From spiking neuron models to linear-nonlinear models.

PubMed

Ostojic, Srdjan; Brunel, Nicolas

2011-01-20

Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.

Estimation of hysteretic damping of structures by stochastic subspace identification

NASA Astrophysics Data System (ADS)

Bajrić, Anela; Høgsberg, Jan

2018-05-01

Output-only system identification techniques can estimate modal parameters of structures represented by linear time-invariant systems. However, the extension of the techniques to structures exhibiting non-linear behavior has not received much attention. This paper presents an output-only system identification method suitable for random response of dynamic systems with hysteretic damping. The method applies the concept of Stochastic Subspace Identification (SSI) to estimate the model parameters of a dynamic system with hysteretic damping. The restoring force is represented by the Bouc-Wen model, for which an equivalent linear relaxation model is derived. Hysteretic properties can be encountered in engineering structures exposed to severe cyclic environmental loads, as well as in vibration mitigation devices, such as Magneto-Rheological (MR) dampers. The identification technique incorporates the equivalent linear damper model in the estimation procedure. Synthetic data, representing the random vibrations of systems with hysteresis, validate the estimated system parameters by the presented identification method at low and high-levels of excitation amplitudes.

State estimation of stochastic non-linear hybrid dynamic system using an interacting multiple model algorithm.

PubMed

Elenchezhiyan, M; Prakash, J

2015-09-01

In this work, state estimation schemes for non-linear hybrid dynamic systems subjected to stochastic state disturbances and random errors in measurements using interacting multiple-model (IMM) algorithms are formulated. In order to compute both discrete modes and continuous state estimates of a hybrid dynamic system either an IMM extended Kalman filter (IMM-EKF) or an IMM based derivative-free Kalman filters is proposed in this study. The efficacy of the proposed IMM based state estimation schemes is demonstrated by conducting Monte-Carlo simulation studies on the two-tank hybrid system and switched non-isothermal continuous stirred tank reactor system. Extensive simulation studies reveal that the proposed IMM based state estimation schemes are able to generate fairly accurate continuous state estimates and discrete modes. In the presence and absence of sensor bias, the simulation studies reveal that the proposed IMM unscented Kalman filter (IMM-UKF) based simultaneous state and parameter estimation scheme outperforms multiple-model UKF (MM-UKF) based simultaneous state and parameter estimation scheme. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Combining experimental techniques with non-linear numerical models to assess the sorption of pesticides on soils

NASA Astrophysics Data System (ADS)

Magga, Zoi; Tzovolou, Dimitra N.; Theodoropoulou, Maria A.; Tsakiroglou, Christos D.

2012-03-01

The risk assessment of groundwater pollution by pesticides may be based on pesticide sorption and biodegradation kinetic parameters estimated with inverse modeling of datasets from either batch or continuous flow soil column experiments. In the present work, a chemical non-equilibrium and non-linear 2-site sorption model is incorporated into solute transport models to invert the datasets of batch and soil column experiments, and estimate the kinetic sorption parameters for two pesticides: N-phosphonomethyl glycine (glyphosate) and 2,4-dichlorophenoxy-acetic acid (2,4-D). When coupling the 2-site sorption model with the 2-region transport model, except of the kinetic sorption parameters, the soil column datasets enable us to estimate the mass-transfer coefficients associated with solute diffusion between mobile and immobile regions. In order to improve the reliability of models and kinetic parameter values, a stepwise strategy that combines batch and continuous flow tests with adequate true-to-the mechanism analytical of numerical models, and decouples the kinetics of purely reactive steps of sorption from physical mass-transfer processes is required.

Weibull Modulus Estimated by the Non-linear Least Squares Method: A Solution to Deviation Occurring in Traditional Weibull Estimation

NASA Astrophysics Data System (ADS)

Li, T.; Griffiths, W. D.; Chen, J.

2017-11-01

The Maximum Likelihood method and the Linear Least Squares (LLS) method have been widely used to estimate Weibull parameters for reliability of brittle and metal materials. In the last 30 years, many researchers focused on the bias of Weibull modulus estimation, and some improvements have been achieved, especially in the case of the LLS method. However, there is a shortcoming in these methods for a specific type of data, where the lower tail deviates dramatically from the well-known linear fit in a classic LLS Weibull analysis. This deviation can be commonly found from the measured properties of materials, and previous applications of the LLS method on this kind of dataset present an unreliable linear regression. This deviation was previously thought to be due to physical flaws ( i.e., defects) contained in materials. However, this paper demonstrates that this deviation can also be caused by the linear transformation of the Weibull function, occurring in the traditional LLS method. Accordingly, it may not be appropriate to carry out a Weibull analysis according to the linearized Weibull function, and the Non-linear Least Squares method (Non-LS) is instead recommended for the Weibull modulus estimation of casting properties.

Estimation of real-time runway surface contamination using flight data recorder parameters

NASA Astrophysics Data System (ADS)

Curry, Donovan

Within this research effort, the development of an analytic process for friction coefficient estimation is presented. Under static equilibrium, the sum of forces and moments acting on the aircraft, in the aircraft body coordinate system, while on the ground at any instant is equal to zero. Under this premise the longitudinal, lateral and normal forces due to landing are calculated along with the individual deceleration components existent when an aircraft comes to a rest during ground roll. In order to validate this hypothesis a six degree of freedom aircraft model had to be created and landing tests had to be simulated on different surfaces. The simulated aircraft model includes a high fidelity aerodynamic model, thrust model, landing gear model, friction model and antiskid model. Three main surfaces were defined in the friction model; dry, wet and snow/ice. Only the parameters recorded by an FDR are used directly from the aircraft model all others are estimated or known a priori. The estimation of unknown parameters is also presented in the research effort. With all needed parameters a comparison and validation with simulated and estimated data, under different runway conditions, is performed. Finally, this report presents results of a sensitivity analysis in order to provide a measure of reliability of the analytic estimation process. Linear and non-linear sensitivity analysis has been performed in order to quantify the level of uncertainty implicit in modeling estimated parameters and how they can affect the calculation of the instantaneous coefficient of friction. Using the approach of force and moment equilibrium about the CG at landing to reconstruct the instantaneous coefficient of friction appears to be a reasonably accurate estimate when compared to the simulated friction coefficient. This is also true when the FDR and estimated parameters are introduced to white noise and when crosswind is introduced to the simulation. After the linear analysis the results show the minimum frequency at which the algorithm still provides moderately accurate data is at 2Hz. In addition, the linear analysis shows that with estimated parameters increased and decreased up to 25% at random, high priority parameters have to be accurate to within at least +/-5% to have an effect of less than 1% change in the average coefficient of friction. Non-linear analysis results show that the algorithm can be considered reasonably accurate for all simulated cases when inaccuracies in the estimated parameters vary randomly and simultaneously up to +/-27%. At worst-case the maximum percentage change in average coefficient of friction is less than 10% for all surfaces.

New non-linear model of groundwater recharge: Inclusion of memory, heterogeneity and visco-elasticity

NASA Astrophysics Data System (ADS)

Spannenberg, Jescica; Atangana, Abdon; Vermeulen, P. D.

2017-09-01

Fractional differentiation has adequate use for investigating real world scenarios related to geological formations associated with elasticity, heterogeneity, viscoelasticity, and the memory effect. Since groundwater systems exist in these geological formations, modelling groundwater recharge as a real world scenario is a challenging task to do because existing recharge estimation methods are governed by linear equations which make use of constant field parameters. This is inadequate because in reality these parameters are a function of both space and time. This study therefore concentrates on modifying the recharge equation governing the EARTH model, by application of the Eton approach. Accordingly, this paper presents a modified equation which is non-linear, and accounts for parameters in a way that it is a function of both space and time. To be more specific, herein, recharge and drainage resistance which are parameters within the equation, became a function of both space and time. Additionally, the study entailed solving the non-linear equation using an iterative method as well as numerical solutions by means of the Crank-Nicolson scheme. The numerical solutions were used alongside the Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu derivatives, so that account was taken for elasticity, heterogeneity, viscoelasticity, and the memory effect. In essence, this paper presents a more adequate model for recharge estimation.

Space Shuttle propulsion parameter estimation using optimal estimation techniques, volume 1

NASA Technical Reports Server (NTRS)

1983-01-01

The mathematical developments and their computer program implementation for the Space Shuttle propulsion parameter estimation project are summarized. The estimation approach chosen is the extended Kalman filtering with a modified Bryson-Frazier smoother. Its use here is motivated by the objective of obtaining better estimates than those available from filtering and to eliminate the lag associated with filtering. The estimation technique uses as the dynamical process the six degree equations-of-motion resulting in twelve state vector elements. In addition to these are mass and solid propellant burn depth as the ""system'' state elements. The ""parameter'' state elements can include aerodynamic coefficient, inertia, center-of-gravity, atmospheric wind, etc. deviations from referenced values. Propulsion parameter state elements have been included not as options just discussed but as the main parameter states to be estimated. The mathematical developments were completed for all these parameters. Since the systems dynamics and measurement processes are non-linear functions of the states, the mathematical developments are taken up almost entirely by the linearization of these equations as required by the estimation algorithms.

Estimation of biological parameters of marine organisms using linear and nonlinear acoustic scattering model-based inversion methods.

PubMed

Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H

2016-05-01

The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel.

Estimating cosmic velocity fields from density fields and tidal tensors

NASA Astrophysics Data System (ADS)

Kitaura, Francisco-Shu; Angulo, Raul E.; Hoffman, Yehuda; Gottlöber, Stefan

2012-10-01

In this work we investigate the non-linear and non-local relation between cosmological density and peculiar velocity fields. Our goal is to provide an algorithm for the reconstruction of the non-linear velocity field from the fully non-linear density. We find that including the gravitational tidal field tensor using second-order Lagrangian perturbation theory based upon an estimate of the linear component of the non-linear density field significantly improves the estimate of the cosmic flow in comparison to linear theory not only in the low density, but also and more dramatically in the high-density regions. In particular we test two estimates of the linear component: the lognormal model and the iterative Lagrangian linearization. The present approach relies on a rigorous higher order Lagrangian perturbation theory analysis which incorporates a non-local relation. It does not require additional fitting from simulations being in this sense parameter free, it is independent of statistical-geometrical optimization and it is straightforward and efficient to compute. The method is demonstrated to yield an unbiased estimator of the velocity field on scales ≳5 h-1 Mpc with closely Gaussian distributed errors. Moreover, the statistics of the divergence of the peculiar velocity field is extremely well recovered showing a good agreement with the true one from N-body simulations. The typical errors of about 10 km s-1 (1σ confidence intervals) are reduced by more than 80 per cent with respect to linear theory in the scale range between 5 and 10 h-1 Mpc in high-density regions (δ > 2). We also find that iterative Lagrangian linearization is significantly superior in the low-density regime with respect to the lognormal model.

Poster — Thur Eve — 44: Linearization of Compartmental Models for More Robust Estimates of Regional Hemodynamic, Metabolic and Functional Parameters using DCE-CT/PET Imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blais, AR; Dekaban, M; Lee, T-Y

2014-08-15

Quantitative analysis of dynamic positron emission tomography (PET) data usually involves minimizing a cost function with nonlinear regression, wherein the choice of starting parameter values and the presence of local minima affect the bias and variability of the estimated kinetic parameters. These nonlinear methods can also require lengthy computation time, making them unsuitable for use in clinical settings. Kinetic modeling of PET aims to estimate the rate parameter k{sub 3}, which is the binding affinity of the tracer to a biological process of interest and is highly susceptible to noise inherent in PET image acquisition. We have developed linearized kineticmore » models for kinetic analysis of dynamic contrast enhanced computed tomography (DCE-CT)/PET imaging, including a 2-compartment model for DCE-CT and a 3-compartment model for PET. Use of kinetic parameters estimated from DCE-CT can stabilize the kinetic analysis of dynamic PET data, allowing for more robust estimation of k{sub 3}. Furthermore, these linearized models are solved with a non-negative least squares algorithm and together they provide other advantages including: 1) only one possible solution and they do not require a choice of starting parameter values, 2) parameter estimates are comparable in accuracy to those from nonlinear models, 3) significantly reduced computational time. Our simulated data show that when blood volume and permeability are estimated with DCE-CT, the bias of k{sub 3} estimation with our linearized model is 1.97 ± 38.5% for 1,000 runs with a signal-to-noise ratio of 10. In summary, we have developed a computationally efficient technique for accurate estimation of k{sub 3} from noisy dynamic PET data.« less

The structural identifiability and parameter estimation of a multispecies model for the transmission of mastitis in dairy cows with postmilking teat disinfection.

PubMed

White, L J; Evans, N D; Lam, T J G M; Schukken, Y H; Medley, G F; Godfrey, K R; Chappell, M J

2002-01-01

A mathematical model for the transmission of two interacting classes of mastitis causing bacterial pathogens in a herd of dairy cows is presented and applied to a specific data set. The data were derived from a field trial of a specific measure used in the control of these pathogens, where half the individuals were subjected to the control and in the others the treatment was discontinued. The resultant mathematical model (eight non-linear simultaneous ordinary differential equations) therefore incorporates heterogeneity in the host as well as the infectious agent and consequently the effects of control are intrinsic in the model structure. A structural identifiability analysis of the model is presented demonstrating that the scope of the novel method used allows application to high order non-linear systems. The results of a simultaneous estimation of six unknown system parameters are presented. Previous work has only estimated a subset of these either simultaneously or individually. Therefore not only are new estimates provided for the parameters relating to the transmission and control of the classes of pathogens under study, but also information about the relationships between them. We exploit the close link between mathematical modelling, structural identifiability analysis, and parameter estimation to obtain biological insights into the system modelled.

Multivariate meta-analysis for non-linear and other multi-parameter associations

PubMed Central

Gasparrini, A; Armstrong, B; Kenward, M G

2012-01-01

In this paper, we formalize the application of multivariate meta-analysis and meta-regression to synthesize estimates of multi-parameter associations obtained from different studies. This modelling approach extends the standard two-stage analysis used to combine results across different sub-groups or populations. The most straightforward application is for the meta-analysis of non-linear relationships, described for example by regression coefficients of splines or other functions, but the methodology easily generalizes to any setting where complex associations are described by multiple correlated parameters. The modelling framework of multivariate meta-analysis is implemented in the package mvmeta within the statistical environment R. As an illustrative example, we propose a two-stage analysis for investigating the non-linear exposure–response relationship between temperature and non-accidental mortality using time-series data from multiple cities. Multivariate meta-analysis represents a useful analytical tool for studying complex associations through a two-stage procedure. Copyright © 2012 John Wiley & Sons, Ltd. PMID:22807043

Linear regression analysis of survival data with missing censoring indicators.

PubMed

Wang, Qihua; Dinse, Gregg E

2011-04-01

Linear regression analysis has been studied extensively in a random censorship setting, but typically all of the censoring indicators are assumed to be observed. In this paper, we develop synthetic data methods for estimating regression parameters in a linear model when some censoring indicators are missing. We define estimators based on regression calibration, imputation, and inverse probability weighting techniques, and we prove all three estimators are asymptotically normal. The finite-sample performance of each estimator is evaluated via simulation. We illustrate our methods by assessing the effects of sex and age on the time to non-ambulatory progression for patients in a brain cancer clinical trial.

Non-linear Growth Models in Mplus and SAS

PubMed Central

Grimm, Kevin J.; Ram, Nilam

2013-01-01

Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included. PMID:23882134

Frequency-domain full-waveform inversion with non-linear descent directions

NASA Astrophysics Data System (ADS)

Geng, Yu; Pan, Wenyong; Innanen, Kristopher A.

2018-05-01

Full-waveform inversion (FWI) is a highly non-linear inverse problem, normally solved iteratively, with each iteration involving an update constructed through linear operations on the residuals. Incorporating a flexible degree of non-linearity within each update may have important consequences for convergence rates, determination of low model wavenumbers and discrimination of parameters. We examine one approach for doing so, wherein higher order scattering terms are included within the sensitivity kernel during the construction of the descent direction, adjusting it away from that of the standard Gauss-Newton approach. These scattering terms are naturally admitted when we construct the sensitivity kernel by varying not the current but the to-be-updated model at each iteration. Linear and/or non-linear inverse scattering methodologies allow these additional sensitivity contributions to be computed from the current data residuals within any given update. We show that in the presence of pre-critical reflection data, the error in a second-order non-linear update to a background of s0 is, in our scheme, proportional to at most (Δs/s0)3 in the actual parameter jump Δs causing the reflection. In contrast, the error in a standard Gauss-Newton FWI update is proportional to (Δs/s0)2. For numerical implementation of more complex cases, we introduce a non-linear frequency-domain scheme, with an inner and an outer loop. A perturbation is determined from the data residuals within the inner loop, and a descent direction based on the resulting non-linear sensitivity kernel is computed in the outer loop. We examine the response of this non-linear FWI using acoustic single-parameter synthetics derived from the Marmousi model. The inverted results vary depending on data frequency ranges and initial models, but we conclude that the non-linear FWI has the capability to generate high-resolution model estimates in both shallow and deep regions, and to converge rapidly, relative to a benchmark FWI approach involving the standard gradient.

Linear regression techniques for use in the EC tracer method of secondary organic aerosol estimation

NASA Astrophysics Data System (ADS)

Saylor, Rick D.; Edgerton, Eric S.; Hartsell, Benjamin E.

A variety of linear regression techniques and simple slope estimators are evaluated for use in the elemental carbon (EC) tracer method of secondary organic carbon (OC) estimation. Linear regression techniques based on ordinary least squares are not suitable for situations where measurement uncertainties exist in both regressed variables. In the past, regression based on the method of Deming [1943. Statistical Adjustment of Data. Wiley, London] has been the preferred choice for EC tracer method parameter estimation. In agreement with Chu [2005. Stable estimate of primary OC/EC ratios in the EC tracer method. Atmospheric Environment 39, 1383-1392], we find that in the limited case where primary non-combustion OC (OC non-comb) is assumed to be zero, the ratio of averages (ROA) approach provides a stable and reliable estimate of the primary OC-EC ratio, (OC/EC) pri. In contrast with Chu [2005. Stable estimate of primary OC/EC ratios in the EC tracer method. Atmospheric Environment 39, 1383-1392], however, we find that the optimal use of Deming regression (and the more general York et al. [2004. Unified equations for the slope, intercept, and standard errors of the best straight line. American Journal of Physics 72, 367-375] regression) provides excellent results as well. For the more typical case where OC non-comb is allowed to obtain a non-zero value, we find that regression based on the method of York is the preferred choice for EC tracer method parameter estimation. In the York regression technique, detailed information on uncertainties in the measurement of OC and EC is used to improve the linear best fit to the given data. If only limited information is available on the relative uncertainties of OC and EC, then Deming regression should be used. On the other hand, use of ROA in the estimation of secondary OC, and thus the assumption of a zero OC non-comb value, generally leads to an overestimation of the contribution of secondary OC to total measured OC.

Fitting a defect non-linear model with or without prior, distinguishing nuclear reaction products as an example.

PubMed

Helgesson, P; Sjöstrand, H

2017-11-01

Fitting a parametrized function to data is important for many researchers and scientists. If the model is non-linear and/or defect, it is not trivial to do correctly and to include an adequate uncertainty analysis. This work presents how the Levenberg-Marquardt algorithm for non-linear generalized least squares fitting can be used with a prior distribution for the parameters and how it can be combined with Gaussian processes to treat model defects. An example, where three peaks in a histogram are to be distinguished, is carefully studied. In particular, the probability r 1 for a nuclear reaction to end up in one out of two overlapping peaks is studied. Synthetic data are used to investigate effects of linearizations and other assumptions. For perfect Gaussian peaks, it is seen that the estimated parameters are distributed close to the truth with good covariance estimates. This assumes that the method is applied correctly; for example, prior knowledge should be implemented using a prior distribution and not by assuming that some parameters are perfectly known (if they are not). It is also important to update the data covariance matrix using the fit if the uncertainties depend on the expected value of the data (e.g., for Poisson counting statistics or relative uncertainties). If a model defect is added to the peaks, such that their shape is unknown, a fit which assumes perfect Gaussian peaks becomes unable to reproduce the data, and the results for r 1 become biased. It is, however, seen that it is possible to treat the model defect with a Gaussian process with a covariance function tailored for the situation, with hyper-parameters determined by leave-one-out cross validation. The resulting estimates for r 1 are virtually unbiased, and the uncertainty estimates agree very well with the underlying uncertainty.

Fitting a defect non-linear model with or without prior, distinguishing nuclear reaction products as an example

NASA Astrophysics Data System (ADS)

Helgesson, P.; Sjöstrand, H.

2017-11-01

Fitting a parametrized function to data is important for many researchers and scientists. If the model is non-linear and/or defect, it is not trivial to do correctly and to include an adequate uncertainty analysis. This work presents how the Levenberg-Marquardt algorithm for non-linear generalized least squares fitting can be used with a prior distribution for the parameters and how it can be combined with Gaussian processes to treat model defects. An example, where three peaks in a histogram are to be distinguished, is carefully studied. In particular, the probability r1 for a nuclear reaction to end up in one out of two overlapping peaks is studied. Synthetic data are used to investigate effects of linearizations and other assumptions. For perfect Gaussian peaks, it is seen that the estimated parameters are distributed close to the truth with good covariance estimates. This assumes that the method is applied correctly; for example, prior knowledge should be implemented using a prior distribution and not by assuming that some parameters are perfectly known (if they are not). It is also important to update the data covariance matrix using the fit if the uncertainties depend on the expected value of the data (e.g., for Poisson counting statistics or relative uncertainties). If a model defect is added to the peaks, such that their shape is unknown, a fit which assumes perfect Gaussian peaks becomes unable to reproduce the data, and the results for r1 become biased. It is, however, seen that it is possible to treat the model defect with a Gaussian process with a covariance function tailored for the situation, with hyper-parameters determined by leave-one-out cross validation. The resulting estimates for r1 are virtually unbiased, and the uncertainty estimates agree very well with the underlying uncertainty.

Height and Weight Estimation From Anthropometric Measurements Using Machine Learning Regressions

PubMed Central

Fernandes, Bruno J. T.; Roque, Alexandre

2018-01-01

Height and weight are measurements explored to tracking nutritional diseases, energy expenditure, clinical conditions, drug dosages, and infusion rates. Many patients are not ambulant or may be unable to communicate, and a sequence of these factors may not allow accurate estimation or measurements; in those cases, it can be estimated approximately by anthropometric means. Different groups have proposed different linear or non-linear equations which coefficients are obtained by using single or multiple linear regressions. In this paper, we present a complete study of the application of different learning models to estimate height and weight from anthropometric measurements: support vector regression, Gaussian process, and artificial neural networks. The predicted values are significantly more accurate than that obtained with conventional linear regressions. In all the cases, the predictions are non-sensitive to ethnicity, and to gender, if more than two anthropometric parameters are analyzed. The learning model analysis creates new opportunities for anthropometric applications in industry, textile technology, security, and health care. PMID:29651366

Linear theory for filtering nonlinear multiscale systems with model error

PubMed Central

Berry, Tyrus; Harlim, John

2014-01-01

In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online, as part of a filtering procedure, simultaneously produce accurate filtering and equilibrium statistical prediction. In contrast, an offline estimation technique based on a linear regression, which fits the parameters to a training dataset without using the filter, yields filter estimates which are worse than the observations or even divergent when the slow variables are not fully observed. This finding does not imply that all offline methods are inherently inferior to the online method for nonlinear estimation problems, it only suggests that an ideal estimation technique should estimate all parameters simultaneously whether it is online or offline. PMID:25002829

Desired Accuracy Estimation of Noise Function from ECG Signal by Fuzzy Approach

PubMed Central

Vahabi, Zahra; Kermani, Saeed

2012-01-01

Unknown noise and artifacts present in medical signals with non-linear fuzzy filter will be estimated and then removed. An adaptive neuro-fuzzy interference system which has a non-linear structure presented for the noise function prediction by before Samples. This paper is about a neuro-fuzzy method to estimate unknown noise of Electrocardiogram signal. Adaptive neural combined with Fuzzy System to construct a fuzzy Predictor. For this system setting parameters such as the number of Membership Functions for each input and output, training epochs, type of MFs for each input and output, learning algorithm and etc. is determined by learning data. At the end simulated experimental results are presented for proper validation. PMID:23717810

Linear and non-linear regression analysis for the sorption kinetics of methylene blue onto activated carbon.

PubMed

Kumar, K Vasanth

2006-10-11

Batch kinetic experiments were carried out for the sorption of methylene blue onto activated carbon. The experimental kinetics were fitted to the pseudo first-order and pseudo second-order kinetics by linear and a non-linear method. The five different types of Ho pseudo second-order expression have been discussed. A comparison of linear least-squares method and a trial and error non-linear method of estimating the pseudo second-order rate kinetic parameters were examined. The sorption process was found to follow a both pseudo first-order kinetic and pseudo second-order kinetic model. Present investigation showed that it is inappropriate to use a type 1 and type pseudo second-order expressions as proposed by Ho and Blanachard et al. respectively for predicting the kinetic rate constants and the initial sorption rate for the studied system. Three correct possible alternate linear expressions (type 2 to type 4) to better predict the initial sorption rate and kinetic rate constants for the studied system (methylene blue/activated carbon) was proposed. Linear method was found to check only the hypothesis instead of verifying the kinetic model. Non-linear regression method was found to be the more appropriate method to determine the rate kinetic parameters.

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

NASA Technical Reports Server (NTRS)

Lisano, Michael E.

2007-01-01

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

Gap-filling methods to impute eddy covariance flux data by preserving variance.

NASA Astrophysics Data System (ADS)

Kunwor, S.; Staudhammer, C. L.; Starr, G.; Loescher, H. W.

2015-12-01

To represent carbon dynamics, in terms of exchange of CO2 between the terrestrial ecosystem and the atmosphere, eddy covariance (EC) data has been collected using eddy flux towers from various sites across globe for more than two decades. However, measurements from EC data are missing for various reasons: precipitation, routine maintenance, or lack of vertical turbulence. In order to have estimates of net ecosystem exchange of carbon dioxide (NEE) with high precision and accuracy, robust gap-filling methods to impute missing data are required. While the methods used so far have provided robust estimates of the mean value of NEE, little attention has been paid to preserving the variance structures embodied by the flux data. Preserving the variance of these data will provide unbiased and precise estimates of NEE over time, which mimic natural fluctuations. We used a non-linear regression approach with moving windows of different lengths (15, 30, and 60-days) to estimate non-linear regression parameters for one year of flux data from a long-leaf pine site at the Joseph Jones Ecological Research Center. We used as our base the Michaelis-Menten and Van't Hoff functions. We assessed the potential physiological drivers of these parameters with linear models using micrometeorological predictors. We then used a parameter prediction approach to refine the non-linear gap-filling equations based on micrometeorological conditions. This provides us an opportunity to incorporate additional variables, such as vapor pressure deficit (VPD) and volumetric water content (VWC) into the equations. Our preliminary results indicate that improvements in gap-filling can be gained with a 30-day moving window with additional micrometeorological predictors (as indicated by lower root mean square error (RMSE) of the predicted values of NEE). Our next steps are to use these parameter predictions from moving windows to gap-fill the data with and without incorporation of potential driver variables of the parameters traditionally used. Then, comparisons of the predicted values from these methods and 'traditional' gap-filling methods (using 12 fixed monthly windows) will be assessed to show the scale of preserving variance. Further, this method will be applied to impute artificially created gaps for analyzing if variance is preserved.

A python framework for environmental model uncertainty analysis

USGS Publications Warehouse

White, Jeremy; Fienen, Michael N.; Doherty, John E.

2016-01-01

We have developed pyEMU, a python framework for Environmental Modeling Uncertainty analyses, open-source tool that is non-intrusive, easy-to-use, computationally efficient, and scalable to highly-parameterized inverse problems. The framework implements several types of linear (first-order, second-moment (FOSM)) and non-linear uncertainty analyses. The FOSM-based analyses can also be completed prior to parameter estimation to help inform important modeling decisions, such as parameterization and objective function formulation. Complete workflows for several types of FOSM-based and non-linear analyses are documented in example notebooks implemented using Jupyter that are available in the online pyEMU repository. Example workflows include basic parameter and forecast analyses, data worth analyses, and error-variance analyses, as well as usage of parameter ensemble generation and management capabilities. These workflows document the necessary steps and provides insights into the results, with the goal of educating users not only in how to apply pyEMU, but also in the underlying theory of applied uncertainty quantification.

Output-only modal parameter estimator of linear time-varying structural systems based on vector TAR model and least squares support vector machine

NASA Astrophysics Data System (ADS)

Zhou, Si-Da; Ma, Yuan-Chen; Liu, Li; Kang, Jie; Ma, Zhi-Sai; Yu, Lei

2018-01-01

Identification of time-varying modal parameters contributes to the structural health monitoring, fault detection, vibration control, etc. of the operational time-varying structural systems. However, it is a challenging task because there is not more information for the identification of the time-varying systems than that of the time-invariant systems. This paper presents a vector time-dependent autoregressive model and least squares support vector machine based modal parameter estimator for linear time-varying structural systems in case of output-only measurements. To reduce the computational cost, a Wendland's compactly supported radial basis function is used to achieve the sparsity of the Gram matrix. A Gamma-test-based non-parametric approach of selecting the regularization factor is adapted for the proposed estimator to replace the time-consuming n-fold cross validation. A series of numerical examples have illustrated the advantages of the proposed modal parameter estimator on the suppression of the overestimate and the short data. A laboratory experiment has further validated the proposed estimator.

Controlling the non-linear intracavity dynamics of large He-Ne laser gyroscopes

NASA Astrophysics Data System (ADS)

Cuccato, D.; Beghi, A.; Belfi, J.; Beverini, N.; Ortolan, A.; Di Virgilio, A.

2014-02-01

A model based on Lamb's theory of gas lasers is applied to a He-Ne ring laser (RL) gyroscope to estimate and remove the laser dynamics contribution from the rotation measurements. The intensities of the counter-propagating laser beams exiting one cavity mirror are continuously observed together with a monitor of the laser population inversion. These observables, once properly calibrated with a dedicated procedure, allow us to estimate cold cavity and active medium parameters driving the main part of the non-linearities of the system. The quantitative estimation of intrinsic non-reciprocal effects due to cavity and active medium non-linear coupling plays a key role in testing fundamental symmetries of space-time with RLs. The parameter identification and noise subtraction procedure has been verified by means of a Monte Carlo study of the system, and experimentally tested on the G-PISA RL oriented with the normal to the ring plane almost parallel to the Earth's rotation axis. In this configuration the Earth's rotation rate provides the maximum Sagnac effect while the contribution of the orientation error is reduced to a minimum. After the subtraction of laser dynamics by a Kalman filter, the relative systematic errors of G-PISA reduce from 50 to 5 parts in 103 and can be attributed to the residual uncertainties on geometrical scale factor and orientation of the ring.

Estimating the kinetic parameters of activated sludge storage using weighted non-linear least-squares and accelerating genetic algorithm.

PubMed

Fang, Fang; Ni, Bing-Jie; Yu, Han-Qing

2009-06-01

In this study, weighted non-linear least-squares analysis and accelerating genetic algorithm are integrated to estimate the kinetic parameters of substrate consumption and storage product formation of activated sludge. A storage product formation equation is developed and used to construct the objective function for the determination of its production kinetics. The weighted least-squares analysis is employed to calculate the differences in the storage product concentration between the model predictions and the experimental data as the sum of squared weighted errors. The kinetic parameters for the substrate consumption and the storage product formation are estimated to be the maximum heterotrophic growth rate of 0.121/h, the yield coefficient of 0.44 mg CODX/mg CODS (COD, chemical oxygen demand) and the substrate half saturation constant of 16.9 mg/L, respectively, by minimizing the objective function using a real-coding-based accelerating genetic algorithm. Also, the fraction of substrate electrons diverted to the storage product formation is estimated to be 0.43 mg CODSTO/mg CODS. The validity of our approach is confirmed by the results of independent tests and the kinetic parameter values reported in literature, suggesting that this approach could be useful to evaluate the product formation kinetics of mixed cultures like activated sludge. More importantly, as this integrated approach could estimate the kinetic parameters rapidly and accurately, it could be applied to other biological processes.

Study of Heart Rate Variability in Bipolar Disorder: Linear and Non-Linear Parameters during Sleep

PubMed Central

Migliorini, Matteo; Mendez, Martin O.; Bianchi, Anna M.

2012-01-01

The aim of the study is to define physiological parameters and vital signs that may be related to the mood and mental status in patients affected by bipolar disorder. In particular we explored the autonomic nervous system through the analysis of the heart rate variability. Many different parameters, in the time and in the frequency domain, linear and non-linear were evaluated during the sleep in a group of normal subject and in one patient in four different conditions. The recording of the signals was performed through a wearable sensorized T-shirt. Heart rate variability (HRV) signal and movement analysis allowed also obtaining sleep staging and the estimation of REM sleep percentage over the total sleep time. A group of eight normal females constituted the control group, on which normality ranges were estimated. The pathologic subject was recorded during four different nights, at time intervals of at least 1 week, and during different phases of the disturbance. Some of the examined parameters (MEANNN, SDNN, RMSSD) confirmed reduced HRV in depression and bipolar disorder. REM sleep percentage was found to be increased. Lempel–Ziv complexity and sample entropy, on the other hand, seem to correlate with the depression level. Even if the number of examined subjects is still small, and the results need further validation, the proposed methodology and the calculated parameters seem promising tools for the monitoring of mood changes in psychiatric disorders. PMID:22291638

Multiparameter Estimation in Networked Quantum Sensors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Proctor, Timothy J.; Knott, Paul A.; Dunningham, Jacob A.

We introduce a general model for a network of quantum sensors, and we use this model to consider the question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. Thismore » immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or non-linear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network.« less

Multiparameter Estimation in Networked Quantum Sensors

DOE PAGES

Proctor, Timothy J.; Knott, Paul A.; Dunningham, Jacob A.

2018-02-21

We introduce a general model for a network of quantum sensors, and we use this model to consider the question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. Thismore » immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or non-linear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network.« less

Generalized massive optimal data compression

NASA Astrophysics Data System (ADS)

Alsing, Justin; Wandelt, Benjamin

2018-05-01

In this paper, we provide a general procedure for optimally compressing N data down to n summary statistics, where n is equal to the number of parameters of interest. We show that compression to the score function - the gradient of the log-likelihood with respect to the parameters - yields n compressed statistics that are optimal in the sense that they preserve the Fisher information content of the data. Our method generalizes earlier work on linear Karhunen-Loéve compression for Gaussian data whilst recovering both lossless linear compression and quadratic estimation as special cases when they are optimal. We give a unified treatment that also includes the general non-Gaussian case as long as mild regularity conditions are satisfied, producing optimal non-linear summary statistics when appropriate. As a worked example, we derive explicitly the n optimal compressed statistics for Gaussian data in the general case where both the mean and covariance depend on the parameters.

Validation of Bayesian analysis of compartmental kinetic models in medical imaging.

PubMed

Sitek, Arkadiusz; Li, Quanzheng; El Fakhri, Georges; Alpert, Nathaniel M

2016-10-01

Kinetic compartmental analysis is frequently used to compute physiologically relevant quantitative values from time series of images. In this paper, a new approach based on Bayesian analysis to obtain information about these parameters is presented and validated. The closed-form of the posterior distribution of kinetic parameters is derived with a hierarchical prior to model the standard deviation of normally distributed noise. Markov chain Monte Carlo methods are used for numerical estimation of the posterior distribution. Computer simulations of the kinetics of F18-fluorodeoxyglucose (FDG) are used to demonstrate drawing statistical inferences about kinetic parameters and to validate the theory and implementation. Additionally, point estimates of kinetic parameters and covariance of those estimates are determined using the classical non-linear least squares approach. Posteriors obtained using methods proposed in this work are accurate as no significant deviation from the expected shape of the posterior was found (one-sided P>0.08). It is demonstrated that the results obtained by the standard non-linear least-square methods fail to provide accurate estimation of uncertainty for the same data set (P<0.0001). The results of this work validate new methods for a computer simulations of FDG kinetics. Results show that in situations where the classical approach fails in accurate estimation of uncertainty, Bayesian estimation provides an accurate information about the uncertainties in the parameters. Although a particular example of FDG kinetics was used in the paper, the methods can be extended for different pharmaceuticals and imaging modalities. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

A hybrid optimization approach to the estimation of distributed parameters in two-dimensional confined aquifers

USGS Publications Warehouse

Heidari, M.; Ranjithan, S.R.

1998-01-01

In using non-linear optimization techniques for estimation of parameters in a distributed ground water model, the initial values of the parameters and prior information about them play important roles. In this paper, the genetic algorithm (GA) is combined with the truncated-Newton search technique to estimate groundwater parameters for a confined steady-state ground water model. Use of prior information about the parameters is shown to be important in estimating correct or near-correct values of parameters on a regional scale. The amount of prior information needed for an accurate solution is estimated by evaluation of the sensitivity of the performance function to the parameters. For the example presented here, it is experimentally demonstrated that only one piece of prior information of the least sensitive parameter is sufficient to arrive at the global or near-global optimum solution. For hydraulic head data with measurement errors, the error in the estimation of parameters increases as the standard deviation of the errors increases. Results from our experiments show that, in general, the accuracy of the estimated parameters depends on the level of noise in the hydraulic head data and the initial values used in the truncated-Newton search technique.In using non-linear optimization techniques for estimation of parameters in a distributed ground water model, the initial values of the parameters and prior information about them play important roles. In this paper, the genetic algorithm (GA) is combined with the truncated-Newton search technique to estimate groundwater parameters for a confined steady-state ground water model. Use of prior information about the parameters is shown to be important in estimating correct or near-correct values of parameters on a regional scale. The amount of prior information needed for an accurate solution is estimated by evaluation of the sensitivity of the performance function to the parameters. For the example presented here, it is experimentally demonstrated that only one piece of prior information of the least sensitive parameter is sufficient to arrive at the global or near-global optimum solution. For hydraulic head data with measurement errors, the error in the estimation of parameters increases as the standard deviation of the errors increases. Results from our experiments show that, in general, the accuracy of the estimated parameters depends on the level of noise in the hydraulic head data and the initial values used in the truncated-Newton search technique.

A Sparse Bayesian Learning Algorithm for White Matter Parameter Estimation from Compressed Multi-shell Diffusion MRI.

PubMed

Pisharady, Pramod Kumar; Sotiropoulos, Stamatios N; Sapiro, Guillermo; Lenglet, Christophe

2017-09-01

We propose a sparse Bayesian learning algorithm for improved estimation of white matter fiber parameters from compressed (under-sampled q-space) multi-shell diffusion MRI data. The multi-shell data is represented in a dictionary form using a non-monoexponential decay model of diffusion, based on continuous gamma distribution of diffusivities. The fiber volume fractions with predefined orientations, which are the unknown parameters, form the dictionary weights. These unknown parameters are estimated with a linear un-mixing framework, using a sparse Bayesian learning algorithm. A localized learning of hyperparameters at each voxel and for each possible fiber orientations improves the parameter estimation. Our experiments using synthetic data from the ISBI 2012 HARDI reconstruction challenge and in-vivo data from the Human Connectome Project demonstrate the improvements.

Estimation of sum-to-one constrained parameters with non-Gaussian extensions of ensemble-based Kalman filters: application to a 1D ocean biogeochemical model

NASA Astrophysics Data System (ADS)

Simon, E.; Bertino, L.; Samuelsen, A.

2011-12-01

Combined state-parameter estimation in ocean biogeochemical models with ensemble-based Kalman filters is a challenging task due to the non-linearity of the models, the constraints of positiveness that apply to the variables and parameters, and the non-Gaussian distribution of the variables in which they result. Furthermore, these models are sensitive to numerous parameters that are poorly known. Previous works [1] demonstrated that the Gaussian anamorphosis extensions of ensemble-based Kalman filters were relevant tools to perform combined state-parameter estimation in such non-Gaussian framework. In this study, we focus on the estimation of the grazing preferences parameters of zooplankton species. These parameters are introduced to model the diet of zooplankton species among phytoplankton species and detritus. They are positive values and their sum is equal to one. Because the sum-to-one constraint cannot be handled by ensemble-based Kalman filters, a reformulation of the parameterization is proposed. We investigate two types of changes of variables for the estimation of sum-to-one constrained parameters. The first one is based on Gelman [2] and leads to the estimation of normal distributed parameters. The second one is based on the representation of the unit sphere in spherical coordinates and leads to the estimation of parameters with bounded distributions (triangular or uniform). These formulations are illustrated and discussed in the framework of twin experiments realized in the 1D coupled model GOTM-NORWECOM with Gaussian anamorphosis extensions of the deterministic ensemble Kalman filter (DEnKF). [1] Simon E., Bertino L. : Gaussian anamorphosis extension of the DEnKF for combined state and parameter estimation : application to a 1D ocean ecosystem model. Journal of Marine Systems, 2011. doi :10.1016/j.jmarsys.2011.07.007 [2] Gelman A. : Method of Moments Using Monte Carlo Simulation. Journal of Computational and Graphical Statistics, 4, 1, 36-54, 1995.

Functional Linear Model with Zero-value Coefficient Function at Sub-regions.

PubMed

Zhou, Jianhui; Wang, Nae-Yuh; Wang, Naisyin

2013-01-01

We propose a shrinkage method to estimate the coefficient function in a functional linear regression model when the value of the coefficient function is zero within certain sub-regions. Besides identifying the null region in which the coefficient function is zero, we also aim to perform estimation and inferences for the nonparametrically estimated coefficient function without over-shrinking the values. Our proposal consists of two stages. In stage one, the Dantzig selector is employed to provide initial location of the null region. In stage two, we propose a group SCAD approach to refine the estimated location of the null region and to provide the estimation and inference procedures for the coefficient function. Our considerations have certain advantages in this functional setup. One goal is to reduce the number of parameters employed in the model. With a one-stage procedure, it is needed to use a large number of knots in order to precisely identify the zero-coefficient region; however, the variation and estimation difficulties increase with the number of parameters. Owing to the additional refinement stage, we avoid this necessity and our estimator achieves superior numerical performance in practice. We show that our estimator enjoys the Oracle property; it identifies the null region with probability tending to 1, and it achieves the same asymptotic normality for the estimated coefficient function on the non-null region as the functional linear model estimator when the non-null region is known. Numerically, our refined estimator overcomes the shortcomings of the initial Dantzig estimator which tends to under-estimate the absolute scale of non-zero coefficients. The performance of the proposed method is illustrated in simulation studies. We apply the method in an analysis of data collected by the Johns Hopkins Precursors Study, where the primary interests are in estimating the strength of association between body mass index in midlife and the quality of life in physical functioning at old age, and in identifying the effective age ranges where such associations exist.

Optimal non-linear health insurance.

PubMed

Blomqvist, A

1997-06-01

Most theoretical and empirical work on efficient health insurance has been based on models with linear insurance schedules (a constant co-insurance parameter). In this paper, dynamic optimization techniques are used to analyse the properties of optimal non-linear insurance schedules in a model similar to one originally considered by Spence and Zeckhauser (American Economic Review, 1971, 61, 380-387) and reminiscent of those that have been used in the literature on optimal income taxation. The results of a preliminary numerical example suggest that the welfare losses from the implicit subsidy to employer-financed health insurance under US tax law may be a good deal smaller than previously estimated using linear models.

Multimodality CT/SPECT Evaluation of Micelle Drug Carriers for Treatment of Breast Tumors

DTIC Science & Technology

2007-07-01

lap diffusion, Dh and Df, were then calculated using non-linear least squares parameter estimation ( Matlab 7.1). Dh and Df were estimated using release... entanglement serves as a much greater impediment to drug transport. 3.4. Mechanism of action of cell death induced by β-lap micelles Growth assays

Improvements in aircraft extraction programs

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.; Maine, R. E.

1976-01-01

Flight data from an F-8 Corsair and a Cessna 172 was analyzed to demonstrate specific improvements in the LRC parameter extraction computer program. The Cramer-Rao bounds were shown to provide a satisfactory relative measure of goodness of parameter estimates. It was not used as an absolute measure due to an inherent uncertainty within a multiplicative factor, traced in turn to the uncertainty in the noise bandwidth in the statistical theory of parameter estimation. The measure was also derived on an entirely nonstatistical basis, yielding thereby also an interpretation of the significance of off-diagonal terms in the dispersion matrix. The distinction between coefficients as linear and non-linear was shown to be important in its implication to a recommended order of parameter iteration. Techniques of improving convergence generally, were developed, and tested out on flight data. In particular, an easily implemented modification incorporating a gradient search was shown to improve initial estimates and thus remove a common cause for lack of convergence.

Estimating parameter of influenza transmission using regularized least square

NASA Astrophysics Data System (ADS)

Nuraini, N.; Syukriah, Y.; Indratno, S. W.

2014-02-01

Transmission process of influenza can be presented in a mathematical model as a non-linear differential equations system. In this model the transmission of influenza is determined by the parameter of contact rate of the infected host and susceptible host. This parameter will be estimated using a regularized least square method where the Finite Element Method and Euler Method are used for approximating the solution of the SIR differential equation. The new infected data of influenza from CDC is used to see the effectiveness of the method. The estimated parameter represents the contact rate proportion of transmission probability in a day which can influence the number of infected people by the influenza. Relation between the estimated parameter and the number of infected people by the influenza is measured by coefficient of correlation. The numerical results show positive correlation between the estimated parameters and the infected people.

DUAL STATE-PARAMETER UPDATING SCHEME ON A CONCEPTUAL HYDROLOGIC MODEL USING SEQUENTIAL MONTE CARLO FILTERS

NASA Astrophysics Data System (ADS)

Noh, Seong Jin; Tachikawa, Yasuto; Shiiba, Michiharu; Kim, Sunmin

Applications of data assimilation techniques have been widely used to improve upon the predictability of hydrologic modeling. Among various data assimilation techniques, sequential Monte Carlo (SMC) filters, known as "particle filters" provide the capability to handle non-linear and non-Gaussian state-space models. This paper proposes a dual state-parameter updating scheme (DUS) based on SMC methods to estimate both state and parameter variables of a hydrologic model. We introduce a kernel smoothing method for the robust estimation of uncertain model parameters in the DUS. The applicability of the dual updating scheme is illustrated using the implementation of the storage function model on a middle-sized Japanese catchment. We also compare performance results of DUS combined with various SMC methods, such as SIR, ASIR and RPF.

ITOUGH2(UNIX). Inverse Modeling for TOUGH2 Family of Multiphase Flow Simulators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Finsterle, S.

1999-03-01

ITOUGH2 provides inverse modeling capabilities for the TOUGH2 family of numerical simulators for non-isothermal multiphase flows in fractured-porous media. The ITOUGH2 can be used for estimating parameters by automatic modeling calibration, for sensitivity analyses, and for uncertainity propagation analyses (linear and Monte Carlo simulations). Any input parameter to the TOUGH2 simulator can be estimated based on any type of observation for which a corresponding TOUGH2 output is calculated. ITOUGH2 solves a non-linear least-squares problem using direct or gradient-based minimization algorithms. A detailed residual and error analysis is performed, which includes the evaluation of model identification criteria. ITOUGH2 can also bemore » run in forward mode, solving subsurface flow problems related to nuclear waste isolation, oil, gas, and geothermal resevoir engineering, and vadose zone hydrology.« less

Parameter estimation procedure for complex non-linear systems: calibration of ASM No. 1 for N-removal in a full-scale oxidation ditch.

PubMed

Abusam, A; Keesman, K J; van Straten, G; Spanjers, H; Meinema, K

2001-01-01

When applied to large simulation models, the process of parameter estimation is also called calibration. Calibration of complex non-linear systems, such as activated sludge plants, is often not an easy task. On the one hand, manual calibration of such complex systems is usually time-consuming, and its results are often not reproducible. On the other hand, conventional automatic calibration methods are not always straightforward and often hampered by local minima problems. In this paper a new straightforward and automatic procedure, which is based on the response surface method (RSM) for selecting the best identifiable parameters, is proposed. In RSM, the process response (output) is related to the levels of the input variables in terms of a first- or second-order regression model. Usually, RSM is used to relate measured process output quantities to process conditions. However, in this paper RSM is used for selecting the dominant parameters, by evaluating parameters sensitivity in a predefined region. Good results obtained in calibration of ASM No. 1 for N-removal in a full-scale oxidation ditch proved that the proposed procedure is successful and reliable.

Non-linear identification of a squeeze-film damper

NASA Technical Reports Server (NTRS)

Stanway, Roger; Mottershead, John; Firoozian, Riaz

1987-01-01

Described is an experimental study to identify the damping laws associated with a squeeze-film vibration damper. This is achieved by using a non-linear filtering algorithm to process displacement responses of the damper ring to synchronous excitation and thus to estimate the parameters in an nth-power velocity model. The experimental facility is described in detail and a representative selection of results is included. The identified models are validated through the prediction of damper-ring orbits and comparison with observed responses.

Non-Linear System Identification for Aeroelastic Systems with Application to Experimental Data

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2008-01-01

Representation and identification of a non-linear aeroelastic pitch-plunge system as a model of the NARMAX class is considered. A non-linear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (i) the outputs of the NARMAX model match closely those generated using continuous-time methods and (ii) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.

Mathematical quantification of the induced stress resistance of microbial populations during non-isothermal stresses.

PubMed

Garre, Alberto; Huertas, Juan Pablo; González-Tejedor, Gerardo A; Fernández, Pablo S; Egea, Jose A; Palop, Alfredo; Esnoz, Arturo

2018-02-02

This contribution presents a mathematical model to describe non-isothermal microbial inactivation processes taking into account the acclimation of the microbial cell to thermal stress. The model extends the log-linear inactivation model including a variable and model parameters quantifying the induced thermal resistance. The model has been tested on cells of Escherichia coli against two families of non-isothermal profiles with different constant heating rates. One of the families was composed of monophasic profiles, consisting of a non-isothermal heating stage from 35 to 70°C; the other family was composed of biphasic profiles, consisting of a non-isothermal heating stage followed by a holding period at constant temperature of 57.5°C. Lower heating rates resulted in a higher thermal resistance of the bacterial population. This was reflected in a higher D-value. The parameter estimation was performed in two steps. Firstly, the D and z-values were estimated from the isothermal experiments. Next, the parameters describing the acclimation were estimated using one of the biphasic profiles. This set of parameters was able to describe the remaining experimental data. Finally, a methodology for the construction of diagrams illustrating the magnitude of the induced thermal resistance is presented. The methodology has been illustrated by building it for a biphasic temperature profile with a linear heating phase and a holding phase. This diagram provides a visualization of how the shape of the temperature profile (heating rate and holding temperature) affects the acclimation of the cell to the thermal stress. This diagram can be used for the design of inactivation treatments by industry taking into account the acclimation of the cell to the thermal stress. Copyright © 2017 Elsevier B.V. All rights reserved.

Non-linear motions in reprocessed GPS station position time series

NASA Astrophysics Data System (ADS)

Rudenko, Sergei; Gendt, Gerd

2010-05-01

Global Positioning System (GPS) data of about 400 globally distributed stations obtained at time span from 1998 till 2007 were reprocessed using GFZ Potsdam EPOS (Earth Parameter and Orbit System) software within International GNSS Service (IGS) Tide Gauge Benchmark Monitoring (TIGA) Pilot Project and IGS Data Reprocessing Campaign with the purpose to determine weekly precise coordinates of GPS stations located at or near tide gauges. Vertical motions of these stations are used to correct the vertical motions of tide gauges for local motions and to tie tide gauge measurements to the geocentric reference frame. Other estimated parameters include daily values of the Earth rotation parameters and their rates, as well as satellite antenna offsets. The solution GT1 derived is based on using absolute phase center variation model, ITRF2005 as a priori reference frame, and other new models. The solution contributed also to ITRF2008. The time series of station positions are analyzed to identify non-linear motions caused by different effects. The paper presents the time series of GPS station coordinates and investigates apparent non-linear motions and their influence on GPS station height rates.

Robust control of the DC-DC boost converter based on the uncertainty and disturbance estimator

NASA Astrophysics Data System (ADS)

Oucheriah, Said

2017-11-01

In this paper, a robust non-linear controller based on the uncertainty and disturbance estimator (UDE) scheme is successfully developed and implemented for the output voltage regulation of the DC-DC boost converter. System uncertainties, external disturbances and unknown non-linear dynamics are lumped as a signal that is accurately estimated using a low-pass filter and their effects are cancelled by the controller. This methodology forms the basis of the UDE-based controller. A simple procedure is also developed that systematically determines the parameters of the controller to meet certain specifications. Using simulation, the effectiveness of the proposed controller is compared against the sliding-mode control (SMC). Experimental tests also show that the proposed controller is robust to system uncertainties, large input and load perturbations.

Variations of cosmic large-scale structure covariance matrices across parameter space

NASA Astrophysics Data System (ADS)

Reischke, Robert; Kiessling, Alina; Schäfer, Björn Malte

2017-03-01

The likelihood function for cosmological parameters, given by e.g. weak lensing shear measurements, depends on contributions to the covariance induced by the non-linear evolution of the cosmic web. As highly non-linear clustering to date has only been described by numerical N-body simulations in a reliable and sufficiently precise way, the necessary computational costs for estimating those covariances at different points in parameter space are tremendous. In this work, we describe the change of the matter covariance and the weak lensing covariance matrix as a function of cosmological parameters by constructing a suitable basis, where we model the contribution to the covariance from non-linear structure formation using Eulerian perturbation theory at third order. We show that our formalism is capable of dealing with large matrices and reproduces expected degeneracies and scaling with cosmological parameters in a reliable way. Comparing our analytical results to numerical simulations, we find that the method describes the variation of the covariance matrix found in the SUNGLASS weak lensing simulation pipeline within the errors at one-loop and tree-level for the spectrum and the trispectrum, respectively, for multipoles up to ℓ ≤ 1300. We show that it is possible to optimize the sampling of parameter space where numerical simulations should be carried out by minimizing interpolation errors and propose a corresponding method to distribute points in parameter space in an economical way.

Temperature profile retrievals with extended Kalman-Bucy filters

NASA Technical Reports Server (NTRS)

Ledsham, W. H.; Staelin, D. H.

1979-01-01

The Extended Kalman-Bucy Filter is a powerful technique for estimating non-stationary random parameters in situations where the received signal is a noisy non-linear function of those parameters. A practical causal filter for retrieving atmospheric temperature profiles from radiances observed at a single scan angle by the Scanning Microwave Spectrometer (SCAMS) carried on the Nimbus 6 satellite typically shows approximately a 10-30% reduction in rms error about the mean at almost all levels below 70 mb when compared with a regression inversion.

Can you trust the parametric standard errors in nonlinear least squares? Yes, with provisos.

PubMed

Tellinghuisen, Joel

2018-04-01

Questions about the reliability of parametric standard errors (SEs) from nonlinear least squares (LS) algorithms have led to a general mistrust of these precision estimators that is often unwarranted. The importance of non-Gaussian parameter distributions is illustrated by converting linear models to nonlinear by substituting e A , ln A, and 1/A for a linear parameter a. Monte Carlo (MC) simulations characterize parameter distributions in more complex cases, including when data have varying uncertainty and should be weighted, but weights are neglected. This situation leads to loss of precision and erroneous parametric SEs, as is illustrated for the Lineweaver-Burk analysis of enzyme kinetics data and the analysis of isothermal titration calorimetry data. Non-Gaussian parameter distributions are generally asymmetric and biased. However, when the parametric SE is <10% of the magnitude of the parameter, both the bias and the asymmetry can usually be ignored. Sometimes nonlinear estimators can be redefined to give more normal distributions and better convergence properties. Variable data uncertainty, or heteroscedasticity, can sometimes be handled by data transforms but more generally requires weighted LS, which in turn require knowledge of the data variance. Parametric SEs are rigorously correct in linear LS under the usual assumptions, and are a trustworthy approximation in nonlinear LS provided they are sufficiently small - a condition favored by the abundant, precise data routinely collected in many modern instrumental methods. Copyright © 2018 Elsevier B.V. All rights reserved.

An extended harmonic balance method based on incremental nonlinear control parameters

NASA Astrophysics Data System (ADS)

Khodaparast, Hamed Haddad; Madinei, Hadi; Friswell, Michael I.; Adhikari, Sondipon; Coggon, Simon; Cooper, Jonathan E.

2017-02-01

A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of 'non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices.

Fast estimation of diffusion tensors under Rician noise by the EM algorithm.

PubMed

Liu, Jia; Gasbarra, Dario; Railavo, Juha

2016-01-15

Diffusion tensor imaging (DTI) is widely used to characterize, in vivo, the white matter of the central nerve system (CNS). This biological tissue contains much anatomic, structural and orientational information of fibers in human brain. Spectral data from the displacement distribution of water molecules located in the brain tissue are collected by a magnetic resonance scanner and acquired in the Fourier domain. After the Fourier inversion, the noise distribution is Gaussian in both real and imaginary parts and, as a consequence, the recorded magnitude data are corrupted by Rician noise. Statistical estimation of diffusion leads a non-linear regression problem. In this paper, we present a fast computational method for maximum likelihood estimation (MLE) of diffusivities under the Rician noise model based on the expectation maximization (EM) algorithm. By using data augmentation, we are able to transform a non-linear regression problem into the generalized linear modeling framework, reducing dramatically the computational cost. The Fisher-scoring method is used for achieving fast convergence of the tensor parameter. The new method is implemented and applied using both synthetic and real data in a wide range of b-amplitudes up to 14,000s/mm(2). Higher accuracy and precision of the Rician estimates are achieved compared with other log-normal based methods. In addition, we extend the maximum likelihood (ML) framework to the maximum a posteriori (MAP) estimation in DTI under the aforementioned scheme by specifying the priors. We will describe how close numerically are the estimators of model parameters obtained through MLE and MAP estimation. Copyright © 2015 Elsevier B.V. All rights reserved.

Audio visual speech source separation via improved context dependent association model

NASA Astrophysics Data System (ADS)

Kazemi, Alireza; Boostani, Reza; Sobhanmanesh, Fariborz

2014-12-01

In this paper, we exploit the non-linear relation between a speech source and its associated lip video as a source of extra information to propose an improved audio-visual speech source separation (AVSS) algorithm. The audio-visual association is modeled using a neural associator which estimates the visual lip parameters from a temporal context of acoustic observation frames. We define an objective function based on mean square error (MSE) measure between estimated and target visual parameters. This function is minimized for estimation of the de-mixing vector/filters to separate the relevant source from linear instantaneous or time-domain convolutive mixtures. We have also proposed a hybrid criterion which uses AV coherency together with kurtosis as a non-Gaussianity measure. Experimental results are presented and compared in terms of visually relevant speech detection accuracy and output signal-to-interference ratio (SIR) of source separation. The suggested audio-visual model significantly improves relevant speech classification accuracy compared to existing GMM-based model and the proposed AVSS algorithm improves the speech separation quality compared to reference ICA- and AVSS-based methods.

Formation of parametric images using mixed-effects models: a feasibility study.

PubMed

Huang, Husan-Ming; Shih, Yi-Yu; Lin, Chieh

2016-03-01

Mixed-effects models have been widely used in the analysis of longitudinal data. By presenting the parameters as a combination of fixed effects and random effects, mixed-effects models incorporating both within- and between-subject variations are capable of improving parameter estimation. In this work, we demonstrate the feasibility of using a non-linear mixed-effects (NLME) approach for generating parametric images from medical imaging data of a single study. By assuming that all voxels in the image are independent, we used simulation and animal data to evaluate whether NLME can improve the voxel-wise parameter estimation. For testing purposes, intravoxel incoherent motion (IVIM) diffusion parameters including perfusion fraction, pseudo-diffusion coefficient and true diffusion coefficient were estimated using diffusion-weighted MR images and NLME through fitting the IVIM model. The conventional method of non-linear least squares (NLLS) was used as the standard approach for comparison of the resulted parametric images. In the simulated data, NLME provides more accurate and precise estimates of diffusion parameters compared with NLLS. Similarly, we found that NLME has the ability to improve the signal-to-noise ratio of parametric images obtained from rat brain data. These data have shown that it is feasible to apply NLME in parametric image generation, and the parametric image quality can be accordingly improved with the use of NLME. With the flexibility to be adapted to other models or modalities, NLME may become a useful tool to improve the parametric image quality in the future. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Mathematical model for the contribution of individual organs to non-zero y-intercepts in single and multi-compartment linear models of whole-body energy expenditure.

PubMed

Kaiyala, Karl J

2014-01-01

Mathematical models for the dependence of energy expenditure (EE) on body mass and composition are essential tools in metabolic phenotyping. EE scales over broad ranges of body mass as a non-linear allometric function. When considered within restricted ranges of body mass, however, allometric EE curves exhibit 'local linearity.' Indeed, modern EE analysis makes extensive use of linear models. Such models typically involve one or two body mass compartments (e.g., fat free mass and fat mass). Importantly, linear EE models typically involve a non-zero (usually positive) y-intercept term of uncertain origin, a recurring theme in discussions of EE analysis and a source of confounding in traditional ratio-based EE normalization. Emerging linear model approaches quantify whole-body resting EE (REE) in terms of individual organ masses (e.g., liver, kidneys, heart, brain). Proponents of individual organ REE modeling hypothesize that multi-organ linear models may eliminate non-zero y-intercepts. This could have advantages in adjusting REE for body mass and composition. Studies reveal that individual organ REE is an allometric function of total body mass. I exploit first-order Taylor linearization of individual organ REEs to model the manner in which individual organs contribute to whole-body REE and to the non-zero y-intercept in linear REE models. The model predicts that REE analysis at the individual organ-tissue level will not eliminate intercept terms. I demonstrate that the parameters of a linear EE equation can be transformed into the parameters of the underlying 'latent' allometric equation. This permits estimates of the allometric scaling of EE in a diverse variety of physiological states that are not represented in the allometric EE literature but are well represented by published linear EE analyses.

The Box-Cox power transformation on nursing sensitive indicators: Does it matter if structural effects are omitted during the estimation of the transformation parameter?

PubMed Central

2011-01-01

Background Many nursing and health related research studies have continuous outcome measures that are inherently non-normal in distribution. The Box-Cox transformation provides a powerful tool for developing a parsimonious model for data representation and interpretation when the distribution of the dependent variable, or outcome measure, of interest deviates from the normal distribution. The objectives of this study was to contrast the effect of obtaining the Box-Cox power transformation parameter and subsequent analysis of variance with or without a priori knowledge of predictor variables under the classic linear or linear mixed model settings. Methods Simulation data from a 3 × 4 factorial treatments design, along with the Patient Falls and Patient Injury Falls from the National Database of Nursing Quality Indicators (NDNQI®) for the 3rd quarter of 2007 from a convenience sample of over one thousand US hospitals were analyzed. The effect of the nonlinear monotonic transformation was contrasted in two ways: a) estimating the transformation parameter along with factors with potential structural effects, and b) estimating the transformation parameter first and then conducting analysis of variance for the structural effect. Results Linear model ANOVA with Monte Carlo simulation and mixed models with correlated error terms with NDNQI examples showed no substantial differences on statistical tests for structural effects if the factors with structural effects were omitted during the estimation of the transformation parameter. Conclusions The Box-Cox power transformation can still be an effective tool for validating statistical inferences with large observational, cross-sectional, and hierarchical or repeated measure studies under the linear or the mixed model settings without prior knowledge of all the factors with potential structural effects. PMID:21854614

The Box-Cox power transformation on nursing sensitive indicators: does it matter if structural effects are omitted during the estimation of the transformation parameter?

PubMed

Hou, Qingjiang; Mahnken, Jonathan D; Gajewski, Byron J; Dunton, Nancy

2011-08-19

Many nursing and health related research studies have continuous outcome measures that are inherently non-normal in distribution. The Box-Cox transformation provides a powerful tool for developing a parsimonious model for data representation and interpretation when the distribution of the dependent variable, or outcome measure, of interest deviates from the normal distribution. The objectives of this study was to contrast the effect of obtaining the Box-Cox power transformation parameter and subsequent analysis of variance with or without a priori knowledge of predictor variables under the classic linear or linear mixed model settings. Simulation data from a 3 × 4 factorial treatments design, along with the Patient Falls and Patient Injury Falls from the National Database of Nursing Quality Indicators (NDNQI® for the 3rd quarter of 2007 from a convenience sample of over one thousand US hospitals were analyzed. The effect of the nonlinear monotonic transformation was contrasted in two ways: a) estimating the transformation parameter along with factors with potential structural effects, and b) estimating the transformation parameter first and then conducting analysis of variance for the structural effect. Linear model ANOVA with Monte Carlo simulation and mixed models with correlated error terms with NDNQI examples showed no substantial differences on statistical tests for structural effects if the factors with structural effects were omitted during the estimation of the transformation parameter. The Box-Cox power transformation can still be an effective tool for validating statistical inferences with large observational, cross-sectional, and hierarchical or repeated measure studies under the linear or the mixed model settings without prior knowledge of all the factors with potential structural effects.

Model-Based Engine Control Architecture with an Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Csank, Jeffrey T.; Connolly, Joseph W.

2016-01-01

This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The non-linear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.

Linear Parameter Varying Control Synthesis for Actuator Failure, Based on Estimated Parameter

NASA Technical Reports Server (NTRS)

Shin, Jong-Yeob; Wu, N. Eva; Belcastro, Christine

2002-01-01

The design of a linear parameter varying (LPV) controller for an aircraft at actuator failure cases is presented. The controller synthesis for actuator failure cases is formulated into linear matrix inequality (LMI) optimizations based on an estimated failure parameter with pre-defined estimation error bounds. The inherent conservatism of an LPV control synthesis methodology is reduced using a scaling factor on the uncertainty block which represents estimated parameter uncertainties. The fault parameter is estimated using the two-stage Kalman filter. The simulation results of the designed LPV controller for a HiMXT (Highly Maneuverable Aircraft Technology) vehicle with the on-line estimator show that the desired performance and robustness objectives are achieved for actuator failure cases.

Stochastic sediment property inversion in Shallow Water 06.

PubMed

Michalopoulou, Zoi-Heleni

2017-11-01

Received time-series at a short distance from the source allow the identification of distinct paths; four of these are direct, surface and bottom reflections, and sediment reflection. In this work, a Gibbs sampling method is used for the estimation of the arrival times of these paths and the corresponding probability density functions. The arrival times for the first three paths are then employed along with linearization for the estimation of source range and depth, water column depth, and sound speed in the water. Propagating densities of arrival times through the linearized inverse problem, densities are also obtained for the above parameters, providing maximum a posteriori estimates. These estimates are employed to calculate densities and point estimates of sediment sound speed and thickness using a non-linear, grid-based model. Density computation is an important aspect of this work, because those densities express the uncertainty in the inversion for sediment properties.

Prediction of HDR quality by combining perceptually transformed display measurements with machine learning

NASA Astrophysics Data System (ADS)

Choudhury, Anustup; Farrell, Suzanne; Atkins, Robin; Daly, Scott

2017-09-01

We present an approach to predict overall HDR display quality as a function of key HDR display parameters. We first performed subjective experiments on a high quality HDR display that explored five key HDR display parameters: maximum luminance, minimum luminance, color gamut, bit-depth and local contrast. Subjects rated overall quality for different combinations of these display parameters. We explored two models | a physical model solely based on physically measured display characteristics and a perceptual model that transforms physical parameters using human vision system models. For the perceptual model, we use a family of metrics based on a recently published color volume model (ICT-CP), which consists of the PQ luminance non-linearity (ST2084) and LMS-based opponent color, as well as an estimate of the display point spread function. To predict overall visual quality, we apply linear regression and machine learning techniques such as Multilayer Perceptron, RBF and SVM networks. We use RMSE and Pearson/Spearman correlation coefficients to quantify performance. We found that the perceptual model is better at predicting subjective quality than the physical model and that SVM is better at prediction than linear regression. The significance and contribution of each display parameter was investigated. In addition, we found that combined parameters such as contrast do not improve prediction. Traditional perceptual models were also evaluated and we found that models based on the PQ non-linearity performed better.

Whole-body PET parametric imaging employing direct 4D nested reconstruction and a generalized non-linear Patlak model

NASA Astrophysics Data System (ADS)

Karakatsanis, Nicolas A.; Rahmim, Arman

2014-03-01

Graphical analysis is employed in the research setting to provide quantitative estimation of PET tracer kinetics from dynamic images at a single bed. Recently, we proposed a multi-bed dynamic acquisition framework enabling clinically feasible whole-body parametric PET imaging by employing post-reconstruction parameter estimation. In addition, by incorporating linear Patlak modeling within the system matrix, we enabled direct 4D reconstruction in order to effectively circumvent noise amplification in dynamic whole-body imaging. However, direct 4D Patlak reconstruction exhibits a relatively slow convergence due to the presence of non-sparse spatial correlations in temporal kinetic analysis. In addition, the standard Patlak model does not account for reversible uptake, thus underestimating the influx rate Ki. We have developed a novel whole-body PET parametric reconstruction framework in the STIR platform, a widely employed open-source reconstruction toolkit, a) enabling accelerated convergence of direct 4D multi-bed reconstruction, by employing a nested algorithm to decouple the temporal parameter estimation from the spatial image update process, and b) enhancing the quantitative performance particularly in regions with reversible uptake, by pursuing a non-linear generalized Patlak 4D nested reconstruction algorithm. A set of published kinetic parameters and the XCAT phantom were employed for the simulation of dynamic multi-bed acquisitions. Quantitative analysis on the Ki images demonstrated considerable acceleration in the convergence of the nested 4D whole-body Patlak algorithm. In addition, our simulated and patient whole-body data in the postreconstruction domain indicated the quantitative benefits of our extended generalized Patlak 4D nested reconstruction for tumor diagnosis and treatment response monitoring.

A Non-linear Geodetic Data Inversion Using ABIC for Slip Distribution on a Fault With an Unknown dip Angle

NASA Astrophysics Data System (ADS)

Fukahata, Y.; Wright, T. J.

2006-12-01

We developed a method of geodetic data inversion for slip distribution on a fault with an unknown dip angle. When fault geometry is unknown, the problem of geodetic data inversion is non-linear. A common strategy for obtaining slip distribution is to first determine the fault geometry by minimizing the square misfit under the assumption of a uniform slip on a rectangular fault, and then apply the usual linear inversion technique to estimate a slip distribution on the determined fault. It is not guaranteed, however, that the fault determined under the assumption of a uniform slip gives the best fault geometry for a spatially variable slip distribution. In addition, in obtaining a uniform slip fault model, we have to simultaneously determine the values of the nine mutually dependent parameters, which is a highly non-linear, complicated process. Although the inverse problem is non-linear for cases with unknown fault geometries, the non-linearity of the problems is actually weak, when we can assume the fault surface to be flat. In particular, when a clear fault trace is observed on the EarthOs surface after an earthquake, we can precisely estimate the strike and the location of the fault. In this case only the dip angle has large ambiguity. In geodetic data inversion we usually need to introduce smoothness constraints in order to compromise reciprocal requirements for model resolution and estimation errors in a natural way. Strictly speaking, the inverse problem with smoothness constraints is also non-linear, even if the fault geometry is known. The non-linearity has been dissolved by introducing AkaikeOs Bayesian Information Criterion (ABIC), with which the optimal value of the relative weight of observed data to smoothness constraints is objectively determined. In this study, using ABIC in determining the optimal dip angle, we dissolved the non-linearity of the inverse problem. We applied the method to the InSAR data of the 1995 Dinar, Turkey earthquake and obtained a much shallower dip angle than before.

Missing-value estimation using linear and non-linear regression with Bayesian gene selection.

PubMed

Zhou, Xiaobo; Wang, Xiaodong; Dougherty, Edward R

2003-11-22

Data from microarray experiments are usually in the form of large matrices of expression levels of genes under different experimental conditions. Owing to various reasons, there are frequently missing values. Estimating these missing values is important because they affect downstream analysis, such as clustering, classification and network design. Several methods of missing-value estimation are in use. The problem has two parts: (1) selection of genes for estimation and (2) design of an estimation rule. We propose Bayesian variable selection to obtain genes to be used for estimation, and employ both linear and nonlinear regression for the estimation rule itself. Fast implementation issues for these methods are discussed, including the use of QR decomposition for parameter estimation. The proposed methods are tested on data sets arising from hereditary breast cancer and small round blue-cell tumors. The results compare very favorably with currently used methods based on the normalized root-mean-square error. The appendix is available from http://gspsnap.tamu.edu/gspweb/zxb/missing_zxb/ (user: gspweb; passwd: gsplab).

Weighted linear least squares estimation of diffusion MRI parameters: strengths, limitations, and pitfalls.

PubMed

Veraart, Jelle; Sijbers, Jan; Sunaert, Stefan; Leemans, Alexander; Jeurissen, Ben

2013-11-01

Linear least squares estimators are widely used in diffusion MRI for the estimation of diffusion parameters. Although adding proper weights is necessary to increase the precision of these linear estimators, there is no consensus on how to practically define them. In this study, the impact of the commonly used weighting strategies on the accuracy and precision of linear diffusion parameter estimators is evaluated and compared with the nonlinear least squares estimation approach. Simulation and real data experiments were done to study the performance of the weighted linear least squares estimators with weights defined by (a) the squares of the respective noisy diffusion-weighted signals; and (b) the squares of the predicted signals, which are reconstructed from a previous estimate of the diffusion model parameters. The negative effect of weighting strategy (a) on the accuracy of the estimator was surprisingly high. Multi-step weighting strategies yield better performance and, in some cases, even outperformed the nonlinear least squares estimator. If proper weighting strategies are applied, the weighted linear least squares approach shows high performance characteristics in terms of accuracy/precision and may even be preferred over nonlinear estimation methods. Copyright © 2013 Elsevier Inc. All rights reserved.

Bypassing the Limits of Ll Regularization: Convex Sparse Signal Processing Using Non-Convex Regularization

NASA Astrophysics Data System (ADS)

Parekh, Ankit

Sparsity has become the basis of some important signal processing methods over the last ten years. Many signal processing problems (e.g., denoising, deconvolution, non-linear component analysis) can be expressed as inverse problems. Sparsity is invoked through the formulation of an inverse problem with suitably designed regularization terms. The regularization terms alone encode sparsity into the problem formulation. Often, the ℓ1 norm is used to induce sparsity, so much so that ℓ1 regularization is considered to be `modern least-squares'. The use of ℓ1 norm, as a sparsity-inducing regularizer, leads to a convex optimization problem, which has several benefits: the absence of extraneous local minima, well developed theory of globally convergent algorithms, even for large-scale problems. Convex regularization via the ℓ1 norm, however, tends to under-estimate the non-zero values of sparse signals. In order to estimate the non-zero values more accurately, non-convex regularization is often favored over convex regularization. However, non-convex regularization generally leads to non-convex optimization, which suffers from numerous issues: convergence may be guaranteed to only a stationary point, problem specific parameters may be difficult to set, and the solution is sensitive to the initialization of the algorithm. The first part of this thesis is aimed toward combining the benefits of non-convex regularization and convex optimization to estimate sparse signals more effectively. To this end, we propose to use parameterized non-convex regularizers with designated non-convexity and provide a range for the non-convex parameter so as to ensure that the objective function is strictly convex. By ensuring convexity of the objective function (sum of data-fidelity and non-convex regularizer), we can make use of a wide variety of convex optimization algorithms to obtain the unique global minimum reliably. The second part of this thesis proposes a non-linear signal decomposition technique for an important biomedical signal processing problem: the detection of sleep spindles and K-complexes in human sleep electroencephalography (EEG). We propose a non-linear model for the EEG consisting of three components: (1) a transient (sparse piecewise constant) component, (2) a low-frequency component, and (3) an oscillatory component. The oscillatory component admits a sparse time-frequency representation. Using a convex objective function, we propose a fast non-linear optimization algorithm to estimate the three components in the proposed signal model. The low-frequency and oscillatory components are then used to estimate the K-complexes and sleep spindles respectively. The proposed detection method is shown to outperform several state-of-the-art automated sleep spindles detection methods.

Parameters estimation for reactive transport: A way to test the validity of a reactive model

NASA Astrophysics Data System (ADS)

Aggarwal, Mohit; Cheikh Anta Ndiaye, Mame; Carrayrou, Jérôme

The chemical parameters used in reactive transport models are not known accurately due to the complexity and the heterogeneous conditions of a real domain. We will present an efficient algorithm in order to estimate the chemical parameters using Monte-Carlo method. Monte-Carlo methods are very robust for the optimisation of the highly non-linear mathematical model describing reactive transport. Reactive transport of tributyltin (TBT) through natural quartz sand at seven different pHs is taken as the test case. Our algorithm will be used to estimate the chemical parameters of the sorption of TBT onto the natural quartz sand. By testing and comparing three models of surface complexation, we show that the proposed adsorption model cannot explain the experimental data.

Non-intrusive parameter identification procedure user's guide

NASA Technical Reports Server (NTRS)

Hanson, G. D.; Jewell, W. F.

1983-01-01

Written in standard FORTRAN, NAS is capable of identifying linear as well as nonlinear relations between input and output parameters; the only restriction is that the input/output relation be linear with respect to the unknown coefficients of the estimation equations. The output of the identification algorithm can be specified to be in either the time domain (i.e., the estimation equation coefficients) or in the frequency domain (i.e., a frequency response of the estimation equation). The frame length ("window") over which the identification procedure is to take place can be specified to be any portion of the input time history, thereby allowing the freedom to start and stop the identification procedure within a time history. There also is an option which allows a sliding window, which gives a moving average over the time history. The NAS software also includes the ability to identify several assumed solutions simultaneously for the same or different input data.

Comparison of least squares and exponential sine sweep methods for Parallel Hammerstein Models estimation

NASA Astrophysics Data System (ADS)

Rebillat, Marc; Schoukens, Maarten

2018-05-01

Linearity is a common assumption for many real-life systems, but in many cases the nonlinear behavior of systems cannot be ignored and must be modeled and estimated. Among the various existing classes of nonlinear models, Parallel Hammerstein Models (PHM) are interesting as they are at the same time easy to interpret as well as to estimate. One way to estimate PHM relies on the fact that the estimation problem is linear in the parameters and thus that classical least squares (LS) estimation algorithms can be used. In that area, this article introduces a regularized LS estimation algorithm inspired on some of the recently developed regularized impulse response estimation techniques. Another mean to estimate PHM consists in using parametric or non-parametric exponential sine sweeps (ESS) based methods. These methods (LS and ESS) are founded on radically different mathematical backgrounds but are expected to tackle the same issue. A methodology is proposed here to compare them with respect to (i) their accuracy, (ii) their computational cost, and (iii) their robustness to noise. Tests are performed on simulated systems for several values of methods respective parameters and of signal to noise ratio. Results show that, for a given set of data points, the ESS method is less demanding in computational resources than the LS method but that it is also less accurate. Furthermore, the LS method needs parameters to be set in advance whereas the ESS method is not subject to conditioning issues and can be fully non-parametric. In summary, for a given set of data points, ESS method can provide a first, automatic, and quick overview of a nonlinear system than can guide more computationally demanding and precise methods, such as the regularized LS one proposed here.

Estimation of parameters in rational reaction rates of molecular biological systems via weighted least squares

NASA Astrophysics Data System (ADS)

Wu, Fang-Xiang; Mu, Lei; Shi, Zhong-Ke

2010-01-01

The models of gene regulatory networks are often derived from statistical thermodynamics principle or Michaelis-Menten kinetics equation. As a result, the models contain rational reaction rates which are nonlinear in both parameters and states. It is challenging to estimate parameters nonlinear in a model although there have been many traditional nonlinear parameter estimation methods such as Gauss-Newton iteration method and its variants. In this article, we develop a two-step method to estimate the parameters in rational reaction rates of gene regulatory networks via weighted linear least squares. This method takes the special structure of rational reaction rates into consideration. That is, in the rational reaction rates, the numerator and the denominator are linear in parameters. By designing a special weight matrix for the linear least squares, parameters in the numerator and the denominator can be estimated by solving two linear least squares problems. The main advantage of the developed method is that it can produce the analytical solutions to the estimation of parameters in rational reaction rates which originally is nonlinear parameter estimation problem. The developed method is applied to a couple of gene regulatory networks. The simulation results show the superior performance over Gauss-Newton method.

Fitting and forecasting coupled dark energy in the non-linear regime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Casas, Santiago; Amendola, Luca; Pettorino, Valeria

2016-01-01

We consider cosmological models in which dark matter feels a fifth force mediated by the dark energy scalar field, also known as coupled dark energy. Our interest resides in estimating forecasts for future surveys like Euclid when we take into account non-linear effects, relying on new fitting functions that reproduce the non-linear matter power spectrum obtained from N-body simulations. We obtain fitting functions for models in which the dark matter-dark energy coupling is constant. Their validity is demonstrated for all available simulations in the redshift range 0z=–1.6 and wave modes below 0k=1 h/Mpc. These fitting formulas can be used tomore » test the predictions of the model in the non-linear regime without the need for additional computing-intensive N-body simulations. We then use these fitting functions to perform forecasts on the constraining power that future galaxy-redshift surveys like Euclid will have on the coupling parameter, using the Fisher matrix method for galaxy clustering (GC) and weak lensing (WL). We find that by using information in the non-linear power spectrum, and combining the GC and WL probes, we can constrain the dark matter-dark energy coupling constant squared, β{sup 2}, with precision smaller than 4% and all other cosmological parameters better than 1%, which is a considerable improvement of more than an order of magnitude compared to corresponding linear power spectrum forecasts with the same survey specifications.« less

Quasi-Newton methods for parameter estimation in functional differential equations

NASA Technical Reports Server (NTRS)

Brewer, Dennis W.

1988-01-01

A state-space approach to parameter estimation in linear functional differential equations is developed using the theory of linear evolution equations. A locally convergent quasi-Newton type algorithm is applied to distributed systems with particular emphasis on parameters that induce unbounded perturbations of the state. The algorithm is computationally implemented on several functional differential equations, including coefficient and delay estimation in linear delay-differential equations.

Difference-based ridge-type estimator of parameters in restricted partial linear model with correlated errors.

PubMed

Wu, Jibo

2016-01-01

In this article, a generalized difference-based ridge estimator is proposed for the vector parameter in a partial linear model when the errors are dependent. It is supposed that some additional linear constraints may hold to the whole parameter space. Its mean-squared error matrix is compared with the generalized restricted difference-based estimator. Finally, the performance of the new estimator is explained by a simulation study and a numerical example.

A simplified method for power-law modelling of metabolic pathways from time-course data and steady-state flux profiles.

PubMed

Kitayama, Tomoya; Kinoshita, Ayako; Sugimoto, Masahiro; Nakayama, Yoichi; Tomita, Masaru

2006-07-17

In order to improve understanding of metabolic systems there have been attempts to construct S-system models from time courses. Conventionally, non-linear curve-fitting algorithms have been used for modelling, because of the non-linear properties of parameter estimation from time series. However, the huge iterative calculations required have hindered the development of large-scale metabolic pathway models. To solve this problem we propose a novel method involving power-law modelling of metabolic pathways from the Jacobian of the targeted system and the steady-state flux profiles by linearization of S-systems. The results of two case studies modelling a straight and a branched pathway, respectively, showed that our method reduced the number of unknown parameters needing to be estimated. The time-courses simulated by conventional kinetic models and those described by our method behaved similarly under a wide range of perturbations of metabolite concentrations. The proposed method reduces calculation complexity and facilitates the construction of large-scale S-system models of metabolic pathways, realizing a practical application of reverse engineering of dynamic simulation models from the Jacobian of the targeted system and steady-state flux profiles.

3D non-linear inversion of magnetic anomalies caused by prismatic bodies using differential evolution algorithm

NASA Astrophysics Data System (ADS)

Balkaya, Çağlayan; Ekinci, Yunus Levent; Göktürkler, Gökhan; Turan, Seçil

2017-01-01

3D non-linear inversion of total field magnetic anomalies caused by vertical-sided prismatic bodies has been achieved by differential evolution (DE), which is one of the population-based evolutionary algorithms. We have demonstrated the efficiency of the algorithm on both synthetic and field magnetic anomalies by estimating horizontal distances from the origin in both north and east directions, depths to the top and bottom of the bodies, inclination and declination angles of the magnetization, and intensity of magnetization of the causative bodies. In the synthetic anomaly case, we have considered both noise-free and noisy data sets due to two vertical-sided prismatic bodies in a non-magnetic medium. For the field case, airborne magnetic anomalies originated from intrusive granitoids at the eastern part of the Biga Peninsula (NW Turkey) which is composed of various kinds of sedimentary, metamorphic and igneous rocks, have been inverted and interpreted. Since the granitoids are the outcropped rocks in the field, the estimations for the top depths of two prisms representing the magnetic bodies were excluded during inversion studies. Estimated bottom depths are in good agreement with the ones obtained by a different approach based on 3D modelling of pseudogravity anomalies. Accuracy of the estimated parameters from both cases has been also investigated via probability density functions. Based on the tests in the present study, it can be concluded that DE is a useful tool for the parameter estimation of source bodies using magnetic anomalies.

Degree-of-Freedom Strengthened Cascade Array for DOD-DOA Estimation in MIMO Array Systems.

PubMed

Yao, Bobin; Dong, Zhi; Zhang, Weile; Wang, Wei; Wu, Qisheng

2018-05-14

In spatial spectrum estimation, difference co-array can provide extra degrees-of-freedom (DOFs) for promoting parameter identifiability and parameter estimation accuracy. For the sake of acquiring as more DOFs as possible with a given number of physical sensors, we herein design a novel sensor array geometry named cascade array. This structure is generated by systematically connecting a uniform linear array (ULA) and a non-uniform linear array, and can provide more DOFs than some exist array structures but less than the upper-bound indicated by minimum redundant array (MRA). We further apply this cascade array into multiple input multiple output (MIMO) array systems, and propose a novel joint direction of departure (DOD) and direction of arrival (DOA) estimation algorithm, which is based on a reduced-dimensional weighted subspace fitting technique. The algorithm is angle auto-paired and computationally efficient. Theoretical analysis and numerical simulations prove the advantages and effectiveness of the proposed array structure and the related algorithm.

Prediction of the sorption capacities and affinities of organic chemicals by XAD-7.

PubMed

Yang, Kun; Qi, Long; Wei, Wei; Wu, Wenhao; Lin, Daohui

2016-01-01

Macro-porous resins are widely used as adsorbents for the treatment of organic contaminants in wastewater and for the pre-concentration of organic solutes from water. However, the sorption mechanisms for organic contaminants on such adsorbents have not been systematically investigated so far. Therefore, in this study, the sorption capacities and affinities of 24 organic chemicals by XAD-7 were investigated and the experimentally obtained sorption isotherms were fitted to the Dubinin-Ashtakhov model. Linear positive correlations were observed between the sorption capacities and the solubilities (SW) of the chemicals in water or octanol and between the sorption affinities and the solvatochromic parameters of the chemicals, indicating that the sorption of various organic compounds by XAD-7 occurred by non-linear partitioning into XAD-7, rather than by adsorption on XAD-7 surfaces. Both specific interactions (i.e., hydrogen-bonding interactions) as well as nonspecific interactions were considered to be responsible for the non-linear partitioning. The correlation equations obtained in this study allow the prediction of non-linear partitioning using well-known chemical parameters, namely SW, octanol-water partition coefficients (KOW), and the hydrogen-bonding donor parameter (αm). The effect of pH on the sorption of ionizable organic compounds (IOCs) could also be predicted by combining the correlation equations with additional equations developed from the estimation of IOC dissociation rates. The prediction equations developed in this study and the proposed non-linear partition mechanism shed new light on the selective removal and pre-concentration of organic solutes from water and on the regeneration of exhausted XAD-7 using solvent extraction.

Technical notes and correspondence: Stochastic robustness of linear time-invariant control systems

NASA Technical Reports Server (NTRS)

Stengel, Robert F.; Ray, Laura R.

1991-01-01

A simple numerical procedure for estimating the stochastic robustness of a linear time-invariant system is described. Monte Carlo evaluations of the system's eigenvalues allows the probability of instability and the related stochastic root locus to be estimated. This analysis approach treats not only Gaussian parameter uncertainties but non-Gaussian cases, including uncertain-but-bounded variation. Confidence intervals for the scalar probability of instability address computational issues inherent in Monte Carlo simulation. Trivial extensions of the procedure admit consideration of alternate discriminants; thus, the probabilities that stipulated degrees of instability will be exceeded or that closed-loop roots will leave desirable regions can also be estimated. Results are particularly amenable to graphical presentation.

Quasi- and pseudo-maximum likelihood estimators for discretely observed continuous-time Markov branching processes

PubMed Central

Chen, Rui; Hyrien, Ollivier

2011-01-01

This article deals with quasi- and pseudo-likelihood estimation in a class of continuous-time multi-type Markov branching processes observed at discrete points in time. “Conventional” and conditional estimation are discussed for both approaches. We compare their properties and identify situations where they lead to asymptotically equivalent estimators. Both approaches possess robustness properties, and coincide with maximum likelihood estimation in some cases. Quasi-likelihood functions involving only linear combinations of the data may be unable to estimate all model parameters. Remedial measures exist, including the resort either to non-linear functions of the data or to conditioning the moments on appropriate sigma-algebras. The method of pseudo-likelihood may also resolve this issue. We investigate the properties of these approaches in three examples: the pure birth process, the linear birth-and-death process, and a two-type process that generalizes the previous two examples. Simulations studies are conducted to evaluate performance in finite samples. PMID:21552356

Scale-up of a physiologically-based pharmacokinetic model to predict the disposition of monoclonal antibodies in monkeys.

PubMed

Glassman, Patrick M; Chen, Yang; Balthasar, Joseph P

2015-10-01

Preclinical assessment of monoclonal antibody (mAb) disposition during drug development often includes investigations in non-human primate models. In many cases, mAb exhibit non-linear disposition that relates to mAb-target binding [i.e., target-mediated disposition (TMD)]. The goal of this work was to develop a physiologically-based pharmacokinetic (PBPK) model to predict non-linear mAb disposition in plasma and in tissues in monkeys. Physiological parameters for monkeys were collected from several sources, and plasma data for several mAbs associated with linear pharmacokinetics were digitized from prior literature reports. The digitized data displayed great variability; therefore, parameters describing inter-antibody variability in the rates of pinocytosis and convection were estimated. For prediction of the disposition of individual antibodies, we incorporated tissue concentrations of target proteins, where concentrations were estimated based on categorical immunohistochemistry scores, and with assumed localization of target within the interstitial space of each organ. Kinetics of target-mAb binding and target turnover, in the presence or absence of mAb, were implemented. The model was then employed to predict concentration versus time data, via Monte Carlo simulation, for two mAb that have been shown to exhibit TMD (2F8 and tocilizumab). Model predictions, performed a priori with no parameter fitting, were found to provide good prediction of dose-dependencies in plasma clearance, the areas under plasma concentration versu time curves, and the time-course of plasma concentration data. This PBPK model may find utility in predicting plasma and tissue concentration versus time data and, potentially, the time-course of receptor occupancy (i.e., mAb-target binding) to support the design and interpretation of preclinical pharmacokinetic-pharmacodynamic investigations in non-human primates.

Mean-square state and parameter estimation for stochastic linear systems with Gaussian and Poisson noises

NASA Astrophysics Data System (ADS)

Basin, M.; Maldonado, J. J.; Zendejo, O.

2016-07-01

This paper proposes new mean-square filter and parameter estimator design for linear stochastic systems with unknown parameters over linear observations, where unknown parameters are considered as combinations of Gaussian and Poisson white noises. The problem is treated by reducing the original problem to a filtering problem for an extended state vector that includes parameters as additional states, modelled as combinations of independent Gaussian and Poisson processes. The solution to this filtering problem is based on the mean-square filtering equations for incompletely polynomial states confused with Gaussian and Poisson noises over linear observations. The resulting mean-square filter serves as an identifier for the unknown parameters. Finally, a simulation example shows effectiveness of the proposed mean-square filter and parameter estimator.

Multi-Axis Identifiability Using Single-Surface Parameter Estimation Maneuvers on the X-48B Blended Wing Body

NASA Technical Reports Server (NTRS)

Ratnayake, Nalin A.; Koshimoto, Ed T.; Taylor, Brian R.

2011-01-01

The problem of parameter estimation on hybrid-wing-body type aircraft is complicated by the fact that many design candidates for such aircraft involve a large number of aero- dynamic control effectors that act in coplanar motion. This fact adds to the complexity already present in the parameter estimation problem for any aircraft with a closed-loop control system. Decorrelation of system inputs must be performed in order to ascertain individual surface derivatives with any sort of mathematical confidence. Non-standard control surface configurations, such as clamshell surfaces and drag-rudder modes, further complicate the modeling task. In this paper, asymmetric, single-surface maneuvers are used to excite multiple axes of aircraft motion simultaneously. Time history reconstructions of the moment coefficients computed by the solved regression models are then compared to each other in order to assess relative model accuracy. The reduced flight-test time required for inner surface parameter estimation using multi-axis methods was found to come at the cost of slightly reduced accuracy and statistical confidence for linear regression methods. Since the multi-axis maneuvers captured parameter estimates similar to both longitudinal and lateral-directional maneuvers combined, the number of test points required for the inner, aileron-like surfaces could in theory have been reduced by 50%. While trends were similar, however, individual parameters as estimated by a multi-axis model were typically different by an average absolute difference of roughly 15-20%, with decreased statistical significance, than those estimated by a single-axis model. The multi-axis model exhibited an increase in overall fit error of roughly 1-5% for the linear regression estimates with respect to the single-axis model, when applied to flight data designed for each, respectively.

Can home-monitoring of sleep predict depressive episodes in bipolar patients?

PubMed

Migliorini, M; Mariani, S; Bertschy, G; Kosel, M; Bianchi, A M

2015-08-01

The aim of this study is the evaluation of the autonomic regulations during depressive stages in bipolar patients in order to test new quantitative and objective measures to detect such events. A sensorized T-shirt was used to record ECG signal and body movements during the night, from which HRV data and sleep macrostructure were estimated and analyzed. 9 out of 20 features extracted resulted to be significant (p<;0.05) in discriminating among depressive and non-depressive states. Such features are representation of HRV dynamics in both linear and non-linear domain and parameters linked to sleep modulations.

Effects of data structure on the estimation of covariance functions to describe genotype by environment interactions in a reaction norm model

PubMed Central

Calus, Mario PL; Bijma, Piter; Veerkamp, Roel F

2004-01-01

Covariance functions have been proposed to predict breeding values and genetic (co)variances as a function of phenotypic within herd-year averages (environmental parameters) to include genotype by environment interaction. The objective of this paper was to investigate the influence of definition of environmental parameters and non-random use of sires on expected breeding values and estimated genetic variances across environments. Breeding values were simulated as a linear function of simulated herd effects. The definition of environmental parameters hardly influenced the results. In situations with random use of sires, estimated genetic correlations between the trait expressed in different environments were 0.93, 0.93 and 0.97 while simulated at 0.89 and estimated genetic variances deviated up to 30% from the simulated values. Non random use of sires, poor genetic connectedness and small herd size had a large impact on the estimated covariance functions, expected breeding values and calculated environmental parameters. Estimated genetic correlations between a trait expressed in different environments were biased upwards and breeding values were more biased when genetic connectedness became poorer and herd composition more diverse. The best possible solution at this stage is to use environmental parameters combining large numbers of animals per herd, while losing some information on genotype by environment interaction in the data. PMID:15339629

Robust estimation of thermodynamic parameters (ΔH, ΔS and ΔCp) for prediction of retention time in gas chromatography - Part I (Theoretical).

PubMed

Claumann, Carlos Alberto; Wüst Zibetti, André; Bolzan, Ariovaldo; Machado, Ricardo A F; Pinto, Leonel Teixeira

2015-12-18

An approach that is commonly used for calculating the retention time of a compound in GC departs from the thermodynamic properties ΔH, ΔS and ΔCp of phase change (from mobile to stationary). Such properties can be estimated by using experimental retention time data, which results in a non-linear regression problem for non-isothermal temperature programs. As shown in this work, the surface of the objective function (approximation error criterion) on the basis of thermodynamic parameters can be divided into three clearly defined regions, and solely in one of them there is a possibility for the global optimum to be found. The main contribution of this study was the development of an algorithm that distinguishes the different regions of the error surface and its use in the robust initialization of the estimation of parameters ΔH, ΔS and ΔCp. Copyright © 2015 Elsevier B.V. All rights reserved.

New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies.

PubMed

Essa, Khalid S

2014-01-01

A new fast least-squares method is developed to estimate the shape factor (q-parameter) of a buried structure using normalized residual anomalies obtained from gravity data. The problem of shape factor estimation is transformed into a problem of finding a solution of a non-linear equation of the form f(q) = 0 by defining the anomaly value at the origin and at different points on the profile (N-value). Procedures are also formulated to estimate the depth (z-parameter) and the amplitude coefficient (A-parameter) of the buried structure. The method is simple and rapid for estimating parameters that produced gravity anomalies. This technique is used for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The technique is tested and verified on theoretical models with and without random errors. It is also successfully applied to real data sets from Senegal and India, and the inverted-parameters are in good agreement with the known actual values.

New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies

PubMed Central

Essa, Khalid S.

2013-01-01

A new fast least-squares method is developed to estimate the shape factor (q-parameter) of a buried structure using normalized residual anomalies obtained from gravity data. The problem of shape factor estimation is transformed into a problem of finding a solution of a non-linear equation of the form f(q) = 0 by defining the anomaly value at the origin and at different points on the profile (N-value). Procedures are also formulated to estimate the depth (z-parameter) and the amplitude coefficient (A-parameter) of the buried structure. The method is simple and rapid for estimating parameters that produced gravity anomalies. This technique is used for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The technique is tested and verified on theoretical models with and without random errors. It is also successfully applied to real data sets from Senegal and India, and the inverted-parameters are in good agreement with the known actual values. PMID:25685472

Optimal HRF and smoothing parameters for fMRI time series within an autoregressive modeling framework.

PubMed

Galka, Andreas; Siniatchkin, Michael; Stephani, Ulrich; Groening, Kristina; Wolff, Stephan; Bosch-Bayard, Jorge; Ozaki, Tohru

2010-12-01

The analysis of time series obtained by functional magnetic resonance imaging (fMRI) may be approached by fitting predictive parametric models, such as nearest-neighbor autoregressive models with exogeneous input (NNARX). As a part of the modeling procedure, it is possible to apply instantaneous linear transformations to the data. Spatial smoothing, a common preprocessing step, may be interpreted as such a transformation. The autoregressive parameters may be constrained, such that they provide a response behavior that corresponds to the canonical haemodynamic response function (HRF). We present an algorithm for estimating the parameters of the linear transformations and of the HRF within a rigorous maximum-likelihood framework. Using this approach, an optimal amount of both the spatial smoothing and the HRF can be estimated simultaneously for a given fMRI data set. An example from a motor-task experiment is discussed. It is found that, for this data set, weak, but non-zero, spatial smoothing is optimal. Furthermore, it is demonstrated that activated regions can be estimated within the maximum-likelihood framework.

Trajectory Reconstruction and Uncertainty Analysis Using Mars Science Laboratory Pre-Flight Scale Model Aeroballistic Testing

NASA Technical Reports Server (NTRS)

Lugo, Rafael A.; Tolson, Robert H.; Schoenenberger, Mark

2013-01-01

As part of the Mars Science Laboratory (MSL) trajectory reconstruction effort at NASA Langley Research Center, free-flight aeroballistic experiments of instrumented MSL scale models was conducted at Aberdeen Proving Ground in Maryland. The models carried an inertial measurement unit (IMU) and a flush air data system (FADS) similar to the MSL Entry Atmospheric Data System (MEADS) that provided data types similar to those from the MSL entry. Multiple sources of redundant data were available, including tracking radar and on-board magnetometers. These experimental data enabled the testing and validation of the various tools and methodologies that will be used for MSL trajectory reconstruction. The aerodynamic parameters Mach number, angle of attack, and sideslip angle were estimated using minimum variance with a priori to combine the pressure data and pre-flight computational fluid dynamics (CFD) data. Both linear and non-linear pressure model terms were also estimated for each pressure transducer as a measure of the errors introduced by CFD and transducer calibration. Parameter uncertainties were estimated using a "consider parameters" approach.

A study on technical efficiency of a DMU (review of literature)

NASA Astrophysics Data System (ADS)

Venkateswarlu, B.; Mahaboob, B.; Subbarami Reddy, C.; Sankar, J. Ravi

2017-11-01

In this research paper the concept of technical efficiency (due to Farell) [1] of a decision making unit (DMU) has been introduced and the measure of technical and cost efficiencies are derived. Timmer’s [2] deterministic approach to estimate the Cobb-Douglas production frontier has been proposed. The idea of extension of Timmer’s [2] method to any production frontier which is linear in parameters has been presented here. The estimation of parameters of Cobb-Douglas production frontier by linear programming approach has been discussed in this paper. Mark et al. [3] proposed a non-parametric method to assess efficiency. Nuti et al. [4] investigated the relationships among technical efficiency scores, weighted per capita cost and overall performance Gahe Zing Samuel Yank et al. [5] used Data envelopment analysis to assess technical assessment in banking sectors.

Mathematical Model for the Contribution of Individual Organs to Non-Zero Y-Intercepts in Single and Multi-Compartment Linear Models of Whole-Body Energy Expenditure

PubMed Central

Kaiyala, Karl J.

2014-01-01

Mathematical models for the dependence of energy expenditure (EE) on body mass and composition are essential tools in metabolic phenotyping. EE scales over broad ranges of body mass as a non-linear allometric function. When considered within restricted ranges of body mass, however, allometric EE curves exhibit ‘local linearity.’ Indeed, modern EE analysis makes extensive use of linear models. Such models typically involve one or two body mass compartments (e.g., fat free mass and fat mass). Importantly, linear EE models typically involve a non-zero (usually positive) y-intercept term of uncertain origin, a recurring theme in discussions of EE analysis and a source of confounding in traditional ratio-based EE normalization. Emerging linear model approaches quantify whole-body resting EE (REE) in terms of individual organ masses (e.g., liver, kidneys, heart, brain). Proponents of individual organ REE modeling hypothesize that multi-organ linear models may eliminate non-zero y-intercepts. This could have advantages in adjusting REE for body mass and composition. Studies reveal that individual organ REE is an allometric function of total body mass. I exploit first-order Taylor linearization of individual organ REEs to model the manner in which individual organs contribute to whole-body REE and to the non-zero y-intercept in linear REE models. The model predicts that REE analysis at the individual organ-tissue level will not eliminate intercept terms. I demonstrate that the parameters of a linear EE equation can be transformed into the parameters of the underlying ‘latent’ allometric equation. This permits estimates of the allometric scaling of EE in a diverse variety of physiological states that are not represented in the allometric EE literature but are well represented by published linear EE analyses. PMID:25068692

Electrostatic interaction between stereocilia: I. Its role in supporting the structure of the hair bundle.

PubMed

Dolgobrodov, S G; Lukashkin, A N; Russell, I J

2000-12-01

This paper provides theoretical estimates for the forces of electrostatic interaction between adjacent stereocilia in auditory and vestibular hair cells. Estimates are given for parameters within the measured physiological range using constraints appropriate for the known geometry of the hair bundle. Stereocilia are assumed to possess an extended, negatively charged surface coat, the glycocalyx. Different charge distribution profiles within the glycocalyx are analysed. It is shown that charged glycocalices on the apical surface of the hair cells can support spatial separation between adjacent stereocilia in the hair bundles through electrostatic repulsion between stereocilia. The charge density profile within the glycocalyx is a crucial parameter. In fact, attraction instead of repulsion between adjacent stereocilia will be observed if the charge of the glycocalyx is concentrated near the membrane of the stereocilia, thereby making this type of charge distribution unlikely. The forces of electrostatic interaction between stereocilia may influence the mechanical properties of the hair bundle and, being strongly non-linear, contribute to the non-linear phenomena that have been recorded from the periphery of the auditory and vestibular systems.

An M-estimator for reduced-rank system identification.

PubMed

Chen, Shaojie; Liu, Kai; Yang, Yuguang; Xu, Yuting; Lee, Seonjoo; Lindquist, Martin; Caffo, Brian S; Vogelstein, Joshua T

2017-01-15

High-dimensional time-series data from a wide variety of domains, such as neuroscience, are being generated every day. Fitting statistical models to such data, to enable parameter estimation and time-series prediction, is an important computational primitive. Existing methods, however, are unable to cope with the high-dimensional nature of these data, due to both computational and statistical reasons. We mitigate both kinds of issues by proposing an M-estimator for Reduced-rank System IDentification ( MR. SID). A combination of low-rank approximations, ℓ 1 and ℓ 2 penalties, and some numerical linear algebra tricks, yields an estimator that is computationally efficient and numerically stable. Simulations and real data examples demonstrate the usefulness of this approach in a variety of problems. In particular, we demonstrate that MR. SID can accurately estimate spatial filters, connectivity graphs, and time-courses from native resolution functional magnetic resonance imaging data. MR. SID therefore enables big time-series data to be analyzed using standard methods, readying the field for further generalizations including non-linear and non-Gaussian state-space models.

An M-estimator for reduced-rank system identification

PubMed Central

Chen, Shaojie; Liu, Kai; Yang, Yuguang; Xu, Yuting; Lee, Seonjoo; Lindquist, Martin; Caffo, Brian S.; Vogelstein, Joshua T.

2018-01-01

High-dimensional time-series data from a wide variety of domains, such as neuroscience, are being generated every day. Fitting statistical models to such data, to enable parameter estimation and time-series prediction, is an important computational primitive. Existing methods, however, are unable to cope with the high-dimensional nature of these data, due to both computational and statistical reasons. We mitigate both kinds of issues by proposing an M-estimator for Reduced-rank System IDentification ( MR. SID). A combination of low-rank approximations, ℓ1 and ℓ2 penalties, and some numerical linear algebra tricks, yields an estimator that is computationally efficient and numerically stable. Simulations and real data examples demonstrate the usefulness of this approach in a variety of problems. In particular, we demonstrate that MR. SID can accurately estimate spatial filters, connectivity graphs, and time-courses from native resolution functional magnetic resonance imaging data. MR. SID therefore enables big time-series data to be analyzed using standard methods, readying the field for further generalizations including non-linear and non-Gaussian state-space models. PMID:29391659

Time-domain induced polarization - an analysis of Cole-Cole parameter resolution and correlation using Markov Chain Monte Carlo inversion

NASA Astrophysics Data System (ADS)

Madsen, Line Meldgaard; Fiandaca, Gianluca; Auken, Esben; Christiansen, Anders Vest

2017-12-01

The application of time-domain induced polarization (TDIP) is increasing with advances in acquisition techniques, data processing and spectral inversion schemes. An inversion of TDIP data for the spectral Cole-Cole parameters is a non-linear problem, but by applying a 1-D Markov Chain Monte Carlo (MCMC) inversion algorithm, a full non-linear uncertainty analysis of the parameters and the parameter correlations can be accessed. This is essential to understand to what degree the spectral Cole-Cole parameters can be resolved from TDIP data. MCMC inversions of synthetic TDIP data, which show bell-shaped probability distributions with a single maximum, show that the Cole-Cole parameters can be resolved from TDIP data if an acquisition range above two decades in time is applied. Linear correlations between the Cole-Cole parameters are observed and by decreasing the acquisitions ranges, the correlations increase and become non-linear. It is further investigated how waveform and parameter values influence the resolution of the Cole-Cole parameters. A limiting factor is the value of the frequency exponent, C. As C decreases, the resolution of all the Cole-Cole parameters decreases and the results become increasingly non-linear. While the values of the time constant, τ, must be in the acquisition range to resolve the parameters well, the choice between a 50 per cent and a 100 per cent duty cycle for the current injection does not have an influence on the parameter resolution. The limits of resolution and linearity are also studied in a comparison between the MCMC and a linearized gradient-based inversion approach. The two methods are consistent for resolved models, but the linearized approach tends to underestimate the uncertainties for poorly resolved parameters due to the corresponding non-linear features. Finally, an MCMC inversion of 1-D field data verifies that spectral Cole-Cole parameters can also be resolved from TD field measurements.

The Routine Fitting of Kinetic Data to Models

PubMed Central

Berman, Mones; Shahn, Ezra; Weiss, Marjory F.

1962-01-01

A mathematical formalism is presented for use with digital computers to permit the routine fitting of data to physical and mathematical models. Given a set of data, the mathematical equations describing a model, initial conditions for an experiment, and initial estimates for the values of model parameters, the computer program automatically proceeds to obtain a least squares fit of the data by an iterative adjustment of the values of the parameters. When the experimental measures are linear combinations of functions, the linear coefficients for a least squares fit may also be calculated. The values of both the parameters of the model and the coefficients for the sum of functions may be unknown independent variables, unknown dependent variables, or known constants. In the case of dependence, only linear dependencies are provided for in routine use. The computer program includes a number of subroutines, each one of which performs a special task. This permits flexibility in choosing various types of solutions and procedures. One subroutine, for example, handles linear differential equations, another, special non-linear functions, etc. The use of analytic or numerical solutions of equations is possible. PMID:13867975

Delineating parameter unidentifiabilities in complex models

NASA Astrophysics Data System (ADS)

Raman, Dhruva V.; Anderson, James; Papachristodoulou, Antonis

2017-03-01

Scientists use mathematical modeling as a tool for understanding and predicting the properties of complex physical systems. In highly parametrized models there often exist relationships between parameters over which model predictions are identical, or nearly identical. These are known as structural or practical unidentifiabilities, respectively. They are hard to diagnose and make reliable parameter estimation from data impossible. They furthermore imply the existence of an underlying model simplification. We describe a scalable method for detecting unidentifiabilities, as well as the functional relations defining them, for generic models. This allows for model simplification, and appreciation of which parameters (or functions thereof) cannot be estimated from data. Our algorithm can identify features such as redundant mechanisms and fast time-scale subsystems, as well as the regimes in parameter space over which such approximations are valid. We base our algorithm on a quantification of regional parametric sensitivity that we call `multiscale sloppiness'. Traditionally, the link between parametric sensitivity and the conditioning of the parameter estimation problem is made locally, through the Fisher information matrix. This is valid in the regime of infinitesimal measurement uncertainty. We demonstrate the duality between multiscale sloppiness and the geometry of confidence regions surrounding parameter estimates made where measurement uncertainty is non-negligible. Further theoretical relationships are provided linking multiscale sloppiness to the likelihood-ratio test. From this, we show that a local sensitivity analysis (as typically done) is insufficient for determining the reliability of parameter estimation, even with simple (non)linear systems. Our algorithm can provide a tractable alternative. We finally apply our methods to a large-scale, benchmark systems biology model of necrosis factor (NF)-κ B , uncovering unidentifiabilities.

Limits of detection and decision. Part 3

NASA Astrophysics Data System (ADS)

Voigtman, E.

2008-02-01

It has been shown that the MARLAP (Multi-Agency Radiological Laboratory Analytical Protocols) for estimating the Currie detection limit, which is based on 'critical values of the non-centrality parameter of the non-central t distribution', is intrinsically biased, even if no calibration curve or regression is used. This completed the refutation of the method, begun in Part 2. With the field cleared of obstructions, the true theory underlying Currie's limits of decision, detection and quantification, as they apply in a simple linear chemical measurement system (CMS) having heteroscedastic, Gaussian measurement noise and using weighted least squares (WLS) processing, was then derived. Extensive Monte Carlo simulations were performed, on 900 million independent calibration curves, for linear, "hockey stick" and quadratic noise precision models (NPMs). With errorless NPM parameters, all the simulation results were found to be in excellent agreement with the derived theoretical expressions. Even with as much as 30% noise on all of the relevant NPM parameters, the worst absolute errors in rates of false positives and false negatives, was only 0.3%.

libSRES: a C library for stochastic ranking evolution strategy for parameter estimation.

PubMed

Ji, Xinglai; Xu, Ying

2006-01-01

Estimation of kinetic parameters in a biochemical pathway or network represents a common problem in systems studies of biological processes. We have implemented a C library, named libSRES, to facilitate a fast implementation of computer software for study of non-linear biochemical pathways. This library implements a (mu, lambda)-ES evolutionary optimization algorithm that uses stochastic ranking as the constraint handling technique. Considering the amount of computing time it might require to solve a parameter-estimation problem, an MPI version of libSRES is provided for parallel implementation, as well as a simple user interface. libSRES is freely available and could be used directly in any C program as a library function. We have extensively tested the performance of libSRES on various pathway parameter-estimation problems and found its performance to be satisfactory. The source code (in C) is free for academic users at http://csbl.bmb.uga.edu/~jix/science/libSRES/

The linearized multistage model and the future of quantitative risk assessment.

PubMed

Crump, K S

1996-10-01

The linearized multistage (LMS) model has for over 15 years been the default dose-response model used by the U.S. Environmental Protection Agency (USEPA) and other federal and state regulatory agencies in the United States for calculating quantitative estimates of low-dose carcinogenic risks from animal data. The LMS model is in essence a flexible statistical model that can describe both linear and non-linear dose-response patterns, and that produces an upper confidence bound on the linear low-dose slope of the dose-response curve. Unlike its namesake, the Armitage-Doll multistage model, the parameters of the LMS do not correspond to actual physiological phenomena. Thus the LMS is 'biological' only to the extent that the true biological dose response is linear at low dose and that low-dose slope is reflected in the experimental data. If the true dose response is non-linear the LMS upper bound may overestimate the true risk by many orders of magnitude. However, competing low-dose extrapolation models, including those derived from 'biologically-based models' that are capable of incorporating additional biological information, have not shown evidence to date of being able to produce quantitative estimates of low-dose risks that are any more accurate than those obtained from the LMS model. Further, even if these attempts were successful, the extent to which more accurate estimates of low-dose risks in a test animal species would translate into improved estimates of human risk is questionable. Thus, it does not appear possible at present to develop a quantitative approach that would be generally applicable and that would offer significant improvements upon the crude bounding estimates of the type provided by the LMS model. Draft USEPA guidelines for cancer risk assessment incorporate an approach similar to the LMS for carcinogens having a linear mode of action. However, under these guidelines quantitative estimates of low-dose risks would not be developed for carcinogens having a non-linear mode of action; instead dose-response modelling would be used in the experimental range to calculate an LED10* (a statistical lower bound on the dose corresponding to a 10% increase in risk), and safety factors would be applied to the LED10* to determine acceptable exposure levels for humans. This approach is very similar to the one presently used by USEPA for non-carcinogens. Rather than using one approach for carcinogens believed to have a linear mode of action and a different approach for all other health effects, it is suggested herein that it would be more appropriate to use an approach conceptually similar to the 'LED10*-safety factor' approach for all health effects, and not to routinely develop quantitative risk estimates from animal data.

Real-Time Parameter Estimation in the Frequency Domain

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.

2000-01-01

A method for real-time estimation of parameters in a linear dynamic state-space model was developed and studied. The application is aircraft dynamic model parameter estimation from measured data in flight. Equation error in the frequency domain was used with a recursive Fourier transform for the real-time data analysis. Linear and nonlinear simulation examples and flight test data from the F-18 High Alpha Research Vehicle were used to demonstrate that the technique produces accurate model parameter estimates with appropriate error bounds. Parameter estimates converged in less than one cycle of the dominant dynamic mode, using no a priori information, with control surface inputs measured in flight during ordinary piloted maneuvers. The real-time parameter estimation method has low computational requirements and could be implemented

Second-order kinetic model for the sorption of cadmium onto tree fern: a comparison of linear and non-linear methods.

PubMed

Ho, Yuh-Shan

2006-01-01

A comparison was made of the linear least-squares method and a trial-and-error non-linear method of the widely used pseudo-second-order kinetic model for the sorption of cadmium onto ground-up tree fern. Four pseudo-second-order kinetic linear equations are discussed. Kinetic parameters obtained from the four kinetic linear equations using the linear method differed but they were the same when using the non-linear method. A type 1 pseudo-second-order linear kinetic model has the highest coefficient of determination. Results show that the non-linear method may be a better way to obtain the desired parameters.

Estimation et validation des derivees de stabilite et controle du modele dynamique non-lineaire d'un drone a voilure fixe

NASA Astrophysics Data System (ADS)

Courchesne, Samuel

Knowledge of the dynamic characteristics of a fixed-wing UAV is necessary to design flight control laws and to conceive a high quality flight simulator. The basic features of a flight mechanic model include the properties of mass, inertia and major aerodynamic terms. They respond to a complex process involving various numerical analysis techniques and experimental procedures. This thesis focuses on the analysis of estimation techniques applied to estimate problems of stability and control derivatives from flight test data provided by an experimental UAV. To achieve this objective, a modern identification methodology (Quad-M) is used to coordinate the processing tasks from multidisciplinary fields, such as parameter estimation modeling, instrumentation, the definition of flight maneuvers and validation. The system under study is a non-linear model with six degrees of freedom with a linear aerodynamic model. The time domain techniques are used for identification of the drone. The first technique, the equation error method is used to determine the structure of the aerodynamic model. Thereafter, the output error method and filter error method are used to estimate the aerodynamic coefficients values. The Matlab scripts for estimating the parameters obtained from the American Institute of Aeronautics and Astronautics (AIAA) are used and modified as necessary to achieve the desired results. A commendable effort in this part of research is devoted to the design of experiments. This includes an awareness of the system data acquisition onboard and the definition of flight maneuvers. The flight tests were conducted under stable flight conditions and with low atmospheric disturbance. Nevertheless, the identification results showed that the filter error method is most effective for estimating the parameters of the drone due to the presence of process noise and measurement. The aerodynamic coefficients are validated using a numerical analysis of the vortex method. In addition, a simulation model incorporating the estimated parameters is used to compare the behavior of states measured. Finally, a good correspondence between the results is demonstrated despite a limited number of flight data. Keywords: drone, identification, estimation, nonlinear, flight test, system, aerodynamic coefficient.

Q estimation of seismic data using the generalized S-transform

NASA Astrophysics Data System (ADS)

Hao, Yaju; Wen, Xiaotao; Zhang, Bo; He, Zhenhua; Zhang, Rui; Zhang, Jinming

2016-12-01

Quality factor, Q, is a parameter that characterizes the energy dissipation during seismic wave propagation. The reservoir pore is one of the main factors that affect the value of Q. Especially, when pore space is filled with oil or gas, the rock usually exhibits a relative low Q value. Such a low Q value has been used as a direct hydrocarbon indicator by many researchers. The conventional Q estimation method based on spectral ratio suffers from the problem of waveform tuning; hence, many researchers have introduced time-frequency analysis techniques to tackle this problem. Unfortunately, the window functions adopted in time-frequency analysis algorithms such as continuous wavelet transform (CWT) and S-transform (ST) contaminate the amplitude spectra because the seismic signal is multiplied by the window functions during time-frequency decomposition. The basic assumption of the spectral ratio method is that there is a linear relationship between natural logarithmic spectral ratio and frequency. However, this assumption does not hold if we take the influence of window functions into consideration. In this paper, we first employ a recently developed two-parameter generalized S-transform (GST) to obtain the time-frequency spectra of seismic traces. We then deduce the non-linear relationship between natural logarithmic spectral ratio and frequency. Finally, we obtain a linear relationship between natural logarithmic spectral ratio and a newly defined parameter γ by ignoring the negligible second order term. The gradient of this linear relationship is 1/Q. Here, the parameter γ is a function of frequency and source wavelet. Numerical examples for VSP and post-stack reflection data confirm that our algorithm is capable of yielding accurate results. The Q-value results estimated from field data acquired in western China show reasonable comparison with oil-producing well location.

Is 3D true non linear traveltime tomography reasonable ?

NASA Astrophysics Data System (ADS)

Herrero, A.; Virieux, J.

2003-04-01

The data sets requiring 3D analysis tools in the context of seismic exploration (both onshore and offshore experiments) or natural seismicity (micro seismicity surveys or post event measurements) are more and more numerous. Classical linearized tomographies and also earthquake localisation codes need an accurate 3D background velocity model. However, if the medium is complex and a priori information not available, a 1D analysis is not able to provide an adequate background velocity image. Moreover, the design of the acquisition layouts is often intrinsically 3D and renders difficult even 2D approaches, especially in natural seismicity cases. Thus, the solution relies on the use of a 3D true non linear approach, which allows to explore the model space and to identify an optimal velocity image. The problem becomes then practical and its feasibility depends on the available computing resources (memory and time). In this presentation, we show that facing a 3D traveltime tomography problem with an extensive non-linear approach combining fast travel time estimators based on level set methods and optimisation techniques such as multiscale strategy is feasible. Moreover, because management of inhomogeneous inversion parameters is more friendly in a non linear approach, we describe how to perform a jointly non-linear inversion for the seismic velocities and the sources locations.

Linear Logistic Test Modeling with R

ERIC Educational Resources Information Center

Baghaei, Purya; Kubinger, Klaus D.

2015-01-01

The present paper gives a general introduction to the linear logistic test model (Fischer, 1973), an extension of the Rasch model with linear constraints on item parameters, along with eRm (an R package to estimate different types of Rasch models; Mair, Hatzinger, & Mair, 2014) functions to estimate the model and interpret its parameters. The…

Nonlinear spectral mixture effects for photosynthetic/non-photosynthetic vegetation cover estimates of typical desert vegetation in western China.

PubMed

Ji, Cuicui; Jia, Yonghong; Gao, Zhihai; Wei, Huaidong; Li, Xiaosong

2017-01-01

Desert vegetation plays significant roles in securing the ecological integrity of oasis ecosystems in western China. Timely monitoring of photosynthetic/non-photosynthetic desert vegetation cover is necessary to guide management practices on land desertification and research into the mechanisms driving vegetation recession. In this study, nonlinear spectral mixture effects for photosynthetic/non-photosynthetic vegetation cover estimates are investigated through comparing the performance of linear and nonlinear spectral mixture models with different endmembers applied to field spectral measurements of two types of typical desert vegetation, namely, Nitraria shrubs and Haloxylon. The main results were as follows. (1) The correct selection of endmembers is important for improving the accuracy of vegetation cover estimates, and in particular, shadow endmembers cannot be neglected. (2) For both the Nitraria shrubs and Haloxylon, the Kernel-based Nonlinear Spectral Mixture Model (KNSMM) with nonlinear parameters was the best unmixing model. In consideration of the computational complexity and accuracy requirements, the Linear Spectral Mixture Model (LSMM) could be adopted for Nitraria shrubs plots, but this will result in significant errors for the Haloxylon plots since the nonlinear spectral mixture effects were more obvious for this vegetation type. (3) The vegetation canopy structure (planophile or erectophile) determines the strength of the nonlinear spectral mixture effects. Therefore, no matter for Nitraria shrubs or Haloxylon, the non-linear spectral mixing effects between the photosynthetic / non-photosynthetic vegetation and the bare soil do exist, and its strength is dependent on the three-dimensional structure of the vegetation canopy. The choice of linear or nonlinear spectral mixture models is up to the consideration of computational complexity and the accuracy requirement.

Nonlinear spectral mixture effects for photosynthetic/non-photosynthetic vegetation cover estimates of typical desert vegetation in western China

PubMed Central

Jia, Yonghong; Gao, Zhihai; Wei, Huaidong

2017-01-01

Desert vegetation plays significant roles in securing the ecological integrity of oasis ecosystems in western China. Timely monitoring of photosynthetic/non-photosynthetic desert vegetation cover is necessary to guide management practices on land desertification and research into the mechanisms driving vegetation recession. In this study, nonlinear spectral mixture effects for photosynthetic/non-photosynthetic vegetation cover estimates are investigated through comparing the performance of linear and nonlinear spectral mixture models with different endmembers applied to field spectral measurements of two types of typical desert vegetation, namely, Nitraria shrubs and Haloxylon. The main results were as follows. (1) The correct selection of endmembers is important for improving the accuracy of vegetation cover estimates, and in particular, shadow endmembers cannot be neglected. (2) For both the Nitraria shrubs and Haloxylon, the Kernel-based Nonlinear Spectral Mixture Model (KNSMM) with nonlinear parameters was the best unmixing model. In consideration of the computational complexity and accuracy requirements, the Linear Spectral Mixture Model (LSMM) could be adopted for Nitraria shrubs plots, but this will result in significant errors for the Haloxylon plots since the nonlinear spectral mixture effects were more obvious for this vegetation type. (3) The vegetation canopy structure (planophile or erectophile) determines the strength of the nonlinear spectral mixture effects. Therefore, no matter for Nitraria shrubs or Haloxylon, the non-linear spectral mixing effects between the photosynthetic / non-photosynthetic vegetation and the bare soil do exist, and its strength is dependent on the three-dimensional structure of the vegetation canopy. The choice of linear or nonlinear spectral mixture models is up to the consideration of computational complexity and the accuracy requirement. PMID:29240777

A theory of fine structure image models with an application to detection and classification of dementia.

PubMed

O'Neill, William; Penn, Richard; Werner, Michael; Thomas, Justin

2015-06-01

Estimation of stochastic process models from data is a common application of time series analysis methods. Such system identification processes are often cast as hypothesis testing exercises whose intent is to estimate model parameters and test them for statistical significance. Ordinary least squares (OLS) regression and the Levenberg-Marquardt algorithm (LMA) have proven invaluable computational tools for models being described by non-homogeneous, linear, stationary, ordinary differential equations. In this paper we extend stochastic model identification to linear, stationary, partial differential equations in two independent variables (2D) and show that OLS and LMA apply equally well to these systems. The method employs an original nonparametric statistic as a test for the significance of estimated parameters. We show gray scale and color images are special cases of 2D systems satisfying a particular autoregressive partial difference equation which estimates an analogous partial differential equation. Several applications to medical image modeling and classification illustrate the method by correctly classifying demented and normal OLS models of axial magnetic resonance brain scans according to subject Mini Mental State Exam (MMSE) scores. Comparison with 13 image classifiers from the literature indicates our classifier is at least 14 times faster than any of them and has a classification accuracy better than all but one. Our modeling method applies to any linear, stationary, partial differential equation and the method is readily extended to 3D whole-organ systems. Further, in addition to being a robust image classifier, estimated image models offer insights into which parameters carry the most diagnostic image information and thereby suggest finer divisions could be made within a class. Image models can be estimated in milliseconds which translate to whole-organ models in seconds; such runtimes could make real-time medicine and surgery modeling possible.

Linear and Nonlinear Time-Frequency Analysis for Parameter Estimation of Resident Space Objects

DTIC Science & Technology

2017-02-22

AFRL-AFOSR-UK-TR-2017-0023 Linear and Nonlinear Time -Frequency Analysis for Parameter Estimation of Resident Space Objects Marco Martorella...estimated to average 1 hour per response, including the time for reviewing instructions, searching existing   data sources, gathering and maintaining the...Nonlinear Time -Frequency Analysis for Parameter Estimation of Resident Space Objects 5a.  CONTRACT NUMBER 5b.  GRANT NUMBER FA9550-14-1-0183 5c.  PROGRAM

Rapid determination of thermodynamic parameters from one-dimensional programmed-temperature gas chromatography for use in retention time prediction in comprehensive multidimensional chromatography.

PubMed

McGinitie, Teague M; Ebrahimi-Najafabadi, Heshmatollah; Harynuk, James J

2014-01-17

A new method for estimating the thermodynamic parameters of ΔH(T0), ΔS(T0), and ΔCP for use in thermodynamic modeling of GC×GC separations has been developed. The method is an alternative to the traditional isothermal separations required to fit a three-parameter thermodynamic model to retention data. Herein, a non-linear optimization technique is used to estimate the parameters from a series of temperature-programmed separations using the Nelder-Mead simplex algorithm. With this method, the time required to obtain estimates of thermodynamic parameters a series of analytes is significantly reduced. This new method allows for precise predictions of retention time with the average error being only 0.2s for 1D separations. Predictions for GC×GC separations were also in agreement with experimental measurements; having an average relative error of 0.37% for (1)tr and 2.1% for (2)tr. Copyright © 2013 Elsevier B.V. All rights reserved.

Thermal Property Parameter Estimation of TPS Materials

NASA Technical Reports Server (NTRS)

Maddren, Jesse

1998-01-01

Accurate knowledge of the thermophysical properties of TPS (thermal protection system) materials is necessary for pre-flight design and post-flight data analysis. Thermal properties, such as thermal conductivity and the volumetric specific heat, can be estimated from transient temperature measurements using non-linear parameter estimation methods. Property values are derived by minimizing a functional of the differences between measured and calculated temperatures. High temperature thermal response testing of TPS materials is usually done in arc-jet or radiant heating facilities which provide a quasi one-dimensional heating environment. Last year, under the NASA-ASEE-Stanford Fellowship Program, my work focused on developing a radiant heating apparatus. This year, I have worked on increasing the fidelity of the experimental measurements, optimizing the experimental procedures and interpreting the data.

On Time Delay Margin Estimation for Adaptive Control and Optimal Control Modification

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.

2011-01-01

This paper presents methods for estimating time delay margin for adaptive control of input delay systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent an adaptive law by a locally bounded linear approximation within a small time window. The time delay margin of this input delay system represents a local stability measure and is computed analytically by three methods: Pade approximation, Lyapunov-Krasovskii method, and the matrix measure method. These methods are applied to the standard model-reference adaptive control, s-modification adaptive law, and optimal control modification adaptive law. The windowing analysis results in non-unique estimates of the time delay margin since it is dependent on the length of a time window and parameters which vary from one time window to the next. The optimal control modification adaptive law overcomes this limitation in that, as the adaptive gain tends to infinity and if the matched uncertainty is linear, then the closed-loop input delay system tends to a LTI system. A lower bound of the time delay margin of this system can then be estimated uniquely without the need for the windowing analysis. Simulation results demonstrates the feasibility of the bounded linear stability method for time delay margin estimation.

Evaluation of the site effect with Heuristic Methods

NASA Astrophysics Data System (ADS)

Torres, N. N.; Ortiz-Aleman, C.

2017-12-01

The seismic site response in an area depends mainly on the local geological and topographical conditions. Estimation of variations in ground motion can lead to significant contributions on seismic hazard assessment, in order to reduce human and economic losses. Site response estimation can be posed as a parameterized inversion approach which allows separating source and path effects. The generalized inversion (Field and Jacob, 1995) represents one of the alternative methods to estimate the local seismic response, which involves solving a strongly non-linear multiparametric problem. In this work, local seismic response was estimated using global optimization methods (Genetic Algorithms and Simulated Annealing) which allowed us to increase the range of explored solutions in a nonlinear search, as compared to other conventional linear methods. By using the VEOX Network velocity records, collected from August 2007 to March 2009, source, path and site parameters corresponding to the amplitude spectra of the S wave of the velocity seismic records are estimated. We can establish that inverted parameters resulting from this simultaneous inversion approach, show excellent agreement, not only in terms of adjustment between observed and calculated spectra, but also when compared to previous work from several authors.

Probabilistic estimation of splitting coefficients of normal modes of the Earth, and their uncertainties, using an autoregressive technique

NASA Astrophysics Data System (ADS)

Pachhai, S.; Masters, G.; Laske, G.

2017-12-01

Earth's normal-mode spectra are crucial to studying the long wavelength structure of the Earth. Such observations have been used extensively to estimate "splitting coefficients" which, in turn, can be used to determine the three-dimensional velocity and density structure. Most past studies apply a non-linear iterative inversion to estimate the splitting coefficients which requires that the earthquake source is known. However, it is challenging to know the source details, particularly for big events as used in normal-mode analyses. Additionally, the final solution of the non-linear inversion can depend on the choice of damping parameter and starting model. To circumvent the need to know the source, a two-step linear inversion has been developed and successfully applied to many mantle and core sensitive modes. The first step takes combinations of the data from a single event to produce spectra known as "receiver strips". The autoregressive nature of the receiver strips can then be used to estimate the structure coefficients without the need to know the source. Based on this approach, we recently employed a neighborhood algorithm to measure the splitting coefficients for an isolated inner-core sensitive mode (13S2). This approach explores the parameter space efficiently without any need of regularization and finds the structure coefficients which best fit the observed strips. Here, we implement a Bayesian approach to data collected for earthquakes from early 2000 and more recent. This approach combines the data (through likelihood) and prior information to provide rigorous parameter values and their uncertainties for both isolated and coupled modes. The likelihood function is derived from the inferred errors of the receiver strips which allows us to retrieve proper uncertainties. Finally, we apply model selection criteria that balance the trade-offs between fit (likelihood) and model complexity to investigate the degree and type of structure (elastic and anelastic) required to explain the data.

Non-linear auto-regressive models for cross-frequency coupling in neural time series

PubMed Central

Tallot, Lucille; Grabot, Laetitia; Doyère, Valérie; Grenier, Yves; Gramfort, Alexandre

2017-01-01

We address the issue of reliably detecting and quantifying cross-frequency coupling (CFC) in neural time series. Based on non-linear auto-regressive models, the proposed method provides a generative and parametric model of the time-varying spectral content of the signals. As this method models the entire spectrum simultaneously, it avoids the pitfalls related to incorrect filtering or the use of the Hilbert transform on wide-band signals. As the model is probabilistic, it also provides a score of the model “goodness of fit” via the likelihood, enabling easy and legitimate model selection and parameter comparison; this data-driven feature is unique to our model-based approach. Using three datasets obtained with invasive neurophysiological recordings in humans and rodents, we demonstrate that these models are able to replicate previous results obtained with other metrics, but also reveal new insights such as the influence of the amplitude of the slow oscillation. Using simulations, we demonstrate that our parametric method can reveal neural couplings with shorter signals than non-parametric methods. We also show how the likelihood can be used to find optimal filtering parameters, suggesting new properties on the spectrum of the driving signal, but also to estimate the optimal delay between the coupled signals, enabling a directionality estimation in the coupling. PMID:29227989

A Two-Stage Algorithm for Origin-Destination Matrices Estimation Considering Dynamic Dispersion Parameter for Route Choice

PubMed Central

Wang, Yong; Ma, Xiaolei; Liu, Yong; Gong, Ke; Henricakson, Kristian C.; Xu, Maozeng; Wang, Yinhai

2016-01-01

This paper proposes a two-stage algorithm to simultaneously estimate origin-destination (OD) matrix, link choice proportion, and dispersion parameter using partial traffic counts in a congested network. A non-linear optimization model is developed which incorporates a dynamic dispersion parameter, followed by a two-stage algorithm in which Generalized Least Squares (GLS) estimation and a Stochastic User Equilibrium (SUE) assignment model are iteratively applied until the convergence is reached. To evaluate the performance of the algorithm, the proposed approach is implemented in a hypothetical network using input data with high error, and tested under a range of variation coefficients. The root mean squared error (RMSE) of the estimated OD demand and link flows are used to evaluate the model estimation results. The results indicate that the estimated dispersion parameter theta is insensitive to the choice of variation coefficients. The proposed approach is shown to outperform two established OD estimation methods and produce parameter estimates that are close to the ground truth. In addition, the proposed approach is applied to an empirical network in Seattle, WA to validate the robustness and practicality of this methodology. In summary, this study proposes and evaluates an innovative computational approach to accurately estimate OD matrices using link-level traffic flow data, and provides useful insight for optimal parameter selection in modeling travelers’ route choice behavior. PMID:26761209

Cosmic velocity-gravity relation in redshift space

NASA Astrophysics Data System (ADS)

Colombi, Stéphane; Chodorowski, Michał J.; Teyssier, Romain

2007-02-01

We propose a simple way to estimate the parameter β ~= Ω0.6/b from 3D galaxy surveys, where Ω is the non-relativistic matter-density parameter of the Universe and b is the bias between the galaxy distribution and the total matter distribution. Our method consists in measuring the relation between the cosmological velocity and gravity fields, and thus requires peculiar velocity measurements. The relation is measured directly in redshift space, so there is no need to reconstruct the density field in real space. In linear theory, the radial components of the gravity and velocity fields in redshift space are expected to be tightly correlated, with a slope given, in the distant observer approximation, by We test extensively this relation using controlled numerical experiments based on a cosmological N-body simulation. To perform the measurements, we propose a new and rather simple adaptive interpolation scheme to estimate the velocity and the gravity field on a grid. One of the most striking results is that non-linear effects, including `fingers of God', affect mainly the tails of the joint probability distribution function (PDF) of the velocity and gravity field: the 1-1.5 σ region around the maximum of the PDF is dominated by the linear theory regime, both in real and redshift space. This is understood explicitly by using the spherical collapse model as a proxy of non-linear dynamics. Applications of the method to real galaxy catalogues are discussed, including a preliminary investigation on homogeneous (volume-limited) `galaxy' samples extracted from the simulation with simple prescriptions based on halo and substructure identification, to quantify the effects of the bias between the galaxy distribution and the total matter distribution, as well as the effects of shot noise.

Predicting response before initiation of neoadjuvant chemotherapy in breast cancer using new methods for the analysis of dynamic contrast enhanced MRI (DCE MRI) data

NASA Astrophysics Data System (ADS)

DeGrandchamp, Joseph B.; Whisenant, Jennifer G.; Arlinghaus, Lori R.; Abramson, V. G.; Yankeelov, Thomas E.; Cárdenas-Rodríguez, Julio

2016-03-01

The pharmacokinetic parameters derived from dynamic contrast enhanced (DCE) MRI have shown promise as biomarkers for tumor response to therapy. However, standard methods of analyzing DCE MRI data (Tofts model) require high temporal resolution, high signal-to-noise ratio (SNR), and the Arterial Input Function (AIF). Such models produce reliable biomarkers of response only when a therapy has a large effect on the parameters. We recently reported a method that solves the limitations, the Linear Reference Region Model (LRRM). Similar to other reference region models, the LRRM needs no AIF. Additionally, the LRRM is more accurate and precise than standard methods at low SNR and slow temporal resolution, suggesting LRRM-derived biomarkers could be better predictors. Here, the LRRM, Non-linear Reference Region Model (NRRM), Linear Tofts model (LTM), and Non-linear Tofts Model (NLTM) were used to estimate the RKtrans between muscle and tumor (or the Ktrans for Tofts) and the tumor kep,TOI for 39 breast cancer patients who received neoadjuvant chemotherapy (NAC). These parameters and the receptor statuses of each patient were used to construct cross-validated predictive models to classify patients as complete pathological responders (pCR) or non-complete pathological responders (non-pCR) to NAC. Model performance was evaluated using area under the ROC curve (AUC). The AUC for receptor status alone was 0.62, while the best performance using predictors from the LRRM, NRRM, LTM, and NLTM were AUCs of 0.79, 0.55, 0.60, and 0.59 respectively. This suggests that the LRRM can be used to predict response to NAC in breast cancer.

Robust geostatistical analysis of spatial data

NASA Astrophysics Data System (ADS)

Papritz, Andreas; Künsch, Hans Rudolf; Schwierz, Cornelia; Stahel, Werner A.

2013-04-01

Most of the geostatistical software tools rely on non-robust algorithms. This is unfortunate, because outlying observations are rather the rule than the exception, in particular in environmental data sets. Outliers affect the modelling of the large-scale spatial trend, the estimation of the spatial dependence of the residual variation and the predictions by kriging. Identifying outliers manually is cumbersome and requires expertise because one needs parameter estimates to decide which observation is a potential outlier. Moreover, inference after the rejection of some observations is problematic. A better approach is to use robust algorithms that prevent automatically that outlying observations have undue influence. Former studies on robust geostatistics focused on robust estimation of the sample variogram and ordinary kriging without external drift. Furthermore, Richardson and Welsh (1995) proposed a robustified version of (restricted) maximum likelihood ([RE]ML) estimation for the variance components of a linear mixed model, which was later used by Marchant and Lark (2007) for robust REML estimation of the variogram. We propose here a novel method for robust REML estimation of the variogram of a Gaussian random field that is possibly contaminated by independent errors from a long-tailed distribution. It is based on robustification of estimating equations for the Gaussian REML estimation (Welsh and Richardson, 1997). Besides robust estimates of the parameters of the external drift and of the variogram, the method also provides standard errors for the estimated parameters, robustified kriging predictions at both sampled and non-sampled locations and kriging variances. Apart from presenting our modelling framework, we shall present selected simulation results by which we explored the properties of the new method. This will be complemented by an analysis a data set on heavy metal contamination of the soil in the vicinity of a metal smelter. Marchant, B.P. and Lark, R.M. 2007. Robust estimation of the variogram by residual maximum likelihood. Geoderma 140: 62-72. Richardson, A.M. and Welsh, A.H. 1995. Robust restricted maximum likelihood in mixed linear models. Biometrics 51: 1429-1439. Welsh, A.H. and Richardson, A.M. 1997. Approaches to the robust estimation of mixed models. In: Handbook of Statistics Vol. 15, Elsevier, pp. 343-384.

Development of a shortleaf pine individual-tree growth equation using non-linear mixed modeling techniques

Treesearch

Chakra B. Budhathoki; Thomas B. Lynch; James M. Guldin

2010-01-01

Nonlinear mixed-modeling methods were used to estimate parameters in an individual-tree basal area growth model for shortleaf pine (Pinus echinata Mill.). Shortleaf pine individual-tree growth data were available from over 200 permanently established 0.2-acre fixed-radius plots located in naturally-occurring even-aged shortleaf pine forests on the...

Estimating monotonic rates from biological data using local linear regression.

PubMed

Olito, Colin; White, Craig R; Marshall, Dustin J; Barneche, Diego R

2017-03-01

Accessing many fundamental questions in biology begins with empirical estimation of simple monotonic rates of underlying biological processes. Across a variety of disciplines, ranging from physiology to biogeochemistry, these rates are routinely estimated from non-linear and noisy time series data using linear regression and ad hoc manual truncation of non-linearities. Here, we introduce the R package LoLinR, a flexible toolkit to implement local linear regression techniques to objectively and reproducibly estimate monotonic biological rates from non-linear time series data, and demonstrate possible applications using metabolic rate data. LoLinR provides methods to easily and reliably estimate monotonic rates from time series data in a way that is statistically robust, facilitates reproducible research and is applicable to a wide variety of research disciplines in the biological sciences. © 2017. Published by The Company of Biologists Ltd.

Modelling non-linear effects of dark energy

NASA Astrophysics Data System (ADS)

Bose, Benjamin; Baldi, Marco; Pourtsidou, Alkistis

2018-04-01

We investigate the capabilities of perturbation theory in capturing non-linear effects of dark energy. We test constant and evolving w models, as well as models involving momentum exchange between dark energy and dark matter. Specifically, we compare perturbative predictions at 1-loop level against N-body results for four non-standard equations of state as well as varying degrees of momentum exchange between dark energy and dark matter. The interaction is modelled phenomenologically using a time dependent drag term in the Euler equation. We make comparisons at the level of the matter power spectrum and the redshift space monopole and quadrupole. The multipoles are modelled using the Taruya, Nishimichi and Saito (TNS) redshift space spectrum. We find perturbation theory does very well in capturing non-linear effects coming from dark sector interaction. We isolate and quantify the 1-loop contribution coming from the interaction and from the non-standard equation of state. We find the interaction parameter ξ amplifies scale dependent signatures in the range of scales considered. Non-standard equations of state also give scale dependent signatures within this same regime. In redshift space the match with N-body is improved at smaller scales by the addition of the TNS free parameter σv. To quantify the importance of modelling the interaction, we create mock data sets for varying values of ξ using perturbation theory. This data is given errors typical of Stage IV surveys. We then perform a likelihood analysis using the first two multipoles on these sets and a ξ=0 modelling, ignoring the interaction. We find the fiducial growth parameter f is generally recovered even for very large values of ξ both at z=0.5 and z=1. The ξ=0 modelling is most biased in its estimation of f for the phantom w=‑1.1 case.

A hybrid robust fault tolerant control based on adaptive joint unscented Kalman filter.

PubMed

Shabbouei Hagh, Yashar; Mohammadi Asl, Reza; Cocquempot, Vincent

2017-01-01

In this paper, a new hybrid robust fault tolerant control scheme is proposed. A robust H ∞ control law is used in non-faulty situation, while a Non-Singular Terminal Sliding Mode (NTSM) controller is activated as soon as an actuator fault is detected. Since a linear robust controller is designed, the system is first linearized through the feedback linearization method. To switch from one controller to the other, a fuzzy based switching system is used. An Adaptive Joint Unscented Kalman Filter (AJUKF) is used for fault detection and diagnosis. The proposed method is based on the simultaneous estimation of the system states and parameters. In order to show the efficiency of the proposed scheme, a simulated 3-DOF robotic manipulator is used. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Evaluation of Specific Absorption Rate as a Dosimetric Quantity for Electromagnetic Fields Bioeffects

PubMed Central

Panagopoulos, Dimitris J.; Johansson, Olle; Carlo, George L.

2013-01-01

Purpose To evaluate SAR as a dosimetric quantity for EMF bioeffects, and identify ways for increasing the precision in EMF dosimetry and bioactivity assessment. Methods We discuss the interaction of man-made electromagnetic waves with biological matter and calculate the energy transferred to a single free ion within a cell. We analyze the physics and biology of SAR and evaluate the methods of its estimation. We discuss the experimentally observed non-linearity between electromagnetic exposure and biological effect. Results We find that: a) The energy absorbed by living matter during exposure to environmentally accounted EMFs is normally well below the thermal level. b) All existing methods for SAR estimation, especially those based upon tissue conductivity and internal electric field, have serious deficiencies. c) The only method to estimate SAR without large error is by measuring temperature increases within biological tissue, which normally are negligible for environmental EMF intensities, and thus cannot be measured. Conclusions SAR actually refers to thermal effects, while the vast majority of the recorded biological effects from man-made non-ionizing environmental radiation are non-thermal. Even if SAR could be accurately estimated for a whole tissue, organ, or body, the biological/health effect is determined by tiny amounts of energy/power absorbed by specific biomolecules, which cannot be calculated. Moreover, it depends upon field parameters not taken into account in SAR calculation. Thus, SAR should not be used as the primary dosimetric quantity, but used only as a complementary measure, always reporting the estimating method and the corresponding error. Radiation/field intensity along with additional physical parameters (such as frequency, modulation etc) which can be directly and in any case more accurately measured on the surface of biological tissues, should constitute the primary measure for EMF exposures, in spite of similar uncertainty to predict the biological effect due to non-linearity. PMID:23750202

Historical HIV incidence modelling in regional subgroups: use of flexible discrete models with penalized splines based on prior curves.

PubMed

Greenland, S

1996-03-15

This paper presents an approach to back-projection (back-calculation) of human immunodeficiency virus (HIV) person-year infection rates in regional subgroups based on combining a log-linear model for subgroup differences with a penalized spline model for trends. The penalized spline approach allows flexible trend estimation but requires far fewer parameters than fully non-parametric smoothers, thus saving parameters that can be used in estimating subgroup effects. Use of reasonable prior curve to construct the penalty function minimizes the degree of smoothing needed beyond model specification. The approach is illustrated in application to acquired immunodeficiency syndrome (AIDS) surveillance data from Los Angeles County.

SNDR enhancement in noisy sinusoidal signals by non-linear processing elements

NASA Astrophysics Data System (ADS)

Martorell, Ferran; McDonnell, Mark D.; Abbott, Derek; Rubio, Antonio

2007-06-01

We investigate the possibility of building linear amplifiers capable of enhancing the Signal-to-Noise and Distortion Ratio (SNDR) of sinusoidal input signals using simple non-linear elements. Other works have proven that it is possible to enhance the Signal-to-Noise Ratio (SNR) by using limiters. In this work we study a soft limiter non-linear element with and without hysteresis. We show that the SNDR of sinusoidal signals can be enhanced by 0.94 dB using a wideband soft limiter and up to 9.68 dB using a wideband soft limiter with hysteresis. These results indicate that linear amplifiers could be constructed using non-linear circuits with hysteresis. This paper presents mathematical descriptions for the non-linear elements using statistical parameters. Using these models, the input-output SNDR enhancement is obtained by optimizing the non-linear transfer function parameters to maximize the output SNDR.

Flexible polyurethane foam modelling and identification of viscoelastic parameters for automotive seating applications

NASA Astrophysics Data System (ADS)

Deng, R.; Davies, P.; Bajaj, A. K.

2003-05-01

A hereditary model and a fractional derivative model for the dynamic properties of flexible polyurethane foams used in automotive seat cushions are presented. Non-linear elastic and linear viscoelastic properties are incorporated into these two models. A polynomial function of compression is used to represent the non-linear elastic behavior. The viscoelastic property is modelled by a hereditary integral with a relaxation kernel consisting of two exponential terms in the hereditary model and by a fractional derivative term in the fractional derivative model. The foam is used as the only viscoelastic component in a foam-mass system undergoing uniaxial compression. One-term harmonic balance solutions are developed to approximate the steady state response of the foam-mass system to the harmonic base excitation. System identification procedures based on the direct non-linear optimization and a sub-optimal method are formulated to estimate the material parameters. The effects of the choice of the cost function, frequency resolution of data and imperfections in experiments are discussed. The system identification procedures are also applied to experimental data from a foam-mass system. The performances of the two models for data at different compression and input excitation levels are compared, and modifications to the structure of the fractional derivative model are briefly explored. The role of the viscous damping term in both types of model is discussed.

The response of a linear monostable system and its application in parameters estimation for PSK signals

NASA Astrophysics Data System (ADS)

Duan, Chaowei; Zhan, Yafeng

2016-03-01

The output characteristics of a linear monostable system driven with a periodic signal and an additive white Gaussian noise are studied in this paper. Theoretical analysis shows that the output signal-to-noise ratio (SNR) decreases monotonously with the increasing noise intensity but the output SNR-gain is stable. Inspired by this high SNR-gain phenomenon, this paper applies the linear monostable system in the parameters estimation algorithm for phase shift keying (PSK) signals and improves the estimation performance.

Parameterizing sorption isotherms using a hybrid global-local fitting procedure.

PubMed

Matott, L Shawn; Singh, Anshuman; Rabideau, Alan J

2017-05-01

Predictive modeling of the transport and remediation of groundwater contaminants requires an accurate description of the sorption process, which is usually provided by fitting an isotherm model to site-specific laboratory data. Commonly used calibration procedures, listed in order of increasing sophistication, include: trial-and-error, linearization, non-linear regression, global search, and hybrid global-local search. Given the considerable variability in fitting procedures applied in published isotherm studies, we investigated the importance of algorithm selection through a series of numerical experiments involving 13 previously published sorption datasets. These datasets, considered representative of state-of-the-art for isotherm experiments, had been previously analyzed using trial-and-error, linearization, or non-linear regression methods. The isotherm expressions were re-fit using a 3-stage hybrid global-local search procedure (i.e. global search using particle swarm optimization followed by Powell's derivative free local search method and Gauss-Marquardt-Levenberg non-linear regression). The re-fitted expressions were then compared to previously published fits in terms of the optimized weighted sum of squared residuals (WSSR) fitness function, the final estimated parameters, and the influence on contaminant transport predictions - where easily computed concentration-dependent contaminant retardation factors served as a surrogate measure of likely transport behavior. Results suggest that many of the previously published calibrated isotherm parameter sets were local minima. In some cases, the updated hybrid global-local search yielded order-of-magnitude reductions in the fitness function. In particular, of the candidate isotherms, the Polanyi-type models were most likely to benefit from the use of the hybrid fitting procedure. In some cases, improvements in fitness function were associated with slight (<10%) changes in parameter values, but in other cases significant (>50%) changes in parameter values were noted. Despite these differences, the influence of isotherm misspecification on contaminant transport predictions was quite variable and difficult to predict from inspection of the isotherms. Copyright © 2017 Elsevier B.V. All rights reserved.

Linear Parameter Varying Control for Actuator Failure

NASA Technical Reports Server (NTRS)

Shin, Jong-Yeob; Wu, N. Eva; Belcastro, Christine; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

A robust linear parameter varying (LPV) control synthesis is carried out for an HiMAT vehicle subject to loss of control effectiveness. The scheduling parameter is selected to be a function of the estimates of the control effectiveness factors. The estimates are provided on-line by a two-stage Kalman estimator. The inherent conservatism of the LPV design is reducing through the use of a scaling factor on the uncertainty block that represents the estimation errors of the effectiveness factors. Simulations of the controlled system with the on-line estimator show that a superior fault-tolerance can be achieved.

Exploration and extension of an improved Riemann track fitting algorithm

NASA Astrophysics Data System (ADS)

Strandlie, A.; Frühwirth, R.

2017-09-01

Recently, a new Riemann track fit which operates on translated and scaled measurements has been proposed. This study shows that the new Riemann fit is virtually as precise as popular approaches such as the Kalman filter or an iterative non-linear track fitting procedure, and significantly more precise than other, non-iterative circular track fitting approaches over a large range of measurement uncertainties. The fit is then extended in two directions: first, the measurements are allowed to lie on plane sensors of arbitrary orientation; second, the full error propagation from the measurements to the estimated circle parameters is computed. The covariance matrix of the estimated track parameters can therefore be computed without recourse to asymptotic properties, and is consequently valid for any number of observation. It does, however, assume normally distributed measurement errors. The calculations are validated on a simulated track sample and show excellent agreement with the theoretical expectations.

Sparse 4D TomoSAR imaging in the presence of non-linear deformation

NASA Astrophysics Data System (ADS)

Khwaja, Ahmed Shaharyar; ćetin, Müjdat

2018-04-01

In this paper, we present a sparse four-dimensional tomographic synthetic aperture radar (4D TomoSAR) imaging scheme that can estimate elevation and linear as well as non-linear seasonal deformation rates of scatterers using the interferometric phase. Unlike existing sparse processing techniques that use fixed dictionaries based on a linear deformation model, we use a variable dictionary for the non-linear deformation in the form of seasonal sinusoidal deformation, in addition to the fixed dictionary for the linear deformation. We estimate the amplitude of the sinusoidal deformation using an optimization method and create the variable dictionary using the estimated amplitude. We show preliminary results using simulated data that demonstrate the soundness of our proposed technique for sparse 4D TomoSAR imaging in the presence of non-linear deformation.

On the Impact of a Quadratic Acceleration Term in the Analysis of Position Time Series

NASA Astrophysics Data System (ADS)

Bogusz, Janusz; Klos, Anna; Bos, Machiel Simon; Hunegnaw, Addisu; Teferle, Felix Norman

2016-04-01

The analysis of Global Navigation Satellite System (GNSS) position time series generally assumes that each of the coordinate component series is described by the sum of a linear rate (velocity) and various periodic terms. The residuals, the deviations between the fitted model and the observations, are then a measure of the epoch-to-epoch scatter and have been used for the analysis of the stochastic character (noise) of the time series. Often the parameters of interest in GNSS position time series are the velocities and their associated uncertainties, which have to be determined with the highest reliability. It is clear that not all GNSS position time series follow this simple linear behaviour. Therefore, we have added an acceleration term in the form of a quadratic polynomial function to the model in order to better describe the non-linear motion in the position time series. This non-linear motion could be a response to purely geophysical processes, for example, elastic rebound of the Earth's crust due to ice mass loss in Greenland, artefacts due to deficiencies in bias mitigation models, for example, of the GNSS satellite and receiver antenna phase centres, or any combination thereof. In this study we have simulated 20 time series with different stochastic characteristics such as white, flicker or random walk noise of length of 23 years. The noise amplitude was assumed at 1 mm/y-/4. Then, we added the deterministic part consisting of a linear trend of 20 mm/y (that represents the averaged horizontal velocity) and accelerations ranging from minus 0.6 to plus 0.6 mm/y2. For all these data we estimated the noise parameters with Maximum Likelihood Estimation (MLE) using the Hector software package without taken into account the non-linear term. In this way we set the benchmark to then investigate how the noise properties and velocity uncertainty may be affected by any un-modelled, non-linear term. The velocities and their uncertainties versus the accelerations for different types of noise are determined. Furthermore, we have selected 40 globally distributed stations that have a clear non-linear behaviour from two different International GNSS Service (IGS) analysis centers: JPL (Jet Propulsion Laboratory) and BLT (British Isles continuous GNSS Facility and University of Luxembourg Tide Gauge Benchmark Monitoring (TIGA) Analysis Center). We obtained maximum accelerations of -1.8±1.2 mm2/y and -4.5±3.3 mm2/y for the horizontal and vertical components, respectively. The noise analysis tests have shown that the addition of the non-linear term has significantly whitened the power spectra of the position time series, i.e. shifted the spectral index from flicker towards white noise.

Monte Carlo simulation of parameter confidence intervals for non-linear regression analysis of biological data using Microsoft Excel.

PubMed

Lambert, Ronald J W; Mytilinaios, Ioannis; Maitland, Luke; Brown, Angus M

2012-08-01

This study describes a method to obtain parameter confidence intervals from the fitting of non-linear functions to experimental data, using the SOLVER and Analysis ToolPaK Add-In of the Microsoft Excel spreadsheet. Previously we have shown that Excel can fit complex multiple functions to biological data, obtaining values equivalent to those returned by more specialized statistical or mathematical software. However, a disadvantage of using the Excel method was the inability to return confidence intervals for the computed parameters or the correlations between them. Using a simple Monte-Carlo procedure within the Excel spreadsheet (without recourse to programming), SOLVER can provide parameter estimates (up to 200 at a time) for multiple 'virtual' data sets, from which the required confidence intervals and correlation coefficients can be obtained. The general utility of the method is exemplified by applying it to the analysis of the growth of Listeria monocytogenes, the growth inhibition of Pseudomonas aeruginosa by chlorhexidine and the further analysis of the electrophysiological data from the compound action potential of the rodent optic nerve. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.

Identification of linear system models and state estimators for controls

NASA Technical Reports Server (NTRS)

Chen, Chung-Wen

1992-01-01

The following paper is presented in viewgraph format and covers topics including: (1) linear state feedback control system; (2) Kalman filter state estimation; (3) relation between residual and stochastic part of output; (4) obtaining Kalman filter gain; (5) state estimation under unknown system model and unknown noises; and (6) relationship between filter Markov parameters and system Markov parameters.

Non-linear matter power spectrum covariance matrix errors and cosmological parameter uncertainties

NASA Astrophysics Data System (ADS)

Blot, L.; Corasaniti, P. S.; Amendola, L.; Kitching, T. D.

2016-06-01

The covariance of the matter power spectrum is a key element of the analysis of galaxy clustering data. Independent realizations of observational measurements can be used to sample the covariance, nevertheless statistical sampling errors will propagate into the cosmological parameter inference potentially limiting the capabilities of the upcoming generation of galaxy surveys. The impact of these errors as function of the number of realizations has been previously evaluated for Gaussian distributed data. However, non-linearities in the late-time clustering of matter cause departures from Gaussian statistics. Here, we address the impact of non-Gaussian errors on the sample covariance and precision matrix errors using a large ensemble of N-body simulations. In the range of modes where finite volume effects are negligible (0.1 ≲ k [h Mpc-1] ≲ 1.2), we find deviations of the variance of the sample covariance with respect to Gaussian predictions above ˜10 per cent at k > 0.3 h Mpc-1. Over the entire range these reduce to about ˜5 per cent for the precision matrix. Finally, we perform a Fisher analysis to estimate the effect of covariance errors on the cosmological parameter constraints. In particular, assuming Euclid-like survey characteristics we find that a number of independent realizations larger than 5000 is necessary to reduce the contribution of sampling errors to the cosmological parameter uncertainties at subpercent level. We also show that restricting the analysis to large scales k ≲ 0.2 h Mpc-1 results in a considerable loss in constraining power, while using the linear covariance to include smaller scales leads to an underestimation of the errors on the cosmological parameters.

Linear and non-linear systems identification for adaptive control in mechanical applications vibration suppression

NASA Astrophysics Data System (ADS)

Cazzulani, Gabriele; Resta, Ferruccio; Ripamonti, Francesco

2012-04-01

During the last years, more and more mechanical applications saw the introduction of active control strategies. In particular, the need of improving the performances and/or the system health is very often associated to vibration suppression. This goal can be achieved considering both passive and active solutions. In this sense, many active control strategies have been developed, such as the Independent Modal Space Control (IMSC) or the resonant controllers (PPF, IRC, . . .). In all these cases, in order to tune and optimize the control strategy, the knowledge of the system dynamic behaviour is very important and it can be achieved both considering a numerical model of the system or through an experimental identification process. Anyway, dealing with non-linear or time-varying systems, a tool able to online identify the system parameters becomes a key-point for the control logic synthesis. The aim of the present work is the definition of a real-time technique, based on ARMAX models, that estimates the system parameters starting from the measurements of piezoelectric sensors. These parameters are returned to the control logic, that automatically adapts itself to the system dynamics. The problem is numerically investigated considering a carbon-fiber plate model forced through a piezoelectric patch.

Multiple linear regression to estimate time-frequency electrophysiological responses in single trials

PubMed Central

Hu, L.; Zhang, Z.G.; Mouraux, A.; Iannetti, G.D.

2015-01-01

Transient sensory, motor or cognitive event elicit not only phase-locked event-related potentials (ERPs) in the ongoing electroencephalogram (EEG), but also induce non-phase-locked modulations of ongoing EEG oscillations. These modulations can be detected when single-trial waveforms are analysed in the time-frequency domain, and consist in stimulus-induced decreases (event-related desynchronization, ERD) or increases (event-related synchronization, ERS) of synchrony in the activity of the underlying neuronal populations. ERD and ERS reflect changes in the parameters that control oscillations in neuronal networks and, depending on the frequency at which they occur, represent neuronal mechanisms involved in cortical activation, inhibition and binding. ERD and ERS are commonly estimated by averaging the time-frequency decomposition of single trials. However, their trial-to-trial variability that can reflect physiologically-important information is lost by across-trial averaging. Here, we aim to (1) develop novel approaches to explore single-trial parameters (including latency, frequency and magnitude) of ERP/ERD/ERS; (2) disclose the relationship between estimated single-trial parameters and other experimental factors (e.g., perceived intensity). We found that (1) stimulus-elicited ERP/ERD/ERS can be correctly separated using principal component analysis (PCA) decomposition with Varimax rotation on the single-trial time-frequency distributions; (2) time-frequency multiple linear regression with dispersion term (TF-MLRd) enhances the signal-to-noise ratio of ERP/ERD/ERS in single trials, and provides an unbiased estimation of their latency, frequency, and magnitude at single-trial level; (3) these estimates can be meaningfully correlated with each other and with other experimental factors at single-trial level (e.g., perceived stimulus intensity and ERP magnitude). The methods described in this article allow exploring fully non-phase-locked stimulus-induced cortical oscillations, obtaining single-trial estimate of response latency, frequency, and magnitude. This permits within-subject statistical comparisons, correlation with pre-stimulus features, and integration of simultaneously-recorded EEG and fMRI. PMID:25665966

An optimally weighted estimator of the linear power spectrum disentangling the growth of density perturbations across galaxy surveys

NASA Astrophysics Data System (ADS)

Sorini, D.

2017-04-01

Measuring the clustering of galaxies from surveys allows us to estimate the power spectrum of matter density fluctuations, thus constraining cosmological models. This requires careful modelling of observational effects to avoid misinterpretation of data. In particular, signals coming from different distances encode information from different epochs. This is known as ``light-cone effect'' and is going to have a higher impact as upcoming galaxy surveys probe larger redshift ranges. Generalising the method by Feldman, Kaiser and Peacock (1994) [1], I define a minimum-variance estimator of the linear power spectrum at a fixed time, properly taking into account the light-cone effect. An analytic expression for the estimator is provided, and that is consistent with the findings of previous works in the literature. I test the method within the context of the Halofit model, assuming Planck 2014 cosmological parameters [2]. I show that the estimator presented recovers the fiducial linear power spectrum at present time within 5% accuracy up to k ~ 0.80 h Mpc-1 and within 10% up to k ~ 0.94 h Mpc-1, well into the non-linear regime of the growth of density perturbations. As such, the method could be useful in the analysis of the data from future large-scale surveys, like Euclid.

[The nonlinear parameters of interference EMG of two day old human newborns].

PubMed

Voroshilov, A S; Meĭgal, A Iu

2011-01-01

Temporal structure of interference electromyogram (iEMG) was studied in healthy two days old human newborns (n = 76) using the non-linear parameters (correlation dimension, fractal dimension, correlation entropy). It has been found that the non-linear parameters of iEMG were time-dependent because they were decreasing within the first two days of life. Also, these parameters were sensitive to muscle function, because correlation dimension, fractal dimension, and correlation entropy of iEMG in gastrocnemius muscle differed from the other muscles. The non-linear parameters were proven to be independent of the iEMG amplitude. That model of early ontogenesis may be of potential use for investigation of anti-gravitation activity.

Sensitivity of tumor motion simulation accuracy to lung biomechanical modeling approaches and parameters.

PubMed

Tehrani, Joubin Nasehi; Yang, Yin; Werner, Rene; Lu, Wei; Low, Daniel; Guo, Xiaohu; Wang, Jing

2015-11-21

Finite element analysis (FEA)-based biomechanical modeling can be used to predict lung respiratory motion. In this technique, elastic models and biomechanical parameters are two important factors that determine modeling accuracy. We systematically evaluated the effects of lung and lung tumor biomechanical modeling approaches and related parameters to improve the accuracy of motion simulation of lung tumor center of mass (TCM) displacements. Experiments were conducted with four-dimensional computed tomography (4D-CT). A Quasi-Newton FEA was performed to simulate lung and related tumor displacements between end-expiration (phase 50%) and other respiration phases (0%, 10%, 20%, 30%, and 40%). Both linear isotropic and non-linear hyperelastic materials, including the neo-Hookean compressible and uncoupled Mooney-Rivlin models, were used to create a finite element model (FEM) of lung and tumors. Lung surface displacement vector fields (SDVFs) were obtained by registering the 50% phase CT to other respiration phases, using the non-rigid demons registration algorithm. The obtained SDVFs were used as lung surface displacement boundary conditions in FEM. The sensitivity of TCM displacement to lung and tumor biomechanical parameters was assessed in eight patients for all three models. Patient-specific optimal parameters were estimated by minimizing the TCM motion simulation errors between phase 50% and phase 0%. The uncoupled Mooney-Rivlin material model showed the highest TCM motion simulation accuracy. The average TCM motion simulation absolute errors for the Mooney-Rivlin material model along left-right, anterior-posterior, and superior-inferior directions were 0.80 mm, 0.86 mm, and 1.51 mm, respectively. The proposed strategy provides a reliable method to estimate patient-specific biomechanical parameters in FEM for lung tumor motion simulation.

Sensitivity of Tumor Motion Simulation Accuracy to Lung Biomechanical Modeling Approaches and Parameters

PubMed Central

Tehrani, Joubin Nasehi; Yang, Yin; Werner, Rene; Lu, Wei; Low, Daniel; Guo, Xiaohu

2015-01-01

Finite element analysis (FEA)-based biomechanical modeling can be used to predict lung respiratory motion. In this technique, elastic models and biomechanical parameters are two important factors that determine modeling accuracy. We systematically evaluated the effects of lung and lung tumor biomechanical modeling approaches and related parameters to improve the accuracy of motion simulation of lung tumor center of mass (TCM) displacements. Experiments were conducted with four-dimensional computed tomography (4D-CT). A Quasi-Newton FEA was performed to simulate lung and related tumor displacements between end-expiration (phase 50%) and other respiration phases (0%, 10%, 20%, 30%, and 40%). Both linear isotropic and non-linear hyperelastic materials, including the Neo-Hookean compressible and uncoupled Mooney-Rivlin models, were used to create a finite element model (FEM) of lung and tumors. Lung surface displacement vector fields (SDVFs) were obtained by registering the 50% phase CT to other respiration phases, using the non-rigid demons registration algorithm. The obtained SDVFs were used as lung surface displacement boundary conditions in FEM. The sensitivity of TCM displacement to lung and tumor biomechanical parameters was assessed in eight patients for all three models. Patient-specific optimal parameters were estimated by minimizing the TCM motion simulation errors between phase 50% and phase 0%. The uncoupled Mooney-Rivlin material model showed the highest TCM motion simulation accuracy. The average TCM motion simulation absolute errors for the Mooney-Rivlin material model along left-right (LR), anterior-posterior (AP), and superior-inferior (SI) directions were 0.80 mm, 0.86 mm, and 1.51 mm, respectively. The proposed strategy provides a reliable method to estimate patient-specific biomechanical parameters in FEM for lung tumor motion simulation. PMID:26531324

Pattern recognition in the ALFALFA.70 and Sloan Digital Sky Surveys: a catalogue of ˜500 000 H I gas fraction estimates based on artificial neural networks

NASA Astrophysics Data System (ADS)

Teimoorinia, Hossen; Ellison, Sara L.; Patton, David R.

2017-02-01

The application of artificial neural networks (ANNs) for the estimation of H I gas mass fraction (M_{H I}/{{M}_{*}}) is investigated, based on a sample of 13 674 galaxies in the Sloan Digital Sky Survey (SDSS) with H I detections or upper limits from the Arecibo Legacy Fast Arecibo L-band Feed Array (ALFALFA). We show that, for an example set of fixed input parameters (g - r colour and I-band surface brightness), a multidimensional quadratic model yields M_{H I}/{{M}_{*}} scaling relations with a smaller scatter (0.22 dex) than traditional linear fits (0.32 dex), demonstrating that non-linear methods can lead to an improved performance over traditional approaches. A more extensive ANN analysis is performed using 15 galaxy parameters that capture variation in stellar mass, internal structure, environment and star formation. Of the 15 parameters investigated, we find that g - r colour, followed by stellar mass surface density, bulge fraction and specific star formation rate have the best connection with M_{H I}/{{M}_{*}}. By combining two control parameters, that indicate how well a given galaxy in SDSS is represented by the ALFALFA training set (PR) and the scatter in the training procedure (σfit), we develop a strategy for quantifying which SDSS galaxies our ANN can be adequately applied to, and the associated errors in the M_{H I}/{{M}_{*}} estimation. In contrast to previous works, our M_{H I}/{{M}_{*}} estimation has no systematic trend with galactic parameters such as M⋆, g - r and star formation rate. We present a catalogue of M_{H I}/{{M}_{*}} estimates for more than half a million galaxies in the SDSS, of which ˜150 000 galaxies have a secure selection parameter with average scatter in the M_{H I}/{{M}_{*}} estimation of 0.22 dex.

State-space models’ dirty little secrets: even simple linear Gaussian models can have estimation problems

NASA Astrophysics Data System (ADS)

Auger-Méthé, Marie; Field, Chris; Albertsen, Christoffer M.; Derocher, Andrew E.; Lewis, Mark A.; Jonsen, Ian D.; Mills Flemming, Joanna

2016-05-01

State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (Ursus maritimus) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results.

Variational Bayesian Parameter Estimation Techniques for the General Linear Model

PubMed Central

Starke, Ludger; Ostwald, Dirk

2017-01-01

Variational Bayes (VB), variational maximum likelihood (VML), restricted maximum likelihood (ReML), and maximum likelihood (ML) are cornerstone parametric statistical estimation techniques in the analysis of functional neuroimaging data. However, the theoretical underpinnings of these model parameter estimation techniques are rarely covered in introductory statistical texts. Because of the widespread practical use of VB, VML, ReML, and ML in the neuroimaging community, we reasoned that a theoretical treatment of their relationships and their application in a basic modeling scenario may be helpful for both neuroimaging novices and practitioners alike. In this technical study, we thus revisit the conceptual and formal underpinnings of VB, VML, ReML, and ML and provide a detailed account of their mathematical relationships and implementational details. We further apply VB, VML, ReML, and ML to the general linear model (GLM) with non-spherical error covariance as commonly encountered in the first-level analysis of fMRI data. To this end, we explicitly derive the corresponding free energy objective functions and ensuing iterative algorithms. Finally, in the applied part of our study, we evaluate the parameter and model recovery properties of VB, VML, ReML, and ML, first in an exemplary setting and then in the analysis of experimental fMRI data acquired from a single participant under visual stimulation. PMID:28966572

Control of Distributed Parameter Systems

DTIC Science & Technology

1990-08-01

vari- ant of the general Lotka - Volterra model for interspecific competition. The variant described the emergence of one subpopulation from another as a...distribut ion unlimited. I&. ARSTRACT (MAUMUnw2O1 A unified arioroximation framework for Parameter estimation In general linear POE models has been completed...unified approximation framework for parameter estimation in general linear PDE models. This framework has provided the theoretical basis for a number of

Dealing with uncertainty in landscape genetic resistance models: a case of three co-occurring marsupials.

PubMed

Dudaniec, Rachael Y; Worthington Wilmer, Jessica; Hanson, Jeffrey O; Warren, Matthew; Bell, Sarah; Rhodes, Jonathan R

2016-01-01

Landscape genetics lacks explicit methods for dealing with the uncertainty in landscape resistance estimation, which is particularly problematic when sample sizes of individuals are small. Unless uncertainty can be quantified, valuable but small data sets may be rendered unusable for conservation purposes. We offer a method to quantify uncertainty in landscape resistance estimates using multimodel inference as an improvement over single model-based inference. We illustrate the approach empirically using co-occurring, woodland-preferring Australian marsupials within a common study area: two arboreal gliders (Petaurus breviceps, and Petaurus norfolcensis) and one ground-dwelling antechinus (Antechinus flavipes). First, we use maximum-likelihood and a bootstrap procedure to identify the best-supported isolation-by-resistance model out of 56 models defined by linear and non-linear resistance functions. We then quantify uncertainty in resistance estimates by examining parameter selection probabilities from the bootstrapped data. The selection probabilities provide estimates of uncertainty in the parameters that drive the relationships between landscape features and resistance. We then validate our method for quantifying uncertainty using simulated genetic and landscape data showing that for most parameter combinations it provides sensible estimates of uncertainty. We conclude that small data sets can be informative in landscape genetic analyses provided uncertainty can be explicitly quantified. Being explicit about uncertainty in landscape genetic models will make results more interpretable and useful for conservation decision-making, where dealing with uncertainty is critical. © 2015 John Wiley & Sons Ltd.

Scattering linear polarization of late-type active stars

NASA Astrophysics Data System (ADS)

Yakobchuk, T. M.; Berdyugina, S. V.

2018-05-01

Context. Many active stars are covered in spots, much more so than the Sun, as indicated by spectroscopic and photometric observations. It has been predicted that star spots induce non-zero intrinsic linear polarization by breaking the visible stellar disk symmetry. Although small, this effect might be useful for star spot studies, and it is particularly significant for a future polarimetric atmosphere characterization of exoplanets orbiting active host stars. Aims: Using models for a center-to-limb variation of the intensity and polarization in presence of continuum scattering and adopting a simplified two-temperature photosphere model, we aim to estimate the intrinsic linear polarization for late-type stars of different gravity, effective temperature, and spottedness. Methods: We developed a code that simulates various spot configurations or uses arbitrary surface maps, performs numerical disk integration, and builds Stokes parameter phase curves for a star over a rotation period for a selected wavelength. It allows estimating minimum and maximum polarization values for a given set of stellar parameters and spot coverages. Results: Based on assumptions about photosphere-to-spot temperature contrasts and spot size distributions, we calculate the linear polarization for late-type stars with Teff = 3500 K-6000 K, log g = 1.0-5.0, using the plane-parallel and spherical atmosphere models. Employing random spot surface distribution, we analyze the relation between spot coverage and polarization and determine the influence of different input parameters on results. Furthermore, we consider spot configurations with polar spots and active latitudes and longitudes.

MEG and fMRI Fusion for Non-Linear Estimation of Neural and BOLD Signal Changes

PubMed Central

Plis, Sergey M.; Calhoun, Vince D.; Weisend, Michael P.; Eichele, Tom; Lane, Terran

2010-01-01

The combined analysis of magnetoencephalography (MEG)/electroencephalography and functional magnetic resonance imaging (fMRI) measurements can lead to improvement in the description of the dynamical and spatial properties of brain activity. In this paper we empirically demonstrate this improvement using simulated and recorded task related MEG and fMRI activity. Neural activity estimates were derived using a dynamic Bayesian network with continuous real valued parameters by means of a sequential Monte Carlo technique. In synthetic data, we show that MEG and fMRI fusion improves estimation of the indirectly observed neural activity and smooths tracking of the blood oxygenation level dependent (BOLD) response. In recordings of task related neural activity the combination of MEG and fMRI produces a result with greater signal-to-noise ratio, that confirms the expectation arising from the nature of the experiment. The highly non-linear model of the BOLD response poses a difficult inference problem for neural activity estimation; computational requirements are also high due to the time and space complexity. We show that joint analysis of the data improves the system's behavior by stabilizing the differential equations system and by requiring fewer computational resources. PMID:21120141

Effects of linear trends on estimation of noise in GNSS position time-series

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dmitrieva, K.; Segall, P.; Bradley, A. M.

A thorough understanding of time-dependent noise in Global Navigation Satellite System (GNSS) position time-series is necessary for computing uncertainties in any signals found in the data. However, estimation of time-correlated noise is a challenging task and is complicated by the difficulty in separating noise from signal, the features of greatest interest in the time-series. In this study, we investigate how linear trends affect the estimation of noise in daily GNSS position time-series. We use synthetic time-series to study the relationship between linear trends and estimates of time-correlated noise for the six most commonly cited noise models. We find that themore » effects of added linear trends, or conversely de-trending, vary depending on the noise model. The commonly adopted model of random walk (RW), flicker noise (FN) and white noise (WN) is the most severely affected by de-trending, with estimates of low-amplitude RW most severely biased. FN plus WN is least affected by adding or removing trends. Non-integer power-law noise estimates are also less affected by de-trending, but are very sensitive to the addition of trend when the spectral index is less than one. We derive an analytical relationship between linear trends and the estimated RW variance for the special case of pure RW noise. Finally, overall, we find that to ascertain the correct noise model for GNSS position time-series and to estimate the correct noise parameters, it is important to have independent constraints on the actual trends in the data.« less

Effects of linear trends on estimation of noise in GNSS position time-series

NASA Astrophysics Data System (ADS)

Dmitrieva, K.; Segall, P.; Bradley, A. M.

2017-01-01

A thorough understanding of time-dependent noise in Global Navigation Satellite System (GNSS) position time-series is necessary for computing uncertainties in any signals found in the data. However, estimation of time-correlated noise is a challenging task and is complicated by the difficulty in separating noise from signal, the features of greatest interest in the time-series. In this paper, we investigate how linear trends affect the estimation of noise in daily GNSS position time-series. We use synthetic time-series to study the relationship between linear trends and estimates of time-correlated noise for the six most commonly cited noise models. We find that the effects of added linear trends, or conversely de-trending, vary depending on the noise model. The commonly adopted model of random walk (RW), flicker noise (FN) and white noise (WN) is the most severely affected by de-trending, with estimates of low-amplitude RW most severely biased. FN plus WN is least affected by adding or removing trends. Non-integer power-law noise estimates are also less affected by de-trending, but are very sensitive to the addition of trend when the spectral index is less than one. We derive an analytical relationship between linear trends and the estimated RW variance for the special case of pure RW noise. Overall, we find that to ascertain the correct noise model for GNSS position time-series and to estimate the correct noise parameters, it is important to have independent constraints on the actual trends in the data.

Effects of linear trends on estimation of noise in GNSS position time-series

DOE PAGES

Dmitrieva, K.; Segall, P.; Bradley, A. M.

2016-10-20

A thorough understanding of time-dependent noise in Global Navigation Satellite System (GNSS) position time-series is necessary for computing uncertainties in any signals found in the data. However, estimation of time-correlated noise is a challenging task and is complicated by the difficulty in separating noise from signal, the features of greatest interest in the time-series. In this study, we investigate how linear trends affect the estimation of noise in daily GNSS position time-series. We use synthetic time-series to study the relationship between linear trends and estimates of time-correlated noise for the six most commonly cited noise models. We find that themore » effects of added linear trends, or conversely de-trending, vary depending on the noise model. The commonly adopted model of random walk (RW), flicker noise (FN) and white noise (WN) is the most severely affected by de-trending, with estimates of low-amplitude RW most severely biased. FN plus WN is least affected by adding or removing trends. Non-integer power-law noise estimates are also less affected by de-trending, but are very sensitive to the addition of trend when the spectral index is less than one. We derive an analytical relationship between linear trends and the estimated RW variance for the special case of pure RW noise. Finally, overall, we find that to ascertain the correct noise model for GNSS position time-series and to estimate the correct noise parameters, it is important to have independent constraints on the actual trends in the data.« less

Linearised and non-linearised isotherm models optimization analysis by error functions and statistical means

PubMed Central

2014-01-01

In adsorption study, to describe sorption process and evaluation of best-fitting isotherm model is a key analysis to investigate the theoretical hypothesis. Hence, numerous statistically analysis have been extensively used to estimate validity of the experimental equilibrium adsorption values with the predicted equilibrium values. Several statistical error analysis were carried out. In the present study, the following statistical analysis were carried out to evaluate the adsorption isotherm model fitness, like the Pearson correlation, the coefficient of determination and the Chi-square test, have been used. The ANOVA test was carried out for evaluating significance of various error functions and also coefficient of dispersion were evaluated for linearised and non-linearised models. The adsorption of phenol onto natural soil (Local name Kalathur soil) was carried out, in batch mode at 30 ± 20 C. For estimating the isotherm parameters, to get a holistic view of the analysis the models were compared between linear and non-linear isotherm models. The result reveled that, among above mentioned error functions and statistical functions were designed to determine the best fitting isotherm. PMID:25018878

An evolutive real-time source inversion based on a linear inverse formulation

NASA Astrophysics Data System (ADS)

Sanchez Reyes, H. S.; Tago, J.; Cruz-Atienza, V. M.; Metivier, L.; Contreras Zazueta, M. A.; Virieux, J.

2016-12-01

Finite source inversion is a steppingstone to unveil earthquake rupture. It is used on ground motion predictions and its results shed light on seismic cycle for better tectonic understanding. It is not yet used for quasi-real-time analysis. Nowadays, significant progress has been made on approaches regarding earthquake imaging, thanks to new data acquisition and methodological advances. However, most of these techniques are posterior procedures once seismograms are available. Incorporating source parameters estimation into early warning systems would require to update the source build-up while recording data. In order to go toward this dynamic estimation, we developed a kinematic source inversion formulated in the time-domain, for which seismograms are linearly related to the slip distribution on the fault through convolutions with Green's functions previously estimated and stored (Perton et al., 2016). These convolutions are performed in the time-domain as we progressively increase the time window of records at each station specifically. Selected unknowns are the spatio-temporal slip-rate distribution to keep the linearity of the forward problem with respect to unknowns, as promoted by Fan and Shearer (2014). Through the spatial extension of the expected rupture zone, we progressively build-up the slip-rate when adding new data by assuming rupture causality. This formulation is based on the adjoint-state method for efficiency (Plessix, 2006). The inverse problem is non-unique and, in most cases, underdetermined. While standard regularization terms are used for stabilizing the inversion, we avoid strategies based on parameter reduction leading to an unwanted non-linear relationship between parameters and seismograms for our progressive build-up. Rise time, rupture velocity and other quantities can be extracted later on as attributs from the slip-rate inversion we perform. Satisfactory results are obtained on a synthetic example (FIgure 1) proposed by the Source Inversion Validation project (Mai et al. 2011). A real case application is currently being explored. Our specific formulation, combined with simple prior information, as well as numerical results obtained so far, yields interesting perspectives for a real-time implementation.

Parameter estimation and forecasting for multiplicative log-normal cascades.

PubMed

Leövey, Andrés E; Lux, Thomas

2012-04-01

We study the well-known multiplicative log-normal cascade process in which the multiplication of Gaussian and log normally distributed random variables yields time series with intermittent bursts of activity. Due to the nonstationarity of this process and the combinatorial nature of such a formalism, its parameters have been estimated mostly by fitting the numerical approximation of the associated non-Gaussian probability density function to empirical data, cf. Castaing et al. [Physica D 46, 177 (1990)]. More recently, alternative estimators based upon various moments have been proposed by Beck [Physica D 193, 195 (2004)] and Kiyono et al. [Phys. Rev. E 76, 041113 (2007)]. In this paper, we pursue this moment-based approach further and develop a more rigorous generalized method of moments (GMM) estimation procedure to cope with the documented difficulties of previous methodologies. We show that even under uncertainty about the actual number of cascade steps, our methodology yields very reliable results for the estimated intermittency parameter. Employing the Levinson-Durbin algorithm for best linear forecasts, we also show that estimated parameters can be used for forecasting the evolution of the turbulent flow. We compare forecasting results from the GMM and Kiyono et al.'s procedure via Monte Carlo simulations. We finally test the applicability of our approach by estimating the intermittency parameter and forecasting of volatility for a sample of financial data from stock and foreign exchange markets.

RBF kernel based support vector regression to estimate the blood volume and heart rate responses during hemodialysis.

PubMed

Javed, Faizan; Chan, Gregory S H; Savkin, Andrey V; Middleton, Paul M; Malouf, Philip; Steel, Elizabeth; Mackie, James; Lovell, Nigel H

2009-01-01

This paper uses non-linear support vector regression (SVR) to model the blood volume and heart rate (HR) responses in 9 hemodynamically stable kidney failure patients during hemodialysis. Using radial bias function (RBF) kernels the non-parametric models of relative blood volume (RBV) change with time as well as percentage change in HR with respect to RBV were obtained. The e-insensitivity based loss function was used for SVR modeling. Selection of the design parameters which includes capacity (C), insensitivity region (e) and the RBF kernel parameter (sigma) was made based on a grid search approach and the selected models were cross-validated using the average mean square error (AMSE) calculated from testing data based on a k-fold cross-validation technique. Linear regression was also applied to fit the curves and the AMSE was calculated for comparison with SVR. For the model based on RBV with time, SVR gave a lower AMSE for both training (AMSE=1.5) as well as testing data (AMSE=1.4) compared to linear regression (AMSE=1.8 and 1.5). SVR also provided a better fit for HR with RBV for both training as well as testing data (AMSE=15.8 and 16.4) compared to linear regression (AMSE=25.2 and 20.1).

A Bayesian approach for estimating under-reported dengue incidence with a focus on non-linear associations between climate and dengue in Dhaka, Bangladesh.

PubMed

Sharmin, Sifat; Glass, Kathryn; Viennet, Elvina; Harley, David

2018-04-01

Determining the relation between climate and dengue incidence is challenging due to under-reporting of disease and consequent biased incidence estimates. Non-linear associations between climate and incidence compound this. Here, we introduce a modelling framework to estimate dengue incidence from passive surveillance data while incorporating non-linear climate effects. We estimated the true number of cases per month using a Bayesian generalised linear model, developed in stages to adjust for under-reporting. A semi-parametric thin-plate spline approach was used to quantify non-linear climate effects. The approach was applied to data collected from the national dengue surveillance system of Bangladesh. The model estimated that only 2.8% (95% credible interval 2.7-2.8) of all cases in the capital Dhaka were reported through passive case reporting. The optimal mean monthly temperature for dengue transmission is 29℃ and average monthly rainfall above 15 mm decreases transmission. Our approach provides an estimate of true incidence and an understanding of the effects of temperature and rainfall on dengue transmission in Dhaka, Bangladesh.

The Inverse Problem for Confined Aquifer Flow: Identification and Estimation With Extensions

NASA Astrophysics Data System (ADS)

Loaiciga, Hugo A.; MariñO, Miguel A.

1987-01-01

The contributions of this work are twofold. First, a methodology for estimating the elements of parameter matrices in the governing equation of flow in a confined aquifer is developed. The estimation techniques for the distributed-parameter inverse problem pertain to linear least squares and generalized least squares methods. The linear relationship among the known heads and unknown parameters of the flow equation provides the background for developing criteria for determining the identifiability status of unknown parameters. Under conditions of exact or overidentification it is possible to develop statistically consistent parameter estimators and their asymptotic distributions. The estimation techniques, namely, two-stage least squares and three stage least squares, are applied to a specific groundwater inverse problem and compared between themselves and with an ordinary least squares estimator. The three-stage estimator provides the closer approximation to the actual parameter values, but it also shows relatively large standard errors as compared to the ordinary and two-stage estimators. The estimation techniques provide the parameter matrices required to simulate the unsteady groundwater flow equation. Second, a nonlinear maximum likelihood estimation approach to the inverse problem is presented. The statistical properties of maximum likelihood estimators are derived, and a procedure to construct confidence intervals and do hypothesis testing is given. The relative merits of the linear and maximum likelihood estimators are analyzed. Other topics relevant to the identification and estimation methodologies, i.e., a continuous-time solution to the flow equation, coping with noise-corrupted head measurements, and extension of the developed theory to nonlinear cases are also discussed. A simulation study is used to evaluate the methods developed in this study.

Quantum State Tomography via Linear Regression Estimation

PubMed Central

Qi, Bo; Hou, Zhibo; Li, Li; Dong, Daoyi; Xiang, Guoyong; Guo, Guangcan

2013-01-01

A simple yet efficient state reconstruction algorithm of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and the least-squares method is employed to estimate the unknown parameters. An asymptotic mean squared error (MSE) upper bound for all possible states to be estimated is given analytically, which depends explicitly upon the involved measurement bases. This analytical MSE upper bound can guide one to choose optimal measurement sets. The computational complexity of LRE is O(d4) where d is the dimension of the quantum state. Numerical examples show that LRE is much faster than maximum-likelihood estimation for quantum state tomography. PMID:24336519

Current Pressure Transducer Application of Model-based Prognostics Using Steady State Conditions

NASA Technical Reports Server (NTRS)

Teubert, Christopher; Daigle, Matthew J.

2014-01-01

Prognostics is the process of predicting a system's future states, health degradation/wear, and remaining useful life (RUL). This information plays an important role in preventing failure, reducing downtime, scheduling maintenance, and improving system utility. Prognostics relies heavily on wear estimation. In some components, the sensors used to estimate wear may not be fast enough to capture brief transient states that are indicative of wear. For this reason it is beneficial to be capable of detecting and estimating the extent of component wear using steady-state measurements. This paper details a method for estimating component wear using steady-state measurements, describes how this is used to predict future states, and presents a case study of a current/pressure (I/P) Transducer. I/P Transducer nominal and off-nominal behaviors are characterized using a physics-based model, and validated against expected and observed component behavior. This model is used to map observed steady-state responses to corresponding fault parameter values in the form of a lookup table. This method was chosen because of its fast, efficient nature, and its ability to be applied to both linear and non-linear systems. Using measurements of the steady state output, and the lookup table, wear is estimated. A regression is used to estimate the wear propagation parameter and characterize the damage progression function, which are used to predict future states and the remaining useful life of the system.

A theory of fine structure image models with an application to detection and classification of dementia

PubMed Central

Penn, Richard; Werner, Michael; Thomas, Justin

2015-01-01

Background Estimation of stochastic process models from data is a common application of time series analysis methods. Such system identification processes are often cast as hypothesis testing exercises whose intent is to estimate model parameters and test them for statistical significance. Ordinary least squares (OLS) regression and the Levenberg-Marquardt algorithm (LMA) have proven invaluable computational tools for models being described by non-homogeneous, linear, stationary, ordinary differential equations. Methods In this paper we extend stochastic model identification to linear, stationary, partial differential equations in two independent variables (2D) and show that OLS and LMA apply equally well to these systems. The method employs an original nonparametric statistic as a test for the significance of estimated parameters. Results We show gray scale and color images are special cases of 2D systems satisfying a particular autoregressive partial difference equation which estimates an analogous partial differential equation. Several applications to medical image modeling and classification illustrate the method by correctly classifying demented and normal OLS models of axial magnetic resonance brain scans according to subject Mini Mental State Exam (MMSE) scores. Comparison with 13 image classifiers from the literature indicates our classifier is at least 14 times faster than any of them and has a classification accuracy better than all but one. Conclusions Our modeling method applies to any linear, stationary, partial differential equation and the method is readily extended to 3D whole-organ systems. Further, in addition to being a robust image classifier, estimated image models offer insights into which parameters carry the most diagnostic image information and thereby suggest finer divisions could be made within a class. Image models can be estimated in milliseconds which translate to whole-organ models in seconds; such runtimes could make real-time medicine and surgery modeling possible. PMID:26029638

Non-linear dynamics of human locomotion: effects of rhythmic auditory cueing on local dynamic stability.

PubMed

Terrier, Philippe; Dériaz, Olivier

2013-01-01

It has been observed that times series of gait parameters [stride length (SL), stride time (ST), and stride speed (SS)], exhibit long-term persistence and fractal-like properties. Synchronizing steps with rhythmic auditory stimuli modifies the persistent fluctuation pattern to anti-persistence. Another non-linear method estimates the degree of resilience of gait control to small perturbations, i.e., the local dynamic stability (LDS). The method makes use of the maximal Lyapunov exponent, which estimates how fast a non-linear system embedded in a reconstructed state space (attractor) diverges after an infinitesimal perturbation. We propose to use an instrumented treadmill to simultaneously measure basic gait parameters (time series of SL, ST, and SS from which the statistical persistence among consecutive strides can be assessed), and the trajectory of the center of pressure (from which the LDS can be estimated). In 20 healthy participants, the response to rhythmic auditory cueing (RAC) of LDS and of statistical persistence [assessed with detrended fluctuation analysis (DFA)] was compared. By analyzing the divergence curves, we observed that long-term LDS (computed as the reverse of the average logarithmic rate of divergence between the 4th and the 10th strides downstream from nearest neighbors in the reconstructed attractor) was strongly enhanced (relative change +73%). That is likely the indication of a more dampened dynamics. The change in short-term LDS (divergence over one step) was smaller (+3%). DFA results (scaling exponents) confirmed an anti-persistent pattern in ST, SL, and SS. Long-term LDS (but not short-term LDS) and scaling exponents exhibited a significant correlation between them (r = 0.7). Both phenomena probably result from the more conscious/voluntary gait control that is required by RAC. We suggest that LDS and statistical persistence should be used to evaluate the efficiency of cueing therapy in patients with neurological gait disorders.

HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python.

PubMed

Wiecki, Thomas V; Sofer, Imri; Frank, Michael J

2013-01-01

The diffusion model is a commonly used tool to infer latent psychological processes underlying decision-making, and to link them to neural mechanisms based on response times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of response time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model), which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject/condition than non-hierarchical methods, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g., fMRI) influence decision-making parameters. This paper will first describe the theoretical background of the drift diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the χ(2)-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at: http://ski.clps.brown.edu/hddm_docs/

Accelerated Microstructure Imaging via Convex Optimization (AMICO) from diffusion MRI data.

PubMed

Daducci, Alessandro; Canales-Rodríguez, Erick J; Zhang, Hui; Dyrby, Tim B; Alexander, Daniel C; Thiran, Jean-Philippe

2015-01-15

Microstructure imaging from diffusion magnetic resonance (MR) data represents an invaluable tool to study non-invasively the morphology of tissues and to provide a biological insight into their microstructural organization. In recent years, a variety of biophysical models have been proposed to associate particular patterns observed in the measured signal with specific microstructural properties of the neuronal tissue, such as axon diameter and fiber density. Despite very appealing results showing that the estimated microstructure indices agree very well with histological examinations, existing techniques require computationally very expensive non-linear procedures to fit the models to the data which, in practice, demand the use of powerful computer clusters for large-scale applications. In this work, we present a general framework for Accelerated Microstructure Imaging via Convex Optimization (AMICO) and show how to re-formulate this class of techniques as convenient linear systems which, then, can be efficiently solved using very fast algorithms. We demonstrate this linearization of the fitting problem for two specific models, i.e. ActiveAx and NODDI, providing a very attractive alternative for parameter estimation in those techniques; however, the AMICO framework is general and flexible enough to work also for the wider space of microstructure imaging methods. Results demonstrate that AMICO represents an effective means to accelerate the fit of existing techniques drastically (up to four orders of magnitude faster) while preserving accuracy and precision in the estimated model parameters (correlation above 0.9). We believe that the availability of such ultrafast algorithms will help to accelerate the spread of microstructure imaging to larger cohorts of patients and to study a wider spectrum of neurological disorders. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Analysis of blood pressure signal in patients with different ventricular ejection fraction using linear and non-linear methods.

PubMed

Arcentales, Andres; Rivera, Patricio; Caminal, Pere; Voss, Andreas; Bayes-Genis, Antonio; Giraldo, Beatriz F

2016-08-01

Changes in the left ventricle function produce alternans in the hemodynamic and electric behavior of the cardiovascular system. A total of 49 cardiomyopathy patients have been studied based on the blood pressure signal (BP), and were classified according to the left ventricular ejection fraction (LVEF) in low risk (LR: LVEF>35%, 17 patients) and high risk (HR: LVEF≤35, 32 patients) groups. We propose to characterize these patients using a linear and a nonlinear methods, based on the spectral estimation and the recurrence plot, respectively. From BP signal, we extracted each systolic time interval (STI), upward systolic slope (BPsl), and the difference between systolic and diastolic BP, defined as pulse pressure (PP). After, the best subset of parameters were obtained through the sequential feature selection (SFS) method. According to the results, the best classification was obtained using a combination of linear and nonlinear features from STI and PP parameters. For STI, the best combination was obtained considering the frequency peak and the diagonal structures of RP, with an area under the curve (AUC) of 79%. The same results were obtained when comparing PP values. Consequently, the use of combined linear and nonlinear parameters could improve the risk stratification of cardiomyopathy patients.

Measures of GCM Performance as Functions of Model Parameters Affecting Clouds and Radiation

NASA Astrophysics Data System (ADS)

Jackson, C.; Mu, Q.; Sen, M.; Stoffa, P.

2002-05-01

This abstract is one of three related presentations at this meeting dealing with several issues surrounding optimal parameter and uncertainty estimation of model predictions of climate. Uncertainty in model predictions of climate depends in part on the uncertainty produced by model approximations or parameterizations of unresolved physics. Evaluating these uncertainties is computationally expensive because one needs to evaluate how arbitrary choices for any given combination of model parameters affects model performance. Because the computational effort grows exponentially with the number of parameters being investigated, it is important to choose parameters carefully. Evaluating whether a parameter is worth investigating depends on two considerations: 1) does reasonable choices of parameter values produce a large range in model response relative to observational uncertainty? and 2) does the model response depend non-linearly on various combinations of model parameters? We have decided to narrow our attention to selecting parameters that affect clouds and radiation, as it is likely that these parameters will dominate uncertainties in model predictions of future climate. We present preliminary results of ~20 to 30 AMIPII style climate model integrations using NCAR's CCM3.10 that show model performance as functions of individual parameters controlling 1) critical relative humidity for cloud formation (RHMIN), and 2) boundary layer critical Richardson number (RICR). We also explore various definitions of model performance that include some or all observational data sources (surface air temperature and pressure, meridional and zonal winds, clouds, long and short-wave cloud forcings, etc...) and evaluate in a few select cases whether the model's response depends non-linearly on the parameter values we have selected.

Exploration of DGVM Parameter Solution Space Using Simulated Annealing: Implications for Forecast Uncertainties

NASA Astrophysics Data System (ADS)

Wells, J. R.; Kim, J. B.

2011-12-01

Parameters in dynamic global vegetation models (DGVMs) are thought to be weakly constrained and can be a significant source of errors and uncertainties. DGVMs use between 5 and 26 plant functional types (PFTs) to represent the average plant life form in each simulated plot, and each PFT typically has a dozen or more parameters that define the way it uses resource and responds to the simulated growing environment. Sensitivity analysis explores how varying parameters affects the output, but does not do a full exploration of the parameter solution space. The solution space for DGVM parameter values are thought to be complex and non-linear; and multiple sets of acceptable parameters may exist. In published studies, PFT parameters are estimated from published literature, and often a parameter value is estimated from a single published value. Further, the parameters are "tuned" using somewhat arbitrary, "trial-and-error" methods. BIOMAP is a new DGVM created by fusing MAPSS biogeography model with Biome-BGC. It represents the vegetation of North America using 26 PFTs. We are using simulated annealing, a global search method, to systematically and objectively explore the solution space for the BIOMAP PFTs and system parameters important for plant water use. We defined the boundaries of the solution space by obtaining maximum and minimum values from published literature, and where those were not available, using +/-20% of current values. We used stratified random sampling to select a set of grid cells representing the vegetation of the conterminous USA. Simulated annealing algorithm is applied to the parameters for spin-up and a transient run during the historical period 1961-1990. A set of parameter values is considered acceptable if the associated simulation run produces a modern potential vegetation distribution map that is as accurate as one produced by trial-and-error calibration. We expect to confirm that the solution space is non-linear and complex, and that multiple acceptable parameter sets exist. Further we expect to demonstrate that the multiple parameter sets produce significantly divergent future forecasts in NEP, C storage, and ET and runoff; and thereby identify a highly important source of DGVM uncertainty

Research on SOC Calibration of Large Capacity Lead Acid Battery

NASA Astrophysics Data System (ADS)

Ye, W. Q.; Guo, Y. X.

2018-05-01

Large capacity lead-acid battery is used in track electric locomotive, and State of Charge (SOC) is an important quantitative parameter of locomotive power output and operating mileage of power emergency recovery vehicle. But State of Charge estimation has been a difficult part in the battery management system. In order to reduce the SOC estimation error better, this paper uses the linear relationship of Open Circuit Voltage (OCV) and State of Charge to fit the SOC-OCV curve equation by MATLAB. The method proposed in this paper is small, easy to implement and can be used in the battery non-working state SOC estimation correction, improve the estimation accuracy of SOC.

PET Pharmacokinetic Modelling

NASA Astrophysics Data System (ADS)

Müller-Schauenburg, Wolfgang; Reimold, Matthias

Positron Emission Tomography is a well-established technique that allows imaging and quantification of tissue properties in-vivo. The goal of pharmacokinetic modelling is to estimate physiological parameters, e.g. perfusion or receptor density from the measured time course of a radiotracer. After a brief overview of clinical application of PET, we summarize the fundamentals of modelling: distribution volume, Fick's principle of local balancing, extraction and perfusion, and how to calculate equilibrium data from measurements after bolus injection. Three fundamental models are considered: (i) the 1-tissue compartment model, e.g. for regional cerebral blood flow (rCBF) with the short-lived tracer [15O]water, (ii) the 2-tissue compartment model accounting for trapping (one exponential + constant), e.g. for glucose metabolism with [18F]FDG, (iii) the reversible 2-tissue compartment model (two exponentials), e.g. for receptor binding. Arterial blood sampling is required for classical PET modelling, but can often be avoided by comparing regions with specific binding with so called reference regions with negligible specific uptake, e.g. in receptor imaging. To estimate the model parameters, non-linear least square fits are the standard. Various linearizations have been proposed for rapid parameter estimation, e.g. on a pixel-by-pixel basis, for the prize of a bias. Such linear approaches exist for all three models; e.g. the PATLAK-plot for trapping substances like FDG, and the LOGAN-plot to obtain distribution volumes for reversibly binding tracers. The description of receptor modelling is dedicated to the approaches of the subsequent lecture (chapter) of Millet, who works in the tradition of Delforge with multiple-injection investigations.

HYDRORECESSION: A toolbox for streamflow recession analysis

NASA Astrophysics Data System (ADS)

Arciniega, S.

2015-12-01

Streamflow recession curves are hydrological signatures allowing to study the relationship between groundwater storage and baseflow and/or low flows at the catchment scale. Recent studies have showed that streamflow recession analysis can be quite sensitive to the combination of different models, extraction techniques and parameter estimation methods. In order to better characterize streamflow recession curves, new methodologies combining multiple approaches have been recommended. The HYDRORECESSION toolbox, presented here, is a Matlab graphical user interface developed to analyse streamflow recession time series with the support of different tools allowing to parameterize linear and nonlinear storage-outflow relationships through four of the most useful recession models (Maillet, Boussinesq, Coutagne and Wittenberg). The toolbox includes four parameter-fitting techniques (linear regression, lower envelope, data binning and mean squared error) and three different methods to extract hydrograph recessions segments (Vogel, Brutsaert and Aksoy). In addition, the toolbox has a module that separates the baseflow component from the observed hydrograph using the inverse reservoir algorithm. Potential applications provided by HYDRORECESSION include model parameter analysis, hydrological regionalization and classification, baseflow index estimates, catchment-scale recharge and low-flows modelling, among others. HYDRORECESSION is freely available for non-commercial and academic purposes.

Comparison of Classifiers for Decoding Sensory and Cognitive Information from Prefrontal Neuronal Populations

PubMed Central

Astrand, Elaine; Enel, Pierre; Ibos, Guilhem; Dominey, Peter Ford; Baraduc, Pierre; Ben Hamed, Suliann

2014-01-01

Decoding neuronal information is important in neuroscience, both as a basic means to understand how neuronal activity is related to cerebral function and as a processing stage in driving neuroprosthetic effectors. Here, we compare the readout performance of six commonly used classifiers at decoding two different variables encoded by the spiking activity of the non-human primate frontal eye fields (FEF): the spatial position of a visual cue, and the instructed orientation of the animal's attention. While the first variable is exogenously driven by the environment, the second variable corresponds to the interpretation of the instruction conveyed by the cue; it is endogenously driven and corresponds to the output of internal cognitive operations performed on the visual attributes of the cue. These two variables were decoded using either a regularized optimal linear estimator in its explicit formulation, an optimal linear artificial neural network estimator, a non-linear artificial neural network estimator, a non-linear naïve Bayesian estimator, a non-linear Reservoir recurrent network classifier or a non-linear Support Vector Machine classifier. Our results suggest that endogenous information such as the orientation of attention can be decoded from the FEF with the same accuracy as exogenous visual information. All classifiers did not behave equally in the face of population size and heterogeneity, the available training and testing trials, the subject's behavior and the temporal structure of the variable of interest. In most situations, the regularized optimal linear estimator and the non-linear Support Vector Machine classifiers outperformed the other tested decoders. PMID:24466019

Asymmetrical effects of mesophyll conductance on fundamental photosynthetic parameters and their relationships estimated from leaf gas exchange measurements.

PubMed

Sun, Ying; Gu, Lianhong; Dickinson, Robert E; Pallardy, Stephen G; Baker, John; Cao, Yonghui; DaMatta, Fábio Murilo; Dong, Xuejun; Ellsworth, David; Van Goethem, Davina; Jensen, Anna M; Law, Beverly E; Loos, Rodolfo; Martins, Samuel C Vitor; Norby, Richard J; Warren, Jeffrey; Weston, David; Winter, Klaus

2014-04-01

Worldwide measurements of nearly 130 C3 species covering all major plant functional types are analysed in conjunction with model simulations to determine the effects of mesophyll conductance (g(m)) on photosynthetic parameters and their relationships estimated from A/Ci curves. We find that an assumption of infinite g(m) results in up to 75% underestimation for maximum carboxylation rate V(cmax), 60% for maximum electron transport rate J(max), and 40% for triose phosphate utilization rate T(u) . V(cmax) is most sensitive, J(max) is less sensitive, and T(u) has the least sensitivity to the variation of g(m). Because of this asymmetrical effect of g(m), the ratios of J(max) to V(cmax), T(u) to V(cmax) and T(u) to J(max) are all overestimated. An infinite g(m) assumption also limits the freedom of variation of estimated parameters and artificially constrains parameter relationships to stronger shapes. These findings suggest the importance of quantifying g(m) for understanding in situ photosynthetic machinery functioning. We show that a nonzero resistance to CO2 movement in chloroplasts has small effects on estimated parameters. A non-linear function with gm as input is developed to convert the parameters estimated under an assumption of infinite gm to proper values. This function will facilitate gm representation in global carbon cycle models. © 2013 John Wiley & Sons Ltd.

A non-linear regression method for CT brain perfusion analysis

NASA Astrophysics Data System (ADS)

Bennink, E.; Oosterbroek, J.; Viergever, M. A.; Velthuis, B. K.; de Jong, H. W. A. M.

2015-03-01

CT perfusion (CTP) imaging allows for rapid diagnosis of ischemic stroke. Generation of perfusion maps from CTP data usually involves deconvolution algorithms providing estimates for the impulse response function in the tissue. We propose the use of a fast non-linear regression (NLR) method that we postulate has similar performance to the current academic state-of-art method (bSVD), but that has some important advantages, including the estimation of vascular permeability, improved robustness to tracer-delay, and very few tuning parameters, that are all important in stroke assessment. The aim of this study is to evaluate the fast NLR method against bSVD and a commercial clinical state-of-art method. The three methods were tested against a published digital perfusion phantom earlier used to illustrate the superiority of bSVD. In addition, the NLR and clinical methods were also tested against bSVD on 20 clinical scans. Pearson correlation coefficients were calculated for each of the tested methods. All three methods showed high correlation coefficients (>0.9) with the ground truth in the phantom. With respect to the clinical scans, the NLR perfusion maps showed higher correlation with bSVD than the perfusion maps from the clinical method. Furthermore, the perfusion maps showed that the fast NLR estimates are robust to tracer-delay. In conclusion, the proposed fast NLR method provides a simple and flexible way of estimating perfusion parameters from CT perfusion scans, with high correlation coefficients. This suggests that it could be a better alternative to the current clinical and academic state-of-art methods.

On the distinguishability of HRF models in fMRI.

PubMed

Rosa, Paulo N; Figueiredo, Patricia; Silvestre, Carlos J

2015-01-01

Modeling the Hemodynamic Response Function (HRF) is a critical step in fMRI studies of brain activity, and it is often desirable to estimate HRF parameters with physiological interpretability. A biophysically informed model of the HRF can be described by a non-linear time-invariant dynamic system. However, the identification of this dynamic system may leave much uncertainty on the exact values of the parameters. Moreover, the high noise levels in the data may hinder the model estimation task. In this context, the estimation of the HRF may be seen as a problem of model falsification or invalidation, where we are interested in distinguishing among a set of eligible models of dynamic systems. Here, we propose a systematic tool to determine the distinguishability among a set of physiologically plausible HRF models. The concept of absolutely input-distinguishable systems is introduced and applied to a biophysically informed HRF model, by exploiting the structure of the underlying non-linear dynamic system. A strategy to model uncertainty in the input time-delay and magnitude is developed and its impact on the distinguishability of two physiologically plausible HRF models is assessed, in terms of the maximum noise amplitude above which it is not possible to guarantee the falsification of one model in relation to another. Finally, a methodology is proposed for the choice of the input sequence, or experimental paradigm, that maximizes the distinguishability of the HRF models under investigation. The proposed approach may be used to evaluate the performance of HRF model estimation techniques from fMRI data.

Sparsity-promoting and edge-preserving maximum a posteriori estimators in non-parametric Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Agapiou, Sergios; Burger, Martin; Dashti, Masoumeh; Helin, Tapio

2018-04-01

We consider the inverse problem of recovering an unknown functional parameter u in a separable Banach space, from a noisy observation vector y of its image through a known possibly non-linear map {{\\mathcal G}} . We adopt a Bayesian approach to the problem and consider Besov space priors (see Lassas et al (2009 Inverse Problems Imaging 3 87-122)), which are well-known for their edge-preserving and sparsity-promoting properties and have recently attracted wide attention especially in the medical imaging community. Our key result is to show that in this non-parametric setup the maximum a posteriori (MAP) estimates are characterized by the minimizers of a generalized Onsager-Machlup functional of the posterior. This is done independently for the so-called weak and strong MAP estimates, which as we show coincide in our context. In addition, we prove a form of weak consistency for the MAP estimators in the infinitely informative data limit. Our results are remarkable for two reasons: first, the prior distribution is non-Gaussian and does not meet the smoothness conditions required in previous research on non-parametric MAP estimates. Second, the result analytically justifies existing uses of the MAP estimate in finite but high dimensional discretizations of Bayesian inverse problems with the considered Besov priors.

On structural identifiability analysis of the cascaded linear dynamic systems in isotopically non-stationary 13C labelling experiments.

PubMed

Lin, Weilu; Wang, Zejian; Huang, Mingzhi; Zhuang, Yingping; Zhang, Siliang

2018-06-01

The isotopically non-stationary 13C labelling experiments, as an emerging experimental technique, can estimate the intracellular fluxes of the cell culture under an isotopic transient period. However, to the best of our knowledge, the issue of the structural identifiability analysis of non-stationary isotope experiments is not well addressed in the literature. In this work, the local structural identifiability analysis for non-stationary cumomer balance equations is conducted based on the Taylor series approach. The numerical rank of the Jacobian matrices of the finite extended time derivatives of the measured fractions with respect to the free parameters is taken as the criterion. It turns out that only one single time point is necessary to achieve the structural identifiability analysis of the cascaded linear dynamic system of non-stationary isotope experiments. The equivalence between the local structural identifiability of the cascaded linear dynamic systems and the local optimum condition of the nonlinear least squares problem is elucidated in the work. Optimal measurements sets can then be determined for the metabolic network. Two simulated metabolic networks are adopted to demonstrate the utility of the proposed method. Copyright © 2018 Elsevier Inc. All rights reserved.

Linearly Supporting Feature Extraction for Automated Estimation of Stellar Atmospheric Parameters

NASA Astrophysics Data System (ADS)

Li, Xiangru; Lu, Yu; Comte, Georges; Luo, Ali; Zhao, Yongheng; Wang, Yongjun

2015-05-01

We describe a scheme to extract linearly supporting (LSU) features from stellar spectra to automatically estimate the atmospheric parameters {{T}{\\tt{eff} }}, log g, and [Fe/H]. “Linearly supporting” means that the atmospheric parameters can be accurately estimated from the extracted features through a linear model. The successive steps of the process are as follow: first, decompose the spectrum using a wavelet packet (WP) and represent it by the derived decomposition coefficients; second, detect representative spectral features from the decomposition coefficients using the proposed method Least Absolute Shrinkage and Selection Operator (LARS)bs; third, estimate the atmospheric parameters {{T}{\\tt{eff} }}, log g, and [Fe/H] from the detected features using a linear regression method. One prominent characteristic of this scheme is its ability to evaluate quantitatively the contribution of each detected feature to the atmospheric parameter estimate and also to trace back the physical significance of that feature. This work also shows that the usefulness of a component depends on both the wavelength and frequency. The proposed scheme has been evaluated on both real spectra from the Sloan Digital Sky Survey (SDSS)/SEGUE and synthetic spectra calculated from Kurucz's NEWODF models. On real spectra, we extracted 23 features to estimate {{T}{\\tt{eff} }}, 62 features for log g, and 68 features for [Fe/H]. Test consistencies between our estimates and those provided by the Spectroscopic Parameter Pipeline of SDSS show that the mean absolute errors (MAEs) are 0.0062 dex for log {{T}{\\tt{eff} }} (83 K for {{T}{\\tt{eff} }}), 0.2345 dex for log g, and 0.1564 dex for [Fe/H]. For the synthetic spectra, the MAE test accuracies are 0.0022 dex for log {{T}{\\tt{eff} }} (32 K for {{T}{\\tt{eff} }}), 0.0337 dex for log g, and 0.0268 dex for [Fe/H].

An optimally weighted estimator of the linear power spectrum disentangling the growth of density perturbations across galaxy surveys

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sorini, D., E-mail: sorini@mpia-hd.mpg.de

2017-04-01

Measuring the clustering of galaxies from surveys allows us to estimate the power spectrum of matter density fluctuations, thus constraining cosmological models. This requires careful modelling of observational effects to avoid misinterpretation of data. In particular, signals coming from different distances encode information from different epochs. This is known as ''light-cone effect'' and is going to have a higher impact as upcoming galaxy surveys probe larger redshift ranges. Generalising the method by Feldman, Kaiser and Peacock (1994) [1], I define a minimum-variance estimator of the linear power spectrum at a fixed time, properly taking into account the light-cone effect. Anmore » analytic expression for the estimator is provided, and that is consistent with the findings of previous works in the literature. I test the method within the context of the Halofit model, assuming Planck 2014 cosmological parameters [2]. I show that the estimator presented recovers the fiducial linear power spectrum at present time within 5% accuracy up to k ∼ 0.80 h Mpc{sup −1} and within 10% up to k ∼ 0.94 h Mpc{sup −1}, well into the non-linear regime of the growth of density perturbations. As such, the method could be useful in the analysis of the data from future large-scale surveys, like Euclid.« less

Statistical behavior of ten million experimental detection limits

NASA Astrophysics Data System (ADS)

Voigtman, Edward; Abraham, Kevin T.

2011-02-01

Using a lab-constructed laser-excited fluorimeter, together with bootstrapping methodology, the authors have generated many millions of experimental linear calibration curves for the detection of rhodamine 6G tetrafluoroborate in ethanol solutions. The detection limits computed from them are in excellent agreement with both previously published theory and with comprehensive Monte Carlo computer simulations. Currie decision levels and Currie detection limits, each in the theoretical, chemical content domain, were found to be simply scaled reciprocals of the non-centrality parameter of the non-central t distribution that characterizes univariate linear calibration curves that have homoscedastic, additive Gaussian white noise. Accurate and precise estimates of the theoretical, content domain Currie detection limit for the experimental system, with 5% (each) probabilities of false positives and false negatives, are presented.

Bayesian deconvolution of [corrected] fMRI data using bilinear dynamical systems.

PubMed

Makni, Salima; Beckmann, Christian; Smith, Steve; Woolrich, Mark

2008-10-01

In Penny et al. [Penny, W., Ghahramani, Z., Friston, K.J. 2005. Bilinear dynamical systems. Philos. Trans. R. Soc. Lond. B Biol. Sci. 360(1457) 983-993], a particular case of the Linear Dynamical Systems (LDSs) was used to model the dynamic behavior of the BOLD response in functional MRI. This state-space model, called bilinear dynamical system (BDS), is used to deconvolve the fMRI time series in order to estimate the neuronal response induced by the different stimuli of the experimental paradigm. The BDS model parameters are estimated using an expectation-maximization (EM) algorithm proposed by Ghahramani and Hinton [Ghahramani, Z., Hinton, G.E. 1996. Parameter Estimation for Linear Dynamical Systems. Technical Report, Department of Computer Science, University of Toronto]. In this paper we introduce modifications to the BDS model in order to explicitly model the spatial variations of the haemodynamic response function (HRF) in the brain using a non-parametric approach. While in Penny et al. [Penny, W., Ghahramani, Z., Friston, K.J. 2005. Bilinear dynamical systems. Philos. Trans. R. Soc. Lond. B Biol. Sci. 360(1457) 983-993] the relationship between neuronal activation and fMRI signals is formulated as a first-order convolution with a kernel expansion using basis functions (typically two or three), in this paper, we argue in favor of a spatially adaptive GLM in which a local non-parametric estimation of the HRF is performed. Furthermore, in order to overcome the overfitting problem typically associated with simple EM estimates, we propose a full Variational Bayes (VB) solution to infer the BDS model parameters. We demonstrate the usefulness of our model which is able to estimate both the neuronal activity and the haemodynamic response function in every voxel of the brain. We first examine the behavior of this approach when applied to simulated data with different temporal and noise features. As an example we will show how this method can be used to improve interpretability of estimates from an independent component analysis (ICA) analysis of fMRI data. We finally demonstrate its use on real fMRI data in one slice of the brain.

Kinematic parameters of internal waves of the second mode in the South China Sea

NASA Astrophysics Data System (ADS)

Kurkina, Oxana; Talipova, Tatyana; Soomere, Tarmo; Giniyatullin, Ayrat; Kurkin, Andrey

2017-10-01

Spatial distributions of the main properties of the mode function and kinematic and non-linear parameters of internal waves of the second mode are derived for the South China Sea for typical summer conditions in July. The calculations are based on the Generalized Digital Environmental Model (GDEM) climatology of hydrological variables, from which the local stratification is evaluated. The focus is on the phase speed of long internal waves and the coefficients at the dispersive, quadratic and cubic terms of the weakly non-linear Gardner model. Spatial distributions of these parameters, except for the coefficient at the cubic term, are qualitatively similar for waves of both modes. The dispersive term of Gardner's equation and phase speed for internal waves of the second mode are about a quarter and half, respectively, of those for waves of the first mode. Similarly to the waves of the first mode, the coefficients at the quadratic and cubic terms of Gardner's equation are practically independent of water depth. In contrast to the waves of the first mode, for waves of the second mode the quadratic term is mostly negative. The results can serve as a basis for expressing estimates of the expected parameters of internal waves for the South China Sea.

Estimating the price elasticity of expenditure for prescription drugs in the presence of non-linear price schedules: an illustration from Quebec, Canada.

PubMed

Contoyannis, Paul; Hurley, Jeremiah; Grootendorst, Paul; Jeon, Sung-Hee; Tamblyn, Robyn

2005-09-01

The price elasticity of demand for prescription drugs is a crucial parameter of interest in designing pharmaceutical benefit plans. Estimating the elasticity using micro-data, however, is challenging because insurance coverage that includes deductibles, co-insurance provisions and maximum expenditure limits create a non-linear price schedule, making price endogenous (a function of drug consumption). In this paper we exploit an exogenous change in cost-sharing within the Quebec (Canada) public Pharmacare program to estimate the price elasticity of expenditure for drugs using IV methods. This approach corrects for the endogeneity of price and incorporates the concept of a 'rational' consumer who factors into consumption decisions the price they expect to face at the margin given their expected needs. The IV method is adapted from an approach developed in the public finance literature used to estimate income responses to changes in tax schedules. The instrument is based on the price an individual would face under the new cost-sharing policy if their consumption remained at the pre-policy level. Our preferred specification leads to expenditure elasticities that are in the low range of previous estimates (between -0.12 and -0.16). Naïve OLS estimates are between 1 and 4 times these magnitudes. (c) 2005 John Wiley & Sons, Ltd.

Lateral-Directional Parameter Estimation on the X-48B Aircraft Using an Abstracted, Multi-Objective Effector Model

NASA Technical Reports Server (NTRS)

Ratnayake, Nalin A.; Waggoner, Erin R.; Taylor, Brian R.

2011-01-01

The problem of parameter estimation on hybrid-wing-body aircraft is complicated by the fact that many design candidates for such aircraft involve a large number of aerodynamic control effectors that act in coplanar motion. This adds to the complexity already present in the parameter estimation problem for any aircraft with a closed-loop control system. Decorrelation of flight and simulation data must be performed in order to ascertain individual surface derivatives with any sort of mathematical confidence. Non-standard control surface configurations, such as clamshell surfaces and drag-rudder modes, further complicate the modeling task. In this paper, time-decorrelation techniques are applied to a model structure selected through stepwise regression for simulated and flight-generated lateral-directional parameter estimation data. A virtual effector model that uses mathematical abstractions to describe the multi-axis effects of clamshell surfaces is developed and applied. Comparisons are made between time history reconstructions and observed data in order to assess the accuracy of the regression model. The Cram r-Rao lower bounds of the estimated parameters are used to assess the uncertainty of the regression model relative to alternative models. Stepwise regression was found to be a useful technique for lateral-directional model design for hybrid-wing-body aircraft, as suggested by available flight data. Based on the results of this study, linear regression parameter estimation methods using abstracted effectors are expected to perform well for hybrid-wing-body aircraft properly equipped for the task.

Quantifying lost information due to covariance matrix estimation in parameter inference

NASA Astrophysics Data System (ADS)

Sellentin, Elena; Heavens, Alan F.

2017-02-01

Parameter inference with an estimated covariance matrix systematically loses information due to the remaining uncertainty of the covariance matrix. Here, we quantify this loss of precision and develop a framework to hypothetically restore it, which allows to judge how far away a given analysis is from the ideal case of a known covariance matrix. We point out that it is insufficient to estimate this loss by debiasing the Fisher matrix as previously done, due to a fundamental inequality that describes how biases arise in non-linear functions. We therefore develop direct estimators for parameter credibility contours and the figure of merit, finding that significantly fewer simulations than previously thought are sufficient to reach satisfactory precisions. We apply our results to DES Science Verification weak lensing data, detecting a 10 per cent loss of information that increases their credibility contours. No significant loss of information is found for KiDS. For a Euclid-like survey, with about 10 nuisance parameters we find that 2900 simulations are sufficient to limit the systematically lost information to 1 per cent, with an additional uncertainty of about 2 per cent. Without any nuisance parameters, 1900 simulations are sufficient to only lose 1 per cent of information. We further derive estimators for all quantities needed for forecasting with estimated covariance matrices. Our formalism allows to determine the sweetspot between running sophisticated simulations to reduce the number of nuisance parameters, and running as many fast simulations as possible.

Probability density of spatially distributed soil moisture inferred from crosshole georadar traveltime measurements

NASA Astrophysics Data System (ADS)

Linde, N.; Vrugt, J. A.

2009-04-01

Geophysical models are increasingly used in hydrological simulations and inversions, where they are typically treated as an artificial data source with known uncorrelated "data errors". The model appraisal problem in classical deterministic linear and non-linear inversion approaches based on linearization is often addressed by calculating model resolution and model covariance matrices. These measures offer only a limited potential to assign a more appropriate "data covariance matrix" for future hydrological applications, simply because the regularization operators used to construct a stable inverse solution bear a strong imprint on such estimates and because the non-linearity of the geophysical inverse problem is not explored. We present a parallelized Markov Chain Monte Carlo (MCMC) scheme to efficiently derive the posterior spatially distributed radar slowness and water content between boreholes given first-arrival traveltimes. This method is called DiffeRential Evolution Adaptive Metropolis (DREAM_ZS) with snooker updater and sampling from past states. Our inverse scheme does not impose any smoothness on the final solution, and uses uniform prior ranges of the parameters. The posterior distribution of radar slowness is converted into spatially distributed soil moisture values using a petrophysical relationship. To benchmark the performance of DREAM_ZS, we first apply our inverse method to a synthetic two-dimensional infiltration experiment using 9421 traveltimes contaminated with Gaussian errors and 80 different model parameters, corresponding to a model discretization of 0.3 m × 0.3 m. After this, the method is applied to field data acquired in the vadose zone during snowmelt. This work demonstrates that fully non-linear stochastic inversion can be applied with few limiting assumptions to a range of common two-dimensional tomographic geophysical problems. The main advantage of DREAM_ZS is that it provides a full view of the posterior distribution of spatially distributed soil moisture, which is key to appropriately treat geophysical parameter uncertainty and infer hydrologic models.

Proceedings of the Annual Precise Time and Time Interval (PTTI) applications and Planning Meeting (20th) Held in Vienna, Virginia on 29 November-1 December 1988

DTIC Science & Technology

1988-12-01

PERFORMANCE IN REAL TIME* Dr. James A. Barnes Austron Boulder, Co. Abstract Kalman filters and ARIMA models provide optimum control and evaluation tech...estimates of the model parameters (e.g., the phi’s and theta’s for an ARIMA model ). These model parameters are often evaluated in a batch mode on a...random walk FM, and linear frequency drift. In ARIMA models , this is equivalent to an ARIMA (0,2,2) with a non-zero average sec- ond difference. Using

Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. II

NASA Astrophysics Data System (ADS)

Kazeykina, Anna; Muñoz, Claudio

2018-04-01

We continue our study on the Cauchy problem for the two-dimensional Novikov-Veselov (NV) equation, integrable via the inverse scattering transform for the two dimensional Schrödinger operator at a fixed energy parameter. This work is concerned with the more involved case of a positive energy parameter. For the solution of the linearized equation we derive smoothing and Strichartz estimates by combining new estimates for two different frequency regimes, extending our previous results for the negative energy case [18]. The low frequency regime, which our previous result was not able to treat, is studied in detail. At non-low frequencies we also derive improved smoothing estimates with gain of almost one derivative. Then we combine the linear estimates with a Fourier decomposition method and Xs,b spaces to obtain local well-posedness of NV at positive energy in Hs, s > 1/2. Our result implies, in particular, that at least for s > 1/2, NV does not change its behavior from semilinear to quasilinear as energy changes sign, in contrast to the closely related Kadomtsev-Petviashvili equations. As a complement to our LWP results, we also provide some new explicit solutions of NV at zero energy, generalizations of the lumps solutions, which exhibit new and nonstandard long time behavior. In particular, these solutions blow up in infinite time in L2.

Do Quercus ilex woodlands undergo abrupt non-linear functional changes in response to human disturbance along a climatic gradient?

NASA Astrophysics Data System (ADS)

Bochet, Esther; García-Fayos, Patricio; José Molina, Maria; Moreno de las Heras, Mariano; Espigares, Tíscar; Nicolau, Jose Manuel; Monleon, Vicente

2017-04-01

Theoretical models predict that drylands are particularly prone to suffer critical transitions with abrupt non-linear changes in their structure and functions as a result of the existing complex interactions between climatic fluctuations and human disturbances. However, so far, few studies provide empirical data to validate these models. We aim at determining how holm oak (Quercus ilex) woodlands undergo changes in their functions in response to human disturbance along an aridity gradient (from semi-arid to sub-humid conditions), in eastern Spain. For that purpose, we used (a) remote-sensing estimations of precipitation-use-efficiency (PUE) from enhanced vegetation index (EVI) observations performed in 231x231 m plots of the Moderate Resolution Imaging Spectroradiometer (MODIS); (b) biological and chemical soil parameter determinations (extracellular soil enzyme activity, soil respiration, nutrient cycling processes) from soil sampled in the same plots; (c) vegetation parameter determinations (ratio of functional groups) from vegetation surveys performed in the same plots. We analyzed and compared the shape of the functional change (in terms of PUE and soil and vegetation parameters) in response to human disturbance intensity for our holm oak sites along the aridity gradient. Overall, our results evidenced important differences in the shape of the functional change in response to human disturbance between climatic conditions. Semi-arid areas experienced a more accelerated non-linear decrease with an increasing disturbance intensity than sub-humid ones. The proportion of functional groups (herbaceous vs. woody cover) played a relevant role in the shape of the functional response of the holm oak sites to human disturbance.

Automated Land Cover Change Detection and Mapping from Hidden Parameter Estimates of Normalized Difference Vegetation Index (NDVI) Time-Series

NASA Astrophysics Data System (ADS)

Chakraborty, S.; Banerjee, A.; Gupta, S. K. S.; Christensen, P. R.; Papandreou-Suppappola, A.

2017-12-01

Multitemporal observations acquired frequently by satellites with short revisit periods such as the Moderate Resolution Imaging Spectroradiometer (MODIS), is an important source for modeling land cover. Due to the inherent seasonality of the land cover, harmonic modeling reveals hidden state parameters characteristic to it, which is used in classifying different land cover types and in detecting changes due to natural or anthropogenic factors. In this work, we use an eight day MODIS composite to create a Normalized Difference Vegetation Index (NDVI) time-series of ten years. Improved hidden parameter estimates of the nonlinear harmonic NDVI model are obtained using the Particle Filter (PF), a sequential Monte Carlo estimator. The nonlinear estimation based on PF is shown to improve parameter estimation for different land cover types compared to existing techniques that use the Extended Kalman Filter (EKF), due to linearization of the harmonic model. As these parameters are representative of a given land cover, its applicability in near real-time detection of land cover change is also studied by formulating a metric that captures parameter deviation due to change. The detection methodology is evaluated by considering change as a rare class problem. This approach is shown to detect change with minimum delay. Additionally, the degree of change within the change perimeter is non-uniform. By clustering the deviation in parameters due to change, this spatial variation in change severity is effectively mapped and validated with high spatial resolution change maps of the given regions.

Parameter estimation and forecasting for multiplicative log-normal cascades

NASA Astrophysics Data System (ADS)

Leövey, Andrés E.; Lux, Thomas

2012-04-01

We study the well-known multiplicative log-normal cascade process in which the multiplication of Gaussian and log normally distributed random variables yields time series with intermittent bursts of activity. Due to the nonstationarity of this process and the combinatorial nature of such a formalism, its parameters have been estimated mostly by fitting the numerical approximation of the associated non-Gaussian probability density function to empirical data, cf. Castaing [Physica DPDNPDT0167-278910.1016/0167-2789(90)90035-N 46, 177 (1990)]. More recently, alternative estimators based upon various moments have been proposed by Beck [Physica DPDNPDT0167-278910.1016/j.physd.2004.01.020 193, 195 (2004)] and Kiyono [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.76.041113 76, 041113 (2007)]. In this paper, we pursue this moment-based approach further and develop a more rigorous generalized method of moments (GMM) estimation procedure to cope with the documented difficulties of previous methodologies. We show that even under uncertainty about the actual number of cascade steps, our methodology yields very reliable results for the estimated intermittency parameter. Employing the Levinson-Durbin algorithm for best linear forecasts, we also show that estimated parameters can be used for forecasting the evolution of the turbulent flow. We compare forecasting results from the GMM and Kiyono 's procedure via Monte Carlo simulations. We finally test the applicability of our approach by estimating the intermittency parameter and forecasting of volatility for a sample of financial data from stock and foreign exchange markets.

Uncertainty Prediction in Passive Target Motion Analysis

DTIC Science & Technology

2016-05-12

fundamental property of bearings- only target motion analysis (TMA) is that bearing B to the Attorney Docket No. 300118 3 of 25 target 10 results...the measurements used to estimate them are often non-linear. This is true for the bearing observation: = tan −1 ( () () ) ( 3 ...Parameter Evaluation Plot ( PEP ) is one example of such a grid-based approach. U.S. Patent No. 7,020,046 discloses one version of this method and is

Bayesian Statistics and Uncertainty Quantification for Safety Boundary Analysis in Complex Systems

NASA Technical Reports Server (NTRS)

He, Yuning; Davies, Misty Dawn

2014-01-01

The analysis of a safety-critical system often requires detailed knowledge of safe regions and their highdimensional non-linear boundaries. We present a statistical approach to iteratively detect and characterize the boundaries, which are provided as parameterized shape candidates. Using methods from uncertainty quantification and active learning, we incrementally construct a statistical model from only few simulation runs and obtain statistically sound estimates of the shape parameters for safety boundaries.

Energy acceptance and on momentum aperture optimization for the Sirius project

NASA Astrophysics Data System (ADS)

Dester, P. S.; Sá, F. H.; Liu, L.

2017-07-01

A fast objective function to calculate Touschek lifetime and on momentum aperture is essential to explore the vast search space of strength of quadrupole and sextupole families in Sirius. Touschek lifetime is estimated by using the energy aperture (dynamic and physical), RF system parameters and driving terms. Non-linear induced betatron oscillations are considered to determine the energy aperture. On momentum aperture is estimated by using a chaos indicator and resonance crossing considerations. Touschek lifetime and on momentum aperture constitute the objective function, which was used in a multi-objective genetic algorithm to perform an optimization for Sirius.

Broad-band simulation of M7.2 earthquake on the North Tehran fault, considering non-linear soil effects

NASA Astrophysics Data System (ADS)

Majidinejad, A.; Zafarani, H.; Vahdani, S.

2018-05-01

The North Tehran fault (NTF) is known to be one of the most drastic sources of seismic hazard on the city of Tehran. In this study, we provide broad-band (0-10 Hz) ground motions for the city as a consequence of probable M7.2 earthquake on the NTF. Low-frequency motions (0-2 Hz) are provided from spectral element dynamic simulation of 17 scenario models. High-frequency (2-10 Hz) motions are calculated with a physics-based method based on S-to-S backscattering theory. Broad-band ground motions at the bedrock level show amplifications, both at low and high frequencies, due to the existence of deep Tehran basin in the vicinity of the NTF. By employing soil profiles obtained from regional studies, effect of shallow soil layers on broad-band ground motions is investigated by both linear and non-linear analyses. While linear soil response overestimate ground motion prediction equations, non-linear response predicts plausible results within one standard deviation of empirical relationships. Average Peak Ground Accelerations (PGAs) at the northern, central and southern parts of the city are estimated about 0.93, 0.59 and 0.4 g, respectively. Increased damping caused by non-linear soil behaviour, reduces the soil linear responses considerably, in particular at frequencies above 3 Hz. Non-linear deamplification reduces linear spectral accelerations up to 63 per cent at stations above soft thick sediments. By performing more general analyses, which exclude source-to-site effects on stations, a correction function is proposed for typical site classes of Tehran. Parameters for the function which reduces linear soil response in order to take into account non-linear soil deamplification are provided for various frequencies in the range of engineering interest. In addition to fully non-linear analyses, equivalent-linear calculations were also conducted which their comparison revealed appropriateness of the method for large peaks and low frequencies, but its shortage for small to medium peaks and motions with higher than 3 Hz frequencies.

A Solution to Separation and Multicollinearity in Multiple Logistic Regression

PubMed Central

Shen, Jianzhao; Gao, Sujuan

2010-01-01

In dementia screening tests, item selection for shortening an existing screening test can be achieved using multiple logistic regression. However, maximum likelihood estimates for such logistic regression models often experience serious bias or even non-existence because of separation and multicollinearity problems resulting from a large number of highly correlated items. Firth (1993, Biometrika, 80(1), 27–38) proposed a penalized likelihood estimator for generalized linear models and it was shown to reduce bias and the non-existence problems. The ridge regression has been used in logistic regression to stabilize the estimates in cases of multicollinearity. However, neither solves the problems for each other. In this paper, we propose a double penalized maximum likelihood estimator combining Firth’s penalized likelihood equation with a ridge parameter. We present a simulation study evaluating the empirical performance of the double penalized likelihood estimator in small to moderate sample sizes. We demonstrate the proposed approach using a current screening data from a community-based dementia study. PMID:20376286

A Solution to Separation and Multicollinearity in Multiple Logistic Regression.

PubMed

Shen, Jianzhao; Gao, Sujuan

2008-10-01

In dementia screening tests, item selection for shortening an existing screening test can be achieved using multiple logistic regression. However, maximum likelihood estimates for such logistic regression models often experience serious bias or even non-existence because of separation and multicollinearity problems resulting from a large number of highly correlated items. Firth (1993, Biometrika, 80(1), 27-38) proposed a penalized likelihood estimator for generalized linear models and it was shown to reduce bias and the non-existence problems. The ridge regression has been used in logistic regression to stabilize the estimates in cases of multicollinearity. However, neither solves the problems for each other. In this paper, we propose a double penalized maximum likelihood estimator combining Firth's penalized likelihood equation with a ridge parameter. We present a simulation study evaluating the empirical performance of the double penalized likelihood estimator in small to moderate sample sizes. We demonstrate the proposed approach using a current screening data from a community-based dementia study.

Water Residence Time estimation by 1D deconvolution in the form of a l2 -regularized inverse problem with smoothness, positivity and causality constraints

NASA Astrophysics Data System (ADS)

Meresescu, Alina G.; Kowalski, Matthieu; Schmidt, Frédéric; Landais, François

2018-06-01

The Water Residence Time distribution is the equivalent of the impulse response of a linear system allowing the propagation of water through a medium, e.g. the propagation of rain water from the top of the mountain towards the aquifers. We consider the output aquifer levels as the convolution between the input rain levels and the Water Residence Time, starting with an initial aquifer base level. The estimation of Water Residence Time is important for a better understanding of hydro-bio-geochemical processes and mixing properties of wetlands used as filters in ecological applications, as well as protecting fresh water sources for wells from pollutants. Common methods of estimating the Water Residence Time focus on cross-correlation, parameter fitting and non-parametric deconvolution methods. Here we propose a 1D full-deconvolution, regularized, non-parametric inverse problem algorithm that enforces smoothness and uses constraints of causality and positivity to estimate the Water Residence Time curve. Compared to Bayesian non-parametric deconvolution approaches, it has a fast runtime per test case; compared to the popular and fast cross-correlation method, it produces a more precise Water Residence Time curve even in the case of noisy measurements. The algorithm needs only one regularization parameter to balance between smoothness of the Water Residence Time and accuracy of the reconstruction. We propose an approach on how to automatically find a suitable value of the regularization parameter from the input data only. Tests on real data illustrate the potential of this method to analyze hydrological datasets.

Efficient Spatiotemporal Clutter Rejection and Nonlinear Filtering-based Dim Resolved and Unresolved Object Tracking Algorithms

NASA Astrophysics Data System (ADS)

Tartakovsky, A.; Tong, M.; Brown, A. P.; Agh, C.

2013-09-01

We develop efficient spatiotemporal image processing algorithms for rejection of non-stationary clutter and tracking of multiple dim objects using non-linear track-before-detect methods. For clutter suppression, we include an innovative image alignment (registration) algorithm. The images are assumed to contain elements of the same scene, but taken at different angles, from different locations, and at different times, with substantial clutter non-stationarity. These challenges are typical for space-based and surface-based IR/EO moving sensors, e.g., highly elliptical orbit or low earth orbit scenarios. The algorithm assumes that the images are related via a planar homography, also known as the projective transformation. The parameters are estimated in an iterative manner, at each step adjusting the parameter vector so as to achieve improved alignment of the images. Operating in the parameter space rather than in the coordinate space is a new idea, which makes the algorithm more robust with respect to noise as well as to large inter-frame disturbances, while operating at real-time rates. For dim object tracking, we include new advancements to a particle non-linear filtering-based track-before-detect (TrbD) algorithm. The new TrbD algorithm includes both real-time full image search for resolved objects not yet in track and joint super-resolution and tracking of individual objects in closely spaced object (CSO) clusters. The real-time full image search provides near-optimal detection and tracking of multiple extremely dim, maneuvering objects/clusters. The super-resolution and tracking CSO TrbD algorithm provides efficient near-optimal estimation of the number of unresolved objects in a CSO cluster, as well as the locations, velocities, accelerations, and intensities of the individual objects. We demonstrate that the algorithm is able to accurately estimate the number of CSO objects and their locations when the initial uncertainty on the number of objects is large. We demonstrate performance of the TrbD algorithm both for satellite-based and surface-based EO/IR surveillance scenarios.

Linear least squares approach for evaluating crack tip fracture parameters using isochromatic and isoclinic data from digital photoelasticity

NASA Astrophysics Data System (ADS)

Patil, Prataprao; Vyasarayani, C. P.; Ramji, M.

2017-06-01

In this work, digital photoelasticity technique is used to estimate the crack tip fracture parameters for different crack configurations. Conventionally, only isochromatic data surrounding the crack tip is used for SIF estimation, but with the advent of digital photoelasticity, pixel-wise availability of both isoclinic and isochromatic data could be exploited for SIF estimation in a novel way. A linear least square approach is proposed to estimate the mixed-mode crack tip fracture parameters by solving the multi-parameter stress field equation. The stress intensity factor (SIF) is extracted from those estimated fracture parameters. The isochromatic and isoclinic data around the crack tip is estimated using the ten-step phase shifting technique. To get the unwrapped data, the adaptive quality guided phase unwrapping algorithm (AQGPU) has been used. The mixed mode fracture parameters, especially SIF are estimated for specimen configurations like single edge notch (SEN), center crack and straight crack ahead of inclusion using the proposed algorithm. The experimental SIF values estimated using the proposed method are compared with analytical/finite element analysis (FEA) results, and are found to be in good agreement.

Comparison of various error functions in predicting the optimum isotherm by linear and non-linear regression analysis for the sorption of basic red 9 by activated carbon.

PubMed

Kumar, K Vasanth; Porkodi, K; Rocha, F

2008-01-15

A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of basic red 9 sorption by activated carbon. The r(2) was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions namely coefficient of determination (r(2)), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), the average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. Non-linear regression was found to be a better way to obtain the parameters involved in the isotherms and also the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r(2) was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K(2) was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.

Incorporation of prior information on parameters into nonlinear regression groundwater flow models: 2. Applications

USGS Publications Warehouse

Cooley, Richard L.

1983-01-01

This paper investigates factors influencing the degree of improvement in estimates of parameters of a nonlinear regression groundwater flow model by incorporating prior information of unknown reliability. Consideration of expected behavior of the regression solutions and results of a hypothetical modeling problem lead to several general conclusions. First, if the parameters are properly scaled, linearized expressions for the mean square error (MSE) in parameter estimates of a nonlinear model will often behave very nearly as if the model were linear. Second, by using prior information, the MSE in properly scaled parameters can be reduced greatly over the MSE of ordinary least squares estimates of parameters. Third, plots of estimated MSE and the estimated standard deviation of MSE versus an auxiliary parameter (the ridge parameter) specifying the degree of influence of the prior information on regression results can help determine the potential for improvement of parameter estimates. Fourth, proposed criteria can be used to make appropriate choices for the ridge parameter and another parameter expressing degree of overall bias in the prior information. Results of a case study of Truckee Meadows, Reno-Sparks area, Washoe County, Nevada, conform closely to the results of the hypothetical problem. In the Truckee Meadows case, incorporation of prior information did not greatly change the parameter estimates from those obtained by ordinary least squares. However, the analysis showed that both sets of estimates are more reliable than suggested by the standard errors from ordinary least squares.

[Evaluation of pendulum testing of spasticity].

PubMed

Le Cavorzin, P; Hernot, X; Bartier, O; Carrault, G; Chagneau, F; Gallien, P; Allain, H; Rochcongar, P

2002-11-01

To identify valid measurements of spasticity derived from the pendulum test of the leg in a representative population of spastic patients. Pendulum testing was performed in 15 spastic and 10 matched healthy subjects. The reflex-mediated torque evoked in quadriceps femoris, as well as muscle mechanical parameters (viscosity and elasticity), were calculated using mathematical modelling. Correlation with the two main measures derived from the pendulum test reported in the literature (the Relaxation Index and the area under the curve) was calculated in order to select the most valid. Among mechanical parameters, only viscosity was found to be significantly higher in the spastic group. As expected, the computed integral of the reflex-mediated torque was found to be larger in spastics than in healthy subjects. A significant non-linear (logarithmic) correlation was found between the clinically-assessed muscle spasticity (Ashworth grading) and the computed reflex-mediated torque, emphasising the non-linear behaviour of this scale. Among measurements derived from the pendulum test which are proposed in the literature for routine estimation of spasticity, the Relaxation Index exhibited an unsuitable U-shaped pattern of variation with increasing reflex-mediated torque. On the opposite, the area under the curve revealed a linear regression, which is more convenient for routine estimation of spasticity. The pendulum test of the leg is a simple technique for the assessment of spastic hypertonia. However, the measurement generally used in the literature (the Relaxation Index) exhibits serious limitations, and would benefit to be replaced by more valid measures, such as the area under the goniometric curve, especially for the assessment of therapeutics.

An alternative method to measure the likelihood of a financial crisis in an emerging market

NASA Astrophysics Data System (ADS)

Özlale, Ümit; Metin-Özcan, Kıvılcım

2007-07-01

This paper utilizes an early warning system in order to measure the likelihood of a financial crisis in an emerging market economy. We introduce a methodology, where we can both obtain a likelihood series and analyze the time-varying effects of several macroeconomic variables on this likelihood. Since the issue is analyzed in a non-linear state space framework, the extended Kalman filter emerges as the optimal estimation algorithm. Taking the Turkish economy as our laboratory, the results indicate that both the derived likelihood measure and the estimated time-varying parameters are meaningful and can successfully explain the path that the Turkish economy had followed between 2000 and 2006. The estimated parameters also suggest that overvalued domestic currency, current account deficit and the increase in the default risk increase the likelihood of having an economic crisis in the economy. Overall, the findings in this paper suggest that the estimation methodology introduced in this paper can also be applied to other emerging market economies as well.

Temporal rainfall estimation using input data reduction and model inversion

NASA Astrophysics Data System (ADS)

Wright, A. J.; Vrugt, J. A.; Walker, J. P.; Pauwels, V. R. N.

2016-12-01

Floods are devastating natural hazards. To provide accurate, precise and timely flood forecasts there is a need to understand the uncertainties associated with temporal rainfall and model parameters. The estimation of temporal rainfall and model parameter distributions from streamflow observations in complex dynamic catchments adds skill to current areal rainfall estimation methods, allows for the uncertainty of rainfall input to be considered when estimating model parameters and provides the ability to estimate rainfall from poorly gauged catchments. Current methods to estimate temporal rainfall distributions from streamflow are unable to adequately explain and invert complex non-linear hydrologic systems. This study uses the Discrete Wavelet Transform (DWT) to reduce rainfall dimensionality for the catchment of Warwick, Queensland, Australia. The reduction of rainfall to DWT coefficients allows the input rainfall time series to be simultaneously estimated along with model parameters. The estimation process is conducted using multi-chain Markov chain Monte Carlo simulation with the DREAMZS algorithm. The use of a likelihood function that considers both rainfall and streamflow error allows for model parameter and temporal rainfall distributions to be estimated. Estimation of the wavelet approximation coefficients of lower order decomposition structures was able to estimate the most realistic temporal rainfall distributions. These rainfall estimates were all able to simulate streamflow that was superior to the results of a traditional calibration approach. It is shown that the choice of wavelet has a considerable impact on the robustness of the inversion. The results demonstrate that streamflow data contains sufficient information to estimate temporal rainfall and model parameter distributions. The extent and variance of rainfall time series that are able to simulate streamflow that is superior to that simulated by a traditional calibration approach is a demonstration of equifinality. The use of a likelihood function that considers both rainfall and streamflow error combined with the use of the DWT as a model data reduction technique allows the joint inference of hydrologic model parameters along with rainfall.

Comparison of linear and non-linear models for the adsorption of fluoride onto geo-material: limonite.

PubMed

Sahin, Rubina; Tapadia, Kavita

2015-01-01

The three widely used isotherms Langmuir, Freundlich and Temkin were examined in an experiment using fluoride (F⁻) ion adsorption on a geo-material (limonite) at four different temperatures by linear and non-linear models. Comparison of linear and non-linear regression models were given in selecting the optimum isotherm for the experimental results. The coefficient of determination, r², was used to select the best theoretical isotherm. The four Langmuir linear equations (1, 2, 3, and 4) are discussed. Langmuir isotherm parameters obtained from the four Langmuir linear equations using the linear model differed but they were the same when using the nonlinear model. Langmuir-2 isotherm is one of the linear forms, and it had the highest coefficient of determination (r² = 0.99) compared to the other Langmuir linear equations (1, 3 and 4) in linear form, whereas, for non-linear, Langmuir-4 fitted best among all the isotherms because it had the highest coefficient of determination (r² = 0.99). The results showed that the non-linear model may be a better way to obtain the parameters. In the present work, the thermodynamic parameters show that the absorption of fluoride onto limonite is both spontaneous (ΔG < 0) and endothermic (ΔH > 0). Scanning electron microscope and X-ray diffraction images also confirm the adsorption of F⁻ ion onto limonite. The isotherm and kinetic study reveals that limonite can be used as an adsorbent for fluoride removal. In future we can develop new technology for fluoride removal in large scale by using limonite which is cost-effective, eco-friendly and is easily available in the study area.

Structural identifiability analyses of candidate models for in vitro Pitavastatin hepatic uptake.

PubMed

Grandjean, Thomas R B; Chappell, Michael J; Yates, James W T; Evans, Neil D

2014-05-01

In this paper a review of the application of four different techniques (a version of the similarity transformation approach for autonomous uncontrolled systems, a non-differential input/output observable normal form approach, the characteristic set differential algebra and a recent algebraic input/output relationship approach) to determine the structural identifiability of certain in vitro nonlinear pharmacokinetic models is provided. The Organic Anion Transporting Polypeptide (OATP) substrate, Pitavastatin, is used as a probe on freshly isolated animal and human hepatocytes. Candidate pharmacokinetic non-linear compartmental models have been derived to characterise the uptake process of Pitavastatin. As a prerequisite to parameter estimation, structural identifiability analyses are performed to establish that all unknown parameters can be identified from the experimental observations available. Copyright © 2013. Published by Elsevier Ireland Ltd.

A matlab framework for estimation of NLME models using stochastic differential equations: applications for estimation of insulin secretion rates.

PubMed

Mortensen, Stig B; Klim, Søren; Dammann, Bernd; Kristensen, Niels R; Madsen, Henrik; Overgaard, Rune V

2007-10-01

The non-linear mixed-effects model based on stochastic differential equations (SDEs) provides an attractive residual error model, that is able to handle serially correlated residuals typically arising from structural mis-specification of the true underlying model. The use of SDEs also opens up for new tools for model development and easily allows for tracking of unknown inputs and parameters over time. An algorithm for maximum likelihood estimation of the model has earlier been proposed, and the present paper presents the first general implementation of this algorithm. The implementation is done in Matlab and also demonstrates the use of parallel computing for improved estimation times. The use of the implementation is illustrated by two examples of application which focus on the ability of the model to estimate unknown inputs facilitated by the extension to SDEs. The first application is a deconvolution-type estimation of the insulin secretion rate based on a linear two-compartment model for C-peptide measurements. In the second application the model is extended to also give an estimate of the time varying liver extraction based on both C-peptide and insulin measurements.

Fuzzy C-mean clustering on kinetic parameter estimation with generalized linear least square algorithm in SPECT

NASA Astrophysics Data System (ADS)

Choi, Hon-Chit; Wen, Lingfeng; Eberl, Stefan; Feng, Dagan

2006-03-01

Dynamic Single Photon Emission Computed Tomography (SPECT) has the potential to quantitatively estimate physiological parameters by fitting compartment models to the tracer kinetics. The generalized linear least square method (GLLS) is an efficient method to estimate unbiased kinetic parameters and parametric images. However, due to the low sensitivity of SPECT, noisy data can cause voxel-wise parameter estimation by GLLS to fail. Fuzzy C-Mean (FCM) clustering and modified FCM, which also utilizes information from the immediate neighboring voxels, are proposed to improve the voxel-wise parameter estimation of GLLS. Monte Carlo simulations were performed to generate dynamic SPECT data with different noise levels and processed by general and modified FCM clustering. Parametric images were estimated by Logan and Yokoi graphical analysis and GLLS. The influx rate (K I), volume of distribution (V d) were estimated for the cerebellum, thalamus and frontal cortex. Our results show that (1) FCM reduces the bias and improves the reliability of parameter estimates for noisy data, (2) GLLS provides estimates of micro parameters (K I-k 4) as well as macro parameters, such as volume of distribution (Vd) and binding potential (BP I & BP II) and (3) FCM clustering incorporating neighboring voxel information does not improve the parameter estimates, but improves noise in the parametric images. These findings indicated that it is desirable for pre-segmentation with traditional FCM clustering to generate voxel-wise parametric images with GLLS from dynamic SPECT data.

Inference regarding multiple structural changes in linear models with endogenous regressors☆

PubMed Central

Hall, Alastair R.; Han, Sanggohn; Boldea, Otilia

2012-01-01

This paper considers the linear model with endogenous regressors and multiple changes in the parameters at unknown times. It is shown that minimization of a Generalized Method of Moments criterion yields inconsistent estimators of the break fractions, but minimization of the Two Stage Least Squares (2SLS) criterion yields consistent estimators of these parameters. We develop a methodology for estimation and inference of the parameters of the model based on 2SLS. The analysis covers the cases where the reduced form is either stable or unstable. The methodology is illustrated via an application to the New Keynesian Phillips Curve for the US. PMID:23805021

MODOPTIM: A general optimization program for ground-water flow model calibration and ground-water management with MODFLOW

USGS Publications Warehouse

Halford, Keith J.

2006-01-01

MODOPTIM is a non-linear ground-water model calibration and management tool that simulates flow with MODFLOW-96 as a subroutine. A weighted sum-of-squares objective function defines optimal solutions for calibration and management problems. Water levels, discharges, water quality, subsidence, and pumping-lift costs are the five direct observation types that can be compared in MODOPTIM. Differences between direct observations of the same type can be compared to fit temporal changes and spatial gradients. Water levels in pumping wells, wellbore storage in the observation wells, and rotational translation of observation wells also can be compared. Negative and positive residuals can be weighted unequally so inequality constraints such as maximum chloride concentrations or minimum water levels can be incorporated in the objective function. Optimization parameters are defined with zones and parameter-weight matrices. Parameter change is estimated iteratively with a quasi-Newton algorithm and is constrained to a user-defined maximum parameter change per iteration. Parameters that are less sensitive than a user-defined threshold are not estimated. MODOPTIM facilitates testing more conceptual models by expediting calibration of each conceptual model. Examples of applying MODOPTIM to aquifer-test analysis, ground-water management, and parameter estimation problems are presented.

Parameter Estimation and Model Selection for Indoor Environments Based on Sparse Observations

NASA Astrophysics Data System (ADS)

Dehbi, Y.; Loch-Dehbi, S.; Plümer, L.

2017-09-01

This paper presents a novel method for the parameter estimation and model selection for the reconstruction of indoor environments based on sparse observations. While most approaches for the reconstruction of indoor models rely on dense observations, we predict scenes of the interior with high accuracy in the absence of indoor measurements. We use a model-based top-down approach and incorporate strong but profound prior knowledge. The latter includes probability density functions for model parameters and sparse observations such as room areas and the building footprint. The floorplan model is characterized by linear and bi-linear relations with discrete and continuous parameters. We focus on the stochastic estimation of model parameters based on a topological model derived by combinatorial reasoning in a first step. A Gauss-Markov model is applied for estimation and simulation of the model parameters. Symmetries are represented and exploited during the estimation process. Background knowledge as well as observations are incorporated in a maximum likelihood estimation and model selection is performed with AIC/BIC. The likelihood is also used for the detection and correction of potential errors in the topological model. Estimation results are presented and discussed.

Genetic covariance components within and among linear type traits differ among contrasting beef cattle breeds.

PubMed

Doyle, Jennifer L; Berry, Donagh P; Walsh, Siobhan W; Veerkamp, Roel F; Evans, Ross D; Carthy, Tara R

2018-05-04

Linear type traits describing the skeletal, muscular, and functional characteristics of an animal are routinely scored on live animals in both the dairy and beef cattle industries. Previous studies have demonstrated that genetic parameters for certain performance traits may differ between breeds; no study, however, has attempted to determine if differences exist in genetic parameters of linear type traits among breeds or sexes. Therefore, the objective of the present study was to determine if genetic covariance components for linear type traits differed among five contrasting cattle breeds, and to also investigate if these components differed by sex. A total of 18 linear type traits scored on 3,356 Angus (AA), 31,049 Charolais (CH), 3,004 Hereford (HE), 35,159 Limousin (LM), and 8,632 Simmental (SI) were used in the analysis. Data were analyzed using animal linear mixed models which included the fixed effects of sex of the animal (except in the investigation into the presence of sexual dimorphism), age at scoring, parity of the dam, and contemporary group of herd-date of scoring. Differences (P < 0.05) in heritability estimates, between at least two breeds, existed for 13 out of 18 linear type traits. Differences (P < 0.05) also existed between the pairwise within-breed genetic correlations among the linear type traits. Overall, the linear type traits in the continental breeds (i.e., CH, LM, SI) tended to have similar heritability estimates to each other as well as similar genetic correlations among the same pairwise traits, as did the traits in the British breeds (i.e., AA, HE). The correlation between a linear function of breeding values computed conditional on covariance parameters estimated from the CH breed with a linear function of breeding values computed conditional on covariance parameters estimated from the other breeds was estimated. Replacing the genetic covariance components estimated in the CH breed with those of the LM had least effect but the impact was considerable when the genetic covariance components of the AA were used. Genetic correlations between the same linear type traits in the two sexes were all close to unity (≥0.90) suggesting little advantage in considering these as separate traits for males and females. Results for the present study indicate the potential increase in accuracy of estimated breeding value prediction from considering, at least, the British breed traits separate to continental breed traits.

The linear relationship between cigarette tar and nicotine yields: regulatory implications for smoke constituent ratios.

PubMed

St Charles, F K; Cook, C J; Clayton, P M

2011-02-01

Cigarette smoke analyte yields are often expressed as ratios relative to tar or nicotine yields, usually to compare different products or to estimate human uptake of smoke in relation to nicotine uptake measurements. The method, however, can lead to distorted interpretations, especially in the case of ratios from ultra-low tar yield cigarettes. In brief, as tar yields decrease below the 5–6 mg per cigarette range, the tar-to-nicotine ratio (TNR) decreases rapidly in a non-linear fashion. If, however, the nicotine yield, rather than the ratio, is plotted versus the tar yield, the non-linearity disappears and a straight line is obtained, with a slight positive intercept for nicotine on the ordinate. Unlike the ratio, the slope appears to depend only on the concentration of the nicotine in the blend and does not appear to vary with smoking parameters such as puff volume, puff interval or length smoked or with cigarette design parameters such as length, circumference or the amount of filtration or filter ventilation. Therefore, such a slope is analogous to the TNR although, unlike that ratio, it is invariant. Even more simply, the concentration of the nicotine in the blend, at least for American blend-style cigarettes, provides a similar index.

THE SUCCESSIVE LINEAR ESTIMATOR: A REVISIT. (R827114)

EPA Science Inventory

This paper examines the theoretical basis of the successive linear estimator (SLE) that has been developed for the inverse problem in subsurface hydrology. We show that the SLE algorithm is a non-linear iterative estimator to the inverse problem. The weights used in the SLE al...

Efficient Levenberg-Marquardt minimization of the maximum likelihood estimator for Poisson deviates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laurence, T; Chromy, B

2009-11-10

Histograms of counted events are Poisson distributed, but are typically fitted without justification using nonlinear least squares fitting. The more appropriate maximum likelihood estimator (MLE) for Poisson distributed data is seldom used. We extend the use of the Levenberg-Marquardt algorithm commonly used for nonlinear least squares minimization for use with the MLE for Poisson distributed data. In so doing, we remove any excuse for not using this more appropriate MLE. We demonstrate the use of the algorithm and the superior performance of the MLE using simulations and experiments in the context of fluorescence lifetime imaging. Scientists commonly form histograms ofmore » counted events from their data, and extract parameters by fitting to a specified model. Assuming that the probability of occurrence for each bin is small, event counts in the histogram bins will be distributed according to the Poisson distribution. We develop here an efficient algorithm for fitting event counting histograms using the maximum likelihood estimator (MLE) for Poisson distributed data, rather than the non-linear least squares measure. This algorithm is a simple extension of the common Levenberg-Marquardt (L-M) algorithm, is simple to implement, quick and robust. Fitting using a least squares measure is most common, but it is the maximum likelihood estimator only for Gaussian-distributed data. Non-linear least squares methods may be applied to event counting histograms in cases where the number of events is very large, so that the Poisson distribution is well approximated by a Gaussian. However, it is not easy to satisfy this criterion in practice - which requires a large number of events. It has been well-known for years that least squares procedures lead to biased results when applied to Poisson-distributed data; a recent paper providing extensive characterization of these biases in exponential fitting is given. The more appropriate measure based on the maximum likelihood estimator (MLE) for the Poisson distribution is also well known, but has not become generally used. This is primarily because, in contrast to non-linear least squares fitting, there has been no quick, robust, and general fitting method. In the field of fluorescence lifetime spectroscopy and imaging, there have been some efforts to use this estimator through minimization routines such as Nelder-Mead optimization, exhaustive line searches, and Gauss-Newton minimization. Minimization based on specific one- or multi-exponential models has been used to obtain quick results, but this procedure does not allow the incorporation of the instrument response, and is not generally applicable to models found in other fields. Methods for using the MLE for Poisson-distributed data have been published by the wider spectroscopic community, including iterative minimization schemes based on Gauss-Newton minimization. The slow acceptance of these procedures for fitting event counting histograms may also be explained by the use of the ubiquitous, fast Levenberg-Marquardt (L-M) fitting procedure for fitting non-linear models using least squares fitting (simple searches obtain {approx}10000 references - this doesn't include those who use it, but don't know they are using it). The benefits of L-M include a seamless transition between Gauss-Newton minimization and downward gradient minimization through the use of a regularization parameter. This transition is desirable because Gauss-Newton methods converge quickly, but only within a limited domain of convergence; on the other hand the downward gradient methods have a much wider domain of convergence, but converge extremely slowly nearer the minimum. L-M has the advantages of both procedures: relative insensitivity to initial parameters and rapid convergence. Scientists, when wanting an answer quickly, will fit data using L-M, get an answer, and move on. Only those that are aware of the bias issues will bother to fit using the more appropriate MLE for Poisson deviates. However, since there is a simple, analytical formula for the appropriate MLE measure for Poisson deviates, it is inexcusable that least squares estimators are used almost exclusively when fitting event counting histograms. There have been ways found to use successive non-linear least squares fitting to obtain similarly unbiased results, but this procedure is justified by simulation, must be re-tested when conditions change significantly, and requires two successive fits. There is a great need for a fitting routine for the MLE estimator for Poisson deviates that has convergence domains and rates comparable to the non-linear least squares L-M fitting. We show in this report that a simple way to achieve that goal is to use the L-M fitting procedure not to minimize the least squares measure, but the MLE for Poisson deviates.« less

Multiscale Roughness Influencing on Transport Behavior of Passive Solute through a Single Self-affine Fracture

NASA Astrophysics Data System (ADS)

Dou, Z.

2017-12-01

In this study, the influence of multi-scale roughness on transport behavior of the passive solute through the self-affine fracture was investigated. The single self-affine fracture was constructed by the successive random additions (SRA) and the fracture roughness was decomposed into two different scales (i.e. large-scale primary roughness and small-scale secondary roughness) by the Wavelet analysis technique. The fluid flow in fractures, which was characterized by the Forchheimer's law, showed the non-linear flow behaviors such as eddies and tortuous streamlines. The results indicated that the small-scale secondary roughness was primarily responsible for the non-linear flow behaviors. The direct simulations of asymptotic passive solute transport represented the Non-Fickian transport characteristics (i.e. early arrivals and long tails) in breakthrough curves (BTCs) and residence time distributions (RTDs) with and without consideration of the secondary roughness. Analysis of multiscale BTCs and RTDs showed that the small-scale secondary roughness played a significant role in enhancing the Non-Fickian transport characteristics. We found that removing small-scale secondary roughness led to the lengthening arrival and shortening tail. The peak concentration in BTCs decreased as the secondary roughness was removed, implying that the secondary could also enhance the solute dilution. The estimated BTCs by the Fickian advection-dispersion equation (ADE) yielded errors which decreased with the small-scale secondary roughness being removed. The mobile-immobile model (MIM) was alternatively implemented to characterize the Non-Fickian transport. We found that the MIM was more capable of estimating Non-Fickian BTCs. The small-scale secondary roughness resulted in the decreasing mobile domain fraction and the increasing mass exchange rate between immobile and mobile domains. The estimated parameters from the MIM could provide insight into the inherent mechanism of roughness-induced Non-Fickian transport behaviors.

Concordance cosmology without dark energy

NASA Astrophysics Data System (ADS)

Rácz, Gábor; Dobos, László; Beck, Róbert; Szapudi, István; Csabai, István

2017-07-01

According to the separate universe conjecture, spherically symmetric sub-regions in an isotropic universe behave like mini-universes with their own cosmological parameters. This is an excellent approximation in both Newtonian and general relativistic theories. We estimate local expansion rates for a large number of such regions, and use a scale parameter calculated from the volume-averaged increments of local scale parameters at each time step in an otherwise standard cosmological N-body simulation. The particle mass, corresponding to a coarse graining scale, is an adjustable parameter. This mean field approximation neglects tidal forces and boundary effects, but it is the first step towards a non-perturbative statistical estimation of the effect of non-linear evolution of structure on the expansion rate. Using our algorithm, a simulation with an initial Ωm = 1 Einstein-de Sitter setting closely tracks the expansion and structure growth history of the Λ cold dark matter (ΛCDM) cosmology. Due to small but characteristic differences, our model can be distinguished from the ΛCDM model by future precision observations. Moreover, our model can resolve the emerging tension between local Hubble constant measurements and the Planck best-fitting cosmology. Further improvements to the simulation are necessary to investigate light propagation and confirm full consistency with cosmic microwave background observations.

Estimating enthalpy of vaporization from vapor pressure using Trouton's rule.

PubMed

MacLeod, Matthew; Scheringer, Martin; Hungerbühler, Konrad

2007-04-15

The enthalpy of vaporization of liquids and subcooled liquids at 298 K (delta H(VAP)) is an important parameter in environmental fate assessments that consider spatial and temporal variability in environmental conditions. It has been shown that delta H(VAP)P for non-hydrogen-bonding substances can be estimated from vapor pressure at 298 K (P(L)) using an empirically derived linear relationship. Here, we demonstrate that the relationship between delta H(VAP)and PL is consistent with Trouton's rule and the ClausiusClapeyron equation under the assumption that delta H(VAP) is linearly dependent on temperature between 298 K and the boiling point temperature. Our interpretation based on Trouton's rule substantiates the empirical relationship between delta H(VAP) degree and P(L) degrees for non-hydrogen-bonding chemicals with subcooled liquid vapor pressures ranging over 15 orders of magnitude. We apply the relationship between delta H(VAP) degrees and P(L) degrees to evaluate data reported in literature reviews for several important classes of semivolatile environmental contaminants, including polycyclic aromatic hydrocarbons, chlorobenzenes, polychlorinated biphenyls and polychlorinated dibenzo-dioxins and -furans and illustrate the temperature dependence of results from a multimedia model presented as a partitioning map. The uncertainty associated with estimating delta H(VAP)degrees from P(L) degrees using this relationship is acceptable for most environmental fate modeling of non-hydrogen-bonding semivolatile organic chemicals.

Robust estimation for partially linear models with large-dimensional covariates

PubMed Central

Zhu, LiPing; Li, RunZe; Cui, HengJian

2014-01-01

We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon-cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of o(n), where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures. PMID:24955087

Robust estimation for partially linear models with large-dimensional covariates.

PubMed

Zhu, LiPing; Li, RunZe; Cui, HengJian

2013-10-01

We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon-cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of [Formula: see text], where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures.

Non-Linear Relationship between Economic Growth and CO2 Emissions in China: An Empirical Study Based on Panel Smooth Transition Regression Models

PubMed Central

Wang, Zheng-Xin; Hao, Peng; Yao, Pei-Yi

2017-01-01

The non-linear relationship between provincial economic growth and carbon emissions is investigated by using panel smooth transition regression (PSTR) models. The research indicates that, on the condition of separately taking Gross Domestic Product per capita (GDPpc), energy structure (Es), and urbanisation level (Ul) as transition variables, three models all reject the null hypothesis of a linear relationship, i.e., a non-linear relationship exists. The results show that the three models all contain only one transition function but different numbers of location parameters. The model taking GDPpc as the transition variable has two location parameters, while the other two models separately considering Es and Ul as the transition variables both contain one location parameter. The three models applied in the study all favourably describe the non-linear relationship between economic growth and CO2 emissions in China. It also can be seen that the conversion rate of the influence of Ul on per capita CO2 emissions is significantly higher than those of GDPpc and Es on per capita CO2 emissions. PMID:29236083

Non-Linear Relationship between Economic Growth and CO₂ Emissions in China: An Empirical Study Based on Panel Smooth Transition Regression Models.

PubMed

Wang, Zheng-Xin; Hao, Peng; Yao, Pei-Yi

2017-12-13

The non-linear relationship between provincial economic growth and carbon emissions is investigated by using panel smooth transition regression (PSTR) models. The research indicates that, on the condition of separately taking Gross Domestic Product per capita (GDPpc), energy structure (Es), and urbanisation level (Ul) as transition variables, three models all reject the null hypothesis of a linear relationship, i.e., a non-linear relationship exists. The results show that the three models all contain only one transition function but different numbers of location parameters. The model taking GDPpc as the transition variable has two location parameters, while the other two models separately considering Es and Ul as the transition variables both contain one location parameter. The three models applied in the study all favourably describe the non-linear relationship between economic growth and CO₂ emissions in China. It also can be seen that the conversion rate of the influence of Ul on per capita CO₂ emissions is significantly higher than those of GDPpc and Es on per capita CO₂ emissions.

Holographic dark energy in higher derivative gravity with time varying model parameter c2

NASA Astrophysics Data System (ADS)

Borah, B.; Ansari, M.

2015-01-01

Purpose of this paper is to study holographic dark energy in higher derivative gravity assuming the model parameter c2 as a slowly time varying function. Since dark energy emerges as combined effect of linear as well as non-linear terms of curvature, therefore it is important to see holographic dark energy at higher derivative gravity, where action contains both linear as well as non-linear terms of Ricci curvature R. We consider non-interacting scenario of the holographic dark energy with dark matter in spatially flat universe and obtain evolution of the equation of state parameter. Also, we determine deceleration parameter as well as the evolution of dark energy density to explain expansion of the universe. Further, we investigate validity of generalized second law of thermodynamics in this scenario. Finally, we find out a cosmological application of our work by evaluating a relation for the equation of state of holographic dark energy for low red-shifts containing c2 correction.

Chaotic non-planar vibrations of the thin elastica. Part I: Experimental observation of planar instability

NASA Astrophysics Data System (ADS)

Cusumano, J. P.; Moon, F. C.

1995-01-01

In this two-part paper, the results of an investigation into the non-linear dynamics of a flexible cantilevered rod (the elastica) with a thin rectangular cross-section are presented. An experimental examination of the dynamics of the elastica over a broad parameter range forms the core of Part I. In Part II, the experimental work is related to a theoretical study of the mechanics of the elastica, and the study of a two-degree-of-freedom model obtained by modal projection. The experimental system used in this investigation is a rod with clamped-free boundary conditions, forced by sinusoidally displacing the clamped end. Planar periodic motions of the driven elastica are shown to lose stability at distinct resonant wedges, and the resulting motions are shown in general to be non-planar, chaotic, bending-torsion oscillations. Non-planar motions in all resonances exhibit energy cascading and dynamic two-well phenomena, and a family of asymmetric, bending-torsion non-linear modes is discovered. Correlation dimension calculations are used to estimate the number of active degrees of freedom in the system.

Investigation of scale effects in the TRF determined by VLBI

NASA Astrophysics Data System (ADS)

Wahl, Daniel; Heinkelmann, Robert; Schuh, Harald

2017-04-01

The improvement of the International Terrestrial Reference Frame (ITRF) is of great significance for Earth sciences and one of the major tasks in geodesy. The translation, rotation and the scale-factor, as well as their linear rates, are solved in a 14-parameter transformation between individual frames of each space geodetic technique and the combined frame. In ITRF2008, as well as in the current release ITRF2014, the scale-factor is provided by Very Long Baseline Interferometry (VLBI) and Satellite Laser Ranging (SLR) in equal shares. Since VLBI measures extremely precise group delays that are transformed to baseline lengths by the velocity of light, a natural constant, VLBI is the most suitable method for providing the scale. The aim of the current work is to identify possible shortcomings in the VLBI scale contribution to ITRF2008. For developing recommendations for an enhanced estimation, scale effects in the Terrestrial Reference Frame (TRF) determined with VLBI are considered in detail and compared to ITRF2008. In contrast to station coordinates, where the scale is defined by a geocentric position vector, pointing from the origin of the reference frame to the station, baselines are not related to the origin. They are describing the absolute scale independently from the datum. The more accurate a baseline length, and consequently the scale, is estimated by VLBI, the better the scale contribution to the ITRF. Considering time series of baseline length between different stations, a non-linear periodic signal can clearly be recognized, caused by seasonal effects at observation sites. Modeling these seasonal effects and subtracting them from the original data enhances the repeatability of single baselines significantly. Other effects influencing the scale strongly, are jumps in the time series of baseline length, mainly evoked by major earthquakes. Co- and post-seismic effects can be identified in the data, having a non-linear character likewise. Modeling the non-linear motion or completely excluding affected stations is another important step for an improved scale determination. In addition to the investigation of single baseline repeatabilities also the spatial transformation, which is performed for determining parameters of the ITRF2008, are considered. Since the reliability of the resulting transformation parameters is higher the more identical points are used in the transformation, an approach where all possible stations are used as control points is comprehensible. Experiments that examine the scale-factor and its spatial behavior between control points in ITRF2008 and coordinates determined by VLBI only showed that the network geometry has a large influence on the outcome as well. Introducing an unequally distributed network for the datum configuration, the correlations between translation parameters and the scale-factor can become remarkably high. Only a homogeneous spatial distribution of participating stations yields a maximally uncorrelated scale-factor that can be interpreted independent from other parameters. In the current release of the ITRF, the ITRF2014, for the first time, non-linear effects in the time series of station coordinates are taken into account. The present work shows the importance and the right direction of the modification of the ITRF calculation. But also further improvements were found which lead to an enhanced scale determination.

Characterizing Detrended Fluctuation Analysis of multifractional Brownian motion

NASA Astrophysics Data System (ADS)

Setty, V. A.; Sharma, A. S.

2015-02-01

The Hurst exponent (H) is widely used to quantify long range dependence in time series data and is estimated using several well known techniques. Recognizing its ability to remove trends the Detrended Fluctuation Analysis (DFA) is used extensively to estimate a Hurst exponent in non-stationary data. Multifractional Brownian motion (mBm) broadly encompasses a set of models of non-stationary data exhibiting time varying Hurst exponents, H(t) as against a constant H. Recently, there has been a growing interest in time dependence of H(t) and sliding window techniques have been used to estimate a local time average of the exponent. This brought to fore the ability of DFA to estimate scaling exponents in systems with time varying H(t) , such as mBm. This paper characterizes the performance of DFA on mBm data with linearly varying H(t) and further test the robustness of estimated time average with respect to data and technique related parameters. Our results serve as a bench-mark for using DFA as a sliding window estimator to obtain H(t) from time series data.

Adaptive non-linear control for cancer therapy through a Fokker-Planck observer.

PubMed

Shakeri, Ehsan; Latif-Shabgahi, Gholamreza; Esmaeili Abharian, Amir

2018-04-01

In recent years, many efforts have been made to present optimal strategies for cancer therapy through the mathematical modelling of tumour-cell population dynamics and optimal control theory. In many cases, therapy effect is included in the drift term of the stochastic Gompertz model. By fitting the model with empirical data, the parameters of therapy function are estimated. The reported research works have not presented any algorithm to determine the optimal parameters of therapy function. In this study, a logarithmic therapy function is entered in the drift term of the Gompertz model. Using the proposed control algorithm, the therapy function parameters are predicted and adaptively adjusted. To control the growth of tumour-cell population, its moments must be manipulated. This study employs the probability density function (PDF) control approach because of its ability to control all the process moments. A Fokker-Planck-based non-linear stochastic observer will be used to determine the PDF of the process. A cost function based on the difference between a predefined desired PDF and PDF of tumour-cell population is defined. Using the proposed algorithm, the therapy function parameters are adjusted in such a manner that the cost function is minimised. The existence of an optimal therapy function is also proved. The numerical results are finally given to demonstrate the effectiveness of the proposed method.

Ghost Dark Energy with Non-Linear Interaction Term

NASA Astrophysics Data System (ADS)

Ebrahimi, E.

2016-06-01

Here we investigate ghost dark energy (GDE) in the presence of a non-linear interaction term between dark matter and dark energy. To this end we take into account a general form for the interaction term. Then we discuss about different features of three choices of the non-linear interacting GDE. In all cases we obtain equation of state parameter, w D = p/ ρ, the deceleration parameter and evolution equation of the dark energy density parameter (Ω D ). We find that in one case, w D cross the phantom line ( w D < -1). However in two other classes w D can not cross the phantom divide. The coincidence problem can be solved in these models completely and there exist good agreement between the models and observational values of w D , q. We study squared sound speed {vs2}, and find that for one case of non-linear interaction term {vs2} can achieves positive values at late time of evolution.

Modeling and quantification of repolarization feature dependency on heart rate.

PubMed

Minchole, A; Zacur, E; Pueyo, E; Laguna, P

2014-01-01

This article is part of the Focus Theme of Methods of Information in Medicine on "Biosignal Interpretation: Advanced Methods for Studying Cardiovascular and Respiratory Systems". This work aims at providing an efficient method to estimate the parameters of a non linear model including memory, previously proposed to characterize rate adaptation of repolarization indices. The physiological restrictions on the model parameters have been included in the cost function in such a way that unconstrained optimization techniques such as descent optimization methods can be used for parameter estimation. The proposed method has been evaluated on electrocardiogram (ECG) recordings of healthy subjects performing a tilt test, where rate adaptation of QT and Tpeak-to-Tend (Tpe) intervals has been characterized. The proposed strategy results in an efficient methodology to characterize rate adaptation of repolarization features, improving the convergence time with respect to previous strategies. Moreover, Tpe interval adapts faster to changes in heart rate than the QT interval. In this work an efficient estimation of the parameters of a model aimed at characterizing rate adaptation of repolarization features has been proposed. The Tpe interval has been shown to be rate related and with a shorter memory lag than the QT interval.

Parameter estimation in spiking neural networks: a reverse-engineering approach.

PubMed

Rostro-Gonzalez, H; Cessac, B; Vieville, T

2012-04-01

This paper presents a reverse engineering approach for parameter estimation in spiking neural networks (SNNs). We consider the deterministic evolution of a time-discretized network with spiking neurons, where synaptic transmission has delays, modeled as a neural network of the generalized integrate and fire type. Our approach aims at by-passing the fact that the parameter estimation in SNN results in a non-deterministic polynomial-time hard problem when delays are to be considered. Here, this assumption has been reformulated as a linear programming (LP) problem in order to perform the solution in a polynomial time. Besides, the LP problem formulation makes the fact that the reverse engineering of a neural network can be performed from the observation of the spike times explicit. Furthermore, we point out how the LP adjustment mechanism is local to each neuron and has the same structure as a 'Hebbian' rule. Finally, we present a generalization of this approach to the design of input-output (I/O) transformations as a practical method to 'program' a spiking network, i.e. find a set of parameters allowing us to exactly reproduce the network output, given an input. Numerical verifications and illustrations are provided.

An adaptive observer for on-line tool wear estimation in turning, Part I: Theory

NASA Astrophysics Data System (ADS)

Danai, Kourosh; Ulsoy, A. Galip

1987-04-01

On-line sensing of tool wear has been a long-standing goal of the manufacturing engineering community. In the absence of any reliable on-line tool wear sensors, a new model-based approach for tool wear estimation has been proposed. This approach is an adaptive observer, based on force measurement, which uses both parameter and state estimation techniques. The design of the adaptive observer is based upon a dynamic state model of tool wear in turning. This paper (Part I) presents the model, and explains its use as the basis for the adaptive observer design. This model uses flank wear and crater wear as state variables, feed as the input, and the cutting force as the output. The suitability of the model as the basis for adaptive observation is also verified. The implementation of the adaptive observer requires the design of a state observer and a parameter estimator. To obtain the model parameters for tuning the adaptive observer procedures for linearisation of the non-linear model are specified. The implementation of the adaptive observer in turning and experimental results are presented in a companion paper (Part II).

On Least Squares Fitting Nonlinear Submodels.

ERIC Educational Resources Information Center

Bechtel, Gordon G.

Three simplifying conditions are given for obtaining least squares (LS) estimates for a nonlinear submodel of a linear model. If these are satisfied, and if the subset of nonlinear parameters may be LS fit to the corresponding LS estimates of the linear model, then one attains the desired LS estimates for the entire submodel. Two illustrative…

Mg1-xZnxFe2O4 nanoparticles: Interplay between cation distribution and magnetic properties

NASA Astrophysics Data System (ADS)

Raghuvanshi, S.; Mazaleyrat, F.; Kane, S. N.

2018-04-01

Correlation between cationic distribution, magnetic properties of Mg1-xZnxFe2O4 (0.0 ≤ x ≤ 1.0) ferrite is demonstrated, hardly shown in literature. X-ray diffraction (XRD) confirms the formation of cubic spinel nano ferrites with grain diameter between 40.8 to 55.4 nm. Energy dispersive spectroscopy (EDS) confirms close agreement of Mg/Fe, Zn/Fe molar ratio, presence of all elements (Mg, Zn, Fe, O), formation of estimated ferrite composition. Zn addition (for Mg) shows: i) linear increase of lattice parameter aexp, accounted for replacement of an ion with higher ionic radius (Zn > Mg); ii) presence of higher population of Fe3+ ions on B site, and unusual occurrence of Zn, Mg on A and B site leads to non-equilibrium cation distribution where we observe inverse to mixed structure, and is in contrast to reported literature where inverse to normal transition is reported; iii) effect on A-A, A-B, B-B exchange interactions, affecting coercivity Hc, Ms. A new empirical relation is also obtained showing linear relation between saturation magnetization Ms - inversion parameter δ, oxygen parameter u4 ¯ 3 m. Non-zero Y-K angle (αYK) values implies Y-K type magnetic ordering in the studied samples.

Derivative-Free Estimation of the Score Vector and Observed Information Matrix with Application to State-Space Models

DTIC Science & Technology

2015-07-14

2008). Sequential Monte Carlo smoothing with applica- tion to parameter estimation in non-linear state space models. Bernoulli , 14, 155-179. [22] Parikh...1BcΣ(θ?,δ)(Θ) ] = o ( τk ) for all k ∈ N. (45) The other integral is over the ball BΣ(θ?, δ), i.e. close to θ?; hence we perform a Taylor expansion of...1] R3 (θ, θ?) = ∑ |α|=4 ∂αϕ (θ? + cθ (θ − θ?)) (θ − θ?)α α! . 26 We now use the symmetry of the normal distribution N ( θ?, τ2Σ ) on the ball BΣ(θ

Added-value joint source modelling of seismic and geodetic data

NASA Astrophysics Data System (ADS)

Sudhaus, Henriette; Heimann, Sebastian; Walter, Thomas R.; Krueger, Frank

2013-04-01

In tectonically active regions earthquake source studies strongly support the analysis of the current faulting processes as they reveal the location and geometry of active faults, the average slip released or more. For source modelling of shallow, moderate to large earthquakes often a combination of geodetic (GPS, InSAR) and seismic data is used. A truly joint use of these data, however, usually takes place only on a higher modelling level, where some of the first-order characteristics (time, centroid location, fault orientation, moment) have been fixed already. These required basis model parameters have to be given, assumed or inferred in a previous, separate and highly non-linear modelling step using one of the these data sets alone. We present a new earthquake rupture model implementation that realizes a fully combined data integration of surface displacement measurements and seismic data in a non-linear optimization of simple but extended planar ruptures. The model implementation allows for fast forward calculations of full seismograms and surface deformation and therefore enables us to use Monte Carlo global search algorithms. Furthermore, we benefit from the complementary character of seismic and geodetic data, e. g. the high definition of the source location from geodetic data and the sensitivity of the resolution of the seismic data on moment releases at larger depth. These increased constraints from the combined dataset make optimizations efficient, even for larger model parameter spaces and with a very limited amount of a priori assumption on the source. A vital part of our approach is rigorous data weighting based on the empirically estimated data errors. We construct full data error variance-covariance matrices for geodetic data to account for correlated data noise and also weight the seismic data based on their signal-to-noise ratio. The estimation of the data errors and the fast forward modelling opens the door for Bayesian inferences of the source model parameters. The source model product then features parameter uncertainty estimates and reveals parameter trade-offs that arise from imperfect data coverage and data errors. We applied our new source modelling approach to the 2010 Haiti earthquake for which a number of apparently different seismic, geodetic and joint source models has been reported already - mostly without any model parameter estimations. We here show that the variability of all these source models seems to arise from inherent model parameter trade-offs and mostly has little statistical significance, e.g. even using a large dataset comprising seismic and geodetic data the confidence interval of the fault dip remains as wide as about 20 degrees.

Accurate electrostatic and van der Waals pull-in prediction for fully clamped nano/micro-beams using linear universal graphs of pull-in instability

NASA Astrophysics Data System (ADS)

Tahani, Masoud; Askari, Amir R.

2014-09-01

In spite of the fact that pull-in instability of electrically actuated nano/micro-beams has been investigated by many researchers to date, no explicit formula has been presented yet which can predict pull-in voltage based on a geometrically non-linear and distributed parameter model. The objective of present paper is to introduce a simple and accurate formula to predict this value for a fully clamped electrostatically actuated nano/micro-beam. To this end, a non-linear Euler-Bernoulli beam model is employed, which accounts for the axial residual stress, geometric non-linearity of mid-plane stretching, distributed electrostatic force and the van der Waals (vdW) attraction. The non-linear boundary value governing equation of equilibrium is non-dimensionalized and solved iteratively through single-term Galerkin based reduced order model (ROM). The solutions are validated thorough direct comparison with experimental and other existing results reported in previous studies. Pull-in instability under electrical and vdW loads are also investigated using universal graphs. Based on the results of these graphs, non-dimensional pull-in and vdW parameters, which are defined in the text, vary linearly versus the other dimensionless parameters of the problem. Using this fact, some linear equations are presented to predict pull-in voltage, the maximum allowable length, the so-called detachment length, and the minimum allowable gap for a nano/micro-system. These linear equations are also reduced to a couple of universal pull-in formulas for systems with small initial gap. The accuracy of the universal pull-in formulas are also validated by comparing its results with available experimental and some previous geometric linear and closed-form findings published in the literature.

Drive Control of an Electric Vehicle by a Non-linear Controller

NASA Astrophysics Data System (ADS)

Mubin, Marizan; Ouchi, Shigeto; Anabuki, Masatoshi; Hirata, Hiroshi

The driving force of automobiles is transmitted by the frictional force between the tires and the road surface. This frictional force is a function of the weight of the car-body and the friction coefficient μ between the tires and the road surface. The friction coefficient μ is also a function of the following parameters: the slip ratio λ determined by the car-body speed and the wheel speed, and the condition of the road surface. Slippage of automobiles which causes much damage often occurs during accelerating and braking. In this paper, we propose a new drive control system which has an effect on acceleration and braking. In the drive control system, a non-linear controller designed by using a Lyapunov function is used. This non-linear controller has two functions: first one is μ control which moves the car-body, another one is λ control. The controller is designed in order that μ and λ work at noslip and with slip respectively. As another controller, a disturbance observer is used for estimating the car-body speed which is difficult to be measured. Then, this lead to the proof of the stability condition of the combined system which consists of two controllers: the non-linear controller and the disturbance observer. Finally, the effectiveness of this control system is proved by a very satisfactory simulation and experimental results for two cases.

Analysis of calibration data for the uranium active neutron coincidence counting collar with attention to errors in the measured neutron coincidence rate

DOE PAGES

Croft, Stephen; Burr, Thomas Lee; Favalli, Andrea; ...

2015-12-10

We report that the declared linear density of 238U and 235U in fresh low enriched uranium light water reactor fuel assemblies can be verified for nuclear safeguards purposes using a neutron coincidence counter collar in passive and active mode, respectively. The active mode calibration of the Uranium Neutron Collar – Light water reactor fuel (UNCL) instrument is normally performed using a non-linear fitting technique. The fitting technique relates the measured neutron coincidence rate (the predictor) to the linear density of 235U (the response) in order to estimate model parameters of the nonlinear Padé equation, which traditionally is used to modelmore » the calibration data. Alternatively, following a simple data transformation, the fitting can also be performed using standard linear fitting methods. This paper compares performance of the nonlinear technique to the linear technique, using a range of possible error variance magnitudes in the measured neutron coincidence rate. We develop the required formalism and then apply the traditional (nonlinear) and alternative approaches (linear) to the same experimental and corresponding simulated representative datasets. Lastly, we find that, in this context, because of the magnitude of the errors in the predictor, it is preferable not to transform to a linear model, and it is preferable not to adjust for the errors in the predictor when inferring the model parameters« less

Three dimensional rotating flow of Powell-Eyring nanofluid with non-Fourier's heat flux and non-Fick's mass flux theory

NASA Astrophysics Data System (ADS)

Ibrahim, Wubshet

2018-03-01

This article numerically examines three dimensional boundary layer flow of a rotating Powell-Eyring nanofluid. In modeling heat transfer processes, non-Fourier heat flux theory and for mass transfer non-Fick's mass flux theory are employed. This theory is recently re-initiated and it becomes the active research area to resolves some drawback associated with the famous Fourier heat flux and mass flux theory. The mathematical model of the flow problem is a system of non-linear partial differential equations which are obtained using the boundary layer analysis. The non-linear partial differential equations have been transformed into non-linear high order ordinary differential equations using similarity transformation. Employing bvp4c algorithm from matlab software routine, the numerical solution of the transformed ordinary differential equations is obtained. The governing equations are constrained by parameters such as rotation parameter λ , the non-Newtonian parameter N, dimensionless thermal relaxation and concentration relaxation parameters δt and δc . The impacts of these parameters have been discussed thoroughly and illustrated using graphs and tables. The findings show that thermal relaxation time δt reduces the thermal and concentration boundary layer thickness. Further, the results reveal that the rotational parameter λ has the effect of decreasing the velocity boundary layer thickness in both x and y directions. Further examination pinpoints that the skin friction coefficient along x-axis is an increasing and skin friction coefficient along y-axis is a decreasing function of rotation parameter λ . Furthermore, the non-Newtonian fluid parameter N has the characteristic of reducing the amount of local Nusselt numbers -f″ (0) and -g″ (0) both in x and y -directions.

Estimation of splitting functions from Earth's normal mode spectra using the neighbourhood algorithm

NASA Astrophysics Data System (ADS)

Pachhai, Surya; Tkalčić, Hrvoje; Masters, Guy

2016-01-01

The inverse problem for Earth structure from normal mode data is strongly non-linear and can be inherently non-unique. Traditionally, the inversion is linearized by taking partial derivatives of the complex spectra with respect to the model parameters (i.e. structure coefficients), and solved in an iterative fashion. This method requires that the earthquake source model is known. However, the release of energy in large earthquakes used for the analysis of Earth's normal modes is not simple. A point source approximation is often inadequate, and a more complete account of energy release at the source is required. In addition, many earthquakes are required for the solution to be insensitive to the initial constraints and regularization. In contrast to an iterative approach, the autoregressive linear inversion technique conveniently avoids the need for earthquake source parameters, but it also requires a number of events to achieve full convergence when a single event does not excite all singlets well. To build on previous improvements, we develop a technique to estimate structure coefficients (and consequently, the splitting functions) using a derivative-free parameter search, known as neighbourhood algorithm (NA). We implement an efficient forward method derived using the autoregresssion of receiver strips, and this allows us to search over a multiplicity of structure coefficients in a relatively short time. After demonstrating feasibility of the use of NA in synthetic cases, we apply it to observations of the inner core sensitive mode 13S2. The splitting function of this mode is dominated by spherical harmonic degree 2 axisymmetric structure and is consistent with the results obtained from the autoregressive linear inversion. The sensitivity analysis of multiple events confirms the importance of the Bolivia, 1994 earthquake. When this event is used in the analysis, as little as two events are sufficient to constrain the splitting functions of 13S2 mode. Apart from not requiring the knowledge of earthquake source, the newly developed technique provides an approximate uncertainty measure of the structure coefficients and allows us to control the type of structure solved for, for example to establish if elastic structure is sufficient.

Multi-objective optimization in quantum parameter estimation

NASA Astrophysics Data System (ADS)

Gong, BeiLi; Cui, Wei

2018-04-01

We investigate quantum parameter estimation based on linear and Kerr-type nonlinear controls in an open quantum system, and consider the dissipation rate as an unknown parameter. We show that while the precision of parameter estimation is improved, it usually introduces a significant deformation to the system state. Moreover, we propose a multi-objective model to optimize the two conflicting objectives: (1) maximizing the Fisher information, improving the parameter estimation precision, and (2) minimizing the deformation of the system state, which maintains its fidelity. Finally, simulations of a simplified ɛ-constrained model demonstrate the feasibility of the Hamiltonian control in improving the precision of the quantum parameter estimation.

Estimation of time- and state-dependent delays and other parameters in functional differential equations

NASA Technical Reports Server (NTRS)

Murphy, K. A.

1988-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Estimation of time- and state-dependent delays and other parameters in functional differential equations

NASA Technical Reports Server (NTRS)

Murphy, K. A.

1990-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Density-dependent host choice by disease vectors: epidemiological implications of the ideal free distribution.

PubMed

Basáñez, María-Gloria; Razali, Karina; Renz, Alfons; Kelly, David

2007-03-01

The proportion of vector blood meals taken on humans (the human blood index, h) appears as a squared term in classical expressions of the basic reproduction ratio (R(0)) for vector-borne infections. Consequently, R(0) varies non-linearly with h. Estimates of h, however, constitute mere snapshots of a parameter that is predicted, from evolutionary theory, to vary with vector and host abundance. We test this prediction using a population dynamics model of river blindness assuming that, before initiation of vector control or chemotherapy, recorded measures of vector density and human infection accurately represent endemic equilibrium. We obtain values of h that satisfy the condition that the effective reproduction ratio (R(e)) must equal 1 at equilibrium. Values of h thus obtained decrease with vector density, decrease with the vector:human ratio and make R(0) respond non-linearly rather than increase linearly with vector density. We conclude that if vectors are less able to obtain human blood meals as their density increases, antivectorial measures may not lead to proportional reductions in R(0) until very low vector levels are achieved. Density dependence in the contact rate of infectious diseases transmitted by insects may be an important non-linear process with implications for their epidemiology and control.

Objective calibration of regional climate models

NASA Astrophysics Data System (ADS)

Bellprat, O.; Kotlarski, S.; Lüthi, D.; SchäR, C.

2012-12-01

Climate models are subject to high parametric uncertainty induced by poorly confined model parameters of parameterized physical processes. Uncertain model parameters are typically calibrated in order to increase the agreement of the model with available observations. The common practice is to adjust uncertain model parameters manually, often referred to as expert tuning, which lacks objectivity and transparency in the use of observations. These shortcomings often haze model inter-comparisons and hinder the implementation of new model parameterizations. Methods which would allow to systematically calibrate model parameters are unfortunately often not applicable to state-of-the-art climate models, due to computational constraints facing the high dimensionality and non-linearity of the problem. Here we present an approach to objectively calibrate a regional climate model, using reanalysis driven simulations and building upon a quadratic metamodel presented by Neelin et al. (2010) that serves as a computationally cheap surrogate of the model. Five model parameters originating from different parameterizations are selected for the optimization according to their influence on the model performance. The metamodel accurately estimates spatial averages of 2 m temperature, precipitation and total cloud cover, with an uncertainty of similar magnitude as the internal variability of the regional climate model. The non-linearities of the parameter perturbations are well captured, such that only a limited number of 20-50 simulations are needed to estimate optimal parameter settings. Parameter interactions are small, which allows to further reduce the number of simulations. In comparison to an ensemble of the same model which has undergone expert tuning, the calibration yields similar optimal model configurations, but leading to an additional reduction of the model error. The performance range captured is much wider than sampled with the expert-tuned ensemble and the presented methodology is effective and objective. It is argued that objective calibration is an attractive tool and could become standard procedure after introducing new model implementations, or after a spatial transfer of a regional climate model. Objective calibration of parameterizations with regional models could also serve as a strategy toward improving parameterization packages of global climate models.

Influence of imperfect end boundary condition on the nonlocal dynamics of CNTs

NASA Astrophysics Data System (ADS)

Fathi, Reza; Lotfan, Saeed; Sadeghi, Morteza H.

2017-03-01

Imperfections that unavoidably occur during the fabrication process of carbon nanotubes (CNTs) have a significant influence on the vibration behavior of CNTs. Among these imperfections, the boundary condition defect is studied in this investigation based on the nonlocal elasticity theory. To this end, a mathematical model of the non-ideal end condition in a cantilever CNT is developed by a strongly non-linear spring to study its effect on the vibration behavior. The weak form equation of motion is derived via Hamilton's principle and solved based on Rayleigh-Ritz approach. Once the frequency response function (FRF) of the CNT is simulated, it is found that the defect parameter injects noise to the FRF in the range of lower frequencies and as a result the small scale effect on the FRF remains undisturbed in high frequency ranges. Besides, in this work a process is introduced to estimate the nonlocal and defect parameters for establishing the mathematical model of the CNT based on FRF, which can be competitive because of its lower instrumentation and data analysis costs. The estimation process relies on the resonance frequencies and the magnitude of noise in the frequency response function of the CNT. The results show that the constructed dynamic response of the system based on estimated parameters is in good agreement with the original response of the CNT.

An Extension of the Partial Credit Model with an Application to the Measurement of Change.

ERIC Educational Resources Information Center

Fischer, Gerhard H.; Ponocny, Ivo

1994-01-01

An extension to the partial credit model, the linear partial credit model, is considered under the assumption of a certain linear decomposition of the item x category parameters into basic parameters. A conditional maximum likelihood algorithm for estimating basic parameters is presented and illustrated with simulation and an empirical study. (SLD)

Approaches to characterise chromatographic column performance based on global parameters accounting for peak broadening and skewness.

PubMed

Baeza-Baeza, J J; Pous-Torres, S; Torres-Lapasió, J R; García-Alvarez-Coque, M C

2010-04-02

Peak broadening and skewness are fundamental parameters in chromatography, since they affect the resolution capability of a chromatographic column. A common practice to characterise chromatographic columns is to estimate the efficiency and asymmetry factor for the peaks of one or more solutes eluted at selected experimental conditions. This has the drawback that the extra-column contributions to the peak variance and skewness make the peak shape parameters depend on the retention time. We propose and discuss here the use of several approaches that allow the estimation of global parameters (non-dependent on the retention time) to describe the column performance. The global parameters arise from different linear relationships that can be established between the peak variance, standard deviation, or half-widths with the retention time. Some of them describe exclusively the column contribution to the peak broadening, whereas others consider the extra-column effects also. The estimation of peak skewness was also possible for the approaches based on the half-widths. The proposed approaches were applied to the characterisation of different columns (Spherisorb, Zorbax SB, Zorbax Eclipse, Kromasil, Chromolith, X-Terra and Inertsil), using the chromatographic data obtained for several diuretics and basic drugs (beta-blockers). Copyright (c) 2010 Elsevier B.V. All rights reserved.

Gompertzian stochastic model with delay effect to cervical cancer growth

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah

2015-02-03

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

Evaluation of Uncertainty and Sensitivity in Environmental Modeling at a Radioactive Waste Management Site

NASA Astrophysics Data System (ADS)

Stockton, T. B.; Black, P. K.; Catlett, K. M.; Tauxe, J. D.

2002-05-01

Environmental modeling is an essential component in the evaluation of regulatory compliance of radioactive waste management sites (RWMSs) at the Nevada Test Site in southern Nevada, USA. For those sites that are currently operating, further goals are to support integrated decision analysis for the development of acceptance criteria for future wastes, as well as site maintenance, closure, and monitoring. At these RWMSs, the principal pathways for release of contamination to the environment are upward towards the ground surface rather than downwards towards the deep water table. Biotic processes, such as burrow excavation and plant uptake and turnover, dominate this upward transport. A combined multi-pathway contaminant transport and risk assessment model was constructed using the GoldSim modeling platform. This platform facilitates probabilistic analysis of environmental systems, and is especially well suited for assessments involving radionuclide decay chains. The model employs probabilistic definitions of key parameters governing contaminant transport, with the goals of quantifying cumulative uncertainty in the estimation of performance measures and providing information necessary to perform sensitivity analyses. This modeling differs from previous radiological performance assessments (PAs) in that the modeling parameters are intended to be representative of the current knowledge, and the uncertainty in that knowledge, of parameter values rather than reflective of a conservative assessment approach. While a conservative PA may be sufficient to demonstrate regulatory compliance, a parametrically honest PA can also be used for more general site decision-making. In particular, a parametrically honest probabilistic modeling approach allows both uncertainty and sensitivity analyses to be explicitly coupled to the decision framework using a single set of model realizations. For example, sensitivity analysis provides a guide for analyzing the value of collecting more information by quantifying the relative importance of each input parameter in predicting the model response. However, in these complex, high dimensional eco-system models, represented by the RWMS model, the dynamics of the systems can act in a non-linear manner. Quantitatively assessing the importance of input variables becomes more difficult as the dimensionality, the non-linearities, and the non-monotonicities of the model increase. Methods from data mining such as Multivariate Adaptive Regression Splines (MARS) and the Fourier Amplitude Sensitivity Test (FAST) provide tools that can be used in global sensitivity analysis in these high dimensional, non-linear situations. The enhanced interpretability of model output provided by the quantitative measures estimated by these global sensitivity analysis tools will be demonstrated using the RWMS model.

Do Quercus ilex Woodlands Undergo Abrupt Non-linear Changes in their Functional Dynamics in Response to Human Disturbance and Climatic Variation?

NASA Astrophysics Data System (ADS)

Bochet, E.; García-Fayos, P.; Molina, M. J.; Moreno de las Heras, M.; Espigares, T.; Nicolau, J. M.; Monleon, V. J.

2017-12-01

Theoretical models predict that drylands are particularly prone to suffer critical transitions with abrupt non-linear changes in their structure and functions as a result of the existing complex interactions between climatic fluctuations and human disturbances. How drylands undergo functional change has become an important issue in ecology which needs empirical data to validate theoretical models. We aim at determining the response of Mediterranean holm oak woodlands to human disturbance in three different climatic areas from Eastern Spain, under the hypothesis that semiarid and dry-transition landscapes are more prone to suffer abrupt functional changes than sub-humid ones. We used (a) remote-sensing estimations of precipitation-use-efficiency (PUE) from enhanced vegetation index (EVI) observations performed in 231 x 231 m plots of the Moderate Resolution Imaging Spectroradiometer (MODIS); (b) soil parameter (enzyme activity, organic matter) and (c) vegetation parameter (functional groups) determinations from soil sampling and vegetation surveys, respectively, performed in the same plots. We analyzed and compared the shape of the functional change (in terms of PUE, soil and vegetation parameters) in response to human disturbance intensity for our holm oak sites in the three climatic areas. Although no threshold of abrupt change is observed, important differences in the functional response of holm oak woodlands to disturbance exist between climatic conditions. Overall, semiarid and dry-transition woodlands suffer a non-linear functional decrease in terms of PUE, soil organic matter and enzyme activity with disturbance intensity. Differently, sub-humid woodlands experience a linear decrease of PUE with disturbance intensity and an increase of both soil parameters at high disturbance intensities after an important decrease at low disturbance intensities. The structural change from woody- to herbaceous-dominated landscapes in sub-humid areas explains the recovery of the functional state of the system at high disturbance intensities. This structural change in the vegetation provides resilience to sub-humid woodlands at high intensity levels where semiarid and dry-transition woodlands suffer a pronounced degradation.

Estimation and Simulation of Slow Crack Growth Parameters from Constant Stress Rate Data

NASA Technical Reports Server (NTRS)

Salem, Jonathan A.; Weaver, Aaron S.

2003-01-01

Closed form, approximate functions for estimating the variances and degrees-of-freedom associated with the slow crack growth parameters n, D, B, and A(sup *) as measured using constant stress rate ('dynamic fatigue') testing were derived by using propagation of errors. Estimates made with the resulting functions and slow crack growth data for a sapphire window were compared to the results of Monte Carlo simulations. The functions for estimation of the variances of the parameters were derived both with and without logarithmic transformation of the initial slow crack growth equations. The transformation was performed to make the functions both more linear and more normal. Comparison of the Monte Carlo results and the closed form expressions derived with propagation of errors indicated that linearization is not required for good estimates of the variances of parameters n and D by the propagation of errors method. However, good estimates variances of the parameters B and A(sup *) could only be made when the starting slow crack growth equation was transformed and the coefficients of variation of the input parameters were not too large. This was partially a result of the skewered distributions of B and A(sup *). Parametric variation of the input parameters was used to determine an acceptable range for using closed form approximate equations derived from propagation of errors.

Envelope of coda waves for a double couple source due to non-linear elasticity

NASA Astrophysics Data System (ADS)

Calisto, Ignacia; Bataille, Klaus

2014-10-01

Non-linear elasticity has recently been considered as a source of scattering, therefore contributing to the coda of seismic waves, in particular for the case of explosive sources. This idea is analysed further here, theoretically solving the expression for the envelope of coda waves generated by a point moment tensor in order to compare with earthquake data. For weak non-linearities, one can consider each point of the non-linear medium as a source of scattering within a homogeneous and linear medium, for which Green's functions can be used to compute the total displacement of scattered waves. These sources of scattering have specific radiation patterns depending on the incident and scattered P or S waves, respectively. In this approach, the coda envelope depends on three scalar parameters related to the specific non-linearity of the medium; however these parameters only change the scale of the coda envelope. The shape of the coda envelope is sensitive to both the source time function and the intrinsic attenuation. We compare simulations using this model with data from earthquakes in Taiwan, with a good fit.

Non-linear dynamic analysis of geared systems, part 2

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

Simplified large African carnivore density estimators from track indices.

PubMed

Winterbach, Christiaan W; Ferreira, Sam M; Funston, Paul J; Somers, Michael J

2016-01-01

The range, population size and trend of large carnivores are important parameters to assess their status globally and to plan conservation strategies. One can use linear models to assess population size and trends of large carnivores from track-based surveys on suitable substrates. The conventional approach of a linear model with intercept may not intercept at zero, but may fit the data better than linear model through the origin. We assess whether a linear regression through the origin is more appropriate than a linear regression with intercept to model large African carnivore densities and track indices. We did simple linear regression with intercept analysis and simple linear regression through the origin and used the confidence interval for ß in the linear model y  =  αx  + ß, Standard Error of Estimate, Mean Squares Residual and Akaike Information Criteria to evaluate the models. The Lion on Clay and Low Density on Sand models with intercept were not significant ( P  > 0.05). The other four models with intercept and the six models thorough origin were all significant ( P  < 0.05). The models using linear regression with intercept all included zero in the confidence interval for ß and the null hypothesis that ß = 0 could not be rejected. All models showed that the linear model through the origin provided a better fit than the linear model with intercept, as indicated by the Standard Error of Estimate and Mean Square Residuals. Akaike Information Criteria showed that linear models through the origin were better and that none of the linear models with intercept had substantial support. Our results showed that linear regression through the origin is justified over the more typical linear regression with intercept for all models we tested. A general model can be used to estimate large carnivore densities from track densities across species and study areas. The formula observed track density = 3.26 × carnivore density can be used to estimate densities of large African carnivores using track counts on sandy substrates in areas where carnivore densities are 0.27 carnivores/100 km 2 or higher. To improve the current models, we need independent data to validate the models and data to test for non-linear relationship between track indices and true density at low densities.

Real-Time Parameter Estimation Method Applied to a MIMO Process and its Comparison with an Offline Identification Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaplanoglu, Erkan; Safak, Koray K.; Varol, H. Selcuk

2009-01-12

An experiment based method is proposed for parameter estimation of a class of linear multivariable systems. The method was applied to a pressure-level control process. Experimental time domain input/output data was utilized in a gray-box modeling approach. Prior knowledge of the form of the system transfer function matrix elements is assumed to be known. Continuous-time system transfer function matrix parameters were estimated in real-time by the least-squares method. Simulation results of experimentally determined system transfer function matrix compare very well with the experimental results. For comparison and as an alternative to the proposed real-time estimation method, we also implemented anmore » offline identification method using artificial neural networks and obtained fairly good results. The proposed methods can be implemented conveniently on a desktop PC equipped with a data acquisition board for parameter estimation of moderately complex linear multivariable systems.« less

A two-stage Monte Carlo approach to the expression of uncertainty with finite sample sizes.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crowder, Stephen Vernon; Moyer, Robert D.

2005-05-01

Proposed supplement I to the GUM outlines a 'propagation of distributions' approach to deriving the distribution of a measurand for any non-linear function and for any set of random inputs. The supplement's proposed Monte Carlo approach assumes that the distributions of the random inputs are known exactly. This implies that the sample sizes are effectively infinite. In this case, the mean of the measurand can be determined precisely using a large number of Monte Carlo simulations. In practice, however, the distributions of the inputs will rarely be known exactly, but must be estimated using possibly small samples. If these approximatedmore » distributions are treated as exact, the uncertainty in estimating the mean is not properly taken into account. In this paper, we propose a two-stage Monte Carlo procedure that explicitly takes into account the finite sample sizes used to estimate parameters of the input distributions. We will illustrate the approach with a case study involving the efficiency of a thermistor mount power sensor. The performance of the proposed approach will be compared to the standard GUM approach for finite samples using simple non-linear measurement equations. We will investigate performance in terms of coverage probabilities of derived confidence intervals.« less

Transformation to equivalent dimensions—a new methodology to study earthquake clustering

NASA Astrophysics Data System (ADS)

Lasocki, Stanislaw

2014-05-01

A seismic event is represented by a point in a parameter space, quantified by the vector of parameter values. Studies of earthquake clustering involve considering distances between such points in multidimensional spaces. However, the metrics of earthquake parameters are different, hence the metric in a multidimensional parameter space cannot be readily defined. The present paper proposes a solution of this metric problem based on a concept of probabilistic equivalence of earthquake parameters. Under this concept the lengths of parameter intervals are equivalent if the probability for earthquakes to take values from either interval is the same. Earthquake clustering is studied in an equivalent rather than the original dimensions space, where the equivalent dimension (ED) of a parameter is its cumulative distribution function. All transformed parameters are of linear scale in [0, 1] interval and the distance between earthquakes represented by vectors in any ED space is Euclidean. The unknown, in general, cumulative distributions of earthquake parameters are estimated from earthquake catalogues by means of the model-free non-parametric kernel estimation method. Potential of the transformation to EDs is illustrated by two examples of use: to find hierarchically closest neighbours in time-space and to assess temporal variations of earthquake clustering in a specific 4-D phase space.

Identification of internal properties of fibers and micro-swimmers

NASA Astrophysics Data System (ADS)

Plouraboue, Franck; Thiam, Ibrahima; Delmotte, Blaise; Climent, Eric; PSC Collaboration

2016-11-01

In this presentation we discuss the identifiability of constitutive parameters of passive or active micro-swimmers. We first present a general framework for describing fibers or micro-swimmers using a bead-model description. Using a kinematic constraint formulation to describe fibers, flagellum or cilia, we find explicit linear relationship between elastic constitutive parameters and generalised velocities from computing contact forces. This linear formulation then permits to address explicitly identifiability conditions and solve for parameter identification. We show that both active forcing and passive parameters are both identifiable independently but not simultaneously. We also provide unbiased estimators for elastic parameters as well as active ones in the presence of Langevin-like forcing with Gaussian noise using normal linear regression models and maximum likelihood method. These theoretical results are illustrated in various configurations of relaxed or actuated passives fibers, and active filament of known passive properties, showing the efficiency of the proposed approach for direct parameter identification. The convergence of the proposed estimators is successfully tested numerically.

An evaluation of bias in propensity score-adjusted non-linear regression models.

PubMed

Wan, Fei; Mitra, Nandita

2018-03-01

Propensity score methods are commonly used to adjust for observed confounding when estimating the conditional treatment effect in observational studies. One popular method, covariate adjustment of the propensity score in a regression model, has been empirically shown to be biased in non-linear models. However, no compelling underlying theoretical reason has been presented. We propose a new framework to investigate bias and consistency of propensity score-adjusted treatment effects in non-linear models that uses a simple geometric approach to forge a link between the consistency of the propensity score estimator and the collapsibility of non-linear models. Under this framework, we demonstrate that adjustment of the propensity score in an outcome model results in the decomposition of observed covariates into the propensity score and a remainder term. Omission of this remainder term from a non-collapsible regression model leads to biased estimates of the conditional odds ratio and conditional hazard ratio, but not for the conditional rate ratio. We further show, via simulation studies, that the bias in these propensity score-adjusted estimators increases with larger treatment effect size, larger covariate effects, and increasing dissimilarity between the coefficients of the covariates in the treatment model versus the outcome model.

Linear and nonlinear ARMA model parameter estimation using an artificial neural network

NASA Technical Reports Server (NTRS)

Chon, K. H.; Cohen, R. J.

1997-01-01

This paper addresses parametric system identification of linear and nonlinear dynamic systems by analysis of the input and output signals. Specifically, we investigate the relationship between estimation of the system using a feedforward neural network model and estimation of the system by use of linear and nonlinear autoregressive moving-average (ARMA) models. By utilizing a neural network model incorporating a polynomial activation function, we show the equivalence of the artificial neural network to the linear and nonlinear ARMA models. We compare the parameterization of the estimated system using the neural network and ARMA approaches by utilizing data generated by means of computer simulations. Specifically, we show that the parameters of a simulated ARMA system can be obtained from the neural network analysis of the simulated data or by conventional least squares ARMA analysis. The feasibility of applying neural networks with polynomial activation functions to the analysis of experimental data is explored by application to measurements of heart rate (HR) and instantaneous lung volume (ILV) fluctuations.

Strengthen forensic entomology in court--the need for data exploration and the validation of a generalised additive mixed model.

PubMed

Baqué, Michèle; Amendt, Jens

2013-01-01

Developmental data of juvenile blow flies (Diptera: Calliphoridae) are typically used to calculate the age of immature stages found on or around a corpse and thus to estimate a minimum post-mortem interval (PMI(min)). However, many of those data sets don't take into account that immature blow flies grow in a non-linear fashion. Linear models do not supply a sufficient reliability on age estimates and may even lead to an erroneous determination of the PMI(min). According to the Daubert standard and the need for improvements in forensic science, new statistic tools like smoothing methods and mixed models allow the modelling of non-linear relationships and expand the field of statistical analyses. The present study introduces into the background and application of these statistical techniques by analysing a model which describes the development of the forensically important blow fly Calliphora vicina at different temperatures. The comparison of three statistical methods (linear regression, generalised additive modelling and generalised additive mixed modelling) clearly demonstrates that only the latter provided regression parameters that reflect the data adequately. We focus explicitly on both the exploration of the data--to assure their quality and to show the importance of checking it carefully prior to conducting the statistical tests--and the validation of the resulting models. Hence, we present a common method for evaluating and testing forensic entomological data sets by using for the first time generalised additive mixed models.

Semiparametric Estimation of the Impacts of Longitudinal Interventions on Adolescent Obesity using Targeted Maximum-Likelihood: Accessible Estimation with the ltmle Package

PubMed Central

Decker, Anna L.; Hubbard, Alan; Crespi, Catherine M.; Seto, Edmund Y.W.; Wang, May C.

2015-01-01

While child and adolescent obesity is a serious public health concern, few studies have utilized parameters based on the causal inference literature to examine the potential impacts of early intervention. The purpose of this analysis was to estimate the causal effects of early interventions to improve physical activity and diet during adolescence on body mass index (BMI), a measure of adiposity, using improved techniques. The most widespread statistical method in studies of child and adolescent obesity is multi-variable regression, with the parameter of interest being the coefficient on the variable of interest. This approach does not appropriately adjust for time-dependent confounding, and the modeling assumptions may not always be met. An alternative parameter to estimate is one motivated by the causal inference literature, which can be interpreted as the mean change in the outcome under interventions to set the exposure of interest. The underlying data-generating distribution, upon which the estimator is based, can be estimated via a parametric or semi-parametric approach. Using data from the National Heart, Lung, and Blood Institute Growth and Health Study, a 10-year prospective cohort study of adolescent girls, we estimated the longitudinal impact of physical activity and diet interventions on 10-year BMI z-scores via a parameter motivated by the causal inference literature, using both parametric and semi-parametric estimation approaches. The parameters of interest were estimated with a recently released R package, ltmle, for estimating means based upon general longitudinal treatment regimes. We found that early, sustained intervention on total calories had a greater impact than a physical activity intervention or non-sustained interventions. Multivariable linear regression yielded inflated effect estimates compared to estimates based on targeted maximum-likelihood estimation and data-adaptive super learning. Our analysis demonstrates that sophisticated, optimal semiparametric estimation of longitudinal treatment-specific means via ltmle provides an incredibly powerful, yet easy-to-use tool, removing impediments for putting theory into practice. PMID:26046009

Are Successive Investments in Education Equally Worthwhile? Endogenous Schooling Decisions and Non-Linearities in the Earnings-Schooling Relationship

ERIC Educational Resources Information Center

Skalli, Ali

2007-01-01

Most of the studies that account for the endogeneity bias when estimating the returns to schooling assume that the relationship between education and earnings is linear. Studies that assume the latter relationship to be non-linear simply ignore the endogeneity bias. Moreover, they either assume an ad-hoc non-linear relationship or argue that…

Comparison of stability and control parameters for a light, single-engine, high-winged aircraft using different flight test and parameter estimation techniques

NASA Technical Reports Server (NTRS)

Suit, W. T.; Cannaday, R. L.

1979-01-01

The longitudinal and lateral stability and control parameters for a high wing, general aviation, airplane are examined. Estimations using flight data obtained at various flight conditions within the normal range of the aircraft are presented. The estimations techniques, an output error technique (maximum likelihood) and an equation error technique (linear regression), are presented. The longitudinal static parameters are estimated from climbing, descending, and quasi steady state flight data. The lateral excitations involve a combination of rudder and ailerons. The sensitivity of the aircraft modes of motion to variations in the parameter estimates are discussed.

Identification of transmissivity fields using a Bayesian strategy and perturbative approach

NASA Astrophysics Data System (ADS)

Zanini, Andrea; Tanda, Maria Giovanna; Woodbury, Allan D.

2017-10-01

The paper deals with the crucial problem of the groundwater parameter estimation that is the basis for efficient modeling and reclamation activities. A hierarchical Bayesian approach is developed: it uses the Akaike's Bayesian Information Criteria in order to estimate the hyperparameters (related to the covariance model chosen) and to quantify the unknown noise variance. The transmissivity identification proceeds in two steps: the first, called empirical Bayesian interpolation, uses Y* (Y = lnT) observations to interpolate Y values on a specified grid; the second, called empirical Bayesian update, improve the previous Y estimate through the addition of hydraulic head observations. The relationship between the head and the lnT has been linearized through a perturbative solution of the flow equation. In order to test the proposed approach, synthetic aquifers from literature have been considered. The aquifers in question contain a variety of boundary conditions (both Dirichelet and Neuman type) and scales of heterogeneities (σY2 = 1.0 and σY2 = 5.3). The estimated transmissivity fields were compared to the true one. The joint use of Y* and head measurements improves the estimation of Y considering both degrees of heterogeneity. Even if the variance of the strong transmissivity field can be considered high for the application of the perturbative approach, the results show the same order of approximation of the non-linear methods proposed in literature. The procedure allows to compute the posterior probability distribution of the target quantities and to quantify the uncertainty in the model prediction. Bayesian updating has advantages related both to the Monte-Carlo (MC) and non-MC approaches. In fact, as the MC methods, Bayesian updating allows computing the direct posterior probability distribution of the target quantities and as non-MC methods it has computational times in the order of seconds.

Random forests in non-invasive sensorimotor rhythm brain-computer interfaces: a practical and convenient non-linear classifier.

PubMed

Steyrl, David; Scherer, Reinhold; Faller, Josef; Müller-Putz, Gernot R

2016-02-01

There is general agreement in the brain-computer interface (BCI) community that although non-linear classifiers can provide better results in some cases, linear classifiers are preferable. Particularly, as non-linear classifiers often involve a number of parameters that must be carefully chosen. However, new non-linear classifiers were developed over the last decade. One of them is the random forest (RF) classifier. Although popular in other fields of science, RFs are not common in BCI research. In this work, we address three open questions regarding RFs in sensorimotor rhythm (SMR) BCIs: parametrization, online applicability, and performance compared to regularized linear discriminant analysis (LDA). We found that the performance of RF is constant over a large range of parameter values. We demonstrate - for the first time - that RFs are applicable online in SMR-BCIs. Further, we show in an offline BCI simulation that RFs statistically significantly outperform regularized LDA by about 3%. These results confirm that RFs are practical and convenient non-linear classifiers for SMR-BCIs. Taking into account further properties of RFs, such as independence from feature distributions, maximum margin behavior, multiclass and advanced data mining capabilities, we argue that RFs should be taken into consideration for future BCIs.

Quantum Chemically Estimated Abraham Solute Parameters Using Multiple Solvent-Water Partition Coefficients and Molecular Polarizability.

PubMed

Liang, Yuzhen; Xiong, Ruichang; Sandler, Stanley I; Di Toro, Dominic M

2017-09-05

Polyparameter Linear Free Energy Relationships (pp-LFERs), also called Linear Solvation Energy Relationships (LSERs), are used to predict many environmentally significant properties of chemicals. A method is presented for computing the necessary chemical parameters, the Abraham parameters (AP), used by many pp-LFERs. It employs quantum chemical calculations and uses only the chemical's molecular structure. The method computes the Abraham E parameter using density functional theory computed molecular polarizability and the Clausius-Mossotti equation relating the index refraction to the molecular polarizability, estimates the Abraham V as the COSMO calculated molecular volume, and computes the remaining AP S, A, and B jointly with a multiple linear regression using sixty-five solvent-water partition coefficients computed using the quantum mechanical COSMO-SAC solvation model. These solute parameters, referred to as Quantum Chemically estimated Abraham Parameters (QCAP), are further adjusted by fitting to experimentally based APs using QCAP parameters as the independent variables so that they are compatible with existing Abraham pp-LFERs. QCAP and adjusted QCAP for 1827 neutral chemicals are included. For 24 solvent-water systems including octanol-water, predicted log solvent-water partition coefficients using adjusted QCAP have the smallest root-mean-square errors (RMSEs, 0.314-0.602) compared to predictions made using APs estimated using the molecular fragment based method ABSOLV (0.45-0.716). For munition and munition-like compounds, adjusted QCAP has much lower RMSE (0.860) than does ABSOLV (4.45) which essentially fails for these compounds.

Stationary and non-stationary extreme value modeling of extreme temperature in Malaysia

NASA Astrophysics Data System (ADS)

Hasan, Husna; Salleh, Nur Hanim Mohd; Kassim, Suraiya

2014-09-01

Extreme annual temperature of eighteen stations in Malaysia is fitted to the Generalized Extreme Value distribution. Stationary and non-stationary models with trend are considered for each station and the Likelihood Ratio test is used to determine the best-fitting model. Results show that three out of eighteen stations i.e. Bayan Lepas, Labuan and Subang favor a model which is linear in the location parameter. A hierarchical cluster analysis is employed to investigate the existence of similar behavior among the stations. Three distinct clusters are found in which one of them consists of the stations that favor the non-stationary model. T-year estimated return levels of the extreme temperature are provided based on the chosen models.

Use of simulation tools to illustrate the effect of data management practices for low and negative plate counts on the estimated parameters of microbial reduction models.

PubMed

Garcés-Vega, Francisco; Marks, Bradley P

2014-08-01

In the last 20 years, the use of microbial reduction models has expanded significantly, including inactivation (linear and nonlinear), survival, and transfer models. However, a major constraint for model development is the impossibility to directly quantify the number of viable microorganisms below the limit of detection (LOD) for a given study. Different approaches have been used to manage this challenge, including ignoring negative plate counts, using statistical estimations, or applying data transformations. Our objective was to illustrate and quantify the effect of negative plate count data management approaches on parameter estimation for microbial reduction models. Because it is impossible to obtain accurate plate counts below the LOD, we performed simulated experiments to generate synthetic data for both log-linear and Weibull-type microbial reductions. We then applied five different, previously reported data management practices and fit log-linear and Weibull models to the resulting data. The results indicated a significant effect (α = 0.05) of the data management practices on the estimated model parameters and performance indicators. For example, when the negative plate counts were replaced by the LOD for log-linear data sets, the slope of the subsequent log-linear model was, on average, 22% smaller than for the original data, the resulting model underpredicted lethality by up to 2.0 log, and the Weibull model was erroneously selected as the most likely correct model for those data. The results demonstrate that it is important to explicitly report LODs and related data management protocols, which can significantly affect model results, interpretation, and utility. Ultimately, we recommend using only the positive plate counts to estimate model parameters for microbial reduction curves and avoiding any data value substitutions or transformations when managing negative plate counts to yield the most accurate model parameters.

Improving Forecasts Through Realistic Uncertainty Estimates: A Novel Data Driven Method for Model Uncertainty Quantification in Data Assimilation

NASA Astrophysics Data System (ADS)

Pathiraja, S. D.; Moradkhani, H.; Marshall, L. A.; Sharma, A.; Geenens, G.

2016-12-01

Effective combination of model simulations and observations through Data Assimilation (DA) depends heavily on uncertainty characterisation. Many traditional methods for quantifying model uncertainty in DA require some level of subjectivity (by way of tuning parameters or by assuming Gaussian statistics). Furthermore, the focus is typically on only estimating the first and second moments. We propose a data-driven methodology to estimate the full distributional form of model uncertainty, i.e. the transition density p(xt|xt-1). All sources of uncertainty associated with the model simulations are considered collectively, without needing to devise stochastic perturbations for individual components (such as model input, parameter and structural uncertainty). A training period is used to derive the distribution of errors in observed variables conditioned on hidden states. Errors in hidden states are estimated from the conditional distribution of observed variables using non-linear optimization. The theory behind the framework and case study applications are discussed in detail. Results demonstrate improved predictions and more realistic uncertainty bounds compared to a standard perturbation approach.

A geometric approach to non-linear correlations with intrinsic scatter

NASA Astrophysics Data System (ADS)

Pihajoki, Pauli

2017-12-01

We propose a new mathematical model for n - k-dimensional non-linear correlations with intrinsic scatter in n-dimensional data. The model is based on Riemannian geometry and is naturally symmetric with respect to the measured variables and invariant under coordinate transformations. We combine the model with a Bayesian approach for estimating the parameters of the correlation relation and the intrinsic scatter. A side benefit of the approach is that censored and truncated data sets and independent, arbitrary measurement errors can be incorporated. We also derive analytic likelihoods for the typical astrophysical use case of linear relations in n-dimensional Euclidean space. We pay particular attention to the case of linear regression in two dimensions and compare our results to existing methods. Finally, we apply our methodology to the well-known MBH-σ correlation between the mass of a supermassive black hole in the centre of a galactic bulge and the corresponding bulge velocity dispersion. The main result of our analysis is that the most likely slope of this correlation is ∼6 for the data sets used, rather than the values in the range of ∼4-5 typically quoted in the literature for these data.

Estimating Shape and Micro-Motion Parameter of Rotationally Symmetric Space Objects from the Infrared Signature

PubMed Central

Wu, Yabei; Lu, Huanzhang; Zhao, Fei; Zhang, Zhiyong

2016-01-01

Shape serves as an important additional feature for space target classification, which is complementary to those made available. Since different shapes lead to different projection functions, the projection property can be regarded as one kind of shape feature. In this work, the problem of estimating the projection function from the infrared signature of the object is addressed. We show that the projection function of any rotationally symmetric object can be approximately represented as a linear combination of some base functions. Based on this fact, the signal model of the emissivity-area product sequence is constructed, which is a particular mathematical function of the linear coefficients and micro-motion parameters. Then, the least square estimator is proposed to estimate the projection function and micro-motion parameters jointly. Experiments validate the effectiveness of the proposed method. PMID:27763500

Non-linear effects of soda taxes on consumption and weight outcomes.

PubMed

Fletcher, Jason M; Frisvold, David E; Tefft, Nathan

2015-05-01

The potential health impacts of imposing large taxes on soda to improve population health have been of interest for over a decade. As estimates of the effects of existing soda taxes with low rates suggest little health improvements, recent proposals suggest that large taxes may be effective in reducing weight because of non-linear consumption responses or threshold effects. This paper tests this hypothesis in two ways. First, we estimate non-linear effects of taxes using the range of current rates. Second, we leverage the sudden, relatively large soda tax increase in two states during the early 1990s combined with new synthetic control methods useful for comparative case studies. Our findings suggest virtually no evidence of non-linear or threshold effects. Copyright © 2014 John Wiley & Sons, Ltd.

Mapping forest canopy fuels in Yellowstone National Park using lidar and hyperspectral data

NASA Astrophysics Data System (ADS)

Halligan, Kerry Quinn

The severity and size of wildland fires in the forested western U.S have increased in recent years despite improvements in fire suppression efficiency. This, along with increased density of homes in the wildland-urban interface, has resulted in high costs for fire management and increased risks to human health, safety and property. Crown fires, in comparison to surface fires, pose an especially high risk due to their intensity and high rate of spread. Crown fire models require a range of quantitative fuel parameters which can be difficult and costly to obtain, but advances in lidar and hyperspectral sensor technologies hold promise for delivering these inputs. Further research is needed, however, to assess the strengths and limitations of these technologies and the most appropriate analysis methodologies for estimating crown fuel parameters from these data. This dissertation focuses on retrieving critical crown fuel parameters, including canopy height, canopy bulk density and proportion of dead canopy fuel, from airborne lidar and hyperspectral data. Remote sensing data were used in conjunction with detailed field data on forest parameters and surface reflectance measurements. A new method was developed for retrieving Digital Surface Model (DSM) and Digital Canopy Models (DCM) from first return lidar data. Validation data on individual tree heights demonstrated the high accuracy (r2 0.95) of the DCMs developed via this new algorithm. Lidar-derived DCMs were used to estimate critical crown fire parameters including available canopy fuel, canopy height and canopy bulk density with linear regression model r2 values ranging from 0.75 to 0.85. Hyperspectral data were used in conjunction with Spectral Mixture Analysis (SMA) to assess fuel quality in the form of live versus dead canopy proportions. Severity and stage of insect-caused forest mortality were estimated using the fractional abundance of green vegetation, non-photosynthetic vegetation and shade obtained from SMA. Proportion of insect attack was estimated with a linear model producing an r2 of 0.6 using SMA and bark endmembers from image and reference libraries. Fraction of red attack, with a possible link to increased crown fire risk, was estimated with an r2 of 0.45.

A statistical methodology for estimating transport parameters: Theory and applications to one-dimensional advectivec-dispersive systems

USGS Publications Warehouse

Wagner, Brian J.; Gorelick, Steven M.

1986-01-01

A simulation nonlinear multiple-regression methodology for estimating parameters that characterize the transport of contaminants is developed and demonstrated. Finite difference contaminant transport simulation is combined with a nonlinear weighted least squares multiple-regression procedure. The technique provides optimal parameter estimates and gives statistics for assessing the reliability of these estimates under certain general assumptions about the distributions of the random measurement errors. Monte Carlo analysis is used to estimate parameter reliability for a hypothetical homogeneous soil column for which concentration data contain large random measurement errors. The value of data collected spatially versus data collected temporally was investigated for estimation of velocity, dispersion coefficient, effective porosity, first-order decay rate, and zero-order production. The use of spatial data gave estimates that were 2–3 times more reliable than estimates based on temporal data for all parameters except velocity. Comparison of estimated linear and nonlinear confidence intervals based upon Monte Carlo analysis showed that the linear approximation is poor for dispersion coefficient and zero-order production coefficient when data are collected over time. In addition, examples demonstrate transport parameter estimation for two real one-dimensional systems. First, the longitudinal dispersivity and effective porosity of an unsaturated soil are estimated using laboratory column data. We compare the reliability of estimates based upon data from individual laboratory experiments versus estimates based upon pooled data from several experiments. Second, the simulation nonlinear regression procedure is extended to include an additional governing equation that describes delayed storage during contaminant transport. The model is applied to analyze the trends, variability, and interrelationship of parameters in a mourtain stream in northern California.

Inverse problem of HIV cell dynamics using Genetic Algorithms

NASA Astrophysics Data System (ADS)

González, J. A.; Guzmán, F. S.

2017-01-01

In order to describe the cell dynamics of T-cells in a patient infected with HIV, we use a flavour of Perelson's model. This is a non-linear system of Ordinary Differential Equations that describes the evolution of healthy, latently infected, infected T-cell concentrations and the free viral cells. Different parameters in the equations give different dynamics. Considering the concentration of these types of cells is known for a particular patient, the inverse problem consists in estimating the parameters in the model. We solve this inverse problem using a Genetic Algorithm (GA) that minimizes the error between the solutions of the model and the data from the patient. These errors depend on the parameters of the GA, like mutation rate and population, although a detailed analysis of this dependence will be described elsewhere.

A non-linear data mining parameter selection algorithm for continuous variables

PubMed Central

Razavi, Marianne; Brady, Sean

2017-01-01

In this article, we propose a new data mining algorithm, by which one can both capture the non-linearity in data and also find the best subset model. To produce an enhanced subset of the original variables, a preferred selection method should have the potential of adding a supplementary level of regression analysis that would capture complex relationships in the data via mathematical transformation of the predictors and exploration of synergistic effects of combined variables. The method that we present here has the potential to produce an optimal subset of variables, rendering the overall process of model selection more efficient. This algorithm introduces interpretable parameters by transforming the original inputs and also a faithful fit to the data. The core objective of this paper is to introduce a new estimation technique for the classical least square regression framework. This new automatic variable transformation and model selection method could offer an optimal and stable model that minimizes the mean square error and variability, while combining all possible subset selection methodology with the inclusion variable transformations and interactions. Moreover, this method controls multicollinearity, leading to an optimal set of explanatory variables. PMID:29131829

Nonlinear method for including the mass uncertainty of standards and the system measurement errors in the fitting of calibration curves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pickles, W.L.; McClure, J.W.; Howell, R.H.

1978-01-01

A sophisticated non-linear multiparameter fitting program has been used to produce a best fit calibration curve for the response of an x-ray fluorescence analyzer to uranium nitrate, freeze dried, 0.2% accurate, gravimetric standards. The program is based on unconstrained minimization subroutine, VA02A. The program considers the mass values of the gravimetric standards as parameters to be fit along with the normal calibration curve parameters. The fitting procedure weights with the system errors and the mass errors in a consistent way. The resulting best fit calibration curve parameters reflect the fact that the masses of the standard samples are measured quantitiesmore » with a known error. Error estimates for the calibration curve parameters can be obtined from the curvature of the Chi-Squared Matrix or from error relaxation techniques. It has been shown that non-dispersive x-ray fluorescence analysis of 0.1 to 1 mg freeze-dried UNO/sub 3/ can have an accuracy of 0.2% in 1000 sec.« less

Use of an anaerobic sequencing batch reactor for parameter estimation in modelling of anaerobic digestion.

PubMed

Batstone, D J; Torrijos, M; Ruiz, C; Schmidt, J E

2004-01-01

The model structure in anaerobic digestion has been clarified following publication of the IWA Anaerobic Digestion Model No. 1 (ADM1). However, parameter values are not well known, and uncertainty and variability in the parameter values given is almost unknown. Additionally, platforms for identification of parameters, namely continuous-flow laboratory digesters, and batch tests suffer from disadvantages such as long run times, and difficulty in defining initial conditions, respectively. Anaerobic sequencing batch reactors (ASBRs) are sequenced into fill-react-settle-decant phases, and offer promising possibilities for estimation of parameters, as they are by nature, dynamic in behaviour, and allow repeatable behaviour to establish initial conditions, and evaluate parameters. In this study, we estimated parameters describing winery wastewater (most COD as ethanol) degradation using data from sequencing operation, and validated these parameters using unsequenced pulses of ethanol and acetate. The model used was the ADM1, with an extension for ethanol degradation. Parameter confidence spaces were found by non-linear, correlated analysis of the two main Monod parameters; maximum uptake rate (k(m)), and half saturation concentration (K(S)). These parameters could be estimated together using only the measured acetate concentration (20 points per cycle). From interpolating the single cycle acetate data to multiple cycles, we estimate that a practical "optimal" identifiability could be achieved after two cycles for the acetate parameters, and three cycles for the ethanol parameters. The parameters found performed well in the short term, and represented the pulses of acetate and ethanol (within 4 days of the winery-fed cycles) very well. The main discrepancy was poor prediction of pH dynamics, which could be due to an unidentified buffer with an overall influence the same as a weak base (possibly CaCO3). Based on this work, ASBR systems are effective for parameter estimation, especially for comparative wastewater characterisation. The main disadvantages are heavy computational requirements for multiple cycles, and difficulty in establishing the correct biomass concentration in the reactor, though the last is also a disadvantage for continuous fixed film reactors, and especially, batch tests.

Estimating neural response functions from fMRI

PubMed Central

Kumar, Sukhbinder; Penny, William

2014-01-01

This paper proposes a methodology for estimating Neural Response Functions (NRFs) from fMRI data. These NRFs describe non-linear relationships between experimental stimuli and neuronal population responses. The method is based on a two-stage model comprising an NRF and a Hemodynamic Response Function (HRF) that are simultaneously fitted to fMRI data using a Bayesian optimization algorithm. This algorithm also produces a model evidence score, providing a formal model comparison method for evaluating alternative NRFs. The HRF is characterized using previously established “Balloon” and BOLD signal models. We illustrate the method with two example applications based on fMRI studies of the auditory system. In the first, we estimate the time constants of repetition suppression and facilitation, and in the second we estimate the parameters of population receptive fields in a tonotopic mapping study. PMID:24847246

Sensitivity-based virtual fields for the non-linear virtual fields method

NASA Astrophysics Data System (ADS)

Marek, Aleksander; Davis, Frances M.; Pierron, Fabrice

2017-09-01

The virtual fields method is an approach to inversely identify material parameters using full-field deformation data. In this manuscript, a new set of automatically-defined virtual fields for non-linear constitutive models has been proposed. These new sensitivity-based virtual fields reduce the influence of noise on the parameter identification. The sensitivity-based virtual fields were applied to a numerical example involving small strain plasticity; however, the general formulation derived for these virtual fields is applicable to any non-linear constitutive model. To quantify the improvement offered by these new virtual fields, they were compared with stiffness-based and manually defined virtual fields. The proposed sensitivity-based virtual fields were consistently able to identify plastic model parameters and outperform the stiffness-based and manually defined virtual fields when the data was corrupted by noise.

Maximum Marginal Likelihood Estimation of a Monotonic Polynomial Generalized Partial Credit Model with Applications to Multiple Group Analysis.

PubMed

Falk, Carl F; Cai, Li

2016-06-01

We present a semi-parametric approach to estimating item response functions (IRF) useful when the true IRF does not strictly follow commonly used functions. Our approach replaces the linear predictor of the generalized partial credit model with a monotonic polynomial. The model includes the regular generalized partial credit model at the lowest order polynomial. Our approach extends Liang's (A semi-parametric approach to estimate IRFs, Unpublished doctoral dissertation, 2007) method for dichotomous item responses to the case of polytomous data. Furthermore, item parameter estimation is implemented with maximum marginal likelihood using the Bock-Aitkin EM algorithm, thereby facilitating multiple group analyses useful in operational settings. Our approach is demonstrated on both educational and psychological data. We present simulation results comparing our approach to more standard IRF estimation approaches and other non-parametric and semi-parametric alternatives.

Optical Method for Estimating the Chlorophyll Contents in Plant Leaves.

PubMed

Pérez-Patricio, Madaín; Camas-Anzueto, Jorge Luis; Sanchez-Alegría, Avisaí; Aguilar-González, Abiel; Gutiérrez-Miceli, Federico; Escobar-Gómez, Elías; Voisin, Yvon; Rios-Rojas, Carlos; Grajales-Coutiño, Ruben

2018-02-22

This work introduces a new vision-based approach for estimating chlorophyll contents in a plant leaf using reflectance and transmittance as base parameters. Images of the top and underside of the leaf are captured. To estimate the base parameters (reflectance/transmittance), a novel optical arrangement is proposed. The chlorophyll content is then estimated by using linear regression where the inputs are the reflectance and transmittance of the leaf. Performance of the proposed method for chlorophyll content estimation was compared with a spectrophotometer and a Soil Plant Analysis Development (SPAD) meter. Chlorophyll content estimation was realized for Lactuca sativa L., Azadirachta indica , Canavalia ensiforme , and Lycopersicon esculentum . Experimental results showed that-in terms of accuracy and processing speed-the proposed algorithm outperformed many of the previous vision-based approach methods that have used SPAD as a reference device. On the other hand, the accuracy reached is 91% for crops such as Azadirachta indica , where the chlorophyll value was obtained using the spectrophotometer. Additionally, it was possible to achieve an estimation of the chlorophyll content in the leaf every 200 ms with a low-cost camera and a simple optical arrangement. This non-destructive method increased accuracy in the chlorophyll content estimation by using an optical arrangement that yielded both the reflectance and transmittance information, while the required hardware is cheap.

Modeling Complex Equilibria in ITC Experiments: Thermodynamic Parameters Estimation for a Three Binding Site Model

PubMed Central

Le, Vu H.; Buscaglia, Robert; Chaires, Jonathan B.; Lewis, Edwin A.

2013-01-01

Isothermal Titration Calorimetry, ITC, is a powerful technique that can be used to estimate a complete set of thermodynamic parameters (e.g. Keq (or ΔG), ΔH, ΔS, and n) for a ligand binding interaction described by a thermodynamic model. Thermodynamic models are constructed by combination of equilibrium constant, mass balance, and charge balance equations for the system under study. Commercial ITC instruments are supplied with software that includes a number of simple interaction models, for example one binding site, two binding sites, sequential sites, and n-independent binding sites. More complex models for example, three or more binding sites, one site with multiple binding mechanisms, linked equilibria, or equilibria involving macromolecular conformational selection through ligand binding need to be developed on a case by case basis by the ITC user. In this paper we provide an algorithm (and a link to our MATLAB program) for the non-linear regression analysis of a multiple binding site model with up to four overlapping binding equilibria. Error analysis demonstrates that fitting ITC data for multiple parameters (e.g. up to nine parameters in the three binding site model) yields thermodynamic parameters with acceptable accuracy. PMID:23262283

A theoretical signal processing framework for linear diffusion MRI: Implications for parameter estimation and experiment design.

PubMed

Varadarajan, Divya; Haldar, Justin P

2017-11-01

The data measured in diffusion MRI can be modeled as the Fourier transform of the Ensemble Average Propagator (EAP), a probability distribution that summarizes the molecular diffusion behavior of the spins within each voxel. This Fourier relationship is potentially advantageous because of the extensive theory that has been developed to characterize the sampling requirements, accuracy, and stability of linear Fourier reconstruction methods. However, existing diffusion MRI data sampling and signal estimation methods have largely been developed and tuned without the benefit of such theory, instead relying on approximations, intuition, and extensive empirical evaluation. This paper aims to address this discrepancy by introducing a novel theoretical signal processing framework for diffusion MRI. The new framework can be used to characterize arbitrary linear diffusion estimation methods with arbitrary q-space sampling, and can be used to theoretically evaluate and compare the accuracy, resolution, and noise-resilience of different data acquisition and parameter estimation techniques. The framework is based on the EAP, and makes very limited modeling assumptions. As a result, the approach can even provide new insight into the behavior of model-based linear diffusion estimation methods in contexts where the modeling assumptions are inaccurate. The practical usefulness of the proposed framework is illustrated using both simulated and real diffusion MRI data in applications such as choosing between different parameter estimation methods and choosing between different q-space sampling schemes. Copyright © 2017 Elsevier Inc. All rights reserved.

A population pharmacokinetic model of valproic acid in pediatric patients with epilepsy: a non-linear pharmacokinetic model based on protein-binding saturation.

PubMed

Ding, Junjie; Wang, Yi; Lin, Weiwei; Wang, Changlian; Zhao, Limei; Li, Xingang; Zhao, Zhigang; Miao, Liyan; Jiao, Zheng

2015-03-01

Valproic acid (VPA) follows a non-linear pharmacokinetic profile in terms of protein-binding saturation. The total daily dose regarding VPA clearance is a simple power function, which may partially explain the non-linearity of the pharmacokinetic profile; however, it may be confounded by the therapeutic drug monitoring effect. The aim of this study was to develop a population pharmacokinetic model for VPA based on protein-binding saturation in pediatric patients with epilepsy. A total of 1,107 VPA serum trough concentrations at steady state were collected from 902 epileptic pediatric patients aged from 3 weeks to 14 years at three hospitals. The population pharmacokinetic model was developed using NONMEM(®) software. The ability of three candidate models (the simple power exponent model, the dose-dependent maximum effect [DDE] model, and the protein-binding model) to describe the non-linear pharmacokinetic profile of VPA was investigated, and potential covariates were screened using a stepwise approach. Bootstrap, normalized prediction distribution errors and external evaluations from two independent studies were performed to determine the stability and predictive performance of the candidate models. The age-dependent exponent model described the effects of body weight and age on the clearance well. Co-medication with carbamazepine was identified as a significant covariate. The DDE model best fitted the aim of this study, although there were no obvious differences in the predictive performances. The condition number was less than 500, and the precision of the parameter estimates was less than 30 %, indicating stability and validity of the final model. The DDE model successfully described the non-linear pharmacokinetics of VPA. Furthermore, the proposed population pharmacokinetic model of VPA can be used to design rational dosage regimens to achieve desirable serum concentrations.

Retrieval of Spatio-temporal Distributions of Particle Parameters from Multiwavelength Lidar Measurements Using the Linear Estimation Technique and Comparison with AERONET

NASA Technical Reports Server (NTRS)

Veselovskii, I.; Whiteman, D. N.; Korenskiy, M.; Kolgotin, A.; Dubovik, O.; Perez-Ramirez, D.; Suvorina, A.

2013-01-01

The results of the application of the linear estimation technique to multiwavelength Raman lidar measurements performed during the summer of 2011 in Greenbelt, MD, USA, are presented. We demonstrate that multiwavelength lidars are capable not only of providing vertical profiles of particle properties but also of revealing the spatio-temporal evolution of aerosol features. The nighttime 3 Beta + 1 alpha lidar measurements on 21 and 22 July were inverted to spatio-temporal distributions of particle microphysical parameters, such as volume, number density, effective radius and the complex refractive index. The particle volume and number density show strong variation during the night, while the effective radius remains approximately constant. The real part of the refractive index demonstrates a slight decreasing tendency in a region of enhanced extinction coefficient. The linear estimation retrievals are stable and provide time series of particle parameters as a function of height at 4 min resolution. AERONET observations are compared with multiwavelength lidar retrievals showing good agreement.

Application of a baseflow filter for evaluating model structure suitability of the IHACRES CMD

NASA Astrophysics Data System (ADS)

Kim, H. S.

2015-02-01

The main objective of this study was to assess the predictive uncertainty from the rainfall-runoff model structure coupling a conceptual module (non-linear module) with a metric transfer function module (linear module). The methodology was primarily based on the comparison between the outputs of the rainfall-runoff model and those from an alternative model approach. An alternative model approach was used to minimise uncertainties arising from data and the model structure. A baseflow filter was adopted to better understand deficiencies in the forms of the rainfall-runoff model by avoiding the uncertainties related to data and the model structure. The predictive uncertainty from the model structure was investigated for representative groups of catchments having similar hydrological response characteristics in the upper Murrumbidgee Catchment. In the assessment of model structure suitability, the consistency (or variability) of catchment response over time and space in model performance and parameter values has been investigated to detect problems related to the temporal and spatial variability of the model accuracy. The predictive error caused by model uncertainty was evaluated through analysis of the variability of the model performance and parameters. A graphical comparison of model residuals, effective rainfall estimates and hydrographs was used to determine a model's ability related to systematic model deviation between simulated and observed behaviours and general behavioural differences in the timing and magnitude of peak flows. The model's predictability was very sensitive to catchment response characteristics. The linear module performs reasonably well in the wetter catchments but has considerable difficulties when applied to the drier catchments where a hydrologic response is dominated by quick flow. The non-linear module has a potential limitation in its capacity to capture non-linear processes for converting observed rainfall into effective rainfall in both the wetter and drier catchments. The comparative study based on a better quantification of the accuracy and precision of hydrological modelling predictions yields a better understanding for the potential improvement of model deficiencies.

Information theoretic analysis of canny edge detection in visual communication

NASA Astrophysics Data System (ADS)

Jiang, Bo; Rahman, Zia-ur

2011-06-01

In general edge detection evaluation, the edge detectors are examined, analyzed, and compared either visually or with a metric for specific an application. This analysis is usually independent of the characteristics of the image-gathering, transmission and display processes that do impact the quality of the acquired image and thus, the resulting edge image. We propose a new information theoretic analysis of edge detection that unites the different components of the visual communication channel and assesses edge detection algorithms in an integrated manner based on Shannon's information theory. The edge detection algorithm here is considered to achieve high performance only if the information rate from the scene to the edge approaches the maximum possible. Thus, by setting initial conditions of the visual communication system as constant, different edge detection algorithms could be evaluated. This analysis is normally limited to linear shift-invariant filters so in order to examine the Canny edge operator in our proposed system, we need to estimate its "power spectral density" (PSD). Since the Canny operator is non-linear and shift variant, we perform the estimation for a set of different system environment conditions using simulations. In our paper we will first introduce the PSD of the Canny operator for a range of system parameters. Then, using the estimated PSD, we will assess the Canny operator using information theoretic analysis. The information-theoretic metric is also used to compare the performance of the Canny operator with other edge-detection operators. This also provides a simple tool for selecting appropriate edgedetection algorithms based on system parameters, and for adjusting their parameters to maximize information throughput.

Trends in hydrological extremes in the Senegal and the Niger Rivers

NASA Astrophysics Data System (ADS)

Wilcox, C.; Bodian, A.; Vischel, T.; Panthou, G.; Quantin, G.

2017-12-01

In recent years, West Africa has witnessed several floods of unprecedented magnitude. Although the evolution of hydrological extremes has been evaluated in the region to some extent, results lack regional coverage, significance levels, uncertainty estimations, model selection criteria, or a combination of the above. In this study, Generalized Extreme Value (GEV) distributions with and without various non-stationary temporal covariates are applied to annual maxima of daily discharge (AMAX) data sets in the Sudano-Guinean part of the Senegal River basin and in the Sahelian part of the Niger River basin. The data ranges from the 1950s to the 2010s. The two models of best fit most often selected (with an alpha=0.05 certainty level) were 1) a double-linear model for the central tendency parameter (μ) with stationary dispersion (σ) and 2) a double-linear model for both parameters. Change points are relatively consistent for the Senegal basin, with stations switching from a decreasing streamflow trend to an increasing streamflow trend in the early 1980s. In the Niger basin the trend in μ was generally positive with an increase in slope after the change point, but the change point location was less consistent. The study clearly demonstrates the significant trends in extreme discharge values in West Africa over the past six decades. Moreover, it proposes a clear methodology for comparing GEV models and selecting the best for use. The return levels generated from the chosen models can be applied to river basin management and hydraulic works sizing. The results provide a first evaluation of non-stationarity in extreme hydrological values in West Africa that is accompanied by significance levels, uncertainties, and non-stationary return level estimations .

Modeling and Compensating Temperature-Dependent Non-Uniformity Noise in IR Microbolometer Cameras

PubMed Central

Wolf, Alejandro; Pezoa, Jorge E.; Figueroa, Miguel

2016-01-01

Images rendered by uncooled microbolometer-based infrared (IR) cameras are severely degraded by the spatial non-uniformity (NU) noise. The NU noise imposes a fixed-pattern over the true images, and the intensity of the pattern changes with time due to the temperature instability of such cameras. In this paper, we present a novel model and a compensation algorithm for the spatial NU noise and its temperature-dependent variations. The model separates the NU noise into two components: a constant term, which corresponds to a set of NU parameters determining the spatial structure of the noise, and a dynamic term, which scales linearly with the fluctuations of the temperature surrounding the array of microbolometers. We use a black-body radiator and samples of the temperature surrounding the IR array to offline characterize both the constant and the temperature-dependent NU noise parameters. Next, the temperature-dependent variations are estimated online using both a spatially uniform Hammerstein-Wiener estimator and a pixelwise least mean squares (LMS) estimator. We compensate for the NU noise in IR images from two long-wave IR cameras. Results show an excellent NU correction performance and a root mean square error of less than 0.25 ∘C, when the array’s temperature varies by approximately 15 ∘C. PMID:27447637

Stochastic Estimation and Non-Linear Wall-Pressure Sources in a Separating/Reattaching Flow

NASA Technical Reports Server (NTRS)

Naguib, A.; Hudy, L.; Humphreys, W. M., Jr.

2002-01-01

Simultaneous wall-pressure and PIV measurements are used to study the conditional flow field associated with surface-pressure generation in a separating/reattaching flow established over a fence-with-splitter-plate geometry. The conditional flow field is captured using linear and quadratic stochastic estimation based on the occurrence of positive and negative pressure events in the vicinity of the mean reattachment location. The results shed light on the dominant flow structures associated with significant wall-pressure generation. Furthermore, analysis based on the individual terms in the stochastic estimation expansion shows that both the linear and non-linear flow sources of the coherent (conditional) velocity field are equally important contributors to the generation of the conditional surface pressure.

Optimal hemodynamic response model for functional near-infrared spectroscopy

PubMed Central

Kamran, Muhammad A.; Jeong, Myung Yung; Mannan, Malik M. N.

2015-01-01

Functional near-infrared spectroscopy (fNIRS) is an emerging non-invasive brain imaging technique and measures brain activities by means of near-infrared light of 650–950 nm wavelengths. The cortical hemodynamic response (HR) differs in attributes at different brain regions and on repetition of trials, even if the experimental paradigm is kept exactly the same. Therefore, an HR model that can estimate such variations in the response is the objective of this research. The canonical hemodynamic response function (cHRF) is modeled by two Gamma functions with six unknown parameters (four of them to model the shape and other two to scale and baseline respectively). The HRF model is supposed to be a linear combination of HRF, baseline, and physiological noises (amplitudes and frequencies of physiological noises are supposed to be unknown). An objective function is developed as a square of the residuals with constraints on 12 free parameters. The formulated problem is solved by using an iterative optimization algorithm to estimate the unknown parameters in the model. Inter-subject variations in HRF and physiological noises have been estimated for better cortical functional maps. The accuracy of the algorithm has been verified using 10 real and 15 simulated data sets. Ten healthy subjects participated in the experiment and their HRF for finger-tapping tasks have been estimated and analyzed. The statistical significance of the estimated activity strength parameters has been verified by employing statistical analysis (i.e., t-value > tcritical and p-value < 0.05). PMID:26136668

Optimal hemodynamic response model for functional near-infrared spectroscopy.

PubMed

Kamran, Muhammad A; Jeong, Myung Yung; Mannan, Malik M N

2015-01-01

Functional near-infrared spectroscopy (fNIRS) is an emerging non-invasive brain imaging technique and measures brain activities by means of near-infrared light of 650-950 nm wavelengths. The cortical hemodynamic response (HR) differs in attributes at different brain regions and on repetition of trials, even if the experimental paradigm is kept exactly the same. Therefore, an HR model that can estimate such variations in the response is the objective of this research. The canonical hemodynamic response function (cHRF) is modeled by two Gamma functions with six unknown parameters (four of them to model the shape and other two to scale and baseline respectively). The HRF model is supposed to be a linear combination of HRF, baseline, and physiological noises (amplitudes and frequencies of physiological noises are supposed to be unknown). An objective function is developed as a square of the residuals with constraints on 12 free parameters. The formulated problem is solved by using an iterative optimization algorithm to estimate the unknown parameters in the model. Inter-subject variations in HRF and physiological noises have been estimated for better cortical functional maps. The accuracy of the algorithm has been verified using 10 real and 15 simulated data sets. Ten healthy subjects participated in the experiment and their HRF for finger-tapping tasks have been estimated and analyzed. The statistical significance of the estimated activity strength parameters has been verified by employing statistical analysis (i.e., t-value > t critical and p-value < 0.05).

Estimation of regression laws for ground motion parameters using as case of study the Amatrice earthquake

NASA Astrophysics Data System (ADS)

Tiberi, Lara; Costa, Giovanni

2017-04-01

The possibility to directly associate the damages to the ground motion parameters is always a great challenge, in particular for civil protections. Indeed a ground motion parameter, estimated in near real time that can express the damages occurred after an earthquake, is fundamental to arrange the first assistance after an event. The aim of this work is to contribute to the estimation of the ground motion parameter that better describes the observed intensity, immediately after an event. This can be done calculating for each ground motion parameter estimated in a near real time mode a regression law which correlates the above-mentioned parameter to the observed macro-seismic intensity. This estimation is done collecting high quality accelerometric data in near field, filtering them at different frequency steps. The regression laws are calculated using two different techniques: the non linear least-squares (NLLS) Marquardt-Levenberg algorithm and the orthogonal distance methodology (ODR). The limits of the first methodology are the needed of initial values for the parameters a and b (set 1.0 in this study), and the constraint that the independent variable must be known with greater accuracy than the dependent variable. While the second algorithm is based on the estimation of the errors perpendicular to the line, rather than just vertically. The vertical errors are just the errors in the 'y' direction, so only for the dependent variable whereas the perpendicular errors take into account errors for both the variables, the dependent and the independent. This makes possible also to directly invert the relation, so the a and b values can be used also to express the gmps as function of I. For each law the standard deviation and R2 value are estimated in order to test the quality and the reliability of the found relation. The Amatrice earthquake of 24th August of 2016 is used as case of study to test the goodness of the calculated regression laws.

Reflectance Estimation from Urban Terrestrial Images: Validation of a Symbolic Ray-Tracing Method on Synthetic Data

NASA Astrophysics Data System (ADS)

Coubard, F.; Brédif, M.; Paparoditis, N.; Briottet, X.

2011-04-01

Terrestrial geolocalized images are nowadays widely used on the Internet, mainly in urban areas, through immersion services such as Google Street View. On the long run, we seek to enhance the visualization of these images; for that purpose, radiometric corrections must be performed to free them from illumination conditions at the time of acquisition. Given the simultaneously acquired 3D geometric model of the scene with LIDAR or vision techniques, we face an inverse problem where the illumination and the geometry of the scene are known and the reflectance of the scene is to be estimated. Our main contribution is the introduction of a symbolic ray-tracing rendering to generate parametric images, for quick evaluation and comparison with the acquired images. The proposed approach is then based on an iterative estimation of the reflectance parameters of the materials, using a single rendering pre-processing. We validate the method on synthetic data with linear BRDF models and discuss the limitations of the proposed approach with more general non-linear BRDF models.

Runoff load estimation of particulate and dissolved nitrogen in Lake Inba watershed using continuous monitoring data on turbidity and electric conductivity.

PubMed

Kim, J; Nagano, Y; Furumai, H

2012-01-01

Easy-to-measure surrogate parameters for water quality indicators are needed for real time monitoring as well as for generating data for model calibration and validation. In this study, a novel linear regression model for estimating total nitrogen (TN) based on two surrogate parameters is proposed based on evaluation of pollutant loads flowing into a eutrophic lake. Based on their runoff characteristics during wet weather, electric conductivity (EC) and turbidity were selected as surrogates for particulate nitrogen (PN) and dissolved nitrogen (DN), respectively. Strong linear relationships were established between PN and turbidity and DN and EC, and both models subsequently combined for estimation of TN. This model was evaluated by comparison of estimated and observed TN runoff loads during rainfall events. This analysis showed that turbidity and EC are viable surrogates for PN and DN, respectively, and that the linear regression model for TN concentration was successful in estimating TN runoff loads during rainfall events and also under dry weather conditions.

Modelling lactation curve for milk fat to protein ratio in Iranian buffaloes (Bubalus bubalis) using non-linear mixed models.

PubMed

Hossein-Zadeh, Navid Ghavi

2016-08-01

The aim of this study was to compare seven non-linear mathematical models (Brody, Wood, Dhanoa, Sikka, Nelder, Rook and Dijkstra) to examine their efficiency in describing the lactation curves for milk fat to protein ratio (FPR) in Iranian buffaloes. Data were 43 818 test-day records for FPR from the first three lactations of Iranian buffaloes which were collected on 523 dairy herds in the period from 1996 to 2012 by the Animal Breeding Center of Iran. Each model was fitted to monthly FPR records of buffaloes using the non-linear mixed model procedure (PROC NLMIXED) in SAS and the parameters were estimated. The models were tested for goodness of fit using Akaike's information criterion (AIC), Bayesian information criterion (BIC) and log maximum likelihood (-2 Log L). The Nelder and Sikka mixed models provided the best fit of lactation curve for FPR in the first and second lactations of Iranian buffaloes, respectively. However, Wood, Dhanoa and Sikka mixed models provided the best fit of lactation curve for FPR in the third parity buffaloes. Evaluation of first, second and third lactation features showed that all models, except for Dijkstra model in the third lactation, under-predicted test time at which daily FPR was minimum. On the other hand, minimum FPR was over-predicted by all equations. Evaluation of the different models used in this study indicated that non-linear mixed models were sufficient for fitting test-day FPR records of Iranian buffaloes.

Non-linear dynamical classification of short time series of the rössler system in high noise regimes.

PubMed

Lainscsek, Claudia; Weyhenmeyer, Jonathan; Hernandez, Manuel E; Poizner, Howard; Sejnowski, Terrence J

2013-01-01

Time series analysis with delay differential equations (DDEs) reveals non-linear properties of the underlying dynamical system and can serve as a non-linear time-domain classification tool. Here global DDE models were used to analyze short segments of simulated time series from a known dynamical system, the Rössler system, in high noise regimes. In a companion paper, we apply the DDE model developed here to classify short segments of encephalographic (EEG) data recorded from patients with Parkinson's disease and healthy subjects. Nine simulated subjects in each of two distinct classes were generated by varying the bifurcation parameter b and keeping the other two parameters (a and c) of the Rössler system fixed. All choices of b were in the chaotic parameter range. We diluted the simulated data using white noise ranging from 10 to -30 dB signal-to-noise ratios (SNR). Structure selection was supervised by selecting the number of terms, delays, and order of non-linearity of the model DDE model that best linearly separated the two classes of data. The distances d from the linear dividing hyperplane was then used to assess the classification performance by computing the area A' under the ROC curve. The selected model was tested on untrained data using repeated random sub-sampling validation. DDEs were able to accurately distinguish the two dynamical conditions, and moreover, to quantify the changes in the dynamics. There was a significant correlation between the dynamical bifurcation parameter b of the simulated data and the classification parameter d from our analysis. This correlation still held for new simulated subjects with new dynamical parameters selected from each of the two dynamical regimes. Furthermore, the correlation was robust to added noise, being significant even when the noise was greater than the signal. We conclude that DDE models may be used as a generalizable and reliable classification tool for even small segments of noisy data.

Non-Linear Dynamical Classification of Short Time Series of the Rössler System in High Noise Regimes

PubMed Central

Lainscsek, Claudia; Weyhenmeyer, Jonathan; Hernandez, Manuel E.; Poizner, Howard; Sejnowski, Terrence J.

2013-01-01

Time series analysis with delay differential equations (DDEs) reveals non-linear properties of the underlying dynamical system and can serve as a non-linear time-domain classification tool. Here global DDE models were used to analyze short segments of simulated time series from a known dynamical system, the Rössler system, in high noise regimes. In a companion paper, we apply the DDE model developed here to classify short segments of encephalographic (EEG) data recorded from patients with Parkinson’s disease and healthy subjects. Nine simulated subjects in each of two distinct classes were generated by varying the bifurcation parameter b and keeping the other two parameters (a and c) of the Rössler system fixed. All choices of b were in the chaotic parameter range. We diluted the simulated data using white noise ranging from 10 to −30 dB signal-to-noise ratios (SNR). Structure selection was supervised by selecting the number of terms, delays, and order of non-linearity of the model DDE model that best linearly separated the two classes of data. The distances d from the linear dividing hyperplane was then used to assess the classification performance by computing the area A′ under the ROC curve. The selected model was tested on untrained data using repeated random sub-sampling validation. DDEs were able to accurately distinguish the two dynamical conditions, and moreover, to quantify the changes in the dynamics. There was a significant correlation between the dynamical bifurcation parameter b of the simulated data and the classification parameter d from our analysis. This correlation still held for new simulated subjects with new dynamical parameters selected from each of the two dynamical regimes. Furthermore, the correlation was robust to added noise, being significant even when the noise was greater than the signal. We conclude that DDE models may be used as a generalizable and reliable classification tool for even small segments of noisy data. PMID:24379798

Aerodynamic parameter estimation via Fourier modulating function techniques

NASA Technical Reports Server (NTRS)

Pearson, A. E.

1995-01-01

Parameter estimation algorithms are developed in the frequency domain for systems modeled by input/output ordinary differential equations. The approach is based on Shinbrot's method of moment functionals utilizing Fourier based modulating functions. Assuming white measurement noises for linear multivariable system models, an adaptive weighted least squares algorithm is developed which approximates a maximum likelihood estimate and cannot be biased by unknown initial or boundary conditions in the data owing to a special property attending Shinbrot-type modulating functions. Application is made to perturbation equation modeling of the longitudinal and lateral dynamics of a high performance aircraft using flight-test data. Comparative studies are included which demonstrate potential advantages of the algorithm relative to some well established techniques for parameter identification. Deterministic least squares extensions of the approach are made to the frequency transfer function identification problem for linear systems and to the parameter identification problem for a class of nonlinear-time-varying differential system models.

System Identification Applied to Dynamic CFD Simulation and Wind Tunnel Data

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.; Klein, Vladislav; Frink, Neal T.; Vicroy, Dan D.

2011-01-01

Demanding aerodynamic modeling requirements for military and civilian aircraft have provided impetus for researchers to improve computational and experimental techniques. Model validation is a key component for these research endeavors so this study is an initial effort to extend conventional time history comparisons by comparing model parameter estimates and their standard errors using system identification methods. An aerodynamic model of an aircraft performing one-degree-of-freedom roll oscillatory motion about its body axes is developed. The model includes linear aerodynamics and deficiency function parameters characterizing an unsteady effect. For estimation of unknown parameters two techniques, harmonic analysis and two-step linear regression, were applied to roll-oscillatory wind tunnel data and to computational fluid dynamics (CFD) simulated data. The model used for this study is a highly swept wing unmanned aerial combat vehicle. Differences in response prediction, parameters estimates, and standard errors are compared and discussed

Standard and goodness-of-fit parameter estimation methods for the three-parameter lognormal distribution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kane, V.E.

1982-01-01

A class of goodness-of-fit estimators is found to provide a useful alternative in certain situations to the standard maximum likelihood method which has some undesirable estimation characteristics for estimation from the three-parameter lognormal distribution. The class of goodness-of-fit tests considered include the Shapiro-Wilk and Filliben tests which reduce to a weighted linear combination of the order statistics that can be maximized in estimation problems. The weighted order statistic estimators are compared to the standard procedures in Monte Carlo simulations. Robustness of the procedures are examined and example data sets analyzed.

Non-linear feedback control of the p53 protein-mdm2 inhibitor system using the derivative-free non-linear Kalman filter.

PubMed

Rigatos, Gerasimos G

2016-06-01

It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.

Selection of optimal oligonucleotide probes for microarrays usingmultiple criteria, global alignment and parameter estimation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Xingyuan; He, Zhili; Zhou, Jizhong

2005-10-30

The oligonucleotide specificity for microarray hybridizationcan be predicted by its sequence identity to non-targets, continuousstretch to non-targets, and/or binding free energy to non-targets. Mostcurrently available programs only use one or two of these criteria, whichmay choose 'false' specific oligonucleotides or miss 'true' optimalprobes in a considerable proportion. We have developed a software tool,called CommOligo using new algorithms and all three criteria forselection of optimal oligonucleotide probes. A series of filters,including sequence identity, free energy, continuous stretch, GC content,self-annealing, distance to the 3'-untranslated region (3'-UTR) andmelting temperature (Tm), are used to check each possibleoligonucleotide. A sequence identity is calculated based onmore » gapped globalalignments. A traversal algorithm is used to generate alignments for freeenergy calculation. The optimal Tm interval is determined based on probecandidates that have passed all other filters. Final probes are pickedusing a combination of user-configurable piece-wise linear functions andan iterative process. The thresholds for identity, stretch and freeenergy filters are automatically determined from experimental data by anaccessory software tool, CommOligo_PE (CommOligo Parameter Estimator).The program was used to design probes for both whole-genome and highlyhomologous sequence data. CommOligo and CommOligo_PE are freely availableto academic users upon request.« less

Reconstructing Information in Large-Scale Structure via Logarithmic Mapping

NASA Astrophysics Data System (ADS)

Szapudi, Istvan

We propose to develop a new method to extract information from large-scale structure data combining two-point statistics and non-linear transformations; before, this information was available only with substantially more complex higher-order statistical methods. Initially, most of the cosmological information in large-scale structure lies in two-point statistics. With non- linear evolution, some of that useful information leaks into higher-order statistics. The PI and group has shown in a series of theoretical investigations how that leakage occurs, and explained the Fisher information plateau at smaller scales. This plateau means that even as more modes are added to the measurement of the power spectrum, the total cumulative information (loosely speaking the inverse errorbar) is not increasing. Recently we have shown in Neyrinck et al. (2009, 2010) that a logarithmic (and a related Gaussianization or Box-Cox) transformation on the non-linear Dark Matter or galaxy field reconstructs a surprisingly large fraction of this missing Fisher information of the initial conditions. This was predicted by the earlier wave mechanical formulation of gravitational dynamics by Szapudi & Kaiser (2003). The present proposal is focused on working out the theoretical underpinning of the method to a point that it can be used in practice to analyze data. In particular, one needs to deal with the usual real-life issues of galaxy surveys, such as complex geometry, discrete sam- pling (Poisson or sub-Poisson noise), bias (linear, or non-linear, deterministic, or stochastic), redshift distortions, pro jection effects for 2D samples, and the effects of photometric redshift errors. We will develop methods for weak lensing and Sunyaev-Zeldovich power spectra as well, the latter specifically targetting Planck. In addition, we plan to investigate the question of residual higher- order information after the non-linear mapping, and possible applications for cosmology. Our aim will be to work out practical methods, with the ultimate goal of cosmological parameter estimation. We will quantify with standard MCMC and Fisher methods (including DETF Figure of merit when applicable) the efficiency of our estimators, comparing with the conventional method, that uses the un-transformed field. Preliminary results indicate that the increase for NASA's WFIRST in the DETF Figure of Merit would be 1.5-4.2 using a range of pessimistic to optimistic assumptions, respectively.

Solution Methods for 3D Tomographic Inversion Using A Highly Non-Linear Ray Tracer

NASA Astrophysics Data System (ADS)

Hipp, J. R.; Ballard, S.; Young, C. J.; Chang, M.

2008-12-01

To develop 3D velocity models to improve nuclear explosion monitoring capability, we have developed a 3D tomographic modeling system that traces rays using an implementation of the Um and Thurber ray pseudo- bending approach, with full enforcement of Snell's Law in 3D at the major discontinuities. Due to the highly non-linear nature of the ray tracer, however, we are forced to substantially damp the inversion in order to converge on a reasonable model. Unfortunately the amount of damping is not known a priori and can significantly extend the number of calls of the computationally expensive ray-tracer and the least squares matrix solver. If the damping term is too small the solution step-size produces either an un-realistic model velocity change or places the solution in or near a local minimum from which extrication is nearly impossible. If the damping term is too large, convergence can be very slow or premature convergence can occur. Standard approaches involve running inversions with a suite of damping parameters to find the best model. A better solution methodology is to take advantage of existing non-linear solution techniques such as Levenberg-Marquardt (LM) or quasi-newton iterative solvers. In particular, the LM algorithm was specifically designed to find the minimum of a multi-variate function that is expressed as the sum of squares of non-linear real-valued functions. It has become a standard technique for solving non-linear least squared problems, and is widely adopted in a broad spectrum of disciplines, including the geosciences. At each iteration, the LM approach dynamically varies the level of damping to optimize convergence. When the current estimate of the solution is far from the ultimate solution LM behaves as a steepest decent method, but transitions to Gauss- Newton behavior, with near quadratic convergence, as the estimate approaches the final solution. We show typical linear solution techniques and how they can lead to local minima if the damping is set too low. We also describe the LM technique and show how it automatically determines the appropriate damping factor as it iteratively converges on the best solution. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04- 94AL85000.

A new Bayesian Earthquake Analysis Tool (BEAT)

NASA Astrophysics Data System (ADS)

Vasyura-Bathke, Hannes; Dutta, Rishabh; Jónsson, Sigurjón; Mai, Martin

2017-04-01

Modern earthquake source estimation studies increasingly use non-linear optimization strategies to estimate kinematic rupture parameters, often considering geodetic and seismic data jointly. However, the optimization process is complex and consists of several steps that need to be followed in the earthquake parameter estimation procedure. These include pre-describing or modeling the fault geometry, calculating the Green's Functions (often assuming a layered elastic half-space), and estimating the distributed final slip and possibly other kinematic source parameters. Recently, Bayesian inference has become popular for estimating posterior distributions of earthquake source model parameters given measured/estimated/assumed data and model uncertainties. For instance, some research groups consider uncertainties of the layered medium and propagate these to the source parameter uncertainties. Other groups make use of informative priors to reduce the model parameter space. In addition, innovative sampling algorithms have been developed that efficiently explore the often high-dimensional parameter spaces. Compared to earlier studies, these improvements have resulted in overall more robust source model parameter estimates that include uncertainties. However, the computational demands of these methods are high and estimation codes are rarely distributed along with the published results. Even if codes are made available, it is often difficult to assemble them into a single optimization framework as they are typically coded in different programing languages. Therefore, further progress and future applications of these methods/codes are hampered, while reproducibility and validation of results has become essentially impossible. In the spirit of providing open-access and modular codes to facilitate progress and reproducible research in earthquake source estimations, we undertook the effort of producing BEAT, a python package that comprises all the above-mentioned features in one single programing environment. The package is build on top of the pyrocko seismological toolbox (www.pyrocko.org) and makes use of the pymc3 module for Bayesian statistical model fitting. BEAT is an open-source package (https://github.com/hvasbath/beat) and we encourage and solicit contributions to the project. In this contribution, we present our strategy for developing BEAT, show application examples, and discuss future developments.

Parameter estimating state reconstruction

NASA Technical Reports Server (NTRS)

George, E. B.

1976-01-01

Parameter estimation is considered for systems whose entire state cannot be measured. Linear observers are designed to recover the unmeasured states to a sufficient accuracy to permit the estimation process. There are three distinct dynamics that must be accommodated in the system design: the dynamics of the plant, the dynamics of the observer, and the system updating of the parameter estimation. The latter two are designed to minimize interaction of the involved systems. These techniques are extended to weakly nonlinear systems. The application to a simulation of a space shuttle POGO system test is of particular interest. A nonlinear simulation of the system is developed, observers designed, and the parameters estimated.

Analysis of randomly time varying systems by gaussian closure technique

NASA Astrophysics Data System (ADS)

Dash, P. K.; Iyengar, R. N.

1982-07-01

The Gaussian probability closure technique is applied to study the random response of multidegree of freedom stochastically time varying systems under non-Gaussian excitations. Under the assumption that the response, the coefficient and the excitation processes are jointly Gaussian, deterministic equations are derived for the first two response moments. It is further shown that this technique leads to the best Gaussian estimate in a minimum mean square error sense. An example problem is solved which demonstrates the capability of this technique for handling non-linearity, stochastic system parameters and amplitude limited responses in a unified manner. Numerical results obtained through the Gaussian closure technique compare well with the exact solutions.

Estimating fractional vegetation cover and the vegetation index of bare soil and highly dense vegetation with a physically based method

NASA Astrophysics Data System (ADS)

Song, Wanjuan; Mu, Xihan; Ruan, Gaiyan; Gao, Zhan; Li, Linyuan; Yan, Guangjian

2017-06-01

Normalized difference vegetation index (NDVI) of highly dense vegetation (NDVIv) and bare soil (NDVIs), identified as the key parameters for Fractional Vegetation Cover (FVC) estimation, are usually obtained with empirical statistical methods However, it is often difficult to obtain reasonable values of NDVIv and NDVIs at a coarse resolution (e.g., 1 km), or in arid, semiarid, and evergreen areas. The uncertainty of estimated NDVIs and NDVIv can cause substantial errors in FVC estimations when a simple linear mixture model is used. To address this problem, this paper proposes a physically based method. The leaf area index (LAI) and directional NDVI are introduced in a gap fraction model and a linear mixture model for FVC estimation to calculate NDVIv and NDVIs. The model incorporates the Moderate Resolution Imaging Spectroradiometer (MODIS) Bidirectional Reflectance Distribution Function (BRDF) model parameters product (MCD43B1) and LAI product, which are convenient to acquire. Two types of evaluation experiments are designed 1) with data simulated by a canopy radiative transfer model and 2) with satellite observations. The root-mean-square deviation (RMSD) for simulated data is less than 0.117, depending on the type of noise added on the data. In the real data experiment, the RMSD for cropland is 0.127, for grassland is 0.075, and for forest is 0.107. The experimental areas respectively lack fully vegetated and non-vegetated pixels at 1 km resolution. Consequently, a relatively large uncertainty is found while using the statistical methods and the RMSD ranges from 0.110 to 0.363 based on the real data. The proposed method is convenient to produce NDVIv and NDVIs maps for FVC estimation on regional and global scales.

A Bayesian least squares support vector machines based framework for fault diagnosis and failure prognosis

NASA Astrophysics Data System (ADS)

Khawaja, Taimoor Saleem

A high-belief low-overhead Prognostics and Health Management (PHM) system is desired for online real-time monitoring of complex non-linear systems operating in a complex (possibly non-Gaussian) noise environment. This thesis presents a Bayesian Least Squares Support Vector Machine (LS-SVM) based framework for fault diagnosis and failure prognosis in nonlinear non-Gaussian systems. The methodology assumes the availability of real-time process measurements, definition of a set of fault indicators and the existence of empirical knowledge (or historical data) to characterize both nominal and abnormal operating conditions. An efficient yet powerful Least Squares Support Vector Machine (LS-SVM) algorithm, set within a Bayesian Inference framework, not only allows for the development of real-time algorithms for diagnosis and prognosis but also provides a solid theoretical framework to address key concepts related to classification for diagnosis and regression modeling for prognosis. SVM machines are founded on the principle of Structural Risk Minimization (SRM) which tends to find a good trade-off between low empirical risk and small capacity. The key features in SVM are the use of non-linear kernels, the absence of local minima, the sparseness of the solution and the capacity control obtained by optimizing the margin. The Bayesian Inference framework linked with LS-SVMs allows a probabilistic interpretation of the results for diagnosis and prognosis. Additional levels of inference provide the much coveted features of adaptability and tunability of the modeling parameters. The two main modules considered in this research are fault diagnosis and failure prognosis. With the goal of designing an efficient and reliable fault diagnosis scheme, a novel Anomaly Detector is suggested based on the LS-SVM machines. The proposed scheme uses only baseline data to construct a 1-class LS-SVM machine which, when presented with online data is able to distinguish between normal behavior and any abnormal or novel data during real-time operation. The results of the scheme are interpreted as a posterior probability of health (1 - probability of fault). As shown through two case studies in Chapter 3, the scheme is well suited for diagnosing imminent faults in dynamical non-linear systems. Finally, the failure prognosis scheme is based on an incremental weighted Bayesian LS-SVR machine. It is particularly suited for online deployment given the incremental nature of the algorithm and the quick optimization problem solved in the LS-SVR algorithm. By way of kernelization and a Gaussian Mixture Modeling (GMM) scheme, the algorithm can estimate "possibly" non-Gaussian posterior distributions for complex non-linear systems. An efficient regression scheme associated with the more rigorous core algorithm allows for long-term predictions, fault growth estimation with confidence bounds and remaining useful life (RUL) estimation after a fault is detected. The leading contributions of this thesis are (a) the development of a novel Bayesian Anomaly Detector for efficient and reliable Fault Detection and Identification (FDI) based on Least Squares Support Vector Machines, (b) the development of a data-driven real-time architecture for long-term Failure Prognosis using Least Squares Support Vector Machines, (c) Uncertainty representation and management using Bayesian Inference for posterior distribution estimation and hyper-parameter tuning, and finally (d) the statistical characterization of the performance of diagnosis and prognosis algorithms in order to relate the efficiency and reliability of the proposed schemes.

Pseudo-second order models for the adsorption of safranin onto activated carbon: comparison of linear and non-linear regression methods.

PubMed

Kumar, K Vasanth

2007-04-02

Kinetic experiments were carried out for the sorption of safranin onto activated carbon particles. The kinetic data were fitted to pseudo-second order model of Ho, Sobkowsk and Czerwinski, Blanchard et al. and Ritchie by linear and non-linear regression methods. Non-linear method was found to be a better way of obtaining the parameters involved in the second order rate kinetic expressions. Both linear and non-linear regression showed that the Sobkowsk and Czerwinski and Ritchie's pseudo-second order models were the same. Non-linear regression analysis showed that both Blanchard et al. and Ho have similar ideas on the pseudo-second order model but with different assumptions. The best fit of experimental data in Ho's pseudo-second order expression by linear and non-linear regression method showed that Ho pseudo-second order model was a better kinetic expression when compared to other pseudo-second order kinetic expressions.

Studies in astronomical time series analysis. IV - Modeling chaotic and random processes with linear filters

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.

1990-01-01

While chaos arises only in nonlinear systems, standard linear time series models are nevertheless useful for analyzing data from chaotic processes. This paper introduces such a model, the chaotic moving average. This time-domain model is based on the theorem that any chaotic process can be represented as the convolution of a linear filter with an uncorrelated process called the chaotic innovation. A technique, minimum phase-volume deconvolution, is introduced to estimate the filter and innovation. The algorithm measures the quality of a model using the volume covered by the phase-portrait of the innovation process. Experiments on synthetic data demonstrate that the algorithm accurately recovers the parameters of simple chaotic processes. Though tailored for chaos, the algorithm can detect both chaos and randomness, distinguish them from each other, and separate them if both are present. It can also recover nonminimum-delay pulse shapes in non-Gaussian processes, both random and chaotic.

Linear model for fast background subtraction in oligonucleotide microarrays.

PubMed

Kroll, K Myriam; Barkema, Gerard T; Carlon, Enrico

2009-11-16

One important preprocessing step in the analysis of microarray data is background subtraction. In high-density oligonucleotide arrays this is recognized as a crucial step for the global performance of the data analysis from raw intensities to expression values. We propose here an algorithm for background estimation based on a model in which the cost function is quadratic in a set of fitting parameters such that minimization can be performed through linear algebra. The model incorporates two effects: 1) Correlated intensities between neighboring features in the chip and 2) sequence-dependent affinities for non-specific hybridization fitted by an extended nearest-neighbor model. The algorithm has been tested on 360 GeneChips from publicly available data of recent expression experiments. The algorithm is fast and accurate. Strong correlations between the fitted values for different experiments as well as between the free-energy parameters and their counterparts in aqueous solution indicate that the model captures a significant part of the underlying physical chemistry.

Combined Yamamoto approach for simultaneous estimation of adsorption isotherm and kinetic parameters in ion-exchange chromatography.

PubMed

Rüdt, Matthias; Gillet, Florian; Heege, Stefanie; Hitzler, Julian; Kalbfuss, Bernd; Guélat, Bertrand

2015-09-25

Application of model-based design is appealing to support the development of protein chromatography in the biopharmaceutical industry. However, the required efforts for parameter estimation are frequently perceived as time-consuming and expensive. In order to speed-up this work, a new parameter estimation approach for modelling ion-exchange chromatography in linear conditions was developed. It aims at reducing the time and protein demand for the model calibration. The method combines the estimation of kinetic and thermodynamic parameters based on the simultaneous variation of the gradient slope and the residence time in a set of five linear gradient elutions. The parameters are estimated from a Yamamoto plot and a gradient-adjusted Van Deemter plot. The combined approach increases the information extracted per experiment compared to the individual methods. As a proof of concept, the combined approach was successfully applied for a monoclonal antibody on a cation-exchanger and for a Fc-fusion protein on an anion-exchange resin. The individual parameter estimations for the mAb confirmed that the new approach maintained the accuracy of the usual Yamamoto and Van Deemter plots. In the second case, offline size-exclusion chromatography was performed in order to estimate the thermodynamic parameters of an impurity (high molecular weight species) simultaneously with the main product. Finally, the parameters obtained from the combined approach were used in a lumped kinetic model to simulate the chromatography runs. The simulated chromatograms obtained for a wide range of gradient lengths and residence times showed only small deviations compared to the experimental data. Copyright © 2015 Elsevier B.V. All rights reserved.

Modern control concepts in hydrology. [parameter identification in adaptive stochastic control approach

NASA Technical Reports Server (NTRS)

Duong, N.; Winn, C. B.; Johnson, G. R.

1975-01-01

Two approaches to an identification problem in hydrology are presented, based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time-invariant or time-dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and confirm the results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise.

Genetic parameters for linear type traits and milk, fat, and protein production in holstein cows in Brazil.

PubMed

Campos, Rafael Viegas; Cobuci, Jaime Araujo; Kern, Elisandra Lurdes; Costa, Cláudio Napolis; McManus, Concepta Margaret

2015-04-01

The objective of this study was to estimate genetic and phenotypic parameters for linear type traits, as well as milk yield (MY), fat yield (FY) and protein yield (PY) in 18,831 Holstein cows reared in 495 herds in Brazil. Restricted maximum likelihood with a bivariate model was used for estimation genetic parameters, including fixed effects of herd-year of classification, period of classification, classifier and stage of lactation for linear type traits and herd-year of calving, season of calving and lactation order effects for production traits. The age of cow at calving was fitted as a covariate (with linear and quadratic terms), common to both models. Heritability estimates varied from 0.09 to 0.38 for linear type traits and from 0.17 to 0.24 for production traits, indicating sufficient genetic variability to achieve genetic gain through selection. In general, estimates of genetic correlations between type and production traits were low, except for udder texture and angularity that showed positive genetic correlations (>0.29) with MY, FY, and PY. Udder depth had the highest negative genetic correlation (-0.30) with production traits. Selection for final score, commonly used by farmers as a practical selection tool to improve type traits, does not lead to significant improvements in production traits, thus the use of selection indices that consider both sets of traits (production and type) seems to be the most adequate to carry out genetic selection of animals in the Brazilian herd.

Genetic Parameters for Linear Type Traits and Milk, Fat, and Protein Production in Holstein Cows in Brazil

PubMed Central

Campos, Rafael Viegas; Cobuci, Jaime Araujo; Kern, Elisandra Lurdes; Costa, Cláudio Napolis; McManus, Concepta Margaret

2015-01-01

The objective of this study was to estimate genetic and phenotypic parameters for linear type traits, as well as milk yield (MY), fat yield (FY) and protein yield (PY) in 18,831 Holstein cows reared in 495 herds in Brazil. Restricted maximum likelihood with a bivariate model was used for estimation genetic parameters, including fixed effects of herd-year of classification, period of classification, classifier and stage of lactation for linear type traits and herd-year of calving, season of calving and lactation order effects for production traits. The age of cow at calving was fitted as a covariate (with linear and quadratic terms), common to both models. Heritability estimates varied from 0.09 to 0.38 for linear type traits and from 0.17 to 0.24 for production traits, indicating sufficient genetic variability to achieve genetic gain through selection. In general, estimates of genetic correlations between type and production traits were low, except for udder texture and angularity that showed positive genetic correlations (>0.29) with MY, FY, and PY. Udder depth had the highest negative genetic correlation (−0.30) with production traits. Selection for final score, commonly used by farmers as a practical selection tool to improve type traits, does not lead to significant improvements in production traits, thus the use of selection indices that consider both sets of traits (production and type) seems to be the most adequate to carry out genetic selection of animals in the Brazilian herd. PMID:25656190

Estimation of the limit of detection in semiconductor gas sensors through linearized calibration models.

PubMed

Burgués, Javier; Jiménez-Soto, Juan Manuel; Marco, Santiago

2018-07-12

The limit of detection (LOD) is a key figure of merit in chemical sensing. However, the estimation of this figure of merit is hindered by the non-linear calibration curve characteristic of semiconductor gas sensor technologies such as, metal oxide (MOX), gasFETs or thermoelectric sensors. Additionally, chemical sensors suffer from cross-sensitivities and temporal stability problems. The application of the International Union of Pure and Applied Chemistry (IUPAC) recommendations for univariate LOD estimation in non-linear semiconductor gas sensors is not straightforward due to the strong statistical requirements of the IUPAC methodology (linearity, homoscedasticity, normality). Here, we propose a methodological approach to LOD estimation through linearized calibration models. As an example, the methodology is applied to the detection of low concentrations of carbon monoxide using MOX gas sensors in a scenario where the main source of error is the presence of uncontrolled levels of humidity. Copyright © 2018 Elsevier B.V. All rights reserved.

The non-linear power spectrum of the Lyman alpha forest

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arinyo-i-Prats, Andreu; Miralda-Escudé, Jordi; Viel, Matteo

2015-12-01

The Lyman alpha forest power spectrum has been measured on large scales by the BOSS survey in SDSS-III at z∼ 2.3, has been shown to agree well with linear theory predictions, and has provided the first measurement of Baryon Acoustic Oscillations at this redshift. However, the power at small scales, affected by non-linearities, has not been well examined so far. We present results from a variety of hydrodynamic simulations to predict the redshift space non-linear power spectrum of the Lyα transmission for several models, testing the dependence on resolution and box size. A new fitting formula is introduced to facilitate themore » comparison of our simulation results with observations and other simulations. The non-linear power spectrum has a generic shape determined by a transition scale from linear to non-linear anisotropy, and a Jeans scale below which the power drops rapidly. In addition, we predict the two linear bias factors of the Lyα forest and provide a better physical interpretation of their values and redshift evolution. The dependence of these bias factors and the non-linear power on the amplitude and slope of the primordial fluctuations power spectrum, the temperature-density relation of the intergalactic medium, and the mean Lyα transmission, as well as the redshift evolution, is investigated and discussed in detail. A preliminary comparison to the observations shows that the predicted redshift distortion parameter is in good agreement with the recent determination of Blomqvist et al., but the density bias factor is lower than observed. We make all our results publicly available in the form of tables of the non-linear power spectrum that is directly obtained from all our simulations, and parameters of our fitting formula.« less

Parameter estimation for lithium ion batteries

NASA Astrophysics Data System (ADS)

Santhanagopalan, Shriram

With an increase in the demand for lithium based batteries at the rate of about 7% per year, the amount of effort put into improving the performance of these batteries from both experimental and theoretical perspectives is increasing. There exist a number of mathematical models ranging from simple empirical models to complicated physics-based models to describe the processes leading to failure of these cells. The literature is also rife with experimental studies that characterize the various properties of the system in an attempt to improve the performance of lithium ion cells. However, very little has been done to quantify the experimental observations and relate these results to the existing mathematical models. In fact, the best of the physics based models in the literature show as much as 20% discrepancy when compared to experimental data. The reasons for such a big difference include, but are not limited to, numerical complexities involved in extracting parameters from experimental data and inconsistencies in interpreting directly measured values for the parameters. In this work, an attempt has been made to implement simplified models to extract parameter values that accurately characterize the performance of lithium ion cells. The validity of these models under a variety of experimental conditions is verified using a model discrimination procedure. Transport and kinetic properties are estimated using a non-linear estimation procedure. The initial state of charge inside each electrode is also maintained as an unknown parameter, since this value plays a significant role in accurately matching experimental charge/discharge curves with model predictions and is not readily known from experimental data. The second part of the dissertation focuses on parameters that change rapidly with time. For example, in the case of lithium ion batteries used in Hybrid Electric Vehicle (HEV) applications, the prediction of the State of Charge (SOC) of the cell under a variety of road conditions is important. An algorithm to predict the SOC in time intervals as small as 5 ms is of critical demand. In such cases, the conventional non-linear estimation procedure is not time-effective. There exist methodologies in the literature, such as those based on fuzzy logic; however, these techniques require a lot of computational storage space. Consequently, it is not possible to implement such techniques on a micro-chip for integration as a part of a real-time device. The Extended Kalman Filter (EKF) based approach presented in this work is a first step towards developing an efficient method to predict online, the State of Charge of a lithium ion cell based on an electrochemical model. The final part of the dissertation focuses on incorporating uncertainty in parameter values into electrochemical models using the polynomial chaos theory (PCT).

Non-Linear Cosmological Power Spectra in Real and Redshift Space

NASA Technical Reports Server (NTRS)

Taylor, A. N.; Hamilton, A. J. S.

1996-01-01

We present an expression for the non-linear evolution of the cosmological power spectrum based on Lagrangian trajectories. This is simplified using the Zel'dovich approximation to trace particle displacements, assuming Gaussian initial conditions. The model is found to exhibit the transfer of power from large to small scales expected in self-gravitating fields. Some exact solutions are found for power-law initial spectra. We have extended this analysis into red-shift space and found a solution for the non-linear, anisotropic redshift-space power spectrum in the limit of plane-parallel redshift distortions. The quadrupole-to-monopole ratio is calculated for the case of power-law initial spectra. We find that the shape of this ratio depends on the shape of the initial spectrum, but when scaled to linear theory depends only weakly on the redshift-space distortion parameter, beta. The point of zero-crossing of the quadrupole, kappa(sub o), is found to obey a simple scaling relation and we calculate this scale in the Zel'dovich approximation. This model is found to be in good agreement with a series of N-body simulations on scales down to the zero-crossing of the quadrupole, although the wavenumber at zero-crossing is underestimated. These results are applied to the quadrupole-to-monopole ratio found in the merged QDOT plus 1.2-Jy-IRAS redshift survey. Using a likelihood technique we have estimated that the distortion parameter is constrained to be beta greater than 0.5 at the 95 percent level. Our results are fairly insensitive to the local primordial spectral slope, but the likelihood analysis suggests n = -2 un the translinear regime. The zero-crossing scale of the quadrupole is k(sub 0) = 0.5 +/- 0.1 h Mpc(exp -1) and from this we infer that the amplitude of clustering is sigma(sub 8) = 0.7 +/- 0.05. We suggest that the success of this model is due to non-linear redshift-space effects arising from infall on to caustic and is not dominated by virialized cluster cores. The latter should start to dominate on scales below the zero-crossing of the quadrupole, where our model breaks down.

Optically induced circular and axial birefringences in achiral fluids: an ab initio study of the optical Faraday effect

NASA Astrophysics Data System (ADS)

Baranowska, Angelika; Rizzo, Antonio; Coriani, Sonia

2006-07-01

A computational analysis of the effects (intensity-dependent change in the refractive index and the optical Faraday effect, OFE) induced in an achiral fluid by circularly polarized, linearly polarized or unpolarized light is presented. The connection between the molecular parameters appearing in the expression of the observable, as derived by Woźniak in the 1990s, and the appropriate linear and cubic frequency dependent response functions is made for the general case of both chiral and non-chiral fluid. The parameters which are non-vanishing in the case of achiral systems are then computed employing a coupled cluster singles and doubles wave function model and a wide choice of correlation consistent basis sets, for a set of reference systems, including a rare gas (neon), a non-dipolar (N2) and a dipolar (CO) molecule. Contributions due to magnetic and quadrupolar interactions between the fields and the gases are neglected, since they are in principle of much less importance than the purely electric dipolar interactions. Nevertheless a rough estimate of their size is given. The aim of the study is to assess the detectability of OFE. To this end, the ab initio results are compared with those obtained in this work for the closely related optical Kerr effect (OKE) and with those yielded by the classical Faraday effect.

Minimum mean squared error (MSE) adjustment and the optimal Tykhonov-Phillips regularization parameter via reproducing best invariant quadratic uniformly unbiased estimates (repro-BIQUUE)

NASA Astrophysics Data System (ADS)

Schaffrin, Burkhard

2008-02-01

In a linear Gauss-Markov model, the parameter estimates from BLUUE (Best Linear Uniformly Unbiased Estimate) are not robust against possible outliers in the observations. Moreover, by giving up the unbiasedness constraint, the mean squared error (MSE) risk may be further reduced, in particular when the problem is ill-posed. In this paper, the α-weighted S-homBLE (Best homogeneously Linear Estimate) is derived via formulas originally used for variance component estimation on the basis of the repro-BIQUUE (reproducing Best Invariant Quadratic Uniformly Unbiased Estimate) principle in a model with stochastic prior information. In the present model, however, such prior information is not included, which allows the comparison of the stochastic approach (α-weighted S-homBLE) with the well-established algebraic approach of Tykhonov-Phillips regularization, also known as R-HAPS (Hybrid APproximation Solution), whenever the inverse of the “substitute matrix” S exists and is chosen as the R matrix that defines the relative impact of the regularizing term on the final result.

A method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1971-01-01

A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

Online vegetation parameter estimation using passive microwave remote sensing observations

USDA-ARS?s Scientific Manuscript database

In adaptive system identification the Kalman filter can be used to identify the coefficient of the observation operator of a linear system. Here the ensemble Kalman filter is tested for adaptive online estimation of the vegetation opacity parameter of a radiative transfer model. A state augmentatio...

Kinetic analysis of non-isothermal solid-state reactions: multi-stage modeling without assumptions in the reaction mechanism.

PubMed

Pomerantsev, Alexey L; Kutsenova, Alla V; Rodionova, Oxana Ye

2017-02-01

A novel non-linear regression method for modeling non-isothermal thermogravimetric data is proposed. Experiments for several heating rates are analyzed simultaneously. The method is applicable to complex multi-stage processes when the number of stages is unknown. Prior knowledge of the type of kinetics is not required. The main idea is a consequent estimation of parameters when the overall model is successively changed from one level of modeling to another. At the first level, the Avrami-Erofeev functions are used. At the second level, the Sestak-Berggren functions are employed with the goal to broaden the overall model. The method is tested using both simulated and real-world data. A comparison of the proposed method with a recently published 'model-free' deconvolution method is presented.

The variance of the locally measured Hubble parameter explained with different estimators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Odderskov, Io; Hannestad, Steen; Brandbyge, Jacob, E-mail: isho07@phys.au.dk, E-mail: sth@phys.au.dk, E-mail: jacobb@phys.au.dk

We study the expected variance of measurements of the Hubble constant, H {sub 0}, as calculated in either linear perturbation theory or using non-linear velocity power spectra derived from N -body simulations. We compare the variance with that obtained by carrying out mock observations in the N-body simulations, and show that the estimator typically used for the local Hubble constant in studies based on perturbation theory is different from the one used in studies based on N-body simulations. The latter gives larger weight to distant sources, which explains why studies based on N-body simulations tend to obtain a smaller variancemore » than that found from studies based on the power spectrum. Although both approaches result in a variance too small to explain the discrepancy between the value of H {sub 0} from CMB measurements and the value measured in the local universe, these considerations are important in light of the percent determination of the Hubble constant in the local universe.« less

Linking aquifer spatial properties and non-Fickian transport in mobile-immobile like alluvial settings

USGS Publications Warehouse

Zhang, Yong; Green, Christopher T.; Baeumer, Boris

2014-01-01

Time-nonlocal transport models can describe non-Fickian diffusion observed in geological media, but the physical meaning of parameters can be ambiguous, and most applications are limited to curve-fitting. This study explores methods for predicting the parameters of a temporally tempered Lévy motion (TTLM) model for transient sub-diffusion in mobile–immobile like alluvial settings represented by high-resolution hydrofacies models. The TTLM model is a concise multi-rate mass transfer (MRMT) model that describes a linear mass transfer process where the transfer kinetics and late-time transport behavior are controlled by properties of the host medium, especially the immobile domain. The intrinsic connection between the MRMT and TTLM models helps to estimate the main time-nonlocal parameters in the TTLM model (which are the time scale index, the capacity coefficient, and the truncation parameter) either semi-analytically or empirically from the measurable aquifer properties. Further applications show that the TTLM model captures the observed solute snapshots, the breakthrough curves, and the spatial moments of plumes up to the fourth order. Most importantly, the a priori estimation of the time-nonlocal parameters outside of any breakthrough fitting procedure provides a reliable “blind” prediction of the late-time dynamics of subdiffusion observed in a spectrum of alluvial settings. Predictability of the time-nonlocal parameters may be due to the fact that the late-time subdiffusion is not affected by the exact location of each immobile zone, but rather is controlled by the time spent in immobile blocks surrounding the pathway of solute particles. Results also show that the effective dispersion coefficient has to be fitted due to the scale effect of transport, and the mean velocity can differ from local measurements or volume averages. The link between medium heterogeneity and time-nonlocal parameters will help to improve model predictability for non-Fickian transport in alluvial settings.

Measurement of picometre non-linearity in an optical grating encoder using x-ray interferometry

NASA Astrophysics Data System (ADS)

Yacoot, Andrew; Cross, Nigel

2003-01-01

X-ray interferometry has been used to characterize the non-linearity in an optical encoder displacement measuring system. Traceable measurements of the non-linearity have been made and an estimation of the uncertainty associated with the measurements is given. Cyclic errors with a magnitude of up to 50 pm and periodicity of the encoder system (128 nm) have been recorded.

Turbulent mixing of a critical fluid: The non-perturbative renormalization

NASA Astrophysics Data System (ADS)

Hnatič, M.; Kalagov, G.; Nalimov, M.

2018-01-01

Non-perturbative Renormalization Group (NPRG) technique is applied to a stochastical model of a non-conserved scalar order parameter near its critical point, subject to turbulent advection. The compressible advecting flow is modeled by a random Gaussian velocity field with zero mean and correlation function 〈υjυi 〉 ∼ (Pji⊥ + αPji∥) /k d + ζ. Depending on the relations between the parameters ζ, α and the space dimensionality d, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow), but there is a new nonequilibrium regime (universality class) associated with new nontrivial fixed points of the renormalization group equations. We have obtained the phase diagram (d, ζ) of possible scaling regimes in the system. The physical point d = 3, ζ = 4 / 3 corresponding to three-dimensional fully developed Kolmogorov's turbulence, where critical fluctuations are irrelevant, is stable for α ≲ 2.26. Otherwise, in the case of "strong compressibility" α ≳ 2.26, the critical fluctuations of the order parameter become relevant for three-dimensional turbulence. Estimations of critical exponents for each scaling regime are presented.

Bridging the gaps between non-invasive genetic sampling and population parameter estimation

Treesearch

Francesca Marucco; Luigi Boitani; Daniel H. Pletscher; Michael K. Schwartz

2011-01-01

Reliable estimates of population parameters are necessary for effective management and conservation actions. The use of genetic data for capture­recapture (CR) analyses has become an important tool to estimate population parameters for elusive species. Strong emphasis has been placed on the genetic analysis of non-invasive samples, or on the CR analysis; however,...

Robust Characterization of Loss Rates

NASA Astrophysics Data System (ADS)

Wallman, Joel J.; Barnhill, Marie; Emerson, Joseph

2015-08-01

Many physical implementations of qubits—including ion traps, optical lattices and linear optics—suffer from loss. A nonzero probability of irretrievably losing a qubit can be a substantial obstacle to fault-tolerant methods of processing quantum information, requiring new techniques to safeguard against loss that introduce an additional overhead that depends upon the loss rate. Here we present a scalable and platform-independent protocol for estimating the average loss rate (averaged over all input states) resulting from an arbitrary Markovian noise process, as well as an independent estimate of detector efficiency. Moreover, we show that our protocol gives an additional constraint on estimated parameters from randomized benchmarking that improves the reliability of the estimated error rate and provides a new indicator for non-Markovian signatures in the experimental data. We also derive a bound for the state-dependent loss rate in terms of the average loss rate.

Deletion Diagnostics for the Generalised Linear Mixed Model with independent random effects

PubMed Central

Ganguli, B.; Roy, S. Sen; Naskar, M.; Malloy, E. J.; Eisen, E. A.

2015-01-01

The Generalised Linear Mixed Model (GLMM) is widely used for modelling environmental data. However, such data are prone to influential observations which can distort the estimated exposure-response curve particularly in regions of high exposure. Deletion diagnostics for iterative estimation schemes commonly derive the deleted estimates based on a single iteration of the full system holding certain pivotal quantities such as the information matrix to be constant. In this paper, we present an approximate formula for the deleted estimates and Cook’s distance for the GLMM which does not assume that the estimates of variance parameters are unaffected by deletion. The procedure allows the user to calculate standardised DFBETAs for mean as well as variance parameters. In certain cases, such as when using the GLMM as a device for smoothing, such residuals for the variance parameters are interesting in their own right. In general, the procedure leads to deleted estimates of mean parameters which are corrected for the effect of deletion on variance components as estimation of the two sets of parameters is interdependent. The probabilistic behaviour of these residuals is investigated and a simulation based procedure suggested for their standardisation. The method is used to identify influential individuals in an occupational cohort exposed to silica. The results show that failure to conduct post model fitting diagnostics for variance components can lead to erroneous conclusions about the fitted curve and unstable confidence intervals. PMID:26626135

Estimating the remaining useful life of bearings using a neuro-local linear estimator-based method.

PubMed

Ahmad, Wasim; Ali Khan, Sheraz; Kim, Jong-Myon

2017-05-01

Estimating the remaining useful life (RUL) of a bearing is required for maintenance scheduling. While the degradation behavior of a bearing changes during its lifetime, it is usually assumed to follow a single model. In this letter, bearing degradation is modeled by a monotonically increasing function that is globally non-linear and locally linearized. The model is generated using historical data that is smoothed with a local linear estimator. A neural network learns this model and then predicts future levels of vibration acceleration to estimate the RUL of a bearing. The proposed method yields reasonably accurate estimates of the RUL of a bearing at different points during its operational life.

Identification of internal properties of fibres and micro-swimmers

NASA Astrophysics Data System (ADS)

Plouraboué, Franck; Thiam, E. Ibrahima; Delmotte, Blaise; Climent, Eric

2017-01-01

In this paper, we address the identifiability of constitutive parameters of passive or active micro-swimmers. We first present a general framework for describing fibres or micro-swimmers using a bead-model description. Using a kinematic constraint formulation to describe fibres, flagellum or cilia, we find explicit linear relationship between elastic constitutive parameters and generalized velocities from computing contact forces. This linear formulation then permits one to address explicitly identifiability conditions and solve for parameter identification. We show that both active forcing and passive parameters are both identifiable independently but not simultaneously. We also provide unbiased estimators for generalized elastic parameters in the presence of Langevin-like forcing with Gaussian noise using a Bayesian approach. These theoretical results are illustrated in various configurations showing the efficiency of the proposed approach for direct parameter identification. The convergence of the proposed estimators is successfully tested numerically.

A new software for deformation source optimization, the Bayesian Earthquake Analysis Tool (BEAT)

NASA Astrophysics Data System (ADS)

Vasyura-Bathke, H.; Dutta, R.; Jonsson, S.; Mai, P. M.

2017-12-01

Modern studies of crustal deformation and the related source estimation, including magmatic and tectonic sources, increasingly use non-linear optimization strategies to estimate geometric and/or kinematic source parameters and often consider both jointly, geodetic and seismic data. Bayesian inference is increasingly being used for estimating posterior distributions of deformation source model parameters, given measured/estimated/assumed data and model uncertainties. For instance, some studies consider uncertainties of a layered medium and propagate these into source parameter uncertainties, while others use informative priors to reduce the model parameter space. In addition, innovative sampling algorithms have been developed to efficiently explore the high-dimensional parameter spaces. Compared to earlier studies, these improvements have resulted in overall more robust source model parameter estimates that include uncertainties. However, the computational burden of these methods is high and estimation codes are rarely made available along with the published results. Even if the codes are accessible, it is usually challenging to assemble them into a single optimization framework as they are typically coded in different programing languages. Therefore, further progress and future applications of these methods/codes are hampered, while reproducibility and validation of results has become essentially impossible. In the spirit of providing open-access and modular codes to facilitate progress and reproducible research in deformation source estimations, we undertook the effort of developing BEAT, a python package that comprises all the above-mentioned features in one single programing environment. The package builds on the pyrocko seismological toolbox (www.pyrocko.org), and uses the pymc3 module for Bayesian statistical model fitting. BEAT is an open-source package (https://github.com/hvasbath/beat), and we encourage and solicit contributions to the project. Here, we present our strategy for developing BEAT and show application examples; especially the effect of including the model prediction uncertainty of the velocity model in following source optimizations: full moment tensor, Mogi source, moderate strike-slip earth-quake.

Log-normal frailty models fitted as Poisson generalized linear mixed models.

PubMed

Hirsch, Katharina; Wienke, Andreas; Kuss, Oliver

2016-12-01

The equivalence of a survival model with a piecewise constant baseline hazard function and a Poisson regression model has been known since decades. As shown in recent studies, this equivalence carries over to clustered survival data: A frailty model with a log-normal frailty term can be interpreted and estimated as a generalized linear mixed model with a binary response, a Poisson likelihood, and a specific offset. Proceeding this way, statistical theory and software for generalized linear mixed models are readily available for fitting frailty models. This gain in flexibility comes at the small price of (1) having to fix the number of pieces for the baseline hazard in advance and (2) having to "explode" the data set by the number of pieces. In this paper we extend the simulations of former studies by using a more realistic baseline hazard (Gompertz) and by comparing the model under consideration with competing models. Furthermore, the SAS macro %PCFrailty is introduced to apply the Poisson generalized linear mixed approach to frailty models. The simulations show good results for the shared frailty model. Our new %PCFrailty macro provides proper estimates, especially in case of 4 events per piece. The suggested Poisson generalized linear mixed approach for log-normal frailty models based on the %PCFrailty macro provides several advantages in the analysis of clustered survival data with respect to more flexible modelling of fixed and random effects, exact (in the sense of non-approximate) maximum likelihood estimation, and standard errors and different types of confidence intervals for all variance parameters. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Sensor fault diagnosis of singular delayed LPV systems with inexact parameters: an uncertain system approach

NASA Astrophysics Data System (ADS)

Hassanabadi, Amir Hossein; Shafiee, Masoud; Puig, Vicenc

2018-01-01

In this paper, sensor fault diagnosis of a singular delayed linear parameter varying (LPV) system is considered. In the considered system, the model matrices are dependent on some parameters which are real-time measurable. The case of inexact parameter measurements is considered which is close to real situations. Fault diagnosis in this system is achieved via fault estimation. For this purpose, an augmented system is created by including sensor faults as additional system states. Then, an unknown input observer (UIO) is designed which estimates both the system states and the faults in the presence of measurement noise, disturbances and uncertainty induced by inexact measured parameters. Error dynamics and the original system constitute an uncertain system due to inconsistencies between real and measured values of the parameters. Then, the robust estimation of the system states and the faults are achieved with H∞ performance and formulated with a set of linear matrix inequalities (LMIs). The designed UIO is also applicable for fault diagnosis of singular delayed LPV systems with unmeasurable scheduling variables. The efficiency of the proposed approach is illustrated with an example.

Parameter estimation of multivariate multiple regression model using bayesian with non-informative Jeffreys’ prior distribution

NASA Astrophysics Data System (ADS)

Saputro, D. R. S.; Amalia, F.; Widyaningsih, P.; Affan, R. C.

2018-05-01

Bayesian method is a method that can be used to estimate the parameters of multivariate multiple regression model. Bayesian method has two distributions, there are prior and posterior distributions. Posterior distribution is influenced by the selection of prior distribution. Jeffreys’ prior distribution is a kind of Non-informative prior distribution. This prior is used when the information about parameter not available. Non-informative Jeffreys’ prior distribution is combined with the sample information resulting the posterior distribution. Posterior distribution is used to estimate the parameter. The purposes of this research is to estimate the parameters of multivariate regression model using Bayesian method with Non-informative Jeffreys’ prior distribution. Based on the results and discussion, parameter estimation of β and Σ which were obtained from expected value of random variable of marginal posterior distribution function. The marginal posterior distributions for β and Σ are multivariate normal and inverse Wishart. However, in calculation of the expected value involving integral of a function which difficult to determine the value. Therefore, approach is needed by generating of random samples according to the posterior distribution characteristics of each parameter using Markov chain Monte Carlo (MCMC) Gibbs sampling algorithm.

Measurement bias detection with Kronecker product restricted models for multivariate longitudinal data: an illustration with health-related quality of life data from thirteen measurement occasions

PubMed Central

Verdam, Mathilde G. E.; Oort, Frans J.

2014-01-01

Highlights Application of Kronecker product to construct parsimonious structural equation models for multivariate longitudinal data. A method for the investigation of measurement bias with Kronecker product restricted models. Application of these methods to health-related quality of life data from bone metastasis patients, collected at 13 consecutive measurement occasions. The use of curves to facilitate substantive interpretation of apparent measurement bias. Assessment of change in common factor means, after accounting for apparent measurement bias. Longitudinal measurement invariance is usually investigated with a longitudinal factor model (LFM). However, with multiple measurement occasions, the number of parameters to be estimated increases with a multiple of the number of measurement occasions. To guard against too low ratios of numbers of subjects and numbers of parameters, we can use Kronecker product restrictions to model the multivariate longitudinal structure of the data. These restrictions can be imposed on all parameter matrices, including measurement invariance restrictions on factor loadings and intercepts. The resulting models are parsimonious and have attractive interpretation, but require different methods for the investigation of measurement bias. Specifically, additional parameter matrices are introduced to accommodate possible violations of measurement invariance. These additional matrices consist of measurement bias parameters that are either fixed at zero or free to be estimated. In cases of measurement bias, it is also possible to model the bias over time, e.g., with linear or non-linear curves. Measurement bias detection with Kronecker product restricted models will be illustrated with multivariate longitudinal data from 682 bone metastasis patients whose health-related quality of life (HRQL) was measured at 13 consecutive weeks. PMID:25295016

Measurement bias detection with Kronecker product restricted models for multivariate longitudinal data: an illustration with health-related quality of life data from thirteen measurement occasions.

PubMed

Verdam, Mathilde G E; Oort, Frans J

2014-01-01

Application of Kronecker product to construct parsimonious structural equation models for multivariate longitudinal data.A method for the investigation of measurement bias with Kronecker product restricted models.Application of these methods to health-related quality of life data from bone metastasis patients, collected at 13 consecutive measurement occasions.The use of curves to facilitate substantive interpretation of apparent measurement bias.Assessment of change in common factor means, after accounting for apparent measurement bias.Longitudinal measurement invariance is usually investigated with a longitudinal factor model (LFM). However, with multiple measurement occasions, the number of parameters to be estimated increases with a multiple of the number of measurement occasions. To guard against too low ratios of numbers of subjects and numbers of parameters, we can use Kronecker product restrictions to model the multivariate longitudinal structure of the data. These restrictions can be imposed on all parameter matrices, including measurement invariance restrictions on factor loadings and intercepts. The resulting models are parsimonious and have attractive interpretation, but require different methods for the investigation of measurement bias. Specifically, additional parameter matrices are introduced to accommodate possible violations of measurement invariance. These additional matrices consist of measurement bias parameters that are either fixed at zero or free to be estimated. In cases of measurement bias, it is also possible to model the bias over time, e.g., with linear or non-linear curves. Measurement bias detection with Kronecker product restricted models will be illustrated with multivariate longitudinal data from 682 bone metastasis patients whose health-related quality of life (HRQL) was measured at 13 consecutive weeks.

Comparison between Linear and Nonlinear Regression in a Laboratory Heat Transfer Experiment

ERIC Educational Resources Information Center

Gonçalves, Carine Messias; Schwaab, Marcio; Pinto, José Carlos

2013-01-01

In order to interpret laboratory experimental data, undergraduate students are used to perform linear regression through linearized versions of nonlinear models. However, the use of linearized models can lead to statistically biased parameter estimates. Even so, it is not an easy task to introduce nonlinear regression and show for the students…

Semi-analytical solution of flow to a well in an unconfined-fractured aquifer system separated by an aquitard

NASA Astrophysics Data System (ADS)

Sedghi, Mohammad M.; Samani, Nozar; Barry, D. A.

2018-04-01

Semi-analytical solutions are presented for flow to a well in an extensive homogeneous and anisotropic unconfined-fractured aquifer system separated by an aquitard. The pumping well is of infinitesimal radius and screened in either the overlying unconfined aquifer or the underlying fractured aquifer. An existing linearization method was used to determine the watertable drainage. The solution was obtained via Laplace and Hankel transforms, with results calculated by numerical inversion. The main findings are presented in the form of non-dimensional drawdown-time curves, as well as scaled sensitivity-dimensionless time curves. The new solution permits determination of the influence of fractures, matrix blocks and watertable drainage parameters on the aquifer drawdown. The effect of the aquitard on the drawdown response of the overlying unconfined aquifer and the underlying fractured aquifer was also explored. The results permit estimation of the unconfined and fractured aquifer hydraulic parameters via type-curve matching or coupling of the solution with a parameter estimation code. The solution can also be used to determine aquifer hydraulic properties from an optimal pumping test set up and duration.

A one-step method for modelling longitudinal data with differential equations.

PubMed

Hu, Yueqin; Treinen, Raymond

2018-04-06

Differential equation models are frequently used to describe non-linear trajectories of longitudinal data. This study proposes a new approach to estimate the parameters in differential equation models. Instead of estimating derivatives from the observed data first and then fitting a differential equation to the derivatives, our new approach directly fits the analytic solution of a differential equation to the observed data, and therefore simplifies the procedure and avoids bias from derivative estimations. A simulation study indicates that the analytic solutions of differential equations (ASDE) approach obtains unbiased estimates of parameters and their standard errors. Compared with other approaches that estimate derivatives first, ASDE has smaller standard error, larger statistical power and accurate Type I error. Although ASDE obtains biased estimation when the system has sudden phase change, the bias is not serious and a solution is also provided to solve the phase problem. The ASDE method is illustrated and applied to a two-week study on consumers' shopping behaviour after a sale promotion, and to a set of public data tracking participants' grammatical facial expression in sign language. R codes for ASDE, recommendations for sample size and starting values are provided. Limitations and several possible expansions of ASDE are also discussed. © 2018 The British Psychological Society.

Estimation of pharmacokinetic parameters from non-compartmental variables using Microsoft Excel.

PubMed

Dansirikul, Chantaratsamon; Choi, Malcolm; Duffull, Stephen B

2005-06-01

This study was conducted to develop a method, termed 'back analysis (BA)', for converting non-compartmental variables to compartment model dependent pharmacokinetic parameters for both one- and two-compartment models. A Microsoft Excel spreadsheet was implemented with the use of Solver and visual basic functions. The performance of the BA method in estimating pharmacokinetic parameter values was evaluated by comparing the parameter values obtained to a standard modelling software program, NONMEM, using simulated data. The results show that the BA method was reasonably precise and provided low bias in estimating fixed and random effect parameters for both one- and two-compartment models. The pharmacokinetic parameters estimated from the BA method were similar to those of NONMEM estimation.

Identification and compensation of friction for a novel two-axis differential micro-feed system

NASA Astrophysics Data System (ADS)

Du, Fuxin; Zhang, Mingyang; Wang, Zhaoguo; Yu, Chen; Feng, Xianying; Li, Peigang

2018-06-01

Non-linear friction in a conventional drive feed system (CDFS) feeding at low speed is one of the main factors that lead to the complexity of the feed drive. The CDFS will inevitably enter or approach a non-linear creeping work area at extremely low speed. A novel two-axis differential micro-feed system (TDMS) is developed in this paper to overcome the accuracy limitation of CDFS. A dynamic model of TDMS is first established. Then, a novel all-component friction parameter identification method (ACFPIM) using a genetic algorithm (GA) to identify the friction parameters of a TDMS is introduced. The friction parameters of the ball screw and linear motion guides are identified independently using the method, assuring the accurate modelling of friction force at all components. A proportional-derivate feed drive position controller with an observer-based friction compensator is implemented to achieve an accurate trajectory tracking performance. Finally, comparative experiments demonstrate the effectiveness of the TDMS in inhibiting the disadvantageous influence of non-linear friction and the validity of the proposed identification method for TDMS.

Spherically symmetric analysis on open FLRW solution in non-linear massive gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin, E-mail: chienichiang@berkeley.edu, E-mail: izumi@phys.ntu.edu.tw, E-mail: chen@slac.stanford.edu

2012-12-01

We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity frommore » general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.« less

Combining markers with and without the limit of detection

PubMed Central

Dong, Ting; Liu, Catherine Chunling; Petricoin, Emanuel F.; Tang, Liansheng Larry

2014-01-01

In this paper, we consider the combination of markers with and without the limit of detection (LOD). LOD is often encountered when measuring proteomic markers. Because of the limited detecting ability of an equipment or instrument, it is difficult to measure markers at a relatively low level. Suppose that after some monotonic transformation, the marker values approximately follow multivariate normal distributions. We propose to estimate distribution parameters while taking the LOD into account, and then combine markers using the results from the linear discriminant analysis. Our simulation results show that the ROC curve parameter estimates generated from the proposed method are much closer to the truth than simply using the linear discriminant analysis to combine markers without considering the LOD. In addition, we propose a procedure to select and combine a subset of markers when many candidate markers are available. The procedure based on the correlation among markers is different from a common understanding that a subset of the most accurate markers should be selected for the combination. The simulation studies show that the accuracy of a combined marker can be largely impacted by the correlation of marker measurements. Our methods are applied to a protein pathway dataset to combine proteomic biomarkers to distinguish cancer patients from non-cancer patients. PMID:24132938

Underwater passive acoustic localization of Pacific walruses in the northeastern Chukchi Sea.

PubMed

Rideout, Brendan P; Dosso, Stan E; Hannay, David E

2013-09-01

This paper develops and applies a linearized Bayesian localization algorithm based on acoustic arrival times of marine mammal vocalizations at spatially-separated receivers which provides three-dimensional (3D) location estimates with rigorous uncertainty analysis. To properly account for uncertainty in receiver parameters (3D hydrophone locations and synchronization times) and environmental parameters (water depth and sound-speed correction), these quantities are treated as unknowns constrained by prior estimates and prior uncertainties. Unknown scaling factors on both the prior and arrival-time uncertainties are estimated by minimizing Akaike's Bayesian information criterion (a maximum entropy condition). Maximum a posteriori estimates for sound source locations and times, receiver parameters, and environmental parameters are calculated simultaneously using measurements of arrival times for direct and interface-reflected acoustic paths. Posterior uncertainties for all unknowns incorporate both arrival time and prior uncertainties. Monte Carlo simulation results demonstrate that, for the cases considered here, linearization errors are small and the lack of an accurate sound-speed profile does not cause significant biases in the estimated locations. A sequence of Pacific walrus vocalizations, recorded in the Chukchi Sea northwest of Alaska, is localized using this technique, yielding a track estimate and uncertainties with an estimated speed comparable to normal walrus swim speeds.

Estimation of octanol/water partition coefficients using LSER parameters

USGS Publications Warehouse

Luehrs, Dean C.; Hickey, James P.; Godbole, Kalpana A.; Rogers, Tony N.

1998-01-01

The logarithms of octanol/water partition coefficients, logKow, were regressed against the linear solvation energy relationship (LSER) parameters for a training set of 981 diverse organic chemicals. The standard deviation for logKow was 0.49. The regression equation was then used to estimate logKow for a test of 146 chemicals which included pesticides and other diverse polyfunctional compounds. Thus the octanol/water partition coefficient may be estimated by LSER parameters without elaborate software but only moderate accuracy should be expected.

Extracting surface diffusion coefficients from batch adsorption measurement data: application of the classic Langmuir kinetics model.

PubMed

Chu, Khim Hoong

2017-11-09

Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the diffusion model's governing equations is generally required. We report here the application of the classic Langmuir kinetics model to extract surface diffusion coefficients from batch kinetic data. The use of the Langmuir kinetics model in lieu of the conventional surface diffusion model allows derivation of an analytical expression. The parameter estimation procedure requires determining the Langmuir rate coefficient from which the pertinent surface diffusion coefficient is calculated. Surface diffusion coefficients within the 10 -9 to 10 -6  cm 2 /s range obtained by fitting the Langmuir kinetics model to experimental kinetic data taken from the literature are found to be consistent with the corresponding values obtained from the traditional surface diffusion model. The virtue of this simplified parameter estimation method is that it reduces the computational complexity as the analytical expression involves only an algebraic equation in closed form which is easily evaluated by spreadsheet computation.

Optimal estimation of parameters and states in stochastic time-varying systems with time delay

NASA Astrophysics Data System (ADS)

Torkamani, Shahab; Butcher, Eric A.

2013-08-01

In this study estimation of parameters and states in stochastic linear and nonlinear delay differential systems with time-varying coefficients and constant delay is explored. The approach consists of first employing a continuous time approximation to approximate the stochastic delay differential equation with a set of stochastic ordinary differential equations. Then the problem of parameter estimation in the resulting stochastic differential system is represented as an optimal filtering problem using a state augmentation technique. By adapting the extended Kalman-Bucy filter to the resulting system, the unknown parameters of the time-delayed system are estimated from noise-corrupted, possibly incomplete measurements of the states.

Noise normalization and windowing functions for VALIDAR in wind parameter estimation

NASA Astrophysics Data System (ADS)

Beyon, Jeffrey Y.; Koch, Grady J.; Li, Zhiwen

2006-05-01

The wind parameter estimates from a state-of-the-art 2-μm coherent lidar system located at NASA Langley, Virginia, named VALIDAR (validation lidar), were compared after normalizing the noise by its estimated power spectra via the periodogram and the linear predictive coding (LPC) scheme. The power spectra and the Doppler shift estimates were the main parameter estimates for comparison. Different types of windowing functions were implemented in VALIDAR data processing algorithm and their impact on the wind parameter estimates was observed. Time and frequency independent windowing functions such as Rectangular, Hanning, and Kaiser-Bessel and time and frequency dependent apodized windowing function were compared. The briefing of current nonlinear algorithm development for Doppler shift correction subsequently follows.

Centroid estimation for a Shack-Hartmann wavefront sensor based on stream processing.

PubMed

Kong, Fanpeng; Polo, Manuel Cegarra; Lambert, Andrew

2017-08-10

Using center of gravity to estimate the centroid of the spot in a Shack-Hartmann wavefront sensor, the measurement corrupts with photon and detector noise. Parameters, like window size, often require careful optimization to balance the noise error, dynamic range, and linearity of the response coefficient under different photon flux. It also needs to be substituted by the correlation method for extended sources. We propose a centroid estimator based on stream processing, where the center of gravity calculation window floats with the incoming pixel from the detector. In comparison with conventional methods, we show that the proposed estimator simplifies the choice of optimized parameters, provides a unit linear coefficient response, and reduces the influence of background and noise. It is shown that the stream-based centroid estimator also works well for limited size extended sources. A hardware implementation of the proposed estimator is discussed.

Genetic parameters for racing records in trotters using linear and generalized linear models.

PubMed

Suontama, M; van der Werf, J H J; Juga, J; Ojala, M

2012-09-01

Heritability and repeatability and genetic and phenotypic correlations were estimated for trotting race records with linear and generalized linear models using 510,519 records on 17,792 Finnhorses and 513,161 records on 25,536 Standardbred trotters. Heritability and repeatability were estimated for single racing time and earnings traits with linear models, and logarithmic scale was used for racing time and fourth-root scale for earnings to correct for nonnormality. Generalized linear models with a gamma distribution were applied for single racing time and with a multinomial distribution for single earnings traits. In addition, genetic parameters for annual earnings were estimated with linear models on the observed and fourth-root scales. Racing success traits of single placings, winnings, breaking stride, and disqualifications were analyzed using generalized linear models with a binomial distribution. Estimates of heritability were greatest for racing time, which ranged from 0.32 to 0.34. Estimates of heritability were low for single earnings with all distributions, ranging from 0.01 to 0.09. Annual earnings were closer to normal distribution than single earnings. Heritability estimates were moderate for annual earnings on the fourth-root scale, 0.19 for Finnhorses and 0.27 for Standardbred trotters. Heritability estimates for binomial racing success variables ranged from 0.04 to 0.12, being greatest for winnings and least for breaking stride. Genetic correlations among racing traits were high, whereas phenotypic correlations were mainly low to moderate, except correlations between racing time and earnings were high. On the basis of a moderate heritability and moderate to high repeatability for racing time and annual earnings, selection of horses for these traits is effective when based on a few repeated records. Because of high genetic correlations, direct selection for racing time and annual earnings would also result in good genetic response in racing success.

A sensitivity analysis for a thermomechanical model of the Antarctic ice sheet and ice shelves

NASA Astrophysics Data System (ADS)

Baratelli, F.; Castellani, G.; Vassena, C.; Giudici, M.

2012-04-01

The outcomes of an ice sheet model depend on a number of parameters and physical quantities which are often estimated with large uncertainty, because of lack of sufficient experimental measurements in such remote environments. Therefore, the efforts to improve the accuracy of the predictions of ice sheet models by including more physical processes and interactions with atmosphere, hydrosphere and lithosphere can be affected by the inaccuracy of the fundamental input data. A sensitivity analysis can help to understand which are the input data that most affect the different predictions of the model. In this context, a finite difference thermomechanical ice sheet model based on the Shallow-Ice Approximation (SIA) and on the Shallow-Shelf Approximation (SSA) has been developed and applied for the simulation of the evolution of the Antarctic ice sheet and ice shelves for the last 200 000 years. The sensitivity analysis of the model outcomes (e.g., the volume of the ice sheet and of the ice shelves, the basal melt rate of the ice sheet, the mean velocity of the Ross and Ronne-Filchner ice shelves, the wet area at the base of the ice sheet) with respect to the model parameters (e.g., the basal sliding coefficient, the geothermal heat flux, the present-day surface accumulation and temperature, the mean ice shelves viscosity, the melt rate at the base of the ice shelves) has been performed by computing three synthetic numerical indices: two local sensitivity indices and a global sensitivity index. Local sensitivity indices imply a linearization of the model and neglect both non-linear and joint effects of the parameters. The global variance-based sensitivity index, instead, takes into account the complete variability of the input parameters but is usually conducted with a Monte Carlo approach which is computationally very demanding for non-linear complex models. Therefore, the global sensitivity index has been computed using a development of the model outputs in a neighborhood of the reference parameter values with a second-order approximation. The comparison of the three sensitivity indices proved that the approximation of the non-linear model with a second-order expansion is sufficient to show some differences between the local and the global indices. As a general result, the sensitivity analysis showed that most of the model outcomes are mainly sensitive to the present-day surface temperature and accumulation, which, in principle, can be measured more easily (e.g., with remote sensing techniques) than the other input parameters considered. On the other hand, the parameters to which the model resulted less sensitive are the basal sliding coefficient and the mean ice shelves viscosity.

Kinetic modeling of the photocatalytic degradation of clofibric acid in a slurry reactor.

PubMed

Manassero, Agustina; Satuf, María Lucila; Alfano, Orlando Mario

2015-01-01

A kinetic study of the photocatalytic degradation of the pharmaceutical clofibric acid is presented. Experiments were carried out under UV radiation employing titanium dioxide in water suspension. The main reaction intermediates were identified and quantified. Intrinsic expressions to represent the kinetics of clofibric acid and the main intermediates were derived. The modeling of the radiation field in the reactor was carried out by Monte Carlo simulation. Experimental runs were performed by varying the catalyst concentration and the incident radiation. Kinetic parameters were estimated from the experiments by applying a non-linear regression procedure. Good agreement was obtained between model predictions and experimental data, with an error of 5.9 % in the estimations of the primary pollutant concentration.

Quadratic semiparametric Von Mises calculus

PubMed Central

Robins, James; Li, Lingling; Tchetgen, Eric

2009-01-01

We discuss a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on U-statistics constructed from quadratic influence functions. The latter extend ordinary linear influence functions of the parameter of interest as defined in semiparametric theory, and represent second order derivatives of this parameter. For parameters for which the matching cannot be perfect the method leads to a bias-variance trade-off, and results in estimators that converge at a slower than n–1/2-rate. In a number of examples the resulting rate can be shown to be optimal. We are particularly interested in estimating parameters in models with a nuisance parameter of high dimension or low regularity, where the parameter of interest cannot be estimated at n–1/2-rate. PMID:23087487

The influence of linear elements on plant species diversity of Mediterranean rural landscapes: assessment of different indices and statistical approaches.

PubMed

García del Barrio, J M; Ortega, M; Vázquez De la Cueva, A; Elena-Rosselló, R

2006-08-01

This paper mainly aims to study the linear element influence on the estimation of vascular plant species diversity in five Mediterranean landscapes modeled as land cover patch mosaics. These landscapes have several core habitats and a different set of linear elements--habitat edges or ecotones, roads or railways, rivers, streams and hedgerows on farm land--whose plant composition were examined. Secondly, it aims to check plant diversity estimation in Mediterranean landscapes using parametric and non-parametric procedures, with two indices: Species richness and Shannon index. Land cover types and landscape linear elements were identified from aerial photographs. Their spatial information was processed using GIS techniques. Field plots were selected using a stratified sampling design according to relieve and tree density of each habitat type. A 50x20 m2 multi-scale sampling plot was designed for the core habitats and across the main landscape linear elements. Richness and diversity of plant species were estimated by comparing the observed field data to ICE (Incidence-based Coverage Estimator) and ACE (Abundance-based Coverage Estimator) non-parametric estimators. The species density, percentage of unique species, and alpha diversity per plot were significantly higher (p < 0.05) in linear elements than in core habitats. ICE estimate of number of species was 32% higher than of ACE estimate, which did not differ significantly from the observed values. Accumulated species richness in core habitats together with linear elements, were significantly higher than those recorded only in the core habitats in all the landscapes. Conversely, Shannon diversity index did not show significant differences.

Hurst Estimation of Scale Invariant Processes with Stationary Increments and Piecewise Linear Drift

NASA Astrophysics Data System (ADS)

Modarresi, N.; Rezakhah, S.

The characteristic feature of the discrete scale invariant (DSI) processes is the invariance of their finite dimensional distributions by dilation for certain scaling factor. DSI process with piecewise linear drift and stationary increments inside prescribed scale intervals is introduced and studied. To identify the structure of the process, first, we determine the scale intervals, their linear drifts and eliminate them. Then, a new method for the estimation of the Hurst parameter of such DSI processes is presented and applied to some period of the Dow Jones indices. This method is based on fixed number equally spaced samples inside successive scale intervals. We also present some efficient method for estimating Hurst parameter of self-similar processes with stationary increments. We compare the performance of this method with the celebrated FA, DFA and DMA on the simulated data of fractional Brownian motion (fBm).

Intelligent, Robust Control of Deteriorated Turbofan Engines via Linear Parameter Varying Quadratic Lyapunov Function Design

NASA Technical Reports Server (NTRS)

Turso, James A.; Litt, Jonathan S.

2004-01-01

A method for accommodating engine deterioration via a scheduled Linear Parameter Varying Quadratic Lyapunov Function (LPVQLF)-Based controller is presented. The LPVQLF design methodology provides a means for developing unconditionally stable, robust control of Linear Parameter Varying (LPV) systems. The controller is scheduled on the Engine Deterioration Index, a function of estimated parameters that relate to engine health, and is computed using a multilayer feedforward neural network. Acceptable thrust response and tight control of exhaust gas temperature (EGT) is accomplished by adjusting the performance weights on these parameters for different levels of engine degradation. Nonlinear simulations demonstrate that the controller achieves specified performance objectives while being robust to engine deterioration as well as engine-to-engine variations.

Financial market dynamics: superdiffusive or not?

NASA Astrophysics Data System (ADS)

Devi, Sandhya

2017-08-01

The behavior of stock market returns over a period of 1-60 d has been investigated for S&P 500 and Nasdaq within the framework of nonextensive Tsallis statistics. Even for such long terms, the distributions of the returns are non-Gaussian. They have fat tails indicating that the stock returns do not follow a random walk model. In this work, a good fit to a Tsallis q-Gaussian distribution is obtained for the distributions of all the returns using the method of Maximum Likelihood Estimate. For all the regions of data considered, the values of the scaling parameter q, estimated from 1 d returns, lie in the range 1.4-1.65. The estimated inverse mean square deviations (beta) show a power law behavior in time with exponent values between  -0.91 and  -1.1 indicating normal to mildly subdiffusive behavior. Quite often, the dynamics of market return distributions is modelled by a Fokker-Plank (FP) equation either with a linear drift and a nonlinear diffusion term or with just a nonlinear diffusion term. Both of these cases support a q-Gaussian distribution as a solution. The distributions obtained from current estimated parameters are compared with the solutions of the FP equations. For negligible drift term, the inverse mean square deviations (betaFP) from the FP model follow a power law with exponent values between  -1.25 and  -1.48 indicating superdiffusion. When the drift term is non-negligible, the corresponding betaFP do not follow a power law and become stationary after certain characteristic times that depend on the values of the drift parameter and q. Neither of these behaviors is supported by the results of the empirical fit.

Longitudinal association of short-term, metronome-paced heart rate variability and echocardiographically assessed cardiac structure at a 4-year follow-up: results from the prospective, population-based CARLA cohort.

PubMed

Medenwald, Daniel; Swenne, Cees A; Frantz, Stefan; Nuding, Sebastian; Kors, Jan A; Pietzner, Diana; Tiller, Daniel; Greiser, Karin H; Kluttig, Alexander; Haerting, Johannes

2017-12-01

To assess the value of cardiac structure/function in predicting heart rate variability (HRV) and the possibly predictive value of HRV on cardiac parameters. Baseline and 4-year follow-up data from the population-based CARLA cohort were used (790 men, 646 women, aged 45-83 years at baseline and 50-87 years at follow-up). Echocardiographic and HRV recordings were performed at baseline and at follow-up. Linear regression models with a quadratic term were used. Crude and covariate adjusted estimates were calculated. Missing values were imputed by means of multiple imputation. Heart rate variability measures taken into account consisted of linear time and frequency domain [standard deviation of normal-to-normal intervals (SDNN), high-frequency power (HF), low-frequency power (LF), LF/HF ratio] and non-linear measures [detrended fluctuation analysis (DFA1), SD1, SD2, SD1/SD2 ratio]. Echocardiographic parameters considered were ventricular mass index, diastolic interventricular septum thickness, left ventricular diastolic dimension, left atrial dimension systolic (LADS), and ejection fraction (Teichholz). A negative quadratic relation between baseline LADS and change in SDNN and HF was observed. The maximum HF and SDNN change (an increase of roughly 0.02%) was predicted at LADS of 3.72 and 3.57 cm, respectively, while the majority of subjects experienced a decrease in HRV. There was no association between further echocardiographic parameters and change in HRV, and there was no evidence of a predictive value of HRV in the prediction of changes in cardiac structure. In the general population, LADS predicts 4-year alteration in SDNN and HF non-linearly. Because of the novelty of the result, analyses should be replicated in other populations. Published on behalf of the European Society of Cardiology. All rights reserved. © The Author 2017. For permissions please email: journals.permissions@oup.com.

Joint constraints on galaxy bias and σ{sub 8} through the N-pdf of the galaxy number density

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arnalte-Mur, Pablo; Martínez, Vicent J.; Vielva, Patricio

We present a full description of the N-probability density function of the galaxy number density fluctuations. This N-pdf is given in terms, on the one hand, of the cold dark matter correlations and, on the other hand, of the galaxy bias parameter. The method relies on the assumption commonly adopted that the dark matter density fluctuations follow a local non-linear transformation of the initial energy density perturbations. The N-pdf of the galaxy number density fluctuations allows for an optimal estimation of the bias parameter (e.g., via maximum-likelihood estimation, or Bayesian inference if there exists any a priori information on themore » bias parameter), and of those parameters defining the dark matter correlations, in particular its amplitude (σ{sub 8}). It also provides the proper framework to perform model selection between two competitive hypotheses. The parameters estimation capabilities of the N-pdf are proved by SDSS-like simulations (both, ideal log-normal simulations and mocks obtained from Las Damas simulations), showing that our estimator is unbiased. We apply our formalism to the 7th release of the SDSS main sample (for a volume-limited subset with absolute magnitudes M{sub r} ≤ −20). We obtain b-circumflex  = 1.193 ± 0.074 and σ-bar{sub 8} = 0.862 ± 0.080, for galaxy number density fluctuations in cells of the size of 30h{sup −1}Mpc. Different model selection criteria show that galaxy biasing is clearly favoured.« less

Integration of measurements with atmospheric dispersion models: Source term estimation for dispersal of (239)Pu due to non-nuclear detonation of high explosive

NASA Astrophysics Data System (ADS)

Edwards, L. L.; Harvey, T. F.; Freis, R. P.; Pitovranov, S. E.; Chernokozhin, E. V.

1992-10-01

The accuracy associated with assessing the environmental consequences of an accidental release of radioactivity is highly dependent on our knowledge of the source term characteristics and, in the case when the radioactivity is condensed on particles, the particle size distribution, all of which are generally poorly known. This paper reports on the development of a numerical technique that integrates the radiological measurements with atmospheric dispersion modeling. This results in a more accurate particle-size distribution and particle injection height estimation when compared with measurements of high explosive dispersal of (239)Pu. The estimation model is based on a non-linear least squares regression scheme coupled with the ARAC three-dimensional atmospheric dispersion models. The viability of the approach is evaluated by estimation of ADPIC model input parameters such as the ADPIC particle size mean aerodynamic diameter, the geometric standard deviation, and largest size. Additionally we estimate an optimal 'coupling coefficient' between the particles and an explosive cloud rise model. The experimental data are taken from the Clean Slate 1 field experiment conducted during 1963 at the Tonopah Test Range in Nevada. The regression technique optimizes the agreement between the measured and model predicted concentrations of (239)Pu by varying the model input parameters within their respective ranges of uncertainties. The technique generally estimated the measured concentrations within a factor of 1.5, with the worst estimate being within a factor of 5, very good in view of the complexity of the concentration measurements, the uncertainties associated with the meteorological data, and the limitations of the models. The best fit also suggest a smaller mean diameter and a smaller geometric standard deviation on the particle size as well as a slightly weaker particle to cloud coupling than previously reported.

Estimation of Fetal Weight during Labor: Still a Challenge.

PubMed

Barros, Joana Goulão; Reis, Inês; Pereira, Isabel; Clode, Nuno; Graça, Luís M

2016-01-01

To evaluate the accuracy of fetal weight prediction by ultrasonography labor employing a formula including the linear measurements of femur length (FL) and mid-thigh soft-tissue thickness (STT). We conducted a prospective study involving singleton uncomplicated term pregnancies within 48 hours of delivery. Only pregnancies with a cephalic fetus admitted in the labor ward for elective cesarean section, induction of labor or spontaneous labor were included. We excluded all non-Caucasian women, the ones previously diagnosed with gestational diabetes and the ones with evidence of ruptured membranes. Fetal weight estimates were calculated using a previously proposed formula [estimated fetal weight = 1687.47 + (54.1 x FL) + (76.68 x STT). The relationship between actual birth weight and estimated fetal weight was analyzed using Pearson's correlation. The formula's performance was assessed by calculating the signed and absolute errors. Mean weight difference and signed percentage error were calculated for birth weight divided into three subgroups: < 3000 g; 3000-4000 g; and > 4000 g. We included for analysis 145 cases and found a significant, yet low, linear relationship between birth weight and estimated fetal weight (p < 0.001; R2 = 0.197) with an absolute mean error of 10.6%. The lowest mean percentage error (0.3%) corresponded to the subgroup with birth weight between 3000 g and 4000 g. This study demonstrates a poor correlation between actual birth weight and the estimated fetal weight using a formula based on femur length and mid-thigh soft-tissue thickness, both linear parameters. Although avoidance of circumferential ultrasound measurements might prove to be beneficial, it is still yet to be found a fetal estimation formula that can be both accurate and simple to perform.

Linear Estimation of Particle Bulk Parameters from Multi-Wavelength Lidar Measurements

NASA Technical Reports Server (NTRS)

Veselovskii, Igor; Dubovik, Oleg; Kolgotin, A.; Korenskiy, M.; Whiteman, D. N.; Allakhverdiev, K.; Huseyinoglu, F.

2012-01-01

An algorithm for linear estimation of aerosol bulk properties such as particle volume, effective radius and complex refractive index from multiwavelength lidar measurements is presented. The approach uses the fact that the total aerosol concentration can well be approximated as a linear combination of aerosol characteristics measured by multiwavelength lidar. Therefore, the aerosol concentration can be estimated from lidar measurements without the need to derive the size distribution, which entails more sophisticated procedures. The definition of the coefficients required for the linear estimates is based on an expansion of the particle size distribution in terms of the measurement kernels. Once the coefficients are established, the approach permits fast retrieval of aerosol bulk properties when compared with the full regularization technique. In addition, the straightforward estimation of bulk properties stabilizes the inversion making it more resistant to noise in the optical data. Numerical tests demonstrate that for data sets containing three aerosol backscattering and two extinction coefficients (so called 3 + 2 ) the uncertainties in the retrieval of particle volume and surface area are below 45% when input data random uncertainties are below 20 %. Moreover, using linear estimates allows reliable retrievals even when the number of input data is reduced. To evaluate the approach, the results obtained using this technique are compared with those based on the previously developed full inversion scheme that relies on the regularization procedure. Both techniques were applied to the data measured by multiwavelength lidar at NASA/GSFC. The results obtained with both methods using the same observations are in good agreement. At the same time, the high speed of the retrieval using linear estimates makes the method preferable for generating aerosol information from extended lidar observations. To demonstrate the efficiency of the method, an extended time series of observations acquired in Turkey in May 2010 was processed using the linear estimates technique permitting, for what we believe to be the first time, temporal-height distributions of particle parameters.

Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thimmisetty, Charanraj A.; Zhao, Wenju; Chen, Xiao

2017-10-18

Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). Thismore » approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.« less

Revisiting linear plasma waves for finite value of the plasma parameter

NASA Astrophysics Data System (ADS)

Grismayer, Thomas; Fahlen, Jay; Decyk, Viktor; Mori, Warren

2010-11-01

We investigate through theory and PIC simulations the Landau-damping of plasma waves with finite plasma parameter. We concentrate on the linear regime, γφB, where the waves are typically small and below the thermal noise. We simulate these condition using 1,2,3D electrostatic PIC codes (BEPS), noting that modern computers now allow us to simulate cases where (nλD^3 = [1e2;1e6]). We study these waves by using a subtraction technique in which two simulations are carried out. In the first, a small wave is initialized or driven, in the second no wave is excited. The results are subtracted to provide a clean signal that can be studied. As nλD^3 is decreased, the number of resonant electrons can be small for linear waves. We show how the damping changes as a result of having few resonant particles. We also find that for small nλD^3 fluctuations can cause the electrons to undergo collisions that eventually destroy the initial wave. A quantity of interest is the the life time of a particular mode which depends on the plasma parameter and the wave number. The life time is estimated and then compared with the numerical results. A surprising result is that even for large values of nλD^3 some non-Vlasov discreteness effects appear to be important.

The Impact of Model Misspecification on Parameter Estimation and Item-Fit Assessment in Log-Linear Diagnostic Classification Models

ERIC Educational Resources Information Center

Kunina-Habenicht, Olga; Rupp, Andre A.; Wilhelm, Oliver

2012-01-01

Using a complex simulation study we investigated parameter recovery, classification accuracy, and performance of two item-fit statistics for correct and misspecified diagnostic classification models within a log-linear modeling framework. The basic manipulated test design factors included the number of respondents (1,000 vs. 10,000), attributes (3…

Three dimensional radiative flow of magnetite-nanofluid with homogeneous-heterogeneous reactions

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Rashid, Madiha; Alsaedi, Ahmed

2018-03-01

Present communication deals with the effects of homogeneous-heterogeneous reactions in flow of nanofluid by non-linear stretching sheet. Water based nanofluid containing magnetite nanoparticles is considered. Non-linear radiation and non-uniform heat sink/source effects are examined. Non-linear differential systems are computed by Optimal homotopy analysis method (OHAM). Convergent solutions of nonlinear systems are established. The optimal data of auxiliary variables is obtained. Impact of several non-dimensional parameters for velocity components, temperature and concentration fields are examined. Graphs are plotted for analysis of surface drag force and heat transfer rate.

Axioms of adaptivity

PubMed Central

Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D.

2014-01-01

This paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of (discrete) lower bounds, inexact solvers, inhomogeneous boundary data, or the use of equivalent error estimators. Solely four axioms guarantee the optimality in terms of the error estimators. Compared to the state of the art in the temporary literature, the improvements of this article can be summarized as follows: First, a general framework is presented which covers the existing literature on optimality of adaptive schemes. The abstract analysis covers linear as well as nonlinear problems and is independent of the underlying finite element or boundary element method. Second, efficiency of the error estimator is neither needed to prove convergence nor quasi-optimal convergence behavior of the error estimator. In this paper, efficiency exclusively characterizes the approximation classes involved in terms of the best-approximation error and data resolution and so the upper bound on the optimal marking parameters does not depend on the efficiency constant. Third, some general quasi-Galerkin orthogonality is not only sufficient, but also necessary for the R-linear convergence of the error estimator, which is a fundamental ingredient in the current quasi-optimality analysis due to Stevenson 2007. Finally, the general analysis allows for equivalent error estimators and inexact solvers as well as different non-homogeneous and mixed boundary conditions. PMID:25983390

Estimating linear temporal trends from aggregated environmental monitoring data

USGS Publications Warehouse

Erickson, Richard A.; Gray, Brian R.; Eager, Eric A.

2017-01-01

Trend estimates are often used as part of environmental monitoring programs. These trends inform managers (e.g., are desired species increasing or undesired species decreasing?). Data collected from environmental monitoring programs is often aggregated (i.e., averaged), which confounds sampling and process variation. State-space models allow sampling variation and process variations to be separated. We used simulated time-series to compare linear trend estimations from three state-space models, a simple linear regression model, and an auto-regressive model. We also compared the performance of these five models to estimate trends from a long term monitoring program. We specifically estimated trends for two species of fish and four species of aquatic vegetation from the Upper Mississippi River system. We found that the simple linear regression had the best performance of all the given models because it was best able to recover parameters and had consistent numerical convergence. Conversely, the simple linear regression did the worst job estimating populations in a given year. The state-space models did not estimate trends well, but estimated population sizes best when the models converged. We found that a simple linear regression performed better than more complex autoregression and state-space models when used to analyze aggregated environmental monitoring data.

Inverse problems-based maximum likelihood estimation of ground reflectivity for selected regions of interest from stripmap SAR data [Regularized maximum likelihood estimation of ground reflectivity from stripmap SAR data

DOE Office of Scientific and Technical Information (OSTI.GOV)

West, R. Derek; Gunther, Jacob H.; Moon, Todd K.

In this study, we derive a comprehensive forward model for the data collected by stripmap synthetic aperture radar (SAR) that is linear in the ground reflectivity parameters. It is also shown that if the noise model is additive, then the forward model fits into the linear statistical model framework, and the ground reflectivity parameters can be estimated by statistical methods. We derive the maximum likelihood (ML) estimates for the ground reflectivity parameters in the case of additive white Gaussian noise. Furthermore, we show that obtaining the ML estimates of the ground reflectivity requires two steps. The first step amounts tomore » a cross-correlation of the data with a model of the data acquisition parameters, and it is shown that this step has essentially the same processing as the so-called convolution back-projection algorithm. The second step is a complete system inversion that is capable of mitigating the sidelobes of the spatially variant impulse responses remaining after the correlation processing. We also state the Cramer-Rao lower bound (CRLB) for the ML ground reflectivity estimates.We show that the CRLB is linked to the SAR system parameters, the flight path of the SAR sensor, and the image reconstruction grid.We demonstrate the ML image formation and the CRLB bound for synthetically generated data.« less

Inverse problems-based maximum likelihood estimation of ground reflectivity for selected regions of interest from stripmap SAR data [Regularized maximum likelihood estimation of ground reflectivity from stripmap SAR data

DOE PAGES

West, R. Derek; Gunther, Jacob H.; Moon, Todd K.

2016-12-01

In this study, we derive a comprehensive forward model for the data collected by stripmap synthetic aperture radar (SAR) that is linear in the ground reflectivity parameters. It is also shown that if the noise model is additive, then the forward model fits into the linear statistical model framework, and the ground reflectivity parameters can be estimated by statistical methods. We derive the maximum likelihood (ML) estimates for the ground reflectivity parameters in the case of additive white Gaussian noise. Furthermore, we show that obtaining the ML estimates of the ground reflectivity requires two steps. The first step amounts tomore » a cross-correlation of the data with a model of the data acquisition parameters, and it is shown that this step has essentially the same processing as the so-called convolution back-projection algorithm. The second step is a complete system inversion that is capable of mitigating the sidelobes of the spatially variant impulse responses remaining after the correlation processing. We also state the Cramer-Rao lower bound (CRLB) for the ML ground reflectivity estimates.We show that the CRLB is linked to the SAR system parameters, the flight path of the SAR sensor, and the image reconstruction grid.We demonstrate the ML image formation and the CRLB bound for synthetically generated data.« less

Genomic prediction based on data from three layer lines using non-linear regression models.

PubMed

Huang, Heyun; Windig, Jack J; Vereijken, Addie; Calus, Mario P L

2014-11-06

Most studies on genomic prediction with reference populations that include multiple lines or breeds have used linear models. Data heterogeneity due to using multiple populations may conflict with model assumptions used in linear regression methods. In an attempt to alleviate potential discrepancies between assumptions of linear models and multi-population data, two types of alternative models were used: (1) a multi-trait genomic best linear unbiased prediction (GBLUP) model that modelled trait by line combinations as separate but correlated traits and (2) non-linear models based on kernel learning. These models were compared to conventional linear models for genomic prediction for two lines of brown layer hens (B1 and B2) and one line of white hens (W1). The three lines each had 1004 to 1023 training and 238 to 240 validation animals. Prediction accuracy was evaluated by estimating the correlation between observed phenotypes and predicted breeding values. When the training dataset included only data from the evaluated line, non-linear models yielded at best a similar accuracy as linear models. In some cases, when adding a distantly related line, the linear models showed a slight decrease in performance, while non-linear models generally showed no change in accuracy. When only information from a closely related line was used for training, linear models and non-linear radial basis function (RBF) kernel models performed similarly. The multi-trait GBLUP model took advantage of the estimated genetic correlations between the lines. Combining linear and non-linear models improved the accuracy of multi-line genomic prediction. Linear models and non-linear RBF models performed very similarly for genomic prediction, despite the expectation that non-linear models could deal better with the heterogeneous multi-population data. This heterogeneity of the data can be overcome by modelling trait by line combinations as separate but correlated traits, which avoids the occasional occurrence of large negative accuracies when the evaluated line was not included in the training dataset. Furthermore, when using a multi-line training dataset, non-linear models provided information on the genotype data that was complementary to the linear models, which indicates that the underlying data distributions of the three studied lines were indeed heterogeneous.

Angular spectra of the intrinsic galaxy ellipticity field, their observability and their impact on lensing in tomographic surveys

NASA Astrophysics Data System (ADS)

Schäfer, Björn Malte; Merkel, Philipp M.

2017-09-01

This paper describes intrinsic ellipticity correlations between galaxies, their statistical properties, their observability with future surveys and their interference with weak gravitational lensing measurements. Using an angular-momentum-based, quadratic intrinsic alignment model we derive correlation functions of the ellipticity components and project them to yield the four non-zero angular ellipticity spectra C^ɛ _E(ℓ), C^ɛ _B(ℓ), C^ɛ _C(ℓ) and C^ɛ _S(ℓ) in their generalization to tomographic surveys. For a Euclid-like survey, these spectra would have amplitudes smaller than the weak lensing effect on non-linear structures, but would constitute an important systematics. Computing estimation biases for cosmological parameters derived from an alignment-contaminated survey suggests biases of +5σw for the dark energy equation of state parameter w, -20σ _{Ω _m} for the matter density Ωm and -12σ _{σ _8} for the spectrum normalization σ8. Intrinsic alignments yield a signal that is easily observable with a survey similar to Euclid: while not independent, significances for estimates of each of the four spectra reach values of tens of σ if weak lensing and shape noise are considered as noise sources, which suggests relative uncertainties on alignment parameters at the percent level, implying that galaxy alignment mechanisms can be investigated by future surveys.

Slip Distribution of the 2008 Iwate-Miyagi Nairiku, Japan, Earthquake Inverted from PALSAR Data

NASA Astrophysics Data System (ADS)

Fukahata, Y.; Fukushima, Y.; Arimoto, M.

2008-12-01

On 14 June 2008, the Iwate-Miyagi Nairiku earthquake struck northeast Japan, where active seismicity has been observed under east-west compressional stress fields. According to the Japan Meteorological Agency, the magnitude and the hypocenter depth of the earthquake are 7.2 and 8 km, respectively. The earthquake is considered to have occurred on a west dipping reverse fault with a roughly north-south strike. The earthquake caused significant surface displacements, which were detected by PALSAR, a Synthetic Aperture Radar (SAR) onboard the Advanced Land Observing Satellite (ALOS) employed by the Japan Aerospace Exploration Agency (JAXA). Several pairs of PALSAR images are available to measure the coseismic displacements. InSAR data show up to 1 m of line-of-sight displacements both for ascending and descending paths. The pixel matching method was also used to obtain range and azimuth offset data around the epicentral region, where displacements were too large for the interferometric technique (see Fukushima (this meeting) in detail). We inverted the obtained SAR interferometric and pixel matching data to estimate slip distribution on the fault. Since the geometry of the fault are not well known, the inverse problem is non-linear. If the fault surface is assumed to be a flat plane, however, the non-linearity is weak. Following the method of Fukahata & Wright (2008), we resolved the weak non-linearity based on ABIC (Akaike"fs Bayesian Information Criterion). That is to say, the fault parameters (e.g. strike, dip and location) as well as the weight of smoothing parameter were objectively determined by minimizing ABIC. We first estimated slip distribution by assuming a pure dip slip for simplicity, since it has been reported that the dip slip component is dominant. Then, the optimal fault geometry was dip 26 and strike 203 degrees with the location passing through (140.90E, 38.97N). The maximum slip was more than 8 m and most slips concentrated at shallow depths (< 4 km). Without fixing the rake, a large slip area with the maximum slip of about 8 m concentrated in the shallow region was obtained again.

Modern control concepts in hydrology

NASA Technical Reports Server (NTRS)

Duong, N.; Johnson, G. R.; Winn, C. B.

1974-01-01

Two approaches to an identification problem in hydrology are presented based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time invariant or time dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and conform with results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second, by using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise.

Hubble Space Telescope Angular Velocity Estimation During the Robotic Servicing Mission

NASA Technical Reports Server (NTRS)

Thienel, Julie K.; Queen, Steven Z.; VanEepoel, John M.; Sanner, Robert M.

2005-01-01

In 2004 NASA began investigation of a robotic servicing mission for the Hubble Space Telescope (HST). Such a mission would require estimates of the HST attitude and rates in order to achieve a capture by the proposed Hubble robotic vehicle (HRV). HRV was to be equipped with vision-based sensors, capable of estimating the relative attitude between HST and HRV. The inertial HST attitude is derived from the measured relative attitude and the HRV computed inertial attitude. However, the relative rate between HST and HRV cannot be measured directly. Therefore, the HST rate with respect to inertial space is not known. Two approaches are developed to estimate the HST rates. Both methods utilize the measured relative attitude and the HRV inertial attitude and rates. First, a non-linear estimator is developed. The nonlinear approach estimates the HST rate through an estimation of the inertial angular momentum. Second, a linearized approach is developed. The linearized approach is a pseudo-linear Kalman filter. Simulation test results for both methods are given. Even though the development began as an application for the HST robotic servicing mission, the methods presented are applicable to any rendezvous/capture mission involving a non-cooperative target spacecraft.

Adding a Parameter Increases the Variance of an Estimated Regression Function

ERIC Educational Resources Information Center

Withers, Christopher S.; Nadarajah, Saralees

2011-01-01

The linear regression model is one of the most popular models in statistics. It is also one of the simplest models in statistics. It has received applications in almost every area of science, engineering and medicine. In this article, the authors show that adding a predictor to a linear model increases the variance of the estimated regression…

Sensitivity Analysis and Parameter Estimation for a Reactive Transport Model of Uranium Bioremediation

NASA Astrophysics Data System (ADS)

Meyer, P. D.; Yabusaki, S.; Curtis, G. P.; Ye, M.; Fang, Y.

2011-12-01

A three-dimensional, variably-saturated flow and multicomponent biogeochemical reactive transport model of uranium bioremediation was used to generate synthetic data . The 3-D model was based on a field experiment at the U.S. Dept. of Energy Rifle Integrated Field Research Challenge site that used acetate biostimulation of indigenous metal reducing bacteria to catalyze the conversion of aqueous uranium in the +6 oxidation state to immobile solid-associated uranium in the +4 oxidation state. A key assumption in past modeling studies at this site was that a comprehensive reaction network could be developed largely through one-dimensional modeling. Sensitivity analyses and parameter estimation were completed for a 1-D reactive transport model abstracted from the 3-D model to test this assumption, to identify parameters with the greatest potential to contribute to model predictive uncertainty, and to evaluate model structure and data limitations. Results showed that sensitivities of key biogeochemical concentrations varied in space and time, that model nonlinearities and/or parameter interactions have a significant impact on calculated sensitivities, and that the complexity of the model's representation of processes affecting Fe(II) in the system may make it difficult to correctly attribute observed Fe(II) behavior to modeled processes. Non-uniformity of the 3-D simulated groundwater flux and averaging of the 3-D synthetic data for use as calibration targets in the 1-D modeling resulted in systematic errors in the 1-D model parameter estimates and outputs. This occurred despite using the same reaction network for 1-D modeling as used in the data-generating 3-D model. Predictive uncertainty of the 1-D model appeared to be significantly underestimated by linear parameter uncertainty estimates.

Discrete-time neural network for fast solving large linear L1 estimation problems and its application to image restoration.

PubMed

Xia, Youshen; Sun, Changyin; Zheng, Wei Xing

2012-05-01

There is growing interest in solving linear L1 estimation problems for sparsity of the solution and robustness against non-Gaussian noise. This paper proposes a discrete-time neural network which can calculate large linear L1 estimation problems fast. The proposed neural network has a fixed computational step length and is proved to be globally convergent to an optimal solution. Then, the proposed neural network is efficiently applied to image restoration. Numerical results show that the proposed neural network is not only efficient in solving degenerate problems resulting from the nonunique solutions of the linear L1 estimation problems but also needs much less computational time than the related algorithms in solving both linear L1 estimation and image restoration problems.

Regional groundwater characteristics and hydraulic conductivity based on geological units in Korean peninsula

NASA Astrophysics Data System (ADS)

Kim, Y.; Suk, H.

2011-12-01

In this study, about 2,000 deep observation wells, stream and/or river distribution, and river's density were analyzed to identify regional groundwater flow trend, based on the regional groundwater survey of four major river watersheds including Geum river, Han river, Youngsan-Seomjin river, and Nakdong river in Korea. Hydrogeologial data were collected to analyze regional groundwater flow characteristics according to geological units. Additionally, hydrological soil type data were collected to estimate direct runoff through SCS-CN method. Temperature and precipitation data were used to quantify infiltration rate. The temperature and precipitation data were also used to quantify evaporation by Thornthwaite method and to evaluate groundwater recharge, respectively. Understanding the regional groundwater characteristics requires the database of groundwater flow parameters, but most hydrogeological data include limited information such as groundwater level and well configuration. In this study, therefore, groundwater flow parameters such as hydraulic conductivities or transmissivities were estimated using observed groundwater level by inverse model, namely PEST (Non-linear Parameter ESTimation). Since groundwater modeling studies have some uncertainties in data collection, conceptualization, and model results, model calibration should be performed. The calibration may be manually performed by changing parameters step by step, or various parameters are simultaneously changed by automatic procedure using PEST program. In this study, both manual and automatic procedures were employed to calibrate and estimate hydraulic parameter distributions. In summary, regional groundwater survey data obtained from four major river watersheds and various data of hydrology, meteorology, geology, soil, and topography in Korea were used to estimate hydraulic conductivities using PEST program. Especially, in order to estimate hydraulic conductivity effectively, it is important to perform in such a way that areas of same or similar hydrogeological characteristics should be grouped into zones. Keywords: regional groundwater, database, hydraulic conductivity, PEST, Korean peninsular Acknowledgements: This work was supported by the Radioactive Waste Management of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge Economy (2011T100200152)

A parameter estimation subroutine package

NASA Technical Reports Server (NTRS)

Bierman, G. J.; Nead, W. M.

1977-01-01

Linear least squares estimation and regression analyses continue to play a major role in orbit determination and related areas. FORTRAN subroutines have been developed to facilitate analyses of a variety of parameter estimation problems. Easy to use multipurpose sets of algorithms are reported that are reasonably efficient and which use a minimal amount of computer storage. Subroutine inputs, outputs, usage and listings are given, along with examples of how these routines can be used.

Population pharmacokinetics of levofloxacin in Korean patients.

PubMed

Kiem, Sungmin; Ryu, Sung-Mun; Lee, Yun-Mi; Schentag, Jerome J; Kim, Yang-Wook; Kim, Hyeon-Kuk; Jang, Hang-Jae; Joo, Yong-Don; Jin, Kyubok; Shin, Jae-Gook; Ghim, Jong-Lyul

2016-08-01

Levofloxacin (LVFX) has different effects depending on the area under the concentration-time curve (AUC)/minimum inhibitory concentration (MIC) ratio. While AUC can be expressed as dose/clearance (CL), we measured serial concentrations of LVFX in Koreans and tried to set a Korean-specific equation, estimating the CL of the antibiotic. In total, 38 patients, aged 18-87 years, received once daily intravenous LVFX doses of 500 mg or 250 mg, depending on their renal function. Four plasma samples were obtained according to a D optimal sampling design. The population pharmacokinetic (PK) parameters of LVFX were estimated using non-linear mixed-effect modeling (NONMEM, ver. 7.2). The CL of LVFX was dependent on creatinine clearance (CLCR) as a covariate. The mean population PK parameters of LVFX in Koreans were as follows: CL (l/hour) = 6.19 ×  (CLCR/75)(1.32). The CL of LVFX in Koreans is expected to be lower than that in Western people.

High dimensional linear regression models under long memory dependence and measurement error

NASA Astrophysics Data System (ADS)

Kaul, Abhishek

This dissertation consists of three chapters. The first chapter introduces the models under consideration and motivates problems of interest. A brief literature review is also provided in this chapter. The second chapter investigates the properties of Lasso under long range dependent model errors. Lasso is a computationally efficient approach to model selection and estimation, and its properties are well studied when the regression errors are independent and identically distributed. We study the case, where the regression errors form a long memory moving average process. We establish a finite sample oracle inequality for the Lasso solution. We then show the asymptotic sign consistency in this setup. These results are established in the high dimensional setup (p> n) where p can be increasing exponentially with n. Finally, we show the consistency, n½ --d-consistency of Lasso, along with the oracle property of adaptive Lasso, in the case where p is fixed. Here d is the memory parameter of the stationary error sequence. The performance of Lasso is also analysed in the present setup with a simulation study. The third chapter proposes and investigates the properties of a penalized quantile based estimator for measurement error models. Standard formulations of prediction problems in high dimension regression models assume the availability of fully observed covariates and sub-Gaussian and homogeneous model errors. This makes these methods inapplicable to measurement errors models where covariates are unobservable and observations are possibly non sub-Gaussian and heterogeneous. We propose weighted penalized corrected quantile estimators for the regression parameter vector in linear regression models with additive measurement errors, where unobservable covariates are nonrandom. The proposed estimators forgo the need for the above mentioned model assumptions. We study these estimators in both the fixed dimension and high dimensional sparse setups, in the latter setup, the dimensionality can grow exponentially with the sample size. In the fixed dimensional setting we provide the oracle properties associated with the proposed estimators. In the high dimensional setting, we provide bounds for the statistical error associated with the estimation, that hold with asymptotic probability 1, thereby providing the ℓ1-consistency of the proposed estimator. We also establish the model selection consistency in terms of the correctly estimated zero components of the parameter vector. A simulation study that investigates the finite sample accuracy of the proposed estimator is also included in this chapter.

A question of separation: disentangling tracer bias and gravitational non-linearity with counts-in-cells statistics

NASA Astrophysics Data System (ADS)

Uhlemann, C.; Feix, M.; Codis, S.; Pichon, C.; Bernardeau, F.; L'Huillier, B.; Kim, J.; Hong, S. E.; Laigle, C.; Park, C.; Shin, J.; Pogosyan, D.

2018-02-01

Starting from a very accurate model for density-in-cells statistics of dark matter based on large deviation theory, a bias model for the tracer density in spheres is formulated. It adopts a mean bias relation based on a quadratic bias model to relate the log-densities of dark matter to those of mass-weighted dark haloes in real and redshift space. The validity of the parametrized bias model is established using a parametrization-independent extraction of the bias function. This average bias model is then combined with the dark matter PDF, neglecting any scatter around it: it nevertheless yields an excellent model for densities-in-cells statistics of mass tracers that is parametrized in terms of the underlying dark matter variance and three bias parameters. The procedure is validated on measurements of both the one- and two-point statistics of subhalo densities in the state-of-the-art Horizon Run 4 simulation showing excellent agreement for measured dark matter variance and bias parameters. Finally, it is demonstrated that this formalism allows for a joint estimation of the non-linear dark matter variance and the bias parameters using solely the statistics of subhaloes. Having verified that galaxy counts in hydrodynamical simulations sampled on a scale of 10 Mpc h-1 closely resemble those of subhaloes, this work provides important steps towards making theoretical predictions for density-in-cells statistics applicable to upcoming galaxy surveys like Euclid or WFIRST.

Parameter estimation using weighted total least squares in the two-compartment exchange model.

PubMed

Garpebring, Anders; Löfstedt, Tommy

2018-01-01

The linear least squares (LLS) estimator provides a fast approach to parameter estimation in the linearized two-compartment exchange model. However, the LLS method may introduce a bias through correlated noise in the system matrix of the model. The purpose of this work is to present a new estimator for the linearized two-compartment exchange model that takes this noise into account. To account for the noise in the system matrix, we developed an estimator based on the weighted total least squares (WTLS) method. Using simulations, the proposed WTLS estimator was compared, in terms of accuracy and precision, to an LLS estimator and a nonlinear least squares (NLLS) estimator. The WTLS method improved the accuracy compared to the LLS method to levels comparable to the NLLS method. This improvement was at the expense of increased computational time; however, the WTLS was still faster than the NLLS method. At high signal-to-noise ratio all methods provided similar precisions while inconclusive results were observed at low signal-to-noise ratio. The proposed method provides improvements in accuracy compared to the LLS method, however, at an increased computational cost. Magn Reson Med 79:561-567, 2017. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

A distributed lag approach to fitting non-linear dose-response models in particulate matter air pollution time series investigations.

PubMed

Roberts, Steven; Martin, Michael A

2007-06-01

The majority of studies that have investigated the relationship between particulate matter (PM) air pollution and mortality have assumed a linear dose-response relationship and have used either a single-day's PM or a 2- or 3-day moving average of PM as the measure of PM exposure. Both of these modeling choices have come under scrutiny in the literature, the linear assumption because it does not allow for non-linearities in the dose-response relationship, and the use of the single- or multi-day moving average PM measure because it does not allow for differential PM-mortality effects spread over time. These two problems have been dealt with on a piecemeal basis with non-linear dose-response models used in some studies and distributed lag models (DLMs) used in others. In this paper, we propose a method for investigating the shape of the PM-mortality dose-response relationship that combines a non-linear dose-response model with a DLM. This combined model will be shown to produce satisfactory estimates of the PM-mortality dose-response relationship in situations where non-linear dose response models and DLMs alone do not; that is, the combined model did not systemically underestimate or overestimate the effect of PM on mortality. The combined model is applied to ten cities in the US and a pooled dose-response model formed. When fitted with a change-point value of 60 microg/m(3), the pooled model provides evidence for a positive association between PM and mortality. The combined model produced larger estimates for the effect of PM on mortality than when using a non-linear dose-response model or a DLM in isolation. For the combined model, the estimated percentage increase in mortality for PM concentrations of 25 and 75 microg/m(3) were 3.3% and 5.4%, respectively. In contrast, the corresponding values from a DLM used in isolation were 1.2% and 3.5%, respectively.

A flexible Bayesian assessment for the expected impact of data on prediction confidence for optimal sampling designs

NASA Astrophysics Data System (ADS)

Leube, Philipp; Geiges, Andreas; Nowak, Wolfgang

2010-05-01

Incorporating hydrogeological data, such as head and tracer data, into stochastic models of subsurface flow and transport helps to reduce prediction uncertainty. Considering limited financial resources available for the data acquisition campaign, information needs towards the prediction goal should be satisfied in a efficient and task-specific manner. For finding the best one among a set of design candidates, an objective function is commonly evaluated, which measures the expected impact of data on prediction confidence, prior to their collection. An appropriate approach to this task should be stochastically rigorous, master non-linear dependencies between data, parameters and model predictions, and allow for a wide variety of different data types. Existing methods fail to fulfill all these requirements simultaneously. For this reason, we introduce a new method, denoted as CLUE (Cross-bred Likelihood Uncertainty Estimator), that derives the essential distributions and measures of data utility within a generalized, flexible and accurate framework. The method makes use of Bayesian GLUE (Generalized Likelihood Uncertainty Estimator) and extends it to an optimal design method by marginalizing over the yet unknown data values. Operating in a purely Bayesian Monte-Carlo framework, CLUE is a strictly formal information processing scheme free of linearizations. It provides full flexibility associated with the type of measurements (linear, non-linear, direct, indirect) and accounts for almost arbitrary sources of uncertainty (e.g. heterogeneity, geostatistical assumptions, boundary conditions, model concepts) via stochastic simulation and Bayesian model averaging. This helps to minimize the strength and impact of possible subjective prior assumptions, that would be hard to defend prior to data collection. Our study focuses on evaluating two different uncertainty measures: (i) expected conditional variance and (ii) expected relative entropy of a given prediction goal. The applicability and advantages are shown in a synthetic example. Therefor, we consider a contaminant source, posing a threat on a drinking water well in an aquifer. Furthermore, we assume uncertainty in geostatistical parameters, boundary conditions and hydraulic gradient. The two mentioned measures evaluate the sensitivity of (1) general prediction confidence and (2) exceedance probability of a legal regulatory threshold value on sampling locations.

Prediction of S-wave velocity using complete ensemble empirical mode decomposition and neural networks

NASA Astrophysics Data System (ADS)

Gaci, Said; Hachay, Olga; Zaourar, Naima

2017-04-01

One of the key elements in hydrocarbon reservoirs characterization is the S-wave velocity (Vs). Since the traditional estimating methods often fail to accurately predict this physical parameter, a new approach that takes into account its non-stationary and non-linear properties is needed. In this view, a prediction model based on complete ensemble empirical mode decomposition (CEEMD) and a multiple layer perceptron artificial neural network (MLP ANN) is suggested to compute Vs from P-wave velocity (Vp). Using a fine-to-coarse reconstruction algorithm based on CEEMD, the Vp log data is decomposed into a high frequency (HF) component, a low frequency (LF) component and a trend component. Then, different combinations of these components are used as inputs of the MLP ANN algorithm for estimating Vs log. Applications on well logs taken from different geological settings illustrate that the predicted Vs values using MLP ANN with the combinations of HF, LF and trend in inputs are more accurate than those obtained with the traditional estimating methods. Keywords: S-wave velocity, CEEMD, multilayer perceptron neural networks.

Bayesian parameter estimation for nonlinear modelling of biological pathways.

PubMed

Ghasemi, Omid; Lindsey, Merry L; Yang, Tianyi; Nguyen, Nguyen; Huang, Yufei; Jin, Yu-Fang

2011-01-01

The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC) method. We applied this approach to the biological pathways involved in the left ventricle (LV) response to myocardial infarction (MI) and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly parameterized dynamic systems. Our proposed Bayesian algorithm successfully estimated parameters in nonlinear mathematical models for biological pathways. This method can be further extended to high order systems and thus provides a useful tool to analyze biological dynamics and extract information using temporal data.

Modeling coupled sorption and transformation of 17β-estradiol-17-sulfate in soil-water systems

NASA Astrophysics Data System (ADS)

Bai, Xuelian; Shrestha, Suman L.; Casey, Francis X. M.; Hakk, Heldur; Fan, Zhaosheng

2014-11-01

Animal manure is the primary source of exogenous free estrogens in the environment, which are known endocrine-disrupting chemicals to disorder the reproduction system of organisms. Conjugated estrogens can act as precursors to free estrogens, which may increase the total estrogenicity in the environment. In this study, a comprehensive model was used to simultaneously simulate the coupled sorption and transformation of a sulfate estrogen conjugate, 17β-estradiol-17-sulfate (E2-17S), in various soil-water systems (non-sterile/sterile; topsoil/subsoil). The simulated processes included multiple transformation pathways (i.e. hydroxylation, hydrolysis, and oxidation) and mass transfer between the aqueous, reversibly sorbed, and irreversibly sorbed phases of all soils for E2-17S and its metabolites. The conceptual model was conceived based on a series of linear sorption and first-order transformation expressions. The model was inversely solved using finite difference to estimate process parameters. A global optimization method was applied for the inverse analysis along with variable model restrictions to estimate 36 parameters. The model provided a satisfactory simultaneous fit (R2adj = 0.93 and d = 0.87) of all the experimental data and reliable parameter estimates. This modeling study improved the understanding on fate and transport of estrogen conjugates under various soil-water conditions.

Adjusting for overdispersion in piecewise exponential regression models to estimate excess mortality rate in population-based research.

PubMed

Luque-Fernandez, Miguel Angel; Belot, Aurélien; Quaresma, Manuela; Maringe, Camille; Coleman, Michel P; Rachet, Bernard

2016-10-01

In population-based cancer research, piecewise exponential regression models are used to derive adjusted estimates of excess mortality due to cancer using the Poisson generalized linear modelling framework. However, the assumption that the conditional mean and variance of the rate parameter given the set of covariates x i are equal is strong and may fail to account for overdispersion given the variability of the rate parameter (the variance exceeds the mean). Using an empirical example, we aimed to describe simple methods to test and correct for overdispersion. We used a regression-based score test for overdispersion under the relative survival framework and proposed different approaches to correct for overdispersion including a quasi-likelihood, robust standard errors estimation, negative binomial regression and flexible piecewise modelling. All piecewise exponential regression models showed the presence of significant inherent overdispersion (p-value <0.001). However, the flexible piecewise exponential model showed the smallest overdispersion parameter (3.2 versus 21.3) for non-flexible piecewise exponential models. We showed that there were no major differences between methods. However, using a flexible piecewise regression modelling, with either a quasi-likelihood or robust standard errors, was the best approach as it deals with both, overdispersion due to model misspecification and true or inherent overdispersion.

A Case Study on the Application of a Structured Experimental Method for Optimal Parameter Design of a Complex Control System

NASA Technical Reports Server (NTRS)

Torres-Pomales, Wilfredo

2015-01-01

This report documents a case study on the application of Reliability Engineering techniques to achieve an optimal balance between performance and robustness by tuning the functional parameters of a complex non-linear control system. For complex systems with intricate and non-linear patterns of interaction between system components, analytical derivation of a mathematical model of system performance and robustness in terms of functional parameters may not be feasible or cost-effective. The demonstrated approach is simple, structured, effective, repeatable, and cost and time efficient. This general approach is suitable for a wide range of systems.

Kalman filter data assimilation: targeting observations and parameter estimation.

PubMed

Bellsky, Thomas; Kostelich, Eric J; Mahalov, Alex

2014-06-01

This paper studies the effect of targeted observations on state and parameter estimates determined with Kalman filter data assimilation (DA) techniques. We first provide an analytical result demonstrating that targeting observations within the Kalman filter for a linear model can significantly reduce state estimation error as opposed to fixed or randomly located observations. We next conduct observing system simulation experiments for a chaotic model of meteorological interest, where we demonstrate that the local ensemble transform Kalman filter (LETKF) with targeted observations based on largest ensemble variance is skillful in providing more accurate state estimates than the LETKF with randomly located observations. Additionally, we find that a hybrid ensemble Kalman filter parameter estimation method accurately updates model parameters within the targeted observation context to further improve state estimation.

Kalman filter data assimilation: Targeting observations and parameter estimation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bellsky, Thomas, E-mail: bellskyt@asu.edu; Kostelich, Eric J.; Mahalov, Alex

2014-06-15

This paper studies the effect of targeted observations on state and parameter estimates determined with Kalman filter data assimilation (DA) techniques. We first provide an analytical result demonstrating that targeting observations within the Kalman filter for a linear model can significantly reduce state estimation error as opposed to fixed or randomly located observations. We next conduct observing system simulation experiments for a chaotic model of meteorological interest, where we demonstrate that the local ensemble transform Kalman filter (LETKF) with targeted observations based on largest ensemble variance is skillful in providing more accurate state estimates than the LETKF with randomly locatedmore » observations. Additionally, we find that a hybrid ensemble Kalman filter parameter estimation method accurately updates model parameters within the targeted observation context to further improve state estimation.« less

Constitutive error based parameter estimation technique for plate structures using free vibration signatures

NASA Astrophysics Data System (ADS)

Guchhait, Shyamal; Banerjee, Biswanath

2018-04-01

In this paper, a variant of constitutive equation error based material parameter estimation procedure for linear elastic plates is developed from partially measured free vibration sig-natures. It has been reported in many research articles that the mode shape curvatures are much more sensitive compared to mode shape themselves to localize inhomogeneity. Complying with this idea, an identification procedure is framed as an optimization problem where the proposed cost function measures the error in constitutive relation due to incompatible curvature/strain and moment/stress fields. Unlike standard constitutive equation error based procedure wherein a solution of a couple system is unavoidable in each iteration, we generate these incompatible fields via two linear solves. A simple, yet effective, penalty based approach is followed to incorporate measured data. The penalization parameter not only helps in incorporating corrupted measurement data weakly but also acts as a regularizer against the ill-posedness of the inverse problem. Explicit linear update formulas are then developed for anisotropic linear elastic material. Numerical examples are provided to show the applicability of the proposed technique. Finally, an experimental validation is also provided.

Analysis and application of minimum variance discrete time system identification

NASA Technical Reports Server (NTRS)

Kaufman, H.; Kotob, S.

1975-01-01

An on-line minimum variance parameter identifier is developed which embodies both accuracy and computational efficiency. The formulation results in a linear estimation problem with both additive and multiplicative noise. The resulting filter which utilizes both the covariance of the parameter vector itself and the covariance of the error in identification is proven to be mean square convergent and mean square consistent. The MV parameter identification scheme is then used to construct a stable state and parameter estimation algorithm.

Constrained Maximum Likelihood Estimation for Two-Level Mean and Covariance Structure Models

ERIC Educational Resources Information Center

Bentler, Peter M.; Liang, Jiajuan; Tang, Man-Lai; Yuan, Ke-Hai

2011-01-01

Maximum likelihood is commonly used for the estimation of model parameters in the analysis of two-level structural equation models. Constraints on model parameters could be encountered in some situations such as equal factor loadings for different factors. Linear constraints are the most common ones and they are relatively easy to handle in…

Identifying Bearing Rotodynamic Coefficients Using an Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Miller, Brad A.; Howard, Samuel A.

2008-01-01

An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter's performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.

Recent developments in learning control and system identification for robots and structures

NASA Technical Reports Server (NTRS)

Phan, M.; Juang, J.-N.; Longman, R. W.

1990-01-01

This paper reviews recent results in learning control and learning system identification, with particular emphasis on discrete-time formulation, and their relation to adaptive theory. Related continuous-time results are also discussed. Among the topics presented are proportional, derivative, and integral learning controllers, time-domain formulation of discrete learning algorithms. Newly developed techniques are described including the concept of the repetition domain, and the repetition domain formulation of learning control by linear feedback, model reference learning control, indirect learning control with parameter estimation, as well as related basic concepts, recursive and non-recursive methods for learning identification.

Camera calibration based on the back projection process

NASA Astrophysics Data System (ADS)

Gu, Feifei; Zhao, Hong; Ma, Yueyang; Bu, Penghui

2015-12-01

Camera calibration plays a crucial role in 3D measurement tasks of machine vision. In typical calibration processes, camera parameters are iteratively optimized in the forward imaging process (FIP). However, the results can only guarantee the minimum of 2D projection errors on the image plane, but not the minimum of 3D reconstruction errors. In this paper, we propose a universal method for camera calibration, which uses the back projection process (BPP). In our method, a forward projection model is used to obtain initial intrinsic and extrinsic parameters with a popular planar checkerboard pattern. Then, the extracted image points are projected back into 3D space and compared with the ideal point coordinates. Finally, the estimation of the camera parameters is refined by a non-linear function minimization process. The proposed method can obtain a more accurate calibration result, which is more physically useful. Simulation and practical data are given to demonstrate the accuracy of the proposed method.

Classical and quantum non-linear optical applications using the Mach-Zehnder interferometer

NASA Astrophysics Data System (ADS)

Prescod, Andru

Mach Zehnder (MZ) modulators are widely employed in a variety of applications, such as optical communications, optical imaging, metrology and encryption. In this dissertation, we explore two non-linear MZ applications; one classified as classical and one as quantum, in which the Mach Zehnder interferometer is used. In the first application, a classical non-linear application, we introduce and study a new electro-optic highly linear (e.g., >130 dB) modulator configuration. This modulator makes use of a phase modulator (PM) in one arm of the MZ interferometer (MZI) and a ring resonator (RR) located on the other arm. The modulator performance is obtained through the control of a combination of internal and external parameters. These parameters include the RR-coupling ratio (internal parameter); the RF power split ratio and the RF phase bias (external parameters). Results show the unique and superior features, such as high linearity (SFDR˜133 dB), modulation bandwidth extension (as much as 70%) over the previously proposed and demonstrated Resonator-Assisted Mach Zehnder (RAMZ) design. Furthermore the proposed electro-optic modulator of this dissertation also provides an inherent SFDR compensation capability, even in cases where a significant waveguide optical loss exists. This design also shows potential for increased flexibility, practicality and ease of use. In the second application, a quantum non-linear application, we experimentally demonstrate quantum optical coherence tomography (QOCT) using a type II non-linear crystal (periodically-poled potassium titanyl phosphate (KTiOPO4) or PPKTP). There have been several publications discussing the merits and disadvantages of QOCT compared to OCT and other imaging techniques. First, we discuss the issues and solutions for increasing the efficiency of the quantum entangled photons. Second, we use a free space QOCT experiment to generate a high flux of these quantum entangled photons in two orthogonal polarizations, by parametric down-conversion. Third, by ensuring that these down-converted photons have the same frequency, spatial-temporal mode, and the same polarization when they interfere at a beam splitter, quantum interference should occur. Quantum interference of these entangled photons enables high resolution probing of dispersive samples.

Log-gamma linear-mixed effects models for multiple outcomes with application to a longitudinal glaucoma study

PubMed Central

Zhang, Peng; Luo, Dandan; Li, Pengfei; Sharpsten, Lucie; Medeiros, Felipe A.

2015-01-01

Glaucoma is a progressive disease due to damage in the optic nerve with associated functional losses. Although the relationship between structural and functional progression in glaucoma is well established, there is disagreement on how this association evolves over time. In addressing this issue, we propose a new class of non-Gaussian linear-mixed models to estimate the correlations among subject-specific effects in multivariate longitudinal studies with a skewed distribution of random effects, to be used in a study of glaucoma. This class provides an efficient estimation of subject-specific effects by modeling the skewed random effects through the log-gamma distribution. It also provides more reliable estimates of the correlations between the random effects. To validate the log-gamma assumption against the usual normality assumption of the random effects, we propose a lack-of-fit test using the profile likelihood function of the shape parameter. We apply this method to data from a prospective observation study, the Diagnostic Innovations in Glaucoma Study, to present a statistically significant association between structural and functional change rates that leads to a better understanding of the progression of glaucoma over time. PMID:26075565

Interseismic Deformation on the San Andreas Fault System

NASA Astrophysics Data System (ADS)

Segall, P.

2001-12-01

Interseismic deformation measurements are most often interpreted in terms of steady slip on buried elastic dislocations. While such models often yield slip-rates that are in reasonable accord with geologic observations, they are: 1) inconsistent with observations of transient deformation following large earthquakes, and 2) tend to predict locking depths significantly deeper than recent large earthquakes. An alternate two-dimensional model of repeating earthquakes that break an elastic plate of thickness H, overlying a viscoelastic half-space with relaxation time tR (Savage and Prescott, 1978) involves 5 parameters; H, tR, t, T, and ˙ {s}, where t is the time since the last quake, T is the earthquake cycle time, and ˙ {s} is the slip-rate. Many parts of the SAF system involve multiple parallel faults, which further increases the number of parameters to be estimated. All hope is not lost, however, if we make use of a priori constraints on slip-rate from geologic studies, and utilize measurements of time dependent strain following the 1906 earthquake, in addition to the present day spatial distribution of deformation-rate. GPS data from the Carrizo Plain segment of the SAF imply a considerably larger relaxation time than inferred from the post-1906 strain-rate transient. This indicates that either the crustal structure differs significantly between northern and central California, or that the simple model is deficient, either due to time-dependent down-dip slip following large earthquakes or non-linear rheology. To test the effect of regional variations in H and tR, I analyze data from the northern San Francisco Bay area (Prescott et al, 2001, JGR), and include the SAF, the Hayward-Rogers Creek (HRC), and Concord-Green Valley faults (CGV). Non-linear optimization using simulated annealing and constrained non-linear least squares yields an optimal model with: H ~ 10 km, tR ~ 34 years, TSAF = 205 years, ˙ {s}SAF ~ 18 mm/yr, tHRC = 225 years, T{ HRC} = 630 years, and ˙ {s}{HRC } ~ 13 mm/yr, ˙ {s}CGV ~ 9 mm/yr. Adding the constraint that the coseismic slip in major Hayward and San Andreas events not exceed 3.0 m and 7.0 m, respectively yields an optimal model with: H ~ 18 km, tR ~ 36 years, TSAF = 280 years, ˙ {s}SAF = 25 mm/yr, tHRC = 225 years, T{ HRC} = 276 years, and ˙ {s}{HRC } ~ 11 mm/yr, ˙ {s}CGV ~ 9 mm/yr. These estimates are in reasonable accord with independent paleoseismic results. The conclusion of this pilot study is that by combining the present day deformation field, post-1906 strain data, and geologic bounds on slip-rate and maximum earthquake slip, we can estimate parameters of considerable geophysical interest, including time since past quakes and average recurrence interval.

A Systematic Approach to Sensor Selection for Aircraft Engine Health Estimation

NASA Technical Reports Server (NTRS)

Simon, Donald L.; Garg, Sanjay

2009-01-01

A systematic approach for selecting an optimal suite of sensors for on-board aircraft gas turbine engine health estimation is presented. The methodology optimally chooses the engine sensor suite and the model tuning parameter vector to minimize the Kalman filter mean squared estimation error in the engine s health parameters or other unmeasured engine outputs. This technique specifically addresses the underdetermined estimation problem where there are more unknown system health parameters representing degradation than available sensor measurements. This paper presents the theoretical estimation error equations, and describes the optimization approach that is applied to select the sensors and model tuning parameters to minimize these errors. Two different model tuning parameter vector selection approaches are evaluated: the conventional approach of selecting a subset of health parameters to serve as the tuning parameters, and an alternative approach that selects tuning parameters as a linear combination of all health parameters. Results from the application of the technique to an aircraft engine simulation are presented, and compared to those from an alternative sensor selection strategy.

Models to describe the thermal development rates of Cycloneda sanguinea L. (Coleoptera: Coccinelidae).

PubMed

Pachú, Jéssica Ks; Malaquias, José B; Godoy, Wesley Ac; de S Ramalho, Francisco; Almeida, Bruna R; Rossi, Fabrício

2018-04-01

Precise estimates of the lower (T min ) and higher (T max ) thermal thresholds as well as the temperature range that provides optimum performance (T opt ) enable to obtain the desired number of individuals in conservation systems, rearing and release of natural enemies. In this study, the relationship between the development rates of Cycloneda sanguinea L. (Coleoptera: Coccinelidae) and temperature was described using non-linear models developed by Analytis, Brière, Lactin, Lamb, Logan and Sharpe & DeMichele. There were differences between the models, considering the estimates of the parameters T min , T max , and T opt . All of the tested models were able to describe non-linear responses involving the development rates of C. sanguinea at constant temperatures. Lactin and Lamb gave the highest z weight for egg, while Analytis, Sharpe & DeMichele and Brière gave the highest values for larvae and pupae. The more realistic T opt estimated by the models varied from 29° to 31°C for egg, 27-28 °C for larvae and 28-29 °C for pupae. The Logan, Lactin and Analytis models estimated the T max for egg, larvae and pupae to be approximately 34 °C, while the T min estimated by the Analytis model was 16 °C for larvae and pupae. The information generated by our research will contribute towards improving the rearing and release of C. sanguinea in biological control programs, accurately controlling the rate of development in laboratory conditions or even scheduling the most favourable this species' release. Copyright © 2018 Elsevier Ltd. All rights reserved.

Effects of non-tidal atmospheric loading on a Kalman filter-based terrestrial reference frame

NASA Astrophysics Data System (ADS)

Abbondanza, C.; Altamimi, Z.; Chin, T. M.; Collilieux, X.; Dach, R.; Heflin, M. B.; Gross, R. S.; König, R.; Lemoine, F. G.; MacMillan, D. S.; Parker, J. W.; van Dam, T. M.; Wu, X.

2013-12-01

The International Terrestrial Reference Frame (ITRF) adopts a piece-wise linear model to parameterize regularized station positions and velocities. The space-geodetic (SG) solutions from VLBI, SLR, GPS and DORIS global networks used as input in the ITRF combination process account for tidal loading deformations, but ignore the non-tidal part. As a result, the non-linear signal observed in the time series of SG-derived station positions in part reflects non-tidal loading displacements not introduced in the SG data reduction. In this analysis, the effect of non-tidal atmospheric loading (NTAL) corrections on the TRF is assessed adopting a Remove/Restore approach: (i) Focusing on the a-posteriori approach, the NTAL model derived from the National Center for Environmental Prediction (NCEP) surface pressure is removed from the SINEX files of the SG solutions used as inputs to the TRF determinations. (ii) Adopting a Kalman-filter based approach, a linear TRF is estimated combining the 4 SG solutions free from NTAL displacements. (iii) Linear fits to the NTAL displacements removed at step (i) are restored to the linear reference frame estimated at (ii). The velocity fields of the (standard) linear reference frame in which the NTAL model has not been removed and the one in which the model has been removed/restored are compared and discussed.

IMNN: Information Maximizing Neural Networks

NASA Astrophysics Data System (ADS)

Charnock, Tom; Lavaux, Guilhem; Wandelt, Benjamin D.

2018-04-01

This software trains artificial neural networks to find non-linear functionals of data that maximize Fisher information: information maximizing neural networks (IMNNs). As compressing large data sets vastly simplifies both frequentist and Bayesian inference, important information may be inadvertently missed. Likelihood-free inference based on automatically derived IMNN summaries produces summaries that are good approximations to sufficient statistics. IMNNs are robustly capable of automatically finding optimal, non-linear summaries of the data even in cases where linear compression fails: inferring the variance of Gaussian signal in the presence of noise, inferring cosmological parameters from mock simulations of the Lyman-α forest in quasar spectra, and inferring frequency-domain parameters from LISA-like detections of gravitational waveforms. In this final case, the IMNN summary outperforms linear data compression by avoiding the introduction of spurious likelihood maxima.

Parameter estimation with bio-inspired meta-heuristic optimization: modeling the dynamics of endocytosis.

PubMed

Tashkova, Katerina; Korošec, Peter; Silc, Jurij; Todorovski, Ljupčo; Džeroski, Sašo

2011-10-11

We address the task of parameter estimation in models of the dynamics of biological systems based on ordinary differential equations (ODEs) from measured data, where the models are typically non-linear and have many parameters, the measurements are imperfect due to noise, and the studied system can often be only partially observed. A representative task is to estimate the parameters in a model of the dynamics of endocytosis, i.e., endosome maturation, reflected in a cut-out switch transition between the Rab5 and Rab7 domain protein concentrations, from experimental measurements of these concentrations. The general parameter estimation task and the specific instance considered here are challenging optimization problems, calling for the use of advanced meta-heuristic optimization methods, such as evolutionary or swarm-based methods. We apply three global-search meta-heuristic algorithms for numerical optimization, i.e., differential ant-stigmergy algorithm (DASA), particle-swarm optimization (PSO), and differential evolution (DE), as well as a local-search derivative-based algorithm 717 (A717) to the task of estimating parameters in ODEs. We evaluate their performance on the considered representative task along a number of metrics, including the quality of reconstructing the system output and the complete dynamics, as well as the speed of convergence, both on real-experimental data and on artificial pseudo-experimental data with varying amounts of noise. We compare the four optimization methods under a range of observation scenarios, where data of different completeness and accuracy of interpretation are given as input. Overall, the global meta-heuristic methods (DASA, PSO, and DE) clearly and significantly outperform the local derivative-based method (A717). Among the three meta-heuristics, differential evolution (DE) performs best in terms of the objective function, i.e., reconstructing the output, and in terms of convergence. These results hold for both real and artificial data, for all observability scenarios considered, and for all amounts of noise added to the artificial data. In sum, the meta-heuristic methods considered are suitable for estimating the parameters in the ODE model of the dynamics of endocytosis under a range of conditions: With the model and conditions being representative of parameter estimation tasks in ODE models of biochemical systems, our results clearly highlight the promise of bio-inspired meta-heuristic methods for parameter estimation in dynamic system models within system biology.

Parameter estimation with bio-inspired meta-heuristic optimization: modeling the dynamics of endocytosis

PubMed Central

2011-01-01

Background We address the task of parameter estimation in models of the dynamics of biological systems based on ordinary differential equations (ODEs) from measured data, where the models are typically non-linear and have many parameters, the measurements are imperfect due to noise, and the studied system can often be only partially observed. A representative task is to estimate the parameters in a model of the dynamics of endocytosis, i.e., endosome maturation, reflected in a cut-out switch transition between the Rab5 and Rab7 domain protein concentrations, from experimental measurements of these concentrations. The general parameter estimation task and the specific instance considered here are challenging optimization problems, calling for the use of advanced meta-heuristic optimization methods, such as evolutionary or swarm-based methods. Results We apply three global-search meta-heuristic algorithms for numerical optimization, i.e., differential ant-stigmergy algorithm (DASA), particle-swarm optimization (PSO), and differential evolution (DE), as well as a local-search derivative-based algorithm 717 (A717) to the task of estimating parameters in ODEs. We evaluate their performance on the considered representative task along a number of metrics, including the quality of reconstructing the system output and the complete dynamics, as well as the speed of convergence, both on real-experimental data and on artificial pseudo-experimental data with varying amounts of noise. We compare the four optimization methods under a range of observation scenarios, where data of different completeness and accuracy of interpretation are given as input. Conclusions Overall, the global meta-heuristic methods (DASA, PSO, and DE) clearly and significantly outperform the local derivative-based method (A717). Among the three meta-heuristics, differential evolution (DE) performs best in terms of the objective function, i.e., reconstructing the output, and in terms of convergence. These results hold for both real and artificial data, for all observability scenarios considered, and for all amounts of noise added to the artificial data. In sum, the meta-heuristic methods considered are suitable for estimating the parameters in the ODE model of the dynamics of endocytosis under a range of conditions: With the model and conditions being representative of parameter estimation tasks in ODE models of biochemical systems, our results clearly highlight the promise of bio-inspired meta-heuristic methods for parameter estimation in dynamic system models within system biology. PMID:21989196

Parameter estimation in linear models of the human operator in a closed loop with application of deterministic test signals

NASA Technical Reports Server (NTRS)

Vanlunteren, A.; Stassen, H. G.

1973-01-01

Parameter estimation techniques are discussed with emphasis on unbiased estimates in the presence of noise. A distinction between open and closed loop systems is made. A method is given based on the application of external forcing functions consisting of a sun of sinusoids; this method is thus based on the estimation of Fourier coefficients and is applicable for models with poles and zeros in open and closed loop systems.

Robust linear parameter-varying control of blood pressure using vasoactive drugs

NASA Astrophysics Data System (ADS)

Luspay, Tamas; Grigoriadis, Karolos

2015-10-01

Resuscitation of emergency care patients requires fast restoration of blood pressure to a target value to achieve hemodynamic stability and vital organ perfusion. A robust control design methodology is presented in this paper for regulating the blood pressure of hypotensive patients by means of the closed-loop administration of vasoactive drugs. To this end, a dynamic first-order delay model is utilised to describe the vasoactive drug response with varying parameters that represent intra-patient and inter-patient variability. The proposed framework consists of two components: first, an online model parameter estimation is carried out using a multiple-model extended Kalman-filter. Second, the estimated model parameters are used for continuously scheduling a robust linear parameter-varying (LPV) controller. The closed-loop behaviour is characterised by parameter-varying dynamic weights designed to regulate the mean arterial pressure to a target value. Experimental data of blood pressure response of anesthetised pigs to phenylephrine injection are used for validating the LPV blood pressure models. Simulation studies are provided to validate the online model estimation and the LPV blood pressure control using phenylephrine drug injection models representing patients showing sensitive, nominal and insensitive response to the drug.

Non-local Second Order Closure Scheme for Boundary Layer Turbulence and Convection

NASA Astrophysics Data System (ADS)

Meyer, Bettina; Schneider, Tapio

2017-04-01

There has been scientific consensus that the uncertainty in the cloud feedback remains the largest source of uncertainty in the prediction of climate parameters like climate sensitivity. To narrow down this uncertainty, not only a better physical understanding of cloud and boundary layer processes is required, but specifically the representation of boundary layer processes in models has to be improved. General climate models use separate parameterisation schemes to model the different boundary layer processes like small-scale turbulence, shallow and deep convection. Small scale turbulence is usually modelled by local diffusive parameterisation schemes, which truncate the hierarchy of moment equations at first order and use second-order equations only to estimate closure parameters. In contrast, the representation of convection requires higher order statistical moments to capture their more complex structure, such as narrow updrafts in a quasi-steady environment. Truncations of moment equations at second order may lead to more accurate parameterizations. At the same time, they offer an opportunity to take spatially correlated structures (e.g., plumes) into account, which are known to be important for convective dynamics. In this project, we study the potential and limits of local and non-local second order closure schemes. A truncation of the momentum equations at second order represents the same dynamics as a quasi-linear version of the equations of motion. We study the three-dimensional quasi-linear dynamics in dry and moist convection by implementing it in a LES model (PyCLES) and compare it to a fully non-linear LES. In the quasi-linear LES, interactions among turbulent eddies are suppressed but nonlinear eddy—mean flow interactions are retained, as they are in the second order closure. In physical terms, suppressing eddy—eddy interactions amounts to suppressing, e.g., interactions among convective plumes, while retaining interactions between plumes and the environment (e.g., entrainment and detrainment). In a second part, we employ the possibility to include non-local statistical correlations in a second-order closure scheme. Such non-local correlations allow to directly incorporate the spatially coherent structures that occur in the form of convective updrafts penetrating the boundary layer. This allows us to extend the work that has been done using assumed-PDF schemes for parameterising boundary layer turbulence and shallow convection in a non-local sense.

Identification of dynamic systems, theory and formulation

NASA Technical Reports Server (NTRS)

Maine, R. E.; Iliff, K. W.

1985-01-01

The problem of estimating parameters of dynamic systems is addressed in order to present the theoretical basis of system identification and parameter estimation in a manner that is complete and rigorous, yet understandable with minimal prerequisites. Maximum likelihood and related estimators are highlighted. The approach used requires familiarity with calculus, linear algebra, and probability, but does not require knowledge of stochastic processes or functional analysis. The treatment emphasizes unification of the various areas in estimation in dynamic systems is treated as a direct outgrowth of the static system theory. Topics covered include basic concepts and definitions; numerical optimization methods; probability; statistical estimators; estimation in static systems; stochastic processes; state estimation in dynamic systems; output error, filter error, and equation error methods of parameter estimation in dynamic systems, and the accuracy of the estimates.

Multi-disease analysis of maternal antibody decay using non-linear mixed models accounting for censoring.

PubMed

Goeyvaerts, Nele; Leuridan, Elke; Faes, Christel; Van Damme, Pierre; Hens, Niel

2015-09-10

Biomedical studies often generate repeated measures of multiple outcomes on a set of subjects. It may be of interest to develop a biologically intuitive model for the joint evolution of these outcomes while assessing inter-subject heterogeneity. Even though it is common for biological processes to entail non-linear relationships, examples of multivariate non-linear mixed models (MNMMs) are still fairly rare. We contribute to this area by jointly analyzing the maternal antibody decay for measles, mumps, rubella, and varicella, allowing for a different non-linear decay model for each infectious disease. We present a general modeling framework to analyze multivariate non-linear longitudinal profiles subject to censoring, by combining multivariate random effects, non-linear growth and Tobit regression. We explore the hypothesis of a common infant-specific mechanism underlying maternal immunity using a pairwise correlated random-effects approach and evaluating different correlation matrix structures. The implied marginal correlation between maternal antibody levels is estimated using simulations. The mean duration of passive immunity was less than 4 months for all diseases with substantial heterogeneity between infants. The maternal antibody levels against rubella and varicella were found to be positively correlated, while little to no correlation could be inferred for the other disease pairs. For some pairs, computational issues occurred with increasing correlation matrix complexity, which underlines the importance of further developing estimation methods for MNMMs. Copyright © 2015 John Wiley & Sons, Ltd.

Performance of maximum likelihood mixture models to estimate nursery habitat contributions to fish stocks: a case study on sea bream Sparus aurata

PubMed Central

Darnaude, Audrey M.

2016-01-01

Background Mixture models (MM) can be used to describe mixed stocks considering three sets of parameters: the total number of contributing sources, their chemical baseline signatures and their mixing proportions. When all nursery sources have been previously identified and sampled for juvenile fish to produce baseline nursery-signatures, mixing proportions are the only unknown set of parameters to be estimated from the mixed-stock data. Otherwise, the number of sources, as well as some/all nursery-signatures may need to be also estimated from the mixed-stock data. Our goal was to assess bias and uncertainty in these MM parameters when estimated using unconditional maximum likelihood approaches (ML-MM), under several incomplete sampling and nursery-signature separation scenarios. Methods We used a comprehensive dataset containing otolith elemental signatures of 301 juvenile Sparus aurata, sampled in three contrasting years (2008, 2010, 2011), from four distinct nursery habitats. (Mediterranean lagoons) Artificial nursery-source and mixed-stock datasets were produced considering: five different sampling scenarios where 0–4 lagoons were excluded from the nursery-source dataset and six nursery-signature separation scenarios that simulated data separated 0.5, 1.5, 2.5, 3.5, 4.5 and 5.5 standard deviations among nursery-signature centroids. Bias (BI) and uncertainty (SE) were computed to assess reliability for each of the three sets of MM parameters. Results Both bias and uncertainty in mixing proportion estimates were low (BI ≤ 0.14, SE ≤ 0.06) when all nursery-sources were sampled but exhibited large variability among cohorts and increased with the number of non-sampled sources up to BI = 0.24 and SE = 0.11. Bias and variability in baseline signature estimates also increased with the number of non-sampled sources, but tended to be less biased, and more uncertain than mixing proportion ones, across all sampling scenarios (BI < 0.13, SE < 0.29). Increasing separation among nursery signatures improved reliability of mixing proportion estimates, but lead to non-linear responses in baseline signature parameters. Low uncertainty, but a consistent underestimation bias affected the estimated number of nursery sources, across all incomplete sampling scenarios. Discussion ML-MM produced reliable estimates of mixing proportions and nursery-signatures under an important range of incomplete sampling and nursery-signature separation scenarios. This method failed, however, in estimating the true number of nursery sources, reflecting a pervasive issue affecting mixture models, within and beyond the ML framework. Large differences in bias and uncertainty found among cohorts were linked to differences in separation of chemical signatures among nursery habitats. Simulation approaches, such as those presented here, could be useful to evaluate sensitivity of MM results to separation and variability in nursery-signatures for other species, habitats or cohorts. PMID:27761305

Smoothing-based compressed state Kalman filter for joint state-parameter estimation: Applications in reservoir characterization and CO2 storage monitoring

NASA Astrophysics Data System (ADS)

Li, Y. J.; Kokkinaki, Amalia; Darve, Eric F.; Kitanidis, Peter K.

2017-08-01

The operation of most engineered hydrogeological systems relies on simulating physical processes using numerical models with uncertain parameters and initial conditions. Predictions by such uncertain models can be greatly improved by Kalman-filter techniques that sequentially assimilate monitoring data. Each assimilation constitutes a nonlinear optimization, which is solved by linearizing an objective function about the model prediction and applying a linear correction to this prediction. However, if model parameters and initial conditions are uncertain, the optimization problem becomes strongly nonlinear and a linear correction may yield unphysical results. In this paper, we investigate the utility of one-step ahead smoothing, a variant of the traditional filtering process, to eliminate nonphysical results and reduce estimation artifacts caused by nonlinearities. We present the smoothing-based compressed state Kalman filter (sCSKF), an algorithm that combines one step ahead smoothing, in which current observations are used to correct the state and parameters one step back in time, with a nonensemble covariance compression scheme, that reduces the computational cost by efficiently exploring the high-dimensional state and parameter space. Numerical experiments show that when model parameters are uncertain and the states exhibit hyperbolic behavior with sharp fronts, as in CO2 storage applications, one-step ahead smoothing reduces overshooting errors and, by design, gives physically consistent state and parameter estimates. We compared sCSKF with commonly used data assimilation methods and showed that for the same computational cost, combining one step ahead smoothing and nonensemble compression is advantageous for real-time characterization and monitoring of large-scale hydrogeological systems with sharp moving fronts.

Scaling up stomatal conductance from leaf to canopy using a dual-leaf model for estimating crop evapotranspiration.

PubMed

Ding, Risheng; Kang, Shaozhong; Du, Taisheng; Hao, Xinmei; Zhang, Yanqun

2014-01-01

The dual-source Shuttleworth-Wallace model has been widely used to estimate and partition crop evapotranspiration (λET). Canopy stomatal conductance (Gsc), an essential parameter of the model, is often calculated by scaling up leaf stomatal conductance, considering the canopy as one single leaf in a so-called "big-leaf" model. However, Gsc can be overestimated or underestimated depending on leaf area index level in the big-leaf model, due to a non-linear stomatal response to light. A dual-leaf model, scaling up Gsc from leaf to canopy, was developed in this study. The non-linear stomata-light relationship was incorporated by dividing the canopy into sunlit and shaded fractions and calculating each fraction separately according to absorbed irradiances. The model includes: (1) the absorbed irradiance, determined by separately integrating the sunlit and shaded leaves with consideration of both beam and diffuse radiation; (2) leaf area for the sunlit and shaded fractions; and (3) a leaf conductance model that accounts for the response of stomata to PAR, vapor pressure deficit and available soil water. In contrast to the significant errors of Gsc in the big-leaf model, the predicted Gsc using the dual-leaf model had a high degree of data-model agreement; the slope of the linear regression between daytime predictions and measurements was 1.01 (R2 = 0.98), with RMSE of 0.6120 mm s-1 for four clear-sky days in different growth stages. The estimates of half-hourly λET using the dual-source dual-leaf model (DSDL) agreed well with measurements and the error was within 5% during two growing seasons of maize with differing hydrometeorological and management strategies. Moreover, the estimates of soil evaporation using the DSDL model closely matched actual measurements. Our results indicate that the DSDL model can produce more accurate estimation of Gsc and λET, compared to the big-leaf model, and thus is an effective alternative approach for estimating and partitioning λET.

Scaling Up Stomatal Conductance from Leaf to Canopy Using a Dual-Leaf Model for Estimating Crop Evapotranspiration

PubMed Central

Ding, Risheng; Kang, Shaozhong; Du, Taisheng; Hao, Xinmei; Zhang, Yanqun

2014-01-01

The dual-source Shuttleworth-Wallace model has been widely used to estimate and partition crop evapotranspiration (λET). Canopy stomatal conductance (Gsc), an essential parameter of the model, is often calculated by scaling up leaf stomatal conductance, considering the canopy as one single leaf in a so-called “big-leaf” model. However, Gsc can be overestimated or underestimated depending on leaf area index level in the big-leaf model, due to a non-linear stomatal response to light. A dual-leaf model, scaling up Gsc from leaf to canopy, was developed in this study. The non-linear stomata-light relationship was incorporated by dividing the canopy into sunlit and shaded fractions and calculating each fraction separately according to absorbed irradiances. The model includes: (1) the absorbed irradiance, determined by separately integrating the sunlit and shaded leaves with consideration of both beam and diffuse radiation; (2) leaf area for the sunlit and shaded fractions; and (3) a leaf conductance model that accounts for the response of stomata to PAR, vapor pressure deficit and available soil water. In contrast to the significant errors of Gsc in the big-leaf model, the predicted Gsc using the dual-leaf model had a high degree of data-model agreement; the slope of the linear regression between daytime predictions and measurements was 1.01 (R2 = 0.98), with RMSE of 0.6120 mm s−1 for four clear-sky days in different growth stages. The estimates of half-hourly λET using the dual-source dual-leaf model (DSDL) agreed well with measurements and the error was within 5% during two growing seasons of maize with differing hydrometeorological and management strategies. Moreover, the estimates of soil evaporation using the DSDL model closely matched actual measurements. Our results indicate that the DSDL model can produce more accurate estimation of Gsc and λET, compared to the big-leaf model, and thus is an effective alternative approach for estimating and partitioning λET. PMID:24752329

Initialization of a fractional order identification algorithm applied for Lithium-ion battery modeling in time domain

NASA Astrophysics Data System (ADS)

Nasser Eddine, Achraf; Huard, Benoît; Gabano, Jean-Denis; Poinot, Thierry

2018-06-01

This paper deals with the initialization of a non linear identification algorithm used to accurately estimate the physical parameters of Lithium-ion battery. A Randles electric equivalent circuit is used to describe the internal impedance of the battery. The diffusion phenomenon related to this modeling is presented using a fractional order method. The battery model is thus reformulated into a transfer function which can be identified through Levenberg-Marquardt algorithm to ensure the algorithm's convergence to the physical parameters. An initialization method is proposed in this paper by taking into account previously acquired information about the static and dynamic system behavior. The method is validated using noisy voltage response, while precision of the final identification results is evaluated using Monte-Carlo method.

Comparison of the A-Cc curve fitting methods in determining maximum ribulose 1.5-bisphosphate carboxylase/oxygenase carboxylation rate, potential light saturated electron transport rate and leaf dark respiration.

PubMed

Miao, Zewei; Xu, Ming; Lathrop, Richard G; Wang, Yufei

2009-02-01

A review of the literature revealed that a variety of methods are currently used for fitting net assimilation of CO2-chloroplastic CO2 concentration (A-Cc) curves, resulting in considerable differences in estimating the A-Cc parameters [including maximum ribulose 1.5-bisphosphate carboxylase/oxygenase (Rubisco) carboxylation rate (Vcmax), potential light saturated electron transport rate (Jmax), leaf dark respiration in the light (Rd), mesophyll conductance (gm) and triose-phosphate utilization (TPU)]. In this paper, we examined the impacts of fitting methods on the estimations of Vcmax, Jmax, TPU, Rd and gm using grid search and non-linear fitting techniques. Our results suggested that the fitting methods significantly affected the predictions of Rubisco-limited (Ac), ribulose 1,5-bisphosphate-limited (Aj) and TPU-limited (Ap) curves and leaf photosynthesis velocities because of the inconsistent estimate of Vcmax, Jmax, TPU, Rd and gm, but they barely influenced the Jmax : Vcmax, Vcmax : Rd and Jmax : TPU ratio. In terms of fitting accuracy, simplicity of fitting procedures and sample size requirement, we recommend to combine grid search and non-linear techniques to directly and simultaneously fit Vcmax, Jmax, TPU, Rd and gm with the whole A-Cc curve in contrast to the conventional method, which fits Vcmax, Rd or gm first and then solves for Vcmax, Jmax and/or TPU with V(cmax), Rd and/or gm held as constants.

Linearized T-Matrix and Mie Scattering Computations

NASA Technical Reports Server (NTRS)

Spurr, R.; Wang, J.; Zeng, J.; Mishchenko, M. I.

2011-01-01

We present a new linearization of T-Matrix and Mie computations for light scattering by non-spherical and spherical particles, respectively. In addition to the usual extinction and scattering cross-sections and the scattering matrix outputs, the linearized models will generate analytical derivatives of these optical properties with respect to the real and imaginary parts of the particle refractive index, and (for non-spherical scatterers) with respect to the ''shape'' parameter (the spheroid aspect ratio, cylinder diameter/height ratio, Chebyshev particle deformation factor). These derivatives are based on the essential linearity of Maxwell's theory. Analytical derivatives are also available for polydisperse particle size distribution parameters such as the mode radius. The T-matrix formulation is based on the NASA Goddard Institute for Space Studies FORTRAN 77 code developed in the 1990s. The linearized scattering codes presented here are in FORTRAN 90 and will be made publicly available.

Communications circuit including a linear quadratic estimator

DOEpatents

Ferguson, Dennis D.

2015-07-07

A circuit includes a linear quadratic estimator (LQE) configured to receive a plurality of measurements a signal. The LQE is configured to weight the measurements based on their respective uncertainties to produce weighted averages. The circuit further includes a controller coupled to the LQE and configured to selectively adjust at least one data link parameter associated with a communication channel in response to receiving the weighted averages.

Detecting chaos in particle accelerators through the frequency map analysis method.

PubMed

Papaphilippou, Yannis

2014-06-01

The motion of beams in particle accelerators is dominated by a plethora of non-linear effects, which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting these effects and thereby increasing the region of beam stability plays an essential role during the accelerator design phase but also their operation. After describing the nature of non-linear effects and their impact on performance parameters of different particle accelerator categories, the theory of non-linear particle motion is outlined. The recent developments on the methods employed for the analysis of chaotic beam motion are detailed. In particular, the ability of the frequency map analysis method to detect chaotic motion and guide the correction of non-linear effects is demonstrated in particle tracking simulations but also experimental data.

WE-H-BRA-01: BEST IN PHYSICS (THERAPY): Nano-Dosimetric Kinetic Model for Variable Relative Biological Effectiveness of Proton and Ion Beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abolfath, R; Bronk, L; Titt, U.

2016-06-15

Purpose: Recent clonogenic cell survival and γH2AX studies suggest proton relative biological effectiveness (RBE) may be a non-linear function of linear energy transfer (LET) in the distal edge of the Bragg peak and beyond. We sought to develop a multiscale model to account for non-linear response phenomena to aid in the optimization of intensity-modulated proton therapy. Methods: The model is based on first-principle simulations of proton track structures, including secondary ions, and an analytical derivation of the dependence on particle LET of the linear-quadratic (LQ) model parameters α and β. The derived formulas are an extension of the microdosimetric kineticmore » (MK) model that captures dissipative track structures and non-Poissonian distribution of DNA damage at the distal edge of the Bragg peak and beyond. Monte Carlo simulations were performed to confirm the non-linear dose-response characteristics arising from the non-Poisson distribution of initial DNA damage. Results: In contrast to low LET segments of the proton depth dose, from the beam entrance to the Bragg peak, strong deviations from non-dissipative track structures and Poisson distribution in the ionization events in the Bragg peak distal edge govern the non-linear cell response and result in the transformation α=(1+c-1 L) α-x+2(c-0 L+c-2 L^2 )(1+c-1 L) β-x and β=(1+c-1 L)^2 β-x. Here L is the charged particle LET, and c-0,c-1, and c-2 are functions of microscopic parameters and can be served as fitting parameters to the cell-survival data. In the low LET limit c-1, and c-2 are negligible hence the linear model proposed and used by Wilkins-Oelfke for the proton treatment planning system can be retrieved. The present model fits well the recent clonogenic survival data measured recently in our group in MDACC. Conclusion: The present hybrid method provides higher accuracy in calculating the RBE-weighted dose in the target and normal tissues.« less

Simultaneous multiple non-crossing quantile regression estimation using kernel constraints

PubMed Central

Liu, Yufeng; Wu, Yichao

2011-01-01

Quantile regression (QR) is a very useful statistical tool for learning the relationship between the response variable and covariates. For many applications, one often needs to estimate multiple conditional quantile functions of the response variable given covariates. Although one can estimate multiple quantiles separately, it is of great interest to estimate them simultaneously. One advantage of simultaneous estimation is that multiple quantiles can share strength among them to gain better estimation accuracy than individually estimated quantile functions. Another important advantage of joint estimation is the feasibility of incorporating simultaneous non-crossing constraints of QR functions. In this paper, we propose a new kernel-based multiple QR estimation technique, namely simultaneous non-crossing quantile regression (SNQR). We use kernel representations for QR functions and apply constraints on the kernel coefficients to avoid crossing. Both unregularised and regularised SNQR techniques are considered. Asymptotic properties such as asymptotic normality of linear SNQR and oracle properties of the sparse linear SNQR are developed. Our numerical results demonstrate the competitive performance of our SNQR over the original individual QR estimation. PMID:22190842

astroABC : An Approximate Bayesian Computation Sequential Monte Carlo sampler for cosmological parameter estimation

NASA Astrophysics Data System (ADS)

Jennings, E.; Madigan, M.

2017-04-01

Given the complexity of modern cosmological parameter inference where we are faced with non-Gaussian data and noise, correlated systematics and multi-probe correlated datasets,the Approximate Bayesian Computation (ABC) method is a promising alternative to traditional Markov Chain Monte Carlo approaches in the case where the Likelihood is intractable or unknown. The ABC method is called "Likelihood free" as it avoids explicit evaluation of the Likelihood by using a forward model simulation of the data which can include systematics. We introduce astroABC, an open source ABC Sequential Monte Carlo (SMC) sampler for parameter estimation. A key challenge in astrophysics is the efficient use of large multi-probe datasets to constrain high dimensional, possibly correlated parameter spaces. With this in mind astroABC allows for massive parallelization using MPI, a framework that handles spawning of processes across multiple nodes. A key new feature of astroABC is the ability to create MPI groups with different communicators, one for the sampler and several others for the forward model simulation, which speeds up sampling time considerably. For smaller jobs the Python multiprocessing option is also available. Other key features of this new sampler include: a Sequential Monte Carlo sampler; a method for iteratively adapting tolerance levels; local covariance estimate using scikit-learn's KDTree; modules for specifying optimal covariance matrix for a component-wise or multivariate normal perturbation kernel and a weighted covariance metric; restart files output frequently so an interrupted sampling run can be resumed at any iteration; output and restart files are backed up at every iteration; user defined distance metric and simulation methods; a module for specifying heterogeneous parameter priors including non-standard prior PDFs; a module for specifying a constant, linear, log or exponential tolerance level; well-documented examples and sample scripts. This code is hosted online at https://github.com/EliseJ/astroABC.

Influence of tire dynamics on slip ratio estimation of independent driving wheel system

NASA Astrophysics Data System (ADS)

Li, Jianqiu; Song, Ziyou; Wei, Yintao; Ouyang, Minggao

2014-11-01

The independent driving wheel system, which is composed of in-wheel permanent magnet synchronous motor(I-PMSM) and tire, is more convenient to estimate the slip ratio because the rotary speed of the rotor can be accurately measured. However, the ring speed of the tire ring doesn't equal to the rotor speed considering the tire deformation. For this reason, a deformable tire and a detailed I-PMSM are modeled by using Matlab/Simulink. Moreover, the tire/road contact interface(a slippery road) is accurately described by the non-linear relaxation length-based model and the Magic Formula pragmatic model. Based on the relatively accurate model, the error of slip ratio estimated by the rotor rotary speed is analyzed in both time and frequency domains when a quarter car is started by the I-PMSM with a definite target torque input curve. In addition, the natural frequencies(NFs) of the driving wheel system with variable parameters are illustrated to present the relationship between the slip ratio estimation error and the NF. According to this relationship, a low-pass filter, whose cut-off frequency corresponds to the NF, is proposed to eliminate the error in the estimated slip ratio. The analysis, concerning the effect of the driving wheel parameters and road conditions on slip ratio estimation, shows that the peak estimation error can be reduced up to 75% when the LPF is adopted. The robustness and effectiveness of the LPF are therefore validated. This paper builds up the deformable tire model and the detailed I-PMSM models, and analyzes the effect of the driving wheel parameters and road conditions on slip ratio estimation.

Improving the quantification of contrast enhanced ultrasound using a Bayesian approach

NASA Astrophysics Data System (ADS)

Rizzo, Gaia; Tonietto, Matteo; Castellaro, Marco; Raffeiner, Bernd; Coran, Alessandro; Fiocco, Ugo; Stramare, Roberto; Grisan, Enrico

2017-03-01

Contrast Enhanced Ultrasound (CEUS) is a sensitive imaging technique to assess tissue vascularity, that can be useful in the quantification of different perfusion patterns. This can be particularly important in the early detection and staging of arthritis. In a recent study we have shown that a Gamma-variate can accurately quantify synovial perfusion and it is flexible enough to describe many heterogeneous patterns. Moreover, we have shown that through a pixel-by-pixel analysis the quantitative information gathered characterizes more effectively the perfusion. However, the SNR ratio of the data and the nonlinearity of the model makes the parameter estimation difficult. Using classical non-linear-leastsquares (NLLS) approach the number of unreliable estimates (those with an asymptotic coefficient of variation greater than a user-defined threshold) is significant, thus affecting the overall description of the perfusion kinetics and of its heterogeneity. In this work we propose to solve the parameter estimation at the pixel level within a Bayesian framework using Variational Bayes (VB), and an automatic and data-driven prior initialization. When evaluating the pixels for which both VB and NLLS provided reliable estimates, we demonstrated that the parameter values provided by the two methods are well correlated (Pearson's correlation between 0.85 and 0.99). Moreover, the mean number of unreliable pixels drastically reduces from 54% (NLLS) to 26% (VB), without increasing the computational time (0.05 s/pixel for NLLS and 0.07 s/pixel for VB). When considering the efficiency of the algorithms as computational time per reliable estimate, VB outperforms NLLS (0.11 versus 0.25 seconds per reliable estimate respectively).

Influence of Non-linear Radiation Heat Flux on Rotating Maxwell Fluid over a Deformable Surface: A Numerical Study

NASA Astrophysics Data System (ADS)

Mustafa, M.; Mushtaq, A.; Hayat, T.; Alsaedi, A.

2018-04-01

Mathematical model for Maxwell fluid flow in rotating frame induced by an isothermal stretching wall is explored numerically. Scale analysis based boundary layer approximations are applied to simplify the conservation relations which are later converted to similar forms via appropriate substitutions. A numerical approach is utilized to derive similarity solutions for broad range of Deborah number. The results predict that velocity distributions are inversely proportional to the stress relaxation time. This outcome is different from that observed for the elastic parameter of second grade fluid. Unlike non-rotating frame, the solution curves are oscillatory decaying functions of similarity variable. As angular velocity enlarges, temperature rises and significant drop in the heat transfer coefficient occurs. We note that the wall slope of temperature has an asymptotically decaying profile against the wall to ambient ratio parameter. From the qualitative view point, temperature ratio parameter and radiation parameter have similar effect on the thermal boundary layer. Furthermore, radiation parameter has a definite role in improving the cooling process of the stretching boundary. A comparative study of current numerical computations and those from the existing studies is also presented in a limiting case. To our knowledge, the phenomenon of non-linear radiation in rotating viscoelastic flow due to linearly stretched plate is just modeled here.

Fully 3D modeling of tokamak vertical displacement events with realistic parameters

NASA Astrophysics Data System (ADS)

Pfefferle, David; Ferraro, Nathaniel; Jardin, Stephen; Bhattacharjee, Amitava

2016-10-01

In this work, we model the complex multi-domain and highly non-linear physics of Vertical Displacement Events (VDEs), one of the most damaging off-normal events in tokamaks, with the implicit 3D extended MHD code M3D-C1. The code has recently acquired the capability to include finite thickness conducting structures within the computational domain. By exploiting the possibility of running a linear 3D calculation on top of a non-linear 2D simulation, we monitor the non-axisymmetric stability and assess the eigen-structure of kink modes as the simulation proceeds. Once a stability boundary is crossed, a fully 3D non-linear calculation is launched for the remainder of the simulation, starting from an earlier time of the 2D run. This procedure, along with adaptive zoning, greatly increases the efficiency of the calculation, and allows to perform VDE simulations with realistic parameters and high resolution. Simulations are being validated with NSTX data where both axisymmetric (toroidally averaged) and non-axisymmetric induced and conductive (halo) currents have been measured. This work is supported by US DOE Grant DE-AC02-09CH11466.

Quantification and parametrization of non-linearity effects by higher-order sensitivity terms in scattered light differential optical absorption spectroscopy

NASA Astrophysics Data System (ADS)

Puķīte, Jānis; Wagner, Thomas

2016-05-01

We address the application of differential optical absorption spectroscopy (DOAS) of scattered light observations in the presence of strong absorbers (in particular ozone), for which the absorption optical depth is a non-linear function of the trace gas concentration. This is the case because Beer-Lambert law generally does not hold for scattered light measurements due to many light paths contributing to the measurement. While in many cases linear approximation can be made, for scenarios with strong absorptions non-linear effects cannot always be neglected. This is especially the case for observation geometries, for which the light contributing to the measurement is crossing the atmosphere under spatially well-separated paths differing strongly in length and location, like in limb geometry. In these cases, often full retrieval algorithms are applied to address the non-linearities, requiring iterative forward modelling of absorption spectra involving time-consuming wavelength-by-wavelength radiative transfer modelling. In this study, we propose to describe the non-linear effects by additional sensitivity parameters that can be used e.g. to build up a lookup table. Together with widely used box air mass factors (effective light paths) describing the linear response to the increase in the trace gas amount, the higher-order sensitivity parameters eliminate the need for repeating the radiative transfer modelling when modifying the absorption scenario even in the presence of a strong absorption background. While the higher-order absorption structures can be described as separate fit parameters in the spectral analysis (so-called DOAS fit), in practice their quantitative evaluation requires good measurement quality (typically better than that available from current measurements). Therefore, we introduce an iterative retrieval algorithm correcting for the higher-order absorption structures not yet considered in the DOAS fit as well as the absorption dependence on temperature and scattering processes.

A stopping criterion for the iterative solution of partial differential equations

NASA Astrophysics Data System (ADS)

Rao, Kaustubh; Malan, Paul; Perot, J. Blair

2018-01-01

A stopping criterion for iterative solution methods is presented that accurately estimates the solution error using low computational overhead. The proposed criterion uses information from prior solution changes to estimate the error. When the solution changes are noisy or stagnating it reverts to a less accurate but more robust, low-cost singular value estimate to approximate the error given the residual. This estimator can also be applied to iterative linear matrix solvers such as Krylov subspace or multigrid methods. Examples of the stopping criterion's ability to accurately estimate the non-linear and linear solution error are provided for a number of different test cases in incompressible fluid dynamics.

Numerical solution of mixed convection flow of an MHD Jeffery fluid over an exponentially stretching sheet in the presence of thermal radiation and chemical reaction

NASA Astrophysics Data System (ADS)

Shateyi, Stanford; Marewo, Gerald T.

2018-05-01

We numerically investigate a mixed convection model for a magnetohydrodynamic (MHD) Jeffery fluid flowing over an exponentially stretching sheet. The influence of thermal radiation and chemical reaction is also considered in this study. The governing non-linear coupled partial differential equations are reduced to a set of coupled non-linear ordinary differential equations by using similarity functions. This new set of ordinary differential equations are solved numerically using the Spectral Quasi-Linearization Method. A parametric study of physical parameters involved in this study is carried out and displayed in tabular and graphical forms. It is observed that the velocity is enhanced with increasing values of the Deborah number, buoyancy and thermal radiation parameters. Furthermore, the temperature and species concentration are decreasing functions of the Deborah number. The skin friction coefficient increases with increasing values of the magnetic parameter and relaxation time. Heat and mass transfer rates increase with increasing values of the Deborah number and buoyancy parameters.

Phase Diagrams and the Non-Linear Dielectric Constant in the Landau-Type Potential Including the Linear-Quadratic Coupling between Order Parameters

NASA Astrophysics Data System (ADS)

Iwata, Makoto; Orihara, Hiroshi; Ishibashi, Yoshihiro

1997-04-01

The phase diagrams in the Landau-type thermodynamic potential including the linear-quadratic coupling between order parameters p and q, i.e., qp2, which is applicable to the phase transition in the benzil, phospholipid bilayers, and the isotropic-nematic phase transition in liquid crystals, are studied. It was found that the phase diagram in the extreme case has one tricritical point c1, one critical end point e1, and two triple points t1 and t2. The linear and nonlinear dielectric constants in the potential are discussed in the case that the order parameter p is the polarization.

Image Based Biomarker of Breast Cancer Risk: Analysis of Risk Disparity Among Minority Populations

DTIC Science & Technology

2014-03-01

attenuation coefficient of calcium hydroxyapatite ; is a parameter controlling the contrast of MCs in synthetic images (0< ə); and is the linear...effect of acquisition parameters and quantum noise," Med Phys, 37, 1591-600 (2010). [13] M. J. Yaffe, J. M. Boone, N. Packard, O. Alonzo-Proulx, S. Y...the acquisition of individual mammograms, the use of linear transformations does not seem appropriate for mammogram registration. Non-linear

A numerical identifiability test for state-space models--application to optimal experimental design.

PubMed

Hidalgo, M E; Ayesa, E

2001-01-01

This paper describes a mathematical tool for identifiability analysis, easily applicable to high order non-linear systems modelled in state-space and implementable in simulators with a time-discrete approach. This procedure also permits a rigorous analysis of the expected estimation errors (average and maximum) in calibration experiments. The methodology is based on the recursive numerical evaluation of the information matrix during the simulation of a calibration experiment and in the setting-up of a group of information parameters based on geometric interpretations of this matrix. As an example of the utility of the proposed test, the paper presents its application to an optimal experimental design of ASM Model No. 1 calibration, in order to estimate the maximum specific growth rate microH and the concentration of heterotrophic biomass XBH.

Comparison of BOD results obtained by dilution and manometric methods in sanitary landfill leachates.

PubMed

Ceçen, F; Yangin, C

2000-12-01

This study examined the determination of BOD in landfill leachates by dilution (D-method) and manometric methods (M-method). The differences in results were discussed based on statistical tests. The effects of sample dilution, seeding, chloride and total Kjeldahl nitrogen (TKN) level were examined. The M-method was found to be more sensitive to increases in chloride and TKN concentrations. However, in the M-method the positive interference of nitrogenous BOD (NBOD) to carbonaceous BOD (CBOD) was more successfully prevented. The BOD rate constant k and the ultimate BOD (BODu) were estimated by non-linear regression. With the M-method these parameters could be more reliably estimated than the D-method. Suggestions were made for BOD analyses in landfill leachates in future studies.

Study of parameter of nonlinearity in 2-chloroethanol with 2-dimethylethanolamine/2-diethylethanolamine at different temperatures

NASA Astrophysics Data System (ADS)

Awasthi, Anjali; Awasthi, Aashees

2017-06-01

The acoustic non-linearity parameter (B/A) for binary mixtures of 2-chloroethanol with 2-dimethylethanolamine (2-DMAE) and 2-diethylethanolamine (2-DEAE) are evaluated using Tong Dong, Beyer and Beyer-Tong Dong coefficients at varying concentrations and temperatures ranging from 293.15 to 313.15 K. The nonlinearity parameter is used to calculate various molecular properties such as internal pressure, cohesive energy density, Van der waals' constant, distance of closest approach, diffusion coefficient and rotational correlation time. Additionally, the intermediate quantities like temperature and pressure derivatives of sound velocity and phase shift parameter as a function of temperature are also deduced. The extent of intermolecular interactions, anharmonicity and structural configuration of the binaries under investigation are discussed in terms of excess non-linearity parameter (B/A)E.

Quantifying uncertainty and sensitivity in sea ice models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Urrego Blanco, Jorge Rolando; Hunke, Elizabeth Clare; Urban, Nathan Mark

The Los Alamos Sea Ice model has a number of input parameters for which accurate values are not always well established. We conduct a variance-based sensitivity analysis of hemispheric sea ice properties to 39 input parameters. The method accounts for non-linear and non-additive effects in the model.

AGARD Flight Test Instrumentation Series. Volume 14. The Analysis of Random Data

DTIC Science & Technology

1981-11-01

obtained at arbitrary times during a number of flights. No constraints have been placed upon the controlling parameters, so that the process is non ...34noisy" environment controlling a non -linear system (the aircraft) using a redundant net of control parameters. when aircraft were flown manually with...structure. Cuse 2. Non -Stationary Measurements. When the 114S value of a random signal varies with parameters which cannot be controlled , then the method

Impact of fitting algorithms on errors of parameter estimates in dynamic contrast-enhanced MRI

NASA Astrophysics Data System (ADS)

Debus, C.; Floca, R.; Nörenberg, D.; Abdollahi, A.; Ingrisch, M.

2017-12-01

Parameter estimation in dynamic contrast-enhanced MRI (DCE MRI) is usually performed by non-linear least square (NLLS) fitting of a pharmacokinetic model to a measured concentration-time curve. The two-compartment exchange model (2CXM) describes the compartments ‘plasma’ and ‘interstitial volume’ and their exchange in terms of plasma flow and capillary permeability. The model function can be defined by either a system of two coupled differential equations or a closed-form analytical solution. The aim of this study was to compare these two representations in terms of accuracy, robustness and computation speed, depending on parameter combination and temporal sampling. The impact on parameter estimation errors was investigated by fitting the 2CXM to simulated concentration-time curves. Parameter combinations representing five tissue types were used, together with two arterial input functions, a measured and a theoretical population based one, to generate 4D concentration images at three different temporal resolutions. Images were fitted by NLLS techniques, where the sum of squared residuals was calculated by either numeric integration with the Runge-Kutta method or convolution. Furthermore two example cases, a prostate carcinoma and a glioblastoma multiforme patient, were analyzed in order to investigate the validity of our findings in real patient data. The convolution approach yields improved results in precision and robustness of determined parameters. Precision and stability are limited in curves with low blood flow. The model parameter ve shows great instability and little reliability in all cases. Decreased temporal resolution results in significant errors for the differential equation approach in several curve types. The convolution excelled in computational speed by three orders of magnitude. Uncertainties in parameter estimation at low temporal resolution cannot be compensated by usage of the differential equations. Fitting with the convolution approach is superior in computational time, with better stability and accuracy at the same time.

Realization of non-linear coherent states by photonic lattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dehdashti, Shahram, E-mail: shdehdashti@zju.edu.cn; Li, Rujiang; Chen, Hongsheng, E-mail: hansomchen@zju.edu.cn

2015-06-15

In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2) and su(1, 1) coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.

Apparent diffusion coefficient (ADC) does not correlate with different serological parameters in myositis and myopathy.

PubMed

Meyer, Hans-Jonas; Ziemann, Oliver; Kornhuber, Malte; Emmer, Alexander; Quäschling, Ulf; Schob, Stefan; Surov, Alexey

2018-06-01

Background Magnetic resonance imaging (MRI) is widely used in several muscle disorders. Diffusion-weighted imaging (DWI) is an imaging modality, which can reflect microstructural tissue composition. The apparent diffusion coefficient (ADC) is used to quantify the random motion of water molecules in tissue. Purpose To investigate ADC values in patients with myositis and non-inflammatory myopathy and to analyze possible associations between ADC and laboratory parameters in these patients. Material and Methods Overall, 17 patients with several myositis entities, eight patients with non-inflammatory myopathies, and nine patients without muscle disorder as a control group were included in the study (mean age = 55.3 ± 14.3 years). The diagnosis was confirmed by histopathology in every case. DWI was obtained in a 1.5-T scanner using two b-values: 0 and 1000 s/mm 2 . In all patients, the blood sample was acquired within three days to the MRI. The following serological parameters were estimated: C-reactive protein, lactate dehydrogenase, alanine aminotransferase, aspartate aminotransferase, creatine kinase, and myoglobine. Results The estimated mean ADC value for the myositis group was 1.89 ± 0.37 × 10 -3  mm 2 /s and for the non-inflammatory myopathy group was 1.79 ± 0.33 × 10 -3  mm 2 /s, respectively. The mean ADC values (1.15 ± 0.37 × 10 -3  mm 2 /s) were significantly higher to unaffected muscles (vs. myositis P = 0.0002 and vs. myopathy P = 0.0021). There were no significant correlations between serological parameters and ADC values. Conclusion Affected muscles showed statistically significantly higher ADC values than normal muscles. No linear correlations between ADC and serological parameters were identified.

On the pth moment estimates of solutions to stochastic functional differential equations in the G-framework.

PubMed

Faizullah, Faiz

2016-01-01

The aim of the current paper is to present the path-wise and moment estimates for solutions to stochastic functional differential equations with non-linear growth condition in the framework of G-expectation and G-Brownian motion. Under the nonlinear growth condition, the pth moment estimates for solutions to SFDEs driven by G-Brownian motion are proved. The properties of G-expectations, Hölder's inequality, Bihari's inequality, Gronwall's inequality and Burkholder-Davis-Gundy inequalities are used to develop the above mentioned theory. In addition, the path-wise asymptotic estimates and continuity of pth moment for the solutions to SFDEs in the G-framework, with non-linear growth condition are shown.

Population pharmacokinetics of methadone hydrochloride after a single intramuscular administration in adult Japanese sika deer (Cervus nippon nippon).

PubMed

Scala, Christopher; Marsot, Amélie; Limoges, Marie-Josée; Locatelli, Yann; Simon, Nicolas; Alvarez, Jean-Claude

2015-03-01

To assess the population pharmacokinetics of methadone in deer. Prospective non-randomized experimental trial. Twelve healthy adult sika deer (nine males and three females). Deer received intramuscular administration of racemic methadone hydrochloride at 0.5 mg kg(-1) or 1 mg kg(-1) . Plasma methadone and its metabolite 2-Ethylidene-1,5-Dimethyl-3,3-Diphenyl-Pyrolidine (EDDP) concentrations were determined by validated liquid chromatography coupled to tandem mass spectrometry methods, at times 0, 30 minutes, 1, 2, 3, 4, 5, 6, 8, 12 and 24 hours. Population pharmacokinetics analysis was undertaken using a non-linear mixed effects modelling (NONMEM). A two-compartment linear disposition model best described observed time-concentration profiles of methadone and EDDP. Population parameter estimates of methadone were elimination clearance (17.3 L hour(-1) ), metabolic clearance (34.6 L hour(-1) ), volume of distribution of compartment 1 (216.0 L) and volume of distribution of compartment 2 (384.0 L). Population parameter estimates of EDDP were elimination clearance (121.0 L hour(-1) ), volume of distribution of compartment 3 (1.08 L) and volume of distribution of compartment 4 (499.5 L). The total clearance and total volume of distribution of methadone and EDDP were 51.9 L hour(-1) , 121.0 L hour (-1) , 600.0 L and 500.6 L, respectively. The methadone terminal elimination half-life was 8.19 hours. No adverse effects were observed after methadone administration. Following intramuscular injection, methadone was characterized by a large total volume of distribution, high systemic clearance and intermediate terminal half-life in sika deer. © 2014 Association of Veterinary Anaesthetists and the American College of Veterinary Anesthesia and Analgesia.

The detectability of baryonic acoustic oscillations in future galaxy surveys

NASA Astrophysics Data System (ADS)

Angulo, R. E.; Baugh, C. M.; Frenk, C. S.; Lacey, C. G.

2008-01-01

We assess the detectability of baryonic acoustic oscillation (BAO) in the power spectrum of galaxies using ultralarge volume N-body simulations of the hierarchical clustering of dark matter and semi-analytical modelling of galaxy formation. A step-by-step illustration is given of the various effects (non-linear fluctuation growth, peculiar motions, non-linear and scale-dependent bias) which systematically change the form of the galaxy power spectrum on large scales from the simple prediction of linear perturbation theory. Using a new method to extract the scale of the oscillations, we nevertheless find that the BAO approach gives an unbiased estimate of the sound horizon scale. Sampling variance remains the dominant source of error despite the huge volume of our simulation box (=2.41h-3Gpc3). We use our results to forecast the accuracy with which forthcoming surveys will be able to measure the sound horizon scale, s, and, hence constrain the dark energy equation of state parameter, w (with simplifying assumptions and without marginalizing over the other cosmological parameters). Pan-STARRS could potentially yield a measurement with an accuracy of Δs/s = 0.5-0.7 per cent (corresponding to Δw ~ 2-3 per cent), which is competitive with the proposed WFMOS survey (Δs/s = 1 per cent Δw ~ 4 per cent). Achieving Δw <= 1 per cent using BAO alone is beyond any currently commissioned project and will require an all-sky spectroscopic survey, such as would be undertaken by the SPACE mission concept under proposal to ESA.

Estimation of white matter fiber parameters from compressed multiresolution diffusion MRI using sparse Bayesian learning.

PubMed

Pisharady, Pramod Kumar; Sotiropoulos, Stamatios N; Duarte-Carvajalino, Julio M; Sapiro, Guillermo; Lenglet, Christophe

2018-02-15

We present a sparse Bayesian unmixing algorithm BusineX: Bayesian Unmixing for Sparse Inference-based Estimation of Fiber Crossings (X), for estimation of white matter fiber parameters from compressed (under-sampled) diffusion MRI (dMRI) data. BusineX combines compressive sensing with linear unmixing and introduces sparsity to the previously proposed multiresolution data fusion algorithm RubiX, resulting in a method for improved reconstruction, especially from data with lower number of diffusion gradients. We formulate the estimation of fiber parameters as a sparse signal recovery problem and propose a linear unmixing framework with sparse Bayesian learning for the recovery of sparse signals, the fiber orientations and volume fractions. The data is modeled using a parametric spherical deconvolution approach and represented using a dictionary created with the exponential decay components along different possible diffusion directions. Volume fractions of fibers along these directions define the dictionary weights. The proposed sparse inference, which is based on the dictionary representation, considers the sparsity of fiber populations and exploits the spatial redundancy in data representation, thereby facilitating inference from under-sampled q-space. The algorithm improves parameter estimation from dMRI through data-dependent local learning of hyperparameters, at each voxel and for each possible fiber orientation, that moderate the strength of priors governing the parameter variances. Experimental results on synthetic and in-vivo data show improved accuracy with a lower uncertainty in fiber parameter estimates. BusineX resolves a higher number of second and third fiber crossings. For under-sampled data, the algorithm is also shown to produce more reliable estimates. Copyright © 2017 Elsevier Inc. All rights reserved.

A computational analysis subject to thermophysical aspects of Sisko fluid flow over a cylindrical surface

NASA Astrophysics Data System (ADS)

Awais, M.; Khalil-Ur-Rehman; Malik, M. Y.; Hussain, Arif; Salahuddin, T.

2017-09-01

The present analysis is devoted to probing the salient features of the mixed convection and non-linear thermal radiation effects on non-Newtonian Sisko fluid flow over a linearly stretching cylindrical surface. Properties of heat transfer are outlined via variable thermal conductivity and convective boundary conditions. The boundary layer approach is implemented to construct the mathematical model in the form of partial differential equations. Then, the requisite PDEs are transmuted into a complex ordinary differential system by invoking appropriate dimensionless variables. Solution of subsequent ODEs is obtained by utilizing the Runge-Kutta algorithm (fifth order) along with the shooting scheme. The graphical illustrations are presented to interpret the features of the involved pertinent flow parameters on concerning profiles. For a better description of the fluid flow, numerical variations in local skin friction coefficient and local Nusselt number are scrutinized in tables. From thorough analysis, it is inferred that the mixed convection parameter and the curvature parameter increase the velocity while temperature shows a different behavior. Additionally, both momentum and thermal distribution of fluid flow decrease with increasing values of the non-linearity index. Furthermore, variable thermal parameter and heat generation/absorption parameter amplify the temperature significantly. The skin friction is an increasing function of all momentum controlling parameters. The local Nusselt number also shows a similar behavior against heat radiation parameter and variable thermal conductivity parameter while it shows a dual nature for the heat generation/absorption parameter. Finally, the obtained results are validated by comparison with the existing literature and hence the correctness of the analysis is proved.

Near real-time estimation of the seismic source parameters in a compressed domain

NASA Astrophysics Data System (ADS)

Rodriguez, Ismael A. Vera

Seismic events can be characterized by its origin time, location and moment tensor. Fast estimations of these source parameters are important in areas of geophysics like earthquake seismology, and the monitoring of seismic activity produced by volcanoes, mining operations and hydraulic injections in geothermal and oil and gas reservoirs. Most available monitoring systems estimate the source parameters in a sequential procedure: first determining origin time and location (e.g., epicentre, hypocentre or centroid of the stress glut density), and then using this information to initialize the evaluation of the moment tensor. A more efficient estimation of the source parameters requires a concurrent evaluation of the three variables. The main objective of the present thesis is to address the simultaneous estimation of origin time, location and moment tensor of seismic events. The proposed method displays the benefits of being: 1) automatic, 2) continuous and, depending on the scale of application, 3) of providing results in real-time or near real-time. The inversion algorithm is based on theoretical results from sparse representation theory and compressive sensing. The feasibility of implementation is determined through the analysis of synthetic and real data examples. The numerical experiments focus on the microseismic monitoring of hydraulic fractures in oil and gas wells, however, an example using real earthquake data is also presented for validation. The thesis is complemented with a resolvability analysis of the moment tensor. The analysis targets common monitoring geometries employed in hydraulic fracturing in oil wells. Additionally, it is presented an application of sparse representation theory for the denoising of one-component and three-component microseismicity records, and an algorithm for improved automatic time-picking using non-linear inversion constraints.

Assessing the impact of non-tidal atmospheric loading on a Kalman filter-based terrestrial reference frame

NASA Astrophysics Data System (ADS)

Abbondanza, Claudio; Altamimi, Zuheir; Chin, Toshio; Collilieux, Xavier; Dach, Rolf; Gross, Richard; Heflin, Michael; König, Rolf; Lemoine, Frank; Macmillan, Dan; Parker, Jay; van Dam, Tonie; Wu, Xiaoping

2014-05-01

The International Terrestrial Reference Frame (ITRF) adopts a piece-wise linear model to parameterize regularized station positions and velocities. The space-geodetic (SG) solutions from VLBI, SLR, GPS and DORIS used as input in the ITRF combination process account for tidal loading deformations, but ignore the non-tidal part. As a result, the non-linear signal observed in the time series of SG-derived station positions in part reflects non-tidal loading displacements not introduced in the SG data reduction. In this analysis, we assess the impact of non-tidal atmospheric loading (NTAL) corrections on the TRF computation. Focusing on the a-posteriori approach, (i) the NTAL model derived from the National Centre for Environmental Prediction (NCEP) surface pressure is removed from the SINEX files of the SG solutions used as inputs to the TRF determinations; (ii) adopting a Kalman-filter based approach, two distinct linear TRFs are estimated combining the 4 SG solutions with (corrected TRF solution) and without the NTAL displacements (standard TRF solution). Linear fits (offset and atmospheric velocity) of the NTAL displacements removed during step (i) are estimated accounting for the station position discontinuities introduced in the SG solutions and adopting different weighting strategies. The NTAL-derived (atmospheric) velocity fields are compared to those obtained from the TRF reductions during step (ii). The consistency between the atmospheric and the TRF-derived velocity fields is examined. We show how the presence of station position discontinuities in SG solutions degrades the agreement between the velocity fields and compare the effect of different weighting structure adopted while estimating the linear fits to the NTAL displacements. Finally, we evaluate the effect of restoring the atmospheric velocities determined through the linear fits of the NTAL displacements to the single-technique linear reference frames obtained by stacking the standard SG SINEX files. Differences between the velocity fields obtained restoring the NTAL displacements and the standard stacked linear reference frames are discussed.

Entropy Analysis in Mixed Convection MHD flow of Nanofluid over a Non-linear Stretching Sheet

NASA Astrophysics Data System (ADS)

Matin, Meisam Habibi; Nobari, Mohammad Reza Heirani; Jahangiri, Pouyan

This article deals with a numerical study of entropy analysis in mixed convection MHD flow of nanofluid over a non-linear stretching sheet taking into account the effects of viscous dissipation and variable magnetic field. The nanofluid is made of such nano particles as SiO2 with pure water as a base fluid. To analyze the problem, at first the boundary layer equations are transformed into non-linear ordinary equations using a similarity transformation. The resultant equations are then solved numerically using the Keller-Box scheme based on the implicit finite-difference method. The effects of different non-dimensional governing parameters such as magnetic parameter, nanoparticles volume fraction, Nusselt, Richardson, Eckert, Hartman, Brinkman, Reynolds and entropy generation numbers are investigated in details. The results indicate that increasing the nano particles to the base fluids causes the reduction in shear forces and a decrease in stretching sheet heat transfer coefficient. Also, decreasing the magnetic parameter and increasing the Eckert number result in improves heat transfer rate. Furthermore, the surface acts as a strong source of irreversibility due to the higher entropy generation number near the surface.

Non-Linear Dynamics and Emergence in Laboratory Fusion Plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hnat, B.

2011-09-22

Turbulent behaviour of laboratory fusion plasma system is modelled using extended Hasegawa-Wakatani equations. The model is solved numerically using finite difference techniques. We discuss non-linear effects in such a system in the presence of the micro-instabilities, specifically a drift wave instability. We explore particle dynamics in different range of parameters and show that the transport changes from diffusive to non-diffusive when large directional flows are developed.

MODELING H-ARS USING HEMATOLOGICAL PARAMETERS: A COMPARISON BETWEEN THE NON-HUMAN PRIMATE AND MINIPIG.

PubMed

Bolduc, David L; Bünger, Rolf; Moroni, Maria; Blakely, William F

2016-12-01

Multiple hematological biomarkers (i.e. complete blood counts and serum chemistry parameters) were used in a multivariate linear-regression fit to create predictive algorithms for estimating the severity of hematopoietic acute radiation syndrome (H-ARS) using two different species (i.e. Göttingen Minipig and non-human primate (NHP) (Macacca mulatta)). Biomarker data were analyzed prior to irradiation and between 1-60 days (minipig) and 1-30 days (NHP) after irradiation exposures of 1.6-3.5 Gy (minipig) and 6.5 Gy (NHP) 60 Co gamma ray doses at 0.5-0.6 Gy min -1 and 0.4 Gy min -1 , respectively. Fitted radiation risk and injury categorization (RRIC) values and RRIC prediction percent accuracies were compared between the two models. Both models estimated H-ARS severity with over 80% overall predictive power and with receiver operating characteristic curve area values of 0.884 and 0.825. These results based on two animal radiation models support the concept for the use of a hematopoietic-based algorithm for predicting the risk of H-ARS in humans. Published by Oxford University Press 2016. This work is written by (a) US Government employee(s) and is in the public domain in the US.

Secreted Klotho and FGF23 in chronic kidney disease Stage 1 to 5: a sequence suggested from a cross-sectional study.

PubMed

Pavik, Ivana; Jaeger, Philippe; Ebner, Lena; Wagner, Carsten A; Petzold, Katja; Spichtig, Daniela; Poster, Diane; Wüthrich, Rudolf P; Russmann, Stefan; Serra, Andreas L

2013-02-01

Klotho and fibroblast growth factor 23 (FGF23) are key regulators of mineral metabolism in renal insufficiency. FGF23 levels have been shown to increase early in chronic kidney disease (CKD); however, the corresponding soluble Klotho levels at the different CKD stages are not known. Soluble Klotho, FGF23, parathyroid hormone (PTH), 1,25-dihydroxy vitamin D(3) (1,25D) and other parameters of mineral metabolism were measured in an observational cross-sectional study in 87 patients. Locally weighted scatter plot smoothing function of these parameters were plotted versus estimated glomerular filtration rate (eGFR) to illustrate the pattern of the relationship. Linear and non-linear regression analyses were performed to estimate changes in mineral metabolism parameters per 1mL/min/1.73 m(2) decline. In CKD 1-5, Klotho and 1,25D linearly decreased, whereas both FGF23 and PTH showed a baseline at early CKD stages and then a curvilinear increase. Crude mean Klotho level declined by 4.8 pg/mL (95% CI 3.5-6.2 pg/mL, P < 0.0001) and 1,25D levels by 0.30 ng/L (95% CI 0.18-0.41 ng/L, P < 0.0001) as GFR declined by 1 mL/min/1.73 m(2). After adjustment for age, gender, serum 25-hydroxyvitamin D levels and concomitant medications (calcium, supplemental vitamin D and calcitriol), we estimated that the mean Klotho change was 3.2 pg/mL (95% CI 1.2-5.2 pg/mL, P = 0.0019) for each 1 mL/min/1.73 m(2) GFR change. FGF23 departed from the baseline at an eGFR of 47 mL/min/1.73 m(2) (95% CI 39-56 mL/min/1.73 m(2)), whereas PTH departed at an eGFR of 34 mL/min/1.73 m(2) (95% CI 19-50 mL/min/1.73 m(2)). Soluble Klotho and 1,25D levels decrease and FGF23 levels increase at early CKD stages, whereas PTH levels increase at more advanced CKD stages.

Two is better than one: joint statistics of density and velocity in concentric spheres as a cosmological probe

NASA Astrophysics Data System (ADS)

Uhlemann, C.; Codis, S.; Hahn, O.; Pichon, C.; Bernardeau, F.

2017-08-01

The analytical formalism to obtain the probability distribution functions (PDFs) of spherically averaged cosmic densities and velocity divergences in the mildly non-linear regime is presented. A large-deviation principle is applied to those cosmic fields assuming their most likely dynamics in spheres is set by the spherical collapse model. We validate our analytical results using state-of-the-art dark matter simulations with a phase-space resolved velocity field finding a 2 per cent level agreement for a wide range of velocity divergences and densities in the mildly non-linear regime (˜10 Mpc h-1 at redshift zero), usually inaccessible to perturbation theory. From the joint PDF of densities and velocity divergences measured in two concentric spheres, we extract with the same accuracy velocity profiles and conditional velocity PDF subject to a given over/underdensity that are of interest to understand the non-linear evolution of velocity flows. Both PDFs are used to build a simple but accurate maximum likelihood estimator for the redshift evolution of the variance of both the density and velocity divergence fields, which have smaller relative errors than their sample variances when non-linearities appear. Given the dependence of the velocity divergence on the growth rate, there is a significant gain in using the full knowledge of both PDFs to derive constraints on the equation of state-of-dark energy. Thanks to the insensitivity of the velocity divergence to bias, its PDF can be used to obtain unbiased constraints on the growth of structures (σ8, f) or it can be combined with the galaxy density PDF to extract bias parameters.

Estimation of genetic parameters and their sampling variances of quantitative traits in the type 2 modified augmented design

USDA-ARS?s Scientific Manuscript database

We proposed a method to estimate the error variance among non-replicated genotypes, thus to estimate the genetic parameters by using replicated controls. We derived formulas to estimate sampling variances of the genetic parameters. Computer simulation indicated that the proposed methods of estimatin...

Pseudo second order kinetics and pseudo isotherms for malachite green onto activated carbon: comparison of linear and non-linear regression methods.

PubMed

Kumar, K Vasanth; Sivanesan, S

2006-08-25

Pseudo second order kinetic expressions of Ho, Sobkowsk and Czerwinski, Blanachard et al. and Ritchie were fitted to the experimental kinetic data of malachite green onto activated carbon by non-linear and linear method. Non-linear method was found to be a better way of obtaining the parameters involved in the second order rate kinetic expressions. Both linear and non-linear regression showed that the Sobkowsk and Czerwinski and Ritchie's pseudo second order model were the same. Non-linear regression analysis showed that both Blanachard et al. and Ho have similar ideas on the pseudo second order model but with different assumptions. The best fit of experimental data in Ho's pseudo second order expression by linear and non-linear regression method showed that Ho pseudo second order model was a better kinetic expression when compared to other pseudo second order kinetic expressions. The amount of dye adsorbed at equilibrium, q(e), was predicted from Ho pseudo second order expression and were fitted to the Langmuir, Freundlich and Redlich Peterson expressions by both linear and non-linear method to obtain the pseudo isotherms. The best fitting pseudo isotherm was found to be the Langmuir and Redlich Peterson isotherm. Redlich Peterson is a special case of Langmuir when the constant g equals unity.

Modelling hydrological extremes under non-stationary conditions using climate covariates

NASA Astrophysics Data System (ADS)

Vasiliades, Lampros; Galiatsatou, Panagiota; Loukas, Athanasios

2013-04-01

Extreme value theory is a probabilistic theory that can interpret the future probabilities of occurrence of extreme events (e.g. extreme precipitation and streamflow) using past observed records. Traditionally, extreme value theory requires the assumption of temporal stationarity. This assumption implies that the historical patterns of recurrence of extreme events are static over time. However, the hydroclimatic system is nonstationary on time scales that are relevant to extreme value analysis, due to human-mediated and natural environmental change. In this study the generalized extreme value (GEV) distribution is used to assess nonstationarity in annual maximum daily rainfall and streamflow timeseries at selected meteorological and hydrometric stations in Greece and Cyprus. The GEV distribution parameters (location, scale, and shape) are specified as functions of time-varying covariates and estimated using the conditional density network (CDN) as proposed by Cannon (2010). The CDN is a probabilistic extension of the multilayer perceptron neural network. Model parameters are estimated via the generalized maximum likelihood (GML) approach using the quasi-Newton BFGS optimization algorithm, and the appropriate GEV-CDN model architecture for the selected meteorological and hydrometric stations is selected by fitting increasingly complicated models and choosing the one that minimizes the Akaike information criterion with small sample size correction. For all case studies in Greece and Cyprus different formulations are tested with combinational cases of stationary and nonstationary parameters of the GEV distribution, linear and non-linear architecture of the CDN and combinations of the input climatic covariates. Climatic indices such as the Southern Oscillation Index (SOI), which describes atmospheric circulation in the eastern tropical pacific related to El Niño Southern Oscillation (ENSO), the Pacific Decadal Oscillation (PDO) index that varies on an interdecadal rather than interannual time scale and the atmospheric circulation patterns as expressed by the North Atlantic Oscillation (NAO) index are used to express the GEV parameters as functions of the covariates. Results show that the nonstationary GEV model can be an efficient tool to take into account the dependencies between extreme value random variables and the temporal evolution of the climate.

Sugeno-Fuzzy Expert System Modeling for Quality Prediction of Non-Contact Machining Process

NASA Astrophysics Data System (ADS)

Sivaraos; Khalim, A. Z.; Salleh, M. S.; Sivakumar, D.; Kadirgama, K.

2018-03-01

Modeling can be categorised into four main domains: prediction, optimisation, estimation and calibration. In this paper, the Takagi-Sugeno-Kang (TSK) fuzzy logic method is examined as a prediction modelling method to investigate the taper quality of laser lathing, which seeks to replace traditional lathe machines with 3D laser lathing in order to achieve the desired cylindrical shape of stock materials. Three design parameters were selected: feed rate, cutting speed and depth of cut. A total of twenty-four experiments were conducted with eight sequential runs and replicated three times. The results were found to be 99% of accuracy rate of the TSK fuzzy predictive model, which suggests that the model is a suitable and practical method for non-linear laser lathing process.

Parameter Recovery for the 1-P HGLLM with Non-Normally Distributed Level-3 Residuals

ERIC Educational Resources Information Center

Kara, Yusuf; Kamata, Akihito

2017-01-01

A multilevel Rasch model using a hierarchical generalized linear model is one approach to multilevel item response theory (IRT) modeling and is referred to as a one-parameter hierarchical generalized linear logistic model (1-P HGLLM). Although it has the flexibility to model nested structure of data with covariates, the model assumes the normality…

Genetic Algorithm Based Framework for Automation of Stochastic Modeling of Multi-Season Streamflows

NASA Astrophysics Data System (ADS)

Srivastav, R. K.; Srinivasan, K.; Sudheer, K.

2009-05-01

Synthetic streamflow data generation involves the synthesis of likely streamflow patterns that are statistically indistinguishable from the observed streamflow data. The various kinds of stochastic models adopted for multi-season streamflow generation in hydrology are: i) parametric models which hypothesize the form of the periodic dependence structure and the distributional form a priori (examples are PAR, PARMA); disaggregation models that aim to preserve the correlation structure at the periodic level and the aggregated annual level; ii) Nonparametric models (examples are bootstrap/kernel based methods), which characterize the laws of chance, describing the stream flow process, without recourse to prior assumptions as to the form or structure of these laws; (k-nearest neighbor (k-NN), matched block bootstrap (MABB)); non-parametric disaggregation model. iii) Hybrid models which blend both parametric and non-parametric models advantageously to model the streamflows effectively. Despite many of these developments that have taken place in the field of stochastic modeling of streamflows over the last four decades, accurate prediction of the storage and the critical drought characteristics has been posing a persistent challenge to the stochastic modeler. This is partly because, usually, the stochastic streamflow model parameters are estimated by minimizing a statistically based objective function (such as maximum likelihood (MLE) or least squares (LS) estimation) and subsequently the efficacy of the models is being validated based on the accuracy of prediction of the estimates of the water-use characteristics, which requires large number of trial simulations and inspection of many plots and tables. Still accurate prediction of the storage and the critical drought characteristics may not be ensured. In this study a multi-objective optimization framework is proposed to find the optimal hybrid model (blend of a simple parametric model, PAR(1) model and matched block bootstrap (MABB) ) based on the explicit objective functions of minimizing the relative bias and relative root mean square error in estimating the storage capacity of the reservoir. The optimal parameter set of the hybrid model is obtained based on the search over a multi- dimensional parameter space (involving simultaneous exploration of the parametric (PAR(1)) as well as the non-parametric (MABB) components). This is achieved using the efficient evolutionary search based optimization tool namely, non-dominated sorting genetic algorithm - II (NSGA-II). This approach helps in reducing the drudgery involved in the process of manual selection of the hybrid model, in addition to predicting the basic summary statistics dependence structure, marginal distribution and water-use characteristics accurately. The proposed optimization framework is used to model the multi-season streamflows of River Beaver and River Weber of USA. In case of both the rivers, the proposed GA-based hybrid model yields a much better prediction of the storage capacity (where simultaneous exploration of both parametric and non-parametric components is done) when compared with the MLE-based hybrid models (where the hybrid model selection is done in two stages, thus probably resulting in a sub-optimal model). This framework can be further extended to include different linear/non-linear hybrid stochastic models at other temporal and spatial scales as well.

Estimation of Gravity Parameters Related to Simple Geometrical Structures by Developing an Approach Based on Deconvolution and Linear Optimization Techniques

NASA Astrophysics Data System (ADS)

Asfahani, J.; Tlas, M.

2015-10-01

An easy and practical method for interpreting residual gravity anomalies due to simple geometrically shaped models such as cylinders and spheres has been proposed in this paper. This proposed method is based on both the deconvolution technique and the simplex algorithm for linear optimization to most effectively estimate the model parameters, e.g., the depth from the surface to the center of a buried structure (sphere or horizontal cylinder) or the depth from the surface to the top of a buried object (vertical cylinder), and the amplitude coefficient from the residual gravity anomaly profile. The method was tested on synthetic data sets corrupted by different white Gaussian random noise levels to demonstrate the capability and reliability of the method. The results acquired show that the estimated parameter values derived by this proposed method are close to the assumed true parameter values. The validity of this method is also demonstrated using real field residual gravity anomalies from Cuba and Sweden. Comparable and acceptable agreement is shown between the results derived by this method and those derived from real field data.

Models for estimation of the presence of non-regulated disinfection by-products in small drinking water systems.

PubMed

Guilherme, Stéphanie; Rodriguez, Manuel J

2017-10-23

Among all the organic disinfection by-products (DBPs), only trihalomethanes (THMs) and haloacetic acids (HAAs) are regulated in drinking water, while most DBPs are not. Very little information exists on the occurrence of non-regulated DBPs, particularly in small water systems (SWS). Paradoxically, SWS are more vulnerable to DBPs because of a low capacity to implement adequate treatment technologies to remove DBP precursors. Since DBP analyses are expensive, usually SWS have difficulties to implement a rigorous characterization of these contaminants. The purpose of this study was to estimate non-regulated DBP levels in SWS from easy measurements of relevant parameters regularly monitored. Since no information on non-regulated DBPs in SWS was available, a sampling program was carried out in 25 SWS in two provinces of Canada. Five DBP families were investigated: THMs, HAAs, haloacetonitriles (HANs), halonitromethanes (HNMs), and haloketones (HKs). Multivariate linear mixed regression models were developed to estimate HAN, HK, and HNM levels from water quality characteristics in the water treatment plant, concentrations of regulated DBPs, and residual disinfectant levels. The models obtained have a good explanatory capacity since R 2 varies from 0.77 to 0.91 according to compounds and conditions for application (season and type of treatment). Model validation with an independent database suggested their ability for generalization in similar SWS in North America.

Analyzing Multilevel Data: An Empirical Comparison of Parameter Estimates of Hierarchical Linear Modeling and Ordinary Least Squares Regression

ERIC Educational Resources Information Center

Rocconi, Louis M.

2011-01-01

Hierarchical linear models (HLM) solve the problems associated with the unit of analysis problem such as misestimated standard errors, heterogeneity of regression and aggregation bias by modeling all levels of interest simultaneously. Hierarchical linear modeling resolves the problem of misestimated standard errors by incorporating a unique random…

A class of non-linear exposure-response models suitable for health impact assessment applicable to large cohort studies of ambient air pollution.

PubMed

Nasari, Masoud M; Szyszkowicz, Mieczysław; Chen, Hong; Crouse, Daniel; Turner, Michelle C; Jerrett, Michael; Pope, C Arden; Hubbell, Bryan; Fann, Neal; Cohen, Aaron; Gapstur, Susan M; Diver, W Ryan; Stieb, David; Forouzanfar, Mohammad H; Kim, Sun-Young; Olives, Casey; Krewski, Daniel; Burnett, Richard T

2016-01-01

The effectiveness of regulatory actions designed to improve air quality is often assessed by predicting changes in public health resulting from their implementation. Risk of premature mortality from long-term exposure to ambient air pollution is the single most important contributor to such assessments and is estimated from observational studies generally assuming a log-linear, no-threshold association between ambient concentrations and death. There has been only limited assessment of this assumption in part because of a lack of methods to estimate the shape of the exposure-response function in very large study populations. In this paper, we propose a new class of variable coefficient risk functions capable of capturing a variety of potentially non-linear associations which are suitable for health impact assessment. We construct the class by defining transformations of concentration as the product of either a linear or log-linear function of concentration multiplied by a logistic weighting function. These risk functions can be estimated using hazard regression survival models with currently available computer software and can accommodate large population-based cohorts which are increasingly being used for this purpose. We illustrate our modeling approach with two large cohort studies of long-term concentrations of ambient air pollution and mortality: the American Cancer Society Cancer Prevention Study II (CPS II) cohort and the Canadian Census Health and Environment Cohort (CanCHEC). We then estimate the number of deaths attributable to changes in fine particulate matter concentrations over the 2000 to 2010 time period in both Canada and the USA using both linear and non-linear hazard function models.

System health monitoring using multiple-model adaptive estimation techniques

NASA Astrophysics Data System (ADS)

Sifford, Stanley Ryan

Monitoring system health for fault detection and diagnosis by tracking system parameters concurrently with state estimates is approached using a new multiple-model adaptive estimation (MMAE) method. This novel method is called GRid-based Adaptive Parameter Estimation (GRAPE). GRAPE expands existing MMAE methods by using new techniques to sample the parameter space. GRAPE expands on MMAE with the hypothesis that sample models can be applied and resampled without relying on a predefined set of models. GRAPE is initially implemented in a linear framework using Kalman filter models. A more generalized GRAPE formulation is presented using extended Kalman filter (EKF) models to represent nonlinear systems. GRAPE can handle both time invariant and time varying systems as it is designed to track parameter changes. Two techniques are presented to generate parameter samples for the parallel filter models. The first approach is called selected grid-based stratification (SGBS). SGBS divides the parameter space into equally spaced strata. The second approach uses Latin Hypercube Sampling (LHS) to determine the parameter locations and minimize the total number of required models. LHS is particularly useful when the parameter dimensions grow. Adding more parameters does not require the model count to increase for LHS. Each resample is independent of the prior sample set other than the location of the parameter estimate. SGBS and LHS can be used for both the initial sample and subsequent resamples. Furthermore, resamples are not required to use the same technique. Both techniques are demonstrated for both linear and nonlinear frameworks. The GRAPE framework further formalizes the parameter tracking process through a general approach for nonlinear systems. These additional methods allow GRAPE to either narrow the focus to converged values within a parameter range or expand the range in the appropriate direction to track the parameters outside the current parameter range boundary. Customizable rules define the specific resample behavior when the GRAPE parameter estimates converge. Convergence itself is determined from the derivatives of the parameter estimates using a simple moving average window to filter out noise. The system can be tuned to match the desired performance goals by making adjustments to parameters such as the sample size, convergence criteria, resample criteria, initial sampling method, resampling method, confidence in prior sample covariances, sample delay, and others.

Genetic parameters for direct and maternal calving ease in Walloon dairy cattle based on linear and threshold models.

PubMed

Vanderick, S; Troch, T; Gillon, A; Glorieux, G; Gengler, N

2014-12-01

Calving ease scores from Holstein dairy cattle in the Walloon Region of Belgium were analysed using univariate linear and threshold animal models. Variance components and derived genetic parameters were estimated from a data set including 33,155 calving records. Included in the models were season, herd and sex of calf × age of dam classes × group of calvings interaction as fixed effects, herd × year of calving, maternal permanent environment and animal direct and maternal additive genetic as random effects. Models were fitted with the genetic correlation between direct and maternal additive genetic effects either estimated or constrained to zero. Direct heritability for calving ease was approximately 8% with linear models and approximately 12% with threshold models. Maternal heritabilities were approximately 2 and 4%, respectively. Genetic correlation between direct and maternal additive effects was found to be not significantly different from zero. Models were compared in terms of goodness of fit and predictive ability. Criteria of comparison such as mean squared error, correlation between observed and predicted calving ease scores as well as between estimated breeding values were estimated from 85,118 calving records. The results provided few differences between linear and threshold models even though correlations between estimated breeding values from subsets of data for sires with progeny from linear model were 17 and 23% greater for direct and maternal genetic effects, respectively, than from threshold model. For the purpose of genetic evaluation for calving ease in Walloon Holstein dairy cattle, the linear animal model without covariance between direct and maternal additive effects was found to be the best choice. © 2014 Blackwell Verlag GmbH.

Population Dynamics and Temperature-Dependent Development of Chrysomphalus aonidum (L.) to Aid Sustainable Pest Management Decisions.

PubMed

Campolo, O; Malacrinò, A; Laudani, F; Maione, V; Zappalà, L; Palmeri, V

2014-10-01

The increasing worldwide trades progressively led to decreased impact of natural barriers on wild species movement. The exotic scale Chrysomphalus aonidum (L.) (Hemiptera: Diaspididae), recently reported on citrus in southern Italy, may represent a new threat to Mediterranean citriculture. We studied C. aonidum population dynamics under field conditions and documented its development under various temperatures. To enable describing temperature-dependent development through the use of linear and non-linear models, low temperature thresholds and thermal constants for each developmental stage were estimated. Chrysomphalus aonidum was able to perform four generations on green parts (leaves, sprouts) of citrus trees and three on fruits. In addition, an overall higher population density was observed on samples collected in the southern part of the tree canopy. Temperature had a significant effect on the developmental rate; female needed 625 degree days (DD) to complete its development, while male needed 833 DD. The low threshold temperatures, together with data from population dynamics, demonstrated that C. aonidum is able to overwinter as second instar and as an adult. The results obtained, validated by those collected in the field, revealed few differences between predicted and observed dates of first occurrence of each C. aonidum instar in citrus orchards. Data on C. aonidum phenology and the definition of the thermal parameters (lower and upper threshold temperatures, optimum temperature, and the thermal constant) by non-linear models could allow the estimation of the occurrence in the field of each life stage and would be helpful in developing effective integrated control strategies.

An Index and Test of Linear Moderated Mediation.

PubMed

Hayes, Andrew F

2015-01-01

I describe a test of linear moderated mediation in path analysis based on an interval estimate of the parameter of a function linking the indirect effect to values of a moderator-a parameter that I call the index of moderated mediation. This test can be used for models that integrate moderation and mediation in which the relationship between the indirect effect and the moderator is estimated as linear, including many of the models described by Edwards and Lambert ( 2007 ) and Preacher, Rucker, and Hayes ( 2007 ) as well as extensions of these models to processes involving multiple mediators operating in parallel or in serial. Generalization of the method to latent variable models is straightforward. Three empirical examples describe the computation of the index and the test, and its implementation is illustrated using Mplus and the PROCESS macro for SPSS and SAS.