Stable Lévy motion with inverse Gaussian subordinator

NASA Astrophysics Data System (ADS)

Kumar, A.; Wyłomańska, A.; Gajda, J.

2017-09-01

In this paper we study the stable Lévy motion subordinated by the so-called inverse Gaussian process. This process extends the well known normal inverse Gaussian (NIG) process introduced by Barndorff-Nielsen, which arises by subordinating ordinary Brownian motion (with drift) with inverse Gaussian process. The NIG process found many interesting applications, especially in financial data description. We discuss here the main features of the introduced subordinated process, such as distributional properties, existence of fractional order moments and asymptotic tail behavior. We show the connection of the process with continuous time random walk. Further, the governing fractional partial differential equations for the probability density function is also obtained. Moreover, we discuss the asymptotic distribution of sample mean square displacement, the main tool in detection of anomalous diffusion phenomena (Metzler et al., 2014). In order to apply the stable Lévy motion time-changed by inverse Gaussian subordinator we propose a step-by-step procedure of parameters estimation. At the end, we show how the examined process can be useful to model financial time series.

Gaussian mixture models as flux prediction method for central receivers

NASA Astrophysics Data System (ADS)

Grobler, Annemarie; Gauché, Paul; Smit, Willie

2016-05-01

Flux prediction methods are crucial to the design and operation of central receiver systems. Current methods such as the circular and elliptical (bivariate) Gaussian prediction methods are often used in field layout design and aiming strategies. For experimental or small central receiver systems, the flux profile of a single heliostat often deviates significantly from the circular and elliptical Gaussian models. Therefore a novel method of flux prediction was developed by incorporating the fitting of Gaussian mixture models onto flux profiles produced by flux measurement or ray tracing. A method was also developed to predict the Gaussian mixture model parameters of a single heliostat for a given time using image processing. Recording the predicted parameters in a database ensures that more accurate predictions are made in a shorter time frame.

Kinect Posture Reconstruction Based on a Local Mixture of Gaussian Process Models.

PubMed

Liu, Zhiguang; Zhou, Liuyang; Leung, Howard; Shum, Hubert P H

2016-11-01

Depth sensor based 3D human motion estimation hardware such as Kinect has made interactive applications more popular recently. However, it is still challenging to accurately recognize postures from a single depth camera due to the inherently noisy data derived from depth images and self-occluding action performed by the user. In this paper, we propose a new real-time probabilistic framework to enhance the accuracy of live captured postures that belong to one of the action classes in the database. We adopt the Gaussian Process model as a prior to leverage the position data obtained from Kinect and marker-based motion capture system. We also incorporate a temporal consistency term into the optimization framework to constrain the velocity variations between successive frames. To ensure that the reconstructed posture resembles the accurate parts of the observed posture, we embed a set of joint reliability measurements into the optimization framework. A major drawback of Gaussian Process is its cubic learning complexity when dealing with a large database due to the inverse of a covariance matrix. To solve the problem, we propose a new method based on a local mixture of Gaussian Processes, in which Gaussian Processes are defined in local regions of the state space. Due to the significantly decreased sample size in each local Gaussian Process, the learning time is greatly reduced. At the same time, the prediction speed is enhanced as the weighted mean prediction for a given sample is determined by the nearby local models only. Our system also allows incrementally updating a specific local Gaussian Process in real time, which enhances the likelihood of adapting to run-time postures that are different from those in the database. Experimental results demonstrate that our system can generate high quality postures even under severe self-occlusion situations, which is beneficial for real-time applications such as motion-based gaming and sport training.

Semisupervised Gaussian Process for Automated Enzyme Search.

PubMed

Mellor, Joseph; Grigoras, Ioana; Carbonell, Pablo; Faulon, Jean-Loup

2016-06-17

Synthetic biology is today harnessing the design of novel and greener biosynthesis routes for the production of added-value chemicals and natural products. The design of novel pathways often requires a detailed selection of enzyme sequences to import into the chassis at each of the reaction steps. To address such design requirements in an automated way, we present here a tool for exploring the space of enzymatic reactions. Given a reaction and an enzyme the tool provides a probability estimate that the enzyme catalyzes the reaction. Our tool first considers the similarity of a reaction to known biochemical reactions with respect to signatures around their reaction centers. Signatures are defined based on chemical transformation rules by using extended connectivity fingerprint descriptors. A semisupervised Gaussian process model associated with the similar known reactions then provides the probability estimate. The Gaussian process model uses information about both the reaction and the enzyme in providing the estimate. These estimates were validated experimentally by the application of the Gaussian process model to a newly identified metabolite in Escherichia coli in order to search for the enzymes catalyzing its associated reactions. Furthermore, we show with several pathway design examples how such ability to assign probability estimates to enzymatic reactions provides the potential to assist in bioengineering applications, providing experimental validation to our proposed approach. To the best of our knowledge, the proposed approach is the first application of Gaussian processes dealing with biological sequences and chemicals, the use of a semisupervised Gaussian process framework is also novel in the context of machine learning applied to bioinformatics. However, the ability of an enzyme to catalyze a reaction depends on the affinity between the substrates of the reaction and the enzyme. This affinity is generally quantified by the Michaelis constant KM. Therefore, we also demonstrate using Gaussian process regression to predict KM given a substrate-enzyme pair.

Random Process Simulation for stochastic fatigue analysis. Ph.D. Thesis - Rice Univ., Houston, Tex.

NASA Technical Reports Server (NTRS)

Larsen, Curtis E.

1988-01-01

A simulation technique is described which directly synthesizes the extrema of a random process and is more efficient than the Gaussian simulation method. Such a technique is particularly useful in stochastic fatigue analysis because the required stress range moment E(R sup m), is a function only of the extrema of the random stress process. The family of autoregressive moving average (ARMA) models is reviewed and an autoregressive model is presented for modeling the extrema of any random process which has a unimodal power spectral density (psd). The proposed autoregressive technique is found to produce rainflow stress range moments which compare favorably with those computed by the Gaussian technique and to average 11.7 times faster than the Gaussian technique. The autoregressive technique is also adapted for processes having bimodal psd's. The adaptation involves using two autoregressive processes to simulate the extrema due to each mode and the superposition of these two extrema sequences. The proposed autoregressive superposition technique is 9 to 13 times faster than the Gaussian technique and produces comparable values for E(R sup m) for bimodal psd's having the frequency of one mode at least 2.5 times that of the other mode.

Flexible link functions in nonparametric binary regression with Gaussian process priors.

PubMed

Li, Dan; Wang, Xia; Lin, Lizhen; Dey, Dipak K

2016-09-01

In many scientific fields, it is a common practice to collect a sequence of 0-1 binary responses from a subject across time, space, or a collection of covariates. Researchers are interested in finding out how the expected binary outcome is related to covariates, and aim at better prediction in the future 0-1 outcomes. Gaussian processes have been widely used to model nonlinear systems; in particular to model the latent structure in a binary regression model allowing nonlinear functional relationship between covariates and the expectation of binary outcomes. A critical issue in modeling binary response data is the appropriate choice of link functions. Commonly adopted link functions such as probit or logit links have fixed skewness and lack the flexibility to allow the data to determine the degree of the skewness. To address this limitation, we propose a flexible binary regression model which combines a generalized extreme value link function with a Gaussian process prior on the latent structure. Bayesian computation is employed in model estimation. Posterior consistency of the resulting posterior distribution is demonstrated. The flexibility and gains of the proposed model are illustrated through detailed simulation studies and two real data examples. Empirical results show that the proposed model outperforms a set of alternative models, which only have either a Gaussian process prior on the latent regression function or a Dirichlet prior on the link function. © 2015, The International Biometric Society.

Flexible Link Functions in Nonparametric Binary Regression with Gaussian Process Priors

PubMed Central

Li, Dan; Lin, Lizhen; Dey, Dipak K.

2015-01-01

Summary In many scientific fields, it is a common practice to collect a sequence of 0-1 binary responses from a subject across time, space, or a collection of covariates. Researchers are interested in finding out how the expected binary outcome is related to covariates, and aim at better prediction in the future 0-1 outcomes. Gaussian processes have been widely used to model nonlinear systems; in particular to model the latent structure in a binary regression model allowing nonlinear functional relationship between covariates and the expectation of binary outcomes. A critical issue in modeling binary response data is the appropriate choice of link functions. Commonly adopted link functions such as probit or logit links have fixed skewness and lack the flexibility to allow the data to determine the degree of the skewness. To address this limitation, we propose a flexible binary regression model which combines a generalized extreme value link function with a Gaussian process prior on the latent structure. Bayesian computation is employed in model estimation. Posterior consistency of the resulting posterior distribution is demonstrated. The flexibility and gains of the proposed model are illustrated through detailed simulation studies and two real data examples. Empirical results show that the proposed model outperforms a set of alternative models, which only have either a Gaussian process prior on the latent regression function or a Dirichlet prior on the link function. PMID:26686333

Bayesian Computation for Log-Gaussian Cox Processes: A Comparative Analysis of Methods

PubMed Central

Teng, Ming; Nathoo, Farouk S.; Johnson, Timothy D.

2017-01-01

The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point pattern data. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the first level and a Gaussian Process at the second level. Various methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulation studies as well as through two applications, the first examining ecological data and the second involving neuroimaging data. PMID:29200537

PERIOD ESTIMATION FOR SPARSELY SAMPLED QUASI-PERIODIC LIGHT CURVES APPLIED TO MIRAS

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

He, Shiyuan; Huang, Jianhua Z.; Long, James

2016-12-01

We develop a nonlinear semi-parametric Gaussian process model to estimate periods of Miras with sparsely sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum likelihood to estimate the period and the parameters of the Gaussian process, while integrating out the effects of other nuisance parameters in the model with respect to a suitable prior distribution obtained from earlier studies. Since the likelihood is highly multimodal for period, we implement a hybrid method that applies the quasi-Newton algorithm for Gaussian process parameters and search the period/frequencymore » parameter space over a dense grid. A large-scale, high-fidelity simulation is conducted to mimic the sampling quality of Mira light curves obtained by the M33 Synoptic Stellar Survey. The simulated data set is publicly available and can serve as a testbed for future evaluation of different period estimation methods. The semi-parametric model outperforms an existing algorithm on this simulated test data set as measured by period recovery rate and quality of the resulting period–luminosity relations.« less

'A device for being able to book P&L': the organizational embedding of the Gaussian copula.

PubMed

MacKenzie, Donald; Spears, Taylor

2014-06-01

This article, the second of two articles on the Gaussian copula family of models, discusses the attitude of 'quants' (modellers) to these models, showing that contrary to some accounts, those quants were not 'model dopes' who uncritically accepted the outputs of the models. Although sometimes highly critical of Gaussian copulas - even 'othering' them as not really being models --they nevertheless nearly all kept using them, an outcome we explain with reference to the embedding of these models in inter- and intra-organizational processes: communication, risk control and especially the setting of bonuses. The article also examines the role of Gaussian copula models in the 2007-2008 global crisis and in a 2005 episode known as 'the correlation crisis'. We end with the speculation that all widely used derivatives models (and indeed the evaluation culture in which they are embedded) help generate inter-organizational co-ordination, and all that is special in this respect about the Gaussian copula is that its status as 'other' makes this role evident.

Gaussian Process Interpolation for Uncertainty Estimation in Image Registration

PubMed Central

Wachinger, Christian; Golland, Polina; Reuter, Martin; Wells, William

2014-01-01

Intensity-based image registration requires resampling images on a common grid to evaluate the similarity function. The uncertainty of interpolation varies across the image, depending on the location of resampled points relative to the base grid. We propose to perform Bayesian inference with Gaussian processes, where the covariance matrix of the Gaussian process posterior distribution estimates the uncertainty in interpolation. The Gaussian process replaces a single image with a distribution over images that we integrate into a generative model for registration. Marginalization over resampled images leads to a new similarity measure that includes the uncertainty of the interpolation. We demonstrate that our approach increases the registration accuracy and propose an efficient approximation scheme that enables seamless integration with existing registration methods. PMID:25333127

Robust radio interferometric calibration using the t-distribution

NASA Astrophysics Data System (ADS)

Kazemi, S.; Yatawatta, S.

2013-10-01

A major stage of radio interferometric data processing is calibration or the estimation of systematic errors in the data and the correction for such errors. A stochastic error (noise) model is assumed, and in most cases, this underlying model is assumed to be Gaussian. However, outliers in the data due to interference or due to errors in the sky model would have adverse effects on processing based on a Gaussian noise model. Most of the shortcomings of calibration such as the loss in flux or coherence, and the appearance of spurious sources, could be attributed to the deviations of the underlying noise model. In this paper, we propose to improve the robustness of calibration by using a noise model based on Student's t-distribution. Student's t-noise is a special case of Gaussian noise when the variance is unknown. Unlike Gaussian-noise-model-based calibration, traditional least-squares minimization would not directly extend to a case when we have a Student's t-noise model. Therefore, we use a variant of the expectation-maximization algorithm, called the expectation-conditional maximization either algorithm, when we have a Student's t-noise model and use the Levenberg-Marquardt algorithm in the maximization step. We give simulation results to show the robustness of the proposed calibration method as opposed to traditional Gaussian-noise-model-based calibration, especially in preserving the flux of weaker sources that are not included in the calibration model.

Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets.

PubMed

Datta, Abhirup; Banerjee, Sudipto; Finley, Andrew O; Gelfand, Alan E

2016-01-01

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive U.S. Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods. Supplementary materials for this article are available online.

Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets

PubMed Central

Datta, Abhirup; Banerjee, Sudipto; Finley, Andrew O.; Gelfand, Alan E.

2018-01-01

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive U.S. Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods. Supplementary materials for this article are available online. PMID:29720777

Simulation of the usage of Gaussian mixture models for the purpose of modelling virtual mass spectrometry data.

PubMed

Plechawska, Małgorzata; Polańska, Joanna

2009-01-01

This article presents the method of the processing of mass spectrometry data. Mass spectra are modelled with Gaussian Mixture Models. Every peak of the spectrum is represented by a single Gaussian. Its parameters describe the location, height and width of the corresponding peak of the spectrum. An authorial version of the Expectation Maximisation Algorithm was used to perform all calculations. Errors were estimated with a virtual mass spectrometer. The discussed tool was originally designed to generate a set of spectra within defined parameters.

Gaussian temporal modulation for the behavior of multi-sinc Schell-model pulses in dispersive media

NASA Astrophysics Data System (ADS)

Liu, Xiayin; Zhao, Daomu; Tian, Kehan; Pan, Weiqing; Zhang, Kouwen

2018-06-01

A new class of pulse source with correlation being modeled by the convolution operation of two legitimate temporal correlation function is proposed. Particularly, analytical formulas for the Gaussian temporally modulated multi-sinc Schell-model (MSSM) pulses generated by such pulse source propagating in dispersive media are derived. It is demonstrated that the average intensity of MSSM pulses on propagation are reshaped from flat profile or a train to a distribution with a Gaussian temporal envelope by adjusting the initial correlation width of the Gaussian pulse. The effects of the Gaussian temporal modulation on the temporal degree of coherence of the MSSM pulse are also analyzed. The results presented here show the potential of coherence modulation for pulse shaping and pulsed laser material processing.

Revisiting non-Gaussianity from non-attractor inflation models

NASA Astrophysics Data System (ADS)

Cai, Yi-Fu; Chen, Xingang; Namjoo, Mohammad Hossein; Sasaki, Misao; Wang, Dong-Gang; Wang, Ziwei

2018-05-01

Non-attractor inflation is known as the only single field inflationary scenario that can violate non-Gaussianity consistency relation with the Bunch-Davies vacuum state and generate large local non-Gaussianity. However, it is also known that the non-attractor inflation by itself is incomplete and should be followed by a phase of slow-roll attractor. Moreover, there is a transition process between these two phases. In the past literature, this transition was approximated as instant and the evolution of non-Gaussianity in this phase was not fully studied. In this paper, we follow the detailed evolution of the non-Gaussianity through the transition phase into the slow-roll attractor phase, considering different types of transition. We find that the transition process has important effect on the size of the local non-Gaussianity. We first compute the net contribution of the non-Gaussianities at the end of inflation in canonical non-attractor models. If the curvature perturbations keep evolving during the transition—such as in the case of smooth transition or some sharp transition scenarios—the Script O(1) local non-Gaussianity generated in the non-attractor phase can be completely erased by the subsequent evolution, although the consistency relation remains violated. In extremal cases of sharp transition where the super-horizon modes freeze immediately right after the end of the non-attractor phase, the original non-attractor result can be recovered. We also study models with non-canonical kinetic terms, and find that the transition can typically contribute a suppression factor in the squeezed bispectrum, but the final local non-Gaussianity can still be made parametrically large.

Mixed-effects Gaussian process functional regression models with application to dose-response curve prediction.

PubMed

Shi, J Q; Wang, B; Will, E J; West, R M

2012-11-20

We propose a new semiparametric model for functional regression analysis, combining a parametric mixed-effects model with a nonparametric Gaussian process regression model, namely a mixed-effects Gaussian process functional regression model. The parametric component can provide explanatory information between the response and the covariates, whereas the nonparametric component can add nonlinearity. We can model the mean and covariance structures simultaneously, combining the information borrowed from other subjects with the information collected from each individual subject. We apply the model to dose-response curves that describe changes in the responses of subjects for differing levels of the dose of a drug or agent and have a wide application in many areas. We illustrate the method for the management of renal anaemia. An individual dose-response curve is improved when more information is included by this mechanism from the subject/patient over time, enabling a patient-specific treatment regime. Copyright © 2012 John Wiley & Sons, Ltd.

Remaining Useful Life Prediction for Lithium-Ion Batteries Based on Gaussian Processes Mixture

PubMed Central

Li, Lingling; Wang, Pengchong; Chao, Kuei-Hsiang; Zhou, Yatong; Xie, Yang

2016-01-01

The remaining useful life (RUL) prediction of Lithium-ion batteries is closely related to the capacity degeneration trajectories. Due to the self-charging and the capacity regeneration, the trajectories have the property of multimodality. Traditional prediction models such as the support vector machines (SVM) or the Gaussian Process regression (GPR) cannot accurately characterize this multimodality. This paper proposes a novel RUL prediction method based on the Gaussian Process Mixture (GPM). It can process multimodality by fitting different segments of trajectories with different GPR models separately, such that the tiny differences among these segments can be revealed. The method is demonstrated to be effective for prediction by the excellent predictive result of the experiments on the two commercial and chargeable Type 1850 Lithium-ion batteries, provided by NASA. The performance comparison among the models illustrates that the GPM is more accurate than the SVM and the GPR. In addition, GPM can yield the predictive confidence interval, which makes the prediction more reliable than that of traditional models. PMID:27632176

Bayesian Analysis of Non-Gaussian Long-Range Dependent Processes

NASA Astrophysics Data System (ADS)

Graves, Timothy; Watkins, Nicholas; Franzke, Christian; Gramacy, Robert

2013-04-01

Recent studies [e.g. the Antarctic study of Franzke, J. Climate, 2010] have strongly suggested that surface temperatures exhibit long-range dependence (LRD). The presence of LRD would hamper the identification of deterministic trends and the quantification of their significance. It is well established that LRD processes exhibit stochastic trends over rather long periods of time. Thus, accurate methods for discriminating between physical processes that possess long memory and those that do not are an important adjunct to climate modeling. As we briefly review, the LRD idea originated at the same time as H-selfsimilarity, so it is often not realised that a model does not have to be H-self similar to show LRD [e.g. Watkins, GRL Frontiers, 2013]. We have used Markov Chain Monte Carlo algorithms to perform a Bayesian analysis of Auto-Regressive Fractionally-Integrated Moving-Average ARFIMA(p,d,q) processes, which are capable of modeling LRD. Our principal aim is to obtain inference about the long memory parameter, d, with secondary interest in the scale and location parameters. We have developed a reversible-jump method enabling us to integrate over different model forms for the short memory component. We initially assume Gaussianity, and have tested the method on both synthetic and physical time series. Many physical processes, for example the Faraday Antarctic time series, are significantly non-Gaussian. We have therefore extended this work by weakening the Gaussianity assumption, assuming an alpha-stable distribution for the innovations, and performing joint inference on d and alpha. Such a modified FARIMA(p,d,q) process is a flexible, initial model for non-Gaussian processes with long memory. We will present a study of the dependence of the posterior variance of the memory parameter d on the length of the time series considered. This will be compared with equivalent error diagnostics for other measures of d.

Multi-pose facial correction based on Gaussian process with combined kernel function

NASA Astrophysics Data System (ADS)

Shi, Shuyan; Ji, Ruirui; Zhang, Fan

2018-04-01

In order to improve the recognition rate of various postures, this paper proposes a method of facial correction based on Gaussian Process which build a nonlinear regression model between the front and the side face with combined kernel function. The face images with horizontal angle from -45° to +45° can be properly corrected to front faces. Finally, Support Vector Machine is employed for face recognition. Experiments on CAS PEAL R1 face database show that Gaussian process can weaken the influence of pose changes and improve the accuracy of face recognition to certain extent.

Improved Gaussian Beam-Scattering Algorithm

NASA Technical Reports Server (NTRS)

Lock, James A.

1995-01-01

The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.

Separation of components from a scale mixture of Gaussian white noises

NASA Astrophysics Data System (ADS)

Vamoş, Călin; Crăciun, Maria

2010-05-01

The time evolution of a physical quantity associated with a thermodynamic system whose equilibrium fluctuations are modulated in amplitude by a slowly varying phenomenon can be modeled as the product of a Gaussian white noise {Zt} and a stochastic process with strictly positive values {Vt} referred to as volatility. The probability density function (pdf) of the process Xt=VtZt is a scale mixture of Gaussian white noises expressed as a time average of Gaussian distributions weighted by the pdf of the volatility. The separation of the two components of {Xt} can be achieved by imposing the condition that the absolute values of the estimated white noise be uncorrelated. We apply this method to the time series of the returns of the daily S&P500 index, which has also been analyzed by means of the superstatistics method that imposes the condition that the estimated white noise be Gaussian. The advantage of our method is that this financial time series is processed without partitioning or removal of the extreme events and the estimated white noise becomes almost Gaussian only as result of the uncorrelation condition.

Revisiting Gaussian Process Regression Modeling for Localization in Wireless Sensor Networks

PubMed Central

Richter, Philipp; Toledano-Ayala, Manuel

2015-01-01

Signal strength-based positioning in wireless sensor networks is a key technology for seamless, ubiquitous localization, especially in areas where Global Navigation Satellite System (GNSS) signals propagate poorly. To enable wireless local area network (WLAN) location fingerprinting in larger areas while maintaining accuracy, methods to reduce the effort of radio map creation must be consolidated and automatized. Gaussian process regression has been applied to overcome this issue, also with auspicious results, but the fit of the model was never thoroughly assessed. Instead, most studies trained a readily available model, relying on the zero mean and squared exponential covariance function, without further scrutinization. This paper studies the Gaussian process regression model selection for WLAN fingerprinting in indoor and outdoor environments. We train several models for indoor/outdoor- and combined areas; we evaluate them quantitatively and compare them by means of adequate model measures, hence assessing the fit of these models directly. To illuminate the quality of the model fit, the residuals of the proposed model are investigated, as well. Comparative experiments on the positioning performance verify and conclude the model selection. In this way, we show that the standard model is not the most appropriate, discuss alternatives and present our best candidate. PMID:26370996

Computationally efficient algorithm for Gaussian Process regression in case of structured samples

NASA Astrophysics Data System (ADS)

Belyaev, M.; Burnaev, E.; Kapushev, Y.

2016-04-01

Surrogate modeling is widely used in many engineering problems. Data sets often have Cartesian product structure (for instance factorial design of experiments with missing points). In such case the size of the data set can be very large. Therefore, one of the most popular algorithms for approximation-Gaussian Process regression-can be hardly applied due to its computational complexity. In this paper a computationally efficient approach for constructing Gaussian Process regression in case of data sets with Cartesian product structure is presented. Efficiency is achieved by using a special structure of the data set and operations with tensors. Proposed algorithm has low computational as well as memory complexity compared to existing algorithms. In this work we also introduce a regularization procedure allowing to take into account anisotropy of the data set and avoid degeneracy of regression model.

Predicting Error Bars for QSAR Models

NASA Astrophysics Data System (ADS)

Schroeter, Timon; Schwaighofer, Anton; Mika, Sebastian; Ter Laak, Antonius; Suelzle, Detlev; Ganzer, Ursula; Heinrich, Nikolaus; Müller, Klaus-Robert

2007-09-01

Unfavorable physicochemical properties often cause drug failures. It is therefore important to take lipophilicity and water solubility into account early on in lead discovery. This study presents log D7 models built using Gaussian Process regression, Support Vector Machines, decision trees and ridge regression algorithms based on 14556 drug discovery compounds of Bayer Schering Pharma. A blind test was conducted using 7013 new measurements from the last months. We also present independent evaluations using public data. Apart from accuracy, we discuss the quality of error bars that can be computed by Gaussian Process models, and ensemble and distance based techniques for the other modelling approaches.

Bayesian non-parametric inference for stochastic epidemic models using Gaussian Processes.

PubMed

Xu, Xiaoguang; Kypraios, Theodore; O'Neill, Philip D

2016-10-01

This paper considers novel Bayesian non-parametric methods for stochastic epidemic models. Many standard modeling and data analysis methods use underlying assumptions (e.g. concerning the rate at which new cases of disease will occur) which are rarely challenged or tested in practice. To relax these assumptions, we develop a Bayesian non-parametric approach using Gaussian Processes, specifically to estimate the infection process. The methods are illustrated with both simulated and real data sets, the former illustrating that the methods can recover the true infection process quite well in practice, and the latter illustrating that the methods can be successfully applied in different settings. © The Author 2016. Published by Oxford University Press.

A fast elitism Gaussian estimation of distribution algorithm and application for PID optimization.

PubMed

Xu, Qingyang; Zhang, Chengjin; Zhang, Li

2014-01-01

Estimation of distribution algorithm (EDA) is an intelligent optimization algorithm based on the probability statistics theory. A fast elitism Gaussian estimation of distribution algorithm (FEGEDA) is proposed in this paper. The Gaussian probability model is used to model the solution distribution. The parameters of Gaussian come from the statistical information of the best individuals by fast learning rule. A fast learning rule is used to enhance the efficiency of the algorithm, and an elitism strategy is used to maintain the convergent performance. The performances of the algorithm are examined based upon several benchmarks. In the simulations, a one-dimensional benchmark is used to visualize the optimization process and probability model learning process during the evolution, and several two-dimensional and higher dimensional benchmarks are used to testify the performance of FEGEDA. The experimental results indicate the capability of FEGEDA, especially in the higher dimensional problems, and the FEGEDA exhibits a better performance than some other algorithms and EDAs. Finally, FEGEDA is used in PID controller optimization of PMSM and compared with the classical-PID and GA.

A Fast Elitism Gaussian Estimation of Distribution Algorithm and Application for PID Optimization

PubMed Central

Xu, Qingyang; Zhang, Chengjin; Zhang, Li

2014-01-01

Estimation of distribution algorithm (EDA) is an intelligent optimization algorithm based on the probability statistics theory. A fast elitism Gaussian estimation of distribution algorithm (FEGEDA) is proposed in this paper. The Gaussian probability model is used to model the solution distribution. The parameters of Gaussian come from the statistical information of the best individuals by fast learning rule. A fast learning rule is used to enhance the efficiency of the algorithm, and an elitism strategy is used to maintain the convergent performance. The performances of the algorithm are examined based upon several benchmarks. In the simulations, a one-dimensional benchmark is used to visualize the optimization process and probability model learning process during the evolution, and several two-dimensional and higher dimensional benchmarks are used to testify the performance of FEGEDA. The experimental results indicate the capability of FEGEDA, especially in the higher dimensional problems, and the FEGEDA exhibits a better performance than some other algorithms and EDAs. Finally, FEGEDA is used in PID controller optimization of PMSM and compared with the classical-PID and GA. PMID:24892059

A Gaussian Processes Technique for Short-term Load Forecasting with Considerations of Uncertainty

NASA Astrophysics Data System (ADS)

Ohmi, Masataro; Mori, Hiroyuki

In this paper, an efficient method is proposed to deal with short-term load forecasting with the Gaussian Processes. Short-term load forecasting plays a key role to smooth power system operation such as economic load dispatching, unit commitment, etc. Recently, the deregulated and competitive power market increases the degree of uncertainty. As a result, it is more important to obtain better prediction results to save the cost. One of the most important aspects is that power system operator needs the upper and lower bounds of the predicted load to deal with the uncertainty while they require more accurate predicted values. The proposed method is based on the Bayes model in which output is expressed in a distribution rather than a point. To realize the model efficiently, this paper proposes the Gaussian Processes that consists of the Bayes linear model and kernel machine to obtain the distribution of the predicted value. The proposed method is successively applied to real data of daily maximum load forecasting.

Neural pulse frequency modulation of an exponentially correlated Gaussian process

NASA Technical Reports Server (NTRS)

Hutchinson, C. E.; Chon, Y.-T.

1976-01-01

The effect of NPFM (Neural Pulse Frequency Modulation) on a stationary Gaussian input, namely an exponentially correlated Gaussian input, is investigated with special emphasis on the determination of the average number of pulses in unit time, known also as the average frequency of pulse occurrence. For some classes of stationary input processes where the formulation of the appropriate multidimensional Markov diffusion model of the input-plus-NPFM system is possible, the average impulse frequency may be obtained by a generalization of the approach adopted. The results are approximate and numerical, but are in close agreement with Monte Carlo computer simulation results.

Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising.

PubMed

Zhang, Kai; Zuo, Wangmeng; Chen, Yunjin; Meng, Deyu; Zhang, Lei

2017-07-01

The discriminative model learning for image denoising has been recently attracting considerable attentions due to its favorable denoising performance. In this paper, we take one step forward by investigating the construction of feed-forward denoising convolutional neural networks (DnCNNs) to embrace the progress in very deep architecture, learning algorithm, and regularization method into image denoising. Specifically, residual learning and batch normalization are utilized to speed up the training process as well as boost the denoising performance. Different from the existing discriminative denoising models which usually train a specific model for additive white Gaussian noise at a certain noise level, our DnCNN model is able to handle Gaussian denoising with unknown noise level (i.e., blind Gaussian denoising). With the residual learning strategy, DnCNN implicitly removes the latent clean image in the hidden layers. This property motivates us to train a single DnCNN model to tackle with several general image denoising tasks, such as Gaussian denoising, single image super-resolution, and JPEG image deblocking. Our extensive experiments demonstrate that our DnCNN model can not only exhibit high effectiveness in several general image denoising tasks, but also be efficiently implemented by benefiting from GPU computing.

Soft Mixer Assignment in a Hierarchical Generative Model of Natural Scene Statistics

PubMed Central

Schwartz, Odelia; Sejnowski, Terrence J.; Dayan, Peter

2010-01-01

Gaussian scale mixture models offer a top-down description of signal generation that captures key bottom-up statistical characteristics of filter responses to images. However, the pattern of dependence among the filters for this class of models is prespecified. We propose a novel extension to the gaussian scale mixture model that learns the pattern of dependence from observed inputs and thereby induces a hierarchical representation of these inputs. Specifically, we propose that inputs are generated by gaussian variables (modeling local filter structure), multiplied by a mixer variable that is assigned probabilistically to each input from a set of possible mixers. We demonstrate inference of both components of the generative model, for synthesized data and for different classes of natural images, such as a generic ensemble and faces. For natural images, the mixer variable assignments show invariances resembling those of complex cells in visual cortex; the statistics of the gaussian components of the model are in accord with the outputs of divisive normalization models. We also show how our model helps interrelate a wide range of models of image statistics and cortical processing. PMID:16999575

Gaussian Process Regression Model in Spatial Logistic Regression

NASA Astrophysics Data System (ADS)

Sofro, A.; Oktaviarina, A.

2018-01-01

Spatial analysis has developed very quickly in the last decade. One of the favorite approaches is based on the neighbourhood of the region. Unfortunately, there are some limitations such as difficulty in prediction. Therefore, we offer Gaussian process regression (GPR) to accommodate the issue. In this paper, we will focus on spatial modeling with GPR for binomial data with logit link function. The performance of the model will be investigated. We will discuss the inference of how to estimate the parameters and hyper-parameters and to predict as well. Furthermore, simulation studies will be explained in the last section.

Predicting Error Bars for QSAR Models

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

Schroeter, Timon; Technische Universitaet Berlin, Department of Computer Science, Franklinstrasse 28/29, 10587 Berlin; Schwaighofer, Anton

2007-09-18

Unfavorable physicochemical properties often cause drug failures. It is therefore important to take lipophilicity and water solubility into account early on in lead discovery. This study presents log D{sub 7} models built using Gaussian Process regression, Support Vector Machines, decision trees and ridge regression algorithms based on 14556 drug discovery compounds of Bayer Schering Pharma. A blind test was conducted using 7013 new measurements from the last months. We also present independent evaluations using public data. Apart from accuracy, we discuss the quality of error bars that can be computed by Gaussian Process models, and ensemble and distance based techniquesmore » for the other modelling approaches.« less

On the Bayesian Treed Multivariate Gaussian Process with Linear Model of Coregionalization

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

Konomi, Bledar A.; Karagiannis, Georgios; Lin, Guang

2015-02-01

The Bayesian treed Gaussian process (BTGP) has gained popularity in recent years because it provides a straightforward mechanism for modeling non-stationary data and can alleviate computational demands by fitting models to less data. The extension of BTGP to the multivariate setting requires us to model the cross-covariance and to propose efficient algorithms that can deal with trans-dimensional MCMC moves. In this paper we extend the cross-covariance of the Bayesian treed multivariate Gaussian process (BTMGP) to that of linear model of Coregionalization (LMC) cross-covariances. Different strategies have been developed to improve the MCMC mixing and invert smaller matrices in the Bayesianmore » inference. Moreover, we compare the proposed BTMGP with existing multiple BTGP and BTMGP in test cases and multiphase flow computer experiment in a full scale regenerator of a carbon capture unit. The use of the BTMGP with LMC cross-covariance helped to predict the computer experiments relatively better than existing competitors. The proposed model has a wide variety of applications, such as computer experiments and environmental data. In the case of computer experiments we also develop an adaptive sampling strategy for the BTMGP with LMC cross-covariance function.« less

The application of feature selection to the development of Gaussian process models for percutaneous absorption.

PubMed

Lam, Lun Tak; Sun, Yi; Davey, Neil; Adams, Rod; Prapopoulou, Maria; Brown, Marc B; Moss, Gary P

2010-06-01

The aim was to employ Gaussian processes to assess mathematically the nature of a skin permeability dataset and to employ these methods, particularly feature selection, to determine the key physicochemical descriptors which exert the most significant influence on percutaneous absorption, and to compare such models with established existing models. Gaussian processes, including automatic relevance detection (GPRARD) methods, were employed to develop models of percutaneous absorption that identified key physicochemical descriptors of percutaneous absorption. Using MatLab software, the statistical performance of these models was compared with single linear networks (SLN) and quantitative structure-permeability relationships (QSPRs). Feature selection methods were used to examine in more detail the physicochemical parameters used in this study. A range of statistical measures to determine model quality were used. The inherently nonlinear nature of the skin data set was confirmed. The Gaussian process regression (GPR) methods yielded predictive models that offered statistically significant improvements over SLN and QSPR models with regard to predictivity (where the rank order was: GPR > SLN > QSPR). Feature selection analysis determined that the best GPR models were those that contained log P, melting point and the number of hydrogen bond donor groups as significant descriptors. Further statistical analysis also found that great synergy existed between certain parameters. It suggested that a number of the descriptors employed were effectively interchangeable, thus questioning the use of models where discrete variables are output, usually in the form of an equation. The use of a nonlinear GPR method produced models with significantly improved predictivity, compared with SLN or QSPR models. Feature selection methods were able to provide important mechanistic information. However, it was also shown that significant synergy existed between certain parameters, and as such it was possible to interchange certain descriptors (i.e. molecular weight and melting point) without incurring a loss of model quality. Such synergy suggested that a model constructed from discrete terms in an equation may not be the most appropriate way of representing mechanistic understandings of skin absorption.

Bayesian Treed Multivariate Gaussian Process with Adaptive Design: Application to a Carbon Capture Unit

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

Konomi, Bledar A.; Karagiannis, Georgios; Sarkar, Avik

2014-05-16

Computer experiments (numerical simulations) are widely used in scientific research to study and predict the behavior of complex systems, which usually have responses consisting of a set of distinct outputs. The computational cost of the simulations at high resolution are often expensive and become impractical for parametric studies at different input values. To overcome these difficulties we develop a Bayesian treed multivariate Gaussian process (BTMGP) as an extension of the Bayesian treed Gaussian process (BTGP) in order to model and evaluate a multivariate process. A suitable choice of covariance function and the prior distributions facilitates the different Markov chain Montemore » Carlo (MCMC) movements. We utilize this model to sequentially sample the input space for the most informative values, taking into account model uncertainty and expertise gained. A simulation study demonstrates the use of the proposed method and compares it with alternative approaches. We apply the sequential sampling technique and BTMGP to model the multiphase flow in a full scale regenerator of a carbon capture unit. The application presented in this paper is an important tool for research into carbon dioxide emissions from thermal power plants.« less

A stochastic-geometric model of soil variation in Pleistocene patterned ground

NASA Astrophysics Data System (ADS)

Lark, Murray; Meerschman, Eef; Van Meirvenne, Marc

2013-04-01

In this paper we examine the spatial variability of soil in parent material with complex spatial structure which arises from complex non-linear geomorphic processes. We show that this variability can be better-modelled by a stochastic-geometric model than by a standard Gaussian random field. The benefits of the new model are seen in the reproduction of features of the target variable which influence processes like water movement and pollutant dispersal. Complex non-linear processes in the soil give rise to properties with non-Gaussian distributions. Even under a transformation to approximate marginal normality, such variables may have a more complex spatial structure than the Gaussian random field model of geostatistics can accommodate. In particular the extent to which extreme values of the variable are connected in spatially coherent regions may be misrepresented. As a result, for example, geostatistical simulation generally fails to reproduce the pathways for preferential flow in an environment where coarse infill of former fluvial channels or coarse alluvium of braided streams creates pathways for rapid movement of water. Multiple point geostatistics has been developed to deal with this problem. Multiple point methods proceed by sampling from a set of training images which can be assumed to reproduce the non-Gaussian behaviour of the target variable. The challenge is to identify appropriate sources of such images. In this paper we consider a mode of soil variation in which the soil varies continuously, exhibiting short-range lateral trends induced by local effects of the factors of soil formation which vary across the region of interest in an unpredictable way. The trends in soil variation are therefore only apparent locally, and the soil variation at regional scale appears random. We propose a stochastic-geometric model for this mode of soil variation called the Continuous Local Trend (CLT) model. We consider a case study of soil formed in relict patterned ground with pronounced lateral textural variations arising from the presence of infilled ice-wedges of Pleistocene origin. We show how knowledge of the pedogenetic processes in this environment, along with some simple descriptive statistics, can be used to select and fit a CLT model for the apparent electrical conductivity (ECa) of the soil. We use the model to simulate realizations of the CLT process, and compare these with realizations of a fitted Gaussian random field. We show how statistics that summarize the spatial coherence of regions with small values of ECa, which are expected to have coarse texture and so larger saturated hydraulic conductivity, are better reproduced by the CLT model than by the Gaussian random field. This suggests that the CLT model could be used to generate an unlimited supply of training images to allow multiple point geostatistical simulation or prediction of this or similar variables.

New deconvolution method for microscopic images based on the continuous Gaussian radial basis function interpolation model.

PubMed

Chen, Zhaoxue; Chen, Hao

2014-01-01

A deconvolution method based on the Gaussian radial basis function (GRBF) interpolation is proposed. Both the original image and Gaussian point spread function are expressed as the same continuous GRBF model, thus image degradation is simplified as convolution of two continuous Gaussian functions, and image deconvolution is converted to calculate the weighted coefficients of two-dimensional control points. Compared with Wiener filter and Lucy-Richardson algorithm, the GRBF method has an obvious advantage in the quality of restored images. In order to overcome such a defect of long-time computing, the method of graphic processing unit multithreading or increasing space interval of control points is adopted, respectively, to speed up the implementation of GRBF method. The experiments show that based on the continuous GRBF model, the image deconvolution can be efficiently implemented by the method, which also has a considerable reference value for the study of three-dimensional microscopic image deconvolution.

DESCRIPTION OF ATMOSPHERIC TRANSPORT PROCESSES IN EULERIAN AIR QUALITY MODELS

EPA Science Inventory

Key differences among many types of air quality models are the way atmospheric advection and turbulent diffusion processes are treated. Gaussian models use analytical solutions of the advection-diffusion equations. Lagrangian models use a hypothetical air parcel concept effecti...

Brownian motion under dynamic disorder: effects of memory on the decay of the non-Gaussianity parameter

NASA Astrophysics Data System (ADS)

Tyagi, Neha; Cherayil, Binny J.

2018-03-01

The increasingly widespread occurrence in complex fluids of particle motion that is both Brownian and non-Gaussian has recently been found to be successfully modeled by a process (frequently referred to as ‘diffusing diffusivity’) in which the white noise that governs Brownian diffusion is itself stochastically modulated by either Ornstein–Uhlenbeck dynamics or by two-state noise. But the model has so far not been able to account for an aspect of non-Gaussian Brownian motion that is also commonly observed: a non-monotonic decay of the parameter that quantifies the extent of deviation from Gaussian behavior. In this paper, we show that the inclusion of memory effects in the model—via a generalized Langevin equation—can rationalise this phenomenon.

Designing Multi-target Compound Libraries with Gaussian Process Models.

PubMed

Bieler, Michael; Reutlinger, Michael; Rodrigues, Tiago; Schneider, Petra; Kriegl, Jan M; Schneider, Gisbert

2016-05-01

We present the application of machine learning models to selecting G protein-coupled receptor (GPCR)-focused compound libraries. The library design process was realized by ant colony optimization. A proprietary Boehringer-Ingelheim reference set consisting of 3519 compounds tested in dose-response assays at 11 GPCR targets served as training data for machine learning and activity prediction. We compared the usability of the proprietary data with a public data set from ChEMBL. Gaussian process models were trained to prioritize compounds from a virtual combinatorial library. We obtained meaningful models for three of the targets (5-HT2c , MCH, A1), which were experimentally confirmed for 12 of 15 selected and synthesized or purchased compounds. Overall, the models trained on the public data predicted the observed assay results more accurately. The results of this study motivate the use of Gaussian process regression on public data for virtual screening and target-focused compound library design. © 2016 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA. This is an open access article under the terms of the Creative Commons Attribution Non-Commercial NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

Real-time model learning using Incremental Sparse Spectrum Gaussian Process Regression.

PubMed

Gijsberts, Arjan; Metta, Giorgio

2013-05-01

Novel applications in unstructured and non-stationary human environments require robots that learn from experience and adapt autonomously to changing conditions. Predictive models therefore not only need to be accurate, but should also be updated incrementally in real-time and require minimal human intervention. Incremental Sparse Spectrum Gaussian Process Regression is an algorithm that is targeted specifically for use in this context. Rather than developing a novel algorithm from the ground up, the method is based on the thoroughly studied Gaussian Process Regression algorithm, therefore ensuring a solid theoretical foundation. Non-linearity and a bounded update complexity are achieved simultaneously by means of a finite dimensional random feature mapping that approximates a kernel function. As a result, the computational cost for each update remains constant over time. Finally, algorithmic simplicity and support for automated hyperparameter optimization ensures convenience when employed in practice. Empirical validation on a number of synthetic and real-life learning problems confirms that the performance of Incremental Sparse Spectrum Gaussian Process Regression is superior with respect to the popular Locally Weighted Projection Regression, while computational requirements are found to be significantly lower. The method is therefore particularly suited for learning with real-time constraints or when computational resources are limited. Copyright © 2012 Elsevier Ltd. All rights reserved.

Edge detection - Image-plane versus digital processing

NASA Technical Reports Server (NTRS)

Huck, Friedrich O.; Fales, Carl L.; Park, Stephen K.; Triplett, Judith A.

1987-01-01

To optimize edge detection with the familiar Laplacian-of-Gaussian operator, it has become common to implement this operator with a large digital convolution mask followed by some interpolation of the processed data to determine the zero crossings that locate edges. It is generally recognized that this large mask causes substantial blurring of fine detail. It is shown that the spatial detail can be improved by a factor of about four with either the Wiener-Laplacian-of-Gaussian filter or an image-plane processor. The Wiener-Laplacian-of-Gaussian filter minimizes the image-gathering degradations if the scene statistics are at least approximately known and also serves as an interpolator to determine the desired zero crossings directly. The image-plane processor forms the Laplacian-of-Gaussian response by properly combining the optical design of the image-gathering system with a minimal three-by-three lateral-inhibitory processing mask. This approach, which is suggested by Marr's model of early processing in human vision, also reduces data processing by about two orders of magnitude and data transmission by up to an order of magnitude.

Gaussian Processes for Prediction of Homing Pigeon Flight Trajectories

NASA Astrophysics Data System (ADS)

Mann, Richard; Freeman, Robin; Osborne, Michael; Garnett, Roman; Meade, Jessica; Armstrong, Chris; Biro, Dora; Guilford, Tim; Roberts, Stephen

2009-12-01

We construct and apply a stochastic Gaussian Process (GP) model of flight trajectory generation for pigeons trained to home from specific release sites. The model shows increasing predictive power as the birds become familiar with the sites, mirroring the animal's learning process. We show how the increasing similarity between successive flight trajectories can be used to infer, with increasing accuracy, an idealised route that captures the repeated spatial aspects of the bird's flight. We subsequently use techniques associated with reduced-rank GP approximations to objectively identify the key waypoints used by each bird to memorise its idiosyncratic habitual route between the release site and the home loft.

Event rate and reaction time performance in ADHD: Testing predictions from the state regulation deficit hypothesis using an ex-Gaussian model.

PubMed

Metin, Baris; Wiersema, Jan R; Verguts, Tom; Gasthuys, Roos; van Der Meere, Jacob J; Roeyers, Herbert; Sonuga-Barke, Edmund

2016-01-01

According to the state regulation deficit (SRD) account, ADHD is associated with a problem using effort to maintain an optimal activation state under demanding task settings such as very fast or very slow event rates. This leads to a prediction of disrupted performance at event rate extremes reflected in higher Gaussian response variability that is a putative marker of activation during motor preparation. In the current study, we tested this hypothesis using ex-Gaussian modeling, which distinguishes Gaussian from non-Gaussian variability. Twenty-five children with ADHD and 29 typically developing controls performed a simple Go/No-Go task under four different event-rate conditions. There was an accentuated quadratic relationship between event rate and Gaussian variability in the ADHD group compared to the controls. The children with ADHD had greater Gaussian variability at very fast and very slow event rates but not at moderate event rates. The results provide evidence for the SRD account of ADHD. However, given that this effect did not explain all group differences (some of which were independent of event rate) other cognitive and/or motivational processes are also likely implicated in ADHD performance deficits.

A non-Gaussian option pricing model based on Kaniadakis exponential deformation

NASA Astrophysics Data System (ADS)

Moretto, Enrico; Pasquali, Sara; Trivellato, Barbara

2017-09-01

A way to make financial models effective is by letting them to represent the so called "fat tails", i.e., extreme changes in stock prices that are regarded as almost impossible by the standard Gaussian distribution. In this article, the Kaniadakis deformation of the usual exponential function is used to define a random noise source in the dynamics of price processes capable of capturing such real market phenomena.

GaussianCpG: a Gaussian model for detection of CpG island in human genome sequences.

PubMed

Yu, Ning; Guo, Xuan; Zelikovsky, Alexander; Pan, Yi

2017-05-24

As crucial markers in identifying biological elements and processes in mammalian genomes, CpG islands (CGI) play important roles in DNA methylation, gene regulation, epigenetic inheritance, gene mutation, chromosome inactivation and nuclesome retention. The generally accepted criteria of CGI rely on: (a) %G+C content is ≥ 50%, (b) the ratio of the observed CpG content and the expected CpG content is ≥ 0.6, and (c) the general length of CGI is greater than 200 nucleotides. Most existing computational methods for the prediction of CpG island are programmed on these rules. However, many experimentally verified CpG islands deviate from these artificial criteria. Experiments indicate that in many cases %G+C is < 50%, CpG obs /CpG exp varies, and the length of CGI ranges from eight nucleotides to a few thousand of nucleotides. It implies that CGI detection is not just a straightly statistical task and some unrevealed rules probably are hidden. A novel Gaussian model, GaussianCpG, is developed for detection of CpG islands on human genome. We analyze the energy distribution over genomic primary structure for each CpG site and adopt the parameters from statistics of Human genome. The evaluation results show that the new model can predict CpG islands efficiently by balancing both sensitivity and specificity over known human CGI data sets. Compared with other models, GaussianCpG can achieve better performance in CGI detection. Our Gaussian model aims to simplify the complex interaction between nucleotides. The model is computed not by the linear statistical method but by the Gaussian energy distribution and accumulation. The parameters of Gaussian function are not arbitrarily designated but deliberately chosen by optimizing the biological statistics. By using the pseudopotential analysis on CpG islands, the novel model is validated on both the real and artificial data sets.

TH-C-BRD-04: Beam Modeling and Validation with Triple and Double Gaussian Dose Kernel for Spot Scanning Proton Beams

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

Hirayama, S; Takayanagi, T; Fujii, Y

2014-06-15

Purpose: To present the validity of our beam modeling with double and triple Gaussian dose kernels for spot scanning proton beams in Nagoya Proton Therapy Center. This study investigates the conformance between the measurements and calculation results in absolute dose with two types of beam kernel. Methods: A dose kernel is one of the important input data required for the treatment planning software. The dose kernel is the 3D dose distribution of an infinitesimal pencil beam of protons in water and consists of integral depth doses and lateral distributions. We have adopted double and triple Gaussian model as lateral distributionmore » in order to take account of the large angle scattering due to nuclear reaction by fitting simulated inwater lateral dose profile for needle proton beam at various depths. The fitted parameters were interpolated as a function of depth in water and were stored as a separate look-up table for the each beam energy. The process of beam modeling is based on the method of MDACC [X.R.Zhu 2013]. Results: From the comparison results between the absolute doses calculated by double Gaussian model and those measured at the center of SOBP, the difference is increased up to 3.5% in the high-energy region because the large angle scattering due to nuclear reaction is not sufficiently considered at intermediate depths in the double Gaussian model. In case of employing triple Gaussian dose kernels, the measured absolute dose at the center of SOBP agrees with calculation within ±1% regardless of the SOBP width and maximum range. Conclusion: We have demonstrated the beam modeling results of dose distribution employing double and triple Gaussian dose kernel. Treatment planning system with the triple Gaussian dose kernel has been successfully verified and applied to the patient treatment with a spot scanning technique in Nagoya Proton Therapy Center.« less

Dirichlet Process Gaussian-mixture model: An application to localizing coalescing binary neutron stars with gravitational-wave observations

NASA Astrophysics Data System (ADS)

Del Pozzo, W.; Berry, C. P. L.; Ghosh, A.; Haines, T. S. F.; Singer, L. P.; Vecchio, A.

2018-06-01

We reconstruct posterior distributions for the position (sky area and distance) of a simulated set of binary neutron-star gravitational-waves signals observed with Advanced LIGO and Advanced Virgo. We use a Dirichlet Process Gaussian-mixture model, a fully Bayesian non-parametric method that can be used to estimate probability density functions with a flexible set of assumptions. The ability to reliably reconstruct the source position is important for multimessenger astronomy, as recently demonstrated with GW170817. We show that for detector networks comparable to the early operation of Advanced LIGO and Advanced Virgo, typical localization volumes are ˜104-105 Mpc3 corresponding to ˜102-103 potential host galaxies. The localization volume is a strong function of the network signal-to-noise ratio, scaling roughly ∝ϱnet-6. Fractional localizations improve with the addition of further detectors to the network. Our Dirichlet Process Gaussian-mixture model can be adopted for localizing events detected during future gravitational-wave observing runs, and used to facilitate prompt multimessenger follow-up.

celerite: Scalable 1D Gaussian Processes in C++, Python, and Julia

NASA Astrophysics Data System (ADS)

Foreman-Mackey, Daniel; Agol, Eric; Ambikasaran, Sivaram; Angus, Ruth

2017-09-01

celerite provides fast and scalable Gaussian Process (GP) Regression in one dimension and is implemented in C++, Python, and Julia. The celerite API is designed to be familiar to users of george and, like george, celerite is designed to efficiently evaluate the marginalized likelihood of a dataset under a GP model. This is then be used alongside a non-linear optimization or posterior inference library for the best results.

Direct Importance Estimation with Gaussian Mixture Models

NASA Astrophysics Data System (ADS)

Yamada, Makoto; Sugiyama, Masashi

The ratio of two probability densities is called the importance and its estimation has gathered a great deal of attention these days since the importance can be used for various data processing purposes. In this paper, we propose a new importance estimation method using Gaussian mixture models (GMMs). Our method is an extention of the Kullback-Leibler importance estimation procedure (KLIEP), an importance estimation method using linear or kernel models. An advantage of GMMs is that covariance matrices can also be learned through an expectation-maximization procedure, so the proposed method — which we call the Gaussian mixture KLIEP (GM-KLIEP) — is expected to work well when the true importance function has high correlation. Through experiments, we show the validity of the proposed approach.

Noise effects in nonlinear biochemical signaling

NASA Astrophysics Data System (ADS)

Bostani, Neda; Kessler, David A.; Shnerb, Nadav M.; Rappel, Wouter-Jan; Levine, Herbert

2012-01-01

It has been generally recognized that stochasticity can play an important role in the information processing accomplished by reaction networks in biological cells. Most treatments of that stochasticity employ Gaussian noise even though it is a priori obvious that this approximation can violate physical constraints, such as the positivity of chemical concentrations. Here, we show that even when such nonphysical fluctuations are rare, an exact solution of the Gaussian model shows that the model can yield unphysical results. This is done in the context of a simple incoherent-feedforward model which exhibits perfect adaptation in the deterministic limit. We show how one can use the natural separation of time scales in this model to yield an approximate model, that is analytically solvable, including its dynamical response to an environmental change. Alternatively, one can employ a cutoff procedure to regularize the Gaussian result.

Monte Carlo based toy model for fission process

NASA Astrophysics Data System (ADS)

Kurniadi, R.; Waris, A.; Viridi, S.

2014-09-01

There are many models and calculation techniques to obtain visible image of fission yield process. In particular, fission yield can be calculated by using two calculations approach, namely macroscopic approach and microscopic approach. This work proposes another calculation approach in which the nucleus is treated as a toy model. Hence, the fission process does not represent real fission process in nature completely. The toy model is formed by Gaussian distribution of random number that randomizes distance likesthe distance between particle and central point. The scission process is started by smashing compound nucleus central point into two parts that are left central and right central points. These three points have different Gaussian distribution parameters such as mean (μCN, μL, μR), and standard deviation (σCN, σL, σR). By overlaying of three distributions, the number of particles (NL, NR) that are trapped by central points can be obtained. This process is iterated until (NL, NR) become constant numbers. Smashing process is repeated by changing σL and σR, randomly.

Stable radiation pressure acceleration of ions by suppressing transverse Rayleigh-Taylor instability with multiple Gaussian pulses

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

Zhou, M. L.; Liu, B.; Hu, R. H.

In the case of a thin plasma slab accelerated by the radiation pressure of an ultra-intense laser pulse, the development of Rayleigh-Taylor instability (RTI) will destroy the acceleration structure and terminate the acceleration process much sooner than theoretical limit. In this paper, a new scheme using multiple Gaussian pulses for ion acceleration in a radiation pressure acceleration regime is investigated with particle-in-cell simulation. We found that with multiple Gaussian pulses, the instability could be efficiently suppressed and the divergence of the ion bunch is greatly reduced, resulting in a longer acceleration time and much more collimated ion bunch with highermore » energy than using a single Gaussian pulse. An analytical model is developed to describe the suppression of RTI at the laser-plasma interface. The model shows that the suppression of RTI is due to the introduction of the long wavelength mode RTI by the multiple Gaussian pulses.« less

An unbiased risk estimator for image denoising in the presence of mixed poisson-gaussian noise.

PubMed

Le Montagner, Yoann; Angelini, Elsa D; Olivo-Marin, Jean-Christophe

2014-03-01

The behavior and performance of denoising algorithms are governed by one or several parameters, whose optimal settings depend on the content of the processed image and the characteristics of the noise, and are generally designed to minimize the mean squared error (MSE) between the denoised image returned by the algorithm and a virtual ground truth. In this paper, we introduce a new Poisson-Gaussian unbiased risk estimator (PG-URE) of the MSE applicable to a mixed Poisson-Gaussian noise model that unifies the widely used Gaussian and Poisson noise models in fluorescence bioimaging applications. We propose a stochastic methodology to evaluate this estimator in the case when little is known about the internal machinery of the considered denoising algorithm, and we analyze both theoretically and empirically the characteristics of the PG-URE estimator. Finally, we evaluate the PG-URE-driven parametrization for three standard denoising algorithms, with and without variance stabilizing transforms, and different characteristics of the Poisson-Gaussian noise mixture.

Is There a Critical Distance for Fickian Transport? - a Statistical Approach to Sub-Fickian Transport Modelling in Porous Media

NASA Astrophysics Data System (ADS)

Most, S.; Nowak, W.; Bijeljic, B.

2014-12-01

Transport processes in porous media are frequently simulated as particle movement. This process can be formulated as a stochastic process of particle position increments. At the pore scale, the geometry and micro-heterogeneities prohibit the commonly made assumption of independent and normally distributed increments to represent dispersion. Many recent particle methods seek to loosen this assumption. Recent experimental data suggest that we have not yet reached the end of the need to generalize, because particle increments show statistical dependency beyond linear correlation and over many time steps. The goal of this work is to better understand the validity regions of commonly made assumptions. We are investigating after what transport distances can we observe: A statistical dependence between increments, that can be modelled as an order-k Markov process, boils down to order 1. This would be the Markovian distance for the process, where the validity of yet-unexplored non-Gaussian-but-Markovian random walks would start. A bivariate statistical dependence that simplifies to a multi-Gaussian dependence based on simple linear correlation (validity of correlated PTRW). Complete absence of statistical dependence (validity of classical PTRW/CTRW). The approach is to derive a statistical model for pore-scale transport from a powerful experimental data set via copula analysis. The model is formulated as a non-Gaussian, mutually dependent Markov process of higher order, which allows us to investigate the validity ranges of simpler models.

Ship Detection in SAR Image Based on the Alpha-stable Distribution

PubMed Central

Wang, Changcheng; Liao, Mingsheng; Li, Xiaofeng

2008-01-01

This paper describes an improved Constant False Alarm Rate (CFAR) ship detection algorithm in spaceborne synthetic aperture radar (SAR) image based on Alpha-stable distribution model. Typically, the CFAR algorithm uses the Gaussian distribution model to describe statistical characteristics of a SAR image background clutter. However, the Gaussian distribution is only valid for multilook SAR images when several radar looks are averaged. As sea clutter in SAR images shows spiky or heavy-tailed characteristics, the Gaussian distribution often fails to describe background sea clutter. In this study, we replace the Gaussian distribution with the Alpha-stable distribution, which is widely used in impulsive or spiky signal processing, to describe the background sea clutter in SAR images. In our proposed algorithm, an initial step for detecting possible ship targets is employed. Then, similar to the typical two-parameter CFAR algorithm, a local process is applied to the pixel identified as possible target. A RADARSAT-1 image is used to validate this Alpha-stable distribution based algorithm. Meanwhile, known ship location data during the time of RADARSAT-1 SAR image acquisition is used to validate ship detection results. Validation results show improvements of the new CFAR algorithm based on the Alpha-stable distribution over the CFAR algorithm based on the Gaussian distribution. PMID:27873794

Surrogate modelling for the prediction of spatial fields based on simultaneous dimensionality reduction of high-dimensional input/output spaces.

PubMed

Crevillén-García, D

2018-04-01

Time-consuming numerical simulators for solving groundwater flow and dissolution models of physico-chemical processes in deep aquifers normally require some of the model inputs to be defined in high-dimensional spaces in order to return realistic results. Sometimes, the outputs of interest are spatial fields leading to high-dimensional output spaces. Although Gaussian process emulation has been satisfactorily used for computing faithful and inexpensive approximations of complex simulators, these have been mostly applied to problems defined in low-dimensional input spaces. In this paper, we propose a method for simultaneously reducing the dimensionality of very high-dimensional input and output spaces in Gaussian process emulators for stochastic partial differential equation models while retaining the qualitative features of the original models. This allows us to build a surrogate model for the prediction of spatial fields in such time-consuming simulators. We apply the methodology to a model of convection and dissolution processes occurring during carbon capture and storage.

Multi-fidelity Gaussian process regression for prediction of random fields

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

Parussini, L.; Venturi, D., E-mail: venturi@ucsc.edu; Perdikaris, P.

We propose a new multi-fidelity Gaussian process regression (GPR) approach for prediction of random fields based on observations of surrogate models or hierarchies of surrogate models. Our method builds upon recent work on recursive Bayesian techniques, in particular recursive co-kriging, and extends it to vector-valued fields and various types of covariances, including separable and non-separable ones. The framework we propose is general and can be used to perform uncertainty propagation and quantification in model-based simulations, multi-fidelity data fusion, and surrogate-based optimization. We demonstrate the effectiveness of the proposed recursive GPR techniques through various examples. Specifically, we study the stochastic Burgersmore » equation and the stochastic Oberbeck–Boussinesq equations describing natural convection within a square enclosure. In both cases we find that the standard deviation of the Gaussian predictors as well as the absolute errors relative to benchmark stochastic solutions are very small, suggesting that the proposed multi-fidelity GPR approaches can yield highly accurate results.« less

The Mass-dependent Star Formation Histories of Disk Galaxies: Infall Model Versus Observations

NASA Astrophysics Data System (ADS)

Chang, R. X.; Hou, J. L.; Shen, S. Y.; Shu, C. G.

2010-10-01

We introduce a simple model to explore the star formation histories of disk galaxies. We assume that the disk originate and grows by continuous gas infall. The gas infall rate is parameterized by the Gaussian formula with one free parameter: the infall-peak time tp . The Kennicutt star formation law is adopted to describe how much cold gas turns into stars. The gas outflow process is also considered in our model. We find that, at a given galactic stellar mass M *, the model adopting a late infall-peak time tp results in blue colors, low-metallicity, high specific star formation rate (SFR), and high gas fraction, while the gas outflow rate mainly influences the gas-phase metallicity and star formation efficiency mainly influences the gas fraction. Motivated by the local observed scaling relations, we "construct" a mass-dependent model by assuming that the low-mass galaxy has a later infall-peak time tp and a larger gas outflow rate than massive systems. It is shown that this model can be in agreement with not only the local observations, but also with the observed correlations between specific SFR and galactic stellar mass SFR/M * ~ M * at intermediate redshifts z < 1. Comparison between the Gaussian-infall model and the exponential-infall model is also presented. It shows that the exponential-infall model predicts a higher SFR at early stage and a lower SFR later than that of Gaussian infall. Our results suggest that the Gaussian infall rate may be more reasonable in describing the gas cooling process than the exponential infall rate, especially for low-mass systems.

The Prediction of Length-of-day Variations Based on Gaussian Processes

NASA Astrophysics Data System (ADS)

Lei, Y.; Zhao, D. N.; Gao, Y. P.; Cai, H. B.

2015-01-01

Due to the complicated time-varying characteristics of the length-of-day (LOD) variations, the accuracies of traditional strategies for the prediction of the LOD variations such as the least squares extrapolation model, the time-series analysis model, and so on, have not met the requirements for real-time and high-precision applications. In this paper, a new machine learning algorithm --- the Gaussian process (GP) model is employed to forecast the LOD variations. Its prediction precisions are analyzed and compared with those of the back propagation neural networks (BPNN), general regression neural networks (GRNN) models, and the Earth Orientation Parameters Prediction Comparison Campaign (EOP PCC). The results demonstrate that the application of the GP model to the prediction of the LOD variations is efficient and feasible.

Poisson-Gaussian Noise Reduction Using the Hidden Markov Model in Contourlet Domain for Fluorescence Microscopy Images

PubMed Central

Yang, Sejung; Lee, Byung-Uk

2015-01-01

In certain image acquisitions processes, like in fluorescence microscopy or astronomy, only a limited number of photons can be collected due to various physical constraints. The resulting images suffer from signal dependent noise, which can be modeled as a Poisson distribution, and a low signal-to-noise ratio. However, the majority of research on noise reduction algorithms focuses on signal independent Gaussian noise. In this paper, we model noise as a combination of Poisson and Gaussian probability distributions to construct a more accurate model and adopt the contourlet transform which provides a sparse representation of the directional components in images. We also apply hidden Markov models with a framework that neatly describes the spatial and interscale dependencies which are the properties of transformation coefficients of natural images. In this paper, an effective denoising algorithm for Poisson-Gaussian noise is proposed using the contourlet transform, hidden Markov models and noise estimation in the transform domain. We supplement the algorithm by cycle spinning and Wiener filtering for further improvements. We finally show experimental results with simulations and fluorescence microscopy images which demonstrate the improved performance of the proposed approach. PMID:26352138

Modeling and forecasting foreign exchange daily closing prices with normal inverse Gaussian

NASA Astrophysics Data System (ADS)

Teneng, Dean

2013-09-01

We fit the normal inverse Gaussian(NIG) distribution to foreign exchange closing prices using the open software package R and select best models by Käärik and Umbleja (2011) proposed strategy. We observe that daily closing prices (12/04/2008 - 07/08/2012) of CHF/JPY, AUD/JPY, GBP/JPY, NZD/USD, QAR/CHF, QAR/EUR, SAR/CHF, SAR/EUR, TND/CHF and TND/EUR are excellent fits while EGP/EUR and EUR/GBP are good fits with a Kolmogorov-Smirnov test p-value of 0.062 and 0.08 respectively. It was impossible to estimate normal inverse Gaussian parameters (by maximum likelihood; computational problem) for JPY/CHF but CHF/JPY was an excellent fit. Thus, while the stochastic properties of an exchange rate can be completely modeled with a probability distribution in one direction, it may be impossible the other way around. We also demonstrate that foreign exchange closing prices can be forecasted with the normal inverse Gaussian (NIG) Lévy process, both in cases where the daily closing prices can and cannot be modeled by NIG distribution.

A continuous mixing model for pdf simulations and its applications to combusting shear flows

NASA Technical Reports Server (NTRS)

Hsu, A. T.; Chen, J.-Y.

1991-01-01

The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in this work. A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models.

Suborbital spaceplane optimization using non-stationary Gaussian processes

NASA Astrophysics Data System (ADS)

Dufour, Robin; de Muelenaere, Julien; Elham, Ali

2014-10-01

This paper presents multidisciplinary design optimization of a sub-orbital spaceplane. The optimization includes three disciplines: the aerodynamics, the structure and the trajectory. An Adjoint Euler code is used to calculate the aerodynamic lift and drag of the vehicle as well as their derivatives with respect to the design variables. A new surrogate model has been developed based on a non-stationary Gaussian process. That model was used to estimate the aerodynamic characteristics of the vehicle during the trajectory optimization. The trajectory of thevehicle has been optimized together with its geometry in order to maximize the amount of payload that can be carried by the spaceplane.

Prediction of temperature and HAZ in thermal-based processes with Gaussian heat source by a hybrid GA-ANN model

NASA Astrophysics Data System (ADS)

Fazli Shahri, Hamid Reza; Mahdavinejad, Ramezanali

2018-02-01

Thermal-based processes with Gaussian heat source often produce excessive temperature which can impose thermally-affected layers in specimens. Therefore, the temperature distribution and Heat Affected Zone (HAZ) of materials are two critical factors which are influenced by different process parameters. Measurement of the HAZ thickness and temperature distribution within the processes are not only difficult but also expensive. This research aims at finding a valuable knowledge on these factors by prediction of the process through a novel combinatory model. In this study, an integrated Artificial Neural Network (ANN) and genetic algorithm (GA) was used to predict the HAZ and temperature distribution of the specimens. To end this, a series of full factorial design of experiments were conducted by applying a Gaussian heat flux on Ti-6Al-4 V at first, then the temperature of the specimen was measured by Infrared thermography. The HAZ width of each sample was investigated through measuring the microhardness. Secondly, the experimental data was used to create a GA-ANN model. The efficiency of GA in design and optimization of the architecture of ANN was investigated. The GA was used to determine the optimal number of neurons in hidden layer, learning rate and momentum coefficient of both output and hidden layers of ANN. Finally, the reliability of models was assessed according to the experimental results and statistical indicators. The results demonstrated that the combinatory model predicted the HAZ and temperature more effective than a trial-and-error ANN model.

a Gaussian Process Based Multi-Person Interaction Model

NASA Astrophysics Data System (ADS)

Klinger, T.; Rottensteiner, F.; Heipke, C.

2016-06-01

Online multi-person tracking in image sequences is commonly guided by recursive filters, whose predictive models define the expected positions of future states. When a predictive model deviates too much from the true motion of a pedestrian, which is often the case in crowded scenes due to unpredicted accelerations, the data association is prone to fail. In this paper we propose a novel predictive model on the basis of Gaussian Process Regression. The model takes into account the motion of every tracked pedestrian in the scene and the prediction is executed with respect to the velocities of all interrelated persons. As shown by the experiments, the model is capable of yielding more plausible predictions even in the presence of mutual occlusions or missing measurements. The approach is evaluated on a publicly available benchmark and outperforms other state-of-the-art trackers.

Theory and generation of conditional, scalable sub-Gaussian random fields

NASA Astrophysics Data System (ADS)

Panzeri, M.; Riva, M.; Guadagnini, A.; Neuman, S. P.

2016-03-01

Many earth and environmental (as well as a host of other) variables, Y, and their spatial (or temporal) increments, ΔY, exhibit non-Gaussian statistical scaling. Previously we were able to capture key aspects of such non-Gaussian scaling by treating Y and/or ΔY as sub-Gaussian random fields (or processes). This however left unaddressed the empirical finding that whereas sample frequency distributions of Y tend to display relatively mild non-Gaussian peaks and tails, those of ΔY often reveal peaks that grow sharper and tails that become heavier with decreasing separation distance or lag. Recently we proposed a generalized sub-Gaussian model (GSG) which resolves this apparent inconsistency between the statistical scaling behaviors of observed variables and their increments. We presented an algorithm to generate unconditional random realizations of statistically isotropic or anisotropic GSG functions and illustrated it in two dimensions. Most importantly, we demonstrated the feasibility of estimating all parameters of a GSG model underlying a single realization of Y by analyzing jointly spatial moments of Y data and corresponding increments, ΔY. Here, we extend our GSG model to account for noisy measurements of Y at a discrete set of points in space (or time), present an algorithm to generate conditional realizations of corresponding isotropic or anisotropic random fields, introduce two approximate versions of this algorithm to reduce CPU time, and explore them on one and two-dimensional synthetic test cases.

Separation of the atmospheric variability into non-Gaussian multidimensional sources by projection pursuit techniques

NASA Astrophysics Data System (ADS)

Pires, Carlos A. L.; Ribeiro, Andreia F. S.

2017-02-01

We develop an expansion of space-distributed time series into statistically independent uncorrelated subspaces (statistical sources) of low-dimension and exhibiting enhanced non-Gaussian probability distributions with geometrically simple chosen shapes (projection pursuit rationale). The method relies upon a generalization of the principal component analysis that is optimal for Gaussian mixed signals and of the independent component analysis (ICA), optimized to split non-Gaussian scalar sources. The proposed method, supported by information theory concepts and methods, is the independent subspace analysis (ISA) that looks for multi-dimensional, intrinsically synergetic subspaces such as dyads (2D) and triads (3D), not separable by ICA. Basically, we optimize rotated variables maximizing certain nonlinear correlations (contrast functions) coming from the non-Gaussianity of the joint distribution. As a by-product, it provides nonlinear variable changes `unfolding' the subspaces into nearly Gaussian scalars of easier post-processing. Moreover, the new variables still work as nonlinear data exploratory indices of the non-Gaussian variability of the analysed climatic and geophysical fields. The method (ISA, followed by nonlinear unfolding) is tested into three datasets. The first one comes from the Lorenz'63 three-dimensional chaotic model, showing a clear separation into a non-Gaussian dyad plus an independent scalar. The second one is a mixture of propagating waves of random correlated phases in which the emergence of triadic wave resonances imprints a statistical signature in terms of a non-Gaussian non-separable triad. Finally the method is applied to the monthly variability of a high-dimensional quasi-geostrophic (QG) atmospheric model, applied to the Northern Hemispheric winter. We find that quite enhanced non-Gaussian dyads of parabolic shape, perform much better than the unrotated variables in which concerns the separation of the four model's centroid regimes (positive and negative phases of the Arctic Oscillation and of the North Atlantic Oscillation). Triads are also likely in the QG model but of weaker expression than dyads due to the imposed shape and dimension. The study emphasizes the existence of nonlinear dyadic and triadic nonlinear teleconnections.

An adaptive Gaussian process-based method for efficient Bayesian experimental design in groundwater contaminant source identification problems: ADAPTIVE GAUSSIAN PROCESS-BASED INVERSION

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

Zhang, Jiangjiang; Li, Weixuan; Zeng, Lingzao

Surrogate models are commonly used in Bayesian approaches such as Markov Chain Monte Carlo (MCMC) to avoid repetitive CPU-demanding model evaluations. However, the approximation error of a surrogate may lead to biased estimations of the posterior distribution. This bias can be corrected by constructing a very accurate surrogate or implementing MCMC in a two-stage manner. Since the two-stage MCMC requires extra original model evaluations, the computational cost is still high. If the information of measurement is incorporated, a locally accurate approximation of the original model can be adaptively constructed with low computational cost. Based on this idea, we propose amore » Gaussian process (GP) surrogate-based Bayesian experimental design and parameter estimation approach for groundwater contaminant source identification problems. A major advantage of the GP surrogate is that it provides a convenient estimation of the approximation error, which can be incorporated in the Bayesian formula to avoid over-confident estimation of the posterior distribution. The proposed approach is tested with a numerical case study. Without sacrificing the estimation accuracy, the new approach achieves about 200 times of speed-up compared to our previous work using two-stage MCMC.« less

A Prediction Model for Functional Outcomes in Spinal Cord Disorder Patients Using Gaussian Process Regression.

PubMed

Lee, Sunghoon Ivan; Mortazavi, Bobak; Hoffman, Haydn A; Lu, Derek S; Li, Charles; Paak, Brian H; Garst, Jordan H; Razaghy, Mehrdad; Espinal, Marie; Park, Eunjeong; Lu, Daniel C; Sarrafzadeh, Majid

2016-01-01

Predicting the functional outcomes of spinal cord disorder patients after medical treatments, such as a surgical operation, has always been of great interest. Accurate posttreatment prediction is especially beneficial for clinicians, patients, care givers, and therapists. This paper introduces a prediction method for postoperative functional outcomes by a novel use of Gaussian process regression. The proposed method specifically considers the restricted value range of the target variables by modeling the Gaussian process based on a truncated Normal distribution, which significantly improves the prediction results. The prediction has been made in assistance with target tracking examinations using a highly portable and inexpensive handgrip device, which greatly contributes to the prediction performance. The proposed method has been validated through a dataset collected from a clinical cohort pilot involving 15 patients with cervical spinal cord disorder. The results show that the proposed method can accurately predict postoperative functional outcomes, Oswestry disability index and target tracking scores, based on the patient's preoperative information with a mean absolute error of 0.079 and 0.014 (out of 1.0), respectively.

A Modularized Efficient Framework for Non-Markov Time Series Estimation

NASA Astrophysics Data System (ADS)

Schamberg, Gabriel; Ba, Demba; Coleman, Todd P.

2018-06-01

We present a compartmentalized approach to finding the maximum a-posteriori (MAP) estimate of a latent time series that obeys a dynamic stochastic model and is observed through noisy measurements. We specifically consider modern signal processing problems with non-Markov signal dynamics (e.g. group sparsity) and/or non-Gaussian measurement models (e.g. point process observation models used in neuroscience). Through the use of auxiliary variables in the MAP estimation problem, we show that a consensus formulation of the alternating direction method of multipliers (ADMM) enables iteratively computing separate estimates based on the likelihood and prior and subsequently "averaging" them in an appropriate sense using a Kalman smoother. As such, this can be applied to a broad class of problem settings and only requires modular adjustments when interchanging various aspects of the statistical model. Under broad log-concavity assumptions, we show that the separate estimation problems are convex optimization problems and that the iterative algorithm converges to the MAP estimate. As such, this framework can capture non-Markov latent time series models and non-Gaussian measurement models. We provide example applications involving (i) group-sparsity priors, within the context of electrophysiologic specrotemporal estimation, and (ii) non-Gaussian measurement models, within the context of dynamic analyses of learning with neural spiking and behavioral observations.

Application of multivariate Gaussian detection theory to known non-Gaussian probability density functions

NASA Astrophysics Data System (ADS)

Schwartz, Craig R.; Thelen, Brian J.; Kenton, Arthur C.

1995-06-01

A statistical parametric multispectral sensor performance model was developed by ERIM to support mine field detection studies, multispectral sensor design/performance trade-off studies, and target detection algorithm development. The model assumes target detection algorithms and their performance models which are based on data assumed to obey multivariate Gaussian probability distribution functions (PDFs). The applicability of these algorithms and performance models can be generalized to data having non-Gaussian PDFs through the use of transforms which convert non-Gaussian data to Gaussian (or near-Gaussian) data. An example of one such transform is the Box-Cox power law transform. In practice, such a transform can be applied to non-Gaussian data prior to the introduction of a detection algorithm that is formally based on the assumption of multivariate Gaussian data. This paper presents an extension of these techniques to the case where the joint multivariate probability density function of the non-Gaussian input data is known, and where the joint estimate of the multivariate Gaussian statistics, under the Box-Cox transform, is desired. The jointly estimated multivariate Gaussian statistics can then be used to predict the performance of a target detection algorithm which has an associated Gaussian performance model.

Statistics of a neuron model driven by asymmetric colored noise.

PubMed

Müller-Hansen, Finn; Droste, Felix; Lindner, Benjamin

2015-02-01

Irregular firing of neurons can be modeled as a stochastic process. Here we study the perfect integrate-and-fire neuron driven by dichotomous noise, a Markovian process that jumps between two states (i.e., possesses a non-Gaussian statistics) and exhibits nonvanishing temporal correlations (i.e., represents a colored noise). Specifically, we consider asymmetric dichotomous noise with two different transition rates. Using a first-passage-time formulation, we derive exact expressions for the probability density and the serial correlation coefficient of the interspike interval (time interval between two subsequent neural action potentials) and the power spectrum of the spike train. Furthermore, we extend the model by including additional Gaussian white noise, and we give approximations for the interspike interval (ISI) statistics in this case. Numerical simulations are used to validate the exact analytical results for pure dichotomous noise, and to test the approximations of the ISI statistics when Gaussian white noise is included. The results may help to understand how correlations and asymmetry of noise and signals in nerve cells shape neuronal firing statistics.

Gaussian process based independent analysis for temporal source separation in fMRI.

PubMed

Hald, Ditte Høvenhoff; Henao, Ricardo; Winther, Ole

2017-05-15

Functional Magnetic Resonance Imaging (fMRI) gives us a unique insight into the processes of the brain, and opens up for analyzing the functional activation patterns of the underlying sources. Task-inferred supervised learning with restrictive assumptions in the regression set-up, restricts the exploratory nature of the analysis. Fully unsupervised independent component analysis (ICA) algorithms, on the other hand, can struggle to detect clear classifiable components on single-subject data. We attribute this shortcoming to inadequate modeling of the fMRI source signals by failing to incorporate its temporal nature. fMRI source signals, biological stimuli and non-stimuli-related artifacts are all smooth over a time-scale compatible with the sampling time (TR). We therefore propose Gaussian process ICA (GPICA), which facilitates temporal dependency by the use of Gaussian process source priors. On two fMRI data sets with different sampling frequency, we show that the GPICA-inferred temporal components and associated spatial maps allow for a more definite interpretation than standard temporal ICA methods. The temporal structures of the sources are controlled by the covariance of the Gaussian process, specified by a kernel function with an interpretable and controllable temporal length scale parameter. We propose a hierarchical model specification, considering both instantaneous and convolutive mixing, and we infer source spatial maps, temporal patterns and temporal length scale parameters by Markov Chain Monte Carlo. A companion implementation made as a plug-in for SPM can be downloaded from https://github.com/dittehald/GPICA. Copyright © 2017 Elsevier Inc. All rights reserved.

Segmenting Continuous Motions with Hidden Semi-markov Models and Gaussian Processes

PubMed Central

Nakamura, Tomoaki; Nagai, Takayuki; Mochihashi, Daichi; Kobayashi, Ichiro; Asoh, Hideki; Kaneko, Masahide

2017-01-01

Humans divide perceived continuous information into segments to facilitate recognition. For example, humans can segment speech waves into recognizable morphemes. Analogously, continuous motions are segmented into recognizable unit actions. People can divide continuous information into segments without using explicit segment points. This capacity for unsupervised segmentation is also useful for robots, because it enables them to flexibly learn languages, gestures, and actions. In this paper, we propose a Gaussian process-hidden semi-Markov model (GP-HSMM) that can divide continuous time series data into segments in an unsupervised manner. Our proposed method consists of a generative model based on the hidden semi-Markov model (HSMM), the emission distributions of which are Gaussian processes (GPs). Continuous time series data is generated by connecting segments generated by the GP. Segmentation can be achieved by using forward filtering-backward sampling to estimate the model's parameters, including the lengths and classes of the segments. In an experiment using the CMU motion capture dataset, we tested GP-HSMM with motion capture data containing simple exercise motions; the results of this experiment showed that the proposed GP-HSMM was comparable with other methods. We also conducted an experiment using karate motion capture data, which is more complex than exercise motion capture data; in this experiment, the segmentation accuracy of GP-HSMM was 0.92, which outperformed other methods. PMID:29311889

Sequencing batch-reactor control using Gaussian-process models.

PubMed

Kocijan, Juš; Hvala, Nadja

2013-06-01

This paper presents a Gaussian-process (GP) model for the design of sequencing batch-reactor (SBR) control for wastewater treatment. The GP model is a probabilistic, nonparametric model with uncertainty predictions. In the case of SBR control, it is used for the on-line optimisation of the batch-phases duration. The control algorithm follows the course of the indirect process variables (pH, redox potential and dissolved oxygen concentration) and recognises the characteristic patterns in their time profile. The control algorithm uses GP-based regression to smooth the signals and GP-based classification for the pattern recognition. When tested on the signals from an SBR laboratory pilot plant, the control algorithm provided a satisfactory agreement between the proposed completion times and the actual termination times of the biodegradation processes. In a set of tested batches the final ammonia and nitrate concentrations were below 1 and 0.5 mg L(-1), respectively, while the aeration time was shortened considerably. Copyright © 2013 Elsevier Ltd. All rights reserved.

ENSO's non-stationary and non-Gaussian character: the role of climate shifts

NASA Astrophysics Data System (ADS)

Boucharel, J.; Dewitte, B.; Garel, B.; Du Penhoat, Y.

2009-07-01

El Niño Southern Oscillation (ENSO) is the dominant mode of climate variability in the Pacific, having socio-economic impacts on surrounding regions. ENSO exhibits significant modulation on decadal to inter-decadal time scales which is related to changes in its characteristics (onset, amplitude, frequency, propagation, and predictability). Some of these characteristics tend to be overlooked in ENSO studies, such as its asymmetry (the number and amplitude of warm and cold events are not equal) and the deviation of its statistics from those of the Gaussian distribution. These properties could be related to the ability of the current generation of coupled models to predict ENSO and its modulation. Here, ENSO's non-Gaussian nature and asymmetry are diagnosed from in situ data and a variety of models (from intermediate complexity models to full-physics coupled general circulation models (CGCMs)) using robust statistical tools initially designed for financial mathematics studies. In particular α-stable laws are used as theoretical background material to measure (and quantify) the non-Gaussian character of ENSO time series and to estimate the skill of ``naïve'' statistical models in producing deviation from Gaussian laws and asymmetry. The former are based on non-stationary processes dominated by abrupt changes in mean state and empirical variance. It is shown that the α-stable character of ENSO may result from the presence of climate shifts in the time series. Also, cool (warm) periods are associated with ENSO statistics having a stronger (weaker) tendency towards Gaussianity and lower (greater) asymmetry. This supports the hypothesis of ENSO being rectified by changes in mean state through nonlinear processes. The relationship between changes in mean state and nonlinearity (skewness) is further investigated both in the Zebiak and Cane (1987)'s model and the models of the Intergovernmental Panel for Climate Change (IPCC). Whereas there is a clear relationship in all models between ENSO asymmetry (as measured by skewness or nonlinear advection) and changes in mean state, they exhibit a variety of behaviour with regard to α-stability. This suggests that the dynamics associated with climate shifts and the occurrence of extreme events involve higher-order statistical moments that cannot be accounted for solely by nonlinear advection.

Gaussian Process Model for Antarctic Surface Mass Balance and Ice Core Site Selection

NASA Astrophysics Data System (ADS)

White, P. A.; Reese, S.; Christensen, W. F.; Rupper, S.

2017-12-01

Surface mass balance (SMB) is an important factor in the estimation of sea level change, and data are collected to estimate models for prediction of SMB on the Antarctic ice sheet. Using Favier et al.'s (2013) quality-controlled aggregate data set of SMB field measurements, a fully Bayesian spatial model is posed to estimate Antarctic SMB and propose new field measurement locations. Utilizing Nearest-Neighbor Gaussian process (NNGP) models, SMB is estimated over the Antarctic ice sheet. An Antarctic SMB map is rendered using this model and is compared with previous estimates. A prediction uncertainty map is created to identify regions of high SMB uncertainty. The model estimates net SMB to be 2173 Gton yr-1 with 95% credible interval (2021,2331) Gton yr-1. On average, these results suggest lower Antarctic SMB and higher uncertainty than previously purported [Vaughan et al. (1999); Van de Berg et al. (2006); Arthern, Winebrenner and Vaughan (2006); Bromwich et al. (2004); Lenaerts et al. (2012)], even though this model utilizes significantly more observations than previous models. Using the Gaussian process' uncertainty and model parameters, we propose 15 new measurement locations for field study utilizing a maximin space-filling, error-minimizing design; these potential measurements are identied to minimize future estimation uncertainty. Using currently accepted Antarctic mass balance estimates and our SMB estimate, we estimate net mass loss [Shepherd et al. (2012); Jacob et al. (2012)]. Furthermore, we discuss modeling details for both space-time data and combining field measurement data with output from mathematical models using the NNGP framework.

Reduced Wiener Chaos representation of random fields via basis adaptation and projection

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

Tsilifis, Panagiotis, E-mail: tsilifis@usc.edu; Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089; Ghanem, Roger G., E-mail: ghanem@usc.edu

2017-07-15

A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.

Reduced Wiener Chaos representation of random fields via basis adaptation and projection

NASA Astrophysics Data System (ADS)

Tsilifis, Panagiotis; Ghanem, Roger G.

2017-07-01

A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.

Covariances and spectra of the kinematics and dynamics of nonlinear waves

NASA Technical Reports Server (NTRS)

Tung, C. C.; Huang, N. E.

1985-01-01

Using the Stokes waves as a model of nonlinear waves and considering the linear component as a narrow-band Gaussian process, the covariances and spectra of velocity and acceleration components and pressure for points in the vicinity of still water level were derived taking into consideration the effects of free surface fluctuations. The results are compared with those obtained earlier using linear Gaussian waves.

Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion

NASA Astrophysics Data System (ADS)

Sposini, Vittoria; Chechkin, Aleksei V.; Seno, Flavio; Pagnini, Gianni; Metzler, Ralf

2018-04-01

A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential (Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time-dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.

Semiparametric Identification of Human Arm Dynamics for Flexible Control of a Functional Electrical Stimulation Neuroprosthesis

PubMed Central

Schearer, Eric M.; Liao, Yu-Wei; Perreault, Eric J.; Tresch, Matthew C.; Memberg, William D.; Kirsch, Robert F.; Lynch, Kevin M.

2016-01-01

We present a method to identify the dynamics of a human arm controlled by an implanted functional electrical stimulation neuroprosthesis. The method uses Gaussian process regression to predict shoulder and elbow torques given the shoulder and elbow joint positions and velocities and the electrical stimulation inputs to muscles. We compare the accuracy of torque predictions of nonparametric, semiparametric, and parametric model types. The most accurate of the three model types is a semiparametric Gaussian process model that combines the flexibility of a black box function approximator with the generalization power of a parameterized model. The semiparametric model predicted torques during stimulation of multiple muscles with errors less than 20% of the total muscle torque and passive torque needed to drive the arm. The identified model allows us to define an arbitrary reaching trajectory and approximately determine the muscle stimulations required to drive the arm along that trajectory. PMID:26955041

Non-Gaussian analysis of diffusion weighted imaging in head and neck at 3T: a pilot study in patients with nasopharyngeal carcinoma.

PubMed

Yuan, Jing; Yeung, David Ka Wai; Mok, Greta S P; Bhatia, Kunwar S; Wang, Yi-Xiang J; Ahuja, Anil T; King, Ann D

2014-01-01

To technically investigate the non-Gaussian diffusion of head and neck diffusion weighted imaging (DWI) at 3 Tesla and compare advanced non-Gaussian diffusion models, including diffusion kurtosis imaging (DKI), stretched-exponential model (SEM), intravoxel incoherent motion (IVIM) and statistical model in the patients with nasopharyngeal carcinoma (NPC). After ethics approval was granted, 16 patients with NPC were examined using DWI performed at 3T employing an extended b-value range from 0 to 1500 s/mm(2). DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models on primary tumor, metastatic node, spinal cord and muscle. Non-Gaussian parameter maps were generated and compared to apparent diffusion coefficient (ADC) maps in NPC. Diffusion in NPC exhibited non-Gaussian behavior at the extended b-value range. Non-Gaussian models achieved significantly better fitting of DWI signal than the mono-exponential model. Non-Gaussian diffusion coefficients were substantially different from mono-exponential ADC both in magnitude and histogram distribution. Non-Gaussian diffusivity in head and neck tissues and NPC lesions could be assessed by using non-Gaussian diffusion models. Non-Gaussian DWI analysis may reveal additional tissue properties beyond ADC and holds potentials to be used as a complementary tool for NPC characterization.

Evaluation of the influence of double and triple Gaussian proton kernel models on accuracy of dose calculations for spot scanning technique.

PubMed

Hirayama, Shusuke; Takayanagi, Taisuke; Fujii, Yusuke; Fujimoto, Rintaro; Fujitaka, Shinichiro; Umezawa, Masumi; Nagamine, Yoshihiko; Hosaka, Masahiro; Yasui, Keisuke; Omachi, Chihiro; Toshito, Toshiyuki

2016-03-01

The main purpose in this study was to present the results of beam modeling and how the authors systematically investigated the influence of double and triple Gaussian proton kernel models on the accuracy of dose calculations for spot scanning technique. The accuracy of calculations was important for treatment planning software (TPS) because the energy, spot position, and absolute dose had to be determined by TPS for the spot scanning technique. The dose distribution was calculated by convolving in-air fluence with the dose kernel. The dose kernel was the in-water 3D dose distribution of an infinitesimal pencil beam and consisted of an integral depth dose (IDD) and a lateral distribution. Accurate modeling of the low-dose region was important for spot scanning technique because the dose distribution was formed by cumulating hundreds or thousands of delivered beams. The authors employed a double Gaussian function as the in-air fluence model of an individual beam. Double and triple Gaussian kernel models were also prepared for comparison. The parameters of the kernel lateral model were derived by fitting a simulated in-water lateral dose profile induced by an infinitesimal proton beam, whose emittance was zero, at various depths using Monte Carlo (MC) simulation. The fitted parameters were interpolated as a function of depth in water and stored as a separate look-up table. These stored parameters for each energy and depth in water were acquired from the look-up table when incorporating them into the TPS. The modeling process for the in-air fluence and IDD was based on the method proposed in the literature. These were derived using MC simulation and measured data. The authors compared the measured and calculated absolute doses at the center of the spread-out Bragg peak (SOBP) under various volumetric irradiation conditions to systematically investigate the influence of the two types of kernel models on the dose calculations. The authors investigated the difference between double and triple Gaussian kernel models. The authors found that the difference between the two studied kernel models appeared at mid-depths and the accuracy of predicting the double Gaussian model deteriorated at the low-dose bump that appeared at mid-depths. When the authors employed the double Gaussian kernel model, the accuracy of calculations for the absolute dose at the center of the SOBP varied with irradiation conditions and the maximum difference was 3.4%. In contrast, the results obtained from calculations with the triple Gaussian kernel model indicated good agreement with the measurements within ±1.1%, regardless of the irradiation conditions. The difference between the results obtained with the two types of studied kernel models was distinct in the high energy region. The accuracy of calculations with the double Gaussian kernel model varied with the field size and SOBP width because the accuracy of prediction with the double Gaussian model was insufficient at the low-dose bump. The evaluation was only qualitative under limited volumetric irradiation conditions. Further accumulation of measured data would be needed to quantitatively comprehend what influence the double and triple Gaussian kernel models had on the accuracy of dose calculations.

Gaussian random bridges and a geometric model for information equilibrium

NASA Astrophysics Data System (ADS)

Mengütürk, Levent Ali

2018-03-01

The paper introduces a class of conditioned stochastic processes that we call Gaussian random bridges (GRBs) and proves some of their properties. Due to the anticipative representation of any GRB as the sum of a random variable and a Gaussian (T , 0) -bridge, GRBs can model noisy information processes in partially observed systems. In this spirit, we propose an asset pricing model with respect to what we call information equilibrium in a market with multiple sources of information. The idea is to work on a topological manifold endowed with a metric that enables us to systematically determine an equilibrium point of a stochastic system that can be represented by multiple points on that manifold at each fixed time. In doing so, we formulate GRB-based information diversity over a Riemannian manifold and show that it is pinned to zero over the boundary determined by Dirac measures. We then define an influence factor that controls the dominance of an information source in determining the best estimate of a signal in the L2-sense. When there are two sources, this allows us to construct information equilibrium as a functional of a geodesic-valued stochastic process, which is driven by an equilibrium convergence rate representing the signal-to-noise ratio. This leads us to derive price dynamics under what can be considered as an equilibrium probability measure. We also provide a semimartingale representation of Markovian GRBs associated with Gaussian martingales and a non-anticipative representation of fractional Brownian random bridges that can incorporate degrees of information coupling in a given system via the Hurst exponent.

Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation

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

Ruban, V. P., E-mail: ruban@itp.ac.ru

2015-05-15

The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrödinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of roguemore » wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves.« less

Model selection using cosmic chronometers with Gaussian Processes

NASA Astrophysics Data System (ADS)

Melia, Fulvio; Yennapureddy, Manoj K.

2018-02-01

The use of Gaussian Processes with a measurement of the cosmic expansion rate based solely on the observation of cosmic chronometers provides a completely cosmology-independent reconstruction of the Hubble constant H(z) suitable for testing different models. The corresponding dispersion σH is smaller than ~ 9% over the entire redshift range (lesssim zlesssim 20) of the observations, rivaling many kinds of cosmological measurements available today. We use the reconstructed H(z) function to test six different cosmologies, and show that it favours the Rh=ct universe, which has only one free parameter (i.e., H0) over other models, including Planck ΛCDM . The parameters of the standard model may be re-optimized to improve the fits to the reconstructed H(z) function, but the results have smaller p-values than one finds with Rh=ct.

Numerical modeling of macrodispersion in heterogeneous media: a comparison of multi-Gaussian and non-multi-Gaussian models

NASA Astrophysics Data System (ADS)

Wen, Xian-Huan; Gómez-Hernández, J. Jaime

1998-03-01

The macrodispersion of an inert solute in a 2-D heterogeneous porous media is estimated numerically in a series of fields of varying heterogeneity. Four different random function (RF) models are used to model log-transmissivity (ln T) spatial variability, and for each of these models, ln T variance is varied from 0.1 to 2.0. The four RF models share the same univariate Gaussian histogram and the same isotropic covariance, but differ from one another in terms of the spatial connectivity patterns at extreme transmissivity values. More specifically, model A is a multivariate Gaussian model for which, by definition, extreme values (both high and low) are spatially uncorrelated. The other three models are non-multi-Gaussian: model B with high connectivity of high extreme values, model C with high connectivity of low extreme values, and model D with high connectivities of both high and low extreme values. Residence time distributions (RTDs) and macrodispersivities (longitudinal and transverse) are computed on ln T fields corresponding to the different RF models, for two different flow directions and at several scales. They are compared with each other, as well as with predicted values based on first-order analytical results. Numerically derived RTDs and macrodispersivities for the multi-Gaussian model are in good agreement with analytically derived values using first-order theories for log-transmissivity variance up to 2.0. The results from the non-multi-Gaussian models differ from each other and deviate largely from the multi-Gaussian results even when ln T variance is small. RTDs in non-multi-Gaussian realizations with high connectivity at high extreme values display earlier breakthrough than in multi-Gaussian realizations, whereas later breakthrough and longer tails are observed for RTDs from non-multi-Gaussian realizations with high connectivity at low extreme values. Longitudinal macrodispersivities in the non-multi-Gaussian realizations are, in general, larger than in the multi-Gaussian ones, while transverse macrodispersivities in the non-multi-Gaussian realizations can be larger or smaller than in the multi-Gaussian ones depending on the type of connectivity at extreme values. Comparing the numerical results for different flow directions, it is confirmed that macrodispersivities in multi-Gaussian realizations with isotropic spatial correlation are not flow direction-dependent. Macrodispersivities in the non-multi-Gaussian realizations, however, are flow direction-dependent although the covariance of ln T is isotropic (the same for all four models). It is important to account for high connectivities at extreme transmissivity values, a likely situation in some geological formations. Some of the discrepancies between first-order-based analytical results and field-scale tracer test data may be due to the existence of highly connected paths of extreme conductivity values.

Electrospining of polyaniline/poly(lactic acid) ultrathin fibers: process and statistical modeling using a non-gaussian approach

USDA-ARS?s Scientific Manuscript database

Cover: The electrospinning technique was employed to obtain conducting nanofibers based on polyaniline and poly(lactic acid). A statistical model was employed to describe how the process factors (solution concentration, applied voltage, and flow rate) govern the fiber dimensions. Nanofibers down to ...

Sensor Fusion of Gaussian Mixtures for Ballistic Target Tracking in the Re-Entry Phase

PubMed Central

Lu, Kelin; Zhou, Rui

2016-01-01

A sensor fusion methodology for the Gaussian mixtures model is proposed for ballistic target tracking with unknown ballistic coefficients. To improve the estimation accuracy, a track-to-track fusion architecture is proposed to fuse tracks provided by the local interacting multiple model filters. During the fusion process, the duplicate information is removed by considering the first order redundant information between the local tracks. With extensive simulations, we show that the proposed algorithm improves the tracking accuracy in ballistic target tracking in the re-entry phase applications. PMID:27537883

Sensor Fusion of Gaussian Mixtures for Ballistic Target Tracking in the Re-Entry Phase.

PubMed

Lu, Kelin; Zhou, Rui

2016-08-15

A sensor fusion methodology for the Gaussian mixtures model is proposed for ballistic target tracking with unknown ballistic coefficients. To improve the estimation accuracy, a track-to-track fusion architecture is proposed to fuse tracks provided by the local interacting multiple model filters. During the fusion process, the duplicate information is removed by considering the first order redundant information between the local tracks. With extensive simulations, we show that the proposed algorithm improves the tracking accuracy in ballistic target tracking in the re-entry phase applications.

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.

Non-Gaussian Analysis of Diffusion Weighted Imaging in Head and Neck at 3T: A Pilot Study in Patients with Nasopharyngeal Carcinoma

PubMed Central

Yuan, Jing; Yeung, David Ka Wai; Mok, Greta S. P.; Bhatia, Kunwar S.; Wang, Yi-Xiang J.; Ahuja, Anil T.; King, Ann D.

2014-01-01

Purpose To technically investigate the non-Gaussian diffusion of head and neck diffusion weighted imaging (DWI) at 3 Tesla and compare advanced non-Gaussian diffusion models, including diffusion kurtosis imaging (DKI), stretched-exponential model (SEM), intravoxel incoherent motion (IVIM) and statistical model in the patients with nasopharyngeal carcinoma (NPC). Materials and Methods After ethics approval was granted, 16 patients with NPC were examined using DWI performed at 3T employing an extended b-value range from 0 to 1500 s/mm2. DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models on primary tumor, metastatic node, spinal cord and muscle. Non-Gaussian parameter maps were generated and compared to apparent diffusion coefficient (ADC) maps in NPC. Results Diffusion in NPC exhibited non-Gaussian behavior at the extended b-value range. Non-Gaussian models achieved significantly better fitting of DWI signal than the mono-exponential model. Non-Gaussian diffusion coefficients were substantially different from mono-exponential ADC both in magnitude and histogram distribution. Conclusion Non-Gaussian diffusivity in head and neck tissues and NPC lesions could be assessed by using non-Gaussian diffusion models. Non-Gaussian DWI analysis may reveal additional tissue properties beyond ADC and holds potentials to be used as a complementary tool for NPC characterization. PMID:24466318

Model-checking techniques based on cumulative residuals.

PubMed

Lin, D Y; Wei, L J; Ying, Z

2002-03-01

Residuals have long been used for graphical and numerical examinations of the adequacy of regression models. Conventional residual analysis based on the plots of raw residuals or their smoothed curves is highly subjective, whereas most numerical goodness-of-fit tests provide little information about the nature of model misspecification. In this paper, we develop objective and informative model-checking techniques by taking the cumulative sums of residuals over certain coordinates (e.g., covariates or fitted values) or by considering some related aggregates of residuals, such as moving sums and moving averages. For a variety of statistical models and data structures, including generalized linear models with independent or dependent observations, the distributions of these stochastic processes tinder the assumed model can be approximated by the distributions of certain zero-mean Gaussian processes whose realizations can be easily generated by computer simulation. Each observed process can then be compared, both graphically and numerically, with a number of realizations from the Gaussian process. Such comparisons enable one to assess objectively whether a trend seen in a residual plot reflects model misspecification or natural variation. The proposed techniques are particularly useful in checking the functional form of a covariate and the link function. Illustrations with several medical studies are provided.

Analysis of Flow and Transport in non-Gaussian Heterogeneous Formations Using a Generalized Sub-Gaussian Model

NASA Astrophysics Data System (ADS)

Guadagnini, A.; Riva, M.; Neuman, S. P.

2016-12-01

Environmental quantities such as log hydraulic conductivity (or transmissivity), Y(x) = ln K(x), and their spatial (or temporal) increments, ΔY, are known to be generally non-Gaussian. Documented evidence of such behavior includes symmetry of increment distributions at all separation scales (or lags) between incremental values of Y with sharp peaks and heavy tails that decay asymptotically as lag increases. This statistical scaling occurs in porous as well as fractured media characterized by either one or a hierarchy of spatial correlation scales. In hierarchical media one observes a range of additional statistical ΔY scaling phenomena, all of which are captured comprehensibly by a novel generalized sub-Gaussian (GSG) model. In this model Y forms a mixture Y(x) = U(x) G(x) of single- or multi-scale Gaussian processes G having random variances, U being a non-negative subordinator independent of G. Elsewhere we developed ways to generate unconditional and conditional random realizations of isotropic or anisotropic GSG fields which can be embedded in numerical Monte Carlo flow and transport simulations. Here we present and discuss expressions for probability distribution functions of Y and ΔY as well as their lead statistical moments. We then focus on a simple flow setting of mean uniform steady state flow in an unbounded, two-dimensional domain, exploring ways in which non-Gaussian heterogeneity affects stochastic flow and transport descriptions. Our expressions represent (a) lead order autocovariance and cross-covariance functions of hydraulic head, velocity and advective particle displacement as well as (b) analogues of preasymptotic and asymptotic Fickian dispersion coefficients. We compare them with corresponding expressions developed in the literature for Gaussian Y.

Inverse Gaussian gamma distribution model for turbulence-induced fading in free-space optical communication.

PubMed

Cheng, Mingjian; Guo, Ya; Li, Jiangting; Zheng, Xiaotong; Guo, Lixin

2018-04-20

We introduce an alternative distribution to the gamma-gamma (GG) distribution, called inverse Gaussian gamma (IGG) distribution, which can efficiently describe moderate-to-strong irradiance fluctuations. The proposed stochastic model is based on a modulation process between small- and large-scale irradiance fluctuations, which are modeled by gamma and inverse Gaussian distributions, respectively. The model parameters of the IGG distribution are directly related to atmospheric parameters. The accuracy of the fit among the IGG, log-normal, and GG distributions with the experimental probability density functions in moderate-to-strong turbulence are compared, and results indicate that the newly proposed IGG model provides an excellent fit to the experimental data. As the receiving diameter is comparable with the atmospheric coherence radius, the proposed IGG model can reproduce the shape of the experimental data, whereas the GG and LN models fail to match the experimental data. The fundamental channel statistics of a free-space optical communication system are also investigated in an IGG-distributed turbulent atmosphere, and a closed-form expression for the outage probability of the system is derived with Meijer's G-function.

Assessment of parametric uncertainty for groundwater reactive transport modeling,

USGS Publications Warehouse

Shi, Xiaoqing; Ye, Ming; Curtis, Gary P.; Miller, Geoffery L.; Meyer, Philip D.; Kohler, Matthias; Yabusaki, Steve; Wu, Jichun

2014-01-01

The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gaussian assumption, Gaussian residuals are widely used. This paper shows that the residuals of the reactive transport model are non-Gaussian, heteroscedastic, and correlated in time; characterizing them requires using a generalized likelihood function such as the formal generalized likelihood function developed by Schoups and Vrugt (2010). For the surface complexation model considered in this study for simulating uranium reactive transport in groundwater, parametric uncertainty is quantified using the least squares regression methods and Bayesian methods with both Gaussian and formal generalized likelihood functions. While the least squares methods and Bayesian methods with Gaussian likelihood function produce similar Gaussian parameter distributions, the parameter distributions of Bayesian uncertainty quantification using the formal generalized likelihood function are non-Gaussian. In addition, predictive performance of formal generalized likelihood function is superior to that of least squares regression and Bayesian methods with Gaussian likelihood function. The Bayesian uncertainty quantification is conducted using the differential evolution adaptive metropolis (DREAM(zs)) algorithm; as a Markov chain Monte Carlo (MCMC) method, it is a robust tool for quantifying uncertainty in groundwater reactive transport models. For the surface complexation model, the regression-based local sensitivity analysis and Morris- and DREAM(ZS)-based global sensitivity analysis yield almost identical ranking of parameter importance. The uncertainty analysis may help select appropriate likelihood functions, improve model calibration, and reduce predictive uncertainty in other groundwater reactive transport and environmental modeling.

Common inputs in subthreshold membrane potential: The role of quiescent states in neuronal activity

NASA Astrophysics Data System (ADS)

Montangie, Lisandro; Montani, Fernando

2018-06-01

Experiments in certain regions of the cerebral cortex suggest that the spiking activity of neuronal populations is regulated by common non-Gaussian inputs across neurons. We model these deviations from random-walk processes with q -Gaussian distributions into simple threshold neurons, and investigate the scaling properties in large neural populations. We show that deviations from the Gaussian statistics provide a natural framework to regulate population statistics such as sparsity, entropy, and specific heat. This type of description allows us to provide an adequate strategy to explain the information encoding in the case of low neuronal activity and its possible implications on information transmission.

Inferring probabilistic stellar rotation periods using Gaussian processes

NASA Astrophysics Data System (ADS)

Angus, Ruth; Morton, Timothy; Aigrain, Suzanne; Foreman-Mackey, Daniel; Rajpaul, Vinesh

2018-02-01

Variability in the light curves of spotted, rotating stars is often non-sinusoidal and quasi-periodic - spots move on the stellar surface and have finite lifetimes, causing stellar flux variations to slowly shift in phase. A strictly periodic sinusoid therefore cannot accurately model a rotationally modulated stellar light curve. Physical models of stellar surfaces have many drawbacks preventing effective inference, such as highly degenerate or high-dimensional parameter spaces. In this work, we test an appropriate effective model: a Gaussian Process with a quasi-periodic covariance kernel function. This highly flexible model allows sampling of the posterior probability density function of the periodic parameter, marginalizing over the other kernel hyperparameters using a Markov Chain Monte Carlo approach. To test the effectiveness of this method, we infer rotation periods from 333 simulated stellar light curves, demonstrating that the Gaussian process method produces periods that are more accurate than both a sine-fitting periodogram and an autocorrelation function method. We also demonstrate that it works well on real data, by inferring rotation periods for 275 Kepler stars with previously measured periods. We provide a table of rotation periods for these and many more, altogether 1102 Kepler objects of interest, and their posterior probability density function samples. Because this method delivers posterior probability density functions, it will enable hierarchical studies involving stellar rotation, particularly those involving population modelling, such as inferring stellar ages, obliquities in exoplanet systems, or characterizing star-planet interactions. The code used to implement this method is available online.

Dynamic cardiac PET imaging: extraction of time-activity curves using ICA and a generalized Gaussian distribution model.

PubMed

Mabrouk, Rostom; Dubeau, François; Bentabet, Layachi

2013-01-01

Kinetic modeling of metabolic and physiologic cardiac processes in small animals requires an input function (IF) and a tissue time-activity curves (TACs). In this paper, we present a mathematical method based on independent component analysis (ICA) to extract the IF and the myocardium's TACs directly from dynamic positron emission tomography (PET) images. The method assumes a super-Gaussian distribution model for the blood activity, and a sub-Gaussian distribution model for the tissue activity. Our appreach was applied on 22 PET measurement sets of small animals, which were obtained from the three most frequently used cardiac radiotracers, namely: desoxy-fluoro-glucose ((18)F-FDG), [(13)N]-ammonia, and [(11)C]-acetate. Our study was extended to PET human measurements obtained with the Rubidium-82 ((82) Rb) radiotracer. The resolved mathematical IF values compare favorably to those derived from curves extracted from regions of interest (ROI), suggesting that the procedure presents a reliable alternative to serial blood sampling for small-animal cardiac PET studies.

Model Checking Techniques for Assessing Functional Form Specifications in Censored Linear Regression Models.

PubMed

León, Larry F; Cai, Tianxi

2012-04-01

In this paper we develop model checking techniques for assessing functional form specifications of covariates in censored linear regression models. These procedures are based on a censored data analog to taking cumulative sums of "robust" residuals over the space of the covariate under investigation. These cumulative sums are formed by integrating certain Kaplan-Meier estimators and may be viewed as "robust" censored data analogs to the processes considered by Lin, Wei & Ying (2002). The null distributions of these stochastic processes can be approximated by the distributions of certain zero-mean Gaussian processes whose realizations can be generated by computer simulation. Each observed process can then be graphically compared with a few realizations from the Gaussian process. We also develop formal test statistics for numerical comparison. Such comparisons enable one to assess objectively whether an apparent trend seen in a residual plot reects model misspecification or natural variation. We illustrate the methods with a well known dataset. In addition, we examine the finite sample performance of the proposed test statistics in simulation experiments. In our simulation experiments, the proposed test statistics have good power of detecting misspecification while at the same time controlling the size of the test.

NGMIX: Gaussian mixture models for 2D images

NASA Astrophysics Data System (ADS)

Sheldon, Erin

2015-08-01

NGMIX implements Gaussian mixture models for 2D images. Both the PSF profile and the galaxy are modeled using mixtures of Gaussians. Convolutions are thus performed analytically, resulting in fast model generation as compared to methods that perform the convolution in Fourier space. For the galaxy model, NGMIX supports exponential disks and de Vaucouleurs and Sérsic profiles; these are implemented approximately as a sum of Gaussians using the fits from Hogg & Lang (2013). Additionally, any number of Gaussians can be fit, either completely free or constrained to be cocentric and co-elliptical.

Clinical time series prediction: Toward a hierarchical dynamical system framework.

PubMed

Liu, Zitao; Hauskrecht, Milos

2015-09-01

Developing machine learning and data mining algorithms for building temporal models of clinical time series is important for understanding of the patient condition, the dynamics of a disease, effect of various patient management interventions and clinical decision making. In this work, we propose and develop a novel hierarchical framework for modeling clinical time series data of varied length and with irregularly sampled observations. Our hierarchical dynamical system framework for modeling clinical time series combines advantages of the two temporal modeling approaches: the linear dynamical system and the Gaussian process. We model the irregularly sampled clinical time series by using multiple Gaussian process sequences in the lower level of our hierarchical framework and capture the transitions between Gaussian processes by utilizing the linear dynamical system. The experiments are conducted on the complete blood count (CBC) panel data of 1000 post-surgical cardiac patients during their hospitalization. Our framework is evaluated and compared to multiple baseline approaches in terms of the mean absolute prediction error and the absolute percentage error. We tested our framework by first learning the time series model from data for the patients in the training set, and then using it to predict future time series values for the patients in the test set. We show that our model outperforms multiple existing models in terms of its predictive accuracy. Our method achieved a 3.13% average prediction accuracy improvement on ten CBC lab time series when it was compared against the best performing baseline. A 5.25% average accuracy improvement was observed when only short-term predictions were considered. A new hierarchical dynamical system framework that lets us model irregularly sampled time series data is a promising new direction for modeling clinical time series and for improving their predictive performance. Copyright © 2014 Elsevier B.V. All rights reserved.

Generalized Processing Tree Models: Jointly Modeling Discrete and Continuous Variables.

PubMed

Heck, Daniel W; Erdfelder, Edgar; Kieslich, Pascal J

2018-05-24

Multinomial processing tree models assume that discrete cognitive states determine observed response frequencies. Generalized processing tree (GPT) models extend this conceptual framework to continuous variables such as response times, process-tracing measures, or neurophysiological variables. GPT models assume finite-mixture distributions, with weights determined by a processing tree structure, and continuous components modeled by parameterized distributions such as Gaussians with separate or shared parameters across states. We discuss identifiability, parameter estimation, model testing, a modeling syntax, and the improved precision of GPT estimates. Finally, a GPT version of the feature comparison model of semantic categorization is applied to computer-mouse trajectories.

Investigation of non-Gaussian effects in the Brazilian option market

NASA Astrophysics Data System (ADS)

Sosa-Correa, William O.; Ramos, Antônio M. T.; Vasconcelos, Giovani L.

2018-04-01

An empirical study of the Brazilian option market is presented in light of three option pricing models, namely the Black-Scholes model, the exponential model, and a model based on a power law distribution, the so-called q-Gaussian distribution or Tsallis distribution. It is found that the q-Gaussian model performs better than the Black-Scholes model in about one third of the option chains analyzed. But among these cases, the exponential model performs better than the q-Gaussian model in 75% of the time. The superiority of the exponential model over the q-Gaussian model is particularly impressive for options close to the expiration date, where its success rate rises above ninety percent.

Mathematic model analysis of Gaussian beam propagation through an arbitrary thickness random phase screen.

PubMed

Tian, Yuzhen; Guo, Jin; Wang, Rui; Wang, Tingfeng

2011-09-12

In order to research the statistical properties of Gaussian beam propagation through an arbitrary thickness random phase screen for adaptive optics and laser communication application in the laboratory, we establish mathematic models of statistical quantities, which are based on the Rytov method and the thin phase screen model, involved in the propagation process. And the analytic results are developed for an arbitrary thickness phase screen based on the Kolmogorov power spectrum. The comparison between the arbitrary thickness phase screen and the thin phase screen shows that it is more suitable for our results to describe the generalized case, especially the scintillation index.

Approximate bandpass and frequency response models of the difference of Gaussian filter

NASA Astrophysics Data System (ADS)

Birch, Philip; Mitra, Bhargav; Bangalore, Nagachetan M.; Rehman, Saad; Young, Rupert; Chatwin, Chris

2010-12-01

The Difference of Gaussian (DOG) filter is widely used in optics and image processing as, among other things, an edge detection and correlation filter. It has important biological applications and appears to be part of the mammalian vision system. In this paper we analyse the filter and provide details of the full width half maximum, bandwidth and frequency response in order to aid the full characterisation of its performance.

Nonlinear and non-Gaussian Bayesian based handwriting beautification

NASA Astrophysics Data System (ADS)

Shi, Cao; Xiao, Jianguo; Xu, Canhui; Jia, Wenhua

2013-03-01

A framework is proposed in this paper to effectively and efficiently beautify handwriting by means of a novel nonlinear and non-Gaussian Bayesian algorithm. In the proposed framework, format and size of handwriting image are firstly normalized, and then typeface in computer system is applied to optimize vision effect of handwriting. The Bayesian statistics is exploited to characterize the handwriting beautification process as a Bayesian dynamic model. The model parameters to translate, rotate and scale typeface in computer system are controlled by state equation, and the matching optimization between handwriting and transformed typeface is employed by measurement equation. Finally, the new typeface, which is transformed from the original one and gains the best nonlinear and non-Gaussian optimization, is the beautification result of handwriting. Experimental results demonstrate the proposed framework provides a creative handwriting beautification methodology to improve visual acceptance.

Gaussian process tomography for soft x-ray spectroscopy at WEST without equilibrium information

NASA Astrophysics Data System (ADS)

Wang, T.; Mazon, D.; Svensson, J.; Li, D.; Jardin, A.; Verdoolaege, G.

2018-06-01

Gaussian process tomography (GPT) is a recently developed tomography method based on the Bayesian probability theory [J. Svensson, JET Internal Report EFDA-JET-PR(11)24, 2011 and Li et al., Rev. Sci. Instrum. 84, 083506 (2013)]. By modeling the soft X-ray (SXR) emissivity field in a poloidal cross section as a Gaussian process, the Bayesian SXR tomography can be carried out in a robust and extremely fast way. Owing to the short execution time of the algorithm, GPT is an important candidate for providing real-time reconstructions with a view to impurity transport and fast magnetohydrodynamic control. In addition, the Bayesian formalism allows quantifying uncertainty on the inferred parameters. In this paper, the GPT technique is validated using a synthetic data set expected from the WEST tokamak, and the results are shown of its application to the reconstruction of SXR emissivity profiles measured on Tore Supra. The method is compared with the standard algorithm based on minimization of the Fisher information.

Assessment of DPOAE test-retest difference curves via hierarchical Gaussian processes.

PubMed

Bao, Junshu; Hanson, Timothy; McMillan, Garnett P; Knight, Kristin

2017-03-01

Distortion product otoacoustic emissions (DPOAE) testing is a promising alternative to behavioral hearing tests and auditory brainstem response testing of pediatric cancer patients. The central goal of this study is to assess whether significant changes in the DPOAE frequency/emissions curve (DP-gram) occur in pediatric patients in a test-retest scenario. This is accomplished through the construction of normal reference charts, or credible regions, that DP-gram differences lie in, as well as contour probabilities that measure how abnormal (or in a certain sense rare) a test-retest difference is. A challenge is that the data were collected over varying frequencies, at different time points from baseline, and on possibly one or both ears. A hierarchical structural equation Gaussian process model is proposed to handle the different sources of correlation in the emissions measurements, wherein both subject-specific random effects and variance components governing the smoothness and variability of each child's Gaussian process are coupled together. © 2016, The International Biometric Society.

Recovering Galaxy Properties Using Gaussian Process SED Fitting

NASA Astrophysics Data System (ADS)

Iyer, Kartheik; Awan, Humna

2018-01-01

Information about physical quantities like the stellar mass, star formation rates, and ages for distant galaxies is contained in their spectral energy distributions (SEDs), obtained through photometric surveys like SDSS, CANDELS, LSST etc. However, noise in the photometric observations often is a problem, and using naive machine learning methods to estimate physical quantities can result in overfitting the noise, or converging on solutions that lie outside the physical regime of parameter space.We use Gaussian Process regression trained on a sample of SEDs corresponding to galaxies from a Semi-Analytic model (Somerville+15a) to estimate their stellar masses, and compare its performance to a variety of different methods, including simple linear regression, Random Forests, and k-Nearest Neighbours. We find that the Gaussian Process method is robust to noise and predicts not only stellar masses but also their uncertainties. The method is also robust in the cases where the distribution of the training data is not identical to the target data, which can be extremely useful when generalized to more subtle galaxy properties.

Truncated Gaussians as tolerance sets

NASA Technical Reports Server (NTRS)

Cozman, Fabio; Krotkov, Eric

1994-01-01

This work focuses on the use of truncated Gaussian distributions as models for bounded data measurements that are constrained to appear between fixed limits. The authors prove that the truncated Gaussian can be viewed as a maximum entropy distribution for truncated bounded data, when mean and covariance are given. The characteristic function for the truncated Gaussian is presented; from this, algorithms are derived for calculation of mean, variance, summation, application of Bayes rule and filtering with truncated Gaussians. As an example of the power of their methods, a derivation of the disparity constraint (used in computer vision) from their models is described. The authors' approach complements results in Statistics, but their proposal is not only to use the truncated Gaussian as a model for selected data; they propose to model measurements as fundamentally in terms of truncated Gaussians.

Yes, the GIGP Really Does Work--And Is Workable!

ERIC Educational Resources Information Center

Burrell, Quentin L.; Fenton, Michael R.

1993-01-01

Discusses the generalized inverse Gaussian-Poisson (GIGP) process for informetric modeling. Negative binomial distribution is discussed, construction of the GIGP process is explained, zero-truncated GIGP is considered, and applications of the process with journals, library circulation statistics, and database index terms are described. (50…

Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment.

PubMed

Wang, Fei; Liang, Chunhao; Yuan, Yangsheng; Cai, Yangjian

2014-09-22

A new kind of partially coherent beam with non-conventional correlation function named generalized multi-Gaussian correlated Schell-model (GMGCSM) beam is proposed. The GMGCSM beam of the first or second kind is capable of producing dark hollow or flat-topped beam profile in the focal plane (or in the far field). Furthermore, we carry out experimental generation of a GMGCSM beam of the first or second kind, and measure its focused intensity. Our experimental results verify theoretical predictions. The GMGCSM beam will be useful for free-space optical communications, material thermal processing, particle or atom trapping.

Bayesian modelling of the emission spectrum of the Joint European Torus Lithium Beam Emission Spectroscopy system.

PubMed

Kwak, Sehyun; Svensson, J; Brix, M; Ghim, Y-C

2016-02-01

A Bayesian model of the emission spectrum of the JET lithium beam has been developed to infer the intensity of the Li I (2p-2s) line radiation and associated uncertainties. The detected spectrum for each channel of the lithium beam emission spectroscopy system is here modelled by a single Li line modified by an instrumental function, Bremsstrahlung background, instrumental offset, and interference filter curve. Both the instrumental function and the interference filter curve are modelled with non-parametric Gaussian processes. All free parameters of the model, the intensities of the Li line, Bremsstrahlung background, and instrumental offset, are inferred using Bayesian probability theory with a Gaussian likelihood for photon statistics and electronic background noise. The prior distributions of the free parameters are chosen as Gaussians. Given these assumptions, the intensity of the Li line and corresponding uncertainties are analytically available using a Bayesian linear inversion technique. The proposed approach makes it possible to extract the intensity of Li line without doing a separate background subtraction through modulation of the Li beam.

Long-Term Deflection Prediction from Computer Vision-Measured Data History for High-Speed Railway Bridges

PubMed Central

Lee, Jaebeom; Lee, Young-Joo

2018-01-01

Management of the vertical long-term deflection of a high-speed railway bridge is a crucial factor to guarantee traffic safety and passenger comfort. Therefore, there have been efforts to predict the vertical deflection of a railway bridge based on physics-based models representing various influential factors to vertical deflection such as concrete creep and shrinkage. However, it is not an easy task because the vertical deflection of a railway bridge generally involves several sources of uncertainty. This paper proposes a probabilistic method that employs a Gaussian process to construct a model to predict the vertical deflection of a railway bridge based on actual vision-based measurement and temperature. To deal with the sources of uncertainty which may cause prediction errors, a Gaussian process is modeled with multiple kernels and hyperparameters. Once the hyperparameters are identified through the Gaussian process regression using training data, the proposed method provides a 95% prediction interval as well as a predictive mean about the vertical deflection of the bridge. The proposed method is applied to an arch bridge under operation for high-speed trains in South Korea. The analysis results obtained from the proposed method show good agreement with the actual measurement data on the vertical deflection of the example bridge, and the prediction results can be utilized for decision-making on railway bridge maintenance. PMID:29747421

Long-Term Deflection Prediction from Computer Vision-Measured Data History for High-Speed Railway Bridges.

PubMed

Lee, Jaebeom; Lee, Kyoung-Chan; Lee, Young-Joo

2018-05-09

Management of the vertical long-term deflection of a high-speed railway bridge is a crucial factor to guarantee traffic safety and passenger comfort. Therefore, there have been efforts to predict the vertical deflection of a railway bridge based on physics-based models representing various influential factors to vertical deflection such as concrete creep and shrinkage. However, it is not an easy task because the vertical deflection of a railway bridge generally involves several sources of uncertainty. This paper proposes a probabilistic method that employs a Gaussian process to construct a model to predict the vertical deflection of a railway bridge based on actual vision-based measurement and temperature. To deal with the sources of uncertainty which may cause prediction errors, a Gaussian process is modeled with multiple kernels and hyperparameters. Once the hyperparameters are identified through the Gaussian process regression using training data, the proposed method provides a 95% prediction interval as well as a predictive mean about the vertical deflection of the bridge. The proposed method is applied to an arch bridge under operation for high-speed trains in South Korea. The analysis results obtained from the proposed method show good agreement with the actual measurement data on the vertical deflection of the example bridge, and the prediction results can be utilized for decision-making on railway bridge maintenance.

A qualitative assessment of a random process proposed as an atmospheric turbulence model

NASA Technical Reports Server (NTRS)

Sidwell, K.

1977-01-01

A random process is formed by the product of two Gaussian processes and the sum of that product with a third Gaussian process. The resulting total random process is interpreted as the sum of an amplitude modulated process and a slowly varying, random mean value. The properties of the process are examined, including an interpretation of the process in terms of the physical structure of atmospheric motions. The inclusion of the mean value variation gives an improved representation of the properties of atmospheric motions, since the resulting process can account for the differences in the statistical properties of atmospheric velocity components and their gradients. The application of the process to atmospheric turbulence problems, including the response of aircraft dynamic systems, is examined. The effects of the mean value variation upon aircraft loads are small in most cases, but can be important in the measurement and interpretation of atmospheric turbulence data.

The area of isodensity contours in cosmological models and galaxy surveys

NASA Technical Reports Server (NTRS)

Ryden, Barbara S.; Melott, Adrian L.; Craig, David A.; Gott, J. Richard, III; Weinberg, David H.

1989-01-01

The contour crossing statistic, defined as the mean number of times per unit length that a straight line drawn through the field crosses a given contour, is applied to model density fields and to smoothed samples of galaxies. Models in which the matter is in a bubble structure, in a filamentary net, or in clusters can be distinguished from Gaussian density distributions. The shape of the contour crossing curve in the initially Gaussian fields considered remains Gaussian after gravitational evolution and biasing, as long as the smoothing length is longer than the mass correlation length. With a smoothing length of 5/h Mpc, models containing cosmic strings are indistinguishable from Gaussian distributions. Cosmic explosion models are significantly non-Gaussian, having a bubbly structure. Samples from the CfA survey and the Haynes and Giovanelli (1986) survey are more strongly non-Gaussian at a smoothing length of 6/h Mpc than any of the models examined. At a smoothing length of 12/h Mpc, the Haynes and Giovanelli sample appears Gaussian.

Connections between Graphical Gaussian Models and Factor Analysis

ERIC Educational Resources Information Center

Salgueiro, M. Fatima; Smith, Peter W. F.; McDonald, John W.

2010-01-01

Connections between graphical Gaussian models and classical single-factor models are obtained by parameterizing the single-factor model as a graphical Gaussian model. Models are represented by independence graphs, and associations between each manifest variable and the latent factor are measured by factor partial correlations. Power calculations…

A path integral approach to the Hodgkin-Huxley model

NASA Astrophysics Data System (ADS)

Baravalle, Roman; Rosso, Osvaldo A.; Montani, Fernando

2017-11-01

To understand how single neurons process sensory information, it is necessary to develop suitable stochastic models to describe the response variability of the recorded spike trains. Spikes in a given neuron are produced by the synergistic action of sodium and potassium of the voltage-dependent channels that open or close the gates. Hodgkin and Huxley (HH) equations describe the ionic mechanisms underlying the initiation and propagation of action potentials, through a set of nonlinear ordinary differential equations that approximate the electrical characteristics of the excitable cell. Path integral provides an adequate approach to compute quantities such as transition probabilities, and any stochastic system can be expressed in terms of this methodology. We use the technique of path integrals to determine the analytical solution driven by a non-Gaussian colored noise when considering the HH equations as a stochastic system. The different neuronal dynamics are investigated by estimating the path integral solutions driven by a non-Gaussian colored noise q. More specifically we take into account the correlational structures of the complex neuronal signals not just by estimating the transition probability associated to the Gaussian approach of the stochastic HH equations, but instead considering much more subtle processes accounting for the non-Gaussian noise that could be induced by the surrounding neural network and by feedforward correlations. This allows us to investigate the underlying dynamics of the neural system when different scenarios of noise correlations are considered.

Modeling methods for merging computational and experimental aerodynamic pressure data

NASA Astrophysics Data System (ADS)

Haderlie, Jacob C.

This research describes a process to model surface pressure data sets as a function of wing geometry from computational and wind tunnel sources and then merge them into a single predicted value. The described merging process will enable engineers to integrate these data sets with the goal of utilizing the advantages of each data source while overcoming the limitations of both; this provides a single, combined data set to support analysis and design. The main challenge with this process is accurately representing each data source everywhere on the wing. Additionally, this effort demonstrates methods to model wind tunnel pressure data as a function of angle of attack as an initial step towards a merging process that uses both location on the wing and flow conditions (e.g., angle of attack, flow velocity or Reynold's number) as independent variables. This surrogate model of pressure as a function of angle of attack can be useful for engineers that need to predict the location of zero-order discontinuities, e.g., flow separation or normal shocks. Because, to the author's best knowledge, there is no published, well-established merging method for aerodynamic pressure data (here, the coefficient of pressure Cp), this work identifies promising modeling and merging methods, and then makes a critical comparison of these methods. Surrogate models represent the pressure data for both data sets. Cubic B-spline surrogate models represent the computational simulation results. Machine learning and multi-fidelity surrogate models represent the experimental data. This research compares three surrogates for the experimental data (sequential--a.k.a. online--Gaussian processes, batch Gaussian processes, and multi-fidelity additive corrector) on the merits of accuracy and computational cost. The Gaussian process (GP) methods employ cubic B-spline CFD surrogates as a model basis function to build a surrogate model of the WT data, and this usage of the CFD surrogate in building the WT data could serve as a "merging" because the resulting WT pressure prediction uses information from both sources. In the GP approach, this model basis function concept seems to place more "weight" on the Cp values from the wind tunnel (WT) because the GP surrogate uses the CFD to approximate the WT data values. Conversely, the computationally inexpensive additive corrector method uses the CFD B-spline surrogate to define the shape of the spanwise distribution of the Cp while minimizing prediction error at all spanwise locations for a given arc length position; this, too, combines information from both sources to make a prediction of the 2-D WT-based Cp distribution, but the additive corrector approach gives more weight to the CFD prediction than to the WT data. Three surrogate models of the experimental data as a function of angle of attack are also compared for accuracy and computational cost. These surrogates are a single Gaussian process model (a single "expert"), product of experts, and generalized product of experts. The merging approach provides a single pressure distribution that combines experimental and computational data. The batch Gaussian process method provides a relatively accurate surrogate that is computationally acceptable, and can receive wind tunnel data from port locations that are not necessarily parallel to a variable direction. On the other hand, the sequential Gaussian process and additive corrector methods must receive a sufficient number of data points aligned with one direction, e.g., from pressure port bands (tap rows) aligned with the freestream. The generalized product of experts best represents wind tunnel pressure as a function of angle of attack, but at higher computational cost than the single expert approach. The format of the application data from computational and experimental sources in this work precluded the merging process from including flow condition variables (e.g., angle of attack) in the independent variables, so the merging process is only conducted in the wing geometry variables of arc length and span. The merging process of Cp data allows a more "hands-off" approach to aircraft design and analysis, (i.e., not as many engineers needed to debate the Cp distribution shape) and generates Cp predictions at any location on the wing. However, the cost with these benefits are engineer time (learning how to build surrogates), computational time in constructing the surrogates, and surrogate accuracy (surrogates introduce error into data predictions). This dissertation effort used the Trap Wing / First AIAA CFD High-Lift Prediction Workshop as a relevant transonic wing with a multi-element high-lift system, and this work identified that the batch GP model for the WT data and the B-spline surrogate for the CFD might best be combined using expert belief weights to describe Cp as a function of location on the wing element surface. (Abstract shortened by ProQuest.).

Cosmology on ultralarge scales with intensity mapping of the neutral hydrogen 21 cm emission: limits on primordial non-Gaussianity.

PubMed

Camera, Stefano; Santos, Mário G; Ferreira, Pedro G; Ferramacho, Luís

2013-10-25

The large-scale structure of the Universe supplies crucial information about the physical processes at play at early times. Unresolved maps of the intensity of 21 cm emission from neutral hydrogen HI at redshifts z=/~1-5 are the best hope of accessing the ultralarge-scale information, directly related to the early Universe. A purpose-built HI intensity experiment may be used to detect the large scale effects of primordial non-Gaussianity, placing stringent bounds on different models of inflation. We argue that it may be possible to place tight constraints on the non-Gaussianity parameter f(NL), with an error close to σ(f(NL))~1.

Comparisons of non-Gaussian statistical models in DNA methylation analysis.

PubMed

Ma, Zhanyu; Teschendorff, Andrew E; Yu, Hong; Taghia, Jalil; Guo, Jun

2014-06-16

As a key regulatory mechanism of gene expression, DNA methylation patterns are widely altered in many complex genetic diseases, including cancer. DNA methylation is naturally quantified by bounded support data; therefore, it is non-Gaussian distributed. In order to capture such properties, we introduce some non-Gaussian statistical models to perform dimension reduction on DNA methylation data. Afterwards, non-Gaussian statistical model-based unsupervised clustering strategies are applied to cluster the data. Comparisons and analysis of different dimension reduction strategies and unsupervised clustering methods are presented. Experimental results show that the non-Gaussian statistical model-based methods are superior to the conventional Gaussian distribution-based method. They are meaningful tools for DNA methylation analysis. Moreover, among several non-Gaussian methods, the one that captures the bounded nature of DNA methylation data reveals the best clustering performance.

Comparisons of Non-Gaussian Statistical Models in DNA Methylation Analysis

PubMed Central

Ma, Zhanyu; Teschendorff, Andrew E.; Yu, Hong; Taghia, Jalil; Guo, Jun

2014-01-01

As a key regulatory mechanism of gene expression, DNA methylation patterns are widely altered in many complex genetic diseases, including cancer. DNA methylation is naturally quantified by bounded support data; therefore, it is non-Gaussian distributed. In order to capture such properties, we introduce some non-Gaussian statistical models to perform dimension reduction on DNA methylation data. Afterwards, non-Gaussian statistical model-based unsupervised clustering strategies are applied to cluster the data. Comparisons and analysis of different dimension reduction strategies and unsupervised clustering methods are presented. Experimental results show that the non-Gaussian statistical model-based methods are superior to the conventional Gaussian distribution-based method. They are meaningful tools for DNA methylation analysis. Moreover, among several non-Gaussian methods, the one that captures the bounded nature of DNA methylation data reveals the best clustering performance. PMID:24937687

Gaussian process based intelligent sampling for measuring nano-structure surfaces

NASA Astrophysics Data System (ADS)

Sun, L. J.; Ren, M. J.; Yin, Y. H.

2016-09-01

Nanotechnology is the science and engineering that manipulate matters at nano scale, which can be used to create many new materials and devices with a vast range of applications. As the nanotech product increasingly enters the commercial marketplace, nanometrology becomes a stringent and enabling technology for the manipulation and the quality control of the nanotechnology. However, many measuring instruments, for instance scanning probe microscopy, are limited to relatively small area of hundreds of micrometers with very low efficiency. Therefore some intelligent sampling strategies should be required to improve the scanning efficiency for measuring large area. This paper presents a Gaussian process based intelligent sampling method to address this problem. The method makes use of Gaussian process based Bayesian regression as a mathematical foundation to represent the surface geometry, and the posterior estimation of Gaussian process is computed by combining the prior probability distribution with the maximum likelihood function. Then each sampling point is adaptively selected by determining the position which is the most likely outside of the required tolerance zone among the candidates and then inserted to update the model iteratively. Both simulationson the nominal surface and manufactured surface have been conducted on nano-structure surfaces to verify the validity of the proposed method. The results imply that the proposed method significantly improves the measurement efficiency in measuring large area structured surfaces.

Gaussian Process Regression (GPR) Representation in Predictive Model Markup Language (PMML)

PubMed Central

Lechevalier, D.; Ak, R.; Ferguson, M.; Law, K. H.; Lee, Y.-T. T.; Rachuri, S.

2017-01-01

This paper describes Gaussian process regression (GPR) models presented in predictive model markup language (PMML). PMML is an extensible-markup-language (XML) -based standard language used to represent data-mining and predictive analytic models, as well as pre- and post-processed data. The previous PMML version, PMML 4.2, did not provide capabilities for representing probabilistic (stochastic) machine-learning algorithms that are widely used for constructing predictive models taking the associated uncertainties into consideration. The newly released PMML version 4.3, which includes the GPR model, provides new features: confidence bounds and distribution for the predictive estimations. Both features are needed to establish the foundation for uncertainty quantification analysis. Among various probabilistic machine-learning algorithms, GPR has been widely used for approximating a target function because of its capability of representing complex input and output relationships without predefining a set of basis functions, and predicting a target output with uncertainty quantification. GPR is being employed to various manufacturing data-analytics applications, which necessitates representing this model in a standardized form for easy and rapid employment. In this paper, we present a GPR model and its representation in PMML. Furthermore, we demonstrate a prototype using a real data set in the manufacturing domain. PMID:29202125

Gaussian Process Regression (GPR) Representation in Predictive Model Markup Language (PMML).

PubMed

Park, J; Lechevalier, D; Ak, R; Ferguson, M; Law, K H; Lee, Y-T T; Rachuri, S

2017-01-01

This paper describes Gaussian process regression (GPR) models presented in predictive model markup language (PMML). PMML is an extensible-markup-language (XML) -based standard language used to represent data-mining and predictive analytic models, as well as pre- and post-processed data. The previous PMML version, PMML 4.2, did not provide capabilities for representing probabilistic (stochastic) machine-learning algorithms that are widely used for constructing predictive models taking the associated uncertainties into consideration. The newly released PMML version 4.3, which includes the GPR model, provides new features: confidence bounds and distribution for the predictive estimations. Both features are needed to establish the foundation for uncertainty quantification analysis. Among various probabilistic machine-learning algorithms, GPR has been widely used for approximating a target function because of its capability of representing complex input and output relationships without predefining a set of basis functions, and predicting a target output with uncertainty quantification. GPR is being employed to various manufacturing data-analytics applications, which necessitates representing this model in a standardized form for easy and rapid employment. In this paper, we present a GPR model and its representation in PMML. Furthermore, we demonstrate a prototype using a real data set in the manufacturing domain.

Towards better modelling of drug-loading in solid lipid nanoparticles: Molecular dynamics, docking experiments and Gaussian Processes machine learning.

PubMed

Hathout, Rania M; Metwally, Abdelkader A

2016-11-01

This study represents one of the series applying computer-oriented processes and tools in digging for information, analysing data and finally extracting correlations and meaningful outcomes. In this context, binding energies could be used to model and predict the mass of loaded drugs in solid lipid nanoparticles after molecular docking of literature-gathered drugs using MOE® software package on molecularly simulated tripalmitin matrices using GROMACS®. Consequently, Gaussian processes as a supervised machine learning artificial intelligence technique were used to correlate the drugs' descriptors (e.g. M.W., xLogP, TPSA and fragment complexity) with their molecular docking binding energies. Lower percentage bias was obtained compared to previous studies which allows the accurate estimation of the loaded mass of any drug in the investigated solid lipid nanoparticles by just projecting its chemical structure to its main features (descriptors). Copyright © 2016 Elsevier B.V. All rights reserved.

Recognition Memory zROC Slopes for Items with Correct versus Incorrect Source Decisions Discriminate the Dual Process and Unequal Variance Signal Detection Models

ERIC Educational Resources Information Center

Starns, Jeffrey J.; Rotello, Caren M.; Hautus, Michael J.

2014-01-01

We tested the dual process and unequal variance signal detection models by jointly modeling recognition and source confidence ratings. The 2 approaches make unique predictions for the slope of the recognition memory zROC function for items with correct versus incorrect source decisions. The standard bivariate Gaussian version of the unequal…

Adaptive design of an X-ray magnetic circular dichroism spectroscopy experiment with Gaussian process modelling

NASA Astrophysics Data System (ADS)

Ueno, Tetsuro; Hino, Hideitsu; Hashimoto, Ai; Takeichi, Yasuo; Sawada, Masahiro; Ono, Kanta

2018-01-01

Spectroscopy is a widely used experimental technique, and enhancing its efficiency can have a strong impact on materials research. We propose an adaptive design for spectroscopy experiments that uses a machine learning technique to improve efficiency. We examined X-ray magnetic circular dichroism (XMCD) spectroscopy for the applicability of a machine learning technique to spectroscopy. An XMCD spectrum was predicted by Gaussian process modelling with learning of an experimental spectrum using a limited number of observed data points. Adaptive sampling of data points with maximum variance of the predicted spectrum successfully reduced the total data points for the evaluation of magnetic moments while providing the required accuracy. The present method reduces the time and cost for XMCD spectroscopy and has potential applicability to various spectroscopies.

Random mechanics: Nonlinear vibrations, turbulences, seisms, swells, fatigue

NASA Astrophysics Data System (ADS)

Kree, P.; Soize, C.

The random modeling of physical phenomena, together with probabilistic methods for the numerical calculation of random mechanical forces, are analytically explored. Attention is given to theoretical examinations such as probabilistic concepts, linear filtering techniques, and trajectory statistics. Applications of the methods to structures experiencing atmospheric turbulence, the quantification of turbulence, and the dynamic responses of the structures are considered. A probabilistic approach is taken to study the effects of earthquakes on structures and to the forces exerted by ocean waves on marine structures. Theoretical analyses by means of vector spaces and stochastic modeling are reviewed, as are Markovian formulations of Gaussian processes and the definition of stochastic differential equations. Finally, random vibrations with a variable number of links and linear oscillators undergoing the square of Gaussian processes are investigated.

Adaptive Sensing of Time Series with Application to Remote Exploration

NASA Technical Reports Server (NTRS)

Thompson, David R.; Cabrol, Nathalie A.; Furlong, Michael; Hardgrove, Craig; Low, Bryan K. H.; Moersch, Jeffrey; Wettergreen, David

2013-01-01

We address the problem of adaptive informationoptimal data collection in time series. Here a remote sensor or explorer agent throttles its sampling rate in order to track anomalous events while obeying constraints on time and power. This problem is challenging because the agent has limited visibility -- all collected datapoints lie in the past, but its resource allocation decisions require predicting far into the future. Our solution is to continually fit a Gaussian process model to the latest data and optimize the sampling plan on line to maximize information gain. We compare the performance characteristics of stationary and nonstationary Gaussian process models. We also describe an application based on geologic analysis during planetary rover exploration. Here adaptive sampling can improve coverage of localized anomalies and potentially benefit mission science yield of long autonomous traverses.

Gaussian process-based surrogate modeling framework for process planning in laser powder-bed fusion additive manufacturing of 316L stainless steel

DOE PAGES

Tapia, Gustavo; Khairallah, Saad A.; Matthews, Manyalibo J.; ...

2017-09-22

Here, Laser Powder-Bed Fusion (L-PBF) metal-based additive manufacturing (AM) is complex and not fully understood. Successful processing for one material, might not necessarily apply to a different material. This paper describes a workflow process that aims at creating a material data sheet standard that describes regimes where the process can be expected to be robust. The procedure consists of building a Gaussian process-based surrogate model of the L-PBF process that predicts melt pool depth in single-track experiments given a laser power, scan speed, and laser beam size combination. The predictions are then mapped onto a power versus scan speed diagrammore » delimiting the conduction from the keyhole melting controlled regimes. This statistical framework is shown to be robust even for cases where experimental training data might be suboptimal in quality, if appropriate physics-based filters are applied. Additionally, it is demonstrated that a high-fidelity simulation model of L-PBF can equally be successfully used for building a surrogate model, which is beneficial since simulations are getting more efficient and are more practical to study the response of different materials, than to re-tool an AM machine for new material powder.« less

Gaussian process-based surrogate modeling framework for process planning in laser powder-bed fusion additive manufacturing of 316L stainless steel

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

Tapia, Gustavo; Khairallah, Saad A.; Matthews, Manyalibo J.

Here, Laser Powder-Bed Fusion (L-PBF) metal-based additive manufacturing (AM) is complex and not fully understood. Successful processing for one material, might not necessarily apply to a different material. This paper describes a workflow process that aims at creating a material data sheet standard that describes regimes where the process can be expected to be robust. The procedure consists of building a Gaussian process-based surrogate model of the L-PBF process that predicts melt pool depth in single-track experiments given a laser power, scan speed, and laser beam size combination. The predictions are then mapped onto a power versus scan speed diagrammore » delimiting the conduction from the keyhole melting controlled regimes. This statistical framework is shown to be robust even for cases where experimental training data might be suboptimal in quality, if appropriate physics-based filters are applied. Additionally, it is demonstrated that a high-fidelity simulation model of L-PBF can equally be successfully used for building a surrogate model, which is beneficial since simulations are getting more efficient and are more practical to study the response of different materials, than to re-tool an AM machine for new material powder.« less

A comparative assessment of preclinical chemotherapeutic response of tumors using quantitative non-Gaussian diffusion MRI

PubMed Central

Xu, Junzhong; Li, Ke; Smith, R. Adam; Waterton, John C.; Zhao, Ping; Ding, Zhaohua; Does, Mark D.; Manning, H. Charles; Gore, John C.

2016-01-01

Background Diffusion-weighted MRI (DWI) signal attenuation is often not mono-exponential (i.e. non-Gaussian diffusion) with stronger diffusion weighting. Several non-Gaussian diffusion models have been developed and may provide new information or higher sensitivity compared with the conventional apparent diffusion coefficient (ADC) method. However the relative merits of these models to detect tumor therapeutic response is not fully clear. Methods Conventional ADC, and three widely-used non-Gaussian models, (bi-exponential, stretched exponential, and statistical model), were implemented and compared for assessing SW620 human colon cancer xenografts responding to barasertib, an agent known to induce apoptosis via polyploidy. Bayesian Information Criterion (BIC) was used for model selection among all three non-Gaussian models. Results All of tumor volume, histology, conventional ADC, and three non-Gaussian DWI models could show significant differences between control and treatment groups after four days of treatment. However, only the non-Gaussian models detected significant changes after two days of treatment. For any treatment or control group, over 65.7% of tumor voxels indicate the bi-exponential model is strongly or very strongly preferred. Conclusion Non-Gaussian DWI model-derived biomarkers are capable of detecting tumor earlier chemotherapeutic response of tumors compared with conventional ADC and tumor volume. The bi-exponential model provides better fitting compared with statistical and stretched exponential models for the tumor and treatment models used in the current work. PMID:27919785

Angle-domain common-image gathers from anisotropic Gaussian beam migration and its application to anisotropy-induced imaging errors analysis

NASA Astrophysics Data System (ADS)

Han, Jianguang; Wang, Yun; Yu, Changqing; Chen, Peng

2017-02-01

An approach for extracting angle-domain common-image gathers (ADCIGs) from anisotropic Gaussian beam prestack depth migration (GB-PSDM) is presented in this paper. The propagation angle is calculated in the process of migration using the real-value traveltime information of Gaussian beam. Based on the above, we further investigate the effects of anisotropy on GB-PSDM, where the corresponding ADCIGs are extracted to assess the quality of migration images. The test results of the VTI syncline model and the TTI thrust sheet model show that anisotropic parameters ɛ, δ, and tilt angle 𝜃, have a great influence on the accuracy of the migrated image in anisotropic media, and ignoring any one of them will cause obvious imaging errors. The anisotropic GB-PSDM with the true anisotropic parameters can obtain more accurate seismic images of subsurface structures in anisotropic media.

Thermal time constant: optimising the skin temperature predictive modelling in lower limb prostheses using Gaussian processes

PubMed Central

Buis, Arjan

2016-01-01

Elevated skin temperature at the body/device interface of lower-limb prostheses is one of the major factors that affect tissue health. The heat dissipation in prosthetic sockets is greatly influenced by the thermal conductive properties of the hard socket and liner material employed. However, monitoring of the interface temperature at skin level in lower-limb prosthesis is notoriously complicated. This is due to the flexible nature of the interface liners used which requires consistent positioning of sensors during donning and doffing. Predicting the residual limb temperature by monitoring the temperature between socket and liner rather than skin and liner could be an important step in alleviating complaints on increased temperature and perspiration in prosthetic sockets. To predict the residual limb temperature, a machine learning algorithm – Gaussian processes is employed, which utilizes the thermal time constant values of commonly used socket and liner materials. This Letter highlights the relevance of thermal time constant of prosthetic materials in Gaussian processes technique which would be useful in addressing the challenge of non-invasively monitoring the residual limb skin temperature. With the introduction of thermal time constant, the model can be optimised and generalised for a given prosthetic setup, thereby making the predictions more reliable. PMID:27695626

EMG prediction from Motor Cortical Recordings via a Non-Negative Point Process Filter

PubMed Central

Nazarpour, Kianoush; Ethier, Christian; Paninski, Liam; Rebesco, James M.; Miall, R. Chris; Miller, Lee E.

2012-01-01

A constrained point process filtering mechanism for prediction of electromyogram (EMG) signals from multi-channel neural spike recordings is proposed here. Filters from the Kalman family are inherently sub-optimal in dealing with non-Gaussian observations, or a state evolution that deviates from the Gaussianity assumption. To address these limitations, we modeled the non-Gaussian neural spike train observations by using a generalized linear model (GLM) that encapsulates covariates of neural activity, including the neurons’ own spiking history, concurrent ensemble activity, and extrinsic covariates (EMG signals). In order to predict the envelopes of EMGs, we reformulated the Kalman filter (KF) in an optimization framework and utilized a non-negativity constraint. This structure characterizes the non-linear correspondence between neural activity and EMG signals reasonably. The EMGs were recorded from twelve forearm and hand muscles of a behaving monkey during a grip-force task. For the case of limited training data, the constrained point process filter improved the prediction accuracy when compared to a conventional Wiener cascade filter (a linear causal filter followed by a static non-linearity) for different bin sizes and delays between input spikes and EMG output. For longer training data sets, results of the proposed filter and that of the Wiener cascade filter were comparable. PMID:21659018

Thermal time constant: optimising the skin temperature predictive modelling in lower limb prostheses using Gaussian processes.

PubMed

Mathur, Neha; Glesk, Ivan; Buis, Arjan

2016-06-01

Elevated skin temperature at the body/device interface of lower-limb prostheses is one of the major factors that affect tissue health. The heat dissipation in prosthetic sockets is greatly influenced by the thermal conductive properties of the hard socket and liner material employed. However, monitoring of the interface temperature at skin level in lower-limb prosthesis is notoriously complicated. This is due to the flexible nature of the interface liners used which requires consistent positioning of sensors during donning and doffing. Predicting the residual limb temperature by monitoring the temperature between socket and liner rather than skin and liner could be an important step in alleviating complaints on increased temperature and perspiration in prosthetic sockets. To predict the residual limb temperature, a machine learning algorithm - Gaussian processes is employed, which utilizes the thermal time constant values of commonly used socket and liner materials. This Letter highlights the relevance of thermal time constant of prosthetic materials in Gaussian processes technique which would be useful in addressing the challenge of non-invasively monitoring the residual limb skin temperature. With the introduction of thermal time constant, the model can be optimised and generalised for a given prosthetic setup, thereby making the predictions more reliable.

Image interpolation and denoising for division of focal plane sensors using Gaussian processes.

PubMed

Gilboa, Elad; Cunningham, John P; Nehorai, Arye; Gruev, Viktor

2014-06-16

Image interpolation and denoising are important techniques in image processing. These methods are inherent to digital image acquisition as most digital cameras are composed of a 2D grid of heterogeneous imaging sensors. Current polarization imaging employ four different pixelated polarization filters, commonly referred to as division of focal plane polarization sensors. The sensors capture only partial information of the true scene, leading to a loss of spatial resolution as well as inaccuracy of the captured polarization information. Interpolation is a standard technique to recover the missing information and increase the accuracy of the captured polarization information. Here we focus specifically on Gaussian process regression as a way to perform a statistical image interpolation, where estimates of sensor noise are used to improve the accuracy of the estimated pixel information. We further exploit the inherent grid structure of this data to create a fast exact algorithm that operates in ����(N(3/2)) (vs. the naive ���� (N³)), thus making the Gaussian process method computationally tractable for image data. This modeling advance and the enabling computational advance combine to produce significant improvements over previously published interpolation methods for polarimeters, which is most pronounced in cases of low signal-to-noise ratio (SNR). We provide the comprehensive mathematical model as well as experimental results of the GP interpolation performance for division of focal plane polarimeter.

The Laplace method for probability measures in Banach spaces

NASA Astrophysics Data System (ADS)

Piterbarg, V. I.; Fatalov, V. R.

1995-12-01

Contents §1. Introduction Chapter I. Asymptotic analysis of continual integrals in Banach space, depending on a large parameter §2. The large deviation principle and logarithmic asymptotics of continual integrals §3. Exact asymptotics of Gaussian integrals in Banach spaces: the Laplace method 3.1. The Laplace method for Gaussian integrals taken over the whole Hilbert space: isolated minimum points ([167], I) 3.2. The Laplace method for Gaussian integrals in Hilbert space: the manifold of minimum points ([167], II) 3.3. The Laplace method for Gaussian integrals in Banach space ([90], [174], [176]) 3.4. Exact asymptotics of large deviations of Gaussian norms §4. The Laplace method for distributions of sums of independent random elements with values in Banach space 4.1. The case of a non-degenerate minimum point ([137], I) 4.2. A degenerate isolated minimum point and the manifold of minimum points ([137], II) §5. Further examples 5.1. The Laplace method for the local time functional of a Markov symmetric process ([217]) 5.2. The Laplace method for diffusion processes, a finite number of non-degenerate minimum points ([116]) 5.3. Asymptotics of large deviations for Brownian motion in the Hölder norm 5.4. Non-asymptotic expansion of a strong stable law in Hilbert space ([41]) Chapter II. The double sum method - a version of the Laplace method in the space of continuous functions §6. Pickands' method of double sums 6.1. General situations 6.2. Asymptotics of the distribution of the maximum of a Gaussian stationary process 6.3. Asymptotics of the probability of a large excursion of a Gaussian non-stationary process §7. Probabilities of large deviations of trajectories of Gaussian fields 7.1. Homogeneous fields and fields with constant dispersion 7.2. Finitely many maximum points of dispersion 7.3. Manifold of maximum points of dispersion 7.4. Asymptotics of distributions of maxima of Wiener fields §8. Exact asymptotics of large deviations of the norm of Gaussian vectors and processes with values in the spaces L_k^p and l^2. Gaussian fields with the set of parameters in Hilbert space 8.1 Exact asymptotics of the distribution of the l_k^p-norm of a Gaussian finite-dimensional vector with dependent coordinates, p > 1 8.2. Exact asymptotics of probabilities of high excursions of trajectories of processes of type \\chi^2 8.3. Asymptotics of the probabilities of large deviations of Gaussian processes with a set of parameters in Hilbert space [74] 8.4. Asymptotics of distributions of maxima of the norms of l^2-valued Gaussian processes 8.5. Exact asymptotics of large deviations for the l^2-valued Ornstein-Uhlenbeck process Bibliography

Continuous-variable quantum Gaussian process regression and quantum singular value decomposition of nonsparse low-rank matrices

NASA Astrophysics Data System (ADS)

Das, Siddhartha; Siopsis, George; Weedbrook, Christian

2018-02-01

With the significant advancement in quantum computation during the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used technique in supervised classical machine learning. Here we introduce an algorithm for Gaussian process regression using continuous-variable quantum systems that can be realized with technology based on photonic quantum computers under certain assumptions regarding distribution of data and availability of efficient quantum access. Our algorithm shows that by using a continuous-variable quantum computer a dramatic speedup in computing Gaussian process regression can be achieved, i.e., the possibility of exponentially reducing the time to compute. Furthermore, our results also include a continuous-variable quantum-assisted singular value decomposition method of nonsparse low rank matrices and forms an important subroutine in our Gaussian process regression algorithm.

Probabilistic Estimates of Global Mean Sea Level and its Underlying Processes

NASA Astrophysics Data System (ADS)

Hay, C.; Morrow, E.; Kopp, R. E.; Mitrovica, J. X.

2015-12-01

Local sea level can vary significantly from the global mean value due to a suite of processes that includes ongoing sea-level changes due to the last ice age, land water storage, ocean circulation changes, and non-uniform sea-level changes that arise when modern-day land ice rapidly melts. Understanding these sources of spatial and temporal variability is critical to estimating past and present sea-level change and projecting future sea-level rise. Using two probabilistic techniques, a multi-model Kalman smoother and Gaussian process regression, we have reanalyzed 20th century tide gauge observations to produce a new estimate of global mean sea level (GMSL). Our methods allow us to extract global information from the sparse tide gauge field by taking advantage of the physics-based and model-derived geometry of the contributing processes. Both methods provide constraints on the sea-level contribution of glacial isostatic adjustment (GIA). The Kalman smoother tests multiple discrete models of glacial isostatic adjustment (GIA), probabilistically computing the most likely GIA model given the observations, while the Gaussian process regression characterizes the prior covariance structure of a suite of GIA models and then uses this structure to estimate the posterior distribution of local rates of GIA-induced sea-level change. We present the two methodologies, the model-derived geometries of the underlying processes, and our new probabilistic estimates of GMSL and GIA.

Accounting for Non-Gaussian Sources of Spatial Correlation in Parametric Functional Magnetic Resonance Imaging Paradigms II: A Method to Obtain First-Level Analysis Residuals with Uniform and Gaussian Spatial Autocorrelation Function and Independent and Identically Distributed Time-Series.

PubMed

Gopinath, Kaundinya; Krishnamurthy, Venkatagiri; Lacey, Simon; Sathian, K

2018-02-01

In a recent study Eklund et al. have shown that cluster-wise family-wise error (FWE) rate-corrected inferences made in parametric statistical method-based functional magnetic resonance imaging (fMRI) studies over the past couple of decades may have been invalid, particularly for cluster defining thresholds less stringent than p < 0.001; principally because the spatial autocorrelation functions (sACFs) of fMRI data had been modeled incorrectly to follow a Gaussian form, whereas empirical data suggest otherwise. Hence, the residuals from general linear model (GLM)-based fMRI activation estimates in these studies may not have possessed a homogenously Gaussian sACF. Here we propose a method based on the assumption that heterogeneity and non-Gaussianity of the sACF of the first-level GLM analysis residuals, as well as temporal autocorrelations in the first-level voxel residual time-series, are caused by unmodeled MRI signal from neuronal and physiological processes as well as motion and other artifacts, which can be approximated by appropriate decompositions of the first-level residuals with principal component analysis (PCA), and removed. We show that application of this method yields GLM residuals with significantly reduced spatial correlation, nearly Gaussian sACF and uniform spatial smoothness across the brain, thereby allowing valid cluster-based FWE-corrected inferences based on assumption of Gaussian spatial noise. We further show that application of this method renders the voxel time-series of first-level GLM residuals independent, and identically distributed across time (which is a necessary condition for appropriate voxel-level GLM inference), without having to fit ad hoc stochastic colored noise models. Furthermore, the detection power of individual subject brain activation analysis is enhanced. This method will be especially useful for case studies, which rely on first-level GLM analysis inferences.

An efficient background modeling approach based on vehicle detection

NASA Astrophysics Data System (ADS)

Wang, Jia-yan; Song, Li-mei; Xi, Jiang-tao; Guo, Qing-hua

2015-10-01

The existing Gaussian Mixture Model(GMM) which is widely used in vehicle detection suffers inefficiency in detecting foreground image during the model phase, because it needs quite a long time to blend the shadows in the background. In order to overcome this problem, an improved method is proposed in this paper. First of all, each frame is divided into several areas(A, B, C and D), Where area A, B, C and D are decided by the frequency and the scale of the vehicle access. For each area, different new learning rate including weight, mean and variance is applied to accelerate the elimination of shadows. At the same time, the measure of adaptive change for Gaussian distribution is taken to decrease the total number of distributions and save memory space effectively. With this method, different threshold value and different number of Gaussian distribution are adopted for different areas. The results show that the speed of learning and the accuracy of the model using our proposed algorithm surpass the traditional GMM. Probably to the 50th frame, interference with the vehicle has been eliminated basically, and the model number only 35% to 43% of the standard, the processing speed for every frame approximately has a 20% increase than the standard. The proposed algorithm has good performance in terms of elimination of shadow and processing speed for vehicle detection, it can promote the development of intelligent transportation, which is very meaningful to the other Background modeling methods.

Non-stationary noise estimation using dictionary learning and Gaussian mixture models

NASA Astrophysics Data System (ADS)

Hughes, James M.; Rockmore, Daniel N.; Wang, Yang

2014-02-01

Stationarity of the noise distribution is a common assumption in image processing. This assumption greatly simplifies denoising estimators and other model parameters and consequently assuming stationarity is often a matter of convenience rather than an accurate model of noise characteristics. The problematic nature of this assumption is exacerbated in real-world contexts, where noise is often highly non-stationary and can possess time- and space-varying characteristics. Regardless of model complexity, estimating the parameters of noise dis- tributions in digital images is a difficult task, and estimates are often based on heuristic assumptions. Recently, sparse Bayesian dictionary learning methods were shown to produce accurate estimates of the level of additive white Gaussian noise in images with minimal assumptions. We show that a similar model is capable of accu- rately modeling certain kinds of non-stationary noise processes, allowing for space-varying noise in images to be estimated, detected, and removed. We apply this modeling concept to several types of non-stationary noise and demonstrate the model's effectiveness on real-world problems, including denoising and segmentation of images according to noise characteristics, which has applications in image forensics.

Non-Gaussian Analysis of Turbulent Boundary Layer Fluctuating Pressure on Aircraft Skin Panels

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Steinwolf, Alexander

2005-01-01

The purpose of the study is to investigate the probability density function (PDF) of turbulent boundary layer fluctuating pressures measured on the outer sidewall of a supersonic transport aircraft and to approximate these PDFs by analytical models. Experimental flight results show that the fluctuating pressure PDFs differ from the Gaussian distribution even for standard smooth surface conditions. The PDF tails are wider and longer than those of the Gaussian model. For pressure fluctuations in front of forward-facing step discontinuities, deviations from the Gaussian model are more significant and the PDFs become asymmetrical. There is a certain spatial pattern of the skewness and kurtosis behavior depending on the distance upstream from the step. All characteristics related to non-Gaussian behavior are highly dependent upon the distance from the step and the step height, less dependent on aircraft speed, and not dependent on the fuselage location. A Hermite polynomial transform model and a piecewise-Gaussian model fit the flight data well both for the smooth and stepped conditions. The piecewise-Gaussian approximation can be additionally regarded for convenience in usage after the model is constructed.

Fast machine-learning online optimization of ultra-cold-atom experiments.

PubMed

Wigley, P B; Everitt, P J; van den Hengel, A; Bastian, J W; Sooriyabandara, M A; McDonald, G D; Hardman, K S; Quinlivan, C D; Manju, P; Kuhn, C C N; Petersen, I R; Luiten, A N; Hope, J J; Robins, N P; Hush, M R

2016-05-16

We apply an online optimization process based on machine learning to the production of Bose-Einstein condensates (BEC). BEC is typically created with an exponential evaporation ramp that is optimal for ergodic dynamics with two-body s-wave interactions and no other loss rates, but likely sub-optimal for real experiments. Through repeated machine-controlled scientific experimentation and observations our 'learner' discovers an optimal evaporation ramp for BEC production. In contrast to previous work, our learner uses a Gaussian process to develop a statistical model of the relationship between the parameters it controls and the quality of the BEC produced. We demonstrate that the Gaussian process machine learner is able to discover a ramp that produces high quality BECs in 10 times fewer iterations than a previously used online optimization technique. Furthermore, we show the internal model developed can be used to determine which parameters are essential in BEC creation and which are unimportant, providing insight into the optimization process of the system.

Fast machine-learning online optimization of ultra-cold-atom experiments

PubMed Central

Wigley, P. B.; Everitt, P. J.; van den Hengel, A.; Bastian, J. W.; Sooriyabandara, M. A.; McDonald, G. D.; Hardman, K. S.; Quinlivan, C. D.; Manju, P.; Kuhn, C. C. N.; Petersen, I. R.; Luiten, A. N.; Hope, J. J.; Robins, N. P.; Hush, M. R.

2016-01-01

We apply an online optimization process based on machine learning to the production of Bose-Einstein condensates (BEC). BEC is typically created with an exponential evaporation ramp that is optimal for ergodic dynamics with two-body s-wave interactions and no other loss rates, but likely sub-optimal for real experiments. Through repeated machine-controlled scientific experimentation and observations our ‘learner’ discovers an optimal evaporation ramp for BEC production. In contrast to previous work, our learner uses a Gaussian process to develop a statistical model of the relationship between the parameters it controls and the quality of the BEC produced. We demonstrate that the Gaussian process machine learner is able to discover a ramp that produces high quality BECs in 10 times fewer iterations than a previously used online optimization technique. Furthermore, we show the internal model developed can be used to determine which parameters are essential in BEC creation and which are unimportant, providing insight into the optimization process of the system. PMID:27180805

A New Non-gaussian Turbulent Wind Field Generator to Estimate Design-Loads of Wind-Turbines

NASA Astrophysics Data System (ADS)

Schaffarczyk, A. P.; Gontier, H.; Kleinhans, D.; Friedrich, R.

Climate change and finite fossil fuel resources make it urgent to turn into electricity generation from mostly renewable energies. One major part will play wind-energy supplied by wind-turbines of rated power up to 10 MW. For their design and development wind field models have to be used. The standard models are based on the empirical spectra, for example by von Karman or Kaimal. From investigation of measured data it is clear that gusts are underrepresented in such models. Based on some fundamental discoveries of the nature of turbulence by Friedrich [1] derived from the Navier-Stokes equation directly, we used the concept of Continuous Time Random Walks to construct three dimensional wind fields obeying non-Gaussian statistics. These wind fields were used to estimate critical fatigue loads necessary within the certification process. Calculations are carried out with an implementation of a beam-model (FLEX5) for two types of state-of-the-art wind turbines The authors considered the edgewise and flapwise blade-root bending moments as well as tilt moment at tower top due to the standard wind field models and our new non-Gaussian wind field model. Clear differences in the loads were found.

A clustering-based fuzzy wavelet neural network model for short-term load forecasting.

PubMed

Kodogiannis, Vassilis S; Amina, Mahdi; Petrounias, Ilias

2013-10-01

Load forecasting is a critical element of power system operation, involving prediction of the future level of demand to serve as the basis for supply and demand planning. This paper presents the development of a novel clustering-based fuzzy wavelet neural network (CB-FWNN) model and validates its prediction on the short-term electric load forecasting of the Power System of the Greek Island of Crete. The proposed model is obtained from the traditional Takagi-Sugeno-Kang fuzzy system by replacing the THEN part of fuzzy rules with a "multiplication" wavelet neural network (MWNN). Multidimensional Gaussian type of activation functions have been used in the IF part of the fuzzyrules. A Fuzzy Subtractive Clustering scheme is employed as a pre-processing technique to find out the initial set and adequate number of clusters and ultimately the number of multiplication nodes in MWNN, while Gaussian Mixture Models with the Expectation Maximization algorithm are utilized for the definition of the multidimensional Gaussians. The results corresponding to the minimum and maximum power load indicate that the proposed load forecasting model provides significantly accurate forecasts, compared to conventional neural networks models.

Gaussian covariance graph models accounting for correlated marker effects in genome-wide prediction.

PubMed

Martínez, C A; Khare, K; Rahman, S; Elzo, M A

2017-10-01

Several statistical models used in genome-wide prediction assume uncorrelated marker allele substitution effects, but it is known that these effects may be correlated. In statistics, graphical models have been identified as a useful tool for covariance estimation in high-dimensional problems and it is an area that has recently experienced a great expansion. In Gaussian covariance graph models (GCovGM), the joint distribution of a set of random variables is assumed to be Gaussian and the pattern of zeros of the covariance matrix is encoded in terms of an undirected graph G. In this study, methods adapting the theory of GCovGM to genome-wide prediction were developed (Bayes GCov, Bayes GCov-KR and Bayes GCov-H). In simulated data sets, improvements in correlation between phenotypes and predicted breeding values and accuracies of predicted breeding values were found. Our models account for correlation of marker effects and permit to accommodate general structures as opposed to models proposed in previous studies, which consider spatial correlation only. In addition, they allow incorporation of biological information in the prediction process through its use when constructing graph G, and their extension to the multi-allelic loci case is straightforward. © 2017 Blackwell Verlag GmbH.

Gaussian decomposition of high-resolution melt curve derivatives for measuring genome-editing efficiency

PubMed Central

Zaboikin, Michail; Freter, Carl

2018-01-01

We describe a method for measuring genome editing efficiency from in silico analysis of high-resolution melt curve data. The melt curve data derived from amplicons of genome-edited or unmodified target sites were processed to remove the background fluorescent signal emanating from free fluorophore and then corrected for temperature-dependent quenching of fluorescence of double-stranded DNA-bound fluorophore. Corrected data were normalized and numerically differentiated to obtain the first derivatives of the melt curves. These were then mathematically modeled as a sum or superposition of minimal number of Gaussian components. Using Gaussian parameters determined by modeling of melt curve derivatives of unedited samples, we were able to model melt curve derivatives from genetically altered target sites where the mutant population could be accommodated using an additional Gaussian component. From this, the proportion contributed by the mutant component in the target region amplicon could be accurately determined. Mutant component computations compared well with the mutant frequency determination from next generation sequencing data. The results were also consistent with our earlier studies that used difference curve areas from high-resolution melt curves for determining the efficiency of genome-editing reagents. The advantage of the described method is that it does not require calibration curves to estimate proportion of mutants in amplicons of genome-edited target sites. PMID:29300734

Unified theory for stochastic modelling of hydroclimatic processes: Preserving marginal distributions, correlation structures, and intermittency

NASA Astrophysics Data System (ADS)

Papalexiou, Simon Michael

2018-05-01

Hydroclimatic processes come in all "shapes and sizes". They are characterized by different spatiotemporal correlation structures and probability distributions that can be continuous, mixed-type, discrete or even binary. Simulating such processes by reproducing precisely their marginal distribution and linear correlation structure, including features like intermittency, can greatly improve hydrological analysis and design. Traditionally, modelling schemes are case specific and typically attempt to preserve few statistical moments providing inadequate and potentially risky distribution approximations. Here, a single framework is proposed that unifies, extends, and improves a general-purpose modelling strategy, based on the assumption that any process can emerge by transforming a specific "parent" Gaussian process. A novel mathematical representation of this scheme, introducing parametric correlation transformation functions, enables straightforward estimation of the parent-Gaussian process yielding the target process after the marginal back transformation, while it provides a general description that supersedes previous specific parameterizations, offering a simple, fast and efficient simulation procedure for every stationary process at any spatiotemporal scale. This framework, also applicable for cyclostationary and multivariate modelling, is augmented with flexible parametric correlation structures that parsimoniously describe observed correlations. Real-world simulations of various hydroclimatic processes with different correlation structures and marginals, such as precipitation, river discharge, wind speed, humidity, extreme events per year, etc., as well as a multivariate example, highlight the flexibility, advantages, and complete generality of the method.

Gaussian process regression for tool wear prediction

NASA Astrophysics Data System (ADS)

Kong, Dongdong; Chen, Yongjie; Li, Ning

2018-05-01

To realize and accelerate the pace of intelligent manufacturing, this paper presents a novel tool wear assessment technique based on the integrated radial basis function based kernel principal component analysis (KPCA_IRBF) and Gaussian process regression (GPR) for real-timely and accurately monitoring the in-process tool wear parameters (flank wear width). The KPCA_IRBF is a kind of new nonlinear dimension-increment technique and firstly proposed for feature fusion. The tool wear predictive value and the corresponding confidence interval are both provided by utilizing the GPR model. Besides, GPR performs better than artificial neural networks (ANN) and support vector machines (SVM) in prediction accuracy since the Gaussian noises can be modeled quantitatively in the GPR model. However, the existence of noises will affect the stability of the confidence interval seriously. In this work, the proposed KPCA_IRBF technique helps to remove the noises and weaken its negative effects so as to make the confidence interval compressed greatly and more smoothed, which is conducive for monitoring the tool wear accurately. Moreover, the selection of kernel parameter in KPCA_IRBF can be easily carried out in a much larger selectable region in comparison with the conventional KPCA_RBF technique, which helps to improve the efficiency of model construction. Ten sets of cutting tests are conducted to validate the effectiveness of the presented tool wear assessment technique. The experimental results show that the in-process flank wear width of tool inserts can be monitored accurately by utilizing the presented tool wear assessment technique which is robust under a variety of cutting conditions. This study lays the foundation for tool wear monitoring in real industrial settings.

Modeling Array Stations in SIG-VISA

NASA Astrophysics Data System (ADS)

Ding, N.; Moore, D.; Russell, S.

2013-12-01

We add support for array stations to SIG-VISA, a system for nuclear monitoring using probabilistic inference on seismic signals. Array stations comprise a large portion of the IMS network; they can provide increased sensitivity and more accurate directional information compared to single-component stations. Our existing model assumed that signals were independent at each station, which is false when lots of stations are close together, as in an array. The new model removes that assumption by jointly modeling signals across array elements. This is done by extending our existing Gaussian process (GP) regression models, also known as kriging, from a 3-dimensional single-component space of events to a 6-dimensional space of station-event pairs. For each array and each event attribute (including coda decay, coda height, amplitude transfer and travel time), we model the joint distribution across array elements using a Gaussian process that learns the correlation lengthscale across the array, thereby incorporating information of array stations into the probabilistic inference framework. To evaluate the effectiveness of our model, we perform ';probabilistic beamforming' on new events using our GP model, i.e., we compute the event azimuth having highest posterior probability under the model, conditioned on the signals at array elements. We compare the results from our probabilistic inference model to the beamforming currently performed by IMS station processing.

A Concept for Measuring Electron Distribution Functions Using Collective Thomson Scattering

NASA Astrophysics Data System (ADS)

Milder, A. L.; Froula, D. H.

2017-10-01

A.B. Langdon proposed that stable non-Maxwellian distribution functions are realized in coronal inertial confinement fusion plasmas via inverse bremsstrahlung heating. For Zvosc2 Zvosc2 vth2 > 1 , vth2 > 1 , the inverse bremsstrahlung heating rate is sufficiently fast to compete with electron-electron collisions. This process preferentially heats the subthermal electrons leading to super-Gaussian distribution functions. A method to identify the super-Gaussian order of the distribution functions in these plasmas using collective Thomson scattering will be proposed. By measuring the collective Thomson spectra over a range of angles the density, temperature and super-Gaussian order can be determined. This is accomplished by fitting non-Maxwellian distribution data with a super-Gaussian model; in order to match the density and electron temperature to within 10%, the super-Gaussian order must be varied. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.

Numerical investigations of non-collinear optical parametric chirped pulse amplification for Laguerre-Gaussian vortex beam

NASA Astrophysics Data System (ADS)

Xu, Lu; Yu, Lianghong; Liang, Xiaoyan

2016-04-01

We present for the first time a scheme to amplify a Laguerre-Gaussian vortex beam based on non-collinear optical parametric chirped pulse amplification (OPCPA). In addition, a three-dimensional numerical model of non-collinear optical parametric amplification was deduced in the frequency domain, in which the effects of non-collinear configuration, temporal and spatial walk-off, group-velocity dispersion and diffraction were also taken into account, to trace the dynamics of the Laguerre-Gaussian vortex beam and investigate its critical parameters in the non-collinear OPCPA process. Based on the numerical simulation results, the scheme shows promise for implementation in a relativistic twisted laser pulse system, which will diversify the light-matter interaction field.

Stationary moments, diffusion limits, and extinction times for logistic growth with random catastrophes.

PubMed

Schlomann, Brandon H

2018-06-06

A central problem in population ecology is understanding the consequences of stochastic fluctuations. Analytically tractable models with Gaussian driving noise have led to important, general insights, but they fail to capture rare, catastrophic events, which are increasingly observed at scales ranging from global fisheries to intestinal microbiota. Due to mathematical challenges, growth processes with random catastrophes are less well characterized and it remains unclear how their consequences differ from those of Gaussian processes. In the face of a changing climate and predicted increases in ecological catastrophes, as well as increased interest in harnessing microbes for therapeutics, these processes have never been more relevant. To better understand them, I revisit here a differential equation model of logistic growth coupled to density-independent catastrophes that arrive as a Poisson process, and derive new analytic results that reveal its statistical structure. First, I derive exact expressions for the model's stationary moments, revealing a single effective catastrophe parameter that largely controls low order statistics. Then, I use weak convergence theorems to construct its Gaussian analog in a limit of frequent, small catastrophes, keeping the stationary population mean constant for normalization. Numerically computing statistics along this limit shows how they transform as the dynamics shifts from catastrophes to diffusions, enabling quantitative comparisons. For example, the mean time to extinction increases monotonically by orders of magnitude, demonstrating significantly higher extinction risk under catastrophes than under diffusions. Together, these results provide insight into a wide range of stochastic dynamical systems important for ecology and conservation. Copyright © 2018 Elsevier Ltd. All rights reserved.

Clinical time series prediction: towards a hierarchical dynamical system framework

PubMed Central

Liu, Zitao; Hauskrecht, Milos

2014-01-01

Objective Developing machine learning and data mining algorithms for building temporal models of clinical time series is important for understanding of the patient condition, the dynamics of a disease, effect of various patient management interventions and clinical decision making. In this work, we propose and develop a novel hierarchical framework for modeling clinical time series data of varied length and with irregularly sampled observations. Materials and methods Our hierarchical dynamical system framework for modeling clinical time series combines advantages of the two temporal modeling approaches: the linear dynamical system and the Gaussian process. We model the irregularly sampled clinical time series by using multiple Gaussian process sequences in the lower level of our hierarchical framework and capture the transitions between Gaussian processes by utilizing the linear dynamical system. The experiments are conducted on the complete blood count (CBC) panel data of 1000 post-surgical cardiac patients during their hospitalization. Our framework is evaluated and compared to multiple baseline approaches in terms of the mean absolute prediction error and the absolute percentage error. Results We tested our framework by first learning the time series model from data for the patient in the training set, and then applying the model in order to predict future time series values on the patients in the test set. We show that our model outperforms multiple existing models in terms of its predictive accuracy. Our method achieved a 3.13% average prediction accuracy improvement on ten CBC lab time series when it was compared against the best performing baseline. A 5.25% average accuracy improvement was observed when only short-term predictions were considered. Conclusion A new hierarchical dynamical system framework that lets us model irregularly sampled time series data is a promising new direction for modeling clinical time series and for improving their predictive performance. PMID:25534671

Modeling stock return distributions with a quantum harmonic oscillator

NASA Astrophysics Data System (ADS)

Ahn, K.; Choi, M. Y.; Dai, B.; Sohn, S.; Yang, B.

2017-11-01

We propose a quantum harmonic oscillator as a model for the market force which draws a stock return from short-run fluctuations to the long-run equilibrium. The stochastic equation governing our model is transformed into a Schrödinger equation, the solution of which features “quantized” eigenfunctions. Consequently, stock returns follow a mixed χ distribution, which describes Gaussian and non-Gaussian features. Analyzing the Financial Times Stock Exchange (FTSE) All Share Index, we demonstrate that our model outperforms traditional stochastic process models, e.g., the geometric Brownian motion and the Heston model, with smaller fitting errors and better goodness-of-fit statistics. In addition, making use of analogy, we provide an economic rationale of the physics concepts such as the eigenstate, eigenenergy, and angular frequency, which sheds light on the relationship between finance and econophysics literature.

Gaussian process model for extrapolation of scattering observables for complex molecules: From benzene to benzonitrile

NASA Astrophysics Data System (ADS)

Cui, Jie; Li, Zhiying; Krems, Roman V.

2015-10-01

We consider a problem of extrapolating the collision properties of a large polyatomic molecule A-H to make predictions of the dynamical properties for another molecule related to A-H by the substitution of the H atom with a small molecular group X, without explicitly computing the potential energy surface for A-X. We assume that the effect of the -H →-X substitution is embodied in a multidimensional function with unknown parameters characterizing the change of the potential energy surface. We propose to apply the Gaussian Process model to determine the dependence of the dynamical observables on the unknown parameters. This can be used to produce an interval of the observable values which corresponds to physical variations of the potential parameters. We show that the Gaussian Process model combined with classical trajectory calculations can be used to obtain the dependence of the cross sections for collisions of C6H5CN with He on the unknown parameters describing the interaction of the He atom with the CN fragment of the molecule. The unknown parameters are then varied within physically reasonable ranges to produce a prediction uncertainty of the cross sections. The results are normalized to the cross sections for He — C6H6 collisions obtained from quantum scattering calculations in order to provide a prediction interval of the thermally averaged cross sections for collisions of C6H5CN with He.

Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes.

PubMed

Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon

2017-12-01

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes. © 2017, The International Biometric Society.

Temporal self-splitting of optical pulses

NASA Astrophysics Data System (ADS)

Ding, Chaoliang; Koivurova, Matias; Turunen, Jari; Pan, Liuzhan

2018-05-01

We present mathematical models for temporally and spectrally partially coherent pulse trains with Laguerre-Gaussian and Hermite-Gaussian Schell-model statistics as extensions of the standard Gaussian Schell model for pulse trains. We derive propagation formulas of both classes of pulsed fields in linearly dispersive media and in temporal optical systems. It is found that, in general, both types of fields exhibit time-domain self-splitting upon propagation. The Laguerre-Gaussian model leads to multiply peaked pulses, while the Hermite-Gaussian model leads to doubly peaked pulses, in the temporal far field (in dispersive media) or at the Fourier plane of a temporal system. In both model fields the character of the self-splitting phenomenon depends both on the degree of temporal and spectral coherence and on the power spectrum of the field.

Linear velocity fields in non-Gaussian models for large-scale structure

NASA Technical Reports Server (NTRS)

Scherrer, Robert J.

1992-01-01

Linear velocity fields in two types of physically motivated non-Gaussian models are examined for large-scale structure: seed models, in which the density field is a convolution of a density profile with a distribution of points, and local non-Gaussian fields, derived from a local nonlinear transformation on a Gaussian field. The distribution of a single component of the velocity is derived for seed models with randomly distributed seeds, and these results are applied to the seeded hot dark matter model and the global texture model with cold dark matter. An expression for the distribution of a single component of the velocity in arbitrary local non-Gaussian models is given, and these results are applied to such fields with chi-squared and lognormal distributions. It is shown that all seed models with randomly distributed seeds and all local non-Guassian models have single-component velocity distributions with positive kurtosis.

Stochastic resonance in a piecewise nonlinear model driven by multiplicative non-Gaussian noise and additive white noise

NASA Astrophysics Data System (ADS)

Guo, Yongfeng; Shen, Yajun; Tan, Jianguo

2016-09-01

The phenomenon of stochastic resonance (SR) in a piecewise nonlinear model driven by a periodic signal and correlated noises for the cases of a multiplicative non-Gaussian noise and an additive Gaussian white noise is investigated. Applying the path integral approach, the unified colored noise approximation and the two-state model theory, the analytical expression of the signal-to-noise ratio (SNR) is derived. It is found that conventional stochastic resonance exists in this system. From numerical computations we obtain that: (i) As a function of the non-Gaussian noise intensity, the SNR is increased when the non-Gaussian noise deviation parameter q is increased. (ii) As a function of the Gaussian noise intensity, the SNR is decreased when q is increased. This demonstrates that the effect of the non-Gaussian noise on SNR is different from that of the Gaussian noise in this system. Moreover, we further discuss the effect of the correlation time of the non-Gaussian noise, cross-correlation strength, the amplitude and frequency of the periodic signal on SR.

Skewness in large-scale structure and non-Gaussian initial conditions

NASA Technical Reports Server (NTRS)

Fry, J. N.; Scherrer, Robert J.

1994-01-01

We compute the skewness of the galaxy distribution arising from the nonlinear evolution of arbitrary non-Gaussian intial conditions to second order in perturbation theory including the effects of nonlinear biasing. The result contains a term identical to that for a Gaussian initial distribution plus terms which depend on the skewness and kurtosis of the initial conditions. The results are model dependent; we present calculations for several toy models. At late times, the leading contribution from the initial skewness decays away relative to the other terms and becomes increasingly unimportant, but the contribution from initial kurtosis, previously overlooked, has the same time dependence as the Gaussian terms. Observations of a linear dependence of the normalized skewness on the rms density fluctuation therefore do not necessarily rule out initially non-Gaussian models. We also show that with non-Gaussian initial conditions the first correction to linear theory for the mean square density fluctuation is larger than for Gaussian models.

A Surrogate-based Adaptive Sampling Approach for History Matching and Uncertainty Quantification

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

Li, Weixuan; Zhang, Dongxiao; Lin, Guang

A critical procedure in reservoir simulations is history matching (or data assimilation in a broader sense), which calibrates model parameters such that the simulation results are consistent with field measurements, and hence improves the credibility of the predictions given by the simulations. Often there exist non-unique combinations of parameter values that all yield the simulation results matching the measurements. For such ill-posed history matching problems, Bayesian theorem provides a theoretical foundation to represent different solutions and to quantify the uncertainty with the posterior PDF. Lacking an analytical solution in most situations, the posterior PDF may be characterized with a samplemore » of realizations, each representing a possible scenario. A novel sampling algorithm is presented here for the Bayesian solutions to history matching problems. We aim to deal with two commonly encountered issues: 1) as a result of the nonlinear input-output relationship in a reservoir model, the posterior distribution could be in a complex form, such as multimodal, which violates the Gaussian assumption required by most of the commonly used data assimilation approaches; 2) a typical sampling method requires intensive model evaluations and hence may cause unaffordable computational cost. In the developed algorithm, we use a Gaussian mixture model as the proposal distribution in the sampling process, which is simple but also flexible to approximate non-Gaussian distributions and is particularly efficient when the posterior is multimodal. Also, a Gaussian process is utilized as a surrogate model to speed up the sampling process. Furthermore, an iterative scheme of adaptive surrogate refinement and re-sampling ensures sampling accuracy while keeping the computational cost at a minimum level. The developed approach is demonstrated with an illustrative example and shows its capability in handling the above-mentioned issues. Multimodal posterior of the history matching problem is captured and are used to give a reliable production prediction with uncertainty quantification. The new algorithm reveals a great improvement in terms of computational efficiency comparing previously studied approaches for the sample problem.« less

A novel multitarget model of radiation-induced cell killing based on the Gaussian distribution.

PubMed

Zhao, Lei; Mi, Dong; Sun, Yeqing

2017-05-07

The multitarget version of the traditional target theory based on the Poisson distribution is still used to describe the dose-survival curves of cells after ionizing radiation in radiobiology and radiotherapy. However, noting that the usual ionizing radiation damage is the result of two sequential stochastic processes, the probability distribution of the damage number per cell should follow a compound Poisson distribution, like e.g. Neyman's distribution of type A (N. A.). In consideration of that the Gaussian distribution can be considered as the approximation of the N. A. in the case of high flux, a multitarget model based on the Gaussian distribution is proposed to describe the cell inactivation effects in low linear energy transfer (LET) radiation with high dose-rate. Theoretical analysis and experimental data fitting indicate that the present theory is superior to the traditional multitarget model and similar to the Linear - Quadratic (LQ) model in describing the biological effects of low-LET radiation with high dose-rate, and the parameter ratio in the present model can be used as an alternative indicator to reflect the radiation damage and radiosensitivity of the cells. Copyright © 2017 Elsevier Ltd. All rights reserved.

Nested polynomial trends for the improvement of Gaussian process-based predictors

NASA Astrophysics Data System (ADS)

Perrin, G.; Soize, C.; Marque-Pucheu, S.; Garnier, J.

2017-10-01

The role of simulation keeps increasing for the sensitivity analysis and the uncertainty quantification of complex systems. Such numerical procedures are generally based on the processing of a huge amount of code evaluations. When the computational cost associated with one particular evaluation of the code is high, such direct approaches based on the computer code only, are not affordable. Surrogate models have therefore to be introduced to interpolate the information given by a fixed set of code evaluations to the whole input space. When confronted to deterministic mappings, the Gaussian process regression (GPR), or kriging, presents a good compromise between complexity, efficiency and error control. Such a method considers the quantity of interest of the system as a particular realization of a Gaussian stochastic process, whose mean and covariance functions have to be identified from the available code evaluations. In this context, this work proposes an innovative parametrization of this mean function, which is based on the composition of two polynomials. This approach is particularly relevant for the approximation of strongly non linear quantities of interest from very little information. After presenting the theoretical basis of this method, this work compares its efficiency to alternative approaches on a series of examples.

Normal and tumoral melanocytes exhibit q-Gaussian random search patterns.

PubMed

da Silva, Priscila C A; Rosembach, Tiago V; Santos, Anésia A; Rocha, Márcio S; Martins, Marcelo L

2014-01-01

In multicellular organisms, cell motility is central in all morphogenetic processes, tissue maintenance, wound healing and immune surveillance. Hence, failures in its regulation potentiates numerous diseases. Here, cell migration assays on plastic 2D surfaces were performed using normal (Melan A) and tumoral (B16F10) murine melanocytes in random motility conditions. The trajectories of the centroids of the cell perimeters were tracked through time-lapse microscopy. The statistics of these trajectories was analyzed by building velocity and turn angle distributions, as well as velocity autocorrelations and the scaling of mean-squared displacements. We find that these cells exhibit a crossover from a normal to a super-diffusive motion without angular persistence at long time scales. Moreover, these melanocytes move with non-Gaussian velocity distributions. This major finding indicates that amongst those animal cells supposedly migrating through Lévy walks, some of them can instead perform q-Gaussian walks. Furthermore, our results reveal that B16F10 cells infected by mycoplasmas exhibit essentially the same diffusivity than their healthy counterparts. Finally, a q-Gaussian random walk model was proposed to account for these melanocytic migratory traits. Simulations based on this model correctly describe the crossover to super-diffusivity in the cell migration tracks.

Latent degradation indicators estimation and prediction: A Monte Carlo approach

NASA Astrophysics Data System (ADS)

Zhou, Yifan; Sun, Yong; Mathew, Joseph; Wolff, Rodney; Ma, Lin

2011-01-01

Asset health inspections can produce two types of indicators: (1) direct indicators (e.g. the thickness of a brake pad, and the crack depth on a gear) which directly relate to a failure mechanism; and (2) indirect indicators (e.g. the indicators extracted from vibration signals and oil analysis data) which can only partially reveal a failure mechanism. While direct indicators enable more precise references to asset health condition, they are often more difficult to obtain than indirect indicators. The state space model provides an efficient approach to estimating direct indicators by using indirect indicators. However, existing state space models to estimate direct indicators largely depend on assumptions such as, discrete time, discrete state, linearity, and Gaussianity. The discrete time assumption requires fixed inspection intervals. The discrete state assumption entails discretising continuous degradation indicators, which often introduces additional errors. The linear and Gaussian assumptions are not consistent with nonlinear and irreversible degradation processes in most engineering assets. This paper proposes a state space model without these assumptions. Monte Carlo-based algorithms are developed to estimate the model parameters and the remaining useful life. These algorithms are evaluated for performance using numerical simulations through MATLAB. The result shows that both the parameters and the remaining useful life are estimated accurately. Finally, the new state space model is used to process vibration and crack depth data from an accelerated test of a gearbox. During this application, the new state space model shows a better fitness result than the state space model with linear and Gaussian assumption.

White Gaussian Noise - Models for Engineers

NASA Astrophysics Data System (ADS)

Jondral, Friedrich K.

2018-04-01

This paper assembles some information about white Gaussian noise (WGN) and its applications. It starts from a description of thermal noise, i. e. the irregular motion of free charge carriers in electronic devices. In a second step, mathematical models of WGN processes and their most important parameters, especially autocorrelation functions and power spectrum densities, are introduced. In order to proceed from mathematical models to simulations, we discuss the generation of normally distributed random numbers. The signal-to-noise ratio as the most important quality measure used in communications, control or measurement technology is accurately introduced. As a practical application of WGN, the transmission of quadrature amplitude modulated (QAM) signals over additive WGN channels together with the optimum maximum likelihood (ML) detector is considered in a demonstrative and intuitive way.

Formation of primordial black holes from non-Gaussian perturbations produced in a waterfall transition

NASA Astrophysics Data System (ADS)

Bugaev, Edgar; Klimai, Peter

2012-05-01

We consider the process of primordial black hole (PBH) formation originated from primordial curvature perturbations produced during waterfall transition (with tachyonic instability), at the end of hybrid inflation. It is known that in such inflation models, rather large values of curvature perturbation amplitudes can be reached, which can potentially cause a significant PBH production in the early Universe. The probability distributions of density perturbation amplitudes in this case can be strongly non-Gaussian, which requires a special treatment. We calculated PBH abundances and PBH mass spectra for the model and analyzed their dependence on model parameters. We obtained the constraints on the parameters of the inflationary potential, using the available limits on βPBH.

Galaxy formation

PubMed Central

Peebles, P. J. E.

1998-01-01

It is argued that within the standard Big Bang cosmological model the bulk of the mass of the luminous parts of the large galaxies likely had been assembled by redshift z ∼ 10. Galaxy assembly this early would be difficult to fit in the widely discussed adiabatic cold dark matter model for structure formation, but it could agree with an isocurvature version in which the cold dark matter is the remnant of a massive scalar field frozen (or squeezed) from quantum fluctuations during inflation. The squeezed field fluctuations would be Gaussian with zero mean, and the distribution of the field mass therefore would be the square of a random Gaussian process. This offers a possibly interesting new direction for the numerical exploration of models for cosmic structure formation. PMID:9419326

How Many Separable Sources? Model Selection In Independent Components Analysis

PubMed Central

Woods, Roger P.; Hansen, Lars Kai; Strother, Stephen

2015-01-01

Unlike mixtures consisting solely of non-Gaussian sources, mixtures including two or more Gaussian components cannot be separated using standard independent components analysis methods that are based on higher order statistics and independent observations. The mixed Independent Components Analysis/Principal Components Analysis (mixed ICA/PCA) model described here accommodates one or more Gaussian components in the independent components analysis model and uses principal components analysis to characterize contributions from this inseparable Gaussian subspace. Information theory can then be used to select from among potential model categories with differing numbers of Gaussian components. Based on simulation studies, the assumptions and approximations underlying the Akaike Information Criterion do not hold in this setting, even with a very large number of observations. Cross-validation is a suitable, though computationally intensive alternative for model selection. Application of the algorithm is illustrated using Fisher's iris data set and Howells' craniometric data set. Mixed ICA/PCA is of potential interest in any field of scientific investigation where the authenticity of blindly separated non-Gaussian sources might otherwise be questionable. Failure of the Akaike Information Criterion in model selection also has relevance in traditional independent components analysis where all sources are assumed non-Gaussian. PMID:25811988

Gaussian fitting for carotid and radial artery pressure waveforms: comparison between normal subjects and heart failure patients.

PubMed

Liu, Chengyu; Zheng, Dingchang; Zhao, Lina; Liu, Changchun

2014-01-01

It has been reported that Gaussian functions could accurately and reliably model both carotid and radial artery pressure waveforms (CAPW and RAPW). However, the physiological relevance of the characteristic features from the modeled Gaussian functions has been little investigated. This study thus aimed to determine characteristic features from the Gaussian functions and to make comparisons of them between normal subjects and heart failure patients. Fifty-six normal subjects and 51 patients with heart failure were studied with the CAPW and RAPW signals recorded simultaneously. The two signals were normalized first and then modeled by three positive Gaussian functions, with their peak amplitude, peak time, and half-width determined. Comparisons of these features were finally made between the two groups. Results indicated that the peak amplitude of the first Gaussian curve was significantly decreased in heart failure patients compared with normal subjects (P<0.001). Significantly increased peak amplitude of the second Gaussian curves (P<0.001) and significantly shortened peak times of the second and third Gaussian curves (both P<0.001) were also presented in heart failure patients. These results were true for both CAPW and RAPW signals, indicating the clinical significance of the Gaussian modeling, which should provide essential tools for further understanding the underlying physiological mechanisms of the artery pressure waveform.

Model fitting for small skin permeability data sets: hyperparameter optimisation in Gaussian Process Regression.

PubMed

Ashrafi, Parivash; Sun, Yi; Davey, Neil; Adams, Roderick G; Wilkinson, Simon C; Moss, Gary Patrick

2018-03-01

The aim of this study was to investigate how to improve predictions from Gaussian Process models by optimising the model hyperparameters. Optimisation methods, including Grid Search, Conjugate Gradient, Random Search, Evolutionary Algorithm and Hyper-prior, were evaluated and applied to previously published data. Data sets were also altered in a structured manner to reduce their size, which retained the range, or 'chemical space' of the key descriptors to assess the effect of the data range on model quality. The Hyper-prior Smoothbox kernel results in the best models for the majority of data sets, and they exhibited significantly better performance than benchmark quantitative structure-permeability relationship (QSPR) models. When the data sets were systematically reduced in size, the different optimisation methods generally retained their statistical quality, whereas benchmark QSPR models performed poorly. The design of the data set, and possibly also the approach to validation of the model, is critical in the development of improved models. The size of the data set, if carefully controlled, was not generally a significant factor for these models and that models of excellent statistical quality could be produced from substantially smaller data sets. © 2018 Royal Pharmaceutical Society.

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

NASA Technical Reports Server (NTRS)

Semper, Sean R.; Crassidis, John L.; George, Jemin; Mukherjee, Siddharth; Singla, Puneet

2015-01-01

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented.

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.

Static and transient performance prediction for CFB boilers using a Bayesian-Gaussian Neural Network

NASA Astrophysics Data System (ADS)

Ye, Haiwen; Ni, Weidou

1997-06-01

A Bayesian-Gaussian Neural Network (BGNN) is put forward in this paper to predict the static and transient performance of Circulating Fluidized Bed (CFB) boilers. The advantages of this network over Back-Propagation Neural Networks (BPNNs), easier determination of topology, simpler and time saving in training process as well as self-organizing ability, make this network more practical in on-line performance prediction for complicated processes. Simulation shows that this network is comparable to the BPNNs in predicting the performance of CFB boilers. Good and practical on-line performance predictions are essential for operation guide and model predictive control of CFB boilers, which are under research by the authors.

Classification and recognition of dynamical models: the role of phase, independent components, kernels and optimal transport.

PubMed

Bissacco, Alessandro; Chiuso, Alessandro; Soatto, Stefano

2007-11-01

We address the problem of performing decision tasks, and in particular classification and recognition, in the space of dynamical models in order to compare time series of data. Motivated by the application of recognition of human motion in image sequences, we consider a class of models that include linear dynamics, both stable and marginally stable (periodic), both minimum and non-minimum phase, driven by non-Gaussian processes. This requires extending existing learning and system identification algorithms to handle periodic modes and nonminimum phase behavior, while taking into account higher-order statistics of the data. Once a model is identified, we define a kernel-based cord distance between models that includes their dynamics, their initial conditions as well as input distribution. This is made possible by a novel kernel defined between two arbitrary (non-Gaussian) distributions, which is computed by efficiently solving an optimal transport problem. We validate our choice of models, inference algorithm, and distance on the tasks of human motion synthesis (sample paths of the learned models), and recognition (nearest-neighbor classification in the computed distance). However, our work can be applied more broadly where one needs to compare historical data while taking into account periodic trends, non-minimum phase behavior, and non-Gaussian input distributions.

Approximations to camera sensor noise

NASA Astrophysics Data System (ADS)

Jin, Xiaodan; Hirakawa, Keigo

2013-02-01

Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model the combined sensor noise. Though additive Gaussian noise with signal-dependent noise variance (SD-AWGN) and Poisson corruption are two widely used models to approximate the actual sensor noise distribution, the justification given to these types of models are based on limited evidence. The goal of this paper is to provide a more comprehensive characterization of random noise. We concluded by presenting concrete evidence that Poisson model is a better approximation to real camera model than SD-AWGN. We suggest further modification to Poisson that may improve the noise model.

Effects of scale-dependent non-Gaussianity on cosmological structures

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

LoVerde, Marilena; Miller, Amber; Shandera, Sarah

2008-04-15

The detection of primordial non-Gaussianity could provide a powerful means to test various inflationary scenarios. Although scale-invariant non-Gaussianity (often described by the f{sub NL} formalism) is currently best constrained by the CMB, single-field models with changing sound speed can have strongly scale-dependent non-Gaussianity. Such models could evade the CMB constraints but still have important effects at scales responsible for the formation of cosmological objects such as clusters and galaxies. We compute the effect of scale-dependent primordial non-Gaussianity on cluster number counts as a function of redshift, using a simple ansatz to model scale-dependent features. We forecast constraints on these modelsmore » achievable with forthcoming datasets. We also examine consequences for the galaxy bispectrum. Our results are relevant for the Dirac-Born-Infeld model of brane inflation, where the scale dependence of the non-Gaussianity is directly related to the geometry of the extra dimensions.« less

Gaussian statistics of the cosmic microwave background: Correlation of temperature extrema in the COBE DMR two-year sky maps

NASA Technical Reports Server (NTRS)

Kogut, A.; Banday, A. J.; Bennett, C. L.; Hinshaw, G.; Lubin, P. M.; Smoot, G. F.

1995-01-01

We use the two-point correlation function of the extrema points (peaks and valleys) in the Cosmic Background Explorer (COBE) Differential Microwave Radiometers (DMR) 2 year sky maps as a test for non-Gaussian temperature distribution in the cosmic microwave background anisotropy. A maximum-likelihood analysis compares the DMR data to n = 1 toy models whose random-phase spherical harmonic components a(sub lm) are drawn from either Gaussian, chi-square, or log-normal parent populations. The likelihood of the 53 GHz (A+B)/2 data is greatest for the exact Gaussian model. There is less than 10% chance that the non-Gaussian models tested describe the DMR data, limited primarily by type II errors in the statistical inference. The extrema correlation function is a stronger test for this class of non-Gaussian models than topological statistics such as the genus.

Separation of the low-frequency atmospheric variability into non-Gaussian multidimensional sources by Independent Subspace Analysis

NASA Astrophysics Data System (ADS)

Pires, Carlos; Ribeiro, Andreia

2016-04-01

An efficient nonlinear method of statistical source separation of space-distributed non-Gaussian distributed data is proposed. The method relies in the so called Independent Subspace Analysis (ISA), being tested on a long time-series of the stream-function field of an atmospheric quasi-geostrophic 3-level model (QG3) simulating the winter's monthly variability of the Northern Hemisphere. ISA generalizes the Independent Component Analysis (ICA) by looking for multidimensional and minimally dependent, uncorrelated and non-Gaussian distributed statistical sources among the rotated projections or subspaces of the multivariate probability distribution of the leading principal components of the working field whereas ICA restrict to scalar sources. The rationale of that technique relies upon the projection pursuit technique, looking for data projections of enhanced interest. In order to accomplish the decomposition, we maximize measures of the sources' non-Gaussianity by contrast functions which are given by squares of nonlinear, cross-cumulant-based correlations involving the variables spanning the sources. Therefore sources are sought matching certain nonlinear data structures. The maximized contrast function is built in such a way that it provides the minimization of the mean square of the residuals of certain nonlinear regressions. The issuing residuals, followed by spherization, provide a new set of nonlinear variable changes that are at once uncorrelated, quasi-independent and quasi-Gaussian, representing an advantage with respect to the Independent Components (scalar sources) obtained by ICA where the non-Gaussianity is concentrated into the non-Gaussian scalar sources. The new scalar sources obtained by the above process encompass the attractor's curvature thus providing improved nonlinear model indices of the low-frequency atmospheric variability which is useful since large circulation indices are nonlinearly correlated. The non-Gaussian tested sources (dyads and triads, respectively of two and three dimensions) lead to a dense data concentration along certain curves or surfaces, nearby which the clusters' centroids of the joint probability density function tend to be located. That favors a better splitting of the QG3 atmospheric model's weather regimes: the positive and negative phases of the Arctic Oscillation and positive and negative phases of the North Atlantic Oscillation. The leading model's non-Gaussian dyad is associated to a positive correlation between: 1) the squared anomaly of the extratropical jet-stream and 2) the meridional jet-stream meandering. Triadic sources coming from maximized third-order cross cumulants between pairwise uncorrelated components reveal situations of triadic wave resonance and nonlinear triadic teleconnections, only possible thanks to joint non-Gaussianity. That kind of triadic synergies are accounted for an Information-Theoretic measure: the Interaction Information. The dominant model's triad occurs between anomalies of: 1) the North Pole anomaly pressure 2) the jet-stream intensity at the Eastern North-American boundary and 3) the jet-stream intensity at the Eastern Asian boundary. Publication supported by project FCT UID/GEO/50019/2013 - Instituto Dom Luiz.

Comparison of non-Gaussian and Gaussian diffusion models of diffusion weighted imaging of rectal cancer at 3.0 T MRI.

PubMed

Zhang, Guangwen; Wang, Shuangshuang; Wen, Didi; Zhang, Jing; Wei, Xiaocheng; Ma, Wanling; Zhao, Weiwei; Wang, Mian; Wu, Guosheng; Zhang, Jinsong

2016-12-09

Water molecular diffusion in vivo tissue is much more complicated. We aimed to compare non-Gaussian diffusion models of diffusion-weighted imaging (DWI) including intra-voxel incoherent motion (IVIM), stretched-exponential model (SEM) and Gaussian diffusion model at 3.0 T MRI in patients with rectal cancer, and to determine the optimal model for investigating the water diffusion properties and characterization of rectal carcinoma. Fifty-nine consecutive patients with pathologically confirmed rectal adenocarcinoma underwent DWI with 16 b-values at a 3.0 T MRI system. DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models (IVIM-mono, IVIM-bi and SEM) on primary tumor and adjacent normal rectal tissue. Parameters of standard apparent diffusion coefficient (ADC), slow- and fast-ADC, fraction of fast ADC (f), α value and distributed diffusion coefficient (DDC) were generated and compared between the tumor and normal tissues. The SEM exhibited the best fitting results of actual DWI signal in rectal cancer and the normal rectal wall (R 2  = 0.998, 0.999 respectively). The DDC achieved relatively high area under the curve (AUC = 0.980) in differentiating tumor from normal rectal wall. Non-Gaussian diffusion models could assess tissue properties more accurately than the ADC derived Gaussian diffusion model. SEM may be used as a potential optimal model for characterization of rectal cancer.

Some new results on the statistics of radio wave scintillation. I - Empirical evidence for Gaussian statistics

NASA Technical Reports Server (NTRS)

Rino, C. L.; Livingston, R. C.; Whitney, H. E.

1976-01-01

This paper presents an analysis of ionospheric scintillation data which shows that the underlying statistical structure of the signal can be accurately modeled by the additive complex Gaussian perturbation predicted by the Born approximation in conjunction with an application of the central limit theorem. By making use of this fact, it is possible to estimate the in-phase, phase quadrature, and cophased scattered power by curve fitting to measured intensity histograms. By using this procedure, it is found that typically more than 80% of the scattered power is in phase quadrature with the undeviated signal component. Thus, the signal is modeled by a Gaussian, but highly non-Rician process. From simultaneous UHF and VHF data, only a weak dependence of this statistical structure on changes in the Fresnel radius is deduced. The signal variance is found to have a nonquadratic wavelength dependence. It is hypothesized that this latter effect is a subtle manifestation of locally homogeneous irregularity structures, a mathematical model proposed by Kolmogorov (1941) in his early studies of incompressible fluid turbulence.

On the characterization of flowering curves using Gaussian mixture models.

PubMed

Proïa, Frédéric; Pernet, Alix; Thouroude, Tatiana; Michel, Gilles; Clotault, Jérémy

2016-08-07

In this paper, we develop a statistical methodology applied to the characterization of flowering curves using Gaussian mixture models. Our study relies on a set of rosebushes flowering data, and Gaussian mixture models are mainly used to quantify the reblooming properties of each one. In this regard, we also suggest our own selection criterion to take into account the lack of symmetry of most of the flowering curves. Three classes are created on the basis of a principal component analysis conducted on a set of reblooming indicators, and a subclassification is made using a longitudinal k-means algorithm which also highlights the role played by the precocity of the flowering. In this way, we obtain an overview of the correlations between the features we decided to retain on each curve. In particular, results suggest the lack of correlation between reblooming and flowering precocity. The pertinent indicators obtained in this study will be a first step towards the comprehension of the environmental and genetic control of these biological processes. Copyright © 2016 Elsevier Ltd. All rights reserved.

Evaluation of non-Gaussian diffusion in cardiac MRI.

PubMed

McClymont, Darryl; Teh, Irvin; Carruth, Eric; Omens, Jeffrey; McCulloch, Andrew; Whittington, Hannah J; Kohl, Peter; Grau, Vicente; Schneider, Jürgen E

2017-09-01

The diffusion tensor model assumes Gaussian diffusion and is widely applied in cardiac diffusion MRI. However, diffusion in biological tissue deviates from a Gaussian profile as a result of hindrance and restriction from cell and tissue microstructure, and may be quantified better by non-Gaussian modeling. The aim of this study was to investigate non-Gaussian diffusion in healthy and hypertrophic hearts. Thirteen rat hearts (five healthy, four sham, four hypertrophic) were imaged ex vivo. Diffusion-weighted images were acquired at b-values up to 10,000 s/mm 2 . Models of diffusion were fit to the data and ranked based on the Akaike information criterion. The diffusion tensor was ranked best at b-values up to 2000 s/mm 2 but reflected the signal poorly in the high b-value regime, in which the best model was a non-Gaussian "beta distribution" model. Although there was considerable overlap in apparent diffusivities between the healthy, sham, and hypertrophic hearts, diffusion kurtosis and skewness in the hypertrophic hearts were more than 20% higher in the sheetlet and sheetlet-normal directions. Non-Gaussian diffusion models have a higher sensitivity for the detection of hypertrophy compared with the Gaussian model. In particular, diffusion kurtosis may serve as a useful biomarker for characterization of disease and remodeling in the heart. Magn Reson Med 78:1174-1186, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

Nonstationary stochastic charge fluctuations of a dust particle in plasmas.

PubMed

Shotorban, B

2011-06-01

Stochastic charge fluctuations of a dust particle that are due to discreteness of electrons and ions in plasmas can be described by a one-step process master equation [T. Matsoukas and M. Russell, J. Appl. Phys. 77, 4285 (1995)] with no exact solution. In the present work, using the system size expansion method of Van Kampen along with the linear noise approximation, a Fokker-Planck equation with an exact Gaussian solution is developed by expanding the master equation. The Gaussian solution has time-dependent mean and variance governed by two ordinary differential equations modeling the nonstationary process of dust particle charging. The model is tested via the comparison of its results to the results obtained by solving the master equation numerically. The electron and ion currents are calculated through the orbital motion limited theory. At various times of the nonstationary process of charging, the model results are in a very good agreement with the master equation results. The deviation is more significant when the standard deviation of the charge is comparable to the mean charge in magnitude.

The Gaussian atmospheric transport model and its sensitivity to the joint frequency distribution and parametric variability.

PubMed

Hamby, D M

2002-01-01

Reconstructed meteorological data are often used in some form of long-term wind trajectory models for estimating the historical impacts of atmospheric emissions. Meteorological data for the straight-line Gaussian plume model are put into a joint frequency distribution, a three-dimensional array describing atmospheric wind direction, speed, and stability. Methods using the Gaussian model and joint frequency distribution inputs provide reasonable estimates of downwind concentration and have been shown to be accurate to within a factor of four. We have used multiple joint frequency distributions and probabilistic techniques to assess the Gaussian plume model and determine concentration-estimate uncertainty and model sensitivity. We examine the straight-line Gaussian model while calculating both sector-averaged and annual-averaged relative concentrations at various downwind distances. The sector-average concentration model was found to be most sensitive to wind speed, followed by horizontal dispersion (sigmaZ), the importance of which increases as stability increases. The Gaussian model is not sensitive to stack height uncertainty. Precision of the frequency data appears to be most important to meteorological inputs when calculations are made for near-field receptors, increasing as stack height increases.

Optimisation of dispersion parameters of Gaussian plume model for CO₂ dispersion.

PubMed

Liu, Xiong; Godbole, Ajit; Lu, Cheng; Michal, Guillaume; Venton, Philip

2015-11-01

The carbon capture and storage (CCS) and enhanced oil recovery (EOR) projects entail the possibility of accidental release of carbon dioxide (CO2) into the atmosphere. To quantify the spread of CO2 following such release, the 'Gaussian' dispersion model is often used to estimate the resulting CO2 concentration levels in the surroundings. The Gaussian model enables quick estimates of the concentration levels. However, the traditionally recommended values of the 'dispersion parameters' in the Gaussian model may not be directly applicable to CO2 dispersion. This paper presents an optimisation technique to obtain the dispersion parameters in order to achieve a quick estimation of CO2 concentration levels in the atmosphere following CO2 blowouts. The optimised dispersion parameters enable the Gaussian model to produce quick estimates of CO2 concentration levels, precluding the necessity to set up and run much more complicated models. Computational fluid dynamics (CFD) models were employed to produce reference CO2 dispersion profiles in various atmospheric stability classes (ASC), different 'source strengths' and degrees of ground roughness. The performance of the CFD models was validated against the 'Kit Fox' field measurements, involving dispersion over a flat horizontal terrain, both with low and high roughness regions. An optimisation model employing a genetic algorithm (GA) to determine the best dispersion parameters in the Gaussian plume model was set up. Optimum values of the dispersion parameters for different ASCs that can be used in the Gaussian plume model for predicting CO2 dispersion were obtained.

Evolution of CMB spectral distortion anisotropies and tests of primordial non-Gaussianity

NASA Astrophysics Data System (ADS)

Chluba, Jens; Dimastrogiovanni, Emanuela; Amin, Mustafa A.; Kamionkowski, Marc

2017-04-01

Anisotropies in distortions to the frequency spectrum of the cosmic microwave background (CMB) can be created through spatially varying heating processes in the early Universe. For instance, the dissipation of small-scale acoustic modes does create distortion anisotropies, in particular for non-Gaussian primordial perturbations. In this work, we derive approximations that allow describing the associated distortion field. We provide a systematic formulation of the problem using Fourier-space window functions, clarifying and generalizing previous approximations. Our expressions highlight the fact that the amplitudes of the spectral-distortion fluctuations induced by non-Gaussianity depend also on the homogeneous value of those distortions. Absolute measurements are thus required to obtain model-independent distortion constraints on primordial non-Gaussianity. We also include a simple description for the evolution of distortions through photon diffusion, showing that these corrections can usually be neglected. Our formulation provides a systematic framework for computing higher order correlation functions of distortions with CMB temperature anisotropies and can be extended to describe correlations with polarization anisotropies.

Quantum key distillation from Gaussian states by Gaussian operations.

PubMed

Navascués, M; Bae, J; Cirac, J I; Lewestein, M; Sanpera, A; Acín, A

2005-01-14

We study the secrecy properties of Gaussian states under Gaussian operations. Although such operations are useless for quantum distillation, we prove that it is possible to distill a secret key secure against any attack from sufficiently entangled Gaussian states with nonpositive partial transposition. Moreover, all such states allow for key distillation, when Eve is assumed to perform finite-size coherent attacks before the reconciliation process.

Demonstration of emulator-based Bayesian calibration of safety analysis codes: Theory and formulation

DOE PAGES

Yurko, Joseph P.; Buongiorno, Jacopo; Youngblood, Robert

2015-05-28

System codes for simulation of safety performance of nuclear plants may contain parameters whose values are not known very accurately. New information from tests or operating experience is incorporated into safety codes by a process known as calibration, which reduces uncertainty in the output of the code and thereby improves its support for decision-making. The work reported here implements several improvements on classic calibration techniques afforded by modern analysis techniques. The key innovation has come from development of code surrogate model (or code emulator) construction and prediction algorithms. Use of a fast emulator makes the calibration processes used here withmore » Markov Chain Monte Carlo (MCMC) sampling feasible. This study uses Gaussian Process (GP) based emulators, which have been used previously to emulate computer codes in the nuclear field. The present work describes the formulation of an emulator that incorporates GPs into a factor analysis-type or pattern recognition-type model. This “function factorization” Gaussian Process (FFGP) model allows overcoming limitations present in standard GP emulators, thereby improving both accuracy and speed of the emulator-based calibration process. Calibration of a friction-factor example using a Method of Manufactured Solution is performed to illustrate key properties of the FFGP based process.« less

Gaussian Processes for Data-Efficient Learning in Robotics and Control.

PubMed

Deisenroth, Marc Peter; Fox, Dieter; Rasmussen, Carl Edward

2015-02-01

Autonomous learning has been a promising direction in control and robotics for more than a decade since data-driven learning allows to reduce the amount of engineering knowledge, which is otherwise required. However, autonomous reinforcement learning (RL) approaches typically require many interactions with the system to learn controllers, which is a practical limitation in real systems, such as robots, where many interactions can be impractical and time consuming. To address this problem, current learning approaches typically require task-specific knowledge in form of expert demonstrations, realistic simulators, pre-shaped policies, or specific knowledge about the underlying dynamics. In this paper, we follow a different approach and speed up learning by extracting more information from data. In particular, we learn a probabilistic, non-parametric Gaussian process transition model of the system. By explicitly incorporating model uncertainty into long-term planning and controller learning our approach reduces the effects of model errors, a key problem in model-based learning. Compared to state-of-the art RL our model-based policy search method achieves an unprecedented speed of learning. We demonstrate its applicability to autonomous learning in real robot and control tasks.

Resource theory of non-Gaussian operations

NASA Astrophysics Data System (ADS)

Zhuang, Quntao; Shor, Peter W.; Shapiro, Jeffrey H.

2018-05-01

Non-Gaussian states and operations are crucial for various continuous-variable quantum information processing tasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussian operations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operations as resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotone that is nonincreasing under the set of free superoperations, i.e., concatenation and tensoring with Gaussian channels. For conditional unitary maps, this monotone can be analytically calculated. As examples, we show that the non-Gaussianity of ideal photon-number subtraction and photon-number addition equal the non-Gaussianity of the single-photon Fock state. Based on our non-Gaussianity monotone, we divide non-Gaussian operations into two classes: (i) the finite non-Gaussianity class, e.g., photon-number subtraction, photon-number addition, and all Gaussian-dilatable non-Gaussian channels; and (ii) the diverging non-Gaussianity class, e.g., the binary phase-shift channel and the Kerr nonlinearity. This classification also implies that not all non-Gaussian channels are exactly Gaussian dilatable. Our resource theory enables a quantitative characterization and a first classification of non-Gaussian operations, paving the way towards the full understanding of non-Gaussianity.

Increasing accuracy of dispersal kernels in grid-based population models

USGS Publications Warehouse

Slone, D.H.

2011-01-01

Dispersal kernels in grid-based population models specify the proportion, distance and direction of movements within the model landscape. Spatial errors in dispersal kernels can have large compounding effects on model accuracy. Circular Gaussian and Laplacian dispersal kernels at a range of spatial resolutions were investigated, and methods for minimizing errors caused by the discretizing process were explored. Kernels of progressively smaller sizes relative to the landscape grid size were calculated using cell-integration and cell-center methods. These kernels were convolved repeatedly, and the final distribution was compared with a reference analytical solution. For large Gaussian kernels (σ > 10 cells), the total kernel error was <10 &sup-11; compared to analytical results. Using an invasion model that tracked the time a population took to reach a defined goal, the discrete model results were comparable to the analytical reference. With Gaussian kernels that had σ ≤ 0.12 using the cell integration method, or σ ≤ 0.22 using the cell center method, the kernel error was greater than 10%, which resulted in invasion times that were orders of magnitude different than theoretical results. A goal-seeking routine was developed to adjust the kernels to minimize overall error. With this, corrections for small kernels were found that decreased overall kernel error to <10-11 and invasion time error to <5%.

Sequential updating of multimodal hydrogeologic parameter fields using localization and clustering techniques

NASA Astrophysics Data System (ADS)

Sun, Alexander Y.; Morris, Alan P.; Mohanty, Sitakanta

2009-07-01

Estimated parameter distributions in groundwater models may contain significant uncertainties because of data insufficiency. Therefore, adaptive uncertainty reduction strategies are needed to continuously improve model accuracy by fusing new observations. In recent years, various ensemble Kalman filters have been introduced as viable tools for updating high-dimensional model parameters. However, their usefulness is largely limited by the inherent assumption of Gaussian error statistics. Hydraulic conductivity distributions in alluvial aquifers, for example, are usually non-Gaussian as a result of complex depositional and diagenetic processes. In this study, we combine an ensemble Kalman filter with grid-based localization and a Gaussian mixture model (GMM) clustering techniques for updating high-dimensional, multimodal parameter distributions via dynamic data assimilation. We introduce innovative strategies (e.g., block updating and dimension reduction) to effectively reduce the computational costs associated with these modified ensemble Kalman filter schemes. The developed data assimilation schemes are demonstrated numerically for identifying the multimodal heterogeneous hydraulic conductivity distributions in a binary facies alluvial aquifer. Our results show that localization and GMM clustering are very promising techniques for assimilating high-dimensional, multimodal parameter distributions, and they outperform the corresponding global ensemble Kalman filter analysis scheme in all scenarios considered.

An integrated Gaussian process regression for prediction of remaining useful life of slow speed bearings based on acoustic emission

NASA Astrophysics Data System (ADS)

Aye, S. A.; Heyns, P. S.

2017-02-01

This paper proposes an optimal Gaussian process regression (GPR) for the prediction of remaining useful life (RUL) of slow speed bearings based on a novel degradation assessment index obtained from acoustic emission signal. The optimal GPR is obtained from an integration or combination of existing simple mean and covariance functions in order to capture the observed trend of the bearing degradation as well the irregularities in the data. The resulting integrated GPR model provides an excellent fit to the data and improves over the simple GPR models that are based on simple mean and covariance functions. In addition, it achieves a low percentage error prediction of the remaining useful life of slow speed bearings. These findings are robust under varying operating conditions such as loading and speed and can be applied to nonlinear and nonstationary machine response signals useful for effective preventive machine maintenance purposes.

Rockfall travel distances theoretical distributions

NASA Astrophysics Data System (ADS)

Jaboyedoff, Michel; Derron, Marc-Henri; Pedrazzini, Andrea

2017-04-01

The probability of propagation of rockfalls is a key part of hazard assessment, because it permits to extrapolate the probability of propagation of rockfall either based on partial data or simply theoretically. The propagation can be assumed frictional which permits to describe on average the propagation by a line of kinetic energy which corresponds to the loss of energy along the path. But loss of energy can also be assumed as a multiplicative process or a purely random process. The distributions of the rockfall block stop points can be deduced from such simple models, they lead to Gaussian, Inverse-Gaussian, Log-normal or exponential negative distributions. The theoretical background is presented, and the comparisons of some of these models with existing data indicate that these assumptions are relevant. The results are either based on theoretical considerations or by fitting results. They are potentially very useful for rockfall hazard zoning and risk assessment. This approach will need further investigations.

Gaussian processes with optimal kernel construction for neuro-degenerative clinical onset prediction

NASA Astrophysics Data System (ADS)

Canas, Liane S.; Yvernault, Benjamin; Cash, David M.; Molteni, Erika; Veale, Tom; Benzinger, Tammie; Ourselin, Sébastien; Mead, Simon; Modat, Marc

2018-02-01

Gaussian Processes (GP) are a powerful tool to capture the complex time-variations of a dataset. In the context of medical imaging analysis, they allow a robust modelling even in case of highly uncertain or incomplete datasets. Predictions from GP are dependent of the covariance kernel function selected to explain the data variance. To overcome this limitation, we propose a framework to identify the optimal covariance kernel function to model the data.The optimal kernel is defined as a composition of base kernel functions used to identify correlation patterns between data points. Our approach includes a modified version of the Compositional Kernel Learning (CKL) algorithm, in which we score the kernel families using a new energy function that depends both the Bayesian Information Criterion (BIC) and the explained variance score. We applied the proposed framework to model the progression of neurodegenerative diseases over time, in particular the progression of autosomal dominantly-inherited Alzheimer's disease, and use it to predict the time to clinical onset of subjects carrying genetic mutation.

Airborne Detection and Tracking of Geologic Leakage Sites

NASA Astrophysics Data System (ADS)

Jacob, Jamey; Allamraju, Rakshit; Axelrod, Allan; Brown, Calvin; Chowdhary, Girish; Mitchell, Taylor

2014-11-01

Safe storage of CO2 to reduce greenhouse gas emissions without adversely affecting energy use or hindering economic growth requires development of monitoring technology that is capable of validating storage permanence while ensuring the integrity of sequestration operations. Soil gas monitoring has difficulty accurately distinguishing gas flux signals related to leakage from those associated with meteorologically driven changes of soil moisture and temperature. Integrated ground and airborne monitoring systems are being deployed capable of directly detecting CO2 concentration in storage sites. Two complimentary approaches to detecting leaks in the carbon sequestration fields are presented. The first approach focuses on reducing the requisite network communication for fusing individual Gaussian Process (GP) CO2 sensing models into a global GP CO2 model. The GP fusion approach learns how to optimally allocate the static and mobile sensors. The second approach leverages a hierarchical GP-Sigmoidal Gaussian Cox Process for airborne predictive mission planning to optimally reducing the entropy of the global CO2 model. Results from the approaches will be presented.

Synchronic interval Gaussian mixed-integer programming for air quality management.

PubMed

Cheng, Guanhui; Huang, Guohe Gordon; Dong, Cong

2015-12-15

To reveal the synchronism of interval uncertainties, the tradeoff between system optimality and security, the discreteness of facility-expansion options, the uncertainty of pollutant dispersion processes, and the seasonality of wind features in air quality management (AQM) systems, a synchronic interval Gaussian mixed-integer programming (SIGMIP) approach is proposed in this study. A robust interval Gaussian dispersion model is developed for approaching the pollutant dispersion process under interval uncertainties and seasonal variations. The reflection of synchronic effects of interval uncertainties in the programming objective is enabled through introducing interval functions. The proposition of constraint violation degrees helps quantify the tradeoff between system optimality and constraint violation under interval uncertainties. The overall optimality of system profits of an SIGMIP model is achieved based on the definition of an integrally optimal solution. Integer variables in the SIGMIP model are resolved by the existing cutting-plane method. Combining these efforts leads to an effective algorithm for the SIGMIP model. An application to an AQM problem in a region in Shandong Province, China, reveals that the proposed SIGMIP model can facilitate identifying the desired scheme for AQM. The enhancement of the robustness of optimization exercises may be helpful for increasing the reliability of suggested schemes for AQM under these complexities. The interrelated tradeoffs among control measures, emission sources, flow processes, receptors, influencing factors, and economic and environmental goals are effectively balanced. Interests of many stakeholders are reasonably coordinated. The harmony between economic development and air quality control is enabled. Results also indicate that the constraint violation degree is effective at reflecting the compromise relationship between constraint-violation risks and system optimality under interval uncertainties. This can help decision makers mitigate potential risks, e.g. insufficiency of pollutant treatment capabilities, exceedance of air quality standards, deficiency of pollution control fund, or imbalance of economic or environmental stress, in the process of guiding AQM. Copyright © 2015 Elsevier B.V. All rights reserved.

The effect of noise and lipid signals on determination of Gaussian and non-Gaussian diffusion parameters in skeletal muscle.

PubMed

Cameron, Donnie; Bouhrara, Mustapha; Reiter, David A; Fishbein, Kenneth W; Choi, Seongjin; Bergeron, Christopher M; Ferrucci, Luigi; Spencer, Richard G

2017-07-01

This work characterizes the effect of lipid and noise signals on muscle diffusion parameter estimation in several conventional and non-Gaussian models, the ultimate objectives being to characterize popular fat suppression approaches for human muscle diffusion studies, to provide simulations to inform experimental work and to report normative non-Gaussian parameter values. The models investigated in this work were the Gaussian monoexponential and intravoxel incoherent motion (IVIM) models, and the non-Gaussian kurtosis and stretched exponential models. These were evaluated via simulations, and in vitro and in vivo experiments. Simulations were performed using literature input values, modeling fat contamination as an additive baseline to data, whereas phantom studies used a phantom containing aliphatic and olefinic fats and muscle-like gel. Human imaging was performed in the hamstring muscles of 10 volunteers. Diffusion-weighted imaging was applied with spectral attenuated inversion recovery (SPAIR), slice-select gradient reversal and water-specific excitation fat suppression, alone and in combination. Measurement bias (accuracy) and dispersion (precision) were evaluated, together with intra- and inter-scan repeatability. Simulations indicated that noise in magnitude images resulted in <6% bias in diffusion coefficients and non-Gaussian parameters (α, K), whereas baseline fitting minimized fat bias for all models, except IVIM. In vivo, popular SPAIR fat suppression proved inadequate for accurate parameter estimation, producing non-physiological parameter estimates without baseline fitting and large biases when it was used. Combining all three fat suppression techniques and fitting data with a baseline offset gave the best results of all the methods studied for both Gaussian diffusion and, overall, for non-Gaussian diffusion. It produced consistent parameter estimates for all models, except IVIM, and highlighted non-Gaussian behavior perpendicular to muscle fibers (α ~ 0.95, K ~ 3.1). These results show that effective fat suppression is crucial for accurate measurement of non-Gaussian diffusion parameters, and will be an essential component of quantitative studies of human muscle quality. Published 2017. This article is a U.S. Government work and is in the public domain in the USA.

Moving target detection method based on improved Gaussian mixture model

NASA Astrophysics Data System (ADS)

Ma, J. Y.; Jie, F. R.; Hu, Y. J.

2017-07-01

Gaussian Mixture Model is often employed to build background model in background difference methods for moving target detection. This paper puts forward an adaptive moving target detection algorithm based on improved Gaussian Mixture Model. According to the graylevel convergence for each pixel, adaptively choose the number of Gaussian distribution to learn and update background model. Morphological reconstruction method is adopted to eliminate the shadow.. Experiment proved that the proposed method not only has good robustness and detection effect, but also has good adaptability. Even for the special cases when the grayscale changes greatly and so on, the proposed method can also make outstanding performance.

The properties of the anti-tumor model with coupling non-Gaussian noise and Gaussian colored noise

NASA Astrophysics Data System (ADS)

Guo, Qin; Sun, Zhongkui; Xu, Wei

2016-05-01

The anti-tumor model with correlation between multiplicative non-Gaussian noise and additive Gaussian-colored noise has been investigated in this paper. The behaviors of the stationary probability distribution demonstrate that the multiplicative non-Gaussian noise plays a dual role in the development of tumor and an appropriate additive Gaussian colored noise can lead to a minimum of the mean value of tumor cell population. The mean first passage time is calculated to quantify the effects of noises on the transition time of tumors between the stable states. An increase in both the non-Gaussian noise intensity and the departure from the Gaussian noise can accelerate the transition from the disease state to the healthy state. On the contrary, an increase in cross-correlated degree will slow down the transition. Moreover, the correlation time can enhance the stability of the disease state.

Probability density and exceedance rate functions of locally Gaussian turbulence

NASA Technical Reports Server (NTRS)

Mark, W. D.

1989-01-01

A locally Gaussian model of turbulence velocities is postulated which consists of the superposition of a slowly varying strictly Gaussian component representing slow temporal changes in the mean wind speed and a more rapidly varying locally Gaussian turbulence component possessing a temporally fluctuating local variance. Series expansions of the probability density and exceedance rate functions of the turbulence velocity model, based on Taylor's series, are derived. Comparisons of the resulting two-term approximations with measured probability density and exceedance rate functions of atmospheric turbulence velocity records show encouraging agreement, thereby confirming the consistency of the measured records with the locally Gaussian model. Explicit formulas are derived for computing all required expansion coefficients from measured turbulence records.

An End-to-End Model of Plant Pheromone Channel for Long Range Molecular Communication.

PubMed

Unluturk, Bige D; Akyildiz, Ian F

2017-01-01

A new track in molecular communication is using pheromones which can scale up the range of diffusion-based communication from μm meters to meters and enable new applications requiring long range. Pheromone communication is the emission of molecules in the air which trigger behavioral or physiological responses in receiving organisms. The objective of this paper is to introduce a new end-to-end model which incorporates pheromone behavior with communication theory for plants. The proposed model includes both the transmission and reception processes as well as the propagation channel. The transmission process is the emission of pheromones from the leaves of plants. The dispersion of pheromones by the flow of wind constitutes the propagation process. The reception process is the sensing of pheromones by the pheromone receptors of plants. The major difference of pheromone communication from other molecular communication techniques is the dispersion channel acting under the laws of turbulent diffusion. In this paper, the pheromone channel is modeled as a Gaussian puff, i.e., a cloud of pheromone released instantaneously from the source whose dispersion follows a Gaussian distribution. Numerical results on the performance of the overall end-to-end pheromone channel in terms of normalized gain and delay are provided.

Electrospinning of Polyaniline/Poly(Lactic Acid) Ultrathin Fibers: Process and Statistical Modeling using a Non-Gaussian Approach

USDA-ARS?s Scientific Manuscript database

Fibers of poly(lactic acid) (PLA) blended with p-toluenesulfonic acid-doped polyaniline, PAni.TSA, were obtained by lectrospinning, following a factorial design which was used mainly to study the effect of four process parameters (PLA solution concentration, PAni solution concentration, applied volt...

A Maximum Entropy Method for Particle Filtering

NASA Astrophysics Data System (ADS)

Eyink, Gregory L.; Kim, Sangil

2006-06-01

Standard ensemble or particle filtering schemes do not properly represent states of low priori probability when the number of available samples is too small, as is often the case in practical applications. We introduce here a set of parametric resampling methods to solve this problem. Motivated by a general H-theorem for relative entropy, we construct parametric models for the filter distributions as maximum-entropy/minimum-information models consistent with moments of the particle ensemble. When the prior distributions are modeled as mixtures of Gaussians, our method naturally generalizes the ensemble Kalman filter to systems with highly non-Gaussian statistics. We apply the new particle filters presented here to two simple test cases: a one-dimensional diffusion process in a double-well potential and the three-dimensional chaotic dynamical system of Lorenz.

Fractal scaling analysis of groundwater dynamics in confined aquifers

NASA Astrophysics Data System (ADS)

Tu, Tongbi; Ercan, Ali; Kavvas, M. Levent

2017-10-01

Groundwater closely interacts with surface water and even climate systems in most hydroclimatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality, and multifractal detrended fluctuation analysis (MF-DFA) and multiscale multifractal analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation, is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes that can model both the long-memory behavior and the Brownian finite-memory behavior.

Individualized Gaussian process-based prediction and detection of local and global gray matter abnormalities in elderly subjects.

PubMed

Ziegler, G; Ridgway, G R; Dahnke, R; Gaser, C

2014-08-15

Structural imaging based on MRI is an integral component of the clinical assessment of patients with potential dementia. We here propose an individualized Gaussian process-based inference scheme for clinical decision support in healthy and pathological aging elderly subjects using MRI. The approach aims at quantitative and transparent support for clinicians who aim to detect structural abnormalities in patients at risk of Alzheimer's disease or other types of dementia. Firstly, we introduce a generative model incorporating our knowledge about normative decline of local and global gray matter volume across the brain in elderly. By supposing smooth structural trajectories the models account for the general course of age-related structural decline as well as late-life accelerated loss. Considering healthy subjects' demography and global brain parameters as informative about normal brain aging variability affords individualized predictions in single cases. Using Gaussian process models as a normative reference, we predict new subjects' brain scans and quantify the local gray matter abnormalities in terms of Normative Probability Maps (NPM) and global z-scores. By integrating the observed expectation error and the predictive uncertainty, the local maps and global scores exploit the advantages of Bayesian inference for clinical decisions and provide a valuable extension of diagnostic information about pathological aging. We validate the approach in simulated data and real MRI data. We train the GP framework using 1238 healthy subjects with ages 18-94 years, and predict in 415 independent test subjects diagnosed as healthy controls, Mild Cognitive Impairment and Alzheimer's disease. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Individualized Gaussian process-based prediction and detection of local and global gray matter abnormalities in elderly subjects

PubMed Central

Ziegler, G.; Ridgway, G.R.; Dahnke, R.; Gaser, C.

2014-01-01

Structural imaging based on MRI is an integral component of the clinical assessment of patients with potential dementia. We here propose an individualized Gaussian process-based inference scheme for clinical decision support in healthy and pathological aging elderly subjects using MRI. The approach aims at quantitative and transparent support for clinicians who aim to detect structural abnormalities in patients at risk of Alzheimer's disease or other types of dementia. Firstly, we introduce a generative model incorporating our knowledge about normative decline of local and global gray matter volume across the brain in elderly. By supposing smooth structural trajectories the models account for the general course of age-related structural decline as well as late-life accelerated loss. Considering healthy subjects' demography and global brain parameters as informative about normal brain aging variability affords individualized predictions in single cases. Using Gaussian process models as a normative reference, we predict new subjects' brain scans and quantify the local gray matter abnormalities in terms of Normative Probability Maps (NPM) and global z-scores. By integrating the observed expectation error and the predictive uncertainty, the local maps and global scores exploit the advantages of Bayesian inference for clinical decisions and provide a valuable extension of diagnostic information about pathological aging. We validate the approach in simulated data and real MRI data. We train the GP framework using 1238 healthy subjects with ages 18–94 years, and predict in 415 independent test subjects diagnosed as healthy controls, Mild Cognitive Impairment and Alzheimer's disease. PMID:24742919

Gaussian process model for extrapolation of scattering observables for complex molecules: From benzene to benzonitrile

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

Cui, Jie; Krems, Roman V.; Li, Zhiying

2015-10-21

We consider a problem of extrapolating the collision properties of a large polyatomic molecule A–H to make predictions of the dynamical properties for another molecule related to A–H by the substitution of the H atom with a small molecular group X, without explicitly computing the potential energy surface for A–X. We assume that the effect of the −H →−X substitution is embodied in a multidimensional function with unknown parameters characterizing the change of the potential energy surface. We propose to apply the Gaussian Process model to determine the dependence of the dynamical observables on the unknown parameters. This can bemore » used to produce an interval of the observable values which corresponds to physical variations of the potential parameters. We show that the Gaussian Process model combined with classical trajectory calculations can be used to obtain the dependence of the cross sections for collisions of C{sub 6}H{sub 5}CN with He on the unknown parameters describing the interaction of the He atom with the CN fragment of the molecule. The unknown parameters are then varied within physically reasonable ranges to produce a prediction uncertainty of the cross sections. The results are normalized to the cross sections for He — C{sub 6}H{sub 6} collisions obtained from quantum scattering calculations in order to provide a prediction interval of the thermally averaged cross sections for collisions of C{sub 6}H{sub 5}CN with He.« less

A computer program for uncertainty analysis integrating regression and Bayesian methods

USGS Publications Warehouse

Lu, Dan; Ye, Ming; Hill, Mary C.; Poeter, Eileen P.; Curtis, Gary

2014-01-01

This work develops a new functionality in UCODE_2014 to evaluate Bayesian credible intervals using the Markov Chain Monte Carlo (MCMC) method. The MCMC capability in UCODE_2014 is based on the FORTRAN version of the differential evolution adaptive Metropolis (DREAM) algorithm of Vrugt et al. (2009), which estimates the posterior probability density function of model parameters in high-dimensional and multimodal sampling problems. The UCODE MCMC capability provides eleven prior probability distributions and three ways to initialize the sampling process. It evaluates parametric and predictive uncertainties and it has parallel computing capability based on multiple chains to accelerate the sampling process. This paper tests and demonstrates the MCMC capability using a 10-dimensional multimodal mathematical function, a 100-dimensional Gaussian function, and a groundwater reactive transport model. The use of the MCMC capability is made straightforward and flexible by adopting the JUPITER API protocol. With the new MCMC capability, UCODE_2014 can be used to calculate three types of uncertainty intervals, which all can account for prior information: (1) linear confidence intervals which require linearity and Gaussian error assumptions and typically 10s–100s of highly parallelizable model runs after optimization, (2) nonlinear confidence intervals which require a smooth objective function surface and Gaussian observation error assumptions and typically 100s–1,000s of partially parallelizable model runs after optimization, and (3) MCMC Bayesian credible intervals which require few assumptions and commonly 10,000s–100,000s or more partially parallelizable model runs. Ready access allows users to select methods best suited to their work, and to compare methods in many circumstances.

Some error bounds for K-iterated Gaussian recursive filters

NASA Astrophysics Data System (ADS)

Cuomo, Salvatore; Galletti, Ardelio; Giunta, Giulio; Marcellino, Livia

2016-10-01

Recursive filters (RFs) have achieved a central role in several research fields over the last few years. For example, they are used in image processing, in data assimilation and in electrocardiogram denoising. More in particular, among RFs, the Gaussian RFs are an efficient computational tool for approximating Gaussian-based convolutions and are suitable for digital image processing and applications of the scale-space theory. As is a common knowledge, the Gaussian RFs, applied to signals with support in a finite domain, generate distortions and artifacts, mostly localized at the boundaries. Heuristic and theoretical improvements have been proposed in literature to deal with this issue (namely boundary conditions). They include the case in which a Gaussian RF is applied more than once, i.e. the so called K-iterated Gaussian RFs. In this paper, starting from a summary of the comprehensive mathematical background, we consider the case of the K-iterated first-order Gaussian RF and provide the study of its numerical stability and some component-wise theoretical error bounds.

Directionality volatility in electroencephalogram time series

NASA Astrophysics Data System (ADS)

Mansor, Mahayaudin M.; Green, David A.; Metcalfe, Andrew V.

2016-06-01

We compare time series of electroencephalograms (EEGs) from healthy volunteers with EEGs from subjects diagnosed with epilepsy. The EEG time series from the healthy group are recorded during awake state with their eyes open and eyes closed, and the records from subjects with epilepsy are taken from three different recording regions of pre-surgical diagnosis: hippocampal, epileptogenic and seizure zone. The comparisons for these 5 categories are in terms of deviations from linear time series models with constant variance Gaussian white noise error inputs. One feature investigated is directionality, and how this can be modelled by either non-linear threshold autoregressive models or non-Gaussian errors. A second feature is volatility, which is modelled by Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) processes. Other features include the proportion of variability accounted for by time series models, and the skewness and the kurtosis of the residuals. The results suggest these comparisons may have diagnostic potential for epilepsy and provide early warning of seizures.

Multivariate Bayesian analysis of Gaussian, right censored Gaussian, ordered categorical and binary traits using Gibbs sampling

PubMed Central

Korsgaard, Inge Riis; Lund, Mogens Sandø; Sorensen, Daniel; Gianola, Daniel; Madsen, Per; Jensen, Just

2003-01-01

A fully Bayesian analysis using Gibbs sampling and data augmentation in a multivariate model of Gaussian, right censored, and grouped Gaussian traits is described. The grouped Gaussian traits are either ordered categorical traits (with more than two categories) or binary traits, where the grouping is determined via thresholds on the underlying Gaussian scale, the liability scale. Allowances are made for unequal models, unknown covariance matrices and missing data. Having outlined the theory, strategies for implementation are reviewed. These include joint sampling of location parameters; efficient sampling from the fully conditional posterior distribution of augmented data, a multivariate truncated normal distribution; and sampling from the conditional inverse Wishart distribution, the fully conditional posterior distribution of the residual covariance matrix. Finally, a simulated dataset was analysed to illustrate the methodology. This paper concentrates on a model where residuals associated with liabilities of the binary traits are assumed to be independent. A Bayesian analysis using Gibbs sampling is outlined for the model where this assumption is relaxed. PMID:12633531

Gaussian Mixture Model of Heart Rate Variability

PubMed Central

Costa, Tommaso; Boccignone, Giuseppe; Ferraro, Mario

2012-01-01

Heart rate variability (HRV) is an important measure of sympathetic and parasympathetic functions of the autonomic nervous system and a key indicator of cardiovascular condition. This paper proposes a novel method to investigate HRV, namely by modelling it as a linear combination of Gaussians. Results show that three Gaussians are enough to describe the stationary statistics of heart variability and to provide a straightforward interpretation of the HRV power spectrum. Comparisons have been made also with synthetic data generated from different physiologically based models showing the plausibility of the Gaussian mixture parameters. PMID:22666386

Characterizing Mafic, Clay, and Carbonate Components found in MRO/CRISM Images in Libya Montes, Mars, using Advances in Automated Gaussian Modeling of Spectral Features

NASA Astrophysics Data System (ADS)

Makarewicz, H. D.; Parente, M.; Perry, K. A.; McKeown, N. K.; Bishop, J. L.

2009-12-01

Aqueous processes have been inferred at the Libya Montes rim/terrace complex of the southern Isidis Basin due to the dense concentration of valley networks [1]. Coordinated CRISM-HiRISE investigations of this region characterized discrete units of ancient phyllosilicate deposits covered by an olivine-rich material and a pyroxene caprock [2]. CRISM mapping data show minor phyllosilicate abundances widespread throughout the Southern Highlands [3], which are dominated by low-Ca pyroxene bearing material [4,5]. The carbonate magnesite has also been located throughout this area [6] and at Libya Montes [7]. Our current study involves detailed characterization of the minerals present at Libya Montes through implementation of improved automated Gaussian modeling methods. We have developed an automated procedure for modeling spectral features using Gaussians that has been successfully applied to laboratory studies and hyperspectral analyses of Mars [8,9,10,11]. Several studies are being conducted to improve and validate these models. These include a comparison of initialization methods, continuum methods, optimization algorithms, and modeled functions. The modeled functions compared include Gaussians, saturated Gaussians, and Lorentzians. This algorithm and the modeling studies are currently being applied towards analyses of CRISM hyperspectral images of Libya Montes and laboratory spectra of mineral mixtures. Specifically, olivine, pyroxene, phyllosilicate, and carbonate deposits are being modeled and classified by composition in CRISM images. References [1]Crumpler, L. S., and K. L. Tanaka (2003) J. Geophys. Res., 108, DOI: 8010.1029/2002JE002040. [2]Bishop, J. L., et al. (2007) 7th Int'l Mars Conf. [3]Mustard, J. F., et al. (2008) Nature, 454, 07305. [4]Bibring, J.-P., et al. (2005) Science, 307,1576. [5]Mustard, J. F., et al.(2005) Science, 307, 1594. [6]Ehlmann, B. L., et al. (2008) Science, 322, 1828. [7]Perry, K., et al. (2009) AGU Fall Mtng. [8]Makarewicz, H. D., et al. (2009) IEEE Whispers Wkshp. [9]Makarewicz, H. D., et al. (2008) AGU Fall Mtng. [10]Makarewicz, H. D., et al. (2009) LPSC. [11]Makarewicz, H. D., et al. (2009) Lunar Sci Forum.

[Method of correcting sensitivity nonuniformity using gaussian distribution on 3.0 Tesla abdominal MRI].

PubMed

Hayashi, Norio; Miyati, Tosiaki; Takanaga, Masako; Ohno, Naoki; Hamaguchi, Takashi; Kozaka, Kazuto; Sanada, Shigeru; Yamamoto, Tomoyuki; Matsui, Osamu

2011-01-01

In the direction where the phased array coil used in parallel magnetic resonance imaging (MRI) is perpendicular to the arrangement, sensitivity falls significantly. Moreover, in a 3.0 tesla (3T) abdominal MRI, the quality of the image is reduced by changes in the relaxation time, reinforcement of the magnetic susceptibility effect, etc. In a 3T MRI, which has a high resonant frequency, the signal of the depths (central part) is reduced in the trunk part. SCIC, which is sensitivity correction processing, has inadequate correction processing, such as that edges are emphasized and the central part is corrected. Therefore, we used 3T with a Gaussian distribution. The uneven compensation processing for sensitivity of an abdomen MR image was considered. The correction processing consisted of the following methods. 1) The center of gravity of the domain of the human body in an abdomen MR image was calculated. 2) The correction coefficient map was created from the center of gravity using the Gaussian distribution. 3) The sensitivity correction image was created from the correction coefficient map and the original picture image. Using the Gaussian correction to process the image, the uniformity calculated using the NEMA method was improved significantly compared to the original image of a phantom. In a visual evaluation by radiologists, the uniformity was improved significantly using the Gaussian correction processing. Because of the homogeneous improvement of the abdomen image taken using 3T MRI, the Gaussian correction processing is considered to be a very useful technique.

Random medium model for cusping of plane waves.

PubMed

Li, Jia; Korotkova, Olga

2017-09-01

We introduce a model for a three-dimensional (3D) Schell-type stationary medium whose degree of potential's correlation satisfies the Fractional Multi-Gaussian (FMG) function. Compared with the scattered profile produced by the Gaussian Schell-model (GSM) medium, the Fractional Multi-Gaussian Schell-model (FMGSM) medium gives rise to a sharp concave intensity apex in the scattered field. This implies that the FMGSM medium also accounts for a larger than Gaussian's power in the bucket (PIB) in the forward scattering direction, hence being a better candidate than the GSM medium for generating highly-focused (cusp-like) scattered profiles in the far zone. Compared to other mathematical models for the medium's correlation function which can produce similar cusped scattered profiles the FMG function offers unprecedented tractability being the weighted superposition of Gaussian functions. Our results provide useful applications to energy counter problems and particle manipulation by weakly scattered fields.

Characterizing CDOM Spectral Variability Across Diverse Regions and Spectral Ranges

NASA Astrophysics Data System (ADS)

Grunert, Brice K.; Mouw, Colleen B.; Ciochetto, Audrey B.

2018-01-01

Satellite remote sensing of colored dissolved organic matter (CDOM) has focused on CDOM absorption (aCDOM) at a reference wavelength, as its magnitude provides insight into the underwater light field and large-scale biogeochemical processes. CDOM spectral slope, SCDOM, has been treated as a constant or semiconstant parameter in satellite retrievals of aCDOM despite significant regional and temporal variabilities. SCDOM and other optical metrics provide insights into CDOM composition, processing, food web dynamics, and carbon cycling. To date, much of this work relies on fluorescence techniques or aCDOM in spectral ranges unavailable to current and planned satellite sensors (e.g., <300 nm). In preparation for anticipated future hyperspectral satellite missions, we take the first step here of exploring global variability in SCDOM and fit deviations in the aCDOM spectra using the recently proposed Gaussian decomposition method. From this, we investigate if global variability in retrieved SCDOM and Gaussian components is significant and regionally distinct. We iteratively decreased the spectral range considered and analyzed the number, location, and magnitude of fitted Gaussian components to understand if a reduced spectral range impacts information obtained within a common spectral window. We compared the fitted slope from the Gaussian decomposition method to absorption-based indices that indicate CDOM composition to determine the ability of satellite-derived slope to inform the analysis and modeling of large-scale biogeochemical processes. Finally, we present implications of the observed variability for remote sensing of CDOM characteristics via SCDOM.

Summary of tracking and identification methods

NASA Astrophysics Data System (ADS)

Blasch, Erik; Yang, Chun; Kadar, Ivan

2014-06-01

Over the last two decades, many solutions have arisen to combine target tracking estimation with classification methods. Target tracking includes developments from linear to non-linear and Gaussian to non-Gaussian processing. Pattern recognition includes detection, classification, recognition, and identification methods. Integrating tracking and pattern recognition has resulted in numerous approaches and this paper seeks to organize the various approaches. We discuss the terminology so as to have a common framework for various standards such as the NATO STANAG 4162 - Identification Data Combining Process. In a use case, we provide a comparative example highlighting that location information (as an example) with additional mission objectives from geographical, human, social, cultural, and behavioral modeling is needed to determine identification as classification alone does not allow determining identification or intent.

An empirical analysis of the distribution of overshoots in a stationary Gaussian stochastic process

NASA Technical Reports Server (NTRS)

Carter, M. C.; Madison, M. W.

1973-01-01

The frequency distribution of overshoots in a stationary Gaussian stochastic process is analyzed. The primary processes involved in this analysis are computer simulation and statistical estimation. Computer simulation is used to simulate stationary Gaussian stochastic processes that have selected autocorrelation functions. An analysis of the simulation results reveals a frequency distribution for overshoots with a functional dependence on the mean and variance of the process. Statistical estimation is then used to estimate the mean and variance of a process. It is shown that for an autocorrelation function, the mean and the variance for the number of overshoots, a frequency distribution for overshoots can be estimated.

High-Dimensional Intrinsic Interpolation Using Gaussian Process Regression and Diffusion Maps

DOE PAGES

Thimmisetty, Charanraj A.; Ghanem, Roger G.; White, Joshua A.; ...

2017-10-10

This article considers the challenging task of estimating geologic properties of interest using a suite of proxy measurements. The current work recast this task as a manifold learning problem. In this process, this article introduces a novel regression procedure for intrinsic variables constrained onto a manifold embedded in an ambient space. The procedure is meant to sharpen high-dimensional interpolation by inferring non-linear correlations from the data being interpolated. The proposed approach augments manifold learning procedures with a Gaussian process regression. It first identifies, using diffusion maps, a low-dimensional manifold embedded in an ambient high-dimensional space associated with the data. Itmore » relies on the diffusion distance associated with this construction to define a distance function with which the data model is equipped. This distance metric function is then used to compute the correlation structure of a Gaussian process that describes the statistical dependence of quantities of interest in the high-dimensional ambient space. The proposed method is applicable to arbitrarily high-dimensional data sets. Here, it is applied to subsurface characterization using a suite of well log measurements. The predictions obtained in original, principal component, and diffusion space are compared using both qualitative and quantitative metrics. Considerable improvement in the prediction of the geological structural properties is observed with the proposed method.« less

High-Dimensional Intrinsic Interpolation Using Gaussian Process Regression and Diffusion Maps

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

Thimmisetty, Charanraj A.; Ghanem, Roger G.; White, Joshua A.

This article considers the challenging task of estimating geologic properties of interest using a suite of proxy measurements. The current work recast this task as a manifold learning problem. In this process, this article introduces a novel regression procedure for intrinsic variables constrained onto a manifold embedded in an ambient space. The procedure is meant to sharpen high-dimensional interpolation by inferring non-linear correlations from the data being interpolated. The proposed approach augments manifold learning procedures with a Gaussian process regression. It first identifies, using diffusion maps, a low-dimensional manifold embedded in an ambient high-dimensional space associated with the data. Itmore » relies on the diffusion distance associated with this construction to define a distance function with which the data model is equipped. This distance metric function is then used to compute the correlation structure of a Gaussian process that describes the statistical dependence of quantities of interest in the high-dimensional ambient space. The proposed method is applicable to arbitrarily high-dimensional data sets. Here, it is applied to subsurface characterization using a suite of well log measurements. The predictions obtained in original, principal component, and diffusion space are compared using both qualitative and quantitative metrics. Considerable improvement in the prediction of the geological structural properties is observed with the proposed method.« less

Probing the cosmological initial conditions using the CMB

NASA Astrophysics Data System (ADS)

Yadav, Amit P. S.

In the last few decades, advances in observational cosmology have given us a standard model of cosmology. The basic cosmological parameters have been laid out to high precision. Cosmologists have started asking questions about the nature of the cosmological initial conditions. Many ambitious experiments such as Planck satellite, EBEX, ACT, CAPMAP, QUaD, BICEP, SPIDER, QUIET, and GEM are underway. Experiments like these will provide us with a wealth of information about CMB polarization, CMB lensing, and polarization foregrounds. These experiments will be complemented with great observational campaigns to map the 3D structure in the Universe and new particle physics constraints from the Large Hadron Collider. In my graduate work I have made explicit how observations of the CMB temperature and E-polarization anisotropies can be combined to provide optimal constraints on models of the early universe at the highest energies. I have developed new ways of constraining models of the early universe using CMB temperature and polarization data. Inflation is one of the most promising theories of the early universe. Different inflationary models predict different amounts of non-Gaussian perturbations. Although any non-Gaussianity predicted by the canonical inflation model is very small, there exist models which can generate significant amounts of non-Gaussianities. Hence any characterization of non-Gaussianity of the primordial perturbations constrains the models of inflation. The information in the bispectrum (or higher order moments) is completely independent of the power spectrum constraints on the amplitude of primordial power spectrum (A), the scalar spectral index of the primordial power spectrum ns, and the running of the primordial power spectrum. My work has made it possible to extract the bispectrum information from large, high resolution CMB temperature and polarization data. We have demonstrated that the primordial adiabatic perturbations can be reconstructed using CMB temperature and E-polarization information (Yadav and Wandelt 2005). One of the main motivations of reconstructing the primordial perturbations is to study the primordial non-Gaussianities. Since the amplitude of primordial non-Gaussianity is very small, any enhancement in sensitivity to the primordial features is useful because it improves the characterization of the primordial non-Gaussianity. Our reconstruction allows us to be more sensitive to the primordial features, whereas most of the current probes of non-Gaussianity do not specifically select for them. We have also developed a fast cubic (bispectrum) estimator of non-Gaussianity f NL of local type, using combined temperature and E-polarization data (Yadavet al. 2007). The estimator is computationally efficient, scaling as O( N 3/2 ) compared to the O( N 5/2 ) scaling of the brute force bispectrum calculation for sky maps with N pixels. For the Planck satellite, this translates into a speed-up by factors of millions, reducing the required computing time from thousands of years to just hours and thus making f NL estimation feasible. The speed of our estimator allows us to study its statistical properties using Monte Carlo simulations. Our estimator in its original form was optimal for homogeneous noise. In order to apply our estimator to realistic data, the estimator needed to be able to deal with inhomogeneous noise. We have generalized the fast polarized estimator to deal with inhomogeneous noise. The generalized estimator is also computationally efficient, scaling as O( N 3/2 ). Furthermore, we have studied and characterized our estimators in the presence of realistic noise, finite resolution, incomplete sky-coverage, and using non-Gaussian CMB maps (Yadavet al. 2008a). We have also developed a numerical code to generate CMB temperature and polarization non-Gaussian maps starting from a given primordial non-Gaussianity (f NL ) (Liguori et al. 2007). In the process of non-Gaussian CMB map making, the code also generates corresponding non-Gaussian primordial curvature perturbations. We use these curvature perturbations to quantify the quality of the tomographic reconstruction method described in (Yadav and Wandelt 2005). We check whether the tomographic reconstruction method preserves the non-Gaussian features, especially the phase information, in the reconstructed curvature perturbations (Yadav et al. in preparation). Finally, using our estimator we found (Yadav and Wandelt 2008) evidence for primordial non-Gaussianity of the local type (f NL ) in the temperature anisotropy of the Cosmic Microwave Background. Analyzing the bispectrum of the WMAP 3-year data up to l max =750 we find 27< f NL <147 (95% CL). This amounts to a rejection of f NL =0 at 2.8s, disfavoring canonical single field slow-roll inflation. The signal is robust to variations in l max , frequency, and masks. No known foreground, instrument systematic, or secondary anisotropy explains it. We explore the impact of several analysis choices on the quoted significance and find 2.5s to be conservative.

Non-Gaussian PDF Modeling of Turbulent Boundary Layer Fluctuating Pressure Excitation

NASA Technical Reports Server (NTRS)

Steinwolf, Alexander; Rizzi, Stephen A.

2003-01-01

The purpose of the study is to investigate properties of the probability density function (PDF) of turbulent boundary layer fluctuating pressures measured on the exterior of a supersonic transport aircraft. It is shown that fluctuating pressure PDFs differ from the Gaussian distribution even for surface conditions having no significant discontinuities. The PDF tails are wider and longer than those of the Gaussian model. For pressure fluctuations upstream of forward-facing step discontinuities and downstream of aft-facing step discontinuities, deviations from the Gaussian model are more significant and the PDFs become asymmetrical. Various analytical PDF distributions are used and further developed to model this behavior.

Tip-tilt disturbance model identification based on non-linear least squares fitting for Linear Quadratic Gaussian control

NASA Astrophysics Data System (ADS)

Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing

2018-05-01

We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.

Recurrence plots of discrete-time Gaussian stochastic processes

NASA Astrophysics Data System (ADS)

Ramdani, Sofiane; Bouchara, Frédéric; Lagarde, Julien; Lesne, Annick

2016-09-01

We investigate the statistical properties of recurrence plots (RPs) of data generated by discrete-time stationary Gaussian random processes. We analytically derive the theoretical values of the probabilities of occurrence of recurrence points and consecutive recurrence points forming diagonals in the RP, with an embedding dimension equal to 1. These results allow us to obtain theoretical values of three measures: (i) the recurrence rate (REC) (ii) the percent determinism (DET) and (iii) RP-based estimation of the ε-entropy κ(ε) in the sense of correlation entropy. We apply these results to two Gaussian processes, namely first order autoregressive processes and fractional Gaussian noise. For these processes, we simulate a number of realizations and compare the RP-based estimations of the three selected measures to their theoretical values. These comparisons provide useful information on the quality of the estimations, such as the minimum required data length and threshold radius used to construct the RP.

Non-Gaussianities in multifield DBI inflation with a waterfall phase transition

NASA Astrophysics Data System (ADS)

Kidani, Taichi; Koyama, Kazuya; Mizuno, Shuntaro

2012-10-01

We study multifield Dirac-Born-Infeld (DBI) inflation models with a waterfall phase transition. This transition happens for a D3 brane moving in the warped conifold if there is an instability along angular directions. The transition converts the angular perturbations into the curvature perturbation. Thanks to this conversion, multifield models can evade the stringent constraints that strongly disfavor single field ultraviolet (UV) DBI inflation models in string theory. We explicitly demonstrate that our model satisfies current observational constraints on the spectral index and equilateral non-Gaussianity as well as the bound on the tensor to scalar ratio imposed in string theory models. In addition, we show that large local type non-Gaussianity is generated together with equilateral non-Gaussianity in this model.

A model of the human in a cognitive prediction task.

NASA Technical Reports Server (NTRS)

Rouse, W. B.

1973-01-01

The human decision maker's behavior when predicting future states of discrete linear dynamic systems driven by zero-mean Gaussian processes is modeled. The task is on a slow enough time scale that physiological constraints are insignificant compared with cognitive limitations. The model is basically a linear regression system identifier with a limited memory and noisy observations. Experimental data are presented and compared to the model.

Gaussian process regression of chirplet decomposed ultrasonic B-scans of a simulated design case

NASA Astrophysics Data System (ADS)

Wertz, John; Homa, Laura; Welter, John; Sparkman, Daniel; Aldrin, John

2018-04-01

The US Air Force seeks to implement damage tolerant lifecycle management of composite structures. Nondestructive characterization of damage is a key input to this framework. One approach to characterization is model-based inversion of the ultrasonic response from damage features; however, the computational expense of modeling the ultrasonic waves within composites is a major hurdle to implementation. A surrogate forward model with sufficient accuracy and greater computational efficiency is therefore critical to enabling model-based inversion and damage characterization. In this work, a surrogate model is developed on the simulated ultrasonic response from delamination-like structures placed at different locations within a representative composite layup. The resulting B-scans are decomposed via the chirplet transform, and a Gaussian process model is trained on the chirplet parameters. The quality of the surrogate is tested by comparing the B-scan for a delamination configuration not represented within the training data set. The estimated B-scan has a maximum error of ˜15% for an estimated reduction in computational runtime of ˜95% for 200 function calls. This considerable reduction in computational expense makes full 3D characterization of impact damage tractable.

Statistical modelling of networked human-automation performance using working memory capacity.

PubMed

Ahmed, Nisar; de Visser, Ewart; Shaw, Tyler; Mohamed-Ameen, Amira; Campbell, Mark; Parasuraman, Raja

2014-01-01

This study examines the challenging problem of modelling the interaction between individual attentional limitations and decision-making performance in networked human-automation system tasks. Analysis of real experimental data from a task involving networked supervision of multiple unmanned aerial vehicles by human participants shows that both task load and network message quality affect performance, but that these effects are modulated by individual differences in working memory (WM) capacity. These insights were used to assess three statistical approaches for modelling and making predictions with real experimental networked supervisory performance data: classical linear regression, non-parametric Gaussian processes and probabilistic Bayesian networks. It is shown that each of these approaches can help designers of networked human-automated systems cope with various uncertainties in order to accommodate future users by linking expected operating conditions and performance from real experimental data to observable cognitive traits like WM capacity. Practitioner Summary: Working memory (WM) capacity helps account for inter-individual variability in operator performance in networked unmanned aerial vehicle supervisory tasks. This is useful for reliable performance prediction near experimental conditions via linear models; robust statistical prediction beyond experimental conditions via Gaussian process models and probabilistic inference about unknown task conditions/WM capacities via Bayesian network models.

Multiview road sign detection via self-adaptive color model and shape context matching

NASA Astrophysics Data System (ADS)

Liu, Chunsheng; Chang, Faliang; Liu, Chengyun

2016-09-01

The multiview appearance of road signs in uncontrolled environments has made the detection of road signs a challenging problem in computer vision. We propose a road sign detection method to detect multiview road signs. This method is based on several algorithms, including the classical cascaded detector, the self-adaptive weighted Gaussian color model (SW-Gaussian model), and a shape context matching method. The classical cascaded detector is used to detect the frontal road signs in video sequences and obtain the parameters for the SW-Gaussian model. The proposed SW-Gaussian model combines the two-dimensional Gaussian model and the normalized red channel together, which can largely enhance the contrast between the red signs and background. The proposed shape context matching method can match shapes with big noise, which is utilized to detect road signs in different directions. The experimental results show that compared with previous detection methods, the proposed multiview detection method can reach higher detection rate in detecting signs with different directions.

Robust nonlinear system identification: Bayesian mixture of experts using the t-distribution

NASA Astrophysics Data System (ADS)

Baldacchino, Tara; Worden, Keith; Rowson, Jennifer

2017-02-01

A novel variational Bayesian mixture of experts model for robust regression of bifurcating and piece-wise continuous processes is introduced. The mixture of experts model is a powerful model which probabilistically splits the input space allowing different models to operate in the separate regions. However, current methods have no fail-safe against outliers. In this paper, a robust mixture of experts model is proposed which consists of Student-t mixture models at the gates and Student-t distributed experts, trained via Bayesian inference. The Student-t distribution has heavier tails than the Gaussian distribution, and so it is more robust to outliers, noise and non-normality in the data. Using both simulated data and real data obtained from the Z24 bridge this robust mixture of experts performs better than its Gaussian counterpart when outliers are present. In particular, it provides robustness to outliers in two forms: unbiased parameter regression models, and robustness to overfitting/complex models.

Flat-top beam for laser-stimulated pain

NASA Astrophysics Data System (ADS)

McCaughey, Ryan; Nadeau, Valerie; Dickinson, Mark

2005-04-01

One of the main problems during laser stimulation in human pain research is the risk of tissue damage caused by excessive heating of the skin. This risk has been reduced by using a laser beam with a flattop (or superGaussian) intensity profile, instead of the conventional Gaussian beam. A finite difference approximation to the heat conduction equation has been applied to model the temperature distribution in skin as a result of irradiation by flattop and Gaussian profile CO2 laser beams. The model predicts that a 15 mm diameter, 15 W, 100 ms CO2 laser pulse with an order 6 superGaussian profile produces a maximum temperature 6 oC less than a Gaussian beam with the same energy density. A superGaussian profile was created by passing a Gaussian beam through a pair of zinc selenide aspheric lenses which refract the more intense central region of the beam towards the less intense periphery. The profiles of the lenses were determined by geometrical optics. In human pain trials the superGaussian beam required more power than the Gaussian beam to reach sensory and pain thresholds.

Gaussian-input Gaussian mixture model for representing density maps and atomic models.

PubMed

Kawabata, Takeshi

2018-07-01

A new Gaussian mixture model (GMM) has been developed for better representations of both atomic models and electron microscopy 3D density maps. The standard GMM algorithm employs an EM algorithm to determine the parameters. It accepted a set of 3D points with weights, corresponding to voxel or atomic centers. Although the standard algorithm worked reasonably well; however, it had three problems. First, it ignored the size (voxel width or atomic radius) of the input, and thus it could lead to a GMM with a smaller spread than the input. Second, the algorithm had a singularity problem, as it sometimes stopped the iterative procedure due to a Gaussian function with almost zero variance. Third, a map with a large number of voxels required a long computation time for conversion to a GMM. To solve these problems, we have introduced a Gaussian-input GMM algorithm, which considers the input atoms or voxels as a set of Gaussian functions. The standard EM algorithm of GMM was extended to optimize the new GMM. The new GMM has identical radius of gyration to the input, and does not suddenly stop due to the singularity problem. For fast computation, we have introduced a down-sampled Gaussian functions (DSG) by merging neighboring voxels into an anisotropic Gaussian function. It provides a GMM with thousands of Gaussian functions in a short computation time. We also have introduced a DSG-input GMM: the Gaussian-input GMM with the DSG as the input. This new algorithm is much faster than the standard algorithm. Copyright © 2018 The Author(s). Published by Elsevier Inc. All rights reserved.

Gaussian Process Regression for Uncertainty Estimation on Ecosystem Data

NASA Astrophysics Data System (ADS)

Menzer, O.; Moffat, A.; Lasslop, G.; Reichstein, M.

2011-12-01

The flow of carbon between terrestrial ecosystems and the atmosphere is mainly driven by nonlinear, complex and time-lagged processes. Understanding the associated ecosystem responses and climatic feedbacks is a key challenge regarding climate change questions such as increasing atmospheric CO2 levels. Usually, the underlying relationships are implemented in models as prescribed functions which interlink numerous meteorological, radiative and gas exchange variables. In contrast, supervised Machine Learning algorithms, such as Artificial Neural Networks or Gaussian Processes, allow for an insight into the relationships directly from a data perspective. Micrometeorological, high resolution measurements at flux towers of the FLUXNET observational network are an essential tool for obtaining quantifications of the ecosystem variables, as they continuously record e.g. CO2 exchange, solar radiation and air temperature. In order to facilitate the investigation of the interactions and feedbacks between these variables, several challenging data properties need to be taken into account: noisy, multidimensional and incomplete (Moffat, Accepted). The task of estimating uncertainties in such micrometeorological measurements can be addressed by Gaussian Processes (GPs), a modern nonparametric method for nonlinear regression. The GP approach has recently been shown to be a powerful modeling tool, regardless of the input dimensionality, the degree of nonlinearity and the noise level (Rasmussen and Williams, 2006). Heteroscedastic Gaussian Processes (HGPs) are a specialized GP method for data with a varying, inhomogeneous noise variance (Goldberg et al., 1998; Kersting et al., 2007), as usually observed in CO2 flux measurements (Richardson et al., 2006). Here, we showed by an evaluation of the HGP performance in several artificial experiments and a comparison to existing nonlinear regression methods, that their outstanding ability is to capture measurement noise levels, concurrently providing reasonable data fits under relatively few assumptions. On the basis of incomplete, half-hourly measured ecosystem data, a HGP was trained to model NEP (Net Ecosystem Production), only with the drivers PPFD (Photosynthetic Photon Flux Density) and Air Temperature. Time information was added to account for the autocorrelation in the flux measurements. Provided with a gap-filled, meteorological time series, NEP and the corresponding random error estimates can then be predicted empirically at high temporal resolution. We report uncertainties in annual sums of CO2 exchange at two flux tower sites in Hainich, Germany and Hesse, France. Similar noise patterns, but different magnitudes between sites were detected, with annual random error estimates of +/- 14.1 gCm^-2yr^-1 and +/- 23.5 gCm^-2yr^-1, respectively, for the year 2001. Existing models calculate uncertainties by evaluating the standard deviation of the model residuals. A comparison to the methods of Reichstein et al. (2005) and Lasslop et al. (2008) showed confidence both in the predictive uncertainties and the annual sums modeled with the HGP approach.

'The formula that killed Wall Street': the Gaussian copula and modelling practices in investment banking.

PubMed

MacKenzie, Donald; Spears, Taylor

2014-06-01

Drawing on documentary sources and 114 interviews with market participants, this and a companion article discuss the development and use in finance of the Gaussian copula family of models, which are employed to estimate the probability distribution of losses on a pool of loans or bonds, and which were centrally involved in the credit crisis. This article, which explores how and why the Gaussian copula family developed in the way it did, employs the concept of 'evaluation culture', a set of practices, preferences and beliefs concerning how to determine the economic value of financial instruments that is shared by members of multiple organizations. We identify an evaluation culture, dominant within the derivatives departments of investment banks, which we call the 'culture of no-arbitrage modelling', and explore its relation to the development of Gaussian copula models. The article suggests that two themes from the science and technology studies literature on models (modelling as 'impure' bricolage, and modelling as articulating with heterogeneous objectives and constraints) help elucidate the history of Gaussian copula models in finance.

Robust Library Building for Autonomous Classification of Downhole Geophysical Logs Using Gaussian Processes

NASA Astrophysics Data System (ADS)

Silversides, Katherine L.; Melkumyan, Arman

2017-03-01

Machine learning techniques such as Gaussian Processes can be used to identify stratigraphically important features in geophysical logs. The marker shales in the banded iron formation hosted iron ore deposits of the Hamersley Ranges, Western Australia, form distinctive signatures in the natural gamma logs. The identification of these marker shales is important for stratigraphic identification of unit boundaries for the geological modelling of the deposit. Machine learning techniques each have different unique properties that will impact the results. For Gaussian Processes (GPs), the output values are inclined towards the mean value, particularly when there is not sufficient information in the library. The impact that these inclinations have on the classification can vary depending on the parameter values selected by the user. Therefore, when applying machine learning techniques, care must be taken to fit the technique to the problem correctly. This study focuses on optimising the settings and choices for training a GPs system to identify a specific marker shale. We show that the final results converge even when different, but equally valid starting libraries are used for the training. To analyse the impact on feature identification, GP models were trained so that the output was inclined towards a positive, neutral or negative output. For this type of classification, the best results were when the pull was towards a negative output. We also show that the GP output can be adjusted by using a standard deviation coefficient that changes the balance between certainty and accuracy in the results.

A dynamic feedforward neural network based on gaussian particle swarm optimization and its application for predictive control.

PubMed

Han, Min; Fan, Jianchao; Wang, Jun

2011-09-01

A dynamic feedforward neural network (DFNN) is proposed for predictive control, whose adaptive parameters are adjusted by using Gaussian particle swarm optimization (GPSO) in the training process. Adaptive time-delay operators are added in the DFNN to improve its generalization for poorly known nonlinear dynamic systems with long time delays. Furthermore, GPSO adopts a chaotic map with Gaussian function to balance the exploration and exploitation capabilities of particles, which improves the computational efficiency without compromising the performance of the DFNN. The stability of the particle dynamics is analyzed, based on the robust stability theory, without any restrictive assumption. A stability condition for the GPSO+DFNN model is derived, which ensures a satisfactory global search and quick convergence, without the need for gradients. The particle velocity ranges could change adaptively during the optimization process. The results of a comparative study show that the performance of the proposed algorithm can compete with selected algorithms on benchmark problems. Additional simulation results demonstrate the effectiveness and accuracy of the proposed combination algorithm in identifying and controlling nonlinear systems with long time delays.

Parametric adaptive filtering and data validation in the bar GW detector AURIGA

NASA Astrophysics Data System (ADS)

Ortolan, A.; Baggio, L.; Cerdonio, M.; Prodi, G. A.; Vedovato, G.; Vitale, S.

2002-04-01

We report on our experience gained in the signal processing of the resonant GW detector AURIGA. Signal amplitude and arrival time are estimated by means of a matched-adaptive Wiener filter. The detector noise, entering in the filter set-up, is modelled as a parametric ARMA process; to account for slow non-stationarity of the noise, the ARMA parameters are estimated on an hourly basis. A requirement of the set-up of an unbiased Wiener filter is the separation of time spans with 'almost Gaussian' noise from non-Gaussian and/or strongly non-stationary time spans. The separation algorithm consists basically of a variance estimate with the Chauvenet convergence method and a threshold on the Curtosis index. The subsequent validation of data is strictly connected with the separation procedure: in fact, by injecting a large number of artificial GW signals into the 'almost Gaussian' part of the AURIGA data stream, we have demonstrated that the effective probability distributions of the signal-to-noise ratio χ2 and the time of arrival are those that are expected.

Warped linear mixed models for the genetic analysis of transformed phenotypes

PubMed Central

Fusi, Nicolo; Lippert, Christoph; Lawrence, Neil D.; Stegle, Oliver

2014-01-01

Linear mixed models (LMMs) are a powerful and established tool for studying genotype–phenotype relationships. A limitation of the LMM is that the model assumes Gaussian distributed residuals, a requirement that rarely holds in practice. Violations of this assumption can lead to false conclusions and loss in power. To mitigate this problem, it is common practice to pre-process the phenotypic values to make them as Gaussian as possible, for instance by applying logarithmic or other nonlinear transformations. Unfortunately, different phenotypes require different transformations, and choosing an appropriate transformation is challenging and subjective. Here we present an extension of the LMM that estimates an optimal transformation from the observed data. In simulations and applications to real data from human, mouse and yeast, we show that using transformations inferred by our model increases power in genome-wide association studies and increases the accuracy of heritability estimation and phenotype prediction. PMID:25234577

Warped linear mixed models for the genetic analysis of transformed phenotypes.

PubMed

Fusi, Nicolo; Lippert, Christoph; Lawrence, Neil D; Stegle, Oliver

2014-09-19

Linear mixed models (LMMs) are a powerful and established tool for studying genotype-phenotype relationships. A limitation of the LMM is that the model assumes Gaussian distributed residuals, a requirement that rarely holds in practice. Violations of this assumption can lead to false conclusions and loss in power. To mitigate this problem, it is common practice to pre-process the phenotypic values to make them as Gaussian as possible, for instance by applying logarithmic or other nonlinear transformations. Unfortunately, different phenotypes require different transformations, and choosing an appropriate transformation is challenging and subjective. Here we present an extension of the LMM that estimates an optimal transformation from the observed data. In simulations and applications to real data from human, mouse and yeast, we show that using transformations inferred by our model increases power in genome-wide association studies and increases the accuracy of heritability estimation and phenotype prediction.

Response of Electrical Activity in an Improved Neuron Model under Electromagnetic Radiation and Noise

PubMed Central

Zhan, Feibiao; Liu, Shenquan

2017-01-01

Electrical activities are ubiquitous neuronal bioelectric phenomena, which have many different modes to encode the expression of biological information, and constitute the whole process of signal propagation between neurons. Therefore, we focus on the electrical activities of neurons, which is also causing widespread concern among neuroscientists. In this paper, we mainly investigate the electrical activities of the Morris-Lecar (M-L) model with electromagnetic radiation or Gaussian white noise, which can restore the authenticity of neurons in realistic neural network. First, we explore dynamical response of the whole system with electromagnetic induction (EMI) and Gaussian white noise. We find that there are slight differences in the discharge behaviors via comparing the response of original system with that of improved system, and electromagnetic induction can transform bursting or spiking state to quiescent state and vice versa. Furthermore, we research bursting transition mode and the corresponding periodic solution mechanism for the isolated neuron model with electromagnetic induction by using one-parameter and bi-parameters bifurcation analysis. Finally, we analyze the effects of Gaussian white noise on the original system and coupled system, which is conducive to understand the actual discharge properties of realistic neurons. PMID:29209192

Response of Electrical Activity in an Improved Neuron Model under Electromagnetic Radiation and Noise.

PubMed

Zhan, Feibiao; Liu, Shenquan

2017-01-01

Electrical activities are ubiquitous neuronal bioelectric phenomena, which have many different modes to encode the expression of biological information, and constitute the whole process of signal propagation between neurons. Therefore, we focus on the electrical activities of neurons, which is also causing widespread concern among neuroscientists. In this paper, we mainly investigate the electrical activities of the Morris-Lecar (M-L) model with electromagnetic radiation or Gaussian white noise, which can restore the authenticity of neurons in realistic neural network. First, we explore dynamical response of the whole system with electromagnetic induction (EMI) and Gaussian white noise. We find that there are slight differences in the discharge behaviors via comparing the response of original system with that of improved system, and electromagnetic induction can transform bursting or spiking state to quiescent state and vice versa. Furthermore, we research bursting transition mode and the corresponding periodic solution mechanism for the isolated neuron model with electromagnetic induction by using one-parameter and bi-parameters bifurcation analysis. Finally, we analyze the effects of Gaussian white noise on the original system and coupled system, which is conducive to understand the actual discharge properties of realistic neurons.

Quantum entanglement beyond Gaussian criteria

PubMed Central

Gomes, R. M.; Salles, A.; Toscano, F.; Souto Ribeiro, P. H.; Walborn, S. P.

2009-01-01

Most of the attention given to continuous variable systems for quantum information processing has traditionally been focused on Gaussian states. However, non-Gaussianity is an essential requirement for universal quantum computation and entanglement distillation, and can improve the efficiency of other quantum information tasks. Here we report the experimental observation of genuine non-Gaussian entanglement using spatially entangled photon pairs. The quantum correlations are invisible to all second-order tests, which identify only Gaussian entanglement, and are revealed only under application of a higher-order entanglement criterion. Thus, the photons exhibit a variety of entanglement that cannot be reproduced by Gaussian states. PMID:19995963

Quantum entanglement beyond Gaussian criteria.

PubMed

Gomes, R M; Salles, A; Toscano, F; Souto Ribeiro, P H; Walborn, S P

2009-12-22

Most of the attention given to continuous variable systems for quantum information processing has traditionally been focused on Gaussian states. However, non-Gaussianity is an essential requirement for universal quantum computation and entanglement distillation, and can improve the efficiency of other quantum information tasks. Here we report the experimental observation of genuine non-Gaussian entanglement using spatially entangled photon pairs. The quantum correlations are invisible to all second-order tests, which identify only Gaussian entanglement, and are revealed only under application of a higher-order entanglement criterion. Thus, the photons exhibit a variety of entanglement that cannot be reproduced by Gaussian states.

A mathematical study of a random process proposed as an atmospheric turbulence model

NASA Technical Reports Server (NTRS)

Sidwell, K.

1977-01-01

A random process is formed by the product of a local Gaussian process and a random amplitude process, and the sum of that product with an independent mean value process. The mathematical properties of the resulting process are developed, including the first and second order properties and the characteristic function of general order. An approximate method for the analysis of the response of linear dynamic systems to the process is developed. The transition properties of the process are also examined.

Modeling of a UV laser beam—silicon nitride interaction

NASA Astrophysics Data System (ADS)

Dgheim, J. A.

2016-11-01

A numerical model is developed to study heat and radiation transfers during the interaction between a UV laser beam and silicon nitride. The laser beam has temporal Gaussian or Gate shapes of a wavelength of 247 nm, with pulse duration of 27 ns. The mathematical model is based on the heat equation coupled to Lambert-Beer relationship by taking into account the conduction, convection and radiation phenomena. The resulting equations are schemed by the finite element method. Comparison with the literature shows qualitative and quantitative agreements. The investigated parameters are the temperature, the timing of the melting process and the melting phase thickness. The effects of the laser fluences, ranging from 500 to 16 000 J.m-2, the Gaussian and Gate shapes on the heat transfer, and the melting phenomenon are studied.

Diffusion weighted imaging in patients with rectal cancer: Comparison between Gaussian and non-Gaussian models

PubMed Central

Marias, Kostas; Lambregts, Doenja M. J.; Nikiforaki, Katerina; van Heeswijk, Miriam M.; Bakers, Frans C. H.; Beets-Tan, Regina G. H.

2017-01-01

Purpose The purpose of this study was to compare the performance of four diffusion models, including mono and bi-exponential both Gaussian and non-Gaussian models, in diffusion weighted imaging of rectal cancer. Material and methods Nineteen patients with rectal adenocarcinoma underwent MRI examination of the rectum before chemoradiation therapy including a 7 b-value diffusion sequence (0, 25, 50, 100, 500, 1000 and 2000 s/mm2) at a 1.5T scanner. Four different diffusion models including mono- and bi-exponential Gaussian (MG and BG) and non-Gaussian (MNG and BNG) were applied on whole tumor volumes of interest. Two different statistical criteria were recruited to assess their fitting performance, including the adjusted-R2 and Root Mean Square Error (RMSE). To decide which model better characterizes rectal cancer, model selection was relied on Akaike Information Criteria (AIC) and F-ratio. Results All candidate models achieved a good fitting performance with the two most complex models, the BG and the BNG, exhibiting the best fitting performance. However, both criteria for model selection indicated that the MG model performed better than any other model. In particular, using AIC Weights and F-ratio, the pixel-based analysis demonstrated that tumor areas better described by the simplest MG model in an average area of 53% and 33%, respectively. Non-Gaussian behavior was illustrated in an average area of 37% according to the F-ratio, and 7% using AIC Weights. However, the distributions of the pixels best fitted by each of the four models suggest that MG failed to perform better than any other model in all patients, and the overall tumor area. Conclusion No single diffusion model evaluated herein could accurately describe rectal tumours. These findings probably can be explained on the basis of increased tumour heterogeneity, where areas with high vascularity could be fitted better with bi-exponential models, and areas with necrosis would mostly follow mono-exponential behavior. PMID:28863161

Diffusion weighted imaging in patients with rectal cancer: Comparison between Gaussian and non-Gaussian models.

PubMed

Manikis, Georgios C; Marias, Kostas; Lambregts, Doenja M J; Nikiforaki, Katerina; van Heeswijk, Miriam M; Bakers, Frans C H; Beets-Tan, Regina G H; Papanikolaou, Nikolaos

2017-01-01

The purpose of this study was to compare the performance of four diffusion models, including mono and bi-exponential both Gaussian and non-Gaussian models, in diffusion weighted imaging of rectal cancer. Nineteen patients with rectal adenocarcinoma underwent MRI examination of the rectum before chemoradiation therapy including a 7 b-value diffusion sequence (0, 25, 50, 100, 500, 1000 and 2000 s/mm2) at a 1.5T scanner. Four different diffusion models including mono- and bi-exponential Gaussian (MG and BG) and non-Gaussian (MNG and BNG) were applied on whole tumor volumes of interest. Two different statistical criteria were recruited to assess their fitting performance, including the adjusted-R2 and Root Mean Square Error (RMSE). To decide which model better characterizes rectal cancer, model selection was relied on Akaike Information Criteria (AIC) and F-ratio. All candidate models achieved a good fitting performance with the two most complex models, the BG and the BNG, exhibiting the best fitting performance. However, both criteria for model selection indicated that the MG model performed better than any other model. In particular, using AIC Weights and F-ratio, the pixel-based analysis demonstrated that tumor areas better described by the simplest MG model in an average area of 53% and 33%, respectively. Non-Gaussian behavior was illustrated in an average area of 37% according to the F-ratio, and 7% using AIC Weights. However, the distributions of the pixels best fitted by each of the four models suggest that MG failed to perform better than any other model in all patients, and the overall tumor area. No single diffusion model evaluated herein could accurately describe rectal tumours. These findings probably can be explained on the basis of increased tumour heterogeneity, where areas with high vascularity could be fitted better with bi-exponential models, and areas with necrosis would mostly follow mono-exponential behavior.

Spherical Deconvolution of Multichannel Diffusion MRI Data with Non-Gaussian Noise Models and Spatial Regularization

PubMed Central

Canales-Rodríguez, Erick J.; Caruyer, Emmanuel; Aja-Fernández, Santiago; Radua, Joaquim; Yurramendi Mendizabal, Jesús M.; Iturria-Medina, Yasser; Melie-García, Lester; Alemán-Gómez, Yasser; Thiran, Jean-Philippe; Sarró, Salvador; Pomarol-Clotet, Edith; Salvador, Raymond

2015-01-01

Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on many factors such as the number of coils and the methodology used to combine multichannel MRI signals. Indeed, the two prevailing methods for multichannel signal combination lead to noise patterns better described by Rician and noncentral Chi distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in human brain data. PMID:26470024

Human Language Technology: Opportunities and Challenges

DTIC Science & Technology

2005-01-01

because of the connections to and reliance on signal processing. Audio diarization critically includes indexing of speakers [12], since speaker ...to reduce inter- speaker variability in training. Standard techniques include vocal-tract length normalization, adaptation of acoustic models using...maximum likelihood linear regression (MLLR), and speaker -adaptive training based on MLLR. The acoustic models are mixtures of Gaussians, typically with

Examining the effect of initialization strategies on the performance of Gaussian mixture modeling.

PubMed

Shireman, Emilie; Steinley, Douglas; Brusco, Michael J

2017-02-01

Mixture modeling is a popular technique for identifying unobserved subpopulations (e.g., components) within a data set, with Gaussian (normal) mixture modeling being the form most widely used. Generally, the parameters of these Gaussian mixtures cannot be estimated in closed form, so estimates are typically obtained via an iterative process. The most common estimation procedure is maximum likelihood via the expectation-maximization (EM) algorithm. Like many approaches for identifying subpopulations, finite mixture modeling can suffer from locally optimal solutions, and the final parameter estimates are dependent on the initial starting values of the EM algorithm. Initial values have been shown to significantly impact the quality of the solution, and researchers have proposed several approaches for selecting the set of starting values. Five techniques for obtaining starting values that are implemented in popular software packages are compared. Their performances are assessed in terms of the following four measures: (1) the ability to find the best observed solution, (2) settling on a solution that classifies observations correctly, (3) the number of local solutions found by each technique, and (4) the speed at which the start values are obtained. On the basis of these results, a set of recommendations is provided to the user.

[Gaussian process regression and its application in near-infrared spectroscopy analysis].

PubMed

Feng, Ai-Ming; Fang, Li-Min; Lin, Min

2011-06-01

Gaussian process (GP) is applied in the present paper as a chemometric method to explore the complicated relationship between the near infrared (NIR) spectra and ingredients. After the outliers were detected by Monte Carlo cross validation (MCCV) method and removed from dataset, different preprocessing methods, such as multiplicative scatter correction (MSC), smoothing and derivate, were tried for the best performance of the models. Furthermore, uninformative variable elimination (UVE) was introduced as a variable selection technique and the characteristic wavelengths obtained were further employed as input for modeling. A public dataset with 80 NIR spectra of corn was introduced as an example for evaluating the new algorithm. The optimal models for oil, starch and protein were obtained by the GP regression method. The performance of the final models were evaluated according to the root mean square error of calibration (RMSEC), root mean square error of cross-validation (RMSECV), root mean square error of prediction (RMSEP) and correlation coefficient (r). The models give good calibration ability with r values above 0.99 and the prediction ability is also satisfactory with r values higher than 0.96. The overall results demonstrate that GP algorithm is an effective chemometric method and is promising for the NIR analysis.

A Novel Signal Modeling Approach for Classification of Seizure and Seizure-Free EEG Signals.

PubMed

Gupta, Anubha; Singh, Pushpendra; Karlekar, Mandar

2018-05-01

This paper presents a signal modeling-based new methodology of automatic seizure detection in EEG signals. The proposed method consists of three stages. First, a multirate filterbank structure is proposed that is constructed using the basis vectors of discrete cosine transform. The proposed filterbank decomposes EEG signals into its respective brain rhythms: delta, theta, alpha, beta, and gamma. Second, these brain rhythms are statistically modeled with the class of self-similar Gaussian random processes, namely, fractional Brownian motion and fractional Gaussian noises. The statistics of these processes are modeled using a single parameter called the Hurst exponent. In the last stage, the value of Hurst exponent and autoregressive moving average parameters are used as features to design a binary support vector machine classifier to classify pre-ictal, inter-ictal (epileptic with seizure free interval), and ictal (seizure) EEG segments. The performance of the classifier is assessed via extensive analysis on two widely used data set and is observed to provide good accuracy on both the data set. Thus, this paper proposes a novel signal model for EEG data that best captures the attributes of these signals and hence, allows to boost the classification accuracy of seizure and seizure-free epochs.

Automatic image equalization and contrast enhancement using Gaussian mixture modeling.

PubMed

Celik, Turgay; Tjahjadi, Tardi

2012-01-01

In this paper, we propose an adaptive image equalization algorithm that automatically enhances the contrast in an input image. The algorithm uses the Gaussian mixture model to model the image gray-level distribution, and the intersection points of the Gaussian components in the model are used to partition the dynamic range of the image into input gray-level intervals. The contrast equalized image is generated by transforming the pixels' gray levels in each input interval to the appropriate output gray-level interval according to the dominant Gaussian component and the cumulative distribution function of the input interval. To take account of the hypothesis that homogeneous regions in the image represent homogeneous silences (or set of Gaussian components) in the image histogram, the Gaussian components with small variances are weighted with smaller values than the Gaussian components with larger variances, and the gray-level distribution is also used to weight the components in the mapping of the input interval to the output interval. Experimental results show that the proposed algorithm produces better or comparable enhanced images than several state-of-the-art algorithms. Unlike the other algorithms, the proposed algorithm is free of parameter setting for a given dynamic range of the enhanced image and can be applied to a wide range of image types.

A flexible cure rate model for spatially correlated survival data based on generalized extreme value distribution and Gaussian process priors.

PubMed

Li, Dan; Wang, Xia; Dey, Dipak K

2016-09-01

Our present work proposes a new survival model in a Bayesian context to analyze right-censored survival data for populations with a surviving fraction, assuming that the log failure time follows a generalized extreme value distribution. Many applications require a more flexible modeling of covariate information than a simple linear or parametric form for all covariate effects. It is also necessary to include the spatial variation in the model, since it is sometimes unexplained by the covariates considered in the analysis. Therefore, the nonlinear covariate effects and the spatial effects are incorporated into the systematic component of our model. Gaussian processes (GPs) provide a natural framework for modeling potentially nonlinear relationship and have recently become extremely powerful in nonlinear regression. Our proposed model adopts a semiparametric Bayesian approach by imposing a GP prior on the nonlinear structure of continuous covariate. With the consideration of data availability and computational complexity, the conditionally autoregressive distribution is placed on the region-specific frailties to handle spatial correlation. The flexibility and gains of our proposed model are illustrated through analyses of simulated data examples as well as a dataset involving a colon cancer clinical trial from the state of Iowa. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Gaussian mixtures on tensor fields for segmentation: applications to medical imaging.

PubMed

de Luis-García, Rodrigo; Westin, Carl-Fredrik; Alberola-López, Carlos

2011-01-01

In this paper, we introduce a new approach for tensor field segmentation based on the definition of mixtures of Gaussians on tensors as a statistical model. Working over the well-known Geodesic Active Regions segmentation framework, this scheme presents several interesting advantages. First, it yields a more flexible model than the use of a single Gaussian distribution, which enables the method to better adapt to the complexity of the data. Second, it can work directly on tensor-valued images or, through a parallel scheme that processes independently the intensity and the local structure tensor, on scalar textured images. Two different applications have been considered to show the suitability of the proposed method for medical imaging segmentation. First, we address DT-MRI segmentation on a dataset of 32 volumes, showing a successful segmentation of the corpus callosum and favourable comparisons with related approaches in the literature. Second, the segmentation of bones from hand radiographs is studied, and a complete automatic-semiautomatic approach has been developed that makes use of anatomical prior knowledge to produce accurate segmentation results. Copyright © 2010 Elsevier Ltd. All rights reserved.

Squared exponential covariance function for prediction of hydrocarbon in seabed logging application

NASA Astrophysics Data System (ADS)

Mukhtar, Siti Mariam; Daud, Hanita; Dass, Sarat Chandra

2016-11-01

Seabed Logging technology (SBL) has progressively emerged as one of the demanding technologies in Exploration and Production (E&P) industry. Hydrocarbon prediction in deep water areas is crucial task for a driller in any oil and gas company as drilling cost is very expensive. Simulation data generated by Computer Software Technology (CST) is used to predict the presence of hydrocarbon where the models replicate real SBL environment. These models indicate that the hydrocarbon filled reservoirs are more resistive than surrounding water filled sediments. Then, as hydrocarbon depth is increased, it is more challenging to differentiate data with and without hydrocarbon. MATLAB is used for data extractions for curve fitting process using Gaussian process (GP). GP can be classified into regression and classification problems, where this work only focuses on Gaussian process regression (GPR) problem. Most popular choice to supervise GPR is squared exponential (SE), as it provides stability and probabilistic prediction in huge amounts of data. Hence, SE is used to predict the presence or absence of hydrocarbon in the reservoir from the data generated.

Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.

PubMed

García, Constantino A; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G

2017-08-01

The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.

Estimating Mixture of Gaussian Processes by Kernel Smoothing

PubMed Central

Huang, Mian; Li, Runze; Wang, Hansheng; Yao, Weixin

2014-01-01

When the functional data are not homogeneous, e.g., there exist multiple classes of functional curves in the dataset, traditional estimation methods may fail. In this paper, we propose a new estimation procedure for the Mixture of Gaussian Processes, to incorporate both functional and inhomogeneous properties of the data. Our method can be viewed as a natural extension of high-dimensional normal mixtures. However, the key difference is that smoothed structures are imposed for both the mean and covariance functions. The model is shown to be identifiable, and can be estimated efficiently by a combination of the ideas from EM algorithm, kernel regression, and functional principal component analysis. Our methodology is empirically justified by Monte Carlo simulations and illustrated by an analysis of a supermarket dataset. PMID:24976675

American option pricing in Gauss-Markov interest rate models

NASA Astrophysics Data System (ADS)

Galluccio, Stefano

1999-07-01

In the context of Gaussian non-homogeneous interest-rate models, we study the problem of American bond option pricing. In particular, we show how to efficiently compute the exercise boundary in these models in order to decompose the price as a sum of a European option and an American premium. Generalizations to coupon-bearing bonds and jump-diffusion processes for the interest rates are also discussed.

Fractional Brownian motion time-changed by gamma and inverse gamma process

NASA Astrophysics Data System (ADS)

Kumar, A.; Wyłomańska, A.; Połoczański, R.; Sundar, S.

2017-02-01

Many real time-series exhibit behavior adequate to long range dependent data. Additionally very often these time-series have constant time periods and also have characteristics similar to Gaussian processes although they are not Gaussian. Therefore there is need to consider new classes of systems to model these kinds of empirical behavior. Motivated by this fact in this paper we analyze two processes which exhibit long range dependence property and have additional interesting characteristics which may be observed in real phenomena. Both of them are constructed as the superposition of fractional Brownian motion (FBM) and other process. In the first case the internal process, which plays role of the time, is the gamma process while in the second case the internal process is its inverse. We present in detail their main properties paying main attention to the long range dependence property. Moreover, we show how to simulate these processes and estimate their parameters. We propose to use a novel method based on rescaled modified cumulative distribution function for estimation of parameters of the second considered process. This method is very useful in description of rounded data, like waiting times of subordinated processes delayed by inverse subordinators. By using the Monte Carlo method we show the effectiveness of proposed estimation procedures. Finally, we present the applications of proposed models to real time series.

Optimum Laser Beam Characteristics for Achieving Smoother Ablations in Laser Vision Correction.

PubMed

Verma, Shwetabh; Hesser, Juergen; Arba-Mosquera, Samuel

2017-04-01

Controversial opinions exist regarding optimum laser beam characteristics for achieving smoother ablations in laser-based vision correction. The purpose of the study was to outline a rigorous simulation model for simulating shot-by-shot ablation process. The impact of laser beam characteristics like super Gaussian order, truncation radius, spot geometry, spot overlap, and lattice geometry were tested on ablation smoothness. Given the super Gaussian order, the theoretical beam profile was determined following Lambert-Beer model. The intensity beam profile originating from an excimer laser was measured with a beam profiler camera. For both, the measured and theoretical beam profiles, two spot geometries (round and square spots) were considered, and two types of lattices (reticular and triangular) were simulated with varying spot overlaps and ablated material (cornea or polymethylmethacrylate [PMMA]). The roughness in ablation was determined by the root-mean-square per square root of layer depth. Truncating the beam profile increases the roughness in ablation, Gaussian profiles theoretically result in smoother ablations, round spot geometries produce lower roughness in ablation compared to square geometry, triangular lattices theoretically produce lower roughness in ablation compared to the reticular lattice, theoretically modeled beam profiles show lower roughness in ablation compared to the measured beam profile, and the simulated roughness in ablation on PMMA tends to be lower than on human cornea. For given input parameters, proper optimum parameters for minimizing the roughness have been found. Theoretically, the proposed model can be used for achieving smoothness with laser systems used for ablation processes at relatively low cost. This model may improve the quality of results and could be directly applied for improving postoperative surface quality.

Approximating high angular resolution apparent diffusion coefficient profiles using spherical harmonics under BiGaussian assumption

NASA Astrophysics Data System (ADS)

Cao, Ning; Liang, Xuwei; Zhuang, Qi; Zhang, Jun

2009-02-01

Magnetic Resonance Imaging (MRI) techniques have achieved much importance in providing visual and quantitative information of human body. Diffusion MRI is the only non-invasive tool to obtain information of the neural fiber networks of the human brain. The traditional Diffusion Tensor Imaging (DTI) is only capable of characterizing Gaussian diffusion. High Angular Resolution Diffusion Imaging (HARDI) extends its ability to model more complex diffusion processes. Spherical harmonic series truncated to a certain degree is used in recent studies to describe the measured non-Gaussian Apparent Diffusion Coefficient (ADC) profile. In this study, we use the sampling theorem on band-limited spherical harmonics to choose a suitable degree to truncate the spherical harmonic series in the sense of Signal-to-Noise Ratio (SNR), and use Monte Carlo integration to compute the spherical harmonic transform of human brain data obtained from icosahedral schema.

Gaussian process based modeling and experimental design for sensor calibration in drifting environments

PubMed Central

Geng, Zongyu; Yang, Feng; Chen, Xi; Wu, Nianqiang

2016-01-01

It remains a challenge to accurately calibrate a sensor subject to environmental drift. The calibration task for such a sensor is to quantify the relationship between the sensor’s response and its exposure condition, which is specified by not only the analyte concentration but also the environmental factors such as temperature and humidity. This work developed a Gaussian Process (GP)-based procedure for the efficient calibration of sensors in drifting environments. Adopted as the calibration model, GP is not only able to capture the possibly nonlinear relationship between the sensor responses and the various exposure-condition factors, but also able to provide valid statistical inference for uncertainty quantification of the target estimates (e.g., the estimated analyte concentration of an unknown environment). Built on GP’s inference ability, an experimental design method was developed to achieve efficient sampling of calibration data in a batch sequential manner. The resulting calibration procedure, which integrates the GP-based modeling and experimental design, was applied on a simulated chemiresistor sensor to demonstrate its effectiveness and its efficiency over the traditional method. PMID:26924894

Radiation Transport in Random Media With Large Fluctuations

NASA Astrophysics Data System (ADS)

Olson, Aaron; Prinja, Anil; Franke, Brian

2017-09-01

Neutral particle transport in media exhibiting large and complex material property spatial variation is modeled by representing cross sections as lognormal random functions of space and generated through a nonlinear memory-less transformation of a Gaussian process with covariance uniquely determined by the covariance of the cross section. A Karhunen-Loève decomposition of the Gaussian process is implemented to effciently generate realizations of the random cross sections and Woodcock Monte Carlo used to transport particles on each realization and generate benchmark solutions for the mean and variance of the particle flux as well as probability densities of the particle reflectance and transmittance. A computationally effcient stochastic collocation method is implemented to directly compute the statistical moments such as the mean and variance, while a polynomial chaos expansion in conjunction with stochastic collocation provides a convenient surrogate model that also produces probability densities of output quantities of interest. Extensive numerical testing demonstrates that use of stochastic reduced-order modeling provides an accurate and cost-effective alternative to random sampling for particle transport in random media.

A novel optimization algorithm for MIMO Hammerstein model identification under heavy-tailed noise.

PubMed

Jin, Qibing; Wang, Hehe; Su, Qixin; Jiang, Beiyan; Liu, Qie

2018-01-01

In this paper, we study the system identification of multi-input multi-output (MIMO) Hammerstein processes under the typical heavy-tailed noise. To the best of our knowledge, there is no general analytical method to solve this identification problem. Motivated by this, we propose a general identification method to solve this problem based on a Gaussian-Mixture Distribution intelligent optimization algorithm (GMDA). The nonlinear part of Hammerstein process is modeled by a Radial Basis Function (RBF) neural network, and the identification problem is converted to an optimization problem. To overcome the drawbacks of analytical identification method in the presence of heavy-tailed noise, a meta-heuristic optimization algorithm, Cuckoo search (CS) algorithm is used. To improve its performance for this identification problem, the Gaussian-mixture Distribution (GMD) and the GMD sequences are introduced to improve the performance of the standard CS algorithm. Numerical simulations for different MIMO Hammerstein models are carried out, and the simulation results verify the effectiveness of the proposed GMDA. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Topology of large-scale structure in seeded hot dark matter models

NASA Technical Reports Server (NTRS)

Beaky, Matthew M.; Scherrer, Robert J.; Villumsen, Jens V.

1992-01-01

The topology of the isodensity surfaces in seeded hot dark matter models, in which static seed masses provide the density perturbations in a universe dominated by massive neutrinos is examined. When smoothed with a Gaussian window, the linear initial conditions in these models show no trace of non-Gaussian behavior for r0 equal to or greater than 5 Mpc (h = 1/2), except for very low seed densities, which show a shift toward isolated peaks. An approximate analytic expression is given for the genus curve expected in linear density fields from randomly distributed seed masses. The evolved models have a Gaussian topology for r0 = 10 Mpc, but show a shift toward a cellular topology with r0 = 5 Mpc; Gaussian models with an identical power spectrum show the same behavior.

Fast genomic predictions via Bayesian G-BLUP and multilocus models of threshold traits including censored Gaussian data.

PubMed

Kärkkäinen, Hanni P; Sillanpää, Mikko J

2013-09-04

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed.

Fast Genomic Predictions via Bayesian G-BLUP and Multilocus Models of Threshold Traits Including Censored Gaussian Data

PubMed Central

Kärkkäinen, Hanni P.; Sillanpää, Mikko J.

2013-01-01

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed. PMID:23821618

Statistical Orbit Determination using the Particle Filter for Incorporating Non-Gaussian Uncertainties

NASA Technical Reports Server (NTRS)

Mashiku, Alinda; Garrison, James L.; Carpenter, J. Russell

2012-01-01

The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.

Bayesian Treed Calibration: An Application to Carbon Capture With AX Sorbent

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

Konomi, Bledar A.; Karagiannis, Georgios; Lai, Kevin

2017-01-02

In cases where field or experimental measurements are not available, computer models can model real physical or engineering systems to reproduce their outcomes. They are usually calibrated in light of experimental data to create a better representation of the real system. Statistical methods, based on Gaussian processes, for calibration and prediction have been especially important when the computer models are expensive and experimental data limited. In this paper, we develop the Bayesian treed calibration (BTC) as an extension of standard Gaussian process calibration methods to deal with non-stationarity computer models and/or their discrepancy from the field (or experimental) data. Ourmore » proposed method partitions both the calibration and observable input space, based on a binary tree partitioning, into sub-regions where existing model calibration methods can be applied to connect a computer model with the real system. The estimation of the parameters in the proposed model is carried out using Markov chain Monte Carlo (MCMC) computational techniques. Different strategies have been applied to improve mixing. We illustrate our method in two artificial examples and a real application that concerns the capture of carbon dioxide with AX amine based sorbents. The source code and the examples analyzed in this paper are available as part of the supplementary materials.« less

Estimation of continuous multi-DOF finger joint kinematics from surface EMG using a multi-output Gaussian Process.

PubMed

Ngeo, Jimson; Tamei, Tomoya; Shibata, Tomohiro

2014-01-01

Surface electromyographic (EMG) signals have often been used in estimating upper and lower limb dynamics and kinematics for the purpose of controlling robotic devices such as robot prosthesis and finger exoskeletons. However, in estimating multiple and a high number of degrees-of-freedom (DOF) kinematics from EMG, output DOFs are usually estimated independently. In this study, we estimate finger joint kinematics from EMG signals using a multi-output convolved Gaussian Process (Multi-output Full GP) that considers dependencies between outputs. We show that estimation of finger joints from muscle activation inputs can be improved by using a regression model that considers inherent coupling or correlation within the hand and finger joints. We also provide a comparison of estimation performance between different regression methods, such as Artificial Neural Networks (ANN) which is used by many of the related studies. We show that using a multi-output GP gives improved estimation compared to multi-output ANN and even dedicated or independent regression models.

Non-gaussianity versus nonlinearity of cosmological perturbations.

PubMed

Verde, L

2001-06-01

Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us toward a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, nonlinear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but galaxies might not be faithful tracers of the underlying mass distribution. The relationship between fluctuations in the mass and in the galaxies distribution (bias), is often assumed to be local, but could well be nonlinear. Moreover, galaxy catalogues use the redshift as third spatial coordinate: the resulting redshift-space map of the galaxy distribution is nonlinearly distorted by peculiar velocities. Nonlinear gravitational evolution, biasing, and redshift-space distortion introduce non-gaussianity, even in an initially gaussian fluctuation field. I investigate the statistical tools that allow us, in principle, to disentangle the above different effects, and the observational datasets we require to do so in practice.

Can a numerically stable subgrid-scale model for turbulent flow computation be ideally accurate?: a preliminary theoretical study for the Gaussian filtered Navier-Stokes equations.

PubMed

Ida, Masato; Taniguchi, Nobuyuki

2003-09-01

This paper introduces a candidate for the origin of the numerical instabilities in large eddy simulation repeatedly observed in academic and practical industrial flow computations. Without resorting to any subgrid-scale modeling, but based on a simple assumption regarding the streamwise component of flow velocity, it is shown theoretically that in a channel-flow computation, the application of the Gaussian filtering to the incompressible Navier-Stokes equations yields a numerically unstable term, a cross-derivative term, which is similar to one appearing in the Gaussian filtered Vlasov equation derived by Klimas [J. Comput. Phys. 68, 202 (1987)] and also to one derived recently by Kobayashi and Shimomura [Phys. Fluids 15, L29 (2003)] from the tensor-diffusivity subgrid-scale term in a dynamic mixed model. The present result predicts that not only the numerical methods and the subgrid-scale models employed but also only the applied filtering process can be a seed of this numerical instability. An investigation concerning the relationship between the turbulent energy scattering and the unstable term shows that the instability of the term does not necessarily represent the backscatter of kinetic energy which has been considered a possible origin of numerical instabilities in large eddy simulation. The present findings raise the question whether a numerically stable subgrid-scale model can be ideally accurate.

Analytical performance specifications for changes in assay bias (Δbias) for data with logarithmic distributions as assessed by effects on reference change values.

PubMed

Petersen, Per H; Lund, Flemming; Fraser, Callum G; Sölétormos, György

2016-11-01

Background The distributions of within-subject biological variation are usually described as coefficients of variation, as are analytical performance specifications for bias, imprecision and other characteristics. Estimation of specifications required for reference change values is traditionally done using relationship between the batch-related changes during routine performance, described as Δbias, and the coefficients of variation for analytical imprecision (CV A ): the original theory is based on standard deviations or coefficients of variation calculated as if distributions were Gaussian. Methods The distribution of between-subject biological variation can generally be described as log-Gaussian. Moreover, recent analyses of within-subject biological variation suggest that many measurands have log-Gaussian distributions. In consequence, we generated a model for the estimation of analytical performance specifications for reference change value, with combination of Δbias and CV A based on log-Gaussian distributions of CV I as natural logarithms. The model was tested using plasma prolactin and glucose as examples. Results Analytical performance specifications for reference change value generated using the new model based on log-Gaussian distributions were practically identical with the traditional model based on Gaussian distributions. Conclusion The traditional and simple to apply model used to generate analytical performance specifications for reference change value, based on the use of coefficients of variation and assuming Gaussian distributions for both CV I and CV A , is generally useful.

Mean Field Variational Bayesian Data Assimilation

NASA Astrophysics Data System (ADS)

Vrettas, M.; Cornford, D.; Opper, M.

2012-04-01

Current data assimilation schemes propose a range of approximate solutions to the classical data assimilation problem, particularly state estimation. Broadly there are three main active research areas: ensemble Kalman filter methods which rely on statistical linearization of the model evolution equations, particle filters which provide a discrete point representation of the posterior filtering or smoothing distribution and 4DVAR methods which seek the most likely posterior smoothing solution. In this paper we present a recent extension to our variational Bayesian algorithm which seeks the most probably posterior distribution over the states, within the family of non-stationary Gaussian processes. Our original work on variational Bayesian approaches to data assimilation sought the best approximating time varying Gaussian process to the posterior smoothing distribution for stochastic dynamical systems. This approach was based on minimising the Kullback-Leibler divergence between the true posterior over paths, and our Gaussian process approximation. So long as the observation density was sufficiently high to bring the posterior smoothing density close to Gaussian the algorithm proved very effective, on lower dimensional systems. However for higher dimensional systems, the algorithm was computationally very demanding. We have been developing a mean field version of the algorithm which treats the state variables at a given time as being independent in the posterior approximation, but still accounts for their relationships between each other in the mean solution arising from the original dynamical system. In this work we present the new mean field variational Bayesian approach, illustrating its performance on a range of classical data assimilation problems. We discuss the potential and limitations of the new approach. We emphasise that the variational Bayesian approach we adopt, in contrast to other variational approaches, provides a bound on the marginal likelihood of the observations given parameters in the model which also allows inference of parameters such as observation errors, and parameters in the model and model error representation, particularly if this is written as a deterministic form with small additive noise. We stress that our approach can address very long time window and weak constraint settings. However like traditional variational approaches our Bayesian variational method has the benefit of being posed as an optimisation problem. We finish with a sketch of the future directions for our approach.

Simulation of time series by distorted Gaussian processes

NASA Technical Reports Server (NTRS)

Greenhall, C. A.

1977-01-01

Distorted stationary Gaussian process can be used to provide computer-generated imitations of experimental time series. A method of analyzing a source time series and synthesizing an imitation is shown, and an example using X-band radiometer data is given.

Nonturbulent dispersion processes in complex terrain

Treesearch

Michael A. Fosberg; Douglas G. Fox; E.A. Howard; Jack D. Cohen

1976-01-01

Mass divergence influences on plume dispersion modify classic Gaussian calculations by as much as a factor of two in complex terrain. The Gaussian plume was derived in flux form to include this process.Authors' response to comments and criticism received following this publication:

Occupancy mapping and surface reconstruction using local Gaussian processes with Kinect sensors.

PubMed

Kim, Soohwan; Kim, Jonghyuk

2013-10-01

Although RGB-D sensors have been successfully applied to visual SLAM and surface reconstruction, most of the applications aim at visualization. In this paper, we propose a noble method of building continuous occupancy maps and reconstructing surfaces in a single framework for both navigation and visualization. Particularly, we apply a Bayesian nonparametric approach, Gaussian process classification, to occupancy mapping. However, it suffers from high-computational complexity of O(n(3))+O(n(2)m), where n and m are the numbers of training and test data, respectively, limiting its use for large-scale mapping with huge training data, which is common with high-resolution RGB-D sensors. Therefore, we partition both training and test data with a coarse-to-fine clustering method and apply Gaussian processes to each local clusters. In addition, we consider Gaussian processes as implicit functions, and thus extract iso-surfaces from the scalar fields, continuous occupancy maps, using marching cubes. By doing that, we are able to build two types of map representations within a single framework of Gaussian processes. Experimental results with 2-D simulated data show that the accuracy of our approximated method is comparable to previous work, while the computational time is dramatically reduced. We also demonstrate our method with 3-D real data to show its feasibility in large-scale environments.

How to model moon signals using 2-dimensional Gaussian function: Classroom activity for measuring nighttime cloud cover

NASA Astrophysics Data System (ADS)

Gacal, G. F. B.; Lagrosas, N.

2016-12-01

Nowadays, cameras are commonly used by students. In this study, we use this instrument to look at moon signals and relate these signals to Gaussian functions. To implement this as a classroom activity, students need computers, computer software to visualize signals, and moon images. A normalized Gaussian function is often used to represent probability density functions of normal distribution. It is described by its mean m and standard deviation s. The smaller standard deviation implies less spread from the mean. For the 2-dimensional Gaussian function, the mean can be described by coordinates (x0, y0), while the standard deviations can be described by sx and sy. In modelling moon signals obtained from sky-cameras, the position of the mean (x0, y0) is solved by locating the coordinates of the maximum signal of the moon. The two standard deviations are the mean square weighted deviation based from the sum of total pixel values of all rows/columns. If visualized in three dimensions, the 2D Gaussian function appears as a 3D bell surface (Fig. 1a). This shape is similar to the pixel value distribution of moon signals as captured by a sky-camera. An example of this is illustrated in Fig 1b taken around 22:20 (local time) of January 31, 2015. The local time is 8 hours ahead of coordinated universal time (UTC). This image is produced by a commercial camera (Canon Powershot A2300) with 1s exposure time, f-stop of f/2.8, and 5mm focal length. One has to chose a camera with high sensitivity when operated at nighttime to effectively detect these signals. Fig. 1b is obtained by converting the red-green-blue (RGB) photo to grayscale values. The grayscale values are then converted to a double data type matrix. The last conversion process is implemented for the purpose of having the same scales for both Gaussian model and pixel distribution of raw signals. Subtraction of the Gaussian model from the raw data produces a moonless image as shown in Fig. 1c. This moonless image can be used for quantifying cloud cover as captured by ordinary cameras (Gacal et al, 2016). Cloud cover can be defined as the ratio of number of pixels whose values exceeds 0.07 and the total number of pixels. In this particular image, cloud cover value is 0.67.

Variational Gaussian approximation for Poisson data

NASA Astrophysics Data System (ADS)

Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

2018-02-01

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

Hierarchical Bayesian modelling of gene expression time series across irregularly sampled replicates and clusters.

PubMed

Hensman, James; Lawrence, Neil D; Rattray, Magnus

2013-08-20

Time course data from microarrays and high-throughput sequencing experiments require simple, computationally efficient and powerful statistical models to extract meaningful biological signal, and for tasks such as data fusion and clustering. Existing methodologies fail to capture either the temporal or replicated nature of the experiments, and often impose constraints on the data collection process, such as regularly spaced samples, or similar sampling schema across replications. We propose hierarchical Gaussian processes as a general model of gene expression time-series, with application to a variety of problems. In particular, we illustrate the method's capacity for missing data imputation, data fusion and clustering.The method can impute data which is missing both systematically and at random: in a hold-out test on real data, performance is significantly better than commonly used imputation methods. The method's ability to model inter- and intra-cluster variance leads to more biologically meaningful clusters. The approach removes the necessity for evenly spaced samples, an advantage illustrated on a developmental Drosophila dataset with irregular replications. The hierarchical Gaussian process model provides an excellent statistical basis for several gene-expression time-series tasks. It has only a few additional parameters over a regular GP, has negligible additional complexity, is easily implemented and can be integrated into several existing algorithms. Our experiments were implemented in python, and are available from the authors' website: http://staffwww.dcs.shef.ac.uk/people/J.Hensman/.

Parallel logic gates in synthetic gene networks induced by non-Gaussian noise.

PubMed

Xu, Yong; Jin, Xiaoqin; Zhang, Huiqing

2013-11-01

The recent idea of logical stochastic resonance is verified in synthetic gene networks induced by non-Gaussian noise. We realize the switching between two kinds of logic gates under optimal moderate noise intensity by varying two different tunable parameters in a single gene network. Furthermore, in order to obtain more logic operations, thus providing additional information processing capacity, we obtain in a two-dimensional toggle switch model two complementary logic gates and realize the transformation between two logic gates via the methods of changing different parameters. These simulated results contribute to improve the computational power and functionality of the networks.

Time-resolved measurements of statistics for a Nd:YAG laser.

PubMed

Hubschmid, W; Bombach, R; Gerber, T

1994-08-20

Time-resolved measurements of the fluctuating intensity of a multimode frequency-doubled Nd:YAG laser have been performed. For various operating conditions the enhancement factors in nonlinear optical processes that use a fluctuating instead of a single-mode laser have been determined up to the sixth order. In the case of reduced flash-lamp excitation and a switched-off laser amplifier, the intensity fluctuations agree with the normalized Gaussian model for the fluctuations of the fundamental frequency, whereas strong deviations are found under usual operating conditions. The frequencydoubled light has in the latter case enhancement factors not so far from values of Gaussian statistics.

Extinction time of a stochastic predator-prey model by the generalized cell mapping method

NASA Astrophysics Data System (ADS)

Han, Qun; Xu, Wei; Hu, Bing; Huang, Dongmei; Sun, Jian-Qiao

2018-03-01

The stochastic response and extinction time of a predator-prey model with Gaussian white noise excitations are studied by the generalized cell mapping (GCM) method based on the short-time Gaussian approximation (STGA). The methods for stochastic response probability density functions (PDFs) and extinction time statistics are developed. The Taylor expansion is used to deal with non-polynomial nonlinear terms of the model for deriving the moment equations with Gaussian closure, which are needed for the STGA in order to compute the one-step transition probabilities. The work is validated with direct Monte Carlo simulations. We have presented the transient responses showing the evolution from a Gaussian initial distribution to a non-Gaussian steady-state one. The effects of the model parameter and noise intensities on the steady-state PDFs are discussed. It is also found that the effects of noise intensities on the extinction time statistics are opposite to the effects on the limit probability distributions of the survival species.

Integration of Advanced Statistical Analysis Tools and Geophysical Modeling

DTIC Science & Technology

2012-08-01

Carin Duke University Douglas Oldenburg University of British Columbia Stephen Billings Leonard Pasion Laurens Beran Sky Research...data processing for UXO discrimination is the time (or frequency) dependent dipole model (Bell and Barrow (2001), Pasion and Oldenburg (2001), Zhang...described by a bimodal distribution (i.e. two Gaussians, see Pasion (2007)). Data features are nonetheless useful when data quality is not sufficient

Kullback-Leibler divergence measure of intermittency: Application to turbulence

NASA Astrophysics Data System (ADS)

Granero-Belinchón, Carlos; Roux, Stéphane G.; Garnier, Nicolas B.

2018-01-01

For generic systems exhibiting power law behaviors, and hence multiscale dependencies, we propose a simple tool to analyze multifractality and intermittency, after noticing that these concepts are directly related to the deformation of a probability density function from Gaussian at large scales to non-Gaussian at smaller scales. Our framework is based on information theory and uses Shannon entropy and Kullback-Leibler divergence. We provide an extensive application to three-dimensional fully developed turbulence, seen here as a paradigmatic complex system where intermittency was historically defined and the concepts of scale invariance and multifractality were extensively studied and benchmarked. We compute our quantity on experimental Eulerian velocity measurements, as well as on synthetic processes and phenomenological models of fluid turbulence. Our approach is very general and does not require any underlying model of the system, although it can probe the relevance of such a model.

Penalized gaussian process regression and classification for high-dimensional nonlinear data.

PubMed

Yi, G; Shi, J Q; Choi, T

2011-12-01

The model based on Gaussian process (GP) prior and a kernel covariance function can be used to fit nonlinear data with multidimensional covariates. It has been used as a flexible nonparametric approach for curve fitting, classification, clustering, and other statistical problems, and has been widely applied to deal with complex nonlinear systems in many different areas particularly in machine learning. However, it is a challenging problem when the model is used for the large-scale data sets and high-dimensional data, for example, for the meat data discussed in this article that have 100 highly correlated covariates. For such data, it suffers from large variance of parameter estimation and high predictive errors, and numerically, it suffers from unstable computation. In this article, penalized likelihood framework will be applied to the model based on GPs. Different penalties will be investigated, and their ability in application given to suit the characteristics of GP models will be discussed. The asymptotic properties will also be discussed with the relevant proofs. Several applications to real biomechanical and bioinformatics data sets will be reported. © 2011, The International Biometric Society No claim to original US government works.

An adaptive Gaussian process-based iterative ensemble smoother for data assimilation

NASA Astrophysics Data System (ADS)

Ju, Lei; Zhang, Jiangjiang; Meng, Long; Wu, Laosheng; Zeng, Lingzao

2018-05-01

Accurate characterization of subsurface hydraulic conductivity is vital for modeling of subsurface flow and transport. The iterative ensemble smoother (IES) has been proposed to estimate the heterogeneous parameter field. As a Monte Carlo-based method, IES requires a relatively large ensemble size to guarantee its performance. To improve the computational efficiency, we propose an adaptive Gaussian process (GP)-based iterative ensemble smoother (GPIES) in this study. At each iteration, the GP surrogate is adaptively refined by adding a few new base points chosen from the updated parameter realizations. Then the sensitivity information between model parameters and measurements is calculated from a large number of realizations generated by the GP surrogate with virtually no computational cost. Since the original model evaluations are only required for base points, whose number is much smaller than the ensemble size, the computational cost is significantly reduced. The applicability of GPIES in estimating heterogeneous conductivity is evaluated by the saturated and unsaturated flow problems, respectively. Without sacrificing estimation accuracy, GPIES achieves about an order of magnitude of speed-up compared with the standard IES. Although subsurface flow problems are considered in this study, the proposed method can be equally applied to other hydrological models.

A novel Gaussian process regression model for state-of-health estimation of lithium-ion battery using charging curve

NASA Astrophysics Data System (ADS)

Yang, Duo; Zhang, Xu; Pan, Rui; Wang, Yujie; Chen, Zonghai

2018-04-01

The state-of-health (SOH) estimation is always a crucial issue for lithium-ion batteries. In order to provide an accurate and reliable SOH estimation, a novel Gaussian process regression (GPR) model based on charging curve is proposed in this paper. Different from other researches where SOH is commonly estimated by cycle life, in this work four specific parameters extracted from charging curves are used as inputs of the GPR model instead of cycle numbers. These parameters can reflect the battery aging phenomenon from different angles. The grey relational analysis method is applied to analyze the relational grade between selected features and SOH. On the other hand, some adjustments are made in the proposed GPR model. Covariance function design and the similarity measurement of input variables are modified so as to improve the SOH estimate accuracy and adapt to the case of multidimensional input. Several aging data from NASA data repository are used for demonstrating the estimation effect by the proposed method. Results show that the proposed method has high SOH estimation accuracy. Besides, a battery with dynamic discharging profile is used to verify the robustness and reliability of this method.

Modeling Multi-Variate Gaussian Distributions and Analysis of Higgs Boson Couplings with the ATLAS Detector

NASA Astrophysics Data System (ADS)

Krohn, Olivia; Armbruster, Aaron; Gao, Yongsheng; Atlas Collaboration

2017-01-01

Software tools developed for the purpose of modeling CERN LHC pp collision data to aid in its interpretation are presented. Some measurements are not adequately described by a Gaussian distribution; thus an interpretation assuming Gaussian uncertainties will inevitably introduce bias, necessitating analytical tools to recreate and evaluate non-Gaussian features. One example is the measurements of Higgs boson production rates in different decay channels, and the interpretation of these measurements. The ratios of data to Standard Model expectations (μ) for five arbitrary signals were modeled by building five Poisson distributions with mixed signal contributions such that the measured values of μ are correlated. Algorithms were designed to recreate probability distribution functions of μ as multi-variate Gaussians, where the standard deviation (σ) and correlation coefficients (ρ) are parametrized. There was good success with modeling 1-D likelihood contours of μ, and the multi-dimensional distributions were well modeled within 1- σ but the model began to diverge after 2- σ due to unmerited assumptions in developing ρ. Future plans to improve the algorithms and develop a user-friendly analysis package will also be discussed. NSF International Research Experiences for Students

Implication of observed cloud variability for parameterizations of microphysical and radiative transfer processes in climate models

NASA Astrophysics Data System (ADS)

Huang, D.; Liu, Y.

2014-12-01

The effects of subgrid cloud variability on grid-average microphysical rates and radiative fluxes are examined by use of long-term retrieval products at the Tropical West Pacific (TWP), Southern Great Plains (SGP), and North Slope of Alaska (NSA) sites of the Department of Energy's Atmospheric Radiation Measurement (ARM) Program. Four commonly used distribution functions, the truncated Gaussian, Gamma, lognormal, and Weibull distributions, are constrained to have the same mean and standard deviation as observed cloud liquid water content. The PDFs are then used to upscale relevant physical processes to obtain grid-average process rates. It is found that the truncated Gaussian representation results in up to 30% mean bias in autoconversion rate whereas the mean bias for the lognormal representation is about 10%. The Gamma and Weibull distribution function performs the best for the grid-average autoconversion rate with the mean relative bias less than 5%. For radiative fluxes, the lognormal and truncated Gaussian representations perform better than the Gamma and Weibull representations. The results show that the optimal choice of subgrid cloud distribution function depends on the nonlinearity of the process of interest and thus there is no single distribution function that works best for all parameterizations. Examination of the scale (window size) dependence of the mean bias indicates that the bias in grid-average process rates monotonically increases with increasing window sizes, suggesting the increasing importance of subgrid variability with increasing grid sizes.

DEVELOPMENT OF A MODEL THAT CONTAINS BOTH MULTIPOLE MOMENTS AND GAUSSIANS FOR THE CALCULATION OF MOLECULAR ELECTROSTATIC POTENTIALS

EPA Science Inventory

The electrostatic interaction is a critical component of intermolecular interactions in biological processes. Rapid methods for the computation and characterization of the molecular electrostatic potential (MEP) that segment the molecular charge distribution and replace this cont...

Bayesian Travel Time Inversion adopting Gaussian Process Regression

NASA Astrophysics Data System (ADS)

Mauerberger, S.; Holschneider, M.

2017-12-01

A major application in seismology is the determination of seismic velocity models. Travel time measurements are putting an integral constraint on the velocity between source and receiver. We provide insight into travel time inversion from a correlation-based Bayesian point of view. Therefore, the concept of Gaussian process regression is adopted to estimate a velocity model. The non-linear travel time integral is approximated by a 1st order Taylor expansion. A heuristic covariance describes correlations amongst observations and a priori model. That approach enables us to assess a proxy of the Bayesian posterior distribution at ordinary computational costs. No multi dimensional numeric integration nor excessive sampling is necessary. Instead of stacking the data, we suggest to progressively build the posterior distribution. Incorporating only a single evidence at a time accounts for the deficit of linearization. As a result, the most probable model is given by the posterior mean whereas uncertainties are described by the posterior covariance.As a proof of concept, a synthetic purely 1d model is addressed. Therefore a single source accompanied by multiple receivers is considered on top of a model comprising a discontinuity. We consider travel times of both phases - direct and reflected wave - corrupted by noise. Left and right of the interface are assumed independent where the squared exponential kernel serves as covariance.

A Joint Gaussian Process Model for Active Visual Recognition with Expertise Estimation in Crowdsourcing

PubMed Central

Long, Chengjiang; Hua, Gang; Kapoor, Ashish

2015-01-01

We present a noise resilient probabilistic model for active learning of a Gaussian process classifier from crowds, i.e., a set of noisy labelers. It explicitly models both the overall label noise and the expertise level of each individual labeler with two levels of flip models. Expectation propagation is adopted for efficient approximate Bayesian inference of our probabilistic model for classification, based on which, a generalized EM algorithm is derived to estimate both the global label noise and the expertise of each individual labeler. The probabilistic nature of our model immediately allows the adoption of the prediction entropy for active selection of data samples to be labeled, and active selection of high quality labelers based on their estimated expertise to label the data. We apply the proposed model for four visual recognition tasks, i.e., object category recognition, multi-modal activity recognition, gender recognition, and fine-grained classification, on four datasets with real crowd-sourced labels from the Amazon Mechanical Turk. The experiments clearly demonstrate the efficacy of the proposed model. In addition, we extend the proposed model with the Predictive Active Set Selection Method to speed up the active learning system, whose efficacy is verified by conducting experiments on the first three datasets. The results show our extended model can not only preserve a higher accuracy, but also achieve a higher efficiency. PMID:26924892

A Gaussian framework for modeling effects of frequency-dependent attenuation, frequency-dependent scattering, and gating.

PubMed

Wear, Keith A

2002-11-01

For a wide range of applications in medical ultrasound, power spectra of received signals are approximately Gaussian. It has been established previously that an ultrasound beam with a Gaussian spectrum propagating through a medium with linear attenuation remains Gaussian. In this paper, Gaussian transformations are derived to model the effects of scattering (according to a power law, as is commonly applicable in soft tissues, especially over limited frequency ranges) and gating (with a Hamming window, a commonly used gate function). These approximations are shown to be quite accurate even for relatively broad band systems with fractional bandwidths approaching 100%. The theory is validated by experiments in phantoms consisting of glass particles suspended in agar.

Laguerre-Gaussian, Hermite-Gaussian, Bessel-Gaussian, and Finite-Energy Airy Beams Carrying Orbital Angular Momentum in Strongly Nonlocal Nonlinear Media

NASA Astrophysics Data System (ADS)

Wu, Zhenkun; Gu, Yuzong

2016-12-01

The propagation of two-dimensional beams is analytically and numerically investigated in strongly nonlocal nonlinear media (SNNM) based on the ABCD matrix. The two-dimensional beams reported in this paper are described by the product of the superposition of generalized Laguerre-Gaussian (LG), Hermite-Gaussian (HG), Bessel-Gaussian (BG), and circular Airy (CA) beams, carrying an orbital angular momentum (OAM). Owing to OAM and the modulation of SNNM, we find that the propagation of these two-dimensional beams exhibits complete rotation and periodic inversion: the spatial intensity profile first extends and then diminishes, and during the propagation the process repeats to form a breath-like phenomenon.

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.

Formation of doughnut and super-Gaussian intensity distributions of laser radiation in the far field using a bimorph mirror

NASA Astrophysics Data System (ADS)

Lylova, A. N.; Sheldakova, Yu. V.; Kudryashov, A. V.; Samarkin, V. V.

2018-01-01

We consider the methods for modelling doughnut and super-Gaussian intensity distributions in the far field by means of deformable bimorph mirrors. A method for the rapid formation of a specified intensity distribution using a Shack - Hartmann sensor is proposed, and the results of the modelling of doughnut and super-Gaussian intensity distributions are presented.

Efficient, adaptive estimation of two-dimensional firing rate surfaces via Gaussian process methods.

PubMed

Rad, Kamiar Rahnama; Paninski, Liam

2010-01-01

Estimating two-dimensional firing rate maps is a common problem, arising in a number of contexts: the estimation of place fields in hippocampus, the analysis of temporally nonstationary tuning curves in sensory and motor areas, the estimation of firing rates following spike-triggered covariance analyses, etc. Here we introduce methods based on Gaussian process nonparametric Bayesian techniques for estimating these two-dimensional rate maps. These techniques offer a number of advantages: the estimates may be computed efficiently, come equipped with natural errorbars, adapt their smoothness automatically to the local density and informativeness of the observed data, and permit direct fitting of the model hyperparameters (e.g., the prior smoothness of the rate map) via maximum marginal likelihood. We illustrate the method's flexibility and performance on a variety of simulated and real data.

Electronically nonadiabatic wave packet propagation using frozen Gaussian scattering

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

Kondorskiy, Alexey D., E-mail: kondor@sci.lebedev.ru; Nanbu, Shinkoh, E-mail: shinkoh.nanbu@sophia.ac.jp

2015-09-21

We present an approach, which allows to employ the adiabatic wave packet propagation technique and semiclassical theory to treat the nonadiabatic processes by using trajectory hopping. The approach developed generates a bunch of hopping trajectories and gives all additional information to incorporate the effect of nonadiabatic coupling into the wave packet dynamics. This provides an interface between a general adiabatic frozen Gaussian wave packet propagation method and the trajectory surface hopping technique. The basic idea suggested in [A. D. Kondorskiy and H. Nakamura, J. Chem. Phys. 120, 8937 (2004)] is revisited and complemented in the present work by the elaborationmore » of efficient numerical algorithms. We combine our approach with the adiabatic Herman-Kluk frozen Gaussian approximation. The efficiency and accuracy of the resulting method is demonstrated by applying it to popular benchmark model systems including three Tully’s models and 24D model of pyrazine. It is shown that photoabsorption spectrum is successfully reproduced by using a few hundreds of trajectories. We employ the compact finite difference Hessian update scheme to consider feasibility of the ab initio “on-the-fly” simulations. It is found that this technique allows us to obtain the reliable final results using several Hessian matrix calculations per trajectory.« less

Evolution of the frequency chirp of Gaussian pulses and beams when passing through a pulse compressor.

PubMed

Li, Derong; Lv, Xiaohua; Bowlan, Pamela; Du, Rui; Zeng, Shaoqun; Luo, Qingming

2009-09-14

The evolution of the frequency chirp of a laser pulse inside a classical pulse compressor is very different for plane waves and Gaussian beams, although after propagating through the last (4th) dispersive element, the two models give the same results. In this paper, we have analyzed the evolution of the frequency chirp of Gaussian pulses and beams using a method which directly obtains the spectral phase acquired by the compressor. We found the spatiotemporal couplings in the phase to be the fundamental reason for the difference in the frequency chirp acquired by a Gaussian beam and a plane wave. When the Gaussian beam propagates, an additional frequency chirp will be introduced if any spatiotemporal couplings (i.e. angular dispersion, spatial chirp or pulse front tilt) are present. However, if there are no couplings present, the chirp of the Gaussian beam is the same as that of a plane wave. When the Gaussian beam is well collimated, the introduced frequency chirp predicted by the plane wave and Gaussian beam models are in closer agreement. This work improves our understanding of pulse compressors and should be helpful for optimizing dispersion compensation schemes in many applications of femtosecond laser pulses.

Bayesian nonparametric regression with varying residual density

PubMed Central

Pati, Debdeep; Dunson, David B.

2013-01-01

We consider the problem of robust Bayesian inference on the mean regression function allowing the residual density to change flexibly with predictors. The proposed class of models is based on a Gaussian process prior for the mean regression function and mixtures of Gaussians for the collection of residual densities indexed by predictors. Initially considering the homoscedastic case, we propose priors for the residual density based on probit stick-breaking (PSB) scale mixtures and symmetrized PSB (sPSB) location-scale mixtures. Both priors restrict the residual density to be symmetric about zero, with the sPSB prior more flexible in allowing multimodal densities. We provide sufficient conditions to ensure strong posterior consistency in estimating the regression function under the sPSB prior, generalizing existing theory focused on parametric residual distributions. The PSB and sPSB priors are generalized to allow residual densities to change nonparametrically with predictors through incorporating Gaussian processes in the stick-breaking components. This leads to a robust Bayesian regression procedure that automatically down-weights outliers and influential observations in a locally-adaptive manner. Posterior computation relies on an efficient data augmentation exact block Gibbs sampler. The methods are illustrated using simulated and real data applications. PMID:24465053

Transient Calibration of a Variably-Saturated Groundwater Flow Model By Iterative Ensemble Smoothering: Synthetic Case and Application to the Flow Induced During Shaft Excavation and Operation of the Bure Underground Research Laboratory

NASA Astrophysics Data System (ADS)

Lam, D. T.; Kerrou, J.; Benabderrahmane, H.; Perrochet, P.

2017-12-01

The calibration of groundwater flow models in transient state can be motivated by the expected improved characterization of the aquifer hydraulic properties, especially when supported by a rich transient dataset. In the prospect of setting up a calibration strategy for a variably-saturated transient groundwater flow model of the area around the ANDRA's Bure Underground Research Laboratory, we wish to take advantage of the long hydraulic head and flowrate time series collected near and at the access shafts in order to help inform the model hydraulic parameters. A promising inverse approach for such high-dimensional nonlinear model, and which applicability has been illustrated more extensively in other scientific fields, could be an iterative ensemble smoother algorithm initially developed for a reservoir engineering problem. Furthermore, the ensemble-based stochastic framework will allow to address to some extent the uncertainty of the calibration for a subsequent analysis of a flow process dependent prediction. By assimilating the available data in one single step, this method iteratively updates each member of an initial ensemble of stochastic realizations of parameters until the minimization of an objective function. However, as it is well known for ensemble-based Kalman methods, this correction computed from approximations of covariance matrices is most efficient when the ensemble realizations are multi-Gaussian. As shown by the comparison of the updated ensemble mean obtained for our simplified synthetic model of 2D vertical flow by using either multi-Gaussian or multipoint simulations of parameters, the ensemble smoother fails to preserve the initial connectivity of the facies and the parameter bimodal distribution. Given the geological structures depicted by the multi-layered geological model built for the real case, our goal is to find how to still best leverage the performance of the ensemble smoother while using an initial ensemble of conditional multi-Gaussian simulations or multipoint simulations as conceptually consistent as possible. Performance of the algorithm including additional steps to help mitigate the effects of non-Gaussian patterns, such as Gaussian anamorphosis, or resampling of facies from the training image using updated local probability constraints will be assessed.

A Bernoulli Gaussian Watermark for Detecting Integrity Attacks in Control Systems

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

Weerakkody, Sean; Ozel, Omur; Sinopoli, Bruno

We examine the merit of Bernoulli packet drops in actively detecting integrity attacks on control systems. The aim is to detect an adversary who delivers fake sensor measurements to a system operator in order to conceal their effect on the plant. Physical watermarks, or noisy additive Gaussian inputs, have been previously used to detect several classes of integrity attacks in control systems. In this paper, we consider the analysis and design of Gaussian physical watermarks in the presence of packet drops at the control input. On one hand, this enables analysis in a more general network setting. On the othermore » hand, we observe that in certain cases, Bernoulli packet drops can improve detection performance relative to a purely Gaussian watermark. This motivates the joint design of a Bernoulli-Gaussian watermark which incorporates both an additive Gaussian input and a Bernoulli drop process. We characterize the effect of such a watermark on system performance as well as attack detectability in two separate design scenarios. Here, we consider a correlation detector for attack recognition. We then propose efficiently solvable optimization problems to intelligently select parameters of the Gaussian input and the Bernoulli drop process while addressing security and performance trade-offs. Finally, we provide numerical results which illustrate that a watermark with packet drops can indeed outperform a Gaussian watermark.« less

Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile

NASA Astrophysics Data System (ADS)

Borges, G. M.; Ferreira, A. S.; da Silva, M. A. A.; Cressoni, J. C.; Viswanathan, G. M.; Mariz, A. M.

2012-09-01

Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e.g., fractional Brownian motion, Lévy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation σt which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.

Gaussian process models for reference ET estimation from alternative meteorological data sources

USDA-ARS?s Scientific Manuscript database

Accurate estimates of daily crop evapotranspiration (ET) are needed for efficient irrigation management, especially in arid and semi-arid regions where crop water demand exceeds rainfall. Daily grass or alfalfa reference ET values and crop coefficients are widely used to estimate crop water demand. ...

Modeling laser velocimeter signals as triply stochastic Poisson processes

NASA Technical Reports Server (NTRS)

Mayo, W. T., Jr.

1976-01-01

Previous models of laser Doppler velocimeter (LDV) systems have not adequately described dual-scatter signals in a manner useful for analysis and simulation of low-level photon-limited signals. At low photon rates, an LDV signal at the output of a photomultiplier tube is a compound nonhomogeneous filtered Poisson process, whose intensity function is another (slower) Poisson process with the nonstationary rate and frequency parameters controlled by a random flow (slowest) process. In the present paper, generalized Poisson shot noise models are developed for low-level LDV signals. Theoretical results useful in detection error analysis and simulation are presented, along with measurements of burst amplitude statistics. Computer generated simulations illustrate the difference between Gaussian and Poisson models of low-level signals.

Revealing transient strain in geodetic data with Gaussian process regression

NASA Astrophysics Data System (ADS)

Hines, T. T.; Hetland, E. A.

2018-03-01

Transient strain derived from global navigation satellite system (GNSS) data can be used to detect and understand geophysical processes such as slow slip events and post-seismic deformation. Here we propose using Gaussian process regression (GPR) as a tool for estimating transient strain from GNSS data. GPR is a non-parametric, Bayesian method for interpolating scattered data. In our approach, we assume a stochastic prior model for transient displacements. The prior describes how much we expect transient displacements to covary spatially and temporally. A posterior estimate of transient strain is obtained by differentiating the posterior transient displacements, which are formed by conditioning the prior with the GNSS data. As a demonstration, we use GPR to detect transient strain resulting from slow slip events in the Pacific Northwest. Maximum likelihood methods are used to constrain a prior model for transient displacements in this region. The temporal covariance of our prior model is described by a compact Wendland covariance function, which significantly reduces the computational burden that can be associated with GPR. Our results reveal the spatial and temporal evolution of strain from slow slip events. We verify that the transient strain estimated with GPR is in fact geophysical signal by comparing it to the seismic tremor that is associated with Pacific Northwest slow slip events.

ExGUtils: A Python Package for Statistical Analysis With the ex-Gaussian Probability Density.

PubMed

Moret-Tatay, Carmen; Gamermann, Daniel; Navarro-Pardo, Esperanza; Fernández de Córdoba Castellá, Pedro

2018-01-01

The study of reaction times and their underlying cognitive processes is an important field in Psychology. Reaction times are often modeled through the ex-Gaussian distribution, because it provides a good fit to multiple empirical data. The complexity of this distribution makes the use of computational tools an essential element. Therefore, there is a strong need for efficient and versatile computational tools for the research in this area. In this manuscript we discuss some mathematical details of the ex-Gaussian distribution and apply the ExGUtils package, a set of functions and numerical tools, programmed for python, developed for numerical analysis of data involving the ex-Gaussian probability density. In order to validate the package, we present an extensive analysis of fits obtained with it, discuss advantages and differences between the least squares and maximum likelihood methods and quantitatively evaluate the goodness of the obtained fits (which is usually an overlooked point in most literature in the area). The analysis done allows one to identify outliers in the empirical datasets and criteriously determine if there is a need for data trimming and at which points it should be done.

ExGUtils: A Python Package for Statistical Analysis With the ex-Gaussian Probability Density

PubMed Central

Moret-Tatay, Carmen; Gamermann, Daniel; Navarro-Pardo, Esperanza; Fernández de Córdoba Castellá, Pedro

2018-01-01

The study of reaction times and their underlying cognitive processes is an important field in Psychology. Reaction times are often modeled through the ex-Gaussian distribution, because it provides a good fit to multiple empirical data. The complexity of this distribution makes the use of computational tools an essential element. Therefore, there is a strong need for efficient and versatile computational tools for the research in this area. In this manuscript we discuss some mathematical details of the ex-Gaussian distribution and apply the ExGUtils package, a set of functions and numerical tools, programmed for python, developed for numerical analysis of data involving the ex-Gaussian probability density. In order to validate the package, we present an extensive analysis of fits obtained with it, discuss advantages and differences between the least squares and maximum likelihood methods and quantitatively evaluate the goodness of the obtained fits (which is usually an overlooked point in most literature in the area). The analysis done allows one to identify outliers in the empirical datasets and criteriously determine if there is a need for data trimming and at which points it should be done. PMID:29765345

Enhancing interaural-delay-based extents of laterality at high frequencies by using ``transposed stimuli''

NASA Astrophysics Data System (ADS)

Bernstein, Leslie R.; Trahiotis, Constantine

2003-06-01

An acoustic pointing task was used to determine whether interaural temporal disparities (ITDs) conveyed by high-frequency ``transposed'' stimuli would produce larger extents of laterality than ITDs conveyed by bands of high-frequency Gaussian noise. The envelopes of transposed stimuli are designed to provide high-frequency channels with information similar to that conveyed by the waveforms of low-frequency stimuli. Lateralization was measured for low-frequency Gaussian noises, the same noises transposed to 4 kHz, and high-frequency Gaussian bands of noise centered at 4 kHz. Extents of laterality obtained with the transposed stimuli were greater than those obtained with bands of Gaussian noise centered at 4 kHz and, in some cases, were equivalent to those obtained with low-frequency stimuli. In a second experiment, the general effects on lateral position produced by imposed combinations of bandwidth, ITD, and interaural phase disparities (IPDs) on low-frequency stimuli remained when those stimuli were transposed to 4 kHz. Overall, the data were fairly well accounted for by a model that computes the cross-correlation subsequent to known stages of peripheral auditory processing augmented by low-pass filtering of the envelopes within the high-frequency channels of each ear.

Infrared maritime target detection using a probabilistic single Gaussian model of sea clutter in Fourier domain

NASA Astrophysics Data System (ADS)

Zhou, Anran; Xie, Weixin; Pei, Jihong; Chen, Yapei

2018-02-01

For ship targets detection in cluttered infrared image sequences, a robust detection method, based on the probabilistic single Gaussian model of sea background in Fourier domain, is put forward. The amplitude spectrum sequences at each frequency point of the pure seawater images in Fourier domain, being more stable than the gray value sequences of each background pixel in the spatial domain, are regarded as a Gaussian model. Next, a probability weighted matrix is built based on the stability of the pure seawater's total energy spectrum in the row direction, to make the Gaussian model more accurate. Then, the foreground frequency points are separated from the background frequency points by the model. Finally, the false-alarm points are removed utilizing ships' shape features. The performance of the proposed method is tested by visual and quantitative comparisons with others.

On the application of Rice's exceedance statistics to atmospheric turbulence.

NASA Technical Reports Server (NTRS)

Chen, W. Y.

1972-01-01

Discrepancies produced by the application of Rice's exceedance statistics to atmospheric turbulence are examined. First- and second-order densities from several data sources have been measured for this purpose. Particular care was paid to each selection of turbulence that provides stationary mean and variance over the entire segment. Results show that even for a stationary segment of turbulence, the process is still highly non-Gaussian, in spite of a Gaussian appearance for its first-order distribution. Data also indicate strongly non-Gaussian second-order distributions. It is therefore concluded that even stationary atmospheric turbulence with a normal first-order distribution cannot be considered a Gaussian process, and consequently the application of Rice's exceedance statistics should be approached with caution.

A Heavy Tailed Expectation Maximization Hidden Markov Random Field Model with Applications to Segmentation of MRI

PubMed Central

Castillo-Barnes, Diego; Peis, Ignacio; Martínez-Murcia, Francisco J.; Segovia, Fermín; Illán, Ignacio A.; Górriz, Juan M.; Ramírez, Javier; Salas-Gonzalez, Diego

2017-01-01

A wide range of segmentation approaches assumes that intensity histograms extracted from magnetic resonance images (MRI) have a distribution for each brain tissue that can be modeled by a Gaussian distribution or a mixture of them. Nevertheless, intensity histograms of White Matter and Gray Matter are not symmetric and they exhibit heavy tails. In this work, we present a hidden Markov random field model with expectation maximization (EM-HMRF) modeling the components using the α-stable distribution. The proposed model is a generalization of the widely used EM-HMRF algorithm with Gaussian distributions. We test the α-stable EM-HMRF model in synthetic data and brain MRI data. The proposed methodology presents two main advantages: Firstly, it is more robust to outliers. Secondly, we obtain similar results than using Gaussian when the Gaussian assumption holds. This approach is able to model the spatial dependence between neighboring voxels in tomographic brain MRI. PMID:29209194

Statistical description of non-Gaussian samples in the F2 layer of the ionosphere during heliogeophysical disturbances

NASA Astrophysics Data System (ADS)

Sergeenko, N. P.

2017-11-01

An adequate statistical method should be developed in order to predict probabilistically the range of ionospheric parameters. This problem is solved in this paper. The time series of the critical frequency of the layer F2- foF2( t) were subjected to statistical processing. For the obtained samples {δ foF2}, statistical distributions and invariants up to the fourth order are calculated. The analysis shows that the distributions differ from the Gaussian law during the disturbances. At levels of sufficiently small probability distributions, there are arbitrarily large deviations from the model of the normal process. Therefore, it is attempted to describe statistical samples {δ foF2} based on the Poisson model. For the studied samples, the exponential characteristic function is selected under the assumption that time series are a superposition of some deterministic and random processes. Using the Fourier transform, the characteristic function is transformed into a nonholomorphic excessive-asymmetric probability-density function. The statistical distributions of the samples {δ foF2} calculated for the disturbed periods are compared with the obtained model distribution function. According to the Kolmogorov's criterion, the probabilities of the coincidence of a posteriori distributions with the theoretical ones are P 0.7-0.9. The conducted analysis makes it possible to draw a conclusion about the applicability of a model based on the Poisson random process for the statistical description and probabilistic variation estimates during heliogeophysical disturbances of the variations {δ foF2}.

Advanced Machine Learning Emulators of Radiative Transfer Models

NASA Astrophysics Data System (ADS)

Camps-Valls, G.; Verrelst, J.; Martino, L.; Vicent, J.

2017-12-01

Physically-based model inversion methodologies are based on physical laws and established cause-effect relationships. A plethora of remote sensing applications rely on the physical inversion of a Radiative Transfer Model (RTM), which lead to physically meaningful bio-geo-physical parameter estimates. The process is however computationally expensive, needs expert knowledge for both the selection of the RTM, its parametrization and the the look-up table generation, as well as its inversion. Mimicking complex codes with statistical nonlinear machine learning algorithms has become the natural alternative very recently. Emulators are statistical constructs able to approximate the RTM, although at a fraction of the computational cost, providing an estimation of uncertainty, and estimations of the gradient or finite integral forms. We review the field and recent advances of emulation of RTMs with machine learning models. We posit Gaussian processes (GPs) as the proper framework to tackle the problem. Furthermore, we introduce an automatic methodology to construct emulators for costly RTMs. The Automatic Gaussian Process Emulator (AGAPE) methodology combines the interpolation capabilities of GPs with the accurate design of an acquisition function that favours sampling in low density regions and flatness of the interpolation function. We illustrate the good capabilities of our emulators in toy examples, leaf and canopy levels PROSPECT and PROSAIL RTMs, and for the construction of an optimal look-up-table for atmospheric correction based on MODTRAN5.

Anomalous scaling of a passive scalar advected by the Navier-Stokes velocity field: two-loop approximation.

PubMed

Adzhemyan, L Ts; Antonov, N V; Honkonen, J; Kim, T L

2005-01-01

The field theoretic renormalization group and operator-product expansion are applied to the model of a passive scalar quantity advected by a non-Gaussian velocity field with finite correlation time. The velocity is governed by the Navier-Stokes equation, subject to an external random stirring force with the correlation function proportional to delta(t- t')k(4-d-2epsilon). It is shown that the scalar field is intermittent already for small epsilon, its structure functions display anomalous scaling behavior, and the corresponding exponents can be systematically calculated as series in epsilon. The practical calculation is accomplished to order epsilon2 (two-loop approximation), including anisotropic sectors. As for the well-known Kraichnan rapid-change model, the anomalous scaling results from the existence in the model of composite fields (operators) with negative scaling dimensions, identified with the anomalous exponents. Thus the mechanism of the origin of anomalous scaling appears similar for the Gaussian model with zero correlation time and the non-Gaussian model with finite correlation time. It should be emphasized that, in contrast to Gaussian velocity ensembles with finite correlation time, the model and the perturbation theory discussed here are manifestly Galilean covariant. The relevance of these results for real passive advection and comparison with the Gaussian models and experiments are briefly discussed.

Soft sensor modeling based on variable partition ensemble method for nonlinear batch processes

NASA Astrophysics Data System (ADS)

Wang, Li; Chen, Xiangguang; Yang, Kai; Jin, Huaiping

2017-01-01

Batch processes are always characterized by nonlinear and system uncertain properties, therefore, the conventional single model may be ill-suited. A local learning strategy soft sensor based on variable partition ensemble method is developed for the quality prediction of nonlinear and non-Gaussian batch processes. A set of input variable sets are obtained by bootstrapping and PMI criterion. Then, multiple local GPR models are developed based on each local input variable set. When a new test data is coming, the posterior probability of each best performance local model is estimated based on Bayesian inference and used to combine these local GPR models to get the final prediction result. The proposed soft sensor is demonstrated by applying to an industrial fed-batch chlortetracycline fermentation process.

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.

Langevin equation with fluctuating diffusivity: A two-state model

NASA Astrophysics Data System (ADS)

Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji

2016-07-01

Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.

Curvaton scenario within the minimal supersymmetric standard model and predictions for non-Gaussianity.

PubMed

Mazumdar, Anupam; Nadathur, Seshadri

2012-03-16

We provide a model in which both the inflaton and the curvaton are obtained from within the minimal supersymmetric standard model, with known gauge and Yukawa interactions. Since now both the inflaton and curvaton fields are successfully embedded within the same sector, their decay products thermalize very quickly before the electroweak scale. This results in two important features of the model: first, there will be no residual isocurvature perturbations, and second, observable non-Gaussianities can be generated with the non-Gaussianity parameter f(NL)~O(5-1000) being determined solely by the combination of weak-scale physics and the standard model Yukawa interactions.

An adaptive Hinfinity controller design for bank-to-turn missiles using ridge Gaussian neural networks.

PubMed

Lin, Chuan-Kai; Wang, Sheng-De

2004-11-01

A new autopilot design for bank-to-turn (BTT) missiles is presented. In the design of autopilot, a ridge Gaussian neural network with local learning capability and fewer tuning parameters than Gaussian neural networks is proposed to model the controlled nonlinear systems. We prove that the proposed ridge Gaussian neural network, which can be a universal approximator, equals the expansions of rotated and scaled Gaussian functions. Although ridge Gaussian neural networks can approximate the nonlinear and complex systems accurately, the small approximation errors may affect the tracking performance significantly. Therefore, by employing the Hinfinity control theory, it is easy to attenuate the effects of the approximation errors of the ridge Gaussian neural networks to a prescribed level. Computer simulation results confirm the effectiveness of the proposed ridge Gaussian neural networks-based autopilot with Hinfinity stabilization.

Non-Gaussian lineshapes and dynamics of time-resolved linear and nonlinear (correlation) spectra.

PubMed

Dinpajooh, Mohammadhasan; Matyushov, Dmitry V

2014-07-17

Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.

Gaussian signal relaxation around spin echoes: Implications for precise reversible transverse relaxation quantification of pulmonary tissue at 1.5 and 3 Tesla.

PubMed

Zapp, Jascha; Domsch, Sebastian; Weingärtner, Sebastian; Schad, Lothar R

2017-05-01

To characterize the reversible transverse relaxation in pulmonary tissue and to study the benefit of a quadratic exponential (Gaussian) model over the commonly used linear exponential model for increased quantification precision. A point-resolved spectroscopy sequence was used for comprehensive sampling of the relaxation around spin echoes. Measurements were performed in an ex vivo tissue sample and in healthy volunteers at 1.5 Tesla (T) and 3 T. The goodness of fit using χred2 and the precision of the fitted relaxation time by means of its confidence interval were compared between the two relaxation models. The Gaussian model provides enhanced descriptions of pulmonary relaxation with lower χred2 by average factors of 4 ex vivo and 3 in volunteers. The Gaussian model indicates higher sensitivity to tissue structure alteration with increased precision of reversible transverse relaxation time measurements also by average factors of 4 ex vivo and 3 in volunteers. The mean relaxation times of the Gaussian model in volunteers are T2,G' = (1.97 ± 0.27) msec at 1.5 T and T2,G' = (0.83 ± 0.21) msec at 3 T. Pulmonary signal relaxation was found to be accurately modeled as Gaussian, providing a potential biomarker T2,G' with high sensitivity. Magn Reson Med 77:1938-1945, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Equivalent linearization for fatigue life estimates of a nonlinear structure

NASA Technical Reports Server (NTRS)

Miles, R. N.

1989-01-01

An analysis is presented of the suitability of the method of equivalent linearization for estimating the fatigue life of a nonlinear structure. Comparisons are made of the fatigue life of a nonlinear plate as predicted using conventional equivalent linearization and three other more accurate methods. The excitation of the plate is assumed to be Gaussian white noise and the plate response is modeled using a single resonant mode. The methods used for comparison consist of numerical simulation, a probabalistic formulation, and a modification of equivalent linearization which avoids the usual assumption that the response process is Gaussian. Remarkably close agreement is obtained between all four methods, even for cases where the response is significantly linear.

Analysis of low altitude atmospheric turbulence data measured in flight

NASA Technical Reports Server (NTRS)

Ganzer, V. M.; Joppa, R. G.; Vanderwees, G.

1977-01-01

All three components of turbulence were measured simultaneously in flight at each wing tip of a Beech D-18 aircraft. The flights were conducted at low altitude, 30.5 - 61.0 meters (100-200 ft.), over water in the presence of wind driven turbulence. Statistical properties of flight measured turbulence were compared with Gaussian and non-Gaussian turbulence models. Spatial characteristics of the turbulence were analyzed using the data from flight perpendicular and parallel to the wind. The probability density distributions of the vertical gusts show distinctly non-Gaussian characteristics. The distributions of the longitudinal and lateral gusts are generally Gaussian. The power spectra compare in the inertial subrange at some points better with the Dryden spectrum, while at other points the von Karman spectrum is a better approximation. In the low frequency range the data show peaks or dips in the power spectral density. The cross between vertical gusts in the direction of the mean wind were compared with a matched non-Gaussian model. The real component of the cross spectrum is in general close to the non-Gaussian model. The imaginary component, however, indicated a larger phase shift between these two gust components than was found in previous research.

Smoothing the Marmousi Model

NASA Astrophysics Data System (ADS)

Žáček, K.

Summary- The only way to make an excessively complex velocity model suitable for application of ray-based methods, such as the Gaussian beam or Gaussian packet methods, is to smooth it. We have smoothed the Marmousi model by choosing a coarser grid and by minimizing the second spatial derivatives of the slowness. This was done by minimizing the relevant Sobolev norm of slowness. We show that minimizing the relevant Sobolev norm of slowness is a suitable technique for preparing the optimum models for asymptotic ray theory methods. However, the price we pay for a model suitable for ray tracing is an increase of the difference between the smoothed and original model. Similarly, the estimated error in the travel time also increases due to the difference between the models. In smoothing the Marmousi model, we have found the estimated error of travel times at the verge of acceptability. Due to the low frequencies in the wavefield of the original Marmousi data set, we have found the Gaussian beams and Gaussian packets at the verge of applicability even in models sufficiently smoothed for ray tracing.

Topology in two dimensions. IV - CDM models with non-Gaussian initial conditions

NASA Astrophysics Data System (ADS)

Coles, Peter; Moscardini, Lauro; Plionis, Manolis; Lucchin, Francesco; Matarrese, Sabino; Messina, Antonio

1993-02-01

The results of N-body simulations with both Gaussian and non-Gaussian initial conditions are used here to generate projected galaxy catalogs with the same selection criteria as the Shane-Wirtanen counts of galaxies. The Euler-Poincare characteristic is used to compare the statistical nature of the projected galaxy clustering in these simulated data sets with that of the observed galaxy catalog. All the models produce a topology dominated by a meatball shift when normalized to the known small-scale clustering properties of galaxies. Models characterized by a positive skewness of the distribution of primordial density perturbations are inconsistent with the Lick data, suggesting problems in reconciling models based on cosmic textures with observations. Gaussian CDM models fit the distribution of cell counts only if they have a rather high normalization but possess too low a coherence length compared with the Lick counts. This suggests that a CDM model with extra large scale power would probably fit the available data.

Simplified model of statistically stationary spacecraft rotation and associated induced gravity environments

NASA Technical Reports Server (NTRS)

Fichtl, G. H.; Holland, R. L.

1978-01-01

A stochastic model of spacecraft motion was developed based on the assumption that the net torque vector due to crew activity and rocket thruster firings is a statistically stationary Gaussian vector process. The process had zero ensemble mean value, and the components of the torque vector were mutually stochastically independent. The linearized rigid-body equations of motion were used to derive the autospectral density functions of the components of the spacecraft rotation vector. The cross-spectral density functions of the components of the rotation vector vanish for all frequencies so that the components of rotation were mutually stochastically independent. The autospectral and cross-spectral density functions of the induced gravity environment imparted to scientific apparatus rigidly attached to the spacecraft were calculated from the rotation rate spectral density functions via linearized inertial frame to body-fixed principal axis frame transformation formulae. The induced gravity process was a Gaussian one with zero mean value. Transformation formulae were used to rotate the principal axis body-fixed frame to which the rotation rate and induced gravity vector were referred to a body-fixed frame in which the components of the induced gravity vector were stochastically independent. Rice's theory of exceedances was used to calculate expected exceedance rates of the components of the rotation and induced gravity vector processes.

Constructing a cosmological model-independent Hubble diagram of type Ia supernovae with cosmic chronometers

NASA Astrophysics Data System (ADS)

Li, Zhengxiang; Gonzalez, J. E.; Yu, Hongwei; Zhu, Zong-Hong; Alcaniz, J. S.

2016-02-01

We apply two methods, i.e., the Gaussian processes and the nonparametric smoothing procedure, to reconstruct the Hubble parameter H (z ) as a function of redshift from 15 measurements of the expansion rate obtained from age estimates of passively evolving galaxies. These reconstructions enable us to derive the luminosity distance to a certain redshift z , calibrate the light-curve fitting parameters accounting for the (unknown) intrinsic magnitude of type Ia supernova (SNe Ia), and construct cosmological model-independent Hubble diagrams of SNe Ia. In order to test the compatibility between the reconstructed functions of H (z ), we perform a statistical analysis considering the latest SNe Ia sample, the so-called joint light-curve compilation. We find that, for the Gaussian processes, the reconstructed functions of Hubble parameter versus redshift, and thus the following analysis on SNe Ia calibrations and cosmological implications, are sensitive to prior mean functions. However, for the nonparametric smoothing method, the reconstructed functions are not dependent on initial guess models, and consistently require high values of H0, which are in excellent agreement with recent measurements of this quantity from Cepheids and other local distance indicators.

Gaussian process regression for forecasting battery state of health

NASA Astrophysics Data System (ADS)

Richardson, Robert R.; Osborne, Michael A.; Howey, David A.

2017-07-01

Accurately predicting the future capacity and remaining useful life of batteries is necessary to ensure reliable system operation and to minimise maintenance costs. The complex nature of battery degradation has meant that mechanistic modelling of capacity fade has thus far remained intractable; however, with the advent of cloud-connected devices, data from cells in various applications is becoming increasingly available, and the feasibility of data-driven methods for battery prognostics is increasing. Here we propose Gaussian process (GP) regression for forecasting battery state of health, and highlight various advantages of GPs over other data-driven and mechanistic approaches. GPs are a type of Bayesian non-parametric method, and hence can model complex systems whilst handling uncertainty in a principled manner. Prior information can be exploited by GPs in a variety of ways: explicit mean functions can be used if the functional form of the underlying degradation model is available, and multiple-output GPs can effectively exploit correlations between data from different cells. We demonstrate the predictive capability of GPs for short-term and long-term (remaining useful life) forecasting on a selection of capacity vs. cycle datasets from lithium-ion cells.

Gyrator transform of generalized sine-Gaussian beams and conversion an edge-dislocation into a vortex

NASA Astrophysics Data System (ADS)

Zhu, Kaicheng; Tang, Huiqin; Tang, Ying; Xia, Hui

2014-12-01

We proposed a scheme that converts a sine-Gaussian beam with an edge dislocation into a dark hollow beam with a vortex. Based on the gyrator transform (GT) relation, the closed-form field distribution of generalized sine-Gaussian beams passing through a GT system is derived; the intensity distribution and the corresponding phase distribution associated with the transforming generalized sine-Gaussian beams are analyzed. According to the numerical method, the distributions are graphically demonstrated and found that, for appropriate beam parameters and the GT angle, dark hollow vortex beams with topological charge 1 can be achieved using sine-Gaussian beams carrying an edge dislocation. Moreover, the orbital angular momentum content of a GT sine-Gaussian beam is analyzed. It is proved that the GT retains the odd- or even-order spiral harmonics structures of generalized sine-Gaussian beams in the transform process. In particular, it is wholly possible to convert an edge dislocation embedded in sine-Gaussian beams into a vortex with GT. The study also reveals that to obtain a dark hollow beam making use of GT of cos-Gaussian beams is impossible.

Capacity of PPM on Gaussian and Webb Channels

NASA Technical Reports Server (NTRS)

Divsalar, D.; Dolinar, S.; Pollara, F.; Hamkins, J.

2000-01-01

This paper computes and compares the capacities of M-ary PPM on various idealized channels that approximate the optical communication channel: (1) the standard additive white Gaussian noise (AWGN) channel;(2) a more general AWGN channel (AWGN2) allowing different variances in signal and noise slots;(3) a Webb-distributed channel (Webb2);(4) a Webb+Gaussian channel, modeling Gaussian thermal noise added to Webb-distributed channel outputs.

Effective squeezing enhancement via measurement-induced non-Gaussian operation and its application to the dense coding scheme

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

Kitagawa, Akira; Takeoka, Masahiro; Sasaki, Masahide

2005-08-15

We study the measurement-induced non-Gaussian operation on the single- and two-mode Gaussian squeezed vacuum states with beam splitters and on-off type photon detectors, with which mixed non-Gaussian states are generally obtained in the conditional process. It is known that the entanglement can be enhanced via this non-Gaussian operation on the two-mode squeezed vacuum state. We show that, in the range of practical squeezing parameters, the conditional outputs are still close to Gaussian states, but their second order variances of quantum fluctuations and correlations are effectively suppressed and enhanced, respectively. To investigate an operational meaning of these states, especially entangled states,more » we also evaluate the quantum dense coding scheme from the viewpoint of the mutual information, and we show that non-Gaussian entangled state can be advantageous compared with the original two-mode squeezed state.« less

Simulation and analysis of scalable non-Gaussian statistically anisotropic random functions

NASA Astrophysics Data System (ADS)

Riva, Monica; Panzeri, Marco; Guadagnini, Alberto; Neuman, Shlomo P.

2015-12-01

Many earth and environmental (as well as other) variables, Y, and their spatial or temporal increments, ΔY, exhibit non-Gaussian statistical scaling. Previously we were able to capture some key aspects of such scaling by treating Y or ΔY as standard sub-Gaussian random functions. We were however unable to reconcile two seemingly contradictory observations, namely that whereas sample frequency distributions of Y (or its logarithm) exhibit relatively mild non-Gaussian peaks and tails, those of ΔY display peaks that grow sharper and tails that become heavier with decreasing separation distance or lag. Recently we overcame this difficulty by developing a new generalized sub-Gaussian model which captures both behaviors in a unified and consistent manner, exploring it on synthetically generated random functions in one dimension (Riva et al., 2015). Here we extend our generalized sub-Gaussian model to multiple dimensions, present an algorithm to generate corresponding random realizations of statistically isotropic or anisotropic sub-Gaussian functions and illustrate it in two dimensions. We demonstrate the accuracy of our algorithm by comparing ensemble statistics of Y and ΔY (such as, mean, variance, variogram and probability density function) with those of Monte Carlo generated realizations. We end by exploring the feasibility of estimating all relevant parameters of our model by analyzing jointly spatial moments of Y and ΔY obtained from a single realization of Y.

Receiver design for SPAD-based VLC systems under Poisson-Gaussian mixed noise model.

PubMed

Mao, Tianqi; Wang, Zhaocheng; Wang, Qi

2017-01-23

Single-photon avalanche diode (SPAD) is a promising photosensor because of its high sensitivity to optical signals in weak illuminance environment. Recently, it has drawn much attention from researchers in visible light communications (VLC). However, existing literature only deals with the simplified channel model, which only considers the effects of Poisson noise introduced by SPAD, but neglects other noise sources. Specifically, when an analog SPAD detector is applied, there exists Gaussian thermal noise generated by the transimpedance amplifier (TIA) and the digital-to-analog converter (D/A). Therefore, in this paper, we propose an SPAD-based VLC system with pulse-amplitude-modulation (PAM) under Poisson-Gaussian mixed noise model, where Gaussian-distributed thermal noise at the receiver is also investigated. The closed-form conditional likelihood of received signals is derived using the Laplace transform and the saddle-point approximation method, and the corresponding quasi-maximum-likelihood (quasi-ML) detector is proposed. Furthermore, the Poisson-Gaussian-distributed signals are converted to Gaussian variables with the aid of the generalized Anscombe transform (GAT), leading to an equivalent additive white Gaussian noise (AWGN) channel, and a hard-decision-based detector is invoked. Simulation results demonstrate that, the proposed GAT-based detector can reduce the computational complexity with marginal performance loss compared with the proposed quasi-ML detector, and both detectors are capable of accurately demodulating the SPAD-based PAM signals.

On the lorentzian versus Gaussian character of time-domain spin-echo signals from the brain as sampled by means of gradient-echoes: Implications for quantitative transverse relaxation studies.

PubMed

Mulkern, Robert V; Balasubramanian, Mukund; Mitsouras, Dimitrios

2014-07-30

To determine whether Lorentzian or Gaussian intra-voxel frequency distributions are better suited for modeling data acquired with gradient-echo sampling of single spin-echoes for the simultaneous characterization of irreversible and reversible relaxation rates. Clinical studies (e.g., of brain iron deposition) using such acquisition schemes have typically assumed Lorentzian distributions. Theoretical expressions of the time-domain spin-echo signal for intra-voxel Lorentzian and Gaussian distributions were used to fit data from a human brain scanned at both 1.5 Tesla (T) and 3T, resulting in maps of irreversible and reversible relaxation rates for each model. The relative merits of the Lorentzian versus Gaussian model were compared by means of quality of fit considerations. Lorentzian fits were equivalent to Gaussian fits primarily in regions of the brain where irreversible relaxation dominated. In the multiple brain regions where reversible relaxation effects become prominent, however, Gaussian fits were clearly superior. The widespread assumption that a Lorentzian distribution is suitable for quantitative transverse relaxation studies of the brain should be reconsidered, particularly at 3T and higher field strengths as reversible relaxation effects become more prominent. Gaussian distributions offer alternate fits of experimental data that should prove quite useful in general. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc. © 2014 Wiley Periodicals, Inc.

Hermite-Gaussian beams with self-forming spiral phase distribution

NASA Astrophysics Data System (ADS)

Zinchik, Alexander A.; Muzychenko, Yana B.

2014-05-01

Spiral laser beams is a family of laser beams that preserve the structural stability up to scale and rotate with the propagation. Properties of spiral beams are of practical interest for laser technology, medicine and biotechnology. Researchers use a spiral beams for movement and manipulation of microparticles. Spiral beams have a complicated phase distribution in cross section. This paper describes the results of analytical and computer simulation of Hermite-Gaussian beams with self-forming spiral phase distribution. In the simulation used a laser beam consisting of the sum of the two modes HG TEMnm and TEMn1m1. The coefficients n1, n, m1, m were varied. Additional phase depending from the coefficients n, m, m1, n1 imposed on the resulting beam. As a result, formed the Hermite Gaussian beam phase distribution which takes the form of a spiral in the process of distribution. For modeling was used VirtualLab 5.0 (manufacturer LightTrans GmbH).

Renyi entropy measures of heart rate Gaussianity.

PubMed

Lake, Douglas E

2006-01-01

Sample entropy and approximate entropy are measures that have been successfully utilized to study the deterministic dynamics of heart rate (HR). A complementary stochastic point of view and a heuristic argument using the Central Limit Theorem suggests that the Gaussianity of HR is a complementary measure of the physiological complexity of the underlying signal transduction processes. Renyi entropy (or q-entropy) is a widely used measure of Gaussianity in many applications. Particularly important members of this family are differential (or Shannon) entropy (q = 1) and quadratic entropy (q = 2). We introduce the concepts of differential and conditional Renyi entropy rate and, in conjunction with Burg's theorem, develop a measure of the Gaussianity of a linear random process. Robust algorithms for estimating these quantities are presented along with estimates of their standard errors.

MuLoG, or How to Apply Gaussian Denoisers to Multi-Channel SAR Speckle Reduction?

PubMed

Deledalle, Charles-Alban; Denis, Loic; Tabti, Sonia; Tupin, Florence

2017-09-01

Speckle reduction is a longstanding topic in synthetic aperture radar (SAR) imaging. Since most current and planned SAR imaging satellites operate in polarimetric, interferometric, or tomographic modes, SAR images are multi-channel and speckle reduction techniques must jointly process all channels to recover polarimetric and interferometric information. The distinctive nature of SAR signal (complex-valued, corrupted by multiplicative fluctuations) calls for the development of specialized methods for speckle reduction. Image denoising is a very active topic in image processing with a wide variety of approaches and many denoising algorithms available, almost always designed for additive Gaussian noise suppression. This paper proposes a general scheme, called MuLoG (MUlti-channel LOgarithm with Gaussian denoising), to include such Gaussian denoisers within a multi-channel SAR speckle reduction technique. A new family of speckle reduction algorithms can thus be obtained, benefiting from the ongoing progress in Gaussian denoising, and offering several speckle reduction results often displaying method-specific artifacts that can be dismissed by comparison between results.

Bayesian soft X-ray tomography using non-stationary Gaussian Processes

NASA Astrophysics Data System (ADS)

Li, Dong; Svensson, J.; Thomsen, H.; Medina, F.; Werner, A.; Wolf, R.

2013-08-01

In this study, a Bayesian based non-stationary Gaussian Process (GP) method for the inference of soft X-ray emissivity distribution along with its associated uncertainties has been developed. For the investigation of equilibrium condition and fast magnetohydrodynamic behaviors in nuclear fusion plasmas, it is of importance to infer, especially in the plasma center, spatially resolved soft X-ray profiles from a limited number of noisy line integral measurements. For this ill-posed inversion problem, Bayesian probability theory can provide a posterior probability distribution over all possible solutions under given model assumptions. Specifically, the use of a non-stationary GP to model the emission allows the model to adapt to the varying length scales of the underlying diffusion process. In contrast to other conventional methods, the prior regularization is realized in a probability form which enhances the capability of uncertainty analysis, in consequence, scientists who concern the reliability of their results will benefit from it. Under the assumption of normally distributed noise, the posterior distribution evaluated at a discrete number of points becomes a multivariate normal distribution whose mean and covariance are analytically available, making inversions and calculation of uncertainty fast. Additionally, the hyper-parameters embedded in the model assumption can be optimized through a Bayesian Occam's Razor formalism and thereby automatically adjust the model complexity. This method is shown to produce convincing reconstructions and good agreements with independently calculated results from the Maximum Entropy and Equilibrium-Based Iterative Tomography Algorithm methods.

Bayesian soft X-ray tomography using non-stationary Gaussian Processes.

PubMed

Li, Dong; Svensson, J; Thomsen, H; Medina, F; Werner, A; Wolf, R

2013-08-01

In this study, a Bayesian based non-stationary Gaussian Process (GP) method for the inference of soft X-ray emissivity distribution along with its associated uncertainties has been developed. For the investigation of equilibrium condition and fast magnetohydrodynamic behaviors in nuclear fusion plasmas, it is of importance to infer, especially in the plasma center, spatially resolved soft X-ray profiles from a limited number of noisy line integral measurements. For this ill-posed inversion problem, Bayesian probability theory can provide a posterior probability distribution over all possible solutions under given model assumptions. Specifically, the use of a non-stationary GP to model the emission allows the model to adapt to the varying length scales of the underlying diffusion process. In contrast to other conventional methods, the prior regularization is realized in a probability form which enhances the capability of uncertainty analysis, in consequence, scientists who concern the reliability of their results will benefit from it. Under the assumption of normally distributed noise, the posterior distribution evaluated at a discrete number of points becomes a multivariate normal distribution whose mean and covariance are analytically available, making inversions and calculation of uncertainty fast. Additionally, the hyper-parameters embedded in the model assumption can be optimized through a Bayesian Occam's Razor formalism and thereby automatically adjust the model complexity. This method is shown to produce convincing reconstructions and good agreements with independently calculated results from the Maximum Entropy and Equilibrium-Based Iterative Tomography Algorithm methods.

Interactive Gaussian Graphical Models for Discovering Depth Trends in ChemCam Data

NASA Astrophysics Data System (ADS)

Oyen, D. A.; Komurlu, C.; Lanza, N. L.

2018-04-01

Interactive Gaussian graphical models discover surface compositional features on rocks in ChemCam targets. Our approach visualizes shot-to-shot relationships among LIBS observations, and identifies the wavelengths involved in the trend.

Gaussian process surrogates for failure detection: A Bayesian experimental design approach

NASA Astrophysics Data System (ADS)

Wang, Hongqiao; Lin, Guang; Li, Jinglai

2016-05-01

An important task of uncertainty quantification is to identify the probability of undesired events, in particular, system failures, caused by various sources of uncertainties. In this work we consider the construction of Gaussian process surrogates for failure detection and failure probability estimation. In particular, we consider the situation that the underlying computer models are extremely expensive, and in this setting, determining the sampling points in the state space is of essential importance. We formulate the problem as an optimal experimental design for Bayesian inferences of the limit state (i.e., the failure boundary) and propose an efficient numerical scheme to solve the resulting optimization problem. In particular, the proposed limit-state inference method is capable of determining multiple sampling points at a time, and thus it is well suited for problems where multiple computer simulations can be performed in parallel. The accuracy and performance of the proposed method is demonstrated by both academic and practical examples.

Reconstructing the interaction between dark energy and dark matter using Gaussian processes

NASA Astrophysics Data System (ADS)

Yang, Tao; Guo, Zong-Kuan; Cai, Rong-Gen

2015-06-01

We present a nonparametric approach to reconstruct the interaction between dark energy and dark matter directly from SNIa Union 2.1 data using Gaussian processes, which is a fully Bayesian approach for smoothing data. In this method, once the equation of state (w ) of dark energy is specified, the interaction can be reconstructed as a function of redshift. For the decaying vacuum energy case with w =-1 , the reconstructed interaction is consistent with the standard Λ CDM model, namely, there is no evidence for the interaction. This also holds for the constant w cases from -0.9 to -1.1 and for the Chevallier-Polarski-Linder (CPL) parametrization case. If the equation of state deviates obviously from -1 , the reconstructed interaction exists at 95% confidence level. This shows the degeneracy between the interaction and the equation of state of dark energy when they get constraints from the observational data.

The impact of compression of speech signal, background noise and acoustic disturbances on the effectiveness of speaker identification

NASA Astrophysics Data System (ADS)

Kamiński, K.; Dobrowolski, A. P.

2017-04-01

The paper presents the architecture and the results of optimization of selected elements of the Automatic Speaker Recognition (ASR) system that uses Gaussian Mixture Models (GMM) in the classification process. Optimization was performed on the process of selection of individual characteristics using the genetic algorithm and the parameters of Gaussian distributions used to describe individual voices. The system that was developed was tested in order to evaluate the impact of different compression methods used, among others, in landline, mobile, and VoIP telephony systems, on effectiveness of the speaker identification. Also, the results were presented of effectiveness of speaker identification at specific levels of noise with the speech signal and occurrence of other disturbances that could appear during phone calls, which made it possible to specify the spectrum of applications of the presented ASR system.

Construction of reactive potential energy surfaces with Gaussian process regression: active data selection

NASA Astrophysics Data System (ADS)

Guan, Yafu; Yang, Shuo; Zhang, Dong H.

2018-04-01

Gaussian process regression (GPR) is an efficient non-parametric method for constructing multi-dimensional potential energy surfaces (PESs) for polyatomic molecules. Since not only the posterior mean but also the posterior variance can be easily calculated, GPR provides a well-established model for active learning, through which PESs can be constructed more efficiently and accurately. We propose a strategy of active data selection for the construction of PESs with emphasis on low energy regions. Through three-dimensional (3D) example of H3, the validity of this strategy is verified. The PESs for two prototypically reactive systems, namely, H + H2O ↔ H2 + OH reaction and H + CH4 ↔ H2 + CH3 reaction are reconstructed. Only 920 and 4000 points are assembled to reconstruct these two PESs respectively. The accuracy of the GP PESs is not only tested by energy errors but also validated by quantum scattering calculations.

The Common Patterns of Nature

PubMed Central

Frank, Steven A.

2010-01-01

We typically observe large-scale outcomes that arise from the interactions of many hidden, small-scale processes. Examples include age of disease onset, rates of amino acid substitutions, and composition of ecological communities. The macroscopic patterns in each problem often vary around a characteristic shape that can be generated by neutral processes. A neutral generative model assumes that each microscopic process follows unbiased or random stochastic fluctuations: random connections of network nodes; amino acid substitutions with no effect on fitness; species that arise or disappear from communities randomly. These neutral generative models often match common patterns of nature. In this paper, I present the theoretical background by which we can understand why these neutral generative models are so successful. I show where the classic patterns come from, such as the Poisson pattern, the normal or Gaussian pattern, and many others. Each classic pattern was often discovered by a simple neutral generative model. The neutral patterns share a special characteristic: they describe the patterns of nature that follow from simple constraints on information. For example, any aggregation of processes that preserves information only about the mean and variance attracts to the Gaussian pattern; any aggregation that preserves information only about the mean attracts to the exponential pattern; any aggregation that preserves information only about the geometric mean attracts to the power law pattern. I present a simple and consistent informational framework of the common patterns of nature based on the method of maximum entropy. This framework shows that each neutral generative model is a special case that helps to discover a particular set of informational constraints; those informational constraints define a much wider domain of non-neutral generative processes that attract to the same neutral pattern. PMID:19538344

Vegetation Monitoring with Gaussian Processes and Latent Force Models

NASA Astrophysics Data System (ADS)

Camps-Valls, Gustau; Svendsen, Daniel; Martino, Luca; Campos, Manuel; Luengo, David

2017-04-01

Monitoring vegetation by biophysical parameter retrieval from Earth observation data is a challenging problem, where machine learning is currently a key player. Neural networks, kernel methods, and Gaussian Process (GP) regression have excelled in parameter retrieval tasks at both local and global scales. GP regression is based on solid Bayesian statistics, yield efficient and accurate parameter estimates, and provides interesting advantages over competing machine learning approaches such as confidence intervals. However, GP models are hampered by lack of interpretability, that prevented the widespread adoption by a larger community. In this presentation we will summarize some of our latest developments to address this issue. We will review the main characteristics of GPs and their advantages in vegetation monitoring standard applications. Then, three advanced GP models will be introduced. First, we will derive sensitivity maps for the GP predictive function that allows us to obtain feature ranking from the model and to assess the influence of examples in the solution. Second, we will introduce a Joint GP (JGP) model that combines in situ measurements and simulated radiative transfer data in a single GP model. The JGP regression provides more sensible confidence intervals for the predictions, respects the physics of the underlying processes, and allows for transferability across time and space. Finally, a latent force model (LFM) for GP modeling that encodes ordinary differential equations to blend data-driven modeling and physical models of the system is presented. The LFM performs multi-output regression, adapts to the signal characteristics, is able to cope with missing data in the time series, and provides explicit latent functions that allow system analysis and evaluation. Empirical evidence of the performance of these models will be presented through illustrative examples.

Gaussian processes-based predictive models to estimate reference ET from alternative meteorological data sources for irrigation scheduling

USDA-ARS?s Scientific Manuscript database

Accurate estimates of daily crop evapotranspiration (ET) are needed for efficient irrigation management, especially in arid and semi-arid irrigated regions where crop water demand exceeds rainfall. The impact of inaccurate ET estimates can be tremendous in both irrigation cost and the increased dema...

Proactive Control Processes in Event-Based Prospective Memory: Evidence from Intraindividual Variability and Ex-Gaussian Analyses

ERIC Educational Resources Information Center

Ball, B. Hunter; Brewer, Gene A.

2018-01-01

The present study implemented an individual differences approach in conjunction with response time (RT) variability and distribution modeling techniques to better characterize the cognitive control dynamics underlying ongoing task cost (i.e., slowing) and cue detection in event-based prospective memory (PM). Three experiments assessed the relation…

Gaussian Process modelling of blood glucose response to free-living physical activity data in people with type 1 diabetes.

PubMed

Valletta, John Joseph; Chipperfield, Andrew J; Byrne, Christopher D

2009-01-01

Good blood glucose control is important to people with type 1 diabetes to prevent diabetes-related complications. Too much blood glucose (hyperglycaemia) causes long-term micro-vascular complications, while a severe drop in blood glucose (hypoglycaemia) can cause life-threatening coma. Finding the right balance between quantity and type of food intake, physical activity levels and insulin dosage, is a daily challenge. Increased physical activity levels often cause changes in blood glucose due to increased glucose uptake into tissues such as muscle. To date we have limited knowledge about the minute by minute effects of exercise on blood glucose levels, in part due to the difficulty in measuring glucose and physical activity levels continuously, in a free-living environment. By using a light and user-friendly armband we can record physical activity energy expenditure on a minute-by-minute basis. Simultaneously, by using a continuous glucose monitoring system we can record glucose concentrations. In this paper, Gaussian Processes are used to model the glucose excursions in response to physical activity data, to study its effect on glycaemic control.

Characterization of Adrenal Adenoma by Gaussian Model-Based Algorithm.

PubMed

Hsu, Larson D; Wang, Carolyn L; Clark, Toshimasa J

2016-01-01

We confirmed that computed tomography (CT) attenuation values of pixels in an adrenal nodule approximate a Gaussian distribution. Building on this and the previously described histogram analysis method, we created an algorithm that uses mean and standard deviation to estimate the percentage of negative attenuation pixels in an adrenal nodule, thereby allowing differentiation of adenomas and nonadenomas. The institutional review board approved both components of this study in which we developed and then validated our criteria. In the first, we retrospectively assessed CT attenuation values of adrenal nodules for normality using a 2-sample Kolmogorov-Smirnov test. In the second, we evaluated a separate cohort of patients with adrenal nodules using both the conventional 10HU unit mean attenuation method and our Gaussian model-based algorithm. We compared the sensitivities of the 2 methods using McNemar's test. A total of 183 of 185 observations (98.9%) demonstrated a Gaussian distribution in adrenal nodule pixel attenuation values. The sensitivity and specificity of our Gaussian model-based algorithm for identifying adrenal adenoma were 86.1% and 83.3%, respectively. The sensitivity and specificity of the mean attenuation method were 53.2% and 94.4%, respectively. The sensitivities of the 2 methods were significantly different (P value < 0.001). In conclusion, the CT attenuation values within an adrenal nodule follow a Gaussian distribution. Our Gaussian model-based algorithm can characterize adrenal adenomas with higher sensitivity than the conventional mean attenuation method. The use of our algorithm, which does not require additional postprocessing, may increase workflow efficiency and reduce unnecessary workup of benign nodules. Copyright © 2016 Elsevier Inc. All rights reserved.

Assimilating every-30-second 100-m-mesh radar observations for convective weather: implications to non-Gaussian PDF

NASA Astrophysics Data System (ADS)

Miyoshi, T.; Teramura, T.; Ruiz, J.; Kondo, K.; Lien, G. Y.

2016-12-01

Convective weather is known to be highly nonlinear and chaotic, and it is hard to predict their location and timing precisely. Our Big Data Assimilation (BDA) effort has been exploring to use dense and frequent observations to avoid non-Gaussian probability density function (PDF) and to apply an ensemble Kalman filter under the Gaussian error assumption. The phased array weather radar (PAWR) can observe a dense three-dimensional volume scan with 100-m range resolution and 100 elevation angles in only 30 seconds. The BDA system assimilates the PAWR reflectivity and Doppler velocity observations every 30 seconds into 100 ensemble members of storm-scale numerical weather prediction (NWP) model at 100-m grid spacing. The 30-second-update, 100-m-mesh BDA system has been quite successful in multiple case studies of local severe rainfall events. However, with 1000 ensemble members, the reduced-resolution BDA system at 1-km grid spacing showed significant non-Gaussian PDF with every-30-second updates. With a 10240-member ensemble Kalman filter with a global NWP model at 112-km grid spacing, we found roughly 1000 members satisfactory to capture the non-Gaussian error structures. With these in mind, we explore how the density of observations in space and time affects the non-Gaussianity in an ensemble Kalman filter with a simple toy model. In this presentation, we will present the most up-to-date results of the BDA research, as well as the investigation with the toy model on the non-Gaussianity with dense and frequent observations.

Experimental study of the focusing properties of a Gaussian Schell-model vortex beam

NASA Astrophysics Data System (ADS)

Wang, Fei; Zhu, Shijun; Cai, Yangjian

2011-08-01

We carry out an experimental and theoretical study of the focusing properties of a Gaussian Schell-model (GSM) vortex beam. It is found that we can shape the beam profile of the focused GSM vortex beam by varying its initial spatial coherence width. Focused dark hollow, flat-topped, and Gaussian beam spots can be obtained in our experiment, which will be useful for trapping particles. The experimental results agree well with the theoretical results.

Multimodality Prediction of Chaotic Time Series with Sparse Hard-Cut EM Learning of the Gaussian Process Mixture Model

NASA Astrophysics Data System (ADS)

Zhou, Ya-Tong; Fan, Yu; Chen, Zi-Yi; Sun, Jian-Cheng

2017-05-01

The contribution of this work is twofold: (1) a multimodality prediction method of chaotic time series with the Gaussian process mixture (GPM) model is proposed, which employs a divide and conquer strategy. It automatically divides the chaotic time series into multiple modalities with different extrinsic patterns and intrinsic characteristics, and thus can more precisely fit the chaotic time series. (2) An effective sparse hard-cut expectation maximization (SHC-EM) learning algorithm for the GPM model is proposed to improve the prediction performance. SHC-EM replaces a large learning sample set with fewer pseudo inputs, accelerating model learning based on these pseudo inputs. Experiments on Lorenz and Chua time series demonstrate that the proposed method yields not only accurate multimodality prediction, but also the prediction confidence interval. SHC-EM outperforms the traditional variational learning in terms of both prediction accuracy and speed. In addition, SHC-EM is more robust and insusceptible to noise than variational learning. Supported by the National Natural Science Foundation of China under Grant No 60972106, the China Postdoctoral Science Foundation under Grant No 2014M561053, the Humanity and Social Science Foundation of Ministry of Education of China under Grant No 15YJA630108, and the Hebei Province Natural Science Foundation under Grant No E2016202341.

Probabilistic Space Weather Forecasting: a Bayesian Perspective

NASA Astrophysics Data System (ADS)

Camporeale, E.; Chandorkar, M.; Borovsky, J.; Care', A.

2017-12-01

Most of the Space Weather forecasts, both at operational and research level, are not probabilistic in nature. Unfortunately, a prediction that does not provide a confidence level is not very useful in a decision-making scenario. Nowadays, forecast models range from purely data-driven, machine learning algorithms, to physics-based approximation of first-principle equations (and everything that sits in between). Uncertainties pervade all such models, at every level: from the raw data to finite-precision implementation of numerical methods. The most rigorous way of quantifying the propagation of uncertainties is by embracing a Bayesian probabilistic approach. One of the simplest and most robust machine learning technique in the Bayesian framework is Gaussian Process regression and classification. Here, we present the application of Gaussian Processes to the problems of the DST geomagnetic index forecast, the solar wind type classification, and the estimation of diffusion parameters in radiation belt modeling. In each of these very diverse problems, the GP approach rigorously provide forecasts in the form of predictive distributions. In turn, these distributions can be used as input for ensemble simulations in order to quantify the amplification of uncertainties. We show that we have achieved excellent results in all of the standard metrics to evaluate our models, with very modest computational cost.

Brownian motion with adaptive drift for remaining useful life prediction: Revisited

NASA Astrophysics Data System (ADS)

Wang, Dong; Tsui, Kwok-Leung

2018-01-01

Linear Brownian motion with constant drift is widely used in remaining useful life predictions because its first hitting time follows the inverse Gaussian distribution. State space modelling of linear Brownian motion was proposed to make the drift coefficient adaptive and incorporate on-line measurements into the first hitting time distribution. Here, the drift coefficient followed the Gaussian distribution, and it was iteratively estimated by using Kalman filtering once a new measurement was available. Then, to model nonlinear degradation, linear Brownian motion with adaptive drift was extended to nonlinear Brownian motion with adaptive drift. However, in previous studies, an underlying assumption used in the state space modelling was that in the update phase of Kalman filtering, the predicted drift coefficient at the current time exactly equalled the posterior drift coefficient estimated at the previous time, which caused a contradiction with the predicted drift coefficient evolution driven by an additive Gaussian process noise. In this paper, to alleviate such an underlying assumption, a new state space model is constructed. As a result, in the update phase of Kalman filtering, the predicted drift coefficient at the current time evolves from the posterior drift coefficient at the previous time. Moreover, the optimal Kalman filtering gain for iteratively estimating the posterior drift coefficient at any time is mathematically derived. A discussion that theoretically explains the main reasons why the constructed state space model can result in high remaining useful life prediction accuracies is provided. Finally, the proposed state space model and its associated Kalman filtering gain are applied to battery prognostics.

INPUFF: A SINGLE SOURCE GAUSSIAN PUFF DISPERSION ALGORITHM. USER'S GUIDE

EPA Science Inventory

INPUFF is a Gaussian INtegrated PUFF model. The Gaussian puff diffusion equation is used to compute the contribution to the concentration at each receptor from each puff every time step. Computations in INPUFF can be made for a single point source at up to 25 receptor locations. ...

Stress-induced electric current fluctuations in rocks: a superstatistical model

NASA Astrophysics Data System (ADS)

Cartwright-Taylor, Alexis; Vallianatos, Filippos; Sammonds, Peter

2017-04-01

We recorded spontaneous electric current flow in non-piezoelectric Carrara marble samples during triaxial deformation. Mechanical data, ultrasonic velocities and acoustic emissions were acquired simultaneously with electric current to constrain the relationship between electric current flow, differential stress and damage. Under strain-controlled loading, spontaneous electric current signals (nA) were generated and sustained under all conditions tested. In dry samples, a detectable electric current arises only during dilatancy and the overall signal is correlated with the damage induced by microcracking. Our results show that fracture plays a key role in the generation of electric currents in deforming rocks (Cartwright-Taylor et al., in prep). We also analysed the high-frequency fluctuations of these electric current signals and found that they are not normally distributed - they exhibit power-law tails (Cartwright-Taylor et al., 2014). We modelled these distributions with q-Gaussian statistics, derived by maximising the Tsallis entropy. This definition of entropy is particularly applicable to systems which are strongly correlated and far from equilibrium. Good agreement, at all experimental conditions, between the distributions of electric current fluctuations and the q-Gaussian function with q-values far from one, illustrates the highly correlated, fractal nature of the electric source network within the samples and provides further evidence that the source of the electric signals is the developing fractal network of cracks. It has been shown (Beck, 2001) that q-Gaussian distributions can arise from the superposition of local relaxations in the presence of a slowly varying driving force, thus providing a dynamic reason for the appearance of Tsallis statistics in systems with a fluctuating energy dissipation rate. So, the probability distribution for a dynamic variable, u under some external slow forcing, β, can be obtained as a superposition of temporary local equilibrium processes whose variance fluctuates over time. The appearance of q-Gaussian statistics are caused by the fluctuating β parameter, which effectively models the fluctuating energy dissipation rate in the system. This concept is known as superstatistics and is physically relevant for modelling driven non-equilibrium systems where the environmental conditions fluctuate on a large scale. The idea is that the environmental variable, such as temperature or pressure, changes so slowly that a rapidly fluctuating variable within that environment has time to relax back to equilibrium between each change in the environment. The application of superstatistical techniques to our experimental electric current fluctuations show that they can indeed be described, to good approximation, by the superposition of local Gaussian processes with fluctuating variance. We conclude, then, that the measured electric current fluctuates in response to intermittent energy dissipation and is driven to varying temporary local equilibria during deformation by the variations in stress intensity. The advantage of this technique is that, once the model has been established to be a good description of the system in question, the average β parameter (a measure of the average energy dissipation rate) for the system can be obtained simply from the macroscopic q-Gaussian distribution parameters.

Improved Discrete Approximation of Laplacian of Gaussian

NASA Technical Reports Server (NTRS)

Shuler, Robert L., Jr.

2004-01-01

An improved method of computing a discrete approximation of the Laplacian of a Gaussian convolution of an image has been devised. The primary advantage of the method is that without substantially degrading the accuracy of the end result, it reduces the amount of information that must be processed and thus reduces the amount of circuitry needed to perform the Laplacian-of- Gaussian (LOG) operation. Some background information is necessary to place the method in context. The method is intended for application to the LOG part of a process of real-time digital filtering of digitized video data that represent brightnesses in pixels in a square array. The particular filtering process of interest is one that converts pixel brightnesses to binary form, thereby reducing the amount of information that must be performed in subsequent correlation processing (e.g., correlations between images in a stereoscopic pair for determining distances or correlations between successive frames of the same image for detecting motions). The Laplacian is often included in the filtering process because it emphasizes edges and textures, while the Gaussian is often included because it smooths out noise that might not be consistent between left and right images or between successive frames of the same image.

Unfolding of Proteins: Thermal and Mechanical Unfolding

NASA Technical Reports Server (NTRS)

Hur, Joe S.; Darve, Eric

2004-01-01

We have employed a Hamiltonian model based on a self-consistent Gaussian appoximation to examine the unfolding process of proteins in external - both mechanical and thermal - force elds. The motivation was to investigate the unfolding pathways of proteins by including only the essence of the important interactions of the native-state topology. Furthermore, if such a model can indeed correctly predict the physics of protein unfolding, it can complement more computationally expensive simulations and theoretical work. The self-consistent Gaussian approximation by Micheletti et al. has been incorporated in our model to make the model mathematically tractable by signi cantly reducing the computational cost. All thermodynamic properties and pair contact probabilities are calculated by simply evaluating the values of a series of Incomplete Gamma functions in an iterative manner. We have compared our results to previous molecular dynamics simulation and experimental data for the mechanical unfolding of the giant muscle protein Titin (1TIT). Our model, especially in light of its simplicity and excellent agreement with experiment and simulation, demonstrates the basic physical elements necessary to capture the mechanism of protein unfolding in an external force field.

Investigating task inhibition in children versus adults: A diffusion model analysis.

PubMed

Schuch, Stefanie; Konrad, Kerstin

2017-04-01

One can take n-2 task repetition costs as a measure of inhibition on the level of task sets. When switching back to a Task A after only one intermediate trial (ABA task sequence), Task A is thought to still be inhibited, leading to performance costs relative to task sequences where switching back to Task A is preceded by at least two intermediary trials (CBA). The current study investigated differences in inhibitory ability between children and adults by comparing n-2 task repetition costs in children (9-11years of age, N=32) and young adults (21-30years of age, N=32). The mean reaction times and error rate differences between ABA and CBA sequences did not differ between the two age groups. However, diffusion model analysis revealed that different cognitive processes contribute to the inhibition effect in the two age groups: The adults, but not the children, showed a smaller drift rate in ABA than in CBA, suggesting that persisting task inhibition is associated with slower response selection in adults. In children, non-decision time was longer in ABA than in CBA, possibly reflecting longer task preparation in ABA than in CBA. In addition, Ex-Gaussian functions were fitted to the distributions of correct reaction times. In adults, the ABA-CBA difference was reflected in the exponential parameter of the distribution; in children, the ABA-CBA difference was found in the Gaussian mu parameter. Hence, Ex-Gaussian analysis, although noisier, was generally in line with diffusion model analysis. Taken together, the data suggest that the task inhibition effect found in mean performance is mediated by different cognitive processes in children versus adults. Copyright © 2016 Elsevier Inc. All rights reserved.

A feedback control strategy for the airfoil system under non-Gaussian colored noise excitation.

PubMed

Huang, Yong; Tao, Gang

2014-09-01

The stability of a binary airfoil with feedback control under stochastic disturbances, a non-Gaussian colored noise, is studied in this paper. First, based on some approximated theories and methods the non-Gaussian colored noise is simplified to an Ornstein-Uhlenbeck process. Furthermore, via the stochastic averaging method and the logarithmic polar transformation, one dimensional diffusion process can be obtained. At last by applying the boundary conditions, the largest Lyapunov exponent which can determine the almost-sure stability of the system and the effective region of control parameters is calculated.

A feedback control strategy for the airfoil system under non-Gaussian colored noise excitation

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

Huang, Yong, E-mail: hy@njust.edu.cn, E-mail: taogang@njust.edu.cn; Tao, Gang, E-mail: hy@njust.edu.cn, E-mail: taogang@njust.edu.cn

2014-09-01

The stability of a binary airfoil with feedback control under stochastic disturbances, a non-Gaussian colored noise, is studied in this paper. First, based on some approximated theories and methods the non-Gaussian colored noise is simplified to an Ornstein-Uhlenbeck process. Furthermore, via the stochastic averaging method and the logarithmic polar transformation, one dimensional diffusion process can be obtained. At last by applying the boundary conditions, the largest Lyapunov exponent which can determine the almost-sure stability of the system and the effective region of control parameters is calculated.

Sparse covariance estimation in heterogeneous samples*

PubMed Central

Rodríguez, Abel; Lenkoski, Alex; Dobra, Adrian

2015-01-01

Standard Gaussian graphical models implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected from heterogeneous populations where such an assumption is not satisfied, leading in turn to nonlinear relationships among variables. To address such situations we explore mixtures of Gaussian graphical models; in particular, we consider both infinite mixtures and infinite hidden Markov models where the emission distributions correspond to Gaussian graphical models. Such models allow us to divide a heterogeneous population into homogenous groups, with each cluster having its own conditional independence structure. As an illustration, we study the trends in foreign exchange rate fluctuations in the pre-Euro era. PMID:26925189

Local spectrum analysis of field propagation in an anisotropic medium. Part I. Time-harmonic fields.

PubMed

Tinkelman, Igor; Melamed, Timor

2005-06-01

The phase-space beam summation is a general analytical framework for local analysis and modeling of radiation from extended source distributions. In this formulation, the field is expressed as a superposition of beam propagators that emanate from all points in the source domain and in all directions. In this Part I of a two-part investigation, the theory is extended to include propagation in anisotropic medium characterized by a generic wave-number profile for time-harmonic fields; in a companion paper [J. Opt. Soc. Am. A 22, 1208 (2005)], the theory is extended to time-dependent fields. The propagation characteristics of the beam propagators in a homogeneous anisotropic medium are considered. With use of Gaussian windows for the local processing of either ordinary or extraordinary electromagnetic field distributions, the field is represented by a phase-space spectral distribution in which the propagating elements are Gaussian beams that are formulated by using Gaussian plane-wave spectral distributions over the extended source plane. By applying saddle-point asymptotics, we extract the Gaussian beam phenomenology in the anisotropic environment. The resulting field is parameterized in terms of the spatial evolution of the beam curvature, beam width, etc., which are mapped to local geometrical properties of the generic wave-number profile. The general results are applied to the special case of uniaxial crystal, and it is found that the asymptotics for the Gaussian beam propagators, as well as the physical phenomenology attached, perform remarkably well.

SU-F-T-158: Experimental Characterization of Field Size Dependence of Dose and Lateral Beam Profiles of Scanning Proton and Carbon Ion Beams for Empirical Model in Air

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

Li, Y; Hsi, W; Zhao, J

2016-06-15

Purpose: The Gaussian model for the lateral profiles in air is crucial for an accurate treatment planning system. The field size dependence of dose and the lateral beam profiles of scanning proton and carbon ion beams are due mainly to particles undergoing multiple Coulomb scattering in the beam line components and secondary particles produced by nuclear interactions in the target, both of which depend upon the energy and species of the beam. In this work, lateral profile shape parameters were fitted to measurements of field size dependence dose at the center of field size in air. Methods: Previous studies havemore » employed empirical fits to measured profile data to significantly reduce the QA time required for measurements. From this approach to derive the weight and sigma of lateral profiles in air, empirical model formulations were simulated for three selected energies for both proton and carbon beams. Results: The 20%–80% lateral penumbras predicted by the double model for proton and single model for carbon with the error functions agreed with the measurements within 1 mm. The standard deviation between measured and fitted field size dependence of dose for empirical model in air has a maximum accuracy of 0.74% for proton with double Gaussian, and of 0.57% for carbon with single Gaussian. Conclusion: We have demonstrated that the double Gaussian model of lateral beam profiles is significantly better than the single Gaussian model for proton while a single Gaussian model is sufficient for carbon. The empirical equation may be used to double check the separately obtained model that is currently used by the planning system. The empirical model in air for dose of spot scanning proton and carbon ion beams cannot be directly used for irregular shaped patient fields, but can be to provide reference values for clinical use and quality assurance.« less

Fractional Gaussian noise-enhanced information capacity of a nonlinear neuron model with binary signal input

NASA Astrophysics Data System (ADS)

Gao, Feng-Yin; Kang, Yan-Mei; Chen, Xi; Chen, Guanrong

2018-05-01

This paper reveals the effect of fractional Gaussian noise with Hurst exponent H ∈(1 /2 ,1 ) on the information capacity of a general nonlinear neuron model with binary signal input. The fGn and its corresponding fractional Brownian motion exhibit long-range, strong-dependent increments. It extends standard Brownian motion to many types of fractional processes found in nature, such as the synaptic noise. In the paper, for the subthreshold binary signal, sufficient conditions are given based on the "forbidden interval" theorem to guarantee the occurrence of stochastic resonance, while for the suprathreshold binary signal, the simulated results show that additive fGn with Hurst exponent H ∈(1 /2 ,1 ) could increase the mutual information or bits count. The investigation indicated that the synaptic noise with the characters of long-range dependence and self-similarity might be the driving factor for the efficient encoding and decoding of the nervous system.

Connectivity ranking of heterogeneous random conductivity models

NASA Astrophysics Data System (ADS)

Rizzo, C. B.; de Barros, F.

2017-12-01

To overcome the challenges associated with hydrogeological data scarcity, the hydraulic conductivity (K) field is often represented by a spatial random process. The state-of-the-art provides several methods to generate 2D or 3D random K-fields, such as the classic multi-Gaussian fields or non-Gaussian fields, training image-based fields and object-based fields. We provide a systematic comparison of these models based on their connectivity. We use the minimum hydraulic resistance as a connectivity measure, which it has been found to be strictly correlated with early time arrival of dissolved contaminants. A computationally efficient graph-based algorithm is employed, allowing a stochastic treatment of the minimum hydraulic resistance through a Monte-Carlo approach and therefore enabling the computation of its uncertainty. The results show the impact of geostatistical parameters on the connectivity for each group of random fields, being able to rank the fields according to their minimum hydraulic resistance.

Combining MLC and SVM Classifiers for Learning Based Decision Making: Analysis and Evaluations

PubMed Central

Zhang, Yi; Ren, Jinchang; Jiang, Jianmin

2015-01-01

Maximum likelihood classifier (MLC) and support vector machines (SVM) are two commonly used approaches in machine learning. MLC is based on Bayesian theory in estimating parameters of a probabilistic model, whilst SVM is an optimization based nonparametric method in this context. Recently, it is found that SVM in some cases is equivalent to MLC in probabilistically modeling the learning process. In this paper, MLC and SVM are combined in learning and classification, which helps to yield probabilistic output for SVM and facilitate soft decision making. In total four groups of data are used for evaluations, covering sonar, vehicle, breast cancer, and DNA sequences. The data samples are characterized in terms of Gaussian/non-Gaussian distributed and balanced/unbalanced samples which are then further used for performance assessment in comparing the SVM and the combined SVM-MLC classifier. Interesting results are reported to indicate how the combined classifier may work under various conditions. PMID:26089862

Combining MLC and SVM Classifiers for Learning Based Decision Making: Analysis and Evaluations.

PubMed

Zhang, Yi; Ren, Jinchang; Jiang, Jianmin

2015-01-01

Maximum likelihood classifier (MLC) and support vector machines (SVM) are two commonly used approaches in machine learning. MLC is based on Bayesian theory in estimating parameters of a probabilistic model, whilst SVM is an optimization based nonparametric method in this context. Recently, it is found that SVM in some cases is equivalent to MLC in probabilistically modeling the learning process. In this paper, MLC and SVM are combined in learning and classification, which helps to yield probabilistic output for SVM and facilitate soft decision making. In total four groups of data are used for evaluations, covering sonar, vehicle, breast cancer, and DNA sequences. The data samples are characterized in terms of Gaussian/non-Gaussian distributed and balanced/unbalanced samples which are then further used for performance assessment in comparing the SVM and the combined SVM-MLC classifier. Interesting results are reported to indicate how the combined classifier may work under various conditions.

Almost sure convergence in quantum spin glasses

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

Buzinski, David, E-mail: dab197@case.edu; Meckes, Elizabeth, E-mail: elizabeth.meckes@case.edu

2015-12-15

Recently, Keating, Linden, and Wells [Markov Processes Relat. Fields 21(3), 537-555 (2015)] showed that the density of states measure of a nearest-neighbor quantum spin glass model is approximately Gaussian when the number of particles is large. The density of states measure is the ensemble average of the empirical spectral measure of a random matrix; in this paper, we use concentration of measure and entropy techniques together with the result of Keating, Linden, and Wells to show that in fact the empirical spectral measure of such a random matrix is almost surely approximately Gaussian itself with no ensemble averaging. We alsomore » extend this result to a spherical quantum spin glass model and to the more general coupling geometries investigated by Erdős and Schröder [Math. Phys., Anal. Geom. 17(3-4), 441–464 (2014)].« less

On the numbers of images of two stochastic gravitational lensing models

NASA Astrophysics Data System (ADS)

Wei, Ang

2017-02-01

We study two gravitational lensing models with Gaussian randomness: the continuous mass fluctuation model and the floating black hole model. The lens equations of these models are related to certain random harmonic functions. Using Rice's formula and Gaussian techniques, we obtain the expected numbers of zeros of these functions, which indicate the amounts of images in the corresponding lens systems.

Numerical model estimating the capabilities and limitations of the fast Fourier transform technique in absolute interferometry

NASA Astrophysics Data System (ADS)

Talamonti, James J.; Kay, Richard B.; Krebs, Danny J.

1996-05-01

A numerical model was developed to emulate the capabilities of systems performing noncontact absolute distance measurements. The model incorporates known methods to minimize signal processing and digital sampling errors and evaluates the accuracy limitations imposed by spectral peak isolation by using Hanning, Blackman, and Gaussian windows in the fast Fourier transform technique. We applied this model to the specific case of measuring the relative lengths of a compound Michelson interferometer. By processing computer-simulated data through our model, we project the ultimate precision for ideal data, and data containing AM-FM noise. The precision is shown to be limited by nonlinearities in the laser scan. absolute distance, interferometer.

Solute Concentration at a Pumping Well in Non-Gaussian Random Aquifers under Time-Varying Operational Schedules

NASA Astrophysics Data System (ADS)

Libera, A.; de Barros, F.; Riva, M.; Guadagnini, A.

2016-12-01

Managing contaminated groundwater systems is an arduous task for multiple reasons. First, subsurface hydraulic properties are heterogeneous and the high costs associated with site characterization leads to data scarcity (therefore, model predictions are uncertain). Second, it is common for water agencies to schedule groundwater extraction through a temporal sequence of pumping rates to maximize the benefits to anthropogenic activities and minimize the environmental footprint of the withdrawal operations. The temporal variability in pumping rates and aquifer heterogeneity affect dilution rates of contaminant plumes and chemical concentration breakthrough curves (BTCs) at the well. While contaminant transport under steady-state pumping is widely studied, the manner in which a given time-varying pumping schedule affects contaminant plume behavior is tackled only marginally. At the same time, most studies focus on the impact of Gaussian random hydraulic conductivity (K) fields on transport. Here, we systematically analyze the significance of the random space function (RSF) model characterizing K in the presence of distinct pumping operations on the uncertainty of the concentration BTC at the operating well. We juxtapose Monte Carlo based numerical results associated with two models: (a) a recently proposed Generalized Sub-Gaussian model which allows capturing non-Gaussian statistical scaling features of RSFs such as hydraulic conductivity, and (b) the commonly used Gaussian field approximation. Our novel results include an appraisal of the coupled effect of (a) the model employed to depict the random spatial variability of K and (b) transient flow regime, as induced by a temporally varying pumping schedule, on the concentration BTC at the operating well. We systematically quantify the sensitivity of the uncertainty in the contaminant BTC to the RSF model adopted for K (non-Gaussian or Gaussian) in the presence of diverse well pumping schedules. Results contribute to determine conditions under which any of these two key factors prevails on the other.

Numerical modeling of Gaussian beam propagation and diffraction in inhomogeneous media based on the complex eikonal equation

NASA Astrophysics Data System (ADS)

Huang, Xingguo; Sun, Hui

2018-05-01

Gaussian beam is an important complex geometrical optical technology for modeling seismic wave propagation and diffraction in the subsurface with complex geological structure. Current methods for Gaussian beam modeling rely on the dynamic ray tracing and the evanescent wave tracking. However, the dynamic ray tracing method is based on the paraxial ray approximation and the evanescent wave tracking method cannot describe strongly evanescent fields. This leads to inaccuracy of the computed wave fields in the region with a strong inhomogeneous medium. To address this problem, we compute Gaussian beam wave fields using the complex phase by directly solving the complex eikonal equation. In this method, the fast marching method, which is widely used for phase calculation, is combined with Gauss-Newton optimization algorithm to obtain the complex phase at the regular grid points. The main theoretical challenge in combination of this method with Gaussian beam modeling is to address the irregular boundary near the curved central ray. To cope with this challenge, we present the non-uniform finite difference operator and a modified fast marching method. The numerical results confirm the proposed approach.

Gaussian mixed model in support of semiglobal matching leveraged by ground control points

NASA Astrophysics Data System (ADS)

Ma, Hao; Zheng, Shunyi; Li, Chang; Li, Yingsong; Gui, Li

2017-04-01

Semiglobal matching (SGM) has been widely applied in large aerial images because of its good tradeoff between complexity and robustness. The concept of ground control points (GCPs) is adopted to make SGM more robust. We model the effect of GCPs as two data terms for stereo matching between high-resolution aerial epipolar images in an iterative scheme. One term based on GCPs is formulated by Gaussian mixture model, which strengths the relation between GCPs and the pixels to be estimated and encodes some degree of consistency between them with respect to disparity values. Another term depends on pixel-wise confidence, and we further design a confidence updating equation based on three rules. With this confidence-based term, the assignment of disparity can be heuristically selected among disparity search ranges during the iteration process. Several iterations are sufficient to bring out satisfactory results according to our experiments. Experimental results validate that the proposed method outperforms surface reconstruction, which is a representative variant of SGM and behaves excellently on aerial images.

Sparsity-based Poisson denoising with dictionary learning.

PubMed

Giryes, Raja; Elad, Michael

2014-12-01

The problem of Poisson denoising appears in various imaging applications, such as low-light photography, medical imaging, and microscopy. In cases of high SNR, several transformations exist so as to convert the Poisson noise into an additive-independent identically distributed. Gaussian noise, for which many effective algorithms are available. However, in a low-SNR regime, these transformations are significantly less accurate, and a strategy that relies directly on the true noise statistics is required. Salmon et al took this route, proposing a patch-based exponential image representation model based on Gaussian mixture model, leading to state-of-the-art results. In this paper, we propose to harness sparse-representation modeling to the image patches, adopting the same exponential idea. Our scheme uses a greedy pursuit with boot-strapping-based stopping condition and dictionary learning within the denoising process. The reconstruction performance of the proposed scheme is competitive with leading methods in high SNR and achieving state-of-the-art results in cases of low SNR.

Quantifying parameter uncertainty in stochastic models using the Box Cox transformation

NASA Astrophysics Data System (ADS)

Thyer, Mark; Kuczera, George; Wang, Q. J.

2002-08-01

The Box-Cox transformation is widely used to transform hydrological data to make it approximately Gaussian. Bayesian evaluation of parameter uncertainty in stochastic models using the Box-Cox transformation is hindered by the fact that there is no analytical solution for the posterior distribution. However, the Markov chain Monte Carlo method known as the Metropolis algorithm can be used to simulate the posterior distribution. This method properly accounts for the nonnegativity constraint implicit in the Box-Cox transformation. Nonetheless, a case study using the AR(1) model uncovered a practical problem with the implementation of the Metropolis algorithm. The use of a multivariate Gaussian jump distribution resulted in unacceptable convergence behaviour. This was rectified by developing suitable parameter transformations for the mean and variance of the AR(1) process to remove the strong nonlinear dependencies with the Box-Cox transformation parameter. Applying this methodology to the Sydney annual rainfall data and the Burdekin River annual runoff data illustrates the efficacy of these parameter transformations and demonstrate the value of quantifying parameter uncertainty.

Establishment and application of the estimation model for pollutant concentrfation in agriculture drain

NASA Astrophysics Data System (ADS)

Li, Qiangkun; Hu, Yawei; Jia, Qian; Song, Changji

2018-02-01

It is the key point of quantitative research on agricultural non-point source pollution load, the estimation of pollutant concentration in agricultural drain. In the guidance of uncertainty theory, the synthesis of fertilization and irrigation is used as an impulse input to the farmland, meanwhile, the pollutant concentration in agricultural drain is looked as the response process corresponding to the impulse input. The migration and transformation of pollutant in soil is expressed by Inverse Gaussian Probability Density Function. The law of pollutants migration and transformation in soil at crop different growth periods is reflected by adjusting parameters of Inverse Gaussian Distribution. Based on above, the estimation model for pollutant concentration in agricultural drain at field scale was constructed. Taking the of Qing Tong Xia Irrigation District in Ningxia as an example, the concentration of nitrate nitrogen and total phosphorus in agricultural drain was simulated by this model. The results show that the simulated results accorded with measured data approximately and Nash-Sutcliffe coefficients were 0.972 and 0.964, respectively.

Stochastic inflation lattice simulations - Ultra-large scale structure of the universe

NASA Technical Reports Server (NTRS)

Salopek, D. S.

1991-01-01

Non-Gaussian fluctuations for structure formation may arise in inflation from the nonlinear interaction of long wavelength gravitational and scalar fields. Long wavelength fields have spatial gradients, a (exp -1), small compared to the Hubble radius, and they are described in terms of classical random fields that are fed by short wavelength quantum noise. Lattice Langevin calculations are given for a toy model with a scalar field interacting with an exponential potential where one can obtain exact analytic solutions of the Fokker-Planck equation. For single scalar field models that are consistent with current microwave background fluctuations, the fluctuations are Gaussian. However, for scales much larger than our observable Universe, one expects large metric fluctuations that are non-Gaussian. This example illuminates non-Gaussian models involving multiple scalar fields which are consistent with current microwave background limits.

Fast Low-Rank Bayesian Matrix Completion With Hierarchical Gaussian Prior Models

NASA Astrophysics Data System (ADS)

Yang, Linxiao; Fang, Jun; Duan, Huiping; Li, Hongbin; Zeng, Bing

2018-06-01

The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a Wishart distribution is specified as a hyperprior over the precision matrix. We show that such a hierarchical Gaussian prior has the potential to encourage a low-rank solution. Based on the proposed hierarchical prior model, a variational Bayesian method is developed for matrix completion, where the generalized approximate massage passing (GAMP) technique is embedded into the variational Bayesian inference in order to circumvent cumbersome matrix inverse operations. Simulation results show that our proposed method demonstrates superiority over existing state-of-the-art matrix completion methods.

Dynamic Socialized Gaussian Process Models for Human Behavior Prediction in a Health Social Network

PubMed Central

Shen, Yelong; Phan, NhatHai; Xiao, Xiao; Jin, Ruoming; Sun, Junfeng; Piniewski, Brigitte; Kil, David; Dou, Dejing

2016-01-01

Modeling and predicting human behaviors, such as the level and intensity of physical activity, is a key to preventing the cascade of obesity and helping spread healthy behaviors in a social network. In our conference paper, we have developed a social influence model, named Socialized Gaussian Process (SGP), for socialized human behavior modeling. Instead of explicitly modeling social influence as individuals' behaviors influenced by their friends' previous behaviors, SGP models the dynamic social correlation as the result of social influence. The SGP model naturally incorporates personal behavior factor and social correlation factor (i.e., the homophily principle: Friends tend to perform similar behaviors) into a unified model. And it models the social influence factor (i.e., an individual's behavior can be affected by his/her friends) implicitly in dynamic social correlation schemes. The detailed experimental evaluation has shown the SGP model achieves better prediction accuracy compared with most of baseline methods. However, a Socialized Random Forest model may perform better at the beginning compared with the SGP model. One of the main reasons is the dynamic social correlation function is purely based on the users' sequential behaviors without considering other physical activity-related features. To address this issue, we further propose a novel “multi-feature SGP model” (mfSGP) which improves the SGP model by using multiple physical activity-related features in the dynamic social correlation learning. Extensive experimental results illustrate that the mfSGP model clearly outperforms all other models in terms of prediction accuracy and running time. PMID:27746515

EM in high-dimensional spaces.

PubMed

Draper, Bruce A; Elliott, Daniel L; Hayes, Jeremy; Baek, Kyungim

2005-06-01

This paper considers fitting a mixture of Gaussians model to high-dimensional data in scenarios where there are fewer data samples than feature dimensions. Issues that arise when using principal component analysis (PCA) to represent Gaussian distributions inside Expectation-Maximization (EM) are addressed, and a practical algorithm results. Unlike other algorithms that have been proposed, this algorithm does not try to compress the data to fit low-dimensional models. Instead, it models Gaussian distributions in the (N - 1)-dimensional space spanned by the N data samples. We are able to show that this algorithm converges on data sets where low-dimensional techniques do not.

Long-ranged Fermi-Pasta-Ulam systems in thermal contact: Crossover from q-statistics to Boltzmann-Gibbs statistics

NASA Astrophysics Data System (ADS)

Bagchi, Debarshee; Tsallis, Constantino

2017-04-01

The relaxation to equilibrium of two long-range-interacting Fermi-Pasta-Ulam-like models (β type) in thermal contact is numerically studied. These systems, with different sizes and energy densities, are coupled to each other by a few thermal contacts which are short-range harmonic springs. By using the kinetic definition of temperature, we compute the time evolution of temperature and energy density of the two systems. Eventually, for some time t >teq, the temperature and energy density of the coupled system equilibrate to values consistent with standard Boltzmann-Gibbs thermostatistics. The equilibration time teq depends on the system size N as teq ∼Nγ where γ ≃ 1.8. We compute the velocity distribution P (v) of the oscillators of the two systems during the relaxation process. We find that P (v) is non-Gaussian and is remarkably close to a q-Gaussian distribution for all times before thermal equilibrium is reached. During the relaxation process we observe q > 1 while close to t =teq the value of q converges to unity and P (v) approaches a Gaussian. Thus the relaxation phenomenon in long-ranged systems connected by a thermal contact can be generically described as a crossover from q-statistics to Boltzmann-Gibbs statistics.

Experimental study of the focusing properties of a Gaussian Schell-model vortex beam.

PubMed

Wang, Fei; Zhu, Shijun; Cai, Yangjian

2011-08-15

We carry out an experimental and theoretical study of the focusing properties of a Gaussian Schell-model (GSM) vortex beam. It is found that we can shape the beam profile of the focused GSM vortex beam by varying its initial spatial coherence width. Focused dark hollow, flat-topped, and Gaussian beam spots can be obtained in our experiment, which will be useful for trapping particles. The experimental results agree well with the theoretical results. © 2011 Optical Society of America

Study of Gaussian Doped Double Gate JunctionLess (GD-DG-JL) transistor including source drain depletion length: Model for sub-threshold behavior

NASA Astrophysics Data System (ADS)

Kumari, Vandana; Kumar, Ayush; Saxena, Manoj; Gupta, Mridula

2018-01-01

The sub-threshold model formulation of Gaussian Doped Double Gate JunctionLess (GD-DG-JL) FET including source/drain depletion length is reported in the present work under the assumption that the ungated regions are fully depleted. To provide deeper insight into the device performance, the impact of gaussian straggle, channel length, oxide and channel thickness and high-k gate dielectric has been studied using extensive TCAD device simulation.

High-Performance Clock Synchronization Algorithms for Distributed Wireless Airborne Computer Networks with Applications to Localization and Tracking of Targets

DTIC Science & Technology

2010-06-01

GMKPF represents a better and more flexible alternative to the Gaussian Maximum Likelihood (GML), and Exponential Maximum Likelihood ( EML ...accurate results relative to GML and EML when the network delays are modeled in terms of a single non-Gaussian/non-exponential distribution or as a...to the Gaussian Maximum Likelihood (GML), and Exponential Maximum Likelihood ( EML ) estimators for clock offset estimation in non-Gaussian or non

Signal Partitioning Algorithm for Highly Efficient Gaussian Mixture Modeling in Mass Spectrometry

PubMed Central

Polanski, Andrzej; Marczyk, Michal; Pietrowska, Monika; Widlak, Piotr; Polanska, Joanna

2015-01-01

Mixture - modeling of mass spectra is an approach with many potential applications including peak detection and quantification, smoothing, de-noising, feature extraction and spectral signal compression. However, existing algorithms do not allow for automated analyses of whole spectra. Therefore, despite highlighting potential advantages of mixture modeling of mass spectra of peptide/protein mixtures and some preliminary results presented in several papers, the mixture modeling approach was so far not developed to the stage enabling systematic comparisons with existing software packages for proteomic mass spectra analyses. In this paper we present an efficient algorithm for Gaussian mixture modeling of proteomic mass spectra of different types (e.g., MALDI-ToF profiling, MALDI-IMS). The main idea is automated partitioning of protein mass spectral signal into fragments. The obtained fragments are separately decomposed into Gaussian mixture models. The parameters of the mixture models of fragments are then aggregated to form the mixture model of the whole spectrum. We compare the elaborated algorithm to existing algorithms for peak detection and we demonstrate improvements of peak detection efficiency obtained by using Gaussian mixture modeling. We also show applications of the elaborated algorithm to real proteomic datasets of low and high resolution. PMID:26230717

Modeling Non-Gaussian Time Series with Nonparametric Bayesian Model.

PubMed

Xu, Zhiguang; MacEachern, Steven; Xu, Xinyi

2015-02-01

We present a class of Bayesian copula models whose major components are the marginal (limiting) distribution of a stationary time series and the internal dynamics of the series. We argue that these are the two features with which an analyst is typically most familiar, and hence that these are natural components with which to work. For the marginal distribution, we use a nonparametric Bayesian prior distribution along with a cdf-inverse cdf transformation to obtain large support. For the internal dynamics, we rely on the traditionally successful techniques of normal-theory time series. Coupling the two components gives us a family of (Gaussian) copula transformed autoregressive models. The models provide coherent adjustments of time scales and are compatible with many extensions, including changes in volatility of the series. We describe basic properties of the models, show their ability to recover non-Gaussian marginal distributions, and use a GARCH modification of the basic model to analyze stock index return series. The models are found to provide better fit and improved short-range and long-range predictions than Gaussian competitors. The models are extensible to a large variety of fields, including continuous time models, spatial models, models for multiple series, models driven by external covariate streams, and non-stationary models.

Representation of Arctic mixed-phase clouds and the Wegener-Bergeron-Findeisen process in climate models: Perspectives from a cloud-resolving study

NASA Astrophysics Data System (ADS)

Fan, Jiwen; Ghan, Steven; Ovchinnikov, Mikhail; Liu, Xiaohong; Rasch, Philip J.; Korolev, Alexei

2011-01-01

Two types of Arctic mixed-phase clouds observed during the ISDAC and M-PACE field campaigns are simulated using a 3-dimensional cloud-resolving model (CRM) with size-resolved cloud microphysics. The modeled cloud properties agree reasonably well with aircraft measurements and surface-based retrievals. Cloud properties such as the probability density function (PDF) of vertical velocity (w), cloud liquid and ice, regimes of cloud particle growth, including the Wegener-Bergeron-Findeisen (WBF) process, and the relationships among properties/processes in mixed-phase clouds are examined to gain insights for improving their representation in General Circulation Models (GCMs). The PDF of the simulated w is well represented by a Gaussian function, validating, at least for arctic clouds, the subgrid treatment used in GCMs. The PDFs of liquid and ice water contents can be approximated by Gamma functions, and a Gaussian function can describe the total water distribution, but a fixed variance assumption should be avoided in both cases. The CRM results support the assumption frequently used in GCMs that mixed phase clouds maintain water vapor near liquid saturation. Thus, ice continues to grow throughout the stratiform cloud but the WBF process occurs in about 50% of cloud volume where liquid and ice co-exist, predominantly in downdrafts. In updrafts, liquid and ice particles grow simultaneously. The relationship between the ice depositional growth rate and cloud ice strongly depends on the capacitance of ice particles. The simplified size-independent capacitance of ice particles used in GCMs could lead to large deviations in ice depositional growth.

The formation of cosmic structure in a texture-seeded cold dark matter cosmogony

NASA Technical Reports Server (NTRS)

Gooding, Andrew K.; Park, Changbom; Spergel, David N.; Turok, Neil; Gott, Richard, III

1992-01-01

The growth of density fluctuations induced by global texture in an Omega = 1 cold dark matter (CDM) cosmogony is calculated. The resulting power spectra are in good agreement with each other, with more power on large scales than in the standard inflation plus CDM model. Calculation of related statistics (two-point correlation functions, mass variances, cosmic Mach number) indicates that the texture plus CDM model compares more favorably than standard CDM with observations of large-scale structure. Texture produces coherent velocity fields on large scales, as observed. Excessive small-scale velocity dispersions, and voids less empty than those observed may be remedied by including baryonic physics. The topology of the cosmic structure agrees well with observation. The non-Gaussian texture induced density fluctuations lead to earlier nonlinear object formation than in Gaussian models and may also be more compatible with recent evidence that the galaxy density field is non-Gaussian on large scales. On smaller scales the density field is strongly non-Gaussian, but this appears to be primarily due to nonlinear gravitational clustering. The velocity field on smaller scales is surprisingly Gaussian.

Non-Gaussian microwave background fluctuations from nonlinear gravitational effects

NASA Technical Reports Server (NTRS)

Salopek, D. S.; Kunstatter, G. (Editor)

1991-01-01

Whether the statistics of primordial fluctuations for structure formation are Gaussian or otherwise may be determined if the Cosmic Background Explorer (COBE) Satellite makes a detection of the cosmic microwave-background temperature anisotropy delta T(sub CMB)/T(sub CMB). Non-Gaussian fluctuations may be generated in the chaotic inflationary model if two scalar fields interact nonlinearly with gravity. Theoretical contour maps are calculated for the resulting Sachs-Wolfe temperature fluctuations at large angular scales (greater than 3 degrees). In the long-wavelength approximation, one can confidently determine the nonlinear evolution of quantum noise with gravity during the inflationary epoch because: (1) different spatial points are no longer in causal contact; and (2) quantum gravity corrections are typically small-- it is sufficient to model the system using classical random fields. If the potential for two scalar fields V(phi sub 1, phi sub 2) possesses a sharp feature, then non-Gaussian fluctuations may arise. An explicit model is given where cold spots in delta T(sub CMB)/T(sub CMB) maps are suppressed as compared to the Gaussian case. The fluctuations are essentially scale-invariant.

Computational thermochemistry: Automated generation of scale factors for vibrational frequencies calculated by electronic structure model chemistries

NASA Astrophysics Data System (ADS)

Yu, Haoyu S.; Fiedler, Lucas J.; Alecu, I. M.; Truhlar, Donald G.

2017-01-01

We present a Python program, FREQ, for calculating the optimal scale factors for calculating harmonic vibrational frequencies, fundamental vibrational frequencies, and zero-point vibrational energies from electronic structure calculations. The program utilizes a previously published scale factor optimization model (Alecu et al., 2010) to efficiently obtain all three scale factors from a set of computed vibrational harmonic frequencies. In order to obtain the three scale factors, the user only needs to provide zero-point energies of 15 or 6 selected molecules. If the user has access to the Gaussian 09 or Gaussian 03 program, we provide the option for the user to run the program by entering the keywords for a certain method and basis set in the Gaussian 09 or Gaussian 03 program. Four other Python programs, input.py, input6, pbs.py, and pbs6.py, are also provided for generating Gaussian 09 or Gaussian 03 input and PBS files. The program can also be used with data from any other electronic structure package. A manual of how to use this program is included in the code package.

Non-Gaussian spatiotemporal simulation of multisite daily precipitation: downscaling framework

NASA Astrophysics Data System (ADS)

Ben Alaya, M. A.; Ouarda, T. B. M. J.; Chebana, F.

2018-01-01

Probabilistic regression approaches for downscaling daily precipitation are very useful. They provide the whole conditional distribution at each forecast step to better represent the temporal variability. The question addressed in this paper is: how to simulate spatiotemporal characteristics of multisite daily precipitation from probabilistic regression models? Recent publications point out the complexity of multisite properties of daily precipitation and highlight the need for using a non-Gaussian flexible tool. This work proposes a reasonable compromise between simplicity and flexibility avoiding model misspecification. A suitable nonparametric bootstrapping (NB) technique is adopted. A downscaling model which merges a vector generalized linear model (VGLM as a probabilistic regression tool) and the proposed bootstrapping technique is introduced to simulate realistic multisite precipitation series. The model is applied to data sets from the southern part of the province of Quebec, Canada. It is shown that the model is capable of reproducing both at-site properties and the spatial structure of daily precipitations. Results indicate the superiority of the proposed NB technique, over a multivariate autoregressive Gaussian framework (i.e. Gaussian copula).

Efficient gaussian density formulation of volume and surface areas of macromolecules on graphical processing units.

PubMed

Zhang, Baofeng; Kilburg, Denise; Eastman, Peter; Pande, Vijay S; Gallicchio, Emilio

2017-04-15

We present an algorithm to efficiently compute accurate volumes and surface areas of macromolecules on graphical processing unit (GPU) devices using an analytic model which represents atomic volumes by continuous Gaussian densities. The volume of the molecule is expressed by means of the inclusion-exclusion formula, which is based on the summation of overlap integrals among multiple atomic densities. The surface area of the molecule is obtained by differentiation of the molecular volume with respect to atomic radii. The many-body nature of the model makes a port to GPU devices challenging. To our knowledge, this is the first reported full implementation of this model on GPU hardware. To accomplish this, we have used recursive strategies to construct the tree of overlaps and to accumulate volumes and their gradients on the tree data structures so as to minimize memory contention. The algorithm is used in the formulation of a surface area-based non-polar implicit solvent model implemented as an open source plug-in (named GaussVol) for the popular OpenMM library for molecular mechanics modeling. GaussVol is 50 to 100 times faster than our best optimized implementation for the CPUs, achieving speeds in excess of 100 ns/day with 1 fs time-step for protein-sized systems on commodity GPUs. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Fast and Scalable Gaussian Process Modeling with Applications to Astronomical Time Series

NASA Astrophysics Data System (ADS)

Foreman-Mackey, Daniel; Agol, Eric; Ambikasaran, Sivaram; Angus, Ruth

2017-12-01

The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large data sets. Gaussian processes (GPs) are a popular class of models used for this purpose, but since the computational cost scales, in general, as the cube of the number of data points, their application has been limited to small data sets. In this paper, we present a novel method for GPs modeling in one dimension where the computational requirements scale linearly with the size of the data set. We demonstrate the method by applying it to simulated and real astronomical time series data sets. These demonstrations are examples of probabilistic inference of stellar rotation periods, asteroseismic oscillation spectra, and transiting planet parameters. The method exploits structure in the problem when the covariance function is expressed as a mixture of complex exponentials, without requiring evenly spaced observations or uniform noise. This form of covariance arises naturally when the process is a mixture of stochastically driven damped harmonic oscillators—providing a physical motivation for and interpretation of this choice—but we also demonstrate that it can be a useful effective model in some other cases. We present a mathematical description of the method and compare it to existing scalable GP methods. The method is fast and interpretable, with a range of potential applications within astronomical data analysis and beyond. We provide well-tested and documented open-source implementations of this method in C++, Python, and Julia.

Human motion tracking by temporal-spatial local gaussian process experts.

PubMed

Zhao, Xu; Fu, Yun; Liu, Yuncai

2011-04-01

Human pose estimation via motion tracking systems can be considered as a regression problem within a discriminative framework. It is always a challenging task to model the mapping from observation space to state space because of the high-dimensional characteristic in the multimodal conditional distribution. In order to build the mapping, existing techniques usually involve a large set of training samples in the learning process which are limited in their capability to deal with multimodality. We propose, in this work, a novel online sparse Gaussian Process (GP) regression model to recover 3-D human motion in monocular videos. Particularly, we investigate the fact that for a given test input, its output is mainly determined by the training samples potentially residing in its local neighborhood and defined in the unified input-output space. This leads to a local mixture GP experts system composed of different local GP experts, each of which dominates a mapping behavior with the specific covariance function adapting to a local region. To handle the multimodality, we combine both temporal and spatial information therefore to obtain two categories of local experts. The temporal and spatial experts are integrated into a seamless hybrid system, which is automatically self-initialized and robust for visual tracking of nonlinear human motion. Learning and inference are extremely efficient as all the local experts are defined online within very small neighborhoods. Extensive experiments on two real-world databases, HumanEva and PEAR, demonstrate the effectiveness of our proposed model, which significantly improve the performance of existing models.

Infinite von Mises-Fisher Mixture Modeling of Whole Brain fMRI Data.

PubMed

Røge, Rasmus E; Madsen, Kristoffer H; Schmidt, Mikkel N; Mørup, Morten

2017-10-01

Cluster analysis of functional magnetic resonance imaging (fMRI) data is often performed using gaussian mixture models, but when the time series are standardized such that the data reside on a hypersphere, this modeling assumption is questionable. The consequences of ignoring the underlying spherical manifold are rarely analyzed, in part due to the computational challenges imposed by directional statistics. In this letter, we discuss a Bayesian von Mises-Fisher (vMF) mixture model for data on the unit hypersphere and present an efficient inference procedure based on collapsed Markov chain Monte Carlo sampling. Comparing the vMF and gaussian mixture models on synthetic data, we demonstrate that the vMF model has a slight advantage inferring the true underlying clustering when compared to gaussian-based models on data generated from both a mixture of vMFs and a mixture of gaussians subsequently normalized. Thus, when performing model selection, the two models are not in agreement. Analyzing multisubject whole brain resting-state fMRI data from healthy adult subjects, we find that the vMF mixture model is considerably more reliable than the gaussian mixture model when comparing solutions across models trained on different groups of subjects, and again we find that the two models disagree on the optimal number of components. The analysis indicates that the fMRI data support more than a thousand clusters, and we confirm this is not a result of overfitting by demonstrating better prediction on data from held-out subjects. Our results highlight the utility of using directional statistics to model standardized fMRI data and demonstrate that whole brain segmentation of fMRI data requires a very large number of functional units in order to adequately account for the discernible statistical patterns in the data.

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

Tuo, Rui; Wu, C. F. Jeff

Many computer models contain unknown parameters which need to be estimated using physical observations. Furthermore, the calibration method based on Gaussian process models may lead to unreasonable estimate for imperfect computer models. In this work, we extend their study to calibration problems with stochastic physical data. We propose a novel method, called the L 2 calibration, and show its semiparametric efficiency. The conventional method of the ordinary least squares is also studied. Theoretical analysis shows that it is consistent but not efficient. Here, numerical examples show that the proposed method outperforms the existing ones.

Random scalar fields and hyperuniformity

NASA Astrophysics Data System (ADS)

Ma, Zheng; Torquato, Salvatore

2017-06-01

Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystals and liquids. Hyperuniform systems have attracted recent attention because they are endowed with novel transport and optical properties. Recently, the hyperuniformity concept has been generalized to characterize two-phase media, scalar fields, and random vector fields. In this paper, we devise methods to explicitly construct hyperuniform scalar fields. Specifically, we analyze spatial patterns generated from Gaussian random fields, which have been used to model the microwave background radiation and heterogeneous materials, the Cahn-Hilliard equation for spinodal decomposition, and Swift-Hohenberg equations that have been used to model emergent pattern formation, including Rayleigh-Bénard convection. We show that the Gaussian random scalar fields can be constructed to be hyperuniform. We also numerically study the time evolution of spinodal decomposition patterns and demonstrate that they are hyperuniform in the scaling regime. Moreover, we find that labyrinth-like patterns generated by the Swift-Hohenberg equation are effectively hyperuniform. We show that thresholding (level-cutting) a hyperuniform Gaussian random field to produce a two-phase random medium tends to destroy the hyperuniformity of the progenitor scalar field. We then propose guidelines to achieve effectively hyperuniform two-phase media derived from thresholded non-Gaussian fields. Our investigation paves the way for new research directions to characterize the large-structure spatial patterns that arise in physics, chemistry, biology, and ecology. Moreover, our theoretical results are expected to guide experimentalists to synthesize new classes of hyperuniform materials with novel physical properties via coarsening processes and using state-of-the-art techniques, such as stereolithography and 3D printing.

Upscaling from particle models to entropic gradient flows

NASA Astrophysics Data System (ADS)

Dirr, Nicolas; Laschos, Vaios; Zimmer, Johannes

2012-06-01

We prove that, for the case of Gaussians on the real line, the functional derived by a time discretization of the diffusion equation as entropic gradient flow is asymptotically equivalent to the rate functional derived from the underlying microscopic process. This result strengthens a conjecture that the same statement is actually true for all measures with second finite moment.

Future constraints on angle-dependent non-Gaussianity from large radio surveys

NASA Astrophysics Data System (ADS)

Raccanelli, Alvise; Shiraishi, Maresuke; Bartolo, Nicola; Bertacca, Daniele; Liguori, Michele; Matarrese, Sabino; Norris, Ray P.; Parkinson, David

2017-03-01

We investigate how well future large-scale radio surveys could measure different shapes of primordial non-Gaussianity; in particular we focus on angle-dependent non-Gaussianity arising from primordial anisotropic sources, whose bispectrum has an angle dependence between the three wavevectors that is characterized by Legendre polynomials PL and expansion coefficients cL. We provide forecasts for measurements of galaxy power spectrum, finding that Large-Scale Structure (LSS) data could allow measurements of primordial non-Gaussianity that would be competitive with, or improve upon, current constraints set by CMB experiments, for all the shapes considered. We argue that the best constraints will come from the possibility to assign redshift information to radio galaxy surveys, and investigate a few possible scenarios for the EMU and SKA surveys. A realistic (futuristic) modeling could provide constraints of fNLloc ≈ 1(0 . 5) for the local shape, fNL of O(10) (O(1)) for the orthogonal, equilateral and folded shapes, and cL=1 ≈ 80(2) , cL=2 ≈ 400(10) for angle-dependent non-Gaussianity showing that only futuristic galaxy surveys will be able to set strong constraints on these models. Nevertheless, the more futuristic forecasts show the potential of LSS analyses to considerably improve current constraints on non-Gaussianity, and so on models of the primordial Universe. Finally, we find the minimum requirements that would be needed to reach σ(cL=1) = 10, which can be considered as a typical (lower) value predicted by some (inflationary) models.

Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States

NASA Astrophysics Data System (ADS)

Walschaers, Mattia; Fabre, Claude; Parigi, Valentina; Treps, Nicolas

2017-11-01

Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.

Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States.

PubMed

Walschaers, Mattia; Fabre, Claude; Parigi, Valentina; Treps, Nicolas

2017-11-03

Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.

A Nonlinear Framework of Delayed Particle Smoothing Method for Vehicle Localization under Non-Gaussian Environment.

PubMed

Xiao, Zhu; Havyarimana, Vincent; Li, Tong; Wang, Dong

2016-05-13

In this paper, a novel nonlinear framework of smoothing method, non-Gaussian delayed particle smoother (nGDPS), is proposed, which enables vehicle state estimation (VSE) with high accuracy taking into account the non-Gaussianity of the measurement and process noises. Within the proposed method, the multivariate Student's t-distribution is adopted in order to compute the probability distribution function (PDF) related to the process and measurement noises, which are assumed to be non-Gaussian distributed. A computation approach based on Ensemble Kalman Filter (EnKF) is designed to cope with the mean and the covariance matrix of the proposal non-Gaussian distribution. A delayed Gibbs sampling algorithm, which incorporates smoothing of the sampled trajectories over a fixed-delay, is proposed to deal with the sample degeneracy of particles. The performance is investigated based on the real-world data, which is collected by low-cost on-board vehicle sensors. The comparison study based on the real-world experiments and the statistical analysis demonstrates that the proposed nGDPS has significant improvement on the vehicle state accuracy and outperforms the existing filtering and smoothing methods.

Comparing fixed and variable-width Gaussian networks.

PubMed

Kůrková, Věra; Kainen, Paul C

2014-09-01

The role of width of Gaussians in two types of computational models is investigated: Gaussian radial-basis-functions (RBFs) where both widths and centers vary and Gaussian kernel networks which have fixed widths but varying centers. The effect of width on functional equivalence, universal approximation property, and form of norms in reproducing kernel Hilbert spaces (RKHS) is explored. It is proven that if two Gaussian RBF networks have the same input-output functions, then they must have the same numbers of units with the same centers and widths. Further, it is shown that while sets of input-output functions of Gaussian kernel networks with two different widths are disjoint, each such set is large enough to be a universal approximator. Embedding of RKHSs induced by "flatter" Gaussians into RKHSs induced by "sharper" Gaussians is described and growth of the ratios of norms on these spaces with increasing input dimension is estimated. Finally, large sets of argminima of error functionals in sets of input-output functions of Gaussian RBFs are described. Copyright © 2014 Elsevier Ltd. All rights reserved.

Simultaneous masking additivity for short Gaussian-shaped tones: spectral effects.

PubMed

Laback, Bernhard; Necciari, Thibaud; Balazs, Peter; Savel, Sophie; Ystad, Sølvi

2013-08-01

Laback et al. [(2011). J. Acoust. Soc. Am. 129, 888-897] investigated the additivity of nonsimultaneous masking using short Gaussian-shaped tones as maskers and target. The present study involved Gaussian stimuli to measure the additivity of simultaneous masking for combinations of up to four spectrally separated maskers. According to most basilar membrane measurements, the maskers should be processed linearly at the characteristic frequency (CF) of the target. Assuming also compression of the target, all masker combinations should produce excess masking (exceeding linear additivity). The results for a pair of maskers flanking the target indeed showed excess masking. The amount of excess masking could be predicted by a model assuming summation of masker-evoked excitations in intensity units at the target CF and compression of the target, using compressive input/output functions derived from the nonsimultaneous masking study. However, the combinations of lower-frequency maskers showed much less excess masking than predicted by the model. This cannot easily be attributed to factors like off-frequency listening, combination tone perception, or between-masker suppression. It was better predicted, however, by assuming weighted intensity summation of masker excitations. The optimum weights for the lower-frequency maskers were smaller than one, consistent with partial masker compression as indicated by recent psychoacoustic data.

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

Lange, R.; Dickerson, M.A.; Peterson, K.R.

Two numerical models for the calculation of air concentration and ground deposition of airborne effluent releases are compared. The Particle-in-Cell (PIC) model and the Straight-Line Airflow Gaussian model were used for the simulation. Two sites were selected for comparison: the Hudson River Valley, New York, and the area around the Savannah River Plant, South Carolina. Input for the models was synthesized from meteorological data gathered in previous studies by various investigators. It was found that the PIC model more closely simulated the three-dimensional effects of the meteorology and topography. Overall, the Gaussian model calculated higher concentrations under stable conditions withmore » better agreement between the two methods during neutral to unstable conditions. In addition, because of its consideration of exposure from the returning plume after flow reversal, the PIC model calculated air concentrations over larger areas than did the Gaussian model.« less

Extracting features of Gaussian self-similar stochastic processes via the Bandt-Pompe approach.

PubMed

Rosso, O A; Zunino, L; Pérez, D G; Figliola, A; Larrondo, H A; Garavaglia, M; Martín, M T; Plastino, A

2007-12-01

By recourse to appropriate information theory quantifiers (normalized Shannon entropy and Martín-Plastino-Rosso intensive statistical complexity measure), we revisit the characterization of Gaussian self-similar stochastic processes from a Bandt-Pompe viewpoint. We show that the ensuing approach exhibits considerable advantages with respect to other treatments. In particular, clear quantifiers gaps are found in the transition between the continuous processes and their associated noises.

A high-frequency warm shallow water acoustic communications channel model and measurements.

PubMed

Chitre, Mandar

2007-11-01

Underwater acoustic communication is a core enabling technology with applications in ocean monitoring using remote sensors and autonomous underwater vehicles. One of the more challenging underwater acoustic communication channels is the medium-range very shallow warm-water channel, common in tropical coastal regions. This channel exhibits two key features-extensive time-varying multipath and high levels of non-Gaussian ambient noise due to snapping shrimp-both of which limit the performance of traditional communication techniques. A good understanding of the communications channel is key to the design of communication systems. It aids in the development of signal processing techniques as well as in the testing of the techniques via simulation. In this article, a physics-based channel model for the very shallow warm-water acoustic channel at high frequencies is developed, which are of interest to medium-range communication system developers. The model is based on ray acoustics and includes time-varying statistical effects as well as non-Gaussian ambient noise statistics observed during channel studies. The model is calibrated and its accuracy validated using measurements made at sea.

Bayesian spatial transformation models with applications in neuroimaging data

PubMed Central

Miranda, Michelle F.; Zhu, Hongtu; Ibrahim, Joseph G.

2013-01-01

Summary The aim of this paper is to develop a class of spatial transformation models (STM) to spatially model the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) and a set of covariates. Our STMs include a varying Box-Cox transformation model for dealing with the issue of non-Gaussian distributed imaging data and a Gaussian Markov Random Field model for incorporating spatial smoothness of the imaging data. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. Simulations and real data analysis demonstrate that the STM significantly outperforms the voxel-wise linear model with Gaussian noise in recovering meaningful geometric patterns. Our STM is able to reveal important brain regions with morphological changes in children with attention deficit hyperactivity disorder. PMID:24128143

Gaussian Finite Element Method for Description of Underwater Sound Diffraction

NASA Astrophysics Data System (ADS)

Huang, Dehua

A new method for solving diffraction problems is presented in this dissertation. It is based on the use of Gaussian diffraction theory. The Rayleigh integral is used to prove the core of Gaussian theory: the diffraction field of a Gaussian is described by a Gaussian function. The parabolic approximation used by previous authors is not necessary to this proof. Comparison of the Gaussian beam expansion and Fourier series expansion reveals that the Gaussian expansion is a more general and more powerful technique. The method combines the Gaussian beam superposition technique (Wen and Breazeale, J. Acoust. Soc. Am. 83, 1752-1756 (1988)) and the Finite element solution to the parabolic equation (Huang, J. Acoust. Soc. Am. 84, 1405-1413 (1988)). Computer modeling shows that the new method is capable of solving for the sound field even in an inhomogeneous medium, whether the source is a Gaussian source or a distributed source. It can be used for horizontally layered interfaces or irregular interfaces. Calculated results are compared with experimental results by use of a recently designed and improved Gaussian transducer in a laboratory water tank. In addition, the power of the Gaussian Finite element method is demonstrated by comparing numerical results with experimental results from use of a piston transducer in a water tank.

Coherence degree of the fundamental Bessel-Gaussian beam in turbulent atmosphere

NASA Astrophysics Data System (ADS)

Lukin, Igor P.

2017-11-01

In this article the coherence of a fundamental Bessel-Gaussian optical beam in turbulent atmosphere is analyzed. The problem analysis is based on the solution of the equation for the transverse second-order mutual coherence function of a fundamental Bessel-Gaussian optical beam of optical radiation. The behavior of a coherence degree of a fundamental Bessel-Gaussian optical beam depending on parameters of an optical beam and characteristics of turbulent atmosphere is examined. It was revealed that at low levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam has the characteristic oscillating appearance. At high levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam is described by an one-scale decreasing curve which in process of increase of level of fluctuations on a line of formation of a laser beam becomes closer to the same characteristic of a spherical optical wave.

Radiation pressure acceleration of corrugated thin foils by Gaussian and super-Gaussian beams

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

Adusumilli, K.; Goyal, D.; Tripathi, V. K.

Rayleigh-Taylor instability of radiation pressure accelerated ultrathin foils by laser having Gaussian and super-Gaussian intensity distribution is investigated using a single fluid code. The foil is allowed to have ring shaped surface ripples. The radiation pressure force on such a foil is non-uniform with finite transverse component F{sub r}; F{sub r} varies periodically with r. Subsequently, the ripple grows as the foil moves ahead along z. With a Gaussian beam, the foil acquires an overall curvature due to non-uniformity in radiation pressure and gets thinner. In the process, the ripple perturbation is considerably washed off. With super-Gaussian beam, the ripplemore » is found to be more strongly washed out. In order to avoid transmission of the laser through the thinning foil, a criterion on the foil thickness is obtained.« less

Disentangling inhibition-based and retrieval-based aftereffects of distractors: Cognitive versus motor processes.

PubMed

Singh, Tarini; Laub, Ruth; Burgard, Jan Pablo; Frings, Christian

2018-05-01

Selective attention refers to the ability to selectively act upon relevant information at the expense of irrelevant information. Yet, in many experimental tasks, what happens to the representation of the irrelevant information is still debated. Typically, 2 approaches to distractor processing have been suggested, namely distractor inhibition and distractor-based retrieval. However, it is also typical that both processes are hard to disentangle. For instance, in the negative priming literature (for a review Frings, Schneider, & Fox, 2015) this has been a continuous debate since the early 1980s. In the present study, we attempted to prove that both processes exist, but that they reflect distractor processing at different levels of representation. Distractor inhibition impacts stimulus representation, whereas distractor-based retrieval impacts mainly motor processes. We investigated both processes in a distractor-priming task, which enables an independent measurement of both processes. For our argument that both processes impact different levels of distractor representation, we estimated the exponential parameter (τ) and Gaussian components (μ, σ) of the exponential Gaussian reaction-time (RT) distribution, which have previously been used to independently test the effects of cognitive and motor processes (e.g., Moutsopoulou & Waszak, 2012). The distractor-based retrieval effect was evident for the Gaussian component, which is typically discussed as reflecting motor processes, but not for the exponential parameter, whereas the inhibition component was evident for the exponential parameter, which is typically discussed as reflecting cognitive processes, but not for the Gaussian parameter. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Weakly anomalous diffusion with non-Gaussian propagators

NASA Astrophysics Data System (ADS)

Cressoni, J. C.; Viswanathan, G. M.; Ferreira, A. S.; da Silva, M. A. A.

2012-08-01

A poorly understood phenomenon seen in complex systems is diffusion characterized by Hurst exponent H≈1/2 but with non-Gaussian statistics. Motivated by such empirical findings, we report an exact analytical solution for a non-Markovian random walk model that gives rise to weakly anomalous diffusion with H=1/2 but with a non-Gaussian propagator.

Nonparametric Bayesian Segmentation of a Multivariate Inhomogeneous Space-Time Poisson Process.

PubMed

Ding, Mingtao; He, Lihan; Dunson, David; Carin, Lawrence

2012-12-01

A nonparametric Bayesian model is proposed for segmenting time-evolving multivariate spatial point process data. An inhomogeneous Poisson process is assumed, with a logistic stick-breaking process (LSBP) used to encourage piecewise-constant spatial Poisson intensities. The LSBP explicitly favors spatially contiguous segments, and infers the number of segments based on the observed data. The temporal dynamics of the segmentation and of the Poisson intensities are modeled with exponential correlation in time, implemented in the form of a first-order autoregressive model for uniformly sampled discrete data, and via a Gaussian process with an exponential kernel for general temporal sampling. We consider and compare two different inference techniques: a Markov chain Monte Carlo sampler, which has relatively high computational complexity; and an approximate and efficient variational Bayesian analysis. The model is demonstrated with a simulated example and a real example of space-time crime events in Cincinnati, Ohio, USA.

Processor core for real time background identification of HD video based on OpenCV Gaussian mixture model algorithm

NASA Astrophysics Data System (ADS)

Genovese, Mariangela; Napoli, Ettore

2013-05-01

The identification of moving objects is a fundamental step in computer vision processing chains. The development of low cost and lightweight smart cameras steadily increases the request of efficient and high performance circuits able to process high definition video in real time. The paper proposes two processor cores aimed to perform the real time background identification on High Definition (HD, 1920 1080 pixel) video streams. The implemented algorithm is the OpenCV version of the Gaussian Mixture Model (GMM), an high performance probabilistic algorithm for the segmentation of the background that is however computationally intensive and impossible to implement on general purpose CPU with the constraint of real time processing. In the proposed paper, the equations of the OpenCV GMM algorithm are optimized in such a way that a lightweight and low power implementation of the algorithm is obtained. The reported performances are also the result of the use of state of the art truncated binary multipliers and ROM compression techniques for the implementation of the non-linear functions. The first circuit has commercial FPGA devices as a target and provides speed and logic resource occupation that overcome previously proposed implementations. The second circuit is oriented to an ASIC (UMC-90nm) standard cell implementation. Both implementations are able to process more than 60 frames per second in 1080p format, a frame rate compatible with HD television.

Moving vehicles segmentation based on Gaussian motion model

NASA Astrophysics Data System (ADS)

Zhang, Wei; Fang, Xiang Z.; Lin, Wei Y.

2005-07-01

Moving objects segmentation is a challenge in computer vision. This paper focuses on the segmentation of moving vehicles in dynamic scene. We analyses the psychology of human vision and present a framework for segmenting moving vehicles in the highway. The proposed framework consists of two parts. Firstly, we propose an adaptive background update method in which the background is updated according to the change of illumination conditions and thus can adapt to the change of illumination sensitively. Secondly, we construct a Gaussian motion model to segment moving vehicles, in which the motion vectors of the moving pixels are modeled as a Gaussian model and an on-line EM algorithm is used to update the model. The Gaussian distribution of the adaptive model is elevated to determine which moving vectors result from moving vehicles and which from other moving objects such as waving trees. Finally, the pixels with motion vector result from the moving vehicles are segmented. Experimental results of several typical scenes show that the proposed model can detect the moving vehicles correctly and is immune from influence of the moving objects caused by the waving trees and the vibration of camera.

Efficient calibration for imperfect computer models

DOE PAGES

Tuo, Rui; Wu, C. F. Jeff

2015-12-01

Many computer models contain unknown parameters which need to be estimated using physical observations. Furthermore, the calibration method based on Gaussian process models may lead to unreasonable estimate for imperfect computer models. In this work, we extend their study to calibration problems with stochastic physical data. We propose a novel method, called the L 2 calibration, and show its semiparametric efficiency. The conventional method of the ordinary least squares is also studied. Theoretical analysis shows that it is consistent but not efficient. Here, numerical examples show that the proposed method outperforms the existing ones.

A new estimator method for GARCH models

NASA Astrophysics Data System (ADS)

Onody, R. N.; Favaro, G. M.; Cazaroto, E. R.

2007-06-01

The GARCH (p, q) model is a very interesting stochastic process with widespread applications and a central role in empirical finance. The Markovian GARCH (1, 1) model has only 3 control parameters and a much discussed question is how to estimate them when a series of some financial asset is given. Besides the maximum likelihood estimator technique, there is another method which uses the variance, the kurtosis and the autocorrelation time to determine them. We propose here to use the standardized 6th moment. The set of parameters obtained in this way produces a very good probability density function and a much better time autocorrelation function. This is true for both studied indexes: NYSE Composite and FTSE 100. The probability of return to the origin is investigated at different time horizons for both Gaussian and Laplacian GARCH models. In spite of the fact that these models show almost identical performances with respect to the final probability density function and to the time autocorrelation function, their scaling properties are, however, very different. The Laplacian GARCH model gives a better scaling exponent for the NYSE time series, whereas the Gaussian dynamics fits better the FTSE scaling exponent.

Strategy and model building in the fourth dimension: a null model for genotype x age interaction as a Gaussian stationary stochastic process.

PubMed

Diego, Vincent P; Almasy, Laura; Dyer, Thomas D; Soler, Júlia M P; Blangero, John

2003-12-31

Using univariate and multivariate variance components linkage analysis methods, we studied possible genotype x age interaction in cardiovascular phenotypes related to the aging process from the Framingham Heart Study. We found evidence for genotype x age interaction for fasting glucose and systolic blood pressure. There is polygenic genotype x age interaction for fasting glucose and systolic blood pressure and quantitative trait locus x age interaction for a linkage signal for systolic blood pressure phenotypes located on chromosome 17 at 67 cM.

Diffusion of Super-Gaussian Profiles

ERIC Educational Resources Information Center

Rosenberg, C.-J.; Anderson, D.; Desaix, M.; Johannisson, P.; Lisak, M.

2007-01-01

The present analysis describes an analytically simple and systematic approximation procedure for modelling the free diffusive spreading of initially super-Gaussian profiles. The approach is based on a self-similar ansatz for the evolution of the diffusion profile, and the parameter functions involved in the modelling are determined by suitable…

Gaussian copula as a likelihood function for environmental models

NASA Astrophysics Data System (ADS)

Wani, O.; Espadas, G.; Cecinati, F.; Rieckermann, J.

2017-12-01

Parameter estimation of environmental models always comes with uncertainty. To formally quantify this parametric uncertainty, a likelihood function needs to be formulated, which is defined as the probability of observations given fixed values of the parameter set. A likelihood function allows us to infer parameter values from observations using Bayes' theorem. The challenge is to formulate a likelihood function that reliably describes the error generating processes which lead to the observed monitoring data, such as rainfall and runoff. If the likelihood function is not representative of the error statistics, the parameter inference will give biased parameter values. Several uncertainty estimation methods that are currently being used employ Gaussian processes as a likelihood function, because of their favourable analytical properties. Box-Cox transformation is suggested to deal with non-symmetric and heteroscedastic errors e.g. for flow data which are typically more uncertain in high flows than in periods with low flows. Problem with transformations is that the results are conditional on hyper-parameters, for which it is difficult to formulate the analyst's belief a priori. In an attempt to address this problem, in this research work we suggest learning the nature of the error distribution from the errors made by the model in the "past" forecasts. We use a Gaussian copula to generate semiparametric error distributions . 1) We show that this copula can be then used as a likelihood function to infer parameters, breaking away from the practice of using multivariate normal distributions. Based on the results from a didactical example of predicting rainfall runoff, 2) we demonstrate that the copula captures the predictive uncertainty of the model. 3) Finally, we find that the properties of autocorrelation and heteroscedasticity of errors are captured well by the copula, eliminating the need to use transforms. In summary, our findings suggest that copulas are an interesting departure from the usage of fully parametric distributions as likelihood functions - and they could help us to better capture the statistical properties of errors and make more reliable predictions.

Kinetic and energy production analysis of pyrolysis of lignocellulosic biomass using a three-parallel Gaussian reaction model.

PubMed

Chen, Tianju; Zhang, Jinzhi; Wu, Jinhu

2016-07-01

The kinetic and energy productions of pyrolysis of a lignocellulosic biomass were investigated using a three-parallel Gaussian distribution method in this work. The pyrolysis experiment of the pine sawdust was performed using a thermogravimetric-mass spectroscopy (TG-MS) analyzer. A three-parallel Gaussian distributed activation energy model (DAEM)-reaction model was used to describe thermal decomposition behaviors of the three components, hemicellulose, cellulose and lignin. The first, second and third pseudocomponents represent the fractions of hemicellulose, cellulose and lignin, respectively. It was found that the model is capable of predicting the pyrolysis behavior of the pine sawdust. The activation energy distribution peaks for the three pseudo-components were centered at 186.8, 197.5 and 203.9kJmol(-1) for the pine sawdust, respectively. The evolution profiles of H2, CH4, CO, and CO2 were well predicted using the three-parallel Gaussian distribution model. In addition, the chemical composition of bio-oil was also obtained by pyrolysis-gas chromatography/mass spectrometry instrument (Py-GC/MS). Copyright © 2016 Elsevier Ltd. All rights reserved.

Estimation of High-Dimensional Graphical Models Using Regularized Score Matching

PubMed Central

Lin, Lina; Drton, Mathias; Shojaie, Ali

2017-01-01

Graphical models are widely used to model stochastic dependences among large collections of variables. We introduce a new method of estimating undirected conditional independence graphs based on the score matching loss, introduced by Hyvärinen (2005), and subsequently extended in Hyvärinen (2007). The regularized score matching method we propose applies to settings with continuous observations and allows for computationally efficient treatment of possibly non-Gaussian exponential family models. In the well-explored Gaussian setting, regularized score matching avoids issues of asymmetry that arise when applying the technique of neighborhood selection, and compared to existing methods that directly yield symmetric estimates, the score matching approach has the advantage that the considered loss is quadratic and gives piecewise linear solution paths under ℓ1 regularization. Under suitable irrepresentability conditions, we show that ℓ1-regularized score matching is consistent for graph estimation in sparse high-dimensional settings. Through numerical experiments and an application to RNAseq data, we confirm that regularized score matching achieves state-of-the-art performance in the Gaussian case and provides a valuable tool for computationally efficient estimation in non-Gaussian graphical models. PMID:28638498

Geographically weighted regression model on poverty indicator

NASA Astrophysics Data System (ADS)

Slamet, I.; Nugroho, N. F. T. A.; Muslich

2017-12-01

In this research, we applied geographically weighted regression (GWR) for analyzing the poverty in Central Java. We consider Gaussian Kernel as weighted function. The GWR uses the diagonal matrix resulted from calculating kernel Gaussian function as a weighted function in the regression model. The kernel weights is used to handle spatial effects on the data so that a model can be obtained for each location. The purpose of this paper is to model of poverty percentage data in Central Java province using GWR with Gaussian kernel weighted function and to determine the influencing factors in each regency/city in Central Java province. Based on the research, we obtained geographically weighted regression model with Gaussian kernel weighted function on poverty percentage data in Central Java province. We found that percentage of population working as farmers, population growth rate, percentage of households with regular sanitation, and BPJS beneficiaries are the variables that affect the percentage of poverty in Central Java province. In this research, we found the determination coefficient R2 are 68.64%. There are two categories of district which are influenced by different of significance factors.

Robust Linear Models for Cis-eQTL Analysis.

PubMed

Rantalainen, Mattias; Lindgren, Cecilia M; Holmes, Christopher C

2015-01-01

Expression Quantitative Trait Loci (eQTL) analysis enables characterisation of functional genetic variation influencing expression levels of individual genes. In outbread populations, including humans, eQTLs are commonly analysed using the conventional linear model, adjusting for relevant covariates, assuming an allelic dosage model and a Gaussian error term. However, gene expression data generally have noise that induces heavy-tailed errors relative to the Gaussian distribution and often include atypical observations, or outliers. Such departures from modelling assumptions can lead to an increased rate of type II errors (false negatives), and to some extent also type I errors (false positives). Careful model checking can reduce the risk of type-I errors but often not type II errors, since it is generally too time-consuming to carefully check all models with a non-significant effect in large-scale and genome-wide studies. Here we propose the application of a robust linear model for eQTL analysis to reduce adverse effects of deviations from the assumption of Gaussian residuals. We present results from a simulation study as well as results from the analysis of real eQTL data sets. Our findings suggest that in many situations robust models have the potential to provide more reliable eQTL results compared to conventional linear models, particularly in respect to reducing type II errors due to non-Gaussian noise. Post-genomic data, such as that generated in genome-wide eQTL studies, are often noisy and frequently contain atypical observations. Robust statistical models have the potential to provide more reliable results and increased statistical power under non-Gaussian conditions. The results presented here suggest that robust models should be considered routinely alongside other commonly used methodologies for eQTL analysis.

Statistical description of turbulent transport for flux driven toroidal plasmas

NASA Astrophysics Data System (ADS)

Anderson, J.; Imadera, K.; Kishimoto, Y.; Li, J. Q.; Nordman, H.

2017-06-01

A novel methodology to analyze non-Gaussian probability distribution functions (PDFs) of intermittent turbulent transport in global full-f gyrokinetic simulations is presented. In this work, the auto-regressive integrated moving average (ARIMA) model is applied to time series data of intermittent turbulent heat transport to separate noise and oscillatory trends, allowing for the extraction of non-Gaussian features of the PDFs. It was shown that non-Gaussian tails of the PDFs from first principles based gyrokinetic simulations agree with an analytical estimation based on a two fluid model.

Speech Enhancement Using Gaussian Scale Mixture Models

PubMed Central

Hao, Jiucang; Lee, Te-Won; Sejnowski, Terrence J.

2011-01-01

This paper presents a novel probabilistic approach to speech enhancement. Instead of a deterministic logarithmic relationship, we assume a probabilistic relationship between the frequency coefficients and the log-spectra. The speech model in the log-spectral domain is a Gaussian mixture model (GMM). The frequency coefficients obey a zero-mean Gaussian whose covariance equals to the exponential of the log-spectra. This results in a Gaussian scale mixture model (GSMM) for the speech signal in the frequency domain, since the log-spectra can be regarded as scaling factors. The probabilistic relation between frequency coefficients and log-spectra allows these to be treated as two random variables, both to be estimated from the noisy signals. Expectation-maximization (EM) was used to train the GSMM and Bayesian inference was used to compute the posterior signal distribution. Because exact inference of this full probabilistic model is computationally intractable, we developed two approaches to enhance the efficiency: the Laplace method and a variational approximation. The proposed methods were applied to enhance speech corrupted by Gaussian noise and speech-shaped noise (SSN). For both approximations, signals reconstructed from the estimated frequency coefficients provided higher signal-to-noise ratio (SNR) and those reconstructed from the estimated log-spectra produced lower word recognition error rate because the log-spectra fit the inputs to the recognizer better. Our algorithms effectively reduced the SSN, which algorithms based on spectral analysis were not able to suppress. PMID:21359139

Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels

NASA Astrophysics Data System (ADS)

Sabapathy, Krishna Kumar; Winter, Andreas

2017-06-01

We present a framework for studying bosonic non-Gaussian channels of continuous-variable systems. Our emphasis is on a class of channels that we call photon-added Gaussian channels, which are experimentally viable with current quantum-optical technologies. A strong motivation for considering these channels is the fact that it is compulsory to go beyond the Gaussian domain for numerous tasks in continuous-variable quantum information processing such as entanglement distillation from Gaussian states and universal quantum computation. The single-mode photon-added channels we consider are obtained by using two-mode beam splitters and squeezing operators with photon addition applied to the ancilla ports giving rise to families of non-Gaussian channels. For each such channel, we derive its operator-sum representation, indispensable in the present context. We observe that these channels are Fock preserving (coherence nongenerating). We then report two examples of activation using our scheme of photon addition, that of quantum-optical nonclassicality at outputs of channels that would otherwise output only classical states and of both the quantum and private communication capacities, hinting at far-reaching applications for quantum-optical communication. Further, we see that noisy Gaussian channels can be expressed as a convex mixture of these non-Gaussian channels. We also present other physical and information-theoretic properties of these channels.

q-Gaussian distributions and multiplicative stochastic processes for analysis of multiple financial time series

NASA Astrophysics Data System (ADS)

Sato, Aki-Hiro

2010-12-01

This study considers q-Gaussian distributions and stochastic differential equations with both multiplicative and additive noises. In the M-dimensional case a q-Gaussian distribution can be theoretically derived as a stationary probability distribution of the multiplicative stochastic differential equation with both mutually independent multiplicative and additive noises. By using the proposed stochastic differential equation a method to evaluate a default probability under a given risk buffer is proposed.

A simulation of water pollution model parameter estimation

NASA Technical Reports Server (NTRS)

Kibler, J. F.

1976-01-01

A parameter estimation procedure for a water pollution transport model is elaborated. A two-dimensional instantaneous-release shear-diffusion model serves as representative of a simple transport process. Pollution concentration levels are arrived at via modeling of a remote-sensing system. The remote-sensed data are simulated by adding Gaussian noise to the concentration level values generated via the transport model. Model parameters are estimated from the simulated data using a least-squares batch processor. Resolution, sensor array size, and number and location of sensor readings can be found from the accuracies of the parameter estimates.

A Gaussian Approximation Potential for Silicon

NASA Astrophysics Data System (ADS)

Bernstein, Noam; Bartók, Albert; Kermode, James; Csányi, Gábor

We present an interatomic potential for silicon using the Gaussian Approximation Potential (GAP) approach, which uses the Gaussian process regression method to approximate the reference potential energy surface as a sum of atomic energies. Each atomic energy is approximated as a function of the local environment around the atom, which is described with the smooth overlap of atomic environments (SOAP) descriptor. The potential is fit to a database of energies, forces, and stresses calculated using density functional theory (DFT) on a wide range of configurations from zero and finite temperature simulations. These include crystalline phases, liquid, amorphous, and low coordination structures, and diamond-structure point defects, dislocations, surfaces, and cracks. We compare the results of the potential to DFT calculations, as well as to previously published models including Stillinger-Weber, Tersoff, modified embedded atom method (MEAM), and ReaxFF. We show that it is very accurate as compared to the DFT reference results for a wide range of properties, including low energy bulk phases, liquid structure, as well as point, line, and plane defects in the diamond structure.

Leading non-Gaussian corrections for diffusion orientation distribution function.

PubMed

Jensen, Jens H; Helpern, Joseph A; Tabesh, Ali

2014-02-01

An analytical representation of the leading non-Gaussian corrections for a class of diffusion orientation distribution functions (dODFs) is presented. This formula is constructed from the diffusion and diffusional kurtosis tensors, both of which may be estimated with diffusional kurtosis imaging (DKI). By incorporating model-independent non-Gaussian diffusion effects, it improves on the Gaussian approximation used in diffusion tensor imaging (DTI). This analytical representation therefore provides a natural foundation for DKI-based white matter fiber tractography, which has potential advantages over conventional DTI-based fiber tractography in generating more accurate predictions for the orientations of fiber bundles and in being able to directly resolve intra-voxel fiber crossings. The formula is illustrated with numerical simulations for a two-compartment model of fiber crossings and for human brain data. These results indicate that the inclusion of the leading non-Gaussian corrections can significantly affect fiber tractography in white matter regions, such as the centrum semiovale, where fiber crossings are common. 2013 John Wiley & Sons, Ltd.

Leading Non-Gaussian Corrections for Diffusion Orientation Distribution Function

PubMed Central

Jensen, Jens H.; Helpern, Joseph A.; Tabesh, Ali

2014-01-01

An analytical representation of the leading non-Gaussian corrections for a class of diffusion orientation distribution functions (dODFs) is presented. This formula is constructed out of the diffusion and diffusional kurtosis tensors, both of which may be estimated with diffusional kurtosis imaging (DKI). By incorporating model-independent non-Gaussian diffusion effects, it improves upon the Gaussian approximation used in diffusion tensor imaging (DTI). This analytical representation therefore provides a natural foundation for DKI-based white matter fiber tractography, which has potential advantages over conventional DTI-based fiber tractography in generating more accurate predictions for the orientations of fiber bundles and in being able to directly resolve intra-voxel fiber crossings. The formula is illustrated with numerical simulations for a two-compartment model of fiber crossings and for human brain data. These results indicate that the inclusion of the leading non-Gaussian corrections can significantly affect fiber tractography in white matter regions, such as the centrum semiovale, where fiber crossings are common. PMID:24738143

Laser Raman detection for oral cancer based on an adaptive Gaussian process classification method with posterior probabilities

NASA Astrophysics Data System (ADS)

Du, Zhanwei; Yang, Yongjian; Bai, Yuan; Wang, Lijun; Su, Le; Chen, Yong; Li, Xianchang; Zhou, Xiaodong; Jia, Jun; Shen, Aiguo; Hu, Jiming

2013-03-01

The existing methods for early and differential diagnosis of oral cancer are limited due to the unapparent early symptoms and the imperfect imaging examination methods. In this paper, the classification models of oral adenocarcinoma, carcinoma tissues and a control group with just four features are established by utilizing the hybrid Gaussian process (HGP) classification algorithm, with the introduction of the mechanisms of noise reduction and posterior probability. HGP shows much better performance in the experimental results. During the experimental process, oral tissues were divided into three groups, adenocarcinoma (n = 87), carcinoma (n = 100) and the control group (n = 134). The spectral data for these groups were collected. The prospective application of the proposed HGP classification method improved the diagnostic sensitivity to 56.35% and the specificity to about 70.00%, and resulted in a Matthews correlation coefficient (MCC) of 0.36. It is proved that the utilization of HGP in LRS detection analysis for the diagnosis of oral cancer gives accurate results. The prospect of application is also satisfactory.

Modeling of dispersion near roadways based on the vehicle-induced turbulence concept

NASA Astrophysics Data System (ADS)

Sahlodin, Ali M.; Sotudeh-Gharebagh, Rahmat; Zhu, Yifang

A mathematical model is developed for dispersion near roadways by incorporating vehicle-induced turbulence (VIT) into Gaussian dispersion modeling using computational fluid dynamics (CFD). The model is based on the Gaussian plume equation in which roadway is regarded as a series of point sources. The Gaussian dispersion parameters are modified by simulation of the roadway using CFD in order to evaluate turbulent kinetic energy (TKE) as a measure of VIT. The model was evaluated against experimental carbon monoxide concentrations downwind of two major freeways reported in the literature. Good agreements were achieved between model results and the literature data. A significant difference was observed between the model results with and without considering VIT. The difference is rather high for data very close to the freeways. This model, after evaluation with additional data, may be used as a framework for predicting dispersion and deposition from any roadway for different traffic (vehicle type and speed) conditions.

Cosmic microwave background power asymmetry from non-Gaussian modulation.

PubMed

Schmidt, Fabian; Hui, Lam

2013-01-04

Non-Gaussianity in the inflationary perturbations can couple observable scales to modes of much longer wavelength (even superhorizon), leaving as a signature a large-angle modulation of the observed cosmic microwave background power spectrum. This provides an alternative origin for a power asymmetry that is otherwise often ascribed to a breaking of statistical isotropy. The non-Gaussian modulation effect can be significant even for typical ~10(-5) perturbations while respecting current constraints on non-Gaussianity if the squeezed limit of the bispectrum is sufficiently infrared divergent. Just such a strongly infrared-divergent bispectrum has been claimed for inflation models with a non-Bunch-Davies initial state, for instance. Upper limits on the observed cosmic microwave background power asymmetry place stringent constraints on the duration of inflation in such models.

Command Generator Tracker Synthesis Methods Using an LQG (Linear System Model, Quadratic Cost, and Gaussian Noise Process) Derived Proportional Plus Integral Controller Based on the Integral of the Regulation Error.

DTIC Science & Technology

1983-12-01

34 M4 + + Z + + + E + ass + + Z + + + osi " " + + Z + + + + 9tr"- + t + Z + ++ +" + + L + Z + +0+ + : :L:+: • +: E. . :ce + L+ Z+ + E+ 9 " + L z + K...this guide.) The truth model description is identified by the heading "TRUTH MODELO . The matrices of the continuous-time system are listed first. The

Degeneracy of energy levels of pseudo-Gaussian oscillators

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

Iacob, Theodor-Felix; Iacob, Felix, E-mail: felix@physics.uvt.ro; Lute, Marina

2015-12-07

We study the main features of the isotropic radial pseudo-Gaussian oscillators spectral properties. This study is made upon the energy levels degeneracy with respect to orbital angular momentum quantum number. In a previous work [6] we have shown that the pseudo-Gaussian oscillators belong to the class of quasi-exactly solvable models and an exact solution has been found.

Recent advances in scalable non-Gaussian geostatistics: The generalized sub-Gaussian model

NASA Astrophysics Data System (ADS)

Guadagnini, Alberto; Riva, Monica; Neuman, Shlomo P.

2018-07-01

Geostatistical analysis has been introduced over half a century ago to allow quantifying seemingly random spatial variations in earth quantities such as rock mineral content or permeability. The traditional approach has been to view such quantities as multivariate Gaussian random functions characterized by one or a few well-defined spatial correlation scales. There is, however, mounting evidence that many spatially varying quantities exhibit non-Gaussian behavior over a multiplicity of scales. The purpose of this minireview is not to paint a broad picture of the subject and its treatment in the literature. Instead, we focus on very recent advances in the recognition and analysis of this ubiquitous phenomenon, which transcends hydrology and the Earth sciences, brought about largely by our own work. In particular, we use porosity data from a deep borehole to illustrate typical aspects of such scalable non-Gaussian behavior, describe a very recent theoretical model that (for the first time) captures all these behavioral aspects in a comprehensive manner, show how this allows generating random realizations of the quantity conditional on sampled values, point toward ways of incorporating scalable non-Gaussian behavior in hydrologic analysis, highlight the significance of doing so, and list open questions requiring further research.

Bayesian spatial transformation models with applications in neuroimaging data.

PubMed

Miranda, Michelle F; Zhu, Hongtu; Ibrahim, Joseph G

2013-12-01

The aim of this article is to develop a class of spatial transformation models (STM) to spatially model the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) and a set of covariates. The proposed STM include a varying Box-Cox transformation model for dealing with the issue of non-Gaussian distributed imaging data and a Gaussian Markov random field model for incorporating spatial smoothness of the imaging data. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. Simulations and real data analysis demonstrate that the STM significantly outperforms the voxel-wise linear model with Gaussian noise in recovering meaningful geometric patterns. Our STM is able to reveal important brain regions with morphological changes in children with attention deficit hyperactivity disorder. © 2013, The International Biometric Society.

Adaptive Gaussian mixture models for pre-screening in GPR data

NASA Astrophysics Data System (ADS)

Torrione, Peter; Morton, Kenneth, Jr.; Besaw, Lance E.

2011-06-01

Due to the large amount of data generated by vehicle-mounted ground penetrating radar (GPR) antennae arrays, advanced feature extraction and classification can only be performed on a small subset of data during real-time operation. As a result, most GPR based landmine detection systems implement "pre-screening" algorithms to processes all of the data generated by the antennae array and identify locations with anomalous signatures for more advanced processing. These pre-screening algorithms must be computationally efficient and obtain high probability of detection, but can permit a false alarm rate which might be higher than the total system requirements. Many approaches to prescreening have previously been proposed, including linear prediction coefficients, the LMS algorithm, and CFAR-based approaches. Similar pre-screening techniques have also been developed in the field of video processing to identify anomalous behavior or anomalous objects. One such algorithm, an online k-means approximation to an adaptive Gaussian mixture model (GMM), is particularly well-suited to application for pre-screening in GPR data due to its computational efficiency, non-linear nature, and relevance of the logic underlying the algorithm to GPR processing. In this work we explore the application of an adaptive GMM-based approach for anomaly detection from the video processing literature to pre-screening in GPR data. Results with the ARA Nemesis landmine detection system demonstrate significant pre-screening performance improvements compared to alternative approaches, and indicate that the proposed algorithm is a complimentary technique to existing methods.

Research in Stochastic Processes and their Applications

DTIC Science & Technology

1993-01-01

goal is to learn how Gaussian and linear signal processing methodologies should be adapted to deal with non-Gaussian regimes. Part III continues the... smoothi fmictions in /I, ami we have a chain C ... C tir C ... C /I’) C 11_ C ... C 1t_, C_ ... C ¢’, 10 4o = fH,; H =H;, H, (Hilbert space). 4ý is a Fr

Testing for the Gaussian nature of cosmological density perturbations through the three-point temperature correlation function

NASA Technical Reports Server (NTRS)

Luo, Xiaochun; Schramm, David N.

1993-01-01

One of the crucial aspects of density perturbations that are produced by the standard inflation scenario is that they are Gaussian where seeds produced by topological defects tend to be non-Gaussian. The three-point correlation function of the temperature anisotropy of the cosmic microwave background radiation (CBR) provides a sensitive test of this aspect of the primordial density field. In this paper, this function is calculated in the general context of various allowed non-Gaussian models. It is shown that the Cosmic Background Explorer and the forthcoming South Pole and balloon CBR anisotropy data may be able to provide a crucial test of the Gaussian nature of the perturbations.

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.

Application of a statistical emulator to fire emission modeling

Treesearch

Marwan Katurji; Jovanka Nikolic; Shiyuan Zhong; Scott Pratt; Lejiang Yu; Warren E. Heilman

2015-01-01

We have demonstrated the use of an advanced Gaussian-Process (GP) emulator to estimate wildland fire emissions over a wide range of fuel and atmospheric conditions. The Fire Emission Production Simulator, or FEPS, is used to produce an initial set of emissions data that correspond to some selected values in the domain of the input fuel and atmospheric parameters for...

Rate Constants for Fine-Structure Excitations in O - H Collisions with Error Bars Obtained by Machine Learning

NASA Astrophysics Data System (ADS)

Vieira, Daniel; Krems, Roman

2017-04-01

Fine-structure transitions in collisions of O(3Pj) with atomic hydrogen are an important cooling mechanism in the interstellar medium; knowledge of the rate coefficients for these transitions has a wide range of astrophysical applications. The accuracy of the theoretical calculation is limited by inaccuracy in the ab initio interaction potentials used in the coupled-channel quantum scattering calculations from which the rate coefficients can be obtained. In this work we use the latest ab initio results for the O(3Pj) + H interaction potentials to improve on previous calculations of the rate coefficients. We further present a machine-learning technique based on Gaussian Process regression to determine the sensitivity of the rate coefficients to variations of the underlying adiabatic interaction potentials. To account for the inaccuracy inherent in the ab initio calculations we compute error bars for the rate coefficients corresponding to 20% variation in each of the interaction potentials. We obtain these error bars by fitting a Gaussian Process model to a data set of potential curves and rate constants. We use the fitted model to do sensitivity analysis, determining the relative importance of individual adiabatic potential curves to a given fine-structure transition. NSERC.

Bayesian nonparametric adaptive control using Gaussian processes.

PubMed

Chowdhary, Girish; Kingravi, Hassan A; How, Jonathan P; Vela, Patricio A

2015-03-01

Most current model reference adaptive control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element is radial basis function networks (RBFNs), with RBF centers preallocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become noneffective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semiglobal in nature. This paper investigates a Gaussian process-based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. The GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed-loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.

Gaussian entanglement generation from coherence using beam-splitters

PubMed Central

Wang, Zhong-Xiao; Wang, Shuhao; Ma, Teng; Wang, Tie-Jun; Wang, Chuan

2016-01-01

The generation and quantification of quantum entanglement is crucial for quantum information processing. Here we study the transition of Gaussian correlation under the effect of linear optical beam-splitters. We find the single-mode Gaussian coherence acts as the resource in generating Gaussian entanglement for two squeezed states as the input states. With the help of consecutive beam-splitters, single-mode coherence and quantum entanglement can be converted to each other. Our results reveal that by using finite number of beam-splitters, it is possible to extract all the entanglement from the single-mode coherence even if the entanglement is wiped out before each beam-splitter. PMID:27892537

Non-Gaussian probabilistic MEG source localisation based on kernel density estimation☆

PubMed Central

Mohseni, Hamid R.; Kringelbach, Morten L.; Woolrich, Mark W.; Baker, Adam; Aziz, Tipu Z.; Probert-Smith, Penny

2014-01-01

There is strong evidence to suggest that data recorded from magnetoencephalography (MEG) follows a non-Gaussian distribution. However, existing standard methods for source localisation model the data using only second order statistics, and therefore use the inherent assumption of a Gaussian distribution. In this paper, we present a new general method for non-Gaussian source estimation of stationary signals for localising brain activity from MEG data. By providing a Bayesian formulation for MEG source localisation, we show that the source probability density function (pdf), which is not necessarily Gaussian, can be estimated using multivariate kernel density estimators. In the case of Gaussian data, the solution of the method is equivalent to that of widely used linearly constrained minimum variance (LCMV) beamformer. The method is also extended to handle data with highly correlated sources using the marginal distribution of the estimated joint distribution, which, in the case of Gaussian measurements, corresponds to the null-beamformer. The proposed non-Gaussian source localisation approach is shown to give better spatial estimates than the LCMV beamformer, both in simulations incorporating non-Gaussian signals, and in real MEG measurements of auditory and visual evoked responses, where the highly correlated sources are known to be difficult to estimate. PMID:24055702

Gaussian or non-Gaussian logconductivity distribution at the MADE site: What is its impact on the breakthrough curve?

PubMed

Fiori, Aldo; Volpi, Elena; Zarlenga, Antonio; Bohling, Geoffrey C

2015-08-01

The impact of the logconductivity (Y=ln K) distribution fY on transport at the MADE site is analyzed. Our principal interest is in non-Gaussian fY characterized by heavier tails than the Gaussian. Both the logconductivity moments and fY itself are inferred, taking advantage of the detailed measurements of Bohling et al. (2012). The resulting logconductivity distribution displays heavier tails than the Gaussian, although the departure from Gaussianity is not significant. The effect of the logconductivity distribution on the breakthrough curve (BTC) is studied through an analytical, physically based model. It is found that the non-Gaussianity of the MADE logconductivity distribution does not strongly affect the BTC. Counterintuitively, assuming heavier tailed distributions for Y, with same variance, leads to BTCs which are more symmetrical than those for the Gaussian fY, with less pronounced preferential flow. Results indicate that the impact of strongly non-Gaussian, heavy tailed distributions on solute transport in heterogeneous porous formations can be significant, especially in the presence of high heterogeneity, resulting in reduced preferential flow and retarded peak arrivals. Copyright © 2015 Elsevier B.V. All rights reserved.

Precision process calibration and CD predictions for low-k1 lithography

NASA Astrophysics Data System (ADS)

Chen, Ting; Park, Sangbong; Berger, Gabriel; Coskun, Tamer H.; de Vocht, Joep; Chen, Fung; Yu, Linda; Hsu, Stephen; van den Broeke, Doug; Socha, Robert; Park, Jungchul; Gronlund, Keith; Davis, Todd; Plachecki, Vince; Harris, Tom; Hansen, Steve; Lambson, Chuck

2005-06-01

Leading resist calibration for sub-0.3 k1 lithography demands accuracy <2nm for CD through pitch. An accurately calibrated resist process is the prerequisite for establishing production-worthy manufacturing under extreme low k1. From an integrated imaging point of view, the following key components must be simultaneously considered during the calibration - high numerical aperture (NA>0.8) imaging characteristics, customized illuminations (measured vs. modeled pupil profiles), resolution enhancement technology (RET) mask with OPC, reticle metrology, and resist thin film substrate. For imaging at NA approaching unity, polarized illumination can impact significantly the contrast formation in the resist film stack, and therefore it is an important factor to consider in the CD-based resist calibration. For aggressive DRAM memory core designs at k1<0.3, pattern-specific illumination optimization has proven to be critical for achieving the required imaging performance. Various optimization techniques from source profile optimization with fixed mask design to the combined source and mask optimization have been considered for customer designs and available imaging capabilities. For successful low-k1 process development, verification of the optimization results can only be made with a sufficiently tunable resist model that can predicate the wafer printing accurately under various optimized process settings. We have developed, for resist patterning under aggressive low-k1 conditions, a novel 3D diffusion model equipped with double-Gaussian convolution in each dimension. Resist calibration with the new diffusion model has demonstrated a fitness and CD predication accuracy that rival or outperform the traditional 3D physical resist models. In this work, we describe our empirical approach to achieving the nm-scale precision for advanced lithography process calibrations, using either measured 1D CD through-pitch or 2D memory core patterns. We show that for ArF imaging, the current resist development and diffusion modeling can readily achieve ~1-2nm max CD errors for common 1D through-pitch and aggressive 2D memory core resist patterns. Sensitivities of the calibrated models to various process parameters are analyzed, including the comparison between the measured and modeled (Gaussian or GRAIL) pupil profiles. We also report our preliminary calibration results under selected polarized illumination conditions.

A Non-Gaussian Stock Price Model: Options, Credit and a Multi-Timescale Memory

NASA Astrophysics Data System (ADS)

Borland, L.

We review a recently proposed model of stock prices, based on astatistical feedback model that results in a non-Gaussian distribution of price changes. Applications to option pricing and the pricing of debt is discussed. A generalization to account for feedback effects over multiple timescales is also presented. This model reproduces most of the stylized facts (ie statistical anomalies) observed in real financial markets.

Mean First Passage Time and Stochastic Resonance in a Transcriptional Regulatory System with Non-Gaussian Noise

NASA Astrophysics Data System (ADS)

Kang, Yan-Mei; Chen, Xi; Lin, Xu-Dong; Tan, Ning

The mean first passage time (MFPT) in a phenomenological gene transcriptional regulatory model with non-Gaussian noise is analytically investigated based on the singular perturbation technique. The effect of the non-Gaussian noise on the phenomenon of stochastic resonance (SR) is then disclosed based on a new combination of adiabatic elimination and linear response approximation. Compared with the results in the Gaussian noise case, it is found that bounded non-Gaussian noise inhibits the transition between different concentrations of protein, while heavy-tailed non-Gaussian noise accelerates the transition. It is also found that the optimal noise intensity for SR in the heavy-tailed noise case is smaller, while the optimal noise intensity in the bounded noise case is larger. These observations can be explained by the heavy-tailed noise easing random transitions.

Test of the cosmic evolution using Gaussian processes

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

Zhang, Ming-Jian; Xia, Jun-Qing, E-mail: zhangmj@ihep.ac.cn, E-mail: xiajq@bnu.edu.cn

2016-12-01

Much focus was on the possible slowing down of cosmic acceleration under the dark energy parametrization. In the present paper, we investigate this subject using the Gaussian processes (GP), without resorting to a particular template of dark energy. The reconstruction is carried out by abundant data including luminosity distance from Union2, Union2.1 compilation and gamma-ray burst, and dynamical Hubble parameter. It suggests that slowing down of cosmic acceleration cannot be presented within 95% C.L., in considering the influence of spatial curvature and Hubble constant. In order to reveal the reason of tension between our reconstruction and previous parametrization constraint formore » Union2 data, we compare them and find that slowing down of acceleration in some parametrization is only a ''mirage'. Although these parameterizations fits well with the observational data, their tension can be revealed by high order derivative of distance D. Instead, GP method is able to faithfully model the cosmic expansion history.« less

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.

An Effective Post-Filtering Framework for 3-D PET Image Denoising Based on Noise and Sensitivity Characteristics

NASA Astrophysics Data System (ADS)

Kim, Ji Hye; Ahn, Il Jun; Nam, Woo Hyun; Ra, Jong Beom

2015-02-01

Positron emission tomography (PET) images usually suffer from a noticeable amount of statistical noise. In order to reduce this noise, a post-filtering process is usually adopted. However, the performance of this approach is limited because the denoising process is mostly performed on the basis of the Gaussian random noise. It has been reported that in a PET image reconstructed by the expectation-maximization (EM), the noise variance of each voxel depends on its mean value, unlike in the case of Gaussian noise. In addition, we observe that the variance also varies with the spatial sensitivity distribution in a PET system, which reflects both the solid angle determined by a given scanner geometry and the attenuation information of a scanned object. Thus, if a post-filtering process based on the Gaussian random noise is applied to PET images without consideration of the noise characteristics along with the spatial sensitivity distribution, the spatially variant non-Gaussian noise cannot be reduced effectively. In the proposed framework, to effectively reduce the noise in PET images reconstructed by the 3-D ordinary Poisson ordered subset EM (3-D OP-OSEM), we first denormalize an image according to the sensitivity of each voxel so that the voxel mean value can represent its statistical properties reliably. Based on our observation that each noisy denormalized voxel has a linear relationship between the mean and variance, we try to convert this non-Gaussian noise image to a Gaussian noise image. We then apply a block matching 4-D algorithm that is optimized for noise reduction of the Gaussian noise image, and reconvert and renormalize the result to obtain a final denoised image. Using simulated phantom data and clinical patient data, we demonstrate that the proposed framework can effectively suppress the noise over the whole region of a PET image while minimizing degradation of the image resolution.

Statistics of Advective Stretching in Three-dimensional Incompressible Flows

NASA Astrophysics Data System (ADS)

Subramanian, Natarajan; Kellogg, Louise H.; Turcotte, Donald L.

2009-09-01

We present a method to quantify kinematic stretching in incompressible, unsteady, isoviscous, three-dimensional flows. We extend the method of Kellogg and Turcotte (J. Geophys. Res. 95:421-432, 1990) to compute the axial stretching/thinning experienced by infinitesimal ellipsoidal strain markers in arbitrary three-dimensional incompressible flows and discuss the differences between our method and the computation of Finite Time Lyapunov Exponent (FTLE). We use the cellular flow model developed in Solomon and Mezic (Nature 425:376-380, 2003) to study the statistics of stretching in a three-dimensional unsteady cellular flow. We find that the probability density function of the logarithm of normalised cumulative stretching (log S) for a globally chaotic flow, with spatially heterogeneous stretching behavior, is not Gaussian and that the coefficient of variation of the Gaussian distribution does not decrease with time as t^{-1/2} . However, it is observed that stretching becomes exponential log S˜ t and the probability density function of log S becomes Gaussian when the time dependence of the flow and its three-dimensionality are increased to make the stretching behaviour of the flow more spatially uniform. We term these behaviors weak and strong chaotic mixing respectively. We find that for strongly chaotic mixing, the coefficient of variation of the Gaussian distribution decreases with time as t^{-1/2} . This behavior is consistent with a random multiplicative stretching process.

Antimicrobial peptides and induced membrane curvature: geometry, coordination chemistry, and molecular engineering

PubMed Central

Schmidt, Nathan W.; Wong, Gerard C. L.

2013-01-01

Short cationic, amphipathic antimicrobial peptides are multi-functional molecules that have roles in host defense as direct microbicides and modulators of the immune response. While a general mechanism of microbicidal activity involves the selective disruption and permeabilization of cell membranes, the relationships between peptide sequence and membrane activity are still under investigation. Here, we review the diverse functions that AMPs collectively have in host defense, and show that these functions can be multiplexed with a membrane mechanism of activity derived from the generation of negative Gaussian membrane curvature. As AMPs preferentially generate this curvature in model bacterial cell membranes, the selective generation of negative Gaussian curvature provides AMPs with a broad mechanism to target microbial membranes. The amino acid constraints placed on AMPs by the geometric requirement to induce negative Gaussian curvature are consistent with known AMP sequences. This ‘saddle-splay curvature selection rule’ is not strongly restrictive so AMPs have significant compositional freedom to multiplex membrane activity with other useful functions. The observation that certain proteins involved in cellular processes which require negative Gaussian curvature contain domains with similar motifs as AMPs, suggests this rule may be applicable to other curvature-generating proteins. Since our saddle-splay curvature design rule is based upon both a mechanism of activity and the existing motifs of natural AMPs, we believe it will assist the development of synthetic antimicrobials. PMID:24778573

Statistics of the geomagnetic secular variation for the past 5Ma

NASA Technical Reports Server (NTRS)

Constable, C. G.; Parker, R. L.

1986-01-01

A new statistical model is proposed for the geomagnetic secular variation over the past 5Ma. Unlike previous models, the model makes use of statistical characteristics of the present day geomagnetic field. The spatial power spectrum of the non-dipole field is consistent with a white source near the core-mantle boundary with Gaussian distribution. After a suitable scaling, the spherical harmonic coefficients may be regarded as statistical samples from a single giant Gaussian process; this is the model of the non-dipole field. The model can be combined with an arbitrary statistical description of the dipole and probability density functions and cumulative distribution functions can be computed for declination and inclination that would be observed at any site on Earth's surface. Global paleomagnetic data spanning the past 5Ma are used to constrain the statistics of the dipole part of the field. A simple model is found to be consistent with the available data. An advantage of specifying the model in terms of the spherical harmonic coefficients is that it is a complete statistical description of the geomagnetic field, enabling us to test specific properties for a general description. Both intensity and directional data distributions may be tested to see if they satisfy the expected model distributions.

Statistics of the geomagnetic secular variation for the past 5 m.y

NASA Technical Reports Server (NTRS)

Constable, C. G.; Parker, R. L.

1988-01-01

A new statistical model is proposed for the geomagnetic secular variation over the past 5Ma. Unlike previous models, the model makes use of statistical characteristics of the present day geomagnetic field. The spatial power spectrum of the non-dipole field is consistent with a white source near the core-mantle boundary with Gaussian distribution. After a suitable scaling, the spherical harmonic coefficients may be regarded as statistical samples from a single giant Gaussian process; this is the model of the non-dipole field. The model can be combined with an arbitrary statistical description of the dipole and probability density functions and cumulative distribution functions can be computed for declination and inclination that would be observed at any site on Earth's surface. Global paleomagnetic data spanning the past 5Ma are used to constrain the statistics of the dipole part of the field. A simple model is found to be consistent with the available data. An advantage of specifying the model in terms of the spherical harmonic coefficients is that it is a complete statistical description of the geomagnetic field, enabling us to test specific properties for a general description. Both intensity and directional data distributions may be tested to see if they satisfy the expected model distributions.