An Application to the Prediction of LOD Change Based on General Regression Neural Network

NASA Astrophysics Data System (ADS)

Zhang, X. H.; Wang, Q. J.; Zhu, J. J.; Zhang, H.

2011-07-01

Traditional prediction of the LOD (length of day) change was based on linear models, such as the least square model and the autoregressive technique, etc. Due to the complex non-linear features of the LOD variation, the performances of the linear model predictors are not fully satisfactory. This paper applies a non-linear neural network - general regression neural network (GRNN) model to forecast the LOD change, and the results are analyzed and compared with those obtained with the back propagation neural network and other models. The comparison shows that the performance of the GRNN model in the prediction of the LOD change is efficient and feasible.

Accuracy assessment of the linear Poisson-Boltzmann equation and reparametrization of the OBC generalized Born model for nucleic acids and nucleic acid-protein complexes.

PubMed

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2015-04-05

The generalized Born model in the Onufriev, Bashford, and Case (Onufriev et al., Proteins: Struct Funct Genet 2004, 55, 383) implementation has emerged as one of the best compromises between accuracy and speed of computation. For simulations of nucleic acids, however, a number of issues should be addressed: (1) the generalized Born model is based on a linear model and the linearization of the reference Poisson-Boltmann equation may be questioned for highly charged systems as nucleic acids; (2) although much attention has been given to potentials, solvation forces could be much less sensitive to linearization than the potentials; and (3) the accuracy of the Onufriev-Bashford-Case (OBC) model for nucleic acids depends on fine tuning of parameters. Here, we show that the linearization of the Poisson Boltzmann equation has mild effects on computed forces, and that with optimal choice of the OBC model parameters, solvation forces, essential for molecular dynamics simulations, agree well with those computed using the reference Poisson-Boltzmann model. © 2015 Wiley Periodicals, Inc.

Application of General Regression Neural Network to the Prediction of LOD Change

NASA Astrophysics Data System (ADS)

Zhang, Xiao-Hong; Wang, Qi-Jie; Zhu, Jian-Jun; Zhang, Hao

2012-01-01

Traditional methods for predicting the change in length of day (LOD change) are mainly based on some linear models, such as the least square model and autoregression model, etc. However, the LOD change comprises complicated non-linear factors and the prediction effect of the linear models is always not so ideal. Thus, a kind of non-linear neural network — general regression neural network (GRNN) model is tried to make the prediction of the LOD change and the result is compared with the predicted results obtained by taking advantage of the BP (back propagation) neural network model and other models. The comparison result shows that the application of the GRNN to the prediction of the LOD change is highly effective and feasible.

A Constrained Linear Estimator for Multiple Regression

ERIC Educational Resources Information Center

Davis-Stober, Clintin P.; Dana, Jason; Budescu, David V.

2010-01-01

"Improper linear models" (see Dawes, Am. Psychol. 34:571-582, "1979"), such as equal weighting, have garnered interest as alternatives to standard regression models. We analyze the general circumstances under which these models perform well by recasting a class of "improper" linear models as "proper" statistical models with a single predictor. We…

Convex set and linear mixing model

NASA Technical Reports Server (NTRS)

Xu, P.; Greeley, R.

1993-01-01

A major goal of optical remote sensing is to determine surface compositions of the earth and other planetary objects. For assessment of composition, single pixels in multi-spectral images usually record a mixture of the signals from various materials within the corresponding surface area. In this report, we introduce a closed and bounded convex set as a mathematical model for linear mixing. This model has a clear geometric implication because the closed and bounded convex set is a natural generalization of a triangle in n-space. The endmembers are extreme points of the convex set. Every point in the convex closure of the endmembers is a linear mixture of those endmembers, which is exactly how linear mixing is defined. With this model, some general criteria for selecting endmembers could be described. This model can lead to a better understanding of linear mixing models.

Derivation of the linear-logistic model and Cox's proportional hazard model from a canonical system description.

PubMed

Voit, E O; Knapp, R G

1997-08-15

The linear-logistic regression model and Cox's proportional hazard model are widely used in epidemiology. Their successful application leaves no doubt that they are accurate reflections of observed disease processes and their associated risks or incidence rates. In spite of their prominence, it is not a priori evident why these models work. This article presents a derivation of the two models from the framework of canonical modeling. It begins with a general description of the dynamics between risk sources and disease development, formulates this description in the canonical representation of an S-system, and shows how the linear-logistic model and Cox's proportional hazard model follow naturally from this representation. The article interprets the model parameters in terms of epidemiological concepts as well as in terms of general systems theory and explains the assumptions and limitations generally accepted in the application of these epidemiological models.

Commentary on the statistical properties of noise and its implication on general linear models in functional near-infrared spectroscopy.

PubMed

Huppert, Theodore J

2016-01-01

Functional near-infrared spectroscopy (fNIRS) is a noninvasive neuroimaging technique that uses low levels of light to measure changes in cerebral blood oxygenation levels. In the majority of NIRS functional brain studies, analysis of this data is based on a statistical comparison of hemodynamic levels between a baseline and task or between multiple task conditions by means of a linear regression model: the so-called general linear model. Although these methods are similar to their implementation in other fields, particularly for functional magnetic resonance imaging, the specific application of these methods in fNIRS research differs in several key ways related to the sources of noise and artifacts unique to fNIRS. In this brief communication, we discuss the application of linear regression models in fNIRS and the modifications needed to generalize these models in order to deal with structured (colored) noise due to systemic physiology and noise heteroscedasticity due to motion artifacts. The objective of this work is to present an overview of these noise properties in the context of the linear model as it applies to fNIRS data. This work is aimed at explaining these mathematical issues to the general fNIRS experimental researcher but is not intended to be a complete mathematical treatment of these concepts.

The Development of Web-based Graphical User Interface for Unified Modeling Data with Multi (Correlated) Responses

NASA Astrophysics Data System (ADS)

Made Tirta, I.; Anggraeni, Dian

2018-04-01

Statistical models have been developed rapidly into various directions to accommodate various types of data. Data collected from longitudinal, repeated measured, clustered data (either continuous, binary, count, or ordinal), are more likely to be correlated. Therefore statistical model for independent responses, such as Generalized Linear Model (GLM), Generalized Additive Model (GAM) are not appropriate. There are several models available to apply for correlated responses including GEEs (Generalized Estimating Equations), for marginal model and various mixed effect model such as GLMM (Generalized Linear Mixed Models) and HGLM (Hierarchical Generalized Linear Models) for subject spesific models. These models are available on free open source software R, but they can only be accessed through command line interface (using scrit). On the othe hand, most practical researchers very much rely on menu based or Graphical User Interface (GUI). We develop, using Shiny framework, standard pull down menu Web-GUI that unifies most models for correlated responses. The Web-GUI has accomodated almost all needed features. It enables users to do and compare various modeling for repeated measure data (GEE, GLMM, HGLM, GEE for nominal responses) much more easily trough online menus. This paper discusses the features of the Web-GUI and illustrates the use of them. In General we find that GEE, GLMM, HGLM gave very closed results.

Linear Logistic Test Modeling with R

ERIC Educational Resources Information Center

Baghaei, Purya; Kubinger, Klaus D.

2015-01-01

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

Defining a Family of Cognitive Diagnosis Models Using Log-Linear Models with Latent Variables

ERIC Educational Resources Information Center

Henson, Robert A.; Templin, Jonathan L.; Willse, John T.

2009-01-01

This paper uses log-linear models with latent variables (Hagenaars, in "Loglinear Models with Latent Variables," 1993) to define a family of cognitive diagnosis models. In doing so, the relationship between many common models is explicitly defined and discussed. In addition, because the log-linear model with latent variables is a general model for…

Posterior propriety for hierarchical models with log-likelihoods that have norm bounds

DOE PAGES

Michalak, Sarah E.; Morris, Carl N.

2015-07-17

Statisticians often use improper priors to express ignorance or to provide good frequency properties, requiring that posterior propriety be verified. Our paper addresses generalized linear mixed models, GLMMs, when Level I parameters have Normal distributions, with many commonly-used hyperpriors. It provides easy-to-verify sufficient posterior propriety conditions based on dimensions, matrix ranks, and exponentiated norm bounds, ENBs, for the Level I likelihood. Since many familiar likelihoods have ENBs, which is often verifiable via log-concavity and MLE finiteness, our novel use of ENBs permits unification of posterior propriety results and posterior MGF/moment results for many useful Level I distributions, including those commonlymore » used with multilevel generalized linear models, e.g., GLMMs and hierarchical generalized linear models, HGLMs. Furthermore, those who need to verify existence of posterior distributions or of posterior MGFs/moments for a multilevel generalized linear model given a proper or improper multivariate F prior as in Section 1 should find the required results in Sections 1 and 2 and Theorem 3 (GLMMs), Theorem 4 (HGLMs), or Theorem 5 (posterior MGFs/moments).« less

A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence.

PubMed

Nikoloulopoulos, Aristidis K

2017-10-01

A bivariate copula mixed model has been recently proposed to synthesize diagnostic test accuracy studies and it has been shown that it is superior to the standard generalized linear mixed model in this context. Here, we call trivariate vine copulas to extend the bivariate meta-analysis of diagnostic test accuracy studies by accounting for disease prevalence. Our vine copula mixed model includes the trivariate generalized linear mixed model as a special case and can also operate on the original scale of sensitivity, specificity, and disease prevalence. Our general methodology is illustrated by re-analyzing the data of two published meta-analyses. Our study suggests that there can be an improvement on trivariate generalized linear mixed model in fit to data and makes the argument for moving to vine copula random effects models especially because of their richness, including reflection asymmetric tail dependence, and computational feasibility despite their three dimensionality.

Modelling female fertility traits in beef cattle using linear and non-linear models.

PubMed

Naya, H; Peñagaricano, F; Urioste, J I

2017-06-01

Female fertility traits are key components of the profitability of beef cattle production. However, these traits are difficult and expensive to measure, particularly under extensive pastoral conditions, and consequently, fertility records are in general scarce and somehow incomplete. Moreover, fertility traits are usually dominated by the effects of herd-year environment, and it is generally assumed that relatively small margins are kept for genetic improvement. New ways of modelling genetic variation in these traits are needed. Inspired in the methodological developments made by Prof. Daniel Gianola and co-workers, we assayed linear (Gaussian), Poisson, probit (threshold), censored Poisson and censored Gaussian models to three different kinds of endpoints, namely calving success (CS), number of days from first calving (CD) and number of failed oestrus (FE). For models involving FE and CS, non-linear models overperformed their linear counterparts. For models derived from CD, linear versions displayed better adjustment than the non-linear counterparts. Non-linear models showed consistently higher estimates of heritability and repeatability in all cases (h 2  < 0.08 and r < 0.13, for linear models; h 2  > 0.23 and r > 0.24, for non-linear models). While additive and permanent environment effects showed highly favourable correlations between all models (>0.789), consistency in selecting the 10% best sires showed important differences, mainly amongst the considered endpoints (FE, CS and CD). In consequence, endpoints should be considered as modelling different underlying genetic effects, with linear models more appropriate to describe CD and non-linear models better for FE and CS. © 2017 Blackwell Verlag GmbH.

Regression Is a Univariate General Linear Model Subsuming Other Parametric Methods as Special Cases.

ERIC Educational Resources Information Center

Vidal, Sherry

Although the concept of the general linear model (GLM) has existed since the 1960s, other univariate analyses such as the t-test and the analysis of variance models have remained popular. The GLM produces an equation that minimizes the mean differences of independent variables as they are related to a dependent variable. From a computer printout…

Non-Linear Approach in Kinesiology Should Be Preferred to the Linear--A Case of Basketball.

PubMed

Trninić, Marko; Jeličić, Mario; Papić, Vladan

2015-07-01

In kinesiology, medicine, biology and psychology, in which research focus is on dynamical self-organized systems, complex connections exist between variables. Non-linear nature of complex systems has been discussed and explained by the example of non-linear anthropometric predictors of performance in basketball. Previous studies interpreted relations between anthropometric features and measures of effectiveness in basketball by (a) using linear correlation models, and by (b) including all basketball athletes in the same sample of participants regardless of their playing position. In this paper the significance and character of linear and non-linear relations between simple anthropometric predictors (AP) and performance criteria consisting of situation-related measures of effectiveness (SE) in basketball were determined and evaluated. The sample of participants consisted of top-level junior basketball players divided in three groups according to their playing time (8 minutes and more per game) and playing position: guards (N = 42), forwards (N = 26) and centers (N = 40). Linear (general model) and non-linear (general model) regression models were calculated simultaneously and separately for each group. The conclusion is viable: non-linear regressions are frequently superior to linear correlations when interpreting actual association logic among research variables.

The Linear Bias in the Zeldovich Approximation and a Relation between the Number Density and the Linear Bias of Dark Halos

NASA Astrophysics Data System (ADS)

Fan, Zuhui

2000-01-01

The linear bias of the dark halos from a model under the Zeldovich approximation is derived and compared with the fitting formula of simulation results. While qualitatively similar to the Press-Schechter formula, this model gives a better description for the linear bias around the turnaround point. This advantage, however, may be compromised by the large uncertainty of the actual behavior of the linear bias near the turnaround point. For a broad class of structure formation models in the cold dark matter framework, a general relation exists between the number density and the linear bias of dark halos. This relation can be readily tested by numerical simulations. Thus, instead of laboriously checking these models one by one, numerical simulation studies can falsify a whole category of models. The general validity of this relation is important in identifying key physical processes responsible for the large-scale structure formation in the universe.

TI-59 Programs for Multiple Regression.

DTIC Science & Technology

1980-05-01

general linear hypothesis model of full rank [ Graybill , 19611 can be written as Y = x 8 + C , s-N(O,o 2I) nxl nxk kxl nxl where Y is the vector of n...a "reduced model " solution, and confidence intervals for linear functions of the coefficients can be obtained using (x’x) and a2, based on the t...O107)l UA.LLL. Library ModuIe NASTER -Puter 0NTINA Cards 1 PROGRAM DESCRIPTION (s s 2 ror the general linear hypothesis model Y - XO + C’ calculates

Development and validation of a general purpose linearization program for rigid aircraft models

NASA Technical Reports Server (NTRS)

Duke, E. L.; Antoniewicz, R. F.

1985-01-01

A FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft models is discussed. The program LINEAR numerically determines a linear systems model using nonlinear equations of motion and a user-supplied, nonlinear aerodynamic model. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model. Also, included in the report is a comparison of linear and nonlinear models for a high performance aircraft.

Do bioclimate variables improve performance of climate envelope models?

USGS Publications Warehouse

Watling, James I.; Romañach, Stephanie S.; Bucklin, David N.; Speroterra, Carolina; Brandt, Laura A.; Pearlstine, Leonard G.; Mazzotti, Frank J.

2012-01-01

Climate envelope models are widely used to forecast potential effects of climate change on species distributions. A key issue in climate envelope modeling is the selection of predictor variables that most directly influence species. To determine whether model performance and spatial predictions were related to the selection of predictor variables, we compared models using bioclimate variables with models constructed from monthly climate data for twelve terrestrial vertebrate species in the southeastern USA using two different algorithms (random forests or generalized linear models), and two model selection techniques (using uncorrelated predictors or a subset of user-defined biologically relevant predictor variables). There were no differences in performance between models created with bioclimate or monthly variables, but one metric of model performance was significantly greater using the random forest algorithm compared with generalized linear models. Spatial predictions between maps using bioclimate and monthly variables were very consistent using the random forest algorithm with uncorrelated predictors, whereas we observed greater variability in predictions using generalized linear models.

Confidence Intervals for Assessing Heterogeneity in Generalized Linear Mixed Models

ERIC Educational Resources Information Center

Wagler, Amy E.

2014-01-01

Generalized linear mixed models are frequently applied to data with clustered categorical outcomes. The effect of clustering on the response is often difficult to practically assess partly because it is reported on a scale on which comparisons with regression parameters are difficult to make. This article proposes confidence intervals for…

Estimation of Complex Generalized Linear Mixed Models for Measurement and Growth

ERIC Educational Resources Information Center

Jeon, Minjeong

2012-01-01

Maximum likelihood (ML) estimation of generalized linear mixed models (GLMMs) is technically challenging because of the intractable likelihoods that involve high dimensional integrations over random effects. The problem is magnified when the random effects have a crossed design and thus the data cannot be reduced to small independent clusters. A…

Application of the Hyper-Poisson Generalized Linear Model for Analyzing Motor Vehicle Crashes.

PubMed

Khazraee, S Hadi; Sáez-Castillo, Antonio Jose; Geedipally, Srinivas Reddy; Lord, Dominique

2015-05-01

The hyper-Poisson distribution can handle both over- and underdispersion, and its generalized linear model formulation allows the dispersion of the distribution to be observation-specific and dependent on model covariates. This study's objective is to examine the potential applicability of a newly proposed generalized linear model framework for the hyper-Poisson distribution in analyzing motor vehicle crash count data. The hyper-Poisson generalized linear model was first fitted to intersection crash data from Toronto, characterized by overdispersion, and then to crash data from railway-highway crossings in Korea, characterized by underdispersion. The results of this study are promising. When fitted to the Toronto data set, the goodness-of-fit measures indicated that the hyper-Poisson model with a variable dispersion parameter provided a statistical fit as good as the traditional negative binomial model. The hyper-Poisson model was also successful in handling the underdispersed data from Korea; the model performed as well as the gamma probability model and the Conway-Maxwell-Poisson model previously developed for the same data set. The advantages of the hyper-Poisson model studied in this article are noteworthy. Unlike the negative binomial model, which has difficulties in handling underdispersed data, the hyper-Poisson model can handle both over- and underdispersed crash data. Although not a major issue for the Conway-Maxwell-Poisson model, the effect of each variable on the expected mean of crashes is easily interpretable in the case of this new model. © 2014 Society for Risk Analysis.

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

PubMed

Wu, Jibo

2016-01-01

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

A methodology for evaluation of parent-mutant competition using a generalized non-linear ecosystem model

Treesearch

Raymond L. Czaplewski

1973-01-01

A generalized, non-linear population dynamics model of an ecosystem is used to investigate the direction of selective pressures upon a mutant by studying the competition between parent and mutant populations. The model has the advantages of considering selection as operating on the phenotype, of retaining the interaction of the mutant population with the ecosystem as a...

Comparison of linear and nonlinear models for coherent hemodynamics spectroscopy (CHS)

NASA Astrophysics Data System (ADS)

Sassaroli, Angelo; Kainerstorfer, Jana; Fantini, Sergio

2015-03-01

A recently proposed linear time-invariant hemodynamic model for coherent hemodynamics spectroscopy1 (CHS) relates the tissue concentrations of oxy- and deoxy-hemoglobin (outputs of the system) to given dynamics of the tissue blood volume, blood flow and rate constant of oxygen diffusion (inputs of the system). This linear model was derived in the limit of "small" perturbations in blood flow velocity. We have extended this model to a more general model (which will be referred to as the nonlinear extension to the original model) that yields the time-dependent changes of oxy and deoxy-hemoglobin concentrations in response to arbitrary dynamic changes in capillary blood flow velocity. The nonlinear extension to the model relies on a general solution of the partial differential equation that governs the spatio-temporal behavior of oxygen saturation of hemoglobin in capillaries and venules on the basis of dynamic (or time resolved) blood transit time. We show preliminary results where the CHS spectra obtained from the linear and nonlinear models are compared to quantify the limits of applicability of the linear model.

A generalized interval fuzzy mixed integer programming model for a multimodal transportation problem under uncertainty

NASA Astrophysics Data System (ADS)

Tian, Wenli; Cao, Chengxuan

2017-03-01

A generalized interval fuzzy mixed integer programming model is proposed for the multimodal freight transportation problem under uncertainty, in which the optimal mode of transport and the optimal amount of each type of freight transported through each path need to be decided. For practical purposes, three mathematical methods, i.e. the interval ranking method, fuzzy linear programming method and linear weighted summation method, are applied to obtain equivalents of constraints and parameters, and then a fuzzy expected value model is presented. A heuristic algorithm based on a greedy criterion and the linear relaxation algorithm are designed to solve the model.

A General Linear Model Approach to Adjusting the Cumulative GPA.

ERIC Educational Resources Information Center

Young, John W.

A general linear model (GLM), using least-squares techniques, was used to develop a criterion measure to replace freshman year grade point average (GPA) in college admission predictive validity studies. Problems with the use of GPA include those associated with the combination of grades from different courses and disciplines into a single measure,…

Genetic parameters for racing records in trotters using linear and generalized linear models.

PubMed

Suontama, M; van der Werf, J H J; Juga, J; Ojala, M

2012-09-01

Heritability and repeatability and genetic and phenotypic correlations were estimated for trotting race records with linear and generalized linear models using 510,519 records on 17,792 Finnhorses and 513,161 records on 25,536 Standardbred trotters. Heritability and repeatability were estimated for single racing time and earnings traits with linear models, and logarithmic scale was used for racing time and fourth-root scale for earnings to correct for nonnormality. Generalized linear models with a gamma distribution were applied for single racing time and with a multinomial distribution for single earnings traits. In addition, genetic parameters for annual earnings were estimated with linear models on the observed and fourth-root scales. Racing success traits of single placings, winnings, breaking stride, and disqualifications were analyzed using generalized linear models with a binomial distribution. Estimates of heritability were greatest for racing time, which ranged from 0.32 to 0.34. Estimates of heritability were low for single earnings with all distributions, ranging from 0.01 to 0.09. Annual earnings were closer to normal distribution than single earnings. Heritability estimates were moderate for annual earnings on the fourth-root scale, 0.19 for Finnhorses and 0.27 for Standardbred trotters. Heritability estimates for binomial racing success variables ranged from 0.04 to 0.12, being greatest for winnings and least for breaking stride. Genetic correlations among racing traits were high, whereas phenotypic correlations were mainly low to moderate, except correlations between racing time and earnings were high. On the basis of a moderate heritability and moderate to high repeatability for racing time and annual earnings, selection of horses for these traits is effective when based on a few repeated records. Because of high genetic correlations, direct selection for racing time and annual earnings would also result in good genetic response in racing success.

Application of conditional moment tests to model checking for generalized linear models.

PubMed

Pan, Wei

2002-06-01

Generalized linear models (GLMs) are increasingly being used in daily data analysis. However, model checking for GLMs with correlated discrete response data remains difficult. In this paper, through a case study on marginal logistic regression using a real data set, we illustrate the flexibility and effectiveness of using conditional moment tests (CMTs), along with other graphical methods, to do model checking for generalized estimation equation (GEE) analyses. Although CMTs provide an array of powerful diagnostic tests for model checking, they were originally proposed in the econometrics literature and, to our knowledge, have never been applied to GEE analyses. CMTs cover many existing tests, including the (generalized) score test for an omitted covariate, as special cases. In summary, we believe that CMTs provide a class of useful model checking tools.

Linear Equating for the NEAT Design: Parameter Substitution Models and Chained Linear Relationship Models

ERIC Educational Resources Information Center

Kane, Michael T.; Mroch, Andrew A.; Suh, Youngsuk; Ripkey, Douglas R.

2009-01-01

This paper analyzes five linear equating models for the "nonequivalent groups with anchor test" (NEAT) design with internal anchors (i.e., the anchor test is part of the full test). The analysis employs a two-dimensional framework. The first dimension contrasts two general approaches to developing the equating relationship. Under a "parameter…

Latent log-linear models for handwritten digit classification.

PubMed

Deselaers, Thomas; Gass, Tobias; Heigold, Georg; Ney, Hermann

2012-06-01

We present latent log-linear models, an extension of log-linear models incorporating latent variables, and we propose two applications thereof: log-linear mixture models and image deformation-aware log-linear models. The resulting models are fully discriminative, can be trained efficiently, and the model complexity can be controlled. Log-linear mixture models offer additional flexibility within the log-linear modeling framework. Unlike previous approaches, the image deformation-aware model directly considers image deformations and allows for a discriminative training of the deformation parameters. Both are trained using alternating optimization. For certain variants, convergence to a stationary point is guaranteed and, in practice, even variants without this guarantee converge and find models that perform well. We tune the methods on the USPS data set and evaluate on the MNIST data set, demonstrating the generalization capabilities of our proposed models. Our models, although using significantly fewer parameters, are able to obtain competitive results with models proposed in the literature.

Linear and Nonlinear Thinking: A Multidimensional Model and Measure

ERIC Educational Resources Information Center

Groves, Kevin S.; Vance, Charles M.

2015-01-01

Building upon previously developed and more general dual-process models, this paper provides empirical support for a multidimensional thinking style construct comprised of linear thinking and multiple dimensions of nonlinear thinking. A self-report assessment instrument (Linear/Nonlinear Thinking Style Profile; LNTSP) is presented and…

Assessing the Tangent Linear Behaviour of Common Tracer Transport Schemes and Their Use in a Linearised Atmospheric General Circulation Model

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Kent, James

2015-01-01

The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5). All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have nonlinear behaviour. The piecewise parabolic method (PPM) with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM) is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.

General linear methods and friends: Toward efficient solutions of multiphysics problems

NASA Astrophysics Data System (ADS)

Sandu, Adrian

2017-07-01

Time dependent multiphysics partial differential equations are of great practical importance as they model diverse phenomena that appear in mechanical and chemical engineering, aeronautics, astrophysics, meteorology and oceanography, financial modeling, environmental sciences, etc. There is no single best time discretization for the complex multiphysics systems of practical interest. We discuss "multimethod" approaches that combine different time steps and discretizations using the rigourous frameworks provided by Partitioned General Linear Methods and Generalize-structure Additive Runge Kutta Methods..

Estimation of Standard Error of Regression Effects in Latent Regression Models Using Binder's Linearization. Research Report. ETS RR-07-09

ERIC Educational Resources Information Center

Li, Deping; Oranje, Andreas

2007-01-01

Two versions of a general method for approximating standard error of regression effect estimates within an IRT-based latent regression model are compared. The general method is based on Binder's (1983) approach, accounting for complex samples and finite populations by Taylor series linearization. In contrast, the current National Assessment of…

Escaping the snare of chronological growth and launching a free curve alternative: general deviance as latent growth model.

PubMed

Wood, Phillip Karl; Jackson, Kristina M

2013-08-01

Researchers studying longitudinal relationships among multiple problem behaviors sometimes characterize autoregressive relationships across constructs as indicating "protective" or "launch" factors or as "developmental snares." These terms are used to indicate that initial or intermediary states of one problem behavior subsequently inhibit or promote some other problem behavior. Such models are contrasted with models of "general deviance" over time in which all problem behaviors are viewed as indicators of a common linear trajectory. When fit of the "general deviance" model is poor and fit of one or more autoregressive models is good, this is taken as support for the inhibitory or enhancing effect of one construct on another. In this paper, we argue that researchers consider competing models of growth before comparing deviance and time-bound models. Specifically, we propose use of the free curve slope intercept (FCSI) growth model (Meredith & Tisak, 1990) as a general model to typify change in a construct over time. The FCSI model includes, as nested special cases, several statistical models often used for prospective data, such as linear slope intercept models, repeated measures multivariate analysis of variance, various one-factor models, and hierarchical linear models. When considering models involving multiple constructs, we argue the construct of "general deviance" can be expressed as a single-trait multimethod model, permitting a characterization of the deviance construct over time without requiring restrictive assumptions about the form of growth over time. As an example, prospective assessments of problem behaviors from the Dunedin Multidisciplinary Health and Development Study (Silva & Stanton, 1996) are considered and contrasted with earlier analyses of Hussong, Curran, Moffitt, and Caspi (2008), which supported launch and snare hypotheses. For antisocial behavior, the FCSI model fit better than other models, including the linear chronometric growth curve model used by Hussong et al. For models including multiple constructs, a general deviance model involving a single trait and multimethod factors (or a corresponding hierarchical factor model) fit the data better than either the "snares" alternatives or the general deviance model previously considered by Hussong et al. Taken together, the analyses support the view that linkages and turning points cannot be contrasted with general deviance models absent additional experimental intervention or control.

Escaping the snare of chronological growth and launching a free curve alternative: General deviance as latent growth model

PubMed Central

WOOD, PHILLIP KARL; JACKSON, KRISTINA M.

2014-01-01

Researchers studying longitudinal relationships among multiple problem behaviors sometimes characterize autoregressive relationships across constructs as indicating “protective” or “launch” factors or as “developmental snares.” These terms are used to indicate that initial or intermediary states of one problem behavior subsequently inhibit or promote some other problem behavior. Such models are contrasted with models of “general deviance” over time in which all problem behaviors are viewed as indicators of a common linear trajectory. When fit of the “general deviance” model is poor and fit of one or more autoregressive models is good, this is taken as support for the inhibitory or enhancing effect of one construct on another. In this paper, we argue that researchers consider competing models of growth before comparing deviance and time-bound models. Specifically, we propose use of the free curve slope intercept (FCSI) growth model (Meredith & Tisak, 1990) as a general model to typify change in a construct over time. The FCSI model includes, as nested special cases, several statistical models often used for prospective data, such as linear slope intercept models, repeated measures multivariate analysis of variance, various one-factor models, and hierarchical linear models. When considering models involving multiple constructs, we argue the construct of “general deviance” can be expressed as a single-trait multimethod model, permitting a characterization of the deviance construct over time without requiring restrictive assumptions about the form of growth over time. As an example, prospective assessments of problem behaviors from the Dunedin Multidisciplinary Health and Development Study (Silva & Stanton, 1996) are considered and contrasted with earlier analyses of Hussong, Curran, Moffitt, and Caspi (2008), which supported launch and snare hypotheses. For antisocial behavior, the FCSI model fit better than other models, including the linear chronometric growth curve model used by Hussong et al. For models including multiple constructs, a general deviance model involving a single trait and multimethod factors (or a corresponding hierarchical factor model) fit the data better than either the “snares” alternatives or the general deviance model previously considered by Hussong et al. Taken together, the analyses support the view that linkages and turning points cannot be contrasted with general deviance models absent additional experimental intervention or control. PMID:23880389

The general linear inverse problem - Implication of surface waves and free oscillations for earth structure.

NASA Technical Reports Server (NTRS)

Wiggins, R. A.

1972-01-01

The discrete general linear inverse problem reduces to a set of m equations in n unknowns. There is generally no unique solution, but we can find k linear combinations of parameters for which restraints are determined. The parameter combinations are given by the eigenvectors of the coefficient matrix. The number k is determined by the ratio of the standard deviations of the observations to the allowable standard deviations in the resulting solution. Various linear combinations of the eigenvectors can be used to determine parameter resolution and information distribution among the observations. Thus we can determine where information comes from among the observations and exactly how it constraints the set of possible models. The application of such analyses to surface-wave and free-oscillation observations indicates that (1) phase, group, and amplitude observations for any particular mode provide basically the same type of information about the model; (2) observations of overtones can enhance the resolution considerably; and (3) the degree of resolution has generally been overestimated for many model determinations made from surface waves.

Estimation and Selection via Absolute Penalized Convex Minimization And Its Multistage Adaptive Applications

PubMed Central

Huang, Jian; Zhang, Cun-Hui

2013-01-01

The ℓ1-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of high-dimensional statistical problems. In this article, we consider a class of weighted ℓ1-penalized estimators for convex loss functions of a general form, including the generalized linear models. We study the estimation, prediction, selection and sparsity properties of the weighted ℓ1-penalized estimator in sparse, high-dimensional settings where the number of predictors p can be much larger than the sample size n. Adaptive Lasso is considered as a special case. A multistage method is developed to approximate concave regularized estimation by applying an adaptive Lasso recursively. We provide prediction and estimation oracle inequalities for single- and multi-stage estimators, a general selection consistency theorem, and an upper bound for the dimension of the Lasso estimator. Important models including the linear regression, logistic regression and log-linear models are used throughout to illustrate the applications of the general results. PMID:24348100

Methodological quality and reporting of generalized linear mixed models in clinical medicine (2000-2012): a systematic review.

PubMed

Casals, Martí; Girabent-Farrés, Montserrat; Carrasco, Josep L

2014-01-01

Modeling count and binary data collected in hierarchical designs have increased the use of Generalized Linear Mixed Models (GLMMs) in medicine. This article presents a systematic review of the application and quality of results and information reported from GLMMs in the field of clinical medicine. A search using the Web of Science database was performed for published original articles in medical journals from 2000 to 2012. The search strategy included the topic "generalized linear mixed models","hierarchical generalized linear models", "multilevel generalized linear model" and as a research domain we refined by science technology. Papers reporting methodological considerations without application, and those that were not involved in clinical medicine or written in English were excluded. A total of 443 articles were detected, with an increase over time in the number of articles. In total, 108 articles fit the inclusion criteria. Of these, 54.6% were declared to be longitudinal studies, whereas 58.3% and 26.9% were defined as repeated measurements and multilevel design, respectively. Twenty-two articles belonged to environmental and occupational public health, 10 articles to clinical neurology, 8 to oncology, and 7 to infectious diseases and pediatrics. The distribution of the response variable was reported in 88% of the articles, predominantly Binomial (n = 64) or Poisson (n = 22). Most of the useful information about GLMMs was not reported in most cases. Variance estimates of random effects were described in only 8 articles (9.2%). The model validation, the method of covariate selection and the method of goodness of fit were only reported in 8.0%, 36.8% and 14.9% of the articles, respectively. During recent years, the use of GLMMs in medical literature has increased to take into account the correlation of data when modeling qualitative data or counts. According to the current recommendations, the quality of reporting has room for improvement regarding the characteristics of the analysis, estimation method, validation, and selection of the model.

A heteroscedastic generalized linear model with a non-normal speed factor for responses and response times.

PubMed

Molenaar, Dylan; Bolsinova, Maria

2017-05-01

In generalized linear modelling of responses and response times, the observed response time variables are commonly transformed to make their distribution approximately normal. A normal distribution for the transformed response times is desirable as it justifies the linearity and homoscedasticity assumptions in the underlying linear model. Past research has, however, shown that the transformed response times are not always normal. Models have been developed to accommodate this violation. In the present study, we propose a modelling approach for responses and response times to test and model non-normality in the transformed response times. Most importantly, we distinguish between non-normality due to heteroscedastic residual variances, and non-normality due to a skewed speed factor. In a simulation study, we establish parameter recovery and the power to separate both effects. In addition, we apply the model to a real data set. © 2017 The Authors. British Journal of Mathematical and Statistical Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.

A simple and exploratory way to determine the mean-variance relationship in generalized linear models.

PubMed

Tsou, Tsung-Shan

2007-03-30

This paper introduces an exploratory way to determine how variance relates to the mean in generalized linear models. This novel method employs the robust likelihood technique introduced by Royall and Tsou.A urinary data set collected by Ginsberg et al. and the fabric data set analysed by Lee and Nelder are considered to demonstrate the applicability and simplicity of the proposed technique. Application of the proposed method could easily reveal a mean-variance relationship that would generally be left unnoticed, or that would require more complex modelling to detect. Copyright (c) 2006 John Wiley & Sons, Ltd.

Symposium on General Linear Model Approach to the Analysis of Experimental Data in Educational Research (Athens, Georgia, June 29-July 1, 1967). Final Report.

ERIC Educational Resources Information Center

Bashaw, W. L., Ed.; Findley, Warren G., Ed.

This volume contains the five major addresses and subsequent discussion from the Symposium on the General Linear Models Approach to the Analysis of Experimental Data in Educational Research, which was held in 1967 in Athens, Georgia. The symposium was designed to produce systematic information, including new methodology, for dissemination to the…

Derivation and definition of a linear aircraft model

NASA Technical Reports Server (NTRS)

Duke, Eugene L.; Antoniewicz, Robert F.; Krambeer, Keith D.

1988-01-01

A linear aircraft model for a rigid aircraft of constant mass flying over a flat, nonrotating earth is derived and defined. The derivation makes no assumptions of reference trajectory or vehicle symmetry. The linear system equations are derived and evaluated along a general trajectory and include both aircraft dynamics and observation variables.

On the Relation between the Linear Factor Model and the Latent Profile Model

ERIC Educational Resources Information Center

Halpin, Peter F.; Dolan, Conor V.; Grasman, Raoul P. P. P.; De Boeck, Paul

2011-01-01

The relationship between linear factor models and latent profile models is addressed within the context of maximum likelihood estimation based on the joint distribution of the manifest variables. Although the two models are well known to imply equivalent covariance decompositions, in general they do not yield equivalent estimates of the…

Phylogenetic mixtures and linear invariants for equal input models.

PubMed

Casanellas, Marta; Steel, Mike

2017-04-01

The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of [Formula: see text] leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987).

MULTIVARIATE LINEAR MIXED MODELS FOR MULTIPLE OUTCOMES. (R824757)

EPA Science Inventory

We propose a multivariate linear mixed (MLMM) for the analysis of multiple outcomes, which generalizes the latent variable model of Sammel and Ryan. The proposed model assumes a flexible correlation structure among the multiple outcomes, and allows a global test of the impact of ...

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

Grenon, Cedric; Lake, Kayll

We generalize the Swiss-cheese cosmologies so as to include nonzero linear momenta of the associated boundary surfaces. The evolution of mass scales in these generalized cosmologies is studied for a variety of models for the background without having to specify any details within the local inhomogeneities. We find that the final effective gravitational mass and size of the evolving inhomogeneities depends on their linear momenta but these properties are essentially unaffected by the details of the background model.

Modeling the frequency of opposing left-turn conflicts at signalized intersections using generalized linear regression models.

PubMed

Zhang, Xin; Liu, Pan; Chen, Yuguang; Bai, Lu; Wang, Wei

2014-01-01

The primary objective of this study was to identify whether the frequency of traffic conflicts at signalized intersections can be modeled. The opposing left-turn conflicts were selected for the development of conflict predictive models. Using data collected at 30 approaches at 20 signalized intersections, the underlying distributions of the conflicts under different traffic conditions were examined. Different conflict-predictive models were developed to relate the frequency of opposing left-turn conflicts to various explanatory variables. The models considered include a linear regression model, a negative binomial model, and separate models developed for four traffic scenarios. The prediction performance of different models was compared. The frequency of traffic conflicts follows a negative binominal distribution. The linear regression model is not appropriate for the conflict frequency data. In addition, drivers behaved differently under different traffic conditions. Accordingly, the effects of conflicting traffic volumes on conflict frequency vary across different traffic conditions. The occurrences of traffic conflicts at signalized intersections can be modeled using generalized linear regression models. The use of conflict predictive models has potential to expand the uses of surrogate safety measures in safety estimation and evaluation.

A Linear Variable-[theta] Model for Measuring Individual Differences in Response Precision

ERIC Educational Resources Information Center

Ferrando, Pere J.

2011-01-01

Models for measuring individual response precision have been proposed for binary and graded responses. However, more continuous formats are quite common in personality measurement and are usually analyzed with the linear factor analysis model. This study extends the general Gaussian person-fluctuation model to the continuous-response case and…

Generalized Path Analysis and Generalized Simultaneous Equations Model for Recursive Systems with Responses of Mixed Types

ERIC Educational Resources Information Center

Tsai, Tien-Lung; Shau, Wen-Yi; Hu, Fu-Chang

2006-01-01

This article generalizes linear path analysis (PA) and simultaneous equations models (SiEM) to deal with mixed responses of different types in a recursive or triangular system. An efficient instrumental variable (IV) method for estimating the structural coefficients of a 2-equation partially recursive generalized path analysis (GPA) model and…

Statistical inference for template aging

NASA Astrophysics Data System (ADS)

Schuckers, Michael E.

2006-04-01

A change in classification error rates for a biometric device is often referred to as template aging. Here we offer two methods for determining whether the effect of time is statistically significant. The first of these is the use of a generalized linear model to determine if these error rates change linearly over time. This approach generalizes previous work assessing the impact of covariates using generalized linear models. The second approach uses of likelihood ratio tests methodology. The focus here is on statistical methods for estimation not the underlying cause of the change in error rates over time. These methodologies are applied to data from the National Institutes of Standards and Technology Biometric Score Set Release 1. The results of these applications are discussed.

Generalized Kapchinskij-Vladimirskij Distribution and Beam Matrix for Phase-Space Manipulations of High-Intensity Beams

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

Chung, Moses; Qin, Hong; Davidson, Ronald C.

In an uncoupled linear lattice system, the Kapchinskij-Vladimirskij (KV) distribution formulated on the basis of the single-particle Courant-Snyder invariants has served as a fundamental theoretical basis for the analyses of the equilibrium, stability, and transport properties of high-intensity beams for the past several decades. Recent applications of high-intensity beams, however, require beam phase-space manipulations by intentionally introducing strong coupling. Here in this Letter, we report the full generalization of the KV model by including all of the linear (both external and space-charge) coupling forces, beam energy variations, and arbitrary emittance partition, which all form essential elements for phase-space manipulations. Themore » new generalized KV model yields spatially uniform density profiles and corresponding linear self-field forces as desired. Finally, the corresponding matrix envelope equations and beam matrix for the generalized KV model provide important new theoretical tools for the detailed design and analysis of high-intensity beam manipulations, for which previous theoretical models are not easily applicable.« less

Generalized Kapchinskij-Vladimirskij Distribution and Beam Matrix for Phase-Space Manipulations of High-Intensity Beams

DOE PAGES

Chung, Moses; Qin, Hong; Davidson, Ronald C.; ...

2016-11-23

In an uncoupled linear lattice system, the Kapchinskij-Vladimirskij (KV) distribution formulated on the basis of the single-particle Courant-Snyder invariants has served as a fundamental theoretical basis for the analyses of the equilibrium, stability, and transport properties of high-intensity beams for the past several decades. Recent applications of high-intensity beams, however, require beam phase-space manipulations by intentionally introducing strong coupling. Here in this Letter, we report the full generalization of the KV model by including all of the linear (both external and space-charge) coupling forces, beam energy variations, and arbitrary emittance partition, which all form essential elements for phase-space manipulations. Themore » new generalized KV model yields spatially uniform density profiles and corresponding linear self-field forces as desired. Finally, the corresponding matrix envelope equations and beam matrix for the generalized KV model provide important new theoretical tools for the detailed design and analysis of high-intensity beam manipulations, for which previous theoretical models are not easily applicable.« less

Aircraft Airframe Cost Estimation Using a Random Coefficients Model

DTIC Science & Technology

1979-12-01

approach will also be used here. 2 Model Formulation Several different types of equations could be used for the basic form of the CER, such as linear ...5) Marcotte developed several CER’s for fighter aircraft airframes using the log- linear model . A plot of the residuals from the CER for recurring...of the natural logarithm. Ordinary Least Squares The ordinary least squares procedure starts with the equation for the general linear model . The

Optical linear algebra processors: noise and error-source modeling.

PubMed

Casasent, D; Ghosh, A

1985-06-01

The modeling of system and component noise and error sources in optical linear algebra processors (OLAP's) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.

Optical linear algebra processors - Noise and error-source modeling

NASA Technical Reports Server (NTRS)

Casasent, D.; Ghosh, A.

1985-01-01

The modeling of system and component noise and error sources in optical linear algebra processors (OLAPs) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.

Artificial Neural Network versus Linear Models Forecasting Doha Stock Market

NASA Astrophysics Data System (ADS)

Yousif, Adil; Elfaki, Faiz

2017-12-01

The purpose of this study is to determine the instability of Doha stock market and develop forecasting models. Linear time series models are used and compared with a nonlinear Artificial Neural Network (ANN) namely Multilayer Perceptron (MLP) Technique. It aims to establish the best useful model based on daily and monthly data which are collected from Qatar exchange for the period starting from January 2007 to January 2015. Proposed models are for the general index of Qatar stock exchange and also for the usages in other several sectors. With the help of these models, Doha stock market index and other various sectors were predicted. The study was conducted by using various time series techniques to study and analyze data trend in producing appropriate results. After applying several models, such as: Quadratic trend model, double exponential smoothing model, and ARIMA, it was concluded that ARIMA (2,2) was the most suitable linear model for the daily general index. However, ANN model was found to be more accurate than time series models.

Electromagnetic axial anomaly in a generalized linear sigma model

NASA Astrophysics Data System (ADS)

Fariborz, Amir H.; Jora, Renata

2017-06-01

We construct the electromagnetic anomaly effective term for a generalized linear sigma model with two chiral nonets, one with a quark-antiquark structure, the other one with a four-quark content. We compute in the leading order of this framework the decays into two photons of six pseudoscalars: π0(137 ), π0(1300 ), η (547 ), η (958 ), η (1295 ) and η (1760 ). Our results agree well with the available experimental data.

Integrable generalizations of non-linear multiple three-wave interaction models

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1989-07-01

Integrable generalizations of multiple three-wave interaction models in terms of r-matrix formulation are investigated. The Lax representations, complete sets of first integrals in involution are constructed, the quantization leading to Gaudin's models is discussed.

Modeling non-linear growth responses to temperature and hydrology in wetland trees

NASA Astrophysics Data System (ADS)

Keim, R.; Allen, S. T.

2016-12-01

Growth responses of wetland trees to flooding and climate variations are difficult to model because they depend on multiple, apparently interacting factors, but are a critical link in hydrological control of wetland carbon budgets. To more generally understand tree growth to hydrological forcing, we modeled non-linear responses of tree ring growth to flooding and climate at sub-annual time steps, using Vaganov-Shashkin response functions. We calibrated the model to six baldcypress tree-ring chronologies from two hydrologically distinct sites in southern Louisiana, and tested several hypotheses of plasticity in wetlands tree responses to interacting environmental variables. The model outperformed traditional multiple linear regression. More importantly, optimized response parameters were generally similar among sites with varying hydrological conditions, suggesting generality to the functions. Model forms that included interacting responses to multiple forcing factors were more effective than were single response functions, indicating the principle of a single limiting factor is not correct in wetlands and both climatic and hydrological variables must be considered in predicting responses to hydrological or climate change.

Modeling Linguistic Variables With Regression Models: Addressing Non-Gaussian Distributions, Non-independent Observations, and Non-linear Predictors With Random Effects and Generalized Additive Models for Location, Scale, and Shape

PubMed Central

Coupé, Christophe

2018-01-01

As statistical approaches are getting increasingly used in linguistics, attention must be paid to the choice of methods and algorithms used. This is especially true since they require assumptions to be satisfied to provide valid results, and because scientific articles still often fall short of reporting whether such assumptions are met. Progress is being, however, made in various directions, one of them being the introduction of techniques able to model data that cannot be properly analyzed with simpler linear regression models. We report recent advances in statistical modeling in linguistics. We first describe linear mixed-effects regression models (LMM), which address grouping of observations, and generalized linear mixed-effects models (GLMM), which offer a family of distributions for the dependent variable. Generalized additive models (GAM) are then introduced, which allow modeling non-linear parametric or non-parametric relationships between the dependent variable and the predictors. We then highlight the possibilities offered by generalized additive models for location, scale, and shape (GAMLSS). We explain how they make it possible to go beyond common distributions, such as Gaussian or Poisson, and offer the appropriate inferential framework to account for ‘difficult’ variables such as count data with strong overdispersion. We also demonstrate how they offer interesting perspectives on data when not only the mean of the dependent variable is modeled, but also its variance, skewness, and kurtosis. As an illustration, the case of phonemic inventory size is analyzed throughout the article. For over 1,500 languages, we consider as predictors the number of speakers, the distance from Africa, an estimation of the intensity of language contact, and linguistic relationships. We discuss the use of random effects to account for genealogical relationships, the choice of appropriate distributions to model count data, and non-linear relationships. Relying on GAMLSS, we assess a range of candidate distributions, including the Sichel, Delaporte, Box-Cox Green and Cole, and Box-Cox t distributions. We find that the Box-Cox t distribution, with appropriate modeling of its parameters, best fits the conditional distribution of phonemic inventory size. We finally discuss the specificities of phoneme counts, weak effects, and how GAMLSS should be considered for other linguistic variables. PMID:29713298

Modeling Linguistic Variables With Regression Models: Addressing Non-Gaussian Distributions, Non-independent Observations, and Non-linear Predictors With Random Effects and Generalized Additive Models for Location, Scale, and Shape.

PubMed

Coupé, Christophe

2018-01-01

As statistical approaches are getting increasingly used in linguistics, attention must be paid to the choice of methods and algorithms used. This is especially true since they require assumptions to be satisfied to provide valid results, and because scientific articles still often fall short of reporting whether such assumptions are met. Progress is being, however, made in various directions, one of them being the introduction of techniques able to model data that cannot be properly analyzed with simpler linear regression models. We report recent advances in statistical modeling in linguistics. We first describe linear mixed-effects regression models (LMM), which address grouping of observations, and generalized linear mixed-effects models (GLMM), which offer a family of distributions for the dependent variable. Generalized additive models (GAM) are then introduced, which allow modeling non-linear parametric or non-parametric relationships between the dependent variable and the predictors. We then highlight the possibilities offered by generalized additive models for location, scale, and shape (GAMLSS). We explain how they make it possible to go beyond common distributions, such as Gaussian or Poisson, and offer the appropriate inferential framework to account for 'difficult' variables such as count data with strong overdispersion. We also demonstrate how they offer interesting perspectives on data when not only the mean of the dependent variable is modeled, but also its variance, skewness, and kurtosis. As an illustration, the case of phonemic inventory size is analyzed throughout the article. For over 1,500 languages, we consider as predictors the number of speakers, the distance from Africa, an estimation of the intensity of language contact, and linguistic relationships. We discuss the use of random effects to account for genealogical relationships, the choice of appropriate distributions to model count data, and non-linear relationships. Relying on GAMLSS, we assess a range of candidate distributions, including the Sichel, Delaporte, Box-Cox Green and Cole, and Box-Cox t distributions. We find that the Box-Cox t distribution, with appropriate modeling of its parameters, best fits the conditional distribution of phonemic inventory size. We finally discuss the specificities of phoneme counts, weak effects, and how GAMLSS should be considered for other linguistic variables.

Real-time Adaptive Control Using Neural Generalized Predictive Control

NASA Technical Reports Server (NTRS)

Haley, Pam; Soloway, Don; Gold, Brian

1999-01-01

The objective of this paper is to demonstrate the feasibility of a Nonlinear Generalized Predictive Control algorithm by showing real-time adaptive control on a plant with relatively fast time-constants. Generalized Predictive Control has classically been used in process control where linear control laws were formulated for plants with relatively slow time-constants. The plant of interest for this paper is a magnetic levitation device that is nonlinear and open-loop unstable. In this application, the reference model of the plant is a neural network that has an embedded nominal linear model in the network weights. The control based on the linear model provides initial stability at the beginning of network training. In using a neural network the control laws are nonlinear and online adaptation of the model is possible to capture unmodeled or time-varying dynamics. Newton-Raphson is the minimization algorithm. Newton-Raphson requires the calculation of the Hessian, but even with this computational expense the low iteration rate make this a viable algorithm for real-time control.

Comparing Regression Coefficients between Nested Linear Models for Clustered Data with Generalized Estimating Equations

ERIC Educational Resources Information Center

Yan, Jun; Aseltine, Robert H., Jr.; Harel, Ofer

2013-01-01

Comparing regression coefficients between models when one model is nested within another is of great practical interest when two explanations of a given phenomenon are specified as linear models. The statistical problem is whether the coefficients associated with a given set of covariates change significantly when other covariates are added into…

Variable Selection with Prior Information for Generalized Linear Models via the Prior LASSO Method.

PubMed

Jiang, Yuan; He, Yunxiao; Zhang, Heping

LASSO is a popular statistical tool often used in conjunction with generalized linear models that can simultaneously select variables and estimate parameters. When there are many variables of interest, as in current biological and biomedical studies, the power of LASSO can be limited. Fortunately, so much biological and biomedical data have been collected and they may contain useful information about the importance of certain variables. This paper proposes an extension of LASSO, namely, prior LASSO (pLASSO), to incorporate that prior information into penalized generalized linear models. The goal is achieved by adding in the LASSO criterion function an additional measure of the discrepancy between the prior information and the model. For linear regression, the whole solution path of the pLASSO estimator can be found with a procedure similar to the Least Angle Regression (LARS). Asymptotic theories and simulation results show that pLASSO provides significant improvement over LASSO when the prior information is relatively accurate. When the prior information is less reliable, pLASSO shows great robustness to the misspecification. We illustrate the application of pLASSO using a real data set from a genome-wide association study.

A comparison of methods for the analysis of binomial clustered outcomes in behavioral research.

PubMed

Ferrari, Alberto; Comelli, Mario

2016-12-01

In behavioral research, data consisting of a per-subject proportion of "successes" and "failures" over a finite number of trials often arise. This clustered binary data are usually non-normally distributed, which can distort inference if the usual general linear model is applied and sample size is small. A number of more advanced methods is available, but they are often technically challenging and a comparative assessment of their performances in behavioral setups has not been performed. We studied the performances of some methods applicable to the analysis of proportions; namely linear regression, Poisson regression, beta-binomial regression and Generalized Linear Mixed Models (GLMMs). We report on a simulation study evaluating power and Type I error rate of these models in hypothetical scenarios met by behavioral researchers; plus, we describe results from the application of these methods on data from real experiments. Our results show that, while GLMMs are powerful instruments for the analysis of clustered binary outcomes, beta-binomial regression can outperform them in a range of scenarios. Linear regression gave results consistent with the nominal level of significance, but was overall less powerful. Poisson regression, instead, mostly led to anticonservative inference. GLMMs and beta-binomial regression are generally more powerful than linear regression; yet linear regression is robust to model misspecification in some conditions, whereas Poisson regression suffers heavily from violations of the assumptions when used to model proportion data. We conclude providing directions to behavioral scientists dealing with clustered binary data and small sample sizes. Copyright © 2016 Elsevier B.V. All rights reserved.

Analyzing longitudinal data with the linear mixed models procedure in SPSS.

PubMed

West, Brady T

2009-09-01

Many applied researchers analyzing longitudinal data share a common misconception: that specialized statistical software is necessary to fit hierarchical linear models (also known as linear mixed models [LMMs], or multilevel models) to longitudinal data sets. Although several specialized statistical software programs of high quality are available that allow researchers to fit these models to longitudinal data sets (e.g., HLM), rapid advances in general purpose statistical software packages have recently enabled analysts to fit these same models when using preferred packages that also enable other more common analyses. One of these general purpose statistical packages is SPSS, which includes a very flexible and powerful procedure for fitting LMMs to longitudinal data sets with continuous outcomes. This article aims to present readers with a practical discussion of how to analyze longitudinal data using the LMMs procedure in the SPSS statistical software package.

Anomaly General Circulation Models.

NASA Astrophysics Data System (ADS)

Navarra, Antonio

The feasibility of the anomaly model is assessed using barotropic and baroclinic models. In the barotropic case, both a stationary and a time-dependent model has been formulated and constructed, whereas only the stationary, linear case is considered in the baroclinic case. Results from the barotropic model indicate that a relation between the stationary solution and the time-averaged non-linear solution exists. The stationary linear baroclinic solution can therefore be considered with some confidence. The linear baroclinic anomaly model poses a formidable mathematical problem because it is necessary to solve a gigantic linear system to obtain the solution. A new method to find solution of large linear system, based on a projection on the Krylov subspace is shown to be successful when applied to the linearized baroclinic anomaly model. The scheme consists of projecting the original linear system on the Krylov subspace, thereby reducing the dimensionality of the matrix to be inverted to obtain the solution. With an appropriate setting of the damping parameters, the iterative Krylov method reaches a solution even using a Krylov subspace ten times smaller than the original space of the problem. This generality allows the treatment of the important problem of linear waves in the atmosphere. A larger class (nonzonally symmetric) of basic states can now be treated for the baroclinic primitive equations. These problem leads to large unsymmetrical linear systems of order 10000 and more which can now be successfully tackled by the Krylov method. The (R7) linear anomaly model is used to investigate extensively the linear response to equatorial and mid-latitude prescribed heating. The results indicate that the solution is deeply affected by the presence of the stationary waves in the basic state. The instability of the asymmetric flows, first pointed out by Simmons et al. (1983), is active also in the baroclinic case. However, the presence of baroclinic processes modifies the dominant response. The most sensitive areas are identified; they correspond to north Japan, the Pole and Greenland regions. A limited set of higher resolution (R15) experiments indicate that this situation is still present and enhanced at higher resolution. The linear anomaly model is also applied to a realistic case. (Abstract shortened with permission of author.).

Bayesian Correction for Misclassification in Multilevel Count Data Models.

PubMed

Nelson, Tyler; Song, Joon Jin; Chin, Yoo-Mi; Stamey, James D

2018-01-01

Covariate misclassification is well known to yield biased estimates in single level regression models. The impact on hierarchical count models has been less studied. A fully Bayesian approach to modeling both the misclassified covariate and the hierarchical response is proposed. Models with a single diagnostic test and with multiple diagnostic tests are considered. Simulation studies show the ability of the proposed model to appropriately account for the misclassification by reducing bias and improving performance of interval estimators. A real data example further demonstrated the consequences of ignoring the misclassification. Ignoring misclassification yielded a model that indicated there was a significant, positive impact on the number of children of females who observed spousal abuse between their parents. When the misclassification was accounted for, the relationship switched to negative, but not significant. Ignoring misclassification in standard linear and generalized linear models is well known to lead to biased results. We provide an approach to extend misclassification modeling to the important area of hierarchical generalized linear models.

Frequency Response of Synthetic Vocal Fold Models with Linear and Nonlinear Material Properties

PubMed Central

Shaw, Stephanie M.; Thomson, Scott L.; Dromey, Christopher; Smith, Simeon

2014-01-01

Purpose The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency during anterior-posterior stretching. Method Three materially linear and three materially nonlinear models were created and stretched up to 10 mm in 1 mm increments. Phonation onset pressure (Pon) and fundamental frequency (F0) at Pon were recorded for each length. Measurements were repeated as the models were relaxed in 1 mm increments back to their resting lengths, and tensile tests were conducted to determine the stress-strain responses of linear versus nonlinear models. Results Nonlinear models demonstrated a more substantial frequency response than did linear models and a more predictable pattern of F0 increase with respect to increasing length (although range was inconsistent across models). Pon generally increased with increasing vocal fold length for nonlinear models, whereas for linear models, Pon decreased with increasing length. Conclusions Nonlinear synthetic models appear to more accurately represent the human vocal folds than linear models, especially with respect to F0 response. PMID:22271874

Frequency response of synthetic vocal fold models with linear and nonlinear material properties.

PubMed

Shaw, Stephanie M; Thomson, Scott L; Dromey, Christopher; Smith, Simeon

2012-10-01

The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency (F0) during anterior-posterior stretching. Three materially linear and 3 materially nonlinear models were created and stretched up to 10 mm in 1-mm increments. Phonation onset pressure (Pon) and F0 at Pon were recorded for each length. Measurements were repeated as the models were relaxed in 1-mm increments back to their resting lengths, and tensile tests were conducted to determine the stress-strain responses of linear versus nonlinear models. Nonlinear models demonstrated a more substantial frequency response than did linear models and a more predictable pattern of F0 increase with respect to increasing length (although range was inconsistent across models). Pon generally increased with increasing vocal fold length for nonlinear models, whereas for linear models, Pon decreased with increasing length. Nonlinear synthetic models appear to more accurately represent the human vocal folds than do linear models, especially with respect to F0 response.

Credibility analysis of risk classes by generalized linear model

NASA Astrophysics Data System (ADS)

Erdemir, Ovgucan Karadag; Sucu, Meral

2016-06-01

In this paper generalized linear model (GLM) and credibility theory which are frequently used in nonlife insurance pricing are combined for reliability analysis. Using full credibility standard, GLM is associated with limited fluctuation credibility approach. Comparison criteria such as asymptotic variance and credibility probability are used to analyze the credibility of risk classes. An application is performed by using one-year claim frequency data of a Turkish insurance company and results of credible risk classes are interpreted.

Evaluation of airborne lidar data to predict vegetation Presence/Absence

USGS Publications Warehouse

Palaseanu-Lovejoy, M.; Nayegandhi, A.; Brock, J.; Woodman, R.; Wright, C.W.

2009-01-01

This study evaluates the capabilities of the Experimental Advanced Airborne Research Lidar (EAARL) in delineating vegetation assemblages in Jean Lafitte National Park, Louisiana. Five-meter-resolution grids of bare earth, canopy height, canopy-reflection ratio, and height of median energy were derived from EAARL data acquired in September 2006. Ground-truth data were collected along transects to assess species composition, canopy cover, and ground cover. To decide which model is more accurate, comparisons of general linear models and generalized additive models were conducted using conventional evaluation methods (i.e., sensitivity, specificity, Kappa statistics, and area under the curve) and two new indexes, net reclassification improvement and integrated discrimination improvement. Generalized additive models were superior to general linear models in modeling presence/absence in training vegetation categories, but no statistically significant differences between the two models were achieved in determining the classification accuracy at validation locations using conventional evaluation methods, although statistically significant improvements in net reclassifications were observed. ?? 2009 Coastal Education and Research Foundation.

Resource Allocation Modelling in Vocational Rehabilitation: A Prototype Developed with the Michigan and Rhode Island VR Agencies.

ERIC Educational Resources Information Center

Leff, H. Stephen; Turner, Ralph R.

This report focuses on the use of linear programming models to address the issues of how vocational rehabilitation (VR) resources should be allocated in order to maximize program efficiency within given resource constraints. A general introduction to linear programming models is first presented that describes the major types of models available,…

On Generalizations of Cochran’s Theorem and Projection Matrices.

DTIC Science & Technology

1980-08-01

Definiteness of the Estimated Dispersion Matrix in a Multivariate Linear Model ," F. Pukelsheim and George P.H. Styan, May 1978. TECHNICAL REPORTS...with applications to the analysis of covariance," Proc. Cambridge Philos. Soc., 30, pp. 178-191. Graybill , F. A. and Marsaglia, G. (1957...34Idempotent matrices and quad- ratic forms in the general linear hypothesis," Ann. Math. Statist., 28, pp. 678-686. Greub, W. (1975). Linear Algebra (4th ed

SCI Identification (SCIDNT) program user's guide. [maximum likelihood method for linear rotorcraft models

NASA Technical Reports Server (NTRS)

1979-01-01

The computer program Linear SCIDNT which evaluates rotorcraft stability and control coefficients from flight or wind tunnel test data is described. It implements the maximum likelihood method to maximize the likelihood function of the parameters based on measured input/output time histories. Linear SCIDNT may be applied to systems modeled by linear constant-coefficient differential equations. This restriction in scope allows the application of several analytical results which simplify the computation and improve its efficiency over the general nonlinear case.

Right-Sizing Statistical Models for Longitudinal Data

PubMed Central

Wood, Phillip K.; Steinley, Douglas; Jackson, Kristina M.

2015-01-01

Arguments are proposed that researchers using longitudinal data should consider more and less complex statistical model alternatives to their initially chosen techniques in an effort to “right-size” the model to the data at hand. Such model comparisons may alert researchers who use poorly fitting overly parsimonious models to more complex better fitting alternatives, and, alternatively, may identify more parsimonious alternatives to overly complex (and perhaps empirically under-identified and/or less powerful) statistical models. A general framework is proposed for considering (often nested) relationships between a variety of psychometric and growth curve models. A three-step approach is proposed in which models are evaluated based on the number and patterning of variance components prior to selection of better-fitting growth models that explain both mean and variation/covariation patterns. The orthogonal, free-curve slope-intercept (FCSI) growth model is considered as a general model which includes, as special cases, many models including the Factor Mean model (FM, McArdle & Epstein, 1987), McDonald's (1967) linearly constrained factor model, Hierarchical Linear Models (HLM), Repeated Measures MANOVA, and the Linear Slope Intercept (LinearSI) Growth Model. The FCSI model, in turn, is nested within the Tuckerized factor model. The approach is illustrated by comparing alternative models in a longitudinal study of children's vocabulary and by comparison of several candidate parametric growth and chronometric models in a Monte Carlo study. PMID:26237507

Right-sizing statistical models for longitudinal data.

PubMed

Wood, Phillip K; Steinley, Douglas; Jackson, Kristina M

2015-12-01

Arguments are proposed that researchers using longitudinal data should consider more and less complex statistical model alternatives to their initially chosen techniques in an effort to "right-size" the model to the data at hand. Such model comparisons may alert researchers who use poorly fitting, overly parsimonious models to more complex, better-fitting alternatives and, alternatively, may identify more parsimonious alternatives to overly complex (and perhaps empirically underidentified and/or less powerful) statistical models. A general framework is proposed for considering (often nested) relationships between a variety of psychometric and growth curve models. A 3-step approach is proposed in which models are evaluated based on the number and patterning of variance components prior to selection of better-fitting growth models that explain both mean and variation-covariation patterns. The orthogonal free curve slope intercept (FCSI) growth model is considered a general model that includes, as special cases, many models, including the factor mean (FM) model (McArdle & Epstein, 1987), McDonald's (1967) linearly constrained factor model, hierarchical linear models (HLMs), repeated-measures multivariate analysis of variance (MANOVA), and the linear slope intercept (linearSI) growth model. The FCSI model, in turn, is nested within the Tuckerized factor model. The approach is illustrated by comparing alternative models in a longitudinal study of children's vocabulary and by comparing several candidate parametric growth and chronometric models in a Monte Carlo study. (c) 2015 APA, all rights reserved).

Low dose radiation risks for women surviving the a-bombs in Japan: generalized additive model.

PubMed

Dropkin, Greg

2016-11-24

Analyses of cancer mortality and incidence in Japanese A-bomb survivors have been used to estimate radiation risks, which are generally higher for women. Relative Risk (RR) is usually modelled as a linear function of dose. Extrapolation from data including high doses predicts small risks at low doses. Generalized Additive Models (GAMs) are flexible methods for modelling non-linear behaviour. GAMs are applied to cancer incidence in female low dose subcohorts, using anonymous public data for the 1958 - 1998 Life Span Study, to test for linearity, explore interactions, adjust for the skewed dose distribution, examine significance below 100 mGy, and estimate risks at 10 mGy. For all solid cancer incidence, RR estimated from 0 - 100 mGy and 0 - 20 mGy subcohorts is significantly raised. The response tapers above 150 mGy. At low doses, RR increases with age-at-exposure and decreases with time-since-exposure, the preferred covariate. Using the empirical cumulative distribution of dose improves model fit, and capacity to detect non-linear responses. RR is elevated over wide ranges of covariate values. Results are stable under simulation, or when removing exceptional data cells, or adjusting neutron RBE. Estimates of Excess RR at 10 mGy using the cumulative dose distribution are 10 - 45 times higher than extrapolations from a linear model fitted to the full cohort. Below 100 mGy, quasipoisson models find significant effects for all solid, squamous, uterus, corpus, and thyroid cancers, and for respiratory cancers when age-at-exposure > 35 yrs. Results for the thyroid are compatible with studies of children treated for tinea capitis, and Chernobyl survivors. Results for the uterus are compatible with studies of UK nuclear workers and the Techa River cohort. Non-linear models find large, significant cancer risks for Japanese women exposed to low dose radiation from the atomic bombings. The risks should be reflected in protection standards.

Generalized linear mixed models with varying coefficients for longitudinal data.

PubMed

Zhang, Daowen

2004-03-01

The routinely assumed parametric functional form in the linear predictor of a generalized linear mixed model for longitudinal data may be too restrictive to represent true underlying covariate effects. We relax this assumption by representing these covariate effects by smooth but otherwise arbitrary functions of time, with random effects used to model the correlation induced by among-subject and within-subject variation. Due to the usually intractable integration involved in evaluating the quasi-likelihood function, the double penalized quasi-likelihood (DPQL) approach of Lin and Zhang (1999, Journal of the Royal Statistical Society, Series B61, 381-400) is used to estimate the varying coefficients and the variance components simultaneously by representing a nonparametric function by a linear combination of fixed effects and random effects. A scaled chi-squared test based on the mixed model representation of the proposed model is developed to test whether an underlying varying coefficient is a polynomial of certain degree. We evaluate the performance of the procedures through simulation studies and illustrate their application with Indonesian children infectious disease data.

Restricted DCJ-indel model: sorting linear genomes with DCJ and indels

PubMed Central

2012-01-01

Background The double-cut-and-join (DCJ) is a model that is able to efficiently sort a genome into another, generalizing the typical mutations (inversions, fusions, fissions, translocations) to which genomes are subject, but allowing the existence of circular chromosomes at the intermediate steps. In the general model many circular chromosomes can coexist in some intermediate step. However, when the compared genomes are linear, it is more plausible to use the so-called restricted DCJ model, in which we proceed the reincorporation of a circular chromosome immediately after its creation. These two consecutive DCJ operations, which create and reincorporate a circular chromosome, mimic a transposition or a block-interchange. When the compared genomes have the same content, it is known that the genomic distance for the restricted DCJ model is the same as the distance for the general model. If the genomes have unequal contents, in addition to DCJ it is necessary to consider indels, which are insertions and deletions of DNA segments. Linear time algorithms were proposed to compute the distance and to find a sorting scenario in a general, unrestricted DCJ-indel model that considers DCJ and indels. Results In the present work we consider the restricted DCJ-indel model for sorting linear genomes with unequal contents. We allow DCJ operations and indels with the following constraint: if a circular chromosome is created by a DCJ, it has to be reincorporated in the next step (no other DCJ or indel can be applied between the creation and the reincorporation of a circular chromosome). We then develop a sorting algorithm and give a tight upper bound for the restricted DCJ-indel distance. Conclusions We have given a tight upper bound for the restricted DCJ-indel distance. The question whether this bound can be reduced so that both the general and the restricted DCJ-indel distances are equal remains open. PMID:23281630

A Refined Model for Radar Homing Intercepts.

DTIC Science & Technology

1983-10-27

Helge Toutenburq, Prior Information in Linear Models ,(Wiley, NY, 1982). 7. F. A. Graybill , Introduction to Matrices with Applications in StatisticF... linear target trajectory model z i = 0 + 1 r i + wi () where w i i=I,..., N is a sequence of uncorrelated zero-mean A noise, the general formula for...z i (i=l,..., N) at r. and a linear regression model 1 z i = a0 + a1 r i + w i =(Al) where wi is the corruption noise; the problem is to estimate a0

Modeling Learning in Doubly Multilevel Binary Longitudinal Data Using Generalized Linear Mixed Models: An Application to Measuring and Explaining Word Learning.

PubMed

Cho, Sun-Joo; Goodwin, Amanda P

2016-04-01

When word learning is supported by instruction in experimental studies for adolescents, word knowledge outcomes tend to be collected from complex data structure, such as multiple aspects of word knowledge, multilevel reader data, multilevel item data, longitudinal design, and multiple groups. This study illustrates how generalized linear mixed models can be used to measure and explain word learning for data having such complexity. Results from this application provide deeper understanding of word knowledge than could be attained from simpler models and show that word knowledge is multidimensional and depends on word characteristics and instructional contexts.

Use of instrumental variables in the analysis of generalized linear models in the presence of unmeasured confounding with applications to epidemiological research.

PubMed

Johnston, K M; Gustafson, P; Levy, A R; Grootendorst, P

2008-04-30

A major, often unstated, concern of researchers carrying out epidemiological studies of medical therapy is the potential impact on validity if estimates of treatment are biased due to unmeasured confounders. One technique for obtaining consistent estimates of treatment effects in the presence of unmeasured confounders is instrumental variables analysis (IVA). This technique has been well developed in the econometrics literature and is being increasingly used in epidemiological studies. However, the approach to IVA that is most commonly used in such studies is based on linear models, while many epidemiological applications make use of non-linear models, specifically generalized linear models (GLMs) such as logistic or Poisson regression. Here we present a simple method for applying IVA within the class of GLMs using the generalized method of moments approach. We explore some of the theoretical properties of the method and illustrate its use within both a simulation example and an epidemiological study where unmeasured confounding is suspected to be present. We estimate the effects of beta-blocker therapy on one-year all-cause mortality after an incident hospitalization for heart failure, in the absence of data describing disease severity, which is believed to be a confounder. 2008 John Wiley & Sons, Ltd

Perfect commuting-operator strategies for linear system games

NASA Astrophysics Data System (ADS)

Cleve, Richard; Liu, Li; Slofstra, William

2017-01-01

Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely presented group associated with the linear system which arises from the non-commutative equations.

Description of a computer program and numerical techniques for developing linear perturbation models from nonlinear systems simulations

NASA Technical Reports Server (NTRS)

Dieudonne, J. E.

1978-01-01

A numerical technique was developed which generates linear perturbation models from nonlinear aircraft vehicle simulations. The technique is very general and can be applied to simulations of any system that is described by nonlinear differential equations. The computer program used to generate these models is discussed, with emphasis placed on generation of the Jacobian matrices, calculation of the coefficients needed for solving the perturbation model, and generation of the solution of the linear differential equations. An example application of the technique to a nonlinear model of the NASA terminal configured vehicle is included.

Generalized linear and generalized additive models in studies of species distributions: Setting the scene

USGS Publications Warehouse

Guisan, Antoine; Edwards, T.C.; Hastie, T.

2002-01-01

An important statistical development of the last 30 years has been the advance in regression analysis provided by generalized linear models (GLMs) and generalized additive models (GAMs). Here we introduce a series of papers prepared within the framework of an international workshop entitled: Advances in GLMs/GAMs modeling: from species distribution to environmental management, held in Riederalp, Switzerland, 6-11 August 2001. We first discuss some general uses of statistical models in ecology, as well as provide a short review of several key examples of the use of GLMs and GAMs in ecological modeling efforts. We next present an overview of GLMs and GAMs, and discuss some of their related statistics used for predictor selection, model diagnostics, and evaluation. Included is a discussion of several new approaches applicable to GLMs and GAMs, such as ridge regression, an alternative to stepwise selection of predictors, and methods for the identification of interactions by a combined use of regression trees and several other approaches. We close with an overview of the papers and how we feel they advance our understanding of their application to ecological modeling. ?? 2002 Elsevier Science B.V. All rights reserved.

Linear Mixed Models: Gum and Beyond

NASA Astrophysics Data System (ADS)

Arendacká, Barbora; Täubner, Angelika; Eichstädt, Sascha; Bruns, Thomas; Elster, Clemens

2014-04-01

In Annex H.5, the Guide to the Evaluation of Uncertainty in Measurement (GUM) [1] recognizes the necessity to analyze certain types of experiments by applying random effects ANOVA models. These belong to the more general family of linear mixed models that we focus on in the current paper. Extending the short introduction provided by the GUM, our aim is to show that the more general, linear mixed models cover a wider range of situations occurring in practice and can be beneficial when employed in data analysis of long-term repeated experiments. Namely, we point out their potential as an aid in establishing an uncertainty budget and as means for gaining more insight into the measurement process. We also comment on computational issues and to make the explanations less abstract, we illustrate all the concepts with the help of a measurement campaign conducted in order to challenge the uncertainty budget in calibration of accelerometers.

Explicit criteria for prioritization of cataract surgery

PubMed Central

Ma Quintana, José; Escobar, Antonio; Bilbao, Amaia

2006-01-01

Background Consensus techniques have been used previously to create explicit criteria to prioritize cataract extraction; however, the appropriateness of the intervention was not included explicitly in previous studies. We developed a prioritization tool for cataract extraction according to the RAND method. Methods Criteria were developed using a modified Delphi panel judgment process. A panel of 11 ophthalmologists was assembled. Ratings were analyzed regarding the level of agreement among panelists. We studied the effect of all variables on the final panel score using general linear and logistic regression models. Priority scoring systems were developed by means of optimal scaling and general linear models. The explicit criteria developed were summarized by means of regression tree analysis. Results Eight variables were considered to create the indications. Of the 310 indications that the panel evaluated, 22.6% were considered high priority, 52.3% intermediate priority, and 25.2% low priority. Agreement was reached for 31.9% of the indications and disagreement for 0.3%. Logistic regression and general linear models showed that the preoperative visual acuity of the cataractous eye, visual function, and anticipated visual acuity postoperatively were the most influential variables. Alternative and simple scoring systems were obtained by optimal scaling and general linear models where the previous variables were also the most important. The decision tree also shows the importance of the previous variables and the appropriateness of the intervention. Conclusion Our results showed acceptable validity as an evaluation and management tool for prioritizing cataract extraction. It also provides easy algorithms for use in clinical practice. PMID:16512893

Competing regression models for longitudinal data.

PubMed

Alencar, Airlane P; Singer, Julio M; Rocha, Francisco Marcelo M

2012-03-01

The choice of an appropriate family of linear models for the analysis of longitudinal data is often a matter of concern for practitioners. To attenuate such difficulties, we discuss some issues that emerge when analyzing this type of data via a practical example involving pretest-posttest longitudinal data. In particular, we consider log-normal linear mixed models (LNLMM), generalized linear mixed models (GLMM), and models based on generalized estimating equations (GEE). We show how some special features of the data, like a nonconstant coefficient of variation, may be handled in the three approaches and evaluate their performance with respect to the magnitude of standard errors of interpretable and comparable parameters. We also show how different diagnostic tools may be employed to identify outliers and comment on available software. We conclude by noting that the results are similar, but that GEE-based models may be preferable when the goal is to compare the marginal expected responses. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Commensurate Priors for Incorporating Historical Information in Clinical Trials Using General and Generalized Linear Models

PubMed Central

Hobbs, Brian P.; Sargent, Daniel J.; Carlin, Bradley P.

2014-01-01

Assessing between-study variability in the context of conventional random-effects meta-analysis is notoriously difficult when incorporating data from only a small number of historical studies. In order to borrow strength, historical and current data are often assumed to be fully homogeneous, but this can have drastic consequences for power and Type I error if the historical information is biased. In this paper, we propose empirical and fully Bayesian modifications of the commensurate prior model (Hobbs et al., 2011) extending Pocock (1976), and evaluate their frequentist and Bayesian properties for incorporating patient-level historical data using general and generalized linear mixed regression models. Our proposed commensurate prior models lead to preposterior admissible estimators that facilitate alternative bias-variance trade-offs than those offered by pre-existing methodologies for incorporating historical data from a small number of historical studies. We also provide a sample analysis of a colon cancer trial comparing time-to-disease progression using a Weibull regression model. PMID:24795786

Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

PubMed

Pei, Soo-Chang; Ding, Jian-Jiun

2005-03-01

Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

A comparative study of generalized linear mixed modelling and artificial neural network approach for the joint modelling of survival and incidence of Dengue patients in Sri Lanka

NASA Astrophysics Data System (ADS)

Hapugoda, J. C.; Sooriyarachchi, M. R.

2017-09-01

Survival time of patients with a disease and the incidence of that particular disease (count) is frequently observed in medical studies with the data of a clustered nature. In many cases, though, the survival times and the count can be correlated in a way that, diseases that occur rarely could have shorter survival times or vice versa. Due to this fact, joint modelling of these two variables will provide interesting and certainly improved results than modelling these separately. Authors have previously proposed a methodology using Generalized Linear Mixed Models (GLMM) by joining the Discrete Time Hazard model with the Poisson Regression model to jointly model survival and count model. As Aritificial Neural Network (ANN) has become a most powerful computational tool to model complex non-linear systems, it was proposed to develop a new joint model of survival and count of Dengue patients of Sri Lanka by using that approach. Thus, the objective of this study is to develop a model using ANN approach and compare the results with the previously developed GLMM model. As the response variables are continuous in nature, Generalized Regression Neural Network (GRNN) approach was adopted to model the data. To compare the model fit, measures such as root mean square error (RMSE), absolute mean error (AME) and correlation coefficient (R) were used. The measures indicate the GRNN model fits the data better than the GLMM model.

Local influence for generalized linear models with missing covariates.

PubMed

Shi, Xiaoyan; Zhu, Hongtu; Ibrahim, Joseph G

2009-12-01

In the analysis of missing data, sensitivity analyses are commonly used to check the sensitivity of the parameters of interest with respect to the missing data mechanism and other distributional and modeling assumptions. In this article, we formally develop a general local influence method to carry out sensitivity analyses of minor perturbations to generalized linear models in the presence of missing covariate data. We examine two types of perturbation schemes (the single-case and global perturbation schemes) for perturbing various assumptions in this setting. We show that the metric tensor of a perturbation manifold provides useful information for selecting an appropriate perturbation. We also develop several local influence measures to identify influential points and test model misspecification. Simulation studies are conducted to evaluate our methods, and real datasets are analyzed to illustrate the use of our local influence measures.

Multilayer neural networks for reduced-rank approximation.

PubMed

Diamantaras, K I; Kung, S Y

1994-01-01

This paper is developed in two parts. First, the authors formulate the solution to the general reduced-rank linear approximation problem relaxing the invertibility assumption of the input autocorrelation matrix used by previous authors. The authors' treatment unifies linear regression, Wiener filtering, full rank approximation, auto-association networks, SVD and principal component analysis (PCA) as special cases. The authors' analysis also shows that two-layer linear neural networks with reduced number of hidden units, trained with the least-squares error criterion, produce weights that correspond to the generalized singular value decomposition of the input-teacher cross-correlation matrix and the input data matrix. As a corollary the linear two-layer backpropagation model with reduced hidden layer extracts an arbitrary linear combination of the generalized singular vector components. Second, the authors investigate artificial neural network models for the solution of the related generalized eigenvalue problem. By introducing and utilizing the extended concept of deflation (originally proposed for the standard eigenvalue problem) the authors are able to find that a sequential version of linear BP can extract the exact generalized eigenvector components. The advantage of this approach is that it's easier to update the model structure by adding one more unit or pruning one or more units when the application requires it. An alternative approach for extracting the exact components is to use a set of lateral connections among the hidden units trained in such a way as to enforce orthogonality among the upper- and lower-layer weights. The authors call this the lateral orthogonalization network (LON) and show via theoretical analysis-and verify via simulation-that the network extracts the desired components. The advantage of the LON-based model is that it can be applied in a parallel fashion so that the components are extracted concurrently. Finally, the authors show the application of their results to the solution of the identification problem of systems whose excitation has a non-invertible autocorrelation matrix. Previous identification methods usually rely on the invertibility assumption of the input autocorrelation, therefore they can not be applied to this case.

Dimensional Reduction for the General Markov Model on Phylogenetic Trees.

PubMed

Sumner, Jeremy G

2017-03-01

We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables (site pattern counts) reduces the dimensionality of the model from exponential in the number of extant taxa, to quadratic in the number of taxa, while retaining the ability to statistically identify phylogenetic divergence events. A key feature is the identification of an invariant subspace which depends only bilinearly on the model parameters, in contrast to the usual multi-linear dependence in the full space. We discuss potential applications including the computation of split (edge) weights on phylogenetic trees from observed sequence data.

Linear approximations of nonlinear systems

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Su, R.

1983-01-01

The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model.

Modification of 2-D Time-Domain Shallow Water Wave Equation using Asymptotic Expansion Method

NASA Astrophysics Data System (ADS)

Khairuman, Teuku; Nasruddin, MN; Tulus; Ramli, Marwan

2018-01-01

Generally, research on the tsunami wave propagation model can be conducted by using a linear model of shallow water theory, where a non-linear side on high order is ignored. In line with research on the investigation of the tsunami waves, the Boussinesq equation model underwent a change aimed to obtain an improved quality of the dispersion relation and non-linearity by increasing the order to be higher. To solve non-linear sides at high order is used a asymptotic expansion method. This method can be used to solve non linear partial differential equations. In the present work, we found that this method needs much computational time and memory with the increase of the number of elements.

Structural Equation Modeling: A Framework for Ocular and Other Medical Sciences Research

PubMed Central

Christ, Sharon L.; Lee, David J.; Lam, Byron L.; Diane, Zheng D.

2017-01-01

Structural equation modeling (SEM) is a modeling framework that encompasses many types of statistical models and can accommodate a variety of estimation and testing methods. SEM has been used primarily in social sciences but is increasingly used in epidemiology, public health, and the medical sciences. SEM provides many advantages for the analysis of survey and clinical data, including the ability to model latent constructs that may not be directly observable. Another major feature is simultaneous estimation of parameters in systems of equations that may include mediated relationships, correlated dependent variables, and in some instances feedback relationships. SEM allows for the specification of theoretically holistic models because multiple and varied relationships may be estimated together in the same model. SEM has recently expanded by adding generalized linear modeling capabilities that include the simultaneous estimation of parameters of different functional form for outcomes with different distributions in the same model. Therefore, mortality modeling and other relevant health outcomes may be evaluated. Random effects estimation using latent variables has been advanced in the SEM literature and software. In addition, SEM software has increased estimation options. Therefore, modern SEM is quite general and includes model types frequently used by health researchers, including generalized linear modeling, mixed effects linear modeling, and population average modeling. This article does not present any new information. It is meant as an introduction to SEM and its uses in ocular and other health research. PMID:24467557

Deformation-Aware Log-Linear Models

NASA Astrophysics Data System (ADS)

Gass, Tobias; Deselaers, Thomas; Ney, Hermann

In this paper, we present a novel deformation-aware discriminative model for handwritten digit recognition. Unlike previous approaches our model directly considers image deformations and allows discriminative training of all parameters, including those accounting for non-linear transformations of the image. This is achieved by extending a log-linear framework to incorporate a latent deformation variable. The resulting model has an order of magnitude less parameters than competing approaches to handling image deformations. We tune and evaluate our approach on the USPS task and show its generalization capabilities by applying the tuned model to the MNIST task. We gain interesting insights and achieve highly competitive results on both tasks.

Further advances in predicting species distributions

Treesearch

Gretchen G. Moisen; Thomas C. Edwards; Patrick E. Osborne

2006-01-01

In 2001, a workshop focused on the use of generalized linear models (GLM: McCullagh and Nelder, 1989) and generalized additive models (GAM: Hastie and Tibshirani, 1986, 1990) for predicting species distributions was held in Riederalp, Switzerland. This topic led to the publication of special issues in Ecological Modelling (Guisan et al., 2002) and Biodiversity and...

Non-linear regime of the Generalized Minimal Massive Gravity in critical points

NASA Astrophysics Data System (ADS)

Setare, M. R.; Adami, H.

2016-03-01

The Generalized Minimal Massive Gravity (GMMG) theory is realized by adding the CS deformation term, the higher derivative deformation term, and an extra term to pure Einstein gravity with a negative cosmological constant. In the present paper we obtain exact solutions to the GMMG field equations in the non-linear regime of the model. GMMG model about AdS_3 space is conjectured to be dual to a 2-dimensional CFT. We study the theory in critical points corresponding to the central charges c_-=0 or c_+=0, in the non-linear regime. We show that AdS_3 wave solutions are present, and have logarithmic form in critical points. Then we study the AdS_3 non-linear deformation solution. Furthermore we obtain logarithmic deformation of extremal BTZ black hole. After that using Abbott-Deser-Tekin method we calculate the energy and angular momentum of these types of black hole solutions.

Testing concordance of instrumental variable effects in generalized linear models with application to Mendelian randomization

PubMed Central

Dai, James Y.; Chan, Kwun Chuen Gary; Hsu, Li

2014-01-01

Instrumental variable regression is one way to overcome unmeasured confounding and estimate causal effect in observational studies. Built on structural mean models, there has been considerale work recently developed for consistent estimation of causal relative risk and causal odds ratio. Such models can sometimes suffer from identification issues for weak instruments. This hampered the applicability of Mendelian randomization analysis in genetic epidemiology. When there are multiple genetic variants available as instrumental variables, and causal effect is defined in a generalized linear model in the presence of unmeasured confounders, we propose to test concordance between instrumental variable effects on the intermediate exposure and instrumental variable effects on the disease outcome, as a means to test the causal effect. We show that a class of generalized least squares estimators provide valid and consistent tests of causality. For causal effect of a continuous exposure on a dichotomous outcome in logistic models, the proposed estimators are shown to be asymptotically conservative. When the disease outcome is rare, such estimators are consistent due to the log-linear approximation of the logistic function. Optimality of such estimators relative to the well-known two-stage least squares estimator and the double-logistic structural mean model is further discussed. PMID:24863158

Genomic prediction based on data from three layer lines using non-linear regression models.

PubMed

Huang, Heyun; Windig, Jack J; Vereijken, Addie; Calus, Mario P L

2014-11-06

Most studies on genomic prediction with reference populations that include multiple lines or breeds have used linear models. Data heterogeneity due to using multiple populations may conflict with model assumptions used in linear regression methods. In an attempt to alleviate potential discrepancies between assumptions of linear models and multi-population data, two types of alternative models were used: (1) a multi-trait genomic best linear unbiased prediction (GBLUP) model that modelled trait by line combinations as separate but correlated traits and (2) non-linear models based on kernel learning. These models were compared to conventional linear models for genomic prediction for two lines of brown layer hens (B1 and B2) and one line of white hens (W1). The three lines each had 1004 to 1023 training and 238 to 240 validation animals. Prediction accuracy was evaluated by estimating the correlation between observed phenotypes and predicted breeding values. When the training dataset included only data from the evaluated line, non-linear models yielded at best a similar accuracy as linear models. In some cases, when adding a distantly related line, the linear models showed a slight decrease in performance, while non-linear models generally showed no change in accuracy. When only information from a closely related line was used for training, linear models and non-linear radial basis function (RBF) kernel models performed similarly. The multi-trait GBLUP model took advantage of the estimated genetic correlations between the lines. Combining linear and non-linear models improved the accuracy of multi-line genomic prediction. Linear models and non-linear RBF models performed very similarly for genomic prediction, despite the expectation that non-linear models could deal better with the heterogeneous multi-population data. This heterogeneity of the data can be overcome by modelling trait by line combinations as separate but correlated traits, which avoids the occasional occurrence of large negative accuracies when the evaluated line was not included in the training dataset. Furthermore, when using a multi-line training dataset, non-linear models provided information on the genotype data that was complementary to the linear models, which indicates that the underlying data distributions of the three studied lines were indeed heterogeneous.

A generalized linear factor model approach to the hierarchical framework for responses and response times.

PubMed

Molenaar, Dylan; Tuerlinckx, Francis; van der Maas, Han L J

2015-05-01

We show how the hierarchical model for responses and response times as developed by van der Linden (2007), Fox, Klein Entink, and van der Linden (2007), Klein Entink, Fox, and van der Linden (2009), and Glas and van der Linden (2010) can be simplified to a generalized linear factor model with only the mild restriction that there is no hierarchical model at the item side. This result is valuable as it enables all well-developed modelling tools and extensions that come with these methods. We show that the restriction we impose on the hierarchical model does not influence parameter recovery under realistic circumstances. In addition, we present two illustrative real data analyses to demonstrate the practical benefits of our approach. © 2014 The British Psychological Society.

Normality of raw data in general linear models: The most widespread myth in statistics

USGS Publications Warehouse

Kery, Marc; Hatfield, Jeff S.

2003-01-01

In years of statistical consulting for ecologists and wildlife biologists, by far the most common misconception we have come across has been the one about normality in general linear models. These comprise a very large part of the statistical models used in ecology and include t tests, simple and multiple linear regression, polynomial regression, and analysis of variance (ANOVA) and covariance (ANCOVA). There is a widely held belief that the normality assumption pertains to the raw data rather than to the model residuals. We suspect that this error may also occur in countless published studies, whenever the normality assumption is tested prior to analysis. This may lead to the use of nonparametric alternatives (if there are any), when parametric tests would indeed be appropriate, or to use of transformations of raw data, which may introduce hidden assumptions such as multiplicative effects on the natural scale in the case of log-transformed data. Our aim here is to dispel this myth. We very briefly describe relevant theory for two cases of general linear models to show that the residuals need to be normally distributed if tests requiring normality are to be used, such as t and F tests. We then give two examples demonstrating that the distribution of the response variable may be nonnormal, and yet the residuals are well behaved. We do not go into the issue of how to test normality; instead we display the distributions of response variables and residuals graphically.

Order Selection for General Expression of Nonlinear Autoregressive Model Based on Multivariate Stepwise Regression

NASA Astrophysics Data System (ADS)

Shi, Jinfei; Zhu, Songqing; Chen, Ruwen

2017-12-01

An order selection method based on multiple stepwise regressions is proposed for General Expression of Nonlinear Autoregressive model which converts the model order problem into the variable selection of multiple linear regression equation. The partial autocorrelation function is adopted to define the linear term in GNAR model. The result is set as the initial model, and then the nonlinear terms are introduced gradually. Statistics are chosen to study the improvements of both the new introduced and originally existed variables for the model characteristics, which are adopted to determine the model variables to retain or eliminate. So the optimal model is obtained through data fitting effect measurement or significance test. The simulation and classic time-series data experiment results show that the method proposed is simple, reliable and can be applied to practical engineering.

Fuzzy branching temporal logic.

PubMed

Moon, Seong-ick; Lee, Kwang H; Lee, Doheon

2004-04-01

Intelligent systems require a systematic way to represent and handle temporal information containing uncertainty. In particular, a logical framework is needed that can represent uncertain temporal information and its relationships with logical formulae. Fuzzy linear temporal logic (FLTL), a generalization of propositional linear temporal logic (PLTL) with fuzzy temporal events and fuzzy temporal states defined on a linear time model, was previously proposed for this purpose. However, many systems are best represented by branching time models in which each state can have more than one possible future path. In this paper, fuzzy branching temporal logic (FBTL) is proposed to address this problem. FBTL adopts and generalizes concurrent tree logic (CTL*), which is a classical branching temporal logic. The temporal model of FBTL is capable of representing fuzzy temporal events and fuzzy temporal states, and the order relation among them is represented as a directed graph. The utility of FBTL is demonstrated using a fuzzy job shop scheduling problem as an example.

Exact solutions of the Navier-Stokes equations generalized for flow in porous media

NASA Astrophysics Data System (ADS)

Daly, Edoardo; Basser, Hossein; Rudman, Murray

2018-05-01

Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.

Meta-analysis of studies with bivariate binary outcomes: a marginal beta-binomial model approach

PubMed Central

Chen, Yong; Hong, Chuan; Ning, Yang; Su, Xiao

2018-01-01

When conducting a meta-analysis of studies with bivariate binary outcomes, challenges arise when the within-study correlation and between-study heterogeneity should be taken into account. In this paper, we propose a marginal beta-binomial model for the meta-analysis of studies with binary outcomes. This model is based on the composite likelihood approach, and has several attractive features compared to the existing models such as bivariate generalized linear mixed model (Chu and Cole, 2006) and Sarmanov beta-binomial model (Chen et al., 2012). The advantages of the proposed marginal model include modeling the probabilities in the original scale, not requiring any transformation of probabilities or any link function, having closed-form expression of likelihood function, and no constraints on the correlation parameter. More importantly, since the marginal beta-binomial model is only based on the marginal distributions, it does not suffer from potential misspecification of the joint distribution of bivariate study-specific probabilities. Such misspecification is difficult to detect and can lead to biased inference using currents methods. We compare the performance of the marginal beta-binomial model with the bivariate generalized linear mixed model and the Sarmanov beta-binomial model by simulation studies. Interestingly, the results show that the marginal beta-binomial model performs better than the Sarmanov beta-binomial model, whether or not the true model is Sarmanov beta-binomial, and the marginal beta-binomial model is more robust than the bivariate generalized linear mixed model under model misspecifications. Two meta-analyses of diagnostic accuracy studies and a meta-analysis of case-control studies are conducted for illustration. PMID:26303591

Global identifiability of linear compartmental models--a computer algebra algorithm.

PubMed

Audoly, S; D'Angiò, L; Saccomani, M P; Cobelli, C

1998-01-01

A priori global identifiability deals with the uniqueness of the solution for the unknown parameters of a model and is, thus, a prerequisite for parameter estimation of biological dynamic models. Global identifiability is however difficult to test, since it requires solving a system of algebraic nonlinear equations which increases both in nonlinearity degree and number of terms and unknowns with increasing model order. In this paper, a computer algebra tool, GLOBI (GLOBal Identifiability) is presented, which combines the topological transfer function method with the Buchberger algorithm, to test global identifiability of linear compartmental models. GLOBI allows for the automatic testing of a priori global identifiability of general structure compartmental models from general multi input-multi output experiments. Examples of usage of GLOBI to analyze a priori global identifiability of some complex biological compartmental models are provided.

Flexible Approaches to Computing Mediated Effects in Generalized Linear Models: Generalized Estimating Equations and Bootstrapping

ERIC Educational Resources Information Center

Schluchter, Mark D.

2008-01-01

In behavioral research, interest is often in examining the degree to which the effect of an independent variable X on an outcome Y is mediated by an intermediary or mediator variable M. This article illustrates how generalized estimating equations (GEE) modeling can be used to estimate the indirect or mediated effect, defined as the amount by…

Real-time imaging of human brain function by near-infrared spectroscopy using an adaptive general linear model

PubMed Central

Abdelnour, A. Farras; Huppert, Theodore

2009-01-01

Near-infrared spectroscopy is a non-invasive neuroimaging method which uses light to measure changes in cerebral blood oxygenation associated with brain activity. In this work, we demonstrate the ability to record and analyze images of brain activity in real-time using a 16-channel continuous wave optical NIRS system. We propose a novel real-time analysis framework using an adaptive Kalman filter and a state–space model based on a canonical general linear model of brain activity. We show that our adaptive model has the ability to estimate single-trial brain activity events as we apply this method to track and classify experimental data acquired during an alternating bilateral self-paced finger tapping task. PMID:19457389

On Fitting Generalized Linear Mixed-effects Models for Binary Responses using Different Statistical Packages

PubMed Central

Zhang, Hui; Lu, Naiji; Feng, Changyong; Thurston, Sally W.; Xia, Yinglin; Tu, Xin M.

2011-01-01

Summary The generalized linear mixed-effects model (GLMM) is a popular paradigm to extend models for cross-sectional data to a longitudinal setting. When applied to modeling binary responses, different software packages and even different procedures within a package may give quite different results. In this report, we describe the statistical approaches that underlie these different procedures and discuss their strengths and weaknesses when applied to fit correlated binary responses. We then illustrate these considerations by applying these procedures implemented in some popular software packages to simulated and real study data. Our simulation results indicate a lack of reliability for most of the procedures considered, which carries significant implications for applying such popular software packages in practice. PMID:21671252

Gain optimization with non-linear controls

NASA Technical Reports Server (NTRS)

Slater, G. L.; Kandadai, R. D.

1984-01-01

An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.

A General Approach to Causal Mediation Analysis

ERIC Educational Resources Information Center

Imai, Kosuke; Keele, Luke; Tingley, Dustin

2010-01-01

Traditionally in the social sciences, causal mediation analysis has been formulated, understood, and implemented within the framework of linear structural equation models. We argue and demonstrate that this is problematic for 3 reasons: the lack of a general definition of causal mediation effects independent of a particular statistical model, the…

Robust Weak Chimeras in Oscillator Networks with Delayed Linear and Quadratic Interactions

NASA Astrophysics Data System (ADS)

Bick, Christian; Sebek, Michael; Kiss, István Z.

2017-10-01

We present an approach to generate chimera dynamics (localized frequency synchrony) in oscillator networks with two populations of (at least) two elements using a general method based on a delayed interaction with linear and quadratic terms. The coupling design yields robust chimeras through a phase-model-based design of the delay and the ratio of linear and quadratic components of the interactions. We demonstrate the method in the Brusselator model and experiments with electrochemical oscillators. The technique opens the way to directly bridge chimera dynamics in phase models and real-world oscillator networks.

High Fidelity Modeling of Field Reversed Configuration (FRC) Thrusters

DTIC Science & Technology

2017-04-22

signatures which can be used for direct, non -invasive, comparison with experimental diagnostics can be produced. This research will be directly... experimental campaign is critical to developing general design philosophies for low-power plasmoid formation, the complexity of non -linear plasma processes...advanced space propulsion. The work consists of numerical method development, physical model development, and systematic studies of the non -linear

Spatially resolved regression analysis of pre-treatment FDG, FLT and Cu-ATSM PET from post-treatment FDG PET: an exploratory study

PubMed Central

Bowen, Stephen R; Chappell, Richard J; Bentzen, Søren M; Deveau, Michael A; Forrest, Lisa J; Jeraj, Robert

2012-01-01

Purpose To quantify associations between pre-radiotherapy and post-radiotherapy PET parameters via spatially resolved regression. Materials and methods Ten canine sinonasal cancer patients underwent PET/CT scans of [18F]FDG (FDGpre), [18F]FLT (FLTpre), and [61Cu]Cu-ATSM (Cu-ATSMpre). Following radiotherapy regimens of 50 Gy in 10 fractions, veterinary patients underwent FDG PET/CT scans at three months (FDGpost). Regression of standardized uptake values in baseline FDGpre, FLTpre and Cu-ATSMpre tumour voxels to those in FDGpost images was performed for linear, log-linear, generalized-linear and mixed-fit linear models. Goodness-of-fit in regression coefficients was assessed by R2. Hypothesis testing of coefficients over the patient population was performed. Results Multivariate linear model fits of FDGpre to FDGpost were significantly positive over the population (FDGpost~0.17 FDGpre, p=0.03), and classified slopes of RECIST non-responders and responders to be different (0.37 vs. 0.07, p=0.01). Generalized-linear model fits related FDGpre to FDGpost by a linear power law (FDGpost~FDGpre0.93, p<0.001). Univariate mixture model fits of FDGpre improved R2 from 0.17 to 0.52. Neither baseline FLT PET nor Cu-ATSM PET uptake contributed statistically significant multivariate regression coefficients. Conclusions Spatially resolved regression analysis indicates that pre-treatment FDG PET uptake is most strongly associated with three-month post-treatment FDG PET uptake in this patient population, though associations are histopathology-dependent. PMID:22682748

A generalized linear integrate-and-fire neural model produces diverse spiking behaviors.

PubMed

Mihalaş, Stefan; Niebur, Ernst

2009-03-01

For simulations of neural networks, there is a trade-off between the size of the network that can be simulated and the complexity of the model used for individual neurons. In this study, we describe a generalization of the leaky integrate-and-fire model that produces a wide variety of spiking behaviors while still being analytically solvable between firings. For different parameter values, the model produces spiking or bursting, tonic, phasic or adapting responses, depolarizing or hyperpolarizing after potentials and so forth. The model consists of a diagonalizable set of linear differential equations describing the time evolution of membrane potential, a variable threshold, and an arbitrary number of firing-induced currents. Each of these variables is modified by an update rule when the potential reaches threshold. The variables used are intuitive and have biological significance. The model's rich behavior does not come from the differential equations, which are linear, but rather from complex update rules. This single-neuron model can be implemented using algorithms similar to the standard integrate-and-fire model. It is a natural match with event-driven algorithms for which the firing times are obtained as a solution of a polynomial equation.

Modeling exposure–lag–response associations with distributed lag non-linear models

PubMed Central

Gasparrini, Antonio

2014-01-01

In biomedical research, a health effect is frequently associated with protracted exposures of varying intensity sustained in the past. The main complexity of modeling and interpreting such phenomena lies in the additional temporal dimension needed to express the association, as the risk depends on both intensity and timing of past exposures. This type of dependency is defined here as exposure–lag–response association. In this contribution, I illustrate a general statistical framework for such associations, established through the extension of distributed lag non-linear models, originally developed in time series analysis. This modeling class is based on the definition of a cross-basis, obtained by the combination of two functions to flexibly model linear or nonlinear exposure-responses and the lag structure of the relationship, respectively. The methodology is illustrated with an example application to cohort data and validated through a simulation study. This modeling framework generalizes to various study designs and regression models, and can be applied to study the health effects of protracted exposures to environmental factors, drugs or carcinogenic agents, among others. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24027094

Detecting treatment-subgroup interactions in clustered data with generalized linear mixed-effects model trees.

PubMed

Fokkema, M; Smits, N; Zeileis, A; Hothorn, T; Kelderman, H

2017-10-25

Identification of subgroups of patients for whom treatment A is more effective than treatment B, and vice versa, is of key importance to the development of personalized medicine. Tree-based algorithms are helpful tools for the detection of such interactions, but none of the available algorithms allow for taking into account clustered or nested dataset structures, which are particularly common in psychological research. Therefore, we propose the generalized linear mixed-effects model tree (GLMM tree) algorithm, which allows for the detection of treatment-subgroup interactions, while accounting for the clustered structure of a dataset. The algorithm uses model-based recursive partitioning to detect treatment-subgroup interactions, and a GLMM to estimate the random-effects parameters. In a simulation study, GLMM trees show higher accuracy in recovering treatment-subgroup interactions, higher predictive accuracy, and lower type II error rates than linear-model-based recursive partitioning and mixed-effects regression trees. Also, GLMM trees show somewhat higher predictive accuracy than linear mixed-effects models with pre-specified interaction effects, on average. We illustrate the application of GLMM trees on an individual patient-level data meta-analysis on treatments for depression. We conclude that GLMM trees are a promising exploratory tool for the detection of treatment-subgroup interactions in clustered datasets.

Finite element modelling of non-linear magnetic circuits using Cosmic NASTRAN

NASA Technical Reports Server (NTRS)

Sheerer, T. J.

1986-01-01

The general purpose Finite Element Program COSMIC NASTRAN currently has the ability to model magnetic circuits with constant permeablilities. An approach was developed which, through small modifications to the program, allows modelling of non-linear magnetic devices including soft magnetic materials, permanent magnets and coils. Use of the NASTRAN code resulted in output which can be used for subsequent mechanical analysis using a variation of the same computer model. Test problems were found to produce theoretically verifiable results.

An Application of the H-Function to Curve-Fitting and Density Estimation.

DTIC Science & Technology

1983-12-01

equations into a model that is linear in its coefficients. Nonlinear least squares estimation is a relatively new area developed to accomodate models which...to converge on a solution (10:9-10). For the simple linear model and when general assump- tions are made, the Gauss-Markov theorem states that the...distribution. For example, if the analyst wants to model the time between arrivals to a queue for a computer simulation, he infers the true probability

Dynamical localization of coupled relativistic kicked rotors

NASA Astrophysics Data System (ADS)

Rozenbaum, Efim B.; Galitski, Victor

2017-02-01

A periodically driven rotor is a prototypical model that exhibits a transition to chaos in the classical regime and dynamical localization (related to Anderson localization) in the quantum regime. In a recent work [Phys. Rev. B 94, 085120 (2016), 10.1103/PhysRevB.94.085120], A. C. Keser et al. considered a many-body generalization of coupled quantum kicked rotors, and showed that in the special integrable linear case, dynamical localization survives interactions. By analogy with many-body localization, the phenomenon was dubbed dynamical many-body localization. In the present work, we study nonintegrable models of single and coupled quantum relativistic kicked rotors (QRKRs) that bridge the gap between the conventional quadratic rotors and the integrable linear models. For a single QRKR, we supplement the recent analysis of the angular-momentum-space dynamics with a study of the spin dynamics. Our analysis of two and three coupled QRKRs along with the proved localization in the many-body linear model indicate that dynamical localization exists in few-body systems. Moreover, the relation between QRKR and linear rotor models implies that dynamical many-body localization can exist in generic, nonintegrable many-body systems. And localization can generally result from a complicated interplay between Anderson mechanism and limiting integrability, since the many-body linear model is a high-angular-momentum limit of many-body QRKRs. We also analyze the dynamics of two coupled QRKRs in the highly unusual superballistic regime and find that the resonance conditions are relaxed due to interactions. Finally, we propose experimental realizations of the QRKR model in cold atoms in optical lattices.

Meta-analysis for the comparison of two diagnostic tests to a common gold standard: A generalized linear mixed model approach.

PubMed

Hoyer, Annika; Kuss, Oliver

2018-05-01

Meta-analysis of diagnostic studies is still a rapidly developing area of biostatistical research. Especially, there is an increasing interest in methods to compare different diagnostic tests to a common gold standard. Restricting to the case of two diagnostic tests, in these meta-analyses the parameters of interest are the differences of sensitivities and specificities (with their corresponding confidence intervals) between the two diagnostic tests while accounting for the various associations across single studies and between the two tests. We propose statistical models with a quadrivariate response (where sensitivity of test 1, specificity of test 1, sensitivity of test 2, and specificity of test 2 are the four responses) as a sensible approach to this task. Using a quadrivariate generalized linear mixed model naturally generalizes the common standard bivariate model of meta-analysis for a single diagnostic test. If information on several thresholds of the tests is available, the quadrivariate model can be further generalized to yield a comparison of full receiver operating characteristic (ROC) curves. We illustrate our model by an example where two screening methods for the diagnosis of type 2 diabetes are compared.

Meta-analysis of studies with bivariate binary outcomes: a marginal beta-binomial model approach.

PubMed

Chen, Yong; Hong, Chuan; Ning, Yang; Su, Xiao

2016-01-15

When conducting a meta-analysis of studies with bivariate binary outcomes, challenges arise when the within-study correlation and between-study heterogeneity should be taken into account. In this paper, we propose a marginal beta-binomial model for the meta-analysis of studies with binary outcomes. This model is based on the composite likelihood approach and has several attractive features compared with the existing models such as bivariate generalized linear mixed model (Chu and Cole, 2006) and Sarmanov beta-binomial model (Chen et al., 2012). The advantages of the proposed marginal model include modeling the probabilities in the original scale, not requiring any transformation of probabilities or any link function, having closed-form expression of likelihood function, and no constraints on the correlation parameter. More importantly, because the marginal beta-binomial model is only based on the marginal distributions, it does not suffer from potential misspecification of the joint distribution of bivariate study-specific probabilities. Such misspecification is difficult to detect and can lead to biased inference using currents methods. We compare the performance of the marginal beta-binomial model with the bivariate generalized linear mixed model and the Sarmanov beta-binomial model by simulation studies. Interestingly, the results show that the marginal beta-binomial model performs better than the Sarmanov beta-binomial model, whether or not the true model is Sarmanov beta-binomial, and the marginal beta-binomial model is more robust than the bivariate generalized linear mixed model under model misspecifications. Two meta-analyses of diagnostic accuracy studies and a meta-analysis of case-control studies are conducted for illustration. Copyright © 2015 John Wiley & Sons, Ltd.

A Generalized Linear Integrate-and-Fire Neural Model Produces Diverse Spiking Behaviors

PubMed Central

Mihalaş, Ştefan; Niebur, Ernst

2010-01-01

For simulations of neural networks, there is a trade-off between the size of the network that can be simulated and the complexity of the model used for individual neurons. In this study, we describe a generalization of the leaky integrate-and-fire model that produces a wide variety of spiking behaviors while still being analytically solvable between firings. For different parameter values, the model produces spiking or bursting, tonic, phasic or adapting responses, depolarizing or hyperpolarizing after potentials and so forth. The model consists of a diagonalizable set of linear differential equations describing the time evolution of membrane potential, a variable threshold, and an arbitrary number of firing-induced currents. Each of these variables is modified by an update rule when the potential reaches threshold. The variables used are intuitive and have biological significance. The model’s rich behavior does not come from the differential equations, which are linear, but rather from complex update rules. This single-neuron model can be implemented using algorithms similar to the standard integrate-and-fire model. It is a natural match with event-driven algorithms for which the firing times are obtained as a solution of a polynomial equation. PMID:18928368

Machine Learning-based discovery of closures for reduced models of dynamical systems

NASA Astrophysics Data System (ADS)

Pan, Shaowu; Duraisamy, Karthik

2017-11-01

Despite the successful application of machine learning (ML) in fields such as image processing and speech recognition, only a few attempts has been made toward employing ML to represent the dynamics of complex physical systems. Previous attempts mostly focus on parameter calibration or data-driven augmentation of existing models. In this work we present a ML framework to discover closure terms in reduced models of dynamical systems and provide insights into potential problems associated with data-driven modeling. Based on exact closure models for linear system, we propose a general linear closure framework from viewpoint of optimization. The framework is based on trapezoidal approximation of convolution term. Hyperparameters that need to be determined include temporal length of memory effect, number of sampling points, and dimensions of hidden states. To circumvent the explicit specification of memory effect, a general framework inspired from neural networks is also proposed. We conduct both a priori and posteriori evaluations of the resulting model on a number of non-linear dynamical systems. This work was supported in part by AFOSR under the project ``LES Modeling of Non-local effects using Statistical Coarse-graining'' with Dr. Jean-Luc Cambier as the technical monitor.

Linear network representation of multistate models of transport.

PubMed Central

Sandblom, J; Ring, A; Eisenman, G

1982-01-01

By introducing external driving forces in rate-theory models of transport we show how the Eyring rate equations can be transformed into Ohm's law with potentials that obey Kirchhoff's second law. From such a formalism the state diagram of a multioccupancy multicomponent system can be directly converted into linear network with resistors connecting nodal (branch) points and with capacitances connecting each nodal point with a reference point. The external forces appear as emf or current generators in the network. This theory allows the algebraic methods of linear network theory to be used in solving the flux equations for multistate models and is particularly useful for making proper simplifying approximation in models of complex membrane structure. Some general properties of linear network representation are also deduced. It is shown, for instance, that Maxwell's reciprocity relationships of linear networks lead directly to Onsager's relationships in the near equilibrium region. Finally, as an example of the procedure, the equivalent circuit method is used to solve the equations for a few transport models. PMID:7093425

Order-constrained linear optimization.

PubMed

Tidwell, Joe W; Dougherty, Michael R; Chrabaszcz, Jeffrey S; Thomas, Rick P

2017-11-01

Despite the fact that data and theories in the social, behavioural, and health sciences are often represented on an ordinal scale, there has been relatively little emphasis on modelling ordinal properties. The most common analytic framework used in psychological science is the general linear model, whose variants include ANOVA, MANOVA, and ordinary linear regression. While these methods are designed to provide the best fit to the metric properties of the data, they are not designed to maximally model ordinal properties. In this paper, we develop an order-constrained linear least-squares (OCLO) optimization algorithm that maximizes the linear least-squares fit to the data conditional on maximizing the ordinal fit based on Kendall's τ. The algorithm builds on the maximum rank correlation estimator (Han, 1987, Journal of Econometrics, 35, 303) and the general monotone model (Dougherty & Thomas, 2012, Psychological Review, 119, 321). Analyses of simulated data indicate that when modelling data that adhere to the assumptions of ordinary least squares, OCLO shows minimal bias, little increase in variance, and almost no loss in out-of-sample predictive accuracy. In contrast, under conditions in which data include a small number of extreme scores (fat-tailed distributions), OCLO shows less bias and variance, and substantially better out-of-sample predictive accuracy, even when the outliers are removed. We show that the advantages of OCLO over ordinary least squares in predicting new observations hold across a variety of scenarios in which researchers must decide to retain or eliminate extreme scores when fitting data. © 2017 The British Psychological Society.

On fitting generalized linear mixed-effects models for binary responses using different statistical packages.

PubMed

Zhang, Hui; Lu, Naiji; Feng, Changyong; Thurston, Sally W; Xia, Yinglin; Zhu, Liang; Tu, Xin M

2011-09-10

The generalized linear mixed-effects model (GLMM) is a popular paradigm to extend models for cross-sectional data to a longitudinal setting. When applied to modeling binary responses, different software packages and even different procedures within a package may give quite different results. In this report, we describe the statistical approaches that underlie these different procedures and discuss their strengths and weaknesses when applied to fit correlated binary responses. We then illustrate these considerations by applying these procedures implemented in some popular software packages to simulated and real study data. Our simulation results indicate a lack of reliability for most of the procedures considered, which carries significant implications for applying such popular software packages in practice. Copyright © 2011 John Wiley & Sons, Ltd.

Closed-loop stability of linear quadratic optimal systems in the presence of modeling errors

NASA Technical Reports Server (NTRS)

Toda, M.; Patel, R.; Sridhar, B.

1976-01-01

The well-known stabilizing property of linear quadratic state feedback design is utilized to evaluate the robustness of a linear quadratic feedback design in the presence of modeling errors. Two general conditions are obtained for allowable modeling errors such that the resulting closed-loop system remains stable. One of these conditions is applied to obtain two more particular conditions which are readily applicable to practical situations where a designer has information on the bounds of modeling errors. Relations are established between the allowable parameter uncertainty and the weighting matrices of the quadratic performance index, thereby enabling the designer to select appropriate weighting matrices to attain a robust feedback design.

Probabilistic inference using linear Gaussian importance sampling for hybrid Bayesian networks

NASA Astrophysics Data System (ADS)

Sun, Wei; Chang, K. C.

2005-05-01

Probabilistic inference for Bayesian networks is in general NP-hard using either exact algorithms or approximate methods. However, for very complex networks, only the approximate methods such as stochastic sampling could be used to provide a solution given any time constraint. There are several simulation methods currently available. They include logic sampling (the first proposed stochastic method for Bayesian networks, the likelihood weighting algorithm) the most commonly used simulation method because of its simplicity and efficiency, the Markov blanket scoring method, and the importance sampling algorithm. In this paper, we first briefly review and compare these available simulation methods, then we propose an improved importance sampling algorithm called linear Gaussian importance sampling algorithm for general hybrid model (LGIS). LGIS is aimed for hybrid Bayesian networks consisting of both discrete and continuous random variables with arbitrary distributions. It uses linear function and Gaussian additive noise to approximate the true conditional probability distribution for continuous variable given both its parents and evidence in a Bayesian network. One of the most important features of the newly developed method is that it can adaptively learn the optimal important function from the previous samples. We test the inference performance of LGIS using a 16-node linear Gaussian model and a 6-node general hybrid model. The performance comparison with other well-known methods such as Junction tree (JT) and likelihood weighting (LW) shows that LGIS-GHM is very promising.

Simplified large African carnivore density estimators from track indices.

PubMed

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

2016-01-01

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

Linear Sigma Model Toolshed for D-brane Physics

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

Hellerman, Simeon

Building on earlier work, we construct linear sigma models for strings on curved spaces in the presence of branes. Our models include an extremely general class of brane-worldvolume gauge field configurations. We explain in an accessible manner the mathematical ideas which suggest appropriate worldsheet interactions for generating a given open string background. This construction provides an explanation for the appearance of the derived category in D-brane physic complementary to that of recent work of Douglas.

Minimal agent based model for financial markets II. Statistical properties of the linear and multiplicative dynamics

NASA Astrophysics Data System (ADS)

Alfi, V.; Cristelli, M.; Pietronero, L.; Zaccaria, A.

2009-02-01

We present a detailed study of the statistical properties of the Agent Based Model introduced in paper I [Eur. Phys. J. B, DOI: 10.1140/epjb/e2009-00028-4] and of its generalization to the multiplicative dynamics. The aim of the model is to consider the minimal elements for the understanding of the origin of the stylized facts and their self-organization. The key elements are fundamentalist agents, chartist agents, herding dynamics and price behavior. The first two elements correspond to the competition between stability and instability tendencies in the market. The herding behavior governs the possibility of the agents to change strategy and it is a crucial element of this class of models. We consider a linear approximation for the price dynamics which permits a simple interpretation of the model dynamics and, for many properties, it is possible to derive analytical results. The generalized non linear dynamics results to be extremely more sensible to the parameter space and much more difficult to analyze and control. The main results for the nature and self-organization of the stylized facts are, however, very similar in the two cases. The main peculiarity of the non linear dynamics is an enhancement of the fluctuations and a more marked evidence of the stylized facts. We will also discuss some modifications of the model to introduce more realistic elements with respect to the real markets.

Transfer matrix method for dynamics modeling and independent modal space vibration control design of linear hybrid multibody system

NASA Astrophysics Data System (ADS)

Rong, Bao; Rui, Xiaoting; Lu, Kun; Tao, Ling; Wang, Guoping; Ni, Xiaojun

2018-05-01

In this paper, an efficient method of dynamics modeling and vibration control design of a linear hybrid multibody system (MS) is studied based on the transfer matrix method. The natural vibration characteristics of a linear hybrid MS are solved by using low-order transfer equations. Then, by constructing the brand-new body dynamics equation, augmented operator and augmented eigenvector, the orthogonality of augmented eigenvector of a linear hybrid MS is satisfied, and its state space model expressed in each independent model space is obtained easily. According to this dynamics model, a robust independent modal space-fuzzy controller is designed for vibration control of a general MS, and the genetic optimization of some critical control parameters of fuzzy tuners is also presented. Two illustrative examples are performed, which results show that this method is computationally efficient and with perfect control performance.

Statistical Methods for Generalized Linear Models with Covariates Subject to Detection Limits.

PubMed

Bernhardt, Paul W; Wang, Huixia J; Zhang, Daowen

2015-05-01

Censored observations are a common occurrence in biomedical data sets. Although a large amount of research has been devoted to estimation and inference for data with censored responses, very little research has focused on proper statistical procedures when predictors are censored. In this paper, we consider statistical methods for dealing with multiple predictors subject to detection limits within the context of generalized linear models. We investigate and adapt several conventional methods and develop a new multiple imputation approach for analyzing data sets with predictors censored due to detection limits. We establish the consistency and asymptotic normality of the proposed multiple imputation estimator and suggest a computationally simple and consistent variance estimator. We also demonstrate that the conditional mean imputation method often leads to inconsistent estimates in generalized linear models, while several other methods are either computationally intensive or lead to parameter estimates that are biased or more variable compared to the proposed multiple imputation estimator. In an extensive simulation study, we assess the bias and variability of different approaches within the context of a logistic regression model and compare variance estimation methods for the proposed multiple imputation estimator. Lastly, we apply several methods to analyze the data set from a recently-conducted GenIMS study.

A generalized fuzzy credibility-constrained linear fractional programming approach for optimal irrigation water allocation under uncertainty

NASA Astrophysics Data System (ADS)

Zhang, Chenglong; Guo, Ping

2017-10-01

The vague and fuzzy parametric information is a challenging issue in irrigation water management problems. In response to this problem, a generalized fuzzy credibility-constrained linear fractional programming (GFCCFP) model is developed for optimal irrigation water allocation under uncertainty. The model can be derived from integrating generalized fuzzy credibility-constrained programming (GFCCP) into a linear fractional programming (LFP) optimization framework. Therefore, it can solve ratio optimization problems associated with fuzzy parameters, and examine the variation of results under different credibility levels and weight coefficients of possibility and necessary. It has advantages in: (1) balancing the economic and resources objectives directly; (2) analyzing system efficiency; (3) generating more flexible decision solutions by giving different credibility levels and weight coefficients of possibility and (4) supporting in-depth analysis of the interrelationships among system efficiency, credibility level and weight coefficient. The model is applied to a case study of irrigation water allocation in the middle reaches of Heihe River Basin, northwest China. Therefore, optimal irrigation water allocation solutions from the GFCCFP model can be obtained. Moreover, factorial analysis on the two parameters (i.e. λ and γ) indicates that the weight coefficient is a main factor compared with credibility level for system efficiency. These results can be effective for support reasonable irrigation water resources management and agricultural production.

Finite-time H∞ filtering for non-linear stochastic systems

NASA Astrophysics Data System (ADS)

Hou, Mingzhe; Deng, Zongquan; Duan, Guangren

2016-09-01

This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

The Fermi-Pasta-Ulam Problem and Its Underlying Integrable Dynamics: An Approach Through Lyapunov Exponents

NASA Astrophysics Data System (ADS)

Benettin, G.; Pasquali, S.; Ponno, A.

2018-05-01

FPU models, in dimension one, are perturbations either of the linear model or of the Toda model; perturbations of the linear model include the usual β -model, perturbations of Toda include the usual α +β model. In this paper we explore and compare two families, or hierarchies, of FPU models, closer and closer to either the linear or the Toda model, by computing numerically, for each model, the maximal Lyapunov exponent χ . More precisely, we consider statistically typical trajectories and study the asymptotics of χ for large N (the number of particles) and small ɛ (the specific energy E / N), and find, for all models, asymptotic power laws χ ˜eq Cɛ ^a, C and a depending on the model. The asymptotics turns out to be, in general, rather slow, and producing accurate results requires a great computational effort. We also revisit and extend the analytic computation of χ introduced by Casetti, Livi and Pettini, originally formulated for the β -model. With great evidence the theory extends successfully to all models of the linear hierarchy, but not to models close to Toda.

Longitudinal data analyses using linear mixed models in SPSS: concepts, procedures and illustrations.

PubMed

Shek, Daniel T L; Ma, Cecilia M S

2011-01-05

Although different methods are available for the analyses of longitudinal data, analyses based on generalized linear models (GLM) are criticized as violating the assumption of independence of observations. Alternatively, linear mixed models (LMM) are commonly used to understand changes in human behavior over time. In this paper, the basic concepts surrounding LMM (or hierarchical linear models) are outlined. Although SPSS is a statistical analyses package commonly used by researchers, documentation on LMM procedures in SPSS is not thorough or user friendly. With reference to this limitation, the related procedures for performing analyses based on LMM in SPSS are described. To demonstrate the application of LMM analyses in SPSS, findings based on six waves of data collected in the Project P.A.T.H.S. (Positive Adolescent Training through Holistic Social Programmes) in Hong Kong are presented.

Longitudinal Data Analyses Using Linear Mixed Models in SPSS: Concepts, Procedures and Illustrations

PubMed Central

Shek, Daniel T. L.; Ma, Cecilia M. S.

2011-01-01

Although different methods are available for the analyses of longitudinal data, analyses based on generalized linear models (GLM) are criticized as violating the assumption of independence of observations. Alternatively, linear mixed models (LMM) are commonly used to understand changes in human behavior over time. In this paper, the basic concepts surrounding LMM (or hierarchical linear models) are outlined. Although SPSS is a statistical analyses package commonly used by researchers, documentation on LMM procedures in SPSS is not thorough or user friendly. With reference to this limitation, the related procedures for performing analyses based on LMM in SPSS are described. To demonstrate the application of LMM analyses in SPSS, findings based on six waves of data collected in the Project P.A.T.H.S. (Positive Adolescent Training through Holistic Social Programmes) in Hong Kong are presented. PMID:21218263

A single-degree-of-freedom model for non-linear soil amplification

USGS Publications Warehouse

Erdik, Mustafa Ozder

1979-01-01

For proper understanding of soil behavior during earthquakes and assessment of a realistic surface motion, studies of the large-strain dynamic response of non-linear hysteretic soil systems are indispensable. Most of the presently available studies are based on the assumption that the response of a soil deposit is mainly due to the upward propagation of horizontally polarized shear waves from the underlying bedrock. Equivalent-linear procedures, currently in common use in non-linear soil response analysis, provide a simple approach and have been favorably compared with the actual recorded motions in some particular cases. Strain compatibility in these equivalent-linear approaches is maintained by selecting values of shear moduli and damping ratios in accordance with the average soil strains, in an iterative manner. Truly non-linear constitutive models with complete strain compatibility have also been employed. The equivalent-linear approaches often raise some doubt as to the reliability of their results concerning the system response in high frequency regions. In these frequency regions the equivalent-linear methods may underestimate the surface motion by as much as a factor of two or more. Although studies are complete in their methods of analysis, they inevitably provide applications pertaining only to a few specific soil systems, and do not lead to general conclusions about soil behavior. This report attempts to provide a general picture of the soil response through the use of a single-degree-of-freedom non-linear-hysteretic model. Although the investigation is based on a specific type of nonlinearity and a set of dynamic soil properties, the method described does not limit itself to these assumptions and is equally applicable to other types of nonlinearity and soil parameters.

hi-class: Horndeski in the Cosmic Linear Anisotropy Solving System

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

Zumalacárregui, Miguel; Bellini, Emilio; Sawicki, Ignacy

We present the public version of hi-class (www.hiclass-code.net), an extension of the Boltzmann code CLASS to a broad ensemble of modifications to general relativity. In particular, hi-class can calculate predictions for models based on Horndeski's theory, which is the most general scalar-tensor theory described by second-order equations of motion and encompasses any perfect-fluid dark energy, quintessence, Brans-Dicke, f ( R ) and covariant Galileon models. hi-class has been thoroughly tested and can be readily used to understand the impact of alternative theories of gravity on linear structure formation as well as for cosmological parameter extraction.

Quantum description of light propagation in generalized media

NASA Astrophysics Data System (ADS)

Häyrynen, Teppo; Oksanen, Jani

2016-02-01

Linear quantum input-output relation based models are widely applied to describe the light propagation in a lossy medium. The details of the interaction and the associated added noise depend on whether the device is configured to operate as an amplifier or an attenuator. Using the traveling wave (TW) approach, we generalize the linear material model to simultaneously account for both the emission and absorption processes and to have point-wise defined noise field statistics and intensity dependent interaction strengths. Thus, our approach describes the quantum input-output relations of linear media with net attenuation, amplification or transparency without pre-selection of the operation point. The TW approach is then applied to investigate materials at thermal equilibrium, inverted materials, the transparency limit where losses are compensated, and the saturating amplifiers. We also apply the approach to investigate media in nonuniform states which can be e.g. consequences of a temperature gradient over the medium or a position dependent inversion of the amplifier. Furthermore, by using the generalized model we investigate devices with intensity dependent interactions and show how an initial thermal field transforms to a field having coherent statistics due to gain saturation.

Rhombic micro-displacement amplifier for piezoelectric actuator and its linear and hybrid model

NASA Astrophysics Data System (ADS)

Chen, Jinglong; Zhang, Chunlin; Xu, Minglong; Zi, Yanyang; Zhang, Xinong

2015-01-01

This paper proposes rhombic micro-displacement amplifier (RMDA) for piezoelectric actuator (PA). First, the geometric amplification relations are analyzed and linear model is built to analyze the mechanical and electrical properties of this amplifier. Next, the accurate modeling method of amplifier is studied for important application of precise servo control. The classical Preisach model (CPM) is generally implemented using a numerical technique based on the first-order reversal curves (FORCs). The accuracy of CPM mainly depends on the number of FORCs. However, it is generally difficult to achieve enough number of FORCs in practice. So, Support Vector Machine (SVM) is employed in the work to circumvent the deficiency of the CPM. Then the hybrid model, which is based on discrete CPM and SVM is developed to account for hysteresis and dynamic effects. Finally, experimental validation is carried out. The analyzed result shows that this amplifier with the hybrid model is suitable for control application.

A generalized partially linear mean-covariance regression model for longitudinal proportional data, with applications to the analysis of quality of life data from cancer clinical trials.

PubMed

Zheng, Xueying; Qin, Guoyou; Tu, Dongsheng

2017-05-30

Motivated by the analysis of quality of life data from a clinical trial on early breast cancer, we propose in this paper a generalized partially linear mean-covariance regression model for longitudinal proportional data, which are bounded in a closed interval. Cholesky decomposition of the covariance matrix for within-subject responses and generalized estimation equations are used to estimate unknown parameters and the nonlinear function in the model. Simulation studies are performed to evaluate the performance of the proposed estimation procedures. Our new model is also applied to analyze the data from the cancer clinical trial that motivated this research. In comparison with available models in the literature, the proposed model does not require specific parametric assumptions on the density function of the longitudinal responses and the probability function of the boundary values and can capture dynamic changes of time or other interested variables on both mean and covariance of the correlated proportional responses. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

A Dynamic Model for Modern Military Conflict.

DTIC Science & Technology

1982-10-01

within the generalized form of the Lotka - Volterra equations, that can account for the important interactions of modern military conflicts described in...Mx + These equations are seen to be of the generalized Lotka - Volterra form; however, only 20 of the 32 parameters that might possibly be included...determine one equilibrium as the solution of a system of linear equations. The method is derived for the general nth order Lotka - Volterra model in

The mathematical formulation of a generalized Hooke's law for blood vessels.

PubMed

Zhang, Wei; Wang, Chong; Kassab, Ghassan S

2007-08-01

It is well known that the stress-strain relationship of blood vessels is highly nonlinear. To linearize the relationship, the Hencky strain tensor is generalized to a logarithmic-exponential (log-exp) strain tensor to absorb the nonlinearity. A quadratic nominal strain potential is proposed to derive the second Piola-Kirchhoff stresses by differentiating the potential with respect to the log-exp strains. The resulting constitutive equation is a generalized Hooke's law. Ten material constants are needed for the three-dimensional orthotropic model. The nondimensional constant used in the log-exp strain definition is interpreted as a nonlinearity parameter. The other nine constants are the elastic moduli with respect to the log-exp strains. In this paper, the proposed linear stress-strain relation is shown to represent the pseudoelastic Fung model very well.

Noise limitations in optical linear algebra processors.

PubMed

Batsell, S G; Jong, T L; Walkup, J F; Krile, T F

1990-05-10

A general statistical noise model is presented for optical linear algebra processors. A statistical analysis which includes device noise, the multiplication process, and the addition operation is undertaken. We focus on those processes which are architecturally independent. Finally, experimental results which verify the analytical predictions are also presented.

Anisotropic k-essence cosmologies

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

Chimento, Luis P.; Forte, Monica

We investigate a Bianchi type-I cosmology with k-essence and find the set of models which dissipate the initial anisotropy. There are cosmological models with extended tachyon fields and k-essence having a constant barotropic index. We obtain the conditions leading to a regular bounce of the average geometry and the residual anisotropy on the bounce. For constant potential, we develop purely kinetic k-essence models which are dust dominated in their early stages, dissipate the initial anisotropy, and end in a stable de Sitter accelerated expansion scenario. We show that linear k-field and polynomial kinetic function models evolve asymptotically to Friedmann-Robertson-Walker cosmologies.more » The linear case is compatible with an asymptotic potential interpolating between V{sub l}{proportional_to}{phi}{sup -{gamma}{sub l}}, in the shear dominated regime, and V{sub l}{proportional_to}{phi}{sup -2} at late time. In the polynomial case, the general solution contains cosmological models with an oscillatory average geometry. For linear k-essence, we find the general solution in the Bianchi type-I cosmology when the k field is driven by an inverse square potential. This model shares the same geometry as a quintessence field driven by an exponential potential.« less

A generalized fuzzy linear programming approach for environmental management problem under uncertainty.

PubMed

Fan, Yurui; Huang, Guohe; Veawab, Amornvadee

2012-01-01

In this study, a generalized fuzzy linear programming (GFLP) method was developed to deal with uncertainties expressed as fuzzy sets that exist in the constraints and objective function. A stepwise interactive algorithm (SIA) was advanced to solve GFLP model and generate solutions expressed as fuzzy sets. To demonstrate its application, the developed GFLP method was applied to a regional sulfur dioxide (SO2) control planning model to identify effective SO2 mitigation polices with a minimized system performance cost under uncertainty. The results were obtained to represent the amount of SO2 allocated to different control measures from different sources. Compared with the conventional interval-parameter linear programming (ILP) approach, the solutions obtained through GFLP were expressed as fuzzy sets, which can provide intervals for the decision variables and objective function, as well as related possibilities. Therefore, the decision makers can make a tradeoff between model stability and the plausibility based on solutions obtained through GFLP and then identify desired policies for SO2-emission control under uncertainty.

A general science-based framework for dynamical spatio-temporal models

USGS Publications Warehouse

Wikle, C.K.; Hooten, M.B.

2010-01-01

Spatio-temporal statistical models are increasingly being used across a wide variety of scientific disciplines to describe and predict spatially-explicit processes that evolve over time. Correspondingly, in recent years there has been a significant amount of research on new statistical methodology for such models. Although descriptive models that approach the problem from the second-order (covariance) perspective are important, and innovative work is being done in this regard, many real-world processes are dynamic, and it can be more efficient in some cases to characterize the associated spatio-temporal dependence by the use of dynamical models. The chief challenge with the specification of such dynamical models has been related to the curse of dimensionality. Even in fairly simple linear, first-order Markovian, Gaussian error settings, statistical models are often over parameterized. Hierarchical models have proven invaluable in their ability to deal to some extent with this issue by allowing dependency among groups of parameters. In addition, this framework has allowed for the specification of science based parameterizations (and associated prior distributions) in which classes of deterministic dynamical models (e. g., partial differential equations (PDEs), integro-difference equations (IDEs), matrix models, and agent-based models) are used to guide specific parameterizations. Most of the focus for the application of such models in statistics has been in the linear case. The problems mentioned above with linear dynamic models are compounded in the case of nonlinear models. In this sense, the need for coherent and sensible model parameterizations is not only helpful, it is essential. Here, we present an overview of a framework for incorporating scientific information to motivate dynamical spatio-temporal models. First, we illustrate the methodology with the linear case. We then develop a general nonlinear spatio-temporal framework that we call general quadratic nonlinearity and demonstrate that it accommodates many different classes of scientific-based parameterizations as special cases. The model is presented in a hierarchical Bayesian framework and is illustrated with examples from ecology and oceanography. ?? 2010 Sociedad de Estad??stica e Investigaci??n Operativa.

GVE-Based Dynamics and Control for Formation Flying Spacecraft

NASA Technical Reports Server (NTRS)

Breger, Louis; How, Jonathan P.

2004-01-01

Formation flying is an enabling technology for many future space missions. This paper presents extensions to the equations of relative motion expressed in Keplerian orbital elements, including new initialization techniques for general formation configurations. A new linear time-varying form of the equations of relative motion is developed from Gauss Variational Equations and used in a model predictive controller. The linearizing assumptions for these equations are shown to be consistent with typical formation flying scenarios. Several linear, convex initialization techniques are presented, as well as a general, decentralized method for coordinating a tetrahedral formation using differential orbital elements. Control methods are validated using a commercial numerical propagator.

FAST TRACK PAPER: Non-iterative multiple-attenuation methods: linear inverse solutions to non-linear inverse problems - II. BMG approximation

NASA Astrophysics Data System (ADS)

Ikelle, Luc T.; Osen, Are; Amundsen, Lasse; Shen, Yunqing

2004-12-01

The classical linear solutions to the problem of multiple attenuation, like predictive deconvolution, τ-p filtering, or F-K filtering, are generally fast, stable, and robust compared to non-linear solutions, which are generally either iterative or in the form of a series with an infinite number of terms. These qualities have made the linear solutions more attractive to seismic data-processing practitioners. However, most linear solutions, including predictive deconvolution or F-K filtering, contain severe assumptions about the model of the subsurface and the class of free-surface multiples they can attenuate. These assumptions limit their usefulness. In a recent paper, we described an exception to this assertion for OBS data. We showed in that paper that a linear and non-iterative solution to the problem of attenuating free-surface multiples which is as accurate as iterative non-linear solutions can be constructed for OBS data. We here present a similar linear and non-iterative solution for attenuating free-surface multiples in towed-streamer data. For most practical purposes, this linear solution is as accurate as the non-linear ones.

A Generalization of Pythagoras's Theorem and Application to Explanations of Variance Contributions in Linear Models. Research Report. ETS RR-14-18

ERIC Educational Resources Information Center

Carlson, James E.

2014-01-01

Many aspects of the geometry of linear statistical models and least squares estimation are well known. Discussions of the geometry may be found in many sources. Some aspects of the geometry relating to the partitioning of variation that can be explained using a little-known theorem of Pappus and have not been discussed previously are the topic of…

Modelling of Asphalt Concrete Stiffness in the Linear Viscoelastic Region

NASA Astrophysics Data System (ADS)

Mazurek, Grzegorz; Iwański, Marek

2017-10-01

Stiffness modulus is a fundamental parameter used in the modelling of the viscoelastic behaviour of bituminous mixtures. On the basis of the master curve in the linear viscoelasticity range, the mechanical properties of asphalt concrete at different loading times and temperatures can be predicted. This paper discusses the construction of master curves under rheological mathematical models i.e. the sigmoidal function model (MEPDG), the fractional model, and Bahia and co-workers’ model in comparison to the results from mechanistic rheological models i.e. the generalized Huet-Sayegh model, the generalized Maxwell model and the Burgers model. For the purposes of this analysis, the reference asphalt concrete mix (denoted as AC16W) intended for the binder coarse layer and for traffic category KR3 (5×105

Identifiability of large-scale non-linear dynamic network models applied to the ADM1-case study.

PubMed

Nimmegeers, Philippe; Lauwers, Joost; Telen, Dries; Logist, Filip; Impe, Jan Van

2017-06-01

In this work, both the structural and practical identifiability of the Anaerobic Digestion Model no. 1 (ADM1) is investigated, which serves as a relevant case study of large non-linear dynamic network models. The structural identifiability is investigated using the probabilistic algorithm, adapted to deal with the specifics of the case study (i.e., a large-scale non-linear dynamic system of differential and algebraic equations). The practical identifiability is analyzed using a Monte Carlo parameter estimation procedure for a 'non-informative' and 'informative' experiment, which are heuristically designed. The model structure of ADM1 has been modified by replacing parameters by parameter combinations, to provide a generally locally structurally identifiable version of ADM1. This means that in an idealized theoretical situation, the parameters can be estimated accurately. Furthermore, the generally positive structural identifiability results can be explained from the large number of interconnections between the states in the network structure. This interconnectivity, however, is also observed in the parameter estimates, making uncorrelated parameter estimations in practice difficult. Copyright © 2017. Published by Elsevier Inc.

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

Suhara, Tadahiro; Kanada-En'yo, Yoshiko

We investigate the linear-chain structures in highly excited states of {sup 14}C using a generalized molecular-orbital model, by which we incorporate an asymmetric configuration of three {alpha} clusters in the linear-chain states. By applying this model to the {sup 14}C system, we study the {sup 10}Be+{alpha} correlation in the linear-chain state of {sup 14}C. To clarify the origin of the {sup 10}Be+{alpha} correlation in the {sup 14}C linear-chain state, we analyze linear 3 {alpha} and 3{alpha} + n systems in a similar way. We find that a linear 3{alpha} system prefers the asymmetric 2{alpha} + {alpha} configuration, whose origin ismore » the many-body correlation incorporated by the parity projection. This configuration causes an asymmetric mean field for two valence neutrons, which induces the concentration of valence neutron wave functions around the correlating 2{alpha}. A linear-chain structure of {sup 16}C is also discussed.« less

Single-phase power distribution system power flow and fault analysis

NASA Technical Reports Server (NTRS)

Halpin, S. M.; Grigsby, L. L.

1992-01-01

Alternative methods for power flow and fault analysis of single-phase distribution systems are presented. The algorithms for both power flow and fault analysis utilize a generalized approach to network modeling. The generalized admittance matrix, formed using elements of linear graph theory, is an accurate network model for all possible single-phase network configurations. Unlike the standard nodal admittance matrix formulation algorithms, the generalized approach uses generalized component models for the transmission line and transformer. The standard assumption of a common node voltage reference point is not required to construct the generalized admittance matrix. Therefore, truly accurate simulation results can be obtained for networks that cannot be modeled using traditional techniques.

Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations.

PubMed

Henry, B I; Langlands, T A M; Wearne, S L

2006-09-01

We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a nonstandard diffusion term. Results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term. We have also developed further extensions of the CTRW model to include more general reaction dynamics.

Information Fusion from the Point of View of Communication Theory; Fusing Information to Trade-Off the Resolution of Assessments Against the Probability of Mis-Assessment

DTIC Science & Technology

2013-08-19

excellence in linear models , 2010. She successfully defended her dissertation, Linear System Design for Fusion and Compression, on Aug 13, 2013. Her work was...measurements into canonical coordinates, scaling, and rotation; there is a water-filling interpretation; (3) the optimum design of a linear secondary channel of...measurements to fuse with a primary linear channel of measurements maximizes a generalized Rayleigh quotient; (4) the asymptotically optimum

Reduced-order modeling of soft robots

PubMed Central

Chenevier, Jean; González, David; Aguado, J. Vicente; Chinesta, Francisco

2018-01-01

We present a general strategy for the modeling and simulation-based control of soft robots. Although the presented methodology is completely general, we restrict ourselves to the analysis of a model robot made of hyperelastic materials and actuated by cables or tendons. To comply with the stringent real-time constraints imposed by control algorithms, a reduced-order modeling strategy is proposed that allows to minimize the amount of online CPU cost. Instead, an offline training procedure is proposed that allows to determine a sort of response surface that characterizes the response of the robot. Contrarily to existing strategies, the proposed methodology allows for a fully non-linear modeling of the soft material in a hyperelastic setting as well as a fully non-linear kinematic description of the movement without any restriction nor simplifying assumption. Examples of different configurations of the robot were analyzed that show the appeal of the method. PMID:29470496

Unification of the general non-linear sigma model and the Virasoro master equation

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

Boer, J. de; Halpern, M.B.

1997-06-01

The Virasoro master equation describes a large set of conformal field theories known as the affine-Virasoro constructions, in the operator algebra (affinie Lie algebra) of the WZW model, while the einstein equations of the general non-linear sigma model describe another large set of conformal field theories. This talk summarizes recent work which unifies these two sets of conformal field theories, together with a presumable large class of new conformal field theories. The basic idea is to consider spin-two operators of the form L{sub ij}{partial_derivative}x{sup i}{partial_derivative}x{sup j} in the background of a general sigma model. The requirement that these operators satisfymore » the Virasoro algebra leads to a set of equations called the unified Einstein-Virasoro master equation, in which the spin-two spacetime field L{sub ij} cuples to the usual spacetime fields of the sigma model. The one-loop form of this unified system is presented, and some of its algebraic and geometric properties are discussed.« less

Electricity Consumption in the Industrial Sector of Jordan: Application of Multivariate Linear Regression and Adaptive Neuro-Fuzzy Techniques

NASA Astrophysics Data System (ADS)

Samhouri, M.; Al-Ghandoor, A.; Fouad, R. H.

2009-08-01

In this study two techniques, for modeling electricity consumption of the Jordanian industrial sector, are presented: (i) multivariate linear regression and (ii) neuro-fuzzy models. Electricity consumption is modeled as function of different variables such as number of establishments, number of employees, electricity tariff, prevailing fuel prices, production outputs, capacity utilizations, and structural effects. It was found that industrial production and capacity utilization are the most important variables that have significant effect on future electrical power demand. The results showed that both the multivariate linear regression and neuro-fuzzy models are generally comparable and can be used adequately to simulate industrial electricity consumption. However, comparison that is based on the square root average squared error of data suggests that the neuro-fuzzy model performs slightly better for future prediction of electricity consumption than the multivariate linear regression model. Such results are in full agreement with similar work, using different methods, for other countries.

Size effects in non-linear heat conduction with flux-limited behaviors

NASA Astrophysics Data System (ADS)

Li, Shu-Nan; Cao, Bing-Yang

2017-11-01

Size effects are discussed for several non-linear heat conduction models with flux-limited behaviors, including the phonon hydrodynamic, Lagrange multiplier, hierarchy moment, nonlinear phonon hydrodynamic, tempered diffusion, thermon gas and generalized nonlinear models. For the phonon hydrodynamic, Lagrange multiplier and tempered diffusion models, heat flux will not exist in problems with sufficiently small scale. The existence of heat flux needs the sizes of heat conduction larger than their corresponding critical sizes, which are determined by the physical properties and boundary temperatures. The critical sizes can be regarded as the theoretical limits of the applicable ranges for these non-linear heat conduction models with flux-limited behaviors. For sufficiently small scale heat conduction, the phonon hydrodynamic and Lagrange multiplier models can also predict the theoretical possibility of violating the second law and multiplicity. Comparisons are also made between these non-Fourier models and non-linear Fourier heat conduction in the type of fast diffusion, which can also predict flux-limited behaviors.

A penalized framework for distributed lag non-linear models.

PubMed

Gasparrini, Antonio; Scheipl, Fabian; Armstrong, Ben; Kenward, Michael G

2017-09-01

Distributed lag non-linear models (DLNMs) are a modelling tool for describing potentially non-linear and delayed dependencies. Here, we illustrate an extension of the DLNM framework through the use of penalized splines within generalized additive models (GAM). This extension offers built-in model selection procedures and the possibility of accommodating assumptions on the shape of the lag structure through specific penalties. In addition, this framework includes, as special cases, simpler models previously proposed for linear relationships (DLMs). Alternative versions of penalized DLNMs are compared with each other and with the standard unpenalized version in a simulation study. Results show that this penalized extension to the DLNM class provides greater flexibility and improved inferential properties. The framework exploits recent theoretical developments of GAMs and is implemented using efficient routines within freely available software. Real-data applications are illustrated through two reproducible examples in time series and survival analysis. © 2017 The Authors Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society.

Evaluation of confidence intervals for a steady-state leaky aquifer model

USGS Publications Warehouse

Christensen, S.; Cooley, R.L.

1999-01-01

The fact that dependent variables of groundwater models are generally nonlinear functions of model parameters is shown to be a potentially significant factor in calculating accurate confidence intervals for both model parameters and functions of the parameters, such as the values of dependent variables calculated by the model. The Lagrangian method of Vecchia and Cooley [Vecchia, A.V. and Cooley, R.L., Water Resources Research, 1987, 23(7), 1237-1250] was used to calculate nonlinear Scheffe-type confidence intervals for the parameters and the simulated heads of a steady-state groundwater flow model covering 450 km2 of a leaky aquifer. The nonlinear confidence intervals are compared to corresponding linear intervals. As suggested by the significant nonlinearity of the regression model, linear confidence intervals are often not accurate. The commonly made assumption that widths of linear confidence intervals always underestimate the actual (nonlinear) widths was not correct. Results show that nonlinear effects can cause the nonlinear intervals to be asymmetric and either larger or smaller than the linear approximations. Prior information on transmissivities helps reduce the size of the confidence intervals, with the most notable effects occurring for the parameters on which there is prior information and for head values in parameter zones for which there is prior information on the parameters.The fact that dependent variables of groundwater models are generally nonlinear functions of model parameters is shown to be a potentially significant factor in calculating accurate confidence intervals for both model parameters and functions of the parameters, such as the values of dependent variables calculated by the model. The Lagrangian method of Vecchia and Cooley was used to calculate nonlinear Scheffe-type confidence intervals for the parameters and the simulated heads of a steady-state groundwater flow model covering 450 km2 of a leaky aquifer. The nonlinear confidence intervals are compared to corresponding linear intervals. As suggested by the significant nonlinearity of the regression model, linear confidence intervals are often not accurate. The commonly made assumption that widths of linear confidence intervals always underestimate the actual (nonlinear) widths was not correct. Results show that nonlinear effects can cause the nonlinear intervals to be asymmetric and either larger or smaller than the linear approximations. Prior information on transmissivities helps reduce the size of the confidence intervals, with the most notable effects occurring for the parameters on which there is prior information and for head values in parameter zones for which there is prior information on the parameters.

Focal activation of primary visual cortex following supra-choroidal electrical stimulation of the retina: Intrinsic signal imaging and linear model analysis.

PubMed

Cloherty, Shaun L; Hietanen, Markus A; Suaning, Gregg J; Ibbotson, Michael R

2010-01-01

We performed optical intrinsic signal imaging of cat primary visual cortex (Area 17 and 18) while delivering bipolar electrical stimulation to the retina by way of a supra-choroidal electrode array. Using a general linear model (GLM) analysis we identified statistically significant (p < 0.01) activation in a localized region of cortex following supra-threshold electrical stimulation at a single retinal locus. (1) demonstrate that intrinsic signal imaging combined with linear model analysis provides a powerful tool for assessing cortical responses to prosthetic stimulation, and (2) confirm that supra-choroidal electrical stimulation can achieve localized activation of the cortex consistent with focal activation of the retina.

Beta Regression Finite Mixture Models of Polarization and Priming

ERIC Educational Resources Information Center

Smithson, Michael; Merkle, Edgar C.; Verkuilen, Jay

2011-01-01

This paper describes the application of finite-mixture general linear models based on the beta distribution to modeling response styles, polarization, anchoring, and priming effects in probability judgments. These models, in turn, enhance our capacity for explicitly testing models and theories regarding the aforementioned phenomena. The mixture…

Unification theory of optimal life histories and linear demographic models in internal stochasticity.

PubMed

Oizumi, Ryo

2014-01-01

Life history of organisms is exposed to uncertainty generated by internal and external stochasticities. Internal stochasticity is generated by the randomness in each individual life history, such as randomness in food intake, genetic character and size growth rate, whereas external stochasticity is due to the environment. For instance, it is known that the external stochasticity tends to affect population growth rate negatively. It has been shown in a recent theoretical study using path-integral formulation in structured linear demographic models that internal stochasticity can affect population growth rate positively or negatively. However, internal stochasticity has not been the main subject of researches. Taking account of effect of internal stochasticity on the population growth rate, the fittest organism has the optimal control of life history affected by the stochasticity in the habitat. The study of this control is known as the optimal life schedule problems. In order to analyze the optimal control under internal stochasticity, we need to make use of "Stochastic Control Theory" in the optimal life schedule problem. There is, however, no such kind of theory unifying optimal life history and internal stochasticity. This study focuses on an extension of optimal life schedule problems to unify control theory of internal stochasticity into linear demographic models. First, we show the relationship between the general age-states linear demographic models and the stochastic control theory via several mathematical formulations, such as path-integral, integral equation, and transition matrix. Secondly, we apply our theory to a two-resource utilization model for two different breeding systems: semelparity and iteroparity. Finally, we show that the diversity of resources is important for species in a case. Our study shows that this unification theory can address risk hedges of life history in general age-states linear demographic models.

Unification Theory of Optimal Life Histories and Linear Demographic Models in Internal Stochasticity

PubMed Central

Oizumi, Ryo

2014-01-01

Life history of organisms is exposed to uncertainty generated by internal and external stochasticities. Internal stochasticity is generated by the randomness in each individual life history, such as randomness in food intake, genetic character and size growth rate, whereas external stochasticity is due to the environment. For instance, it is known that the external stochasticity tends to affect population growth rate negatively. It has been shown in a recent theoretical study using path-integral formulation in structured linear demographic models that internal stochasticity can affect population growth rate positively or negatively. However, internal stochasticity has not been the main subject of researches. Taking account of effect of internal stochasticity on the population growth rate, the fittest organism has the optimal control of life history affected by the stochasticity in the habitat. The study of this control is known as the optimal life schedule problems. In order to analyze the optimal control under internal stochasticity, we need to make use of “Stochastic Control Theory” in the optimal life schedule problem. There is, however, no such kind of theory unifying optimal life history and internal stochasticity. This study focuses on an extension of optimal life schedule problems to unify control theory of internal stochasticity into linear demographic models. First, we show the relationship between the general age-states linear demographic models and the stochastic control theory via several mathematical formulations, such as path–integral, integral equation, and transition matrix. Secondly, we apply our theory to a two-resource utilization model for two different breeding systems: semelparity and iteroparity. Finally, we show that the diversity of resources is important for species in a case. Our study shows that this unification theory can address risk hedges of life history in general age-states linear demographic models. PMID:24945258

A primer for biomedical scientists on how to execute model II linear regression analysis.

PubMed

Ludbrook, John

2012-04-01

1. There are two very different ways of executing linear regression analysis. One is Model I, when the x-values are fixed by the experimenter. The other is Model II, in which the x-values are free to vary and are subject to error. 2. I have received numerous complaints from biomedical scientists that they have great difficulty in executing Model II linear regression analysis. This may explain the results of a Google Scholar search, which showed that the authors of articles in journals of physiology, pharmacology and biochemistry rarely use Model II regression analysis. 3. I repeat my previous arguments in favour of using least products linear regression analysis for Model II regressions. I review three methods for executing ordinary least products (OLP) and weighted least products (WLP) regression analysis: (i) scientific calculator and/or computer spreadsheet; (ii) specific purpose computer programs; and (iii) general purpose computer programs. 4. Using a scientific calculator and/or computer spreadsheet, it is easy to obtain correct values for OLP slope and intercept, but the corresponding 95% confidence intervals (CI) are inaccurate. 5. Using specific purpose computer programs, the freeware computer program smatr gives the correct OLP regression coefficients and obtains 95% CI by bootstrapping. In addition, smatr can be used to compare the slopes of OLP lines. 6. When using general purpose computer programs, I recommend the commercial programs systat and Statistica for those who regularly undertake linear regression analysis and I give step-by-step instructions in the Supplementary Information as to how to use loss functions. © 2011 The Author. Clinical and Experimental Pharmacology and Physiology. © 2011 Blackwell Publishing Asia Pty Ltd.

[Analysis of binary classification repeated measurement data with GEE and GLMMs using SPSS software].

PubMed

An, Shengli; Zhang, Yanhong; Chen, Zheng

2012-12-01

To analyze binary classification repeated measurement data with generalized estimating equations (GEE) and generalized linear mixed models (GLMMs) using SPSS19.0. GEE and GLMMs models were tested using binary classification repeated measurement data sample using SPSS19.0. Compared with SAS, SPSS19.0 allowed convenient analysis of categorical repeated measurement data using GEE and GLMMs.

Study report on guidelines and test procedures for investigating stability of nonlinear cardiovascular control system models

NASA Technical Reports Server (NTRS)

Fitzjerrell, D. G.

1974-01-01

A general study of the stability of nonlinear as compared to linear control systems is presented. The analysis is general and, therefore, applies to other types of nonlinear biological control systems as well as the cardiovascular control system models. Both inherent and numerical stability are discussed for corresponding analytical and graphic methods and numerical methods.

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.

Bayesian inference on risk differences: an application to multivariate meta-analysis of adverse events in clinical trials.

PubMed

Chen, Yong; Luo, Sheng; Chu, Haitao; Wei, Peng

2013-05-01

Multivariate meta-analysis is useful in combining evidence from independent studies which involve several comparisons among groups based on a single outcome. For binary outcomes, the commonly used statistical models for multivariate meta-analysis are multivariate generalized linear mixed effects models which assume risks, after some transformation, follow a multivariate normal distribution with possible correlations. In this article, we consider an alternative model for multivariate meta-analysis where the risks are modeled by the multivariate beta distribution proposed by Sarmanov (1966). This model have several attractive features compared to the conventional multivariate generalized linear mixed effects models, including simplicity of likelihood function, no need to specify a link function, and has a closed-form expression of distribution functions for study-specific risk differences. We investigate the finite sample performance of this model by simulation studies and illustrate its use with an application to multivariate meta-analysis of adverse events of tricyclic antidepressants treatment in clinical trials.

A new formalism for modelling parameters α and β of the linear-quadratic model of cell survival for hadron therapy

NASA Astrophysics Data System (ADS)

Vassiliev, Oleg N.; Grosshans, David R.; Mohan, Radhe

2017-10-01

We propose a new formalism for calculating parameters α and β of the linear-quadratic model of cell survival. This formalism, primarily intended for calculating relative biological effectiveness (RBE) for treatment planning in hadron therapy, is based on a recently proposed microdosimetric revision of the single-target multi-hit model. The main advantage of our formalism is that it reliably produces α and β that have correct general properties with respect to their dependence on physical properties of the beam, including the asymptotic behavior for very low and high linear energy transfer (LET) beams. For example, in the case of monoenergetic beams, our formalism predicts that, as a function of LET, (a) α has a maximum and (b) the α/β ratio increases monotonically with increasing LET. No prior models reviewed in this study predict both properties (a) and (b) correctly, and therefore, these prior models are valid only within a limited LET range. We first present our formalism in a general form, for polyenergetic beams. A significant new result in this general case is that parameter β is represented as an average over the joint distribution of energies E 1 and E 2 of two particles in the beam. This result is consistent with the role of the quadratic term in the linear-quadratic model. It accounts for the two-track mechanism of cell kill, in which two particles, one after another, damage the same site in the cell nucleus. We then present simplified versions of the formalism, and discuss predicted properties of α and β. Finally, to demonstrate consistency of our formalism with experimental data, we apply it to fit two sets of experimental data: (1) α for heavy ions, covering a broad range of LETs, and (2) β for protons. In both cases, good agreement is achieved.

Spatial Assessment of Model Errors from Four Regression Techniques

Treesearch

Lianjun Zhang; Jeffrey H. Gove; Jeffrey H. Gove

2005-01-01

Fomst modelers have attempted to account for the spatial autocorrelations among trees in growth and yield models by applying alternative regression techniques such as linear mixed models (LMM), generalized additive models (GAM), and geographicalIy weighted regression (GWR). However, the model errors are commonly assessed using average errors across the entire study...

Logit Models for the Analysis of Two-Way Categorical Data

ERIC Educational Resources Information Center

Draxler, Clemens

2011-01-01

This article discusses the application of logit models for the analyses of 2-way categorical observations. The models described are generalized linear models using the logit link function. One of the models is the Rasch model (Rasch, 1960). The objective is to test hypotheses of marginal and conditional independence between explanatory quantities…

Wavelet regression model in forecasting crude oil price

NASA Astrophysics Data System (ADS)

Hamid, Mohd Helmie; Shabri, Ani

2017-05-01

This study presents the performance of wavelet multiple linear regression (WMLR) technique in daily crude oil forecasting. WMLR model was developed by integrating the discrete wavelet transform (DWT) and multiple linear regression (MLR) model. The original time series was decomposed to sub-time series with different scales by wavelet theory. Correlation analysis was conducted to assist in the selection of optimal decomposed components as inputs for the WMLR model. The daily WTI crude oil price series has been used in this study to test the prediction capability of the proposed model. The forecasting performance of WMLR model were also compared with regular multiple linear regression (MLR), Autoregressive Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) using root mean square errors (RMSE) and mean absolute errors (MAE). Based on the experimental results, it appears that the WMLR model performs better than the other forecasting technique tested in this study.

Sea surface temperature anomalies, planetary waves, and air-sea feedback in the middle latitudes

NASA Technical Reports Server (NTRS)

Frankignoul, C.

1985-01-01

Current analytical models for large-scale air-sea interactions in the middle latitudes are reviewed in terms of known sea-surface temperature (SST) anomalies. The scales and strength of different atmospheric forcing mechanisms are discussed, along with the damping and feedback processes controlling the evolution of the SST. Difficulties with effective SST modeling are described in terms of the techniques and results of case studies, numerical simulations of mixed-layer variability and statistical modeling. The relationship between SST and diabatic heating anomalies is considered and a linear model is developed for the response of the stationary atmosphere to the air-sea feedback. The results obtained with linear wave models are compared with the linear model results. Finally, sample data are presented from experiments with general circulation models into which specific SST anomaly data for the middle latitudes were introduced.

Linear hypergeneralization of learned dynamics across movement speeds reveals anisotropic, gain-encoding primitives for motor adaptation.

PubMed

Joiner, Wilsaan M; Ajayi, Obafunso; Sing, Gary C; Smith, Maurice A

2011-01-01

The ability to generalize learned motor actions to new contexts is a key feature of the motor system. For example, the ability to ride a bicycle or swing a racket is often first developed at lower speeds and later applied to faster velocities. A number of previous studies have examined the generalization of motor adaptation across movement directions and found that the learned adaptation decays in a pattern consistent with the existence of motor primitives that display narrow Gaussian tuning. However, few studies have examined the generalization of motor adaptation across movement speeds. Following adaptation to linear velocity-dependent dynamics during point-to-point reaching arm movements at one speed, we tested the ability of subjects to transfer this adaptation to short-duration higher-speed movements aimed at the same target. We found near-perfect linear extrapolation of the trained adaptation with respect to both the magnitude and the time course of the velocity profiles associated with the high-speed movements: a 69% increase in movement speed corresponded to a 74% extrapolation of the trained adaptation. The close match between the increase in movement speed and the corresponding increase in adaptation beyond what was trained indicates linear hypergeneralization. Computational modeling shows that this pattern of linear hypergeneralization across movement speeds is not compatible with previous models of adaptation in which motor primitives display isotropic Gaussian tuning of motor output around their preferred velocities. Instead, we show that this generalization pattern indicates that the primitives involved in the adaptation to viscous dynamics display anisotropic tuning in velocity space and encode the gain between motor output and motion state rather than motor output itself.

A comparison of Heuristic method and Llewellyn’s rules for identification of redundant constraints

NASA Astrophysics Data System (ADS)

Estiningsih, Y.; Farikhin; Tjahjana, R. H.

2018-03-01

Important techniques in linear programming is modelling and solving practical optimization. Redundant constraints are consider for their effects on general linear programming problems. Identification and reduce redundant constraints are for avoidance of all the calculations associated when solving an associated linear programming problems. Many researchers have been proposed for identification redundant constraints. This paper a compararison of Heuristic method and Llewellyn’s rules for identification of redundant constraints.

Variability simulations with a steady, linearized primitive equations model

NASA Technical Reports Server (NTRS)

Kinter, J. L., III; Nigam, S.

1985-01-01

Solutions of the steady, primitive equations on a sphere, linearized about a zonally symmetric basic state are computed for the purpose of simulating monthly mean variability in the troposphere. The basic states are observed, winter monthly mean, zonal means of zontal and meridional velocities, temperatures and surface pressures computed from the 15 year NMC time series. A least squares fit to a series of Legendre polynomials is used to compute the basic states between 20 H and the equator, and the hemispheres are assumed symmetric. The model is spectral in the zonal direction, and centered differences are employed in the meridional and vertical directions. Since the model is steady and linear, the solution is obtained by inversion of a block, pente-diagonal matrix. The model simulates the climatology of the GFDL nine level, spectral general circulation model quite closely, particularly in middle latitudes above the boundary layer. This experiment is an extension of that simulation to examine variability of the steady, linear solution.

[Application of SAS macro to evaluated multiplicative and additive interaction in logistic and Cox regression in clinical practices].

PubMed

Nie, Z Q; Ou, Y Q; Zhuang, J; Qu, Y J; Mai, J Z; Chen, J M; Liu, X Q

2016-05-01

Conditional logistic regression analysis and unconditional logistic regression analysis are commonly used in case control study, but Cox proportional hazard model is often used in survival data analysis. Most literature only refer to main effect model, however, generalized linear model differs from general linear model, and the interaction was composed of multiplicative interaction and additive interaction. The former is only statistical significant, but the latter has biological significance. In this paper, macros was written by using SAS 9.4 and the contrast ratio, attributable proportion due to interaction and synergy index were calculated while calculating the items of logistic and Cox regression interactions, and the confidence intervals of Wald, delta and profile likelihood were used to evaluate additive interaction for the reference in big data analysis in clinical epidemiology and in analysis of genetic multiplicative and additive interactions.

A note about high blood pressure in childhood

NASA Astrophysics Data System (ADS)

Teodoro, M. Filomena; Simão, Carla

2017-06-01

In medical, behavioral and social sciences it is usual to get a binary outcome. In the present work is collected information where some of the outcomes are binary variables (1='yes'/ 0='no'). In [14] a preliminary study about the caregivers perception of pediatric hypertension was introduced. An experimental questionnaire was designed to be answered by the caregivers of routine pediatric consultation attendees in the Santa Maria's hospital (HSM). The collected data was statistically analyzed, where a descriptive analysis and a predictive model were performed. Significant relations between some socio-demographic variables and the assessed knowledge were obtained. In [14] can be found a statistical data analysis using partial questionnaire's information. The present article completes the statistical approach estimating a model for relevant remaining questions of questionnaire by Generalized Linear Models (GLM). Exploring the binary outcome issue, we intend to extend this approach using Generalized Linear Mixed Models (GLMM), but the process is still ongoing.

Fair Package Assignment

NASA Astrophysics Data System (ADS)

Lahaie, Sébastien; Parkes, David C.

We consider the problem of fair allocation in the package assignment model, where a set of indivisible items, held by single seller, must be efficiently allocated to agents with quasi-linear utilities. A fair assignment is one that is efficient and envy-free. We consider a model where bidders have superadditive valuations, meaning that items are pure complements. Our central result is that core outcomes are fair and even coalition-fair over this domain, while fair distributions may not even exist for general valuations. Of relevance to auction design, we also establish that the core is equivalent to the set of anonymous-price competitive equilibria, and that superadditive valuations are a maximal domain that guarantees the existence of anonymous-price competitive equilibrium. Our results are analogs of core equivalence results for linear prices in the standard assignment model, and for nonlinear, non-anonymous prices in the package assignment model with general valuations.

Ancestral haplotype-based association mapping with generalized linear mixed models accounting for stratification.

PubMed

Zhang, Z; Guillaume, F; Sartelet, A; Charlier, C; Georges, M; Farnir, F; Druet, T

2012-10-01

In many situations, genome-wide association studies are performed in populations presenting stratification. Mixed models including a kinship matrix accounting for genetic relatedness among individuals have been shown to correct for population and/or family structure. Here we extend this methodology to generalized linear mixed models which properly model data under various distributions. In addition we perform association with ancestral haplotypes inferred using a hidden Markov model. The method was shown to properly account for stratification under various simulated scenari presenting population and/or family structure. Use of ancestral haplotypes resulted in higher power than SNPs on simulated datasets. Application to real data demonstrates the usefulness of the developed model. Full analysis of a dataset with 4600 individuals and 500 000 SNPs was performed in 2 h 36 min and required 2.28 Gb of RAM. The software GLASCOW can be freely downloaded from www.giga.ulg.ac.be/jcms/prod_381171/software. francois.guillaume@jouy.inra.fr Supplementary data are available at Bioinformatics online.

Optimal Scaling of Interaction Effects in Generalized Linear Models

ERIC Educational Resources Information Center

van Rosmalen, Joost; Koning, Alex J.; Groenen, Patrick J. F.

2009-01-01

Multiplicative interaction models, such as Goodman's (1981) RC(M) association models, can be a useful tool for analyzing the content of interaction effects. However, most models for interaction effects are suitable only for data sets with two or three predictor variables. Here, we discuss an optimal scaling model for analyzing the content of…

Extended Mixed-Efects Item Response Models with the MH-RM Algorithm

ERIC Educational Resources Information Center

Chalmers, R. Philip

2015-01-01

A mixed-effects item response theory (IRT) model is presented as a logical extension of the generalized linear mixed-effects modeling approach to formulating explanatory IRT models. Fixed and random coefficients in the extended model are estimated using a Metropolis-Hastings Robbins-Monro (MH-RM) stochastic imputation algorithm to accommodate for…

Bayesian Model Comparison for the Order Restricted RC Association Model

ERIC Educational Resources Information Center

Iliopoulos, G.; Kateri, M.; Ntzoufras, I.

2009-01-01

Association models constitute an attractive alternative to the usual log-linear models for modeling the dependence between classification variables. They impose special structure on the underlying association by assigning scores on the levels of each classification variable, which can be fixed or parametric. Under the general row-column (RC)…

Theory of the lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability

NASA Technical Reports Server (NTRS)

Lallemand, Pierre; Luo, Li-Shi

2000-01-01

The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyper-viscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters which optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some 2D LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long wave-length limit (wave vector k = 0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis.

Interpreting the g loadings of intelligence test composite scores in light of Spearman's law of diminishing returns.

PubMed

Reynolds, Matthew R

2013-03-01

The linear loadings of intelligence test composite scores on a general factor (g) have been investigated recently in factor analytic studies. Spearman's law of diminishing returns (SLODR), however, implies that the g loadings of test scores likely decrease in magnitude as g increases, or they are nonlinear. The purpose of this study was to (a) investigate whether the g loadings of composite scores from the Differential Ability Scales (2nd ed.) (DAS-II, C. D. Elliott, 2007a, Differential Ability Scales (2nd ed.). San Antonio, TX: Pearson) were nonlinear and (b) if they were nonlinear, to compare them with linear g loadings to demonstrate how SLODR alters the interpretation of these loadings. Linear and nonlinear confirmatory factor analysis (CFA) models were used to model Nonverbal Reasoning, Verbal Ability, Visual Spatial Ability, Working Memory, and Processing Speed composite scores in four age groups (5-6, 7-8, 9-13, and 14-17) from the DAS-II norming sample. The nonlinear CFA models provided better fit to the data than did the linear models. In support of SLODR, estimates obtained from the nonlinear CFAs indicated that g loadings decreased as g level increased. The nonlinear portion for the nonverbal reasoning loading, however, was not statistically significant across the age groups. Knowledge of general ability level informs composite score interpretation because g is less likely to produce differences, or is measured less, in those scores at higher g levels. One implication is that it may be more important to examine the pattern of specific abilities at higher general ability levels. PsycINFO Database Record (c) 2013 APA, all rights reserved.

Generalized Structured Component Analysis

ERIC Educational Resources Information Center

Hwang, Heungsun; Takane, Yoshio

2004-01-01

We propose an alternative method to partial least squares for path analysis with components, called generalized structured component analysis. The proposed method replaces factors by exact linear combinations of observed variables. It employs a well-defined least squares criterion to estimate model parameters. As a result, the proposed method…

State variable modeling of the integrated engine and aircraft dynamics

NASA Astrophysics Data System (ADS)

Rotaru, Constantin; Sprinţu, Iuliana

2014-12-01

This study explores the dynamic characteristics of the combined aircraft-engine system, based on the general theory of the state variables for linear and nonlinear systems, with details leading first to the separate formulation of the longitudinal and the lateral directional state variable models, followed by the merging of the aircraft and engine models into a single state variable model. The linearized equations were expressed in a matrix form and the engine dynamics was included in terms of variation of thrust following a deflection of the throttle. The linear model of the shaft dynamics for a two-spool jet engine was derived by extending the one-spool model. The results include the discussion of the thrust effect upon the aircraft response when the thrust force associated with the engine has a sizable moment arm with respect to the aircraft center of gravity for creating a compensating moment.

Majorization Minimization by Coordinate Descent for Concave Penalized Generalized Linear Models

PubMed Central

Jiang, Dingfeng; Huang, Jian

2013-01-01

Recent studies have demonstrated theoretical attractiveness of a class of concave penalties in variable selection, including the smoothly clipped absolute deviation and minimax concave penalties. The computation of the concave penalized solutions in high-dimensional models, however, is a difficult task. We propose a majorization minimization by coordinate descent (MMCD) algorithm for computing the concave penalized solutions in generalized linear models. In contrast to the existing algorithms that use local quadratic or local linear approximation to the penalty function, the MMCD seeks to majorize the negative log-likelihood by a quadratic loss, but does not use any approximation to the penalty. This strategy makes it possible to avoid the computation of a scaling factor in each update of the solutions, which improves the efficiency of coordinate descent. Under certain regularity conditions, we establish theoretical convergence property of the MMCD. We implement this algorithm for a penalized logistic regression model using the SCAD and MCP penalties. Simulation studies and a data example demonstrate that the MMCD works sufficiently fast for the penalized logistic regression in high-dimensional settings where the number of covariates is much larger than the sample size. PMID:25309048

Robust root clustering for linear uncertain systems using generalized Lyapunov theory

NASA Technical Reports Server (NTRS)

Yedavalli, R. K.

1993-01-01

Consideration is given to the problem of matrix root clustering in subregions of a complex plane for linear state space models with real parameter uncertainty. The nominal matrix root clustering theory of Gutman & Jury (1981) using the generalized Liapunov equation is extended to the perturbed matrix case, and bounds are derived on the perturbation to maintain root clustering inside a given region. The theory makes it possible to obtain an explicit relationship between the parameters of the root clustering region and the uncertainty range of the parameter space.

Linearized Programming of Memristors for Artificial Neuro-Sensor Signal Processing

PubMed Central

Yang, Changju; Kim, Hyongsuk

2016-01-01

A linearized programming method of memristor-based neural weights is proposed. Memristor is known as an ideal element to implement a neural synapse due to its embedded functions of analog memory and analog multiplication. Its resistance variation with a voltage input is generally a nonlinear function of time. Linearization of memristance variation about time is very important for the easiness of memristor programming. In this paper, a method utilizing an anti-serial architecture for linear programming is proposed. The anti-serial architecture is composed of two memristors with opposite polarities. It linearizes the variation of memristance due to complimentary actions of two memristors. For programming a memristor, additional memristor with opposite polarity is employed. The linearization effect of weight programming of an anti-serial architecture is investigated and memristor bridge synapse which is built with two sets of anti-serial memristor architecture is taken as an application example of the proposed method. Simulations are performed with memristors of both linear drift model and nonlinear model. PMID:27548186

Linearized Programming of Memristors for Artificial Neuro-Sensor Signal Processing.

PubMed

Yang, Changju; Kim, Hyongsuk

2016-08-19

A linearized programming method of memristor-based neural weights is proposed. Memristor is known as an ideal element to implement a neural synapse due to its embedded functions of analog memory and analog multiplication. Its resistance variation with a voltage input is generally a nonlinear function of time. Linearization of memristance variation about time is very important for the easiness of memristor programming. In this paper, a method utilizing an anti-serial architecture for linear programming is proposed. The anti-serial architecture is composed of two memristors with opposite polarities. It linearizes the variation of memristance due to complimentary actions of two memristors. For programming a memristor, additional memristor with opposite polarity is employed. The linearization effect of weight programming of an anti-serial architecture is investigated and memristor bridge synapse which is built with two sets of anti-serial memristor architecture is taken as an application example of the proposed method. Simulations are performed with memristors of both linear drift model and nonlinear model.

Extending local canonical correlation analysis to handle general linear contrasts for FMRI data.

PubMed

Jin, Mingwu; Nandy, Rajesh; Curran, Tim; Cordes, Dietmar

2012-01-01

Local canonical correlation analysis (CCA) is a multivariate method that has been proposed to more accurately determine activation patterns in fMRI data. In its conventional formulation, CCA has several drawbacks that limit its usefulness in fMRI. A major drawback is that, unlike the general linear model (GLM), a test of general linear contrasts of the temporal regressors has not been incorporated into the CCA formalism. To overcome this drawback, a novel directional test statistic was derived using the equivalence of multivariate multiple regression (MVMR) and CCA. This extension will allow CCA to be used for inference of general linear contrasts in more complicated fMRI designs without reparameterization of the design matrix and without reestimating the CCA solutions for each particular contrast of interest. With the proper constraints on the spatial coefficients of CCA, this test statistic can yield a more powerful test on the inference of evoked brain regional activations from noisy fMRI data than the conventional t-test in the GLM. The quantitative results from simulated and pseudoreal data and activation maps from fMRI data were used to demonstrate the advantage of this novel test statistic.

Extending Local Canonical Correlation Analysis to Handle General Linear Contrasts for fMRI Data

PubMed Central

Jin, Mingwu; Nandy, Rajesh; Curran, Tim; Cordes, Dietmar

2012-01-01

Local canonical correlation analysis (CCA) is a multivariate method that has been proposed to more accurately determine activation patterns in fMRI data. In its conventional formulation, CCA has several drawbacks that limit its usefulness in fMRI. A major drawback is that, unlike the general linear model (GLM), a test of general linear contrasts of the temporal regressors has not been incorporated into the CCA formalism. To overcome this drawback, a novel directional test statistic was derived using the equivalence of multivariate multiple regression (MVMR) and CCA. This extension will allow CCA to be used for inference of general linear contrasts in more complicated fMRI designs without reparameterization of the design matrix and without reestimating the CCA solutions for each particular contrast of interest. With the proper constraints on the spatial coefficients of CCA, this test statistic can yield a more powerful test on the inference of evoked brain regional activations from noisy fMRI data than the conventional t-test in the GLM. The quantitative results from simulated and pseudoreal data and activation maps from fMRI data were used to demonstrate the advantage of this novel test statistic. PMID:22461786

Chemical networks with inflows and outflows: a positive linear differential inclusions approach.

PubMed

Angeli, David; De Leenheer, Patrick; Sontag, Eduardo D

2009-01-01

Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to a ubiquitous biochemical reaction network with inflows and outflows, known as the futile cycle. We also provide a characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle. 2009 American Institute of Chemical Engineers

Stability margin of linear systems with parameters described by fuzzy numbers.

PubMed

Husek, Petr

2011-10-01

This paper deals with the linear systems with uncertain parameters described by fuzzy numbers. The problem of determining the stability margin of those systems with linear affine dependence of the coefficients of a characteristic polynomial on system parameters is studied. Fuzzy numbers describing the system parameters are allowed to be characterized by arbitrary nonsymmetric membership functions. An elegant solution, graphical in nature, based on generalization of the Tsypkin-Polyak plot is presented. The advantage of the presented approach over the classical robust concept is demonstrated on a control of the Fiat Dedra engine model and a control of the quarter car suspension model.

Simple, Efficient Estimators of Treatment Effects in Randomized Trials Using Generalized Linear Models to Leverage Baseline Variables

PubMed Central

Rosenblum, Michael; van der Laan, Mark J.

2010-01-01

Models, such as logistic regression and Poisson regression models, are often used to estimate treatment effects in randomized trials. These models leverage information in variables collected before randomization, in order to obtain more precise estimates of treatment effects. However, there is the danger that model misspecification will lead to bias. We show that certain easy to compute, model-based estimators are asymptotically unbiased even when the working model used is arbitrarily misspecified. Furthermore, these estimators are locally efficient. As a special case of our main result, we consider a simple Poisson working model containing only main terms; in this case, we prove the maximum likelihood estimate of the coefficient corresponding to the treatment variable is an asymptotically unbiased estimator of the marginal log rate ratio, even when the working model is arbitrarily misspecified. This is the log-linear analog of ANCOVA for linear models. Our results demonstrate one application of targeted maximum likelihood estimation. PMID:20628636

General job stress: a unidimensional measure and its non-linear relations with outcome variables.

PubMed

Yankelevich, Maya; Broadfoot, Alison; Gillespie, Jennifer Z; Gillespie, Michael A; Guidroz, Ashley

2012-04-01

This article aims to examine the non-linear relations between a general measure of job stress [Stress in General (SIG)] and two outcome variables: intentions to quit and job satisfaction. In so doing, we also re-examine the factor structure of the SIG and determine that, as a two-factor scale, it obscures non-linear relations with outcomes. Thus, in this research, we not only test for non-linear relations between stress and outcome variables but also present an updated version of the SIG scale. Using two distinct samples of working adults (sample 1, N = 589; sample 2, N = 4322), results indicate that a more parsimonious eight-item SIG has better model-data fit than the 15-item two-factor SIG and that the eight-item SIG has non-linear relations with job satisfaction and intentions to quit. Specifically, the revised SIG has an inverted curvilinear J-shaped relation with job satisfaction such that job satisfaction drops precipitously after a certain level of stress; the SIG has a J-shaped curvilinear relation with intentions to quit such that turnover intentions increase exponentially after a certain level of stress. Copyright © 2011 John Wiley & Sons, Ltd.

Nonlinear time series modeling and forecasting the seismic data of the Hindu Kush region

NASA Astrophysics Data System (ADS)

Khan, Muhammad Yousaf; Mittnik, Stefan

2018-01-01

In this study, we extended the application of linear and nonlinear time models in the field of earthquake seismology and examined the out-of-sample forecast accuracy of linear Autoregressive (AR), Autoregressive Conditional Duration (ACD), Self-Exciting Threshold Autoregressive (SETAR), Threshold Autoregressive (TAR), Logistic Smooth Transition Autoregressive (LSTAR), Additive Autoregressive (AAR), and Artificial Neural Network (ANN) models for seismic data of the Hindu Kush region. We also extended the previous studies by using Vector Autoregressive (VAR) and Threshold Vector Autoregressive (TVAR) models and compared their forecasting accuracy with linear AR model. Unlike previous studies that typically consider the threshold model specifications by using internal threshold variable, we specified these models with external transition variables and compared their out-of-sample forecasting performance with the linear benchmark AR model. The modeling results show that time series models used in the present study are capable of capturing the dynamic structure present in the seismic data. The point forecast results indicate that the AR model generally outperforms the nonlinear models. However, in some cases, threshold models with external threshold variables specification produce more accurate forecasts, indicating that specification of threshold time series models is of crucial importance. For raw seismic data, the ACD model does not show an improved out-of-sample forecasting performance over the linear AR model. The results indicate that the AR model is the best forecasting device to model and forecast the raw seismic data of the Hindu Kush region.

A generalized reaction diffusion model for spatial structure formed by motile cells.

PubMed

Ochoa, F L

1984-01-01

A non-linear stability analysis using a multi-scale perturbation procedure is carried out on a model of a generalized reaction diffusion mechanism which involves only a single equation but which nevertheless exhibits bifurcation to non-uniform states. The patterns generated by this model by variation in a parameter related to the scalar dimensions of domain of definition, indicate its capacity to represent certain key morphogenetic features of multicellular systems formed by motile cells.

Profile-Likelihood Approach for Estimating Generalized Linear Mixed Models with Factor Structures

ERIC Educational Resources Information Center

Jeon, Minjeong; Rabe-Hesketh, Sophia

2012-01-01

In this article, the authors suggest a profile-likelihood approach for estimating complex models by maximum likelihood (ML) using standard software and minimal programming. The method works whenever setting some of the parameters of the model to known constants turns the model into a standard model. An important class of models that can be…

Directed electromagnetic wave propagation in 1D metamaterial: Projecting operators method

NASA Astrophysics Data System (ADS)

Ampilogov, Dmitrii; Leble, Sergey

2016-07-01

We consider a boundary problem for 1D electrodynamics modeling of a pulse propagation in a metamaterial medium. We build and apply projecting operators to a Maxwell system in time domain that allows to split the linear propagation problem to directed waves for a material relations with general dispersion. Matrix elements of the projectors act as convolution integral operators. For a weak nonlinearity we generalize the linear results still for arbitrary dispersion and derive the system of interacting right/left waves with combined (hybrid) amplitudes. The result is specified for the popular metamaterial model with Drude formula for both permittivity and permeability coefficients. We also discuss and investigate stationary solutions of the system related to some boundary regimes.

Novel forecasting approaches using combination of machine learning and statistical models for flood susceptibility mapping.

PubMed

Shafizadeh-Moghadam, Hossein; Valavi, Roozbeh; Shahabi, Himan; Chapi, Kamran; Shirzadi, Ataollah

2018-07-01

In this research, eight individual machine learning and statistical models are implemented and compared, and based on their results, seven ensemble models for flood susceptibility assessment are introduced. The individual models included artificial neural networks, classification and regression trees, flexible discriminant analysis, generalized linear model, generalized additive model, boosted regression trees, multivariate adaptive regression splines, and maximum entropy, and the ensemble models were Ensemble Model committee averaging (EMca), Ensemble Model confidence interval Inferior (EMciInf), Ensemble Model confidence interval Superior (EMciSup), Ensemble Model to estimate the coefficient of variation (EMcv), Ensemble Model to estimate the mean (EMmean), Ensemble Model to estimate the median (EMmedian), and Ensemble Model based on weighted mean (EMwmean). The data set covered 201 flood events in the Haraz watershed (Mazandaran province in Iran) and 10,000 randomly selected non-occurrence points. Among the individual models, the Area Under the Receiver Operating Characteristic (AUROC), which showed the highest value, belonged to boosted regression trees (0.975) and the lowest value was recorded for generalized linear model (0.642). On the other hand, the proposed EMmedian resulted in the highest accuracy (0.976) among all models. In spite of the outstanding performance of some models, nevertheless, variability among the prediction of individual models was considerable. Therefore, to reduce uncertainty, creating more generalizable, more stable, and less sensitive models, ensemble forecasting approaches and in particular the EMmedian is recommended for flood susceptibility assessment. Copyright © 2018 Elsevier Ltd. All rights reserved.

ADME evaluation in drug discovery. 1. Applications of genetic algorithms to the prediction of blood-brain partitioning of a large set of drugs.

PubMed

Hou, Tingjun; Xu, Xiaojie

2002-12-01

In this study, the relationships between the brain-blood concentration ratio of 96 structurally diverse compounds with a large number of structurally derived descriptors were investigated. The linear models were based on molecular descriptors that can be calculated for any compound simply from a knowledge of its molecular structure. The linear correlation coefficients of the models were optimized by genetic algorithms (GAs), and the descriptors used in the linear models were automatically selected from 27 structurally derived descriptors. The GA optimizations resulted in a group of linear models with three or four molecular descriptors with good statistical significance. The change of descriptor use as the evolution proceeds demonstrates that the octane/water partition coefficient and the partial negative solvent-accessible surface area multiplied by the negative charge are crucial to brain-blood barrier permeability. Moreover, we found that the predictions using multiple QSPR models from GA optimization gave quite good results in spite of the diversity of structures, which was better than the predictions using the best single model. The predictions for the two external sets with 37 diverse compounds using multiple QSPR models indicate that the best linear models with four descriptors are sufficiently effective for predictive use. Considering the ease of computation of the descriptors, the linear models may be used as general utilities to screen the blood-brain barrier partitioning of drugs in a high-throughput fashion.

Estimating PM2.5 Concentrations in Xi'an City Using a Generalized Additive Model with Multi-Source Monitoring Data

PubMed Central

Song, Yong-Ze; Yang, Hong-Lei; Peng, Jun-Huan; Song, Yi-Rong; Sun, Qian; Li, Yuan

2015-01-01

Particulate matter with an aerodynamic diameter <2.5 μm (PM2.5) represents a severe environmental problem and is of negative impact on human health. Xi'an City, with a population of 6.5 million, is among the highest concentrations of PM2.5 in China. In 2013, in total, there were 191 days in Xi’an City on which PM2.5 concentrations were greater than 100 μg/m3. Recently, a few studies have explored the potential causes of high PM2.5 concentration using remote sensing data such as the MODIS aerosol optical thickness (AOT) product. Linear regression is a commonly used method to find statistical relationships among PM2.5 concentrations and other pollutants, including CO, NO2, SO2, and O3, which can be indicative of emission sources. The relationships of these variables, however, are usually complicated and non-linear. Therefore, a generalized additive model (GAM) is used to estimate the statistical relationships between potential variables and PM2.5 concentrations. This model contains linear functions of SO2 and CO, univariate smoothing non-linear functions of NO2, O3, AOT and temperature, and bivariate smoothing non-linear functions of location and wind variables. The model can explain 69.50% of PM2.5 concentrations, with R2 = 0.691, which improves the result of a stepwise linear regression (R2 = 0.582) by 18.73%. The two most significant variables, CO concentration and AOT, represent 20.65% and 19.54% of the deviance, respectively, while the three other gas-phase concentrations, SO2, NO2, and O3 account for 10.88% of the total deviance. These results show that in Xi'an City, the traffic and other industrial emissions are the primary source of PM2.5. Temperature, location, and wind variables also non-linearly related with PM2.5. PMID:26540446

SOCR Analyses - an Instructional Java Web-based Statistical Analysis Toolkit.

PubMed

Chu, Annie; Cui, Jenny; Dinov, Ivo D

2009-03-01

The Statistical Online Computational Resource (SOCR) designs web-based tools for educational use in a variety of undergraduate courses (Dinov 2006). Several studies have demonstrated that these resources significantly improve students' motivation and learning experiences (Dinov et al. 2008). SOCR Analyses is a new component that concentrates on data modeling and analysis using parametric and non-parametric techniques supported with graphical model diagnostics. Currently implemented analyses include commonly used models in undergraduate statistics courses like linear models (Simple Linear Regression, Multiple Linear Regression, One-Way and Two-Way ANOVA). In addition, we implemented tests for sample comparisons, such as t-test in the parametric category; and Wilcoxon rank sum test, Kruskal-Wallis test, Friedman's test, in the non-parametric category. SOCR Analyses also include several hypothesis test models, such as Contingency tables, Friedman's test and Fisher's exact test.The code itself is open source (http://socr.googlecode.com/), hoping to contribute to the efforts of the statistical computing community. The code includes functionality for each specific analysis model and it has general utilities that can be applied in various statistical computing tasks. For example, concrete methods with API (Application Programming Interface) have been implemented in statistical summary, least square solutions of general linear models, rank calculations, etc. HTML interfaces, tutorials, source code, activities, and data are freely available via the web (www.SOCR.ucla.edu). Code examples for developers and demos for educators are provided on the SOCR Wiki website.In this article, the pedagogical utilization of the SOCR Analyses is discussed, as well as the underlying design framework. As the SOCR project is on-going and more functions and tools are being added to it, these resources are constantly improved. The reader is strongly encouraged to check the SOCR site for most updated information and newly added models.

Linear-time reconstruction of zero-recombinant Mendelian inheritance on pedigrees without mating loops.

PubMed

Liu, Lan; Jiang, Tao

2007-01-01

With the launch of the international HapMap project, the haplotype inference problem has attracted a great deal of attention in the computational biology community recently. In this paper, we study the question of how to efficiently infer haplotypes from genotypes of individuals related by a pedigree without mating loops, assuming that the hereditary process was free of mutations (i.e. the Mendelian law of inheritance) and recombinants. We model the haplotype inference problem as a system of linear equations as in [10] and present an (optimal) linear-time (i.e. O(mn) time) algorithm to generate a particular solution (A particular solution of any linear system is an assignment of numerical values to the variables in the system which satisfies the equations in the system.) to the haplotype inference problem, where m is the number of loci (or markers) in a genotype and n is the number of individuals in the pedigree. Moreover, the algorithm also provides a general solution (A general solution of any linear system is denoted by the span of a basis in the solution space to its associated homogeneous system, offset from the origin by a vector, namely by any particular solution. A general solution for ZRHC is very useful in practice because it allows the end user to efficiently enumerate all solutions for ZRHC and performs tasks such as random sampling.) in O(mn2) time, which is optimal because the size of a general solution could be as large as Theta(mn2). The key ingredients of our construction are (i) a fast consistency checking procedure for the system of linear equations introduced in [10] based on a careful investigation of the relationship between the equations (ii) a novel linear-time method for solving linear equations without invoking the Gaussian elimination method. Although such a fast method for solving equations is not known for general systems of linear equations, we take advantage of the underlying loop-free pedigree graph and some special properties of the linear equations.

Diagnostics for generalized linear hierarchical models in network meta-analysis.

PubMed

Zhao, Hong; Hodges, James S; Carlin, Bradley P

2017-09-01

Network meta-analysis (NMA) combines direct and indirect evidence comparing more than 2 treatments. Inconsistency arises when these 2 information sources differ. Previous work focuses on inconsistency detection, but little has been done on how to proceed after identifying inconsistency. The key issue is whether inconsistency changes an NMA's substantive conclusions. In this paper, we examine such discrepancies from a diagnostic point of view. Our methods seek to detect influential and outlying observations in NMA at a trial-by-arm level. These observations may have a large effect on the parameter estimates in NMA, or they may deviate markedly from other observations. We develop formal diagnostics for a Bayesian hierarchical model to check the effect of deleting any observation. Diagnostics are specified for generalized linear hierarchical NMA models and investigated for both published and simulated datasets. Results from our example dataset using either contrast- or arm-based models and from the simulated datasets indicate that the sources of inconsistency in NMA tend not to be influential, though results from the example dataset suggest that they are likely to be outliers. This mimics a familiar result from linear model theory, in which outliers with low leverage are not influential. Future extensions include incorporating baseline covariates and individual-level patient data. Copyright © 2017 John Wiley & Sons, Ltd.

Gravitational field of static p -branes in linearized ghost-free gravity

NASA Astrophysics Data System (ADS)

Boos, Jens; Frolov, Valeri P.; Zelnikov, Andrei

2018-04-01

We study the gravitational field of static p -branes in D -dimensional Minkowski space in the framework of linearized ghost-free (GF) gravity. The concrete models of GF gravity we consider are parametrized by the nonlocal form factors exp (-□/μ2) and exp (□2/μ4) , where μ-1 is the scale of nonlocality. We show that the singular behavior of the gravitational field of p -branes in general relativity is cured by short-range modifications introduced by the nonlocalities, and we derive exact expressions of the regularized gravitational fields, whose geometry can be written as a warped metric. For large distances compared to the scale of nonlocality, μ r →∞ , our solutions approach those found in linearized general relativity.

A generalized Lyapunov theory for robust root clustering of linear state space models with real parameter uncertainty

NASA Technical Reports Server (NTRS)

Yedavalli, R. K.

1992-01-01

The problem of analyzing and designing controllers for linear systems subject to real parameter uncertainty is considered. An elegant, unified theory for robust eigenvalue placement is presented for a class of D-regions defined by algebraic inequalities by extending the nominal matrix root clustering theory of Gutman and Jury (1981) to linear uncertain time systems. The author presents explicit conditions for matrix root clustering for different D-regions and establishes the relationship between the eigenvalue migration range and the parameter range. The bounds are all obtained by one-shot computation in the matrix domain and do not need any frequency sweeping or parameter gridding. The method uses the generalized Lyapunov theory for getting the bounds.

Two-dimensional motion of Brownian swimmers in linear flows.

PubMed

Sandoval, Mario; Jimenez, Alonso

2016-03-01

The motion of viruses and bacteria and even synthetic microswimmers can be affected by thermal fluctuations and by external flows. In this work, we study the effect of linear external flows and thermal fluctuations on the diffusion of those swimmers modeled as spherical active (self-propelled) particles moving in two dimensions. General formulae for their mean-square displacement under a general linear flow are presented. We also provide, at short and long times, explicit expressions for the mean-square displacement of a swimmer immersed in three canonical flows, namely, solid-body rotation, shear and extensional flows. These expressions can now be used to estimate the effect of external flows on the displacement of Brownian microswimmers. Finally, our theoretical results are validated by using Brownian dynamics simulations.

A new Newton-like method for solving nonlinear equations.

PubMed

Saheya, B; Chen, Guo-Qing; Sui, Yun-Kang; Wu, Cai-Ying

2016-01-01

This paper presents an iterative scheme for solving nonline ar equations. We establish a new rational approximation model with linear numerator and denominator which has generalizes the local linear model. We then employ the new approximation for nonlinear equations and propose an improved Newton's method to solve it. The new method revises the Jacobian matrix by a rank one matrix each iteration and obtains the quadratic convergence property. The numerical performance and comparison show that the proposed method is efficient.

Measures and models for angular correlation and angular-linear correlation. [correlation of random variables

NASA Technical Reports Server (NTRS)

Johnson, R. A.; Wehrly, T.

1976-01-01

Population models for dependence between two angular measurements and for dependence between an angular and a linear observation are proposed. The method of canonical correlations first leads to new population and sample measures of dependence in this latter situation. An example relating wind direction to the level of a pollutant is given. Next, applied to pairs of angular measurements, the method yields previously proposed sample measures in some special cases and a new sample measure in general.

The Fisher-KPP problem with doubly nonlinear diffusion

NASA Astrophysics Data System (ADS)

Audrito, Alessandro; Vázquez, Juan Luis

2017-12-01

The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it possesses a family of travelling waves that describe the asymptotic behaviour of a large class solutions 0 ≤ u (x , t) ≤ 1 of the problem posed in the real line. The existence of propagation waves with finite speed has been confirmed in some related models and disproved in others. We investigate here the corresponding theory when the linear diffusion is replaced by the "slow" doubly nonlinear diffusion and we find travelling waves that represent the wave propagation of more general solutions even when we extend the study to several space dimensions. A similar study is performed in the critical case that we call "pseudo-linear", i.e., when the operator is still nonlinear but has homogeneity one. With respect to the classical model and the "pseudo-linear" case, the "slow" travelling waves exhibit free boundaries.

Control for Population Structure and Relatedness for Binary Traits in Genetic Association Studies via Logistic Mixed Models

PubMed Central

Chen, Han; Wang, Chaolong; Conomos, Matthew P.; Stilp, Adrienne M.; Li, Zilin; Sofer, Tamar; Szpiro, Adam A.; Chen, Wei; Brehm, John M.; Celedón, Juan C.; Redline, Susan; Papanicolaou, George J.; Thornton, Timothy A.; Laurie, Cathy C.; Rice, Kenneth; Lin, Xihong

2016-01-01

Linear mixed models (LMMs) are widely used in genome-wide association studies (GWASs) to account for population structure and relatedness, for both continuous and binary traits. Motivated by the failure of LMMs to control type I errors in a GWAS of asthma, a binary trait, we show that LMMs are generally inappropriate for analyzing binary traits when population stratification leads to violation of the LMM’s constant-residual variance assumption. To overcome this problem, we develop a computationally efficient logistic mixed model approach for genome-wide analysis of binary traits, the generalized linear mixed model association test (GMMAT). This approach fits a logistic mixed model once per GWAS and performs score tests under the null hypothesis of no association between a binary trait and individual genetic variants. We show in simulation studies and real data analysis that GMMAT effectively controls for population structure and relatedness when analyzing binary traits in a wide variety of study designs. PMID:27018471

Practical robustness measures in multivariable control system analysis. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Lehtomaki, N. A.

1981-01-01

The robustness of the stability of multivariable linear time invariant feedback control systems with respect to model uncertainty is considered using frequency domain criteria. Available robustness tests are unified under a common framework based on the nature and structure of model errors. These results are derived using a multivariable version of Nyquist's stability theorem in which the minimum singular value of the return difference transfer matrix is shown to be the multivariable generalization of the distance to the critical point on a single input, single output Nyquist diagram. Using the return difference transfer matrix, a very general robustness theorem is presented from which all of the robustness tests dealing with specific model errors may be derived. The robustness tests that explicitly utilized model error structure are able to guarantee feedback system stability in the face of model errors of larger magnitude than those robustness tests that do not. The robustness of linear quadratic Gaussian control systems are analyzed.

Modeling demand for public transit services in rural areas

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

Attaluri, P.; Seneviratne, P.N.; Javid, M.

1997-05-01

Accurate estimates of demand are critical for planning, designing, and operating public transit systems. Previous research has demonstrated that the expected demand in rural areas is a function of both demographic and transit system variables. Numerous models have been proposed to describe the relationship between the aforementioned variables. However, most of them are site specific and their validity over time and space is not reported or perhaps has not been tested. Moreover, input variables in some cases are extremely difficult to quantify. In this article, the estimation of demand using the generalized linear modeling technique is discussed. Two separate models,more » one for fixed-route and another for demand-responsive services, are presented. These models, calibrated with data from systems in nine different states, are used to demonstrate the appropriateness and validity of generalized linear models compared to the regression models. They explain over 70% of the variation in expected demand for fixed-route services and 60% of the variation in expected demand for demand-responsive services. It was found that the models are spatially transferable and that data for calibration are easily obtainable.« less

Mediation analysis when a continuous mediator is measured with error and the outcome follows a generalized linear model

PubMed Central

Valeri, Linda; Lin, Xihong; VanderWeele, Tyler J.

2014-01-01

Mediation analysis is a popular approach to examine the extent to which the effect of an exposure on an outcome is through an intermediate variable (mediator) and the extent to which the effect is direct. When the mediator is mis-measured the validity of mediation analysis can be severely undermined. In this paper we first study the bias of classical, non-differential measurement error on a continuous mediator in the estimation of direct and indirect causal effects in generalized linear models when the outcome is either continuous or discrete and exposure-mediator interaction may be present. Our theoretical results as well as a numerical study demonstrate that in the presence of non-linearities the bias of naive estimators for direct and indirect effects that ignore measurement error can take unintuitive directions. We then develop methods to correct for measurement error. Three correction approaches using method of moments, regression calibration and SIMEX are compared. We apply the proposed method to the Massachusetts General Hospital lung cancer study to evaluate the effect of genetic variants mediated through smoking on lung cancer risk. PMID:25220625

Modeling Systematicity and Individuality in Nonlinear Second Language Development: The Case of English Grammatical Morphemes

ERIC Educational Resources Information Center

Murakami, Akira

2016-01-01

This article introduces two sophisticated statistical modeling techniques that allow researchers to analyze systematicity, individual variation, and nonlinearity in second language (L2) development. Generalized linear mixed-effects models can be used to quantify individual variation and examine systematic effects simultaneously, and generalized…

Stochastic field-line wandering in magnetic turbulence with shear. I. Quasi-linear theory

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

Shalchi, A.; Negrea, M.; Petrisor, I.

2016-07-15

We investigate the random walk of magnetic field lines in magnetic turbulence with shear. In the first part of the series, we develop a quasi-linear theory in order to compute the diffusion coefficient of magnetic field lines. We derive general formulas for the diffusion coefficients in the different directions of space. We like to emphasize that we expect that quasi-linear theory is only valid if the so-called Kubo number is small. We consider two turbulence models as examples, namely, a noisy slab model as well as a Gaussian decorrelation model. For both models we compute the field line diffusion coefficientsmore » and we show how they depend on the aforementioned Kubo number as well as a shear parameter. It is demonstrated that the shear effect reduces all field line diffusion coefficients.« less

An Index and Test of Linear Moderated Mediation.

PubMed

Hayes, Andrew F

2015-01-01

I describe a test of linear moderated mediation in path analysis based on an interval estimate of the parameter of a function linking the indirect effect to values of a moderator-a parameter that I call the index of moderated mediation. This test can be used for models that integrate moderation and mediation in which the relationship between the indirect effect and the moderator is estimated as linear, including many of the models described by Edwards and Lambert ( 2007 ) and Preacher, Rucker, and Hayes ( 2007 ) as well as extensions of these models to processes involving multiple mediators operating in parallel or in serial. Generalization of the method to latent variable models is straightforward. Three empirical examples describe the computation of the index and the test, and its implementation is illustrated using Mplus and the PROCESS macro for SPSS and SAS.

Endoreversible quantum heat engines in the linear response regime.

PubMed

Wang, Honghui; He, Jizhou; Wang, Jianhui

2017-07-01

We analyze general models of quantum heat engines operating a cycle of two adiabatic and two isothermal processes. We use the quantum master equation for a system to describe heat transfer current during a thermodynamic process in contact with a heat reservoir, with no use of phenomenological thermal conduction. We apply the endoreversibility description to such engine models working in the linear response regime and derive expressions of the efficiency and the power. By analyzing the entropy production rate along a single cycle, we identify the thermodynamic flux and force that a linear relation connects. From maximizing the power output, we find that such heat engines satisfy the tight-coupling condition and the efficiency at maximum power agrees with the Curzon-Ahlborn efficiency known as the upper bound in the linear response regime.

Feature extraction with deep neural networks by a generalized discriminant analysis.

PubMed

Stuhlsatz, André; Lippel, Jens; Zielke, Thomas

2012-04-01

We present an approach to feature extraction that is a generalization of the classical linear discriminant analysis (LDA) on the basis of deep neural networks (DNNs). As for LDA, discriminative features generated from independent Gaussian class conditionals are assumed. This modeling has the advantages that the intrinsic dimensionality of the feature space is bounded by the number of classes and that the optimal discriminant function is linear. Unfortunately, linear transformations are insufficient to extract optimal discriminative features from arbitrarily distributed raw measurements. The generalized discriminant analysis (GerDA) proposed in this paper uses nonlinear transformations that are learnt by DNNs in a semisupervised fashion. We show that the feature extraction based on our approach displays excellent performance on real-world recognition and detection tasks, such as handwritten digit recognition and face detection. In a series of experiments, we evaluate GerDA features with respect to dimensionality reduction, visualization, classification, and detection. Moreover, we show that GerDA DNNs can preprocess truly high-dimensional input data to low-dimensional representations that facilitate accurate predictions even if simple linear predictors or measures of similarity are used.

Aspects of job scheduling

NASA Technical Reports Server (NTRS)

Phillips, K.

1976-01-01

A mathematical model for job scheduling in a specified context is presented. The model uses both linear programming and combinatorial methods. While designed with a view toward optimization of scheduling of facility and plant operations at the Deep Space Communications Complex, the context is sufficiently general to be widely applicable. The general scheduling problem including options for scheduling objectives is discussed and fundamental parameters identified. Mathematical algorithms for partitioning problems germane to scheduling are presented.

On the linear relation between the mean and the standard deviation of a response time distribution.

PubMed

Wagenmakers, Eric-Jan; Brown, Scott

2007-07-01

Although it is generally accepted that the spread of a response time (RT) distribution increases with the mean, the precise nature of this relation remains relatively unexplored. The authors show that in several descriptive RT distributions, the standard deviation increases linearly with the mean. Results from a wide range of tasks from different experimental paradigms support a linear relation between RT mean and RT standard deviation. Both R. Ratcliff's (1978) diffusion model and G. D. Logan's (1988) instance theory of automatization provide explanations for this linear relation. The authors identify and discuss 3 specific boundary conditions for the linear law to hold. The law constrains RT models and supports the use of the coefficient of variation to (a) compare variability while controlling for differences in baseline speed of processing and (b) assess whether changes in performance with practice are due to quantitative speedup or qualitative reorganization. Copyright 2007 APA.

Wave kinetics of random fibre lasers

PubMed Central

Churkin, D V.; Kolokolov, I V.; Podivilov, E V.; Vatnik, I D.; Nikulin, M A.; Vergeles, S S.; Terekhov, I S.; Lebedev, V V.; Falkovich, G.; Babin, S A.; Turitsyn, S K.

2015-01-01

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics. PMID:25645177

The use of generalized linear models and generalized estimating equations in bioarchaeological studies.

PubMed

Nikita, Efthymia

2014-03-01

The current article explores whether the application of generalized linear models (GLM) and generalized estimating equations (GEE) can be used in place of conventional statistical analyses in the study of ordinal data that code an underlying continuous variable, like entheseal changes. The analysis of artificial data and ordinal data expressing entheseal changes in archaeological North African populations gave the following results. Parametric and nonparametric tests give convergent results particularly for P values <0.1, irrespective of whether the underlying variable is normally distributed or not under the condition that the samples involved in the tests exhibit approximately equal sizes. If this prerequisite is valid and provided that the samples are of equal variances, analysis of covariance may be adopted. GLM are not subject to constraints and give results that converge to those obtained from all nonparametric tests. Therefore, they can be used instead of traditional tests as they give the same amount of information as them, but with the advantage of allowing the study of the simultaneous impact of multiple predictors and their interactions and the modeling of the experimental data. However, GLM should be replaced by GEE for the study of bilateral asymmetry and in general when paired samples are tested, because GEE are appropriate for correlated data. Copyright © 2013 Wiley Periodicals, Inc.

Neuroimaging Research: from Null-Hypothesis Falsification to Out-Of-Sample Generalization

ERIC Educational Resources Information Center

Bzdok, Danilo; Varoquaux, Gaël; Thirion, Bertrand

2017-01-01

Brain-imaging technology has boosted the quantification of neurobiological phenomena underlying human mental operations and their disturbances. Since its inception, drawing inference on neurophysiological effects hinged on classical statistical methods, especially, the general linear model. The tens of thousands of variables per brain scan were…

Semilinear programming: applications and implementation

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

Mohan, S.

Semilinear programming is a method of solving optimization problems with linear constraints where the non-negativity restrictions on the variables are dropped and the objective function coefficients can take on different values depending on whether the variable is positive or negative. The simplex method for linear programming is modified in this thesis to solve general semilinear and piecewise linear programs efficiently without having to transform them into equivalent standard linear programs. Several models in widely different areas of optimization such as production smoothing, facility locations, goal programming and L/sub 1/ estimation are presented first to demonstrate the compact formulation that arisesmore » when such problems are formulated as semilinear programs. A code SLP is constructed using the semilinear programming techniques. Problems in aggregate planning and L/sub 1/ estimation are solved using SLP and equivalent linear programs using a linear programming simplex code. Comparisons of CPU times and number iterations indicate SLP to be far superior. The semilinear programming techniques are extended to piecewise linear programming in the implementation of the code PLP. Piecewise linear models in aggregate planning are solved using PLP and equivalent standard linear programs using a simple upper bounded linear programming code SUBLP.« less

A Search for Mountain Waves in MLS Stratospheric Limb Radiances from the Winter Northern Hemisphere: Data Analysis and Global Mountain Wave Modeling

DTIC Science & Technology

2004-02-11

the general circulation of the middle atmosphere, Philos. Trans. R. Soc. London, Ser. A, 323, 693–705. Anton , H. (2000), Elementary Linear Algebra ...Because the saturated radiances may depend slightly on tangent height as the limb path length decreases, a linear trend (described by parameters a and b...track days and interpolated onto the same limb-track orbits. The color bar scale for radiance variance is linear . (b) Digital elevations of northern

Non-Linear Concentration-Response Relationships between Ambient Ozone and Daily Mortality.

PubMed

Bae, Sanghyuk; Lim, Youn-Hee; Kashima, Saori; Yorifuji, Takashi; Honda, Yasushi; Kim, Ho; Hong, Yun-Chul

2015-01-01

Ambient ozone (O3) concentration has been reported to be significantly associated with mortality. However, linearity of the relationships and the presence of a threshold has been controversial. The aim of the present study was to examine the concentration-response relationship and threshold of the association between ambient O3 concentration and non-accidental mortality in 13 Japanese and Korean cities from 2000 to 2009. We selected Japanese and Korean cities which have population of over 1 million. We constructed Poisson regression models adjusting daily mean temperature, daily mean PM10, humidity, time trend, season, year, day of the week, holidays and yearly population. The association between O3 concentration and mortality was examined using linear, spline and linear-threshold models. The thresholds were estimated for each city, by constructing linear-threshold models. We also examined the city-combined association using a generalized additive mixed model. The mean O3 concentration did not differ greatly between Korea and Japan, which were 26.2 ppb and 24.2 ppb, respectively. Seven out of 13 cities showed better fits for the spline model compared with the linear model, supporting a non-linear relationships between O3 concentration and mortality. All of the 7 cities showed J or U shaped associations suggesting the existence of thresholds. The range of city-specific thresholds was from 11 to 34 ppb. The city-combined analysis also showed a non-linear association with a threshold around 30-40 ppb. We have observed non-linear concentration-response relationship with thresholds between daily mean ambient O3 concentration and daily number of non-accidental death in Japanese and Korean cities.

Shear-flexible finite-element models of laminated composite plates and shells

NASA Technical Reports Server (NTRS)

Noor, A. K.; Mathers, M. D.

1975-01-01

Several finite-element models are applied to the linear static, stability, and vibration analysis of laminated composite plates and shells. The study is based on linear shallow-shell theory, with the effects of shear deformation, anisotropic material behavior, and bending-extensional coupling included. Both stiffness (displacement) and mixed finite-element models are considered. Discussion is focused on the effects of shear deformation and anisotropic material behavior on the accuracy and convergence of different finite-element models. Numerical studies are presented which show the effects of increasing the order of the approximating polynomials, adding internal degrees of freedom, and using derivatives of generalized displacements as nodal parameters.

Model Analysis and Model Creation: Capturing the Task-Model Structure of Quantitative Item Domains. Research Report. ETS RR-06-11

ERIC Educational Resources Information Center

Deane, Paul; Graf, Edith Aurora; Higgins, Derrick; Futagi, Yoko; Lawless, René

2006-01-01

This study focuses on the relationship between item modeling and evidence-centered design (ECD); it considers how an appropriately generalized item modeling software tool can support systematic identification and exploitation of task-model variables, and then examines the feasibility of this goal, using linear-equation items as a test case. The…

On the repeated measures designs and sample sizes for randomized controlled trials.

PubMed

Tango, Toshiro

2016-04-01

For the analysis of longitudinal or repeated measures data, generalized linear mixed-effects models provide a flexible and powerful tool to deal with heterogeneity among subject response profiles. However, the typical statistical design adopted in usual randomized controlled trials is an analysis of covariance type analysis using a pre-defined pair of "pre-post" data, in which pre-(baseline) data are used as a covariate for adjustment together with other covariates. Then, the major design issue is to calculate the sample size or the number of subjects allocated to each treatment group. In this paper, we propose a new repeated measures design and sample size calculations combined with generalized linear mixed-effects models that depend not only on the number of subjects but on the number of repeated measures before and after randomization per subject used for the analysis. The main advantages of the proposed design combined with the generalized linear mixed-effects models are (1) it can easily handle missing data by applying the likelihood-based ignorable analyses under the missing at random assumption and (2) it may lead to a reduction in sample size, compared with the simple pre-post design. The proposed designs and the sample size calculations are illustrated with real data arising from randomized controlled trials. © The Author 2015. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Multishaker modal testing

NASA Technical Reports Server (NTRS)

Craig, Roy R., Jr.

1987-01-01

The major accomplishments of this research are: (1) the refinement and documentation of a multi-input, multi-output modal parameter estimation algorithm which is applicable to general linear, time-invariant dynamic systems; (2) the development and testing of an unsymmetric block-Lanzcos algorithm for reduced-order modeling of linear systems with arbitrary damping; and (3) the development of a control-structure-interaction (CSI) test facility.

Assessing variance components in multilevel linear models using approximate Bayes factors: A case study of ethnic disparities in birthweight

PubMed Central

Saville, Benjamin R.; Herring, Amy H.; Kaufman, Jay S.

2013-01-01

Racial/ethnic disparities in birthweight are a large source of differential morbidity and mortality worldwide and have remained largely unexplained in epidemiologic models. We assess the impact of maternal ancestry and census tract residence on infant birth weights in New York City and the modifying effects of race and nativity by incorporating random effects in a multilevel linear model. Evaluating the significance of these predictors involves the test of whether the variances of the random effects are equal to zero. This is problematic because the null hypothesis lies on the boundary of the parameter space. We generalize an approach for assessing random effects in the two-level linear model to a broader class of multilevel linear models by scaling the random effects to the residual variance and introducing parameters that control the relative contribution of the random effects. After integrating over the random effects and variance components, the resulting integrals needed to calculate the Bayes factor can be efficiently approximated with Laplace’s method. PMID:24082430

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

PubMed Central

2011-01-01

Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task. PMID:21867520

Query construction, entropy, and generalization in neural-network models

NASA Astrophysics Data System (ADS)

Sollich, Peter

1994-05-01

We study query construction algorithms, which aim at improving the generalization ability of systems that learn from examples by choosing optimal, nonredundant training sets. We set up a general probabilistic framework for deriving such algorithms from the requirement of optimizing a suitable objective function; specifically, we consider the objective functions entropy (or information gain) and generalization error. For two learning scenarios, the high-low game and the linear perceptron, we evaluate the generalization performance obtained by applying the corresponding query construction algorithms and compare it to training on random examples. We find qualitative differences between the two scenarios due to the different structure of the underlying rules (nonlinear and ``noninvertible'' versus linear); in particular, for the linear perceptron, random examples lead to the same generalization ability as a sequence of queries in the limit of an infinite number of examples. We also investigate learning algorithms which are ill matched to the learning environment and find that, in this case, minimum entropy queries can in fact yield a lower generalization ability than random examples. Finally, we study the efficiency of single queries and its dependence on the learning history, i.e., on whether the previous training examples were generated randomly or by querying, and the difference between globally and locally optimal query construction.

Meteorological influences on the interannual variability of meningitis incidence in northwest Nigeria.

NASA Astrophysics Data System (ADS)

Abdussalam, Auwal; Monaghan, Andrew; Dukic, Vanja; Hayden, Mary; Hopson, Thomas; Leckebusch, Gregor

2013-04-01

Northwest Nigeria is a region with high risk of bacterial meningitis. Since the first documented epidemic of meningitis in Nigeria in 1905, the disease has been endemic in the northern part of the country, with epidemics occurring regularly. In this study we examine the influence of climate on the interannual variability of meningitis incidence and epidemics. Monthly aggregate counts of clinically confirmed hospital-reported cases of meningitis were collected in northwest Nigeria for the 22-year period spanning 1990-2011. Several generalized linear statistical models were fit to the monthly meningitis counts, including generalized additive models. Explanatory variables included monthly records of temperatures, humidity, rainfall, wind speed, sunshine and dustiness from weather stations nearest to the hospitals, and a time series of polysaccharide vaccination efficacy. The effects of other confounding factors -- i.e., mainly non-climatic factors for which records were not available -- were estimated as a smooth, monthly-varying function of time in the generalized additive models. Results reveal that the most important explanatory climatic variables are mean maximum monthly temperature, relative humidity and dustiness. Accounting for confounding factors (e.g., social processes) in the generalized additive models explains more of the year-to-year variation of meningococcal disease compared to those generalized linear models that do not account for such factors. Promising results from several models that included only explanatory variables that preceded the meningitis case data by 1-month suggest there may be potential for prediction of meningitis in northwest Nigeria to aid decision makers on this time scale.

Development of control strategies for safe microburst penetration: A progress report

NASA Technical Reports Server (NTRS)

Psiaki, Mark L.

1987-01-01

A single-engine, propeller-driven, general-aviation model was incorporated into the nonlinear simulation and into the linear analysis of root loci and frequency response. Full-scale wind tunnel data provided its aerodynamic model, and the thrust model included the airspeed dependent effects of power and propeller efficiency. Also, the parameters of the Jet Transport model were changed to correspond more closely to the Boeing 727. In order to study their effects on steady-state repsonse to vertical wind inputs, altitude and total specific energy (air-relative and inertial) feedback capabilities were added to the nonlinear and linear models. Multiloop system design goals were defined. Attempts were made to develop controllers which achieved these goals.

Simulation of extreme rainfall and projection of future changes using the GLIMCLIM model

NASA Astrophysics Data System (ADS)

Rashid, Md. Mamunur; Beecham, Simon; Chowdhury, Rezaul Kabir

2017-10-01

In this study, the performance of the Generalized LInear Modelling of daily CLImate sequence (GLIMCLIM) statistical downscaling model was assessed to simulate extreme rainfall indices and annual maximum daily rainfall (AMDR) when downscaled daily rainfall from National Centers for Environmental Prediction (NCEP) reanalysis and Coupled Model Intercomparison Project Phase 5 (CMIP5) general circulation models (GCM) (four GCMs and two scenarios) output datasets and then their changes were estimated for the future period 2041-2060. The model was able to reproduce the monthly variations in the extreme rainfall indices reasonably well when forced by the NCEP reanalysis datasets. Frequency Adapted Quantile Mapping (FAQM) was used to remove bias in the simulated daily rainfall when forced by CMIP5 GCMs, which reduced the discrepancy between observed and simulated extreme rainfall indices. Although the observed AMDR were within the 2.5th and 97.5th percentiles of the simulated AMDR, the model consistently under-predicted the inter-annual variability of AMDR. A non-stationary model was developed using the generalized linear model for local, shape and scale to estimate the AMDR with an annual exceedance probability of 0.01. The study shows that in general, AMDR is likely to decrease in the future. The Onkaparinga catchment will also experience drier conditions due to an increase in consecutive dry days coinciding with decreases in heavy (>long term 90th percentile) rainfall days, empirical 90th quantile of rainfall and maximum 5-day consecutive total rainfall for the future period (2041-2060) compared to the base period (1961-2000).

A conformal approach for the analysis of the non-linear stability of radiation cosmologies

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

Luebbe, Christian, E-mail: c.luebbe@ucl.ac.uk; Department of Mathematics, University of Leicester, University Road, LE1 8RH; Valiente Kroon, Juan Antonio, E-mail: j.a.valiente-kroon@qmul.ac.uk

2013-01-15

The conformal Einstein equations for a trace-free (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de Sitter-like trace-free (radiation) perfect fluid Friedman-Lemaitre-Robertson-Walker cosmological models. The solutions thus obtained exist globally towards the future and are future geodesically complete. - Highlights: Black-Right-Pointing-Pointer We study the Einstein-Euler system in General Relativity using conformal methods. Black-Right-Pointing-Pointer We analyze the structural properties of the associated evolution equations. Black-Right-Pointing-Pointer We establish the non-linear stability of pure radiation cosmological models.

Thermospheric dynamics - A system theory approach

NASA Technical Reports Server (NTRS)

Codrescu, M.; Forbes, J. M.; Roble, R. G.

1990-01-01

A system theory approach to thermospheric modeling is developed, based upon a linearization method which is capable of preserving nonlinear features of a dynamical system. The method is tested using a large, nonlinear, time-varying system, namely the thermospheric general circulation model (TGCM) of the National Center for Atmospheric Research. In the linearized version an equivalent system, defined for one of the desired TGCM output variables, is characterized by a set of response functions that is constructed from corresponding quasi-steady state and unit sample response functions. The linearized version of the system runs on a personal computer and produces an approximation of the desired TGCM output field height profile at a given geographic location.

A Thermodynamic Theory Of Solid Viscoelasticity. Part 1: Linear Viscoelasticity.

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Leonov, Arkady I.

2002-01-01

The present series of three consecutive papers develops a general theory for linear and finite solid viscoelasticity. Because the most important object for nonlinear studies are rubber-like materials, the general approach is specified in a form convenient for solving problems important for many industries that involve rubber-like materials. General linear and nonlinear theories for non-isothermal deformations of viscoelastic solids are developed based on the quasi-linear approach of non-equilibrium thermodynamics. In this, the first paper of the series, we analyze non-isothermal linear viscoelasticity, which is applicable in a range of small strains not only to all synthetic polymers and bio-polymers but also to some non-polymeric materials. Although the linear case seems to be well developed, there still are some reasons to implement a thermodynamic derivation of constitutive equations for solid-like, non-isothermal, linear viscoelasticity. The most important is the thermodynamic modeling of thermo-rheological complexity , i.e. different temperature dependences of relaxation parameters in various parts of relaxation spectrum. A special structure of interaction matrices is established for different physical mechanisms contributed to the normal relaxation modes. This structure seems to be in accord with observations, and creates a simple mathematical framework for both continuum and molecular theories of the thermo-rheological complex relaxation phenomena. Finally, a unified approach is briefly discussed that, in principle, allows combining both the long time (discrete) and short time (continuous) descriptions of relaxation behaviors for polymers in the rubbery and glassy regions.

Effect Sizes for Growth-Modeling Analysis for Controlled Clinical Trials in the Same Metric as for Classical Analysis

ERIC Educational Resources Information Center

Feingold, Alan

2009-01-01

The use of growth-modeling analysis (GMA)--including hierarchical linear models, latent growth models, and general estimating equations--to evaluate interventions in psychology, psychiatry, and prevention science has grown rapidly over the last decade. However, an effect size associated with the difference between the trajectories of the…

Spatial regression methods capture prediction uncertainty in species distribution model projections through time

Treesearch

Alan K. Swanson; Solomon Z. Dobrowski; Andrew O. Finley; James H. Thorne; Michael K. Schwartz

2013-01-01

The uncertainty associated with species distribution model (SDM) projections is poorly characterized, despite its potential value to decision makers. Error estimates from most modelling techniques have been shown to be biased due to their failure to account for spatial autocorrelation (SAC) of residual error. Generalized linear mixed models (GLMM) have the ability to...

Dynamical Analysis in the Mathematical Modelling of Human Blood Glucose

ERIC Educational Resources Information Center

Bae, Saebyok; Kang, Byungmin

2012-01-01

We want to apply the geometrical method to a dynamical system of human blood glucose. Due to the educational importance of model building, we show a relatively general modelling process using observational facts. Next, two models of some concrete forms are analysed in the phase plane by means of linear stability, phase portrait and vector…

Center for Parallel Optimization.

DTIC Science & Technology

1996-03-19

A NEW OPTIMIZATION BASED APPROACH TO IMPROVING GENERALIZATION IN MACHINE LEARNING HAS BEEN PROPOSED AND COMPUTATIONALLY VALIDATED ON SIMPLE LINEAR MODELS AS WELL AS ON HIGHLY NONLINEAR SYSTEMS SUCH AS NEURAL NETWORKS.

Using a generalized linear mixed model approach to explore the role of age, motor proficiency, and cognitive styles in children's reach estimation accuracy.

PubMed

Caçola, Priscila M; Pant, Mohan D

2014-10-01

The purpose was to use a multi-level statistical technique to analyze how children's age, motor proficiency, and cognitive styles interact to affect accuracy on reach estimation tasks via Motor Imagery and Visual Imagery. Results from the Generalized Linear Mixed Model analysis (GLMM) indicated that only the 7-year-old age group had significant random intercepts for both tasks. Motor proficiency predicted accuracy in reach tasks, and cognitive styles (object scale) predicted accuracy in the motor imagery task. GLMM analysis is suitable to explore age and other parameters of development. In this case, it allowed an assessment of motor proficiency interacting with age to shape how children represent, plan, and act on the environment.

Analysis and comparison of end effects in linear switched reluctance and hybrid motors

NASA Astrophysics Data System (ADS)

Barhoumi, El Manaa; Abo-Khalil, Ahmed Galal; Berrouche, Youcef; Wurtz, Frederic

2017-03-01

This paper presents and discusses the longitudinal and transversal end effects which affects the propulsive force of linear motors. Generally, the modeling of linear machine considers the forces distortion due to the specific geometry of linear actuators. The insertion of permanent magnets on the stator allows improving the propulsive force produced by switched reluctance linear motors. Also, the inserted permanent magnets in the hybrid structure allow reducing considerably the ends effects observed in linear motors. The analysis was conducted using 2D and 3D finite elements method. The permanent magnet reinforces the flux produced by the winding and reorients it which allows modifying the impact of end effects. Presented simulations and discussions show the importance of this study to characterize the end effects in two different linear motors.

Modelling leaf photosynthetic and transpiration temperature-dependent responses in Vitis vinifera cv. Semillon grapevines growing in hot, irrigated vineyard conditions

PubMed Central

Greer, Dennis H.

2012-01-01

Background and aims Grapevines growing in Australia are often exposed to very high temperatures and the question of how the gas exchange processes adjust to these conditions is not well understood. The aim was to develop a model of photosynthesis and transpiration in relation to temperature to quantify the impact of the growing conditions on vine performance. Methodology Leaf gas exchange was measured along the grapevine shoots in accordance with their growth and development over several growing seasons. Using a general linear statistical modelling approach, photosynthesis and transpiration were modelled against leaf temperature separated into bands and the model parameters and coefficients applied to independent datasets to validate the model. Principal results Photosynthesis, transpiration and stomatal conductance varied along the shoot, with early emerging leaves having the highest rates, but these declined as later emerging leaves increased their gas exchange capacities in accordance with development. The general linear modelling approach applied to these data revealed that photosynthesis at each temperature was additively dependent on stomatal conductance, internal CO2 concentration and photon flux density. The temperature-dependent coefficients for these parameters applied to other datasets gave a predicted rate of photosynthesis that was linearly related to the measured rates, with a 1 : 1 slope. Temperature-dependent transpiration was multiplicatively related to stomatal conductance and the leaf to air vapour pressure deficit and applying the coefficients also showed a highly linear relationship, with a 1 : 1 slope between measured and modelled rates, when applied to independent datasets. Conclusions The models developed for the grapevines were relatively simple but accounted for much of the seasonal variation in photosynthesis and transpiration. The goodness of fit in each case demonstrated that explicitly selecting leaf temperature as a model parameter, rather than including temperature intrinsically as is usually done in more complex models, was warranted. PMID:22567220

Principal Curves on Riemannian Manifolds.

PubMed

Hauberg, Soren

2016-09-01

Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimizes a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend to imply that the methods only work well when the manifold is mostly flat within the support of the generating distribution. We argue that instead of generalizing linear Euclidean models, it is more fruitful to generalize non-linear Euclidean models. Specifically, we extend the classic Principal Curves from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls of traditional geodesic approaches. We empirically demonstrate the effectiveness of the Riemannian principal curves on several manifolds and datasets.

The Log-Linear Cognitive Diagnostic Model (LCDM) as a Special Case of The General Diagnostic Model (GDM). Research Report. ETS RR-14-40

ERIC Educational Resources Information Center

von Davier, Matthias

2014-01-01

Diagnostic models combine multiple binary latent variables in an attempt to produce a latent structure that provides more information about test takers' performance than do unidimensional latent variable models. Recent developments in diagnostic modeling emphasize the possibility that multiple skills may interact in a conjunctive way within the…

Underground Mathematics

ERIC Educational Resources Information Center

Hadlock, Charles R

2013-01-01

The movement of groundwater in underground aquifers is an ideal physical example of many important themes in mathematical modeling, ranging from general principles (like Occam's Razor) to specific techniques (such as geometry, linear equations, and the calculus). This article gives a self-contained introduction to groundwater modeling with…

A General Multidimensional Model for the Measurement of Cultural Differences.

ERIC Educational Resources Information Center

Olmedo, Esteban L.; Martinez, Sergio R.

A multidimensional model for measuring cultural differences (MCD) based on factor analytic theory and techniques is proposed. The model assumes that a cultural space may be defined by means of a relatively small number of orthogonal dimensions which are linear combinations of a much larger number of cultural variables. Once a suitable,…

Prescriptive Statements and Educational Practice: What Can Structural Equation Modeling (SEM) Offer?

ERIC Educational Resources Information Center

Martin, Andrew J.

2011-01-01

Longitudinal structural equation modeling (SEM) can be a basis for making prescriptive statements on educational practice and offers yields over "traditional" statistical techniques under the general linear model. The extent to which prescriptive statements can be made will rely on the appropriate accommodation of key elements of research design,…

Power Analysis for Complex Mediational Designs Using Monte Carlo Methods

ERIC Educational Resources Information Center

Thoemmes, Felix; MacKinnon, David P.; Reiser, Mark R.

2010-01-01

Applied researchers often include mediation effects in applications of advanced methods such as latent variable models and linear growth curve models. Guidance on how to estimate statistical power to detect mediation for these models has not yet been addressed in the literature. We describe a general framework for power analyses for complex…

Detection of genomic loci associated with environmental variables using generalized linear mixed models.

PubMed

Lobréaux, Stéphane; Melodelima, Christelle

2015-02-01

We tested the use of Generalized Linear Mixed Models to detect associations between genetic loci and environmental variables, taking into account the population structure of sampled individuals. We used a simulation approach to generate datasets under demographically and selectively explicit models. These datasets were used to analyze and optimize GLMM capacity to detect the association between markers and selective coefficients as environmental data in terms of false and true positive rates. Different sampling strategies were tested, maximizing the number of populations sampled, sites sampled per population, or individuals sampled per site, and the effect of different selective intensities on the efficiency of the method was determined. Finally, we apply these models to an Arabidopsis thaliana SNP dataset from different accessions, looking for loci associated with spring minimal temperature. We identified 25 regions that exhibit unusual correlations with the climatic variable and contain genes with functions related to temperature stress. Copyright © 2014 Elsevier Inc. All rights reserved.

Generalized soldering of {+-}2 helicity states in D=2+1

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

Dalmazi, D.; Mendonca, Elias L.

2009-07-15

The direct sum of a couple of Maxwell-Chern-Simons gauge theories of opposite helicities {+-}1 does not lead to a Proca theory in D=2+1, although both theories share the same spectrum. However, it is known that by adding an interference term between both helicities we can join the complementary pieces together and obtain the physically expected result. A generalized soldering procedure can be defined to generate the missing interference term. Here, we show that the same procedure can be applied to join together {+-}2 helicity states in a full off-shell manner. In particular, by using second-order (in derivatives) self-dual models ofmore » helicities {+-}2 (spin-2 analogues of Maxwell-Chern-Simmons models) the Fierz-Pauli theory is obtained after soldering. Remarkably, if we replace the second-order models by third-order self-dual models (linearized topologically massive gravity) of opposite helicities, after soldering, we end up exactly with the new massive gravity theory of Bergshoeff, Hohm, and Townsend in its linearized approximation.« less

Phenomenology of stochastic exponential growth

NASA Astrophysics Data System (ADS)

Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya

2017-06-01

Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.

Conditional Monte Carlo randomization tests for regression models.

PubMed

Parhat, Parwen; Rosenberger, William F; Diao, Guoqing

2014-08-15

We discuss the computation of randomization tests for clinical trials of two treatments when the primary outcome is based on a regression model. We begin by revisiting the seminal paper of Gail, Tan, and Piantadosi (1988), and then describe a method based on Monte Carlo generation of randomization sequences. The tests based on this Monte Carlo procedure are design based, in that they incorporate the particular randomization procedure used. We discuss permuted block designs, complete randomization, and biased coin designs. We also use a new technique by Plamadeala and Rosenberger (2012) for simple computation of conditional randomization tests. Like Gail, Tan, and Piantadosi, we focus on residuals from generalized linear models and martingale residuals from survival models. Such techniques do not apply to longitudinal data analysis, and we introduce a method for computation of randomization tests based on the predicted rate of change from a generalized linear mixed model when outcomes are longitudinal. We show, by simulation, that these randomization tests preserve the size and power well under model misspecification. Copyright © 2014 John Wiley & Sons, Ltd.

Linear analysis of auto-organization in Hebbian neural networks.

PubMed

Carlos Letelier, J; Mpodozis, J

1995-01-01

The self-organization of neurotopies where neural connections follow Hebbian dynamics is framed in terms of linear operator theory. A general and exact equation describing the time evolution of the overall synaptic strength connecting two neural laminae is derived. This linear matricial equation, which is similar to the equations used to describe oscillating systems in physics, is modified by the introduction of non-linear terms, in order to capture self-organizing (or auto-organizing) processes. The behavior of a simple and small system, that contains a non-linearity that mimics a metabolic constraint, is analyzed by computer simulations. The emergence of a simple "order" (or degree of organization) in this low-dimensionality model system is discussed.

Generalized Predictive and Neural Generalized Predictive Control of Aerospace Systems

NASA Technical Reports Server (NTRS)

Kelkar, Atul G.

2000-01-01

The research work presented in this thesis addresses the problem of robust control of uncertain linear and nonlinear systems using Neural network-based Generalized Predictive Control (NGPC) methodology. A brief overview of predictive control and its comparison with Linear Quadratic (LQ) control is given to emphasize advantages and drawbacks of predictive control methods. It is shown that the Generalized Predictive Control (GPC) methodology overcomes the drawbacks associated with traditional LQ control as well as conventional predictive control methods. It is shown that in spite of the model-based nature of GPC it has good robustness properties being special case of receding horizon control. The conditions for choosing tuning parameters for GPC to ensure closed-loop stability are derived. A neural network-based GPC architecture is proposed for the control of linear and nonlinear uncertain systems. A methodology to account for parametric uncertainty in the system is proposed using on-line training capability of multi-layer neural network. Several simulation examples and results from real-time experiments are given to demonstrate the effectiveness of the proposed methodology.

Multi-disease analysis of maternal antibody decay using non-linear mixed models accounting for censoring.

PubMed

Goeyvaerts, Nele; Leuridan, Elke; Faes, Christel; Van Damme, Pierre; Hens, Niel

2015-09-10

Biomedical studies often generate repeated measures of multiple outcomes on a set of subjects. It may be of interest to develop a biologically intuitive model for the joint evolution of these outcomes while assessing inter-subject heterogeneity. Even though it is common for biological processes to entail non-linear relationships, examples of multivariate non-linear mixed models (MNMMs) are still fairly rare. We contribute to this area by jointly analyzing the maternal antibody decay for measles, mumps, rubella, and varicella, allowing for a different non-linear decay model for each infectious disease. We present a general modeling framework to analyze multivariate non-linear longitudinal profiles subject to censoring, by combining multivariate random effects, non-linear growth and Tobit regression. We explore the hypothesis of a common infant-specific mechanism underlying maternal immunity using a pairwise correlated random-effects approach and evaluating different correlation matrix structures. The implied marginal correlation between maternal antibody levels is estimated using simulations. The mean duration of passive immunity was less than 4 months for all diseases with substantial heterogeneity between infants. The maternal antibody levels against rubella and varicella were found to be positively correlated, while little to no correlation could be inferred for the other disease pairs. For some pairs, computational issues occurred with increasing correlation matrix complexity, which underlines the importance of further developing estimation methods for MNMMs. Copyright © 2015 John Wiley & Sons, Ltd.

Advanced statistics: linear regression, part II: multiple linear regression.

PubMed

Marill, Keith A

2004-01-01

The applications of simple linear regression in medical research are limited, because in most situations, there are multiple relevant predictor variables. Univariate statistical techniques such as simple linear regression use a single predictor variable, and they often may be mathematically correct but clinically misleading. Multiple linear regression is a mathematical technique used to model the relationship between multiple independent predictor variables and a single dependent outcome variable. It is used in medical research to model observational data, as well as in diagnostic and therapeutic studies in which the outcome is dependent on more than one factor. Although the technique generally is limited to data that can be expressed with a linear function, it benefits from a well-developed mathematical framework that yields unique solutions and exact confidence intervals for regression coefficients. Building on Part I of this series, this article acquaints the reader with some of the important concepts in multiple regression analysis. These include multicollinearity, interaction effects, and an expansion of the discussion of inference testing, leverage, and variable transformations to multivariate models. Examples from the first article in this series are expanded on using a primarily graphic, rather than mathematical, approach. The importance of the relationships among the predictor variables and the dependence of the multivariate model coefficients on the choice of these variables are stressed. Finally, concepts in regression model building are discussed.

Reprint of Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-04-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-03-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

A novel heuristic for optimization aggregate production problem: Evidence from flat panel display in Malaysia

NASA Astrophysics Data System (ADS)

Al-Kuhali, K.; Hussain M., I.; Zain Z., M.; Mullenix, P.

2015-05-01

Aim: This paper contribute to the flat panel display industry it terms of aggregate production planning. Methodology: For the minimization cost of total production of LCD manufacturing, a linear programming was applied. The decision variables are general production costs, additional cost incurred for overtime production, additional cost incurred for subcontracting, inventory carrying cost, backorder costs and adjustments for changes incurred within labour levels. Model has been developed considering a manufacturer having several product types, which the maximum types are N, along a total time period of T. Results: Industrial case study based on Malaysia is presented to test and to validate the developed linear programming model for aggregate production planning. Conclusion: The model development is fit under stable environment conditions. Overall it can be recommended to adapt the proven linear programming model to production planning of Malaysian flat panel display industry.

A comparison of optimal MIMO linear and nonlinear models for brain machine interfaces

NASA Astrophysics Data System (ADS)

Kim, S.-P.; Sanchez, J. C.; Rao, Y. N.; Erdogmus, D.; Carmena, J. M.; Lebedev, M. A.; Nicolelis, M. A. L.; Principe, J. C.

2006-06-01

The field of brain-machine interfaces requires the estimation of a mapping from spike trains collected in motor cortex areas to the hand kinematics of the behaving animal. This paper presents a systematic investigation of several linear (Wiener filter, LMS adaptive filters, gamma filter, subspace Wiener filters) and nonlinear models (time-delay neural network and local linear switching models) applied to datasets from two experiments in monkeys performing motor tasks (reaching for food and target hitting). Ensembles of 100-200 cortical neurons were simultaneously recorded in these experiments, and even larger neuronal samples are anticipated in the future. Due to the large size of the models (thousands of parameters), the major issue studied was the generalization performance. Every parameter of the models (not only the weights) was selected optimally using signal processing and machine learning techniques. The models were also compared statistically with respect to the Wiener filter as the baseline. Each of the optimization procedures produced improvements over that baseline for either one of the two datasets or both.

A comparison of optimal MIMO linear and nonlinear models for brain-machine interfaces.

PubMed

Kim, S-P; Sanchez, J C; Rao, Y N; Erdogmus, D; Carmena, J M; Lebedev, M A; Nicolelis, M A L; Principe, J C

2006-06-01

The field of brain-machine interfaces requires the estimation of a mapping from spike trains collected in motor cortex areas to the hand kinematics of the behaving animal. This paper presents a systematic investigation of several linear (Wiener filter, LMS adaptive filters, gamma filter, subspace Wiener filters) and nonlinear models (time-delay neural network and local linear switching models) applied to datasets from two experiments in monkeys performing motor tasks (reaching for food and target hitting). Ensembles of 100-200 cortical neurons were simultaneously recorded in these experiments, and even larger neuronal samples are anticipated in the future. Due to the large size of the models (thousands of parameters), the major issue studied was the generalization performance. Every parameter of the models (not only the weights) was selected optimally using signal processing and machine learning techniques. The models were also compared statistically with respect to the Wiener filter as the baseline. Each of the optimization procedures produced improvements over that baseline for either one of the two datasets or both.

Identification of Linear and Nonlinear Sensory Processing Circuits from Spiking Neuron Data.

PubMed

Florescu, Dorian; Coca, Daniel

2018-03-01

Inferring mathematical models of sensory processing systems directly from input-output observations, while making the fewest assumptions about the model equations and the types of measurements available, is still a major issue in computational neuroscience. This letter introduces two new approaches for identifying sensory circuit models consisting of linear and nonlinear filters in series with spiking neuron models, based only on the sampled analog input to the filter and the recorded spike train output of the spiking neuron. For an ideal integrate-and-fire neuron model, the first algorithm can identify the spiking neuron parameters as well as the structure and parameters of an arbitrary nonlinear filter connected to it. The second algorithm can identify the parameters of the more general leaky integrate-and-fire spiking neuron model, as well as the parameters of an arbitrary linear filter connected to it. Numerical studies involving simulated and real experimental recordings are used to demonstrate the applicability and evaluate the performance of the proposed algorithms.

Stable static structures in models with higher-order derivatives

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

Bazeia, D., E-mail: bazeia@fisica.ufpb.br; Departamento de Física, Universidade Federal de Campina Grande, 58109-970 Campina Grande, PB; Lobão, A.S.

2015-09-15

We investigate the presence of static solutions in generalized models described by a real scalar field in four-dimensional space–time. We study models in which the scalar field engenders higher-order derivatives and spontaneous symmetry breaking, inducing the presence of domain walls. Despite the presence of higher-order derivatives, the models keep to equations of motion second-order differential equations, so we focus on the presence of first-order equations that help us to obtain analytical solutions and investigate linear stability on general grounds. We then illustrate the general results with some specific examples, showing that the domain wall may become compact and that themore » zero mode may split. Moreover, if the model is further generalized to include k-field behavior, it may contribute to split the static structure itself.« less

Integration of system identification and finite element modelling of nonlinear vibrating structures

NASA Astrophysics Data System (ADS)

Cooper, Samson B.; DiMaio, Dario; Ewins, David J.

2018-03-01

The Finite Element Method (FEM), Experimental modal analysis (EMA) and other linear analysis techniques have been established as reliable tools for the dynamic analysis of engineering structures. They are often used to provide solutions to small and large structures and other variety of cases in structural dynamics, even those exhibiting a certain degree of nonlinearity. Unfortunately, when the nonlinear effects are substantial or the accuracy of the predicted response is of vital importance, a linear finite element model will generally prove to be unsatisfactory. As a result, the validated linear FE model requires further enhancement so that it can represent and predict the nonlinear behaviour exhibited by the structure. In this paper, a pragmatic approach to integrating test-based system identification and FE modelling of a nonlinear structure is presented. This integration is based on three different phases: the first phase involves the derivation of an Underlying Linear Model (ULM) of the structure, the second phase includes experiment-based nonlinear identification using measured time series and the third phase covers augmenting the linear FE model and experimental validation of the nonlinear FE model. The proposed case study is demonstrated on a twin cantilever beam assembly coupled with a flexible arch shaped beam. In this case, polynomial-type nonlinearities are identified and validated with force-controlled stepped-sine test data at several excitation levels.

A flexible count data regression model for risk analysis.

PubMed

Guikema, Seth D; Coffelt, Jeremy P; Goffelt, Jeremy P

2008-02-01

In many cases, risk and reliability analyses involve estimating the probabilities of discrete events such as hardware failures and occurrences of disease or death. There is often additional information in the form of explanatory variables that can be used to help estimate the likelihood of different numbers of events in the future through the use of an appropriate regression model, such as a generalized linear model. However, existing generalized linear models (GLM) are limited in their ability to handle the types of variance structures often encountered in using count data in risk and reliability analysis. In particular, standard models cannot handle both underdispersed data (variance less than the mean) and overdispersed data (variance greater than the mean) in a single coherent modeling framework. This article presents a new GLM based on a reformulation of the Conway-Maxwell Poisson (COM) distribution that is useful for both underdispersed and overdispersed count data and demonstrates this model by applying it to the assessment of electric power system reliability. The results show that the proposed COM GLM can provide as good of fits to data as the commonly used existing models for overdispered data sets while outperforming these commonly used models for underdispersed data sets.

The Determination of the Large-Scale Circulation of the Pacific Ocean from Satellite Altimetry using Model Green's Functions

NASA Technical Reports Server (NTRS)

Stammer, Detlef; Wunsch, Carl

1996-01-01

A Green's function method for obtaining an estimate of the ocean circulation using both a general circulation model and altimetric data is demonstrated. The fundamental assumption is that the model is so accurate that the differences between the observations and the model-estimated fields obey a linear dynamics. In the present case, the calculations are demonstrated for model/data differences occurring on very a large scale, where the linearization hypothesis appears to be a good one. A semi-automatic linearization of the Bryan/Cox general circulation model is effected by calculating the model response to a series of isolated (in both space and time) geostrophically balanced vortices. These resulting impulse responses or 'Green's functions' then provide the kernels for a linear inverse problem. The method is first demonstrated with a set of 'twin experiments' and then with real data spanning the entire model domain and a year of TOPEX/POSEIDON observations. Our present focus is on the estimate of the time-mean and annual cycle of the model. Residuals of the inversion/assimilation are largest in the western tropical Pacific, and are believed to reflect primarily geoid error. Vertical resolution diminishes with depth with 1 year of data. The model mean is modified such that the subtropical gyre is weakened by about 1 cm/s and the center of the gyre shifted southward by about 10 deg. Corrections to the flow field at the annual cycle suggest that the dynamical response is weak except in the tropics, where the estimated seasonal cycle of the low-latitude current system is of the order of 2 cm/s. The underestimation of observed fluctuations can be related to the inversion on the coarse spatial grid, which does not permit full resolution of the tropical physics. The methodology is easily extended to higher resolution, to use of spatially correlated errors, and to other data types.

On Markov parameters in system identification

NASA Technical Reports Server (NTRS)

Phan, Minh; Juang, Jer-Nan; Longman, Richard W.

1991-01-01

A detailed discussion of Markov parameters in system identification is given. Different forms of input-output representation of linear discrete-time systems are reviewed and discussed. Interpretation of sampled response data as Markov parameters is presented. Relations between the state-space model and particular linear difference models via the Markov parameters are formulated. A generalization of Markov parameters to observer and Kalman filter Markov parameters for system identification is explained. These extended Markov parameters play an important role in providing not only a state-space realization, but also an observer/Kalman filter for the system of interest.

Dynamics of thin-shell wormholes with different cosmological models

NASA Astrophysics Data System (ADS)

Sharif, Muhammad; Mumtaz, Saadia

This work is devoted to investigate the stability of thin-shell wormholes in Einstein-Hoffmann-Born-Infeld electrodynamics. We also study the attractive and repulsive characteristics of these configurations. A general equation-of-state is considered in the form of linear perturbation which explores the stability of the respective wormhole solutions. We assume Chaplygin, linear and logarithmic gas models to study exotic matter at thin-shell and evaluate stability regions for different values of the involved parameters. It is concluded that the Hoffmann-Born-Infeld parameter and electric charge enhance the stability regions.

A Galerkin approximation for linear elastic shallow shells

NASA Astrophysics Data System (ADS)

Figueiredo, I. N.; Trabucho, L.

1992-03-01

This work is a generalization to shallow shell models of previous results for plates by B. Miara (1989). Using the same basis functions as in the plate case, we construct a Galerkin approximation of the three-dimensional linearized elasticity problem, and establish some error estimates as a function of the thickness, the curvature, the geometry of the shell, the forces and the Lamé costants.

Nonlinear changes in brain activity during continuous word repetition: an event-related multiparametric functional MR imaging study.

PubMed

Hagenbeek, R E; Rombouts, S A R B; Veltman, D J; Van Strien, J W; Witter, M P; Scheltens, P; Barkhof, F

2007-10-01

Changes in brain activation as a function of continuous multiparametric word recognition have not been studied before by using functional MR imaging (fMRI), to our knowledge. Our aim was to identify linear changes in brain activation and, what is more interesting, nonlinear changes in brain activation as a function of extended word repetition. Fifteen healthy young right-handed individuals participated in this study. An event-related extended continuous word-recognition task with 30 target words was used to study the parametric effect of word recognition on brain activation. Word-recognition-related brain activation was studied as a function of 9 word repetitions. fMRI data were analyzed with a general linear model with regressors for linearly changing signal intensity and nonlinearly changing signal intensity, according to group average reaction time (RT) and individual RTs. A network generally associated with episodic memory recognition showed either constant or linearly decreasing brain activation as a function of word repetition. Furthermore, both anterior and posterior cingulate cortices and the left middle frontal gyrus followed the nonlinear curve of the group RT, whereas the anterior cingulate cortex was also associated with individual RT. Linear alteration in brain activation as a function of word repetition explained most changes in blood oxygen level-dependent signal intensity. Using a hierarchically orthogonalized model, we found evidence for nonlinear activation associated with both group and individual RTs.

Biomechanically based simulation of brain deformations for intraoperative image correction: coupling of elastic and fluid models

NASA Astrophysics Data System (ADS)

Hagemann, Alexander; Rohr, Karl; Stiehl, H. Siegfried

2000-06-01

In order to improve the accuracy of image-guided neurosurgery, different biomechanical models have been developed to correct preoperative images w.r.t. intraoperative changes like brain shift or tumor resection. All existing biomechanical models simulate different anatomical structures by using either appropriate boundary conditions or by spatially varying material parameter values, while assuming the same physical model for all anatomical structures. In general, this leads to physically implausible results, especially in the case of adjacent elastic and fluid structures. Therefore, we propose a new approach which allows to couple different physical models. In our case, we simulate rigid, elastic, and fluid regions by using the appropriate physical description for each material, namely either the Navier equation or the Stokes equation. To solve the resulting differential equations, we derive a linear matrix system for each region by applying the finite element method (FEM). Thereafter, the linear matrix systems are linked together, ending up with one overall linear matrix system. Our approach has been tested using synthetic as well as tomographic images. It turns out from experiments, that the integrated treatment of rigid, elastic, and fluid regions significantly improves the prediction results in comparison to a pure linear elastic model.

A powerful and flexible approach to the analysis of RNA sequence count data.

PubMed

Zhou, Yi-Hui; Xia, Kai; Wright, Fred A

2011-10-01

A number of penalization and shrinkage approaches have been proposed for the analysis of microarray gene expression data. Similar techniques are now routinely applied to RNA sequence transcriptional count data, although the value of such shrinkage has not been conclusively established. If penalization is desired, the explicit modeling of mean-variance relationships provides a flexible testing regimen that 'borrows' information across genes, while easily incorporating design effects and additional covariates. We describe BBSeq, which incorporates two approaches: (i) a simple beta-binomial generalized linear model, which has not been extensively tested for RNA-Seq data and (ii) an extension of an expression mean-variance modeling approach to RNA-Seq data, involving modeling of the overdispersion as a function of the mean. Our approaches are flexible, allowing for general handling of discrete experimental factors and continuous covariates. We report comparisons with other alternate methods to handle RNA-Seq data. Although penalized methods have advantages for very small sample sizes, the beta-binomial generalized linear model, combined with simple outlier detection and testing approaches, appears to have favorable characteristics in power and flexibility. An R package containing examples and sample datasets is available at http://www.bios.unc.edu/research/genomic_software/BBSeq yzhou@bios.unc.edu; fwright@bios.unc.edu Supplementary data are available at Bioinformatics online.

Special Holonomy and Two-Dimensional Supersymmetric Sigma-Models

NASA Astrophysics Data System (ADS)

Stojevic, Vid

2006-11-01

Two-dimensional sigma-models describing superstrings propagating on manifolds of special holonomy are characterized by symmetries related to covariantly constant forms that these manifolds hold, which are generally non-linear and close in a field dependent sense. The thesis explores various aspects of the special holonomy symmetries.

General Multivariate Linear Modeling of Surface Shapes Using SurfStat

PubMed Central

Chung, Moo K.; Worsley, Keith J.; Nacewicz, Brendon, M.; Dalton, Kim M.; Davidson, Richard J.

2010-01-01

Although there are many imaging studies on traditional ROI-based amygdala volumetry, there are very few studies on modeling amygdala shape variations. This paper present a unified computational and statistical framework for modeling amygdala shape variations in a clinical population. The weighted spherical harmonic representation is used as to parameterize, to smooth out, and to normalize amygdala surfaces. The representation is subsequently used as an input for multivariate linear models accounting for nuisance covariates such as age and brain size difference using SurfStat package that completely avoids the complexity of specifying design matrices. The methodology has been applied for quantifying abnormal local amygdala shape variations in 22 high functioning autistic subjects. PMID:20620211

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Power Laws, Scale Invariance and the Generalized Frobenius Series:

NASA Astrophysics Data System (ADS)

Visser, Matt; Yunes, Nicolas

We present a self-contained formalism for calculating the background solution, the linearized solutions and a class of generalized Frobenius-like solutions to a system of scale-invariant differential equations. We first cast the scale-invariant model into its equidimensional and autonomous forms, find its fixed points, and then obtain power-law background solutions. After linearizing about these fixed points, we find a second linearized solution, which provides a distinct collection of power laws characterizing the deviations from the fixed point. We prove that generically there will be a region surrounding the fixed point in which the complete general solution can be represented as a generalized Frobenius-like power series with exponents that are integer multiples of the exponents arising in the linearized problem. While discussions of the linearized system are common, and one can often find a discussion of power-series with integer exponents, power series with irrational (indeed complex) exponents are much rarer in the extant literature. The Frobenius-like series we encounter can be viewed as a variant of the rarely-discussed Liapunov expansion theorem (not to be confused with the more commonly encountered Liapunov functions and Liapunov exponents). As specific examples we apply these ideas to Newtonian and relativistic isothermal stars and construct two separate power series with the overlapping radius of convergence. The second of these power series solutions represents an expansion around "spatial infinity," and in realistic models it is this second power series that gives information about the stellar core, and the damped oscillations in core mass and core radius as the central pressure goes to infinity. The power-series solutions we obtain extend classical results; as exemplified for instance by the work of Lane, Emden, and Chandrasekhar in the Newtonian case, and that of Harrison, Thorne, Wakano, and Wheeler in the relativistic case. We also indicate how to extend these ideas to situations where fixed points may not exist — either due to "monotone" flow or due to the presence of limit cycles. Monotone flow generically leads to logarithmic deviations from scaling, while limit cycles generally lead to discrete self-similar solutions.

Estimation of Quasi-Stiffness of the Human Hip in the Stance Phase of Walking

PubMed Central

Shamaei, Kamran; Sawicki, Gregory S.; Dollar, Aaron M.

2013-01-01

This work presents a framework for selection of subject-specific quasi-stiffness of hip orthoses and exoskeletons, and other devices that are intended to emulate the biological performance of this joint during walking. The hip joint exhibits linear moment-angular excursion behavior in both the extension and flexion stages of the resilient loading-unloading phase that consists of terminal stance and initial swing phases. Here, we establish statistical models that can closely estimate the slope of linear fits to the moment-angle graph of the hip in this phase, termed as the quasi-stiffness of the hip. Employing an inverse dynamics analysis, we identify a series of parameters that can capture the nearly linear hip quasi-stiffnesses in the resilient loading phase. We then employ regression analysis on experimental moment-angle data of 216 gait trials across 26 human adults walking over a wide range of gait speeds (0.75–2.63 m/s) to obtain a set of general-form statistical models that estimate the hip quasi-stiffnesses using body weight and height, gait speed, and hip excursion. We show that the general-form models can closely estimate the hip quasi-stiffness in the extension (R2 = 92%) and flexion portions (R2 = 89%) of the resilient loading phase of the gait. We further simplify the general-form models and present a set of stature-based models that can estimate the hip quasi-stiffness for the preferred gait speed using only body weight and height with an average error of 27% for the extension stage and 37% for the flexion stage. PMID:24349136

Forecasting paratransit services demand : review and recommendations.

DOT National Transportation Integrated Search

2013-06-01

Travel demand forecasting tools for Floridas paratransit services are outdated, utilizing old national trip : generation rate generalities and simple linear regression models. In its guidance for the development of : mandated Transportation Disadv...

On testing an unspecified function through a linear mixed effects model with multiple variance components

PubMed Central

Wang, Yuanjia; Chen, Huaihou

2012-01-01

Summary We examine a generalized F-test of a nonparametric function through penalized splines and a linear mixed effects model representation. With a mixed effects model representation of penalized splines, we imbed the test of an unspecified function into a test of some fixed effects and a variance component in a linear mixed effects model with nuisance variance components under the null. The procedure can be used to test a nonparametric function or varying-coefficient with clustered data, compare two spline functions, test the significance of an unspecified function in an additive model with multiple components, and test a row or a column effect in a two-way analysis of variance model. Through a spectral decomposition of the residual sum of squares, we provide a fast algorithm for computing the null distribution of the test, which significantly improves the computational efficiency over bootstrap. The spectral representation reveals a connection between the likelihood ratio test (LRT) in a multiple variance components model and a single component model. We examine our methods through simulations, where we show that the power of the generalized F-test may be higher than the LRT, depending on the hypothesis of interest and the true model under the alternative. We apply these methods to compute the genome-wide critical value and p-value of a genetic association test in a genome-wide association study (GWAS), where the usual bootstrap is computationally intensive (up to 108 simulations) and asymptotic approximation may be unreliable and conservative. PMID:23020801

On testing an unspecified function through a linear mixed effects model with multiple variance components.

PubMed

Wang, Yuanjia; Chen, Huaihou

2012-12-01

We examine a generalized F-test of a nonparametric function through penalized splines and a linear mixed effects model representation. With a mixed effects model representation of penalized splines, we imbed the test of an unspecified function into a test of some fixed effects and a variance component in a linear mixed effects model with nuisance variance components under the null. The procedure can be used to test a nonparametric function or varying-coefficient with clustered data, compare two spline functions, test the significance of an unspecified function in an additive model with multiple components, and test a row or a column effect in a two-way analysis of variance model. Through a spectral decomposition of the residual sum of squares, we provide a fast algorithm for computing the null distribution of the test, which significantly improves the computational efficiency over bootstrap. The spectral representation reveals a connection between the likelihood ratio test (LRT) in a multiple variance components model and a single component model. We examine our methods through simulations, where we show that the power of the generalized F-test may be higher than the LRT, depending on the hypothesis of interest and the true model under the alternative. We apply these methods to compute the genome-wide critical value and p-value of a genetic association test in a genome-wide association study (GWAS), where the usual bootstrap is computationally intensive (up to 10(8) simulations) and asymptotic approximation may be unreliable and conservative. © 2012, The International Biometric Society.

Adaptive convex combination approach for the identification of improper quaternion processes.

PubMed

Ujang, Bukhari Che; Jahanchahi, Cyrus; Took, Clive Cheong; Mandic, Danilo P

2014-01-01

Data-adaptive optimal modeling and identification of real-world vector sensor data is provided by combining the fractional tap-length (FT) approach with model order selection in the quaternion domain. To account rigorously for the generality of such processes, both second-order circular (proper) and noncircular (improper), the proposed approach in this paper combines the FT length optimization with both the strictly linear quaternion least mean square (QLMS) and widely linear QLMS (WL-QLMS). A collaborative approach based on QLMS and WL-QLMS is shown to both identify the type of processes (proper or improper) and to track their optimal parameters in real time. Analysis shows that monitoring the evolution of the convex mixing parameter within the collaborative approach allows us to track the improperness in real time. Further insight into the properties of those algorithms is provided by establishing a relationship between the steady-state error and optimal model order. The approach is supported by simulations on model order selection and identification of both strictly linear and widely linear quaternion-valued systems, such as those routinely used in renewable energy (wind) and human-centered computing (biomechanics).

Inverse scattering method and soliton double solution family for the general symplectic gravity model

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

Gao Yajun

A previously established Hauser-Ernst-type extended double-complex linear system is slightly modified and used to develop an inverse scattering method for the stationary axisymmetric general symplectic gravity model. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method applied fine and effective. As an application, a concrete family of soliton double solutions for the considered theory is obtained.

Unobtrusive Detection of Mild Cognitive Impairment in Older Adults Through Home Monitoring.

PubMed

Akl, Ahmad; Snoek, Jasper; Mihailidis, Alex

2017-03-01

The early detection of dementias such as Alzheimer's disease can in some cases reverse, stop, or slow cognitive decline and in general greatly reduce the burden of care. This is of increasing significance as demographic studies are warning of an aging population in North America and worldwide. Various smart homes and systems have been developed to detect cognitive decline through continuous monitoring of high risk individuals. However, the majority of these smart homes and systems use a number of predefined heuristics to detect changes in cognition, which has been demonstrated to focus on the idiosyncratic nuances of the individual subjects, and thus, does not generalize. In this paper, we address this problem by building generalized linear models of home activity of older adults monitored using unobtrusive sensing technologies. We use inhomogenous Poisson processes to model the presence of the recruited older adults within different rooms throughout the day. We employ an information theoretic approach to compare the generalized linear models learned, and we observe significant statistical differences between the cognitively intact and impaired older adults. Using a simple thresholding approach, we were able to detect mild cognitive impairment in older adults with an average area under the ROC curve of 0.716 and an average area under the precision-recall curve of 0.706 using activity models estimated over a time window of 12 weeks.

The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded.

PubMed

Nakagawa, Shinichi; Johnson, Paul C D; Schielzeth, Holger

2017-09-01

The coefficient of determination R 2 quantifies the proportion of variance explained by a statistical model and is an important summary statistic of biological interest. However, estimating R 2 for generalized linear mixed models (GLMMs) remains challenging. We have previously introduced a version of R 2 that we called [Formula: see text] for Poisson and binomial GLMMs, but not for other distributional families. Similarly, we earlier discussed how to estimate intra-class correlation coefficients (ICCs) using Poisson and binomial GLMMs. In this paper, we generalize our methods to all other non-Gaussian distributions, in particular to negative binomial and gamma distributions that are commonly used for modelling biological data. While expanding our approach, we highlight two useful concepts for biologists, Jensen's inequality and the delta method, both of which help us in understanding the properties of GLMMs. Jensen's inequality has important implications for biologically meaningful interpretation of GLMMs, whereas the delta method allows a general derivation of variance associated with non-Gaussian distributions. We also discuss some special considerations for binomial GLMMs with binary or proportion data. We illustrate the implementation of our extension by worked examples from the field of ecology and evolution in the R environment. However, our method can be used across disciplines and regardless of statistical environments. © 2017 The Author(s).

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

PubMed Central

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

2012-01-01

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

Economic policy optimization based on both one stochastic model and the parametric control theory

NASA Astrophysics Data System (ADS)

Ashimov, Abdykappar; Borovskiy, Yuriy; Onalbekov, Mukhit

2016-06-01

A nonlinear dynamic stochastic general equilibrium model with financial frictions is developed to describe two interacting national economies in the environment of the rest of the world. Parameters of nonlinear model are estimated based on its log-linearization by the Bayesian approach. The nonlinear model is verified by retroprognosis, estimation of stability indicators of mappings specified by the model, and estimation the degree of coincidence for results of internal and external shocks' effects on macroeconomic indicators on the basis of the estimated nonlinear model and its log-linearization. On the base of the nonlinear model, the parametric control problems of economic growth and volatility of macroeconomic indicators of Kazakhstan are formulated and solved for two exchange rate regimes (free floating and managed floating exchange rates)

Bianchi type-VIh string cloud cosmological models with bulk viscosity

NASA Astrophysics Data System (ADS)

Tripathy, Sunil K.; Behera, Dipanjali

2010-11-01

String cloud cosmological models are studied using spatially homogeneous and anisotropic Bianchi type VIh metric in the frame work of general relativity. The field equations are solved for massive string cloud in presence of bulk viscosity. A general linear equation of state of the cosmic string tension density with the proper energy density of the universe is considered. The physical and kinematical properties of the models have been discussed in detail and the limits of the anisotropic parameter responsible for different phases of the universe are explored.

Brittle failure of rock: A review and general linear criterion

NASA Astrophysics Data System (ADS)

Labuz, Joseph F.; Zeng, Feitao; Makhnenko, Roman; Li, Yuan

2018-07-01

A failure criterion typically is phenomenological since few models exist to theoretically derive the mathematical function. Indeed, a successful failure criterion is a generalization of experimental data obtained from strength tests on specimens subjected to known stress states. For isotropic rock that exhibits a pressure dependence on strength, a popular failure criterion is a linear equation in major and minor principal stresses, independent of the intermediate principal stress. A general linear failure criterion called Paul-Mohr-Coulomb (PMC) contains all three principal stresses with three material constants: friction angles for axisymmetric compression ϕc and extension ϕe and isotropic tensile strength V0. PMC provides a framework to describe a nonlinear failure surface by a set of planes "hugging" the curved surface. Brittle failure of rock is reviewed and multiaxial test methods are summarized. Equations are presented to implement PMC for fitting strength data and determining the three material parameters. A piecewise linear approximation to a nonlinear failure surface is illustrated by fitting two planes with six material parameters to form either a 6- to 12-sided pyramid or a 6- to 12- to 6-sided pyramid. The particular nature of the failure surface is dictated by the experimental data.

Control for Population Structure and Relatedness for Binary Traits in Genetic Association Studies via Logistic Mixed Models.

PubMed

Chen, Han; Wang, Chaolong; Conomos, Matthew P; Stilp, Adrienne M; Li, Zilin; Sofer, Tamar; Szpiro, Adam A; Chen, Wei; Brehm, John M; Celedón, Juan C; Redline, Susan; Papanicolaou, George J; Thornton, Timothy A; Laurie, Cathy C; Rice, Kenneth; Lin, Xihong

2016-04-07

Linear mixed models (LMMs) are widely used in genome-wide association studies (GWASs) to account for population structure and relatedness, for both continuous and binary traits. Motivated by the failure of LMMs to control type I errors in a GWAS of asthma, a binary trait, we show that LMMs are generally inappropriate for analyzing binary traits when population stratification leads to violation of the LMM's constant-residual variance assumption. To overcome this problem, we develop a computationally efficient logistic mixed model approach for genome-wide analysis of binary traits, the generalized linear mixed model association test (GMMAT). This approach fits a logistic mixed model once per GWAS and performs score tests under the null hypothesis of no association between a binary trait and individual genetic variants. We show in simulation studies and real data analysis that GMMAT effectively controls for population structure and relatedness when analyzing binary traits in a wide variety of study designs. Copyright © 2016 The American Society of Human Genetics. Published by Elsevier Inc. All rights reserved.

Quasi-Linear Parameter Varying Representation of General Aircraft Dynamics Over Non-Trim Region

NASA Technical Reports Server (NTRS)

Shin, Jong-Yeob

2007-01-01

For applying linear parameter varying (LPV) control synthesis and analysis to a nonlinear system, it is required that a nonlinear system be represented in the form of an LPV model. In this paper, a new representation method is developed to construct an LPV model from a nonlinear mathematical model without the restriction that an operating point must be in the neighborhood of equilibrium points. An LPV model constructed by the new method preserves local stabilities of the original nonlinear system at "frozen" scheduling parameters and also represents the original nonlinear dynamics of a system over a non-trim region. An LPV model of the motion of FASER (Free-flying Aircraft for Subscale Experimental Research) is constructed by the new method.

Alternative Models for Small Samples in Psychological Research: Applying Linear Mixed Effects Models and Generalized Estimating Equations to Repeated Measures Data

ERIC Educational Resources Information Center

Muth, Chelsea; Bales, Karen L.; Hinde, Katie; Maninger, Nicole; Mendoza, Sally P.; Ferrer, Emilio

2016-01-01

Unavoidable sample size issues beset psychological research that involves scarce populations or costly laboratory procedures. When incorporating longitudinal designs these samples are further reduced by traditional modeling techniques, which perform listwise deletion for any instance of missing data. Moreover, these techniques are limited in their…

Using Generalized Additive Models to Analyze Single-Case Designs

ERIC Educational Resources Information Center

Shadish, William; Sullivan, Kristynn

2013-01-01

Many analyses for single-case designs (SCDs)--including nearly all the effect size indicators-- currently assume no trend in the data. Regression and multilevel models allow for trend, but usually test only linear trend and have no principled way of knowing if higher order trends should be represented in the model. This paper shows how Generalized…

The Convergence Model of Communication. Papers of the East-West Communication Institute, No. 18.

ERIC Educational Resources Information Center

Kincaid, D. Lawrence

Expressing the need for a description of communication that is equally applicable to all the social sciences, this report develops a general model of the communication process based upon the principle of convergence as derived from basic information theory and cybernetics. It criticizes the linear, one-way models of communication that have…

A sequential linear optimization approach for controller design

NASA Technical Reports Server (NTRS)

Horta, L. G.; Juang, J.-N.; Junkins, J. L.

1985-01-01

A linear optimization approach with a simple real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam finite element model for the optimal sizing and placement of active/passive-structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to initial conditions of the linear optimization approach is also demonstrated.

Solving large mixed linear models using preconditioned conjugate gradient iteration.

PubMed

Strandén, I; Lidauer, M

1999-12-01

Continuous evaluation of dairy cattle with a random regression test-day model requires a fast solving method and algorithm. A new computing technique feasible in Jacobi and conjugate gradient based iterative methods using iteration on data is presented. In the new computing technique, the calculations in multiplication of a vector by a matrix were recorded to three steps instead of the commonly used two steps. The three-step method was implemented in a general mixed linear model program that used preconditioned conjugate gradient iteration. Performance of this program in comparison to other general solving programs was assessed via estimation of breeding values using univariate, multivariate, and random regression test-day models. Central processing unit time per iteration with the new three-step technique was, at best, one-third that needed with the old technique. Performance was best with the test-day model, which was the largest and most complex model used. The new program did well in comparison to other general software. Programs keeping the mixed model equations in random access memory required at least 20 and 435% more time to solve the univariate and multivariate animal models, respectively. Computations of the second best iteration on data took approximately three and five times longer for the animal and test-day models, respectively, than did the new program. Good performance was due to fast computing time per iteration and quick convergence to the final solutions. Use of preconditioned conjugate gradient based methods in solving large breeding value problems is supported by our findings.

Modeling of Geometric Error in Linear Guide Way to Improved the vertical three-axis CNC Milling machine’s accuracy

NASA Astrophysics Data System (ADS)

Kwintarini, Widiyanti; Wibowo, Agung; Arthaya, Bagus M.; Yuwana Martawirya, Yatna

2018-03-01

The purpose of this study was to improve the accuracy of three-axis CNC Milling Vertical engines with a general approach by using mathematical modeling methods of machine tool geometric errors. The inaccuracy of CNC machines can be caused by geometric errors that are an important factor during the manufacturing process and during the assembly phase, and are factors for being able to build machines with high-accuracy. To improve the accuracy of the three-axis vertical milling machine, by knowing geometric errors and identifying the error position parameters in the machine tool by arranging the mathematical modeling. The geometric error in the machine tool consists of twenty-one error parameters consisting of nine linear error parameters, nine angle error parameters and three perpendicular error parameters. The mathematical modeling approach of geometric error with the calculated alignment error and angle error in the supporting components of the machine motion is linear guide way and linear motion. The purpose of using this mathematical modeling approach is the identification of geometric errors that can be helpful as reference during the design, assembly and maintenance stages to improve the accuracy of CNC machines. Mathematically modeling geometric errors in CNC machine tools can illustrate the relationship between alignment error, position and angle on a linear guide way of three-axis vertical milling machines.

An approximation of herd effect due to vaccinating children against seasonal influenza - a potential solution to the incorporation of indirect effects into static models.

PubMed

Van Vlaenderen, Ilse; Van Bellinghen, Laure-Anne; Meier, Genevieve; Nautrup, Barbara Poulsen

2013-01-22

Indirect herd effect from vaccination of children offers potential for improving the effectiveness of influenza prevention in the remaining unvaccinated population. Static models used in cost-effectiveness analyses cannot dynamically capture herd effects. The objective of this study was to develop a methodology to allow herd effect associated with vaccinating children against seasonal influenza to be incorporated into static models evaluating the cost-effectiveness of influenza vaccination. Two previously published linear equations for approximation of herd effects in general were compared with the results of a structured literature review undertaken using PubMed searches to identify data on herd effects specific to influenza vaccination. A linear function was fitted to point estimates from the literature using the sum of squared residuals. The literature review identified 21 publications on 20 studies for inclusion. Six studies provided data on a mathematical relationship between effective vaccine coverage in subgroups and reduction of influenza infection in a larger unvaccinated population. These supported a linear relationship when effective vaccine coverage in a subgroup population was between 20% and 80%. Three studies evaluating herd effect at a community level, specifically induced by vaccinating children, provided point estimates for fitting linear equations. The fitted linear equation for herd protection in the target population for vaccination (children) was slightly less conservative than a previously published equation for herd effects in general. The fitted linear equation for herd protection in the non-target population was considerably less conservative than the previously published equation. This method of approximating herd effect requires simple adjustments to the annual baseline risk of influenza in static models: (1) for the age group targeted by the childhood vaccination strategy (i.e. children); and (2) for other age groups not targeted (e.g. adults and/or elderly). Two approximations provide a linear relationship between effective coverage and reduction in the risk of infection. The first is a conservative approximation, recommended as a base-case for cost-effectiveness evaluations. The second, fitted to data extracted from a structured literature review, provides a less conservative estimate of herd effect, recommended for sensitivity analyses.

INTERANNUAL VARIATION IN METEOROLOGICALLY ADJUSTED OZONE LEVELS IN THE EASTERN UNITED STATES: A COMPARISON OF TWO APPROACHED

EPA Science Inventory

Assessing the influence of abatement efforts and other human activities on ozone levels is complicated by the atmosphere's changeable nature. Two statistical methods, the dynamic linear model(DLM) and the generalized additive model (GAM), are used to estimate ozone trends in the...

Orthonormal vector general polynomials derived from the Cartesian gradient of the orthonormal Zernike-based polynomials.

PubMed

Mafusire, Cosmas; Krüger, Tjaart P J

2018-06-01

The concept of orthonormal vector circle polynomials is revisited by deriving a set from the Cartesian gradient of Zernike polynomials in a unit circle using a matrix-based approach. The heart of this model is a closed-form matrix equation of the gradient of Zernike circle polynomials expressed as a linear combination of lower-order Zernike circle polynomials related through a gradient matrix. This is a sparse matrix whose elements are two-dimensional standard basis transverse Euclidean vectors. Using the outer product form of the Cholesky decomposition, the gradient matrix is used to calculate a new matrix, which we used to express the Cartesian gradient of the Zernike circle polynomials as a linear combination of orthonormal vector circle polynomials. Since this new matrix is singular, the orthonormal vector polynomials are recovered by reducing the matrix to its row echelon form using the Gauss-Jordan elimination method. We extend the model to derive orthonormal vector general polynomials, which are orthonormal in a general pupil by performing a similarity transformation on the gradient matrix to give its equivalent in the general pupil. The outer form of the Gram-Schmidt procedure and the Gauss-Jordan elimination method are then applied to the general pupil to generate the orthonormal vector general polynomials from the gradient of the orthonormal Zernike-based polynomials. The performance of the model is demonstrated with a simulated wavefront in a square pupil inscribed in a unit circle.

Decomposition and model selection for large contingency tables.

PubMed

Dahinden, Corinne; Kalisch, Markus; Bühlmann, Peter

2010-04-01

Large contingency tables summarizing categorical variables arise in many areas. One example is in biology, where large numbers of biomarkers are cross-tabulated according to their discrete expression level. Interactions of the variables are of great interest and are generally studied with log-linear models. The structure of a log-linear model can be visually represented by a graph from which the conditional independence structure can then be easily read off. However, since the number of parameters in a saturated model grows exponentially in the number of variables, this generally comes with a heavy computational burden. Even if we restrict ourselves to models of lower-order interactions or other sparse structures, we are faced with the problem of a large number of cells which play the role of sample size. This is in sharp contrast to high-dimensional regression or classification procedures because, in addition to a high-dimensional parameter, we also have to deal with the analogue of a huge sample size. Furthermore, high-dimensional tables naturally feature a large number of sampling zeros which often leads to the nonexistence of the maximum likelihood estimate. We therefore present a decomposition approach, where we first divide the problem into several lower-dimensional problems and then combine these to form a global solution. Our methodology is computationally feasible for log-linear interaction models with many categorical variables each or some of them having many levels. We demonstrate the proposed method on simulated data and apply it to a bio-medical problem in cancer research.

Modeling Aircraft Wing Loads from Flight Data Using Neural Networks

NASA Technical Reports Server (NTRS)

Allen, Michael J.; Dibley, Ryan P.

2003-01-01

Neural networks were used to model wing bending-moment loads, torsion loads, and control surface hinge-moments of the Active Aeroelastic Wing (AAW) aircraft. Accurate loads models are required for the development of control laws designed to increase roll performance through wing twist while not exceeding load limits. Inputs to the model include aircraft rates, accelerations, and control surface positions. Neural networks were chosen to model aircraft loads because they can account for uncharacterized nonlinear effects while retaining the capability to generalize. The accuracy of the neural network models was improved by first developing linear loads models to use as starting points for network training. Neural networks were then trained with flight data for rolls, loaded reversals, wind-up-turns, and individual control surface doublets for load excitation. Generalization was improved by using gain weighting and early stopping. Results are presented for neural network loads models of four wing loads and four control surface hinge moments at Mach 0.90 and an altitude of 15,000 ft. An average model prediction error reduction of 18.6 percent was calculated for the neural network models when compared to the linear models. This paper documents the input data conditioning, input parameter selection, structure, training, and validation of the neural network models.

A hierarchy for modeling high speed propulsion systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Deabreu, Alex

1991-01-01

General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery such as inlets, ramjets, and scramjets. The discussion is separated into four sections: (1) computational fluid dynamics model for the entire nonlinear system or high order nonlinear models; (2) high order linearized model derived from fundamental physics; (3) low order linear models obtained from other high order models; and (4) low order nonlinear models. Included are special considerations on any relevant control system designs. The methods discussed are for the quasi-one dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, moving normal shocks, hammershocks, subsonic combustion via heat addition, temperature dependent gases, detonation, and thermal choking.

A formulation of rotor-airframe coupling for design analysis of vibrations of helicopter airframes

NASA Technical Reports Server (NTRS)

Kvaternik, R. G.; Walton, W. C., Jr.

1982-01-01

A linear formulation of rotor airframe coupling intended for vibration analysis in airframe structural design is presented. The airframe is represented by a finite element analysis model; the rotor is represented by a general set of linear differential equations with periodic coefficients; and the connections between the rotor and airframe are specified through general linear equations of constraint. Coupling equations are applied to the rotor and airframe equations to produce one set of linear differential equations governing vibrations of the combined rotor airframe system. These equations are solved by the harmonic balance method for the system steady state vibrations. A feature of the solution process is the representation of the airframe in terms of forced responses calculated at the rotor harmonics of interest. A method based on matrix partitioning is worked out for quick recalculations of vibrations in design studies when only relatively few airframe members are varied. All relations are presented in forms suitable for direct computer implementation.

Heuristics for Understanding the Concepts of Interaction, Polynomial Trend, and the General Linear Model.

ERIC Educational Resources Information Center

Thompson, Bruce

The relationship between analysis of variance (ANOVA) methods and their analogs (analysis of covariance and multiple analyses of variance and covariance--collectively referred to as OVA methods) and the more general analytic case is explored. A small heuristic data set is used, with a hypothetical sample of 20 subjects, randomly assigned to five…

Does Access Matter? Time in General Education and Achievement for Students with Disabilities

ERIC Educational Resources Information Center

Cosier, Meghan; Causton-Theoharis, Julie; Theoharis, George

2013-01-01

This study examined the relationship between hours in general education and achievement in reading and mathematics for students with disabilities. The study population included more than 1,300 students between the ages of 6 and 9 years old within 180 school districts. Hierarchical linear modeling (HLM) was utilized with the Pre-Elementary…

Linear stability and nonlinear analyses of traffic waves for the general nonlinear car-following model with multi-time delays

NASA Astrophysics Data System (ADS)

Sun, Dihua; Chen, Dong; Zhao, Min; Liu, Weining; Zheng, Linjiang

2018-07-01

In this paper, the general nonlinear car-following model with multi-time delays is investigated in order to describe the reactions of vehicle to driving behavior. Platoon stability and string stability criteria are obtained for the general nonlinear car-following model. Burgers equation and Korteweg de Vries (KdV) equation and their solitary wave solutions are derived adopting the reductive perturbation method. We investigate the properties of typical optimal velocity model using both analytic and numerical methods, which estimates the impact of delays about the evolution of traffic congestion. The numerical results show that time delays in sensing relative movement is more sensitive to the stability of traffic flow than time delays in sensing host motion.

Neutron star dynamics under time-dependent external torques

NASA Astrophysics Data System (ADS)

Gügercinoǧlu, Erbil; Alpar, M. Ali

2017-11-01

The two-component model describes neutron star dynamics incorporating the response of the superfluid interior. Conventional solutions and applications involve constant external torques, as appropriate for radio pulsars on dynamical time-scales. We present the general solution of two-component dynamics under arbitrary time-dependent external torques, with internal torques that are linear in the rotation rates, or with the extremely non-linear internal torques due to vortex creep. The two-component model incorporating the response of linear or non-linear internal torques can now be applied not only to radio pulsars but also to magnetars and to neutron stars in binary systems, with strong observed variability and noise in the spin-down or spin-up rates. Our results allow the extraction of the time-dependent external torques from the observed spin-down (or spin-up) time series, \\dot{Ω }(t). Applications are discussed.

SOCR Analyses – an Instructional Java Web-based Statistical Analysis Toolkit

PubMed Central

Chu, Annie; Cui, Jenny; Dinov, Ivo D.

2011-01-01

The Statistical Online Computational Resource (SOCR) designs web-based tools for educational use in a variety of undergraduate courses (Dinov 2006). Several studies have demonstrated that these resources significantly improve students' motivation and learning experiences (Dinov et al. 2008). SOCR Analyses is a new component that concentrates on data modeling and analysis using parametric and non-parametric techniques supported with graphical model diagnostics. Currently implemented analyses include commonly used models in undergraduate statistics courses like linear models (Simple Linear Regression, Multiple Linear Regression, One-Way and Two-Way ANOVA). In addition, we implemented tests for sample comparisons, such as t-test in the parametric category; and Wilcoxon rank sum test, Kruskal-Wallis test, Friedman's test, in the non-parametric category. SOCR Analyses also include several hypothesis test models, such as Contingency tables, Friedman's test and Fisher's exact test. The code itself is open source (http://socr.googlecode.com/), hoping to contribute to the efforts of the statistical computing community. The code includes functionality for each specific analysis model and it has general utilities that can be applied in various statistical computing tasks. For example, concrete methods with API (Application Programming Interface) have been implemented in statistical summary, least square solutions of general linear models, rank calculations, etc. HTML interfaces, tutorials, source code, activities, and data are freely available via the web (www.SOCR.ucla.edu). Code examples for developers and demos for educators are provided on the SOCR Wiki website. In this article, the pedagogical utilization of the SOCR Analyses is discussed, as well as the underlying design framework. As the SOCR project is on-going and more functions and tools are being added to it, these resources are constantly improved. The reader is strongly encouraged to check the SOCR site for most updated information and newly added models. PMID:21546994

Response statistics of rotating shaft with non-linear elastic restoring forces by path integration

NASA Astrophysics Data System (ADS)

Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael

2017-07-01

Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.

Estimation for general birth-death processes

PubMed Central

Crawford, Forrest W.; Minin, Vladimir N.; Suchard, Marc A.

2013-01-01

Birth-death processes (BDPs) are continuous-time Markov chains that track the number of “particles” in a system over time. While widely used in population biology, genetics and ecology, statistical inference of the instantaneous particle birth and death rates remains largely limited to restrictive linear BDPs in which per-particle birth and death rates are constant. Researchers often observe the number of particles at discrete times, necessitating data augmentation procedures such as expectation-maximization (EM) to find maximum likelihood estimates. For BDPs on finite state-spaces, there are powerful matrix methods for computing the conditional expectations needed for the E-step of the EM algorithm. For BDPs on infinite state-spaces, closed-form solutions for the E-step are available for some linear models, but most previous work has resorted to time-consuming simulation. Remarkably, we show that the E-step conditional expectations can be expressed as convolutions of computable transition probabilities for any general BDP with arbitrary rates. This important observation, along with a convenient continued fraction representation of the Laplace transforms of the transition probabilities, allows for novel and efficient computation of the conditional expectations for all BDPs, eliminating the need for truncation of the state-space or costly simulation. We use this insight to derive EM algorithms that yield maximum likelihood estimation for general BDPs characterized by various rate models, including generalized linear models. We show that our Laplace convolution technique outperforms competing methods when they are available and demonstrate a technique to accelerate EM algorithm convergence. We validate our approach using synthetic data and then apply our methods to cancer cell growth and estimation of mutation parameters in microsatellite evolution. PMID:25328261

Estimation for general birth-death processes.

PubMed

Crawford, Forrest W; Minin, Vladimir N; Suchard, Marc A

2014-04-01

Birth-death processes (BDPs) are continuous-time Markov chains that track the number of "particles" in a system over time. While widely used in population biology, genetics and ecology, statistical inference of the instantaneous particle birth and death rates remains largely limited to restrictive linear BDPs in which per-particle birth and death rates are constant. Researchers often observe the number of particles at discrete times, necessitating data augmentation procedures such as expectation-maximization (EM) to find maximum likelihood estimates. For BDPs on finite state-spaces, there are powerful matrix methods for computing the conditional expectations needed for the E-step of the EM algorithm. For BDPs on infinite state-spaces, closed-form solutions for the E-step are available for some linear models, but most previous work has resorted to time-consuming simulation. Remarkably, we show that the E-step conditional expectations can be expressed as convolutions of computable transition probabilities for any general BDP with arbitrary rates. This important observation, along with a convenient continued fraction representation of the Laplace transforms of the transition probabilities, allows for novel and efficient computation of the conditional expectations for all BDPs, eliminating the need for truncation of the state-space or costly simulation. We use this insight to derive EM algorithms that yield maximum likelihood estimation for general BDPs characterized by various rate models, including generalized linear models. We show that our Laplace convolution technique outperforms competing methods when they are available and demonstrate a technique to accelerate EM algorithm convergence. We validate our approach using synthetic data and then apply our methods to cancer cell growth and estimation of mutation parameters in microsatellite evolution.

Modeling the Non-Linear Response of Fiber-Reinforced Laminates Using a Combined Damage/Plasticity Model

NASA Technical Reports Server (NTRS)

Schuecker, Clara; Davila, Carlos G.; Pettermann, Heinz E.

2008-01-01

The present work is concerned with modeling the non-linear response of fiber reinforced polymer laminates. Recent experimental data suggests that the non-linearity is not only caused by matrix cracking but also by matrix plasticity due to shear stresses. To capture the effects of those two mechanisms, a model combining a plasticity formulation with continuum damage has been developed to simulate the non-linear response of laminates under plane stress states. The model is used to compare the predicted behavior of various laminate lay-ups to experimental data from the literature by looking at the degradation of axial modulus and Poisson s ratio of the laminates. The influence of residual curing stresses and in-situ effect on the predicted response is also investigated. It is shown that predictions of the combined damage/plasticity model, in general, correlate well with the experimental data. The test data shows that there are two different mechanisms that can have opposite effects on the degradation of the laminate Poisson s ratio which is captured correctly by the damage/plasticity model. Residual curing stresses are found to have a minor influence on the predicted response for the cases considered here. Some open questions remain regarding the prediction of damage onset.

Prediction of siRNA potency using sparse logistic regression.

PubMed

Hu, Wei; Hu, John

2014-06-01

RNA interference (RNAi) can modulate gene expression at post-transcriptional as well as transcriptional levels. Short interfering RNA (siRNA) serves as a trigger for the RNAi gene inhibition mechanism, and therefore is a crucial intermediate step in RNAi. There have been extensive studies to identify the sequence characteristics of potent siRNAs. One such study built a linear model using LASSO (Least Absolute Shrinkage and Selection Operator) to measure the contribution of each siRNA sequence feature. This model is simple and interpretable, but it requires a large number of nonzero weights. We have introduced a novel technique, sparse logistic regression, to build a linear model using single-position specific nucleotide compositions which has the same prediction accuracy of the linear model based on LASSO. The weights in our new model share the same general trend as those in the previous model, but have only 25 nonzero weights out of a total 84 weights, a 54% reduction compared to the previous model. Contrary to the linear model based on LASSO, our model suggests that only a few positions are influential on the efficacy of the siRNA, which are the 5' and 3' ends and the seed region of siRNA sequences. We also employed sparse logistic regression to build a linear model using dual-position specific nucleotide compositions, a task LASSO is not able to accomplish well due to its high dimensional nature. Our results demonstrate the superiority of sparse logistic regression as a technique for both feature selection and regression over LASSO in the context of siRNA design.

Transverse instability of periodic and generalized solitary waves for a fifth-order KP model

NASA Astrophysics Data System (ADS)

Haragus, Mariana; Wahlén, Erik

2017-02-01

We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic waves at infinity. We prove that these solitary waves are transversely spectrally unstable and that this instability is induced by the transverse instability of the periodic tails. We rely upon a detailed spectral analysis of some suitably chosen linear operators.

Drivers willingness to pay progressive rate for street parking.

DOT National Transportation Integrated Search

2015-01-01

This study finds willingness to pay and price elasticity for on-street parking demand using stated : preference data obtained from 238 respondents. Descriptive, statistical and economic analyses including : regression, generalized linear model, and f...

Analytical methods in multivariate highway safety exposure data estimation

DOT National Transportation Integrated Search

1984-01-01

Three general analytical techniques which may be of use in : extending, enhancing, and combining highway accident exposure data are : discussed. The techniques are log-linear modelling, iterative propor : tional fitting and the expectation maximizati...

Markov and semi-Markov switching linear mixed models used to identify forest tree growth components.

PubMed

Chaubert-Pereira, Florence; Guédon, Yann; Lavergne, Christian; Trottier, Catherine

2010-09-01

Tree growth is assumed to be mainly the result of three components: (i) an endogenous component assumed to be structured as a succession of roughly stationary phases separated by marked change points that are asynchronous among individuals, (ii) a time-varying environmental component assumed to take the form of synchronous fluctuations among individuals, and (iii) an individual component corresponding mainly to the local environment of each tree. To identify and characterize these three components, we propose to use semi-Markov switching linear mixed models, i.e., models that combine linear mixed models in a semi-Markovian manner. The underlying semi-Markov chain represents the succession of growth phases and their lengths (endogenous component) whereas the linear mixed models attached to each state of the underlying semi-Markov chain represent-in the corresponding growth phase-both the influence of time-varying climatic covariates (environmental component) as fixed effects, and interindividual heterogeneity (individual component) as random effects. In this article, we address the estimation of Markov and semi-Markov switching linear mixed models in a general framework. We propose a Monte Carlo expectation-maximization like algorithm whose iterations decompose into three steps: (i) sampling of state sequences given random effects, (ii) prediction of random effects given state sequences, and (iii) maximization. The proposed statistical modeling approach is illustrated by the analysis of successive annual shoots along Corsican pine trunks influenced by climatic covariates. © 2009, The International Biometric Society.

On a generalized laminate theory with application to bending, vibration, and delamination buckling in composite laminates

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

Barbero, E.J.

1989-01-01

In this study, a computational model for accurate analysis of composite laminates and laminates with including delaminated interfaces is developed. An accurate prediction of stress distributions, including interlaminar stresses, is obtained by using the Generalized Laminate Plate Theory of Reddy in which layer-wise linear approximation of the displacements through the thickness is used. Analytical as well as finite-element solutions of the theory are developed for bending and vibrations of laminated composite plates for the linear theory. Geometrical nonlinearity, including buckling and postbuckling are included and used to perform stress analysis of laminated plates. A general two dimensional theory of laminatedmore » cylindrical shells is also developed in this study. Geometrical nonlinearity and transverse compressibility are included. Delaminations between layers of composite plates are modelled by jump discontinuity conditions at the interfaces. The theory includes multiple delaminations through the thickness. Geometric nonlinearity is included to capture layer buckling. The strain energy release rate distribution along the boundary of delaminations is computed by a novel algorithm. The computational models presented herein are accurate for global behavior and particularly appropriate for the study of local effects.« less

Validating the applicability of the GUM procedure

NASA Astrophysics Data System (ADS)

Cox, Maurice G.; Harris, Peter M.

2014-08-01

This paper is directed at practitioners seeking a degree of assurance in the quality of the results of an uncertainty evaluation when using the procedure in the Guide to the Expression of Uncertainty in Measurement (GUM) (JCGM 100 : 2008). Such assurance is required in adhering to general standards such as International Standard ISO/IEC 17025 or other sector-specific standards. We investigate the extent to which such assurance can be given. For many practical cases, a measurement result incorporating an evaluated uncertainty that is correct to one significant decimal digit would be acceptable. Any quantification of the numerical precision of an uncertainty statement is naturally relative to the adequacy of the measurement model and the knowledge used of the quantities in that model. For general univariate and multivariate measurement models, we emphasize the use of a Monte Carlo method, as recommended in GUM Supplements 1 and 2. One use of this method is as a benchmark in terms of which measurement results provided by the GUM can be assessed in any particular instance. We mainly consider measurement models that are linear in the input quantities, or have been linearized and the linearization process is deemed to be adequate. When the probability distributions for those quantities are independent, we indicate the use of other approaches such as convolution methods based on the fast Fourier transform and, particularly, Chebyshev polynomials as benchmarks.

Simplified model to describe the dissociative recombination of linear polyatomic ions of astrophysical interest

NASA Astrophysics Data System (ADS)

Fonseca Dos Santos, Samantha; Douguet, Nicolas; Kokoouline, Viatcheslav; Orel, Ann

2013-05-01

We will present theoretical results on the dissociative recombination (DR) of the linear polyatomic ions HCNH+, HCO+ and N2H+. Besides their astrophysical importance, they also share the characteristic that at low electronic impact energies their DR process happens via the indirect DR mechanism. We apply a general simplified model successfully implemented to treat the DR process of the highly symmetric non-linear molecules H3+, CH3+, H3O+ and NH4+ to calculated cross sections and DR rates for these ions. The model is based on multichannel quantum defect theory and accounts for all the main ingredients of indirect DR. New perspectives on dissociative recombination of HCO+ will also be discussed, including the possible role of HOC+ in storage ring experimental results. This work is supported by the DOE Office of Basic Energy Science and the National Science Foundation, Grant No's PHY-11-60611 and PHY-10-68785.

Linear regression in astronomy. II

NASA Technical Reports Server (NTRS)

Feigelson, Eric D.; Babu, Gutti J.

1992-01-01

A wide variety of least-squares linear regression procedures used in observational astronomy, particularly investigations of the cosmic distance scale, are presented and discussed. The classes of linear models considered are (1) unweighted regression lines, with bootstrap and jackknife resampling; (2) regression solutions when measurement error, in one or both variables, dominates the scatter; (3) methods to apply a calibration line to new data; (4) truncated regression models, which apply to flux-limited data sets; and (5) censored regression models, which apply when nondetections are present. For the calibration problem we develop two new procedures: a formula for the intercept offset between two parallel data sets, which propagates slope errors from one regression to the other; and a generalization of the Working-Hotelling confidence bands to nonstandard least-squares lines. They can provide improved error analysis for Faber-Jackson, Tully-Fisher, and similar cosmic distance scale relations.

Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models

NASA Astrophysics Data System (ADS)

Boudineau, Mégane; Carfantan, Hervé; Bourguignon, Sébastien; Bazot, Michael

2016-06-01

We address the sparse approximation problem in the case where the data are approximated by the linear combination of a small number of elementary signals, each of these signals depending non-linearly on additional parameters. Sparsity is explicitly expressed through a Bernoulli-Gaussian hierarchical model in a Bayesian framework. Posterior mean estimates are computed using Markov Chain Monte-Carlo algorithms. We generalize the partially marginalized Gibbs sampler proposed in the linear case in [1], and build an hybrid Hastings-within-Gibbs algorithm in order to account for the nonlinear parameters. All model parameters are then estimated in an unsupervised procedure. The resulting method is evaluated on a sparse spectral analysis problem. It is shown to converge more efficiently than the classical joint estimation procedure, with only a slight increase of the computational cost per iteration, consequently reducing the global cost of the estimation procedure.

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

Bose, Benjamin; Koyama, Kazuya, E-mail: benjamin.bose@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk

We develop a code to produce the power spectrum in redshift space based on standard perturbation theory (SPT) at 1-loop order. The code can be applied to a wide range of modified gravity and dark energy models using a recently proposed numerical method by A.Taruya to find the SPT kernels. This includes Horndeski's theory with a general potential, which accommodates both chameleon and Vainshtein screening mechanisms and provides a non-linear extension of the effective theory of dark energy up to the third order. Focus is on a recent non-linear model of the redshift space power spectrum which has been shownmore » to model the anisotropy very well at relevant scales for the SPT framework, as well as capturing relevant non-linear effects typical of modified gravity theories. We provide consistency checks of the code against established results and elucidate its application within the light of upcoming high precision RSD data.« less

Venus Chasmata: A Lithospheric Stretching Model

NASA Technical Reports Server (NTRS)

Solomon, S. C.; Head, J. W.

1985-01-01

An outstanding problem for Venus is the characterization of its style of global tectonics, an issue intimately related to the dominant mechanism of lithospheric heat loss. Among the most spectacular and extensive of the major tectonic features on Venus are the chasmata, deep linear valleys generally interpreted to be the products of lithospheric extension and rifting. Systems of chasmata and related features can be traced along several tectonic zones up to 20,000 km in linear extent. A lithospheric stretching model was developed to explain the topographic characteristics of Venus chasmata and to constrain the physical properties of the Venus crust and lithosphere.

Estimating a graphical intra-class correlation coefficient (GICC) using multivariate probit-linear mixed models.

PubMed

Yue, Chen; Chen, Shaojie; Sair, Haris I; Airan, Raag; Caffo, Brian S

2015-09-01

Data reproducibility is a critical issue in all scientific experiments. In this manuscript, the problem of quantifying the reproducibility of graphical measurements is considered. The image intra-class correlation coefficient (I2C2) is generalized and the graphical intra-class correlation coefficient (GICC) is proposed for such purpose. The concept for GICC is based on multivariate probit-linear mixed effect models. A Markov Chain Monte Carlo EM (mcm-cEM) algorithm is used for estimating the GICC. Simulation results with varied settings are demonstrated and our method is applied to the KIRBY21 test-retest dataset.

Quantum criticality of the two-channel pseudogap Anderson model: universal scaling in linear and non-linear conductance.

PubMed

Wu, Tsan-Pei; Wang, Xiao-Qun; Guo, Guang-Yu; Anders, Frithjof; Chung, Chung-Hou

2016-05-05

The quantum criticality of the two-lead two-channel pseudogap Anderson impurity model is studied. Based on the non-crossing approximation (NCA) and numerical renormalization group (NRG) approaches, we calculate both the linear and nonlinear conductance of the model at finite temperatures with a voltage bias and a power-law vanishing conduction electron density of states, ρc(ω) proportional |ω − μF|(r) (0 < r < 1) near the Fermi energy μF. At a fixed lead-impurity hybridization, a quantum phase transition from the two-channel Kondo (2CK) to the local moment (LM) phase is observed with increasing r from r = 0 to r = rc < 1. Surprisingly, in the 2CK phase, different power-law scalings from the well-known [Formula: see text] or [Formula: see text] form is found. Moreover, novel power-law scalings in conductances at the 2CK-LM quantum critical point are identified. Clear distinctions are found on the critical exponents between linear and non-linear conductance at criticality. The implications of these two distinct quantum critical properties for the non-equilibrium quantum criticality in general are discussed.

Modelling and economic evaluation of forest biome shifts under climate change in Southwest Germany

Treesearch

Marc Hanewinkel; Susan Hummel; Dominik Cullmann

2010-01-01

We evaluated the economic effects of a predicted shift from Norway spruce (Picea abies) to European beech (Fagus sylvatica) for a forest area of 1.3 million ha in southwest Germany. The shift was modelled with a generalized linear model (GLM) by using presence/absence data from the National Forest Inventory in Baden-Wurttemberg...

Economic Planning for Multicounty Rural Areas: Application of a Linear Programming Model in Northwest Arkansas. Technical Bulletin No. 1653.

ERIC Educational Resources Information Center

Williams, Daniel G.

Planners in multicounty rural areas can use the Rural Development, Activity Analysis Planning (RDAAP) model to try to influence the optimal growth of their areas among different general economic goals. The model implies that best industries for rural areas have: high proportion of imported inputs; low transportation costs; high value added/output…

Some aspects of mathematical and chemical modeling of complex chemical processes

NASA Technical Reports Server (NTRS)

Nemes, I.; Botar, L.; Danoczy, E.; Vidoczy, T.; Gal, D.

1983-01-01

Some theoretical questions involved in the mathematical modeling of the kinetics of complex chemical process are discussed. The analysis is carried out for the homogeneous oxidation of ethylbenzene in the liquid phase. Particular attention is given to the determination of the general characteristics of chemical systems from an analysis of mathematical models developed on the basis of linear algebra.

Building out a Measurement Model to Incorporate Complexities of Testing in the Language Domain

ERIC Educational Resources Information Center

Wilson, Mark; Moore, Stephen

2011-01-01

This paper provides a summary of a novel and integrated way to think about the item response models (most often used in measurement applications in social science areas such as psychology, education, and especially testing of various kinds) from the viewpoint of the statistical theory of generalized linear and nonlinear mixed models. In addition,…

General Model of Photon-Pair Detection with an Image Sensor

NASA Astrophysics Data System (ADS)

Defienne, Hugo; Reichert, Matthew; Fleischer, Jason W.

2018-05-01

We develop an analytic model that relates intensity correlation measurements performed by an image sensor to the properties of photon pairs illuminating it. Experiments using an effective single-photon counting camera, a linear electron-multiplying charge-coupled device camera, and a standard CCD camera confirm the model. The results open the field of quantum optical sensing using conventional detectors.

Financial Distress Prediction using Linear Discriminant Analysis and Support Vector Machine

NASA Astrophysics Data System (ADS)

Santoso, Noviyanti; Wibowo, Wahyu

2018-03-01

A financial difficulty is the early stages before the bankruptcy. Bankruptcies caused by the financial distress can be seen from the financial statements of the company. The ability to predict financial distress became an important research topic because it can provide early warning for the company. In addition, predicting financial distress is also beneficial for investors and creditors. This research will be made the prediction model of financial distress at industrial companies in Indonesia by comparing the performance of Linear Discriminant Analysis (LDA) and Support Vector Machine (SVM) combined with variable selection technique. The result of this research is prediction model based on hybrid Stepwise-SVM obtains better balance among fitting ability, generalization ability and model stability than the other models.

A Flight Dynamics Model for a Multi-Actuated Flexible Rocket Vehicle

NASA Technical Reports Server (NTRS)

Orr, Jeb S.

2011-01-01

A comprehensive set of motion equations for a multi-actuated flight vehicle is presented. The dynamics are derived from a vector approach that generalizes the classical linear perturbation equations for flexible launch vehicles into a coupled three-dimensional model. The effects of nozzle and aerosurface inertial coupling, sloshing propellant, and elasticity are incorporated without restrictions on the position, orientation, or number of model elements. The present formulation is well suited to matrix implementation for large-scale linear stability and sensitivity analysis and is also shown to be extensible to nonlinear time-domain simulation through the application of a special form of Lagrange s equations in quasi-coordinates. The model is validated through frequency-domain response comparison with a high-fidelity planar implementation.

An Efficient Test for Gene-Environment Interaction in Generalized Linear Mixed Models with Family Data.

PubMed

Mazo Lopera, Mauricio A; Coombes, Brandon J; de Andrade, Mariza

2017-09-27

Gene-environment (GE) interaction has important implications in the etiology of complex diseases that are caused by a combination of genetic factors and environment variables. Several authors have developed GE analysis in the context of independent subjects or longitudinal data using a gene-set. In this paper, we propose to analyze GE interaction for discrete and continuous phenotypes in family studies by incorporating the relatedness among the relatives for each family into a generalized linear mixed model (GLMM) and by using a gene-based variance component test. In addition, we deal with collinearity problems arising from linkage disequilibrium among single nucleotide polymorphisms (SNPs) by considering their coefficients as random effects under the null model estimation. We show that the best linear unbiased predictor (BLUP) of such random effects in the GLMM is equivalent to the ridge regression estimator. This equivalence provides a simple method to estimate the ridge penalty parameter in comparison to other computationally-demanding estimation approaches based on cross-validation schemes. We evaluated the proposed test using simulation studies and applied it to real data from the Baependi Heart Study consisting of 76 families. Using our approach, we identified an interaction between BMI and the Peroxisome Proliferator Activated Receptor Gamma ( PPARG ) gene associated with diabetes.

PDE-based geophysical modelling using finite elements: examples from 3D resistivity and 2D magnetotellurics

NASA Astrophysics Data System (ADS)

Schaa, R.; Gross, L.; du Plessis, J.

2016-04-01

We present a general finite-element solver, escript, tailored to solve geophysical forward and inverse modeling problems in terms of partial differential equations (PDEs) with suitable boundary conditions. Escript’s abstract interface allows geoscientists to focus on solving the actual problem without being experts in numerical modeling. General-purpose finite element solvers have found wide use especially in engineering fields and find increasing application in the geophysical disciplines as these offer a single interface to tackle different geophysical problems. These solvers are useful for data interpretation and for research, but can also be a useful tool in educational settings. This paper serves as an introduction into PDE-based modeling with escript where we demonstrate in detail how escript is used to solve two different forward modeling problems from applied geophysics (3D DC resistivity and 2D magnetotellurics). Based on these two different cases, other geophysical modeling work can easily be realized. The escript package is implemented as a Python library and allows the solution of coupled, linear or non-linear, time-dependent PDEs. Parallel execution for both shared and distributed memory architectures is supported and can be used without modifications to the scripts.

Non Abelian T-duality in Gauged Linear Sigma Models

NASA Astrophysics Data System (ADS)

Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando; Santos-Silva, Roberto

2018-04-01

Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM's as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they depend in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.

Item Response Theory Using Hierarchical Generalized Linear Models

ERIC Educational Resources Information Center

Ravand, Hamdollah

2015-01-01

Multilevel models (MLMs) are flexible in that they can be employed to obtain item and person parameters, test for differential item functioning (DIF) and capture both local item and person dependence. Papers on the MLM analysis of item response data have focused mostly on theoretical issues where applications have been add-ons to simulation…

Modeling Agrilus planipennis within-tree colonization patterns and development of a systematic subsampling plan

USDA-ARS?s Scientific Manuscript database

Emerald ash borer, Agrilus planipennis Fairmaire, an insect native to central Asia, was first detected in southeast Michigan in 2002, and has since killed millions of ash trees, Fraxinus spp., throughout eastern North America. Here, we use generalized linear mixed models to predict the presence or a...

The Effects of Measurement Error on Statistical Models for Analyzing Change. Final Report.

ERIC Educational Resources Information Center

Dunivant, Noel

The results of six major projects are discussed including a comprehensive mathematical and statistical analysis of the problems caused by errors of measurement in linear models for assessing change. In a general matrix representation of the problem, several new analytic results are proved concerning the parameters which affect bias in…

The evaluation of the OSGLR algorithm for restructurable controls

NASA Technical Reports Server (NTRS)

Bonnice, W. F.; Wagner, E.; Hall, S. R.; Motyka, P.

1986-01-01

The detection and isolation of commercial aircraft control surface and actuator failures using the orthogonal series generalized likelihood ratio (OSGLR) test was evaluated. The OSGLR algorithm was chosen as the most promising algorithm based on a preliminary evaluation of three failure detection and isolation (FDI) algorithms (the detection filter, the generalized likelihood ratio test, and the OSGLR test) and a survey of the literature. One difficulty of analytic FDI techniques and the OSGLR algorithm in particular is their sensitivity to modeling errors. Therefore, methods of improving the robustness of the algorithm were examined with the incorporation of age-weighting into the algorithm being the most effective approach, significantly reducing the sensitivity of the algorithm to modeling errors. The steady-state implementation of the algorithm based on a single cruise linear model was evaluated using a nonlinear simulation of a C-130 aircraft. A number of off-nominal no-failure flight conditions including maneuvers, nonzero flap deflections, different turbulence levels and steady winds were tested. Based on the no-failure decision functions produced by off-nominal flight conditions, the failure detection performance at the nominal flight condition was determined. The extension of the algorithm to a wider flight envelope by scheduling the linear models used by the algorithm on dynamic pressure and flap deflection was also considered. Since simply scheduling the linear models over the entire flight envelope is unlikely to be adequate, scheduling of the steady-state implentation of the algorithm was briefly investigated.

Linear mixed model for heritability estimation that explicitly addresses environmental variation.

PubMed

Heckerman, David; Gurdasani, Deepti; Kadie, Carl; Pomilla, Cristina; Carstensen, Tommy; Martin, Hilary; Ekoru, Kenneth; Nsubuga, Rebecca N; Ssenyomo, Gerald; Kamali, Anatoli; Kaleebu, Pontiano; Widmer, Christian; Sandhu, Manjinder S

2016-07-05

The linear mixed model (LMM) is now routinely used to estimate heritability. Unfortunately, as we demonstrate, LMM estimates of heritability can be inflated when using a standard model. To help reduce this inflation, we used a more general LMM with two random effects-one based on genomic variants and one based on easily measured spatial location as a proxy for environmental effects. We investigated this approach with simulated data and with data from a Uganda cohort of 4,778 individuals for 34 phenotypes including anthropometric indices, blood factors, glycemic control, blood pressure, lipid tests, and liver function tests. For the genomic random effect, we used identity-by-descent estimates from accurately phased genome-wide data. For the environmental random effect, we constructed a covariance matrix based on a Gaussian radial basis function. Across the simulated and Ugandan data, narrow-sense heritability estimates were lower using the more general model. Thus, our approach addresses, in part, the issue of "missing heritability" in the sense that much of the heritability previously thought to be missing was fictional. Software is available at https://github.com/MicrosoftGenomics/FaST-LMM.

Missing Data in Clinical Studies: Issues and Methods

PubMed Central

Ibrahim, Joseph G.; Chu, Haitao; Chen, Ming-Hui

2012-01-01

Missing data are a prevailing problem in any type of data analyses. A participant variable is considered missing if the value of the variable (outcome or covariate) for the participant is not observed. In this article, various issues in analyzing studies with missing data are discussed. Particularly, we focus on missing response and/or covariate data for studies with discrete, continuous, or time-to-event end points in which generalized linear models, models for longitudinal data such as generalized linear mixed effects models, or Cox regression models are used. We discuss various classifications of missing data that may arise in a study and demonstrate in several situations that the commonly used method of throwing out all participants with any missing data may lead to incorrect results and conclusions. The methods described are applied to data from an Eastern Cooperative Oncology Group phase II clinical trial of liver cancer and a phase III clinical trial of advanced non–small-cell lung cancer. Although the main area of application discussed here is cancer, the issues and methods we discuss apply to any type of study. PMID:22649133

Symmetry groups of integro-differential equations for linear thermoviscoelastic materials with memory

NASA Astrophysics Data System (ADS)

Zhou, L.-Q.; Meleshko, S. V.

2017-07-01

The group analysis method is applied to a system of integro-differential equations corresponding to a linear thermoviscoelastic model. A recently developed approach for calculating the symmetry groups of such equations is used. The general solution of the determining equations for the system is obtained. Using subalgebras of the admitted Lie algebra, two classes of partially invariant solutions of the considered system of integro-differential equations are studied.

Guidelines and Procedures for Computing Time-Series Suspended-Sediment Concentrations and Loads from In-Stream Turbidity-Sensor and Streamflow Data

USGS Publications Warehouse

Rasmussen, Patrick P.; Gray, John R.; Glysson, G. Douglas; Ziegler, Andrew C.

2009-01-01

In-stream continuous turbidity and streamflow data, calibrated with measured suspended-sediment concentration data, can be used to compute a time series of suspended-sediment concentration and load at a stream site. Development of a simple linear (ordinary least squares) regression model for computing suspended-sediment concentrations from instantaneous turbidity data is the first step in the computation process. If the model standard percentage error (MSPE) of the simple linear regression model meets a minimum criterion, this model should be used to compute a time series of suspended-sediment concentrations. Otherwise, a multiple linear regression model using paired instantaneous turbidity and streamflow data is developed and compared to the simple regression model. If the inclusion of the streamflow variable proves to be statistically significant and the uncertainty associated with the multiple regression model results in an improvement over that for the simple linear model, the turbidity-streamflow multiple linear regression model should be used to compute a suspended-sediment concentration time series. The computed concentration time series is subsequently used with its paired streamflow time series to compute suspended-sediment loads by standard U.S. Geological Survey techniques. Once an acceptable regression model is developed, it can be used to compute suspended-sediment concentration beyond the period of record used in model development with proper ongoing collection and analysis of calibration samples. Regression models to compute suspended-sediment concentrations are generally site specific and should never be considered static, but they represent a set period in a continually dynamic system in which additional data will help verify any change in sediment load, type, and source.

Mean-force-field and mean-spherical approximations for the electric microfield distribution at a charged point in the charged-hard-particles fluid

NASA Astrophysics Data System (ADS)

Rosenfeld, Yaakov

1989-01-01

The linearized mean-force-field approximation, leading to a Gaussian distribution, provides an exact formal solution to the mean-spherical integral equation model for the electric microfield distribution at a charged point in the general charged-hard-particles fluid. Lado's explicit solution for plasmas immediately follows this general observation.

Reader Reaction On the generalized Kruskal-Wallis test for genetic association studies incorporating group uncertainty

PubMed Central

Wu, Baolin; Guan, Weihua

2015-01-01

Summary Acar and Sun (2013, Biometrics, 69, 427-435) presented a generalized Kruskal-Wallis (GKW) test for genetic association studies that incorporated the genotype uncertainty and showed its robust and competitive performance compared to existing methods. We present another interesting way to derive the GKW test via a rank linear model. PMID:25351417

Reader reaction on the generalized Kruskal-Wallis test for genetic association studies incorporating group uncertainty.

PubMed

Wu, Baolin; Guan, Weihua

2015-06-01

Acar and Sun (2013, Biometrics 69, 427-435) presented a generalized Kruskal-Wallis (GKW) test for genetic association studies that incorporated the genotype uncertainty and showed its robust and competitive performance compared to existing methods. We present another interesting way to derive the GKW test via a rank linear model. © 2014, The International Biometric Society.

A quasi-likelihood approach to non-negative matrix factorization

PubMed Central

Devarajan, Karthik; Cheung, Vincent C.K.

2017-01-01

A unified approach to non-negative matrix factorization based on the theory of generalized linear models is proposed. This approach embeds a variety of statistical models, including the exponential family, within a single theoretical framework and provides a unified view of such factorizations from the perspective of quasi-likelihood. Using this framework, a family of algorithms for handling signal-dependent noise is developed and its convergence proven using the Expectation-Maximization algorithm. In addition, a measure to evaluate the goodness-of-fit of the resulting factorization is described. The proposed methods allow modeling of non-linear effects via appropriate link functions and are illustrated using an application in biomedical signal processing. PMID:27348511

Feature Extraction of Event-Related Potentials Using Wavelets: An Application to Human Performance Monitoring

NASA Technical Reports Server (NTRS)

Trejo, Leonard J.; Shensa, Mark J.; Remington, Roger W. (Technical Monitor)

1998-01-01

This report describes the development and evaluation of mathematical models for predicting human performance from discrete wavelet transforms (DWT) of event-related potentials (ERP) elicited by task-relevant stimuli. The DWT was compared to principal components analysis (PCA) for representation of ERPs in linear regression and neural network models developed to predict a composite measure of human signal detection performance. Linear regression models based on coefficients of the decimated DWT predicted signal detection performance with half as many f ree parameters as comparable models based on PCA scores. In addition, the DWT-based models were more resistant to model degradation due to over-fitting than PCA-based models. Feed-forward neural networks were trained using the backpropagation,-, algorithm to predict signal detection performance based on raw ERPs, PCA scores, or high-power coefficients of the DWT. Neural networks based on high-power DWT coefficients trained with fewer iterations, generalized to new data better, and were more resistant to overfitting than networks based on raw ERPs. Networks based on PCA scores did not generalize to new data as well as either the DWT network or the raw ERP network. The results show that wavelet expansions represent the ERP efficiently and extract behaviorally important features for use in linear regression or neural network models of human performance. The efficiency of the DWT is discussed in terms of its decorrelation and energy compaction properties. In addition, the DWT models provided evidence that a pattern of low-frequency activity (1 to 3.5 Hz) occurring at specific times and scalp locations is a reliable correlate of human signal detection performance.

Feature extraction of event-related potentials using wavelets: an application to human performance monitoring

NASA Technical Reports Server (NTRS)

Trejo, L. J.; Shensa, M. J.

1999-01-01

This report describes the development and evaluation of mathematical models for predicting human performance from discrete wavelet transforms (DWT) of event-related potentials (ERP) elicited by task-relevant stimuli. The DWT was compared to principal components analysis (PCA) for representation of ERPs in linear regression and neural network models developed to predict a composite measure of human signal detection performance. Linear regression models based on coefficients of the decimated DWT predicted signal detection performance with half as many free parameters as comparable models based on PCA scores. In addition, the DWT-based models were more resistant to model degradation due to over-fitting than PCA-based models. Feed-forward neural networks were trained using the backpropagation algorithm to predict signal detection performance based on raw ERPs, PCA scores, or high-power coefficients of the DWT. Neural networks based on high-power DWT coefficients trained with fewer iterations, generalized to new data better, and were more resistant to overfitting than networks based on raw ERPs. Networks based on PCA scores did not generalize to new data as well as either the DWT network or the raw ERP network. The results show that wavelet expansions represent the ERP efficiently and extract behaviorally important features for use in linear regression or neural network models of human performance. The efficiency of the DWT is discussed in terms of its decorrelation and energy compaction properties. In addition, the DWT models provided evidence that a pattern of low-frequency activity (1 to 3.5 Hz) occurring at specific times and scalp locations is a reliable correlate of human signal detection performance. Copyright 1999 Academic Press.

A powerful and flexible approach to the analysis of RNA sequence count data

PubMed Central

Zhou, Yi-Hui; Xia, Kai; Wright, Fred A.

2011-01-01

Motivation: A number of penalization and shrinkage approaches have been proposed for the analysis of microarray gene expression data. Similar techniques are now routinely applied to RNA sequence transcriptional count data, although the value of such shrinkage has not been conclusively established. If penalization is desired, the explicit modeling of mean–variance relationships provides a flexible testing regimen that ‘borrows’ information across genes, while easily incorporating design effects and additional covariates. Results: We describe BBSeq, which incorporates two approaches: (i) a simple beta-binomial generalized linear model, which has not been extensively tested for RNA-Seq data and (ii) an extension of an expression mean–variance modeling approach to RNA-Seq data, involving modeling of the overdispersion as a function of the mean. Our approaches are flexible, allowing for general handling of discrete experimental factors and continuous covariates. We report comparisons with other alternate methods to handle RNA-Seq data. Although penalized methods have advantages for very small sample sizes, the beta-binomial generalized linear model, combined with simple outlier detection and testing approaches, appears to have favorable characteristics in power and flexibility. Availability: An R package containing examples and sample datasets is available at http://www.bios.unc.edu/research/genomic_software/BBSeq Contact: yzhou@bios.unc.edu; fwright@bios.unc.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:21810900

Linear discriminant analysis with misallocation in training samples

NASA Technical Reports Server (NTRS)

Chhikara, R. (Principal Investigator); Mckeon, J.

1982-01-01

Linear discriminant analysis for a two-class case is studied in the presence of misallocation in training samples. A general appraoch to modeling of mislocation is formulated, and the mean vectors and covariance matrices of the mixture distributions are derived. The asymptotic distribution of the discriminant boundary is obtained and the asymptotic first two moments of the two types of error rate given. Certain numerical results for the error rates are presented by considering the random and two non-random misallocation models. It is shown that when the allocation procedure for training samples is objectively formulated, the effect of misallocation on the error rates of the Bayes linear discriminant rule can almost be eliminated. If, however, this is not possible, the use of Fisher rule may be preferred over the Bayes rule.

The decline and fall of Type II error rates

Treesearch

Steve Verrill; Mark Durst

2005-01-01

For general linear models with normally distributed random errors, the probability of a Type II error decreases exponentially as a function of sample size. This potentially rapid decline reemphasizes the importance of performing power calculations.

Quasi-likelihood generalized linear regression analysis of fatality risk data

DOT National Transportation Integrated Search

2009-01-01

Transportation-related fatality risks is a function of many interacting human, vehicle, and environmental factors. Statisitcally valid analysis of such data is challenged both by the complexity of plausable structural models relating fatality rates t...

Generalized cable equation model for myelinated nerve fiber.

PubMed

Einziger, Pinchas D; Livshitz, Leonid M; Mizrahi, Joseph

2005-10-01

Herein, the well-known cable equation for nonmyelinated axon model is extended analytically for myelinated axon formulation. The myelinated membrane conductivity is represented via the Fourier series expansion. The classical cable equation is thereby modified into a linear second order ordinary differential equation with periodic coefficients, known as Hill's equation. The general internal source response, expressed via repeated convolutions, uniformly converges provided that the entire periodic membrane is passive. The solution can be interpreted as an extended source response in an equivalent nonmyelinated axon (i.e., the response is governed by the classical cable equation). The extended source consists of the original source and a novel activation function, replacing the periodic membrane in the myelinated axon model. Hill's equation is explicitly integrated for the specific choice of piecewise constant membrane conductivity profile, thereby resulting in an explicit closed form expression for the transmembrane potential in terms of trigonometric functions. The Floquet's modes are recognized as the nerve fiber activation modes, which are conventionally associated with the nonlinear Hodgkin-Huxley formulation. They can also be incorporated in our linear model, provided that the periodic membrane point-wise passivity constraint is properly modified. Indeed, the modified condition, enforcing the periodic membrane passivity constraint on the average conductivity only leads, for the first time, to the inclusion of the nerve fiber activation modes in our novel model. The validity of the generalized transmission-line and cable equation models for a myelinated nerve fiber, is verified herein through a rigorous Green's function formulation and numerical simulations for transmembrane potential induced in three-dimensional myelinated cylindrical cell. It is shown that the dominant pole contribution of the exact modal expansion is the transmembrane potential solution of our generalized model.

Dissipation models for central difference schemes

NASA Astrophysics Data System (ADS)

Eliasson, Peter

1992-12-01

In this paper different flux limiters are used to construct dissipation models. The flux limiters are usually of Total Variation Diminishing (TVD type and are applied to the characteristic variables for the hyperbolic Euler equations in one, two or three dimensions. A number of simplified dissipation models with a reduced number of limiters are considered to reduce the computational effort. The most simplified methods use only one limiter, the dissipation model by Jameson belongs to this class since the Jameson pressure switch is considered as a limiter, not TVD though. Other one-limiter models with TVD limiters are also investigated. Models in between the most simplified one-limiter models and the full model with limiters on all the different characteristics are considered where different dissipation models are applied to the linear and non-linear characteristcs. In this paper the theory by Yee is extended to a general explicit Runge-Kutta type of schemes.

Learning quadratic receptive fields from neural responses to natural stimuli.

PubMed

Rajan, Kanaka; Marre, Olivier; Tkačik, Gašper

2013-07-01

Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are selective for only a small number of linear projections of a potentially high-dimensional input. In this review, we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection, that is, the neuron is sensitive to the local covariance structure of the signal preceding the spike. To infer this quadratic dependence in the presence of arbitrary (e.g., naturalistic) stimulus distribution, we review several inference methods, focusing in particular on two information theory-based approaches (maximization of stimulus energy and of noise entropy) and two likelihood-based approaches (Bayesian spike-triggered covariance and extensions of generalized linear models). We analyze the formal relationship between the likelihood-based and information-based approaches to demonstrate how they lead to consistent inference. We demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus.

Estimating linear-nonlinear models using Rényi divergences

PubMed Central

Kouh, Minjoon; Sharpee, Tatyana O.

2009-01-01

This paper compares a family of methods for characterizing neural feature selectivity using natural stimuli in the framework of the linear-nonlinear model. In this model, the spike probability depends in a nonlinear way on a small number of stimulus dimensions. The relevant stimulus dimensions can be found by optimizing a Rényi divergence that quantifies a change in the stimulus distribution associated with the arrival of single spikes. Generally, good reconstructions can be obtained based on optimization of Rényi divergence of any order, even in the limit of small numbers of spikes. However, the smallest error is obtained when the Rényi divergence of order 1 is optimized. This type of optimization is equivalent to information maximization, and is shown to saturate the Cramér-Rao bound describing the smallest error allowed for any unbiased method. We also discuss conditions under which information maximization provides a convenient way to perform maximum likelihood estimation of linear-nonlinear models from neural data. PMID:19568981

Estimating linear-nonlinear models using Renyi divergences.

PubMed

Kouh, Minjoon; Sharpee, Tatyana O

2009-01-01

This article compares a family of methods for characterizing neural feature selectivity using natural stimuli in the framework of the linear-nonlinear model. In this model, the spike probability depends in a nonlinear way on a small number of stimulus dimensions. The relevant stimulus dimensions can be found by optimizing a Rényi divergence that quantifies a change in the stimulus distribution associated with the arrival of single spikes. Generally, good reconstructions can be obtained based on optimization of Rényi divergence of any order, even in the limit of small numbers of spikes. However, the smallest error is obtained when the Rényi divergence of order 1 is optimized. This type of optimization is equivalent to information maximization, and is shown to saturate the Cramer-Rao bound describing the smallest error allowed for any unbiased method. We also discuss conditions under which information maximization provides a convenient way to perform maximum likelihood estimation of linear-nonlinear models from neural data.

Cell kill by megavoltage protons with high LET.

PubMed

Kuperman, Vadim Y

2016-07-21

The aim of the current study is to develop a radiobiological model which describes the effect of linear energy transfer (LET) on cell survival and relative biological effectiveness (RBE) of megavoltage protons. By assuming the existence of critical sites within a cell, analytical expression for cell survival S as a function of LET is derived. The obtained results indicate that in cases where dose per fraction is small, [Formula: see text] is a linear-quadratic (LQ) function of dose while both alpha and beta radio-sensitivities are non-linearly dependent on LET. In particular, in the current model alpha increases with increasing LET while beta decreases. Conversely, in the case of large dose per fraction, the LQ dependence of [Formula: see text] on dose is invalid. The proposed radiobiological model predicts cell survival probability and RBE which, in general, deviate from the results obtained by using conventional LQ formalism. The differences between the LQ model and that described in the current study are reflected in the calculated RBE of protons.

Nanoscale swimmers: hydrodynamic interactions and propulsion of molecular machines

NASA Astrophysics Data System (ADS)

Sakaue, T.; Kapral, R.; Mikhailov, A. S.

2010-06-01

Molecular machines execute nearly regular cyclic conformational changes as a result of ligand binding and product release. This cyclic conformational dynamics is generally non-reciprocal so that under time reversal a different sequence of machine conformations is visited. Since such changes occur in a solvent, coupling to solvent hydrodynamic modes will generally result in self-propulsion of the molecular machine. These effects are investigated for a class of coarse grained models of protein machines consisting of a set of beads interacting through pair-wise additive potentials. Hydrodynamic effects are incorporated through a configuration-dependent mobility tensor, and expressions for the propulsion linear and angular velocities, as well as the stall force, are obtained. In the limit where conformational changes are small so that linear response theory is applicable, it is shown that propulsion is exponentially small; thus, propulsion is nonlinear phenomenon. The results are illustrated by computations on a simple model molecular machine.

MSC products for the simulation of tire behavior

NASA Technical Reports Server (NTRS)

Muskivitch, John C.

1995-01-01

The modeling of tires and the simulation of tire behavior are complex problems. The MacNeal-Schwendler Corporation (MSC) has a number of finite element analysis products that can be used to address the complexities of tire modeling and simulation. While there are many similarities between the products, each product has a number of capabilities that uniquely enable it to be used for a specific aspect of tire behavior. This paper discusses the following programs: (1) MSC/NASTRAN - general purpose finite element program for linear and nonlinear static and dynamic analysis; (2) MSC/ADAQUS - nonlinear statics and dynamics finite element program; (3) MSC/PATRAN AFEA (Advanced Finite Element Analysis) - general purpose finite element program with a subset of linear and nonlinear static and dynamic analysis capabilities with an integrated version of MSC/PATRAN for pre- and post-processing; and (4) MSC/DYTRAN - nonlinear explicit transient dynamics finite element program.

Constraints to solve parallelogram grid problems in 2D non separable linear canonical transform

NASA Astrophysics Data System (ADS)

Zhao, Liang; Healy, John J.; Muniraj, Inbarasan; Cui, Xiao-Guang; Malallah, Ra'ed; Ryle, James P.; Sheridan, John T.

2017-05-01

The 2D non-separable linear canonical transform (2D-NS-LCT) can model a range of various paraxial optical systems. Digital algorithms to evaluate the 2D-NS-LCTs are important in modeling the light field propagations and also of interest in many digital signal processing applications. In [Zhao 14] we have reported that a given 2D input image with rectangular shape/boundary, in general, results in a parallelogram output sampling grid (generally in an affine coordinates rather than in a Cartesian coordinates) thus limiting the further calculations, e.g. inverse transform. One possible solution is to use the interpolation techniques; however, it reduces the speed and accuracy of the numerical approximations. To alleviate this problem, in this paper, some constraints are derived under which the output samples are located in the Cartesian coordinates. Therefore, no interpolation operation is required and thus the calculation error can be significantly eliminated.

Massive parallelization of serial inference algorithms for a complex generalized linear model

PubMed Central

Suchard, Marc A.; Simpson, Shawn E.; Zorych, Ivan; Ryan, Patrick; Madigan, David

2014-01-01

Following a series of high-profile drug safety disasters in recent years, many countries are redoubling their efforts to ensure the safety of licensed medical products. Large-scale observational databases such as claims databases or electronic health record systems are attracting particular attention in this regard, but present significant methodological and computational concerns. In this paper we show how high-performance statistical computation, including graphics processing units, relatively inexpensive highly parallel computing devices, can enable complex methods in large databases. We focus on optimization and massive parallelization of cyclic coordinate descent approaches to fit a conditioned generalized linear model involving tens of millions of observations and thousands of predictors in a Bayesian context. We find orders-of-magnitude improvement in overall run-time. Coordinate descent approaches are ubiquitous in high-dimensional statistics and the algorithms we propose open up exciting new methodological possibilities with the potential to significantly improve drug safety. PMID:25328363

A polymer, random walk model for the size-distribution of large DNA fragments after high linear energy transfer radiation

NASA Technical Reports Server (NTRS)

Ponomarev, A. L.; Brenner, D.; Hlatky, L. R.; Sachs, R. K.

2000-01-01

DNA double-strand breaks (DSBs) produced by densely ionizing radiation are not located randomly in the genome: recent data indicate DSB clustering along chromosomes. Stochastic DSB clustering at large scales, from > 100 Mbp down to < 0.01 Mbp, is modeled using computer simulations and analytic equations. A random-walk, coarse-grained polymer model for chromatin is combined with a simple track structure model in Monte Carlo software called DNAbreak and is applied to data on alpha-particle irradiation of V-79 cells. The chromatin model neglects molecular details but systematically incorporates an increase in average spatial separation between two DNA loci as the number of base-pairs between the loci increases. Fragment-size distributions obtained using DNAbreak match data on large fragments about as well as distributions previously obtained with a less mechanistic approach. Dose-response relations, linear at small doses of high linear energy transfer (LET) radiation, are obtained. They are found to be non-linear when the dose becomes so large that there is a significant probability of overlapping or close juxtaposition, along one chromosome, for different DSB clusters from different tracks. The non-linearity is more evident for large fragments than for small. The DNAbreak results furnish an example of the RLC (randomly located clusters) analytic formalism, which generalizes the broken-stick fragment-size distribution of the random-breakage model that is often applied to low-LET data.

Bayesian block-diagonal variable selection and model averaging

PubMed Central

Papaspiliopoulos, O.; Rossell, D.

2018-01-01

Summary We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general designs. In block-diagonal designs our approach returns the most probable model of any given size without resorting to numerical integration. The algorithm also provides a novel and efficient solution to the frequentist best subset selection problem for block-diagonal designs. Posterior probabilities for any number of models are obtained by evaluating a single one-dimensional integral, and other quantities of interest such as variable inclusion probabilities and model-averaged regression estimates are obtained by an adaptive, deterministic one-dimensional numerical integration. The overall computational cost scales linearly with the number of blocks, which can be processed in parallel, and exponentially with the block size, rendering it most adequate in situations where predictors are organized in many moderately-sized blocks. For general designs, we approximate the Gram matrix by a block-diagonal matrix using spectral clustering and propose an iterative algorithm that capitalizes on the block-diagonal algorithms to explore efficiently the model space. All methods proposed in this paper are implemented in the R library mombf. PMID:29861501

Theoretical foundations of apparent-damping phenomena and nearly irreversible energy exchange in linear conservative systems.

PubMed

Carcaterra, A; Akay, A

2007-04-01

This paper discusses a class of unexpected irreversible phenomena that can develop in linear conservative systems and provides a theoretical foundation that explains the underlying principles. Recent studies have shown that energy can be introduced to a linear system with near irreversibility, or energy within a system can migrate to a subsystem nearly irreversibly, even in the absence of dissipation, provided that the system has a particular natural frequency distribution. The present work introduces a general theory that provides a mathematical foundation and a physical explanation for the near irreversibility phenomena observed and reported in previous publications. Inspired by the properties of probability distribution functions, the general formulation developed here is based on particular properties of harmonic series, which form the common basis of linear dynamic system models. The results demonstrate the existence of a special class of linear nondissipative dynamic systems that exhibit nearly irreversible energy exchange and possess a decaying impulse response. In addition to uncovering a new class of dynamic system properties, the results have far-reaching implications in engineering applications where classical vibration damping or absorption techniques may not be effective. Furthermore, the results also support the notion of nearly irreversible energy transfer in conservative linear systems, which until now has been a concept associated exclusively with nonlinear systems.

Steady induction effects in geomagnetism. Part 1B: Geomagnetic estimation of steady surficial core motions: A non-linear inverse problem

NASA Technical Reports Server (NTRS)

Voorhies, Coerte V.

1993-01-01

The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.

Chemical oscillator as a generalized Rayleigh oscillator.

PubMed

Ghosh, Shyamolina; Ray, Deb Shankar

2013-10-28

We derive the conditions under which a set of arbitrary two dimensional autonomous kinetic equations can be reduced to the form of a generalized Rayleigh oscillator which admits of limit cycle solution. This is based on a linear transformation of field variables which can be found by inspection of the kinetic equations. We illustrate the scheme with the help of several chemical and bio-chemical oscillator models to show how they can be cast as a generalized Rayleigh oscillator.

General theories of linear gravitational perturbations to a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Tattersall, Oliver J.; Ferreira, Pedro G.; Lagos, Macarena

2018-02-01

We use the covariant formulation proposed by Tattersall, Lagos, and Ferreira [Phys. Rev. D 96, 064011 (2017), 10.1103/PhysRevD.96.064011] to analyze the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasinormal modes of perturbed black holes may be affected by modifications to general relativity. We restrict ourselves to single-tensor, scalar-tensor and vector-tensor diffeomorphism-invariant gravity models in a Schwarzschild black hole background. We show explicitly the full covariant form of the quadratic actions in such cases, which allow us to then analyze odd parity (axial) and even parity (polar) perturbations simultaneously in a straightforward manner.

Fit Point-Wise AB Initio Calculation Potential Energies to a Multi-Dimension Long-Range Model

NASA Astrophysics Data System (ADS)

Zhai, Yu; Li, Hui; Le Roy, Robert J.

2016-06-01

A potential energy surface (PES) is a fundamental tool and source of understanding for theoretical spectroscopy and for dynamical simulations. Making correct assignments for high-resolution rovibrational spectra of floppy polyatomic and van der Waals molecules often relies heavily on predictions generated from a high quality ab initio potential energy surface. Moreover, having an effective analytic model to represent such surfaces can be as important as the ab initio results themselves. For the one-dimensional potentials of diatomic molecules, the most successful such model to date is arguably the ``Morse/Long-Range'' (MLR) function developed by R. J. Le Roy and coworkers. It is very flexible, is everywhere differentiable to all orders. It incorporates correct predicted long-range behaviour, extrapolates sensibly at both large and small distances, and two of its defining parameters are always the physically meaningful well depth {D}_e and equilibrium distance r_e. Extensions of this model, called the Multi-Dimension Morse/Long-Range (MD-MLR) function, linear molecule-linear molecule systems and atom-non-linear molecule system. have been applied successfully to atom-plus-linear molecule, linear molecule-linear molecule and atom-non-linear molecule systems. However, there are several technical challenges faced in modelling the interactions of general molecule-molecule systems, such as the absence of radial minima for some relative alignments, difficulties in fitting short-range potential energies, and challenges in determining relative-orientation dependent long-range coefficients. This talk will illustrate some of these challenges and describe our ongoing work in addressing them. Mol. Phys. 105, 663 (2007); J. Chem. Phys. 131, 204309 (2009); Mol. Phys. 109, 435 (2011). Phys. Chem. Chem. Phys. 10, 4128 (2008); J. Chem. Phys. 130, 144305 (2009) J. Chem. Phys. 132, 214309 (2010) J. Chem. Phys. 140, 214309 (2010)

Generalized two-dimensional (2D) linear system analysis metrics (GMTF, GDQE) for digital radiography systems including the effect of focal spot, magnification, scatter, and detector characteristics.

PubMed

Jain, Amit; Kuhls-Gilcrist, Andrew T; Gupta, Sandesh K; Bednarek, Daniel R; Rudin, Stephen

2010-03-01

The MTF, NNPS, and DQE are standard linear system metrics used to characterize intrinsic detector performance. To evaluate total system performance for actual clinical conditions, generalized linear system metrics (GMTF, GNNPS and GDQE) that include the effect of the focal spot distribution, scattered radiation, and geometric unsharpness are more meaningful and appropriate. In this study, a two-dimensional (2D) generalized linear system analysis was carried out for a standard flat panel detector (FPD) (194-micron pixel pitch and 600-micron thick CsI) and a newly-developed, high-resolution, micro-angiographic fluoroscope (MAF) (35-micron pixel pitch and 300-micron thick CsI). Realistic clinical parameters and x-ray spectra were used. The 2D detector MTFs were calculated using the new Noise Response method and slanted edge method and 2D focal spot distribution measurements were done using a pin-hole assembly. The scatter fraction, generated for a uniform head equivalent phantom, was measured and the scatter MTF was simulated with a theoretical model. Different magnifications and scatter fractions were used to estimate the 2D GMTF, GNNPS and GDQE for both detectors. Results show spatial non-isotropy for the 2D generalized metrics which provide a quantitative description of the performance of the complete imaging system for both detectors. This generalized analysis demonstrated that the MAF and FPD have similar capabilities at lower spatial frequencies, but that the MAF has superior performance over the FPD at higher frequencies even when considering focal spot blurring and scatter. This 2D generalized performance analysis is a valuable tool to evaluate total system capabilities and to enable optimized design for specific imaging tasks.

Plant uptake of elements in soil and pore water: field observations versus model assumptions.

PubMed

Raguž, Veronika; Jarsjö, Jerker; Grolander, Sara; Lindborg, Regina; Avila, Rodolfo

2013-09-15

Contaminant concentrations in various edible plant parts transfer hazardous substances from polluted areas to animals and humans. Thus, the accurate prediction of plant uptake of elements is of significant importance. The processes involved contain many interacting factors and are, as such, complex. In contrast, the most common way to currently quantify element transfer from soils into plants is relatively simple, using an empirical soil-to-plant transfer factor (TF). This practice is based on theoretical assumptions that have been previously shown to not generally be valid. Using field data on concentrations of 61 basic elements in spring barley, soil and pore water at four agricultural sites in mid-eastern Sweden, we quantify element-specific TFs. Our aim is to investigate to which extent observed element-specific uptake is consistent with TF model assumptions and to which extent TF's can be used to predict observed differences in concentrations between different plant parts (root, stem and ear). Results show that for most elements, plant-ear concentrations are not linearly related to bulk soil concentrations, which is congruent with previous studies. This behaviour violates a basic TF model assumption of linearity. However, substantially better linear correlations are found when weighted average element concentrations in whole plants are used for TF estimation. The highest number of linearly-behaving elements was found when relating average plant concentrations to soil pore-water concentrations. In contrast to other elements, essential elements (micronutrients and macronutrients) exhibited relatively small differences in concentration between different plant parts. Generally, the TF model was shown to work reasonably well for micronutrients, whereas it did not for macronutrients. The results also suggest that plant uptake of elements from sources other than the soil compartment (e.g. from air) may be non-negligible. Copyright © 2013 Elsevier Ltd. All rights reserved.

Conceptual Foundations of Soliton Versus Particle Dualities Toward a Topological Model for Matter

NASA Astrophysics Data System (ADS)

Kouneiher, Joseph

2016-06-01

The idea that fermions could be solitons was actually confirmed in theoretical models in 1975 in the case when the space-time is two-dimensional and with the sine-Gordon model. More precisely S. Coleman showed that two different classical models end up describing the same fermions particle, when the quantum theory is constructed. But in one model the fermion is a quantum excitation of the field and in the other model the particle is a soliton. Hence both points of view can be reconciliated.The principal aim in this paper is to exhibit a solutions of topological type for the fermions in the wave zone, where the equations of motion are non-linear field equations, i.e. using a model generalizing sine- Gordon model to four dimensions, and describe the solutions for linear and circular polarized waves. In other words, the paper treat fermions as topological excitations of a bosonic field.

Neural-Based Compensation of Nonlinearities in an Airplane Longitudinal Model with Dynamic-Inversion Control

PubMed Central

Li, YuHui; Jin, FeiTeng

2017-01-01

The inversion design approach is a very useful tool for the complex multiple-input-multiple-output nonlinear systems to implement the decoupling control goal, such as the airplane model and spacecraft model. In this work, the flight control law is proposed using the neural-based inversion design method associated with the nonlinear compensation for a general longitudinal model of the airplane. First, the nonlinear mathematic model is converted to the equivalent linear model based on the feedback linearization theory. Then, the flight control law integrated with this inversion model is developed to stabilize the nonlinear system and relieve the coupling effect. Afterwards, the inversion control combined with the neural network and nonlinear portion is presented to improve the transient performance and attenuate the uncertain effects on both external disturbances and model errors. Finally, the simulation results demonstrate the effectiveness of this controller. PMID:29410680

Efficient polarimetric BRDF model.

PubMed

Renhorn, Ingmar G E; Hallberg, Tomas; Boreman, Glenn D

2015-11-30

The purpose of the present manuscript is to present a polarimetric bidirectional reflectance distribution function (BRDF) model suitable for hyperspectral and polarimetric signature modelling. The model is based on a further development of a previously published four-parameter model that has been generalized in order to account for different types of surface structures (generalized Gaussian distribution). A generalization of the Lambertian diffuse model is presented. The pBRDF-functions are normalized using numerical integration. Using directional-hemispherical reflectance (DHR) measurements, three of the four basic parameters can be determined for any wavelength. This simplifies considerably the development of multispectral polarimetric BRDF applications. The scattering parameter has to be determined from at least one BRDF measurement. The model deals with linear polarized radiation; and in similarity with e.g. the facet model depolarization is not included. The model is very general and can inherently model extreme surfaces such as mirrors and Lambertian surfaces. The complex mixture of sources is described by the sum of two basic models, a generalized Gaussian/Fresnel model and a generalized Lambertian model. Although the physics inspired model has some ad hoc features, the predictive power of the model is impressive over a wide range of angles and scattering magnitudes. The model has been applied successfully to painted surfaces, both dull and glossy and also on metallic bead blasted surfaces. The simple and efficient model should be attractive for polarimetric simulations and polarimetric remote sensing.

Visibility vs. biomass in flowers: exploring corolla allocation in Mediterranean entomophilous plants.

PubMed

Herrera, Javier

2009-05-01

While pollinators may in general select for large, morphologically uniform floral phenotypes, drought stress has been proposed as a destabilizing force that may favour small flowers and/or promote floral variation within species. The general validity of this concept was checked by surveying a taxonomically diverse array of 38 insect-pollinated Mediterranean species. The interplay between fresh biomass investment, linear size and percentage corolla allocation was studied. Allometric relationships between traits were investigated by reduced major-axis regression, and qualitative correlates of floral variation explored using general linear-model MANOVA. Across species, flowers were perfectly isometrical with regard to corolla allocation (i.e. larger flowers were just scaled-up versions of smaller ones and vice versa). In contrast, linear size and biomass varied allometrically (i.e. there were shape variations, in addition to variations in size). Most floral variables correlated positively and significantly across species, except corolla allocation, which was largely determined by family membership and floral symmetry. On average, species with bilateral flowers allocated more to the corolla than those with radial flowers. Plant life-form was immaterial to all of the studied traits. Flower linear size variation was in general low among conspecifics (coefficients of variation around 10 %), whereas biomass was in general less uniform (e.g. 200-400 mg in Cistus salvifolius). Significant among-population differences were detected for all major quantitative floral traits. Flower miniaturization can allow an improved use of reproductive resources under prevailingly stressful conditions. The hypothesis that flower size reflects a compromise between pollinator attraction, water requirements and allometric constraints among floral parts is discussed.

Linear and Poisson models for genetic evaluation of tick resistance in cross-bred Hereford x Nellore cattle.

PubMed

Ayres, D R; Pereira, R J; Boligon, A A; Silva, F F; Schenkel, F S; Roso, V M; Albuquerque, L G

2013-12-01

Cattle resistance to ticks is measured by the number of ticks infesting the animal. The model used for the genetic analysis of cattle resistance to ticks frequently requires logarithmic transformation of the observations. The objective of this study was to evaluate the predictive ability and goodness of fit of different models for the analysis of this trait in cross-bred Hereford x Nellore cattle. Three models were tested: a linear model using logarithmic transformation of the observations (MLOG); a linear model without transformation of the observations (MLIN); and a generalized linear Poisson model with residual term (MPOI). All models included the classificatory effects of contemporary group and genetic group and the covariates age of animal at the time of recording and individual heterozygosis, as well as additive genetic effects as random effects. Heritability estimates were 0.08 ± 0.02, 0.10 ± 0.02 and 0.14 ± 0.04 for MLIN, MLOG and MPOI models, respectively. The model fit quality, verified by deviance information criterion (DIC) and residual mean square, indicated fit superiority of MPOI model. The predictive ability of the models was compared by validation test in independent sample. The MPOI model was slightly superior in terms of goodness of fit and predictive ability, whereas the correlations between observed and predicted tick counts were practically the same for all models. A higher rank correlation between breeding values was observed between models MLOG and MPOI. Poisson model can be used for the selection of tick-resistant animals. © 2013 Blackwell Verlag GmbH.

Fractional Gaussian model in global optimization

NASA Astrophysics Data System (ADS)

Dimri, V. P.; Srivastava, R. P.

2009-12-01

Earth system is inherently non-linear and it can be characterized well if we incorporate no-linearity in the formulation and solution of the problem. General tool often used for characterization of the earth system is inversion. Traditionally inverse problems are solved using least-square based inversion by linearizing the formulation. The initial model in such inversion schemes is often assumed to follow posterior Gaussian probability distribution. It is now well established that most of the physical properties of the earth follow power law (fractal distribution). Thus, the selection of initial model based on power law probability distribution will provide more realistic solution. We present a new method which can draw samples of posterior probability density function very efficiently using fractal based statistics. The application of the method has been demonstrated to invert band limited seismic data with well control. We used fractal based probability density function which uses mean, variance and Hurst coefficient of the model space to draw initial model. Further this initial model is used in global optimization inversion scheme. Inversion results using initial models generated by our method gives high resolution estimates of the model parameters than the hitherto used gradient based liner inversion method.

Assessment of bias correction under transient climate change

NASA Astrophysics Data System (ADS)

Van Schaeybroeck, Bert; Vannitsem, Stéphane

2015-04-01

Calibration of climate simulations is necessary since large systematic discrepancies are generally found between the model climate and the observed climate. Recent studies have cast doubt upon the common assumption of the bias being stationary when the climate changes. This led to the development of new methods, mostly based on linear sensitivity of the biases as a function of time or forcing (Kharin et al. 2012). However, recent studies uncovered more fundamental problems using both low-order systems (Vannitsem 2011) and climate models, showing that the biases may display complicated non-linear variations under climate change. This last analysis focused on biases derived from the equilibrium climate sensitivity, thereby ignoring the effect of the transient climate sensitivity. Based on the linear response theory, a general method of bias correction is therefore proposed that can be applied on any climate forcing scenario. The validity of the method is addressed using twin experiments with a climate model of intermediate complexity LOVECLIM (Goosse et al., 2010). We evaluate to what extent the bias change is sensitive to the structure (frequency) of the applied forcing (here greenhouse gases) and whether the linear response theory is valid for global and/or local variables. To answer these question we perform large-ensemble simulations using different 300-year scenarios of forced carbon-dioxide concentrations. Reality and simulations are assumed to differ by a model error emulated as a parametric error in the wind drag or in the radiative scheme. References [1] H. Goosse et al., 2010: Description of the Earth system model of intermediate complexity LOVECLIM version 1.2, Geosci. Model Dev., 3, 603-633. [2] S. Vannitsem, 2011: Bias correction and post-processing under climate change, Nonlin. Processes Geophys., 18, 911-924. [3] V.V. Kharin, G. J. Boer, W. J. Merryfield, J. F. Scinocca, and W.-S. Lee, 2012: Statistical adjustment of decadal predictions in a changing climate, Geophys. Res. Lett., 39, L19705.

Profile local linear estimation of generalized semiparametric regression model for longitudinal data.

PubMed

Sun, Yanqing; Sun, Liuquan; Zhou, Jie

2013-07-01

This paper studies the generalized semiparametric regression model for longitudinal data where the covariate effects are constant for some and time-varying for others. Different link functions can be used to allow more flexible modelling of longitudinal data. The nonparametric components of the model are estimated using a local linear estimating equation and the parametric components are estimated through a profile estimating function. The method automatically adjusts for heterogeneity of sampling times, allowing the sampling strategy to depend on the past sampling history as well as possibly time-dependent covariates without specifically model such dependence. A [Formula: see text]-fold cross-validation bandwidth selection is proposed as a working tool for locating an appropriate bandwidth. A criteria for selecting the link function is proposed to provide better fit of the data. Large sample properties of the proposed estimators are investigated. Large sample pointwise and simultaneous confidence intervals for the regression coefficients are constructed. Formal hypothesis testing procedures are proposed to check for the covariate effects and whether the effects are time-varying. A simulation study is conducted to examine the finite sample performances of the proposed estimation and hypothesis testing procedures. The methods are illustrated with a data example.

Removing an intersubject variance component in a general linear model improves multiway factoring of event-related spectral perturbations in group EEG studies.

PubMed

Spence, Jeffrey S; Brier, Matthew R; Hart, John; Ferree, Thomas C

2013-03-01

Linear statistical models are used very effectively to assess task-related differences in EEG power spectral analyses. Mixed models, in particular, accommodate more than one variance component in a multisubject study, where many trials of each condition of interest are measured on each subject. Generally, intra- and intersubject variances are both important to determine correct standard errors for inference on functions of model parameters, but it is often assumed that intersubject variance is the most important consideration in a group study. In this article, we show that, under common assumptions, estimates of some functions of model parameters, including estimates of task-related differences, are properly tested relative to the intrasubject variance component only. A substantial gain in statistical power can arise from the proper separation of variance components when there is more than one source of variability. We first develop this result analytically, then show how it benefits a multiway factoring of spectral, spatial, and temporal components from EEG data acquired in a group of healthy subjects performing a well-studied response inhibition task. Copyright © 2011 Wiley Periodicals, Inc.

Statistical downscaling of precipitation using long short-term memory recurrent neural networks

NASA Astrophysics Data System (ADS)

Misra, Saptarshi; Sarkar, Sudeshna; Mitra, Pabitra

2017-11-01

Hydrological impacts of global climate change on regional scale are generally assessed by downscaling large-scale climatic variables, simulated by General Circulation Models (GCMs), to regional, small-scale hydrometeorological variables like precipitation, temperature, etc. In this study, we propose a new statistical downscaling model based on Recurrent Neural Network with Long Short-Term Memory which captures the spatio-temporal dependencies in local rainfall. The previous studies have used several other methods such as linear regression, quantile regression, kernel regression, beta regression, and artificial neural networks. Deep neural networks and recurrent neural networks have been shown to be highly promising in modeling complex and highly non-linear relationships between input and output variables in different domains and hence we investigated their performance in the task of statistical downscaling. We have tested this model on two datasets—one on precipitation in Mahanadi basin in India and the second on precipitation in Campbell River basin in Canada. Our autoencoder coupled long short-term memory recurrent neural network model performs the best compared to other existing methods on both the datasets with respect to temporal cross-correlation, mean squared error, and capturing the extremes.

Comparisons of a Constrained Least Squares Model versus Human-in-the-Loop for Spectral Unmixing to Determine Material Type of GEO Debris

NASA Technical Reports Server (NTRS)

Abercromby, Kira J.; Rapp, Jason; Bedard, Donald; Seitzer, Patrick; Cardona, Tommaso; Cowardin, Heather; Barker, Ed; Lederer, Susan

2013-01-01

Constrained Linear Least Squares model is generally more accurate than the "human-in-the-loop". However, "human-in-the-loop" can remove materials that make no sense. The speed of the model in determining a "first cut" at the material ID makes it a viable option for spectral unmixing of debris objects.

The microcomputer scientific software series 3: general linear model--analysis of variance.

Treesearch

Harold M. Rauscher

1985-01-01

A BASIC language set of programs, designed for use on microcomputers, is presented. This set of programs will perform the analysis of variance for any statistical model describing either balanced or unbalanced designs. The program computes and displays the degrees of freedom, Type I sum of squares, and the mean square for the overall model, the error, and each factor...

A generalized target theory and its applications.

PubMed

Zhao, Lei; Mi, Dong; Hu, Bei; Sun, Yeqing

2015-09-28

Different radiobiological models have been proposed to estimate the cell-killing effects, which are very important in radiotherapy and radiation risk assessment. However, most applied models have their own scopes of application. In this work, by generalizing the relationship between "hit" and "survival" in traditional target theory with Yager negation operator in Fuzzy mathematics, we propose a generalized target model of radiation-induced cell inactivation that takes into account both cellular repair effects and indirect effects of radiation. The simulation results of the model and the rethinking of "the number of targets in a cell" and "the number of hits per target" suggest that it is only necessary to investigate the generalized single-hit single-target (GSHST) in the present theoretical frame. Analysis shows that the GSHST model can be reduced to the linear quadratic model and multitarget model in the low-dose and high-dose regions, respectively. The fitting results show that the GSHST model agrees well with the usual experimental observations. In addition, the present model can be used to effectively predict cellular repair capacity, radiosensitivity, target size, especially the biologically effective dose for the treatment planning in clinical applications.

A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account non-local dispersion effects

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

Schmitt, Nikolai; Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder; Scheid, Claire

2016-07-01

The interaction of light with metallic nanostructures is increasingly attracting interest because of numerous potential applications. Sub-wavelength metallic structures, when illuminated with a frequency close to the plasma frequency of the metal, present resonances that cause extreme local field enhancements. Exploiting the latter in applications of interest requires a detailed knowledge about the occurring fields which can actually not be obtained analytically. For the latter mentioned reason, numerical tools are thus an absolute necessity. The insight they provide is very often the only way to get a deep enough understanding of the very rich physics at play. For the numericalmore » modeling of light-structure interaction on the nanoscale, the choice of an appropriate material model is a crucial point. Approaches that are adopted in a first instance are based on local (i.e. with no interaction between electrons) dispersive models, e.g. Drude or Drude–Lorentz models. From the mathematical point of view, when a time-domain modeling is considered, these models lead to an additional system of ordinary differential equations coupled to Maxwell's equations. However, recent experiments have shown that the repulsive interaction between electrons inside the metal makes the response of metals intrinsically non-local and that this effect cannot generally be overlooked. Technological achievements have enabled the consideration of metallic structures in a regime where such non-localities have a significant influence on the structures' optical response. This leads to an additional, in general non-linear, system of partial differential equations which is, when coupled to Maxwell's equations, significantly more difficult to treat. Nevertheless, dealing with a linearized non-local dispersion model already opens the route to numerous practical applications of plasmonics. In this work, we present a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell's equations coupled to a linearized non-local dispersion model relevant to plasmonics. While the method is presented in the general 3D case, numerical results are given for 2D simulation settings.« less

The Elementary Operations of Human Vision Are Not Reducible to Template-Matching

PubMed Central

Neri, Peter

2015-01-01

It is generally acknowledged that biological vision presents nonlinear characteristics, yet linear filtering accounts of visual processing are ubiquitous. The template-matching operation implemented by the linear-nonlinear cascade (linear filter followed by static nonlinearity) is the most widely adopted computational tool in systems neuroscience. This simple model achieves remarkable explanatory power while retaining analytical tractability, potentially extending its reach to a wide range of systems and levels in sensory processing. The extent of its applicability to human behaviour, however, remains unclear. Because sensory stimuli possess multiple attributes (e.g. position, orientation, size), the issue of applicability may be asked by considering each attribute one at a time in relation to a family of linear-nonlinear models, or by considering all attributes collectively in relation to a specified implementation of the linear-nonlinear cascade. We demonstrate that human visual processing can operate under conditions that are indistinguishable from linear-nonlinear transduction with respect to substantially different stimulus attributes of a uniquely specified target signal with associated behavioural task. However, no specific implementation of a linear-nonlinear cascade is able to account for the entire collection of results across attributes; a satisfactory account at this level requires the introduction of a small gain-control circuit, resulting in a model that no longer belongs to the linear-nonlinear family. Our results inform and constrain efforts at obtaining and interpreting comprehensive characterizations of the human sensory process by demonstrating its inescapably nonlinear nature, even under conditions that have been painstakingly fine-tuned to facilitate template-matching behaviour and to produce results that, at some level of inspection, do conform to linear filtering predictions. They also suggest that compliance with linear transduction may be the targeted outcome of carefully crafted nonlinear circuits, rather than default behaviour exhibited by basic components. PMID:26556758

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

NASA Astrophysics Data System (ADS)

Kim, H. S.

2015-02-01

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

Geometry of the scalar sector

DOE PAGES

Alonso, Rodrigo; Jenkins, Elizabeth E.; Manohar, Aneesh V.

2016-08-17

The S-matrix of a quantum field theory is unchanged by field redefinitions, and so it only depends on geometric quantities such as the curvature of field space. Whether the Higgs multiplet transforms linearly or non-linearly under electroweak symmetry is a subtle question since one can make a coordinate change to convert a field that transforms linearly into one that transforms non-linearly. Renormalizability of the Standard Model (SM) does not depend on the choice of scalar fields or whether the scalar fields transform linearly or non-linearly under the gauge group, but only on the geometric requirement that the scalar field manifoldmore » M is flat. Standard Model Effective Field Theory (SMEFT) and Higgs Effective Field Theory (HEFT) have curved M, since they parametrize deviations from the flat SM case. We show that the HEFT Lagrangian can be written in SMEFT form if and only ifMhas a SU(2) L U(1) Y invariant fixed point. Experimental observables in HEFT depend on local geometric invariants of M such as sectional curvatures, which are of order 1/Λ 2 , where Λ is the EFT scale. We give explicit expressions for these quantities in terms of the structure constants for a general G → H symmetry breaking pattern. The one-loop radiative correction in HEFT is determined using a covariant expansion which preserves manifest invariance of M under coordinate redefinitions. The formula for the radiative correction is simple when written in terms of the curvature of M and the gauge curvature field strengths. We also extend the CCWZ formalism to non-compact groups, and generalize the HEFT curvature computation to the case of multiple singlet scalar fields.« less

An overview of longitudinal data analysis methods for neurological research.

PubMed

Locascio, Joseph J; Atri, Alireza

2011-01-01

The purpose of this article is to provide a concise, broad and readily accessible overview of longitudinal data analysis methods, aimed to be a practical guide for clinical investigators in neurology. In general, we advise that older, traditional methods, including (1) simple regression of the dependent variable on a time measure, (2) analyzing a single summary subject level number that indexes changes for each subject and (3) a general linear model approach with a fixed-subject effect, should be reserved for quick, simple or preliminary analyses. We advocate the general use of mixed-random and fixed-effect regression models for analyses of most longitudinal clinical studies. Under restrictive situations or to provide validation, we recommend: (1) repeated-measure analysis of covariance (ANCOVA), (2) ANCOVA for two time points, (3) generalized estimating equations and (4) latent growth curve/structural equation models.

A Generalized Acoustic Analogy

NASA Technical Reports Server (NTRS)

Goldstein, M. E.

2003-01-01

The purpose of this article is to show that the Navier-Stokes equations can be rewritten as a set of linearized inhomogeneous Euler equations (in convective form) with source terms that are exactly the same as those that would result from externally imposed shear stress and energy flux perturbations. These results are used to develop a mathematical basis for some existing and potential new jet noise models by appropriately choosing the base flow about which the linearization is carried out.

Optimal Artificial Boundary Condition Configurations for Sensitivity-Based Model Updating and Damage Detection

DTIC Science & Technology

2010-09-01

matrix is used in many methods, like Jacobi or Gauss Seidel , for solving linear systems. Also, no partial pivoting is necessary for a strictly column...problems that arise during the procedure, which in general, converges to the solving of a linear system. The most common issue with the solution is the... iterative procedure to find an appropriate subset of parameters that produce an optimal solution commonly known as forward selection. Then, the

Approximate reduction of linear population models governed by stochastic differential equations: application to multiregional models.

PubMed

Sanz, Luis; Alonso, Juan Antonio

2017-12-01

In this work we develop approximate aggregation techniques in the context of slow-fast linear population models governed by stochastic differential equations and apply the results to the treatment of populations with spatial heterogeneity. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a simpler reduced model with a fewer number of 'global' variables, in such a way that the dynamics of the former can be approximated by that of the latter. In our model we contemplate a linear fast deterministic process together with a linear slow process in which the parameters are affected by additive noise, and give conditions for the solutions corresponding to positive initial conditions to remain positive for all times. By letting the fast process reach equilibrium we build a reduced system with a lesser number of variables, and provide results relating the asymptotic behaviour of the first- and second-order moments of the population vector for the original and the reduced system. The general technique is illustrated by analysing a multiregional stochastic system in which dispersal is deterministic and the rate growth of the populations in each patch is affected by additive noise.

Background history and cosmic perturbations for a general system of self-conserved dynamical dark energy and matter

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

Gómez-Valent, Adrià; Karimkhani, Elahe; Solà, Joan, E-mail: adriagova@ecm.ub.edu, E-mail: e.karimkhani91@basu.ac.ir, E-mail: sola@ecm.ub.edu

We determine the Hubble expansion and the general cosmic perturbation equations for a general system consisting of self-conserved matter, ρ{sub m}, and self-conserved dark energy (DE), ρ{sub D}. While at the background level the two components are non-interacting, they do interact at the perturbations level. We show that the coupled system of matter and DE perturbations can be transformed into a single, third order, matter perturbation equation, which reduces to the (derivative of the) standard one in the case that the DE is just a cosmological constant. As a nontrivial application we analyze a class of dynamical models whose DEmore » density ρ{sub D}(H) consists of a constant term, C{sub 0}, and a series of powers of the Hubble rate. These models were previously analyzed from the point of view of dynamical vacuum models, but here we treat them as self-conserved DE models with a dynamical equation of state. We fit them to the wealth of expansion history and linear structure formation data and compare their fit quality with that of the concordance ΛCDM model. Those with C{sub 0}=0 include the so-called ''entropic-force'' and ''QCD-ghost'' DE models, as well as the pure linear model ρ{sub D}∼H, all of which appear strongly disfavored. The models with C{sub 0}≠0 , in contrast, emerge as promising dynamical DE candidates whose phenomenological performance is highly competitive with the rigid Λ-term inherent to the ΛCDM.« less

Modeling the effects of AADT on predicting multiple-vehicle crashes at urban and suburban signalized intersections.

PubMed

Chen, Chen; Xie, Yuanchang

2016-06-01

Annual Average Daily Traffic (AADT) is often considered as a main covariate for predicting crash frequencies at urban and suburban intersections. A linear functional form is typically assumed for the Safety Performance Function (SPF) to describe the relationship between the natural logarithm of expected crash frequency and covariates derived from AADTs. Such a linearity assumption has been questioned by many researchers. This study applies Generalized Additive Models (GAMs) and Piecewise Linear Negative Binomial (PLNB) regression models to fit intersection crash data. Various covariates derived from minor-and major-approach AADTs are considered. Three different dependent variables are modeled, which are total multiple-vehicle crashes, rear-end crashes, and angle crashes. The modeling results suggest that a nonlinear functional form may be more appropriate. Also, the results show that it is important to take into consideration the joint safety effects of multiple covariates. Additionally, it is found that the ratio of minor to major-approach AADT has a varying impact on intersection safety and deserves further investigations. Copyright © 2016 Elsevier Ltd. All rights reserved.

Spike-train spectra and network response functions for non-linear integrate-and-fire neurons.

PubMed

Richardson, Magnus J E

2008-11-01

Reduced models have long been used as a tool for the analysis of the complex activity taking place in neurons and their coupled networks. Recent advances in experimental and theoretical techniques have further demonstrated the usefulness of this approach. Despite the often gross simplification of the underlying biophysical properties, reduced models can still present significant difficulties in their analysis, with the majority of exact and perturbative results available only for the leaky integrate-and-fire model. Here an elementary numerical scheme is demonstrated which can be used to calculate a number of biologically important properties of the general class of non-linear integrate-and-fire models. Exact results for the first-passage-time density and spike-train spectrum are derived, as well as the linear response properties and emergent states of recurrent networks. Given that the exponential integrate-fire model has recently been shown to agree closely with the experimentally measured response of pyramidal cells, the methodology presented here promises to provide a convenient tool to facilitate the analysis of cortical-network dynamics.

Analytical modelling of Halbach linear generator incorporating pole shifting and piece-wise spring for ocean wave energy harvesting

NASA Astrophysics Data System (ADS)

Tan, Yimin; Lin, Kejian; Zu, Jean W.

2018-05-01

Halbach permanent magnet (PM) array has attracted tremendous research attention in the development of electromagnetic generators for its unique properties. This paper has proposed a generalized analytical model for linear generators. The slotted stator pole-shifting and implementation of Halbach array have been combined for the first time. Initially, the magnetization components of the Halbach array have been determined using Fourier decomposition. Then, based on the magnetic scalar potential method, the magnetic field distribution has been derived employing specially treated boundary conditions. FEM analysis has been conducted to verify the analytical model. A slotted linear PM generator with Halbach PM has been constructed to validate the model and further improved using piece-wise springs to trigger full range reciprocating motion. A dynamic model has been developed to characterize the dynamic behavior of the slider. This analytical method provides an effective tool in development and optimization of Halbach PM generator. The experimental results indicate that piece-wise springs can be employed to improve generator performance under low excitation frequency.

Mum, why do you keep on growing? Impacts of environmental variability on optimal growth and reproduction allocation strategies of annual plants.

PubMed

De Lara, Michel

2006-05-01

In their 1990 paper Optimal reproductive efforts and the timing of reproduction of annual plants in randomly varying environments, Amir and Cohen considered stochastic environments consisting of i.i.d. sequences in an optimal allocation discrete-time model. We suppose here that the sequence of environmental factors is more generally described by a Markov chain. Moreover, we discuss the connection between the time interval of the discrete-time dynamic model and the ability of the plant to rebuild completely its vegetative body (from reserves). We formulate a stochastic optimization problem covering the so-called linear and logarithmic fitness (corresponding to variation within and between years), which yields optimal strategies. For "linear maximizers'', we analyse how optimal strategies depend upon the environmental variability type: constant, random stationary, random i.i.d., random monotonous. We provide general patterns in terms of targets and thresholds, including both determinate and indeterminate growth. We also provide a partial result on the comparison between ;"linear maximizers'' and "log maximizers''. Numerical simulations are provided, allowing to give a hint at the effect of different mathematical assumptions.

No association of smoke-free ordinances with profits from bingo and charitable games in Massachusetts.

PubMed

Glantz, S A; Wilson-Loots, R

2003-12-01

Because it is widely played, claims that smoking restrictions will adversely affect bingo games is used as an argument against these policies. We used publicly available data from Massachusetts to assess the impact of 100% smoke-free ordinances on profits from bingo and other gambling sponsored by charitable organisations between 1985 and 2001. We conducted two analyses: (1) a general linear model implementation of a time series analysis with net profits (adjusted to 2001 dollars) as the dependent variable, and community (as a fixed effect), year, lagged net profits, and the length of time the ordinance had been in force as the independent variables; (2) multiple linear regression of total state profits against time, lagged profits, and the percentage of the entire state population in communities that allow charitable gaming but prohibit smoking. The general linear model analysis of data from individual communities showed that, while adjusted profits fell over time, this effect was not related to the presence of an ordinance. The analysis in terms of the fraction of the population living in communities with ordinances yielded the same result. Policymakers can implement smoke-free policies without concern that these policies will affect charitable gaming.

A general U-block model-based design procedure for nonlinear polynomial control systems

NASA Astrophysics Data System (ADS)

Zhu, Q. M.; Zhao, D. Y.; Zhang, Jianhua

2016-10-01

The proposition of U-model concept (in terms of 'providing concise and applicable solutions for complex problems') and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work - using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.

Tracking Electroencephalographic Changes Using Distributions of Linear Models: Application to Propofol-Based Depth of Anesthesia Monitoring.

PubMed

Kuhlmann, Levin; Manton, Jonathan H; Heyse, Bjorn; Vereecke, Hugo E M; Lipping, Tarmo; Struys, Michel M R F; Liley, David T J

2017-04-01

Tracking brain states with electrophysiological measurements often relies on short-term averages of extracted features and this may not adequately capture the variability of brain dynamics. The objective is to assess the hypotheses that this can be overcome by tracking distributions of linear models using anesthesia data, and that anesthetic brain state tracking performance of linear models is comparable to that of a high performing depth of anesthesia monitoring feature. Individuals' brain states are classified by comparing the distribution of linear (auto-regressive moving average-ARMA) model parameters estimated from electroencephalographic (EEG) data obtained with a sliding window to distributions of linear model parameters for each brain state. The method is applied to frontal EEG data from 15 subjects undergoing propofol anesthesia and classified by the observers assessment of alertness/sedation (OAA/S) scale. Classification of the OAA/S score was performed using distributions of either ARMA parameters or the benchmark feature, Higuchi fractal dimension. The highest average testing sensitivity of 59% (chance sensitivity: 17%) was found for ARMA (2,1) models and Higuchi fractal dimension achieved 52%, however, no statistical difference was observed. For the same ARMA case, there was no statistical difference if medians are used instead of distributions (sensitivity: 56%). The model-based distribution approach is not necessarily more effective than a median/short-term average approach, however, it performs well compared with a distribution approach based on a high performing anesthesia monitoring measure. These techniques hold potential for anesthesia monitoring and may be generally applicable for tracking brain states.

Parameterization of Model Validating Sets for Uncertainty Bound Optimizations. Revised

NASA Technical Reports Server (NTRS)

Lim, K. B.; Giesy, D. P.

2000-01-01

Given measurement data, a nominal model and a linear fractional transformation uncertainty structure with an allowance on unknown but bounded exogenous disturbances, easily computable tests for the existence of a model validating uncertainty set are given. Under mild conditions, these tests are necessary and sufficient for the case of complex, nonrepeated, block-diagonal structure. For the more general case which includes repeated and/or real scalar uncertainties, the tests are only necessary but become sufficient if a collinearity condition is also satisfied. With the satisfaction of these tests, it is shown that a parameterization of all model validating sets of plant models is possible. The new parameterization is used as a basis for a systematic way to construct or perform uncertainty tradeoff with model validating uncertainty sets which have specific linear fractional transformation structure for use in robust control design and analysis. An illustrative example which includes a comparison of candidate model validating sets is given.

Fuzzy linear model for production optimization of mining systems with multiple entities

NASA Astrophysics Data System (ADS)

Vujic, Slobodan; Benovic, Tomo; Miljanovic, Igor; Hudej, Marjan; Milutinovic, Aleksandar; Pavlovic, Petar

2011-12-01

Planning and production optimization within multiple mines or several work sites (entities) mining systems by using fuzzy linear programming (LP) was studied. LP is the most commonly used operations research methods in mining engineering. After the introductory review of properties and limitations of applying LP, short reviews of the general settings of deterministic and fuzzy LP models are presented. With the purpose of comparative analysis, the application of both LP models is presented using the example of the Bauxite Basin Niksic with five mines. After the assessment, LP is an efficient mathematical modeling tool in production planning and solving many other single-criteria optimization problems of mining engineering. After the comparison of advantages and deficiencies of both deterministic and fuzzy LP models, the conclusion presents benefits of the fuzzy LP model but is also stating that seeking the optimal plan of production means to accomplish the overall analysis that will encompass the LP model approaches.

Quasi-Linear Vacancy Dynamics Modeling and Circuit Analysis of the Bipolar Memristor

PubMed Central

Abraham, Isaac

2014-01-01

The quasi-linear transport equation is investigated for modeling the bipolar memory resistor. The solution accommodates vacancy and circuit level perspectives on memristance. For the first time in literature the component resistors that constitute the contemporary dual variable resistor circuit model are quantified using vacancy parameters and derived from a governing partial differential equation. The model describes known memristor dynamics even as it generates new insight about vacancy migration, bottlenecks to switching speed and elucidates subtle relationships between switching resistance range and device parameters. The model is shown to comply with Chua's generalized equations for the memristor. Independent experimental results are used throughout, to validate the insights obtained from the model. The paper concludes by implementing a memristor-capacitor filter and compares its performance to a reference resistor-capacitor filter to demonstrate that the model is usable for practical circuit analysis. PMID:25390634

Polar versus Cartesian velocity models for maneuvering target tracking with IMM

NASA Astrophysics Data System (ADS)

Laneuville, Dann

This paper compares various model sets in different IMM filters for the maneuvering target tracking problem. The aim is to see whether we can improve the tracking performance of what is certainly the most widely used model set in the literature for the maneuvering target tracking problem: a Nearly Constant Velocity model and a Nearly Coordinated Turn model. Our new challenger set consists of a mixed Cartesian position and polar velocity state vector to describe the uniform motion segments and is augmented with the turn rate to obtain the second model for the maneuvering segments. This paper also gives a general procedure to discretize up to second order any non-linear continuous time model with linear diffusion. Comparative simulations on an air defence scenario with a 2D radar, show that this new approach improves significantly the tracking performance in this case.

Quasi-linear vacancy dynamics modeling and circuit analysis of the bipolar memristor.

PubMed

Abraham, Isaac

2014-01-01

The quasi-linear transport equation is investigated for modeling the bipolar memory resistor. The solution accommodates vacancy and circuit level perspectives on memristance. For the first time in literature the component resistors that constitute the contemporary dual variable resistor circuit model are quantified using vacancy parameters and derived from a governing partial differential equation. The model describes known memristor dynamics even as it generates new insight about vacancy migration, bottlenecks to switching speed and elucidates subtle relationships between switching resistance range and device parameters. The model is shown to comply with Chua's generalized equations for the memristor. Independent experimental results are used throughout, to validate the insights obtained from the model. The paper concludes by implementing a memristor-capacitor filter and compares its performance to a reference resistor-capacitor filter to demonstrate that the model is usable for practical circuit analysis.

Building a Multicontextual Model of Latino College Enrollment: Student, School, and State-Level Effects

ERIC Educational Resources Information Center

Nunez, Anne-Marie; Kim, Dongbin

2012-01-01

Latinos' college enrollment rates, particularly in four-year institutions, have not kept pace with their population growth in the United States. Using three-level hierarchical generalized linear modeling, this study analyzes data from the Educational Longitudinal Study (ELS) to examine the influence of high school and state contexts, in addition…

Using Stocking or Harvesting to Reverse Period-Doubling Bifurcations in Discrete Population Models

Treesearch

James F. Selgrade

1998-01-01

This study considers a general class of 2-dimensional, discrete population models where each per capita transition function (fitness) depends on a linear combination of the densities of the interacting populations. The fitness functions are either monotone decreasing functions (pioneer fitnesses) or one-humped functions (climax fitnesses). Four sets of necessary...

Reversing Period-Doubling Bifurcations in Models of Population Interactions Using Constant Stocking or Harvesting

Treesearch

James F. Selgrade; James H. Roberds

1998-01-01

This study considers a general class of two-dimensional, discrete population models where each per capita transition function (fitness) depends on a linear combination of the densities of the interacting populations. The fitness functions are either monotone decreasing functions (pioneer fitnesses) or one-humped functions (climax fitnesses). Conditions are derived...

A generalized analog implementation of piecewise linear neuron models using CCII building blocks.

PubMed

Soleimani, Hamid; Ahmadi, Arash; Bavandpour, Mohammad; Sharifipoor, Ozra

2014-03-01

This paper presents a set of reconfigurable analog implementations of piecewise linear spiking neuron models using second generation current conveyor (CCII) building blocks. With the same topology and circuit elements, without W/L modification which is impossible after circuit fabrication, these circuits can produce different behaviors, similar to the biological neurons, both for a single neuron as well as a network of neurons just by tuning reference current and voltage sources. The models are investigated, in terms of analog implementation feasibility and costs, targeting large scale hardware implementations. Results show that, in order to gain the best performance, area and accuracy; these models can be compromised. Simulation results are presented for different neuron behaviors with CMOS 350 nm technology. Copyright © 2013 Elsevier Ltd. All rights reserved.

Aerodynamic mathematical modeling - basic concepts

NASA Technical Reports Server (NTRS)

Tobak, M.; Schiff, L. B.

1981-01-01

The mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers is reviewed. Bryan's original formulation, linear aerodynamic indicial functions, and superposition are considered. These concepts are extended into the nonlinear regime. The nonlinear generalization yields a form for the aerodynamic response that can be built up from the responses to a limited number of well defined characteristic motions, reproducible in principle either in wind tunnel experiments or flow field computations. A further generalization leads to a form accommodating the discontinuous and double valued behavior characteristics of hysteresis in the steady state aerodynamic response.

A land use regression model for ambient ultrafine particles in Montreal, Canada: A comparison of linear regression and a machine learning approach.

PubMed

Weichenthal, Scott; Ryswyk, Keith Van; Goldstein, Alon; Bagg, Scott; Shekkarizfard, Maryam; Hatzopoulou, Marianne

2016-04-01

Existing evidence suggests that ambient ultrafine particles (UFPs) (<0.1µm) may contribute to acute cardiorespiratory morbidity. However, few studies have examined the long-term health effects of these pollutants owing in part to a need for exposure surfaces that can be applied in large population-based studies. To address this need, we developed a land use regression model for UFPs in Montreal, Canada using mobile monitoring data collected from 414 road segments during the summer and winter months between 2011 and 2012. Two different approaches were examined for model development including standard multivariable linear regression and a machine learning approach (kernel-based regularized least squares (KRLS)) that learns the functional form of covariate impacts on ambient UFP concentrations from the data. The final models included parameters for population density, ambient temperature and wind speed, land use parameters (park space and open space), length of local roads and rail, and estimated annual average NOx emissions from traffic. The final multivariable linear regression model explained 62% of the spatial variation in ambient UFP concentrations whereas the KRLS model explained 79% of the variance. The KRLS model performed slightly better than the linear regression model when evaluated using an external dataset (R(2)=0.58 vs. 0.55) or a cross-validation procedure (R(2)=0.67 vs. 0.60). In general, our findings suggest that the KRLS approach may offer modest improvements in predictive performance compared to standard multivariable linear regression models used to estimate spatial variations in ambient UFPs. However, differences in predictive performance were not statistically significant when evaluated using the cross-validation procedure. Crown Copyright © 2015. Published by Elsevier Inc. All rights reserved.

Deformed coset models from gauged WZW actions

NASA Astrophysics Data System (ADS)

Park, Q.-Han

1994-06-01

A general Lagrangian formulation of integrably deformed G/H-coset models is given. We consider the G/H-coset model in terms of the gauged Wess-Zumino-Witten action and obtain an integrable deformation by adding a potential energy term Tr(gTg -1overlineT) , where algebra elements T, overlineT belong to the center of the algebra h associated with the subgroup H. We show that the classical equation of motion of the deformed coset model can be identified with the integrability condition of certain linear equations which makes the use of the inverse scattering method possible. Using the linear equation, we give a systematic way to construct infinitely many conserved currents as well as soliton solutions. In the case of the parafermionic SU(2)/U(1)-coset model, we derive n-solitons and conserved currents explicitly.

Passive dendrites enable single neurons to compute linearly non-separable functions.

PubMed

Cazé, Romain Daniel; Humphries, Mark; Gutkin, Boris

2013-01-01

Local supra-linear summation of excitatory inputs occurring in pyramidal cell dendrites, the so-called dendritic spikes, results in independent spiking dendritic sub-units, which turn pyramidal neurons into two-layer neural networks capable of computing linearly non-separable functions, such as the exclusive OR. Other neuron classes, such as interneurons, may possess only a few independent dendritic sub-units, or only passive dendrites where input summation is purely sub-linear, and where dendritic sub-units are only saturating. To determine if such neurons can also compute linearly non-separable functions, we enumerate, for a given parameter range, the Boolean functions implementable by a binary neuron model with a linear sub-unit and either a single spiking or a saturating dendritic sub-unit. We then analytically generalize these numerical results to an arbitrary number of non-linear sub-units. First, we show that a single non-linear dendritic sub-unit, in addition to the somatic non-linearity, is sufficient to compute linearly non-separable functions. Second, we analytically prove that, with a sufficient number of saturating dendritic sub-units, a neuron can compute all functions computable with purely excitatory inputs. Third, we show that these linearly non-separable functions can be implemented with at least two strategies: one where a dendritic sub-unit is sufficient to trigger a somatic spike; another where somatic spiking requires the cooperation of multiple dendritic sub-units. We formally prove that implementing the latter architecture is possible with both types of dendritic sub-units whereas the former is only possible with spiking dendrites. Finally, we show how linearly non-separable functions can be computed by a generic two-compartment biophysical model and a realistic neuron model of the cerebellar stellate cell interneuron. Taken together our results demonstrate that passive dendrites are sufficient to enable neurons to compute linearly non-separable functions.

Passive Dendrites Enable Single Neurons to Compute Linearly Non-separable Functions

PubMed Central

Cazé, Romain Daniel; Humphries, Mark; Gutkin, Boris

2013-01-01

Local supra-linear summation of excitatory inputs occurring in pyramidal cell dendrites, the so-called dendritic spikes, results in independent spiking dendritic sub-units, which turn pyramidal neurons into two-layer neural networks capable of computing linearly non-separable functions, such as the exclusive OR. Other neuron classes, such as interneurons, may possess only a few independent dendritic sub-units, or only passive dendrites where input summation is purely sub-linear, and where dendritic sub-units are only saturating. To determine if such neurons can also compute linearly non-separable functions, we enumerate, for a given parameter range, the Boolean functions implementable by a binary neuron model with a linear sub-unit and either a single spiking or a saturating dendritic sub-unit. We then analytically generalize these numerical results to an arbitrary number of non-linear sub-units. First, we show that a single non-linear dendritic sub-unit, in addition to the somatic non-linearity, is sufficient to compute linearly non-separable functions. Second, we analytically prove that, with a sufficient number of saturating dendritic sub-units, a neuron can compute all functions computable with purely excitatory inputs. Third, we show that these linearly non-separable functions can be implemented with at least two strategies: one where a dendritic sub-unit is sufficient to trigger a somatic spike; another where somatic spiking requires the cooperation of multiple dendritic sub-units. We formally prove that implementing the latter architecture is possible with both types of dendritic sub-units whereas the former is only possible with spiking dendrites. Finally, we show how linearly non-separable functions can be computed by a generic two-compartment biophysical model and a realistic neuron model of the cerebellar stellate cell interneuron. Taken together our results demonstrate that passive dendrites are sufficient to enable neurons to compute linearly non-separable functions. PMID:23468600

An approximation of herd effect due to vaccinating children against seasonal influenza – a potential solution to the incorporation of indirect effects into static models

PubMed Central

2013-01-01

Background Indirect herd effect from vaccination of children offers potential for improving the effectiveness of influenza prevention in the remaining unvaccinated population. Static models used in cost-effectiveness analyses cannot dynamically capture herd effects. The objective of this study was to develop a methodology to allow herd effect associated with vaccinating children against seasonal influenza to be incorporated into static models evaluating the cost-effectiveness of influenza vaccination. Methods Two previously published linear equations for approximation of herd effects in general were compared with the results of a structured literature review undertaken using PubMed searches to identify data on herd effects specific to influenza vaccination. A linear function was fitted to point estimates from the literature using the sum of squared residuals. Results The literature review identified 21 publications on 20 studies for inclusion. Six studies provided data on a mathematical relationship between effective vaccine coverage in subgroups and reduction of influenza infection in a larger unvaccinated population. These supported a linear relationship when effective vaccine coverage in a subgroup population was between 20% and 80%. Three studies evaluating herd effect at a community level, specifically induced by vaccinating children, provided point estimates for fitting linear equations. The fitted linear equation for herd protection in the target population for vaccination (children) was slightly less conservative than a previously published equation for herd effects in general. The fitted linear equation for herd protection in the non-target population was considerably less conservative than the previously published equation. Conclusions This method of approximating herd effect requires simple adjustments to the annual baseline risk of influenza in static models: (1) for the age group targeted by the childhood vaccination strategy (i.e. children); and (2) for other age groups not targeted (e.g. adults and/or elderly). Two approximations provide a linear relationship between effective coverage and reduction in the risk of infection. The first is a conservative approximation, recommended as a base-case for cost-effectiveness evaluations. The second, fitted to data extracted from a structured literature review, provides a less conservative estimate of herd effect, recommended for sensitivity analyses. PMID:23339290

Thermal analyses of the International Ultraviolet Explorer (IUE) scientific instrument using the NASTRAN thermal analyzer (NTA): A general purpose summary

NASA Technical Reports Server (NTRS)

Jackson, C. E., Jr.

1976-01-01

The NTA Level 15.5.2/3, was used to provide non-linear steady-state (NLSS) and non-linear transient (NLTR) thermal predictions for the International Ultraviolet Explorer (IUE) Scientific Instrument (SI). NASTRAN structural models were used as the basis for the thermal models, which were produced by a straight forward conversion procedure. The accuracy of this technique was sub-sequently demonstrated by a comparison of NTA predicts with the results of a thermal vacuum test of the IUE Engineering Test Unit (ETU). Completion of these tasks was aided by the use of NTA subroutines.

Non-Asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso.

PubMed

Kong, Shengchun; Nan, Bin

2014-01-01

We consider finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival data, however, are neither iid nor Lipschitz.We first approximate the negative log partial likelihood function by a sum of iid non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the lasso penalized Cox regression using pointwise arguments to tackle the difficulties caused by lacking iid Lipschitz losses.

Non-Asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso

PubMed Central

Kong, Shengchun; Nan, Bin

2013-01-01

We consider finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival data, however, are neither iid nor Lipschitz.We first approximate the negative log partial likelihood function by a sum of iid non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the lasso penalized Cox regression using pointwise arguments to tackle the difficulties caused by lacking iid Lipschitz losses. PMID:24516328

A nonlinear model for analysis of slug-test data

USGS Publications Warehouse

McElwee, C.D.; Zenner, M.A.

1998-01-01

While doing slug tests in high-permeability aquifers, we have consistently seen deviations from the expected response of linear theoretical models. Normalized curves do not coincide for various initial heads, as would be predicted by linear theories, and are shifted to larger times for higher initial heads. We have developed a general nonlinear model based on the Navier-Stokes equation, nonlinear frictional loss, non-Darcian flow, acceleration effects, radius changes in the well bore, and a Hvorslev model for the aquifer, which explains these data features. The model produces a very good fit for both oscillatory and nonoscillatory field data, using a single set of physical parameters to predict the field data for various initial displacements at a given well. This is in contrast to linear models which have a systematic lack of fit and indicate that hydraulic conductivity varies with the initial displacement. We recommend multiple slug tests with a considerable variation in initial head displacement to evaluate the possible presence of nonlinear effects. Our conclusion is that the nonlinear model presented here is an excellent tool to analyze slug tests, covering the range from the underdamped region to the overdamped region.

Analysing the Costs of Integrated Care: A Case on Model Selection for Chronic Care Purposes

PubMed Central

Sánchez-Pérez, Inma; Ibern, Pere; Coderch, Jordi; Inoriza, José María

2016-01-01

Background: The objective of this study is to investigate whether the algorithm proposed by Manning and Mullahy, a consolidated health economics procedure, can also be used to estimate individual costs for different groups of healthcare services in the context of integrated care. Methods: A cross-sectional study focused on the population of the Baix Empordà (Catalonia-Spain) for the year 2012 (N = 92,498 individuals). A set of individual cost models as a function of sex, age and morbidity burden were adjusted and individual healthcare costs were calculated using a retrospective full-costing system. The individual morbidity burden was inferred using the Clinical Risk Groups (CRG) patient classification system. Results: Depending on the characteristics of the data, and according to the algorithm criteria, the choice of model was a linear model on the log of costs or a generalized linear model with a log link. We checked for goodness of fit, accuracy, linear structure and heteroscedasticity for the models obtained. Conclusion: The proposed algorithm identified a set of suitable cost models for the distinct groups of services integrated care entails. The individual morbidity burden was found to be indispensable when allocating appropriate resources to targeted individuals. PMID:28316542

Modeling soybean canopy resistance from micrometeorological and plant variables for estimating evapotranspiration using one-step Penman-Monteith approach

NASA Astrophysics Data System (ADS)

Irmak, Suat; Mutiibwa, Denis; Payero, Jose; Marek, Thomas; Porter, Dana

2013-12-01

Canopy resistance (rc) is one of the most important variables in evapotranspiration, agronomy, hydrology and climate change studies that link vegetation response to changing environmental and climatic variables. This study investigates the concept of generalized nonlinear/linear modeling approach of rc from micrometeorological and plant variables for soybean [Glycine max (L.) Merr.] canopy at different climatic zones in Nebraska, USA (Clay Center, Geneva, Holdrege and North Platte). Eight models estimating rc as a function of different combination of micrometeorological and plant variables are presented. The models integrated the linear and non-linear effects of regulating variables (net radiation, Rn; relative humidity, RH; wind speed, U3; air temperature, Ta; vapor pressure deficit, VPD; leaf area index, LAI; aerodynamic resistance, ra; and solar zenith angle, Za) to predict hourly rc. The most complex rc model has all regulating variables and the simplest model has only Rn, Ta and RH. The rc models were developed at Clay Center in the growing season of 2007 and applied to other independent sites and years. The predicted rc for the growing seasons at four locations were then used to estimate actual crop evapotranspiration (ETc) as a one-step process using the Penman-Monteith model and compared to the measured data at all locations. The models were able to account for 66-93% of the variability in measured hourly ETc across locations. Models without LAI generally underperformed and underestimated due to overestimation of rc, especially during full canopy cover stage. Using vapor pressure deficit or relative humidity in the models had similar effect on estimating rc. The root squared error (RSE) between measured and estimated ETc was about 0.07 mm h-1 for most of the models at Clay Center, Geneva and Holdrege. At North Platte, RSE was above 0.10 mm h-1. The results at different sites and different growing seasons demonstrate the robustness and consistency of the models in estimating soybean rc, which is encouraging towards the general application of one-step estimation of soybean canopy ETc in practice using the Penman-Monteith model and could aid in enhancing the utilization of the approach by irrigation and water management community.

Hydrostatic calculations of axisymmetric flow and its stability for the AGCE model

NASA Technical Reports Server (NTRS)

Miller, T. L.; Gall, R. L.

1981-01-01

Baroclinic waves in the atmospherics general circulation experiment (AGCE) apparatus by the use of numerical hydrostatic primitive equation models were determined. The calculation is accomplished by using an axisymmetric primitive equation model to compute, for a given set of experimental parameters, a steady state axisymmetric flow and then testing this axisymmetric flow for stability using a linear primitive equation model. Some axisymmetric flows are presented together with preliminary stability calculations.

Ordinal probability effect measures for group comparisons in multinomial cumulative link models.

PubMed

Agresti, Alan; Kateri, Maria

2017-03-01

We consider simple ordinal model-based probability effect measures for comparing distributions of two groups, adjusted for explanatory variables. An "ordinal superiority" measure summarizes the probability that an observation from one distribution falls above an independent observation from the other distribution, adjusted for explanatory variables in a model. The measure applies directly to normal linear models and to a normal latent variable model for ordinal response variables. It equals Φ(β/2) for the corresponding ordinal model that applies a probit link function to cumulative multinomial probabilities, for standard normal cdf Φ and effect β that is the coefficient of the group indicator variable. For the more general latent variable model for ordinal responses that corresponds to a linear model with other possible error distributions and corresponding link functions for cumulative multinomial probabilities, the ordinal superiority measure equals exp(β)/[1+exp(β)] with the log-log link and equals approximately exp(β/2)/[1+exp(β/2)] with the logit link, where β is the group effect. Another ordinal superiority measure generalizes the difference of proportions from binary to ordinal responses. We also present related measures directly for ordinal models for the observed response that need not assume corresponding latent response models. We present confidence intervals for the measures and illustrate with an example. © 2016, The International Biometric Society.

A comparative analysis of predictive models of morbidity in intensive care unit after cardiac surgery - part II: an illustrative example.

PubMed

Cevenini, Gabriele; Barbini, Emanuela; Scolletta, Sabino; Biagioli, Bonizella; Giomarelli, Pierpaolo; Barbini, Paolo

2007-11-22

Popular predictive models for estimating morbidity probability after heart surgery are compared critically in a unitary framework. The study is divided into two parts. In the first part modelling techniques and intrinsic strengths and weaknesses of different approaches were discussed from a theoretical point of view. In this second part the performances of the same models are evaluated in an illustrative example. Eight models were developed: Bayes linear and quadratic models, k-nearest neighbour model, logistic regression model, Higgins and direct scoring systems and two feed-forward artificial neural networks with one and two layers. Cardiovascular, respiratory, neurological, renal, infectious and hemorrhagic complications were defined as morbidity. Training and testing sets each of 545 cases were used. The optimal set of predictors was chosen among a collection of 78 preoperative, intraoperative and postoperative variables by a stepwise procedure. Discrimination and calibration were evaluated by the area under the receiver operating characteristic curve and Hosmer-Lemeshow goodness-of-fit test, respectively. Scoring systems and the logistic regression model required the largest set of predictors, while Bayesian and k-nearest neighbour models were much more parsimonious. In testing data, all models showed acceptable discrimination capacities, however the Bayes quadratic model, using only three predictors, provided the best performance. All models showed satisfactory generalization ability: again the Bayes quadratic model exhibited the best generalization, while artificial neural networks and scoring systems gave the worst results. Finally, poor calibration was obtained when using scoring systems, k-nearest neighbour model and artificial neural networks, while Bayes (after recalibration) and logistic regression models gave adequate results. Although all the predictive models showed acceptable discrimination performance in the example considered, the Bayes and logistic regression models seemed better than the others, because they also had good generalization and calibration. The Bayes quadratic model seemed to be a convincing alternative to the much more usual Bayes linear and logistic regression models. It showed its capacity to identify a minimum core of predictors generally recognized as essential to pragmatically evaluate the risk of developing morbidity after heart surgery.

Predictive IP controller for robust position control of linear servo system.

PubMed

Lu, Shaowu; Zhou, Fengxing; Ma, Yajie; Tang, Xiaoqi

2016-07-01

Position control is a typical application of linear servo system. In this paper, to reduce the system overshoot, an integral plus proportional (IP) controller is used in the position control implementation. To further improve the control performance, a gain-tuning IP controller based on a generalized predictive control (GPC) law is proposed. Firstly, to represent the dynamics of the position loop, a second-order linear model is used and its model parameters are estimated on-line by using a recursive least squares method. Secondly, based on the GPC law, an optimal control sequence is obtained by using receding horizon, then directly supplies the IP controller with the corresponding control parameters in the real operations. Finally, simulation and experimental results are presented to show the efficiency of proposed scheme. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

A three operator split-step method covering a larger set of non-linear partial differential equations

NASA Astrophysics Data System (ADS)

Zia, Haider

2017-06-01

This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.

Non-linear corrections to the time-covariance function derived from a multi-state chemical master equation.

PubMed

Scott, M

2012-08-01

The time-covariance function captures the dynamics of biochemical fluctuations and contains important information about the underlying kinetic rate parameters. Intrinsic fluctuations in biochemical reaction networks are typically modelled using a master equation formalism. In general, the equation cannot be solved exactly and approximation methods are required. For small fluctuations close to equilibrium, a linearisation of the dynamics provides a very good description of the relaxation of the time-covariance function. As the number of molecules in the system decrease, deviations from the linear theory appear. Carrying out a systematic perturbation expansion of the master equation to capture these effects results in formidable algebra; however, symbolic mathematics packages considerably expedite the computation. The authors demonstrate that non-linear effects can reveal features of the underlying dynamics, such as reaction stoichiometry, not available in linearised theory. Furthermore, in models that exhibit noise-induced oscillations, non-linear corrections result in a shift in the base frequency along with the appearance of a secondary harmonic.

Ghost Dark Energy with Non-Linear Interaction Term

NASA Astrophysics Data System (ADS)

Ebrahimi, E.

2016-06-01

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

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

NASA Astrophysics Data System (ADS)

Borah, B.; Ansari, M.

2015-01-01

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

Discrete quasi-linear viscoelastic damping analysis of connective tissues, and the biomechanics of stretching.

PubMed

Babaei, Behzad; Velasquez-Mao, Aaron J; Thomopoulos, Stavros; Elson, Elliot L; Abramowitch, Steven D; Genin, Guy M

2017-05-01

The time- and frequency-dependent properties of connective tissue define their physiological function, but are notoriously difficult to characterize. Well-established tools such as linear viscoelasticity and the Fung quasi-linear viscoelastic (QLV) model impose forms on responses that can mask true tissue behavior. Here, we applied a more general discrete quasi-linear viscoelastic (DQLV) model to identify the static and dynamic time- and frequency-dependent behavior of rabbit medial collateral ligaments. Unlike the Fung QLV approach, the DQLV approach revealed that energy dissipation is elevated at a loading period of ∼10s. The fitting algorithm was applied to the entire loading history on each specimen, enabling accurate estimation of the material's viscoelastic relaxation spectrum from data gathered from transient rather than only steady states. The application of the DQLV method to cyclically loading regimens has broad applicability for the characterization of biological tissues, and the results suggest a mechanistic basis for the stretching regimens most favored by athletic trainers. Copyright © 2017 Elsevier Ltd. All rights reserved.

Discrete quasi-linear viscoelastic damping analysis of connective tissues, and the biomechanics of stretching

PubMed Central

Babaei, Behzad; Velasquez-Mao, Aaron J.; Thomopoulos, Stavros; Elson, Elliot L.; Abramowitch, Steven D.; Genin, Guy M.

2017-01-01

The time- and frequency-dependent properties of connective tissue define their physiological function, but are notoriously difficult to characterize. Well-established tools such as linear viscoelasticity and the Fung quasi-linear viscoelastic (QLV) model impose forms on responses that can mask true tissue behavior. Here, we applied a more general discrete quasi-linear viscoelastic (DQLV) model to identify the static and dynamic time- and frequency-dependent behavior of rabbit medial collateral ligaments. Unlike the Fung QLV approach, the DQLV approach revealed that energy dissipation is elevated at a loading period of ~10 seconds. The fitting algorithm was applied to the entire loading history on each specimen, enabling accurate estimation of the material's viscoelastic relaxation spectrum from data gathered from transient rather than only steady states. The application of the DQLV method to cyclically loading regimens has broad applicability for the characterization of biological tissues, and the results suggest a mechanistic basis for the stretching regimens most favored by athletic trainers. PMID:28088071

A unified view on weakly correlated recurrent networks

PubMed Central

Grytskyy, Dmytro; Tetzlaff, Tom; Diesmann, Markus; Helias, Moritz

2013-01-01

The diversity of neuron models used in contemporary theoretical neuroscience to investigate specific properties of covariances in the spiking activity raises the question how these models relate to each other. In particular it is hard to distinguish between generic properties of covariances and peculiarities due to the abstracted model. Here we present a unified view on pairwise covariances in recurrent networks in the irregular regime. We consider the binary neuron model, the leaky integrate-and-fire (LIF) model, and the Hawkes process. We show that linear approximation maps each of these models to either of two classes of linear rate models (LRM), including the Ornstein–Uhlenbeck process (OUP) as a special case. The distinction between both classes is the location of additive noise in the rate dynamics, which is located on the output side for spiking models and on the input side for the binary model. Both classes allow closed form solutions for the covariance. For output noise it separates into an echo term and a term due to correlated input. The unified framework enables us to transfer results between models. For example, we generalize the binary model and the Hawkes process to the situation with synaptic conduction delays and simplify derivations for established results. Our approach is applicable to general network structures and suitable for the calculation of population averages. The derived averages are exact for fixed out-degree network architectures and approximate for fixed in-degree. We demonstrate how taking into account fluctuations in the linearization procedure increases the accuracy of the effective theory and we explain the class dependent differences between covariances in the time and the frequency domain. Finally we show that the oscillatory instability emerging in networks of LIF models with delayed inhibitory feedback is a model-invariant feature: the same structure of poles in the complex frequency plane determines the population power spectra. PMID:24151463

Reductions in finite-dimensional integrable systems and special points of classical r-matrices

NASA Astrophysics Data System (ADS)

Skrypnyk, T.

2016-12-01

For a given 𝔤 ⊗ 𝔤-valued non-skew-symmetric non-dynamical classical r-matrices r(u, v) with spectral parameters, we construct the general form of 𝔤-valued Lax matrices of finite-dimensional integrable systems satisfying linear r-matrix algebra. We show that the reduction in the corresponding finite-dimensional integrable systems is connected with "the special points" of the classical r-matrices in which they become degenerated. We also propose a systematic way of the construction of additional integrals of the Lax-integrable systems associated with the symmetries of the corresponding r-matrices. We consider examples of the Lax matrices and integrable systems that are obtained in the framework of the general scheme. Among them there are such physically important systems as generalized Gaudin systems in an external magnetic field, ultimate integrable generalization of Toda-type chains (including "modified" or "deformed" Toda chains), generalized integrable Jaynes-Cummings-Dicke models, integrable boson models generalizing Bose-Hubbard dimer models, etc.

Treatment of systematic errors in land data assimilation systems

NASA Astrophysics Data System (ADS)

Crow, W. T.; Yilmaz, M.

2012-12-01

Data assimilation systems are generally designed to minimize the influence of random error on the estimation of system states. Yet, experience with land data assimilation systems has also revealed the presence of large systematic differences between model-derived and remotely-sensed estimates of land surface states. Such differences are commonly resolved prior to data assimilation through implementation of a pre-processing rescaling step whereby observations are scaled (or non-linearly transformed) to somehow "match" comparable predictions made by an assimilation model. While the rationale for removing systematic differences in means (i.e., bias) between models and observations is well-established, relatively little theoretical guidance is currently available to determine the appropriate treatment of higher-order moments during rescaling. This talk presents a simple analytical argument to define an optimal linear-rescaling strategy for observations prior to their assimilation into a land surface model. While a technique based on triple collocation theory is shown to replicate this optimal strategy, commonly-applied rescaling techniques (e.g., so called "least-squares regression" and "variance matching" approaches) are shown to represent only sub-optimal approximations to it. Since the triple collocation approach is likely infeasible in many real-world circumstances, general advice for deciding between various feasible (yet sub-optimal) rescaling approaches will be presented with an emphasis of the implications of this work for the case of directly assimilating satellite radiances. While the bulk of the analysis will deal with linear rescaling techniques, its extension to nonlinear cases will also be discussed.

On the classification of the spectrally stable standing waves of the Hartree problem

NASA Astrophysics Data System (ADS)

Georgiev, Vladimir; Stefanov, Atanas

2018-05-01

We consider the fractional Hartree model, with general power non-linearity and arbitrary spatial dimension. We construct variationally the "normalized" solutions for the corresponding Choquard-Pekar model-in particular a number of key properties, like smoothness and bell-shapedness are established. As a consequence of the construction, we show that these solitons are spectrally stable as solutions to the time-dependent Hartree model. In addition, we analyze the spectral stability of the Moroz-Van Schaftingen solitons of the classical Hartree problem, in any dimensions and power non-linearity. A full classification is obtained, the main conclusion of which is that only and exactly the "normalized" solutions (which exist only in a portion of the range) are spectrally stable.

Linear analysis of a force reflective teleoperator

NASA Technical Reports Server (NTRS)

Biggers, Klaus B.; Jacobsen, Stephen C.; Davis, Clark C.

1989-01-01

Complex force reflective teleoperation systems are often very difficult to analyze due to the large number of components and control loops involved. One mode of a force reflective teleoperator is described. An analysis of the performance of the system based on a linear analysis of the general full order model is presented. Reduced order models are derived and correlated with the full order models. Basic effects of force feedback and position feedback are examined and the effects of time delays between the master and slave are studied. The results show that with symmetrical position-position control of teleoperators, a basic trade off must be made between the intersystem stiffness of the teleoperator, and the impedance felt by the operator in free space.

A comparison of methods to handle skew distributed cost variables in the analysis of the resource consumption in schizophrenia treatment.

PubMed

Kilian, Reinhold; Matschinger, Herbert; Löeffler, Walter; Roick, Christiane; Angermeyer, Matthias C

2002-03-01

Transformation of the dependent cost variable is often used to solve the problems of heteroscedasticity and skewness in linear ordinary least square regression of health service cost data. However, transformation may cause difficulties in the interpretation of regression coefficients and the retransformation of predicted values. The study compares the advantages and disadvantages of different methods to estimate regression based cost functions using data on the annual costs of schizophrenia treatment. Annual costs of psychiatric service use and clinical and socio-demographic characteristics of the patients were assessed for a sample of 254 patients with a diagnosis of schizophrenia (ICD-10 F 20.0) living in Leipzig. The clinical characteristics of the participants were assessed by means of the BPRS 4.0, the GAF, and the CAN for service needs. Quality of life was measured by WHOQOL-BREF. A linear OLS regression model with non-parametric standard errors, a log-transformed OLS model and a generalized linear model with a log-link and a gamma distribution were used to estimate service costs. For the estimation of robust non-parametric standard errors, the variance estimator by White and a bootstrap estimator based on 2000 replications were employed. Models were evaluated by the comparison of the R2 and the root mean squared error (RMSE). RMSE of the log-transformed OLS model was computed with three different methods of bias-correction. The 95% confidence intervals for the differences between the RMSE were computed by means of bootstrapping. A split-sample-cross-validation procedure was used to forecast the costs for the one half of the sample on the basis of a regression equation computed for the other half of the sample. All three methods showed significant positive influences of psychiatric symptoms and met psychiatric service needs on service costs. Only the log- transformed OLS model showed a significant negative impact of age, and only the GLM shows a significant negative influences of employment status and partnership on costs. All three models provided a R2 of about.31. The Residuals of the linear OLS model revealed significant deviances from normality and homoscedasticity. The residuals of the log-transformed model are normally distributed but still heteroscedastic. The linear OLS model provided the lowest prediction error and the best forecast of the dependent cost variable. The log-transformed model provided the lowest RMSE if the heteroscedastic bias correction was used. The RMSE of the GLM with a log link and a gamma distribution was higher than those of the linear OLS model and the log-transformed OLS model. The difference between the RMSE of the linear OLS model and that of the log-transformed OLS model without bias correction was significant at the 95% level. As result of the cross-validation procedure, the linear OLS model provided the lowest RMSE followed by the log-transformed OLS model with a heteroscedastic bias correction. The GLM showed the weakest model fit again. None of the differences between the RMSE resulting form the cross- validation procedure were found to be significant. The comparison of the fit indices of the different regression models revealed that the linear OLS model provided a better fit than the log-transformed model and the GLM, but the differences between the models RMSE were not significant. Due to the small number of cases in the study the lack of significance does not sufficiently proof that the differences between the RSME for the different models are zero and the superiority of the linear OLS model can not be generalized. The lack of significant differences among the alternative estimators may reflect a lack of sample size adequate to detect important differences among the estimators employed. Further studies with larger case number are necessary to confirm the results. Specification of an adequate regression models requires a careful examination of the characteristics of the data. Estimation of standard errors and confidence intervals by nonparametric methods which are robust against deviations from the normal distribution and the homoscedasticity of residuals are suitable alternatives to the transformation of the skew distributed dependent variable. Further studies with more adequate case numbers are needed to confirm the results.

A flexible Bayesian assessment for the expected impact of data on prediction confidence for optimal sampling designs

NASA Astrophysics Data System (ADS)

Leube, Philipp; Geiges, Andreas; Nowak, Wolfgang

2010-05-01

Incorporating hydrogeological data, such as head and tracer data, into stochastic models of subsurface flow and transport helps to reduce prediction uncertainty. Considering limited financial resources available for the data acquisition campaign, information needs towards the prediction goal should be satisfied in a efficient and task-specific manner. For finding the best one among a set of design candidates, an objective function is commonly evaluated, which measures the expected impact of data on prediction confidence, prior to their collection. An appropriate approach to this task should be stochastically rigorous, master non-linear dependencies between data, parameters and model predictions, and allow for a wide variety of different data types. Existing methods fail to fulfill all these requirements simultaneously. For this reason, we introduce a new method, denoted as CLUE (Cross-bred Likelihood Uncertainty Estimator), that derives the essential distributions and measures of data utility within a generalized, flexible and accurate framework. The method makes use of Bayesian GLUE (Generalized Likelihood Uncertainty Estimator) and extends it to an optimal design method by marginalizing over the yet unknown data values. Operating in a purely Bayesian Monte-Carlo framework, CLUE is a strictly formal information processing scheme free of linearizations. It provides full flexibility associated with the type of measurements (linear, non-linear, direct, indirect) and accounts for almost arbitrary sources of uncertainty (e.g. heterogeneity, geostatistical assumptions, boundary conditions, model concepts) via stochastic simulation and Bayesian model averaging. This helps to minimize the strength and impact of possible subjective prior assumptions, that would be hard to defend prior to data collection. Our study focuses on evaluating two different uncertainty measures: (i) expected conditional variance and (ii) expected relative entropy of a given prediction goal. The applicability and advantages are shown in a synthetic example. Therefor, we consider a contaminant source, posing a threat on a drinking water well in an aquifer. Furthermore, we assume uncertainty in geostatistical parameters, boundary conditions and hydraulic gradient. The two mentioned measures evaluate the sensitivity of (1) general prediction confidence and (2) exceedance probability of a legal regulatory threshold value on sampling locations.

Using generalized additive (mixed) models to analyze single case designs.

PubMed

Shadish, William R; Zuur, Alain F; Sullivan, Kristynn J

2014-04-01

This article shows how to apply generalized additive models and generalized additive mixed models to single-case design data. These models excel at detecting the functional form between two variables (often called trend), that is, whether trend exists, and if it does, what its shape is (e.g., linear and nonlinear). In many respects, however, these models are also an ideal vehicle for analyzing single-case designs because they can consider level, trend, variability, overlap, immediacy of effect, and phase consistency that single-case design researchers examine when interpreting a functional relation. We show how these models can be implemented in a wide variety of ways to test whether treatment is effective, whether cases differ from each other, whether treatment effects vary over cases, and whether trend varies over cases. We illustrate diagnostic statistics and graphs, and we discuss overdispersion of data in detail, with examples of quasibinomial models for overdispersed data, including how to compute dispersion and quasi-AIC fit indices in generalized additive models. We show how generalized additive mixed models can be used to estimate autoregressive models and random effects and discuss the limitations of the mixed models compared to generalized additive models. We provide extensive annotated syntax for doing all these analyses in the free computer program R. Copyright © 2013 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.

Validation of drift and diffusion coefficients from experimental data

NASA Astrophysics Data System (ADS)

Riera, R.; Anteneodo, C.

2010-04-01

Many fluctuation phenomena, in physics and other fields, can be modeled by Fokker-Planck or stochastic differential equations whose coefficients, associated with drift and diffusion components, may be estimated directly from the observed time series. Its correct characterization is crucial to determine the system quantifiers. However, due to the finite sampling rates of real data, the empirical estimates may significantly differ from their true functional forms. In the literature, low-order corrections, or even no corrections, have been applied to the finite-time estimates. A frequent outcome consists of linear drift and quadratic diffusion coefficients. For this case, exact corrections have been recently found, from Itô-Taylor expansions. Nevertheless, model validation constitutes a necessary step before determining and applying the appropriate corrections. Here, we exploit the consequences of the exact theoretical results obtained for the linear-quadratic model. In particular, we discuss whether the observed finite-time estimates are actually a manifestation of that model. The relevance of this analysis is put into evidence by its application to two contrasting real data examples in which finite-time linear drift and quadratic diffusion coefficients are observed. In one case the linear-quadratic model is readily rejected while in the other, although the model constitutes a very good approximation, low-order corrections are inappropriate. These examples give warning signs about the proper interpretation of finite-time analysis even in more general diffusion processes.

Non Abelian T-duality in Gauged Linear Sigma Models

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

Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando

Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM’s as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they dependmore » in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.« less

Using generalized linear models to estimate selectivity from short-term recoveries of tagged red drum Sciaenops ocellatus: Effects of gear, fate, and regulation period

USGS Publications Warehouse

Bacheler, N.M.; Hightower, J.E.; Burdick, S.M.; Paramore, L.M.; Buckel, J.A.; Pollock, K.H.

2010-01-01

Estimating the selectivity patterns of various fishing gears is a critical component of fisheries stock assessment due to the difficulty in obtaining representative samples from most gears. We used short-term recoveries (n = 3587) of tagged red drum Sciaenops ocellatus to directly estimate age- and length-based selectivity patterns using generalized linear models. The most parsimonious models were selected using AIC, and standard deviations were estimated using simulations. Selectivity of red drum was dependent upon the regulation period in which the fish was caught, the gear used to catch the fish (i.e., hook-and-line, gill nets, pound nets), and the fate of the fish upon recovery (i.e., harvested or released); models including all first-order interactions between main effects outperformed models without interactions. Selectivity of harvested fish was generally dome-shaped and shifted toward larger, older fish in response to regulation changes. Selectivity of caught-and-released red drum was highest on the youngest and smallest fish in the early and middle regulation periods, but increased on larger, legal-sized fish in the late regulation period. These results suggest that catch-and-release mortality has consistently been high for small, young red drum, but has recently become more common in larger, older fish. This method of estimating selectivity from short-term tag recoveries is valuable because it is simpler than full tag-return models, and may be more robust because yearly fishing and natural mortality rates do not need to be modeled and estimated. ?? 2009 Elsevier B.V.

Using generalized linear models to estimate selectivity from short-term recoveries of tagged red drum Sciaenops ocellatus: Effects of gear, fate, and regulation period

USGS Publications Warehouse

Burdick, Summer M.; Hightower, Joseph E.; Bacheler, Nathan M.; Paramore, Lee M.; Buckel, Jeffrey A.; Pollock, Kenneth H.

2010-01-01

Estimating the selectivity patterns of various fishing gears is a critical component of fisheries stock assessment due to the difficulty in obtaining representative samples from most gears. We used short-term recoveries (n = 3587) of tagged red drum Sciaenops ocellatus to directly estimate age- and length-based selectivity patterns using generalized linear models. The most parsimonious models were selected using AIC, and standard deviations were estimated using simulations. Selectivity of red drum was dependent upon the regulation period in which the fish was caught, the gear used to catch the fish (i.e., hook-and-line, gill nets, pound nets), and the fate of the fish upon recovery (i.e., harvested or released); models including all first-order interactions between main effects outperformed models without interactions. Selectivity of harvested fish was generally dome-shaped and shifted toward larger, older fish in response to regulation changes. Selectivity of caught-and-released red drum was highest on the youngest and smallest fish in the early and middle regulation periods, but increased on larger, legal-sized fish in the late regulation period. These results suggest that catch-and-release mortality has consistently been high for small, young red drum, but has recently become more common in larger, older fish. This method of estimating selectivity from short-term tag recoveries is valuable because it is simpler than full tag-return models, and may be more robust because yearly fishing and natural mortality rates do not need to be modeled and estimated.

Validated linear dynamic model of electrically-shunted magnetostrictive transducers with application to structural vibration control

NASA Astrophysics Data System (ADS)

Scheidler, Justin J.; Asnani, Vivake M.

2017-03-01

This paper presents a linear model of the fully-coupled electromechanical behavior of a generally-shunted magnetostrictive transducer. The impedance and admittance representations of the model are reported. The model is used to derive the effect of the shunt’s electrical impedance on the storage modulus and loss factor of the transducer without neglecting the inherent resistance of the transducer’s coil. The expressions are normalized and then shown to also represent generally-shunted piezoelectric materials that have a finite leakage resistance. The generalized expressions are simplified for three shunts: resistive, series resistive-capacitive, and inductive, which are considered for shunt damping, resonant shunt damping, and stiffness tuning, respectively. For each shunt, the storage modulus and loss factor are plotted for a wide range of the normalized parameters. Then, important trends and their impact on different applications are discussed. An experimental validation of the transducer model is presented for the case of resistive and resonant shunts. The model closely predicts the measured response for a variety of operating conditions. This paper also introduces a model for the dynamic compliance of a vibrating structure that is coupled to a magnetostrictive transducer for shunt damping and resonant shunt damping applications. This compliance is normalized and then shown to be analogous to that of a structure that is coupled to a piezoelectric material. The derived analogies allow for the observations and equations in the existing literature on structural vibration control using shunted piezoelectric materials to be directly applied to the case of shunted magnetostrictive transducers.

Non Abelian T-duality in Gauged Linear Sigma Models

DOE PAGES

Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando; ...

2018-04-01

Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM’s as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they dependmore » in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.« less

A quasi-chemical model for the growth and death of microorganisms in foods by non-thermal and high-pressure processing.

PubMed

Doona, Christopher J; Feeherry, Florence E; Ross, Edward W

2005-04-15

Predictive microbial models generally rely on the growth of bacteria in laboratory broth to approximate the microbial growth kinetics expected to take place in actual foods under identical environmental conditions. Sigmoidal functions such as the Gompertz or logistics equation accurately model the typical microbial growth curve from the lag to the stationary phase and provide the mathematical basis for estimating parameters such as the maximum growth rate (MGR). Stationary phase data can begin to show a decline and make it difficult to discern which data to include in the analysis of the growth curve, a factor that influences the calculated values of the growth parameters. In contradistinction, the quasi-chemical kinetics model provides additional capabilities in microbial modelling and fits growth-death kinetics (all four phases of the microbial lifecycle continuously) for a general set of microorganisms in a variety of actual food substrates. The quasi-chemical model is differential equations (ODEs) that derives from a hypothetical four-step chemical mechanism involving an antagonistic metabolite (quorum sensing) and successfully fits the kinetics of pathogens (Staphylococcus aureus, Escherichia coli and Listeria monocytogenes) in various foods (bread, turkey meat, ham and cheese) as functions of different hurdles (a(w), pH, temperature and anti-microbial lactate). The calculated value of the MGR depends on whether growth-death data or only growth data are used in the fitting procedure. The quasi-chemical kinetics model is also exploited for use with the novel food processing technology of high-pressure processing. The high-pressure inactivation kinetics of E. coli are explored in a model food system over the pressure (P) range of 207-345 MPa (30,000-50,000 psi) and the temperature (T) range of 30-50 degrees C. In relatively low combinations of P and T, the inactivation curves are non-linear and exhibit a shoulder prior to a more rapid rate of microbial destruction. In the higher P, T regime, the inactivation plots tend to be linear. In all cases, the quasi-chemical model successfully fit the linear and curvi-linear inactivation plots for E. coli in model food systems. The experimental data and the quasi-chemical mathematical model described herein are candidates for inclusion in ComBase, the developing database that combines data and models from the USDA Pathogen Modeling Program and the UK Food MicroModel.

Variable selection for marginal longitudinal generalized linear models.

PubMed

Cantoni, Eva; Flemming, Joanna Mills; Ronchetti, Elvezio

2005-06-01

Variable selection is an essential part of any statistical analysis and yet has been somewhat neglected in the context of longitudinal data analysis. In this article, we propose a generalized version of Mallows's C(p) (GC(p)) suitable for use with both parametric and nonparametric models. GC(p) provides an estimate of a measure of model's adequacy for prediction. We examine its performance with popular marginal longitudinal models (fitted using GEE) and contrast results with what is typically done in practice: variable selection based on Wald-type or score-type tests. An application to real data further demonstrates the merits of our approach while at the same time emphasizing some important robust features inherent to GC(p).

Mathematical modeling of spinning elastic bodies for modal analysis.

NASA Technical Reports Server (NTRS)

Likins, P. W.; Barbera, F. J.; Baddeley, V.

1973-01-01

The problem of modal analysis of an elastic appendage on a rotating base is examined to establish the relative advantages of various mathematical models of elastic structures and to extract general inferences concerning the magnitude and character of the influence of spin on the natural frequencies and mode shapes of rotating structures. In realization of the first objective, it is concluded that except for a small class of very special cases the elastic continuum model is devoid of useful results, while for constant nominal spin rate the distributed-mass finite-element model is quite generally tractable, since in the latter case the governing equations are always linear, constant-coefficient, ordinary differential equations. Although with both of these alternatives the details of the formulation generally obscure the essence of the problem and permit very little engineering insight to be gained without extensive computation, this difficulty is not encountered when dealing with simple concentrated mass models.

Theoretical and software considerations for nonlinear dynamic analysis

NASA Technical Reports Server (NTRS)

Schmidt, R. J.; Dodds, R. H., Jr.

1983-01-01

In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented.

Equivalent circuit simulation of HPEM-induced transient responses at nonlinear loads

NASA Astrophysics Data System (ADS)

Kotzev, Miroslav; Bi, Xiaotang; Kreitlow, Matthias; Gronwald, Frank

2017-09-01

In this paper the equivalent circuit modeling of a nonlinearly loaded loop antenna and its transient responses to HPEM field excitations are investigated. For the circuit modeling the general strategy to characterize the nonlinearly loaded antenna by a linear and a nonlinear circuit part is pursued. The linear circuit part can be determined by standard methods of antenna theory and numerical field computation. The modeling of the nonlinear circuit part requires realistic circuit models of the nonlinear loads that are given by Schottky diodes. Combining both parts, appropriate circuit models are obtained and analyzed by means of a standard SPICE circuit simulator. It is the main result that in this way full-wave simulation results can be reproduced. Furthermore it is clearly seen that the equivalent circuit modeling offers considerable advantages with respect to computation speed and also leads to improved physical insights regarding the coupling between HPEM field excitation and nonlinearly loaded loop antenna.

Prediction of High-Lift Flows using Turbulent Closure Models

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.; Gatski, Thomas B.; Ying, Susan X.; Bertelrud, Arild

1997-01-01

The flow over two different multi-element airfoil configurations is computed using linear eddy viscosity turbulence models and a nonlinear explicit algebraic stress model. A subset of recently-measured transition locations using hot film on a McDonnell Douglas configuration is presented, and the effect of transition location on the computed solutions is explored. Deficiencies in wake profile computations are found to be attributable in large part to poor boundary layer prediction on the generating element, and not necessarily inadequate turbulence modeling in the wake. Using measured transition locations for the main element improves the prediction of its boundary layer thickness, skin friction, and wake profile shape. However, using measured transition locations on the slat still yields poor slat wake predictions. The computation of the slat flow field represents a key roadblock to successful predictions of multi-element flows. In general, the nonlinear explicit algebraic stress turbulence model gives very similar results to the linear eddy viscosity models.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev, , Dr.

2017-10-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ω_i while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev, , Dr.

2017-09-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ωi while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev

2017-11-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ωi while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

Documenting Differences between Early Stone Age Flake Production Systems: An Experimental Model and Archaeological Verification.

PubMed

Presnyakova, Darya; Archer, Will; Braun, David R; Flear, Wesley

2015-01-01

This study investigates morphological differences between flakes produced via "core and flake" technologies and those resulting from bifacial shaping strategies. We investigate systematic variation between two technological groups of flakes using experimentally produced assemblages, and then apply the experimental model to the Cutting 10 Mid -Pleistocene archaeological collection from Elandsfontein, South Africa. We argue that a specific set of independent variables--and their interactions--including external platform angle, platform depth, measures of thickness variance and flake curvature should distinguish between these two technological groups. The role of these variables in technological group separation was further investigated using the Generalized Linear Model as well as Linear Discriminant Analysis. The Discriminant model was used to classify archaeological flakes from the Cutting 10 locality in terms of their probability of association, within either experimentally developed technological group. The results indicate that the selected independent variables play a central role in separating core and flake from bifacial technologies. Thickness evenness and curvature had the greatest effect sizes in both the Generalized Linear and Discriminant models. Interestingly the interaction between thickness evenness and platform depth was significant and played an important role in influencing technological group membership. The identified interaction emphasizes the complexity in attempting to distinguish flake production strategies based on flake morphological attributes. The results of the discriminant function analysis demonstrate that the majority of flakes at the Cutting 10 locality were not associated with the production of the numerous Large Cutting Tools found at the site, which corresponds with previous suggestions regarding technological behaviors reflected in this assemblage.

Documenting Differences between Early Stone Age Flake Production Systems: An Experimental Model and Archaeological Verification

PubMed Central

Presnyakova, Darya; Archer, Will; Braun, David R.; Flear, Wesley

2015-01-01

This study investigates morphological differences between flakes produced via “core and flake” technologies and those resulting from bifacial shaping strategies. We investigate systematic variation between two technological groups of flakes using experimentally produced assemblages, and then apply the experimental model to the Cutting 10 Mid -Pleistocene archaeological collection from Elandsfontein, South Africa. We argue that a specific set of independent variables—and their interactions—including external platform angle, platform depth, measures of thickness variance and flake curvature should distinguish between these two technological groups. The role of these variables in technological group separation was further investigated using the Generalized Linear Model as well as Linear Discriminant Analysis. The Discriminant model was used to classify archaeological flakes from the Cutting 10 locality in terms of their probability of association, within either experimentally developed technological group. The results indicate that the selected independent variables play a central role in separating core and flake from bifacial technologies. Thickness evenness and curvature had the greatest effect sizes in both the Generalized Linear and Discriminant models. Interestingly the interaction between thickness evenness and platform depth was significant and played an important role in influencing technological group membership. The identified interaction emphasizes the complexity in attempting to distinguish flake production strategies based on flake morphological attributes. The results of the discriminant function analysis demonstrate that the majority of flakes at the Cutting 10 locality were not associated with the production of the numerous Large Cutting Tools found at the site, which corresponds with previous suggestions regarding technological behaviors reflected in this assemblage. PMID:26111251

Planck constant as spectral parameter in integrable systems and KZB equations

NASA Astrophysics Data System (ADS)

Levin, A.; Olshanetsky, M.; Zotov, A.

2014-10-01

We construct special rational gl N Knizhnik-Zamolodchikov-Bernard (KZB) equations with Ñ punctures by deformation of the corresponding quantum gl N rational R-matrix. They have two parameters. The limit of the first one brings the model to the ordinary rational KZ equation. Another one is τ. At the level of classical mechanics the deformation parameter τ allows to extend the previously obtained modified Gaudin models to the modified Schlesinger systems. Next, we notice that the identities underlying generic (elliptic) KZB equations follow from some additional relations for the properly normalized R-matrices. The relations are noncommutative analogues of identities for (scalar) elliptic functions. The simplest one is the unitarity condition. The quadratic (in R matrices) relations are generated by noncommutative Fay identities. In particular, one can derive the quantum Yang-Baxter equations from the Fay identities. The cubic relations provide identities for the KZB equations as well as quadratic relations for the classical r-matrices which can be treated as halves of the classical Yang-Baxter equation. At last we discuss the R-matrix valued linear problems which provide gl Ñ CM models and Painlevé equations via the above mentioned identities. The role of the spectral parameter plays the Planck constant of the quantum R-matrix. When the quantum gl N R-matrix is scalar ( N = 1) the linear problem reproduces the Krichever's ansatz for the Lax matrices with spectral parameter for the gl Ñ CM models. The linear problems for the quantum CM models generalize the KZ equations in the same way as the Lax pairs with spectral parameter generalize those without it.

Optimal exponential synchronization of general chaotic delayed neural networks: an LMI approach.

PubMed

Liu, Meiqin

2009-09-01

This paper investigates the optimal exponential synchronization problem of general chaotic neural networks with or without time delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. This general model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, and recurrent multilayer perceptrons (RMLPs) with or without delays. Using the drive-response concept, time-delay feedback controllers are designed to synchronize two identical chaotic neural networks as quickly as possible. The control design equations are shown to be a generalized eigenvalue problem (GEVP) which can be easily solved by various convex optimization algorithms to determine the optimal control law and the optimal exponential synchronization rate. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.