Sample records for graphical gaussian model
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Connections between Graphical Gaussian Models and Factor Analysis
ERIC Educational Resources Information Center
Salgueiro, M. Fatima; Smith, Peter W. F.; McDonald, John W.
2010-01-01
Connections between graphical Gaussian models and classical single-factor models are obtained by parameterizing the single-factor model as a graphical Gaussian model. Models are represented by independence graphs, and associations between each manifest variable and the latent factor are measured by factor partial correlations. Power calculations…
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Robust Gaussian Graphical Modeling via l1 Penalization
Sun, Hokeun; Li, Hongzhe
2012-01-01
Summary Gaussian graphical models have been widely used as an effective method for studying the conditional independency structure among genes and for constructing genetic networks. However, gene expression data typically have heavier tails or more outlying observations than the standard Gaussian distribution. Such outliers in gene expression data can lead to wrong inference on the dependency structure among the genes. We propose a l1 penalized estimation procedure for the sparse Gaussian graphical models that is robustified against possible outliers. The likelihood function is weighted according to how the observation is deviated, where the deviation of the observation is measured based on its own likelihood. An efficient computational algorithm based on the coordinate gradient descent method is developed to obtain the minimizer of the negative penalized robustified-likelihood, where nonzero elements of the concentration matrix represents the graphical links among the genes. After the graphical structure is obtained, we re-estimate the positive definite concentration matrix using an iterative proportional fitting algorithm. Through simulations, we demonstrate that the proposed robust method performs much better than the graphical Lasso for the Gaussian graphical models in terms of both graph structure selection and estimation when outliers are present. We apply the robust estimation procedure to an analysis of yeast gene expression data and show that the resulting graph has better biological interpretation than that obtained from the graphical Lasso. PMID:23020775
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GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models
Mukherjee, Chiranjit; Rodriguez, Abel
2016-01-01
Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful. PMID:28626348
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GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models.
Mukherjee, Chiranjit; Rodriguez, Abel
2016-01-01
Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful.
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Interactive Gaussian Graphical Models for Discovering Depth Trends in ChemCam Data
NASA Astrophysics Data System (ADS)
Oyen, D. A.; Komurlu, C.; Lanza, N. L.
2018-04-01
Interactive Gaussian graphical models discover surface compositional features on rocks in ChemCam targets. Our approach visualizes shot-to-shot relationships among LIBS observations, and identifies the wavelengths involved in the trend.
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Sparse covariance estimation in heterogeneous samples*
Rodríguez, Abel; Lenkoski, Alex; Dobra, Adrian
2015-01-01
Standard Gaussian graphical models implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected from heterogeneous populations where such an assumption is not satisfied, leading in turn to nonlinear relationships among variables. To address such situations we explore mixtures of Gaussian graphical models; in particular, we consider both infinite mixtures and infinite hidden Markov models where the emission distributions correspond to Gaussian graphical models. Such models allow us to divide a heterogeneous population into homogenous groups, with each cluster having its own conditional independence structure. As an illustration, we study the trends in foreign exchange rate fluctuations in the pre-Euro era. PMID:26925189
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On an Additive Semigraphoid Model for Statistical Networks With Application to Pathway Analysis.
Li, Bing; Chun, Hyonho; Zhao, Hongyu
2014-09-01
We introduce a nonparametric method for estimating non-gaussian graphical models based on a new statistical relation called additive conditional independence, which is a three-way relation among random vectors that resembles the logical structure of conditional independence. Additive conditional independence allows us to use one-dimensional kernel regardless of the dimension of the graph, which not only avoids the curse of dimensionality but also simplifies computation. It also gives rise to a parallel structure to the gaussian graphical model that replaces the precision matrix by an additive precision operator. The estimators derived from additive conditional independence cover the recently introduced nonparanormal graphical model as a special case, but outperform it when the gaussian copula assumption is violated. We compare the new method with existing ones by simulations and in genetic pathway analysis.
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Estimation of High-Dimensional Graphical Models Using Regularized Score Matching
Lin, Lina; Drton, Mathias; Shojaie, Ali
2017-01-01
Graphical models are widely used to model stochastic dependences among large collections of variables. We introduce a new method of estimating undirected conditional independence graphs based on the score matching loss, introduced by Hyvärinen (2005), and subsequently extended in Hyvärinen (2007). The regularized score matching method we propose applies to settings with continuous observations and allows for computationally efficient treatment of possibly non-Gaussian exponential family models. In the well-explored Gaussian setting, regularized score matching avoids issues of asymmetry that arise when applying the technique of neighborhood selection, and compared to existing methods that directly yield symmetric estimates, the score matching approach has the advantage that the considered loss is quadratic and gives piecewise linear solution paths under ℓ1 regularization. Under suitable irrepresentability conditions, we show that ℓ1-regularized score matching is consistent for graph estimation in sparse high-dimensional settings. Through numerical experiments and an application to RNAseq data, we confirm that regularized score matching achieves state-of-the-art performance in the Gaussian case and provides a valuable tool for computationally efficient estimation in non-Gaussian graphical models. PMID:28638498
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Graphical Models for Ordinal Data
Guo, Jian; Levina, Elizaveta; Michailidis, George; Zhu, Ji
2014-01-01
A graphical model for ordinal variables is considered, where it is assumed that the data are generated by discretizing the marginal distributions of a latent multivariate Gaussian distribution. The relationships between these ordinal variables are then described by the underlying Gaussian graphical model and can be inferred by estimating the corresponding concentration matrix. Direct estimation of the model is computationally expensive, but an approximate EM-like algorithm is developed to provide an accurate estimate of the parameters at a fraction of the computational cost. Numerical evidence based on simulation studies shows the strong performance of the algorithm, which is also illustrated on data sets on movie ratings and an educational survey. PMID:26120267
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On an additive partial correlation operator and nonparametric estimation of graphical models.
Lee, Kuang-Yao; Li, Bing; Zhao, Hongyu
2016-09-01
We introduce an additive partial correlation operator as an extension of partial correlation to the nonlinear setting, and use it to develop a new estimator for nonparametric graphical models. Our graphical models are based on additive conditional independence, a statistical relation that captures the spirit of conditional independence without having to resort to high-dimensional kernels for its estimation. The additive partial correlation operator completely characterizes additive conditional independence, and has the additional advantage of putting marginal variation on appropriate scales when evaluating interdependence, which leads to more accurate statistical inference. We establish the consistency of the proposed estimator. Through simulation experiments and analysis of the DREAM4 Challenge dataset, we demonstrate that our method performs better than existing methods in cases where the Gaussian or copula Gaussian assumption does not hold, and that a more appropriate scaling for our method further enhances its performance.
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On an additive partial correlation operator and nonparametric estimation of graphical models
Li, Bing; Zhao, Hongyu
2016-01-01
Abstract We introduce an additive partial correlation operator as an extension of partial correlation to the nonlinear setting, and use it to develop a new estimator for nonparametric graphical models. Our graphical models are based on additive conditional independence, a statistical relation that captures the spirit of conditional independence without having to resort to high-dimensional kernels for its estimation. The additive partial correlation operator completely characterizes additive conditional independence, and has the additional advantage of putting marginal variation on appropriate scales when evaluating interdependence, which leads to more accurate statistical inference. We establish the consistency of the proposed estimator. Through simulation experiments and analysis of the DREAM4 Challenge dataset, we demonstrate that our method performs better than existing methods in cases where the Gaussian or copula Gaussian assumption does not hold, and that a more appropriate scaling for our method further enhances its performance. PMID:29422689
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The Gaussian Graphical Model in Cross-Sectional and Time-Series Data.
Epskamp, Sacha; Waldorp, Lourens J; Mõttus, René; Borsboom, Denny
2018-04-16
We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse modeling of covariance structures, and may highlight potential causal relationships between observed variables. We describe the utility in three kinds of psychological data sets: data sets in which consecutive cases are assumed independent (e.g., cross-sectional data), temporally ordered data sets (e.g., n = 1 time series), and a mixture of the 2 (e.g., n > 1 time series). In time-series analysis, the GGM can be used to model the residual structure of a vector-autoregression analysis (VAR), also termed graphical VAR. Two network models can then be obtained: a temporal network and a contemporaneous network. When analyzing data from multiple subjects, a GGM can also be formed on the covariance structure of stationary means-the between-subjects network. We discuss the interpretation of these models and propose estimation methods to obtain these networks, which we implement in the R packages graphicalVAR and mlVAR. The methods are showcased in two empirical examples, and simulation studies on these methods are included in the supplementary materials.
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Werhli, Adriano V; Grzegorczyk, Marco; Husmeier, Dirk
2006-10-15
An important problem in systems biology is the inference of biochemical pathways and regulatory networks from postgenomic data. Various reverse engineering methods have been proposed in the literature, and it is important to understand their relative merits and shortcomings. In the present paper, we compare the accuracy of reconstructing gene regulatory networks with three different modelling and inference paradigms: (1) Relevance networks (RNs): pairwise association scores independent of the remaining network; (2) graphical Gaussian models (GGMs): undirected graphical models with constraint-based inference, and (3) Bayesian networks (BNs): directed graphical models with score-based inference. The evaluation is carried out on the Raf pathway, a cellular signalling network describing the interaction of 11 phosphorylated proteins and phospholipids in human immune system cells. We use both laboratory data from cytometry experiments as well as data simulated from the gold-standard network. We also compare passive observations with active interventions. On Gaussian observational data, BNs and GGMs were found to outperform RNs. The difference in performance was not significant for the non-linear simulated data and the cytoflow data, though. Also, we did not observe a significant difference between BNs and GGMs on observational data in general. However, for interventional data, BNs outperform GGMs and RNs, especially when taking the edge directions rather than just the skeletons of the graphs into account. This suggests that the higher computational costs of inference with BNs over GGMs and RNs are not justified when using only passive observations, but that active interventions in the form of gene knockouts and over-expressions are required to exploit the full potential of BNs. Data, software and supplementary material are available from http://www.bioss.sari.ac.uk/staff/adriano/research.html
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Chen, Zhaoxue; Chen, Hao
2014-01-01
A deconvolution method based on the Gaussian radial basis function (GRBF) interpolation is proposed. Both the original image and Gaussian point spread function are expressed as the same continuous GRBF model, thus image degradation is simplified as convolution of two continuous Gaussian functions, and image deconvolution is converted to calculate the weighted coefficients of two-dimensional control points. Compared with Wiener filter and Lucy-Richardson algorithm, the GRBF method has an obvious advantage in the quality of restored images. In order to overcome such a defect of long-time computing, the method of graphic processing unit multithreading or increasing space interval of control points is adopted, respectively, to speed up the implementation of GRBF method. The experiments show that based on the continuous GRBF model, the image deconvolution can be efficiently implemented by the method, which also has a considerable reference value for the study of three-dimensional microscopic image deconvolution.
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Zhang, Xiao-Fei; Ou-Yang, Le; Yan, Hong
2017-08-15
Understanding how gene regulatory networks change under different cellular states is important for revealing insights into network dynamics. Gaussian graphical models, which assume that the data follow a joint normal distribution, have been used recently to infer differential networks. However, the distributions of the omics data are non-normal in general. Furthermore, although much biological knowledge (or prior information) has been accumulated, most existing methods ignore the valuable prior information. Therefore, new statistical methods are needed to relax the normality assumption and make full use of prior information. We propose a new differential network analysis method to address the above challenges. Instead of using Gaussian graphical models, we employ a non-paranormal graphical model that can relax the normality assumption. We develop a principled model to take into account the following prior information: (i) a differential edge less likely exists between two genes that do not participate together in the same pathway; (ii) changes in the networks are driven by certain regulator genes that are perturbed across different cellular states and (iii) the differential networks estimated from multi-view gene expression data likely share common structures. Simulation studies demonstrate that our method outperforms other graphical model-based algorithms. We apply our method to identify the differential networks between platinum-sensitive and platinum-resistant ovarian tumors, and the differential networks between the proneural and mesenchymal subtypes of glioblastoma. Hub nodes in the estimated differential networks rediscover known cancer-related regulator genes and contain interesting predictions. The source code is at https://github.com/Zhangxf-ccnu/pDNA. szuouyl@gmail.com. Supplementary data are available at Bioinformatics online. © The Author (2017). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com
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Model-checking techniques based on cumulative residuals.
Lin, D Y; Wei, L J; Ying, Z
2002-03-01
Residuals have long been used for graphical and numerical examinations of the adequacy of regression models. Conventional residual analysis based on the plots of raw residuals or their smoothed curves is highly subjective, whereas most numerical goodness-of-fit tests provide little information about the nature of model misspecification. In this paper, we develop objective and informative model-checking techniques by taking the cumulative sums of residuals over certain coordinates (e.g., covariates or fitted values) or by considering some related aggregates of residuals, such as moving sums and moving averages. For a variety of statistical models and data structures, including generalized linear models with independent or dependent observations, the distributions of these stochastic processes tinder the assumed model can be approximated by the distributions of certain zero-mean Gaussian processes whose realizations can be easily generated by computer simulation. Each observed process can then be compared, both graphically and numerically, with a number of realizations from the Gaussian process. Such comparisons enable one to assess objectively whether a trend seen in a residual plot reflects model misspecification or natural variation. The proposed techniques are particularly useful in checking the functional form of a covariate and the link function. Illustrations with several medical studies are provided.
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Gaussian Graphical Models Identify Networks of Dietary Intake in a German Adult Population.
Iqbal, Khalid; Buijsse, Brian; Wirth, Janine; Schulze, Matthias B; Floegel, Anna; Boeing, Heiner
2016-03-01
Data-reduction methods such as principal component analysis are often used to derive dietary patterns. However, such methods do not assess how foods are consumed in relation to each other. Gaussian graphical models (GGMs) are a set of novel methods that can address this issue. We sought to apply GGMs to derive sex-specific dietary intake networks representing consumption patterns in a German adult population. Dietary intake data from 10,780 men and 16,340 women of the European Prospective Investigation into Cancer and Nutrition (EPIC)-Potsdam cohort were cross-sectionally analyzed to construct dietary intake networks. Food intake for each participant was estimated using a 148-item food-frequency questionnaire that captured the intake of 49 food groups. GGMs were applied to log-transformed intakes (grams per day) of 49 food groups to construct sex-specific food networks. Semiparametric Gaussian copula graphical models (SGCGMs) were used to confirm GGM results. In men, GGMs identified 1 major dietary network that consisted of intakes of red meat, processed meat, cooked vegetables, sauces, potatoes, cabbage, poultry, legumes, mushrooms, soup, and whole-grain and refined breads. For women, a similar network was identified with the addition of fried potatoes. Other identified networks consisted of dairy products and sweet food groups. SGCGMs yielded results comparable to those of GGMs. GGMs are a powerful exploratory method that can be used to construct dietary networks representing dietary intake patterns that reveal how foods are consumed in relation to each other. GGMs indicated an apparent major role of red meat intake in a consumption pattern in the studied population. In the future, identified networks might be transformed into pattern scores for investigating their associations with health outcomes. © 2016 American Society for Nutrition.
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Hollow sinh-Gaussian beams and their paraxial properties.
Sun, Qiongge; Zhou, Keya; Fang, Guangyu; Zhang, Guoqiang; Liu, Zhengjun; Liu, Shutian
2012-04-23
A new mathematical model of dark-hollow beams, described as hollow sinh-Gaussian (HsG) beams, has been introduced. The intensity distributions of HsG beams are characterized by a single bright ring along the propagation whose size is determined by the order of beams; the shape of the ring can be controlled by beam width and this leads to the elliptical HsG beams. Propagation characteristics of HsG beams through an ABCD optical system have been researched, they can be regarded as superposition of a series of Hypergeometric-Gaussian (HyGG) beams. As a numerical example, the propagation characteristics of HsG beams in free space have been demonstrated graphically. © 2012 Optical Society of America
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Gene network inference by fusing data from diverse distributions
Žitnik, Marinka; Zupan, Blaž
2015-01-01
Motivation: Markov networks are undirected graphical models that are widely used to infer relations between genes from experimental data. Their state-of-the-art inference procedures assume the data arise from a Gaussian distribution. High-throughput omics data, such as that from next generation sequencing, often violates this assumption. Furthermore, when collected data arise from multiple related but otherwise nonidentical distributions, their underlying networks are likely to have common features. New principled statistical approaches are needed that can deal with different data distributions and jointly consider collections of datasets. Results: We present FuseNet, a Markov network formulation that infers networks from a collection of nonidentically distributed datasets. Our approach is computationally efficient and general: given any number of distributions from an exponential family, FuseNet represents model parameters through shared latent factors that define neighborhoods of network nodes. In a simulation study, we demonstrate good predictive performance of FuseNet in comparison to several popular graphical models. We show its effectiveness in an application to breast cancer RNA-sequencing and somatic mutation data, a novel application of graphical models. Fusion of datasets offers substantial gains relative to inference of separate networks for each dataset. Our results demonstrate that network inference methods for non-Gaussian data can help in accurate modeling of the data generated by emergent high-throughput technologies. Availability and implementation: Source code is at https://github.com/marinkaz/fusenet. Contact: blaz.zupan@fri.uni-lj.si Supplementary information: Supplementary information is available at Bioinformatics online. PMID:26072487
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A semiparametric graphical modelling approach for large-scale equity selection.
Liu, Han; Mulvey, John; Zhao, Tianqi
2016-01-01
We propose a new stock selection strategy that exploits rebalancing returns and improves portfolio performance. To effectively harvest rebalancing gains, we apply ideas from elliptical-copula graphical modelling and stability inference to select stocks that are as independent as possible. The proposed elliptical-copula graphical model has a latent Gaussian representation; its structure can be effectively inferred using the regularized rank-based estimators. The resulting algorithm is computationally efficient and scales to large data-sets. To show the efficacy of the proposed method, we apply it to conduct equity selection based on a 16-year health care stock data-set and a large 34-year stock data-set. Empirical tests show that the proposed method is superior to alternative strategies including a principal component analysis-based approach and the classical Markowitz strategy based on the traditional buy-and-hold assumption.
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Inouye, David I.; Ravikumar, Pradeep; Dhillon, Inderjit S.
2016-01-01
We develop Square Root Graphical Models (SQR), a novel class of parametric graphical models that provides multivariate generalizations of univariate exponential family distributions. Previous multivariate graphical models (Yang et al., 2015) did not allow positive dependencies for the exponential and Poisson generalizations. However, in many real-world datasets, variables clearly have positive dependencies. For example, the airport delay time in New York—modeled as an exponential distribution—is positively related to the delay time in Boston. With this motivation, we give an example of our model class derived from the univariate exponential distribution that allows for almost arbitrary positive and negative dependencies with only a mild condition on the parameter matrix—a condition akin to the positive definiteness of the Gaussian covariance matrix. Our Poisson generalization allows for both positive and negative dependencies without any constraints on the parameter values. We also develop parameter estimation methods using node-wise regressions with ℓ1 regularization and likelihood approximation methods using sampling. Finally, we demonstrate our exponential generalization on a synthetic dataset and a real-world dataset of airport delay times. PMID:27563373
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Hollow Gaussian beams and their propagation properties
NASA Astrophysics Data System (ADS)
Cai, Yangjian; Lu, Xuanhui; Lin, Qiang
2003-07-01
A new mathematical model, described as hollow Gaussian beams (HGBs), is proposed to describe a dark hollow laser beam (DHB). The area of the dark region across the HGBs can easily be controlled by proper choice of the beam parameters. Based on the Collins integral, an analytical propagation formula for the HGBs through a paraxial optical system is derived. The HGBs also can be expressed as a superposition of a series of Lagurerre-Gaussian modes by use of a polynomial expansion. As a numerical example, the propagation properties of a DHB in free space are illustrated graphically. The HGBs provide a convenient and powerful way to describe and treat the propagation of DHBs and can be used conveniently to analyze atoms manipulated with a DHB.
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Hollow Gaussian beams and their propagation properties.
Cai, Yangjian; Lu, Xuanhui; Lin, Qiang
2003-07-01
A new mathematical model, described as hollow Gaussian beams (HGBs), is proposed to describe a dark hollow laser beam (DHB). The area of the dark region across the HGBs can easily be controlled by proper choice of the beam parameters. Based on the Collins integral, an analytical propagation formula for the HGBs through a paraxial optical system is derived. The HGBs also can be expressed as a superposition of a series of Lagurerre-Gaussian modes by use of a polynomial expansion. As a numerical example, the propagation properties of a DHB in free space are illustrated graphically. The HGBs provide a convenient and powerful way to describe and treat the propagation of DHBs and can be used conveniently to analyze atoms manipulated with a DHB.
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A semiparametric graphical modelling approach for large-scale equity selection
Liu, Han; Mulvey, John; Zhao, Tianqi
2016-01-01
We propose a new stock selection strategy that exploits rebalancing returns and improves portfolio performance. To effectively harvest rebalancing gains, we apply ideas from elliptical-copula graphical modelling and stability inference to select stocks that are as independent as possible. The proposed elliptical-copula graphical model has a latent Gaussian representation; its structure can be effectively inferred using the regularized rank-based estimators. The resulting algorithm is computationally efficient and scales to large data-sets. To show the efficacy of the proposed method, we apply it to conduct equity selection based on a 16-year health care stock data-set and a large 34-year stock data-set. Empirical tests show that the proposed method is superior to alternative strategies including a principal component analysis-based approach and the classical Markowitz strategy based on the traditional buy-and-hold assumption. PMID:28316507
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Gaussian covariance graph models accounting for correlated marker effects in genome-wide prediction.
Martínez, C A; Khare, K; Rahman, S; Elzo, M A
2017-10-01
Several statistical models used in genome-wide prediction assume uncorrelated marker allele substitution effects, but it is known that these effects may be correlated. In statistics, graphical models have been identified as a useful tool for covariance estimation in high-dimensional problems and it is an area that has recently experienced a great expansion. In Gaussian covariance graph models (GCovGM), the joint distribution of a set of random variables is assumed to be Gaussian and the pattern of zeros of the covariance matrix is encoded in terms of an undirected graph G. In this study, methods adapting the theory of GCovGM to genome-wide prediction were developed (Bayes GCov, Bayes GCov-KR and Bayes GCov-H). In simulated data sets, improvements in correlation between phenotypes and predicted breeding values and accuracies of predicted breeding values were found. Our models account for correlation of marker effects and permit to accommodate general structures as opposed to models proposed in previous studies, which consider spatial correlation only. In addition, they allow incorporation of biological information in the prediction process through its use when constructing graph G, and their extension to the multi-allelic loci case is straightforward. © 2017 Blackwell Verlag GmbH.
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Zhang, Baofeng; Kilburg, Denise; Eastman, Peter; Pande, Vijay S; Gallicchio, Emilio
2017-04-15
We present an algorithm to efficiently compute accurate volumes and surface areas of macromolecules on graphical processing unit (GPU) devices using an analytic model which represents atomic volumes by continuous Gaussian densities. The volume of the molecule is expressed by means of the inclusion-exclusion formula, which is based on the summation of overlap integrals among multiple atomic densities. The surface area of the molecule is obtained by differentiation of the molecular volume with respect to atomic radii. The many-body nature of the model makes a port to GPU devices challenging. To our knowledge, this is the first reported full implementation of this model on GPU hardware. To accomplish this, we have used recursive strategies to construct the tree of overlaps and to accumulate volumes and their gradients on the tree data structures so as to minimize memory contention. The algorithm is used in the formulation of a surface area-based non-polar implicit solvent model implemented as an open source plug-in (named GaussVol) for the popular OpenMM library for molecular mechanics modeling. GaussVol is 50 to 100 times faster than our best optimized implementation for the CPUs, achieving speeds in excess of 100 ns/day with 1 fs time-step for protein-sized systems on commodity GPUs. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
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NASA Astrophysics Data System (ADS)
Simon, E.; Bertino, L.; Samuelsen, A.
2011-12-01
Combined state-parameter estimation in ocean biogeochemical models with ensemble-based Kalman filters is a challenging task due to the non-linearity of the models, the constraints of positiveness that apply to the variables and parameters, and the non-Gaussian distribution of the variables in which they result. Furthermore, these models are sensitive to numerous parameters that are poorly known. Previous works [1] demonstrated that the Gaussian anamorphosis extensions of ensemble-based Kalman filters were relevant tools to perform combined state-parameter estimation in such non-Gaussian framework. In this study, we focus on the estimation of the grazing preferences parameters of zooplankton species. These parameters are introduced to model the diet of zooplankton species among phytoplankton species and detritus. They are positive values and their sum is equal to one. Because the sum-to-one constraint cannot be handled by ensemble-based Kalman filters, a reformulation of the parameterization is proposed. We investigate two types of changes of variables for the estimation of sum-to-one constrained parameters. The first one is based on Gelman [2] and leads to the estimation of normal distributed parameters. The second one is based on the representation of the unit sphere in spherical coordinates and leads to the estimation of parameters with bounded distributions (triangular or uniform). These formulations are illustrated and discussed in the framework of twin experiments realized in the 1D coupled model GOTM-NORWECOM with Gaussian anamorphosis extensions of the deterministic ensemble Kalman filter (DEnKF). [1] Simon E., Bertino L. : Gaussian anamorphosis extension of the DEnKF for combined state and parameter estimation : application to a 1D ocean ecosystem model. Journal of Marine Systems, 2011. doi :10.1016/j.jmarsys.2011.07.007 [2] Gelman A. : Method of Moments Using Monte Carlo Simulation. Journal of Computational and Graphical Statistics, 4, 1, 36-54, 1995.
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Fixing convergence of Gaussian belief propagation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Johnson, Jason K; Bickson, Danny; Dolev, Danny
Gaussian belief propagation (GaBP) is an iterative message-passing algorithm for inference in Gaussian graphical models. It is known that when GaBP converges it converges to the correct MAP estimate of the Gaussian random vector and simple sufficient conditions for its convergence have been established. In this paper we develop a double-loop algorithm for forcing convergence of GaBP. Our method computes the correct MAP estimate even in cases where standard GaBP would not have converged. We further extend this construction to compute least-squares solutions of over-constrained linear systems. We believe that our construction has numerous applications, since the GaBP algorithm ismore » linked to solution of linear systems of equations, which is a fundamental problem in computer science and engineering. As a case study, we discuss the linear detection problem. We show that using our new construction, we are able to force convergence of Montanari's linear detection algorithm, in cases where it would originally fail. As a consequence, we are able to increase significantly the number of users that can transmit concurrently.« less
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Gaussian graphical modeling reconstructs pathway reactions from high-throughput metabolomics data
2011-01-01
Background With the advent of high-throughput targeted metabolic profiling techniques, the question of how to interpret and analyze the resulting vast amount of data becomes more and more important. In this work we address the reconstruction of metabolic reactions from cross-sectional metabolomics data, that is without the requirement for time-resolved measurements or specific system perturbations. Previous studies in this area mainly focused on Pearson correlation coefficients, which however are generally incapable of distinguishing between direct and indirect metabolic interactions. Results In our new approach we propose the application of a Gaussian graphical model (GGM), an undirected probabilistic graphical model estimating the conditional dependence between variables. GGMs are based on partial correlation coefficients, that is pairwise Pearson correlation coefficients conditioned against the correlation with all other metabolites. We first demonstrate the general validity of the method and its advantages over regular correlation networks with computer-simulated reaction systems. Then we estimate a GGM on data from a large human population cohort, covering 1020 fasting blood serum samples with 151 quantified metabolites. The GGM is much sparser than the correlation network, shows a modular structure with respect to metabolite classes, and is stable to the choice of samples in the data set. On the example of human fatty acid metabolism, we demonstrate for the first time that high partial correlation coefficients generally correspond to known metabolic reactions. This feature is evaluated both manually by investigating specific pairs of high-scoring metabolites, and then systematically on a literature-curated model of fatty acid synthesis and degradation. Our method detects many known reactions along with possibly novel pathway interactions, representing candidates for further experimental examination. Conclusions In summary, we demonstrate strong signatures of intracellular pathways in blood serum data, and provide a valuable tool for the unbiased reconstruction of metabolic reactions from large-scale metabolomics data sets. PMID:21281499
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NASA Astrophysics Data System (ADS)
Urunkar, T. U.; Valkunde, A. T.; Vhanmore, B. D.; Gavade, K. M.; Patil, S. D.; Takale, M. V.
2018-05-01
It is quite known that critical power of the laser plays vital role in the propagation of Gaussian laser beam in collisionless plasma. The nonlinearity in dielectric constant considered herein is due to the ponderomotive force. In the present analysis, the interval of critical beam power has been explored to sustain the competition between diffraction and self-focusing of Gaussian laser beam during propagation in collisionless magnetized plasma. Differential equation for beam-width parameter has been established by using WKB and paraxial approximations under parabolic equation approach. The effect of critical power on the propagation of Gaussian laser beam has been presented graphically and discussed.
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NASA Astrophysics Data System (ADS)
Zhu, Kaicheng; Tang, Huiqin; Tang, Ying; Xia, Hui
2014-12-01
We proposed a scheme that converts a sine-Gaussian beam with an edge dislocation into a dark hollow beam with a vortex. Based on the gyrator transform (GT) relation, the closed-form field distribution of generalized sine-Gaussian beams passing through a GT system is derived; the intensity distribution and the corresponding phase distribution associated with the transforming generalized sine-Gaussian beams are analyzed. According to the numerical method, the distributions are graphically demonstrated and found that, for appropriate beam parameters and the GT angle, dark hollow vortex beams with topological charge 1 can be achieved using sine-Gaussian beams carrying an edge dislocation. Moreover, the orbital angular momentum content of a GT sine-Gaussian beam is analyzed. It is proved that the GT retains the odd- or even-order spiral harmonics structures of generalized sine-Gaussian beams in the transform process. In particular, it is wholly possible to convert an edge dislocation embedded in sine-Gaussian beams into a vortex with GT. The study also reveals that to obtain a dark hollow beam making use of GT of cos-Gaussian beams is impossible.
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Deng, Wenping; Zhang, Kui; Liu, Sanzhen; Zhao, Patrick; Xu, Shizhong; Wei, Hairong
2018-04-30
Joint reconstruction of multiple gene regulatory networks (GRNs) using gene expression data from multiple tissues/conditions is very important for understanding common and tissue/condition-specific regulation. However, there are currently no computational models and methods available for directly constructing such multiple GRNs that not only share some common hub genes but also possess tissue/condition-specific regulatory edges. In this paper, we proposed a new graphic Gaussian model for joint reconstruction of multiple gene regulatory networks (JRmGRN), which highlighted hub genes, using gene expression data from several tissues/conditions. Under the framework of Gaussian graphical model, JRmGRN method constructs the GRNs through maximizing a penalized log likelihood function. We formulated it as a convex optimization problem, and then solved it with an alternating direction method of multipliers (ADMM) algorithm. The performance of JRmGRN was first evaluated with synthetic data and the results showed that JRmGRN outperformed several other methods for reconstruction of GRNs. We also applied our method to real Arabidopsis thaliana RNA-seq data from two light regime conditions in comparison with other methods, and both common hub genes and some conditions-specific hub genes were identified with higher accuracy and precision. JRmGRN is available as a R program from: https://github.com/wenpingd. hairong@mtu.edu. Proof of theorem, derivation of algorithm and supplementary data are available at Bioinformatics online.
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Node-Based Learning of Multiple Gaussian Graphical Models
Mohan, Karthik; London, Palma; Fazel, Maryam; Witten, Daniela; Lee, Su-In
2014-01-01
We consider the problem of estimating high-dimensional Gaussian graphical models corresponding to a single set of variables under several distinct conditions. This problem is motivated by the task of recovering transcriptional regulatory networks on the basis of gene expression data containing heterogeneous samples, such as different disease states, multiple species, or different developmental stages. We assume that most aspects of the conditional dependence networks are shared, but that there are some structured differences between them. Rather than assuming that similarities and differences between networks are driven by individual edges, we take a node-based approach, which in many cases provides a more intuitive interpretation of the network differences. We consider estimation under two distinct assumptions: (1) differences between the K networks are due to individual nodes that are perturbed across conditions, or (2) similarities among the K networks are due to the presence of common hub nodes that are shared across all K networks. Using a row-column overlap norm penalty function, we formulate two convex optimization problems that correspond to these two assumptions. We solve these problems using an alternating direction method of multipliers algorithm, and we derive a set of necessary and sufficient conditions that allows us to decompose the problem into independent subproblems so that our algorithm can be scaled to high-dimensional settings. Our proposal is illustrated on synthetic data, a webpage data set, and a brain cancer gene expression data set. PMID:25309137
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A Hierarchical Poisson Log-Normal Model for Network Inference from RNA Sequencing Data
Gallopin, Mélina; Rau, Andrea; Jaffrézic, Florence
2013-01-01
Gene network inference from transcriptomic data is an important methodological challenge and a key aspect of systems biology. Although several methods have been proposed to infer networks from microarray data, there is a need for inference methods able to model RNA-seq data, which are count-based and highly variable. In this work we propose a hierarchical Poisson log-normal model with a Lasso penalty to infer gene networks from RNA-seq data; this model has the advantage of directly modelling discrete data and accounting for inter-sample variance larger than the sample mean. Using real microRNA-seq data from breast cancer tumors and simulations, we compare this method to a regularized Gaussian graphical model on log-transformed data, and a Poisson log-linear graphical model with a Lasso penalty on power-transformed data. For data simulated with large inter-sample dispersion, the proposed model performs better than the other methods in terms of sensitivity, specificity and area under the ROC curve. These results show the necessity of methods specifically designed for gene network inference from RNA-seq data. PMID:24147011
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Hypergeometric Gaussian beam and its propagation in turbulence
NASA Astrophysics Data System (ADS)
Eyyuboğlu, Halil Tanyer; Cai, Yangjian
2012-10-01
We study propagation characteristics of hypergeometric Gaussian beam in turbulence. In this context, we formulate the receiver plane intensity using extended Huygens-Fresnel integral. From the graphical results, it is seen that, after propagation, hypergeometric Gaussian will in general assume the shape of a dark hollow beam at topological charges other than zero. Increasing values of topological charge will make the beam broader with steeper walls. On the other hand, higher values of hollowness parameter will contract into a narrower shape. Raising the topological charge or the hollowness parameter individually will cause outer rings to appear. Both increased levels of turbulence and longer propagation distances will accelerate the beam evolution and help reach the final Gaussian shape sooner. At lower wavelengths, there will be less beam spreading.
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NASA Astrophysics Data System (ADS)
Maneri, E.; Gawronski, W.
1999-10-01
The linear quadratic Gaussian (LQG) design algorithms described in [2] and [5] have been used in the controller design of JPL's beam-waveguide [5] and 70-m [6] antennas. This algorithm significantly improves tracking precision in a windy environment. This article describes the graphical user interface (GUI) software for the design LQG controllers. It consists of two parts: the basic LQG design and the fine-tuning of the basic design using a constrained optimization algorithm. The presented GUI was developed to simplify the design process, to make the design process user-friendly, and to enable design of an LQG controller for one with a limited control engineering background. The user is asked to manipulate the GUI sliders and radio buttons to watch the antenna performance. Simple rules are given at the GUI display.
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Andrade, Xavier; Aspuru-Guzik, Alán
2013-10-08
We discuss the application of graphical processing units (GPUs) to accelerate real-space density functional theory (DFT) calculations. To make our implementation efficient, we have developed a scheme to expose the data parallelism available in the DFT approach; this is applied to the different procedures required for a real-space DFT calculation. We present results for current-generation GPUs from AMD and Nvidia, which show that our scheme, implemented in the free code Octopus, can reach a sustained performance of up to 90 GFlops for a single GPU, representing a significant speed-up when compared to the CPU version of the code. Moreover, for some systems, our implementation can outperform a GPU Gaussian basis set code, showing that the real-space approach is a competitive alternative for DFT simulations on GPUs.
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Gaussian graphical modeling reveals specific lipid correlations in glioblastoma cells
NASA Astrophysics Data System (ADS)
Mueller, Nikola S.; Krumsiek, Jan; Theis, Fabian J.; Böhm, Christian; Meyer-Bäse, Anke
2011-06-01
Advances in high-throughput measurements of biological specimens necessitate the development of biologically driven computational techniques. To understand the molecular level of many human diseases, such as cancer, lipid quantifications have been shown to offer an excellent opportunity to reveal disease-specific regulations. The data analysis of the cell lipidome, however, remains a challenging task and cannot be accomplished solely based on intuitive reasoning. We have developed a method to identify a lipid correlation network which is entirely disease-specific. A powerful method to correlate experimentally measured lipid levels across the various samples is a Gaussian Graphical Model (GGM), which is based on partial correlation coefficients. In contrast to regular Pearson correlations, partial correlations aim to identify only direct correlations while eliminating indirect associations. Conventional GGM calculations on the entire dataset can, however, not provide information on whether a correlation is truly disease-specific with respect to the disease samples and not a correlation of control samples. Thus, we implemented a novel differential GGM approach unraveling only the disease-specific correlations, and applied it to the lipidome of immortal Glioblastoma tumor cells. A large set of lipid species were measured by mass spectrometry in order to evaluate lipid remodeling as a result to a combination of perturbation of cells inducing programmed cell death, while the other perturbations served solely as biological controls. With the differential GGM, we were able to reveal Glioblastoma-specific lipid correlations to advance biomedical research on novel gene therapies.
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León, Larry F; Cai, Tianxi
2012-04-01
In this paper we develop model checking techniques for assessing functional form specifications of covariates in censored linear regression models. These procedures are based on a censored data analog to taking cumulative sums of "robust" residuals over the space of the covariate under investigation. These cumulative sums are formed by integrating certain Kaplan-Meier estimators and may be viewed as "robust" censored data analogs to the processes considered by Lin, Wei & Ying (2002). The null distributions of these stochastic processes can be approximated by the distributions of certain zero-mean Gaussian processes whose realizations can be generated by computer simulation. Each observed process can then be graphically compared with a few realizations from the Gaussian process. We also develop formal test statistics for numerical comparison. Such comparisons enable one to assess objectively whether an apparent trend seen in a residual plot reects model misspecification or natural variation. We illustrate the methods with a well known dataset. In addition, we examine the finite sample performance of the proposed test statistics in simulation experiments. In our simulation experiments, the proposed test statistics have good power of detecting misspecification while at the same time controlling the size of the test.
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Generation of dark hollow beams by using a fractional radial Hilbert transform system
NASA Astrophysics Data System (ADS)
Xie, Qiansen; Zhao, Daomu
2007-07-01
The radial Hilbert transform has been extend to the fractional field, which could be called the fractional radial Hilbert transform (FRHT). Using edge-enhancement characteristics of this transform, we convert a Gaussian light beam into a variety of dark hollow beams (DHBs). Based on the fact that a hard-edged aperture can be expanded approximately as a finite sum of complex Gaussian functions, the analytical expression of a Gaussian beam passing through a FRHT system has been derived. As a numerical example, the properties of the DHBs with different fractional orders are illustrated graphically. The calculation results obtained by use of the analytical method and the integral method are also compared.
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Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization
NASA Technical Reports Server (NTRS)
Simpson, Timothy W.; Korte, John J.; Mauery, Timothy M.; Mistree, Farrokh
1998-01-01
In this paper, we compare and contrast the use of second-order response surface models and kriging models for approximating non-random, deterministic computer analyses. After reviewing the response surface method for constructing polynomial approximations, kriging is presented as an alternative approximation method for the design and analysis of computer experiments. Both methods are applied to the multidisciplinary design of an aerospike nozzle which consists of a computational fluid dynamics model and a finite-element model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations, and four optimization problems m formulated and solved using both sets of approximation models. The second-order response surface models and kriging models-using a constant underlying global model and a Gaussian correlation function-yield comparable results.
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Ortiz, Andrés; Munilla, Jorge; Álvarez-Illán, Ignacio; Górriz, Juan M; Ramírez, Javier
2015-01-01
Alzheimer's Disease (AD) is the most common neurodegenerative disease in elderly people. Its development has been shown to be closely related to changes in the brain connectivity network and in the brain activation patterns along with structural changes caused by the neurodegenerative process. Methods to infer dependence between brain regions are usually derived from the analysis of covariance between activation levels in the different areas. However, these covariance-based methods are not able to estimate conditional independence between variables to factor out the influence of other regions. Conversely, models based on the inverse covariance, or precision matrix, such as Sparse Gaussian Graphical Models allow revealing conditional independence between regions by estimating the covariance between two variables given the rest as constant. This paper uses Sparse Inverse Covariance Estimation (SICE) methods to learn undirected graphs in order to derive functional and structural connectivity patterns from Fludeoxyglucose (18F-FDG) Position Emission Tomography (PET) data and segmented Magnetic Resonance images (MRI), drawn from the ADNI database, for Control, MCI (Mild Cognitive Impairment Subjects), and AD subjects. Sparse computation fits perfectly here as brain regions usually only interact with a few other areas. The models clearly show different metabolic covariation patters between subject groups, revealing the loss of strong connections in AD and MCI subjects when compared to Controls. Similarly, the variance between GM (Gray Matter) densities of different regions reveals different structural covariation patterns between the different groups. Thus, the different connectivity patterns for controls and AD are used in this paper to select regions of interest in PET and GM images with discriminative power for early AD diagnosis. Finally, functional an structural models are combined to leverage the classification accuracy. The results obtained in this work show the usefulness of the Sparse Gaussian Graphical models to reveal functional and structural connectivity patterns. This information provided by the sparse inverse covariance matrices is not only used in an exploratory way but we also propose a method to use it in a discriminative way. Regression coefficients are used to compute reconstruction errors for the different classes that are then introduced in a SVM for classification. Classification experiments performed using 68 Controls, 70 AD, and 111 MCI images and assessed by cross-validation show the effectiveness of the proposed method.
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Lactation is associated with altered metabolomic signatures in women with gestational diabetes.
Much, Daniela; Beyerlein, Andreas; Kindt, Alida; Krumsiek, Jan; Stückler, Ferdinand; Rossbauer, Michaela; Hofelich, Anna; Wiesenäcker, David; Hivner, Susanne; Herbst, Melanie; Römisch-Margl, Werner; Prehn, Cornelia; Adamski, Jerzy; Kastenmüller, Gabi; Theis, Fabian; Ziegler, Anette-G; Hummel, Sandra
2016-10-01
Lactation for >3 months in women with gestational diabetes is associated with a reduced risk of type 2 diabetes that persists for up to 15 years postpartum. However, the underlying mechanisms are unknown. We examined whether in women with gestational diabetes lactation for >3 months is associated with altered metabolomic signatures postpartum. We enrolled 197 women with gestational diabetes at a median of 3.6 years (interquartile range 0.7-6.5 years) after delivery. Targeted metabolomics profiles (including 156 metabolites) were obtained during a glucose challenge test. Comparisons of metabolite concentrations and ratios between women who lactated for >3 months and women who lactated for ≤3 months or not at all were performed using linear regression with adjustment for age and BMI at the postpartum visit, time since delivery, and maternal education level, and correction for multiple testing. Gaussian graphical modelling was used to generate metabolite networks. Lactation for >3 months was associated with a higher total lysophosphatidylcholine/total phosphatidylcholine ratio; in women with short-term follow-up, it was also associated with lower leucine concentrations and a lower total branched-chain amino acid concentration. Gaussian graphical modelling identified subgroups of closely linked metabolites within phosphatidylcholines and branched-chain amino acids that were affected by lactation for >3 months and have been linked to the pathophysiology of type 2 diabetes in previous studies. Lactation for >3 months in women with gestational diabetes is associated with changes in the metabolomics profile that have been linked to the early pathogenesis of type 2 diabetes.
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Beam wander of dark hollow, flat-topped and annular beams
NASA Astrophysics Data System (ADS)
Eyyuboğlu, H. T.; Çil, C. Z.
2008-11-01
Benefiting from the earlier derivations for the Gaussian beam, we formulate beam wander for dark hollow (DH) and flat-topped (FT) beams, also covering the annular Gaussian (AG) beam as a special case. Via graphical illustrations, beam wander variations of these beams are analyzed and compared among themselves and to the fundamental Gaussian beam against changes in propagation length, amplitude factor, source size, wavelength of operation, inner and outer scales of turbulence. These comparisons show that in relation to the fundamental Gaussian beam, DH and FT beams will exhibit less beam wander, particularly at small primary beam source sizes, lower amplitude factors of the secondary beam and higher beam orders. Furthermore, DH and FT beams will continue to preserve this advantageous position all throughout the considered range of wavelengths, inner and outer scales of turbulence. FT beams, in particular, are observed to have the smallest beam wander values among all, up to certain source sizes.
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NASA Astrophysics Data System (ADS)
Mao, Jin-Jin; Tian, Shou-Fu; Zou, Li; Zhang, Tian-Tian
2018-05-01
In this paper, we consider a generalized Hirota equation with a bounded potential, which can be used to describe the propagation properties of optical soliton solutions. By employing the hypothetical method and the sub-equation method, we construct the bright soliton, dark soliton, complexitons and Gaussian soliton solutions of the Hirota equation. Moreover, we explicitly derive the power series solutions with their convergence analysis. Finally, we provide the graphical analysis of such soliton solutions in order to better understand their dynamical behavior.
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A Poisson Log-Normal Model for Constructing Gene Covariation Network Using RNA-seq Data.
Choi, Yoonha; Coram, Marc; Peng, Jie; Tang, Hua
2017-07-01
Constructing expression networks using transcriptomic data is an effective approach for studying gene regulation. A popular approach for constructing such a network is based on the Gaussian graphical model (GGM), in which an edge between a pair of genes indicates that the expression levels of these two genes are conditionally dependent, given the expression levels of all other genes. However, GGMs are not appropriate for non-Gaussian data, such as those generated in RNA-seq experiments. We propose a novel statistical framework that maximizes a penalized likelihood, in which the observed count data follow a Poisson log-normal distribution. To overcome the computational challenges, we use Laplace's method to approximate the likelihood and its gradients, and apply the alternating directions method of multipliers to find the penalized maximum likelihood estimates. The proposed method is evaluated and compared with GGMs using both simulated and real RNA-seq data. The proposed method shows improved performance in detecting edges that represent covarying pairs of genes, particularly for edges connecting low-abundant genes and edges around regulatory hubs.
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Theoretical analysis of non-Gaussian heterogeneity effects on subsurface flow and transport
NASA Astrophysics Data System (ADS)
Riva, Monica; Guadagnini, Alberto; Neuman, Shlomo P.
2017-04-01
Much of the stochastic groundwater literature is devoted to the analysis of flow and transport in Gaussian or multi-Gaussian log hydraulic conductivity (or transmissivity) fields, Y(x)=ln\\func K(x) (x being a position vector), characterized by one or (less frequently) a multiplicity of spatial correlation scales. Yet Y and many other variables and their (spatial or temporal) increments, ΔY, are known to be generally non-Gaussian. One common manifestation of non-Gaussianity is that whereas frequency distributions of Y often exhibit mild peaks and light tails, those of increments ΔY are generally symmetric with peaks that grow sharper, and tails that become heavier, as separation scale or lag between pairs of Y values decreases. A statistical model that captures these disparate, scale-dependent distributions of Y and ΔY in a unified and consistent manner has been recently proposed by us. This new "generalized sub-Gaussian (GSG)" model has the form Y(x)=U(x)G(x) where G(x) is (generally, but not necessarily) a multiscale Gaussian random field and U(x) is a nonnegative subordinator independent of G. The purpose of this paper is to explore analytically, in an elementary manner, lead-order effects that non-Gaussian heterogeneity described by the GSG model have on the stochastic description of flow and transport. Recognizing that perturbation expansion of hydraulic conductivity K=eY diverges when Y is sub-Gaussian, we render the expansion convergent by truncating Y's domain of definition. We then demonstrate theoretically and illustrate by way of numerical examples that, as the domain of truncation expands, (a) the variance of truncated Y (denoted by Yt) approaches that of Y and (b) the pdf (and thereby moments) of Yt increments approach those of Y increments and, as a consequence, the variogram of Yt approaches that of Y. This in turn guarantees that perturbing Kt=etY to second order in σYt (the standard deviation of Yt) yields results which approach those we obtain upon perturbing K=eY to second order in σY even as the corresponding series diverges. Our analysis is rendered mathematically tractable by considering mean-uniform steady state flow in an unbounded, two-dimensional domain of mildly heterogeneous Y with a single-scale function G having an isotropic exponential covariance. Results consist of expressions for (a) lead-order autocovariance and cross-covariance functions of hydraulic head, velocity, and advective particle displacement and (b) analogues of preasymptotic as well as asymptotic Fickian dispersion coefficients. We compare these theoretically and graphically with corresponding expressions developed in the literature for Gaussian Y. We find the former to differ from the latter by a factor k =
/2 ( <> denoting ensemble expectation) and the GSG covariance of longitudinal velocity to contain an additional nugget term depending on this same factor. In the limit as Y becomes Gaussian, k reduces to one and the nugget term drops out. -
NASA Astrophysics Data System (ADS)
Franta, Daniel; Nečas, David; Giglia, Angelo; Franta, Pavel; Ohlídal, Ivan
2017-11-01
Optical characterization of magnesium fluoride thin films is performed in a wide spectral range from far infrared to extreme ultraviolet (0.01-45 eV) utilizing the universal dispersion model. Two film defects, i.e. random roughness of the upper boundaries and defect transition layer at lower boundary are taken into account. An extension of universal dispersion model consisting in expressing the excitonic contributions as linear combinations of Gaussian and truncated Lorentzian terms is introduced. The spectral dependencies of the optical constants are presented in a graphical form and by the complete set of dispersion parameters that allows generating tabulated optical constants with required range and step using a simple utility in the newAD2 software package.
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GPU-based optimal control for RWM feedback in tokamaks
Clement, Mitchell; Hanson, Jeremy; Bialek, Jim; ...
2017-08-23
The design and implementation of a Graphics Processing Unit (GPU) based Resistive Wall Mode (RWM) controller to perform feedback control on the RWM using Linear Quadratic Gaussian (LQG) control is reported herein. Also, the control algorithm is based on a simplified DIII-D VALEN model. By using NVIDIA’s GPUDirect RDMA framework, the digitizer and output module are able to write and read directly to and from GPU memory, eliminating memory transfers between host and GPU. In conclusion, the system and algorithm was able to reduce plasma response excited by externally applied fields by 32% during development experiments.
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GPU-based optimal control for RWM feedback in tokamaks
DOE Office of Scientific and Technical Information (OSTI.GOV)
Clement, Mitchell; Hanson, Jeremy; Bialek, Jim
The design and implementation of a Graphics Processing Unit (GPU) based Resistive Wall Mode (RWM) controller to perform feedback control on the RWM using Linear Quadratic Gaussian (LQG) control is reported herein. Also, the control algorithm is based on a simplified DIII-D VALEN model. By using NVIDIA’s GPUDirect RDMA framework, the digitizer and output module are able to write and read directly to and from GPU memory, eliminating memory transfers between host and GPU. In conclusion, the system and algorithm was able to reduce plasma response excited by externally applied fields by 32% during development experiments.
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Circular Probable Error for Circular and Noncircular Gaussian Impacts
2012-09-01
1M simulated impacts ph(k)=mean(imp(:,1).^2+imp(:,2).^2<=CEP^2); % hit frequency on CEP end phit (j)=mean(ph...avg 100 hit frequencies to “incr n” end % GRAPHICS plot(i, phit ,’r-’); % error exponent versus Ph estimate
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NASA Technical Reports Server (NTRS)
Simpson, Timothy W.
1998-01-01
The use of response surface models and kriging models are compared for approximating non-random, deterministic computer analyses. After discussing the traditional response surface approach for constructing polynomial models for approximation, kriging is presented as an alternative statistical-based approximation method for the design and analysis of computer experiments. Both approximation methods are applied to the multidisciplinary design and analysis of an aerospike nozzle which consists of a computational fluid dynamics model and a finite element analysis model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations. Four optimization problems are formulated and solved using both approximation models. While neither approximation technique consistently outperforms the other in this example, the kriging models using only a constant for the underlying global model and a Gaussian correlation function perform as well as the second order polynomial response surface models.
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Profiler - A Fast and Versatile New Program for Decomposing Galaxy Light Profiles
NASA Astrophysics Data System (ADS)
Ciambur, Bogdan C.
2016-12-01
I introduce Profiler, a user-friendly program designed to analyse the radial surface brightness profiles of galaxies. With an intuitive graphical user interface, Profiler can accurately model galaxies of a broad range of morphological types, with various parametric functions routinely employed in the field (Sérsic, core-Sérsic, exponential, Gaussian, Moffat, and Ferrers). In addition to these, Profiler can employ the broken exponential model for disc truncations or anti-truncations, and two special cases of the edge-on disc model: along the disc's major or minor axis. The convolution of (circular or elliptical) models with the point spread function is performed in 2D, and offers a choice between Gaussian, Moffat or a user-provided profile for the point spread function. Profiler is optimised to work with galaxy light profiles obtained from isophotal measurements, which allow for radial gradients in the geometric parameters of the isophotes, and are thus often better at capturing the total light than 2D image-fitting programs. Additionally, the 1D approach is generally less computationally expensive and more stable. I demonstrate Profiler's features by decomposing three case-study galaxies: the cored elliptical galaxy NGC 3348, the nucleated dwarf Seyfert I galaxy Pox 52, and NGC 2549, a double-barred galaxy with an edge-on, truncated disc.
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Optimizing Cubature for Efficient Integration of Subspace Deformations
An, Steven S.; Kim, Theodore; James, Doug L.
2009-01-01
We propose an efficient scheme for evaluating nonlinear subspace forces (and Jacobians) associated with subspace deformations. The core problem we address is efficient integration of the subspace force density over the 3D spatial domain. Similar to Gaussian quadrature schemes that efficiently integrate functions that lie in particular polynomial subspaces, we propose cubature schemes (multi-dimensional quadrature) optimized for efficient integration of force densities associated with particular subspace deformations, particular materials, and particular geometric domains. We support generic subspace deformation kinematics, and nonlinear hyperelastic materials. For an r-dimensional deformation subspace with O(r) cubature points, our method is able to evaluate subspace forces at O(r2) cost. We also describe composite cubature rules for runtime error estimation. Results are provided for various subspace deformation models, several hyperelastic materials (St.Venant-Kirchhoff, Mooney-Rivlin, Arruda-Boyce), and multimodal (graphics, haptics, sound) applications. We show dramatically better efficiency than traditional Monte Carlo integration. CR Categories: I.6.8 [Simulation and Modeling]: Types of Simulation—Animation, I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Physically based modeling G.1.4 [Mathematics of Computing]: Numerical Analysis—Quadrature and Numerical Differentiation PMID:19956777
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NASA Astrophysics Data System (ADS)
Mert, Bayram Ali; Dag, Ahmet
2017-12-01
In this study, firstly, a practical and educational geostatistical program (JeoStat) was developed, and then example analysis of porosity parameter distribution, using oilfield data, was presented. With this program, two or three-dimensional variogram analysis can be performed by using normal, log-normal or indicator transformed data. In these analyses, JeoStat offers seven commonly used theoretical variogram models (Spherical, Gaussian, Exponential, Linear, Generalized Linear, Hole Effect and Paddington Mix) to the users. These theoretical models can be easily and quickly fitted to experimental models using a mouse. JeoStat uses ordinary kriging interpolation technique for computation of point or block estimate, and also uses cross-validation test techniques for validation of the fitted theoretical model. All the results obtained by the analysis as well as all the graphics such as histogram, variogram and kriging estimation maps can be saved to the hard drive, including digitised graphics and maps. As such, the numerical values of any point in the map can be monitored using a mouse and text boxes. This program is available to students, researchers, consultants and corporations of any size free of charge. The JeoStat software package and source codes available at: http://www.jeostat.com/JeoStat_2017.0.rar.
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Effects of the interaction range on structural phases of flexible polymers.
Gross, J; Neuhaus, T; Vogel, T; Bachmann, M
2013-02-21
We systematically investigate how the range of interaction between non-bonded monomers influences the formation of structural phases of elastic, flexible polymers. Massively parallel replica-exchange simulations of a generic, coarse-grained model, performed partly on graphics processing units and in multiple-gaussian modified ensembles, pave the way for the construction of the structural phase diagram, parametrized by interaction range and temperature. Conformational transitions between gas-like, liquid, and diverse solid (pseudo) phases are identified by microcanonical statistical inflection-point analysis. We find evidence for finite-size effects that cause the crossover of "collapse" and "freezing" transitions for very short interaction ranges.
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GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA
NASA Astrophysics Data System (ADS)
Spiechowicz, J.; Kostur, M.; Machura, L.
2015-06-01
This work presents an updated and extended guide on methods of a proper acceleration of the Monte Carlo integration of stochastic differential equations with the commonly available NVIDIA Graphics Processing Units using the CUDA programming environment. We outline the general aspects of the scientific computing on graphics cards and demonstrate them with two models of a well known phenomenon of the noise induced transport of Brownian motors in periodic structures. As a source of fluctuations in the considered systems we selected the three most commonly occurring noises: the Gaussian white noise, the white Poissonian noise and the dichotomous process also known as a random telegraph signal. The detailed discussion on various aspects of the applied numerical schemes is also presented. The measured speedup can be of the astonishing order of about 3000 when compared to a typical CPU. This number significantly expands the range of problems solvable by use of stochastic simulations, allowing even an interactive research in some cases.
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High-performance dynamic quantum clustering on graphics processors
DOE Office of Scientific and Technical Information (OSTI.GOV)
Wittek, Peter, E-mail: peterwittek@acm.org
2013-01-15
Clustering methods in machine learning may benefit from borrowing metaphors from physics. Dynamic quantum clustering associates a Gaussian wave packet with the multidimensional data points and regards them as eigenfunctions of the Schroedinger equation. The clustering structure emerges by letting the system evolve and the visual nature of the algorithm has been shown to be useful in a range of applications. Furthermore, the method only uses matrix operations, which readily lend themselves to parallelization. In this paper, we develop an implementation on graphics hardware and investigate how this approach can accelerate the computations. We achieve a speedup of up tomore » two magnitudes over a multicore CPU implementation, which proves that quantum-like methods and acceleration by graphics processing units have a great relevance to machine learning.« less
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A Graphical Model of Smoking-Induced Global Instability in Lung Cancer.
Wang, Yanbo; Qian, Weikang; Yuan, Bo
2018-01-01
Smoking is the major cause of lung cancer and the leading cause of cancer-related death in the world. The most current view about lung cancer is no longer limited to individual genes being mutated by any carcinogenic insults from smoking. Instead, tumorigenesis is a phenotype conferred by many systematic and global alterations, leading to extensive heterogeneity and variation for both the genotypes and phenotypes of individual cancer cells. Thus, strategically it is foremost important to develop a methodology to capture any consistent and global alterations presumably shared by most of the cancerous cells for a given population. This is particularly true that almost all of the data collected from solid cancers (including lung cancers) are usually distant apart over a large span of temporal or even spatial contexts. Here, we report a multiple non-Gaussian graphical model to reconstruct the gene interaction network using two previously published gene expression datasets. Our graphical model aims to selectively detect gross structural changes at the level of gene interaction networks. Our methodology is extensively validated, demonstrating good robustness, as well as the selectivity and specificity expected based on our biological insights. In summary, gene regulatory networks are still relatively stable during presumably the early stage of neoplastic transformation. But drastic structural differences can be found between lung cancer and its normal control, including the gain of functional modules for cellular proliferations such as EGFR and PDGFRA, as well as the lost of the important IL6 module, supporting their roles as potential drug targets. Interestingly, our method can also detect early modular changes, with the ALDH3A1 and its associated interactions being strongly implicated as a potential early marker, whose activations appear to alter LCN2 module as well as its interactions with the important TP53-MDM2 circuitry. Our strategy using the graphical model to reconstruct gene interaction work with biologically-inspired constraints exemplifies the importance and beauty of biology in developing any bio-computational approach.
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NASA Astrophysics Data System (ADS)
Jain, Varun; Biesinger, Mark C.; Linford, Matthew R.
2018-07-01
X-ray photoelectron spectroscopy (XPS) is arguably the most important vacuum technique for surface chemical analysis, and peak fitting is an indispensable part of XPS data analysis. Functions that have been widely explored and used in XPS peak fitting include the Gaussian, Lorentzian, Gaussian-Lorentzian sum (GLS), Gaussian-Lorentzian product (GLP), and Voigt functions, where the Voigt function is a convolution of a Gaussian and a Lorentzian function. In this article we discuss these functions from a graphical perspective. Arguments based on convolution and the Central Limit Theorem are made to justify the use of functions that are intermediate between pure Gaussians and pure Lorentzians in XPS peak fitting. Mathematical forms for the GLS and GLP functions are presented with a mixing parameter m. Plots are shown for GLS and GLP functions with mixing parameters ranging from 0 to 1. There are fundamental differences between the GLS and GLP functions. The GLS function better follows the 'wings' of the Lorentzian, while these 'wings' are suppressed in the GLP. That is, these two functions are not interchangeable. The GLS and GLP functions are compared to the Voigt function, where the GLS is shown to be a decent approximation of it. Practically, both the GLS and the GLP functions can be useful for XPS peak fitting. Examples of the uses of these functions are provided herein.
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Technical notes and correspondence: Stochastic robustness of linear time-invariant control systems
NASA Technical Reports Server (NTRS)
Stengel, Robert F.; Ray, Laura R.
1991-01-01
A simple numerical procedure for estimating the stochastic robustness of a linear time-invariant system is described. Monte Carlo evaluations of the system's eigenvalues allows the probability of instability and the related stochastic root locus to be estimated. This analysis approach treats not only Gaussian parameter uncertainties but non-Gaussian cases, including uncertain-but-bounded variation. Confidence intervals for the scalar probability of instability address computational issues inherent in Monte Carlo simulation. Trivial extensions of the procedure admit consideration of alternate discriminants; thus, the probabilities that stipulated degrees of instability will be exceeded or that closed-loop roots will leave desirable regions can also be estimated. Results are particularly amenable to graphical presentation.
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Stable stress‐drop measurements and their variability: Implications for ground‐motion prediction
Hanks, Thomas C.; Baltay, Annemarie S.; Beroza, Gregory C.
2013-01-01
We estimate the arms‐stress drop, Graphic, (Hanks, 1979) using acceleration time records of 59 earthquakes from two earthquake sequences in eastern Honshu, Japan. These acceleration‐based static stress drops compare well to stress drops calculated for the same events by Baltay et al. (2011) using an empirical Green’s function (eGf) approach. This agreement supports the assumption that earthquake acceleration time histories in the bandwidth between the corner frequency and a maximum observed frequency can be considered white, Gaussian, noise. Although the Graphic is computationally simpler than the eGf‐based Graphic‐stress drop, and is used as the “stress parameter” to describe the earthquake source in ground‐motion prediction equations, we find that it only compares well to the Graphic at source‐station distances of ∼20 km or less because there is no consideration of whole‐path anelastic attenuation or scattering. In these circumstances, the correlation between the Graphic and Graphic is strong. Events with high and low stress drops obtained through the eGf method have similarly high and low Graphic. We find that the inter‐event standard deviation of stress drop, for the population of earthquakes considered, is similar for both methods, 0.40 for the Graphic method and 0.42 for the Graphic, in log10 units, provided we apply the ∼20 km distance restriction to Graphic. This indicates that the observed variability is inherent to the source, rather than attributable to uncertainties in stress‐drop estimates
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Statistical, Graphical, and Learning Methods for Sensing, Surveillance, and Navigation Systems
2016-06-28
harsh propagation environments. Conventional filtering techniques fail to provide satisfactory performance in many important nonlinear or non...Gaussian scenarios. In addition, there is a lack of a unified methodology for the design and analysis of different filtering techniques. To address...these problems, we have proposed a new filtering methodology called belief condensation (BC) DISTRIBUTION A: Distribution approved for public release
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Study of information transfer optimization for communication satellites
NASA Technical Reports Server (NTRS)
Odenwalder, J. P.; Viterbi, A. J.; Jacobs, I. M.; Heller, J. A.
1973-01-01
The results are presented of a study of source coding, modulation/channel coding, and systems techniques for application to teleconferencing over high data rate digital communication satellite links. Simultaneous transmission of video, voice, data, and/or graphics is possible in various teleconferencing modes and one-way, two-way, and broadcast modes are considered. A satellite channel model including filters, limiter, a TWT, detectors, and an optimized equalizer is treated in detail. A complete analysis is presented for one set of system assumptions which exclude nonlinear gain and phase distortion in the TWT. Modulation, demodulation, and channel coding are considered, based on an additive white Gaussian noise channel model which is an idealization of an equalized channel. Source coding with emphasis on video data compression is reviewed, and the experimental facility utilized to test promising techniques is fully described.
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A comparative study of nonparametric methods for pattern recognition
NASA Technical Reports Server (NTRS)
Hahn, S. F.; Nelson, G. D.
1972-01-01
The applied research discussed in this report determines and compares the correct classification percentage of the nonparametric sign test, Wilcoxon's signed rank test, and K-class classifier with the performance of the Bayes classifier. The performance is determined for data which have Gaussian, Laplacian and Rayleigh probability density functions. The correct classification percentage is shown graphically for differences in modes and/or means of the probability density functions for four, eight and sixteen samples. The K-class classifier performed very well with respect to the other classifiers used. Since the K-class classifier is a nonparametric technique, it usually performed better than the Bayes classifier which assumes the data to be Gaussian even though it may not be. The K-class classifier has the advantage over the Bayes in that it works well with non-Gaussian data without having to determine the probability density function of the data. It should be noted that the data in this experiment was always unimodal.
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NASA Astrophysics Data System (ADS)
Patil, S. D.; Valkunde, A. T.; Vhanmore, B. D.; Urunkar, T. U.; Gavade, K. M.; Takale, M. V.
2018-05-01
When inter particle distance is comparable to the de Broglies wavelength of charged particles, quantum effects in plasmas are unavoidable. We have exploited an influence of light absorption on self-focusing of Gaussian laser beam in cold quantum plasma by considering relativistic nonlinearity. Nonlinear differential equation governing beam-width parameter has been established by using parabolic equation approach under paraxial and WKB approximations. The effect of light absorption on variation of beam-width parameter with dimensionless distance of propagation is presented graphically and discussed. It is found that light absorption plays vital role in weakening the relativistic self-focusing of laser beam during propagation in cold quantum plasma and gives reasonably interesting results.
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SMURC: High-Dimension Small-Sample Multivariate Regression With Covariance Estimation.
Bayar, Belhassen; Bouaynaya, Nidhal; Shterenberg, Roman
2017-03-01
We consider a high-dimension low sample-size multivariate regression problem that accounts for correlation of the response variables. The system is underdetermined as there are more parameters than samples. We show that the maximum likelihood approach with covariance estimation is senseless because the likelihood diverges. We subsequently propose a normalization of the likelihood function that guarantees convergence. We call this method small-sample multivariate regression with covariance (SMURC) estimation. We derive an optimization problem and its convex approximation to compute SMURC. Simulation results show that the proposed algorithm outperforms the regularized likelihood estimator with known covariance matrix and the sparse conditional Gaussian graphical model. We also apply SMURC to the inference of the wing-muscle gene network of the Drosophila melanogaster (fruit fly).
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NASA Astrophysics Data System (ADS)
Schwartz, Craig R.; Thelen, Brian J.; Kenton, Arthur C.
1995-06-01
A statistical parametric multispectral sensor performance model was developed by ERIM to support mine field detection studies, multispectral sensor design/performance trade-off studies, and target detection algorithm development. The model assumes target detection algorithms and their performance models which are based on data assumed to obey multivariate Gaussian probability distribution functions (PDFs). The applicability of these algorithms and performance models can be generalized to data having non-Gaussian PDFs through the use of transforms which convert non-Gaussian data to Gaussian (or near-Gaussian) data. An example of one such transform is the Box-Cox power law transform. In practice, such a transform can be applied to non-Gaussian data prior to the introduction of a detection algorithm that is formally based on the assumption of multivariate Gaussian data. This paper presents an extension of these techniques to the case where the joint multivariate probability density function of the non-Gaussian input data is known, and where the joint estimate of the multivariate Gaussian statistics, under the Box-Cox transform, is desired. The jointly estimated multivariate Gaussian statistics can then be used to predict the performance of a target detection algorithm which has an associated Gaussian performance model.
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Particle Filtering for Model-Based Anomaly Detection in Sensor Networks
NASA Technical Reports Server (NTRS)
Solano, Wanda; Banerjee, Bikramjit; Kraemer, Landon
2012-01-01
A novel technique has been developed for anomaly detection of rocket engine test stand (RETS) data. The objective was to develop a system that postprocesses a csv file containing the sensor readings and activities (time-series) from a rocket engine test, and detects any anomalies that might have occurred during the test. The output consists of the names of the sensors that show anomalous behavior, and the start and end time of each anomaly. In order to reduce the involvement of domain experts significantly, several data-driven approaches have been proposed where models are automatically acquired from the data, thus bypassing the cost and effort of building system models. Many supervised learning methods can efficiently learn operational and fault models, given large amounts of both nominal and fault data. However, for domains such as RETS data, the amount of anomalous data that is actually available is relatively small, making most supervised learning methods rather ineffective, and in general met with limited success in anomaly detection. The fundamental problem with existing approaches is that they assume that the data are iid, i.e., independent and identically distributed, which is violated in typical RETS data. None of these techniques naturally exploit the temporal information inherent in time series data from the sensor networks. There are correlations among the sensor readings, not only at the same time, but also across time. However, these approaches have not explicitly identified and exploited such correlations. Given these limitations of model-free methods, there has been renewed interest in model-based methods, specifically graphical methods that explicitly reason temporally. The Gaussian Mixture Model (GMM) in a Linear Dynamic System approach assumes that the multi-dimensional test data is a mixture of multi-variate Gaussians, and fits a given number of Gaussian clusters with the help of the wellknown Expectation Maximization (EM) algorithm. The parameters thus learned are used for calculating the joint distribution of the observations. However, this GMM assumption is essentially an approximation and signals the potential viability of non-parametric density estimators. This is the key idea underlying the new approach.
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Yuan, Jing; Yeung, David Ka Wai; Mok, Greta S P; Bhatia, Kunwar S; Wang, Yi-Xiang J; Ahuja, Anil T; King, Ann D
2014-01-01
To technically investigate the non-Gaussian diffusion of head and neck diffusion weighted imaging (DWI) at 3 Tesla and compare advanced non-Gaussian diffusion models, including diffusion kurtosis imaging (DKI), stretched-exponential model (SEM), intravoxel incoherent motion (IVIM) and statistical model in the patients with nasopharyngeal carcinoma (NPC). After ethics approval was granted, 16 patients with NPC were examined using DWI performed at 3T employing an extended b-value range from 0 to 1500 s/mm(2). DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models on primary tumor, metastatic node, spinal cord and muscle. Non-Gaussian parameter maps were generated and compared to apparent diffusion coefficient (ADC) maps in NPC. Diffusion in NPC exhibited non-Gaussian behavior at the extended b-value range. Non-Gaussian models achieved significantly better fitting of DWI signal than the mono-exponential model. Non-Gaussian diffusion coefficients were substantially different from mono-exponential ADC both in magnitude and histogram distribution. Non-Gaussian diffusivity in head and neck tissues and NPC lesions could be assessed by using non-Gaussian diffusion models. Non-Gaussian DWI analysis may reveal additional tissue properties beyond ADC and holds potentials to be used as a complementary tool for NPC characterization.
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Inferring network structure in non-normal and mixed discrete-continuous genomic data.
Bhadra, Anindya; Rao, Arvind; Baladandayuthapani, Veerabhadran
2018-03-01
Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional independence has been studied using sparse Gaussian graphical models for continuous data and sparse Ising models for discrete data. However, there are two clear situations when these approaches are inadequate. The first occurs when the data are continuous but display non-normal marginal behavior such as heavy tails or skewness, rendering an assumption of normality inappropriate. The second occurs when a part of the data is ordinal or discrete (e.g., presence or absence of a mutation) and the other part is continuous (e.g., expression levels of genes or proteins). In this case, the existing Bayesian approaches typically employ a latent variable framework for the discrete part that precludes inferring conditional independence among the data that are actually observed. The current article overcomes these two challenges in a unified framework using Gaussian scale mixtures. Our framework is able to handle continuous data that are not normal and data that are of mixed continuous and discrete nature, while still being able to infer a sparse conditional sign independence structure among the observed data. Extensive performance comparison in simulations with alternative techniques and an analysis of a real cancer genomics data set demonstrate the effectiveness of the proposed approach. © 2017, The International Biometric Society.
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NASA Astrophysics Data System (ADS)
Yu, Jian; Yin, Qian; Guo, Ping; Luo, A.-li
2014-09-01
This paper presents an efficient method for the extraction of astronomical spectra from two-dimensional (2D) multifibre spectrographs based on the regularized least-squares QR-factorization (LSQR) algorithm. We address two issues: we propose a modified Gaussian point spread function (PSF) for modelling the 2D PSF from multi-emission-line gas-discharge lamp images (arc images), and we develop an efficient deconvolution method to extract spectra in real circumstances. The proposed modified 2D Gaussian PSF model can fit various types of 2D PSFs, including different radial distortion angles and ellipticities. We adopt the regularized LSQR algorithm to solve the sparse linear equations constructed from the sparse convolution matrix, which we designate the deconvolution spectrum extraction method. Furthermore, we implement a parallelized LSQR algorithm based on graphics processing unit programming in the Compute Unified Device Architecture to accelerate the computational processing. Experimental results illustrate that the proposed extraction method can greatly reduce the computational cost and memory use of the deconvolution method and, consequently, increase its efficiency and practicability. In addition, the proposed extraction method has a stronger noise tolerance than other methods, such as the boxcar (aperture) extraction and profile extraction methods. Finally, we present an analysis of the sensitivity of the extraction results to the radius and full width at half-maximum of the 2D PSF.
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Inferring network structure in non-normal and mixed discrete-continuous genomic data
Bhadra, Anindya; Rao, Arvind; Baladandayuthapani, Veerabhadran
2017-01-01
Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional independence has been studied using sparse Gaussian graphical models for continuous data and sparse Ising models for discrete data. However, there are two clear situations when these approaches are inadequate. The first occurs when the data are continuous but display non-normal marginal behavior such as heavy tails or skewness, rendering an assumption of normality inappropriate. The second occurs when a part of the data is ordinal or discrete (e.g., presence or absence of a mutation) and the other part is continuous (e.g., expression levels of genes or proteins). In this case, the existing Bayesian approaches typically employ a latent variable framework for the discrete part that precludes inferring conditional independence among the data that are actually observed. The current article overcomes these two challenges in a unified framework using Gaussian scale mixtures. Our framework is able to handle continuous data that are not normal and data that are of mixed continuous and discrete nature, while still being able to infer a sparse conditional sign independence structure among the observed data. Extensive performance comparison in simulations with alternative techniques and an analysis of a real cancer genomics data set demonstrate the effectiveness of the proposed approach. PMID:28437848
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NASA Astrophysics Data System (ADS)
Wen, Xian-Huan; Gómez-Hernández, J. Jaime
1998-03-01
The macrodispersion of an inert solute in a 2-D heterogeneous porous media is estimated numerically in a series of fields of varying heterogeneity. Four different random function (RF) models are used to model log-transmissivity (ln T) spatial variability, and for each of these models, ln T variance is varied from 0.1 to 2.0. The four RF models share the same univariate Gaussian histogram and the same isotropic covariance, but differ from one another in terms of the spatial connectivity patterns at extreme transmissivity values. More specifically, model A is a multivariate Gaussian model for which, by definition, extreme values (both high and low) are spatially uncorrelated. The other three models are non-multi-Gaussian: model B with high connectivity of high extreme values, model C with high connectivity of low extreme values, and model D with high connectivities of both high and low extreme values. Residence time distributions (RTDs) and macrodispersivities (longitudinal and transverse) are computed on ln T fields corresponding to the different RF models, for two different flow directions and at several scales. They are compared with each other, as well as with predicted values based on first-order analytical results. Numerically derived RTDs and macrodispersivities for the multi-Gaussian model are in good agreement with analytically derived values using first-order theories for log-transmissivity variance up to 2.0. The results from the non-multi-Gaussian models differ from each other and deviate largely from the multi-Gaussian results even when ln T variance is small. RTDs in non-multi-Gaussian realizations with high connectivity at high extreme values display earlier breakthrough than in multi-Gaussian realizations, whereas later breakthrough and longer tails are observed for RTDs from non-multi-Gaussian realizations with high connectivity at low extreme values. Longitudinal macrodispersivities in the non-multi-Gaussian realizations are, in general, larger than in the multi-Gaussian ones, while transverse macrodispersivities in the non-multi-Gaussian realizations can be larger or smaller than in the multi-Gaussian ones depending on the type of connectivity at extreme values. Comparing the numerical results for different flow directions, it is confirmed that macrodispersivities in multi-Gaussian realizations with isotropic spatial correlation are not flow direction-dependent. Macrodispersivities in the non-multi-Gaussian realizations, however, are flow direction-dependent although the covariance of ln T is isotropic (the same for all four models). It is important to account for high connectivities at extreme transmissivity values, a likely situation in some geological formations. Some of the discrepancies between first-order-based analytical results and field-scale tracer test data may be due to the existence of highly connected paths of extreme conductivity values.
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Yuan, Jing; Yeung, David Ka Wai; Mok, Greta S. P.; Bhatia, Kunwar S.; Wang, Yi-Xiang J.; Ahuja, Anil T.; King, Ann D.
2014-01-01
Purpose To technically investigate the non-Gaussian diffusion of head and neck diffusion weighted imaging (DWI) at 3 Tesla and compare advanced non-Gaussian diffusion models, including diffusion kurtosis imaging (DKI), stretched-exponential model (SEM), intravoxel incoherent motion (IVIM) and statistical model in the patients with nasopharyngeal carcinoma (NPC). Materials and Methods After ethics approval was granted, 16 patients with NPC were examined using DWI performed at 3T employing an extended b-value range from 0 to 1500 s/mm2. DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models on primary tumor, metastatic node, spinal cord and muscle. Non-Gaussian parameter maps were generated and compared to apparent diffusion coefficient (ADC) maps in NPC. Results Diffusion in NPC exhibited non-Gaussian behavior at the extended b-value range. Non-Gaussian models achieved significantly better fitting of DWI signal than the mono-exponential model. Non-Gaussian diffusion coefficients were substantially different from mono-exponential ADC both in magnitude and histogram distribution. Conclusion Non-Gaussian diffusivity in head and neck tissues and NPC lesions could be assessed by using non-Gaussian diffusion models. Non-Gaussian DWI analysis may reveal additional tissue properties beyond ADC and holds potentials to be used as a complementary tool for NPC characterization. PMID:24466318
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Assessment of parametric uncertainty for groundwater reactive transport modeling,
Shi, Xiaoqing; Ye, Ming; Curtis, Gary P.; Miller, Geoffery L.; Meyer, Philip D.; Kohler, Matthias; Yabusaki, Steve; Wu, Jichun
2014-01-01
The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gaussian assumption, Gaussian residuals are widely used. This paper shows that the residuals of the reactive transport model are non-Gaussian, heteroscedastic, and correlated in time; characterizing them requires using a generalized likelihood function such as the formal generalized likelihood function developed by Schoups and Vrugt (2010). For the surface complexation model considered in this study for simulating uranium reactive transport in groundwater, parametric uncertainty is quantified using the least squares regression methods and Bayesian methods with both Gaussian and formal generalized likelihood functions. While the least squares methods and Bayesian methods with Gaussian likelihood function produce similar Gaussian parameter distributions, the parameter distributions of Bayesian uncertainty quantification using the formal generalized likelihood function are non-Gaussian. In addition, predictive performance of formal generalized likelihood function is superior to that of least squares regression and Bayesian methods with Gaussian likelihood function. The Bayesian uncertainty quantification is conducted using the differential evolution adaptive metropolis (DREAM(zs)) algorithm; as a Markov chain Monte Carlo (MCMC) method, it is a robust tool for quantifying uncertainty in groundwater reactive transport models. For the surface complexation model, the regression-based local sensitivity analysis and Morris- and DREAM(ZS)-based global sensitivity analysis yield almost identical ranking of parameter importance. The uncertainty analysis may help select appropriate likelihood functions, improve model calibration, and reduce predictive uncertainty in other groundwater reactive transport and environmental modeling.
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NGMIX: Gaussian mixture models for 2D images
NASA Astrophysics Data System (ADS)
Sheldon, Erin
2015-08-01
NGMIX implements Gaussian mixture models for 2D images. Both the PSF profile and the galaxy are modeled using mixtures of Gaussians. Convolutions are thus performed analytically, resulting in fast model generation as compared to methods that perform the convolution in Fourier space. For the galaxy model, NGMIX supports exponential disks and de Vaucouleurs and Sérsic profiles; these are implemented approximately as a sum of Gaussians using the fits from Hogg & Lang (2013). Additionally, any number of Gaussians can be fit, either completely free or constrained to be cocentric and co-elliptical.
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Investigation of non-Gaussian effects in the Brazilian option market
NASA Astrophysics Data System (ADS)
Sosa-Correa, William O.; Ramos, Antônio M. T.; Vasconcelos, Giovani L.
2018-04-01
An empirical study of the Brazilian option market is presented in light of three option pricing models, namely the Black-Scholes model, the exponential model, and a model based on a power law distribution, the so-called q-Gaussian distribution or Tsallis distribution. It is found that the q-Gaussian model performs better than the Black-Scholes model in about one third of the option chains analyzed. But among these cases, the exponential model performs better than the q-Gaussian model in 75% of the time. The superiority of the exponential model over the q-Gaussian model is particularly impressive for options close to the expiration date, where its success rate rises above ninety percent.
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NASA Astrophysics Data System (ADS)
Skataric, Maja; Bose, Sandip; Zeroug, Smaine; Tilke, Peter
2017-02-01
It is not uncommon in the field of non-destructive evaluation that multiple measurements encompassing a variety of modalities are available for analysis and interpretation for determining the underlying states of nature of the materials or parts being tested. Despite and sometimes due to the richness of data, significant challenges arise in the interpretation manifested as ambiguities and inconsistencies due to various uncertain factors in the physical properties (inputs), environment, measurement device properties, human errors, and the measurement data (outputs). Most of these uncertainties cannot be described by any rigorous mathematical means, and modeling of all possibilities is usually infeasible for many real time applications. In this work, we will discuss an approach based on Hierarchical Bayesian Graphical Models (HBGM) for the improved interpretation of complex (multi-dimensional) problems with parametric uncertainties that lack usable physical models. In this setting, the input space of the physical properties is specified through prior distributions based on domain knowledge and expertise, which are represented as Gaussian mixtures to model the various possible scenarios of interest for non-destructive testing applications. Forward models are then used offline to generate the expected distribution of the proposed measurements which are used to train a hierarchical Bayesian network. In Bayesian analysis, all model parameters are treated as random variables, and inference of the parameters is made on the basis of posterior distribution given the observed data. Learned parameters of the posterior distribution obtained after the training can therefore be used to build an efficient classifier for differentiating new observed data in real time on the basis of pre-trained models. We will illustrate the implementation of the HBGM approach to ultrasonic measurements used for cement evaluation of cased wells in the oil industry.
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Gstat: a program for geostatistical modelling, prediction and simulation
NASA Astrophysics Data System (ADS)
Pebesma, Edzer J.; Wesseling, Cees G.
1998-01-01
Gstat is a computer program for variogram modelling, and geostatistical prediction and simulation. It provides a generic implementation of the multivariable linear model with trends modelled as a linear function of coordinate polynomials or of user-defined base functions, and independent or dependent, geostatistically modelled, residuals. Simulation in gstat comprises conditional or unconditional (multi-) Gaussian sequential simulation of point values or block averages, or (multi-) indicator sequential simulation. Besides many of the popular options found in other geostatistical software packages, gstat offers the unique combination of (i) an interactive user interface for modelling variograms and generalized covariances (residual variograms), that uses the device-independent plotting program gnuplot for graphical display, (ii) support for several ascii and binary data and map file formats for input and output, (iii) a concise, intuitive and flexible command language, (iv) user customization of program defaults, (v) no built-in limits, and (vi) free, portable ANSI-C source code. This paper describes the class of problems gstat can solve, and addresses aspects of efficiency and implementation, managing geostatistical projects, and relevant technical details.
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A non-gaussian model of continuous atmospheric turbulence for use in aircraft design
NASA Technical Reports Server (NTRS)
Reeves, P. M.; Joppa, R. G.; Ganzer, V. M.
1976-01-01
A non-Gaussian model of atmospheric turbulence is presented and analyzed. The model is restricted to the regions of the atmosphere where the turbulence is steady or continuous, and the assumptions of homogeneity and stationarity are justified. Also spatial distribution of turbulence is neglected, so the model consists of three independent, stationary stochastic processes which represent the vertical, lateral, and longitudinal gust components. The non-Gaussian and Gaussian models are compared with experimental data, and it is shown that the Gaussian model underestimates the number of high velocity gusts which occur in the atmosphere, while the non-Gaussian model can be adjusted to match the observed high velocity gusts more satisfactorily. Application of the proposed model to aircraft response is investigated, with particular attention to the response power spectral density, the probability distribution, and the level crossing frequency. A numerical example is presented which illustrates the application of the non-Gaussian model to the study of an aircraft autopilot system. Listings and sample results of a number of computer programs used in working with the model are included.
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Truncated Gaussians as tolerance sets
NASA Technical Reports Server (NTRS)
Cozman, Fabio; Krotkov, Eric
1994-01-01
This work focuses on the use of truncated Gaussian distributions as models for bounded data measurements that are constrained to appear between fixed limits. The authors prove that the truncated Gaussian can be viewed as a maximum entropy distribution for truncated bounded data, when mean and covariance are given. The characteristic function for the truncated Gaussian is presented; from this, algorithms are derived for calculation of mean, variance, summation, application of Bayes rule and filtering with truncated Gaussians. As an example of the power of their methods, a derivation of the disparity constraint (used in computer vision) from their models is described. The authors' approach complements results in Statistics, but their proposal is not only to use the truncated Gaussian as a model for selected data; they propose to model measurements as fundamentally in terms of truncated Gaussians.
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Higher-order cumulants and spectral kurtosis for early detection of subterranean termites
NASA Astrophysics Data System (ADS)
de la Rosa, Juan José González; Moreno Muñoz, Antonio
2008-02-01
This paper deals with termite detection in non-favorable SNR scenarios via signal processing using higher-order statistics. The results could be extrapolated to all impulse-like insect emissions; the situation involves non-destructive termite detection. Fourth-order cumulants in time and frequency domains enhance the detection and complete the characterization of termite emissions, non-Gaussian in essence. Sliding higher-order cumulants offer distinctive time instances, as a complement to the sliding variance, which only reveal power excesses in the signal; even for low-amplitude impulses. The spectral kurtosis reveals non-Gaussian characteristics (the peakedness of the probability density function) associated to these non-stationary measurements, specially in the near ultrasound frequency band. Contrasted estimators have been used to compute the higher-order statistics. The inedited findings are shown via graphical examples.
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The area of isodensity contours in cosmological models and galaxy surveys
NASA Technical Reports Server (NTRS)
Ryden, Barbara S.; Melott, Adrian L.; Craig, David A.; Gott, J. Richard, III; Weinberg, David H.
1989-01-01
The contour crossing statistic, defined as the mean number of times per unit length that a straight line drawn through the field crosses a given contour, is applied to model density fields and to smoothed samples of galaxies. Models in which the matter is in a bubble structure, in a filamentary net, or in clusters can be distinguished from Gaussian density distributions. The shape of the contour crossing curve in the initially Gaussian fields considered remains Gaussian after gravitational evolution and biasing, as long as the smoothing length is longer than the mass correlation length. With a smoothing length of 5/h Mpc, models containing cosmic strings are indistinguishable from Gaussian distributions. Cosmic explosion models are significantly non-Gaussian, having a bubbly structure. Samples from the CfA survey and the Haynes and Giovanelli (1986) survey are more strongly non-Gaussian at a smoothing length of 6/h Mpc than any of the models examined. At a smoothing length of 12/h Mpc, the Haynes and Giovanelli sample appears Gaussian.
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Sign: large-scale gene network estimation environment for high performance computing.
Tamada, Yoshinori; Shimamura, Teppei; Yamaguchi, Rui; Imoto, Seiya; Nagasaki, Masao; Miyano, Satoru
2011-01-01
Our research group is currently developing software for estimating large-scale gene networks from gene expression data. The software, called SiGN, is specifically designed for the Japanese flagship supercomputer "K computer" which is planned to achieve 10 petaflops in 2012, and other high performance computing environments including Human Genome Center (HGC) supercomputer system. SiGN is a collection of gene network estimation software with three different sub-programs: SiGN-BN, SiGN-SSM and SiGN-L1. In these three programs, five different models are available: static and dynamic nonparametric Bayesian networks, state space models, graphical Gaussian models, and vector autoregressive models. All these models require a huge amount of computational resources for estimating large-scale gene networks and therefore are designed to be able to exploit the speed of 10 petaflops. The software will be available freely for "K computer" and HGC supercomputer system users. The estimated networks can be viewed and analyzed by Cell Illustrator Online and SBiP (Systems Biology integrative Pipeline). The software project web site is available at http://sign.hgc.jp/ .
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Comparisons of non-Gaussian statistical models in DNA methylation analysis.
Ma, Zhanyu; Teschendorff, Andrew E; Yu, Hong; Taghia, Jalil; Guo, Jun
2014-06-16
As a key regulatory mechanism of gene expression, DNA methylation patterns are widely altered in many complex genetic diseases, including cancer. DNA methylation is naturally quantified by bounded support data; therefore, it is non-Gaussian distributed. In order to capture such properties, we introduce some non-Gaussian statistical models to perform dimension reduction on DNA methylation data. Afterwards, non-Gaussian statistical model-based unsupervised clustering strategies are applied to cluster the data. Comparisons and analysis of different dimension reduction strategies and unsupervised clustering methods are presented. Experimental results show that the non-Gaussian statistical model-based methods are superior to the conventional Gaussian distribution-based method. They are meaningful tools for DNA methylation analysis. Moreover, among several non-Gaussian methods, the one that captures the bounded nature of DNA methylation data reveals the best clustering performance.
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Comparisons of Non-Gaussian Statistical Models in DNA Methylation Analysis
Ma, Zhanyu; Teschendorff, Andrew E.; Yu, Hong; Taghia, Jalil; Guo, Jun
2014-01-01
As a key regulatory mechanism of gene expression, DNA methylation patterns are widely altered in many complex genetic diseases, including cancer. DNA methylation is naturally quantified by bounded support data; therefore, it is non-Gaussian distributed. In order to capture such properties, we introduce some non-Gaussian statistical models to perform dimension reduction on DNA methylation data. Afterwards, non-Gaussian statistical model-based unsupervised clustering strategies are applied to cluster the data. Comparisons and analysis of different dimension reduction strategies and unsupervised clustering methods are presented. Experimental results show that the non-Gaussian statistical model-based methods are superior to the conventional Gaussian distribution-based method. They are meaningful tools for DNA methylation analysis. Moreover, among several non-Gaussian methods, the one that captures the bounded nature of DNA methylation data reveals the best clustering performance. PMID:24937687
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NASA Astrophysics Data System (ADS)
Woodbury, D.; Kubota, S.; Johnson, I.
2014-10-01
Computer simulations of electromagnetic wave propagation in magnetized plasmas are an important tool for both plasma heating and diagnostics. For active millimeter-wave and microwave diagnostics, accurately modeling the evolution of the beam parameters for launched, reflected or scattered waves in a toroidal plasma requires that calculations be done using the full 3-D geometry. Previously, we reported on the application of GPGPU (General-Purpose computing on Graphics Processing Units) to a 3-D vacuum Maxwell code using the FDTD (Finite-Difference Time-Domain) method. Tests were done for Gaussian beam propagation with a hard source antenna, utilizing the parallel processing capabilities of the NVIDIA K20M. In the current study, we have modified the 3-D code to include a soft source antenna and an induced current density based on the cold plasma approximation. Results from Gaussian beam propagation in an inhomogeneous anisotropic plasma, along with comparisons to ray- and beam-tracing calculations will be presented. Additional enhancements, such as advanced coding techniques for improved speedup, will also be investigated. Supported by U.S. DoE Grant DE-FG02-99-ER54527 and in part by the U.S. DoE, Office of Science, WDTS under the Science Undergraduate Laboratory Internship program.
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Xu, Junzhong; Li, Ke; Smith, R. Adam; Waterton, John C.; Zhao, Ping; Ding, Zhaohua; Does, Mark D.; Manning, H. Charles; Gore, John C.
2016-01-01
Background Diffusion-weighted MRI (DWI) signal attenuation is often not mono-exponential (i.e. non-Gaussian diffusion) with stronger diffusion weighting. Several non-Gaussian diffusion models have been developed and may provide new information or higher sensitivity compared with the conventional apparent diffusion coefficient (ADC) method. However the relative merits of these models to detect tumor therapeutic response is not fully clear. Methods Conventional ADC, and three widely-used non-Gaussian models, (bi-exponential, stretched exponential, and statistical model), were implemented and compared for assessing SW620 human colon cancer xenografts responding to barasertib, an agent known to induce apoptosis via polyploidy. Bayesian Information Criterion (BIC) was used for model selection among all three non-Gaussian models. Results All of tumor volume, histology, conventional ADC, and three non-Gaussian DWI models could show significant differences between control and treatment groups after four days of treatment. However, only the non-Gaussian models detected significant changes after two days of treatment. For any treatment or control group, over 65.7% of tumor voxels indicate the bi-exponential model is strongly or very strongly preferred. Conclusion Non-Gaussian DWI model-derived biomarkers are capable of detecting tumor earlier chemotherapeutic response of tumors compared with conventional ADC and tumor volume. The bi-exponential model provides better fitting compared with statistical and stretched exponential models for the tumor and treatment models used in the current work. PMID:27919785
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2012-01-01
Background Starch serves as a temporal storage of carbohydrates in plant leaves during day/night cycles. To study transcriptional regulatory modules of this dynamic metabolic process, we conducted gene regulation network analysis based on small-sample inference of graphical Gaussian model (GGM). Results Time-series significant analysis was applied for Arabidopsis leaf transcriptome data to obtain a set of genes that are highly regulated under a diurnal cycle. A total of 1,480 diurnally regulated genes included 21 starch metabolic enzymes, 6 clock-associated genes, and 106 transcription factors (TF). A starch-clock-TF gene regulation network comprising 117 nodes and 266 edges was constructed by GGM from these 133 significant genes that are potentially related to the diurnal control of starch metabolism. From this network, we found that β-amylase 3 (b-amy3: At4g17090), which participates in starch degradation in chloroplast, is the most frequently connected gene (a hub gene). The robustness of gene-to-gene regulatory network was further analyzed by TF binding site prediction and by evaluating global co-expression of TFs and target starch metabolic enzymes. As a result, two TFs, indeterminate domain 5 (AtIDD5: At2g02070) and constans-like (COL: At2g21320), were identified as positive regulators of starch synthase 4 (SS4: At4g18240). The inference model of AtIDD5-dependent positive regulation of SS4 gene expression was experimentally supported by decreased SS4 mRNA accumulation in Atidd5 mutant plants during the light period of both short and long day conditions. COL was also shown to positively control SS4 mRNA accumulation. Furthermore, the knockout of AtIDD5 and COL led to deformation of chloroplast and its contained starch granules. This deformity also affected the number of starch granules per chloroplast, which increased significantly in both knockout mutant lines. Conclusions In this study, we utilized a systematic approach of microarray analysis to discover the transcriptional regulatory network of starch metabolism in Arabidopsis leaves. With this inference method, the starch regulatory network of Arabidopsis was found to be strongly associated with clock genes and TFs, of which AtIDD5 and COL were evidenced to control SS4 gene expression and starch granule formation in chloroplasts. PMID:22898356
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Non-Gaussian Analysis of Turbulent Boundary Layer Fluctuating Pressure on Aircraft Skin Panels
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Steinwolf, Alexander
2005-01-01
The purpose of the study is to investigate the probability density function (PDF) of turbulent boundary layer fluctuating pressures measured on the outer sidewall of a supersonic transport aircraft and to approximate these PDFs by analytical models. Experimental flight results show that the fluctuating pressure PDFs differ from the Gaussian distribution even for standard smooth surface conditions. The PDF tails are wider and longer than those of the Gaussian model. For pressure fluctuations in front of forward-facing step discontinuities, deviations from the Gaussian model are more significant and the PDFs become asymmetrical. There is a certain spatial pattern of the skewness and kurtosis behavior depending on the distance upstream from the step. All characteristics related to non-Gaussian behavior are highly dependent upon the distance from the step and the step height, less dependent on aircraft speed, and not dependent on the fuselage location. A Hermite polynomial transform model and a piecewise-Gaussian model fit the flight data well both for the smooth and stepped conditions. The piecewise-Gaussian approximation can be additionally regarded for convenience in usage after the model is constructed.
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Computer generated hologram from point cloud using graphics processor.
Chen, Rick H-Y; Wilkinson, Timothy D
2009-12-20
Computer generated holography is an extremely demanding and complex task when it comes to providing realistic reconstructions with full parallax, occlusion, and shadowing. We present an algorithm designed for data-parallel computing on modern graphics processing units to alleviate the computational burden. We apply Gaussian interpolation to create a continuous surface representation from discrete input object points. The algorithm maintains a potential occluder list for each individual hologram plane sample to keep the number of visibility tests to a minimum. We experimented with two approximations that simplify and accelerate occlusion computation. It is observed that letting several neighboring hologram plane samples share visibility information on object points leads to significantly faster computation without causing noticeable artifacts in the reconstructed images. Computing a reduced sample set via nonuniform sampling is also found to be an effective acceleration technique.
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Automated Weather Observing System (AWOS) Demonstration Program.
1984-09-01
month "bur:-in" r "debugging" period and a 10-month ’usefu I life " period. Fhe butrn- in pr i ,J was i sed to establish the Data Acquisition System...Histograms. Histograms provide a graphical means of showing how well the probability distribution of residu : , approaches a normal or Gaussian distribution...Organization Report No. 7- Author’s) Paul .J. O t Brien et al. DOT/FAA/CT-84/20 9. Performing Organlzation Name and Address 10. Work Unit No. (TRAIS
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Temporal self-splitting of optical pulses
NASA Astrophysics Data System (ADS)
Ding, Chaoliang; Koivurova, Matias; Turunen, Jari; Pan, Liuzhan
2018-05-01
We present mathematical models for temporally and spectrally partially coherent pulse trains with Laguerre-Gaussian and Hermite-Gaussian Schell-model statistics as extensions of the standard Gaussian Schell model for pulse trains. We derive propagation formulas of both classes of pulsed fields in linearly dispersive media and in temporal optical systems. It is found that, in general, both types of fields exhibit time-domain self-splitting upon propagation. The Laguerre-Gaussian model leads to multiply peaked pulses, while the Hermite-Gaussian model leads to doubly peaked pulses, in the temporal far field (in dispersive media) or at the Fourier plane of a temporal system. In both model fields the character of the self-splitting phenomenon depends both on the degree of temporal and spectral coherence and on the power spectrum of the field.
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Linear velocity fields in non-Gaussian models for large-scale structure
NASA Technical Reports Server (NTRS)
Scherrer, Robert J.
1992-01-01
Linear velocity fields in two types of physically motivated non-Gaussian models are examined for large-scale structure: seed models, in which the density field is a convolution of a density profile with a distribution of points, and local non-Gaussian fields, derived from a local nonlinear transformation on a Gaussian field. The distribution of a single component of the velocity is derived for seed models with randomly distributed seeds, and these results are applied to the seeded hot dark matter model and the global texture model with cold dark matter. An expression for the distribution of a single component of the velocity in arbitrary local non-Gaussian models is given, and these results are applied to such fields with chi-squared and lognormal distributions. It is shown that all seed models with randomly distributed seeds and all local non-Guassian models have single-component velocity distributions with positive kurtosis.
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Colclough, Giles L; Woolrich, Mark W; Harrison, Samuel J; Rojas López, Pedro A; Valdes-Sosa, Pedro A; Smith, Stephen M
2018-05-07
A Bayesian model for sparse, hierarchical, inver-covariance estimation is presented, and applied to multi-subject functional connectivity estimation in the human brain. It enables simultaneous inference of the strength of connectivity between brain regions at both subject and population level, and is applicable to fMRI, MEG and EEG data. Two versions of the model can encourage sparse connectivity, either using continuous priors to suppress irrelevant connections, or using an explicit description of the network structure to estimate the connection probability between each pair of regions. A large evaluation of this model, and thirteen methods that represent the state of the art of inverse covariance modelling, is conducted using both simulated and resting-state functional imaging datasets. Our novel Bayesian approach has similar performance to the best extant alternative, Ng et al.'s Sparse Group Gaussian Graphical Model algorithm, which also is based on a hierarchical structure. Using data from the Human Connectome Project, we show that these hierarchical models are able to reduce the measurement error in MEG beta-band functional networks by 10%, producing concomitant increases in estimates of the genetic influence on functional connectivity. Copyright © 2018. Published by Elsevier Inc.
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NASA Astrophysics Data System (ADS)
Guo, Yongfeng; Shen, Yajun; Tan, Jianguo
2016-09-01
The phenomenon of stochastic resonance (SR) in a piecewise nonlinear model driven by a periodic signal and correlated noises for the cases of a multiplicative non-Gaussian noise and an additive Gaussian white noise is investigated. Applying the path integral approach, the unified colored noise approximation and the two-state model theory, the analytical expression of the signal-to-noise ratio (SNR) is derived. It is found that conventional stochastic resonance exists in this system. From numerical computations we obtain that: (i) As a function of the non-Gaussian noise intensity, the SNR is increased when the non-Gaussian noise deviation parameter q is increased. (ii) As a function of the Gaussian noise intensity, the SNR is decreased when q is increased. This demonstrates that the effect of the non-Gaussian noise on SNR is different from that of the Gaussian noise in this system. Moreover, we further discuss the effect of the correlation time of the non-Gaussian noise, cross-correlation strength, the amplitude and frequency of the periodic signal on SR.
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Skewness in large-scale structure and non-Gaussian initial conditions
NASA Technical Reports Server (NTRS)
Fry, J. N.; Scherrer, Robert J.
1994-01-01
We compute the skewness of the galaxy distribution arising from the nonlinear evolution of arbitrary non-Gaussian intial conditions to second order in perturbation theory including the effects of nonlinear biasing. The result contains a term identical to that for a Gaussian initial distribution plus terms which depend on the skewness and kurtosis of the initial conditions. The results are model dependent; we present calculations for several toy models. At late times, the leading contribution from the initial skewness decays away relative to the other terms and becomes increasingly unimportant, but the contribution from initial kurtosis, previously overlooked, has the same time dependence as the Gaussian terms. Observations of a linear dependence of the normalized skewness on the rms density fluctuation therefore do not necessarily rule out initially non-Gaussian models. We also show that with non-Gaussian initial conditions the first correction to linear theory for the mean square density fluctuation is larger than for Gaussian models.
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Arbitrage with fractional Gaussian processes
NASA Astrophysics Data System (ADS)
Zhang, Xili; Xiao, Weilin
2017-04-01
While the arbitrage opportunity in the Black-Scholes model driven by fractional Brownian motion has a long history, the arbitrage strategy in the Black-Scholes model driven by general fractional Gaussian processes is in its infancy. The development of stochastic calculus with respect to fractional Gaussian processes allowed us to study such models. In this paper, following the idea of Shiryaev (1998), an arbitrage strategy is constructed for the Black-Scholes model driven by fractional Gaussian processes, when the stochastic integral is interpreted in the Riemann-Stieltjes sense. Arbitrage opportunities in some fractional Gaussian processes, including fractional Brownian motion, sub-fractional Brownian motion, bi-fractional Brownian motion, weighted-fractional Brownian motion and tempered fractional Brownian motion, are also investigated.
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How Many Separable Sources? Model Selection In Independent Components Analysis
Woods, Roger P.; Hansen, Lars Kai; Strother, Stephen
2015-01-01
Unlike mixtures consisting solely of non-Gaussian sources, mixtures including two or more Gaussian components cannot be separated using standard independent components analysis methods that are based on higher order statistics and independent observations. The mixed Independent Components Analysis/Principal Components Analysis (mixed ICA/PCA) model described here accommodates one or more Gaussian components in the independent components analysis model and uses principal components analysis to characterize contributions from this inseparable Gaussian subspace. Information theory can then be used to select from among potential model categories with differing numbers of Gaussian components. Based on simulation studies, the assumptions and approximations underlying the Akaike Information Criterion do not hold in this setting, even with a very large number of observations. Cross-validation is a suitable, though computationally intensive alternative for model selection. Application of the algorithm is illustrated using Fisher's iris data set and Howells' craniometric data set. Mixed ICA/PCA is of potential interest in any field of scientific investigation where the authenticity of blindly separated non-Gaussian sources might otherwise be questionable. Failure of the Akaike Information Criterion in model selection also has relevance in traditional independent components analysis where all sources are assumed non-Gaussian. PMID:25811988
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Liu, Chengyu; Zheng, Dingchang; Zhao, Lina; Liu, Changchun
2014-01-01
It has been reported that Gaussian functions could accurately and reliably model both carotid and radial artery pressure waveforms (CAPW and RAPW). However, the physiological relevance of the characteristic features from the modeled Gaussian functions has been little investigated. This study thus aimed to determine characteristic features from the Gaussian functions and to make comparisons of them between normal subjects and heart failure patients. Fifty-six normal subjects and 51 patients with heart failure were studied with the CAPW and RAPW signals recorded simultaneously. The two signals were normalized first and then modeled by three positive Gaussian functions, with their peak amplitude, peak time, and half-width determined. Comparisons of these features were finally made between the two groups. Results indicated that the peak amplitude of the first Gaussian curve was significantly decreased in heart failure patients compared with normal subjects (P<0.001). Significantly increased peak amplitude of the second Gaussian curves (P<0.001) and significantly shortened peak times of the second and third Gaussian curves (both P<0.001) were also presented in heart failure patients. These results were true for both CAPW and RAPW signals, indicating the clinical significance of the Gaussian modeling, which should provide essential tools for further understanding the underlying physiological mechanisms of the artery pressure waveform.
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MSEE: Stochastic Cognitive Linguistic Behavior Models for Semantic Sensing
2013-09-01
recognition, a Gaussian Process Dynamic Model with Social Network Analysis (GPDM-SNA) for a small human group action recognition, an extended GPDM-SNA...44 3.2. Small Human Group Activity Modeling Based on Gaussian Process Dynamic Model and Social Network Analysis (SN-GPDM...51 Approved for public release; distribution unlimited. 3 3.2.3. Gaussian Process Dynamical Model and
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Effects of scale-dependent non-Gaussianity on cosmological structures
DOE Office of Scientific and Technical Information (OSTI.GOV)
LoVerde, Marilena; Miller, Amber; Shandera, Sarah
2008-04-15
The detection of primordial non-Gaussianity could provide a powerful means to test various inflationary scenarios. Although scale-invariant non-Gaussianity (often described by the f{sub NL} formalism) is currently best constrained by the CMB, single-field models with changing sound speed can have strongly scale-dependent non-Gaussianity. Such models could evade the CMB constraints but still have important effects at scales responsible for the formation of cosmological objects such as clusters and galaxies. We compute the effect of scale-dependent primordial non-Gaussianity on cluster number counts as a function of redshift, using a simple ansatz to model scale-dependent features. We forecast constraints on these modelsmore » achievable with forthcoming datasets. We also examine consequences for the galaxy bispectrum. Our results are relevant for the Dirac-Born-Infeld model of brane inflation, where the scale dependence of the non-Gaussianity is directly related to the geometry of the extra dimensions.« less
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NASA Technical Reports Server (NTRS)
Kogut, A.; Banday, A. J.; Bennett, C. L.; Hinshaw, G.; Lubin, P. M.; Smoot, G. F.
1995-01-01
We use the two-point correlation function of the extrema points (peaks and valleys) in the Cosmic Background Explorer (COBE) Differential Microwave Radiometers (DMR) 2 year sky maps as a test for non-Gaussian temperature distribution in the cosmic microwave background anisotropy. A maximum-likelihood analysis compares the DMR data to n = 1 toy models whose random-phase spherical harmonic components a(sub lm) are drawn from either Gaussian, chi-square, or log-normal parent populations. The likelihood of the 53 GHz (A+B)/2 data is greatest for the exact Gaussian model. There is less than 10% chance that the non-Gaussian models tested describe the DMR data, limited primarily by type II errors in the statistical inference. The extrema correlation function is a stronger test for this class of non-Gaussian models than topological statistics such as the genus.
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Zhang, Guangwen; Wang, Shuangshuang; Wen, Didi; Zhang, Jing; Wei, Xiaocheng; Ma, Wanling; Zhao, Weiwei; Wang, Mian; Wu, Guosheng; Zhang, Jinsong
2016-12-09
Water molecular diffusion in vivo tissue is much more complicated. We aimed to compare non-Gaussian diffusion models of diffusion-weighted imaging (DWI) including intra-voxel incoherent motion (IVIM), stretched-exponential model (SEM) and Gaussian diffusion model at 3.0 T MRI in patients with rectal cancer, and to determine the optimal model for investigating the water diffusion properties and characterization of rectal carcinoma. Fifty-nine consecutive patients with pathologically confirmed rectal adenocarcinoma underwent DWI with 16 b-values at a 3.0 T MRI system. DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models (IVIM-mono, IVIM-bi and SEM) on primary tumor and adjacent normal rectal tissue. Parameters of standard apparent diffusion coefficient (ADC), slow- and fast-ADC, fraction of fast ADC (f), α value and distributed diffusion coefficient (DDC) were generated and compared between the tumor and normal tissues. The SEM exhibited the best fitting results of actual DWI signal in rectal cancer and the normal rectal wall (R 2 = 0.998, 0.999 respectively). The DDC achieved relatively high area under the curve (AUC = 0.980) in differentiating tumor from normal rectal wall. Non-Gaussian diffusion models could assess tissue properties more accurately than the ADC derived Gaussian diffusion model. SEM may be used as a potential optimal model for characterization of rectal cancer.
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Evaluation of non-Gaussian diffusion in cardiac MRI.
McClymont, Darryl; Teh, Irvin; Carruth, Eric; Omens, Jeffrey; McCulloch, Andrew; Whittington, Hannah J; Kohl, Peter; Grau, Vicente; Schneider, Jürgen E
2017-09-01
The diffusion tensor model assumes Gaussian diffusion and is widely applied in cardiac diffusion MRI. However, diffusion in biological tissue deviates from a Gaussian profile as a result of hindrance and restriction from cell and tissue microstructure, and may be quantified better by non-Gaussian modeling. The aim of this study was to investigate non-Gaussian diffusion in healthy and hypertrophic hearts. Thirteen rat hearts (five healthy, four sham, four hypertrophic) were imaged ex vivo. Diffusion-weighted images were acquired at b-values up to 10,000 s/mm 2 . Models of diffusion were fit to the data and ranked based on the Akaike information criterion. The diffusion tensor was ranked best at b-values up to 2000 s/mm 2 but reflected the signal poorly in the high b-value regime, in which the best model was a non-Gaussian "beta distribution" model. Although there was considerable overlap in apparent diffusivities between the healthy, sham, and hypertrophic hearts, diffusion kurtosis and skewness in the hypertrophic hearts were more than 20% higher in the sheetlet and sheetlet-normal directions. Non-Gaussian diffusion models have a higher sensitivity for the detection of hypertrophy compared with the Gaussian model. In particular, diffusion kurtosis may serve as a useful biomarker for characterization of disease and remodeling in the heart. Magn Reson Med 78:1174-1186, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.
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Hamby, D M
2002-01-01
Reconstructed meteorological data are often used in some form of long-term wind trajectory models for estimating the historical impacts of atmospheric emissions. Meteorological data for the straight-line Gaussian plume model are put into a joint frequency distribution, a three-dimensional array describing atmospheric wind direction, speed, and stability. Methods using the Gaussian model and joint frequency distribution inputs provide reasonable estimates of downwind concentration and have been shown to be accurate to within a factor of four. We have used multiple joint frequency distributions and probabilistic techniques to assess the Gaussian plume model and determine concentration-estimate uncertainty and model sensitivity. We examine the straight-line Gaussian model while calculating both sector-averaged and annual-averaged relative concentrations at various downwind distances. The sector-average concentration model was found to be most sensitive to wind speed, followed by horizontal dispersion (sigmaZ), the importance of which increases as stability increases. The Gaussian model is not sensitive to stack height uncertainty. Precision of the frequency data appears to be most important to meteorological inputs when calculations are made for near-field receptors, increasing as stack height increases.
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Optimisation of dispersion parameters of Gaussian plume model for CO₂ dispersion.
Liu, Xiong; Godbole, Ajit; Lu, Cheng; Michal, Guillaume; Venton, Philip
2015-11-01
The carbon capture and storage (CCS) and enhanced oil recovery (EOR) projects entail the possibility of accidental release of carbon dioxide (CO2) into the atmosphere. To quantify the spread of CO2 following such release, the 'Gaussian' dispersion model is often used to estimate the resulting CO2 concentration levels in the surroundings. The Gaussian model enables quick estimates of the concentration levels. However, the traditionally recommended values of the 'dispersion parameters' in the Gaussian model may not be directly applicable to CO2 dispersion. This paper presents an optimisation technique to obtain the dispersion parameters in order to achieve a quick estimation of CO2 concentration levels in the atmosphere following CO2 blowouts. The optimised dispersion parameters enable the Gaussian model to produce quick estimates of CO2 concentration levels, precluding the necessity to set up and run much more complicated models. Computational fluid dynamics (CFD) models were employed to produce reference CO2 dispersion profiles in various atmospheric stability classes (ASC), different 'source strengths' and degrees of ground roughness. The performance of the CFD models was validated against the 'Kit Fox' field measurements, involving dispersion over a flat horizontal terrain, both with low and high roughness regions. An optimisation model employing a genetic algorithm (GA) to determine the best dispersion parameters in the Gaussian plume model was set up. Optimum values of the dispersion parameters for different ASCs that can be used in the Gaussian plume model for predicting CO2 dispersion were obtained.
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'A device for being able to book P&L': the organizational embedding of the Gaussian copula.
MacKenzie, Donald; Spears, Taylor
2014-06-01
This article, the second of two articles on the Gaussian copula family of models, discusses the attitude of 'quants' (modellers) to these models, showing that contrary to some accounts, those quants were not 'model dopes' who uncritically accepted the outputs of the models. Although sometimes highly critical of Gaussian copulas - even 'othering' them as not really being models --they nevertheless nearly all kept using them, an outcome we explain with reference to the embedding of these models in inter- and intra-organizational processes: communication, risk control and especially the setting of bonuses. The article also examines the role of Gaussian copula models in the 2007-2008 global crisis and in a 2005 episode known as 'the correlation crisis'. We end with the speculation that all widely used derivatives models (and indeed the evaluation culture in which they are embedded) help generate inter-organizational co-ordination, and all that is special in this respect about the Gaussian copula is that its status as 'other' makes this role evident.
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F-MAP: A Bayesian approach to infer the gene regulatory network using external hints
Shahdoust, Maryam; Mahjub, Hossein; Sadeghi, Mehdi
2017-01-01
The Common topological features of related species gene regulatory networks suggest reconstruction of the network of one species by using the further information from gene expressions profile of related species. We present an algorithm to reconstruct the gene regulatory network named; F-MAP, which applies the knowledge about gene interactions from related species. Our algorithm sets a Bayesian framework to estimate the precision matrix of one species microarray gene expressions dataset to infer the Gaussian Graphical model of the network. The conjugate Wishart prior is used and the information from related species is applied to estimate the hyperparameters of the prior distribution by using the factor analysis. Applying the proposed algorithm on six related species of drosophila shows that the precision of reconstructed networks is improved considerably compared to the precision of networks constructed by other Bayesian approaches. PMID:28938012
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Cameron, Donnie; Bouhrara, Mustapha; Reiter, David A; Fishbein, Kenneth W; Choi, Seongjin; Bergeron, Christopher M; Ferrucci, Luigi; Spencer, Richard G
2017-07-01
This work characterizes the effect of lipid and noise signals on muscle diffusion parameter estimation in several conventional and non-Gaussian models, the ultimate objectives being to characterize popular fat suppression approaches for human muscle diffusion studies, to provide simulations to inform experimental work and to report normative non-Gaussian parameter values. The models investigated in this work were the Gaussian monoexponential and intravoxel incoherent motion (IVIM) models, and the non-Gaussian kurtosis and stretched exponential models. These were evaluated via simulations, and in vitro and in vivo experiments. Simulations were performed using literature input values, modeling fat contamination as an additive baseline to data, whereas phantom studies used a phantom containing aliphatic and olefinic fats and muscle-like gel. Human imaging was performed in the hamstring muscles of 10 volunteers. Diffusion-weighted imaging was applied with spectral attenuated inversion recovery (SPAIR), slice-select gradient reversal and water-specific excitation fat suppression, alone and in combination. Measurement bias (accuracy) and dispersion (precision) were evaluated, together with intra- and inter-scan repeatability. Simulations indicated that noise in magnitude images resulted in <6% bias in diffusion coefficients and non-Gaussian parameters (α, K), whereas baseline fitting minimized fat bias for all models, except IVIM. In vivo, popular SPAIR fat suppression proved inadequate for accurate parameter estimation, producing non-physiological parameter estimates without baseline fitting and large biases when it was used. Combining all three fat suppression techniques and fitting data with a baseline offset gave the best results of all the methods studied for both Gaussian diffusion and, overall, for non-Gaussian diffusion. It produced consistent parameter estimates for all models, except IVIM, and highlighted non-Gaussian behavior perpendicular to muscle fibers (α ~ 0.95, K ~ 3.1). These results show that effective fat suppression is crucial for accurate measurement of non-Gaussian diffusion parameters, and will be an essential component of quantitative studies of human muscle quality. Published 2017. This article is a U.S. Government work and is in the public domain in the USA.
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NASA Astrophysics Data System (ADS)
Rivera-Ortega, Uriel; Dirckx, Joris
2015-09-01
In this manuscript a computer based simulation is proposed for teaching concepts of interference of light (under the scheme of a Michelson interferometer), phase-shifting and polarization states. The user can change some parameters of the interfering waves, such as their amplitude and phase difference in order to graphically represent the polarization state of a simulated travelling wave. Regarding to the interference simulation, the user is able to change the wavelength and type of the interfering waves by selecting combinations between planar and Gaussian profiles, as well as the optical path difference by translating or tilting one of the two mirrors in the interferometer setup, all of this via a graphical user interface (GUI) designed in MATLAB. A theoretical introduction and simulation results for each phenomenon will be shown. Due to the simulation characteristics, this GUI can be a very good non-formal learning resource.
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Moving target detection method based on improved Gaussian mixture model
NASA Astrophysics Data System (ADS)
Ma, J. Y.; Jie, F. R.; Hu, Y. J.
2017-07-01
Gaussian Mixture Model is often employed to build background model in background difference methods for moving target detection. This paper puts forward an adaptive moving target detection algorithm based on improved Gaussian Mixture Model. According to the graylevel convergence for each pixel, adaptively choose the number of Gaussian distribution to learn and update background model. Morphological reconstruction method is adopted to eliminate the shadow.. Experiment proved that the proposed method not only has good robustness and detection effect, but also has good adaptability. Even for the special cases when the grayscale changes greatly and so on, the proposed method can also make outstanding performance.
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The properties of the anti-tumor model with coupling non-Gaussian noise and Gaussian colored noise
NASA Astrophysics Data System (ADS)
Guo, Qin; Sun, Zhongkui; Xu, Wei
2016-05-01
The anti-tumor model with correlation between multiplicative non-Gaussian noise and additive Gaussian-colored noise has been investigated in this paper. The behaviors of the stationary probability distribution demonstrate that the multiplicative non-Gaussian noise plays a dual role in the development of tumor and an appropriate additive Gaussian colored noise can lead to a minimum of the mean value of tumor cell population. The mean first passage time is calculated to quantify the effects of noises on the transition time of tumors between the stable states. An increase in both the non-Gaussian noise intensity and the departure from the Gaussian noise can accelerate the transition from the disease state to the healthy state. On the contrary, an increase in cross-correlated degree will slow down the transition. Moreover, the correlation time can enhance the stability of the disease state.
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Probability density and exceedance rate functions of locally Gaussian turbulence
NASA Technical Reports Server (NTRS)
Mark, W. D.
1989-01-01
A locally Gaussian model of turbulence velocities is postulated which consists of the superposition of a slowly varying strictly Gaussian component representing slow temporal changes in the mean wind speed and a more rapidly varying locally Gaussian turbulence component possessing a temporally fluctuating local variance. Series expansions of the probability density and exceedance rate functions of the turbulence velocity model, based on Taylor's series, are derived. Comparisons of the resulting two-term approximations with measured probability density and exceedance rate functions of atmospheric turbulence velocity records show encouraging agreement, thereby confirming the consistency of the measured records with the locally Gaussian model. Explicit formulas are derived for computing all required expansion coefficients from measured turbulence records.
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Gaussian mixture models as flux prediction method for central receivers
NASA Astrophysics Data System (ADS)
Grobler, Annemarie; Gauché, Paul; Smit, Willie
2016-05-01
Flux prediction methods are crucial to the design and operation of central receiver systems. Current methods such as the circular and elliptical (bivariate) Gaussian prediction methods are often used in field layout design and aiming strategies. For experimental or small central receiver systems, the flux profile of a single heliostat often deviates significantly from the circular and elliptical Gaussian models. Therefore a novel method of flux prediction was developed by incorporating the fitting of Gaussian mixture models onto flux profiles produced by flux measurement or ray tracing. A method was also developed to predict the Gaussian mixture model parameters of a single heliostat for a given time using image processing. Recording the predicted parameters in a database ensures that more accurate predictions are made in a shorter time frame.
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Korsgaard, Inge Riis; Lund, Mogens Sandø; Sorensen, Daniel; Gianola, Daniel; Madsen, Per; Jensen, Just
2003-01-01
A fully Bayesian analysis using Gibbs sampling and data augmentation in a multivariate model of Gaussian, right censored, and grouped Gaussian traits is described. The grouped Gaussian traits are either ordered categorical traits (with more than two categories) or binary traits, where the grouping is determined via thresholds on the underlying Gaussian scale, the liability scale. Allowances are made for unequal models, unknown covariance matrices and missing data. Having outlined the theory, strategies for implementation are reviewed. These include joint sampling of location parameters; efficient sampling from the fully conditional posterior distribution of augmented data, a multivariate truncated normal distribution; and sampling from the conditional inverse Wishart distribution, the fully conditional posterior distribution of the residual covariance matrix. Finally, a simulated dataset was analysed to illustrate the methodology. This paper concentrates on a model where residuals associated with liabilities of the binary traits are assumed to be independent. A Bayesian analysis using Gibbs sampling is outlined for the model where this assumption is relaxed. PMID:12633531
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Gaussian Mixture Model of Heart Rate Variability
Costa, Tommaso; Boccignone, Giuseppe; Ferraro, Mario
2012-01-01
Heart rate variability (HRV) is an important measure of sympathetic and parasympathetic functions of the autonomic nervous system and a key indicator of cardiovascular condition. This paper proposes a novel method to investigate HRV, namely by modelling it as a linear combination of Gaussians. Results show that three Gaussians are enough to describe the stationary statistics of heart variability and to provide a straightforward interpretation of the HRV power spectrum. Comparisons have been made also with synthetic data generated from different physiologically based models showing the plausibility of the Gaussian mixture parameters. PMID:22666386
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Random medium model for cusping of plane waves.
Li, Jia; Korotkova, Olga
2017-09-01
We introduce a model for a three-dimensional (3D) Schell-type stationary medium whose degree of potential's correlation satisfies the Fractional Multi-Gaussian (FMG) function. Compared with the scattered profile produced by the Gaussian Schell-model (GSM) medium, the Fractional Multi-Gaussian Schell-model (FMGSM) medium gives rise to a sharp concave intensity apex in the scattered field. This implies that the FMGSM medium also accounts for a larger than Gaussian's power in the bucket (PIB) in the forward scattering direction, hence being a better candidate than the GSM medium for generating highly-focused (cusp-like) scattered profiles in the far zone. Compared to other mathematical models for the medium's correlation function which can produce similar cusped scattered profiles the FMG function offers unprecedented tractability being the weighted superposition of Gaussian functions. Our results provide useful applications to energy counter problems and particle manipulation by weakly scattered fields.
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Orthogonal Gaussian process models
Plumlee, Matthew; Joseph, V. Roshan
2017-01-01
Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads to poor estimation of the coefficients in the mean model, and thus the estimated mean model loses interpretability. This paper introduces a new Gaussian process model whose stochastic part is orthogonal to the mean part to address this issue. As a result, this paper also discusses applications to multi-fidelity simulations using data examples.
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Orthogonal Gaussian process models
DOE Office of Scientific and Technical Information (OSTI.GOV)
Plumlee, Matthew; Joseph, V. Roshan
Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads to poor estimation of the coefficients in the mean model, and thus the estimated mean model loses interpretability. This paper introduces a new Gaussian process model whose stochastic part is orthogonal to the mean part to address this issue. As a result, this paper also discusses applications to multi-fidelity simulations using data examples.
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Poly-Gaussian model of randomly rough surface in rarefied gas flow
DOE Office of Scientific and Technical Information (OSTI.GOV)
Aksenova, Olga A.; Khalidov, Iskander A.
2014-12-09
Surface roughness is simulated by the model of non-Gaussian random process. Our results for the scattering of rarefied gas atoms from a rough surface using modified approach to the DSMC calculation of rarefied gas flow near a rough surface are developed and generalized applying the poly-Gaussian model representing probability density as the mixture of Gaussian densities. The transformation of the scattering function due to the roughness is characterized by the roughness operator. Simulating rough surface of the walls by the poly-Gaussian random field expressed as integrated Wiener process, we derive a representation of the roughness operator that can be appliedmore » in numerical DSMC methods as well as in analytical investigations.« less
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Non-Gaussian PDF Modeling of Turbulent Boundary Layer Fluctuating Pressure Excitation
NASA Technical Reports Server (NTRS)
Steinwolf, Alexander; Rizzi, Stephen A.
2003-01-01
The purpose of the study is to investigate properties of the probability density function (PDF) of turbulent boundary layer fluctuating pressures measured on the exterior of a supersonic transport aircraft. It is shown that fluctuating pressure PDFs differ from the Gaussian distribution even for surface conditions having no significant discontinuities. The PDF tails are wider and longer than those of the Gaussian model. For pressure fluctuations upstream of forward-facing step discontinuities and downstream of aft-facing step discontinuities, deviations from the Gaussian model are more significant and the PDFs become asymmetrical. Various analytical PDF distributions are used and further developed to model this behavior.
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NASA Astrophysics Data System (ADS)
Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing
2018-05-01
We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.
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Non-Gaussianities in multifield DBI inflation with a waterfall phase transition
NASA Astrophysics Data System (ADS)
Kidani, Taichi; Koyama, Kazuya; Mizuno, Shuntaro
2012-10-01
We study multifield Dirac-Born-Infeld (DBI) inflation models with a waterfall phase transition. This transition happens for a D3 brane moving in the warped conifold if there is an instability along angular directions. The transition converts the angular perturbations into the curvature perturbation. Thanks to this conversion, multifield models can evade the stringent constraints that strongly disfavor single field ultraviolet (UV) DBI inflation models in string theory. We explicitly demonstrate that our model satisfies current observational constraints on the spectral index and equilateral non-Gaussianity as well as the bound on the tensor to scalar ratio imposed in string theory models. In addition, we show that large local type non-Gaussianity is generated together with equilateral non-Gaussianity in this model.
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Multiview road sign detection via self-adaptive color model and shape context matching
NASA Astrophysics Data System (ADS)
Liu, Chunsheng; Chang, Faliang; Liu, Chengyun
2016-09-01
The multiview appearance of road signs in uncontrolled environments has made the detection of road signs a challenging problem in computer vision. We propose a road sign detection method to detect multiview road signs. This method is based on several algorithms, including the classical cascaded detector, the self-adaptive weighted Gaussian color model (SW-Gaussian model), and a shape context matching method. The classical cascaded detector is used to detect the frontal road signs in video sequences and obtain the parameters for the SW-Gaussian model. The proposed SW-Gaussian model combines the two-dimensional Gaussian model and the normalized red channel together, which can largely enhance the contrast between the red signs and background. The proposed shape context matching method can match shapes with big noise, which is utilized to detect road signs in different directions. The experimental results show that compared with previous detection methods, the proposed multiview detection method can reach higher detection rate in detecting signs with different directions.
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Sparse network-based models for patient classification using fMRI
Rosa, Maria J.; Portugal, Liana; Hahn, Tim; Fallgatter, Andreas J.; Garrido, Marta I.; Shawe-Taylor, John; Mourao-Miranda, Janaina
2015-01-01
Pattern recognition applied to whole-brain neuroimaging data, such as functional Magnetic Resonance Imaging (fMRI), has proved successful at discriminating psychiatric patients from healthy participants. However, predictive patterns obtained from whole-brain voxel-based features are difficult to interpret in terms of the underlying neurobiology. Many psychiatric disorders, such as depression and schizophrenia, are thought to be brain connectivity disorders. Therefore, pattern recognition based on network models might provide deeper insights and potentially more powerful predictions than whole-brain voxel-based approaches. Here, we build a novel sparse network-based discriminative modeling framework, based on Gaussian graphical models and L1-norm regularized linear Support Vector Machines (SVM). In addition, the proposed framework is optimized in terms of both predictive power and reproducibility/stability of the patterns. Our approach aims to provide better pattern interpretation than voxel-based whole-brain approaches by yielding stable brain connectivity patterns that underlie discriminative changes in brain function between the groups. We illustrate our technique by classifying patients with major depressive disorder (MDD) and healthy participants, in two (event- and block-related) fMRI datasets acquired while participants performed a gender discrimination and emotional task, respectively, during the visualization of emotional valent faces. PMID:25463459
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Non-Gaussian Multi-resolution Modeling of Magnetosphere-Ionosphere Coupling Processes
NASA Astrophysics Data System (ADS)
Fan, M.; Paul, D.; Lee, T. C. M.; Matsuo, T.
2016-12-01
The most dynamic coupling between the magnetosphere and ionosphere occurs in the Earth's polar atmosphere. Our objective is to model scale-dependent stochastic characteristics of high-latitude ionospheric electric fields that originate from solar wind magnetosphere-ionosphere interactions. The Earth's high-latitude ionospheric electric field exhibits considerable variability, with increasing non-Gaussian characteristics at decreasing spatio-temporal scales. Accurately representing the underlying stochastic physical process through random field modeling is crucial not only for scientific understanding of the energy, momentum and mass exchanges between the Earth's magnetosphere and ionosphere, but also for modern technological systems including telecommunication, navigation, positioning and satellite tracking. While a lot of efforts have been made to characterize the large-scale variability of the electric field in the context of Gaussian processes, no attempt has been made so far to model the small-scale non-Gaussian stochastic process observed in the high-latitude ionosphere. We construct a novel random field model using spherical needlets as building blocks. The double localization of spherical needlets in both spatial and frequency domains enables the model to capture the non-Gaussian and multi-resolutional characteristics of the small-scale variability. The estimation procedure is computationally feasible due to the utilization of an adaptive Gibbs sampler. We apply the proposed methodology to the computational simulation output from the Lyon-Fedder-Mobarry (LFM) global magnetohydrodynamics (MHD) magnetosphere model. Our non-Gaussian multi-resolution model results in characterizing significantly more energy associated with the small-scale ionospheric electric field variability in comparison to Gaussian models. By accurately representing unaccounted-for additional energy and momentum sources to the Earth's upper atmosphere, our novel random field modeling approach will provide a viable remedy to the current numerical models' systematic biases resulting from the underestimation of high-latitude energy and momentum sources.
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Flat-top beam for laser-stimulated pain
NASA Astrophysics Data System (ADS)
McCaughey, Ryan; Nadeau, Valerie; Dickinson, Mark
2005-04-01
One of the main problems during laser stimulation in human pain research is the risk of tissue damage caused by excessive heating of the skin. This risk has been reduced by using a laser beam with a flattop (or superGaussian) intensity profile, instead of the conventional Gaussian beam. A finite difference approximation to the heat conduction equation has been applied to model the temperature distribution in skin as a result of irradiation by flattop and Gaussian profile CO2 laser beams. The model predicts that a 15 mm diameter, 15 W, 100 ms CO2 laser pulse with an order 6 superGaussian profile produces a maximum temperature 6 oC less than a Gaussian beam with the same energy density. A superGaussian profile was created by passing a Gaussian beam through a pair of zinc selenide aspheric lenses which refract the more intense central region of the beam towards the less intense periphery. The profiles of the lenses were determined by geometrical optics. In human pain trials the superGaussian beam required more power than the Gaussian beam to reach sensory and pain thresholds.
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Gaussian-input Gaussian mixture model for representing density maps and atomic models.
Kawabata, Takeshi
2018-07-01
A new Gaussian mixture model (GMM) has been developed for better representations of both atomic models and electron microscopy 3D density maps. The standard GMM algorithm employs an EM algorithm to determine the parameters. It accepted a set of 3D points with weights, corresponding to voxel or atomic centers. Although the standard algorithm worked reasonably well; however, it had three problems. First, it ignored the size (voxel width or atomic radius) of the input, and thus it could lead to a GMM with a smaller spread than the input. Second, the algorithm had a singularity problem, as it sometimes stopped the iterative procedure due to a Gaussian function with almost zero variance. Third, a map with a large number of voxels required a long computation time for conversion to a GMM. To solve these problems, we have introduced a Gaussian-input GMM algorithm, which considers the input atoms or voxels as a set of Gaussian functions. The standard EM algorithm of GMM was extended to optimize the new GMM. The new GMM has identical radius of gyration to the input, and does not suddenly stop due to the singularity problem. For fast computation, we have introduced a down-sampled Gaussian functions (DSG) by merging neighboring voxels into an anisotropic Gaussian function. It provides a GMM with thousands of Gaussian functions in a short computation time. We also have introduced a DSG-input GMM: the Gaussian-input GMM with the DSG as the input. This new algorithm is much faster than the standard algorithm. Copyright © 2018 The Author(s). Published by Elsevier Inc. All rights reserved.
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MacKenzie, Donald; Spears, Taylor
2014-06-01
Drawing on documentary sources and 114 interviews with market participants, this and a companion article discuss the development and use in finance of the Gaussian copula family of models, which are employed to estimate the probability distribution of losses on a pool of loans or bonds, and which were centrally involved in the credit crisis. This article, which explores how and why the Gaussian copula family developed in the way it did, employs the concept of 'evaluation culture', a set of practices, preferences and beliefs concerning how to determine the economic value of financial instruments that is shared by members of multiple organizations. We identify an evaluation culture, dominant within the derivatives departments of investment banks, which we call the 'culture of no-arbitrage modelling', and explore its relation to the development of Gaussian copula models. The article suggests that two themes from the science and technology studies literature on models (modelling as 'impure' bricolage, and modelling as articulating with heterogeneous objectives and constraints) help elucidate the history of Gaussian copula models in finance.
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NASA Astrophysics Data System (ADS)
Nishimura, Tomoaki
2016-03-01
A computer simulation program for ion scattering and its graphical user interface (MEISwin) has been developed. Using this program, researchers have analyzed medium-energy ion scattering and Rutherford backscattering spectrometry at Ritsumeikan University since 1998, and at Rutgers University since 2007. The main features of the program are as follows: (1) stopping power can be chosen from five datasets spanning several decades (from 1977 to 2011), (2) straggling can be chosen from two datasets, (3) spectral shape can be selected as Gaussian or exponentially modified Gaussian, (4) scattering cross sections can be selected as Coulomb or screened, (5) simulations adopt the resonant elastic scattering cross section of 16O(4He, 4He)16O, (6) pileup simulation for RBS spectra is supported, (7) natural and specific isotope abundances are supported, and (8) the charge fraction can be chosen from three patterns (fixed, energy-dependent, and ion fraction with charge-exchange parameters for medium-energy ion scattering). This study demonstrates and discusses the simulations and their results.
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Gaussian temporal modulation for the behavior of multi-sinc Schell-model pulses in dispersive media
NASA Astrophysics Data System (ADS)
Liu, Xiayin; Zhao, Daomu; Tian, Kehan; Pan, Weiqing; Zhang, Kouwen
2018-06-01
A new class of pulse source with correlation being modeled by the convolution operation of two legitimate temporal correlation function is proposed. Particularly, analytical formulas for the Gaussian temporally modulated multi-sinc Schell-model (MSSM) pulses generated by such pulse source propagating in dispersive media are derived. It is demonstrated that the average intensity of MSSM pulses on propagation are reshaped from flat profile or a train to a distribution with a Gaussian temporal envelope by adjusting the initial correlation width of the Gaussian pulse. The effects of the Gaussian temporal modulation on the temporal degree of coherence of the MSSM pulse are also analyzed. The results presented here show the potential of coherence modulation for pulse shaping and pulsed laser material processing.
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Marias, Kostas; Lambregts, Doenja M. J.; Nikiforaki, Katerina; van Heeswijk, Miriam M.; Bakers, Frans C. H.; Beets-Tan, Regina G. H.
2017-01-01
Purpose The purpose of this study was to compare the performance of four diffusion models, including mono and bi-exponential both Gaussian and non-Gaussian models, in diffusion weighted imaging of rectal cancer. Material and methods Nineteen patients with rectal adenocarcinoma underwent MRI examination of the rectum before chemoradiation therapy including a 7 b-value diffusion sequence (0, 25, 50, 100, 500, 1000 and 2000 s/mm2) at a 1.5T scanner. Four different diffusion models including mono- and bi-exponential Gaussian (MG and BG) and non-Gaussian (MNG and BNG) were applied on whole tumor volumes of interest. Two different statistical criteria were recruited to assess their fitting performance, including the adjusted-R2 and Root Mean Square Error (RMSE). To decide which model better characterizes rectal cancer, model selection was relied on Akaike Information Criteria (AIC) and F-ratio. Results All candidate models achieved a good fitting performance with the two most complex models, the BG and the BNG, exhibiting the best fitting performance. However, both criteria for model selection indicated that the MG model performed better than any other model. In particular, using AIC Weights and F-ratio, the pixel-based analysis demonstrated that tumor areas better described by the simplest MG model in an average area of 53% and 33%, respectively. Non-Gaussian behavior was illustrated in an average area of 37% according to the F-ratio, and 7% using AIC Weights. However, the distributions of the pixels best fitted by each of the four models suggest that MG failed to perform better than any other model in all patients, and the overall tumor area. Conclusion No single diffusion model evaluated herein could accurately describe rectal tumours. These findings probably can be explained on the basis of increased tumour heterogeneity, where areas with high vascularity could be fitted better with bi-exponential models, and areas with necrosis would mostly follow mono-exponential behavior. PMID:28863161
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Manikis, Georgios C; Marias, Kostas; Lambregts, Doenja M J; Nikiforaki, Katerina; van Heeswijk, Miriam M; Bakers, Frans C H; Beets-Tan, Regina G H; Papanikolaou, Nikolaos
2017-01-01
The purpose of this study was to compare the performance of four diffusion models, including mono and bi-exponential both Gaussian and non-Gaussian models, in diffusion weighted imaging of rectal cancer. Nineteen patients with rectal adenocarcinoma underwent MRI examination of the rectum before chemoradiation therapy including a 7 b-value diffusion sequence (0, 25, 50, 100, 500, 1000 and 2000 s/mm2) at a 1.5T scanner. Four different diffusion models including mono- and bi-exponential Gaussian (MG and BG) and non-Gaussian (MNG and BNG) were applied on whole tumor volumes of interest. Two different statistical criteria were recruited to assess their fitting performance, including the adjusted-R2 and Root Mean Square Error (RMSE). To decide which model better characterizes rectal cancer, model selection was relied on Akaike Information Criteria (AIC) and F-ratio. All candidate models achieved a good fitting performance with the two most complex models, the BG and the BNG, exhibiting the best fitting performance. However, both criteria for model selection indicated that the MG model performed better than any other model. In particular, using AIC Weights and F-ratio, the pixel-based analysis demonstrated that tumor areas better described by the simplest MG model in an average area of 53% and 33%, respectively. Non-Gaussian behavior was illustrated in an average area of 37% according to the F-ratio, and 7% using AIC Weights. However, the distributions of the pixels best fitted by each of the four models suggest that MG failed to perform better than any other model in all patients, and the overall tumor area. No single diffusion model evaluated herein could accurately describe rectal tumours. These findings probably can be explained on the basis of increased tumour heterogeneity, where areas with high vascularity could be fitted better with bi-exponential models, and areas with necrosis would mostly follow mono-exponential behavior.
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Gaussian processes: a method for automatic QSAR modeling of ADME properties.
Obrezanova, Olga; Csanyi, Gabor; Gola, Joelle M R; Segall, Matthew D
2007-01-01
In this article, we discuss the application of the Gaussian Process method for the prediction of absorption, distribution, metabolism, and excretion (ADME) properties. On the basis of a Bayesian probabilistic approach, the method is widely used in the field of machine learning but has rarely been applied in quantitative structure-activity relationship and ADME modeling. The method is suitable for modeling nonlinear relationships, does not require subjective determination of the model parameters, works for a large number of descriptors, and is inherently resistant to overtraining. The performance of Gaussian Processes compares well with and often exceeds that of artificial neural networks. Due to these features, the Gaussian Processes technique is eminently suitable for automatic model generation-one of the demands of modern drug discovery. Here, we describe the basic concept of the method in the context of regression problems and illustrate its application to the modeling of several ADME properties: blood-brain barrier, hERG inhibition, and aqueous solubility at pH 7.4. We also compare Gaussian Processes with other modeling techniques.
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Automatic image equalization and contrast enhancement using Gaussian mixture modeling.
Celik, Turgay; Tjahjadi, Tardi
2012-01-01
In this paper, we propose an adaptive image equalization algorithm that automatically enhances the contrast in an input image. The algorithm uses the Gaussian mixture model to model the image gray-level distribution, and the intersection points of the Gaussian components in the model are used to partition the dynamic range of the image into input gray-level intervals. The contrast equalized image is generated by transforming the pixels' gray levels in each input interval to the appropriate output gray-level interval according to the dominant Gaussian component and the cumulative distribution function of the input interval. To take account of the hypothesis that homogeneous regions in the image represent homogeneous silences (or set of Gaussian components) in the image histogram, the Gaussian components with small variances are weighted with smaller values than the Gaussian components with larger variances, and the gray-level distribution is also used to weight the components in the mapping of the input interval to the output interval. Experimental results show that the proposed algorithm produces better or comparable enhanced images than several state-of-the-art algorithms. Unlike the other algorithms, the proposed algorithm is free of parameter setting for a given dynamic range of the enhanced image and can be applied to a wide range of image types.
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Spatio-Temporal Data Analysis at Scale Using Models Based on Gaussian Processes
DOE Office of Scientific and Technical Information (OSTI.GOV)
Stein, Michael
Gaussian processes are the most commonly used statistical model for spatial and spatio-temporal processes that vary continuously. They are broadly applicable in the physical sciences and engineering and are also frequently used to approximate the output of complex computer models, deterministic or stochastic. We undertook research related to theory, computation, and applications of Gaussian processes as well as some work on estimating extremes of distributions for which a Gaussian process assumption might be inappropriate. Our theoretical contributions include the development of new classes of spatial-temporal covariance functions with desirable properties and new results showing that certain covariance models lead tomore » predictions with undesirable properties. To understand how Gaussian process models behave when applied to deterministic computer models, we derived what we believe to be the first significant results on the large sample properties of estimators of parameters of Gaussian processes when the actual process is a simple deterministic function. Finally, we investigated some theoretical issues related to maxima of observations with varying upper bounds and found that, depending on the circumstances, standard large sample results for maxima may or may not hold. Our computational innovations include methods for analyzing large spatial datasets when observations fall on a partially observed grid and methods for estimating parameters of a Gaussian process model from observations taken by a polar-orbiting satellite. In our application of Gaussian process models to deterministic computer experiments, we carried out some matrix computations that would have been infeasible using even extended precision arithmetic by focusing on special cases in which all elements of the matrices under study are rational and using exact arithmetic. The applications we studied include total column ozone as measured from a polar-orbiting satellite, sea surface temperatures over the Pacific Ocean, and annual temperature extremes at a site in New York City. In each of these applications, our theoretical and computational innovations were directly motivated by the challenges posed by analyzing these and similar types of data.« less
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Topology of large-scale structure in seeded hot dark matter models
NASA Technical Reports Server (NTRS)
Beaky, Matthew M.; Scherrer, Robert J.; Villumsen, Jens V.
1992-01-01
The topology of the isodensity surfaces in seeded hot dark matter models, in which static seed masses provide the density perturbations in a universe dominated by massive neutrinos is examined. When smoothed with a Gaussian window, the linear initial conditions in these models show no trace of non-Gaussian behavior for r0 equal to or greater than 5 Mpc (h = 1/2), except for very low seed densities, which show a shift toward isolated peaks. An approximate analytic expression is given for the genus curve expected in linear density fields from randomly distributed seed masses. The evolved models have a Gaussian topology for r0 = 10 Mpc, but show a shift toward a cellular topology with r0 = 5 Mpc; Gaussian models with an identical power spectrum show the same behavior.
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Deng, Wenping; Zhang, Kui; Busov, Victor; Wei, Hairong
2017-01-01
Present knowledge indicates a multilayered hierarchical gene regulatory network (ML-hGRN) often operates above a biological pathway. Although the ML-hGRN is very important for understanding how a pathway is regulated, there is almost no computational algorithm for directly constructing ML-hGRNs. A backward elimination random forest (BWERF) algorithm was developed for constructing the ML-hGRN operating above a biological pathway. For each pathway gene, the BWERF used a random forest model to calculate the importance values of all transcription factors (TFs) to this pathway gene recursively with a portion (e.g. 1/10) of least important TFs being excluded in each round of modeling, during which, the importance values of all TFs to the pathway gene were updated and ranked until only one TF was remained in the list. The above procedure, termed BWERF. After that, the importance values of a TF to all pathway genes were aggregated and fitted to a Gaussian mixture model to determine the TF retention for the regulatory layer immediately above the pathway layer. The acquired TFs at the secondary layer were then set to be the new bottom layer to infer the next upper layer, and this process was repeated until a ML-hGRN with the expected layers was obtained. BWERF improved the accuracy for constructing ML-hGRNs because it used backward elimination to exclude the noise genes, and aggregated the individual importance values for determining the TFs retention. We validated the BWERF by using it for constructing ML-hGRNs operating above mouse pluripotency maintenance pathway and Arabidopsis lignocellulosic pathway. Compared to GENIE3, BWERF showed an improvement in recognizing authentic TFs regulating a pathway. Compared to the bottom-up Gaussian graphical model algorithm we developed for constructing ML-hGRNs, the BWERF can construct ML-hGRNs with significantly reduced edges that enable biologists to choose the implicit edges for experimental validation.
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NASA Astrophysics Data System (ADS)
Dehbi, Y.; Haunert, J.-H.; Plümer, L.
2017-10-01
3D city and building models according to CityGML encode the geometry, represent the structure and model semantically relevant building parts such as doors, windows and balconies. Building information models support the building design, construction and the facility management. In contrast to CityGML, they include also objects which cannot be observed from the outside. The three dimensional indoor models characterize a missing link between both worlds. Their derivation, however, is expensive. The semantic automatic interpretation of 3D point clouds of indoor environments is a methodically demanding task. The data acquisition is costly and difficult. The laser scanners and image-based methods require the access to every room. Based on an approach which does not require an additional geometry acquisition of building indoors, we propose an attempt for filling the gaps between 3D building models and building information models. Based on sparse observations such as the building footprint and room areas, 3D indoor models are generated using combinatorial and stochastic reasoning. The derived models are expanded by a-priori not observable structures such as electric installation. Gaussian mixtures, linear and bi-linear constraints are used to represent the background knowledge and structural regularities. The derivation of hypothesised models is performed by stochastic reasoning using graphical models, Gauss-Markov models and MAP-estimators.
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Kärkkäinen, Hanni P; Sillanpää, Mikko J
2013-09-04
Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed.
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Kärkkäinen, Hanni P.; Sillanpää, Mikko J.
2013-01-01
Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed. PMID:23821618
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Non-gaussianity versus nonlinearity of cosmological perturbations.
Verde, L
2001-06-01
Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us toward a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, nonlinear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but galaxies might not be faithful tracers of the underlying mass distribution. The relationship between fluctuations in the mass and in the galaxies distribution (bias), is often assumed to be local, but could well be nonlinear. Moreover, galaxy catalogues use the redshift as third spatial coordinate: the resulting redshift-space map of the galaxy distribution is nonlinearly distorted by peculiar velocities. Nonlinear gravitational evolution, biasing, and redshift-space distortion introduce non-gaussianity, even in an initially gaussian fluctuation field. I investigate the statistical tools that allow us, in principle, to disentangle the above different effects, and the observational datasets we require to do so in practice.
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Techniques and software tools for estimating ultrasonic signal-to-noise ratios
NASA Astrophysics Data System (ADS)
Chiou, Chien-Ping; Margetan, Frank J.; McKillip, Matthew; Engle, Brady J.; Roberts, Ronald A.
2016-02-01
At Iowa State University's Center for Nondestructive Evaluation (ISU CNDE), the use of models to simulate ultrasonic inspections has played a key role in R&D efforts for over 30 years. To this end a series of wave propagation models, flaw response models, and microstructural backscatter models have been developed to address inspection problems of interest. One use of the combined models is the estimation of signal-to-noise ratios (S/N) in circumstances where backscatter from the microstructure (grain noise) acts to mask sonic echoes from internal defects. Such S/N models have been used in the past to address questions of inspection optimization and reliability. Under the sponsorship of the National Science Foundation's Industry/University Cooperative Research Center at ISU, an effort was recently initiated to improve existing research-grade software by adding graphical user interface (GUI) to become user friendly tools for the rapid estimation of S/N for ultrasonic inspections of metals. The software combines: (1) a Python-based GUI for specifying an inspection scenario and displaying results; and (2) a Fortran-based engine for computing defect signal and backscattered grain noise characteristics. The latter makes use of several models including: the Multi-Gaussian Beam Model for computing sonic fields radiated by commercial transducers; the Thompson-Gray Model for the response from an internal defect; the Independent Scatterer Model for backscattered grain noise; and the Stanke-Kino Unified Model for attenuation. The initial emphasis was on reformulating the research-grade code into a suitable modular form, adding the graphical user interface and performing computations rapidly and robustly. Thus the initial inspection problem being addressed is relatively simple. A normal-incidence pulse/echo immersion inspection is simulated for a curved metal component having a non-uniform microstructure, specifically an equiaxed, untextured microstructure in which the average grain size may vary with depth. The defect may be a flat-bottomed-hole reference reflector, a spherical void or a spherical inclusion. In future generations of the software, microstructures and defect types will be generalized and oblique incidence inspections will be treated as well. This paper provides an overview of the modeling approach and presents illustrative results output by the first-generation software.
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Petersen, Per H; Lund, Flemming; Fraser, Callum G; Sölétormos, György
2016-11-01
Background The distributions of within-subject biological variation are usually described as coefficients of variation, as are analytical performance specifications for bias, imprecision and other characteristics. Estimation of specifications required for reference change values is traditionally done using relationship between the batch-related changes during routine performance, described as Δbias, and the coefficients of variation for analytical imprecision (CV A ): the original theory is based on standard deviations or coefficients of variation calculated as if distributions were Gaussian. Methods The distribution of between-subject biological variation can generally be described as log-Gaussian. Moreover, recent analyses of within-subject biological variation suggest that many measurands have log-Gaussian distributions. In consequence, we generated a model for the estimation of analytical performance specifications for reference change value, with combination of Δbias and CV A based on log-Gaussian distributions of CV I as natural logarithms. The model was tested using plasma prolactin and glucose as examples. Results Analytical performance specifications for reference change value generated using the new model based on log-Gaussian distributions were practically identical with the traditional model based on Gaussian distributions. Conclusion The traditional and simple to apply model used to generate analytical performance specifications for reference change value, based on the use of coefficients of variation and assuming Gaussian distributions for both CV I and CV A , is generally useful.
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GaussianCpG: a Gaussian model for detection of CpG island in human genome sequences.
Yu, Ning; Guo, Xuan; Zelikovsky, Alexander; Pan, Yi
2017-05-24
As crucial markers in identifying biological elements and processes in mammalian genomes, CpG islands (CGI) play important roles in DNA methylation, gene regulation, epigenetic inheritance, gene mutation, chromosome inactivation and nuclesome retention. The generally accepted criteria of CGI rely on: (a) %G+C content is ≥ 50%, (b) the ratio of the observed CpG content and the expected CpG content is ≥ 0.6, and (c) the general length of CGI is greater than 200 nucleotides. Most existing computational methods for the prediction of CpG island are programmed on these rules. However, many experimentally verified CpG islands deviate from these artificial criteria. Experiments indicate that in many cases %G+C is < 50%, CpG obs /CpG exp varies, and the length of CGI ranges from eight nucleotides to a few thousand of nucleotides. It implies that CGI detection is not just a straightly statistical task and some unrevealed rules probably are hidden. A novel Gaussian model, GaussianCpG, is developed for detection of CpG islands on human genome. We analyze the energy distribution over genomic primary structure for each CpG site and adopt the parameters from statistics of Human genome. The evaluation results show that the new model can predict CpG islands efficiently by balancing both sensitivity and specificity over known human CGI data sets. Compared with other models, GaussianCpG can achieve better performance in CGI detection. Our Gaussian model aims to simplify the complex interaction between nucleotides. The model is computed not by the linear statistical method but by the Gaussian energy distribution and accumulation. The parameters of Gaussian function are not arbitrarily designated but deliberately chosen by optimizing the biological statistics. By using the pseudopotential analysis on CpG islands, the novel model is validated on both the real and artificial data sets.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Hirayama, S; Takayanagi, T; Fujii, Y
2014-06-15
Purpose: To present the validity of our beam modeling with double and triple Gaussian dose kernels for spot scanning proton beams in Nagoya Proton Therapy Center. This study investigates the conformance between the measurements and calculation results in absolute dose with two types of beam kernel. Methods: A dose kernel is one of the important input data required for the treatment planning software. The dose kernel is the 3D dose distribution of an infinitesimal pencil beam of protons in water and consists of integral depth doses and lateral distributions. We have adopted double and triple Gaussian model as lateral distributionmore » in order to take account of the large angle scattering due to nuclear reaction by fitting simulated inwater lateral dose profile for needle proton beam at various depths. The fitted parameters were interpolated as a function of depth in water and were stored as a separate look-up table for the each beam energy. The process of beam modeling is based on the method of MDACC [X.R.Zhu 2013]. Results: From the comparison results between the absolute doses calculated by double Gaussian model and those measured at the center of SOBP, the difference is increased up to 3.5% in the high-energy region because the large angle scattering due to nuclear reaction is not sufficiently considered at intermediate depths in the double Gaussian model. In case of employing triple Gaussian dose kernels, the measured absolute dose at the center of SOBP agrees with calculation within ±1% regardless of the SOBP width and maximum range. Conclusion: We have demonstrated the beam modeling results of dose distribution employing double and triple Gaussian dose kernel. Treatment planning system with the triple Gaussian dose kernel has been successfully verified and applied to the patient treatment with a spot scanning technique in Nagoya Proton Therapy Center.« less
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Brookes, Emre; Pérez, Javier; Cardinali, Barbara; Profumo, Aldo; Vachette, Patrice; Rocco, Mattia
2013-12-01
Fibrinogen is a large heterogeneous aggregation/degradation-prone protein playing a central role in blood coagulation and associated pathologies, whose structure is not completely resolved. When a high-molecular-weight fraction was analyzed by size-exclusion high-performance liquid chromatography/small-angle X-ray scattering (HPLC-SAXS), several composite peaks were apparent and because of the stickiness of fibrinogen the analysis was complicated by severe capillary fouling. Novel SAS analysis tools developed as a part of the UltraScan Solution Modeler ( US-SOMO ; http://somo.uthscsa.edu/), an open-source suite of utilities with advanced graphical user interfaces whose initial goal was the hydrodynamic modeling of biomacromolecules, were implemented and applied to this problem. They include the correction of baseline drift due to the accumulation of material on the SAXS capillary walls, and the Gaussian decomposition of non-baseline-resolved HPLC-SAXS elution peaks. It was thus possible to resolve at least two species co-eluting under the fibrinogen main monomer peak, probably resulting from in-column degradation, and two others under an oligomers peak. The overall and cross-sectional radii of gyration, molecular mass and mass/length ratio of all species were determined using the manual or semi-automated procedures available within the US-SOMO SAS module. Differences between monomeric species and linear and sideways oligomers were thus identified and rationalized. This new US-SOMO version additionally contains several computational and graphical tools, implementing functionalities such as the mapping of residues contributing to particular regions of P ( r ), and an advanced module for the comparison of primary I ( q ) versus q data with model curves computed from atomic level structures or bead models. It should be of great help in multi-resolution studies involving hydrodynamics, solution scattering and crystallographic/NMR data.
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Variational Gaussian approximation for Poisson data
NASA Astrophysics Data System (ADS)
Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen
2018-02-01
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.
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Extinction time of a stochastic predator-prey model by the generalized cell mapping method
NASA Astrophysics Data System (ADS)
Han, Qun; Xu, Wei; Hu, Bing; Huang, Dongmei; Sun, Jian-Qiao
2018-03-01
The stochastic response and extinction time of a predator-prey model with Gaussian white noise excitations are studied by the generalized cell mapping (GCM) method based on the short-time Gaussian approximation (STGA). The methods for stochastic response probability density functions (PDFs) and extinction time statistics are developed. The Taylor expansion is used to deal with non-polynomial nonlinear terms of the model for deriving the moment equations with Gaussian closure, which are needed for the STGA in order to compute the one-step transition probabilities. The work is validated with direct Monte Carlo simulations. We have presented the transient responses showing the evolution from a Gaussian initial distribution to a non-Gaussian steady-state one. The effects of the model parameter and noise intensities on the steady-state PDFs are discussed. It is also found that the effects of noise intensities on the extinction time statistics are opposite to the effects on the limit probability distributions of the survival species.
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NASA Astrophysics Data System (ADS)
Krohn, Olivia; Armbruster, Aaron; Gao, Yongsheng; Atlas Collaboration
2017-01-01
Software tools developed for the purpose of modeling CERN LHC pp collision data to aid in its interpretation are presented. Some measurements are not adequately described by a Gaussian distribution; thus an interpretation assuming Gaussian uncertainties will inevitably introduce bias, necessitating analytical tools to recreate and evaluate non-Gaussian features. One example is the measurements of Higgs boson production rates in different decay channels, and the interpretation of these measurements. The ratios of data to Standard Model expectations (μ) for five arbitrary signals were modeled by building five Poisson distributions with mixed signal contributions such that the measured values of μ are correlated. Algorithms were designed to recreate probability distribution functions of μ as multi-variate Gaussians, where the standard deviation (σ) and correlation coefficients (ρ) are parametrized. There was good success with modeling 1-D likelihood contours of μ, and the multi-dimensional distributions were well modeled within 1- σ but the model began to diverge after 2- σ due to unmerited assumptions in developing ρ. Future plans to improve the algorithms and develop a user-friendly analysis package will also be discussed. NSF International Research Experiences for Students
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Hirayama, Shusuke; Takayanagi, Taisuke; Fujii, Yusuke; Fujimoto, Rintaro; Fujitaka, Shinichiro; Umezawa, Masumi; Nagamine, Yoshihiko; Hosaka, Masahiro; Yasui, Keisuke; Omachi, Chihiro; Toshito, Toshiyuki
2016-03-01
The main purpose in this study was to present the results of beam modeling and how the authors systematically investigated the influence of double and triple Gaussian proton kernel models on the accuracy of dose calculations for spot scanning technique. The accuracy of calculations was important for treatment planning software (TPS) because the energy, spot position, and absolute dose had to be determined by TPS for the spot scanning technique. The dose distribution was calculated by convolving in-air fluence with the dose kernel. The dose kernel was the in-water 3D dose distribution of an infinitesimal pencil beam and consisted of an integral depth dose (IDD) and a lateral distribution. Accurate modeling of the low-dose region was important for spot scanning technique because the dose distribution was formed by cumulating hundreds or thousands of delivered beams. The authors employed a double Gaussian function as the in-air fluence model of an individual beam. Double and triple Gaussian kernel models were also prepared for comparison. The parameters of the kernel lateral model were derived by fitting a simulated in-water lateral dose profile induced by an infinitesimal proton beam, whose emittance was zero, at various depths using Monte Carlo (MC) simulation. The fitted parameters were interpolated as a function of depth in water and stored as a separate look-up table. These stored parameters for each energy and depth in water were acquired from the look-up table when incorporating them into the TPS. The modeling process for the in-air fluence and IDD was based on the method proposed in the literature. These were derived using MC simulation and measured data. The authors compared the measured and calculated absolute doses at the center of the spread-out Bragg peak (SOBP) under various volumetric irradiation conditions to systematically investigate the influence of the two types of kernel models on the dose calculations. The authors investigated the difference between double and triple Gaussian kernel models. The authors found that the difference between the two studied kernel models appeared at mid-depths and the accuracy of predicting the double Gaussian model deteriorated at the low-dose bump that appeared at mid-depths. When the authors employed the double Gaussian kernel model, the accuracy of calculations for the absolute dose at the center of the SOBP varied with irradiation conditions and the maximum difference was 3.4%. In contrast, the results obtained from calculations with the triple Gaussian kernel model indicated good agreement with the measurements within ±1.1%, regardless of the irradiation conditions. The difference between the results obtained with the two types of studied kernel models was distinct in the high energy region. The accuracy of calculations with the double Gaussian kernel model varied with the field size and SOBP width because the accuracy of prediction with the double Gaussian model was insufficient at the low-dose bump. The evaluation was only qualitative under limited volumetric irradiation conditions. Further accumulation of measured data would be needed to quantitatively comprehend what influence the double and triple Gaussian kernel models had on the accuracy of dose calculations.
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Bayesian sensitivity analysis of bifurcating nonlinear models
NASA Astrophysics Data System (ADS)
Becker, W.; Worden, K.; Rowson, J.
2013-01-01
Sensitivity analysis allows one to investigate how changes in input parameters to a system affect the output. When computational expense is a concern, metamodels such as Gaussian processes can offer considerable computational savings over Monte Carlo methods, albeit at the expense of introducing a data modelling problem. In particular, Gaussian processes assume a smooth, non-bifurcating response surface. This work highlights a recent extension to Gaussian processes which uses a decision tree to partition the input space into homogeneous regions, and then fits separate Gaussian processes to each region. In this way, bifurcations can be modelled at region boundaries and different regions can have different covariance properties. To test this method, both the treed and standard methods were applied to the bifurcating response of a Duffing oscillator and a bifurcating FE model of a heart valve. It was found that the treed Gaussian process provides a practical way of performing uncertainty and sensitivity analysis on large, potentially-bifurcating models, which cannot be dealt with by using a single GP, although an open problem remains how to manage bifurcation boundaries that are not parallel to coordinate axes.
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Wear, Keith A
2002-11-01
For a wide range of applications in medical ultrasound, power spectra of received signals are approximately Gaussian. It has been established previously that an ultrasound beam with a Gaussian spectrum propagating through a medium with linear attenuation remains Gaussian. In this paper, Gaussian transformations are derived to model the effects of scattering (according to a power law, as is commonly applicable in soft tissues, especially over limited frequency ranges) and gating (with a Hamming window, a commonly used gate function). These approximations are shown to be quite accurate even for relatively broad band systems with fractional bandwidths approaching 100%. The theory is validated by experiments in phantoms consisting of glass particles suspended in agar.
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Plechawska, Małgorzata; Polańska, Joanna
2009-01-01
This article presents the method of the processing of mass spectrometry data. Mass spectra are modelled with Gaussian Mixture Models. Every peak of the spectrum is represented by a single Gaussian. Its parameters describe the location, height and width of the corresponding peak of the spectrum. An authorial version of the Expectation Maximisation Algorithm was used to perform all calculations. Errors were estimated with a virtual mass spectrometer. The discussed tool was originally designed to generate a set of spectra within defined parameters.
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NASA Astrophysics Data System (ADS)
Lylova, A. N.; Sheldakova, Yu. V.; Kudryashov, A. V.; Samarkin, V. V.
2018-01-01
We consider the methods for modelling doughnut and super-Gaussian intensity distributions in the far field by means of deformable bimorph mirrors. A method for the rapid formation of a specified intensity distribution using a Shack - Hartmann sensor is proposed, and the results of the modelling of doughnut and super-Gaussian intensity distributions are presented.
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Revisiting non-Gaussianity from non-attractor inflation models
NASA Astrophysics Data System (ADS)
Cai, Yi-Fu; Chen, Xingang; Namjoo, Mohammad Hossein; Sasaki, Misao; Wang, Dong-Gang; Wang, Ziwei
2018-05-01
Non-attractor inflation is known as the only single field inflationary scenario that can violate non-Gaussianity consistency relation with the Bunch-Davies vacuum state and generate large local non-Gaussianity. However, it is also known that the non-attractor inflation by itself is incomplete and should be followed by a phase of slow-roll attractor. Moreover, there is a transition process between these two phases. In the past literature, this transition was approximated as instant and the evolution of non-Gaussianity in this phase was not fully studied. In this paper, we follow the detailed evolution of the non-Gaussianity through the transition phase into the slow-roll attractor phase, considering different types of transition. We find that the transition process has important effect on the size of the local non-Gaussianity. We first compute the net contribution of the non-Gaussianities at the end of inflation in canonical non-attractor models. If the curvature perturbations keep evolving during the transition—such as in the case of smooth transition or some sharp transition scenarios—the Script O(1) local non-Gaussianity generated in the non-attractor phase can be completely erased by the subsequent evolution, although the consistency relation remains violated. In extremal cases of sharp transition where the super-horizon modes freeze immediately right after the end of the non-attractor phase, the original non-attractor result can be recovered. We also study models with non-canonical kinetic terms, and find that the transition can typically contribute a suppression factor in the squeezed bispectrum, but the final local non-Gaussianity can still be made parametrically large.
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Li, Derong; Lv, Xiaohua; Bowlan, Pamela; Du, Rui; Zeng, Shaoqun; Luo, Qingming
2009-09-14
The evolution of the frequency chirp of a laser pulse inside a classical pulse compressor is very different for plane waves and Gaussian beams, although after propagating through the last (4th) dispersive element, the two models give the same results. In this paper, we have analyzed the evolution of the frequency chirp of Gaussian pulses and beams using a method which directly obtains the spectral phase acquired by the compressor. We found the spatiotemporal couplings in the phase to be the fundamental reason for the difference in the frequency chirp acquired by a Gaussian beam and a plane wave. When the Gaussian beam propagates, an additional frequency chirp will be introduced if any spatiotemporal couplings (i.e. angular dispersion, spatial chirp or pulse front tilt) are present. However, if there are no couplings present, the chirp of the Gaussian beam is the same as that of a plane wave. When the Gaussian beam is well collimated, the introduced frequency chirp predicted by the plane wave and Gaussian beam models are in closer agreement. This work improves our understanding of pulse compressors and should be helpful for optimizing dispersion compensation schemes in many applications of femtosecond laser pulses.
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Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising.
Zhang, Kai; Zuo, Wangmeng; Chen, Yunjin; Meng, Deyu; Zhang, Lei
2017-07-01
The discriminative model learning for image denoising has been recently attracting considerable attentions due to its favorable denoising performance. In this paper, we take one step forward by investigating the construction of feed-forward denoising convolutional neural networks (DnCNNs) to embrace the progress in very deep architecture, learning algorithm, and regularization method into image denoising. Specifically, residual learning and batch normalization are utilized to speed up the training process as well as boost the denoising performance. Different from the existing discriminative denoising models which usually train a specific model for additive white Gaussian noise at a certain noise level, our DnCNN model is able to handle Gaussian denoising with unknown noise level (i.e., blind Gaussian denoising). With the residual learning strategy, DnCNN implicitly removes the latent clean image in the hidden layers. This property motivates us to train a single DnCNN model to tackle with several general image denoising tasks, such as Gaussian denoising, single image super-resolution, and JPEG image deblocking. Our extensive experiments demonstrate that our DnCNN model can not only exhibit high effectiveness in several general image denoising tasks, but also be efficiently implemented by benefiting from GPU computing.
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NASA Astrophysics Data System (ADS)
Sandoz, J.-P.; Steenaart, W.
1984-12-01
The nonuniform sampling digital phase-locked loop (DPLL) with sequential loop filter, in which the correction sizes are controlled by the accumulated differences of two additional phase comparators, is graphically analyzed. In the absence of noise and frequency drift, the analysis gives some physical insight into the acquisition and tracking behavior. Taking noise into account, a mathematical model is derived and a random walk technique is applied to evaluate the rms phase error and the mean acquisition time. Experimental results confirm the appropriate simplifying hypotheses used in the numerical analysis. Two related performance measures defined in terms of the rms phase error and the acquisition time for a given SNR are used. These measures provide a common basis for comparing different digital loops and, to a limited extent, also with a first-order linear loop. Finally, the behavior of a modified DPLL under frequency deviation in the presence of Gaussian noise is tested experimentally and by computer simulation.
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Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile
NASA Astrophysics Data System (ADS)
Borges, G. M.; Ferreira, A. S.; da Silva, M. A. A.; Cressoni, J. C.; Viswanathan, G. M.; Mariz, A. M.
2012-09-01
Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e.g., fractional Brownian motion, Lévy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation σt which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.
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Robust radio interferometric calibration using the t-distribution
NASA Astrophysics Data System (ADS)
Kazemi, S.; Yatawatta, S.
2013-10-01
A major stage of radio interferometric data processing is calibration or the estimation of systematic errors in the data and the correction for such errors. A stochastic error (noise) model is assumed, and in most cases, this underlying model is assumed to be Gaussian. However, outliers in the data due to interference or due to errors in the sky model would have adverse effects on processing based on a Gaussian noise model. Most of the shortcomings of calibration such as the loss in flux or coherence, and the appearance of spurious sources, could be attributed to the deviations of the underlying noise model. In this paper, we propose to improve the robustness of calibration by using a noise model based on Student's t-distribution. Student's t-noise is a special case of Gaussian noise when the variance is unknown. Unlike Gaussian-noise-model-based calibration, traditional least-squares minimization would not directly extend to a case when we have a Student's t-noise model. Therefore, we use a variant of the expectation-maximization algorithm, called the expectation-conditional maximization either algorithm, when we have a Student's t-noise model and use the Levenberg-Marquardt algorithm in the maximization step. We give simulation results to show the robustness of the proposed calibration method as opposed to traditional Gaussian-noise-model-based calibration, especially in preserving the flux of weaker sources that are not included in the calibration model.
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NASA Astrophysics Data System (ADS)
Zhou, Anran; Xie, Weixin; Pei, Jihong; Chen, Yapei
2018-02-01
For ship targets detection in cluttered infrared image sequences, a robust detection method, based on the probabilistic single Gaussian model of sea background in Fourier domain, is put forward. The amplitude spectrum sequences at each frequency point of the pure seawater images in Fourier domain, being more stable than the gray value sequences of each background pixel in the spatial domain, are regarded as a Gaussian model. Next, a probability weighted matrix is built based on the stability of the pure seawater's total energy spectrum in the row direction, to make the Gaussian model more accurate. Then, the foreground frequency points are separated from the background frequency points by the model. Finally, the false-alarm points are removed utilizing ships' shape features. The performance of the proposed method is tested by visual and quantitative comparisons with others.
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Leong, Siow Hoo; Ong, Seng Huat
2017-01-01
This paper considers three crucial issues in processing scaled down image, the representation of partial image, similarity measure and domain adaptation. Two Gaussian mixture model based algorithms are proposed to effectively preserve image details and avoids image degradation. Multiple partial images are clustered separately through Gaussian mixture model clustering with a scan and select procedure to enhance the inclusion of small image details. The local image features, represented by maximum likelihood estimates of the mixture components, are classified by using the modified Bayes factor (MBF) as a similarity measure. The detection of novel local features from MBF will suggest domain adaptation, which is changing the number of components of the Gaussian mixture model. The performance of the proposed algorithms are evaluated with simulated data and real images and it is shown to perform much better than existing Gaussian mixture model based algorithms in reproducing images with higher structural similarity index.
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Leong, Siow Hoo
2017-01-01
This paper considers three crucial issues in processing scaled down image, the representation of partial image, similarity measure and domain adaptation. Two Gaussian mixture model based algorithms are proposed to effectively preserve image details and avoids image degradation. Multiple partial images are clustered separately through Gaussian mixture model clustering with a scan and select procedure to enhance the inclusion of small image details. The local image features, represented by maximum likelihood estimates of the mixture components, are classified by using the modified Bayes factor (MBF) as a similarity measure. The detection of novel local features from MBF will suggest domain adaptation, which is changing the number of components of the Gaussian mixture model. The performance of the proposed algorithms are evaluated with simulated data and real images and it is shown to perform much better than existing Gaussian mixture model based algorithms in reproducing images with higher structural similarity index. PMID:28686634
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Castillo-Barnes, Diego; Peis, Ignacio; Martínez-Murcia, Francisco J.; Segovia, Fermín; Illán, Ignacio A.; Górriz, Juan M.; Ramírez, Javier; Salas-Gonzalez, Diego
2017-01-01
A wide range of segmentation approaches assumes that intensity histograms extracted from magnetic resonance images (MRI) have a distribution for each brain tissue that can be modeled by a Gaussian distribution or a mixture of them. Nevertheless, intensity histograms of White Matter and Gray Matter are not symmetric and they exhibit heavy tails. In this work, we present a hidden Markov random field model with expectation maximization (EM-HMRF) modeling the components using the α-stable distribution. The proposed model is a generalization of the widely used EM-HMRF algorithm with Gaussian distributions. We test the α-stable EM-HMRF model in synthetic data and brain MRI data. The proposed methodology presents two main advantages: Firstly, it is more robust to outliers. Secondly, we obtain similar results than using Gaussian when the Gaussian assumption holds. This approach is able to model the spatial dependence between neighboring voxels in tomographic brain MRI. PMID:29209194
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Improved Gaussian Beam-Scattering Algorithm
NASA Technical Reports Server (NTRS)
Lock, James A.
1995-01-01
The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.
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Adzhemyan, L Ts; Antonov, N V; Honkonen, J; Kim, T L
2005-01-01
The field theoretic renormalization group and operator-product expansion are applied to the model of a passive scalar quantity advected by a non-Gaussian velocity field with finite correlation time. The velocity is governed by the Navier-Stokes equation, subject to an external random stirring force with the correlation function proportional to delta(t- t')k(4-d-2epsilon). It is shown that the scalar field is intermittent already for small epsilon, its structure functions display anomalous scaling behavior, and the corresponding exponents can be systematically calculated as series in epsilon. The practical calculation is accomplished to order epsilon2 (two-loop approximation), including anisotropic sectors. As for the well-known Kraichnan rapid-change model, the anomalous scaling results from the existence in the model of composite fields (operators) with negative scaling dimensions, identified with the anomalous exponents. Thus the mechanism of the origin of anomalous scaling appears similar for the Gaussian model with zero correlation time and the non-Gaussian model with finite correlation time. It should be emphasized that, in contrast to Gaussian velocity ensembles with finite correlation time, the model and the perturbation theory discussed here are manifestly Galilean covariant. The relevance of these results for real passive advection and comparison with the Gaussian models and experiments are briefly discussed.
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Soft Mixer Assignment in a Hierarchical Generative Model of Natural Scene Statistics
Schwartz, Odelia; Sejnowski, Terrence J.; Dayan, Peter
2010-01-01
Gaussian scale mixture models offer a top-down description of signal generation that captures key bottom-up statistical characteristics of filter responses to images. However, the pattern of dependence among the filters for this class of models is prespecified. We propose a novel extension to the gaussian scale mixture model that learns the pattern of dependence from observed inputs and thereby induces a hierarchical representation of these inputs. Specifically, we propose that inputs are generated by gaussian variables (modeling local filter structure), multiplied by a mixer variable that is assigned probabilistically to each input from a set of possible mixers. We demonstrate inference of both components of the generative model, for synthesized data and for different classes of natural images, such as a generic ensemble and faces. For natural images, the mixer variable assignments show invariances resembling those of complex cells in visual cortex; the statistics of the gaussian components of the model are in accord with the outputs of divisive normalization models. We also show how our model helps interrelate a wide range of models of image statistics and cortical processing. PMID:16999575
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Mazumdar, Anupam; Nadathur, Seshadri
2012-03-16
We provide a model in which both the inflaton and the curvaton are obtained from within the minimal supersymmetric standard model, with known gauge and Yukawa interactions. Since now both the inflaton and curvaton fields are successfully embedded within the same sector, their decay products thermalize very quickly before the electroweak scale. This results in two important features of the model: first, there will be no residual isocurvature perturbations, and second, observable non-Gaussianities can be generated with the non-Gaussianity parameter f(NL)~O(5-1000) being determined solely by the combination of weak-scale physics and the standard model Yukawa interactions.
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Lin, Chuan-Kai; Wang, Sheng-De
2004-11-01
A new autopilot design for bank-to-turn (BTT) missiles is presented. In the design of autopilot, a ridge Gaussian neural network with local learning capability and fewer tuning parameters than Gaussian neural networks is proposed to model the controlled nonlinear systems. We prove that the proposed ridge Gaussian neural network, which can be a universal approximator, equals the expansions of rotated and scaled Gaussian functions. Although ridge Gaussian neural networks can approximate the nonlinear and complex systems accurately, the small approximation errors may affect the tracking performance significantly. Therefore, by employing the Hinfinity control theory, it is easy to attenuate the effects of the approximation errors of the ridge Gaussian neural networks to a prescribed level. Computer simulation results confirm the effectiveness of the proposed ridge Gaussian neural networks-based autopilot with Hinfinity stabilization.
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Non-Gaussian lineshapes and dynamics of time-resolved linear and nonlinear (correlation) spectra.
Dinpajooh, Mohammadhasan; Matyushov, Dmitry V
2014-07-17
Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.
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Zapp, Jascha; Domsch, Sebastian; Weingärtner, Sebastian; Schad, Lothar R
2017-05-01
To characterize the reversible transverse relaxation in pulmonary tissue and to study the benefit of a quadratic exponential (Gaussian) model over the commonly used linear exponential model for increased quantification precision. A point-resolved spectroscopy sequence was used for comprehensive sampling of the relaxation around spin echoes. Measurements were performed in an ex vivo tissue sample and in healthy volunteers at 1.5 Tesla (T) and 3 T. The goodness of fit using χred2 and the precision of the fitted relaxation time by means of its confidence interval were compared between the two relaxation models. The Gaussian model provides enhanced descriptions of pulmonary relaxation with lower χred2 by average factors of 4 ex vivo and 3 in volunteers. The Gaussian model indicates higher sensitivity to tissue structure alteration with increased precision of reversible transverse relaxation time measurements also by average factors of 4 ex vivo and 3 in volunteers. The mean relaxation times of the Gaussian model in volunteers are T2,G' = (1.97 ± 0.27) msec at 1.5 T and T2,G' = (0.83 ± 0.21) msec at 3 T. Pulmonary signal relaxation was found to be accurately modeled as Gaussian, providing a potential biomarker T2,G' with high sensitivity. Magn Reson Med 77:1938-1945, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.
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NASA Astrophysics Data System (ADS)
Pires, Carlos A. L.; Ribeiro, Andreia F. S.
2017-02-01
We develop an expansion of space-distributed time series into statistically independent uncorrelated subspaces (statistical sources) of low-dimension and exhibiting enhanced non-Gaussian probability distributions with geometrically simple chosen shapes (projection pursuit rationale). The method relies upon a generalization of the principal component analysis that is optimal for Gaussian mixed signals and of the independent component analysis (ICA), optimized to split non-Gaussian scalar sources. The proposed method, supported by information theory concepts and methods, is the independent subspace analysis (ISA) that looks for multi-dimensional, intrinsically synergetic subspaces such as dyads (2D) and triads (3D), not separable by ICA. Basically, we optimize rotated variables maximizing certain nonlinear correlations (contrast functions) coming from the non-Gaussianity of the joint distribution. As a by-product, it provides nonlinear variable changes `unfolding' the subspaces into nearly Gaussian scalars of easier post-processing. Moreover, the new variables still work as nonlinear data exploratory indices of the non-Gaussian variability of the analysed climatic and geophysical fields. The method (ISA, followed by nonlinear unfolding) is tested into three datasets. The first one comes from the Lorenz'63 three-dimensional chaotic model, showing a clear separation into a non-Gaussian dyad plus an independent scalar. The second one is a mixture of propagating waves of random correlated phases in which the emergence of triadic wave resonances imprints a statistical signature in terms of a non-Gaussian non-separable triad. Finally the method is applied to the monthly variability of a high-dimensional quasi-geostrophic (QG) atmospheric model, applied to the Northern Hemispheric winter. We find that quite enhanced non-Gaussian dyads of parabolic shape, perform much better than the unrotated variables in which concerns the separation of the four model's centroid regimes (positive and negative phases of the Arctic Oscillation and of the North Atlantic Oscillation). Triads are also likely in the QG model but of weaker expression than dyads due to the imposed shape and dimension. The study emphasizes the existence of nonlinear dyadic and triadic nonlinear teleconnections.
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Erickson, Collin B; Ankenman, Bruce E; Sanchez, Susan M
2018-06-01
This data article provides the summary data from tests comparing various Gaussian process software packages. Each spreadsheet represents a single function or type of function using a particular input sample size. In each spreadsheet, a row gives the results for a particular replication using a single package. Within each spreadsheet there are the results from eight Gaussian process model-fitting packages on five replicates of the surface. There is also one spreadsheet comparing the results from two packages performing stochastic kriging. These data enable comparisons between the packages to determine which package will give users the best results.
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Analysis of low altitude atmospheric turbulence data measured in flight
NASA Technical Reports Server (NTRS)
Ganzer, V. M.; Joppa, R. G.; Vanderwees, G.
1977-01-01
All three components of turbulence were measured simultaneously in flight at each wing tip of a Beech D-18 aircraft. The flights were conducted at low altitude, 30.5 - 61.0 meters (100-200 ft.), over water in the presence of wind driven turbulence. Statistical properties of flight measured turbulence were compared with Gaussian and non-Gaussian turbulence models. Spatial characteristics of the turbulence were analyzed using the data from flight perpendicular and parallel to the wind. The probability density distributions of the vertical gusts show distinctly non-Gaussian characteristics. The distributions of the longitudinal and lateral gusts are generally Gaussian. The power spectra compare in the inertial subrange at some points better with the Dryden spectrum, while at other points the von Karman spectrum is a better approximation. In the low frequency range the data show peaks or dips in the power spectral density. The cross between vertical gusts in the direction of the mean wind were compared with a matched non-Gaussian model. The real component of the cross spectrum is in general close to the non-Gaussian model. The imaginary component, however, indicated a larger phase shift between these two gust components than was found in previous research.
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NASA Astrophysics Data System (ADS)
Žáček, K.
Summary- The only way to make an excessively complex velocity model suitable for application of ray-based methods, such as the Gaussian beam or Gaussian packet methods, is to smooth it. We have smoothed the Marmousi model by choosing a coarser grid and by minimizing the second spatial derivatives of the slowness. This was done by minimizing the relevant Sobolev norm of slowness. We show that minimizing the relevant Sobolev norm of slowness is a suitable technique for preparing the optimum models for asymptotic ray theory methods. However, the price we pay for a model suitable for ray tracing is an increase of the difference between the smoothed and original model. Similarly, the estimated error in the travel time also increases due to the difference between the models. In smoothing the Marmousi model, we have found the estimated error of travel times at the verge of acceptability. Due to the low frequencies in the wavefield of the original Marmousi data set, we have found the Gaussian beams and Gaussian packets at the verge of applicability even in models sufficiently smoothed for ray tracing.
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Topology in two dimensions. IV - CDM models with non-Gaussian initial conditions
NASA Astrophysics Data System (ADS)
Coles, Peter; Moscardini, Lauro; Plionis, Manolis; Lucchin, Francesco; Matarrese, Sabino; Messina, Antonio
1993-02-01
The results of N-body simulations with both Gaussian and non-Gaussian initial conditions are used here to generate projected galaxy catalogs with the same selection criteria as the Shane-Wirtanen counts of galaxies. The Euler-Poincare characteristic is used to compare the statistical nature of the projected galaxy clustering in these simulated data sets with that of the observed galaxy catalog. All the models produce a topology dominated by a meatball shift when normalized to the known small-scale clustering properties of galaxies. Models characterized by a positive skewness of the distribution of primordial density perturbations are inconsistent with the Lick data, suggesting problems in reconciling models based on cosmic textures with observations. Gaussian CDM models fit the distribution of cell counts only if they have a rather high normalization but possess too low a coherence length compared with the Lick counts. This suggests that a CDM model with extra large scale power would probably fit the available data.
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Capacity of PPM on Gaussian and Webb Channels
NASA Technical Reports Server (NTRS)
Divsalar, D.; Dolinar, S.; Pollara, F.; Hamkins, J.
2000-01-01
This paper computes and compares the capacities of M-ary PPM on various idealized channels that approximate the optical communication channel: (1) the standard additive white Gaussian noise (AWGN) channel;(2) a more general AWGN channel (AWGN2) allowing different variances in signal and noise slots;(3) a Webb-distributed channel (Webb2);(4) a Webb+Gaussian channel, modeling Gaussian thermal noise added to Webb-distributed channel outputs.
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Simulation and analysis of scalable non-Gaussian statistically anisotropic random functions
NASA Astrophysics Data System (ADS)
Riva, Monica; Panzeri, Marco; Guadagnini, Alberto; Neuman, Shlomo P.
2015-12-01
Many earth and environmental (as well as other) variables, Y, and their spatial or temporal increments, ΔY, exhibit non-Gaussian statistical scaling. Previously we were able to capture some key aspects of such scaling by treating Y or ΔY as standard sub-Gaussian random functions. We were however unable to reconcile two seemingly contradictory observations, namely that whereas sample frequency distributions of Y (or its logarithm) exhibit relatively mild non-Gaussian peaks and tails, those of ΔY display peaks that grow sharper and tails that become heavier with decreasing separation distance or lag. Recently we overcame this difficulty by developing a new generalized sub-Gaussian model which captures both behaviors in a unified and consistent manner, exploring it on synthetically generated random functions in one dimension (Riva et al., 2015). Here we extend our generalized sub-Gaussian model to multiple dimensions, present an algorithm to generate corresponding random realizations of statistically isotropic or anisotropic sub-Gaussian functions and illustrate it in two dimensions. We demonstrate the accuracy of our algorithm by comparing ensemble statistics of Y and ΔY (such as, mean, variance, variogram and probability density function) with those of Monte Carlo generated realizations. We end by exploring the feasibility of estimating all relevant parameters of our model by analyzing jointly spatial moments of Y and ΔY obtained from a single realization of Y.
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Receiver design for SPAD-based VLC systems under Poisson-Gaussian mixed noise model.
Mao, Tianqi; Wang, Zhaocheng; Wang, Qi
2017-01-23
Single-photon avalanche diode (SPAD) is a promising photosensor because of its high sensitivity to optical signals in weak illuminance environment. Recently, it has drawn much attention from researchers in visible light communications (VLC). However, existing literature only deals with the simplified channel model, which only considers the effects of Poisson noise introduced by SPAD, but neglects other noise sources. Specifically, when an analog SPAD detector is applied, there exists Gaussian thermal noise generated by the transimpedance amplifier (TIA) and the digital-to-analog converter (D/A). Therefore, in this paper, we propose an SPAD-based VLC system with pulse-amplitude-modulation (PAM) under Poisson-Gaussian mixed noise model, where Gaussian-distributed thermal noise at the receiver is also investigated. The closed-form conditional likelihood of received signals is derived using the Laplace transform and the saddle-point approximation method, and the corresponding quasi-maximum-likelihood (quasi-ML) detector is proposed. Furthermore, the Poisson-Gaussian-distributed signals are converted to Gaussian variables with the aid of the generalized Anscombe transform (GAT), leading to an equivalent additive white Gaussian noise (AWGN) channel, and a hard-decision-based detector is invoked. Simulation results demonstrate that, the proposed GAT-based detector can reduce the computational complexity with marginal performance loss compared with the proposed quasi-ML detector, and both detectors are capable of accurately demodulating the SPAD-based PAM signals.
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Mulkern, Robert V; Balasubramanian, Mukund; Mitsouras, Dimitrios
2014-07-30
To determine whether Lorentzian or Gaussian intra-voxel frequency distributions are better suited for modeling data acquired with gradient-echo sampling of single spin-echoes for the simultaneous characterization of irreversible and reversible relaxation rates. Clinical studies (e.g., of brain iron deposition) using such acquisition schemes have typically assumed Lorentzian distributions. Theoretical expressions of the time-domain spin-echo signal for intra-voxel Lorentzian and Gaussian distributions were used to fit data from a human brain scanned at both 1.5 Tesla (T) and 3T, resulting in maps of irreversible and reversible relaxation rates for each model. The relative merits of the Lorentzian versus Gaussian model were compared by means of quality of fit considerations. Lorentzian fits were equivalent to Gaussian fits primarily in regions of the brain where irreversible relaxation dominated. In the multiple brain regions where reversible relaxation effects become prominent, however, Gaussian fits were clearly superior. The widespread assumption that a Lorentzian distribution is suitable for quantitative transverse relaxation studies of the brain should be reconsidered, particularly at 3T and higher field strengths as reversible relaxation effects become more prominent. Gaussian distributions offer alternate fits of experimental data that should prove quite useful in general. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc. © 2014 Wiley Periodicals, Inc.
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Characterization of Adrenal Adenoma by Gaussian Model-Based Algorithm.
Hsu, Larson D; Wang, Carolyn L; Clark, Toshimasa J
2016-01-01
We confirmed that computed tomography (CT) attenuation values of pixels in an adrenal nodule approximate a Gaussian distribution. Building on this and the previously described histogram analysis method, we created an algorithm that uses mean and standard deviation to estimate the percentage of negative attenuation pixels in an adrenal nodule, thereby allowing differentiation of adenomas and nonadenomas. The institutional review board approved both components of this study in which we developed and then validated our criteria. In the first, we retrospectively assessed CT attenuation values of adrenal nodules for normality using a 2-sample Kolmogorov-Smirnov test. In the second, we evaluated a separate cohort of patients with adrenal nodules using both the conventional 10HU unit mean attenuation method and our Gaussian model-based algorithm. We compared the sensitivities of the 2 methods using McNemar's test. A total of 183 of 185 observations (98.9%) demonstrated a Gaussian distribution in adrenal nodule pixel attenuation values. The sensitivity and specificity of our Gaussian model-based algorithm for identifying adrenal adenoma were 86.1% and 83.3%, respectively. The sensitivity and specificity of the mean attenuation method were 53.2% and 94.4%, respectively. The sensitivities of the 2 methods were significantly different (P value < 0.001). In conclusion, the CT attenuation values within an adrenal nodule follow a Gaussian distribution. Our Gaussian model-based algorithm can characterize adrenal adenomas with higher sensitivity than the conventional mean attenuation method. The use of our algorithm, which does not require additional postprocessing, may increase workflow efficiency and reduce unnecessary workup of benign nodules. Copyright © 2016 Elsevier Inc. All rights reserved.
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NASA Astrophysics Data System (ADS)
Miyoshi, T.; Teramura, T.; Ruiz, J.; Kondo, K.; Lien, G. Y.
2016-12-01
Convective weather is known to be highly nonlinear and chaotic, and it is hard to predict their location and timing precisely. Our Big Data Assimilation (BDA) effort has been exploring to use dense and frequent observations to avoid non-Gaussian probability density function (PDF) and to apply an ensemble Kalman filter under the Gaussian error assumption. The phased array weather radar (PAWR) can observe a dense three-dimensional volume scan with 100-m range resolution and 100 elevation angles in only 30 seconds. The BDA system assimilates the PAWR reflectivity and Doppler velocity observations every 30 seconds into 100 ensemble members of storm-scale numerical weather prediction (NWP) model at 100-m grid spacing. The 30-second-update, 100-m-mesh BDA system has been quite successful in multiple case studies of local severe rainfall events. However, with 1000 ensemble members, the reduced-resolution BDA system at 1-km grid spacing showed significant non-Gaussian PDF with every-30-second updates. With a 10240-member ensemble Kalman filter with a global NWP model at 112-km grid spacing, we found roughly 1000 members satisfactory to capture the non-Gaussian error structures. With these in mind, we explore how the density of observations in space and time affects the non-Gaussianity in an ensemble Kalman filter with a simple toy model. In this presentation, we will present the most up-to-date results of the BDA research, as well as the investigation with the toy model on the non-Gaussianity with dense and frequent observations.
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Experimental study of the focusing properties of a Gaussian Schell-model vortex beam
NASA Astrophysics Data System (ADS)
Wang, Fei; Zhu, Shijun; Cai, Yangjian
2011-08-01
We carry out an experimental and theoretical study of the focusing properties of a Gaussian Schell-model (GSM) vortex beam. It is found that we can shape the beam profile of the focused GSM vortex beam by varying its initial spatial coherence width. Focused dark hollow, flat-topped, and Gaussian beam spots can be obtained in our experiment, which will be useful for trapping particles. The experimental results agree well with the theoretical results.
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Layer-by-layer design method for soft-X-ray multilayers
NASA Technical Reports Server (NTRS)
Yamamoto, Masaki; Namioka, Takeshi
1992-01-01
A new design method effective for a nontransparent system has been developed for soft-X-ray multilayers with the aid of graphic representation of the complex amplitude reflectance in a Gaussian plane. The method provides an effective means of attaining the absolute maximum reflectance on a layer-by-layer basis and also gives clear insight into the evolution of the amplitude reflectance on a multilayer as it builds up. An optical criterion is derived for the selection of a proper pair of materials needed for designing a high-reflectance multilayer. Some examples are given to illustrate the usefulness of this design method.
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Metin, Baris; Wiersema, Jan R; Verguts, Tom; Gasthuys, Roos; van Der Meere, Jacob J; Roeyers, Herbert; Sonuga-Barke, Edmund
2016-01-01
According to the state regulation deficit (SRD) account, ADHD is associated with a problem using effort to maintain an optimal activation state under demanding task settings such as very fast or very slow event rates. This leads to a prediction of disrupted performance at event rate extremes reflected in higher Gaussian response variability that is a putative marker of activation during motor preparation. In the current study, we tested this hypothesis using ex-Gaussian modeling, which distinguishes Gaussian from non-Gaussian variability. Twenty-five children with ADHD and 29 typically developing controls performed a simple Go/No-Go task under four different event-rate conditions. There was an accentuated quadratic relationship between event rate and Gaussian variability in the ADHD group compared to the controls. The children with ADHD had greater Gaussian variability at very fast and very slow event rates but not at moderate event rates. The results provide evidence for the SRD account of ADHD. However, given that this effect did not explain all group differences (some of which were independent of event rate) other cognitive and/or motivational processes are also likely implicated in ADHD performance deficits.
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INPUFF: A SINGLE SOURCE GAUSSIAN PUFF DISPERSION ALGORITHM. USER'S GUIDE
INPUFF is a Gaussian INtegrated PUFF model. The Gaussian puff diffusion equation is used to compute the contribution to the concentration at each receptor from each puff every time step. Computations in INPUFF can be made for a single point source at up to 25 receptor locations. ...
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Li, Y; Hsi, W; Zhao, J
2016-06-15
Purpose: The Gaussian model for the lateral profiles in air is crucial for an accurate treatment planning system. The field size dependence of dose and the lateral beam profiles of scanning proton and carbon ion beams are due mainly to particles undergoing multiple Coulomb scattering in the beam line components and secondary particles produced by nuclear interactions in the target, both of which depend upon the energy and species of the beam. In this work, lateral profile shape parameters were fitted to measurements of field size dependence dose at the center of field size in air. Methods: Previous studies havemore » employed empirical fits to measured profile data to significantly reduce the QA time required for measurements. From this approach to derive the weight and sigma of lateral profiles in air, empirical model formulations were simulated for three selected energies for both proton and carbon beams. Results: The 20%–80% lateral penumbras predicted by the double model for proton and single model for carbon with the error functions agreed with the measurements within 1 mm. The standard deviation between measured and fitted field size dependence of dose for empirical model in air has a maximum accuracy of 0.74% for proton with double Gaussian, and of 0.57% for carbon with single Gaussian. Conclusion: We have demonstrated that the double Gaussian model of lateral beam profiles is significantly better than the single Gaussian model for proton while a single Gaussian model is sufficient for carbon. The empirical equation may be used to double check the separately obtained model that is currently used by the planning system. The empirical model in air for dose of spot scanning proton and carbon ion beams cannot be directly used for irregular shaped patient fields, but can be to provide reference values for clinical use and quality assurance.« less
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National Centers for Environmental Prediction
Products Operational Forecast Graphics Experimental Forecast Graphics Verification and Diagnostics Model PARALLEL/EXPERIMENTAL MODEL FORECAST GRAPHICS OPERATIONAL VERIFICATION / DIAGNOSTICS PARALLEL VERIFICATION Developmental Air Quality Forecasts and Verification Back to Table of Contents 2. PARALLEL/EXPERIMENTAL GRAPHICS
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National Centers for Environmental Prediction
Operational Forecast Graphics Experimental Forecast Graphics Verification and Diagnostics Model Configuration /EXPERIMENTAL MODEL FORECAST GRAPHICS OPERATIONAL VERIFICATION / DIAGNOSTICS PARALLEL VERIFICATION / DIAGNOSTICS Developmental Air Quality Forecasts and Verification Back to Table of Contents 2. PARALLEL/EXPERIMENTAL GRAPHICS
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On the numbers of images of two stochastic gravitational lensing models
NASA Astrophysics Data System (ADS)
Wei, Ang
2017-02-01
We study two gravitational lensing models with Gaussian randomness: the continuous mass fluctuation model and the floating black hole model. The lens equations of these models are related to certain random harmonic functions. Using Rice's formula and Gaussian techniques, we obtain the expected numbers of zeros of these functions, which indicate the amounts of images in the corresponding lens systems.
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Structural modeling of djenkolic acid with sulfur replaced by selenium and tellurium.
Melnikov, Petr; Nascimento, Valter A; Silva, Anderson F; Consolo, Lourdes Z Z
2014-04-17
The comparative structural modeling of djenkolic acid and its derivatives containing selenium and tellurium in chalcogen sites (Ch=Se, Te) has provided detailed information about the bond lengths and bond angles, filling the gap in what we know about the structural characteristics of these aminoacids. The investigation using the molecular mechanics technique with good approximation confirmed the available information on X-ray refinements for the related compounds methionine and selenomethionine, as well as for an estimate made earlier for telluromethionine. It was shown that the Ch-C(3) and Ch-C(4) bond lengths grow in parallel with the increasing anionic radii. Although the distances C-C, C-O, and C-N are very similar, the geometry of conformers is quite different owing to the possibility of rotation about four carbon atoms, hence the remarkable variability observed in dihedral angles. It was shown that the compounds contain a rigid block with two Ch atoms connected through a methylene group. The standard program Gaussian 03 with graphical interface Gaussview 4.1.2 has proved to be satisfactory tool for the structural description of less-common bioactive compositions when direct X-ray results are absent.
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Implementation of GPU accelerated SPECT reconstruction with Monte Carlo-based scatter correction.
Bexelius, Tobias; Sohlberg, Antti
2018-06-01
Statistical SPECT reconstruction can be very time-consuming especially when compensations for collimator and detector response, attenuation, and scatter are included in the reconstruction. This work proposes an accelerated SPECT reconstruction algorithm based on graphics processing unit (GPU) processing. Ordered subset expectation maximization (OSEM) algorithm with CT-based attenuation modelling, depth-dependent Gaussian convolution-based collimator-detector response modelling, and Monte Carlo-based scatter compensation was implemented using OpenCL. The OpenCL implementation was compared against the existing multi-threaded OSEM implementation running on a central processing unit (CPU) in terms of scatter-to-primary ratios, standardized uptake values (SUVs), and processing speed using mathematical phantoms and clinical multi-bed bone SPECT/CT studies. The difference in scatter-to-primary ratios, visual appearance, and SUVs between GPU and CPU implementations was minor. On the other hand, at its best, the GPU implementation was noticed to be 24 times faster than the multi-threaded CPU version on a normal 128 × 128 matrix size 3 bed bone SPECT/CT data set when compensations for collimator and detector response, attenuation, and scatter were included. GPU SPECT reconstructions show great promise as an every day clinical reconstruction tool.
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NASA Astrophysics Data System (ADS)
Libera, A.; de Barros, F.; Riva, M.; Guadagnini, A.
2016-12-01
Managing contaminated groundwater systems is an arduous task for multiple reasons. First, subsurface hydraulic properties are heterogeneous and the high costs associated with site characterization leads to data scarcity (therefore, model predictions are uncertain). Second, it is common for water agencies to schedule groundwater extraction through a temporal sequence of pumping rates to maximize the benefits to anthropogenic activities and minimize the environmental footprint of the withdrawal operations. The temporal variability in pumping rates and aquifer heterogeneity affect dilution rates of contaminant plumes and chemical concentration breakthrough curves (BTCs) at the well. While contaminant transport under steady-state pumping is widely studied, the manner in which a given time-varying pumping schedule affects contaminant plume behavior is tackled only marginally. At the same time, most studies focus on the impact of Gaussian random hydraulic conductivity (K) fields on transport. Here, we systematically analyze the significance of the random space function (RSF) model characterizing K in the presence of distinct pumping operations on the uncertainty of the concentration BTC at the operating well. We juxtapose Monte Carlo based numerical results associated with two models: (a) a recently proposed Generalized Sub-Gaussian model which allows capturing non-Gaussian statistical scaling features of RSFs such as hydraulic conductivity, and (b) the commonly used Gaussian field approximation. Our novel results include an appraisal of the coupled effect of (a) the model employed to depict the random spatial variability of K and (b) transient flow regime, as induced by a temporally varying pumping schedule, on the concentration BTC at the operating well. We systematically quantify the sensitivity of the uncertainty in the contaminant BTC to the RSF model adopted for K (non-Gaussian or Gaussian) in the presence of diverse well pumping schedules. Results contribute to determine conditions under which any of these two key factors prevails on the other.
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NASA Astrophysics Data System (ADS)
Huang, Xingguo; Sun, Hui
2018-05-01
Gaussian beam is an important complex geometrical optical technology for modeling seismic wave propagation and diffraction in the subsurface with complex geological structure. Current methods for Gaussian beam modeling rely on the dynamic ray tracing and the evanescent wave tracking. However, the dynamic ray tracing method is based on the paraxial ray approximation and the evanescent wave tracking method cannot describe strongly evanescent fields. This leads to inaccuracy of the computed wave fields in the region with a strong inhomogeneous medium. To address this problem, we compute Gaussian beam wave fields using the complex phase by directly solving the complex eikonal equation. In this method, the fast marching method, which is widely used for phase calculation, is combined with Gauss-Newton optimization algorithm to obtain the complex phase at the regular grid points. The main theoretical challenge in combination of this method with Gaussian beam modeling is to address the irregular boundary near the curved central ray. To cope with this challenge, we present the non-uniform finite difference operator and a modified fast marching method. The numerical results confirm the proposed approach.
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Stochastic inflation lattice simulations - Ultra-large scale structure of the universe
NASA Technical Reports Server (NTRS)
Salopek, D. S.
1991-01-01
Non-Gaussian fluctuations for structure formation may arise in inflation from the nonlinear interaction of long wavelength gravitational and scalar fields. Long wavelength fields have spatial gradients, a (exp -1), small compared to the Hubble radius, and they are described in terms of classical random fields that are fed by short wavelength quantum noise. Lattice Langevin calculations are given for a toy model with a scalar field interacting with an exponential potential where one can obtain exact analytic solutions of the Fokker-Planck equation. For single scalar field models that are consistent with current microwave background fluctuations, the fluctuations are Gaussian. However, for scales much larger than our observable Universe, one expects large metric fluctuations that are non-Gaussian. This example illuminates non-Gaussian models involving multiple scalar fields which are consistent with current microwave background limits.
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Fast Low-Rank Bayesian Matrix Completion With Hierarchical Gaussian Prior Models
NASA Astrophysics Data System (ADS)
Yang, Linxiao; Fang, Jun; Duan, Huiping; Li, Hongbin; Zeng, Bing
2018-06-01
The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a Wishart distribution is specified as a hyperprior over the precision matrix. We show that such a hierarchical Gaussian prior has the potential to encourage a low-rank solution. Based on the proposed hierarchical prior model, a variational Bayesian method is developed for matrix completion, where the generalized approximate massage passing (GAMP) technique is embedded into the variational Bayesian inference in order to circumvent cumbersome matrix inverse operations. Simulation results show that our proposed method demonstrates superiority over existing state-of-the-art matrix completion methods.
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EM in high-dimensional spaces.
Draper, Bruce A; Elliott, Daniel L; Hayes, Jeremy; Baek, Kyungim
2005-06-01
This paper considers fitting a mixture of Gaussians model to high-dimensional data in scenarios where there are fewer data samples than feature dimensions. Issues that arise when using principal component analysis (PCA) to represent Gaussian distributions inside Expectation-Maximization (EM) are addressed, and a practical algorithm results. Unlike other algorithms that have been proposed, this algorithm does not try to compress the data to fit low-dimensional models. Instead, it models Gaussian distributions in the (N - 1)-dimensional space spanned by the N data samples. We are able to show that this algorithm converges on data sets where low-dimensional techniques do not.
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Experimental study of the focusing properties of a Gaussian Schell-model vortex beam.
Wang, Fei; Zhu, Shijun; Cai, Yangjian
2011-08-15
We carry out an experimental and theoretical study of the focusing properties of a Gaussian Schell-model (GSM) vortex beam. It is found that we can shape the beam profile of the focused GSM vortex beam by varying its initial spatial coherence width. Focused dark hollow, flat-topped, and Gaussian beam spots can be obtained in our experiment, which will be useful for trapping particles. The experimental results agree well with the theoretical results. © 2011 Optical Society of America
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NASA Astrophysics Data System (ADS)
Kumari, Vandana; Kumar, Ayush; Saxena, Manoj; Gupta, Mridula
2018-01-01
The sub-threshold model formulation of Gaussian Doped Double Gate JunctionLess (GD-DG-JL) FET including source/drain depletion length is reported in the present work under the assumption that the ungated regions are fully depleted. To provide deeper insight into the device performance, the impact of gaussian straggle, channel length, oxide and channel thickness and high-k gate dielectric has been studied using extensive TCAD device simulation.
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Probabilistic Graphical Model Representation in Phylogenetics
Höhna, Sebastian; Heath, Tracy A.; Boussau, Bastien; Landis, Michael J.; Ronquist, Fredrik; Huelsenbeck, John P.
2014-01-01
Recent years have seen a rapid expansion of the model space explored in statistical phylogenetics, emphasizing the need for new approaches to statistical model representation and software development. Clear communication and representation of the chosen model is crucial for: (i) reproducibility of an analysis, (ii) model development, and (iii) software design. Moreover, a unified, clear and understandable framework for model representation lowers the barrier for beginners and nonspecialists to grasp complex phylogenetic models, including their assumptions and parameter/variable dependencies. Graphical modeling is a unifying framework that has gained in popularity in the statistical literature in recent years. The core idea is to break complex models into conditionally independent distributions. The strength lies in the comprehensibility, flexibility, and adaptability of this formalism, and the large body of computational work based on it. Graphical models are well-suited to teach statistical models, to facilitate communication among phylogeneticists and in the development of generic software for simulation and statistical inference. Here, we provide an introduction to graphical models for phylogeneticists and extend the standard graphical model representation to the realm of phylogenetics. We introduce a new graphical model component, tree plates, to capture the changing structure of the subgraph corresponding to a phylogenetic tree. We describe a range of phylogenetic models using the graphical model framework and introduce modules to simplify the representation of standard components in large and complex models. Phylogenetic model graphs can be readily used in simulation, maximum likelihood inference, and Bayesian inference using, for example, Metropolis–Hastings or Gibbs sampling of the posterior distribution. [Computation; graphical models; inference; modularization; statistical phylogenetics; tree plate.] PMID:24951559
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2010-06-01
GMKPF represents a better and more flexible alternative to the Gaussian Maximum Likelihood (GML), and Exponential Maximum Likelihood ( EML ...accurate results relative to GML and EML when the network delays are modeled in terms of a single non-Gaussian/non-exponential distribution or as a...to the Gaussian Maximum Likelihood (GML), and Exponential Maximum Likelihood ( EML ) estimators for clock offset estimation in non-Gaussian or non
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Fast and robust group-wise eQTL mapping using sparse graphical models.
Cheng, Wei; Shi, Yu; Zhang, Xiang; Wang, Wei
2015-01-16
Genome-wide expression quantitative trait loci (eQTL) studies have emerged as a powerful tool to understand the genetic basis of gene expression and complex traits. The traditional eQTL methods focus on testing the associations between individual single-nucleotide polymorphisms (SNPs) and gene expression traits. A major drawback of this approach is that it cannot model the joint effect of a set of SNPs on a set of genes, which may correspond to hidden biological pathways. We introduce a new approach to identify novel group-wise associations between sets of SNPs and sets of genes. Such associations are captured by hidden variables connecting SNPs and genes. Our model is a linear-Gaussian model and uses two types of hidden variables. One captures the set associations between SNPs and genes, and the other captures confounders. We develop an efficient optimization procedure which makes this approach suitable for large scale studies. Extensive experimental evaluations on both simulated and real datasets demonstrate that the proposed methods can effectively capture both individual and group-wise signals that cannot be identified by the state-of-the-art eQTL mapping methods. Considering group-wise associations significantly improves the accuracy of eQTL mapping, and the successful multi-layer regression model opens a new approach to understand how multiple SNPs interact with each other to jointly affect the expression level of a group of genes.
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Signal Partitioning Algorithm for Highly Efficient Gaussian Mixture Modeling in Mass Spectrometry
Polanski, Andrzej; Marczyk, Michal; Pietrowska, Monika; Widlak, Piotr; Polanska, Joanna
2015-01-01
Mixture - modeling of mass spectra is an approach with many potential applications including peak detection and quantification, smoothing, de-noising, feature extraction and spectral signal compression. However, existing algorithms do not allow for automated analyses of whole spectra. Therefore, despite highlighting potential advantages of mixture modeling of mass spectra of peptide/protein mixtures and some preliminary results presented in several papers, the mixture modeling approach was so far not developed to the stage enabling systematic comparisons with existing software packages for proteomic mass spectra analyses. In this paper we present an efficient algorithm for Gaussian mixture modeling of proteomic mass spectra of different types (e.g., MALDI-ToF profiling, MALDI-IMS). The main idea is automated partitioning of protein mass spectral signal into fragments. The obtained fragments are separately decomposed into Gaussian mixture models. The parameters of the mixture models of fragments are then aggregated to form the mixture model of the whole spectrum. We compare the elaborated algorithm to existing algorithms for peak detection and we demonstrate improvements of peak detection efficiency obtained by using Gaussian mixture modeling. We also show applications of the elaborated algorithm to real proteomic datasets of low and high resolution. PMID:26230717
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Modeling Non-Gaussian Time Series with Nonparametric Bayesian Model.
Xu, Zhiguang; MacEachern, Steven; Xu, Xinyi
2015-02-01
We present a class of Bayesian copula models whose major components are the marginal (limiting) distribution of a stationary time series and the internal dynamics of the series. We argue that these are the two features with which an analyst is typically most familiar, and hence that these are natural components with which to work. For the marginal distribution, we use a nonparametric Bayesian prior distribution along with a cdf-inverse cdf transformation to obtain large support. For the internal dynamics, we rely on the traditionally successful techniques of normal-theory time series. Coupling the two components gives us a family of (Gaussian) copula transformed autoregressive models. The models provide coherent adjustments of time scales and are compatible with many extensions, including changes in volatility of the series. We describe basic properties of the models, show their ability to recover non-Gaussian marginal distributions, and use a GARCH modification of the basic model to analyze stock index return series. The models are found to provide better fit and improved short-range and long-range predictions than Gaussian competitors. The models are extensible to a large variety of fields, including continuous time models, spatial models, models for multiple series, models driven by external covariate streams, and non-stationary models.
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The formation of cosmic structure in a texture-seeded cold dark matter cosmogony
NASA Technical Reports Server (NTRS)
Gooding, Andrew K.; Park, Changbom; Spergel, David N.; Turok, Neil; Gott, Richard, III
1992-01-01
The growth of density fluctuations induced by global texture in an Omega = 1 cold dark matter (CDM) cosmogony is calculated. The resulting power spectra are in good agreement with each other, with more power on large scales than in the standard inflation plus CDM model. Calculation of related statistics (two-point correlation functions, mass variances, cosmic Mach number) indicates that the texture plus CDM model compares more favorably than standard CDM with observations of large-scale structure. Texture produces coherent velocity fields on large scales, as observed. Excessive small-scale velocity dispersions, and voids less empty than those observed may be remedied by including baryonic physics. The topology of the cosmic structure agrees well with observation. The non-Gaussian texture induced density fluctuations lead to earlier nonlinear object formation than in Gaussian models and may also be more compatible with recent evidence that the galaxy density field is non-Gaussian on large scales. On smaller scales the density field is strongly non-Gaussian, but this appears to be primarily due to nonlinear gravitational clustering. The velocity field on smaller scales is surprisingly Gaussian.
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Non-Gaussian microwave background fluctuations from nonlinear gravitational effects
NASA Technical Reports Server (NTRS)
Salopek, D. S.; Kunstatter, G. (Editor)
1991-01-01
Whether the statistics of primordial fluctuations for structure formation are Gaussian or otherwise may be determined if the Cosmic Background Explorer (COBE) Satellite makes a detection of the cosmic microwave-background temperature anisotropy delta T(sub CMB)/T(sub CMB). Non-Gaussian fluctuations may be generated in the chaotic inflationary model if two scalar fields interact nonlinearly with gravity. Theoretical contour maps are calculated for the resulting Sachs-Wolfe temperature fluctuations at large angular scales (greater than 3 degrees). In the long-wavelength approximation, one can confidently determine the nonlinear evolution of quantum noise with gravity during the inflationary epoch because: (1) different spatial points are no longer in causal contact; and (2) quantum gravity corrections are typically small-- it is sufficient to model the system using classical random fields. If the potential for two scalar fields V(phi sub 1, phi sub 2) possesses a sharp feature, then non-Gaussian fluctuations may arise. An explicit model is given where cold spots in delta T(sub CMB)/T(sub CMB) maps are suppressed as compared to the Gaussian case. The fluctuations are essentially scale-invariant.
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NASA Astrophysics Data System (ADS)
Yu, Haoyu S.; Fiedler, Lucas J.; Alecu, I. M.; Truhlar, Donald G.
2017-01-01
We present a Python program, FREQ, for calculating the optimal scale factors for calculating harmonic vibrational frequencies, fundamental vibrational frequencies, and zero-point vibrational energies from electronic structure calculations. The program utilizes a previously published scale factor optimization model (Alecu et al., 2010) to efficiently obtain all three scale factors from a set of computed vibrational harmonic frequencies. In order to obtain the three scale factors, the user only needs to provide zero-point energies of 15 or 6 selected molecules. If the user has access to the Gaussian 09 or Gaussian 03 program, we provide the option for the user to run the program by entering the keywords for a certain method and basis set in the Gaussian 09 or Gaussian 03 program. Four other Python programs, input.py, input6, pbs.py, and pbs6.py, are also provided for generating Gaussian 09 or Gaussian 03 input and PBS files. The program can also be used with data from any other electronic structure package. A manual of how to use this program is included in the code package.
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Non-Gaussian spatiotemporal simulation of multisite daily precipitation: downscaling framework
NASA Astrophysics Data System (ADS)
Ben Alaya, M. A.; Ouarda, T. B. M. J.; Chebana, F.
2018-01-01
Probabilistic regression approaches for downscaling daily precipitation are very useful. They provide the whole conditional distribution at each forecast step to better represent the temporal variability. The question addressed in this paper is: how to simulate spatiotemporal characteristics of multisite daily precipitation from probabilistic regression models? Recent publications point out the complexity of multisite properties of daily precipitation and highlight the need for using a non-Gaussian flexible tool. This work proposes a reasonable compromise between simplicity and flexibility avoiding model misspecification. A suitable nonparametric bootstrapping (NB) technique is adopted. A downscaling model which merges a vector generalized linear model (VGLM as a probabilistic regression tool) and the proposed bootstrapping technique is introduced to simulate realistic multisite precipitation series. The model is applied to data sets from the southern part of the province of Quebec, Canada. It is shown that the model is capable of reproducing both at-site properties and the spatial structure of daily precipitations. Results indicate the superiority of the proposed NB technique, over a multivariate autoregressive Gaussian framework (i.e. Gaussian copula).
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The display of molecular models with the Ames Interactive Modeling System (AIMS)
NASA Technical Reports Server (NTRS)
Egan, J. T.; Hart, J.; Burt, S. K.; Macelroy, R. D.
1982-01-01
A visualization of molecular models can lead to a clearer understanding of the models. Sophisticated graphics devices supported by minicomputers make it possible for the chemist to interact with the display of a very large model, altering its structure. In addition to user interaction, the need arises also for other ways of displaying information. These include the production of viewgraphs, film presentation, as well as publication quality prints of various models. To satisfy these needs, the display capability of the Ames Interactive Modeling System (AIMS) has been enhanced to provide a wide range of graphics and plotting capabilities. Attention is given to an overview of the AIMS system, graphics hardware used by the AIMS display subsystem, a comparison of graphics hardware, the representation of molecular models, graphics software used by the AIMS display subsystem, the display of a model obtained from data stored in molecule data base, a graphics feature for obtaining single frame permanent copy displays, and a feature for producing multiple frame displays.
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Infinite von Mises-Fisher Mixture Modeling of Whole Brain fMRI Data.
Røge, Rasmus E; Madsen, Kristoffer H; Schmidt, Mikkel N; Mørup, Morten
2017-10-01
Cluster analysis of functional magnetic resonance imaging (fMRI) data is often performed using gaussian mixture models, but when the time series are standardized such that the data reside on a hypersphere, this modeling assumption is questionable. The consequences of ignoring the underlying spherical manifold are rarely analyzed, in part due to the computational challenges imposed by directional statistics. In this letter, we discuss a Bayesian von Mises-Fisher (vMF) mixture model for data on the unit hypersphere and present an efficient inference procedure based on collapsed Markov chain Monte Carlo sampling. Comparing the vMF and gaussian mixture models on synthetic data, we demonstrate that the vMF model has a slight advantage inferring the true underlying clustering when compared to gaussian-based models on data generated from both a mixture of vMFs and a mixture of gaussians subsequently normalized. Thus, when performing model selection, the two models are not in agreement. Analyzing multisubject whole brain resting-state fMRI data from healthy adult subjects, we find that the vMF mixture model is considerably more reliable than the gaussian mixture model when comparing solutions across models trained on different groups of subjects, and again we find that the two models disagree on the optimal number of components. The analysis indicates that the fMRI data support more than a thousand clusters, and we confirm this is not a result of overfitting by demonstrating better prediction on data from held-out subjects. Our results highlight the utility of using directional statistics to model standardized fMRI data and demonstrate that whole brain segmentation of fMRI data requires a very large number of functional units in order to adequately account for the discernible statistical patterns in the data.
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Teaching "Instant Experience" with Graphical Model Validation Techniques
ERIC Educational Resources Information Center
Ekstrøm, Claus Thorn
2014-01-01
Graphical model validation techniques for linear normal models are often used to check the assumptions underlying a statistical model. We describe an approach to provide "instant experience" in looking at a graphical model validation plot, so it becomes easier to validate if any of the underlying assumptions are violated.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Faculjak, D.A.
1988-03-01
Graphics Manager (GFXMGR) is menu-driven, user-friendly software designed to interactively create, edit, and delete graphics displays on the Advanced Electronics Design (AED) graphics controller, Model 767. The software runs on the VAX family of computers and has been used successfully in security applications to create and change site layouts (maps) of specific facilities. GFXMGR greatly benefits graphics development by minimizing display-development time, reducing tedium on the part of the user, and improving system performance. It is anticipated that GFXMGR can be used to create graphics displays for many types of applications. 8 figs., 2 tabs.
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Future constraints on angle-dependent non-Gaussianity from large radio surveys
NASA Astrophysics Data System (ADS)
Raccanelli, Alvise; Shiraishi, Maresuke; Bartolo, Nicola; Bertacca, Daniele; Liguori, Michele; Matarrese, Sabino; Norris, Ray P.; Parkinson, David
2017-03-01
We investigate how well future large-scale radio surveys could measure different shapes of primordial non-Gaussianity; in particular we focus on angle-dependent non-Gaussianity arising from primordial anisotropic sources, whose bispectrum has an angle dependence between the three wavevectors that is characterized by Legendre polynomials PL and expansion coefficients cL. We provide forecasts for measurements of galaxy power spectrum, finding that Large-Scale Structure (LSS) data could allow measurements of primordial non-Gaussianity that would be competitive with, or improve upon, current constraints set by CMB experiments, for all the shapes considered. We argue that the best constraints will come from the possibility to assign redshift information to radio galaxy surveys, and investigate a few possible scenarios for the EMU and SKA surveys. A realistic (futuristic) modeling could provide constraints of fNLloc ≈ 1(0 . 5) for the local shape, fNL of O(10) (O(1)) for the orthogonal, equilateral and folded shapes, and cL=1 ≈ 80(2) , cL=2 ≈ 400(10) for angle-dependent non-Gaussianity showing that only futuristic galaxy surveys will be able to set strong constraints on these models. Nevertheless, the more futuristic forecasts show the potential of LSS analyses to considerably improve current constraints on non-Gaussianity, and so on models of the primordial Universe. Finally, we find the minimum requirements that would be needed to reach σ(cL=1) = 10, which can be considered as a typical (lower) value predicted by some (inflationary) models.
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Comparing fixed and variable-width Gaussian networks.
Kůrková, Věra; Kainen, Paul C
2014-09-01
The role of width of Gaussians in two types of computational models is investigated: Gaussian radial-basis-functions (RBFs) where both widths and centers vary and Gaussian kernel networks which have fixed widths but varying centers. The effect of width on functional equivalence, universal approximation property, and form of norms in reproducing kernel Hilbert spaces (RKHS) is explored. It is proven that if two Gaussian RBF networks have the same input-output functions, then they must have the same numbers of units with the same centers and widths. Further, it is shown that while sets of input-output functions of Gaussian kernel networks with two different widths are disjoint, each such set is large enough to be a universal approximator. Embedding of RKHSs induced by "flatter" Gaussians into RKHSs induced by "sharper" Gaussians is described and growth of the ratios of norms on these spaces with increasing input dimension is estimated. Finally, large sets of argminima of error functionals in sets of input-output functions of Gaussian RBFs are described. Copyright © 2014 Elsevier Ltd. All rights reserved.
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NASA Technical Reports Server (NTRS)
1974-01-01
The present form of this cardiovascular model simulates both 1-g and zero-g LBNP (lower body negative pressure) experiments and tilt experiments. In addition, the model simulates LBNP experiments at any body angle. The model is currently accessible on the Univac 1110 Time-Shared System in an interactive operational mode. Model output may be in tabular form and/or graphic form. The graphic capabilities are programmed for the Tektronix 4010 graphics terminal and the Univac 1110.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Lange, R.; Dickerson, M.A.; Peterson, K.R.
Two numerical models for the calculation of air concentration and ground deposition of airborne effluent releases are compared. The Particle-in-Cell (PIC) model and the Straight-Line Airflow Gaussian model were used for the simulation. Two sites were selected for comparison: the Hudson River Valley, New York, and the area around the Savannah River Plant, South Carolina. Input for the models was synthesized from meteorological data gathered in previous studies by various investigators. It was found that the PIC model more closely simulated the three-dimensional effects of the meteorology and topography. Overall, the Gaussian model calculated higher concentrations under stable conditions withmore » better agreement between the two methods during neutral to unstable conditions. In addition, because of its consideration of exposure from the returning plume after flow reversal, the PIC model calculated air concentrations over larger areas than did the Gaussian model.« less
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Bayesian spatial transformation models with applications in neuroimaging data
Miranda, Michelle F.; Zhu, Hongtu; Ibrahim, Joseph G.
2013-01-01
Summary The aim of this paper is to develop a class of spatial transformation models (STM) to spatially model the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) and a set of covariates. Our STMs include a varying Box-Cox transformation model for dealing with the issue of non-Gaussian distributed imaging data and a Gaussian Markov Random Field model for incorporating spatial smoothness of the imaging data. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. Simulations and real data analysis demonstrate that the STM significantly outperforms the voxel-wise linear model with Gaussian noise in recovering meaningful geometric patterns. Our STM is able to reveal important brain regions with morphological changes in children with attention deficit hyperactivity disorder. PMID:24128143
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Gaussian Finite Element Method for Description of Underwater Sound Diffraction
NASA Astrophysics Data System (ADS)
Huang, Dehua
A new method for solving diffraction problems is presented in this dissertation. It is based on the use of Gaussian diffraction theory. The Rayleigh integral is used to prove the core of Gaussian theory: the diffraction field of a Gaussian is described by a Gaussian function. The parabolic approximation used by previous authors is not necessary to this proof. Comparison of the Gaussian beam expansion and Fourier series expansion reveals that the Gaussian expansion is a more general and more powerful technique. The method combines the Gaussian beam superposition technique (Wen and Breazeale, J. Acoust. Soc. Am. 83, 1752-1756 (1988)) and the Finite element solution to the parabolic equation (Huang, J. Acoust. Soc. Am. 84, 1405-1413 (1988)). Computer modeling shows that the new method is capable of solving for the sound field even in an inhomogeneous medium, whether the source is a Gaussian source or a distributed source. It can be used for horizontally layered interfaces or irregular interfaces. Calculated results are compared with experimental results by use of a recently designed and improved Gaussian transducer in a laboratory water tank. In addition, the power of the Gaussian Finite element method is demonstrated by comparing numerical results with experimental results from use of a piston transducer in a water tank.
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Weakly anomalous diffusion with non-Gaussian propagators
NASA Astrophysics Data System (ADS)
Cressoni, J. C.; Viswanathan, G. M.; Ferreira, A. S.; da Silva, M. A. A.
2012-08-01
A poorly understood phenomenon seen in complex systems is diffusion characterized by Hurst exponent H≈1/2 but with non-Gaussian statistics. Motivated by such empirical findings, we report an exact analytical solution for a non-Markovian random walk model that gives rise to weakly anomalous diffusion with H=1/2 but with a non-Gaussian propagator.
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A Program of Continuing Research on Representing, Manipulating, and Reasoning about Physical Objects
1991-09-30
graphics with the goal of automatically converting complex graphics models into forms more appropriate for radiosity computation. 2.4 Least Constraint We...to computer graphics with the goal of automatically 7 converting complex graphics models into forms more appropriate for radiosity com- putation. 8 4
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Building Regression Models: The Importance of Graphics.
ERIC Educational Resources Information Center
Dunn, Richard
1989-01-01
Points out reasons for using graphical methods to teach simple and multiple regression analysis. Argues that a graphically oriented approach has considerable pedagogic advantages in the exposition of simple and multiple regression. Shows that graphical methods may play a central role in the process of building regression models. (Author/LS)
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Engineering Graphics Educational Outcomes for the Global Engineer: An Update
ERIC Educational Resources Information Center
Barr, R. E.
2012-01-01
This paper discusses the formulation of educational outcomes for engineering graphics that span the global enterprise. Results of two repeated faculty surveys indicate that new computer graphics tools and techniques are now the preferred mode of engineering graphical communication. Specifically, 3-D computer modeling, assembly modeling, and model…
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Moving vehicles segmentation based on Gaussian motion model
NASA Astrophysics Data System (ADS)
Zhang, Wei; Fang, Xiang Z.; Lin, Wei Y.
2005-07-01
Moving objects segmentation is a challenge in computer vision. This paper focuses on the segmentation of moving vehicles in dynamic scene. We analyses the psychology of human vision and present a framework for segmenting moving vehicles in the highway. The proposed framework consists of two parts. Firstly, we propose an adaptive background update method in which the background is updated according to the change of illumination conditions and thus can adapt to the change of illumination sensitively. Secondly, we construct a Gaussian motion model to segment moving vehicles, in which the motion vectors of the moving pixels are modeled as a Gaussian model and an on-line EM algorithm is used to update the model. The Gaussian distribution of the adaptive model is elevated to determine which moving vectors result from moving vehicles and which from other moving objects such as waving trees. Finally, the pixels with motion vector result from the moving vehicles are segmented. Experimental results of several typical scenes show that the proposed model can detect the moving vehicles correctly and is immune from influence of the moving objects caused by the waving trees and the vibration of camera.
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Diffusion of Super-Gaussian Profiles
ERIC Educational Resources Information Center
Rosenberg, C.-J.; Anderson, D.; Desaix, M.; Johannisson, P.; Lisak, M.
2007-01-01
The present analysis describes an analytically simple and systematic approximation procedure for modelling the free diffusive spreading of initially super-Gaussian profiles. The approach is based on a self-similar ansatz for the evolution of the diffusion profile, and the parameter functions involved in the modelling are determined by suitable…
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Chen, Tianju; Zhang, Jinzhi; Wu, Jinhu
2016-07-01
The kinetic and energy productions of pyrolysis of a lignocellulosic biomass were investigated using a three-parallel Gaussian distribution method in this work. The pyrolysis experiment of the pine sawdust was performed using a thermogravimetric-mass spectroscopy (TG-MS) analyzer. A three-parallel Gaussian distributed activation energy model (DAEM)-reaction model was used to describe thermal decomposition behaviors of the three components, hemicellulose, cellulose and lignin. The first, second and third pseudocomponents represent the fractions of hemicellulose, cellulose and lignin, respectively. It was found that the model is capable of predicting the pyrolysis behavior of the pine sawdust. The activation energy distribution peaks for the three pseudo-components were centered at 186.8, 197.5 and 203.9kJmol(-1) for the pine sawdust, respectively. The evolution profiles of H2, CH4, CO, and CO2 were well predicted using the three-parallel Gaussian distribution model. In addition, the chemical composition of bio-oil was also obtained by pyrolysis-gas chromatography/mass spectrometry instrument (Py-GC/MS). Copyright © 2016 Elsevier Ltd. All rights reserved.
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Geographically weighted regression model on poverty indicator
NASA Astrophysics Data System (ADS)
Slamet, I.; Nugroho, N. F. T. A.; Muslich
2017-12-01
In this research, we applied geographically weighted regression (GWR) for analyzing the poverty in Central Java. We consider Gaussian Kernel as weighted function. The GWR uses the diagonal matrix resulted from calculating kernel Gaussian function as a weighted function in the regression model. The kernel weights is used to handle spatial effects on the data so that a model can be obtained for each location. The purpose of this paper is to model of poverty percentage data in Central Java province using GWR with Gaussian kernel weighted function and to determine the influencing factors in each regency/city in Central Java province. Based on the research, we obtained geographically weighted regression model with Gaussian kernel weighted function on poverty percentage data in Central Java province. We found that percentage of population working as farmers, population growth rate, percentage of households with regular sanitation, and BPJS beneficiaries are the variables that affect the percentage of poverty in Central Java province. In this research, we found the determination coefficient R2 are 68.64%. There are two categories of district which are influenced by different of significance factors.
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Robust Linear Models for Cis-eQTL Analysis.
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.
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Statistical description of turbulent transport for flux driven toroidal plasmas
NASA Astrophysics Data System (ADS)
Anderson, J.; Imadera, K.; Kishimoto, Y.; Li, J. Q.; Nordman, H.
2017-06-01
A novel methodology to analyze non-Gaussian probability distribution functions (PDFs) of intermittent turbulent transport in global full-f gyrokinetic simulations is presented. In this work, the auto-regressive integrated moving average (ARIMA) model is applied to time series data of intermittent turbulent heat transport to separate noise and oscillatory trends, allowing for the extraction of non-Gaussian features of the PDFs. It was shown that non-Gaussian tails of the PDFs from first principles based gyrokinetic simulations agree with an analytical estimation based on a two fluid model.
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Speech Enhancement Using Gaussian Scale Mixture Models
Hao, Jiucang; Lee, Te-Won; Sejnowski, Terrence J.
2011-01-01
This paper presents a novel probabilistic approach to speech enhancement. Instead of a deterministic logarithmic relationship, we assume a probabilistic relationship between the frequency coefficients and the log-spectra. The speech model in the log-spectral domain is a Gaussian mixture model (GMM). The frequency coefficients obey a zero-mean Gaussian whose covariance equals to the exponential of the log-spectra. This results in a Gaussian scale mixture model (GSMM) for the speech signal in the frequency domain, since the log-spectra can be regarded as scaling factors. The probabilistic relation between frequency coefficients and log-spectra allows these to be treated as two random variables, both to be estimated from the noisy signals. Expectation-maximization (EM) was used to train the GSMM and Bayesian inference was used to compute the posterior signal distribution. Because exact inference of this full probabilistic model is computationally intractable, we developed two approaches to enhance the efficiency: the Laplace method and a variational approximation. The proposed methods were applied to enhance speech corrupted by Gaussian noise and speech-shaped noise (SSN). For both approximations, signals reconstructed from the estimated frequency coefficients provided higher signal-to-noise ratio (SNR) and those reconstructed from the estimated log-spectra produced lower word recognition error rate because the log-spectra fit the inputs to the recognizer better. Our algorithms effectively reduced the SSN, which algorithms based on spectral analysis were not able to suppress. PMID:21359139
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Theory and generation of conditional, scalable sub-Gaussian random fields
NASA Astrophysics Data System (ADS)
Panzeri, M.; Riva, M.; Guadagnini, A.; Neuman, S. P.
2016-03-01
Many earth and environmental (as well as a host of other) variables, Y, and their spatial (or temporal) increments, ΔY, exhibit non-Gaussian statistical scaling. Previously we were able to capture key aspects of such non-Gaussian scaling by treating Y and/or ΔY as sub-Gaussian random fields (or processes). This however left unaddressed the empirical finding that whereas sample frequency distributions of Y tend to display relatively mild non-Gaussian peaks and tails, those of ΔY often reveal peaks that grow sharper and tails that become heavier with decreasing separation distance or lag. Recently we proposed a generalized sub-Gaussian model (GSG) which resolves this apparent inconsistency between the statistical scaling behaviors of observed variables and their increments. We presented an algorithm to generate unconditional random realizations of statistically isotropic or anisotropic GSG functions and illustrated it in two dimensions. Most importantly, we demonstrated the feasibility of estimating all parameters of a GSG model underlying a single realization of Y by analyzing jointly spatial moments of Y data and corresponding increments, ΔY. Here, we extend our GSG model to account for noisy measurements of Y at a discrete set of points in space (or time), present an algorithm to generate conditional realizations of corresponding isotropic or anisotropic random fields, introduce two approximate versions of this algorithm to reduce CPU time, and explore them on one and two-dimensional synthetic test cases.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Zhou, M. L.; Liu, B.; Hu, R. H.
In the case of a thin plasma slab accelerated by the radiation pressure of an ultra-intense laser pulse, the development of Rayleigh-Taylor instability (RTI) will destroy the acceleration structure and terminate the acceleration process much sooner than theoretical limit. In this paper, a new scheme using multiple Gaussian pulses for ion acceleration in a radiation pressure acceleration regime is investigated with particle-in-cell simulation. We found that with multiple Gaussian pulses, the instability could be efficiently suppressed and the divergence of the ion bunch is greatly reduced, resulting in a longer acceleration time and much more collimated ion bunch with highermore » energy than using a single Gaussian pulse. An analytical model is developed to describe the suppression of RTI at the laser-plasma interface. The model shows that the suppression of RTI is due to the introduction of the long wavelength mode RTI by the multiple Gaussian pulses.« less
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An unbiased risk estimator for image denoising in the presence of mixed poisson-gaussian noise.
Le Montagner, Yoann; Angelini, Elsa D; Olivo-Marin, Jean-Christophe
2014-03-01
The behavior and performance of denoising algorithms are governed by one or several parameters, whose optimal settings depend on the content of the processed image and the characteristics of the noise, and are generally designed to minimize the mean squared error (MSE) between the denoised image returned by the algorithm and a virtual ground truth. In this paper, we introduce a new Poisson-Gaussian unbiased risk estimator (PG-URE) of the MSE applicable to a mixed Poisson-Gaussian noise model that unifies the widely used Gaussian and Poisson noise models in fluorescence bioimaging applications. We propose a stochastic methodology to evaluate this estimator in the case when little is known about the internal machinery of the considered denoising algorithm, and we analyze both theoretically and empirically the characteristics of the PG-URE estimator. Finally, we evaluate the PG-URE-driven parametrization for three standard denoising algorithms, with and without variance stabilizing transforms, and different characteristics of the Poisson-Gaussian noise mixture.
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Leading non-Gaussian corrections for diffusion orientation distribution function.
Jensen, Jens H; Helpern, Joseph A; Tabesh, Ali
2014-02-01
An analytical representation of the leading non-Gaussian corrections for a class of diffusion orientation distribution functions (dODFs) is presented. This formula is constructed from the diffusion and diffusional kurtosis tensors, both of which may be estimated with diffusional kurtosis imaging (DKI). By incorporating model-independent non-Gaussian diffusion effects, it improves on the Gaussian approximation used in diffusion tensor imaging (DTI). This analytical representation therefore provides a natural foundation for DKI-based white matter fiber tractography, which has potential advantages over conventional DTI-based fiber tractography in generating more accurate predictions for the orientations of fiber bundles and in being able to directly resolve intra-voxel fiber crossings. The formula is illustrated with numerical simulations for a two-compartment model of fiber crossings and for human brain data. These results indicate that the inclusion of the leading non-Gaussian corrections can significantly affect fiber tractography in white matter regions, such as the centrum semiovale, where fiber crossings are common. 2013 John Wiley & Sons, Ltd.
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Leading Non-Gaussian Corrections for Diffusion Orientation Distribution Function
Jensen, Jens H.; Helpern, Joseph A.; Tabesh, Ali
2014-01-01
An analytical representation of the leading non-Gaussian corrections for a class of diffusion orientation distribution functions (dODFs) is presented. This formula is constructed out of the diffusion and diffusional kurtosis tensors, both of which may be estimated with diffusional kurtosis imaging (DKI). By incorporating model-independent non-Gaussian diffusion effects, it improves upon the Gaussian approximation used in diffusion tensor imaging (DTI). This analytical representation therefore provides a natural foundation for DKI-based white matter fiber tractography, which has potential advantages over conventional DTI-based fiber tractography in generating more accurate predictions for the orientations of fiber bundles and in being able to directly resolve intra-voxel fiber crossings. The formula is illustrated with numerical simulations for a two-compartment model of fiber crossings and for human brain data. These results indicate that the inclusion of the leading non-Gaussian corrections can significantly affect fiber tractography in white matter regions, such as the centrum semiovale, where fiber crossings are common. PMID:24738143
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Modeling of dispersion near roadways based on the vehicle-induced turbulence concept
NASA Astrophysics Data System (ADS)
Sahlodin, Ali M.; Sotudeh-Gharebagh, Rahmat; Zhu, Yifang
A mathematical model is developed for dispersion near roadways by incorporating vehicle-induced turbulence (VIT) into Gaussian dispersion modeling using computational fluid dynamics (CFD). The model is based on the Gaussian plume equation in which roadway is regarded as a series of point sources. The Gaussian dispersion parameters are modified by simulation of the roadway using CFD in order to evaluate turbulent kinetic energy (TKE) as a measure of VIT. The model was evaluated against experimental carbon monoxide concentrations downwind of two major freeways reported in the literature. Good agreements were achieved between model results and the literature data. A significant difference was observed between the model results with and without considering VIT. The difference is rather high for data very close to the freeways. This model, after evaluation with additional data, may be used as a framework for predicting dispersion and deposition from any roadway for different traffic (vehicle type and speed) conditions.
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NASA Astrophysics Data System (ADS)
Tyagi, Neha; Cherayil, Binny J.
2018-03-01
The increasingly widespread occurrence in complex fluids of particle motion that is both Brownian and non-Gaussian has recently been found to be successfully modeled by a process (frequently referred to as ‘diffusing diffusivity’) in which the white noise that governs Brownian diffusion is itself stochastically modulated by either Ornstein–Uhlenbeck dynamics or by two-state noise. But the model has so far not been able to account for an aspect of non-Gaussian Brownian motion that is also commonly observed: a non-monotonic decay of the parameter that quantifies the extent of deviation from Gaussian behavior. In this paper, we show that the inclusion of memory effects in the model—via a generalized Langevin equation—can rationalise this phenomenon.
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Cosmic microwave background power asymmetry from non-Gaussian modulation.
Schmidt, Fabian; Hui, Lam
2013-01-04
Non-Gaussianity in the inflationary perturbations can couple observable scales to modes of much longer wavelength (even superhorizon), leaving as a signature a large-angle modulation of the observed cosmic microwave background power spectrum. This provides an alternative origin for a power asymmetry that is otherwise often ascribed to a breaking of statistical isotropy. The non-Gaussian modulation effect can be significant even for typical ~10(-5) perturbations while respecting current constraints on non-Gaussianity if the squeezed limit of the bispectrum is sufficiently infrared divergent. Just such a strongly infrared-divergent bispectrum has been claimed for inflation models with a non-Bunch-Davies initial state, for instance. Upper limits on the observed cosmic microwave background power asymmetry place stringent constraints on the duration of inflation in such models.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Patil, S. D., E-mail: sdpatilphy@gmail.com; Takale, M. V.
2016-05-06
This paper presents an influence of light absorption on self-focusing of laser beam propagation in plasma. The differential equation for beam-width parameter is obtained using the Wentzel-Kramers-Brillouin and paraxial approximations through parabolic equation approach. The nonlinearity in dielectric function is assumed to be aroused due to the combined effect of weakly relativistic and ponderomotive regime. To highlight the nature of propagation, behavior of beam-width parameter with dimensionless distance of propagation is presented graphically and discussed. The present work is helpful to understand issues related to the beam propagation in laser plasma interaction experiments where light absorption plays a vital role.
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Degeneracy of energy levels of pseudo-Gaussian oscillators
DOE Office of Scientific and Technical Information (OSTI.GOV)
Iacob, Theodor-Felix; Iacob, Felix, E-mail: felix@physics.uvt.ro; Lute, Marina
2015-12-07
We study the main features of the isotropic radial pseudo-Gaussian oscillators spectral properties. This study is made upon the energy levels degeneracy with respect to orbital angular momentum quantum number. In a previous work [6] we have shown that the pseudo-Gaussian oscillators belong to the class of quasi-exactly solvable models and an exact solution has been found.
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Recent advances in scalable non-Gaussian geostatistics: The generalized sub-Gaussian model
NASA Astrophysics Data System (ADS)
Guadagnini, Alberto; Riva, Monica; Neuman, Shlomo P.
2018-07-01
Geostatistical analysis has been introduced over half a century ago to allow quantifying seemingly random spatial variations in earth quantities such as rock mineral content or permeability. The traditional approach has been to view such quantities as multivariate Gaussian random functions characterized by one or a few well-defined spatial correlation scales. There is, however, mounting evidence that many spatially varying quantities exhibit non-Gaussian behavior over a multiplicity of scales. The purpose of this minireview is not to paint a broad picture of the subject and its treatment in the literature. Instead, we focus on very recent advances in the recognition and analysis of this ubiquitous phenomenon, which transcends hydrology and the Earth sciences, brought about largely by our own work. In particular, we use porosity data from a deep borehole to illustrate typical aspects of such scalable non-Gaussian behavior, describe a very recent theoretical model that (for the first time) captures all these behavioral aspects in a comprehensive manner, show how this allows generating random realizations of the quantity conditional on sampled values, point toward ways of incorporating scalable non-Gaussian behavior in hydrologic analysis, highlight the significance of doing so, and list open questions requiring further research.
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The order of three lowest-energy states of the six-electron harmonium at small force constant
DOE Office of Scientific and Technical Information (OSTI.GOV)
Strasburger, Krzysztof
2016-06-21
The order of low-energy states of six-electron harmonium is uncertain in the case of strong correlation, which is not a desired situation for the model system being considered for future testing of approximate methods of quantum chemistry. The computational study of these states has been carried out at the frequency parameter ω = 0.01, using the variational method with the basis of symmetry-projected, explicitly correlated Gaussian (ECG) lobe functions. It has revealed that the six-electron harmonium at this confinement strength is an octahedral Wigner molecule, whose order of states is different than in the strong confinement regime and does notmore » agree with the earlier predictions. The results obtained for ω = 0.5 and 10 are consistent with the findings based on the Hund’s rules for the s{sup 2}p{sup 4} electron configuration. Substantial part of the computations has been carried out on the graphical processing units and the efficiency of these devices in calculation of the integrals over ECG functions has been compared with traditional processors.« less
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Study of In-Trap Ion Clouds by Ion Trajectory Simulations.
Zhou, Xiaoyu; Liu, Xinwei; Cao, Wenbo; Wang, Xiao; Li, Ming; Qiao, Haoxue; Ouyang, Zheng
2018-02-01
Gaussian distribution has been utilized to describe the global number density distribution of ion cloud in the Paul trap, which is known as the thermal equilibrium theory and widely used in theoretical modeling of ion clouds in the ion traps. Using ion trajectory simulations, however, the ion clouds can now also be treated as a dynamic ion flow field and the location-dependent features could now be characterized. This study was carried out to better understand the in-trap ion cloud properties, such as the local particle velocity and temperature. The local ion number densities were found to be heterogeneously distributed in terms of mean and distribution width; the velocity and temperature of the ion flow varied with pressure depending on the flow type of the neutral molecules; and the "quasi-static" equilibrium status can only be achieved after a certain number of collisions, for which the time period is pressure-dependent. This work provides new insights of the ion clouds that are globally stable but subjected to local rf heating and collisional cooling. Graphical Abstract ᅟ.
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Bayesian spatial transformation models with applications in neuroimaging data.
Miranda, Michelle F; Zhu, Hongtu; Ibrahim, Joseph G
2013-12-01
The aim of this article is to develop a class of spatial transformation models (STM) to spatially model the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) and a set of covariates. The proposed STM include a varying Box-Cox transformation model for dealing with the issue of non-Gaussian distributed imaging data and a Gaussian Markov random field model for incorporating spatial smoothness of the imaging data. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. Simulations and real data analysis demonstrate that the STM significantly outperforms the voxel-wise linear model with Gaussian noise in recovering meaningful geometric patterns. Our STM is able to reveal important brain regions with morphological changes in children with attention deficit hyperactivity disorder. © 2013, The International Biometric Society.
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NASA Technical Reports Server (NTRS)
Luo, Xiaochun; Schramm, David N.
1993-01-01
One of the crucial aspects of density perturbations that are produced by the standard inflation scenario is that they are Gaussian where seeds produced by topological defects tend to be non-Gaussian. The three-point correlation function of the temperature anisotropy of the cosmic microwave background radiation (CBR) provides a sensitive test of this aspect of the primordial density field. In this paper, this function is calculated in the general context of various allowed non-Gaussian models. It is shown that the Cosmic Background Explorer and the forthcoming South Pole and balloon CBR anisotropy data may be able to provide a crucial test of the Gaussian nature of the perturbations.
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Yang, Sejung; Lee, Byung-Uk
2015-01-01
In certain image acquisitions processes, like in fluorescence microscopy or astronomy, only a limited number of photons can be collected due to various physical constraints. The resulting images suffer from signal dependent noise, which can be modeled as a Poisson distribution, and a low signal-to-noise ratio. However, the majority of research on noise reduction algorithms focuses on signal independent Gaussian noise. In this paper, we model noise as a combination of Poisson and Gaussian probability distributions to construct a more accurate model and adopt the contourlet transform which provides a sparse representation of the directional components in images. We also apply hidden Markov models with a framework that neatly describes the spatial and interscale dependencies which are the properties of transformation coefficients of natural images. In this paper, an effective denoising algorithm for Poisson-Gaussian noise is proposed using the contourlet transform, hidden Markov models and noise estimation in the transform domain. We supplement the algorithm by cycle spinning and Wiener filtering for further improvements. We finally show experimental results with simulations and fluorescence microscopy images which demonstrate the improved performance of the proposed approach. PMID:26352138
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Non-Gaussian probabilistic MEG source localisation based on kernel density estimation☆
Mohseni, Hamid R.; Kringelbach, Morten L.; Woolrich, Mark W.; Baker, Adam; Aziz, Tipu Z.; Probert-Smith, Penny
2014-01-01
There is strong evidence to suggest that data recorded from magnetoencephalography (MEG) follows a non-Gaussian distribution. However, existing standard methods for source localisation model the data using only second order statistics, and therefore use the inherent assumption of a Gaussian distribution. In this paper, we present a new general method for non-Gaussian source estimation of stationary signals for localising brain activity from MEG data. By providing a Bayesian formulation for MEG source localisation, we show that the source probability density function (pdf), which is not necessarily Gaussian, can be estimated using multivariate kernel density estimators. In the case of Gaussian data, the solution of the method is equivalent to that of widely used linearly constrained minimum variance (LCMV) beamformer. The method is also extended to handle data with highly correlated sources using the marginal distribution of the estimated joint distribution, which, in the case of Gaussian measurements, corresponds to the null-beamformer. The proposed non-Gaussian source localisation approach is shown to give better spatial estimates than the LCMV beamformer, both in simulations incorporating non-Gaussian signals, and in real MEG measurements of auditory and visual evoked responses, where the highly correlated sources are known to be difficult to estimate. PMID:24055702
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Fiori, Aldo; Volpi, Elena; Zarlenga, Antonio; Bohling, Geoffrey C
2015-08-01
The impact of the logconductivity (Y=ln K) distribution fY on transport at the MADE site is analyzed. Our principal interest is in non-Gaussian fY characterized by heavier tails than the Gaussian. Both the logconductivity moments and fY itself are inferred, taking advantage of the detailed measurements of Bohling et al. (2012). The resulting logconductivity distribution displays heavier tails than the Gaussian, although the departure from Gaussianity is not significant. The effect of the logconductivity distribution on the breakthrough curve (BTC) is studied through an analytical, physically based model. It is found that the non-Gaussianity of the MADE logconductivity distribution does not strongly affect the BTC. Counterintuitively, assuming heavier tailed distributions for Y, with same variance, leads to BTCs which are more symmetrical than those for the Gaussian fY, with less pronounced preferential flow. Results indicate that the impact of strongly non-Gaussian, heavy tailed distributions on solute transport in heterogeneous porous formations can be significant, especially in the presence of high heterogeneity, resulting in reduced preferential flow and retarded peak arrivals. Copyright © 2015 Elsevier B.V. All rights reserved.
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A Non-Gaussian Stock Price Model: Options, Credit and a Multi-Timescale Memory
NASA Astrophysics Data System (ADS)
Borland, L.
We review a recently proposed model of stock prices, based on astatistical feedback model that results in a non-Gaussian distribution of price changes. Applications to option pricing and the pricing of debt is discussed. A generalization to account for feedback effects over multiple timescales is also presented. This model reproduces most of the stylized facts (ie statistical anomalies) observed in real financial markets.
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NASA Astrophysics Data System (ADS)
Kang, Yan-Mei; Chen, Xi; Lin, Xu-Dong; Tan, Ning
The mean first passage time (MFPT) in a phenomenological gene transcriptional regulatory model with non-Gaussian noise is analytically investigated based on the singular perturbation technique. The effect of the non-Gaussian noise on the phenomenon of stochastic resonance (SR) is then disclosed based on a new combination of adiabatic elimination and linear response approximation. Compared with the results in the Gaussian noise case, it is found that bounded non-Gaussian noise inhibits the transition between different concentrations of protein, while heavy-tailed non-Gaussian noise accelerates the transition. It is also found that the optimal noise intensity for SR in the heavy-tailed noise case is smaller, while the optimal noise intensity in the bounded noise case is larger. These observations can be explained by the heavy-tailed noise easing random transitions.
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Modeling Sea-Level Change using Errors-in-Variables Integrated Gaussian Processes
NASA Astrophysics Data System (ADS)
Cahill, Niamh; Parnell, Andrew; Kemp, Andrew; Horton, Benjamin
2014-05-01
We perform Bayesian inference on historical and late Holocene (last 2000 years) rates of sea-level change. The data that form the input to our model are tide-gauge measurements and proxy reconstructions from cores of coastal sediment. To accurately estimate rates of sea-level change and reliably compare tide-gauge compilations with proxy reconstructions it is necessary to account for the uncertainties that characterize each dataset. Many previous studies used simple linear regression models (most commonly polynomial regression) resulting in overly precise rate estimates. The model we propose uses an integrated Gaussian process approach, where a Gaussian process prior is placed on the rate of sea-level change and the data itself is modeled as the integral of this rate process. The non-parametric Gaussian process model is known to be well suited to modeling time series data. The advantage of using an integrated Gaussian process is that it allows for the direct estimation of the derivative of a one dimensional curve. The derivative at a particular time point will be representative of the rate of sea level change at that time point. The tide gauge and proxy data are complicated by multiple sources of uncertainty, some of which arise as part of the data collection exercise. Most notably, the proxy reconstructions include temporal uncertainty from dating of the sediment core using techniques such as radiocarbon. As a result of this, the integrated Gaussian process model is set in an errors-in-variables (EIV) framework so as to take account of this temporal uncertainty. The data must be corrected for land-level change known as glacio-isostatic adjustment (GIA) as it is important to isolate the climate-related sea-level signal. The correction for GIA introduces covariance between individual age and sea level observations into the model. The proposed integrated Gaussian process model allows for the estimation of instantaneous rates of sea-level change and accounts for all available sources of uncertainty in tide-gauge and proxy-reconstruction data. Our response variable is sea level after correction for GIA. By embedding the integrated process in an errors-in-variables (EIV) framework, and removing the estimate of GIA, we can quantify rates with better estimates of uncertainty than previously possible. The model provides a flexible fit and enables us to estimate rates of change at any given time point, thus observing how rates have been evolving from the past to present day.
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Yu, Wenxi; Liu, Yang; Ma, Zongwei; Bi, Jun
2017-08-01
Using satellite-based aerosol optical depth (AOD) measurements and statistical models to estimate ground-level PM 2.5 is a promising way to fill the areas that are not covered by ground PM 2.5 monitors. The statistical models used in previous studies are primarily Linear Mixed Effects (LME) and Geographically Weighted Regression (GWR) models. In this study, we developed a new regression model between PM 2.5 and AOD using Gaussian processes in a Bayesian hierarchical setting. Gaussian processes model the stochastic nature of the spatial random effects, where the mean surface and the covariance function is specified. The spatial stochastic process is incorporated under the Bayesian hierarchical framework to explain the variation of PM 2.5 concentrations together with other factors, such as AOD, spatial and non-spatial random effects. We evaluate the results of our model and compare them with those of other, conventional statistical models (GWR and LME) by within-sample model fitting and out-of-sample validation (cross validation, CV). The results show that our model possesses a CV result (R 2 = 0.81) that reflects higher accuracy than that of GWR and LME (0.74 and 0.48, respectively). Our results indicate that Gaussian process models have the potential to improve the accuracy of satellite-based PM 2.5 estimates.
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Back to Normal! Gaussianizing posterior distributions for cosmological probes
NASA Astrophysics Data System (ADS)
Schuhmann, Robert L.; Joachimi, Benjamin; Peiris, Hiranya V.
2014-05-01
We present a method to map multivariate non-Gaussian posterior probability densities into Gaussian ones via nonlinear Box-Cox transformations, and generalizations thereof. This is analogous to the search for normal parameters in the CMB, but can in principle be applied to any probability density that is continuous and unimodal. The search for the optimally Gaussianizing transformation amongst the Box-Cox family is performed via a maximum likelihood formalism. We can judge the quality of the found transformation a posteriori: qualitatively via statistical tests of Gaussianity, and more illustratively by how well it reproduces the credible regions. The method permits an analytical reconstruction of the posterior from a sample, e.g. a Markov chain, and simplifies the subsequent joint analysis with other experiments. Furthermore, it permits the characterization of a non-Gaussian posterior in a compact and efficient way. The expression for the non-Gaussian posterior can be employed to find analytic formulae for the Bayesian evidence, and consequently be used for model comparison.
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Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
NASA Astrophysics Data System (ADS)
Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin
2018-02-01
Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.
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Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations
DOE Office of Scientific and Technical Information (OSTI.GOV)
Verde, Licia; Jimenez, Raul; Alvarez-Gaume, Luis
2013-06-01
We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non-Gaussianity estimation from Cosmic Microwave Background maps and the halo mass function where we obtain analytical expressions. We also provide analytic approximations and their range of validity. For the Cosmic Microwave Background we give a fast way to compute the PDF which is valid up to more than 7σ for f{sub NL} values (both true and sampled) not ruledmore » out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.« less
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Gaussian-Beam Laser-Resonator Program
NASA Technical Reports Server (NTRS)
Cross, Patricia L.; Bair, Clayton H.; Barnes, Norman
1989-01-01
Gaussian Beam Laser Resonator Program models laser resonators by use of Gaussian-beam-propagation techniques. Used to determine radii of beams as functions of position in laser resonators. Algorithm used in program has three major components. First, ray-transfer matrix for laser resonator must be calculated. Next, initial parameters of beam calculated. Finally, propagation of beam through optical elements computed. Written in Microsoft FORTRAN (Version 4.01).
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NASA Astrophysics Data System (ADS)
Guadagnini, A.; Riva, M.; Neuman, S. P.
2016-12-01
Environmental quantities such as log hydraulic conductivity (or transmissivity), Y(x) = ln K(x), and their spatial (or temporal) increments, ΔY, are known to be generally non-Gaussian. Documented evidence of such behavior includes symmetry of increment distributions at all separation scales (or lags) between incremental values of Y with sharp peaks and heavy tails that decay asymptotically as lag increases. This statistical scaling occurs in porous as well as fractured media characterized by either one or a hierarchy of spatial correlation scales. In hierarchical media one observes a range of additional statistical ΔY scaling phenomena, all of which are captured comprehensibly by a novel generalized sub-Gaussian (GSG) model. In this model Y forms a mixture Y(x) = U(x) G(x) of single- or multi-scale Gaussian processes G having random variances, U being a non-negative subordinator independent of G. Elsewhere we developed ways to generate unconditional and conditional random realizations of isotropic or anisotropic GSG fields which can be embedded in numerical Monte Carlo flow and transport simulations. Here we present and discuss expressions for probability distribution functions of Y and ΔY as well as their lead statistical moments. We then focus on a simple flow setting of mean uniform steady state flow in an unbounded, two-dimensional domain, exploring ways in which non-Gaussian heterogeneity affects stochastic flow and transport descriptions. Our expressions represent (a) lead order autocovariance and cross-covariance functions of hydraulic head, velocity and advective particle displacement as well as (b) analogues of preasymptotic and asymptotic Fickian dispersion coefficients. We compare them with corresponding expressions developed in the literature for Gaussian Y.
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Period Estimation for Sparsely-sampled Quasi-periodic Light Curves Applied to Miras
NASA Astrophysics Data System (ADS)
He, Shiyuan; Yuan, Wenlong; Huang, Jianhua Z.; Long, James; Macri, Lucas M.
2016-12-01
We develop a nonlinear semi-parametric Gaussian process model to estimate periods of Miras with sparsely sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum likelihood to estimate the period and the parameters of the Gaussian process, while integrating out the effects of other nuisance parameters in the model with respect to a suitable prior distribution obtained from earlier studies. Since the likelihood is highly multimodal for period, we implement a hybrid method that applies the quasi-Newton algorithm for Gaussian process parameters and search the period/frequency parameter space over a dense grid. A large-scale, high-fidelity simulation is conducted to mimic the sampling quality of Mira light curves obtained by the M33 Synoptic Stellar Survey. The simulated data set is publicly available and can serve as a testbed for future evaluation of different period estimation methods. The semi-parametric model outperforms an existing algorithm on this simulated test data set as measured by period recovery rate and quality of the resulting period-luminosity relations.
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Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA
DOE Office of Scientific and Technical Information (OSTI.GOV)
Thimmisetty, Charanraj A.; Zhao, Wenju; Chen, Xiao
2017-10-18
Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). Thismore » approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.« less
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Modeling and forecasting foreign exchange daily closing prices with normal inverse Gaussian
NASA Astrophysics Data System (ADS)
Teneng, Dean
2013-09-01
We fit the normal inverse Gaussian(NIG) distribution to foreign exchange closing prices using the open software package R and select best models by Käärik and Umbleja (2011) proposed strategy. We observe that daily closing prices (12/04/2008 - 07/08/2012) of CHF/JPY, AUD/JPY, GBP/JPY, NZD/USD, QAR/CHF, QAR/EUR, SAR/CHF, SAR/EUR, TND/CHF and TND/EUR are excellent fits while EGP/EUR and EUR/GBP are good fits with a Kolmogorov-Smirnov test p-value of 0.062 and 0.08 respectively. It was impossible to estimate normal inverse Gaussian parameters (by maximum likelihood; computational problem) for JPY/CHF but CHF/JPY was an excellent fit. Thus, while the stochastic properties of an exchange rate can be completely modeled with a probability distribution in one direction, it may be impossible the other way around. We also demonstrate that foreign exchange closing prices can be forecasted with the normal inverse Gaussian (NIG) Lévy process, both in cases where the daily closing prices can and cannot be modeled by NIG distribution.
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Model-independent test for scale-dependent non-Gaussianities in the cosmic microwave background.
Räth, C; Morfill, G E; Rossmanith, G; Banday, A J; Górski, K M
2009-04-03
We present a model-independent method to test for scale-dependent non-Gaussianities in combination with scaling indices as test statistics. Therefore, surrogate data sets are generated, in which the power spectrum of the original data is preserved, while the higher order correlations are partly randomized by applying a scale-dependent shuffling procedure to the Fourier phases. We apply this method to the Wilkinson Microwave Anisotropy Probe data of the cosmic microwave background and find signatures for non-Gaussianities on large scales. Further tests are required to elucidate the origin of the detected anomalies.
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Probing the cosmological initial conditions using the CMB
NASA Astrophysics Data System (ADS)
Yadav, Amit P. S.
In the last few decades, advances in observational cosmology have given us a standard model of cosmology. The basic cosmological parameters have been laid out to high precision. Cosmologists have started asking questions about the nature of the cosmological initial conditions. Many ambitious experiments such as Planck satellite, EBEX, ACT, CAPMAP, QUaD, BICEP, SPIDER, QUIET, and GEM are underway. Experiments like these will provide us with a wealth of information about CMB polarization, CMB lensing, and polarization foregrounds. These experiments will be complemented with great observational campaigns to map the 3D structure in the Universe and new particle physics constraints from the Large Hadron Collider. In my graduate work I have made explicit how observations of the CMB temperature and E-polarization anisotropies can be combined to provide optimal constraints on models of the early universe at the highest energies. I have developed new ways of constraining models of the early universe using CMB temperature and polarization data. Inflation is one of the most promising theories of the early universe. Different inflationary models predict different amounts of non-Gaussian perturbations. Although any non-Gaussianity predicted by the canonical inflation model is very small, there exist models which can generate significant amounts of non-Gaussianities. Hence any characterization of non-Gaussianity of the primordial perturbations constrains the models of inflation. The information in the bispectrum (or higher order moments) is completely independent of the power spectrum constraints on the amplitude of primordial power spectrum (A), the scalar spectral index of the primordial power spectrum ns, and the running of the primordial power spectrum. My work has made it possible to extract the bispectrum information from large, high resolution CMB temperature and polarization data. We have demonstrated that the primordial adiabatic perturbations can be reconstructed using CMB temperature and E-polarization information (Yadav and Wandelt 2005). One of the main motivations of reconstructing the primordial perturbations is to study the primordial non-Gaussianities. Since the amplitude of primordial non-Gaussianity is very small, any enhancement in sensitivity to the primordial features is useful because it improves the characterization of the primordial non-Gaussianity. Our reconstruction allows us to be more sensitive to the primordial features, whereas most of the current probes of non-Gaussianity do not specifically select for them. We have also developed a fast cubic (bispectrum) estimator of non-Gaussianity f NL of local type, using combined temperature and E-polarization data (Yadavet al. 2007). The estimator is computationally efficient, scaling as O( N 3/2 ) compared to the O( N 5/2 ) scaling of the brute force bispectrum calculation for sky maps with N pixels. For the Planck satellite, this translates into a speed-up by factors of millions, reducing the required computing time from thousands of years to just hours and thus making f NL estimation feasible. The speed of our estimator allows us to study its statistical properties using Monte Carlo simulations. Our estimator in its original form was optimal for homogeneous noise. In order to apply our estimator to realistic data, the estimator needed to be able to deal with inhomogeneous noise. We have generalized the fast polarized estimator to deal with inhomogeneous noise. The generalized estimator is also computationally efficient, scaling as O( N 3/2 ). Furthermore, we have studied and characterized our estimators in the presence of realistic noise, finite resolution, incomplete sky-coverage, and using non-Gaussian CMB maps (Yadavet al. 2008a). We have also developed a numerical code to generate CMB temperature and polarization non-Gaussian maps starting from a given primordial non-Gaussianity (f NL ) (Liguori et al. 2007). In the process of non-Gaussian CMB map making, the code also generates corresponding non-Gaussian primordial curvature perturbations. We use these curvature perturbations to quantify the quality of the tomographic reconstruction method described in (Yadav and Wandelt 2005). We check whether the tomographic reconstruction method preserves the non-Gaussian features, especially the phase information, in the reconstructed curvature perturbations (Yadav et al. in preparation). Finally, using our estimator we found (Yadav and Wandelt 2008) evidence for primordial non-Gaussianity of the local type (f NL ) in the temperature anisotropy of the Cosmic Microwave Background. Analyzing the bispectrum of the WMAP 3-year data up to l max =750 we find 27< f NL <147 (95% CL). This amounts to a rejection of f NL =0 at 2.8s, disfavoring canonical single field slow-roll inflation. The signal is robust to variations in l max , frequency, and masks. No known foreground, instrument systematic, or secondary anisotropy explains it. We explore the impact of several analysis choices on the quoted significance and find 2.5s to be conservative.
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Teaching Real Business Cycles to Undergraduates
ERIC Educational Resources Information Center
Brevik, Frode; Gartner, Manfred
2007-01-01
The authors review the graphical approach to teaching the real business cycle model introduced in Barro. They then look at where this approach cuts corners and suggest refinements. Finally, they compare graphical and exact models by means of impulse-response functions. The graphical models yield reliable qualitative results. Sizable quantitative…
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Graphics modelling of non-contact thickness measuring robotics work cell
NASA Technical Reports Server (NTRS)
Warren, Charles W.
1990-01-01
A system was developed for measuring, in real time, the thickness of a sprayable insulation during its application. The system was graphically modelled, off-line, using a state-of-the-art graphics workstation and associated software. This model was to contain a 3D color model of a workcell containing a robot and an air bearing turntable. A communication link was established between the graphics workstations and the robot's controller. Sequences of robot motion generated by the computer simulation are transmitted to the robot for execution.
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NASA Astrophysics Data System (ADS)
Piretzidis, Dimitrios; Sideris, Michael G.
2016-04-01
This study investigates the possibilities of local hydrology signal extraction using GRACE data and conventional filtering techniques. The impact of the basin shape has also been studied in order to derive empirical rules for tuning the GRACE filter parameters. GRACE CSR Release 05 monthly solutions were used from April 2002 to August 2015 (161 monthly solutions in total). SLR data were also used to replace the GRACE C2,0 coefficient, and a de-correlation filter with optimal parameters for CSR Release 05 data was applied to attenuate the correlation errors of monthly mass differences. For basins located at higher latitudes, the effect of Glacial Isostatic Adjustment (GIA) was taken into account using the ICE-6G model. The study focuses on three geometric properties, i.e., the area, the convexity and the width in the longitudinal direction, of 100 basins with global distribution. Two experiments have been performed. The first one deals with the determination of the Gaussian smoothing radius that minimizes the gaussianity of GRACE equivalent water height (EWH) over the selected basins. The EWH kurtosis was selected as a metric of gaussianity. The second experiment focuses on the derivation of the Gaussian smoothing radius that minimizes the RMS difference between GRACE data and a hydrology model. The GLDAS 1.0 Noah hydrology model was chosen, which shows good agreement with GRACE data according to previous studies. Early results show that there is an apparent relation between the geometric attributes of the basins examined and the Gaussian radius derived from the two experiments. The kurtosis analysis experiment tends to underestimate the optimal Gaussian radius, which is close to 200-300 km in many cases. Empirical rules for the selection of the Gaussian radius have been also developed for sub-regional scale basins.
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Gaussian solitary waves and compactons in Fermi–Pasta–Ulam lattices with Hertzian potentials
James, Guillaume; Pelinovsky, Dmitry
2014-01-01
We consider a class of fully nonlinear Fermi–Pasta–Ulam (FPU) lattices, consisting of a chain of particles coupled by fractional power nonlinearities of order α>1. This class of systems incorporates a classical Hertzian model describing acoustic wave propagation in chains of touching beads in the absence of precompression. We analyse the propagation of localized waves when α is close to unity. Solutions varying slowly in space and time are searched with an appropriate scaling, and two asymptotic models of the chain of particles are derived consistently. The first one is a logarithmic Korteweg–de Vries (KdV) equation and possesses linearly orbitally stable Gaussian solitary wave solutions. The second model consists of a generalized KdV equation with Hölder-continuous fractional power nonlinearity and admits compacton solutions, i.e. solitary waves with compact support. When , we numerically establish the asymptotically Gaussian shape of exact FPU solitary waves with near-sonic speed and analytically check the pointwise convergence of compactons towards the limiting Gaussian profile. PMID:24808748
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Chialvo, Ariel A.; Vlcek, Lukas
2014-11-01
We present a detailed derivation of the complete set of expressions required for the implementation of an Ewald summation approach to handle the long-range electrostatic interactions of polar and ionic model systems involving Gaussian charges and induced dipole moments with a particular application to the isobaricisothermal molecular dynamics simulation of our Gaussian Charge Polarizable (GCP) water model and its extension to aqueous electrolytes solutions. The set comprises the individual components of the potential energy, electrostatic potential, electrostatic field and gradient, the electrostatic force and the corresponding virial. Moreover, we show how the derived expressions converge to known point-based electrostatic counterpartsmore » when the parameters, defining the Gaussian charge and induced-dipole distributions, are extrapolated to their limiting point values. Finally, we illustrate the Ewald implementation against the current reaction field approach by isothermal-isobaric molecular dynamics of ambient GCP water for which we compared the outcomes of the thermodynamic, microstructural, and polarization behavior.« less
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Noise effects in nonlinear biochemical signaling
NASA Astrophysics Data System (ADS)
Bostani, Neda; Kessler, David A.; Shnerb, Nadav M.; Rappel, Wouter-Jan; Levine, Herbert
2012-01-01
It has been generally recognized that stochasticity can play an important role in the information processing accomplished by reaction networks in biological cells. Most treatments of that stochasticity employ Gaussian noise even though it is a priori obvious that this approximation can violate physical constraints, such as the positivity of chemical concentrations. Here, we show that even when such nonphysical fluctuations are rare, an exact solution of the Gaussian model shows that the model can yield unphysical results. This is done in the context of a simple incoherent-feedforward model which exhibits perfect adaptation in the deterministic limit. We show how one can use the natural separation of time scales in this model to yield an approximate model, that is analytically solvable, including its dynamical response to an environmental change. Alternatively, one can employ a cutoff procedure to regularize the Gaussian result.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Passos de Figueiredo, Leandro, E-mail: leandrop.fgr@gmail.com; Grana, Dario; Santos, Marcio
We propose a Bayesian approach for seismic inversion to estimate acoustic impedance, porosity and lithofacies within the reservoir conditioned to post-stack seismic and well data. The link between elastic and petrophysical properties is given by a joint prior distribution for the logarithm of impedance and porosity, based on a rock-physics model. The well conditioning is performed through a background model obtained by well log interpolation. Two different approaches are presented: in the first approach, the prior is defined by a single Gaussian distribution, whereas in the second approach it is defined by a Gaussian mixture to represent the well datamore » multimodal distribution and link the Gaussian components to different geological lithofacies. The forward model is based on a linearized convolutional model. For the single Gaussian case, we obtain an analytical expression for the posterior distribution, resulting in a fast algorithm to compute the solution of the inverse problem, i.e. the posterior distribution of acoustic impedance and porosity as well as the facies probability given the observed data. For the Gaussian mixture prior, it is not possible to obtain the distributions analytically, hence we propose a Gibbs algorithm to perform the posterior sampling and obtain several reservoir model realizations, allowing an uncertainty analysis of the estimated properties and lithofacies. Both methodologies are applied to a real seismic dataset with three wells to obtain 3D models of acoustic impedance, porosity and lithofacies. The methodologies are validated through a blind well test and compared to a standard Bayesian inversion approach. Using the probability of the reservoir lithofacies, we also compute a 3D isosurface probability model of the main oil reservoir in the studied field.« less
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The Gaussian Laser Angular Distribution in HYDRA's 3D Laser Ray Trace Package
DOE Office of Scientific and Technical Information (OSTI.GOV)
Sepke, Scott M.
In this note, the angular distribution of rays launched by the 3D LZR ray trace package is derived for Gaussian beams (npower==2) with bm model=3±. Beams with bm model=+3 have a nearly at distribution, and beams with bm model=-3 have a nearly linear distribution when the spot size is large compared to the wavelength.
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National Centers for Environmental Prediction
/ VISION | About EMC EMC > NAM > EXPERIMENTAL DATA Home NAM Operational Products HIRESW Operational Products Operational Forecast Graphics Experimental Forecast Graphics Verification and Diagnostics Model PARALLEL/EXPERIMENTAL MODEL FORECAST GRAPHICS OPERATIONAL VERIFICATION / DIAGNOSTICS PARALLEL VERIFICATION
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Wang, Shijun; Liu, Peter; Turkbey, Baris; Choyke, Peter; Pinto, Peter; Summers, Ronald M
2012-01-01
In this paper, we propose a new pharmacokinetic model for parameter estimation of dynamic contrast-enhanced (DCE) MRI by using Gaussian process inference. Our model is based on the Tofts dual-compartment model for the description of tracer kinetics and the observed time series from DCE-MRI is treated as a Gaussian stochastic process. The parameter estimation is done through a maximum likelihood approach and we propose a variant of the coordinate descent method to solve this likelihood maximization problem. The new model was shown to outperform a baseline method on simulated data. Parametric maps generated on prostate DCE data with the new model also provided better enhancement of tumors, lower intensity on false positives, and better boundary delineation when compared with the baseline method. New statistical parameter maps from the process model were also found to be informative, particularly when paired with the PK parameter maps.
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Tests for Gaussianity of the MAXIMA-1 cosmic microwave background map.
Wu, J H; Balbi, A; Borrill, J; Ferreira, P G; Hanany, S; Jaffe, A H; Lee, A T; Rabii, B; Richards, P L; Smoot, G F; Stompor, R; Winant, C D
2001-12-17
Gaussianity of the cosmological perturbations is one of the key predictions of standard inflation, but it is violated by other models of structure formation such as cosmic defects. We present the first test of the Gaussianity of the cosmic microwave background (CMB) on subdegree angular scales, where deviations from Gaussianity are most likely to occur. We apply the methods of moments, cumulants, the Kolmogorov test, the chi(2) test, and Minkowski functionals in eigen, real, Wiener-filtered, and signal-whitened spaces, to the MAXIMA-1 CMB anisotropy data. We find that the data, which probe angular scales between 10 arcmin and 5 deg, are consistent with Gaussianity. These results show consistency with the standard inflation and place constraints on the existence of cosmic defects.
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Genomic Prediction of Genotype × Environment Interaction Kernel Regression Models.
Cuevas, Jaime; Crossa, José; Soberanis, Víctor; Pérez-Elizalde, Sergio; Pérez-Rodríguez, Paulino; Campos, Gustavo de Los; Montesinos-López, O A; Burgueño, Juan
2016-11-01
In genomic selection (GS), genotype × environment interaction (G × E) can be modeled by a marker × environment interaction (M × E). The G × E may be modeled through a linear kernel or a nonlinear (Gaussian) kernel. In this study, we propose using two nonlinear Gaussian kernels: the reproducing kernel Hilbert space with kernel averaging (RKHS KA) and the Gaussian kernel with the bandwidth estimated through an empirical Bayesian method (RKHS EB). We performed single-environment analyses and extended to account for G × E interaction (GBLUP-G × E, RKHS KA-G × E and RKHS EB-G × E) in wheat ( L.) and maize ( L.) data sets. For single-environment analyses of wheat and maize data sets, RKHS EB and RKHS KA had higher prediction accuracy than GBLUP for all environments. For the wheat data, the RKHS KA-G × E and RKHS EB-G × E models did show up to 60 to 68% superiority over the corresponding single environment for pairs of environments with positive correlations. For the wheat data set, the models with Gaussian kernels had accuracies up to 17% higher than that of GBLUP-G × E. For the maize data set, the prediction accuracy of RKHS EB-G × E and RKHS KA-G × E was, on average, 5 to 6% higher than that of GBLUP-G × E. The superiority of the Gaussian kernel models over the linear kernel is due to more flexible kernels that accounts for small, more complex marker main effects and marker-specific interaction effects. Copyright © 2016 Crop Science Society of America.
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Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels
NASA Astrophysics Data System (ADS)
De Palma, Giacomo; Trevisan, Dario; Giovannetti, Vittorio
2017-04-01
We prove the long-standing conjecture stating that Gaussian thermal input states minimize the output von Neumann entropy of one-mode phase-covariant quantum Gaussian channels among all the input states with a given entropy. Phase-covariant quantum Gaussian channels model the attenuation and the noise that affect any electromagnetic signal in the quantum regime. Our result is crucial to prove the converse theorems for both the triple trade-off region and the capacity region for broadcast communication of the Gaussian quantum-limited amplifier. Our result extends to the quantum regime the entropy power inequality that plays a key role in classical information theory. Our proof exploits a completely new technique based on the recent determination of the p →q norms of the quantum-limited amplifier [De Palma et al., arXiv:1610.09967]. This technique can be applied to any quantum channel.
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Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels.
De Palma, Giacomo; Trevisan, Dario; Giovannetti, Vittorio
2017-04-21
We prove the long-standing conjecture stating that Gaussian thermal input states minimize the output von Neumann entropy of one-mode phase-covariant quantum Gaussian channels among all the input states with a given entropy. Phase-covariant quantum Gaussian channels model the attenuation and the noise that affect any electromagnetic signal in the quantum regime. Our result is crucial to prove the converse theorems for both the triple trade-off region and the capacity region for broadcast communication of the Gaussian quantum-limited amplifier. Our result extends to the quantum regime the entropy power inequality that plays a key role in classical information theory. Our proof exploits a completely new technique based on the recent determination of the p→q norms of the quantum-limited amplifier [De Palma et al., arXiv:1610.09967]. This technique can be applied to any quantum channel.
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Improving stability of prediction models based on correlated omics data by using network approaches.
Tissier, Renaud; Houwing-Duistermaat, Jeanine; Rodríguez-Girondo, Mar
2018-01-01
Building prediction models based on complex omics datasets such as transcriptomics, proteomics, metabolomics remains a challenge in bioinformatics and biostatistics. Regularized regression techniques are typically used to deal with the high dimensionality of these datasets. However, due to the presence of correlation in the datasets, it is difficult to select the best model and application of these methods yields unstable results. We propose a novel strategy for model selection where the obtained models also perform well in terms of overall predictability. Several three step approaches are considered, where the steps are 1) network construction, 2) clustering to empirically derive modules or pathways, and 3) building a prediction model incorporating the information on the modules. For the first step, we use weighted correlation networks and Gaussian graphical modelling. Identification of groups of features is performed by hierarchical clustering. The grouping information is included in the prediction model by using group-based variable selection or group-specific penalization. We compare the performance of our new approaches with standard regularized regression via simulations. Based on these results we provide recommendations for selecting a strategy for building a prediction model given the specific goal of the analysis and the sizes of the datasets. Finally we illustrate the advantages of our approach by application of the methodology to two problems, namely prediction of body mass index in the DIetary, Lifestyle, and Genetic determinants of Obesity and Metabolic syndrome study (DILGOM) and prediction of response of each breast cancer cell line to treatment with specific drugs using a breast cancer cell lines pharmacogenomics dataset.
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Flexible link functions in nonparametric binary regression with Gaussian process priors.
Li, Dan; Wang, Xia; Lin, Lizhen; Dey, Dipak K
2016-09-01
In many scientific fields, it is a common practice to collect a sequence of 0-1 binary responses from a subject across time, space, or a collection of covariates. Researchers are interested in finding out how the expected binary outcome is related to covariates, and aim at better prediction in the future 0-1 outcomes. Gaussian processes have been widely used to model nonlinear systems; in particular to model the latent structure in a binary regression model allowing nonlinear functional relationship between covariates and the expectation of binary outcomes. A critical issue in modeling binary response data is the appropriate choice of link functions. Commonly adopted link functions such as probit or logit links have fixed skewness and lack the flexibility to allow the data to determine the degree of the skewness. To address this limitation, we propose a flexible binary regression model which combines a generalized extreme value link function with a Gaussian process prior on the latent structure. Bayesian computation is employed in model estimation. Posterior consistency of the resulting posterior distribution is demonstrated. The flexibility and gains of the proposed model are illustrated through detailed simulation studies and two real data examples. Empirical results show that the proposed model outperforms a set of alternative models, which only have either a Gaussian process prior on the latent regression function or a Dirichlet prior on the link function. © 2015, The International Biometric Society.
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Flexible Link Functions in Nonparametric Binary Regression with Gaussian Process Priors
Li, Dan; Lin, Lizhen; Dey, Dipak K.
2015-01-01
Summary In many scientific fields, it is a common practice to collect a sequence of 0-1 binary responses from a subject across time, space, or a collection of covariates. Researchers are interested in finding out how the expected binary outcome is related to covariates, and aim at better prediction in the future 0-1 outcomes. Gaussian processes have been widely used to model nonlinear systems; in particular to model the latent structure in a binary regression model allowing nonlinear functional relationship between covariates and the expectation of binary outcomes. A critical issue in modeling binary response data is the appropriate choice of link functions. Commonly adopted link functions such as probit or logit links have fixed skewness and lack the flexibility to allow the data to determine the degree of the skewness. To address this limitation, we propose a flexible binary regression model which combines a generalized extreme value link function with a Gaussian process prior on the latent structure. Bayesian computation is employed in model estimation. Posterior consistency of the resulting posterior distribution is demonstrated. The flexibility and gains of the proposed model are illustrated through detailed simulation studies and two real data examples. Empirical results show that the proposed model outperforms a set of alternative models, which only have either a Gaussian process prior on the latent regression function or a Dirichlet prior on the link function. PMID:26686333
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Loop corrections to primordial non-Gaussianity
NASA Astrophysics Data System (ADS)
Boran, Sibel; Kahya, E. O.
2018-02-01
We discuss quantum gravitational loop effects to observable quantities such as curvature power spectrum and primordial non-Gaussianity of cosmic microwave background (CMB) radiation. We first review the previously shown case where one gets a time dependence for zeta-zeta correlator due to loop corrections. Then we investigate the effect of loop corrections to primordial non-Gaussianity of CMB. We conclude that, even with a single scalar inflaton, one might get a huge value for non-Gaussianity which would exceed the observed value by at least 30 orders of magnitude. Finally we discuss the consequences of this result for scalar driven inflationary models.
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Understanding of Relation Structures of Graphical Models by Lower Secondary Students
ERIC Educational Resources Information Center
van Buuren, Onne; Heck, André; Ellermeijer, Ton
2016-01-01
A learning path has been developed on system dynamical graphical modelling, integrated into the Dutch lower secondary physics curriculum. As part of the developmental research for this learning path, students' understanding of the relation structures shown in the diagrams of graphical system dynamics based models has been investigated. One of our…
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Narayan, Manjari; Allen, Genevera I.
2016-01-01
Many complex brain disorders, such as autism spectrum disorders, exhibit a wide range of symptoms and disability. To understand how brain communication is impaired in such conditions, functional connectivity studies seek to understand individual differences in brain network structure in terms of covariates that measure symptom severity. In practice, however, functional connectivity is not observed but estimated from complex and noisy neural activity measurements. Imperfect subject network estimates can compromise subsequent efforts to detect covariate effects on network structure. We address this problem in the case of Gaussian graphical models of functional connectivity, by proposing novel two-level models that treat both subject level networks and population level covariate effects as unknown parameters. To account for imperfectly estimated subject level networks when fitting these models, we propose two related approaches—R2 based on resampling and random effects test statistics, and R3 that additionally employs random adaptive penalization. Simulation studies using realistic graph structures reveal that R2 and R3 have superior statistical power to detect covariate effects compared to existing approaches, particularly when the number of within subject observations is comparable to the size of subject networks. Using our novel models and methods to study parts of the ABIDE dataset, we find evidence of hypoconnectivity associated with symptom severity in autism spectrum disorders, in frontoparietal and limbic systems as well as in anterior and posterior cingulate cortices. PMID:27147940
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Parametric inference for biological sequence analysis.
Pachter, Lior; Sturmfels, Bernd
2004-11-16
One of the major successes in computational biology has been the unification, by using the graphical model formalism, of a multitude of algorithms for annotating and comparing biological sequences. Graphical models that have been applied to these problems include hidden Markov models for annotation, tree models for phylogenetics, and pair hidden Markov models for alignment. A single algorithm, the sum-product algorithm, solves many of the inference problems that are associated with different statistical models. This article introduces the polytope propagation algorithm for computing the Newton polytope of an observation from a graphical model. This algorithm is a geometric version of the sum-product algorithm and is used to analyze the parametric behavior of maximum a posteriori inference calculations for graphical models.
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Gopinath, Kaundinya; Krishnamurthy, Venkatagiri; Sathian, K
2018-02-01
In a recent study, Eklund et al. employed resting-state functional magnetic resonance imaging data as a surrogate for null functional magnetic resonance imaging (fMRI) datasets and posited that cluster-wise family-wise error (FWE) rate-corrected inferences made by using parametric statistical methods in fMRI studies over the past two decades may have been invalid, particularly for cluster defining thresholds less stringent than p < 0.001; this was principally because the spatial autocorrelation functions (sACF) of fMRI data had been modeled incorrectly to follow a Gaussian form, whereas empirical data suggested otherwise. Here, we show that accounting for non-Gaussian signal components such as those arising from resting-state neural activity as well as physiological responses and motion artifacts in the null fMRI datasets yields first- and second-level general linear model analysis residuals with nearly uniform and Gaussian sACF. Further comparison with nonparametric permutation tests indicates that cluster-based FWE corrected inferences made with Gaussian spatial noise approximations are valid.
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Blended particle filters for large-dimensional chaotic dynamical systems
Majda, Andrew J.; Qi, Di; Sapsis, Themistoklis P.
2014-01-01
A major challenge in contemporary data science is the development of statistically accurate particle filters to capture non-Gaussian features in large-dimensional chaotic dynamical systems. Blended particle filters that capture non-Gaussian features in an adaptively evolving low-dimensional subspace through particles interacting with evolving Gaussian statistics on the remaining portion of phase space are introduced here. These blended particle filters are constructed in this paper through a mathematical formalism involving conditional Gaussian mixtures combined with statistically nonlinear forecast models compatible with this structure developed recently with high skill for uncertainty quantification. Stringent test cases for filtering involving the 40-dimensional Lorenz 96 model with a 5-dimensional adaptive subspace for nonlinear blended filtering in various turbulent regimes with at least nine positive Lyapunov exponents are used here. These cases demonstrate the high skill of the blended particle filter algorithms in capturing both highly non-Gaussian dynamical features as well as crucial nonlinear statistics for accurate filtering in extreme filtering regimes with sparse infrequent high-quality observations. The formalism developed here is also useful for multiscale filtering of turbulent systems and a simple application is sketched below. PMID:24825886
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A 2D Gaussian-Beam-Based Method for Modeling the Dichroic Surfaces of Quasi-Optical Systems
NASA Astrophysics Data System (ADS)
Elis, Kevin; Chabory, Alexandre; Sokoloff, Jérôme; Bolioli, Sylvain
2016-08-01
In this article, we propose an approach in the spectral domain to treat the interaction of a field with a dichroic surface in two dimensions. For a Gaussian beam illumination of the surface, the reflected and transmitted fields are approximated by one reflected and one transmitted Gaussian beams. Their characteristics are determined by means of a matching in the spectral domain, which requires a second-order approximation of the dichroic surface response when excited by plane waves. This approximation is of the same order as the one used in Gaussian beam shooting algorithm to model curved interfaces associated with lenses, reflector, etc. The method uses general analytical formulations for the GBs that depend either on a paraxial or far-field approximation. Numerical experiments are led to test the efficiency of the method in terms of accuracy and computation time. They include a parametric study and a case for which the illumination is provided by a horn antenna. For the latter, the incident field is firstly expressed as a sum of Gaussian beams by means of Gabor frames.
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Time-domain least-squares migration using the Gaussian beam summation method
NASA Astrophysics Data System (ADS)
Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo
2018-04-01
With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modeling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modeling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a preconditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.
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Time-domain least-squares migration using the Gaussian beam summation method
NASA Astrophysics Data System (ADS)
Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo
2018-07-01
With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modelling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modelling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a pre-conditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.
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Direct Importance Estimation with Gaussian Mixture Models
NASA Astrophysics Data System (ADS)
Yamada, Makoto; Sugiyama, Masashi
The ratio of two probability densities is called the importance and its estimation has gathered a great deal of attention these days since the importance can be used for various data processing purposes. In this paper, we propose a new importance estimation method using Gaussian mixture models (GMMs). Our method is an extention of the Kullback-Leibler importance estimation procedure (KLIEP), an importance estimation method using linear or kernel models. An advantage of GMMs is that covariance matrices can also be learned through an expectation-maximization procedure, so the proposed method — which we call the Gaussian mixture KLIEP (GM-KLIEP) — is expected to work well when the true importance function has high correlation. Through experiments, we show the validity of the proposed approach.
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A Graphical Analysis of the Cournot-Nash and Stackelberg Models.
ERIC Educational Resources Information Center
Fulton, Murray
1997-01-01
Shows how the Cournot-Nash and Stackelberg equilibria can be represented in the familiar supply-demand graphical framework, allowing a direct comparison with the monopoly, competitive, and industrial organization models. This graphical analysis is represented throughout the article. (MJP)
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The information content of cosmic microwave background anisotropies
NASA Astrophysics Data System (ADS)
Scott, Douglas; Contreras, Dagoberto; Narimani, Ali; Ma, Yin-Zhe
2016-06-01
The cosmic microwave background (CMB) contains perturbations that are close to Gaussian and isotropic. This means that its information content, in the sense of the ability to constrain cosmological models, is closely related to the number of modes probed in CMB power spectra. Rather than making forecasts for specific experimental setups, here we take a more pedagogical approach and ask how much information we can extract from the CMB if we are only limited by sample variance. We show that, compared with temperature measurements, the addition of E-mode polarization doubles the number of modes available out to a fixed maximum multipole, provided that all of the TT, TE, and EE power spectra are measured. However, the situation in terms of constraints on particular parameters is more complicated, as we explain and illustrate graphically. We also discuss the enhancements in information that can come from adding B-mode polarization and gravitational lensing. We show how well one could ever determine the basic cosmological parameters from CMB data compared with what has been achieved with Planck, which has already probed a substantial fraction of the TT information. Lastly, we look at constraints on neutrino mass as a specific example of how lensing information improves future prospects beyond the current 6-parameter model.
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The information content of cosmic microwave background anisotropies
DOE Office of Scientific and Technical Information (OSTI.GOV)
Scott, Douglas; Contreras, Dagoberto; Narimani, Ali
The cosmic microwave background (CMB) contains perturbations that are close to Gaussian and isotropic. This means that its information content, in the sense of the ability to constrain cosmological models, is closely related to the number of modes probed in CMB power spectra. Rather than making forecasts for specific experimental setups, here we take a more pedagogical approach and ask how much information we can extract from the CMB if we are only limited by sample variance. We show that, compared with temperature measurements, the addition of E -mode polarization doubles the number of modes available out to a fixedmore » maximum multipole, provided that all of the TT , TE , and EE power spectra are measured. However, the situation in terms of constraints on particular parameters is more complicated, as we explain and illustrate graphically. We also discuss the enhancements in information that can come from adding B -mode polarization and gravitational lensing. We show how well one could ever determine the basic cosmological parameters from CMB data compared with what has been achieved with Planck , which has already probed a substantial fraction of the TT information. Lastly, we look at constraints on neutrino mass as a specific example of how lensing information improves future prospects beyond the current 6-parameter model.« less
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Consistency of biological networks inferred from microarray and sequencing data.
Vinciotti, Veronica; Wit, Ernst C; Jansen, Rick; de Geus, Eco J C N; Penninx, Brenda W J H; Boomsma, Dorret I; 't Hoen, Peter A C
2016-06-24
Sparse Gaussian graphical models are popular for inferring biological networks, such as gene regulatory networks. In this paper, we investigate the consistency of these models across different data platforms, such as microarray and next generation sequencing, on the basis of a rich dataset containing samples that are profiled under both techniques as well as a large set of independent samples. Our analysis shows that individual node variances can have a remarkable effect on the connectivity of the resulting network. Their inconsistency across platforms and the fact that the variability level of a node may not be linked to its regulatory role mean that, failing to scale the data prior to the network analysis, leads to networks that are not reproducible across different platforms and that may be misleading. Moreover, we show how the reproducibility of networks across different platforms is significantly higher if networks are summarised in terms of enrichment amongst functional groups of interest, such as pathways, rather than at the level of individual edges. Careful pre-processing of transcriptional data and summaries of networks beyond individual edges can improve the consistency of network inference across platforms. However, caution is needed at this stage in the (over)interpretation of gene regulatory networks inferred from biological data.
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Comparative simulation study of chemical synthesis of functional DADNE material.
Liu, Min Hsien; Liu, Chuan Wen
2017-01-01
Amorphous molecular simulation to model the reaction species in the synthesis of chemically inert and energetic 1,1-diamino-2,2-dinitroethene (DADNE) explosive material was performed in this work. Nitromethane was selected as the starting reactant to undergo halogenation, nitration, deprotonation, intermolecular condensation, and dehydration to produce the target DADNE product. The Materials Studio (MS) forcite program allowed fast energy calculations and reliable geometric optimization of all aqueous molecular reaction systems (0.1-0.5 M) at 283 K and 298 K. The MS forcite-computed and Gaussian polarizable continuum model (PCM)-computed results were analyzed and compared in order to explore feasible reaction pathways under suitable conditions for the synthesis of DADNE. Through theoretical simulation, the findings revealed that synthesis was possible, and a total energy barrier of 449.6 kJ mol -1 needed to be overcome in order to carry out the reaction according to MS calculation of the energy barriers at each stage at 283 K, as shown by the reaction profiles. Local analysis of intermolecular interaction, together with calculation of the stabilization energy of each reaction system, provided information that can be used as a reference regarding molecular integrated stability. Graphical Abstract Materials Studio software has been suggested for the computation and simulation of DADNE synthesis.
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Biktashev, Vadim N
2014-04-01
We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.
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NASA Astrophysics Data System (ADS)
Rychlik, Igor; Mao, Wengang
2018-02-01
The wind speed variability in the North Atlantic has been successfully modelled using a spatio-temporal transformed Gaussian field. However, this type of model does not correctly describe the extreme wind speeds attributed to tropical storms and hurricanes. In this study, the transformed Gaussian model is further developed to include the occurrence of severe storms. In this new model, random components are added to the transformed Gaussian field to model rare events with extreme wind speeds. The resulting random field is locally stationary and homogeneous. The localized dependence structure is described by time- and space-dependent parameters. The parameters have a natural physical interpretation. To exemplify its application, the model is fitted to the ECMWF ERA-Interim reanalysis data set. The model is applied to compute long-term wind speed distributions and return values, e.g., 100- or 1000-year extreme wind speeds, and to simulate random wind speed time series at a fixed location or spatio-temporal wind fields around that location.
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NASA Astrophysics Data System (ADS)
Pires, Carlos; Ribeiro, Andreia
2016-04-01
An efficient nonlinear method of statistical source separation of space-distributed non-Gaussian distributed data is proposed. The method relies in the so called Independent Subspace Analysis (ISA), being tested on a long time-series of the stream-function field of an atmospheric quasi-geostrophic 3-level model (QG3) simulating the winter's monthly variability of the Northern Hemisphere. ISA generalizes the Independent Component Analysis (ICA) by looking for multidimensional and minimally dependent, uncorrelated and non-Gaussian distributed statistical sources among the rotated projections or subspaces of the multivariate probability distribution of the leading principal components of the working field whereas ICA restrict to scalar sources. The rationale of that technique relies upon the projection pursuit technique, looking for data projections of enhanced interest. In order to accomplish the decomposition, we maximize measures of the sources' non-Gaussianity by contrast functions which are given by squares of nonlinear, cross-cumulant-based correlations involving the variables spanning the sources. Therefore sources are sought matching certain nonlinear data structures. The maximized contrast function is built in such a way that it provides the minimization of the mean square of the residuals of certain nonlinear regressions. The issuing residuals, followed by spherization, provide a new set of nonlinear variable changes that are at once uncorrelated, quasi-independent and quasi-Gaussian, representing an advantage with respect to the Independent Components (scalar sources) obtained by ICA where the non-Gaussianity is concentrated into the non-Gaussian scalar sources. The new scalar sources obtained by the above process encompass the attractor's curvature thus providing improved nonlinear model indices of the low-frequency atmospheric variability which is useful since large circulation indices are nonlinearly correlated. The non-Gaussian tested sources (dyads and triads, respectively of two and three dimensions) lead to a dense data concentration along certain curves or surfaces, nearby which the clusters' centroids of the joint probability density function tend to be located. That favors a better splitting of the QG3 atmospheric model's weather regimes: the positive and negative phases of the Arctic Oscillation and positive and negative phases of the North Atlantic Oscillation. The leading model's non-Gaussian dyad is associated to a positive correlation between: 1) the squared anomaly of the extratropical jet-stream and 2) the meridional jet-stream meandering. Triadic sources coming from maximized third-order cross cumulants between pairwise uncorrelated components reveal situations of triadic wave resonance and nonlinear triadic teleconnections, only possible thanks to joint non-Gaussianity. That kind of triadic synergies are accounted for an Information-Theoretic measure: the Interaction Information. The dominant model's triad occurs between anomalies of: 1) the North Pole anomaly pressure 2) the jet-stream intensity at the Eastern North-American boundary and 3) the jet-stream intensity at the Eastern Asian boundary. Publication supported by project FCT UID/GEO/50019/2013 - Instituto Dom Luiz.
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Fast Component Pursuit for Large-Scale Inverse Covariance Estimation.
Han, Lei; Zhang, Yu; Zhang, Tong
2016-08-01
The maximum likelihood estimation (MLE) for the Gaussian graphical model, which is also known as the inverse covariance estimation problem, has gained increasing interest recently. Most existing works assume that inverse covariance estimators contain sparse structure and then construct models with the ℓ 1 regularization. In this paper, different from existing works, we study the inverse covariance estimation problem from another perspective by efficiently modeling the low-rank structure in the inverse covariance, which is assumed to be a combination of a low-rank part and a diagonal matrix. One motivation for this assumption is that the low-rank structure is common in many applications including the climate and financial analysis, and another one is that such assumption can reduce the computational complexity when computing its inverse. Specifically, we propose an efficient COmponent Pursuit (COP) method to obtain the low-rank part, where each component can be sparse. For optimization, the COP method greedily learns a rank-one component in each iteration by maximizing the log-likelihood. Moreover, the COP algorithm enjoys several appealing properties including the existence of an efficient solution in each iteration and the theoretical guarantee on the convergence of this greedy approach. Experiments on large-scale synthetic and real-world datasets including thousands of millions variables show that the COP method is faster than the state-of-the-art techniques for the inverse covariance estimation problem when achieving comparable log-likelihood on test data.
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Graphical workstation capability for reliability modeling
NASA Technical Reports Server (NTRS)
Bavuso, Salvatore J.; Koppen, Sandra V.; Haley, Pamela J.
1992-01-01
In addition to computational capabilities, software tools for estimating the reliability of fault-tolerant digital computer systems must also provide a means of interfacing with the user. Described here is the new graphical interface capability of the hybrid automated reliability predictor (HARP), a software package that implements advanced reliability modeling techniques. The graphics oriented (GO) module provides the user with a graphical language for modeling system failure modes through the selection of various fault-tree gates, including sequence-dependency gates, or by a Markov chain. By using this graphical input language, a fault tree becomes a convenient notation for describing a system. In accounting for any sequence dependencies, HARP converts the fault-tree notation to a complex stochastic process that is reduced to a Markov chain, which it can then solve for system reliability. The graphics capability is available for use on an IBM-compatible PC, a Sun, and a VAX workstation. The GO module is written in the C programming language and uses the graphical kernal system (GKS) standard for graphics implementation. The PC, VAX, and Sun versions of the HARP GO module are currently in beta-testing stages.
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Messaoudi, Noureddine; Bekka, Raïs El'hadi; Ravier, Philippe; Harba, Rachid
2017-02-01
The purpose of this paper was to evaluate the effects of the longitudinal single differential (LSD), the longitudinal double differential (LDD) and the normal double differential (NDD) spatial filters, the electrode shape, the inter-electrode distance (IED) on non-Gaussianity and non-linearity levels of simulated surface EMG (sEMG) signals when the maximum voluntary contraction (MVC) varied from 10% to 100% by a step of 10%. The effects of recruitment range thresholds (RR), the firing rate (FR) strategy and the peak firing rate (PFR) of motor units were also considered. A cylindrical multilayer model of the volume conductor and a model of motor unit (MU) recruitment and firing rate were used to simulate sEMG signals in a pool of 120 MUs for 5s. Firstly, the stationarity of sEMG signals was tested by the runs, the reverse arrangements (RA) and the modified reverse arrangements (MRA) tests. Then the non-Gaussianity was characterised with bicoherence and kurtosis, and non-linearity levels was evaluated with linearity test. The kurtosis analysis showed that the sEMG signals detected by the LSD filter were the most Gaussian and those detected by the NDD filter were the least Gaussian. In addition, the sEMG signals detected by the LSD filter were the most linear. For a given filter, the sEMG signals detected by using rectangular electrodes were more Gaussian and more linear than that detected with circular electrodes. Moreover, the sEMG signals are less non-Gaussian and more linear with reverse onion-skin firing rate strategy than those with onion-skin strategy. The levels of sEMG signal Gaussianity and linearity increased with the increase of the IED, RR and PFR. Copyright © 2016 Elsevier Ltd. All rights reserved.
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NASA Astrophysics Data System (ADS)
Eyyuboğlu, Halil Tanyer
2008-02-01
We formulate and evaluate in terms of graphical outputs, source and receiver plane expressions, the complex degree of coherence, beam size variation and power in bucket performance for higher order partially coherent dark hollow beams propagating in turbulent atmosphere. Our formulation is able to cover square, rectangular, circular, elliptical geometries for dark hollow and flat-topped beams in one single expression. From the graphical outputs of the receiver plane, it is observed that higher order partially coherent dark hollow beams will initially develop an outer ring around a central lobe, but will eventually evolve towards a Gaussian shape as the propagation distance is extended. It is further observed that stronger turbulence levels and greater partial coherence have similar effects on beam profile. During propagation, modulus of complex degree of coherence of partially coherent dark hollow beams appears to rise above that of the source plane values, reaching as high as near unity. Beam size analysis shows that, among the types examined, (nearly) flat-topped beam experiences the least beam expansion. Power in bucket analysis indicates that lowest order square fully coherent dark beam offers the best power capturing.
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Chialvo, Ariel A.; Moucka, Filip; Vlcek, Lukas; ...
2015-03-24
Here we implemented the Gaussian charge-on-spring (GCOS) version of the original self-consistent field implementation of the Gaussian Charge Polarizable water model and test its accuracy to represent the polarization behavior of the original model involving smeared charges and induced dipole moments. Moreover, for that purpose we adapted the recently developed multiple-particle-move (MPM) within the Gibbs and isochoric-isothermal ensembles Monte Carlo methods for the efficient simulation of polarizable fluids. We also assessed the accuracy of the GCOS representation by a direct comparison of the resulting vapor-liquid phase envelope, microstructure, and relevant microscopic descriptors of water polarization along the orthobaric curve againstmore » the corresponding quantities from the actual GCP water model.« less
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Nuclear DNA contents of Echinchloa crus-galli and its Gaussian relationships with environments
NASA Astrophysics Data System (ADS)
Li, Dan-Dan; Lu, Yong-Liang; Guo, Shui-Liang; Yin, Li-Ping; Zhou, Ping; Lou, Yu-Xia
2017-02-01
Previous studies on plant nuclear DNA content variation and its relationships with environmental gradients produced conflicting results. We speculated that the relationships between nuclear DNA content of a widely-distributed species and its environmental gradients might be non-linear if it was sampled in a large geographical gradient. Echinochloa crus-galli (L.) P. Beauv. is a worldwide species, but without documents on its intraspecific variation of nuclear DNA content. Our objectives are: 1) to detect intraspecific variation scope of E. crus-galli in its nuclear DNA content, and 2) to testify whether nuclear DNA content of the species changes with environmental gradients following Gaussian models if its populations were sampled in a large geographical gradient. We collected seeds of 36 Chinese populations of E. crus-galli across a wide geographical gradient, and sowed them in a homogeneous field to get their offspring to determine their nuclear DNA content. We analyzed the relationships of nuclear DNA content of these populations with latitude, longitude, and nineteen bioclimatic variables by using Gaussian and linear models. (1) Nuclear DNA content varied from 2.113 to 2.410 pg among 36 Chinese populations of E. crus-galli, with a mean value of 2.256 pg. (2) Gaussian correlations of nuclear DNA content (y) with geographical gradients were detected, with latitude (x) following y = 2.2923*e -(x - 24.9360)2/2*63.79452 (r = 0.546, P < 0.001), and with longitude (x) following y = 2.2933*e -(x - 116.1801)2/2*44.74502 (r = 0.672, P < 0.001). (3) Among the nineteen bioclimatic variables, except temperature isothermality, precipitations of the wettest month, the wettest quarter and the warmest quarter, the others could be better fit with nuclear DNA content by using Gaussian models than by linear models. There exists intra-specific variation among 36 Chinese populations of E. crus-galli, Gaussian models could be applied to fit the correlations of its Nuclear DNA content with geographical and most bioclimatic gradients.
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Shi, J Q; Wang, B; Will, E J; West, R M
2012-11-20
We propose a new semiparametric model for functional regression analysis, combining a parametric mixed-effects model with a nonparametric Gaussian process regression model, namely a mixed-effects Gaussian process functional regression model. The parametric component can provide explanatory information between the response and the covariates, whereas the nonparametric component can add nonlinearity. We can model the mean and covariance structures simultaneously, combining the information borrowed from other subjects with the information collected from each individual subject. We apply the model to dose-response curves that describe changes in the responses of subjects for differing levels of the dose of a drug or agent and have a wide application in many areas. We illustrate the method for the management of renal anaemia. An individual dose-response curve is improved when more information is included by this mechanism from the subject/patient over time, enabling a patient-specific treatment regime. Copyright © 2012 John Wiley & Sons, Ltd.
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Computational algorithms for simulations in atmospheric optics.
Konyaev, P A; Lukin, V P
2016-04-20
A computer simulation technique for atmospheric and adaptive optics based on parallel programing is discussed. A parallel propagation algorithm is designed and a modified spectral-phase method for computer generation of 2D time-variant random fields is developed. Temporal power spectra of Laguerre-Gaussian beam fluctuations are considered as an example to illustrate the applications discussed. Implementation of the proposed algorithms using Intel MKL and IPP libraries and NVIDIA CUDA technology is shown to be very fast and accurate. The hardware system for the computer simulation is an off-the-shelf desktop with an Intel Core i7-4790K CPU operating at a turbo-speed frequency up to 5 GHz and an NVIDIA GeForce GTX-960 graphics accelerator with 1024 1.5 GHz processors.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Habibi, M.; Ghamari, F.
2012-11-15
The authors have investigated the non-stationary self-focusing of Gaussian laser pulse in cold quantum plasma. In case of high dense plasma, the nonlinearity in the dielectric constant is mainly due to relativistic high intense interactions and quantum effects. In this paper, we have introduced a ramp density profile for plasma and presented graphically the behavior of spot size oscillations of pulse at rear and front portions of the pulse. It is observed that the ramp density profile and quantum effects play a vital role in stronger and better focusing at the rear of the pulse than at the front inmore » cold quantum plasmas.« less
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Data Analysis with Graphical Models: Software Tools
NASA Technical Reports Server (NTRS)
Buntine, Wray L.
1994-01-01
Probabilistic graphical models (directed and undirected Markov fields, and combined in chain graphs) are used widely in expert systems, image processing and other areas as a framework for representing and reasoning with probabilities. They come with corresponding algorithms for performing probabilistic inference. This paper discusses an extension to these models by Spiegelhalter and Gilks, plates, used to graphically model the notion of a sample. This offers a graphical specification language for representing data analysis problems. When combined with general methods for statistical inference, this also offers a unifying framework for prototyping and/or generating data analysis algorithms from graphical specifications. This paper outlines the framework and then presents some basic tools for the task: a graphical version of the Pitman-Koopman Theorem for the exponential family, problem decomposition, and the calculation of exact Bayes factors. Other tools already developed, such as automatic differentiation, Gibbs sampling, and use of the EM algorithm, make this a broad basis for the generation of data analysis software.
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A graphical language for reliability model generation
NASA Technical Reports Server (NTRS)
Howell, Sandra V.; Bavuso, Salvatore J.; Haley, Pamela J.
1990-01-01
A graphical interface capability of the hybrid automated reliability predictor (HARP) is described. The graphics-oriented (GO) module provides the user with a graphical language for modeling system failure modes through the selection of various fault tree gates, including sequence dependency gates, or by a Markov chain. With this graphical input language, a fault tree becomes a convenient notation for describing a system. In accounting for any sequence dependencies, HARP converts the fault-tree notation to a complex stochastic process that is reduced to a Markov chain which it can then solve for system reliability. The graphics capability is available for use on an IBM-compatible PC, a Sun, and a VAX workstation. The GO module is written in the C programming language and uses the Graphical Kernel System (GKS) standard for graphics implementation. The PC, VAX, and Sun versions of the HARP GO module are currently in beta-testing.
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Bayesian Analysis of Non-Gaussian Long-Range Dependent Processes
NASA Astrophysics Data System (ADS)
Graves, T.; Franzke, C.; Gramacy, R. B.; Watkins, N. W.
2012-12-01
Recent studies have strongly suggested that surface temperatures exhibit long-range dependence (LRD). The presence of LRD would hamper the identification of deterministic trends and the quantification of their significance. It is well established that LRD processes exhibit stochastic trends over rather long periods of time. Thus, accurate methods for discriminating between physical processes that possess long memory and those that do not are an important adjunct to climate modeling. We have used Markov Chain Monte Carlo algorithms to perform a Bayesian analysis of Auto-Regressive Fractionally-Integrated Moving-Average (ARFIMA) processes, which are capable of modeling LRD. Our principal aim is to obtain inference about the long memory parameter, d,with secondary interest in the scale and location parameters. We have developed a reversible-jump method enabling us to integrate over different model forms for the short memory component. We initially assume Gaussianity, and have tested the method on both synthetic and physical time series such as the Central England Temperature. Many physical processes, for example the Faraday time series from Antarctica, are highly non-Gaussian. We have therefore extended this work by weakening the Gaussianity assumption. Specifically, we assume a symmetric α -stable distribution for the innovations. Such processes provide good, flexible, initial models for non-Gaussian processes with long memory. We will present a study of the dependence of the posterior variance σ d of the memory parameter d on the length of the time series considered. This will be compared with equivalent error diagnostics for other measures of d.
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PERIOD ESTIMATION FOR SPARSELY SAMPLED QUASI-PERIODIC LIGHT CURVES APPLIED TO MIRAS
DOE Office of Scientific and Technical Information (OSTI.GOV)
He, Shiyuan; Huang, Jianhua Z.; Long, James
2016-12-01
We develop a nonlinear semi-parametric Gaussian process model to estimate periods of Miras with sparsely sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum likelihood to estimate the period and the parameters of the Gaussian process, while integrating out the effects of other nuisance parameters in the model with respect to a suitable prior distribution obtained from earlier studies. Since the likelihood is highly multimodal for period, we implement a hybrid method that applies the quasi-Newton algorithm for Gaussian process parameters and search the period/frequencymore » parameter space over a dense grid. A large-scale, high-fidelity simulation is conducted to mimic the sampling quality of Mira light curves obtained by the M33 Synoptic Stellar Survey. The simulated data set is publicly available and can serve as a testbed for future evaluation of different period estimation methods. The semi-parametric model outperforms an existing algorithm on this simulated test data set as measured by period recovery rate and quality of the resulting period–luminosity relations.« less
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Accretion rates of protoplanets. II - Gaussian distributions of planetesimal velocities
NASA Technical Reports Server (NTRS)
Greenzweig, Yuval; Lissauer, Jack J.
1992-01-01
In the present growth-rate calculations for a protoplanet that is embedded in a disk of planetesimals with triaxial Gaussian velocity dispersion and uniform surface density, the protoplanet is on a circular orbit. The accretion rate in the two-body approximation is found to be enhanced by a factor of about 3 relative to the case where all planetesimals' eccentricities and inclinations are equal to the rms values of those disk variables having locally Gaussian velocity dispersion. This accretion-rate enhancement should be incorporated by all models that assume a single random velocity for all planetesimals in lieu of a Gaussian distribution.
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Interactive graphic editing tools in bioluminescent imaging simulation
NASA Astrophysics Data System (ADS)
Li, Hui; Tian, Jie; Luo, Jie; Wang, Ge; Cong, Wenxiang
2005-04-01
It is a challenging task to accurately describe complicated biological tissues and bioluminescent sources in bioluminescent imaging simulation. Several graphic editing tools have been developed to efficiently model each part of the bioluminescent simulation environment and to interactively correct or improve the initial models of anatomical structures or bioluminescent sources. There are two major types of graphic editing tools: non-interactive tools and interactive tools. Geometric building blocks (i.e. regular geometric graphics and superquadrics) are applied as non-interactive tools. To a certain extent, complicated anatomical structures and bioluminescent sources can be approximately modeled by combining a sufficient large number of geometric building blocks with Boolean operators. However, those models are too simple to describe the local features and fine changes in 2D/3D irregular contours. Therefore, interactive graphic editing tools have been developed to facilitate the local modifications of any initial surface model. With initial models composed of geometric building blocks, interactive spline mode is applied to conveniently perform dragging and compressing operations on 2D/3D local surface of biological tissues and bioluminescent sources inside the region/volume of interest. Several applications of the interactive graphic editing tools will be presented in this article.
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SIGMA--A Graphical Approach to Teaching Simulation.
ERIC Educational Resources Information Center
Schruben, Lee W.
1992-01-01
SIGMA (Simulation Graphical Modeling and Analysis) is a computer graphics environment for building, testing, and experimenting with discrete event simulation models on personal computers. It uses symbolic representations (computer animation) to depict the logic of large, complex discrete event systems for easier understanding and has proven itself…
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A fast elitism Gaussian estimation of distribution algorithm and application for PID optimization.
Xu, Qingyang; Zhang, Chengjin; Zhang, Li
2014-01-01
Estimation of distribution algorithm (EDA) is an intelligent optimization algorithm based on the probability statistics theory. A fast elitism Gaussian estimation of distribution algorithm (FEGEDA) is proposed in this paper. The Gaussian probability model is used to model the solution distribution. The parameters of Gaussian come from the statistical information of the best individuals by fast learning rule. A fast learning rule is used to enhance the efficiency of the algorithm, and an elitism strategy is used to maintain the convergent performance. The performances of the algorithm are examined based upon several benchmarks. In the simulations, a one-dimensional benchmark is used to visualize the optimization process and probability model learning process during the evolution, and several two-dimensional and higher dimensional benchmarks are used to testify the performance of FEGEDA. The experimental results indicate the capability of FEGEDA, especially in the higher dimensional problems, and the FEGEDA exhibits a better performance than some other algorithms and EDAs. Finally, FEGEDA is used in PID controller optimization of PMSM and compared with the classical-PID and GA.
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A Fast Elitism Gaussian Estimation of Distribution Algorithm and Application for PID Optimization
Xu, Qingyang; Zhang, Chengjin; Zhang, Li
2014-01-01
Estimation of distribution algorithm (EDA) is an intelligent optimization algorithm based on the probability statistics theory. A fast elitism Gaussian estimation of distribution algorithm (FEGEDA) is proposed in this paper. The Gaussian probability model is used to model the solution distribution. The parameters of Gaussian come from the statistical information of the best individuals by fast learning rule. A fast learning rule is used to enhance the efficiency of the algorithm, and an elitism strategy is used to maintain the convergent performance. The performances of the algorithm are examined based upon several benchmarks. In the simulations, a one-dimensional benchmark is used to visualize the optimization process and probability model learning process during the evolution, and several two-dimensional and higher dimensional benchmarks are used to testify the performance of FEGEDA. The experimental results indicate the capability of FEGEDA, especially in the higher dimensional problems, and the FEGEDA exhibits a better performance than some other algorithms and EDAs. Finally, FEGEDA is used in PID controller optimization of PMSM and compared with the classical-PID and GA. PMID:24892059
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Following a trend with an exponential moving average: Analytical results for a Gaussian model
NASA Astrophysics Data System (ADS)
Grebenkov, Denis S.; Serror, Jeremy
2014-01-01
We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean, variance, skewness and kurtosis) and asymptotic behavior (quantiles). We show that the asymmetry of the distribution (with often small losses and less frequent but significant profits) is reminiscent to trend following strategies and less dependent on peculiarities of price variations. At short times, trend following strategies admit larger losses than one may anticipate from standard Gaussian estimates, while smaller losses are ensured at longer times. Simple explicit formulas characterizing the distribution of P&Ls illustrate the basic mechanisms of momentum trading, while general matrix representations can be applied to arbitrary Gaussian models. We also compute explicitly annualized risk adjusted P&L and strategy turnover to account for transaction costs. We deduce the trend following optimal timescale and its dependence on both auto-correlation level and transaction costs. Theoretical results are illustrated on the Dow Jones index.
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A Gaussian Mixture Model Representation of Endmember Variability in Hyperspectral Unmixing
NASA Astrophysics Data System (ADS)
Zhou, Yuan; Rangarajan, Anand; Gader, Paul D.
2018-05-01
Hyperspectral unmixing while considering endmember variability is usually performed by the normal compositional model (NCM), where the endmembers for each pixel are assumed to be sampled from unimodal Gaussian distributions. However, in real applications, the distribution of a material is often not Gaussian. In this paper, we use Gaussian mixture models (GMM) to represent the endmember variability. We show, given the GMM starting premise, that the distribution of the mixed pixel (under the linear mixing model) is also a GMM (and this is shown from two perspectives). The first perspective originates from the random variable transformation and gives a conditional density function of the pixels given the abundances and GMM parameters. With proper smoothness and sparsity prior constraints on the abundances, the conditional density function leads to a standard maximum a posteriori (MAP) problem which can be solved using generalized expectation maximization. The second perspective originates from marginalizing over the endmembers in the GMM, which provides us with a foundation to solve for the endmembers at each pixel. Hence, our model can not only estimate the abundances and distribution parameters, but also the distinct endmember set for each pixel. We tested the proposed GMM on several synthetic and real datasets, and showed its potential by comparing it to current popular methods.
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Briët, Olivier J T; Amerasinghe, Priyanie H; Vounatsou, Penelope
2013-01-01
With the renewed drive towards malaria elimination, there is a need for improved surveillance tools. While time series analysis is an important tool for surveillance, prediction and for measuring interventions' impact, approximations by commonly used Gaussian methods are prone to inaccuracies when case counts are low. Therefore, statistical methods appropriate for count data are required, especially during "consolidation" and "pre-elimination" phases. Generalized autoregressive moving average (GARMA) models were extended to generalized seasonal autoregressive integrated moving average (GSARIMA) models for parsimonious observation-driven modelling of non Gaussian, non stationary and/or seasonal time series of count data. The models were applied to monthly malaria case time series in a district in Sri Lanka, where malaria has decreased dramatically in recent years. The malaria series showed long-term changes in the mean, unstable variance and seasonality. After fitting negative-binomial Bayesian models, both a GSARIMA and a GARIMA deterministic seasonality model were selected based on different criteria. Posterior predictive distributions indicated that negative-binomial models provided better predictions than Gaussian models, especially when counts were low. The G(S)ARIMA models were able to capture the autocorrelation in the series. G(S)ARIMA models may be particularly useful in the drive towards malaria elimination, since episode count series are often seasonal and non-stationary, especially when control is increased. Although building and fitting GSARIMA models is laborious, they may provide more realistic prediction distributions than do Gaussian methods and may be more suitable when counts are low.
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Briët, Olivier J. T.; Amerasinghe, Priyanie H.; Vounatsou, Penelope
2013-01-01
Introduction With the renewed drive towards malaria elimination, there is a need for improved surveillance tools. While time series analysis is an important tool for surveillance, prediction and for measuring interventions’ impact, approximations by commonly used Gaussian methods are prone to inaccuracies when case counts are low. Therefore, statistical methods appropriate for count data are required, especially during “consolidation” and “pre-elimination” phases. Methods Generalized autoregressive moving average (GARMA) models were extended to generalized seasonal autoregressive integrated moving average (GSARIMA) models for parsimonious observation-driven modelling of non Gaussian, non stationary and/or seasonal time series of count data. The models were applied to monthly malaria case time series in a district in Sri Lanka, where malaria has decreased dramatically in recent years. Results The malaria series showed long-term changes in the mean, unstable variance and seasonality. After fitting negative-binomial Bayesian models, both a GSARIMA and a GARIMA deterministic seasonality model were selected based on different criteria. Posterior predictive distributions indicated that negative-binomial models provided better predictions than Gaussian models, especially when counts were low. The G(S)ARIMA models were able to capture the autocorrelation in the series. Conclusions G(S)ARIMA models may be particularly useful in the drive towards malaria elimination, since episode count series are often seasonal and non-stationary, especially when control is increased. Although building and fitting GSARIMA models is laborious, they may provide more realistic prediction distributions than do Gaussian methods and may be more suitable when counts are low. PMID:23785448
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Application of selection and estimation regular vine copula on go public company share
NASA Astrophysics Data System (ADS)
Hasna Afifah, R.; Noviyanti, Lienda; Bachrudin, Achmad
2018-03-01
The accuracy of financial risk management involving a large number of assets is needed, but information about dependencies among assets cannot be adequately analyzed. To analyze dependencies on a number of assets, several tools have been added to standard multivariate copula. However, these tools have not been adequately used in apps with higher dimensions. The bivariate parametric copula families can be used to solve it. The multivariate copula can be built from the bivariate parametric copula which is connected by a graphical representation to become Pair Copula Constructions (PCCs) or vine copula. The application of C-vine and D-vine copula have been used in some researches, but the use of C-vine and D-vine copula is more limited than R-vine copula. Therefore, this study used R-vine copula to provide flexibility for modeling complex dependencies on a high dimension. Since copula is a static model, while stock values change over time, then copula should be combined with the ARMA- GARCH model for modeling the movement of shares (volatility). The objective of this paper is to select and estimate R-vine copula which is used to analyze PT Jasa Marga (Persero) Tbk (JSMR), PT Waskita Karya (Persero) Tbk (WSKT), and PT Bank Mandiri (Persero) Tbk (BMRI) from august 31, 2014 to august 31, 2017. From the method it is obtained that the selected copulas for 2 edges at the first tree are survival Gumbel and the copula for edge at the second tree is Gaussian.
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NASA Astrophysics Data System (ADS)
Uhlemann, C.; Pajer, E.; Pichon, C.; Nishimichi, T.; Codis, S.; Bernardeau, F.
2018-03-01
Non-Gaussianities of dynamical origin are disentangled from primordial ones using the formalism of large deviation statistics with spherical collapse dynamics. This is achieved by relying on accurate analytical predictions for the one-point probability distribution function and the two-point clustering of spherically averaged cosmic densities (sphere bias). Sphere bias extends the idea of halo bias to intermediate density environments and voids as underdense regions. In the presence of primordial non-Gaussianity, sphere bias displays a strong scale dependence relevant for both high- and low-density regions, which is predicted analytically. The statistics of densities in spheres are built to model primordial non-Gaussianity via an initial skewness with a scale dependence that depends on the bispectrum of the underlying model. The analytical formulas with the measured non-linear dark matter variance as input are successfully tested against numerical simulations. For local non-Gaussianity with a range from fNL = -100 to +100, they are found to agree within 2 per cent or better for densities ρ ∈ [0.5, 3] in spheres of radius 15 Mpc h-1 down to z = 0.35. The validity of the large deviation statistics formalism is thereby established for all observationally relevant local-type departures from perfectly Gaussian initial conditions. The corresponding estimators for the amplitude of the non-linear variance σ8 and primordial skewness fNL are validated using a fiducial joint maximum likelihood experiment. The influence of observational effects and the prospects for a future detection of primordial non-Gaussianity from joint one- and two-point densities-in-spheres statistics are discussed.
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Albin, Thomas J; Vink, Peter
2015-01-01
Anthropometric data are assumed to have a Gaussian (Normal) distribution, but if non-Gaussian, accommodation estimates are affected. When data are limited, users may choose to combine anthropometric elements by Combining Percentiles (CP) (adding or subtracting), despite known adverse effects. This study examined whether global anthropometric data are Gaussian distributed. It compared the Median Correlation Method (MCM) of combining anthropometric elements with unknown correlations to CP to determine if MCM provides better estimates of percentile values and accommodation. Percentile values of 604 male and female anthropometric data drawn from seven countries worldwide were expressed as standard scores. The standard scores were tested to determine if they were consistent with a Gaussian distribution. Empirical multipliers for determining percentile values were developed.In a test case, five anthropometric elements descriptive of seating were combined in addition and subtraction models. Percentile values were estimated for each model by CP, MCM with Gaussian distributed data, or MCM with empirically distributed data. The 5th and 95th percentile values of a dataset of global anthropometric data are shown to be asymmetrically distributed. MCM with empirical multipliers gave more accurate estimates of 5th and 95th percentiles values. Anthropometric data are not Gaussian distributed. The MCM method is more accurate than adding or subtracting percentiles.
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Gaussianization for fast and accurate inference from cosmological data
NASA Astrophysics Data System (ADS)
Schuhmann, Robert L.; Joachimi, Benjamin; Peiris, Hiranya V.
2016-06-01
We present a method to transform multivariate unimodal non-Gaussian posterior probability densities into approximately Gaussian ones via non-linear mappings, such as Box-Cox transformations and generalizations thereof. This permits an analytical reconstruction of the posterior from a point sample, like a Markov chain, and simplifies the subsequent joint analysis with other experiments. This way, a multivariate posterior density can be reported efficiently, by compressing the information contained in Markov Chain Monte Carlo samples. Further, the model evidence integral (I.e. the marginal likelihood) can be computed analytically. This method is analogous to the search for normal parameters in the cosmic microwave background, but is more general. The search for the optimally Gaussianizing transformation is performed computationally through a maximum-likelihood formalism; its quality can be judged by how well the credible regions of the posterior are reproduced. We demonstrate that our method outperforms kernel density estimates in this objective. Further, we select marginal posterior samples from Planck data with several distinct strongly non-Gaussian features, and verify the reproduction of the marginal contours. To demonstrate evidence computation, we Gaussianize the joint distribution of data from weak lensing and baryon acoustic oscillations, for different cosmological models, and find a preference for flat Λcold dark matter. Comparing to values computed with the Savage-Dickey density ratio, and Population Monte Carlo, we find good agreement of our method within the spread of the other two.
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A Gaussian Model-Based Probabilistic Approach for Pulse Transit Time Estimation.
Jang, Dae-Geun; Park, Seung-Hun; Hahn, Minsoo
2016-01-01
In this paper, we propose a new probabilistic approach to pulse transit time (PTT) estimation using a Gaussian distribution model. It is motivated basically by the hypothesis that PTTs normalized by RR intervals follow the Gaussian distribution. To verify the hypothesis, we demonstrate the effects of arterial compliance on the normalized PTTs using the Moens-Korteweg equation. Furthermore, we observe a Gaussian distribution of the normalized PTTs on real data. In order to estimate the PTT using the hypothesis, we first assumed that R-waves in the electrocardiogram (ECG) can be correctly identified. The R-waves limit searching ranges to detect pulse peaks in the photoplethysmogram (PPG) and to synchronize the results with cardiac beats--i.e., the peaks of the PPG are extracted within the corresponding RR interval of the ECG as pulse peak candidates. Their probabilities of being the actual pulse peak are then calculated using a Gaussian probability function. The parameters of the Gaussian function are automatically updated when a new pulse peak is identified. This update makes the probability function adaptive to variations of cardiac cycles. Finally, the pulse peak is identified as the candidate with the highest probability. The proposed approach is tested on a database where ECG and PPG waveforms are collected simultaneously during the submaximal bicycle ergometer exercise test. The results are promising, suggesting that the method provides a simple but more accurate PTT estimation in real applications.
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Improved Scheme of Modified Gaussian Deconvolution for Reflectance Spectra of Lunar Soils
NASA Technical Reports Server (NTRS)
Hiroi, T.; Pieters, C. M.; Noble, S. K.
2000-01-01
In our continuing effort for deconvolving reflectance spectra of lunar soils using the modified Gaussian model, a new scheme has been developed, including a new form of continuum. All the parameters are optimized with certain constraints.
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On the robustness of the q-Gaussian family
NASA Astrophysics Data System (ADS)
Sicuro, Gabriele; Tempesta, Piergiulio; Rodríguez, Antonio; Tsallis, Constantino
2015-12-01
We introduce three deformations, called α-, β- and γ-deformation respectively, of a N-body probabilistic model, first proposed by Rodríguez et al. (2008), having q-Gaussians as N → ∞ limiting probability distributions. The proposed α- and β-deformations are asymptotically scale-invariant, whereas the γ-deformation is not. We prove that, for both α- and β-deformations, the resulting deformed triangles still have q-Gaussians as limiting distributions, with a value of q independent (dependent) on the deformation parameter in the α-case (β-case). In contrast, the γ-case, where we have used the celebrated Q-numbers and the Gauss binomial coefficients, yields other limiting probability distribution functions, outside the q-Gaussian family. These results suggest that scale-invariance might play an important role regarding the robustness of the q-Gaussian family.
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NASA Astrophysics Data System (ADS)
Premkumar, S.; Jawahar, A.; Mathavan, T.; Kumara Dhas, M.; Sathe, V. G.; Milton Franklin Benial, A.
2014-08-01
The molecular structure of 2-(tert-butoxycarbonyl (Boc) -amino)-5-bromopyridine (BABP) was optimized by the DFT/B3LYP method with 6-311G (d,p), 6-311++G (d,p) and cc-pVTZ basis sets using the Gaussian 09 program. The most stable optimized structure of the molecule was predicted by the DFT/B3LYP method with cc-pVTZ basis set. The vibrational frequencies, Mulliken atomic charge distribution, frontier molecular orbitals and thermodynamical parameters were calculated. These calculations were done at the ground state energy level of BABP without applying any constraint on the potential energy surface. The vibrational spectra were experimentally recorded using Fourier Transform-Infrared (FT-IR) and micro-Raman spectrometer. The computed vibrational frequencies were scaled by scale factors to yield a good agreement with observed experimental vibrational frequencies. The complete theoretically calculated and experimentally observed vibrational frequencies were assigned on the basis of Potential Energy Distribution (PED) calculation using the VEDA 4.0 program. The vibrational modes assignments were performed by using the animation option of GaussView 05 graphical interface for Gaussian program. The Mulliken atomic charge distribution was calculated for BABP molecule. The molecular reactivity and stability of BABP were also studied by frontier molecular orbitals (FMOs) analysis.
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Kinect Posture Reconstruction Based on a Local Mixture of Gaussian Process Models.
Liu, Zhiguang; Zhou, Liuyang; Leung, Howard; Shum, Hubert P H
2016-11-01
Depth sensor based 3D human motion estimation hardware such as Kinect has made interactive applications more popular recently. However, it is still challenging to accurately recognize postures from a single depth camera due to the inherently noisy data derived from depth images and self-occluding action performed by the user. In this paper, we propose a new real-time probabilistic framework to enhance the accuracy of live captured postures that belong to one of the action classes in the database. We adopt the Gaussian Process model as a prior to leverage the position data obtained from Kinect and marker-based motion capture system. We also incorporate a temporal consistency term into the optimization framework to constrain the velocity variations between successive frames. To ensure that the reconstructed posture resembles the accurate parts of the observed posture, we embed a set of joint reliability measurements into the optimization framework. A major drawback of Gaussian Process is its cubic learning complexity when dealing with a large database due to the inverse of a covariance matrix. To solve the problem, we propose a new method based on a local mixture of Gaussian Processes, in which Gaussian Processes are defined in local regions of the state space. Due to the significantly decreased sample size in each local Gaussian Process, the learning time is greatly reduced. At the same time, the prediction speed is enhanced as the weighted mean prediction for a given sample is determined by the nearby local models only. Our system also allows incrementally updating a specific local Gaussian Process in real time, which enhances the likelihood of adapting to run-time postures that are different from those in the database. Experimental results demonstrate that our system can generate high quality postures even under severe self-occlusion situations, which is beneficial for real-time applications such as motion-based gaming and sport training.
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Gopinath, Kaundinya; Krishnamurthy, Venkatagiri; Lacey, Simon; Sathian, K
2018-02-01
In a recent study Eklund et al. have shown that cluster-wise family-wise error (FWE) rate-corrected inferences made in parametric statistical method-based functional magnetic resonance imaging (fMRI) studies over the past couple of decades may have been invalid, particularly for cluster defining thresholds less stringent than p < 0.001; principally because the spatial autocorrelation functions (sACFs) of fMRI data had been modeled incorrectly to follow a Gaussian form, whereas empirical data suggest otherwise. Hence, the residuals from general linear model (GLM)-based fMRI activation estimates in these studies may not have possessed a homogenously Gaussian sACF. Here we propose a method based on the assumption that heterogeneity and non-Gaussianity of the sACF of the first-level GLM analysis residuals, as well as temporal autocorrelations in the first-level voxel residual time-series, are caused by unmodeled MRI signal from neuronal and physiological processes as well as motion and other artifacts, which can be approximated by appropriate decompositions of the first-level residuals with principal component analysis (PCA), and removed. We show that application of this method yields GLM residuals with significantly reduced spatial correlation, nearly Gaussian sACF and uniform spatial smoothness across the brain, thereby allowing valid cluster-based FWE-corrected inferences based on assumption of Gaussian spatial noise. We further show that application of this method renders the voxel time-series of first-level GLM residuals independent, and identically distributed across time (which is a necessary condition for appropriate voxel-level GLM inference), without having to fit ad hoc stochastic colored noise models. Furthermore, the detection power of individual subject brain activation analysis is enhanced. This method will be especially useful for case studies, which rely on first-level GLM analysis inferences.
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Semisupervised Gaussian Process for Automated Enzyme Search.
Mellor, Joseph; Grigoras, Ioana; Carbonell, Pablo; Faulon, Jean-Loup
2016-06-17
Synthetic biology is today harnessing the design of novel and greener biosynthesis routes for the production of added-value chemicals and natural products. The design of novel pathways often requires a detailed selection of enzyme sequences to import into the chassis at each of the reaction steps. To address such design requirements in an automated way, we present here a tool for exploring the space of enzymatic reactions. Given a reaction and an enzyme the tool provides a probability estimate that the enzyme catalyzes the reaction. Our tool first considers the similarity of a reaction to known biochemical reactions with respect to signatures around their reaction centers. Signatures are defined based on chemical transformation rules by using extended connectivity fingerprint descriptors. A semisupervised Gaussian process model associated with the similar known reactions then provides the probability estimate. The Gaussian process model uses information about both the reaction and the enzyme in providing the estimate. These estimates were validated experimentally by the application of the Gaussian process model to a newly identified metabolite in Escherichia coli in order to search for the enzymes catalyzing its associated reactions. Furthermore, we show with several pathway design examples how such ability to assign probability estimates to enzymatic reactions provides the potential to assist in bioengineering applications, providing experimental validation to our proposed approach. To the best of our knowledge, the proposed approach is the first application of Gaussian processes dealing with biological sequences and chemicals, the use of a semisupervised Gaussian process framework is also novel in the context of machine learning applied to bioinformatics. However, the ability of an enzyme to catalyze a reaction depends on the affinity between the substrates of the reaction and the enzyme. This affinity is generally quantified by the Michaelis constant KM. Therefore, we also demonstrate using Gaussian process regression to predict KM given a substrate-enzyme pair.
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Gaussian noise and time-reversal symmetry in nonequilibrium Langevin models.
Vainstein, M H; Rubí, J M
2007-03-01
We show that in driven systems the Gaussian nature of the fluctuating force and time reversibility are equivalent properties. This result together with the potential condition of the external force drastically restricts the form of the probability distribution function, which can be shown to satisfy time-independent relations. We have corroborated this feature by explicitly analyzing a model for the stretching of a polymer and a model for a suspension of noninteracting Brownian particles in steady flow.
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NASA Technical Reports Server (NTRS)
Reeves, P. M.; Campbell, G. S.; Ganzer, V. M.; Joppa, R. G.
1974-01-01
A method is described for generating time histories which model the frequency content and certain non-Gaussian probability characteristics of atmospheric turbulence including the large gusts and patchy nature of turbulence. Methods for time histories using either analog or digital computation are described. A STOL airplane was programmed into a 6-degree-of-freedom flight simulator, and turbulence time histories from several atmospheric turbulence models were introduced. The pilots' reactions are described.
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Fitted Hanbury-Brown Twiss radii versus space-time variances in flow-dominated models
NASA Astrophysics Data System (ADS)
Frodermann, Evan; Heinz, Ulrich; Lisa, Michael Annan
2006-04-01
The inability of otherwise successful dynamical models to reproduce the Hanbury-Brown Twiss (HBT) radii extracted from two-particle correlations measured at the Relativistic Heavy Ion Collider (RHIC) is known as the RHIC HBT Puzzle. Most comparisons between models and experiment exploit the fact that for Gaussian sources the HBT radii agree with certain combinations of the space-time widths of the source that can be directly computed from the emission function without having to evaluate, at significant expense, the two-particle correlation function. We here study the validity of this approach for realistic emission function models, some of which exhibit significant deviations from simple Gaussian behavior. By Fourier transforming the emission function, we compute the two-particle correlation function, and fit it with a Gaussian to partially mimic the procedure used for measured correlation functions. We describe a novel algorithm to perform this Gaussian fit analytically. We find that for realistic hydrodynamic models the HBT radii extracted from this procedure agree better with the data than the values previously extracted from the space-time widths of the emission function. Although serious discrepancies between the calculated and the measured HBT radii remain, we show that a more apples-to-apples comparison of models with data can play an important role in any eventually successful theoretical description of RHIC HBT data.
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Fitted Hanbury-Brown-Twiss radii versus space-time variances in flow-dominated models
DOE Office of Scientific and Technical Information (OSTI.GOV)
Frodermann, Evan; Heinz, Ulrich; Lisa, Michael Annan
2006-04-15
The inability of otherwise successful dynamical models to reproduce the Hanbury-Brown-Twiss (HBT) radii extracted from two-particle correlations measured at the Relativistic Heavy Ion Collider (RHIC) is known as the RHIC HBT Puzzle. Most comparisons between models and experiment exploit the fact that for Gaussian sources the HBT radii agree with certain combinations of the space-time widths of the source that can be directly computed from the emission function without having to evaluate, at significant expense, the two-particle correlation function. We here study the validity of this approach for realistic emission function models, some of which exhibit significant deviations from simplemore » Gaussian behavior. By Fourier transforming the emission function, we compute the two-particle correlation function, and fit it with a Gaussian to partially mimic the procedure used for measured correlation functions. We describe a novel algorithm to perform this Gaussian fit analytically. We find that for realistic hydrodynamic models the HBT radii extracted from this procedure agree better with the data than the values previously extracted from the space-time widths of the emission function. Although serious discrepancies between the calculated and the measured HBT radii remain, we show that a more apples-to-apples comparison of models with data can play an important role in any eventually successful theoretical description of RHIC HBT data.« less
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A Gaussian beam method for ultrasonic non-destructive evaluation modeling
NASA Astrophysics Data System (ADS)
Jacquet, O.; Leymarie, N.; Cassereau, D.
2018-05-01
The propagation of high-frequency ultrasonic body waves can be efficiently estimated with a semi-analytic Dynamic Ray Tracing approach using paraxial approximation. Although this asymptotic field estimation avoids the computational cost of numerical methods, it may encounter several limitations in reproducing identified highly interferential features. Nevertheless, some can be managed by allowing paraxial quantities to be complex-valued. This gives rise to localized solutions, known as paraxial Gaussian beams. Whereas their propagation and transmission/reflection laws are well-defined, the fact remains that the adopted complexification introduces additional initial conditions. While their choice is usually performed according to strategies specifically tailored to limited applications, a Gabor frame method has been implemented to indiscriminately initialize a reasonable number of paraxial Gaussian beams. Since this method can be applied for an usefully wide range of ultrasonic transducers, the typical case of the time-harmonic piston radiator is investigated. Compared to the commonly used Multi-Gaussian Beam model [1], a better agreement is obtained throughout the radiated field between the results of numerical integration (or analytical on-axis solution) and the resulting Gaussian beam superposition. Sparsity of the proposed solution is also discussed.
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A Guide to the Literature on Learning Graphical Models
NASA Technical Reports Server (NTRS)
Buntine, Wray L.; Friedland, Peter (Technical Monitor)
1994-01-01
This literature review discusses different methods under the general rubric of learning Bayesian networks from data, and more generally, learning probabilistic graphical models. Because many problems in artificial intelligence, statistics and neural networks can be represented as a probabilistic graphical model, this area provides a unifying perspective on learning. This paper organizes the research in this area along methodological lines of increasing complexity.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Wang, Yi; Xue, Wei, E-mail: yw366@cam.ac.uk, E-mail: wei.xue@sissa.it
We study the tilt of the primordial gravitational waves spectrum. A hint of blue tilt is shown from analyzing the BICEP2 and POLARBEAR data. Motivated by this, we explore the possibilities of blue tensor spectra from the very early universe cosmology models, including null energy condition violating inflation, inflation with general initial conditions, and string gas cosmology, etc. For the simplest G-inflation, blue tensor spectrum also implies blue scalar spectrum. In general, the inflation models with blue tensor spectra indicate large non-Gaussianities. On the other hand, string gas cosmology predicts blue tensor spectrum with highly Gaussian fluctuations. If further experimentsmore » do confirm the blue tensor spectrum, non-Gaussianity becomes a distinguishing test between inflation and alternatives.« less
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Chaudret, Robin; Gresh, Nohad; Narth, Christophe; Lagardère, Louis; Darden, Thomas A; Cisneros, G Andrés; Piquemal, Jean-Philip
2014-09-04
We demonstrate as a proof of principle the capabilities of a novel hybrid MM'/MM polarizable force field to integrate short-range quantum effects in molecular mechanics (MM) through the use of Gaussian electrostatics. This lead to a further gain in accuracy in the representation of the first coordination shell of metal ions. It uses advanced electrostatics and couples two point dipole polarizable force fields, namely, the Gaussian electrostatic model (GEM), a model based on density fitting, which uses fitted electronic densities to evaluate nonbonded interactions, and SIBFA (sum of interactions between fragments ab initio computed), which resorts to distributed multipoles. To understand the benefits of the use of Gaussian electrostatics, we evaluate first the accuracy of GEM, which is a pure density-based Gaussian electrostatics model on a test Ca(II)-H2O complex. GEM is shown to further improve the agreement of MM polarization with ab initio reference results. Indeed, GEM introduces nonclassical effects by modeling the short-range quantum behavior of electric fields and therefore enables a straightforward (and selective) inclusion of the sole overlap-dependent exchange-polarization repulsive contribution by means of a Gaussian damping function acting on the GEM fields. The S/G-1 scheme is then introduced. Upon limiting the use of Gaussian electrostatics to metal centers only, it is shown to be able to capture the dominant quantum effects at play on the metal coordination sphere. S/G-1 is able to accurately reproduce ab initio total interaction energies within closed-shell metal complexes regarding each individual contribution including the separate contributions of induction, polarization, and charge-transfer. Applications of the method are provided for various systems including the HIV-1 NCp7-Zn(II) metalloprotein. S/G-1 is then extended to heavy metal complexes. Tested on Hg(II) water complexes, S/G-1 is shown to accurately model polarization up to quadrupolar response level. This opens up the possibility of embodying explicit scalar relativistic effects in molecular mechanics thanks to the direct transferability of ab initio pseudopotentials. Therefore, incorporating GEM-like electron density for a metal cation enable the introduction of nonambiguous short-range quantum effects within any point-dipole based polarizable force field without the need of an extensive parametrization.
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Errors associated with fitting Gaussian profiles to noisy emission-line spectra
NASA Technical Reports Server (NTRS)
Lenz, Dawn D.; Ayres, Thomas R.
1992-01-01
Landman et al. (1982) developed prescriptions to predict profile fitting errors for Gaussian emission lines perturbed by white noise. We show that their scaling laws can be generalized to more complicated signal-dependent 'noise models' of common astronomical detector systems.
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NASA Astrophysics Data System (ADS)
Fallah-Shorshani, Masoud; Shekarrizfard, Maryam; Hatzopoulou, Marianne
2017-10-01
Dispersion of road transport emissions in urban metropolitan areas is typically simulated using Gaussian models that ignore the turbulence and drag induced by buildings, which are especially relevant for areas with dense downtown cores. To consider the effect of buildings, street canyon models are used but often at the level of single urban corridors and small road networks. In this paper, we compare and validate two dispersion models with widely varying algorithms, across a modelling domain consisting of the City of Montreal, Canada accounting for emissions of more 40,000 roads. The first dispersion model is based on flow decomposition into the urban canopy sub-flow as well as overlying airflow. It takes into account the specific height and geometry of buildings along each road. The second model is a Gaussian puff dispersion model, which handles complex terrain and incorporates three-dimensional meteorology, but accounts for buildings only through variations in the initial vertical mixing coefficient. Validation against surface observations indicated that both models under-predicted measured concentrations. Average weekly exposure surfaces derived from both models were found to be reasonably correlated (r = 0.8) although the Gaussian dispersion model tended to underestimate concentrations around the roadways compared to the street canyon model. In addition, both models were used to estimate exposures of a representative sample of the Montreal population composed of 1319 individuals. Large differences were noted whereby exposures derived from the Gaussian puff model were significantly lower than exposures derived from the street canyon model, an expected result considering the concentration of population around roadways. These differences have large implications for the analyses of health effects associated with NO2 exposure.
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Hybrid automated reliability predictor integrated work station (HiREL)
NASA Technical Reports Server (NTRS)
Bavuso, Salvatore J.
1991-01-01
The Hybrid Automated Reliability Predictor (HARP) integrated reliability (HiREL) workstation tool system marks another step toward the goal of producing a totally integrated computer aided design (CAD) workstation design capability. Since a reliability engineer must generally graphically represent a reliability model before he can solve it, the use of a graphical input description language increases productivity and decreases the incidence of error. The captured image displayed on a cathode ray tube (CRT) screen serves as a documented copy of the model and provides the data for automatic input to the HARP reliability model solver. The introduction of dependency gates to a fault tree notation allows the modeling of very large fault tolerant system models using a concise and visually recognizable and familiar graphical language. In addition to aiding in the validation of the reliability model, the concise graphical representation presents company management, regulatory agencies, and company customers a means of expressing a complex model that is readily understandable. The graphical postprocessor computer program HARPO (HARP Output) makes it possible for reliability engineers to quickly analyze huge amounts of reliability/availability data to observe trends due to exploratory design changes.
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An analytic linear accelerator source model for GPU-based Monte Carlo dose calculations.
Tian, Zhen; Li, Yongbao; Folkerts, Michael; Shi, Feng; Jiang, Steve B; Jia, Xun
2015-10-21
Recently, there has been a lot of research interest in developing fast Monte Carlo (MC) dose calculation methods on graphics processing unit (GPU) platforms. A good linear accelerator (linac) source model is critical for both accuracy and efficiency considerations. In principle, an analytical source model should be more preferred for GPU-based MC dose engines than a phase-space file-based model, in that data loading and CPU-GPU data transfer can be avoided. In this paper, we presented an analytical field-independent source model specifically developed for GPU-based MC dose calculations, associated with a GPU-friendly sampling scheme. A key concept called phase-space-ring (PSR) was proposed. Each PSR contained a group of particles that were of the same type, close in energy and reside in a narrow ring on the phase-space plane located just above the upper jaws. The model parameterized the probability densities of particle location, direction and energy for each primary photon PSR, scattered photon PSR and electron PSR. Models of one 2D Gaussian distribution or multiple Gaussian components were employed to represent the particle direction distributions of these PSRs. A method was developed to analyze a reference phase-space file and derive corresponding model parameters. To efficiently use our model in MC dose calculations on GPU, we proposed a GPU-friendly sampling strategy, which ensured that the particles sampled and transported simultaneously are of the same type and close in energy to alleviate GPU thread divergences. To test the accuracy of our model, dose distributions of a set of open fields in a water phantom were calculated using our source model and compared to those calculated using the reference phase-space files. For the high dose gradient regions, the average distance-to-agreement (DTA) was within 1 mm and the maximum DTA within 2 mm. For relatively low dose gradient regions, the root-mean-square (RMS) dose difference was within 1.1% and the maximum dose difference within 1.7%. The maximum relative difference of output factors was within 0.5%. Over 98.5% passing rate was achieved in 3D gamma-index tests with 2%/2 mm criteria in both an IMRT prostate patient case and a head-and-neck case. These results demonstrated the efficacy of our model in terms of accurately representing a reference phase-space file. We have also tested the efficiency gain of our source model over our previously developed phase-space-let file source model. The overall efficiency of dose calculation was found to be improved by ~1.3-2.2 times in water and patient cases using our analytical model.
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NASA Astrophysics Data System (ADS)
Simon, P.; Semboloni, E.; van Waerbeke, L.; Hoekstra, H.; Erben, T.; Fu, L.; Harnois-Déraps, J.; Heymans, C.; Hildebrandt, H.; Kilbinger, M.; Kitching, T. D.; Miller, L.; Schrabback, T.
2015-05-01
We study the correlations of the shear signal between triplets of sources in the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) to probe cosmological parameters via the matter bispectrum. In contrast to previous studies, we adopt a non-Gaussian model of the data likelihood which is supported by our simulations of the survey. We find that for state-of-the-art surveys, similar to CFHTLenS, a Gaussian likelihood analysis is a reasonable approximation, albeit small differences in the parameter constraints are already visible. For future surveys we expect that a Gaussian model becomes inaccurate. Our algorithm for a refined non-Gaussian analysis and data compression is then of great utility especially because it is not much more elaborate if simulated data are available. Applying this algorithm to the third-order correlations of shear alone in a blind analysis, we find a good agreement with the standard cosmological model: Σ _8=σ _8(Ω _m/0.27)^{0.64}=0.79^{+0.08}_{-0.11} for a flat Λ cold dark matter cosmology with h = 0.7 ± 0.04 (68 per cent credible interval). Nevertheless our models provide only moderately good fits as indicated by χ2/dof = 2.9, including a 20 per cent rms uncertainty in the predicted signal amplitude. The models cannot explain a signal drop on scales around 15 arcmin, which may be caused by systematics. It is unclear whether the discrepancy can be fully explained by residual point spread function systematics of which we find evidence at least on scales of a few arcmin. Therefore we need a better understanding of higher order correlations of cosmic shear and their systematics to confidently apply them as cosmological probes.
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2013-01-01
Background Arguably, genotypes and phenotypes may be linked in functional forms that are not well addressed by the linear additive models that are standard in quantitative genetics. Therefore, developing statistical learning models for predicting phenotypic values from all available molecular information that are capable of capturing complex genetic network architectures is of great importance. Bayesian kernel ridge regression is a non-parametric prediction model proposed for this purpose. Its essence is to create a spatial distance-based relationship matrix called a kernel. Although the set of all single nucleotide polymorphism genotype configurations on which a model is built is finite, past research has mainly used a Gaussian kernel. Results We sought to investigate the performance of a diffusion kernel, which was specifically developed to model discrete marker inputs, using Holstein cattle and wheat data. This kernel can be viewed as a discretization of the Gaussian kernel. The predictive ability of the diffusion kernel was similar to that of non-spatial distance-based additive genomic relationship kernels in the Holstein data, but outperformed the latter in the wheat data. However, the difference in performance between the diffusion and Gaussian kernels was negligible. Conclusions It is concluded that the ability of a diffusion kernel to capture the total genetic variance is not better than that of a Gaussian kernel, at least for these data. Although the diffusion kernel as a choice of basis function may have potential for use in whole-genome prediction, our results imply that embedding genetic markers into a non-Euclidean metric space has very small impact on prediction. Our results suggest that use of the black box Gaussian kernel is justified, given its connection to the diffusion kernel and its similar predictive performance. PMID:23763755
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ENSO's non-stationary and non-Gaussian character: the role of climate shifts
NASA Astrophysics Data System (ADS)
Boucharel, J.; Dewitte, B.; Garel, B.; Du Penhoat, Y.
2009-07-01
El Niño Southern Oscillation (ENSO) is the dominant mode of climate variability in the Pacific, having socio-economic impacts on surrounding regions. ENSO exhibits significant modulation on decadal to inter-decadal time scales which is related to changes in its characteristics (onset, amplitude, frequency, propagation, and predictability). Some of these characteristics tend to be overlooked in ENSO studies, such as its asymmetry (the number and amplitude of warm and cold events are not equal) and the deviation of its statistics from those of the Gaussian distribution. These properties could be related to the ability of the current generation of coupled models to predict ENSO and its modulation. Here, ENSO's non-Gaussian nature and asymmetry are diagnosed from in situ data and a variety of models (from intermediate complexity models to full-physics coupled general circulation models (CGCMs)) using robust statistical tools initially designed for financial mathematics studies. In particular α-stable laws are used as theoretical background material to measure (and quantify) the non-Gaussian character of ENSO time series and to estimate the skill of ``naïve'' statistical models in producing deviation from Gaussian laws and asymmetry. The former are based on non-stationary processes dominated by abrupt changes in mean state and empirical variance. It is shown that the α-stable character of ENSO may result from the presence of climate shifts in the time series. Also, cool (warm) periods are associated with ENSO statistics having a stronger (weaker) tendency towards Gaussianity and lower (greater) asymmetry. This supports the hypothesis of ENSO being rectified by changes in mean state through nonlinear processes. The relationship between changes in mean state and nonlinearity (skewness) is further investigated both in the Zebiak and Cane (1987)'s model and the models of the Intergovernmental Panel for Climate Change (IPCC). Whereas there is a clear relationship in all models between ENSO asymmetry (as measured by skewness or nonlinear advection) and changes in mean state, they exhibit a variety of behaviour with regard to α-stability. This suggests that the dynamics associated with climate shifts and the occurrence of extreme events involve higher-order statistical moments that cannot be accounted for solely by nonlinear advection.
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An interactive graphics system to facilitate finite element structural analysis
NASA Technical Reports Server (NTRS)
Burk, R. C.; Held, F. H.
1973-01-01
The characteristics of an interactive graphics systems to facilitate the finite element method of structural analysis are described. The finite element model analysis consists of three phases: (1) preprocessing (model generation), (2) problem solution, and (3) postprocessing (interpretation of results). The advantages of interactive graphics to finite element structural analysis are defined.
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User-Extensible Graphics Using Abstract Structure,
1987-08-01
Flex 6 The Algol68 model of the graphical abstract structure 5 The creation of a PictureDefinition 6 The making of a picture from a PictureDefinition 7...data together with the operations that can be performed on that data. i 7! ś I _ § 4, The Alqol68 model of the graphical abstract structure Every
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Writing a Scientific Paper II. Communication by Graphics
NASA Astrophysics Data System (ADS)
Sterken, C.
2011-07-01
This paper discusses facets of visual communication by way of images, graphs, diagrams and tabular material. Design types and elements of graphical images are presented, along with advice on how to create graphs, and on how to read graphical illustrations. This is done in astronomical context, using case studies and historical examples of good and bad graphics. Design types of graphs (scatter and vector plots, histograms, pie charts, ternary diagrams and three-dimensional surface graphs) are explicated, as well as the major components of graphical images (axes, legends, textual parts, etc.). The basic features of computer graphics (image resolution, vector images, bitmaps, graphical file formats and file conversions) are explained, as well as concepts of color models and of color spaces (with emphasis on aspects of readability of color graphics by viewers suffering from color-vision deficiencies). Special attention is given to the verity of graphical content, and to misrepresentations and errors in graphics and associated basic statistics. Dangers of dot joining and curve fitting are discussed, with emphasis on the perception of linearity, the issue of nonsense correlations, and the handling of outliers. Finally, the distinction between data, fits and models is illustrated.
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Model-independent analyses of non-Gaussianity in Planck CMB maps using Minkowski functionals
NASA Astrophysics Data System (ADS)
Buchert, Thomas; France, Martin J.; Steiner, Frank
2017-05-01
Despite the wealth of Planck results, there are difficulties in disentangling the primordial non-Gaussianity of the Cosmic Microwave Background (CMB) from the secondary and the foreground non-Gaussianity (NG). For each of these forms of NG the lack of complete data introduces model-dependences. Aiming at detecting the NGs of the CMB temperature anisotropy δ T , while paying particular attention to a model-independent quantification of NGs, our analysis is based upon statistical and morphological univariate descriptors, respectively: the probability density function P(δ T) , related to v0, the first Minkowski Functional (MF), and the two other MFs, v1 and v2. From their analytical Gaussian predictions we build the discrepancy functions {{ Δ }k} (k = P, 0, 1, 2) which are applied to an ensemble of 105 CMB realization maps of the Λ CDM model and to the Planck CMB maps. In our analysis we use general Hermite expansions of the {{ Δ }k} up to the 12th order, where the coefficients are explicitly given in terms of cumulants. Assuming hierarchical ordering of the cumulants, we obtain the perturbative expansions generalizing the second order expansions of Matsubara to arbitrary order in the standard deviation {σ0} for P(δ T) and v0, where the perturbative expansion coefficients are explicitly given in terms of complete Bell polynomials. The comparison of the Hermite expansions and the perturbative expansions is performed for the Λ CDM map sample and the Planck data. We confirm the weak level of non-Gaussianity (1-2)σ of the foreground corrected masked Planck 2015 maps.
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The Topology of Large-Scale Structure in the 1.2 Jy IRAS Redshift Survey
NASA Astrophysics Data System (ADS)
Protogeros, Zacharias A. M.; Weinberg, David H.
1997-11-01
We measure the topology (genus) of isodensity contour surfaces in volume-limited subsets of the 1.2 Jy IRAS redshift survey, for smoothing scales λ = 4, 7, and 12 h-1 Mpc. At 12 h-1 Mpc, the observed genus curve has a symmetric form similar to that predicted for a Gaussian random field. At the shorter smoothing lengths, the observed genus curve shows a modest shift in the direction of an isolated cluster or ``meatball'' topology. We use mock catalogs drawn from cosmological N-body simulations to investigate the systematic biases that affect topology measurements in samples of this size and to determine the full covariance matrix of the expected random errors. We incorporate the error correlations into our evaluations of theoretical models, obtaining both frequentist assessments of absolute goodness of fit and Bayesian assessments of models' relative likelihoods. We compare the observed topology of the 1.2 Jy survey to the predictions of dynamically evolved, unbiased, gravitational instability models that have Gaussian initial conditions. The model with an n = -1 power-law initial power spectrum achieves the best overall agreement with the data, though models with a low-density cold dark matter power spectrum and an n = 0 power-law spectrum are also consistent. The observed topology is inconsistent with an initially Gaussian model that has n = -2, and it is strongly inconsistent with a Voronoi foam model, which has a non-Gaussian, bubble topology.
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Action detection by double hierarchical multi-structure space-time statistical matching model
NASA Astrophysics Data System (ADS)
Han, Jing; Zhu, Junwei; Cui, Yiyin; Bai, Lianfa; Yue, Jiang
2018-03-01
Aimed at the complex information in videos and low detection efficiency, an actions detection model based on neighboring Gaussian structure and 3D LARK features is put forward. We exploit a double hierarchical multi-structure space-time statistical matching model (DMSM) in temporal action localization. First, a neighboring Gaussian structure is presented to describe the multi-scale structural relationship. Then, a space-time statistical matching method is proposed to achieve two similarity matrices on both large and small scales, which combines double hierarchical structural constraints in model by both the neighboring Gaussian structure and the 3D LARK local structure. Finally, the double hierarchical similarity is fused and analyzed to detect actions. Besides, the multi-scale composite template extends the model application into multi-view. Experimental results of DMSM on the complex visual tracker benchmark data sets and THUMOS 2014 data sets show the promising performance. Compared with other state-of-the-art algorithm, DMSM achieves superior performances.
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Estimating Risk of Natural Gas Portfolios by Using GARCH-EVT-Copula Model.
Tang, Jiechen; Zhou, Chao; Yuan, Xinyu; Sriboonchitta, Songsak
2015-01-01
This paper concentrates on estimating the risk of Title Transfer Facility (TTF) Hub natural gas portfolios by using the GARCH-EVT-copula model. We first use the univariate ARMA-GARCH model to model each natural gas return series. Second, the extreme value distribution (EVT) is fitted to the tails of the residuals to model marginal residual distributions. Third, multivariate Gaussian copula and Student t-copula are employed to describe the natural gas portfolio risk dependence structure. Finally, we simulate N portfolios and estimate value at risk (VaR) and conditional value at risk (CVaR). Our empirical results show that, for an equally weighted portfolio of five natural gases, the VaR and CVaR values obtained from the Student t-copula are larger than those obtained from the Gaussian copula. Moreover, when minimizing the portfolio risk, the optimal natural gas portfolio weights are found to be similar across the multivariate Gaussian copula and Student t-copula and different confidence levels.
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Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets.
Datta, Abhirup; Banerjee, Sudipto; Finley, Andrew O; Gelfand, Alan E
2016-01-01
Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive U.S. Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods. Supplementary materials for this article are available online.
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Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets
Datta, Abhirup; Banerjee, Sudipto; Finley, Andrew O.; Gelfand, Alan E.
2018-01-01
Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive U.S. Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods. Supplementary materials for this article are available online. PMID:29720777
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Estimating Risk of Natural Gas Portfolios by Using GARCH-EVT-Copula Model
Tang, Jiechen; Zhou, Chao; Yuan, Xinyu; Sriboonchitta, Songsak
2015-01-01
This paper concentrates on estimating the risk of Title Transfer Facility (TTF) Hub natural gas portfolios by using the GARCH-EVT-copula model. We first use the univariate ARMA-GARCH model to model each natural gas return series. Second, the extreme value distribution (EVT) is fitted to the tails of the residuals to model marginal residual distributions. Third, multivariate Gaussian copula and Student t-copula are employed to describe the natural gas portfolio risk dependence structure. Finally, we simulate N portfolios and estimate value at risk (VaR) and conditional value at risk (CVaR). Our empirical results show that, for an equally weighted portfolio of five natural gases, the VaR and CVaR values obtained from the Student t-copula are larger than those obtained from the Gaussian copula. Moreover, when minimizing the portfolio risk, the optimal natural gas portfolio weights are found to be similar across the multivariate Gaussian copula and Student t-copula and different confidence levels. PMID:26351652
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Action detection by double hierarchical multi-structure space–time statistical matching model
NASA Astrophysics Data System (ADS)
Han, Jing; Zhu, Junwei; Cui, Yiyin; Bai, Lianfa; Yue, Jiang
2018-06-01
Aimed at the complex information in videos and low detection efficiency, an actions detection model based on neighboring Gaussian structure and 3D LARK features is put forward. We exploit a double hierarchical multi-structure space-time statistical matching model (DMSM) in temporal action localization. First, a neighboring Gaussian structure is presented to describe the multi-scale structural relationship. Then, a space-time statistical matching method is proposed to achieve two similarity matrices on both large and small scales, which combines double hierarchical structural constraints in model by both the neighboring Gaussian structure and the 3D LARK local structure. Finally, the double hierarchical similarity is fused and analyzed to detect actions. Besides, the multi-scale composite template extends the model application into multi-view. Experimental results of DMSM on the complex visual tracker benchmark data sets and THUMOS 2014 data sets show the promising performance. Compared with other state-of-the-art algorithm, DMSM achieves superior performances.
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NASA Astrophysics Data System (ADS)
Fallah-Shorshani, Masoud; Shekarrizfard, Maryam; Hatzopoulou, Marianne
2017-03-01
The development and use of dispersion models that simulate traffic-related air pollution in urban areas has risen significantly in support of air pollution exposure research. In order to accurately estimate population exposure, it is important to generate concentration surfaces that take into account near-road concentrations as well as the transport of pollutants throughout an urban region. In this paper, an integrated modelling chain was developed to simulate ambient Nitrogen Dioxide (NO2) in a dense urban neighbourhood while taking into account traffic emissions, the regional background, and the transport of pollutants within the urban canopy. For this purpose, we developed a hybrid configuration including 1) a street canyon model, which simulates pollutant transfer along streets and intersections, taking into account the geometry of buildings and other obstacles, and 2) a Gaussian puff model, which resolves the transport of contaminants at the top of the urban canopy and accounts for regional meteorology. Each dispersion model was validated against measured concentrations and compared against the hybrid configuration. Our results demonstrate that the hybrid approach significantly improves the output of each model on its own. An underestimation appears clearly for the Gaussian model and street-canyon model compared to observed data. This is due to ignoring the building effect by the Gaussian model and undermining the contribution of other roads by the canyon model. The hybrid approach reduced the RMSE (of observed vs. predicted concentrations) by 16%-25% compared to each model on its own, and increased FAC2 (fraction of predictions within a factor of two of the observations) by 10%-34%.
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Charged particle dynamics in the presence of non-Gaussian Lévy electrostatic fluctuations
Del-Castillo-Negrete, Diego B.; Moradi, Sara; Anderson, Johan
2016-09-01
Full orbit dynamics of charged particles in a 3-dimensional helical magnetic field in the presence of -stable Levy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The Levy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of Levy fluctuations. The absolute value ofmore » the power law decay exponents are linearly proportional to the Levy index. Furthermore, the observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian Levy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.« less
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Charged particle dynamics in the presence of non-Gaussian Lévy electrostatic fluctuations
NASA Astrophysics Data System (ADS)
Moradi, Sara; del-Castillo-Negrete, Diego; Anderson, Johan
2016-09-01
Full orbit dynamics of charged particles in a 3-dimensional helical magnetic field in the presence of α-stable Lévy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of Lévy fluctuations. The absolute value of the power law decay exponents is linearly proportional to the Lévy index α. The observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian Lévy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Ruban, V. P., E-mail: ruban@itp.ac.ru
2015-05-15
The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrödinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of roguemore » wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves.« less
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Dietz, Karl-Josef; Vogel, Marc Oliver; Viehhauser, Andrea
2010-09-01
To optimize acclimation responses to environmental growth conditions, plants integrate and weigh a diversity of input signals. Signal integration within the signalling networks occurs at different sites including the level of transcription factor activation. Accumulating evidence assigns a major and diversified role in environmental signal integration to the family of APETALA 2/ethylene response element binding protein (AP2/EREBP) transcription factors. Presently, the Plant Transcription Factor Database 3.0 assigns 147 gene loci to this family in Arabidopsis thaliana, 200 in Populus trichocarpa and 163 in Oryza sativa subsp. japonica as compared to 13 to 14 in unicellular algae ( http://plntfdb.bio.uni-potsdam.de/v3.0/ ). AP2/EREBP transcription factors have been implicated in hormone, sugar and redox signalling in context of abiotic stresses such as cold and drought. This review exemplarily addresses present-day knowledge of selected AP2/EREBP with focus on a function in stress signal integration and retrograde signalling and defines AP2/EREBP-linked gene networks from transcriptional profiling-based graphical Gaussian models. The latter approach suggests highly interlinked functions of AP2/EREBPs in retrograde and stress signalling.
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Detection of multiple perturbations in multi-omics biological networks.
Griffin, Paula J; Zhang, Yuqing; Johnson, William Evan; Kolaczyk, Eric D
2018-05-17
Cellular mechanism-of-action is of fundamental concern in many biological studies. It is of particular interest for identifying the cause of disease and learning the way in which treatments act against disease. However, pinpointing such mechanisms is difficult, due to the fact that small perturbations to the cell can have wide-ranging downstream effects. Given a snapshot of cellular activity, it can be challenging to tell where a disturbance originated. The presence of an ever-greater variety of high-throughput biological data offers an opportunity to examine cellular behavior from multiple angles, but also presents the statistical challenge of how to effectively analyze data from multiple sources. In this setting, we propose a method for mechanism-of-action inference by extending network filtering to multi-attribute data. We first estimate a joint Gaussian graphical model across multiple data types using penalized regression and filter for network effects. We then apply a set of likelihood ratio tests to identify the most likely site of the original perturbation. In addition, we propose a conditional testing procedure to allow for detection of multiple perturbations. We demonstrate this methodology on paired gene expression and methylation data from The Cancer Genome Atlas (TCGA). © 2018, The International Biometric Society.
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Optimal modeling of 1D azimuth correlations in the context of Bayesian inference
NASA Astrophysics Data System (ADS)
De Kock, Michiel B.; Eggers, Hans C.; Trainor, Thomas A.
2015-09-01
Analysis and interpretation of spectrum and correlation data from high-energy nuclear collisions is currently controversial because two opposing physics narratives derive contradictory implications from the same data, one narrative claiming collision dynamics is dominated by dijet production and projectile-nucleon fragmentation, the other claiming collision dynamics is dominated by a dense, flowing QCD medium. Opposing interpretations seem to be supported by alternative data models, and current model-comparison schemes are unable to distinguish between them. There is clearly need for a convincing new methodology to break the deadlock. In this study we introduce Bayesian inference (BI) methods applied to angular correlation data as a basis to evaluate competing data models. For simplicity the data considered are projections of two-dimensional (2D) angular correlations onto a 1D azimuth from three centrality classes of 200-GeV Au-Au collisions. We consider several data models typical of current model choices, including Fourier series (FS) and a Gaussian plus various combinations of individual cosine components. We evaluate model performance with BI methods and with power-spectrum analysis. We find that FS-only models are rejected in all cases by Bayesian analysis, which always prefers a Gaussian. A cylindrical quadrupole cos(2 ϕ ) is required in some cases but rejected for 0%-5%-central Au-Au collisions. Given a Gaussian centered at the azimuth origin, "higher harmonics" cos(m ϕ ) for m >2 are rejected. A model consisting of Gaussian +dipole cos(ϕ )+quadrupole cos(2 ϕ ) provides good 1D data descriptions in all cases.
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The Mass-dependent Star Formation Histories of Disk Galaxies: Infall Model Versus Observations
NASA Astrophysics Data System (ADS)
Chang, R. X.; Hou, J. L.; Shen, S. Y.; Shu, C. G.
2010-10-01
We introduce a simple model to explore the star formation histories of disk galaxies. We assume that the disk originate and grows by continuous gas infall. The gas infall rate is parameterized by the Gaussian formula with one free parameter: the infall-peak time tp . The Kennicutt star formation law is adopted to describe how much cold gas turns into stars. The gas outflow process is also considered in our model. We find that, at a given galactic stellar mass M *, the model adopting a late infall-peak time tp results in blue colors, low-metallicity, high specific star formation rate (SFR), and high gas fraction, while the gas outflow rate mainly influences the gas-phase metallicity and star formation efficiency mainly influences the gas fraction. Motivated by the local observed scaling relations, we "construct" a mass-dependent model by assuming that the low-mass galaxy has a later infall-peak time tp and a larger gas outflow rate than massive systems. It is shown that this model can be in agreement with not only the local observations, but also with the observed correlations between specific SFR and galactic stellar mass SFR/M * ~ M * at intermediate redshifts z < 1. Comparison between the Gaussian-infall model and the exponential-infall model is also presented. It shows that the exponential-infall model predicts a higher SFR at early stage and a lower SFR later than that of Gaussian infall. Our results suggest that the Gaussian infall rate may be more reasonable in describing the gas cooling process than the exponential infall rate, especially for low-mass systems.
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XDGMM: eXtreme Deconvolution Gaussian Mixture Modeling
NASA Astrophysics Data System (ADS)
Holoien, Thomas W.-S.; Marshall, Philip J.; Wechsler, Risa H.
2017-08-01
XDGMM uses Gaussian mixtures to do density estimation of noisy, heterogenous, and incomplete data using extreme deconvolution (XD) algorithms which is compatible with the scikit-learn machine learning methods. It implements both the astroML and Bovy et al. (2011) algorithms, and extends the BaseEstimator class from scikit-learn so that cross-validation methods work. It allows the user to produce a conditioned model if values of some parameters are known.
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A non-Gaussian option pricing model based on Kaniadakis exponential deformation
NASA Astrophysics Data System (ADS)
Moretto, Enrico; Pasquali, Sara; Trivellato, Barbara
2017-09-01
A way to make financial models effective is by letting them to represent the so called "fat tails", i.e., extreme changes in stock prices that are regarded as almost impossible by the standard Gaussian distribution. In this article, the Kaniadakis deformation of the usual exponential function is used to define a random noise source in the dynamics of price processes capable of capturing such real market phenomena.
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NASA Astrophysics Data System (ADS)
Nguyen, Ngoc Minh; Corff, Sylvain Le; Moulines, Éric
2017-12-01
This paper focuses on sequential Monte Carlo approximations of smoothing distributions in conditionally linear and Gaussian state spaces. To reduce Monte Carlo variance of smoothers, it is typical in these models to use Rao-Blackwellization: particle approximation is used to sample sequences of hidden regimes while the Gaussian states are explicitly integrated conditional on the sequence of regimes and observations, using variants of the Kalman filter/smoother. The first successful attempt to use Rao-Blackwellization for smoothing extends the Bryson-Frazier smoother for Gaussian linear state space models using the generalized two-filter formula together with Kalman filters/smoothers. More recently, a forward-backward decomposition of smoothing distributions mimicking the Rauch-Tung-Striebel smoother for the regimes combined with backward Kalman updates has been introduced. This paper investigates the benefit of introducing additional rejuvenation steps in all these algorithms to sample at each time instant new regimes conditional on the forward and backward particles. This defines particle-based approximations of the smoothing distributions whose support is not restricted to the set of particles sampled in the forward or backward filter. These procedures are applied to commodity markets which are described using a two-factor model based on the spot price and a convenience yield for crude oil data.
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Rabbani, Hossein; Sonka, Milan; Abramoff, Michael D
2013-01-01
In this paper, MMSE estimator is employed for noise-free 3D OCT data recovery in 3D complex wavelet domain. Since the proposed distribution for noise-free data plays a key role in the performance of MMSE estimator, a priori distribution for the pdf of noise-free 3D complex wavelet coefficients is proposed which is able to model the main statistical properties of wavelets. We model the coefficients with a mixture of two bivariate Gaussian pdfs with local parameters which are able to capture the heavy-tailed property and inter- and intrascale dependencies of coefficients. In addition, based on the special structure of OCT images, we use an anisotropic windowing procedure for local parameters estimation that results in visual quality improvement. On this base, several OCT despeckling algorithms are obtained based on using Gaussian/two-sided Rayleigh noise distribution and homomorphic/nonhomomorphic model. In order to evaluate the performance of the proposed algorithm, we use 156 selected ROIs from 650 × 512 × 128 OCT dataset in the presence of wet AMD pathology. Our simulations show that the best MMSE estimator using local bivariate mixture prior is for the nonhomomorphic model in the presence of Gaussian noise which results in an improvement of 7.8 ± 1.7 in CNR.
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Cheng, Mingjian; Guo, Ya; Li, Jiangting; Zheng, Xiaotong; Guo, Lixin
2018-04-20
We introduce an alternative distribution to the gamma-gamma (GG) distribution, called inverse Gaussian gamma (IGG) distribution, which can efficiently describe moderate-to-strong irradiance fluctuations. The proposed stochastic model is based on a modulation process between small- and large-scale irradiance fluctuations, which are modeled by gamma and inverse Gaussian distributions, respectively. The model parameters of the IGG distribution are directly related to atmospheric parameters. The accuracy of the fit among the IGG, log-normal, and GG distributions with the experimental probability density functions in moderate-to-strong turbulence are compared, and results indicate that the newly proposed IGG model provides an excellent fit to the experimental data. As the receiving diameter is comparable with the atmospheric coherence radius, the proposed IGG model can reproduce the shape of the experimental data, whereas the GG and LN models fail to match the experimental data. The fundamental channel statistics of a free-space optical communication system are also investigated in an IGG-distributed turbulent atmosphere, and a closed-form expression for the outage probability of the system is derived with Meijer's G-function.
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Revisiting Gaussian Process Regression Modeling for Localization in Wireless Sensor Networks
Richter, Philipp; Toledano-Ayala, Manuel
2015-01-01
Signal strength-based positioning in wireless sensor networks is a key technology for seamless, ubiquitous localization, especially in areas where Global Navigation Satellite System (GNSS) signals propagate poorly. To enable wireless local area network (WLAN) location fingerprinting in larger areas while maintaining accuracy, methods to reduce the effort of radio map creation must be consolidated and automatized. Gaussian process regression has been applied to overcome this issue, also with auspicious results, but the fit of the model was never thoroughly assessed. Instead, most studies trained a readily available model, relying on the zero mean and squared exponential covariance function, without further scrutinization. This paper studies the Gaussian process regression model selection for WLAN fingerprinting in indoor and outdoor environments. We train several models for indoor/outdoor- and combined areas; we evaluate them quantitatively and compare them by means of adequate model measures, hence assessing the fit of these models directly. To illuminate the quality of the model fit, the residuals of the proposed model are investigated, as well. Comparative experiments on the positioning performance verify and conclude the model selection. In this way, we show that the standard model is not the most appropriate, discuss alternatives and present our best candidate. PMID:26370996
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Chen, Nan; Majda, Andrew J
2017-12-05
Solving the Fokker-Planck equation for high-dimensional complex dynamical systems is an important issue. Recently, the authors developed efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures, which contain many strong non-Gaussian features such as intermittency and fat-tailed probability density functions (PDFs). The algorithms involve a hybrid strategy with a small number of samples [Formula: see text], where a conditional Gaussian mixture in a high-dimensional subspace via an extremely efficient parametric method is combined with a judicious Gaussian kernel density estimation in the remaining low-dimensional subspace. In this article, two effective strategies are developed and incorporated into these algorithms. The first strategy involves a judicious block decomposition of the conditional covariance matrix such that the evolutions of different blocks have no interactions, which allows an extremely efficient parallel computation due to the small size of each individual block. The second strategy exploits statistical symmetry for a further reduction of [Formula: see text] The resulting algorithms can efficiently solve the Fokker-Planck equation with strongly non-Gaussian PDFs in much higher dimensions even with orders in the millions and thus beat the curse of dimension. The algorithms are applied to a [Formula: see text]-dimensional stochastic coupled FitzHugh-Nagumo model for excitable media. An accurate recovery of both the transient and equilibrium non-Gaussian PDFs requires only [Formula: see text] samples! In addition, the block decomposition facilitates the algorithms to efficiently capture the distinct non-Gaussian features at different locations in a [Formula: see text]-dimensional two-layer inhomogeneous Lorenz 96 model, using only [Formula: see text] samples. Copyright © 2017 the Author(s). Published by PNAS.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Harlim, John, E-mail: jharlim@psu.edu; Mahdi, Adam, E-mail: amahdi@ncsu.edu; Majda, Andrew J., E-mail: jonjon@cims.nyu.edu
2014-01-15
A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partialmore » noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model.« less
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Squeezing and its graphical representations in the anharmonic oscillator model
NASA Astrophysics Data System (ADS)
Tanaś, R.; Miranowicz, A.; Kielich, S.
1991-04-01
The problem of squeezing and its graphical representations in the anharmonic oscillator model is considered. Explicit formulas for squeezing, principal squeezing, and the quasiprobability distribution (QPD) function are given and illustrated graphically. Approximate analytical formulas for the variances, extremal variances, and QPD are obtained for the case of small nonlinearities and large numbers of photons. The possibility of almost perfect squeezing in the model is demonstrated and its graphical representations in the form of variance lemniscates and QPD contours are plotted. For large numbers of photons the crescent shape of the QPD contours is hardly visible and quite regular ellipses are obtained.
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The Concurrent Engineering Design Paradigm Is Now Fully Functional for Graphics Education
ERIC Educational Resources Information Center
Krueger, Thomas J.; Barr, Ronald E.
2007-01-01
Engineering design graphics education has come a long way in the past two decades. The emergence of solid geometric modeling technology has become the focal point for the graphical development of engineering design ideas. The main attraction of this 3-D modeling approach is the downstream application of the data base to analysis and…
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A continuous mixing model for pdf simulations and its applications to combusting shear flows
NASA Technical Reports Server (NTRS)
Hsu, A. T.; Chen, J.-Y.
1991-01-01
The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in this work. A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models.
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Non-Gaussian bias: insights from discrete density peaks
DOE Office of Scientific and Technical Information (OSTI.GOV)
Desjacques, Vincent; Riotto, Antonio; Gong, Jinn-Ouk, E-mail: Vincent.Desjacques@unige.ch, E-mail: jinn-ouk.gong@apctp.org, E-mail: Antonio.Riotto@unige.ch
2013-09-01
Corrections induced by primordial non-Gaussianity to the linear halo bias can be computed from a peak-background split or the widespread local bias model. However, numerical simulations clearly support the prediction of the former, in which the non-Gaussian amplitude is proportional to the linear halo bias. To understand better the reasons behind the failure of standard Lagrangian local bias, in which the halo overdensity is a function of the local mass overdensity only, we explore the effect of a primordial bispectrum on the 2-point correlation of discrete density peaks. We show that the effective local bias expansion to peak clustering vastlymore » simplifies the calculation. We generalize this approach to excursion set peaks and demonstrate that the resulting non-Gaussian amplitude, which is a weighted sum of quadratic bias factors, precisely agrees with the peak-background split expectation, which is a logarithmic derivative of the halo mass function with respect to the normalisation amplitude. We point out that statistics of thresholded regions can be computed using the same formalism. Our results suggest that halo clustering statistics can be modelled consistently (in the sense that the Gaussian and non-Gaussian bias factors agree with peak-background split expectations) from a Lagrangian bias relation only if the latter is specified as a set of constraints imposed on the linear density field. This is clearly not the case of standard Lagrangian local bias. Therefore, one is led to consider additional variables beyond the local mass overdensity.« less
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NASA Astrophysics Data System (ADS)
Ortiz-Jaramillo, B.; Fandiño Toro, H. A.; Benitez-Restrepo, H. D.; Orjuela-Vargas, S. A.; Castellanos-Domínguez, G.; Philips, W.
2012-03-01
Infrared Non-Destructive Testing (INDT) is known as an effective and rapid method for nondestructive inspection. It can detect a broad range of near-surface structuring flaws in metallic and composite components. Those flaws are modeled as a smooth contour centered at peaks of stored thermal energy, termed Regions of Interest (ROI). Dedicated methodologies must detect the presence of those ROIs. In this paper, we present a methodology for ROI extraction in INDT tasks. The methodology deals with the difficulties due to the non-uniform heating. The non-uniform heating affects low spatial/frequencies and hinders the detection of relevant points in the image. In this paper, a methodology for ROI extraction in INDT using multi-resolution analysis is proposed, which is robust to ROI low contrast and non-uniform heating. The former methodology includes local correlation, Gaussian scale analysis and local edge detection. In this methodology local correlation between image and Gaussian window provides interest points related to ROIs. We use a Gaussian window because thermal behavior is well modeled by Gaussian smooth contours. Also, the Gaussian scale is used to analyze details in the image using multi-resolution analysis avoiding low contrast, non-uniform heating and selection of the Gaussian window size. Finally, local edge detection is used to provide a good estimation of the boundaries in the ROI. Thus, we provide a methodology for ROI extraction based on multi-resolution analysis that is better or equal compared with the other dedicate algorithms proposed in the state of art.
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On the cause of the non-Gaussian distribution of residuals in geomagnetism
NASA Astrophysics Data System (ADS)
Hulot, G.; Khokhlov, A.
2017-12-01
To describe errors in the data, Gaussian distributions naturally come to mind. In many practical instances, indeed, Gaussian distributions are appropriate. In the broad field of geomagnetism, however, it has repeatedly been noted that residuals between data and models often display much sharper distributions, sometimes better described by a Laplace distribution. In the present study, we make the case that such non-Gaussian behaviors are very likely the result of what is known as mixture of distributions in the statistical literature. Mixtures arise as soon as the data do not follow a common distribution or are not properly normalized, the resulting global distribution being a mix of the various distributions followed by subsets of the data, or even individual datum. We provide examples of the way such mixtures can lead to distributions that are much sharper than Gaussian distributions and discuss the reasons why such mixtures are likely the cause of the non-Gaussian distributions observed in geomagnetism. We also show that when properly selecting sub-datasets based on geophysical criteria, statistical mixture can sometimes be avoided and much more Gaussian behaviors recovered. We conclude with some general recommendations and point out that although statistical mixture always tends to sharpen the resulting distribution, it does not necessarily lead to a Laplacian distribution. This needs to be taken into account when dealing with such non-Gaussian distributions.
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A general graphical user interface for automatic reliability modeling
NASA Technical Reports Server (NTRS)
Liceaga, Carlos A.; Siewiorek, Daniel P.
1991-01-01
Reported here is a general Graphical User Interface (GUI) for automatic reliability modeling of Processor Memory Switch (PMS) structures using a Markov model. This GUI is based on a hierarchy of windows. One window has graphical editing capabilities for specifying the system's communication structure, hierarchy, reconfiguration capabilities, and requirements. Other windows have field texts, popup menus, and buttons for specifying parameters and selecting actions. An example application of the GUI is given.
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Learning Layouts for Single-Page Graphic Designs.
O'Donovan, Peter; Agarwala, Aseem; Hertzmann, Aaron
2014-08-01
This paper presents an approach for automatically creating graphic design layouts using a new energy-based model derived from design principles. The model includes several new algorithms for analyzing graphic designs, including the prediction of perceived importance, alignment detection, and hierarchical segmentation. Given the model, we use optimization to synthesize new layouts for a variety of single-page graphic designs. Model parameters are learned with Nonlinear Inverse Optimization (NIO) from a small number of example layouts. To demonstrate our approach, we show results for applications including generating design layouts in various styles, retargeting designs to new sizes, and improving existing designs. We also compare our automatic results with designs created using crowdsourcing and show that our approach performs slightly better than novice designers.
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Random Process Simulation for stochastic fatigue analysis. Ph.D. Thesis - Rice Univ., Houston, Tex.
NASA Technical Reports Server (NTRS)
Larsen, Curtis E.
1988-01-01
A simulation technique is described which directly synthesizes the extrema of a random process and is more efficient than the Gaussian simulation method. Such a technique is particularly useful in stochastic fatigue analysis because the required stress range moment E(R sup m), is a function only of the extrema of the random stress process. The family of autoregressive moving average (ARMA) models is reviewed and an autoregressive model is presented for modeling the extrema of any random process which has a unimodal power spectral density (psd). The proposed autoregressive technique is found to produce rainflow stress range moments which compare favorably with those computed by the Gaussian technique and to average 11.7 times faster than the Gaussian technique. The autoregressive technique is also adapted for processes having bimodal psd's. The adaptation involves using two autoregressive processes to simulate the extrema due to each mode and the superposition of these two extrema sequences. The proposed autoregressive superposition technique is 9 to 13 times faster than the Gaussian technique and produces comparable values for E(R sup m) for bimodal psd's having the frequency of one mode at least 2.5 times that of the other mode.
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Consistency relation and non-Gaussianity in a Galileon inflation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Asadi, Kosar; Nozari, Kourosh, E-mail: k.asadi@stu.umz.ac.ir, E-mail: knozari@umz.ac.ir
2016-12-01
We study a particular Galileon inflation in the light of Planck2015 observational data in order to constraint the model parameter space. We study the spectrum of the primordial modes of the density perturbations by expanding the action up to the second order in perturbations. Then we pursue by expanding the action up to the third order and find the three point correlation functions to find the amplitude of the non-Gaussianity of the primordial perturbations in this setup. We study the amplitude of the non-Gaussianity both in equilateral and orthogonal configurations and test the model with recent observational data. Our analysismore » shows that for some ranges of the non-minimal coupling parameter, the model is consistent with observation and it is also possible to have large non-Gaussianity which would be observable by future improvements in experiments. Moreover, we obtain the tilt of the tensor power spectrum and test the standard inflationary consistency relation ( r = −8 n {sub T} ) against the latest bounds from the Planck2015 dataset. We find a slight deviation from the standard consistency relation in this setup. Nevertheless, such a deviation seems not to be sufficiently remarkable to be detected confidently.« less
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A relativistic signature in large-scale structure
NASA Astrophysics Data System (ADS)
Bartolo, Nicola; Bertacca, Daniele; Bruni, Marco; Koyama, Kazuya; Maartens, Roy; Matarrese, Sabino; Sasaki, Misao; Verde, Licia; Wands, David
2016-09-01
In General Relativity, the constraint equation relating metric and density perturbations is inherently nonlinear, leading to an effective non-Gaussianity in the dark matter density field on large scales-even if the primordial metric perturbation is Gaussian. Intrinsic non-Gaussianity in the large-scale dark matter overdensity in GR is real and physical. However, the variance smoothed on a local physical scale is not correlated with the large-scale curvature perturbation, so that there is no relativistic signature in the galaxy bias when using the simplest model of bias. It is an open question whether the observable mass proxies such as luminosity or weak lensing correspond directly to the physical mass in the simple halo bias model. If not, there may be observables that encode this relativistic signature.
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Ionospheric scintillation studies
NASA Technical Reports Server (NTRS)
Rino, C. L.; Freemouw, E. J.
1973-01-01
The diffracted field of a monochromatic plane wave was characterized by two complex correlation functions. For a Gaussian complex field, these quantities suffice to completely define the statistics of the field. Thus, one can in principle calculate the statistics of any measurable quantity in terms of the model parameters. The best data fits were achieved for intensity statistics derived under the Gaussian statistics hypothesis. The signal structure that achieved the best fit was nearly invariant with scintillation level and irregularity source (ionosphere or solar wind). It was characterized by the fact that more than 80% of the scattered signal power is in phase quadrature with the undeviated or coherent signal component. Thus, the Gaussian-statistics hypothesis is both convenient and accurate for channel modeling work.
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NASA Astrophysics Data System (ADS)
Aygun, M.; Kucuk, Y.; Boztosun, I.; Ibraheem, Awad A.
2010-12-01
The elastic scattering angular distributions of 6He projectile on different medium and heavy mass target nuclei including 12C, 27Al, 58Ni, 64Zn, 65Cu, 197Au, 208Pb and 209Bi have been examined by using the few-body and Gaussian-shaped density distributions at various energies. The microscopic real parts of the complex nuclear optical potential have been obtained by using the double-folding model for each of the density distributions and the phenomenological imaginary potentials have been taken as the Woods-Saxon type. Comparative results of the few-body and Gaussian-shaped density distributions together with the experimental data are presented within the framework of the optical model.
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Effect of lensing non-Gaussianity on the CMB power spectra
DOE Office of Scientific and Technical Information (OSTI.GOV)
Lewis, Antony; Pratten, Geraint, E-mail: antony@cosmologist.info, E-mail: geraint.pratten@gmail.com
2016-12-01
Observed CMB anisotropies are lensed, and the lensed power spectra can be calculated accurately assuming the lensing deflections are Gaussian. However, the lensing deflections are actually slightly non-Gaussian due to both non-linear large-scale structure growth and post-Born corrections. We calculate the leading correction to the lensed CMB power spectra from the non-Gaussianity, which is determined by the lensing bispectrum. Assuming no primordial non-Gaussianity, the lowest-order result gives ∼ 0.3% corrections to the BB and EE polarization spectra on small-scales. However we show that the effect on EE is reduced by about a factor of two by higher-order Gaussian lensing smoothing,more » rendering the total effect safely negligible for the foreseeable future. We give a simple analytic model for the signal expected from skewness of the large-scale lensing field; the effect is similar to a net demagnification and hence a small change in acoustic scale (and therefore out of phase with the dominant lensing smoothing that predominantly affects the peaks and troughs of the power spectrum).« less
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Non-Gaussian Methods for Causal Structure Learning.
Shimizu, Shohei
2018-05-22
Causal structure learning is one of the most exciting new topics in the fields of machine learning and statistics. In many empirical sciences including prevention science, the causal mechanisms underlying various phenomena need to be studied. Nevertheless, in many cases, classical methods for causal structure learning are not capable of estimating the causal structure of variables. This is because it explicitly or implicitly assumes Gaussianity of data and typically utilizes only the covariance structure. In many applications, however, non-Gaussian data are often obtained, which means that more information may be contained in the data distribution than the covariance matrix is capable of containing. Thus, many new methods have recently been proposed for using the non-Gaussian structure of data and inferring the causal structure of variables. This paper introduces prevention scientists to such causal structure learning methods, particularly those based on the linear, non-Gaussian, acyclic model known as LiNGAM. These non-Gaussian data analysis tools can fully estimate the underlying causal structures of variables under assumptions even in the presence of unobserved common causes. This feature is in contrast to other approaches. A simulated example is also provided.
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Biasing and the search for primordial non-Gaussianity beyond the local type
DOE Office of Scientific and Technical Information (OSTI.GOV)
Gleyzes, Jérôme; De Putter, Roland; Doré, Olivier
Primordial non-Gaussianity encodes valuable information about the physics of inflation, including the spectrum of particles and interactions. Significant improvements in our understanding of non-Gaussanity beyond Planck require information from large-scale structure. The most promising approach to utilize this information comes from the scale-dependent bias of halos. For local non-Gaussanity, the improvements available are well studied but the potential for non-Gaussianity beyond the local type, including equilateral and quasi-single field inflation, is much less well understood. In this paper, we forecast the capabilities of large-scale structure surveys to detect general non-Gaussianity through galaxy/halo power spectra. We study how non-Gaussanity can bemore » distinguished from a general biasing model and where the information is encoded. For quasi-single field inflation, significant improvements over Planck are possible in some regions of parameter space. We also show that the multi-tracer technique can significantly improve the sensitivity for all non-Gaussianity types, providing up to an order of magnitude improvement for equilateral non-Gaussianity over the single-tracer measurement.« less
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Kurtosis, skewness, and non-Gaussian cosmological density perturbations
NASA Technical Reports Server (NTRS)
Luo, Xiaochun; Schramm, David N.
1993-01-01
Cosmological topological defects as well as some nonstandard inflation models can give rise to non-Gaussian density perturbations. Skewness and kurtosis are the third and fourth moments that measure the deviation of a distribution from a Gaussian. Measurement of these moments for the cosmological density field and for the microwave background temperature anisotropy can provide a test of the Gaussian nature of the primordial fluctuation spectrum. In the case of the density field, the importance of measuring the kurtosis is stressed since it will be preserved through the weakly nonlinear gravitational evolution epoch. Current constraints on skewness and kurtosis of primeval perturbations are obtained from the observed density contrast on small scales and from recent COBE observations of temperature anisotropies on large scales. It is also shown how, in principle, future microwave anisotropy experiments might be able to reveal the initial skewness and kurtosis. It is shown that present data argue that if the initial spectrum is adiabatic, then it is probably Gaussian, but non-Gaussian isocurvature fluctuations are still allowed, and these are what topological defects provide.
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Separation of components from a scale mixture of Gaussian white noises
NASA Astrophysics Data System (ADS)
Vamoş, Călin; Crăciun, Maria
2010-05-01
The time evolution of a physical quantity associated with a thermodynamic system whose equilibrium fluctuations are modulated in amplitude by a slowly varying phenomenon can be modeled as the product of a Gaussian white noise {Zt} and a stochastic process with strictly positive values {Vt} referred to as volatility. The probability density function (pdf) of the process Xt=VtZt is a scale mixture of Gaussian white noises expressed as a time average of Gaussian distributions weighted by the pdf of the volatility. The separation of the two components of {Xt} can be achieved by imposing the condition that the absolute values of the estimated white noise be uncorrelated. We apply this method to the time series of the returns of the daily S&P500 index, which has also been analyzed by means of the superstatistics method that imposes the condition that the estimated white noise be Gaussian. The advantage of our method is that this financial time series is processed without partitioning or removal of the extreme events and the estimated white noise becomes almost Gaussian only as result of the uncorrelation condition.
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gWEGA: GPU-accelerated WEGA for molecular superposition and shape comparison.
Yan, Xin; Li, Jiabo; Gu, Qiong; Xu, Jun
2014-06-05
Virtual screening of a large chemical library for drug lead identification requires searching/superimposing a large number of three-dimensional (3D) chemical structures. This article reports a graphic processing unit (GPU)-accelerated weighted Gaussian algorithm (gWEGA) that expedites shape or shape-feature similarity score-based virtual screening. With 86 GPU nodes (each node has one GPU card), gWEGA can screen 110 million conformations derived from an entire ZINC drug-like database with diverse antidiabetic agents as query structures within 2 s (i.e., screening more than 55 million conformations per second). The rapid screening speed was accomplished through the massive parallelization on multiple GPU nodes and rapid prescreening of 3D structures (based on their shape descriptors and pharmacophore feature compositions). Copyright © 2014 Wiley Periodicals, Inc.
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Statistical Modeling of Retinal Optical Coherence Tomography.
Amini, Zahra; Rabbani, Hossein
2016-06-01
In this paper, a new model for retinal Optical Coherence Tomography (OCT) images is proposed. This statistical model is based on introducing a nonlinear Gaussianization transform to convert the probability distribution function (pdf) of each OCT intra-retinal layer to a Gaussian distribution. The retina is a layered structure and in OCT each of these layers has a specific pdf which is corrupted by speckle noise, therefore a mixture model for statistical modeling of OCT images is proposed. A Normal-Laplace distribution, which is a convolution of a Laplace pdf and Gaussian noise, is proposed as the distribution of each component of this model. The reason for choosing Laplace pdf is the monotonically decaying behavior of OCT intensities in each layer for healthy cases. After fitting a mixture model to the data, each component is gaussianized and all of them are combined by Averaged Maximum A Posterior (AMAP) method. To demonstrate the ability of this method, a new contrast enhancement method based on this statistical model is proposed and tested on thirteen healthy 3D OCTs taken by the Topcon 3D OCT and five 3D OCTs from Age-related Macular Degeneration (AMD) patients, taken by Zeiss Cirrus HD-OCT. Comparing the results with two contending techniques, the prominence of the proposed method is demonstrated both visually and numerically. Furthermore, to prove the efficacy of the proposed method for a more direct and specific purpose, an improvement in the segmentation of intra-retinal layers using the proposed contrast enhancement method as a preprocessing step, is demonstrated.
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State estimation and prediction using clustered particle filters.
Lee, Yoonsang; Majda, Andrew J
2016-12-20
Particle filtering is an essential tool to improve uncertain model predictions by incorporating noisy observational data from complex systems including non-Gaussian features. A class of particle filters, clustered particle filters, is introduced for high-dimensional nonlinear systems, which uses relatively few particles compared with the standard particle filter. The clustered particle filter captures non-Gaussian features of the true signal, which are typical in complex nonlinear dynamical systems such as geophysical systems. The method is also robust in the difficult regime of high-quality sparse and infrequent observations. The key features of the clustered particle filtering are coarse-grained localization through the clustering of the state variables and particle adjustment to stabilize the method; each observation affects only neighbor state variables through clustering and particles are adjusted to prevent particle collapse due to high-quality observations. The clustered particle filter is tested for the 40-dimensional Lorenz 96 model with several dynamical regimes including strongly non-Gaussian statistics. The clustered particle filter shows robust skill in both achieving accurate filter results and capturing non-Gaussian statistics of the true signal. It is further extended to multiscale data assimilation, which provides the large-scale estimation by combining a cheap reduced-order forecast model and mixed observations of the large- and small-scale variables. This approach enables the use of a larger number of particles due to the computational savings in the forecast model. The multiscale clustered particle filter is tested for one-dimensional dispersive wave turbulence using a forecast model with model errors.
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State estimation and prediction using clustered particle filters
Lee, Yoonsang; Majda, Andrew J.
2016-01-01
Particle filtering is an essential tool to improve uncertain model predictions by incorporating noisy observational data from complex systems including non-Gaussian features. A class of particle filters, clustered particle filters, is introduced for high-dimensional nonlinear systems, which uses relatively few particles compared with the standard particle filter. The clustered particle filter captures non-Gaussian features of the true signal, which are typical in complex nonlinear dynamical systems such as geophysical systems. The method is also robust in the difficult regime of high-quality sparse and infrequent observations. The key features of the clustered particle filtering are coarse-grained localization through the clustering of the state variables and particle adjustment to stabilize the method; each observation affects only neighbor state variables through clustering and particles are adjusted to prevent particle collapse due to high-quality observations. The clustered particle filter is tested for the 40-dimensional Lorenz 96 model with several dynamical regimes including strongly non-Gaussian statistics. The clustered particle filter shows robust skill in both achieving accurate filter results and capturing non-Gaussian statistics of the true signal. It is further extended to multiscale data assimilation, which provides the large-scale estimation by combining a cheap reduced-order forecast model and mixed observations of the large- and small-scale variables. This approach enables the use of a larger number of particles due to the computational savings in the forecast model. The multiscale clustered particle filter is tested for one-dimensional dispersive wave turbulence using a forecast model with model errors. PMID:27930332
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Gaussian Process Interpolation for Uncertainty Estimation in Image Registration
Wachinger, Christian; Golland, Polina; Reuter, Martin; Wells, William
2014-01-01
Intensity-based image registration requires resampling images on a common grid to evaluate the similarity function. The uncertainty of interpolation varies across the image, depending on the location of resampled points relative to the base grid. We propose to perform Bayesian inference with Gaussian processes, where the covariance matrix of the Gaussian process posterior distribution estimates the uncertainty in interpolation. The Gaussian process replaces a single image with a distribution over images that we integrate into a generative model for registration. Marginalization over resampled images leads to a new similarity measure that includes the uncertainty of the interpolation. We demonstrate that our approach increases the registration accuracy and propose an efficient approximation scheme that enables seamless integration with existing registration methods. PMID:25333127
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Robot graphic simulation testbed
NASA Technical Reports Server (NTRS)
Cook, George E.; Sztipanovits, Janos; Biegl, Csaba; Karsai, Gabor; Springfield, James F.
1991-01-01
The objective of this research was twofold. First, the basic capabilities of ROBOSIM (graphical simulation system) were improved and extended by taking advantage of advanced graphic workstation technology and artificial intelligence programming techniques. Second, the scope of the graphic simulation testbed was extended to include general problems of Space Station automation. Hardware support for 3-D graphics and high processing performance make high resolution solid modeling, collision detection, and simulation of structural dynamics computationally feasible. The Space Station is a complex system with many interacting subsystems. Design and testing of automation concepts demand modeling of the affected processes, their interactions, and that of the proposed control systems. The automation testbed was designed to facilitate studies in Space Station automation concepts.
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Souza, W.R.
1999-01-01
This report documents a graphical display post-processor (SutraPlot) for the U.S. Geological Survey Saturated-Unsaturated flow and solute or energy TRAnsport simulation model SUTRA, Version 2D3D.1. This version of SutraPlot is an upgrade to SutraPlot for the 2D-only SUTRA model (Souza, 1987). It has been modified to add 3D functionality, a graphical user interface (GUI), and enhanced graphic output options. Graphical options for 2D SUTRA (2-dimension) simulations include: drawing the 2D finite-element mesh, mesh boundary, and velocity vectors; plots of contours for pressure, saturation, concentration, and temperature within the model region; 2D finite-element based gridding and interpolation; and 2D gridded data export files. Graphical options for 3D SUTRA (3-dimension) simulations include: drawing the 3D finite-element mesh; plots of contours for pressure, saturation, concentration, and temperature in 2D sections of the 3D model region; 3D finite-element based gridding and interpolation; drawing selected regions of velocity vectors (projected on principal coordinate planes); and 3D gridded data export files. Installation instructions and a description of all graphic options are presented. A sample SUTRA problem is described and three step-by-step SutraPlot applications are provided. In addition, the methodology and numerical algorithms for the 2D and 3D finite-element based gridding and interpolation, developed for SutraPlot, are described. 1
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Non-local bias in the halo bispectrum with primordial non-Gaussianity
DOE Office of Scientific and Technical Information (OSTI.GOV)
Tellarini, Matteo; Ross, Ashley J.; Wands, David
2015-07-01
Primordial non-Gaussianity can lead to a scale-dependent bias in the density of collapsed halos relative to the underlying matter density. The galaxy power spectrum already provides constraints on local-type primordial non-Gaussianity complementary those from the cosmic microwave background (CMB), while the bispectrum contains additional shape information and has the potential to outperform CMB constraints in future. We develop the bias model for the halo density contrast in the presence of local-type primordial non-Gaussianity, deriving a bivariate expansion up to second order in terms of the local linear matter density contrast and the local gravitational potential in Lagrangian coordinates. Nonlinear evolutionmore » of the matter density introduces a non-local tidal term in the halo model. Furthermore, the presence of local-type non-Gaussianity in the Lagrangian frame leads to a novel non-local convective term in the Eulerian frame, that is proportional to the displacement field when going beyond the spherical collapse approximation. We use an extended Press-Schechter approach to evaluate the halo mass function and thus the halo bispectrum. We show that including these non-local terms in the halo bispectra can lead to corrections of up to 25% for some configurations, on large scales or at high redshift.« less
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Ship Detection in SAR Image Based on the Alpha-stable Distribution
Wang, Changcheng; Liao, Mingsheng; Li, Xiaofeng
2008-01-01
This paper describes an improved Constant False Alarm Rate (CFAR) ship detection algorithm in spaceborne synthetic aperture radar (SAR) image based on Alpha-stable distribution model. Typically, the CFAR algorithm uses the Gaussian distribution model to describe statistical characteristics of a SAR image background clutter. However, the Gaussian distribution is only valid for multilook SAR images when several radar looks are averaged. As sea clutter in SAR images shows spiky or heavy-tailed characteristics, the Gaussian distribution often fails to describe background sea clutter. In this study, we replace the Gaussian distribution with the Alpha-stable distribution, which is widely used in impulsive or spiky signal processing, to describe the background sea clutter in SAR images. In our proposed algorithm, an initial step for detecting possible ship targets is employed. Then, similar to the typical two-parameter CFAR algorithm, a local process is applied to the pixel identified as possible target. A RADARSAT-1 image is used to validate this Alpha-stable distribution based algorithm. Meanwhile, known ship location data during the time of RADARSAT-1 SAR image acquisition is used to validate ship detection results. Validation results show improvements of the new CFAR algorithm based on the Alpha-stable distribution over the CFAR algorithm based on the Gaussian distribution. PMID:27873794
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Discrimination of numerical proportions: A comparison of binomial and Gaussian models.
Raidvee, Aire; Lember, Jüri; Allik, Jüri
2017-01-01
Observers discriminated the numerical proportion of two sets of elements (N = 9, 13, 33, and 65) that differed either by color or orientation. According to the standard Thurstonian approach, the accuracy of proportion discrimination is determined by irreducible noise in the nervous system that stochastically transforms the number of presented visual elements onto a continuum of psychological states representing numerosity. As an alternative to this customary approach, we propose a Thurstonian-binomial model, which assumes discrete perceptual states, each of which is associated with a certain visual element. It is shown that the probability β with which each visual element can be noticed and registered by the perceptual system can explain data of numerical proportion discrimination at least as well as the continuous Thurstonian-Gaussian model, and better, if the greater parsimony of the Thurstonian-binomial model is taken into account using AIC model selection. We conclude that Gaussian and binomial models represent two different fundamental principles-internal noise vs. using only a fraction of available information-which are both plausible descriptions of visual perception.
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Review and developments of dissemination models for airborne carbon fibers
NASA Technical Reports Server (NTRS)
Elber, W.
1980-01-01
Dissemination prediction models were reviewed to determine their applicability to a risk assessment for airborne carbon fibers. The review showed that the Gaussian prediction models using partial reflection at the ground agreed very closely with a more elaborate diffusion analysis developed for the study. For distances beyond 10,000 m the Gaussian models predicted a slower fall-off in exposure levels than the diffusion models. This resulting level of conservatism was preferred for the carbon fiber risk assessment. The results also showed that the perfect vertical-mixing models developed herein agreed very closely with the diffusion analysis for all except the most stable atmospheric conditions.
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NASA Astrophysics Data System (ADS)
Mitchell, Noah; Koning, Vinzenz; Vitelli, Vincenzo; Irvine, William T. M.
2014-03-01
When an elastic film conforms to a surface with Gaussian curvature, stresses arise in the film. As a result, cracks--typically studied in flat materials--interact with curvature when propagating through the system. Using silicone elastomer sheets that conform to the surface of a Gaussian bump, we find experimental evidence for the deflection of a crack propagating through the material. We interpret our experiments with reference to analytical modeling and simulations of a simplified model system.
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Autonomous detection of crowd anomalies in multiple-camera surveillance feeds
NASA Astrophysics Data System (ADS)
Nordlöf, Jonas; Andersson, Maria
2016-10-01
A novel approach for autonomous detection of anomalies in crowded environments is presented in this paper. The proposed models uses a Gaussian mixture probability hypothesis density (GM-PHD) filter as feature extractor in conjunction with different Gaussian mixture hidden Markov models (GM-HMMs). Results, based on both simulated and recorded data, indicate that this method can track and detect anomalies on-line in individual crowds through multiple camera feeds in a crowded environment.
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Steve P. Verrill; James W. Evans; David E. Kretschmann; Cherilyn A. Hatfield
2014-01-01
Two important wood properties are the modulus of elasticity (MOE) and the modulus of rupture (MOR). In the past, the statistical distribution of the MOE has often been modeled as Gaussian, and that of the MOR as lognormal or as a two- or three-parameter Weibull distribution. It is well known that MOE and MOR are positively correlated. To model the simultaneous behavior...
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Steve P. Verrill; David E. Kretschmann; James W. Evans
2016-01-01
Two important wood properties are stiffness (modulus of elasticity, MOE) and bending strength (modulus of rupture, MOR). In the past, MOE has often been modeled as a Gaussian and MOR as a lognormal or a two- or threeparameter Weibull. It is well known that MOE and MOR are positively correlated. To model the simultaneous behavior of MOE and MOR for the purposes of wood...
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Bayesian Computation for Log-Gaussian Cox Processes: A Comparative Analysis of Methods
Teng, Ming; Nathoo, Farouk S.; Johnson, Timothy D.
2017-01-01
The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point pattern data. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the first level and a Gaussian Process at the second level. Various methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulation studies as well as through two applications, the first examining ecological data and the second involving neuroimaging data. PMID:29200537
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Model for non-Gaussian intraday stock returns
NASA Astrophysics Data System (ADS)
Gerig, Austin; Vicente, Javier; Fuentes, Miguel A.
2009-12-01
Stock prices are known to exhibit non-Gaussian dynamics, and there is much interest in understanding the origin of this behavior. Here, we present a model that explains the shape and scaling of the distribution of intraday stock price fluctuations (called intraday returns) and verify the model using a large database for several stocks traded on the London Stock Exchange. We provide evidence that the return distribution for these stocks is non-Gaussian and similar in shape and that the distribution appears stable over intraday time scales. We explain these results by assuming the volatility of returns is constant intraday but varies over longer periods such that its inverse square follows a gamma distribution. This produces returns that are Student distributed for intraday time scales. The predicted results show excellent agreement with the data for all stocks in our study and over all regions of the return distribution.
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Research on Bayes matting algorithm based on Gaussian mixture model
NASA Astrophysics Data System (ADS)
Quan, Wei; Jiang, Shan; Han, Cheng; Zhang, Chao; Jiang, Zhengang
2015-12-01
The digital matting problem is a classical problem of imaging. It aims at separating non-rectangular foreground objects from a background image, and compositing with a new background image. Accurate matting determines the quality of the compositing image. A Bayesian matting Algorithm Based on Gaussian Mixture Model is proposed to solve this matting problem. Firstly, the traditional Bayesian framework is improved by introducing Gaussian mixture model. Then, a weighting factor is added in order to suppress the noises of the compositing images. Finally, the effect is further improved by regulating the user's input. This algorithm is applied to matting jobs of classical images. The results are compared to the traditional Bayesian method. It is shown that our algorithm has better performance in detail such as hair. Our algorithm eliminates the noise well. And it is very effectively in dealing with the kind of work, such as interested objects with intricate boundaries.
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Sparkle model for AM1 calculation of lanthanide complexes: improved parameters for europium.
Rocha, Gerd B; Freire, Ricardo O; Da Costa, Nivan B; De Sá, Gilberto F; Simas, Alfredo M
2004-04-05
In the present work, we sought to improve our sparkle model for the calculation of lanthanide complexes, SMLC,in various ways: (i) inclusion of the europium atomic mass, (ii) reparametrization of the model within AM1 from a new response function including all distances of the coordination polyhedron for tris(acetylacetonate)(1,10-phenanthroline) europium(III), (iii) implementation of the model in the software package MOPAC93r2, and (iv) inclusion of spherical Gaussian functions in the expression which computes the core-core repulsion energy. The parametrization results indicate that SMLC II is superior to the previous version of the model because Gaussian functions proved essential if one requires a better description of the geometries of the complexes. In order to validate our parametrization, we carried out calculations on 96 europium(III) complexes, selected from Cambridge Structural Database 2003, and compared our predicted ground state geometries with the experimental ones. Our results show that this new parametrization of the SMLC model, with the inclusion of spherical Gaussian functions in the core-core repulsion energy, is better capable of predicting the Eu-ligand distances than the previous version. The unsigned mean error for all interatomic distances Eu-L, in all 96 complexes, which, for the original SMLC is 0.3564 A, is lowered to 0.1993 A when the model was parametrized with the inclusion of two Gaussian functions. Our results also indicate that this model is more applicable to europium complexes with beta-diketone ligands. As such, we conclude that this improved model can be considered a powerful tool for the study of lanthanide complexes and their applications, such as the modeling of light conversion molecular devices.
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ERIC Educational Resources Information Center
Crow, Wendell C.
This paper suggests ways in which manifest, physical attributes of graphic elements can be described and measured. It also proposes a preliminary conceptual model that accounts for the readily apparent, measurable variables in a visual message. The graphic elements that are described include format, typeface, and photographs/artwork. The…
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Cosine-Gaussian Schell-model sources.
Mei, Zhangrong; Korotkova, Olga
2013-07-15
We introduce a new class of partially coherent sources of Schell type with cosine-Gaussian spectral degree of coherence and confirm that such sources are physically genuine. Further, we derive the expression for the cross-spectral density function of a beam generated by the novel source propagating in free space and analyze the evolution of the spectral density and the spectral degree of coherence. It is shown that at sufficiently large distances from the source the degree of coherence of the propagating beam assumes Gaussian shape while the spectral density takes on the dark-hollow profile.
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Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution.
García-Patrón, Raúl; Cerf, Nicolas J
2006-11-10
A fully general approach to the security analysis of continuous-variable quantum key distribution (CV-QKD) is presented. Provided that the quantum channel is estimated via the covariance matrix of the quadratures, Gaussian attacks are shown to be optimal against all collective eavesdropping strategies. The proof is made strikingly simple by combining a physical model of measurement, an entanglement-based description of CV-QKD, and a recent powerful result on the extremality of Gaussian states [M. M. Wolf, Phys. Rev. Lett. 96, 080502 (2006)10.1103/PhysRevLett.96.080502].
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Classification of ECG beats using deep belief network and active learning.
G, Sayantan; T, Kien P; V, Kadambari K
2018-04-12
A new semi-supervised approach based on deep learning and active learning for classification of electrocardiogram signals (ECG) is proposed. The objective of the proposed work is to model a scientific method for classification of cardiac irregularities using electrocardiogram beats. The model follows the Association for the Advancement of medical instrumentation (AAMI) standards and consists of three phases. In phase I, feature representation of ECG is learnt using Gaussian-Bernoulli deep belief network followed by a linear support vector machine (SVM) training in the consecutive phase. It yields three deep models which are based on AAMI-defined classes, namely N, V, S, and F. In the last phase, a query generator is introduced to interact with the expert to label few beats to improve accuracy and sensitivity. The proposed approach depicts significant improvement in accuracy with minimal queries posed to the expert and fast online training as tested on the MIT-BIH Arrhythmia Database and the MIT-BIH Supra-ventricular Arrhythmia Database (SVDB). With 100 queries labeled by the expert in phase III, the method achieves an accuracy of 99.5% in "S" versus all classifications (SVEB) and 99.4% accuracy in "V " versus all classifications (VEB) on MIT-BIH Arrhythmia Database. In a similar manner, it is attributed that an accuracy of 97.5% for SVEB and 98.6% for VEB on SVDB database is achieved respectively. Graphical Abstract Reply- Deep belief network augmented by active learning for efficient prediction of arrhythmia.
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Henao-Holguín, Laura Verónica; Basiuk, Vladimir A
2015-06-01
Nickel(II) complex of 5,14-dihydro-6,8,15,17-tetramethyldibenzo[b,i][1,4,8,11] tetraazacyclotetradecine (NiTMTAA), which can be employed for noncovalent functionalization of carbon nanotubes (CNTs), represents a more complex and interesting case in terms of structure of the resulting nanohybrids, as compared to the related materials functionalized with porphyrins and phthalocyanines. Due to its saddle shape, the NiTMTAA molecule adsorbed can adopt different, energetically non-equivalent orientations with respect to CNT, depending on whether CH3 or C6H4 groups contact the latter. The main goal of the present work was to provide information on the interactions of NiTMTAA with simple single-walled CNT (SWNT) models accessible for dispersion-corrected DFT calculations. For reasons of comparison, we employed three such functionals: M06-2X and LC-BLYP as implemented in Gaussian 09 package, and PBE-G as implemented in Materials Studio 6.0. In order to roughly estimate the effect of nanotube chirality on the interaction strenght, we considered two short closed-end SWNT models (also referred to as 'elongated fullerenes'), one armchair and one zigzag, derived from C60 and C80 hemispheres. In addition, we calculated similar complexes with C60, as well as I h and D 5h isomers of C80. The results were analyzed in terms of optimized geometries, formation energies, HOMO-LUMO gap energies, and intermolecular separations. Graphical Abstract Interaction of Ni(II) tetraazaannulene complex with elongated fullerenes.
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NASA Astrophysics Data System (ADS)
Selim, M. M.; Bezák, V.
2003-06-01
The one-dimensional version of the radiative transfer problem (i.e. the so-called rod model) is analysed with a Gaussian random extinction function (x). Then the optical length X = 0 Ldx(x) is a Gaussian random variable. The transmission and reflection coefficients, T(X) and R(X), are taken as infinite series. When these series (and also when the series representing T 2(X), T 2(X), R(X)T(X), etc.) are averaged, term by term, according to the Gaussian statistics, the series become divergent after averaging. As it was shown in a former paper by the authors (in Acta Physica Slovaca (2003)), a rectification can be managed when a `modified' Gaussian probability density function is used, equal to zero for X > 0 and proportional to the standard Gaussian probability density for X > 0. In the present paper, the authors put forward an alternative, showing that if the m.s.r. of X is sufficiently small in comparison with & $bar X$ ; , the standard Gaussian averaging is well functional provided that the summation in the series representing the variable T m-j (X)R j (X) (m = 1,2,..., j = 1,...,m) is truncated at a well-chosen finite term. The authors exemplify their analysis by some numerical calculations.
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Aberration analysis and calculation in system of Gaussian beam illuminates lenslet array
NASA Astrophysics Data System (ADS)
Zhao, Zhu; Hui, Mei; Zhou, Ping; Su, Tianquan; Feng, Yun; Zhao, Yuejin
2014-09-01
Low order aberration was founded when focused Gaussian beam imaging at Kodak KAI -16000 image detector, which is integrated with lenslet array. Effect of focused Gaussian beam and numerical simulation calculation of the aberration were presented in this paper. First, we set up a model of optical imaging system based on previous experiment. Focused Gaussian beam passed through a pinhole and was received by Kodak KAI -16000 image detector whose microlenses of lenslet array were exactly focused on sensor surface. Then, we illustrated the characteristics of focused Gaussian beam and the effect of relative space position relations between waist of Gaussian beam and front spherical surface of microlenses to the aberration. Finally, we analyzed the main element of low order aberration and calculated the spherical aberration caused by lenslet array according to the results of above two steps. Our theoretical calculations shown that , the numerical simulation had a good agreement with the experimental result. Our research results proved that spherical aberration was the main element and made up about 93.44% of the 48 nm error, which was demonstrated in previous experiment. The spherical aberration is inversely proportional to the value of divergence distance between microlens and waist, and directly proportional to the value of the Gaussian beam waist radius.
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Mabrouk, Rostom; Dubeau, François; Bentabet, Layachi
2013-01-01
Kinetic modeling of metabolic and physiologic cardiac processes in small animals requires an input function (IF) and a tissue time-activity curves (TACs). In this paper, we present a mathematical method based on independent component analysis (ICA) to extract the IF and the myocardium's TACs directly from dynamic positron emission tomography (PET) images. The method assumes a super-Gaussian distribution model for the blood activity, and a sub-Gaussian distribution model for the tissue activity. Our appreach was applied on 22 PET measurement sets of small animals, which were obtained from the three most frequently used cardiac radiotracers, namely: desoxy-fluoro-glucose ((18)F-FDG), [(13)N]-ammonia, and [(11)C]-acetate. Our study was extended to PET human measurements obtained with the Rubidium-82 ((82) Rb) radiotracer. The resolved mathematical IF values compare favorably to those derived from curves extracted from regions of interest (ROI), suggesting that the procedure presents a reliable alternative to serial blood sampling for small-animal cardiac PET studies.
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Remaining Useful Life Prediction for Lithium-Ion Batteries Based on Gaussian Processes Mixture
Li, Lingling; Wang, Pengchong; Chao, Kuei-Hsiang; Zhou, Yatong; Xie, Yang
2016-01-01
The remaining useful life (RUL) prediction of Lithium-ion batteries is closely related to the capacity degeneration trajectories. Due to the self-charging and the capacity regeneration, the trajectories have the property of multimodality. Traditional prediction models such as the support vector machines (SVM) or the Gaussian Process regression (GPR) cannot accurately characterize this multimodality. This paper proposes a novel RUL prediction method based on the Gaussian Process Mixture (GPM). It can process multimodality by fitting different segments of trajectories with different GPR models separately, such that the tiny differences among these segments can be revealed. The method is demonstrated to be effective for prediction by the excellent predictive result of the experiments on the two commercial and chargeable Type 1850 Lithium-ion batteries, provided by NASA. The performance comparison among the models illustrates that the GPM is more accurate than the SVM and the GPR. In addition, GPM can yield the predictive confidence interval, which makes the prediction more reliable than that of traditional models. PMID:27632176
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Liu, T; Yu, D; Beitler, J
Purpose: Xerostomia (dry mouth), secondary to parotid-gland injury, is a distressing side-effect in head-and-neck radiotherapy (RT). This study's purpose is to develop a novel ultrasound technique to quantitatively evaluate post-RT parotid-gland injury. Methods: Recent ultrasound studies have shown that healthy parotid glands exhibit homogeneous echotexture, whereas post-RT parotid glands are often heterogeneous, with multiple hypoechoic (inflammation) or hyperechoic (fibrosis) regions. We propose to use a Gaussian mixture model to analyze the ultrasonic echo-histogram of the parotid glands. An IRB-approved clinical study was conducted: (1) control-group: 13 healthy-volunteers, served as the control; (2) acutetoxicity group − 20 patients (mean age: 62.5more » ± 8.9 years, follow-up: 2.0±0.8 months); and (3) late-toxicity group − 18 patients (mean age: 60.7 ± 7.3 years, follow-up: 20.1±10.4 months). All patients experienced RTOG grade 1 or 2 salivary-gland toxicity. Each participant underwent an ultrasound scan (10 MHz) of the bilateral parotid glands. An echo-intensity histogram was derived for each parotid and a Gaussian mixture model was used to fit the histogram using expectation maximization (EM) algorithm. The quality of the fitting was evaluated with the R-squared value. Results: (1) Controlgroup: all parotid glands fitted well with one Gaussian component, with a mean intensity of 79.8±4.9 (R-squared>0.96). (2) Acute-toxicity group: 37 of the 40 post-RT parotid glands fitted well with two Gaussian components, with a mean intensity of 42.9±7.4, 73.3±12.2 (R-squared>0.95). (3) Latetoxicity group: 32 of the 36 post-RT parotid fitted well with 3 Gaussian components, with mean intensities of 49.7±7.6, 77.2±8.7, and 118.6±11.8 (R-squared>0.98). Conclusion: RT-associated parotid-gland injury is common in head-and-neck RT, but challenging to assess. This work has demonstrated that the Gaussian mixture model of the echo-histogram could quantify acute and late toxicity of the parotid glands. This study provides meaningful preliminary data from future observational and interventional clinical research.« less
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Han, Fang; Liu, Han
2017-02-01
Correlation matrix plays a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson's sample correlation matrix. Although Pearson's sample correlation matrix enjoys various good properties under Gaussian models, its not an effective estimator when facing heavy-tail distributions with possible outliers. As a robust alternative, Han and Liu (2013b) advocated the use of a transformed version of the Kendall's tau sample correlation matrix in estimating high dimensional latent generalized correlation matrix under the transelliptical distribution family (or elliptical copula). The transelliptical family assumes that after unspecified marginal monotone transformations, the data follow an elliptical distribution. In this paper, we study the theoretical properties of the Kendall's tau sample correlation matrix and its transformed version proposed in Han and Liu (2013b) for estimating the population Kendall's tau correlation matrix and the latent Pearson's correlation matrix under both spectral and restricted spectral norms. With regard to the spectral norm, we highlight the role of "effective rank" in quantifying the rate of convergence. With regard to the restricted spectral norm, we for the first time present a "sign subgaussian condition" which is sufficient to guarantee that the rank-based correlation matrix estimator attains the optimal rate of convergence. In both cases, we do not need any moment condition.
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Transformation of Graphical ECA Policies into Executable PonderTalk Code
NASA Astrophysics Data System (ADS)
Romeikat, Raphael; Sinsel, Markus; Bauer, Bernhard
Rules are becoming more and more important in business modeling and systems engineering and are recognized as a high-level programming paradigma. For the effective development of rules it is desired to start at a high level, e.g. with graphical rules, and to refine them into code of a particular rule language for implementation purposes later. An model-driven approach is presented in this paper to transform graphical rules into executable code in a fully automated way. The focus is on event-condition-action policies as a special rule type. These are modeled graphically and translated into the PonderTalk language. The approach may be extended to integrate other rule types and languages as well.
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Hollow Gaussian Schell-model beam and its propagation
NASA Astrophysics Data System (ADS)
Wang, Li-Gang; Wang, Li-Qin
2008-03-01
In this paper, we present a new model, hollow Gaussian Schell-model beams (HGSMBs), to describe the practical dark hollow beams. An analytical propagation formula for HGSMBs passing through a paraxial first-order optical system is derived based on the theory of coherence. Based on the derived formula, an application example showing the influence of spatial coherence on the propagation of beams is illustrated. It is found that the beam propagating properties of HGSMBs will be greatly affected by their spatial coherence. Our model provides a very convenient way for analyzing the propagation properties of partially coherent dark hollow beams.
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Predicting Error Bars for QSAR Models
NASA Astrophysics Data System (ADS)
Schroeter, Timon; Schwaighofer, Anton; Mika, Sebastian; Ter Laak, Antonius; Suelzle, Detlev; Ganzer, Ursula; Heinrich, Nikolaus; Müller, Klaus-Robert
2007-09-01
Unfavorable physicochemical properties often cause drug failures. It is therefore important to take lipophilicity and water solubility into account early on in lead discovery. This study presents log D7 models built using Gaussian Process regression, Support Vector Machines, decision trees and ridge regression algorithms based on 14556 drug discovery compounds of Bayer Schering Pharma. A blind test was conducted using 7013 new measurements from the last months. We also present independent evaluations using public data. Apart from accuracy, we discuss the quality of error bars that can be computed by Gaussian Process models, and ensemble and distance based techniques for the other modelling approaches.
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Jackson, M E; Gnadt, J W
1999-03-01
The object-oriented graphical programming language LabView was used to implement the numerical solution to a computational model of saccade generation in primates. The computational model simulates the activity and connectivity of anatomical strictures known to be involved in saccadic eye movements. The LabView program provides a graphical user interface to the model that makes it easy to observe and modify the behavior of each element of the model. Essential elements of the source code of the LabView program are presented and explained. A copy of the model is available for download from the internet.
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Interactive voxel graphics in virtual reality
NASA Astrophysics Data System (ADS)
Brody, Bill; Chappell, Glenn G.; Hartman, Chris
2002-06-01
Interactive voxel graphics in virtual reality poses significant research challenges in terms of interface, file I/O, and real-time algorithms. Voxel graphics is not so new, as it is the focus of a good deal of scientific visualization. Interactive voxel creation and manipulation is a more innovative concept. Scientists are understandably reluctant to manipulate data. They collect or model data. A scientific analogy to interactive graphics is the generation of initial conditions for some model. It is used as a method to test those models. We, however, are in the business of creating new data in the form of graphical imagery. In our endeavor, science is a tool and not an end. Nevertheless, there is a whole class of interactions and associated data generation scenarios that are natural to our way of working and that are also appropriate to scientific inquiry. Annotation by sketching or painting to point to and distinguish interesting and important information is very significant for science as well as art. Annotation in 3D is difficult without a good 3D interface. Interactive graphics in virtual reality is an appropriate approach to this problem.
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Working covariance model selection for generalized estimating equations.
Carey, Vincent J; Wang, You-Gan
2011-11-20
We investigate methods for data-based selection of working covariance models in the analysis of correlated data with generalized estimating equations. We study two selection criteria: Gaussian pseudolikelihood and a geodesic distance based on discrepancy between model-sensitive and model-robust regression parameter covariance estimators. The Gaussian pseudolikelihood is found in simulation to be reasonably sensitive for several response distributions and noncanonical mean-variance relations for longitudinal data. Application is also made to a clinical dataset. Assessment of adequacy of both correlation and variance models for longitudinal data should be routine in applications, and we describe open-source software supporting this practice. Copyright © 2011 John Wiley & Sons, Ltd.
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NASA Astrophysics Data System (ADS)
M, H. Moghtader Dindarlu; M Kavosh, Tehrani; H, Saghafifar; A, Maleki
2015-12-01
In this paper, according to the temperature and strain distribution obtained by considering the Gaussian pump profile and dependence of physical properties on temperature, we derive an analytical model for refractive index variations of the diode side-pumped Nd:YAG laser rod. Then we evaluate this model by numerical solution and our maximum relative errors are 5% and 10% for variations caused by thermo-optical and thermo-mechanical effects; respectively. Finally, we present an analytical model for calculating the focal length of the thermal lens and spherical aberration. This model is evaluated by experimental results.
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NASA Technical Reports Server (NTRS)
Hirt, E. F.; Fox, G. L.
1982-01-01
Two specific NASTRAN preprocessors and postprocessors are examined. A postprocessor for dynamic analysis and a graphical interactive package for model generation and review of resuls are presented. A computer program that provides response spectrum analysis capability based on data from NASTRAN finite element model is described and the GIFTS system, a graphic processor to augment NASTRAN is introduced.
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2017-08-01
access to the GPU for general purpose processing .5 CUDA is designed to work easily with multiple programming languages , including Fortran. CUDA is a...Using Graphics Processing Unit (GPU) Computing by Leelinda P Dawson Approved for public release; distribution unlimited...The Performance Improvement of the Lagrangian Particle Dispersion Model (LPDM) Using Graphics Processing Unit (GPU) Computing by Leelinda
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Propagation of flat-topped multi-Gaussian beams through a double-lens system with apertures.
Gao, Yanqi; Zhu, Baoqiang; Liu, Daizhong; Lin, Zunqi
2009-07-20
A general model for different apertures and flat-topped laser beams based on the multi-Gaussian function is developed. The general analytical expression for the propagation of a flat-topped beam through a general double-lens system with apertures is derived using the above model. Then, the propagation characteristics of the flat-topped beam through a spatial filter are investigated by using a simplified analytical expression. Based on the Fluence beam contrast and the Fill factor, the influences of a pinhole size on the propagation of the flat-topped multi-Gaussian beam (FMGB) through the spatial filter are illustrated. An analytical expression for the propagation of the FMGB through the spatial filter with a misaligned pinhole is presented, and the influences of the pinhole offset are evaluated.
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NASA Astrophysics Data System (ADS)
Weitzen, J. A.; Bourque, S.; Ostergaard, J. C.; Bench, P. M.; Baily, A. D.
1991-04-01
Analysis of data from recent experiments leads to the observation that distributions of underdense meteor trail peak signal amplitudes differ from classic predictions. In this paper the distribution of trail amplitudes in decibels relative 1 W (dBw) is considered, and it is shown that Lindberg's theorem can be used to apply central limit arguments to this problem. It is illustrated that a Gaussian model for the distribution of the logarithm of the peak received signal level of underdense trails provides a better fit to data than classic approaches. Distributions of underdense meteor trail amplitudes at five frequencies are compared to a Gaussian distribution and the classic model. Implications of the Gaussian assumption on the design of communication systems are discussed.
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NASA Astrophysics Data System (ADS)
Makarewicz, H. D.; Parente, M.; Perry, K. A.; McKeown, N. K.; Bishop, J. L.
2009-12-01
Aqueous processes have been inferred at the Libya Montes rim/terrace complex of the southern Isidis Basin due to the dense concentration of valley networks [1]. Coordinated CRISM-HiRISE investigations of this region characterized discrete units of ancient phyllosilicate deposits covered by an olivine-rich material and a pyroxene caprock [2]. CRISM mapping data show minor phyllosilicate abundances widespread throughout the Southern Highlands [3], which are dominated by low-Ca pyroxene bearing material [4,5]. The carbonate magnesite has also been located throughout this area [6] and at Libya Montes [7]. Our current study involves detailed characterization of the minerals present at Libya Montes through implementation of improved automated Gaussian modeling methods. We have developed an automated procedure for modeling spectral features using Gaussians that has been successfully applied to laboratory studies and hyperspectral analyses of Mars [8,9,10,11]. Several studies are being conducted to improve and validate these models. These include a comparison of initialization methods, continuum methods, optimization algorithms, and modeled functions. The modeled functions compared include Gaussians, saturated Gaussians, and Lorentzians. This algorithm and the modeling studies are currently being applied towards analyses of CRISM hyperspectral images of Libya Montes and laboratory spectra of mineral mixtures. Specifically, olivine, pyroxene, phyllosilicate, and carbonate deposits are being modeled and classified by composition in CRISM images. References [1]Crumpler, L. S., and K. L. Tanaka (2003) J. Geophys. Res., 108, DOI: 8010.1029/2002JE002040. [2]Bishop, J. L., et al. (2007) 7th Int'l Mars Conf. [3]Mustard, J. F., et al. (2008) Nature, 454, 07305. [4]Bibring, J.-P., et al. (2005) Science, 307,1576. [5]Mustard, J. F., et al.(2005) Science, 307, 1594. [6]Ehlmann, B. L., et al. (2008) Science, 322, 1828. [7]Perry, K., et al. (2009) AGU Fall Mtng. [8]Makarewicz, H. D., et al. (2009) IEEE Whispers Wkshp. [9]Makarewicz, H. D., et al. (2008) AGU Fall Mtng. [10]Makarewicz, H. D., et al. (2009) LPSC. [11]Makarewicz, H. D., et al. (2009) Lunar Sci Forum.
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Geometric database maintenance using CCTV cameras and overlay graphics
NASA Astrophysics Data System (ADS)
Oxenberg, Sheldon C.; Landell, B. Patrick; Kan, Edwin
1988-01-01
An interactive graphics system using closed circuit television (CCTV) cameras for remote verification and maintenance of a geometric world model database has been demonstrated in GE's telerobotics testbed. The database provides geometric models and locations of objects viewed by CCTV cameras and manipulated by telerobots. To update the database, an operator uses the interactive graphics system to superimpose a wireframe line drawing of an object with known dimensions on a live video scene containing that object. The methodology used is multipoint positioning to easily superimpose a wireframe graphic on the CCTV image of an object in the work scene. An enhanced version of GE's interactive graphics system will provide the object designation function for the operator control station of the Jet Propulsion Laboratory's telerobot demonstration system.
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NASA Astrophysics Data System (ADS)
Tripathi, Bharat B.; Marchiano, Régis; Baskar, Sambandam; Coulouvrat, François
2015-10-01
Propagation of acoustical shock waves in complex geometry is a topic of interest in the field of nonlinear acoustics. For instance, simulation of Buzz Saw Noice requires the treatment of shock waves generated by the turbofan through the engines of aeroplanes with complex geometries and wall liners. Nevertheless, from a numerical point of view it remains a challenge. The two main hurdles are to take into account the complex geometry of the domain and to deal with the spurious oscillations (Gibbs phenomenon) near the discontinuities. In this work, first we derive the conservative hyperbolic system of nonlinear acoustics (up to quadratic nonlinear terms) using the fundamental equations of fluid dynamics. Then, we propose to adapt the classical nodal discontinuous Galerkin method to develop a high fidelity solver for nonlinear acoustics. The discontinuous Galerkin method is a hybrid of finite element and finite volume method and is very versatile to handle complex geometry. In order to obtain better performance, the method is parallelized on Graphical Processing Units. Like other numerical methods, discontinuous Galerkin method suffers with the problem of Gibbs phenomenon near the shock, which is a numerical artifact. Among the various ways to manage these spurious oscillations, we choose the method of parabolic regularization. Although, the introduction of artificial viscosity into the system is a popular way of managing shocks, we propose a new approach of introducing smooth artificial viscosity locally in each element, wherever needed. Firstly, a shock sensor using the linear coefficients of the spectral solution is used to locate the position of the discontinuities. Then, a viscosity coefficient depending on the shock sensor is introduced into the hyperbolic system of equations, only in the elements near the shock. The viscosity is applied as a two-dimensional Gaussian patch with its shape parameters depending on the element dimensions, referred here as Element Centered Smooth Artificial Viscosity. Using this numerical solver, various numerical experiments are presented for one and two-dimensional test cases in homogeneous and quiescent medium. This work is funded by CEFIPRA (Indo-French Centre for the Promotion of Advance Research) and partially aided by EGIDE (Campus France).
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NASA Astrophysics Data System (ADS)
Waubke, Holger; Kasess, Christian H.
2016-11-01
Devices that emit structure-borne sound are commonly decoupled by elastic components to shield the environment from acoustical noise and vibrations. The elastic elements often have a hysteretic behavior that is typically neglected. In order to take hysteretic behavior into account, Bouc developed a differential equation for such materials, especially joints made of rubber or equipped with dampers. In this work, the Bouc model is solved by means of the Gaussian closure technique based on the Kolmogorov equation. Kolmogorov developed a method to derive probability density functions for arbitrary explicit first-order vector differential equations under white noise excitation using a partial differential equation of a multivariate conditional probability distribution. Up to now no analytical solution of the Kolmogorov equation in conjunction with the Bouc model exists. Therefore a wide range of approximate solutions, especially the statistical linearization, were developed. Using the Gaussian closure technique that is an approximation to the Kolmogorov equation assuming a multivariate Gaussian distribution an analytic solution is derived in this paper for the Bouc model. For the stationary case the two methods yield equivalent results, however, in contrast to statistical linearization the presented solution allows to calculate the transient behavior explicitly. Further, stationary case leads to an implicit set of equations that can be solved iteratively with a small number of iterations and without instabilities for specific parameter sets.
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Sonka, Milan; Abramoff, Michael D.
2013-01-01
In this paper, MMSE estimator is employed for noise-free 3D OCT data recovery in 3D complex wavelet domain. Since the proposed distribution for noise-free data plays a key role in the performance of MMSE estimator, a priori distribution for the pdf of noise-free 3D complex wavelet coefficients is proposed which is able to model the main statistical properties of wavelets. We model the coefficients with a mixture of two bivariate Gaussian pdfs with local parameters which are able to capture the heavy-tailed property and inter- and intrascale dependencies of coefficients. In addition, based on the special structure of OCT images, we use an anisotropic windowing procedure for local parameters estimation that results in visual quality improvement. On this base, several OCT despeckling algorithms are obtained based on using Gaussian/two-sided Rayleigh noise distribution and homomorphic/nonhomomorphic model. In order to evaluate the performance of the proposed algorithm, we use 156 selected ROIs from 650 × 512 × 128 OCT dataset in the presence of wet AMD pathology. Our simulations show that the best MMSE estimator using local bivariate mixture prior is for the nonhomomorphic model in the presence of Gaussian noise which results in an improvement of 7.8 ± 1.7 in CNR. PMID:24222760
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GAUSSIAN BEAM LASER RESONATOR PROGRAM
NASA Technical Reports Server (NTRS)
Cross, P. L.
1994-01-01
In designing a laser cavity, the laser engineer is frequently concerned with more than the stability of the resonator. Other considerations include the size of the beam at various optical surfaces within the resonator or the performance of intracavity line-narrowing or other optical elements. Laser resonators obey the laws of Gaussian beam propagation, not geometric optics. The Gaussian Beam Laser Resonator Program models laser resonators using Gaussian ray trace techniques. It can be used to determine the propagation of radiation through laser resonators. The algorithm used in the Gaussian Beam Resonator program has three major components. First, the ray transfer matrix for the laser resonator must be calculated. Next calculations of the initial beam parameters, specifically, the beam stability, the beam waist size and location for the resonator input element, and the wavefront curvature and beam radius at the input surface to the first resonator element are performed. Finally the propagation of the beam through the optical elements is computed. The optical elements can be modeled as parallel plates, lenses, mirrors, dummy surfaces, or Gradient Index (GRIN) lenses. A Gradient Index lens is a good approximation of a laser rod operating under a thermal load. The optical system may contain up to 50 elements. In addition to the internal beam elements the optical system may contain elements external to the resonator. The Gaussian Beam Resonator program was written in Microsoft FORTRAN (Version 4.01). It was developed for the IBM PS/2 80-071 microcomputer and has been implemented on an IBM PC compatible under MS DOS 3.21. The program was developed in 1988 and requires approximately 95K bytes to operate.
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Near grazing scattering from non-Gaussian ocean surfaces
NASA Technical Reports Server (NTRS)
Kim, Yunjin; Rodriguez, Ernesto
1993-01-01
We investigate the behavior of the scattered electromagnetic waves from non-Gaussian ocean surfaces at near grazing incidence. Even though the scattering mechanisms at moderate incidence angles are relatively well understood, the same is not true for near grazing rough surface scattering. However, from the experimental ocean scattering data, it has been observed that the backscattering cross section of a horizontally polarized wave can be as large as the vertical counterpart at near grazing incidence. In addition, these returns are highly intermittent in time. There have been some suggestions that these unexpected effects may come from shadowing or feature scattering. Using numerical scattering simulations, it can be shown that the horizontal backscattering cannot be larger than the vertical one for the Gaussian surfaces. Our main objective of this study is to gain a clear understanding of scattering mechanisms underlying the near grazing ocean scattering. In order to evaluate the backscattering cross section from ocean surfaces at near grazing incidence, both the hydrodynamic modeling of ocean surfaces and an accurate near grazing scattering theory are required. For the surface modeling, we generate Gaussian surfaces from the ocean surface power spectrum which is derived using several experimental data. Then, weakly nonlinear large scale ocean surfaces are generated following Longuet-Higgins. In addition, the modulation of small waves by large waves is included using the conservation of wave action. For surface scattering, we use MOM (Method of Moments) to calculate the backscattering from scattering patches with the two scale shadowing approximation. The differences between Gaussian and non-Gaussian surface scattering at near grazing incidence are presented.
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A stochastic-geometric model of soil variation in Pleistocene patterned ground
NASA Astrophysics Data System (ADS)
Lark, Murray; Meerschman, Eef; Van Meirvenne, Marc
2013-04-01
In this paper we examine the spatial variability of soil in parent material with complex spatial structure which arises from complex non-linear geomorphic processes. We show that this variability can be better-modelled by a stochastic-geometric model than by a standard Gaussian random field. The benefits of the new model are seen in the reproduction of features of the target variable which influence processes like water movement and pollutant dispersal. Complex non-linear processes in the soil give rise to properties with non-Gaussian distributions. Even under a transformation to approximate marginal normality, such variables may have a more complex spatial structure than the Gaussian random field model of geostatistics can accommodate. In particular the extent to which extreme values of the variable are connected in spatially coherent regions may be misrepresented. As a result, for example, geostatistical simulation generally fails to reproduce the pathways for preferential flow in an environment where coarse infill of former fluvial channels or coarse alluvium of braided streams creates pathways for rapid movement of water. Multiple point geostatistics has been developed to deal with this problem. Multiple point methods proceed by sampling from a set of training images which can be assumed to reproduce the non-Gaussian behaviour of the target variable. The challenge is to identify appropriate sources of such images. In this paper we consider a mode of soil variation in which the soil varies continuously, exhibiting short-range lateral trends induced by local effects of the factors of soil formation which vary across the region of interest in an unpredictable way. The trends in soil variation are therefore only apparent locally, and the soil variation at regional scale appears random. We propose a stochastic-geometric model for this mode of soil variation called the Continuous Local Trend (CLT) model. We consider a case study of soil formed in relict patterned ground with pronounced lateral textural variations arising from the presence of infilled ice-wedges of Pleistocene origin. We show how knowledge of the pedogenetic processes in this environment, along with some simple descriptive statistics, can be used to select and fit a CLT model for the apparent electrical conductivity (ECa) of the soil. We use the model to simulate realizations of the CLT process, and compare these with realizations of a fitted Gaussian random field. We show how statistics that summarize the spatial coherence of regions with small values of ECa, which are expected to have coarse texture and so larger saturated hydraulic conductivity, are better reproduced by the CLT model than by the Gaussian random field. This suggests that the CLT model could be used to generate an unlimited supply of training images to allow multiple point geostatistical simulation or prediction of this or similar variables.
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The Gaussian copula model for the joint deficit index for droughts
NASA Astrophysics Data System (ADS)
Van de Vyver, H.; Van den Bergh, J.
2018-06-01
The characterization of droughts and their impacts is very dependent on the time scale that is involved. In order to obtain an overall drought assessment, the cumulative effects of water deficits over different times need to be examined together. For example, the recently developed joint deficit index (JDI) is based on multivariate probabilities of precipitation over various time scales from 1- to 12-months, and was constructed from empirical copulas. In this paper, we examine the Gaussian copula model for the JDI. We model the covariance across the temporal scales with a two-parameter function that is commonly used in the specific context of spatial statistics or geostatistics. The validity of the covariance models is demonstrated with long-term precipitation series. Bootstrap experiments indicate that the Gaussian copula model has advantages over the empirical copula method in the context of drought severity assessment: (i) it is able to quantify droughts outside the range of the empirical copula, (ii) provides adequate drought quantification, and (iii) provides a better understanding of the uncertainty in the estimation.
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Kwak, Sehyun; Svensson, J; Brix, M; Ghim, Y-C
2016-02-01
A Bayesian model of the emission spectrum of the JET lithium beam has been developed to infer the intensity of the Li I (2p-2s) line radiation and associated uncertainties. The detected spectrum for each channel of the lithium beam emission spectroscopy system is here modelled by a single Li line modified by an instrumental function, Bremsstrahlung background, instrumental offset, and interference filter curve. Both the instrumental function and the interference filter curve are modelled with non-parametric Gaussian processes. All free parameters of the model, the intensities of the Li line, Bremsstrahlung background, and instrumental offset, are inferred using Bayesian probability theory with a Gaussian likelihood for photon statistics and electronic background noise. The prior distributions of the free parameters are chosen as Gaussians. Given these assumptions, the intensity of the Li line and corresponding uncertainties are analytically available using a Bayesian linear inversion technique. The proposed approach makes it possible to extract the intensity of Li line without doing a separate background subtraction through modulation of the Li beam.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Friberg, Ari T.; Visser, Taco D.; Wolf, Emil
A reciprocity inequality is derived, involving the effective size of a planar, secondary, Gaussian Schell-model source and the effective angular spread of the beam that the source generates. The analysis is shown to imply that a fully spatially coherent source of that class (which generates the lowest-order Hermite-Gaussian laser mode) has certain minimal properties. (c) 2000 Optical Society of America.
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NASA Astrophysics Data System (ADS)
Basin, M.; Maldonado, J. J.; Zendejo, O.
2016-07-01
This paper proposes new mean-square filter and parameter estimator design for linear stochastic systems with unknown parameters over linear observations, where unknown parameters are considered as combinations of Gaussian and Poisson white noises. The problem is treated by reducing the original problem to a filtering problem for an extended state vector that includes parameters as additional states, modelled as combinations of independent Gaussian and Poisson processes. The solution to this filtering problem is based on the mean-square filtering equations for incompletely polynomial states confused with Gaussian and Poisson noises over linear observations. The resulting mean-square filter serves as an identifier for the unknown parameters. Finally, a simulation example shows effectiveness of the proposed mean-square filter and parameter estimator.
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Gyrator transform of Gaussian beams with phase difference and generation of hollow beam
NASA Astrophysics Data System (ADS)
Xiao, Zhiyu; Xia, Hui; Yu, Tao; Xie, Ding; Xie, Wenke
2018-03-01
The optical expression of Gaussian beams with phase difference, which is caused by gyrator transform (GT), has been obtained. The intensity and phase distribution of transform Gaussian beams are analyzed. It is found that the circular hollow vortex beam can be obtained by overlapping two GT Gaussian beams with π phase difference. The effect of parameters on the intensity and phase distributions of the hollow vortex beam are discussed. The results show that the shape of intensity distribution is significantly influenced by GT angle α and propagation distance z. The size of the hollow vortex beam can be adjusted by waist width ω 0. Compared with previously reported results, the work shows that the hollow vortex beam can be obtained without any model conversion of the light source.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Zentner, I.; Ferré, G., E-mail: gregoire.ferre@ponts.org; Poirion, F.
2016-06-01
In this paper, a new method for the identification and simulation of non-Gaussian and non-stationary stochastic fields given a database is proposed. It is based on two successive biorthogonal decompositions aiming at representing spatio–temporal stochastic fields. The proposed double expansion allows to build the model even in the case of large-size problems by separating the time, space and random parts of the field. A Gaussian kernel estimator is used to simulate the high dimensional set of random variables appearing in the decomposition. The capability of the method to reproduce the non-stationary and non-Gaussian features of random phenomena is illustrated bymore » applications to earthquakes (seismic ground motion) and sea states (wave heights).« less
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Accretion rates of protoplanets 2: Gaussian distribution of planestesimal velocities
NASA Technical Reports Server (NTRS)
Greenzweig, Yuval; Lissauer, Jack J.
1991-01-01
The growth rate of a protoplanet embedded in a uniform surface density disk of planetesimals having a triaxial Gaussian velocity distribution was calculated. The longitudes of the aspses and nodes of the planetesimals are uniformly distributed, and the protoplanet is on a circular orbit. The accretion rate in the two body approximation is enhanced by a factor of approximately 3, compared to the case where all planetesimals have eccentricity and inclination equal to the root mean square (RMS) values of those variables in the Gaussian distribution disk. Numerical three body integrations show comparable enhancements, except when the RMS initial planetesimal eccentricities are extremely small. This enhancement in accretion rate should be incorporated by all models, analytical or numerical, which assume a single random velocity for all planetesimals, in lieu of a Gaussian distribution.
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Gyrator transform of Gaussian beams with phase difference and generation of hollow beam
NASA Astrophysics Data System (ADS)
Xiao, Zhiyu; Xia, Hui; Yu, Tao; Xie, Ding; Xie, Wenke
2018-06-01
The optical expression of Gaussian beams with phase difference, which is caused by gyrator transform (GT), has been obtained. The intensity and phase distribution of transform Gaussian beams are analyzed. It is found that the circular hollow vortex beam can be obtained by overlapping two GT Gaussian beams with π phase difference. The effect of parameters on the intensity and phase distributions of the hollow vortex beam are discussed. The results show that the shape of intensity distribution is significantly influenced by GT angle α and propagation distance z. The size of the hollow vortex beam can be adjusted by waist width ω 0. Compared with previously reported results, the work shows that the hollow vortex beam can be obtained without any model conversion of the light source.
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Stable Lévy motion with inverse Gaussian subordinator
NASA Astrophysics Data System (ADS)
Kumar, A.; Wyłomańska, A.; Gajda, J.
2017-09-01
In this paper we study the stable Lévy motion subordinated by the so-called inverse Gaussian process. This process extends the well known normal inverse Gaussian (NIG) process introduced by Barndorff-Nielsen, which arises by subordinating ordinary Brownian motion (with drift) with inverse Gaussian process. The NIG process found many interesting applications, especially in financial data description. We discuss here the main features of the introduced subordinated process, such as distributional properties, existence of fractional order moments and asymptotic tail behavior. We show the connection of the process with continuous time random walk. Further, the governing fractional partial differential equations for the probability density function is also obtained. Moreover, we discuss the asymptotic distribution of sample mean square displacement, the main tool in detection of anomalous diffusion phenomena (Metzler et al., 2014). In order to apply the stable Lévy motion time-changed by inverse Gaussian subordinator we propose a step-by-step procedure of parameters estimation. At the end, we show how the examined process can be useful to model financial time series.
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Ince Gaussian beams in strongly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Deng, Dongmei; Guo, Qi
2008-07-01
Based on the Snyder-Mitchell model that describes the beam propagation in strongly nonlocal nonlinear media, the close forms of Ince-Gaussian (IG) beams have been found. The transverse structures of the IG beams are described by the product of the Ince polynomials and the Gaussian function. Depending on the input power of the beams, the IG beams can be either a soliton state or a breather state. The IG beams constitute the exact and continuous transition modes between Hermite-Gaussian beams and Laguerre-Gaussian beams. The IG vortex beams can be constructed by a linear combination of the even and odd IG beams. The transverse intensity pattern of IG vortex beams consists of elliptic rings, whose number and ellipticity can be controlled, and a phase displaying a number of in-line vortices, each with a unitary topological charge. The analytical solutions of the IG beams are confirmed by the numerical simulations of the nonlocal nonlinear Schr\\rm \\ddot{o} dinger equation.
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Conversion of the high-mode solitons in strongly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Zhang, Xiaping
2017-01-01
The conversion of high-mode solitons propagating in Strongly Nonlocal Nonlinear Media (SNNM) in three coordinate systems, namely, the elliptic coordinate system, the rectangular coordinate system and the cylindrical coordinate system, based on the Snyder-Mitchell Model that describes the paraxial beam propagating in SNNM, is discussed. Through constituting the trial solution with modulating the Gaussian beam by Ince polynomials, the closed-solution of Gaussian beams in elliptic coordinate is accessed. The Ince-Gaussian (IG) beams constitute the exact and continuous transition modes between Hermite-Gaussian beams and Laguerre-Gaussian (LG) beams, which is controlled by the elliptic parameter. The conditions of conversion in the three types of solitons are given in relation to the Gouy phase invariability in stable propagation. The profiles of the IG breather at a different propagating distance are numerically obtained, and the conversions of a few IG solitons are illustrated. The difference between the IG soliton and the corresponding LG soliton is remarkable from the Poynting vector and phase plots at their profiles along the propagating axis.
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Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation
NASA Technical Reports Server (NTRS)
Semper, Sean R.; Crassidis, John L.; George, Jemin; Mukherjee, Siddharth; Singla, Puneet
2015-01-01
When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented.
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NASA Astrophysics Data System (ADS)
Holoien, Thomas W.-S.; Marshall, Philip J.; Wechsler, Risa H.
2017-06-01
We describe two new open-source tools written in Python for performing extreme deconvolution Gaussian mixture modeling (XDGMM) and using a conditioned model to re-sample observed supernova and host galaxy populations. XDGMM is new program that uses Gaussian mixtures to perform density estimation of noisy data using extreme deconvolution (XD) algorithms. Additionally, it has functionality not available in other XD tools. It allows the user to select between the AstroML and Bovy et al. fitting methods and is compatible with scikit-learn machine learning algorithms. Most crucially, it allows the user to condition a model based on the known values of a subset of parameters. This gives the user the ability to produce a tool that can predict unknown parameters based on a model that is conditioned on known values of other parameters. EmpiriciSN is an exemplary application of this functionality, which can be used to fit an XDGMM model to observed supernova/host data sets and predict likely supernova parameters using a model conditioned on observed host properties. It is primarily intended to simulate realistic supernovae for LSST data simulations based on empirical galaxy properties.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Holoien, Thomas W. -S.; Marshall, Philip J.; Wechsler, Risa H.
We describe two new open-source tools written in Python for performing extreme deconvolution Gaussian mixture modeling (XDGMM) and using a conditioned model to re-sample observed supernova and host galaxy populations. XDGMM is new program that uses Gaussian mixtures to perform density estimation of noisy data using extreme deconvolution (XD) algorithms. Additionally, it has functionality not available in other XD tools. It allows the user to select between the AstroML and Bovy et al. fitting methods and is compatible with scikit-learn machine learning algorithms. Most crucially, it allows the user to condition a model based on the known values of amore » subset of parameters. This gives the user the ability to produce a tool that can predict unknown parameters based on a model that is conditioned on known values of other parameters. EmpiriciSN is an exemplary application of this functionality, which can be used to fit an XDGMM model to observed supernova/host data sets and predict likely supernova parameters using a model conditioned on observed host properties. It is primarily intended to simulate realistic supernovae for LSST data simulations based on empirical galaxy properties.« less
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NASA Astrophysics Data System (ADS)
Park, Subok; Badano, Aldo; Gallas, Brandon D.; Myers, Kyle J.
2007-03-01
Previously, a non-prewhitening matched filter (NPWMF) incorporating a model for the contrast sensitivity of the human visual system was introduced for modeling human performance in detection tasks with different viewing angles and white-noise backgrounds by Badano et al. But NPWMF observers do not perform well detection tasks involving complex backgrounds since they do not account for random backgrounds. A channelized-Hotelling observer (CHO) using difference-of-Gaussians (DOG) channels has been shown to track human performance well in detection tasks using lumpy backgrounds. In this work, a CHO with DOG channels, incorporating the model of the human contrast sensitivity, was developed similarly. We call this new observer a contrast-sensitive CHO (CS-CHO). The Barten model was the basis of our human contrast sensitivity model. A scalar was multiplied to the Barten model and varied to control the thresholding effect of the contrast sensitivity on luminance-valued images and hence the performance-prediction ability of the CS-CHO. The performance of the CS-CHO was compared to the average human performance from the psychophysical study by Park et al., where the task was to detect a known Gaussian signal in non-Gaussian distributed lumpy backgrounds. Six different signal-intensity values were used in this study. We chose the free parameter of our model to match the mean human performance in the detection experiment at the strongest signal intensity. Then we compared the model to the human at five different signal-intensity values in order to see if the performance of the CS-CHO matched human performance. Our results indicate that the CS-CHO with the chosen scalar for the contrast sensitivity predicts human performance closely as a function of signal intensity.
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Exploring super-Gaussianity toward robust information-theoretical time delay estimation.
Petsatodis, Theodoros; Talantzis, Fotios; Boukis, Christos; Tan, Zheng-Hua; Prasad, Ramjee
2013-03-01
Time delay estimation (TDE) is a fundamental component of speaker localization and tracking algorithms. Most of the existing systems are based on the generalized cross-correlation method assuming gaussianity of the source. It has been shown that the distribution of speech, captured with far-field microphones, is highly varying, depending on the noise and reverberation conditions. Thus the performance of TDE is expected to fluctuate depending on the underlying assumption for the speech distribution, being also subject to multi-path reflections and competitive background noise. This paper investigates the effect upon TDE when modeling the source signal with different speech-based distributions. An information theoretical TDE method indirectly encapsulating higher order statistics (HOS) formed the basis of this work. The underlying assumption of Gaussian distributed source has been replaced by that of generalized Gaussian distribution that allows evaluating the problem under a larger set of speech-shaped distributions, ranging from Gaussian to Laplacian and Gamma. Closed forms of the univariate and multivariate entropy expressions of the generalized Gaussian distribution are derived to evaluate the TDE. The results indicate that TDE based on the specific criterion is independent of the underlying assumption for the distribution of the source, for the same covariance matrix.
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The impact of non-Gaussianity upon cosmological forecasts
NASA Astrophysics Data System (ADS)
Repp, A.; Szapudi, I.; Carron, J.; Wolk, M.
2015-12-01
The primary science driver for 3D galaxy surveys is their potential to constrain cosmological parameters. Forecasts of these surveys' effectiveness typically assume Gaussian statistics for the underlying matter density, despite the fact that the actual distribution is decidedly non-Gaussian. To quantify the effect of this assumption, we employ an analytic expression for the power spectrum covariance matrix to calculate the Fisher information for Baryon Acoustic Oscillation (BAO)-type model surveys. We find that for typical number densities, at kmax = 0.5h Mpc-1, Gaussian assumptions significantly overestimate the information on all parameters considered, in some cases by up to an order of magnitude. However, after marginalizing over a six-parameter set, the form of the covariance matrix (dictated by N-body simulations) causes the majority of the effect to shift to the `amplitude-like' parameters, leaving the others virtually unaffected. We find that Gaussian assumptions at such wavenumbers can underestimate the dark energy parameter errors by well over 50 per cent, producing dark energy figures of merit almost three times too large. Thus, for 3D galaxy surveys probing the non-linear regime, proper consideration of non-Gaussian effects is essential.
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Premkumar, S; Jawahar, A; Mathavan, T; Kumara Dhas, M; Sathe, V G; Milton Franklin Benial, A
2014-08-14
The molecular structure of 2-(tert-butoxycarbonyl (Boc) -amino)-5-bromopyridine (BABP) was optimized by the DFT/B3LYP method with 6-311G (d,p), 6-311++G (d,p) and cc-pVTZ basis sets using the Gaussian 09 program. The most stable optimized structure of the molecule was predicted by the DFT/B3LYP method with cc-pVTZ basis set. The vibrational frequencies, Mulliken atomic charge distribution, frontier molecular orbitals and thermodynamical parameters were calculated. These calculations were done at the ground state energy level of BABP without applying any constraint on the potential energy surface. The vibrational spectra were experimentally recorded using Fourier Transform-Infrared (FT-IR) and micro-Raman spectrometer. The computed vibrational frequencies were scaled by scale factors to yield a good agreement with observed experimental vibrational frequencies. The complete theoretically calculated and experimentally observed vibrational frequencies were assigned on the basis of Potential Energy Distribution (PED) calculation using the VEDA 4.0 program. The vibrational modes assignments were performed by using the animation option of GaussView 05 graphical interface for Gaussian program. The Mulliken atomic charge distribution was calculated for BABP molecule. The molecular reactivity and stability of BABP were also studied by frontier molecular orbitals (FMOs) analysis. Copyright © 2014 Elsevier B.V. All rights reserved.
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Process and representation in graphical displays
NASA Technical Reports Server (NTRS)
Gillan, Douglas J.; Lewis, Robert; Rudisill, Marianne
1993-01-01
Our initial model of graphic comprehension has focused on statistical graphs. Like other models of human-computer interaction, models of graphical comprehension can be used by human-computer interface designers and developers to create interfaces that present information in an efficient and usable manner. Our investigation of graph comprehension addresses two primary questions: how do people represent the information contained in a data graph?; and how do they process information from the graph? The topics of focus for graphic representation concern the features into which people decompose a graph and the representations of the graph in memory. The issue of processing can be further analyzed as two questions: what overall processing strategies do people use?; and what are the specific processing skills required?
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Wang, Hue-Yu; Wen, Ching-Feng; Chiu, Yu-Hsien; Lee, I-Nong; Kao, Hao-Yun; Lee, I-Chen; Ho, Wen-Hsien
2013-01-01
An adaptive-network-based fuzzy inference system (ANFIS) was compared with an artificial neural network (ANN) in terms of accuracy in predicting the combined effects of temperature (10.5 to 24.5°C), pH level (5.5 to 7.5), sodium chloride level (0.25% to 6.25%) and sodium nitrite level (0 to 200 ppm) on the growth rate of Leuconostoc mesenteroides under aerobic and anaerobic conditions. THE ANFIS AND ANN MODELS WERE COMPARED IN TERMS OF SIX STATISTICAL INDICES CALCULATED BY COMPARING THEIR PREDICTION RESULTS WITH ACTUAL DATA: mean absolute percentage error (MAPE), root mean square error (RMSE), standard error of prediction percentage (SEP), bias factor (Bf), accuracy factor (Af), and absolute fraction of variance (R (2)). Graphical plots were also used for model comparison. The learning-based systems obtained encouraging prediction results. Sensitivity analyses of the four environmental factors showed that temperature and, to a lesser extent, NaCl had the most influence on accuracy in predicting the growth rate of Leuconostoc mesenteroides under aerobic and anaerobic conditions. The observed effectiveness of ANFIS for modeling microbial kinetic parameters confirms its potential use as a supplemental tool in predictive mycology. Comparisons between growth rates predicted by ANFIS and actual experimental data also confirmed the high accuracy of the Gaussian membership function in ANFIS. Comparisons of the six statistical indices under both aerobic and anaerobic conditions also showed that the ANFIS model was better than all ANN models in predicting the four kinetic parameters. Therefore, the ANFIS model is a valuable tool for quickly predicting the growth rate of Leuconostoc mesenteroides under aerobic and anaerobic conditions.
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Wang, Hue-Yu; Wen, Ching-Feng; Chiu, Yu-Hsien; Lee, I-Nong; Kao, Hao-Yun; Lee, I-Chen; Ho, Wen-Hsien
2013-01-01
Background An adaptive-network-based fuzzy inference system (ANFIS) was compared with an artificial neural network (ANN) in terms of accuracy in predicting the combined effects of temperature (10.5 to 24.5°C), pH level (5.5 to 7.5), sodium chloride level (0.25% to 6.25%) and sodium nitrite level (0 to 200 ppm) on the growth rate of Leuconostoc mesenteroides under aerobic and anaerobic conditions. Methods The ANFIS and ANN models were compared in terms of six statistical indices calculated by comparing their prediction results with actual data: mean absolute percentage error (MAPE), root mean square error (RMSE), standard error of prediction percentage (SEP), bias factor (Bf), accuracy factor (Af), and absolute fraction of variance (R 2). Graphical plots were also used for model comparison. Conclusions The learning-based systems obtained encouraging prediction results. Sensitivity analyses of the four environmental factors showed that temperature and, to a lesser extent, NaCl had the most influence on accuracy in predicting the growth rate of Leuconostoc mesenteroides under aerobic and anaerobic conditions. The observed effectiveness of ANFIS for modeling microbial kinetic parameters confirms its potential use as a supplemental tool in predictive mycology. Comparisons between growth rates predicted by ANFIS and actual experimental data also confirmed the high accuracy of the Gaussian membership function in ANFIS. Comparisons of the six statistical indices under both aerobic and anaerobic conditions also showed that the ANFIS model was better than all ANN models in predicting the four kinetic parameters. Therefore, the ANFIS model is a valuable tool for quickly predicting the growth rate of Leuconostoc mesenteroides under aerobic and anaerobic conditions. PMID:23705023
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CO2 laser nerve stimulator with flat-top irradiance profile for human pain research
NASA Astrophysics Data System (ADS)
McCaughey, Ryan Gerard
Human pain research aims to further the understanding of how pain is processed by the body. Studies require a reproducible, quantifiable, scalable, pain specific and safe stimulus. Using laser light to raise the temperature of the skin to painful levels is a good method of satisfying these conditions. The CO[2] laser is an ideal source because its infrared radiation is readily absorbed in the upper layers of the skin, where the free nerve endings of pain-conveying fibres are located, causing localised heating and evoking pain. A pain stimulator based on a CO[2] laser has been developed. It is computer controlled with a graphical interface so that non specialists can easily operate the laser. Safety features have been incorporated to protect the operator and the subject. These include activation of a shutter to block the beam and shut-down of the laser, when, for example, potentially harmful laser parameters are selected or abnormal signals are sent to the laser. The CO[2] laser normally operates in TEM[00] mode, i.e. the irradiance of the beam decreases roughly exponentially from the centre. This is not ideal for thermal stimulation, since it will generate a temperature that also has a peak in the centre of the beam. This will result in non-uniform activation of nerve fibres. Lenses have been developed to redistribute the energy of the beam to produce a flattened super Gaussian irradiance profile for uniform heating of the skin. The shape of the lenses was determined by geometrical optics. They work by refracting the more intense central part of the beam towards the periphery. Solution of the heat transfer equation by a finite differences method, confirmed that the super Gaussian profile generated by the bean shaper produces a more uniform temperature distribution in skin. The model was also used to predict how varying skin parameters, such as thickness and water content, affects the temperature generated by irradiation with a CO[2] laser beam. The predicted skin temperatures matched the temperatures measured during thermal stimulation with the laser. The risk of damaging the tissue was also calculated from the modelled temperature distribution. Psychophysical techniques were used to characterise the laser stimulator compared to an existing laser stimulator. Differences in the temporal provides of the lasers resulted in different pain sensations for beams of the same energy. The conduction velocities of thermally stimulated fibres were estimated by recording the reaction time to laser irradiation. It was found that the super Gaussian beam evokes pain at a lower temperature than a TEM[00] beam. It is, therefore, a safer source for evoking pain in human pain studies.
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Zaboikin, Michail; Freter, Carl
2018-01-01
We describe a method for measuring genome editing efficiency from in silico analysis of high-resolution melt curve data. The melt curve data derived from amplicons of genome-edited or unmodified target sites were processed to remove the background fluorescent signal emanating from free fluorophore and then corrected for temperature-dependent quenching of fluorescence of double-stranded DNA-bound fluorophore. Corrected data were normalized and numerically differentiated to obtain the first derivatives of the melt curves. These were then mathematically modeled as a sum or superposition of minimal number of Gaussian components. Using Gaussian parameters determined by modeling of melt curve derivatives of unedited samples, we were able to model melt curve derivatives from genetically altered target sites where the mutant population could be accommodated using an additional Gaussian component. From this, the proportion contributed by the mutant component in the target region amplicon could be accurately determined. Mutant component computations compared well with the mutant frequency determination from next generation sequencing data. The results were also consistent with our earlier studies that used difference curve areas from high-resolution melt curves for determining the efficiency of genome-editing reagents. The advantage of the described method is that it does not require calibration curves to estimate proportion of mutants in amplicons of genome-edited target sites. PMID:29300734
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Cosmological information in Gaussianized weak lensing signals
NASA Astrophysics Data System (ADS)
Joachimi, B.; Taylor, A. N.; Kiessling, A.
2011-11-01
Gaussianizing the one-point distribution of the weak gravitational lensing convergence has recently been shown to increase the signal-to-noise ratio contained in two-point statistics. We investigate the information on cosmology that can be extracted from the transformed convergence fields. Employing Box-Cox transformations to determine optimal transformations to Gaussianity, we develop analytical models for the transformed power spectrum, including effects of noise and smoothing. We find that optimized Box-Cox transformations perform substantially better than an offset logarithmic transformation in Gaussianizing the convergence, but both yield very similar results for the signal-to-noise ratio. None of the transformations is capable of eliminating correlations of the power spectra between different angular frequencies, which we demonstrate to have a significant impact on the errors in cosmology. Analytic models of the Gaussianized power spectrum yield good fits to the simulations and produce unbiased parameter estimates in the majority of cases, where the exceptions can be traced back to the limitations in modelling the higher order correlations of the original convergence. In the ideal case, without galaxy shape noise, we find an increase in the cumulative signal-to-noise ratio by a factor of 2.6 for angular frequencies up to ℓ= 1500, and a decrease in the area of the confidence region in the Ωm-σ8 plane, measured in terms of q-values, by a factor of 4.4 for the best performing transformation. When adding a realistic level of shape noise, all transformations perform poorly with little decorrelation of angular frequencies, a maximum increase in signal-to-noise ratio of 34 per cent, and even slightly degraded errors on cosmological parameters. We argue that to find Gaussianizing transformations of practical use, it will be necessary to go beyond transformations of the one-point distribution of the convergence, extend the analysis deeper into the non-linear regime and resort to an exploration of parameter space via simulations.
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ModelMate - A graphical user interface for model analysis
Banta, Edward R.
2011-01-01
ModelMate is a graphical user interface designed to facilitate use of model-analysis programs with models. This initial version of ModelMate supports one model-analysis program, UCODE_2005, and one model software program, MODFLOW-2005. ModelMate can be used to prepare input files for UCODE_2005, run UCODE_2005, and display analysis results. A link to the GW_Chart graphing program facilitates visual interpretation of results. ModelMate includes capabilities for organizing directories used with the parallel-processing capabilities of UCODE_2005 and for maintaining files in those directories to be identical to a set of files in a master directory. ModelMate can be used on its own or in conjunction with ModelMuse, a graphical user interface for MODFLOW-2005 and PHAST.
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Lam, Lun Tak; Sun, Yi; Davey, Neil; Adams, Rod; Prapopoulou, Maria; Brown, Marc B; Moss, Gary P
2010-06-01
The aim was to employ Gaussian processes to assess mathematically the nature of a skin permeability dataset and to employ these methods, particularly feature selection, to determine the key physicochemical descriptors which exert the most significant influence on percutaneous absorption, and to compare such models with established existing models. Gaussian processes, including automatic relevance detection (GPRARD) methods, were employed to develop models of percutaneous absorption that identified key physicochemical descriptors of percutaneous absorption. Using MatLab software, the statistical performance of these models was compared with single linear networks (SLN) and quantitative structure-permeability relationships (QSPRs). Feature selection methods were used to examine in more detail the physicochemical parameters used in this study. A range of statistical measures to determine model quality were used. The inherently nonlinear nature of the skin data set was confirmed. The Gaussian process regression (GPR) methods yielded predictive models that offered statistically significant improvements over SLN and QSPR models with regard to predictivity (where the rank order was: GPR > SLN > QSPR). Feature selection analysis determined that the best GPR models were those that contained log P, melting point and the number of hydrogen bond donor groups as significant descriptors. Further statistical analysis also found that great synergy existed between certain parameters. It suggested that a number of the descriptors employed were effectively interchangeable, thus questioning the use of models where discrete variables are output, usually in the form of an equation. The use of a nonlinear GPR method produced models with significantly improved predictivity, compared with SLN or QSPR models. Feature selection methods were able to provide important mechanistic information. However, it was also shown that significant synergy existed between certain parameters, and as such it was possible to interchange certain descriptors (i.e. molecular weight and melting point) without incurring a loss of model quality. Such synergy suggested that a model constructed from discrete terms in an equation may not be the most appropriate way of representing mechanistic understandings of skin absorption.
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Bayesian Analysis of Non-Gaussian Long-Range Dependent Processes
NASA Astrophysics Data System (ADS)
Graves, Timothy; Watkins, Nicholas; Franzke, Christian; Gramacy, Robert
2013-04-01
Recent studies [e.g. the Antarctic study of Franzke, J. Climate, 2010] have strongly suggested that surface temperatures exhibit long-range dependence (LRD). The presence of LRD would hamper the identification of deterministic trends and the quantification of their significance. It is well established that LRD processes exhibit stochastic trends over rather long periods of time. Thus, accurate methods for discriminating between physical processes that possess long memory and those that do not are an important adjunct to climate modeling. As we briefly review, the LRD idea originated at the same time as H-selfsimilarity, so it is often not realised that a model does not have to be H-self similar to show LRD [e.g. Watkins, GRL Frontiers, 2013]. We have used Markov Chain Monte Carlo algorithms to perform a Bayesian analysis of Auto-Regressive Fractionally-Integrated Moving-Average ARFIMA(p,d,q) processes, which are capable of modeling LRD. Our principal aim is to obtain inference about the long memory parameter, d, with secondary interest in the scale and location parameters. We have developed a reversible-jump method enabling us to integrate over different model forms for the short memory component. We initially assume Gaussianity, and have tested the method on both synthetic and physical time series. Many physical processes, for example the Faraday Antarctic time series, are significantly non-Gaussian. We have therefore extended this work by weakening the Gaussianity assumption, assuming an alpha-stable distribution for the innovations, and performing joint inference on d and alpha. Such a modified FARIMA(p,d,q) process is a flexible, initial model for non-Gaussian processes with long memory. We will present a study of the dependence of the posterior variance of the memory parameter d on the length of the time series considered. This will be compared with equivalent error diagnostics for other measures of d.
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Task-Analytic Design of Graphic Presentations
1990-05-18
important premise of Larkin and Simon’s work is that, when comparing alternative presentations, it is fruitful to characterize graphic-based problem solving...using the same information-processing models used to help understand problem solving using other representations [Newell and Simon, 19721...luring execution of graphic presentation- 4 based problem -solving procedures. Chapter 2 reviews other work related to the problem of designing graphic
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Ellingson, B M; Sahebjam, S; Kim, H J; Pope, W B; Harris, R J; Woodworth, D C; Lai, A; Nghiemphu, P L; Mason, W P; Cloughesy, T F
2014-04-01
Pre-treatment ADC characteristics have been shown to predict response to bevacizumab in recurrent glioblastoma multiforme. However, no studies have examined whether ADC characteristics are specific to this particular treatment. The purpose of the current study was to determine whether ADC histogram analysis is a bevacizumab-specific or treatment-independent biomarker of treatment response in recurrent glioblastoma multiforme. Eighty-nine bevacizumab-treated and 43 chemotherapy-treated recurrent glioblastoma multiformes never exposed to bevacizumab were included in this study. In all patients, ADC values in contrast-enhancing ROIs from MR imaging examinations performed at the time of recurrence, immediately before commencement of treatment for recurrence, were extracted and the resulting histogram was fitted to a mixed model with a double Gaussian distribution. Mean ADC in the lower Gaussian curve was used as the primary biomarker of interest. The Cox proportional hazards model and log-rank tests were used for survival analysis. Cox multivariate regression analysis accounting for the interaction between bevacizumab- and non-bevacizumab-treated patients suggested that the ability of the lower Gaussian curve to predict survival is dependent on treatment (progression-free survival, P = .045; overall survival, P = .003). Patients with bevacizumab-treated recurrent glioblastoma multiforme with a pretreatment lower Gaussian curve > 1.2 μm(2)/ms had a significantly longer progression-free survival and overall survival compared with bevacizumab-treated patients with a lower Gaussian curve < 1.2 μm(2)/ms. No differences in progression-free survival or overall survival were observed in the chemotherapy-treated cohort. Bevacizumab-treated patients with a mean lower Gaussian curve > 1.2 μm(2)/ms had a significantly longer progression-free survival and overall survival compared with chemotherapy-treated patients. The mean lower Gaussian curve from ADC histogram analysis is a predictive imaging biomarker for bevacizumab-treated, not chemotherapy-treated, recurrent glioblastoma multiforme. Patients with recurrent glioblastoma multiforme with a mean lower Gaussian curve > 1.2 μm(2)/ms have a survival advantage when treated with bevacizumab.
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Reduced Wiener Chaos representation of random fields via basis adaptation and projection
DOE Office of Scientific and Technical Information (OSTI.GOV)
Tsilifis, Panagiotis, E-mail: tsilifis@usc.edu; Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089; Ghanem, Roger G., E-mail: ghanem@usc.edu
2017-07-15
A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.
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Neural pulse frequency modulation of an exponentially correlated Gaussian process
NASA Technical Reports Server (NTRS)
Hutchinson, C. E.; Chon, Y.-T.
1976-01-01
The effect of NPFM (Neural Pulse Frequency Modulation) on a stationary Gaussian input, namely an exponentially correlated Gaussian input, is investigated with special emphasis on the determination of the average number of pulses in unit time, known also as the average frequency of pulse occurrence. For some classes of stationary input processes where the formulation of the appropriate multidimensional Markov diffusion model of the input-plus-NPFM system is possible, the average impulse frequency may be obtained by a generalization of the approach adopted. The results are approximate and numerical, but are in close agreement with Monte Carlo computer simulation results.
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Multi-pose facial correction based on Gaussian process with combined kernel function
NASA Astrophysics Data System (ADS)
Shi, Shuyan; Ji, Ruirui; Zhang, Fan
2018-04-01
In order to improve the recognition rate of various postures, this paper proposes a method of facial correction based on Gaussian Process which build a nonlinear regression model between the front and the side face with combined kernel function. The face images with horizontal angle from -45° to +45° can be properly corrected to front faces. Finally, Support Vector Machine is employed for face recognition. Experiments on CAS PEAL R1 face database show that Gaussian process can weaken the influence of pose changes and improve the accuracy of face recognition to certain extent.
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Reduced Wiener Chaos representation of random fields via basis adaptation and projection
NASA Astrophysics Data System (ADS)
Tsilifis, Panagiotis; Ghanem, Roger G.
2017-07-01
A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.
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Effect of polarization on the evolution of electromagnetic hollow Gaussian Schell-model beam
NASA Astrophysics Data System (ADS)
Long, Xuewen; Lu, Keqing; Zhang, Yuhong; Guo, Jianbang; Li, Kehao
2011-02-01
Based on the theory of coherence, an analytical propagation formula for partially polarized and partially coherent hollow Gaussian Schell-model beams (HGSMBs) passing through a paraxial optical system is derived. Furthermore, we show that the degree of polarization of source may affect the evolution of HGSMBs and a tunable dark region may exist. For two special cases of fully coherent and partially coherent δxx = δyy, normalized intensity distributions are independent of the polarization of source.
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Stereoscopic 3D graphics generation
NASA Astrophysics Data System (ADS)
Li, Zhi; Liu, Jianping; Zan, Y.
1997-05-01
Stereoscopic display technology is one of the key techniques of areas such as simulation, multimedia, entertainment, virtual reality, and so on. Moreover, stereoscopic 3D graphics generation is an important part of stereoscopic 3D display system. In this paper, at first, we describe the principle of stereoscopic display and summarize some methods to generate stereoscopic 3D graphics. Secondly, to overcome the problems which came from the methods of user defined models (such as inconvenience, long modifying period and so on), we put forward the vector graphics files defined method. Thus we can design more directly; modify the model simply and easily; generate more conveniently; furthermore, we can make full use of graphics accelerator card and so on. Finally, we discuss the problem of how to speed up the generation.
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Daneshzand, Mohammad; Faezipour, Miad; Barkana, Buket D.
2017-01-01
Deep brain stimulation (DBS) has compelling results in the desynchronization of the basal ganglia neuronal activities and thus, is used in treating the motor symptoms of Parkinson's disease (PD). Accurate definition of DBS waveform parameters could avert tissue or electrode damage, increase the neuronal activity and reduce energy cost which will prolong the battery life, hence avoiding device replacement surgeries. This study considers the use of a charge balanced Gaussian waveform pattern as a method to disrupt the firing patterns of neuronal cell activity. A computational model was created to simulate ganglia cells and their interactions with thalamic neurons. From the model, we investigated the effects of modified DBS pulse shapes and proposed a delay period between the cathodic and anodic parts of the charge balanced Gaussian waveform to desynchronize the firing patterns of the GPe and GPi cells. The results of the proposed Gaussian waveform with delay outperformed that of rectangular DBS waveforms used in in-vivo experiments. The Gaussian Delay Gaussian (GDG) waveforms achieved lower number of misses in eliciting action potential while having a lower amplitude and shorter length of delay compared to numerous different pulse shapes. The amount of energy consumed in the basal ganglia network due to GDG waveforms was dropped by 22% in comparison with charge balanced Gaussian waveforms without any delay between the cathodic and anodic parts and was also 60% lower than a rectangular charged balanced pulse with a delay between the cathodic and anodic parts of the waveform. Furthermore, by defining a Synchronization Level metric, we observed that the GDG waveform was able to reduce the synchronization of GPi neurons more effectively than any other waveform. The promising results of GDG waveforms in terms of eliciting action potential, desynchronization of the basal ganglia neurons and reduction of energy consumption can potentially enhance the performance of DBS devices. PMID:28848417
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Daneshzand, Mohammad; Faezipour, Miad; Barkana, Buket D
2017-01-01
Deep brain stimulation (DBS) has compelling results in the desynchronization of the basal ganglia neuronal activities and thus, is used in treating the motor symptoms of Parkinson's disease (PD). Accurate definition of DBS waveform parameters could avert tissue or electrode damage, increase the neuronal activity and reduce energy cost which will prolong the battery life, hence avoiding device replacement surgeries. This study considers the use of a charge balanced Gaussian waveform pattern as a method to disrupt the firing patterns of neuronal cell activity. A computational model was created to simulate ganglia cells and their interactions with thalamic neurons. From the model, we investigated the effects of modified DBS pulse shapes and proposed a delay period between the cathodic and anodic parts of the charge balanced Gaussian waveform to desynchronize the firing patterns of the GPe and GPi cells. The results of the proposed Gaussian waveform with delay outperformed that of rectangular DBS waveforms used in in-vivo experiments. The Gaussian Delay Gaussian (GDG) waveforms achieved lower number of misses in eliciting action potential while having a lower amplitude and shorter length of delay compared to numerous different pulse shapes. The amount of energy consumed in the basal ganglia network due to GDG waveforms was dropped by 22% in comparison with charge balanced Gaussian waveforms without any delay between the cathodic and anodic parts and was also 60% lower than a rectangular charged balanced pulse with a delay between the cathodic and anodic parts of the waveform. Furthermore, by defining a Synchronization Level metric, we observed that the GDG waveform was able to reduce the synchronization of GPi neurons more effectively than any other waveform. The promising results of GDG waveforms in terms of eliciting action potential, desynchronization of the basal ganglia neurons and reduction of energy consumption can potentially enhance the performance of DBS devices.
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Spainhour, John Christian G; Janech, Michael G; Schwacke, John H; Velez, Juan Carlos Q; Ramakrishnan, Viswanathan
2014-01-01
Matrix assisted laser desorption/ionization time-of-flight (MALDI-TOF) coupled with stable isotope standards (SIS) has been used to quantify native peptides. This peptide quantification by MALDI-TOF approach has difficulties quantifying samples containing peptides with ion currents in overlapping spectra. In these overlapping spectra the currents sum together, which modify the peak heights and make normal SIS estimation problematic. An approach using Gaussian mixtures based on known physical constants to model the isotopic cluster of a known compound is proposed here. The characteristics of this approach are examined for single and overlapping compounds. The approach is compared to two commonly used SIS quantification methods for single compound, namely Peak Intensity method and Riemann sum area under the curve (AUC) method. For studying the characteristics of the Gaussian mixture method, Angiotensin II, Angiotensin-2-10, and Angiotenisn-1-9 and their associated SIS peptides were used. The findings suggest, Gaussian mixture method has similar characteristics as the two methods compared for estimating the quantity of isolated isotopic clusters for single compounds. All three methods were tested using MALDI-TOF mass spectra collected for peptides of the renin-angiotensin system. The Gaussian mixture method accurately estimated the native to labeled ratio of several isolated angiotensin peptides (5.2% error in ratio estimation) with similar estimation errors to those calculated using peak intensity and Riemann sum AUC methods (5.9% and 7.7%, respectively). For overlapping angiotensin peptides, (where the other two methods are not applicable) the estimation error of the Gaussian mixture was 6.8%, which is within the acceptable range. In summary, for single compounds the Gaussian mixture method is equivalent or marginally superior compared to the existing methods of peptide quantification and is capable of quantifying overlapping (convolved) peptides within the acceptable margin of error.
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NASA Astrophysics Data System (ADS)
Libera, Arianna; de Barros, Felipe P. J.; Riva, Monica; Guadagnini, Alberto
2017-10-01
Our study is keyed to the analysis of the interplay between engineering factors (i.e., transient pumping rates versus less realistic but commonly analyzed uniform extraction rates) and the heterogeneous structure of the aquifer (as expressed by the probability distribution characterizing transmissivity) on contaminant transport. We explore the joint influence of diverse (a) groundwater pumping schedules (constant and variable in time) and (b) representations of the stochastic heterogeneous transmissivity (T) field on temporal histories of solute concentrations observed at an extraction well. The stochastic nature of T is rendered by modeling its natural logarithm, Y = ln T, through a typical Gaussian representation and the recently introduced Generalized sub-Gaussian (GSG) model. The latter has the unique property to embed scale-dependent non-Gaussian features of the main statistics of Y and its (spatial) increments, which have been documented in a variety of studies. We rely on numerical Monte Carlo simulations and compute the temporal evolution at the well of low order moments of the solute concentration (C), as well as statistics of the peak concentration (Cp), identified as the environmental performance metric of interest in this study. We show that the pumping schedule strongly affects the pattern of the temporal evolution of the first two statistical moments of C, regardless the nature (Gaussian or non-Gaussian) of the underlying Y field, whereas the latter quantitatively influences their magnitude. Our results show that uncertainty associated with C and Cp estimates is larger when operating under a transient extraction scheme than under the action of a uniform withdrawal schedule. The probability density function (PDF) of Cp displays a long positive tail in the presence of time-varying pumping schedule. All these aspects are magnified in the presence of non-Gaussian Y fields. Additionally, the PDF of Cp displays a bimodal shape for all types of pumping schemes analyzed, independent of the type of heterogeneity considered.
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An alternative theoretical model for an anomalous hollow beam.
Cai, Yangjian; Wang, Zhaoying; Lin, Qiang
2008-09-15
An alternative and convenient theoretical model is proposed to describe a flexible anomalous hollow beam of elliptical symmetry with an elliptical solid core, which was observed in experiment recently (Phys. Rev. Lett, 94 (2005) 134802). In this model, the electric field of anomalous hollow beam is expressed as a finite sum of elliptical Gaussian modes. Flattopped beams, dark hollow beams and Gaussian beams are special cases of our model. Analytical propagation formulae for coherent and partially coherent anomalous hollow beams passing through astigmatic ABCD optical systems are derived. Some numerical examples are calculated to show the propagation and focusing properties of coherent and partially coherent anomalous hollow beams.
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Predicting Error Bars for QSAR Models
DOE Office of Scientific and Technical Information (OSTI.GOV)
Schroeter, Timon; Technische Universitaet Berlin, Department of Computer Science, Franklinstrasse 28/29, 10587 Berlin; Schwaighofer, Anton
2007-09-18
Unfavorable physicochemical properties often cause drug failures. It is therefore important to take lipophilicity and water solubility into account early on in lead discovery. This study presents log D{sub 7} models built using Gaussian Process regression, Support Vector Machines, decision trees and ridge regression algorithms based on 14556 drug discovery compounds of Bayer Schering Pharma. A blind test was conducted using 7013 new measurements from the last months. We also present independent evaluations using public data. Apart from accuracy, we discuss the quality of error bars that can be computed by Gaussian Process models, and ensemble and distance based techniquesmore » for the other modelling approaches.« less
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Nosedal-Sanchez, Alvaro; Jackson, Charles S.; Huerta, Gabriel
2016-07-20
A new test statistic for climate model evaluation has been developed that potentially mitigates some of the limitations that exist for observing and representing field and space dependencies of climate phenomena. Traditionally such dependencies have been ignored when climate models have been evaluated against observational data, which makes it difficult to assess whether any given model is simulating observed climate for the right reasons. The new statistic uses Gaussian Markov random fields for estimating field and space dependencies within a first-order grid point neighborhood structure. We illustrate the ability of Gaussian Markov random fields to represent empirical estimates of fieldmore » and space covariances using "witch hat" graphs. We further use the new statistic to evaluate the tropical response of a climate model (CAM3.1) to changes in two parameters important to its representation of cloud and precipitation physics. Overall, the inclusion of dependency information did not alter significantly the recognition of those regions of parameter space that best approximated observations. However, there were some qualitative differences in the shape of the response surface that suggest how such a measure could affect estimates of model uncertainty.« less
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A New Non-gaussian Turbulent Wind Field Generator to Estimate Design-Loads of Wind-Turbines
NASA Astrophysics Data System (ADS)
Schaffarczyk, A. P.; Gontier, H.; Kleinhans, D.; Friedrich, R.
Climate change and finite fossil fuel resources make it urgent to turn into electricity generation from mostly renewable energies. One major part will play wind-energy supplied by wind-turbines of rated power up to 10 MW. For their design and development wind field models have to be used. The standard models are based on the empirical spectra, for example by von Karman or Kaimal. From investigation of measured data it is clear that gusts are underrepresented in such models. Based on some fundamental discoveries of the nature of turbulence by Friedrich [1] derived from the Navier-Stokes equation directly, we used the concept of Continuous Time Random Walks to construct three dimensional wind fields obeying non-Gaussian statistics. These wind fields were used to estimate critical fatigue loads necessary within the certification process. Calculations are carried out with an implementation of a beam-model (FLEX5) for two types of state-of-the-art wind turbines The authors considered the edgewise and flapwise blade-root bending moments as well as tilt moment at tower top due to the standard wind field models and our new non-Gaussian wind field model. Clear differences in the loads were found.
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A clustering-based fuzzy wavelet neural network model for short-term load forecasting.
Kodogiannis, Vassilis S; Amina, Mahdi; Petrounias, Ilias
2013-10-01
Load forecasting is a critical element of power system operation, involving prediction of the future level of demand to serve as the basis for supply and demand planning. This paper presents the development of a novel clustering-based fuzzy wavelet neural network (CB-FWNN) model and validates its prediction on the short-term electric load forecasting of the Power System of the Greek Island of Crete. The proposed model is obtained from the traditional Takagi-Sugeno-Kang fuzzy system by replacing the THEN part of fuzzy rules with a "multiplication" wavelet neural network (MWNN). Multidimensional Gaussian type of activation functions have been used in the IF part of the fuzzyrules. A Fuzzy Subtractive Clustering scheme is employed as a pre-processing technique to find out the initial set and adequate number of clusters and ultimately the number of multiplication nodes in MWNN, while Gaussian Mixture Models with the Expectation Maximization algorithm are utilized for the definition of the multidimensional Gaussians. The results corresponding to the minimum and maximum power load indicate that the proposed load forecasting model provides significantly accurate forecasts, compared to conventional neural networks models.
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On the Bayesian Treed Multivariate Gaussian Process with Linear Model of Coregionalization
DOE Office of Scientific and Technical Information (OSTI.GOV)
Konomi, Bledar A.; Karagiannis, Georgios; Lin, Guang
2015-02-01
The Bayesian treed Gaussian process (BTGP) has gained popularity in recent years because it provides a straightforward mechanism for modeling non-stationary data and can alleviate computational demands by fitting models to less data. The extension of BTGP to the multivariate setting requires us to model the cross-covariance and to propose efficient algorithms that can deal with trans-dimensional MCMC moves. In this paper we extend the cross-covariance of the Bayesian treed multivariate Gaussian process (BTMGP) to that of linear model of Coregionalization (LMC) cross-covariances. Different strategies have been developed to improve the MCMC mixing and invert smaller matrices in the Bayesianmore » inference. Moreover, we compare the proposed BTMGP with existing multiple BTGP and BTMGP in test cases and multiphase flow computer experiment in a full scale regenerator of a carbon capture unit. The use of the BTMGP with LMC cross-covariance helped to predict the computer experiments relatively better than existing competitors. The proposed model has a wide variety of applications, such as computer experiments and environmental data. In the case of computer experiments we also develop an adaptive sampling strategy for the BTMGP with LMC cross-covariance function.« less
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Nosedal-Sanchez, Alvaro; Jackson, Charles S.; Huerta, Gabriel
A new test statistic for climate model evaluation has been developed that potentially mitigates some of the limitations that exist for observing and representing field and space dependencies of climate phenomena. Traditionally such dependencies have been ignored when climate models have been evaluated against observational data, which makes it difficult to assess whether any given model is simulating observed climate for the right reasons. The new statistic uses Gaussian Markov random fields for estimating field and space dependencies within a first-order grid point neighborhood structure. We illustrate the ability of Gaussian Markov random fields to represent empirical estimates of fieldmore » and space covariances using "witch hat" graphs. We further use the new statistic to evaluate the tropical response of a climate model (CAM3.1) to changes in two parameters important to its representation of cloud and precipitation physics. Overall, the inclusion of dependency information did not alter significantly the recognition of those regions of parameter space that best approximated observations. However, there were some qualitative differences in the shape of the response surface that suggest how such a measure could affect estimates of model uncertainty.« less
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Karabatsos, George
2017-02-01
Most of applied statistics involves regression analysis of data. In practice, it is important to specify a regression model that has minimal assumptions which are not violated by data, to ensure that statistical inferences from the model are informative and not misleading. This paper presents a stand-alone and menu-driven software package, Bayesian Regression: Nonparametric and Parametric Models, constructed from MATLAB Compiler. Currently, this package gives the user a choice from 83 Bayesian models for data analysis. They include 47 Bayesian nonparametric (BNP) infinite-mixture regression models; 5 BNP infinite-mixture models for density estimation; and 31 normal random effects models (HLMs), including normal linear models. Each of the 78 regression models handles either a continuous, binary, or ordinal dependent variable, and can handle multi-level (grouped) data. All 83 Bayesian models can handle the analysis of weighted observations (e.g., for meta-analysis), and the analysis of left-censored, right-censored, and/or interval-censored data. Each BNP infinite-mixture model has a mixture distribution assigned one of various BNP prior distributions, including priors defined by either the Dirichlet process, Pitman-Yor process (including the normalized stable process), beta (two-parameter) process, normalized inverse-Gaussian process, geometric weights prior, dependent Dirichlet process, or the dependent infinite-probits prior. The software user can mouse-click to select a Bayesian model and perform data analysis via Markov chain Monte Carlo (MCMC) sampling. After the sampling completes, the software automatically opens text output that reports MCMC-based estimates of the model's posterior distribution and model predictive fit to the data. Additional text and/or graphical output can be generated by mouse-clicking other menu options. This includes output of MCMC convergence analyses, and estimates of the model's posterior predictive distribution, for selected functionals and values of covariates. The software is illustrated through the BNP regression analysis of real data.
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NASA Astrophysics Data System (ADS)
Cui, Shuya; Wang, Tao; Hu, Xiaoli
2014-12-01
A new chiral ionic liquid was synthesized from (S)-1-phenylethylamine and it was studied by IR, Raman, polarimetry, NMR and X-ray crystal diffraction. Its vibrational spectral bands are precisely ascribed to the studied structure with the aid of DFT theoretical calculations. The optimized geometries and calculated vibrational frequencies are evaluated via comparison with experimental values. The vibrational spectral data obtained from IR and Raman spectra are assigned based on the results of the theoretical calculations by the DFT-B3LYP method at 6-311G(d,p) level. The computed vibrational frequencies were scaled by scale factors to yield a good agreement with observed experimental vibrational frequencies. The vibrational modes assignments were performed by using the animation option of GaussView5.0 graphical interface for Gaussian program.
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Polarization characteristics of double-clad elliptical fibers.
Zhang, F; Lit, J W
1990-12-20
A scalar variational analysis based on a Gaussian approximation of the fundamental mode of a double-clad elliptical fiber with a depressed inner cladding is studied. The polarization properties and graphic results are presented; they are given in terms of three parameters: the ratio of the major axis to the minor axis of the core, the ratio of the inner cladding major axis to the core major axis, and the difference between the core index and the inner cladding index. The variations of both the spot size and the field intensity with core ellipticity are examined. It is shown that high birefringence and dispersion-free orthogonal polarization modes can be obtained within the single-mode region and that the field intensity distribution may be more confined to the fiber center than in a single-clad elliptical fiber.
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Implicit Multibody Penalty-BasedDistributed Contact.
Xu, Hongyi; Zhao, Yili; Barbic, Jernej
2014-09-01
The penalty method is a simple and popular approach to resolving contact in computer graphics and robotics. Penalty-based contact, however, suffers from stability problems due to the highly variable and unpredictable net stiffness, and this is particularly pronounced in simulations with time-varying distributed geometrically complex contact. We employ semi-implicit integration, exact analytical contact gradients, symbolic Gaussian elimination and a SVD solver to simulate stable penalty-based frictional contact with large, time-varying contact areas, involving many rigid objects and articulated rigid objects in complex conforming contact and self-contact. We also derive implicit proportional-derivative control forces for real-time control of articulated structures with loops. We present challenging contact scenarios such as screwing a hexbolt into a hole, bowls stacked in perfectly conforming configurations, and manipulating many objects using actively controlled articulated mechanisms in real time.
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Computationally efficient algorithm for Gaussian Process regression in case of structured samples
NASA Astrophysics Data System (ADS)
Belyaev, M.; Burnaev, E.; Kapushev, Y.
2016-04-01
Surrogate modeling is widely used in many engineering problems. Data sets often have Cartesian product structure (for instance factorial design of experiments with missing points). In such case the size of the data set can be very large. Therefore, one of the most popular algorithms for approximation-Gaussian Process regression-can be hardly applied due to its computational complexity. In this paper a computationally efficient approach for constructing Gaussian Process regression in case of data sets with Cartesian product structure is presented. Efficiency is achieved by using a special structure of the data set and operations with tensors. Proposed algorithm has low computational as well as memory complexity compared to existing algorithms. In this work we also introduce a regularization procedure allowing to take into account anisotropy of the data set and avoid degeneracy of regression model.
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Nonlinear and non-Gaussian Bayesian based handwriting beautification
NASA Astrophysics Data System (ADS)
Shi, Cao; Xiao, Jianguo; Xu, Canhui; Jia, Wenhua
2013-03-01
A framework is proposed in this paper to effectively and efficiently beautify handwriting by means of a novel nonlinear and non-Gaussian Bayesian algorithm. In the proposed framework, format and size of handwriting image are firstly normalized, and then typeface in computer system is applied to optimize vision effect of handwriting. The Bayesian statistics is exploited to characterize the handwriting beautification process as a Bayesian dynamic model. The model parameters to translate, rotate and scale typeface in computer system are controlled by state equation, and the matching optimization between handwriting and transformed typeface is employed by measurement equation. Finally, the new typeface, which is transformed from the original one and gains the best nonlinear and non-Gaussian optimization, is the beautification result of handwriting. Experimental results demonstrate the proposed framework provides a creative handwriting beautification methodology to improve visual acceptance.
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Limits of Gaussian fluctuations in the cosmic microwave background at 19.2 GHz
NASA Technical Reports Server (NTRS)
Boughn, S. P.; Cheng, E. S.; Cottingham, D. A.; Fixsen, D. J.
1992-01-01
The Northern Hemisphere data from the 19.2 GHz full sky survey are analyzed to place limits on the magnitude of Gaussian fluctuations in the cosmic microwave background implied by a variety of correlation functions. Included among the models tested are the monochromatic and Gaussian-shaped families, and those with power-law spectra for n values between -2 and 1. An upper bound is placed on the quadrupole anisotropy of Delta T/T less than 3.2 x 10 exp -5 rms, and an upper bound on scale-invariant (n = 1) fluctuations of a2 less than 4.5 x 10 exp -5 (95 percent confidence level). There is significant contamination of these data from Galactic emission, and improvement of the modeling of the Galaxy could yield a significant reduction of these upper bounds.
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Limits on Gaussian fluctuations in the cosmic microwave background at 19.2 GHz
NASA Technical Reports Server (NTRS)
Boughn, S. P.; Cheng, E. S.; Cottingham, D. A.; Fixsen, D. J.
1991-01-01
The Northern Hemisphere data from the 19.2 GHz full sky survey are analyzed to place limits on the magnitude of Gaussian fluctuations in the cosmic microwave background implied by a variety of correlation functions. Included among the models tested are the monochromatic and Gaussian-shaped families, and those with power law spectra for n from -2 to 1. We place an upper bound on the quadrupole anisotropy of DeltaT/T less than 3.2 x 10 exp -5 rms, and an upper bound on scale-invariant (n = 1) fluctuations of a2 less than 4.5 x 10 exp -5 (95 percent confidence level). There is significant contamination of these data from Galactic emission, and improvement of our modeling of the Galaxy could yield a significant reduction of these upper bounds.
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What Can Causal Networks Tell Us about Metabolic Pathways?
Blair, Rachael Hageman; Kliebenstein, Daniel J.; Churchill, Gary A.
2012-01-01
Graphical models describe the linear correlation structure of data and have been used to establish causal relationships among phenotypes in genetic mapping populations. Data are typically collected at a single point in time. Biological processes on the other hand are often non-linear and display time varying dynamics. The extent to which graphical models can recapitulate the architecture of an underlying biological processes is not well understood. We consider metabolic networks with known stoichiometry to address the fundamental question: “What can causal networks tell us about metabolic pathways?”. Using data from an Arabidopsis BaySha population and simulated data from dynamic models of pathway motifs, we assess our ability to reconstruct metabolic pathways using graphical models. Our results highlight the necessity of non-genetic residual biological variation for reliable inference. Recovery of the ordering within a pathway is possible, but should not be expected. Causal inference is sensitive to subtle patterns in the correlation structure that may be driven by a variety of factors, which may not emphasize the substrate-product relationship. We illustrate the effects of metabolic pathway architecture, epistasis and stochastic variation on correlation structure and graphical model-derived networks. We conclude that graphical models should be interpreted cautiously, especially if the implied causal relationships are to be used in the design of intervention strategies. PMID:22496633
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Cortical circuitry implementing graphical models.
Litvak, Shai; Ullman, Shimon
2009-11-01
In this letter, we develop and simulate a large-scale network of spiking neurons that approximates the inference computations performed by graphical models. Unlike previous related schemes, which used sum and product operations in either the log or linear domains, the current model uses an inference scheme based on the sum and maximization operations in the log domain. Simulations show that using these operations, a large-scale circuit, which combines populations of spiking neurons as basic building blocks, is capable of finding close approximations to the full mathematical computations performed by graphical models within a few hundred milliseconds. The circuit is general in the sense that it can be wired for any graph structure, it supports multistate variables, and it uses standard leaky integrate-and-fire neuronal units. Following previous work, which proposed relations between graphical models and the large-scale cortical anatomy, we focus on the cortical microcircuitry and propose how anatomical and physiological aspects of the local circuitry may map onto elements of the graphical model implementation. We discuss in particular the roles of three major types of inhibitory neurons (small fast-spiking basket cells, large layer 2/3 basket cells, and double-bouquet neurons), subpopulations of strongly interconnected neurons with their unique connectivity patterns in different cortical layers, and the possible role of minicolumns in the realization of the population-based maximum operation.
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High-Order Local Pooling and Encoding Gaussians Over a Dictionary of Gaussians.
Li, Peihua; Zeng, Hui; Wang, Qilong; Shiu, Simon C K; Zhang, Lei
2017-07-01
Local pooling (LP) in configuration (feature) space proposed by Boureau et al. explicitly restricts similar features to be aggregated, which can preserve as much discriminative information as possible. At the time it appeared, this method combined with sparse coding achieved competitive classification results with only a small dictionary. However, its performance lags far behind the state-of-the-art results as only the zero-order information is exploited. Inspired by the success of high-order statistical information in existing advanced feature coding or pooling methods, we make an attempt to address the limitation of LP. To this end, we present a novel method called high-order LP (HO-LP) to leverage the information higher than the zero-order one. Our idea is intuitively simple: we compute the first- and second-order statistics per configuration bin and model them as a Gaussian. Accordingly, we employ a collection of Gaussians as visual words to represent the universal probability distribution of features from all classes. Our problem is naturally formulated as encoding Gaussians over a dictionary of Gaussians as visual words. This problem, however, is challenging since the space of Gaussians is not a Euclidean space but forms a Riemannian manifold. We address this challenge by mapping Gaussians into the Euclidean space, which enables us to perform coding with common Euclidean operations rather than complex and often expensive Riemannian operations. Our HO-LP preserves the advantages of the original LP: pooling only similar features and using a small dictionary. Meanwhile, it achieves very promising performance on standard benchmarks, with either conventional, hand-engineered features or deep learning-based features.
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Naaz, Farah; Chariker, Julia H.; Pani, John R.
2013-01-01
A study was conducted to test the hypothesis that instruction with graphically integrated representations of whole and sectional neuroanatomy is especially effective for learning to recognize neural structures in sectional imagery (such as MRI images). Neuroanatomy was taught to two groups of participants using computer graphical models of the human brain. Both groups learned whole anatomy first with a three-dimensional model of the brain. One group then learned sectional anatomy using two-dimensional sectional representations, with the expectation that there would be transfer of learning from whole to sectional anatomy. The second group learned sectional anatomy by moving a virtual cutting plane through the three-dimensional model. In tests of long-term retention of sectional neuroanatomy, the group with graphically integrated representation recognized more neural structures that were known to be challenging to learn. This study demonstrates the use of graphical representation to facilitate a more elaborated (deeper) understanding of complex spatial relations. PMID:24563579
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Gaussian Process Regression Model in Spatial Logistic Regression
NASA Astrophysics Data System (ADS)
Sofro, A.; Oktaviarina, A.
2018-01-01
Spatial analysis has developed very quickly in the last decade. One of the favorite approaches is based on the neighbourhood of the region. Unfortunately, there are some limitations such as difficulty in prediction. Therefore, we offer Gaussian process regression (GPR) to accommodate the issue. In this paper, we will focus on spatial modeling with GPR for binomial data with logit link function. The performance of the model will be investigated. We will discuss the inference of how to estimate the parameters and hyper-parameters and to predict as well. Furthermore, simulation studies will be explained in the last section.