Polynomial decay rate of a thermoelastic Mindlin-Timoshenko plate model with Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Grobbelaar-Van Dalsen, Marié

2015-02-01

In this article, we are concerned with the polynomial stabilization of a two-dimensional thermoelastic Mindlin-Timoshenko plate model with no mechanical damping. The model is subject to Dirichlet boundary conditions on the elastic as well as the thermal variables. The work complements our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 64:1305-1325, 2013) on the polynomial stabilization of a Mindlin-Timoshenko model in a radially symmetric domain under Dirichlet boundary conditions on the displacement and thermal variables and free boundary conditions on the shear angle variables. In particular, our aim is to investigate the effect of the Dirichlet boundary conditions on all the variables on the polynomial decay rate of the model. By once more applying a frequency domain method in which we make critical use of an inequality for the trace of Sobolev functions on the boundary of a bounded, open connected set we show that the decay is slower than in the model considered in the cited work. A comparison of our result with our polynomial decay result for a magnetoelastic Mindlin-Timoshenko model subject to Dirichlet boundary conditions on the elastic variables in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) also indicates a correlation between the robustness of the coupling between parabolic and hyperbolic dynamics and the polynomial decay rate in the two models.

An incremental DPMM-based method for trajectory clustering, modeling, and retrieval.

PubMed

Hu, Weiming; Li, Xi; Tian, Guodong; Maybank, Stephen; Zhang, Zhongfei

2013-05-01

Trajectory analysis is the basis for many applications, such as indexing of motion events in videos, activity recognition, and surveillance. In this paper, the Dirichlet process mixture model (DPMM) is applied to trajectory clustering, modeling, and retrieval. We propose an incremental version of a DPMM-based clustering algorithm and apply it to cluster trajectories. An appropriate number of trajectory clusters is determined automatically. When trajectories belonging to new clusters arrive, the new clusters can be identified online and added to the model without any retraining using the previous data. A time-sensitive Dirichlet process mixture model (tDPMM) is applied to each trajectory cluster for learning the trajectory pattern which represents the time-series characteristics of the trajectories in the cluster. Then, a parameterized index is constructed for each cluster. A novel likelihood estimation algorithm for the tDPMM is proposed, and a trajectory-based video retrieval model is developed. The tDPMM-based probabilistic matching method and the DPMM-based model growing method are combined to make the retrieval model scalable and adaptable. Experimental comparisons with state-of-the-art algorithms demonstrate the effectiveness of our algorithm.

Dual Sticky Hierarchical Dirichlet Process Hidden Markov Model and Its Application to Natural Language Description of Motions.

PubMed

Hu, Weiming; Tian, Guodong; Kang, Yongxin; Yuan, Chunfeng; Maybank, Stephen

2017-09-25

In this paper, a new nonparametric Bayesian model called the dual sticky hierarchical Dirichlet process hidden Markov model (HDP-HMM) is proposed for mining activities from a collection of time series data such as trajectories. All the time series data are clustered. Each cluster of time series data, corresponding to a motion pattern, is modeled by an HMM. Our model postulates a set of HMMs that share a common set of states (topics in an analogy with topic models for document processing), but have unique transition distributions. For the application to motion trajectory modeling, topics correspond to motion activities. The learnt topics are clustered into atomic activities which are assigned predicates. We propose a Bayesian inference method to decompose a given trajectory into a sequence of atomic activities. On combining the learnt sources and sinks, semantic motion regions, and the learnt sequence of atomic activities, the action represented by the trajectory can be described in natural language in as automatic a way as possible. The effectiveness of our dual sticky HDP-HMM is validated on several trajectory datasets. The effectiveness of the natural language descriptions for motions is demonstrated on the vehicle trajectories extracted from a traffic scene.

A Bayesian Semiparametric Item Response Model with Dirichlet Process Priors

ERIC Educational Resources Information Center

Miyazaki, Kei; Hoshino, Takahiro

2009-01-01

In Item Response Theory (IRT), item characteristic curves (ICCs) are illustrated through logistic models or normal ogive models, and the probability that examinees give the correct answer is usually a monotonically increasing function of their ability parameters. However, since only limited patterns of shapes can be obtained from logistic models…

Using Dirichlet Processes for Modeling Heterogeneous Treatment Effects across Sites

ERIC Educational Resources Information Center

Miratrix, Luke; Feller, Avi; Pillai, Natesh; Pati, Debdeep

2016-01-01

Modeling the distribution of site level effects is an important problem, but it is also an incredibly difficult one. Current methods rely on distributional assumptions in multilevel models for estimation. There it is hoped that the partial pooling of site level estimates with overall estimates, designed to take into account individual variation as…

A Hierarchical Bayesian Model for Calibrating Estimates of Species Divergence Times

PubMed Central

Heath, Tracy A.

2012-01-01

In Bayesian divergence time estimation methods, incorporating calibrating information from the fossil record is commonly done by assigning prior densities to ancestral nodes in the tree. Calibration prior densities are typically parametric distributions offset by minimum age estimates provided by the fossil record. Specification of the parameters of calibration densities requires the user to quantify his or her prior knowledge of the age of the ancestral node relative to the age of its calibrating fossil. The values of these parameters can, potentially, result in biased estimates of node ages if they lead to overly informative prior distributions. Accordingly, determining parameter values that lead to adequate prior densities is not straightforward. In this study, I present a hierarchical Bayesian model for calibrating divergence time analyses with multiple fossil age constraints. This approach applies a Dirichlet process prior as a hyperprior on the parameters of calibration prior densities. Specifically, this model assumes that the rate parameters of exponential prior distributions on calibrated nodes are distributed according to a Dirichlet process, whereby the rate parameters are clustered into distinct parameter categories. Both simulated and biological data are analyzed to evaluate the performance of the Dirichlet process hyperprior. Compared with fixed exponential prior densities, the hierarchical Bayesian approach results in more accurate and precise estimates of internal node ages. When this hyperprior is applied using Markov chain Monte Carlo methods, the ages of calibrated nodes are sampled from mixtures of exponential distributions and uncertainty in the values of calibration density parameters is taken into account. PMID:22334343

A Novel Information-Theoretic Approach for Variable Clustering and Predictive Modeling Using Dirichlet Process Mixtures

PubMed Central

Chen, Yun; Yang, Hui

2016-01-01

In the era of big data, there are increasing interests on clustering variables for the minimization of data redundancy and the maximization of variable relevancy. Existing clustering methods, however, depend on nontrivial assumptions about the data structure. Note that nonlinear interdependence among variables poses significant challenges on the traditional framework of predictive modeling. In the present work, we reformulate the problem of variable clustering from an information theoretic perspective that does not require the assumption of data structure for the identification of nonlinear interdependence among variables. Specifically, we propose the use of mutual information to characterize and measure nonlinear correlation structures among variables. Further, we develop Dirichlet process (DP) models to cluster variables based on the mutual-information measures among variables. Finally, orthonormalized variables in each cluster are integrated with group elastic-net model to improve the performance of predictive modeling. Both simulation and real-world case studies showed that the proposed methodology not only effectively reveals the nonlinear interdependence structures among variables but also outperforms traditional variable clustering algorithms such as hierarchical clustering. PMID:27966581

A Novel Information-Theoretic Approach for Variable Clustering and Predictive Modeling Using Dirichlet Process Mixtures.

PubMed

Chen, Yun; Yang, Hui

2016-12-14

In the era of big data, there are increasing interests on clustering variables for the minimization of data redundancy and the maximization of variable relevancy. Existing clustering methods, however, depend on nontrivial assumptions about the data structure. Note that nonlinear interdependence among variables poses significant challenges on the traditional framework of predictive modeling. In the present work, we reformulate the problem of variable clustering from an information theoretic perspective that does not require the assumption of data structure for the identification of nonlinear interdependence among variables. Specifically, we propose the use of mutual information to characterize and measure nonlinear correlation structures among variables. Further, we develop Dirichlet process (DP) models to cluster variables based on the mutual-information measures among variables. Finally, orthonormalized variables in each cluster are integrated with group elastic-net model to improve the performance of predictive modeling. Both simulation and real-world case studies showed that the proposed methodology not only effectively reveals the nonlinear interdependence structures among variables but also outperforms traditional variable clustering algorithms such as hierarchical clustering.

Decomposing biodiversity data using the Latent Dirichlet Allocation model, a probabilistic multivariate statistical method

Treesearch

Denis Valle; Benjamin Baiser; Christopher W. Woodall; Robin Chazdon; Jerome Chave

2014-01-01

We propose a novel multivariate method to analyse biodiversity data based on the Latent Dirichlet Allocation (LDA) model. LDA, a probabilistic model, reduces assemblages to sets of distinct component communities. It produces easily interpretable results, can represent abrupt and gradual changes in composition, accommodates missing data and allows for coherent estimates...

An improved approximate-Bayesian model-choice method for estimating shared evolutionary history

PubMed Central

2014-01-01

Background To understand biological diversification, it is important to account for large-scale processes that affect the evolutionary history of groups of co-distributed populations of organisms. Such events predict temporally clustered divergences times, a pattern that can be estimated using genetic data from co-distributed species. I introduce a new approximate-Bayesian method for comparative phylogeographical model-choice that estimates the temporal distribution of divergences across taxa from multi-locus DNA sequence data. The model is an extension of that implemented in msBayes. Results By reparameterizing the model, introducing more flexible priors on demographic and divergence-time parameters, and implementing a non-parametric Dirichlet-process prior over divergence models, I improved the robustness, accuracy, and power of the method for estimating shared evolutionary history across taxa. Conclusions The results demonstrate the improved performance of the new method is due to (1) more appropriate priors on divergence-time and demographic parameters that avoid prohibitively small marginal likelihoods for models with more divergence events, and (2) the Dirichlet-process providing a flexible prior on divergence histories that does not strongly disfavor models with intermediate numbers of divergence events. The new method yields more robust estimates of posterior uncertainty, and thus greatly reduces the tendency to incorrectly estimate models of shared evolutionary history with strong support. PMID:24992937

A Dirichlet-Multinomial Bayes Classifier for Disease Diagnosis with Microbial Compositions.

PubMed

Gao, Xiang; Lin, Huaiying; Dong, Qunfeng

2017-01-01

Dysbiosis of microbial communities is associated with various human diseases, raising the possibility of using microbial compositions as biomarkers for disease diagnosis. We have developed a Bayes classifier by modeling microbial compositions with Dirichlet-multinomial distributions, which are widely used to model multicategorical count data with extra variation. The parameters of the Dirichlet-multinomial distributions are estimated from training microbiome data sets based on maximum likelihood. The posterior probability of a microbiome sample belonging to a disease or healthy category is calculated based on Bayes' theorem, using the likelihood values computed from the estimated Dirichlet-multinomial distribution, as well as a prior probability estimated from the training microbiome data set or previously published information on disease prevalence. When tested on real-world microbiome data sets, our method, called DMBC (for Dirichlet-multinomial Bayes classifier), shows better classification accuracy than the only existing Bayesian microbiome classifier based on a Dirichlet-multinomial mixture model and the popular random forest method. The advantage of DMBC is its built-in automatic feature selection, capable of identifying a subset of microbial taxa with the best classification accuracy between different classes of samples based on cross-validation. This unique ability enables DMBC to maintain and even improve its accuracy at modeling species-level taxa. The R package for DMBC is freely available at https://github.com/qunfengdong/DMBC. IMPORTANCE By incorporating prior information on disease prevalence, Bayes classifiers have the potential to estimate disease probability better than other common machine-learning methods. Thus, it is important to develop Bayes classifiers specifically tailored for microbiome data. Our method shows higher classification accuracy than the only existing Bayesian classifier and the popular random forest method, and thus provides an alternative option for using microbial compositions for disease diagnosis.

Modeling virtual organizations with Latent Dirichlet Allocation: a case for natural language processing.

PubMed

Gross, Alexander; Murthy, Dhiraj

2014-10-01

This paper explores a variety of methods for applying the Latent Dirichlet Allocation (LDA) automated topic modeling algorithm to the modeling of the structure and behavior of virtual organizations found within modern social media and social networking environments. As the field of Big Data reveals, an increase in the scale of social data available presents new challenges which are not tackled by merely scaling up hardware and software. Rather, they necessitate new methods and, indeed, new areas of expertise. Natural language processing provides one such method. This paper applies LDA to the study of scientific virtual organizations whose members employ social technologies. Because of the vast data footprint in these virtual platforms, we found that natural language processing was needed to 'unlock' and render visible latent, previously unseen conversational connections across large textual corpora (spanning profiles, discussion threads, forums, and other social media incarnations). We introduce variants of LDA and ultimately make the argument that natural language processing is a critical interdisciplinary methodology to make better sense of social 'Big Data' and we were able to successfully model nested discussion topics from forums and blog posts using LDA. Importantly, we found that LDA can move us beyond the state-of-the-art in conventional Social Network Analysis techniques. Copyright © 2014 Elsevier Ltd. All rights reserved.

Diffusion Processes Satisfying a Conservation Law Constraint

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2014-03-04

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Diffusion Processes Satisfying a Conservation Law Constraint

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

Bakosi, J.; Ristorcelli, J. R.

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Latent Dirichlet Allocation (LDA) Model and kNN Algorithm to Classify Research Project Selection

NASA Astrophysics Data System (ADS)

Safi’ie, M. A.; Utami, E.; Fatta, H. A.

2018-03-01

Universitas Sebelas Maret has a teaching staff more than 1500 people, and one of its tasks is to carry out research. In the other side, the funding support for research and service is limited, so there is need to be evaluated to determine the Research proposal submission and devotion on society (P2M). At the selection stage, research proposal documents are collected as unstructured data and the data stored is very large. To extract information contained in the documents therein required text mining technology. This technology applied to gain knowledge to the documents by automating the information extraction. In this articles we use Latent Dirichlet Allocation (LDA) to the documents as a model in feature extraction process, to get terms that represent its documents. Hereafter we use k-Nearest Neighbour (kNN) algorithm to classify the documents based on its terms.

Neighbor-Dependent Ramachandran Probability Distributions of Amino Acids Developed from a Hierarchical Dirichlet Process Model

PubMed Central

Mitra, Rajib; Jordan, Michael I.; Dunbrack, Roland L.

2010-01-01

Distributions of the backbone dihedral angles of proteins have been studied for over 40 years. While many statistical analyses have been presented, only a handful of probability densities are publicly available for use in structure validation and structure prediction methods. The available distributions differ in a number of important ways, which determine their usefulness for various purposes. These include: 1) input data size and criteria for structure inclusion (resolution, R-factor, etc.); 2) filtering of suspect conformations and outliers using B-factors or other features; 3) secondary structure of input data (e.g., whether helix and sheet are included; whether beta turns are included); 4) the method used for determining probability densities ranging from simple histograms to modern nonparametric density estimation; and 5) whether they include nearest neighbor effects on the distribution of conformations in different regions of the Ramachandran map. In this work, Ramachandran probability distributions are presented for residues in protein loops from a high-resolution data set with filtering based on calculated electron densities. Distributions for all 20 amino acids (with cis and trans proline treated separately) have been determined, as well as 420 left-neighbor and 420 right-neighbor dependent distributions. The neighbor-independent and neighbor-dependent probability densities have been accurately estimated using Bayesian nonparametric statistical analysis based on the Dirichlet process. In particular, we used hierarchical Dirichlet process priors, which allow sharing of information between densities for a particular residue type and different neighbor residue types. The resulting distributions are tested in a loop modeling benchmark with the program Rosetta, and are shown to improve protein loop conformation prediction significantly. The distributions are available at http://dunbrack.fccc.edu/hdp. PMID:20442867

Stochastic search, optimization and regression with energy applications

NASA Astrophysics Data System (ADS)

Hannah, Lauren A.

Designing clean energy systems will be an important task over the next few decades. One of the major roadblocks is a lack of mathematical tools to economically evaluate those energy systems. However, solutions to these mathematical problems are also of interest to the operations research and statistical communities in general. This thesis studies three problems that are of interest to the energy community itself or provide support for solution methods: R&D portfolio optimization, nonparametric regression and stochastic search with an observable state variable. First, we consider the one stage R&D portfolio optimization problem to avoid the sequential decision process associated with the multi-stage. The one stage problem is still difficult because of a non-convex, combinatorial decision space and a non-convex objective function. We propose a heuristic solution method that uses marginal project values---which depend on the selected portfolio---to create a linear objective function. In conjunction with the 0-1 decision space, this new problem can be solved as a knapsack linear program. This method scales well to large decision spaces. We also propose an alternate, provably convergent algorithm that does not exploit problem structure. These methods are compared on a solid oxide fuel cell R&D portfolio problem. Next, we propose Dirichlet Process mixtures of Generalized Linear Models (DPGLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We prove conditions for the asymptotic unbiasedness of the DP-GLM regression mean function estimate. We also give examples for when those conditions hold, including models for compactly supported continuous distributions and a model with continuous covariates and categorical response. We empirically analyze the properties of the DP-GLM and why it provides better results than existing Dirichlet process mixture regression models. We evaluate DP-GLM on several data sets, comparing it to modern methods of nonparametric regression like CART, Bayesian trees and Gaussian processes. Compared to existing techniques, the DP-GLM provides a single model (and corresponding inference algorithms) that performs well in many regression settings. Finally, we study convex stochastic search problems where a noisy objective function value is observed after a decision is made. There are many stochastic search problems whose behavior depends on an exogenous state variable which affects the shape of the objective function. Currently, there is no general purpose algorithm to solve this class of problems. We use nonparametric density estimation to take observations from the joint state-outcome distribution and use them to infer the optimal decision for a given query state. We propose two solution methods that depend on the problem characteristics: function-based and gradient-based optimization. We examine two weighting schemes, kernel-based weights and Dirichlet process-based weights, for use with the solution methods. The weights and solution methods are tested on a synthetic multi-product newsvendor problem and the hour-ahead wind commitment problem. Our results show that in some cases Dirichlet process weights offer substantial benefits over kernel based weights and more generally that nonparametric estimation methods provide good solutions to otherwise intractable problems.

DIMM-SC: a Dirichlet mixture model for clustering droplet-based single cell transcriptomic data.

PubMed

Sun, Zhe; Wang, Ting; Deng, Ke; Wang, Xiao-Feng; Lafyatis, Robert; Ding, Ying; Hu, Ming; Chen, Wei

2018-01-01

Single cell transcriptome sequencing (scRNA-Seq) has become a revolutionary tool to study cellular and molecular processes at single cell resolution. Among existing technologies, the recently developed droplet-based platform enables efficient parallel processing of thousands of single cells with direct counting of transcript copies using Unique Molecular Identifier (UMI). Despite the technology advances, statistical methods and computational tools are still lacking for analyzing droplet-based scRNA-Seq data. Particularly, model-based approaches for clustering large-scale single cell transcriptomic data are still under-explored. We developed DIMM-SC, a Dirichlet Mixture Model for clustering droplet-based Single Cell transcriptomic data. This approach explicitly models UMI count data from scRNA-Seq experiments and characterizes variations across different cell clusters via a Dirichlet mixture prior. We performed comprehensive simulations to evaluate DIMM-SC and compared it with existing clustering methods such as K-means, CellTree and Seurat. In addition, we analyzed public scRNA-Seq datasets with known cluster labels and in-house scRNA-Seq datasets from a study of systemic sclerosis with prior biological knowledge to benchmark and validate DIMM-SC. Both simulation studies and real data applications demonstrated that overall, DIMM-SC achieves substantially improved clustering accuracy and much lower clustering variability compared to other existing clustering methods. More importantly, as a model-based approach, DIMM-SC is able to quantify the clustering uncertainty for each single cell, facilitating rigorous statistical inference and biological interpretations, which are typically unavailable from existing clustering methods. DIMM-SC has been implemented in a user-friendly R package with a detailed tutorial available on www.pitt.edu/∼wec47/singlecell.html. wei.chen@chp.edu or hum@ccf.org. Supplementary data are available at Bioinformatics online. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Entity Relation Detection with Factorial Hidden Markov Models and Maximum Entropy Discriminant Latent Dirichlet Allocations

ERIC Educational Resources Information Center

Li, Dingcheng

2011-01-01

Coreference resolution (CR) and entity relation detection (ERD) aim at finding predefined relations between pairs of entities in text. CR focuses on resolving identity relations while ERD focuses on detecting non-identity relations. Both CR and ERD are important as they can potentially improve other natural language processing (NLP) related tasks…

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

Matthias C. M. Troffaes; Gero Walter; Dana Kelly

In a standard Bayesian approach to the alpha-factor model for common-cause failure, a precise Dirichlet prior distribution models epistemic uncertainty in the alpha-factors. This Dirichlet prior is then updated with observed data to obtain a posterior distribution, which forms the basis for further inferences. In this paper, we adapt the imprecise Dirichlet model of Walley to represent epistemic uncertainty in the alpha-factors. In this approach, epistemic uncertainty is expressed more cautiously via lower and upper expectations for each alpha-factor, along with a learning parameter which determines how quickly the model learns from observed data. For this application, we focus onmore » elicitation of the learning parameter, and find that values in the range of 1 to 10 seem reasonable. The approach is compared with Kelly and Atwood's minimally informative Dirichlet prior for the alpha-factor model, which incorporated precise mean values for the alpha-factors, but which was otherwise quite diffuse. Next, we explore the use of a set of Gamma priors to model epistemic uncertainty in the marginal failure rate, expressed via a lower and upper expectation for this rate, again along with a learning parameter. As zero counts are generally less of an issue here, we find that the choice of this learning parameter is less crucial. Finally, we demonstrate how both epistemic uncertainty models can be combined to arrive at lower and upper expectations for all common-cause failure rates. Thereby, we effectively provide a full sensitivity analysis of common-cause failure rates, properly reflecting epistemic uncertainty of the analyst on all levels of the common-cause failure model.« less

A menu-driven software package of Bayesian nonparametric (and parametric) mixed models for regression analysis and density estimation.

PubMed

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.

Bayesian parameter estimation for the Wnt pathway: an infinite mixture models approach.

PubMed

Koutroumpas, Konstantinos; Ballarini, Paolo; Votsi, Irene; Cournède, Paul-Henry

2016-09-01

Likelihood-free methods, like Approximate Bayesian Computation (ABC), have been extensively used in model-based statistical inference with intractable likelihood functions. When combined with Sequential Monte Carlo (SMC) algorithms they constitute a powerful approach for parameter estimation and model selection of mathematical models of complex biological systems. A crucial step in the ABC-SMC algorithms, significantly affecting their performance, is the propagation of a set of parameter vectors through a sequence of intermediate distributions using Markov kernels. In this article, we employ Dirichlet process mixtures (DPMs) to design optimal transition kernels and we present an ABC-SMC algorithm with DPM kernels. We illustrate the use of the proposed methodology using real data for the canonical Wnt signaling pathway. A multi-compartment model of the pathway is developed and it is compared to an existing model. The results indicate that DPMs are more efficient in the exploration of the parameter space and can significantly improve ABC-SMC performance. In comparison to alternative sampling schemes that are commonly used, the proposed approach can bring potential benefits in the estimation of complex multimodal distributions. The method is used to estimate the parameters and the initial state of two models of the Wnt pathway and it is shown that the multi-compartment model fits better the experimental data. Python scripts for the Dirichlet Process Gaussian Mixture model and the Gibbs sampler are available at https://sites.google.com/site/kkoutroumpas/software konstantinos.koutroumpas@ecp.fr. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Multimodal brain-tumor segmentation based on Dirichlet process mixture model with anisotropic diffusion and Markov random field prior.

PubMed

Lu, Yisu; Jiang, Jun; Yang, Wei; Feng, Qianjin; Chen, Wufan

2014-01-01

Brain-tumor segmentation is an important clinical requirement for brain-tumor diagnosis and radiotherapy planning. It is well-known that the number of clusters is one of the most important parameters for automatic segmentation. However, it is difficult to define owing to the high diversity in appearance of tumor tissue among different patients and the ambiguous boundaries of lesions. In this study, a nonparametric mixture of Dirichlet process (MDP) model is applied to segment the tumor images, and the MDP segmentation can be performed without the initialization of the number of clusters. Because the classical MDP segmentation cannot be applied for real-time diagnosis, a new nonparametric segmentation algorithm combined with anisotropic diffusion and a Markov random field (MRF) smooth constraint is proposed in this study. Besides the segmentation of single modal brain-tumor images, we developed the algorithm to segment multimodal brain-tumor images by the magnetic resonance (MR) multimodal features and obtain the active tumor and edema in the same time. The proposed algorithm is evaluated using 32 multimodal MR glioma image sequences, and the segmentation results are compared with other approaches. The accuracy and computation time of our algorithm demonstrates very impressive performance and has a great potential for practical real-time clinical use.

Multimodal Brain-Tumor Segmentation Based on Dirichlet Process Mixture Model with Anisotropic Diffusion and Markov Random Field Prior

PubMed Central

Lu, Yisu; Jiang, Jun; Chen, Wufan

2014-01-01

Brain-tumor segmentation is an important clinical requirement for brain-tumor diagnosis and radiotherapy planning. It is well-known that the number of clusters is one of the most important parameters for automatic segmentation. However, it is difficult to define owing to the high diversity in appearance of tumor tissue among different patients and the ambiguous boundaries of lesions. In this study, a nonparametric mixture of Dirichlet process (MDP) model is applied to segment the tumor images, and the MDP segmentation can be performed without the initialization of the number of clusters. Because the classical MDP segmentation cannot be applied for real-time diagnosis, a new nonparametric segmentation algorithm combined with anisotropic diffusion and a Markov random field (MRF) smooth constraint is proposed in this study. Besides the segmentation of single modal brain-tumor images, we developed the algorithm to segment multimodal brain-tumor images by the magnetic resonance (MR) multimodal features and obtain the active tumor and edema in the same time. The proposed algorithm is evaluated using 32 multimodal MR glioma image sequences, and the segmentation results are compared with other approaches. The accuracy and computation time of our algorithm demonstrates very impressive performance and has a great potential for practical real-time clinical use. PMID:25254064

Quantum "violation" of Dirichlet boundary condition

NASA Astrophysics Data System (ADS)

Park, I. Y.

2017-02-01

Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a tension between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum-corrected black hole solution of the 1PI action no longer obeys, in the naive manner one may expect, the Dirichlet boundary conditions imposed at the classical level. We attribute the 'violation' of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.

USING DIRICHLET TESSELLATION TO HELP ESTIMATE MICROBIAL BIOMASS CONCENTRATIONS

EPA Science Inventory

Dirichlet tessellation was applied to estimate microbial concentrations from microscope well slides. The use of microscopy/Dirichlet tessellation to quantify biomass was illustrated with two species of morphologically distinct cyanobacteria, and validated empirically by compariso...

A classical Perron method for existence of smooth solutions to boundary value and obstacle problems for degenerate-elliptic operators via holomorphic maps

NASA Astrophysics Data System (ADS)

Feehan, Paul M. N.

2017-09-01

We prove existence of solutions to boundary value problems and obstacle problems for degenerate-elliptic, linear, second-order partial differential operators with partial Dirichlet boundary conditions using a new version of the Perron method. The elliptic operators considered have a degeneracy along a portion of the domain boundary which is similar to the degeneracy of a model linear operator identified by Daskalopoulos and Hamilton [9] in their study of the porous medium equation or the degeneracy of the Heston operator [21] in mathematical finance. Existence of a solution to the partial Dirichlet problem on a half-ball, where the operator becomes degenerate on the flat boundary and a Dirichlet condition is only imposed on the spherical boundary, provides the key additional ingredient required for our Perron method. Surprisingly, proving existence of a solution to this partial Dirichlet problem with ;mixed; boundary conditions on a half-ball is more challenging than one might expect. Due to the difficulty in developing a global Schauder estimate and due to compatibility conditions arising where the ;degenerate; and ;non-degenerate boundaries; touch, one cannot directly apply the continuity or approximate solution methods. However, in dimension two, there is a holomorphic map from the half-disk onto the infinite strip in the complex plane and one can extend this definition to higher dimensions to give a diffeomorphism from the half-ball onto the infinite ;slab;. The solution to the partial Dirichlet problem on the half-ball can thus be converted to a partial Dirichlet problem on the slab, albeit for an operator which now has exponentially growing coefficients. The required Schauder regularity theory and existence of a solution to the partial Dirichlet problem on the slab can nevertheless be obtained using previous work of the author and C. Pop [16]. Our Perron method relies on weak and strong maximum principles for degenerate-elliptic operators, concepts of continuous subsolutions and supersolutions for boundary value and obstacle problems for degenerate-elliptic operators, and maximum and comparison principle estimates previously developed by the author [13].

Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming

2017-12-01

In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.

Stability and Hopf Bifurcation in a Reaction-Diffusion Model with Chemotaxis and Nonlocal Delay Effect

NASA Astrophysics Data System (ADS)

Li, Dong; Guo, Shangjiang

Chemotaxis is an observed phenomenon in which a biological individual moves preferentially toward a relatively high concentration, which is contrary to the process of natural diffusion. In this paper, we study a reaction-diffusion model with chemotaxis and nonlocal delay effect under Dirichlet boundary condition by using Lyapunov-Schmidt reduction and the implicit function theorem. The existence, multiplicity, stability and Hopf bifurcation of spatially nonhomogeneous steady state solutions are investigated. Moreover, our results are illustrated by an application to the model with a logistic source, homogeneous kernel and one-dimensional spatial domain.

Explicit treatment for Dirichlet, Neumann and Cauchy boundary conditions in POD-based reduction of groundwater models

NASA Astrophysics Data System (ADS)

Gosses, Moritz; Nowak, Wolfgang; Wöhling, Thomas

2018-05-01

In recent years, proper orthogonal decomposition (POD) has become a popular model reduction method in the field of groundwater modeling. It is used to mitigate the problem of long run times that are often associated with physically-based modeling of natural systems, especially for parameter estimation and uncertainty analysis. POD-based techniques reproduce groundwater head fields sufficiently accurate for a variety of applications. However, no study has investigated how POD techniques affect the accuracy of different boundary conditions found in groundwater models. We show that the current treatment of boundary conditions in POD causes inaccuracies for these boundaries in the reduced models. We provide an improved method that splits the POD projection space into a subspace orthogonal to the boundary conditions and a separate subspace that enforces the boundary conditions. To test the method for Dirichlet, Neumann and Cauchy boundary conditions, four simple transient 1D-groundwater models, as well as a more complex 3D model, are set up and reduced both by standard POD and POD with the new extension. We show that, in contrast to standard POD, the new method satisfies both Dirichlet and Neumann boundary conditions. It can also be applied to Cauchy boundaries, where the flux error of standard POD is reduced by its head-independent contribution. The extension essentially shifts the focus of the projection towards the boundary conditions. Therefore, we see a slight trade-off between errors at model boundaries and overall accuracy of the reduced model. The proposed POD extension is recommended where exact treatment of boundary conditions is required.

Spectral multigrid methods for elliptic equations 2

NASA Technical Reports Server (NTRS)

Zang, T. A.; Wong, Y. S.; Hussaini, M. Y.

1983-01-01

A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.

Quantum Gravitational Effects on the Boundary

NASA Astrophysics Data System (ADS)

James, F.; Park, I. Y.

2018-04-01

Quantum gravitational effects might hold the key to some of the outstanding problems in theoretical physics. We analyze the perturbative quantum effects on the boundary of a gravitational system and the Dirichlet boundary condition imposed at the classical level. Our analysis reveals that for a black hole solution, there is a contradiction between the quantum effects and the Dirichlet boundary condition: the black hole solution of the one-particle-irreducible action no longer satisfies the Dirichlet boundary condition as would be expected without going into details. The analysis also suggests that the tension between the Dirichlet boundary condition and loop effects is connected with a certain mechanism of information storage on the boundary.

Linguistic Extensions of Topic Models

ERIC Educational Resources Information Center

Boyd-Graber, Jordan

2010-01-01

Topic models like latent Dirichlet allocation (LDA) provide a framework for analyzing large datasets where observations are collected into groups. Although topic modeling has been fruitfully applied to problems social science, biology, and computer vision, it has been most widely used to model datasets where documents are modeled as exchangeable…

Using Bayesian Nonparametric Hidden Semi-Markov Models to Disentangle Affect Processes during Marital Interaction

PubMed Central

Griffin, William A.; Li, Xun

2016-01-01

Sequential affect dynamics generated during the interaction of intimate dyads, such as married couples, are associated with a cascade of effects—some good and some bad—on each partner, close family members, and other social contacts. Although the effects are well documented, the probabilistic structures associated with micro-social processes connected to the varied outcomes remain enigmatic. Using extant data we developed a method of classifying and subsequently generating couple dynamics using a Hierarchical Dirichlet Process Hidden semi-Markov Model (HDP-HSMM). Our findings indicate that several key aspects of existing models of marital interaction are inadequate: affect state emissions and their durations, along with the expected variability differences between distressed and nondistressed couples are present but highly nuanced; and most surprisingly, heterogeneity among highly satisfied couples necessitate that they be divided into subgroups. We review how this unsupervised learning technique generates plausible dyadic sequences that are sensitive to relationship quality and provide a natural mechanism for computational models of behavioral and affective micro-social processes. PMID:27187319

Regularization of moving boundaries in a laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results.

PubMed

Meulenbroek, Bernard; Ebert, Ute; Schäfer, Lothar

2005-11-04

The dynamics of ionization fronts that generate a conducting body are in the simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact uniformly propagating solutions of this problem in 2D and construct a single partial differential equation governing small perturbations of these solutions. For some parameter value, this equation can be solved analytically, which shows rigorously that the uniformly propagating solution is linearly convectively stable and that the asymptotic relaxation is universal and exponential in time.

A Dirichlet process model for classifying and forecasting epidemic curves.

PubMed

Nsoesie, Elaine O; Leman, Scotland C; Marathe, Madhav V

2014-01-09

A forecast can be defined as an endeavor to quantitatively estimate a future event or probabilities assigned to a future occurrence. Forecasting stochastic processes such as epidemics is challenging since there are several biological, behavioral, and environmental factors that influence the number of cases observed at each point during an epidemic. However, accurate forecasts of epidemics would impact timely and effective implementation of public health interventions. In this study, we introduce a Dirichlet process (DP) model for classifying and forecasting influenza epidemic curves. The DP model is a nonparametric Bayesian approach that enables the matching of current influenza activity to simulated and historical patterns, identifies epidemic curves different from those observed in the past and enables prediction of the expected epidemic peak time. The method was validated using simulated influenza epidemics from an individual-based model and the accuracy was compared to that of the tree-based classification technique, Random Forest (RF), which has been shown to achieve high accuracy in the early prediction of epidemic curves using a classification approach. We also applied the method to forecasting influenza outbreaks in the United States from 1997-2013 using influenza-like illness (ILI) data from the Centers for Disease Control and Prevention (CDC). We made the following observations. First, the DP model performed as well as RF in identifying several of the simulated epidemics. Second, the DP model correctly forecasted the peak time several days in advance for most of the simulated epidemics. Third, the accuracy of identifying epidemics different from those already observed improved with additional data, as expected. Fourth, both methods correctly classified epidemics with higher reproduction numbers (R) with a higher accuracy compared to epidemics with lower R values. Lastly, in the classification of seasonal influenza epidemics based on ILI data from the CDC, the methods' performance was comparable. Although RF requires less computational time compared to the DP model, the algorithm is fully supervised implying that epidemic curves different from those previously observed will always be misclassified. In contrast, the DP model can be unsupervised, semi-supervised or fully supervised. Since both methods have their relative merits, an approach that uses both RF and the DP model could be beneficial.

A Case Study on Sepsis Using PubMed and Deep Learning for Ontology Learning.

PubMed

Arguello Casteleiro, Mercedes; Maseda Fernandez, Diego; Demetriou, George; Read, Warren; Fernandez Prieto, Maria Jesus; Des Diz, Julio; Nenadic, Goran; Keane, John; Stevens, Robert

2017-01-01

We investigate the application of distributional semantics models for facilitating unsupervised extraction of biomedical terms from unannotated corpora. Term extraction is used as the first step of an ontology learning process that aims to (semi-)automatic annotation of biomedical concepts and relations from more than 300K PubMed titles and abstracts. We experimented with both traditional distributional semantics methods such as Latent Semantic Analysis (LSA) and Latent Dirichlet Allocation (LDA) as well as the neural language models CBOW and Skip-gram from Deep Learning. The evaluation conducted concentrates on sepsis, a major life-threatening condition, and shows that Deep Learning models outperform LSA and LDA with much higher precision.

Study of a mixed dispersal population dynamics model

DOE PAGES

Chugunova, Marina; Jadamba, Baasansuren; Kao, Chiu -Yen; ...

2016-08-27

In this study, we consider a mixed dispersal model with periodic and Dirichlet boundary conditions and its corresponding linear eigenvalue problem. This model describes the time evolution of a population which disperses both locally and non-locally. We investigate how long time dynamics depend on the parameter values. Furthermore, we study the minimization of the principal eigenvalue under the constraints that the resource function is bounded from above and below, and with a fixed total integral. Biologically, this minimization problem is motivated by the question of determining the optimal spatial arrangement of favorable and unfavorable regions for the species to diemore » out more slowly or survive more easily. Our numerical simulations indicate that the optimal favorable region tends to be a simply-connected domain. Numerous results are shown to demonstrate various scenarios of optimal favorable regions for periodic and Dirichlet boundary conditions.« less

Dirichlet Component Regression and its Applications to Psychiatric Data.

PubMed

Gueorguieva, Ralitza; Rosenheck, Robert; Zelterman, Daniel

2008-08-15

We describe a Dirichlet multivariable regression method useful for modeling data representing components as a percentage of a total. This model is motivated by the unmet need in psychiatry and other areas to simultaneously assess the effects of covariates on the relative contributions of different components of a measure. The model is illustrated using the Positive and Negative Syndrome Scale (PANSS) for assessment of schizophrenia symptoms which, like many other metrics in psychiatry, is composed of a sum of scores on several components, each in turn, made up of sums of evaluations on several questions. We simultaneously examine the effects of baseline socio-demographic and co-morbid correlates on all of the components of the total PANSS score of patients from a schizophrenia clinical trial and identify variables associated with increasing or decreasing relative contributions of each component. Several definitions of residuals are provided. Diagnostics include measures of overdispersion, Cook's distance, and a local jackknife influence metric.

Stability estimate for the aligned magnetic field in a periodic quantum waveguide from Dirichlet-to-Neumann map

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

Mejri, Youssef, E-mail: josef-bizert@hotmail.fr; Dép. des Mathématiques, Faculté des Sciences de Bizerte, 7021 Jarzouna; Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l’Ingénieur, ENIT BP 37, Le Belvedere, 1002 Tunis

In this article, we study the boundary inverse problem of determining the aligned magnetic field appearing in the magnetic Schrödinger equation in a periodic quantum cylindrical waveguide, by knowledge of the Dirichlet-to-Neumann map. We prove a Hölder stability estimate with respect to the Dirichlet-to-Neumann map, by means of the geometrical optics solutions of the magnetic Schrödinger equation.

Constructing Weyl group multiple Dirichlet series

NASA Astrophysics Data System (ADS)

Chinta, Gautam; Gunnells, Paul E.

2010-01-01

Let Phi be a reduced root system of rank r . A Weyl group multiple Dirichlet series for Phi is a Dirichlet series in r complex variables s_1,dots,s_r , initially converging for {Re}(s_i) sufficiently large, that has meromorphic continuation to {{C}}^r and satisfies functional equations under the transformations of {{C}}^r corresponding to the Weyl group of Phi . A heuristic definition of such a series was given by Brubaker, Bump, Chinta, Friedberg, and Hoffstein, and they have been investigated in certain special cases by others. In this paper we generalize results by Chinta and Gunnells to construct Weyl group multiple Dirichlet series by a uniform method and show in all cases that they have the expected properties.

Partial Membership Latent Dirichlet Allocation for Soft Image Segmentation.

PubMed

Chen, Chao; Zare, Alina; Trinh, Huy N; Omotara, Gbenga O; Cobb, James Tory; Lagaunne, Timotius A

2017-12-01

Topic models [e.g., probabilistic latent semantic analysis, latent Dirichlet allocation (LDA), and supervised LDA] have been widely used for segmenting imagery. However, these models are confined to crisp segmentation, forcing a visual word (i.e., an image patch) to belong to one and only one topic. Yet, there are many images in which some regions cannot be assigned a crisp categorical label (e.g., transition regions between a foggy sky and the ground or between sand and water at a beach). In these cases, a visual word is best represented with partial memberships across multiple topics. To address this, we present a partial membership LDA (PM-LDA) model and an associated parameter estimation algorithm. This model can be useful for imagery, where a visual word may be a mixture of multiple topics. Experimental results on visual and sonar imagery show that PM-LDA can produce both crisp and soft semantic image segmentations; a capability previous topic modeling methods do not have.

Modeling Information Content Via Dirichlet-Multinomial Regression Analysis.

PubMed

Ferrari, Alberto

2017-01-01

Shannon entropy is being increasingly used in biomedical research as an index of complexity and information content in sequences of symbols, e.g. languages, amino acid sequences, DNA methylation patterns and animal vocalizations. Yet, distributional properties of information entropy as a random variable have seldom been the object of study, leading to researchers mainly using linear models or simulation-based analytical approach to assess differences in information content, when entropy is measured repeatedly in different experimental conditions. Here a method to perform inference on entropy in such conditions is proposed. Building on results coming from studies in the field of Bayesian entropy estimation, a symmetric Dirichlet-multinomial regression model, able to deal efficiently with the issue of mean entropy estimation, is formulated. Through a simulation study the model is shown to outperform linear modeling in a vast range of scenarios and to have promising statistical properties. As a practical example, the method is applied to a data set coming from a real experiment on animal communication.

What to Do When K-Means Clustering Fails: A Simple yet Principled Alternative Algorithm.

PubMed

Raykov, Yordan P; Boukouvalas, Alexis; Baig, Fahd; Little, Max A

The K-means algorithm is one of the most popular clustering algorithms in current use as it is relatively fast yet simple to understand and deploy in practice. Nevertheless, its use entails certain restrictive assumptions about the data, the negative consequences of which are not always immediately apparent, as we demonstrate. While more flexible algorithms have been developed, their widespread use has been hindered by their computational and technical complexity. Motivated by these considerations, we present a flexible alternative to K-means that relaxes most of the assumptions, whilst remaining almost as fast and simple. This novel algorithm which we call MAP-DP (maximum a-posteriori Dirichlet process mixtures), is statistically rigorous as it is based on nonparametric Bayesian Dirichlet process mixture modeling. This approach allows us to overcome most of the limitations imposed by K-means. The number of clusters K is estimated from the data instead of being fixed a-priori as in K-means. In addition, while K-means is restricted to continuous data, the MAP-DP framework can be applied to many kinds of data, for example, binary, count or ordinal data. Also, it can efficiently separate outliers from the data. This additional flexibility does not incur a significant computational overhead compared to K-means with MAP-DP convergence typically achieved in the order of seconds for many practical problems. Finally, in contrast to K-means, since the algorithm is based on an underlying statistical model, the MAP-DP framework can deal with missing data and enables model testing such as cross validation in a principled way. We demonstrate the simplicity and effectiveness of this algorithm on the health informatics problem of clinical sub-typing in a cluster of diseases known as parkinsonism.

What to Do When K-Means Clustering Fails: A Simple yet Principled Alternative Algorithm

PubMed Central

Baig, Fahd; Little, Max A.

2016-01-01

The K-means algorithm is one of the most popular clustering algorithms in current use as it is relatively fast yet simple to understand and deploy in practice. Nevertheless, its use entails certain restrictive assumptions about the data, the negative consequences of which are not always immediately apparent, as we demonstrate. While more flexible algorithms have been developed, their widespread use has been hindered by their computational and technical complexity. Motivated by these considerations, we present a flexible alternative to K-means that relaxes most of the assumptions, whilst remaining almost as fast and simple. This novel algorithm which we call MAP-DP (maximum a-posteriori Dirichlet process mixtures), is statistically rigorous as it is based on nonparametric Bayesian Dirichlet process mixture modeling. This approach allows us to overcome most of the limitations imposed by K-means. The number of clusters K is estimated from the data instead of being fixed a-priori as in K-means. In addition, while K-means is restricted to continuous data, the MAP-DP framework can be applied to many kinds of data, for example, binary, count or ordinal data. Also, it can efficiently separate outliers from the data. This additional flexibility does not incur a significant computational overhead compared to K-means with MAP-DP convergence typically achieved in the order of seconds for many practical problems. Finally, in contrast to K-means, since the algorithm is based on an underlying statistical model, the MAP-DP framework can deal with missing data and enables model testing such as cross validation in a principled way. We demonstrate the simplicity and effectiveness of this algorithm on the health informatics problem of clinical sub-typing in a cluster of diseases known as parkinsonism. PMID:27669525

Comparing Latent Dirichlet Allocation and Latent Semantic Analysis as Classifiers

ERIC Educational Resources Information Center

Anaya, Leticia H.

2011-01-01

In the Information Age, a proliferation of unstructured text electronic documents exists. Processing these documents by humans is a daunting task as humans have limited cognitive abilities for processing large volumes of documents that can often be extremely lengthy. To address this problem, text data computer algorithms are being developed.…

Numerical Study of Periodic Traveling Wave Solutions for the Predator-Prey Model with Landscape Features

NASA Astrophysics Data System (ADS)

Yun, Ana; Shin, Jaemin; Li, Yibao; Lee, Seunggyu; Kim, Junseok

We numerically investigate periodic traveling wave solutions for a diffusive predator-prey system with landscape features. The landscape features are modeled through the homogeneous Dirichlet boundary condition which is imposed at the edge of the obstacle domain. To effectively treat the Dirichlet boundary condition, we employ a robust and accurate numerical technique by using a boundary control function. We also propose a robust algorithm for calculating the numerical periodicity of the traveling wave solution. In numerical experiments, we show that periodic traveling waves which move out and away from the obstacle are effectively generated. We explain the formation of the traveling waves by comparing the wavelengths. The spatial asynchrony has been shown in quantitative detail for various obstacles. Furthermore, we apply our numerical technique to the complicated real landscape features.

Using Dirichlet Priors to Improve Model Parameter Plausibility

ERIC Educational Resources Information Center

Rai, Dovan; Gong, Yue; Beck, Joseph E.

2009-01-01

Student modeling is a widely used approach to make inference about a student's attributes like knowledge, learning, etc. If we wish to use these models to analyze and better understand student learning there are two problems. First, a model's ability to predict student performance is at best weakly related to the accuracy of any one of its…

Bounded solutions in a T-shaped waveguide and the spectral properties of the Dirichlet ladder

NASA Astrophysics Data System (ADS)

Nazarov, S. A.

2014-08-01

The Dirichlet problem is considered on the junction of thin quantum waveguides (of thickness h ≪ 1) in the shape of an infinite two-dimensional ladder. Passage to the limit as h → +0 is discussed. It is shown that the asymptotically correct transmission conditions at nodes of the corresponding one-dimensional quantum graph are Dirichlet conditions rather than the conventional Kirchhoff transmission conditions. The result is obtained by analyzing bounded solutions of a problem in the T-shaped waveguide that the boundary layer phenomenon.

General stability of memory-type thermoelastic Timoshenko beam acting on shear force

NASA Astrophysics Data System (ADS)

Apalara, Tijani A.

2018-03-01

In this paper, we consider a linear thermoelastic Timoshenko system with memory effects where the thermoelastic coupling is acting on shear force under Neumann-Dirichlet-Dirichlet boundary conditions. The same system with fully Dirichlet boundary conditions was considered by Messaoudi and Fareh (Nonlinear Anal TMA 74(18):6895-6906, 2011, Acta Math Sci 33(1):23-40, 2013), but they obtained a general stability result which depends on the speeds of wave propagation. In our case, we obtained a general stability result irrespective of the wave speeds of the system.

First-passage dynamics of linear stochastic interface models: weak-noise theory and influence of boundary conditions

NASA Astrophysics Data System (ADS)

Gross, Markus

2018-03-01

We consider a one-dimensional fluctuating interfacial profile governed by the Edwards–Wilkinson or the stochastic Mullins-Herring equation for periodic, standard Dirichlet and Dirichlet no-flux boundary conditions. The minimum action path of an interfacial fluctuation conditioned to reach a given maximum height M at a finite (first-passage) time T is calculated within the weak-noise approximation. Dynamic and static scaling functions for the profile shape are obtained in the transient and the equilibrium regime, i.e. for first-passage times T smaller or larger than the characteristic relaxation time, respectively. In both regimes, the profile approaches the maximum height M with a universal algebraic time dependence characterized solely by the dynamic exponent of the model. It is shown that, in the equilibrium regime, the spatial shape of the profile depends sensitively on boundary conditions and conservation laws, but it is essentially independent of them in the transient regime.

A generalized Poisson solver for first-principles device simulations

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

Bani-Hashemian, Mohammad Hossein; VandeVondele, Joost, E-mail: joost.vandevondele@mat.ethz.ch; Brück, Sascha

2016-01-28

Electronic structure calculations of atomistic systems based on density functional theory involve solving the Poisson equation. In this paper, we present a plane-wave based algorithm for solving the generalized Poisson equation subject to periodic or homogeneous Neumann conditions on the boundaries of the simulation cell and Dirichlet type conditions imposed at arbitrary subdomains. In this way, source, drain, and gate voltages can be imposed across atomistic models of electronic devices. Dirichlet conditions are enforced as constraints in a variational framework giving rise to a saddle point problem. The resulting system of equations is then solved using a stationary iterative methodmore » in which the generalized Poisson operator is preconditioned with the standard Laplace operator. The solver can make use of any sufficiently smooth function modelling the dielectric constant, including density dependent dielectric continuum models. For all the boundary conditions, consistent derivatives are available and molecular dynamics simulations can be performed. The convergence behaviour of the scheme is investigated and its capabilities are demonstrated.« less

Dirichlet Component Regression and its Applications to Psychiatric Data

PubMed Central

Gueorguieva, Ralitza; Rosenheck, Robert; Zelterman, Daniel

2011-01-01

Summary We describe a Dirichlet multivariable regression method useful for modeling data representing components as a percentage of a total. This model is motivated by the unmet need in psychiatry and other areas to simultaneously assess the effects of covariates on the relative contributions of different components of a measure. The model is illustrated using the Positive and Negative Syndrome Scale (PANSS) for assessment of schizophrenia symptoms which, like many other metrics in psychiatry, is composed of a sum of scores on several components, each in turn, made up of sums of evaluations on several questions. We simultaneously examine the effects of baseline socio-demographic and co-morbid correlates on all of the components of the total PANSS score of patients from a schizophrenia clinical trial and identify variables associated with increasing or decreasing relative contributions of each component. Several definitions of residuals are provided. Diagnostics include measures of overdispersion, Cook’s distance, and a local jackknife influence metric. PMID:22058582

Pareto genealogies arising from a Poisson branching evolution model with selection.

PubMed

Huillet, Thierry E

2014-02-01

We study a class of coalescents derived from a sampling procedure out of N i.i.d. Pareto(α) random variables, normalized by their sum, including β-size-biasing on total length effects (β < α). Depending on the range of α we derive the large N limit coalescents structure, leading either to a discrete-time Poisson-Dirichlet (α, -β) Ξ-coalescent (α ε[0, 1)), or to a family of continuous-time Beta (2 - α, α - β)Λ-coalescents (α ε[1, 2)), or to the Kingman coalescent (α ≥ 2). We indicate that this class of coalescent processes (and their scaling limits) may be viewed as the genealogical processes of some forward in time evolving branching population models including selection effects. In such constant-size population models, the reproduction step, which is based on a fitness-dependent Poisson Point Process with scaling power-law(α) intensity, is coupled to a selection step consisting of sorting out the N fittest individuals issued from the reproduction step.

A Meinardus Theorem with Multiple Singularities

NASA Astrophysics Data System (ADS)

Granovsky, Boris L.; Stark, Dudley

2012-09-01

Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing (Granovsky et al., Adv. Appl. Math. 41:307-328, 2008), we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size n, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.

A Dirichlet process model for classifying and forecasting epidemic curves

PubMed Central

2014-01-01

Background A forecast can be defined as an endeavor to quantitatively estimate a future event or probabilities assigned to a future occurrence. Forecasting stochastic processes such as epidemics is challenging since there are several biological, behavioral, and environmental factors that influence the number of cases observed at each point during an epidemic. However, accurate forecasts of epidemics would impact timely and effective implementation of public health interventions. In this study, we introduce a Dirichlet process (DP) model for classifying and forecasting influenza epidemic curves. Methods The DP model is a nonparametric Bayesian approach that enables the matching of current influenza activity to simulated and historical patterns, identifies epidemic curves different from those observed in the past and enables prediction of the expected epidemic peak time. The method was validated using simulated influenza epidemics from an individual-based model and the accuracy was compared to that of the tree-based classification technique, Random Forest (RF), which has been shown to achieve high accuracy in the early prediction of epidemic curves using a classification approach. We also applied the method to forecasting influenza outbreaks in the United States from 1997–2013 using influenza-like illness (ILI) data from the Centers for Disease Control and Prevention (CDC). Results We made the following observations. First, the DP model performed as well as RF in identifying several of the simulated epidemics. Second, the DP model correctly forecasted the peak time several days in advance for most of the simulated epidemics. Third, the accuracy of identifying epidemics different from those already observed improved with additional data, as expected. Fourth, both methods correctly classified epidemics with higher reproduction numbers (R) with a higher accuracy compared to epidemics with lower R values. Lastly, in the classification of seasonal influenza epidemics based on ILI data from the CDC, the methods’ performance was comparable. Conclusions Although RF requires less computational time compared to the DP model, the algorithm is fully supervised implying that epidemic curves different from those previously observed will always be misclassified. In contrast, the DP model can be unsupervised, semi-supervised or fully supervised. Since both methods have their relative merits, an approach that uses both RF and the DP model could be beneficial. PMID:24405642

Differential Topic Models.

PubMed

Chen, Changyou; Buntine, Wray; Ding, Nan; Xie, Lexing; Du, Lan

2015-02-01

In applications we may want to compare different document collections: they could have shared content but also different and unique aspects in particular collections. This task has been called comparative text mining or cross-collection modeling. We present a differential topic model for this application that models both topic differences and similarities. For this we use hierarchical Bayesian nonparametric models. Moreover, we found it was important to properly model power-law phenomena in topic-word distributions and thus we used the full Pitman-Yor process rather than just a Dirichlet process. Furthermore, we propose the transformed Pitman-Yor process (TPYP) to incorporate prior knowledge such as vocabulary variations in different collections into the model. To deal with the non-conjugate issue between model prior and likelihood in the TPYP, we thus propose an efficient sampling algorithm using a data augmentation technique based on the multinomial theorem. Experimental results show the model discovers interesting aspects of different collections. We also show the proposed MCMC based algorithm achieves a dramatically reduced test perplexity compared to some existing topic models. Finally, we show our model outperforms the state-of-the-art for document classification/ideology prediction on a number of text collections.

Application of the perfectly matched layer in 2.5D marine controlled-source electromagnetic modeling

NASA Astrophysics Data System (ADS)

Li, Gang; Han, Bo

2017-09-01

For the traditional framework of EM modeling algorithms, the Dirichlet boundary is usually used which assumes the field values are zero at the boundaries. This crude condition requires that the boundaries should be sufficiently far away from the area of interest. Although cell sizes could become larger toward the boundaries as electromagnetic wave is propagated diffusively, a large modeling area may still be necessary to mitigate the boundary artifacts. In this paper, the complex frequency-shifted perfectly matched layer (CFS-PML) in stretching Cartesian coordinates is successfully applied to 2.5D frequency-domain marine controlled-source electromagnetic (CSEM) field modeling. By using this PML boundary, one can restrict the modeling area of interest to the target region. Only a few absorbing layers surrounding the computational area can effectively depress the artificial boundary effect without losing the numerical accuracy. A 2.5D marine CSEM modeling scheme with the CFS-PML is developed by using the staggered finite-difference discretization. This modeling algorithm using the CFS-PML is of high accuracy, and shows advantages in computational time and memory saving than that using the Dirichlet boundary. For 3D problem, this computation time and memory saving should be more significant.

A simple way to unify multicriteria decision analysis (MCDA) and stochastic multicriteria acceptability analysis (SMAA) using a Dirichlet distribution in benefit-risk assessment.

PubMed

Saint-Hilary, Gaelle; Cadour, Stephanie; Robert, Veronique; Gasparini, Mauro

2017-05-01

Quantitative methodologies have been proposed to support decision making in drug development and monitoring. In particular, multicriteria decision analysis (MCDA) and stochastic multicriteria acceptability analysis (SMAA) are useful tools to assess the benefit-risk ratio of medicines according to the performances of the treatments on several criteria, accounting for the preferences of the decision makers regarding the relative importance of these criteria. However, even in its probabilistic form, MCDA requires the exact elicitations of the weights of the criteria by the decision makers, which may be difficult to achieve in practice. SMAA allows for more flexibility and can be used with unknown or partially known preferences, but it is less popular due to its increased complexity and the high degree of uncertainty in its results. In this paper, we propose a simple model as a generalization of MCDA and SMAA, by applying a Dirichlet distribution to the weights of the criteria and by making its parameters vary. This unique model permits to fit both MCDA and SMAA, and allows for a more extended exploration of the benefit-risk assessment of treatments. The precision of its results depends on the precision parameter of the Dirichlet distribution, which could be naturally interpreted as the strength of confidence of the decision makers in their elicitation of preferences. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Infinite hidden conditional random fields for human behavior analysis.

PubMed

Bousmalis, Konstantinos; Zafeiriou, Stefanos; Morency, Louis-Philippe; Pantic, Maja

2013-01-01

Hidden conditional random fields (HCRFs) are discriminative latent variable models that have been shown to successfully learn the hidden structure of a given classification problem (provided an appropriate validation of the number of hidden states). In this brief, we present the infinite HCRF (iHCRF), which is a nonparametric model based on hierarchical Dirichlet processes and is capable of automatically learning the optimal number of hidden states for a classification task. We show how we learn the model hyperparameters with an effective Markov-chain Monte Carlo sampling technique, and we explain the process that underlines our iHCRF model with the Restaurant Franchise Rating Agencies analogy. We show that the iHCRF is able to converge to a correct number of represented hidden states, and outperforms the best finite HCRFs--chosen via cross-validation--for the difficult tasks of recognizing instances of agreement, disagreement, and pain. Moreover, the iHCRF manages to achieve this performance in significantly less total training, validation, and testing time.

Dirichlet boundary conditions for arbitrary-shaped boundaries in stellarator-like magnetic fields for the Flux-Coordinate Independent method

NASA Astrophysics Data System (ADS)

Hill, Peter; Shanahan, Brendan; Dudson, Ben

2017-04-01

We present a technique for handling Dirichlet boundary conditions with the Flux Coordinate Independent (FCI) parallel derivative operator with arbitrary-shaped material geometry in general 3D magnetic fields. The FCI method constructs a finite difference scheme for ∇∥ by following field lines between poloidal planes and interpolating within planes. Doing so removes the need for field-aligned coordinate systems that suffer from singularities in the metric tensor at null points in the magnetic field (or equivalently, when q → ∞). One cost of this method is that as the field lines are not on the mesh, they may leave the domain at any point between neighbouring planes, complicating the application of boundary conditions. The Leg Value Fill (LVF) boundary condition scheme presented here involves an extrapolation/interpolation of the boundary value onto the field line end point. The usual finite difference scheme can then be used unmodified. We implement the LVF scheme in BOUT++ and use the Method of Manufactured Solutions to verify the implementation in a rectangular domain, and show that it does not modify the error scaling of the finite difference scheme. The use of LVF for arbitrary wall geometry is outlined. We also demonstrate the feasibility of using the FCI approach in no n-axisymmetric configurations for a simple diffusion model in a "straight stellarator" magnetic field. A Gaussian blob diffuses along the field lines, tracing out flux surfaces. Dirichlet boundary conditions impose a last closed flux surface (LCFS) that confines the density. Including a poloidal limiter moves the LCFS to a smaller radius. The expected scaling of the numerical perpendicular diffusion, which is a consequence of the FCI method, in stellarator-like geometry is recovered. A novel technique for increasing the parallel resolution during post-processing, in order to reduce artefacts in visualisations, is described.

Stable, high-order computation of impedance-impedance operators for three-dimensional layered medium simulations.

PubMed

Nicholls, David P

2018-04-01

The faithful modelling of the propagation of linear waves in a layered, periodic structure is of paramount importance in many branches of the applied sciences. In this paper, we present a novel numerical algorithm for the simulation of such problems which is free of the artificial singularities present in related approaches. We advocate for a surface integral formulation which is phrased in terms of impedance-impedance operators that are immune to the Dirichlet eigenvalues which plague the Dirichlet-Neumann operators that appear in classical formulations. We demonstrate a high-order spectral algorithm to simulate these latter operators based upon a high-order perturbation of surfaces methodology which is rapid, robust and highly accurate. We demonstrate the validity and utility of our approach with a sequence of numerical simulations.

A three-dimensional Dirichlet-to-Neumann operator for water waves over topography

NASA Astrophysics Data System (ADS)

Andrade, D.; Nachbin, A.

2018-06-01

Surface water waves are considered propagating over highly variable non-smooth topographies. For this three dimensional problem a Dirichlet-to-Neumann (DtN) operator is constructed reducing the numerical modeling and evolution to the two dimensional free surface. The corresponding Fourier-type operator is defined through a matrix decomposition. The topographic component of the decomposition requires special care and a Galerkin method is provided accordingly. One dimensional numerical simulations, along the free surface, validate the DtN formulation in the presence of a large amplitude, rapidly varying topography. An alternative, conformal mapping based, method is used for benchmarking. A two dimensional simulation in the presence of a Luneburg lens (a particular submerged mound) illustrates the accurate performance of the three dimensional DtN operator.

Stable, high-order computation of impedance-impedance operators for three-dimensional layered medium simulations

NASA Astrophysics Data System (ADS)

Nicholls, David P.

2018-04-01

The faithful modelling of the propagation of linear waves in a layered, periodic structure is of paramount importance in many branches of the applied sciences. In this paper, we present a novel numerical algorithm for the simulation of such problems which is free of the artificial singularities present in related approaches. We advocate for a surface integral formulation which is phrased in terms of impedance-impedance operators that are immune to the Dirichlet eigenvalues which plague the Dirichlet-Neumann operators that appear in classical formulations. We demonstrate a high-order spectral algorithm to simulate these latter operators based upon a high-order perturbation of surfaces methodology which is rapid, robust and highly accurate. We demonstrate the validity and utility of our approach with a sequence of numerical simulations.

A Dirichlet process mixture model for automatic (18)F-FDG PET image segmentation: Validation study on phantoms and on lung and esophageal lesions.

PubMed

Giri, Maria Grazia; Cavedon, Carlo; Mazzarotto, Renzo; Ferdeghini, Marco

2016-05-01

The aim of this study was to implement a Dirichlet process mixture (DPM) model for automatic tumor edge identification on (18)F-fluorodeoxyglucose positron emission tomography ((18)F-FDG PET) images by optimizing the parameters on which the algorithm depends, to validate it experimentally, and to test its robustness. The DPM model belongs to the class of the Bayesian nonparametric models and uses the Dirichlet process prior for flexible nonparametric mixture modeling, without any preliminary choice of the number of mixture components. The DPM algorithm implemented in the statistical software package R was used in this work. The contouring accuracy was evaluated on several image data sets: on an IEC phantom (spherical inserts with diameter in the range 10-37 mm) acquired by a Philips Gemini Big Bore PET-CT scanner, using 9 different target-to-background ratios (TBRs) from 2.5 to 70; on a digital phantom simulating spherical/uniform lesions and tumors, irregular in shape and activity; and on 20 clinical cases (10 lung and 10 esophageal cancer patients). The influence of the DPM parameters on contour generation was studied in two steps. In the first one, only the IEC spheres having diameters of 22 and 37 mm and a sphere of the digital phantom (41.6 mm diameter) were studied by varying the main parameters until the diameter of the spheres was obtained within 0.2% of the true value. In the second step, the results obtained for this training set were applied to the entire data set to determine DPM based volumes of all available lesions. These volumes were compared to those obtained by applying already known algorithms (Gaussian mixture model and gradient-based) and to true values, when available. Only one parameter was found able to significantly influence segmentation accuracy (ANOVA test). This parameter was linearly connected to the uptake variance of the tested region of interest (ROI). In the first step of the study, a calibration curve was determined to automatically generate the optimal parameter from the variance of the ROI. This "calibration curve" was then applied to contour the whole data set. The accuracy (mean discrepancy between DPM model-based contours and reference contours) of volume estimation was below (1 ± 7)% on the whole data set (1 SD). The overlap between true and automatically segmented contours, measured by the Dice similarity coefficient, was 0.93 with a SD of 0.03. The proposed DPM model was able to accurately reproduce known volumes of FDG concentration, with high overlap between segmented and true volumes. For all the analyzed inserts of the IEC phantom, the algorithm proved to be robust to variations in radius and in TBR. The main advantage of this algorithm was that no setting of DPM parameters was required in advance, since the proper setting of the only parameter that could significantly influence the segmentation results was automatically related to the uptake variance of the chosen ROI. Furthermore, the algorithm did not need any preliminary choice of the optimum number of classes to describe the ROIs within PET images and no assumption about the shape of the lesion and the uptake heterogeneity of the tracer was required.

A Dirichlet process mixture model for automatic {sup 18}F-FDG PET image segmentation: Validation study on phantoms and on lung and esophageal lesions

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

Giri, Maria Grazia, E-mail: mariagrazia.giri@ospedaleuniverona.it; Cavedon, Carlo; Mazzarotto, Renzo

Purpose: The aim of this study was to implement a Dirichlet process mixture (DPM) model for automatic tumor edge identification on {sup 18}F-fluorodeoxyglucose positron emission tomography ({sup 18}F-FDG PET) images by optimizing the parameters on which the algorithm depends, to validate it experimentally, and to test its robustness. Methods: The DPM model belongs to the class of the Bayesian nonparametric models and uses the Dirichlet process prior for flexible nonparametric mixture modeling, without any preliminary choice of the number of mixture components. The DPM algorithm implemented in the statistical software package R was used in this work. The contouring accuracymore » was evaluated on several image data sets: on an IEC phantom (spherical inserts with diameter in the range 10–37 mm) acquired by a Philips Gemini Big Bore PET-CT scanner, using 9 different target-to-background ratios (TBRs) from 2.5 to 70; on a digital phantom simulating spherical/uniform lesions and tumors, irregular in shape and activity; and on 20 clinical cases (10 lung and 10 esophageal cancer patients). The influence of the DPM parameters on contour generation was studied in two steps. In the first one, only the IEC spheres having diameters of 22 and 37 mm and a sphere of the digital phantom (41.6 mm diameter) were studied by varying the main parameters until the diameter of the spheres was obtained within 0.2% of the true value. In the second step, the results obtained for this training set were applied to the entire data set to determine DPM based volumes of all available lesions. These volumes were compared to those obtained by applying already known algorithms (Gaussian mixture model and gradient-based) and to true values, when available. Results: Only one parameter was found able to significantly influence segmentation accuracy (ANOVA test). This parameter was linearly connected to the uptake variance of the tested region of interest (ROI). In the first step of the study, a calibration curve was determined to automatically generate the optimal parameter from the variance of the ROI. This “calibration curve” was then applied to contour the whole data set. The accuracy (mean discrepancy between DPM model-based contours and reference contours) of volume estimation was below (1 ± 7)% on the whole data set (1 SD). The overlap between true and automatically segmented contours, measured by the Dice similarity coefficient, was 0.93 with a SD of 0.03. Conclusions: The proposed DPM model was able to accurately reproduce known volumes of FDG concentration, with high overlap between segmented and true volumes. For all the analyzed inserts of the IEC phantom, the algorithm proved to be robust to variations in radius and in TBR. The main advantage of this algorithm was that no setting of DPM parameters was required in advance, since the proper setting of the only parameter that could significantly influence the segmentation results was automatically related to the uptake variance of the chosen ROI. Furthermore, the algorithm did not need any preliminary choice of the optimum number of classes to describe the ROIs within PET images and no assumption about the shape of the lesion and the uptake heterogeneity of the tracer was required.« less

Nonparametric Bayesian models for a spatial covariance.

PubMed

Reich, Brian J; Fuentes, Montserrat

2012-01-01

A crucial step in the analysis of spatial data is to estimate the spatial correlation function that determines the relationship between a spatial process at two locations. The standard approach to selecting the appropriate correlation function is to use prior knowledge or exploratory analysis, such as a variogram analysis, to select the correct parametric correlation function. Rather that selecting a particular parametric correlation function, we treat the covariance function as an unknown function to be estimated from the data. We propose a flexible prior for the correlation function to provide robustness to the choice of correlation function. We specify the prior for the correlation function using spectral methods and the Dirichlet process prior, which is a common prior for an unknown distribution function. Our model does not require Gaussian data or spatial locations on a regular grid. The approach is demonstrated using a simulation study as well as an analysis of California air pollution data.

Sine-gordon type field in spacetime of arbitrary dimension. II: Stochastic quantization

NASA Astrophysics Data System (ADS)

Kirillov, A. I.

1995-11-01

Using the theory of Dirichlet forms, we prove the existence of a distribution-valued diffusion process such that the Nelson measure of a field with a bounded interaction density is its invariant probability measure. A Langevin equation in mathematically correct form is formulated which is satisfied by the process. The drift term of the equation is interpreted as a renormalized Euclidean current operator.

Null boundary controllability of a one-dimensional heat equation with an internal point mass and variable coefficients

NASA Astrophysics Data System (ADS)

Ben Amara, Jamel; Bouzidi, Hedi

2018-01-01

In this paper, we consider a linear hybrid system which is composed by two non-homogeneous rods connected by a point mass with Dirichlet boundary conditions on the left end and a boundary control acts on the right end. We prove that this system is null controllable with Dirichlet or Neumann boundary controls. Our approach is mainly based on a detailed spectral analysis together with the moment method. In particular, we show that the associated spectral gap in both cases (Dirichlet or Neumann boundary controls) is positive without further conditions on the coefficients other than the regularities.

The Dirichlet-Multinomial Model for Multivariate Randomized Response Data and Small Samples

ERIC Educational Resources Information Center

Avetisyan, Marianna; Fox, Jean-Paul

2012-01-01

In survey sampling the randomized response (RR) technique can be used to obtain truthful answers to sensitive questions. Although the individual answers are masked due to the RR technique, individual (sensitive) response rates can be estimated when observing multivariate response data. The beta-binomial model for binary RR data will be generalized…

New solutions to the constant-head test performed at a partially penetrating well

NASA Astrophysics Data System (ADS)

Chang, Y. C.; Yeh, H. D.

2009-05-01

SummaryThe mathematical model describing the aquifer response to a constant-head test performed at a fully penetrating well can be easily solved by the conventional integral transform technique. In addition, the Dirichlet-type condition should be chosen as the boundary condition along the rim of wellbore for such a test well. However, the boundary condition for a test well with partial penetration must be considered as a mixed-type condition. Generally, the Dirichlet condition is prescribed along the well screen and the Neumann type no-flow condition is specified over the unscreened part of the test well. The model for such a mixed boundary problem in a confined aquifer system of infinite radial extent and finite vertical extent is solved by the dual series equations and perturbation method. This approach provides analytical results for the drawdown in the partially penetrating well and the well discharge along the screen. The semi-analytical solutions are particularly useful for the practical applications from the computational point of view.

Probabilistic sensitivity analysis for decision trees with multiple branches: use of the Dirichlet distribution in a Bayesian framework.

PubMed

Briggs, Andrew H; Ades, A E; Price, Martin J

2003-01-01

In structuring decision models of medical interventions, it is commonly recommended that only 2 branches be used for each chance node to avoid logical inconsistencies that can arise during sensitivity analyses if the branching probabilities do not sum to 1. However, information may be naturally available in an unconditional form, and structuring a tree in conditional form may complicate rather than simplify the sensitivity analysis of the unconditional probabilities. Current guidance emphasizes using probabilistic sensitivity analysis, and a method is required to provide probabilistic probabilities over multiple branches that appropriately represents uncertainty while satisfying the requirement that mutually exclusive event probabilities should sum to 1. The authors argue that the Dirichlet distribution, the multivariate equivalent of the beta distribution, is appropriate for this purpose and illustrate its use for generating a fully probabilistic transition matrix for a Markov model. Furthermore, they demonstrate that by adopting a Bayesian approach, the problem of observing zero counts for transitions of interest can be overcome.

The Smoothed Dirichlet Distribution: Understanding Cross-Entropy Ranking in Information Retrieval

DTIC Science & Technology

2006-07-01

reflect those of the spon- sor. viii ABSTRACT Unigram Language modeling is a successful probabilistic framework for Information Retrieval (IR) that uses...the Relevance model (RM), a state-of-the-art model for IR in the language modeling framework that uses the same cross-entropy as its ranking function...In addition, the SD based classifier provides more flexibility than RM in modeling documents owing to a consistent generative framework . We

Nonparametric Bayesian predictive distributions for future order statistics

Treesearch

Richard A. Johnson; James W. Evans; David W. Green

1999-01-01

We derive the predictive distribution for a specified order statistic, determined from a future random sample, under a Dirichlet process prior. Two variants of the approach are treated and some limiting cases studied. A practical application to monitoring the strength of lumber is discussed including choices of prior expectation and comparisons made to a Bayesian...

On the Dirichlet's Box Principle

ERIC Educational Resources Information Center

Poon, Kin-Keung; Shiu, Wai-Chee

2008-01-01

In this note, we will focus on several applications on the Dirichlet's box principle in Discrete Mathematics lesson and number theory lesson. In addition, the main result is an innovative game on a triangular board developed by the authors. The game has been used in teaching and learning mathematics in Discrete Mathematics and some high schools in…

Characterization and Modeling of Thoraco-Abdominal Response to Blast Waves. Volume 4. Biomechanical Model of Thorax Response to Blast Loading

DTIC Science & Technology

1985-05-01

non- zero Dirichlet boundary conditions and/or general mixed type boundary conditions. Note that Neumann type boundary condi- tion enters the problem by...Background ................................. ................... I 1.3 General Description ..... ............ ........... . ....... ...... 2 2. ANATOMICAL...human and varions loading conditions for the definition of a generalized safety guideline of blast exposure. To model the response of a sheep torso

Test Design Project: Studies in Test Adequacy. Annual Report.

ERIC Educational Resources Information Center

Wilcox, Rand R.

These studies in test adequacy focus on two problems: procedures for estimating reliability, and techniques for identifying ineffective distractors. Fourteen papers are presented on recent advances in measuring achievement (a response to Molenaar); "an extension of the Dirichlet-multinomial model that allows true score and guessing to be…

The Casimir effect for parallel plates revisited

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

Kawakami, N. A.; Nemes, M. C.; Wreszinski, Walter F.

2007-10-15

The Casimir effect for a massless scalar field with Dirichlet and periodic boundary conditions (bc's) on infinite parallel plates is revisited in the local quantum field theory (lqft) framework introduced by Kay [Phys. Rev. D 20, 3052 (1979)]. The model displays a number of more realistic features than the ones he treated. In addition to local observables, as the energy density, we propose to consider intensive variables, such as the energy per unit area {epsilon}, as fundamental observables. Adopting this view, lqft rejects Dirichlet (the same result may be proved for Neumann or mixed) bc, and accepts periodic bc: inmore » the former case {epsilon} diverges, in the latter it is finite, as is shown by an expression for the local energy density obtained from lqft through the use of the Poisson summation formula. Another way to see this uses methods from the Euler summation formula: in the proof of regularization independence of the energy per unit area, a regularization-dependent surface term arises upon use of Dirichlet bc, but not periodic bc. For the conformally invariant scalar quantum field, this surface term is absent due to the condition of zero trace of the energy momentum tensor, as remarked by De Witt [Phys. Rep. 19, 295 (1975)]. The latter property does not hold in the application to the dark energy problem in cosmology, in which we argue that periodic bc might play a distinguished role.« less

Uniform gradient estimates on manifolds with a boundary and applications

NASA Astrophysics Data System (ADS)

Cheng, Li-Juan; Thalmaier, Anton; Thompson, James

2018-04-01

We revisit the problem of obtaining uniform gradient estimates for Dirichlet and Neumann heat semigroups on Riemannian manifolds with boundary. As applications, we obtain isoperimetric inequalities, using Ledoux's argument, and uniform quantitative gradient estimates, firstly for C^2_b functions with boundary conditions and then for the unit spectral projection operators of Dirichlet and Neumann Laplacians.

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

PubMed

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

2016-09-01

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

Flexible Link Functions in Nonparametric Binary Regression with Gaussian Process Priors

PubMed Central

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

2015-01-01

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

Using phrases and document metadata to improve topic modeling of clinical reports.

PubMed

Speier, William; Ong, Michael K; Arnold, Corey W

2016-06-01

Probabilistic topic models provide an unsupervised method for analyzing unstructured text, which have the potential to be integrated into clinical automatic summarization systems. Clinical documents are accompanied by metadata in a patient's medical history and frequently contains multiword concepts that can be valuable for accurately interpreting the included text. While existing methods have attempted to address these problems individually, we present a unified model for free-text clinical documents that integrates contextual patient- and document-level data, and discovers multi-word concepts. In the proposed model, phrases are represented by chained n-grams and a Dirichlet hyper-parameter is weighted by both document-level and patient-level context. This method and three other Latent Dirichlet allocation models were fit to a large collection of clinical reports. Examples of resulting topics demonstrate the results of the new model and the quality of the representations are evaluated using empirical log likelihood. The proposed model was able to create informative prior probabilities based on patient and document information, and captured phrases that represented various clinical concepts. The representation using the proposed model had a significantly higher empirical log likelihood than the compared methods. Integrating document metadata and capturing phrases in clinical text greatly improves the topic representation of clinical documents. The resulting clinically informative topics may effectively serve as the basis for an automatic summarization system for clinical reports. Copyright © 2016 Elsevier Inc. All rights reserved.

Augmenting Latent Dirichlet Allocation and Rank Threshold Detection with Ontologies

DTIC Science & Technology

2010-03-01

Probabilistic Latent Semantic Indexing (PLSI) is an automated indexing information retrieval model [20]. It is based on a statistical latent class model which is...uses a statistical foundation that is more accurate in finding hidden semantic relationships [20]. The model uses factor analysis of count data, number...principle of statistical infer- ence which asserts that all of the information in a sample is contained in the likelihood function [20]. The statistical

Bayesian Ensemble Trees (BET) for Clustering and Prediction in Heterogeneous Data

PubMed Central

Duan, Leo L.; Clancy, John P.; Szczesniak, Rhonda D.

2016-01-01

We propose a novel “tree-averaging” model that utilizes the ensemble of classification and regression trees (CART). Each constituent tree is estimated with a subset of similar data. We treat this grouping of subsets as Bayesian Ensemble Trees (BET) and model them as a Dirichlet process. We show that BET determines the optimal number of trees by adapting to the data heterogeneity. Compared with the other ensemble methods, BET requires much fewer trees and shows equivalent prediction accuracy using weighted averaging. Moreover, each tree in BET provides variable selection criterion and interpretation for each subset. We developed an efficient estimating procedure with improved estimation strategies in both CART and mixture models. We demonstrate these advantages of BET with simulations and illustrate the approach with a real-world data example involving regression of lung function measurements obtained from patients with cystic fibrosis. Supplemental materials are available online. PMID:27524872

Dirichlet to Neumann operator for Abelian Yang-Mills gauge fields

NASA Astrophysics Data System (ADS)

Díaz-Marín, Homero G.

We consider the Dirichlet to Neumann operator for Abelian Yang-Mills boundary conditions. The aim is constructing a complex structure for the symplectic space of boundary conditions of Euler-Lagrange solutions modulo gauge for space-time manifolds with smooth boundary. Thus we prepare a suitable scenario for geometric quantization within the reduced symplectic space of boundary conditions of Abelian gauge fields.

A characteristic based volume penalization method for general evolution problems applied to compressible viscous flows

NASA Astrophysics Data System (ADS)

Brown-Dymkoski, Eric; Kasimov, Nurlybek; Vasilyev, Oleg V.

2014-04-01

In order to introduce solid obstacles into flows, several different methods are used, including volume penalization methods which prescribe appropriate boundary conditions by applying local forcing to the constitutive equations. One well known method is Brinkman penalization, which models solid obstacles as porous media. While it has been adapted for compressible, incompressible, viscous and inviscid flows, it is limited in the types of boundary conditions that it imposes, as are most volume penalization methods. Typically, approaches are limited to Dirichlet boundary conditions. In this paper, Brinkman penalization is extended for generalized Neumann and Robin boundary conditions by introducing hyperbolic penalization terms with characteristics pointing inward on solid obstacles. This Characteristic-Based Volume Penalization (CBVP) method is a comprehensive approach to conditions on immersed boundaries, providing for homogeneous and inhomogeneous Dirichlet, Neumann, and Robin boundary conditions on hyperbolic and parabolic equations. This CBVP method can be used to impose boundary conditions for both integrated and non-integrated variables in a systematic manner that parallels the prescription of exact boundary conditions. Furthermore, the method does not depend upon a physical model, as with porous media approach for Brinkman penalization, and is therefore flexible for various physical regimes and general evolutionary equations. Here, the method is applied to scalar diffusion and to direct numerical simulation of compressible, viscous flows. With the Navier-Stokes equations, both homogeneous and inhomogeneous Neumann boundary conditions are demonstrated through external flow around an adiabatic and heated cylinder. Theoretical and numerical examination shows that the error from penalized Neumann and Robin boundary conditions can be rigorously controlled through an a priori penalization parameter η. The error on a transient boundary is found to converge as O(η), which is more favorable than the error convergence of the already established Dirichlet boundary condition.

Extending information retrieval methods to personalized genomic-based studies of disease.

PubMed

Ye, Shuyun; Dawson, John A; Kendziorski, Christina

2014-01-01

Genomic-based studies of disease now involve diverse types of data collected on large groups of patients. A major challenge facing statistical scientists is how best to combine the data, extract important features, and comprehensively characterize the ways in which they affect an individual's disease course and likelihood of response to treatment. We have developed a survival-supervised latent Dirichlet allocation (survLDA) modeling framework to address these challenges. Latent Dirichlet allocation (LDA) models have proven extremely effective at identifying themes common across large collections of text, but applications to genomics have been limited. Our framework extends LDA to the genome by considering each patient as a "document" with "text" detailing his/her clinical events and genomic state. We then further extend the framework to allow for supervision by a time-to-event response. The model enables the efficient identification of collections of clinical and genomic features that co-occur within patient subgroups, and then characterizes each patient by those features. An application of survLDA to The Cancer Genome Atlas ovarian project identifies informative patient subgroups showing differential response to treatment, and validation in an independent cohort demonstrates the potential for patient-specific inference.

Knowledge-based probabilistic representations of branching ratios in chemical networks: The case of dissociative recombinations

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

Plessis, Sylvain; Carrasco, Nathalie; Pernot, Pascal

Experimental data about branching ratios for the products of dissociative recombination of polyatomic ions are presently the unique information source available to modelers of natural or laboratory chemical plasmas. Yet, because of limitations in the measurement techniques, data for many ions are incomplete. In particular, the repartition of hydrogen atoms among the fragments of hydrocarbons ions is often not available. A consequence is that proper implementation of dissociative recombination processes in chemical models is difficult, and many models ignore invaluable data. We propose a novel probabilistic approach based on Dirichlet-type distributions, enabling modelers to fully account for the available information.more » As an application, we consider the production rate of radicals through dissociative recombination in an ionospheric chemistry model of Titan, the largest moon of Saturn. We show how the complete scheme of dissociative recombination products derived with our method dramatically affects these rates in comparison with the simplistic H-loss mechanism implemented by default in all recent models.« less

Knowledge-based probabilistic representations of branching ratios in chemical networks: the case of dissociative recombinations.

PubMed

Plessis, Sylvain; Carrasco, Nathalie; Pernot, Pascal

2010-10-07

Experimental data about branching ratios for the products of dissociative recombination of polyatomic ions are presently the unique information source available to modelers of natural or laboratory chemical plasmas. Yet, because of limitations in the measurement techniques, data for many ions are incomplete. In particular, the repartition of hydrogen atoms among the fragments of hydrocarbons ions is often not available. A consequence is that proper implementation of dissociative recombination processes in chemical models is difficult, and many models ignore invaluable data. We propose a novel probabilistic approach based on Dirichlet-type distributions, enabling modelers to fully account for the available information. As an application, we consider the production rate of radicals through dissociative recombination in an ionospheric chemistry model of Titan, the largest moon of Saturn. We show how the complete scheme of dissociative recombination products derived with our method dramatically affects these rates in comparison with the simplistic H-loss mechanism implemented by default in all recent models.

Bayesian hierarchical functional data analysis via contaminated informative priors.

PubMed

Scarpa, Bruno; Dunson, David B

2009-09-01

A variety of flexible approaches have been proposed for functional data analysis, allowing both the mean curve and the distribution about the mean to be unknown. Such methods are most useful when there is limited prior information. Motivated by applications to modeling of temperature curves in the menstrual cycle, this article proposes a flexible approach for incorporating prior information in semiparametric Bayesian analyses of hierarchical functional data. The proposed approach is based on specifying the distribution of functions as a mixture of a parametric hierarchical model and a nonparametric contamination. The parametric component is chosen based on prior knowledge, while the contamination is characterized as a functional Dirichlet process. In the motivating application, the contamination component allows unanticipated curve shapes in unhealthy menstrual cycles. Methods are developed for posterior computation, and the approach is applied to data from a European fecundability study.

Bayesian inference on multiscale models for poisson intensity estimation: applications to photon-limited image denoising.

PubMed

Lefkimmiatis, Stamatios; Maragos, Petros; Papandreou, George

2009-08-01

We present an improved statistical model for analyzing Poisson processes, with applications to photon-limited imaging. We build on previous work, adopting a multiscale representation of the Poisson process in which the ratios of the underlying Poisson intensities (rates) in adjacent scales are modeled as mixtures of conjugate parametric distributions. Our main contributions include: 1) a rigorous and robust regularized expectation-maximization (EM) algorithm for maximum-likelihood estimation of the rate-ratio density parameters directly from the noisy observed Poisson data (counts); 2) extension of the method to work under a multiscale hidden Markov tree model (HMT) which couples the mixture label assignments in consecutive scales, thus modeling interscale coefficient dependencies in the vicinity of image edges; 3) exploration of a 2-D recursive quad-tree image representation, involving Dirichlet-mixture rate-ratio densities, instead of the conventional separable binary-tree image representation involving beta-mixture rate-ratio densities; and 4) a novel multiscale image representation, which we term Poisson-Haar decomposition, that better models the image edge structure, thus yielding improved performance. Experimental results on standard images with artificially simulated Poisson noise and on real photon-limited images demonstrate the effectiveness of the proposed techniques.

Repeated Red-Black ordering

NASA Astrophysics Data System (ADS)

Ciarlet, P.

1994-09-01

Hereafter, we describe and analyze, from both a theoretical and a numerical point of view, an iterative method for efficiently solving symmetric elliptic problems with possibly discontinuous coefficients. In the following, we use the Preconditioned Conjugate Gradient method to solve the symmetric positive definite linear systems which arise from the finite element discretization of the problems. We focus our interest on sparse and efficient preconditioners. In order to define the preconditioners, we perform two steps: first we reorder the unknowns and then we carry out a (modified) incomplete factorization of the original matrix. We study numerically and theoretically two preconditioners, the second preconditioner corresponding to the one investigated by Brand and Heinemann [2]. We prove convergence results about the Poisson equation with either Dirichlet or periodic boundary conditions. For a meshsizeh, Brand proved that the condition number of the preconditioned system is bounded byO(h-1/2) for Dirichlet boundary conditions. By slightly modifying the preconditioning process, we prove that the condition number is bounded byO(h-1/3).

Poisson Coordinates.

PubMed

Li, Xian-Ying; Hu, Shi-Min

2013-02-01

Harmonic functions are the critical points of a Dirichlet energy functional, the linear projections of conformal maps. They play an important role in computer graphics, particularly for gradient-domain image processing and shape-preserving geometric computation. We propose Poisson coordinates, a novel transfinite interpolation scheme based on the Poisson integral formula, as a rapid way to estimate a harmonic function on a certain domain with desired boundary values. Poisson coordinates are an extension of the Mean Value coordinates (MVCs) which inherit their linear precision, smoothness, and kernel positivity. We give explicit formulas for Poisson coordinates in both continuous and 2D discrete forms. Superior to MVCs, Poisson coordinates are proved to be pseudoharmonic (i.e., they reproduce harmonic functions on n-dimensional balls). Our experimental results show that Poisson coordinates have lower Dirichlet energies than MVCs on a number of typical 2D domains (particularly convex domains). As well as presenting a formula, our approach provides useful insights for further studies on coordinates-based interpolation and fast estimation of harmonic functions.

Theoretical aspect of suitable spatial boundary condition specified for adjoint model on limited area

NASA Astrophysics Data System (ADS)

Wang, Yuan; Wu, Rongsheng

2001-12-01

Theoretical argumentation for so-called suitable spatial condition is conducted by the aid of homotopy framework to demonstrate that the proposed boundary condition does guarantee that the over-specification boundary condition resulting from an adjoint model on a limited-area is no longer an issue, and yet preserve its well-poseness and optimal character in the boundary setting. The ill-poseness of over-specified spatial boundary condition is in a sense, inevitable from an adjoint model since data assimilation processes have to adapt prescribed observations that used to be over-specified at the spatial boundaries of the modeling domain. In the view of pragmatic implement, the theoretical framework of our proposed condition for spatial boundaries indeed can be reduced to the hybrid formulation of nudging filter, radiation condition taking account of ambient forcing, together with Dirichlet kind of compatible boundary condition to the observations prescribed in data assimilation procedure. All of these treatments, no doubt, are very familiar to mesoscale modelers.

Existence and uniqueness of steady state solutions of a nonlocal diffusive logistic equation

NASA Astrophysics Data System (ADS)

Sun, Linan; Shi, Junping; Wang, Yuwen

2013-08-01

In this paper, we consider a dynamical model of population biology which is of the classical Fisher type, but the competition interaction between individuals is nonlocal. The existence, uniqueness, and stability of the steady state solution of the nonlocal problem on a bounded interval with homogeneous Dirichlet boundary conditions are studied.

Generalized Riemann hypothesis and stochastic time series

NASA Astrophysics Data System (ADS)

Mussardo, Giuseppe; LeClair, André

2018-06-01

Using the Dirichlet theorem on the equidistribution of residue classes modulo q and the Lemke Oliver–Soundararajan conjecture on the distribution of pairs of residues on consecutive primes, we show that the domain of convergence of the infinite product of Dirichlet L-functions of non-principal characters can be extended from down to , without encountering any zeros before reaching this critical line. The possibility of doing so can be traced back to a universal diffusive random walk behavior of a series C N over the primes which underlies the convergence of the infinite product of the Dirichlet functions. The series C N presents several aspects in common with stochastic time series and its control requires to address a problem similar to the single Brownian trajectory problem in statistical mechanics. In the case of the Dirichlet functions of non principal characters, we show that this problem can be solved in terms of a self-averaging procedure based on an ensemble of block variables computed on extended intervals of primes. Those intervals, called inertial intervals, ensure the ergodicity and stationarity of the time series underlying the quantity C N . The infinity of primes also ensures the absence of rare events which would have been responsible for a different scaling behavior than the universal law of the random walks.

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

Yang, Dr. Li; Cui, Xiaohui; Cemerlic, Alma

Ad hoc networks are very helpful in situations when no fixed network infrastructure is available, such as natural disasters and military conflicts. In such a network, all wireless nodes are equal peers simultaneously serving as both senders and routers for other nodes. Therefore, how to route packets through reliable paths becomes a fundamental problems when behaviors of certain nodes deviate from wireless ad hoc routing protocols. We proposed a novel Dirichlet reputation model based on Bayesian inference theory which evaluates reliability of each node in terms of packet delivery. Our system offers a way to predict and select a reliablemore » path through combination of first-hand observation and second-hand reputation reports. We also proposed moving window mechanism which helps to adjust ours responsiveness of our system to changes of node behaviors. We integrated the Dirichlet reputation into routing protocol of wireless ad hoc networks. Our extensive simulation indicates that our proposed reputation system can improve good throughput of the network and reduce negative impacts caused by misbehaving nodes.« less

The spectra of rectangular lattices of quantum waveguides

NASA Astrophysics Data System (ADS)

Nazarov, S. A.

2017-02-01

We obtain asymptotic formulae for the spectral segments of a thin (h\\ll 1) rectangular lattice of quantum waveguides which is described by a Dirichlet problem for the Laplacian. We establish that the structure of the spectrum of the lattice is incorrectly described by the commonly accepted quantum graph model with the traditional Kirchhoff conditions at the vertices. It turns out that the lengths of the spectral segments are infinitesimals of order O(e-δ/h), δ> 0, and O(h) as h\\to+0, and gaps of width O(h-2) and O(1) arise between them in the low- frequency and middle- frequency spectral ranges respectively. The first spectral segment is generated by the (unique) eigenvalue in the discrete spectrum of an infinite cross-shaped waveguide \\Theta. The absence of bounded solutions of the problem in \\Theta at the threshold frequency means that the correct model of the lattice is a graph with Dirichlet conditions at the vertices which splits into two infinite subsets of identical edges- intervals. By using perturbations of finitely many joints, we construct any given number of discrete spectrum points of the lattice below the essential spectrum as well as inside the gaps.

Knowledge-Based Topic Model for Unsupervised Object Discovery and Localization.

PubMed

Niu, Zhenxing; Hua, Gang; Wang, Le; Gao, Xinbo

Unsupervised object discovery and localization is to discover some dominant object classes and localize all of object instances from a given image collection without any supervision. Previous work has attempted to tackle this problem with vanilla topic models, such as latent Dirichlet allocation (LDA). However, in those methods no prior knowledge for the given image collection is exploited to facilitate object discovery. On the other hand, the topic models used in those methods suffer from the topic coherence issue-some inferred topics do not have clear meaning, which limits the final performance of object discovery. In this paper, prior knowledge in terms of the so-called must-links are exploited from Web images on the Internet. Furthermore, a novel knowledge-based topic model, called LDA with mixture of Dirichlet trees, is proposed to incorporate the must-links into topic modeling for object discovery. In particular, to better deal with the polysemy phenomenon of visual words, the must-link is re-defined as that one must-link only constrains one or some topic(s) instead of all topics, which leads to significantly improved topic coherence. Moreover, the must-links are built and grouped with respect to specific object classes, thus the must-links in our approach are semantic-specific , which allows to more efficiently exploit discriminative prior knowledge from Web images. Extensive experiments validated the efficiency of our proposed approach on several data sets. It is shown that our method significantly improves topic coherence and outperforms the unsupervised methods for object discovery and localization. In addition, compared with discriminative methods, the naturally existing object classes in the given image collection can be subtly discovered, which makes our approach well suited for realistic applications of unsupervised object discovery.Unsupervised object discovery and localization is to discover some dominant object classes and localize all of object instances from a given image collection without any supervision. Previous work has attempted to tackle this problem with vanilla topic models, such as latent Dirichlet allocation (LDA). However, in those methods no prior knowledge for the given image collection is exploited to facilitate object discovery. On the other hand, the topic models used in those methods suffer from the topic coherence issue-some inferred topics do not have clear meaning, which limits the final performance of object discovery. In this paper, prior knowledge in terms of the so-called must-links are exploited from Web images on the Internet. Furthermore, a novel knowledge-based topic model, called LDA with mixture of Dirichlet trees, is proposed to incorporate the must-links into topic modeling for object discovery. In particular, to better deal with the polysemy phenomenon of visual words, the must-link is re-defined as that one must-link only constrains one or some topic(s) instead of all topics, which leads to significantly improved topic coherence. Moreover, the must-links are built and grouped with respect to specific object classes, thus the must-links in our approach are semantic-specific , which allows to more efficiently exploit discriminative prior knowledge from Web images. Extensive experiments validated the efficiency of our proposed approach on several data sets. It is shown that our method significantly improves topic coherence and outperforms the unsupervised methods for object discovery and localization. In addition, compared with discriminative methods, the naturally existing object classes in the given image collection can be subtly discovered, which makes our approach well suited for realistic applications of unsupervised object discovery.

Ages of Records in Random Walks

NASA Astrophysics Data System (ADS)

Szabó, Réka; Vető, Bálint

2016-12-01

We consider random walks with continuous and symmetric step distributions. We prove universal asymptotics for the average proportion of the age of the kth longest lasting record for k=1,2,ldots and for the probability that the record of the kth longest age is broken at step n. Due to the relation to the Chinese restaurant process, the ranked sequence of proportions of ages converges to the Poisson-Dirichlet distribution.

Laplace-Beltrami Eigenvalues and Topological Features of Eigenfunctions for Statistical Shape Analysis

PubMed Central

Reuter, Martin; Wolter, Franz-Erich; Shenton, Martha; Niethammer, Marc

2009-01-01

This paper proposes the use of the surface based Laplace-Beltrami and the volumetric Laplace eigenvalues and -functions as shape descriptors for the comparison and analysis of shapes. These spectral measures are isometry invariant and therefore allow for shape comparisons with minimal shape pre-processing. In particular, no registration, mapping, or remeshing is necessary. The discriminatory power of the 2D surface and 3D solid methods is demonstrated on a population of female caudate nuclei (a subcortical gray matter structure of the brain, involved in memory function, emotion processing, and learning) of normal control subjects and of subjects with schizotypal personality disorder. The behavior and properties of the Laplace-Beltrami eigenvalues and -functions are discussed extensively for both the Dirichlet and Neumann boundary condition showing advantages of the Neumann vs. the Dirichlet spectra in 3D. Furthermore, topological analyses employing the Morse-Smale complex (on the surfaces) and the Reeb graph (in the solids) are performed on selected eigenfunctions, yielding shape descriptors, that are capable of localizing geometric properties and detecting shape differences by indirectly registering topological features such as critical points, level sets and integral lines of the gradient field across subjects. The use of these topological features of the Laplace-Beltrami eigenfunctions in 2D and 3D for statistical shape analysis is novel. PMID:20161035

Complex temporal topic evolution modelling using the Kullback-Leibler divergence and the Bhattacharyya distance.

PubMed

Andrei, Victor; Arandjelović, Ognjen

2016-12-01

The rapidly expanding corpus of medical research literature presents major challenges in the understanding of previous work, the extraction of maximum information from collected data, and the identification of promising research directions. We present a case for the use of advanced machine learning techniques as an aide in this task and introduce a novel methodology that is shown to be capable of extracting meaningful information from large longitudinal corpora and of tracking complex temporal changes within it. Our framework is based on (i) the discretization of time into epochs, (ii) epoch-wise topic discovery using a hierarchical Dirichlet process-based model, and (iii) a temporal similarity graph which allows for the modelling of complex topic changes. More specifically, this is the first work that discusses and distinguishes between two groups of particularly challenging topic evolution phenomena: topic splitting and speciation and topic convergence and merging, in addition to the more widely recognized emergence and disappearance and gradual evolution. The proposed framework is evaluated on a public medical literature corpus.

Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities

NASA Astrophysics Data System (ADS)

Alessandrini, Giovanni; de Hoop, Maarten V.; Gaburro, Romina

2017-12-01

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body Ω\\subset{R}n when the so-called Neumann-to-Dirichlet map is locally given on a non-empty curved portion Σ of the boundary \\partialΩ . We prove that anisotropic conductivities that are a priori known to be piecewise constant matrices on a given partition of Ω with curved interfaces can be uniquely determined in the interior from the knowledge of the local Neumann-to-Dirichlet map.

Quasi-measures on the group G{sup m}, Dirichlet sets, and uniqueness problems for multiple Walsh series

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

Plotnikov, Mikhail G

2011-02-11

Multiple Walsh series (S) on the group G{sup m} are studied. It is proved that every at most countable set is a uniqueness set for series (S) under convergence over cubes. The recovery problem is solved for the coefficients of series (S) that converge outside countable sets or outside sets of Dirichlet type. A number of analogues of the de la Vallee Poussin theorem are established for series (S). Bibliography: 28 titles.

Effect of background dielectric on TE-polarized photonic bandgap of metallodielectric photonic crystals using Dirichlet-to-Neumann map method.

PubMed

Sedghi, Aliasghar; Rezaei, Behrooz

2016-11-20

Using the Dirichlet-to-Neumann map method, we have calculated the photonic band structure of two-dimensional metallodielectric photonic crystals having the square and triangular lattices of circular metal rods in a dielectric background. We have selected the transverse electric mode of electromagnetic waves, and the resulting band structures showed the existence of photonic bandgap in these structures. We theoretically study the effect of background dielectric on the photonic bandgap.

Manifold Matching: Joint Optimization of Fidelity and Commensurability

DTIC Science & Technology

2011-11-12

identified separately in p◦m, will be geometrically incommensurate (see Figure 7). Thus the null distribution of the test statistic will be inflated...into the objective function obviates the geometric incommensurability phenomenon. Thus we can es- tablish that, for a range of Dirichlet product model...from the geometric incommensu- rability phenomenon. Then q p implies that cca suffers from the spurious correlation phe- nomenon with high probability

Incorporating Topic Assignment Constraint and Topic Correlation Limitation into Clinical Goal Discovering for Clinical Pathway Mining.

PubMed

Xu, Xiao; Jin, Tao; Wei, Zhijie; Wang, Jianmin

2017-01-01

Clinical pathways are widely used around the world for providing quality medical treatment and controlling healthcare cost. However, the expert-designed clinical pathways can hardly deal with the variances among hospitals and patients. It calls for more dynamic and adaptive process, which is derived from various clinical data. Topic-based clinical pathway mining is an effective approach to discover a concise process model. Through this approach, the latent topics found by latent Dirichlet allocation (LDA) represent the clinical goals. And process mining methods are used to extract the temporal relations between these topics. However, the topic quality is usually not desirable due to the low performance of the LDA in clinical data. In this paper, we incorporate topic assignment constraint and topic correlation limitation into the LDA to enhance the ability of discovering high-quality topics. Two real-world datasets are used to evaluate the proposed method. The results show that the topics discovered by our method are with higher coherence, informativeness, and coverage than the original LDA. These quality topics are suitable to represent the clinical goals. Also, we illustrate that our method is effective in generating a comprehensive topic-based clinical pathway model.

Incorporating Topic Assignment Constraint and Topic Correlation Limitation into Clinical Goal Discovering for Clinical Pathway Mining

PubMed Central

Xu, Xiao; Wei, Zhijie

2017-01-01

Clinical pathways are widely used around the world for providing quality medical treatment and controlling healthcare cost. However, the expert-designed clinical pathways can hardly deal with the variances among hospitals and patients. It calls for more dynamic and adaptive process, which is derived from various clinical data. Topic-based clinical pathway mining is an effective approach to discover a concise process model. Through this approach, the latent topics found by latent Dirichlet allocation (LDA) represent the clinical goals. And process mining methods are used to extract the temporal relations between these topics. However, the topic quality is usually not desirable due to the low performance of the LDA in clinical data. In this paper, we incorporate topic assignment constraint and topic correlation limitation into the LDA to enhance the ability of discovering high-quality topics. Two real-world datasets are used to evaluate the proposed method. The results show that the topics discovered by our method are with higher coherence, informativeness, and coverage than the original LDA. These quality topics are suitable to represent the clinical goals. Also, we illustrate that our method is effective in generating a comprehensive topic-based clinical pathway model. PMID:29065617

Chemistry in Titan

NASA Astrophysics Data System (ADS)

Plessis, S.; Carrasco, N.; Pernot, P.

2009-04-01

Modelling the chemical composition of Titan's ionosphere is a very challenging issue. Latest works perform either inversion of CASSINI's INMS mass spectra (neutral[1] or ion[2]), or design coupled ion-neutral chemistry models[3]. Coupling ionic and neutral chemistry has been reported to be an essential feature of accurate modelling[3]. Electron Dissociative Recombination (EDR), where free electrons recombine with positive ions to produce neutral species, is a key component of ion-neutral coupling. There is a major difficulty in EDR modelling: for heavy ions, the distribution of neutral products is incompletely characterized by experiments. For instance, for some hydrocarbon ions only the carbon repartition is measured, leaving the hydrogen repartition and thus the exact neutral species identity unknown[4]. This precludes reliable deterministic modelling of this process and of ion-neutral coupling. We propose a novel stochastic description of the EDR chemical reactions which enables efficient representation and simulation of the partial experimental knowledge. The description of products distribution in multi-pathways reactions is based on branching ratios, which should sum to unity. The keystone of our approach is the design of a probability density function accounting for all available informations and physical constrains. This is done by Dirichlet modelling which enables one to sample random variables whose sum is constant[5]. The specifics of EDR partial uncertainty call for a hierarchiral Dirichlet representation, which generalizes our previous work[5]. We present results on the importance of ion-neutral coupling based on our stochastic model. C repartition H repartition (measured) (unknown ) → C4H2 + 3H2 + H .. -→ C4 . → C4H2 + 7H → C3H8. + CH C4H+9 + e- -→ C3 + C .. → C3H3 + CH2 + 2H2 → C2H6 + C2H2 + H .. -→ C2 + C2 . → 2C2H2 + 2H2 + H (1) References [1] J. Cui, R.V. Yelle, V. Vuitton, J.H. Waite Jr., W.T. Kasprzak, D.A. Gell, H.B. Niemann, I.C.F. Müller-Wodarg, N. Borggren, G.G. Fletcher, E.L. Patrick, E. Raaen, and B.A. Magee. Analysis of Titan's neutral upper atmosphere from Cassini ion neutral mass spectrometer measurements. Icarus, In Press, Accepted Manuscript:-, 2008. [2] V. Vuitton, R. V. Yelle, and M.J. McEwan. Ion chemistry and N-containing molecules in Titan's upper atmosphere. Icarus, 191:722-742, 2007. [3] V. De La Haye, J.H. Waite Jr., T.E. Cravens, I.P. Robertson, and S. Lebonnois. Coupled ion and neutral rotating model of Titan's upper atmosphere. Icarus, 197(1):110 - 136, 2008. [4] J. B. A. Mitchell, C. Rebrion-Rowe, J. L. Le Garrec, G. Angelova, H. Bluhme, K. Seiersen, and L. H. Andersen. Branching ratios for the dissociative recombination of hydrocarbon ions. I: The cases of C4H9+ and C4H5+. International Journal of Mass Spectrometry, 227(2):273-279, June 2003. [5] N. Carrasco and P. Pernot. Modeling of branching ratio uncertainty in chemical networks by Dirichlet distributions. Journal of Physical Chemistry A, 11(18):3507-3512, 2007.

Parameter Estimation for the Dirichlet-Multinomial Distribution Using Supplementary Beta-Binomial Data.

DTIC Science & Technology

1987-07-01

multinomial distribution as a magazine exposure model. J. of Marketing Research . 21, 100-106. Lehmann, E.L. (1983). Theory of Point Estimation. John Wiley and... Marketing Research . 21, 89-99. V I flWflW WflW~WWMWSS tWN ,rw fl rwwrwwr-w~ w-. ~. - - -- .~ 𔃾 4’.) ~a 4’ ., 𔃾. ’-4. .4.: .4~ I .4. ~J3iAf a,’ -a’ 4

Multimodal Hierarchical Dirichlet Process-Based Active Perception by a Robot

PubMed Central

Taniguchi, Tadahiro; Yoshino, Ryo; Takano, Toshiaki

2018-01-01

In this paper, we propose an active perception method for recognizing object categories based on the multimodal hierarchical Dirichlet process (MHDP). The MHDP enables a robot to form object categories using multimodal information, e.g., visual, auditory, and haptic information, which can be observed by performing actions on an object. However, performing many actions on a target object requires a long time. In a real-time scenario, i.e., when the time is limited, the robot has to determine the set of actions that is most effective for recognizing a target object. We propose an active perception for MHDP method that uses the information gain (IG) maximization criterion and lazy greedy algorithm. We show that the IG maximization criterion is optimal in the sense that the criterion is equivalent to a minimization of the expected Kullback–Leibler divergence between a final recognition state and the recognition state after the next set of actions. However, a straightforward calculation of IG is practically impossible. Therefore, we derive a Monte Carlo approximation method for IG by making use of a property of the MHDP. We also show that the IG has submodular and non-decreasing properties as a set function because of the structure of the graphical model of the MHDP. Therefore, the IG maximization problem is reduced to a submodular maximization problem. This means that greedy and lazy greedy algorithms are effective and have a theoretical justification for their performance. We conducted an experiment using an upper-torso humanoid robot and a second one using synthetic data. The experimental results show that the method enables the robot to select a set of actions that allow it to recognize target objects quickly and accurately. The numerical experiment using the synthetic data shows that the proposed method can work appropriately even when the number of actions is large and a set of target objects involves objects categorized into multiple classes. The results support our theoretical outcomes. PMID:29872389

Multimodal Hierarchical Dirichlet Process-Based Active Perception by a Robot.

PubMed

Taniguchi, Tadahiro; Yoshino, Ryo; Takano, Toshiaki

2018-01-01

In this paper, we propose an active perception method for recognizing object categories based on the multimodal hierarchical Dirichlet process (MHDP). The MHDP enables a robot to form object categories using multimodal information, e.g., visual, auditory, and haptic information, which can be observed by performing actions on an object. However, performing many actions on a target object requires a long time. In a real-time scenario, i.e., when the time is limited, the robot has to determine the set of actions that is most effective for recognizing a target object. We propose an active perception for MHDP method that uses the information gain (IG) maximization criterion and lazy greedy algorithm. We show that the IG maximization criterion is optimal in the sense that the criterion is equivalent to a minimization of the expected Kullback-Leibler divergence between a final recognition state and the recognition state after the next set of actions. However, a straightforward calculation of IG is practically impossible. Therefore, we derive a Monte Carlo approximation method for IG by making use of a property of the MHDP. We also show that the IG has submodular and non-decreasing properties as a set function because of the structure of the graphical model of the MHDP. Therefore, the IG maximization problem is reduced to a submodular maximization problem. This means that greedy and lazy greedy algorithms are effective and have a theoretical justification for their performance. We conducted an experiment using an upper-torso humanoid robot and a second one using synthetic data. The experimental results show that the method enables the robot to select a set of actions that allow it to recognize target objects quickly and accurately. The numerical experiment using the synthetic data shows that the proposed method can work appropriately even when the number of actions is large and a set of target objects involves objects categorized into multiple classes. The results support our theoretical outcomes.

Resolving an ostensible inconsistency in calculating the evaporation rate of sessile drops.

PubMed

Chini, S F; Amirfazli, A

2017-05-01

This paper resolves an ostensible inconsistency in the literature in calculating the evaporation rate for sessile drops in a quiescent environment. The earlier models in the literature have shown that adapting the evaporation flux model for a suspended spherical drop to calculate the evaporation rate of a sessile drop needs a correction factor; the correction factor was shown to be a function of the drop contact angle, i.e. f(θ). However, there seemed to be a problem as none of the earlier models explicitly or implicitly mentioned the evaporation flux variations along the surface of a sessile drop. The more recent evaporation models include this variation using an electrostatic analogy, i.e. the Laplace equation (steady-state continuity) in a domain with a known boundary condition value, or known as the Dirichlet problem for Laplace's equation. The challenge is that the calculated evaporation rates using the earlier models seemed to differ from that of the recent models (note both types of models were validated in the literature by experiments). We have reinvestigated the recent models and found that the mathematical simplifications in solving the Dirichlet problem in toroidal coordinates have created the inconsistency. We also proposed a closed form approximation for f(θ) which is valid in a wide range, i.e. 8°≤θ≤131°. Using the proposed model in this study, theoretically, it was shown that the evaporation rate in the CWA (constant wetted area) mode is faster than the evaporation rate in the CCA (constant contact angle) mode for a sessile drop. Copyright © 2016 Elsevier B.V. All rights reserved.

Leveraging constraints and biotelemetry data to pinpoint repetitively used spatial features

USGS Publications Warehouse

Brost, Brian M.; Hooten, Mevin B.; Small, Robert J.

2016-01-01

Satellite telemetry devices collect valuable information concerning the sites visited by animals, including the location of central places like dens, nests, rookeries, or haul‐outs. Existing methods for estimating the location of central places from telemetry data require user‐specified thresholds and ignore common nuances like measurement error. We present a fully model‐based approach for locating central places from telemetry data that accounts for multiple sources of uncertainty and uses all of the available locational data. Our general framework consists of an observation model to account for large telemetry measurement error and animal movement, and a highly flexible mixture model specified using a Dirichlet process to identify the location of central places. We also quantify temporal patterns in central place use by incorporating ancillary behavioral data into the model; however, our framework is also suitable when no such behavioral data exist. We apply the model to a simulated data set as proof of concept. We then illustrate our framework by analyzing an Argos satellite telemetry data set on harbor seals (Phoca vitulina) in the Gulf of Alaska, a species that exhibits fidelity to terrestrial haul‐out sites.

Boundary conditions and formation of pure spin currents in magnetic field

NASA Astrophysics Data System (ADS)

Eliashvili, Merab; Tsitsishvili, George

2017-09-01

Schrödinger equation for an electron confined to a two-dimensional strip is considered in the presence of homogeneous orthogonal magnetic field. Since the system has edges, the eigenvalue problem is supplied by the boundary conditions (BC) aimed in preventing the leakage of matter away across the edges. In the case of spinless electrons the Dirichlet and Neumann BC are considered. The Dirichlet BC result in the existence of charge carrying edge states. For the Neumann BC each separate edge comprises two counterflow sub-currents which precisely cancel out each other provided the system is populated by electrons up to certain Fermi level. Cancelation of electric current is a good starting point for developing the spin-effects. In this scope we reconsider the problem for a spinning electron with Rashba coupling. The Neumann BC are replaced by Robin BC. Again, the two counterflow electric sub-currents cancel out each other for a separate edge, while the spin current survives thus modeling what is known as pure spin current - spin flow without charge flow.

Breast Histopathological Image Retrieval Based on Latent Dirichlet Allocation.

PubMed

Ma, Yibing; Jiang, Zhiguo; Zhang, Haopeng; Xie, Fengying; Zheng, Yushan; Shi, Huaqiang; Zhao, Yu

2017-07-01

In the field of pathology, whole slide image (WSI) has become the major carrier of visual and diagnostic information. Content-based image retrieval among WSIs can aid the diagnosis of an unknown pathological image by finding its similar regions in WSIs with diagnostic information. However, the huge size and complex content of WSI pose several challenges for retrieval. In this paper, we propose an unsupervised, accurate, and fast retrieval method for a breast histopathological image. Specifically, the method presents a local statistical feature of nuclei for morphology and distribution of nuclei, and employs the Gabor feature to describe the texture information. The latent Dirichlet allocation model is utilized for high-level semantic mining. Locality-sensitive hashing is used to speed up the search. Experiments on a WSI database with more than 8000 images from 15 types of breast histopathology demonstrate that our method achieves about 0.9 retrieval precision as well as promising efficiency. Based on the proposed framework, we are developing a search engine for an online digital slide browsing and retrieval platform, which can be applied in computer-aided diagnosis, pathology education, and WSI archiving and management.

Estimating the Term Structure With a Semiparametric Bayesian Hierarchical Model: An Application to Corporate Bonds.

PubMed

Cruz-Marcelo, Alejandro; Ensor, Katherine B; Rosner, Gary L

2011-06-01

The term structure of interest rates is used to price defaultable bonds and credit derivatives, as well as to infer the quality of bonds for risk management purposes. We introduce a model that jointly estimates term structures by means of a Bayesian hierarchical model with a prior probability model based on Dirichlet process mixtures. The modeling methodology borrows strength across term structures for purposes of estimation. The main advantage of our framework is its ability to produce reliable estimators at the company level even when there are only a few bonds per company. After describing the proposed model, we discuss an empirical application in which the term structure of 197 individual companies is estimated. The sample of 197 consists of 143 companies with only one or two bonds. In-sample and out-of-sample tests are used to quantify the improvement in accuracy that results from approximating the term structure of corporate bonds with estimators by company rather than by credit rating, the latter being a popular choice in the financial literature. A complete description of a Markov chain Monte Carlo (MCMC) scheme for the proposed model is available as Supplementary Material.

Estimating the Term Structure With a Semiparametric Bayesian Hierarchical Model: An Application to Corporate Bonds1

PubMed Central

Cruz-Marcelo, Alejandro; Ensor, Katherine B.; Rosner, Gary L.

2011-01-01

The term structure of interest rates is used to price defaultable bonds and credit derivatives, as well as to infer the quality of bonds for risk management purposes. We introduce a model that jointly estimates term structures by means of a Bayesian hierarchical model with a prior probability model based on Dirichlet process mixtures. The modeling methodology borrows strength across term structures for purposes of estimation. The main advantage of our framework is its ability to produce reliable estimators at the company level even when there are only a few bonds per company. After describing the proposed model, we discuss an empirical application in which the term structure of 197 individual companies is estimated. The sample of 197 consists of 143 companies with only one or two bonds. In-sample and out-of-sample tests are used to quantify the improvement in accuracy that results from approximating the term structure of corporate bonds with estimators by company rather than by credit rating, the latter being a popular choice in the financial literature. A complete description of a Markov chain Monte Carlo (MCMC) scheme for the proposed model is available as Supplementary Material. PMID:21765566

A New Family of Solvable Pearson-Dirichlet Random Walks

NASA Astrophysics Data System (ADS)

Le Caër, Gérard

2011-07-01

An n-step Pearson-Gamma random walk in ℝ d starts at the origin and consists of n independent steps with gamma distributed lengths and uniform orientations. The gamma distribution of each step length has a shape parameter q>0. Constrained random walks of n steps in ℝ d are obtained from the latter walks by imposing that the sum of the step lengths is equal to a fixed value. Simple closed-form expressions were obtained in particular for the distribution of the endpoint of such constrained walks for any d≥ d 0 and any n≥2 when q is either q = d/2 - 1 ( d 0=3) or q= d-1 ( d 0=2) (Le Caër in J. Stat. Phys. 140:728-751, 2010). When the total walk length is chosen, without loss of generality, to be equal to 1, then the constrained step lengths have a Dirichlet distribution whose parameters are all equal to q and the associated walk is thus named a Pearson-Dirichlet random walk. The density of the endpoint position of a n-step planar walk of this type ( n≥2), with q= d=2, was shown recently to be a weighted mixture of 1+ floor( n/2) endpoint densities of planar Pearson-Dirichlet walks with q=1 (Beghin and Orsingher in Stochastics 82:201-229, 2010). The previous result is generalized to any walk space dimension and any number of steps n≥2 when the parameter of the Pearson-Dirichlet random walk is q= d>1. We rely on the connection between an unconstrained random walk and a constrained one, which have both the same n and the same q= d, to obtain a closed-form expression of the endpoint density. The latter is a weighted mixture of 1+ floor( n/2) densities with simple forms, equivalently expressed as a product of a power and a Gauss hypergeometric function. The weights are products of factors which depends both on d and n and Bessel numbers independent of d.

Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics

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

Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro

2017-04-01

We present an efficient implicit incompressible smoothed particle hydrodynamics (I2SPH) discretization of Navier-Stokes, Poisson-Boltzmann, and advection-diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The I2SPH's accuracy and convergence are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. The new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.

Decoding brain activity using a large-scale probabilistic functional-anatomical atlas of human cognition

PubMed Central

Jones, Michael N.

2017-01-01

A central goal of cognitive neuroscience is to decode human brain activity—that is, to infer mental processes from observed patterns of whole-brain activation. Previous decoding efforts have focused on classifying brain activity into a small set of discrete cognitive states. To attain maximal utility, a decoding framework must be open-ended, systematic, and context-sensitive—that is, capable of interpreting numerous brain states, presented in arbitrary combinations, in light of prior information. Here we take steps towards this objective by introducing a probabilistic decoding framework based on a novel topic model—Generalized Correspondence Latent Dirichlet Allocation—that learns latent topics from a database of over 11,000 published fMRI studies. The model produces highly interpretable, spatially-circumscribed topics that enable flexible decoding of whole-brain images. Importantly, the Bayesian nature of the model allows one to “seed” decoder priors with arbitrary images and text—enabling researchers, for the first time, to generate quantitative, context-sensitive interpretations of whole-brain patterns of brain activity. PMID:29059185

Transport dissipative particle dynamics model for mesoscopic advection- diffusion-reaction problems

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

Zhen, Li; Yazdani, Alireza; Tartakovsky, Alexandre M.

2015-07-07

We present a transport dissipative particle dynamics (tDPD) model for simulating mesoscopic problems involving advection-diffusion-reaction (ADR) processes, along with a methodology for implementation of the correct Dirichlet and Neumann boundary conditions in tDPD simulations. tDPD is an extension of the classic DPD framework with extra variables for describing the evolution of concentration fields. The transport of concentration is modeled by a Fickian flux and a random flux between particles, and an analytical formula is proposed to relate the mesoscopic concentration friction to the effective diffusion coefficient. To validate the present tDPD model and the boundary conditions, we perform three tDPDmore » simulations of one-dimensional diffusion with different boundary conditions, and the results show excellent agreement with the theoretical solutions. We also performed two-dimensional simulations of ADR systems and the tDPD simulations agree well with the results obtained by the spectral element method. Finally, we present an application of the tDPD model to the dynamic process of blood coagulation involving 25 reacting species in order to demonstrate the potential of tDPD in simulating biological dynamics at the mesoscale. We find that the tDPD solution of this comprehensive 25-species coagulation model is only twice as computationally expensive as the DPD simulation of the hydrodynamics only, which is a significant advantage over available continuum solvers.« less

Faà di Bruno's formula and the distributions of random partitions in population genetics and physics.

PubMed

Hoppe, Fred M

2008-06-01

We show that the formula of Faà di Bruno for the derivative of a composite function gives, in special cases, the sampling distributions in population genetics that are due to Ewens and to Pitman. The composite function is the same in each case. Other sampling distributions also arise in this way, such as those arising from Dirichlet, multivariate hypergeometric, and multinomial models, special cases of which correspond to Bose-Einstein, Fermi-Dirac, and Maxwell-Boltzmann distributions in physics. Connections are made to compound sampling models.

Thermodynamic Identities and Symmetry Breaking in Short-Range Spin Glasses

NASA Astrophysics Data System (ADS)

Arguin, L.-P.; Newman, C. M.; Stein, D. L.

2015-10-01

We present a technique to generate relations connecting pure state weights, overlaps, and correlation functions in short-range spin glasses. These are obtained directly from the unperturbed Hamiltonian and hold for general coupling distributions. All are satisfied in phases with simple thermodynamic structure, such as the droplet-scaling and chaotic pairs pictures. If instead nontrivial mixed-state pictures hold, the relations suggest that replica symmetry is broken as described by a Derrida-Ruelle cascade, with pure state weights distributed as a Poisson-Dirichlet process.

Low frequency acoustic and electromagnetic scattering

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Maccamy, R. C.

1986-01-01

This paper deals with two classes of problems arising from acoustics and electromagnetics scattering in the low frequency stations. The first class of problem is solving Helmholtz equation with Dirichlet boundary conditions on an arbitrary two dimensional body while the second one is an interior-exterior interface problem with Helmholtz equation in the exterior. Low frequency analysis show that there are two intermediate problems which solve the above problems accurate to 0(k/2/ log k) where k is the frequency. These solutions greatly differ from the zero frequency approximations. For the Dirichlet problem numerical examples are shown to verify the theoretical estimates.

The first eigenvalue of the p-Laplacian on quantum graphs

NASA Astrophysics Data System (ADS)

Del Pezzo, Leandro M.; Rossi, Julio D.

2016-12-01

We study the first eigenvalue of the p-Laplacian (with 1

Detecting Anisotropic Inclusions Through EIT

NASA Astrophysics Data System (ADS)

Cristina, Jan; Päivärinta, Lassi

2017-12-01

We study the evolution equation {partialtu=-Λtu} where {Λt} is the Dirichlet-Neumann operator of a decreasing family of Riemannian manifolds with boundary {Σt}. We derive a lower bound for the solution of such an equation, and apply it to a quantitative density estimate for the restriction of harmonic functions on M}=Σ_{0 to the boundaries of {partialΣt}. Consequently we are able to derive a lower bound for the difference of the Dirichlet-Neumann maps in terms of the difference of a background metrics g and an inclusion metric {g+χ_{Σ}(h-g)} on a manifold M.

Nonparametric Hierarchical Bayesian Model for Functional Brain Parcellation

PubMed Central

Lashkari, Danial; Sridharan, Ramesh; Vul, Edward; Hsieh, Po-Jang; Kanwisher, Nancy; Golland, Polina

2011-01-01

We develop a method for unsupervised analysis of functional brain images that learns group-level patterns of functional response. Our algorithm is based on a generative model that comprises two main layers. At the lower level, we express the functional brain response to each stimulus as a binary activation variable. At the next level, we define a prior over the sets of activation variables in all subjects. We use a Hierarchical Dirichlet Process as the prior in order to simultaneously learn the patterns of response that are shared across the group, and to estimate the number of these patterns supported by data. Inference based on this model enables automatic discovery and characterization of salient and consistent patterns in functional signals. We apply our method to data from a study that explores the response of the visual cortex to a collection of images. The discovered profiles of activation correspond to selectivity to a number of image categories such as faces, bodies, and scenes. More generally, our results appear superior to the results of alternative data-driven methods in capturing the category structure in the space of stimuli. PMID:21841977

A Semiparametric Approach to Simultaneous Covariance Estimation for Bivariate Sparse Longitudinal Data

PubMed Central

Das, Kiranmoy; Daniels, Michael J.

2014-01-01

Summary Estimation of the covariance structure for irregular sparse longitudinal data has been studied by many authors in recent years but typically using fully parametric specifications. In addition, when data are collected from several groups over time, it is known that assuming the same or completely different covariance matrices over groups can lead to loss of efficiency and/or bias. Nonparametric approaches have been proposed for estimating the covariance matrix for regular univariate longitudinal data by sharing information across the groups under study. For the irregular case, with longitudinal measurements that are bivariate or multivariate, modeling becomes more difficult. In this article, to model bivariate sparse longitudinal data from several groups, we propose a flexible covariance structure via a novel matrix stick-breaking process for the residual covariance structure and a Dirichlet process mixture of normals for the random effects. Simulation studies are performed to investigate the effectiveness of the proposed approach over more traditional approaches. We also analyze a subset of Framingham Heart Study data to examine how the blood pressure trajectories and covariance structures differ for the patients from different BMI groups (high, medium and low) at baseline. PMID:24400941

Systematic identification of latent disease-gene associations from PubMed articles.

PubMed

Zhang, Yuji; Shen, Feichen; Mojarad, Majid Rastegar; Li, Dingcheng; Liu, Sijia; Tao, Cui; Yu, Yue; Liu, Hongfang

2018-01-01

Recent scientific advances have accumulated a tremendous amount of biomedical knowledge providing novel insights into the relationship between molecular and cellular processes and diseases. Literature mining is one of the commonly used methods to retrieve and extract information from scientific publications for understanding these associations. However, due to large data volume and complicated associations with noises, the interpretability of such association data for semantic knowledge discovery is challenging. In this study, we describe an integrative computational framework aiming to expedite the discovery of latent disease mechanisms by dissecting 146,245 disease-gene associations from over 25 million of PubMed indexed articles. We take advantage of both Latent Dirichlet Allocation (LDA) modeling and network-based analysis for their capabilities of detecting latent associations and reducing noises for large volume data respectively. Our results demonstrate that (1) the LDA-based modeling is able to group similar diseases into disease topics; (2) the disease-specific association networks follow the scale-free network property; (3) certain subnetwork patterns were enriched in the disease-specific association networks; and (4) genes were enriched in topic-specific biological processes. Our approach offers promising opportunities for latent disease-gene knowledge discovery in biomedical research.

Systematic identification of latent disease-gene associations from PubMed articles

PubMed Central

Mojarad, Majid Rastegar; Li, Dingcheng; Liu, Sijia; Tao, Cui; Yu, Yue; Liu, Hongfang

2018-01-01

Recent scientific advances have accumulated a tremendous amount of biomedical knowledge providing novel insights into the relationship between molecular and cellular processes and diseases. Literature mining is one of the commonly used methods to retrieve and extract information from scientific publications for understanding these associations. However, due to large data volume and complicated associations with noises, the interpretability of such association data for semantic knowledge discovery is challenging. In this study, we describe an integrative computational framework aiming to expedite the discovery of latent disease mechanisms by dissecting 146,245 disease-gene associations from over 25 million of PubMed indexed articles. We take advantage of both Latent Dirichlet Allocation (LDA) modeling and network-based analysis for their capabilities of detecting latent associations and reducing noises for large volume data respectively. Our results demonstrate that (1) the LDA-based modeling is able to group similar diseases into disease topics; (2) the disease-specific association networks follow the scale-free network property; (3) certain subnetwork patterns were enriched in the disease-specific association networks; and (4) genes were enriched in topic-specific biological processes. Our approach offers promising opportunities for latent disease-gene knowledge discovery in biomedical research. PMID:29373609

Water Flow in Karst Aquifer Considering Dynamically Variable Saturation Conduit

NASA Astrophysics Data System (ADS)

Tan, Chaoqun; Hu, Bill X.

2017-04-01

The karst system is generally conceptualized as dual-porosity system, which is characterized by low conductivity and high storage continuum matrix and high conductivity and quick flow conduit networks. And so far, a common numerical model for simulating flow in karst aquifer is MODFLOW2005-CFP, which is released by USGS in 2008. However, the steady-state approach for conduit flow in CFP is physically impractical when simulating very dynamic hydraulics with variable saturation conduit. So, we adopt the method proposed by Reimann et al. (2011) to improve current model, in which Saint-Venant equations are used to model the flow in conduit. Considering the actual background that the conduit is very big and varies along flow path and the Dirichlet boundary varies with rainfall in our study area in Southwest China, we further investigate the influence of conduit diameter and outflow boundary on numerical model. And we also analyze the hydraulic process in multi-precipitation events. We find that the numerical model here corresponds well with CFP for saturated conduit, and it could depict the interaction between matrix and conduit during very dynamic hydraulics pretty well compare with CFP.

Numerical reconstruction of unknown Robin inclusions inside a heat conductor by a non-iterative method

NASA Astrophysics Data System (ADS)

Nakamura, Gen; Wang, Haibing

2017-05-01

Consider the problem of reconstructing unknown Robin inclusions inside a heat conductor from boundary measurements. This problem arises from active thermography and is formulated as an inverse boundary value problem for the heat equation. In our previous works, we proposed a sampling-type method for reconstructing the boundary of the Robin inclusion and gave its rigorous mathematical justification. This method is non-iterative and based on the characterization of the solution to the so-called Neumann- to-Dirichlet map gap equation. In this paper, we give a further investigation of the reconstruction method from both the theoretical and numerical points of view. First, we clarify the solvability of the Neumann-to-Dirichlet map gap equation and establish a relation of its solution to the Green function associated with an initial-boundary value problem for the heat equation inside the Robin inclusion. This naturally provides a way of computing this Green function from the Neumann-to-Dirichlet map and explains what is the input for the linear sampling method. Assuming that the Neumann-to-Dirichlet map gap equation has a unique solution, we also show the convergence of our method for noisy measurements. Second, we give the numerical implementation of the reconstruction method for two-dimensional spatial domains. The measurements for our inverse problem are simulated by solving the forward problem via the boundary integral equation method. Numerical results are presented to illustrate the efficiency and stability of the proposed method. By using a finite sequence of transient input over a time interval, we propose a new sampling method over the time interval by single measurement which is most likely to be practical.

A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions

NASA Astrophysics Data System (ADS)

Reimer, Ashton S.; Cheviakov, Alexei F.

2013-03-01

A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.

Research of the multimodal brain-tumor segmentation algorithm

NASA Astrophysics Data System (ADS)

Lu, Yisu; Chen, Wufan

2015-12-01

It is well-known that the number of clusters is one of the most important parameters for automatic segmentation. However, it is difficult to define owing to the high diversity in appearance of tumor tissue among different patients and the ambiguous boundaries of lesions. In this study, a nonparametric mixture of Dirichlet process (MDP) model is applied to segment the tumor images, and the MDP segmentation can be performed without the initialization of the number of clusters. A new nonparametric segmentation algorithm combined with anisotropic diffusion and a Markov random field (MRF) smooth constraint is proposed in this study. Besides the segmentation of single modal brain tumor images, we developed the algorithm to segment multimodal brain tumor images by the magnetic resonance (MR) multimodal features and obtain the active tumor and edema in the same time. The proposed algorithm is evaluated and compared with other approaches. The accuracy and computation time of our algorithm demonstrates very impressive performance.

Behavior Based Social Dimensions Extraction for Multi-Label Classification

PubMed Central

Li, Le; Xu, Junyi; Xiao, Weidong; Ge, Bin

2016-01-01

Classification based on social dimensions is commonly used to handle the multi-label classification task in heterogeneous networks. However, traditional methods, which mostly rely on the community detection algorithms to extract the latent social dimensions, produce unsatisfactory performance when community detection algorithms fail. In this paper, we propose a novel behavior based social dimensions extraction method to improve the classification performance in multi-label heterogeneous networks. In our method, nodes’ behavior features, instead of community memberships, are used to extract social dimensions. By introducing Latent Dirichlet Allocation (LDA) to model the network generation process, nodes’ connection behaviors with different communities can be extracted accurately, which are applied as latent social dimensions for classification. Experiments on various public datasets reveal that the proposed method can obtain satisfactory classification results in comparison to other state-of-the-art methods on smaller social dimensions. PMID:27049849

Repulsive Casimir effect from extra dimensions and Robin boundary conditions: From branes to pistons

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

Elizalde, E.; Odintsov, S. D.; Institucio Catalana de Recerca i Estudis Avanccats

2009-03-15

We evaluate the Casimir energy and force for a massive scalar field with general curvature coupling parameter, subject to Robin boundary conditions on two codimension-one parallel plates, located on a (D+1)-dimensional background spacetime with an arbitrary internal space. The most general case of different Robin coefficients on the two separate plates is considered. With independence of the geometry of the internal space, the Casimir forces are seen to be attractive for special cases of Dirichlet or Neumann boundary conditions on both plates and repulsive for Dirichlet boundary conditions on one plate and Neumann boundary conditions on the other. For Robinmore » boundary conditions, the Casimir forces can be either attractive or repulsive, depending on the Robin coefficients and the separation between the plates, what is actually remarkable and useful. Indeed, we demonstrate the existence of an equilibrium point for the interplate distance, which is stabilized due to the Casimir force, and show that stability is enhanced by the presence of the extra dimensions. Applications of these properties in braneworld models are discussed. Finally, the corresponding results are generalized to the geometry of a piston of arbitrary cross section.« less

Latent Dirichlet Allocation (LDA) for Sentiment Analysis Toward Tourism Review in Indonesia

NASA Astrophysics Data System (ADS)

Putri, IR; Kusumaningrum, R.

2017-01-01

The tourism industry is one of foreign exchange sector, which has considerable potential development in Indonesia. Compared to other Southeast Asia countries such as Malaysia with 18 million tourists and Singapore 20 million tourists, Indonesia which is the largest Southeast Asia’s country have failed to attract higher tourist numbers compared to its regional peers. Indonesia only managed to attract 8,8 million foreign tourists in 2013, with the value of foreign tourists each year which is likely to decrease. Apart from the infrastructure problems, marketing and managing also form of obstacles for tourism growth. An evaluation and self-analysis should be done by the stakeholder to respond toward this problem and capture opportunities that related to tourism satisfaction from tourists review. Recently, one of technology to answer this problem only relying on the subjective of statistical data which collected by voting or grading from user randomly. So the result is still not to be accountable. Thus, we proposed sentiment analysis with probabilistic topic model using Latent Dirichlet Allocation (LDA) method to be applied for reading general tendency from tourist review into certain topics that can be classified toward positive and negative sentiment.

A new analytical solution solved by triple series equations method for constant-head tests in confined aquifers

NASA Astrophysics Data System (ADS)

Chang, Ya-Chi; Yeh, Hund-Der

2010-06-01

The constant-head pumping tests are usually employed to determine the aquifer parameters and they can be performed in fully or partially penetrating wells. Generally, the Dirichlet condition is prescribed along the well screen and the Neumann type no-flow condition is specified over the unscreened part of the test well. The mathematical model describing the aquifer response to a constant-head test performed in a fully penetrating well can be easily solved by the conventional integral transform technique under the uniform Dirichlet-type condition along the rim of wellbore. However, the boundary condition for a test well with partial penetration should be considered as a mixed-type condition. This mixed boundary value problem in a confined aquifer system of infinite radial extent and finite vertical extent is solved by the Laplace and finite Fourier transforms in conjunction with the triple series equations method. This approach provides analytical results for the drawdown in a partially penetrating well for arbitrary location of the well screen in a finite thickness aquifer. The semi-analytical solutions are particularly useful for the practical applications from the computational point of view.

Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics

DOE PAGES

Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro; ...

2017-01-03

In this paper, we present a consistent implicit incompressible smoothed particle hydrodynamics (I 2SPH) discretization of Navier–Stokes, Poisson–Boltzmann, and advection–diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The accuracy and convergence of the consistent I 2SPH are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. Lastly, the new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.

Effects of degeneracy and response function in a diffusion predator-prey model

NASA Astrophysics Data System (ADS)

Li, Shanbing; Wu, Jianhua; Dong, Yaying

2018-04-01

In this paper, we consider positive solutions of a diffusion predator-prey model with a degeneracy under the Dirichlet boundary conditions. We first obtain sufficient conditions of the existence of positive solutions by the Leray-Schauder degree theory, and then analyze the limiting behavior of positive solutions as the growth rate of the predator goes to infinity and the conversion rates of the predator goes to zero, respectively. It is shown that these results for Holling II response function (i.e. m  >  0) reveal interesting contrast with that for the classical Lotka-Volterra predator-prey model (i.e. m  =  0).

A finite element algorithm for high-lying eigenvalues with Neumann and Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Báez, G.; Méndez-Sánchez, R. A.; Leyvraz, F.; Seligman, T. H.

2014-01-01

We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions, or combinations of either for different parts of the boundary. We use an inverse power plus Gauss-Seidel algorithm to solve the generalized eigenvalue problem. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We checked the algorithm by comparing the cumulative level density of the spectrum obtained numerically with the theoretical prediction given by the Weyl formula. We found a systematic deviation due to the discretization, not to the algorithm itself.

On the exterior Dirichlet problem for Hessian quotient equations

NASA Astrophysics Data System (ADS)

Li, Dongsheng; Li, Zhisu

2018-06-01

In this paper, we establish the existence and uniqueness theorem for solutions of the exterior Dirichlet problem for Hessian quotient equations with prescribed asymptotic behavior at infinity. This extends the previous related results on the Monge-Ampère equations and on the Hessian equations, and rearranges them in a systematic way. Based on the Perron's method, the main ingredient of this paper is to construct some appropriate subsolutions of the Hessian quotient equation, which is realized by introducing some new quantities about the elementary symmetric polynomials and using them to analyze the corresponding ordinary differential equation related to the generalized radially symmetric subsolutions of the original equation.

A three dimensional Dirichlet-to-Neumann map for surface waves over topography

NASA Astrophysics Data System (ADS)

Nachbin, Andre; Andrade, David

2016-11-01

We consider three dimensional surface water waves in the potential theory regime. The bottom topography can have a quite general profile. In the case of linear waves the Dirichlet-to-Neumann operator is formulated in a matrix decomposition form. Computational simulations illustrate the performance of the method. Two dimensional periodic bottom variations are considered in both the Bragg resonance regime as well as the rapidly varying (homogenized) regime. In the three-dimensional case we use the Luneburg lens-shaped submerged mound, which promotes the focusing of the underlying rays. FAPERJ Cientistas do Nosso Estado Grant 102917/2011 and ANP/PRH-32.

Two-point correlation function for Dirichlet L-functions

NASA Astrophysics Data System (ADS)

Bogomolny, E.; Keating, J. P.

2013-03-01

The two-point correlation function for the zeros of Dirichlet L-functions at a height E on the critical line is calculated heuristically using a generalization of the Hardy-Littlewood conjecture for pairs of primes in arithmetic progression. The result matches the conjectured random-matrix form in the limit as E → ∞ and, importantly, includes finite-E corrections. These finite-E corrections differ from those in the case of the Riemann zeta-function, obtained in Bogomolny and Keating (1996 Phys. Rev. Lett. 77 1472), by certain finite products of primes which divide the modulus of the primitive character used to construct the L-function in question.

Synchronization of Reaction-Diffusion Neural Networks With Dirichlet Boundary Conditions and Infinite Delays.

PubMed

Sheng, Yin; Zhang, Hao; Zeng, Zhigang

2017-10-01

This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.

Theory of multicolor lattice gas - A cellular automaton Poisson solver

NASA Technical Reports Server (NTRS)

Chen, H.; Matthaeus, W. H.; Klein, L. W.

1990-01-01

The present class of models for cellular automata involving a quiescent hydrodynamic lattice gas with multiple-valued passive labels termed 'colors', the lattice collisions change individual particle colors while preserving net color. The rigorous proofs of the multicolor lattice gases' essential features are rendered more tractable by an equivalent subparticle representation in which the color is represented by underlying two-state 'spins'. Schemes for the introduction of Dirichlet and Neumann boundary conditions are described, and two illustrative numerical test cases are used to verify the theory. The lattice gas model is equivalent to a Poisson equation solution.

RB Particle Filter Time Synchronization Algorithm Based on the DPM Model.

PubMed

Guo, Chunsheng; Shen, Jia; Sun, Yao; Ying, Na

2015-09-03

Time synchronization is essential for node localization, target tracking, data fusion, and various other Wireless Sensor Network (WSN) applications. To improve the estimation accuracy of continuous clock offset and skew of mobile nodes in WSNs, we propose a novel time synchronization algorithm, the Rao-Blackwellised (RB) particle filter time synchronization algorithm based on the Dirichlet process mixture (DPM) model. In a state-space equation with a linear substructure, state variables are divided into linear and non-linear variables by the RB particle filter algorithm. These two variables can be estimated using Kalman filter and particle filter, respectively, which improves the computational efficiency more so than if only the particle filter was used. In addition, the DPM model is used to describe the distribution of non-deterministic delays and to automatically adjust the number of Gaussian mixture model components based on the observational data. This improves the estimation accuracy of clock offset and skew, which allows achieving the time synchronization. The time synchronization performance of this algorithm is also validated by computer simulations and experimental measurements. The results show that the proposed algorithm has a higher time synchronization precision than traditional time synchronization algorithms.

Stochastic species abundance models involving special copulas

NASA Astrophysics Data System (ADS)

Huillet, Thierry E.

2018-01-01

Copulas offer a very general tool to describe the dependence structure of random variables supported by the hypercube. Inspired by problems of species abundances in Biology, we study three distinct toy models where copulas play a key role. In a first one, a Marshall-Olkin copula arises in a species extinction model with catastrophe. In a second one, a quasi-copula problem arises in a flagged species abundance model. In a third model, we study completely random species abundance models in the hypercube as those, not of product type, with uniform margins and singular. These can be understood from a singular copula supported by an inflated simplex. An exchangeable singular Dirichlet copula is also introduced, together with its induced completely random species abundance vector.

Transport dissipative particle dynamics model for mesoscopic advection-diffusion-reaction problems

PubMed Central

Yazdani, Alireza; Tartakovsky, Alexandre; Karniadakis, George Em

2015-01-01

We present a transport dissipative particle dynamics (tDPD) model for simulating mesoscopic problems involving advection-diffusion-reaction (ADR) processes, along with a methodology for implementation of the correct Dirichlet and Neumann boundary conditions in tDPD simulations. tDPD is an extension of the classic dissipative particle dynamics (DPD) framework with extra variables for describing the evolution of concentration fields. The transport of concentration is modeled by a Fickian flux and a random flux between tDPD particles, and the advection is implicitly considered by the movements of these Lagrangian particles. An analytical formula is proposed to relate the tDPD parameters to the effective diffusion coefficient. To validate the present tDPD model and the boundary conditions, we perform three tDPD simulations of one-dimensional diffusion with different boundary conditions, and the results show excellent agreement with the theoretical solutions. We also performed two-dimensional simulations of ADR systems and the tDPD simulations agree well with the results obtained by the spectral element method. Finally, we present an application of the tDPD model to the dynamic process of blood coagulation involving 25 reacting species in order to demonstrate the potential of tDPD in simulating biological dynamics at the mesoscale. We find that the tDPD solution of this comprehensive 25-species coagulation model is only twice as computationally expensive as the conventional DPD simulation of the hydrodynamics only, which is a significant advantage over available continuum solvers. PMID:26156459

Locating Temporal Functional Dynamics of Visual Short-Term Memory Binding using Graph Modular Dirichlet Energy

NASA Astrophysics Data System (ADS)

Smith, Keith; Ricaud, Benjamin; Shahid, Nauman; Rhodes, Stephen; Starr, John M.; Ibáñez, Augustin; Parra, Mario A.; Escudero, Javier; Vandergheynst, Pierre

2017-02-01

Visual short-term memory binding tasks are a promising early marker for Alzheimer’s disease (AD). To uncover functional deficits of AD in these tasks it is meaningful to first study unimpaired brain function. Electroencephalogram recordings were obtained from encoding and maintenance periods of tasks performed by healthy young volunteers. We probe the task’s transient physiological underpinnings by contrasting shape only (Shape) and shape-colour binding (Bind) conditions, displayed in the left and right sides of the screen, separately. Particularly, we introduce and implement a novel technique named Modular Dirichlet Energy (MDE) which allows robust and flexible analysis of the functional network with unprecedented temporal precision. We find that connectivity in the Bind condition is less integrated with the global network than in the Shape condition in occipital and frontal modules during the encoding period of the right screen condition. Using MDE we are able to discern driving effects in the occipital module between 100-140 ms, coinciding with the P100 visually evoked potential, followed by a driving effect in the frontal module between 140-180 ms, suggesting that the differences found constitute an information processing difference between these modules. This provides temporally precise information over a heterogeneous population in promising tasks for the detection of AD.

Strong Asymmetric Limit of the Quasi-Potential of the Boundary Driven Weakly Asymmetric Exclusion Process

NASA Astrophysics Data System (ADS)

Bertini, Lorenzo; Gabrielli, Davide; Landim, Claudio

2009-07-01

We consider the weakly asymmetric exclusion process on a bounded interval with particles reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by the viscous Burgers equation with Dirichlet boundary conditions. In the case in which the bulk asymmetry is in the same direction as the drift due to the boundary reservoirs, we prove that the quasi-potential can be expressed in terms of the solution to a one-dimensional boundary value problem which has been introduced by Enaud and Derrida [16]. We consider the strong asymmetric limit of the quasi-potential and recover the functional derived by Derrida, Lebowitz, and Speer [15] for the asymmetric exclusion process.

Characterizing Twitter Discussions About HPV Vaccines Using Topic Modeling and Community Detection.

PubMed

Surian, Didi; Nguyen, Dat Quoc; Kennedy, Georgina; Johnson, Mark; Coiera, Enrico; Dunn, Adam G

2016-08-29

In public health surveillance, measuring how information enters and spreads through online communities may help us understand geographical variation in decision making associated with poor health outcomes. Our aim was to evaluate the use of community structure and topic modeling methods as a process for characterizing the clustering of opinions about human papillomavirus (HPV) vaccines on Twitter. The study examined Twitter posts (tweets) collected between October 2013 and October 2015 about HPV vaccines. We tested Latent Dirichlet Allocation and Dirichlet Multinomial Mixture (DMM) models for inferring topics associated with tweets, and community agglomeration (Louvain) and the encoding of random walks (Infomap) methods to detect community structure of the users from their social connections. We examined the alignment between community structure and topics using several common clustering alignment measures and introduced a statistical measure of alignment based on the concentration of specific topics within a small number of communities. Visualizations of the topics and the alignment between topics and communities are presented to support the interpretation of the results in context of public health communication and identification of communities at risk of rejecting the safety and efficacy of HPV vaccines. We analyzed 285,417 Twitter posts (tweets) about HPV vaccines from 101,519 users connected by 4,387,524 social connections. Examining the alignment between the community structure and the topics of tweets, the results indicated that the Louvain community detection algorithm together with DMM produced consistently higher alignment values and that alignments were generally higher when the number of topics was lower. After applying the Louvain method and DMM with 30 topics and grouping semantically similar topics in a hierarchy, we characterized 163,148 (57.16%) tweets as evidence and advocacy, and 6244 (2.19%) tweets describing personal experiences. Among the 4548 users who posted experiential tweets, 3449 users (75.84%) were found in communities where the majority of tweets were about evidence and advocacy. The use of community detection in concert with topic modeling appears to be a useful way to characterize Twitter communities for the purpose of opinion surveillance in public health applications. Our approach may help identify online communities at risk of being influenced by negative opinions about public health interventions such as HPV vaccines.

Characterizing Twitter Discussions About HPV Vaccines Using Topic Modeling and Community Detection

PubMed Central

Nguyen, Dat Quoc; Kennedy, Georgina; Johnson, Mark; Coiera, Enrico; Dunn, Adam G

2016-01-01

Background In public health surveillance, measuring how information enters and spreads through online communities may help us understand geographical variation in decision making associated with poor health outcomes. Objective Our aim was to evaluate the use of community structure and topic modeling methods as a process for characterizing the clustering of opinions about human papillomavirus (HPV) vaccines on Twitter. Methods The study examined Twitter posts (tweets) collected between October 2013 and October 2015 about HPV vaccines. We tested Latent Dirichlet Allocation and Dirichlet Multinomial Mixture (DMM) models for inferring topics associated with tweets, and community agglomeration (Louvain) and the encoding of random walks (Infomap) methods to detect community structure of the users from their social connections. We examined the alignment between community structure and topics using several common clustering alignment measures and introduced a statistical measure of alignment based on the concentration of specific topics within a small number of communities. Visualizations of the topics and the alignment between topics and communities are presented to support the interpretation of the results in context of public health communication and identification of communities at risk of rejecting the safety and efficacy of HPV vaccines. Results We analyzed 285,417 Twitter posts (tweets) about HPV vaccines from 101,519 users connected by 4,387,524 social connections. Examining the alignment between the community structure and the topics of tweets, the results indicated that the Louvain community detection algorithm together with DMM produced consistently higher alignment values and that alignments were generally higher when the number of topics was lower. After applying the Louvain method and DMM with 30 topics and grouping semantically similar topics in a hierarchy, we characterized 163,148 (57.16%) tweets as evidence and advocacy, and 6244 (2.19%) tweets describing personal experiences. Among the 4548 users who posted experiential tweets, 3449 users (75.84%) were found in communities where the majority of tweets were about evidence and advocacy. Conclusions The use of community detection in concert with topic modeling appears to be a useful way to characterize Twitter communities for the purpose of opinion surveillance in public health applications. Our approach may help identify online communities at risk of being influenced by negative opinions about public health interventions such as HPV vaccines. PMID:27573910

Condition Monitoring for Helicopter Data. Appendix A

NASA Technical Reports Server (NTRS)

Wen, Fang; Willett, Peter; Deb, Somnath

2000-01-01

In this paper the classical "Westland" set of empirical accelerometer helicopter data is analyzed with the aim of condition monitoring for diagnostic purposes. The goal is to determine features for failure events from these data, via a proprietary signal processing toolbox, and to weigh these according to a variety of classification algorithms. As regards signal processing, it appears that the autoregressive (AR) coefficients from a simple linear model encapsulate a great deal of information in a relatively few measurements; it has also been found that augmentation of these by harmonic and other parameters can improve classification significantly. As regards classification, several techniques have been explored, among these restricted Coulomb energy (RCE) networks, learning vector quantization (LVQ), Gaussian mixture classifiers and decision trees. A problem with these approaches, and in common with many classification paradigms, is that augmentation of the feature dimension can degrade classification ability. Thus, we also introduce the Bayesian data reduction algorithm (BDRA), which imposes a Dirichlet prior on training data and is thus able to quantify probability of error in an exact manner, such that features may be discarded or coarsened appropriately.

Comparing and improving proper orthogonal decomposition (POD) to reduce the complexity of groundwater models

NASA Astrophysics Data System (ADS)

Gosses, Moritz; Nowak, Wolfgang; Wöhling, Thomas

2017-04-01

Physically-based modeling is a wide-spread tool in understanding and management of natural systems. With the high complexity of many such models and the huge amount of model runs necessary for parameter estimation and uncertainty analysis, overall run times can be prohibitively long even on modern computer systems. An encouraging strategy to tackle this problem are model reduction methods. In this contribution, we compare different proper orthogonal decomposition (POD, Siade et al. (2010)) methods and their potential applications to groundwater models. The POD method performs a singular value decomposition on system states as simulated by the complex (e.g., PDE-based) groundwater model taken at several time-steps, so-called snapshots. The singular vectors with the highest information content resulting from this decomposition are then used as a basis for projection of the system of model equations onto a subspace of much lower dimensionality than the original complex model, thereby greatly reducing complexity and accelerating run times. In its original form, this method is only applicable to linear problems. Many real-world groundwater models are non-linear, tough. These non-linearities are introduced either through model structure (unconfined aquifers) or boundary conditions (certain Cauchy boundaries, like rivers with variable connection to the groundwater table). To date, applications of POD focused on groundwater models simulating pumping tests in confined aquifers with constant head boundaries. In contrast, POD model reduction either greatly looses accuracy or does not significantly reduce model run time if the above-mentioned non-linearities are introduced. We have also found that variable Dirichlet boundaries are problematic for POD model reduction. An extension to the POD method, called POD-DEIM, has been developed for non-linear groundwater models by Stanko et al. (2016). This method uses spatial interpolation points to build the equation system in the reduced model space, thereby allowing the recalculation of system matrices at every time-step necessary for non-linear models while retaining the speed of the reduced model. This makes POD-DEIM applicable for groundwater models simulating unconfined aquifers. However, in our analysis, the method struggled to reproduce variable river boundaries accurately and gave no advantage for variable Dirichlet boundaries compared to the original POD method. We have developed another extension for POD that targets to address these remaining problems by performing a second POD operation on the model matrix on the left-hand side of the equation. The method aims to at least reproduce the accuracy of the other methods where they are applicable while outperforming them for setups with changing river boundaries or variable Dirichlet boundaries. We compared the new extension with original POD and POD-DEIM for different combinations of model structures and boundary conditions. The new method shows the potential of POD extensions for applications to non-linear groundwater systems and complex boundary conditions that go beyond the current, relatively limited range of applications. References: Siade, A. J., Putti, M., and Yeh, W. W.-G. (2010). Snapshot selection for groundwater model reduction using proper orthogonal decomposition. Water Resour. Res., 46(8):W08539. Stanko, Z. P., Boyce, S. E., and Yeh, W. W.-G. (2016). Nonlinear model reduction of unconfined groundwater flow using pod and deim. Advances in Water Resources, 97:130 - 143.

Asymptotic stability of a nonlinear Korteweg-de Vries equation with critical lengths

NASA Astrophysics Data System (ADS)

Chu, Jixun; Coron, Jean-Michel; Shang, Peipei

2015-10-01

We study an initial-boundary-value problem of a nonlinear Korteweg-de Vries equation posed on the finite interval (0, 2 kπ) where k is a positive integer. The whole system has Dirichlet boundary condition at the left end-point, and both of Dirichlet and Neumann homogeneous boundary conditions at the right end-point. It is known that the origin is not asymptotically stable for the linearized system around the origin. We prove that the origin is (locally) asymptotically stable for the nonlinear system if the integer k is such that the kernel of the linear Korteweg-de Vries stationary equation is of dimension 1. This is for example the case if k = 1.

Marginally specified priors for non-parametric Bayesian estimation

PubMed Central

Kessler, David C.; Hoff, Peter D.; Dunson, David B.

2014-01-01

Summary Prior specification for non-parametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. A statistician is unlikely to have informed opinions about all aspects of such a parameter but will have real information about functionals of the parameter, such as the population mean or variance. The paper proposes a new framework for non-parametric Bayes inference in which the prior distribution for a possibly infinite dimensional parameter is decomposed into two parts: an informative prior on a finite set of functionals, and a non-parametric conditional prior for the parameter given the functionals. Such priors can be easily constructed from standard non-parametric prior distributions in common use and inherit the large support of the standard priors on which they are based. Additionally, posterior approximations under these informative priors can generally be made via minor adjustments to existing Markov chain approximation algorithms for standard non-parametric prior distributions. We illustrate the use of such priors in the context of multivariate density estimation using Dirichlet process mixture models, and in the modelling of high dimensional sparse contingency tables. PMID:25663813

Evolutionary dynamics of language systems

PubMed Central

Wu, Chieh-Hsi; Hua, Xia; Dunn, Michael; Levinson, Stephen C.; Gray, Russell D.

2017-01-01

Understanding how and why language subsystems differ in their evolutionary dynamics is a fundamental question for historical and comparative linguistics. One key dynamic is the rate of language change. While it is commonly thought that the rapid rate of change hampers the reconstruction of deep language relationships beyond 6,000–10,000 y, there are suggestions that grammatical structures might retain more signal over time than other subsystems, such as basic vocabulary. In this study, we use a Dirichlet process mixture model to infer the rates of change in lexical and grammatical data from 81 Austronesian languages. We show that, on average, most grammatical features actually change faster than items of basic vocabulary. The grammatical data show less schismogenesis, higher rates of homoplasy, and more bursts of contact-induced change than the basic vocabulary data. However, there is a core of grammatical and lexical features that are highly stable. These findings suggest that different subsystems of language have differing dynamics and that careful, nuanced models of language change will be needed to extract deeper signal from the noise of parallel evolution, areal readaptation, and contact. PMID:29073028

An efficient algorithm for accurate computation of the Dirichlet-multinomial log-likelihood function.

PubMed

Yu, Peng; Shaw, Chad A

2014-06-01

The Dirichlet-multinomial (DMN) distribution is a fundamental model for multicategory count data with overdispersion. This distribution has many uses in bioinformatics including applications to metagenomics data, transctriptomics and alternative splicing. The DMN distribution reduces to the multinomial distribution when the overdispersion parameter ψ is 0. Unfortunately, numerical computation of the DMN log-likelihood function by conventional methods results in instability in the neighborhood of [Formula: see text]. An alternative formulation circumvents this instability, but it leads to long runtimes that make it impractical for large count data common in bioinformatics. We have developed a new method for computation of the DMN log-likelihood to solve the instability problem without incurring long runtimes. The new approach is composed of a novel formula and an algorithm to extend its applicability. Our numerical experiments show that this new method both improves the accuracy of log-likelihood evaluation and the runtime by several orders of magnitude, especially in high-count data situations that are common in deep sequencing data. Using real metagenomic data, our method achieves manyfold runtime improvement. Our method increases the feasibility of using the DMN distribution to model many high-throughput problems in bioinformatics. We have included in our work an R package giving access to this method and a vingette applying this approach to metagenomic data. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Seawater intrusion in karstic, coastal aquifers: Current challenges and future scenarios in the Taranto area (southern Italy).

PubMed

De Filippis, Giovanna; Foglia, Laura; Giudici, Mauro; Mehl, Steffen; Margiotta, Stefano; Negri, Sergio Luigi

2016-12-15

Mediterranean areas are characterized by complex hydrogeological systems, where management of freshwater resources, mostly stored in karstic, coastal aquifers, is necessary and requires the application of numerical tools to detect and prevent deterioration of groundwater, mostly caused by overexploitation. In the Taranto area (southern Italy), the deep, karstic aquifer is the only source of freshwater and satisfies the main human activities. Preserving quantity and quality of this system through management policies is so necessary and such task can be addressed through modeling tools which take into account human impacts and the effects of climate changes. A variable-density flow model was developed with SEAWAT to depict the "current" status of the saltwater intrusion, namely the status simulated over an average hydrogeological year. Considering the goals of this analysis and the scale at which the model was built, the equivalent porous medium approach was adopted to represent the deep aquifer. The effects that different flow boundary conditions along the coast have on the transport model were assessed. Furthermore, salinity stratification occurs within a strip spreading between 4km and 7km from the coast in the deep aquifer. The model predicts a similar phenomenon for some submarine freshwater springs and modeling outcomes were positively compared with measurements found in the literature. Two scenarios were simulated to assess the effects of decreased rainfall and increased pumping on saline intrusion. Major differences in the concentration field with respect to the "current" status were found where the hydraulic conductivity of the deep aquifer is higher and such differences are higher when Dirichlet flow boundary conditions are assigned. Furthermore, the Dirichlet boundary condition along the coast for transport modeling influences the concentration field in different scenarios at shallow depths; as such, concentration values simulated under stressed conditions are lower than those simulated under undisturbed conditions. Copyright © 2016 Elsevier B.V. All rights reserved.

Two-Dimensional Model for Reactive-Sorption Columns of Cylindrical Geometry: Analytical Solutions and Moment Analysis.

PubMed

Khan, Farman U; Qamar, Shamsul

2017-05-01

A set of analytical solutions are presented for a model describing the transport of a solute in a fixed-bed reactor of cylindrical geometry subjected to the first (Dirichlet) and third (Danckwerts) type inlet boundary conditions. Linear sorption kinetic process and first-order decay are considered. Cylindrical geometry allows the use of large columns to investigate dispersion, adsorption/desorption and reaction kinetic mechanisms. The finite Hankel and Laplace transform techniques are adopted to solve the model equations. For further analysis, statistical temporal moments are derived from the Laplace-transformed solutions. The developed analytical solutions are compared with the numerical solutions of high-resolution finite volume scheme. Different case studies are presented and discussed for a series of numerical values corresponding to a wide range of mass transfer and reaction kinetics. A good agreement was observed in the analytical and numerical concentration profiles and moments. The developed solutions are efficient tools for analyzing numerical algorithms, sensitivity analysis and simultaneous determination of the longitudinal and transverse dispersion coefficients from a laboratory-scale radial column experiment. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Scalar Casimir densities and forces for parallel plates in cosmic string spacetime

NASA Astrophysics Data System (ADS)

Bezerra de Mello, E. R.; Saharian, A. A.; Abajyan, S. V.

2018-04-01

We analyze the Green function, the Casimir densities and forces associated with a massive scalar quantum field confined between two parallel plates in a higher dimensional cosmic string spacetime. The plates are placed orthogonal to the string, and the field obeys the Robin boundary conditions on them. The boundary-induced contributions are explicitly extracted in the vacuum expectation values (VEVs) of the field squared and of the energy-momentum tensor for both the single plate and two plates geometries. The VEV of the energy-momentum tensor, in additional to the diagonal components, contains an off diagonal component corresponding to the shear stress. The latter vanishes on the plates in special cases of Dirichlet and Neumann boundary conditions. For points outside the string core the topological contributions in the VEVs are finite on the plates. Near the string the VEVs are dominated by the boundary-free part, whereas at large distances the boundary-induced contributions dominate. Due to the nonzero off diagonal component of the vacuum energy-momentum tensor, in addition to the normal component, the Casimir forces have nonzero component parallel to the boundary (shear force). Unlike the problem on the Minkowski bulk, the normal forces acting on the separate plates, in general, do not coincide if the corresponding Robin coefficients are different. Another difference is that in the presence of the cosmic string the Casimir forces for Dirichlet and Neumann boundary conditions differ. For Dirichlet boundary condition the normal Casimir force does not depend on the curvature coupling parameter. This is not the case for other boundary conditions. A new qualitative feature induced by the cosmic string is the appearance of the shear stress acting on the plates. The corresponding force is directed along the radial coordinate and vanishes for Dirichlet and Neumann boundary conditions. Depending on the parameters of the problem, the radial component of the shear force can be either positive or negative.

Bayesian clustering of DNA sequences using Markov chains and a stochastic partition model.

PubMed

Jääskinen, Väinö; Parkkinen, Ville; Cheng, Lu; Corander, Jukka

2014-02-01

In many biological applications it is necessary to cluster DNA sequences into groups that represent underlying organismal units, such as named species or genera. In metagenomics this grouping needs typically to be achieved on the basis of relatively short sequences which contain different types of errors, making the use of a statistical modeling approach desirable. Here we introduce a novel method for this purpose by developing a stochastic partition model that clusters Markov chains of a given order. The model is based on a Dirichlet process prior and we use conjugate priors for the Markov chain parameters which enables an analytical expression for comparing the marginal likelihoods of any two partitions. To find a good candidate for the posterior mode in the partition space, we use a hybrid computational approach which combines the EM-algorithm with a greedy search. This is demonstrated to be faster and yield highly accurate results compared to earlier suggested clustering methods for the metagenomics application. Our model is fairly generic and could also be used for clustering of other types of sequence data for which Markov chains provide a reasonable way to compress information, as illustrated by experiments on shotgun sequence type data from an Escherichia coli strain.

Mappings of Least Dirichlet Energy and their Hopf Differentials

NASA Astrophysics Data System (ADS)

Iwaniec, Tadeusz; Onninen, Jani

2013-08-01

The paper is concerned with mappings {h \\colon {X}} {{begin{array}{ll} onto \\ longrightarrow }} {{Y}} between planar domains having least Dirichlet energy. The existence and uniqueness (up to a conformal change of variables in {{X}}) of the energy-minimal mappings is established within the class {overline{fancyscript{H}}_2({X}, {Y})} of strong limits of homeomorphisms in the Sobolev space {fancyscript{W}^{1,2}({X}, {Y})} , a result of considerable interest in the mathematical models of nonlinear elasticity. The inner variation of the independent variable in {{X}} leads to the Hopf differential {hz overline{h_{bar{z}}} dz ⊗ dz} and its trajectories. For a pair of doubly connected domains, in which {{X}} has finite conformal modulus, we establish the following principle: A mapping {h in overline{fancyscript{H}}2 ({X}, {Y})} is energy-minimal if and only if its Hopf-differential is analytic in {{X}} and real along {partial {X}} . In general, the energy-minimal mappings may not be injective, in which case one observes the occurrence of slits in {{X}} (cognate with cracks). Slits are triggered by points of concavity of {{Y}} . They originate from {partial {X}} and advance along vertical trajectories of the Hopf differential toward {{X}} where they eventually terminate, so no crosscuts are created.

Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Ding, Xiao-Li; Nieto, Juan J.

2017-11-01

In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.

Machine Learning-Based Classification of 38 Years of Spine-Related Literature Into 100 Research Topics.

PubMed

Sing, David C; Metz, Lionel N; Dudli, Stefan

2017-06-01

Retrospective review. To identify the top 100 spine research topics. Recent advances in "machine learning," or computers learning without explicit instructions, have yielded broad technological advances. Topic modeling algorithms can be applied to large volumes of text to discover quantifiable themes and trends. Abstracts were extracted from the National Library of Medicine PubMed database from five prominent peer-reviewed spine journals (European Spine Journal [ESJ], The Spine Journal [SpineJ], Spine, Journal of Spinal Disorders and Techniques [JSDT], Journal of Neurosurgery: Spine [JNS]). Each abstract was entered into a latent Dirichlet allocation model specified to discover 100 topics, resulting in each abstract being assigned a probability of belonging in a topic. Topics were named using the five most frequently appearing terms within that topic. Significance of increasing ("hot") or decreasing ("cold") topic popularity over time was evaluated with simple linear regression. From 1978 to 2015, 25,805 spine-related research articles were extracted and classified into 100 topics. Top two most published topics included "clinical, surgeons, guidelines, information, care" (n = 496 articles) and "pain, back, low, treatment, chronic" (424). Top two hot trends included "disc, cervical, replacement, level, arthroplasty" (+0.05%/yr, P < 0.001), and "minimally, invasive, approach, technique" (+0.05%/yr, P < 0.001). By journal, the most published topics were ESJ-"operative, surgery, postoperative, underwent, preoperative"; SpineJ-"clinical, surgeons, guidelines, information, care"; Spine-"pain, back, low, treatment, chronic"; JNS- "tumor, lesions, rare, present, diagnosis"; JSDT-"cervical, anterior, plate, fusion, ACDF." Topics discovered through latent Dirichlet allocation modeling represent unbiased meaningful themes relevant to spine care. Topic dynamics can provide historical context and direction for future research for aspiring investigators and trainees interested in spine careers. Please explore https://singdc.shinyapps.io/spinetopics. N A.

Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images

PubMed Central

Zhou, Mingyuan; Chen, Haojun; Paisley, John; Ren, Lu; Li, Lingbo; Xing, Zhengming; Dunson, David; Sapiro, Guillermo; Carin, Lawrence

2013-01-01

Nonparametric Bayesian methods are considered for recovery of imagery based upon compressive, incomplete, and/or noisy measurements. A truncated beta-Bernoulli process is employed to infer an appropriate dictionary for the data under test and also for image recovery. In the context of compressive sensing, significant improvements in image recovery are manifested using learned dictionaries, relative to using standard orthonormal image expansions. The compressive-measurement projections are also optimized for the learned dictionary. Additionally, we consider simpler (incomplete) measurements, defined by measuring a subset of image pixels, uniformly selected at random. Spatial interrelationships within imagery are exploited through use of the Dirichlet and probit stick-breaking processes. Several example results are presented, with comparisons to other methods in the literature. PMID:21693421

User's guide to the Variably Saturated Flow (VSF) process to MODFLOW

USGS Publications Warehouse

Thoms, R. Brad; Johnson, Richard L.; Healy, Richard W.

2006-01-01

A new process for simulating three-dimensional (3-D) variably saturated flow (VSF) using Richards' equation has been added to the 3-D modular finite-difference ground-water model MODFLOW. Five new packages are presented here as part of the VSF Process--the Richards' Equation Flow (REF1) Package, the Seepage Face (SPF1) Package, the Surface Ponding (PND1) Package, the Surface Evaporation (SEV1) Package, and the Root Zone Evapotranspiration (RZE1) Package. Additionally, a new Adaptive Time-Stepping (ATS1) Package is presented for use by both the Ground-Water Flow (GWF) Process and VSF. The VSF Process allows simulation of flow in unsaturated media above the ground-water zone and facilitates modeling of ground-water/surface-water interactions. Model performance is evaluated by comparison to an analytical solution for one-dimensional (1-D) constant-head infiltration (Dirichlet boundary condition), field experimental data for a 1-D constant-head infiltration, laboratory experimental data for two-dimensional (2-D) constant-flux infiltration (Neumann boundary condition), laboratory experimental data for 2-D transient drainage through a seepage face, and numerical model results (VS2DT) of a 2-D flow-path simulation using realistic surface boundary conditions. A hypothetical 3-D example case also is presented to demonstrate the new capability using periodic boundary conditions (for example, daily precipitation) and varied surface topography over a larger spatial scale (0.133 square kilometer). The new model capabilities retain the modular structure of the MODFLOW code and preserve MODFLOW's existing capabilities as well as compatibility with commercial pre-/post-processors. The overall success of the VSF Process in simulating mixed boundary conditions and variable soil types demonstrates its utility for future hydrologic investigations. This report presents a new flow package implementing the governing equations for variably saturated ground-water flow, four new boundary condition packages unique to unsaturated flow, the Adaptive Time-Stepping Package for use with both the GWF Process and the new VSF Process, detailed descriptions of the input and output files for each package, and six simulation examples verifying model performance.

Potential usefulness of a topic model-based categorization of lung cancers as quantitative CT biomarkers for predicting the recurrence risk after curative resection

NASA Astrophysics Data System (ADS)

Kawata, Y.; Niki, N.; Ohmatsu, H.; Satake, M.; Kusumoto, M.; Tsuchida, T.; Aokage, K.; Eguchi, K.; Kaneko, M.; Moriyama, N.

2014-03-01

In this work, we investigate a potential usefulness of a topic model-based categorization of lung cancers as quantitative CT biomarkers for predicting the recurrence risk after curative resection. The elucidation of the subcategorization of a pulmonary nodule type in CT images is an important preliminary step towards developing the nodule managements that are specific to each patient. We categorize lung cancers by analyzing volumetric distributions of CT values within lung cancers via a topic model such as latent Dirichlet allocation. Through applying our scheme to 3D CT images of nonsmall- cell lung cancer (maximum lesion size of 3 cm) , we demonstrate the potential usefulness of the topic model-based categorization of lung cancers as quantitative CT biomarkers.

Nonparametric Bayesian inference for mean residual life functions in survival analysis.

PubMed

Poynor, Valerie; Kottas, Athanasios

2018-01-19

Modeling and inference for survival analysis problems typically revolves around different functions related to the survival distribution. Here, we focus on the mean residual life (MRL) function, which provides the expected remaining lifetime given that a subject has survived (i.e. is event-free) up to a particular time. This function is of direct interest in reliability, medical, and actuarial fields. In addition to its practical interpretation, the MRL function characterizes the survival distribution. We develop general Bayesian nonparametric inference for MRL functions built from a Dirichlet process mixture model for the associated survival distribution. The resulting model for the MRL function admits a representation as a mixture of the kernel MRL functions with time-dependent mixture weights. This model structure allows for a wide range of shapes for the MRL function. Particular emphasis is placed on the selection of the mixture kernel, taken to be a gamma distribution, to obtain desirable properties for the MRL function arising from the mixture model. The inference method is illustrated with a data set of two experimental groups and a data set involving right censoring. The supplementary material available at Biostatistics online provides further results on empirical performance of the model, using simulated data examples. © The Author 2018. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Modification of Classical SPM for Slightly Rough Surface Scattering with Low Grazing Angle Incidence

NASA Astrophysics Data System (ADS)

Guo, Li-Xin; Wei, Guo-Hui; Kim, Cheyoung; Wu, Zhen-Sen

2005-11-01

Based on the impedance/admittance rough boundaries, the reflection coefficients and the scattering cross section with low grazing angle incidence are obtained for both VV and HH polarizations. The error of the classical perturbation method at grazing angle is overcome for the vertical polarization at a rough Neumann boundary of infinite extent. The derivation of the formulae and the numerical results show that the backscattering cross section depends on the grazing angle to the fourth power for both Neumann and Dirichlet boundary conditions with low grazing angle incidence. Our results can reduce to that of the classical small perturbation method by neglecting the Neumann and Dirichlet boundary conditions. The project supported by National Natural Science Foundation of China under Grant No. 60101001 and the National Defense Foundation of China

Predicting inpatient clinical order patterns with probabilistic topic models vs conventional order sets.

PubMed

Chen, Jonathan H; Goldstein, Mary K; Asch, Steven M; Mackey, Lester; Altman, Russ B

2017-05-01

Build probabilistic topic model representations of hospital admissions processes and compare the ability of such models to predict clinical order patterns as compared to preconstructed order sets. The authors evaluated the first 24 hours of structured electronic health record data for > 10 K inpatients. Drawing an analogy between structured items (e.g., clinical orders) to words in a text document, the authors performed latent Dirichlet allocation probabilistic topic modeling. These topic models use initial clinical information to predict clinical orders for a separate validation set of > 4 K patients. The authors evaluated these topic model-based predictions vs existing human-authored order sets by area under the receiver operating characteristic curve, precision, and recall for subsequent clinical orders. Existing order sets predict clinical orders used within 24 hours with area under the receiver operating characteristic curve 0.81, precision 16%, and recall 35%. This can be improved to 0.90, 24%, and 47% ( P  < 10 -20 ) by using probabilistic topic models to summarize clinical data into up to 32 topics. Many of these latent topics yield natural clinical interpretations (e.g., "critical care," "pneumonia," "neurologic evaluation"). Existing order sets tend to provide nonspecific, process-oriented aid, with usability limitations impairing more precise, patient-focused support. Algorithmic summarization has the potential to breach this usability barrier by automatically inferring patient context, but with potential tradeoffs in interpretability. Probabilistic topic modeling provides an automated approach to detect thematic trends in patient care and generate decision support content. A potential use case finds related clinical orders for decision support. © The Author 2016. Published by Oxford University Press on behalf of the American Medical Informatics Association.

Predicting inpatient clinical order patterns with probabilistic topic models vs conventional order sets

PubMed Central

Goldstein, Mary K; Asch, Steven M; Mackey, Lester; Altman, Russ B

2017-01-01

Objective: Build probabilistic topic model representations of hospital admissions processes and compare the ability of such models to predict clinical order patterns as compared to preconstructed order sets. Materials and Methods: The authors evaluated the first 24 hours of structured electronic health record data for > 10 K inpatients. Drawing an analogy between structured items (e.g., clinical orders) to words in a text document, the authors performed latent Dirichlet allocation probabilistic topic modeling. These topic models use initial clinical information to predict clinical orders for a separate validation set of > 4 K patients. The authors evaluated these topic model-based predictions vs existing human-authored order sets by area under the receiver operating characteristic curve, precision, and recall for subsequent clinical orders. Results: Existing order sets predict clinical orders used within 24 hours with area under the receiver operating characteristic curve 0.81, precision 16%, and recall 35%. This can be improved to 0.90, 24%, and 47% (P < 10−20) by using probabilistic topic models to summarize clinical data into up to 32 topics. Many of these latent topics yield natural clinical interpretations (e.g., “critical care,” “pneumonia,” “neurologic evaluation”). Discussion: Existing order sets tend to provide nonspecific, process-oriented aid, with usability limitations impairing more precise, patient-focused support. Algorithmic summarization has the potential to breach this usability barrier by automatically inferring patient context, but with potential tradeoffs in interpretability. Conclusion: Probabilistic topic modeling provides an automated approach to detect thematic trends in patient care and generate decision support content. A potential use case finds related clinical orders for decision support. PMID:27655861

Wireless Wearable Multisensory Suite and Real-Time Prediction of Obstructive Sleep Apnea Episodes.

PubMed

Le, Trung Q; Cheng, Changqing; Sangasoongsong, Akkarapol; Wongdhamma, Woranat; Bukkapatnam, Satish T S

2013-01-01

Obstructive sleep apnea (OSA) is a common sleep disorder found in 24% of adult men and 9% of adult women. Although continuous positive airway pressure (CPAP) has emerged as a standard therapy for OSA, a majority of patients are not tolerant to this treatment, largely because of the uncomfortable nasal air delivery during their sleep. Recent advances in wireless communication and advanced ("bigdata") preditive analytics technologies offer radically new point-of-care treatment approaches for OSA episodes with unprecedented comfort and afforadability. We introduce a Dirichlet process-based mixture Gaussian process (DPMG) model to predict the onset of sleep apnea episodes based on analyzing complex cardiorespiratory signals gathered from a custom-designed wireless wearable multisensory suite. Extensive testing with signals from the multisensory suite as well as PhysioNet's OSA database suggests that the accuracy of offline OSA classification is 88%, and accuracy for predicting an OSA episode 1-min ahead is 83% and 3-min ahead is 77%. Such accurate prediction of an impending OSA episode can be used to adaptively adjust CPAP airflow (toward improving the patient's adherence) or the torso posture (e.g., minor chin adjustments to maintain steady levels of the airflow).

A Non-hydrostatic Atmospheric Model for Global High-resolution Simulation

NASA Astrophysics Data System (ADS)

Peng, X.; Li, X.

2017-12-01

A three-dimensional non-hydrostatic atmosphere model, GRAPES_YY, is developed on the spherical Yin-Yang grid system in order to enforce global high-resolution weather simulation or forecasting at the CAMS/CMA. The quasi-uniform grid makes the computation be of high efficiency and free of pole problem. Full representation of the three-dimensional Coriolis force is considered in the governing equations. Under the constraint of third-order boundary interpolation, the model is integrated with the semi-implicit semi-Lagrangian method using the same code on both zones. A static halo region is set to ensure computation of cross-boundary transport and updating Dirichlet-type boundary conditions in the solution process of elliptical equations with the Schwarz method. A series of dynamical test cases, including the solid-body advection, the balanced geostrophic flow, zonal flow over an isolated mountain, development of the Rossby-Haurwitz wave and a baroclinic wave, are carried out, and excellent computational stability and accuracy of the dynamic core has been confirmed. After implementation of the physical processes of long and short-wave radiation, cumulus convection, micro-physical transformation of water substances and the turbulent processes in the planetary boundary layer include surface layer vertical fluxes parameterization, a long-term run of the model is then put forward under an idealized aqua-planet configuration to test the model physics and model ability in both short-term and long-term integrations. In the aqua-planet experiment, the model shows an Earth-like structure of circulation. The time-zonal mean temperature, wind components and humidity illustrate reasonable subtropical zonal westerly jet, meridional three-cell circulation, tropical convection and thermodynamic structures. The specific SST and solar insolation being symmetric about the equator enhance the ITCZ and tropical precipitation, which concentrated in tropical region. Additional analysis and tuning of the model is still going on, and preliminary results have demonstrated the possibility of high-resolution application of the model to global weather prediction and even seasonal climate projection.

Use of dirichlet distributions and orthogonal projection techniques for the fluctuation analysis of steady-state multivariate birth-death systems

NASA Astrophysics Data System (ADS)

Palombi, Filippo; Toti, Simona

2015-05-01

Approximate weak solutions of the Fokker-Planck equation represent a useful tool to analyze the equilibrium fluctuations of birth-death systems, as they provide a quantitative knowledge lying in between numerical simulations and exact analytic arguments. In this paper, we adapt the general mathematical formalism known as the Ritz-Galerkin method for partial differential equations to the Fokker-Planck equation with time-independent polynomial drift and diffusion coefficients on the simplex. Then, we show how the method works in two examples, namely the binary and multi-state voter models with zealots.

Sound-turbulence interaction in transonic boundary layers

NASA Astrophysics Data System (ADS)

Lelostec, Ludovic; Scalo, Carlo; Lele, Sanjiva

2014-11-01

Acoustic wave scattering in a transonic boundary layer is investigated through a novel approach. Instead of simulating directly the interaction of an incoming oblique acoustic wave with a turbulent boundary layer, suitable Dirichlet conditions are imposed at the wall to reproduce only the reflected wave resulting from the interaction of the incident wave with the boundary layer. The method is first validated using the laminar boundary layer profiles in a parallel flow approximation. For this scattering problem an exact inviscid solution can be found in the frequency domain which requires numerical solution of an ODE. The Dirichlet conditions are imposed in a high-fidelity unstructured compressible flow solver for Large Eddy Simulation (LES), CharLESx. The acoustic field of the reflected wave is then solved and the interaction between the boundary layer and sound scattering can be studied.

Step scaling and the Yang-Mills gradient flow

NASA Astrophysics Data System (ADS)

Lüscher, Martin

2014-06-01

The use of the Yang-Mills gradient flow in step-scaling studies of lattice QCD is expected to lead to results of unprecedented precision. Step scaling is usually based on the Schrödinger functional, where time ranges over an interval [0 , T] and all fields satisfy Dirichlet boundary conditions at time 0 and T. In these calculations, potentially important sources of systematic errors are boundary lattice effects and the infamous topology-freezing problem. The latter is here shown to be absent if Neumann instead of Dirichlet boundary conditions are imposed on the gauge field at time 0. Moreover, the expectation values of gauge-invariant local fields at positive flow time (and of other well localized observables) that reside in the center of the space-time volume are found to be largely insensitive to the boundary lattice effects.

Heat kernel for the elliptic system of linear elasticity with boundary conditions

NASA Astrophysics Data System (ADS)

Taylor, Justin; Kim, Seick; Brown, Russell

2014-10-01

We consider the elliptic system of linear elasticity with bounded measurable coefficients in a domain where the second Korn inequality holds. We construct heat kernel of the system subject to Dirichlet, Neumann, or mixed boundary condition under the assumption that weak solutions of the elliptic system are Hölder continuous in the interior. Moreover, we show that if weak solutions of the mixed problem are Hölder continuous up to the boundary, then the corresponding heat kernel has a Gaussian bound. In particular, if the domain is a two dimensional Lipschitz domain satisfying a corkscrew or non-tangential accessibility condition on the set where we specify Dirichlet boundary condition, then we show that the heat kernel has a Gaussian bound. As an application, we construct Green's function for elliptic mixed problem in such a domain.

Topic Modeling of NASA Space System Problem Reports: Research in Practice

NASA Technical Reports Server (NTRS)

Layman, Lucas; Nikora, Allen P.; Meek, Joshua; Menzies, Tim

2016-01-01

Problem reports at NASA are similar to bug reports: they capture defects found during test, post-launch operational anomalies, and document the investigation and corrective action of the issue. These artifacts are a rich source of lessons learned for NASA, but are expensive to analyze since problem reports are comprised primarily of natural language text. We apply topic modeling to a corpus of NASA problem reports to extract trends in testing and operational failures. We collected 16,669 problem reports from six NASA space flight missions and applied Latent Dirichlet Allocation topic modeling to the document corpus. We analyze the most popular topics within and across missions, and how popular topics changed over the lifetime of a mission. We find that hardware material and flight software issues are common during the integration and testing phase, while ground station software and equipment issues are more common during the operations phase. We identify a number of challenges in topic modeling for trend analysis: 1) that the process of selecting the topic modeling parameters lacks definitive guidance, 2) defining semantically-meaningful topic labels requires nontrivial effort and domain expertise, 3) topic models derived from the combined corpus of the six missions were biased toward the larger missions, and 4) topics must be semantically distinct as well as cohesive to be useful. Nonetheless,topic modeling can identify problem themes within missions and across mission lifetimes, providing useful feedback to engineers and project managers.

Multiple Positive Solutions in the Second Order Autonomous Nonlinear Boundary Value Problems

NASA Astrophysics Data System (ADS)

Atslega, Svetlana; Sadyrbaev, Felix

2009-09-01

We construct the second order autonomous equations with arbitrarily large number of positive solutions satisfying homogeneous Dirichlet boundary conditions. Phase plane approach and bifurcation of solutions are the main tools.

Variational Problems with Long-Range Interaction

NASA Astrophysics Data System (ADS)

Soave, Nicola; Tavares, Hugo; Terracini, Susanna; Zilio, Alessandro

2018-06-01

We consider a class of variational problems for densities that repel each other at a distance. Typical examples are given by the Dirichlet functional and the Rayleigh functional D(u) = \\sum_{i=1}^k \\int_{Ω} |\

High-Reproducibility and High-Accuracy Method for Automated Topic Classification

NASA Astrophysics Data System (ADS)

Lancichinetti, Andrea; Sirer, M. Irmak; Wang, Jane X.; Acuna, Daniel; Körding, Konrad; Amaral, Luís A. Nunes

2015-01-01

Much of human knowledge sits in large databases of unstructured text. Leveraging this knowledge requires algorithms that extract and record metadata on unstructured text documents. Assigning topics to documents will enable intelligent searching, statistical characterization, and meaningful classification. Latent Dirichlet allocation (LDA) is the state of the art in topic modeling. Here, we perform a systematic theoretical and numerical analysis that demonstrates that current optimization techniques for LDA often yield results that are not accurate in inferring the most suitable model parameters. Adapting approaches from community detection in networks, we propose a new algorithm that displays high reproducibility and high accuracy and also has high computational efficiency. We apply it to a large set of documents in the English Wikipedia and reveal its hierarchical structure.

Stochastic Model for Phonemes Uncovers an Author-Dependency of Their Usage.

PubMed

Deng, Weibing; Allahverdyan, Armen E

2016-01-01

We study rank-frequency relations for phonemes, the minimal units that still relate to linguistic meaning. We show that these relations can be described by the Dirichlet distribution, a direct analogue of the ideal-gas model in statistical mechanics. This description allows us to demonstrate that the rank-frequency relations for phonemes of a text do depend on its author. The author-dependency effect is not caused by the author's vocabulary (common words used in different texts), and is confirmed by several alternative means. This suggests that it can be directly related to phonemes. These features contrast to rank-frequency relations for words, which are both author and text independent and are governed by the Zipf's law.

AdOn HDP-HMM: An Adaptive Online Model for Segmentation and Classification of Sequential Data.

PubMed

Bargi, Ava; Xu, Richard Yi Da; Piccardi, Massimo

2017-09-21

Recent years have witnessed an increasing need for the automated classification of sequential data, such as activities of daily living, social media interactions, financial series, and others. With the continuous flow of new data, it is critical to classify the observations on-the-fly and without being limited by a predetermined number of classes. In addition, a model should be able to update its parameters in response to a possible evolution in the distributions of the classes. This compelling problem, however, does not seem to have been adequately addressed in the literature, since most studies focus on offline classification over predefined class sets. In this paper, we present a principled solution for this problem based on an adaptive online system leveraging Markov switching models and hierarchical Dirichlet process priors. This adaptive online approach is capable of classifying the sequential data over an unlimited number of classes while meeting the memory and delay constraints typical of streaming contexts. In this paper, we introduce an adaptive ''learning rate'' that is responsible for balancing the extent to which the model retains its previous parameters or adapts to new observations. Experimental results on stationary and evolving synthetic data and two video data sets, TUM Assistive Kitchen and collated Weizmann, show a remarkable performance in terms of segmentation and classification, particularly for sequences from evolutionary distributions and/or those containing previously unseen classes.

Classification and Clustering Methods for Multiple Environmental Factors in Gene-Environment Interaction: Application to the Multi-Ethnic Study of Atherosclerosis.

PubMed

Ko, Yi-An; Mukherjee, Bhramar; Smith, Jennifer A; Kardia, Sharon L R; Allison, Matthew; Diez Roux, Ana V

2016-11-01

There has been an increased interest in identifying gene-environment interaction (G × E) in the context of multiple environmental exposures. Most G × E studies analyze one exposure at a time, but we are exposed to multiple exposures in reality. Efficient analysis strategies for complex G × E with multiple environmental factors in a single model are still lacking. Using the data from the Multiethnic Study of Atherosclerosis, we illustrate a two-step approach for modeling G × E with multiple environmental factors. First, we utilize common clustering and classification strategies (e.g., k-means, latent class analysis, classification and regression trees, Bayesian clustering using Dirichlet Process) to define subgroups corresponding to distinct environmental exposure profiles. Second, we illustrate the use of an additive main effects and multiplicative interaction model, instead of the conventional saturated interaction model using product terms of factors, to study G × E with the data-driven exposure subgroups defined in the first step. We demonstrate useful analytical approaches to translate multiple environmental exposures into one summary class. These tools not only allow researchers to consider several environmental exposures in G × E analysis but also provide some insight into how genes modify the effect of a comprehensive exposure profile instead of examining effect modification for each exposure in isolation.

FUN-LDA: A Latent Dirichlet Allocation Model for Predicting Tissue-Specific Functional Effects of Noncoding Variation: Methods and Applications.

PubMed

Backenroth, Daniel; He, Zihuai; Kiryluk, Krzysztof; Boeva, Valentina; Pethukova, Lynn; Khurana, Ekta; Christiano, Angela; Buxbaum, Joseph D; Ionita-Laza, Iuliana

2018-05-03

We describe a method based on a latent Dirichlet allocation model for predicting functional effects of noncoding genetic variants in a cell-type- and/or tissue-specific way (FUN-LDA). Using this unsupervised approach, we predict tissue-specific functional effects for every position in the human genome in 127 different tissues and cell types. We demonstrate the usefulness of our predictions by using several validation experiments. Using eQTL data from several sources, including the GTEx project, Geuvadis project, and TwinsUK cohort, we show that eQTLs in specific tissues tend to be most enriched among the predicted functional variants in relevant tissues in Roadmap. We further show how these integrated functional scores can be used for (1) deriving the most likely cell or tissue type causally implicated for a complex trait by using summary statistics from genome-wide association studies and (2) estimating a tissue-based correlation matrix of various complex traits. We found large enrichment of heritability in functional components of relevant tissues for various complex traits, and FUN-LDA yielded higher enrichment estimates than existing methods. Finally, using experimentally validated functional variants from the literature and variants possibly implicated in disease by previous studies, we rigorously compare FUN-LDA with state-of-the-art functional annotation methods and show that FUN-LDA has better prediction accuracy and higher resolution than these methods. In particular, our results suggest that tissue- and cell-type-specific functional prediction methods tend to have substantially better prediction accuracy than organism-level prediction methods. Scores for each position in the human genome and for each ENCODE and Roadmap tissue are available online (see Web Resources). Copyright © 2018 American Society of Human Genetics. Published by Elsevier Inc. All rights reserved.

The spectrum, radiation conditions and the Fredholm property for the Dirichlet Laplacian in a perforated plane with semi-infinite inclusions

NASA Astrophysics Data System (ADS)

Cardone, G.; Durante, T.; Nazarov, S. A.

2017-07-01

We consider the spectral Dirichlet problem for the Laplace operator in the plane Ω∘ with double-periodic perforation but also in the domain Ω• with a semi-infinite foreign inclusion so that the Floquet-Bloch technique and the Gelfand transform do not apply directly. We describe waves which are localized near the inclusion and propagate along it. We give a formulation of the problem with radiation conditions that provides a Fredholm operator of index zero. The main conclusion concerns the spectra σ∘ and σ• of the problems in Ω∘ and Ω•, namely we present a concrete geometry which supports the relation σ∘ ⫋σ• due to a new non-empty spectral band caused by the semi-infinite inclusion called an open waveguide in the double-periodic medium.

Unstable Mode Solutions to the Klein-Gordon Equation in Kerr-anti-de Sitter Spacetimes

NASA Astrophysics Data System (ADS)

Dold, Dominic

2017-03-01

For any cosmological constant {Λ = -3/ℓ2 < 0} and any {α < 9/4}, we find a Kerr-AdS spacetime {({M}, g_{KAdS})}, in which the Klein-Gordon equation {Box_{g_{KAdS}}ψ + α/ℓ2ψ = 0} has an exponentially growing mode solution satisfying a Dirichlet boundary condition at infinity. The spacetime violates the Hawking-Reall bound {r+2 > |a|ℓ}. We obtain an analogous result for Neumann boundary conditions if {5/4 < α < 9/4}. Moreover, in the Dirichlet case, one can prove that, for any Kerr-AdS spacetime violating the Hawking-Reall bound, there exists an open family of masses {α} such that the corresponding Klein-Gordon equation permits exponentially growing mode solutions. Our result adopts methods of Shlapentokh-Rothman developed in (Commun. Math. Phys. 329:859-891, 2014) and provides the first rigorous construction of a superradiant instability for negative cosmological constant.

Stereochemistry of silicon in oxygen-containing compounds

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

Serezhkin, V. N., E-mail: Serezhkin@samsu.ru; Urusov, V. S.

2017-01-15

Specific stereochemical features of silicon in oxygen-containing compounds, including hybrid silicates with all oxygen atoms of SiO{sub n} groups ({sub n} = 4, 5, or 6) entering into the composition of organic anions or molecules, are described by characteristics of Voronoi—Dirichlet polyhedra. It is found that in rutile-like stishovite and post-stishovite phases with the structures similar to those of СаСl{sub 2}, α-PbO{sub 2}, or pyrite FeS{sub 2}, the volume of Voronoi—Dirichlet polyhedra of silicon and oxygen atoms decreases linearly with pressure increasing to 268 GPa. Based on these results, the possibility of formation of new post-stishovite phases is shown, namely,more » the fluorite-like structure (transition predicted at ~400 GPa) and a body-centered cubic lattice with statistical arrangement of silicon and oxygen atoms (~900 GPa).« less

A unified Bayesian semiparametric approach to assess discrimination ability in survival analysis

PubMed Central

Zhao, Lili; Feng, Dai; Chen, Guoan; Taylor, Jeremy M.G.

2015-01-01

Summary The discriminatory ability of a marker for censored survival data is routinely assessed by the time-dependent ROC curve and the c-index. The time-dependent ROC curve evaluates the ability of a biomarker to predict whether a patient lives past a particular time t. The c-index measures the global concordance of the marker and the survival time regardless of the time point. We propose a Bayesian semiparametric approach to estimate these two measures. The proposed estimators are based on the conditional distribution of the survival time given the biomarker and the empirical biomarker distribution. The conditional distribution is estimated by a linear dependent Dirichlet process mixture model. The resulting ROC curve is smooth as it is estimated by a mixture of parametric functions. The proposed c-index estimator is shown to be more efficient than the commonly used Harrell's c-index since it uses all pairs of data rather than only informative pairs. The proposed estimators are evaluated through simulations and illustrated using a lung cancer dataset. PMID:26676324

A practical guide to big data research in psychology.

PubMed

Chen, Eric Evan; Wojcik, Sean P

2016-12-01

The massive volume of data that now covers a wide variety of human behaviors offers researchers in psychology an unprecedented opportunity to conduct innovative theory- and data-driven field research. This article is a practical guide to conducting big data research, covering data management, acquisition, processing, and analytics (including key supervised and unsupervised learning data mining methods). It is accompanied by walkthrough tutorials on data acquisition, text analysis with latent Dirichlet allocation topic modeling, and classification with support vector machines. Big data practitioners in academia, industry, and the community have built a comprehensive base of tools and knowledge that makes big data research accessible to researchers in a broad range of fields. However, big data research does require knowledge of software programming and a different analytical mindset. For those willing to acquire the requisite skills, innovative analyses of unexpected or previously untapped data sources can offer fresh ways to develop, test, and extend theories. When conducted with care and respect, big data research can become an essential complement to traditional research. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Latent topic discovery of clinical concepts from hospital discharge summaries of a heterogeneous patient cohort.

PubMed

Lehman, Li-Wei; Long, William; Saeed, Mohammed; Mark, Roger

2014-01-01

Patients in critical care often exhibit complex disease patterns. A fundamental challenge in clinical research is to identify clinical features that may be characteristic of adverse patient outcomes. In this work, we propose a data-driven approach for phenotype discovery of patients in critical care. We used Hierarchical Dirichlet Process (HDP) as a non-parametric topic modeling technique to automatically discover the latent "topic" structure of diseases, symptoms, and findings documented in hospital discharge summaries. We show that the latent topic structure can be used to reveal phenotypic patterns of diseases and symptoms shared across subgroups of a patient cohort, and may contain prognostic value in stratifying patients' post hospital discharge mortality risks. Using discharge summaries of a large patient cohort from the MIMIC II database, we evaluate the clinical utility of the discovered topic structure in identifying patients who are at high risk of mortality within one year post hospital discharge. We demonstrate that the learned topic structure has statistically significant associations with mortality post hospital discharge, and may provide valuable insights in defining new feature sets for predicting patient outcomes.

Geometry Processing of Conventionally Produced Mouse Brain Slice Images.

PubMed

Agarwal, Nitin; Xu, Xiangmin; Gopi, M

2018-04-21

Brain mapping research in most neuroanatomical laboratories relies on conventional processing techniques, which often introduce histological artifacts such as tissue tears and tissue loss. In this paper we present techniques and algorithms for automatic registration and 3D reconstruction of conventionally produced mouse brain slices in a standardized atlas space. This is achieved first by constructing a virtual 3D mouse brain model from annotated slices of Allen Reference Atlas (ARA). Virtual re-slicing of the reconstructed model generates ARA-based slice images corresponding to the microscopic images of histological brain sections. These image pairs are aligned using a geometric approach through contour images. Histological artifacts in the microscopic images are detected and removed using Constrained Delaunay Triangulation before performing global alignment. Finally, non-linear registration is performed by solving Laplace's equation with Dirichlet boundary conditions. Our methods provide significant improvements over previously reported registration techniques for the tested slices in 3D space, especially on slices with significant histological artifacts. Further, as one of the application we count the number of neurons in various anatomical regions using a dataset of 51 microscopic slices from a single mouse brain. To the best of our knowledge the presented work is the first that automatically registers both clean as well as highly damaged high-resolutions histological slices of mouse brain to a 3D annotated reference atlas space. This work represents a significant contribution to this subfield of neuroscience as it provides tools to neuroanatomist for analyzing and processing histological data. Copyright © 2018 Elsevier B.V. All rights reserved.

A theoretical model for investigating the effect of vacuum fluctuations on the electromechanical stability of nanotweezers

NASA Astrophysics Data System (ADS)

Farrokhabadi, A.; Mokhtari, J.; Koochi, A.; Abadyan, M.

2015-06-01

In this paper, the impact of the Casimir attraction on the electromechanical stability of nanowire-fabricated nanotweezers is investigated using a theoretical continuum mechanics model. The Dirichlet mode is considered and an asymptotic solution, based on path integral approach, is applied to consider the effect of vacuum fluctuations in the model. The Euler-Bernoulli beam theory is employed to derive the nonlinear governing equation of the nanotweezers. The governing equations are solved by three different approaches, i.e. the modified variation iteration method, generalized differential quadrature method and using a lumped parameter model. Various perspectives of the problem, including the comparison with the van der Waals force regime, the variation of instability parameters and effects of geometry are addressed in present paper. The proposed approach is beneficial for the precise determination of the electrostatic response of the nanotweezers in the presence of Casimir force.

On the connection between multigrid and cyclic reduction

NASA Technical Reports Server (NTRS)

Merriam, M. L.

1984-01-01

A technique is shown whereby it is possible to relate a particular multigrid process to cyclic reduction using purely mathematical arguments. This technique suggest methods for solving Poisson's equation in 1-, 2-, or 3-dimensions with Dirichlet or Neumann boundary conditions. In one dimension the method is exact and, in fact, reduces to cyclic reduction. This provides a valuable reference point for understanding multigrid techniques. The particular multigrid process analyzed is referred to here as Approximate Cyclic Reduction (ACR) and is one of a class known as Multigrid Reduction methods in the literature. It involves one approximation with a known error term. It is possible to relate the error term in this approximation with certain eigenvector components of the error. These are sharply reduced in amplitude by classical relaxation techniques. The approximation can thus be made a very good one.

Recognition of a person named entity from the text written in a natural language

NASA Astrophysics Data System (ADS)

Dolbin, A. V.; Rozaliev, V. L.; Orlova, Y. A.

2017-01-01

This work is devoted to the semantic analysis of texts, which were written in a natural language. The main goal of the research was to compare latent Dirichlet allocation and latent semantic analysis to identify elements of the human appearance in the text. The completeness of information retrieval was chosen as the efficiency criteria for methods comparison. However, it was insufficient to choose only one method for achieving high recognition rates. Thus, additional methods were used for finding references to the personality in the text. All these methods are based on the created information model, which represents person’s appearance.

Greedy feature selection for glycan chromatography data with the generalized Dirichlet distribution

PubMed Central

2013-01-01

Background Glycoproteins are involved in a diverse range of biochemical and biological processes. Changes in protein glycosylation are believed to occur in many diseases, particularly during cancer initiation and progression. The identification of biomarkers for human disease states is becoming increasingly important, as early detection is key to improving survival and recovery rates. To this end, the serum glycome has been proposed as a potential source of biomarkers for different types of cancers. High-throughput hydrophilic interaction liquid chromatography (HILIC) technology for glycan analysis allows for the detailed quantification of the glycan content in human serum. However, the experimental data from this analysis is compositional by nature. Compositional data are subject to a constant-sum constraint, which restricts the sample space to a simplex. Statistical analysis of glycan chromatography datasets should account for their unusual mathematical properties. As the volume of glycan HILIC data being produced increases, there is a considerable need for a framework to support appropriate statistical analysis. Proposed here is a methodology for feature selection in compositional data. The principal objective is to provide a template for the analysis of glycan chromatography data that may be used to identify potential glycan biomarkers. Results A greedy search algorithm, based on the generalized Dirichlet distribution, is carried out over the feature space to search for the set of “grouping variables” that best discriminate between known group structures in the data, modelling the compositional variables using beta distributions. The algorithm is applied to two glycan chromatography datasets. Statistical classification methods are used to test the ability of the selected features to differentiate between known groups in the data. Two well-known methods are used for comparison: correlation-based feature selection (CFS) and recursive partitioning (rpart). CFS is a feature selection method, while recursive partitioning is a learning tree algorithm that has been used for feature selection in the past. Conclusions The proposed feature selection method performs well for both glycan chromatography datasets. It is computationally slower, but results in a lower misclassification rate and a higher sensitivity rate than both correlation-based feature selection and the classification tree method. PMID:23651459

On degenerate coupled transport processes in porous media with memory phenomena

NASA Astrophysics Data System (ADS)

Beneš, Michal; Pažanin, Igor

2018-06-01

In this paper we prove the existence of weak solutions to degenerate parabolic systems arising from the fully coupled moisture movement, solute transport of dissolved species and heat transfer through porous materials. Physically relevant mixed Dirichlet-Neumann boundary conditions and initial conditions are considered. Existence of a global weak solution of the problem is proved by means of semidiscretization in time, proving necessary uniform estimates and by passing to the limit from discrete approximations. Degeneration occurs in the nonlinear transport coefficients which are not assumed to be bounded below and above by positive constants. Degeneracies in transport coefficients are overcome by proving suitable a-priori $L^{\\infty}$-estimates based on De Giorgi and Moser iteration technique.

Casimir interaction between spheres in ( D + 1)-dimensional Minkowski spacetime

NASA Astrophysics Data System (ADS)

Teo, L. P.

2014-05-01

We consider the Casimir interaction between two spheres in ( D + 1)-dimensional Minkowski spacetime due to the vacuum fluctuations of scalar fields. We consider combinations of Dirichlet and Neumann boundary conditions. The TGTG formula of the Casimir interaction energy is derived. The computations of the T matrices of the two spheres are straightforward. To compute the two G matrices, known as translation matrices, which relate the hyper-spherical waves in two spherical coordinate frames differ by a translation, we generalize the operator approach employed in [39]. The result is expressed in terms of an integral over Gegenbauer polynomials. In contrast to the D=3 case, we do not re-express the integral in terms of 3 j-symbols and hyper-spherical waves, which in principle, can be done but does not simplify the formula. Using our expression for the Casimir interaction energy, we derive the large separation and small separation asymptotic expansions of the Casimir interaction energy. In the large separation regime, we find that the Casimir interaction energy is of order L -2 D+3, L -2 D+1 and L -2 D-1 respectively for Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions, where L is the center-to-center distance of the two spheres. In the small separation regime, we confirm that the leading term of the Casimir interaction agrees with the proximity force approximation, which is of order , where d is the distance between the two spheres. Another main result of this work is the analytic computations of the next-to-leading order term in the small separation asymptotic expansion. This term is computed using careful order analysis as well as perturbation method. In the case the radius of one of the sphere goes to infinity, we find that the results agree with the one we derive for sphere-plate configuration. When D=3, we also recover previously known results. We find that when D is large, the ratio of the next-to-leading order term to the leading order term is linear in D, indicating a larger correction at higher dimensions. The methodologies employed in this work and the results obtained can be used to study the one-loop effective action of the system of two spherical objects in the universe.

Spark formation as a moving boundary process

NASA Astrophysics Data System (ADS)

Ebert, Ute

2006-03-01

The growth process of spark channels recently becomes accessible through complementary methods. First, I will review experiments with nanosecond photographic resolution and with fast and well defined power supplies that appropriately resolve the dynamics of electric breakdown [1]. Second, I will discuss the elementary physical processes as well as present computations of spark growth and branching with adaptive grid refinement [2]. These computations resolve three well separated scales of the process that emerge dynamically. Third, this scale separation motivates a hierarchy of models on different length scales. In particular, I will discuss a moving boundary approximation for the ionization fronts that generate the conducting channel. The resulting moving boundary problem shows strong similarities with classical viscous fingering. For viscous fingering, it is known that the simplest model forms unphysical cusps within finite time that are suppressed by a regularizing condition on the moving boundary. For ionization fronts, we derive a new condition on the moving boundary of mixed Dirichlet-Neumann type (φ=ɛnφ) that indeed regularizes all structures investigated so far. In particular, we present compact analytical solutions with regularization, both for uniformly translating shapes and for their linear perturbations [3]. These solutions are so simple that they may acquire a paradigmatic role in the future. Within linear perturbation theory, they explicitly show the convective stabilization of a curved front while planar fronts are linearly unstable against perturbations of arbitrary wave length. [1] T.M.P. Briels, E.M. van Veldhuizen, U. Ebert, TU Eindhoven. [2] C. Montijn, J. Wackers, W. Hundsdorfer, U. Ebert, CWI Amsterdam. [3] B. Meulenbroek, U. Ebert, L. Schäfer, Phys. Rev. Lett. 95, 195004 (2005).

Learning topic models by belief propagation.

PubMed

Zeng, Jia; Cheung, William K; Liu, Jiming

2013-05-01

Latent Dirichlet allocation (LDA) is an important hierarchical Bayesian model for probabilistic topic modeling, which attracts worldwide interest and touches on many important applications in text mining, computer vision and computational biology. This paper represents the collapsed LDA as a factor graph, which enables the classic loopy belief propagation (BP) algorithm for approximate inference and parameter estimation. Although two commonly used approximate inference methods, such as variational Bayes (VB) and collapsed Gibbs sampling (GS), have gained great success in learning LDA, the proposed BP is competitive in both speed and accuracy, as validated by encouraging experimental results on four large-scale document datasets. Furthermore, the BP algorithm has the potential to become a generic scheme for learning variants of LDA-based topic models in the collapsed space. To this end, we show how to learn two typical variants of LDA-based topic models, such as author-topic models (ATM) and relational topic models (RTM), using BP based on the factor graph representations.

Detecting Adaptation in Protein-Coding Genes Using a Bayesian Site-Heterogeneous Mutation-Selection Codon Substitution Model.

PubMed

Rodrigue, Nicolas; Lartillot, Nicolas

2017-01-01

Codon substitution models have traditionally attempted to uncover signatures of adaptation within protein-coding genes by contrasting the rates of synonymous and non-synonymous substitutions. Another modeling approach, known as the mutation-selection framework, attempts to explicitly account for selective patterns at the amino acid level, with some approaches allowing for heterogeneity in these patterns across codon sites. Under such a model, substitutions at a given position occur at the neutral or nearly neutral rate when they are synonymous, or when they correspond to replacements between amino acids of similar fitness; substitutions from high to low (low to high) fitness amino acids have comparatively low (high) rates. Here, we study the use of such a mutation-selection framework as a null model for the detection of adaptation. Following previous works in this direction, we include a deviation parameter that has the effect of capturing the surplus, or deficit, in non-synonymous rates, relative to what would be expected under a mutation-selection modeling framework that includes a Dirichlet process approach to account for across-codon-site variation in amino acid fitness profiles. We use simulations, along with a few real data sets, to study the behavior of the approach, and find it to have good power with a low false-positive rate. Altogether, we emphasize the potential of recent mutation-selection models in the detection of adaptation, calling for further model refinements as well as large-scale applications. © The Author 2016. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.

Boundary conditions in Chebyshev and Legendre methods

NASA Technical Reports Server (NTRS)

Canuto, C.

1984-01-01

Two different ways of treating non-Dirichlet boundary conditions in Chebyshev and Legendre collocation methods are discussed for second order differential problems. An error analysis is provided. The effect of preconditioning the corresponding spectral operators by finite difference matrices is also investigated.

Simple diffusion can support the pitchfork, the flip bifurcations, and the chaos

NASA Astrophysics Data System (ADS)

Meng, Lili; Li, Xinfu; Zhang, Guang

2017-12-01

In this paper, a discrete rational fration population model with the Dirichlet boundary conditions will be considered. According to the discrete maximum principle and the sub- and supper-solution method, the necessary and sufficient conditions of uniqueness and existence of positive steady state solutions will be obtained. In addition, the dynamical behavior of a special two patch metapopulation model is investigated by using the bifurcation method, the center manifold theory, the bifurcation diagrams and the largest Lyapunov exponent. The results show that there exist the pitchfork, the flip bifurcations, and the chaos. Clearly, these phenomena are caused by the simple diffusion. The theoretical analysis of chaos is very imortant, unfortunately, there is not any results in this hand. However, some open problems are given.

Investigation occurrences of turing pattern in Schnakenberg and Gierer-Meinhardt equation

NASA Astrophysics Data System (ADS)

Nurahmi, Annisa Fitri; Putra, Prama Setia; Nuraini, Nuning

2018-03-01

There are several types of animals with unusual, varied patterns on their skin. The skin pigmentation system influences this in the animal. On the other side, in 1950 Alan Turing formulated the mathematical theory of morphogenesis, where this model can bring up a spatial pattern or so-called Turing pattern. This research discusses the identification of Turing's model that can produce animal skin pattern. Investigations conducted on two types of equations: Schnakenberg (1979), and Gierer-Meinhardt (1972). In this research, parameters were explored to produce Turing's patter on that both equation. The numerical simulation in this research done using Neumann Homogeneous and Dirichlet Homogeneous boundary condition. The investigation of Schnakenberg equation yielded poison dart frog (Andinobates dorisswansonae) and ladybird (Coccinellidae septempunctata) pattern while skin fish pattern was showed by Gierer-Meinhardt equation.

Discontinuous Galerkin Methods for Turbulence Simulation

NASA Technical Reports Server (NTRS)

Collis, S. Scott

2002-01-01

A discontinuous Galerkin (DG) method is formulated, implemented, and tested for simulation of compressible turbulent flows. The method is applied to turbulent channel flow at low Reynolds number, where it is found to successfully predict low-order statistics with fewer degrees of freedom than traditional numerical methods. This reduction is achieved by utilizing local hp-refinement such that the computational grid is refined simultaneously in all three spatial coordinates with decreasing distance from the wall. Another advantage of DG is that Dirichlet boundary conditions can be enforced weakly through integrals of the numerical fluxes. Both for a model advection-diffusion problem and for turbulent channel flow, weak enforcement of wall boundaries is found to improve results at low resolution. Such weak boundary conditions may play a pivotal role in wall modeling for large-eddy simulation.

Two-scale homogenization to determine effective parameters of thin metallic-structured films

PubMed Central

Marigo, Jean-Jacques

2016-01-01

We present a homogenization method based on matched asymptotic expansion technique to derive effective transmission conditions of thin structured films. The method leads unambiguously to effective parameters of the interface which define jump conditions or boundary conditions at an equivalent zero thickness interface. The homogenized interface model is presented in the context of electromagnetic waves for metallic inclusions associated with Neumann or Dirichlet boundary conditions for transverse electric or transverse magnetic wave polarization. By comparison with full-wave simulations, the model is shown to be valid for thin interfaces up to thicknesses close to the wavelength. We also compare our effective conditions with the two-sided impedance conditions obtained in transmission line theory and to the so-called generalized sheet transition conditions. PMID:27616916

A numerical technique for linear elliptic partial differential equations in polygonal domains.

PubMed

Hashemzadeh, P; Fokas, A S; Smitheman, S A

2015-03-08

Integral representations for the solution of linear elliptic partial differential equations (PDEs) can be obtained using Green's theorem. However, these representations involve both the Dirichlet and the Neumann values on the boundary, and for a well-posed boundary-value problem (BVPs) one of these functions is unknown. A new transform method for solving BVPs for linear and integrable nonlinear PDEs usually referred to as the unified transform ( or the Fokas transform ) was introduced by the second author in the late Nineties. For linear elliptic PDEs, this method can be considered as the analogue of Green's function approach but now it is formulated in the complex Fourier plane instead of the physical plane. It employs two global relations also formulated in the Fourier plane which couple the Dirichlet and the Neumann boundary values. These relations can be used to characterize the unknown boundary values in terms of the given boundary data, yielding an elegant approach for determining the Dirichlet to Neumann map . The numerical implementation of the unified transform can be considered as the counterpart in the Fourier plane of the well-known boundary integral method which is formulated in the physical plane. For this implementation, one must choose (i) a suitable basis for expanding the unknown functions and (ii) an appropriate set of complex values, which we refer to as collocation points, at which to evaluate the global relations. Here, by employing a variety of examples we present simple guidelines of how the above choices can be made. Furthermore, we provide concrete rules for choosing the collocation points so that the condition number of the matrix of the associated linear system remains low.

A multiscale model for reinforced concrete with macroscopic variation of reinforcement slip

NASA Astrophysics Data System (ADS)

Sciegaj, Adam; Larsson, Fredrik; Lundgren, Karin; Nilenius, Filip; Runesson, Kenneth

2018-06-01

A single-scale model for reinforced concrete, comprising the plain concrete continuum, reinforcement bars and the bond between them, is used as a basis for deriving a two-scale model. The large-scale problem, representing the "effective" reinforced concrete solid, is enriched by an effective reinforcement slip variable. The subscale problem on a Representative Volume Element (RVE) is defined by Dirichlet boundary conditions. The response of the RVEs of different sizes was investigated by means of pull-out tests. The resulting two-scale formulation was used in an FE^2 analysis of a deep beam. Load-deflection relations, crack widths, and strain fields were compared to those obtained from a single-scale analysis. Incorporating the independent macroscopic reinforcement slip variable resulted in a more pronounced localisation of the effective strain field. This produced a more accurate estimation of the crack widths than the two-scale formulation neglecting the effective reinforcement slip variable.

DUTIR at TREC 2009: Chemical IR Track

DTIC Science & Technology

2009-11-01

We set the Dirichlet prior empirically at 1,500 as recommended in [2]. For example, Topic 15 “ Betaines for peripheral arterial disease” is...converted into the following Indri query: # (combine betaines for peripheral arterial disease ) which produces results rank-equivalent to a simple query

Modifications to holographic entanglement entropy in warped CFT

NASA Astrophysics Data System (ADS)

Song, Wei; Wen, Qiang; Xu, Jianfei

2017-02-01

In [1] it was observed that asymptotic boundary conditions play an important role in the study of holographic entanglement beyond AdS/CFT. In particular, the Ryu-Takayanagi proposal must be modified for warped AdS3 (WAdS3) with Dirichlet boundary conditions. In this paper, we consider AdS3 and WAdS3 with Dirichlet-Neumann boundary conditions. The conjectured holographic duals are warped conformal field theories (WCFTs), featuring a Virasoro-Kac-Moody algebra. We provide a holographic calculation of the entanglement entropy and Rényi entropy using AdS3/WCFT and WAdS3/WCFT dualities. Our bulk results are consistent with the WCFT results derived by Castro-Hofman-Iqbal using the Rindler method. Comparing with [1], we explicitly show that the holographic entanglement entropy is indeed affected by boundary conditions. Both results differ from the Ryu-Takayanagi proposal, indicating new relations between spacetime geometry and quantum entanglement for holographic dualities beyond AdS/CFT.

Positivity and Almost Positivity of Biharmonic Green's Functions under Dirichlet Boundary Conditions

NASA Astrophysics Data System (ADS)

Grunau, Hans-Christoph; Robert, Frédéric

2010-03-01

In general, for higher order elliptic equations and boundary value problems like the biharmonic equation and the linear clamped plate boundary value problem, neither a maximum principle nor a comparison principle or—equivalently—a positivity preserving property is available. The problem is rather involved since the clamped boundary conditions prevent the boundary value problem from being reasonably written as a system of second order boundary value problems. It is shown that, on the other hand, for bounded smooth domains {Ω subsetmathbb{R}^n} , the negative part of the corresponding Green’s function is “small” when compared with its singular positive part, provided {n≥q 3} . Moreover, the biharmonic Green’s function in balls {Bsubsetmathbb{R}^n} under Dirichlet (that is, clamped) boundary conditions is known explicitly and is positive. It has been known for some time that positivity is preserved under small regular perturbations of the domain, if n = 2. In the present paper, such a stability result is proved for {n≥q 3}.

Exact harmonic solutions to Guyer-Krumhansl-type equation and application to heat transport in thin films

NASA Astrophysics Data System (ADS)

Zhukovsky, K.; Oskolkov, D.

2018-03-01

A system of hyperbolic-type inhomogeneous differential equations (DE) is considered for non-Fourier heat transfer in thin films. Exact harmonic solutions to Guyer-Krumhansl-type heat equation and to the system of inhomogeneous DE are obtained in Cauchy- and Dirichlet-type conditions. The contribution of the ballistic-type heat transport, of the Cattaneo heat waves and of the Fourier heat diffusion is discussed and compared with each other in various conditions. The application of the study to the ballistic heat transport in thin films is performed. Rapid evolution of the ballistic quasi-temperature component in low-dimensional systems is elucidated and compared with slow evolution of its diffusive counterpart. The effect of the ballistic quasi-temperature component on the evolution of the complete quasi-temperature is explored. In this context, the influence of the Knudsen number and of Cauchy- and Dirichlet-type conditions on the evolution of the temperature distribution is explored. The comparative analysis of the obtained solutions is performed.

Exclusion Process with Slow Boundary

NASA Astrophysics Data System (ADS)

Baldasso, Rangel; Menezes, Otávio; Neumann, Adriana; Souza, Rafael R.

2017-06-01

We study the hydrodynamic and the hydrostatic behavior of the simple symmetric exclusion process with slow boundary. The term slow boundary means that particles can be born or die at the boundary sites, at a rate proportional to N^{-θ }, where θ > 0 and N is the scaling parameter. In the bulk, the particles exchange rate is equal to 1. In the hydrostatic scenario, we obtain three different linear profiles, depending on the value of the parameter θ ; in the hydrodynamic scenario, we obtain that the time evolution of the spatial density of particles, in the diffusive scaling, is given by the weak solution of the heat equation, with boundary conditions that depend on θ . If θ \\in (0,1), we get Dirichlet boundary conditions, (which is the same behavior if θ =0, see Farfán in Hydrostatics, statical and dynamical large deviations of boundary driven gradient symmetric exclusion processes, 2008); if θ =1, we get Robin boundary conditions; and, if θ \\in (1,∞), we get Neumann boundary conditions.

Posterior consistency in conditional distribution estimation

PubMed Central

Pati, Debdeep; Dunson, David B.; Tokdar, Surya T.

2014-01-01

A wide variety of priors have been proposed for nonparametric Bayesian estimation of conditional distributions, and there is a clear need for theorems providing conditions on the prior for large support, as well as posterior consistency. Estimation of an uncountable collection of conditional distributions across different regions of the predictor space is a challenging problem, which differs in some important ways from density and mean regression estimation problems. Defining various topologies on the space of conditional distributions, we provide sufficient conditions for posterior consistency focusing on a broad class of priors formulated as predictor-dependent mixtures of Gaussian kernels. This theory is illustrated by showing that the conditions are satisfied for a class of generalized stick-breaking process mixtures in which the stick-breaking lengths are monotone, differentiable functions of a continuous stochastic process. We also provide a set of sufficient conditions for the case where stick-breaking lengths are predictor independent, such as those arising from a fixed Dirichlet process prior. PMID:25067858

Automated airplane surface generation

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

Smith, R.E.; Cordero, Y.; Jones, W.

1996-12-31

An efficient methodology and software axe presented for defining a class of airplane configurations. A small set of engineering design parameters and grid control parameters govern the process. The general airplane configuration has wing, fuselage, vertical tall, horizontal tail, and canard components. Wing, canard, and tail surface grids axe manifested by solving a fourth-order partial differential equation subject to Dirichlet and Neumann boundary conditions. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage is described by an algebraic function with four design parameters. The computed surface grids are suitablemore » for a wide range of Computational Fluid Dynamics simulation and configuration optimizations. Both batch and interactive software are discussed for applying the methodology.« less

Mechanisms for the target patterns formation in a stochastic bistable excitable medium

NASA Astrophysics Data System (ADS)

Verisokin, Andrey Yu.; Verveyko, Darya V.; Postnov, Dmitry E.

2018-04-01

We study the features of formation and evolution of spatiotemporal chaotic regime generated by autonomous pacemakers in excitable deterministic and stochastic bistable active media using the example of the FitzHugh - Nagumo biological neuron model under discrete medium conditions. The following possible mechanisms for the formation of autonomous pacemakers have been studied: 1) a temporal external force applied to a small region of the medium, 2) geometry of the solution region (the medium contains regions with Dirichlet or Neumann boundaries). In our work we explore the conditions for the emergence of pacemakers inducing target patterns in a stochastic bistable excitable system and propose the algorithm for their analysis.

Impulsive synchronization of stochastic reaction-diffusion neural networks with mixed time delays.

PubMed

Sheng, Yin; Zeng, Zhigang

2018-07-01

This paper discusses impulsive synchronization of stochastic reaction-diffusion neural networks with Dirichlet boundary conditions and hybrid time delays. By virtue of inequality techniques, theories of stochastic analysis, linear matrix inequalities, and the contradiction method, sufficient criteria are proposed to ensure exponential synchronization of the addressed stochastic reaction-diffusion neural networks with mixed time delays via a designed impulsive controller. Compared with some recent studies, the neural network models herein are more general, some restrictions are relaxed, and the obtained conditions enhance and generalize some published ones. Finally, two numerical simulations are performed to substantiate the validity and merits of the developed theoretical analysis. Copyright © 2018 Elsevier Ltd. All rights reserved.

Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom

NASA Astrophysics Data System (ADS)

Compelli, A.; Ivanov, R.; Todorov, M.

2017-12-01

A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to approximations of Boussinesq and Korteweg-de Vries (KdV) types, taking into account the effect of the slowly varying bottom. The arising KdV equation with variable coefficients is studied numerically when the initial condition is in the form of the one-soliton solution for the initial depth. This article is part of the theme issue 'Nonlinear water waves'.

Probabilistic treatment of the uncertainty from the finite size of weighted Monte Carlo data

NASA Astrophysics Data System (ADS)

Glüsenkamp, Thorsten

2018-06-01

Parameter estimation in HEP experiments often involves Monte Carlo simulation to model the experimental response function. A typical application are forward-folding likelihood analyses with re-weighting, or time-consuming minimization schemes with a new simulation set for each parameter value. Problematically, the finite size of such Monte Carlo samples carries intrinsic uncertainty that can lead to a substantial bias in parameter estimation if it is neglected and the sample size is small. We introduce a probabilistic treatment of this problem by replacing the usual likelihood functions with novel generalized probability distributions that incorporate the finite statistics via suitable marginalization. These new PDFs are analytic, and can be used to replace the Poisson, multinomial, and sample-based unbinned likelihoods, which covers many use cases in high-energy physics. In the limit of infinite statistics, they reduce to the respective standard probability distributions. In the general case of arbitrary Monte Carlo weights, the expressions involve the fourth Lauricella function FD, for which we find a new finite-sum representation in a certain parameter setting. The result also represents an exact form for Carlson's Dirichlet average Rn with n > 0, and thereby an efficient way to calculate the probability generating function of the Dirichlet-multinomial distribution, the extended divided difference of a monomial, or arbitrary moments of univariate B-splines. We demonstrate the bias reduction of our approach with a typical toy Monte Carlo problem, estimating the normalization of a peak in a falling energy spectrum, and compare the results with previously published methods from the literature.

Dimension Reduction for the Landau-de Gennes Model in Planar Nematic Thin Films

NASA Astrophysics Data System (ADS)

Golovaty, Dmitry; Montero, José Alberto; Sternberg, Peter

2015-12-01

We use the method of Γ -convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film in the limit of vanishing thickness. In this asymptotic regime, surface energy plays a greater role, and we take particular care in understanding its influence on the structure of the minimizers of the derived two-dimensional energy. We assume general weak anchoring conditions on the top and the bottom surfaces of the film and the strong Dirichlet boundary conditions on the lateral boundary of the film. The constants in the weak anchoring conditions are chosen so as to enforce that a surface-energy-minimizing nematic Q-tensor has the normal to the film as one of its eigenvectors. We establish a general convergence result and then discuss the limiting problem in several parameter regimes.

Mathematical and computational aspects of nonuniform frictional slip modeling

NASA Astrophysics Data System (ADS)

Gorbatikh, Larissa

2004-07-01

A mechanics-based model of non-uniform frictional sliding is studied from the mathematical/computational analysis point of view. This problem is of a key importance for a number of applications (particularly geomechanical ones), where materials interfaces undergo partial frictional sliding under compression and shear. We show that the problem is reduced to Dirichlet's problem for monotonic loading and to Riemman's problem for cyclic loading. The problem may look like a traditional crack interaction problem, however, it is confounded by the fact that locations of n sliding intervals are not known. They are to be determined from the condition for the stress intensity factors: KII=0 at the ends of the sliding zones. Computationally, it reduces to solving a system of 2n coupled non-linear algebraic equations involving singular integrals with unknown limits of integration.

Bounded Partial Sums?

ERIC Educational Resources Information Center

Brilleslyper, Michael A.; Wolverton, Robert H.

2008-01-01

In this article we consider an example suitable for investigation in many mid and upper level undergraduate mathematics courses. Fourier series provide an excellent example of the differences between uniform and non-uniform convergence. We use Dirichlet's test to investigate the convergence of the Fourier series for a simple periodic saw tooth…

UTOPIAN: user-driven topic modeling based on interactive nonnegative matrix factorization.

PubMed

Choo, Jaegul; Lee, Changhyun; Reddy, Chandan K; Park, Haesun

2013-12-01

Topic modeling has been widely used for analyzing text document collections. Recently, there have been significant advancements in various topic modeling techniques, particularly in the form of probabilistic graphical modeling. State-of-the-art techniques such as Latent Dirichlet Allocation (LDA) have been successfully applied in visual text analytics. However, most of the widely-used methods based on probabilistic modeling have drawbacks in terms of consistency from multiple runs and empirical convergence. Furthermore, due to the complicatedness in the formulation and the algorithm, LDA cannot easily incorporate various types of user feedback. To tackle this problem, we propose a reliable and flexible visual analytics system for topic modeling called UTOPIAN (User-driven Topic modeling based on Interactive Nonnegative Matrix Factorization). Centered around its semi-supervised formulation, UTOPIAN enables users to interact with the topic modeling method and steer the result in a user-driven manner. We demonstrate the capability of UTOPIAN via several usage scenarios with real-world document corpuses such as InfoVis/VAST paper data set and product review data sets.

Materials Processing in Magnetic Fields

NASA Astrophysics Data System (ADS)

Schneider-Muntau, Hans J.; Wada, Hitoshi

The latest in lattice QCD -- Quark-gluon plasma physics -- String theory and exact results in quantum field theory -- The status of local supersymmetry.Supersymmetry in nuclei -- Inflation, dark matter, dark energy -- How many dimensions are really compactified? -- Horizons -- Neutrino oscillations physics -- Fundamental constants and their possible time dependence.Highlights from BNL. new phenomena at RHIC -- Highlights from BABAR -- Diffraction studied with a hard scale at HERA -- The large hadron collider: a status report -- Status of non-LHC experiments at CERN -- Highlights from Gran Sass.Fast automatic systems for nuclear emulsion scanning: technique and experiments -- Probing the QGP with charm at ALICE-LHC -- magnetic screening length in hot QCD -- Non-supersymmetric deformation of the Klebanov-Strassler model and the related plane wave theory -- Holographic renormalization made simple: an example -- The kamLAND impact on neutrino oscillations -- Particle identification with the ALIC TOF detector at very high multiplicity -- Superpotentials of N = 1 SUSY gauge theories -- Measurement of the proton structure function F2 in QED compton scattering at HERA -- Yang-Mills effective action at high temperature -- The time of flight (TOF) system of the ALICE experiment -- Almost product manifolds as the low energy geometry of Dirichlet Brane.

Quasi-equilibrium theory for the distribution of rare alleles in a subdivided population: justification and implications.

PubMed

Burr, T L

2000-05-01

This paper examines a quasi-equilibrium theory of rare alleles for subdivided populations that follow an island-model version of the Wright-Fisher model of evolution. All mutations are assumed to create new alleles. We present four results: (1) conditions for the theory to apply are formally established using properties of the moments of the binomial distribution; (2) approximations currently in the literature can be replaced with exact results that are in better agreement with our simulations; (3) a modified maximum likelihood estimator of migration rate exhibits the same good performance on island-model data or on data simulated from the multinomial mixed with the Dirichlet distribution, and (4) a connection between the rare-allele method and the Ewens Sampling Formula for the infinite-allele mutation model is made. This introduces a new and simpler proof for the expected number of alleles implied by the Ewens Sampling Formula. Copyright 2000 Academic Press.

Robin Gravity

NASA Astrophysics Data System (ADS)

Krishnan, Chethan; Maheshwari, Shubham; Bala Subramanian, P. N.

2017-08-01

We write down a Robin boundary term for general relativity. The construction relies on the Neumann result of arXiv:1605.01603 in an essential way. This is unlike in mechanics and (polynomial) field theory, where two formulations of the Robin problem exist: one with Dirichlet as the natural limiting case, and another with Neumann.

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

Manjunath, Naren; Samajdar, Rhine; Jain, Sudhir R., E-mail: srjain@barc.gov.in

Recently, the nodal domain counts of planar, integrable billiards with Dirichlet boundary conditions were shown to satisfy certain difference equations in Samajdar and Jain (2014). The exact solutions of these equations give the number of domains explicitly. For complete generality, we demonstrate this novel formulation for three additional separable systems and thus extend the statement to all integrable billiards.

A weighted anisotropic variant of the Caffarelli-Kohn-Nirenberg inequality and applications

NASA Astrophysics Data System (ADS)

Bahrouni, Anouar; Rădulescu, Vicenţiu D.; Repovš, Dušan D.

2018-04-01

We present a weighted version of the Caffarelli-Kohn-Nirenberg inequality in the framework of variable exponents. The combination of this inequality with a variant of the fountain theorem, yields the existence of infinitely many solutions for a class of non-homogeneous problems with Dirichlet boundary condition.

The use of MACSYMA for solving elliptic boundary value problems

NASA Technical Reports Server (NTRS)

Thejll, Peter; Gilbert, Robert P.

1990-01-01

A boundary method is presented for the solution of elliptic boundary value problems. An approach based on the use of complete systems of solutions is emphasized. The discussion is limited to the Dirichlet problem, even though the present method can possibly be adapted to treat other boundary value problems.

Solution of a Nonlinear Heat Conduction Equation for a Curvilinear Region with Dirichlet Conditions by the Fast-Expansion Method

NASA Astrophysics Data System (ADS)

Chernyshov, A. D.

2018-05-01

The analytical solution of the nonlinear heat conduction problem for a curvilinear region is obtained with the use of the fast-expansion method together with the method of extension of boundaries and pointwise technique of computing Fourier coefficients.

Pig Data and Bayesian Inference on Multinomial Probabilities

ERIC Educational Resources Information Center

Kern, John C.

2006-01-01

Bayesian inference on multinomial probabilities is conducted based on data collected from the game Pass the Pigs[R]. Prior information on these probabilities is readily available from the instruction manual, and is easily incorporated in a Dirichlet prior. Posterior analysis of the scoring probabilities quantifies the discrepancy between empirical…

Comment Data Mining to Estimate Student Performance Considering Consecutive Lessons

ERIC Educational Resources Information Center

Sorour, Shaymaa E.; Goda, Kazumasa; Mine, Tsunenori

2017-01-01

The purpose of this study is to examine different formats of comment data to predict student performance. Having students write comment data after every lesson can reflect students' learning attitudes, tendencies and learning activities involved with the lesson. In this research, Latent Dirichlet Allocation (LDA) and Probabilistic Latent Semantic…

Automatic sleep classification using a data-driven topic model reveals latent sleep states.

PubMed

Koch, Henriette; Christensen, Julie A E; Frandsen, Rune; Zoetmulder, Marielle; Arvastson, Lars; Christensen, Soren R; Jennum, Poul; Sorensen, Helge B D

2014-09-30

The golden standard for sleep classification uses manual scoring of polysomnography despite points of criticism such as oversimplification, low inter-rater reliability and the standard being designed on young and healthy subjects. To meet the criticism and reveal the latent sleep states, this study developed a general and automatic sleep classifier using a data-driven approach. Spectral EEG and EOG measures and eye correlation in 1s windows were calculated and each sleep epoch was expressed as a mixture of probabilities of latent sleep states by using the topic model Latent Dirichlet Allocation. Model application was tested on control subjects and patients with periodic leg movements (PLM) representing a non-neurodegenerative group, and patients with idiopathic REM sleep behavior disorder (iRBD) and Parkinson's Disease (PD) representing a neurodegenerative group. The model was optimized using 50 subjects and validated on 76 subjects. The optimized sleep model used six topics, and the topic probabilities changed smoothly during transitions. According to the manual scorings, the model scored an overall subject-specific accuracy of 68.3 ± 7.44 (% μ ± σ) and group specific accuracies of 69.0 ± 4.62 (control), 70.1 ± 5.10 (PLM), 67.2 ± 8.30 (iRBD) and 67.7 ± 9.07 (PD). Statistics of the latent sleep state content showed accordances to the sleep stages defined in the golden standard. However, this study indicates that sleep contains six diverse latent sleep states and that state transitions are continuous processes. The model is generally applicable and may contribute to the research in neurodegenerative diseases and sleep disorders. Copyright © 2014 Elsevier B.V. All rights reserved.

3D Numerical Simulation of the Wave and Current Loads on a Truss Foundation of the Offshore Wind Turbine During the Extreme Typhoon Event

NASA Astrophysics Data System (ADS)

Lin, C. W.; Wu, T. R.; Chuang, M. H.; Tsai, Y. L.

2015-12-01

The wind in Taiwan Strait is strong and stable which offers an opportunity to build offshore wind farms. However, frequently visited typhoons and strong ocean current require more attentions on the wave force and local scour around the foundation of the turbine piles. In this paper, we introduce an in-house, multi-phase CFD model, Splash3D, for solving the flow field with breaking wave, strong turbulent, and scour phenomena. Splash3D solves Navier-Stokes Equation with Large-Eddy Simulation (LES) for the fluid domain, and uses volume of fluid (VOF) with piecewise linear interface reconstruction (PLIC) method to describe the break free-surface. The waves were generated inside the computational domain by internal wave maker with a mass-source function. This function is designed to adequately simulate the wave condition under observed extreme events based on JONSWAP spectrum and dispersion relationship. Dirichlet velocity boundary condition is assigned at the upper stream boundary to induce the ocean current. At the downstream face, the sponge-layer method combined with pressure Dirichlet boundary condition is specified for dissipating waves and conducting current out of the domain. Numerical pressure gauges are uniformly set on the structure surface to obtain the force distribution on the structure. As for the local scour around the foundation, we developed Discontinuous Bi-viscous Model (DBM) for the development of the scour hole. Model validations were presented as well. The force distribution under observed irregular wave condition was extracted by the irregular-surface force extraction (ISFE) method, which provides a fast and elegant way to integrate the force acting on the surface of irregular structure. From the Simulation results, we found that the total force is mainly induced by the impinging waves, and the force from the ocean current is about 2 order of magnitude smaller than the wave force. We also found the dynamic pressure, wave height, and the projection area of the structure are the main factors to the total force. Detailed results and discussion are presented as well.

FINDING POTENTIALLY UNSAFE NUTRITIONAL SUPPLEMENTS FROM USER REVIEWS WITH TOPIC MODELING.

PubMed

Sullivan, Ryan; Sarker, Abeed; O'Connor, Karen; Goodin, Amanda; Karlsrud, Mark; Gonzalez, Graciela

2016-01-01

Although dietary supplements are widely used and generally are considered safe, some supplements have been identified as causative agents for adverse reactions, some of which may even be fatal. The Food and Drug Administration (FDA) is responsible for monitoring supplements and ensuring that supplements are safe. However, current surveillance protocols are not always effective. Leveraging user-generated textual data, in the form of Amazon.com reviews for nutritional supplements, we use natural language processing techniques to develop a system for the monitoring of dietary supplements. We use topic modeling techniques, specifically a variation of Latent Dirichlet Allocation (LDA), and background knowledge in the form of an adverse reaction dictionary to score products based on their potential danger to the public. Our approach generates topics that semantically capture adverse reactions from a document set consisting of reviews posted by users of specific products, and based on these topics, we propose a scoring mechanism to categorize products as "high potential danger", "average potential danger" and "low potential danger." We evaluate our system by comparing the system categorization with human annotators, and we find that the our system agrees with the annotators 69.4% of the time. With these results, we demonstrate that our methods show promise and that our system represents a proof of concept as a viable low-cost, active approach for dietary supplement monitoring.

Topic detection using paragraph vectors to support active learning in systematic reviews.

PubMed

Hashimoto, Kazuma; Kontonatsios, Georgios; Miwa, Makoto; Ananiadou, Sophia

2016-08-01

Systematic reviews require expert reviewers to manually screen thousands of citations in order to identify all relevant articles to the review. Active learning text classification is a supervised machine learning approach that has been shown to significantly reduce the manual annotation workload by semi-automating the citation screening process of systematic reviews. In this paper, we present a new topic detection method that induces an informative representation of studies, to improve the performance of the underlying active learner. Our proposed topic detection method uses a neural network-based vector space model to capture semantic similarities between documents. We firstly represent documents within the vector space, and cluster the documents into a predefined number of clusters. The centroids of the clusters are treated as latent topics. We then represent each document as a mixture of latent topics. For evaluation purposes, we employ the active learning strategy using both our novel topic detection method and a baseline topic model (i.e., Latent Dirichlet Allocation). Results obtained demonstrate that our method is able to achieve a high sensitivity of eligible studies and a significantly reduced manual annotation cost when compared to the baseline method. This observation is consistent across two clinical and three public health reviews. The tool introduced in this work is available from https://nactem.ac.uk/pvtopic/. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Signatures of ecological processes in microbial community time series.

PubMed

Faust, Karoline; Bauchinger, Franziska; Laroche, Béatrice; de Buyl, Sophie; Lahti, Leo; Washburne, Alex D; Gonze, Didier; Widder, Stefanie

2018-06-28

Growth rates, interactions between community members, stochasticity, and immigration are important drivers of microbial community dynamics. In sequencing data analysis, such as network construction and community model parameterization, we make implicit assumptions about the nature of these drivers and thereby restrict model outcome. Despite apparent risk of methodological bias, the validity of the assumptions is rarely tested, as comprehensive procedures are lacking. Here, we propose a classification scheme to determine the processes that gave rise to the observed time series and to enable better model selection. We implemented a three-step classification scheme in R that first determines whether dependence between successive time steps (temporal structure) is present in the time series and then assesses with a recently developed neutrality test whether interactions between species are required for the dynamics. If the first and second tests confirm the presence of temporal structure and interactions, then parameters for interaction models are estimated. To quantify the importance of temporal structure, we compute the noise-type profile of the community, which ranges from black in case of strong dependency to white in the absence of any dependency. We applied this scheme to simulated time series generated with the Dirichlet-multinomial (DM) distribution, Hubbell's neutral model, the generalized Lotka-Volterra model and its discrete variant (the Ricker model), and a self-organized instability model, as well as to human stool microbiota time series. The noise-type profiles for all but DM data clearly indicated distinctive structures. The neutrality test correctly classified all but DM and neutral time series as non-neutral. The procedure reliably identified time series for which interaction inference was suitable. Both tests were required, as we demonstrated that all structured time series, including those generated with the neutral model, achieved a moderate to high goodness of fit to the Ricker model. We present a fast and robust scheme to classify community structure and to assess the prevalence of interactions directly from microbial time series data. The procedure not only serves to determine ecological drivers of microbial dynamics, but also to guide selection of appropriate community models for prediction and follow-up analysis.

The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation

NASA Astrophysics Data System (ADS)

Oliveira, F. De; Franco, S. R.; Pinto, M. A. Villela

2018-02-01

The aim of this paper is to reduce the necessary CPU time to solve the three-dimensional heat diffusion equation using Dirichlet boundary conditions. The finite difference method (FDM) is used to discretize the differential equations with a second-order accuracy central difference scheme (CDS). The algebraic equations systems are solved using the lexicographical and red-black Gauss-Seidel methods, associated with the geometric multigrid method with a correction scheme (CS) and V-cycle. Comparisons are made between two types of restriction: injection and full weighting. The used prolongation process is the trilinear interpolation. This work is concerned with the study of the influence of the smoothing value (v), number of mesh levels (L) and number of unknowns (N) on the CPU time, as well as the analysis of algorithm complexity.

Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom.

PubMed

Compelli, A; Ivanov, R; Todorov, M

2018-01-28

A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to approximations of Boussinesq and Korteweg-de Vries (KdV) types, taking into account the effect of the slowly varying bottom. The arising KdV equation with variable coefficients is studied numerically when the initial condition is in the form of the one-soliton solution for the initial depth.This article is part of the theme issue 'Nonlinear water waves'. © 2017 The Author(s).

Detection of dominant flow and abnormal events in surveillance video

NASA Astrophysics Data System (ADS)

Kwak, Sooyeong; Byun, Hyeran

2011-02-01

We propose an algorithm for abnormal event detection in surveillance video. The proposed algorithm is based on a semi-unsupervised learning method, a kind of feature-based approach so that it does not detect the moving object individually. The proposed algorithm identifies dominant flow without individual object tracking using a latent Dirichlet allocation model in crowded environments. It can also automatically detect and localize an abnormally moving object in real-life video. The performance tests are taken with several real-life databases, and their results show that the proposed algorithm can efficiently detect abnormally moving objects in real time. The proposed algorithm can be applied to any situation in which abnormal directions or abnormal speeds are detected regardless of direction.

Topic Model for Graph Mining.

PubMed

Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Luo, Xiangfeng

2015-12-01

Graph mining has been a popular research area because of its numerous application scenarios. Many unstructured and structured data can be represented as graphs, such as, documents, chemical molecular structures, and images. However, an issue in relation to current research on graphs is that they cannot adequately discover the topics hidden in graph-structured data which can be beneficial for both the unsupervised learning and supervised learning of the graphs. Although topic models have proved to be very successful in discovering latent topics, the standard topic models cannot be directly applied to graph-structured data due to the "bag-of-word" assumption. In this paper, an innovative graph topic model (GTM) is proposed to address this issue, which uses Bernoulli distributions to model the edges between nodes in a graph. It can, therefore, make the edges in a graph contribute to latent topic discovery and further improve the accuracy of the supervised and unsupervised learning of graphs. The experimental results on two different types of graph datasets show that the proposed GTM outperforms the latent Dirichlet allocation on classification by using the unveiled topics of these two models to represent graphs.

Infrared length scale and extrapolations for the no-core shell model

DOE PAGES

Wendt, K. A.; Forssén, C.; Papenbrock, T.; ...

2015-06-03

In this paper, we precisely determine the infrared (IR) length scale of the no-core shell model (NCSM). In the NCSM, the A-body Hilbert space is truncated by the total energy, and the IR length can be determined by equating the intrinsic kinetic energy of A nucleons in the NCSM space to that of A nucleons in a 3(A-1)-dimensional hyper-radial well with a Dirichlet boundary condition for the hyper radius. We demonstrate that this procedure indeed yields a very precise IR length by performing large-scale NCSM calculations for 6Li. We apply our result and perform accurate IR extrapolations for bound statesmore » of 4He, 6He, 6Li, and 7Li. Finally, we also attempt to extrapolate NCSM results for 10B and 16O with bare interactions from chiral effective field theory over tens of MeV.« less

Recommender system based on scarce information mining.

PubMed

Lu, Wei; Chung, Fu-Lai; Lai, Kunfeng; Zhang, Liang

2017-09-01

Guessing what user may like is now a typical interface for video recommendation. Nowadays, the highly popular user generated content sites provide various sources of information such as tags for recommendation tasks. Motivated by a real world online video recommendation problem, this work targets at the long tail phenomena of user behavior and the sparsity of item features. A personalized compound recommendation framework for online video recommendation called Dirichlet mixture probit model for information scarcity (DPIS) is hence proposed. Assuming that each clicking sample is generated from a representation of user preferences, DPIS models the sample level topic proportions as a multinomial item vector, and utilizes topical clustering on the user part for recommendation through a probit classifier. As demonstrated by the real-world application, the proposed DPIS achieves better performance in accuracy, perplexity as well as diversity in coverage than traditional methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

The Riemann-Hilbert approach to the Helmholtz equation in a quarter-plane: Neumann, Robin and Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Its, Alexander; Its, Elizabeth

2018-04-01

We revisit the Helmholtz equation in a quarter-plane in the framework of the Riemann-Hilbert approach to linear boundary value problems suggested in late 1990s by A. Fokas. We show the role of the Sommerfeld radiation condition in Fokas' scheme.

Vectorized multigrid Poisson solver for the CDC CYBER 205

NASA Technical Reports Server (NTRS)

Barkai, D.; Brandt, M. A.

1984-01-01

The full multigrid (FMG) method is applied to the two dimensional Poisson equation with Dirichlet boundary conditions. This has been chosen as a relatively simple test case for examining the efficiency of fully vectorizing of the multigrid method. Data structure and programming considerations and techniques are discussed, accompanied by performance details.

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C072)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C048)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

pong: fast analysis and visualization of latent clusters in population genetic data.

PubMed

Behr, Aaron A; Liu, Katherine Z; Liu-Fang, Gracie; Nakka, Priyanka; Ramachandran, Sohini

2016-09-15

A series of methods in population genetics use multilocus genotype data to assign individuals membership in latent clusters. These methods belong to a broad class of mixed-membership models, such as latent Dirichlet allocation used to analyze text corpora. Inference from mixed-membership models can produce different output matrices when repeatedly applied to the same inputs, and the number of latent clusters is a parameter that is often varied in the analysis pipeline. For these reasons, quantifying, visualizing, and annotating the output from mixed-membership models are bottlenecks for investigators across multiple disciplines from ecology to text data mining. We introduce pong, a network-graphical approach for analyzing and visualizing membership in latent clusters with a native interactive D3.js visualization. pong leverages efficient algorithms for solving the Assignment Problem to dramatically reduce runtime while increasing accuracy compared with other methods that process output from mixed-membership models. We apply pong to 225 705 unlinked genome-wide single-nucleotide variants from 2426 unrelated individuals in the 1000 Genomes Project, and identify previously overlooked aspects of global human population structure. We show that pong outpaces current solutions by more than an order of magnitude in runtime while providing a customizable and interactive visualization of population structure that is more accurate than those produced by current tools. pong is freely available and can be installed using the Python package management system pip. pong's source code is available at https://github.com/abehr/pong aaron_behr@alumni.brown.edu or sramachandran@brown.edu Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press.

Revealing common disease mechanisms shared by tumors of different tissues of origin through semantic representation of genomic alterations and topic modeling.

PubMed

Chen, Vicky; Paisley, John; Lu, Xinghua

2017-03-14

Cancer is a complex disease driven by somatic genomic alterations (SGAs) that perturb signaling pathways and consequently cellular function. Identifying patterns of pathway perturbations would provide insights into common disease mechanisms shared among tumors, which is important for guiding treatment and predicting outcome. However, identifying perturbed pathways is challenging, because different tumors can have the same perturbed pathways that are perturbed by different SGAs. Here, we designed novel semantic representations that capture the functional similarity of distinct SGAs perturbing a common pathway in different tumors. Combining this representation with topic modeling would allow us to identify patterns in altered signaling pathways. We represented each gene with a vector of words describing its function, and we represented the SGAs of a tumor as a text document by pooling the words representing individual SGAs. We applied the nested hierarchical Dirichlet process (nHDP) model to a collection of tumors of 5 cancer types from TCGA. We identified topics (consisting of co-occurring words) representing the common functional themes of different SGAs. Tumors were clustered based on their topic associations, such that each cluster consists of tumors sharing common functional themes. The resulting clusters contained mixtures of cancer types, which indicates that different cancer types can share disease mechanisms. Survival analysis based on the clusters revealed significant differences in survival among the tumors of the same cancer type that were assigned to different clusters. The results indicate that applying topic modeling to semantic representations of tumors identifies patterns in the combinations of altered functional pathways in cancer.

Inverse scattering for an exterior Dirichlet program

NASA Technical Reports Server (NTRS)

Hariharan, S. I.

1981-01-01

Scattering due to a metallic cylinder which is in the field of a wire carrying a periodic current is considered. The location and shape of the cylinder is obtained with a far field measurement in between the wire and the cylinder. The same analysis is applicable in acoustics in the situation that the cylinder is a soft wall body and the wire is a line source. The associated direct problem in this situation is an exterior Dirichlet problem for the Helmholtz equation in two dimensions. An improved low frequency estimate for the solution of this problem using integral equation methods is presented. The far field measurements are related to the solutions of boundary integral equations in the low frequency situation. These solutions are expressed in terms of mapping function which maps the exterior of the unknown curve onto the exterior of a unit disk. The coefficients of the Laurent expansion of the conformal transformations are related to the far field coefficients. The first far field coefficient leads to the calculation of the distance between the source and the cylinder.

Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics

NASA Astrophysics Data System (ADS)

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-07-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.

The impact of the rate prior on Bayesian estimation of divergence times with multiple Loci.

PubMed

Dos Reis, Mario; Zhu, Tianqi; Yang, Ziheng

2014-07-01

Bayesian methods provide a powerful way to estimate species divergence times by combining information from molecular sequences with information from the fossil record. With the explosive increase of genomic data, divergence time estimation increasingly uses data of multiple loci (genes or site partitions). Widely used computer programs to estimate divergence times use independent and identically distributed (i.i.d.) priors on the substitution rates for different loci. The i.i.d. prior is problematic. As the number of loci (L) increases, the prior variance of the average rate across all loci goes to zero at the rate 1/L. As a consequence, the rate prior dominates posterior time estimates when many loci are analyzed, and if the rate prior is misspecified, the estimated divergence times will converge to wrong values with very narrow credibility intervals. Here we develop a new prior on the locus rates based on the Dirichlet distribution that corrects the problematic behavior of the i.i.d. prior. We use computer simulation and real data analysis to highlight the differences between the old and new priors. For a dataset for six primate species, we show that with the old i.i.d. prior, if the prior rate is too high (or too low), the estimated divergence times are too young (or too old), outside the bounds imposed by the fossil calibrations. In contrast, with the new Dirichlet prior, posterior time estimates are insensitive to the rate prior and are compatible with the fossil calibrations. We re-analyzed a phylogenomic data set of 36 mammal species and show that using many fossil calibrations can alleviate the adverse impact of a misspecified rate prior to some extent. We recommend the use of the new Dirichlet prior in Bayesian divergence time estimation. [Bayesian inference, divergence time, relaxed clock, rate prior, partition analysis.]. © The Author(s) 2014. Published by Oxford University Press, on behalf of the Society of Systematic Biologists.

Atmospheric effect in three-space scenario for the Stokes-Helmert method of geoid determination

NASA Astrophysics Data System (ADS)

Yang, H.; Tenzer, R.; Vanicek, P.; Santos, M.

2004-05-01

: According to the Stokes-Helmert method for the geoid determination by Vanicek and Martinec (1994) and Vanicek et al. (1999), the Helmert gravity anomalies are computed at the earth surface. To formulate the fundamental formula of physical geodesy, Helmert's gravity anomalies are then downward continued from the earth surface onto the geoid. This procedure, i.e., the inverse Dirichlet's boundary value problem, is realized by solving the Poisson integral equation. The above mentioned "classical" approach can be modified so that the inverse Dirichlet's boundary value problem is solved in the No Topography (NT) space (Vanicek et al., 2004) instead of in the Helmert (H) space. This technique has been introduced by Vanicek et al. (2003) and was used by Tenzer and Vanicek (2003) for the determination of the geoid in the region of the Canadian Rocky Mountains. According to this new approach, the gravity anomalies referred to the earth surface are first transformed into the NT-space. This transformation is realized by subtracting the gravitational attraction of topographical and atmospheric masses from the gravity anomalies at the earth surface. Since the NT-anomalies are harmonic above the geoid, the Dirichlet boundary value problem is solved in the NT-space instead of the Helmert space according to the standard formulation. After being obtained on the geoid, the NT-anomalies are transformed into the H-space to minimize the indirect effect on the geoidal heights. This step, i.e., transformation from NT-space to H-space is realized by adding the gravitational attraction of condensed topographical and condensed atmospheric masses to the NT-anomalies at the geoid. The effects of atmosphere in the standard Stokes-Helmert method was intensively investigated by Sjöberg (1998 and 1999), and Novák (2000). In this presentation, the effect of the atmosphere in the three-space scenario for the Stokes-Helmert method is discussed and the numerical results over Canada are shown. Key words: Atmosphere - Geoid - Gravity

Exploiting Language Models to Classify Events from Twitter

PubMed Central

Vo, Duc-Thuan; Hai, Vo Thuan; Ock, Cheol-Young

2015-01-01

Classifying events is challenging in Twitter because tweets texts have a large amount of temporal data with a lot of noise and various kinds of topics. In this paper, we propose a method to classify events from Twitter. We firstly find the distinguishing terms between tweets in events and measure their similarities with learning language models such as ConceptNet and a latent Dirichlet allocation method for selectional preferences (LDA-SP), which have been widely studied based on large text corpora within computational linguistic relations. The relationship of term words in tweets will be discovered by checking them under each model. We then proposed a method to compute the similarity between tweets based on tweets' features including common term words and relationships among their distinguishing term words. It will be explicit and convenient for applying to k-nearest neighbor techniques for classification. We carefully applied experiments on the Edinburgh Twitter Corpus to show that our method achieves competitive results for classifying events. PMID:26451139

Mapping annotations with textual evidence using an scLDA model.

PubMed

Jin, Bo; Chen, Vicky; Chen, Lujia; Lu, Xinghua

2011-01-01

Most of the knowledge regarding genes and proteins is stored in biomedical literature as free text. Extracting information from complex biomedical texts demands techniques capable of inferring biological concepts from local text regions and mapping them to controlled vocabularies. To this end, we present a sentence-based correspondence latent Dirichlet allocation (scLDA) model which, when trained with a corpus of PubMed documents with known GO annotations, performs the following tasks: 1) learning major biological concepts from the corpus, 2) inferring the biological concepts existing within text regions (sentences), and 3) identifying the text regions in a document that provides evidence for the observed annotations. When applied to new gene-related documents, a trained scLDA model is capable of predicting GO annotations and identifying text regions as textual evidence supporting the predicted annotations. This study uses GO annotation data as a testbed; the approach can be generalized to other annotated data, such as MeSH and MEDLINE documents.

Spectral decompositions of multiple time series: a Bayesian non-parametric approach.

PubMed

Macaro, Christian; Prado, Raquel

2014-01-01

We consider spectral decompositions of multiple time series that arise in studies where the interest lies in assessing the influence of two or more factors. We write the spectral density of each time series as a sum of the spectral densities associated to the different levels of the factors. We then use Whittle's approximation to the likelihood function and follow a Bayesian non-parametric approach to obtain posterior inference on the spectral densities based on Bernstein-Dirichlet prior distributions. The prior is strategically important as it carries identifiability conditions for the models and allows us to quantify our degree of confidence in such conditions. A Markov chain Monte Carlo (MCMC) algorithm for posterior inference within this class of frequency-domain models is presented.We illustrate the approach by analyzing simulated and real data via spectral one-way and two-way models. In particular, we present an analysis of functional magnetic resonance imaging (fMRI) brain responses measured in individuals who participated in a designed experiment to study pain perception in humans.

Skin Effect Modeling in Conductors of Arbitrary Shape Through a Surface Admittance Operator and the Contour Integral Method

NASA Astrophysics Data System (ADS)

Patel, Utkarsh R.; Triverio, Piero

2016-09-01

An accurate modeling of skin effect inside conductors is of capital importance to solve transmission line and scattering problems. This paper presents a surface-based formulation to model skin effect in conductors of arbitrary cross section, and compute the per-unit-length impedance of a multiconductor transmission line. The proposed formulation is based on the Dirichlet-Neumann operator that relates the longitudinal electric field to the tangential magnetic field on the boundary of a conductor. We demonstrate how the surface operator can be obtained through the contour integral method for conductors of arbitrary shape. The proposed algorithm is simple to implement, efficient, and can handle arbitrary cross-sections, which is a main advantage over the existing approach based on eigenfunctions, which is available only for canonical conductor's shapes. The versatility of the method is illustrated through a diverse set of examples, which includes transmission lines with trapezoidal, curved, and V-shaped conductors. Numerical results demonstrate the accuracy, versatility, and efficiency of the proposed technique.

The MUSIC algorithm for impedance tomography of small inclusions from discrete data

NASA Astrophysics Data System (ADS)

Lechleiter, A.

2015-09-01

We consider a point-electrode model for electrical impedance tomography and show that current-to-voltage measurements from finitely many electrodes are sufficient to characterize the positions of a finite number of point-like inclusions. More precisely, we consider an asymptotic expansion with respect to the size of the small inclusions of the relative Neumann-to-Dirichlet operator in the framework of the point electrode model. This operator is naturally finite-dimensional and models difference measurements by finitely many small electrodes of the electric potential with and without the small inclusions. Moreover, its leading-order term explicitly characterizes the centers of the small inclusions if the (finite) number of point electrodes is large enough. This characterization is based on finite-dimensional test vectors and leads naturally to a MUSIC algorithm for imaging the inclusion centers. We show both the feasibility and limitations of this imaging technique via two-dimensional numerical experiments, considering in particular the influence of the number of point electrodes on the algorithm’s images.

Identifying biological concepts from a protein-related corpus with a probabilistic topic model

PubMed Central

Zheng, Bin; McLean, David C; Lu, Xinghua

2006-01-01

Background Biomedical literature, e.g., MEDLINE, contains a wealth of knowledge regarding functions of proteins. Major recurring biological concepts within such text corpora represent the domains of this body of knowledge. The goal of this research is to identify the major biological topics/concepts from a corpus of protein-related MEDLINE© titles and abstracts by applying a probabilistic topic model. Results The latent Dirichlet allocation (LDA) model was applied to the corpus. Based on the Bayesian model selection, 300 major topics were extracted from the corpus. The majority of identified topics/concepts was found to be semantically coherent and most represented biological objects or concepts. The identified topics/concepts were further mapped to the controlled vocabulary of the Gene Ontology (GO) terms based on mutual information. Conclusion The major and recurring biological concepts within a collection of MEDLINE documents can be extracted by the LDA model. The identified topics/concepts provide parsimonious and semantically-enriched representation of the texts in a semantic space with reduced dimensionality and can be used to index text. PMID:16466569

Multiscale modeling of electroosmotic flow: Effects of discrete ion, enhanced viscosity, and surface friction

NASA Astrophysics Data System (ADS)

Bhadauria, Ravi; Aluru, N. R.

2017-05-01

We propose an isothermal, one-dimensional, electroosmotic flow model for slit-shaped nanochannels. Nanoscale confinement effects are embedded into the transport model by incorporating the spatially varying solvent and ion concentration profiles that correspond to the electrochemical potential of mean force. The local viscosity is dependent on the solvent local density and is modeled using the local average density method. Excess contributions to the local viscosity are included using the Onsager-Fuoss expression that is dependent on the local ionic strength. A Dirichlet-type boundary condition is provided in the form of the slip velocity that is dependent on the macroscopic interfacial friction. This solvent-surface specific interfacial friction is estimated using a dynamical generalized Langevin equation based framework. The electroosmotic flow of Na+ and Cl- as single counterions and NaCl salt solvated in Extended Simple Point Charge (SPC/E) water confined between graphene and silicon slit-shaped nanochannels are considered as examples. The proposed model yields a good quantitative agreement with the solvent velocity profiles obtained from the non-equilibrium molecular dynamics simulations.

Bayesian correlated clustering to integrate multiple datasets

PubMed Central

Kirk, Paul; Griffin, Jim E.; Savage, Richard S.; Ghahramani, Zoubin; Wild, David L.

2012-01-01

Motivation: The integration of multiple datasets remains a key challenge in systems biology and genomic medicine. Modern high-throughput technologies generate a broad array of different data types, providing distinct—but often complementary—information. We present a Bayesian method for the unsupervised integrative modelling of multiple datasets, which we refer to as MDI (Multiple Dataset Integration). MDI can integrate information from a wide range of different datasets and data types simultaneously (including the ability to model time series data explicitly using Gaussian processes). Each dataset is modelled using a Dirichlet-multinomial allocation (DMA) mixture model, with dependencies between these models captured through parameters that describe the agreement among the datasets. Results: Using a set of six artificially constructed time series datasets, we show that MDI is able to integrate a significant number of datasets simultaneously, and that it successfully captures the underlying structural similarity between the datasets. We also analyse a variety of real Saccharomyces cerevisiae datasets. In the two-dataset case, we show that MDI’s performance is comparable with the present state-of-the-art. We then move beyond the capabilities of current approaches and integrate gene expression, chromatin immunoprecipitation–chip and protein–protein interaction data, to identify a set of protein complexes for which genes are co-regulated during the cell cycle. Comparisons to other unsupervised data integration techniques—as well as to non-integrative approaches—demonstrate that MDI is competitive, while also providing information that would be difficult or impossible to extract using other methods. Availability: A Matlab implementation of MDI is available from http://www2.warwick.ac.uk/fac/sci/systemsbiology/research/software/. Contact: D.L.Wild@warwick.ac.uk Supplementary information: Supplementary data are available at Bioinformatics online. PMID:23047558

Local recovery of the compressional and shear speeds from the hyperbolic DN map

NASA Astrophysics Data System (ADS)

Stefanov, Plamen; Uhlmann, Gunther; Vasy, Andras

2018-01-01

We study the isotropic elastic wave equation in a bounded domain with boundary. We show that local knowledge of the Dirichlet-to-Neumann map determines uniquely the speed of the p-wave locally if there is a strictly convex foliation with respect to it, and similarly for the s-wave speed.

Quantum field between moving mirrors: A three dimensional example

NASA Technical Reports Server (NTRS)

Hacyan, S.; Jauregui, Roco; Villarreal, Carlos

1995-01-01

The scalar quantum field uniformly moving plates in three dimensional space is studied. Field equations for Dirichlet boundary conditions are solved exactly. Comparison of the resulting wavefunctions with their instantaneous static counterpart is performed via Bogolubov coefficients. Unlike the one dimensional problem, 'particle' creation as well as squeezing may occur. The time dependent Casimir energy is also evaluated.

Einstein-Gauss-Bonnet theory of gravity: The Gauss-Bonnet-Katz boundary term

NASA Astrophysics Data System (ADS)

Deruelle, Nathalie; Merino, Nelson; Olea, Rodrigo

2018-05-01

We propose a boundary term to the Einstein-Gauss-Bonnet action for gravity, which uses the Chern-Weil theorem plus a dimensional continuation process, such that the extremization of the full action yields the equations of motion when Dirichlet boundary conditions are imposed. When translated into tensorial language, this boundary term is the generalization to this theory of the Katz boundary term and vector for general relativity. The boundary term constructed in this paper allows to deal with a general background and is not equivalent to the Gibbons-Hawking-Myers boundary term. However, we show that they coincide if one replaces the background of the Katz procedure by a product manifold. As a first application we show that this Einstein Gauss-Bonnet Katz action yields, without any extra ingredients, the expected mass of the Boulware-Deser black hole.

A Probabilistic Approach to Interior Regularity of Fully Nonlinear Degenerate Elliptic Equations in Smooth Domains

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

Zhou Wei, E-mail: zhoux123@umn.edu

2013-06-15

We consider the value function of a stochastic optimal control of degenerate diffusion processes in a domain D. We study the smoothness of the value function, under the assumption of the non-degeneracy of the diffusion term along the normal to the boundary and an interior condition weaker than the non-degeneracy of the diffusion term. When the diffusion term, drift term, discount factor, running payoff and terminal payoff are all in the class of C{sup 1,1}( D-bar ) , the value function turns out to be the unique solution in the class of C{sub loc}{sup 1,1}(D) Intersection C{sup 0,1}( D-bar )more » to the associated degenerate Bellman equation with Dirichlet boundary data. Our approach is probabilistic.« less

Identifying synonymy between relational phrases using word embeddings.

PubMed

Nguyen, Nhung T H; Miwa, Makoto; Tsuruoka, Yoshimasa; Tojo, Satoshi

2015-08-01

Many text mining applications in the biomedical domain benefit from automatic clustering of relational phrases into synonymous groups, since it alleviates the problem of spurious mismatches caused by the diversity of natural language expressions. Most of the previous work that has addressed this task of synonymy resolution uses similarity metrics between relational phrases based on textual strings or dependency paths, which, for the most part, ignore the context around the relations. To overcome this shortcoming, we employ a word embedding technique to encode relational phrases. We then apply the k-means algorithm on top of the distributional representations to cluster the phrases. Our experimental results show that this approach outperforms state-of-the-art statistical models including latent Dirichlet allocation and Markov logic networks. Copyright © 2015 Elsevier Inc. All rights reserved.

An Eigenvalue Analysis of finite-difference approximations for hyperbolic IBVPs

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1989-01-01

The eigenvalue spectrum associated with a linear finite-difference approximation plays a crucial role in the stability analysis and in the actual computational performance of the discrete approximation. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is analytically intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L(sub 2) stability on a finite domain.

Robust boundary treatment for open-channel flows in divergence-free incompressible SPH

NASA Astrophysics Data System (ADS)

Pahar, Gourabananda; Dhar, Anirban

2017-03-01

A robust Incompressible Smoothed Particle Hydrodynamics (ISPH) framework is developed to simulate specified inflow and outflow boundary conditions for open-channel flow. Being purely divergence-free, the framework offers smoothed and structured pressure distribution. An implicit treatment of Pressure Poison Equation and Dirichlet boundary condition is applied on free-surface to minimize error in velocity-divergence. Beyond inflow and outflow threshold, multiple layers of dummy particles are created according to specified boundary condition. Inflow boundary acts as a soluble wave-maker. Fluid particles beyond outflow threshold are removed and replaced with dummy particles with specified boundary velocity. The framework is validated against different cases of open channel flow with different boundary conditions. The model can efficiently capture flow evolution and vortex generation for random geometry and variable boundary conditions.

Discrete cosine and sine transforms generalized to honeycomb lattice

NASA Astrophysics Data System (ADS)

Hrivnák, Jiří; Motlochová, Lenka

2018-06-01

The discrete cosine and sine transforms are generalized to a triangular fragment of the honeycomb lattice. The honeycomb point sets are constructed by subtracting the root lattice from the weight lattice points of the crystallographic root system A2. The two-variable orbit functions of the Weyl group of A2, discretized simultaneously on the weight and root lattices, induce a novel parametric family of extended Weyl orbit functions. The periodicity and von Neumann and Dirichlet boundary properties of the extended Weyl orbit functions are detailed. Three types of discrete complex Fourier-Weyl transforms and real-valued Hartley-Weyl transforms are described. Unitary transform matrices and interpolating behavior of the discrete transforms are exemplified. Consequences of the developed discrete transforms for transversal eigenvibrations of the mechanical graphene model are discussed.

A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

NASA Astrophysics Data System (ADS)

Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

2018-06-01

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

On two mathematical problems of canonical quantization. IV

NASA Astrophysics Data System (ADS)

Kirillov, A. I.

1992-11-01

A method for solving the problem of reconstructing a measure beginning with its logarithmic derivative is presented. The method completes that of solving the stochastic differential equation via Dirichlet forms proposed by S. Albeverio and M. Rockner. As a result one obtains the mathematical apparatus for the stochastic quantization. The apparatus is applied to prove the existence of the Feynman-Kac measure of the sine-Gordon and λφ2n/(1 + K2φ2n)-models. A synthesis of both mathematical problems of canonical quantization is obtained in the form of a second-order martingale problem for vacuum noise. It is shown that in stochastic mechanics the martingale problem is an analog of Newton's second law and enables us to find the Nelson's stochastic trajectories without determining the wave functions.

Hybrid generative-discriminative human action recognition by combining spatiotemporal words with supervised topic models

NASA Astrophysics Data System (ADS)

Sun, Hao; Wang, Cheng; Wang, Boliang

2011-02-01

We present a hybrid generative-discriminative learning method for human action recognition from video sequences. Our model combines a bag-of-words component with supervised latent topic models. A video sequence is represented as a collection of spatiotemporal words by extracting space-time interest points and describing these points using both shape and motion cues. The supervised latent Dirichlet allocation (sLDA) topic model, which employs discriminative learning using labeled data under a generative framework, is introduced to discover the latent topic structure that is most relevant to action categorization. The proposed algorithm retains most of the desirable properties of generative learning while increasing the classification performance though a discriminative setting. It has also been extended to exploit both labeled data and unlabeled data to learn human actions under a unified framework. We test our algorithm on three challenging data sets: the KTH human motion data set, the Weizmann human action data set, and a ballet data set. Our results are either comparable to or significantly better than previously published results on these data sets and reflect the promise of hybrid generative-discriminative learning approaches.

Concurrent multiscale modeling of microstructural effects on localization behavior in finite deformation solid mechanics

DOE PAGES

Alleman, Coleman N.; Foulk, James W.; Mota, Alejandro; ...

2017-11-06

The heterogeneity in mechanical fields introduced by microstructure plays a critical role in the localization of deformation. In order to resolve this incipient stage of failure, it is therefore necessary to incorporate microstructure with sufficient resolution. On the other hand, computational limitations make it infeasible to represent the microstructure in the entire domain at the component scale. Here, the authors demonstrate the use of concurrent multiscale modeling to incorporate explicit, finely resolved microstructure in a critical region while resolving the smoother mechanical fields outside this region with a coarser discretization to limit computational cost. The microstructural physics is modeled withmore » a high-fidelity model that incorporates anisotropic crystal elasticity and rate-dependent crystal plasticity to simulate the behavior of a stainless steel alloy. The component-scale material behavior is treated with a lower fidelity model incorporating isotropic linear elasticity and rate-independent J 2 plasticity. The microstructural and component scale subdomains are modeled concurrently, with coupling via the Schwarz alternating method, which solves boundary-value problems in each subdomain separately and transfers solution information between subdomains via Dirichlet boundary conditions. In this study, the framework is applied to model incipient localization in tensile specimens during necking.« less

A tree-parenchyma coupled model for lung ventilation simulation.

PubMed

Pozin, Nicolas; Montesantos, Spyridon; Katz, Ira; Pichelin, Marine; Vignon-Clementel, Irene; Grandmont, Céline

2017-11-01

In this article, we develop a lung ventilation model. The parenchyma is described as an elastic homogenized media. It is irrigated by a space-filling dyadic resistive pipe network, which represents the tracheobronchial tree. In this model, the tree and the parenchyma are strongly coupled. The tree induces an extra viscous term in the system constitutive relation, which leads, in the finite element framework, to a full matrix. We consider an efficient algorithm that takes advantage of the tree structure to enable a fast matrix-vector product computation. This framework can be used to model both free and mechanically induced respiration, in health and disease. Patient-specific lung geometries acquired from computed tomography scans are considered. Realistic Dirichlet boundary conditions can be deduced from surface registration on computed tomography images. The model is compared to a more classical exit compartment approach. Results illustrate the coupling between the tree and the parenchyma, at global and regional levels, and how conditions for the purely 0D model can be inferred. Different types of boundary conditions are tested, including a nonlinear Robin model of the surrounding lung structures. Copyright © 2017 John Wiley & Sons, Ltd.

Concurrent multiscale modeling of microstructural effects on localization behavior in finite deformation solid mechanics

NASA Astrophysics Data System (ADS)

Alleman, Coleman N.; Foulk, James W.; Mota, Alejandro; Lim, Hojun; Littlewood, David J.

2018-02-01

The heterogeneity in mechanical fields introduced by microstructure plays a critical role in the localization of deformation. To resolve this incipient stage of failure, it is therefore necessary to incorporate microstructure with sufficient resolution. On the other hand, computational limitations make it infeasible to represent the microstructure in the entire domain at the component scale. In this study, the authors demonstrate the use of concurrent multiscale modeling to incorporate explicit, finely resolved microstructure in a critical region while resolving the smoother mechanical fields outside this region with a coarser discretization to limit computational cost. The microstructural physics is modeled with a high-fidelity model that incorporates anisotropic crystal elasticity and rate-dependent crystal plasticity to simulate the behavior of a stainless steel alloy. The component-scale material behavior is treated with a lower fidelity model incorporating isotropic linear elasticity and rate-independent J2 plasticity. The microstructural and component scale subdomains are modeled concurrently, with coupling via the Schwarz alternating method, which solves boundary-value problems in each subdomain separately and transfers solution information between subdomains via Dirichlet boundary conditions. In this study, the framework is applied to model incipient localization in tensile specimens during necking.

Concurrent multiscale modeling of microstructural effects on localization behavior in finite deformation solid mechanics

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

Alleman, Coleman N.; Foulk, James W.; Mota, Alejandro

The heterogeneity in mechanical fields introduced by microstructure plays a critical role in the localization of deformation. In order to resolve this incipient stage of failure, it is therefore necessary to incorporate microstructure with sufficient resolution. On the other hand, computational limitations make it infeasible to represent the microstructure in the entire domain at the component scale. Here, the authors demonstrate the use of concurrent multiscale modeling to incorporate explicit, finely resolved microstructure in a critical region while resolving the smoother mechanical fields outside this region with a coarser discretization to limit computational cost. The microstructural physics is modeled withmore » a high-fidelity model that incorporates anisotropic crystal elasticity and rate-dependent crystal plasticity to simulate the behavior of a stainless steel alloy. The component-scale material behavior is treated with a lower fidelity model incorporating isotropic linear elasticity and rate-independent J 2 plasticity. The microstructural and component scale subdomains are modeled concurrently, with coupling via the Schwarz alternating method, which solves boundary-value problems in each subdomain separately and transfers solution information between subdomains via Dirichlet boundary conditions. In this study, the framework is applied to model incipient localization in tensile specimens during necking.« less

Search for Patterns of Functional Specificity in the Brain: A Nonparametric Hierarchical Bayesian Model for Group fMRI Data

PubMed Central

Sridharan, Ramesh; Vul, Edward; Hsieh, Po-Jang; Kanwisher, Nancy; Golland, Polina

2012-01-01

Functional MRI studies have uncovered a number of brain areas that demonstrate highly specific functional patterns. In the case of visual object recognition, small, focal regions have been characterized with selectivity for visual categories such as human faces. In this paper, we develop an algorithm that automatically learns patterns of functional specificity from fMRI data in a group of subjects. The method does not require spatial alignment of functional images from different subjects. The algorithm is based on a generative model that comprises two main layers. At the lower level, we express the functional brain response to each stimulus as a binary activation variable. At the next level, we define a prior over sets of activation variables in all subjects. We use a Hierarchical Dirichlet Process as the prior in order to learn the patterns of functional specificity shared across the group, which we call functional systems, and estimate the number of these systems. Inference based on our model enables automatic discovery and characterization of dominant and consistent functional systems. We apply the method to data from a visual fMRI study comprised of 69 distinct stimulus images. The discovered system activation profiles correspond to selectivity for a number of image categories such as faces, bodies, and scenes. Among systems found by our method, we identify new areas that are deactivated by face stimuli. In empirical comparisons with perviously proposed exploratory methods, our results appear superior in capturing the structure in the space of visual categories of stimuli. PMID:21884803

SIBIS: a Bayesian model for inconsistent protein sequence estimation.

PubMed

Khenoussi, Walyd; Vanhoutrève, Renaud; Poch, Olivier; Thompson, Julie D

2014-09-01

The prediction of protein coding genes is a major challenge that depends on the quality of genome sequencing, the accuracy of the model used to elucidate the exonic structure of the genes and the complexity of the gene splicing process leading to different protein variants. As a consequence, today's protein databases contain a huge amount of inconsistency, due to both natural variants and sequence prediction errors. We have developed a new method, called SIBIS, to detect such inconsistencies based on the evolutionary information in multiple sequence alignments. A Bayesian framework, combined with Dirichlet mixture models, is used to estimate the probability of observing specific amino acids and to detect inconsistent or erroneous sequence segments. We evaluated the performance of SIBIS on a reference set of protein sequences with experimentally validated errors and showed that the sensitivity is significantly higher than previous methods, with only a small loss of specificity. We also assessed a large set of human sequences from the UniProt database and found evidence of inconsistency in 48% of the previously uncharacterized sequences. We conclude that the integration of quality control methods like SIBIS in automatic analysis pipelines will be critical for the robust inference of structural, functional and phylogenetic information from these sequences. Source code, implemented in C on a linux system, and the datasets of protein sequences are freely available for download at http://www.lbgi.fr/∼julie/SIBIS. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Rotationally symmetric viscous gas flows

NASA Astrophysics Data System (ADS)

Weigant, W.; Plotnikov, P. I.

2017-03-01

The Dirichlet boundary value problem for the Navier-Stokes equations of a barotropic viscous compressible fluid is considered. The flow region and the data of the problem are assumed to be invariant under rotations about a fixed axis. The existence of rotationally symmetric weak solutions for all adiabatic exponents from the interval (γ*,∞) with a critical exponent γ* < 4/3 is proved.

Thermoelectric DC conductivities in hyperscaling violating Lifshitz theories

NASA Astrophysics Data System (ADS)

Cremonini, Sera; Cvetič, Mirjam; Papadimitriou, Ioannis

2018-04-01

We analytically compute the thermoelectric conductivities at zero frequency (DC) in the holographic dual of a four dimensional Einstein-Maxwell-Axion-Dilaton theory that admits a class of asymptotically hyperscaling violating Lifshitz backgrounds with a dynamical exponent z and hyperscaling violating parameter θ. We show that the heat current in the dual Lifshitz theory involves the energy flux, which is an irrelevant operator for z > 1. The linearized fluctuations relevant for computing the thermoelectric conductivities turn on a source for this irrelevant operator, leading to several novel and non-trivial aspects in the holographic renormalization procedure and the identification of the physical observables in the dual theory. Moreover, imposing Dirichlet or Neumann boundary conditions on the spatial components of one of the two Maxwell fields present leads to different thermoelectric conductivities. Dirichlet boundary conditions reproduce the thermoelectric DC conductivities obtained from the near horizon analysis of Donos and Gauntlett, while Neumann boundary conditions result in a new set of DC conductivities. We make preliminary analytical estimates for the temperature behavior of the thermoelectric matrix in appropriate regions of parameter space. In particular, at large temperatures we find that the only case which could lead to a linear resistivity ρ ˜ T corresponds to z = 4 /3.

Synthesis and X-ray Crystallography of [Mg(H2O)6][AnO2(C2H5COO)3]2 (An = U, Np, or Pu).

PubMed

Serezhkin, Viktor N; Grigoriev, Mikhail S; Abdulmyanov, Aleksey R; Fedoseev, Aleksandr M; Savchenkov, Anton V; Serezhkina, Larisa B

2016-08-01

Synthesis and X-ray crystallography of single crystals of [Mg(H2O)6][AnO2(C2H5COO)3]2, where An = U (I), Np (II), or Pu (III), are reported. Compounds I-III are isostructural and crystallize in the trigonal crystal system. The structures of I-III are built of hydrated magnesium cations [Mg(H2O)6](2+) and mononuclear [AnO2(C2H5COO)3](-) complexes, which belong to the AB(01)3 crystallochemical group of uranyl complexes (A = AnO2(2+), B(01) = C2H5COO(-)). Peculiarities of intermolecular interactions in the structures of [Mg(H2O)6][UO2(L)3]2 complexes depending on the carboxylate ion L (acetate, propionate, or n-butyrate) are investigated using the method of molecular Voronoi-Dirichlet polyhedra. Actinide contraction in the series of U(VI)-Np(VI)-Pu(VI) in compounds I-III is reflected in a decrease in the mean An═O bond lengths and in the volume and sphericity degree of Voronoi-Dirichlet polyhedra of An atoms.

Brain Surface Conformal Parameterization Using Riemann Surface Structure

PubMed Central

Wang, Yalin; Lui, Lok Ming; Gu, Xianfeng; Hayashi, Kiralee M.; Chan, Tony F.; Toga, Arthur W.; Thompson, Paul M.; Yau, Shing-Tung

2011-01-01

In medical imaging, parameterized 3-D surface models are useful for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on Riemann surface structure, which uses a special curvilinear net structure (conformal net) to partition the surface into a set of patches that can each be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable (their solutions tend to be smooth functions and the boundary conditions of the Dirichlet problem can be enforced). Conformal parameterization also helps transform partial differential equations (PDEs) that may be defined on 3-D brain surface manifolds to modified PDEs on a two-dimensional parameter domain. Since the Jacobian matrix of a conformal parameterization is diagonal, the modified PDE on the parameter domain is readily solved. To illustrate our techniques, we computed parameterizations for several types of anatomical surfaces in 3-D magnetic resonance imaging scans of the brain, including the cerebral cortex, hippocampi, and lateral ventricles. For surfaces that are topologically homeomorphic to each other and have similar geometrical structures, we show that the parameterization results are consistent and the subdivided surfaces can be matched to each other. Finally, we present an automatic sulcal landmark location algorithm by solving PDEs on cortical surfaces. The landmark detection results are used as constraints for building conformal maps between surfaces that also match explicitly defined landmarks. PMID:17679336

Detecting Hotspot Information Using Multi-Attribute Based Topic Model

PubMed Central

Wang, Jing; Li, Li; Tan, Feng; Zhu, Ying; Feng, Weisi

2015-01-01

Microblogging as a kind of social network has become more and more important in our daily lives. Enormous amounts of information are produced and shared on a daily basis. Detecting hot topics in the mountains of information can help people get to the essential information more quickly. However, due to short and sparse features, a large number of meaningless tweets and other characteristics of microblogs, traditional topic detection methods are often ineffective in detecting hot topics. In this paper, we propose a new topic model named multi-attribute latent dirichlet allocation (MA-LDA), in which the time and hashtag attributes of microblogs are incorporated into LDA model. By introducing time attribute, MA-LDA model can decide whether a word should appear in hot topics or not. Meanwhile, compared with the traditional LDA model, applying hashtag attribute in MA-LDA model gives the core words an artificially high ranking in results meaning the expressiveness of outcomes can be improved. Empirical evaluations on real data sets demonstrate that our method is able to detect hot topics more accurately and efficiently compared with several baselines. Our method provides strong evidence of the importance of the temporal factor in extracting hot topics. PMID:26496635

Traffic Behavior Recognition Using the Pachinko Allocation Model

PubMed Central

Huynh-The, Thien; Banos, Oresti; Le, Ba-Vui; Bui, Dinh-Mao; Yoon, Yongik; Lee, Sungyoung

2015-01-01

CCTV-based behavior recognition systems have gained considerable attention in recent years in the transportation surveillance domain for identifying unusual patterns, such as traffic jams, accidents, dangerous driving and other abnormal behaviors. In this paper, a novel approach for traffic behavior modeling is presented for video-based road surveillance. The proposed system combines the pachinko allocation model (PAM) and support vector machine (SVM) for a hierarchical representation and identification of traffic behavior. A background subtraction technique using Gaussian mixture models (GMMs) and an object tracking mechanism based on Kalman filters are utilized to firstly construct the object trajectories. Then, the sparse features comprising the locations and directions of the moving objects are modeled by PAM into traffic topics, namely activities and behaviors. As a key innovation, PAM captures not only the correlation among the activities, but also among the behaviors based on the arbitrary directed acyclic graph (DAG). The SVM classifier is then utilized on top to train and recognize the traffic activity and behavior. The proposed model shows more flexibility and greater expressive power than the commonly-used latent Dirichlet allocation (LDA) approach, leading to a higher recognition accuracy in the behavior classification. PMID:26151213

Extensively Parameterized Mutation-Selection Models Reliably Capture Site-Specific Selective Constraint.

PubMed

Spielman, Stephanie J; Wilke, Claus O

2016-11-01

The mutation-selection model of coding sequence evolution has received renewed attention for its use in estimating site-specific amino acid propensities and selection coefficient distributions. Two computationally tractable mutation-selection inference frameworks have been introduced: One framework employs a fixed-effects, highly parameterized maximum likelihood approach, whereas the other employs a random-effects Bayesian Dirichlet Process approach. While both implementations follow the same model, they appear to make distinct predictions about the distribution of selection coefficients. The fixed-effects framework estimates a large proportion of highly deleterious substitutions, whereas the random-effects framework estimates that all substitutions are either nearly neutral or weakly deleterious. It remains unknown, however, how accurately each method infers evolutionary constraints at individual sites. Indeed, selection coefficient distributions pool all site-specific inferences, thereby obscuring a precise assessment of site-specific estimates. Therefore, in this study, we use a simulation-based strategy to determine how accurately each approach recapitulates the selective constraint at individual sites. We find that the fixed-effects approach, despite its extensive parameterization, consistently and accurately estimates site-specific evolutionary constraint. By contrast, the random-effects Bayesian approach systematically underestimates the strength of natural selection, particularly for slowly evolving sites. We also find that, despite the strong differences between their inferred selection coefficient distributions, the fixed- and random-effects approaches yield surprisingly similar inferences of site-specific selective constraint. We conclude that the fixed-effects mutation-selection framework provides the more reliable software platform for model application and future development. © The Author 2016. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Spiritual and ceremonial plants in North America: an assessment of Moerman's ethnobotanical database comparing Residual, Binomial, Bayesian and Imprecise Dirichlet Model (IDM) analysis.

PubMed

Turi, Christina E; Murch, Susan J

2013-07-09

Ethnobotanical research and the study of plants used for rituals, ceremonies and to connect with the spirit world have led to the discovery of many novel psychoactive compounds such as nicotine, caffeine, and cocaine. In North America, spiritual and ceremonial uses of plants are well documented and can be accessed online via the University of Michigan's Native American Ethnobotany Database. The objective of the study was to compare Residual, Bayesian, Binomial and Imprecise Dirichlet Model (IDM) analyses of ritual, ceremonial and spiritual plants in Moerman's ethnobotanical database and to identify genera that may be good candidates for the discovery of novel psychoactive compounds. The database was queried with the following format "Family Name AND Ceremonial OR Spiritual" for 263 North American botanical families. Spiritual and ceremonial flora consisted of 86 families with 517 species belonging to 292 genera. Spiritual taxa were then grouped further into ceremonial medicines and items categories. Residual, Bayesian, Binomial and IDM analysis were performed to identify over and under-utilized families. The 4 statistical approaches were in good agreement when identifying under-utilized families but large families (>393 species) were underemphasized by Binomial, Bayesian and IDM approaches for over-utilization. Residual, Binomial, and IDM analysis identified similar families as over-utilized in the medium (92-392 species) and small (<92 species) classes. The families Apiaceae, Asteraceae, Ericacea, Pinaceae and Salicaceae were identified as significantly over-utilized as ceremonial medicines in medium and large sized families. Analysis of genera within the Apiaceae and Asteraceae suggest that the genus Ligusticum and Artemisia are good candidates for facilitating the discovery of novel psychoactive compounds. The 4 statistical approaches were not consistent in the selection of over-utilization of flora. Residual analysis revealed overall trends that were supported by Binomial analysis when separated into small, medium and large families. The Bayesian, Binomial and IDM approaches identified different genera as potentially important. Species belonging to the genus Artemisia and Ligusticum were most consistently identified and may be valuable in future studies of the ethnopharmacology. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

A Deep and Autoregressive Approach for Topic Modeling of Multimodal Data.

PubMed

Zheng, Yin; Zhang, Yu-Jin; Larochelle, Hugo

2016-06-01

Topic modeling based on latent Dirichlet allocation (LDA) has been a framework of choice to deal with multimodal data, such as in image annotation tasks. Another popular approach to model the multimodal data is through deep neural networks, such as the deep Boltzmann machine (DBM). Recently, a new type of topic model called the Document Neural Autoregressive Distribution Estimator (DocNADE) was proposed and demonstrated state-of-the-art performance for text document modeling. In this work, we show how to successfully apply and extend this model to multimodal data, such as simultaneous image classification and annotation. First, we propose SupDocNADE, a supervised extension of DocNADE, that increases the discriminative power of the learned hidden topic features and show how to employ it to learn a joint representation from image visual words, annotation words and class label information. We test our model on the LabelMe and UIUC-Sports data sets and show that it compares favorably to other topic models. Second, we propose a deep extension of our model and provide an efficient way of training the deep model. Experimental results show that our deep model outperforms its shallow version and reaches state-of-the-art performance on the Multimedia Information Retrieval (MIR) Flickr data set.

3D variational brain tumor segmentation using Dirichlet priors on a clustered feature set.

PubMed

Popuri, Karteek; Cobzas, Dana; Murtha, Albert; Jägersand, Martin

2012-07-01

Brain tumor segmentation is a required step before any radiation treatment or surgery. When performed manually, segmentation is time consuming and prone to human errors. Therefore, there have been significant efforts to automate the process. But, automatic tumor segmentation from MRI data is a particularly challenging task. Tumors have a large diversity in shape and appearance with intensities overlapping the normal brain tissues. In addition, an expanding tumor can also deflect and deform nearby tissue. In our work, we propose an automatic brain tumor segmentation method that addresses these last two difficult problems. We use the available MRI modalities (T1, T1c, T2) and their texture characteristics to construct a multidimensional feature set. Then, we extract clusters which provide a compact representation of the essential information in these features. The main idea in this work is to incorporate these clustered features into the 3D variational segmentation framework. In contrast to previous variational approaches, we propose a segmentation method that evolves the contour in a supervised fashion. The segmentation boundary is driven by the learned region statistics in the cluster space. We incorporate prior knowledge about the normal brain tissue appearance during the estimation of these region statistics. In particular, we use a Dirichlet prior that discourages the clusters from the normal brain region to be in the tumor region. This leads to a better disambiguation of the tumor from brain tissue. We evaluated the performance of our automatic segmentation method on 15 real MRI scans of brain tumor patients, with tumors that are inhomogeneous in appearance, small in size and in proximity to the major structures in the brain. Validation with the expert segmentation labels yielded encouraging results: Jaccard (58%), Precision (81%), Recall (67%), Hausdorff distance (24 mm). Using priors on the brain/tumor appearance, our proposed automatic 3D variational segmentation method was able to better disambiguate the tumor from the surrounding tissue.

Estimation of population trajectories from count data

USGS Publications Warehouse

Link, W.A.; Sauer, J.R.

1997-01-01

Monitoring of changes in animal population size is rarely possible through complete censuses; frequently, the only feasible means of monitoring changes in population size is to use counts of animals obtained by skilled observers as indices to abundance. Analysis of changes in population size can be severely biased if factors related to the acquisition of data are not adequately controlled for. In particular we identify two types of observer effects: these correspond to baseline differences in observer competence, and to changes through time in the ability of individual observers. We present a family of models for count data in which the first of these observer effects is treated as a nuisance parameter. Conditioning on totals of negative binomial counts yields a Dirichlet compound multinomial vector for each observer. Quasi-likelihood is used to estimate parameters related to population trajectory and other parameters of interest; model selection is carried out on the basis of Akaike's information criterion. An example is presented using data on Wood thrush from the North American Breeding Bird Survey.

Multiclass Data Segmentation using Diffuse Interface Methods on Graphs

DTIC Science & Technology

2014-01-01

37] that performs interac- tive image segmentation using the solution to a combinatorial Dirichlet problem. Elmoataz et al . have developed general...izations of the graph Laplacian [25] for image denoising and manifold smoothing. Couprie et al . in [18] define a conve- niently parameterized graph...continuous setting carry over to the discrete graph representation. For general data segmentation, Bresson et al . in [8], present rigorous convergence

On the Effective Construction of Compactly Supported Wavelets Satisfying Homogenous Boundary Conditions on the Interval

NASA Technical Reports Server (NTRS)

Chiavassa, G.; Liandrat, J.

1996-01-01

We construct compactly supported wavelet bases satisfying homogeneous boundary conditions on the interval (0,1). The maximum features of multiresolution analysis on the line are retained, including polynomial approximation and tree algorithms. The case of H(sub 0)(sup 1)(0, 1)is detailed, and numerical values, required for the implementation, are provided for the Neumann and Dirichlet boundary conditions.

Interactions between Mathematics and Physics: The History of the Concept of Function--Teaching with and about Nature of Mathematics

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-01-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another…

The accurate solution of Poisson's equation by expansion in Chebyshev polynomials

NASA Technical Reports Server (NTRS)

Haidvogel, D. B.; Zang, T.

1979-01-01

A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways - by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.

The tunneling effect for a class of difference operators

NASA Astrophysics Data System (ADS)

Klein, Markus; Rosenberger, Elke

We analyze a general class of self-adjoint difference operators H𝜀 = T𝜀 + V𝜀 on ℓ2((𝜀ℤ)d), where V𝜀 is a multi-well potential and 𝜀 is a small parameter. We give a coherent review of our results on tunneling up to new sharp results on the level of complete asymptotic expansions (see [30-35]).Our emphasis is on general ideas and strategy, possibly of interest for a broader range of readers, and less on detailed mathematical proofs. The wells are decoupled by introducing certain Dirichlet operators on regions containing only one potential well. Then the eigenvalue problem for the Hamiltonian H𝜀 is treated as a small perturbation of these comparison problems. After constructing a Finslerian distance d induced by H𝜀, we show that Dirichlet eigenfunctions decay exponentially with a rate controlled by this distance to the well. It follows with microlocal techniques that the first n eigenvalues of H𝜀 converge to the first n eigenvalues of the direct sum of harmonic oscillators on ℝd located at several wells. In a neighborhood of one well, we construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low-lying eigenvalues of H𝜀. These are obtained from eigenfunctions or quasimodes for the operator H𝜀, acting on L2(ℝd), via restriction to the lattice (𝜀ℤ)d. Tunneling is then described by a certain interaction matrix, similar to the analysis for the Schrödinger operator (see [22]), the remainder is exponentially small and roughly quadratic compared with the interaction matrix. We give weighted ℓ2-estimates for the difference of eigenfunctions of Dirichlet-operators in neighborhoods of the different wells and the associated WKB-expansions at the wells. In the last step, we derive full asymptotic expansions for interactions between two “wells” (minima) of the potential energy, in particular for the discrete tunneling effect. Here we essentially use analysis on phase space, complexified in the momentum variable. These results are as sharp as the classical results for the Schrödinger operator in [22].

Spreading and vanishing in a West Nile virus model with expanding fronts

NASA Astrophysics Data System (ADS)

Tarboush, Abdelrazig K.; Lin, ZhiGui; Zhang, MengYun

2017-05-01

In this paper, we study a simplified version of a West Nile virus model discussed by Lewis et al. [28], which was considered as a first approximation for the spatial spread of WNv. The basic reproduction number $R_0$ for the non-spatial epidemic model is defined and a threshold parameter $R_0 ^D$ for the corresponding problem with null Dirichlet boundary condition is introduced. We consider a free boundary problem with coupled system, which describes the diffusion of birds by a PDE and the movement of mosquitoes by a ODE. The risk index $R_0^F (t)$ associated with the disease in spatial setting is represented. Sufficient conditions for the WNv to eradicate or to spread are given. The asymptotic behavior of the solution to system when the spreading occurs are considered. It is shown that the initial number of infected populations, the diffusion rate of birds and the length of initial habitat exhibit important impacts on the vanishing or spreading of the virus. Numerical simulations are presented to illustrate the analytical results.

An Optimization-based Atomistic-to-Continuum Coupling Method

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

Olson, Derek; Bochev, Pavel B.; Luskin, Mitchell

2014-08-21

In this paper, we present a new optimization-based method for atomistic-to-continuum (AtC) coupling. The main idea is to cast the latter as a constrained optimization problem with virtual Dirichlet controls on the interfaces between the atomistic and continuum subdomains. The optimization objective is to minimize the error between the atomistic and continuum solutions on the overlap between the two subdomains, while the atomistic and continuum force balance equations provide the constraints. Separation, rather then blending of the atomistic and continuum problems, and their subsequent use as constraints in the optimization problem distinguishes our approach from the existing AtC formulations. Finally,more » we present and analyze the method in the context of a one-dimensional chain of atoms modeled using a linearized two-body potential with next-nearest neighbor interactions.« less

Birkhoff Normal Form for Some Nonlinear PDEs

NASA Astrophysics Data System (ADS)

Bambusi, Dario

We consider the problem of extending to PDEs Birkhoff normal form theorem on Hamiltonian systems close to nonresonant elliptic equilibria. As a model problem we take the nonlinear wave equation with Dirichlet boundary conditions on [0,π] g is an analytic skewsymmetric function which vanishes for u=0 and is periodic with period 2π in the x variable. We prove, under a nonresonance condition which is fulfilled for most g's, that for any integer M there exists a canonical transformation that puts the Hamiltonian in Birkhoff normal form up to a reminder of order M. The canonical transformation is well defined in a neighbourhood of the origin of a Sobolev type phase space of sufficiently high order. Some dynamical consequences are obtained. The technique of proof is applicable to quite general semilinear equations in one space dimension.

Some new results for the one-loop mass correction to the compactified λϕ4 theory

NASA Astrophysics Data System (ADS)

Fucci, Guglielmo; Kirsten, Klaus

2018-03-01

In this work, we consider the one-loop effective action of a self-interacting λϕ4 field propagating in a D dimensional Euclidean space endowed with d ≤ D compact dimensions. The main purpose of this paper is to compute the corrections to the mass of the field due to the presence of the compactified dimensions. Although the results of the one-loop correction to the mass of a λϕ4 field are very well known for compactified toroidal spaces, where the field obeys periodic boundary conditions, similar results do not appear to be readily available for cases in which the scalar field is subject to Dirichlet and Neumann boundary conditions. We apply the results of the one-loop mass correction to the study of the critical temperature in Ginzburg-Landau models.

Analysis of the Westland Data Set

NASA Technical Reports Server (NTRS)

Wen, Fang; Willett, Peter; Deb, Somnath

2001-01-01

The "Westland" set of empirical accelerometer helicopter data with seeded and labeled faults is analyzed with the aim of condition monitoring. The autoregressive (AR) coefficients from a simple linear model encapsulate a great deal of information in a relatively few measurements; and it has also been found that augmentation of these by harmonic and other parameters call improve classification significantly. Several techniques have been explored, among these restricted Coulomb energy (RCE) networks, learning vector quantization (LVQ), Gaussian mixture classifiers and decision trees. A problem with these approaches, and in common with many classification paradigms, is that augmentation of the feature dimension can degrade classification ability. Thus, we also introduce the Bayesian data reduction algorithm (BDRA), which imposes a Dirichlet prior oil training data and is thus able to quantify probability of error in all exact manner, such that features may be discarded or coarsened appropriately.

Microblogging as an extension of science reporting.

PubMed

Büchi, Moritz

2017-11-01

Mass media have long provided general publics with science news. New media such as Twitter have entered this system and provide an additional platform for the dissemination of science information. Based on automated collection and analysis of >900 news articles and 70,000 tweets, this study explores the online communication of current science news. Topic modeling (latent Dirichlet allocation) was used to extract five broad themes of science reporting: space missions, the US government shutdown, cancer research, Nobel Prizes, and climate change. Using content and network analysis, Twitter was found to extend public science communication by providing additional voices and contextualizations of science issues. It serves a recommender role by linking to web resources, connecting users, and directing users' attention. This article suggests that microblogging adds a new and relevant layer to the public communication of science.

Quantitative characterization of the spatial distribution of particles in materials: Application to materials processing

NASA Technical Reports Server (NTRS)

Parse, Joseph B.; Wert, J. A.

1991-01-01

Inhomogeneities in the spatial distribution of second phase particles in engineering materials are known to affect certain mechanical properties. Progress in this area has been hampered by the lack of a convenient method for quantitative description of the spatial distribution of the second phase. This study intends to develop a broadly applicable method for the quantitative analysis and description of the spatial distribution of second phase particles. The method was designed to operate on a desktop computer. The Dirichlet tessellation technique (geometrical method for dividing an area containing an array of points into a set of polygons uniquely associated with the individual particles) was selected as the basis of an analysis technique implemented on a PC. This technique is being applied to the production of Al sheet by PM processing methods; vacuum hot pressing, forging, and rolling. The effect of varying hot working parameters on the spatial distribution of aluminum oxide particles in consolidated sheet is being studied. Changes in distributions of properties such as through-thickness near-neighbor distance correlate with hot-working reduction.

A Non-parametric Cutout Index for Robust Evaluation of Identified Proteins*

PubMed Central

Serang, Oliver; Paulo, Joao; Steen, Hanno; Steen, Judith A.

2013-01-01

This paper proposes a novel, automated method for evaluating sets of proteins identified using mass spectrometry. The remaining peptide-spectrum match score distributions of protein sets are compared to an empirical absent peptide-spectrum match score distribution, and a Bayesian non-parametric method reminiscent of the Dirichlet process is presented to accurately perform this comparison. Thus, for a given protein set, the process computes the likelihood that the proteins identified are correctly identified. First, the method is used to evaluate protein sets chosen using different protein-level false discovery rate (FDR) thresholds, assigning each protein set a likelihood. The protein set assigned the highest likelihood is used to choose a non-arbitrary protein-level FDR threshold. Because the method can be used to evaluate any protein identification strategy (and is not limited to mere comparisons of different FDR thresholds), we subsequently use the method to compare and evaluate multiple simple methods for merging peptide evidence over replicate experiments. The general statistical approach can be applied to other types of data (e.g. RNA sequencing) and generalizes to multivariate problems. PMID:23292186

Daily life activity routine discovery in hemiparetic rehabilitation patients using topic models.

PubMed

Seiter, J; Derungs, A; Schuster-Amft, C; Amft, O; Tröster, G

2015-01-01

Monitoring natural behavior and activity routines of hemiparetic rehabilitation patients across the day can provide valuable progress information for therapists and patients and contribute to an optimized rehabilitation process. In particular, continuous patient monitoring could add type, frequency and duration of daily life activity routines and hence complement standard clinical scores that are assessed for particular tasks only. Machine learning methods have been applied to infer activity routines from sensor data. However, supervised methods require activity annotations to build recognition models and thus require extensive patient supervision. Discovery methods, including topic models could provide patient routine information and deal with variability in activity and movement performance across patients. Topic models have been used to discover characteristic activity routine patterns of healthy individuals using activity primitives recognized from supervised sensor data. Yet, the applicability of topic models for hemiparetic rehabilitation patients and techniques to derive activity primitives without supervision needs to be addressed. We investigate, 1) whether a topic model-based activity routine discovery framework can infer activity routines of rehabilitation patients from wearable motion sensor data. 2) We compare the performance of our topic model-based activity routine discovery using rule-based and clustering-based activity vocabulary. We analyze the activity routine discovery in a dataset recorded with 11 hemiparetic rehabilitation patients during up to ten full recording days per individual in an ambulatory daycare rehabilitation center using wearable motion sensors attached to both wrists and the non-affected thigh. We introduce and compare rule-based and clustering-based activity vocabulary to process statistical and frequency acceleration features to activity words. Activity words were used for activity routine pattern discovery using topic models based on Latent Dirichlet Allocation. Discovered activity routine patterns were then mapped to six categorized activity routines. Using the rule-based approach, activity routines could be discovered with an average accuracy of 76% across all patients. The rule-based approach outperformed clustering by 10% and showed less confusions for predicted activity routines. Topic models are suitable to discover daily life activity routines in hemiparetic rehabilitation patients without trained classifiers and activity annotations. Activity routines show characteristic patterns regarding activity primitives including body and extremity postures and movement. A patient-independent rule set can be derived. Including expert knowledge supports successful activity routine discovery over completely data-driven clustering.

Synthesis and crystal structure analysis of uranyl triple acetates

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

Klepov, Vladislav V., E-mail: vladislavklepov@gmail.com; Department of Chemistry, Samara National Research University, 443086 Samara; Serezhkina, Larisa B.

2016-12-15

Single crystals of triple acetates NaR[UO{sub 2}(CH{sub 3}COO){sub 3}]{sub 3}·6H{sub 2}O (R=Mg, Co, Ni, Zn), well-known for their use as reagents for sodium determination, were grown from aqueous solutions and their structural and spectroscopic properties were studied. Crystal structures of the mentioned phases are based upon (Na[UO{sub 2}(CH{sub 3}COO){sub 3}]{sub 3}){sup 2–} clusters and [R(H{sub 2}O){sub 6}]{sup 2+} aqua-complexes. The cooling of a single crystal of NaMg[UO{sub 2}(CH{sub 3}COO){sub 3}]{sub 3}·6H{sub 2}O from 300 to 100 K leads to a phase transition from trigonal to monoclinic crystal system. Intermolecular interactions between the structural units and their mutual packing were studiedmore » and compared from the point of view of the stereoatomic model of crystal structures based on Voronoi-Dirichlet tessellation. Using this method we compared the crystal structures of the triple acetates with Na[UO{sub 2}(CH{sub 3}COO){sub 3}] and [R(H{sub 2}O){sub 6}][UO{sub 2}(CH{sub 3}COO){sub 3}]{sub 2} and proposed reasons of triple acetates stability. Infrared and Raman spectra were collected and their bands were assigned. - Graphical abstract: Single crystals of uranium based triple acetates, analytical reagents for sodium determination, were synthesized and structurally, spectroscopically and topologically characterized. The structures were compared with the structures of compounds from preceding families [M(H{sub 2}O){sub 6})][UO{sub 2}(CH{sub 3}COO){sub 3}]{sub 2} (M = Mg, Co, Ni, Zn) and Na[UO{sub 2}(CH{sub 3}COO){sub 3}]. Analysis was performed with the method of molecular Voronoi-Dirichlet polyhedra to reveal a large contribution of the hydrogen bonds into intermolecular interactions which can be a reason of low solubility of studied complexes.« less

Multiclass Data Segmentation Using Diffuse Interface Methods on Graphs

DTIC Science & Technology

2014-01-01

interac- tive image segmentation using the solution to a combinatorial Dirichlet problem. Elmoataz et al . have developed general- izations of the graph...Laplacian [25] for image denoising and manifold smoothing. Couprie et al . in [18] define a conve- niently parameterized graph-based energy function that...over to the discrete graph representation. For general data segmentation, Bresson et al . in [8], present rigorous convergence results for two algorithms

Multispike solutions for the Brezis-Nirenberg problem in dimension three

NASA Astrophysics Data System (ADS)

Musso, Monica; Salazar, Dora

2018-06-01

We consider the problem Δu + λu +u5 = 0, u > 0, in a smooth bounded domain Ω in R3, under zero Dirichlet boundary conditions. We obtain solutions to this problem exhibiting multiple bubbling behavior at k different points of the domain as λ tends to a special positive value λ0, which we characterize in terms of the Green function of - Δ - λ.

Visibility of quantum graph spectrum from the vertices

NASA Astrophysics Data System (ADS)

Kühn, Christian; Rohleder, Jonathan

2018-03-01

We investigate the relation between the eigenvalues of the Laplacian with Kirchhoff vertex conditions on a finite metric graph and a corresponding Titchmarsh-Weyl function (a parameter-dependent Neumann-to-Dirichlet map). We give a complete description of all real resonances, including multiplicities, in terms of the edge lengths and the connectivity of the graph, and apply it to characterize all eigenvalues which are visible for the Titchmarsh-Weyl function.

A nonlinear ordinary differential equation associated with the quantum sojourn time

NASA Astrophysics Data System (ADS)

Benguria, Rafael D.; Duclos, Pierre; Fernández, Claudio; Sing-Long, Carlos

2010-11-01

We study a nonlinear ordinary differential equation on the half-line, with the Dirichlet boundary condition at the origin. This equation arises when studying the local maxima of the sojourn time for a free quantum particle whose states belong to an adequate subspace of the unit sphere of the corresponding Hilbert space. We establish several results concerning the existence and asymptotic behavior of the solutions.

An ill-posed parabolic evolution system for dispersive deoxygenation-reaeration in water

NASA Astrophysics Data System (ADS)

Azaïez, M.; Ben Belgacem, F.; Hecht, F.; Le Bot, C.

2014-01-01

We consider an inverse problem that arises in the management of water resources and pertains to the analysis of surface water pollution by organic matter. Most physically relevant models used by engineers derive from various additions and corrections to enhance the earlier deoxygenation-reaeration model proposed by Streeter and Phelps in 1925, the unknowns being the biochemical oxygen demand (BOD) and the dissolved oxygen (DO) concentrations. The one we deal with includes Taylor’s dispersion to account for the heterogeneity of the contamination in all space directions. The system we obtain is then composed of two reaction-dispersion equations. The particularity is that both Neumann and Dirichlet boundary conditions are available on the DO tracer while the BOD density is free of any conditions. In fact, for real-life concerns, measurements on the DO are easy to obtain and to save. On the contrary, collecting data on the BOD is a sensitive task and turns out to be a lengthy process. The global model pursues the reconstruction of the BOD density, and especially of its flux along the boundary. Not only is this problem plainly worth studying for its own interest but it could also be a mandatory step in other applications such as the identification of the location of pollution sources. The non-standard boundary conditions generate two difficulties in mathematical and computational grounds. They set up a severe coupling between both equations and they are the cause of the ill-posed data reconstruction problem. Existence and stability fail. Identifiability is therefore the only positive result one can search for; it is the central purpose of the paper. Finally, we have performed some computational experiments to assess the capability of the mixed finite element in missing data recovery.

Exactly solvable model of the two-dimensional electrical double layer.

PubMed

Samaj, L; Bajnok, Z

2005-12-01

We consider equilibrium statistical mechanics of a simplified model for the ideal conductor electrode in an interface contact with a classical semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of pointlike unit charges in the stability-against-collapse regime of reduced inverse temperatures 0< or = beta < 2. If there is a potential difference between the bulk interior of the electrolyte and the grounded electrode, the electrolyte region close to the electrode (known as the electrical double layer) carries some nonzero surface charge density. The model is mappable onto an integrable semi-infinite sine-Gordon theory with Dirichlet boundary conditions. The exact form-factor and boundary state information gained from the mapping provide asymptotic forms of the charge and number density profiles of electrolyte particles at large distances from the interface. The result for the asymptotic behavior of the induced electric potential, related to the charge density via the Poisson equation, confirms the validity of the concept of renormalized charge and the corresponding saturation hypothesis. It is documented on the nonperturbative result for the asymptotic density profile at a strictly nonzero beta that the Debye-Hückel beta-->0 limit is a delicate issue.

Clustering and variable selection in the presence of mixed variable types and missing data.

PubMed

Storlie, C B; Myers, S M; Katusic, S K; Weaver, A L; Voigt, R G; Croarkin, P E; Stoeckel, R E; Port, J D

2018-05-17

We consider the problem of model-based clustering in the presence of many correlated, mixed continuous, and discrete variables, some of which may have missing values. Discrete variables are treated with a latent continuous variable approach, and the Dirichlet process is used to construct a mixture model with an unknown number of components. Variable selection is also performed to identify the variables that are most influential for determining cluster membership. The work is motivated by the need to cluster patients thought to potentially have autism spectrum disorder on the basis of many cognitive and/or behavioral test scores. There are a modest number of patients (486) in the data set along with many (55) test score variables (many of which are discrete valued and/or missing). The goal of the work is to (1) cluster these patients into similar groups to help identify those with similar clinical presentation and (2) identify a sparse subset of tests that inform the clusters in order to eliminate unnecessary testing. The proposed approach compares very favorably with other methods via simulation of problems of this type. The results of the autism spectrum disorder analysis suggested 3 clusters to be most likely, while only 4 test scores had high (>0.5) posterior probability of being informative. This will result in much more efficient and informative testing. The need to cluster observations on the basis of many correlated, continuous/discrete variables with missing values is a common problem in the health sciences as well as in many other disciplines. Copyright © 2018 John Wiley & Sons, Ltd.

Investigation of Coupled model of Pore network and Continuum in shale gas

NASA Astrophysics Data System (ADS)

Cao, G.; Lin, M.

2016-12-01

Flow in shale spanning over many scales, makes the majority of conventional treatment methods disabled. For effectively simulating, a coupled model of pore-scale and continuum-scale was proposed in this paper. Based on the SEM image, we decompose organic-rich-shale into two subdomains: kerogen and inorganic matrix. In kerogen, the nanoscale pore-network is the main storage space and migration pathway so that the molecular phenomena (slip and diffusive transport) is significant. Whereas, inorganic matrix, with relatively large pores and micro fractures, the flow is approximate to Darcy. We use pore-scale network models (PNM) to represent kerogen and continuum-scale models (FVM or FEM) to represent matrix. Finite element mortars are employed to couple pore- and continuum-scale models by enforcing continuity of pressures and fluxes at shared boundary interfaces. In our method, the process in the coupled model is described by pressure square equation, and uses Dirichlet boundary conditions. We discuss several problems: the optimal element number of mortar faces, two categories boundary faces of pore network, the difference between 2D and 3D models, and the difference between continuum models FVM and FEM in mortars. We conclude that: (1) too coarse mesh in mortars will decrease the accuracy, while too fine mesh will lead to an ill-condition even singular system, the optimal element number is depended on boundary pores and nodes number. (2) pore network models are adjacent to two different mortar faces (PNM to PNM, PNM to continuum model), incidental repeated mortar nodes must be deleted. (3) 3D models can be replaced by 2D models under certain condition. (4) FVM is more convenient than FEM, for its simplicity in assigning interface nodes pressure and calculating interface fluxes. This work is supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB10020302), the 973 Program (2014CB239004), the Key Instrument Developing Project of the CAS (ZDYZ2012-1-08-02), the National Natural Science Foundation of China (41574129).

Asymptotic analysis of the narrow escape problem in dendritic spine shaped domain: three dimensions

NASA Astrophysics Data System (ADS)

Li, Xiaofei; Lee, Hyundae; Wang, Yuliang

2017-08-01

This paper deals with the three-dimensional narrow escape problem in a dendritic spine shaped domain, which is composed of a relatively big head and a thin neck. The narrow escape problem is to compute the mean first passage time of Brownian particles traveling from inside the head to the end of the neck. The original model is to solve a mixed Dirichlet-Neumann boundary value problem for the Poisson equation in the composite domain, and is computationally challenging. In this paper we seek to transfer the original problem to a mixed Robin-Neumann boundary value problem by dropping the thin neck part, and rigorously derive the asymptotic expansion of the mean first passage time with high order terms. This study is a nontrivial three-dimensional generalization of the work in Li (2014 J. Phys. A: Math. Theor. 47 505202), where a two-dimensional analogue domain is considered.

A local crack-tracking strategy to model three-dimensional crack propagation with embedded methods

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

Annavarapu, Chandrasekhar; Settgast, Randolph R.; Vitali, Efrem

We develop a local, implicit crack tracking approach to propagate embedded failure surfaces in three-dimensions. We build on the global crack-tracking strategy of Oliver et al. (Int J. Numer. Anal. Meth. Geomech., 2004; 28:609–632) that tracks all potential failure surfaces in a problem at once by solving a Laplace equation with anisotropic conductivity. We discuss important modifications to this algorithm with a particular emphasis on the effect of the Dirichlet boundary conditions for the Laplace equation on the resultant crack path. Algorithmic and implementational details of the proposed method are provided. Finally, several three-dimensional benchmark problems are studied and resultsmore » are compared with available literature. Lastly, the results indicate that the proposed method addresses pathological cases, exhibits better behavior in the presence of closely interacting fractures, and provides a viable strategy to robustly evolve embedded failure surfaces in 3D.« less

A local crack-tracking strategy to model three-dimensional crack propagation with embedded methods

DOE PAGES

Annavarapu, Chandrasekhar; Settgast, Randolph R.; Vitali, Efrem; ...

2016-09-29

We develop a local, implicit crack tracking approach to propagate embedded failure surfaces in three-dimensions. We build on the global crack-tracking strategy of Oliver et al. (Int J. Numer. Anal. Meth. Geomech., 2004; 28:609–632) that tracks all potential failure surfaces in a problem at once by solving a Laplace equation with anisotropic conductivity. We discuss important modifications to this algorithm with a particular emphasis on the effect of the Dirichlet boundary conditions for the Laplace equation on the resultant crack path. Algorithmic and implementational details of the proposed method are provided. Finally, several three-dimensional benchmark problems are studied and resultsmore » are compared with available literature. Lastly, the results indicate that the proposed method addresses pathological cases, exhibits better behavior in the presence of closely interacting fractures, and provides a viable strategy to robustly evolve embedded failure surfaces in 3D.« less

Isomorphism of dimer configurations and spanning trees on finite square lattices

NASA Astrophysics Data System (ADS)

Brankov, J. G.

1995-09-01

One-to-one mappings of the close-packed dimer configurations on a finite square lattice with free boundaries L onto the spanning trees of a related graph (or two-graph) G are found. The graph (two-graph) G can be constructed from L by: (1) deleting all the vertices of L with arbitrarily fixed parity of the row and column numbers; (2) suppressing all the vertices of degree 2 except those of degree 2 in L; (3) merging all the vertices of degree 1 into a single vertex g. The matrix Kirchhoff theorem reduces the enumeration problem for the spanning trees on G to the eigenvalue problem for the discrete Laplacian on the square lattice L'=G g with mixed Dirichlet-Neumann boundary conditions in at least one direction. That fact explains some of the unusual finite-size properties of the dimer model.

UTD at TREC 2014: Query Expansion for Clinical Decision Support

DTIC Science & Technology

2014-11-01

Description: A 62-year-old man sees a neurologist for progressive memory loss and jerking movements of the lower ex- tremities. Neurologic examination confirms...infiltration. Summary: 62-year-old man with progressive memory loss and in- voluntary leg movements. Brain MRI reveals cortical atrophy, and cortical...latent topics produced by the Latent Dirichlet Allocation (LDA) on the TREC-CDS corpus of scientific articles. The position of words “ loss ” and “ memory

Nondestructive Testing and Target Identification

DTIC Science & Technology

2016-12-21

Dirichlet obstacle coated by a thin layer of non-absorbing media, IMA J. Appl. Math , 80, 1063-1098, (2015). Abstract: We consider the transmission...F. Cakoni, I. De Teresa, H. Haddar and P. Monk, Nondestructive testing of the delami- nated interface between two materials, SIAM J. Appl. Math ., 76...then they form a discrete set. 22. F. Cakoni, D. Colton, S. Meng and P. Monk, Steklov eigenvalues in inverse scattering, SIAM J. Appl. Math . 76, 1737

Single-grid spectral collocation for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bernardi, Christine; Canuto, Claudio; Maday, Yvon; Metivet, Brigitte

1988-01-01

The aim of the paper is to study a collocation spectral method to approximate the Navier-Stokes equations: only one grid is used, which is built from the nodes of a Gauss-Lobatto quadrature formula, either of Legendre or of Chebyshev type. The convergence is proven for the Stokes problem provided with inhomogeneous Dirichlet conditions, then thoroughly analyzed for the Navier-Stokes equations. The practical implementation algorithm is presented, together with numerical results.

Quantum dynamics in continuum for proton transport—Generalized correlation

NASA Astrophysics Data System (ADS)

Chen, Duan; Wei, Guo-Wei

2012-04-01

As a key process of many biological reactions such as biological energy transduction or human sensory systems, proton transport has attracted much research attention in biological, biophysical, and mathematical fields. A quantum dynamics in continuum framework has been proposed to study proton permeation through membrane proteins in our earlier work and the present work focuses on the generalized correlation of protons with their environment. Being complementary to electrostatic potentials, generalized correlations consist of proton-proton, proton-ion, proton-protein, and proton-water interactions. In our approach, protons are treated as quantum particles while other components of generalized correlations are described classically and in different levels of approximations upon simulation feasibility and difficulty. Specifically, the membrane protein is modeled as a group of discrete atoms, while ion densities are approximated by Boltzmann distributions, and water molecules are represented as a dielectric continuum. These proton-environment interactions are formulated as convolutions between number densities of species and their corresponding interaction kernels, in which parameters are obtained from experimental data. In the present formulation, generalized correlations are important components in the total Hamiltonian of protons, and thus is seamlessly embedded in the multiscale/multiphysics total variational model of the system. It takes care of non-electrostatic interactions, including the finite size effect, the geometry confinement induced channel barriers, dehydration and hydrogen bond effects, etc. The variational principle or the Euler-Lagrange equation is utilized to minimize the total energy functional, which includes the total Hamiltonian of protons, and obtain a new version of generalized Laplace-Beltrami equation, generalized Poisson-Boltzmann equation and generalized Kohn-Sham equation. A set of numerical algorithms, such as the matched interface and boundary method, the Dirichlet to Neumann mapping, Gummel iteration, and Krylov space techniques, is employed to improve the accuracy, efficiency, and robustness of model simulations. Finally, comparisons between the present model predictions and experimental data of current-voltage curves, as well as current-concentration curves of the Gramicidin A channel, verify our new model.

Spectral Learning for Supervised Topic Models.

PubMed

Ren, Yong; Wang, Yining; Zhu, Jun

2018-03-01

Supervised topic models simultaneously model the latent topic structure of large collections of documents and a response variable associated with each document. Existing inference methods are based on variational approximation or Monte Carlo sampling, which often suffers from the local minimum defect. Spectral methods have been applied to learn unsupervised topic models, such as latent Dirichlet allocation (LDA), with provable guarantees. This paper investigates the possibility of applying spectral methods to recover the parameters of supervised LDA (sLDA). We first present a two-stage spectral method, which recovers the parameters of LDA followed by a power update method to recover the regression model parameters. Then, we further present a single-phase spectral algorithm to jointly recover the topic distribution matrix as well as the regression weights. Our spectral algorithms are provably correct and computationally efficient. We prove a sample complexity bound for each algorithm and subsequently derive a sufficient condition for the identifiability of sLDA. Thorough experiments on synthetic and real-world datasets verify the theory and demonstrate the practical effectiveness of the spectral algorithms. In fact, our results on a large-scale review rating dataset demonstrate that our single-phase spectral algorithm alone gets comparable or even better performance than state-of-the-art methods, while previous work on spectral methods has rarely reported such promising performance.

Heuristic Bayesian segmentation for discovery of coexpressed genes within genomic regions.

PubMed

Pehkonen, Petri; Wong, Garry; Törönen, Petri

2010-01-01

Segmentation aims to separate homogeneous areas from the sequential data, and plays a central role in data mining. It has applications ranging from finance to molecular biology, where bioinformatics tasks such as genome data analysis are active application fields. In this paper, we present a novel application of segmentation in locating genomic regions with coexpressed genes. We aim at automated discovery of such regions without requirement for user-given parameters. In order to perform the segmentation within a reasonable time, we use heuristics. Most of the heuristic segmentation algorithms require some decision on the number of segments. This is usually accomplished by using asymptotic model selection methods like the Bayesian information criterion. Such methods are based on some simplification, which can limit their usage. In this paper, we propose a Bayesian model selection to choose the most proper result from heuristic segmentation. Our Bayesian model presents a simple prior for the segmentation solutions with various segment numbers and a modified Dirichlet prior for modeling multinomial data. We show with various artificial data sets in our benchmark system that our model selection criterion has the best overall performance. The application of our method in yeast cell-cycle gene expression data reveals potential active and passive regions of the genome.

Fluctuation-induced forces in confined ideal and imperfect Bose gases

NASA Astrophysics Data System (ADS)

Diehl, H. W.; Rutkevich, Sergei B.

2017-06-01

Fluctuation-induced ("Casimir") forces caused by thermal and quantum fluctuations are investigated for ideal and imperfect Bose gases confined to d -dimensional films of size ∞d -1×D under periodic (P), antiperiodic (A), Dirichlet-Dirichlet (DD), Neumann-Neumann (NN), and Robin (R) boundary conditions (BCs). The full scaling functions ΥdBC(xλ=D /λth ,xξ=D /ξ ) of the residual reduced grand potential per area φres,dBC(T ,μ ,D ) =D-(d -1 )ΥdBC(xλ,xξ) are determined for the ideal gas case with these BCs, where λth and ξ are the thermal de Broglie wavelength and the bulk correlation length, respectively. The associated limiting scaling functions ΘdBC(xξ) ≡ΥdBC(∞ ,xξ) describing the critical behavior at the bulk condensation transition are shown to agree with those previously determined from a massive free O (2 ) theory for BC=P,A,DD,DN,NN . For d =3 , they are expressed in closed analytical form in terms of polylogarithms. The analogous scaling functions ΥdBC(xλ,xξ,c1D ,c2D ) and ΘdR(xξ,c1D ,c2D ) under the RBCs (∂z-c1) ϕ |z=0=(∂z+c2) ϕ | z =D=0 with c1≥0 and c2≥0 are also determined. The corresponding scaling functions Υ∞,d P(xλ,xξ) and Θ∞,d P(xξ) for the imperfect Bose gas are shown to agree with those of the interacting Bose gas with n internal degrees of freedom in the limit n →∞ . Hence, for d =3 , Θ∞,d P(xξ) is known exactly in closed analytic form. To account for the breakdown of translation invariance in the direction perpendicular to the boundary planes implied by free BCs such as DDBCs, a modified imperfect Bose gas model is introduced that corresponds to the limit n →∞ of this interacting Bose gas. Numerically and analytically exact results for the scaling function Θ∞,3 DD(xξ) therefore follow from those of the O (2 n ) ϕ4 model for n →∞ .

Fluctuation-induced forces in confined ideal and imperfect Bose gases.

PubMed

Diehl, H W; Rutkevich, Sergei B

2017-06-01

Fluctuation-induced ("Casimir") forces caused by thermal and quantum fluctuations are investigated for ideal and imperfect Bose gases confined to d-dimensional films of size ∞^{d-1}×D under periodic (P), antiperiodic (A), Dirichlet-Dirichlet (DD), Neumann-Neumann (NN), and Robin (R) boundary conditions (BCs). The full scaling functions Υ_{d}^{BC}(x_{λ}=D/λ_{th},x_{ξ}=D/ξ) of the residual reduced grand potential per area φ_{res,d}^{BC}(T,μ,D)=D^{-(d-1)}Υ_{d}^{BC}(x_{λ},x_{ξ}) are determined for the ideal gas case with these BCs, where λ_{th} and ξ are the thermal de Broglie wavelength and the bulk correlation length, respectively. The associated limiting scaling functions Θ_{d}^{BC}(x_{ξ})≡Υ_{d}^{BC}(∞,x_{ξ}) describing the critical behavior at the bulk condensation transition are shown to agree with those previously determined from a massive free O(2) theory for BC=P,A,DD,DN,NN. For d=3, they are expressed in closed analytical form in terms of polylogarithms. The analogous scaling functions Υ_{d}^{BC}(x_{λ},x_{ξ},c_{1}D,c_{2}D) and Θ_{d}^{R}(x_{ξ},c_{1}D,c_{2}D) under the RBCs (∂_{z}-c_{1})ϕ|_{z=0}=(∂_{z}+c_{2})ϕ|_{z=D}=0 with c_{1}≥0 and c_{2}≥0 are also determined. The corresponding scaling functions Υ_{∞,d}^{P}(x_{λ},x_{ξ}) and Θ_{∞,d}^{P}(x_{ξ}) for the imperfect Bose gas are shown to agree with those of the interacting Bose gas with n internal degrees of freedom in the limit n→∞. Hence, for d=3, Θ_{∞,d}^{P}(x_{ξ}) is known exactly in closed analytic form. To account for the breakdown of translation invariance in the direction perpendicular to the boundary planes implied by free BCs such as DDBCs, a modified imperfect Bose gas model is introduced that corresponds to the limit n→∞ of this interacting Bose gas. Numerically and analytically exact results for the scaling function Θ_{∞,3}^{DD}(x_{ξ}) therefore follow from those of the O(2n)ϕ^{4} model for n→∞.

A Pearson Random Walk with Steps of Uniform Orientation and Dirichlet Distributed Lengths

NASA Astrophysics Data System (ADS)

Le Caër, Gérard

2010-08-01

A constrained diffusive random walk of n steps in ℝ d and a random flight in ℝ d , which are equivalent, were investigated independently in recent papers (J. Stat. Phys. 127:813, 2007; J. Theor. Probab. 20:769, 2007, and J. Stat. Phys. 131:1039, 2008). The n steps of the walk are independent and identically distributed random vectors of exponential length and uniform orientation. Conditioned on the sum of their lengths being equal to a given value l, closed-form expressions for the distribution of the endpoint of the walk were obtained altogether for any n for d=1,2,4. Uniform distributions of the endpoint inside a ball of radius l were evidenced for a walk of three steps in 2D and of two steps in 4D. The previous walk is generalized by considering step lengths which have independent and identical gamma distributions with a shape parameter q>0. Given the total walk length being equal to 1, the step lengths have a Dirichlet distribution whose parameters are all equal to q. The walk and the flight above correspond to q=1. Simple analytical expressions are obtained for any d≥2 and n≥2 for the endpoint distributions of two families of walks whose q are integers or half-integers which depend solely on d. These endpoint distributions have a simple geometrical interpretation. Expressed for a two-step planar walk whose q=1, it means that the distribution of the endpoint on a disc of radius 1 is identical to the distribution of the projection on the disc of a point M uniformly distributed over the surface of the 3D unit sphere. Five additional walks, with a uniform distribution of the endpoint in the inside of a ball, are found from known finite integrals of products of powers and Bessel functions of the first kind. They include four different walks in ℝ3, two of two steps and two of three steps, and one walk of two steps in ℝ4. Pearson-Liouville random walks, obtained by distributing the total lengths of the previous Pearson-Dirichlet walks according to some specified probability law are finally discussed. Examples of unconstrained random walks, whose step lengths are gamma distributed, are more particularly considered.

Clinical progress of human papillomavirus genotypes and their persistent infection in subjects with atypical squamous cells of undetermined significance cytology: Statistical and latent Dirichlet allocation analysis

PubMed Central

Kim, Yee Suk; Lee, Sungin; Zong, Nansu; Kahng, Jimin

2017-01-01

The present study aimed to investigate differences in prognosis based on human papillomavirus (HPV) infection, persistent infection and genotype variations for patients exhibiting atypical squamous cells of undetermined significance (ASCUS) in their initial Papanicolaou (PAP) test results. A latent Dirichlet allocation (LDA)-based tool was developed that may offer a facilitated means of communication to be employed during patient-doctor consultations. The present study assessed 491 patients (139 HPV-positive and 352 HPV-negative cases) with a PAP test result of ASCUS with a follow-up period ≥2 years. Patients underwent PAP and HPV DNA chip tests between January 2006 and January 2009. The HPV-positive subjects were followed up with at least 2 instances of PAP and HPV DNA chip tests. The most common genotypes observed were HPV-16 (25.9%, 36/139), HPV-52 (14.4%, 20/139), HPV-58 (13.7%, 19/139), HPV-56 (11.5%, 16/139), HPV-51 (9.4%, 13/139) and HPV-18 (8.6%, 12/139). A total of 33.3% (12/36) patients positive for HPV-16 had cervical intraepithelial neoplasia (CIN)2 or a worse result, which was significantly higher than the prevalence of CIN2 of 1.8% (8/455) in patients negative for HPV-16 (P<0.001), while no significant association was identified for other genotypes in terms of genotype and clinical progress. There was a significant association between clearance and good prognosis (P<0.001). Persistent infection was higher in patients aged ≥51 years (38.7%) than in those aged ≤50 years (20.4%; P=0.036). Progression from persistent infection to CIN2 or worse (19/34, 55.9%) was higher than clearance (0/105, 0.0%; P<0.001). In the LDA analysis, using symmetric Dirichlet priors α=0.1 and β=0.01, and clusters (k)=5 or 10 provided the most meaningful groupings. Statistical and LDA analyses produced consistent results regarding the association between persistent infection of HPV-16, old age and long infection period with a clinical progression of CIN2 or worse. Therefore, LDA results may be presented as explanatory evidence during time-constrained patient-doctor consultations in order to deliver information regarding the patient's status. PMID:28587376

Mining Adverse Events of Dietary Supplements from Product Labels by Topic Modeling.

PubMed

Wang, Yefeng; Gunashekar, Divya R; Adam, Terrence J; Zhang, Rui

2017-01-01

The adverse events of the dietary supplements should be subject to scrutiny due to their growing clinical application and consumption among U.S. adults. An effective method for mining and grouping the adverse events of the dietary supplements is to evaluate product labeling for the rapidly increasing number of new products available in the market. In this study, the adverse events information was extracted from the product labels stored in the Dietary Supplement Label Data-base (DSLD) and analyzed by topic modeling techniques, specifically Latent Dirichlet Allocation (LDA). Among the 50 topics generated by LDA, eight topics were manually evaluated, with topic relatedness ranging from 58.8% to 100% on the product level, and 57.1% to 100% on the ingredient level. Five out of these eight topics were coherent groupings of the dietary supplements based on their adverse events. The results demonstrated that LDA is able to group supplements with similar adverse events based on the dietary supplement labels. Such information can be potentially used by consumers to more safely use dietary supplements.

Organizing Books and Authors by Multilayer SOM.

PubMed

Zhang, Haijun; Chow, Tommy W S; Wu, Q M Jonathan

2016-12-01

This paper introduces a new framework for the organization of electronic books (e-books) and their corresponding authors using a multilayer self-organizing map (MLSOM). An author is modeled by a rich tree-structured representation, and an MLSOM-based system is used as an efficient solution to the organizational problem of structured data. The tree-structured representation formulates author features in a hierarchy of author biography, books, pages, and paragraphs. To efficiently tackle the tree-structured representation, we used an MLSOM algorithm that serves as a clustering technique to handle e-books and their corresponding authors. A book and author recommender system is then implemented using the proposed framework. The effectiveness of our approach was examined in a large-scale data set containing 3868 authors along with the 10500 e-books that they wrote. We also provided visualization results of MLSOM for revealing the relevance patterns hidden from presented author clusters. The experimental results corroborate that the proposed method outperforms other content-based models (e.g., rate adapting poisson, latent Dirichlet allocation, probabilistic latent semantic indexing, and so on) and offers a promising solution to book recommendation, author recommendation, and visualization.

Mining Adverse Events of Dietary Supplements from Product Labels by Topic Modeling

PubMed Central

Wang, Yefeng; Gunashekar, Divya R.; Adam, Terrence J.; Zhang, Rui

2018-01-01

The adverse events of the dietary supplements should be subject to scrutiny due to their growing clinical application and consumption among U.S. adults. An effective method for mining and grouping the adverse events of the dietary supplements is to evaluate product labeling for the rapidly increasing number of new products available in the market. In this study, the adverse events information was extracted from the product labels stored in the Dietary Supplement Label Database (DSLD) and analyzed by topic modeling techniques, specifically Latent Dirichlet Allocation (LDA). Among the 50 topics generated by LDA, eight topics were manually evaluated, with topic relatedness ranging from 58.8% to 100% on the product level, and 57.1% to 100% on the ingredient level. Five out of these eight topics were coherent groupings of the dietary supplements based on their adverse events. The results demonstrated that LDA is able to group supplements with similar adverse events based on the dietary supplement labels. Such information can be potentially used by consumers to more safely use dietary supplements. PMID:29295169

A Stationary One-Equation Turbulent Model with Applications in Porous Media

NASA Astrophysics Data System (ADS)

de Oliveira, H. B.; Paiva, A.

2018-06-01

A one-equation turbulent model is studied in this work in the steady-state and with homogeneous Dirichlet boundary conditions. The considered problem generalizes two distinct approaches that are being used with success in the applications to model different flows through porous media. The novelty of the problem relies on the consideration of the classical Navier-Stokes equations with a feedback forces field, whose presence in the momentum equation will affect the equation for the turbulent kinetic energy (TKE) with a new term that is known as the production and represents the rate at which TKE is transferred from the mean flow to the turbulence. By assuming suitable growth conditions on the feedback forces field and on the function that describes the rate of dissipation of the TKE, as well as on the production term, we will prove the existence of the velocity field and of the TKE. The proof of their uniqueness is made by assuming monotonicity conditions on the feedback forces field and on the turbulent dissipation function, together with a condition of Lipschitz continuity on the production term. The existence of a unique pressure, will follow by the application of a standard version of de Rham's lemma.

Analyzing research trends on drug safety using topic modeling.

PubMed

Zou, Chen

2018-06-01

Published drug safety data has evolved in the past decade due to scientific and technological advances in the relevant research fields. Considering that a vast amount of scientific literature has been published in this area, it is not easy to identify the key information. Topic modeling has emerged as a powerful tool to extract meaningful information from a large volume of unstructured texts. Areas covered: We analyzed the titles and abstracts of 4347 articles in four journals dedicated to drug safety from 2007 to 2016. We applied Latent Dirichlet allocation (LDA) model to extract 50 main topics, and conducted trend analysis to explore the temporal popularity of these topics over years. Expert Opinion/Commentary: We found that 'benefit-risk assessment and communication', 'diabetes' and 'biologic therapy for autoimmune diseases' are the top 3 most published topics. The topics relevant to the use of electronic health records/observational data for safety surveillance are becoming increasingly popular over time. Meanwhile, there is a slight decrease in research on signal detection based on spontaneous reporting, although spontaneous reporting still plays an important role in benefit-risk assessment. The topics related to medical conditions and treatment showed highly dynamic patterns over time.

Diversifying customer review rankings.

PubMed

Krestel, Ralf; Dokoohaki, Nima

2015-06-01

E-commerce Web sites owe much of their popularity to consumer reviews accompanying product descriptions. On-line customers spend hours and hours going through heaps of textual reviews to decide which products to buy. At the same time, each popular product has thousands of user-generated reviews, making it impossible for a buyer to read everything. Current approaches to display reviews to users or recommend an individual review for a product are based on the recency or helpfulness of each review. In this paper, we present a framework to rank product reviews by optimizing the coverage of the ranking with respect to sentiment or aspects, or by summarizing all reviews with the top-K reviews in the ranking. To accomplish this, we make use of the assigned star rating for a product as an indicator for a review's sentiment polarity and compare bag-of-words (language model) with topic models (latent Dirichlet allocation) as a mean to represent aspects. Our evaluation on manually annotated review data from a commercial review Web site demonstrates the effectiveness of our approach, outperforming plain recency ranking by 30% and obtaining best results by combining language and topic model representations. Copyright © 2015 Elsevier Ltd. All rights reserved.

Global Binary Optimization on Graphs for Classification of High Dimensional Data

DTIC Science & Technology

2014-09-01

Buades et al . in [10] introduce a new non-local means algorithm for image denoising and compare it to some of the best methods. In [28], Grady de...scribes a random walk algorithm for image seg- mentation using the solution to a Dirichlet prob- lem. Elmoataz et al . present generalizations of the...graph Laplacian [19] for image denoising and man- ifold smoothing. Couprie et al . in [16] propose a parameterized graph-based energy function that unifies

Implementation of Nonhomogeneous Dirichlet Boundary Conditions in the p- Version of the Finite Element Method

DTIC Science & Technology

1988-09-01

Institute for Physical Science and Teennology rUniversity of Maryland o College Park, MD 20742 B. Gix) Engineering Mechanics Research Corporation Troy...OF THE FINITE ELEMENT METHOD by Ivo Babuska Institute for Physical Science and Technology University of Maryland College Park, MD 20742 B. Guo 2...2Research partially supported by the National Science Foundation under Grant DMS-85-16191 during the stay at the Institute for Physical Science and

Lifshits Tails for Randomly Twisted Quantum Waveguides

NASA Astrophysics Data System (ADS)

Kirsch, Werner; Krejčiřík, David; Raikov, Georgi

2018-03-01

We consider the Dirichlet Laplacian H_γ on a 3D twisted waveguide with random Anderson-type twisting γ . We introduce the integrated density of states N_γ for the operator H_γ , and investigate the Lifshits tails of N_γ , i.e. the asymptotic behavior of N_γ (E) as E \\downarrow \\inf supp dN_γ . In particular, we study the dependence of the Lifshits exponent on the decay rate of the single-site twisting at infinity.

Evaluation of the path integral for flow through random porous media

NASA Astrophysics Data System (ADS)

Westbroek, Marise J. E.; Coche, Gil-Arnaud; King, Peter R.; Vvedensky, Dimitri D.

2018-04-01

We present a path integral formulation of Darcy's equation in one dimension with random permeability described by a correlated multivariate lognormal distribution. This path integral is evaluated with the Markov chain Monte Carlo method to obtain pressure distributions, which are shown to agree with the solutions of the corresponding stochastic differential equation for Dirichlet and Neumann boundary conditions. The extension of our approach to flow through random media in two and three dimensions is discussed.

Nonlocal Reformulations of Water and Internal Waves and Asymptotic Reductions

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.

2009-09-01

Nonlocal reformulations of the classical equations of water waves and two ideal fluids separated by a free interface, bounded above by either a rigid lid or a free surface, are obtained. The kinematic equations may be written in terms of integral equations with a free parameter. By expressing the pressure, or Bernoulli, equation in terms of the surface/interface variables, a closed system is obtained. An advantage of this formulation, referred to as the nonlocal spectral (NSP) formulation, is that the vertical component is eliminated, thus reducing the dimensionality and fixing the domain in which the equations are posed. The NSP equations and the Dirichlet-Neumann operators associated with the water wave or two-fluid equations can be related to each other and the Dirichlet-Neumann series can be obtained from the NSP equations. Important asymptotic reductions obtained from the two-fluid nonlocal system include the generalizations of the Benney-Luke and Kadomtsev-Petviashvili (KP) equations, referred to as intermediate-long wave (ILW) generalizations. These 2+1 dimensional equations possess lump type solutions. In the water wave problem high-order asymptotic series are obtained for two and three dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known hyperbolic secant squared solution of the KdV equation; in three dimensions, the first term is the rational lump solution of the KP equation.

Boundary Regularity for the Porous Medium Equation

NASA Astrophysics Data System (ADS)

Björn, Anders; Björn, Jana; Gianazza, Ugo; Siljander, Juhana

2018-05-01

We study the boundary regularity of solutions to the porous medium equation {u_t = Δ u^m} in the degenerate range {m > 1} . In particular, we show that in cylinders the Dirichlet problem with positive continuous boundary data on the parabolic boundary has a solution which attains the boundary values, provided that the spatial domain satisfies the elliptic Wiener criterion. This condition is known to be optimal, and it is a consequence of our main theorem which establishes a barrier characterization of regular boundary points for general—not necessarily cylindrical—domains in {{R}^{n+1}} . One of our fundamental tools is a new strict comparison principle between sub- and superparabolic functions, which makes it essential for us to study both nonstrict and strict Perron solutions to be able to develop a fruitful boundary regularity theory. Several other comparison principles and pasting lemmas are also obtained. In the process we obtain a rather complete picture of the relation between sub/superparabolic functions and weak sub/supersolutions.

Fungi diversity from different depths and times in chicken manure waste static aerobic composting.

PubMed

Gu, Wenjie; Lu, Yusheng; Tan, Zhiyuan; Xu, Peizhi; Xie, Kaizhi; Li, Xia; Sun, Lili

2017-09-01

The Dirichlet multinomial mixtures mode was used to analyse illumina sequencing data to reveal both temporal and spatial variations of the fungi community present in the aerobic composting. Results showed that 670 operational taxonomic units (OTUs) were detected, and the dominant phylum was Ascomycota. There were four types of samples fungi communities during the composting process. Samples from the early composting stage were mainly grouped into type I and Saccharomycetales sp. was dominant. Fungi community in the medium composting stage were fallen into type II and III, Sordariales sp. and Acremonium alcalophilum, Saccharomycetales sp. and Scedosporium minutisporum were the dominant OTUs respectively. Samples from the late composting stage were mainly grouped into type IV and Scedosporium minutisporum was the dominant OTU; Scedosporium minutisporum was significantly affected by depth (P<0.05). Results indicate that time and depth both are factors that influence fungi distribution and variation in c waste during static aerobic composting. Copyright © 2017. Published by Elsevier Ltd.

Rapid Airplane Parametric Input Design(RAPID)

NASA Technical Reports Server (NTRS)

Smith, Robert E.; Bloor, Malcolm I. G.; Wilson, Michael J.; Thomas, Almuttil M.

2004-01-01

An efficient methodology is presented for defining a class of airplane configurations. Inclusive in this definition are surface grids, volume grids, and grid sensitivity. A small set of design parameters and grid control parameters govern the process. The general airplane configuration has wing, fuselage, vertical tail, horizontal tail, and canard components. The wing, tail, and canard components are manifested by solving a fourth-order partial differential equation subject to Dirichlet and Neumann boundary conditions. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage has circular cross section, and the radius is an algebraic function of four design parameters and an independent computational variable. Volume grids are obtained through an application of the Control Point Form method. Grid sensitivity is obtained by applying the automatic differentiation precompiler ADIFOR to software for the grid generation. The computed surface grids, volume grids, and sensitivity derivatives are suitable for a wide range of Computational Fluid Dynamics simulation and configuration optimizations.

3DFEMWATER: A three-dimensional finite element model of water flow through saturated-unsaturated media

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

Yeh, G.T.

1987-08-01

The 3DFEMWATER model is designed to treat heterogeneous and anisotropic media consisting of as many geologic formations as desired, consider both distributed and point sources/sinks that are spatially and temporally dependent, accept the prescribed initial conditions or obtain them by simulating a steady state version of the system under consideration, deal with a transient head distributed over the Dirichlet boundary, handle time-dependent fluxes due to pressure gradient varying along the Neumann boundary, treat time-dependent total fluxes distributed over the Cauchy boundary, automatically determine variable boundary conditions of evaporation, infiltration, or seepage on the soil-air interface, include the off-diagonal hydraulic conductivitymore » components in the modified Richards equation for dealing with cases when the coordinate system does not coincide with the principal directions of the hydraulic conductivity tensor, give three options for estimating the nonlinear matrix, include two options (successive subregion block iterations and successive point interactions) for solving the linearized matrix equations, automatically reset time step size when boundary conditions or source/sinks change abruptly, and check the mass balance computation over the entire region for every time step. The model is verified with analytical solutions or other numerical models for three examples.« less

Functional level-set derivative for a polymer self consistent field theory Hamiltonian

NASA Astrophysics Data System (ADS)

Ouaknin, Gaddiel; Laachi, Nabil; Bochkov, Daniil; Delaney, Kris; Fredrickson, Glenn H.; Gibou, Frederic

2017-09-01

We derive functional level-set derivatives for the Hamiltonian arising in self-consistent field theory, which are required to solve free boundary problems in the self-assembly of polymeric systems such as block copolymer melts. In particular, we consider Dirichlet, Neumann and Robin boundary conditions. We provide numerical examples that illustrate how these shape derivatives can be used to find equilibrium and metastable structures of block copolymer melts with a free surface in both two and three spatial dimensions.

Image Annotation and Topic Extraction Using Super-Word Latent Dirichlet Allocation

DTIC Science & Technology

2013-09-01

an image can be used to improve automated image annotation performance over existing generalized annotators. Second, image anno - 3 tations can be used...the other variables. The first ratio in the sampling Equation 2.18 uses word frequency by total words, φ̂ (w) j . The second ratio divides word...topics by total words in that document θ̂ (d) j . Both leave out the current assignment of zi and the results are used to randomly choose a new topic

Time-Bound Analytic Tasks on Large Data Sets Through Dynamic Configuration of Workflows

DTIC Science & Technology

2013-11-01

Assessment and Efficient Retrieval of Semantic Workflows.” Information Systems Journal, . 2012. [2] Blei, D., Ng, A., and M . Jordan. “Latent Dirichlet...25 (561-567), 2009. [5] Furlani, T. R., Jones, M . D., Gallo, S. M ., Bruno, A. E., Lu, C., Ghadersohi, A., Gentner, R. J., Patra, A., DeLeon, R. L...Proceedings of the IEEE e- Science Conference, Oxford, UK, pages 244–351. 2009. [8] Gil, Y.; Deelman, E.; Ellisman, M . H.; Fahringer, T.; Fox, G.; Gannon, D

Moving finite elements in 2-D

NASA Technical Reports Server (NTRS)

Gelinas, R. J.; Doss, S. K.; Vajk, J. P.; Djomehri, J.; Miller, K.

1983-01-01

The mathematical background regarding the moving finite element (MFE) method of Miller and Miller (1981) is discussed, taking into account a general system of partial differential equations (PDE) and the amenability of the MFE method in two dimensions to code modularization and to semiautomatic user-construction of numerous PDE systems for both Dirichlet and zero-Neumann boundary conditions. A description of test problem results is presented, giving attention to aspects of single square wave propagation, and a solution of the heat equation.

On the Boussinesq-Burgers equations driven by dynamic boundary conditions

NASA Astrophysics Data System (ADS)

Zhu, Neng; Liu, Zhengrong; Zhao, Kun

2018-02-01

We study the qualitative behavior of the Boussinesq-Burgers equations on a finite interval subject to the Dirichlet type dynamic boundary conditions. Assuming H1 ×H2 initial data which are compatible with boundary conditions and utilizing energy methods, we show that under appropriate conditions on the dynamic boundary data, there exist unique global-in-time solutions to the initial-boundary value problem, and the solutions converge to the boundary data as time goes to infinity, regardless of the magnitude of the initial data.

Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies

NASA Astrophysics Data System (ADS)

Chang, Jing; Gao, Yixian; Li, Yong

2015-05-01

Consider the one dimensional nonlinear beam equation utt + uxxxx + mu + u3 = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form.

Multi-Dimensional Asymptotically Stable 4th Order Accurate Schemes for the Diffusion Equation

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Ditkowski, Adi

1996-01-01

An algorithm is presented which solves the multi-dimensional diffusion equation on co mplex shapes to 4th-order accuracy and is asymptotically stable in time. This bounded-error result is achieved by constructing, on a rectangular grid, a differentiation matrix whose symmetric part is negative definite. The differentiation matrix accounts for the Dirichlet boundary condition by imposing penalty like terms. Numerical examples in 2-D show that the method is effective even where standard schemes, stable by traditional definitions fail.

Optimal decay rate for the wave equation on a square with constant damping on a strip

NASA Astrophysics Data System (ADS)

Stahn, Reinhard

2017-04-01

We consider the damped wave equation with Dirichlet boundary conditions on the unit square parametrized by Cartesian coordinates x and y. We assume the damping a to be strictly positive and constant for x<σ and zero for x>σ . We prove the exact t^{-4/3}-decay rate for the energy of classical solutions. Our main result (Theorem 1) answers question (1) of Anantharaman and Léautaud (Anal PDE 7(1):159-214, 2014, Section 2C).

Interactive Tooth Separation from Dental Model Using Segmentation Field

PubMed Central

2016-01-01

Tooth segmentation on dental model is an essential step of computer-aided-design systems for orthodontic virtual treatment planning. However, fast and accurate identifying cutting boundary to separate teeth from dental model still remains a challenge, due to various geometrical shapes of teeth, complex tooth arrangements, different dental model qualities, and varying degrees of crowding problems. Most segmentation approaches presented before are not able to achieve a balance between fine segmentation results and simple operating procedures with less time consumption. In this article, we present a novel, effective and efficient framework that achieves tooth segmentation based on a segmentation field, which is solved by a linear system defined by a discrete Laplace-Beltrami operator with Dirichlet boundary conditions. A set of contour lines are sampled from the smooth scalar field, and candidate cutting boundaries can be detected from concave regions with large variations of field data. The sensitivity to concave seams of the segmentation field facilitates effective tooth partition, as well as avoids obtaining appropriate curvature threshold value, which is unreliable in some case. Our tooth segmentation algorithm is robust to dental models with low quality, as well as is effective to dental models with different levels of crowding problems. The experiments, including segmentation tests of varying dental models with different complexity, experiments on dental meshes with different modeling resolutions and surface noises and comparison between our method and the morphologic skeleton segmentation method are conducted, thus demonstrating the effectiveness of our method. PMID:27532266

An explicit dissipation-preserving method for Riesz space-fractional nonlinear wave equations in multiple dimensions

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2018-06-01

In this work, we investigate numerically a model governed by a multidimensional nonlinear wave equation with damping and fractional diffusion. The governing partial differential equation considers the presence of Riesz space-fractional derivatives of orders in (1, 2], and homogeneous Dirichlet boundary data are imposed on a closed and bounded spatial domain. The model under investigation possesses an energy function which is preserved in the undamped regime. In the damped case, we establish the property of energy dissipation of the model using arguments from functional analysis. Motivated by these results, we propose an explicit finite-difference discretization of our fractional model based on the use of fractional centered differences. Associated to our discrete model, we also propose discretizations of the energy quantities. We establish that the discrete energy is conserved in the undamped regime, and that it dissipates in the damped scenario. Among the most important numerical features of our scheme, we show that the method has a consistency of second order, that it is stable and that it has a quadratic order of convergence. Some one- and two-dimensional simulations are shown in this work to illustrate the fact that the technique is capable of preserving the discrete energy in the undamped regime. For the sake of convenience, we provide a Matlab implementation of our method for the one-dimensional scenario.

Analytical solutions for sequentially coupled one-dimensional reactive transport problems Part I: Mathematical derivations

NASA Astrophysics Data System (ADS)

Srinivasan, V.; Clement, T. P.

2008-02-01

Multi-species reactive transport equations coupled through sorption and sequential first-order reactions are commonly used to model sites contaminated with radioactive wastes, chlorinated solvents and nitrogenous species. Although researchers have been attempting to solve various forms of these reactive transport equations for over 50 years, a general closed-form analytical solution to this problem is not available in the published literature. In Part I of this two-part article, we derive a closed-form analytical solution to this problem for spatially-varying initial conditions. The proposed solution procedure employs a combination of Laplace and linear transform methods to uncouple and solve the system of partial differential equations. Two distinct solutions are derived for Dirichlet and Cauchy boundary conditions each with Bateman-type source terms. We organize and present the final solutions in a common format that represents the solutions to both boundary conditions. In addition, we provide the mathematical concepts for deriving the solution within a generic framework that can be used for solving similar transport problems.

Gravitational Casimir-Polder effect

NASA Astrophysics Data System (ADS)

Hu, Jiawei; Yu, Hongwei

2017-04-01

The interaction due to quantum gravitational vacuum fluctuations between a gravitationally polarizable object modelled as a two-level system and a gravitational boundary is investigated. This quantum gravitational interaction is found to be position-dependent, which induces a force in close analogy to the Casimir-Polder force in the electromagnetic case. For a Dirichlet boundary, the quantum gravitational potential for the polarizable object in its ground-state is shown to behave like z-5 in the near zone, and z-6 in the far zone, where z is the distance to the boundary. For a concrete example, where a Bose-Einstein condensate is taken as a gravitationally polarizable object, the relative correction to the radius of the BEC caused by fluctuating quantum gravitational waves in vacuum is found to be of order 10-21. Although the correction is far too small to observe in comparison with its electromagnetic counterpart, it is nevertheless of the order of the gravitational strain caused by a recently detected black hole merger on the arms of the LIGO.

“Hybrid Topics” -- Facilitating the Interpretation of Topics Through the Addition of MeSH Descriptors to Bags of Words

PubMed Central

Yu, Zhiguo; Nguyen, Thang; Dhombres, Ferdinand; Johnson, Todd; Bodenreider, Olivier

2018-01-01

Extracting and understanding information, themes and relationships from large collections of documents is an important task for biomedical researchers. Latent Dirichlet Allocation is an unsupervised topic modeling technique using the bag-of-words assumption that has been applied extensively to unveil hidden thematic information within large sets of documents. In this paper, we added MeSH descriptors to the bag-of-words assumption to generate ‘hybrid topics’, which are mixed vectors of words and descriptors. We evaluated this approach on the quality and interpretability of topics in both a general corpus and a specialized corpus. Our results demonstrated that the coherence of ‘hybrid topics’ is higher than that of regular bag-of-words topics in the specialized corpus. We also found that the proportion of topics that are not associated with MeSH descriptors is higher in the specialized corpus than in the general corpus. PMID:29295179

Large eddy simulation of turbulent premixed combustion using tabulated detailed chemistry and presumed probability density function

NASA Astrophysics Data System (ADS)

Zhang, Hongda; Han, Chao; Ye, Taohong; Ren, Zhuyin

2016-03-01

A method of chemistry tabulation combined with presumed probability density function (PDF) is applied to simulate piloted premixed jet burner flames with high Karlovitz number using large eddy simulation. Thermo-chemistry states are tabulated by the combination of auto-ignition and extended auto-ignition model. To evaluate the predictive capability of the proposed tabulation method to represent the thermo-chemistry states under the condition of different fresh gases temperature, a-priori study is conducted by performing idealised transient one-dimensional premixed flame simulations. Presumed PDF is used to involve the interaction of turbulence and flame with beta PDF to model the reaction progress variable distribution. Two presumed PDF models, Dirichlet distribution and independent beta distribution, respectively, are applied for representing the interaction between two mixture fractions that are associated with three inlet streams. Comparisons of statistical results show that two presumed PDF models for the two mixture fractions are both capable of predicting temperature and major species profiles, however, they are shown to have a significant effect on the predictions for intermediate species. An analysis of the thermo-chemical state-space representation of the sub-grid scale (SGS) combustion model is performed by comparing correlations between the carbon monoxide mass fraction and temperature. The SGS combustion model based on the proposed chemistry tabulation can reasonably capture the peak value and change trend of intermediate species. Aspects regarding model extensions to adequately predict the peak location of intermediate species are discussed.

sourceR: Classification and source attribution of infectious agents among heterogeneous populations

PubMed Central

French, Nigel

2017-01-01

Zoonotic diseases are a major cause of morbidity, and productivity losses in both human and animal populations. Identifying the source of food-borne zoonoses (e.g. an animal reservoir or food product) is crucial for the identification and prioritisation of food safety interventions. For many zoonotic diseases it is difficult to attribute human cases to sources of infection because there is little epidemiological information on the cases. However, microbial strain typing allows zoonotic pathogens to be categorised, and the relative frequencies of the strain types among the sources and in human cases allows inference on the likely source of each infection. We introduce sourceR, an R package for quantitative source attribution, aimed at food-borne diseases. It implements a Bayesian model using strain-typed surveillance data from both human cases and source samples, capable of identifying important sources of infection. The model measures the force of infection from each source, allowing for varying survivability, pathogenicity and virulence of pathogen strains, and varying abilities of the sources to act as vehicles of infection. A Bayesian non-parametric (Dirichlet process) approach is used to cluster pathogen strain types by epidemiological behaviour, avoiding model overfitting and allowing detection of strain types associated with potentially high “virulence”. sourceR is demonstrated using Campylobacter jejuni isolate data collected in New Zealand between 2005 and 2008. Chicken from a particular poultry supplier was identified as the major source of campylobacteriosis, which is qualitatively similar to results of previous studies using the same dataset. Additionally, the software identifies a cluster of 9 multilocus sequence types with abnormally high ‘virulence’ in humans. sourceR enables straightforward attribution of cases of zoonotic infection to putative sources of infection. As sourceR develops, we intend it to become an important and flexible resource for food-borne disease attribution studies. PMID:28558033

Unified solver for fluid dynamics and aeroacoustics in isentropic gas flows

NASA Astrophysics Data System (ADS)

Pont, Arnau; Codina, Ramon; Baiges, Joan; Guasch, Oriol

2018-06-01

The high computational cost of solving numerically the fully compressible Navier-Stokes equations, together with the poor performance of most numerical formulations for compressible flow in the low Mach number regime, has led to the necessity for more affordable numerical models for Computational Aeroacoustics. For low Mach number subsonic flows with neither shocks nor thermal coupling, both flow dynamics and wave propagation can be considered isentropic. Therefore, a joint isentropic formulation for flow and aeroacoustics can be devised which avoids the need for segregating flow and acoustic scales. Under these assumptions density and pressure fluctuations are directly proportional, and a two field velocity-pressure compressible formulation can be derived as an extension of an incompressible solver. Moreover, the linear system of equations which arises from the proposed isentropic formulation is better conditioned than the homologous incompressible one due to the presence of a pressure time derivative. Similarly to other compressible formulations the prescription of boundary conditions will have to deal with the backscattering of acoustic waves. In this sense, a separated imposition of boundary conditions for flow and acoustic scales which allows the evacuation of waves through Dirichlet boundaries without using any tailored damping model will be presented.

Dimers in Piecewise Temperleyan Domains

NASA Astrophysics Data System (ADS)

Russkikh, Marianna

2018-03-01

We study the large-scale behavior of the height function in the dimer model on the square lattice. Richard Kenyon has shown that the fluctuations of the height function on Temperleyan discretizations of a planar domain converge in the scaling limit (as the mesh size tends to zero) to the Gaussian Free Field with Dirichlet boundary conditions. We extend Kenyon's result to a more general class of discretizations. Moreover, we introduce a new factorization of the coupling function of the double-dimer model into two discrete holomorphic functions, which are similar to discrete fermions defined in Smirnov (Proceedings of the international congress of mathematicians (ICM), Madrid, Spain, 2006; Ann Math (2) 172:1435-1467, 2010). For Temperleyan discretizations with appropriate boundary modifications, the results of Kenyon imply that the expectation of the double-dimer height function converges to a harmonic function in the scaling limit. We use the above factorization to extend this result to the class of all polygonal discretizations, that are not necessarily Temperleyan. Furthermore, we show that, quite surprisingly, the expectation of the double-dimer height function in the Temperleyan case is exactly discrete harmonic (for an appropriate choice of Laplacian) even before taking the scaling limit.

Dimension Reduction for the Landau-de Gennes Model on Curved Nematic Thin Films

NASA Astrophysics Data System (ADS)

Golovaty, Dmitry; Montero, José Alberto; Sternberg, Peter

2017-12-01

We use the method of Γ -convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film attached to a general fixed surface in the limit of vanishing thickness. This paper generalizes the approach in Golovaty et al. (J Nonlinear Sci 25(6):1431-1451, 2015) where we considered a similar problem for a planar surface. Since the anchoring energy dominates when the thickness of the film is small, it is essential to understand its influence on the structure of the minimizers of the limiting energy. In particular, the anchoring energy dictates the class of admissible competitors and the structure of the limiting problem. We assume general weak anchoring conditions on the top and the bottom surfaces of the film and strong Dirichlet boundary conditions on the lateral boundary of the film when the surface is not closed. We establish a general convergence result to an energy defined on the surface that involves a somewhat surprising remnant of the normal component of the tensor gradient. Then we exhibit one effect of curvature through an analysis of the behavior of minimizers to the limiting problem when the substrate is a frustum.

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

Stagg, Alan K; Yoon, Su-Jong

This report describes the Consortium for Advanced Simulation of Light Water Reactors (CASL) work conducted for completion of the Thermal Hydraulics Methods (THM) Level 3 Milestone THM.CFD.P11.02: Hydra-TH Extensions for Multispecies and Thermosolutal Convection. A critical requirement for modeling reactor thermal hydraulics is to account for species transport within the fluid. In particular, this capability is needed for modeling transport and diffusion of boric acid within water for emergency, reactivity-control scenarios. To support this need, a species transport capability has been implemented in Hydra-TH for binary systems (for example, solute within a solvent). A species transport equation is solved formore » the species (solute) mass fraction, and both thermal and solutal buoyancy effects are handled with specification of a Boussinesq body force. Species boundary conditions can be specified with a Dirichlet condition on mass fraction or a Neumann condition on diffusion flux. To enable enhanced species/fluid mixing in turbulent flow, the molecular diffusivity for the binary system is augmented with a turbulent diffusivity in the species transport calculation. The new capabilities are demonstrated by comparison of Hydra-TH calculations to the analytic solution for a thermosolutal convection problem, and excellent agreement is obtained.« less

The island dynamics model on parallel quadtree grids

NASA Astrophysics Data System (ADS)

Mistani, Pouria; Guittet, Arthur; Bochkov, Daniil; Schneider, Joshua; Margetis, Dionisios; Ratsch, Christian; Gibou, Frederic

2018-05-01

We introduce an approach for simulating epitaxial growth by use of an island dynamics model on a forest of quadtree grids, and in a parallel environment. To this end, we use a parallel framework introduced in the context of the level-set method. This framework utilizes: discretizations that achieve a second-order accurate level-set method on non-graded adaptive Cartesian grids for solving the associated free boundary value problem for surface diffusion; and an established library for the partitioning of the grid. We consider the cases with: irreversible aggregation, which amounts to applying Dirichlet boundary conditions at the island boundary; and an asymmetric (Ehrlich-Schwoebel) energy barrier for attachment/detachment of atoms at the island boundary, which entails the use of a Robin boundary condition. We provide the scaling analyses performed on the Stampede supercomputer and numerical examples that illustrate the capability of our methodology to efficiently simulate different aspects of epitaxial growth. The combination of adaptivity and parallelism in our approach enables simulations that are several orders of magnitude faster than those reported in the recent literature and, thus, provides a viable framework for the systematic study of mound formation on crystal surfaces.

Simulation of Thin Film Equations on an Eye-Shaped Domain with Moving Boundary

NASA Astrophysics Data System (ADS)

Brosch, Joseph; Driscoll, Tobin; Braun, Richard

During a normal eye blink, the upper lid moves, and during the upstroke the lid paints a thin tear film over the exposed corneal and conjunctival surfaces. This thin tear film may be modeled by a nonlinear fourth-order PDE derived from lubrication theory. A major stumbling block in the numerical simulation of this model is to include both the geometry of the eye and the movement of the eyelid. Using a pair of orthogonal and conformal maps, we transform a computational box into a rough representation of a human eye where we proceed to simulate the thin tear film equations. Although we give up some realism, we gain spectrally accurate numerical methods on the computational box. We have applied this method to the heat equation on the blinking domain with both Dirichlet and no-flux boundary conditions, in each case demonstrating at least 10 digits of accuracy.. We are able to perform these simulations very quickly (generally in under a minute) using a desktop version of MATLAB. This project was supported by Grant 1022706 (R.J.B., T.A.D., J.K.B.) from the NSF.

The forces on a single interacting Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Thu, Nguyen Van

2018-04-01

Using double parabola approximation for a single Bose-Einstein condensate confined between double slabs we proved that in grand canonical ensemble (GCE) the ground state with Robin boundary condition (BC) is favored, whereas in canonical ensemble (CE) our system undergoes from ground state with Robin BC to the one with Dirichlet BC in small-L region and vice versa for large-L region and phase transition in space of the ground state is the first order. The surface tension force and Casimir force are also considered in both CE and GCE in detail.

Application of fractional derivative with exponential law to bi-fractional-order wave equation with frictional memory kernel

NASA Astrophysics Data System (ADS)

Cuahutenango-Barro, B.; Taneco-Hernández, M. A.; Gómez-Aguilar, J. F.

2017-12-01

Analytical solutions of the wave equation with bi-fractional-order and frictional memory kernel of Mittag-Leffler type are obtained via Caputo-Fabrizio fractional derivative in the Liouville-Caputo sense. Through the method of separation of variables and Laplace transform method we derive closed-form solutions and establish fundamental solutions. Special cases with homogeneous Dirichlet boundary conditions and nonhomogeneous initial conditions, as well as for the external force are considered. Numerical simulations of the special solutions were done and novel behaviors are obtained.

Vacuum Energy Induced by AN Impenetrable Flux Tube of Finite Radius

NASA Astrophysics Data System (ADS)

Gorkavenko, V. M.; Sitenko, Yu. A.; Stepanov, O. B.

2011-06-01

We consider the effect of the magnetic field background in the form of a tube of the finite transverse size on the vacuum of the quantized charged massive scalar field which is subject to the Dirichlet boundary condition at the edge of the tube. The vacuum energy is induced, being periodic in the value of the magnetic flux enclosed in the tube. The dependence of the vacuum energy density on the distance from the tube and on the coupling to the space-time curvature scalar is comprehensively analyzed.

Vacuum Energy Induced by AN Impenetrable Flux Tube of Finite Radius

NASA Astrophysics Data System (ADS)

Gorkavenko, V. M.; Sitenko, Yu. A.; Stepanov, O. B.

We consider the effect of the magnetic field background in the form of a tube of the finite transverse size on the vacuum of the quantized charged massive scalar field which is subject to the Dirichlet boundary condition at the edge of the tube. The vacuum energy is induced, being periodic in the value of the magnetic flux enclosed in the tube. The dependence of the vacuum energy density on the distance from the tube and on the coupling to the space-time curvature scalar is comprehensively analyzed.

Conference on Ordinary and Partial Differential Equations, 29 March to 2 April 1982.

DTIC Science & Technology

1982-04-02

Azztr. Boundary value problems for elliptic and parabolic equations in domains with corners The paper concerns initial - Dirichlet and initial - mixed...boundary value problems for parabolic equations. a ij(x,t)u x + ai(x,t)Ux. + a(x,t)u-u = f(x,t) i3 1 x Xl,...,Xn , n 2. We consider the case of...moment II Though it is well known, that the electron possesses an anomalous magnetic moment, this term has not been considered so far in the mathematical

Introduction to Real Orthogonal Polynomials

DTIC Science & Technology

1992-06-01

uses Green’s functions. As motivation , consider the Dirichlet problem for the unit circle in the plane, which involves finding a harmonic function u(r...xv ; a, b ; q) - TO [q-N ab+’q ; q, xq b. Orthogoy RMotion O0 (bq :q)x p.(q* ; a, b ; q) pg(q’ ; a, b ; q) (q "q), (aq)x (q ; q), (I -abq) (bq ; q... motivation and justi- fication for continued study of the intrinsic structure of orthogonal polynomials. 99 LIST OF REFERENCES 1. Deyer, W. M., ed., CRC

On the existence of mosaic-skeleton approximations for discrete analogues of integral operators

NASA Astrophysics Data System (ADS)

Kashirin, A. A.; Taltykina, M. Yu.

2017-09-01

Exterior three-dimensional Dirichlet problems for the Laplace and Helmholtz equations are considered. By applying methods of potential theory, they are reduced to equivalent Fredholm boundary integral equations of the first kind, for which discrete analogues, i.e., systems of linear algebraic equations (SLAEs) are constructed. The existence of mosaic-skeleton approximations for the matrices of the indicated systems is proved. These approximations make it possible to reduce the computational complexity of an iterative solution of the SLAEs. Numerical experiments estimating the capabilities of the proposed approach are described.

The Theory and Practice of the h-p Version of Finite Element Method.

DTIC Science & Technology

1987-04-01

1Wr-194 ’The problem with none-hmogeneous Dirichlet problem is to find the finite element solution u. £ data was studied by Babuika, Guo.im- 4401 The h...implemented in the coasmercial code PROOE . by Noetic Tech., St. Louis. See (27,281. The commer- IuS -u 01 1 C(SIS2)Z(u0,HI,S1) (2.3) cial program FIESTA...collaboration with govern- ment agencies such as the National Bureau of Standards. o To be an international center of study and research for foreign

Global bifurcation of solutions of the mean curvature spacelike equation in certain Friedmann-Lemaître-Robertson-Walker spacetimes

NASA Astrophysics Data System (ADS)

Dai, Guowei; Romero, Alfonso; Torres, Pedro J.

2018-06-01

We study the existence of spacelike graphs for the prescribed mean curvature equation in the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. By using a conformal change of variable, this problem is translated into an equivalent problem in the Lorentz-Minkowski spacetime. Then, by using Rabinowitz's global bifurcation method, we obtain the existence and multiplicity of positive solutions for this equation with 0-Dirichlet boundary condition on a ball. Moreover, the global structure of the positive solution set is studied.

Numerical simulation of the generation, propagation, and diffraction of nonlinear waves in a rectangular basin: A three-dimensional numerical wave tank

NASA Astrophysics Data System (ADS)

Darwiche, Mahmoud Khalil M.

The research presented herein is a contribution to the understanding of the numerical modeling of fully nonlinear, transient water waves. The first part of the work involves the development of a time-domain model for the numerical generation of fully nonlinear, transient waves by a piston type wavemaker in a three-dimensional, finite, rectangular tank. A time-domain boundary-integral model is developed for simulating the evolving fluid field. A robust nonsingular, adaptive integration technique for the assembly of the boundary-integral coefficient matrix is developed and tested. A parametric finite-difference technique for calculating the fluid- particle kinematics is also developed and tested. A novel compatibility and continuity condition is implemented to minimize the effect of the singularities that are inherent at the intersections of the various Dirichlet and/or Neumann subsurfaces. Results are presented which demonstrate the accuracy and convergence of the numerical model. The second portion of the work is a study of the interaction of the numerically-generated, fully nonlinear, transient waves with a bottom-mounted, surface-piercing, vertical, circular cylinder. The numerical model developed in the first part of this dissertation is extended to include the presence of the cylinder at the centerline of the basin. The diffraction of the numerically generated waves by the cylinder is simulated, and the particle kinematics of the diffracted flow field are calculated and reported. Again, numerical results showing the accuracy and convergence of the extended model are presented.

Spheroidal Integral Equations for Geodetic Inversion of Geopotential Gradients

NASA Astrophysics Data System (ADS)

Novák, Pavel; Šprlák, Michal

2018-03-01

The static Earth's gravitational field has traditionally been described in geodesy and geophysics by the gravitational potential (geopotential for short), a scalar function of 3-D position. Although not directly observable, geopotential functionals such as its first- and second-order gradients are routinely measured by ground, airborne and/or satellite sensors. In geodesy, these observables are often used for recovery of the static geopotential at some simple reference surface approximating the actual Earth's surface. A generalized mathematical model is represented by a surface integral equation which originates in solving Dirichlet's boundary-value problem of the potential theory defined for the harmonic geopotential, spheroidal boundary and globally distributed gradient data. The mathematical model can be used for combining various geopotential gradients without necessity of their re-sampling or prior continuation in space. The model extends the apparatus of integral equations which results from solving boundary-value problems of the potential theory to all geopotential gradients observed by current ground, airborne and satellite sensors. Differences between spherical and spheroidal formulations of integral kernel functions of Green's kind are investigated. Estimated differences reach relative values at the level of 3% which demonstrates the significance of spheroidal approximation for flattened bodies such as the Earth. The observation model can be used for combined inversion of currently available geopotential gradients while exploring their spectral and stochastic characteristics. The model would be even more relevant to gravitational field modelling of other bodies in space with more pronounced spheroidal geometry than that of the Earth.

Downscaling modelling system for multi-scale air quality forecasting

NASA Astrophysics Data System (ADS)

Nuterman, R.; Baklanov, A.; Mahura, A.; Amstrup, B.; Weismann, J.

2010-09-01

Urban modelling for real meteorological situations, in general, considers only a small part of the urban area in a micro-meteorological model, and urban heterogeneities outside a modelling domain affect micro-scale processes. Therefore, it is important to build a chain of models of different scales with nesting of higher resolution models into larger scale lower resolution models. Usually, the up-scaled city- or meso-scale models consider parameterisations of urban effects or statistical descriptions of the urban morphology, whereas the micro-scale (street canyon) models are obstacle-resolved and they consider a detailed geometry of the buildings and the urban canopy. The developed system consists of the meso-, urban- and street-scale models. First, it is the Numerical Weather Prediction (HIgh Resolution Limited Area Model) model combined with Atmospheric Chemistry Transport (the Comprehensive Air quality Model with extensions) model. Several levels of urban parameterisation are considered. They are chosen depending on selected scales and resolutions. For regional scale, the urban parameterisation is based on the roughness and flux corrections approach; for urban scale - building effects parameterisation. Modern methods of computational fluid dynamics allow solving environmental problems connected with atmospheric transport of pollutants within urban canopy in a presence of penetrable (vegetation) and impenetrable (buildings) obstacles. For local- and micro-scales nesting the Micro-scale Model for Urban Environment is applied. This is a comprehensive obstacle-resolved urban wind-flow and dispersion model based on the Reynolds averaged Navier-Stokes approach and several turbulent closures, i.e. k -ɛ linear eddy-viscosity model, k - ɛ non-linear eddy-viscosity model and Reynolds stress model. Boundary and initial conditions for the micro-scale model are used from the up-scaled models with corresponding interpolation conserving the mass. For the boundaries a kind of Dirichlet condition is chosen to provide the values based on interpolation from the coarse to the fine grid. When the roughness approach is changed to the obstacle-resolved one in the nested model, the interpolation procedure will increase the computational time (due to additional iterations) for meteorological/ chemical fields inside the urban sub-layer. In such situations, as a possible alternative, the perturbation approach can be applied. Here, the effects of main meteorological variables and chemical species are considered as a sum of two components: background (large-scale) values, described by the coarse-resolution model, and perturbations (micro-scale) features, obtained from the nested fine resolution model.

Mining FDA drug labels using an unsupervised learning technique--topic modeling.

PubMed

Bisgin, Halil; Liu, Zhichao; Fang, Hong; Xu, Xiaowei; Tong, Weida

2011-10-18

The Food and Drug Administration (FDA) approved drug labels contain a broad array of information, ranging from adverse drug reactions (ADRs) to drug efficacy, risk-benefit consideration, and more. However, the labeling language used to describe these information is free text often containing ambiguous semantic descriptions, which poses a great challenge in retrieving useful information from the labeling text in a consistent and accurate fashion for comparative analysis across drugs. Consequently, this task has largely relied on the manual reading of the full text by experts, which is time consuming and labor intensive. In this study, a novel text mining method with unsupervised learning in nature, called topic modeling, was applied to the drug labeling with a goal of discovering "topics" that group drugs with similar safety concerns and/or therapeutic uses together. A total of 794 FDA-approved drug labels were used in this study. First, the three labeling sections (i.e., Boxed Warning, Warnings and Precautions, Adverse Reactions) of each drug label were processed by the Medical Dictionary for Regulatory Activities (MedDRA) to convert the free text of each label to the standard ADR terms. Next, the topic modeling approach with latent Dirichlet allocation (LDA) was applied to generate 100 topics, each associated with a set of drugs grouped together based on the probability analysis. Lastly, the efficacy of the topic modeling was evaluated based on known information about the therapeutic uses and safety data of drugs. The results demonstrate that drugs grouped by topics are associated with the same safety concerns and/or therapeutic uses with statistical significance (P<0.05). The identified topics have distinct context that can be directly linked to specific adverse events (e.g., liver injury or kidney injury) or therapeutic application (e.g., antiinfectives for systemic use). We were also able to identify potential adverse events that might arise from specific medications via topics. The successful application of topic modeling on the FDA drug labeling demonstrates its potential utility as a hypothesis generation means to infer hidden relationships of concepts such as, in this study, drug safety and therapeutic use in the study of biomedical documents.

Output Feedback-Based Boundary Control of Uncertain Coupled Semilinear Parabolic PDE Using Neurodynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

In this paper, neurodynamic programming-based output feedback boundary control of distributed parameter systems governed by uncertain coupled semilinear parabolic partial differential equations (PDEs) under Neumann or Dirichlet boundary control conditions is introduced. First, Hamilton-Jacobi-Bellman (HJB) equation is formulated in the original PDE domain and the optimal control policy is derived using the value functional as the solution of the HJB equation. Subsequently, a novel observer is developed to estimate the system states given the uncertain nonlinearity in PDE dynamics and measured outputs. Consequently, the suboptimal boundary control policy is obtained by forward-in-time estimation of the value functional using a neural network (NN)-based online approximator and estimated state vector obtained from the NN observer. Novel adaptive tuning laws in continuous time are proposed for learning the value functional online to satisfy the HJB equation along system trajectories while ensuring the closed-loop stability. Local uniformly ultimate boundedness of the closed-loop system is verified by using Lyapunov theory. The performance of the proposed controller is verified via simulation on an unstable coupled diffusion reaction process.

Smooth operator: The effects of different 3D mesh retriangulation protocols on the computation of Dirichlet normal energy.

PubMed

Spradley, Jackson P; Pampush, James D; Morse, Paul E; Kay, Richard F

2017-05-01

Dirichlet normal energy (DNE) is a metric of surface topography that has been used to evaluate the relationship between the surface complexity of primate cheek teeth and dietary categories. This study examines the effects of different 3D mesh retriangulation protocols on DNE. We examine how different protocols influence the DNE of a simple geometric shape-a hemisphere-to gain a more thorough understanding than can be achieved by investigating a complex biological surface such as a tooth crown. We calculate DNE on 3D surface meshes of hemispheres and on primate molars subjected to various retriangulation protocols, including smoothing algorithms, smoothing amounts, target face counts, and criteria for boundary face exclusion. Software used includes R, MorphoTester, Avizo, and MeshLab. DNE was calculated using the R package "molaR." In all cases, smoothing as performed in Avizo sharply decreases DNE initially, after which DNE becomes stable. Using a broader boundary exclusion criterion or performing additional smoothing (using "mesh fairing" methods) further decreases DNE. Increasing the mesh face count also results in increased DNE on tooth surfaces. Different retriangulation protocols yield different DNE values for the same surfaces, and should not be combined in meta-analyses. Increasing face count will capture surface microfeatures, but at the expense of computational speed. More aggressive smoothing is more likely to alter the essential geometry of the surface. A protocol is proposed that limits potential artifacts created during surface production while preserving pertinent features on the occlusal surface. © 2017 Wiley Periodicals, Inc.

A new model for the blown film process

NASA Astrophysics Data System (ADS)

Demay, Yves; Clamond, Didier

2011-11-01

Polymer films are generally manufactured by film blowing. In this process the polymer (a polyethylene for example) is molten in a screw extruder and forced into a tubular die (typical dimensions are several decimeters in diameter and about one mm in thickness). At extrusion, it forms a liquid tube which is simultaneously drawn in the vertical direction by nip rolls, inflated by an internal pressure and cooled by external air rings. Typical dimensions of the bubble at take up are 1 m or more in diameter and several 10 μm in thickness. From a mechanical point of view, it is an extensional thin layer flow. Readers not familiar with this process will find easily pictures and schematic descriptions with a web research using keywords blown film extrusion. In order to simplify, it is assumed that the temperature profile is known and that the molten polymer behaves as a Newtonian fluid. This crude rheological behavior allows to capture qualitatively an important part of observed phenomena. The classical model introduced by Pearson and Petrie in 1970 is based on three hypothesis: the polymer flow in air is steady and axisymmetric and the film is thin. It uses a tangent frame affixed to the membrane to describe kinematics and to compute stress and strain tensors. In this model the balance equations are written using a stretching force and a curvature equation. It results in a nonlinear system of differential equations for velocity, thickness, radius and stress components according to distance z to extrusion. Solution is then computed using a tedious shooting method to determine force and internal pressure. For stability reasons this system of equations is solved from take up to extrusion. In this Note we derive also balance equations according to a curvilinear abscissa s. It allows us to derive a coupled system of equations for velocity and geometry according to radius r. This strategy which is classically used to determine surfaces of revolution with given mean curvature is rather disconcerting to compute a stretching flow in z direction. However it leads to a model constituted of two coupled equations: Velocity is then solution of a Dirichlet boundary value problem of order two easily solved using a finite elements method; The profile curve of the bubble is solution of a highly nonlinear differential equation of order one leading to a singular integral. Internal pressure appears as a parameter allowing to impose an additional boundary condition. Despite the fact that the computation of the solution remains technical, this new model seems more natural from a mathematical point of view as it leads, on the one hand, to an elliptic equation to compute velocity, and on the other hand, to an equation of a classical type in differential geometry to determine the generatrix.

Recommending Education Materials for Diabetic Questions Using Information Retrieval Approaches

PubMed Central

Wang, Yanshan; Shen, Feichen; Liu, Sijia; Rastegar-Mojarad, Majid; Wang, Liwei

2017-01-01

Background Self-management is crucial to diabetes care and providing expert-vetted content for answering patients’ questions is crucial in facilitating patient self-management. Objective The aim is to investigate the use of information retrieval techniques in recommending patient education materials for diabetic questions of patients. Methods We compared two retrieval algorithms, one based on Latent Dirichlet Allocation topic modeling (topic modeling-based model) and one based on semantic group (semantic group-based model), with the baseline retrieval models, vector space model (VSM), in recommending diabetic patient education materials to diabetic questions posted on the TuDiabetes forum. The evaluation was based on a gold standard dataset consisting of 50 randomly selected diabetic questions where the relevancy of diabetic education materials to the questions was manually assigned by two experts. The performance was assessed using precision of top-ranked documents. Results We retrieved 7510 diabetic questions on the forum and 144 diabetic patient educational materials from the patient education database at Mayo Clinic. The mapping rate of words in each corpus mapped to the Unified Medical Language System (UMLS) was significantly different (P<.001). The topic modeling-based model outperformed the other retrieval algorithms. For example, for the top-retrieved document, the precision of the topic modeling-based, semantic group-based, and VSM models was 67.0%, 62.8%, and 54.3%, respectively. Conclusions This study demonstrated that topic modeling can mitigate the vocabulary difference and it achieved the best performance in recommending education materials for answering patients’ questions. One direction for future work is to assess the generalizability of our findings and to extend our study to other disease areas, other patient education material resources, and online forums. PMID:29038097

Near-Native Protein Loop Sampling Using Nonparametric Density Estimation Accommodating Sparcity

PubMed Central

Day, Ryan; Lennox, Kristin P.; Sukhanov, Paul; Dahl, David B.; Vannucci, Marina; Tsai, Jerry

2011-01-01

Unlike the core structural elements of a protein like regular secondary structure, template based modeling (TBM) has difficulty with loop regions due to their variability in sequence and structure as well as the sparse sampling from a limited number of homologous templates. We present a novel, knowledge-based method for loop sampling that leverages homologous torsion angle information to estimate a continuous joint backbone dihedral angle density at each loop position. The φ,ψ distributions are estimated via a Dirichlet process mixture of hidden Markov models (DPM-HMM). Models are quickly generated based on samples from these distributions and were enriched using an end-to-end distance filter. The performance of the DPM-HMM method was evaluated against a diverse test set in a leave-one-out approach. Candidates as low as 0.45 Å RMSD and with a worst case of 3.66 Å were produced. For the canonical loops like the immunoglobulin complementarity-determining regions (mean RMSD <2.0 Å), the DPM-HMM method performs as well or better than the best templates, demonstrating that our automated method recaptures these canonical loops without inclusion of any IgG specific terms or manual intervention. In cases with poor or few good templates (mean RMSD >7.0 Å), this sampling method produces a population of loop structures to around 3.66 Å for loops up to 17 residues. In a direct test of sampling to the Loopy algorithm, our method demonstrates the ability to sample nearer native structures for both the canonical CDRH1 and non-canonical CDRH3 loops. Lastly, in the realistic test conditions of the CASP9 experiment, successful application of DPM-HMM for 90 loops from 45 TBM targets shows the general applicability of our sampling method in loop modeling problem. These results demonstrate that our DPM-HMM produces an advantage by consistently sampling near native loop structure. The software used in this analysis is available for download at http://www.stat.tamu.edu/~dahl/software/cortorgles/. PMID:22028638

Positivity results for indefinite sublinear elliptic problems via a continuity argument

NASA Astrophysics Data System (ADS)

Kaufmann, U.; Ramos Quoirin, H.; Umezu, K.

2017-10-01

We establish a positivity property for a class of semilinear elliptic problems involving indefinite sublinear nonlinearities. Namely, we show that any nontrivial nonnegative solution is positive for a class of problems the strong maximum principle does not apply to. Our approach is based on a continuity argument combined with variational techniques, the sub and supersolutions method and some a priori bounds. Both Dirichlet and Neumann homogeneous boundary conditions are considered. As a byproduct, we deduce some existence and uniqueness results. Finally, as an application, we derive some positivity results for indefinite concave-convex type problems.

The existence of semiregular solutions to elliptic spectral problems with discontinuous nonlinearities

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

Pavlenko, V N; Potapov, D K

2015-09-30

This paper is concerned with the existence of semiregular solutions to the Dirichlet problem for an equation of elliptic type with discontinuous nonlinearity and when the differential operator is not assumed to be formally self-adjoint. Theorems on the existence of semiregular (positive and negative) solutions for the problem under consideration are given, and a principle of upper and lower solutions giving the existence of semiregular solutions is established. For positive values of the spectral parameter, elliptic spectral problems with discontinuous nonlinearities are shown to have nontrivial semiregular (positive and negative) solutions. Bibliography: 32 titles.

The Cr dependence problem of eigenvalues of the Laplace operator on domains in the plane

NASA Astrophysics Data System (ADS)

Haddad, Julian; Montenegro, Marcos

2018-03-01

The Cr dependence problem of multiple Dirichlet eigenvalues on domains is discussed for elliptic operators by regarding C r + 1-smooth one-parameter families of C1 perturbations of domains in Rn. As applications of our main theorem (Theorem 1), we provide a fairly complete description for all eigenvalues of the Laplace operator on disks and squares in R2 and also for its second eigenvalue on balls in Rn for any n ≥ 3. The central tool used in our proof is a degenerate implicit function theorem on Banach spaces (Theorem 2) of independent interest.

Regular Inversion of the Divergence Operator with Dirichlet Boundary Conditions on a Polygon,

DTIC Science & Technology

1987-04-01

E c- xC 0 Czt C- -- &C -nC CL C~ E C - U U C U C0 V C ( C CC C L 6- - C C- 1 -CLL r = .c L C A C *C CCC F 4 C CC> C C 4D C3 1 ZC -’ c OC.LL fUC I...Iil Moreover by Lemmna 2.1, there is a single cons aiit C such that IIIIIPpV Chi 1 /, p e < CII, 1 2/P p. holds for all such 9. Thus / . af l( I-,0)1

Second-Order Two-Sided Estimates in Nonlinear Elliptic Problems

NASA Astrophysics Data System (ADS)

Cianchi, Andrea; Maz'ya, Vladimir G.

2018-05-01

Best possible second-order regularity is established for solutions to p-Laplacian type equations with {p \\in (1, ∞)} and a square-integrable right-hand side. Our results provide a nonlinear counterpart of the classical L 2-coercivity theory for linear problems, which is missing in the existing literature. Both local and global estimates are obtained. The latter apply to solutions to either Dirichlet or Neumann boundary value problems. Minimal regularity on the boundary of the domain is required, although our conclusions are new even for smooth domains. If the domain is convex, no regularity of its boundary is needed at all.

Flattening maps for the visualization of multibranched vessels.

PubMed

Zhu, Lei; Haker, Steven; Tannenbaum, Allen

2005-02-01

In this paper, we present two novel algorithms which produce flattened visualizations of branched physiological surfaces, such as vessels. The first approach is a conformal mapping algorithm based on the minimization of two Dirichlet functionals. From a triangulated representation of vessel surfaces, we show how the algorithm can be implemented using a finite element technique. The second method is an algorithm which adjusts the conformal mapping to produce a flattened representation of the original surface while preserving areas. This approach employs the theory of optimal mass transport. Furthermore, a new way of extracting center lines for vessel fly-throughs is provided.

Flattening Maps for the Visualization of Multibranched Vessels

PubMed Central

Zhu, Lei; Haker, Steven; Tannenbaum, Allen

2013-01-01

In this paper, we present two novel algorithms which produce flattened visualizations of branched physiological surfaces, such as vessels. The first approach is a conformal mapping algorithm based on the minimization of two Dirichlet functionals. From a triangulated representation of vessel surfaces, we show how the algorithm can be implemented using a finite element technique. The second method is an algorithm which adjusts the conformal mapping to produce a flattened representation of the original surface while preserving areas. This approach employs the theory of optimal mass transport. Furthermore, a new way of extracting center lines for vessel fly-throughs is provided. PMID:15707245

Globally Convergent Inverse Reconstruction Algorithm for Detection of IEDs via Imaging of Spatially Distributed Dielectric Constants using Microwave

DTIC Science & Technology

2010-04-27

Dirichlet boundary data DP̃ (x, y) at the entire plane P̃ . Then one can solve the following boundary value problem in the half space below P̃ ∆w − s2w...which we wanted to be a plane wave when reaching the bottom side of the prism of Figure 1, where measurements were conducted. But actually this 14 was a...initializing wave field is a plane wave. On the other hand, a visual inspection of the output experimental data has revealed to us that actually we had a

Comment on "Exact solution of resonant modes in a rectangular resonator".

PubMed

Gutiérrez-Vega, Julio C; Bandres, Miguel A

2006-08-15

We comment on the recent Letter by J. Wu and A. Liu [Opt. Lett. 31, 1720 (2006)] in which an exact scalar solution to the resonant modes and the resonant frequencies in a two-dimensional rectangular microcavity were presented. The analysis is incorrect because (a) the field solutions were imposed to satisfy simultaneously both Dirichlet and Neumann boundary conditions at the four sides of the rectangle, leading to an overdetermined problem, and (b) the modes in the cavity were expanded using an incorrect series ansatz, leading to an expression for the mode fields that does not satisfy the Helmholtz equation.

Evaluating topic model interpretability from a primary care physician perspective.

PubMed

Arnold, Corey W; Oh, Andrea; Chen, Shawn; Speier, William

2016-02-01

Probabilistic topic models provide an unsupervised method for analyzing unstructured text. These models discover semantically coherent combinations of words (topics) that could be integrated in a clinical automatic summarization system for primary care physicians performing chart review. However, the human interpretability of topics discovered from clinical reports is unknown. Our objective is to assess the coherence of topics and their ability to represent the contents of clinical reports from a primary care physician's point of view. Three latent Dirichlet allocation models (50 topics, 100 topics, and 150 topics) were fit to a large collection of clinical reports. Topics were manually evaluated by primary care physicians and graduate students. Wilcoxon Signed-Rank Tests for Paired Samples were used to evaluate differences between different topic models, while differences in performance between students and primary care physicians (PCPs) were tested using Mann-Whitney U tests for each of the tasks. While the 150-topic model produced the best log likelihood, participants were most accurate at identifying words that did not belong in topics learned by the 100-topic model, suggesting that 100 topics provides better relative granularity of discovered semantic themes for the data set used in this study. Models were comparable in their ability to represent the contents of documents. Primary care physicians significantly outperformed students in both tasks. This work establishes a baseline of interpretability for topic models trained with clinical reports, and provides insights on the appropriateness of using topic models for informatics applications. Our results indicate that PCPs find discovered topics more coherent and representative of clinical reports relative to students, warranting further research into their use for automatic summarization. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Evaluating Topic Model Interpretability from a Primary Care Physician Perspective

PubMed Central

Arnold, Corey W.; Oh, Andrea; Chen, Shawn; Speier, William

2015-01-01

Background and Objective Probabilistic topic models provide an unsupervised method for analyzing unstructured text. These models discover semantically coherent combinations of words (topics) that could be integrated in a clinical automatic summarization system for primary care physicians performing chart review. However, the human interpretability of topics discovered from clinical reports is unknown. Our objective is to assess the coherence of topics and their ability to represent the contents of clinical reports from a primary care physician’s point of view. Methods Three latent Dirichlet allocation models (50 topics, 100 topics, and 150 topics) were fit to a large collection of clinical reports. Topics were manually evaluated by primary care physicians and graduate students. Wilcoxon Signed-Rank Tests for Paired Samples were used to evaluate differences between different topic models, while differences in performance between students and primary care physicians (PCPs) were tested using Mann-Whitney U tests for each of the tasks. Results While the 150-topic model produced the best log likelihood, participants were most accurate at identifying words that did not belong in topics learned by the 100-topic model, suggesting that 100 topics provides better relative granularity of discovered semantic themes for the data set used in this study. Models were comparable in their ability to represent the contents of documents. Primary care physicians significantly outperformed students in both tasks. Conclusion This work establishes a baseline of interpretability for topic models trained with clinical reports, and provides insights on the appropriateness of using topic models for informatics applications. Our results indicate that PCPs find discovered topics more coherent and representative of clinical reports relative to students, warranting further research into their use for automatic summarization. PMID:26614020

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

Callias, C.J.

It has been known for a long time that the spectrum of the Sturm-Liouville operator {minus}{partial_derivative}{sub x}{sup 2}+ v(x) on a finite interval does not uniquely determine the potential v(x). In fact there are infinite-dimensional isospectral classes of potentials [PT]. Highly singular problems have been addressed as well, notably the question of the isospectral classes of the harmonic oscillator on the real line [McK-T], and, more recently, of the singular Sturm-Liouville operator {minus}{partial_derivative}{sub x}{sup 2} + {ell}({ell}+1)/x{sup 2} + v(x) on [0,1][GR]. In this paper we examine the question of whether the structure of isolated singularities in the potential ismore » spectrally determined. As an example of the fruits of our efforts we were able to prove the following result for the Dirichlet problem: Suppose that v(x) {epsilon} C{sup {infinity}}([-1,1]/(0)) is real-valued and v{sup (k)}(1) for all k. Suppose that xv(x) is infinitely differentiable at x = 0 from the right and from the left and lim{sub x}{r_arrow}0+ (d/{sub dx}){sup K}xv(x) = (-1){sup k+1}lim{sub x{r_arrow}0}-(d/dx){sup k}xv(x), so that v(x) {approximately} {Sigma}{sub k}{sup {infinity}}=-1{sup vk}{center_dot}{vert_bar}x{vert_bar}{sup k} as x {r_arrow} 0, for some constants v{sub k}. Suppose that v{sub {minus}1}{ne}0. Then the spectrum of the Sturm-Liousville operator with periodic boundary conditions at {plus_minus}1 and Dirichlet conditions at x = 0 uniquely determines the sequence of asymptotic coefficients v{sub {minus}1}, v{sub 0}, v{sub 1},...Potentials with the 1/x singularity arise in the wave equation for a vibrating rod of variable cross-section, when the cross-sectional area of the rod vanishes quadratically (as a function of the distance from the end of the rod) at one point. The main reason why we look at this problem is as a model that will give us an idea of what can be expected when one attempts to get information about singularities from the spectrum.« less

Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer

NASA Astrophysics Data System (ADS)

Huang, C.-S.; Yang, S.-Y.; Yeh, H.-D.

2015-03-01

An aquifer consisting of a skin zone and a formation zone is considered as a two-zone aquifer. Existing solutions for the problem of constant-flux pumping (CFP) in a two-zone confined aquifer involve laborious calculation. This study develops a new approximate solution for the problem based on a mathematical model including two steady-state flow equations with different hydraulic parameters for the skin and formation zones. A partially penetrating well may be treated as the Neumann condition with a known flux along the screened part and zero flux along the unscreened part. The aquifer domain is finite with an outer circle boundary treated as the Dirichlet condition. The steady-state drawdown solution of the model is derived by the finite Fourier cosine transform. Then, an approximate transient solution is developed by replacing the radius of the boundary in the steady-state solution with an analytical expression for a dimensionless time-dependent radius of influence. The approximate solution is capable of predicting good temporal drawdown distributions over the whole pumping period except at the early stage. A quantitative criterion for the validity of neglecting the vertical flow component due to a partially penetrating well is also provided. Conventional models considering radial flow without the vertical component for the CFP have good accuracy if satisfying the criterion.

Peripheral nerve magnetic stimulation: influence of tissue non-homogeneity

PubMed Central

Krasteva, Vessela TZ; Papazov, Sava P; Daskalov, Ivan K

2003-01-01

Background Peripheral nerves are situated in a highly non-homogeneous environment, including muscles, bones, blood vessels, etc. Time-varying magnetic field stimulation of the median and ulnar nerves in the carpal region is studied, with special consideration of the influence of non-homogeneities. Methods A detailed three-dimensional finite element model (FEM) of the anatomy of the wrist region was built to assess the induced currents distribution by external magnetic stimulation. The electromagnetic field distribution in the non-homogeneous domain was defined as an internal Dirichlet problem using the finite element method. The boundary conditions were obtained by analysis of the vector potential field excited by external current-driven coils. Results The results include evaluation and graphical representation of the induced current field distribution at various stimulation coil positions. Comparative study for the real non-homogeneous structure with anisotropic conductivities of the tissues and a mock homogeneous media is also presented. The possibility of achieving selective stimulation of either of the two nerves is assessed. Conclusion The model developed could be useful in theoretical prediction of the current distribution in the nerves during diagnostic stimulation and therapeutic procedures involving electromagnetic excitation. The errors in applying homogeneous domain modeling rather than real non-homogeneous biological structures are demonstrated. The practical implications of the applied approach are valid for any arbitrary weakly conductive medium. PMID:14693034

Redundancy-Aware Topic Modeling for Patient Record Notes

PubMed Central

Cohen, Raphael; Aviram, Iddo; Elhadad, Michael; Elhadad, Noémie

2014-01-01

The clinical notes in a given patient record contain much redundancy, in large part due to clinicians’ documentation habit of copying from previous notes in the record and pasting into a new note. Previous work has shown that this redundancy has a negative impact on the quality of text mining and topic modeling in particular. In this paper we describe a novel variant of Latent Dirichlet Allocation (LDA) topic modeling, Red-LDA, which takes into account the inherent redundancy of patient records when modeling content of clinical notes. To assess the value of Red-LDA, we experiment with three baselines and our novel redundancy-aware topic modeling method: given a large collection of patient records, (i) apply vanilla LDA to all documents in all input records; (ii) identify and remove all redundancy by chosing a single representative document for each record as input to LDA; (iii) identify and remove all redundant paragraphs in each record, leaving partial, non-redundant documents as input to LDA; and (iv) apply Red-LDA to all documents in all input records. Both quantitative evaluation carried out through log-likelihood on held-out data and topic coherence of produced topics and qualitative assessement of topics carried out by physicians show that Red-LDA produces superior models to all three baseline strategies. This research contributes to the emerging field of understanding the characteristics of the electronic health record and how to account for them in the framework of data mining. The code for the two redundancy-elimination baselines and Red-LDA is made publicly available to the community. PMID:24551060

Redundancy-aware topic modeling for patient record notes.

PubMed

Cohen, Raphael; Aviram, Iddo; Elhadad, Michael; Elhadad, Noémie

2014-01-01

The clinical notes in a given patient record contain much redundancy, in large part due to clinicians' documentation habit of copying from previous notes in the record and pasting into a new note. Previous work has shown that this redundancy has a negative impact on the quality of text mining and topic modeling in particular. In this paper we describe a novel variant of Latent Dirichlet Allocation (LDA) topic modeling, Red-LDA, which takes into account the inherent redundancy of patient records when modeling content of clinical notes. To assess the value of Red-LDA, we experiment with three baselines and our novel redundancy-aware topic modeling method: given a large collection of patient records, (i) apply vanilla LDA to all documents in all input records; (ii) identify and remove all redundancy by chosing a single representative document for each record as input to LDA; (iii) identify and remove all redundant paragraphs in each record, leaving partial, non-redundant documents as input to LDA; and (iv) apply Red-LDA to all documents in all input records. Both quantitative evaluation carried out through log-likelihood on held-out data and topic coherence of produced topics and qualitative assessment of topics carried out by physicians show that Red-LDA produces superior models to all three baseline strategies. This research contributes to the emerging field of understanding the characteristics of the electronic health record and how to account for them in the framework of data mining. The code for the two redundancy-elimination baselines and Red-LDA is made publicly available to the community.

Modeling of various heat adapter plate 4 and 6 array for optimization of thermoelectric generator element using modified diffusion equation

NASA Astrophysics Data System (ADS)

Defrianto; Tambunan, W.; Lazuardi

2017-07-01

The use of waste heat from exhaust gas and converting it to electricity is now an alternative to harvest a cheap and clean energy. Thermoelectric generator (TEG) has the ability to directly recover such waste heat and generate electricity. The aim of this study is to simulate the heat transfer on the aluminum adapter plate for homogeneity temperature distribution coupled with hot side of TEG type 40-40-10/100 from Firma Eureka and adjust their high temperatures to the TEG operating temperature to avoid the element damage. Modelling was carried out using MATLAB modified diffusion equation with Dirichlet boundary conditions at defined temperature which has been set at the ends of the heat source at 463K and 373K ± 10% on the hot side of the TEG element. The use of nylon insulated material is modeled after Neumann boundary condition in which the temperature gradient is ∂T/∂n = 0 out of boundary. Realization of the modelling is done by designing a heat conductive plate using software ACAD 2015 and converted into a binary file format of Mathlab to form a finite element mesh with geometry variations of solid model. The solid cubic model of aluminum adapter plate has a dimension of 40mm length, 40mm width and also 20mm, 30mm and 40mm thickness arranged in two arrays of 2×2 and 2×3 of TEG elements. Results showed a temperature decrease about 40.95% and 50.02% respectively from the initial source and appropriate with TEG temperature tolerance.

Temperature field determination in slabs, circular plates and spheres with saw tooth heat generating sources

NASA Astrophysics Data System (ADS)

Diestra Cruz, Heberth Alexander

The Green's functions integral technique is used to determine the conduction heat transfer temperature field in flat plates, circular plates, and solid spheres with saw tooth heat generating sources. In all cases the boundary temperature is specified (Dirichlet's condition) and the thermal conductivity is constant. The method of images is used to find the Green's function in infinite solids, semi-infinite solids, infinite quadrants, circular plates, and solid spheres. The saw tooth heat generation source has been modeled using Dirac delta function and Heaviside step function. The use of Green's functions allows obtain the temperature distribution in the form of an integral that avoids the convergence problems of infinite series. For the infinite solid and the sphere, the temperature distribution is three-dimensional and in the cases of semi-infinite solid, infinite quadrant and circular plate the distribution is two-dimensional. The method used in this work is superior to other methods because it obtains elegant analytical or quasi-analytical solutions to complex heat conduction problems with less computational effort and more accuracy than the use of fully numerical methods.

Effects of Time-Dependent Inflow Perturbations on Turbulent Flow in a Street Canyon

NASA Astrophysics Data System (ADS)

Duan, G.; Ngan, K.

2017-12-01

Urban flow and turbulence are driven by atmospheric flows with larger horizontal scales. Since building-resolving computational fluid dynamics models typically employ steady Dirichlet boundary conditions or forcing, the accuracy of numerical simulations may be limited by the neglect of perturbations. We investigate the sensitivity of flow within a unit-aspect-ratio street canyon to time-dependent perturbations near the inflow boundary. Using large-eddy simulation, time-periodic perturbations to the streamwise velocity component are incorporated via the nudging technique. Spatial averages of pointwise differences between unperturbed and perturbed velocity fields (i.e., the error kinetic energy) show a clear dependence on the perturbation period, though spatial structures are largely insensitive to the time-dependent forcing. The response of the error kinetic energy is maximized for perturbation periods comparable to the time scale of the mean canyon circulation. Frequency spectra indicate that this behaviour arises from a resonance between the inflow forcing and the mean motion around closed streamlines. The robustness of the results is confirmed using perturbations derived from measurements of roof-level wind speed.

Identifying Indicators of Progress in Thermal Spray Research Using Bibliometrics Analysis

NASA Astrophysics Data System (ADS)

Li, R.-T.; Khor, K. A.; Yu, L.-G.

2016-12-01

We investigated the research publications on thermal spray in the period of 1985-2015 using the data from Web of Science, Scopus and SciVal®. Bibliometrics analysis was employed to elucidate the country and institution distribution in various thermal spray research areas and to characterize the trends of topic change and technology progress. Results show that China, USA, Japan, Germany, India and France were the top countries in thermal spray research, and Xi'an Jiaotong University, Universite de Technologie Belfort-Montbeliard, Shanghai Institute of Ceramics, ETH Zurich, National Research Council of Canada, University of Limoges were among the top institutions that had high scholarly research output during 2005-2015. The terms of the titles, keywords and abstracts of the publications were analyzed by the Latent Dirichlet Allocation model and visually mapped using the VOSviewer software to reveal the progress of thermal spray technology. It is found that thermal barrier coating was consistently the main research area in thermal spray, and high-velocity oxy-fuel spray and cold spray developed rapidly in the last 10 years.

Axial charges of N(1535) and N(1650) in lattice QCD with two flavors of dynamical quarks

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

Takahashi, Toru T.; Kunihiro, Teiji

2008-07-01

We show the first lattice QCD results on the axial charge g{sub A}{sup N}*{sup N}* of N*(1535) and N*(1650). The measurements are performed with two flavors of dynamical quarks employing the renormalization-group improved gauge action at {beta}=1.95 and the mean-field improved clover quark action with the hopping parameters, {kappa}=0.1375, 0.1390, and 0.1400. In order to properly separate signals of N*(1535) and N*(1650), we construct 2x2 correlation matrices and diagonalize them. Wraparound contributions in the correlator, which can be another source of signal contaminations, are eliminated by imposing the Dirichlet boundary condition in the temporal direction. We find that the axialmore » charge of N*(1535) takes small values such as g{sub A}{sup N}*{sup N}*{approx}O(0.1), whereas that of N*(1650) is about 0.5, which is found independent of quark masses and consistent with the predictions by the naive nonrelativistic quark model.« less

Use of a Latent Topic Model for Characteristic Extraction from Health Checkup Questionnaire Data.

PubMed

Hatakeyama, Y; Miyano, I; Kataoka, H; Nakajima, N; Watabe, T; Yasuda, N; Okuhara, Y

2015-01-01

When patients complete questionnaires during health checkups, many of their responses are subjective, making topic extraction difficult. Therefore, the purpose of this study was to develop a model capable of extracting appropriate topics from subjective data in questionnaires conducted during health checkups. We employed a latent topic model to group the lifestyle habits of the study participants and represented their responses to items on health checkup questionnaires as a probability model. For the probability model, we used latent Dirichlet allocation to extract 30 topics from the questionnaires. According to the model parameters, a total of 4381 study participants were then divided into groups based on these topics. Results from laboratory tests, including blood glucose level, triglycerides, and estimated glomerular filtration rate, were compared between each group, and these results were then compared with those obtained by hierarchical clustering. If a significant (p < 0.05) difference was observed in any of the laboratory measurements between groups, it was considered to indicate a questionnaire response pattern corresponding to the value of the test result. A comparison between the latent topic model and hierarchical clustering grouping revealed that, in the latent topic model method, a small group of participants who reported having subjective signs of urinary disorder were allocated to a single group. The latent topic model is useful for extracting characteristics from a small number of groups from questionnaires with a large number of items. These results show that, in addition to chief complaints and history of past illness, questionnaire data obtained during medical checkups can serve as useful judgment criteria for assessing the conditions of patients.

Content Coding of Psychotherapy Transcripts Using Labeled Topic Models.

PubMed

Gaut, Garren; Steyvers, Mark; Imel, Zac E; Atkins, David C; Smyth, Padhraic

2017-03-01

Psychotherapy represents a broad class of medical interventions received by millions of patients each year. Unlike most medical treatments, its primary mechanisms are linguistic; i.e., the treatment relies directly on a conversation between a patient and provider. However, the evaluation of patient-provider conversation suffers from critical shortcomings, including intensive labor requirements, coder error, nonstandardized coding systems, and inability to scale up to larger data sets. To overcome these shortcomings, psychotherapy analysis needs a reliable and scalable method for summarizing the content of treatment encounters. We used a publicly available psychotherapy corpus from Alexander Street press comprising a large collection of transcripts of patient-provider conversations to compare coding performance for two machine learning methods. We used the labeled latent Dirichlet allocation (L-LDA) model to learn associations between text and codes, to predict codes in psychotherapy sessions, and to localize specific passages of within-session text representative of a session code. We compared the L-LDA model to a baseline lasso regression model using predictive accuracy and model generalizability (measured by calculating the area under the curve (AUC) from the receiver operating characteristic curve). The L-LDA model outperforms the lasso logistic regression model at predicting session-level codes with average AUC scores of 0.79, and 0.70, respectively. For fine-grained level coding, L-LDA and logistic regression are able to identify specific talk-turns representative of symptom codes. However, model performance for talk-turn identification is not yet as reliable as human coders. We conclude that the L-LDA model has the potential to be an objective, scalable method for accurate automated coding of psychotherapy sessions that perform better than comparable discriminative methods at session-level coding and can also predict fine-grained codes.

A heuristic approach to determine an appropriate number of topics in topic modeling

PubMed Central

2015-01-01

Background Topic modelling is an active research field in machine learning. While mainly used to build models from unstructured textual data, it offers an effective means of data mining where samples represent documents, and different biological endpoints or omics data represent words. Latent Dirichlet Allocation (LDA) is the most commonly used topic modelling method across a wide number of technical fields. However, model development can be arduous and tedious, and requires burdensome and systematic sensitivity studies in order to find the best set of model parameters. Often, time-consuming subjective evaluations are needed to compare models. Currently, research has yielded no easy way to choose the proper number of topics in a model beyond a major iterative approach. Methods and results Based on analysis of variation of statistical perplexity during topic modelling, a heuristic approach is proposed in this study to estimate the most appropriate number of topics. Specifically, the rate of perplexity change (RPC) as a function of numbers of topics is proposed as a suitable selector. We test the stability and effectiveness of the proposed method for three markedly different types of grounded-truth datasets: Salmonella next generation sequencing, pharmacological side effects, and textual abstracts on computational biology and bioinformatics (TCBB) from PubMed. Conclusion The proposed RPC-based method is demonstrated to choose the best number of topics in three numerical experiments of widely different data types, and for databases of very different sizes. The work required was markedly less arduous than if full systematic sensitivity studies had been carried out with number of topics as a parameter. We understand that additional investigation is needed to substantiate the method's theoretical basis, and to establish its generalizability in terms of dataset characteristics. PMID:26424364

Content Coding of Psychotherapy Transcripts Using Labeled Topic Models

PubMed Central

Gaut, Garren; Steyvers, Mark; Imel, Zac E; Atkins, David C; Smyth, Padhraic

2016-01-01

Psychotherapy represents a broad class of medical interventions received by millions of patients each year. Unlike most medical treatments, its primary mechanisms are linguistic; i.e., the treatment relies directly on a conversation between a patient and provider. However, the evaluation of patient-provider conversation suffers from critical shortcomings, including intensive labor requirements, coder error, non-standardized coding systems, and inability to scale up to larger data sets. To overcome these shortcomings, psychotherapy analysis needs a reliable and scalable method for summarizing the content of treatment encounters. We used a publicly-available psychotherapy corpus from Alexander Street press comprising a large collection of transcripts of patient-provider conversations to compare coding performance for two machine learning methods. We used the Labeled Latent Dirichlet Allocation (L-LDA) model to learn associations between text and codes, to predict codes in psychotherapy sessions, and to localize specific passages of within-session text representative of a session code. We compared the L-LDA model to a baseline lasso regression model using predictive accuracy and model generalizability (measured by calculating the area under the curve (AUC) from the receiver operating characteristic (ROC) curve). The L-LDA model outperforms the lasso logistic regression model at predicting session-level codes with average AUC scores of .79, and .70, respectively. For fine-grained level coding, L-LDA and logistic regression are able to identify specific talk-turns representative of symptom codes. However, model performance for talk-turn identification is not yet as reliable as human coders. We conclude that the L-LDA model has the potential to be an objective, scaleable method for accurate automated coding of psychotherapy sessions that performs better than comparable discriminative methods at session-level coding and can also predict fine-grained codes. PMID:26625437

Theoretical modeling of the effect of Casimir attraction on the electrostatic instability of nanowire-fabricated actuators

NASA Astrophysics Data System (ADS)

Mokhtari, J.; Farrokhabadi, A.; Rach, R.; Abadyan, M.

2015-04-01

The presence of the quantum vacuum fluctuations, i.e. the Casimir attraction, can strongly affect the performance of ultra-small actuators. The strength of the Casimir force is significantly influenced by the geometries of interacting bodies. Previous research has exclusively studied the impact of the vacuum fluctuations on the instability of nanoactuators with planar geometries. However, no work has yet considered this phenomenon in actuators fabricated from nanowires/nanotubes with cylindrical geometries. In our present work, the influence of the Casimir attraction on the electrostatic stability of nanoactuators fabricated from cylindrical conductive nanowire/nanotube is investigated. The Dirichlet mode is considered and an asymptotic solution, based on scattering theory, is applied to consider the effect of vacuum fluctuations in the theoretical model. The size-dependent modified couple stress theory is employed to derive the constitutive equation of the actuator. The governing nonlinear equations are solved by two different approaches, i.e. the finite difference method and modified Adomian-Padé method. Various aspects of the problem, i.e. comparison with the van der Waals force regime, the variation of instability parameters, effect of geometry and coupling between the Casimir force and size dependency are discussed. This work is beneficial to determine the impact of Casimir force on nanowire/nanotube-fabricated actuators.

Predicting structured metadata from unstructured metadata.

PubMed

Posch, Lisa; Panahiazar, Maryam; Dumontier, Michel; Gevaert, Olivier

2016-01-01

Enormous amounts of biomedical data have been and are being produced by investigators all over the world. However, one crucial and limiting factor in data reuse is accurate, structured and complete description of the data or data about the data-defined as metadata. We propose a framework to predict structured metadata terms from unstructured metadata for improving quality and quantity of metadata, using the Gene Expression Omnibus (GEO) microarray database. Our framework consists of classifiers trained using term frequency-inverse document frequency (TF-IDF) features and a second approach based on topics modeled using a Latent Dirichlet Allocation model (LDA) to reduce the dimensionality of the unstructured data. Our results on the GEO database show that structured metadata terms can be the most accurately predicted using the TF-IDF approach followed by LDA both outperforming the majority vote baseline. While some accuracy is lost by the dimensionality reduction of LDA, the difference is small for elements with few possible values, and there is a large improvement over the majority classifier baseline. Overall this is a promising approach for metadata prediction that is likely to be applicable to other datasets and has implications for researchers interested in biomedical metadata curation and metadata prediction. © The Author(s) 2016. Published by Oxford University Press.

Predicting structured metadata from unstructured metadata

PubMed Central

Posch, Lisa; Panahiazar, Maryam; Dumontier, Michel; Gevaert, Olivier

2016-01-01

Enormous amounts of biomedical data have been and are being produced by investigators all over the world. However, one crucial and limiting factor in data reuse is accurate, structured and complete description of the data or data about the data—defined as metadata. We propose a framework to predict structured metadata terms from unstructured metadata for improving quality and quantity of metadata, using the Gene Expression Omnibus (GEO) microarray database. Our framework consists of classifiers trained using term frequency-inverse document frequency (TF-IDF) features and a second approach based on topics modeled using a Latent Dirichlet Allocation model (LDA) to reduce the dimensionality of the unstructured data. Our results on the GEO database show that structured metadata terms can be the most accurately predicted using the TF-IDF approach followed by LDA both outperforming the majority vote baseline. While some accuracy is lost by the dimensionality reduction of LDA, the difference is small for elements with few possible values, and there is a large improvement over the majority classifier baseline. Overall this is a promising approach for metadata prediction that is likely to be applicable to other datasets and has implications for researchers interested in biomedical metadata curation and metadata prediction. Database URL: http://www.yeastgenome.org/ PMID:28637268

Classification of iRBD and Parkinson's disease patients based on eye movements during sleep.

PubMed

Christensen, Julie A E; Koch, Henriette; Frandsen, Rune; Kempfner, Jacob; Arvastson, Lars; Christensen, Soren R; Sorensen, Helge B D; Jennum, Poul

2013-01-01

Patients suffering from the sleep disorder idiopathic rapid-eye-movement sleep behavior disorder (iRBD) have been observed to be in high risk of developing Parkinson's disease (PD). This makes it essential to analyze them in the search for PD biomarkers. This study aims at classifying patients suffering from iRBD or PD based on features reflecting eye movements (EMs) during sleep. A Latent Dirichlet Allocation (LDA) topic model was developed based on features extracted from two electrooculographic (EOG) signals measured as parts in full night polysomnographic (PSG) recordings from ten control subjects. The trained model was tested on ten other control subjects, ten iRBD patients and ten PD patients, obtaining a EM topic mixture diagram for each subject in the test dataset. Three features were extracted from the topic mixture diagrams, reflecting "certainty", "fragmentation" and "stability" in the timely distribution of the EM topics. Using a Naive Bayes (NB) classifier and the features "certainty" and "stability" yielded the best classification result and the subjects were classified with a sensitivity of 95 %, a specificity of 80% and an accuracy of 90 %. This study demonstrates in a data-driven approach, that iRBD and PD patients may exhibit abnorm form and/or timely distribution of EMs during sleep.

An Optimization-Based Framework for the Transformation of Incomplete Biological Knowledge into a Probabilistic Structure and Its Application to the Utilization of Gene/Protein Signaling Pathways in Discrete Phenotype Classification.

PubMed

Esfahani, Mohammad Shahrokh; Dougherty, Edward R

2015-01-01

Phenotype classification via genomic data is hampered by small sample sizes that negatively impact classifier design. Utilization of prior biological knowledge in conjunction with training data can improve both classifier design and error estimation via the construction of the optimal Bayesian classifier. In the genomic setting, gene/protein signaling pathways provide a key source of biological knowledge. Although these pathways are neither complete, nor regulatory, with no timing associated with them, they are capable of constraining the set of possible models representing the underlying interaction between molecules. The aim of this paper is to provide a framework and the mathematical tools to transform signaling pathways to prior probabilities governing uncertainty classes of feature-label distributions used in classifier design. Structural motifs extracted from the signaling pathways are mapped to a set of constraints on a prior probability on a Multinomial distribution. Being the conjugate prior for the Multinomial distribution, we propose optimization paradigms to estimate the parameters of a Dirichlet distribution in the Bayesian setting. The performance of the proposed methods is tested on two widely studied pathways: mammalian cell cycle and a p53 pathway model.

Analysing the health effects of simultaneous exposure to physical and chemical properties of airborne particles

PubMed Central

Pirani, Monica; Best, Nicky; Blangiardo, Marta; Liverani, Silvia; Atkinson, Richard W.; Fuller, Gary W.

2015-01-01

Background Airborne particles are a complex mix of organic and inorganic compounds, with a range of physical and chemical properties. Estimation of how simultaneous exposure to air particles affects the risk of adverse health response represents a challenge for scientific research and air quality management. In this paper, we present a Bayesian approach that can tackle this problem within the framework of time series analysis. Methods We used Dirichlet process mixture models to cluster time points with similar multipollutant and response profiles, while adjusting for seasonal cycles, trends and temporal components. Inference was carried out via Markov Chain Monte Carlo methods. We illustrated our approach using daily data of a range of particle metrics and respiratory mortality for London (UK) 2002–2005. To better quantify the average health impact of these particles, we measured the same set of metrics in 2012, and we computed and compared the posterior predictive distributions of mortality under the exposure scenario in 2012 vs 2005. Results The model resulted in a partition of the days into three clusters. We found a relative risk of 1.02 (95% credible intervals (CI): 1.00, 1.04) for respiratory mortality associated with days characterised by high posterior estimates of non-primary particles, especially nitrate and sulphate. We found a consistent reduction in the airborne particles in 2012 vs 2005 and the analysis of the posterior predictive distributions of respiratory mortality suggested an average annual decrease of − 3.5% (95% CI: − 0.12%, − 5.74%). Conclusions We proposed an effective approach that enabled the better understanding of hidden structures in multipollutant health effects within time series analysis. It allowed the identification of exposure metrics associated with respiratory mortality and provided a tool to assess the changes in health effects from various policies to control the ambient particle matter mixtures. PMID:25795926

Analysing the health effects of simultaneous exposure to physical and chemical properties of airborne particles.

PubMed

Pirani, Monica; Best, Nicky; Blangiardo, Marta; Liverani, Silvia; Atkinson, Richard W; Fuller, Gary W

2015-06-01

Airborne particles are a complex mix of organic and inorganic compounds, with a range of physical and chemical properties. Estimation of how simultaneous exposure to air particles affects the risk of adverse health response represents a challenge for scientific research and air quality management. In this paper, we present a Bayesian approach that can tackle this problem within the framework of time series analysis. We used Dirichlet process mixture models to cluster time points with similar multipollutant and response profiles, while adjusting for seasonal cycles, trends and temporal components. Inference was carried out via Markov Chain Monte Carlo methods. We illustrated our approach using daily data of a range of particle metrics and respiratory mortality for London (UK) 2002-2005. To better quantify the average health impact of these particles, we measured the same set of metrics in 2012, and we computed and compared the posterior predictive distributions of mortality under the exposure scenario in 2012 vs 2005. The model resulted in a partition of the days into three clusters. We found a relative risk of 1.02 (95% credible intervals (CI): 1.00, 1.04) for respiratory mortality associated with days characterised by high posterior estimates of non-primary particles, especially nitrate and sulphate. We found a consistent reduction in the airborne particles in 2012 vs 2005 and the analysis of the posterior predictive distributions of respiratory mortality suggested an average annual decrease of -3.5% (95% CI: -0.12%, -5.74%). We proposed an effective approach that enabled the better understanding of hidden structures in multipollutant health effects within time series analysis. It allowed the identification of exposure metrics associated with respiratory mortality and provided a tool to assess the changes in health effects from various policies to control the ambient particle matter mixtures. Copyright © 2015. Published by Elsevier Ltd.

On the Hilbert-Huang Transform Theoretical Developments

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Blank, Karin; Flatley, Thomas; Huang, Norden E.; Patrick, David; Hestnes, Phyllis

2005-01-01

One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as linearity, of being stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposition data, the HHT allows spectrum analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a near orthogonal adaptive basis, a basis that is derived from the data. The IMFs can be further analyzed for spectrum interpretation by the classical Hilbert Transform. A new engineering spectrum analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications post additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs near orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the developments of new HHT processing options, such as real-time and 2-D processing using Field Programmable Array (FPGA) computational resources, enhanced HHT synthesis, and broaden the scope of HHT applications for signal processing.

On the Aharonov-Bohm Operators with Varying Poles: The Boundary Behavior of Eigenvalues

NASA Astrophysics Data System (ADS)

Noris, Benedetta; Nys, Manon; Terracini, Susanna

2015-11-01

We consider a magnetic Schrödinger operator with magnetic field concentrated at one point (the pole) of a domain and half integer circulation, and we focus on the behavior of Dirichlet eigenvalues as functions of the pole. Although the magnetic field vanishes almost everywhere, it is well known that it affects the operator at the spectral level (the Aharonov-Bohm effect, Phys Rev (2) 115:485-491, 1959). Moreover, the numerical computations performed in (Bonnaillie-Noël et al., Anal PDE 7(6):1365-1395, 2014; Noris and Terracini, Indiana Univ Math J 59(4):1361-1403, 2010) show a rather complex behavior of the eigenvalues as the pole varies in a planar domain. In this paper, in continuation of the analysis started in (Bonnaillie-Noël et al., Anal PDE 7(6):1365-1395, 2014; Noris and Terracini, Indiana Univ Math J 59(4):1361-1403, 2010), we analyze the relation between the variation of the eigenvalue and the nodal structure of the associated eigenfunctions. We deal with planar domains with Dirichlet boundary conditions and we focus on the case when the singular pole approaches the boundary of the domain: then, the operator loses its singular character and the k-th magnetic eigenvalue converges to that of the standard Laplacian. We can predict both the rate of convergence and whether the convergence happens from above or from below, in relation with the number of nodal lines of the k-th eigenfunction of the Laplacian. The proof relies on the variational characterization of eigenvalues, together with a detailed asymptotic analysis of the eigenfunctions, based on an Almgren-type frequency formula for magnetic eigenfunctions and on the blow-up technique.

Extant ape dental topography and its implications for reconstructing the emergence of early Homo.

PubMed

Berthaume, Michael A; Schroer, Kes

2017-11-01

Dental topography reflects diet accurately in several extant and extinct mammalian clades. However, dental topographic dietary reconstructions have high success rates only when closely related taxa are compared. Given the dietary breadth that exists among extant apes and likely existed among fossil hominins, dental topographic values from many species and subspecies of great apes are necessary for making dietary inferences about the hominin fossil record. Here, we present the results of one metric of dental topography, Dirichlet normal energy (DNE), for seven groups of great apes (Pongo pygmaeus pygmaeus, Pan paniscus, Pan troglodytes troglodytes and schweinfurthii, Gorilla gorilla gorilla, Gorilla beringei graueri and beringei). Dirichlet normal energy was inadequate at differentiating folivores from frugivores, but was adequate at predicting which groups had more fibrous diets among sympatric African apes. Character displacement analyses confirmed there is substantial dental topographic and relative molar size (M 1 :M 2 ratio; length, width, and area) divergence in sympatric apes when compared to their allopatric counterparts, but character displacement is only present in relative molar size when DNE is also considered. Presence of character displacement is likely due to indirect competition over similar food resources. Assuming similar ecological conditions in the Plio-Pleistocene, the derived masticatory apparatuses of the robust australopiths and early Homo may be due to indirect competition over dietary resources between the taxa, causing dietary niche partitioning. Our results imply that dental topography cannot be used to predict dietary categories in fossil hominins without consideration of ecological factors, such as dietary and geographic overlap. In addition, our results may open new avenues for understanding the community compositions of early hominins and the formation of specific ecological niches among hominin taxa. Copyright © 2017 Elsevier Ltd. All rights reserved.

Casimir effect due to a single boundary as a manifestation of the Weyl problem

NASA Astrophysics Data System (ADS)

Kolomeisky, Eugene B.; Straley, Joseph P.; Langsjoen, Luke S.; Zaidi, Hussain

2010-09-01

The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases, the divergences can be eliminated by methods such as zeta-function regularization or through physical arguments (ultraviolet transparency of the boundary would provide a cutoff). Using the example of a massless scalar field theory with a single Dirichlet boundary, we explore the relationship between such approaches, with the goal of better understanding of the origin of the divergences. We are guided by the insight due to Dowker and Kennedy (1978 J. Phys. A: Math. Gen. 11 895) and Deutsch and Candelas (1979 Phys. Rev. D 20 3063) that the divergences represent measurable effects that can be interpreted with the aid of the theory of the asymptotic distribution of eigenvalues of the Laplacian discussed by Weyl. In many cases, the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having a geometrical origin, and an 'intrinsic' term that is independent of the cutoff. The Weyl terms make a measurable contribution to the physical situation even when regularization methods succeed in isolating the intrinsic part. Regularization methods fail when the Weyl terms and intrinsic parts of the Casimir effect cannot be clearly separated. Specifically, we demonstrate that the Casimir self-energy of a smooth boundary in two dimensions is a sum of two Weyl terms (exhibiting quadratic and logarithmic cutoff dependence), a geometrical term that is independent of cutoff and a non-geometrical intrinsic term. As by-products, we resolve the puzzle of the divergent Casimir force on a ring and correct the sign of the coefficient of linear tension of the Dirichlet line predicted in earlier treatments.

Low- and high-order accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes

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

Silva, Goncalo, E-mail: goncalo.nuno.silva@gmail.com; Talon, Laurent, E-mail: talon@fast.u-psud.fr; Ginzburg, Irina, E-mail: irina.ginzburg@irstea.fr

The present contribution focuses on the accuracy of reflection-type boundary conditions in the Stokes–Brinkman–Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the two-relaxation-time (TRT) collision and the Brinkman-force based scheme (BF), called BF-TRT scheme. In parallel, we compare it with the Stokes–Brinkman–Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BF-TRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocity-proportional resistance force. This correction modifies themore » effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in lattice-aligned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the no-slip wall condition supported by traditional LBM boundary schemes, such as the bounce-back rule. For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition at an arbitrary wall/boundary-node distance and that supports a higher order accuracy in the accommodation of the TRT-Brinkman solutions. For their modeling, we consider the standard BF scheme and its improved version, called IBF; this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows. Our framework extends the one- and two-point families of linear and parabolic link-wise boundary schemes, respectively called B-LI and B-MLI, which avoid the interference of the Brinkman viscosity correction in their closure relations. The performance of LBM and FEM is thoroughly evaluated in three benchmark tests, which are run throughout three distinctive permeability regimes. The first configuration is a horizontal porous channel, studied with a symbolic approach, where we construct the exact solutions of FEM and BF/IBF with different boundary schemes. The second problem refers to an inclined porous channel flow, which brings in as new challenge the formation of spurious boundary layers in LBM; that is, numerical artefacts that arise due to a deficient accommodation of the bulk solution by the low-accurate boundary scheme. The third problem considers a porous flow past a periodic square array of solid cylinders, which intensifies the previous two tests with the simulation of a more complex flow pattern. The ensemble of numerical tests provides guidelines on the effect of grid resolution and the TRT free collision parameter over the accuracy and the quality of the velocity field, spanning from Stokes to Darcy permeability regimes. It is shown that, with the use of the high-order accurate boundary schemes, the simple, uniform-mesh-based TRT-LBM formulation can even surpass the accuracy of FEM employing hardworking body-fitted meshes.« less

Low- and high-order accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes

NASA Astrophysics Data System (ADS)

Silva, Goncalo; Talon, Laurent; Ginzburg, Irina

2017-04-01

The present contribution focuses on the accuracy of reflection-type boundary conditions in the Stokes-Brinkman-Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the two-relaxation-time (TRT) collision and the Brinkman-force based scheme (BF), called BF-TRT scheme. In parallel, we compare it with the Stokes-Brinkman-Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BF-TRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocity-proportional resistance force. This correction modifies the effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in lattice-aligned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the no-slip wall condition supported by traditional LBM boundary schemes, such as the bounce-back rule. For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition at an arbitrary wall/boundary-node distance and that supports a higher order accuracy in the accommodation of the TRT-Brinkman solutions. For their modeling, we consider the standard BF scheme and its improved version, called IBF; this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows. Our framework extends the one- and two-point families of linear and parabolic link-wise boundary schemes, respectively called B-LI and B-MLI, which avoid the interference of the Brinkman viscosity correction in their closure relations. The performance of LBM and FEM is thoroughly evaluated in three benchmark tests, which are run throughout three distinctive permeability regimes. The first configuration is a horizontal porous channel, studied with a symbolic approach, where we construct the exact solutions of FEM and BF/IBF with different boundary schemes. The second problem refers to an inclined porous channel flow, which brings in as new challenge the formation of spurious boundary layers in LBM; that is, numerical artefacts that arise due to a deficient accommodation of the bulk solution by the low-accurate boundary scheme. The third problem considers a porous flow past a periodic square array of solid cylinders, which intensifies the previous two tests with the simulation of a more complex flow pattern. The ensemble of numerical tests provides guidelines on the effect of grid resolution and the TRT free collision parameter over the accuracy and the quality of the velocity field, spanning from Stokes to Darcy permeability regimes. It is shown that, with the use of the high-order accurate boundary schemes, the simple, uniform-mesh-based TRT-LBM formulation can even surpass the accuracy of FEM employing hardworking body-fitted meshes.

Discovering temporal patterns in water quality time series, focusing on floods with the LDA method

NASA Astrophysics Data System (ADS)

Hélène Aubert, Alice; Tavenard, Romain; Emonet, Rémi; Malinowski, Simon; Guyet, Thomas; Quiniou, René; Odobez, Jean-Marc; Gascuel-Odoux, Chantal

2013-04-01

Studying floods has been a major issue in hydrological research for years. It is often done in terms of water quantity but it is also of interest in terms of water quality. Stream chemistry is a mix of solutes. They originate from various sources in the catchment, reach the stream by various flow pathways and are transformed by biogeochemical reactions at different locations. Therefore, we hypothesized that reaction of the stream chemistry to a rainfall event is not unique but varies according to the season (1), and the global meteorological conditions of the year (2). Identifying a typology of temporal chemical patterns of reaction to a rainfall event is a way to better understand catchment processes at the flood time scale. To answer this issue, we applied a probabilistic model (Latent Dirichlet Allocation or LDA (3)) mining recurrent sequential patterns to a dataset of floods. The dataset is 12 years long and daily recorded. It gathers a broad range of parameters from which we selected rainfall, discharge, water table depth, temperature as well as nitrate, dissolved organic carbon, sulphate and chloride concentrations. It comes from a long-term hydrological observatory (AgrHys, western France) located at Kervidy-Naizin. A set of 472 floods was automatically extracted (4). From each flood, a document has been generated that is made of a set of "hydrological words". Each hydrological word corresponds to a measurement: it is a triplet made of the considered variable, the time at which the measurement is made (relative to the beginning of the flood), and its magnitude (that can be low, medium or high). The documents are used as input data to the LDA algorithm. LDA relies on spotting co-occurrences (as an alternative to the more traditional study of correlation) between words that appear within the flood documents. It has two nice properties that are its ability to easily deal with missing data and its additive property that allows a document to be seen as a mixture of several flood patterns. The output of LDA is a set of patterns that can easily be represented in graphics. These patterns correspond to typical reactions to rainfall events. The patterns themselves are carefully studied, as well as their repartition along the year and along the 12 years of the dataset. The novelties are fourfold. First, as a methodological point of view, we learn that hydrological data can be analyzed with this LDA model giving a typology of a multivariate chemical signature of floods. Second, we outline that chemistry parameters are sufficient to obtain meaningful patterns. There is no need to include hydro-meteorological parameters to define the patterns. However, hydro-meteorological parameters are useful to understand the processes leading to these patterns. Third, our hypothesis of seasonal specific reaction to rainfall is verified, moreover detailed; so is our hypothesis of different reactions to rainfall for years with different hydro-meteorological conditions. Fourth, this method allows the consideration of overlapping floods that are usually not studied. We would recommend the use of such model to study chemical reactions of stream after rainfall events, or more broadly after any hydrological events. The typology that has been provided by this method is a kind of bar code of water chemistry during floods. It could be well suited to compare different geographical locations by using the same patterns and analysing the resulting different pattern distributions. (1) Aubert, A.H. et al., 2012. The chemical signature of a livestock farming catchment: synthesis from a high-frequency multi-element long term monitoring. HESSD, 9(8): 9715 - 9741. (2) Aubert, A.H., Gascuel-Odoux, C., Merot, P., 2013. Annual hysteresis of water quality: A method to analyse the effect of intra- and inter-annual climatic conditions. Journal of Hydrology, 478(0): 29-39. (3) Blei, D. M.; Ng, A. Y.; Jordan, M. I., 2003. Latent Dirichlet allocation. Journal of Machine Learning Research, 3(4-5): 993-1022. (4) de Lavenne, A., Cudennec, C., Streamflow velocity estimation in GIUH-type approach: what can neighbouring basins tell us? Poster Presentation - EGU General Assembly, 22-27 April 2012, Vienna, Austria.

On Certain Theoretical Developments Underlying the Hilbert-Huang Transform

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Blank, Karin; Flatley, Thomas; Huang, Norden E.; Petrick, David; Hestness, Phyllis

2006-01-01

One of the main traditional tools used in scientific and engineering data spectral analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as being linear and stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectral analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposed data, the HHT allows spectral analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real-value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a nearly orthogonal derived from the data (adaptive) basis. The IMFs can be further analyzed for spectrum content by using the classical Hilbert Transform. A new engineering spectral analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications pose additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs nearly orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the development of new HHT processing options, such as real-time and 2-D processing using Field Programmable Gate Array (FPGA) computational resources,

Identifying Topics in Microblogs Using Wikipedia.

PubMed

Yıldırım, Ahmet; Üsküdarlı, Suzan; Özgür, Arzucan

2016-01-01

Twitter is an extremely high volume platform for user generated contributions regarding any topic. The wealth of content created at real-time in massive quantities calls for automated approaches to identify the topics of the contributions. Such topics can be utilized in numerous ways, such as public opinion mining, marketing, entertainment, and disaster management. Towards this end, approaches to relate single or partial posts to knowledge base items have been proposed. However, in microblogging systems like Twitter, topics emerge from the culmination of a large number of contributions. Therefore, identifying topics based on collections of posts, where individual posts contribute to some aspect of the greater topic is necessary. Models, such as Latent Dirichlet Allocation (LDA), propose algorithms for relating collections of posts to sets of keywords that represent underlying topics. In these approaches, figuring out what the specific topic(s) the keyword sets represent remains as a separate task. Another issue in topic detection is the scope, which is often limited to specific domain, such as health. This work proposes an approach for identifying domain-independent specific topics related to sets of posts. In this approach, individual posts are processed and then aggregated to identify key tokens, which are then mapped to specific topics. Wikipedia article titles are selected to represent topics, since they are up to date, user-generated, sophisticated articles that span topics of human interest. This paper describes the proposed approach, a prototype implementation, and a case study based on data gathered during the heavily contributed periods corresponding to the four US election debates in 2012. The manually evaluated results (0.96 precision) and other observations from the study are discussed in detail.

Identifying Topics in Microblogs Using Wikipedia

PubMed Central

Yıldırım, Ahmet; Üsküdarlı, Suzan; Özgür, Arzucan

2016-01-01

Twitter is an extremely high volume platform for user generated contributions regarding any topic. The wealth of content created at real-time in massive quantities calls for automated approaches to identify the topics of the contributions. Such topics can be utilized in numerous ways, such as public opinion mining, marketing, entertainment, and disaster management. Towards this end, approaches to relate single or partial posts to knowledge base items have been proposed. However, in microblogging systems like Twitter, topics emerge from the culmination of a large number of contributions. Therefore, identifying topics based on collections of posts, where individual posts contribute to some aspect of the greater topic is necessary. Models, such as Latent Dirichlet Allocation (LDA), propose algorithms for relating collections of posts to sets of keywords that represent underlying topics. In these approaches, figuring out what the specific topic(s) the keyword sets represent remains as a separate task. Another issue in topic detection is the scope, which is often limited to specific domain, such as health. This work proposes an approach for identifying domain-independent specific topics related to sets of posts. In this approach, individual posts are processed and then aggregated to identify key tokens, which are then mapped to specific topics. Wikipedia article titles are selected to represent topics, since they are up to date, user-generated, sophisticated articles that span topics of human interest. This paper describes the proposed approach, a prototype implementation, and a case study based on data gathered during the heavily contributed periods corresponding to the four US election debates in 2012. The manually evaluated results (0.96 precision) and other observations from the study are discussed in detail. PMID:26991442

Estimation from incomplete multinomial data. Ph.D. Thesis - Harvard Univ.

NASA Technical Reports Server (NTRS)

Credeur, K. R.

1978-01-01

The vector of multinomial cell probabilities was estimated from incomplete data, incomplete in that it contains partially classified observations. Each such partially classified observation was observed to fall in one of two or more selected categories but was not classified further into a single category. The data were assumed to be incomplete at random. The estimation criterion was minimization of risk for quadratic loss. The estimators were the classical maximum likelihood estimate, the Bayesian posterior mode, and the posterior mean. An approximation was developed for the posterior mean. The Dirichlet, the conjugate prior for the multinomial distribution, was assumed for the prior distribution.

Improved definition of crustal magnetic anomalies for MAGSAT data

NASA Technical Reports Server (NTRS)

Brown, R. D.; Frawley, J. F.; Davis, W. M.; Ray, R. D.; Didwall, E.; Regan, R. D. (Principal Investigator)

1982-01-01

The routine correction of MAGSAT vector magnetometer data for external field effects such as the ring current and the daily variation by filtering long wavelength harmonics from the data is described. Separation of fields due to low altitude sources from those caused by high altitude sources is affected by means of dual harmonic expansions in the solution of Dirichlet's problem. This regression/harmonic filter procedure is applied on an orbit by orbit basis, and initial tests on MAGSAT data from orbit 1176 show reduction in external field residuals by 24.33 nT RMS in the horizontal component, and 10.95 nT RMS in the radial component.

Repulsive Casimir force in Bose–Einstein Condensate

NASA Astrophysics Data System (ADS)

Mehedi Faruk, Mir; Biswas, Shovon

2018-04-01

We study the Casimir effect for a three dimensional system of ideal free massive Bose gas in a slab geometry with Zaremba and anti-periodic boundary conditions. It is found that for these type of boundary conditions the resulting Casimir force is repulsive in nature, in contrast with usual periodic, Dirichlet or Neumann boundary condition where the Casimir force is attractive (Martin and Zagrebnov 2006 Europhys. Lett. 73 15). Casimir forces in these boundary conditions also maintain a power law decay function below condensation temperature and exponential decay function above the condensation temperature albeit with a positive sign, identifying the repulsive nature of the force.

A Duality Theory for Non-convex Problems in the Calculus of Variations

NASA Astrophysics Data System (ADS)

Bouchitté, Guy; Fragalà, Ilaria

2018-07-01

We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no duality gap. Further, we provide necessary and sufficient optimality conditions, and we show that our duality principle can be reformulated as a min-max result which is quite useful for numerical implementations. As an example, we illustrate the application of our method to a celebrated free boundary problem. The results were announced in Bouchitté and Fragalà (C R Math Acad Sci Paris 353(4):375-379, 2015).

Hilbert complexes of nonlinear elasticity

NASA Astrophysics Data System (ADS)

Angoshtari, Arzhang; Yavari, Arash

2016-12-01

We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.

Interaction of a conductive crack and of an electrode at a piezoelectric bimaterial interface

NASA Astrophysics Data System (ADS)

Onopriienko, Oleg; Loboda, Volodymyr; Sheveleva, Alla; Lapusta, Yuri

2018-06-01

The interaction of a conductive crack and an electrode at a piezoelectric bi-material interface is studied. The bimaterial is subjected to an in-plane electrical field parallel to the interface and an anti-plane mechanical loading. The problem is formulated and reduced, via the application of sectionally analytic vector functions, to a combined Dirichlet-Riemann boundary value problem. Simple analytical expressions for the stress, the electric field, and their intensity factors as well as for the crack faces' displacement jump are derived. Our numerical results illustrate the proposed approach and permit to draw some conclusions on the crack-electrode interaction.

Acoustic response of a rectangular levitator with orifices

NASA Technical Reports Server (NTRS)

El-Raheb, Michael; Wagner, Paul

1990-01-01

The acoustic response of a rectangular cavity to speaker-generated excitation through waveguides terminating at orifices in the cavity walls is analyzed. To find the effects of orifices, acoustic pressure is expressed by eigenfunctions satisfying Neumann boundary conditions as well as by those satisfying Dirichlet ones. Some of the excess unknowns can be eliminated by point constraints set over the boundary, by appeal to Lagrange undetermined multipliers. The resulting transfer matrix must be further reduced by partial condensation to the order of a matrix describing unmixed boundary conditions. If the cavity is subjected to an axial temperature dependence, the transfer matrix is determined numerically.

The Kirkwood{endash}Buckingham variational method and the boundary value problems for the molecular Schr{umlt o}dinger equation

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

Pupyshev, V.I.; Scherbinin, A.V.; Stepanov, N.F.

1997-11-01

The approach based on the multiplicative form of a trial wave function within the framework of the variational method, initially proposed by Kirkwood and Buckingham, is shown to be an effective analytical tool in the quantum mechanical study of atoms and molecules. As an example, the elementary proof is given to the fact that the ground state energy of a molecular system placed into the box with walls of finite height goes to the corresponding eigenvalue of the Dirichlet boundary value problem when the height of the walls is growing up to infinity. {copyright} {ital 1997 American Institute of Physics.}

The Calderón problem with corrupted data

NASA Astrophysics Data System (ADS)

Caro, Pedro; Garcia, Andoni

2017-08-01

We consider the inverse Calderón problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, one usually assumes the data to be given by such a map. This situation corresponds to having access to infinite-precision measurements, which is totally unrealistic. In this paper, we study the Calderón problem assuming the data to contain measurement errors and provide formulas to reconstruct the conductivity and its normal derivative on the surface. Additionally, we state the rate convergence of the method. Our approach is theoretical and has a stochastic flavour.

A Duality Theory for Non-convex Problems in the Calculus of Variations

NASA Astrophysics Data System (ADS)

Bouchitté, Guy; Fragalà, Ilaria

2018-02-01

We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no duality gap. Further, we provide necessary and sufficient optimality conditions, and we show that our duality principle can be reformulated as a min-max result which is quite useful for numerical implementations. As an example, we illustrate the application of our method to a celebrated free boundary problem. The results were announced in Bouchitté and Fragalà (C R Math Acad Sci Paris 353(4):375-379, 2015).

What Makes You Tick? An Empirical Study of Space Science Related Social Media Communications Using Machine Learning

NASA Astrophysics Data System (ADS)

Hwong, Y. L.; Oliver, C.; Van Kranendonk, M. J.

2016-12-01

The rise of social media has transformed the way the public engages with scientists and science organisations. `Retweet', `Like', `Share' and `Comment' are a few ways users engage with messages on Twitter and Facebook, two of the most popular social media platforms. Despite the availability of big data from these digital footprints, research into social media science communication is scant. This paper presents the results of an empirical study into the processes and outcomes of space science related social media communications using machine learning. The study is divided into two main parts. The first part is dedicated to the use of supervised learning methods to investigate the features of highly engaging messages., e.g. highly retweeted tweets and shared Facebook posts. It is hypothesised that these messages contain certain psycholinguistic features that are unique to the field of space science. We built a predictive model to forecast the engagement levels of social media posts. By using four feature sets (n-grams, psycholinguistics, grammar and social media), we were able to achieve prediction accuracies in the vicinity of 90% using three supervised learning algorithms (Naive Bayes, linear classifier and decision tree). We conducted the same experiments on social media messages from three other fields (politics, business and non-profit) and discovered several features that are exclusive to space science communications: anger, authenticity, hashtags, visual descriptions and a tentative tone. The second part of the study focuses on the extraction of topics from a corpus of texts using topic modelling. This part of the study is exploratory in nature and uses an unsupervised method called Latent Dirichlet Allocation (LDA) to uncover previously unknown topics within a large body of documents. Preliminary results indicate a strong potential of topic model algorithms to automatically uncover themes hidden within social media chatters on space related issues, with keywords such as `exoplanet', `water' and `life' being clustered together forming a topic (i.e. 'Astrobiology'). Results also demonstrate the freewheeling nature of social media conversations, while providing evidence for the role of these platforms in facilitating meaningful exchanges among science audience.

Rapid processing of data based on high-performance algorithms for solving inverse problems and 3D-simulation of the tsunami and earthquakes

NASA Astrophysics Data System (ADS)

Marinin, I. V.; Kabanikhin, S. I.; Krivorotko, O. I.; Karas, A.; Khidasheli, D. G.

2012-04-01

We consider new techniques and methods for earthquake and tsunami related problems, particularly - inverse problems for the determination of tsunami source parameters, numerical simulation of long wave propagation in soil and water and tsunami risk estimations. In addition, we will touch upon the issue of database management and destruction scenario visualization. New approaches and strategies, as well as mathematical tools and software are to be shown. The long joint investigations by researchers of the Institute of Mathematical Geophysics and Computational Mathematics SB RAS and specialists from WAPMERR and Informap have produced special theoretical approaches, numerical methods, and software tsunami and earthquake modeling (modeling of propagation and run-up of tsunami waves on coastal areas), visualization, risk estimation of tsunami, and earthquakes. Algorithms are developed for the operational definition of the origin and forms of the tsunami source. The system TSS numerically simulates the source of tsunami and/or earthquakes and includes the possibility to solve the direct and the inverse problem. It becomes possible to involve advanced mathematical results to improve models and to increase the resolution of inverse problems. Via TSS one can construct maps of risks, the online scenario of disasters, estimation of potential damage to buildings and roads. One of the main tools for the numerical modeling is the finite volume method (FVM), which allows us to achieve stability with respect to possible input errors, as well as to achieve optimum computing speed. Our approach to the inverse problem of tsunami and earthquake determination is based on recent theoretical results concerning the Dirichlet problem for the wave equation. This problem is intrinsically ill-posed. We use the optimization approach to solve this problem and SVD-analysis to estimate the degree of ill-posedness and to find the quasi-solution. The software system we developed is intended to create technology «no frost», realizing a steady stream of direct and inverse problems: solving the direct problem, the visualization and comparison with observed data, to solve the inverse problem (correction of the model parameters). The main objective of further work is the creation of a workstation operating emergency tool that could be used by an emergency duty person in real time.

Probabilistic topic modeling for the analysis and classification of genomic sequences

PubMed Central

2015-01-01

Background Studies on genomic sequences for classification and taxonomic identification have a leading role in the biomedical field and in the analysis of biodiversity. These studies are focusing on the so-called barcode genes, representing a well defined region of the whole genome. Recently, alignment-free techniques are gaining more importance because they are able to overcome the drawbacks of sequence alignment techniques. In this paper a new alignment-free method for DNA sequences clustering and classification is proposed. The method is based on k-mers representation and text mining techniques. Methods The presented method is based on Probabilistic Topic Modeling, a statistical technique originally proposed for text documents. Probabilistic topic models are able to find in a document corpus the topics (recurrent themes) characterizing classes of documents. This technique, applied on DNA sequences representing the documents, exploits the frequency of fixed-length k-mers and builds a generative model for a training group of sequences. This generative model, obtained through the Latent Dirichlet Allocation (LDA) algorithm, is then used to classify a large set of genomic sequences. Results and conclusions We performed classification of over 7000 16S DNA barcode sequences taken from Ribosomal Database Project (RDP) repository, training probabilistic topic models. The proposed method is compared to the RDP tool and Support Vector Machine (SVM) classification algorithm in a extensive set of trials using both complete sequences and short sequence snippets (from 400 bp to 25 bp). Our method reaches very similar results to RDP classifier and SVM for complete sequences. The most interesting results are obtained when short sequence snippets are considered. In these conditions the proposed method outperforms RDP and SVM with ultra short sequences and it exhibits a smooth decrease of performance, at every taxonomic level, when the sequence length is decreased. PMID:25916734

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

Wilson, Andrew T.; Robinson, David Gerald

Most topic modeling algorithms that address the evolution of documents over time use the same number of topics at all times. This obscures the common occurrence in the data where new subjects arise and old ones diminish or disappear entirely. We propose an algorithm to model the birth and death of topics within an LDA-like framework. The user selects an initial number of topics, after which new topics are created and retired without further supervision. Our approach also accommodates many of the acceleration and parallelization schemes developed in recent years for standard LDA. In recent years, topic modeling algorithms suchmore » as latent semantic analysis (LSA)[17], latent Dirichlet allocation (LDA)[10] and their descendants have offered a powerful way to explore and interrogate corpora far too large for any human to grasp without assistance. Using such algorithms we are able to search for similar documents, model and track the volume of topics over time, search for correlated topics or model them with a hierarchy. Most of these algorithms are intended for use with static corpora where the number of documents and the size of the vocabulary are known in advance. Moreover, almost all current topic modeling algorithms fix the number of topics as one of the input parameters and keep it fixed across the entire corpus. While this is appropriate for static corpora, it becomes a serious handicap when analyzing time-varying data sets where topics come and go as a matter of course. This is doubly true for online algorithms that may not have the option of revising earlier results in light of new data. To be sure, these algorithms will account for changing data one way or another, but without the ability to adapt to structural changes such as entirely new topics they may do so in counterintuitive ways.« less

Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer

NASA Astrophysics Data System (ADS)

Huang, C.-S.; Yang, S.-Y.; Yeh, H.-D.

2015-06-01

An aquifer consisting of a skin zone and a formation zone is considered as a two-zone aquifer. Existing solutions for the problem of constant-flux pumping in a two-zone confined aquifer involve laborious calculation. This study develops a new approximate solution for the problem based on a mathematical model describing steady-state radial and vertical flows in a two-zone aquifer. Hydraulic parameters in these two zones can be different but are assumed homogeneous in each zone. A partially penetrating well may be treated as the Neumann condition with a known flux along the screened part and zero flux along the unscreened part. The aquifer domain is finite with an outer circle boundary treated as the Dirichlet condition. The steady-state drawdown solution of the model is derived by the finite Fourier cosine transform. Then, an approximate transient solution is developed by replacing the radius of the aquifer domain in the steady-state solution with an analytical expression for a dimensionless time-dependent radius of influence. The approximate solution is capable of predicting good temporal drawdown distributions over the whole pumping period except at the early stage. A quantitative criterion for the validity of neglecting the vertical flow due to a partially penetrating well is also provided. Conventional models considering radial flow without the vertical component for the constant-flux pumping have good accuracy if satisfying the criterion.

SPOTting model parameters using a ready-made Python package

NASA Astrophysics Data System (ADS)

Houska, Tobias; Kraft, Philipp; Breuer, Lutz

2015-04-01

The selection and parameterization of reliable process descriptions in ecological modelling is driven by several uncertainties. The procedure is highly dependent on various criteria, like the used algorithm, the likelihood function selected and the definition of the prior parameter distributions. A wide variety of tools have been developed in the past decades to optimize parameters. Some of the tools are closed source. Due to this, the choice for a specific parameter estimation method is sometimes more dependent on its availability than the performance. A toolbox with a large set of methods can support users in deciding about the most suitable method. Further, it enables to test and compare different methods. We developed the SPOT (Statistical Parameter Optimization Tool), an open source python package containing a comprehensive set of modules, to analyze and optimize parameters of (environmental) models. SPOT comes along with a selected set of algorithms for parameter optimization and uncertainty analyses (Monte Carlo, MC; Latin Hypercube Sampling, LHS; Maximum Likelihood, MLE; Markov Chain Monte Carlo, MCMC; Scuffled Complex Evolution, SCE-UA; Differential Evolution Markov Chain, DE-MCZ), together with several likelihood functions (Bias, (log-) Nash-Sutcliff model efficiency, Correlation Coefficient, Coefficient of Determination, Covariance, (Decomposed-, Relative-, Root-) Mean Squared Error, Mean Absolute Error, Agreement Index) and prior distributions (Binomial, Chi-Square, Dirichlet, Exponential, Laplace, (log-, multivariate-) Normal, Pareto, Poisson, Cauchy, Uniform, Weibull) to sample from. The model-independent structure makes it suitable to analyze a wide range of applications. We apply all algorithms of the SPOT package in three different case studies. Firstly, we investigate the response of the Rosenbrock function, where the MLE algorithm shows its strengths. Secondly, we study the Griewank function, which has a challenging response surface for optimization methods. Here we see simple algorithms like the MCMC struggling to find the global optimum of the function, while algorithms like SCE-UA and DE-MCZ show their strengths. Thirdly, we apply an uncertainty analysis of a one-dimensional physically based hydrological model build with the Catchment Modelling Framework (CMF). The model is driven by meteorological and groundwater data from a Free Air Carbon Enrichment (FACE) experiment in Linden (Hesse, Germany). Simulation results are evaluated with measured soil moisture data. We search for optimal parameter sets of the van Genuchten-Mualem function and find different equally optimal solutions with some of the algorithms. The case studies reveal that the implemented SPOT methods work sufficiently well. They further show the benefit of having one tool at hand that includes a number of parameter search methods, likelihood functions and a priori parameter distributions within one platform independent package.

A methodology for constraining power in finite element modeling of radiofrequency ablation.

PubMed

Jiang, Yansheng; Possebon, Ricardo; Mulier, Stefaan; Wang, Chong; Chen, Feng; Feng, Yuanbo; Xia, Qian; Liu, Yewei; Yin, Ting; Oyen, Raymond; Ni, Yicheng

2017-07-01

Radiofrequency ablation (RFA) is a minimally invasive thermal therapy for the treatment of cancer, hyperopia, and cardiac tachyarrhythmia. In RFA, the power delivered to the tissue is a key parameter. The objective of this study was to establish a methodology for the finite element modeling of RFA with constant power. Because of changes in the electric conductivity of tissue with temperature, a nonconventional boundary value problem arises in the mathematic modeling of RFA: neither the voltage (Dirichlet condition) nor the current (Neumann condition), but the power, that is, the product of voltage and current was prescribed on part of boundary. We solved the problem using Lagrange multiplier: the product of the voltage and current on the electrode surface is constrained to be equal to the Joule heating. We theoretically proved the equality between the product of the voltage and current on the surface of the electrode and the Joule heating in the domain. We also proved the well-posedness of the problem of solving the Laplace equation for the electric potential under a constant power constraint prescribed on the electrode surface. The Pennes bioheat transfer equation and the Laplace equation for electric potential augmented with the constraint of constant power were solved simultaneously using the Newton-Raphson algorithm. Three problems for validation were solved. Numerical results were compared either with an analytical solution deduced in this study or with results obtained by ANSYS or experiments. This work provides the finite element modeling of constant power RFA with a firm mathematical basis and opens pathway for achieving the optimal RFA power. Copyright © 2016 John Wiley & Sons, Ltd.

Electroneutral models for dynamic Poisson-Nernst-Planck systems

NASA Astrophysics Data System (ADS)

Song, Zilong; Cao, Xiulei; Huang, Huaxiong

2018-01-01

The Poisson-Nernst-Planck (PNP) system is a standard model for describing ion transport. In many applications, e.g., ions in biological tissues, the presence of thin boundary layers poses both modeling and computational challenges. In this paper, we derive simplified electroneutral (EN) models where the thin boundary layers are replaced by effective boundary conditions. There are two major advantages of EN models. First, it is much cheaper to solve them numerically. Second, EN models are easier to deal with compared to the original PNP system; therefore, it would also be easier to derive macroscopic models for cellular structures using EN models. Even though the approach used here is applicable to higher-dimensional cases, this paper mainly focuses on the one-dimensional system, including the general multi-ion case. Using systematic asymptotic analysis, we derive a variety of effective boundary conditions directly applicable to the EN system for the bulk region. This EN system can be solved directly and efficiently without computing the solution in the boundary layer. The derivation is based on matched asymptotics, and the key idea is to bring back higher-order contributions into the effective boundary conditions. For Dirichlet boundary conditions, the higher-order terms can be neglected and the classical results (continuity of electrochemical potential) are recovered. For flux boundary conditions, higher-order terms account for the accumulation of ions in boundary layer and neglecting them leads to physically incorrect solutions. To validate the EN model, numerical computations are carried out for several examples. Our results show that solving the EN model is much more efficient than the original PNP system. Implemented with the Hodgkin-Huxley model, the computational time for solving the EN model is significantly reduced without sacrificing the accuracy of the solution due to the fact that it allows for relatively large mesh and time-step sizes.

LDA boost classification: boosting by topics

NASA Astrophysics Data System (ADS)

Lei, La; Qiao, Guo; Qimin, Cao; Qitao, Li

2012-12-01

AdaBoost is an efficacious classification algorithm especially in text categorization (TC) tasks. The methodology of setting up a classifier committee and voting on the documents for classification can achieve high categorization precision. However, traditional Vector Space Model can easily lead to the curse of dimensionality and feature sparsity problems; so it affects classification performance seriously. This article proposed a novel classification algorithm called LDABoost based on boosting ideology which uses Latent Dirichlet Allocation (LDA) to modeling the feature space. Instead of using words or phrase, LDABoost use latent topics as the features. In this way, the feature dimension is significantly reduced. Improved Naïve Bayes (NB) is designed as the weaker classifier which keeps the efficiency advantage of classic NB algorithm and has higher precision. Moreover, a two-stage iterative weighted method called Cute Integration in this article is proposed for improving the accuracy by integrating weak classifiers into strong classifier in a more rational way. Mutual Information is used as metrics of weights allocation. The voting information and the categorization decision made by basis classifiers are fully utilized for generating the strong classifier. Experimental results reveals LDABoost making categorization in a low-dimensional space, it has higher accuracy than traditional AdaBoost algorithms and many other classic classification algorithms. Moreover, its runtime consumption is lower than different versions of AdaBoost, TC algorithms based on support vector machine and Neural Networks.

Recommending Education Materials for Diabetic Questions Using Information Retrieval Approaches.

PubMed

Zeng, Yuqun; Liu, Xusheng; Wang, Yanshan; Shen, Feichen; Liu, Sijia; Rastegar-Mojarad, Majid; Wang, Liwei; Liu, Hongfang

2017-10-16

Self-management is crucial to diabetes care and providing expert-vetted content for answering patients' questions is crucial in facilitating patient self-management. The aim is to investigate the use of information retrieval techniques in recommending patient education materials for diabetic questions of patients. We compared two retrieval algorithms, one based on Latent Dirichlet Allocation topic modeling (topic modeling-based model) and one based on semantic group (semantic group-based model), with the baseline retrieval models, vector space model (VSM), in recommending diabetic patient education materials to diabetic questions posted on the TuDiabetes forum. The evaluation was based on a gold standard dataset consisting of 50 randomly selected diabetic questions where the relevancy of diabetic education materials to the questions was manually assigned by two experts. The performance was assessed using precision of top-ranked documents. We retrieved 7510 diabetic questions on the forum and 144 diabetic patient educational materials from the patient education database at Mayo Clinic. The mapping rate of words in each corpus mapped to the Unified Medical Language System (UMLS) was significantly different (P<.001). The topic modeling-based model outperformed the other retrieval algorithms. For example, for the top-retrieved document, the precision of the topic modeling-based, semantic group-based, and VSM models was 67.0%, 62.8%, and 54.3%, respectively. This study demonstrated that topic modeling can mitigate the vocabulary difference and it achieved the best performance in recommending education materials for answering patients' questions. One direction for future work is to assess the generalizability of our findings and to extend our study to other disease areas, other patient education material resources, and online forums. ©Yuqun Zeng, Xusheng Liu, Yanshan Wang, Feichen Shen, Sijia Liu, Majid Rastegar Mojarad, Liwei Wang, Hongfang Liu. Originally published in the Journal of Medical Internet Research (http://www.jmir.org), 16.10.2017.

Utility-based designs for randomized comparative trials with categorical outcomes

PubMed Central

Murray, Thomas A.; Thall, Peter F.; Yuan, Ying

2016-01-01

A general utility-based testing methodology for design and conduct of randomized comparative clinical trials with categorical outcomes is presented. Numerical utilities of all elementary events are elicited to quantify their desirabilities. These numerical values are used to map the categorical outcome probability vector of each treatment to a mean utility, which is used as a one-dimensional criterion for constructing comparative tests. Bayesian tests are presented, including fixed sample and group sequential procedures, assuming Dirichlet-multinomial models for the priors and likelihoods. Guidelines are provided for establishing priors, eliciting utilities, and specifying hypotheses. Efficient posterior computation is discussed, and algorithms are provided for jointly calibrating test cutoffs and sample size to control overall type I error and achieve specified power. Asymptotic approximations for the power curve are used to initialize the algorithms. The methodology is applied to re-design a completed trial that compared two chemotherapy regimens for chronic lymphocytic leukemia, in which an ordinal efficacy outcome was dichotomized and toxicity was ignored to construct the trial’s design. The Bayesian tests also are illustrated by several types of categorical outcomes arising in common clinical settings. Freely available computer software for implementation is provided. PMID:27189672

Explicit error bounds for the α-quasi-periodic Helmholtz problem.

PubMed

Lord, Natacha H; Mulholland, Anthony J

2013-10-01

This paper considers a finite element approach to modeling electromagnetic waves in a periodic diffraction grating. In particular, an a priori error estimate associated with the α-quasi-periodic transformation is derived. This involves the solution of the associated Helmholtz problem being written as a product of e(iαx) and an unknown function called the α-quasi-periodic solution. To begin with, the well-posedness of the continuous problem is examined using a variational formulation. The problem is then discretized, and a rigorous a priori error estimate, which guarantees the uniqueness of this approximate solution, is derived. In previous studies, the continuity of the Dirichlet-to-Neumann map has simply been assumed and the dependency of the regularity constant on the system parameters, such as the wavenumber, has not been shown. To address this deficiency, in this paper an explicit dependence on the wavenumber and the degree of the polynomial basis in the a priori error estimate is obtained. Since the finite element method is well known for dealing with any geometries, comparison of numerical results obtained using the α-quasi-periodic transformation with a lattice sum technique is then presented.

Hello, Who is Calling?: Can Words Reveal the Social Nature of Conversations?

PubMed

Stark, Anthony; Shafran, Izhak; Kaye, Jeffrey

2012-01-01

This study aims to infer the social nature of conversations from their content automatically. To place this work in context, our motivation stems from the need to understand how social disengagement affects cognitive decline or depression among older adults. For this purpose, we collected a comprehensive and naturalistic corpus comprising of all the incoming and outgoing telephone calls from 10 subjects over the duration of a year. As a first step, we learned a binary classifier to filter out business related conversation, achieving an accuracy of about 85%. This classification task provides a convenient tool to probe the nature of telephone conversations. We evaluated the utility of openings and closing in differentiating personal calls, and find that empirical results on a large corpus do not support the hypotheses by Schegloff and Sacks that personal conversations are marked by unique closing structures. For classifying different types of social relationships such as family vs other, we investigated features related to language use (entropy), hand-crafted dictionary (LIWC) and topics learned using unsupervised latent Dirichlet models (LDA). Our results show that the posteriors over topics from LDA provide consistently higher accuracy (60-81%) compared to LIWC or language use features in distinguishing different types of conversations.

Airframe Noise Prediction by Acoustic Analogy: Revisited

NASA Technical Reports Server (NTRS)

Farassat, F.; Casper, Jay H.; Tinetti, A.; Dunn, M. H.

2006-01-01

The present work follows a recent survey of airframe noise prediction methodologies. In that survey, Lighthill s acoustic analogy was identified as the most prominent analytical basis for current approaches to airframe noise research. Within this approach, a problem is typically modeled with the Ffowcs Williams and Hawkings (FW-H) equation, for which a geometry-independent solution is obtained by means of the use of the free-space Green function (FSGF). Nonetheless, the aeroacoustic literature would suggest some interest in the use of tailored or exact Green s function (EGF) for aerodynamic noise problems involving solid boundaries, in particular, for trailing edge (TE) noise. A study of possible applications of EGF for prediction of broadband noise from turbulent flow over an airfoil surface and the TE is, therefore, the primary topic of the present work. Typically, the applications of EGF in the literature have been limited to TE noise prediction at low Mach numbers assuming that the normal derivative of the pressure vanishes on the airfoil surface. To extend the application of EGF to higher Mach numbers, the uniqueness of the solution of the wave equation when either the Dirichlet or the Neumann boundary condition (BC) is specified on a deformable surface in motion. The solution of Lighthill s equation with either the Dirichlet or the Neumann BC is given for such a surface using EGFs. These solutions involve both surface and volume integrals just like the solution of FW-H equation using FSGF. Insight drawn from this analysis is evoked to discuss the potential application of EGF to broadband noise prediction. It appears that the use of a EGF offers distinct advantages for predicting TE noise of an airfoil when the normal pressure gradient vanishes on the airfoil surface. It is argued that such an approach may also apply to an airfoil in motion. However, for the prediction of broadband noise not directly associated with a trailing edge, the use of EGF does not appear to offer any advantages over the use of FSGF at the present stage of development. It is suggested here that the applications of EGF for airframe noise analysis be continued. As an example pertinent to airframe noise prediction, the Fast Scattering Code of NASA Langley is utilized to obtain the EGF numerically on the surface of a three dimensional wing with a flap and leading edge slat in uniform rectilinear motion. The interpretation and use of these numerical Green functions are then discussed.

Development of the FHR advanced natural circulation analysis code and application to FHR safety analysis

DOE PAGES

Guo, Z.; Zweibaum, N.; Shao, M.; ...

2016-04-19

The University of California, Berkeley (UCB) is performing thermal hydraulics safety analysis to develop the technical basis for design and licensing of fluoride-salt-cooled, high-temperature reactors (FHRs). FHR designs investigated by UCB use natural circulation for emergency, passive decay heat removal when normal decay heat removal systems fail. The FHR advanced natural circulation analysis (FANCY) code has been developed for assessment of passive decay heat removal capability and safety analysis of these innovative system designs. The FANCY code uses a one-dimensional, semi-implicit scheme to solve for pressure-linked mass, momentum and energy conservation equations. Graph theory is used to automatically generate amore » staggered mesh for complicated pipe network systems. Heat structure models have been implemented for three types of boundary conditions (Dirichlet, Neumann and Robin boundary conditions). Heat structures can be composed of several layers of different materials, and are used for simulation of heat structure temperature distribution and heat transfer rate. Control models are used to simulate sequences of events or trips of safety systems. A proportional-integral controller is also used to automatically make thermal hydraulic systems reach desired steady state conditions. A point kinetics model is used to model reactor kinetics behavior with temperature reactivity feedback. The underlying large sparse linear systems in these models are efficiently solved by using direct and iterative solvers provided by the SuperLU code on high performance machines. Input interfaces are designed to increase the flexibility of simulation for complicated thermal hydraulic systems. In conclusion, this paper mainly focuses on the methodology used to develop the FANCY code, and safety analysis of the Mark 1 pebble-bed FHR under development at UCB is performed.« less

A novel procedure on next generation sequencing data analysis using text mining algorithm.

PubMed

Zhao, Weizhong; Chen, James J; Perkins, Roger; Wang, Yuping; Liu, Zhichao; Hong, Huixiao; Tong, Weida; Zou, Wen

2016-05-13

Next-generation sequencing (NGS) technologies have provided researchers with vast possibilities in various biological and biomedical research areas. Efficient data mining strategies are in high demand for large scale comparative and evolutional studies to be performed on the large amounts of data derived from NGS projects. Topic modeling is an active research field in machine learning and has been mainly used as an analytical tool to structure large textual corpora for data mining. We report a novel procedure to analyse NGS data using topic modeling. It consists of four major procedures: NGS data retrieval, preprocessing, topic modeling, and data mining using Latent Dirichlet Allocation (LDA) topic outputs. The NGS data set of the Salmonella enterica strains were used as a case study to show the workflow of this procedure. The perplexity measurement of the topic numbers and the convergence efficiencies of Gibbs sampling were calculated and discussed for achieving the best result from the proposed procedure. The output topics by LDA algorithms could be treated as features of Salmonella strains to accurately describe the genetic diversity of fliC gene in various serotypes. The results of a two-way hierarchical clustering and data matrix analysis on LDA-derived matrices successfully classified Salmonella serotypes based on the NGS data. The implementation of topic modeling in NGS data analysis procedure provides a new way to elucidate genetic information from NGS data, and identify the gene-phenotype relationships and biomarkers, especially in the era of biological and medical big data. The implementation of topic modeling in NGS data analysis provides a new way to elucidate genetic information from NGS data, and identify the gene-phenotype relationships and biomarkers, especially in the era of biological and medical big data.

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

Guo, Z.; Zweibaum, N.; Shao, M.

The University of California, Berkeley (UCB) is performing thermal hydraulics safety analysis to develop the technical basis for design and licensing of fluoride-salt-cooled, high-temperature reactors (FHRs). FHR designs investigated by UCB use natural circulation for emergency, passive decay heat removal when normal decay heat removal systems fail. The FHR advanced natural circulation analysis (FANCY) code has been developed for assessment of passive decay heat removal capability and safety analysis of these innovative system designs. The FANCY code uses a one-dimensional, semi-implicit scheme to solve for pressure-linked mass, momentum and energy conservation equations. Graph theory is used to automatically generate amore » staggered mesh for complicated pipe network systems. Heat structure models have been implemented for three types of boundary conditions (Dirichlet, Neumann and Robin boundary conditions). Heat structures can be composed of several layers of different materials, and are used for simulation of heat structure temperature distribution and heat transfer rate. Control models are used to simulate sequences of events or trips of safety systems. A proportional-integral controller is also used to automatically make thermal hydraulic systems reach desired steady state conditions. A point kinetics model is used to model reactor kinetics behavior with temperature reactivity feedback. The underlying large sparse linear systems in these models are efficiently solved by using direct and iterative solvers provided by the SuperLU code on high performance machines. Input interfaces are designed to increase the flexibility of simulation for complicated thermal hydraulic systems. In conclusion, this paper mainly focuses on the methodology used to develop the FANCY code, and safety analysis of the Mark 1 pebble-bed FHR under development at UCB is performed.« less

Discovering functional modules by topic modeling RNA-Seq based toxicogenomic data.

PubMed

Yu, Ke; Gong, Binsheng; Lee, Mikyung; Liu, Zhichao; Xu, Joshua; Perkins, Roger; Tong, Weida

2014-09-15

Toxicogenomics (TGx) endeavors to elucidate the underlying molecular mechanisms through exploring gene expression profiles in response to toxic substances. Recently, RNA-Seq is increasingly regarded as a more powerful alternative to microarrays in TGx studies. However, realizing RNA-Seq's full potential requires novel approaches to extracting information from the complex TGx data. Considering read counts as the number of times a word occurs in a document, gene expression profiles from RNA-Seq are analogous to a word by document matrix used in text mining. Topic modeling aiming at to discover the latent structures in text corpora would be helpful to explore RNA-Seq based TGx data. In this study, topic modeling was applied on a typical RNA-Seq based TGx data set to discover hidden functional modules. The RNA-Seq based gene expression profiles were transformed into "documents", on which latent Dirichlet allocation (LDA) was used to build a topic model. We found samples treated by the compounds with the same modes of actions (MoAs) could be clustered based on topic similarities. The topic most relevant to each cluster was identified as a "marker" topic, which was interpreted by gene enrichment analysis with MoAs then confirmed by compound and pathways associations mined from literature. To further validate the "marker" topics, we tested topic transferability from RNA-Seq to microarrays. The RNA-Seq based gene expression profile of a topic specifically associated with peroxisome proliferator-activated receptors (PPAR) signaling pathway was used to query samples with similar expression profiles in two different microarray data sets, yielding accuracy of about 85%. This proof-of-concept study demonstrates the applicability of topic modeling to discover functional modules in RNA-Seq data and suggests a valuable computational tool for leveraging information within TGx data in RNA-Seq era.

Developing strong concurrent multiphysics multiscale coupling to understand the impact of microstructural mechanisms on the structural scale

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

Foulk, James W.; Alleman, Coleman N.; Mota, Alejandro

The heterogeneity in mechanical fields introduced by microstructure plays a critical role in the localization of deformation. To resolve this incipient stage of failure, it is therefore necessary to incorporate microstructure with sufficient resolution. On the other hand, computational limitations make it infeasible to represent the microstructure in the entire domain at the component scale. In this study, the authors demonstrate the use of concurrent multi- scale modeling to incorporate explicit, finely resolved microstructure in a critical region while resolving the smoother mechanical fields outside this region with a coarser discretization to limit computational cost. The microstructural physics is modeledmore » with a high-fidelity model that incorporates anisotropic crystal elasticity and rate-dependent crystal plasticity to simulate the behavior of a stainless steel alloy. The component-scale material behavior is treated with a lower fidelity model incorporating isotropic linear elasticity and rate-independent J 2 plas- ticity. The microstructural and component scale subdomains are modeled concurrently, with coupling via the Schwarz alternating method, which solves boundary-value problems in each subdomain separately and transfers solution information between subdomains via Dirichlet boundary conditions. Beyond cases studies in concurrent multiscale, we explore progress in crystal plastic- ity through modular designs, solution methodologies, model verification, and extensions to Sierra/SM and manycore applications. Advances in conformal microstructures having both hexahedral and tetrahedral workflows in Sculpt and Cubit are highlighted. A structure-property case study in two-phase metallic composites applies the Materials Knowledge System to local metrics for void evolution. Discussion includes lessons learned, future work, and a summary of funded efforts and proposed work. Finally, an appendix illustrates the need for two-way coupling through a single degree of freedom.« less

Empirical performance of the multivariate normal universal portfolio

NASA Astrophysics Data System (ADS)

Tan, Choon Peng; Pang, Sook Theng

2013-09-01

Universal portfolios generated by the multivariate normal distribution are studied with emphasis on the case where variables are dependent, namely, the covariance matrix is not diagonal. The moving-order multivariate normal universal portfolio requires very long implementation time and large computer memory in its implementation. With the objective of reducing memory and implementation time, the finite-order universal portfolio is introduced. Some stock-price data sets are selected from the local stock exchange and the finite-order universal portfolio is run on the data sets, for small finite order. Empirically, it is shown that the portfolio can outperform the moving-order Dirichlet universal portfolio of Cover and Ordentlich[2] for certain parameters in the selected data sets.

Kinetic and dynamic Delaunay tetrahedralizations in three dimensions

NASA Astrophysics Data System (ADS)

Schaller, Gernot; Meyer-Hermann, Michael

2004-09-01

We describe algorithms to implement fully dynamic and kinetic three-dimensional unconstrained Delaunay triangulations, where the time evolution of the triangulation is not only governed by moving vertices but also by a changing number of vertices. We use three-dimensional simplex flip algorithms, a stochastic visibility walk algorithm for point location and in addition, we propose a new simple method of deleting vertices from an existing three-dimensional Delaunay triangulation while maintaining the Delaunay property. As an example, we analyse the performance in various cases of practical relevance. The dual Dirichlet tessellation can be used to solve differential equations on an irregular grid, to define partitions in cell tissue simulations, for collision detection etc.

Bounded Error Schemes for the Wave Equation on Complex Domains

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Ditkowski, Adi; Yefet, Amir

1998-01-01

This paper considers the application of the method of boundary penalty terms ("SAT") to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error-bound. A numerical example, involving the solution of Maxwell's equations inside a 2-D circular wave-guide demonstrates the efficacy of this method in comparison to others (e.g. the staggered Yee scheme) - we achieve a decrease of two orders of magnitude in the level of the L2-error.

Supervised Semantic Classification for Nuclear Proliferation Monitoring

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

Vatsavai, Raju; Cheriyadat, Anil M; Gleason, Shaun Scott

2010-01-01

Existing feature extraction and classification approaches are not suitable for monitoring proliferation activity using high-resolution multi-temporal remote sensing imagery. In this paper we present a supervised semantic labeling framework based on the Latent Dirichlet Allocation method. This framework is used to analyze over 120 images collected under different spatial and temporal settings over the globe representing three major semantic categories: airports, nuclear, and coal power plants. Initial experimental results show a reasonable discrimination of these three categories even though coal and nuclear images share highly common and overlapping objects. This research also identified several research challenges associated with nuclear proliferationmore » monitoring using high resolution remote sensing images.« less

Radial rescaling approach for the eigenvalue problem of a particle in an arbitrarily shaped box.

PubMed

Lijnen, Erwin; Chibotaru, Liviu F; Ceulemans, Arnout

2008-01-01

In the present work we introduce a methodology for solving a quantum billiard with Dirichlet boundary conditions. The procedure starts from the exactly known solutions for the particle in a circular disk, which are subsequently radially rescaled in such a way that they obey the new boundary conditions. In this way one constructs a complete basis set which can be used to obtain the eigenstates and eigenenergies of the corresponding quantum billiard to a high level of precision. Test calculations for several regular polygons show the efficiency of the method which often requires one or two basis functions to describe the lowest eigenstates with high accuracy.

Convergence of spectra of graph-like thin manifolds

NASA Astrophysics Data System (ADS)

Exner, Pavel; Post, Olaf

2005-05-01

We consider a family of compact manifolds which shrinks with respect to an appropriate parameter to a graph. The main result is that the spectrum of the Laplace-Beltrami operator converges to the spectrum of the (differential) Laplacian on the graph with Kirchhoff boundary conditions at the vertices. On the other hand, if the shrinking at the vertex parts of the manifold is sufficiently slower comparing to that of the edge parts, the limiting spectrum corresponds to decoupled edges with Dirichlet boundary conditions at the endpoints. At the borderline between the two regimes we have a third possibility when the limiting spectrum can be described by a nontrivial coupling at the vertices.

Creation and perturbation of planar networks of chemical oscillators

PubMed Central

Tompkins, Nathan; Cambria, Matthew Carl; Wang, Adam L.; Heymann, Michael; Fraden, Seth

2015-01-01

Methods for creating custom planar networks of diffusively coupled chemical oscillators and perturbing individual oscillators within the network are presented. The oscillators consist of the Belousov-Zhabotinsky (BZ) reaction contained in an emulsion. Networks of drops of the BZ reaction are created with either Dirichlet (constant-concentration) or Neumann (no-flux) boundary conditions in a custom planar configuration using programmable illumination for the perturbations. The differences between the observed network dynamics for each boundary condition are described. Using light, we demonstrate the ability to control the initial conditions of the network and to cause individual oscillators within the network to undergo sustained period elongation or a one-time phase delay. PMID:26117136

A fast approach to designing airfoils from given pressure distribution in compressible flows

NASA Technical Reports Server (NTRS)

Daripa, Prabir

1987-01-01

A new inverse method for aerodynamic design of airfols is presented for subcritical flows. The pressure distribution in this method can be prescribed as a function of the arc length of the as-yet unknown body. This inverse problem is shown to be mathematically equivalent to solving only one nonlinear boundary value problem subject to known Dirichlet data on the boundary. The solution to this problem determines the airfoil, the freestream Mach number, and the upstream flow direction. The existence of a solution to a given pressure distribution is discussed. The method is easy to implement and extremely efficient. A series of results for which comparisons are made with the known airfoils is presented.

A contour for the entanglement entropies in harmonic lattices

NASA Astrophysics Data System (ADS)

Coser, Andrea; De Nobili, Cristiano; Tonni, Erik

2017-08-01

We construct a contour function for the entanglement entropies in generic harmonic lattices. In one spatial dimension, numerical analysis are performed by considering harmonic chains with either periodic or Dirichlet boundary conditions. In the massless regime and for some configurations where the subsystem is a single interval, the numerical results for the contour function are compared to the inverse of the local weight function which multiplies the energy-momentum tensor in the corresponding entanglement hamiltonian, found through conformal field theory methods, and a good agreement is observed. A numerical analysis of the contour function for the entanglement entropy is performed also in a massless harmonic chain for a subsystem made by two disjoint intervals.

Applying the method of fundamental solutions to harmonic problems with singular boundary conditions

NASA Astrophysics Data System (ADS)

Valtchev, Svilen S.; Alves, Carlos J. S.

2017-07-01

The method of fundamental solutions (MFS) is known to produce highly accurate numerical results for elliptic boundary value problems (BVP) with smooth boundary conditions, posed in analytic domains. However, due to the analyticity of the shape functions in its approximation basis, the MFS is usually disregarded when the boundary functions possess singularities. In this work we present a modification of the classical MFS which can be applied for the numerical solution of the Laplace BVP with Dirichlet boundary conditions exhibiting jump discontinuities. In particular, a set of harmonic functions with discontinuous boundary traces is added to the MFS basis. The accuracy of the proposed method is compared with the results form the classical MFS.

Scaling laws and properties of compositional data

NASA Astrophysics Data System (ADS)

Buccianti, Antonella; Albanese, Stefano; Lima, AnnaMaria; Minolfi, Giulia; De Vivo, Benedetto

2016-04-01

Many random processes occur in geochemistry. Accurate predictions of the manner in which elements or chemical species interact each other are needed to construct models able to treat presence of random components. Geochemical variables actually observed are the consequence of several events, some of which may be poorly defined or imperfectly understood. Variables tend to change with time/space but, despite their complexity, may share specific common traits and it is possible to model them stochastically. Description of the frequency distribution of the geochemical abundances has been an important target of research, attracting attention for at least 100 years, starting with CLARKE (1889) and continued by GOLDSCHMIDT (1933) and WEDEPOHL (1955). However, it was AHRENS (1954a,b) who focussed on the effect of skewness distributions, for example the log-normal distribution, regarded by him as a fundamental law of geochemistry. Although modeling of frequency distributions with some probabilistic models (for example Gaussian, log-normal, Pareto) has been well discussed in several fields of application, little attention has been devoted to the features of compositional data. When compositional nature of data is taken into account, the most typical distribution models for compositions are the Dirichlet and the additive logistic normal (or normal on the simplex) (AITCHISON et al. 2003; MATEU-FIGUERAS et al. 2005; MATEU-FIGUERAS and PAWLOWSKY-GLAHN 2008; MATEU-FIGUERAS et al. 2013). As an alternative, because compositional data have to be transformed from simplex space to real space, coordinates obtained by the ilr transformation or by application of the concept of balance can be analyzed by classical methods (EGOZCUE et al. 2003). In this contribution an approach coherent with the properties of compositional information is proposed and used to investigate the shape of the frequency distribution of compositional data. The purpose is to understand data-generation processes from the perspective of compositional theory. The approach is based on the use of the isometric log-ratio transformation, characterized by theoretical and practical advantages, but requiring a more complex geochemical interpretation compared with the investigation of single variables. The proposed methodology directs attention to model the frequency distributions of more complex indices, linking all the terms of the composition to better represent the dynamics of geochemical processes. An example of its application is presented and discussed by considering topsoil geochemistry of Campania Region (southern Italy). The investigated multi-element data archive contains, among others, Al, As, B, Ba, Ca, Co, Cr, Cu, Fe, K, La, Mg, Mn, Mo, Na, Ni, P, Pb, Sr, Th, Ti, V and Zn (mg/kg) contents determined in 3535 new topsoils as well as information on coordinates, geology, land cover. (BUCCIANTI et al., 2015). AHRENS, L. ,1954a. Geochim. Cosm. Acta 6, 121-131. AHRENS, L., 1954b. Geochim. Cosm. Acta 5, 49-73. AITCHISON, J., et al., 2003. Math Geol 35(6), 667-680. BUCCIANTI et al., 2015. Jour. Geoch. Explor., 159, 302-316. CLARKE, F., 1889. Phil. Society of Washington Bull. 11, 131-142. EGOZCUE, J.J. et al., 2003. Math Geol 35(3), 279-300. MATEU-FIGUERAS, G. et al, (2005), Stoch. Environ. Res. Risk Ass. 19(3), 205-214.

A new multi-domain method based on an analytical control surface for linear and second-order mean drift wave loads on floating bodies

NASA Astrophysics Data System (ADS)

Liang, Hui; Chen, Xiaobo

2017-10-01

A novel multi-domain method based on an analytical control surface is proposed by combining the use of free-surface Green function and Rankine source function. A cylindrical control surface is introduced to subdivide the fluid domain into external and internal domains. Unlike the traditional domain decomposition strategy or multi-block method, the control surface here is not panelized, on which the velocity potential and normal velocity components are analytically expressed as a series of base functions composed of Laguerre function in vertical coordinate and Fourier series in the circumference. Free-surface Green function is applied in the external domain, and the boundary integral equation is constructed on the control surface in the sense of Galerkin collocation via integrating test functions orthogonal to base functions over the control surface. The external solution gives rise to the so-called Dirichlet-to-Neumann [DN2] and Neumann-to-Dirichlet [ND2] relations on the control surface. Irregular frequencies, which are only dependent on the radius of the control surface, are present in the external solution, and they are removed by extending the boundary integral equation to the interior free surface (circular disc) on which the null normal derivative of potential is imposed, and the dipole distribution is expressed as Fourier-Bessel expansion on the disc. In the internal domain, where the Rankine source function is adopted, new boundary integral equations are formulated. The point collocation is imposed over the body surface and free surface, while the collocation of the Galerkin type is applied on the control surface. The present method is valid in the computation of both linear and second-order mean drift wave loads. Furthermore, the second-order mean drift force based on the middle-field formulation can be calculated analytically by using the coefficients of the Fourier-Laguerre expansion.

What are we ‘tweeting’ about obesity? Mapping tweets with Topic Modeling and Geographic Information System

PubMed Central

Ghosh, Debarchana (Debs); Guha, Rajarshi

2014-01-01

Public health related tweets are difficult to identify in large conversational datasets like Twitter.com. Even more challenging is the visualization and analyses of the spatial patterns encoded in tweets. This study has the following objectives: How can topic modeling be used to identify relevant public health topics such as obesity on Twitter.com? What are the common obesity related themes? What is the spatial pattern of the themes? What are the research challenges of using large conversational datasets from social networking sites? Obesity is chosen as a test theme to demonstrate the effectiveness of topic modeling using Latent Dirichlet Allocation (LDA) and spatial analysis using Geographic Information System (GIS). The dataset is constructed from tweets (originating from the United States) extracted from Twitter.com on obesity-related queries. Examples of such queries are ‘food deserts’, ‘fast food’, and ‘childhood obesity’. The tweets are also georeferenced and time stamped. Three cohesive and meaningful themes such as ‘childhood obesity and schools’, ‘obesity prevention’, and ‘obesity and food habits’ are extracted from the LDA model. The GIS analysis of the extracted themes show distinct spatial pattern between rural and urban areas, northern and southern states, and between coasts and inland states. Further, relating the themes with ancillary datasets such as US census and locations of fast food restaurants based upon the location of the tweets in a GIS environment opened new avenues for spatial analyses and mapping. Therefore the techniques used in this study provide a possible toolset for computational social scientists in general and health researchers in specific to better understand health problems from large conversational datasets. PMID:25126022

What are we 'tweeting' about obesity? Mapping tweets with Topic Modeling and Geographic Information System.

PubMed

Ghosh, Debarchana Debs; Guha, Rajarshi

2013-01-01

Public health related tweets are difficult to identify in large conversational datasets like Twitter.com. Even more challenging is the visualization and analyses of the spatial patterns encoded in tweets. This study has the following objectives: How can topic modeling be used to identify relevant public health topics such as obesity on Twitter.com? What are the common obesity related themes? What is the spatial pattern of the themes? What are the research challenges of using large conversational datasets from social networking sites? Obesity is chosen as a test theme to demonstrate the effectiveness of topic modeling using Latent Dirichlet Allocation (LDA) and spatial analysis using Geographic Information System (GIS). The dataset is constructed from tweets (originating from the United States) extracted from Twitter.com on obesity-related queries. Examples of such queries are 'food deserts', 'fast food', and 'childhood obesity'. The tweets are also georeferenced and time stamped. Three cohesive and meaningful themes such as 'childhood obesity and schools', 'obesity prevention', and 'obesity and food habits' are extracted from the LDA model. The GIS analysis of the extracted themes show distinct spatial pattern between rural and urban areas, northern and southern states, and between coasts and inland states. Further, relating the themes with ancillary datasets such as US census and locations of fast food restaurants based upon the location of the tweets in a GIS environment opened new avenues for spatial analyses and mapping. Therefore the techniques used in this study provide a possible toolset for computational social scientists in general and health researchers in specific to better understand health problems from large conversational datasets.

Detecting Spatial Patterns of Natural Hazards from the Wikipedia Knowledge Base

NASA Astrophysics Data System (ADS)

Fan, J.; Stewart, K.

2015-07-01

The Wikipedia database is a data source of immense richness and variety. Included in this database are thousands of geotagged articles, including, for example, almost real-time updates on current and historic natural hazards. This includes usercontributed information about the location of natural hazards, the extent of the disasters, and many details relating to response, impact, and recovery. In this research, a computational framework is proposed to detect spatial patterns of natural hazards from the Wikipedia database by combining topic modeling methods with spatial analysis techniques. The computation is performed on the Neon Cluster, a high performance-computing cluster at the University of Iowa. This work uses wildfires as the exemplar hazard, but this framework is easily generalizable to other types of hazards, such as hurricanes or flooding. Latent Dirichlet Allocation (LDA) modeling is first employed to train the entire English Wikipedia dump, transforming the database dump into a 500-dimension topic model. Over 230,000 geo-tagged articles are then extracted from the Wikipedia database, spatially covering the contiguous United States. The geo-tagged articles are converted into an LDA topic space based on the topic model, with each article being represented as a weighted multidimension topic vector. By treating each article's topic vector as an observed point in geographic space, a probability surface is calculated for each of the topics. In this work, Wikipedia articles about wildfires are extracted from the Wikipedia database, forming a wildfire corpus and creating a basis for the topic vector analysis. The spatial distribution of wildfire outbreaks in the US is estimated by calculating the weighted sum of the topic probability surfaces using a map algebra approach, and mapped using GIS. To provide an evaluation of the approach, the estimation is compared to wildfire hazard potential maps created by the USDA Forest service.

Clusternomics: Integrative context-dependent clustering for heterogeneous datasets

PubMed Central

Wernisch, Lorenz

2017-01-01

Integrative clustering is used to identify groups of samples by jointly analysing multiple datasets describing the same set of biological samples, such as gene expression, copy number, methylation etc. Most existing algorithms for integrative clustering assume that there is a shared consistent set of clusters across all datasets, and most of the data samples follow this structure. However in practice, the structure across heterogeneous datasets can be more varied, with clusters being joined in some datasets and separated in others. In this paper, we present a probabilistic clustering method to identify groups across datasets that do not share the same cluster structure. The proposed algorithm, Clusternomics, identifies groups of samples that share their global behaviour across heterogeneous datasets. The algorithm models clusters on the level of individual datasets, while also extracting global structure that arises from the local cluster assignments. Clusters on both the local and the global level are modelled using a hierarchical Dirichlet mixture model to identify structure on both levels. We evaluated the model both on simulated and on real-world datasets. The simulated data exemplifies datasets with varying degrees of common structure. In such a setting Clusternomics outperforms existing algorithms for integrative and consensus clustering. In a real-world application, we used the algorithm for cancer subtyping, identifying subtypes of cancer from heterogeneous datasets. We applied the algorithm to TCGA breast cancer dataset, integrating gene expression, miRNA expression, DNA methylation and proteomics. The algorithm extracted clinically meaningful clusters with significantly different survival probabilities. We also evaluated the algorithm on lung and kidney cancer TCGA datasets with high dimensionality, again showing clinically significant results and scalability of the algorithm. PMID:29036190

Clusternomics: Integrative context-dependent clustering for heterogeneous datasets.

PubMed

Gabasova, Evelina; Reid, John; Wernisch, Lorenz

2017-10-01

Integrative clustering is used to identify groups of samples by jointly analysing multiple datasets describing the same set of biological samples, such as gene expression, copy number, methylation etc. Most existing algorithms for integrative clustering assume that there is a shared consistent set of clusters across all datasets, and most of the data samples follow this structure. However in practice, the structure across heterogeneous datasets can be more varied, with clusters being joined in some datasets and separated in others. In this paper, we present a probabilistic clustering method to identify groups across datasets that do not share the same cluster structure. The proposed algorithm, Clusternomics, identifies groups of samples that share their global behaviour across heterogeneous datasets. The algorithm models clusters on the level of individual datasets, while also extracting global structure that arises from the local cluster assignments. Clusters on both the local and the global level are modelled using a hierarchical Dirichlet mixture model to identify structure on both levels. We evaluated the model both on simulated and on real-world datasets. The simulated data exemplifies datasets with varying degrees of common structure. In such a setting Clusternomics outperforms existing algorithms for integrative and consensus clustering. In a real-world application, we used the algorithm for cancer subtyping, identifying subtypes of cancer from heterogeneous datasets. We applied the algorithm to TCGA breast cancer dataset, integrating gene expression, miRNA expression, DNA methylation and proteomics. The algorithm extracted clinically meaningful clusters with significantly different survival probabilities. We also evaluated the algorithm on lung and kidney cancer TCGA datasets with high dimensionality, again showing clinically significant results and scalability of the algorithm.

DEIsoM: a hierarchical Bayesian model for identifying differentially expressed isoforms using biological replicates

PubMed Central

Peng, Hao; Yang, Yifan; Zhe, Shandian; Wang, Jian; Gribskov, Michael; Qi, Yuan

2017-01-01

Abstract Motivation High-throughput mRNA sequencing (RNA-Seq) is a powerful tool for quantifying gene expression. Identification of transcript isoforms that are differentially expressed in different conditions, such as in patients and healthy subjects, can provide insights into the molecular basis of diseases. Current transcript quantification approaches, however, do not take advantage of the shared information in the biological replicates, potentially decreasing sensitivity and accuracy. Results We present a novel hierarchical Bayesian model called Differentially Expressed Isoform detection from Multiple biological replicates (DEIsoM) for identifying differentially expressed (DE) isoforms from multiple biological replicates representing two conditions, e.g. multiple samples from healthy and diseased subjects. DEIsoM first estimates isoform expression within each condition by (1) capturing common patterns from sample replicates while allowing individual differences, and (2) modeling the uncertainty introduced by ambiguous read mapping in each replicate. Specifically, we introduce a Dirichlet prior distribution to capture the common expression pattern of replicates from the same condition, and treat the isoform expression of individual replicates as samples from this distribution. Ambiguous read mapping is modeled as a multinomial distribution, and ambiguous reads are assigned to the most probable isoform in each replicate. Additionally, DEIsoM couples an efficient variational inference and a post-analysis method to improve the accuracy and speed of identification of DE isoforms over alternative methods. Application of DEIsoM to an hepatocellular carcinoma (HCC) dataset identifies biologically relevant DE isoforms. The relevance of these genes/isoforms to HCC are supported by principal component analysis (PCA), read coverage visualization, and the biological literature. Availability and implementation The software is available at https://github.com/hao-peng/DEIsoM Contact pengh@alumni.purdue.edu Supplementary information Supplementary data are available at Bioinformatics online. PMID:28595376

A systems approach for analysis of high content screening assay data with topic modeling.

PubMed

Bisgin, Halil; Chen, Minjun; Wang, Yuping; Kelly, Reagan; Fang, Hong; Xu, Xiaowei; Tong, Weida

2013-01-01

High Content Screening (HCS) has become an important tool for toxicity assessment, partly due to its advantage of handling multiple measurements simultaneously. This approach has provided insight and contributed to the understanding of systems biology at cellular level. To fully realize this potential, the simultaneously measured multiple endpoints from a live cell should be considered in a probabilistic relationship to assess the cell's condition to response stress from a treatment, which poses a great challenge to extract hidden knowledge and relationships from these measurements. In this work, we applied a text mining method of Latent Dirichlet Allocation (LDA) to analyze cellular endpoints from in vitro HCS assays and related to the findings to in vivo histopathological observations. We measured multiple HCS assay endpoints for 122 drugs. Since LDA requires the data to be represented in document-term format, we first converted the continuous value of the measurements to the word frequency that can processed by the text mining tool. For each of the drugs, we generated a document for each of the 4 time points. Thus, we ended with 488 documents (drug-hour) each having different values for the 10 endpoints which are treated as words. We extracted three topics using LDA and examined these to identify diagnostic topics for 45 common drugs located in vivo experiments from the Japanese Toxicogenomics Project (TGP) observing their necrosis findings at 6 and 24 hours after treatment. We found that assay endpoints assigned to particular topics were in concordance with the histopathology observed. Drugs showing necrosis at 6 hour were linked to severe damage events such as Steatosis, DNA Fragmentation, Mitochondrial Potential, and Lysosome Mass. DNA Damage and Apoptosis were associated with drugs causing necrosis at 24 hours, suggesting an interplay of the two pathways in these drugs. Drugs with no sign of necrosis we related to the Cell Loss and Nuclear Size assays, which is suggestive of hepatocyte regeneration. The evidence from this study suggests that topic modeling with LDA can enable us to interpret relationships of endpoints of in vitro assays along with an in vivo histological finding, necrosis. Effectiveness of this approach may add substantially to our understanding of systems biology.

Recurrence relations for orthogonal polynomials for PDEs in polar and cylindrical geometries.

PubMed

Richardson, Megan; Lambers, James V

2016-01-01

This paper introduces two families of orthogonal polynomials on the interval (-1,1), with weight function [Formula: see text]. The first family satisfies the boundary condition [Formula: see text], and the second one satisfies the boundary conditions [Formula: see text]. These boundary conditions arise naturally from PDEs defined on a disk with Dirichlet boundary conditions and the requirement of regularity in Cartesian coordinates. The families of orthogonal polynomials are obtained by orthogonalizing short linear combinations of Legendre polynomials that satisfy the same boundary conditions. Then, the three-term recurrence relations are derived. Finally, it is shown that from these recurrence relations, one can efficiently compute the corresponding recurrences for generalized Jacobi polynomials that satisfy the same boundary conditions.

Initial-Boundary Value Problem for Two-Component Gerdjikov-Ivanov Equation with 3 × 3 Lax Pair on Half-Line

NASA Astrophysics Data System (ADS)

Zhu, Qiao-Zhen; Fan, En-Gui; Xu, Jian

2017-10-01

The Fokas unified method is used to analyze the initial-boundary value problem of two-component Gerdjikov-Ivanonv equation on the half-line. It is shown that the solution of the initial-boundary problem can be expressed in terms of the solution of a 3 × 3 Riemann-Hilbert problem. The Dirichlet to Neumann map is obtained through the global relation. Supported by grants from the National Science Foundation of China under Grant No. 11671095, National Science Foundation of China under Grant No. 11501365, Shanghai Sailing Program supported by Science and Technology Commission of Shanghai Municipality under Grant No 15YF1408100, and the Hujiang Foundation of China (B14005)

Regularity gradient estimates for weak solutions of singular quasi-linear parabolic equations

NASA Astrophysics Data System (ADS)

Phan, Tuoc

2017-12-01

This paper studies the Sobolev regularity for weak solutions of a class of singular quasi-linear parabolic problems of the form ut -div [ A (x , t , u , ∇u) ] =div [ F ] with homogeneous Dirichlet boundary conditions over bounded spatial domains. Our main focus is on the case that the vector coefficients A are discontinuous and singular in (x , t)-variables, and dependent on the solution u. Global and interior weighted W 1 , p (ΩT , ω)-regularity estimates are established for weak solutions of these equations, where ω is a weight function in some Muckenhoupt class of weights. The results obtained are even new for linear equations, and for ω = 1, because of the singularity of the coefficients in (x , t)-variables.

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1987-01-01

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

A general panel method for the analysis and design of arbitrary configurations in incompressible flows. [boundary value problem

NASA Technical Reports Server (NTRS)

Johnson, F. T.

1980-01-01

A method for solving the linear integral equations of incompressible potential flow in three dimensions is presented. Both analysis (Neumann) and design (Dirichlet) boundary conditions are treated in a unified approach to the general flow problem. The method is an influence coefficient scheme which employs source and doublet panels as boundary surfaces. Curved panels possessing singularity strengths, which vary as polynomials are used, and all influence coefficients are derived in closed form. These and other features combine to produce an efficient scheme which is not only versatile but eminently suited to the practical realities of a user-oriented environment. A wide variety of numerical results demonstrating the method is presented.

Preconditioned conjugate residual methods for the solution of spectral equations

NASA Technical Reports Server (NTRS)

Wong, Y. S.; Zang, T. A.; Hussaini, M. Y.

1986-01-01

Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

Modeling and simulation of electronic structure, material interface and random doping in nano electronic devices

PubMed Central

Chen, Duan; Wei, Guo-Wei

2010-01-01

The miniaturization of nano-scale electronic devices, such as metal oxide semiconductor field effect transistors (MOSFETs), has given rise to a pressing demand in the new theoretical understanding and practical tactic for dealing with quantum mechanical effects in integrated circuits. Modeling and simulation of this class of problems have emerged as an important topic in applied and computational mathematics. This work presents mathematical models and computational algorithms for the simulation of nano-scale MOSFETs. We introduce a unified two-scale energy functional to describe the electrons and the continuum electrostatic potential of the nano-electronic device. This framework enables us to put microscopic and macroscopic descriptions in an equal footing at nano scale. By optimization of the energy functional, we derive consistently-coupled Poisson-Kohn-Sham equations. Additionally, layered structures are crucial to the electrostatic and transport properties of nano transistors. A material interface model is proposed for more accurate description of the electrostatics governed by the Poisson equation. Finally, a new individual dopant model that utilizes the Dirac delta function is proposed to understand the random doping effect in nano electronic devices. Two mathematical algorithms, the matched interface and boundary (MIB) method and the Dirichlet-to-Neumann mapping (DNM) technique, are introduced to improve the computational efficiency of nano-device simulations. Electronic structures are computed via subband decomposition and the transport properties, such as the I-V curves and electron density, are evaluated via the non-equilibrium Green's functions (NEGF) formalism. Two distinct device configurations, a double-gate MOSFET and a four-gate MOSFET, are considered in our three-dimensional numerical simulations. For these devices, the current fluctuation and voltage threshold lowering effect induced by the discrete dopant model are explored. Numerical convergence and model well-posedness are also investigated in the present work. PMID:20396650