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.

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…

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.

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

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

Application of the perfectly matched layer in 3-D marine controlled-source electromagnetic modelling

NASA Astrophysics Data System (ADS)

Li, Gang; Li, Yuguo; Han, Bo; Liu, Zhan

2018-01-01

In this study, the complex frequency-shifted perfectly matched layer (CFS-PML) in stretching Cartesian coordinates is successfully applied to 3-D frequency-domain marine controlled-source electromagnetic (CSEM) field modelling. The Dirichlet boundary, which is usually used within the traditional framework of EM modelling algorithms, assumes that the electric or magnetic field values are zero at the boundaries. This requires the boundaries to be sufficiently far away from the area of interest. To mitigate the boundary artefacts, a large modelling area may be necessary even though cell sizes are allowed to grow toward the boundaries due to the diffusion of the electromagnetic wave propagation. Compared with the conventional Dirichlet boundary, the PML boundary is preferred as the modelling area of interest could be restricted to the target region and only a few absorbing layers surrounding can effectively depress the artificial boundary effect without losing the numerical accuracy. Furthermore, for joint inversion of seismic and marine CSEM data, if we use the PML for CSEM field simulation instead of the conventional Dirichlet, the modelling area for these two different geophysical data collected from the same survey area could be the same, which is convenient for joint inversion grid matching. We apply the CFS-PML boundary to 3-D marine CSEM modelling by using the staggered finite-difference discretization. Numerical test indicates that the modelling algorithm using the CFS-PML also shows good accuracy compared to the Dirichlet. Furthermore, the modelling algorithm using the CFS-PML shows advantages in computational time and memory saving than that using the Dirichlet boundary. For the 3-D example in this study, the memory saving using the PML is nearly 42 per cent and the time saving is around 48 per cent compared to using the Dirichlet.

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.

Prior Design for Dependent Dirichlet Processes: An Application to Marathon Modeling

PubMed Central

F. Pradier, Melanie; J. R. Ruiz, Francisco; Perez-Cruz, Fernando

2016-01-01

This paper presents a novel application of Bayesian nonparametrics (BNP) for marathon data modeling. We make use of two well-known BNP priors, the single-p dependent Dirichlet process and the hierarchical Dirichlet process, in order to address two different problems. First, we study the impact of age, gender and environment on the runners’ performance. We derive a fair grading method that allows direct comparison of runners regardless of their age and gender. Unlike current grading systems, our approach is based not only on top world records, but on the performances of all runners. The presented methodology for comparison of densities can be adopted in many other applications straightforwardly, providing an interesting perspective to build dependent Dirichlet processes. Second, we analyze the running patterns of the marathoners in time, obtaining information that can be valuable for training purposes. We also show that these running patterns can be used to predict finishing time given intermediate interval measurements. We apply our models to New York City, Boston and London marathons. PMID:26821155

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].

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.

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.

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…

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.

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...

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.

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.

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.

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.

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.

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.

GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models

PubMed Central

Mukherjee, Chiranjit; Rodriguez, Abel

2016-01-01

Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful. PMID:28626348

GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models.

PubMed

Mukherjee, Chiranjit; Rodriguez, Abel

2016-01-01

Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful.

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.

On selecting a prior for the precision parameter of Dirichlet process mixture models

USGS Publications Warehouse

Dorazio, R.M.

2009-01-01

In hierarchical mixture models the Dirichlet process is used to specify latent patterns of heterogeneity, particularly when the distribution of latent parameters is thought to be clustered (multimodal). The parameters of a Dirichlet process include a precision parameter ?? and a base probability measure G0. In problems where ?? is unknown and must be estimated, inferences about the level of clustering can be sensitive to the choice of prior assumed for ??. In this paper an approach is developed for computing a prior for the precision parameter ?? that can be used in the presence or absence of prior information about the level of clustering. This approach is illustrated in an analysis of counts of stream fishes. The results of this fully Bayesian analysis are compared with an empirical Bayes analysis of the same data and with a Bayesian analysis based on an alternative commonly used prior.

Effective implementation of wavelet Galerkin method

NASA Astrophysics Data System (ADS)

Finěk, Václav; Šimunková, Martina

2012-11-01

It was proved by W. Dahmen et al. that an adaptive wavelet scheme is asymptotically optimal for a wide class of elliptic equations. This scheme approximates the solution u by a linear combination of N wavelets and a benchmark for its performance is the best N-term approximation, which is obtained by retaining the N largest wavelet coefficients of the unknown solution. Moreover, the number of arithmetic operations needed to compute the approximate solution is proportional to N. The most time consuming part of this scheme is the approximate matrix-vector multiplication. In this contribution, we will introduce our implementation of wavelet Galerkin method for Poisson equation -Δu = f on hypercube with homogeneous Dirichlet boundary conditions. In our implementation, we identified nonzero elements of stiffness matrix corresponding to the above problem and we perform matrix-vector multiplication only with these nonzero elements.

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.}

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.

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.

Generalized species sampling priors with latent Beta reinforcements

PubMed Central

Airoldi, Edoardo M.; Costa, Thiago; Bassetti, Federico; Leisen, Fabrizio; Guindani, Michele

2014-01-01

Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a novel and probabilistically coherent family of non-exchangeable species sampling sequences characterized by a tractable predictive probability function with weights driven by a sequence of independent Beta random variables. We compare their theoretical clustering properties with those of the Dirichlet Process and the two parameters Poisson-Dirichlet process. The proposed construction provides a complete characterization of the joint process, differently from existing work. We then propose the use of such process as prior distribution in a hierarchical Bayes modeling framework, and we describe a Markov Chain Monte Carlo sampler for posterior inference. We evaluate the performance of the prior and the robustness of the resulting inference in a simulation study, providing a comparison with popular Dirichlet Processes mixtures and Hidden Markov Models. Finally, we develop an application to the detection of chromosomal aberrations in breast cancer by leveraging array CGH data. PMID:25870462

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.

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.

Analysis of Classes of Singular Steady State Reaction Diffusion Equations

NASA Astrophysics Data System (ADS)

Son, Byungjae

We study positive radial solutions to classes of steady state reaction diffusion problems on the exterior of a ball with both Dirichlet and nonlinear boundary conditions. We study both Laplacian as well as p-Laplacian problems with reaction terms that are p-sublinear at infinity. We consider both positone and semipositone reaction terms and establish existence, multiplicity and uniqueness results. Our existence and multiplicity results are achieved by a method of sub-supersolutions and uniqueness results via a combination of maximum principles, comparison principles, energy arguments and a-priori estimates. Our results significantly enhance the literature on p-sublinear positone and semipositone problems. Finally, we provide exact bifurcation curves for several one-dimensional problems. In the autonomous case, we extend and analyze a quadrature method, and in the nonautonomous case, we employ shooting methods. We use numerical solvers in Mathematica to generate the bifurcation curves.

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.

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

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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.

Determinants and conformal anomalies of GJMS operators on spheres

NASA Astrophysics Data System (ADS)

Dowker, J. S.

2011-03-01

The conformal anomalies and functional determinants of the Branson-GJMS operators, P2k, on the d-dimensional sphere are evaluated in explicit terms for any d and k such that k <= d/2 (if d is even). The determinants are given in terms of multiple gamma functions and a rational multiplicative anomaly, which vanishes for odd d. Taking the mode system on the sphere as the union of Neumann and Dirichlet ones on the hemisphere is a basic part of the method and leads to a heuristic explanation of the non-existence of 'super-critical' operators, 2k > d for even d. Significant use is made of the Barnes zeta function. The results are given in terms of ratios of determinants of operators on a (d + 1)-dimensional bulk dual sphere. For odd dimensions, the log determinant is written in terms of multiple sine functions and agreement is found with holographic computations, yielding an integral over a Plancherel measure. The N-D determinant ratio is also found explicitly for even dimensions. Ehrhart polynomials are encountered.

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

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.

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.

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.

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.

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.

Modeling unobserved sources of heterogeneity in animal abundance using a Dirichlet process prior

USGS Publications Warehouse

Dorazio, R.M.; Mukherjee, B.; Zhang, L.; Ghosh, M.; Jelks, H.L.; Jordan, F.

2008-01-01

In surveys of natural populations of animals, a sampling protocol is often spatially replicated to collect a representative sample of the population. In these surveys, differences in abundance of animals among sample locations may induce spatial heterogeneity in the counts associated with a particular sampling protocol. For some species, the sources of heterogeneity in abundance may be unknown or unmeasurable, leading one to specify the variation in abundance among sample locations stochastically. However, choosing a parametric model for the distribution of unmeasured heterogeneity is potentially subject to error and can have profound effects on predictions of abundance at unsampled locations. In this article, we develop an alternative approach wherein a Dirichlet process prior is assumed for the distribution of latent abundances. This approach allows for uncertainty in model specification and for natural clustering in the distribution of abundances in a data-adaptive way. We apply this approach in an analysis of counts based on removal samples of an endangered fish species, the Okaloosa darter. Results of our data analysis and simulation studies suggest that our implementation of the Dirichlet process prior has several attractive features not shared by conventional, fully parametric alternatives. ?? 2008, The International Biometric Society.

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.

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.

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.

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.

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.

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.

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.

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

Relating zeta functions of discrete and quantum graphs

NASA Astrophysics Data System (ADS)

Harrison, Jonathan; Weyand, Tracy

2018-02-01

We write the spectral zeta function of the Laplace operator on an equilateral metric graph in terms of the spectral zeta function of the normalized Laplace operator on the corresponding discrete graph. To do this, we apply a relation between the spectrum of the Laplacian on a discrete graph and that of the Laplacian on an equilateral metric graph. As a by-product, we determine how the multiplicity of eigenvalues of the quantum graph, that are also in the spectrum of the graph with Dirichlet conditions at the vertices, depends on the graph geometry. Finally we apply the result to calculate the vacuum energy and spectral determinant of a complete bipartite graph and compare our results with those for a star graph, a graph in which all vertices are connected to a central vertex by a single edge.

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.

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.

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

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

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.

Hierarchical Dirichlet process model for gene expression clustering

PubMed Central

2013-01-01

Clustering is an important data processing tool for interpreting microarray data and genomic network inference. In this article, we propose a clustering algorithm based on the hierarchical Dirichlet processes (HDP). The HDP clustering introduces a hierarchical structure in the statistical model which captures the hierarchical features prevalent in biological data such as the gene express data. We develop a Gibbs sampling algorithm based on the Chinese restaurant metaphor for the HDP clustering. We apply the proposed HDP algorithm to both regulatory network segmentation and gene expression clustering. The HDP algorithm is shown to outperform several popular clustering algorithms by revealing the underlying hierarchical structure of the data. For the yeast cell cycle data, we compare the HDP result to the standard result and show that the HDP algorithm provides more information and reduces the unnecessary clustering fragments. PMID:23587447

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.

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.

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Z.; Manteuffel, T. A.; McCormick, S. F.

1996-01-01

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.

A resilient domain decomposition polynomial chaos solver for uncertain elliptic PDEs

NASA Astrophysics Data System (ADS)

Mycek, Paul; Contreras, Andres; Le Maître, Olivier; Sargsyan, Khachik; Rizzi, Francesco; Morris, Karla; Safta, Cosmin; Debusschere, Bert; Knio, Omar

2017-07-01

A resilient method is developed for the solution of uncertain elliptic PDEs on extreme scale platforms. The method is based on a hybrid domain decomposition, polynomial chaos (PC) framework that is designed to address soft faults. Specifically, parallel and independent solves of multiple deterministic local problems are used to define PC representations of local Dirichlet boundary-to-boundary maps that are used to reconstruct the global solution. A LAD-lasso type regression is developed for this purpose. The performance of the resulting algorithm is tested on an elliptic equation with an uncertain diffusivity field. Different test cases are considered in order to analyze the impacts of correlation structure of the uncertain diffusivity field, the stochastic resolution, as well as the probability of soft faults. In particular, the computations demonstrate that, provided sufficiently many samples are generated, the method effectively overcomes the occurrence of soft faults.

Electromagnetic MUSIC-type imaging of perfectly conducting, arc-like cracks at single frequency

NASA Astrophysics Data System (ADS)

Park, Won-Kwang; Lesselier, Dominique

2009-11-01

We propose a non-iterative MUSIC (MUltiple SIgnal Classification)-type algorithm for the time-harmonic electromagnetic imaging of one or more perfectly conducting, arc-like cracks found within a homogeneous space R2. The algorithm is based on a factorization of the Multi-Static Response (MSR) matrix collected in the far-field at a single, nonzero frequency in either Transverse Magnetic (TM) mode (Dirichlet boundary condition) or Transverse Electric (TE) mode (Neumann boundary condition), followed by the calculation of a MUSIC cost functional expected to exhibit peaks along the crack curves each half a wavelength. Numerical experimentation from exact, noiseless and noisy data shows that this is indeed the case and that the proposed algorithm behaves in robust manner, with better results in the TM mode than in the TE mode for which one would have to estimate the normal to the crack to get the most optimal results.

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} |\

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

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.

Dynamic classification of fetal heart rates by hierarchical Dirichlet process mixture models.

PubMed

Yu, Kezi; Quirk, J Gerald; Djurić, Petar M

2017-01-01

In this paper, we propose an application of non-parametric Bayesian (NPB) models for classification of fetal heart rate (FHR) recordings. More specifically, we propose models that are used to differentiate between FHR recordings that are from fetuses with or without adverse outcomes. In our work, we rely on models based on hierarchical Dirichlet processes (HDP) and the Chinese restaurant process with finite capacity (CRFC). Two mixture models were inferred from real recordings, one that represents healthy and another, non-healthy fetuses. The models were then used to classify new recordings and provide the probability of the fetus being healthy. First, we compared the classification performance of the HDP models with that of support vector machines on real data and concluded that the HDP models achieved better performance. Then we demonstrated the use of mixture models based on CRFC for dynamic classification of the performance of (FHR) recordings in a real-time setting.

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

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.

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.

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.

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.

Dynamic classification of fetal heart rates by hierarchical Dirichlet process mixture models

PubMed Central

Yu, Kezi; Quirk, J. Gerald

2017-01-01

In this paper, we propose an application of non-parametric Bayesian (NPB) models for classification of fetal heart rate (FHR) recordings. More specifically, we propose models that are used to differentiate between FHR recordings that are from fetuses with or without adverse outcomes. In our work, we rely on models based on hierarchical Dirichlet processes (HDP) and the Chinese restaurant process with finite capacity (CRFC). Two mixture models were inferred from real recordings, one that represents healthy and another, non-healthy fetuses. The models were then used to classify new recordings and provide the probability of the fetus being healthy. First, we compared the classification performance of the HDP models with that of support vector machines on real data and concluded that the HDP models achieved better performance. Then we demonstrated the use of mixture models based on CRFC for dynamic classification of the performance of (FHR) recordings in a real-time setting. PMID:28953927

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.

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.

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.

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.

A SEMIPARAMETRIC BAYESIAN MODEL FOR CIRCULAR-LINEAR REGRESSION

EPA Science Inventory

We present a Bayesian approach to regress a circular variable on a linear predictor. The regression coefficients are assumed to have a nonparametric distribution with a Dirichlet process prior. The semiparametric Bayesian approach gives added flexibility to the model and is usefu...

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.

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

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 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

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.

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

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).

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

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

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.

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}.

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.

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.

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.

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.

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.

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.

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

Memoized Online Variational Inference for Dirichlet Process Mixture Models

DTIC Science & Technology

2014-06-27

breaking process [7], which places artifically large mass on the final component. It is more efficient and broadly applicable than an alternative trunction...models. In Uncertainty in Artificial Intelligence , 2008. [13] N. Le Roux, M. Schmidt, and F. Bach. A stochastic gradient method with an exponential

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…

Scalable Topic Modeling: Online Learning, Diagnostics, and Recommendation

DTIC Science & Technology

2017-03-01

Chinese restaurant processes. Journal of Machine Learning Research, 12:2461–2488, 2011. 15. L. Hannah, D. Blei and W. Powell. Dirichlet process mixtures of...34. S. Ghosh, A. Ungureanu, E. Sudderth, and D. Blei. A Spatial distance dependent Chinese restaurant process for image segmentation. In Neural

On functional determinants of matrix differential operators with multiple zero modes

NASA Astrophysics Data System (ADS)

Falco, G. M.; Fedorenko, Andrei A.; Gruzberg, Ilya A.

2017-12-01

We generalize the method of computing functional determinants with a single excluded zero eigenvalue developed by McKane and Tarlie to differential operators with multiple zero eigenvalues. We derive general formulas for such functional determinants of r× r matrix second order differential operators O with 0 < n ≤slant 2r linearly independent zero modes. We separately discuss the cases of the homogeneous Dirichlet boundary conditions, when the number of zero modes cannot exceed r, and the case of twisted boundary conditions, including the periodic and anti-periodic ones, when the number of zero modes is bounded above by 2r. In all cases the determinants with excluded zero eigenvalues can be expressed only in terms of the n zero modes and other r-n or 2r-n (depending on the boundary conditions) solutions of the homogeneous equation O h=0 , in the spirit of Gel’fand-Yaglom approach. In instanton calculations, the contribution of the zero modes is taken into account by introducing the so-called collective coordinates. We show that there is a remarkable cancellation of a factor (involving scalar products of zero modes) between the Jacobian of the transformation to the collective coordinates and the functional fluctuation determinant with excluded zero eigenvalues. This cancellation drastically simplifies instanton calculations when one uses our formulas.

Structural study of polymorphism in methylprednisolone aceponate

NASA Astrophysics Data System (ADS)

Knyazev, A. V.; Somov, N. V.; Shipilova, A. S.; Gusarova, E. V.; Knyazeva, S. S.; Stepanova, O. V.; Chuprunov, E. V.

2017-08-01

The crystal structures of methylprednisolone aceponate were determined by X-ray diffraction analysis at temperatures 90 K and 150 K: space group P212121, a = 14.8592(2), b = 19.6844(5), c = 26.1626(4) Å, Z = 12; R = 0.0598 (T = 90 K); space group P212121, a = 6.57348(14), b = 14.8295(3), c = 26.2214(5) Å, Z = 4; R = 0.0518 (T = 150 K). Features of structural changes in the phase transition were revealed. The abrupt change in the unit cell parameters in the phase transition was shown by low-temperature X-ray powder. The methods of degree of invariance of crystal electron density and molecular Voronoi-Dirichlet polyhedra were used for the analysis of polymorphism in methylprednisolone aceponate. The atomic structure at 90 K have a translational pseudosymmetry of electron density η = 0.329(1). The decrease of number of intermolecular contacts in the high-temperature modification due to rupture of intermolecular non-valence contacts C/O was observed.

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.

Estimates of segregation and overlap of functional connectivity networks in the human cerebral cortex.

PubMed

Yeo, B T Thomas; Krienen, Fenna M; Chee, Michael W L; Buckner, Randy L

2014-03-01

The organization of the human cerebral cortex has recently been explored using techniques for parcellating the cortex into distinct functionally coupled networks. The divergent and convergent nature of cortico-cortical anatomic connections suggests the need to consider the possibility of regions belonging to multiple networks and hierarchies among networks. Here we applied the Latent Dirichlet Allocation (LDA) model and spatial independent component analysis (ICA) to solve for functionally coupled cerebral networks without assuming that cortical regions belong to a single network. Data analyzed included 1000 subjects from the Brain Genomics Superstruct Project (GSP) and 12 high quality individual subjects from the Human Connectome Project (HCP). The organization of the cerebral cortex was similar regardless of whether a winner-take-all approach or the more relaxed constraints of LDA (or ICA) were imposed. This suggests that large-scale networks may function as partially isolated modules. Several notable interactions among networks were uncovered by the LDA analysis. Many association regions belong to at least two networks, while somatomotor and early visual cortices are especially isolated. As examples of interaction, the precuneus, lateral temporal cortex, medial prefrontal cortex and posterior parietal cortex participate in multiple paralimbic networks that together comprise subsystems of the default network. In addition, regions at or near the frontal eye field and human lateral intraparietal area homologue participate in multiple hierarchically organized networks. These observations were replicated in both datasets and could be detected (and replicated) in individual subjects from the HCP. © 2013.

Estimates of Segregation and Overlap of Functional Connectivity Networks in the Human Cerebral Cortex

PubMed Central

Yeo, BT Thomas; Krienen, Fenna M; Chee, Michael WL; Buckner, Randy L

2014-01-01

The organization of the human cerebral cortex has recently been explored using techniques for parcellating the cortex into distinct functionally coupled networks. The divergent and convergent nature of cortico-cortical anatomic connections suggests the need to consider the possibility of regions belonging to multiple networks and hierarchies among networks. Here we applied the Latent Dirichlet Allocation (LDA) model and spatial independent component analysis (ICA) to solve for functionally coupled cerebral networks without assuming that cortical regions belong to a single network. Data analyzed included 1,000 subjects from the Brain Genomics Superstruct Project (GSP) and 12 high quality individual subjects from the Human Connectome Project (HCP). The organization of the cerebral cortex was similar regardless of whether a winner-take-all approach or the more relaxed constraints of LDA (or ICA) were imposed. This suggests that large-scale networks may function as partially isolated modules. Several notable interactions among networks were uncovered by the LDA analysis. Many association regions belong to at least two networks, while somatomotor and early visual cortices are especially isolated. As examples of interaction, the precuneus, lateral temporal cortex, medial prefrontal cortex and posterior parietal cortex participate in multiple paralimbic networks that together comprise subsystems of the default network. In addition, regions at or near the frontal eye field and human lateral intraparietal area homologue participate in multiple hierarchically organized networks. These observations were replicated in both datasets and could be detected (and replicated) in individual subjects from the HCP. PMID:24185018

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.

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…

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…

Automated assessment of medical training evaluation text.

PubMed

Zhang, Rui; Pakhomov, Serguei; Gladding, Sophia; Aylward, Michael; Borman-Shoap, Emily; Melton, Genevieve B

2012-01-01

Medical post-graduate residency training and medical student training increasingly utilize electronic systems to evaluate trainee performance based on defined training competencies with quantitative and qualitative data, the later of which typically consists of text comments. Medical education is concomitantly becoming a growing area of clinical research. While electronic systems have proliferated in number, little work has been done to help manage and analyze qualitative data from these evaluations. We explored the use of text-mining techniques to assist medical education researchers in sentiment analysis and topic analysis of residency evaluations with a sample of 812 evaluation statements. While comments were predominantly positive, sentiment analysis improved the ability to discriminate statements with 93% accuracy. Similar to other domains, Latent Dirichlet Analysis and Information Gain revealed groups of core subjects and appear to be useful for identifying topics from this data.

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.

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…

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.…

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.

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…

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...

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.

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.

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.

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.

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

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

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.

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

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.

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…

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.

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…

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…

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.

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.

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.

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

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 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

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

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.

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.

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.

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.

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.

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.

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

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

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.

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.

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

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].

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

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

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

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.

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

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.

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.

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

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.

Negative Binomial Process Count and Mixture Modeling.

PubMed

Zhou, Mingyuan; Carin, Lawrence

2015-02-01

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process for count modeling. A draw from the NB process consists of a Poisson distributed finite number of distinct atoms, each of which is associated with a logarithmic distributed number of data samples. We reveal relationships between various count- and mixture-modeling distributions and construct a Poisson-logarithmic bivariate distribution that connects the NB and Chinese restaurant table distributions. Fundamental properties of the models are developed, and we derive efficient Bayesian inference. It is shown that with augmentation and normalization, the NB process and gamma-NB process can be reduced to the Dirichlet process and hierarchical Dirichlet process, respectively. These relationships highlight theoretical, structural, and computational advantages of the NB process. A variety of NB processes, including the beta-geometric, beta-NB, marked-beta-NB, marked-gamma-NB and zero-inflated-NB processes, with distinct sharing mechanisms, are also constructed. These models are applied to topic modeling, with connections made to existing algorithms under Poisson factor analysis. Example results show the importance of inferring both the NB dispersion and probability parameters.

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.

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

Cracks in Complex Bodies: Covariance of Tip Balances

NASA Astrophysics Data System (ADS)

Mariano, Paolo Maria

2008-04-01

In complex bodies, actions due to substructural changes alter (in some cases drastically) the force driving the tip of macroscopic cracks in quasi-static and dynamic growth, and must be represented directly. Here it is proven that tip balances of standard and substructural interactions are covariant. In fact, the former balance follows from the Lagrangian density’s requirement of invariance with respect to the action of the group of diffeomorphisms of the ambient space to itself, the latter balance accrues from an analogous invariance with respect to the action of a Lie group over the manifold of substructural shapes. The evolution equation of the crack tip can be obtained by exploiting invariance with respect to relabeling the material elements in the reference place. The analysis is developed by first focusing on general complex bodies that admit metastable states with substructural dissipation of viscous-like type inside each material element. Then we account for gradient dissipative effects that induce nonconservative stresses; the covariance of tip balances in simple bodies follows as a corollary. When body actions and boundary data of Dirichlet type are absent, the standard variational description of quasi-static crack growth is simply extended to the case of complex materials.

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.

Analysis of MUSIC-type imaging functional for single, thin electromagnetic inhomogeneity in limited-view inverse scattering problem

NASA Astrophysics Data System (ADS)

Ahn, Chi Young; Jeon, Kiwan; Park, Won-Kwang

2015-06-01

This study analyzes the well-known MUltiple SIgnal Classification (MUSIC) algorithm to identify unknown support of thin penetrable electromagnetic inhomogeneity from scattered field data collected within the so-called multi-static response matrix in limited-view inverse scattering problems. The mathematical theories of MUSIC are partially discovered, e.g., in the full-view problem, for an unknown target of dielectric contrast or a perfectly conducting crack with the Dirichlet boundary condition (Transverse Magnetic-TM polarization) and so on. Hence, we perform further research to analyze the MUSIC-type imaging functional and to certify some well-known but theoretically unexplained phenomena. For this purpose, we establish a relationship between the MUSIC imaging functional and an infinite series of Bessel functions of integer order of the first kind. This relationship is based on the rigorous asymptotic expansion formula in the existence of a thin inhomogeneity with a smooth supporting curve. Various results of numerical simulation are presented in order to support the identified structure of MUSIC. Although a priori information of the target is needed, we suggest a least condition of range of incident and observation directions to apply MUSIC in the limited-view problem.

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.

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.

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.

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.

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

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

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.

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.

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.

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.

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.

Analytical Solutions for an Escape Problem in a Disc with an Arbitrary Distribution of Exit Holes Along Its Boundary

NASA Astrophysics Data System (ADS)

Marshall, J. S.

2016-12-01

We analytically construct solutions for the mean first-passage time and splitting probabilities for the escape problem of a particle moving with continuous Brownian motion in a confining planar disc with an arbitrary distribution (i.e., of any number, size and spacing) of exit holes/absorbing sections along its boundary. The governing equations for these quantities are Poisson's equation with a (non-zero) constant forcing term and Laplace's equation, respectively, and both are subject to a mixture of homogeneous Neumann and Dirichlet boundary conditions. Our solutions are expressed as explicit closed formulae written in terms of a parameterising variable via a conformal map, using special transcendental functions that are defined in terms of an associated Schottky group. They are derived by exploiting recent results for a related problem of fluid mechanics that describes a unidirectional flow over "no-slip/no-shear" surfaces, as well as results from potential theory, all of which were themselves derived using the same theory of Schottky groups. They are exact up to the determination of a finite set of mapping parameters, which is performed numerically. Their evaluation also requires the numerical inversion of the parameterising conformal map. Computations for a series of illustrative examples are also presented.

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.

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.

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.

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).

Homogenization of Winkler-Steklov spectral conditions in three-dimensional linear elasticity

NASA Astrophysics Data System (ADS)

Gómez, D.; Nazarov, S. A.; Pérez, M. E.

2018-04-01

We consider a homogenization Winkler-Steklov spectral problem that consists of the elasticity equations for a three-dimensional homogeneous anisotropic elastic body which has a plane part of the surface subject to alternating boundary conditions on small regions periodically placed along the plane. These conditions are of the Dirichlet type and of the Winkler-Steklov type, the latter containing the spectral parameter. The rest of the boundary of the body is fixed, and the period and size of the regions, where the spectral parameter arises, are of order ɛ . For fixed ɛ , the problem has a discrete spectrum, and we address the asymptotic behavior of the eigenvalues {β _k^ɛ }_{k=1}^{∞} as ɛ → 0. We show that β _k^ɛ =O(ɛ ^{-1}) for each fixed k, and we observe a common limit point for all the rescaled eigenvalues ɛ β _k^ɛ while we make it evident that, although the periodicity of the structure only affects the boundary conditions, a band-gap structure of the spectrum is inherited asymptotically. Also, we provide the asymptotic behavior for certain "groups" of eigenmodes.

Topic Repetition in Conversations on Different Days as a Sign of Dementia.

PubMed

Shinkawa, Kaoru; Yamada, Yasunori

2018-01-01

Detecting early signs of dementia in everyday situations becomes more and more important in a rapidly aging society. Language dysfunctions are recognized as the prominent signs of dementia. Previous computational studies characterized these language dysfunctions by using acoustic and linguistic features for detecting dementia. However, they mainly investigated language dysfunctions collected from patients during neuropsychological tests. Language dysfunctions observed during regular conversations in everyday situations received little attention. One of the dysfunctions associated with dementia which is frequently observed in regular conversations is the repetition of a topic on different days. In this study, we propose a feature to characterize topic repetition in conversations on different days. We used conversational data obtained from a daily monitoring service of eight elderly people, two of whom had dementia. Through the analysis of topic extraction with latent Dirichlet allocation, we found that the frequency of topic repetition was significantly higher in people with dementia than in the control group. The results suggest that our proposed feature for identifying topic repetition in regular conversations on different days might be used for detecting dementia.

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

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.

Straight velocity boundaries in the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Latt, Jonas; Chopard, Bastien; Malaspinas, Orestis; Deville, Michel; Michler, Andreas

2008-05-01

Various ways of implementing boundary conditions for the numerical solution of the Navier-Stokes equations by a lattice Boltzmann method are discussed. Five commonly adopted approaches are reviewed, analyzed, and compared, including local and nonlocal methods. The discussion is restricted to velocity Dirichlet boundary conditions, and to straight on-lattice boundaries which are aligned with the horizontal and vertical lattice directions. The boundary conditions are first inspected analytically by applying systematically the results of a multiscale analysis to boundary nodes. This procedure makes it possible to compare boundary conditions on an equal footing, although they were originally derived from very different principles. It is concluded that all five boundary conditions exhibit second-order accuracy, consistent with the accuracy of the lattice Boltzmann method. The five methods are then compared numerically for accuracy and stability through benchmarks of two-dimensional and three-dimensional flows. None of the methods is found to be throughout superior to the others. Instead, the choice of a best boundary condition depends on the flow geometry, and on the desired trade-off between accuracy and stability. From the findings of the benchmarks, the boundary conditions can be classified into two major groups. The first group comprehends boundary conditions that preserve the information streaming from the bulk into boundary nodes and complete the missing information through closure relations. Boundary conditions in this group are found to be exceptionally accurate at low Reynolds number. Boundary conditions of the second group replace all variables on boundary nodes by new values. They exhibit generally much better numerical stability and are therefore dedicated for use in high Reynolds number flows.

Structure of complexes of uranyl succinate with carbamide and dimethylurea

NASA Astrophysics Data System (ADS)

Serezhkina, L. B.; Grigor'ev, M. S.; Seliverstova, N. V.; Serezhkin, V. N.

2017-09-01

Three new succinate-containing complexes of uranyl with carbamide ( Urea) and N,N'-dimethylurea ( s-Dmur) are synthesized and studied by IR spectroscopy and X-ray diffraction. Structures of the same type, [UO2( Urea)4(H2O)][(UO2)2(C4H4O4)3] · 3H2O and [UO2( Urea)4(H2O)][(UO2)2(C4H4O4)3] · 2 Urea contain two sorts of uranium-containing complex groups, namely, mononuclear [UO2( Urea)4(H2O)]2+ cations and two-dimensional [(UO2)2(C4H4O4)3]2- anions described by crystal-chemical formulas AM 5 1 and A 2 Q 3 02, respectively ( A = UO2 2+, M 1 = Urea or H2O, Q 02 = C4H4O4 2-), and differ only in the nature of noncoordinated molecules—water and carbamide. The main structural groups of the [(UO2)2(C4H4O4)2( s-Dmur)3] crystals are [(UO2)2(C4H4O4)2( s-Dmur)3] chains belonging to the A 2 Q 2 02 M 3 1 ( A = UO2 2+, Q 02 = C4H4O4 2-, M 1 = s-Dmur) crystal-chemical group. Specific features of intermolecular interactions in the crystal structures are revealed using the Voronoi-Dirichlet method of molecular polyhedra.

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

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.

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.

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

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.

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.

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.

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.

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

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

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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 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 impact do assumptions about missing data have on conclusions? A practical sensitivity analysis for a cancer survival registry.

PubMed

Smuk, M; Carpenter, J R; Morris, T P

2017-02-06

Within epidemiological and clinical research, missing data are a common issue and often over looked in publications. When the issue of missing observations is addressed it is usually assumed that the missing data are 'missing at random' (MAR). This assumption should be checked for plausibility, however it is untestable, thus inferences should be assessed for robustness to departures from missing at random. We highlight the method of pattern mixture sensitivity analysis after multiple imputation using colorectal cancer data as an example. We focus on the Dukes' stage variable which has the highest proportion of missing observations. First, we find the probability of being in each Dukes' stage given the MAR imputed dataset. We use these probabilities in a questionnaire to elicit prior beliefs from experts on what they believe the probability would be in the missing data. The questionnaire responses are then used in a Dirichlet draw to create a Bayesian 'missing not at random' (MNAR) prior to impute the missing observations. The model of interest is applied and inferences are compared to those from the MAR imputed data. The inferences were largely insensitive to departure from MAR. Inferences under MNAR suggested a smaller association between Dukes' stage and death, though the association remained positive and with similarly low p values. We conclude by discussing the positives and negatives of our method and highlight the importance of making people aware of the need to test the MAR assumption.

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.

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

Worldwide F(ST) estimates relative to five continental-scale populations.

PubMed

Steele, Christopher D; Court, Denise Syndercombe; Balding, David J

2014-11-01

We estimate the population genetics parameter FST (also referred to as the fixation index) from short tandem repeat (STR) allele frequencies, comparing many worldwide human subpopulations at approximately the national level with continental-scale populations. FST is commonly used to measure population differentiation, and is important in forensic DNA analysis to account for remote shared ancestry between a suspect and an alternative source of the DNA. We estimate FST comparing subpopulations with a hypothetical ancestral population, which is the approach most widely used in population genetics, and also compare a subpopulation with a sampled reference population, which is more appropriate for forensic applications. Both estimation methods are likelihood-based, in which FST is related to the variance of the multinomial-Dirichlet distribution for allele counts. Overall, we find low FST values, with posterior 97.5 percentiles < 3% when comparing a subpopulation with the most appropriate population, and even for inter-population comparisons we find FST < 5%. These are much smaller than single nucleotide polymorphism-based inter-continental FST estimates, and are also about half the magnitude of STR-based estimates from population genetics surveys that focus on distinct ethnic groups rather than a general population. Our findings support the use of FST up to 3% in forensic calculations, which corresponds to some current practice.

Anisotropic crystal structure distortion of the monoclinic polymorph of acetaminophen at high hydrostatic pressures.

PubMed

Boldyreva, E V; Shakhtshneider, T P; Vasilchenko, M A; Ahsbahs, H; Uchtmann, H

2000-04-01

The anisotropy of structural distortion of the monoclinic polymorph of acetaminophen induced by hydrostatic pressure up to 4.0 GPa was studied by single-crystal X-ray diffraction in a Merrill-Bassett diamond anvil cell (DAC). The space group (P2(1)/n) and the general structural pattern remained unchanged with pressure. Despite the overall decrease in the molar volume with pressure, the structure expanded in particular crystallographic directions. One of the linear cell parameters (c) passed through a minimum as the pressure increased. The intramolecular bond lengths changed only slightly with pressure, but the changes in the dihedral and torsion angles were very large. The compressibility of the intermolecular hydrogen bonds NH...O and OH...O was measured. NH...O bonds were shown to be slightly more compressible than OH...O bonds. The anisotropy of structural distortion was analysed in detail in relation to the pressure-induced changes in the molecular conformations, to the compression of the hydrogen-bond network, and to the changes in the orientation of molecules with respect to each other in the pleated sheets in the structure. Dirichlet domains were calculated in order to analyse the relative shifts of the centroids of the hydrogen-bonded cycles and of the centroids of the benzene rings with pressure.

Bacterial diversity among four healthcare-associated institutes in Taiwan.

PubMed

Chen, Chang-Hua; Lin, Yaw-Ling; Chen, Kuan-Hsueh; Chen, Wen-Pei; Chen, Zhao-Feng; Kuo, Han-Yueh; Hung, Hsueh-Fen; Tang, Chuan Yi; Liou, Ming-Li

2017-08-15

Indoor microbial communities have important implications for human health, especially in health-care institutes (HCIs). The factors that determine the diversity and composition of microbiomes in a built environment remain unclear. Herein, we used 16S rRNA amplicon sequencing to investigate the relationships between building attributes and surface bacterial communities among four HCIs located in three buildings. We examined the surface bacterial communities and environmental parameters in the buildings supplied with different ventilation types and compared the results using a Dirichlet multinomial mixture (DMM)-based approach. A total of 203 samples from the four HCIs were analyzed. Four bacterial communities were grouped using the DMM-based approach, which were highly similar to those in the 4 HCIs. The α-diversity and β-diversity in the naturally ventilated building were different from the conditioner-ventilated building. The bacterial source composition varied across each building. Nine genera were found as the core microbiota shared by all the areas, of which Acinetobacter, Enterobacter, Pseudomonas, and Staphylococcus are regarded as healthcare-associated pathogens (HAPs). The observed relationship between environmental parameters such as core microbiota and surface bacterial diversity suggests that we might manage indoor environments by creating new sanitation protocols, adjusting the ventilation design, and further understanding the transmission routes of HAPs.

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.

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.

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.

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.

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

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'.

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.

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.

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.

LDA-Based Unified Topic Modeling for Similar TV User Grouping and TV Program Recommendation.

PubMed

Pyo, Shinjee; Kim, Eunhui; Kim, Munchurl

2015-08-01

Social TV is a social media service via TV and social networks through which TV users exchange their experiences about TV programs that they are viewing. For social TV service, two technical aspects are envisioned: grouping of similar TV users to create social TV communities and recommending TV programs based on group and personal interests for personalizing TV. In this paper, we propose a unified topic model based on grouping of similar TV users and recommending TV programs as a social TV service. The proposed unified topic model employs two latent Dirichlet allocation (LDA) models. One is a topic model of TV users, and the other is a topic model of the description words for viewed TV programs. The two LDA models are then integrated via a topic proportion parameter for TV programs, which enforces the grouping of similar TV users and associated description words for watched TV programs at the same time in a unified topic modeling framework. The unified model identifies the semantic relation between TV user groups and TV program description word groups so that more meaningful TV program recommendations can be made. The unified topic model also overcomes an item ramp-up problem such that new TV programs can be reliably recommended to TV users. Furthermore, from the topic model of TV users, TV users with similar tastes can be grouped as topics, which can then be recommended as social TV communities. To verify our proposed method of unified topic-modeling-based TV user grouping and TV program recommendation for social TV services, in our experiments, we used real TV viewing history data and electronic program guide data from a seven-month period collected by a TV poll agency. The experimental results show that the proposed unified topic model yields an average 81.4% precision for 50 topics in TV program recommendation and its performance is an average of 6.5% higher than that of the topic model of TV users only. For TV user prediction with new TV programs, the average prediction precision was 79.6%. Also, we showed the superiority of our proposed model in terms of both topic modeling performance and recommendation performance compared to two related topic models such as polylingual topic model and bilingual topic model.

Testing Group Mean Differences of Latent Variables in Multilevel Data Using Multiple-Group Multilevel CFA and Multilevel MIMIC Modeling.

PubMed

Kim, Eun Sook; Cao, Chunhua

2015-01-01

Considering that group comparisons are common in social science, we examined two latent group mean testing methods when groups of interest were either at the between or within level of multilevel data: multiple-group multilevel confirmatory factor analysis (MG ML CFA) and multilevel multiple-indicators multiple-causes modeling (ML MIMIC). The performance of these methods were investigated through three Monte Carlo studies. In Studies 1 and 2, either factor variances or residual variances were manipulated to be heterogeneous between groups. In Study 3, which focused on within-level multiple-group analysis, six different model specifications were considered depending on how to model the intra-class group correlation (i.e., correlation between random effect factors for groups within cluster). The results of simulations generally supported the adequacy of MG ML CFA and ML MIMIC for multiple-group analysis with multilevel data. The two methods did not show any notable difference in the latent group mean testing across three studies. Finally, a demonstration with real data and guidelines in selecting an appropriate approach to multilevel multiple-group analysis are provided.

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.

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.

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.

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.

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.

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

Multiple Group Membership and Well-Being: Is There Always Strength in Numbers?

PubMed Central

Sønderlund, Anders L.; Morton, Thomas A.; Ryan, Michelle K.

2017-01-01

A growing body of research points to the value of multiple group memberships for individual well-being. However, much of this work considers group memberships very broadly and in terms of number alone. We conducted two correlational studies exploring how the relationship between multiple group membership and well-being is shaped by (a) the complexity of those groups within the overall self-concept (i.e., social identity complexity: SIC), and (b) the perceived value and visibility of individual group memberships to others (i.e., stigma). Study 1 (N = 112) found a positive relationship between multiple group membership and well-being, but only for individuals high in SIC. This effect was mediated by perceived identity expression and access to social support. Study 2 (N = 104) also found that multiple group memberships indirectly contributed to well-being via perceived identity expression and social support, as well as identity compatibility and perceived social inclusion. But, in this study the relationship between multiple group memberships and well-being outcomes was moderated by the perceived value and visibility of group memberships to others. Specifically, possessing multiple, devalued and visible group memberships compromised well-being relative to multiple valued group memberships, or devalued group memberships that were invisible. Together, these studies suggest that the benefits of multiple group membership depend on factors beyond their number. Specifically, the features of group memberships, individually and in combination, and the way in which these guide self-expression and social action, determine whether these are a benefit or burden for individual well-being. PMID:28680414

Shot Group Statistics for Small Arms Applications

DTIC Science & Technology

2017-06-01

standard deviation. Analysis is presented as applied to one , n-round shot group and then is extended to treat multiple, n-round shot groups. A...dispersion measure for multiple, n-round shot groups can be constructed by selecting one of the dispersion measures listed above, measuring the dispersion of...as applied to one , n-round shot group and then is extended to treat multiple, n-round shot groups. A dispersion measure for multiple, n- round shot

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.

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.

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.

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.

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.

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).

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

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

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.

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.

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.

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.

SU-G-TeP1-15: Toward a Novel GPU Accelerated Deterministic Solution to the Linear Boltzmann Transport Equation

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

Yang, R; Fallone, B; Cross Cancer Institute, Edmonton, AB

Purpose: To develop a Graphic Processor Unit (GPU) accelerated deterministic solution to the Linear Boltzmann Transport Equation (LBTE) for accurate dose calculations in radiotherapy (RT). A deterministic solution yields the potential for major speed improvements due to the sparse matrix-vector and vector-vector multiplications and would thus be of benefit to RT. Methods: In order to leverage the massively parallel architecture of GPUs, the first order LBTE was reformulated as a second order self-adjoint equation using the Least Squares Finite Element Method (LSFEM). This produces a symmetric positive-definite matrix which is efficiently solved using a parallelized conjugate gradient (CG) solver. Themore » LSFEM formalism is applied in space, discrete ordinates is applied in angle, and the Multigroup method is applied in energy. The final linear system of equations produced is tightly coupled in space and angle. Our code written in CUDA-C was benchmarked on an Nvidia GeForce TITAN-X GPU against an Intel i7-6700K CPU. A spatial mesh of 30,950 tetrahedral elements was used with an S4 angular approximation. Results: To avoid repeating a full computationally intensive finite element matrix assembly at each Multigroup energy, a novel mapping algorithm was developed which minimized the operations required at each energy. Additionally, a parallelized memory mapping for the kronecker product between the sparse spatial and angular matrices, including Dirichlet boundary conditions, was created. Atomicity is preserved by graph-coloring overlapping nodes into separate kernel launches. The one-time mapping calculations for matrix assembly, kronecker product, and boundary condition application took 452±1ms on GPU. Matrix assembly for 16 energy groups took 556±3s on CPU, and 358±2ms on GPU using the mappings developed. The CG solver took 93±1s on CPU, and 468±2ms on GPU. Conclusion: Three computationally intensive subroutines in deterministically solving the LBTE have been formulated on GPU, resulting in two orders of magnitude speedup. Funding support from Natural Sciences and Engineering Research Council and Alberta Innovates Health Solutions. Dr. Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization).« less

Synthesis and X-ray diffraction study of new uranyl malonate and oxalate complexes with carbamide

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

Medvedkov, Ya. A.; Serezhkina, L. B., E-mail: Lserezh@samsu.ru; Grigor’ev, M. S.

2016-05-15

Two new malonate-containing uranyl complexes with carbamide of the formulas [UO{sub 2}(C{sub 3}H{sub 2}O{sub 4})(Urea){sub 2}] (I) and [UO{sub 2}(C{sub 3}H{sub 2}O{sub 4})(Urea){sub 3}] (II), where Urea is carbamide, and one uranyl oxalate complex of the formula [UO{sub 2}(C{sub 2}O{sub 4})(Urea){sub 3}] (III) were synthesized, and their crystals were studied by X-ray diffraction. The main structural units in crystals I are the electroneutral chains [UO{sub 2}(C{sub 3}H{sub 2}O{sub 4})(Urea){sub 2}]{sub ∞} belonging to the crystal-chemical group AT{sup 11}M{sub 2}{sup 1} (A = UO{sub 2}{sup 2+}, T{sup 11} = C{sub 3}H{sub 2}O{sub 4}{sup 2-}, M{sup 1} = Urea) of uranyl complexes.more » Crystals II and III are composed of the molecular complexes [UO{sub 2}(L)(Urea){sub 3}], where L = C{sub 3}H{sub 2}O{sub 4}{sup 2-} or C{sub 2}O{sub 4}{sup 2-}, belonging to the crystal-chemical group AB{sup 01}M{sub 3}{sup 1} (A = UO{sub 2}{sup 2+}, B{sup 01} = C{sub 3}H{sub 2}O{sub 4}{sup 2-} or C{sub 2}O{sub 4}{sup 2-}, M{sup 1} = Urea). The characteristic features of the packing of the uranium-containing complexes are discussed in terms of molecular Voronoi–Dirichlet polyhedra. The effect of the Urea: U ratio on the structure of uranium-containing structural units is considered.« less

Spectral algorithms for multiple scale localized eigenfunctions in infinitely long, slightly bent quantum waveguides

NASA Astrophysics Data System (ADS)

Boyd, John P.; Amore, Paolo; Fernández, Francisco M.

2018-03-01

A "bent waveguide" in the sense used here is a small perturbation of a two-dimensional rectangular strip which is infinitely long in the down-channel direction and has a finite, constant width in the cross-channel coordinate. The goal is to calculate the smallest ("ground state") eigenvalue of the stationary Schrödinger equation which here is a two-dimensional Helmholtz equation, ψxx +ψyy + Eψ = 0 where E is the eigenvalue and homogeneous Dirichlet boundary conditions are imposed on the walls of the waveguide. Perturbation theory gives a good description when the "bending strength" parameter ɛ is small as described in our previous article (Amore et al., 2017) and other works cited therein. However, such series are asymptotic, and it is often impractical to calculate more than a handful of terms. It is therefore useful to develop numerical methods for the perturbed strip to cover intermediate ɛ where the perturbation series may be inaccurate and also to check the pertubation expansion when ɛ is small. The perturbation-induced change-in-eigenvalue, δ ≡ E(ɛ) - E(0) , is O(ɛ2) . We show that the computation becomes very challenging as ɛ → 0 because (i) the ground state eigenfunction varies on both O(1) and O(1 / ɛ) length scales and (ii) high accuracy is needed to compute several correct digits in δ, which is itself small compared to the eigenvalue E. The multiple length scales are not geographically separate, but rather are inextricably commingled in the neighborhood of the boundary deformation. We show that coordinate mapping and immersed boundary strategies both reduce the computational domain to the uniform strip, allowing application of pseudospectral methods on tensor product grids with tensor product basis functions. We compared different basis sets; Chebyshev polynomials are best in the cross-channel direction. However, sine functions generate rather accurate analytical approximations with just a single basis function. In the down-channel coordinate, X ∈ [ - ∞ , ∞ ] , Fourier domain truncation using the change of coordinate X = sinh(Lt) is considerably more efficient than rational Chebyshev functions TBn(X ; L) . All the spectral methods, however, yielded the required accuracy on a desktop computer.

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.

Physical and mental health status of survivors of multiple cancer diagnoses: findings from the National Health Interview Survey.

PubMed

Andrykowski, Michael A

2012-07-15

Little research has identified the physical and mental health status of survivors of multiple primary cancer diagnoses. By using data from the population-based 2009 National Health Information Survey, 154 survivors of multiple primary cancer diagnoses, 1427 survivors of a single cancer diagnosis, and 25,004 individuals without a history of cancer diagnosis were identified. The multiple cancer group was compared with the single cancer and no cancer groups with regard to physical and mental health status using analysis of covariance and binary logistic regression. Relative to the no cancer group, the multiple cancer group reported significantly poorer mental health status, greater lifetime, recent, and current prevalence of a variety of medical conditions and comorbidities, and more health-related disability. Although observed group differences between the multiple cancer and single cancer groups were less pronounced than those between the multiple cancer and no cancer groups, a consistent pattern was also evident; the multiple cancer group reported significantly poorer status relative to the single cancer group across a range of mental and physical health and illness-related disability indices. Diagnosis of 2 or more primary cancers (excluding nonmelanoma skin cancers) is associated with increased risk for poorer physical and mental health status over and above that associated with diagnosis of a single primary cancer. Survivors of multiple and single primary cancer diagnoses should be considered as distinct subgroups, and increased attention should be devoted to the unique status and needs of survivors of multiple primary cancer diagnoses. Copyright © 2011 American Cancer Society.

Improvements in cognition, quality of life, and physical performance with clinical Pilates in multiple sclerosis: a randomized controlled trial

PubMed Central

Küçük, Fadime; Kara, Bilge; Poyraz, Esra Çoşkuner; İdiman, Egemen

2016-01-01

[Purpose] The aim of this study was to determine the effects of clinical Pilates in multiple sclerosis patients. [Subjects and Methods] Twenty multiple sclerosis patients were enrolled in this study. The participants were divided into two groups as the clinical Pilates and control groups. Cognition (Multiple Sclerosis Functional Composite), balance (Berg Balance Scale), physical performance (timed performance tests, Timed up and go test), tiredness (Modified Fatigue Impact scale), depression (Beck Depression Inventory), and quality of life (Multiple Sclerosis International Quality of Life Questionnaire) were measured before and after treatment in all participants. [Results] There were statistically significant differences in balance, timed performance, tiredness and Multiple Sclerosis Functional Composite tests between before and after treatment in the clinical Pilates group. We also found significant differences in timed performance tests, the Timed up and go test and the Multiple Sclerosis Functional Composite between before and after treatment in the control group. According to the difference analyses, there were significant differences in Multiple Sclerosis Functional Composite and Multiple Sclerosis International Quality of Life Questionnaire scores between the two groups in favor of the clinical Pilates group. There were statistically significant clinical differences in favor of the clinical Pilates group in comparison of measurements between the groups. Clinical Pilates improved cognitive functions and quality of life compared with traditional exercise. [Conclusion] In Multiple Sclerosis treatment, clinical Pilates should be used as a holistic approach by physical therapists. PMID:27134355

Improvements in cognition, quality of life, and physical performance with clinical Pilates in multiple sclerosis: a randomized controlled trial.

PubMed

Küçük, Fadime; Kara, Bilge; Poyraz, Esra Çoşkuner; İdiman, Egemen

2016-03-01

[Purpose] The aim of this study was to determine the effects of clinical Pilates in multiple sclerosis patients. [Subjects and Methods] Twenty multiple sclerosis patients were enrolled in this study. The participants were divided into two groups as the clinical Pilates and control groups. Cognition (Multiple Sclerosis Functional Composite), balance (Berg Balance Scale), physical performance (timed performance tests, Timed up and go test), tiredness (Modified Fatigue Impact scale), depression (Beck Depression Inventory), and quality of life (Multiple Sclerosis International Quality of Life Questionnaire) were measured before and after treatment in all participants. [Results] There were statistically significant differences in balance, timed performance, tiredness and Multiple Sclerosis Functional Composite tests between before and after treatment in the clinical Pilates group. We also found significant differences in timed performance tests, the Timed up and go test and the Multiple Sclerosis Functional Composite between before and after treatment in the control group. According to the difference analyses, there were significant differences in Multiple Sclerosis Functional Composite and Multiple Sclerosis International Quality of Life Questionnaire scores between the two groups in favor of the clinical Pilates group. There were statistically significant clinical differences in favor of the clinical Pilates group in comparison of measurements between the groups. Clinical Pilates improved cognitive functions and quality of life compared with traditional exercise. [Conclusion] In Multiple Sclerosis treatment, clinical Pilates should be used as a holistic approach by physical therapists.

Temporal Variability of Oral Microbiota over 10 Months and the Implications for Future Epidemiologic Studies.

PubMed

Vogtmann, Emily; Hua, Xing; Zhou, Liang; Wan, Yunhu; Suman, Shalabh; Zhu, Bin; Dagnall, Casey L; Hutchinson, Amy; Jones, Kristine; Hicks, Belynda D; Sinha, Rashmi; Shi, Jianxin; Abnet, Christian C

2018-05-01

Background: Few studies have prospectively evaluated the association between oral microbiota and health outcomes. Precise estimates of the intrasubject microbial metric stability will allow better study planning. Therefore, we conducted a study to evaluate the temporal variability of oral microbiota. Methods: Forty individuals provided six oral samples using the OMNIgene ORAL kit and Scope mouthwash oral rinses approximately every two months over 10 months. DNA was extracted using the QIAsymphony and the V4 region of the 16S rRNA gene was amplified and sequenced using the MiSeq. To estimate temporal variation, we calculated intraclass correlation coefficients (ICCs) for a variety of metrics and examined stability after clustering samples into distinct community types using Dirichlet multinomial models (DMMs). Results: The ICCs for the alpha diversity measures were high, including for number of observed bacterial species [0.74; 95% confidence interval (CI): 0.65-0.82 and 0.79; 95% CI: 0.75-0.94] from OMNIgene ORAL and Scope mouthwash, respectively. The ICCs for the relative abundance of the top four phyla and beta diversity matrices were lower. Three clusters provided the best model fit for the DMM from the OMNIgene ORAL samples, and the probability of remaining in a specific cluster was high (59.5%-80.7%). Conclusions: The oral microbiota appears to be stable over time for multiple metrics, but some measures, particularly relative abundance, were less stable. Impact: We used this information to calculate stability-adjusted power calculations that will inform future field study protocols and experimental analytic designs. Cancer Epidemiol Biomarkers Prev; 27(5); 594-600. ©2018 AACR . ©2018 American Association for Cancer Research.

Hierarchical brain mapping via a generalized Dirichlet solution for mapping brain manifolds

NASA Astrophysics Data System (ADS)

Joshi, Sarang C.; Miller, Michael I.; Christensen, Gary E.; Banerjee, Ayan; Coogan, Tom; Grenander, Ulf

1995-08-01

In this paper we present a coarse-to-fine approach for the transformation of digital anatomical textbooks from the ideal to the individual that unifies the work on landmark deformations and volume based transformation. The Hierarchical approach is linked to the Biological problem itself, coming out of the various kinds of information which is provided by the anatomists. This information is in the form of points, lines, surfaces and sub-volumes corresponding to 0, 1, 2, and 3 dimensional sub-manifolds respectively. The algorithm is driven by these sub- manifolds. We follow the approach that the highest dimensional transformation is a result from the solution of a sequence of lower dimensional problems driven by successive refinements or partitions of the images into various Biologically meaningful sub-structures.

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.

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.

Event-triggered synchronization for reaction-diffusion complex networks via random sampling

NASA Astrophysics Data System (ADS)

Dong, Tao; Wang, Aijuan; Zhu, Huiyun; Liao, Xiaofeng

2018-04-01

In this paper, the synchronization problem of the reaction-diffusion complex networks (RDCNs) with Dirichlet boundary conditions is considered, where the data is sampled randomly. An event-triggered controller based on the sampled data is proposed, which can reduce the number of controller and the communication load. Under this strategy, the synchronization problem of the diffusion complex network is equivalently converted to the stability of a of reaction-diffusion complex dynamical systems with time delay. By using the matrix inequality technique and Lyapunov method, the synchronization conditions of the RDCNs are derived, which are dependent on the diffusion term. Moreover, it is found the proposed control strategy can get rid of the Zeno behavior naturally. Finally, a numerical example is given to verify the obtained results.

Hypergeometric Forms for Ising-Class Integrals

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

Bailey, David H.; Borwein, David; Borwein, Jonathan M.

2006-07-01

We apply experimental-mathematical principles to analyzecertain integrals relevant to the Ising theory of solid-state physics. Wefind representations of the these integrals in terms of MeijerG-functions and nested-Barnes integrals. Our investigations began bycomputing 500-digit numerical values of Cn,k,namely a 2-D array of Isingintegrals for all integers n, k where n is in [2,12]and k is in [0,25].We found that some Cn,k enjoy exact evaluations involving DirichletL-functions or the Riemann zeta function. In theprocess of analyzinghypergeometric representations, we found -- experimentally and strikingly-- that the Cn,k almost certainly satisfy certain inter-indicialrelations including discrete k-recursions. Using generating functions,differential theory, complex analysis, and Wilf-Zeilbergermore » algorithms weare able to prove some central cases of these relations.« less

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.

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.

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

Superradiance of charged black holes in Einstein–Gauss–Bonnet gravity

NASA Astrophysics Data System (ADS)

Fierro, Octavio; Grandi, Nicolás; Oliva, Julio

2018-05-01

In this paper we show that electrically charged black holes in Einstein–Gauss–Bonnet gravity suffer from a superradiant instability. It is triggered by a charged scalar field that fulfils Dirichlet boundary conditions at a mirror located outside the horizon. As in general relativity, the unstable modes exist provided that the mirror is located beyond a critical radius, making the instability a long wavelength one. We explore the effects of the Gauss–Bonnet corrections on the critical radius and find evidence that the critical radius decreases as the Gauss–Bonnet coupling α increases. Due to the, up to date, lack of an analytic rotating solution for Einstein–Gauss–Bonnet theory, this is the first example of a superradiant instability in the presence of higher curvature terms in the action.

An empirical investigation of methods for nonsymmetric linear systems

NASA Technical Reports Server (NTRS)

Sherman, A. H.

1981-01-01

The present investigation is concerned with a comparison of methods for solving linear algebraic systems which arise from finite difference discretizations of the elliptic convection-diffusion equation in a planar region Omega with Dirichlet boundary conditions. Such linear systems are typically of the form Ax = b where A is an N x N sparse nonsymmetric matrix. In a discussion of discretizations, it is assumed that a regular rectilinear mesh of width h has been imposed on Omega. The discretizations considered include central differences, upstream differences, and modified upstream differences. Six methods for solving Ax = b are considered. Three variants of Gaussian elimination have been chosen as representatives of state-of-the-art software for direct methods under different assumptions about pivoting. Three iterative methods are also included.

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.

LES, DNS and RANS for the analysis of high-speed turbulent reacting flows

NASA Technical Reports Server (NTRS)

Givi, Peyman; Taulbee, Dale B.; Adumitroaie, Virgil; Sabini, George J.; Shieh, Geoffrey S.

1994-01-01

The purpose of this research is to continue our efforts in advancing the state of knowledge in large eddy simulation (LES), direct numerical simulation (DNS), and Reynolds averaged Navier Stokes (RANS) methods for the computational analysis of high-speed reacting turbulent flows. In the second phase of this work, covering the period 1 Sep. 1993 - 1 Sep. 1994, we have focused our efforts on two research problems: (1) developments of 'algebraic' moment closures for statistical descriptions of nonpremixed reacting systems, and (2) assessments of the Dirichlet frequency in presumed scalar probability density function (PDF) methods in stochastic description of turbulent reacting flows. This report provides a complete description of our efforts during this past year as supported by the NASA Langley Research Center under Grant NAG1-1122.

Generalised solutions for fully nonlinear PDE systems and existence-uniqueness theorems

NASA Astrophysics Data System (ADS)

Katzourakis, Nikos

2017-07-01

We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as solutions. This approach bypasses the standard problems arising by the application of Distributions to PDEs and is not based on either integration by parts or on the maximum principle. Instead, our starting point builds on the probabilistic representation of derivatives via limits of difference quotients in the Young measures over a toric compactification of the space of jets. After developing some basic theory, as a first application we consider the Dirichlet problem and we prove existence-uniqueness-partial regularity of solutions to fully nonlinear degenerate elliptic 2nd order systems and also existence of solutions to the ∞-Laplace system of vectorial Calculus of Variations in L∞.

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.

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.

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.

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.

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

Percolation galaxy groups and clusters in the sdss redshift survey: identification, catalogs, and the multiplicity function

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

Berlind, Andreas A.; Frieman, Joshua A.; Weinberg, David H.

2006-01-01

We identify galaxy groups and clusters in volume-limited samples of the SDSS redshift survey, using a redshift-space friends-of-friends algorithm. We optimize the friends-of-friends linking lengths to recover galaxy systems that occupy the same dark matter halos, using a set of mock catalogs created by populating halos of N-body simulations with galaxies. Extensive tests with these mock catalogs show that no combination of perpendicular and line-of-sight linking lengths is able to yield groups and clusters that simultaneously recover the true halo multiplicity function, projected size distribution, and velocity dispersion. We adopt a linking length combination that yields, for galaxy groups withmore » ten or more members: a group multiplicity function that is unbiased with respect to the true halo multiplicity function; an unbiased median relation between the multiplicities of groups and their associated halos; a spurious group fraction of less than {approx}1%; a halo completeness of more than {approx}97%; the correct projected size distribution as a function of multiplicity; and a velocity dispersion distribution that is {approx}20% too low at all multiplicities. These results hold over a range of mock catalogs that use different input recipes of populating halos with galaxies. We apply our group-finding algorithm to the SDSS data and obtain three group and cluster catalogs for three volume-limited samples that cover 3495.1 square degrees on the sky. We correct for incompleteness caused by fiber collisions and survey edges, and obtain measurements of the group multiplicity function, with errors calculated from realistic mock catalogs. These multiplicity function measurements provide a key constraint on the relation between galaxy populations and dark matter halos.« less

Having a Lot of a Good Thing: Multiple Important Group Memberships as a Source of Self-Esteem

PubMed Central

Jetten, Jolanda; Branscombe, Nyla R.; Haslam, S. Alexander; Haslam, Catherine; Cruwys, Tegan; Jones, Janelle M.; Cui, Lijuan; Dingle, Genevieve; Liu, James; Murphy, Sean; Thai, Anh; Walter, Zoe; Zhang, Airong

2015-01-01

Membership in important social groups can promote a positive identity. We propose and test an identity resource model in which personal self-esteem is boosted by membership in additional important social groups. Belonging to multiple important group memberships predicts personal self-esteem in children (Study 1a), older adults (Study 1b), and former residents of a homeless shelter (Study 1c). Study 2 shows that the effects of multiple important group memberships on personal self-esteem are not reducible to number of interpersonal ties. Studies 3a and 3b provide longitudinal evidence that multiple important group memberships predict personal self-esteem over time. Studies 4 and 5 show that collective self-esteem mediates this effect, suggesting that membership in multiple important groups boosts personal self-esteem because people take pride in, and derive meaning from, important group memberships. Discussion focuses on when and why important group memberships act as a social resource that fuels personal self-esteem. PMID:26017554

Bridges or Barriers? Conceptualization of the Role of Multiple Identity Gateway Groups in Intergroup Relations.

PubMed

Levy, Aharon; Saguy, Tamar; Halperin, Eran; van Zomeren, Martijn

2017-01-01

The modern era of globalization has been accompanied by a massive growth in interconnections between groups, and has led to the sharing of multiple identities by individuals and groups. Following these developments, research has focused on the issue of multiple identities, and has shed important light on how individuals who hold these complex forms of identity feel and behave, and on the reactions they elicit from members of other groups. However, the potential of groups with such multiple identities (e.g., biracials, immigrants, etc.) to affect the intergroup relations between the groups that represent the respective sources of the different identities (e.g., Blacks and Whites, country of origin and country of residence, etc.) has not been examined to date. Accordingly, in this paper, we first systematically explore the potential of groups in which people identify with multiple social categories, or groups that are perceived as such by others, to play a role in intergroup dynamics. Next, we offer a theoretical framework outlining what functions groups of people with shared multiple identities may serve (as bridges or barriers ) by proposing how their presence may facilitate or deteriorate intergroup relations. Finally, we present recent empirical research examining how groups of people with shared multiple identities can act as gateways and bridge the cleft between two separate groups that represent the respective sources of their different identities, and discuss the theoretical and practical implications for the field of intergroup relations.

Bridges or Barriers? Conceptualization of the Role of Multiple Identity Gateway Groups in Intergroup Relations

PubMed Central

Levy, Aharon; Saguy, Tamar; Halperin, Eran; van Zomeren, Martijn

2017-01-01

The modern era of globalization has been accompanied by a massive growth in interconnections between groups, and has led to the sharing of multiple identities by individuals and groups. Following these developments, research has focused on the issue of multiple identities, and has shed important light on how individuals who hold these complex forms of identity feel and behave, and on the reactions they elicit from members of other groups. However, the potential of groups with such multiple identities (e.g., biracials, immigrants, etc.) to affect the intergroup relations between the groups that represent the respective sources of the different identities (e.g., Blacks and Whites, country of origin and country of residence, etc.) has not been examined to date. Accordingly, in this paper, we first systematically explore the potential of groups in which people identify with multiple social categories, or groups that are perceived as such by others, to play a role in intergroup dynamics. Next, we offer a theoretical framework outlining what functions groups of people with shared multiple identities may serve (as bridges or barriers) by proposing how their presence may facilitate or deteriorate intergroup relations. Finally, we present recent empirical research examining how groups of people with shared multiple identities can act as gateways and bridge the cleft between two separate groups that represent the respective sources of their different identities, and discuss the theoretical and practical implications for the field of intergroup relations. PMID:28706501

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.

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.

Using multiple group modeling to test moderators in meta-analysis.

PubMed

Schoemann, Alexander M

2016-12-01

Meta-analysis is a popular and flexible analysis that can be fit in many modeling frameworks. Two methods of fitting meta-analyses that are growing in popularity are structural equation modeling (SEM) and multilevel modeling (MLM). By using SEM or MLM to fit a meta-analysis researchers have access to powerful techniques associated with SEM and MLM. This paper details how to use one such technique, multiple group analysis, to test categorical moderators in meta-analysis. In a multiple group meta-analysis a model is fit to each level of the moderator simultaneously. By constraining parameters across groups any model parameter can be tested for equality. Using multiple groups to test for moderators is especially relevant in random-effects meta-analysis where both the mean and the between studies variance of the effect size may be compared across groups. A simulation study and the analysis of a real data set are used to illustrate multiple group modeling with both SEM and MLM. Issues related to multiple group meta-analysis and future directions for research are discussed. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Multiple-Group Analysis Using the sem Package in the R System

ERIC Educational Resources Information Center

Evermann, Joerg

2010-01-01

Multiple-group analysis in covariance-based structural equation modeling (SEM) is an important technique to ensure the invariance of latent construct measurements and the validity of theoretical models across different subpopulations. However, not all SEM software packages provide multiple-group analysis capabilities. The sem package for the R…

Multiple Group Counseling with Discharged Schizophrenic Adolescents and their Parents.

ERIC Educational Resources Information Center

Lurie, Abraham; Harold, Ron

Discharged adolescent schizophrenics (17) and their families participated in a pilot program of multiple group counseling, planned to help ex-patients reintegrate into the community. Patients were selected prior to discharge and randomly divided into three multiple-family groups. Each participating family had had a severe breakdown in the…

Social identity continuity and mental health among Syrian refugees in Turkey.

PubMed

Smeekes, Anouk; Verkuyten, Maykel; Çelebi, Elif; Acartürk, Ceren; Onkun, Samed

2017-10-01

Building upon social psychological work on social identity and mental health, this study among Syrian refugees in Turkey examined the importance of multiple group memberships and identity continuity for mental health and well-being. A survey study was conducted among the very difficult to reach population of Syrian refugees (N = 361). With path analysis in AMOS the associations were examined between multiple group memberships, social identity continuity and mental health and psychological well-being. Indicate that belonging to multiple groups before migration was related to a higher likelihood of having preserved group memberships after migration (i.e., sense of social identity continuity), which, in turn, predicted greater life satisfaction and lower levels of depression. Multiple group membership, however, was also directly related to higher depression. Findings are discussed in relation to the importance of multiple group membership and feelings of identity continuity for refugees.

Summary from Working Group on Multiple Beams and Funneling

NASA Technical Reports Server (NTRS)

Wangler, T. P.

1985-01-01

The working group on Multiple Beams and Funneling discussed various topics related to multiple beams and funneling, including (1) design considerations for multiple-beam accelerators; (2) scaling of current, emittance, and brightness for multiple-beam systems; (3) funneling lines using either discrete components or a radiofrequency quadrupole (RFQ) funneling structure; and (4) alternatives to funneling.

Superradiance in the BTZ black hole with Robin boundary conditions

NASA Astrophysics Data System (ADS)

Dappiaggi, Claudio; Ferreira, Hugo R. C.; Herdeiro, Carlos A. R.

2018-03-01

We show the existence of superradiant modes of massive scalar fields propagating in BTZ black holes when certain Robin boundary conditions, which never include the commonly considered Dirichlet boundary conditions, are imposed at spatial infinity. These superradiant modes are defined as those solutions whose energy flux across the horizon is towards the exterior region. Differently from rotating, asymptotically flat black holes, we obtain that not all modes which grow up exponentially in time are superradiant; for some of these, the growth is sourced by a bulk instability of AdS3, triggered by the scalar field with Robin boundary conditions, rather than by energy extraction from the BTZ black hole. Thus, this setup provides an example wherein Bosonic modes with low frequency are pumping energy into, rather than extracting energy from, a rotating black hole.

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

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 High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions

NASA Technical Reports Server (NTRS)

Sun, Xian-He; Zhuang, Yu

1997-01-01

In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments are then introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern, and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.

A fictitious domain approach for the Stokes problem based on the extended finite element method

NASA Astrophysics Data System (ADS)

Court, Sébastien; Fournié, Michel; Lozinski, Alexei

2014-01-01

In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries do not match. A mixed finite element method is used for fluid flow. The interface between the fluid and the structure is localized by a level-set function. Dirichlet boundary conditions are taken into account using Lagrange multiplier. A stabilization term is introduced to improve the approximation of the normal trace of the Cauchy stress tensor at the interface and avoid the inf-sup condition between the spaces for velocity and the Lagrange multiplier. Convergence analysis is given and several numerical tests are performed to illustrate the capabilities of the method.

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.

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.

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.

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.

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.

Induced charge electrophoresis of a conducting cylinder in a nonconducting cylindrical pore and its micromotoring application

NASA Astrophysics Data System (ADS)

Feng, Huicheng; Wong, Teck Neng; Che, Zhizhao

2016-08-01

Induced charge electrophoresis of a conducting cylinder suspended in a nonconducting cylindrical pore is theoretically analyzed and a micromotor is proposed that utilizes the cylinder rotation. The cylinder velocities are analytically obtained in the Dirichlet and the Neumann boundary conditions of the electric field on the cylindrical pore. The results show that the cylinder not only translates but also rotates when it is eccentric with respect to the cylindrical pore. The influences of a number of parameters on the cylinder velocities are characterized in detail. The cylinder trajectories show that the cylinder approaches and becomes stationary at certain positions within the cylindrical pore. The proposed micromotor is capable of working under a heavy load with a high rotational velocity when the eccentricity is large and the applied electric field is strong.

On the use of reverse Brownian motion to accelerate hybrid simulations

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

Bakarji, Joseph; Tartakovsky, Daniel M., E-mail: tartakovsky@stanford.edu

Multiscale and multiphysics simulations are two rapidly developing fields of scientific computing. Efficient coupling of continuum (deterministic or stochastic) constitutive solvers with their discrete (stochastic, particle-based) counterparts is a common challenge in both kinds of simulations. We focus on interfacial, tightly coupled simulations of diffusion that combine continuum and particle-based solvers. The latter employs the reverse Brownian motion (rBm), a Monte Carlo approach that allows one to enforce inhomogeneous Dirichlet, Neumann, or Robin boundary conditions and is trivially parallelizable. We discuss numerical approaches for improving the accuracy of rBm in the presence of inhomogeneous Neumann boundary conditions and alternative strategiesmore » for coupling the rBm solver with its continuum counterpart. Numerical experiments are used to investigate the convergence, stability, and computational efficiency of the proposed hybrid algorithm.« less

Black branes in a box: hydrodynamics, stability, and criticality

NASA Astrophysics Data System (ADS)

Emparan, Roberto; Martınez, Marina

2012-07-01

We study the effective hydrodynamics of neutral black branes enclosed in a finite cylindrical cavity with Dirichlet boundary conditions. We focus on how the Gregory-Laflamme instability changes as we vary the cavity radius R. Fixing the metric at the cavity wall increases the rigidity of the black brane by hindering gradients of the redshift on the wall. In the effective fluid, this is reflected in the growth of the squared speed of sound. As a consequence, when the cavity is smaller than a critical radius the black brane becomes dynamically stable. The correlation with the change in thermodynamic stability is transparent in our approach. We compute the bulk and shear viscosities of the black brane and find that they do not run with R. We find mean-field theory critical exponents near the critical point.

The Bloch Approximation in Periodically Perforated Media

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

Conca, C.; Gomez, D., E-mail: gomezdel@unican.es; Lobo, M.

2005-06-15

We consider a periodically heterogeneous and perforated medium filling an open domain {omega} of R{sup N}. Assuming that the size of the periodicity of the structure and of the holes is O({epsilon}),we study the asymptotic behavior, as {epsilon} {sup {yields}} 0, of the solution of an elliptic boundary value problem with strongly oscillating coefficients posed in {omega}{sup {epsilon}}({omega}{sup {epsilon}} being {omega} minus the holes) with a Neumann condition on the boundary of the holes. We use Bloch wave decomposition to introduce an approximation of the solution in the energy norm which can be computed from the homogenized solution and themore » first Bloch eigenfunction. We first consider the case where {omega}is R{sup N} and then localize the problem for abounded domain {omega}, considering a homogeneous Dirichlet condition on the boundary of {omega}.« less

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.

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

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.

Non-localization of eigenfunctions for Sturm-Liouville operators and applications

NASA Astrophysics Data System (ADS)

Liard, Thibault; Lissy, Pierre; Privat, Yannick

2018-02-01

In this article, we investigate a non-localization property of the eigenfunctions of Sturm-Liouville operators Aa = -∂xx + a (ṡ) Id with Dirichlet boundary conditions, where a (ṡ) runs over the bounded nonnegative potential functions on the interval (0 , L) with L > 0. More precisely, we address the extremal spectral problem of minimizing the L2-norm of a function e (ṡ) on a measurable subset ω of (0 , L), where e (ṡ) runs over all eigenfunctions of Aa, at the same time with respect to all subsets ω having a prescribed measure and all L∞ potential functions a (ṡ) having a prescribed essentially upper bound. We provide some existence and qualitative properties of the minimizers, as well as precise lower and upper estimates on the optimal value. Several consequences in control and stabilization theory are then highlighted.

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.

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

Caravelli, Francesco

The dynamics of purely memristive circuits has been shown to depend on a projection operator which expresses the Kirchhoff constraints, is naturally non-local in nature, and does represent the interaction between memristors. In the present paper we show that for the case of planar circuits, for which a meaningful Hamming distance can be defined, the elements of such projector can be bounded by exponentially decreasing functions of the distance. We provide a geometrical interpretation of the projector elements in terms of determinants of Dirichlet Laplacian of the dual circuit. For the case of linearized dynamics of the circuit for whichmore » a solution is known, this can be shown to provide a light cone bound for the interaction between memristors. Furthermore, this result establishes a finite speed of propagation of signals across the network, despite the non-local nature of the system.« less

Specific features of nonvalent interactions in orthorhombic perovskites

NASA Astrophysics Data System (ADS)

Serezhkin, V. N.; Pushkin, D. V.; Serezhkina, L. B.

2014-07-01

It is established that isostructural orthorhombic perovskites ABO3 (sp. gr. Pnma in different systems, no. 62, Z = 4), depending on the specificity of nonvalent interactions (which determine the combinatorial-topological type of the Voronoi-Dirichlet polyhedra (VDPs) of four basis atoms), are divided into ten different stereotypes. It is shown by the example of 259 perovskites belonging to the DyCrO3 stereotype that VDP characteristics can be used to quantitatively estimate the distortion of BO6 octahedra, including that caused by the Jahn-Teller effect. It is found that one of the causes of the distortion of the coordination polyhedra of atoms in the structure of orthorhombic perovskites is heteroatomic metal-metal interactions, for which the interatomic distances are much shorter than the sum of the Slater radii of A and B atoms.

Should multiple imputation be the method of choice for handling missing data in randomized trials?

PubMed Central

Sullivan, Thomas R; White, Ian R; Salter, Amy B; Ryan, Philip; Lee, Katherine J

2016-01-01

The use of multiple imputation has increased markedly in recent years, and journal reviewers may expect to see multiple imputation used to handle missing data. However in randomized trials, where treatment group is always observed and independent of baseline covariates, other approaches may be preferable. Using data simulation we evaluated multiple imputation, performed both overall and separately by randomized group, across a range of commonly encountered scenarios. We considered both missing outcome and missing baseline data, with missing outcome data induced under missing at random mechanisms. Provided the analysis model was correctly specified, multiple imputation produced unbiased treatment effect estimates, but alternative unbiased approaches were often more efficient. When the analysis model overlooked an interaction effect involving randomized group, multiple imputation produced biased estimates of the average treatment effect when applied to missing outcome data, unless imputation was performed separately by randomized group. Based on these results, we conclude that multiple imputation should not be seen as the only acceptable way to handle missing data in randomized trials. In settings where multiple imputation is adopted, we recommend that imputation is carried out separately by randomized group. PMID:28034175

Should multiple imputation be the method of choice for handling missing data in randomized trials?

PubMed

Sullivan, Thomas R; White, Ian R; Salter, Amy B; Ryan, Philip; Lee, Katherine J

2016-01-01

The use of multiple imputation has increased markedly in recent years, and journal reviewers may expect to see multiple imputation used to handle missing data. However in randomized trials, where treatment group is always observed and independent of baseline covariates, other approaches may be preferable. Using data simulation we evaluated multiple imputation, performed both overall and separately by randomized group, across a range of commonly encountered scenarios. We considered both missing outcome and missing baseline data, with missing outcome data induced under missing at random mechanisms. Provided the analysis model was correctly specified, multiple imputation produced unbiased treatment effect estimates, but alternative unbiased approaches were often more efficient. When the analysis model overlooked an interaction effect involving randomized group, multiple imputation produced biased estimates of the average treatment effect when applied to missing outcome data, unless imputation was performed separately by randomized group. Based on these results, we conclude that multiple imputation should not be seen as the only acceptable way to handle missing data in randomized trials. In settings where multiple imputation is adopted, we recommend that imputation is carried out separately by randomized group.

Changes of procalcitonin level in multiple trauma patients.

PubMed

Wojtaszek, Marek; Staśkiewicz, Grzegorz; Torres, Kamil; Jakubowski, Krzysztof; Rácz, Oliver; Cipora, Elżbieta

2014-01-01

Some aspects of the pathophysiology of complications in multiple-trauma patients still remain unclear. Mediators of inflammation have been postulated as playing a key role in being responsible for life threatening complications of multiple trauma patients. The objective of this study was to evaluate the prognostic value of procalcitonin (PCT) level in multiple trauma patients. A prospective study took place including patients with multiple trauma hospitalised in several hospital units. PCT level was measured in blood from 45 patients, aged 18-70 years using enzyme-linked immunoassay. The patients were divided into three groups: group I - individuals with multiple trauma with central nervous system injury; group II - those with multiple trauma without CNS injury; and group III - patients with isolated central nervous system injury. Initial PCT levels were below 0.5 ng mL(-1) regardless of the cause of trauma. In the 24th hour of observation, a statistically significant increase of PCT concentration vs. initial levels was recorded in all groups of patients. Then PCT levels decreased significantly at the 3rd measurement point in all groups, and they remained unchanged until the last measurement. The highest levels of PCT were observed in multiple trauma patients without CNS injury (group II). In this group of patients, a significantly longer duration of surgery in the post-trauma period affected PCT levels. PCT concentrations in patients who died were significantly greater than in survivors. A long lasting elevated concentration of procalcitonin in the post-traumatic period, or its repeated increase, is a good marker of developing complications observed earlier than clinical manifestations.

Analytical group decision making in natural resources: methodology and application

Treesearch

Daniel L. Schmoldt; David L. Peterson

2000-01-01

Group decision making is becoming increasingly important in natural resource management and associated scientific applications, because multiple values are treated coincidentally in time and space, multiple resource specialists are needed, and multiple stakeholders must be included in the decision process. Decades of social science research on decision making in groups...

Narcotic Use and Postoperative Doctor Shopping in the Orthopaedic Trauma Population.

PubMed

Morris, Brent J; Zumsteg, Justin W; Archer, Kristin R; Cash, Brian; Mir, Hassan R

2014-08-06

The negative consequences of narcotic use and diversion for nonmedical use are on the rise. A growing number of narcotic abusers obtain narcotic prescriptions from multiple providers ("doctor shopping"). This study sought to determine the effects of multiple postoperative narcotic providers on the number of narcotic prescriptions, duration of narcotics, and morphine equivalent dose per day in the orthopaedic trauma population. Our prospective cohort study used the state-controlled substance monitoring database to identify all narcotic prescriptions filled three months prior to admission and six months following discharge for enrolled patients. Patients were assigned into two groups: a single narcotic provider group with prescriptions only from the treating surgeon (or extenders) or a multiple narcotic provider group with prescriptions from both the treating surgeon and an additional provider or providers. Complete data were available for 130 of 151 eligible patients. Preoperative narcotic use, defined by three or more narcotic prescriptions within three months of admission, was noted in 8.5% of patients. Overall, 20.8% of patients sought multiple narcotic providers postoperatively. There were significant increases in postoperative narcotic prescriptions (p < 0.001) between the single narcotic provider group (two prescriptions) and the multiple narcotic provider group (seven prescriptions), in duration of postoperative narcotic use (p < 0.001) between the single narcotic provider group (twenty-eight days) and the multiple narcotic provider group (110 days), and in morphine equivalent dose per day (p = 0.002) between the single narcotic provider group (26 mg) and the multiple narcotic provider group (43 mg). Patients with a high school education or less were 3.2 times more likely to seek multiple providers (p = 0.02), and patients with a history of preoperative narcotic use were 4.5 times more likely to seek multiple providers (p < 0.001). There is a 20.8% prevalence of postoperative doctor shopping in the orthopaedic trauma population. Patients with multiple postoperative narcotic providers had a significant increase in postoperative narcotic prescriptions, duration of narcotics, and morphine equivalent dose per day. Copyright © 2014 by The Journal of Bone and Joint Surgery, Incorporated.

Multiple Intelligences Profiles of Children with Attention Deficit and Hyperactivity Disorder in Comparison with Nonattention Deficit and Hyperactivity Disorder.

PubMed

Najafi, Mostafa; Akouchekian, Shahla; Ghaderi, Alireza; Mahaki, Behzad; Rezaei, Mariam

2017-01-01

Attention deficit and hyperactivity disorder (ADHD) is a common psychological problem during childhood. This study aimed to evaluate multiple intelligences profiles of children with ADHD in comparison with non-ADHD. This cross-sectional descriptive analytical study was done on 50 children of 6-13 years old in two groups of with and without ADHD. Children with ADHD were referred to Clinics of Child and Adolescent Psychiatry, Isfahan University of Medical Sciences, in 2014. Samples were selected based on clinical interview (based on Diagnostic and Statistical Manual of Mental Disorders IV and parent-teacher strengths and difficulties questionnaire), which was done by psychiatrist and psychologist. Raven intelligence quotient (IQ) test was used, and the findings were compared to the results of multiple intelligences test. Data analysis was done using a multivariate analysis of covariance using SPSS20 software. Comparing the profiles of multiple intelligence among two groups, there are more kinds of multiple intelligences in control group than ADHD group, a difference which has been more significant in logical, interpersonal, and intrapersonal intelligence ( P < 0.05). There was no significant difference with the other kinds of multiple intelligences in two groups ( P > 0.05). The IQ average score in the control group and ADHD group was 102.42 ± 16.26 and 96.72 ± 16.06, respectively, that reveals the negative effect of ADHD on IQ average value. There was an insignificance relationship between linguistic and naturalist intelligence ( P > 0.05). However, in other kinds of multiple intelligences, direct and significant relationships were observed ( P < 0.05). Since the levels of IQ (Raven test) and MI in control group were more significant than ADHD group, ADHD is likely to be associated with logical-mathematical, interpersonal, and intrapersonal profiles.

Poisson-Boltzmann-Nernst-Planck model

NASA Astrophysics Data System (ADS)

Zheng, Qiong; Wei, Guo-Wei

2011-05-01

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time.

Poisson-Boltzmann-Nernst-Planck model

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

Zheng Qiong; Wei Guowei; Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824

2011-05-21

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species inmore » the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time.« less

Poisson–Boltzmann–Nernst–Planck model

PubMed Central

Zheng, Qiong; Wei, Guo-Wei

2011-01-01

The Poisson–Nernst–Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst–Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst–Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst–Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson–Boltzmann and Nernst–Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current–voltage (I–V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I–V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time. PMID:21599038

Poisson-Boltzmann-Nernst-Planck model.

PubMed

Zheng, Qiong; Wei, Guo-Wei

2011-05-21

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time. © 2011 American Institute of Physics.

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.

Memory, Multiplication and Mnemonics: A Study into the Recall of Basic Multiplication Facts

ERIC Educational Resources Information Center

Brewer, Robert A.

2004-01-01

The purpose of this study is to examine what effects the mnemonic devices of pictures and stories have on the memorization and recall of multiplication facts. This study was conducted on a fourth grade classroom in which the students were divided into three groups. The first group was given standard flashcards, the second group was given a set of…

Multitrace/singletrace formulations and Domain Decomposition Methods for the solution of Helmholtz transmission problems for bounded composite scatterers

NASA Astrophysics Data System (ADS)

Jerez-Hanckes, Carlos; Pérez-Arancibia, Carlos; Turc, Catalin

2017-12-01

We present Nyström discretizations of multitrace/singletrace formulations and non-overlapping Domain Decomposition Methods (DDM) for the solution of Helmholtz transmission problems for bounded composite scatterers with piecewise constant material properties. We investigate the performance of DDM with both classical Robin and optimized transmission boundary conditions. The optimized transmission boundary conditions incorporate square root Fourier multiplier approximations of Dirichlet to Neumann operators. While the multitrace/singletrace formulations as well as the DDM that use classical Robin transmission conditions are not particularly well suited for Krylov subspace iterative solutions of high-contrast high-frequency Helmholtz transmission problems, we provide ample numerical evidence that DDM with optimized transmission conditions constitute efficient computational alternatives for these type of applications. In the case of large numbers of subdomains with different material properties, we show that the associated DDM linear system can be efficiently solved via hierarchical Schur complements elimination.

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.

Stationary scalar clouds around a BTZ black hole

NASA Astrophysics Data System (ADS)

Ferreira, Hugo R. C.; Herdeiro, Carlos A. R.

2017-10-01

We establish the existence of stationary clouds of massive test scalar fields around BTZ black holes. These clouds are zero-modes of the superradiant instability and are possible when Robin boundary conditions (RBCs) are considered at the AdS boundary. These boundary conditions are the most general ones that ensure the AdS space is an isolated system, and include, as a particular case, the commonly considered Dirichlet or Neumann-type boundary conditions (DBCs or NBCs). We obtain an explicit, closed form, resonance condition, relating the RBCs that allow the existence of normalizable (and regular on and outside the horizon) clouds to the system's parameters. Such RBCs never include pure DBCs or NBCs. We illustrate the spatial distribution of these clouds, their energy and angular momentum density for some cases. Our results show that BTZ black holes with scalar hair can be constructed, as the non-linear realization of these clouds.

Conical : An extended module for computing a numerically satisfactory pair of solutions of the differential equation for conical functions

NASA Astrophysics Data System (ADS)

Dunster, T. M.; Gil, A.; Segura, J.; Temme, N. M.

2017-08-01

Conical functions appear in a large number of applications in physics and engineering. In this paper we describe an extension of our module Conical (Gil et al., 2012) for the computation of conical functions. Specifically, the module includes now a routine for computing the function R-1/2+ iτ m (x) , a real-valued numerically satisfactory companion of the function P-1/2+ iτ m (x) for x > 1. In this way, a natural basis for solving Dirichlet problems bounded by conical domains is provided. The module also improves the performance of our previous algorithm for the conical function P-1/2+ iτ m (x) and it includes now the computation of the first order derivative of the function. This is also considered for the function R-1/2+ iτ m (x) in the extended algorithm.

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

The Path Resistance Method for Bounding the Smallest Nontrivial Eigenvalue of a Laplacian

NASA Technical Reports Server (NTRS)

Guattery, Stephen; Leighton, Tom; Miller, Gary L.

1997-01-01

We introduce the path resistance method for lower bounds on the smallest nontrivial eigenvalue of the Laplacian matrix of a graph. The method is based on viewing the graph in terms of electrical circuits; it uses clique embeddings to produce lower bounds on lambda(sub 2) and star embeddings to produce lower bounds on the smallest Rayleigh quotient when there is a zero Dirichlet boundary condition. The method assigns priorities to the paths in the embedding; we show that, for an unweighted tree T, using uniform priorities for a clique embedding produces a lower bound on lambda(sub 2) that is off by at most an 0(log diameter(T)) factor. We show that the best bounds this method can produce for clique embeddings are the same as for a related method that uses clique embeddings and edge lengths to produce bounds.

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.

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

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

Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces

NASA Astrophysics Data System (ADS)

Mantile, Andrea; Posilicano, Andrea; Sini, Mourad

2016-07-01

The theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic differential operator on Rn with linear boundary conditions on (a relatively open part of) a compact hypersurface. Our approach allows to obtain Kreĭn-like resolvent formulae where the reference operator coincides with the ;free; operator with domain H2 (Rn); this provides an useful tool for the scattering problem from a hypersurface. Concrete examples of this construction are developed in connection with the standard boundary conditions, Dirichlet, Neumann, Robin, δ and δ‧-type, assigned either on a (n - 1) dimensional compact boundary Γ = ∂ Ω or on a relatively open part Σ ⊂ Γ. Schatten-von Neumann estimates for the difference of the powers of resolvents of the free and the perturbed operators are also proven; these give existence and completeness of the wave operators of the associated scattering systems.

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.

A Liouville type theorem for Lane-Emden systems involving the fractional Laplacian

NASA Astrophysics Data System (ADS)

Quaas, Alexander; Xia, Aliang

2016-08-01

We establish a Liouville type theorem for the fractional Lane-Emden system: {(-Δ)αu=vqin  RN,(-Δ)αv=upin  RN, where α \\in (0,1) , N>2α and p, q are positive real numbers and in an appropriate new range. To prove our result we will use the local realization of fractional Laplacian, which can be constructed as a Dirichlet-to-Neumann operator of a degenerate elliptic equation in the spirit of Caffarelli and Silvestre (2007 Commun. PDE 32 1245-60). Our proof is based on a monotonicity argument for suitable transformed functions and the method of moving planes in a half infinite cylinder ({IR}× S+N , where S+N is the half unit sphere in {{{R}}N+1} ) based on maximum principles which are obtained by barrier functions and a coupling argument using a fractional Sobolev trace inequality.

Eigenspace-based fuzzy c-means for sensing trending topics in Twitter

NASA Astrophysics Data System (ADS)

Muliawati, T.; Murfi, H.

2017-07-01

As the information and communication technology are developed, the fulfillment of information can be obtained through social media, like Twitter. The enormous number of internet users has triggered fast and large data flow, thus making the manual analysis is difficult or even impossible. An automated methods for data analysis is needed, one of which is the topic detection and tracking. An alternative method other than latent Dirichlet allocation (LDA) is a soft clustering approach using Fuzzy C-Means (FCM). FCM meets the assumption that a document may consist of several topics. However, FCM works well in low-dimensional data but fails in high-dimensional data. Therefore, we propose an approach where FCM works on low-dimensional data by reducing the data using singular value decomposition (SVD). Our simulations show that this approach gives better accuracies in term of topic recall than LDA for sensing trending topic in Twitter about an event.

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.

Regularity results for the minimum time function with Hörmander vector fields

NASA Astrophysics Data System (ADS)

Albano, Paolo; Cannarsa, Piermarco; Scarinci, Teresa

2018-03-01

In a bounded domain of Rn with boundary given by a smooth (n - 1)-dimensional manifold, we consider the homogeneous Dirichlet problem for the eikonal equation associated with a family of smooth vector fields {X1 , … ,XN } subject to Hörmander's bracket generating condition. We investigate the regularity of the viscosity solution T of such problem. Due to the presence of characteristic boundary points, singular trajectories may occur. First, we characterize these trajectories as the closed set of all points at which the solution loses point-wise Lipschitz continuity. Then, we prove that the local Lipschitz continuity of T, the local semiconcavity of T, and the absence of singular trajectories are equivalent properties. Finally, we show that the last condition is satisfied whenever the characteristic set of {X1 , … ,XN } is a symplectic manifold. We apply our results to several examples.

Parametric embedding for class visualization.

PubMed

Iwata, Tomoharu; Saito, Kazumi; Ueda, Naonori; Stromsten, Sean; Griffiths, Thomas L; Tenenbaum, Joshua B

2007-09-01

We propose a new method, parametric embedding (PE), that embeds objects with the class structure into a low-dimensional visualization space. PE takes as input a set of class conditional probabilities for given data points and tries to preserve the structure in an embedding space by minimizing a sum of Kullback-Leibler divergences, under the assumption that samples are generated by a gaussian mixture with equal covariances in the embedding space. PE has many potential uses depending on the source of the input data, providing insight into the classifier's behavior in supervised, semisupervised, and unsupervised settings. The PE algorithm has a computational advantage over conventional embedding methods based on pairwise object relations since its complexity scales with the product of the number of objects and the number of classes. We demonstrate PE by visualizing supervised categorization of Web pages, semisupervised categorization of digits, and the relations of words and latent topics found by an unsupervised algorithm, latent Dirichlet allocation.

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.

Exponential convergence through linear finite element discretization of stratified subdomains

NASA Astrophysics Data System (ADS)

Guddati, Murthy N.; Druskin, Vladimir; Vaziri Astaneh, Ali

2016-10-01

Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The key features of the discretization are (a) use of midpoint integration to evaluate the contribution matrices, and (b) an unconventional mapping of the mesh into complex space. Named complex-length finite element method (CFEM), the technique is linked to Padé approximants that provide exponential convergence of the Dirichlet-to-Neumann maps and thus the solution at specified points in the domain. Exponential convergence facilitates drastic reduction in the number of elements. This, combined with sparse computation associated with linear finite elements, results in significant reduction in the computational cost. The paper presents the basic ideas of the method as well as illustration of its effectiveness for a variety of problems involving Laplace, Helmholtz and elastodynamics equations.

Tweaking one-loop determinants in AdS3

NASA Astrophysics Data System (ADS)

Castro, Alejandra; Keeler, Cynthia; Szepietowski, Phillip

2017-10-01

We revisit the subject of one-loop determinants in AdS3 gravity via the quasi-normal mode method. Our goal is to evaluate a one-loop determinant with chiral boundary conditions for the metric field; chirality is achieved by imposing Dirichlet boundary conditions on certain components while others satisfy Neumann. Along the way, we give a generalization of the quasinormal mode method for stationary (non-static) thermal backgrounds, and propose a treatment for Neumann boundary conditions in this framework. We evaluate the graviton one-loop determinant on the Euclidean BTZ background with parity-violating boundary conditions (CSS), and find excellent agreement with the dual warped CFT. We also discuss a more general falloff in AdS3 that is related to two dimensional quantum gravity in lightcone gauge. The behavior of the ghost fields under both sets of boundary conditions is novel and we discuss potential interpretations.

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

Existence of evolutionary variational solutions via the calculus of variations

NASA Astrophysics Data System (ADS)

Bögelein, Verena; Duzaar, Frank; Marcellini, Paolo

In this paper we introduce a purely variational approach to time dependent problems, yielding the existence of global parabolic minimizers, that is ∫0T ∫Ω [uṡ∂tφ+f(x,Du)] dx dt⩽∫0T ∫Ω f(x,Du+Dφ) dx dt, whenever T>0 and φ∈C0∞(Ω×(0,T),RN). For the integrand f:Ω×R→[0,∞] we merely assume convexity with respect to the gradient variable and coercivity. These evolutionary variational solutions are obtained as limits of maps depending on space and time minimizing certain convex variational functionals. In the simplest situation, with some growth conditions on f, the method provides the existence of global weak solutions to Cauchy-Dirichlet problems of parabolic systems of the type ∂tu-divDξf(x,Du)=0 in Ω×(0,∞).

Topology and static response of interaction networks in molecular biology

PubMed Central

Radulescu, Ovidiu; Lagarrigue, Sandrine; Siegel, Anne; Veber, Philippe; Le Borgne, Michel

2005-01-01

We introduce a mathematical framework describing static response of networks occurring in molecular biology. This formalism has many similarities with the Laplace–Kirchhoff equations for electrical networks. We introduce the concept of graph boundary and we show how the response of the biological networks to external perturbations can be related to the Dirichlet or Neumann problems for the corresponding equations on the interaction graph. Solutions to these two problems are given in terms of path moduli (measuring path rigidity with respect to the propagation of interaction along the graph). Path moduli are related to loop products in the interaction graph via generalized Mason–Coates formulae. We apply our results to two specific biological examples: the lactose operon and the genetic regulation of lipogenesis. Our applications show consistency with experimental results and in the case of lipogenesis check some hypothesis on the behaviour of hepatic fatty acids on fasting. PMID:16849230

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.

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.

A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Zaky, M. A.

2015-01-01

In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives are presented. By using these operational matrices, we propose a shifted Jacobi tau method for both temporal and spatial discretizations, which allows us to present an efficient spectral method for solving such problem. Furthermore, the error is estimated and the proposed method has reasonable convergence rates in spatial and temporal discretizations. In addition, some known spectral tau approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters θ and ϑ. Finally, in order to demonstrate its accuracy, we compare our method with those reported in the literature.

Closed-form analytical solutions incorporating pumping and tidal effects in various coastal aquifer systems

NASA Astrophysics Data System (ADS)

Wang, Chaoyue; Li, Hailong; Wan, Li; Wang, Xusheng; Jiang, Xiaowei

2014-07-01

Pumping wells are common in coastal aquifers affected by tides. Here we present analytical solutions of groundwater table or head variations during a constant rate pumping from a single, fully-penetrating well in coastal aquifer systems comprising an unconfined aquifer, a confined aquifer and semi-permeable layer between them. The unconfined aquifer terminates at the coastline (or river bank) and the other two layers extend under tidal water (sea or tidal river) for a certain distance L. Analytical solutions are derived for 11 reasonable combinations of different situations of the L-value (zero, finite, and infinite), of the middle layer's permeability (semi-permeable and impermeable), of the boundary condition at the aquifer's submarine terminal (Dirichlet describing direct connection with seawater and no-flow describing the existence of an impermeable capping), and of the tidal water body (sea and tidal river). Solutions are discussed with application examples in fitting field observations and parameter estimations.

Transversally periodic solitary gravity–capillary waves

PubMed Central

Milewski, Paul A.; Wang, Zhan

2014-01-01

When both gravity and surface tension effects are present, surface solitary water waves are known to exist in both two- and three-dimensional infinitely deep fluids. We describe here solutions bridging these two cases: travelling waves which are localized in the propagation direction and periodic in the transverse direction. These transversally periodic gravity–capillary solitary waves are found to be of either elevation or depression type, tend to plane waves below a critical transverse period and tend to solitary lumps as the transverse period tends to infinity. The waves are found numerically in a Hamiltonian system for water waves simplified by a cubic truncation of the Dirichlet-to-Neumann operator. This approximation has been proved to be very accurate for both two- and three-dimensional computations of fully localized gravity–capillary solitary waves. The stability properties of these waves are then investigated via the time evolution of perturbed wave profiles. PMID:24399922

Locality of interactions for planar memristive circuits

DOE PAGES

Caravelli, Francesco

2017-11-08

The dynamics of purely memristive circuits has been shown to depend on a projection operator which expresses the Kirchhoff constraints, is naturally non-local in nature, and does represent the interaction between memristors. In the present paper we show that for the case of planar circuits, for which a meaningful Hamming distance can be defined, the elements of such projector can be bounded by exponentially decreasing functions of the distance. We provide a geometrical interpretation of the projector elements in terms of determinants of Dirichlet Laplacian of the dual circuit. For the case of linearized dynamics of the circuit for whichmore » a solution is known, this can be shown to provide a light cone bound for the interaction between memristors. Furthermore, this result establishes a finite speed of propagation of signals across the network, despite the non-local nature of the system.« less

Pentadiagonal alternating-direction-implicit finite-difference time-domain method for two-dimensional Schrödinger equation

NASA Astrophysics Data System (ADS)

Tay, Wei Choon; Tan, Eng Leong

2014-07-01

In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is further simplified into pentadiagonal fundamental ADI (Penta-FADI) method, which has matrix-operator-free right-hand-sides (RHS), leading to the simplest and most concise update equations. As the Penta-FADI method involves five stencils in the left-hand-sides (LHS) of the pentadiagonal update equations, special treatments that are required for the implementation of the Dirichlet's boundary conditions will be discussed. Using the Penta-FADI method, a significantly higher efficiency gain can be achieved over the conventional Tri-ADI method, which involves a tridiagonal system of equations.

A high-order perturbation of surfaces method for scattering of linear waves by periodic multiply layered gratings in two and three dimensions

NASA Astrophysics Data System (ADS)

Hong, Youngjoon; Nicholls, David P.

2017-09-01

The capability to rapidly and robustly simulate the scattering of linear waves by periodic, multiply layered media in two and three dimensions is crucial in many engineering applications. In this regard, we present a High-Order Perturbation of Surfaces method for linear wave scattering in a multiply layered periodic medium to find an accurate numerical solution of the governing Helmholtz equations. For this we truncate the bi-infinite computational domain to a finite one with artificial boundaries, above and below the structure, and enforce transparent boundary conditions there via Dirichlet-Neumann Operators. This is followed by a Transformed Field Expansion resulting in a Fourier collocation, Legendre-Galerkin, Taylor series method for solving the problem in a transformed set of coordinates. Assorted numerical simulations display the spectral convergence of the proposed algorithm.

Effectiveness of applying progressive muscle relaxation technique on quality of life of patients with multiple sclerosis.

PubMed

Ghafari, Somayeh; Ahmadi, Fazlolah; Nabavi, Masoud; Anoshirvan, Kazemnejad; Memarian, Robabe; Rafatbakhsh, Mohamad

2009-08-01

To identify the effects of applying Progressive Muscle Relaxation Technique on Quality of Life of patients with multiple Sclerosis. In view of the growing caring options in Multiple Sclerosis, improvement of quality of life has become increasingly relevant as a caring intervention. Complementary therapies are widely used by multiple sclerosis patients and Progressive Muscle Relaxation Technique is a form of complementary therapies. Quasi-experimental study. Multiple Sclerosis patients (n = 66) were selected with no probability sampling then assigned to experimental and control groups (33 patients in each group). Means of data collection included: Individual Information Questionnaire, SF-8 Health Survey, Self-reported checklist. PMRT performed for 63 sessions by experimental group during two months but no intervention was done for control group. Statistical analysis was done by SPSS software. Student t-test showed that there was no significant difference between two groups in mean scores of health-related quality of life before the study but this test showed a significant difference between two groups, one and two months after intervention (p < 0.05). anova test with repeated measurements showed that there is a significant difference in mean score of whole and dimensions of health-related quality of life between two groups in three times (p < 0.05). Although this study provides modest support for the effectiveness of Progressive Muscle Relaxation Technique on quality of life of multiple sclerosis patients, further research is required to determine better methods to promote quality of life of patients suffer multiple sclerosis and other chronic disease. Progressive Muscle Relaxation Technique is practically feasible and is associated with increase of life quality of multiple sclerosis patients; so that health professionals need to update their knowledge about complementary therapies.

Low symptomatic premature stent occlusion of multiple plastic stents for benign biliary strictures: comparing standard and prolonged stent change intervals.

PubMed

Lawrence, Christopher; Romagnuolo, Joseph; Payne, K Mark; Hawes, Robert H; Cotton, Peter B

2010-09-01

Benign biliary strictures are typically managed endoscopically whereby an increasing size or number of plastic stents is placed at ERCP. Stents are often changed every 3 to 4 months based on the known median patency of a single biliary stent, but patency data for multiple biliary stents are lacking. To assess the incidence of occlusion-free survival of multiple plastic biliary stents and the rate of premature occlusion if left in longer than 6 months. Retrospective. Tertiary-care medical center (Charleston, SC). Consecutive patients who received multiple plastic stents for benign nonhilar biliary strictures from 1994 to 2008 were identified. Exchange of multiple plastic biliary stents within 6 months (group 1) or 6 months or longer (group 2) after placement. Symptomatic stent occlusion. Seventy-nine patients with nonhilar extrahepatic benign biliary stricture underwent 125 ERCPs with multiple plastic biliary stents. Stents were scheduled for removal/exchange within 6 months in 52 patients (86 ERCPs) compared with after 6 months in 22 patients (26 ERCPs). The median interval between multiple stent placement and removal/exchange was 90 days for group 1 and 242 days for group 2. Premature stent occlusion occurred in 4 of 52 (7.7%) patients in group 1 versus 1 of 22 (4.5%) in group 2, with significantly longer occlusion-free survival in group 2 (log-rank P < .0001). Retrospective study at a single tertiary referral center. Multiple plastic biliary stents for benign nonhilar strictures were associated with a low rate of premature symptomatic stent occlusion at more than 6 months and a longer occlusion-free survival. Copyright 2010 American Society for Gastrointestinal Endoscopy. Published by Mosby, Inc. All rights reserved.

Automated Discovery of Functional Generality of Human Gene Expression Programs

PubMed Central

Gerber, Georg K; Dowell, Robin D; Jaakkola, Tommi S; Gifford, David K

2007-01-01

An important research problem in computational biology is the identification of expression programs, sets of co-expressed genes orchestrating normal or pathological processes, and the characterization of the functional breadth of these programs. The use of human expression data compendia for discovery of such programs presents several challenges including cellular inhomogeneity within samples, genetic and environmental variation across samples, uncertainty in the numbers of programs and sample populations, and temporal behavior. We developed GeneProgram, a new unsupervised computational framework based on Hierarchical Dirichlet Processes that addresses each of the above challenges. GeneProgram uses expression data to simultaneously organize tissues into groups and genes into overlapping programs with consistent temporal behavior, to produce maps of expression programs, which are sorted by generality scores that exploit the automatically learned groupings. Using synthetic and real gene expression data, we showed that GeneProgram outperformed several popular expression analysis methods. We applied GeneProgram to a compendium of 62 short time-series gene expression datasets exploring the responses of human cells to infectious agents and immune-modulating molecules. GeneProgram produced a map of 104 expression programs, a substantial number of which were significantly enriched for genes involved in key signaling pathways and/or bound by NF-κB transcription factors in genome-wide experiments. Further, GeneProgram discovered expression programs that appear to implicate surprising signaling pathways or receptor types in the response to infection, including Wnt signaling and neurotransmitter receptors. We believe the discovered map of expression programs involved in the response to infection will be useful for guiding future biological experiments; genes from programs with low generality scores might serve as new drug targets that exhibit minimal “cross-talk,” and genes from high generality programs may maintain common physiological responses that go awry in disease states. Further, our method is multipurpose, and can be applied readily to novel compendia of biological data. PMID:17696603

Effects of prolonged exercise versus multiple short exercise sessions on risk for metabolic syndrome and the atherogenic index in middle-aged obese women: a randomised controlled trial.

PubMed

Chung, JinWook; Kim, KwangJun; Hong, Jeeyoung; Kong, Hyoun-Joong

2017-08-22

Many people, although they may recognise the positive effects of exercise, do not exercise regularly owing to lack of time. This study aimed to investigate the effects of prolonged single-session exercise and multiple short sessions of exercise on the risk of metabolic syndrome and the atherogenic index in middle-aged obese women. Thirty-six participants were divided into the single-session group, multiple-session group, and control group. The single-session group engaged in one session of treadmill exercise for 30 min a day; the multiple-session group had three sessions of 10 min a day. Both groups exercised 3 days/week for 12 weeks. The control group did not perform any exercise. The single-session group showed decreases in weight (0.97 kg [95% C.I. = 0.09-1.83], p < .05), body mass index (0.43 kg/m 2 [95% C.I. = 0.03-0.81], p < .05), and fat mass (1.65 kg, [95% C.I. = 0.78-2.51], p < .01). Systolic blood pressure dropped in the single-session group (6.66 mmHg, [95% C.I. = 1.44-11.88], p < .05), and diastolic blood pressure dropped in the multiple-session group (3.38 mmHg, [95% C.I. = 1.44-5.88], p < .01). High-density lipoprotein cholesterol rose in the single-session group (4.08 mg/dL, [95% C.I. = -8.08-(-)0.07], p < .05) and dropped in the control group (10.75 mg/dL [95% C.I. = 1.95-19.54], p < .01). According to post hoc analysis, high-density lipoprotein cholesterol increased more in the single-session group than the control group (95% C.I. = 0.61-21.88, p < .05). Glucose levels decreased in both the single-session group (16 mg/dL [95% C.I. = 5.64-26.35], p < .01) and the multiple-session group (12.16 mg/dL, [95% C.I. = 2.18-22.14], p < .05). Waist circumference decreased in the single-session group (2.65 cm [95% C.I. = 1.46-3.83], p < .001) and multiple-session group (2.04 cm, [95% C.I. = 1.51-2.73], p < .001). Low-density lipoprotein cholesterol levels rose in both the multiple-session group (-15.79 mg/dL [95% C.I. = -34.24-(-)3.78], p < .05) and the control group (-22.94 mg/dL [95% C.I. = -44.63-(-)1.24], p < .05). The atherogenic index increased in the control group (-1.06 [95% C.I. = -1.69-(-)0.41], p < .01). The findings indicate that prolonged exercise is superior to multiple short sessions for improving the risk of metabolic syndrome and the atherogenic index in middle-aged obese women. However, multiple short sessions can be recommended as an alternative to prolonged exercise when the goal is to decrease blood glucose or waist circumference.

Glucose uptake heterogeneity of the leg muscles is similar between patients with multiple sclerosis and healthy controls during walking.

PubMed

Kindred, John H; Ketelhut, Nathaniel B; Rudroff, Thorsten

2015-02-01

Difficulties in ambulation are one of the main problems reported by patients with multiple sclerosis. A previous study by our research group showed increased recruitment of muscle groups during walking, but the influence of skeletal muscle properties, such as muscle fiber activity, has not been fully elucidated. The purpose of this investigation was to use the novel method of calculating glucose uptake heterogeneity in the leg muscles of patients with multiple sclerosis and compare these results to healthy controls. Eight patients with multiple sclerosis (4 men) and 8 healthy controls (4 men) performed 15 min of treadmill walking at a comfortable self-selected speed following muscle strength tests. Participants were injected with ≈ 8 mCi of [(18)F]-fluorodeoxyglucose during walking after which positron emission tomography/computed tomography imaging was performed. No differences in muscle strength were detected between multiple sclerosis and control groups (P>0.27). Within the multiple sclerosis, group differences in muscle volume existed between the stronger and weaker legs in the vastus lateralis, semitendinosus, and semimembranosus (P<0.03). Glucose uptake heterogeneity between the groups was not different for any muscle group or individual muscle of the legs (P>0.16, P≥0.05). Patients with multiple sclerosis and healthy controls showed similar muscle fiber activity during walking. Interpretations of these results, with respect to our previous study, suggest that walking difficulties in patients with multiple sclerosis may be more associated with altered central nervous system motor patterns rather than alterations in skeletal muscle properties. Published by Elsevier Ltd.

An innovative training program based on virtual reality and treadmill: effects on gait of persons with multiple sclerosis.

PubMed

Peruzzi, Agnese; Zarbo, Ignazio Roberto; Cereatti, Andrea; Della Croce, Ugo; Mirelman, Anat

2017-07-01

In this single blind randomized controlled trial, we examined the effect of a virtual reality-based training on gait of people with multiple sclerosis. Twenty-five individuals with multiple sclerosis with mild to moderate disability were randomly assigned to either the control group (n = 11) or the experimental group (n = 14). The subjects in the control group received treadmill training. Subjects in the experimental group received virtual reality based treadmill training. Clinical measures and gait parameters were evaluated. Subjects in both the groups significantly improved the walking endurance and speed, cadence and stride length, lower limb joint ranges of motion and powers, during single and dual task gait. Moreover, subjects in the experimental group also improved balance, as indicated by the results of the clinical motor tests (p < 0.05). Between-group comparisons revealed that the experimental group improved significantly more than control group in hip range of motion and hip generated power at terminal stance at post-training. Our results support the perceived benefits of training programs that incorporate virtual reality to improve gait measures in individuals with multiple sclerosis. Implication of rehabilitation Gait deficits are common in multiple sclerosis (85%) and worsen during dual task activities. Intensive and progressive treadmill training, with and without virtual reality, is effective on dual task gait in persons with multiple sclerosis. Virtual reality-based treadmill training requiring obstacle negotiation increases the range of motion and the power generated at the hip, consequently allowing longer stride length and, consequently, higher gait speed.

On Finite Groups and Finite Fields.

ERIC Educational Resources Information Center

Reid, J. D.

1991-01-01

Given a multiplicative group of nonzero elements with order n, the explicit relationship between the number of cyclic subgroups of order d, which divides n, is used in the proof concerning the cyclic nature of that given multiplicative group. (JJK)

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.

Exploring asynchronous brainstorming in large groups: a field comparison of serial and parallel subgroups.

PubMed

de Vreede, Gert-Jan; Briggs, Robert O; Reiter-Palmon, Roni

2010-04-01

The aim of this study was to compare the results of two different modes of using multiple groups (instead of one large group) to identify problems and develop solutions. Many of the complex problems facing organizations today require the use of very large groups or collaborations of groups from multiple organizations. There are many logistical problems associated with the use of such large groups, including the ability to bring everyone together at the same time and location. A field study involved two different organizations and compared productivity and satisfaction of group. The approaches included (a) multiple small groups, each completing the entire process from start to end and combining the results at the end (parallel mode); and (b) multiple subgroups, each building on the work provided by previous subgroups (serial mode). Groups using the serial mode produced more elaborations compared with parallel groups, whereas parallel groups produced more unique ideas compared with serial groups. No significant differences were found related to satisfaction with process and outcomes between the two modes. Preferred mode depends on the type of task facing the group. Parallel groups are more suited for tasks for which a variety of new ideas are needed, whereas serial groups are best suited when elaboration and in-depth thinking on the solution are required. Results of this research can guide the development of facilitated sessions of large groups or "teams of teams."

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

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

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→∞.

Multiple Intelligences Profiles of Children with Attention Deficit and Hyperactivity Disorder in Comparison with Nonattention Deficit and Hyperactivity Disorder

PubMed Central

Najafi, Mostafa; Akouchekian, Shahla; Ghaderi, Alireza; Mahaki, Behzad; Rezaei, Mariam

2017-01-01

Background: Attention deficit and hyperactivity disorder (ADHD) is a common psychological problem during childhood. This study aimed to evaluate multiple intelligences profiles of children with ADHD in comparison with non-ADHD. Materials and Methods: This cross-sectional descriptive analytical study was done on 50 children of 6–13 years old in two groups of with and without ADHD. Children with ADHD were referred to Clinics of Child and Adolescent Psychiatry, Isfahan University of Medical Sciences, in 2014. Samples were selected based on clinical interview (based on Diagnostic and Statistical Manual of Mental Disorders IV and parent–teacher strengths and difficulties questionnaire), which was done by psychiatrist and psychologist. Raven intelligence quotient (IQ) test was used, and the findings were compared to the results of multiple intelligences test. Data analysis was done using a multivariate analysis of covariance using SPSS20 software. Results: Comparing the profiles of multiple intelligence among two groups, there are more kinds of multiple intelligences in control group than ADHD group, a difference which has been more significant in logical, interpersonal, and intrapersonal intelligence (P < 0.05). There was no significant difference with the other kinds of multiple intelligences in two groups (P > 0.05). The IQ average score in the control group and ADHD group was 102.42 ± 16.26 and 96.72 ± 16.06, respectively, that reveals the negative effect of ADHD on IQ average value. There was an insignificance relationship between linguistic and naturalist intelligence (P > 0.05). However, in other kinds of multiple intelligences, direct and significant relationships were observed (P < 0.05). Conclusions: Since the levels of IQ (Raven test) and MI in control group were more significant than ADHD group, ADHD is likely to be associated with logical-mathematical, interpersonal, and intrapersonal profiles. PMID:29285478

Exploring change in a group-based psychological intervention for multiple sclerosis patients.

PubMed

Borghi, Martina; Bonino, Silvia; Graziano, Federica; Calandri, Emanuela

2018-07-01

The study is focused on a group-based cognitive behavioral intervention aimed at promoting the quality of life and psychological well-being of multiple sclerosis patients. The study investigates how the group intervention promoted change among participants and fostered their adjustment to the illness. The intervention involved six groups of patients (a total of 41 patients) and included four consecutive sessions and a 6-month follow-up. To explore change, verbatim transcripts of the intervention sessions were analyzed using a mixed-methods content analysis with qualitative data combined with descriptive statistics. The categories of resistance and openness to change were used to describe the process of change. Resistance and openness to change coexisted during the intervention. Only in the first session did resistance prevail over openness to change; thereafter, openness to change gradually increased and stabilized over time, and openness to change was then always stronger than resistance. The study builds on previous research on the effectiveness of group-based psychological interventions for multiple sclerosis patients and gives methodological and clinical suggestions to health care professionals working with multiple sclerosis patients. Implications for rehabilitation The study suggests that a group-based cognitive behavioral intervention for multiple sclerosis patients focused on the promotion of identity redefinition, a sense of coherence and self-efficacy in dealing with multiple sclerosis fosters the process of change and may be effective in promoting patients' adjustment to their illness. Health care professionals leading group-based psychological interventions for multiple sclerosis patients should be aware that resistance and openness to change coexist in the process of change. The study suggests that the duration of the intervention is a crucial factor: a minimum of three sessions appears to be necessary for group participants to develop greater openness to change and follow-up sessions should be implemented to maintain positive changes among participants. The use of qualitative instruments to evaluate group interventions captures the complexity of processes and gives useful indications to health professionals to improve rehabilitation programs.

Academic Achievement from Using the Learning Medium Via a Tablet Device Based on Multiple Intelligences in Grade 1 Elementary Student.

PubMed

Nuallaong, Winitra; Nuallaong, Thanya; Preechadirek, Nongluck

2015-04-01

To measure academic achievement of the multiple intelligence-based learning medium via a tablet device. This is a quasi-experimental research study (non-randomized control group pretest-posttest design) in 62 grade 1 elementary students (33 males and 29 females). Thirty-one students were included in an experimental group using purposive sampling by choosing a student who had highest multiple intelligence test scores in logical-mathematic. Then, this group learned by the new learning medium via a tablet which the application matched to logical-mathematic multiple intelligence. Another 31 students were included in a control group using simple random sampling and then learning by recitation. Both groups did pre-test and post-test vocabulary. Thirty students in the experimental group and 24 students in the control group increased post-test scores (odds ratio = 8.75). Both groups made significant increasing in post-test scores. The experimental group increased 9.07 marks (95% CI 8.20-9.93) significantly higher than the control group which increased 4.39 marks (95% CI 3.06-5.72) (t = -6.032, df = 51.481, p < 0.001). Although learning from either multiple intelligence-based learning medium via a tablet or recitation can contribute academic achievement, learningfrom the new medium contributed more achievement than recitation. The new learning medium group had higher post-test scores 8.75 times than the recitation group. Therefore, the new learning medium is more effective than the traditional recitation in terms of academic achievement. This study has limitations because samples came from the same school. However, the previous study in Thailand did notfind a logical-mathematical multiple intelligence difference among schools. In the future, long-term research to find how the new learning medium affects knowledge retention will support the advantage for life-long learning.

Effect of multiple infections with white spot syndrome virus and Vibrio anguillarum on Pacific white shrimp Litopenaeus vannamei (L.): mortality and viral replication.

PubMed

Jang, I K; Qiao, G; Kim, S-K

2014-10-01

Multiple infections are commonly found in practical shrimp culture and may cause more serious consequences than infections by one pathogen only. Therefore, this study was conducted to evaluate the effect of multiple infections with white spot syndrome virus (WSSV) and Vibrio anguillarum on Pacific white shrimp Litopenaeus vannamei (L.), mortality, WSSV replication in vivo and host immune response. In the WSSV single-infection group (WSSV load, 2 × 10(2) copies μL(-1)), mean cumulative mortality was 29.2%. In the V. anguillarum single-infection group, cumulative mortality was 12.5% when shrimp were challenged by 10(5) CFU mL(-1) of bacteria. In the co- and super-infection groups, 37.5% and 50% cumulative mortalities, respectively, were observed at a lower bacterial concentration of 10(3) CFU mL(-1), suggesting that shrimp with multiple infections died earlier and more frequently than singly infected shrimp. WSSV load after injection was tracked over time by TaqMan quantitative PCR. WSSV load increased more rapidly in the multiple-infection groups than in the single-infection group. Additionally, mRNA expression of the genes encoding prophenoloxidase 1 and 2, which are closely involved in innate immunity in shrimp, was down-regulated more extensively in multiple-infection groups than in single-infection groups, as indicated by quantitative reverse-transcription PCR. © 2013 John Wiley & Sons Ltd.

Multiple-modality exercise and mind-motor training to improve cardiovascular health and fitness in older adults at risk for cognitive impairment: A randomized controlled trial.

PubMed

Boa Sorte Silva, Narlon C; Gregory, Michael A; Gill, Dawn P; Petrella, Robert J

The effects of multiple-modality exercise on arterial stiffening and cardiovascular fitness has not been fully explored. To explore the influence of a 24-week multiple-modality exercise program associated with a mind-motor training in cardiovascular health and fitness in community-dwelling older adults, compared to multiple-modality exercise (M2) alone. Participants (n=127, aged 67.5 [7.3] years, 71% females) were randomized to either M4 or M2 groups. Both groups received multiple-modality exercise intervention (60min/day, 3days/week for 24-weeks); however, the M4 group underwent additional 15min of mind-motor training, whereas the M2 group received 15min of balance training. Participants were assessed at 24-weeks and after a 28-week non-contact follow-up (52-weeks). at 52-weeks, the M4 group demonstrated a greater VO2max (ml/kg/min) compared to the M2 group (mean difference: 2.39, 95% CI: 0. 61 to 4.16, p=0.009). Within-group analysis indicated that the M4 group demonstrated a positive change in VO2max at 24-weeks (mean change: 1.93, 95% CI: 0.82 to 3.05, p=0.001) and 52-weeks (4.02, 95% CI: 2.71 to 5.32, p=0.001). Similarly, the M2 group increased VO2max at 24-weeks (2.28, 95% CI: 1.23 to 3.32, p<0.001) and 52-weeks (1.63, 95% CI: 0.43 to 2.83, p=0.008). Additionally, the M2 group decreased 24h SBP (mmHg) at 24-weeks (-2.31, 95% CI: -4.61 to -0.01, p=0.049); whereas the M4 group improved 24h DBP (-1.6, 95% CI: -3.03 to -0.17, p=0.028) at 52-weeks. Mind-motor training associated with multiple-modality exercise can positively impact cardiovascular fitness to the same extent as multiple-modality exercise alone. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Is There A Difference Between Presence of Single Stone And Multiple Stones in Flexible Ureterorenoscopy And Laser Lithotripsy For Renal Stone Burden < 300mm2 ?

PubMed

Ozgor, Faruk; Kucuktopcu, Onur; Ucpinar, Burak; Gurbuz, Zafer Gokhan; Sarilar, Omer; Berberoglu, Ahmet Yalcin; Baykal, Murat; Binbay, Murat

2016-01-01

In this study, we aim to evaluate and compare the effectiveness of flexible ureterorenoscopy (f-URS) for solitary and multiple renal stones with < 300 mm2 stone burden. Patients' charts who treated with f-URS for kidney stone between January 2010 and June 2015 were reviewed, retrospectively. Patients with solitary kidney stones (n:111) were enrolled in group 1. We selected 111 patients with multiple kidney stones to serve as the control group and the patients were matched at a 1:1 ratio with respect to the patient's age, gender, body mass index and stone burden. Additionally, patients with multiple stones were divided into two groups according to the presence or abscence of lower pole stones. Stone free status was accepted as complete stone clearence and presence of residual fragments < 2 mm. According to the study design; age, stone burden, body mass index were comparable between groups. The mean operation time was longer in group 2 (p= 0.229). However, the mean fluoroscopy screening time in group 1 and in group 2 was 2.1±1.7 and 2.6±1.5 min, respectively and significantly longer in patients with multiple renal stones (P=0.043). The stone-free status was significantly higher in patients with solitary renal stones after a single session procedure (p=0.02). After third month follow up, overall success rate was 92.7% in Group 1 and 86.4% in Group 2. Our study revealed that F-URS achieved better stone free status in solitary renal stones < 300 mm2. However, outcomes of F-URS were acceptable in patients with multiple stones. Copyright® by the International Brazilian Journal of Urology.

The Effect Of The Materials Based On Multiple Intelligence Theory Upon The Intelligence Groups' Learning Process

NASA Astrophysics Data System (ADS)

Oral, I.; Dogan, O.

2007-04-01

The aim of this study is to find out the effect of the course materials based on Multiple Intelligence Theory upon the intelligence groups' learning process. In conclusion, the results proved that the materials prepared according to Multiple Intelligence Theory have a considerable effect on the students' learning process. This effect was particularly seen on the student groups of the musical-rhythmic, verbal-linguistic, interpersonal-social and naturalist intelligence.

Multiple comparison analysis testing in ANOVA.

PubMed

McHugh, Mary L

2011-01-01

The Analysis of Variance (ANOVA) test has long been an important tool for researchers conducting studies on multiple experimental groups and one or more control groups. However, ANOVA cannot provide detailed information on differences among the various study groups, or on complex combinations of study groups. To fully understand group differences in an ANOVA, researchers must conduct tests of the differences between particular pairs of experimental and control groups. Tests conducted on subsets of data tested previously in another analysis are called post hoc tests. A class of post hoc tests that provide this type of detailed information for ANOVA results are called "multiple comparison analysis" tests. The most commonly used multiple comparison analysis statistics include the following tests: Tukey, Newman-Keuls, Scheffee, Bonferroni and Dunnett. These statistical tools each have specific uses, advantages and disadvantages. Some are best used for testing theory while others are useful in generating new theory. Selection of the appropriate post hoc test will provide researchers with the most detailed information while limiting Type 1 errors due to alpha inflation.

Developing a technique to master multiplication facts 6 to 9 for year 5 pupils

NASA Astrophysics Data System (ADS)

Ahmat, Norhayati; Mohamed, Nurul Huda; Azmee, Nor Afzalina; Adham, Sarah Mohd

2017-05-01

This study was performed to enhance the mastery of multiplication facts 6 to 9 amongst the year 5 pupils. The samples of this study were 40 pupils of year 5 from one of primary school at Teluk Intan, Perak. The samples were divided into two groups, the control group and the treatment group where each group consists of 20 pupils respectively. In this study, new multiplication facts technique, known as `Teknik Sifir Jari' has been introduced to the treatment group. The objectives of the study are to test the effectiveness of the new technique and to increase multiplication fact fluency among pupils. The instruments that have been used in this study are the achievement tests (pre-test and post-test). The data obtained were collected and analyzed using SPSS version 21.A t-test had also been carried out to test the null hypothesis. The results showed that there was an increment in the students' achievement for the students who were taught using the `Teknik Sifir Jari'. Therefore, the `Teknik Sifir Jari' has proved its effectiveness to support students in mastering multiplication facts.

Consensus Recommendations of the Multiple Sclerosis Study Group and Portuguese Neuroradiological Society for the Use of the Magnetic Resonance Imaging in Multiple Sclerosis in Clinical Practice: Part 1.

PubMed

Abreu, Pedro; Pedrosa, Rui; Sá, Maria José; Cerqueira, João; Sousa, Lívia; Da Silva, Ana Martins; Pinheiro, Joaquim; De Sá, João; Batista, Sónia; Simões, Rita Moiron; Pereira, Daniela Jardim; Vilela, Pedro; Vale, José

2018-05-30

Magnetic resonance imaging is established as a recognizable tool in the diagnosis and monitoring of multiple sclerosis patients. In the present, among multiple sclerosis centers, there are different magnetic resonance imaging sequences and protocols used to study multiple sclerosis that may hamper the optimal use of magnetic resonance imaging in multiple sclerosis. In this context, the Group of Studies of Multiple Sclerosis and the Portuguese Society of Neuroradiology, after a joint discussion, appointed a committee of experts to create recommendations adapted to the national reality on the use of magnetic resonance imaging in multiple sclerosis. The purpose of this document is to publish the first Portuguese consensus recommendations on the use of magnetic resonance imaging in multiple sclerosis in clinical practice. The Group of Studies of Multiple Sclerosis and the Portuguese Society of Neuroradiology, after discussion of the topic in national meetings and after a working group meeting held in Figueira da Foz on May 2017, have appointed a committee of experts that have developed by consensus several standard protocols on the use of magnetic resonance imaging in the diagnosis and follow-up of multiple sclerosis. The document obtained was based on the best scientific evidence and expert opinion. Subsequently, the majority of Portuguese multiple sclerosis consultants and departments of neuroradiology scrutinized and reviewed the consensus paper; comments and suggestions were considered. Technical magnetic resonance imaging protocols regarding diagnostic, monitoring and the recommended information to be included in the magnetic resonance imaging report will be published in a separate paper. We provide some practical guidelines to promote standardized strategies to be applied in the clinical practice setting of Portuguese healthcare professionals regarding the use of magnetic resonance imaging in multiple sclerosis. We hope that these first Portuguese magnetic resonance imaging guidelines, based in the best available clinical evidence and practices, will serve to optimize multiple sclerosis management and improve multiple sclerosis patient care across Portugal.

Text Mining to inform construction of Earth and Environmental Science Ontologies

NASA Astrophysics Data System (ADS)

Schildhauer, M.; Adams, B.; Rebich Hespanha, S.

2013-12-01

There is a clear need for better semantic representation of Earth and environmental concepts, to facilitate more effective discovery and re-use of information resources relevant to scientists doing integrative research. In order to develop general-purpose Earth and environmental science ontologies, however, it is necessary to represent concepts and relationships that span usage across multiple disciplines and scientific specialties. Traditional knowledge modeling through ontologies utilizes expert knowledge but inevitably favors the particular perspectives of the ontology engineers, as well as the domain experts who interacted with them. This often leads to ontologies that lack robust coverage of synonymy, while also missing important relationships among concepts that can be extremely useful for working scientists to be aware of. In this presentation we will discuss methods we have developed that utilize statistical topic modeling on a large corpus of Earth and environmental science articles, to expand coverage and disclose relationships among concepts in the Earth sciences. For our work we collected a corpus of over 121,000 abstracts from many of the top Earth and environmental science journals. We performed latent Dirichlet allocation topic modeling on this corpus to discover a set of latent topics, which consist of terms that commonly co-occur in abstracts. We match terms in the topics to concept labels in existing ontologies to reveal gaps, and we examine which terms are commonly associated in natural language discourse, to identify relationships that are important to formally model in ontologies. Our text mining methodology uncovers significant gaps in the content of some popular existing ontologies, and we show how, through a workflow involving human interpretation of topic models, we can bootstrap ontologies to have much better coverage and richer semantics. Because we base our methods directly on what working scientists are communicating about their research, it gives us an alternative bottom-up approach to populating and enriching ontologies, that complements more traditional knowledge modeling endeavors.

QCAD simulation and optimization of semiconductor double quantum dots

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

Nielsen, Erik; Gao, Xujiao; Kalashnikova, Irina

2013-12-01

We present the Quantum Computer Aided Design (QCAD) simulator that targets modeling quantum devices, particularly silicon double quantum dots (DQDs) developed for quantum qubits. The simulator has three di erentiating features: (i) its core contains nonlinear Poisson, e ective mass Schrodinger, and Con guration Interaction solvers that have massively parallel capability for high simulation throughput, and can be run individually or combined self-consistently for 1D/2D/3D quantum devices; (ii) the core solvers show superior convergence even at near-zero-Kelvin temperatures, which is critical for modeling quantum computing devices; (iii) it couples with an optimization engine Dakota that enables optimization of gate voltagesmore » in DQDs for multiple desired targets. The Poisson solver includes Maxwell- Boltzmann and Fermi-Dirac statistics, supports Dirichlet, Neumann, interface charge, and Robin boundary conditions, and includes the e ect of dopant incomplete ionization. The solver has shown robust nonlinear convergence even in the milli-Kelvin temperature range, and has been extensively used to quickly obtain the semiclassical electrostatic potential in DQD devices. The self-consistent Schrodinger-Poisson solver has achieved robust and monotonic convergence behavior for 1D/2D/3D quantum devices at very low temperatures by using a predictor-correct iteration scheme. The QCAD simulator enables the calculation of dot-to-gate capacitances, and comparison with experiment and between solvers. It is observed that computed capacitances are in the right ballpark when compared to experiment, and quantum con nement increases capacitance when the number of electrons is xed in a quantum dot. In addition, the coupling of QCAD with Dakota allows to rapidly identify which device layouts are more likely leading to few-electron quantum dots. Very efficient QCAD simulations on a large number of fabricated and proposed Si DQDs have made it possible to provide fast feedback for design comparison and optimization.« less

42 CFR 411.352 - Group practice.

Code of Federal Regulations, 2010 CFR

2010-10-01

... considered to be a single legal entity notwithstanding that it is composed of multiple legal entities... ownership, governance, and operation; and (3) Organization of the group practice into multiple entities is...). (f) Unified business. (1) The group practice must be a unified business having at least the following...

Comprehension of confidence intervals - development and piloting of patient information materials for people with multiple sclerosis: qualitative study and pilot randomised controlled trial.

PubMed

Rahn, Anne C; Backhus, Imke; Fuest, Franz; Riemann-Lorenz, Karin; Köpke, Sascha; van de Roemer, Adrianus; Mühlhauser, Ingrid; Heesen, Christoph

2016-09-20

Presentation of confidence intervals alongside information about treatment effects can support informed treatment choices in people with multiple sclerosis. We aimed to develop and pilot-test different written patient information materials explaining confidence intervals in people with relapsing-remitting multiple sclerosis. Further, a questionnaire on comprehension of confidence intervals was developed and piloted. We developed different patient information versions aiming to explain confidence intervals. We used an illustrative example to test three different approaches: (1) short version, (2) "average weight" version and (3) "worm prophylaxis" version. Interviews were conducted using think-aloud and teach-back approaches to test feasibility and analysed using qualitative content analysis. To assess comprehension of confidence intervals, a six-item multiple choice questionnaire was developed and tested in a pilot randomised controlled trial using the online survey software UNIPARK. Here, the average weight version (intervention group) was tested against a standard patient information version on confidence intervals (control group). People with multiple sclerosis were invited to take part using existing mailing-lists of people with multiple sclerosis in Germany and were randomised using the UNIPARK algorithm. Participants were blinded towards group allocation. Primary endpoint was comprehension of confidence intervals, assessed with the six-item multiple choice questionnaire with six points representing perfect knowledge. Feasibility of the patient information versions was tested with 16 people with multiple sclerosis. For the pilot randomised controlled trial, 64 people with multiple sclerosis were randomised (intervention group: n = 36; control group: n = 28). More questions were answered correctly in the intervention group compared to the control group (mean 4.8 vs 3.8, mean difference 1.1 (95 % CI 0.42-1.69), p = 0.002). The questionnaire's internal consistency was moderate (Cronbach's alpha = 0.56). The pilot-phase shows promising results concerning acceptability and feasibility. Pilot randomised controlled trial results indicate that the patient information is well understood and that knowledge gain on confidence intervals can be assessed with a set of six questions. German Clinical Trials Register: DRKS00008561 . Registered 8th of June 2015.

Learning and serial effects on verbal memory in mild cognitive impairment.

PubMed

Campos-Magdaleno, María; Díaz-Bóveda, Rosalía; Juncos-Rabadán, Onésimo; Facal, David; Pereiro, Arturo X

2016-01-01

The objective of this study was to examine different patterns of learning and episodic memory in 3 mild cognitive impairment (MCI) groups and a control group by administering the California Verbal Learning Test (CVLT) and using serial position effect as a principal variable. The study sample included 3 groups of patients with MCI (n = 90) divided into single-domain amnestic, multiple-domain amnestic, and multiple-domain nonamnestic MCI and a group of healthy controls (n = 60). We compared the performance of each group on several CVLT measures used in previous research, and we included a new measure that provides specific information about the serial effect. Data showed a similar pattern of learning and memory impairment in both amnestic MCI groups (i.e., no differences between the multiple-domain and single-domain subtypes); the recency effect was significantly higher in both amnestic MCI groups than in all other groups, and the primacy effect was only lower in the multiple-domain amnestic MCI subtype. Verbal learning and memory profiles of patients with amnestic MCI were very similar, independent of the presence of deficits in cognitive domains other than episodic memory. Results are discussed in light of the unitary-store model of memory.

Whole-body multislice computed tomography (MSCT) improves trauma care in patients requiring surgery after multiple trauma.

PubMed

Wurmb, T E; Quaisser, C; Balling, H; Kredel, M; Muellenbach, R; Kenn, W; Roewer, N; Brederlau, J

2011-04-01

Whole-body multislice helical CT becomes increasingly important as a diagnostic tool in patients with multiple injuries. Time gain in multiple-trauma patients who require emergency surgery might improve outcome. The authors hypothesised that whole-body multislice computed tomography (MSCT) (MSCT trauma protocol) as the initial diagnostic tool reduces the interval to start emergency surgery (tOR) if compared to conventional radiography, combined with abdominal ultrasound and organ-focused CT (conventional trauma protocol). The second goal of the study was to investigate whether the diagnostic approach chosen has an impact on outcome. The authors' level 1 trauma centre uses whole-body MSCT for initial radiological diagnostic work-up for patients with suspected multiple trauma. Before the introduction of MSCT in 2004, a conventional approach was used. Group I: data of trauma patients treated with conventional trauma protocol from 2001 to 2003. Group II: data from trauma patients treated with whole-body MSCT trauma protocol from 2004 to 2006. tOR in group I (n=155) was 120 (90-150) min (median and IQR) and 105 (85-133) min (median and IQR) in group II (n=163), respectively (p<0.05). Patients of group II had significantly more serious injuries. No difference in outcome data was found. 14 patients died in both groups within the first 30 days; five of these died within the first 24 h. A whole-body MSCT-based diagnostic approach to multiple trauma shortens the time interval to start emergency surgery in patients with multiple injuries. Mortality remained unchanged in both groups. Patients of group II were more seriously injured; an improvement of outcome might be assumed.

Multiple Family Group Counseling

ERIC Educational Resources Information Center

Sauber, S. Richard

1971-01-01

This article describes the innovative, short term approach of multiple family group counseling in which the counseling applies the principles and dynamics found in family and group counseling to the treatment of the student and his family. Several family units met together to discuss the problems that adversely affect the adolescent and result in…

Tests of Multiplicative Models in Psychology: A Case Study Using the Unified Theory of Implicit Attitudes, Stereotypes, Self-Esteem, and Self-Concept

ERIC Educational Resources Information Center

Blanton, Hart; Jaccard, James

2006-01-01

Theories that posit multiplicative relationships between variables are common in psychology. A. G. Greenwald et al. recently presented a theory that explicated relationships between group identification, group attitudes, and self-esteem. Their theory posits a multiplicative relationship between concepts when predicting a criterion variable.…

Comparative analysis of primary hepatocellular carcinoma with single and multiple lesions by iTRAQ-based quantitative proteomics.

PubMed

Xing, Xiaohua; Huang, Yao; Wang, Sen; Chi, Minhui; Zeng, Yongyi; Chen, Lihong; Li, Ling; Zeng, Jinhua; Lin, Minjie; Han, Xiao; Liu, Xiaolong; Liu, Jingfeng

2015-10-14

In clinical practices, the therapeutic outcomes and prognosis of hepatocellular carcinoma (HCC) patients with different tumor numbers after surgery are very different; however, the underlying mechanisms of the tumorigenesis and development of HCC with different tumor numbers are still not well understood. Here, we systematically compared the overall proteome profiles between the primary HCC with single and multiple lesions using iTRAQ-based quantitative proteomics approach. We identified that 107 and 330 proteins were dysregulated in HCC tissue with multiple lesions (MC group) and HCC tissue with a single lesion (SC group), compared with their non-cancerous tissue (MN and SN groups) respectively. The dysregulated proteins in MC group are concentrated in UBC signaling pathway and NFκB signaling pathway, but the dysregulated proteins in SC group are more concentrated in ERK signaling pathway and the NFκB signaling pathway. These information revealed that there might be different molecular mechanisms of the tumorigenesis and development of the HCC with single and multiple lesions. Furthermore, HSD17B13 were only down-regulated in MC group while HK2 were only up-regulated in SC group among these dysregulated proteins. Therefore, the protein HSD17B13 and HK2 might be potential biomarkers for the primary HCC with single and multiple lesions. Copyright © 2015 Elsevier B.V. All rights reserved.

The effects of pranayama, hatha and raja yoga on physical pain and the quality of life of women with multiple sclerosis.

PubMed

Doulatabad, Shahla Najafi; Nooreyan, Khirollah; Doulatabad, Ardavan Najafi; Noubandegani, Zinat Mohebbi

2012-01-01

In a clinical trial carried out on 60 women with multiple sclerosis, the researchers obtained data using survey questionnaires. In addition to demographic data, the Multiple Sclerosis Quality of Life-54 (MSQoL-54) instrument was used to determine how multiple sclerosis influences the quality of life of the studied women. Within the frame of this randomized controlled trial, the participants were divided into two equally sized groups (the case and the control group) in which the level of pain and the quality of life were evaluated. The case group exercised pain-managing Yoga methods for three months, keeping the pace of eight 90-minute sessions per month. The control participants were subjected to no intervention. One month after the Yoga therapy, the level of pain and the quality of life were evaluated in both groups and compared to the baseline data. Data were analyzed using SPSS software and paired t-tests. After the Yoga therapy, the case group showed a significant improvement in physical pain management (P=0.007) and the quality of life (P=0.001) as compared to the control group. The results showed that Yoga techniques can alleviate physical pain and improve the quality of life of multiple sclerosis patients.

Multiple drilling combined with simvastatin versus multiple drilling alone for the treatment of avascular osteonecrosis of the femoral head: 3-year follow-up study.

PubMed

Yin, Han; Yuan, Zhenfeng; Wang, Dawei

2016-08-15

Multiple small drilling for core decompression is widely used to preserve the femoral head in patients with avascular necrosis of the femoral head (ANFH). Nevertheless, the clinical outcome remains controversial. Simvastatin has been demonstrated to promote bone formation and reduce bone adsorption. The purpose of this study was to determine whether simvastatin enhanced the effect of multiple decompressions in preventing progression of ANFH and to identify independent risk factors associated with poor results. We retrospectively analyzed 58 hips in 36 patients, with a follow-up of 36 months. 20 patients (32 hips) underwent multiple drilling combined with simvastatin treatment (SIM group); 16 patients (26 hips) underwent multiple drilling alone (MD group). We defined clinical failure as a requirement for subsequent hip surgery or Harris Hip Score < 75. New occurrence of collapse or increased collapse > 2 mm on plain radiographs was defined as radiological failure. Successful clinical results were achieved in 27 of 32 hips (84 %) in the SIM group compared with 15 of 26 hips (58 %) in the MD group (OR = 0.2, CI (0.1, 0.6.), P = 0.032). Successful radiological results were achieved in 27 of 32 hips (84 %) in the SIM group and in 16 of 26 hips (61.5 %) in the MD group (P = 0.048). Body mass index, disease stage and location of lesion were independent prognostic factors for overall survival. We believe that simvastatin could enhance the effects of multiple decompressions in preventing progression of ANFH and reducing the risk of femoral head collapse.

Intersections of discrimination due to unemployment and mental health problems: the role of double stigma for job- and help-seeking behaviors.

PubMed

Staiger, Tobias; Waldmann, Tamara; Oexle, Nathalie; Wigand, Moritz; Rüsch, Nicolas

2018-05-21

The everyday lives of unemployed people with mental health problems can be affected by multiple discrimination, but studies about double stigma-an overlap of identities and experiences of discrimination-in this group are lacking. We therefore studied multiple discrimination among unemployed people with mental health problems and its consequences for job- and help-seeking behaviors. Everyday discrimination and attributions of discrimination to unemployment and/or to mental health problems were examined among 301 unemployed individuals with mental health problems. Job search self-efficacy, barriers to care, and perceived need for treatment were compared among four subgroups, depending on attributions of experienced discrimination to unemployment and to mental health problems (group i); neither to unemployment nor to mental health problems (group ii); mainly to unemployment (group iii); or mainly to mental health problems (group iv). In multiple regressions among all participants, higher levels of discrimination predicted reduced job search self-efficacy and higher barriers to care; and attributions of discrimination to unemployment were associated with increased barriers to care. In ANOVAs for subgroup comparisons, group i participants, who attributed discrimination to both unemployment and mental health problems, reported lower job search self-efficacy, more perceived stigma-related barriers to care and more need for treatment than group iii participants, as well as more stigma-related barriers to care than group iv. Multiple discrimination may affect job search and help-seeking among unemployed individuals with mental health problems. Interventions to reduce public stigma and to improve coping with multiple discrimination for this group should be developed.

Effects of exposure in single and multiple contexts on fear renewal: The moderating role of threat-specific and nonspecific emotionality.

PubMed

Olatunji, Bunmi O; Tomarken, Andrew; Wentworth, Brian; Fritzsche, Laura

2017-03-01

The current study examines effects of exposure in multiple contexts on fear reduction and renewal and the moderating effect of baseline threat-specific and nonspecific emotionality. Snake-fearful participants received a negative or neutral emotion induction and were randomized to video exposure to a snake in a single context, multiple context, or a no exposure control group. Anxiety in response to video presentations of a snake was significantly reduced in the two exposure groups compared to the control group, especially among those with heightened baseline threat-specific emotionality as indicated by snake anxiety ratings at baseline. Although the two exposure groups did not differ in responding when confronted with a novel snake, both exposure groups reported significantly lower snake anxiety and arousal than the control group. Subsequent analysis did show that compared to controls, the single context group demonstrated greater increase in anxiety and arousal from post-exposure to exposure to the novel snake among those with heightened snake anxiety at baseline. Furthermore, the multiple context group was less avoidant and less fearful than the single context group on a post-exposure behavioral test. The study used an analogue exposure paradigm with an analogue sample and findings may not be generalizable to a clinical population. These findings suggest that baseline threat-specific emotionality influences fear reduction and renewal. The benefits of exposure in multiple contexts are discussed in relation to a distinct pattern of symptom change that is in line with an inhibitory learning approach. Copyright © 2016 Elsevier Ltd. All rights reserved.

[Effects of pamidronate disodium (Bonin) combined with chemotherapy on bone pain in multiple myeloma].

PubMed

Leng, Yun; Chen, Shi-lun; Shi, Hong-zhi

2002-10-01

Objective. To evaluate the therapeutic effects of Disodium Pamidronate (Bonin) on bone pain in multiple myeloma. Method. 18 patients received only chemotherapy and 16 patients with addition of Bonin were compared. Result. The bone pain was significantly relieved both in chemotherapy alone group and in the combination group of Bonin with chemotherapy after treatment (P<0.01, as compared with before therapy). However, the effects of combination group were more dramatical than that of the other group (P<0.05). No obvious side-effects were observed except mild fever in one patient in the combination group. Conclusion. Bonin, as a safe and effective Bisphosphonates preparation, could relieve bone pain in multiple myeloma more effectively when combined with chemotherapy.

Sensor-augmented pump therapy lowers HbA(1c) in suboptimally controlled Type 1 diabetes; a randomized controlled trial.

PubMed

Hermanides, J; Nørgaard, K; Bruttomesso, D; Mathieu, C; Frid, A; Dayan, C M; Diem, P; Fermon, C; Wentholt, I M E; Hoekstra, J B L; DeVries, J H

2011-10-01

To investigate the efficacy of sensor-augmented pump therapy vs. multiple daily injection therapy in patients with suboptimally controlled Type 1 diabetes. In this investigator-initiated multi-centre trial (the Eurythmics Trial) in eight outpatient centres in Europe, we randomized 83 patients with Type 1 diabetes (40 women) currently treated with multiple daily injections, age 18-65 years and HbA(1c) ≥ 8.2% (≥ 66 mmol/mol) to 26 weeks of treatment with either a sensor-augmented insulin pump (n = 44) (Paradigm(®) REAL-Time) or continued with multiple daily injections (n = 39). Change in HbA(1c) between baseline and 26 weeks, sensor-derived endpoints and patient-reported outcomes were assessed. The trial was completed by 43/44 (98%) patients in the sensor-augmented insulin pump group and 35/39 (90%) patients in the multiple daily injections group. Mean HbA(1c) at baseline and at 26 weeks changed from 8.46% (SD 0.95) (69 mmol/mol) to 7.23% (SD 0.65) (56 mmol/mol) in the sensor-augmented insulin pump group and from 8.59% (SD 0.82) (70 mmol/mol) to 8.46% (SD 1.04) (69 mmol/mol) in the multiple daily injections group. Mean difference in change in HbA(1c) after 26 weeks was -1.21% (95% confidence interval -1.52 to -0.90, P < 0.001) in favour of the sensor-augmented insulin pump group. This was achieved without an increase in percentage of time spent in hypoglycaemia: between-group difference 0.0% (95% confidence interval -1.6 to 1.7, P = 0.96). There were four episodes of severe hypoglycaemia in the sensor-augmented insulin pump group and one episode in the multiple daily injections group (P = 0.21). Problem Areas in Diabetes and Diabetes Treatment Satisfaction Questionnaire scores improved in the sensor-augmented insulin pump group. Sensor augmented pump therapy effectively lowers HbA(1c) in patients with Type 1 diabetes suboptimally controlled with multiple daily injections. © 2011 The Authors. Diabetic Medicine © 2011 Diabetes UK.

Multi-Population Invariance with Dichotomous Measures: Combining Multi-Group and MIMIC Methodologies in Evaluating the General Aptitude Test in the Arabic Language

ERIC Educational Resources Information Center

Sideridis, Georgios D.; Tsaousis, Ioannis; Al-harbi, Khaleel A.

2015-01-01

The purpose of the present study was to extend the model of measurement invariance by simultaneously estimating invariance across multiple populations in the dichotomous instrument case using multi-group confirmatory factor analytic and multiple indicator multiple causes (MIMIC) methodologies. Using the Arabic version of the General Aptitude Test…

Group Therapy with Multiple Therapists in A Large Group.

ERIC Educational Resources Information Center

Herschleman, Philip; Freundlich, David

The utilization of multiple therapists in large group therapy meetings has been found to be a significant improvement over the traditional ward meeting or patient-staff conference. The initially limited goals of reducing ward tension and acting out by means of patients ventilation were surpassed. Despite the size of the meetings it was often…

Statistical Power in Evaluations That Investigate Effects on Multiple Outcomes: A Guide for Researchers

ERIC Educational Resources Information Center

Porter, Kristin E.

2018-01-01

Researchers are often interested in testing the effectiveness of an intervention on multiple outcomes, for multiple subgroups, at multiple points in time, or across multiple treatment groups. The resulting multiplicity of statistical hypothesis tests can lead to spurious findings of effects. Multiple testing procedures (MTPs) are statistical…

Assigning unique identification numbers to new user accounts and groups in a computing environment with multiple registries

DOEpatents

DeRobertis, Christopher V.; Lu, Yantian T.

2010-02-23

A method, system, and program storage device for creating a new user account or user group with a unique identification number in a computing environment having multiple user registries is provided. In response to receiving a command to create a new user account or user group, an operating system of a clustered computing environment automatically checks multiple registries configured for the operating system to determine whether a candidate identification number for the new user account or user group has been assigned already to one or more existing user accounts or groups, respectively. The operating system automatically assigns the candidate identification number to the new user account or user group created in a target user registry if the checking indicates that the candidate identification number has not been assigned already to any of the existing user accounts or user groups, respectively.

Estimating vehicle height using homographic projections

DOEpatents

Cunningham, Mark F; Fabris, Lorenzo; Gee, Timothy F; Ghebretati, Jr., Frezghi H; Goddard, James S; Karnowski, Thomas P; Ziock, Klaus-peter

2013-07-16

Multiple homography transformations corresponding to different heights are generated in the field of view. A group of salient points within a common estimated height range is identified in a time series of video images of a moving object. Inter-salient point distances are measured for the group of salient points under the multiple homography transformations corresponding to the different heights. Variations in the inter-salient point distances under the multiple homography transformations are compared. The height of the group of salient points is estimated to be the height corresponding to the homography transformation that minimizes the variations.

Microwave ablation with multiple simultaneously powered small-gauge triaxial antennas: results from an in vivo swine liver model.

PubMed

Brace, Christopher L; Laeseke, Paul F; Sampson, Lisa A; Frey, Tina M; van der Weide, Daniel W; Lee, Fred T

2007-07-01

To prospectively investigate the ability of a single generator to power multiple small-diameter antennas and create large zones of ablation in an in vivo swine liver model. Thirteen female domestic swine (mean weight, 70 kg) were used for the study as approved by the animal care and use committee. A single generator was used to simultaneously power three triaxial antennas at 55 W per antenna for 10 minutes in three groups: a control group where antennas were spaced to eliminate ablation zone overlap (n=6; 18 individual zones of ablation) and experimental groups where antennas were spaced 2.5 cm (n=7) or 3.0 cm (n=5) apart. Animals were euthanized after ablation, and ablation zones were sectioned and measured. A mixed linear model was used to test for differences in size and circularity among groups. Mean (+/-standard deviation) cross-sectional areas of multiple-antenna zones of ablation at 2.5- and 3.0-cm spacing (26.6 cm(2) +/- 9.7 and 32.2 cm(2) +/- 8.1, respectively) were significantly larger than individual ablation zones created with single antennas (6.76 cm(2) +/- 2.8, P<.001) and were 31% (2.5-cm spacing group: multiple antenna mean area, 26.6 cm(2); 3 x single antenna mean area, 20.28 cm(2)) to 59% (3.0-cm spacing group: multiple antenna mean area, 32.2 cm(2); 3 x single antenna mean area, 20.28 cm(2)) larger than 3 times the mean area of the single-antenna zones. Zones of ablation were found to be very circular, and vessels as large as 1.1 cm were completely coagulated with multiple antennas. A single generator may effectively deliver microwave power to multiple antennas. Large volumes of tissue may be ablated and large vessels coagulated with multiple-antenna ablation in the same time as single-antenna ablation. (c) RSNA, 2007.

Multiple Free Internal Limiting Membrane Flap Insertion in the Treatment of Macular Hole-Associated Retinal Detachment in High Myopia.

PubMed

Chen, San-Ni; Hsieh, Yi-Ting; Yang, Chung-May

2018-06-06

The aim of this paper was to evaluate the efficacy of multiple free internal limiting membrane (ILM) flap insertion in the management of macular hole-associated retinal detachment in high myopia. Eyes receiving operation for macular hole-associated retinal detachment were retrospectively recruited. Those in the study group received ILM peeling and multiple free ILM flap insertion, while those in the control group received ILM peeling only. Postoperative anatomical outcomes and best-corrected visual acuity were compared between the 2 groups. Twenty-seven eyes of 27 patients were recruited in this study (13 in the study group, 14 in the control group). After the operation, the retina was reattached in all cases in both groups. The macular hole closure rate was 100% in the study group but only 42.9% in the control group (adjusted p < 0.001). The eyes in the study group had better visual improvement (logMAR -0.58 ± 0.43) than those in the control group (logMAR -0.31 ± 0.50) with borderline significance (adjusted p = 0.078). For macular hole-associated retinal detachment in highly myopic eyes, the multiple free ILM flap insertion technique offers an effective way to close macular holes. Whether this result also means better visual outcome remains to be seen. © 2018 S. Karger AG, Basel.

Estimating Statistical Power When Making Adjustments for Multiple Tests

ERIC Educational Resources Information Center

Porter, Kristin E.

2016-01-01

In recent years, there has been increasing focus on the issue of multiple hypotheses testing in education evaluation studies. In these studies, researchers are typically interested in testing the effectiveness of an intervention on multiple outcomes, for multiple subgroups, at multiple points in time or across multiple treatment groups. When…

[Anatomy character of renal artery and treatment of living-donor renal transplantation].

PubMed

Zhang, Lei; Fei, Ji-guang; Chen, Li-zhong; Wang, Chang-xi; Deng, Su-xiong; Qiu, Jiang; Li, Jun; Chen, Guo-dong; Huang, Gang

2009-12-15

To study the anatomy characters of renal artery and the treatment of multiple arteries in living donor renal grafts. Records of 142 living donors were analyzed in our center. We analyzed the anatomic structure of renal arteries by DSA and CTA pre-transplantation. Thirty-one kidneys with multiple arteries were transplanted after reconstruction. Then clinical effects were compared between multiple-renal-arteries group (n=31) and single-renal-artery group (n=111). The incidence of multiple renal artery was 30.99%, and there was no difference between both sides (left kidney 22.54%, right kidney 22.13%). If the multiple artery occurred in left or right kidney, the incidence of the multiple artery occurred in the other side was 56.25% and 60.00%, respectively. The diameter of left main renal artery was more magnanimous (P=0.001) and the first branch was more closed to abdominal aorta (P=0.004). Operation time and warm/cool ischemia time were longer in the multiple-renal-arteries group. However, estimated blood loss, delayed graft function, acute rejection and flow rate of arcuate artery were similar in both groups, the same as serum creatinine and serum creatinine clearance rate on day 7, 1 month and 3 month post-operation. It was shown by repeated measures ANOVA that graft with multiple arteries didn't affect the tendency of renal function at early time post-operation. Comprehending the character of renal artery and accurate treatment of multiple artery anastomosis are critical for the effect of the living kidney transplantation.

Multiple-, But Not Single-, Dose of Parecoxib Reduces Shoulder Pain after Gynecologic Laparoscopy

PubMed Central

Zhang, Hufei; Shu, Haihua; Yang, Lu; Cao, Minghui; Zhang, Jingjun; Liu, Kexuan; Xiao, Liangcan; Zhang, Xuyu

2012-01-01

Background: The aim of this study was to investigate effect of single- and multiple-dose of parecoxib on shoulder pain after gynecologic laparoscopy. Methods: 126 patients requiring elective gynecologic laparoscopy were randomly allocated to three groups. Group M (multiple-dose): receiving parecoxib 40mg at 30min before the end of surgery, at 8 and 20hr after surgery, respectively; Group S (single-dose): receiving parecoxib 40mg at 30min before the end of surgery and normal saline at the corresponding time points; Group C (control): receiving normal saline at the same three time points. The shoulder pain was evaluated, both at rest and with motion, at postoperative 6, 24 and 48hr. The impact of shoulder pain on patients' recovery (activity, mood, walking and sleep) was also evaluated. Meanwhile, rescue analgesics and complications were recorded. Results: The overall incidence of shoulder pain in group M (37.5%) was lower than that in group C (61.9%) (difference=-24.4%; 95% CI: 3.4~45.4%; P=0.023). Whereas, single-dose regimen (61.0%) showed no significant reduction (difference with control=-0.9%; 95% CI: -21.9~20.0%; P=0.931). Moreover, multiple-dose regimen reduced the maximal intensity of shoulder pain and the impact for activity and mood in comparison to the control. Multiple-dose of parecoxib decreased the consumption of rescue analgesics. The complications were similar among all groups and no severe complications were observed. Conclusions: Multiple-, but not single-, dose of parecoxib may attenuate the incidence and intensity of shoulder pain and thereby improve patients' quality of recovery following gynecologic laparoscopy. PMID:23136538

Efficacy of rasagiline in patients with the parkinsonian variant of multiple system atrophy: a randomised, placebo-controlled trial.

PubMed

Poewe, Werner; Seppi, Klaus; Fitzer-Attas, Cheryl J; Wenning, Gregor K; Gilman, Sid; Low, Phillip A; Giladi, Nir; Barone, Paolo; Sampaio, Cristina; Eyal, Eli; Rascol, Olivier

2015-02-01

Multiple system atrophy is a complex neurodegenerative disorder for which no effective treatment exists. We aimed to assess the effect of rasagiline on symptoms and progression of the parkinsonian variant of multiple system atrophy. We did this randomised, double-blind, placebo-controlled trial between Dec 15, 2009, and Oct 20, 2011, at 40 academic sites specialised in the care of patients with multiple systemic atrophy across 12 countries. Eligible participants aged 30 years or older with possible or probable parkinsonian variant multiple system atrophy were randomly assigned (1:1), via computer-generated block randomisation (block size of four), to receive either rasagiline 1 mg per day or placebo. Randomisation was stratified by study centre. The investigators, study funder, and personnel involved in patient assessment, monitoring, analysis and data management were masked to group assignment. The primary endpoint was change from baseline to study end in total Unified Multiple System Atrophy Rating Scale (UMSARS) score (parts I and II). Analysis was by modified intention to treat. The trial is registered with ClinicalTrials.gov, number NCT00977665. We randomly assigned 174 participants to the rasagiline group (n=84) or the placebo group (n=90); 21 (25%) patients in the rasagiline group and 15 (17%) in the placebo group withdrew from the study early. At week 48, patients in the rasagiline group had progressed by an adjusted mean of 7·2 (SE 1·2) total UMSARS units versus 7·8 (1·1) units in those in the placebo group. This treatment difference of -0·60 (95% CI -3·68 to 2·47; p=0·70) was not significant. 68 (81%) patients in the rasagiline group and 67 (74%) patients in the placebo group reported adverse events, and we recorded serious adverse events in 29 (35%) versus 23 (26%) patients. The most common adverse events in the rasagiline group were dizziness (n=10 [12%]), peripheral oedema (n=9 [11%]), urinary tract infections (n=9 [11%]), and orthostatic hypotension (n=8 [10%]). In this population of patients with the parkinsonian variant of multiple system atrophy, treatment with rasagiline 1 mg per day did not show a significant benefit as assessed by UMSARS. The study confirms the sensitivity of clinical outcomes for multiple system atrophy to detect clinically significant decline, even in individuals with early disease. Teva Pharmaceutical Industries and H Lundbeck A/S. Copyright © 2015 Elsevier Ltd. All rights reserved.

Effects on Cognition of Stereotactic Lesional Surgery For the Treatment of Tremor in Multiple Sclerosis

PubMed Central

Jahanshahi, Marjan; Pieter, Socorro; Alusi, Sundus H.; Jones, Catherine R. G.; Glickman, Scott; Stein, John; Aziz, Tipu; Bain, Peter G.

2008-01-01

Objective: To assess the effect of stereotactic lesional surgery for treatment of tremor in multiple sclerosis on cognition. Methods: Eleven patients (3 males, 8 females) with multiple sclerosis participated in the study. Six subjects comprised the surgical group and five the matched control group. All patients were assessed at baseline and three months using a neuropsychological test battery that included measures of intellectual ability, memory, language, perception and executive function. Results: There were no significant differences between the surgical and control groups and no change from pre to post testing except for a decline in scores on the Mini-Mental State Examination (MMSE), WAIS-R Digit Span and Verbal Fluency in the surgical group. Conclusions: The results indicate that stereotactic lesional surgery does not result in major cognitive impairment in multiple sclerosis. However, the decline in MMSE scores, digit span and verbal fluency require further investigation in a larger sample. PMID:19491469

Influence of multiple antenatal counselling sessions on modern contraceptive uptake in Nigeria.

PubMed

Adanikin, Abiodun I; Onwudiegwu, Uche; Loto, Olabisi M

2013-10-01

To determine the influence of multiple contraceptive counselling sessions during antenatal care on use of modern postpartum contraception. A total of 216 eligible pregnant women were randomised into antenatal and postnatal counselling groups. The 'Antenatal group' received one-to-one antenatal contraceptive counselling on several occasions while the 'Postnatal group' received a single one-to-one contraceptive counselling session at the sixth week postnatal check, as is routinely practised. All participants were contacted six months postpartum by telephone or personal visit, and questioned about their contraceptive use, if any. More women who had multiple antenatal contraceptive counselling sessions used modern contraceptive methods than those who had a single postnatal counselling session (57% vs. 35%; p = 0.002). There was also a significantly more frequent use of contraception among previously undecided patients in the Antenatal group (p = 0.014). Multiple antenatal contraceptive counselling sessions improve the use of modern postpartum contraception.

Beyond Group: Multiple Person Tracking via Minimal Topology-Energy-Variation.

PubMed

Gao, Shan; Ye, Qixiang; Xing, Junliang; Kuijper, Arjan; Han, Zhenjun; Jiao, Jianbin; Ji, Xiangyang

2017-12-01

Tracking multiple persons is a challenging task when persons move in groups and occlude each other. Existing group-based methods have extensively investigated how to make group division more accurately in a tracking-by-detection framework; however, few of them quantify the group dynamics from the perspective of targets' spatial topology or consider the group in a dynamic view. Inspired by the sociological properties of pedestrians, we propose a novel socio-topology model with a topology-energy function to factor the group dynamics of moving persons and groups. In this model, minimizing the topology-energy-variance in a two-level energy form is expected to produce smooth topology transitions, stable group tracking, and accurate target association. To search for the strong minimum in energy variation, we design the discrete group-tracklet jump moves embedded in the gradient descent method, which ensures that the moves reduce the energy variation of group and trajectory alternately in the varying topology dimension. Experimental results on both RGB and RGB-D data sets show the superiority of our proposed model for multiple person tracking in crowd scenes.

A risk-adapted approach is beneficial in the management of bilateral femoral shaft fractures in multiple trauma patients: an analysis based on the trauma registry of the German Trauma Society.

PubMed

Steinhausen, Eva; Lefering, Rolf; Tjardes, Thorsten; Neugebauer, Edmund A M; Bouillon, Bertil; Rixen, Dieter

2014-05-01

Today, there is a trend toward damage-control orthopedics (DCO) in the management of multiple trauma patients with long bone fractures. However, there is no widely accepted concept. A risk-adapted approach seems to result in low acute morbidity and mortality. Multiple trauma patients with bilateral femoral shaft fractures (FSFs) are considered to be more severely injured. The objective of this study was to validate the risk-adapted approach in the management of multiple trauma patients with bilateral FSF. Data analysis is based on the trauma registry of the German Trauma Society (1993-2008, n = 42,248). Multiple trauma patients with bilateral FSF were analyzed in subgroups according to the type of primary operative strategy. Outcome parameters were mortality and major complications as (multiple) organ failure and sepsis. A total of 379 patients with bilateral FSF were divided into four groups as follows: (1) no operation (8.4%), (2) bilateral temporary external fixation (DCO) (50.9%), bilateral primary definitive osteosynthesis (early total care [ETC]) (25.1%), and primary definitive osteosynthesis of one FSF and DCO contralaterally (mixed) (15.6%). Compared with the ETC group, the DCO group was more severely injured. The incidence of (multiple) organ failure and mortality rates were higher in the DCO group but without significance. Adjusted for injury severity, there was no significant difference of mortality rates between DCO and ETC. Injury severity and mortality rates were significantly increased in the no-operation group. The mixed group was similar to the ETC group regarding injury severity and outcome. In Germany, both DCO and ETC are practiced in multiple trauma patients with bilateral FSF so far. The unstable or potentially unstable patient is reasonably treated with DCO. The clearly stable patient is reasonably treated with nailing. When in doubt, the patient is probably not totally stable, and the safest precaution may be to use DCO as a risk-adapted approach. Therapeutic study, level IV. Epidemiologic study, level III.

Effect of differing PowerPoint slide design on multiple-choice test scores for assessment of knowledge and retention in a theriogenology course.

PubMed

Root Kustritz, Margaret V

2014-01-01

Third-year veterinary students in a required theriogenology diagnostics course were allowed to self-select attendance at a lecture in either the evening or the next morning. One group was presented with PowerPoint slides in a traditional format (T group), and the other group was presented with PowerPoint slides in the assertion-evidence format (A-E group), which uses a single sentence and a highly relevant graphic on each slide to ensure attention is drawn to the most important points in the presentation. Students took a multiple-choice pre-test, attended lecture, and then completed a take-home assignment. All students then completed an online multiple-choice post-test and, one month later, a different online multiple-choice test to evaluate retention. Groups did not differ on pre-test, assignment, or post-test scores, and both groups showed significant gains from pre-test to post-test and from pre-test to retention test. However, the T group showed significant decline from post-test to retention test, while the A-E group did not. Short-term differences between slide designs were most likely unaffected due to required coursework immediately after lecture, but retention of material was superior with the assertion-evidence slide design.

Multiple marker screening test: identification of fetal cystic hygroma, hydrops, and sex chromosome aneuploidy.

PubMed

Wenstrom, K D; Boots, L R; Cosper, P C

1996-01-01

The goal of this study was to determine if the multiple marker screening test (maternal serum alpha-fetoprotein, unconjugated estriol, human chorionic gonadotrophin, and maternal age) detects fetal Turner syndrome or just cystic hygroma/hydrops. Multiple marker screening tests from 4 groups were compared: 1) Turner syndrome with hydrops/ hygroma group (n = 10) = fetuses with cystic hygroma/hydrops and a 45X karyotype, 2) Turner syndrome without hydrops/hygroma (n = 9) = sonographically unremarkable fetal Turner syndrome or Turner mosaic, 3) hydrops group (n = 8) = all cases of fetal cystic hygroma/hydrops excluding Turner syndrome, 4) sex chromosome aneuploidy group (n = 16) = other sonographically normal fetal sex chromosome aneuploidies. Positive screening tests (Down syndrome risk > or = 1:190 or MSAFP > or = 2.5 MOM) were found in 60% (6/10) of the Turner syndrome with hydrops/hygroma group, but only 11% (1/9) of the Turner syndrome without hydrops/hygroma group (P = .04). The incidence of positive screening tests in the Hydrops group was 75% (6/8), while it was only 12.5% (2/16) in the other sex chromosome aneuploidy group. We conclude that the multiple marker screening test identifies fetuses with cystic hygroma/hydrops, and may do so independently of the etiology of the hydrops.

Comparing Multiple-Group Multinomial Log-Linear Models for Multidimensional Skill Distributions in the General Diagnostic Model. Research Report. ETS RR-08-35

ERIC Educational Resources Information Center

Xu, Xueli; von Davier, Matthias

2008-01-01

The general diagnostic model (GDM) utilizes located latent classes for modeling a multidimensional proficiency variable. In this paper, the GDM is extended by employing a log-linear model for multiple populations that assumes constraints on parameters across multiple groups. This constrained model is compared to log-linear models that assume…

Sensitivity Analysis of Multiple Informant Models When Data Are Not Missing at Random

ERIC Educational Resources Information Center

Blozis, Shelley A.; Ge, Xiaojia; Xu, Shu; Natsuaki, Misaki N.; Shaw, Daniel S.; Neiderhiser, Jenae M.; Scaramella, Laura V.; Leve, Leslie D.; Reiss, David

2013-01-01

Missing data are common in studies that rely on multiple informant data to evaluate relationships among variables for distinguishable individuals clustered within groups. Estimation of structural equation models using raw data allows for incomplete data, and so all groups can be retained for analysis even if only 1 member of a group contributes…

Structural Equivalence of Involvement in Problem Behavior by Adolescents across Racial Groups Using Multiple Group Confirmatory Factor Analysis.

ERIC Educational Resources Information Center

Williams, James H.; And Others

1996-01-01

Problem behavior theory predicts that adolescent problem behaviors are manifestations of a single behavioral syndrome. This study tested the validity of the theory across racial groups. Results indicate that multiple pathways are necessary to account for the problem behaviors and they support previous research indicating system response bias in…

Risk factors for retinal breaks in patients with symptom of floaters.

PubMed

Singalavanija, Apichart; Amornrattanapan, Chutiwan; Nitiruangjarus, Kanjanee; Tongsai, Sasima

2010-06-01

To identify the risk factors of retinal breaks in patients with the symptom of floaters, and to determine the association between those risk factors and retinal breaks. A retrospective analytic study of 184 patients (55 males and 129 females) that included 220 eyes was conducted. Patient information such as age, symptoms (multiple floaters, flashing), duration of symptom, refractive error, history of cataract surgery, family history of retinal detachment, and complete eye examination were recorded. The patients were divided into two groups, the first group (control group) had symptoms of floaters and no retinal breaks, the second group (retinal breaks group) had symptoms of floaters with retinal breaks. Chi-square test, and the multiple logistic regression were used for statistical analysis. Two hundred twenty eyes, 175 eyes of the control group and 45 eyes of the retinal breaks group were examined and included in this study. The multiple logistic regression analysis revealed that patients with multiple floaters, and floaters and flashing increased the risk of retinal breaks to 5.8 and 4.3 times, respectively, when compared to patients with single floater or floaters alone. Lattice degeneration increased the risk of retinal breaks to 5.9 times when compared to eyes that did not have lattice degeneration. Multiple floaters, flashing and lattice degeneration are risk factors of retinal breaks in patients with symptoms of floaters. Therefore, it is important for the ophthalmologists to be aware of these risk factors and the patients at risk should have follow-up examinations.

Discrimination and well-being amongst the homeless: the role of multiple group membership

PubMed Central

Johnstone, Melissa; Jetten, Jolanda; Dingle, Genevieve A.; Parsell, Cameron; Walter, Zoe C.

2015-01-01

The homeless are a vulnerable population in many respects. Those experiencing homelessness not only experience personal and economic hardship they also frequently face discrimination and exclusion because of their housing status. Although past research has shown that identifying with multiple groups can buffer against the negative consequences of discrimination on well-being, it remains to be seen whether such strategies protect well-being of people who are homeless. We investigate this issue in a longitudinal study of 119 individuals who were homeless. The results showed that perceived group-based discrimination at T1 was associated with fewer group memberships, and lower subsequent well-being at T2. There was no relationship between personal discrimination at T1 on multiple group memberships at T2. The findings suggest that the experience of group-based discrimination may hinder connecting with groups in the broader social world — groups that could potentially protect the individual against the negative impact of homelessness and discrimination. PMID:26082741