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AuthorDeVore, Ronald (3)Cohen, Albert (2)Douglas, C. (2)Genton, Marc G. (2)Guermond, Jean-Luc (2)View MoreJournalComputing and Visualization in Science (3)Statistics and Computing (3)BMC Bioinformatics (2)Constructive Approximation (2)International Journal of Fracture (2)View MoreKAUST Grant Number

KUS-C1-016-04 (23)

Publisher
Springer Nature (23)

SubjectActive learning (1)Adaptivity (1)Approximation (1)Approximation classes (1)Asymmetric loss function (1)View MoreType
Article (23)

Year (Issue Date)2013 (4)2012 (3)2011 (6)2010 (6)2009 (3)View MoreItem AvailabilityMetadata Only (20)Open Access (3)

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Whole-genome sequencing and genetic variant analysis of a Quarter Horse mare.

Doan, Ryan; Cohen, Noah D; Sawyer, Jason; Ghaffari, Noushin; Johnson, Charlie D; Dindot, Scott V (BMC Genomics, Springer Nature, 2012-02-17) [Article]

BACKGROUND: The catalog of genetic variants in the horse genome originates from a few select animals, the majority originating from the Thoroughbred mare used for the equine genome sequencing project. The purpose of this study was to identify genetic variants, including single nucleotide polymorphisms (SNPs), insertion/deletion polymorphisms (INDELs), and copy number variants (CNVs) in the genome of an individual Quarter Horse mare sequenced by next-generation sequencing. RESULTS: Using massively parallel paired-end sequencing, we generated 59.6 Gb of DNA sequence from a Quarter Horse mare resulting in an average of 24.7X sequence coverage. Reads were mapped to approximately 97% of the reference Thoroughbred genome. Unmapped reads were de novo assembled resulting in 19.1 Mb of new genomic sequence in the horse. Using a stringent filtering method, we identified 3.1 million SNPs, 193 thousand INDELs, and 282 CNVs. Genetic variants were annotated to determine their impact on gene structure and function. Additionally, we genotyped this Quarter Horse for mutations of known diseases and for variants associated with particular traits. Functional clustering analysis of genetic variants revealed that most of the genetic variation in the horse's genome was enriched in sensory perception, signal transduction, and immunity and defense pathways. CONCLUSIONS: This is the first sequencing of a horse genome by next-generation sequencing and the first genomic sequence of an individual Quarter Horse mare. We have increased the catalog of genetic variants for use in equine genomics by the addition of novel SNPs, INDELs, and CNVs. The genetic variants described here will be a useful resource for future studies of genetic variation regulating performance traits and diseases in equids.

A boundary integral method for a dynamic, transient mode I crack problem with viscoelastic cohesive zone

Leise, Tanya L.; Walton, Jay R.; Gorb, Yuliya (International Journal of Fracture, Springer Nature, 2009-08-19) [Article]

We consider the problem of the dynamic, transient propagation of a semi-infinite, mode I crack in an infinite elastic body with a nonlinear, viscoelastic cohesize zone. Our problem formulation includes boundary conditions that preclude crack face interpenetration, in contrast to the usual mode I boundary conditions that assume all unloaded crack faces are stress-free. The nonlinear viscoelastic cohesive zone behavior is motivated by dynamic fracture in brittle polymers in which crack propagation is preceeded by significant crazing in a thin region surrounding the crack tip. We present a combined analytical/numerical solution method that involves reducing the problem to a Dirichlet-to-Neumann map along the crack face plane, resulting in a differo-integral equation relating the displacement and stress along the crack faces and within the cohesive zone. © 2009 Springer Science+Business Media B.V.

Capturing Ridge Functions in High Dimensions from Point Queries

Cohen, Albert; Daubechies, Ingrid; DeVore, Ronald; Kerkyacharian, Gerard; Picard, Dominique (Constructive Approximation, Springer Nature, 2011-12-21) [Article]

Constructing a good approximation to a function of many variables suffers from the "curse of dimensionality". Namely, functions on ℝ N with smoothness of order s can in general be captured with accuracy at most O(n -s/N) using linear spaces or nonlinear manifolds of dimension n. If N is large and s is not, then n has to be chosen inordinately large for good accuracy. The large value of N often precludes reasonable numerical procedures. On the other hand, there is the common belief that real world problems in high dimensions have as their solution, functions which are more amenable to numerical recovery. This has led to the introduction of models for these functions that do not depend on smoothness alone but also involve some form of variable reduction. In these models it is assumed that, although the function depends on N variables, only a small number of them are significant. Another variant of this principle is that the function lives on a low dimensional manifold. Since the dominant variables (respectively the manifold) are unknown, this leads to new problems of how to organize point queries to capture such functions. The present paper studies where to query the values of a ridge function f(x)=g(a · x) when both a∈ℝ N and g ∈ C[0,1] are unknown. We establish estimates on how well f can be approximated using these point queries under the assumptions that g ∈ C s[0,1]. We also study the role of sparsity or compressibility of a in such query problems. © 2011 Springer Science+Business Media, LLC.

An efficient and extensible approach for compressing phylogenetic trees

Matthews, Suzanne J; Williams, Tiffani L (BMC Bioinformatics, Springer Nature, 2011) [Article]

Background: Biologists require new algorithms to efficiently compress and store their large collections of phylogenetic trees. Our previous work showed that TreeZip is a promising approach for compressing phylogenetic trees. In this paper, we extend our TreeZip algorithm by handling trees with weighted branches. Furthermore, by using the compressed TreeZip file as input, we have designed an extensible decompressor that can extract subcollections of trees, compute majority and strict consensus trees, and merge tree collections using set operations such as union, intersection, and set difference.Results: On unweighted phylogenetic trees, TreeZip is able to compress Newick files in excess of 98%. On weighted phylogenetic trees, TreeZip is able to compress a Newick file by at least 73%. TreeZip can be combined with 7zip with little overhead, allowing space savings in excess of 99% (unweighted) and 92%(weighted). Unlike TreeZip, 7zip is not immune to branch rotations, and performs worse as the level of variability in the Newick string representation increases. Finally, since the TreeZip compressed text (TRZ) file contains all the semantic information in a collection of trees, we can easily filter and decompress a subset of trees of interest (such as the set of unique trees), or build the resulting consensus tree in a matter of seconds. We also show the ease of which set operations can be performed on TRZ files, at speeds quicker than those performed on Newick or 7zip compressed Newick files, and without loss of space savings.Conclusions: TreeZip is an efficient approach for compressing large collections of phylogenetic trees. The semantic and compact nature of the TRZ file allow it to be operated upon directly and quickly, without a need to decompress the original Newick file. We believe that TreeZip will be vital for compressing and archiving trees in the biological community. © 2011 Matthews and Williams; licensee BioMed Central Ltd.

A Non-Gaussian Spatial Generalized Linear Latent Variable Model

Irincheeva, Irina; Cantoni, Eva; Genton, Marc G. (Journal of Agricultural, Biological, and Environmental Statistics, Springer Nature, 2012-08-03) [Article]

We consider a spatial generalized linear latent variable model with and without normality distributional assumption on the latent variables. When the latent variables are assumed to be multivariate normal, we apply a Laplace approximation. To relax the assumption of marginal normality in favor of a mixture of normals, we construct a multivariate density with Gaussian spatial dependence and given multivariate margins. We use the pairwise likelihood to estimate the corresponding spatial generalized linear latent variable model. The properties of the resulting estimators are explored by simulations. In the analysis of an air pollution data set the proposed methodology uncovers weather conditions to be a more important source of variability than air pollution in explaining all the causes of non-accidental mortality excluding accidents. © 2012 International Biometric Society.

A note on the Stokes operator and its powers

Guermond, Jean-Luc; Salgado, Abner (Journal of Applied Mathematics and Computing, Springer Nature, 2010-04-28) [Article]

The so-called Stokes operator is an important tool in the analysis of the solutions of the Navier-Stokes equations and their numerical approximation. The aim of this note is to clarify certain properties of the fractional powers of this operator which are sometimes misused. © 2010 Korean Society for Computational and Applied Mathematics.

A stochastic model for transmission, extinction and outbreak of Escherichia coli O157:H7 in cattle as affected by ambient temperature and cleaning practices

Wang, Xueying; Gautam, Raju; Pinedo, Pablo J.; Allen, Linda J. S.; Ivanek, Renata (Journal of Mathematical Biology, Springer Nature, 2013-07-18) [Article]

Many infectious agents transmitting through a contaminated environment are able to persist in the environment depending on the temperature and sanitation determined rates of their replication and clearance, respectively. There is a need to elucidate the effect of these factors on the infection transmission dynamics in terms of infection outbreaks and extinction while accounting for the random nature of the process. Also, it is important to distinguish between the true and apparent extinction, where the former means pathogen extinction in both the host and the environment while the latter means extinction only in the host population. This study proposes a stochastic-differential equation model as an approximation to a Markov jump process model, using Escherichia coli O157:H7 in cattle as a model system. In the model, the host population infection dynamics are described using the standard susceptible-infected-susceptible framework, and the E. coli O157:H7 population in the environment is represented by an additional variable. The backward Kolmogorov equations that determine the probability distribution and the expectation of the first passage time are provided in a general setting. The outbreak and apparent extinction of infection are investigated by numerically solving the Kolmogorov equations for the probability density function of the associated process and the expectation of the associated stopping time. The results provide insight into E. coli O157:H7 transmission and apparent extinction, and suggest ways for controlling the spread of infection in a cattle herd. Specifically, this study highlights the importance of ambient temperature and sanitation, especially during summer. © 2013 Springer-Verlag Berlin Heidelberg.

An Equal-Order DG Method for the Incompressible Navier-Stokes Equations

Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik (Journal of Scientific Computing, Springer Nature, 2008-12-20) [Article]

We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability of this equal-order approach is ensured by a pressure stabilization term. A simple element-by-element post-processing procedure is used to provide globally divergence-free velocity approximations. For small data, we prove the existence and uniqueness of discrete solutions and carry out an error analysis of the method. A series of numerical results are presented that validate our theoretical findings. © 2008 Springer Science+Business Media, LLC.

Annealing evolutionary stochastic approximation Monte Carlo for global optimization

Liang, Faming (Statistics and Computing, Springer Nature, 2010-04-08) [Article]

In this paper, we propose a new algorithm, the so-called annealing evolutionary stochastic approximation Monte Carlo (AESAMC) algorithm as a general optimization technique, and study its convergence. AESAMC possesses a self-adjusting mechanism, whose target distribution can be adapted at each iteration according to the current samples. Thus, AESAMC falls into the class of adaptive Monte Carlo methods. This mechanism also makes AESAMC less trapped by local energy minima than nonadaptive MCMC algorithms. Under mild conditions, we show that AESAMC can converge weakly toward a neighboring set of global minima in the space of energy. AESAMC is tested on multiple optimization problems. The numerical results indicate that AESAMC can potentially outperform simulated annealing, the genetic algorithm, annealing stochastic approximation Monte Carlo, and some other metaheuristics in function optimization. © 2010 Springer Science+Business Media, LLC.

Convergence Rates of AFEM with H −1 Data

Cohen, Albert; DeVore, Ronald; Nochetto, Ricardo H. (Foundations of Computational Mathematics, Springer Nature, 2012-06-29) [Article]

This paper studies adaptive finite element methods (AFEMs), based on piecewise linear elements and newest vertex bisection, for solving second order elliptic equations with piecewise constant coefficients on a polygonal domain Ω⊂ℝ2. The main contribution is to build algorithms that hold for a general right-hand side f∈H-1(Ω). Prior work assumes almost exclusively that f∈L2(Ω). New data indicators based on local H-1 norms are introduced, and then the AFEMs are based on a standard bulk chasing strategy (or Dörfler marking) combined with a procedure that adapts the mesh to reduce these new indicators. An analysis of our AFEM is given which establishes a contraction property and optimal convergence rates N-s with 0<s≤1/2. In contrast to previous work, it is shown that it is not necessary to assume a compatible decay s<1/2 of the data estimator, but rather that this is automatically guaranteed by the approximability assumptions on the solution by adaptive meshes, without further assumptions on f; the borderline case s=1/2 yields an additional factor logN. Computable surrogates for the data indicators are introduced and shown to also yield optimal convergence rates N-s with s≤1/2. © 2012 SFoCM.

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