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Numerical Analysis and Computation

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Articles 1201 - 1230 of 1368

Full-Text Articles in Applied Mathematics

Greedy Signal Recovery And Uncertainty Principles, Deanna Needell, Roman Vershynin Jul 2007

Greedy Signal Recovery And Uncertainty Principles, Deanna Needell, Roman Vershynin

CMC Faculty Publications and Research

This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements – L1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of the Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of the L1-minimization. Our algorithm ROMP reconstructs a sparse signal in a number of iterations linear in the sparsity, and the reconstruction is exact provided the linear measurements satisfy the Uniform Uncertainty Principle. In the case of inaccurate measurements and approximately sparse …

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Survival Analysis With Large Dimensional Covariates: An Application In Microarray Studies, David A. Engler, Yi Li Jul 2007

Survival Analysis With Large Dimensional Covariates: An Application In Microarray Studies, David A. Engler, Yi Li

Harvard University Biostatistics Working Paper Series

Use of microarray technology often leads to high-dimensional and low- sample size data settings. Over the past several years, a variety of novel approaches have been proposed for variable selection in this context. However, only a small number of these have been adapted for time-to-event data where censoring is present. Among standard variable selection methods shown both to have good predictive accuracy and to be computationally efficient is the elastic net penalization approach. In this paper, adaptation of the elastic net approach is presented for variable selection both under the Cox proportional hazards model and under an accelerated failure time …

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Preliminary Estimates Of Building Cost And The Lowest Evaluated Tender, Harriet Eliufoo Jun 2007

Preliminary Estimates Of Building Cost And The Lowest Evaluated Tender, Harriet Eliufoo

Tanzania Journal of Engineering and Technology (TJET)

The paper has investigated and established to what extent are preliminary estimates of building costs close to the lowest evaluated tender and how geographical proximity influences the variance between preliminary estimate and the lowest evaluated tender. A multiple case study constituting 43 building projects in Tanzania were statistically analysed covering a period from 1995- 1999. Findings reveal a significant variance exists between the quantity surveyor’s preliminary estimate figure and the lowest evaluated tender; and that the variance between the quantity surveyor’s figure and the bidder is small when the proposed building project is geographically closer to the quantity surveyor’s base. …

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Simultaneous Confidence Intervals Based On The Percentile Bootstrap Approach, Micha Mandel, Rebecca A. Betensky Jun 2007

Simultaneous Confidence Intervals Based On The Percentile Bootstrap Approach, Micha Mandel, Rebecca A. Betensky

Harvard University Biostatistics Working Paper Series

No abstract provided.

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Distributed Reproducible Research Using Cached Computations, Roger Peng, Sandrah P. Eckel Jun 2007

Distributed Reproducible Research Using Cached Computations, Roger Peng, Sandrah P. Eckel

Johns Hopkins University, Dept. of Biostatistics Working Papers

The ability to make scientific findings reproducible is increasingly important in areas where substantive results are the product of complex statistical computations. Reproducibility can allow others to verify the published findings and conduct alternate analyses of the same data. A question that arises naturally is how can one conduct and distribute reproducible research? This question is relevant from the point of view of both the authors who want to make their research reproducible and readers who want to reproduce relevant findings reported in the scientific literature. We present a framework in which reproducible research can be conducted and distributed via …

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Numerical Simulation Of Waves And Fronts In Inhomogeneous Solids, A. Berezovski, M. Berezovski, J. Engelbrecht, G. A. Maugin Jun 2007

Numerical Simulation Of Waves And Fronts In Inhomogeneous Solids, A. Berezovski, M. Berezovski, J. Engelbrecht, G. A. Maugin

Publications

Dynamic response of inhomogeneous materials exhibits new effects, which often do not exist in homogeneous media. It is quite natural that most of studies of wave and front propagation in inhomogeneous materials are associated with numerical simulations. To develop a numerical algorithm and to perform the numerical simulations of moving fronts we need to formulate a kinetic law of progress relating the driving force and the velocity of the discontinuity. The velocity of discontinuity is determined by means of the non-equilibrium jump relations at the front. The obtained numerical method generalizes the wave-propagation algorithm to the case of moving discontinuities …

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Parameter Estimation In Nonlinear Coupled Advection-Diffusion Equation, Robert R. Ferdinand Jun 2007

Parameter Estimation In Nonlinear Coupled Advection-Diffusion Equation, Robert R. Ferdinand

Applications and Applied Mathematics: An International Journal (AAM)

In this paper a coupled system of two nonlinear advection-diffusion equations is presented. Such systems of equations have been used in mathematical literature to describe the dynamics of contaminant present in groundwater flowing through cracks in a porous rock matrix and getting absorbed into it. An inverse method procedure that approximates infinite-dimensional model parameters is described and convergence results for the parameter approximants are proved. This is finally followed by a computational experiment to compare theoretical and numerical results to verify accuracy of the mathematics analysis presented.

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Intelligence Through Interaction: Towards A Unified Theory For Learning, Ah-Hwee Tan, Gail A. Carpenter, Stephen Grossberg Jun 2007

Intelligence Through Interaction: Towards A Unified Theory For Learning, Ah-Hwee Tan, Gail A. Carpenter, Stephen Grossberg

Research Collection School Of Computing and Information Systems

Machine learning, a cornerstone of intelligent systems, has typically been studied in the context of specific tasks, including clustering (unsupervised learning), classification (supervised learning), and control (reinforcement learning). This paper presents a learning architecture within which a universal adaptation mechanism unifies a rich set of traditionally distinct learning paradigms, including learning by matching, learning by association, learning by instruction, and learning by reinforcement. In accordance with the notion of embodied intelligence, such a learning theory provides a computational account of how an autonomous agent may acquire the knowledge of its environment in a real-time, incremental, and continuous manner. Through a …

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Utilizing Thermal Testing For Recovering, James Preciado, Thomas Werne May 2007

Utilizing Thermal Testing For Recovering, James Preciado, Thomas Werne

Mathematical Sciences Technical Reports (MSTR)

Given a two-dimensional region that contains one or more circular voids, we develop mathematical methods to locate the center and radius of the voids based on thermal boundary data. These methods can be readily applied in the field of non-destructive evaluation.

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Some Results Of Backward Itô Formula, Guiseppe Da Prato, Jose-Luis Menaldi, Luciano Tubaro May 2007

Some Results Of Backward Itô Formula, Guiseppe Da Prato, Jose-Luis Menaldi, Luciano Tubaro

Mathematics Faculty Research Publications

We use the notion of backward integration, with respect to a general Lévy process, to treat, in a simpler and unifying way, various classical topics as: Girsanov theorem, rst order partial differential equations, the Liouville (or Lyapunov) equations and the stochastic characteristic method.

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A Reproducible Research Toolkit For R, Roger Peng May 2007

A Reproducible Research Toolkit For R, Roger Peng

Johns Hopkins University, Dept. of Biostatistics Working Papers

We present a collection of R packages for conducting and distributing reproducible research using R, Sweave, and LaTeX. The collection consists of the cacheSweave, stashR, and SRPM packages which allow for the caching of computations in Sweave documents and the distribution of those cached computations via remotely accessible key-value databases. We describe the caching mechanism used by the cacheSweave package and tools that we have developed for authors and readers for the purposes of creating and interacting with reproducible documents.

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Mathematical Methods In Composing Melodies, Thomas Brown Apr 2007

Mathematical Methods In Composing Melodies, Thomas Brown

Undergraduate Theses and Capstone Projects

This thesis, “Mathematical Methods in Composing Melodies,” explores the different ways in which mathematics can be used to create music. Some research has been done in this field already. Richard F. Voss and John Clarke used fractals and different frequencies of noise to create music. The Greek composer Iannis Xenakis used Markovian Stochastic trees to create some of his compositions. Explored in this thesis are seven different methods to compose melodies. After compiling the different melodies, they were categorized by different musical periods based on the musical characteristics found in the melody. This thesis differs from other research that deals …

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Surrogate Strategies For Computationally Expensive Optimization Problems With Cpu-Time Correlated Functions, Raymond Magallanez Jr. Mar 2007

Surrogate Strategies For Computationally Expensive Optimization Problems With Cpu-Time Correlated Functions, Raymond Magallanez Jr.

Theses and Dissertations

This research focuses on numerically solving a class of computationally expensive optimization problems that possesses a unique characteristic: as the optimal solution is approached, the computational time required to compute an objective function value decreases. This is motivated by an application in which each objective function evaluation requires both a numerical fluid dynamics simulation and an image registration and comparison process. The goal is to find the parameters of a predetermined image by comparing the flow dynamics from the numerical simulation and the predetermined image through the image comparison process. The generalized pattern search and mesh adaptive direct search methods …

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Approximations Of Continuous Newton's Method: An Extension Of Cayley's Problem, Jon T. Jacobsen, Owen Lewis '05, Bradley Tennis '06 Feb 2007

Approximations Of Continuous Newton's Method: An Extension Of Cayley's Problem, Jon T. Jacobsen, Owen Lewis '05, Bradley Tennis '06

All HMC Faculty Publications and Research

Continuous Newton's Method refers to a certain dynamical system whose associated flow generically tends to the roots of a given polynomial. An Euler approximation of this system, with step size h=1, yields the discrete Newton's method algorithm for finding roots. In this note we contrast Euler approximations with several different approximations of the continuous ODE system and, using computer experiments, consider their impact on the associated fractal basin boundaries of the roots

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A Distributed Parabolic Control With Mixed Boundary Conditions, Jose-Luis Menaldi, Domingo Alberto Tarzia Jan 2007

A Distributed Parabolic Control With Mixed Boundary Conditions, Jose-Luis Menaldi, Domingo Alberto Tarzia

Mathematics Faculty Research Publications

We study the asymptotic behavior of an optimal distributed control problem where the state is given by the heat equation with mixed boundary conditions. The parameter α intervenes in the Robin boundary condition and it represents the heat transfer coefficient on a portion Γ1 of the boundary of a given regular n-dimensional domain. For each α, the distributed parabolic control problem optimizes the internal energy g. It is proven that the optimal control ĝα with optimal state uĝαα and optimal adjoint state pĝαα are convergent as α → 1 …

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Diffusion And Fractional Diffusion Based Models For Multiple Light Scattering And Image Analysis, Jonathan Blackledge Jan 2007

Diffusion And Fractional Diffusion Based Models For Multiple Light Scattering And Image Analysis, Jonathan Blackledge

Articles

This paper considers a fractional light diffusion model as an approach to characterizing the case when intermediate scattering processes are present, i.e. the scattering regime is neither strong nor weak. In order to introduce the basis for this approach, we revisit the elements of formal scattering theory and the classical diffusion problem in terms of solutions to the inhomogeneous wave and diffusion equations respectively. We then address the significance of these equations in terms of a random walk model for multiple scattering. This leads to the proposition of a fractional diffusion equation for modelling intermediate strength scattering that is based …

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Multiphoton Response Of Retinal Rod Photoreceptors, Vasilios Alexiades, Harihar Khanal Jan 2007

Multiphoton Response Of Retinal Rod Photoreceptors, Vasilios Alexiades, Harihar Khanal

Publications

Phototransduction is the process by which light is converted into an electrical response in retinal photoreceptors. Rod photoreceptors contain a stack of (about 1000) disc membranes packed with photopigment rhodopsin molecules, which absorb the photons. We present computational experiments which show the profound effect on the response of the distances (how many discs apart) photons happen to be absorbed at. This photon-distribution effect alone can account for much of the observed variability in response.

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Interacting With Local And Remote Data Respositories Using The Stashr Package, Sandrah P. Eckel, Roger Peng Dec 2006

Interacting With Local And Remote Data Respositories Using The Stashr Package, Sandrah P. Eckel, Roger Peng

Johns Hopkins University, Dept. of Biostatistics Working Papers

The stashR package (a Set of Tools for Administering SHared Repositories) for R implements a simple key-value style database where character string keys are associated with data values. The key-value databases can be either stored locally on the user's computer or accessed remotely via the Internet. Methods specific to the stashR package allow users to share data repositories or access previously created remote data repositories. In particular, methods are available for the S4 classes localDB and remoteDB to insert, retrieve, or delete data from the database as well as to synchronize local copies of the data to the remote version …

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A Partially Discretized Age-Dependent Population Model With An Additional Stucture, Jean Tchuenche Dec 2006

A Partially Discretized Age-Dependent Population Model With An Additional Stucture, Jean Tchuenche

Applications and Applied Mathematics: An International Journal (AAM)

A semi-discretization method for solving an age-dependent population dynamics model with an additional structure is proposed. This method, unlike previous ones, considers the partial discretization which reduces the model equation into a first order ordinary differential equation. The latter is then solved explicitly and conditions under which second order accuracy arises are given. While the approach adopted is basically analytical, the main result shows that the sum of errors is bounded. An extension to the non-trivial case where growth depends on the additional parameter leads to a Riccati equation, and the existence and
convergence of solutions are proved.

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Epi-Convergent Discretization Of The Generalizaed Bolza Problem In Dynamic Optimization, Boris S. Mordukhovich, Teemu Pennanen Dec 2006

Epi-Convergent Discretization Of The Generalizaed Bolza Problem In Dynamic Optimization, Boris S. Mordukhovich, Teemu Pennanen

Mathematics Research Reports

The paper is devoted to well-posed discrete approximations of the so-called generalized Bolza problem of minimizing variational functionals defined via extended-real-valued functions. This problem covers more conventional Bolza-type problems in the calculus of variations and optimal control of differential inclusions as well of parameterized differential equations. Our main goal is find efficient conditions ensuring an appropriate epi-convergence of discrete approximations, which plays a significant role in both the qualitative theory and numerical algorithms of optimization and optimal control. The paper seems to be the first attempt to study epi-convergent discretizations of the generalized Bolza problem; it establishes several rather general …

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Spatio-Temporal Analysis Of Areal Data And Discovery Of Neighborhood Relationships In Conditionally Autoregressive Models, Subharup Guha, Louise Ryan Nov 2006

Spatio-Temporal Analysis Of Areal Data And Discovery Of Neighborhood Relationships In Conditionally Autoregressive Models, Subharup Guha, Louise Ryan

Harvard University Biostatistics Working Paper Series

No abstract provided.

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Bayesian Smoothing Of Irregularly-Spaced Data Using Fourier Basis Functions, Christopher J. Paciorek Aug 2006

Bayesian Smoothing Of Irregularly-Spaced Data Using Fourier Basis Functions, Christopher J. Paciorek

Harvard University Biostatistics Working Paper Series

No abstract provided.

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Can We Have Superconvergent Gradient Recovery Under Adaptive Meshes?, Haijun Wu, Zhimin Zhang Aug 2006

Can We Have Superconvergent Gradient Recovery Under Adaptive Meshes?, Haijun Wu, Zhimin Zhang

Mathematics Research Reports

We study adaptive finite element methods for elliptic problems with domain corner singularities. Our model problem is the two dimensional Poisson equation. Results of this paper are two folds. First, we prove that there exists an adaptive mesh (gauged by a discrete mesh density function) under which the recovered.gradient by the Polynomial Preserving Recovery (PPR) is superconvergent. Secondly, we demonstrate by numerical examples that an adaptive procedure with a posteriori error estimator based on PPR does produce adaptive meshes satisfy our mesh density assumption, and the recovered gradient by PPR is indeed supercoveregent in the adaptive process.

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Thermal Imaging To Recover A Defect In Three Dimensional Objects, Breanne Baker Jul 2006

Thermal Imaging To Recover A Defect In Three Dimensional Objects, Breanne Baker

Mathematical Sciences Technical Reports (MSTR)

This paper focuses on the inverse problem of identifying an internal void in a bounded two- or three-dimensional region. Information, in form of a heat flux and temperature, is assumed to be obtainable only on the external boundary of the region. The reciprocity gap approach with a suitable test functions is used in both the two- and three-dimensional cases.

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Non-Destructive Recovery Of Voids Within A Three Dimensional Domain Using Thermal Imaging, Victor B. Oyeyemi Jul 2006

Non-Destructive Recovery Of Voids Within A Three Dimensional Domain Using Thermal Imaging, Victor B. Oyeyemi

Mathematical Sciences Technical Reports (MSTR)

We develop an algorithm capable of detecting the presence of spherical voids in a thermally conducting object. In addition, the process recovers both the radii and locations of each void. Our method involves the application of a known steady state heat flux to the object's boundary and measurement of the induced steady state temperature on the boundary.

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Socio-Economic Impacts Of Computer Viruses In Tanzania, M Victor Jun 2006

Socio-Economic Impacts Of Computer Viruses In Tanzania, M Victor

Tanzania Journal of Engineering and Technology (TJET)

This paper reports on a research project conducted with an objective of identifying and assessing various approaches used by different computer users (Management, System Administrators and end users) in Tanzania to combat computer viruses (CVs), and to assess users' awareness level on CVs. Specifically, the study aimed at assessing the awareness level on CVs to the Tanzanian business community; analyze the socio -economic impact caused by CVs in Tanzania and; assess existing methods, capacity and limitations on controlling CVs in Tanzania. Data was collected using both questionnaires and interview from financial institutions such as NBC and BOT, and telecommunications sector …

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Interacting With Data Using The Filehash Package For R, Roger Peng Jun 2006

Interacting With Data Using The Filehash Package For R, Roger Peng

Johns Hopkins University, Dept. of Biostatistics Working Papers

The filehash package for R implements a simple key-value style database where character string keys are associated with data values that are stored on the disk. A simple interface is provided for inserting, retrieving, and deleting data from the database. Utilities are provided that allow filehash databases to be treated much like environments and lists are already used in R. These utilities are provided to encourage interactive and exploratory analysis on large datasets. Three different file formats for representing the database are currently available and new formats can easily be incorporated by third parties for use in the filehash framework.

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Posterior Simulation In The Generalized Linear Model With Semiparmetric Random Effects, Subharup Guha May 2006

Posterior Simulation In The Generalized Linear Model With Semiparmetric Random Effects, Subharup Guha

Harvard University Biostatistics Working Paper Series

Generalized linear mixed models with semiparametric random effects are useful in a wide variety of Bayesian applications. When the random effects arise from a mixture of Dirichlet process (MDP) model, normal base measures and Gibbs sampling procedures based on the Pólya urn scheme are often used to simulate posterior draws. These algorithms are applicable in the conjugate case when (for a normal base measure) the likelihood is normal. In the non-conjugate case, the algorithms proposed by MacEachern and Müller (1998) and Neal (2000) are often applied to generate posterior samples. Some common problems associated with simulation algorithms for non-conjugate MDP …

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Numerical Simulation Of Nonlinear Elastic Wave Propagation In Piecewise Homogeneous Media, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht Jan 2006

Numerical Simulation Of Nonlinear Elastic Wave Propagation In Piecewise Homogeneous Media, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht

Publications

Systematic experimental work [S. Zhuang, G. Ravichandran, D. Grady, J. Mech. Phys. Solids 51 (2003) 245–265] on laminated composites subjected to high velocity impact loading exhibits the dispersed wave field and the oscillatory behavior of waves with respect to a mean value. Such a behavior is absent in homogeneous solids. An approximate solution to the plate impact in layered heterogeneous solids has been developed in [X. Chen, N. Chandra, A.M. Rajendran, Int. J. Solids Struct. 41 (2004) 4635–4659]. The influence of the particle velocity on many process characteristics was demonstrated. Based on earlier results [A. Berezovski, J. Engelbrecht, G.A. Maugin, …

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Parallel Algorithms For Multicriteria Shortest Path Problems, David L. Sonnier Jan 2006

Parallel Algorithms For Multicriteria Shortest Path Problems, David L. Sonnier

Journal of the Arkansas Academy of Science

This paper presents two strategies for solving multicriteria shortest path problems with more than two criteria. Given an undirected graph within vertices, medges, and a set of K weights associated with each edge, we define a path as a sequence of edges from vertex s to vertex t. We want to find the Pareto-optimal set of paths from s to t. The solutions proposed herein are based on cluster computing using the Message-Passing Interface (MPI) extensions to the C programming language. We solve problems with 3 and 4 criteria, using up to 8 processors in parallel and using solutions based …

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