Information Theoretic Study Of Gaussian Graphical Models And Their Applications, 2017 Louisiana State University and Agricultural and Mechanical College

#### Information Theoretic Study Of Gaussian Graphical Models And Their Applications, Ali Moharrer

*LSU Doctoral Dissertations*

In many problems we are dealing with characterizing a behavior of a complex stochastic system or its response to a set of particular inputs. Such problems span over several topics such as machine learning, complex networks, e.g., social or communication networks; biology, etc. Probabilistic graphical models (PGMs) are powerful tools that offer a compact modeling of complex systems. They are designed to capture the random behavior, i.e., the joint distribution of the system to the best possible accuracy. Our goal is to study certain algebraic and topological properties of a special class of graphical models, known as Gaussian ...

On The Ramberg-Osgood Stress-Strain Model And Large Deformations Of Cantilever Beams, 2017 University of New Orleans

#### On The Ramberg-Osgood Stress-Strain Model And Large Deformations Of Cantilever Beams, Ronald J. Giardina Jr

*University of New Orleans Theses and Dissertations*

In this thesis the Ramberg-Osgood nonlinear model for describing the behavior of many diﬀerent materials is investigated. A brief overview of the model as it is currently used in the literature is undertaken and several misunderstandings and possible pitfalls in its application is pointed out, especially as it pertains to more recent approaches to ﬁnding solutions involving the model. There is an investigation of the displacement of a cantilever beam under a combined loading consisting of a distributed load across the entire length of the beam and a point load at its end and new solutions to this problem are ...

Euler-Richardson Method Preconditioned By Weakly Stochastic Matrix Algebras: A Potential Contribution To Pagerank Computation, 2017 University of Rome Tor Vergata

#### Euler-Richardson Method Preconditioned By Weakly Stochastic Matrix Algebras: A Potential Contribution To Pagerank Computation, Stefano Cipolla, Carmine Di Fiore, Francesco Tudisco

*Electronic Journal of Linear Algebra*

Let S be a column stochastic matrix with at least one full row. Then S describes a Pagerank-like random walk since the computation of the Perron vector x of S can be tackled by solving a suitable M-matrix linear system Mx = y, where M = I − τ A, A is a column stochastic matrix and τ is a positive coefficient smaller than one. The Pagerank centrality index on graphs is a relevant example where these two formulations appear. Previous investigations have shown that the Euler- Richardson (ER) method can be considered in order to approach the Pagerank computation problem by means ...

Efficient Methods For Multidimensional Global Polynomial Approximation With Applications To Random Pdes, 2017 University of Tennessee, Knoxville

#### Efficient Methods For Multidimensional Global Polynomial Approximation With Applications To Random Pdes, Peter A. Jantsch

*Doctoral Dissertations*

In this work, we consider several ways to overcome the challenges associated with polynomial approximation and integration of smooth functions depending on a large number of inputs. We are motivated by the problem of forward uncertainty quantification (UQ), whereby inputs to mathematical models are considered as random variables. With limited resources, finding more efficient and accurate ways to approximate the multidimensional solution to the UQ problem is of crucial importance, due to the “curse of dimensionality” and the cost of solving the underlying deterministic problem.

The first way we overcome the complexity issue is by exploiting the structure of the ...

Numerical Methods For Non-Divergence Form Second Order Linear Elliptic Partial Differential Equations And Discontinuous Ritz Methods For Problems From The Calculus Of Variations, 2017 University of Tennessee, Knoxville

#### Numerical Methods For Non-Divergence Form Second Order Linear Elliptic Partial Differential Equations And Discontinuous Ritz Methods For Problems From The Calculus Of Variations, Stefan Raymond Schnake

*Doctoral Dissertations*

This dissertation consists of three integral parts. Part one studies discontinuous Galerkin approximations of a class of non-divergence form second order linear elliptic PDEs whose coefficients are only continuous. An interior penalty discontinuous Galerkin (IP-DG) method is developed for this class of PDEs. A complete analysis of the proposed IP-DG method is carried out, which includes proving the stability and error estimate in a discrete W^{2;p}-norm [W^2,p-norm]. Part one also studies the convergence of the vanishing moment method for this class of PDEs. The vanishing moment method refers to a PDE technique for approximating these ...

Some Problems Arising From Mathematical Model Of Ductal Carcinoma In Situ., 2017 University of Louisville

#### Some Problems Arising From Mathematical Model Of Ductal Carcinoma In Situ., Heng Li

*Electronic Theses and Dissertations*

Ductal carcinoma in situ (DCIS) is the earliest form of breast cancer. Three mathematical models in the one dimensional case arising from DCIS are proposed. The first two models are in the form of parabolic equation with initial and known moving boundaries. Direct and inverse problems are considered in model 1, existence and uniqueness are proved by using tool from heat potential theory and Volterra integral equations. Also, we discuss the direct problem and nonlocal problem of model 2, existence and uniqueness are proved. And approximation solution of these problems are implemented by Ritz-Galerkin method, which is the first attempt ...

Joint Inversion Of Compact Operators, 2017 Boise State University

#### Joint Inversion Of Compact Operators, James Ford

*Boise State University Theses and Dissertations*

The first mention of joint inversion came in [22], where the authors used the singular value decomposition to determine the degree of ill-conditioning in inverse problems. The authors demonstrated in several examples that combining two models in a joint inversion, and effectively stacking discrete linear models, improved the conditioning of the problem. This thesis extends the notion of using the singular value decomposition to determine the conditioning of discrete joint inversion to using the singular value expansion to determine the well-posedness of joint linear operators. We focus on compact linear operators related to geophysical, electromagnetic subsurface imaging.

The operators are ...

Eignefunctions For Partial Differential Equations On Two-Dimensional Domains With Piecewise Constant Coefficients, 2017 University of Southern Mississippi

#### Eignefunctions For Partial Differential Equations On Two-Dimensional Domains With Piecewise Constant Coefficients, Abdullah M. Aurko

*Master's Theses*

In this thesis, we develop a highly accurate and efficient algorithm for computing the solution of a partial differential equation defined on a two-dimensional domain with discontinuous coefficients. An example of such a problem is for modeling the diffusion of heat energy in two space dimensions, in the case where the spatial domain represents a medium consisting of two different but homogeneous materials, with periodic boundary conditions.

Since diffusivity changes based on the material, it will be represented using a piecewise constant function, and this results in the formation of a complicated mathematical model. Such a model is impossible to ...

Numerical Solution Of Partial Differential Equations Using Polynomial Particular Solutions, 2017 University of Southern Mississippi

#### Numerical Solution Of Partial Differential Equations Using Polynomial Particular Solutions, Thir R. Dangal

*Dissertations*

Polynomial particular solutions have been obtained for certain types of partial differential operators without convection terms. In this dissertation, a closed-form particular solution for more general partial differential operators with constant coefficients has been derived for polynomial basis functions. The newly derived particular solutions are further coupled with the method of particular solutions (MPS) for numerically solving a large class of elliptic partial differential equations. In contrast to the use of Chebyshev polynomial basis functions, the proposed approach is more flexible in selecting the collocation points inside the domain. Polynomial basis functions are well-known for yielding ill-conditioned systems when their ...

An Investigation Of The Accuracy Of Parallel Analysis For Determining The Number Of Factors In A Factor Analysis, 2017 Western Kentucky University

#### An Investigation Of The Accuracy Of Parallel Analysis For Determining The Number Of Factors In A Factor Analysis, Mandy Matsumoto

*Honors College Capstone Experience/Thesis Projects*

Exploratory factor analysis is an analytic technique used to determine the number of factors in a set of data (usually items on a questionnaire) for which the factor structure has not been previously analyzed. Parallel analysis (PA) is a technique used to determine the number of factors in a factor analysis. There are a number of factors that affect the results of a PA: the choice of the eigenvalue percentile, the strength of the factor loadings, the number of variables, and the sample size of the study. Although PA is the most accurate method to date to determine which factors ...

Qualitative Observations Of Dense Particle Motion In A Vibration-Excited Granular Bed, 2017 Iowa State University

#### Qualitative Observations Of Dense Particle Motion In A Vibration-Excited Granular Bed, Timothy B. Morgan, Theodore J. Heindel

*Theodore J. Heindel*

The Brazil nut effect is a classic phenomenon in which larger objects typically migrate to the top of a bed of smaller granular media when exposed to vibration. An example of this phenomenon is finding Brazil nuts on the top of a can of mixed nuts. In this study, the Brazil nut problem is simulated by submerging a large particle in a bed of granular media and then subjecting the system to vibration. Stereoscopic X-ray imaging is used to visualize the large particle motion. These images are then compiled into movies where the particle motion may be tracked. Observations of ...

Shrinkage Function And Its Applications In Matrix Approximation, 2017 University of Florida, Gainesville

#### Shrinkage Function And Its Applications In Matrix Approximation, Toby Boas, Aritra Dutta, Xin Li, Katie Mercier, Eric Niderman

*Electronic Journal of Linear Algebra*

The shrinkage function is widely used in matrix low-rank approximation, compressive sensing, and statistical estimation. In this article, an elementary derivation of the shrinkage function is given. In addition, applications of the shrinkage function are demonstrated in solving several well-known problems, together with a new result in matrix approximation.

Full Wave Modeling Of Ultrasonic Scattering Using Nystrom Method For Nde Applications, 2017 Iowa State University

#### Full Wave Modeling Of Ultrasonic Scattering Using Nystrom Method For Nde Applications, Praveen Gurrala, Kun Chen, Jiming Song, Ron Roberts

*Jiming Song*

Approximate methods for ultrasonic scattering like the Kirchhoff approximation and the geometrical theory of diffraction (GTD) can deliver fast solutions with relatively small computational resources compared to accurate numerical methods. However, these models are prone to inaccuracies in predicting scattered fields from defects that are not very large compared to wavelength. Furthermore, they do not take into account physical phenomena like multiple scattering and surface wave generation on defects. Numerical methods like the finite element method (FEM) and the boundary element method (BEM) can overcome these limitations of approximate models. Commercial softwares such as Abaqus FEA and PZFlex use FEM ...

Fast Algorithms On Random Matrices And Structured Matrices, 2017 The City University of New York

#### Fast Algorithms On Random Matrices And Structured Matrices, Liang Zhao

*All Dissertations, Theses, and Capstone Projects*

Randomization of matrix computations has become a hot research area in the big data era. Sampling with randomly generated matrices has enabled fast algorithms to perform well for some most fundamental problems of numerical algebra with probability close to 1. The dissertation develops a set of algorithms with random and structured matrices for the following applications: 1) We prove that using random sparse and structured sampling enables rank-r approximation of the average input matrix having numerical rank r. 2) We prove that Gaussian elimination with no pivoting (GENP) is numerically safe for the average nonsingular and well-conditioned matrix preprocessed with ...

Large-Scale Online Feature Selection For Ultra-High Dimensional Sparse Data, 2017 Singapore Management University

#### Large-Scale Online Feature Selection For Ultra-High Dimensional Sparse Data, Yue Wu, Steven C. H. Hoi, Tao Mei, Nenghai Yu

*Research Collection School Of Information Systems*

Feature selection (FS) is an important technique in machine learning and data mining, especially for largescale high-dimensional data. Most existing studies have been restricted to batch learning, which is often inefficient and poorly scalable when handling big data in real world. As real data may arrive sequentially and continuously, batch learning has to retrain the model for the new coming data, which is very computationally intensive. Online feature selection (OFS) is a promising new paradigm that is more efficient and scalable than batch learning algorithms. However, existing online algorithms usually fall short in their inferior efficacy. In this article, we ...

Revisiting Assert Use In Github Projects, 2017 Singapore Management University

#### Revisiting Assert Use In Github Projects, Pavneet Singh Kochhar, David Lo

*Research Collection School Of Information Systems*

Assertions are often used to test the assumptions that developers have about a program. An assertion contains a boolean expression which developers believe to be true at a particular program point. It throws an error if the expression is not satisfied, which helps developers to detect and correct bugs. Since assertions make developer assumptions explicit, assertions are also believed to improve under-standability of code. Recently, Casalnuovo et al. analyse C and C++ programs to understand the relationship between assertion usage and defect occurrence. Their results show that asserts have a small effect on reducing the density of bugs and developers ...

High Performance Computation Of Cardiac Models In Real-Time Using Webgl, 2017 Georgia Institute of Technology

#### High Performance Computation Of Cardiac Models In Real-Time Using Webgl, Abouzar Kaboudian, Flavio H. Fenton

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

A Large Reaction-Diffusion Model For Cell Polarization In Yeast, 2017 The Ohio State University

#### A Large Reaction-Diffusion Model For Cell Polarization In Yeast, Marissa Renardy

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Evolution Of Influenza H3n2: A Random Walk In High Dimensions, 2017 Emory University

#### Evolution Of Influenza H3n2: A Random Walk In High Dimensions, James R. Moore

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Building And Validating A Model For Investigating The Dynamics Of Isolated Water Molecules, 2017 Linfield College

#### Building And Validating A Model For Investigating The Dynamics Of Isolated Water Molecules, Grant Cates

*Senior Theses*

Understanding how water molecules behave in isolation is vital to understand many fundamental processes in nature. To that end, scientists have begun studying crystals in which single water molecules become trapped in regularly occurring cavities in the crystal structure. As part of that investigation, numerical models used to investigate the dynamics of isolated water molecules are sought to help bolster our fundamental understanding of how these systems behave. To that end, the efficacy of three computational methods—the Euler Method, the Euler-Aspel Method and the Beeman Method—is compared using a newly defined parameter, called the *predictive stability coefficient ρ ...*