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Dimension Reduction Techniques For High Dimensional And Ultra-High Dimensional Data, Subha Datta

Dissertations

This dissertation introduces two statistical techniques to tackle high-dimensional data, which is very commonplace nowadays. It consists of two topics which are inter-related by a common link, dimension reduction.

The first topic is a recently introduced classification technique, the weighted principal support vector machine (WPSVM), which is incorporated into a spatial point process framework. The WPSVM possesses an additional parameter, a weight parameter, besides the regularization parameter. Most statistical techniques, including WPSVM, have an inherent assumption of independence, which means the data points are not connected with each other in any manner. But spatial data violates this assumption. Correlation between …

Topics On High Dimensional Selective Inference, Yan Zhang

Dissertations

In such applications as identifying differentially expressed genes in micro-array experiments or assessing safety and efficacy of drugs in clinical trials, researchers often report confidence intervals (CIs) and p-values only for the selected parameters, which is called selective inference. While constructing multiple CIs for the selected parameters, it is common practice to ignore issue of selection and multiplicity. Although protection against the effect of selection is sufficient in some cases, simultaneous coverage should be also needed in real applications. For example, in clinical trials, multiple endpoints are considered to assess effects of a drug and the ultimate decision often depends …

Model Selection And Experimental Design Of Biological Networks With Algebraic Geometry, Anyu Zhang

Mathematics Theses and Dissertations

Model selection based on experimental data is an essential challenge in biological data science. In decades, the volume of biological data from varied sources, including laboratory experiments, field observations, and patient health records has seen an unprecedented increase. Mainly when collecting data is expensive or time-consuming, as it is often in the case with clinical trials and biomolecular experiments, the problem of selecting information-rich data becomes crucial for creating relevant models.

Motivated by certain geometric relationships between data, we partitioned input data sets, especially data sets that correspond to a unique basis, into equivalence classes with the same basis to …

Near-To-Far Field Signal Propagation For The Wave And Maxwell Equations, Alhassan Ahmed

Mathematics & Statistics ETDs

The Maxwell equations may be viewed as evolution equations which develop an initial state of the electromagnetic field forward in time. Such evolution can be simulated numerically, that is modeled on a computer, in which case the domain of simulation is typically finite in extent. Nonetheless, one is often interested in the electromagnetic waves which reach infinity (of course which is outside of the simulation domain). Thus we are interested in near-to-far field signal propagation, that is a mathematical process where a signal or solution recorded at a finite radius r = r1 can be converted to a signal at …

Algorithms For Mappings And Symmetries Of Differential Equations, Zahra Mohammadi

Electronic Thesis and Dissertation Repository

Differential Equations are used to mathematically express the laws of physics and models in biology, finance, and many other fields. Examining the solutions of related differential equation systems helps to gain insights into the phenomena described by the differential equations. However, finding exact solutions of differential equations can be extremely difficult and is often impossible. A common approach to addressing this problem is to analyze solutions of differential equations by using their symmetries. In this thesis, we develop algorithms based on analyzing infinitesimal symmetry features of differential equations to determine the existence of invertible mappings of less tractable systems of …

On Improving Performance Of The Binary Logistic Regression Classifier, Michael Chang

UNLV Theses, Dissertations, Professional Papers, and Capstones

Logistic Regression, being both a predictive and an explanatory method, is one of the most commonly used statistical and machine learning method in almost all disciplines. There are many situations, however, when the accuracies of the fitted model are low for predicting either the success event or the failure event. Several statistical and machine learning approaches exist in the literature to handle these situations. This thesis presents several new approaches to improve the performance of the fitted model, and the proposed methods have been applied to real datasets.

Transformations of predictors is a common approach in fitting multiple linear and …

A Pedagogic Analysis Of Linear Algebra Courses, Andrew Taylor

Mathematics & Statistics ETDs

This project is concerned with investigating the question, "Do our applied linear algebra courses (at the University of New Mexico) adequately prepare STEM students for future work in their respective fields?" In order to explore this, surveys were issued to three groups (sections) of students (among two different instructors) at the conclusion of their applied linear algebra course, as well as STEM professors/instructors from a variety of STEM fields. Students were surveyed regarding their perceived mastery of given topics/ideas from the course and professors/instructors were surveyed about the level of mastery they felt was necessary (referred to as ``desired mastery") …

High Strain Dynamic Test On Helical Piles: Analytical And Numerical Investigations, Mohammed Fahad Alwalan

Electronic Thesis and Dissertation Repository

Helical piles are currently considered a preferred foundation option in a wide range of engineering projects to provide high compressive and uplift resistance to static and dynamic loads. In view of the large capacity of large diameter helical piles, there is a need to determine their capacity using accurate and economically feasible testing techniques. The capacity of piles is usually determined by conducting a Static Load Test (SLT). However, the SLT can be costly and time consuming, especially for large capacity piles. The High Strain Dynamic Load Test (HSDT) evaluates the pile capacity using dynamic measurements generated through subjecting the …

Image Restoration Using Automatic Damaged Regions Detection And Machine Learning-Based Inpainting Technique, Chloe Martin-King

Computational and Data Sciences (PhD) Dissertations

In this dissertation we propose two novel image restoration schemes. The first pertains to automatic detection of damaged regions in old photographs and digital images of cracked paintings. In cases when inpainting mask generation cannot be completely automatic, our detection algorithm facilitates precise mask creation, particularly useful for images containing damage that is tedious to annotate or difficult to geometrically define. The main contribution of this dissertation is the development and utilization of a new inpainting technique, region hiding, to repair a single image by training a convolutional neural network on various transformations of that image. Region hiding is also …

Multi-Point Flux Approximations Via The O-Method, Christen Leggett

Master's Theses

When an oil refining company is drilling for oil, much of the oil gets left behind after the first drilling. Enhanced oil recovery techniques can be used to recover more of that oil, but these methods are quite expensive. When a company is deciding if it is worth their time and money to use enhanced oil recovery methods, simulations can be used to model oil flow, showing the behavior and location of the oil. While methods do exist to model this flow, these methods are often very slow and inaccurate due to a large domain and wide variance in coefficients. …

Function Space Tensor Decomposition And Its Application In Sports Analytics, Justin Reising

Electronic Theses and Dissertations

Recent advancements in sports information and technology systems have ushered in a new age of applications of both supervised and unsupervised analytical techniques in the sports domain. These automated systems capture large volumes of data points about competitors during live competition. As a result, multi-relational analyses are gaining popularity in the field of Sports Analytics. We review two case studies of dimensionality reduction with Principal Component Analysis and latent factor analysis with Non-Negative Matrix Factorization applied in sports. Also, we provide a review of a framework for extending these techniques for higher order data structures. The primary scope of this …

Stability Analysis Of Neutral Functional Differential Equations Arising In Partial Element Equivalent Circuit Models, Howard Michael Allison

Theses and Dissertations

Neutral Functional Differential Equations (NFDEs) arise in the study of the Partial Element Equivalent Circuit (PEEC) model with time delays. We present sufficient conditions for asymptotic stability and global stability in the delays of the PEEC NFDE’s, using Lyapunov-Razumikhin function methods.. We develop, for the first time, a standard mixing-type nonlinearity for the PEEC NFDEs. Introducing time invariant and time varying nonlinear perturbation to the PEEC NFDEs, we develop sufficient conditions for stability of the nonlinear perturbed PEEC NFDEs and convergence of the nonlinear system to the original stable linear autonomous system. We also develop sufficient conditions for stability and …

Some Free Boundary Problems For The Nonlinear Degenerate Multidimensional Parabolic Equations Modeling Reaction-Diffusion Processes, Amna Abu Weden

Theses and Dissertations

This dissertation presents a full classification of the short-time behavior of the interfaces or free boundaries for the nonlinear second order degenerate multidimensional parabolic partial differential equation (PDE) ut −∆u m +buβ = 0, x ∈ R N ,0 < t < T (1) with m > 0, β > 0,b ∈ R, arising in various applications in fluid mechanics, filtration of oil or gas in a porous media, plasma physics, reaction-diffusion equations in chemical kinetics, population dynamics in mathematical biology etc. as a mathematical model of nonlinear diffusion phenomena in the presence of the absorption or release of energy. Cauchy problem with compactly supported and nonnegative initial function …

Computational Models For Biological Locomotion In Gels, Hashim Mohammed Alshehri

Theses and Dissertations

We investigated Low Reynold’s Number Locomotion in two-phase biological gels. The gel is composed of two materials: a viscous fluid solvent phase and a viscoelastic polymer network phase. A novel Two-phase Immersed Boundary Method (IBM) is developed to simulate the complicated interactions between an elastic boundary and a mixture of two fluids with very different physical properties. A further extension of the method is developed for the case where fluids satisfy partial-slip and free-slip conditions on the elastic boundary. Our major conclusions are summarized as following: (i) Our numerical scheme is proved to be robust and efficient. It can successfully …

Analysis Of Interfaces For The Nonlinear Degenerate Second Order Parabolic Equations Modeling Diffusion-Convection Processes, Lamees Kadhim Ali Alzaki

Theses and Dissertations

Dissertation pursues analysis of the short-time evolution of interfaces or free boundaries for the non-negative solutions of the nonlinear degenerate second order parabolic partial differential equation (PDE) ut = ( u m ) xx +b ( u γ ) x , x ∈ R,t > 0; m > 1, γ > 0,b ∈ R (1) modeling diffusion-convection processes arising in fluid or gas flow in a porous media, plasma physics, population dynamics in mathematical biology and other applications. Due to the implicit degeneration (m > 1), PDE (1) it possesses a property of the finite speed of propagation and develops interfaces or free boundaries …

Nonlocal Boundary Value Problems For Linear Hyperbolic Systems With Two Independent Variables, Afrah Almutairi

Theses and Dissertations

Nonlocal boundary value problems in a characteristic rectangle for second order linear hyperbolic systems are considered. There are established: (i) Unimprovable sufficient conditions for general boundary value problems to possess the Fredholm property; (ii) Optimal sufficient conditions of unique solvability of general boundary value problems; (iii) Effective sufficient conditions for doubly periodic problems to possess the Fredholm property; (iv) Unimprovable sufficient conditions of unique solvability of doubly periodic problems; (v) Effective sufficient conditions for boundary value problems of periodic type to possess the Fredholm property; (vi) Unimprovable sufficient conditions of unique solvability of boundary value problems of periodic type; (vii) …

Recover Data In Sparse Expansion Forms Modeled By Special Basis Functions, Abdulmtalb Mohamed Hussen

Dissertations

In data analysis and signal processing, the recovery of structured functions (in terms of frequencies and coefficients) with respect to certain basis functions from the given sampling values is a fundamental problem. The original Prony method is the main tool to solve this problem, which requires the equispaced sampling values.

In this dissertation, we use the equispaced sampling values in the frequency domain after the short time Fourier transform in order to reconstruct some signal expansions, such as the exponential expansions and the cosine expansions. In particular, we consider the case that the phase of the cosine expansion is quadratic. …

Dynamical Modeling In Cell Biology With Ordinary Differential Equations, Renee Marie Dale

LSU Doctoral Dissertations

Dynamical systems have been of interest to biologists and mathematicians alike. Many processes in biology lend themselves to dynamical study. Movement, change, and response to stimuli are dynamical characteristics that define what is 'alive'. A scientific relationship between these two fields is therefore natural. In this thesis, I describe how my PhD research variously related to biological, mathematical, and computational problems in cell biology. In chapter 1 I introduce some of the current problems in the field. In chapter 2, my mathematical model of firefly luciferase in vivo shows the importance of dynamical models to understand systems. Data originally collected …

A Parallel Direct Method For Finite Element Electromagnetic Computations Based On Domain Decomposition, Javad Moshfegh

Doctoral Dissertations

High performance parallel computing and direct (factorization-based) solution methods have been the two main trends in electromagnetic computations in recent years. When time-harmonic (frequency-domain) Maxwell's equation are directly discretized with the Finite Element Method (FEM) or other Partial Differential Equation (PDE) methods, the resulting linear system of equations is sparse and indefinite, thus harder to efficiently factorize serially or in parallel than alternative methods e.g. integral equation solutions, that result in dense linear systems. State-of-the-art sparse matrix direct solvers such as MUMPS and PARDISO don't scale favorably, have low parallel efficiency and high memory footprint. This work introduces a new …

Optimal Relaxation Weights For Multigrid Reduction In Time (Mgrit), Masumi Sugiyama

Mathematics & Statistics ETDs

Based on current trends in computer architectures, faster compute speeds must come from increased parallelism rather than increased clock speeds, which are stagnate. This situation has created the well-known bottleneck for sequential time-integration, where each individual time-value (i.e., time-step) is computed sequentially. One approach to alleviate this and achieve parallelism in time is with multigrid. In this work, we consider the scheme known as multigrid-reduction-in-time (MGRIT), but note that there exist other parallel-in-time methods such as parareal and the parallel full approximation scheme in space and time (PFASST). MGRIT is a full multi-level method applied to the time dimension and …

On The Sparre-Andersen Risk Models, Ruixi Zhang

Electronic Thesis and Dissertation Repository

This thesis develops several strategies for calculating ruin-related quantities for a variety of extended risk models. We focus on the Sparre-Andersen risk model, also known as the renewal risk model. The idea of arbitrary distribution for the waiting time between claim payments arose in the 1950’s from the collective risk theory, and received many extensions and modifications in recent years. Our goal is to tackle model assumptions that are either too relaxed for traditional methods to apply, or so complicated that elaborate algebraic tools are needed to obtain explicit solutions.

In Chapter 2, we consider a Lévy risk process and …

Model-Form Uncertainty Quantification For Predictive Probabilistic Graphical Models, Jinchao Feng

Doctoral Dissertations

In this thesis, we focus on Uncertainty Quantification and Sensitivity Analysis, which can provide performance guarantees for predictive models built with both aleatoric and epistemic uncertainties, as well as data, and identify which components in a model have the most influence on predictions of our quantities of interest. In the first part (Chapter 2), we propose non-parametric methods for both local and global sensitivity analysis of chemical reaction models with correlated parameter dependencies. The developed mathematical and statistical tools are applied to a benchmark Langmuir competitive adsorption model on a close packed platinum surface, whose parameters, estimated from quantum-scale computations, …

Adaptive Feature Engineering Modeling For Ultrasound Image Classification For Decision Support, Hatwib Mugasa

Doctoral Dissertations

Ultrasonography is considered a relatively safe option for the diagnosis of benign and malignant cancer lesions due to the low-energy sound waves used. However, the visual interpretation of the ultrasound images is time-consuming and usually has high false alerts due to speckle noise. Improved methods of collection image-based data have been proposed to reduce noise in the images; however, this has proved not to solve the problem due to the complex nature of images and the exponential growth of biomedical datasets. Secondly, the target class in real-world biomedical datasets, that is the focus of interest of a biopsy, is usually …

Electrohydrodynamic Simulations Of The Deformation Of Liquid-Filled Capsules, Pai Song

Mathematics & Statistics Theses & Dissertations

A comprehensive two- and three-dimensional framework for the electrohydrodynamic simulation of deformable capsules is provided. The role of a direct current (DC) electric field on the deformation and orientation of a liquid-filled capsule is thoroughly considered numerically. This framework is based on lattice Boltzmann method for the fluid, finite element method for the membrane structure of the capsule, fast immersed interface method for the electric field and immersed boundary method being used to consider the fluid-structure-electric interaction. Under the effect of electric field, two different types of equilibrium states, prolate or oblate are obtained. The numerical algorithm is also applied …

Computational Analysis Of Antipode Algorithms For The Output Feedback Hopf Algebra, Lance Berlin

Electrical & Computer Engineering Theses & Dissertations

The feedback interconnection of two systems written in terms of Chen-Fliess series can be described explicitly in terms of the antipode of the output feedback Hopf algebra. At present, there are three known computational approaches to calculating this antipode: the left coproduct method, the right coproduct method, and the derivation method. Each of these algorithms is defined recursively, and thus becomes computationally expensive quite quickly. This motivates the need for a more complete understanding of the algorithmic complexity of these methods, as well as the development of new approaches for determining the Hopf algebra antipode. The main goals of this …

Optimal Sampling Paths For Autonomous Vehicles In Uncertain Ocean Flows, Andrew J. De Stefan

Dissertations

Despite an extensive history of oceanic observation, researchers have only begun to build a complete picture of oceanic currents. Sparsity of instrumentation has created the need to maximize the information extracted from every source of data in building this picture. Within the last few decades, autonomous vehicles, or AVs, have been employed as tools to aid in this research initiative. Unmanned and self-propelled, AVs are capable of spending weeks, if not months, exploring and monitoring the oceans. However, the quality of data acquired by these vehicles is highly dependent on the paths along which they collect their observational data. The …

Algebraic Companions And Linearizations, Eunice Y. S. Chan

Electronic Thesis and Dissertation Repository

In this thesis, we look at a novel way of finding roots of a scalar polynomial using eigenvalue techniques. We extended this novel method to the polynomial eigenvalue problem (PEP). PEP have been used in many science and engineering applications such vibrations of structures, computer-aided geometric design, robotics, and machine learning. This thesis explains this idea in the order of which we discovered it.

In Chapter 2, a new kind of companion matrix is introduced for scalar polynomials of the form $c(\lambda) = \lambda a(\lambda)b(\lambda)+c_0$, where upper Hessenberg companions are known for the polynomials $a(\lambda)$ and $b(\lambda)$. This construction can …

Dimension-Breaking For Traveling Waves In Interfacial Flows, Matthew W. Seiders

Theses and Dissertations

Fluid flow models in two spatial dimensions with a one-dimensional interface are known to support overturned traveling solutions. Computational methods of solving the two-dimensional problem are well developed, even in the case of overturned waves. The three-dimensional problem is harder for three prominent reasons. First, some formulations of the two-dimensional problem do not extend to three-dimensions. The technique of conformal mapping is a prime example, as it is very efficient in two dimensions but does not have a three-dimensional equivalent. Second, some three-dimensional models, such as the Transformed Field Expansion method, do not allow for overturned waves. Third, computational time …

Systemic Risk In Financial Networks, Tathagata Banerjee

McKelvey School of Engineering Theses & Dissertations

In this dissertation, I have used the network model based approach to study systemic risk in financial networks. In particular, I have worked on generalized extensions of the Eisenberg--Noe [2001] framework to account for realistic financial situations viz. pricing of corporate debt while accounting for network effects, asset liquidation mechanisms during fire sales, dynamic clearing and impact of contingent payments such as insurance and credit default swaps. First, I present formulas for the valuation of debt and equity of firms in a financial network under comonotonic endowments. I demonstrate that the comonotonic setting provides a lower bound to the price …

Parallel Multipole Expansion Algorithms And Their Biology Applications, Jiahui Chen

Mathematics Theses and Dissertations

N-body pairwise interactions are ubiquitous in scientific areas such as astrophysics, fluids mechanics, electrical engineering, molecular biology, etc. Computing these interactions using direct sum of an O(N) cost is expensive, whereas multipole expansion methods, such as the fast multipole method (FMM) or treecode, can reduce the cost to O(N) or O(N log N). This thesis focuses on developing numerical algorithms of Cartesian FMM and treecode, as well as using these algorithms to directly or implicitly solve biological problems involving pairwise interactions. This thesis consists of the following topics. 1) A cyclic parallel scheme is developed to handle the load balancing …