Physical Sciences and Mathematics Commons^™

Spatiotemporal Subspace Feature Tracking By Mining Discriminatory Characteristics, Richard D. Appiah

Doctoral Dissertations

Recent advancements in data collection technologies have made it possible to collect heterogeneous data at complex levels of abstraction, and at an alarming pace and volume. Data mining, and most recently data science seek to discover hidden patterns and insights from these data by employing a variety of knowledge discovery techniques. At the core of these techniques is the selection and use of features, variables or properties upon which the data were acquired to facilitate effective data modeling. Selecting relevant features in data modeling is critical to ensure an overall model accuracy and optimal predictive performance of future effects. The …

3-Manifold Perspective On Surface Homeomorphisms For Surfaces With Very Negative Euler Characteristic, Michael Harris

Graduate Theses and Dissertations

The goal of this paper is to show for a compact triangulated 3-manifold M with boundary which fibers over the circle that whenever F is a fiber with sufficiently negative Euler characteristic the monodromymaps an essential simple closed curve or an essential simple arc in F to be disjoint from its image (possibly after isotopy). This is shown by applying the theorem of Ichihara, Kobayashi, and Rieck in [10] to the double of M to get a pair of pants. We then find an equivariant pair of pants and use it to find an essential simple closed curve or an …

Interaction Graphs Derived From Activation Functions And Their Application To Gene Regulation, Simon Joyce

Graduate Dissertations and Theses

Interaction graphs are graphic representations of complex networks of mutually interacting components. Their main application is in the field of gene regulatory networks, where they are used to visualize how the expression levels of genes activate or inhibit the expression levels of other genes.

First we develop a natural transformation of activation functions and their derived interaction graphs, called conjugation, that is related to a natural transformation of signed digraphs called switching isomorphism. This is a useful tool for the analysis of interaction graphs used throughout the rest of the dissertation.

We then discuss the question of what restrictions, if …

Implementing And Testing A Panel-Based Method For Modeling Acoustic Scattering From Cfd Input, S. Hales Swift

Open Access Dissertations

Exposure of sailors to high levels of noise in the aircraft carrier deck environment is a problem that has serious human and economic consequences. A variety of approaches to quieting exhausting jets from high-performance aircraft are undergoing development. However, testing of noise abatement solutions at full-scale may be prohibitively costly when many possible nozzle treatments are under consideration. A relatively efficient and accurate means of predicting the noise levels resulting from engine-quieting technologies at personnel locations is needed. This is complicated by the need to model both the direct and the scattered sound field in order to determine the resultant …

On Compactness And Closed-Rangeness Of Composition Operators, Arnab Dutta

Graduate Theses and Dissertations

Let $\phi$ be an analytic self-map of the unit disk $\mathbb{D}:=\{z:\lvert z\rvert

Conformally Invariant Operators In Higher Spin Spaces, Chao Ding

Graduate Theses and Dissertations

In this dissertation, we complete the work of constructing arbitrary order conformally invariant operators in higher spin spaces, where functions take values in irreducible representations of Spin groups. We provide explicit formulas for them.

We first construct the Dirac operator and Rarita-Schwinger operator as Stein Weiss type operators. This motivates us to consider representation theory in higher spin spaces. We provide corrections to the proof of conformal invariance of the Rarita-Schwinger operator in [15]. With the techniques used in the second order case [7, 18], we construct conformally invariant differential operators of arbitrary order with the target space being degree-1 …

The Maximal Thurston-Bennequin Number On Grid Number N Diagrams, Emily Goins Thomas

Graduate Theses and Dissertations

We will prove an upper bound for the Thurston-Bennequin number of Legendrian knots and links on a rectangular grid with arc index n.

TB(n)=CR(n)-[n/2]

In order to prove the bound, we will separate our work for when n is even and when n is odd. After we prove the upper bound, we will show that there are unique knots and links on each grid which achieve the upper bound. When n is even, torus links achieve the maximum, and when n is odd, torus knots achieve the maximum.

Regularity Of Solutions And The Free Boundary For A Class Of Bernoulli-Type Parabolic Free Boundary Problems With Variable Coefficients, Thomas H. Backing

Open Access Dissertations

In this work the regularity of solutions and of the free boundary for a type of parabolic free boundary problem with variable coefficients is proved. After introducing the problem and its history in the introduction, we proceed in Chapter 2 to prove the optimal Lipschitz regularity of viscosity solutions under the main assumption that the free boundary is Lipschitz. In Chapter 3, we prove that Lipschitz free boundaries possess a classical normal in both space and time at each point and that this normal varies with a Hölder modulus of continuity. As a consequence, the viscosity solution is in fact …

Good Stein Neighborhood Bases For Nonsmooth Pseudoconvex Domains, Chizuko Iwaki

Graduate Theses and Dissertations

In 1979, Dufresnoy showed that the existence of a good Stein neighborhood base for Ω ⊂ℂⁿ implies that one can solve the inhomogeneous Cauchy-Riemann equations in C^∞(Ω̄), even if the boundary of Ω is only Lipschitz. In my thesis, I will show sufficient conditions for the existence of a good Stein neighborhood base on a Lipschitz domain satisfying Property (P).

Isometries Of Besov Type Spaces Among Composition Operators, Melissa Ann Shabazz

Graduate Theses and Dissertations

Let Bp,alpha for p >1 and alpha >1 be the Besov type space of holomorphic functions on the unit disk D. Given Phi, a holomorphic self map of D, we show the composition operator CPhi is an isometry on Bp,alpha if and only if the weighted composition operator WPhiPhi, is an isometry on the weighted Bergman space Ap,alpha. We then characterize isometries among composition operators in Bp,alpha in terms of their Nevanlinna type counting function. Finally, we find that the only isometries among composition operators on Bp,alpha, except on B 2,0, are induced by rotations. This extends known results by …

Sensitivity Of Mixed Models To Computational Algorithms Of Time Series Data, Gunaime Nevine

Doctoral Dissertations

Statistical analysis is influenced by implementation of the algorithms used to execute the computations associated with various statistical techniques. Over many years; very important criteria for model comparison has been studied and examined, and two algorithms on a single dataset have been performed numerous times. The goal of this research is not comparing two or more models on one dataset, but comparing models with numerical algorithms that have been used to solve them on the same dataset.

In this research, different models have been broadly applied in modeling and their contrasting which are affected by the numerical algorithms in different …

Prediction Of Time-To-Graduation For Stem Hispanic Undergraduate Students, Gejun Zhu

Theses and Dissertations - UTB/UTPA

In this thesis, we study the time-to-graduation problem for STEM Hispanic undergraduate students. The response, time-to-graduation, was treated in two different ways: as a binary variable with graduated (by the 6th year) and not-graduated values, and as an ordinal variable with values year-4, year-5, year-6, and not-graduate. Mathematics education plays critical role in students’ timely graduation, especially for STEM students. We used students records data obtained from The University of Texas-Pan American to illustrate how mathematics background factors (including SAT math score, ACT math score, TASP math score) and mathematics performance variables (including mathematics GPA, number of dropped mathematics courses, …

The Szego Kernel Of Certain Polynomial Models, And Heat Kernel Estimates For Schrodinger Operators With Reverse Holder Potentials, Michael Tinker

Graduate Theses and Dissertations

We present two different results on operator kernels, each in the context of its relationship to a class of CR manifolds M={z,w1,...wn) element of Cn⁺¹ : Im wifi(Re z)} where n d 2 and (phi)i( x) is subharmonic for i = 1,...,n. Such models have proven useful for studying canonical operators such as the Szegö projection on weakly pseudoconvex domains of finite type in C², and may play a similar role in work on higher codimension CR manifolds in C³. Our study in Part II concerns the Szegö kernel on M for which the (empty set)i are subharmonic nonharmonic polynomials. …

Modeling And Control Of Nanoparticle Bloodstream Concentration For Cancer Therapies, Scarlett S. Bracey

Doctoral Dissertations

Currently, the most commonly used treatments for cancerous tumors (chemotherapy, radiation, etc.) have almost no method of monitoring the administration of the treatment for adverse effects in real time. Without any real time feedback or control, treatment becomes a "guess and check" method with no way of predicting the effects of the drugs based on the actual bioavailability to the patient's body. One particular drug may be effective for one patient, yet provide no benefit to another. Doctors and scientists do not routinely attempt to quantifiably explain this discrepancy. In this work, mathematical modeling and analysis techniques are joined together …

The Word Problem For The Automorphism Groups Of Right-Angled Artin Groups Is In P, Carrie Anne Whittle

Graduate Theses and Dissertations

We provide an algorithm which takes any given automorphism f of any given right-angled Artin group G and determines whether or not f is the identity automorphism, thereby solving the word problem for the automorphism groups of right-angled Artin groups. We do this by solving the compressed word problem for right-angled Artin groups, a more general result. A key piece of this solution is the use of Plandowski's algorithm. We also demonstrate that our algorithm runs in polynomial time in the size of the given automorphism, written as a word in Laurence's generators of the automorphism group of the given …

A Mathematical Model And Numerical Method For Thermoelectric Dna Sequencing, Liwei Shi

Doctoral Dissertations

DNA sequencing is the process of determining the precise order of nucleotide bases, adenine, guanine, cytosine, and thymine within a DNA molecule. It includes any method or technology that is used to determine the order of the four bases in a strand of DNA. The advent of rapid DNA sequencing methods has greatly accelerated biological and medical research and discovery. Thermoelectric DNA sequencing is a novel method to sequence DNA by measuring the heat that is released when DNA polymerase inserts a deoxyribonucleoside triphosphate into a growing DNA strand. The thermoelectric device for this project is composed of four parts: …

Hardy Space Properties Of The Cauchy Kernel Function For A Strictly Convex Planar Domain, Belen Espinosa Lucio

Graduate Theses and Dissertations

This work is based on a paper by Edgar Lee Stout, where it is shown that for every strictly pseudoconvex domain $D$ of class $C^2$ in $\mathbb{C}^N$, the Henkin-Ram\'irez Kernel Function belongs to the Smirnov class, $E^q(D)$, for every $q\in(0,N)$.

The main objective of this dissertation is to show an analogous result for the Cauchy Kernel Function and for any strictly convex bounded domain in the complex plane. Namely, we show that for any strictly convex bounded $D\subset\mathbb{C}$ of class $C^2$ if we fix $\zeta$ in the boundary of $D$ and consider the Cauchy Kernel Function

\mathcal{K}(\zeta,z)=\frac{1}{2\pi i}\frac{1}{\zeta-z}

as a …

The Effect Of Symmetry On The Riemann Map, Jeanine Louise Myers

Graduate Theses and Dissertations

The Riemann mapping theorem guarantees the existence of a conformal mapping or Riemann map in the complex plane from the open unit disk onto an open simply-connected domain, which is not all of the complex plane. Although its existence is guaranteed, the Riemann map is rarely known except for special domains like half-planes, strips, etc. Therefore, any information we can determine about the Riemann map for any class of domains is interesting and useful.

This research investigates how symmetry affects the Riemann map. In particular, we define domains with symmetries called Rectangular Domains or RDs. The Riemann map of an …

Pointwise Schauder Estimates Of Parabolic Equations In Carnot Groups, Heather Arielle Griffin

Graduate Theses and Dissertations

Schauder estimates were a historical stepping stone for establishing uniqueness and smoothness of solutions for certain classes of partial differential equations. Since that time, they have remained an essential tool in the field. Roughly speaking, the estimates state that the Holder continuity of the coefficient functions and inhomogeneous term implies the Holder continuity of the solution and its derivatives. This document establishes pointwise Schauder estimates for second order parabolic equations where the traditional role of derivatives are played by vector fields generated by the first layer of the Lie algebra stratification for a Carnot group. The Schauder estimates are shown …

Border Hispanics’ Physical Activity Improvement In A Chronic Disease Prevention Program, Lu Xu

Theses and Dissertations - UTB/UTPA

In seeking of effective prevention programs to improve physical activities, we want to examine the factors related to physical activities improvement in Alliance for a Healthy Border, a chronic disease prevention program with pre-post-post evaluations through 12 federally qualified community health centers serving primarily Hispanics in communities along the U.S.- Mexico border. Logistic regression was performed to examine the association between physical activity and twenty predictors at baseline. Multinomial regression was used to examine the determinants of physical activities improvement at two time points: program end and post six-months. Socio-demographic, baseline health condition factors, and determination of doing physical activity …

Boundary Element Method (Bem) And Method Of Fundamental Solutions (Mfs) For The Boundary Value Problems Of The 2-D Laplace's Equation, Ermes Anthony Salgado-Ibarra

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis we study the solution of the two dimensional Laplace equation by the boundary Element method (BEM) and the method of fundamental solutions (MFS). Both the BEM and MFS used to solve boundary value problems involving the Laplace equation 2-D settings. Both methods rely on the use of fundamental solution of the Laplace's equation (the solution of Laplace's equation in the distributional sense). We will contrast and compare the results we get using the BEM with results we get using the MFS.

Limiting Behavior Of Nondeterministic Fillings Of The Torus By Colored Squares, Pablo Rosell Gonzalez

Graduate Theses and Dissertations

In this work we study different dynamic processes for filling tori and n×∞ bands with edge-to-edge black and white squares at random. First we present a simulation for the Random Sequential Adsorption (RSA) with nearest-neighbor rejection on n×n tori. We are interested in the ratio of black to total tiles once the domain is saturated for large domains. Next we study the annealing process. Given a random excited tiling of an n×n torus, we show that as t→∞ the system reaches a stable state in which no tile is excited. This stable state can either be a tiling whose tiles …

Essays On Hedge Fund Replication: Methodological Assessment And Development Of The Factor Approach, Nonlinear Modeling And Policy Perspectives, Guillaume Weisang

2011

This dissertation is concerned with hedge fund replication, a subject of a practical and theoretical importance, both from an investment and a risk management point of view. One of our goals is to extend known methodologies in order to enhance our understanding of an industry that is known for its secrecy and its lack of transparency. A second goal is to contribute to the quantitative finance literature with improved techniques for hedge fund replication. Hedge fund replication (HFR) is approached from the methodological as well as from practical and regulatory perspectives. The first two chapters provide the motivation and the …

Holomorphic Hardy Space Representations For Convex Domains In Cn, Jennifer West Paulk

Graduate Theses and Dissertations

This thesis deals with Hardy Spaces of holomorphic functions for a domain in several complex variables, that is, when the complex dimension is greater than or equal to two. The results we obtain are analogous to well known theorems in one complex variable. The domains we are concerned with are strongly convex with real boundary of class C^2. We obtain integral representations utilizing the Leray kernel for Hardy space (p=1) functions on such domains D. Next we define an operator to prove the non-tangential limits of a function in Hardy space (p between 1 and infinity, inclusive) of domain D …

A Comprehensive Uncertainty Analysis And Method Of Geometric Calibration For A Circular Scanning Airborne Lidar, Michael Oliver Gonsalves

Dissertations

This dissertation describes an automated technique for ascertaining the values of the geometric calibration parameters of an airborne lidar. A least squares approach is employed that adjusts the point cloud to a single planar surface which could be either a narrow airport runway or a dynamic sea surface. Going beyond the customary three boresight angles, the proposed adjustment can determine up to eleven calibration parameters to a precision that renders a negligible contribution to the point cloud’s positional uncertainty.

Presently under development is the Coastal Zone Mapping and Imaging Lidar (CZMIL), which, unlike most contemporary systems that use oscillating mirrors …

A Numerical Method For Obtaining An Optimal Temperature Distribution In A Three-Dimensional Triple-Layered Skin Structure Embedded With Multi-Level Blood Vessels, Xingui Tang

Doctoral Dissertations

The research related to hyperthermia has stimulated a lot of interest in recent years because of its application in cancer treatment. When heating the tumor tissue, the crucial problem is keeping the temperature of the surrounding normal tissue below a certain threshold in order to avoid the damage to the normal tissue. Hence, it is important to obtain the temperature field of the entire region during the treatment. The objective of this dissertation is to develop a numerical method for obtaining an optimal temperature distribution in a 3D triple-layered skin structure embedded with multi-level blood vessels where the surface of …

Pattern Recognition For Electric Power System Protection, Yong Sheng

Doctoral Dissertations

The objective of this research is to demonstrate pattern recognition tools such as decision trees (DTs) and neural networks that will improve and automate the design of relay protection functions in electric power systems. Protection functions that will benefit from the research include relay algorithms for high voltage transformer protection (TP) and for high impedance fault (HIF) detection. A methodology, which uses DTs and wavelet analysis to distinguish transformer internal faults from other conditions that are easily mistaken for internal faults, has been developed. Also, a DT based solution is proposed to discriminate HIFs from normal operations that may confuse …