Digital Commons Network^™

Counting Threshold Graphs And Finding Inertia Sets, Christopher Abraham Guzman

Theses and Dissertations

This thesis is separated into two parts: threshold graphs and inertia sets. First we present an algorithmic approach to finding the minimum rank of threshold graphs and then progress to counting the number of threshold graphs with a specific minimum rank. Second, we find an algorithmic and more automated way of determining the inertia set of graphs with seven or fewer vertices using theorems and lemmata found in previous papers. Inertia sets are a relaxation of the inverse eigenvalue problem. Instead of determining all the possible eigenvalues that can be obtained by matrices with a specific zero/nonzero pattern we restrict …

Record Linkage, Stasha Ann Bown Larsen

Theses and Dissertations

This document explains the use of different metrics involved with record linkage. There are two forms of record linkage: deterministic and probabilistic. We will focus on probabilistic record linkage used in merging and updating two databases. Record pairs will be compared using character-based and phonetic-based similarity metrics to determine at what level they match. Performance measures are then calculated and Receiver Operating Characteristic (ROC) curves are formed. Finally, an economic model is applied that returns the optimal tolerance level two databases should use to determine a record pair match in order to maximize profit.

Minimum Rank Problems For Cographs, Nicole Andrea Malloy

Theses and Dissertations

Let G be a simple graph on n vertices, and let S(G) be the class of all real-valued symmetric nxn matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. The smallest rank achieved by a matrix in S(G) is called the minimum rank of G, denoted mr(G). The maximum nullity achieved by a matrix in S(G) is denoted M(G). For each graph G, there is an associated minimum rank class, MR(G) consisting of all matrices A in S(G) with rank A = mr(G). Although no restrictions are applied to the diagonal entries of …

A Crowdsourced Hail Dataset: Potential, Biases, And Inaccuracies, Joseph Robert Pehoski

Theses and Dissertations

Hail is a substantial severe weather hazard in the USA, with significant damage to property and

crops occurring annually. Traditional methods of forecasting hail size have limited accuracy, and despite

improvements in remote sensing of precipitation, the fall characteristics of hail make quantification of

hail imprecise. Research into hail is ongoing, but traditional hail datasets have known biases and low

spatiotemporal resolution. The increased usage of smartphones creates the opportunity to use a

crowdsourced dataset provided by the Precipitation Identification Near the Ground (PING) program, a

program developed by the National Severe Storms Laboratory. PING data is compared to approximate …

An Experimental Investigation Characterizing The Tribological Performance Of Natural And Synthetic Biolubricants Composed Of Carboxylic Acids For Energy Conservation And Sustainability, Carlton Jonathan Reeves

Theses and Dissertations

Over the last several decades the lubrication industry has been striving to bring bio-based lubricants known as biolubricants to prominence. The reasons for the increased environmental initiatives are due to depletion of oil reserves, increases in oil price, stringent government regulations on petroleum-based oils, and most importantly, concerns for protecting the environment. With an estimated, 50% of all lubricants entering the environment and much of these being composed of toxic mineral oils, biolubricants have begun to witness a resurgence. This experimental investigation seeks to develop a new class of ecofriendly biolubricants that are less toxic to the environment, derived from …

A Topics Analysis Model For Health Insurance Claims, Jared Anthony Webb

Theses and Dissertations

Mathematical probability has a rich theory and powerful applications. Of particular note is the Markov chain Monte Carlo (MCMC) method for sampling from high dimensional distributions that may not admit a naive analysis. We develop the theory of the MCMC method from first principles and prove its relevance. We also define a Bayesian hierarchical model for generating data. By understanding how data are generated we may infer hidden structure about these models. We use a specific MCMC method called a Gibbs' sampler to discover topic distributions in a hierarchical Bayesian model called Topics Over Time. We propose an innovative use …

Mathematical Modeling Of Physiological Characteristics In Female Soccer Athletes, Thomas S. Goeppinger

Theses and Dissertations

Intermittent sports create challenges regarding performance measurement. Quantification of various physiological characteristics can lead to increased performance and injury reduction throughout a season of competition. Currently, a variation of an athletes' heart rate is the primary physiological characteristic used for quantifying load on the athlete. With increasing technology, we have the ability to gather additional characteristics regarding the physicality of athletes during competition. This study statistically compares various models using these new characteristics as predictors to the athletes' lactate concentration in their blood. From this comparison, we determine which physiological characteristic(s) best represent the performance and fatigue of these athletes. …

Bi- And Multi Level Game Theoretic Approaches In Mechanical Design, Ehsan Ghotbi

Theses and Dissertations

This dissertation presents a game theoretic approach to solve bi and multi-level optimization problems arising in mechanical design. Toward this end, Stackelberg (leader-follower), Nash, as well as cooperative game formulations are considered. To solve these problems numerically, a sensitivity based approach is developed in this dissertation. Although game theoretic methods have been used by several authors for solving multi-objective problems, numerical methods and the applications of extensive games to engineering design problems are very limited. This dissertation tries to fill this gap by developing the possible scenarios for multi-objective problems and develops new numerical approaches for solving them.

This dissertation …

The Boundedness Of Hausdorff Operators On Function Spaces, Xiaoying Lin

Theses and Dissertations

For a fixed kernel function $\Phi$, the one dimensional Hausdorff operator is defined in the integral form by

\[

\hphi (f)(x)=\int_{0}^{\infty}\frac{\Phi(t)}{t}f(\frac{x}{t})\dt.

\]

By the Minkowski inequality, it is easy to check that the Hausdorff operator is bounded on the Lebesgue spaces $L^{p}$ when $p\geq 1$, with some size condition assumed on the kernel functions $\Phi$. However, people discovered that the above boundedness property is quite different on the Hardy space $H^{p}$ when $0

In this thesis, we first study the boundedness of $\hphi$ on the Hardy space $H^{1}$, and on the local Hardy space $h^{1}(\bbR)$. Our work shows that for …

Constructing Orthogonal Arrays On Non-Abelian Groups, Margaret Ann Mccomack

Theses and Dissertations

For an orthogonal array (or fractional factorial design) on k factors, Xu and Wu (2001) define the array's generalized wordlength pattern (A₁, ..., A_k), by relating a cyclic group to each factor. They prove the property that the array has strength t if and only if A₁ = ... = A_t = 0. In their 2012 paper, Beder and Beder show that this result is independent of the group structure used. Non-abelian groups can be used if the assumption is made that the groups G_i are chosen so that the counting function O …

Invariant Polynomials On Tensors Under The Action Of A Product Of Orthogonal Groups, Lauren Kelly Williams

Theses and Dissertations

Let K be the product O(n₁) × O(n₂) × … × O(n_r) of orthogonal groups. Let V be the r-fold tensor product of defining representations of each orthogonal factor. We compute a stable formula for the dimension of the K-invariant algebra of degree d homogeneous polynomial functions on V. To accomplish this, we compute a formula for the number of matchings which commute with a fixed permutation. Finally, we provide formulas for the invariants and describe a bijection between a basis for the space of invariants and the isomorphism classes of certain r-regular graphs …

Examining Middle School Students' Statistical Thinking While Working In A Technological Environment, Melissa Arnold Scranton

Theses and Dissertations

Examining Middle School Students' Statistical Thinking

While Working in a Technological Environment

Melissa Arnold Scranton

The purpose of this study was to gain a better understanding of how students think in a technological environment. This was accomplished by exploring the differences in the thinking of students while they worked in a technological environment and comparing this to their work in a paper and pencil environment. The software program TinkerPlots: Dynamic Data Exploration (Konold & Miller, 2005), a construction tool that middle school students use for data analysis was the technological environment. In both environments, types of critical, creative, and statistical …

The Minimum Rank Problem For Outerplanar Graphs, John Henry Sinkovic

Theses and Dissertations

Given a simple graph G with vertex set V(G)={1,2,...,n} define S(G) to be the set of all real symmetric matrices A such that for all i not equal to j, the ijth entry of A is nonzero if and only if ij is in E(G). The range of the ranks of matrices in S(G) is of interest and can be determined by finding the minimum rank. The minimum rank of a graph, denoted mr(G), is the minimum rank achieved by a matrix in S(G). The maximum nullity of a graph, denoted M(G), is the maximum nullity achieved by a matrix …

Bounding The Norm Of Matrix Powers, Daniel Ammon Dowler

Theses and Dissertations

In this paper I investigate properties of square complex matrices of the form A^k, where A is also a complex matrix, and k is a nonnegative integer. I look at several ways of representing A^k. In particular, I present an identity expressing the k^th power of the Schur form T of A in terms of the elements of T, which can be used together with the Schur decomposition to provide an expression of A^k. I also explain bounds on the norm of A^k, including some based on the element-based expression of …

A Class Of Univalent Convolutions Of Harmonic Mappings, Matthew Daniel Romney

Theses and Dissertations

A planar harmonic mapping is a complex-valued function ƒ : D → C of the form ƒ(x+iy) = u(x,y) + iv(x,y), where u and v are both real harmonic. Such a function can be written as ƒ = h+g where h and g are both analytic; the function w = g'/h' is called the dilatation of ƒ. This thesis considers the convolution or Hadamard product of planar harmonic mappings that are the vertical shears of the canonical half-plane mapping p;(z) = z/(1-z) with respective dilatations e^iθz and e^ipz, θ, p ∈ R. We prove that any such convolution is univalent. …

Integral Traces Of Weak Maass Forms Of Genus Zero Odd Prime Level, Nathan Eric Green

Theses and Dissertations

Duke and Jenkins defined a family of linear maps from spaces of weakly holomorphic modular forms of negative integral weight and level 1 into spaces of weakly holomorphic modular forms of half integral weight and level 4 and showed that these lifts preserve the integrality of Fourier coefficients. We show that the generalization of these lifts to modular forms of genus 0 odd prime level also preserves the integrality of Fourier coefficients.

Spectral Stability Of Weak Detonations In The Majda Model, Jeffrey James Hendricks

Theses and Dissertations

Using analytical and numerical Evans-function techniques, we examine the spectral stability of weak-detonation-wave solutions of Majda's scalar model for a reacting gas mixture. We provide a proof of monotonicity of solutions. Using monotonicity we obtain a bound on possible unstable eigenvalues for weak-detonation-wave solutions that improves on the more general bound given by Humpherys, Lyng, and Zumbrun. We use a numerical approximation of the Evans function to search for possible unstable eigenvalues in the bounded region obtained by the energy estimate. For the parameter values tested, our results combined with the result of Lyng, Raoofi, Texier, and Zumbrun demonstrate that …

The Frobenius Manifold Structure Of The Landau-Ginzburg A-Model For Sums Of An And Dn Singularities, Rachel Megan Webb

Theses and Dissertations

In this thesis we compute the Frobenius manifold of the Landau-Ginzburg A-model (FJRW theory) for certain polynomials. Specifically, our computations apply to polynomials that are sums of An and Dn singularities, paired with the corresponding maximal symmetry group. In particular this computation applies to several K3 surfaces. We compute the necessary correlators using reconstruction, the concavity axiom, and new techniques. We also compute the Frobenius manifold of the D3 singularity.

Market Dynamics With Non-Homogeneous Poisson Processes, Preston T. Redd

Theses and Dissertations

The Bertrand Duopoly model for demand in economics is a well-used model. Although this model has important insights towards pricing strategy, it does not accurately depict true market behaviors. In this paper, we will examine the advantages and disadvantages of the current model and its assumptions.We then take a whole new approach towards modeling this phenomena, using Poisson processes to model the demand of goods. We will discuss why this is a better approach and explain how we can extend this to better understand pricing strategies and market dynamics. We then apply our findings to the newsvendor problem, a commonly …

Modelling Infertility With Markov Chains, Rebecca Dorff

Theses and Dissertations

Infertility affects approximately 15% of couples. Testing and interventions are costly, in time, money, and emotional energy. This paper will discuss using Markov decision and multi-armed bandit processes to identify a systematic approach of interventions that will lead to the desired baby while minimizing costs.

Investment-Consumption With A Randomly Terminating Income, James Benjamin Taylor Jr.

Theses and Dissertations

We develop a stochastic control model for an investor's optimal investment and consumption over an uncertain planning horizon when the investor is endowed with a defaultable income stream. The distributions of the random time of default and the random terminal time are prescribed by deterministic hazard rates, and the investor makes investments in a standard financial market with a bond and a stock, modeled by geometric Brownian motion. In addition, the investor purchases insurance against both default and the terminal date, the default insurance serving as a proxy for the investor's disutility for default. We approximate the original continuous-time problem …

Poincaré Polynomial Of Fjrw Rings And The Group-Weights Conjecture, Julian Boon Kai Tay

Theses and Dissertations

FJRW-theory is a recent advancement in singularity theory arising from physics. The FJRW-theory is a graded vector space constructed from a quasihomogeneous weighted polynomial and symmetry group, but it has been conjectured that the theory only depends on the weights of the polynomial and the group. In this thesis, I prove this conjecture using Poincaré polynomials and Koszul complexes. By constructing the Koszul complex of the state space, we have found an expression for the Poincaré polynomial of the state space for a given polynomial and associated group. This Poincaré polynomial is defined over the representation ring of a group …

American Spread Option Models And Valuation, Yu Hu

Theses and Dissertations

Spread options are derivative securities, which are written on the difference between the values of two underlying market variables. They are very important tools to hedge the correlation risk. American style spread options allow the holder to exercise the option at any time up to and including maturity. Although they are widely used to hedge and speculate in financial market, the valuation of the American spread option is very challenging. Because even under the classic assumptions that the underlying assets follow the log-normal distribution, the resulting spread doesn't have a distribution with a simple closed formula. In this dissertation, we …

Determining The Alignment Of Math 105 - Intermediate Algebra At The University Of Wisconsin--Milwaukee To The Goals Of The Common Core State Standards, Raymond Dempsey

Theses and Dissertations

In this analysis we examine the Common Core State Standards for Mathematics and compare them to content presented in Math 105 - Intermediate Algebra at the University of Wisconsin-Milwaukee, in order to determine how well the UW-Milwaukee course develops the skills described in the standards. This is done by examining the structure, textbook content, and assessments of the course. Examining relevant high school standards, we determine that many of the procedural elements of these standards are present in the course while many of the conceptual elements are absent or poorly developed. After, we discuss content that is present in the …

Pbw Deformations Of Artin-Schelter Regular Algebras And Their Homogenizations, Jason D. Gaddis

Theses and Dissertations

A central object in the study of noncommutative projective geometry is the (Artin-Schelter) regular algebra, which may be considered as a noncommutative version of a polynomial ring. We extend these ideas to algebras which are not necessarily graded. In particular, we define an algebra to be essentially regular of dimension d if its homogenization is regular of dimension d+1. Essentially regular algebras are described and it is shown that that they are equivalent to PBW deformations of regular algebras. In order to classify essentially regular algebras we introduce a modified version of matrix congruence, called sf-congruence, which is equivalent to …

An Analysis Of The Common Core State Standards For Mathematics And The Content Of Math 095: Essentials Of Algebra At The University Of Wisconsin-Milwaukee, Hayley Nathan

Theses and Dissertations

In this analysis we present the content in Math 095: Essentials of Algebra at the University of Wisconsin-Milwaukee that is aligned to the Common Core State Standards for Mathematics. We find that the content in Math 095 is aligned to a small subset of the high school Number and Quantity, Algebra, and Function standards. We present a representative sample of homework and assessment items from the traditional lecture format of Math 095 and compare them to assessment items released by the Smarter Balanced Assessment Consortium and Illustrative Mathematics. We then discuss content from the Common Core State Standards for Mathematics …

Risk-Based Indifference Pricing In Jump Diffusion Markets With Regime-Switching, Torben Bielert

Theses and Dissertations

This paper is concerned with risk indifference pricing of a European type contingent claim in an incomplete market, where the evolution of the price of the underlying stock is modeled by a regime-switching jump diffusion. The rationale of using such a model is that it can naturally capture the inherent randomness of a prototypical stock market by incorporating both small and big jumps of the prices as well as the qualitative changes of the market. While the model provides a realistic description of the real market, it does introduces substantial difficulty in the analysis. In particular, in contrast with the …

Statistical Investigation Of The Immune Response In Non-Human Primate Models, Annika Laser

Theses and Dissertations

The human immunodeficiency virus (HIV) was first detected more than 30 years ago. Since then, intensive research has been done to develop a broadly protective vaccine, though without success. Our goal is to unveil some features of the protective immunity in non-human primate lentiviral infections in order to emulate HIV-infection. Two primate species have been studied, rhesus macaques (Rh) (Macaca mulatta) and African

green monkeys (Ag) (Chlorocebus spp.). Simian immunodeficiency virus (SIV) infection is non-pathogenic to Ag while Rh develop an AIDS-like illness. In this study, peripheral blood mononuclear cells (PBMC) from 8 Ag and 27 Rh were stimulated with …

Markov Chain Monte Carlo Simulation Of The Wright-Fisher Diffusion, Markus Joseph Wahl

Theses and Dissertations

In population genetics, the proportions of alleles at any given time are of interest. From generation to generation, these proportions vary and over a long time horizon the likelihoods for the proportions are given by a stationary distribution corresponding to the dynamics of the population. We investigate a diffusion approximation for the Wright-Fisher model and develop a Markov chain Monte Carlo simulation to approximate the evolution of the proportions of alleles in the population. Our aim is to estimate the stationary distribution, especially for parameters of the model for which no analytical formulas are known. We discretize the space of …

Category O Representations Of The Lie Superalgebra Osp(3,2), America Masaros

Theses and Dissertations

In his seminal 1977 paper [Kac77], V. G. Kac classified the finite dimensional simple Lie superalgebras over algebraically closed fields of characteristic zero. However, over thirty years later, the representation theory of these algebras is still not completely understood, nor is the structure of their enveloping algebras.

In this thesis, we consider a low-dimensional example, osp(3,2). We compute the composition factors and Jantzen filtrations of Verma modules over osp(3,2) in a variety of cases.