Physical Sciences and Mathematics Commons^™

Mathematical Modeling Of Immune Responses To Hepatitis C Virus Infection, Ivan Ramirez

Electronic Theses and Dissertations

An existing mathematical model of ordinary differential equations was studied to better understand the interactions between hepatitis C virus (HCV) and the immune system cells in the human body. Three possible qualitative scenarios were explored: dominant CTL response, dominant antibody response, and coexistence. Additionally, a sensitivity analysis was carried out to rank model parameters for each of these scenarios. Therapy was addressed as an optimal control problem. Numerical solutions of optimal controls were computed using a forward-backward sweep scheme for each scenario. Model parameters were estimated using ordinary least squares fitting from longitudinal data (serum HCV RNA measurements) given in …

Several Functional Equations Defined On Groups Arising From Stochastic Distance Measures., Heather B. Hunt

Electronic Theses and Dissertations

Several functional equations related to stochastic distance measures have been widely studied when defined on the real line. This dissertation generalizes several of those results to functions defined on groups and fields. Specifically, we consider when the domain is an arbitrary group, G, and the range is the field of complex numbers, C. We begin by looking at the linear functional equation f(pr, qs)+f(ps, qr) = 2f(p, q)+2f(r, s) for all p, q, r, s, € G. The general solution f : G x G → C is given along with a few specific examples. Several generalizations of this equation …

Physiologically-Based Pharmacokinetic Model For Ertapenem, Whitney Forbes

Electronic Theses and Dissertations

Ertapenem is a carbapenem used to treat a wide range of bacterial infections. What sets ertapenem apart from other carbapenems is its longer half-life which implies it need only be administered once daily. We developed a physiologically-based pharmacokinetic model for the distribution of ertapenem within the body. In the model, parameters such as human body weight and height, age, organ volumes, blood flow rates, and partition coefficients of particular tissues are used to examine the absorption, distribution, metabolism, and excretion of ertapenem. The total and free blood concentrations found were then compared to experimental data. We then examined the sensitivity …

Are Highly Dispersed Variables More Extreme? The Case Of Distributions With Compact Support, Benedict E. Adjogah

Electronic Theses and Dissertations

We consider discrete and continuous symmetric random variables X taking values in [0; 1], and thus having expected value 1/2. The main thrust of this investigation is to study the correlation between the variance, Var(X) of X and the value of the expected maximum E(Mn) = E(X1,...,Xn) of n independent and identically distributed random variables X1,X2,...,Xn, each distributed as X. Many special cases are studied, some leading to very interesting alternating sums, and some progress is made towards a general theory.

Topological Ramsey Spaces, Associated Ultrafilters, And Their Applications To The Tukey Theory Of Ultrafilters And Dedekind Cuts Of Nonstandard Arithmetic, Timothy Onofre Trujillo

Electronic Theses and Dissertations

This dissertation makes contributions to the areas of combinatorial set theory, the model theory of arithmetic, and the Tukey theory of ultrafilters. The main results are broken into three parts.

In the first part, we identify some new partition relations among finite trees and use them to answer an open question of Dobrinen; namely, "for n < omega, are the notions of Ramsey for Rn and selective for Rn equivalent?" We show that for each n < omega, it is consistent with ZFC that there exists a selective for Rn ultrafilter which is not Ramsey for Rn.

In the second part, we extend results of Blass concerning Dedekind cuts associated to ultrafilter mappings from p-point and weakly-Ramsey ultrafilters to ultrafilter mappings from Ramsey for R1 ultrafilters. Blass associates to each ultrafilter U on a countable set X and each function g …

Generating Surfaces Of Variable Eccentricity Within A Ray Tracer, Joshua A. Smith

Electronic Theses and Dissertations

Polynomial surfaces used in ray tracing have recently been improved upon allowing for three dimensional applications. Among these are surfaces that have a varying eccentricity. This paper will discuss a method for finding real roots of polynomials [allowing us to create these surfaces]. First, we will give the reader a basic comprehension of the workings of a ray tracer, a general understanding of three dimensional polynomial surfaces, how this newly implemented root finder functions, and how these concepts enable us to create surfaces of variable eccentricity. Then, examples will be provided to demonstrate the capabilities of the program.

Adaptive State Feedback Control Of Lorenz Systems To Its Non-Trivial Equilibrium, Anh V. Tran

Electronic Theses and Dissertations

The complex Lorenz system is a simplified nonlinear dynamical system, which is derived from the Navier-Stokes equations that govern a closed thermal convection loop. The Lorenz system is chaotic for large Rayleigh number. In this chaotic regime, we implement a linear state feedback controller to stabilize the state trajectory at its original nontrivial equilibrium. The state variable for feedback is easily measurable. The system is proved to be globally asymptotically stable with a optimal feedback gain. The stability bound is improved over the previous result. We also established globally stability of the adaptively control system, where the system parameters are …

Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva

Electronic Theses and Dissertations

Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator- prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.

Selection Of Step Size For Total Variation Minimization In Ct, Anna N. Yeboah

Electronic Theses and Dissertations

Medical image reconstruction by total variation minimization is a newly developed area in computed tomography (CT). In compressed sensing literature, it hasbeen shown that signals with sparse representations in an orthonormal basis may be reconstructed via l1-minimization. Furthermore, if an image can be approximately modeled to be piecewise constant, then its gradient is sparse. The application of l1-minimization to a sparse gradient, known as total variation minimization, may then be used to recover the image. In this paper, the steepest descent method is employed to update the approximation of the image. We propose a way to estimate an optimal step …

Structure Vs. Properties Using Chemical Graph Theory, Tabitha N. Williford

Electronic Theses and Dissertations

Chemical graph theory began as a way for mathematicians to bring together the areas of the Physical Sciences and Mathematics. Through its use, mathematicians are able to model chemical systems, predict their properties as well as structure-property relationships. In this dissertation, we consider two questions involving chemical graph theory and its applications. We first look at tree-like polyphenyl systems, which form an important family of compounds in Chemistry, particularly in Material Science. The importance can be seen in LEDs, transmitters, and electronics. In recent years, many extremal results regarding such systems under specific constraints have been reported. More specifically are …