As part of an HHMI funded research project, I showed that overexpression (OE) of actin (ACT2) in Arabidopsis thaliana alters the expression of genes involved in plant immunity. Others have previously shown that knockout (KO) mutants of actin depolymerizing factor 4 are affected in the same gene as ACT2-OE. For...
We consider the problem of wireless spectrum management in cognitive wireless networks that maximizes the revenue for a spectrum operator. Specifically, we study the problem on how a wireless spectrum operator can optimally allocate its limited spectrum to various classes users/devices who pay differently for their spectrum per unit time....
The nonlinear Schrödinger equation is a well-known partial differential equation that provides a successful model in nonlinear optic theory, as well as other applications. In this dissertation, following a survey of mathematical literature, the geometric theory of differential equations is applied to the nonlinear Schrödinger equation. The main result of...
The Alexander polynomial is a well understood classical knot invariant with interesting symmetry properties and recent applications in knot Floer homology. There are many different ways to compute the Alexander polynomial, some involving algebraic techniques and others more geometric or combinatorial approaches. This is an interesting example of how different...
In probability and statistics, Simpson’s paradox is an apparent paradox in which a trend is present in different groups, but is reversed when the groups are combined. Joel Cohen (1986) has shown that continuously distributed lifetimes can never have a Simpson’s paradox. We investigate the same question for discrete random...
String theory, one of the more popular approaches to quantizing gravity, is a highly complex
theory, involving high level mathematics and physics. But the basic ideas of string theory are not inaccessible, even to the undergraduate. This document acts as report to my thesis project, the writing of A Detailed...
The purpose of this thesis is to examine the number of edge-disjoint Hamiltonian cycles in de Bruijn graphs using ideas from finite field theory, particularly linear recurring sequences. It is known that the de Bruijn graph B(d,n) admits d-1 disjoint Hamiltonian cycles when d is a power of 2, and...
Methamphetamine has flooded the media for the past two decades however, this
drug has impacted the nation for many decades prior. Since its synthesis in 1893,
methamphetamine has appealed to various aspects of society including soldiers,
housewives, college students, businessmen, truck drivers, drugged crazed hippies, and
athletes. The extensive effects,...
While the stability of time-homogeneous Markov chains have been extensively studied through the concept of mixing times, the stability of time-inhomogeneous Markov chains has not been studied as in depth. In this manuscript we will introduce special types of time-inhomogeneous Markov chains that are defined through an adiabatic transition. After...
We use the theory of continued fractions over function fields in the setting of hyperelliptic curves of equation y²=f(x), with deg(f)=2g+2. By introducing a new sequence of polynomials defined in terms of the partial quotients of the continued fraction expansion of y, we are able to bound the sum of...