Other Mathematics Commons^™

On 2-Primitive Triangle Decompositions Of Cocktail Party Graphs, Ian P. Waddell

Theses, Dissertations and Capstones

A decomposition of a graph Γ is a collection C of subgraphs, perhaps nonisomorphic, that partition the edges of Γ. Analogously, consider a group of truck drivers whose non-overlapping routes jointly cover all of the roads between a set of cities; that is, each road is traversed by precisely one driver. In this scenario, the cities are the vertices of the graph, the roads are the edges between vertices, and the drivers’ routes are the subgraphs in the decomposition. Given a graph H, we call C an H-decomposition of Γ if each subgraph in C is isomorphic to …

Sensitivity Analysis Of Wolf Restoration In Yellowstone Nation Park Using Omnivory Models, Derek Fields

Theses, Dissertations and Capstones

In the ever-changing world of ecology, species survival often depends on approximations and measurements taken by biologists. These approximations help to ensure and predict the future of that given species. Our ecological community of interest involves wolves, elk, and berry producing shrubs within Yellowstone National Park. We use two different systems of ordinary differential equations, each increasing in complexity to model our community. In each model the predator (wolves) and consumers (elk) compete for a common resource, berry producing shrubs. We call this consumption of resources, from more than one trophic level, omnivory. We approximate each system with parameter values …

Solutions To Dynamic Equations On Varying Times Scales, Sher B. Chhetri

Theses, Dissertations and Capstones

Note: The mathematical symbols could not be represented. See the abstract in the thesis for complete text.

The Dynamics Of Newton's Method On Cubic Polynomials, Shannon N. Miller

Theses, Dissertations and Capstones

The field of dynamics is itself a huge part of many branches of science, including the motion of the planets and galaxies, changing weather patterns, and the growth and decline of populations. Consider a function f and pick x0 in the domain of f . If we iterate this function around the point x0, then we will have the sequence x0, f (x0), f (f (x0)), f (f (f (x0))), ..., which becomes our dynamical system. We are essentially interested in the end behavior of this system. Do …

Convergence Analysis Of Mcmc Method In The Study Of Genetic Linkage With Missing Data, Diana Fisher

Theses, Dissertations and Capstones

Computational infeasibility of exact methods for solving genetic linkage analysis problems has led to the development of a new collection of stochastic methods, all of which require the use of Markov chains. The purpose of this work is to investigate the complexities of missing data in pedigree analysis using the Monte Carlo Markov Chain (MCMC) method as compared to the exact results. Also, we attempt to determine an association between missing data in a familial pedigree and the convergence to stationarity of a descent graph Markov chain implemented in the stochastic method for parametric linkage analysis.

In particular, we will …