Physical Sciences and Mathematics Commons^™

Physically Based Preconditioning Techniques Applied To The First Order Particle Transport And To Fluid Transport In Porous Media, Michael Rigley

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Solving linear systems is at the heart of many scientific applications from the PreAlgebra's student solving for x and y for basic geometry problems to the computational scientist solving billions of equations with billions of variables for weather forecasting, modeling fusion reactions, or web search algorithms. In this study we look at improving the efficiency of solving large linear systems that result from two applications. The first includes linear systems that result from solving differential equations for the movement of atomic particles in particle emitting, void, and absorbing regions. The second includes solving linear systems that result from solving differential …

Computational Topics In Lie Theory And Representation Theory, Thomas J. Apedaile

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The computer algebra system Maple contains a basic set of commands for working with Lie algebras and matrices. The purpose of this thesis was to extend the functionality of these Maple packages in a number of important areas. First, programs for defining multiplication in several different types of algebras were created to allow users to perform a wider variety of calculations. Second, commands were created for calculating some basic properties of matrix representations of semisimple Lie algebras. This allows a user to identify a given matrix representation by a collection of integers which do not change when the basis of …

Family-Wise Error Rate Control In Quantitative Trait Loci (Qtl) Mapping And Gene Ontology Graphs With Remarks On Family Selection, Garrett Saunders

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

One of the great aims of statistics, the science of collecting, analyzing, and interpreting data, is to protect against the probability of falsely rejecting an accepted claim, or hypothesis, given observed data stemming from some experiment. This is generally known as protecting against a Type I Error, or controlling the Type I Error rate. The extension of this protection against Type I Errors to the situation where thousands upon thousands of hypothesis are examined simultaneously is known as multiple hypothesis testing. This dissertation presents an improvement to an existing multiple hypothesis testing approach, the Focus Level method, specific to gene …

Implementation And Application Of The Curds And Whey Algorithm To Regression Problems, John Kidd

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A common statistical problem is trying to predict two or more variables using a set of predictor variables. The simplest model for this situation is called multivariate linear regression. This method uses each set of predictor variables to predict each of the response variables separately. This approach seems counter-intuitive as any possible relationship between the variables being predicted is ignored.

Breiman and Friedman found a way to take advantage of relationships among the response variables to increase the accuracy of the predictions for each of the predicted variables with an algorithm they called Curds and
Whey. It uses other statistical …

Beetles, Fungi And Trees: A Story For The Ages? Modeling And Projecting The Multipartite Symbiosis Between The Mountain Pine Beetle, Dendroctonus Ponderosae, And Its Fungal Symbionts, Grosmannia Clavigera And Ophiostoma Montium, Audrey L. Addison

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

As data collection and modeling improve, ecologists increasingly discover that interspecies dynamics greatly affect the success of individual species. Models accounting for the dynamics of multiple species are becoming more important. In this work, we explore the relationship between mountain pine beetle (MPB, Dendroctonus ponderosae Hopkins) and two mutualistic fungi, Grosmannia clavigera and Ophiostoma montium. These species are involved in a multipartite symbiosis, critical to the survival of MPB, in which each species benefits.

Extensive phenological modeling has been done to determine how temperature affects the timing of life events and cold-weather mortality of MPB. The fungi have also …