Physical Sciences and Mathematics Commons^™

Statistical Dependence In Imputed High-Dimensional Data For A Colorectal Cancer Study, Anvar Suyundikov

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The research objective of this dissertation was to provide novel statistical methods to fill potential gaps in the analyses of micro-ribonucleic acid (miRNA) data, and consequently to identify the miRNAs that contribute to cancer development. Mainly, this dissertation addressed the statistical issues raised by the statistical dependence of imputed (i.e., the missing data were replaced with substituted values) miRNA data in the colorectal cancer study. This dissertation presented a modified imputation method, the weighted KNN imputation accounting for dependence, that predicted the expression levels of missing normal samples with greater imputation accuracy than other imputation methods, and had moderate power …

Tropical Arithmetics And Dot Product Representations Of Graphs, Nicole Turner

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In tropical algebras we substitute min or max for the typical addition and then substitute addition for multiplication. A dot product representation of a graph assigns each vertex of the graph a vector such that two edges are adjacent if and only if the dot product of their vectors is greater than some chosen threshold. The resultS of creating dot product representations of graphs using tropical algebras are examined. In particular we examine the tropical dot product dimensions of graphs and establish connections to threshold graphs and the threshold dimension of a graph.

Classification Of Five-Dimensional Lie Algebras With One-Dimensional Subalgebras Acting As Subalgebras Of The Lorentz Algebra, Jordan Rozum

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Motivated by A. Z. Petrov's classification of four-dimensional Lorentzian metrics, we provide an algebraic classification of the isometry-isotropy pairs of four-dimensional pseudo-Riemannian metrics admitting local slices with five-dimensional isometries contained in the Lorentz algebra. A purely Lie algebraic approach is applied with emphasis on the use of Lie theoretic invariants to distinguish invariant algebra-subalgebra pairs. This method yields an algorithm for identifying isometry-isotropy pairs subject to the aforementioned constraints.

Factors Related To Successful Completion Of Developmental Mathematics Courses, Jason Bagley

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The goal of this research was to identify factors that contribute to students’ achievement in developmental math courses. This research collected information on several factors which have been suggested to have an effect on student achievement, particularly in developmental math courses at Utah State University, and analyzed their effects on student achievement. The literature review identified several factors that appeared related to student achievement, but many of these studies only analyzed a few factors. Very few studies have tried to analyze multiple variables together to try and identify which factors contribute most to student achievement and which observations can be …

Modeling Seed Dispersal And Population Migration Given A Distribution Of Seed Handling Times And Variable Dispersal Motility: Case Study For Pinyon And Juniper In Utah, Ram C. Neupane

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The spread of fruiting tree species is strongly determined by the behavior and range of fruit-eating animals, particularly birds. Birds either consume and digest seeds or carry and cache them at some distance from the source tree. These carried and settled seeds provide some form of distribution which generates tree spread to the new location. Firstly, we modal seed dispersal by birds and introduce it in a dispersal model to estimate seed distribution. Using this distribution, we create a population model to estimate the speed at which juniper and pinyon forest boundaries move.

Secondly, we introduce a fact that bird …

Explicit Construction Of First Integrals For The Toda Flow On A Classical Simple Lie Algebra, Patrick Seegmiller

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Toda flow is a generalization of a dynamical system describing the interaction of particles in a one-dimensional crystal. The concepts and energy and conservation are prominent in the study of dynamical systems, and quantities which remain the same over the evolution of a system provide valuable insights into the system’s behavior. In the realm of mathematics these quantities are called first integrals, or integrals of motion. This paper provides a background for study of the Toda flow, a verification of its integrability, and programming code for finding these quantities which remain unchanged over the evolution of the system.