Mathematics Commons^™

The Minimal Zn-Symmetric Graphs That Are Not Zn-Spherical, Lowell Abrams, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a graph G equipped with faithful and fixed-point-free Γ-action (Γ a finite group) we define an orbit minor H of G to be a minor of G for which the deletion and contraction sets are closed under the Γ-action. The orbit minor H inherits a Γ-symmetry from G, and when the contraction set is acyclic the action inherited by H remains faithful and fixed-point free. When G embeds in the sphere and the Γ-action on G extends to a Γ-action on the entire sphere, we say that G is Γ-spherical. In this paper we determine for every odd value …

Survival Analysis For Truncated Data And Competing Risks, Michael Steelman

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The purpose of this project is to consider the problems of left truncation and competing risks in analyzing censored survival data, and to compare and contrast various approaches for handling these problems. The motivation for this work comes from an analysis of data from the Cache County Memory Study. Study investigators were interested in the association between early-life psychologically stressful events (e.g., parental or sibling death, or parental divorce, among others) and late-life risk of Alzheimer's disease (AD). While conventional methods for censored survival data can be applied, the presence of left truncation and competing risks (i.e., other adverse events …

Comparing Linear Mixed Models To Meta-Regression Analysis In The Greenville Air Quality Study, Lynsie M. Daley

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The effect of air quality on public health is an important issue in need of better understanding. There are many stakeholders, especially in Utah and Cache Valley, where the poor air quality as measured by PM 2.5 levels and consequent inversions can sometimes be the very worst in the nation. This project focuses on comparing two statistical methods used to analyze an important air quality data set from the Greenville Air Quality Study, focusing on a lung function response variable. A linear mixed model, with a random factor for subject, gives slope estimates and their significance for predictor variables of …

On Mikhailov's Reduction Group, Tihomir Valchev

Articles

We present a generalization of the notion of reduction group which allows one to study in a uniform way certain classes of nonlocal $S$-integrable equations like Ablowitz-Musslimani's nonlocal Schr\"odinger equation. Another aspect of the proposed generalization is the possibility to derive in a systematic way solutions to S-integrable equations with prescribed symmetries.

Student Understanding Of Function And Success In Calculus, Daniel I. Drlik

Boise State University Theses and Dissertations

The purpose of this study was to determine if there is a relationship between student success in calculus and student understanding of function. Student understanding of function was measured using two questionnaires, one of which is a modification of an existing measure based on APOS theory. The other I developed with items from the concept image literature. The participants of this study were 116 high school students who were enrolled in a first-year calculus course. The results of the questionnaires were aligned to course exam scores to determine connections between function understanding and rate of success in calculus.

A major …

The Relationship Between Elementary Teachers' Self-Efficacy For Teaching Mathematics And Their Mathematical Knowledge For Teaching, Meagan Mckinney

Boise State University Theses and Dissertations

This study examined the relationship between elementary teachers’ mathematical knowledge for teaching (MKT) and their self-efficacy for teaching mathematics. Self-efficacy and MKT are of high importance with implications in regards to quality of instruction and the Common Core State Standards for mathematics. Using the Content Knowledge for Teaching Mathematics (CKT-M) instrument, data for this study were collected from thirty-five elementary school teachers participating in the Improving Teachers’ Monitoring of Learning Grant at the time. The data were concerned with these teachers’ self-efficacy with the pedagogy and content of mathematics using the Self-Efficacy for Teaching Mathematics Instrument (SETMI). Qualitative data were …

An Investigation Into Vaccination Behavior: Parametrization Of A Samoan Vaccine Scare, Amanda Ruth Spink

Theses and Dissertations

Vaccination behavior can be influenced by many factors. Some examples are vaccine scares, evolutionary game theory, social learning such as media coverage, feedback in the form of infectious cases, and herd immunity. We investigated a previously published model that attempts to explain vaccination behavior based on a game theoretic point of view. The model was applied to a large vaccine scare in the country of Samoa, and a parameter estimation problem was solved for different risk perception scenarios. It was found that the model fit best in the case of no social learning and no feedback. However, adding in these …

Some Results On Pseudo-Collar Structures On High-Dimensional Manifolds, Jeffrey Joseph Rolland

Theses and Dissertations

In this dissertation we outline a partial reverse to Quilen's plus construction in the high-dimensional manifold categor. We show that for any orientable manifold N with fundamental group Q and any fintely presented superperfect group S, there is a 1-sided s-cobordism (W, N, N-) with the fundamental group G of N- a semi-direct product of Q by S, that is, with G satisying 1 -> S -> G -> Q -> 1 and actually a semi-direct product.

We then use a free product of Thompson's group V with itself to form a superperfect group S and start with an orientable …

Counting On R-Fibonacci Numbers, Arthur Benjamin, Curtis Heberle

All HMC Faculty Publications and Research

We prove the r-Fibonacci identities of Howard and Cooper using a combinatorial tiling approach.

Bohr Density Of Simple Linear Group Orbits, Roger Howe, Francois Ziegler

Department of Mathematical Sciences Faculty Publications

We show that any non-zero orbit under a non-compact, simple, irreducible linear group is dense in the Bohr compactification of the ambient space.

Nonlinear Gravitational-Wave Memory From Merging Binary Black Holes, Goran Dojcinoski

Theses, Dissertations and Culminating Projects

Gravitational waves are oscillations in spacetime that propagate throughout the universe at the speed of light. They are a prediction of Einstein’s theory of General Relativity. Detectable sources of gravitational waves are typically collisions of black holes or other compact objects (neutron stars, white dwarfs). While most gravitational-wave signals are expected to be oscillatory in nature, some will exhibit a phenomenon called gravitational-wave memory. This refers to a non-oscillatory component of the gravitational wave signal that can leave a permanent distortion (or “memory” ) in a gravitational-wave detector. The nonlinear memory effect is a type of memory signal that arises …

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.

Interlace Polynomial Of A Special Eulerian Graph, Christian A. Hyra

Theses, Dissertations and Culminating Projects

In a recent paper, Arratia, Bollobas and Sorkin discussed a graph polynomial defined recursively, which they call the interlace polynomial. There have been previous results on the interlace polynomials for special graphs, such as paths, cycles, and trees. Applications have been found in biology and other areas. In this research, I focus on the interlace polynomial of a special type of Eulerian graph, built from one cycle of size n and n cycle three graphs. I developed explicit formulas by implementing the toggling process to the graph. I further investigate the coefficients and special values of the interlace polynomial. Some …

Phantom Maps, Decomposability, And Spaces Meeting Particular Finiteness Conditions, James Schwass

Dissertations

The purpose of this dissertation is to extend principles for detecting the existence of essential phantom maps into spaces meeting particular finiteness conditions. Zabrodsky shows that a space Y having the homotopy type of a finite CW complex is the target of essential phantom maps if and only if Y has a nontrivial rational homology group. We show this observation holds on the collection of finite generalized CW complexes. Similarly, Iriye shows a finite-type, simply connected suspension space is the target of essential phantom maps if and only if it has a nontrivial rational homology group. We show this observation …

Averaged Instrumental Variables Estimators, Yoonseok Lee, Yu Zhou

Center for Policy Research

We develop averaged instrumental variables estimators as a way to deal with many weak instruments. We propose a weighted average of the preliminary k-class estimators, where each estimator is obtained using different subsets of the available instrumental variables. The averaged estimators are shown to be consistent and to satisfy asymptotic normality. Furthermore, its approximate mean squared error reveals that using a small number of instruments for each preliminary k-class estimator reduces the finite sample bias, while averaging prevents the variance from inflating. Monte Carlo simulations find that the averaged estimators compare favorably with alternative instrumental-variable-selection approaches when the strength levels …