Mathematics Commons^™

A Proof Of Concept Study Of Function-Based Statistical Analysis Of Fnirs Data: Syntax Comprehension In Children With Specific Language Impairment Compared To Typically-Developing Controls, Matthew D. Meng, Nicholas J. Wan, Joseph M. Baker, James Montgomery, Julia L. Evans, Ronald Gillam

Mathematics and Statistics Faculty Publications

Functional near infrared spectroscopy (fNIRS) is a neuroimaging techonology that enables investigators to indirectly monitor brain activity in vivo through relative changes in the concentration of oxygenated and deoxygenated hemoglobin. One of the key features of fNIRS is its superior temporal resolution, with dense measurements over very short periods of time (100ms increments). Unfortunately, most statistical analysis approaches in the existing literature have not fully utilized the high temporal resolution of fNIRS. For example, many analysis procedures are based on linearity assumptions that only extract partial information, thereby neglecting the overall dynamic trends in fNIRS trajectories. The main goal of …

The Eyes Have It: Eye Tracking Data Visualizations Of Viewing Patterns Of Statistical Graphics, Trent Fawcett

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

As statistical graphics continue to expand to manage an ever growing amount of diverse data, a need to evaluate the effectiveness of graphics, both basic and complex, has arisen. Technological advancements have given a means to evaluate the effectiveness of graphs and graphical components through eye tracking systems. Eye tracking systems are likewise in need of software that will enable easy evaluation and exploration of data. The focus of this Master's Report is to evaluate the dual solution. An exploration of an eye tracker setup is made, with extensive consideration of testing statistical graphics providing a basis for continued research …

Sexual Assault And The Doctrine Of Chances, Ryan Wallentine

Undergraduate Honors Capstone Projects

Sexual assault is a crime whose offenders often commit multiple acts and its victims experience devastating effects. The doctrine of chances is a rule of evidence that may allow evidences of these past events or circumstances to be presented in a court case given they meet certain criteria. This research argues the probability of being innocently prosecuted for rape multiple times is sufficiently low to meet at least one of the criteria for the doctrine of chances to be used in a sexual assault case. Additional implications and related areas of research are included as well.

Bayesian Models For Repeated Measures Data Using Markov Chain Monte Carlo Methods, Yuanzhi Li

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Bayesian models for repeated measures data are fitted to three different data an analysis projects. Markov Chain Monte Carlo (MCMC) methodology is applied to each case with Gibbs sampling and/or an adaptive Metropolis-Hastings (MH) algorithm used to simulate the posterior distribution of parameters. We implement a Bayesian model with different variance-covariance structures to an audit fee data set. Block structures and linear models for variances are used to examine the linear trend and different behaviors before and after regulatory change during year 2004-2005. We proposed a Bayesian hierarchical model with latent teacher effects, to determine whether teacher professional development (PD) …

Classification Of Spacetimes With Symmetry, Jesse W. Hicks

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Spacetimes with symmetry play a critical role in Einstein's Theory of General Relativity. Missing from the literature is a correct, usable, and computer accessible classification of such spacetimes. This dissertation fills this gap; specifically, we

i) give a new and different approach to the classification of spacetimes with symmetry using modern methods and tools such as the Schmidt method and computer algebra systems, resulting in ninety-two spacetimes;

ii) create digital databases of the classification for easy access and use for researchers;

iii) create software to classify any spacetime metric with symmetry against the new database;

iv) compare results of our …

Definition And Construction Of Entropy Satisfying Multiresolution Analysis (Mra), Ju Y. Yi

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper considers some numerical schemes for the approximate solution of conservation laws and various wavelet methods are reviewed. This is followed by the construction of wavelet spaces based on a polynomial framework for the approximate solution of conservation laws. Construction of a representation of the approximate solution in terms of an entropy satisfying Multiresolution Analysis (MRA) is defined. Finally, a proof of convergence of the approximate solution of conservation laws using the characterization provided by the basis functions in the MRA will be given.

A Spatiotemporal Mountain Pine Beetle Outbreak Model Predicting Severity, Cycle Period, And Invasion Speed, Jacob P. Duncan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The mountain pine beetle (MPB, Dendroctonus ponderosae), a tree-killing bark beetle, has historically been part of the normal disturbance regime in lodgepole pine (Pinus contorta) forests. In recent years, warm winters and summers have allowed MPB populations to achieve synchronous emergence and successful attacks, resulting in widespread population outbreaks and resultant tree mortality across western North America. We develop an age-structured forest demographic model that incorporates temperature-dependent MPB infestations: the Susceptible-Infested-Juvenile (SIJ) model. Stability of equilibria is analyzed as a function of population growth rates, and indicates the existence of periodic outbreaks that intensify as growth rates …

To Dot Product Graphs And Beyond, Sean Bailey

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We will introduce three new vector representations of graphs. These representations are based on relationships between the vectors that are used. Specifically, we will examine scenarios where we ignore specific relationships, where we consider if information is missing, and where we look for when the information in common is not of a specified amount.

Hydra Effects In Stable Communities And Their Implications For System Dynamics, Michael H. Cortez, Peter A. Abrams

Mathematics and Statistics Faculty Publications

A hydra effect occurs when the mean density of a species increases in response to greater mortality. We show that, in a stable multispecies system, a species exhibits a hydra effect only if maintaining that species at its equilibrium density destabilizes the system. The stability of the original system is due to the responses of the hydra-effect species to changes in the other species’ densities. If that dynamical feedback is removed by fixing the density of the hydra-effect species, large changes in the community make-up (including the possibility of species extinction) can occur. This general result has several implications: (1) …

Yeast For Mathematicians - A Ferment Of Discovery, Matthew Lewis, James A. Powell

Mathematics and Statistics Faculty Publications

In addition to the memorization, algorithmic skills and vocabulary which are the default focus in many mathematics classrooms, professional mathematicians are expected to creatively apply known techniques, construct new mathematical approaches and communicate with and about mathematics. We propose that students can learn these professional, higher-level skills through Laboratory Experiences in Mathematical Biology which put students in the role of mathematics researcher creating mathematics to describe and understand biological data. Here we introduce a laboratory experience centered on yeast (Saccharomyces cerevisiae) growing in a small capped flask with a jar to collect carbon dioxide created during yeast growth …

Expression Profiles Of Mirna Subsets Distinguish Human Colorectal Carcinoma And Normal Colonic Mucosa, Daniel F. Pellatt, John R. Stevens, Roger K. Wolff, Lila E. Mullany, Jennifer S. Herrick, Wade Samowitz, Martha L. Slattery

Mathematics and Statistics Faculty Publications

OBJECTIVES: MicroRNAs (miRNAs) are small, non-protein-coding RNA molecules that are commonly dysregulated in colorectal tumors. The objective of this study was to identify smaller subsets of highly predictive miRNAs.

METHODS: Data come from population-based studies of colorectal cancer conducted in Utah and the Kaiser Permanente Medical Care Program. Tissue samples were available for 1,953 individuals, of which 1,894 had carcinoma tissue and 1,599 had normal mucosa available for statistical analysis. Agilent Human miRNA Microarray V.19.0 was used to generate miRNA expression profiles; validation of expression levels was carried out using quantitative PCR. We used random forest analysis and verified findings …

Approximating Optimal Release In A Deterministic Model For The Sterile Insect Technique, Sergio Ramirez, Luis F. Gordillo

Mathematics and Statistics Faculty Publications

Cost/benefit analyses are essential to support management planning and decisions before launching any pest control program. In particular, applications of the sterile insect technique (SIT) are often prevented by the projected economic burden associated with rearing processes. This has had a deep impact on the technique development and its use on insects with long larval periods, as often seen in beetles. Under the assumptions of long adult timespan and multiple mating, we show how to find approximate optimal sterile release policies that minimize costs. The theoretical framework proposed considers the release of insects by pulses and finds approximate optimal release …

An Introduction To Differential Geometry Through Computation, Mark E. Fels

Mathematics and Statistics Faculty Presentations

No abstract provided.

Sexual Assault And The Doctrine Of Chances In The Courtroom, Ryan Wallentine

Research on Capitol Hill

Sexual assault can have devastating and long-lasting effects on victims, but many assailants get away with their crime without being prosecuted.

The doctrine of chances is a rule of evidence allowing evidences of past crimes, wrongs, or acts to show it is unlikely a defendant would be repeatedly and innocently involved in similar, suspicious circumstances.

Given that about 63.3% of assailants are repeat offenders, the doctrine of chances could effectively be used in sexual assault cases.

The main objective is to determine a precise probabilistic threshold for allowing the use of the doctrine of chances in sexual assault cases such …

An Introduction To Differential Geometry Through Computation, Mark E. Fels

Textbooks

The outline of the book is as follows. Chapter 1 reviews some basic facts about smooth functions from IRⁿ to IR^m, as well as the basic facts about vector spaces, basis, and algebras. Chapter 2 introduces tangent vectors and vector fields in IRⁿ using the standard two approaches with curves and derivations. Chapter 3 reviews linear transformations and their matrix representation so that in Chapter 4 the push-forward as an abstract linear transformation can be defined and its matrix representation as the Jacobian can be derived. As an application, the change of variable formula for vector …

Population Density, Not Host Competence, Drives Patterns Of Disease In An Invaded Community, C. L. Searle

Mathematics and Statistics Faculty Presentations

Generalist parasites can strongly influence interactions between native and invasive species. Host competence can be used to predict how an invasive species will affect community disease dynamics; the addition of a highly competent, invasive host is predicted to increase disease. However, densities of invasive and native species can also influence the impacts of invasive species on community disease dynamics. We examined whether information on host competence alone could be used to accurately predict the effects of an invasive host on disease in native hosts. We first characterized the relative competence of an invasive species and a native host species to …

The Kretschmann Scalar, Charles G. Torre

How to... in 10 minutes or less

On a pseudo-Riemannian manifold with metric g, the "Kretschmann scalar" is a quadratic scalar invariant of the Riemann R tensor of g, defined by contracting all indices with g. In this worksheet we show how to calculate the Kretschmann scalar from a metric.

On The Construction Of Simply Connected Solvable Lie Groups, Mark E. Fels

Research Vignettes

This worksheet contains the implementation of Theorems 4.2, 5.4 and 5.7 in the paper On the Construction of Solvable Lie Groups. All the examples in the paper are demonstrated here, along with one in Section 6 that was too long to include in the article.

Differentialgeometry In Brno, Ian M. Anderson

Presentations

This page will provide files supporting Ian Anderson's presentations in Brno, December 2015. The files can be found and downloaded from "Additional Files", below.

The files include:

(1) DifferentialGeometryUSU.mla: This is the Maple Library Archive file which provides all the DifferentialGeometry functionality. Here are Installation Instructions.

(2) DifferentialGeometry.help : this is the latest version of the DifferentialGeometry documentation. Copy this file to the same directory used for DifferentialGeometryUSU.mla (from step (1)).

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.

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.

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 …

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 …

Managing The Spread Of Alfalfa Stem Nematodes Ditylenchus Dipsaci: The Relationship Between Crop Rotation And Pest Re-Emergence, Scott Jordan

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

Alfalfa is a critical cash/rotation crop in the western region of the United States, where it is common to find crops affected by the alfalfa stem nematode (Ditylenchus dipsaci). Understanding the spread dynamics associated with this pest would allow end-users to design better management programs and farming practices. This is of particular importance given that there are no nematicides available against alfalfa stem nematode and control strategies largely rely on crop rotation to non-host crops or by planting resistant varieties. I present a basic host-parasite model that describes the spread of the alfalfa stem nematode on alfalfa crops. With this …

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 …

The Riemann Curvature Tensor, Its Invariants, And Their Use In The Classification Of Spacetimes, Jesse Hicks

Presentations and Publications

The equivalence problem in general relativity is to determine whether two solutions of the Einstein field equations are isometric. Petrov has given a classification of metrics according to their isometry algebras. This talk discusses the use of the Petrov classification scheme, together with the use of scalar curvature invariants, to address the equivalence problem. These are the slides for a presentation at the Mathematics Association of America Spring 2015 conference at Brigham Young University.

Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos

Presentations and Publications

Rainich-type conditions giving a spacetime “geometrization” of matter fields in general relativity are reviewed and extended. Three types of matter are considered: perfect fluids, scalar fields, and elec- tromagnetic fields. Necessary and sufficient conditions on a spacetime metric for it to be part of a perfect fluid solution of the Einstein equa- tions are given. Formulas for constructing the fluid from the metric are obtained. All fluid results hold for any spacetime dimension. Ge- ometric conditions on a metric which are necessary and sufficient for it to define a solution of the Einstein-scalar field equations and for- mulas for constructing …