Physical Sciences and Mathematics Commons^™

Expression Of Wnt-Signaling Pathway Genes And Their Associations With Mirnas In Colorectal Cancer, Martha L. Slattery, Lila E. Mullany, Lori C. Sakoda, Wade S. Samowitz, Roger K. Wolff, John R. Stevens, Jennifer S. Herrick

Mathematics and Statistics Faculty Publications

The Wnt-signaling pathway functions in regulating cell growth and thus is involved in the carcinogenic process of several cancers, including colorectal cancer. We tested the hypothesis that multiple genes in this signaling pathway are dysregulated and that miRNAs are associated with these dysregulated genes. We used data from 217 colorectal cancer (CRC) cases to evaluate differences in Wnt-signaling pathway gene expression between paired CRC and normal mucosa and identify miRNAs that are associated with these genes. Gene expression data from RNA-Seq and miRNA expression data from Agilent Human miRNA Microarray V19.0 were analyzed. We focused on genes most strongly associated …

Introduction To The Usu Library Of Solutions To The Einstein Field Equations, Ian M. Anderson, Charles G. Torre

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This is a Maple worksheet providing an introduction to the USU Library of Solutions to the Einstein Field Equations. The library is part of the DifferentialGeometry software project and is a collection of symbolic data and metadata describing solutions to the Einstein equations.

Novel Statistical Models For Quantitative Shape-Gene Association Selection, Xiaotian Dai

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Other research reported that genetic mechanism plays a major role in the development process of biological shapes. The primary goal of this dissertation is to develop novel statistical models to investigate the quantitative relationships between biological shapes and genetic variants. However, these problems can be extremely challenging to traditional statistical models for a number of reasons: 1) the biological phenotypes cannot be effectively represented by single-valued traits, while traditional regression only handles one dependent variable; 2) in real-life genetic data, the number of candidate genes to be investigated is extremely large, and the signal-to-noise ratio of candidate genes is expected …

Real Simple Lie Algebras: Cartan Subalgebras, Cayley Transforms, And Classification, Hannah M. Lewis

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The differential geometry software package in Maple has the necessary tools and commands to automate the classification process for complex simple Lie algebras. The purpose of this thesis is to write the programs to complete the classification for real simple Lie algebras. This classification is difficult because the Cartan subalgebras are not all conjugate as they are in the complex case. For the process of the real classification, one must first identify a maximally noncompact Cartan subalgebra. The process of the Cayley transform is used to find this specific Cartan subalgebra. This Cartan subalgebra is used to find the simple …

Exact Approaches For Bias Detection And Avoidance With Small, Sparse, Or Correlated Categorical Data, Sarah E. Schwartz

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Every day, traditional statistical methodology are used world wide to study a variety of topics and provides insight regarding countless subjects. Each technique is based on a distinct set of assumptions to ensure valid results. Additionally, many statistical approaches rely on large sample behavior and may collapse or degenerate in the presence of small, spare, or correlated data. This dissertation details several advancements to detect these conditions, avoid their consequences, and analyze data in a different way to yield trustworthy results.

One of the most commonly used modeling techniques for outcomes with only two possible categorical values (eg. live/die, pass/fail, …

Extracting And Visualizing Data From Mobile And Static Eye Trackers In R And Matlab, Chunyang Li

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Eye tracking is the process of measuring where people are looking at with an eye tracker device. Eye tracking has been used in many scientific fields, such as education, usability research, sports, psychology, and marketing. Eye tracking data are often obtained from a static eye tracker or are manually extracted from a mobile eye tracker. Visualization usually plays an important role in the analysis of eye tracking data. So far, there existed no software package that contains a whole collection of eye tracking data processing and visualization tools. In this dissertation, we review the eye tracking technology, the eye tracking …

Extensions And Improvements To Random Forests For Classification, Anna Quach

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The motivation of my dissertation is to improve two weaknesses of Random Forests. One, the failure to detect genetic interactions between two single nucleotide polymorphisms (SNPs) in higher dimensions when the interacting SNPs both have weak main effects and two, the difficulty of interpretation in comparison to parametric methods such as logistic regression, linear discriminant analysis, and linear regression.

We focus on detecting pairwise SNP interactions in genome case-control studies. We determine the best parameter settings to optimize the detection of SNP interactions and improve the efficiency of Random Forests and present an efficient filtering method. The filtering method is …

A Universal Genus-Two Curve From Siegel Modular Forms, Andreas Malmendier, Tony Shaska

Mathematics and Statistics Faculty Publications

Let p be any point in the moduli space of genus-two curves M₂ and K its field of moduli. We provide a universal equation of a genus-two curve C_α,β defined over K(α, β), corresponding to p, where α and β satisfy a quadratic α² + bβ² = c such that b and c are given in terms of ratios of Siegel modular forms. The curve C_α,β is defined over the field of moduli K if and only if the quadratic has a K-rational point (α, β). We discover some interesting …

Stability Of Equilibria In Quantitative Genetic Models Based On Modified-Gradient Systems, Benjamin J. Ridenhour, Jerry R. Ridenhour

Mathematics and Statistics Faculty Publications

Motivated by questions in biology, we investigate the stability of equilibria of the dynamical system x′ = P(t)∇f(x) which arise as critical points of f, under the assumption that P(t) is positive semi-definite. It is shown that the condition ∫^∞λ₁(P(t)) dt = ∞, where λ₁(P(t)) is the smallest eigenvalue of P(t), plays a key role in guaranteeing uniform asymptotic stability and in providing information on the basis of attraction of those equilibria.

Apathy And Concern Over The Future Habitability Of Earth: An Introductory College Assignment Of Forecasting Co2 In The Earth’S Atmosphere, Benjamin J. Burger

Journal on Empowering Teaching Excellence

Non-science, first year regional undergraduate students from rural Utah communities participated in an online introductory geology course and were asked to forecast the rise of CO₂ in the Earth’s atmosphere. The majority of students predicted catastrophic rise to 5,000-ppm sometime over the next 3,100 years, resulting in an atmosphere nearly uninhabitable to human life. However, the level of concern the students exhibited in their answers was not directly proportional with their timing in their forecasted rise of CO₂. This study showcases the importance of presenting students with actual data and using data to develop student forecasted models. …

A Bivariate Hypothesis Testing Approach For Mapping The Trait-Influential Gene, Garrett Saunders, Matthew D. Meng, John R. Stevens

Mathematics and Statistics Faculty Publications

The linkage disequilibrium (LD) based quantitative trait loci (QTL) model involves two indispensable hypothesis tests: the test of whether or not a QTL exists, and the test of the LD strength between the QTaL and the observed marker. The advantage of this two-test framework is to test whether there is an influential QTL around the observed marker instead of just having a QTL by random chance. There exist unsolved, open statistical questions about the inaccurate asymptotic distributions of the test statistics. We propose a bivariate null kernel (BNK) hypothesis testing method, which characterizes the joint distribution of the two test …

Collaborative Research: Mathematics Of Doing, Understanding, Learning And Educating For Secondary Schools, Brynja R. Kohler

Funded Research Records

No abstract provided.

Frg: Collaborative Research: Homotopy Renormalization Of Topological Field Theories, Nathan Geer

Funded Research Records

No abstract provided.

Efficiently Representing The Integer Factorization Problem Using Binary Decision Diagrams, David Skidmore

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

Let p be a prime positive integer and let α be a positive integer greater than 1. A method is given to reduce the problem of finding a nontrivial factorization of α to the problem of finding a solution to a system of modulo p polynomial congruences where each variable in the system is constrained to the set {0,...,p − 1}. In the case that p = 2 it is shown that each polynomial in the system can be represented by an ordered binary decision diagram with size less than 20.25log₂(α)³ + 16.5log₂(α)² + …

A Comparison Of Five Statistical Methods For Predicting Stream Temperature Across Stream Networks, Maike F. Holthuijzen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The health of freshwater aquatic systems, particularly stream networks, is mainly influenced by water temperature, which controls biological processes and influences species distributions and aquatic biodiversity. Thermal regimes of rivers are likely to change in the future, due to climate change and other anthropogenic impacts, and our ability to predict stream temperatures will be critical in understanding distribution shifts of aquatic biota. Spatial statistical network models take into account spatial relationships but have drawbacks, including high computation times and data pre-processing requirements. Machine learning techniques and generalized additive models (GAM) are promising alternatives to the SSN model. Two machine learning …

Physiological Health Parameters Among College Students To Promote Chronic Disease Prevention And Health Promotion, David R. Black, Daniel C. Coster, Samantha R. Paige

Mathematics and Statistics Faculty Publications

This study aimed to provide physiologic health risk parameters by gender and age among college students enrolled in a U.S. Midwestern University to promote chronic disease prevention and ameliorate health. A total of 2615 college students between 18 and 25 years old were recruited annually using a series of cross-sectional designs during the spring semester over an 8-year period. Physiologic parameters measured included body mass index (BMI), percentage body fat (%BF), blood serum cholesterol (BSC), and systolic (SBP) and diastolic (DBP) blood pressure. These measures were compared to data from NHANES to identify differences in physiologic parameters among 18-25 year …

A Stochastic Model For Water-Vegetation Systems And The Effect Of Decreasing Precipitation On Semi-Arid Environments, Shannon A. Dixon

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Current climate change trends are affecting the magnitude and recurrence of extreme weather events. In particular, several semi-arid regions around the planet are confronting more intense and prolonged lack of precipitation, slowly transforming these regions into deserts. Many mathematical models have been developed for purposes of analyzing vegetation-water interactions, particularly in semi-arid landscapes. Most models are based on the average behavior of the system as a whole, and how it is influenced by external changes. These models may be termed "macro-scale" models. Other models have concerned themselves with the interactions between individuals, in this case the interactions between individual plants …

An Exploratory Study Of Fifth-Grade Students’ Reasoning About The Relationship Between Fractions And Decimals When Using Number Line-Based Virtual Manipulatives, Scott Smith

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Understanding the relationship between fractions and decimals is an important step in developing an overall understanding of rational numbers. Research has demonstrated the feasibility of technology in the form of virtual manipulatives for facilitating students’ meaningful understanding of rational number concepts. This exploratory dissertation study was conducted for the two closely related purposes: first, to investigate a sample of fifth-grade students’ reasoning regarding the relationship between fractions and decimals for fractions with terminating decimal representations while using virtual manipulative incorporating parallel number lines; second, to investigate the affordances of the virtual manipulatives for supporting the students’ reasoning about the decimal-fraction …

Combinatorial Games On Graphs, Trevor K. Williams

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Combinatorial Games are intriguing and have a tendency to engross students and lead them into a serious study of mathematics. The engaging nature of games is the basis for this thesis. Two combinatorial games and some educational tools are presented which were developed by the author in the pursuit of the solution of these games.

A Comparison Of Multiple Testing Adjustment Methods With Block-Correlation Positively-Dependent Tests, John R. Stevens, Abdullah Al Masud, Anvar Suyundikov

Mathematics and Statistics Faculty Publications

In high dimensional data analysis (such as gene expression, spatial epidemiology, or brain imaging studies), we often test thousands or more hypotheses simultaneously. As the number of tests increases, the chance of observing some statistically significant tests is very high even when all null hypotheses are true. Consequently, we could reach incorrect conclusions regarding the hypotheses. Researchers frequently use multiplicity adjustment methods to control type I error rates—primarily the family-wise error rate (FWER) or the false discovery rate (FDR)—while still desiring high statistical power. In practice, such studies may have dependent test statistics (or p-values) as tests can be dependent …

An Adaptive Threshold Determination Method Of Feature Screening For Genomic Selection, Matthew D. Meng, Gang Wang, Aaron R. Brough

Mathematics and Statistics Faculty Publications

Background
Although the dimension of the entire genome can be extremely large, only a parsimonious set of influential SNPs are correlated with a particular complex trait and are important to the prediction of the trait. Efficiently and accurately selecting these influential SNPs from millions of candidates is in high demand, but poses challenges. We propose a backward elimination iterative distance correlation (BE-IDC) procedure to select the smallest subset of SNPs that guarantees sufficient prediction accuracy, while also solving the unclear threshold issue for traditional feature screening approaches.

Results
Verified through six simulations, the adaptive threshold estimated by the BE-IDC performed …

Regime Switching In Cointegrated Time Series, Bradley David Zynda Ii

Undergraduate Honors Capstone Projects

Volatile commodities and markets can often be difficult to model and forecast given significant breaks in trends through time. To account such breaks, regime switching methods allow for models to accommodate abrupt changes in behavior of the data. However, the difficulty often arises in beginning the process of choosing a model and its associated parameters with which to represent the data and the objects of interest. To improve model selection for these volatile markets, this research examines time series with regime switching components and argues that a synthesis of vector error correction models with regime switching models with ameliorate financial …

Mass Action In Two-Sex Population Models: Encounters, Mating Encounters And The Associated Numerical Correction, Katherine Snyder, Brynja R. Kohler, Luis F. Gordillo

Mathematics and Statistics Faculty Publications

Ideal gas models are a paradigm used in Biology for the phenomenological modelling of encounters between individuals of different types. These models have been used to approximate encounter rates given densities, velocities and distance within which an encounter certainly occurs. When using mass action in two-sex populations, however, it is necessary to recognize the difference between encounters and mating encounters. While the former refers in general to the (possibly simultaneous) collisions between particles, the latter represents pair formation that will produce offspring. The classical formulation of the law of mass action does not account this difference. In this short paper, …

Analytic Approximation Of Invasion Wave Amplitude Predicts Severity Of Insect Outbreaks, Antje R. H. Graul, James A. Powell

Mathematics and Statistics Faculty Publications

Outbreaks of phytophagous forest insects are largely driven by host demographics and spatial effects of dispersal. We develop a structured integrodifference equation (IDE) outbreak model that tracks the demographics of sedentary hosts under insect infestation pressure. The model is appropriate for a spectrum of pests attacking the later age classes of long-lived hosts, including mountain pine beetle (MPB), spruce budworm, and spruce beetle, which, among them are responsible for more forest damage than fire. The model generates a train of periodic waves of infestation. We approximate the IDE with a partial differential equation and search for traveling wave solutions. The …

A Variant Of Clark's Theorem And Its Applications For Nonsmooth Functionals Without The Palais-Smale Condition, Shaowei Chen, Zhaoli Liu, Zhi-Qiang Wang

Mathematics and Statistics Faculty Publications

By introducing a new notion of the genus with respect to the weak topology in Banach spaces, we prove a variant of Clark's theorem for nonsmooth functionals without the Palais-Smale condition. In this new theorem, the Palais-Smale condition is replaced by a weaker assumption, and a sequence of critical points converging weakly to zero with nonpositive energy is obtained. As applications, we obtain infinitely many solutions for a quasi-linear elliptic equation which is very degenerate and lacks strict convexity, and we also prove the existence of infinitely many homoclinic orbits for a second-order Hamiltonian system for which the functional is …

Predator-Prey Coevolution Drives Productivity-Richness Relationships In Planktonic Systems, Zhichao Pu, Michael H. Cortez, Lin Jiang

Mathematics and Statistics Faculty Publications

The relationship between environmental productivity and species richness often varies among empirical studies, and despite much research, simple explanations for this phenomenon remain elusive. We investigated how phytoplankton and zooplankton coevolution shapes productivity-richness relationships in both phytoplankton and zooplankton, using a simple nutrient-phytoplankton-zooplankton model that incorporates size-dependent metabolic rates summarized from empirical studies. The model allowed comparisons of evolved species richness across productivity levels and at different evolutionary times. Our results show that disruptive selection leads to evolutionary branching of phytoplankton and zooplankton. Both the time required for evolutionary branching and the number of evolved species in phytoplankton and zooplankton …

Perihelion Precession In The General Theory Of Relativity, Charles G. Torre

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This is a relatively quick and informal sketch of a demonstration that general relativistic corrections to the bound Kepler orbits introduce a perihelion precession. Any decent textbook on the general theory of relativity will derive this result. My analysis aligns with that found in the good old text "Introduction to General Relativity", by Adler, Bazin and Schiffer.