Physical Sciences and Mathematics Commons^™

Diet And Lifetyle Factors Associated With Mirna Expression In Colorectal Tissue, Martha L. Slattery, Jennifer S. Herrick, Lila E. Mullany, John R. Stevens, Roger K. Wolff

Mathematics and Statistics Faculty Publications

MicroRNAs (miRNAs) are small non-protein-coding RNA molecules that regulate gene expression. Diet and lifestyle factors have been hypothesized to be involved in the regulation of miRNA expression. In this study it was hypothesized that diet and lifestyle factors are associated with miRNA expression. Data from 1,447 cases of colorectal cancer to evaluate 34 diet and lifestyle variables using miRNA expression in normal colorectal mucosa as well as for differential expression between paired carcinoma and normal tissue were used. miRNA data were obtained using an Agilent platform. Multiple comparisons were adjusted for using the false discovery rate q-value. There were 250 …

Foundations Of Wave Phenomena, Charles G. Torre

Charles G. Torre

This is an undergraduate text on the mathematical foundations of wave phenomena. Version 8.2.

Managing The Spread Of Alfalfa Stem Nematodes (Ditylenchus Dipsaci): The Relationship Between Crop Rotation Periods And Pest Re-Emergence, S. Jordan, Claudia Nischwitz, R. Ramirez, Luis F. Gordillo

Mathematics and Statistics Faculty Publications

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 growers to design better management programs and farming practices. This understanding is of particular importance given that there are no nematicides available against alfalfa stem nematodes and control strategies largely rely on crop rotation to non-host crops or by planting resistant varieties of alfalfa. In this paper we present a basic host-parasite model that describes the spread of the …

Laboratory Experiences In Mathematical Biology For Post-Secondary Mathematics Students, Matthew Lewis

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In addition to the memorization, algorithmic skills and vocabulary which is 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 (LEMBs) which put students in the role of mathematics researcher creating mathematics to describe and understand biological data. LEMBs are constructed so they require no specialized equipment and can easily be run in the context of a college math class. Students collect data and develop mathematical …

On The Geodesic Centers Of Polygonal Domains, Haitao Wang

Computer Science Faculty and Staff Publications

In this paper, we study the problem of computing Euclidean geodesic centers of a polygonal domain P of n vertices. We give a necessary condition for a point being a geodesic center. We show that there is at most one geodesic center among all points of P that have topologically-equivalent shortest path maps. This implies that the total number of geodesic centers is bounded by the size of the shortest path map equivalence decomposition of P, which is known to be O(n^{10}). One key observation is a pi-range property on shortest path lengths when points are moving. With these observations, …

Modeling Zombie Outbreaks: A Problem-Based Approach To Improving Mathematics One Brain At A Time, Matthew Lewis, James A. Powell

Mathematics and Statistics Faculty Publications

A great deal of educational literature has focused on problem-based learning (PBL) in mathematics at the primary and secondary level, but arguably there is an even greater need for PBL in college math courses. We present a project centered around the Humans vs. Zombies moderated tag game played on the USU campus. We discuss the project in the context of an undergraduate differential equations course and discuss how the project is launched. We highlight examples of students mathematical models along with their verbal and written responses as well as discussing assessment and student learning. Results are discussed in the context …

Ε-Kernel Coresets For Stochastic Points, Haitao Wang, Lingxiao Huang, Jian Li, Jeff Mark Phillips

Computer Science Faculty and Staff Publications

With the dramatic growth in the number of application domains that generate probabilistic, noisy and uncertain data, there has been an increasing interest in designing algorithms for geometric or combinatorial optimization problems over such data. In this paper, we initiate the study of constructing epsilon-kernel coresets for uncertain points. We consider uncertainty in the existential model where each point's location is fixed but only occurs with a certain probability, and the locational model where each point has a probability distribution describing its location. An epsilon-kernel coreset approximates the width of a point set in any direction. We consider approximating the …

How The Magnitude Of Prey Genetic Variation Alters Predator-Prey Eco-Evolutionary Dynamics, Michael H. Cortez

Mathematics and Statistics Faculty Publications

Evolution can alter the stability and dynamics of ecological communities; for example, prey evolution can drive cyclic dynamics in predator-prey systems that are not possible in the absence of evolution. However, it is unclear how the magnitude of additive genetic variation in the evolving species mediates those effects. In this study, I explore how the magnitude of prey additive genetic variation determines what effects prey evolution has on the dynamics and stability of predator-prey systems. I use linear stability analysis to decompose the stability of a general eco-evolutionary predator-prey model into components representing the stabilities of the ecological and evolutionary …

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 …

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) …

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 …

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) …

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 …

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.

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 …

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.

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.

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 …

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

Mathematics and Statistics Faculty Presentations

No abstract provided.

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 …

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.

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 …