Mathematics Commons^™

Parametric And Non-Parametric Regression Models With Applications To Climate Change, Osita Eluemuno Onyejekwe

Theses and Dissertations

In this dissertation we have studied the climate factors that contribute to climate change using univariate and multivariate parametric methods as well as nonparametric models. In this study, we have three major contributions. First, the extent of mountain glaciers around the globe and their responses to climate factors are investigated using multivariate methods and we have proposed a predictive model to estimate the mountain glacier response to climate factors. Second, we have addressed the important problem of bandwidth selection in presence of correlated noise in nonparametric regression analysis. We have proposed a denoising method based on an ensemble bandwidth optimization …

On Logconcavity Of Multivariate Discrete Distributions, Majed Ghazi Alharbi

Theses and Dissertations

The contribution of this dissertation to the literature is twofold. First, we use a geometric perspective to present all possible subdivisions of R³ into tetrahedra with disjoint interiors and adopt a combinatorial approach to obtain a special subdivision of Rⁿ into simplices with disjoint interiors, where two simplices are called neighbors if they share a common facet. We then use the neighborhood relationship of the simplices in each subdivision to fully describe the sufficient conditions for the strong unimodality/logconcavity of the trivariate discrete distributions and further extend these results to present a new sufcient condition for the strong unimodality/logconcavity of …

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 …

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 …

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 …

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, …

Tangled Up: Women’S Experiences In Mathematics, Lori Loftin

Honors College

This thesis is a bridge between two disciplines: Women's, Gender, and Sexuality Studies, and Mathematics. The first portion of the work synthesizes both theory and previously done studies to describe the state of women in mathematics as a whole, as well as historicizing the role of women in mathematics. Obstacles to the full and equal participation of women in mathematics are examined through a feminist lens. The second part of the thesis is a feminist biography crafted from an interview with a professor of mathematics, Dr. Erica Flapan. This provides information about her personal experiences as a woman in mathematics …

Do It Today Or Do It Tomorrow: Empirical Non-Exponential Discounting Explained By Symmetry And Fuzzy Ideas, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich, Thongchai Dumrongpokaphan

Departmental Technical Reports (CS)

At first glance, it seems to make sense to conclude that when a 1 dollar reward tomorrow is equivalent to a D < 1 dollar reward today, the day-after-tomorrow's 1 dollar reward would be equivalent to D * D = D² dollars today, and, in general, a reward after time t is equivalent to D(t) = D^t dollars today. This exponential discounting function D(t) was indeed proposed by the economists, but it does not reflect the actual human behavior. Indeed, according to this formula, the effect of distant future events is negligible, and thus, it would be reasonable for a person to take on huge loans or get engaged in unhealthy behavior even when the long-term consequences …

Average Cayley Genus For Groups With Two Generators Of Order Greater Than Two, Dawn Sturgeon

UNLV Theses, Dissertations, Professional Papers, and Capstones

Determining the orientable surfaces on which a particular graph may be imbedded is a basic problem in the area of topological graph theory. We look at groups modeled by Cayley graphs. Imbedding Cayley graphs with symmetry is done using Cayley maps. It is of interest to find the average Cayley genus for a particular group and generating set for the group. We consider the group known as the generalized quaternions with generating set ∆, where ∆ contains two generators with order greater than two. We find a formula for the average Cayley genus of the generalized quaternions. Moreover, we determine …

Investigation Of Finite Groups Through Progenitors, Charles Baccari

Electronic Theses, Projects, and Dissertations

The goal of this presentation is to find original symmetric presentations of finite groups. It is frequently the case, that progenitors factored by appropriate relations produce simple and even sporadic groups as homomorphic images. We have discovered two of the twenty-six sporadic simple groups namely, M₁₂, J₁ and the Lie type group Suz(8). In addition several linear and classical groups will also be presented. We will present several progenitors including: 2^*12: 2² x (3 : 2), 2^*11: PSL₂(11), 2^*5: (5 : 4) which have produced the homomorphic images: …

Construction Of Finite Group, Michelle Soyeong Yeo

Electronic Theses, Projects, and Dissertations

The main goal of this project is to present my investigation of finite images of the progenitor 2^(*n) : N for various N and several values of n. We construct each image by using the technique of double coset enumeration and give a proof of the isomorphism type of the image. We obtain the group 7^2: D_6 as a homomorphic image of the progenitor 2^(*14) : D_14, we obtain the group 2^4 : (5 : 4) as a homomorphic image of the progenitor 2^(*5) : (5 : 4), we obtain the group (10 x10) : ((3 x 4) : 2) …

Neutrosophic Hough Transform, Florentin Smarandache, Umit Budak, Yanhui Guo, Abdulkadir Sengur

Branch Mathematics and Statistics Faculty and Staff Publications

Hough transform (HT) is a useful tool for both pattern recognition and image processing communities. In the view of pattern recognition, it can extract unique features for description of various shapes, such as lines, circles, ellipses, and etc. In the view of image processing, a dozen of applications can be handled with HT, such as lane detection for autonomous cars, blood cell detection in microscope images, and so on. As HT is a straight forward shape detector in a given image, its shape detection ability is low in noisy images. To alleviate its weakness on noisy images and improve its …

An Introduction To Lie Algebra, Amanda Renee Talley

Electronic Theses, Projects, and Dissertations

An (associative) algebra is a vector space over a field equipped with an associative, bilinear multiplication. By use of a new bilinear operation, any associative algebra morphs into a nonassociative abstract Lie algebra, where the new product in terms of the given associative product, is the commutator. The crux of this paper is to investigate the commutator as it pertains to the general linear group and its subalgebras. This forces us to examine properties of ring theory under the lens of linear algebra, as we determine subalgebras, ideals, and solvability as decomposed into an extension of abelian ideals, and nilpotency, …

Making Models With Bayes, Pilar Olid

Electronic Theses, Projects, and Dissertations

Bayesian statistics is an important approach to modern statistical analyses. It allows us to use our prior knowledge of the unknown parameters to construct a model for our data set. The foundation of Bayesian analysis is Bayes' Rule, which in its proportional form indicates that the posterior is proportional to the prior times the likelihood. We will demonstrate how we can apply Bayesian statistical techniques to fit a linear regression model and a hierarchical linear regression model to a data set. We will show how to apply different distributions to Bayesian analyses and how the use of a prior affects …

Statistical Linear Mixed Models For Evaluation Of Training Program In Hand Surgery Chief Residents, Zoe Michelle Ross

Honors Theses

Resident clinics (RCs) are intended to catalyze the achievement of educational milestones through progressively autonomous patient care. However, few studies quantify their effect on competency-based surgical education, and no previous publications focus on hand surgery RCs. This study aims to use statistical theories and knowledge of descriptive statistics and inference statistics, such as confidence intervals, two sample t-tests, correlation and association tests, as well as statistical model building such as analysis of variance with random effects and mixed linear models. We hypothesize that the higher a resident’s training years, the higher the autonomy score (quality of surgery) will be. We …

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 …

Mapping Class Group Orbits Of Curves With Self-Intersections, Patricia Cahn, Federica Fanoni, Bram Petri

Mathematics and Statistics: Faculty Publications

We study mapping class group orbits of homotopy and isotopy classes of curves with self-intersections. We exhibit the asymptotics of the number of such orbits of curves with a bounded number of self-intersections, as the complexity of the surface tends to infinity.

We also consider the minimal genus of a subsurface that contains the curve. We determine the asymptotic number of orbits of curves with a fixed minimal genus and a bounded self-intersection number, as the complexity of the surface tends to infinity.

As a corollary of our methods, we obtain that most curves that are homotopic are also isotopic. …

Infinite-Dimensional Measure Spaces And Frame Analysis, Palle Jorgensen, Myung-Sin Song

SIUE Faculty Research, Scholarship, and Creative Activity

We study certain infinite-dimensional probability measures in connection with frame analysis. Earlier work on frame-measures has so far focused on the case of finite-dimensional frames. We point out that there are good reasons for a sharp distinction between stochastic analysis involving frames in finite vs. infinite dimensions. For the case of infinite-dimensional Hilbert space ℋ, we study three cases of measures. We first show that, for ℋ infinite dimensional, one must resort to infinite dimensional measure spaces which properly contain ℋ. The three cases we consider are: (i) Gaussian frame measures, (ii) Markov path-space measures, and (iii) determinantal measures.

Mode-Sum Prescription For Vacuum Polarization In Black Hole Spacetimes In Even Dimensions, Peter Taylor, Cormac Doran

Articles

We present a mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically symmetric black hole spacetimes in even dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher even dimensions, building upon a previous scheme we developed for odd dimensions. Things are more complicated here since the even-dimensional propagator possesses logarithmic singularities which must be regularized. However, in spite of this complication, the regularization parameters can be computed in closed form in arbitrary even dimensions and for arbitrary metric function f(r). As an explicit example of our method, we …

Mode-Sum Prescription For Vacuum Polarization In Black Hole Spacetimes In Even Dimensions, Peter Taylor, Cormac Breen

Articles

We present a mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically symmetric black hole spacetimes in even dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher even dimensions, building upon a previous scheme we developed for odd dimensions. Things are more complicated here since the even-dimensional propagator possesses logarithmic singularities which must be regularized. However, in spite of this complication, the regularization parameters can be computed in closed form in arbitrary even dimensions and for arbitrary metric function f(r). As an explicit example of our method, we …