Mathematics Commons^™

(Knight)3: A Graphical Perspective Of The Knight's Tour On A Multi-Layered Chess Board, Frederick Scott Neilan

Honors Program Theses and Projects

The Knight’s Tour is an interesting question related to the game of chess. In chess, the Knight must move two squares in one direction (forward, backward, left, right) followed by one square in a perpendicular direction. The question of the Knight’s Tour follows: Does there exist a tour for the Knight that encompasses every single square on the chess board without revisiting any squares? The existence of Knight’s Tours has been proven for the standard 8x8 chess board. Furthermore, the Knight’s Tour can also exist on boards with different sizes and shapes. There has been a lot of research into …

Data Driven Sample Generator Model With Application To Classification, Alvaro Emilio Ulloa Cerna

Mathematics & Statistics ETDs

Despite the rapidly growing interest, progress in the study of relations between physiological abnormalities and mental disorders is hampered by complexity of the human brain and high costs of data collection. The complexity can be captured by machine learning approaches, but they still may require significant amounts of data. In this thesis, we seek to mitigate the latter challenge by developing a data driven sample generator model for the generation of synthetic realistic training data. Our method greatly improves generalization in classification of schizophrenia patients and healthy controls from their structural magnetic resonance images. A feed forward neural network trained …

Model Behavior: The Mathematics Behind Three-Dimensional Modeling And Animation, Kathryn Duff, Vivian Cyrus

Celebration of Student Scholarship Poster Sessions Archive

No abstract provided.

Self-Monitoring Practices, Attitudes, And Needs Of Individuals With Bipolar Disorder: Implications For The Design Of Technologies To Manage Mental Health, Elizabeth L. Murnane, Dan Cosley, Pamara Chang, Shion Guha, Ellen Frank, Geri K. Gay, Mark Matthews

Mathematics, Statistics and Computer Science Faculty Research and Publications

Objective To understand self-monitoring strategies used independently of clinical treatment by individuals with bipolar disorder (BD), in order to recommend technology design principles to support mental health management.

Materials and Methods Participants with BD (N = 552) were recruited through the Depression and Bipolar Support Alliance, the International Bipolar Foundation, and WeSearchTogether.org to complete a survey of closed- and open-ended questions. In this study, we focus on descriptive results and qualitative analyses.

Results Individuals reported primarily self-monitoring items related to their bipolar disorder (mood, sleep, finances, exercise, and social interactions), with an increasing trend towards the use of digital …

Spline Estimation Of Principal Curves, Marcel Andreas Walther

Theses and Dissertations

Finding low-dimensional approximations to high-dimensional data is one of

the most important topics in statistics, which has also multiple applications

in economics, engineering and science. One suggestion in the literature ,based

on kernel smoothing, is a non-linear generalization of principal components.

This kernel-based approach comes with several complications. Therefore the

purpose of this thesis is to provide an alternative based on spline smoothing

which produces more reliable results.

Resonance Varieties Of Pure Braid-Like Groups, Jared Able

Honors Theses

No abstract provided.

Takens Theorem With Singular Spectrum Analysis Applied To Noisy Time Series, Thomas K. Torku

Electronic Theses and Dissertations

The evolution of big data has led to financial time series becoming increasingly complex, noisy, non-stationary and nonlinear. Takens theorem can be used to analyze and forecast nonlinear time series, but even small amounts of noise can hopelessly corrupt a Takens approach. In contrast, Singular Spectrum Analysis is an excellent tool for both forecasting and noise reduction. Fortunately, it is possible to combine the Takens approach with Singular Spectrum analysis (SSA), and in fact, estimation of key parameters in Takens theorem is performed with Singular Spectrum Analysis. In this thesis, we combine the denoising abilities of SSA with the Takens …

Global Supply Sets In Graphs, Christian G. Moore

Electronic Theses and Dissertations

For a graph G=(V,E), a set S⊆V is a global supply set if every vertex v∈V\S has at least one neighbor, say u, in S such that u has at least as many neighbors in S as v has in V \S. The global supply number is the minimum cardinality of a global supply set, denoted γgs (G). We introduce global supply sets and determine the global supply number for selected families of graphs. Also, we give bounds on the global supply number for general graphs, trees, and grid graphs.

Modeling Consequences Of Reduced Vaccination Levels On The Spread Of Measles, Guillermo Ortiz

Honors Program Theses and Projects

Introduction: In this thesis we propose a mathematical model for the spread of measles in a closed population. In section 1 we offer a motivation for the project, describe the measles virus as well as its history in the U.S., and provide a brief summary of three epidemiological models from the literature. In section 2.1 we introduce some probabilistic tools used in our model. Section 2.2.1 outlines our stochastic model used for the spread of measles in a population, which is refined in section 2.2.2 to include health interventions from the CDC. We conclude the thesis by presenting in section …

Polynomials With No Zeros On A Face Of The Bidisk, Jeffrey S. Geronimo, Plamen Iliev, Greg Knese

Mathematics Faculty Publications

We present a Hilbert space geometric approach to the problem of characterizing the positive bivariate trigonometric polynomials that can be represented as the square of a two variable polynomial possessing a certain stability requirement, namely no zeros on a face of the bidisk. Two different characterizations are given using a Hilbert space structure naturally associated to the trigonometric polynomial; one is in terms of a certain orthogonal decomposition the Hilbert space must possess called the “split-shift orthogonality condition” and another is an operator theoretic or matrix condition closely related to an earlier characterization due to the first two authors. This …

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) …

New Flexible Regression Models Generated By Gamma Random Variables With Censored Data, Elizabeth M. Hashimoto, Gauss M. Cordeiro, Edwin M. M. Ortega, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We propose and study a new log-gamma Weibull regression model. We obtain explicit expressions for the raw and incomplete moments, quantile and generating functions and mean deviations of the log-gamma Weibull distribution. We demonstrate that the new regression model can be applied to censored data since it represents a parametric family of models which includes as sub-models several widely-known regression models and therefore can be used more effectively in the analysis of survival data. We obtain the maximum likelihood estimates of the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking …

Distance Density Analysis And Multivariate Mode Detection, Immanuel Torben Lampe

Theses and Dissertations

Finding the mode of the distribution for a sample of points is a very interesting task. In one dimensional problems this can easily be done by estimating the kernel density. Unfortunately this method does not work well in higher dimensions.

This thesis presents a new approach to solve this problem. A method is presented which finds the mode by analyzing the distribution of the distances between each point and the rest of the sample. The idea is that if the i-th sample point, x_i, is in a high-density region, most of these distances should be small, whereas if x_i is …

Homological Properties Of Determinantal Arrangements, Arnold H. Yim

Open Access Dissertations

We study a certain family of hypersurface arrangements known as determinantal arrangements. Determinantal arrangements are a union of varieties defined by minors of a matrix of indeterminates. In particular, we investigate determinantal arrangements using the 2-minors of a 2 × n generic matrix (which can be thought of as natural extensions of braid arrangements), and prove certain statements about their freeness. We also study the topology of these objects. We construct a fibration for the complement of free determinantal arrangements, and use this fibration to prove statements about their homotopy groups. Furthermore, we show that the Poincaré polynomial of the …

Lie Symmetry To Nonlinear Oscillator Systems And Applications, Xiaoyan Li

Theses and Dissertations

In this paper, we apply the theory of Lie symmetry to study a generalized second-order nonlinear differential equation, which includes several physical nonlinear oscillators such as force-free Helmholtz oscillator, force-free Duffing and Duffing-van der Pol oscillators, modified Emden-type equation and its hierarchy etc, and investigate the dynamical properties of this rather general equation. We identify and classify several new integrable cases for arbitrary values of exponents, which determine the tangent vector as well as the infinitesimal generator. Using the Lie point symmetry, we find the useful infinitesimal generators and canonical coordinates, and obtain the first integrals of the second-order nonlinear …

On Hypergroups Of Order At Most 6, Jordy C. Lopez

Theses and Dissertations

This thesis surveys recent results on hypergroups as defined by Frédéric Marty in [3] and [4] and their relation to association schemes as presented in [5]. We show that every association scheme is a hypergroup. Then, we compile a few general results on hypergroups needed for our investigation of hypergroups with three, four and six elements. From [1] and [7], we give examples of hypergroups that do not come from finite schemes and from no scheme at all. Our main result occurs when considering hypergroups S with six elements that have a non-normal closed subset T of order 2 with …

Opinion Formation About Childhood Immunization And Disease Spread On Networks, Shan Shan Zhao

Theses and Dissertations

People are physically and socially connected with each other. Those connections between people represent two, probably overlapping, networks: biological networks, through which physical contacts occur, or social network, through which information diffuse. In my thesis research, I am trying to answer that question in the context of pediatric disease spread on the biological network between households as well as within them and its relationship with information sharing on the social network of households (parents in that case) via "Information Cascades." I mainly focus on the Erdos-Renyi network model. In particular, I use two different but overlapping Erdos-Renyi networks for the …

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 …

Adjusted Empirical Likelihood Method For Comparison Of Treatment Effects In Linear Model Setting, Xi Kang

Theses, Dissertations and Culminating Projects

Empirical likelihood is a nonparametric method of statistical inference which was introduced by Owen. It allows the data analyst to use it without making distribution assumptions. Empirical likelihood method has been widely used not only for nonparametric models but also for semi-parametric models, with the effectiveness of the likelihood approach and good power properties. However, when the sample size is small or the dimension is high, the method is poorly calibrated, producing tests that generally have a higher type I error. In addition, it suffers from a limiting convex hull constraint. Many statisticians have proposed methods to address the performance. …

A Generalized Schur–Horn Theorem And Optimal Frame Completions, Matthew C. Fickus, Justin D. Marks, Miriam J. Poteet

Faculty Publications

The Schur-Horn theorem is a classical result in matrix analysis which characterizes the existence of positive semi-definite matrices with a given diagonal and spectrum. In recent years, this theorem has been used to characterize the existence of finite frames whose elements have given lengths and whose frame operator has a given spectrum. We provide a new generalization of the Schur-Horn theorem which characterizes the spectra of all possible finite frame completions. That is, we characterize the spectra of the frame operators of the finite frames obtained by adding new vectors of given lengths to an existing frame. We then exploit …