Mathematics Commons^™

Noise-Induced Stabilization Of Perturbed Hamiltonian Systems, Tiffany N. Kolba, Anthony Coniglio, Sarah Sparks, Daniel Weithers

Mathematics and Statistics Faculty Publications

Noise-induced stabilization is the phenomenon in which the addition of randomness to an unstable system of ordinary differential equations results in a stable system of stochastic differential equations. With stability defined as global stochastic boundedness, Hamiltonian systems can never be stabilized by the addition of noise that is constant in space. In this article, we investigate how to deterministically perturb a class of unstable Hamiltonian systems in such a way that the qualitative behavior is preserved, but that enables the systems to exhibit noise-induced stabilization.

Scalable Time-Stepping For Navier-Stokes Through High-Frequency Analysis Of Block Arnoldi Iteration, Brianna Bingham

Dissertations

Existing time-stepping methods for PDEs such as Navier-Stokes equations are not as efficient or scalable as they need to be for high-resolution simulation due to stiffness. The failure of existing time-stepping methods to adapt to changes in technology presents a dilemma that is becoming even more problematic over time. By rethinking approaches to time-stepping, dramatic gains in efficiency of simulation methods can be achieved. Krylov subspace spectral (KSS) methods have proven to be effective for solving time-dependent, variable-coefficient PDEs. The objective of this research is to continue the development of KSS methods to provide numerical solution methods that are far …

Geometric Aspects Of Wound Healing, Julio Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we show that many aspects of complex biological processes related to wound healing can be explained in terms of the corresponding geometric symmetries.

Unifications Of Pythagorean Triple Schema, Emily Hammes

Undergraduate Honors Theses

Euclid’s Method of finding Pythagorean triples is a commonly accepted and applied technique. This study focuses on a myriad of other methods behind finding such Pythagorean triples. Specifically, we discover whether or not other ways of finding triples are special cases of Euclid’s Method.

Modeling An M/M/1 Queue With Unreliable Service And A Working Vacation, Joshua Kent Patterson

Mathematics Dissertations - Archive

We define the new term ’unreliable service’ where the service itself is unreliable (i.e. may fail). We discuss how this differs from the current literature, and give examples showing just how common this phenomena is in many real-world scenarios. We first consider the classic M/M/1 queue with unreliable service and find some striking similarities with the well studied M/M/1 derivation. Next, we consider the M/M/1 queue with unreliable service and a working vacation. In each of these cases, surprising explicit results are found including positive recurrence conditions, the stationary queue length distribution, and a decomposition of both the queue length …

On Optimizing The Sum Of Rayleigh Quotients On The Unit Sphere, Aohud Abdulrahman Binbuhaer

Mathematics Dissertations - Archive

Given symmetric matrices and positive definite matrices, we are concerned with the solution of the maximization of the function that is mentioned in the dissertation. We establish necessary optimality conditions for local maximizers. Moreover, a self-consistent-field (SCF) iterative method for solving this maximization problem is introduced and analyzed. We use the Trust-Region SCF iteration to improve the convergence of the SCF method.

Mathematical Modeling Of Zika Virus Transmission And Multiple Pathogen Interactions, Omomayowa Olawoyin

Mathematics Dissertations - Archive

The purpose of this dissertation is twofold: to deepen our understanding of the complex transmission routes of the Zika virus (ZIKV), and to study multiple pathogen interactions (specifically cocirculation of Zika and dengue and discrete-time coinfection models) through the lens of invasion reproductive numbers (IRNs) which measure the ability of a disease to invade a population endemic with another disease(s). In addition to being transmitted to humans through the bite of infected female Aedes aegypti mosquitoes, studies show that the ZIKV can also be sexually and vertically transmitted within both populations. We develop a new mathematical model of the ZIKV …

Modeling The Effects Of The Immune System On Bone Fracture Healing, Imelda Trejo Lorenzo

Mathematics Dissertations - Archive

Bone fracture healing is a complex biological process that results in a full reconstruction of the bone. However, it is not always an easy and successful process. Indeed, in some unfavorable conditions, the bone fracture healing fails with approximately 10% of fractures resulting in nonunion. Furthermore, the risk of nonunion healing increases with age, severe trauma, and immune deficiency. In addition, clinical consequences of fractures include surgical management, prolonged hospitalization, and rehabilitation resulting in high socioeconomic costs. A better understanding of bone healing would enable to find optimal conditions for successful outcomes and to develop strategies for fracture treatments under …

Dynamic Attribute-Level Best Worst Discrete Choice Experiments, Amanda Working, Mohammed Alqawba, Norou Diawara

Mathematics & Statistics Faculty Publications

Dynamic modelling of decision maker choice behavior of best and worst in discrete choice experiments (DCEs) has numerous applications. Such models are proposed under utility function of decision maker and are used in many areas including social sciences, health economics, transportation research, and health systems research. After reviewing references on the study of such experiments, we present example in DCE with emphasis on time dependent best-worst choice and discrimination between choice attributes. Numerical examples of the dynamic DCEs are simulated, and the associated expected utilities over time of the choice models are derived using Markov decision processes. The estimates are …

Simulation As A Predictor In Probability, Xiaona Zhou

Publications and Research

In this study, we simulate bivariate normal data. We gain intuition about the bivariate normal distribution by comparing the generated data to the associated bivariate normal density surface. We also get results about covariance and correlation. We will use tools from linear algebra to discuss transformations of random normal vectors, and the use of contours.

Conjugacy For Homogeneous Ordered Graphs, Samuel Coskey, Paul Ellis

Mathematics Faculty Publications and Presentations

We show that for any countable homogeneous ordered graph G, the conjugacy problem for automorphisms of G is Borel complete. In fact we establish that each such G satisfies a strong extension property called ABAP, which implies that the isomorphism relation on substructures of G is Borel reducible to the conjugacy relation on automorphisms of G.

A Comparative Study Of Incidence Of Domestic Violence Between Immigrant And Non-Immigrant Women In The United States Of America, Nadia A. Gordon, Urmi Ghosh-Dastidar, Janet Liou-Mark, Shamita Dasgupta

Publications and Research

Immigrant women in the USA come from various socio-economic, cultural, and religious backgrounds. Some of these women suffer from domestic violence; however, due to their strict cultural or social structure, they often stay quiet and rarely report these incidents to the authorities. Additionally, since these immigrant women face more challenges than their non-immigrant peers, they are more reluctant or unlikely to leave their abusive partners. An analysis was completed using published data as an attempt to establish if any statistically significant differences exist between reported incidences among immigrant women and non-immigrant women. A chi-square analysis (χ² = 14.53; p-value …

The Most Powerful Thing, Caitlin Jankiewicz

Lake Union Herald

No abstract provided.

One Teacher's Transformation Of Practice Through The Development Of Covariational Thinking And Reasoning In Algebra : A Self-Study, Jacqueline Dauplaise

Theses, Dissertations and Culminating Projects

CCSSM (2010) describes quantitative reasoning as expertise that mathematics educators should seek to develop in their students. Researchers must then understand how to develop covariational reasoning. The problem is that researchers draw from students’ dialogue as the data for understanding quantitative relationships. As a result, the researcher can only conceive the students’ reasoning. The objective of using the self-study research methodology is to examine and improve existing teaching practices. To improve my practice, I reflected upon the implementation of my algebra curriculum through a hermeneutics cycle of my personal history and living educational theory. The critical friend provoked through dialogues …

Sampling Studies For Longitudinal Functional Data, Toni Jassel

Theses, Dissertations and Culminating Projects

We study the data setting consisting of functional data sets repeatedly observed over time. The focus is on the dynamic prediction of the future trajectory for a subject. Regression methods based on dynamic functional models are used for dynamic prediction of individual trajectories. We propose strategies for the selection of the study sampling design in the context of longitudinal functional data. An application to simulated child growth data is presented. The height-for-age z-score (HAZ) was the response variable in the functional dynamic models for prediction. The intent was to recommend four months for removal in our initial historic data set. …

Statistical Modeling Of Count Data With Over-Dispersion Or Zero-Inflation Problems, Chengxin Zhang

Theses, Dissertations and Culminating Projects

In this study, we will analyze a supply retailing company’s data to model the relationship between their customer’s past purchase behavior to predict their future online purchase behavior. The data was divided into time periods from 2016: P1-P6(January 31st to July 30th) and P7(July 31st to August 27th ). Based on customer’s past purchase information from the P1-P6 period, such as money spent, number of cart additions, transactions type, number of unique purchase dates, number of unique purchase skus, number of page views, number browse dates, company size, and number of products purchased, we aim to find if these information …

On The Complexity Of Computing Galois Groups Of Differential Equations, Mengxiao Sun

Dissertations, Theses, and Capstone Projects

The differential Galois group is an analogue for a linear differential equation of the classical Galois group for a polynomial equation. An important application of the differential Galois group is that a linear differential equation can be solved by integrals, exponentials and algebraic functions if and only if the connected component of its differential Galois group is solvable. Computing the differential Galois groups would help us determine the existence of the solutions expressed in terms of elementary functions (integrals, exponentials and algebraic functions) and understand the algebraic relations among the solutions.

Hrushovski first proposed an algorithm for computing the differential …

Stirling Numbers Of Sunflower Graphs, Jose Garcia, Jessica Longo, Matt Phad, Page Wilson

Mathematics Undergraduate Research

A Stirling number of the second kind, S(n, k), is the number of ways to take all of the elements from an n element set and put them into k subsets, so that the subsets are non-empty and pairwise disjoint. To get the graphical Stirling number for a graph G, we add the restriction that any two vertices that are adjacent in G cannot be in the same subset. The traditional Stirling numbers are the graphical Stirling number where the graph is empty. We find graphical Stirling numbers for sunflower graphs, which are powers of paths …

Direct Detection Of Relic Neutrino Background Remains Impossible: A Review Of More Recent Arguments, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The existence of big bang relic neutrinos—exact analogues of the big bang relic photons comprising the cosmic microwave background radiation—is a basic prediction of standard cosmology. The standard big bang theory predicts the existence of 1087 neutrinos per flavour in the visible universe. This is an enormous abundance unrivalled by any other known form of matter, falling second only to the cosmic microwave background (CMB) photon. Yet, unlike the CMB photon which boasts its first (serendipitous) detection in the 1960s and which has since been observed and its properties measured to a high degree of accuracy in a series of …

Lattice-Valued T-Filters And Induced Structures, Frederick Reid

Electronic Theses and Dissertations

A complete lattice is called a frame provided meets distribute over arbitrary joins. The implication operation in this context plays a central role. Intuitively, it measures the degree to which one element is less than or equal to another. In this setting, a category is defined by equipping each set with a T-convergence structure which is defined in terms of T-filters. This category is shown to be topological, strongly Cartesian closed, and extensional. It is well known that the category of topological spaces and continuous maps is neither Cartesian closed nor extensional. Subcategories of compact and of complete spaces are …