Mathematics Commons^™

Periodicity And Invertibility Of Lattice Gas Cellular Automata, Jiawen Wang

Mathematical Sciences Technical Reports (MSTR)

A cellular automaton is a type of mathematical system that models the behavior of a set of cells with discrete values in progressing time steps. The often complicated behaviors of cellular automata are studied in computer science, mathematics, biology, and other science related fields. Lattice gas cellular automata are used to simulate the movements of particles. This thesis aims to discuss the properties of lattice gas models, including periodicity and invertibility, and to examine their accuracy in reflecting the physics of particles in real life. Analysis of elementary cellular automata is presented to introduce the concept of cellular automata and …

Effects Of Framing In Exams On Student Performance, Mariana Lane, Eric Reyes

Mathematical Sciences Technical Reports (MSTR)

No abstract provided.

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.

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 …

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.

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 …

Finding The Symmetry Group Of An Lp With Equality Constraints And Its Application To Classifying Orthogonal Arrays, Andrew J. Geyer, Dursun A. Bulutoglu, Kenneth J. Ryan

Faculty Publications

Excerpt: For a given linear program (LP) a permutation of its variables that sends feasible points to feasible points and preserves the objective function value of each of its feasible points is a symmetry of the LP. The set of all symmetries of an LP, denoted by G^LP, is the symmetry group of the LP. Margot (2010) described a method for computing a subgroup of the symmetry group G^LP of an LP. This method computes G^LP when the LP has only non-redundant inequalities and its feasible set satisfies no equality constraints.

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 …

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 …

On The Fundamental Group Of Plane Curve Complements, Mitchell Scofield

Boise State University Theses and Dissertations

Given a polynomial f(x,y) monic in y of degree d, we study the complement ℂ²-C, where C is the curve defined by the equation f(x,y)=0. The Zariski-Van Kampen theorem gives a presentation of the fundamental group of the complement ℂ²-C. Let NT be be the set of complex numbers x for which f(x,y) has multiple roots (as a polynomial in y). Let : ℂ − NT → ℂ^d − Δ be the map that …

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.

Exotic Phenomena In Dimension Four, Hannah R. Schwartz

Bryn Mawr College Dissertations and Theses

This thesis is a comparison of the smooth and topological categories in dimension 4. We first discuss lists of homeomorphic 4-manifolds with non-equivalent “exotic” smooth structures, and show that any finite list of smooth, closed, simply-connected 4-manifolds that are homeomorphic to a given one X can be obtained by removing a single compact contractible submanifold (or cork) from X, and then regluing it by powers of a boundary diffeomorphism. Furthermore, by allowing the cork to be noncompact, the collection of all the smooth manifolds homeomorphic to X can be obtained in this way. The existence of a universal noncompact cork …

Unbounded Derivations Of C*-Algebras And The Heisenberg Commutation Relation, Lara M. Ismert

Department of Mathematics: Dissertations, Theses, and Student Research

This dissertation investigates the properties of unbounded derivations on C*-algebras, namely the density of their analytic vectors and a property we refer to as "kernel stabilization." We focus on a weakly-defined derivation δ_D which formalizes commutators involving unbounded self-adjoint operators on a Hilbert space. These commutators naturally arise in quantum mechanics, as we briefly describe in the introduction.

A first application of kernel stabilization for δ_D shows that a large class of abstract derivations on unbounded C*-algebras, defined by O. Bratteli and D. Robinson, also have kernel stabilization. A second application of kernel stabilization provides a sufficient condition …

Two-Stage Mixed Integer Stochastic Programming And Its Application To Bond Portfolio Optimization, Nasser Aedh Alreshidi

Theses and Dissertations

We consider a two-stage stochastic bond portfolio optimization problem, where an investor aims to optimize the cost of bond portfolio under different scenarios while ensuring predefined liabilities during a given planning horizon. The investor needs to optimally decide whether to buy, hold, or sell bonds based upon present market conditions under different scenarios and varying assumptions, where the scenarios are determined based on interest rates and buying prices of the bonds. Three stochastic integer programming models are proposed and applied to real-data from Saudi Sukuk (Bond) Market. The case-study results demonstrate the varying optimal decisions made to manage bond portfolio …

Existence And Classification Of Solutions To Nonlinear Elliptic Equations, Haseeb E. Ansari

Theses and Dissertations

The so-called Lane-Emden equation is a model in astrophysics, useful to problems in analysis and conformal geometry, and is closely related to the Yamabe Problem and the Uniformization Theorem. We discuss several important results for the equation, which include proving that the equation admits a distribution solution if and only if p is greater than the Serrin exponent, that classical solutions admit the form of a "bubble function" if p is equal to the Sobolev exponent, and no classical solutions exist for p less than the Sobolev exponent. A new proof of an extended result is also included.

Pm2.5 Data Reliability And Air Quality Improvement Trends In Beijing, Huimin Li

Theses and Dissertations

PM2.5 has been a main environmental concern due to its adverse effects on human health and society. We used data from two sources: monitoring station of the U.S. Embassy in Beijing, and several nearby monitoring stations of the Chinese Ministry of Environmental Protection. This study includes investigating (1) PM2.5 historical data reliability, (2) PM2.5 real-time data reliability, and (3) air quality improvement trends in Beijing over the past decade. We used graphical methods, descriptive statistics, correlation analysis, and inferential analyses including paired samples t-test, ANOVA, and Kruskal-Wallis test. We reported effect sizes to aid study on practical significance. Inferential procedures' …

Generalizations Of The Arcsine Distribution, Rebecca Rasnick

Electronic Theses and Dissertations

The arcsine distribution looks at the fraction of time one player is winning in a fair coin toss game and has been studied for over a hundred years. There has been little further work on how the distribution changes when the coin tosses are not fair or when a player has already won the initial coin tosses or, equivalently, starts with a lead. This thesis will first cover a proof of the arcsine distribution. Then, we explore how the distribution changes when the coin the is unfair. Finally, we will explore the distribution when one person has won the first …

Taking Notes: Generating Twelve-Tone Music With Mathematics, Nathan Molder

Electronic Theses and Dissertations

There has often been a connection between music and mathematics. The world of musical composition is full of combinations of orderings of different musical notes, each of which has different sound quality, length, and em phasis. One of the more intricate composition styles is twelve-tone music, where twelve unique notes (up to octave isomorphism) must be used before they can be repeated. In this thesis, we aim to show multiple ways in which mathematics can be used directly to compose twelve-tone musical scores.

Computable Reducibility Of Equivalence Relations, Marcello Gianni Krakoff

Boise State University Theses and Dissertations

Computable reducibility of equivalence relations is a tool to compare the complexity of equivalence relations on natural numbers. Its use is important to those doing Borel equivalence relation theory, computability theory, and computable structure theory. In this thesis, we compare many naturally occurring equivalence relations with respect to computable reducibility. We will then define a jump operator on equivalence relations and study proprieties of this operation and its iteration. We will then apply this new jump operation by studying its effect on the isomorphism relations of well-founded computable trees.

Formally Verifying Peano Arithmetic, Morgan Sinclaire

Boise State University Theses and Dissertations

This work is concerned with implementing Gentzen’s consistency proof in the Coq theorem prover.

In Chapter 1, we summarize the basic philosophical, historical, and mathematical background behind this theorem. This includes the philosophical motivation for attempting to prove the consistency of Peano arithmetic, which traces itself from the first attempted axiomatizations of mathematics to the maturation of Hilbert’s program. We introduce many of the basic concepts in mathematical logic along the way: first-order logic (FOL), Peano arithmetic (PA), primitive recursive arithmetic (PRA), Gödel's 2nd Incompleteness theorem, and the ordinals below ε₀.

In …

Perfect Double Roman Domination Of Trees, Ayotunde Egunjobi

Electronic Theses and Dissertations

See supplemental content for abstract