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Information Based Approach For Detecting Change Points In Inverse Gaussian Model With Applications, Alexis Anne Wallace
Information Based Approach For Detecting Change Points In Inverse Gaussian Model With Applications, Alexis Anne Wallace
Electronic Theses, Projects, and Dissertations
Change point analysis is a method used to estimate the time point at which a change in the mean or variance of data occurs. It is widely used as changes appear in various datasets such as the stock market, temperature, and quality control, allowing statisticians to take appropriate measures to mitigate financial losses, operational disruptions, or other adverse impacts. In this thesis, we develop a change point detection procedure in the Inverse Gaussian (IG) model using the Modified Information Criterion (MIC). The IG distribution, originating as the distribution of the first passage time of Brownian motion with positive drift, offers …
Statistical Analysis Of Health Habits For Incoming College Students, Wendy Isamara Lizarraga Noriega
Statistical Analysis Of Health Habits For Incoming College Students, Wendy Isamara Lizarraga Noriega
Electronic Theses, Projects, and Dissertations
Health habits among college students are commonly overseen, especially for students transitioning from high school right into college. These students are becoming independent young adults, and learning how to adapt to a different scenery when it comes to their learning environment. As these young adults transition into college, this is the perfect time for the students to become more vulnerable and comfortable with their independence, and their weight begins to fluctuate. Many variables come into consideration when increasing weight as an incoming first-year student. Students are more likely to live alone, get a job, and rely on fast food and …
An Exposition Of The Curvature Of Warped Product Manifolds, Angelina Bisson
An Exposition Of The Curvature Of Warped Product Manifolds, Angelina Bisson
Electronic Theses, Projects, and Dissertations
The field of differential geometry is brimming with compelling objects, among which are warped products. These objects hold a prominent place in differential geometry and have been widely studied, as is evident in the literature. Warped products are topologically the same as the Cartesian product of two manifolds, but with distances in one of the factors in skewed. Our goal is to introduce warped product manifolds and to compute their curvature at any point. We follow recent literature and present a previously known result that classifies all flat warped products to find that there are flat examples of warped products …
Dna Self-Assembly Of Trapezohedral Graphs, Hytham Abdelkarim
Dna Self-Assembly Of Trapezohedral Graphs, Hytham Abdelkarim
Electronic Theses, Projects, and Dissertations
Self-assembly is the process of a collection of components combining to form an organized structure without external direction. DNA self-assembly uses multi-armed DNA molecules as the component building blocks. It is desirable to minimize the material used and to minimize genetic waste in the assembly process. We will be using graph theory as a tool to find optimal solutions to problems in DNA self-assembly. The goal of this research is to develop a method or algorithm that will produce optimal tile sets which will self-assemble into a target DNA complex. We will minimize the number of tile and bond-edge types …
Mathematics Behind Machine Learning, Rim Hammoud
Mathematics Behind Machine Learning, Rim Hammoud
Electronic Theses, Projects, and Dissertations
Artificial intelligence (AI) is a broad field of study that involves developing intelligent
machines that can perform tasks that typically require human intelligence. Machine
learning (ML) is often used as a tool to help create AI systems. The goal of ML is
to create models that can learn and improve to make predictions or decisions based on given data. The goal of this thesis is to build a clear and rigorous exposition of the mathematical underpinnings of support vector machines (SVM), a popular platform used in ML. As we will explore later on in the thesis, SVM can be implemented …
Sum Of Cubes Of The First N Integers, Obiamaka L. Agu
Sum Of Cubes Of The First N Integers, Obiamaka L. Agu
Electronic Theses, Projects, and Dissertations
In Calculus we learned that Sum^{n}_{k=1} k = [n(n+1)]/2 , that Sum^{n}_{k=1} k^2 = [n(n+1)(2n+1)]/6 , and that Sum^{n}_{k=1} k^{3} = (n(n+1)/2)^{2}. These formulas are useful when solving for the area below quadratic or cubic function over an interval [a, b]. This tedious process, solving for areas under a quadratic or a cubic, served as motivation for the introduction of Riemman integrals. For the overzealous math student, these steps were replaced by a simpler method of evaluating antiderivatives at the endpoints a and b. From my recollection, a former instructor informed us to do the value of memorizing these formulas. …
Dna Complexes Of One Bond-Edge Type, Andrew Tyler Lavengood-Ryan
Dna Complexes Of One Bond-Edge Type, Andrew Tyler Lavengood-Ryan
Electronic Theses, Projects, and Dissertations
DNA self-assembly is an important tool used in the building of nanostructures and targeted virotherapies. We use tools from graph theory and number theory to encode the biological process of DNA self-assembly. The principal component of this process is to examine collections of branched junction molecules, called pots, and study the types of structures that such pots can realize. In this thesis, we restrict our attention to pots which contain identical cohesive-ends, or a single bond-edge type, and we demonstrate the types and sizes of structures that can be built based on a single characteristic of the pot that is …
Pascal's Triangle, Pascal's Pyramid, And The Trinomial Triangle, Antonio Saucedo Jr.
Pascal's Triangle, Pascal's Pyramid, And The Trinomial Triangle, Antonio Saucedo Jr.
Electronic Theses, Projects, and Dissertations
Many properties have been found hidden in Pascal's triangle. In this paper, we will present several known properties in Pascal's triangle as well as the properties that lift to different extensions of the triangle, namely Pascal's pyramid and the trinomial triangle. We will tailor our interest towards Fermat numbers and the hockey stick property. We will also show the importance of the hockey stick properties by using them to prove a property in the trinomial triangle.
Progenitors Involving Simple Groups, Nicholas R. Andujo
Progenitors Involving Simple Groups, Nicholas R. Andujo
Electronic Theses, Projects, and Dissertations
I will be going over writing representations of both permutation and monomial progenitors, which include 2^{*4} : D_4, 2^(*7) :L_2 (7) as permutation progenitors, and monomial progenitors 7^(*2) :_m S_3 \times 2, 11^{*2} :_m (5:2)^{*}5, 11^{*3} :_m (25:3), 11^{*4} :_m (4 : 5)^{*}5. Also, the images of these different progenitors at both lower and higher fields and orders. \\ We will also do the double coset enumeration of S5 over D6, S6 over 5 : 4, A_5 x A_5 over (5:2)^{*}5, and go on to also do the double coset enumeration over maximal subgroups for larger constructions. We will also …
Making Models With Bayes, Pilar Olid
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 …
The Evolution Of Cryptology, Gwendolyn Rae Souza
The Evolution Of Cryptology, Gwendolyn Rae Souza
Electronic Theses, Projects, and Dissertations
We live in an age when our most private information is becoming exceedingly difficult to keep private. Cryptology allows for the creation of encryptive barriers that protect this information. Though the information is protected, it is not entirely inaccessible. A recipient may be able to access the information by decoding the message. This possible threat has encouraged cryptologists to evolve and complicate their encrypting methods so that future information can remain safe and become more difficult to decode. There are various methods of encryption that demonstrate how cryptology continues to evolve through time. These methods revolve around different areas of …
Thinking Poker Through Game Theory, Damian Palafox
Thinking Poker Through Game Theory, Damian Palafox
Electronic Theses, Projects, and Dissertations
Poker is a complex game to analyze. In this project we will use the mathematics of game theory to solve some simplified variations of the game. Probability is the building block behind game theory. We must understand a few concepts from probability such as distributions, expected value, variance, and enumeration methods to aid us in studying game theory. We will solve and analyze games through game theory by using different decision methods, decision trees, and the process of domination and simplification. Poker models, with and without cards, will be provided to illustrate optimal strategies. Extensions to those models will be …
On The Evolution Of Virulence, Thi Nguyen
On The Evolution Of Virulence, Thi Nguyen
Electronic Theses, Projects, and Dissertations
The goal of this thesis is to study the dynamics behind the evolution of virulence. We examine first the underlying mechanics of linear systems of ordinary differential equations by investigating the classification of fixed points in these systems, then applying these techniques to nonlinear systems. We then seek to establish the validity of a system that models the population dynamics of uninfected and infected hosts---first with one parasite strain, then n strains. We define the basic reproductive ratio of a parasite, and study its relationship to the evolution of virulence. Lastly, we investigate the mathematics behind superinfection.
Chaos In Dynamics: The Non-Linear Waterwheel, Abraham Romerohernandez
Chaos In Dynamics: The Non-Linear Waterwheel, Abraham Romerohernandez
Theses Digitization Project
In this study basic principles of Chaos in Dynamics will be presented in the context of Lorenz Equations. In particular, we will see a demonstration of chaotic behavior in the Waterwheel Experiment and show how the dynamics of that experiment are a version of the Lorenz Equations.
Comparative Analysis Of Expected Utility Theory Versus Prospect Theory And Critique Of Their Recent Developments, Sassan Sadeghi
Comparative Analysis Of Expected Utility Theory Versus Prospect Theory And Critique Of Their Recent Developments, Sassan Sadeghi
Theses Digitization Project
This study is an investigation of the decision making theories, their developments, and especially, their applications. After locating the two rivals, the Expected Utility Theory (EUT) and the Prospect Theory (PT), within the general context of decision making situations, it compares their main features and examines the PT extensions.
Quenching For Degenerate Semilinear Parabolic Problems With Insulated Boundary Conditions, Bernard Iyawe
Quenching For Degenerate Semilinear Parabolic Problems With Insulated Boundary Conditions, Bernard Iyawe
Theses Digitization Project
This thesis studied the existence, uniqueness, and quenching behavior of the solution to a degenerate equation subject to the initial condition and the second boundary conditions.
Symmetric Presentations Of Finite Groups, Joshua Anthony Roche
Symmetric Presentations Of Finite Groups, Joshua Anthony Roche
Theses Digitization Project
Symmetric presentations of groups allow us to represent, and manipulate, group elements in a manner that is typically more convenient than conventional techniques; in this sense, symmetric presentations are particularly useful in the study of large finite groups.
Blow-Up Behavior Of Solutions For Some Ordinary And Partial Differential Equations, Sarah Y. Bahk
Blow-Up Behavior Of Solutions For Some Ordinary And Partial Differential Equations, Sarah Y. Bahk
Theses Digitization Project
There are two parts in this project. Part 1 the Riccati initial-value problem is looked at. Part 2 considers blow-up property solutions for the degenerate semilinear parabolic initial-boundary value problem.
A Partial Differential Equation To Model The Tacoma Narrows Bridge Failure, James Paul Swatzel
A Partial Differential Equation To Model The Tacoma Narrows Bridge Failure, James Paul Swatzel
Theses Digitization Project
The purpose of this thesis was to examine a partial differential equation to model the Tacoma Narrows bridge failure. This thesis will examine the equation developed by Lazer and McKenna to model a suspension bridge in no wind.
The Mathematics Of Object Recognition In Machine And Human Vision, Sunyoung Kim
The Mathematics Of Object Recognition In Machine And Human Vision, Sunyoung Kim
Theses Digitization Project
The purpose of this project was to see why projective geometry is related to the sort of sensors that machines and humans use for vision.
Numerical Solution Of Markov Chains, Amr Lotfy Elsayad
Numerical Solution Of Markov Chains, Amr Lotfy Elsayad
Theses Digitization Project
This project deals with techniques to solve Markov Chains numerically.
Geodesics Of Ruled Surfaces, Steven John Ramirez
Geodesics Of Ruled Surfaces, Steven John Ramirez
Theses Digitization Project
The focus of this thesis is on the investigation of the geodesics of ruled surfaces.
The Cantor Set, Sam Alfred Pearsall
Chaos And The Stock Market, Brent M. Monte
Chaos And The Stock Market, Brent M. Monte
Theses Digitization Project
No abstract provided.