Applied Mathematics Commons^™

Bivariate Markov Chain Model Of Irritable Bowel Syndrome (Ibs) Subtypes And Abdominal Pain, Ricardo Reyna Jr.

Theses and Dissertations

Researchers use stochastic models like continuous-time Markov chains (CTMC) to model progression of morbidities of public health impact, like HIV and Hepatitis C. Most of the research in that area is done for a single disease. In this research, we use a bivariate continuous-time Markov chain (CTMC) to model progression of co-morbidities. In particular, we use a bivariate CTMC to model the joint progression of Irritable Bowel Syndrome (IBS) and abdominal pain. Symptoms of IBS are known to change throughout the duration of the disorder. Hence, patients are normally asked to make a journal of the stool type, symptoms, and …

Stability Analysis Of Krylov Subspace Spectral Methods For The 1-D Wave Equation In Inhomogeneous Media, Bailey Rester

Master's Theses

Krylov subspace spectral (KSS) methods are high-order accurate, explicit time-stepping methods for partial differential equations (PDEs) that also possess the stability characteristic of implicit methods. Unlike other time-stepping approaches, KSS methods compute each Fourier coefficient of the solution from an individualized approximation of the solution operator of the PDE. As a result, KSS methods scale effectively to higher spatial resolution. This thesis will present a stability analysis of a first-order KSS method applied to the wave equation in inhomogeneous media.

Development Of An Effect Size To Classify The Magnitude Of Dif In Dichotomous And Polytomous Items, James D. Weese

Graduate Theses and Dissertations

A standardized effect size for the SIBTEST/POLYSIBTEST procedure is proposed, allowing for Differential Item Functioning (DIF) to be classified with a single set of DIF heuristics regardless of whether data are dichotomous or polytomous. This proposed standardized effect size accounts for both variability in responses and whether participants are included in the SIBTEST/POLYSIBTEST calculations. First, a new set of unstandardized effect size heuristics are established for dichotomous data that are more aligned with Educational Testing Service (ETS) standards using two and three parameter logistic (2PL and 3PL) models. Second, a standardized effect size is proposed and compared to other DIF …

Rapid Implicit Diagonalization Of Variable-Coefficient Differential Operators Using The Uncertainty Principle, Carley Walker

Master's Theses

We propose to create a new numerical method for a class of time-dependent PDEs (second-order, one space dimension, Dirichlet boundary conditions) that can be used to obtain more accurate and reliable solutions than traditional methods. Previously, it was shown that conventional time-stepping methods could be avoided for time-dependent mathematical models featuring a finite number of homogeneous materials, thus assuming general piecewise constant coefficients. This proposed method will avoid the modeling shortcuts that are traditionally taken, and it will generalize the piecewise constant case of energy diffusion and wave propagation to work for an infinite number of smaller pieces, or a …

Diagonalization Of 1-D Schrodinger Operators With Piecewise Constant Potentials, Sarah Wright

Master's Theses

In today's world our lives are very layered. My research is meant to adapt current inefficient numerical methods to more accurately model the complex situations we encounter. This project focuses on a specific equation that is used to model sound speed in the ocean. As depth increases, the sound speed changes. This means the variable related to the sound speed is not constant. We will modify this variable so that it is piecewise constant. The specific operator in this equation also makes current time-stepping methods not practical. The method used here will apply an eigenfunction expansion technique used in previous …

Inference And Estimation In Change Point Models For Censored Data, Kristine Gierz

Mathematics & Statistics Theses & Dissertations

In general, the change point problem considers inference of a change in distribution for a set of time-ordered observations. This has applications in a large variety of fields and can also apply to survival data. With improvements to medical diagnoses and treatments, incidences and mortality rates have changed. However, the most commonly used analysis methods do not account for such distributional changes. In survival analysis, change point problems can concern a shift in a distribution for a set of time-ordered observations, potentially under censoring or truncation.

In this dissertation, we first propose a sequential testing approach for detecting multiple change …

Conical Orbital Mechanics: A Rework Of Classic Orbit Transfer Mechanics, Cian Anthony Branco

Mechanical & Aerospace Engineering Theses & Dissertations

Simple orbital maneuvers obeying Kepler’s Laws, when taken with respect to Newton’s framework, require considerable time and effort to interpret and understand. Instead of a purely mathematical approach relying on the governing relations, a graphical geometric conceptual representation provides a useful alternative to the physical realities of orbits. Conic sections utilized within the full scope of a modified cone (frustum) were employed to demonstrate and develop a geometric approach to elliptical orbit transformations. The geometric model in-question utilizes the rotation of a plane intersecting the orbital frustum at some angle β (and the change in this angle) in a novel …

Under Frequency Load Shedding Scheme For Islanded Distribution System Based On Mixed Integer Linear Programming, Sohail Sarwar

Student Works (2020-2029)

In recent years, significant climate changes have pivoted the distribution system towards utilization of renewable energy, particularly through distributed generators (DGs). Although DGs offer many benefits, its integration affects the stability of the system, which could lead to blackout, when the grid is disconnected. The system frequency will drop drastically if DG’s generation capacity is less than the total load demand in the network. In order to sustain the system stability, Under Frequency Load Shedding (UFLS) is a commonly used technique to minimize the difference in load demand and power generation. However, existing load shedding techniques are lack in accurate …

Energy-Efficient Communications In Wireless Powered Cognitive Radio Networks Based On Game Theory, Fadhil Mukhlif Aswad Al-Obaidy

Student Works (2020-2029)

There are challenging and prevalent problems related to spectrum resources with the interference of battery-based devices in future wireless networks. To address such challenges, this thesis proposes a theoretical framework for designing and analyzing the distributed power control algorithms in modern 5G cognitive networks. Previous experiments have shown that game theory tools can be used as a suitable and efficient technique to build scalable, balanced, and energy efficient for the distributed power control schemes in order to use it practically in battery-based devices in wireless networks. In reality, the power control issue is constructed as a non-cooperative game for which …

Preludes To Mathematical Biology Education, Timothy Comar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Reactions To A Pandemic: The Coronavirus Brings Mathematicians To The Front Line, Ami Radunskaya

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Asymptotic Analysis Of Radial Point Rupture Solutions For Elliptic Equations, Attou Miloua

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Personalized Immunotherapy Treatment Strategies For A System Of Chronic Myelogenous Leukemia, Paul Valle

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Viewing Ode Models Through A New Lens: The Generalized Linear Chain Trick, Paul Hurtado, Cameron Richards

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Strange Periodic Behavior In An Epilepsy Model, David Chan, Candace Kent, William Strasser

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Applying Immuno-Epidemiology Principles To Violence, Anna H. Sisk, Nina H. Fefferman, Judy Day, Patricia Bamwine

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Various Mathematical Models To Study Covid-19 Pandemic Dynamics With Quarantine, Hospitalized And Non-Pharmaceutical Interventions As Control Strategies, Amit Sharma, Bhanu Gupta

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Stochastic Analysis And Statistical Inference For Seir Models Of Infectious Diseases, Andrés Ríos-Gutiérrez, Viswanathan Arunachalam, Anuj Mubayi

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Malaria-Hiv/Aids Co-Infection Model With Optimal Treatment And Insecticide-Treated Bednets, Eric Numfor

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Pharmacokinetics And Pharmacodynamics Models Of Tumor Growth And Anticancer Effects In Discrete Time, Ngoc Nguyen, Ferhan M. Atici

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.