Other Applied Mathematics Commons^™

Bringing Gans To Medieval Times: Manuscript Translation Models, Tonilynn M. Holtz

College of Graduate Studies: Theses & Dissertations

The Generative Adversarial Networks (GAN) recently emerged as a powerful framework for producing new knowledge from existing knowledge. These models aim to learn patterns from input data then use that knowledge to generate output data samples that plausibly appear to belong to the same set as the input data. Medieval manuscripts study has been an important research area in the humanities field for many decades. These rare manuscripts are often times inaccessible to the general public, including students in scholars, and it is of a great interest to provide digital support (including, but not limited to translation and search) for …

Problems In Chemical Graph Theory Related To The Merrifield-Simmons And Hosoya Topological Indices, William B. O'Reilly

College of Graduate Studies: Theses & Dissertations

In some sense, chemical graph theory applies graph theory to various physical sciences. This interdisciplinary field has significant applications to structure property relationships, as well as mathematical modeling. In particular, we focus on two important indices widely used in chemical graph theory, the Merrifield-Simmons index and Hosoya index. The Merrifield-Simmons index and the Hosoya index are two well-known topological indices used in mathematical chemistry for characterizing specific properties of chemical compounds. Substantial research has been done on the two indices in terms of enumerative problems and extremal questions. In this thesis, we survey known extremal results and consider the generalized …

The Computational Search For Unidentified Central Configurations Of The Newtonian N-Body Problem, Hannah G. Havel

CURE Proceedings

The N-body problem is a field of study in mathematics and physics that involves predicting the motion of particles moving under their mutual gravitational attraction. It is vital in celestial mechanics, such as planning collision-free satellite orbit trajectories. When beginning to understand the N-body problem, we can start by looking at equal masses of these particles or celestial bodies. As particles move, their position and velocity change, both energy and angular momentum are conserved. Sets of constant energy and angular momentum, known as integral manifolds, are higher-dimensional figures that represent constraints of movement to a system. Integral manifolds are described …

A Novel Scheme Based On Bessel Operational Matrices For Solving A Class Of Nonlinear Systems Of Differential Equations, Atallah El-Shenawy, Mohamed El-Gamel, Muhammad E. Anany

Mansoura Engineering Journal

The system of ordinary differential equations arises in many natural phenomena, especially in the field of disease spread. In this paper, a perfect spectral technique is introduced to solve systems of nonlinear differential equations. The technique enhanced the Bessel collocation technique by converting the series notation of unknown variables and their derivatives to matrix relations. The Newton algorithm is developed to solve the resulting nonlinear system of algebraic equations. The effectiveness of the scheme is proved by the convergence analysis and error bound as demonstrated in Theorem 1. The scheme of solution is tested to clarify the efficiency and the …

The Precedence-Constrained Quadratic Knapsack Problem, Changkun Guan

Honors Theses

This thesis investigates the previously unstudied Precedence-Constrained Quadratic Knapsack Problem (PC-QKP), an NP-hard nonlinear combinatorial optimization problem. The PC-QKP is a variation of the traditional Knapsack Problem (KP) that introduces several additional complexities. By developing custom exact and approximate solution methods, and testing these on a wide range of carefully structured PC-QKP problem instances, we seek to identify and understand patterns that make some cases easier or harder to solve than others. The findings aim to help develop better strategies for solving this and similar problems in the future.

Pitching The Use Of Squared And Interaction Terms In Regression Via Baseball Heat Maps, Lucas Chepelsky

Williams Honors College, Honors Research Projects

This project will examine the impact of using second-order terms in regression. For illustration, we use an example of regression where a baseball player's three by three heat map, including the height and distance from inside to outside of the pitch, are variables used to predict batting average. We find that second-order terms are crucial in discovering nonlinear relationships and interaction effects in regression models, and maintain that the common practice of using first-order additive models is insufficient.

Estimating Modeling Parameters For Covid-19 Spread On Campus, Aviel S. Crigger

Honors Undergraduate Theses

Understanding the true burden of community transmission of communicable diseases like COVID-19 is crucial for effective public health response. Clinical cases, while important, only represent a fraction of the actual disease prevalence within a population. In this thesis, we investigate methods to estimate parameters that link clinical cases to the true disease prevalence using a modified compartmental model known as SICR (Susceptible, Infected, Cases, Recovered). We employ Bayesian inference and ensemble Markov chain Monte Carlo (MCMC) simulations to analyze clinical case data provided by the University of Central Florida Health Center from 2020 to 2022. Our goal is to estimate …

Sparse Representation Learning For Temporal Networks, Maxwell Mcneil

Electronic Theses & Dissertations (2024 - present)

Temporal networks arise in many domains including activity of social network users, sensor network readings over time, and time course gene expression within the interaction network of a model organism. Data of this type contains a wealth of prior information such as the connectivity among nodes (e.g., a friendship graph), and prior knowledge of expected temporal patterns (e.g., periodicity). Modeling these temporal and network patterns jointly is essential for state-of-the-art performance in temporal network data analysis and mining. Sparse dictionary encoding is one modeling approach for such underlying patterns. However, most classical approaches consider only one dimension of the data …

Characterizing Probabilities Of Outbreaks Of Dengue In Central Argentina Using A Temperature-Dependent Stochastic Model, Morgan H. Jackson, Elizabet L. Estallo, Cheng Ly, Michael A. Robert

Graduate Research Posters

Dengue virus (DENV) causes over 390 million infections and around 40,000 deaths worldwide each year. DENV is primarily transmitted by the mosquito Aedes aegypti, and both the life cycle of these mosquitoes and dengue transmission are significantly impacted by temperature. In the temperate region of Central Argentina, where dengue outbreaks first began in 2009, outbreaks of dengue can only occur due to new introductions of DENV from other regions. Due to the relationships between temperature and dengue, the risk of outbreak changes throughout the year.

We develop a stochastic model including temperature-dependent mosquito life history traits and transmission-related parameters. …

Simulation Of Wave Propagation In Granular Particles Using A Discrete Element Model, Syed Tahmid Hussan

College of Graduate Studies: Theses & Dissertations

The understanding of Bender Element mechanism and utilization of Particle Flow Code (PFC) to simulate the seismic wave behavior is important to test the dynamic behavior of soil particles. Both discrete and finite element methods can be used to simulate wave behavior. However, Discrete Element Method (DEM) is mostly suitable, as the micro scaled soil particle cannot be fully considered as continuous specimen like a piece of rod or aluminum. Recently DEM has been widely used to study mechanical properties of soils at particle level considering the particles as balls. This study represents a comparative analysis of Voigt and Best …

Penalized Interpolating B-Splines And Their Applications, Kylee L. Hartman-Caballero

Theses and Dissertations

One of the most studied data analysis techniques in Numerical Analysis is interpolation. Interpolation is used in a variety of fields, namely computer graphic design and biomedical research. Among interpolation techniques, cubic splines have been viewed as the standard since at least the 1960s, due to their ease of computation, numerical stability, and the relative smoothness of the interpolating curve. However, cubic splines have notable drawbacks, such as their lack of local control and necessary knowledge of boundary conditions. Arguably a more versatile interpolation technique is the use of B-splines. B-splines, a relative of Bézier curves, allow local control through …

Last Passage Time And Excursion Theory For Solvable Diffusions With Applications In Mathematical Finance, Yaode Sui

Theses and Dissertations (Comprehensive)

In this dissertation, we investigate the properties of last passage times and excursion theory in one-dimensional solvable diffusions, emphasizing their applications in financial modeling, particularly in option pricing. We derive closed-form formulas for the marginal distribution of last passage times and their joint distribution with process values, including the maximum and minimum of the process value. The focus is on time-homogeneous diffusions with various boundaries and imposed killing. Employing spectral expansion theory, we derive explicit formulas for distributions of last passage times in common processes such as Drifted Brownian Motion (BM), Squared Bessel (SQB), Ornstein-Uhlenbeck (OU), and Cox-Ingersoll-Ross (CIR) models. …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Game-Theoretic Approaches To Optimal Resource Allocation And Defense Strategies In Herbaceous Plants, Molly R. Creagar

Department of Mathematics: Dissertations, Theses, and Student Research

Empirical evidence suggests that the attractiveness of a plant to herbivores can be affected by the investment in defense by neighboring plants, as well as investment in defense by the focal plant. Thus, allocation to defense may not only be influenced by the frequency and intensity of herbivory but also by defense strategies employed by other plants in the environment. We incorporate a neighborhood defense effect by applying spatial evolutionary game theory to optimal resource allocation in plants where cooperators are plants investing in defense and defectors are plants that do not. We use a stochastic dynamic programming model, along …

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 …

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

All Dissertations

In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …

Long-Acting Cabotegravir And The Emergence Of Drug-Resistant Hiv, Katharine Gurski

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Incorporating Adaptive Human Behavior Into Epidemiological Models Using Equation Learning, Austin Barton, Jordan Klein, Jonathan Greer, Kevin Flores, Patrick Haughey

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Computational Modeling Using A Novel Continuum Approach Coupled With Pathway-Informed Neural Networks To Optimize Dynein-Mediated Centrosome Positioning In Polarized Cells, Arkaprovo Ghosal, Padmanabhan Seshaiyar Dr., Adriana Dawes Dr., General Genomics Inc.

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Exploring Disease Spread Patterns In A Heterogeneous Environment: The Impact Of Travel Restrictions, Seoyun Choe

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.