Physical Sciences and Mathematics Commons^™

The Effects Of Overwash On Barrier Island Evolution And Building A Barrier Island Measure Of Resistance, Beth Thomas

Theses and Dissertations

Barrier islands are critical for coastal communities, as they serve as a natural buffer against storm surge, waves, and the effects of rising sea levels, protecting life and property. These islands continuously evolve due to both normal and severe environmental conditions; global warming makes it increasingly difficult to predict the evolution of these islands due to increases in storm frequency and intensity. We present a cellular model of barrier island evolution consisting of biotic and abiotic processes including the effects of vegetation, wind, ocean currents, and gravity. The model is used to predict the future evolution of barrier islands off …

Mathematical Models With Clinical Applications For Improving Health Outcomes, Helen Harris

Theses and Dissertations

In clinical settings, patients are exposed to many risks and stressors that could result in adverse health outcomes. Here we present mathematical models that seek to address these risks. First, we present a Markov Chain model to investigate the effect of medication reconciliation (MR) completion on patient health outcomes in the intensive care unit. Using this model, we simulate the annual incidence of adverse drug events (ADEs) for three different ADE rates. Based on the simulated results, we conduct a cost-benefit analysis for various levels of compliance to determine the financial implications of increasing MR completion depending on the baseline …

Advancing Cybersecurity Through Userland Memory Forensics: From Runtime Analysis To Security Applications, Hala Ali

Theses and Dissertations

Memory forensics has become a crucial component of digital investigations, particularly for detecting malware operating solely in system memory. As operating system vendors implemented kernel access restrictions, malware authors shifted to userland malware. However, existing memory forensics techniques have largely focused on kernel-level analysis, leaving userland runtimes insufficiently covered. This dissertation addresses this gap by expanding memory analysis capabilities across two distinct paradigms: interpreted and compiled runtimes. The first phase targets the Python runtime, developing automated recovery techniques that enable several security applications. For malware detection, these techniques extract critical forensic artifacts such as encryption keys and command-and-control configurations. For …

Proof Of Recovery: A Model To Enhance Data Integrity In Data Management Systems, Gustaf Barkstrom

Theses and Dissertations

Businesses lose millions of dollars every year when they can’t restore data from backups. Research shows that Disaster Recovery Plan (DRP) testing is not conducted frequently enough, nor are records maintained that demonstrate full data recovery from backups. This work introduces a design science artifact called PRTOK that aims to increase DRP testing. The design science artifact is a software solution that integrates with Data Management Systems (DMS)

such as iRODS and DSpace, and can work with formats such as HDF5 and BagIt. Proof-of- recovery records, or tokens, are recorded in a replicated, resilient, and indelible proof-of- authority blockchain data …

Generating Synthetic Ct From Mri Data, Foysal Ahmed

Theses and Dissertations

Magnetic resonance imaging (MRI) provides excellent soft tissue contrast without ionizing radiation, making it a strong alternative to computed tomography (CT) in medical imaging workflows. However, CT remains essential for applications requiring electron density information, such as radiation therapy treatment planning. This study investigated the feasibility of generating synthetic CT (sCT) images from MRI using a deep learning-based U-Net architecture. A two-dimensional U-Net was trained on paired MRI-CT data from the SynthRAD 2025 dataset, consisting of 120 T1-weighted (T1W) and 60 T2-weighted (T2W) axial cases, including deformed CT (dCT) aligned to MRI. Model testing used an independent dataset of 30 …

Managing Multi-Drug Resistance: An Evolutionary Game Theory And Optimal Control Approach, Shukhrat Nasrulloev

Theses and Dissertations

Multi-drug resistance is an evolutionary process in which treatment eliminates sensitive cells, allowing resistant clones to dominate. This thesis investigates this process using a framework integrating population dynamics, evolutionary game theory, and optimal control theory. We develop a two-population logistic growth model describing competition between drug-sensitive and drug-resistant cells under treatment, construct dose-dependent payoff matrices and replicator dynamics to characterize evolutionary competition, and derive a critical drug level D_crit = (r_S - rR)/(dS - d_R) at which resistant cells gain a fitness advantage. An optimal control problem is formulated via Pontryagin's Maximum Principle to identify schedules …

Fuchs' Problem For Quasi-Cyclic Groups, Dalen F. Elliott

Theses and Dissertations

Fuchs’ problem asks which groups can arise as the group of units of a ring. Although the finite cyclic case has been completely classified, much less is known in the infinite setting. This thesis contributes to this problem by investigating quasi-cyclic. (Pr¨ufer) groups and their finite direct products. We show that for every odd prime p, there is no commutative ring R such that R×∼= Cp∞. This obstruction arises from characteristic restrictions and the algebraic structure of finite fields. More generally, we prove that any group in which every element has order a power of an odd prime p and …

Data Defines Success: Algorithm For Dataset Quality Assessment In Deep Learning For Malware Detection, Matei Ionescu

Theses and Dissertations

The field of artificial intelligence is based upon the premise of constructing architectures through which to propagate training data. However, the majority of existing research literature is focused on architecture. While necessary, the attention devoted to the architecture should not so precipitously exceed that of the data. It should be noted that this disparity is not without reasonable cause. Data quality is often exceedingly difficult to verify due to particularities of the field or subfield; LLM repositories of text are distinct from image recognition pictures of dog breeds which are distinct from EEG waveforms of human brains which are distinct …

Data-Driven Partitioning In Distributed Optimization For Networked Systems, Prosper Azameti

Theses and Dissertations

The convergence behavior of distributed optimal power flow (OPF) depends strongly on how the power network is partitioned into regions. Classical graph-based methods such as METIS are widely used, but they rely mainly on static topological criteria and do not explicitly incorporate operating-point-dependent information that may affect distributed optimization performance. This thesis develops a data-driven partitioning framework for distributed OPF using graph neural networks (GNNs). Each OPF scenario is represented as a graph in which buses are nodes and transmission lines are edges. Node and edge features capture both structural and operational characteristics of the network. Partition prediction is formulated …

Symmetry In Latin Hypercubes, Levi Neiburger

Theses and Dissertations

Let [n] = {1, ..., n}. A hypercube H of order n and dimension d is a d-dimensional array whose nᵈ cells are indexed by [n]ᵈ. A hyperplane in H is obtained by fixing one coordinate, while allowing the remaining d–1 coordinates to vary. We wish to color each cell of H from a palette of n^d-1 colors such that each hyperplane is polychromatic.

Our main result is the following. Let n be sufficiently large. There exists a symmetric coloring of the d-dimensional hypercubes of order n whose all hyperplanes are polychromatic if and only if: …

Fostering A Growth Mindset In Mathematics: Faculty And Student Experiences, Yolanda G. Rush

Theses and Dissertations

According to the Center for Community College Student Engagement (2019), many students attending two-year institutions need productive persistence strategies, including the development of a growth mindset. Although some growth mindset interventions have been effective in improving academic achievement among students (Boaler, 2016; Canning et al., 2024) and persistence (Lewis, 2019) among students, especially those with developmental needs (Suh et al., 2019) and those in mathematics, little is known about the experiences of students and teachers (i.e., students’ perceptions of teachers’ intentions and implementation) as teachers work to foster a growth mindset culture (Murphy et al., 2021). In this dissertation, I …

Classifying Mathieu-Zhao Subspaces In Products Of Cyclic Rings, Sarah A. Huber

Theses and Dissertations

Mathieu-Zhao subspaces are a generalization of ideals in an algebra and were introduced by Wenhua Zhao in connection to the Jacobian conjecture and its variants. These subspaces have interesting properties, and often the problem of classification is hard. In this thesis, we investigate the structure of Mathieu-Zhao subspaces of the cartesian product of integers modulo powers of a prime p, Zpr × Zps . We will give a complete classification of the subgroups, maximal subgroups, Mathieu-Zhao subspaces, and maximal Mathieu-Zhao subspaces in these rings.

Theoretical Analysis Of Filtering And Smoothing Techniques In Stochastic Time Series, Kaosarat Bola Azeez

Theses and Dissertations

Polynomial-preserving linear filters are fundamental tools for smoothing and trend extraction in noisy time series, particularly when the objective is to reduce short-run variation without distorting underlying low-degree structure. This thesis develops a general framework for such filters based on local polynomial approximation and least-squares estimation. In particular, we establish that the resulting estimators can be represented as symmetric linear filters whose weights satisfy moment conditions that ensure exact polynomial reproduction up to a specified degree. Building on this framework, we derive explicit coefficient vectors for several classical smoothing filters, including the Savitzky-Golay filters SG(5,2) and SG(7,3), as well as …

Schiff Bases As Versatile Platforms: From Multinuclear Dysprosium Complexes To Halogen-Mediated Quasiracemic Crystal Engineering, Macy M. Michorczyk

Theses and Dissertations

Understanding the factors that govern molecular assembly is fundamental in both coordination chemistry and crystal engineering. This thesis investigates these processes through two studies that employ single-crystal X-ray diffraction to elucidate the structural principles underlying the formation of multinuclear metal complexes and the crystal packing of quasiracemates.

The first study examines the unexpected formation of multinuclear metal complexes. Structural characterization of a series of dysprosium complexes was used to compare molecular architectures and identify structural relationships that support a proposed pathway of formation. These findings shed insight into the assembly process that may have lead to their formation.

The second …

Does The Powder River Pass Shear Zone Exist? Geologic Map And Geochronology Of The Bighorn Mountains Caribou Creek 7.5-Minute Quadrangle, Lula G. Staley

Theses and Dissertations

This study produced a 1:24000-scale geologic map of the Caribou Creek 7.5-minute quadrangle in the Bighorn Mountains, Wyoming, by integrating field observation and U-Pb zircon age data. The results of this study will contribute to the USGS EDMAP program by subdividing the southern gneiss terrain. The quadrangle occurs almost entirely in the Bighorn National Forest and is in the drainage of Clear and Crazy Woman creeks. Elevations range from 6,800-9,400 ft. The quadrangle is dominated by Archean crystalline rocks of the Wyoming Province Beartooth-Bighorn Magmatic terrane, mainly granodiorite and tonalite gneiss with lesser migmatite. Several orientations and ages of mafic …

Investigating Phosphorus Load Trends And Driving Factors In Illinois Watersheds Using Machine Learning Algorithms, Hannah Lartey

Theses and Dissertations

Phosphorus (P) pollution in Illinois watersheds has become a significant water quality concern. Recent studies have shown increasing concentrations in streams and rivers, leading to eutrophication, which damages aquatic ecosystems and threatens human health. This study examines temporal trends in total phosphorus loads across 79 monitoring stations in Illinois from 1979 to 2020 and identifies the main environmental factors that influence P load variability. Trend analyses were conducted using the nonparametric Mann-Kendall and Sen’s slope methods. GIS-based climate, hydrology, and soil property datasets were assembled for each monitoring station. These datasets were used to build machine learning models using the …

How And Why Preservice Mathematics Teachers’ Respond To Students’ Statistical Thinking, Radhika Pathak Kharel

Theses and Dissertations

Researchers have found that how preservice teachers (PSTs) respond to students' thinking is crucial to their students' learning and to PSTs' own teaching effectiveness. Although there are some research studies on how teachers respond, there is relatively scarce research on why PSTs respond to students’ thinking the way they do. Such understanding is crucial for designing mathematics methods courses and other professional development opportunities that enable PSTs to create more thoughtful and effective teaching plans. I examined how and why PSTs respond in-the-moment to students’ statistical thinking. The study involved 16 PSTs who enrolled in a middle school mathematics methods …

Structural Framework And Tectonic Implications From Field Investigations In The Ramelau Mountains, Timor-Leste, Tanner A. Nielsen

Theses and Dissertations

Recent advances in petroleum exploration off the southern coast of Timor-Leste and emerging mineral discoveries onshore have underscored the need for a more comprehensive structural understanding of the nation's geology. Although new structural models have been proposed for other parts of Timor, limited progress has been made toward developing detailed models for the Ramelau Mountains, which presents the highest structural relief of the Timor Ranges. Previous mapping in this area has been largely reconnaissance in nature and focused primarily on surface bedrock geology. This study presents a new 1:62,500-scale geologic map and a geometric structural analysis of the Ramelau region …

Perron Theorem Application To A Second-Order Differential Equation With Small Advances, Jason Hendrix

Theses and Dissertations

We analyze a delayed second order differential equation with small delay parameters, proving spectral stability via the characteristic quasi-polynomial and establishing uniform bounds on derivatives of the Green’s function to ensure sign preservation under perturbation, providing a foundation for monotone iteration methods. These results aim to advance the functional-analytic framework for traveling wave solutions in delayed reaction-diffusion systems.

A Systematic Study Of Passkey User Experience Consistency, Bernhardt Ramat

Theses and Dissertations

Passkeys have emerged as a more secure authentication method than passwords, providing a passwordless alternative resistant to phishing and credential theft attacks. Despite their growing adoption, a systematic study into the user experience of passkeys across various websites has yet to be conducted. Usability heuristics suggest that users transfer their expectations from one product to another, and therefore, inconsistencies in passkey deployments can increase cognitive load, resulting in frustration and possible rejection. To address this knowledge gap, this paper presents a comparative analysis of the external functional consistency of the passkey user experience across 111 websites. Our research reveals that …

The Role Of Dust Inputs And Sediment Phosphorus Diffusion Into Utah Lake, Utah, United States Of America, Kristen E. Smith

Theses and Dissertations

Human activities have led to excessive nutrient enrichment which is greater than lake systems can naturally assimilate. This process is known as eutrophication and it is driving significant algae growth resulting in the more common release of harmful toxins. Utah Lake, located in Utah County, UT is one such water body that even after major reductions in anthropogenic phosphorus influent, continues to experience frequent, harmful algal blooms. The extent to which natural processes, like atmospheric dust deposition and sediment recycling, contribute to the lake's phosphorus budget is still poorly understood.

To address this gap of knowledge, this study quantified phosphorus …

Enhancing Silicon Sampling In Large Language Models: Fine-Tuning Techniques Using Survey Data, Davis P. Forster

Theses and Dissertations

Large language models (LLMs) are increasingly used to simulate responses of human demographic groups, a task known as silicon sampling. This paper investigates whether supervised fine-tuning can improve algorithmic fidelity in such settings. We construct a dataset from the General Social Survey (GSS), converting demographic attributes into natural-language backstories and randomly selecting one attribute as a held-out target. Fine-tuning a LLaMA-3.1-70B model on this dataset yields significant improvements on two tasks: (1) imputing missing attributes at the individual level, and (2) reproducing response distributions for demographic slices, such as racial and age groups. Notably, these improvements are achieved with minimal …

Modeling Network Growth Via Generalized Isospectral Reductions, David Thomas Litster

Theses and Dissertations

Many real-world networks also exhibit a variety of symmetries. In this thesis we study equitable partitions and isospectral reductions, both of which are generalizations of symmetries. We formalize the relationship between these two types of generalized symmetry through the study of invariant subspaces. We then use recent results about the presence of equitable partitions in real-world networks to develop a network growth model that introduces similar structures, thereby introducing symmetries similar to those in real world networks.

Intrinsic Stability Of Controlled Systems Via Gershgorin-Type Estimates, David Friedbaum

Theses and Dissertations

Time delays are an inherent feature of real-world dynamical systems, arising whenever information, matter, or energy requires non-negligible time to propagate. Even small delays can destabilize systems that are otherwise well behaved, yet most standard control designs--such as PID or LQR--do not explicitly account for them and may fail when delays are present. This thesis investigates the stability of controlled dynamical systems subject to arbitrary time delays and develops new tools to determine when such systems remain stable. Our approach builds on the notion of intrinsic stability, a strong form of global stability introduced by Webb and Bunimovich, which guaranties …

Game-Theoretically Optimal Strategies In Baseball, William Michael Melville

Theses and Dissertations

Baseball players and their managers make numerous decisions that can have a significant effect on the result of the game. The effectiveness of their decision-making strategies depend on the strategies played by their opponents. For example, throwing a first-pitch fastball down the middle is a good strategy against a hitter who always takes the first pitch, but it is a risky strategy against a hitter who likes to swing at the first pitch and who is good at hitting fastballs. Additionally, any payoff a player receives from playing a strategy comes at the expense of their opponent. A batter cannot …

Play-Based Assessment Of The Cardinal Principle, Allyssa Sonnefeld Leavitt

Theses and Dissertations

Gelman and Gallistel (1986) determined five counting principles that are essential for successful counting, including the cardinal principle where children understand that the last number counted represents the quantity of a set of objects. The traditional How many? task and the Give-n task are the most common tasks that have been used to assess whether children understand the cardinal principle. However, many researchers claim that these tasks either overestimate or underestimate children's understanding of the cardinal principle. Some researchers (Baroody & Pellegrino, 2023) suggest that embedding the traditional How many? task in a game may improve its validity. In this …

An Analysis Of Student Performance In Elementary Linear Algebra At Brigham Young University, Adrienne Irene Christensen

Theses and Dissertations

This study investigates different factors that influence performance in the Elementary Linear Algebra (ELA) course taught at Brigham Young University. These factors include student characteristics such as true freshman status and college enrollment, and content-specific factors such as how performance on essential topics affects overall performance in the course. To analyze the various research questions posed in the study, I used robust linear mixed effects models with random effects controlling for the hierarchical structure of the data. The statistically significant results from these models indicate that (i) true freshmen perform better than other students on exams and in the ELA …

Achieving More Accurate And Interpretable Fraud Detection With Double Machine Learning, Jeremy Andrew Berry

Theses and Dissertations

Fraud detection remains a critical challenge across industries such as insurance, healthcare, finance, and government. Global losses from fraud and financial crime are estimated in the trillions annually, including billions in healthcare and insurance fraud alone. While effective for prediction, traditional machine learning methods often lack causal interpretability and struggle to adapt to evolving fraud tactics. This dissertation investigates the application of Double Machine Learning (DML), an emerging causal inference technique, to enhance both the accuracy and interpretability of fraud analytics. The research compares DML against established causal inference approaches, leveraging a meta-learning framework to evaluate model performance on accuracy, …

Mississippi River Pre-Loess Terrace Deposits: Distribution Of Aggregate Resources, Jonathan Leard

Theses and Dissertations

Pre-loess Terrace Deposits are a Pleistocene, high-quality aggregate resource of gravel, sand, and clay subjacent to loess of varying thickness along the eastern valley wall of the Yazoo Basin in Mississippi. This project delineated 1,230 mi2 of this resource with a volume greater than 33 billion yd3 from the misinterpreted Citronelle Formation in Desoto, Tate, Marshall, Panola, Tallahatchie, Yalobusha, Grenada, Carroll, Holmes, Yazoo, Madison, Hinds, Warren, Jefferson, Claiborne, Adams, Franklin, and Wilkinson Counties with nine terrace base levels at 40, 180, 220, 250, 270, 300, 330, 340, and 370 feet msl indicated by test holes, gravel mine data, outcrop studies, …

Spectral Methods And Wavelets In Quantitative Finance Problems, Davood Damircheli

Theses and Dissertations

This dissertation leverages advanced spectral methods and wavelet techniques to address complex quantitative finance models, enhancing the computation of financial derivatives and risk assessments. Building on foundational studies, this research extends these methods to broader, intricate financial contexts. The first section explores fractional-order generalized Chebyshev wavelets (FOCW) applied to fractional advection equations, relevant in both mathematics and physics. Using a regularized beta function to compute the Riemann-Liouville fractional integral operator, this study introduces a novel numerical scheme with robust accuracy, confirmed through error analysis and empirical tests. The second part examines the fractional Black-Scholes equations for option pricing under subdiffusive …