Physical Sciences and Mathematics Commons^™

Strang-Type Exponential Integrators For Stiff Reaction-Diffusion Systems, Saburi Tolulope Rasheed

Doctoral Dissertations

Reaction-diffusion systems, as examples of semilinear parabolic partial differential equations, have played significant roles in the mathematical modeling of physical, chemical, and biological processes. Several reaction-diffusion systems typically do not have exact solutions in closed form, and numerically solving them also comes with challenges due to the presence of the nonlinear local interaction/chemical reaction dynamics representing the reaction term, coupling between components, multidimensionality of the diffusion operator, and stiffness of the diffusion and/or reaction terms. Wederive and analyze several second-order accurate exponential integrators of the Strang type for the time discretization of stiff reaction-diffusion systems. We utilize the finite difference …

The Interplay Of Seasonality, Evolution, And Density-Dependence In Discrete-Time Predator-Prey Dynamics, Narendra Pant

Doctoral Dissertations

We extend the discrete-time mathematical models developed in (Ackleh et al., 2019) and (Ackleh et al., 2024) to account for seasonal prey reproduction and build a class of discrete-time predator-prey seasonal models. Each model distinguishes between breeding and non-breeding seasons, representing prey reproduction as a periodic function of period 2. Altogether, three different models are analyzed. In the first part, we extend the predator-prey model from (Ackleh et al., 2019) to incorporate seasonality. We study the resulting dynamics and show that when the inherent reproduction number of the prey and the invasion reproduction number of the predator are larger than …

Building And Restoring Trust In Deep Learning: From Multimodal Sensing To Generative Synthesis And Model Integrity, Liqun Shan

Doctoral Dissertations

Deep learning has become a foundational technology for modern intelligent systems used in sensing, authentication, media generation, and automated decision-making. As these systems are increasingly deployed in security- and privacy-sensitive settings, ensuring their trustworthiness has become a critical challenge. Yet deep learning models remain vulnerable to spoofed sensory inputs, synthetic media, and malicious behaviors hidden within trained networks. These vulnerabilities undermine reliability and raise serious concerns about whether such systems can be trusted under adversarial and deceptive scenarios. This dissertation investigates how to build and restore trust in deep learning across three tightly connected dimensions: multimodal sensing, generative authenticity, and …

Learning And Predicting The Performance Of Gradual Type System, Mohammad Wahiduzzaman Khan

Doctoral Dissertations

Gradual typing reconciles the complementary strengths of static and dynamic typing by allowing programmers to incrementally introduce type annotations while preserving the flexibility of dynamically typed code. This approach improves reliability, documentation, and tooling support without sacrificing rapid prototyping. To ensure soundness, gradual type systems enforce annotations through runtime checks, typically implemented via cast insertion. Although these checks guarantee correctness, they can introduce substantial and highly variable runtime overhead, making performance prediction and optimization a central challenge for practical adoption. Prior work has largely focused on coarse-grained (macro-level) configurations, where entire modules are either fully typed or untyped. While such …

Investigating The Distribution And Origin Of Pitted Mounds On Mars Using Machine Learning-Based Mapping And Integrated Geological Analysis: Application To Isidis Planitia, Precious Batubo

Doctoral Dissertations

Pitted mounds are widespread landforms across the northern plains of Mars, yet their origin remains uncertain. These features have been interpreted as possible expressions of subsurface fluid activity, including sedimentary volcanism, magmatic processes, or other fluid-assisted mechanisms. Determining their distribution, morphology, and geology is therefore important for understanding the evolution of subsurface hydrological processes and the planet’s potential for habitability. However, the large spatial extent of mound-bearing terrains makes comprehensive manual mapping impractical. This dissertation presents an automated approach to mound detection using Faster Region-Based Convolutional Neural Network (Faster R-CNN) from high-resolution Context Camera (CTX) images including morphometric and mineralogical …

Emerging Catalysts And System Designs For High-Current-Density Co2 Electroreduction To Multicarbon Fuels And Chemicals Toward Industrial-Scale Applications, Godwin Uche Edor

Masters Theses

Electrochemical CO2 reduction (eCO2RR) offers a sustainable route to convert CO2 into value-added fuels and chemicals, particularly multicarbon (C2+) products due to their higher energy density and economic value compared to C1 counterparts. Industrial adoption of eCO2RR technology is hindered by the difficulty in stably reaching superior Faradaic efficiency (FE) for C2+ products at ≥ 200 mA cm-2 at low applied overpotential due to sluggish C–C coupling kinetics, competing reactions, and catalyst instability. Hence, we examine the recent advances in eCO2RR catalyst engineering strategies, such as nanostructural and electronic modifications of Cu-based catalysts (e.g., interfacial, surface, facet, and defect engineering, …

Micro-Hyperspectral Imaging Of Phytoplankton Enables Deconvolution Of Mixed Communities For Spaceborne Hyperspectral Remote Sensing, Chisom Okwuchi Emeghiebo

Masters Theses

Characterizing phytoplankton diversity is critical for large-scale biodiversity monitoring and harmful algal bloom (HAB) detection. Here, we present a micro hyperspectral imaging method to characterize reflectance signatures, for the first time across major phytoplankton groups. Spectral variability among taxa in laboratory cultures is interpreted using algal pigment and absorption analyses, demonstrating that pigment composition and absorption govern reflectance features. Chlorophytes and cryptophytes exhibit distinct spectral signatures and are readily distinguishable, whereas diatoms and dinoflagellates show greater spectral similarity, with differentiation relying on subtle reflectance features associated with chlorophyll c₁c₂ near ~463 nm and within 620–650 nm. We further applied this …

Linking Greenhouse Gas Fluxes And Plant Responses To Saltwater Intrusion Events Using Remote Sensing, Madeline Jean Moore

Masters Theses

As sea level rise and coastal subsidence increase coastal Louisiana's vulnerability to saltwater intrusion (SWI) events, accurate and rapid monitoring of vegetation responses to these events is becoming increasingly important. In this study, we utilized unmanned aerial vehicle (UAV) multispectral imagery to assess short-term vegetation responses to simulated SWI events in the Visser’s Experimental Wetland Complex in Saint Martinville, Louisiana. Vegetation patches of two common freshwater wetland species, Panicum hemitomon (Maidencane) and Typha domingensis (Southern Cattail), were exposed to 5 ppt salinity for 6-, 10-, and 17-day durations. Multispectral imagery of both species was collected before and after each SWI …

Classifying Storm Surges Along Louisiana Coast Using Machine Learning, Faith Ewere Okunbor

Masters Theses

Storm surges are among the most significant threats to coastal wetlands, causing flooding and saltwater intrusion that alter hydrology, vegetation structure, and long-term ecosystem resilience. Along the Louisiana coast, storm surge effects vary depending on storm behavior, shoreline geometry, and marsh hydrologic connectivity, yet are commonly characterized using broad storm metrics rather than site-specific environmental responses. This study develops a data-driven framework to classify storm surges across coastal Louisiana wetlands using observations from the Coastwide Reference Monitoring System (CRMS). Hourly water-level and salinity time series from twelve hurricanes (2007-2024) were analyzed using a 40-day storm-centered window. Hydrologic and salinity metrics …

Regioselective Tellurination Reactions And Their Utilities, Itunu Comfort Olanrewaju

Masters Theses

This thesis provides a comprehensive study of regioselective tellurination and its applications by integrating experimental and computational techniques, with an aim of synthesizing libraries of organotellurium heterocycles. This study addresses existing challenges in regioselective tellurination, such as unpredictable regioselectivity and avoidance of toxic reagents by harnessing intramolecular Te…O coordination and electrophilic aromatic tellurination. This strategy enables the development of previously poorly accessible compounds including benzotellurazinones, 2-acylaminobenzotellurazoles, and previously unknown 2,3-dihydrobenzo [b] oxatelluranes, which were prepared by antiMarkovnikov anti-addition of TeCl4 to C-C triple bonds. Experimental studies were complemented by computational DFT analyses to provide mechanistic and energetic insight into the …

Stratigraphic Distribution Of Pleistocene Aves At Fossil Lake In Lake County, Oregon, Cole Bradley Phillips

Masters Theses

The Fossil Lake locality in south-central Oregon is rich in many species of fossil remains and is also home to packages of sandstone that grade upward into finer siltstone or claystone. These packages have been interpreted to represent rising and falling lake levels as a result of glacial transgressive and regressive sequences. The fossil vertebrates and invertebrates have also fluctuated because of the different climates at Fossil Lake. Although the stratigraphic distribution of most classes of animals have been determined, fossil birds have not. Here, the distribution of 329 avian fossils is presented in the stratigraphic framework. The species were …

Disparities In The Identification Of Vulnerable Communities Due To Design Storm Methods: A Case Study In The Vermilion River Watershed, South Louisiana, Usa, Claire Orgeron

Masters Theses

Accurately identifying socially vulnerable populations at-risk of flooding is critical for equitable disaster mitigation and planning. This study investigates how the selection of design storm method, which is fundamental to developing flood risk maps used for this identification, influences which socially vulnerable populations are recognized as being at elevated flood risk. The most widely used design storm approach relies on National Oceanic and Atmospheric Administration (NOAA) Atlas 14 point-based rainfall frequency estimates. These estimates are typically applied spatially using areal reduction factors, thereby disregarding rainfall spatial variability in real storms. Stochastic Storm Transposition (SST), an alternative design storm approach that …

Scientific Crosstalk: Natural Language Processing, Praveshika Bhandari

Theses and Dissertations

While sentiment analysis has made significant strides in domains such as social media and personal correspondence, its application to formal scientific writings remains under-explored. The crosstalk between emotional expressions in personal and professional communications has also received limited attention despite its potential to reveal insights into the emotional drivers of scientific creativity. Our research introduces a computational framework designed to detect and quantify emotional expressions across various documents over time. Leveraging state-of-the-art transformer models fine-tuned on domain-specific corpora, the framework models emotional tone distribution. Integrating emotion analysis with knowledge graph modeling enables the exploration of emotional trends alongside key scientific …

Breadquest: Enhancing Roguelike Accessibility Through Procedural Generation And Thematic Design, Hahns Pena

Computer Science and Software Engineering

BreadQuest is a top-down roguelike dungeon crawler with a whimsical dessert theme that aims to make the genre more accessible while preserving strategic depth and replayability. Players explore procedurally generated dungeons, fight pastry-themed enemies, and collect bakery-inspired items that support a flavor-elemental combat system, with each run offering unique layouts, encounters, and rewards. Built in Unity with a modular, data-driven architecture, the game uses procedural generation techniques like Binary Space Partitioning, Voronoi diagrams, and Perlin noise to create varied and replayable levels. The project emphasizes approachable gameplay, cultural dessert inspiration, and replayability, with success evaluated through playtesting and player feedback.

Active Galaxies In A New Light: The Broad Line Region In The Near-Infrared, Sky O'Donnell

Physics

At the center of most massive galaxies, there is a supermassive black hole with a mass millions to billions of times that of the Sun. In some of these galaxies, so-called Active Galactic Nuclei (AGNs), the supermassive black hole is converting the gas that falls toward it into radiation energy, creating large amounts of luminosity. AGNs are composed of the central supermassive black hole, its accretion disk, and a region just outside, composed of fast-moving ionized gas clouds called the Broad Line Region (BLR). Using spectra obtained with NASA’s Infrared Telescope Facility, we use a technique known as reverberation mapping …

Real-Time Simulation Of Bio-Luminescent Light Propagation Using Compute Shaders Within Unreal Engine, Jaden D. Halevi

Computer Science Senior Theses

Presented in this paper is a GPU-native approach to interactive fluid simulation within Unreal Engine 5. The system, BioFluidSim, implements an incompressible Navier-Stokes solver using Unreal’s Niagara Grid2D compute shader pipeline, with a modular biological emission output stage parameterized from experimentally measured Lingulodinium polyedrum bioluminescence behavior. The system is evaluated against FluidNinja Live, a commercially available fragment shader fluid implementation, as a performance baseline. Beyond performance, BioFluidSim offers greater physical fidelity than the fragment shader baseline. Helmholtz–Hodge pressure projection enforces a divergence-free velocity field at runtime, a physical constraint approximated but not enforced by fragment shader approaches. The biological emission …

On The Fractional Laplacian Type Operator, Maysam Abdulnaser Zain

Theses

In this thesis, we study analytical structures arising from Dunkl theory and their

applications to harmonic analysis and fractional Laplacian operators. Dunkl operators are differential–difference operators associated with finite reflection groups, providing a natural generalization of the classical Fourier analysis through the introduction of root systems and multiplicity functions. Within this framework, several classical transforms appear as special cases of the (k,a)-generalized Fourier transform. We study the generalized Fourier transform ��ₖ,ₐ, its kernel B_k,a (x,y), and the associated translation operator and convolution structures. Using these tools, we construct the corresponding heat …

Ai Interview Helper: A Tool For Assisting Search And Rescue Long-Profile Interviews, Dylan P. Starink

Master's Theses

In Search and Rescue (SAR) operations, time pressure and limited interviewer experience can lead to missed opportunities when interviewing a missing person’s friends and family. This thesis presents a real-time, end-to-end system that provides context-aware follow-up question suggestions as interviews unfold. Leveraging large language models (LLMs) and agentic design patterns, the system is intended to support interviewers by helping them identify relevant follow-up questions and pursue potentially overlooked lines of inquiry.

The system was evaluated through three mock interviews with two SAR interviewer participants across two events. Given the limited sample size, the results provide early insights into the feasibility …

Exploring Regenerative Vegetable Systems On The Central Coast Of California, Una S. O'Connell

Master's Theses

As climate change and current agricultural practices place pressure on the long term sustainability and resilience of food production systems, there is growing interest in whether existing agricultural systems can adapt to maintain productivity while improving environmental outcomes.

This study evaluated the effects of regenerative versus standard organic vegetable production systems on yield, insect communities, and weed suppression across three field trials conducted on California's Central Coast. In addition, I collected baseline soil health data for all trials. Trials 1 and 2 were carried out at the Cal Poly San Luis Obispo Organic Farm using cabbage and broccoli as cash …

Equitable Decompositions: A Gateway To Spectral Theory Through Graph Automorphisms, Daniel Ford

Master's Theses

Graphs with symmetry appear throughout mathematics and its applications, from the structure of molecules and network design to combinatorial game theory. A central question in spectral graph theory is how to compute or characterise the eigenvalues of the matrices associated with such graphs. Classical decomposition methods, such as diagonalisation or Jordan normal form, accomplish this but only once some spectral information is already known. A different approach, introduced by Barrett et al. (2015), uses the automorphisms of a graph to block-diagonalise its adjacency matrix without any prior spectral information. Because one of the resulting summands is always the quotient matrix …

Crab: A Novel Clustering Score Using Clustering With Rivals And Buddies For Unsupervised Learning, Allen Choi

Master's Theses

Unsupervised clustering algorithms today are used across a wide variety of fields such as biology, engineering, and industry in order to classify observations into groups where labels are not provided. This can provide important latent information regarding the observations within groups, as well as insight regarding the groups themselves. In order to judge the optimal number of clusters for an unsupervised clustering algorithm, many methods exist such as the Elbow Method and Silhouette Score; however, these methods come with drawbacks and are not necessarily flexible across many unsupervised methods. We present a novel clustering score framework relying on a resampling-based …

Integer Quantization And Embedded Deployment Of Cnn Star Trackers For Cubesats, Meora R. Giusiano

Master's Theses

A star tracker determines spacecraft orientation by photographing the star field, detecting stars in the image, matching them against a catalog, and computing the rotation between observed and cataloged directions. Convolutional neural networks (CNNs) have been proposed as replacements for the detection and centroiding stage, offering improved sub-pixel accuracy and recovering faint stars that classical thresholds lose to stray light and sensor noise. The improvement comes at higher computational cost; the PolySat systemboard targeted in this work lacks the floating-point hardware these networks assume.

This thesis closes the gap between floating-point desktop evaluation and embedded integer deployment. Nine encoder-decoder CNN …

Evaluation Of Solar Reflective Pigments For Use In Direct-To-Metal Coatings, William J. Diment

Master's Theses

Solar reflective coatings offer a promising strategy to mitigate the urban heat island effect by reducing absorption of near-infrared solar energy. This thesis project investigates the feasibility of incorporating near-infrared reflective pigments into waterborne direct-to-metal (DTM) latex coating systems while maintaining acceptable color comparison characteristics and coating performance. An all acrylic latex DTM formulation with titanium dioxide as the sole pigment was prepared and tinted with a variety of conventional and solar reflective commercial colorants across the yellow, red, blue, and green color ranges. Coatings were evaluated for solar reflectance, CIELAB color, gloss, contrast ratio, rheological behavior, accelerated ultraviolet weathering …

Constructing Orthonormal Bases With The Residuals Of Successive Approximations, An Introduction To Multiresolution Analysis, Elijah J. Guptill

Master's Theses

Wavelets and wavelet analysis are used in the study of signal processing, quantum field theory, functional analysis, multifractal analysis, and various other areas of mathematics. Multiresolution analysis provides a framework for building a wavelet basis of $\mathcal{L}^{2}(\mathbb{R})$ from a scaling function $\phi$, whose dyadic dilations and translations, $\{2^{j /2}\phi(2^{j}x-k):j,k\in \mathbb{Z}\}$, approximate $\mathcal{L}^{2}(\mathbb{R})$. One of the key properties of  $\phi$ is that it must satisfy $\phi(x)=\sum_{k\in \mathbb{Z}}{p_{k}2^{j /2}\phi(2^{j}x-k)}$ with respect to the norm on $\mathcal{L}^{2}(\mathbb{R})$. This equation is called a two-scale difference equation. Such equations enforce a regularity on the ordinary generating function $2^{-1 /2}\sum_{k\in \mathbb{Z}}{p_{k}z^{k}}$, known as the quadrature condition. …

What Makes A Modern Attention Implementation?, Brian H. Slonim

Master's Theses

Since the seminal assertion by Vaswani et al. in 2017 that “Attention Is All You Need,” transformer models have risen to ubiquity due to their ability to learn extremely complex patterns from sequence data, culminating in the unprecedented generative capabilities of large language models. These models’ strength lies in their scale: hundreds of millions (e.g., BERT-LARGE) to billions or trillions of learned parameters. Running inference with these models, let alone training them, would be intractable without significant innovations in the hardware and software that support them. This need has driven an enormous demand for GPU compute and associated software ecosystems, …

On M-Estimation: From Theory To Examples, Alexander Yuan

Master's Theses

M-estimation provides a unified framework for statistical procedures defined as optimizers of data-dependent criterion functions. This thesis gives an expository account of M-estimation in classical and high-dimensional settings. The classical part develops weak convergence, empirical process tools, and the argmax framework for studying consistency, rates of convergence, and weak limits. Examples including least squares, maximum likelihood, robust location estimation, change-point estimation, and empirical risk minimization illustrate regular and non-regular asymptotic behavior.

The high-dimensional part studies regularized M-estimators, where the focus shifts to finite-sample error bounds and model selection guarantees. Topics include decomposable regularizers, restricted strong convexity, non-convex penalties, and sparsistency. …

Hot Hands Or Chance Happenings? A Simulation-Based Approach For Wnba Teams, Ruben Jimenez

Master's Theses

The hot hand is a polarizing topic in basketball analytics: fans, stakeholders, and even players themselves assert confidently their belief or disbelief in the idea that players who perform well will continue to do so over an extended period of time. Statistical research has been conducted since as early as 1985 to attempt to disprove or prove the existence of this phenomenon. More recent works have refuted the earliest objections to the hot hand’s existence, with conclusions aided by robust simulation techniques. In this work, we compare hypothesis tests using multiple simulation techniques to explore the hot hand at the …

Is The Hot Hand Real? Evidence From A Permutation And Hierarchical-Based Analysis, Cameron Z. An

Master's Theses

The hot-hand phenomenon, often described as the tendency for individuals to experience prolonged streaks of success that exceed what would be expected under random performance, has been widely studied across many disciplines, particularly basketball. Early studies attempted to evaluate this effect through various techniques, often concluding that the hot-hand phenomenon was largely a myth. However, recent studies have begun to revisit previous analyses using improved statistical techniques, with some claiming evidence of a discernible hot-hand effect. This study examines the presence of the hot-hand effect in the modern NBA by testing whether observed shooting patterns deviate from those simulated under …

Developing A Humpback Whale Vocalization Detector Using Machine Learning Models, Lucas Kantorowski

Master's Theses

Humpback whale songs are notoriously complex. Identification of humpback whale song units requires bioacousticians to tediously listen, analyze, and annotate collected sound data. Even sparse data requires listening to the entirety of the collected acoustic data. In this study, three hours of audio containing over one-thousand humpback whale song units was collected in Monterey Bay, California.

Prior studies have seen success using convolutional neural networks by performing image classification on hundreds of hours worth of spectrograms. Our study uses traditional machine learning models, as they are less computationally demanding, and require less data.

We use time splitting and Mel-frequency cepstrum …

Determining K Clusters In K-Means Clustering With The Crab Algorithm, Jasmine Kristine S. Cabrera

Master's Theses

Unsupervised clustering often faces the challenge of determining the correct number of clusters in the absence of a true target variable. Traditional methods such as the Elbow Method and the Silhouette Score can produce ambiguous results and rely on assumptions about cluster shape or separation. To address this, we created the Clustering Rivals and Buddies (CRAB) algorithm which evaluates clusters based on stability across multiple subsamples. CRAB uses pairwise classifications to identify points that consistently group together called “Buddies” and points that remain separated called “Rivals.” Applied with K-means, CRAB accurately recovers underlying cluster structures in both spherical and non-spherical …