Physical Sciences and Mathematics Commons^™

Representing Lean Proofs: Tactics, Trajectories, Search, Elisaveta Samoylov

Computer Science Senior Theses

In neural theorem proving for interactive proof assistants such as Lean, tactic prediction models score proof steps by surface likelihood, missing whether a move actually advances the proof. This thesis proposes representing each step by the symbolic edit it induces on the proof state rather than by its token-level surface form, and shows that this effect-grounded view yields better tactic embeddings, reveals structured geometry in complete proofs, and enables a practical proof search prior.

We introduce Delta Tokens — token-level state edits augmented with structural indicators — and show they outperform surface-only representations on tactic retrieval and operator-analogy benchmarks. Embedding …

Llzk-Symex: Building A Circuit Verification Framework For The Llzk Zero-Knowledge Intermediate Language, Nicolás Iair Schaievitch

Computer Science Senior Theses

The rising adoption of ZK (Zero-Knowledge) technology has led to a plethora of DSLs (Domain Specific Languages) for facilitating the development of ZK circuits. At the same time, there has also been an increase in the number of compilation targets for these languages, with different cryptographic foundations and performance optimizations. LLZK, by Veridise, aims to unify the ecosystem by providing a single IR (Intermediate Representation) for the different frontend DSLs, that would then also allow choosing between different backends. Given the high stakes (particularly financial) that a lot of ZK circuits are under, together with their high level of complexity, …

Capturing Large Language Model Similarity Through Spectral Analysis, Ishan Verma Prasad

Computer Science Senior Theses

With the rapid development of open-sourced models on Huggingface, there is a strong need for a way to systematically determine the similarity between models. More strongly, for intellectual property and organization, we need a way to determine the "lineage" of models. We borrow principles from Heavy-Tailed Self-Regularization and Random Matrix Theory to provide an inference-free method to accomplish this. We cluster a corpus of several model families by their spectral fingerprints and demonstrate that each model family occupies a distinct region in weight space. This confirms prior ideas of training setups leaving artifacts on model weights and allows us to …

Knockout Tournaments: An Investigation Of Stability, Isabelle Han

Computer Science Senior Theses

Knockout (or single game elimination) tournaments are a competition format widely used to determine a single winner from a pool of participants. However, the seeding, or the initial pairings set by the organizers of the tournament, can dramatically change each participant's probability of winning. This paper introduces stability as a property of tournaments. More specifically, a tournament is stable if no pair of players can be found such that they both wish to swap initial positions. This property is adapted from prior work on stable matchings and is therefore a well-defined structural property.

We investigate three theoretical questions on the …

Reliability-Aware Mixture-Of-Agents For Robust Ai-Generated Image Detection, Jake Jump, Yu-Wing Tai

Computer Science Senior Theses

Detecting AI-generated images requires reasoning across multiple levels of evidence, ranging from low-level statistical artifacts to high-level semantic inconsistencies. Existing approaches typically rely on a single class of signals or emphasize complex multi-agent coordination, which limits robustness under distribution shifts and common image degradations. We propose a reliability-aware Mixture-of-Agents (MoA) framework that treats Vision-Language Model (VLM) agents and computational features as complementary experts and aggregates their predictions based on empirically calibrated reliability. Rather than relying on intricate inter-agent reasoning, our approach centers on structured aggregation: high-precision “anchor” agents drive predictions, while weaker but complementary signals are adaptively incorporated to resolve …

Dancing For The People: A Culturally Grounded Learning-To-Rank Framework For Powwow Dance Evaluation, Avery C. Sutherland

Computer Science Senior Theses

Powwow dance is a form of Indigenous expression that combines movement, storytelling, regalia, and community values. Within competition powwows, dancers are evaluated through a highly subjective judging process that often lacks standardized criteria, creating challenges for consistency, transparency, and fairness. This work investigates whether a learning-to-rank framework can model subjective powwow dance preferences while remaining grounded in the cultural context of the practice. To support this research, a new dataset was constructed consisting of 19 Women's Fancy Shawl dancer profiles and 236 pairwise preference labels collected from experienced members of the powwow community. Each dancer profile combines textual descriptions, images, …

Rscore - A Tool For Learning And Quantifying Software Infrastructure Resiliency, Selena Yujia Zhou

Computer Science Senior Theses

As LLMs take over writing code, infrastructure resilience has become the central challenge of software development, especially for gaming applications, where latency, availability, and scale demands are extreme. However, holistic software infrastructure is difficult to understand for casual developers because of the multiple layers of abstraction that make up an application, and the lack of structured information from proprietary companies. This thesis explores the creation of rscore, a tool that quantifies software infrastructure resiliency and subsequently educates developers about the architecture of any existing gaming application. The tool generates two graphical models of a game’s early versus current infrastructure and …

Mathematical Analysis Of Within-Host Models: Viral–Immune Dynamics, Bifurcations, And Disease Severity, Nazia Afrin

Doctoral Dissertations

My research develops and analyzes ODE-based within-host models at multiple scales. Using dynamical systems theory and numerical methods, I study host–pathogen interactions and immune responses, providing insights into disease dynamics and control. The first model describes the complex dynamics of Hepatitis B virus (HBV) infection and addresses the question: what mechanisms determine whether the infection is cleared during the acute phase or progresses to a chronic state? A key feature of this model is the assumption that all classes of liver cells (uninfected, infected, and protected from reinfection) proliferate at different rates. The findings provide insight into two important aspects …

The Impact Of Evolution And Strong Allee Effects On The Dynamics Of A Discrete-Time Predator-Prey System, Neerob Basak

Doctoral Dissertations

This dissertation investigates the dynamics of discrete-time predator-prey systems, focusing on both evolutionary responses and ecological interactions. The first part of this dissertation, in Chapters 2 and 3, explores how evolutionary processes, particularly the development of resistance to toxicants in predators, influence the persistence and stability of predator-prey populations. In this part, we extend the predator-prey model developed in Ackleh et al., 2019 to incorporate the evolution of a predator's resistance to toxicant effects. We consider three cases: (1) lethal effects, where the toxicant directly influences the predator's survival; (2) sublethal effects, where the toxicant impacts the predator's fecundity, and …

A Bifurcation Theorem And Its Application To Discrete-Time Models In Ecology And Epidemiology, Jenita Jahangir

Doctoral Dissertations

Matrix models are useful for modeling populations or diseases that involve discrete developmental stages, multiple stages of infection, and interactions among species. To study the coexistence dynamics in matrix models, we extend a bifurcation theorem for resident-invader host-parasitoid type populations by allowing every block of the projection matrix, depending on the bifurcation parameter and the off-diagonal blocks, to be nonzero. As an application, in the first part of the dissertation, we propose a discrete-time host-parasitoid model with stage structure in both species. For this model, we establish conditions for the existence and global stability of the extinction and parasitoid-free equilibria. …

Fairness-Aware And Efficient Federated Learning Frameworks For Heterogeneous Systems, Simin Javaherian

Doctoral Dissertations

Federated Learning (FL) enables decentralized clients to collaboratively train machine learning models without sharing raw data, making it a promising paradigm for privacy-preserving intelligence across large-scale, heterogeneous systems. However, practical FL environments face significant challenges arising from variations in client resources, participation patterns, client behavior, and data distributions. These challenges often lead to inefficiency, unbalanced contributions, and unfairness, ultimately degrading model performance and discouraging long-term client participation. This dissertation advances the state of FL by developing a unified suite of fairness-aware and efficiency-driven frameworks tailored for heterogeneous environments. We investigate fairness from multiple perspectives, including client selection, contribution weighting, and …

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 …

C*-Extreme Quantum Instruments; Completion And Disintegration Of Completely Positive Maps, Arghya Chongdar

Doctoral Theses

This thesis develops a comprehensive operator-algebraic framework for the study of completely positive (CP) instruments, with contributions spanning convexity theory, integration theory, completion problems, and disintegration theory. We begin by laying the foundational groundwork in the theory of C*-algebras and von Neumann algebras, introducing key structures such as CP maps, positive operator-valued measures (POVMs), and CP instruments, along with their dilation-theoretic properties. Pure and decomposable instruments are characterized via minimal bi-dilations, and CP instruments are realized as bivariate maps, providing a rigorous quantum analogue of classical joint measures. The thesis then investigates convexity-theoretic aspects of instruments. A structural characterization of …

Deployment-Aware Deep Learning For Computer Vision: Efficient Architectures From 3d Segmentation To Mixed Reality, Bahar Uddin Mahmud

Dissertations

Deep learning has become the dominant approach for solving vision-centric problems; however, its successful deployment in real-world applications remains limited by high computational cost, data dependency, and insufficient integration with practical and human-centered environments. While state-of-the art deep learning models often achieve impressive performance in controlled settings, they frequently fail to generalize or operate efficiently under deployment constraints such as limited resources, complex data modalities, and real-time interaction requirements. These limitations motivate the need for a deployment-oriented deep learning framework that balances accuracy, efficiency, and practical usability.

This dissertation investigates the design and deployment of efficient deep learning architectures for …

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 Number Of Ways To Express A Set As A Union Of Individually Interesting Sets, Alison Watson

Master's Theses

In a dataset that contains what ought rightly to be several distinct datasets placed in juxtaposition with each other, grouping datapoints based on observed similarities can be done in many ways. Topological Data Analysis (TDA) is a field of math that seeks to impose geometric structure onto datasets, thereby translating problems in statistics to problems in geometry or topology. A common truism in this field is “Data has shape and shape has meaning.” In this thesis, we use combinatorial and categorical arguments to demonstrate some shortcomings of a TDA approach on a class of inverse problems inspired by marine wildlife …