Physical Sciences and Mathematics Commons^™

Contributions Toward Understanding The Weak Lefschetz Property For Two Classes Of Almost Complete Intersection Ideals, Matthew Davidson Booth

Theses and Dissertations

In 1980, Richard Stanley proved that Artinian monomial complete intersections enjoy the strong Lefschetz property in characteristic zero. Since his landmark result, the strong and weak Lefschetz properties (SLP and WLP) have garnered attention from an increasing number of mathematicians from an ever-broadening swath of the mathematical community. Indeed, the Lefschetz properties have been scrutinized for their relation to algebraic invariants such as Betti numbers and the Hilbert function as well as their links from commutative algebra to other branches of mathematics.

However, the Lefschetz properties are also quite subtle; the aforementioned result due to Stanely is a rather rare …

Rating Ai Models For Robustness Through A Causal Lens, Kausik Lakkaraju

Theses and Dissertations

As Artificial Intelligence (AI) systems become increasingly powerful and widely accessible, trustworthiness remains a major barrier to their adoption in critical domains such as finance and healthcare. With the advent of large language models (LLMs) that can perform multiple tasks with strong empirical performance, users increasingly rely on these black-box AI services to obtain recommendations, analyze text, and support everyday decisions. However, real-world incidents and empirical studies show that these systems can be overly sensitive to small changes in input, producing outputs that shift substantially under minor perturbations. In addition, models have been reported to exhibit stereotypical behavior and systematic …

Exploring The Efficiency Of Logistic Models With Opt-Out Designs In Discrete Choice Experiment And Their Applications, Dai Fang

Theses and Dissertations

A discrete choice experiment is usually conducted in economics background to measure how consumers would like to trade off attributes of a product, service, or policy. In this experiment, respondents are provided different hypothetical combinations of varied components by using an experimental design such as the full factorial design, which fully represents the all combinations of attributes and levels. The mathematical background of a discrete choice experiments is based random utility theory, in which either positive or negative values are given each characteristic and the weighted sum values of each choice given in the experiment will be compared. This experiment …

Evidence Of Metal-Microcystin Complexation And Its Potential Role In Environmental Fate, Ashley Marie Womer

Theses and Dissertations

Microcystins that enter freshwater systems pose a threat to human health therefore their fate and transport throughout the water column have been intensively studied. While sediment has been regarded as an environmental fate for microcystin (MC), less is known about the molecular mechanisms by which microcystin interacts with the sediment and/or the thermodynamic stability of these interactions. While microcystin has a half-life in lake water on the order of weeks, microcystin adsorbed to sediment can be detected hundreds of years later1-2. Microcystin has been desorbed from these sediments with various EDTA solutions, therefore, work is presented to support the hypothesis …

Surface Salinity Variability And Loop Current Frontal Eddy Activity In The Gulf Of Mexico, Pamela Jo Lee

Theses and Dissertations

The Gulf of Mexico (GoM) is a dynamic semi-enclosed basin where mesoscale and submesoscale circulation regulate the distribution of freshwater, nutrients, and biological productivity. The Loop Current System (LCS), which includes the Loop Current (LC), Loop Current Eddies (LCEs), and Loop Current Frontal Eddies (LCFEs), exerts the dominant control on basin-wide circulation. These features interact with freshwater input from the Mississippi-Atchafalaya River System (MARS) and with saline inflow from the Caribbean, resulting in variability in sea surface salinity (SSS) and chlorophyll-a (Chl-a) across a range of spatial and temporal scales. A primary focus of this work is understanding how the …

A Combined Observational And Reanalysis Approach To Beaufort Gyre Freshening, Christina Mccarty Gregory

Theses and Dissertations

The freshwater (FW) content in the Arctic plays a critical role in the global climate by influencing the regional physical and biological processes, large-scale ocean circulation in the North Atlantic, sea-ice albedo, and other crucial climate parameters. Located in the Canadian Basin, the Beaufort Gyre (BG) is the largest retainer of FW in the Arctic. Here we examine the dynamics of the BG between 2016-2018 using satellite-derived products and ocean reanalysis parameters. Our results demonstrate that the characteristics of BG during the years of this study are a complex combination of various processes. The Ekman-induced FW fluxes were separated into …

Continuous Imaging Of The Shallow Subsurface Of Horry County Using Gpr And Auger Data, Chase William Robinson

Theses and Dissertations

Welded barrier systems are common along passive margins globally and make up approximately 15% of the coastlines around the world. The subsurface facies assemblages of welded barrier systems record depositional histories and past sea-level dynamics, but their complicated depositional architecture can be problematic for understanding aspects like groundwater flow and freshwater-saltwater exchange. Most studies of modern welded barrier sedimentary systems using ground penetrating radar (GPR) rely on a few 100 meters of subsurface data supplemented with a few drill cores. In this study, we used over 75 km of 100MHz and 25MHz GPR data and 195 auger drill logs collected …

A Study Of Type Ia Supernova Spectra, David Edwins

Theses and Dissertations

Type Ia Supernova already represent a valuable tool for astronomical exploration by providing a bright standardizable candle, however, they also represent an opportunity to observe the matter in the universe along the line of sight. A study of the spectra of Type Ia supernovae reveals a variety of contamination of these spectra at a variety of locations, including the Milky Way galaxy, a source likely local to the original supernova and an as yet unidentified source of contamination. Further, Type Ia Supernova appear to change with the redshift of the supernova.

The Use Of Machine-Learning Interatomic Potentials To Study Bulk Properties Of Aqueous Zn Ion Batteries, Ria Vasdev

Theses and Dissertations

Aqueous Zn-ion batteries (AZIBs) have emerged as a promising energy storage tech- nology owing to their high Coulombic efciency and low environmental impact. However, their practical development is impeded by limited cycling stability, pri- marily caused by parasitic side reactions occurring at the anode surface. These side reactions are strongly infuenced by the bulk solvation structure of Zn-based elec- trolytes, which remains challenging to characterize using conventional experimental techniques. Machine-learning interatomic potentials (MLIPs) provide a powerful computational approach to investigate these systems and can be employed to eluci- date the bulk structural properties of Zn electrolytes.

Raman Spectroscopy Of Biological Molecules And Inorganic Compounds, Jasmine Ervin Gardner

Theses and Dissertations

This dissertation describes the use of multiple Raman spectroscopic techniques for the detection and characterization of non-hazardous organic and inorganic compounds. The first two applications involve the use of Raman and surface enhanced Raman spectroscopy to thoroughly analyze autoinducers (AI) produced by gram negative bacteria. The second set of applications involves the use of anti-stokes Raman and resonance Raman spectroscopy to remotely detect inorganic compounds at distances of up to 12 meters away.

This work describes the use of Raman spectroscopy for the characterization and discrimination of signaling molecules used in bacterial communication. Our initial work shows the potential of …

Stimuli-Responsive Hybrid Materials: From Fundamental Photophysics To Tunable Properties, Grace C. Thaggard

Theses and Dissertations

Photochromic materials exhibit properties that can be dynamically tailored as a function of light exposure and represent a rapidly expanding field driven by applications ranging from molecular computing, nanotechnology, or photopharmacology to programable heterogeneous catalysis. For example, the possibility to tune a material’s catalytic activity “on demand” through exposure to a noninvasive stimulus is a transformative concept that could shift the paradigm in chemical industry by allowing for in-situ suppression of byproduct formation, isolation of reactive intermediates, and even control over product yield and selectivity. Development of the mentioned photochromic materials is based on stimuli-responsive molecular building blocks which undergo …

A Dynamical Systems Analysis Of Amyloid-Beta Production, Caroline Lloyd

Theses and Dissertations

Alzheimer’s disease is characterized by the presence of beta-amyloid (A𝛽) plaques in the brain, caused by an accumulation of misfolded A𝛽 proteins. Research suggests that hallmark proteins involved in neurodegenerative disorders such as Alzheimer’s disease, Parkinson’s disease, and Amyotrophic Lateral Sclerosis (ALS) exhibit prion- like behavior. This means that the misfolded, pathogenic proteins influence non- pathogenic proteins to misfold. There is also a small rate of spontaneous conversion which causes A𝛽 to misfold without the presence of pathogenic proteins. Additionally, events that limit blood flow to the brain, such as strokes or direct trauma, are known to increase A𝛽 in …

Quantifying And Characterizing Microplastics In North Inlet And Winyah Bay Estuaries, Sc, Emily Grace Contract

Theses and Dissertations

Microplastics (1 μm to 5 mm) accumulate in the bodies of marine organisms and negatively impact their health. Microplastics have also been linked to birth defects, endocrine disruption, and cancer in humans. This study quantified, characterized, and compared microplastics in a protected estuary (North Inlet Estuary, South Carolina) and an estuary impacted by anthropogenic activities (Winyah Bay, South Carolina). Water samples were taken from three sites in each estuary from February 2025 to December 2025. The samples were digested, filtered, then examined visually for microplastics. Plastic particles were extracted and analyzed by Raman microscopy to obtain polymer content. Results indicate …

Polyvinylidene Difluoride As A Platform For Photonic Circuits, Caleb Duff

Theses and Dissertations

Integrated photonic circuits represent a promising avenue for advancing computing capabilities by replacing electrons with photons as information carriers. This transition necessitates a comprehensive and innovative approach as the well understood requirements for electronic circuits are replaced by the needs of photonic circuits. This work will discuss topological photonics and one of many recent successes in their use to create near scatter free states. This work will then discuss progress towards creating an electromechanical platform using polyvinylidene difluoride [(C2H2F2)n], the platform’s benefits, and how the platform has been tested. This platform would have the potential to create reconfigurable photonic circuits, …

Coastal Development Effects On Estuarine Benthic Microalgal Communities, Henry Christopher Guy

Theses and Dissertations

As key drivers of neritic primary productivity, benthic microalgae (BMA) play essential roles in biogeochemical cycling and estuarine food webs. When considered alongside their shallow, restricted habitats, BMA contribute disproportionately to global carbon fixation. However, the extent of human impact on BMA communities is largely unknown. This study aimed to quantify anthropogenic forcing through specific abiotic drivers of benthic microalgal success. BMA biomass, community composition, porewater nutrients, and sediment composition were measured within two South Carolina Estuaries. North Inlet and Murrells Inlet share similar geographic and morphological characteristics but differ significantly in terms of watershed population. Dissolved phosphate, nitrate, and …

Semi-Supervised Galaxy Morphology Classification Using Convolutional Vision Transformers, Emily Miller Christen

Theses and Dissertations

Galaxy morphology classification is an essential task for understanding galaxy evolution, but modern high-redshift surveys such as JADES produce a large number of unlabeled images that cannot be handled with traditional manual or supervised learning methods. This work explores a semi-supervised transfer learning framework that leverages labeled data from Galaxy Zoo 2 to classify morphologies in James Webb Space Telescope JADES observations. A pretrained Convolutional Vision Transformer is adapted to the new imaging domain and refined using pseudo-labeling on unlabeled data. Experiments simulating JADES imaging conditions show that reduced resolution and noise significantly impact the separability of certain morphology classes, …

Tracing Cosmic Origins: Investigating Carbon Isotopic Ratios To Unlock Universal Insights, Karthik Gananath Putha

Theses and Dissertations

The universe is made up of a vast and diverse collection of elements. All elements with atomic mass number A > 12, ranging from carbon to iron, are continuously enriched over the course of galactic evolution through stellar nucleosynthesis. In contrast, elements heavier than 56 Fe are primarily synthesized via neutron-capture processes, occurring in Asymptotic Giant Branch (AGB) stars, core-collapse supernovae, and more extreme events such as binary neutron star mergers. These elements are later expelled into the surrounding space through powerful supernova explosions. Overtime, these processes enrich the interstellar medium with heavy elements and thus plays an important role in …

Deep Learning Algorithms For Generative Materials Design And Composition Based Property Prediction, Rongzhi Dong

Theses and Dissertations

The accelerated discovery of novel functional materials is critical for advancing trans- formative technologies in energy storage, electronics, and catalysis. Current discovery strategies, whether experimental trial-and-error or DFT-based computational screen- ing, are fundamentally constrained by the limited size and diversity of existing materials databases and the difculty of building predictive models that generalize beyond known compounds. Despite signifcant progress in both experimental and computational approaches, two central challenges persist in modern materials science: generating large numbers of realistic, stable, and synthesizable materials outside existing databases, and developing machine learning models capable of accurately inferring structures and predicting properties under realistic …

Machine Learning Toward Materials Discovery: From Crystal Mapping And Out-Of-Distribution Property Prediction To Radiation Detection And Emerging Foundation Models., Qinyang Li

Theses and Dissertations

The discovery and optimization of advanced materials are central to addressing global challenges in energy, healthcare, and sustainability. This dissertation develops representation-aware and distribution-aware machine learning frameworks to improve robustness, generalization, and interpretability in materials informatics and radiation detection. The work spans crystal structure mapping, adversarial learning for out-of- distribution prediction, foundation-model-based property prediction, and deep neural classifcation of photon interactions.

A global mapping framework is frst introduced to analyze the inorganic materials space using compositional, structural, physical, and neural descriptors derived from the Materials Project database. By embedding materials into low-dimensional mani- folds, the framework reveals clustering behavior and …

From Experience To Reasoning: Offline Rl Subroutines And Llm-Based Grounding For Sample-Efficient Reinforcement Learning, Jianhai Su

Theses and Dissertations

Improving the learning efficiency of reinforcement learning (RL) agents remains a fundamental challenge, particularly in environments characterized by sparse rewards, long horizons, or partial observability. This dissertation investigates how RL agents can learn more efficiently through two complementary forms of guidance: mechanisms derived purely from an agent’s own experience and mechanisms that leverage reasoning priors from pretrained large language models (LLMs).

On the experience-driven side, the frst study develops a general framework for incorporating ofine RL algorithms as subroutines within an online RL process. In this framework, an agent periodically repurposes its replay bufer as an ofine dataset and applies …

Observational Diagnostics And Spectroscopic Detection Of Tropospheric Trace Gases And Oxidation Processes, Callum E. Flowerday

Theses and Dissertations

The troposphere is governed by photochemical and radical-mediated processes that control atmospheric oxidation capacity, secondary pollutant formation, and the chemical lifetime of gases. Quantitative understanding of these processes requires both robust observational frameworks capable of resolving complex precursor–product relationships and instrumentation with sufficient sensitivity and selectivity to detect reactive and low-concentration species. This dissertation advances atmospheric chemistry through the parallel development of quantitative observational methodologies and refined spectroscopic measurement techniques. The first component of this work evaluates atmospheric oxidation systems using long-term monitoring data and empirical diagnostics. Multi-year analyses of ozone and particulate matter trends were conducted to characterize variability …

Development Of Deep Fused Neural Architecture For Ancient Tamil Palm-Leaf Manuscript Recognition, Hariharan P Mr

Theses and Dissertations

Digitizing Tamil palm-leaf manuscripts is important for education, communication, and the preservation of cultural heritage. The complex structure of the Tamil script, the wide range of handwriting styles, and the degradation seen in ancient Tamil palm-leaf manuscripts make these texts very difficult to read and understand. Digital Image Processing (DIP), document analysis techniques, and traditional Optical Character Recognition (OCR) are unable to handle noise, background interference, faded ink, and limited labelled data, motivating the need for robust, effective Deep Learning (DL)- based solutions.

As a prerequisite to understanding and designing effective recognition systems for ancient manuscripts, this thesis first examines …

Objective Conditioning Via Latent-Factor Modeling, Kalman-Smoothing, And Hidden Markov Clustering: An Application To Empirical Asset Pricing, Melanie R. Neller

Theses and Dissertations

Empirical asset pricing relies heavily on conditioning sets--industry groupings, size buckets, valuation screens, and other researcher-defined partitions--to structure cross-sectional tests and portfolio construction. While intuitive, such partitions risk blending heterogeneous firms, masking latent exposures, and introducing omitted-variable bias. This thesis develops an objective, mathematically grounded conditioning pipeline that replaces subjective groupings with latent-factor extraction, Kalman-based data techniques, and probabilistic clustering via Gaussian hidden Markov models (HMMs). Using CRSP monthly returns, the framework stabilizes noisy return data, extracts systematic structure through principal component analysis (PCA), identifies homogeneous stock cohorts through HMM clustering, and models regime persistence using Markov transition matrices. These …

Database-Driven Revelations In Epilepsy: Patient Reporting Accuracy And The Circadian Timing Of Seizures, Ithay Biton

Theses and Dissertations

For over thirty years, patients have been visiting the Arkansas Epilepsy Program for diagnosis and treatment for seizures and seizure-like episodes. As part of their clinical evaluation, patients often undergo ambulatory EEG (electroencephalogram) monitoring. This routine process produces valuable data for treating the patient. In this study, over 2000 ambulatory EEG reports from 1998 to 2016 were reviewed. A large database of seizures was created from the reports, with information on 407 patients, 1611 EEG-confirmed seizures, and 1726 patient-reported seizures (IRB Protocol #17-093). The database was used to address two important issues in epilepsy. The first topic of the study …

Synthesis And Characterization Of Transition Metal Carbide (Max) And Mxene Nanoflakes For Energy Storage And [email protected], Srikanth Ragunath B Mr

Theses and Dissertations

Rapid growth in population and industrialization created a huge demand for superior energy storage devices. Thus, the researchers are in constant search of developing exotic materials towards energy harvesting and storage devices. Batteries, supercapacitors, and fuel cells received a great attention to meet the global demand for energy storage. Among them, supercapacitors are widely preferred as energy storage devices due to higher power density, longer cycle life, and fast charging. The performance of the supercapacitors highly depends on the choice of electrode materials and electrolyte.

Recently, “MXenes”  a new class of layered a new class of layered a new …

Reconstructing Soil Conductivity Profiles From Electromagnetic Induction Data, Tyler Philip Casas

Theses and Dissertations

Construction of infrastructure in cold regions poses a significant challenge, particularly due to permafrost degradation, which can lead to significant structural damage and deterioration to facilities and transportation systems. In recent years, the issue of geophysical hazard detection has been instrumental in minimizing ground subsidence risks when con- structing infrastructure in cold regions. As a commonly used technology for geophysical applications, electromagnetic induction (EMI) can be used for (i) detecting ground subsurface layers and (ii) characterizing soil types via electrical conductivities. However, EMI technology tends to struggle with lower resolution at lower frequencies and shallow depth of penetration at higher …

Metal-Free Nitrogen-Enriched Graphitic Carbon Nitride Architectures For Advanced Supercapacitor Energy Storage: Design, Synthesis, And Electrochemical Performance Optimization, Loujain Gamal Mohamed

Theses and Dissertations

Abstract

This thesis addresses the urgent global requirement for efficient energy storage materials by developing and characterizing advanced graphitic carbon nitride (g-C3N4)-based electrode materials for supercapacitors. A facile, low-cost thermal polymerization method produces 2D nitrogen-rich GCN nanosheets exhibiting excellent electrochemical stability and wide voltage windows, enabling symmetric devices with 19.33 Wh/kg energy density and remarkable cycling stability over 21,000 cycles. To overcome intrinsic limitations of pristine GCN, a 3D/2D metal free composite with bio-derived carbon (Bio-Cx) is synthesized, delivering high capacitance, wide potential windows, and ultrahigh energy density of 53.72 Wh/kg in asymmetric configurations paired with mesoporous nitrogen-doped carbon (MPNDC). …

Electronic Transport In Twisted Bilayer Tungsten Diselenides, Walid Zaher

Theses and Dissertations

This thesis investigates density waves (DWs) in twisted bilayer tungsten diselenide (tWSe₂) using a mean field approximation, with a focus on electron-electron interactions, and the system’s free energy at zero temperature. For the mean field approximation, the study initially employed same-spin nesting vectors, which were found insufficient to induce DWs formation. In contrast, when opposite-spin nesting vectors were used, DWs emerged, indicating that these vectors can support DWs formation. The plots were produced under perfect nesting conditions, where van Hove singularities (VHS) occur. At zero temperature, perfect nesting provides a complete picture of the upper limit of DWs formation, as …

A Virtual-Reality-Based Dental Simulator For Endodontics With Automated Formative Feedback, Yousef Salah Abo El Ela

Theses and Dissertations

Advancements in virtual reality (VR) and haptic technology are transforming the landscape of medical and dental education, offering new avenues for safe, immersive, and repeatable training experiences. Within dentistry, endodontics presents unique challenges for preclinical education due to anatomical complexity, limited access to extracted teeth, ethical concerns, and the shortcomings of conventional plastic models. Despite endodontics specific plastic teeth being available, they fall short of replicating the hardness of real extracted teeth, are relatively costly compared to generic plastic teeth, and are ultimately a disposable item which makes them inadequate as a sustainable long-term solution. Extracted teeth do a much …

A Computational Study Of The Chemomechanics Of Paracetamol Polymorphs: Towards Improving Drug Tabletability, Karim Nader Samra

Theses and Dissertations

The mechanical properties of pharmaceutical crystals are of great importance in tablet manufacturing. Also, knowing the mechanical properties of different polymorphs of the same crystal can reduce the overall production cost. In this study, computational work was done via performing density functional theory calculations on 3 paracetamol crystal polymorphs Form I, II, and III. Understanding the chemical bonding helps in predicting the key elastic properties for different crystallographic directions. In Form II, lattice vector C is dominated with the intermolecular hydrogen bond OH…O giving it the stiffest Young Modulus and the least Poisson’s ratio. Then comes the A-Axis which contains …