Physical Sciences and Mathematics Commons^™

Geometric Structure In High-Dimensional Representations: Theory And Applications To Language, Jiayi Chen

Dartmouth College Ph.D Dissertations

This thesis develops a geometric perspective on high-dimensional representations, motivated by applications to language. Rather than treating representations solely as inputs to predictive models, we view them as structured objects whose geometry encodes meaningful information. In particular, we argue that such representations exhibit organization at multiple scales: at a global level, metric and clustering structure capture relationships such as genre, authorship, and discourse; at a local level, geometric quantities such as intrinsic dimension and curvature describe how these relationships vary across the space.

To study these phenomena, we combine empirical analysis with theoretical development. On the empirical side, we examine …

Unquaint Pigs’ Stakeholder Perspectives On Wild Swine In Central Western Florida, Tyler Koerner

USF Tampa Graduate Theses and Dissertations

The Anthropocene presents important questions for how to address the continuous transferal of new species into new spaces and the cascading impacts of environmental transformations. Novel ecosystems present one such outline for conservation that acknowledges the modification of historic ecosystems and the social entanglements that arrive with new species. I argue that novel ecosystems can benefit from further anthropological integrations that aid in describing the entanglements of introduced species and the pursuit of best managerial outcomes. For wild swine in Florida, the adoption of a novel approach is especially relevant because of entanglements with historic and modern Floridian stakeholders and …

Design And Implementation Of Error Estimators For Finite Element Eigenvalue Problems, Gabriel Esteban Pinochet Soto

Dissertations and Theses

We present three publications, all encompassed under the umbrella of a posteriori error estimation theory for eigenvalue problems for finite element discretizations. The central objective of the research is the development of a general framework for the study of reliable estimation of eigenvalues and eigenspaces. We introduce applications to problems of theoretical interest as well as problems arising in real-life scenarios, such as optical fibers. The first paper focuses on the implementation of a dual-weighted residual error estimator for a nonselfadjoint eigenvalue problems arising from the study of leaky modes in optical fibers---Maxwell's equations, Perfectly Matched Layers, and a conforming …

Improving Explainability And Interpretability Of Neural Networks Via Hyperparameter-Extended Influence Functions, William Breslin

Dissertations and Theses

Understanding how model predictions and training outcomes vary with changes in data, features, and modeling choices is central to explainable artificial intelligence. This dissertation introduces a unified framework for explainability by generalizing classical influence functions to encompass user-defined hyperparameters embedded in the training loss, model architecture, or data representation. By extending influence functions in this way, the framework broadens their applicability and integrates multiple explainability techniques into a single, coherent approach. It provides a common mathematical foundation linking data impact, feature importance, and model design analysis, and supports a broad class of additional explainability analyses beyond these settings. The demonstrated …

An Analytical Framework For Quantifying Urban And Community Resilience To Natural Hazards From Cell-Phone Gps-Location And Traffic-Flow Data, Georgios Chatzikyriakidis

Civil and Environmental Engineering Theses and Dissertations

Urban areas are increasingly exposed to natural hazards while accommodating a growing share of the global population, yet a consistent science-based framework for quantifying urban and community resilience remains lacking. This dissertation develops a physics-based analytical framework grounded in statistical mechanics and the quantitative theory of Brownian motion. A city is conceptualized as a complex medium in which citizens move analogously to Brownian particles within a viscoelastic environment, influenced by socioeconomic interactions and infrastructure functionality.

A central premise is that urban resilience, interpreted as engineering resilience (an outcome), can be quantified through a single metric: the mean-square displacement MSD=⟨r²(t)⟩, of …

Bayesian Spatiotemporal Model For Counterfactual Estimation In Socioeconomic Studies, Duwani W. Gonzalez

Statistical Science Theses and Dissertations

Impact evaluations of regional development programs often require estimating counterfactual outcomes for a small number of treated regions using survey-based areal data. In practice, evaluators typically rely on two-group quasi-experimental methods such as propensity score matching (PSM) and Difference-in-Differences (DiD). These approaches perform poorly when only a few regions receive treatment, and when the set of observed covariates is limited or only partially relevant. Moreover, they typically do not explicitly exploit the spatial and temporal dependence present in survey-based areal data such as in ACS (American Community Survey). This dissertation develops a family of Bayesian spatial predictive models for directly …

Mapping Homogeneous Configuration States For Learning Based Motion Planners, Yazied Hasan

Computer Science ETDs

Reinforcement learning (RL) excels at solving complex tasks, but training times can become prohibitively large for challenging motion-planning problems. Methods that address this cost often require additional training or tuning, counteracting the goal of reducing training time. A more effective approach is to exploit inherent task equivalences: many elements of the state space, dynamics, or structure are functionally interchangeable, enabling simplification or knowledge reuse. We present learning solutions that leverage these equivalences to enhance the RL process. First, we leverage the symmetry of homogeneous multi-agent teams to simplify the task to a single strategy. Second, we map correspondences between distinct …

From Sparse To Precise: Modeling Beam Profiles Using Wavelet-Based Implicit Neural Network (Winn) For Linear Accelerator Commissioning And Quality Assurance, Maryam Ali Albuainin

Computer Science ETDs

Commissioning and routine quality assurance (QA) in radiotherapy require extensive measurements using bulky water tank systems, making the process time-consuming and costly. This research proposes an efficient framework for radiotherapy commissioning and QA by generating complete LINAC physics data from sparse measurements and developing a portable solid-water detector with embedded diodes for high-resolution dosimetry.

At the core of the framework is a Wavelet-based Implicit Neural Network (WINN) that reconstructs full measurement datasets from limited inputs while maintaining clinical accuracy. The model achieves gamma passing rates above 95% (1%/1 mm) and mean absolute errors below 0.5%, while reducing parameters by 99.46% …

Computing Certificates Of Members In Archimedean Quadratic Modules In A[X] And Certifying The Emptiness In Inconsistent Monogenic Archimedean Quadratic Modules In A[X_1, ..., X_N], Jose A. Castellanos Joo

Computer Science ETDs

Polynomials have been found to be a powerful tool over hundreds of years for modeling problems in numerous applications in science, engineering, medicine, and other domains. In the context of formal methods, polynomials arise in modeling in aerospace software and robotics, cyber-physical and hybrid systems, autonomous vehicles and controllers based on neural networks.

A quadratic module is a linear combination of polynomials in a set of generators (including the constant 1) with sum of squares polynomials as multipliers. The membership problem for a finitely generated quadratic module can be decided; however, computing a certificate exhibiting why it is nonnegative under …

Shaping Emergent Competitive And Cooperative Behaviors In Multi-Agent General-Sum Games, Ethan F. Erickson

Honors Projects

Reinforcement learning (RL) algorithms can train agents to solve problems in environments using complex behaviors that are not explicitly programmed, known as emergent behaviors. The goal of our research is to investigate how different RL reward values influence the emergence of competitive and cooperative behaviors in games with teams of multiple agents. Specifically, we focus on general-sum games, in which the sum of gains and losses of each team may be non-zero, allowing situations for agents to mutually benefit or mutually fail. Using Unity’s ML-Agents Toolkit to train agents with RL self-play in bounded 2D environments, we identify high-level behaviors …

Ab Initio Method Development For Electronic Structure Response And Symmetry Quantification, Duc Anh Lai

Chemistry Theses and Dissertations

Electronic structure provides a fundamental framework for understanding molecular properties and reactivity, as it encodes the spatial distribution of electrons and their response to external and internal perturbations. This dissertation develops theoretical and computational frameworks to characterize and manipulate electronic structure through two complementary directions: the response to oriented external electric fields and the quantification of symmetry regulation in electron density.

First, a rigorous theoretical and computational framework is established for treating electric fields with arbitrary orientations relative to molecular structure. The concept of the rotational potential energy surface is introduced to characterize the dependence of molecular energy on field …

Marine Geophysical Studies Of Coupled Tectonic And Sedimentary Processes At Active Plate Boundaries, Sarah R. Rysanek

Earth and Planetary Sciences ETDs

Deep-sea and convergent margin sedimentary systems preserve critical records of tectonic and climatic processes that shape Earth’s surface. This dissertation investigates source-to-sink sediment routing and forearc deformation to better constrain the interplay between sedimentary and tectonic processes, through investigations of a deep-sea fan system, and the forearc geomorphology offshore Nicaragua. In the Gulf of Alaska, we integrate ultra-long-offset and regional multi-channel seismic reflection data, multi-resolution bathymetry, and plate reconstructions to remap the Baranof Fan system. Results show that the fan is larger than previously recognized and constructed by two primary depocenters linked to distinct glacial sediment pathways, with accommodation space …

Constraining Magmatic Processes In The Central American Arc Using Melt Inclusion Vapor Bubble Analysis And Triple Oxygen Isotope Modeling And Exploration Of Volatile Contributions To The Production Of Continual Radio Frequency (Crf) Lightning Events, John M. Hamilton

Earth and Planetary Sciences ETDs

Magmatic volatiles are key to determining the processes happening in the subsurface that we cannot directly sample. Advances in measuring volatile and isotope contents from erupted volcanic samples have given us the ability to understand magmatic processes, mixing components that produce the bulk magma composition and potentially precursors to eruptive hazards, such as lightning.

Through analysis of melt inclusions that sample the melt at depth and triple oxygen isotope quantification of olivine crystals from multiple volcanic edifices, the three following studies display how I have utilized these analytical techniques to help unravel processes happening in the subsurface that lead volcanic …

Stochastic Derivative-Free Deep Learning Methods For Solving High Dimensional Partial Differential Equations, Qing He Mr.

Mathematics Theses and Dissertations

Solving high-dimensional partial differential equations (PDEs) is a fundamental challenge in scientific computing, with applications ranging from quantum chemistry and computational finance to statistical physics and stochastic optimal control.  Classical numerical methods such as finite element or finite difference schemes suffer from the curse of dimensionality, rendering them computationally infeasible when the dimension $d$ exceeds a handful. Physics-informed neural network (PINN) methods alleviate this by embedding the PDE residual directly into a loss function, but they require computing derivatives of the network with respect to its spatial inputs---an operation that scales poorly in high dimensions and demands that the approximate …

Microtubules In Breast Cancer: Exploring The Α/Β-Tubulin Toggle Switch And Its Implications In Human Breast Cancer, Annemarie Ianos

Student Theses and Dissertations

Microtubules, composed of a/b-tubulin heterodimers, play a central role in breast cancer tumor growth by polymerizing, leading to metastasis and depolymerizing, contributing to proliferation. Human enzymes protein kinase Ca (PKC-a) and cyclin-dependent kinase 1 (Cdk-1) mediate phosphorylation at sites a:Ser165 and b:Ser172, respectively, influencing the growth of microtubules. It is possible that alternating phosphorylation at these sites contribute to an a/b-tubulin “toggle switch” that mediates microtubule instability and tumor growth.

The project investigates the influence of the toggle switch model on microtubule stability by determining the impact of mutants (a:S165D, a:S165N, a:S165S_P, b:S172S_P and a:S165S_P/b:S172S …

Computational Design Of Peptides And Proteins Through Machine Learning Approaches, Emily J. Hendrix

Chemistry and Chemical Biology ETDs

Advancements in machine learning have emerged as a pivotal tool in computational biochemistry, offering new advancements to address challenges in protein structure and function. However, current machine-learning approaches offer limited insight in understanding protein dynamics. The purpose of this work is to combine traditional physics-based computational tools, such as molecular dynamics and coarse-grained simulations, with recently developed AI-driven computational tools to bridge gaps and advance the understanding of proteins in both structural and dynamic aspects. I investigated several approaches such as (i) traditional physics-based methods to study protein conformation and ensembles; (ii) identifying a peptide inhibitor for the PICK1 PDZ …

Design, Fabrication, And Characterization Of Silicon Nitride Microresonator Optical Frequency Combs, Lala Rukh

Optical Science and Engineering ETDs

Optical frequency combs consist of equidistant optical frequencies and have numerous applications ranging from optical metrology to medical diagnostics. Initially, frequency combs were based on bulky mode-locked lasers, but advancements in integrated photonics enabled the generation of frequency combs in chip-scale resonators (microcombs) using Kerr nonlinearity. These miniaturized systems present various challenges, including increased propagation losses, enhanced thermal effects, and the extension of microcombs to visible wavelengths. In this dissertation, I will focus on addressing these challenges in silicon nitride (SiN) resonators. First, this thesis focuses on the fabrication of high-Q SiN resonators and the impact of fabrication parameters on …

A Quantum Phase Space Description Of Local Noise In Atomic Ensembles, Andrew Kolmer Forbes

Physics & Astronomy ETDs

Nonclassicality in quantum sensors can improve sensitivity, but often increases susceptibility to noise. Thus, modeling physically relevant noise sources and analyzing their effect on quantum metrology are both of importance to the field of quantum sensing. In this dissertation, I demonstrate that local noise sources, which are present in almost all many-spin systems, can be tractably modeled when assuming permutation symmetry of the noise, and we show that many common local noise sources can be mapped to a Fokker-Planck equation on quantum phase space. We apply this description of noise to study quantum sensing using noisy probe states and establish …

Optical Nuclear Spin Detection In Diamond And Varifocal Metasurface Optics, Maxwell D. Aiello

Physics & Astronomy ETDs

This dissertation presents two experimental investigations at the intersection of quantum sensing and precision optical instrumentation. The primary project demonstrates optically detected nuclear magnetic resonance (NMR) of ¹³C nuclear spins in diamond, using state-selective Landau-Zener transitions under microwave frequency sweeping to bidirectionally transfer spin polarization between nitrogen-vacancy (NV) electron spins and remote ¹³C nuclear spins. This enables optical polarization and readout of large ensembles of polarized nuclear spins at low magnetic fields and room temperature, with spin dephasing times limited by longitudinal relaxation of nearby NV electron spins. The secondary project reports the design, fabrication, and characterization of …

Realizing The Long Wavelength Array Swarm, Craig Anthony Taylor

Physics & Astronomy ETDs

Sensitive modern radio interferometers are costly to build and operate at the university level. The `swarm telescope' concept addresses this challenge by enabling the collaborative use of individual telescope systems, overseen by separate institutions, that come together to form a more powerful and manageable facility. This dissertation focuses on demonstrating this concept using the Long Wavelength Array (LWA) by commissioning an aperture synthesis telescope consisting of interconnected LWA stations, called the LWA Swarm. The presented work details building a cost-efficient prototype LWA platform -- the LWA--North Arm station -- to enable synthesis imaging using the 3-element interferometer comprised of LWA1, …

A Multi-Frequency Investigation Of Compact Symmetric Objects, Evan E. Sheldahl

Physics & Astronomy ETDs

Some of the brightest objects in the radio sky are jetted active galactic nuclei (AGN), supermassive black holes in the centers of galaxies that accelerate relativistic electrons into twin radio jets. One of the biggest questions surrounding AGN is how they produce radio jets in the first place. We search for an answer to this question by exploring a class of AGN that have uniquely well-constrained physical properties and are thought to be in an early stage of AGN development: compact symmetric objects (CSOs). Throughout our journey with these remarkable sources, we quantify their efficacy as calibrator sources for radio …

Quantifying Co2 And Ch4 Fluxes In A Semi-Arid Floodplain: Assessing Spatial And Temporal Drivers, Miles E. Kelsey

Earth and Planetary Sciences ETDs

Rivers transport sediment and carbon across Earth’s surface, and their floodplains can store carbon over decades to millennia, making them important to terrestrial carbon management. While soil carbon can persist long term, it may be released as greenhouse gases through processes like methanogenesis and heterotrophic respiration. Environmental controls on these fluxes remain poorly constrained across floodplains in different climate and geomorphic setting, but especially in semi-arid systems where measurements are limited. To address this gap, we quantified CO₂ and CH₄ fluxes along the Middle Rio Grande (New Mexico, USA) using 227 chamber measurements collected May to November 2025 at three …

Heavy Metal And Metalloid Accumulation In The Gallinas River Following The Hermit's Peak / Calf Canyon Wildfire, Olivia A. Kelly

Geography ETDs

This study evaluates the persistence and bioavailability of heavy metals and metalloids in the Gallinas River three years after the Hermit’s Peak/Calf Canyon Wildfire of 2022 using a multicompartment sampling framework that includes water, sediment, and benthic macroinvertebrate tissue analysis via inductively coupled plasma optical emission spectrometry (ICP-OES) and inductively coupled plasma mass spectrometry (ICP-MS). Results indicate that the Hermit’s Peak/Calf Canyon Fire continues to influence the hydrogeochemical condition of the Gallinas River. Sediments contain elevated concentrations of several metals and metalloids, and these same elements are detectable in macroinvertebrate tissues, linking sediment contamination to biological uptake. Zinc (Zn), silicon …

Nanoscale Structure And Spontaneous Self-Assembly Of Hydrothermal Organic Products, Glorianne P. Dorce

Chemistry and Chemical Biology ETDs

Carbon nanomaterials derived from citric acid and urea exhibit behaviors that challenge conventional structure–property models based on static bulk descriptions. This study examines how precursor pairing and reaction duration, post‑synthetic thermal history, and time‑dependent aging govern nanoscale organization and optical response. Through controlled synthesis and processing, distinct nanostructures with tunable structural and spectroscopic profiles are generated.

A multiscale framework integrating nano‑FTIR, atomic force microscopy, and thermal analysis reveals chemical heterogeneity and continuous structural reorganization across length scales. By correlating local chemical environments with optical behavior, we show that fluorescence efficiency and photostability depend on specific nanoscale architectures rather than average …

Continuous Polygenic Trait Evolution Under Brownian Motion With Gaussian Mixture Models, Mary S. Hopkins

Mathematics & Statistics ETDs

Gaussian mixed-models (GMMs) show promise as a tool for modeling polygenic trait evolution for multiple taxa with established phylogenetic comparative methods (PCMs). When phenotypic traits are influenced by more than one gene, neither a gene tree nor a species tree may be completely adequate to model specific cross-taxa dependencies. In such cases common solutions include using trees inferred from concatenated DNA sequences [35, 95] and consensus gene trees [35]. The GMM-based model, first proposed by Jiang in 2017 [55] allows traits to evolve on more than one tree with distinct topologies. This approach provides a framework for trait evolutionary modeling …

Bayesian Designs For Two-Arm Clinical Trials With Time-To-Event Endpoints: Incorporating Historical Data Through Power Priors, Sara Hajraf H. Almutiri

Mathematics & Statistics ETDs

Bayesian methods provide a flexible framework for time-to-event analysis by incorporating prior information. The power prior offers a systematic way to borrow information from historical data. This approach is especially valuable in clinical research, where historical data can enhance inference in early-phase trials with limited sample sizes. This dissertation develops Bayesian approaches for two-arm survival studies using both closed-form and simulation-based methods. The closed-form inference is derived under exponential and Weibull survival models. Under the proportional hazards framework, the posterior is derived through a normal approximation to the log hazard ratio, allowing inference on the treatment effect when the variance …

Quantum Control Protocols For Robust Quantum Computing, Leeseok Kim

Electrical and Computer Engineering ETDs

The fundamental goal of quantum computing is to precisely control quantum systems to perform meaningful tasks, including implementing high-fidelity quantum gates for reliable quantum computation and accurately simulating complex quantum many- body dynamics. In this dissertation, we develop improved quantum control protocols for three distinct objectives, quantum error suppression, quantum optimal control, and analog quantum algorithms, achieving performance beyond standard approaches. First, we introduce new dynamical decoupling protocols, including both determin- istic and randomized constructions, that can substantially outperform conventional deterministic sequences. We then extend the randomized approach to dynamically corrected gates. Second, we propose a randomized quantum optimal control …

Welcome Tilly Norwood: Forecasting Hollywood’S Ai Policy Futures, Samuel P. Rooker

Senior Honors Projects, 2020-current

In late 2025, weekly trade publication Variety Magazine reported on the announcement of a new acting talent in Hollywood: Tilly Norwood. Norwood is an industry outsider and the pet project of Eline Van der Velden, who unveiled the actress’ existence to the world at the Zurich Film Festival. The announcement quickly gained media coverage while Van der Velden has since faced cyclical backlash from Hollywood trade unions, which does not seem entirely without reason. Tilly Norwood is a digital persona, a generative artificial intelligence (GenAI) program, designed by Van der Velden’s novel AI talent studio, Xicoia, to become the next …

Surface Directed Microwave Assisted Fabrication Of Znmn2o4 And Its Composite As Anode Materials For Lithium Ion Battery, Anirudh Singh

Electronic Theses & Dissertations

The Lithium-ion batteries (LIBs) are widely utilized in portable electronics and electric/hybrid electric vehicles. However, the limited theoretical capacity of graphite (372 mA h g⁻¹) restricts further advancements. In our recent work, a series of ZnMn₂O₄ materials with various additives were synthesized using the microwave reaction method and evaluated as anodes for LIBs. Additives such as 2-methylimidazole (2MIM), polyvinyl alcohol (PVA), and cetyltrimethylammonium bromide (CTAB) were employed to prepare ZnMn₂O₄ with distinct morphologies. Our findings revealed that ZnMn₂O₄  with pure phases was achieved when 2MIM and CTAB were used as additives. …

Degrees Of Access: The Role Of Family Education In Applying To Graduate School, Emma Tweed

Math and Computer Science Honors Theses

Access to graduate education in the United States remains heavily stratified by structural, financial, and informational barriers. While undergraduate first-generation student outcomes are widely studied, fewer structural analyses examine how graduate-level “educational inheritance” shapes prospective applicants' navigational capital, particularly within competitive STEM fields like mathematics. Drawing upon theories of social capital and the “hidden curriculum,” this study investigates the relationship between an individual's knowledge of the graduate school application process and the highest level of education attained by an immediate family member.

Using the Knowledge-GAP survey instrument funded by the National Science Foundation, data were collected from a diverse sample …