Physical Sciences and Mathematics Commons^™

Monoids With K-Strictly Local Geodesic Languages, William M. Hong

Master's Theses

A paper by Gilman, Hermiller, Holt and Rees (2011) prove that a group G finitely generated by X is virtually free if and only if the language of geodesics words in G over X is k-strictly local if and only if the word problem is context-free. If M is a monoid finitely generated by X, we define Γu(M,X) to be the underlying, undirected graph of Γ(M,X). We prove that if the language of geodesics in Γu(M,X) based at the identity is k-strictly local, then the monoid and semi-group word problems are context-free.

Rewriting The Calculus 3 Workshop At San José State University, Moorea Lippert

Master's Theses

Calculus 3 at San José State University is a very important course for any student pursuing a STEM degree. However, the course is very challenging, so the university offers a supplemental workshop course for Calculus 3 students. Unfortunately, this workshop has not aligned with modern research in math education. This thesis documents efforts to recreate the workshop to better align with this modern research.

Fermat's Last Theorem Over Quadratic Number Fields, Richie Tay

Master's Theses

Fermat’s Last Theorem states that the equation xn + yn = zn has no nontrivial integer solutions for n ≥ 3. While the rational case is completely solved, the situation over quadratic number fields is not as straightforward. For some exponents nontrivial solutions exist, while for others they do not. This thesis studies Fermat-type equations over quadratic number fields, combining classical methods with more modern techniques from the theory of elliptic curves. The thesis first reviews the rational cases n = 2, n = 3, n = 4, then develops the necessary background on quadratic number fields, including rings of …

Rational Non-Euclidean Triangles And Elliptic Curves, Tyler Morales

Master's Theses

We say a triangle △ is rational if its side lengths are rational. For a geometry of constant curvature κ, we say △ is a rational triangle if the generalized tangents of its side lengths are rational. We are able to parameterize rational triangles having the same inradius and semiperimeter on an plane curve, write a bijection between the rational points on this curve and triples of side lengths, and show that this curve is an elliptic curve. Then, we write a general transformation for our plane curve to short Weierstrass form to compute ranks and add points easily using …

Match Made In Ml: Developing Compatibility Relationships In Evidential Reasoning Approaches With Machine Learning, Ella Jolie Thomas

Master's Theses

The presented expectation maximization informed evidential reasoning model extends the ability of the evidential reasoning calculus to support decision making by integrating an adaptive model learning capability. Compatibility relationships in Evidential Reasoning models are traditionally built by human domain experts. This process is labor-intensive, especially for large and complex models. Additionally, when new data becomes available, compatibility relationships must be reconstructed. Using machine learning and the expectation maximization algorithm, it is demonstrated that compatibility relationships can be constructed that learn relationships between domain knowledge that is used to make decisions. Using drug development as a domain of application, a traditional …

Superresolution Spectroscopy Of Atomically Thin Semiconductors And Moiré Heterostructures, Chien-Chu (Charity) Wei

Master's Theses

Atomically thin semiconductors and moir’e heterostructures provide an important platform for studying quantum phenomena shaped by reduced dimensionality, interlayer coupling, strain, and local structure. In MoS2, the transition from bulk to monolayer form changes the material from an indirect to a direct band gap, while stacked and strain-engineered systems can produce spatially varying moir’e potentials on nanometer length scales. Because these effects are highly localized, conventional far-field optical spectroscopy is often limited in its ability to resolve them directly. This thesis explores superresolution vibrational spectroscopy as a route toward probing local behavior in atomically thin semiconductors and moir’e heterostructures. Far-field …

The Characterization Of Bridging Waters And Ions In Protein-Rna Complexes, Leslie Duong

Master's Theses

Here we explore the role of bridging waters and ions in protein-RNA complexes. From an initial set of 33 high-resolution X-ray crystal structures, 17 were identified such that protein-RNA complex and component protein and RNA chains were found within 1 pH unit as indicated by crystallization conditions and their diffraction temperatures meeting one of two ranges: above or below freezing. To define an even more realistic set, 12 unbound-unbound and unbound-pseudo-unbound complexes from the 17-set were studied, showing the large fraction of complexes indicating more protein and RNA water hydrogen bonding in their actual interfacial regions as opposed to those …

Accessibility Fairness Practices In Ai Applications For People With Disabilities, Megan Gross

Master's Theses

Advancements in artificial intelligence (AI) improve the lives of people every day with tools like the auto-captioning of videos, improved screen-reader capabilities, and advanced mobility control through speech. However, are all groups of people benefiting from AI or are some being overlooked and left out? Although AI tools made for people with disabilities (PWDs) have improved their lives, AI for the general population generally ignores the experiences of PWDs, making them unable to interact with and benefit from technology. This research evaluates ChatGPT and Gemini in Gmail for usability fairness and analyzes how current regulations and development processes fail to …

Diagrammatic Methods For Calculating Correlation Functions In Low-Dimensional Quantum Gravity, Nicholas A. Parrilla

Master's Theses

This thesis investigates connections between random matrix theory and low-dimensional quantum gravity through the spectral form factor (SFF), a well-studied function that characterizes correlations in the eigenvalue spectrum of an operator. In random matrix ensembles, a feature of the SFF known as the “ramp” is governed by universal spectral correlations, and in Jackiw–Teitelboim (JT) gravity this regime is due to the double-trumpet wormhole geometry. We study the connected correlation functions underlying the SFF using combinatorial, diagrammatic methods from a mathematical formalism known as second-order free probability theory, where they are expressed in terms of annular noncrossing permutations. To access a …

Hydrus Modeling Of A Sahelian Agroforestry System: An Investigation Of Local Water Balance, Nicole A. Butler

Master's Theses

Effects of drought can devastate agricultural productivity in the West African Sahel. Climate complexities, such as lower-than-average rainfall and high winds, can lead to crop failure and low yields, thereby creating food security issues. Agriculture in the Sahel is primarily rainfed, and the rain is becoming increasingly unpredictable due to the changing climate. The method of intercropping groundnut (Arachis hypogea) and pearl millet (Pennisetum glaucum) with the shrub species Piliostigma reticulatum can combat the effects of climate change and restore degraded soil. Intercropping can increase water availability and crop yield when compared to crops grown in the absence of shrubs. …

Fundamental Solutions To The Fractional Heat Operator, Jacob Flores

Math Theses

In this thesis, we are interested in showing the existence of a fundamental solution to the fractional heat operator. The fractional heat operator is a nonlocal linear operator used to model the time evolution of anomalous diffusion processes whose applicability arises in a wide variety of fields in the physical sciences, engineering, economics, and finance. Fundamental solutions to a partial differential operator are a class of generalized solutions formulated with rich mathematical analysis grounded in classes of well-behaved smooth functions referred to as test functions and their continuous linear functionals referred to as distributions. A primary tool that we use …

Continuous 1:1 Sitter Observation Versus Standard Safety Interventions To Reduce Falls In Hospitalized Adults At Risk, Zainab Williams

Student Scholarly Projects

Practice Problem: Patient falls remain a significant patient safety concern among hospitalized adults, particularly those at high risk. Traditional fall-prevention strategies, including continuous 1:1 sitter observation, require evaluation to determine their effectiveness in reducing falls and fall-related injuries.

PICOT: In hospitalized adult patients at high risk for falls (P), does continuous 1:1 sitter observation (I), compared to standard safety interventions (C), reduce fall rates (O) as measured by reported falls per 1,000 patient days during hospitalization over 12 weeks (T)?

Evidence: Current evidence supports multifactorial fall-prevention programs that combine patient assessment, staff engagement, and proactive nursing interventions through intentional rounding. …

Developing An Understanding Of Concavity Built On Covariation, Jade E. Gregg

Theses and Dissertations

This study investigated how six students developed a quantitative understanding of concavity founded in covariational reasoning through a series of task-based teaching interviews. A key finding was the importance of multivariational reasoning--the coordination of more than two variables--in helping students reason deeply about concavity in context. Common difficulties, including confusion about negative rates and overreliance on visual representations, served as productive opportunities for learning when addressed through carefully designed tasks and discussions. The findings extend existing frameworks of covariational reasoning and highlight instructional approaches that can support students in developing a robust, quantity-based understanding of concavity.

Scattered Light Noise At Ligo Livingston Observatory Induced By Microseismic Ground Motion, Debasmita Nandi

LSU Doctoral Dissertations

Gravitational waves are “ripples” in the fabric of spacetime and create a minuscule change in the distance between two points. After publishing his theory of general relativity in 1915, Albert Einstein predicted the existence of gravitational waves as a consequence of the theory. Almost 100 years after the theoretical prediction, gravitational waves were detected for the first time in 2015 by the Advanced LIGO detectors in Livingston, Louisiana, and Hanford, Washington. Gravitational waves have a very small amplitude, making it very challenging to detect them. Different types of noise sources either of instrumental or environmental origin can reduce the astrophysical …

Detecting And Correcting Systematic Image Distortion In Digital Atomic-Resolution Images From Crystals: Projected Symmetry Of Graphite Calibration Samples For Scanning Prove Microscopy And Subperiodic Crystals For Aberration-Corrected Transmission Electron Microscopy, Tyler Michael Bortel

Dissertations and Theses

Though it is an impressive technology, Scanning Tunneling Microscopy (STM) produces images commonly plagued by small systematic errors, often called "drift". These effects have a variety of causes, most notably nonlinear behavior of piezoelectric actuator tubes responsible for the positioning of the scanning probe or sample. One result of these distortions is a potential incorrect classification of the symmetry groups and projected Laue classes of recorded images from crystals—made possible by using recently developed objective methods. An implementation of a known method for detecting and correcting these errors is presented. This method operates strictly in Fourier space so as to …

Pseudodifferential Absorbing Boundary Conditions For Waves, Lauren Taylor

Mechanical Engineering Theses

Absorbing boundary conditions (ABCs) are required to truncate the computational domain when performing Finite Element Analyses of exterior acoustic problems where physical domain is unbounded. ABC is applied on a fictitious boundary containing the scatterer and ideally allows outgoing waves to leave without non-physical reflections. Preventing artificial reflections is essential to benefit from the accuracy of the numerical method used. Otherwise, ABC acts as a reflective surface, and artificial reflections distort the solution in the entire domain which is not recoverable by any type of refinement. Pseudodifferential ABCs were used to describe the Dirichlet-to-Neumann map which maps known boundary values …

Analytic Solutions To Oceanographic Kinematic Property Equations, James Turbett

Theses and Dissertations

With the recent advent of large submesoscale drifter deployments, interpreting the timeseries of kinematic properties (KP) - divergence, vorticity, shear, and normal strain rates observed therein is a pressing issue. The evolution equations for the four KP are derived from the two-dimensional momentum conservation equations. The resulting equations, a nonlinear coupled system of ordinary differential equations, capture the submesoscale motion of drifters along fixed ocean surfaces, with time and space scales on the order of days and kilometers. This thesis builds theory around KP timeseries behavior by solving for the analytic solutions in the particular cases that one KP is …

Numerical Range Of Rank-1 Partial Isometries And Elliptical Range Theorem, Lucas Saone

Theses

The Elliptical Range Theorem states that the numerical range of a 2x2 complex matrix A is an elliptical disc with foci at the eigenvalues of A and center at tr(A)/2. Many proofs have been offered for this theorem. In this paper, we provide another one. The strategy we will use is to decompose the matrix A into the sum of rank-1 operators of the form YxX*, where X and Y are in 2-D complex vectors. When analyzing the numerical range of a rank-1 operator of this form, three results can happen: i) the numerical range forms a disc at the …

Prediction Of Satellite Temperature During An Orbit Of A Cubesat, Michael Reynolds

Honors Theses

This thesis develops a thermal-simulation strategy for predicting CubeSat component temperatures, applied to Jag-Sat-1, a CubeSat developed at the University of South Alabama and deployed from the International Space Station in 2022. The orbit was reconstructed from two-line element (TLE) data using simplified general perturbations (SGP4) propagation, and spacecraft attitude was recovered from onboard gyroscope measurements. Sunlight, penumbra, and umbra intervals were computed geometrically, and the external radiative environment — direct solar, Earth infrared, and albedo heat fluxes — was modeled using orientation-dependent view factors. These time-varying fluxes drove a transient finite-element thermal simulation of the full satellite geometry in …

A Machine-Learning-Based Systematic Framework For Modeling Compression And Recompression Indices For Florida Soils, Michael Morales

Doctoral Dissertations and Master's Theses

This thesis develops a machine-learning framework for estimating the compression index and the recompression index of Florida soils from routinely measured index properties, and reports two studies that build it. Consolidation settlement design requires both indices, and both are obtained from the incremental-loading oedometer test, which occupies a specimen for one to two weeks; the index tests that accompany it are complete within hours. Empirical correlations have filled that interval since the 1950s, but their coefficients are calibrated on specific soil populations and transfer poorly between regions. The first study analyzes 376 consolidation tests compiled for the Florida Department of …

Influence Of Stormwater Flooding Events On The Mobile County School District Student Population, Kadence Kali Johnston

Honors Theses

Mobile County, Alabama, receives among the highest annual rainfall totals in the United States resulting in frequent stormwater flooding that intersects with existing socioeconomic vulnerabilities. Within the Mobile County Public School System (MCPSS), 77% of students are economically disadvantaged and over 10% experience homelessness, creating heightened risk for educational disruption during flood events. This study investigates how stormwater flooding influences school attendance, closures, and academic performance across MCPSS, providing insight into how climate-driven hazards exacerbate educational inequities. The research integrates flood frequency, school performance metrics, and GIS flood-zone mapping and teacher perceptions to understand how flooding affects student learning opportunities. …

Improving Vector Embedding Generation Throughput For Neural Information Retrieval Models, Conrad Tkacz

Theses and Dissertations from DePaul University

For decades, advancements in information retrieval technologies have changed how individuals discover data with computer systems. More recent advancements in artificial intelligence (AI) have also made the benefits of neural information retrieval systems available to millions. These information retrieval systems help empower future discoveries, though this is not the case for scientific data and High-Performance Computing (HPC) systems. HPC systems can generate enormous amounts of data, and no tools are currently available that can ingest data at the rates required to efficiently build an information retrieval system to explore scientific data. This thesis explores the current state of constructing a …

Using Recommender Systems To Help Revitalize Local News, Payam Pourashraf

Theses and Dissertations from DePaul University

Local news outlets have experienced steep declines in readership as national and global online news sources have expanded and consolidated audience attention. Because many local media companies rely primarily on subscription-based business models, they must increase user engagement and provide clearer value to local subscribers. Personalization and recommender systems offer one promising path toward this goal. However, many recommender systems assume that a user’s past behavior can be summarized in a single unified profile. In practice, preferences are often context-dependent: the same person may prefer different content depending on geography, time, task, or situation. Local news offers a socially important …

Analysis Of Clinical Health Worker Notes With Explainable Artificial Intelligence For A Better Perspective In Preventing Readmission, Christopher Scott Klimp

Theses and Dissertations from DePaul University

Emergency Department (ED) readmissions remain a major challenge for healthcare systems, affecting both patient care quality and financial costs. Most prediction models depend largely on structured data from clinical tools that assign points to a small set of predefined factors – such as comorbidities, previous hospital visits, and behaviors such as smoking and drinking – and then sum those points to produce an overall risk score. These point-based tools leave out important information from Social Determinants of Health and a wealth of information from Community Health Workers (Community health workers (CHWs), trusted members of a community who help connect people …

Cdt-1d Cnn Integration With Simpson-Sobolev Regularization For High-Frequency Options Trading: With Fem-Based Heston Option Pricing, Daniel M. Margolis, Johannes Tausch, Arthur K. Selender

Mathematics Theses and Dissertations

This dissertation presents a computational framework for high-frequency options trading that combines Cross-Data-Type 1-D Convolutional Neural Networks (CDT-1D CNN) with Simpson-Sobolev regularization for directional prediction, and finite element methods (FEM) for realistic option pricing during backtesting. The core innovation lies in developing a mathematically rigorous regularization approach that maintains the adaptability of modern deep learning while enabling accurate evaluation through stochastic volatility models. The primary contribution is the Simpson-Sobolev regularization scheme, which extends traditional Sobolev regularization by incorporating Simpson’s rule for numerical integration. This approach achieves higher-order accuracy in approximating the Sobolev norms that control function smoothness. Simpson’s rule attains …

Ethos: A Computational Framework For Material Culture Research, Chelsea L. Grafe

Department of Textiles, Merchandising and Fashion Design: Dissertations, Theses, and Student Research

Museum catalog records make large collections searchable, but they do not always preserve the reasoning behind the claims they contain. A record may present a quilt's identity as settled while leaving the reasoning behind that claim invisible, making it difficult for later researchers to check, question, or reuse. This project asks whether museum catalog data can be analyzed in a way that keeps each analytical claim connected to the evidence that supports it. To test this question, the project applies a material-first computational framework named Ethos. Ethos formalizes an object-centered inquiry sequence in which material dependencies establish where analysis begins …

On The True Interstellar Anisotropy Of Tev Cosmic Rays And Its Implications For The Local Interstellar Medium, Noufel D. Maalal

Theses and Dissertations

Several ground-based cosmic ray (CR) air shower experiments have produced sky maps of intensity anisotropy in the energy range from 1 TeV to a few hundred TeVs with very high statistics and angular resolution. These measurements provide opportunities to study CR sources and propagation in the interstellar medium (ISM). Such studies present two major difficulties. Firstly, CRs are deflected by the heliospheric magnetic field on the last stretch of their journey to Earth. Secondly, measurements at different latitudes are difficult to compare, leading to uncertainties in latitudinal variations on the order of the observed anisotropy. Experiments usually assume latitudinal variations …

Improving Urban Search And Rescue Team Coordination Through Adaptive Context Awareness, Daniel Reyes Duran

Doctoral Dissertations and Master's Theses

Modern multi-agent Urban Search and Rescue (USAR) operations heavily rely on mobile geospatial Common Operating Pictures (COPs) to maintain team coordination and Situational Awareness (SA). However, the proliferation of high-frequency sensor telemetry at the tactical edge has introduced a data saturation paradox challenge: while information theoretically drives informed decision-making, unmanaged data surges induce increased operator cognitive overload and alert fatigue on mobile End-User Devices (EUDs), while downstream data-broadcasting models inherently strain edge processing and viewport environments.

To resolve these constraints, this dissertation presents a context-aware Value of Information (VoI) data-management framework integrated directly with a custom, event-driven Android Team Awareness …

Trustworthy Reinforcement Learning And Communication-Efficient Multi-Agent Systems, Rui Zuo

Dissertations - ALL

The rapid proliferation of autonomous systems, such as Unmanned Aircraft Systems (UAS) transitioning to large-scale Beyond Visual Line of Sight (BVLOS) operations, demands a paradigm shift toward reliable, transparent, and resilient autonomy. While Deep Reinforcement Learning (DRL) and Multi-Agent Reinforcement Learning (MARL) have demonstrated exceptional capabilities in complex decision-making and coordination, their real-world deployment in safety-critical domains is hindered by two fundamental challenges. First, the opaque, "black-box" nature of DRL models prevents human operators from understanding and trusting the agents' underlying logic. Second, as multi-agent operations scale, they become severely constrained by the stochastic link qualities and strict bandwidth limitations …

Atropisomer Mechanochemistry Of Diarylethene Mechanophores: A Study Of Structure-Mechanical Activity Relationships, Cijun Zhang

Dissertations - ALL

Stimuli-responsive organic structures are advanced, intelligent platforms that dynamically adjust their physical or chemical properties—such solubility, or color—in response to external stimuli including light, heat, pH, redox conditions, mechanical force, or magnetic fields. Among these structures, mechanophores represent an important class that is specifically responsive to mechanical force. Synthetic mechanophores can be rationally engineered to exhibit tunable mechanosensitivity as well as tailored chemical and physical properties. In this work, we designed and synthesized a type of atropisomeric mechanophores based on sterically congested diarylethene photoswitches, and systematically investigated their mechanical and photochemical properties. Chapter 1 Chapter 1 provides a general introduction …