Physical Sciences and Mathematics Commons^™

New Distance Distributions Of Asymptotic Giant Branch Stars And Their Role In Tracing Galactic Structure, Rajorshi Bhattacharya

Physics & Astronomy ETDs

Asymptotic giant branch (AGB) stars are among the final evolutionary stages of low- and intermediate-mass stars and among the most luminous cool stellar populations in the Milky Way (MW). Their strong infrared emission allows them to be observed through regions of high interstellar extinction, making them useful tracers of the inner MW. However, their use is limited by unreliable distances because many are dust-obscured and variable, while geometric parallaxes are often unavailable or uncertain. This thesis develops statistical distance-estimation methods for large samples of oxygen-rich AGB stars. The resulting distances broadly agree with literature estimates, supporting their statistical reliability for …

Mining Legacy And Wildfires: Interfacial Reactions Affecting Metal Mobility, Eresay Alcantar-Velasquez

Earth and Planetary Sciences ETDs

We identified water labile interfacial reactions between laboratory burned pinewood ash and mine waste solids that influence metal mobilization. The Upper Gallinas Creek Watershed in New Mexico is affected by wildfires and mining legacy. Pinewood and mine waste sediments were sampled from the area, and the pinewood was burned at 350°C to simulate medium burn intensity ignition. Rapid desorption and gradual dissolution of Mn and Fe was detected by ICP-MS as pH decreased over time. After reacting 18 MΩ ultra-pure water with a mixture of pinewood ash and mine waste sediments Fe (143%) and Mn (89.2%) concentrations increased over time. …

Information Theory Analysis Of Water Vapor Stable Isotopes From The Sail Campaign, Matthew John Rybecky

Earth and Planetary Sciences ETDs

Understanding the processes that control water vapor isotopic composition in mountain environ- ments is essential for interpreting isotope records and predicting water resource responses to cli- mate change. This thesis applies information theory to continuous, high-resolution water vapor stable isotope measurements from the Surface Atmosphere Integrated Field Laboratory (SAIL) campaign in the East River watershed of Colorado’s Upper Gunnison Basin, spanning the winter- to-spring transition of 2022–2023. The analysis employs Shannon entropy, mutual information, transfer entropy, and joint transfer en- tropy (JTE) to quantify how environmental variables, including surface meteorology, radiation, tur- bulent fluxes, and ERA5 reanalysis products, transfer information …

Pebble Accretion: Compositions And Water Origins Of Terrestrial Planets, Susmita Garai

Earth and Planetary Sciences ETDs

Two leading models of planet formation invoke either stochastic collisions among km-sized planetesimals, or pebble accretion of sub-mm-cm solids regulated by gas drag. While collision based models typically require tens to hundreds of millions of years to assemble terrestrial planets, pebble accretion can produce Mars to Jupiter-mass bodies within the lifetime of the protoplanetary disk. Although widely accepted for the rapid growth of giant planet cores, the role of pebble accretion in forming terrestrial planets, including Earth, remains debated. Here, we investigate the consequences of pebble accretion for Earth’s origin. Here, I combine numerical models and laboratory experiments to find …

Gradients Of Abandonment, William Tatman

Geography ETDs

As urban-rural disparities drive depopulation in rural areas worldwide, local strategies emerge as pathways for resilience. Research on Ojika, a Japanese island that has lost 75% of its population since the 1960s, reveals an Abandonment Gradient: a nuanced pattern of disuse adapted to modern polycrises. Extending the concept of "lying fallow" to homes and infrastructure, this thesis focuses on abandonment practices that reflect complex realities of labor, capital, and climate uncertainty. Rather than viewing depopulating communities as passive victims of out-migration, this paper argues they are critical sites for generating crisis response. Communally crafted attitudes toward unused space and more-than-human …

Wildfire Impacts On Fluvial Hydrology From Watershed To National Scales, Paige G. Tunby

Civil Engineering ETDs

Wildfires alter the water quantity and quality in downstream river networks. Fires promote biodiversity, maintain habitat, and provide many ecosystem services in a fire-adapted landscape. However, changes in the natural fire regimes can alter ecosystem function and threaten the water security of impacted downstream communities. The magnitude, timing, and persistence of these impacts are difficult to predict due to the lack of high-resolution datasets with adequate coverage to evaluate spatiotemporal trends after a fire. This dissertation moves us beyond the status quo to evaluate post-fire fluvial responses across scales, from the event-scale impacts after the Hermit’s Peak-Calf Canyon wildfire in …

Boundary Integral Method For A Modified Mullins–Sekerka System, Ly Le

Mathematics & Statistics ETDs

This thesis develops a boundary integral method for a modified Mullins–Sekerka system arising as the sharp-interface limit of a nonreciprocal Cahn–Hilliard model. Nonreciprocal coupling changes the classical Cahn–Hilliard structure by introducing an additional conserved field, leading to coupled elliptic and parabolic dynamics at the interface. Using matched asymptotic expansions, we formally derive the modified Mullins–Sekerka model and then apply the boundary integral method to rewrite it on the moving interface. The elliptic component is represented using the periodic Green’s function for the Laplace equation, while the parabolic component is represented using the periodic heat kernel. This method reduces the bulk …

Nerve Constructions And Mapper, Alexander Bram Fritschi

Mathematics & Statistics ETDs

Mapper is a data visualization tool commonly used in topological data analysis to study large, often high-dimensional datasets. Mapper operates through the selection of a lens function, a clustering algorithm, and a cover. The Mapper graph is constructed using the nerve of the cover after the clustering algorithm is performed; it is therefore useful to study nerves to better understand Mapper. In this thesis, we will utilize the properties of nerves to find the minimal point set that produces a given graph. We will then extend this to Mapper to determine what Mapper graphs may be constructed over a given …

Interpretable Case-Control Inference Through Log-Linear General Location Models, Zacharia Stuart

Mathematics & Statistics ETDs

This dissertation analyzes one of the few publicly available NFL injury datasets to study field type and non-contact lower-limb injuries. Field type is studied jointly with other risk factors to understand how these factors interact to affect injury risk. The data were gathered through a case-control sampling scheme, which limits direct inference on absolute injury probabilities. While not the most common approach for case-control data, this dissertation models the retrospective distribution directly through Log-Linear General Location Models (Log-Linear GLOMs). Through a log-linear structure placed on a log-odds-ratio reparameterization, the model provides directly interpretable marginal and interaction contributions to injury log-odds …

The Uncertainty Principles, Lee Michael Felicetti

Mathematics & Statistics ETDs

The Heisenberg uncertainty principle is a central aspect of quantum mechanics, but also illustrates an essential quality of the Fourier transform. After Heisenberg, a variety of uncertainty inequalities emerged in the fields of physics and mathematics. In this thesis we will analyze the Heisenberg uncertainty principle in both the setting of quantum mechanics and Fourier analysis. We will then look at how the work of Heisenberg has been expanded upon in both physics and mathematics. Particularity, we will see how uncertainty principles can be applied to signal recovery and explore current research in this field.

Simulations Of Atmospheric Pressure Streamer Discharges: Mechanisms Of Streamer Propagation And Related Physics, Dejan Nikic

Electrical and Computer Engineering ETDs

Gas discharge simulations are performed with particular focus on photoionization process in a positive streamer discharge. The effects of this process are investigated by isolating the change in photoionization mean free path (MFP) and keeping the additional processes constant. Furthermore, comparison are made between various effects of simulation parameters, such as initial conditions, geometry extent, simula- tion particle count etc. All of these simulations are performed using a modern Direct Simulation Monte Carlo Particle-in-Cell (DSMC-PIC) code developed by Sandia Na- tional Laboratories. Large scale simulations including 1 cm and 5 cm electrode gaps are performed under standard atmospheric condition air. …

Spatial Heterogeneity And Temporal Trends Of California Extreme Heat Using High-Resolution Earth System Model Simulations, Eleni Konstantelos

Master's Theses

Extreme heat threatens California’s diverse landscapes and populations through intensifying and geographically shifting patterns. This study examined the temporal trend and spatial heterogeneities of California’s extreme heat for 1994–2015. The analysis was based on the fully coupled Energy Exascale Earth System Model version 2 (E3SMv2), specifically its 25-km regionally refined configuration. While the Desert/Inland region exhibited the highest number of days ≥ 35 °C and the highest heatwave severity, Central Valley showed the fastest increase in the number of days ≥ 35 °C and heatwave events, as well as the fastest increases of days exceeding various heat index thresholds over …

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 …

Error-Tolerant Metric Dimension, Leander Ten Hoff

Master's Theses

Metric dimension is a graph parameter that measures the smallest distance-based unique coordinate system on a graph. Fault-tolerant metric dimension is a variant that requires redundancy. Inspired by this idea, we propose and investigate a new variant we call error-tolerant metric dimension. We first prove some fundamental results to gain familiarity with this more complex variant. Then, we use these tools to study relative behaviors of error-tolerant metric dimension. We prove explicit computations for simple graph families, including bipartite complete graphs and paths. Finally, we extend extremal results from previous papers on metric dimension, including a full correction of an …

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 …

The Relationship Between Foliations Of The Plane, Kaplan Diagrams, And Non-Hausdorff 1-Manifolds, Monique Justine Howe

Master's Theses

In this paper we seek to explain the relationship between foliations of the plane, Kaplan diagrams, and simply connected non-Hausdorff 1-manifolds with countable basis that are orientable with an ordering on branch points. We will walk the reader through the definitions of all of these objects, and provide examples with a focus on the motivating example of the Reeb foliation. This paper will describe and define the known bijection from the set of foliations of the plane, F, to the set of Kaplan diagrams, K, its inverse, and the one-to-one map from F to the set of simply connected non-Hausdorff …

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 …

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.

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. …

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.

Probabilistic Metric Dimension, Kyle Worley

Master's Theses

The metric dimension of a graph G is the smallest number of unique vertices (often called “marked vertices” or “landmarks”) such that each vertex has a unique distance to the marked vertices. If a set of vertices S ⊆ V (G) when marked gives all vertices unique distances, it is called a resolving set. Hence if G is a graph with a resolving set S, then for all v, u ∈ V (G) there exists s ∈ S such that d(v, s) ̸= d(u, s). The metric dimension dim(G) = min(|S|). Two widely studied variants exist, one where edges are …

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 …

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 …

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 …

A Dynamics Viewpoint On The Approximation Capabilities Of Infinite-Depth Neural Networks, Andreus Brammer

Electronic Theses and Dissertations 2020 - Present

Neural Ordinary differential equations(Neural ODEs) provide a continuous-time framework for learning dynamical systems by representing the evolution of a state variable through a parameterized differential equation. While most existing methods rely on numerical time stepping methods during training such as RK4, this work investigates an alternate spectral framework where both the solution and the time-dependent network parameters are represented by global polynomial expressions.

Two methods are employed: the first uses Taylor series representations, and the second approach uses Chebyshev polynomial expansions together with fast spectral transforms and efficient polynomial multiplication techniques. In each formulation, the Neural ODE is transformed into …

Enhancing Ecological Resilience: Evaluating Peanut Island's Breakwater Impacts On Coral Reef And Shoreline Dynamics, Dayana Castillo

Electronic Theses and Dissertations 2020 - Present

Anthropogenic shoreline modification and inlet-driven hydrodynamic processes can alter sediment transport pathways and sediment deposition in adjacent coral reef environments. This study evaluated how coastal engineering structures, sediment transport dynamics, and localized hydrodynamic processes influence sediment distribution and coral-associated habitats at Peanut Island, Florida. Beach profile surveys, shoreline mapping, sediment grain size analyses, coral monitoring, and historical aerial imagery were used to assess shoreline variability, sediment characteristics, and long-term shoreline evolution between October 2024 and July 2025. Results indicated that much of the eastern shoreline remained relatively stable, while greater variability was observed along the southern shoreline adjacent to the …

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. …

Improving Cancer Diagnosis And Patient Outcomes With Deep Learning Models, Mariana Arriz-Jorquiera

USF Tampa Graduate Theses and Dissertations

Cancer care depends on timely and reliable decisions, from detection and diagnosis to treatment planning and patient monitoring. These decisions are often made under uncertainty because medical images and healthcare data may be noisy, incomplete, or difficult to interpret. In breast cancer imaging, ultrasound is widely used because it is safe, accessible, and complementary to other imaging modalities. However, variations in image quality, acquisition conditions, and noise can obscure lesion boundaries and texture, affecting human interpretation and artificial intelligence reliability. This dissertation develops deep learning, image-analysis, and optimization methods to improve healthcare decisions under imperfect information. Its primary focus is …