Physical Sciences and Mathematics Commons^™

Topodino: Self-Supervised Topological Representation Learning For Neuronal Morphologies, Yasser Binbisher

Master's Theses

Neuronal cell types are categorized by transcriptomic identity, yet their morphological heterogeneity defies this classification. In response, researchers have adopted unsupervised graph representation learning as a tool to reveal morphological variation within single-class transcriptomic types. However, the complex geometry of neuronal morphology—especially long axons and dense dendrites—challenges graph neural networks, which struggle with message propagation across extended structures. To mitigate this, current approaches enforce sub-sampling on neuronal graphs and omit axons entirely, sacrificing critical biological features for computational efficiency. To overcome this trade-off, this thesis introduces TopoDINO, a self-supervised, topology-aware representation learning model designed to preserve the full hierarchical organization …

Exploiting Compiler-Introduced Vulnerabilities In C: A Cross-Compiler And Cross-Architecture Analysis Of Undefined Behavior, Erik Mccutchen

Master's Theses

Compilers are a critical component in generating secure software across engineering disciplines. However, languages like C that permit undefined behavior introduce a fundamental tension between the compiler’s interpretation of undefined behavior and the security of the generated code. This tension can result in security vulnerabilities that, from the programmer's perspective, are ``created'' by the compiler. The widespread use of these languages, combined with the complexity of modern optimizations and limited developer visibility into compiler behavior, makes these vulnerabilities both pervasive and difficult to detect.

Building on prior work, this thesis refines a dataset of C code snippets that exhibit Compiler-Introduced …

Frequent Itemset Mining With Tidyclust In R, Andrew D. Kerr

Master's Theses

Unsupervised learning is closely associated with clustering, however other methods fall under this umbrella such as data mining. In R, the tidyclust package provides a unified interface for clustering models, yet lacks support for data mining. This thesis addresses this gap by introducing the Apriori and ECLAT algorithms into tidyclust, with a focus on frequent itemset mining. Unlike traditional clustering models, frequent itemsets produce groupings of column variables, rather than cluster labels or partitions of observations. To address this, a novel clustering approach is proposed: items (columns) are grouped based on their ”dominant” frequent itemset. A key contribution is a …

Stability Insights From Modeling Chronic Myelogenous Leukemia, Giovani Thai

Master's Theses

This thesis centers around a model for chronic myelogenous leukemia (CML) as it behaves under imatinib treatment, a common medication for CML patients, and the anti-leukemia immune response. The dynamics are represented with a system of nonlinear delay-differential equations first constructed by Kim et al. in 2008, capturing population changes of T-cells and various CML growth stages. We investigate stability in both the clinical and mathematical sense. Through numerical simulations, we computationally incorporate a supplementary treatment plan to determine its effectiveness in aiding immune response and medication in achieving remission and full elimination. The primary goal is to conduct a …

Structural Color Pigments For Waterborne Coatings, Kyle William Liston

Master's Theses

Structural colors offer unique alternatives to conventional pigments, utilizing their microstructures to produce vibrant colors. These pigments offer an alternative source for colorants without the need for less environmentally friendly conventional pigments. In keeping with the sustainability approach, the use of waterborne coatings was chosen over solvent-based coatings. Here we report the synthesis of brushite platelet, silica supraball, and inverse opal pigments. Brushite platelets were produced through a condensation reaction, while silica supraballs were synthesized via the Stöber process and assembly was attempted using an oil-in-water emulsion. Inverse opal was produced through the templating of silica on poly(methyl methacrylate) (PMMA) …

Langlands Reciprocity And The Splitting Behavior Of Primes In Number Fields, Skip E. Moses

Master's Theses

This thesis explores the evolution of reciprocity laws in number theory in order to provide a conceptual bridge between the classical ideas of quadratic reciprocity and the modern framework of the Langlands program. We develop the necessary algebraic background to understand how the splitting behavior of primes in number fields reflects deep arithmetic structure in ℚ. Starting with quadratic fields and cyclotomic extensions, we motivate the development of the Kronecker–Weber theorem and the characterization of abelian extensions of ℚ. We then introduce Artin reciprocity and show how it generalizes quadratic reciprocity through the formalism of Frobenius elements and Artin L-functions. …

Catalyzed Chemical Recycling Of Poly(Ethylene Terephthalate) For Enhanced Sustainability, Gilberto J. Hernandez-Leypon Jr.

Master's Theses

Plastics are ubiquitous in the production of consumer and industrial products; their chemical stability, low cost of production, and performance versatility make them the best option for many industries. Their inherent benefits, specifically durability, is the basis for the negative environmental impact of polymers. Improper containment of endof-life polymer products causes unintentional migration into the environment. The monomers for many common polymer types are also fossil fuel based further increasing the environmental impact of the plastic lifecycle. Recycling is a possible method of closing the loop of the plastic lifecycle. Currently most recycling is physical, thermally reprocessing used plastics into …

Banach Algebras And The Gelfand Theory Of Group Algebras On Locally Compact Abelian Groups, James Gabriel Bonvanie

Master's Theses

A Banach algebra is a complex algebra that is simultaneously a Banach space in which the norm is submultiplicative. Notably, $L^1(\mathbb{R})$ with the convolutional product is an Abelian, non-unital Banach algebra that admits an approximate identity. We rectify $L^1(\mathbb{R})$ lacking a unit via the unitization $L^1(\mathbb{R})\times\mathbb{C}$ with identity $(0,1)$. Unitization opens the discussion to the spectrum $\sigma(x)$ of a Banach algebra element, in which the spectrum is a nonempty, compact subset of the complex plane. The spectrum of an Abelian Banach algebra is fully characterized with multiplicative linear functionals, and we prove that the Fourier transform is the unique multiplicative …

Spos: An Attestation Solution For The Detection And Mitigation Of Point Of Sale Malware, Damian Singh Dhesi

Master's Theses

Securing 95% of card present transactions, accounting for billions of transactions a year, has made EMV the premier protocol for card-based payment. Created by and named after Europay, Mastercard, and Visa, the EMV protocol provides multiple solutions to resolve security concerns with the outdated, swipe-based, magnetic stripe payment. Such solutions are Chip and PIN which provides a more secure transaction at a significant time cost and EMV contactless which provides improved security to Chip and PIN at greater ease of use with its quick, tap-to-pay based payment. However, regardless of how secure the EMV protocol makes the card side of …

Investigating Social Presence In Collaborative Keys For Asynchronous Courses, Lily P. Cook

Master's Theses

Asynchronous virtual courses have become increasingly popular in the years following the global Covid-19 pandemic. These courses, with no set meeting schedule, offer flexibility to both students and instructors, but pose challenges for developing a collaborative learning environment. The Community of Inquiry framework (Rourke et al., 1999) identifies three essential components in an online course necessary to foster a collaborative environment- teaching presence, cognitive presence, and social presence. Social presence is especially impacted in asynchronous learning settings, which presents challenges for the students to display their personalities and connect with the community. This study investigates Collaborative Keys (CKs), structured collaborative …

On Diffeomorphism Groups Of Surfaces, Madeleine Goertz

Master's Theses

Let $M$ be a closed, connected, smooth manifold. What are the symmetries of $M$? From a geometric viewpoint, the symmetries of $M$ are precisely its isometries, the self maps which preserve lengths and angles. In the smooth category, the symmetries of $M$ are its diffeomorphisms, the self maps which are smooth and have a smooth inverse. Does expanding our notion of symmetries to include diffeomorphisms result in ``more'' symmetries in a meaningful sense? As a formal conjecture, the claim is that the isometry group of $M$ is a deformation retract of the diffeomorphism group of $M$. If $M$ is the …

Filling Gaps In Scientific Data Sets Using Physics Informed Neural Networks: A Case Study In Velocity Fields, Ellen Saunders

Master's Theses

Gaps in scientific data sets are a persistent issue for researchers in a variety of fields, and while nothing makes up for missing out on real data, well-simulated synthetic data can be a useful tool. In the world of image processing, machine learning techniques have become quite sophisticated at taking an image with a missing component and filling in that space with something believable. The aim of this thesis is to take machine learning techniques similar to what gets used in image processing and repurpose them to infill gaps in scientific data sets in a realistic manner. This thesis compares …

Adversarial Deep Reinforcement Learning For Tank Duel Simulation Using Lidar-Based Observations, Braedan Kennedy

Master's Theses

Previous research has demonstrated that reinforcement learning agents can learn to steer differential-drive robots around obstacles using 2D lidar scans as observations. However, these studies typically treat all range returns as undifferentiated obstacles—objects to avoid—without distinguishing between different object types. This thesis builds upon previous research by introducing an adversarial task in which an agent must interpret raw range readings to both avoid static obstacles and identify, pursue, and engage a hostile target.

To investigate this problem, this thesis introduces TankGame, a novel, lightweight 2D tank duel simulator. Each agent receives a 360° lidar scan, controls its motion via tread …

Opening The Black Box With Regal: A Novel Explainable Ai Approach To Uncover Key Predictors In Search And Rescue Success, Brandon Hyunjun Kim

Master's Theses

The outcome of a search and rescue (SAR) operation is influenced by a complex, non-linear interplay among numerous factors, including geographic context, subject-specific characteristics, and environmental conditions. The high dimensionality and intricate dependencies among these variables pose significant challenges to traditional exploratory modeling approaches, limiting their ability to uncover meaningful patterns and relationships associated with mission success. This study introduces Rules Based Explanations for Generated neighborhoods Around Localized cases (REGAL), a novel adaptation of the Local Interpretable Model-agnostic Explanations (LIME) framework to explain deep multimodal neural networks and what key features it assesses to determine search and rescue success. REGAL …

Vertical And Latitudinal Variability Of Marine Heatwaves In The California Current, Gavin M. Plume

Master's Theses

Marine heatwaves (MHWs) are increasing in frequency and intensity globally, with grave effects on marine ecosystems and their dependent industries. There are significant gaps in knowledge of the subsurface behavior and geographic distribution of MHWs, especially in eastern boundary upwelling systems like the California Current. Here, two decades of full water-column temperature observations from a shallow autonomous profiler in San Luis Obispo Bay (~10m) revealed that while MHWs have similar average durations and intensities across all depths, one-third of bottom MHWs occur without a concurrent surface signal. MHWs across the water column initiated during anomalously weak upwelling or downwelling conditions …

Myceli-Yum: Elucidating Structure-Property Relationships For Polymer Degradation By Mycelial Digestion, Jordan Scott Ford

Master's Theses

Since the industrial entrance of polymer plastic materials, plastic has become ubiquitous in both everyday use and waste. Due to inefficiencies and knowledge gaps, current recycling methods are not able to account for the high scale of plastic waste, resulting in the bulk of this waste being landfilled, mishandled, and deposited in the environment. Mycelium, the microorganism responsible for fruiting mushroom bodies and mold growth, holds potential to reduce plastic waste and can potentially be utilized as a method of industrial recycling. Following a drug-design approach, the active site of mycelial enzymes responsible for natural biopolymer degradation have been assessed …

Adaptive Volatility Forecasting Models, Jeffrey K. Tan

Master's Theses

In finance, risk is often quantified by volatility, and computing accurate volatility forecasts — while vital to financial decision making — remains one of the most challenging tasks in financial modeling. This thesis, motivated in part by the Black-Scholes-Merton Model and its limitations, adopts a statistical approach to volatility forecasting. The two main models of interest are the Exponential Weighted Moving Average (EWMA) model and the GARCH(1,1) model. Specifically, this work expands upon a potential adaptive lambda algorithm for EWMA models first proposed by Bernard Bollen (2014), and this work also utilizes the Momentum of Predictability (MoP) to generate adaptive …

The Degrees Of The Irreducible Representations Of The Symmetric Group With Respect To Primes, Vanessa F. Beeler

Master's Theses

In this thesis, we explore the relationship between the degrees of irreducible matrix representations of the symmetric group and prime numbers. We start by building up the required background necessary to construct our results. We dive into topics of discrete mathematics including matrix representations, characters of representations, integer partitions, conjugacy classes, class functions, and tableaux. Some other key ingredients in our work include using character tables to classify the irreducible rep- resentations of the symmetric group and the hook-length formula to easily compute the degrees of these representations. Once we have laid the groundwork for our in- vestigation, we begin …

Comparing Machine Learning Paired Optimization Strategies For Single-Component Waterborne Direct-To-Metal Coatings, Harvir S. Kalkat

Master's Theses

As R&D attempts to fine tune properties before production, the redesign and testing process can become highly iterative. The repetitive nature of formulating can be difficult to escape when relying on chemical intuition alone. To provide some guidance in this process, machine learning (ML) can leverage data from previous trials¹ to design suggestions for subsequent trials. Although ML capabilities have vastly expanded in the last few years, integration of ML into chemistry R&D and education has been slow. Unraveling the mystique of ML can help change what has been a slow embrace in the coatings industry. It is important …

Data Driven Analysis Of Samara Seed Kinematics And Dynamics, Shashwat Sparsh

Master's Theses

Samara Seeds are a class of fruit most famously belonging to the Acer species and are characterized by their single-bladed geometry and their auto-rotation response during descent. This steady-state auto-rotation response is the subject of aerodynamic analysis which aim to quantify the performance. The period prior to the beginning of steady-state auto-rotation is classified as the transition regime and has not been the subject of intense scrutiny.

This thesis employs a data-driven approach to analyzing the kinematic and dynamic response of these seeds during both the transition and auto-rotation stages of flight to quantify the performance with respect to the …

Seoul National University Agn Monitoring Project. V. Velocity-Resolved Hβ Reverberation Mapping And Evidence Of Kinematics Evolution, Shu Wang, Jong-Hak Woo, Aaron J. Barth, Vardha N. Bennert, Elena Gallo, Edmund Hodges-Kluck, Minjin Kim, Suvendu Rakshit, Tommaso Treu, Hojin Cho

Physics

We present velocity-resolved reverberation lags of Hβ for 20 active galactic nuclei (AGNs) from the Seoul National University AGN Monitoring Project. We detect unambiguous velocity-resolved structures in 12 AGNs, among which eight objects exhibit symmetric structures, two objects show inflow-like characteristics, and two objects display outflow-like signatures. For two AGNs, we successfully measure the velocity-resolved lags in different years, revealing evidence of evolving broad-line region (BLR) kinematics. By combining our sample with the literature velocity-resolved lags, we find that the symmetric velocity-resolved lags are the most common (40%) type among this sample. The frequency of inflow kinematics is also …

Climate Change And Variability Drive Increasing Exposure Of Marine Heatwaves Across Us Estuaries, Ricardo U. Nardi, Piero L. F. Mazzini, Ryan K. Walter

Physics

Marine heatwaves (MHWs) are among the greatest threats to marine ecosystems, and while substantial advances have been made in oceanic MHWs, little is known about estuarine MHWs. Utilizing a temperature dataset spanning over two decades and 54 stations distributed across 20 estuaries in the United States National Estuarine Research Reserve System, we present a comprehensive analysis of estuarine MHW characteristics and trends. Long-term climate-change-driven warming is driving more frequent MHWs along the East Coast, and if trends continue, this region will be in a MHW state for ~ 1/3 of the year by the end of the century. In contrast, …

Muon Veto Panel Uniformity Tests At Yale Wright Laboratory For The Cuore And Cupid Experiments And Visualizing Dirac Spinors In The Chiral Basis With The Bloch Sphere, Reagen Neeva Garcia

Physics

This senior project is divided into three sections that describe my path and experiences in under graduate research. The first provides an introduction to the field of particle physics and the search for neutrinoless double beta decay (0νββ) with the Cryogenic Underground Observatory for Rare Events (CUORE) experiment, as well as its upgrade, CUPID (CUORE Upgrade with Particle IDentification). The second section details my contributions to these experiments, including my summer working at Yale’s Wright Laboratory on R&D for the CUPID experiment. In this section I describe my work on the experiment’s muon veto system and on light detector development …

Treating Ground Water For Agricultural And Individual Consumption, Gabby Miller, Bronson Scott, Michael Clawson

Biomedical Engineering

This project, conducted in collaboration with Cal Poly seniors and Da Vinci High School students, aims to develop a solar-powered groundwater purification system. This system is designed to provide clean water for agricultural use and individual consumption, addressing the growing concerns of groundwater contamination and accessibility needs. The final prototype integrates a gravity filtration system combined with chemical purification, utilizing aluminum sulfate and chlorine to remove particulates, bacteria, and organic compounds.

The research phase involved an extensive review of groundwater contamination issues, existing filtration technologies, and market analysis. Key design constraints included cost-effectiveness, ease of maintenance, and minimal energy consumption, …

Vertical Structure Of Subsurface Marine Heatwaves In A Shallow Nearshore Upwelling System, Gavin Plume, Ryan K. Walter, Isabelle Cobb, Michael Dalsin, Piero L. F. Mazzini, Nathan P. Shunk, Ian C. Robbins, Thomas P. Connolly

Physics

Marine heatwaves (MHWs) are increasing in frequency and intensity globally and are among the greatest threats to marine ecosystems. However, limited studies have characterized subsurface MHWs, particularly in shallow waters. We utilized nearly two decades of full water-column (~ 10 m) observations from a unique automated profiler in central California to characterize, for the first time, the vertical structure of MHWs in a shallow nearshore upwelling system. We found MHWs have similar average durations and intensities across all depths, but there were ~ 17% more bottom MHW days than surface MHW days. Nearly one third of bottom MHWs occurred independently …

Offshore Wind Farms Could Impact Coastal Marine Heatwaves In Eastern Boundary Upwelling Systems, Michael Dalsin, Ryan K. Walter, Piero L.F. Mazzini

Physics

Analysis of ecosystem impacts from offshore wind (OSW) farm development has primarily focused on localized effects. However, in Eastern Boundary Current Upwelling Systems (EBUS) like the California Current, OSW farms can modify the intensity and spatial structure of wind-driven upwelling, inducing non-local (tens of kms away) changes to seawater temperature. Recent numerical modeling research determined that a hypothetical upper bound full buildout of OSW farms in central California could warm coastal waters through a reduction in upwelling. Here, we examine the sensitivity of coastal marine heatwaves (MHWs), which are prolonged extreme seawater temperatures that are among the greatest threats to …

Fault Box Modeling Of Dip Slip Faults: A Framework For Fault Box Design And Future Studies, Hailey Pressnell

Master's Theses

The behavior of soils during surface fault rupture is a serious concern in the planning and design of infrastructure that may be located within or near a fault zone. Challenges associated with developing mitigation measures for surface fault rupture include the uncertainty of fault rupture and the variability of fault behavior. Current analytical procedures define surface fault rupture according to the type of fault movement (strike slip, normal or reverse), the amount of displacement on the fault, and the mechanics of the material overlying the fault. The purpose of this thesis is to reconfirm analytical solutions and gain a better …

Combining Direct Black Hole Mass Measurements And Spatially Resolved Stellar Kinematics To Calibrate The Mbh–Σ⋆ Relation Of Active Galaxies, Nico Winkel, Vardha N. Bennert, Raymond P. Remigio, Tommaso Treu, Knud Jahnke, Vivian U, Aaron J. Barth, Matthew Malkan, Bernd Husemann, Xuheng Ding

Physics

The origin of the tight scaling relation between the mass of supermassive black holes (SMBHs; MBH) and their host-galaxy properties remains unclear. Active galactic nuclei (AGNs) probe phases of ongoing SMBH growth and offer the only opportunity to measure MBH beyond the local Universe. However, determining an AGN's host galaxy's stellar velocity dispersion, σ⋆, and its galaxy dynamical mass, Mdyn, is complicated by AGN contamination, aperture effects, and different host-galaxy morphologies. We select a sample of AGNs for which MBH has been independently determined to high accuracy by state-of-the-art techniques: dynamical modeling of the reverberation …

Counting Catalan: An Experimental Evaluation Of The Mixing Time For The Triangulation Markov Chain, Roy Gotlieb

Master's Theses

Monte Carlo Markov chains (MCMCs) are used in many areas as a way to model a system’s behavior. By running a probabilistic simulation on a system’s state space, we can estimate properties of the system that could be untenable to directly compute. It is of interest to determine how quickly a Markov chain mixes\textemdash that is, settles into its stationary distribution. One such chain is induced by taking a binary search tree and performing a rotation or flip on one of its edges. We know that this chain eventually settles into the uniform distribution, but the time complexity bounds on …

Hitch Cart “Landing Gear”, Rebekah White, Jose Raygoza, Randy Hernandez, Brandon Leon

Mechanical Engineering

This report aims to allow our sponsor, to review our design process of the Hitch Cart Landing Gear Prototype. In the design overview section of this report, we discuss the primary design modifications we made to the wheel mechanism of the existing hitch cart prototype, including the addition of the ACME screws and the folding brackets. This allows our sponsor to see the intended improvements made to the past prototype and understand the primary goal of our project. Then, in the implementation section, we cover the entire manufacturing process to allow our sponsor to understand what manufacturing steps must be …