Physical Sciences and Mathematics Commons^™

50,000 Spectra And Counting: Preparing For A Roman Spectral Atlas, Maya Jordan Seagraves

Master's Theses

Slitless spectroscopy with the Hubble Space Telescope's Wide Field Camera 3 \linebreak (WFC3/IR) enables simultaneous spectral coverage of all sources in a field, but large-scale single-orientation datasets remain challenging to process. We developed a pipeline that automates HSTaXe spectral extraction across hundreds of Hubble Space Telescope observations, enabling efficient processing of 84 fields and producing over 50,000 spectra from three filters (F110W, F125W, and F160W) and two grisms (G102 and G141). This was achieved by creating a companion Python package, the Module for Infrared Label Analysis (MILA), that integrates data calibration, extraction, and visualization. To assess the scientific utility of …

Evaluation Of Solar Reflective Pigments For Use In Direct-To-Metal Coatings, William J. Diment

Master's Theses

Solar reflective coatings offer a promising strategy to mitigate the urban heat island effect by reducing absorption of near-infrared solar energy. This thesis project investigates the feasibility of incorporating near-infrared reflective pigments into waterborne direct-to-metal (DTM) latex coating systems while maintaining acceptable color comparison characteristics and coating performance. An all acrylic latex DTM formulation with titanium dioxide as the sole pigment was prepared and tinted with a variety of conventional and solar reflective commercial colorants across the yellow, red, blue, and green color ranges. Coatings were evaluated for solar reflectance, CIELAB color, gloss, contrast ratio, rheological behavior, accelerated ultraviolet weathering …

On M-Estimation: From Theory To Examples, Alexander Yuan

Master's Theses

M-estimation provides a unified framework for statistical procedures defined as optimizers of data-dependent criterion functions. This thesis gives an expository account of M-estimation in classical and high-dimensional settings. The classical part develops weak convergence, empirical process tools, and the argmax framework for studying consistency, rates of convergence, and weak limits. Examples including least squares, maximum likelihood, robust location estimation, change-point estimation, and empirical risk minimization illustrate regular and non-regular asymptotic behavior.

The high-dimensional part studies regularized M-estimators, where the focus shifts to finite-sample error bounds and model selection guarantees. Topics include decomposable regularizers, restricted strong convexity, non-convex penalties, and sparsistency. …

High-Resolution Queries, Low-Resolution Context: Scaling Vision Transformers With Asymmetric Spatial Reduction, James M. Dwyer

Master's Theses

Vision Transformers (ViTs) have demonstrated great performance on image classifica tion benchmarks, however, the quadratic complexity of the self-attention mechanism with respect to sequence length limits their scalability to higher resolution inputs. The attention score matrix grows as O(N2) in both compute and memory, where N is the number of patch tokens, making ViTs computationally expensive and memory intensive for applications that require real-time inference or operate under resource constraints.

This thesis investigates whether the key and value sequences of the self-attention mechanism can be compressed using the local spatial structure of the image — while keeping queries at full …

Scorespeak: An Agentic System For Natural Language Control Of Musical Scores, Nathan S. Lim

Master's Theses

With the recent popularization of large language models (LLMs), natural language has become one of the most accessible and powerful ways for people to interact with creative tools. Although they have become common in mainstream domains like image and audio editing, there is currently no robust AI-based system that can reliably turn free-form language into edits for symbolic musical scores. This gap represents a missed opportunity to improve human workflows for creating and editing sheet music, but it is also a fundamental limitation for other agentic music systems; without a robust mechanism for translating free-form language into structured scores, AI …

Structured Dynamic Factor Analysis Of Environmental Time Series With Application To Morro Bay Estuary, Jose Garcia

Master's Theses

This thesis develops a structured dynamic factor analysis (sDFA) framework for decomposing multivariate environmental time series into latent biological and physical components. The methodology is applied to five years of high-resolution passive monitoring data collected from two sites in Morro Bay, California from 2020 through 2024. Relative contribution indices are developed based on the structured DFA that measure how much each latent process contributes to each observed variable at any given time. Structured DFA models fit to the application data suggest site-specific patterns in how biological and physical processes affect water quality variables. At the bay mouth location, physical processes …

Exploring Regenerative Vegetable Systems On The Central Coast Of California, Una S. O'Connell

Master's Theses

As climate change and current agricultural practices place pressure on the long term sustainability and resilience of food production systems, there is growing interest in whether existing agricultural systems can adapt to maintain productivity while improving environmental outcomes.

This study evaluated the effects of regenerative versus standard organic vegetable production systems on yield, insect communities, and weed suppression across three field trials conducted on California's Central Coast. In addition, I collected baseline soil health data for all trials. Trials 1 and 2 were carried out at the Cal Poly San Luis Obispo Organic Farm using cabbage and broccoli as cash …

Constructing Orthonormal Bases With The Residuals Of Successive Approximations, An Introduction To Multiresolution Analysis, Elijah J. Guptill

Master's Theses

Wavelets and wavelet analysis are used in the study of signal processing, quantum field theory, functional analysis, multifractal analysis, and various other areas of mathematics. Multiresolution analysis provides a framework for building a wavelet basis of $\mathcal{L}^{2}(\mathbb{R})$ from a scaling function $\phi$, whose dyadic dilations and translations, $\{2^{j /2}\phi(2^{j}x-k):j,k\in \mathbb{Z}\}$, approximate $\mathcal{L}^{2}(\mathbb{R})$. One of the key properties of  $\phi$ is that it must satisfy $\phi(x)=\sum_{k\in \mathbb{Z}}{p_{k}2^{j /2}\phi(2^{j}x-k)}$ with respect to the norm on $\mathcal{L}^{2}(\mathbb{R})$. This equation is called a two-scale difference equation. Such equations enforce a regularity on the ordinary generating function $2^{-1 /2}\sum_{k\in \mathbb{Z}}{p_{k}z^{k}}$, known as the quadrature condition. …

Developing A Humpback Whale Vocalization Detector Using Machine Learning Models, Lucas Kantorowski

Master's Theses

Humpback whale songs are notoriously complex. Identification of humpback whale song units requires bioacousticians to tediously listen, analyze, and annotate collected sound data. Even sparse data requires listening to the entirety of the collected acoustic data. In this study, three hours of audio containing over one-thousand humpback whale song units was collected in Monterey Bay, California.

Prior studies have seen success using convolutional neural networks by performing image classification on hundreds of hours worth of spectrograms. Our study uses traditional machine learning models, as they are less computationally demanding, and require less data.

We use time splitting and Mel-frequency cepstrum …

Improving The Reliability And Performance Of A Supersonic Indraft Tube Wind Tunnel, Christian J. Kaml

Master's Theses

Access to supersonic testing is increasing in demand, and wind tunnels remain one of the safest and most cost-effective methods for gathering high-speed flow data. Despite being more economical than alternative options, supersonic wind tunnel facilities often require substantial investment to construct, operate, and maintain.

The novel indraft tube tunnel architecture was conceived as a high-speed flow testbed that incorporates features of both Ludwieg tubes and indraft wind tunnels to maintain costs low enough to be accessible even to small universities. This design was first developed and tested in 2018 at California Polytechnic State University, featuring a cost per test …

An Evaluation Of Road Network Structure As A Predictor Of Traffic Volume, Colin M. Mcdonald

Master's Theses

This thesis evaluates the relationships between various graph theory metrics and taxi traffic volume for the cities of San Francisco, California and Porto, Portugal. We also evaluate a modified betweenness centrality metric which incorporates the count of distinct origin-destination pairs from the taxi data as the weight function. This thesis extends a paper by Pengyao Ye, Bo Wu, and Wenbo Fan by reducing circularity through a temporal train-test split and by comparing both line-graph and primal-graph formulations of betweenness centrality.

We found that past traffic volume is almost perfectly correlated with future traffic volume and that the modified betweenness centrality …

Electrical Resistivity Tomography Investigation Of Hard Rock Aquifers In The Salinian Block, Roxanne C. Chambers

Physics

Identifying a productive groundwater source in hard rock terrain is often a challenge. Conventional hard rock aquifer models commonly describe a weathering derived layered system consisting of a laminated layer, an underlying fractured zone, and a competent granitic basement. This study investigates the applicability of this conceptual model at Lockshaw Ranch, a granitic site within the Salinian Block of central California located near the Rinconada Fault.

Previous electrical resistivity tomography (ERT) surveys and time domain electromagnetic (TDEM) data were integrated with a newly acquired ERT profile (ERT-06) are used to characterize the subsurface structure and identify potential groundwater bearing zones. …

Self-Adjoint Extensions Of Symmetric Operators, Malak Mousa

ETDs from 2020-2029

This thesis introduces operators in Hilbert Space, definitions and properties. And then introduce a method for constructing a self-Adjoint extensions of a symmetric operator and illuminating the method by example.

Experimental Methods For Cryogenic Rare Event Detection: Cuore And Cupid, Alessandro Libenson

Physics

This senior project was written with the primary purpose of serving as a introductory guide for undergraduate students learning about the experimental methods used in the CUORE and CUPID Collaborations. In particular, this project is geared towards getting students in Dr. Gutierrez's research group at Cal Poly up to speed on what CUORE and CUPID actually do. I wrote this as an undergraduate aiming to help future undergraduates. For Cal Poly students, I would suggest the following prerequisites before reading this paper: Electronics and Instrumentation, Quantum Laboratory 1, and the equivalent of the coding/analysis class. It is also important to …

Muon Lifetime: Theory, Experiment, And Simulation, Soren Agustin Munoz

Physics

This senior project investigates the muon lifetime through three complementary approaches: theoretical calculation, laboratory measurement, and computational simulation. The theoretical component develops the necessary background from relativistic field theory to the effective weak interaction, culminating in the leading-order Fermi-theory prediction of τ ≈ 2.2 μs, which explains why the muon lifetime lies on the microsecond scale.

The experimental component measures the lifetime of stopped cosmic-ray muons using a plastic scintillator, photomultiplier tube, and analog timing electronics. A binned Poisson likelihood fit to the primary 15-day acquisition run τ = 2.17^+0.03_-0.09 μs, consistent with the accepted value within the …

Validation Of Electromagnetic Shower Development In A Reduced Alice Focal-E Detector Model Using Geant4, Isaac Lara Romo

Physics

This project focuses on the preliminary simulation of a reduced FoCal-E detector model for the ALICE experiment at CERN. Beamline tests were simulated using an electron gun at various incident energies, and the results were compared with those of the FoCal group. The longitudinal charge deposition per sensor layer was compared between the two setups to verify that the reduced model exhibited expected calorimeter behavior. Additionally, the transverse signal across the high-granularity sensor layers was examined to determine whether the reduced model reproduced the expected lateral development of electromagnetic showers. The results obtained from these measurements show that the reduced …

High-Pressure Studies Of Magnetic Topological Materials, Greeshma Chireckal Jose

ETDs from 2020-2029

Quantum technology leverages the principles of quantum mechanics to transform emerging fields such as quantum computing, spintronics, and next-generation electronics. A crucial step in advancing this frontier is the detailed understanding of fundamental quantum phenomena in materials that can drive quantum innovation. This research aims to systematically investigate quantum phase transitions and unconventional emergent behaviors in magnetic topological materials subjected to external pressure. This study focuses on three representative systems: EuCd2As2, EuMnBi2, and FeSn, each serving as a model for exploring intrinsic magnetic topological states. EuCd2As2, a candidate Weyl semimetal (WSM), is expected to exhibit pressure-induced topological phase transitions, making …

Inverse Modeling The Geo-Spread Of Covid-19 In Brazil, Cameron Keith Mills

ETDs from 2020-2029

In 2021 Fitzgibbon, Morgan, Webb, and Wu used a modified SEIR (susceptible, exposed, infected, and recovered) model to predict how COVID-19 spread through Brazil [12]. For their model, six constant coefficients were used that were fitted, referenced, or assumed. In this thesis, we geo-spatially modify their SEIR model and formulate an inverse problem to recover the now spatial coefficients of the model. We first show there exists a unique solution to the modified model. To solve the inverse problem, we modify an inverse method [17] that focused on minimizing convex functionals. These recovered spatial coefficients can be used with Matlab’s …

Biomedical Applications Of Structurally Defined Natural And Semi-Synthetic Saponins, Chaeeun Lim-Paik

ETDs from 2020-2029

Triterpenoid saponins are amphiphilic glycosides that exhibit a wide range of biological and pharmacological properties, including antifungal, antiviral, molluscicidal, hypoglycemic, and hypocholesterolemic effects. These biological and pharmacological properties make saponins attractive for diverse applications. In this work, we demonstrate three biological applications: (i) immunostimulant vaccine adjuvant, (ii) protein delivery enhancement, and (iii) gene transfection enhancement. In light of the strong structure dependence of saponin activity, expanding the structural diversity of available scaffolds is essential for establishing structure-activity relationships (SAR) across these applications. Here, we expanded our saponin collection through semi-synthetic derivatization and the isolation of new saponins from distinct natural …

Reduced Product Type Monoid-Module Extensions, Darryl Jent

Dissertations

In 1955, I. M. James introduced the James Construction, a free topological monoid that models the loops on the suspension of a given space. In 1969, S. Y. Husseini generalized this idea to RPT monoids: topological monoids with a free-like monoid structure that can be used to model a broader class of loop spaces. In order to prove that these topological monoids are models of loop spaces, both I. M. James and S. Y. Husseini constructed contractible spaces on which these topological monoids act. We define a topological module as a space equipped with an action by a topological monoid. …

From Total Domination To Graph Coloring, Sawyer Isaac Osborn

Dissertations

A question involving a chess piece called a prince on the 8×8 chessboard leads to a concept in graph theory involving total domination. We say a vertex u in a graph G totally dominates a vertex v if u is adjacent to v. A subset S of the vertex set of a graph G is a total dominating set for G if every vertex in G is totally dominated by at least one vertex of S. If S is a total dominating set of G, then σ_S(v) denotes the number of …

Cloud Tank: Virtual Reality Performance Instrument For Embodied Audiovisual Remixing, Asya Ulger

Computer Science Senior Theses

Traditionally, live audiovisual performances are made behind a desk using a laptop and an audio controller. This setup restricts the performer’s movements and separates the artist from their work. Moreover, it narrows what counts as the performance to the output alone — the audience is preconditioned to treat the projected image and sound as the whole event, and not the artist producing it. Cloud Tank challenges this by positioning the performer’s body as the instrument, using virtual reality. As the performer, I mix spatialized audio and drive beat-aligned, reactive video layers through hand movement and hand-pose recognition. The audiovisual output …

Ai Interview Helper: A Tool For Assisting Search And Rescue Long-Profile Interviews, Dylan P. Starink

Master's Theses

In Search and Rescue (SAR) operations, time pressure and limited interviewer experience can lead to missed opportunities when interviewing a missing person’s friends and family. This thesis presents a real-time, end-to-end system that provides context-aware follow-up question suggestions as interviews unfold. Leveraging large language models (LLMs) and agentic design patterns, the system is intended to support interviewers by helping them identify relevant follow-up questions and pursue potentially overlooked lines of inquiry.

The system was evaluated through three mock interviews with two SAR interviewer participants across two events. Given the limited sample size, the results provide early insights into the feasibility …

Equitable Decompositions: A Gateway To Spectral Theory Through Graph Automorphisms, Daniel Ford

Master's Theses

Graphs with symmetry appear throughout mathematics and its applications, from the structure of molecules and network design to combinatorial game theory. A central question in spectral graph theory is how to compute or characterise the eigenvalues of the matrices associated with such graphs. Classical decomposition methods, such as diagonalisation or Jordan normal form, accomplish this but only once some spectral information is already known. A different approach, introduced by Barrett et al. (2015), uses the automorphisms of a graph to block-diagonalise its adjacency matrix without any prior spectral information. Because one of the resulting summands is always the quotient matrix …

Determining K Clusters In K-Means Clustering With The Crab Algorithm, Jasmine Kristine S. Cabrera

Master's Theses

Unsupervised clustering often faces the challenge of determining the correct number of clusters in the absence of a true target variable. Traditional methods such as the Elbow Method and the Silhouette Score can produce ambiguous results and rely on assumptions about cluster shape or separation. To address this, we created the Clustering Rivals and Buddies (CRAB) algorithm which evaluates clusters based on stability across multiple subsamples. CRAB uses pairwise classifications to identify points that consistently group together called “Buddies” and points that remain separated called “Rivals.” Applied with K-means, CRAB accurately recovers underlying cluster structures in both spherical and non-spherical …

Thermally Induced Color Changes In Iron Oxide Containing Coatings, Tabatha Whitfield

Master's Theses

Wildland-urban interface (WUI) fires and residential conflagrations present significant challenges for post-fire damage and fire propagation analysis. CAL FIRE observed reddening in architectural coatings during the 2025 Pacific Palisades fire with no determination of the cause. While heat-induced color change of infrastructure coatings has been studied, its potential use as a thermal exposure indicator in residential fire events remains largely unexplored. The objective of this study was to characterize the heat-induced color change of yellow iron oxide containing coatings subjected to thermal exposures, replicating residential fire conditions. The coatings were applied to commonly used building materials and exposed to direct …

The Implementation Of Scintillation Detectors With The Cuore/Cupid Collaboration In The Search For Neutrinoless Double Beta Decay, Reese Sandra Cormier

Physics

CUORE (Cryogenic Underground Observatory for Rare Events) is an experiment at the Gran Sasso National Laboratory in Assergi, Italy, currently searching for an answer to the matter-antimatter asymmetry problem; the question: why do we exist? One proposed explanation is neutrinoless double beta decay, a theorized exotic decay that would prove that neutrinos are their own antiparticle, violating the current Standard Model for particle physics. However, current detection methods do not distinguish different types of particle interactions, resulting in alpha decays contributing to the background. Therefore, the experimental sensitivity is too limited to make confident determinations about the data. For this …

Gauss Composition And Orthogonal Modular Forms On Binary Lattices, Haochen Wu

Dartmouth College Ph.D Dissertations

We revisit Gauss composition over a general base scheme, with a focus on orthogonal groups. We show that the Clifford and norm functors provide a discriminant-preserving equivalence of categories between binary quadratic modules and pseudoregular modules over quadratic algebras. This perspective synthesizes the constructions of Kneser and Wood, reconciling algebraic and geometric approaches and clarifying the role of orientations and the natural emergence of narrow class groups.

As an application, we restrict to lattices and show that binary orthogonal eigenforms correspond to Hecke characters. Using theta series, we show the explicit connection between Hilbert modular forms and orthogonal modular forms …

Investigating An Energy-Preserving Spectral Finite Difference Numerical Method For A Wave Equation On The Metric Graph, Tue Minh Tran

University Honors Theses

To investigate the accuracy and long-term energy conservation of a spectral finite difference numerical method for a wave equation on metric graphs. In conservative systems, numerical methods should preserve total energy. However, explicit finite difference methods require impractically small space steps and exhibit energy drift at end points. To address these limitations, a spectral finite difference method is implemented using a Fourier transformation. This semi-spectral method improves stability at endpoints while maintaining second-order accuracy, achieving an overall error of O(∆t²). We implement the semi-spectral method on the IEEE14 metric graph and provide visuals showing the initial condition …

Developing A High-Resolution Off-Axis Common-Mode Digital Holographic Microscope, Lucy Cook

University Honors Theses

Off-axis digital holographic microscopy (DHM) is a powerful tool for 3D, non-invasive live-cell tracking without moving parts. However, traditional setups face an inherent dilemma: split-path interferometers offer high spatial resolution but poor temporal stability, while more stable common-mode configurations are historically limited to lower numerical aperture (NA) regimes. This thesis bridges that gap by scaling a common-mode DHM architecture into a high-resolution benchtop instrument featuring NA = 0.65 objectives, paired with a high-power 520 nm laser source to combat transmission losses and sustain imaging frame rates across an expanded optical footprint. We map the multi-variable design space required to satisfy …