Physical Sciences and Mathematics Commons^™

Discovery Of Tidal Disruption Event Candidates In The Hubble Catalog Of Variables, Elliot M. Schweitzer

Pitzer Senior Theses

A tidal disruption event (TDE) occurs when a star passes within the tidal radius of the supermassive black hole (SMBH) likely to reside at the center of most galaxies. Within this radius, the star is torn apart as tidal forces overcome the star's binding energy, and roughly half of the stellar debris spirals back towards the SMBH. The formation of an accretion disk produces bright emissions for months to years, modeled to peak in the ultraviolet and extend well into x-ray and optical wavelengths. TDEs occur only about once every 10⁴-10⁵ years per galaxy. As one of …

Mathematics And Political Ideology: A Historical Argument Against The Cultural Understanding Of Mathematics As An Apolitical Field, And A Journalistic Report On The Impact Of The Trump Administration On American Mathematics In 2026, Philo Judson

Pitzer Senior Theses

The interplay between political ideology and mathematics is a recurring theme throughout the history of the academic field. Mathematics has been used as a tool of empire, while mathematicians have been elevated by states as symbols of national genius for political prestige. Political ideologies have also shaped the field from within, both through the suppression of mathematical thought and the enforcement of mathematical authority. Since 2025, the Trump administration has launched large-scale political attacks on American institutions of higher education, which include lawsuits, discrimination investigations, and the removal of federal funding from certain institutions that don’t adhere to the administration’s …

Modeling French Language Preservation: An Optimal Control Problem, Charlotte Blasi

Scripps Senior Theses

The French language is one of the most globally spoken languages, with over 300 million speakers and designated the official language of 29 nations. French continues to prosper as a result of its titular nations' imperialist history that emphasized linguistic diffusion as well as the support of international organizations dedicated to promoting both the language and the culture of French-speaking nations. In this thesis, we explore the nuanced history of French-speaking countries and one institution dedicated  to promoting the French language, the OIF. We further examine the media mechanism of the OIF and construct a system of Ordinary Differential Equations …

An Introduction To Modern Conversations On Knot Invariants, Stella Shah

Scripps Senior Theses

Knot Theory is a vast and diverse subfield of modern mathematics involving the classification and abstraction of knots and links. In this thesis, we wish to provide the necessary background for and an explanation of two papers in different subfields of knot theory, The Forbidden Quiver of a Link, and Biquandle Fares and Link Invariants.

In Chapter I, we begin with an introduction to knot theory and knot invariants. We continue to present the example of Fox Colorings, and conclude the chapter with an example of the Fox Coloring Number Invariant.

In Chapter II, we explore the derivation and utilization …

Algorithmic Trading In Idiosyncratic-Payoff Markets: A Multi-Agent System For On-Chain Prediction Contracts, Saif Aldeen A.K. Agha

CMC Senior Theses

This thesis documents the design, deployment, and forward-test evaluation of an evolutionary multi-agent algorithmic trading system on Polymarket, the largest decentralized prediction market. The system pairs a locally-hosted 72-billion-parameter language model with a gradient-boosted statistical filter and an evolutionary selection mechanism that maintains a population of approximately 500 autonomous trading agents. Each agent generates a probability estimate for an event, compares it to the prevailing market price, and trades the resulting disagreement.

The central empirical exercise estimates a panel regression of trade-level profit on the absolute disagreement between the agent's probability estimate and the market price, controlling for agent identity, …

Interpretable Sample Uncertainty Measures For Ranked-Choice Election Polls, Jason Liang

CMC Senior Theses

Polling results from traditional single-choice plurality elections are readily interpretable. Simple frequentist population parameters are estimated, including each candidate’s total support and the size of the front runner's lead. If the point estimate for the size of the front runner's lead exceeds the margin of error of the lead, we can conclude that the poll shows a statistically significant front runner. However, the interpretability of these population statistics disappears when applied to ranked-choice voting elections. Because ballots rank multiple candidates and candidates are eliminated in rounds, simple population-wide parameters are not well-defined. In RCV elections, a candidate’s ability to win …

News Media Sentiment Toward Chinese Ai: A Comparative Analysis With Belt And Road Initiative Involvement And Public Opinion On China, Asya Vaisberg

Pomona Senior Theses

This study evaluates different countries' news media’s sentiment towards Chinese AI, between May 2023 and May 2024, by using Microsoft Azure NLP Sentiment Analysis. The results are then compared with the country’s public opinion on China and its involvement in the Belt and Road Initiative (BRI). For this study 12 countries have been selected which are USA, Australia, Pakistan, Peru, Russia, Romania, Italy, Greece, Portugal, Philippines, Brazil, and Egypt. For each one, GNews Application Programming Interface (API), which has access to more than 60,000 global news sources, was used to aggregate relevant news articles based on queried keywords. The collected …

Bail Reform, Large Language Model Risk And Reasoning, William Wyatt

CGU Theses & Dissertations

This dissertation contains three studies. Each asks how rules or language change the choices people and machines make when outcomes are uncertain. The first study, written with Kiran John, evaluates California’s 2020 cashless bail reform. We use propensity score matching on arrestee records from the windows before and after implementation, and we test whether the shift away from cash bail produced any effect on subsequent offending. It did not. Matched comparisons yield small, statistically insignificant differences across every window we examined. That null result cuts against both sides of the public argument. The reform did not drive a spike in …

Volatility Modeling With An Application To Risk Parity Portfolios, Kenneth Hou

CMC Senior Theses

This thesis studies volatility modeling in the context of risk parity portfolio construction. I compare three risk parity portfolios that differ only in their underlying volatility model: a historical covariance baseline, a Bayesian stochastic volatility model, and a GRU–GARCH hybrid neural network. Using daily returns on Kenneth French’s five industry portfolios from January 2016 through December 2025, I construct monthly rebalanced portfolios under each model, with the SV and GRU forecasts embedded in hybrid covariance matrices that combine forecasted volatilities with rolling historical correlations. The results document a divergence between forecast accuracy and portfolio performance: the SV model is the …

Rank Rebalancing In Commodity And Foreign Exchange Markets, Prateek D. Vyas

CMC Senior Theses

This thesis empirically tests the rank-rebalancing mechanism of Stochastic Portfolio Theory (SPT) across commodity futures, foreign exchange futures, and equity ETFs. The Reverse Price-Weighted strategy (RPW) assigns, to each asset, the market weight of the asset at the opposite price rank, and generates an annualized excess return of 2.90% over the price-weighted (MKT) commodity benchmark, during the period of November 1977 to October 2025 (HAC t = 2.058, p = 0.040). The differential Sharpe ratio (dSharpe) of 0.245 is confirmed by a stationary block bootstrap, with a 𝑝-value of 0.015, and factor regressions controlling for carry, momentum, and value yield …

Microbial Community Structure In Global Soils, Matthew Jabro

CMC Senior Theses

Soil harbors the most diverse microbial communities on Earth, yet whether predictable community types exist across biomes and whether taxonomic composition encodes habitat of origin remain open questions at global scale. This thesis addresses both questions by applying unsupervised clustering and supervised classification to transformed 16S ribosomal RNA (rRNA) amplicon profiles from two independent datasets: the global topsoil survey of Bahram et al. (193 samples) and the Earth Microbiome Project (EMP) soil subset of Thompson et al. (2,209 samples). Application of a sample clustering method based on a mixture of Gaussian Graphical Models (MixGGM) identified 19 clusters in the topsoil …

Wiener-Granger Causality To Model Banking Sector Contagion, Riya Bhasin

CMC Senior Theses

In this thesis, we explore the main drivers behind the 2008 Global Financial Crisis and how the interconnectivity of banking sectors contributed to the worldwide spread of its effects. To understand how this became a global phenomenon, we apply linear Wiener-Granger Causality as a form of network analysis, building on pre-existing methodology in order to study continent banking indices. We find connections across locales on the continent and country level, but ones that are weak. Our modelling was insufficient to completely capture existing and well-known relationships accurately. This occurs due to limitations of the data and of the linear models’ …

Analysis Of Δ¹¹B As A Seawater Ph Proxy: Comparing Ocean Circulation Inverse Model Output With Marine Calcifier Geochemistry, Jesse I. Dong

CMC Senior Theses

Increasing anthropogenic carbon flux into the oceans decreases seawater pH, alters dissolved inorganic carbon speciation, and reduces biogenic calcification. The marine calcifiers— specifically corals and coralline algae—incorporate elements from surrounding seawater into their carbonate structures, which preserve past records of ocean carbon chemistry. In particular, boron in biogenic carbonate is a potentially valuable proxy for historical ocean pH across human timescales. Within seawater, boron primarily exists as boric acid B(OH)3 and borate ions B(OH)4 - , where higher pH favors the formation of borate ions. Borate ions preferentially incorporate the heavier ¹¹B isotope over 10B. On the other hand, if …

Doikayt And The Ethics Of Belonging: Lessons In Place-Making From The Jewish Labor Bund, Zoë L. Jacobs

Scripps Senior Theses

This thesis traces the evolution of doikayt—the Bundist principle of hereness—from its origins in the Jewish Labor Bund to contemporary applications in North America. Rooted in a refusal of both assimilation and nationalist escape, doikayt emphasizes cultivating safety, solidarity, and belonging through collective responsibility rather than territorial claims.

Building on this foundation, the exploration situates hereness within a settler-colonial context, where ethical dwelling is complicated by Indigenous dispossession. Drawing on Alexis Shotwell alongside Indigenous thinkers Vanessa Watts and Kyle Whyte, I examine how inhabiting place requires confronting historical injustices and ongoing relational responsibilities. Chapter 3 analyzes Linke Fligl (2016–2022) as …

Spectral Decimation On The Schreier Graphs Of The Basilica Group: A Thesis In Fractal Analysis, Anne D. Bannon

Scripps Senior Theses

This thesis is intended to provide a comprehensive overview of the literature required to fully understand research conducted during the University of Connecticut's Fractals & Stochastics REU in the summer of 2025. The literature review includes a description of Robert Strichartz's seminal work pertaining to the Laplacian spectrum of the Sierpiński Gasket, which provides a framework for how we approach studying the spectrum of the basilica Julia set. Defining the basilica Julia set and the closely-related Basilica group involves graph theory, automata theory, iterated monodromy group theory, and amenable group theory. Further time is dedicated to defining the graph Laplacian …

Real Interpolation: An Approximate Introduction, Madeline Anderson

Scripps Senior Theses

This thesis provides an introduction to real interpolation. We establish

relevant notions in functional analysis first, and use these concepts to study

real interpolation using J. Peetre’s 𝐾-functional in some detail. We also

explore the basics of approximation theory, in particular the connection

between approximation and interpolation results.

Representations Of Finite Groups And Diagrammatic Algebras, Hudson Yeend

CMC Senior Theses

Representation theory allows mathematicians to study abstract mathematical objects using the powerful and concrete tools of linear algebra. This thesis aims to present some foundational concepts in representation theory and apply these concepts to specific groups and algebras. We begin by examining representations of finite groups, culminating with a proof of Maschke's theorem. We then use the correspondence between a group and its group algebra to segue into a study of representations of diagrammatic algebras, where we introduce analogous notions of decomposition. We end with a study of quiver representations, noting that Gabriel's theorem and the kQ-modular structure transcend …

A Nonstandard Exploration Of Approximate Identity And Unitization, Tong (Nicole) Wu

HMC Senior Theses

The goal of this senior thesis is to explore general nonstandard analysis and some possible applications to 𝐶^*-algebras in functional analysis. More specifically, we shall define an approximate identity of a 𝐶^*-algebra using nonstandard analysis and study nonstandard hulls of internal 𝐶^*-algebra in the context of different unitizations. We shall also prove a few results for ideals in 𝐶^*-algebra using nonstandard definitions of approximate identities. We shall also briefly discuss the history and developments of nonstandard analysis.

Driving Into The Past: Road Logs And The History And Geology Of The Eastern Sierra Of California, Char Miller

Eastern Sierra History Journal

Road Logs are a pedagogical tool that geologists use on field trips with their students. Dee Trent's 1982 Road Log, which reproduced in this issue of ESHJ, also functions as a cultural artifact; it demonstrates what was known then, and how that scientific knowledge and the human geography of the region has changed over time.

Road Log For The Natural History Of The Owens Valley And Eastern Sierra Nevada, D. D. Trent

Eastern Sierra History Journal

D.D. Trent, who taught Geology at Citrus College in Southern California for many years, developed this 1982 Road Log for his students for use on field trips. It contains many scientific findings and historical insights about the region and he also contributed hand-drawn maps and illustrations to capture their attention. The Road Log is introduced by Char Miller's essay, "Driving into the Past" and then annotated and updated by Prof. Nicole Moore in an article that follows.

D.D. Trent 1982 Natural History Of Owens Valley/Eastern Sierra: Annotations And Updates, Nicole E. Moore

Eastern Sierra History Journal

Prof. Moore offers some annotations to and updates of D.D. Trent's 1982 Road Log. These revisions are part of the evolution of scientific knowledge and the adaptation of new technologies that enable a deeper understanding of the geology of the Owens Valley and Eastern Sierra. Like Trent, Moore has routinely taken her students up US 395 to explore and assess the region's geological formations.

An Exploratory Approach For Teaching Systems Of Linear Odes With Real Repeated Eigenvalues, Biyong Luo, Li Zhang

CODEE Journal

In this paper, we present a project that aims to pique students' interest and facilitate their engagement in learning. Students will be encouraged to take an active role in their learning of systems of linear ODEs with real repeated Eigenvalues. Through discussion and completion of a set of guided questions given in the project, students will gain a deeper understanding of the topic. Also, students will use the technology tool Bluffton App to draw solution trajectories in a phase plane, and then learn necessary skills for explaining the movements of the trajectories and their long term behaviors. This project may …

Expanding Ode Examples: Introducing Gene Regulation Dynamics Through Hill Functions, Maila Hallare, Jane M. Santamore

CODEE Journal

Gene regulation is a fundamental biological process that controls gene expression. It can explain phenomena such as cell differentiation, circadian rhythms, disease progression, and metabolic control, among many others. Despite their importance in mathematical biology, gene regulation models are rarely featured in traditional ODE textbooks, which focus mainly on examples from engineering, physics, chemistry, and population biology. This article introduces gene regulation dynamics as a valuable addition to ODE curricula, presenting the models from a mathematical perspective and building on properties of the Hill function. These models deepen the understanding of biology-inspired ODE applications, provide accessible research opportunities for students, …

An Ode-Based Analytical Approach To Rayleigh Flow Of Kelvin–Voigt Fluid, Kamille Garcia, Mahanthesh Basavarajappa

CODEE Journal

We present some results from a project carried out in the Under- graduate Research in Mathematics (MATH 4380) course at TAMIU. The main goal of this study is to demonstrate that analytical solutions for a system of partial differential equations (PDEs) can be obtained using methods typically taught in an undergraduate ordinary differential equations (ODE) course, such as power series, undetermined coefficients, and Laplace transforms. In this study, we provide semi-analytical solutions for Rayleigh flow type problem utilizing the Kelvin-Voigt fluid model, which describes the behavior of vis- coelastic materials by incorporating both elastic and viscous properties. Heat transfer analysis …

The 3d Double Spherical Pendulum: Modeling, Analysis, And Simulations, Alexander Gofen

CODEE Journal

This paper presents an inquiry-based research project that develops and analyzes the system of ordinary differential equations governing the motion of the 3D double pendulum, blending computational experiments with applied and theoretical mathematics. We formulate the Lagrangian for the three-dimensional double spherical pendulum and use Maple to derive the four coupled ordinary differential equations (ODEs) in angular variables; for completeness, we also present an equivalent Cartesian formulation. We then compare and visualize the models using the Taylor Center high-order Taylor-series solver, which delivers high-accuracy trajectories and real-time animations in 2D and anaglyph 3D (red/blue). We place the system in context …

Analytical And Numerical Approaches To Parameter Estimation In Damped Oscillatory Systems, Gracie Crooks, F. Ayça Çetinkaya

CODEE Journal

We investigate the inverse problem of identifying damping and stiffness parameters in one-dimensional damped oscillatory systems governed by second-order differential equations. Focusing on mass–spring–damper models, we analyze the qualitative behavior of solutions across underdamped, critically damped, and overdamped regimes, and derive explicit conditions for parameter recovery based on time-domain observations such as equilibrium crossings and turnaround points. Two numerical estimation methods are developed and compared: a finite-difference least-squares approach based on central difference approximations, and a finite element formulation derived from a variational framework using piecewise linear basis functions. Computational experiments using synthetic data assess the accuracy, stability, and noise …

Project-Based Learning With Odes: Modeling Straw Rocket Motion With Air Resistance, Viktoria Savatorova, Ethan Dyer, Aleksei Talonov

CODEE Journal

This paper presents a hands-on project that guides students through building and validating a mathematical model of projectile motion. The project starts with the idealized case of motion under gravity without air resistance and then introduces air drag : first as a linear force, and then as a nonlinear quadratic force, with the Reynolds number providing the justification for the quadratic model. Students perform experiments with vertical and angled launches, capturing and analyzing motion data using video analysis software. Vertical launch data allows parameter estimation via least squares fitting of the nonlinear drag model, yielding values for initial velocity and …

Sulfur Fluoride Exchange With Carbon Pronucleophiles, Joseph R. Novicki, Matthew D. Teeter, Neil J. Baldwin, Christopher W. Am Ende, Alistair D. Richardson, Thomas R. Puleo, Nicholas Ball

Pomona Faculty Publications and Research

Aryl alkyl sulfones are an important class of compounds in drug discovery; thus, new methods toward their synthesis are desirable. A general sulfur fluoride exchange (SuFEx) method to couple aryl sulfonyl fluorides with alkyl carbon pronucleophiles to make aryl alkyl sulfones is described. The reaction was applied to a diverse set of pronucleophiles, including esters, amides, heteroarenes, nitriles, sulfones, sulfoxides, and sulfonamides, at room temperature under mild conditions. We highlight the application of this transformation in parallel medicinal chemistry for the high-throughput generation of a broad array of aryl alkyl sulfones. Lastly, we apply this method to the late-state SuFEx …

Interlace: A Journal Of Mathematics And Fiber Arts, Carolyn Yackel, Sarah-Marie Belcastro

Journal of Humanistic Mathematics

Interlace: A journal of mathematics and fiber arts is a peer-reviewed, open-access completely free journal devoted to publishing high-quality original research at the intersection of mathematics and fiber arts. The journal is now accepting submissions.

Sudoku Grids, David Sheskin

Journal of Humanistic Mathematics

Ten images depicting numerical grids of the mathematical logic puzzle Sudoku are presented. The digit values in each puzzle are represented on either domino tiles, postage stamps, mah-jong tiles, or playing cards.