Physical Sciences and Mathematics Commons^™

Empirical Analysis Of Political Districting Splitability Via Uniform Spanning Trees In Polynomial Time, Brooke C. Feinberg

Scripps Senior Theses

This work expands a recently proven conjecture that a polynomial fraction of all uniform spanning trees (USTs) are splittable into k balanced partitions on grid graphs to real-world political districting plans. We investigate whether similar structural properties hold for the planar dual graphs of U.S. counties (cnty) and tracts (t), using Wilson’s algorithm to generate uniform random spanning trees and Breadth- First Search (BFS) to check for splitability into balanced partitions. Our empirical findings suggest that real-world districting plans can be split into 2-balanced, connected partitions in a fraction of polynomial time. This result highlights the potential for scalable redistricting …

Analyzing Political Sentiment On Micro-Blogging Data: A Lexicon And Machine Learning Approach To The 2024 U.S. Presidential Election, Ava Grey

CMC Senior Theses

This paper explores the trends in sentiment towards U.S. presidential candidates Kamala Harris and Donald Trump through micro-blogging social media text during the five months leading up to the election. Two datasets of varying sizes and origins were used to contextualize and validate analysis findings. The analyses include both a lexicon-based approach and a machine learning predictive method. Common sentiment analysis techniques like term frequency, term frequency inverse, various lexicons, and n-grams were utilized during the lexicon approach. During the modeling, a random forest was utilized in addition to the methods used during the lexicon approach. Results showed that overall …

Neural Correlates Of Attentional Biases In Dietary Choice: Role Of Childhood Socioeconomic Status, Justine Jamie N. Gotico

CMC Senior Theses

Childhood poverty has been shown to increase adult risk for obesity above and beyond its direct effects on adult socioeconomic status (SES). One proposed mechanism of these effects is by shifting behavioral patterns of dietary consumption and choice, for example by increasing rapid attention to high-calorie unhealthy foods. Yet, whether such neural mechanisms can explain observed differences in dietary behavior based on childhood SES remains an open question. Here we used event-related potentials (ERPs) to examine early attentional correlates of low childhood SES during a dietary choice task, based on research suggesting that early attentional biases toward high-calorie foods emerge …

Valuating The Impact Of Unexploded Ordnance (Uxo) In Savannakhet, Laos Through Ecosystem Services Assessments, Nathan Lu

Pitzer Senior Theses

Unexploded ordnance (UXO) impact on countries is not well-documented, since post-war surveys or data collection are often hindered by a lack of appropriate funding and reparation. In Laos, UXO has hardly been cleared since 1964 and thus leaves room for spatially and temporally analyzing the severity of environmental and economic degradation in the area. This study uses the framework of ecosystem services, particularly carbon stock, as a way to provide quantitative metrics of impact to local governments and stakeholders. Through remote sensing data in Savannakhet Province, evidence-based land-use change data was spatially analyzed with geocoded UXO bomb mission locations and …

Untangling The Classification Of Surfaces: An Accessibility-Centered Perspective On Topology, Charlotte N. Richards

Pitzer Senior Theses

Mathematics has clear benefits in education, from preparing students for future careers to teaching them how to problem-solve. While mathematics achievement has been falling in recent decades, students claim that the problem is not the mathematics itself, but the ‘boring’ classroom material that feels removed from real life. More advanced mathematics topics, such as topology, could offer a solution, as their applications lie in countless fields. However, topology has been restricted to upper-level mathematics, disregarding the potential benefits of making this material broadly reachable for a junior high-school audience. In this paper, we analyze five different proofs of the theorem …

The Requirements Of A Nuclear Propulsion System For The Human Exploration Of Mars, Scotia Rollins

Pitzer Senior Theses

This thesis investigates the propulsion requirements for a crewed mission to Mars, focusing on how mission architecture, particularly the choice between opposition- and conjunction-class trajectories, influences the selection between nuclear thermal propulsion (NTP) and nuclear electric propulsion (NEP). By applying the Tsiolkovsky rocket equation, the Delta-V (∆V) needed for efficient interplanetary transfers is shown to exceed the performance limits of chemical propulsion, motivating the need for nuclear alternatives. An engineering comparison of NTP and NEP systems evaluates key parameters including specific impulse, thrust, propellant mass fraction, system mass, and power-to-mass ratios. NTP provides high thrust but moderate efficiency, making it …

Forecasting Equity Betas Using Option-Implied Moments, Ivan Kolesnikov

CMC Senior Theses

Traditional beta estimates are constructed from historical stock‑and‑market returns and therefore adjust only as fast as realized data accrue. This thesis investigates whether the forward‑looking information embedded in equity‑option prices can enhance beta forecasts. Using near‑end‑of‑day quotes for 236 S&P 500 firms between 2007 and 2024, I extract risk‑neutral variance and skewness, construct five alternative beta estimators (historical, option‑implied, and three hybrids), and evaluate them against realized betas over six‑, twelve‑, and twenty‑four‑month windows. Rolling‑OLS beta remains the most accurate benchmark at short horizons, yet option‑implied moments add economically and statistically significant value when systematic exposure is expected to change …

The Coral Porites Lutea As A Regional And Local Proxy For Sea Surface Temperature In Hong Kong, And The Effects Of Typhoons On Proxy Accuracy, Brenna E. Bell

CMC Senior Theses

Proxies related to the climate have been used as a method to observe long-term changes occurring underwater that span long before we had the capability to measure environmental characteristics. Porites corals have been used as sea surface temperature (SST) proxies due to annual cyclicity in their growth process and mineral composition. As the climate differs globally, it is important to ensure that proxies are accurate regardless of location to measure changes in climate. This study examines Porites lutea corals as an SST proxy in the region of Hong Kong. Potential local differences in SST proxy calibrations within the surrounding waters …

Integrating Sentiment Analysis In Predictive Models: A Comparative Study On Game Popularity On Steam, Khaleefa Alhemeiri

CMC Senior Theses

Over the past decades, the gaming industry has managed to evolve into a multi-billion-dollar enterprise. Gaming platforms such as Steam foster unprecedented amounts of engagement among players worldwide daily. In this thesis, we investigate the effect of incorporating sentiment-driven metrics, specifically YouTube view counts and positive reviews, into predictive models for game popularity. In addition, by comparing our linear regression sentiment-based approach to the Bayesian hierarchical folded normal model used by De Luisa et al. (2021), we can understand the many differences, strengths, and limitations of each methodology. In our thesis, we focus on three games. Each is of varying …

Measuring The Similarity Between Trees Of Different Order, Camilo Morales

HMC Senior Theses

Graphs encode relationships between data. However, due to their versatility, it is often difficult to generalize the notion of similarity between two graphs using a distance function. Since graphs can represent various data sets, specific distance metrics need to be tailored for questions we are interested in answering or the data set we are working with. This project is motivated by ongoing investigations into the evolution of female gender representation in mathematics. By building off previous work that has taken data from the Mathematics Genealogy Project and modeled this evolution of representation via a tree, we would like to develop …

World As Other, World As Self: Beyond Dualism In Environmental Narratives, Tamara Wallace Ramirez

CGU Theses & Dissertations

Stories of place matter to the way we live with the Earth. A dualistic perspective that pits "culture" against "nature" enables environmental degradation on small and large scales. Conversely, understanding humans and nonhumans as entwined allows us to think and act differently with our planetary community. This view entails integrating the "self" and the "other." Instead of being antithetical to the other, the self arises through engagement with others, human and nonhuman. Understanding our mutuality with others while respecting their alterity and agency fosters caring and dedication. Our sense of connection with the more-than-human world inspires our compassion. However, such …

Enhancement Of Mechanical, Structural, And Electrical Properties In Advanced Composites And Vat Photopolymerized 3d Printing Nanocomposites, Poom Narongdej

CGU Theses & Dissertations

Advanced composites have gained significant attention across various industries, including aerospace, automotive, clean energy, and healthcare, owing to their exceptional mechanical properties and versatility. Fiber-reinforced polymer (FRP) composites, particularly those reinforced with carbon fibers, are extensively used as structural materials in spacecraft, aircraft, high-performance vehicles, and wind turbines due to their high strength-to-weight ratios, stiffness, durability, and tailorable mechanical characteristics. In healthcare, the advent of additive manufacturing (3D printing) has expanded the utility of advanced composites, enabling precise customization of components to meet patient-specific needs while offering design flexibility and ease of fabrication. Despite these advantages, several challenges hinder the …

Mathematics And Determinism: Chaos, Quantum Mechanics, And The Limits Of Predictive Structure, Jackson T. Salumbides

CMC Senior Theses

This thesis examines the relationship between mathematics and determinism by analyzing how chaos theory, quantum mechanics, and formal mathematical limits challenge traditional conceptions of predictability and causal structure. Chaos theory shows that deterministic systems can exhibit practical unpredictability due to sensitivity to initial conditions. Quantum mechanics introduces probabilistic outcomes that complicate deterministic interpretation, though alternative frameworks such as Bohmian mechanics and superdeterminism attempt to restore determinism at conceptual cost. Additionally, results from mathematical logic, including Gödel’s incompleteness theorems and Turing’s undecidability, demonstrate intrinsic limitations on what can be deduced or computed, even in fully deterministic systems. By synthesizing these areas, …

Demystifying Misconceptions In Introductory Undergraduate Chemistry Education With 3d Printed Molecular Orbitals, Hiwot Endeshaw, Daniel J. O'Leary

Pomona Senior Theses

Spatial abilities are invaluable skills for the science, technology, engineering, and mathematics (STEM) subjects. However, women, people from low socioeconomic backgrounds, and ethnic minorities are more likely to have less developed spatial abilities, which is one of the many contributing factors for the lack of diversity in STEM subjects like chemistry. Teaching spatial skills to undergraduate chemistry students may address this issue and help increase the diversity of students who go on to continue their education in the subject. 3D printing technology in higher education has exploded in recent years, presenting a unique opportunity to teach “hard to grasp” concepts …

Modified N-Heterocyclic Carbene Catalysts For Polyurethane Synthesis, Charise D. Young

Pomona Senior Theses

Polyurethanes are widely used polymers synthesized from diisocyanate and diol molecules. They are ubiquitous polymeric materials with important industrial applications. Their increasing market value prompts the need for selective and efficient production which can be achieved through N-Heterocyclic carbene (NHC) catalysis. N-heterocyclic carbenes are heterocyclic molecules containing a carbene atom and at least one nitrogen adjacent to the carbene center. The nitrogen substituents on the adjacent nitrogen play an important role in influencing their steric and electronic properties and resultant reactivity.^1,2 There is a lack of a comprehensive understanding of the steric and electronic properties of NHCs and how …

Optimizing And Scaling Up Tcfh–Nmi Pyrrole Acylation For Organic Syntheses, Grant H. Miller

Pomona Senior Theses

Traditional ketone synthesis often depends on toxic reagents and hazardous solvents, which limits its scalability and environmental compatibility. The TCFH–NMI method has shown strong potential for amide, ester, and thioester formation, but its use in ketone synthesis has only been recently described, and only on small scales. This thesis addresses that gap by optimizing a scalable synthesis of 2-(monomethyl succinyl)-3,5-dimethylpyrrole using monomethyl succinate and 2,4-dimethylpyrrole as model substrates. Key reaction parameters were systematically refined to improve yield, reproducibility, and sustainability. The final protocol avoids chromatography, operates at room temperature, and consistently delivers high yields. These features position it as a …

Huchum: The Legacy Of Fire Suppression, Indigenous Land Management, And Media Representation, Carolyn Coyne

Pomona Senior Theses

In my thesis, I examine how various forms of news media from the 1900s to present day in Ohlone territory have framed a particular hegemonic ideology around fire that matches early colonial journal entries – an ideology that is fueled by fear, sensationalism, and exclusion and directly commits violence against the Ohlone people. I investigate this time period because this is when modern news corporations, like The New York Times, rose into prominence. Specifically, I question how media representations of fire inform regulations over controlled burns; what are the similarities in discourse between media framing and policy? What tactics are …

Swimming In Sh*T: Quantifying Lagoon Flushing Impacts On Fecal Indicator Bacteria In Surf Zones Of Three Beaches On The East End Of Long Island, Ny, Brody C. Eggert

Pomona Senior Theses

This thesis investigates how lagoon flushing influences fecal indicator bacteria (FIB) concentrations—specifically enterococcus bacteria—in the surf zones of East Hampton and Southampton, New York. Focusing on the coastal lagoons of Georgica Pond, Sagg Pond, and Mecox Bay, the study analyzes how episodic inlet openings and environmental conditions affect enterococcus levels at adjacent recreational beaches. Using over 700 observations from the Surfrider Foundation’s Blue Water Task Force (BWTF) database, I construct a series of statistical models ranging from ordinary least squares to mixed effects frameworks; this thesis shows my process in developing this model. My analysis reveals that open inlets between …

Rwanda's Natural Remedies: A Fresh Look At The Fight Against Malaria, Leandre Nsabimana Ndisanze

Pomona Senior Theses

Malaria remains one of the most devastating parasitic diseases globally, disproportionately affecting sub-Saharan Africa, where Rwanda continues to face high transmission rates and rising resistance to conventional interventions. Despite decades of control efforts, the emergence of drug-resistant Plasmodium falciparum and insecticide-resistant Anopheles mosquitoes threatens to reverse recent gains. This research responds to the urgent need for sustainable and culturally relevant alternatives by exploring the therapeutic potential of Rwandan traditional medicinal plants. These indigenous remedies, long used by local healers, offer an underexplored reservoir of bioactive compounds that may provide the basis for novel antimalarial drugs.

The central hypothesis of this …

A Vascular Flora Of The Sacatar Trail Wilderness, Sierra Nevada, California, Kimberly Schaefer Pivetti

CGU Theses & Dissertations

The Sacatar Trail Wilderness in Inyo and Tulare counties, California, encompasses a bioregional transition zone in the southeastern Sierra Nevada. The ca. 233 km 2 (90 mi 2 ) study area, located 32 km (20 mi) northwest of the city of Ridgecrest, ranges from 930 to 2698 m (3051–8851 ft) in elevation. The highly diverse California Floristic Province, Great Basin, and Mojave Desert converge in the region including the Wilderness creating conditions to support a broad spectrum of vegetation assemblages. The Bureau of Land Management has prohibited vehicular activity in this area since its wilderness designation in 1994; consequently, recent …

Mathematical Modeling Of Cancer Tumor Evolution, Belgacem Al-Azem

CGU Theses & Dissertations

Several mathematical models of cancer tumor evolution are presented. The aim of this endeavor is to write a thesis that fosters numerical and analytical understanding of certain mathematical models in the area of oncology as well as to offer potential predictive tools of therapeutic and clinical applicability. In this work, we give a panoramic view of the cancer phenotype, for to understand cancer, we need to "see" its biophysics. Indeed, the discovery of oncogenes led to the thinking that cancer tumor is perhaps a genetic disease. But the role of angiogenesis and other microenvironment-related discoveries (such as the role of …

Geometric Dimensionality Reduction, Daniel Livschitz

CGU Theses & Dissertations

The emergence of AI models developed through computationally intensive training has resulted in a surge of research into dimensionality reduction techniques that spans across numerous mathematical disciplines. In this thesis we establish Geometric Dimensionality Reduction, a non-linear data compression technique that utilizes low dimensional manifolds embedded in dimensional spaces to form composite contraction-and-projection maps. Geometric Dimensionality Reduction is predominantly demonstrated through a novel algorithm entitled LGE (Livschitz-Gu-Eyunni) that utilizes Multicomplex rotation groups and polyspherical coordinates to define a single tuneable logarithmic map from ℝ 2푛 to ℝ 푛+1 with deterministic time complexity, geometric tunability, and semi-reversibility. Significant breakthroughs in the …

El Maíz Del Abuelo: Fidel Márquez Sanchez’S Legacy And Mexico’S Historical Maize Agriculture, Lucia Marquez-Uppman

Scripps Senior Theses

The Green Revolution was an era of scientific development in productive agricultural methods and technologies in the mid-twentieth century. High-yielding seed varieties, artificial fertilizers, irrigation infrastructure, pesticides, and herbicides all developed from this period. Texcoco, Mexico was the center of much of the Green Revolution's education and research from the 1940s onward at the Autonomous University of Chapingo, a prestigious agricultural school, with funding from the US-based philanthropic Rockefeller Foundation. Powerful consequences in the globe's agriculture emerged from the Green Revolution, including the production of maize, a staple crop in Mexico, especially for Indigenous and campesino populations. My abuelo, Fidel …

Weathering And Beyond: Leveraging Mathematical Modeling To Simulate Erosion In Digital Media, Fiona Irving-Beck

Scripps Senior Theses

How might we bring an idea to life from both a mathematical and an artistic perspective? Within Weathering, I use imagery of environmental erosion to explore the differences between physical and digital forms of representation. I created a physical painting of an abandoned copper mine, digitized the work, and then used a mathematical model to digitally “erode” it, which I re-translated into paintings. While the explicit texture present in physical work speaks best to my practice/intent, the mathematical framework that is the basis for my digital work affords a powerful mode of temporal flexibility. Used in conjunction, these two …

“Regression To The Mean”: The Confluence Of Eugenics And Statistics In The 19th And 20th Centuries, Emrys G. King

Pomona Senior Theses

The work of this thesis is twofold — first, qualitatively characterizing the confluence between the British eugenics and statistics movements in the late 19th and early 20th centuries, and second, quantitatively analyzing the effect of this foundation on pedagogical materials in the growing field of statistics between 1880 and 1970. Towards the first goal, the history of the method of least squares, state statistics, and positive and negative eugenics are outlined, followed by a close reading of the foundational texts authored by Francis Galton and Karl Pearson that introduced linear regression. Towards the latter goal, English-language statistics textbooks published between …

Biomechanics Of The Atherosclerotic Lipidome: (Un)Expected Statin Interactions And Membrane Remodelling, Ethan M. Fong

Pomona Senior Theses

Statins interact with lipid membranes in ways that shape their pharmacokinetics, off-target effects, and pleiotropic actions, yet these interactions' mechanical and biophysical consequences remain poorly understood. This thesis employs a combination of surface plasmon resonance (SPR), quartz crystal microbalance with dissipation monitoring (QCM-D), and rheological modelling to characterize how representative statins intercalate within biomimetic supported lipid bilayers (SLBs) of healthy and diseased composition. SPR reveals that lipophilic statins exhibit higher apparent affinities and slower dissociation kinetics, especially in cholesterol- and anionic lipid-rich membranes. QCM-D analyses demonstrate that statins alter membrane mass, dissipation, and interfacial stiffness in a statin- and membrane-dependent …

Cmc Thesis Chatbot, Luis Gomez

CMC Senior Theses

This GitHub repo is a senior thesis for Claremont McKenna College; it is a thesis about theses. The project is an interactive RAG-based chatbot that helps students, researchers, and faculty explore Claremont McKenna College senior theses. The goal was to create a domain-specific chatbot to show that it is possible to combat the limitations of AI, including hallucinations, outdated data, and lack of domain expertise. The website link is:

CMCThesisChatbot

Mathematical Modeling, Analysis, And Simulation Of Patient Addiction Journey, Adan Baca, Diego Gonzalez, Alonso G. Ogueda, Holly C. Matto, Padmanabhan Seshaiyer

CODEE Journal

This paper aims to develop a mathematical model to study the dynamics of addiction as individuals go through their detox journey. The motivation for this work is three fold. First, there has been a significant increase in drug overdose and drug addiction following the COVID-19 pandemic, and addiction may be interpreted as a infectious disease. Secondly, the dynamics of infectious disease could be modeled via compartmental models described by differential equations and one can therefore leverage the existing analytical and numerical methods to model addiction as a disease. Finally, the work helps to inform how mathematical models governed by differential …

First Diffusion Course: "The Structure Of Language As A Connection Between Artificial Intelligence, Information And Ethics", Dioneia Monte-Serrat

Journal of Humanistic Mathematics

From August 22nd to November 21st, the first Diffusion Course on “The structure of language as a connection between artificial intelligence, information and ethics” will take place on a Thursday of each month, in Ribeirao Preto, Brazil. You are cordially invited to sign up for in-person classes and join other researchers and students on this course.

7th International Conference On Creative Mathematical Sciences Communication (Cmsc`24), Frances A. Rosamond

Journal of Humanistic Mathematics

The 7th International Creative Mathematical Sciences Communication (CMSC) conference is scheduled for October 2024 in Trier, Germany. Initiated in Darwin, Australia in 2013, CMSC aims to explore novel methods of imparting computational thinking to diverse audiences including non-specialists, modern citizens, and children. Participants from around the world and from various and interdisciplinary disciplines such as science, education, dance, drama, and visual arts convene to exchange ideas, present experimental approaches, and collaborate on engaging children in the exploration of ongoing, unresolved research challenges.