Physical Sciences and Mathematics Commons^™

The Sensitivity Of A Laplacian Family Of Ranking Methods, Claire S. Chang

HMC Senior Theses

Ranking from pairwise comparisons is a particularly rich subset of ranking problems. In this work, we focus on a family of ranking methods for pairwise comparisons which encompasses the well-known Massey, Colley, and Markov methods. We will accomplish two objectives to deepen our understanding of this family. First, we will consider its network diffusion interpretation. Second, we will analyze its sensitivity by studying the "maximal upset" where the direction of an arc between the highest and lowest ranked alternatives is flipped. Through these analyses, we will build intuition to answer the question "What are the characteristics of robust ranking methods?" …

Multilayer Network Model Of Gender Bias And Homophily In Hierarchical Structures, Emerson Mcmullen

HMC Senior Theses

Although women have made progress in entering positions in academia and
industry, they are still underrepresented at the highest levels of leadership.
Two factors that may contribute to this leaky pipeline are gender bias,
the tendency to treat individuals differently based on the person’s gender
identity, and homophily, the tendency of people to want to be around those
who are similar to themselves. Here, we present a multilayer network model
of gender representation in professional hierarchies that incorporates these
two factors. This model builds on previous work by Clifton et al. (2019), but
the multilayer network framework allows us to …

Modeling Self-Diffusiophoretic Janus Particles In Fluid, Kausik Das

HMC Senior Theses

We explore spherical Janus particles in which a chemical reaction occurs on one face, depleting a substrate in the suspending fluid, while no reaction occurs on the other face. The steady state concentration field is governed by Laplace’s equation with mixed boundary conditions. We use the collocation method to obtain numerical solutions to the equation in spherical coordinates. The asymmetry of the reaction gives rise to a slip velocity that causes the particle to move spontaneously in the fluid through a process known as self-diffusiophoresis. Using the Lorentz reciprocal theorem, we obtain the swimming velocity of the particle. We extend …

Explorations In Well-Rounded Lattices, Tanis Nielsen

HMC Senior Theses

Lattices are discrete subgroups of Euclidean spaces. Analogously to vector spaces, they can be described as spans of collections of linearly independent vectors, but with integer (instead of real) coefficients. Lattices have many fascinating geometric properties and numerous applications, and lattice theory is a rich and active field of theoretical work. In this thesis, we present an introduction to the theory of Euclidean lattices, along with an overview of some major unsolved problems, such as sphere packing. We then describe several more specialized topics, including prior work on well-rounded ideal lattices and some preliminary results on the study of planar …

Discrete Analogues Of The Poincaré-Hopf Theorem, Kate Perkins

HMC Senior Theses

My thesis unpacks the relationship between two discrete formulations of the Poincaré-Hopf index theorem. Chapter 1 introduces necessary definitions. Chapter 2 describes the discrete analogs and their differences. Chapter 3 contains a proof that one analog implies the other and chapter 4 contains a proof that the Poincaré-Hopf theorem implies the discrete analogs. Finally, chapter 5 presents still open questions and further research directions.

Long Increasing Subsequences, Hannah Friedman

HMC Senior Theses

In my thesis, I investigate long increasing subsequences of permutations from two angles. Motivated by studying interpretations of the longest increasing subsequence statistic across different representations of permutations, we investigate the relationship between reduced words for permutations and their RSK tableaux in Chapter 3. In Chapter 4, we use permutations with long increasing subsequences to construct a basis for the space of ��-local functions.

Permutations, Representations, And Partition Algebras: A Random Walk Through Algebraic Statistics, Ian Shors

HMC Senior Theses

My thesis examines a class of functions on the symmetric group called permutation statistics using tools from representation theory. In 2014, Axel Hultman gave formulas for computing expected values of permutation statistics sampled via random walks. I present analogous formulas for computing variances of these statistics involving Kronecker coefficients – certain numbers that arise in the representation theory of the symmetric group. I also explore deep connections between the study of moments of permutation statistics and the representation theory of the partition algebras, a family of algebras introduced by Paul Martin in 1991. By harnessing these partition algebras, I derive …

Graph Learning On Multi-Modality Medical Data To Generate Clinical Predictions, Justin Jiang

HMC Senior Theses

There exist petabytes of data pertaining to medical visits – everything from blood pressure recordings, X-rays, and doctor’s notes. Electronic health records (EHRs) organize this data into databases, providing an exciting opportunity for machine learning researchers to dive deeper into analyzing human health. There already exist machine learning models that aim to expedite the process of hospital visits; for example, summary models can digest a patient’s medical history and highlight certain parts of their past that merit attention. The current frontier of medical machine learning is combining the various formats of data to generate a clinical prediction – much like …

A Visual Tour Of Dynamical Systems On Color Space, Jonathan Maltsman

HMC Senior Theses

We can think of a pixel as a particle in three dimensional space, where its x, y and z coordinates correspond to its level of red, green, and blue, respectively. Just as a particle’s motion is guided by physical rules like gravity, we can construct rules to guide a pixel’s motion through color space. We can develop striking visuals by applying these rules, called dynamical systems, onto images using animation engines. This project explores a number of these systems while exposing the underlying algebraic structure of color space. We also build and demonstrate a Visual DJ circuit board for …

Stem Education And Retention For Black Women Using High-Impact Practices: Historically Black Colleges And Universities Vs. Predominantly White Liberal Arts Colleges, Annette Njei

CMC Senior Theses

Black women are significantly underrepresented within the fields of science, technology, engineering, and mathematics (STEM). To address this, the Association of American Colleges & Universities crafted ten high-impact practices to increase student engagement and promote retention. This research paper examines how three specific high-impact practices (learning communities, mentoring, and undergraduate research experience) are utilized in STEM education.This research paper explores and compares the best high impact approaches that successfully teach and retain Black women within the various fields of STEM within the differing academic environments of historically Black colleges & universities ( HBCUs) and predominantly white liberal art colleges (PWLACs). …

Maximizing Productivity And Quality In Senior Thesis Writing With Artificial Intelligence And Natural Language Processing Driven Tools, Lauren Leadbetter

CMC Senior Theses

This project is a Python program designed to generate a senior thesis on a user-
inputted topic using natural language processing techniques. The program takes in a
topic from the user and then uses OpenAI API to deploy text models for text genera-
tion and evaluation, such as GPT-3 and Davinci-003. The resulting output is in .tex
format and includes a first-draft outline and paper, followed by self-generated assessment, with scoring, revisions, and feedback comments instructing manual revisions.

This submission is a sample using one available model of the project, meant to
demonstrate it’s functionality and limitations. Further model versions …

Pakistan's Contribution To The Global Rise In Conventional Pollution, Emily Warner

CMC Senior Theses

This thesis examines the impact of conventional pollutants on the environment, communities, and individuals in Pakistan. It begins by investigating the causes of conventional pollutants and exploring Pakistan’s agricultural industry, domestic practices, non-renewable energy sources, and industrial practices (the brick industry, leather tanning industry, and textile industry). It then analyzes factors that continue to contribute to conventional pollution in Pakistan such as economic incentives, politics, and traditional practices within industries. Exploring the measures that have been taken by Pakistan and other organizations to decrease conventional pollutants, it then suggests potential opportunities for improvement.

Can The Xy+Z Heisenberg Model Be Compressed Using The Yang-Baxter Equation? An Exploration Of The Compression Of Quantum Time Dynamic Circuits Describing Heisenberg Spin Chains, Miriam Caron, Bo Peng Dr., Scott Gould Dr., Kevin Setter Dr., Niranjan Govind Dr.

Pitzer Senior Theses

Quantum computing is currently deployed on noisy intermediate-scale quantum (NISQ) devices, which are only able to simulate circuits reliably on shallow depth quantum circuits. A promising problem on near-term quantum computers is quantum time dynamics (QTD). However, QTD circuits grow with increasing time simulations making them difficult to simulate on NISQ devices. This thesis project explores QTD simulations in variations of 1D Heisenberg spin chains with nearest-neighbor and transverse external field interactions with an eye towards studying the dynamics in broader classes of spin models. I first study the quantum Yang-Baxter equation (YBE) and how it has been shown to …

The Green Revolution In California: The Real Costs And Benefits Of Changing Electricity Production, Joseph James Hoffman

CGU Theses & Dissertations

In recent years democratic societies have added concern for the environment to the perennial problems of inequality, economic growth, and law and order. What is often called the Green Revolution has focused on the effect of industrial growth on the health of the individuals living in that society and on the effects on climate. In the United States, the State that was the first to see this problem and the first to make changes to deal with it, was California, where geographical factors ensured that the effects of industrial change on the air were much more severe than anywhere else …

Lattice Extensions And Zeros Of Multilinear Polynomials, Maxwell Forst

CGU Theses & Dissertations

We treat several problems related to the existence of lattice extensions preserving certain geometric properties and small-height zeros of various multilinear polynomials. An extension of a Euclidean lattice $L_1$ is a lattice $L_2$ of higher rank containing $L_1$ so that the intersection of $L_2$ with the subspace spanned by $L_1$ is equal to $L_1$. Our first result provides a counting estimate on the number of ways a primitive collection of vectors in a lattice can be extended to a basis for this lattice. Next, we discuss the existence of lattice extensions with controlled determinant, successive minima and covering radius. In …

On Symmetric Operator Ideals And S-Numbers, Daniel Akech Thiong

CGU Theses & Dissertations

Motivated by the well-known theorem of Schauder, we study the relationship between various s-numbers of an operator T and its adjoint T∗ between Banach spaces. For non-compact operator T ∈ L(X, Y ), we do not have a lot of information about the relationship between n-th s-number, sn(T), with sn(T∗ ), however, in chapter 2, by considering X and Y , with lifting and extension properties, respectively, we were able to obtain a relationship between sn(T) with sn(T∗ ) for certain …

A New Credit Scoring Model To Reduce Potential Predatory Lending: A Design Science Approach, Anna Zakowska

CGU Theses & Dissertations

This research examines the potential impact of implementing a novel credit scoring model that integrates attributes beyond the traditional FICO model. It aims to address issues related to predatory lending and the financial exclusion affecting individuals often categorized as 'credit invisible,' 'credit unscorable,' 'unbanked,' and 'underbanked.' These individuals typically face difficulties in establishing or repairing a credit history, which poses a challenge for financial institutions in accurately evaluating their creditworthiness. This gap in the credit assessment process often opens doors to unfair lending practices. To tackle this problem, a systematically designed, built, tested, and evaluated innovative credit scoring model was …

Graph-Based Acoustic Clustering And Classification, Justin Youngho Sunu

CGU Theses & Dissertations

The rapid growth of audio data collection in various domains necessitates advanced techniquesfor efficient analysis and classification. This dissertation proposes new approaches for categorizing acoustic data, using both unsupervised and semi-supervised learning methods. Starting with raw audio, we preprocess the signal to segment it into time windows, each of which we consider as an independent data point. We use the short-time Fourier transform to describe the signal in a given time window as a set of Fourier coefficients. We interpret the resulting frequency signature as a high-dimensional feature description of each data point. We then develop a graph-based approach for …

The Effect Of Age, Syntax Complexity, And Cognitive Ability On The Rate Of Semantic Illusions, Sara Anne Goring

CGU Theses & Dissertations

Semantic illusions are recognition errors that occur when an individual fails to notice that information contradicts their prior knowledge (Barton & Sanford, 1993; Erickson & Mattson, 1981). For example, after hearing the question, “If a plane crashes while flying over state lines, where should the survivors be buried?” many start to consider the legality or appropriateness of the scenario despite knowing “survivors” should not be buried. Having more knowledge does not necessarily prevent individuals from overlooking illusory information/misinformation. Older adults tend to have greater crystallized intelligence than young adults, yet these age groups appear to detect illusory information at equivalent …

Warehouses In The Inland Empire: Displacing Land And Life, Katherine Gelsey

Pomona Senior Theses

The Inland Empire in Southern California embodies unique spatial and social configurations as a consequence of how settler colonialism has manifested locally in the region since the Spanish Mission Period. This work uses GIS software to estimate patterns of land conversion for residential, agricultural, and warehouse land from 2012 to 2022. Preliminary analysis suggests that thousands of people have been displaced by warehouse expansion over the ten-year period. In the twenty-first century, the Southern California logistics industry continues processes of land dispossession and racialized labor exploitation through displacing agricultural and residential land, exposing disproportionately low-income Black and Latine communities living …

Breakwater: Anti-Blackness In Geoscience Lessons From Long Beach, Ca, Christina Marsh

Pomona Senior Theses

Breakwaters are more than just physical structures that protect against storm surges and in the context of Long Beach, CA, my hometown, they are actualizations of economic, social, environmental, geologic, and policy challenges. Inspired by Trace: Memory, History, Race, and the American Landscape by Lauret Savoy, and Teaching to Transgress by bell hooks, I use an extended metaphor and autoethnographic approach to connect a chronology of my educational life to the physical structure of a breakwater. Where the breakwater also acts as a signifier of my personal experiences of seeing it, questioning its purpose, and not always finding an answer. …

Timber Island: A Screenplay, Lucas Cunningham

Pomona Senior Theses

A screenplay about the legacy of land use in the Pacific Northwest:

A family from old timber money looking to sell their expansive Pacific Northwest island estate. Two Parks Service surveyors, a Native American scientist, and a developer competing for the bid. A forest with its own agenda.

Against a backdrop of cedar trees and saltwater, tensions boil, ideologies clash, and buried secrets bubble to the surface.

Who will walk away with the deed to Timber Island? And what will it cost?

Using Spectroscopy Of Diatomic Molecules To Search For Physics Beyond The Standard Model, Sean Jackson

Pomona Senior Theses

This main focus of this thesis is the use of molecular spectroscopy in the search for New Physics. Diatomic molecules offer interesting experimental opportunities in the search for physics beyond the Standard Model, including CP-violations due to the electric dipole mo- ment of the electron and other parity non-conservation effects. The work presented here concentrates mainly on the PbF molecule. Due to its large internal electric field, low sen- sitivity to external magnetic fields, and the presence of low-lying states of opposite parity in the 207PbF isotopolgue, PbF remains a compelling candidate for parity non-conservation studies. A robust global fit …

Clusters, Curves, And Centroids: Stellar Flare Morphology In The Ultraviolet, Vera Berger

Pomona Senior Theses

With a novel sample of 495 high-cadence light curves for stellar flares in the near-ultraviolet, I explore similarity measures, clustering algorithms, averaging methods, and curve fitting techniques for time series. This work seeks to provide insight into whether stellar flares are similar across stars, if we can identify physically meaningful patterns in their light curves, and how to construct a comprehensive model for flares. I construct the first empirical template for flare light curves in the ultraviolet, and compute ``average elements" of flares displaying complex features such as quasi-periodic oscillations and multipeak structures. Developing accurate models for flares in the …

The Eu's Capacity To Lead The Transatlantic Alliance In Ai Regulation, Varun Roy, Vignesh Sreedhar

Claremont-UC Undergraduate Research Conference on the European Union

In the face of Chinese advances in AI in terms of technological prowess and influence, there has been a call for collaboration between the EU and the US to create a foundation for AI governance based on shared democratic beliefs. This paper maps out the EU, US, and Chinese approaches to AI development and regulation as we analyze the capacity of the US and EU to establish international standards for AI regulation through channels such as the TTC. As the EU rolled out a proportionate and risk-based approach to ensure stricter regulation for high-risk AI technologies, it laid the foundation …

A Generalized Method Of Undetermined Coefficients, James S. Cook, William J. Cook

CODEE Journal

The method of undetermined coefficients is used to solve constant coefficient nonhomogeneous differential equations whose forcing function is itself the solution of a homogeneous constant coefficient differential equation. In this paper, we show that the classical methods for tackling constant coefficient equations, including the method of undetermined coefficients, generalize to much wider class linear differential equations which, for example, include Cauchy-Euler type equations. This general method includes an explicit construction of the fundamental solution sets of such equations. We also briefly consider where this method can be applied by producing the most general second and third order differential equations that …

Mathematical Constants Beyond The Half-Circle: An Open Call For Poetry, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics invites submissions of mathematical poetry for an upcoming poetry folder tentatively titled Mathematical Constants Beyond the Half-Circle. Please send your submissions via email to the editors by November 1, 2022. Publication decisions will be made by December 31, 2022. The folder is expected to appear in January 2023.

Squate, Tom Blackford

Journal of Humanistic Mathematics

This is the story of a middle school student who befriends an irrational number, the square root of eight.

A Topologist’S Broken Heart, Josh Hiller

Journal of Humanistic Mathematics

A poem about a topologist's broken heart.

Perturbation - For Nature Computes On A Straight Line (In Seven Balancing Acts), Vijay Fafat

Journal of Humanistic Mathematics

What if all of our Reality is a simulation? What, perhaps, are the unintended artifacts if we are an "approximate" simulation because God could not muster sufficient computational power for the Equations capturing the ultimate Theory of Everything? Are life and Sentience something She intended, a problem with the simulation's code, or an irreducible, teleological inevitability in Creation?