Physical Sciences and Mathematics Commons^™

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 …

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 …

Application Of Sentiment Analysis And Machine Learning Techniques To Predict Daily Cryptocurrency Price Returns, Edward Wu

CMC Senior Theses

This paper examines the effects of social media sentiment relating to Bitcoin on the daily price returns of Bitcoin and other popular cryptocurrencies by utilizing sentiment analysis and machine learning techniques to predict daily price returns. Many investors think that social media sentiment affects cryptocurrency prices. However, the results of this paper find that social media sentiment relating to Bitcoin does not add significant predictive value to forecasting daily price returns for each of the six cryptocurrencies used for analysis and that machine learning models that do not assume linearity between the current day price return and previous daily price …

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. …

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 …

Counting Spanning Trees On Triangular Lattices, Angie Wang

CMC Senior Theses

This thesis focuses on finding spanning tree counts for triangular lattices and other planar graphs comprised of triangular faces. This topic has applications in redistricting: many proposed algorithmic methods for detecting gerrymandering involve spanning trees, and graphs representing states/regions are often triangulated. First, we present and prove Kirchhoff’s Matrix Tree Theorem, a well known formula for computing the number of spanning trees of a multigraph. Then, we use combinatorial methods to find spanning tree counts for chains of triangles and 3 × n triangular lattices (some limiting formulas exist, but they rely on higher level mathematics). For a chain of …

Utilizing Machine Learning In Healthcare In An Ethical Fashion, Nishka Ayyar

CMC Senior Theses

This thesis paper explores the ethical considerations surrounding the use of machine learning (ML) solutions in healthcare. The background section discusses the basics of machine learning techniques and algorithms, and the increasing interest in their utilization in the healthcare sector. The paper then reviews and critically analyzes four studies that highlight concerns related to using ML in healthcare, including issues of bias, privacy, accountability, and transparency. Based on the analysis of these studies, the paper presents several recommendations for addressing these concerns. The paper concludes with a discussion on the potential benefits of using machine learning technology in healthcare. Ultimately, …

Defining The "Quadruple-A" Player: What Makes A Baseball Player Succeed In The Minor Leagues And Fail In The Major Leagues?, Sam Bogen

CMC Senior Theses

The "Quadruple-A" player is defined as one who is too good to play in Triple-A (the league one step down from Major League Baseball) but not good enough to play consistently in Major League Baseball. This thesis paper attempts to explain the phenomenon of the "Quadruple-A" player. Using Triple-A data from 2013-2022 and Major League data from the "Statcast Era" (2015-2022), I build logistic and linear regression models to predict Major League success based on Triple-A performance data as well as Major League Statcast data, discovering that statistics related to how a player hits the ball such as the speed …

From Bloom To Bouquet: Unearthing The Toxic Cut Flower Industry, Addie Wasikonis

Pitzer Senior Theses

The commercial cut flower industry is an expansive network of growers, laborers, airlines, government workers, wholesalers, retailers, supermarkets, and florists, which deliver a crafted bouquet to the consumer for those special occasions. We often buy flowers during our weekly trip to the supermarket, call our local florist for an arrangement, or make a last-minute order online to be shipped within hours. For this demand to be supplied, the cut flower industry has spread to equator-localized countries where the labor is cheap, the land is plentiful, and the sun shines all year round in order to grow any type of flower …

Decoherence And Preferred Tensor Product Structures For Systems Of Qubits, Marissa M. Singh

Pitzer Senior Theses

In recent decades, the program of Decoherence has helped clarify how features of the classical world emerge from Quantum Mechanics. According to Decoherence, the interaction between a system and its environment dynamically selects certain system states — the pointer states — that exhibit predictable, classical behavior while their superpositions rapidly decohere. However, most Decoherence studies to date pre-suppose a preferred division of the world into “system” and “environment”, corresponding to a preferred choice of Tensor Product Structure (TPS) on the Hilbert Space of states. A few previous works have suggested that the existence of a well-defined pointer observable may be …

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 …

A Study On Global Reef Deterioration: Exploring Coral Bleaching, Emily Fernandez

CMC Senior Theses

This thesis is a study on coral bleaching and coral mortality, studying the relationship between variables such as depth, exposure, distance to shore, and temperature for percent bleaching. All of the analyses were made using two different data sets, that contain information about bleaching events in specific regions, and dates, and provide information factors such as depth, temperature, and exposure. Models were created for different relationships of variables for eco-regions, recent data, and countries. I attempted to find relationships between variables such as depth, temperature, exposure, and distance to shore, and how they affect coral bleaching. Unfortunately, I did not …

Generalized Far-Difference Representations, Prakod Ngamlamai

HMC Senior Theses

Integers are often represented as a base-$b$ representation by the sum $\sum c_ib^i$. Lekkerkerker and Zeckendorf later provided the rules for representing integers as the sum of Fibonacci numbers. Hannah Alpert then introduced the far-difference representation by providing rules for writing an integer with both positive and negative multiples of Fibonacci numbers. Our work aims to generalize her work to a broader family of linear recurrences. To do so, we describe desired properties of the representations, such as lexicographic ordering, and provide a family of algorithms for each linear recurrence that generate unique representations for any integer. We then prove …

Beginner's Analysis Of Financial Stochastic Process Models, David Garcia

HMC Senior Theses

This thesis explores the use of geometric Brownian motion (GBM) as a financial model for predicting stock prices. The model is first introduced and its assumptions and limitations are discussed. Then, it is shown how to simulate GBM in order to predict stock price values. The performance of the GBM model is then evaluated in two different periods of time to determine whether it's accuracy has changed before and after March 23, 2020.

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 …

Analysis Of Biologically Effective Dose For Retroactive Yttrium-90 Trans-Arterial Radioembolization Treatment Optimization, Mj Lindsey

CMC Senior Theses

Trans-arterial radioembolization (TARE) is a protracted modality of radiation therapy where radionuclides labeled with Yttrium-90 (⁹⁰Y) are inserted inside a patient's hepatic artery to treat hepatocellular carcinoma (HCC). While TARE has been shown to be a clinically effective and safe treatment, there is little understanding of the radiobiological relationship between absorbed dose and tissue response, and thus there is no dosimetric standard for treatment planning. The Biologically Effective Dose (BED) formalism, derived from the Linear-Quadratic model of radiobiology, is used to weigh the absorbed dose by the time pattern of delivery. BED is a virtual dose that can …

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). …

Measuring Racial Segregation In Los Angeles County Using Random Walks, Zarina Kismet Dhillon

CMC Senior Theses

As of now there is no universal quantitative measure used to evaluate racial segregation in different regions. This paper begins by providing a history of segregation, with an emphasis on the impact of redlining in the early 20th century. We move to its effect on the current population distribution in Los Angeles, California, and then provide an overview of the mathematical concepts that have been used in previous measurements of segregation. We then introduce a method that we believe encompasses the most representative aspects of preceding work, proposed by Sousa and Nicosia in their work on quantifying ethnic segregation in …

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.

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 …

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 …

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 …

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 …

Partially Filled Latin Squares, Mariam Abu-Adas

Scripps Senior Theses

In this thesis, we analyze various types of Latin squares, their solvability and embeddings. We examine the results by M. Hall, P. Hall, Ryser and Evans first, and apply our understandings to develop an algorithm that the determines the minimum possible embedding of an unsolvable Latin square. We also study Latin squares with missing diagonals in detail.

Optical Tweezers: Exerting Force With Light, Gabriella Seifert

Scripps Senior Theses

Photons carry momentum. When a tightly-focused beam of photons hit a particle, they transfer some of their momentum to the particle, exerting a force. Optical tweezers take advantage of this phenomenon to trap (or “tweeze”) a spherical bead just after the focus of a diverging laser beam, creating a potential well that pulls in beads. In this thesis, I predict the force exerted on trapped beads and measure the actual force using an optical tweezers setup that I built. To predict the force, I follow the path of all possible rays from a diverging beam incident on a spherical bead …

Quantifying The Carbon Stored And Sequestered By The Trees On Pomona College’S Campus, Paola A. Giron-Carson

Scripps Senior Theses

We are experiencing a climate crisis that must be confronted with strategic mitigation. Pomona College contributes to the climate crisis through its emissions for which there is a baseline record. However there is no baseline record of the climate mitigation currently performed by the trees on Pomona’s campus through carbon storage. This study seeks to determine a current baseline quantity of carbon stored and sequestrated by Pomona’s trees as well as possible courses of climate mitigation for Pomona College to take. Initial information gathering was conducted through interviews with several stakeholders. This study was conducted using data collected prior to …

Computational Investigation Of The Ionization Potential Of Lead Sulfide Quantum Dots, Jessica Beyer

Scripps Senior Theses

The purpose of this work was to determine the impact of quantum dot size on ionization potential and to determine how the presence of carbonyl-based ligands affect the ionization potential of lead sulfide quantum dot systems. Ionization potential (IP) is defined as the energy required to remove an electron from an atom, molecule, or material. IP helps scientists determine how reactive the material of interest is, which is crucial information when manufacturing nanomaterials. Accurate quantum chemical calculations of ionization potential are challenging due to the computational cost associated with the numerical solution of the Dyson equation. In this work, 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 …