Physical Sciences and Mathematics Commons^™

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 …

An Inquiry Into Lorentzian Polynomials, Tomás Aguilar-Fraga

HMC Senior Theses

In combinatorics, it is often desirable to show that a sequence is unimodal. One method of establishing this is by proving the stronger yet easier-to-prove condition of being log-concave, or even ultra-log-concave. In 2019, Petter Brändén and June Huh introduced the concept of Lorentzian polynomials, an exciting new tool which can help show that ultra-log-concavity holds in specific cases. My thesis investigates these Lorentzian polynomials, asking in which situations they are broadly useful. It covers topics such as matroid theory, discrete convexity, and Mason’s conjecture, a long-standing open problem in matroid theory. In addition, we discuss interesting applications to known …

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.

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 …

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 …

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 …

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 …

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, …

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 …

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 …

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 …

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 …

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.

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). …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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.

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 …