Physical Sciences and Mathematics Commons^™

Algebraic Invariants Of Knot Diagrams On Surfaces, Ryan Martinez

HMC Senior Theses

In this thesis we first give an introduction to knots, knot diagrams, and algebraic structures defined on them accessible to anyone with knowledge of very basic abstract algebra and topology. Of particular interest in this thesis is the quandle which "colors" knot diagrams. Usually, quandles are only used to color knot diagrams in the plane or on a sphere, so this thesis extends quandles to knot diagrams on any surface and begins to classify the fundamental quandles of knot diagrams on the torus.

This thesis also breifly looks into Niebrzydowski Tribrackets which are a different algebraic structure which, in future …

Results On The Generalized Covering Radius Of Error Correcting Codes, Benjamin Langton

HMC Senior Theses

The recently proposed generalized covering radius is a fundamental property of error correcting codes. This quantity characterizes the trade off between time and space complexity of certain algorithms when a code is used in them. However, for the most part very little is known about the generalized covering radius. My thesis seeks to expand on this field in several ways. First, a new upper bound on this quantity is established and compared to previous bounds. Second, this bound is used to derive a new algorithm for finding codewords within the generalized covering radius of a given vector, and also to …

Examining Soil Microbial Diversity In Transition Zones Between Corn Fields And Restored Prairie In The Upper Midwest, Anna M. Burns

Scripps Senior Theses

Prairies were once the largest ecosystem in North America, but agriculture and settlement has destroyed up to 99% of their pre-colonization extent. Prairie restorations are a strategy to recover the biodiversity and carbon sequestration functions of these grasslands, but typically occur in isolated strips between agricultural fields. My thesis analyzes how effective prairie restorations in the Liberty Prairie (northeastern Illinois) are at recovering the diversity of the prairie soil microbiome, focusing on verrucomicrobia abundance, alpha diversity, and soil physical characteristics.

Power In Numbers: An Abundance Of Small Corals Responsible For Storing Over Half Of The Carbon Stored By All Alaskan Primnoa Pacifica Deep-Sea Corals, Sylvie Alexander

Scripps Senior Theses

Gorgonian deep-sea corals (DSCs) are biologically linked to ocean carbon cycling converting ocean carbon to gorgonin and calcite in their skeletons. As such, gorgonian DSCs likely accumulate and store carbon in their skeleton throughout their lifespans, acting as carbon sinks on historic timescales. Yet, DSC carbon storage hasn’t been investigated to date. This study evaluates gorgonian DSC carbon storage capacity through an evaluation of the carbon stored by Alaskan Primnoa pacifica corals. The development of a model relating coral height to biomass in specimens with this data available was used to determine biomass values in a suite of Alaskan P. …

Here, There, And Everywhere: Probing Ubiquitin-Cavitand Binding Via 15n-1h Hsqc, Julia Didziulis

Scripps Senior Theses

Ubiquitination and other post-translational modifications play a major role in the proliferation of many neurodegenerative diseases, developmental disorders, and cancers, and as such are subjects of recently increased biochemical interest. Expanding upon such research, this study confirmed a robust method of ubiquitin expression and purification, then used 15N-1H HSQC to analyze ubiquitin samples containing varying concentrations of a deep cavitand with affinity for lysine and arginine side chains. In the pure ubiquitin spectrum, arginine side chain chemical shifts were detected in the nitrogen 80-85 ppm range and lysine side chain signals were undetected. However, upon introduction of the cavitand, collection …

Correlation Does Not Imply Correlation: A Thesis On Causal Influence And Simpson’S Paradox, Emily Naitoh

Scripps Senior Theses

In our data-driven world, it has become commonplace to attempt to find
causal relationships. One of the themes of this thesis is to show methods of
determining causation. The second theme follows a saying in mathematics,
"correlation does not imply causation". We will also discuss situations where
correlation does not even imply correlation itself. These cases are described
by Simpson’s paradox in an exploration of different areas of mathematics
and computer coding.

On Multiplication Groups Of Quasigroups, Ahmed Al Fares

CGU Theses & Dissertations

Quasigroups are algebraic structures in which divisibility is always defined. In this thesis we investigate quasigroups using a group-theoretic approach. We first construct a family of quasigroups which behave in a group-like fashion. We then focus on the multiplication groups of quasigroups, which have first appeared in the work of A. A. Albert. These permutation groups allow us to study quasigroups using group theory. We also explore how certain natural operations on quasigroups affect the associated multiplication groups. Along the way we take the time and special care to pose specific questions that may lead to further work in the …

A Framework For And Design Of A Smart Academic Building Using Sensors, Citizen Participation, And Volunteered Geographic Information, Neelam Raigangar

CGU Theses & Dissertations

Population growth and migration patterns have shown an influx of residents from rural to urban environments. To deal with the problems caused by unprecedented urban influx, cities should plan to use technology in a smart and distinctive way. Tackling at the city scale is hard. But a set of smart buildings that are interconnected by technology will lead to smarter communities which are then interconnected to create a smart city. Smart lobby, building, community, or city is distinguished by its application of integrated software, hardware, and network technologies, along with access to real-time data enabling decision-making, facilitating tracing, tracking and …

Data-Driven Methods For Low-Energy Nuclear Theory, Jordan M.R. Fox

CGU Theses & Dissertations

The term data-driven describes computational methods for numerical problem solvingwhich have been developed by the field of data science; these are at the intersection of computer science,mathematics, and statistics. When applied to a domain science like nuclear physics, especially with the goalof deepening scientific insight, data-driven methods form a core pillar of the computational science endeavor.In this dissertation I explore two problems related to theoretical nuclear physics: one in the framework of numerical statistics, and the other in the framework of machine learning. I) Historically our understanding of the structure of the atomic nucleus, the quantum many-body problem, has been …

On The Polytopal Generalization Of Sperner’S Lemma, Amit Harlev

HMC Senior Theses

We introduce and prove Sperner’s lemma, the well known combinatorial analogue of the Brouwer fixed point theorem, and then attempt to gain a better understanding of the polytopal generalization of Sperner’s lemma conjectured in Atanassov (1996) and proven in De Loera et al. (2002). After explaining the polytopal generalization and providing examples, we present a new, simpler proof of a slightly weaker result that helps us better understand the result and why it is correct. Some ideas for how to generalize this proof to the complete result are discussed. In the last two chapters we provide a brief introduction to …

Games For One, Games For Two: Computationally Complex Fun For Polynomial-Hierarchical Families, Kye Shi

HMC Senior Theses

In the first half of this thesis, we explore the polynomial-time hierarchy, emphasizing an intuitive perspective that associates decision problems in the polynomial hierarchy to combinatorial games with fixed numbers of turns. Specifically, problems in 𝐏 are thought of as 0-turn games, 𝐍𝐏 as 1-turn “puzzle” games, and in general 𝚺ₖ𝐏 as 𝑘-turn games, in which decision problems answer the binary question, “can the starting player guarantee a win?” We introduce the formalisms of the polynomial hierarchy through this perspective, alongside definitions of 𝑘-turn CIRCUIT SATISFIABILITY games, whose 𝚺ₖ𝐏-completeness is assumed from prior work (we briefly justify this assumption …

Smoothed Bounded-Confidence Opinion Dynamics On The Complete Graph, Solomon Valore-Caplan

HMC Senior Theses

We present and analyze a model for how opinions might spread throughout a network of people sharing information. Our model is called the smoothed bounded-confidence model and is inspired by the bounded-confidence model of opinion dynamics proposed by Hegselmann and Krause. In the Hegselmann–Krause model, agents move towards the average opinion of their neighbors. However, an agent only factors a neighbor into the average if their opinions are sufficiently similar. In our model, we replace this binary threshold with a logarithmic weighting function that rewards neighbors with similar opinions and minimizes the effect of dissimilar ones. This weighting function can …

An Adaptive Hegselmann–Krause Model Of Opinion Dynamics, Phousawanh Peaungvongpakdy

HMC Senior Theses

Models of opinion dynamics have been used to understand how the spread
of information in a population evolves, such as the classical Hegselmann–
Krause model (Hegselmann and Krause, 2002). One extension of the model
has been used to study the impact of media ideology on social media
networks (Brooks and Porter, 2020). In this thesis, we explore various
models of opinions and propose our own model, which is an adaptive
version of the Hegselmann–Krause model. The adaptive version implements
the social phenomenon of homophily—the tendency for like-minded agents to
associate together. This is done by having agents dissolve connections …

Check Yourself Before You Wrek Yourself: Unpacking And Generalizing Randomized Extended Kaczmarz, William Gilroy

HMC Senior Theses

Linear systems are fundamental in many areas of science and engineering. With the advent of computers there now exist extremely large linear systems that we are interested in. Such linear systems lend themselves to iterative methods. One such method is the family of algorithms called Randomized Kaczmarz methods.
Among this family, there exists a Randomized Kaczmarz variant called Randomized
Extended Kaczmarz which solves for least squares solutions in inconsistent linear systems.
Among Kaczmarz variants, Randomized Extended Kaczmarz is unique in that it modifies input system in a special way to solve for the least squares solution. In this work we …

An Exploration Of Voting With Partial Orders, Mason Acevedo

HMC Senior Theses

In this thesis, we discuss existing ideas and voting systems in social choice theory. Specifically, we focus on the Kemeny rule and the Borda count. Then, we begin trying to understand generalizations of these voting systems in a setting where voters can submit partial rankings on their ballot, instead of complete rankings.

Interpolating The Riemann Zeta Function In The P-Adics, Rebecca Mamlet

Scripps Senior Theses

In this thesis, we develop the Kubota-Leopoldt Riemann zeta function in the p-adic integers. We follow Neil Koblitz's interpolation of Riemann zeta, using Bernoulli measures and p-adic integrals. The underlying goal is to better understand p-adic expansions and computations. We finish by connecting the Riemann zeta function to L-functions and their p-adic interpolations.

An Exponential Formula For Random Variables Generated By Multiple Brownian Motions, Maximilian Lawrence Baroi

CGU Theses & Dissertations

The frozen operator has been used to develop Dyson-series like representations for random variables generated by classical Brownian motion, Lévy processes and fractional Brownian with Hurst index greater than 1/2.The relationship between the conditional expectation of a random variable (or fractional conditional expectation in the case of fractional Brownian motion)and that variable's Dyson-series like representation is the exponential formula. These results had not yet been extended to either fractional Brownian motion with Hurst index less than 1/2, or d-dimensional Brownian motion. The former is still out of reach, but we hope our review of stochastic integration for fractional Brownian motion …

Using Powder Diffraction To Give Insight Into Structures Of Ir2(Diisocyanomenthane)4x2 [Dimen] (X = Cl; Pf6; Bph4), Mairead Brownell

Scripps Senior Theses

Ir2(dimen)42+ (dimen = 1,8-diisocyanomenthane) has been studied extensively as model compound to better understand catalysis of photochemical reactions. Although Ir2(dimen)42+ has been used primarily to observe the photophysical changes of metal-metal transitions, it gives great insight into the transitions that allow other d8-d8 metal complexes to undergo photochemical processes and generate hydrogen gas. The large visible range by which Ir2(dimen)42+ (1) can be electronically excited in solution is indicative of its two solution phase ground states, which interestingly have been hypothesized to resemble two unique packing structures observed in the powder state. In this study, the powder diffraction patterns of …

Footprints On The Prairie: Examining The Interlocking Land Histories Of The Liberty Prairie Reserve, Illinois, Anna M. Burns

Scripps Senior Theses

This thesis begins with the local history of the Liberty Prairie, the land where I conducted the ecological field-work that I later discuss in my second thesis on soil microbiome diversity (“Examining Soil Microbial Diversity in Transition Zones Between Corn Fields and Restored Prairie in the Upper Midwest"). I examine the Indigenous histories of the land, and the conflicts between the Bodwéwadmi and Euro-American settlers that resulted in the land being farmed for cattle, corn, and soy for over a hundred and fifty years. I then take a step back and analyze the broader historical contexts of Midwestern Corn Belt …

The Effects Of "Sticky Stuff" On The Spin Rate And Break Of A Baseball Pitch, Natalie Dale

Scripps Senior Theses

In June 2021, Major League Baseball cracked down on the use of foreign substances by pitchers on the ball (Castrovince, 2021a). It is believed the sticky substances give the pitchers an unfair advantage over batters since they increase spin rate, consequently, through the Magnus Effect, creating more movement or “break” in the pitch, making it harder to hit. There are existing gaps in empirical research on this topic, thus the goal of this project was to determine the effect the banned substances have on the spin rate and related break of the pitches. By using pitch tracking technology, two types …

Examining Bias Against Women In Professional Settings Through Bifurcation Theory, Lauren Cashdan

CMC Senior Theses

When it comes to women in professional hierarchies, it is important to recognize the lack of representation at the higher levels. By modeling these situations we hope to draw attention to the issues currently plaguing professional atmospheres. In a paper by Clifton et. al. (2019), they model the fraction of women at any level in a professional hierarchy using the parameters of hiring gender bias and internal homophily on behalf of the applicant. This thesis will focus on a key theory in Clifton et. al.’s analysis and explain its role in the model, specifically bifrucation analysis. In order to analyze …

Predicting Outcomes Of El Clásico Using Random Forests And Extreme Gradient Boosting, Emanuel Jarquin

CMC Senior Theses

In the modern era, sports betting is becoming increasingly popular. This is especially true in the realm of soccer (or ‘football’ as it is known outside the United States). As a result, the concept of attempting to predict the outcomes of soccer matches using machine learning has garnered much attention in recent years. In this thesis, I utilize well-known machine learning techniques to predict the outcomes of El Clásico matchups and compare the predictive performance of these techniques. The predictive methods employed for this thesis are random forests using the party package in R and extreme gradient boosting using the …

Advanced Full-Text Search Based On Synonyms In Postgres, Joey Bodoia

CMC Senior Theses

This paper discusses the advanced full-text search queries based on synonyms that are supported in Chajda, which is a postgres extension and corresponding python library for highly multi-lingual full-text search in postgres. This discussion will include the motivations for using advanced queries based on synonyms, examples of how to use these advanced queries in Chajda, current limitiations of the advanced queries, and performance testing of the advanced queries.

On Coherence And The Geometry Of Certain Families Of Lattices, David Booth Kogan

CGU Theses & Dissertations

The coherence of a lattice is, roughly speaking, a measure of non-orthogonality of its minimal vectors. It was introduced to lattices (by analogy with frame theory) by L. Fukshansky and others as a possible route to gaining insight into packing density, a central problem in lattice theory. In this work, we introduce the related measure of average coherence, explore connections between packing density and coherence, and prove several properties of certain families of lattices, most notably nearly orthogonal lattices, cyclotomic lattices, and cyclic lattices.

Analyzing Marriage Statistics As Recorded In The Journal Of The American Statistical Association From 1889 To 2012, Annalee Soohoo

CMC Senior Theses

The United States has been tracking American marriage statistics since its founding. According to the United States Census Bureau, “marital status and marital history data help federal agencies understand marriage trends, forecast future needs of programs that have spousal benefits, and measure the effects of policies and programs that focus on the well-being of families, including tax policies and financial assistance programs.”[1] With such a wide scope of applications, it is understandable why marriage statistics are so highly studied and well-documented.

This thesis will analyze American marriage patterns over the past 100 years as documented in the Journal of …

Containing Compounding Container Congestion, Curtis Salinger

CMC Senior Theses

The Covid-19 pandemic caused major disruptions throughout the container shipping supply chain. Professor Dongping Song of Liverpool University wrote a paper discussing the logistical vulnerabilities in the supply chain, including the issue of congestion in ports. This paper examines the Port of Los Angeles from 2018-2021 as it relates to Song’s paper to see how its operations were impacted during the Covid-19 timeframe. It is found that labor shortages, chassis shortages, and change in trade behavior each contributed to the congestion. Unfortunately, the implemented policies were insufficient to bolster the port against sustained challenges and congestion continues to worsen.

Integrating Carbon Pricing Approaches, Amay Shah

CMC Senior Theses

Concerns about global climate change and its effects have been steadily growing around the world in recent years. The Paris Agreement has laid out ambitious targets for countries to cut their emissions in order to limit global warming to 1.5 degrees and to achieve net zero emissions by 2050. Carbon pricing mechanisms are an inventive instrument that can help achieve these emissions reductions by placing a price on greenhouse gas emissions, creating incentives for organizations to reduce their emissions. These mechanisms can also help enable the transfers from wealthy nations to developing nations that will be essential for ensuring a …

Using Short Bursts To Optimize Redistricting In Georgia, Vedika Vishweshwar

CMC Senior Theses

Identifying extreme outliers in large state spaces is a difficult prob-
lem. I consider this problem in the context of finding political district-
ing plans that maximize the number of districts in which the majority
of the population is from a minority group, such as African Americans.
Since the set of all possible districting plans is enormous and unfeasi-
ble to examine in practice, this paper proposes a sampling method to
find these outlying plans. Specifically, this paper experiments with short
bursts in the context of minority voting rights in Georgia. Short bursts
are a type of Markov Chain in …

Parallels Of Quantum Mechanics And Mahāyāna Buddhist Philosophy: An Argument For Relational Quantum Mechanics, Axel I. Palapa

CMC Senior Theses

Western orthodoxy philosophy is based on the principle of noncontradiction and thus, the philosophy of science is as well. The most prominent interpretations of quantum mechanics, since its inception, have followed this principle. In this paper, two quantum phenomena, the Observer Problem (measurement problem) and quantum entanglement will be analyzed from a Mahayana Buddhism ontological perspective. I will analyze the mathematical and philosophical arguments proposed by Graham Priest and Jay Garfield, based on dialethism, pertaining to Nagarjuna and the Net of Indra. Demonstrating the parallels and adaptability of the arguments to further the philosophical groundwork for Carlo Reveille’s Relational Quantum …

Spatial Geochemical Changes In Central And East Texas Soils Over Time Resulting From Human Decomposition, Isabela Marisol Overturf

CMC Senior Theses

Human decomposition is studied to aid forensic investigations and better understand the impact of cemeteries on urban resources like soil and groundwater. The purpose of this study was to identify changes in soil geochemistry at and around a human grave to search for lateral nutrient movement and possibly identify new patterns in elemental concentrations that could be used in estimating post-mortem intervals (PMIs). At the Forensic Anthropology Research Facility (FARF) at Texas State San Marcos, soil samples were collected from a shallow grave over the course of 54 days to conduct analysis for organic matter content, texture, pH, and bulk …