Physical Sciences and Mathematics Commons^™

Drought Tolerant Landscaping Trends In Claremont, California, Serena Myjer

CMC Senior Theses

The environmental impacts of turf grass lawns are particularly important to consider in California, because of its unique Mediterranean climate and ongoing problems with chronic drought. While California is ideal for agriculture, recreation, and year-round living, the occurrence of drought is natural and not uncommon, evident in historical human and paleoclimate records. Drought impacts humans and wildlife including water scarcity, crop failure, water quality, reduced streamflow, and wetland availability. Diverting water from these critical sources for growing turf grass lawns is inappropriate and harmful. This project is the first analysis of landscaping patterns, trends, and changes in Claremont, California using …

Energy As A Limiting Factor In Neuronal Seizure Control: A Mathematical Model, Sophia E. Epstein

CMC Senior Theses

The majority of seizures are self-limiting. Within a few minutes, the observed neuronal synchrony and deviant dynamics of a tonic-clonic or generalized seizure often terminate. However, a small epilesia partialis continua can occur for years. The mechanisms that regulate subcortical activity of neuronal firing and seizure control are poorly understood. Published studies, however, through PET scans, ketogenic treatments, and in vivo mouse experiments, observe hypermetabolism followed by metabolic suppression. These observations indicate that energy can play a key role in mediating seizure dynamics. In this research, I seek to explore this hypothesis and propose a mathematical framework to model how …

Mary Eleanor Spear's Importance To The History Of Statistical Visualization, Melanie Williams

CMC Senior Theses

This paper will demonstrate why Mary Eleanor Spear (1897-1986) is an important figure in the history of statistical visualization. She lead an impressive career working in the federal government as a data analyst before "data analyst" became a thing. She wrote and illustrated two comprehensive textbooks which furthered the art of statistical visualization. Her textbooks cover extensive graphing knowledge still valuable to statisticians and viewers today. Most notable of her works is her development of the box plot. In addition to Spear's career and contributions, this paper will also address the lack of female representation in science, technology, engineering, and …

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 …

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.

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 …

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 …

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 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 �� are thought of as 0-turn games, ���� as 1-turn “puzzle” games, and in general ��ₖ�� as ��-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 ��-turn CIRCUIT SATISFIABILITY games, whose ��ₖ��-completeness is assumed from prior work (we briefly justify this assumption …

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 …

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 …

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 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 …

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 …

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.

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 …

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.

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 …

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 …

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 …

Investigation Of Neutrophil-Like Hl-60 Cell Migration In A 3d Collagen Matrix, Pouye Sedighian

CGU Theses & Dissertations

It is known that cell migration in innate and adaptive immune system plays a fundamental role in human health. Among the immune cells, neutrophils are one of the most essential cells in protecting the body against invading pathogens. In the presence of chemoattractants, these cells are the first responders that start a directed migration toward the injured area. As neutrophils approach the site of infection, they transmigrate to the tissue and follow the chemoattractant concentration gradient to locate and eliminate the invading pathogens. Understanding the patterns and mechanism of neutrophil migration in the presence of chemoattractants could possibly play an …

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.

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 …

Infinitely Many Radial Solutions For A P-Laplacian Problem With Indefinite Weight, Alfonso Castro, Jorge Cossio, Sigifredo Herrón, Carlos Vélez

All HMC Faculty Publications and Research

We prove the existence of infinitely many sign changing radial solutions for a p-Laplacian Dirichlet problem in a ball. Our problem involves a weight function that is positive at the center of the unit ball and negative in its boundary. Standard initial value problems-phase plane analysis arguments do not apply here because solutions to the corresponding initial value problem may blow up near the boundary due to the fact that our weight function is negative at the boundary. We overcome this difficulty by connecting the solutions to a singular initial value problem with those of a regular initial value problem …

Fourth Voices Conference On Teaching Stem With Song, Lawrence M. Lesser

Journal of Humanistic Mathematics

The fourth VOICES (Virtual Ongoing Interdisciplinary Collaborations on Educating with Song) conference will be held September 26, 2021, with its Sunday date especially targeting those whose teaching schedule precludes attendance on a weekday. This online-only conference explores the use of song to teach STEM content at the college or secondary school level and will include reviewed interactive sessions, video-posters, and discussions of interest to both practitioners and researchers.

An Interview With The (Other) Corona Graph, Bonnie Jacob, Jobby Jacob

Journal of Humanistic Mathematics

The following is an interview, conducted in April 2021, with a graph product known as the corona graph. Disclaimer: The views expressed herein are not ours. Actually, this entire interview is fiction, other than the mathematics, of course.

The Music Is All That Counts! A Poem-Collage Pair Created During The Pandemic, Sarah Glaz, Mark Sanders

Journal of Humanistic Mathematics

The poem-collage pair presented here is a work of collaboration between the mathematician and poet, Sarah Glaz, and the collage and ceramic artist, Mark Sanders. The piece is part of their larger joint poem-collage project involving the history of mathematics. Created at the height of the pandemic, the poem-collage pair reflects the reality of living during a plague and embodies the solace offered by long-distance collaboration and by the arts. Included as background is a brief discussion on the history and mathematics involved, information about Sarah’s poem and Mark’s collage, and a reflection on how the pandemic influenced both the …