Physical Sciences and Mathematics Commons^™

Exploring The Structure Of Partial Difference Sets With Denniston Parameters, Nicolas Ferree

Honors Theses

In this work, we investigate the structure of particular partial difference sets (PDS) of size 70 with Denniston parameters in an elementary abelian group and in a nonelementary abelian group. We will make extensive use of character theory in our investigation and ultimately seek to understand the nature of difference sets with these parameters. To begin, we will cover some basic definitions and examples of difference sets and partial difference sets. We will then move on to some basic theorems about partial difference sets before introducing a group ring formalism and using it to explore several important constructions of partial …

The 2015 Ncaa Cost-Of-Attendance Stipend And Its Effects On Institutional Financial Aid Packages, Sara Greene

Honors Theses

In 2015, the National Collegiate Athletic Association (NCAA) allowed “Cost of Attendance” (COA) stipends to be offered to athletic recruits for Division I schools. These stipends are intended to allow schools to grant aid to student-athletes beyond a full-ride scholarship to cover additional costs imposed on student-athletes. These stipends created an opportunity for the “Autonomy” Power 5 programs to utilize a competitive tactic to try to win over the top recruits. There is evidence that these COA stipends have caused an increase in the estimated cost of attendance reported by the university. This paper examines if the COA stipends have …

The Parental Labor Gap: The Impact Of Daycare Access On The Parental Labor Force During The Covid-19 Pandemic, Acacia Wyckoff

Honors Theses

In the two years since the COVID-19 pandemic began, the landscape for work has shifted dramatically. Many companies and employers switched to telework when the pandemic hit, and many still do not require workers to come into the office. Research suggests these COVID-induced changes have led to a closing of the gap in childcare duties between men and women in households. Comparing parents in positions with telework eligibility versus in-person positions, Heggeness and Suri (2022) found that while telework improved the labor participation rate of mothers slightly, there was still a major gap in labor force participation between mothers and …

From Big Farm To Big Pharma: A Differential Equations Model Of Antibiotic-Resistant Salmonella In Industrial Poultry Populations, Rilyn Mckallip

Honors Theses

Antibiotics are used in poultry production as prophylaxis, curative treatment, and growth promotion. The first use is as prophylaxis, or prevention of common bacterial diseases. The crowded conditions in concentrated animal feeding operations necessitate management of infectious disease to ensure overall animal health and the profitability of such operations. In these farms, between 20,000 and 125,000 birds are raised in shed-like enclosures [3], with an average of less than one square foot of space per chicken [34]. Antibiotics are currently used in chicken farms to manage and prevent common bacterial diseases such as respiratory and digestive tract infections, as well …

Length Bias Estimation Of Small Businesses Lifetime, Simeng Li

Honors Theses

Small businesses, particularly restaurants, play a crucial role in the economy by generating employment opportunities, boosting tourism, and contributing to the local economy. However, accurately estimating their lifetimes can be challenging due to the presence of length bias, which occurs when the likelihood of sampling any particular restaurant's closure is influenced by its duration in operation. To address the issue, this study conducts goodness-of-fit tests on exponential/gamma family distributions and employs the Kaplan-Meier method to more accurately estimate the average lifetime of restaurants in Carytown. By providing insights into the challenges of estimating the lifetimes of small businesses, this study …

An Introduction To Obstacle Problems, Calvin Reedy

Honors Theses

The obstacle problem can be used to predict the shape of an elastic membrane lying over an obstacle in a domain Ω. In this paper we introduce and motivate a mathematical formulation for this problem, and give an example to demonstrate the need to search for solutions in non-classical settings. We then introduce Sobolev spaces as the proper setting for solutions, and prove that unique solutions exist in W1,2(Ω).

Overdose Prevention Sites Placement Informed By Simulation, Jing Dong

Honors Theses

In Philadelphia, people are experiencing the greatest opioid crisis in a century. Plac- ing the Overdose Prevention Site (OPS) can alleviate this crisis. However, the journey to the successful launch of the first OPS in the USA is rough. It was first accused of having a collision with federal drug laws. While Safehouse won the lawsuit and the OPS was judged to be legal in 2020, other pressure rose afterward such as the against from the public and the COVID19, which delayed the plan to open the OPS. Without solid research on the effectiveness of OPS, we thought it is …

An Agent-Based Model To Evaluate The Effect Of Socioeconomic Status And Demographic Factors On Covid-19 Prevalence And Mortality, Jonathan Huang, Berke Nouri

Arts & Sciences Student Symposium

The purpose of the project is to discover how the prevalence and mortality of a pandemic change depending on a population’s demographic factors as well as various intervention policies through a NetLogo agent-based model. This model will simulate how demographic factors affect the course of COVID-19 (infection rate, recovery rate, and death rate). Demographic factors of interest will include population density, income distribution, age distribution, and number of hospital beds per capita. Intervention policies include vaccination, social distancing, mask wearing, mass testing, and quarantining. Conclusions about the effect of demographic factors on the infection, recovery, and death rate will be …

Emerald Ash Borer And The Application Of Biological Control In Virginia, Shuheng Chen, Yihui Wu, Shengjie Liu

Arts & Sciences Student Symposium

The emerald ash borer (Agrilus planipennis; EAB) is an invasive wood-boring beetle whose larvae feed on ash phloem. After only 1-5 years of infestation, the larvae create extensive tunnels under the bark that disrupt the tree’s ability to transport water and nutrients, which eventually girdles and kills the tree. Since 2008, EAB has spread to all but the eastern-most counties in Virginia. Bological control is one strategy to limit EAB populations. In this project we study control by native agents (woodpeckers) and imported agents (parasitoid wasps).

Mathematical models of host-parasitoid interactions and simulations based on both models and field studies …

Getting Over It, Thomas Kade, Kevorc Ibrahimian, Max Simpson

Arts & Sciences Student Symposium

The research extended a 2D motion planning system to three dimensional environments. The updated system is now able to plan the motion for robots over 3D terrains modeled by polyhedrons.

The School Mathematics Study Group: Lessons In Mathematics Education, Madeline Polhill

Arts & Sciences Student Symposium

This work argues that the "new math" project called the School Mathematics Study Group offers a valuable case study for mathematics educators seeking to venture into the future better informed about both the successes and failures of previous projects. Understanding this project requires recognizing that the School Mathematics Study Group was wholly a product of the forces—personal, educational, mathematical, and political—that shaped it. Admittedly, some of the SMSG's shortcomings resulted from its members' lack of understanding of the changes needed in mathematics education. Still, the majority of the SMSG's public vilification resulted through no fault of its own, but rather …

The Surface Diffusion And The Willmore Flow For Uniformly Regular Hypersurfaces, Jeremy Lecrone, Yuanzhen Shao, Gieri Simonett

Department of Math & Statistics Faculty Publications

We consider the surface diffusion and Willmore flows acting on a general class of (possibly non–compact) hypersurfaces parameterized over a uniformly regular reference manifold possessing a tubular neighborhood with uniform radius. The surface diffusion and Willmore flows each give rise to a fourth–order quasilinear parabolic equation with nonlinear terms satisfying a specific singular structure. We establish well–posedness of both flows for initial surfaces that are C^1+α–regular and parameterized over a uniformly regular hypersurface. For the Willmore flow, we also show long–term existence for initial surfaces which are C^1+α–close to a sphere, and we prove …

A Template For Success: Celebrating The Work Of Judith Grabiner, Della Dumbaugh, Adrian Rice

Department of Math & Statistics Faculty Publications

Judith Grabiner is a mathematician who specializes in the history of mathematics. She is currently the Flora Sanborn Pitzer Professor Emerita of Mathematics at Pitzer College, one of the Claremont Colleges in Claremont, California. She has authored more than forty articles, as well as three books: The Origins of Cauchy’s Rigorous Calculus (1981), The Calculus as Algebra: J.-L. Lagrange, 1736–1813 (1990), and A Historian Looks Back: The Calculus as Algebra and Selected Writings (2010), which won the Beckenbach Prize from the Mathematical Association of America in 2014. She deliv- ered an invited address titled “The Centrality of Mathemat- ics in …

On Quasilinear Parabolic Equations And Continuous Maximal Regularity, Jeremy Lecrone, Gieri Simonett

Department of Math & Statistics Faculty Publications

We consider a class of abstract quasilinear parabolic problems with lower–order terms exhibiting a prescribed singular structure. We prove well–posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global existence of solutions and we extend the generalized principle of linearized stability to settings with initial values in critical spaces. These general results are applied to the surface diffusion flow in various settings.

Almost Difference Sets In 2-Groups, Xin Yutong

Honors Theses

Difference sets have been studied for decades due to their applications in digital communication, cryptography, algebra, and number theory. More recently, mathematicians have expanded their focus to the field of almost difference sets. Almost difference sets have similar functionalities with difference sets, yet with more potential of finding new constructions. In this paper I will introduce the definitions, properties, and applications of difference sets and almost difference sets, and discuss our effort and results in the exploration of almost difference sets in cyclic and non-cyclic groups.

Internal Migration Of Foreign-Born In Us: Impacts Of Population Concentration And Risk Aversion, Thin Yee Mon Su

Honors Theses

Internal migration in the US has been declining since the 1990s and research has mostly focused on labor market dynamics and aging population to explain the migration trends. This paper analyzes migration patterns of foreign-born groups in the US from 2000 to 2019. Along with the migration determinants such as education and employment, the paper focuses on population concentration as a factor that shapes foreign-born decisions to relocate in the US. Population concertation is defined to be a measure of how geographically concentrated each foreign-born group is across the US. I find that the likelihood of migrating to another state …

Biasing Medial Axis Rapidly-Exploring Random Trees With Safe Hyperspheres, David Qin

Honors Theses

Motion planning is a challenging and widely researched problem in robotics. Motion planning algorithms aim to not only nd unobstructed paths, but also to construct paths with certain qualities, such as maximally avoiding obstacles to improve path safety. One such solution is a Rapidly-Exploring Random Tree (RRT) variant called Medial Axis RRT that generates the safest possible paths, but does so slowly. This paper introduces a RRT variant called Medial Axis Ball RRT (MABallRRT) that uses the concept of clearance -- a robot's distance from its nearest obstacle -- to efficiently construct a roadmap with safe paths. The safety of …

Fast Medial Axis Sampling For Use In Motion Planning, Hanglin Zhou

Honors Theses

Motion planning is a difficult but important problem in robotics. Research has tended toward approximations and randomized algorithms, like sampling-based planning. Probabilistic RoadMaps (PRMs) are one common sampling-based planning approach, but they lack safety guarantees. One main approach, Medial Axis PRM (MAPRM) addressed this deficiency by generating robot configurations as far away from the obstacles as possible, but it introduced an extensive computational burden. We present two techniques, Medial Axis Bridge and Medial Axis Spherical Step, to reduce the computational cost of sampling in MAPRM and additionally propose recycling previously computed clearance information to reduce the cost of connection in …

Estimating Value-At-Risk Of An Unconventional Portfolio, Elizabeth N. Mejía-Ricart

Honors Theses

Since the 2008 financial crisis, interest rates and bond yields have been low all through the recovery and expansion that followed, and they are still low. As a result, more investors have been attracted to US equities, a space of possibly higher returns. However, these returns come with a potential downside: risk of loss. One of the methods to assess this potential downside is value-at-risk (VaR), which gained momentum in the late 1990s. At the time, the market risk amendment to the 1988 Basle Capital Accord required commercial banks with significant trading activities to put aside capital to cover market …

Computer-Assisted Coloring-Graph Generation And Structural Analysis, Wesley Su

Honors Theses

Graphs are a well studied construction in discrete math, with one of the most common areas of study being graph coloring. The graph coloring problem asks for a color to be assigned to each vertex in a graph such that no two adjacent vertices share a color. An assignment of k colors that meets these criteria is called a k-coloring. The coloring graph Ck(G) is defined as the graph where every vertex represents a valid k-coloring of graph G and edges exist between colorings that di↵er by one vertex. We call graph G the base graph of the k-coloring graph …

Identifying Important Parameters In The Inflammatory Process With A Mathematical Model Of Immune Cell Influx And Macrophage Polarization, Marcella Torres, Jing Wang, Paul J. Yannie, Shobha Ghosh, Rebecca A. Segal, Angela M. Reynolds

Department of Math & Statistics Faculty Publications

In an inflammatory setting, macrophages can be polarized to an inflammatory M1 phenotype or to an anti-inflammatory M2 phenotype, as well as existing on a spectrum between these two extremes. Dysfunction of this phenotypic switch can result in a population imbalance that leads to chronic wounds or disease due to unresolved inflammation. Therapeutic interventions that target macrophages have therefore been proposed and implemented in diseases that feature chronic inflammation such as diabetes mellitus and atherosclerosis. We have developed a model for the sequential influx of immune cells in the peritoneal cavity in response to a bacterial stimulus that includes macrophage …

Critical Fault-Detecting Time Evaluation In Software With Discrete Compound Poisson Models, Min-Hsiung Hsieh, Shuen-Lin Jeng, Paul Kvam

Department of Math & Statistics Faculty Publications

Software developers predict their product’s failure rate using reliability growth models that are typically based on nonhomogeneous Poisson (NHP) processes. In this article, we extend that practice to a nonhomogeneous discrete-compound Poisson process that allows for multiple faults of a system at the same time point. Along with traditional reliability metrics such as average number of failures in a time interval, we propose an alternative reliability index called critical fault-detecting time in order to provide more information for software managers making software quality evaluation and critical market policy decisions. We illustrate the significant potential for improved analysis using wireless failure …

Mean Value Theorems For Riemannian Manifolds Via The Obstacle Problem, Brian Benson, Ivan Blank, Jeremy Lecrone

Department of Math & Statistics Faculty Publications

We develop some of the basic theory for the obstacle problem on Riemannian manifolds, and we use it to establish a mean value theorem. Our mean value theorem works for a very wide class of Riemannian manifolds and has no weights at all within the integral.

Perturbed Obstacle Problems In Lipschitz Domains: Linear Stability And Nondegeneracy In Measure, Ivan Blank, Jeremy Lecrone

Department of Math & Statistics Faculty Publications

We consider the classical obstacle problem on bounded, connected Lipschitz domains D⊂Rⁿ. We derive quantitative bounds on the changes to contact sets under general perturbations to both the right-hand side and the boundary data for obstacle problems. In particular, we show that the Lebesgue measure of the symmetric difference between two contact sets is linearly comparable to the L¹-norm of perturbations in the data.

Finite Blaschke Products: A Survey, Stephan Ramon Garcia, Javad Mashreghi, William T. Ross

Department of Math & Statistics Faculty Publications

A finite Blaschke product is a product of finitely many automorphisms of the unit disk. This brief survey covers some of the main topics in the area, including characterizations of Blaschke products, approximation theorems, derivatives and residues of Blaschke products, geometric localization of zeros, and selected other topics.

Multipliers Between Model Spaces, Emmanuel Fricain, Andreas Hartmann, William T. Ross

Department of Math & Statistics Faculty Publications

In this paper we examine the multipliers from one model space to another.

The Range And Valence Of A Real Smirnov Function, Timothy Ferguson, William T. Ross

Department of Math & Statistics Faculty Publications

We give a complete description of the possible ranges of real Smirnov functions (quotients of two bounded analytic functions on the open unit disk where the denominator is outer and such that the radial boundary values are real almost everywhere on the unit circle). Our techniques use the theory of unbounded symmetric Toeplitz operators, some general theory of unbounded symmetric operators, classical Hardy spaces, and an application of the uniformization theorem. In addition, we completely characterize the possible valences for these real Smirnov functions when the valence is finite. To do so we construct Riemann surfaces we call disk trees …

A Probability Model For Strategic Bidding On The Price Is Right, Paul H. Kvam

Department of Math & Statistics Faculty Publications

The TV game show “The Price is Right” features a bidding auction called “Contestants’ Row” that rewards the player (out of 4) who bids closest to an item’s value, without overbidding. This paper considers ways in which players can maximize a winning probability based on the player's bidding order. We consider marginal strategies in which players assume opponents are bidding individually perceived values of the merchandise. Based on preceding bids of others, players have information available to create strategies. We consider conditional strategies in which players adjust bids knowing other players are using strategies. The last bidder has a large …

Optimal Weak Parallelogram Constants For L-P Spaces, Raymond Cheng, Javad Mashreghi, William T. Ross

Department of Math & Statistics Faculty Publications

Inspired by Clarkson's inequalities for L-p and continuing work from [5], this paper computes the optimal constant C in the weak parallelogram laws parallel to f + g parallel to(r )+ C parallel to f - g parallel to(r )= 2(r-1 )(parallel to f parallel to(r) + parallel to g parallel to(r)) for the L-p spaces, 1 < p < infinity.

A Unified Inter-Host And In-Host Model Of Antibiotic Resistance And Infection Spread In A Hospital Ward, Lester Caudill, Barry Lawson

Department of Math & Statistics Faculty Publications

As the battle continues against hospital-acquired infections and the concurrent rise in antibiotic resistance among many of the major causative pathogens, there is a dire need to conduct controlled experiments, in order to compare proposed control strategies. However, cost, time, and ethical considerations make this evaluation strategy either impractical or impossible to implement with living patients. This paper presents a multi-scale model that offers promise as the basis for a tool to simulate these (and other) controlled experiments. This is a “unified” model in two important ways: (i) It combines inter-host and in-host dynamics into a single model, and (ii) …