Physical Sciences and Mathematics Commons^™

Studying Extended Sets From Young Tableaux, Eric S. Nofziger

Undergraduate Honors Thesis Collection

Young tableaux are combinatorial objects related to the partitions of an integer that have various applications in representation theory. These tableaux are defined as a left-justified set of n boxes filled with the numbers 1 through n and organized in rows, with the length of each row corresponding to a summand in the partition. In recent work of Graham–Precup–Russell, an association has been made between a given row-strict tableau and three disjoint subsets I, J, and K, also called extended sets. In this project, we begin to classify which extended sets correlate to a valid row-strict or standard tableau. We …

Identifying How Home Advantage Manifests In Butler Basketball Using Sfa, Emily M. Shoemaker

Undergraduate Honors Thesis Collection

Butler University’s basketball team has been in the Big East Conference since 2013 and is known for having a distinct home court advantage named ‘Hinkle Magic’ by fans. It is of interest to identify how home court advantage affects a Big East team’s ability to play to its full potential for generating wins and what factors are most accurate in measuring this potential. This project will utilize the Stochastic Frontier Approach (SFA) model to identify a team’s efficiency when playing at home vs. away in order to identify when teams meet their potential and if game location has an effect …

Home Sweet Home: A Statistical Analysis Of Home Court Advantage In Division I College Basketball, Lauren Isabel Turnbull

Undergraduate Honors Thesis Collection

Home court advantage is a term that has been used throughout the basketball world by everyone from broadcasters and TV analysts to athletes and coaches to fans. It is a reference to the perceived benefit that the home team receives by playing in their own arena or stadium. Much of the prior research on home court advantage has centered around the reasons that it exists and how it impacts the play on the court through box score statistics. Building on this previous research, this study performs a statistical analysis of men's college basketball to determine if home court advantage is …

Kamila Clustering For A Mixed-Type Data Analysis Of Illinois Medicare Data, Heather Elizabeth Baldacci

Undergraduate Honors Thesis Collection

The Centers for Medicare and Medicare Services (CMS) releases annual reports regarding the Market Saturation and Utilization of nationwide Medicare coverage. CMS data provide an opportunity for an in-depth analysis of Medicare usage patterns within the United States that may provide insight into socioeconomic conditions in certain regions. To discover any potential patterns, the KAMILA (KAy-means for MIxed LArge data sets) clustering algorithm has been utilized within the most recent CMS dataset from 2018. Due to the large size of the original data set, the focus of this research has been limited to Illinois Medicare data, grouped by the 102 …

Model-Based Cluster Analysis Of Indiana Social Security Beneficiary Data, Gwendolyn Spencer

Undergraduate Honors Thesis Collection

Annual reports of the U.S. Old-Age, Survivors, and Disability Insurance (OASDI) program, published by the Social Security Administration, detail the aggregate information about the program for each U.S. Postal ZIP code. This information includes the types of beneficiaries and monthly benefits received. These reports present the opportunity for contemporary analysis of the aggregate information about the OASDI program. To better capture the significance of the most-recent report for 2018, this project will use model-based cluster analysis, the unsupervised machine-learning process of grouping similar data points, to compare the 2017 and 2018 data. Due to the large amount of data, the …

Investigating The Factors That Best Describe Student Experience And Performance In College, Abigale Wynn

Undergraduate Honors Thesis Collection

The National Survey of Student Engagement (NSSE) surveys students at four-year institutions around the United States in order to offer Universities accessible ways to evaluate their students' experiences and performance. The NSSE data is collected in the form of a Likert-scale survey geared towards first year and senior year students. It asks questions about how they spend their time throughout the academic year and how they rate their experience. This thesis looks at the NSSE survey data from Butler University in 2016 and attempts to apply classification techniques and predictive models to draw conclusions about student performance. Methods such as …

Utilizing Multi-Level Classification Techniques To Predict Adverse Drug Effects And Reactions, Victoria Puhl

Undergraduate Honors Thesis Collection

Multi-class classification models are used to predict categorical response variables with more than two possible outcomes. A collection of multi-class classification techniques such as Multinomial Logistic Regression, Na\"{i}ve Bayes, and Support Vector Machine is used in predicting patients’ drug reactions and adverse drug effects based on patients’ demographic and drug administration. The newly released 2018 data on drug reactions and adverse drug effects from U.S. Food and Drug Administration are tested with the models. The applicability of model evaluation measures such as sensitivity, specificity and prediction accuracy in multi-class settings, are also discussed.

Sub-Cloning, Expression, And Purification Of The Wild Type And Mutated Sigma-1 Receptor, Christopher Koch

Undergraduate Honors Thesis Collection

The Sigma-1 receptor (S1R) is an important pharmaceutical target that has been linked to several neurological diseases and drug addiction. It has been proposed that multimerization of S1R is important for attenuating its interactions with the dopamine transporter (DAT) and that S1R agonists promote dissociation to a monomeric form necessary for DAT interaction. This project aims to assess the role of the N-terminal transmembrane domain in oligomerization and binding activity of the mammalian Sigma-1 receptor (S1R). N-terminal truncations lacking the transmembrane domain and the E102Q variant, which displays altered activity and cellular localization, were expressed, purified in order to determine …

Limits Of Julia Sets For Sums Of Power Maps And Polynomials, Micah Brame

Undergraduate Honors Thesis Collection

Suppose f_{n,c} is a complex-valued mapping of one complex variable given by f_{n,c}(z) = z^n + p(z) + c, where p is a polynomial such that p(0) = 0 and c is a complex parameter such that |c| < 1. We provide necessary and sufficient conditions that the geometric limit, as n approaches infinity, of the set of points that remain bounded under iteration by f_{n,c} is the disk of radius 1 centered at the origin.

Crossed Product Algebras Over Dihedral Field Extensions, Kaitlyn Lee

Undergraduate Honors Thesis Collection

Let F be the field of fractions of R, a ring of power series with coefficients in some field. Let K/F be a finite Galois extension, and assume the integral closure S of R in K is also a power series ring.

In this paper, we consider a construction from ring theory called a crossed product algebra and an associated function f: G × G →K called a cocycle that is used to define a multiplication operation for the crossed product algebra. Consider a crossed product algebra whose cocycle f takes values in S. We give a proof concerning which …

Complexities Of Bi-Colored Rubik's Cubes, Taylor Pieper

Undergraduate Honors Thesis Collection

Which of two bi-colored cubes is the simpler puzzle? The differences in the coloring of the cubes creates different symmetries that dramatically reduce the number of states each cube can reach. Which of the symmetries is most reductive? The answer to these questions can be achieved by discovering and comparing the “God’s Number” for these cubes.

A Computational And Theoretical Exploration Of The St. Petersburg Paradox, Alexander Olivero

Undergraduate Honors Thesis Collection

This thesis displays a sample distribution, generated from both a simulation (for large n) by computer program and explicitly calculated (for smaller n), that is not governed by the Central Limit Theorem and, in fact seems to display chaotic behavior. To our knowledge, the explicit calculation of the sample distribution function is new. This project outlines the results that have found a relation to number theory in a probabilistic game that has perplexed mathematicians for hundreds of years.

Symmetries And Patterns In Non-Euclidean Settings, Sarah Elizabeth Stoops

Undergraduate Honors Thesis Collection

From the Megalithic Temples of Malta constructed over 5,500 years ago, to the Pyramid of Djoser in Egypt built some 4,700 years ago, to more recent works of architectural wonder such an the Taj Mahal, the testimonials to the innate human genius for creating beauty through symmetry, color, and patterns abound. Evidently, the mathematical underpinnings of many architectural marvels are mostly rooted in the Euclidean Geometry. Now, as marvelous as these monuments are, one may wonder what would be the concepts of beauty and symmetry in a non-Euclidean universe. It turns out that this is not a far-fetched thought. It …

Generalized Mandelbrot Sets, Aaron Schlenker

Undergraduate Honors Thesis Collection

A complex point Z₀ is defined to be a member of the famous Mandelbrot set fractal when the iterative process using the function Z² stays bounded when applied to Z₀. We investigate what happens if we change the iterative process so that Z² is now composed with, for example, a Mobius transformation, indexed on a parameter a. The Mandelbrot set corresponds to a = O. What happens when we change a = 0 to other values, repeating the iterative process and then drawing the sets? Do these Generalized Mandelbrot sets have similar properties to …

A Three-Part Study In The Connections Between Music And Mathematics, Molly Elizabeth Anderson

Undergraduate Honors Thesis Collection

The idea for this thesis originated from my fascination with the studies of both music and mathematics throughout my entire life. As a triple major in Middle/Secondary Math Education, Mathematics, and Music, I have learned more than I thought possible of music and math. In proposing this thesis, I desired to use my knowledge of arithmetic and aesthetics to research how music and mathematics are intertwined. I am confident that the following three chapters have allowed me to develop as an academic in both music and mathematics. This thesis serves as a presentation of the connections of music and math …

Constructions And Enumeration Methods For Cubic Graphs And Trees, Erica R. Gilliland

Undergraduate Honors Thesis Collection

The goal of this thesis is to study two related problems that, in the broadest terms, lie in a branch of mathematics called graph theory. The first problem examines some new techniques for constructing a Hamilton graph of least possible order and having a preassigned girth, and the second concerns the enumeration of a certain type of graphs called trees.