Physical Sciences and Mathematics Commons^™

Counting The Moduli Space Of Pentagons On Finite Projective Planes, Maxwell Hosler

Senior Independent Study Theses

Finite projective planes are finite incidence structures which generalize the concept of the real projective plane. In this paper, we consider structures of points embedded in these planes. In particular, we investigate pentagons in general position, meaning no three vertices are colinear. We are interested in properties of these pentagons that are preserved by collineation of the plane, and so can be conceived as properties of the equivalence class of polygons up to collineation as a whole. Amongst these are the symmetries of a pentagon and the periodicity of the pentagon under the pentagram map, and a generalization of …

Wildfire Simulation Using Agent Based Modeling: Expanding Controlled Burn Season, Morgan C. Kromer

Senior Independent Study Theses

The United States is home to many different and unique forests. Prior to the 21st century, the United States Forests Service assumed that the best way to protect these forests was to put all efforts to keeping them alive. An enemy to these efforts were wildfires, thus the US adopted a complete fire suppression approach. At the turn of the century, the US realized that wildfires are a necessary part of a forest ecosystem, as they help return nutrients to the soil and reduce ground fuels. However, after suppressing all fires for over 100 years, the forests evolved into a …

Highlights Generation For Tennis Matches Using Computer Vision, Natural Language Processing And Audio Analysis, Alon Liberman

Senior Independent Study Theses

This project uses computer vision, natural language processing and audio analysis to automatize the highlights generation task for tennis matches. Computer vision techniques such as camera shot detection, hough transform and neural networks are used to extract the time intervals of the points. To detect the best points, three approaches are used. Point length suggests which points correspond to rallies and aces. The audio waves are analyzed to search for the highest audio peaks, which indicate the moments where the crowd cheers the most. Sentiment analysis, a natural language processing technique, is used to look for points where the commentators …

The Infinity Conundrum: Understanding Topics In Set Theory And The Continuum Hypothesis, Sabrina Grace Helck

Senior Independent Study Theses

This project is concerned with articulating the necessary background in order to understand the famous result of the undecidability of the continuum hypothesis. The first chapter of this independent study discusses the foundations of set theory, stating fundamental definitions and theorems that will be used throughout the remainder of the project. The second chapter focuses on ordinal and cardinal numbers which will directly relate to the final chapter. First, there is a clear explanation of the notion of order and what it means for a set to be well-ordered. Then ordinal numbers are defined and some properties are listed and …

Stroke Clustering And Fitting In Vector Art, Khandokar Shakib

Senior Independent Study Theses

Vectorization of art involves turning free-hand drawings into vector graphics that can be further scaled and manipulated. In this paper, we explore the concept of vectorization of line drawings and study multiple approaches that attempt to achieve this in the most accurate way possible. We utilize a software called StrokeStrip to discuss the different mathematics behind the parameterization and fitting involved in the drawings.

On Implementing And Testing The Rsa Algorithm, Kien Trung Le

Senior Independent Study Theses

In this work, we give a comprehensive introduction to the RSA cryptosystem, implement it in Java, and compare it empirically to three other RSA implementations. We start by giving an overview of the field of cryptography, from its primitives to the composite constructs used in the field. Then, the paper presents a basic version of the RSA algorithm. With this information in mind, we discuss several problems with this basic conception of RSA, including its speed and some potential attacks that have been attempted. Then, we discuss possible improvements that can make RSA runs faster and more secure. On the …

Option Implied Volatility's Predictability On Monthly Stock Returns, Hung T. Dao

Senior Independent Study Theses

Since the trading of options is based on underlying stocks, it is reasonable to assume that information from the options market can be used to explain the returns in the stock market. Our independent study investigates the relationship between options implied volatility and stock returns. Previous studies have found significant results in using implied volatility in predicting stock returns. This paper provides a discussion of such studies, the theoretical framework for the research topic, and the Black-Scholes model, which is famous for its application in implied volatility calculation. Monthly returns of 20 large US firms are regressed against implied volatility …

Statistical And Machine Learning Approaches To Depressive Disorders Among Adults In The United States: From Factor Discovery To Prediction Evaluation, Minhwa Lee

Senior Independent Study Theses

According to the National Institutes of Mental Health (NIMH), depressive disorders (or major depression) are considered one of the most common and serious health risks in the United States. Our study focuses on extracting non-medical factors of depressive disorders diagnosis, such as overall health states, health risk behaviors, demography, and healthcare access, using the Behavioral Risk Factor Surveillance System (BRFSS) data set collected by the Centers for Disease Control and Prevention (CDC) in 2018.

We set the two objectives of our study about depressive disorders diagnosis in the United States as follows. First, we aim to utilize machine learning algorithms …

A Mathematical Analysis Of The Game Of Santorini, Carson Clyde Geissler

Senior Independent Study Theses

Santorini is a two player combinatorial board game. Santorini bears resemblance to the graph theory game of Geography, a game of moving and deleting vertices on a graph. We explore Santorini with game theory, complexity theory, and artificial intelligence. We present David Lichtenstein’s proof that Geography is PSPACE-hard and adapt the proof for generalized forms of Santorini. Last, we discuss the development of an AI built for a software implementation of Santorini and present a number of improvements to that AI.

Modeling Community Resource Management: An Agent-Based Approach, Maya M. Lapp

Senior Independent Study Theses

As the human population continues increasing rapidly and climate change accelerates, resource depletion is becoming an international problem. Community-based natural resource management (CBNRM) has been suggested as a method to conserve resources while simultaneously empowering traditionally marginalized communities. Because classical equation-based modeling methods fail to capture the complexity of CBNRM, Agent-Based Modeling (ABM) has emerged as a primary method of modeling these systems. In this investigation, we conduct a sensitivity analysis and thorough evaluation of an existing ABM of community forest management. We then modify the original model by providing a new enforcement mechanism that improves the validity of both …

Cheat Detection Using Machine Learning Within Counter-Strike: Global Offensive, Harry Dunham

Senior Independent Study Theses

Deep learning is becoming a steadfast means of solving complex problems that do not have a single concrete or simple solution. One complex problem that fits this description and that has also begun to appear at the forefront of society is cheating, specifically within video games. Therefore, this paper presents a means of developing a deep learning framework that successfully identifies cheaters within the video game CounterStrike: Global Offensive. This approach yields predictive accuracy metrics that range between 80-90% depending on the exact neural network architecture that is employed. This approach is easily scalable and applicable to all types of …

Sports Analytics With Computer Vision, Colby T. Jeffries

Senior Independent Study Theses

Computer vision in sports analytics is a relatively new development. With multi-million dollar systems like STATS’s SportVu, professional basketball teams are able to collect extremely fine-detailed data better than ever before. This concept can be scaled down to provide similar statistics collection to college and high school basketball teams. Here we investigate the creation of such a system using open-source technologies and less expensive hardware. In addition, using a similar technology, we examine basketball free throws to see whether a shooter’s form has a specific relationship to a shot’s outcome. A system that learns this relationship could be used to …

Logic -> Proof -> Rest, Maxwell Taylor

Senior Independent Study Theses

REST is a common architecture for networked applications. Applications that adhere to the REST constraints enjoy significant scaling advantages over other architectures. But REST is not a panacea for the task of building correct software. Algebraic models of computation, particularly CSP, prove useful to describe the composition of applications using REST. CSP enables us to describe and verify the behavior of RESTful systems. The descriptions of each component can be used independently to verify that a system behaves as expected. This thesis demonstrates and develops CSP methodology to verify the behavior of RESTful applications.

Inclusion Of Blocking Power For A Complete Voting Power Analysis In The Imf, Shiwani Varal

Senior Independent Study Theses

The International Monetary Fund (IMF) calculates the voting power of a country by dividing the total of one member's votes by the total of all members' votes. This method of calculating the power of a state judges power as voting weight. However, voting weights are the total number of votes a country has in an institution, while voting power is the influence a country has on a policy decision. A better approach to calculate this voting power within an institution is by using voting power indices. However, literature only calculates the winning power, while voting power is defined as the …

On Degree Bound For Syzygies Of Polynomial Invariants, Zhao Gao

Senior Independent Study Theses

Suppose G is a finite linearly reductive group. The degree bound for the syzygy ideal of the invariant ring of G is given in [2]. We develop the theory of commutative algebra and give the proof from [2] that the ideal of relations of the minimal set of generators of invariant ring of a finite linearly reductive group G is generated in degree at most 2|G|.

Legalization Of Prostitution And Its Impact On The Market For Human Trafficking, Varunavi Newar

Senior Independent Study Theses

No abstract provided.

Optimal Placement Of Family Planning Centers, Kiera Dobbs

Senior Independent Study Theses

This project investigates and begins to solve the problem of access to family planning services in the United States. We research and implement methods in Operations Research to optimize the location of publicly funded family planning centers in the United States by minimizing travel distance. The solution begins with a designated number of family planning centers for the country. An apportionment integer programming algorithm is then exercised to allocate centers to all the states based on population, percent of population in poverty, and state square mileage. At the state level, we use apportionment again to distribute centers to counties. At …

I Don't Play Chess: A Study Of Chess Piece Generating Polynomials, Stephen R. Skoch

Senior Independent Study Theses

This independent study examines counting problems of non-attacking rook, and non-attacking bishop placements. We examine boards for rook and bishop placement with restricted positions and varied dimensions. In this investigation, we discuss the general formula of a generating function for unrestricted, square bishop boards that relies on the Stirling numbers of the second kind. We discuss the maximum number of bishops we can place on a rectangular board, as well as a brief investigation of non-attacking rook placements on three-dimensional boards, drawing a connection to latin squares.

Keeping Your Options Open: An Introduction To Pricing Options, Ryan F. Snyder

Senior Independent Study Theses

An option is a contract which gives the holder of the option the right, but not the obligation, to buy or sell a given security at a given price, which is called the strike price. For example, suppose Yahoo stock is currently trading at $10 per share. A person could buy an option that gives him or her the ability to purchase shares of Yahoo stock for $12 in one year. If the price of Yahoo stock is greater than $12 in one year, the holder of the option will make money. However, he or she will not use the …

A Bayesian Model Of Fertility Decisions In Relationship To Female Labor Force Participation, Rebecca C. Wardrop

Senior Independent Study Theses

Due to the increasing number of women in the labor force, opportunity costs associated with labor force participation are becoming an important factor in fertility decisions. Further, these decisions are assumed to be dynamic as the opportunity costs change as a woman progresses through her career. A Bayesian statistical model , which allows the distribution of the likelihood of having children to be updated as information is gathered, lends itself to the dynamicity of the decision-making process. A generalized model for fertility decisions in terms of labor force participation is created. I also discuss potentials for implementation and furthering the …

Generalist And Specialist Pollination Syndromes: When Are They Favoured? A Theoretical Approach To Predict The Conditions Under Which A Generalist Or Specialist Pollination Syndrome Is Favoured., Tyler L. Poppenwimer

Senior Independent Study Theses

No abstract provided.

Markov Chain Theory With Applications To Baseball, Cal D. Thomay

Senior Independent Study Theses

The applications of Markov chains span a wide range of fields to which models have been designed and implemented to simulate random processes. Markov chains are stochastic processes that are characterized by their memoryless property, where the probability of the process being in the next state of the system depends only on the current state and not on any of the previous states. This property is known as the Markov property. This thesis paper will first introduce the theory of Markov chains, along with explaining two types of Markov chains that will be beneficial in creating a model for analyzing …

The Analytic Hierarchy Process: A Mathematical Model For Decision Making Problems, Giang Huong Nguyen

Senior Independent Study Theses

The ability to make the right decision is an asset in many areas and lines of profession including social work, business, national economics, and international security. However, decision makers often have difficulty choosing the best option since they might not have a full understanding of their preferences, or lack a systematic approach to solve the decision making problems at hand. The Analytic Hierarchy Process (AHP) provides a mathematical model that helps the decision makers arrive at the most logical choice, based on their preferences. We investigate the theory of positive, reciprocal matrices, which provides the theoretical justification of the method …

The Machete Number, David Freund

Senior Independent Study Theses

Knot theory is a branch of topology that deals with the structure and properties of links. Employing a variety of tools, including surfaces, graph theory, and polynomials, we develop and explore classical link invariants. From this foundation, we de fine two novel link invariants, braid height and machete number, and investigate their properties and connection to classical invariants.

Let's Get In The Mood: An Exploration Of Data Mining Techniques To Predict Mood Based On Musical Properties Of Songs, Sarah Smith-Polderman

Senior Independent Study Theses

This thesis explores the possibility of predicting the mood a song will evoke in a person based on certain musical properties that the song exhibits. First, I introduce the topic of data mining and establish its significant relevance in this day and age. Next, I explore the several tasks that data mining can accomplish, and I identify classification and clustering as the two most relevant tasks for mood prediction based on musical properties of songs. Chapter 3 introduces in detail two specific classification techniques: Naive Bayes Classification and k-Nearest Neighbor Classification. Similarly, Chapter 4 introduces two specific clustering techniques: …

The Truth About Lie Symmetries: Solving Differential Equations With Symmetry Methods, Ruth A. Steinhour

Senior Independent Study Theses

Differential equations are vitally important in numerous scientific fields. Oftentimes, they are quite challenging to solve. This Independent Study examines one method for solving differential equations. Norwegian mathematician Sophus Lie developed this method, which uses groups of symmetries, called Lie groups. These symmetries map one solution curve to another. They can be used to determine a canonical coordinate system for a given differential equation. Writing the differential equation in terms of a different coordinate system can make the equation simpler to solve. This I.S. explores techniques for finding a canonical coordinate system and using it to solve a given differential …

Iteration Digraphs, Hannah Roberts

Senior Independent Study Theses

No abstract provided.