Digital Commons Network^™

Backlog Burner: An Adventure Into Automated Scheduling, Anjolaoluwa J. Olubusi

Senior Independent Study Theses

The focus of this independent study is to explain the nurse scheduling problem (NSP) and use it as a basis to create an automated scheduling program. The nurse scheduling problem is an operational research problem that sets to find an optimal hospital schedule that fulfills the needs of the hospital and the personal requests of the nurses. The majority of solutions for the nurse scheduling problem are often designed within a hospital setting. The objective of this independent study is to use the solutions of the nurse scheduling problem to develop an automated scheduling program for the College of Wooster …

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 …

Environmental Socialization In College: A Survey Research And Network Analysis Of Changes In Climate-Conscious Concerns And Behaviors, Bijeta Lamichhane

Senior Independent Study Theses

Studies have established that socialization takes place in different stages of life. This study explores how political socialization occurs at The College of Wooster by examining changes in students' political identities as well as their perceptions towards a politicized issue, that is, climate change. These shifts in beliefs and concerns among students were evaluated by implementing quantitative research tools present in the Statistical Package for Social Sciences (SPSS) and constructing a similarity network using Gephi to explore similarities across students at this institution. The results revealed that students have become more liberal after joining this college. The study also found …

Gaming The System: A Game Theoretic Approach To Risk Management And Cybersecurity, Abigail Breitenbucher

Senior Independent Study Theses

In this independent study, we detail two fields of game theory, traditional and evolutionary. After establishing foundational concepts in both, we explore risk management and cybersecurity through a game theoretic lens, focusing on some current applications in both fields. The research culminates in an application case of a game theoretic model for the 2017 Equifax data breach. To conclude, we discuss the implications of this model and future work involving evolutionary game theory in cybersecurity/risk management.

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 …

The Planar Rook Algebra, Henry Potts-Rubin

Senior Independent Study Theses

No abstract provided.

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 …

A Theory Of Fire Service Provision: With An Empirical Analysis Of Response Time, Suppression Time, And Service Output, Hyong-Gu Hwang

Senior Independent Study Theses

We introduce a two-stage theoretical framework of fire services that justifies the status of response time as a factor input. In the first stage, the provincial government distributes a budget to its cities, resulting in varied numbers of firefighters and fire engines in each city. In the second stage, each city fire department places its fire stations at spatially optimal locations that minimize expected response times. When a fire occurs, the outputs from these two stages are actualized into dispatch level, response time, and suppression time. These intermediate outputs are then transformed into inputs for producing service output, which is …

Developing A Web-Based Application For Finding Meeting Places, Aedan D. Pettit

Senior Independent Study Theses

Midway: Meeting Place Finder is a web application which allows users to supply three or more locations and provides them with a place to meet that minimizes their total driving time. Using techniques from graph theory, an algorithm is developed in order to make this service possible. Then, using Python, this algorithm is implemented into the backend of the web application along with a simple, user-friendly interface. This application has exciting potential to be continually expanded and improved in the future beyond this initial version.

Exploring Topics Of The Art Gallery Problem, Megan Vuich

Senior Independent Study Theses

Created in the 1970's, the Art Gallery Problem seeks to answer the question of how many security guards are necessary to fully survey the floor plan of any building. These floor plans are modeled by polygons, with guards represented by points inside these shapes. Shortly after the creation of the problem, it was theorized that for guards whose positions were limited to the polygon's vertices, the floor of n/3 guards are sufficient to watch any type of polygon, where n is the number of the polygon's vertices. Two proofs accompanied this theorem, drawing from concepts of computational geometry and graph …

Optimizing Timber Harvest Value: A Dynamic Programming Investigation, Kayleigh T. Dietz

Senior Independent Study Theses

Operations research models have been and continue to be integral to the implementation of forest management strategies. Fundamental operations research models such as linear and dynamic programming have respective advantages and disadvantages when applied to any forest system. An overview of five fundamental operations research models are provided in terms of a timber harvesting system. Timber production management is a branch of forest management that seeks to optimize the economic benefits of harvesting timber. The time-stage nature of timber harvesting systems makes dynamic programming a particularly useful model for timber production management. Thus, dynamic programming is the primary model discussed …

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 …

Crime Around The World: Using Mathematical Modeling Techniques To Model Aggregated Worldwide Crime Rates, Kelly M. Steurer

Senior Independent Study Theses

This aim of this study was to determine what affects aggregate crime rates around the world. This thesis used Mathematical Modeling techniques to build generalized linear models for homicide rates and burglary and housebreaking rates using the following predictive factors: economic indicators, education rates, government quality indicators, ethno-linguistic fractionalization, GDP per capita and its growth, drug consumption rates, and age and gender ratios. We used a series of factor selection techniques including linear and stepwise regressions, principal component analysis, and regression analysis to select factors to use to build final models of homicide and burglary and housebreaking.

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|.

Building A Course Recommender System For The College Of Wooster, Nan Jiang

Senior Independent Study Theses

The goal of this project is to investigate the approaches for building recommender systems and to apply them to implement a course recommender system for the College of Wooster. There are three main objectives of this project. The first is to understand the mathematics and computer science aspects behind it. The mathematic concepts built into this project include probability, statistics and linear algebra. The final product is consist of two components: a collection of Python scripts containing the implementation code of the course recommender system, and a simple user interface allowing people to use the recommender system without typing commands. …

The Search For Gto: Determining Optimal Poker Strategy Using Linear Programming, Stuart Young

Senior Independent Study Theses

This project applies techniques from game theory and linear programming to find the optimal strategies of two variants of poker. A set of optimal poker strategies describe a Nash equilibrium, where no player can improve their outcome by changing their own strategy, given the strategies of their opponent(s). We first consider Kuhn Poker as a simple application of our methodology. We then turn our attention to 2-7 Draw Poker, a modern variant onto which little previous research is focused. However, the techniques that we use are incapable of solving large, full-scale variants of poker such as 2-7 Draw. Therefore, we …

Pretending To Be Human: An Automated Theorem Prover To Write Mathematical Proofs, Khoa Nguyen

Senior Independent Study Theses

This project explores the theories of automated theorem proving and lambda calculus, and seeks to improve upon a current implementation of an automated theorem prover that produces human-like output. This software component is based on a published article titled “A Fully Automatic Theorem Prover with Human-Style Output” by M. Ganesalingam and W.T. Gowers [7], which outlines a program called robotone containing a first-order logic system (with a few modifications) able to automatically write simple direct proofs. It is designed to mimic different strategies that a human mathematician would use when facing a problem, and to write human-style proofs. The current …

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

Senior Independent Study Theses

No abstract provided.

A Comparative Analysis Of Photon And Electron Wave Functions In Spherically Symmetric Potentials, Michael Bush

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 …