Physical Sciences and Mathematics Commons^™

An Unsupervised Machine Learning Algorithm For Clustering Low Dimensional Data Points In Euclidean Grid Space, Josef Lazar

Senior Projects Spring 2024

Clustering algorithms provide a useful method for classifying data. The majority of well known clustering algorithms are designed to find globular clusters, however this is not always desirable. In this senior project I present a new clustering algorithm, GBCN (Grid Box Clustering with Noise), which applies a box grid to points in Euclidean space to identify areas of high point density. Points within the grid space that are in adjacent boxes are classified into the same cluster. Conversely, if a path from one point to another can only be completed by traversing an empty grid box, then they are classified …

Comparing Voting Strategies In Blood On The Clocktower, Marty Graham

Senior Projects Spring 2023

This project models a social deduction game called “Blood on the Clocktower.” Simulated players act according to two different algorithms, and the results are recorded across four different variables. The results show that the two algorithms, while constrained to affecting one specific mechanic within the game, produce statistically different results. This model has the potential to be used in simulating group dynamics and modeling the efficacy of certain game strategies.

Writing At The Horizon: How Producing Imagined Narratives Affects Mood, David Yu-Zhong Liang

Senior Projects Fall 2021

The present study explores the effect of three different writing activities and their subsequent effects on participant mood. Writing has been of particular interest for psychologists due to its use in interventions aimed at working through traumatic or stressful periods, and recent research has begun to explore the use of narrative in placing traumatic events and experiences in greater context. However, purely therapeutic, intervention-based writing exercises exclude a large amount of more expressive, imagined creations and narratives, which may have the capacity to reorient, contextualize, and otherwise positively affect a person’s mood. This study investigates whether employing the imagination may …

Chase-Escape On Sparse Networks, Emma Sylvie Bernstein

Senior Projects Spring 2020

Chase-escape is a competitive growth process in which prey spread through an environment while being chased and consumed by predators. The environment is typically modeled by a graph—such as a lattice, tree, or clique—and the species by particles competing to occupy sites. It is arguably more natural to study these dynamics in heterogeneous environments. To this end, we consider chase-escape on a canonical sparse random graph called the Erdo ̋s-R ́enyi graph. We show that if prey spreads too slowly then both species quickly die out. On the other hand, if prey spreads fast enough, then coexistence occurs. Concrete bounds …

Analyzing The Probabilistic Spread Of A Virus On Various Networks, Teagan Decusatis

Senior Projects Spring 2018

In this project we model the spread of a virus on networks as a probabilistic process. We assume the virus breaks out at one vertex on a network and then spreads to neighboring vertices in each time step with a certain probability. Our objective is to find probability distributions that describe the uncertain number of infected vertices at a given time step. The networks we consider are paths, cycles, star graphs, complete graphs, and broom graphs. Through the use of Markov chains and Jordan Normal Form we analyze the probability distribution of these graphs, characterizing the transition matrix for each …

Expected Value And Standard Deviation Of The Center Of Mass Of Random Configurations, Thuy Linh Nguyen

Senior Projects Spring 2018

The goal of this project is to find the expected value and standard deviation of the center of mass in selected random configurations. The center of mass, which is a unique point in a system where the mean distribution of the mass is located, is calculated by dividing the sum of all of the the masses times the position they are at by the total mass of the system. The configurations considered in the paper vary upon the way we choose the positions in the configuration. In his senior project, Finn Hardy determined that the expected value of the center …

Quantifying The Effect Of The Shift In Major League Baseball, Christopher John Hawke Jr.

Senior Projects Spring 2017

Baseball is a very strategic and abstract game, but the baseball world is strangely obsessed with statistics. Modern mainstream statisticians often study offensive data, such as batting average or on-base percentage, in order to evaluate player performance. However, this project observes the game from the opposite perspective: the defensive side of the game. In hopes of analyzing the game from a more concrete perspective, countless mathemeticians - most famously, Bill James - have developed numerous statistical models based on real life data of Major League Baseball (MLB) players. Large numbers of metrics go into these models, but what this project …

On Elegance, Form, And Function: Exploring The Nexus Between Scientific Research And Movement Research, Naja N. Gordon

Senior Projects Fall 2016

Live performance is an inimitable opportunity for a transfer of energy between viewer and performer. Through movement, I attempt to provide a foundation for this transfer. At the heart of my practice is a deep curiosity about movement as it relates to energy, a truly indestructible force. Moreover, systems need energy in order to function. When I think of a dance as a system, or a collection of dancers on stage as a system, the energy that feeds them is the energy that makes a composition .There is kinetic and potential energy within physical practice, incandescent energy from the lights, …

Random Walks On Thompson's Group F, Sarah C. Ghandour

Senior Projects Fall 2016

In this paper we consider the statistical properties of random walks on Thompson’s group F . We use two-way forest diagrams to represent elements of F . First we describe the random walk of F by relating the steps of the walk to the possible interactions between two-way forest diagrams and the elements of {x0,x1}, the finite generating set of F, and their inverses. We then determine the long-term probabilistic and recurrence properties of the walk.

Radical Recognition In Off-Line Handwritten Chinese Characters Using Non-Negative Matrix Factorization, Xiangying Shuai

Senior Projects Spring 2016

In the past decade, handwritten Chinese character recognition has received renewed interest with the emergence of touch screen devices. Other popular applications include on-line Chinese character dictionary look-up and visual translation in mobile phone applications. Due to the complex structure of Chinese characters, this classification task is not exactly an easy one, as it involves knowledge from mathematics, computer science, and linguistics.

Given a large image database of handwritten character data, the goal of my senior project is to use Non-Negative Matrix Factorization (NMF), a recent method for finding a suitable representation (parts-based representation) of image data, to detect specific …