# 2022 College of Engineering and Science Design and Research Conference

## Mathematics and Statistics

### Room 302.

1:00 p.m.

#### Statistical Analysis of Home-Field Advantage in European Soccer

Team Member: Francisco Simoncini

Advisor: Mr. Stan McCaa

Home-field advantage in the sports world is commonly known as a huge factor in determining the final score of any sports game. By using a one-tailed, two-sample t-test, I am analyzing how playing at home generally affects a European soccer team’s performance. I am looking at how these performances are affected across three domestic leagues in Europe. I predict that when teams play at home, there will be a significant difference in their win ratio and goals scored.

1:30 p.m.

#### Predicting Box Office Revenue using Differential Equation Models

Team Member: Brenden David

Advisor: Dr. Dave Meng

The growing popularity of the internet has increased exponentially in the past few decades. This sudden increase in popularity allows for users to gain access to more information than was thought possible in the past, including access to box-office movie revenues of previously released movies. Since we now have access to thousands of movies’ box office revenues, we can analyze some sort of trend within specific genres of movies. With these trends, we developed a differential equations model that will predict the box office revenues of a movie that is in its early stages of the box office. This model can be used to see at which time, during the movie’s box office lifespan, would be the best predictor of movie revenue.

2:00 p.m.

#### A Study of Nash Equilibrium in Discrete Cases

Team Member: Hallye Leleux

Advisor: Dr. Jonathan Walters

In game theory, Nash Equilibrium refers to a set of strategies in a non-cooperative game in which no player can benefit from changing their strategy. This paper examines the payoff matrices of the notable discrete games Battle of the Sexes, Matching Pennies, and The Prisoner’s Dilemma. We then create a custom discrete two-player case and determine the pure and mixed strategy Nash Equilibria. After calculating the probabilities for each mixed strategy, we then determine the resulting payoff for each player and show how deviating from that strategy results in a lower payoff.

2:30 p.m.

#### Flood Risk Prediction in Southern Louisiana using Support Vector Machines

Team Member: Claire Dorsett

Advisor: Dr. Xiyuan Liu

Flooding in Southern Louisiana is a growing concern as violent weather becomes more frequent. According to the Environmental Protection Agency (EPA), Louisiana soils have become drier and annual rainfall trends have increased. The United States Geological Survey (USGS) reports that the protective wetlands of Southern Louisiana are being lost at a rate of 75 square kilometers per year. In light of this change in weather trends and geography, the occurrence of more frequent flooding is likely. Thus, accurate flood prediction has become increasingly important for the public’s safety. The focus of this paper is to apply support vector machines (SVM), a machine learning technique, to classify flood risks based on water gage height, wind speed and direction, and time of the year. In this paper, the methodology of this technique is discussed, and the support vector machine method is applied to data collected by the National Weather Service (NWS) and the US Army Corps of Engineers using the R language. This paper will examine the results of support vector machines of varying kernels to discern which support vector machine is most effective and if this technique is a valid choice for flood risk prediction.

3:00 p.m.

#### Hypothesis Testing of Students’ Mathematical Performance in Relation to the COVID-19 Pandemic

Team Member: Elizabeth Foster

Advisor: Dr. Brian Barron

The COVID-19 Pandemic affected everyone, especially schools and education due to the rapid switch from traditional face-to-face classes to online and hybrid classes. The goal of this study is to see how the pandemic affected students’ grades during distance learning when compared to before. Using hypothesis testing, we will analyze data from 17 sections of MATH 243 classes to determine if the averages went down during the pandemic, specifically in hybrid class settings. Based on the raw data of the test grades in relation to the COVID-19 Pandemic, a significant difference can be found in test scores before and during the Pandemic. The preliminary hypothesis that we will be testing is that the average decreased during hybrid classes compared to face-to-face classes.

3:30 p.m.

#### Factors that Relate to Academic Excellence

Team Member: Matthew Lemoine

Advisor: Mr. Stan McCaa

The American College Testing (ACT) provides university admissions offices a look into a student’s academic ability so that the university can determine admittance and scholarships. The premise of this study is to see whether this is the most effective way to determine academic ability using the logistic regression model. The data was collected from October 21, 2021, to December 31, 2021, at Louisiana Tech University. Using the logistic regression model, predictions of academic excellence are obtained based on the parameters outlined in this paper. After the parameters for the logistic regression model are calculated, conclusions can be drawn that the ACT is not an effective predictor of academic excellence.

4:00 p.m.

#### Implementing a Key Exchange Protocol using Isogenies on Elliptic Curves in Python

Team Member: Thomas Schwartzenburg

Advisor: Dr. Aaron Hutchinson

The study of elliptic curves continues to reveal more secure and efficient methods to encrypt information. For example, in De Feo, Jao, and Plut’s paper “Towards Quantum Resistant Cryptosystems from Supersingular Elliptic Curve Isogenies,” the authors provide an abstract key-exchange protocol using isogonies on supersingular elliptic curves. The main idea of this research is to present an accurate manifestation of the abstract protocol constructed by De Feo et al., which will be realized using Python Programming Language. This protocol is founded in the Diffie-Hellman algorithm using isogenies on elliptic curves as its primary operation. Background on elliptic curve cryptography will also be provided in order to fully understand the presented encryption process.