COLLEGE OF ENGINEERING & SCIENCE
Mathematics & Statistics Presentations
Presentation Schedules
Room 301 Presentations: Join us on Zoom.
1:00 p.m. |
Glucose Regulation Using an Intelligent PID ControllerTeam Members: Parker Willmon |
1:15 p.m. |
The SIR Models, Their Applications, and Approximations of Their RatesTeam Members: Christopher Cano |
1:30 p.m. |
A Novel Method for Computations of Ratios of Jet Cross Sections in Perturbative Quantum ChromodynamicTeam Members: Connor Waits |
1:45 p.m. |
Forecasting Daily Stock Market Return with Multiple Linear RegressionTeam Members: Shengxuan Chen |
2:00 p.m. |
The Shallow Water EquationsTeam Members: Chase Jones |
2:15 p.m. |
The Theory of Cryptography In BTcoinTeam Members: Can Hong |
2:45 p.m. |
Impact of Eating and Sleeping Prior to Test TakingTeam Members: Cassidy Meadows |
3:00 p.m. |
Periodic Points and Sharkovsky’s TheoremTeam Members: Luke J. Seaton |
3:15 p.m. |
The Prediction of Fantasy FootballTeam Members: Chelsea Robinson |
3:30 p.m. |
The Axiom of Choice and Related TopicsTeam Members: Bryan McCormick |
3:45 p.m. |
Strategies and Algorithms of SudokuTeam Members: Callie Weaver |
4:00 p.m. |
Bridge to Bulldogs: A Student and Financial AnalysisTeam Members: Rebekah Moss |
4:15 p.m. |
Predicting and Comparing the Stock Value of Chick-fil-ATeam Members: Mark Yates |
Abstracts
Glucose Regulation Using an Intelligent PID Controller
Type 1 diabetes is a condition characterized by a lack of insulin production. This lack of insulin causes glucose concentration in the blood to increase after meals. In order to maintain blood glucose levels, diabetics must inject insulin using needles or an insulin pump. Additionally, the lack of insulin can cause glucose levels to decrease overnight. This project uses a proportional-integralderivative (PID) controller to modify the rate of insulin and glucagon infusion when glucose levels are increasing or decreasing, respectively.
A system of 12 differential equations was used to anticipate changes in glucose concentration as insulin and glucagon were injected. The system was simulated for virtual patients over a 24-hour time span to test its feasibility in human patients. The PID controller uses the current, past, and anticipated future glucose levels, respectively, to determine the best course of treatment for the virtual patient.
One of the many difficulties in medical technology, however, is everyone is different. These differences are a result of metabolism and other factors. To account for these differences, the controller is designed to change the gain of the different controller components to better tailor the treatment to each patient.
The SIR Models, Their Applications, and Approximations of Their Rates
The SIR (susceptible-infected-recovered) models are used to help predict the spread of diseases. The goals of this paper are: elaborating on the methods of approximating the recovery rate, infection rate, and loss of immunity rate; comparing the SIR models with these approximation methods to real-world data, and determining the most accurate combination of the approximation methods for each SIR model. There are several SIR models such as the Kermack-McKendrick, SIRS, and SI models that are designed for specific diseases. Understanding the parameters of these models will assist us in maximizing their accuracy. For example, there is no explicit formula for any of the rates within the models. Therefore, those rates must be approximated. Using these models to represent real-world situations will explain why each disease needs to be represented by a specific model. Understanding the content and the rate approximations of each model can help determine the level of accuracy the model will have in predicting the spread of the disease.
A Novel Method for Computations of Ratios of Jet Cross Sections in Perturbative Quantum Chromodynamic
The strong interaction is the force responsible for binding quarks to form hadrons, such as protons and neutrons, and also for binding protons and neutrons to form the nuclei of atoms. The properties of the strong interaction can be studied in particle collisions from measurements of the production rates of collimated sprays of particles, called jets. In particular, the ratio of the number of collisions that produce three jets over the number of collisions that produce two jets is a direct measure of the strength of the strong interaction, which is quantified by the strong coupling constant. Determinations of the strong coupling constant from particle collider data require theoretical calculations. In this paper, a new approach for the theoretical calculations that differs from the commonly used approach is investigated. Computations of the results are presented for different ratio measurements performed at the CERN Large Hadron Collider and the Fermilab Tevatron Collider. The results of the two different approaches are compared to each other and to the results of the experimental measurements. It is discussed in which kinematical regions the two approaches agree and where they differ.
Forecasting Daily Stock Market Return with Multiple Linear Regression
The purpose of this project is to use data mining and big data analytic techniques to forecast daily stock market returns with multiple linear regression. Using mathematical and statistical models to analyze the stock market is important and challenging. The accuracy of the final results relies on the quality of the input data and the validity of the methodology. In the report, within a 5-year period, the data regarding eleven financial and economical features are observed and recorded on each trading day. After preprocessing the raw data with the statistical method, we use the multiple linear regression to predict the daily return of the S&P 500 Index ETF (SPY). A model selection procedure is also completed to find the most parsimonious forecasting model.
The Shallow Water Equations
For this project, we are doing research on the shallow water equations: a set of hyperbolic partial differential equations. These equations exist as a set of three primary equations. However, there is another version of the shallow water equations called the Saint Venant’s equations. These equations are similar to the standard shallow water equations but are reduced to one-dimension. The primary goal of our research is to investigate the behavior and mathematical construction of the Saint Venant’s equations and model these equations using COMSOL. Regardless of the equation type, standard or Saint Venant’s, it is useful to note that these equations are only applicable under some restrictions such as hydrostatic balance and the distance from one crest to another, on any two waves, must be greater than the distance from the free surface to the sea floor (bottom topography). These restrictions, along with initial conditions, are also a target in this research, and these conditions and equations can help with flood predictions and regulations not only now, but also in the future.
The Theory of Cryptography in BTcoin
Bitcoin is a well known virtual currency, or cryptocurrency. It was created by a group of people using the name Satoshi Nakamoto in 2008. Currently, many people are utilizing Bitcoin for personal gains and transactions. To keep transactions secure requires techniques from modern cryptography. In this paper, we explain certain aspects of the cryptography of Bitcoin. We are going to discuss two components of the cryptography of Bitcoin— hash functions and signatures. We will describe what the hash function and signature are, give some examples of hash functions, and discuss certain criteria that good hash functions should satisfy.
Impact of Eating and Sleeping Prior to Test Taking
This paper addresses an ongoing issue that many high schools nationwide are having with low test scores in mathematics. There are many different factors that could be contributing to this problem. Questions that we must ask in solving this problem are whether what a student eats and how much sleep they receive are factors?” If the answers to these questions are yes, how beneficial would it be to be able to assist students in their academics by teaching them about the best times to eat and how to improve sleep habits to improve their test scores? Students long for an easy yet efficient way to improve their mathematics test scores, and knowing the best times to eat and sleep could lead to a simple plan that could help without adding additional classroom work or study time. A survey is given to students prior to testing to identify whether they ate and how much sleep they received prior to their exam. The goal of this project is to research and extract data on whether or not eating prior to taking a test is associated with higher mathematics test scores among high school students while also taking sleep into account.
Periodic Points and Sharkovsky’s Theorem
The number of periodic points of a function depends on the context. The number of complex periodic points and rational periodic points have been shown to be infinite and finite, respectively, if f is a polynomial of degree at least 2. However, the number of real periodic points can be either finite or infinite. Sharkovsky’s Theorem states that if p is left of q in the “Sharkovsky ordering” and the continuous function f has a point of period p, then f also has a point of period q. This statement becomes very powerful when considering a function that has points of period 3, all the way to the left side of the Sharkovsky ordering, since having a point of period 3 implies the existence of points of all periods. We explore a continuous function with points of period 3 where the function can be restricted to an interval containing points of period all other natural numbers.
The Prediction of Fantasy Football
In this paper, we consider the game fantasy football, which allows people to simulate being a National Football League team owner. Imaginary owners select from the best players in the NFL and compete on a weekly basis based upon player performances on the field. Fantasy football has become popular over the years. In 2011, according to the Fantasy Sports Trade Association, there were 35 million people that played fantasy sports online in the United States and Canada. Some of the major companies that use fantasy football are Yahoo, ESPN, and the NFL, although there are more platforms. Many people use these platforms to view NFL reporting, preseason rankings, player statistics, fantasy points projections, and expert opinions on drafts. Even though fantasy sports have increased over time and there are various platforms to view stats and predictions, there is no method that provides a strategy to predict the entire fantasy football league.
During this project, we will predict NFL players’ performances on the field and calculate their fantasy points for the next season using the autoregression integrated moving average (ARIMA) models using players’ historical data. We will use the data from these predictions and an algebraic equation to rank players by overall fantasy prediction points for the 2020 fantasy draft.
The Axiom of Choice and Related Topics
This project covers the axiom of choice and two mathematical statements which are equivalent to it. The axiom of choice is an axiom of Zermelo-Fraenkel set theory that states that given a collection of non-empty sets, there exists a choice function which selects one element from each set to form a new set. The equivalents of the axiom of choice that are discussed in this project include Zorn’s Lemma, which states that a partially ordered set with every chain being bounded above contains a maximal element, and the Well-Ordering Theorem, which states that every set has a well ordering. In addition to proving the equivalence of these statements, this project explains the mathematics required to prove them individually, as well as various mathematical consequences of the statements.
Strategies and Algorithms of Sudoku
This paper discusses different strategies for the game of Sudoku and how those strategies relate to other problem-solving techniques while also attempting to use those other techniques in a way that improves the strategies for Sudoku. This includes a thorough analysis of the general algorithm and an algorithm that is formed by the Occupancy Theorem and Preemptive Sets. This paper also compares these algorithms that directly relate to Sudoku with algorithms to similar combinatorial problems such as the Traveling Salesman problem and more. With the study of game theory becoming more popular, these strategies have also been shown to help students in various ways in the classroom. To understand Sudoku on a deeper level, this paper demonstrates ways to model a puzzle by using permutation matrices and different symmetries.
Bridge to Bulldogs: A Student and Financial Analysis
In this paper, we discuss the statistical analysis of the Bridge to Bulldogs program. The program provides prospective students, who do not meet all of the admission requirements, an alternate route of admission to Louisiana Tech University. It is offered over two consecutive quarters, either summer/fall or fall/winter. During the program, students focus on building their math skills through tutoring and special advising. We compare the Bridge students to other first-time freshmen in relation to scores in freshman-level math classes. We also compare composite and Math ACT scores. Finally, we perform a financial analysis, including retention rates, to determine if the Bridge to Bulldogs program is financially beneficial to the university.
Predicting and Comparing the Stock Value of Chick-fil-A
This project focuses on estimating the stock value of Chick-fil-A as if it were a publicly-traded company using a comparable analysis method or CAM. We begin by obtaining financial information from Chick-fil-A as well as the number of locations there are chain-wide. Next, we find two publicly traded fast food companies, one that is larger than, and another that is smaller than Chick-fil-A and obtain the same information from them. The idea is that Chick-fil-A will lie between these two companies, and we can use the CAM to estimate their stock value. The CAM gives us a multiple of the valuation of Chick-fil-A in comparison to the companies we use and that information is used to estimate the stock value. Lastly, we can compare Chick-fil-A with the larger company and then with the smaller company and average the two values which will give us a more accurate estimate.