Moderator names listed below the table.
(You may sort by room or by time of presentation.)Time | Room | Title and speaker | Abstract |
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10:00 | LBJSC 3-10.1 | Ancient and Medieval Indian Mathematics Sydney Smith Hardin-Simmons | Mathematics has been around since ancient civilizations. It has grown and developed over the years to form what we consider mathematics. Ancient and medieval Indian civilizations had their own decimal system and arithmetic algorithms. The way they wrote numbers has evolved over years to more closely resemble the way we write them today. Their math is why we have a base ten system. They have set in place many things that current mathematics has been built upon. |
10:30 | LBJSC 3-10.1 | The Use Of AI In UDL To Benefit Learning In STEM Madeline Haas & John Aguero Sul Ross University | AI has made an impression on students for years, and it’s now time for teachers to accept this and implement it in our everyday math classrooms. The UDL (Universal Design Learning) framework uses the techniques of engagement, representation, and expression to allow students the opportunity to show their mathematical needs and growth in a personalized, hands on way. AI can help teachers implement the UDL framework to each individual students to help improve the overall retention rates for math based lessons. The use of programs such as Chat GPT and other text based AI help students improve conversational skills, math literacy, and absorption of complicated problems that have become a growing issue due to an evolving technological world. Programs such as Quizizz help teachers create competitive, subject based quizzes to help students engage in topics necessary to standardized testing and important key ideas. As well as Prodigy, a math based game system, which helps students with repetition, which is necessary to help retention. All of the programs using AI included automated ways to help teachers and students use the UDL framework to make learning feel unique to them, and help create an inclusive mathematical environment for all types of learning. |
11:00 | LBJSC 3-10.1 | Matrix Diagonalization and the Fibonacci Sequence Christian Lloyd University of Mary Hardin-Baylor | We are going to use Matrix Diagonalization to establish some properties of the Fibonacci Sequence. |
11:30 | LBJSC 3-10.1 | Utilizing Exploratory Data Analysis and Machine Learning to Predict and Summarize College Student Academic Performance with an End-to-End Framework Garrett King Stephen F. Austin University | Stephen F. Austin State University collects a large amount of student information that can be further used to promote academic success. Our project aims to use machine learning and exploratory data analysis to find unseen patterns that may be of interest to advisors to promote student success. We have built an end-to-end framework consisting of a website using a relational database that stores university data along with our model predictions. After testing several different models, the gradient boosting model has been observed to provide the best results on our datasets. The main issue of our data is widespread missing information as well as imbalanced data. Moving forward, implementing time-series deep learning models may lead to more accurate predictions of student success. Finally, maintaining and improving the website and database for advisors is a priority for the future. |
10:00 | LBJSC 3-13.1 | Using Second Order Differential Equations to Build the Trigonometric Functions Austin Brewer Hardin-Simmons | Before the modern definitions of trigonometric functions emerged, power series served as their primary definition. The power series solutions of the second order ordinary differential equation y''+ y=0 can be used to create these functions. We will look at how these are created using initial value problems and how their derivatives are calculated. |
10:30 | LBJSC 3-13.1 | Modeling the Battle of Raate Road Johann Keydel St. Edwards University | We present four Lanchester models of differential equations with estimated parameters to model the Battle of Raate Road, which occurred between the Finnish and Soviet armies from Janauary 1 to January 7, 1940. |
11:00 | LBJSC 3-13.1 | Using Bayesian Methods to Infer Parameters for ODE Epidemic Systems Kyle Earp Tarleton State University | Classical models of disease outbreaks rely on systems of nonlinear ordinary differential equations. ODE models have been widely successful and are credited with saving millions of lives worldwide. However, ODE models involve parameters that are often poorly understood and difficult to infer from limited and noisy data. This is especially problematic for rare, novel, or neglected diseases with unreliable reporting mechanisms. While some parameters can be deduced from biological or social facts, many must be inferred from data. Traditional least-squares point-estimates are fragile when applied to noisy data common in disease modeling. Bayesian inference replaces fragile point-estimates with posterior distributions that are more robust against data quality issues. Whereas point-estimate models produce a single outbreak forecast, Bayesian models generate an ensemble of forecasts through repeatedly sampling model parameters from their posterior distributions and numerically solving the resulting ODE. These multiple forecasts can be pooled and statistically analyzed at each time step (min, max, mean, etc) to give insight into potential outbreak scenarios (best-case, worst-case, most likely, resp). This project aims to create well-functioning ODE models using a new mathematical idea called amortized Bayesian inference implemented in the BayesFlow Python library. This exciting new tool was created in 2020 to help fight Covid-19 and other common diseases. This project will enhance the BayesFlow library to compensate for data quality issues and provide the improved models epidemiologists need to effectively fight NTDs. |
11:30 | LBJSC 3-13.1 | Efficiency of Gauss-Seidel and Convergence of Iterative Methods Itay Kadosh Collin College | Iterative methods play a crucial role in solving linear systems of equations efficiently. Among these methods, Gauss-Seidel stands out for its simplicity and effectiveness. This presentation delves into the efficiency of the Gauss-Seidel iterative method compared to other iterative techniques. By exploring its convergence properties and computational complexities, we illuminate its advantages and limitations in various problem domains. Additionally, we investigate the convergence behavior of iterative methods in general, shedding light on key factors influencing their performance. Through theoretical analysis and practical demonstrations, this presentation aims to provide insights into the practical implications of choosing iterative solvers for solving large-scale linear systems, offering valuable guidance for both theoreticians and practitioners in numerical analysis and scientific computing. |
10:00 | LBJSC Teaching Theater | Area Differences Under Analytic Maps and Operators Luke Duane-Tessier & Daniel Rodriguez Texas A&M | Motivated by the relationship between the area of the image of the unit disk under a holomorphic mapping h and that of zh, we study various L2 norms for Tϕ(h), where Tϕ is the Toeplitz operator on the unit disc with symbol ϕ. Given polynomials p and q we also find a symbol ϕ such that Tϕ(p)=q. We extend some of our results to the polydisc. |
10:30 | LBJSC Teaching Theater | Spiraling Out of Control Hannah Richard Howard Payne University | A closer look into the world of algebraic spirals, how they are derived and how different mathematical operations affect their behavior. Starting with the basic Archimedean spiral to the more complex logarithmic spiral, we will look at how a spiral is graphed and what alterations affect the appearance and categorization of said spirals. |
11:00 | LBJSC Teaching Theater | Heron's Formula Madison Stratton Hardin-Simmons University | Heron's Formula, also known as Hero's Formula, is a fundamental theorem in geometry used to calculate the area of a triangle when the lengths of its three sides are known. My presentation begins with an exploration of the historical background of Heron's Formula, tracing its roots to ancient Greek mathematics. I will then present a detailed break down of the formula, explaining the mathematical principles and reasoning behind its development. Furthermore, my presentation investigates many applications of Heron's Formula in fields ranging from architecture to computer graphics, showcasing how it can be used to solve real-world problems. |
11:30 | LBJSC Teaching Theater | A Dissertation on Spherical Geometry Rachel Tonne Hardin-Simmons University | This will be a presentation on the history, theory, and applications of spherical geometry based on the text titled “Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry” by Glen Van Brummelen. Topics included in the discussion will be Menelaus’s Theorem as well as the spherical Law of Sines. |
10:00 | LBJSC 3-21.3 | Difference Distance Magic Oriented Graphs Kathryn Altman Southwestern University | This work explores a new graph labeling called Difference Distance Magic, where the vertices of an oriented graph are labeled with the set of consecutive positive integers starting at 1, such that the sum of the vertex labels of the in-neighborhood is equal to the sum of the vertex labels of the out-neighborhood at each vertex. We discuss the basic properties of graphs with DDM labelings, as well as proven constructions (or lack thereof) for several classes of graphs. |
10:30 | LBJSC 3-21.3 | Beyond Numbers: Unveiling the Magic of Encryption Rohith Reddy Dasi Reddy Hardin-Simons University | We will embark on a captivating exploration of the intersection between mathematics and encryption, uncovering the allure of 'naked encryption' and its profound implications for data security. |
11:00 | LBJSC 3-21.3 | Panmagic permutations and non-attacking chess queens Jaeho Lee UH – Downtown | How does one place n non-attacking queens on n × n chessboard wrapped around a torus? The answer is a panmagic permutation and such configurations are associated with names of Euler, Gauss and Polya. We will interpret many of them as lines of modular arithmetic, relate those to the symmetry group of regular polygons, and discover when composing them in triples, quadruples and other tuples also gives panmagic permutations. Finally, we will describe how they permute elements in cycles. Some fun concepts of number theory will naturally come up in the process: primitive roots, quadratic residues, square-free numbers and more. |
11:30 | LBJSC 3-21.3 | Subtractive Edge Magic Labelings Alleen Koenig Southwestern University | We look into subtractive edge magic labelings of different directed graphs. A subtractive edge magic labeling of a directed graph with v vertices and e edges is an assignment of the vertices and edges to distinct values from {1,2,...,v+e} such that the weight of each edge in the graph is the same. Here the weight of an edge is the sum of the edge label and the vertex label on the head minus the vertex label of the tail. We will begin by discussing some properties of subtractive edge magic directed graphs and some bounds on the magic constant. Then, we will discuss some classes of graphs and whether or not they have subtractive edge magic labelings including complete bipartite graphs and cycles. |
10:00 | LBJSC 4.19 | Proving the three laws of planetary motion using vector calculus Jonah Hartley Texas State University | In the early 1600s Johannes Kepler(1571-1630) formulated the three principles of celestial harmonies. Then 57 years after his death, Isaac Newton was able to prove these principles using the law of motion and gravitation. Since Newtons proofs, the three principles of celestial harmonies have been referred to as the three laws of planetary motion. In this presentation the history of these laws will be presented and their proofs will be performed using vector calculus. |
10:30 | LBJSC 4.19 | Generating Vascular Models and Assessing Uncertainty in Medical Images Darsh Gandhi UT Arlington | Chronic thromboembolic pulmonary hypertension (CTEPH) is a fatal but curable disease, causing high blood pressure and unresolved lesions in the pulmonary arteries. One way to reduce lesions is via balloon pulmonary angioplasty (BPA), inserting micro-balloons into the arteries to reduce lesion size. Patients typically undergo several treatments each inserting three balloons. However, there is currently no objective way to identify which lesions to treat to minimize blood pressure and maximize perfusion of the lung. To inform this treatment, we develop a patient-specific fluid mechanics model predicting hemodynamics in geometries extracted from computed tomography (CT) images. Using 3D Slicer, we generate a three-dimensional (3D) volumetric surface from the CT image, and using the Vascular Modeling Toolkit, we extract centerlines and junctions creating a tree. Tree labels including vessel radii and length and their uncertainty are obtained using a statistical change point algorithm. This algorithm identifies the segment along each vessel that best represents the vessel radius. We generate 1000 networks by sampling from the distribution of radii from each vessel. For each network configuration, we predict blood pressure and flow in each vessel by solving the one-dimensional Navier-Stokes equations. The microvasculature is represented by an asymmetric bifurcating structured tree in which daughter vessels are scaled relative to their parent. These microvascular trees are attached at the terminal branches of the imaged informed networks, and we solve a linearized wave equation to predict hemodynamics. Perfusion is determined by projecting average flow and pressure at the end of each vessel onto the 3D lung volume. Results show segmentation quality, network size, and changes in radius and length significantly impact hemodynamics. Future work includes optimizing BPA strategies for CTEPH patients, simulating lesion reduction and its hemodynamic impact. |
11:00 | LBJSC 4.19 | Unraveling the Dynamics of Dengue Virus Transmission: Insights into the Influence of Wolbachia Alex Vaesa & Noe Quintanilla UH — Downtown | This research investigates the complexities of Dengue virus transmission in regions where its vector Aedes aegypti mosquito thrives. Focusing on the low presence of the bacterium Wolbachia in this mosquito species, the study explores whether introducing Wolbachia slows down Dengue virus transmission as suggested in many studies in the literature. Mathematical modeling, including ordinary differential equations, is used to understand the interactions between the virus and Wolbachia. The study utilizes MATLAB and R for the data analysis and modeling the Dengue transmission dynamics. |
11:30 | LBJSC 4.19 | Simulating Left Atrial Arrhythmias Using an Interactive N-body Model Leah Rogers Tarleton State University | Heart disease and strokes are the leading global killers, and Supraventricular Tachycardia (SVT) is a leading cause of strokes and heart disease. SVT is defined as arrhythmias originating above the ventricles. Although atrial arrhythmias are not deadly in and of themselves, they can cause the perturbation of blood flow. If this blood stagnates, it can cause clots which can travel to the brain causing a stroke, or to the coronary arteries causing a heart attack. Although medication is vital in managing SVT, cardiac ablation has emerged as the most effective long-term solution. During this procedure, an electrophysiologist places catheters into the heart to create a 3-dimensional map of the heart's electrical activity. Advanced computer software helps identify the source of the irregular electrical activities, allowing electrophysiologists to ablate targeted areas to restore the heart to sinus rhythm. Despite significant advancements in cardiac ablation over the past two decades, understanding the causes and optimal ablation methods for the most prevalent and problematic cardiac arrhythmias, such as Atrial Fibrillation (Afib), remains a modern-day mystery. The most complex arrhythmias originate in the left atrium due to its intricate topology. Therefore, we have developed a computational model of the left atrium to investigate theories related to the mechanisms behind left atrial arrhythmias. Through these efforts, our goal is to shed light on these challenging arrhythmias and utilize our model as a tool to assist doctors, researchers, and medical students in testing ideas and observing outcomes rapidly and inexpensively. |
Moderators
LBJSC | 3-21.2 | Sonalee Bhattacharya |
LBJSC | 3-21.3 | Glen McCabe |
LBJSC | 4-1.9 | Jackson Rebrovich |
LBJSC | 3-13.1 | JiaLong Li |
LBJSC | 3-10.1 | Ellen Couvillion |