SUMS Contributed Talks

Welcome to our Contributed Talk Page!

We've got some great contributed talks this year, and want to thank the 15 teams that invested the time to create their amazing videos and have let us showcase their hard work!

All talks are posted as unlisted videos on YouTube. They are all between 10 and 15 mintues long, and after you watch them, please feel free to leave an encouraging comment or two and ask any questions you have. We will moderate all comments and let the presenters know when they've gotten comments.

Extensions of True Skewness for Unimodal Distributions
Christopher Wang (Columbia University) with Alex Negrón and Clarice Pertel
YouTube Link: https://youtu.be/fxxTG2la6pA

Abstract:In a 2020 paper, Y. Kovchegov introduced the notion of true positive and negative skewness for the distributions of continuous random variables via Fréchet p-means and stochastic dominance criteria. True skewness ensures consistency in sign of widely used but sometimes discrepant measures of the degree of skewness, including Pearson’s moment coefficient of skewness, Pearson mode skewness, and Pearson median skewness. Moreover, unlike Pearson’s measures of skewness, true skewness is well-defined for distributions with infinite integer moments. In this work, we find novel criteria for true skewness, identify a parameter region for true positive skewness of the Weibull distribution, and formally establish positive skewness of the Lévy distribution for the first time. Additionally, we consider the application of true skewness to discrete and multivariate settings and discuss the complications in doing so. An analogous stochastic dominance criterion is proved for the discrete case. In the multivariate case, we propose a notion of a trajectory of true skewness. Finally, we offer a new measure of skewness that is defined for a larger class of distributions based on the notion of true skewness. Several properties of the p-means of random variables are established.

Representation Varieties and the Heisenberg Group
Andre Mas (James Madison University)
YouTube Link: https://youtu.be/s58DtAV6S_g

Abstract:A fundamental goal in mathematics is understanding global actions on spaces. One way this may be done is by studying the maps induced on various related structures, such
as the representation variety, which is constructed from the space’s fundamental group and a matrix Lie group. We will describe how this strategy is used to analyze the fixed point sets of three involutions that generate the mapping class group of a closed, connected, oriented, genus 6 surface. In the process, a case is made for the use of the 3x3 Heisenberg group in the study of representation varieties.

A Tensor SVD-based Classification Algorithm Applied to fMRI Data
Katherine Keegan (Mary Baldwin University) with Tanvi Vishwanath, Vida John, and Yihua Xu
YouTube Link: https://youtu.be/jz2W8kmgIUk

Abstract:To analyze the abundance of multidimensional data, tensor-based frameworks have been developed. Traditionally, the matrix singular value decomposition (SVD) is used to extract the most dominant features from a matrix containing the vectorized data. While the SVD is highly useful for data that can be appropriately represented as a matrix, this step of vectorization causes us to lose the high-dimensional relationships intrinsic to the data. To facilitate efficient multidimensional feature extraction, we utilize a projection-based classification algorithm using the t-SVDM, a tensor analog of the matrix SVD. Our work extends the t-SVDM framework and the classification algorithm, both initially proposed for tensors of order 3, to any number of dimensions. We then apply this algorithm to a classification task using the StarPlus fMRI dataset. Our numerical experiments demonstrate that there exists a superior tensor-based approach to fMRI classification than the best possible equivalent matrix-based approach. Our results illustrate the advantages of our chosen tensor framework, provide insight into beneficial choices of parameters, and could be further developed for classification of more complex imaging data. We provide our Python implementation at https://github.com/elizabethnewman/tensor-fmri.

Chip Firing on Strongly Regular Graphs
William Nettles, Colby Sherwood, Dominic Gammino, Michael Michniak
YouTube Link: https://youtu.be/ODBEWzd-Xrc

Abstract:A Strongly Regular Graph (SRG) is a regular graph such that the number of common neighbors of a pair of vertices depends only on whether the vertices are adjacent or not. A key problem in studying SRGs is the existence and uniqueness of graphs satisfying a given parameter set. Several famous open graph theory problems are existence problems, such as Conway’s 99 graph and the missing Moore graph. We use chip firing groups (critical groups) and their more general form, the Smith group, to study open problems related to SRGs.

A Numerical Study of the SEIQR Model for COVID-19
Caitlin Holt (University of Mary Washington)
YouTube Link: https://youtu.be/ndTxzuS0In0

Abstract:In this research project, we used numerical methods to investigate trends in the susceptible, exposed, infectious, quarantined, recovered, closed cases and insusceptible populations for the COVID-19 pandemic in 2021. We used the SEIQR model containing seven ordinary differential equations, based on the SIR model for epidemics. An analytical solution was derived from a simplified version of the model, created by making various assumptions about the original model. Numerical solutions were generated for the first 100 days of 2021 using algorithms based on Euler's Method, Runge-Kutta Method, and Multistep Methods. Our goal is to show that numerical methods can help us predict trends in the populations we are studying and provide insight for steps that can be taken to reduce the number of infections.

Finding Your Way Back in a Random Forest: Debias Regression Predictors
Hannah Wahl (Tulane University) with John Ryan, Gundeep Singh, and Jessica Zhao
YouTube Link: https://youtu.be/XzHJeE36pYs

Abstract:The random forest can reduce the variance of regression predictors through bagging while leaving the bias little changed. In general, the bias is not negligible and consequently bias correction is necessary. The default bias correction method implemented in the R package randomForest often does not work well and several approaches have been proposed as alternatives. These approaches generally fall into two major categories: univariate smoothing and boosted forest. Previous works only included partial comparisons of these methods without an informative ranking. We conducted a comprehensive comparison of the competitive methods identified in previous studies and identified boosted forest as a general winner. The methods to be compared also included two variants of univariate smoothing we independently proposed. We further explored the iterative performance of boosted forest and developed an easy-to-use stopping rule to avoid overfitting. We also proposed a visualization technique to help users to decide when bias correction was needed.
This work was supported by NSF-REU grant (#1950370)."

Using DEM Derivatives from Quanergy LiDAR Data to Classify Wetlands through Machine Learning
Aidan Lee (Marvin Ridge High School) with Shitij Govil, Aiden MacQueen, and Garrison Payne
YouTube Link: https://youtu.be/TPp9xycoscs

Abstract:Wetlands play a vital role in the environment, providing ecological and economic benefits for the people living on or near them. Despite the vital role they play in the environment, they are underrepresented because of outdated data collection methods, which can leave some wetlands unprotected and vulnerable to legal destruction. As part of the Clean Water Act of 1972, the Environmental Protection Agency protects natural sources of water such as wetlands. The current wetland classification method (NWI) relies on research teams to survey an area and classify it on foot, which is inefficient and potentially harmful to wetlands. The Clean Water Act does not apply to unidentified wetlands, which vastly outnumber the amount of identified wetlands. This project aims to utilize Unmanned Aircraft Systems (UAS) data and Light Detection and Ranging (LiDAR) technology to speed up the process of classifying wetlands and gather more accurate data. We collected DEM(Digital Elevation Model) and multi-spectral data of two wetland sites and broke the sites into hexagon tessellations of various sizes. We used this data along with tree-based machine learning algorithms, such as Gradient Boosting to classify parts of the sites as wetlands or non-wetlands, with the highest accuracy of 96%. This study shows a promising future for machine learning and drone-collected data for the purpose of conserving wetlands.

Approximating a Minimal Path of Fixed Area Loops
William Nettles (James Madison University)
YouTube Link: https://youtu.be/JcsNyTVSVnU

Abstract:A geodesic is a shortest path between two points in some space, and its equation is well known. The space of fixed area n-gons is a path connected space for which the finite-dimensional geodesic equation has solutions. Similarly, the space of fixed area loops is a space for which the infinite dimensional geodesic equation has solutions. We use geodesics in the space of fixed area n-gons to approximate geodesics in the space of fixed area loops.

An epidemiological study on the spread and treatment of treponemal infection in Olive Baboons
Solomaya Schwab (Cedar Crest College) with Diamond Hawkins and Roland Kusi
YouTube Link: https://youtu.be/8j4KuBxCZ2k

Abstract:Yaws is a chronic infection caused by the bacterium Treponema pallidum susp. pertenue (TPE) that was thought to be an exclusive human pathogen but was recently found and confirmed in nonhuman primates. In this paper, we develop the first compartmental ODE model for TPE infection with treatment of wild olive baboons. We solve for disease-free and endemic equilibria and give conditions on local and global stability of the disease-free equilibrium. We calibrate the model based on the data from Lake Manyara National Park in Tanzania. We use the model to help the park managers devise an effective strategy for treatment. We show that an increasing treatment rate yields a decrease in disease prevalence. This indicates that TPE can be eliminated through intense management in closed population. Specifically, we show that if the whole population is treated at least once every 5-6 years, a disease-free equilibrium can be reached. Furthermore, we demonstrate that to see a substantial decrease of TPE infection to near-elimination levels within 15 years, the whole population needs to be treated every 2-3 years.

Machine Aided Detection of Atrial Fibrillation through R-R Intervals
Sahil Patel (John T. Hoggard High School) with Justin Guo and Maximilian Wang
YouTube Link: https://youtu.be/C_PsNnLedG0

Abstract:Atrial Fibrillation (A-FIB) is a heart condition that occurs when the atria fail to beat in coordination with the ventricles, resulting in ""irregularly irregular"" heartbeats. This can lead to blood clotting and potentially a stroke. Since detecting A-FIB is extremely difficult, a possible solution is an application for devices like Apple Watches to constantly track the heart rate of its user. The program would then use the data collected to predict A-FIB based on the R-peaks and the distance between them, otherwise known as R-R intervals. Various features were used in conjunction with numerous classifiers to create models of prediction. The most prominent among these features was transitions, but all the features combined led to a greater overall accuracy. Out of all the classifiers, Light Gradient Boosting (LGBM) and Extreme Gradient Boosting (XGBoost) had the two highest accuracies, at 97.57% and 97.56%, respectively, as well as the two highest sensitivities and specificities. Ensemble models which combined the outputs of many classifiers were also created, none of which outperformed LGBM and XGBoost. Therefore, it was concluded that Light and Extreme Gradient Boosting, when provided with all features, would be the best algorithms for predicting atrial fibrillation.

Picking the Best: Determining an Accurate Measure for the Standard Errors in the Cox PH Model
Ryan Shuman (James Madison University)
YouTube Link: https://youtu.be/bwDVufaoXDs

Abstract:The Cox proportional hazards (PH) model is a popular model to analyze survival data. It is crucial to make a good approximation of the standard errors (SEs) for the regression parameters (β). This work evaluates several methods for estimating the SEs for the βs in Cox PH model. We perform simulation studies and offer general guidance on the selection of the best estimator

An Explicit and Analytical Solution to the Stokes Equations on the Half-Space with Initial Conditions and Boundary Conditions For Velocity using Integral Transforms
Miles Smith (Occidental College) with Clare Spinner and Hannah Stein
YouTube Link: https://youtu.be/saWffaDYaKA

Abstract:In this paper we present explicit and analytical solutions to the Stokes equation on the half-space with data for initial velocity and boundary velocity. Our approach to a solution for velocity and pressure involves integral transformations, Green's functions, and a Helmholtz decomposition. Our main results demonstrate that the velocity derived from this initial value and boundary value problem can be expressed as the curl of the convolution of vorticity and the fundamental solution to the Laplace equation in our domain.

Detecting Woody Plants in Semi-Arid Regions Using Data from the National Ecological Observatory Network (NEON)
Thomas Hutsler and Gordon Hendry (University of North Carolina at Wilmington)
YouTube Link: https://youtu.be/03TzuDew3xw

Abstract: Land cover change has been occurring rapidly in response to human activities throughout the past century. The process of historically non-woody dominant ecosystems transitioning to woody-dominance has been documented throughout the world and is referred to as woody plant encroachment (WPE). WPE has been especially prevalent in semi-arid regions, where changes in precipitation and disturbance patterns can have dramatic effects on vegetation structure. In semi-arid regions, grassland and savanna ecosystems serve as critical habitat for many species and provide area for livestock grazing, offer protection against soil erosion, and facilitate nutrient cycling, among other ecosystem services. These ecosystem services diminish as WPE occurs, therefore it is critical to accurately determine the distribution of woody plants in semi-arid regions. The ideal methodology for monitoring woody plant cover in semi-arid regions should be widely applicable, easily accessible, and accurate. We aim to develop such methods by integrating remote sensing and machine learning techniques and evaluating their efficacy for monitoring woody plant cover at Santa Rita Experimental Range (SRER, Arizona, US), where relatively novel data has been collected by the National Ecological Observatory Network (NEON). Our first objective is to thoroughly understand our data through the process of exploratory data analysis. We then compare multiple classification models to select a model that works best with our dataset. Model performance was compared using standard model assessment metrics such as overall accuracy, sensitivity, and specificity. Software and data used were open source, when possible, to facilitate replicability and accessibility.

Extended SEIR model: Modeling Covid-19 Spread Between University Students
Raina Saha (George Mason University) with Krist Cimbalista, Clarissa Benitez, and Jolypich Pek
YouTube Link: https://youtu.be/AzTpKd5wRSM

Abstract:The SEIR model is a compartmental method used to predict the spread of disease. We constructed an extended form of the SEIR model to model the effect of common mitigation strategies and behaviors on the spread of Covid-19 within a college campus. We found that the inclusion of mitigation strategies like mask use, random testing, and quarantine disobedience was associated with changes in the calculated reproduction number and the peak infected population.

Epidemic spreading on complex networks as front propagation into an unstable state
Ashley Armbruster (Frostburg State University) with Matt Holzer, Noah Roselli, and Lena Underwood
YouTube Link: https://youtu.be/6seKjYQMZlg

Abstract:We study epidemic arrival times in meta-population disease models through the lens of front propagation into unstable states. We demonstrate that several features of invasion fronts in the PDE context are also relevant to the network case. We show that the susceptible-infected-recovered model on a network is linearly determined in the sense that the arrival times in the nonlinear system are approximated by the arrival times of the instability in the system linearized near the disease free state. Arrival time predictions are extended to a susceptible-exposed-infected-recovered model. Finally, we show how inhomogeneities in local infection rates lead to faster average arrival times.