Regional Mathematics and Statistics Conference

Plenary Talk (Saturday)

This year’s plenary speaker is Dr. Paul Bendich. Dr. Bendich is CEO at Geometric Data Analytics, Inc. (GDA) and Adjunct Research Professor of Mathematics at Duke University. He received his Ph.D. in Mathematics from Duke in 2008 and held a postdoctoral position at the Institute for Science and Technology Austria. Dr. Bendich’s doctoral work laid some of the early theoretical foundations for topological data analysis (TDA). Since then, he has been at the forefront of the integration of TDA with more standard machine learning and statistical techniques. This work has found wide application in vehicle tracking, brain imaging, and image simplification, among many other areas. Dr. Bendich oversees all scientific efforts at GDA.

Opening Talk (Friday)

Our opening talk on Friday evening will be delivered by Prof. Adam Graham-Squire from High Point University. The title of his talk will be: Is Democracy a farce? The Mathematics of Voting.

This year’s panel will be on Careers in Mathematics and Statistics Outside of Academia. Come listen to our panel of experts from industry and national labs answer your questions about what it takes to translate your skills in mathematics and statistics into a rewarding career outside of higher eduction. Whether you already are interested in careers outside of academia or are just curious about what’s out there, this is a great chance to learn about the kinds of exciting opportunities available to math & stats graduates.

Our panelists this year are:

• Dagny Grillis. Dagny is a principal at Oliver Wyman Actuarial Consulting in St. Pete, FL, where she leads the health data and analytics team.  She earned her PhD in Mathematical Sciences from Mississippi State University with research focused on partial differential equations. She is a distinguished Fellow of the Society of Actuaries, as well as a member of the American Academy of Actuaries.

• Dana Cella. Dana is a Principal Statistical Scientist at United Therapeutics, where she started after earning her Ph.D. in Statistics from North Carolina State University.

• Stefan Schnake. Stefan is a Research Scientist at Oak Ridge National Laboratory, where he studies discrete model reduction techniques to high-dimensional dynamical systems arising from kinetic problems and neural network training. He earned a Ph.D. in Mathematics from the University of Tennessee, and he completed a postdoctoral fellowship at the University of Oklahoma.

Kristen Abernathy (Winthrop University)
Zach Abernathy (Winthrop University)
Jomi Adejumo (University of Southern Mississippi)
Sean Anderson (Virginia Tech)
Kody Angell (UNC Charlotte)
Angel Antwi-Mensah (Grambling State University)
Gabrielle Armstrong (North Carolina Central University)
Jeeban Bashyal (Alabama A&M University)
James Bird (Winthrop University)
Daniel Blackston (The University of Tennessee)
Patrick Bofah (Grambling State University)
Isabella Bourgeois (Winthrop University)
Kai Bragg (University of North Carolina at Charlotte)
Nicholas Bussberg (Elon University)
Awele Chiekwene (Grambling State University)
Tinodaishe Lincoln Chitswa (Rust College)
Izzy Cole (Towson University)
Joseph Costagliola (University of North Carolina Greensboro)
Enleo Dahal (UNCW)
Owen Deen (University of Maryland)
Taylor Delva (Winthrop University)
Keith Donovan
Suzanne Donovan
Kelly Donovan (Elon University)
Vanessa Ezeh (Grambling State University)
Chidinma Ezugwu (UNC Greensboro)
Matthew Farmer (Anderson University)
Todd Fenstermacher (Anderson University (SC))
Alan Garcia (UNC Greensboro)
Jessie Hamm (Winthrop University)
William Harvell (Anderson University)
Keta Henderson (Elon University)
Ann-Margaret Hill (Anderson University)
Nathan Jagh (Winthrop University)
Siming Jia (UNCG)
Emma Johnson (University of North Carolina – Greensboro)
Lucy Jones (UNC Asheville)
DeAndre Jones (University of North Carolina at Charlotte)
Jakini Kauba (Clemson University)
Nathan Kellerman (Bowdoin College)
Caleb Koment (University of North Carolina at Greensboro)
Wei-Kai Lai (University of South Carolina Salkehatchie)
Amy Lan (UNCW)
Samir Maanaki (Uncg)
Erin Makosiej (Anderson University, SC)
Augustine Manu-Frimpong (Grambling State University)
Jake Matthews (Winthrop University)
Jonathan Milstead (UNCG)
Titania Mlynarczyk (Winthrop University)
KELIE MARLINE Momo Nizegha (Clemson University)
Emiliano Morales-Lopez (Swarthmore College)
Bukata Mubanga (SLAC National Accelerator Laboratory (Stanford University))
Phuong Nguyen (UNC Charlotte)
Gregor Nishino (University of North Carolina Asheville)
Garrett Nix (Winthrop University)
Otutochi Nwadinkpa (University of Arkansas at Pine Bluff)
Dalitso Nyirenda (Grambling State University)
Albert Oganga (Alfred University)
Bushra Orpa (North Carolina central university)
Francis Gyamfi Osei Tutu (Grambling State University)
Oyinkansola Oyedare (Grambling State University)
Zachary Parker (University of North Carolina at Greensboro)
Rishav Patel (University of North Carolina Greensboro)
Aria Petersen (UNCG)
Liam Phillips (University of South Carolina Salkehatchie)
Rishi Ranabothu (UNC Chapel Hill)
Annette Redfern
Larry Redfern
Nyvisalsnuk Rith (Swarthmore College)
Jacob Rodriguez (Winthrop university)
Talya Schillinger (UNC Charlotte)
Stella Sedillo (Winthrop University)
Gihanee Senadheera (Winthrop University)
Elizabeth Skelly-Miles (University of North Carolina at Charlotte)
Lane Smith (University of North Carolina Greensboro)
Clifford Smyth (UNCG)
James Smyth (The Early College at Guilford)
Steven Stokes (Winthrop University)
Shriyans Taduri (UNC Chapel Hill)
Sid Touzeau (University of North Carolina – Wilmington)
Joyce Tran (UNCG)
Isabella Turpen (Anderson University (SC))
Cong Van (University of North Carolina (UNC) at Charlotte)
Savian Viera (University of North Carolina Wilmington)
Lucas Wagner (Duke University)
Keara Walsh (University of North Carolina at Charlotte)
Marley Walter (University of Georgia)
John Paul Ward (North Carolina A&T State University)
Kimberly Weems (North Carolina Central University)
Eddie Wenker (Winthrop University)
Camryn Whipple (Winthrop University)
George Whittington (The University of Georgia)
Yi Zhang (UNC Greensboro)

Name(s): Sean Anderson
Affiliation(s): Virginia Tech
Title: Gymnastics Event Identification Using Topological Data Analysis
Abstract:
Researchers studying gymnastics often rely on hours of practice film to identify skills and assess injury risks, but much of this footage contains downtime such as resting, stretching, etc. To reduce downtime, we developed a machine learning pipeline that classifies segments of practice film as either gymnastics events or downtime. The pipeline uses topological data analysis (TDA) techniques to transform our raw data into classification features. Our dataset, collected by the Wake Forest Biomechanics Lab, consists of ten‑minute recordings of accelerometer and gyroscope signals labeled by skill type. After pre-processing the data, we extracted topological features using TDA methodologies and then used dimension reduction before classification. We tested several machine learning models, including XGBoost and neural networks, to classify both event presence and skill type. Our approach achieved high accuracy in detecting gymnastics events, fully capturing about 99% of true gymnastics events while reducing average video review time from ten minutes to just over one minute. For skill classification across 68 movements, our models reached a weighted F1‑score of about 0.73. These results demonstrate that TDA provides an effective framework for classification problems.

Name(s): Kody Angell
Affiliation(s): UNC Charlotte
Title: Oh Nar! The importance of exogenous inputs in nonlinear autoregressive neural networks
Abstract:
Laser damage induced at blue wavelengths in pigmented biological tissues results in complex interactions between photothermal and photochemical mechanisms. Traditional modeling approaches rely on the Arrhenius equation or zero-order kinetic models which fail to accurately capture experimental data due to their inability to represent the specific nature of biological damage processes. These conventional models cannot adequately account for complex interactions between multiple damage mechanisms occurring simultaneously. Here we applied a nonlinear autoregressive model with exogenous inputs (NARX) to characterize photochemical and photothermal damage in biological tissues under controlled laser light exposure and varying wavelengths. Different kernel types were explored and the optimal result with the lowest root mean squared error (RMSE) was selected. The NARX framework, adapted from Wang et. al., (2022) incorporated memory effects, nonlinear dynamics,and external input variables, enabling better representation of complex biological responses to laser irradiation and capturing both immediate and delayed damage responses. The work incorporates a range of different parameters, enabling comprehensive spectral analysis of cellular damage mechanisms. This approach adapted to the complex differences between damage induced by different wavelengths. The resulting computational framework offered a powerful tool for evaluating phototherapy efficacy with important implications for understanding the interplay between damage types.

Name(s): Daniel Blackston
Affiliation(s): The University of Tennessee
Title: An Improved Linear Combination of Statistics for Binomial Proportion Hypothesis Testing with Partially Overlapping Samples
Abstract:
When comparing two proportions, data often arise that combine both paired and unpaired observations, sometimes called “partially overlapping samples”. New statistical tests are proposed, employing weighted linear combinations of statistics for paired and unpaired data, respectively. The proposed tests are compared to unweighted linear combinations test statistics, as well as tests based on combining all data in a single statistic. Simulation results suggest that the proposed weighted linear combinations are most powerful among all such linear combinations, and can be most powerful overall in select scenarios with high correlation between paired observations.


Name(s): Tinodaishe Lincoln Chitswa
Affiliation(s): Rust College
Title: Mathematical and Statistical Approaches to Student Performance Prediction
Abstract:
Predicting student academic performance is a growing area of research in education, statistics, and computer science. The ability to identify students who may be at risk of underperforming allows educators to design timely interventions and improve learning outcomes. In this project, I developed a student performance predictor using Python and machine learning techniques. The model was trained on publicly available student datasets and included features such as study time, past grades, attendance, and family background. Several algorithms were tested, including logistic regression, decision trees, and random forests, with cross-validation used to measure accuracy and avoid overfitting. In addition to predictive accuracy, the study emphasized interpretability by analyzing which factors contributed most to student outcomes. Results showed that variables such as prior academic performance and study habits had the strongest influence. This work demonstrates how mathematical modeling and statistical learning can be applied to real-world educational challenges, bridging theory with practice while providing valuable tools for supporting student success.


Name(s): Isabel Cole
Affiliation(s): Towson University
Title: Improved Confidence Intervals for Difference of Proportions with Mixed Paired and Unpaired Data
Abstract:
Several adjustments are considered for creating the optimal confidence interval for the difference of two proportions with a mixed paired and unpaired sample design. New adjustments are proposed that include new combinations of previously explored data adjustments and are compared to the adjustments explored in Kathman et al. (2025). A scaled interval incorporating several different adjustments that differ based on paired sample size is the recommended interval estimator for a mixed paired and unpaired sample design.


Name(s): Owen Deen
Affiliation(s): University of Maryland
Title: Automating Scientific Data Access with Multi-Agent Large Language Models
Abstract:
This project presents a multi-agent large language model (LLM) system for natural language querying of a scientific database. The pipeline integrates Retrieval-Augmented Generation (RAG) with a FAISS vector database to improve context retrieval and acronym interpretation. Agent 1 translates plain English into SQL, while Agent 2 interprets results for concise, conversational output. PostgreSQL integration and custom validation ensure accuracy and reliability. Fine-tuning GPT-OSS-20b with LoRA improved dialogue flow and clarity. Despite challenges from schema complexity and retry delays, the system shows that LLMs can effectively automate scientific data access. Future work will explore graph-based schema representations and adaptive retrieval for greater scalability and precision.


Name(s): Kelly M. Donovan
Affiliation(s): Elon University
Title: Novel Missing Data Imputation Method for Deep-Sea Corals: Utilizing Growth Rates to Backfill Values
Abstract:
Missing data, i.e., data values that are not stored for a variable, occur in all fields of data and can lead to a lack of statistical power and produce biased results. Statistical methods are heavily utilized to mitigate issues with missing data, with many methods falling with the classification of imputation techniques. This research investigates missing data issues with the National Oceanic and Atmospheric Administration’s (NOAA) deep-sea coral and sponge dataset. With the prevalence of missing data in the dataset, we propose a novel imputation technique that incorporates biological information of the corals. Because deep-sea corals are slow-growing and stationary animals, we can claim with a degree of certainty that they were present in years prior to observed records at their respective locations. The main idea of the imputation method is to take the average size of a coral species divided by its average growth rate to calculate a ‘backfill range’ for a recorded coral at a certain location and time. Our results show that approximately 9% of data values were original and 91% of values were backfilled for Desmophyllum spp. Our technique will create more robust data sets that will increase scientific understanding of deep-sea coral biodiversity.


Name(s): Chidinma Ezugwu
Affiliation(s): UNC Greensboro
Title: Diffusion Distance and Permutations for Spatial Autocorrelation Analysis
Abstract:
We present a unified framework for analyzing spatial autocorrelation using Markov chains and optimal transport distances between probability distributions. We share new results on the behavior of randomized initial distributions and their evolution under Markov dynamics. In particular, we provide explicit formulas for the expected quadratic deviation (squared distance) between the evolved, randomly permuted initial distribution and a target distribution, as well as related quantities, under a variety of setups, including cases where the initial or target distribution is stationary, uniform, or permuted. We formalize the notion of diffusion distance between distributions and derive bounds on these quantities, enabling precise measurement of spatial autocorrelation and clustering effects. Computational analyses across 100 U.S. cities demonstrate the framework’s utility, with mixing times and distribution evolution visualizations providing insights into how geographic patterns influence convergence. These findings offer practical tools for urban planning, political studies, and environmental policy, bridging traditional spatial statistics with modern probabilistic methods.


Name(s): Ann-Margaret Hill
Affiliation(s): Anderson University
Title: An Extension on the Skolom Sequence Problem
Abstract:
A Skolem sequence is an an integer sequences of length 2n, for some natural number n, for which each each integer 0 ≤ i ≤ n-1 appears exactly twice in the sequence, and there are i integers between each pair of i’s. For instance, the sequence 30023121 is a Skolem sequence. In this presentation, we extend this problem by allowing integers 0 ≤ i ≤ n-1 appear exactly k ≥ 2 times in the sequence such that there are i integers other than the copies of i appearing between all instances of i. Our approach will include showing possible relationships between n and k for which these sequences exists, and we will present some algorithms for construction.


Name(s): Jakini Auset Kauba
Affiliation(s): Clemson University
Title: A Comprehensive Overview of the Effects of Anxiety, Depression, Insomnia, and Trauma on Cognitive Functioning
Abstract:
In a world that has become increasingly stressful, leading to a rise in mental health difficulties, it is important that we make an effort to prioritize our wellness. While it is known that anxiety, depression, insomnia, and trauma all negatively impact cognitive functioning, our model aims to exactly quantify this influence with the hopes of progressively enhancing the nature of academic and professional work spaces. Through the work of Bayesian Inference and techniques from Data Analysis, we conduct cross-sectional, longitudinal, and cluster analyses to highlight some of the mental health disparities of America. This talk serves as an exploratory study to identify statistically significant stressors (individual and intersectional) which negatively impact cognitive functioning. By extracting data from the “NIH All of Us Research” hub and using strategies from machine learning and computational biology, we aim to quantify cognitive brain patterns under “normal/typical” experiences and cognitive brain patterns exposed to stressors associated with anxiety, depression, insomnia, and trauma.


Name(s): Nathan Kellerman
Affiliation(s): Bowdoin College
Title: Size-aware topological analysis with accumulation barcodes
Abstract:
What does it mean to capture the shape of data mathematically? One approach is topological data analysis, which encodes the underlying structure of data through its topological invariants such as connected components, holes, and voids. These characteristics are typically encoded in a persistence diagram, which captures the existence of topological features across different scales of observation. In this talk, we introduce the concept of an accumulation barcode, which extends the standard persistence diagram by including information about the magnitude of each topological feature of the data. Methods for computing and the properties of accumulation barcodes are discussed with a comparison to traditional persistence diagrams. We then apply our methods to problems of (1) clustering major US city populations by demographics, (2) identifying signals of gerrymandering in simulated redistricting plans for the state of North Carolina, and (3) making image classification robust to noise. This work originates from the 2025 UNCG REU under the direction of mentors Dr. Thomas Weighill and Chidinma Ezugwu.


Name(s): Erin Makosiej
Affiliation(s): Anderson University, SC
Title: Steiner n-Skolem Problem on a Grid
Abstract:
We show that grid graphs P_n x P_k can be Steiner k-Skolem labeled. That is, we show that there exists a labeling from the vertices of P_n x P_k to {k-1,k,…,k+n-2} such that for each k-2<i<k+n-1 if S_i is the set of vertices receiving label i, we have that |S_i|=k and d(S_i)=i, where d is the graph Steiner distance.  

Name(s): Augustine Manu-Frimpong and Oyinkansola Oyedare
Affiliation(s): Grambling State University
Title: Adaptive Trend Extraction in Financial Times Series Using ℓ₁ Trend Filtering
Abstract:
This research investigates the application of ℓ₁ trend filtering as an alternative to the Hodrick–Prescott (HP) filter) for extracting meaningful trends from financial time series data. While the HP filter smooths data by penalizing curvature using an ℓ₂ norm, it often over-smooths abrupt market changes, masking structural breaks. ℓ₁ trend filtering replaces the quadratic penalty with an absolute penalty on second-order differences, yielding a piecewise-linear trend that better captures sudden transitions. Using S&P 500 index data, this study compares both methods in terms of adaptability and their ability to detect structural breakpoints in market behavior, demonstrating that ℓ₁ trend filtering provides sharper and more interpretable insights into financial dynamics.

 

Name(s): Emiliano Morales-Lopez
Affiliation(s): Swarthmore College
Title: Modeling the Transmission Dynamics of the Monkeypox Virus Infection with Vaccination and Mask Interventions
Abstract:
Mpox is an infectious disease caused by the monkeypox virus that can be spread between humans and animals, and is endemic to western and central Africa particularly in the Democratic Republic of the Congo (DRC). We develop a deterministic model to analyze the effectiveness of vaccination and other intervention measures for Mpox, while also demonstrating the transmission dynamics including the potential transmission event from a human to an animal. Through mathematical analysis, we show the positivity and boundedness properties of the solutions within the model. Furthermore, we derive the basic reproduction number R_0 using the next generation method, and provide the necessary conditions for disease-free equilibrium to be locally stable through a combination of the linearization method and the Routh-Hurwitz criterion. Additionally, we give sufficient conditions for global stability of the disease-free equilibrium. The model is fitted using the nonlinear least square method to describe the dynamics of the disease based on reported cases of Mpox from DRC between 2023 and May 2025. Sensitivity analysis is performed to show the responsiveness of R_0 with respect to the model parameters.


Name(s): Phuong Mai Nguyen
Affiliation(s): UNC Charlotte
Title: Inverse scattering without phase: Carleman convexification and phase retrieval via the Wentzel–Kramers–Brillouin approximation}
Abstract:
The study addresses the challenging and interesting inverse problem of reconstructing the spatially varying dielectric constant of a medium from phaseless backscattering measurements generated by single-point illumination. The underlying mathematical model is governed by the three-dimensional Helmholtz equation, and the available data consist solely of the magnitude of the scattered wave field. To address the nonlinearity and servere ill-posedness of this phaseless inverse scattering problem, we introduce a robust, globally convergent numerical framework combining several key regularization strategies. Our method first employs a phase retrieval step based on the Wentzel–Kramers–Brillouin (WKB) ansatz, where the lost phase information is reconstructed by solving a nonlinear optimization problem. Subsequently, we implement a Fourier-based dimension reduction technique, transforming the original problem into a more stable system of elliptic equations with Cauchy boundary conditions. To solve this resulting system reliably, we apply the Carleman convexification approach, constructing a strictly convex weighted cost functional whose global minimizer provides an accurate approximation of the true solution. Numerical simulations using synthetic data with high noise levels demonstrate the effectiveness and robustness of the proposed method, confirming its capability to accurately recover both the geometric location and contrast of hidden scatterers.


Name(s): Garrett Nix
Affiliation(s): Winthrop University
Title: Family of Generalized Continuous Bernoulli Distributions: Properties and Applications
Abstract:
Due to data becoming more complex, there is a growing need for flexible models that are able to more accurately describe these data. This research aims to introduce new families of generalized continuous Bernoulli distributions using the T-R{Y} framework. These distributions are called T-continuous Bernoulli{Y} families, and arise from the quantile functions of the exponential, Weibull, logistic, Cauchy, and extreme value distributions, respectively. A few of the general properties of the T-continuous Bernoulli{Y} families are investigated and discussed. Two new generalized continuous Bernoulli distributions are discussed and applied to three different datasets to observe the performance of these generalizations.


Name(s): Albert Oganga
Affiliation(s): Alfred University
Title: An Investigation on the relationship between an airfoil’s upper surface curvature and the lift force it generates, modeled using calculus and Bernoulli’s principle.
Abstract:
This research investigates the relationship between an airfoil’s upper surface curvature and the lift force it generates, modeled using calculus and Bernoulli’s principle. The study focuses on the USA 35B airfoil, used in the Piper J-3 Cub aircraft, which is chosen for its simple, flat-bottom geometry. Polynomial regression and integral calculus were employed to model the airfoil’s shape, calculate planform area, and determine arc length for various curvature factors. By vertically stretching the upper surface polynomial, different thickness ratios (5–30% of chord length) were simulated to analyze their effect on lift. The corresponding airflow velocities above the wing were derived from arc length ratios and applied in Bernoulli’s equation to estimate the lift force. Results revealed an exponential relationship between upper surface curvature and lift, with a strong correlation (R = 0.981). However, the model showed physical limits beyond approximately 11% chord thickness, where the lift increase becomes unrealistic. The findings confirm that moderate curvature enhances lift efficiency, aligning with aerodynamic theory. This study demonstrates how mathematical modeling can effectively approximate aerodynamic phenomena and reinforces the intersection between mathematics and aerospace engineering.


Name(s): Zachary Parker
Affiliation(s): University of North Carolina at Greensboro
Title: Cohomology of $\mathbb{Q}[i]$ with Level
Abstract:
Automorphic forms are intimately linked to the cohomology of arithmetic groups. In this talk, we give an overview of how to explicitly compute such forms. We motivate the objects of interest, then visit the classical case where we illustrate the general approach. We conclude with some collected data, highlighting some exciting surprises, and describe future directions for this work. This project is supervised by Dan Yasaki and is joint with Kalani Thalagoda.


Name(s): Rishav Patel
Affiliation(s): University of North Carolina Greensboro
Title: Effects of density-dependent emigration on models with strong Allee type growth terms
Abstract:
We study positive solutions to a steady state landscape ecological model with a strong Allee type growth term. We consider both positive density-dependent emigration as well as negative density-dependent emigration. Our analysis is restricted to 1-dimensional settings where we use a modified quadrature method and Mathematica computations to obtain bifurcation diagrams for positive solutions in terms of a parameter related to the habitat size. Joint work with Isaac Hammond, Jerome Goddard and R. Shivaji.


Name(s): Liam Phillips
Affiliation(s): University of South Carolina Salkehatchie
Title: No-3-in-a-Wall Problem
Abstract:
In 1976, Martin Gardner proposed the Minimum No-3-in-a-Line Problem: What is the minimum number of counters that can be placed on an n×n chessboard, no three in a line, such that adding one more counter on any vacant square will produce three in a line? We studied this problem, and considered a generalized, but simplified, problem: What is the minimum number of dots that can be placed in an n×n×n cube, no three in a wall, such that adding one more dot in any vacant unit cube will produce three in a wall? In this talk we will introduce some results we found, and a recursive formula that may produce some solutions to this problem.


Name(s): Rishi Ranabothu
Affiliation(s): UNC Chapel Hill
Title: Comparative Analysis of Artificial Pancreas Control Strategies in Simulated Type 1 Diabetes Patients
Abstract:
This study presents a comparative analysis of key control algorithms for Artificial Pancreas (AP) systems by systematically varying both patient-specific and algorithmic parameters to advance fully automated insulin delivery for Type 1 Diabetes. Using the well-established UVA/Padova physiological model implemented within the Simglucose simulation environment, we evaluate algorithm performance across diverse patient conditions. The Simglucose framework includes 30 virtual patients characterized by 44 physiological parameters; in this analysis, we varied two key patient parameters and two algorithm parameters, resulting in 16 simulation scenarios. Each case is assessed using standard clinical performance metrics, including Time in Range, Time in Hyperglycemia, Time in Hypoglycemia, and Glycemic Variability. The findings aim to elucidate how parameter variations influence algorithm adaptability and robustness. These 16 scenarios also serve as a foundation for an extended comparative study involving broader parameter sweeps and multiple control strategies in future simulations.


Name(s): Nyvisalsnuk Rith
Affiliation(s): Swarthmore College
Title: Stability and Bifurcation Analysis on Fishery Models with Strong Allee Effect and Holling’s Type III Functional Response
Abstract:
Fish harvesting is an important economic sector worldwide. They also play an important role in the aquatic ecosystem and over-exploitation could have a devastating consequence in the environment. Therefore, harvesting models has gathered much interest in mathematical bio-economics. In this research, we present differential equation models that describe the dynamics of the fish population under harvesting activity. We assume that the growth of the fish population follows the logistic growth and the strong Allee effect which is the correlation between the population size to its individual fitness. The harvesting rate is given by the Holling’s type III (Sigmoid) functional response where the maximum effort exerted by the predator-human is constant. We provide the conditions for the existence of nonnegative equilibrium solutions and prove the stability of each equilibrium solution. Through bifurcation analysis, we formulate a family of parameter values that guarantees the occurrence of a saddle-node bifurcation within the model. Our results show that the strong Allee effect has a significant impact on the dynamics of the fish population, especially in the extinction and the population threshold within the fishery. Numerical simulations are performed to further comprehend the theoretical result.


Name(s): Steven Stokes
Affiliation(s): Winthrop University
Title: Creating New and Flexible Distributions Using The T-R{Y} Framework
Abstract:
This research explores the utilization of the T-R{Y} Framework, an approach to constructing flexible probability distributions through generational inheritance by compositing three distributions. Each generation inherits parameters, bounds, and graphing power from its predecessor, resulting in a flexible generalization. The Kumaraswamy distribution is given particular emphasis due to its established versatility, and universal bounds so long as data can be scaled to the unit interval. Parameter estimation is carried out using Maximum Likelihood Estimation, supported by optimization methods Differential Evolution and the L-BFGS-B algorithm. The distributions are then evaluated to New York Air Quality Data through AIC and BIC scores. The results confirm that the T–R{Y} Framework consistently yields superior fits, as demonstrated by better fit compared to generic distributions.


Name(s): Shriyans Taduri
Affiliation(s): UNC Chapel Hill
Title: Leveraging Biomedical Language Models to Infer Functional Status: Full-Text vs. ECOG-Relevant Note Segments
Abstract:
Functional status, often expressed as ECOG performance status, is critical for understanding treatment tolerance and outcomes, yet it is rarely stored in structured form. Using de-identified MIMIC-IV discharge notes, I applied NLP methods to extract and impute ECOG values. Weak labels were generated by detecting “ECOG” or “performance status” phrases and extracting nearby numbers. I then fine-tuned Bio-ClinicalBERT using two approaches: (1) full-length notes and (2) ECOG-relevant text segments. The model classified patients as having high vs. low functional status, with patient-level evaluation to avoid data leakage. Early findings indicate that ECOG-focused snippets can match or exceed full-text models while being more interpretable. Future work will extend this approach to predict the full ECOG 0–5 scale, enhancing automated functional status assessment from clinical narratives.


Name(s): Sid Touzeau
Affiliation(s): University of North Carolina – Wilmington
Title: Synthetic Electric Power Interconnect Algorithms
Abstract:
Synthetic Electric Power Interconnect Algorithms (SEPIA) provides researchers with a reliable method of synthetic power grid generation via Exponential Random Graph (ERG) models. Future applications of SEPIA may leverage its versatility to generate synthetic networks with varying structure. Real-world power grid networks are often under restricted access or otherwise considered proprietary. Researchers need many networks with similar properties to determine graph patterns and test theories about information propagation. SEPIA aims to solve this issue by creating a program to generate synthetic outputs which are able to reliably depict grid structure. We find that synthetic graphs display consistently similar average degree values and triangle/2-triangle counts to the measured actual grid networks.


Name(s): Isabella Turpen
Affiliation(s): Anderson University (SC)
Title: The Skolem Sequence Problem on a Torus
Abstract:
In this research, we examine toric grid graphs C_n x C_n. We conjecture that these graphs admit a Steiner n-Skolem labeling. That is, the vertices of G may be labeled by elements of { n-1, … ,2n-2 } such that for each n-1 ≤ I ≤ 2n-2 if S_i is the set of vertices which receive label i, | S_i |=n and d( S_i )=i, where d is the graph Steiner distance. We also provide evidence for this claim.


Name(s): Cong Van
Affiliation(s): University of North Carolina (UNC) at Charlotte
Title: The inverse initial data problem for anisotropic Navier-Stokes equations via Legendre time reduction method
Abstract:
We consider the inverse initial data problem for the compressible anisotropic Navier- Stokes equations, where the goal is to reconstruct the initial velocity field from lateral boundary observations. This problem arises in applications where direct measure- ments of internal fluid states are unavailable. We introduce a novel computational framework based on Legendre time reduction, which projects the velocity field onto an exponentially weighted Legendre basis in time. This transformation reduces the original time-dependent inverse problem to a coupled, time-independent elliptic sys- tem. The resulting reduced model is solved iteratively using a Picard iteration and a stabilized least-squares formulation under noisy boundary data. Numerical exper- iments in two dimensions confirm that the method accurately and robustly recon- structs initial velocity fields, even in the presence of significant measurement noise and complex anisotropic structures. This approach offers a flexible and computa- tionally tractable alternative for inverse modeling in fluid dynamics with anisotropic media.


Name(s): Lucas Wagner
Affiliation(s): Duke University
Title: Ecological Bias in Turnout Modeling: Demographic Structure and Habit Formation in Voting Behavior
Abstract:
Understanding how voter turnout develops and persists across elections is central to both democratic theory and political practice. Turnout underpins the legitimacy of representative institutions, while campaigns and civic organizations rely on turnout models to guide resource allocation and mobilization. This paper revisits recent findings suggesting that aggregate-level demographic composition adds little predictive value for turnout once past participation and registration are known. Using three decades of Minnesota voter file data, I estimate binary response models with out-of-sample validation to test whether individual-level demographics improve prediction beyond voting history. I also examine, mathematically, how ecological aggregation can distort relationships observed at the individual level. Contrary to prior aggregate-level results, I find that demographic features indeed improve model performance and that the strength of “habit formation”, or the persistence of early voting behavior, varies systematically across groups. These findings show that both turnout propensity and civic habit formation are demographically structured in ways that aggregated analyses obscure, with implications for modeling, mobilization, and representation.

Name(s): Keara Walsh
Affiliation(s): University of North Carolina at Charlotte
Title: Modeling the Transition of Laser Damage Mechanisms in Retinal Cells
Abstract:
Photochemical damage is a significant concern for retinal pigmented epithelial (RPE) cells, as it can lead to long-term or permanent cellular effects even at low temperatures and energy levels. We investigated the modeling of the effect of long-pulse, short-wavelength laser exposure to retinal cells, particularly to determine the time duration at which the main damage mechanism transitioned from photothermal to photochemical. Using the rate process model proposed by Clark et al. in 2011, we developed a MATLAB simulation to calculate photothermal and photochemical damage thresholds for a 413nm wavelength laser. The Arrhenius damage integral was utilized to determine the photothermal damage threshold while a two process rate model – a positive rate that is temperature independent and a negative quenching rate – was used to determine the photochemical damage threshold. By implementation of a numerical search algorithm and a binary search, the MATLAB simulation only required input of a time duration vector to compute both the photothermal and photochemical damage thresholds for each time. Additionally, we conducted a study of interpolated points to pinpoint the exact damage transition point. In this study, we also gained insight into the sensitivity of our parameters, the dependence on wavelength, and the limitations of the model.


Name(s): Camryn Whipple, Jake Matthews, and Eddie Wenker
Affiliation(s): Winthrop University
Title: A Dynamics Informed Neural Network Model for Measles Transmission
Abstract:
Dynamics Informed Neural Networks (DINNs) combine traditional compartmental models within the architecture of a neural network. With the outbreak of COVID-19, the use of DINNs have been applied to published COVID data to more accurately predict transmission rates with limited data. In this project, we apply this technique to the study of measles transmission in the United States. We use an SEIRV compartmental model to track the spread of measles through the population. We then construct a DINN that uses the SEIRV compartmental model with current US measles data to predict transmission rates and numbers of infections. We compare the results from the DINN to predictions from a corresponding neural network that excludes the dynamics structure. We find that excluding dynamics in the neural network architecture produces a transmission rate profile and basic reproductive ratio that are not supported by data. Predicted SEIRV compartments without dynamic architecture fail to make sense in a real world setting. With the dynamics architecture, the neural network produces a transmission profile with peaks preceding rises in infection. Additionally, the corresponding basic reproductive ratio is within statistically validated basic reproductive ratio ranges for a measles outbreak.

Participants are responsible for booking their own accommodations. Those who are awarded travel funding can be reimbursed after the conference. Some possible options include:

• Holiday Inn Greensboro Coliseum. Click here to book at a discounted rate. Discount expires October 7th.
• Courtyard by Marriot Greensboro. Click here to book at the UNCG rate.

If you have any trouble with booking or finding accommodations, please reach out to the organizers.

With the support of the National Science Foundation we are able to offer limited travel support to students traveling to RMSC from outside of Greensboro. Travel funding can be used towards mileage or flights, and accommodation. If you would like to apply for funding, please indicate this during registration. We will then let you know prior to the conference how much support we are able to offer you. Priority for travel funding will be given to students who are making a presentation at the conference.

We encourage faculty members to bring groups of students so as to combine travel and accommodation costs. If you are a faculty member and would like to organize funding for bringing multiple students to RMSC, please reach out to the local organizers directly.

Local Organizing Committee

Thomas Weighill (lead) Assistant Professor UNC Greensboro	Igor Erovenko Professor UNC Greensboro	Michael Hull Assistant Professor UNC Greensboro	Jianping Sun Assistant Professor UNC Greensboro

Scientific Committee

Maya Chhetri (UNCG)
Sujit Ghost (NC State)
Kevin Hutson (Furman University)
Jiancheng Jiang (UNC Charlotte)
Taufiquar Khan (UNC Charlotte)
Jimin Lee (UNC Asheville)
Suzanne Lenhart (University of Tennessee, Knoxville)
Tom Lewis (UNCG)
Abhyuday Mandal (University of Georgia, Athens)
Sayed Mostafa (NC A&T)
Ratnasingham Shivaji (UNCG)

UNCG RMSC has a zero-tolerance policy for harassment or discrimination. See the full policy and how to report violations here.