RMSC | Regional Mathematics and Statistics Conference

(Due to unforeseen circumstances, our plenary speaker has changed)

Our Plenary Lecture will be delivered by Dr. Igor Erovenko. Igor Erovenko is a Professor of Mathematics and Associate Department Head in the Department of Mathematics and Statistics at UNC Greensboro. He earned his PhD in mathematics from the University of Virginia.

Dr. Erovenko specializes in mathematical biology. His research centers on behavioral epidemiology, evolutionary game theory, and data-driven machine learning. He develops mathematical and computational models to investigate how individual decisions shape disease transmission and how cooperation evolves in realistic populations. His recent work examines physics-informed machine learning approaches to understanding vaccination behavior.

Dr. Erovenko has contributed to multiple externally funded research and training initiatives, including serving as a principal investigator on the National Science Foundation’s $1 million Project INSIGHT, which incorporates human behavior into epidemiological modeling, and leading an REU program in mathematical biology. He also served as an external supervisor for EvoGamesPlus, a €4 million international research training network funded by the European Union’s Horizon 2020 program.

As a dedicated mentor, Dr. Erovenko has supervised research projects involving 27 undergraduate and four graduate students, with many of these collaborations leading to peer-reviewed publications and conference presentations. In 2021, he received the Career Undergraduate Research Mentor Award from the College of Arts and Sciences. He also served as a Division Representative in Mathematical, Computing, and Statistical Sciences for the Council on Undergraduate Research.

This year’s panel topic is “Math meets biology”. Our panelists have with a diverse set of perspectives, experiences, roles, and backgrounds, and are ready to answer your questions about how mathematics and statistics meets the worlds of biology, health science, pharmaceuticals, and more. Our panelists are:

Jason Pearson is an applied mathematician and physicist using machine learning, mathematical modeling, and fluid dynamics to solve interesting problems that are of benefit to humanity. He is currently a Lead Applied Scientist & Applied Mathematician at Simulations Plus, Inc.

Ivanti (Vee) Galloway is a Biostatistician at Merz Aesthetics and a doctoral researcher in Systems Modeling and Analysis at Virginia Commonwealth University. Her work focuses on applying statistical modeling, systems analysis, and quantitative methods to biological and medical applications, bridging mathematical theory with industry and clinical challenges. She holds a strong interest in biostatistical methodology, data-driven decision-making in clinical sciences, and mentoring students in quantitative fields.

Third panelist TBA.

Abigail Betterton (High Point University)
Aidan Englebretson (Apalachin State University)
Aidan Englebretson (Appalachian State University)
Alan Garcia (UNC Greensboro)
Alana Johnson (North Carolina A&T State University)
Amelia Weaver (NC State University)
Amrit Kaur Dhillon (NC State)
Andreya Daugherty (North Carolina Central University)
Beilong Tang (North Carolina State University)
Carmen Caiseda (Inter American University of Puerto Rico)
Chidinma Williams (UNC Greensboro)
Claire Klein (High Point University)
Daniel Kent (High Point University)
Davina Nti-Gyabaah (Department of Mathematics and Statistics)
Deyaneira Rosario Colón (Interamerican University of Puerto Rico – Bayamón Campus)
Dustin Nichols (High Point University)
Emma Clifton (UNCG)
Erika Gibson (UNCG)
Ethan Botelho (North Carolina State University)
Faharudeen Alhassan (Georgia State University)
Faustus D Maale (NC A&T State University)
Gabriel (UNC Greensboro)
Gire Nyara (UNCG)
Griffin Duncan (Appalachian State University)
Hasini Pasagadugula (NC State University)
Isabelle (University of North Carolina at Greensboro)
Jacob Blazejewski (Appalachian State University)
Jacob Crenshaw (Appalachian State University)
Jeeban Bashyal (Alabama A&M University)
Jeeban Bashyal (Alabama A&M University)
Jerry Moyer (UNCG)
Jesse Paul (University of North Carolina at Greensboro)
Joao Matheus Costa (University of South Carolina Salkehatchie)
Josephine Dial (North Carolina Agricultural and Technical State University)
Katie Pelikan (NC State University)
Keesha Go (UNCG)
KwangHyun Park (Department of Statistics, University of Georgia)
Lily Gregory (UNCG)
Lucas Roney (Appalachian State University)
Mashiwal . M. Issah (Livingstone College)
Md Arifuzzaman (North Carolina State University)
Megan Mueller (High Point University)
Nakul Haridas (North Carolina State University)
Nigar Sultana (Department of Mathematics, North Carolina State University)
Peyton Jackson (Columbia University)
Ravanasamudram Uma (North Carolina Central University)
Samir Maanaki (UNCG)
Siming Jia (University of North Carolina Greensboro)
Sivamurugan Velmurugan (North Carolina School of Science and Mathematics)
Stephen Agyeah (North Carolina Agricultural and Technical State University)
Tamia Stewart-Sellars (UNCG)
Tanner (North Carolina State University)
Thomas Payne (UNCG)
Tianle Chen (Department of Statistical Science, Duke University)
Torre Caparatta (UNCG)
Upasana Aryal (Knox College)
Wei-Kai Lai (University of South Carolina Salkehatchie)
Xiaoqi Wei (North Carolina State University)
Yi Zhang (UNC Greensboro)
Yutong Wu (University of North Carolina at Chapel Hill)
Zehaan Naik (Duke University)
Zijun Qin (University of North Carolina at Charlotte)
ahenderson13@elon.edu (Elon University)
vinodhini Rajasekhar (duke university)

Name(s): Abigail Betterton
Affiliation(s): High Point University
Title: Population Persistence in Two Favorable Patches Separated by a Hostile Matrix
Abstract:
We develop a reaction-diffusion model to study the persistence of a single species inhabiting two favorable patches separated by an interior hostile matrix. The population obeys logistic growth within the patches, while the matrix does not support population growth and is characterized by its own diffusion and mortality rates. The model incorporates density-dependent interface conditions to describe population movement across the patch–matrix interfaces. We utilize a quadrature method to obtain numerical bifurcation diagrams and formulate conjectures about the existence and multiplicity of positive steady-state solutions. In particular, we investigate how the size and properties of the interior matrix influence movement between the patches and how this affects the minimum total favorable patch size required for population persistence.

Name(s): Amrit K Dhillon and Hasini Pasagadugula
Affiliation(s): NC State
Title: Did Duplicated Genomes Keep Mixing? Evidence from Bony Fishes, Ciliates and Bakers’ Yeast
Abstract:
Many successful groups of organisms, including flowering plants and vertebrates, owe part of their evolutionary success to whole genome duplications (WGDs), events in which an organism acquires a complete extra copy of its DNA. Right after such an event, cells often struggle to sort their chromosomes correctly when making eggs and sperm, which can produce inviable gametes. Over time, most lineages solve this problem through a process called diploidization, in which duplicated chromosomes stop pairing with their extra copies. Scientists once thought this happened quickly, but recent studies suggest it may be much more drawn out, with the two subgenomes continuing to exchange genetic material long after the WGD. Here, we look for evidence of this slow resolution in three cases: the WGD in the ancestor of most bony fishes, repeated WGDs in the single-celled paramecia, and a WGD in baker’s yeast. Using a computational tool we developed, we model how each duplication was resolved and compare the evolutionary histories of individual genes with those of the species carrying them. Our results suggest that diploidization was drawn out in all three cases.

Name(s): Amy Heng Lan
Affiliation(s): NC State
Title: Tropical cyclone image comparison using max filtering and learned templates
Abstract:
We apply Max-Filtering, a template-based framework for efficient cyclone pattern matching from large meteorological image archives via dimensionality reduction, to find the top (J) images that are most similar to the query image. We map each image in (\mathbb{R}^{m\times n}) to a (K)-dimensional vector of peak correlation responses, yielding a translation-invariant descriptor for each image. At query time, similarity is measured in feature space to rank top-(J) candidates. Using a 10-year cyclone archive, we benchmark the image matching method against direct correlation and distance-based baselines through brute-force similarity scoring. Experimental results demonstrate both speed and robustness: the precomputation of template responses significantly reduces computation time, while stable retrieval is maintained under shifts, rotations, and noise.We also learn weights for template responses, using separate storms for training, validation, and testing. Experimental results show improved retrieval compared with equal template weighting. Max-Filtering thus provides a practical and efficient framework for interactive cyclone pattern matching.

Name(s): Beilong Tang
Affiliation(s): North Carolina State University
Title: Polar Diffusion: Decoupling radial and tangential denoising in diffusion models
Abstract:
Diffusion models have emerged as a leading approach to generating realistic images by progressively transforming random noise into structured visual content. Conventional diffusion models operate in a Euclidean space, without explicitly distinguishing between changes in image magnitude and structural organization. Yet every nonzero image admits a natural decomposition into two geometrically distinct components: its magnitude, capturing overall intensity, and its direction, encoding its normalized spatial structure. These components may contribute differently to image realism and therefore warrant distinct treatment. We introduce Polar Diffusion, a framework that separates the diffusion process into radial and angular dynamics, allowing their contributions to be modeled and weighted independently. We establish mathematically the relationship between this polar formulation and conventional Euclidean diffusion, providing a principled foundation for extending existing diffusion architectures. Experiments on a synthetic spiral manifold embedded in a high-dimensional space demonstrate substantially improved preservation of the underlying data geometry. Evaluations on CIFAR-10 and ImageNet further show improvements in image generation quality over comparable baselines. Notably, our findings consistently indicate that reducing the relative emphasis on radial errors while prioritizing angular, structure-related errors yields higher-quality generated images.

Name(s): Chidinma Williams
Affiliation(s): UNC Greensboro
Title: Beyond One Step: Diffusion and Transport Distances for Spatial Clustering
Abstract:
We define the diffusion distance between two probability distributions $f$ and $g$ on a graph as the number of steps a graph-constrained Markov chain with stationary distribution $g$ requires to bring $f$ within a prescribed tolerance of $g$, where the chain is taken to be Metropolis–Hastings unless otherwise specified. When $g$ is uniform, the diffusion distance quantifies how strongly $f$ is spatially clustered across the global structure of the graph. Its one-step case recovers Moran’s $I$ under specific spatial weights, while subsequent steps track how the pattern disperses across the full graph. We derive spectral bounds and a stability result, pair the diffusion distance with a complementary geometric measure of clustering—the Wasserstein-$1$ transport deviation from uniformity—and prove a two-sided bound placing it between this deviation and a spectral mixing rate. For inference, exact moments under permutation nulls yield closed-form, conservative significance bounds that require no resampling and scale to large graphs. On stochastic block models, the diffusion-distance test is more powerful than Moran’s $I$. In census data for 100 U.S. cities, the diffusion and transport measures of racial and ethnic population distributions largely agree, and the diffusion distance distinguishes segregation patterns that Moran’s $I$ does not.

Name(s): Deyaneira Rosario Colón
Affiliation(s): Interamerican University of Puerto Rico – Bayamón Campus
Title: Conduction Heat Transfer in Rectangular Plates with Discrete Internal Heat Sources
Abstract:
The purpose of this work is to present analytical and numerical methodologies for solving steady state heat conduction problems in rectangular plates with embedded discrete heat-generation sources. The main objectives are to find the temperature distribution inside the plate with an arbitrarily arrangement of discrete rectangular heating sources analytically and compare it with numerical solutions using Finite Element Analysis (FEA) and Finite Difference Method (FDM). Throughout the investigation, is determined that the location of the heat source affects the symmetry and spatial distribution of the temperature. Also, the largest discrepancies occur near the heat generation regions, where the temperature gradients are the highest. Both FEA and FDM results confirm the accuracy of the analytical solutions with a maximum true error below 0.60%. While the numerical approaches require greater model and computational effort, the analytical formulation offers rapid and clear physical insight into the temperature distribution of the plate. Future work should extend the present formulation to include heat-flux and convection boundary conditions (Neumann or mixed conditions), as well as different geometric configurations and arrangements of discrete heat-generation sources.

Name(s): Erika Gibson
Affiliation(s): UNCG
Title: Improving Detection of Rare Adverse Event Signals in Pharmacovigilance
Abstract:
Rare adverse events are among the most important safety signals to identify in post-marketing surveillance, yet they are also among the most difficult to detect. Sparse reporting, dependence among adverse events, and the large number of simultaneous comparisons can substantially reduce the power of traditional signal-detection methods. This presentation introduces a two-stage hierarchical framework designed to improve the detection of rare adverse event signals while maintaining appropriate control of false discoveries. In Stage 1, adverse events are grouped by System Organ Class and screened using methods that combine evidence from common and heterogeneous effects. Simulation studies show that Adaptive and Optimal combination procedures improve power over the traditional Fisher combination when adverse events are rare, with the Adaptive method providing a favorable balance between statistical performance and computational efficiency. Stage 2 then identifies the individual adverse events contributing to significant group-level signals. A Mid-p test combined with Storey’s q-value procedure demonstrated strong sensitivity and false discovery rate control. Application to 2024 Vaccine Adverse Event Reporting System (VAERS) data illustrates the practical value of the framework, recovering established safety signals while also identifying associations in sparse, low-frequency settings.

Name(s): Ethan Botelho
Affiliation(s): North Carolina State University
Title: Wave Breaking for Perturbed Burgers Equations
Abstract:
Wave breaking refers to the phenomenon in which solutions to certain PDEs remain bounded up to a finite time T^*, while their spatial derivatives become unbounded. Recent work has established wave breaking for several Burgers-type equations, including the Burgers-Hilbert equation, the fractional Korteweg-de Vries (fKdV) equation, and Whitham-type equations. Our goal was to find conditions under which a general Burgers-type equation of the form u_t + u u_x = N[u] exhibits wave breaking in a finite time interval for sufficiently smooth initial data, where N is an essentially bounded linear operator. In this talk, we start with the motivating example of the Burgers-Hilbert equation. Then, we discuss our results for sufficient conditions for wave breaking in the general case and use these results on the fKdV equation and Whitham-type equations. Joint work with Khai T. Nguyen and Madhumita Roy.

Name(s): Faharudeen Alhassan
Affiliation(s): Georgia State University
Title: State-Level Excess Drug Overdose Mortality by Race/Ethnicity in the U.S., 2020–2023: A Population-Scaling Analysis During the COVID-19 Pandemic
Abstract:
The COVID-19 pandemic coincided with a sharp increase in drug overdose deaths in the United States, with substantial differences across racial and ethnic groups. This study examined excess overdose deaths across 47 states and the District of Columbia from 2020 to 2023. Using overdose mortality data from 2014 to 2019, we developed models to estimate the number of deaths expected in the absence of pandemic-era changes. We then compared these estimates with observed deaths and examined how excess mortality varied across racial and ethnic groups and population sizes. White populations experienced the largest number of excess deaths, particularly in 2021. However, excess deaths among Black populations increased sharply in 2021 and 2022, approaching those of White populations by 2023. Black populations also experienced higher excess death rates than White and Hispanic populations. Our findings highlight persistent racial and ethnic disparities in overdose mortality and emphasize the need for targeted public health interventions, improved surveillance, and equitable access to overdose prevention and treatment services.

Name(s): Gabriel Wheeler
Affiliation(s): UNC Greensboro
Title: Exploring the Impact of Adding a Numerical Moment Stabilizer for Approximating Viscosity Solutions
Abstract:
We explore a numerical method to approximate solutions to a class of fully nonlinear boundary value problems. A straightforward approach, which replaces the original problem with a system of algebraic equations based on replacing differential operators with difference operators, has many $\left(2^{N-1}\text{ solutions for }N\text{ nodes}\right)$ solutions, only one of which corresponds to the (physically relevant) viscosity solution. Our method aims to lessen the issue of false solutions by adding a term, called the numerical moment, with coefficient $c\in\mathbb{R}^+$, to the algebraic equations. Others have noted that this method seems to reduce the number of unwanted solutions and make the right one easier to find, but it is difficult to see how the method works in the more often considered higher dimensional cases. So, we consider exclusively one dimensional problems and vary the parameter $c$ to gain understanding into how the solution set of the discrete problem changes and the role that the numerical moment plays in selecting the viscosity solution. For the specific problem that we have mainly focused on, we have shown that when $c$ is large enough, our algebraic system has only two solutions, one of which is the viscosity solution.

Name(s): Griffin Duncan, Lucas Roney, Jacob Crenshaw, and Aidan Englebretson
Affiliation(s): Appalachian State University
Title: From Points to Curves: An Introduction to Interpolation and Approximation Methods
Abstract:
This presentation discusses interpolation as a method for approximating continuous curves from discrete data. This is useful, as it enables informed estimations to be made about missing data values. We will explore two methods for this: polynomial and radial basis function (RBF) interpolation. We will demonstrate how to approximate missing values from tidal wave data with these two methods. In the process, we will explain key features of RBF interpolation, such as the effects of different shape parameters, radial basis function types, and a method for choosing the best shape parameter. Lastly, we will explore how different node sets impact polynomial interpolation.

Name(s): Jeeban Bashyal
Affiliation(s): Alabama A&M University
Title: Improved Upper Bounds on the Independent Domination Number of (k\)-Trees
Abstract:
This paper investigates upper bounds on the independent domination number of k-trees, a class of chordal graphs with important structural properties. The independent domination number of a graph is the minimum size of an independent dominating set: a set of vertices in which no two are adjacent and every vertex outside the set is adjacent to at least one vertex in it. Building on existing results, this study explores how structural parameters, namely simplicial vertices, contractible edges, and the branch number, can be used to derive tighter upper bounds. Using induction, the analysis first establishes a bound for k-trees with no contractible edges and then extends it to general k-trees through an auxiliary graph construction. The resulting bound states that the independent domination number is at most half the quantity obtained by taking the total number of vertices, subtracting the number of vertices of degree k, and adding twice the branch number. Although this bound does not improve on existing results for all values of k, it gives stricter bounds for 2-trees and 3-trees when sufficiently many simplicial vertices are present. Examples involving maximal outerplanar graphs and 3-trees demonstrate its potential to sharpen established estimates and motivate further research into structural bounds for independent domination.

Name(s): Jesse Paul
Affiliation(s): University of North Carolina at Greensboro
Title: A Stable Non-Monotone Narrow-Stencil Method for the Monge–Ampère Equation
Abstract:
The Monge–Ampère equation, which governs optimal transport and the prescription of Gaussian curvature, often has solutions with fewer derivatives than the equation appears to require. Since Barles and Souganidis, convergent finite difference methods for such fully nonlinear equations have relied on monotonicity, which for Monge–Ampère forces wide stencils that are costly and limited to low accuracy. We construct a 17-point narrow-stencil scheme for the two-dimensional Monge–Ampère equation with nonnegative data, stabilized by a numerical moment that steers the scheme toward the convex viscosity solution. We prove the scheme is admissible, stable, and consistent; to our knowledge it is the first non-monotone finite difference method for a fully nonlinear elliptic equation with all three properties.Numerical experiments show convergence across regularity classes, from the smooth prescribed Gaussian curvature equation, to a C^{1,1} optimal transport problem, to the Lipschitz Alexandrov cone, whose gradient singularity lies on the boundary.

Name(s): Joao Matheus Costa
Affiliation(s): University of South Carolina Salkehatchie
Title: A Moving Number Card Puzzle
Abstract:
At 2026 MAA Southeastern Section Spring Meeting, a moving card puzzle was introduced in Math Treasure Hunt. Five cards numbered from 1 to 5 are arranged in the ascending order. In each move, one card from the two ends is inserted into the middle of the other cards. The number of the inserted card stays while the two adjacent cards increase by 1. Players are tasked to find a way to make all numbers 5. In this talk, we will first analyze the solvability of this puzzle and its variations. We will also illustrate the minimum moves needed for all these puzzles. Some possible ways to make the “unsolvable” variations solvable will then be discussed.

Name(s): Keesha Go
Affiliation(s): UNCG
Title: GRIDS: A graph structure learning framework for omics data
Abstract:
Recent development in high-throughput omics technologies has led to advancements in data-driven multi-omics disease subtyping of complex diseases such as cancer. Integrating data from multiple omics perspectives and leveraging graph-based machine learning methods can yield richer patient representations. However, high dimensionality, noise, and cross-omics discrepancies hinder reliable graph construction and alignment, while fixed graph structures fail to capture diverse patient relationships. To address this issue, we propose GRIDS, a graph structure learning framework that builds a separate patient graph for each modality (DNA methylation, mRNA, and miRNA) and uses a multi-head weighted-cosine graph learner anchored to an initial k-NN graph. Each graph is encoded by a two-layer graph convolutional network, and individual predictions are combined with averaged late fusion. We evaluate the model under nested cross-validation on the TCGA-BRCA dataset and achieve an accuracy of 87.96% and a weighted F1 score of 87.83%, outperforming state of the art multi-omics models.

Name(s): Md Arifuzzaman
Affiliation(s): North Carolina State University
Title: Effects of Aortic Coarctation Severity on Pressure, Flow, and Wave Dynamics in One-Dimensional Arterial Network
Abstract:
Aortic coarctation (CoA) is a narrowing of the proximal descending aorta that alters arterial hemodynamics, generating a significant pressure difference between the upper and lower body. This study applies an image-informed 1D fluid dynamics model to predict hemodynamics in a porcine sham and CoA aorta. The aortic, head, and neck vessel geometry is extracted from magnetic resonance images, and smaller vessels are represented by structured trees. A pressure-loss relation accounts for the effects of the CoA. Model predictions are compared with experimental pressure and flow measurements, and wave intensity analysis (WIA) characterizes forward and backward traveling waves. The calibrated model predicts measured flow and the pressure difference across the coarctation. Increasing the CoA severity amplifies the forward and backward compression waves in the ascending aorta and attenuates the WI in the descending aorta. Progressive reduction of the CoA radius from 0.6 to 0.1 cm increases pressure difference from approximately 15 to 60 mmHg. It substantially reduces descending aortic flow, while increasing flow through the head and neck vessels. Because the inlet waveform is prescribed, these simulations isolate the effects of geometric narrowing on downstream flow redistribution, showing how localized narrowing can cause network-wide changes in pressure, flow, and wave dynamics.

Name(s): Nakul Haridas
Affiliation(s): North Carolina State University
Title: Complexity of the Energy Landscape of t-SNE
Abstract:
t-SNE is one of the most widely used tools for visualizing complex, high-dimensional data, with applications ranging from genetics to machine learning. It works by finding a representation of the points in a two or three-dimensional picture so that points which are similar in the original data end up close together. Despite its popularity, t-SNE can produce misleading pictures: it may invent clusters that do not exist, tear apart simple shapes, or give different results each time it is run. Our work aims to explain some of this observed phenomenon mathematically. We show that we can utilize the symmetry of the input space to construct infinitely many distinct critical points of the algorithm, a fact that we can directly illustrate with numerical experiments.

Name(s): Nigar Sultana
Affiliation(s): Department of Mathematics, North Carolina State University
Title: Modeling Pulmonary Hemodynamics and Lung Tissue Perfusion Using a Mixed-Dimensional Computational Approach
Abstract:
Multiscale computational models with anatomically accurate geometries let researchers study blood flow through the lungs and characterize the hemodynamics of the pulmonary circulation. Existing studies often model arterial flow and tissue perfusion separately, leaving a gap in approaches that connect these two scales. This study develops a coupled model that links a one-dimensional (1D) pulmonary arterial network to a three-dimensional (3D) tissue perfusion model. In the arterial network, flow and pressure are predicted using a 1D fluid dynamics model derived from the Navier-Stokes equations for incompressible flow. The lung tissue is modeled as a porous medium, with flow driven by pressure differences between sources (ends of the terminal arterial vessels) and sinks (inflows into the venous network). A 3D Darcy-type equation governs this pressure-driven transport and is solved across the full lung volume using a finite element method. The lung volume, terminal vessel locations, and vascular geometry are obtained by segmenting a CT image from a healthy adult. The model predicts pressure fields and regional blood flow patterns throughout the lung, giving an integrated view of arterial flow and tissue perfusion. It provides a basis for future study of pulmonary vascular conditions such as pulmonary hypertension.

Name(s): Peyton Jackson, Emiliano Mercado
Affiliation(s): Columbia University, UC Berkeley
Title: Optimized Persistence Distance
Abstract:
Topological data analysis (TDA) is frequently used for quantifying the “shape” of data such as latent representations in neural networks or geospatial datasets. Despite the name, existing TDA methods are not invariant to effects such as (anisotropic) scaling, so the true topology of data can be obscured by differences in scale. In particular, topological disparity, typically measured by a persistence distance (bottleneck or Wasserstein distance between persistence diagrams), can be inflated by feature rescaling, while topological similarities can be missed. To address this, we define a new directed discrepancy measure, which minimizes persistence distance over a family of user-defined transformations of the data such as linear, affine, or diagonal transformations, generalizing the dilation-invariant bottleneck dissimilarity of Cao et al. The symmetrized version of this discrepancy, which we call optimized persistence distance (OPD), attempts to resize the topological signal in each dataset for best alignment under a set of constraints, rather than simply normalize the data. We focus on OPD as a comparison tool for neural-network latent representations. Unlike traditional persistence distance, OPD overcomes initialization noise to cluster representations by dataset topology and identifies otherwise hidden trends in data poisoning effects. We also use OPD on a geospatial pollution dataset, where it effectively compares the shape of the data rather than being dominated by differences in overall scale.

Name(s): Samir Maanaki
Affiliation(s): UNCG
Title: Statistical Models and Neural Networks: A Comparative Study in Time Series
Abstract:
Time series forecasting plays an important role in finance, economics, and many other fields. The classical statistical model ARIMA has been widely used, while neural network models that are capable of learning patterns over time, such as LSTM and RNN, have gained recent popularity. However, forecasting research is divided on whether statistical or deep learning approaches perform better. Accurate forecasting models are crucial to allow business and researchers to make informed decisions based on forecasted values. In this study, we simulated time series data generated from multiple ARIMA processes to compare ARIMA, LSTM, and RNN under different sample sizes. We used the RMSE, a common prediction accuracy metric, to evaluate forecasting performance. We found that in large sample size environments, with 9,000 training observations, all three models have similar performance. In small sample size environments, with 100 training observations, we found that LSTM and RNN perform worse than ARIMA. ARIMA requires the forecaster to select specific parameters to perform well, while deep learning models do not require this step. Overall, neither approach demonstrates a clear superiority. Sample size and ease of parameter selection should guide model choice.

Name(s): Siming Jia
Affiliation(s): University of North Carolina Greensboro
Title: Sudoku Number of Rook Graph
Abstract:
Sudoku is a logic puzzle where numbers are placed basic on row, column, and block constraints. A part of sudoku asks what the minimum number of clues is needed in each given row, column, and block constraints of a Sudoku puzzle is. This can be applied to graph theory as a Sudoku Number, which is the number of colored vertices that need to complete proper coloring. This research is about the Sudoku Number of rook graphs. Rook graphs are graphs that have vertices that are represented as cells on a grid, and the edges are the rows and columns. Our goal is to find patterns and formulas to find the Sudoku numbers or these graphs. We use constraint programming to give us the first few Sudoku numbers and possible coloring. We use that to generate more coloring. We found the formula for two row rook graphs and the upper bound for others.

Name(s): Sivamurugan Velmurugan
Affiliation(s): North Carolina School of Science and Mathematics
Title: A Physics Informed Graph Attention Transformer with Weather Driven Delay Propagation for Air Traffic State Prediction
Abstract:
Accurate prediction of air traffic states, including airport queue lengths and cumulative terminal-area travel times, is essential for efficient air traffic management and congestion mitigation. Forecasting remains challenging due to complex spatiotemporal dependencies, and data-driven models often overlook the physics of queue formation and dissipation. Although physics-informed models such as PIGAT (Physics Physics-Informed Graph Attention Transformer) improve prediction accuracy by incorporating queue dynamics, they do not explicitly model how weather-induced delays propagate through interconnected airport networks. Delays rarely stay local: an aircraft delayed at one airport carries that delay to its next destination, spreading disruptions across the network. We introduce a novel weather-driven delay propagation equation as an additional physics-informed loss within PIGAT. The proposed equation combines local queue congestion, weather conditions, and inbound delays from connected airports. These interactions are weighted using PIGAT’s existing blended flow-based and learned adjacency matrices, which incorporate observed air traffic flows and relationships learned by the model. This enables the model to better capture cascading weather-related delays across the national air transportation network. Computational results demonstrate improved prediction accuracy compared with the baseline, particularly during periods of severe weather and network congestion.

Name(s): Stephen Agyeah
Affiliation(s): North Carolina Agricultural and Technical State University
Title: Distribution Function Estimation for Sensitive Quantitative Variables Using Item Sum Techniques and Item Sum Double List Technique
Abstract:
Sensitive quantitative data are often difficult to collect accurately because respondents may misreport private, stigmatizing, or socially undesirable behaviors under direct questioning. This study considers estimation of the cumulative distribution function (CDF) of a sensitive quantitative variable using two indirect questioning methods: the Item Sum Technique (IST) and the Item Sum Double List Technique (ISDLT). Unlike approaches that focus mainly on the mean, the goal is to estimate the full distribution while preserving respondent privacy. Empirical CDF estimators are developed for IST and ISDLT using long list and short list responses, with truncated versions used to keep estimates within [0,1]. Kernel based versions are also considered. Performance is studied through bias, variance, and mean squared error. A Monte Carlo simulation study examines Beta, Gamma, Normal, and Chi-square settings under different sample sizes, allocation probabilities, control variable variability, and dependence structures. Results show that performance depends strongly on survey design. Lower control variability improves stability, while larger variability increases estimation error. Negative dependence can reduce error, whereas positive dependence can increase it. ISDLT generally improves efficiency by combining two complementary list structures. The methods are also applied to real sensitive-behavior data involving sexual partners and pornography consumption.

Name(s): Tanner Byer
Affiliation(s): North Carolina State University
Title: Adaptive Meshes: Task-Aware, Interpretable Featurization of Persistence Diagrams.
Abstract:
Topological Data Analysis (TDA) provides a powerful framework for capturing multi-scale structural features of complex datasets across dimensions. Persistent homology, a cornerstone of TDA, encapsulates the evolution of these topological signatures in a persistence diagram (PD). These summaries are variable-sized multisets of persistence pairs (discrete point measures) and are therefore not readily compatible with common deep learning models. Several featurization methods exist to convert PDs into vector representations. However, these approaches often rely on fixed discretizations or manual hyperparameter tuning, and do not leverage data labels in a supervised setting. In this work, we propose a supervised, data-driven framework for task-aware, adaptive representation learning directly on the space of persistence diagrams. We introduce Adaptive Meshes (AM), an approach that sequentially refines a nonuniform discretization of persistence diagram space, guided by a downstream classification objective. Drawing on ensemble learning, AM propagates this refinement across stratified data subsets and progressively concentrates it on misclassified instances, producing an aggregated collection of task-informed, discriminative features. Empirical evaluations across benchmark data modalities demonstrate that our adaptive featurization yields competitive classification accuracy while preserving interpretability by isolating globally discriminative regions of the persistence domain.

Name(s): Thomas Payne
Affiliation(s): UNCG
Title: Deciding Automorphic Equivalency
Abstract:
We overview progress on an algorithm constructing if possible an automorphism mapping one group element to another, given a pair of elements in a large family of groups of interest to geometric group theorists. This work is placed in the context of newly published results on graph product of group automorphisms, and we draw comparisons with solutions to this problem in simpler cases such as for free groups and general linear groups over the integers. The challenge and role of decision problems in the theory of infinite, finitely presented groups is sketched, as well as how the combinatorial technique of peak reduction can be used to solve this specific problem.

Name(s): Upasana Aryal
Affiliation(s): Knox College
Title: Reversed Dickson polynomials and Differential Equations
Abstract:
Dickson polynomials are an important family of special polynomials with applications in algebra, number theory, coding theory, cryptography, and the study of finite fields. Classical Dickson polynomials of the first and second kinds are known to satisfy certain differential equations, which provide useful information about their mathematical structure. Reversed Dickson polynomials were introduced in 2009 by exchanging the roles of the variable and parameter in the classical Dickson polynomials. Most previous research has focused on their behaviour over finite fields, while their differential properties have received much less attention. In this work, we investigate differential equations associated with reversed Dickson polynomials. In particular, we study the reversed Dickson polynomials of the first kind, second kind, and more general higher kinds, with the aim of extending known differential properties of classical Dickson polynomials to their reversed counterparts.

Name(s): Yutong Wu
Affiliation(s): University of North Carolina at Chapel Hill
Title: A Real-Time Learner-Aware Adaptive Tutoring Prototype Using Facial Behavior and Large Language Models
Abstract:
Most AI-powered tutoring systems respond to students only after they explicitly ask for help. However, students may struggle without recognizing when they need assistance or knowing how to ask for it. This project develops a real-time adaptive tutoring prototype that uses facial behavior to identify potential confusion and provide timely, personalized learning support. Using video recordings of students completing programming tasks, we trained a machine learning model to estimate confusion from facial features. The model was integrated into a prototype that continuously monitors facial behavior, tracks changes in estimated confusion over time, and determines when additional support may be helpful. Based on the learner’s estimated state, a large language model generates responses such as hints, alternative explanations, or examples. Preliminary results demonstrate the feasibility of combining facial analysis, learner-state estimation, and AI-generated instructional support in a real-time system. Future work will improve the accuracy of confusion detection, refine intervention strategies, and evaluate the system through student interactions. Ultimately, this research aims to make AI tutoring more responsive to individual learning needs.

Name(s): Zehaan Naik
Affiliation(s): Duke University
Title: Least Absolute Deviations Estimation for Linear and Sinusoidal Models
Abstract:
Statistical models are often fit by minimizing squared errors, but this approach can be strongly affected by outliers and unusually large errors in the data. This project develops robust alternatives based on least absolute deviations, estimating model parameters by minimizing the total absolute error. We first develop an efficient computational method for least absolute deviations regression in linear models, including settings where the number of predictors is large relative to the number of observations. Our algorithm avoids matrix inversion and specialized optimization software, while achieving a per-iteration computational complexity of order n p log n and remaining applicable even when the number of predictors exceeds the number of observations. We then extend this framework to sinusoidal models, developing a similarly efficient approach for robust estimation of periodic signals. The proposed methods combine computational scalability with theoretical guarantees and demonstrate strong performance against traditional optimization-based approaches. Applications to real-world time series show that these methods can provide substantially more reliable parameter estimates in the presence of outliers and non-Gaussian noise, offering a unified and practical framework for robust statistical estimation.

Participants are responsible for booking their own accommodations. Those who are awarded travel funding can be reimbursed after the conference. UNCG has pre-arranged rates with the following places, but you are welcome to shop around.

• Comfort Inn Greensboro-Kernersville. Click here. ***This hotel allows 18+ to stay.
• DoubleTree by Hilton. Click here. ***This hotel requires someone 21+ to stay.
• Drury Inn & Suites Greensboro. Click here. ***This hotel allows 18+ to stay.

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
Associate Professor
UNC Greensboro

Jianping Sun
Associate 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.