Contributed Session 2
Session 2.0
8:35 to 8:55
9-201
Audrey Eley*
Florida Institute of Technology
Evaluating Synthetic Data Augmentation Methods in Radiomics-Based Lung Staging
This study compares Bootstrap resampling and SMOTE for data augmentation for imbalanced medical data where Lung1 cancer dataset was used for case study and classification of cancer stage was performed using XGBoost. Post-hoc analyses examined majority voting across models, error overlap, and misclassification patterns using 100 Monte Carlo train–test splits. Synthetic radiomics data generated via SMOTE were visualized and assessed for randomness and feature fidelity across multiple runs. While SMOTE produced sufficiently random datasets similar to the original distribution, Bootstrap augmentation consistently yielded greater model-stability and slightly superior performance. These results suggest resampling-based-augmentation may better justify synthetic-generation for clinical-radiomics.
Session 2.0
8:35 to 8:55
9-202
Furio Gerwitz*
University of North Florida
The Chromatic Number and Its Bounds
A proper vertex coloring of a simple graph assigns colors to the vertices such that no adjacent vertices share the same color. The chromatic number of a graph is the minimum number of colors for which such a coloring exists. The chromatic number is a fundamental characteristic of a graph, related to the NP-Complete k-colorability problem, with numerous applications in computing and optimization. This presentation discusses bounds for the chromatic number, including Brook’s theorem for an upper bound and clique-based theorems for lower bounds, ultimately providing insight into the relationship between graph properties, colorings, and the chromatic number.
Session 2.0
8:35 to 8:55
9-203
Brian Curtin
University of South Florida
Bitrades for cooperative pairs
Borrowing from the theory of Latin bitrades, we develop a corresponding theory for a generalization of a Latin square dubbed a cooperative pair. A cooperative pair consists of a column Latin matrix and a row Latin matrix such that every possible pair of entries appears exactly once in some position. Roughly speaking, the first part of the bitrade is a substructure that can be excised from a cooperative pair and a second part can be substituted to preserve the cooperative pair property. We shall survey a few of our results and offer some examples.
Session 2.0
8:35 to 8:55
9-211
Fernanda Rocha Miranda*
Florida Institute of Technology
Distributional Survival Analysis and Risk Stratification in Lung Cancer
This study examines overall survival in a cohort of lung cancer patients using classical survival analysis methods. Data from 398 patients were analyzed, with overall survival defined as time from baseline assessment to death, and right- censoring applied for incomplete follow-up. Survival functions were estimated using the Kaplan–Meier method, and group differences were assessed via log-rank tests. Statistically significant survival differences were observed by age group and gender, while no significant differences were found across histological subtypes or clinical stages. A Cox proportional hazards model identified age as the primary independent predictor of mortality risk.
Session 2.0
8:35 to 8:55
9-218
Brandon Cribbs*
University of North Florida
Reed-Solomon Error-Correcting Codes
Brandon Cribbs - University of North Florida (Graduate Student) Reed-Solomon Error-Correcting Codes Unlike Hamming Codes which correct data one bit at a time, Reed and Solomon proposed an algorithm that corrects multiple bits at a time. The Reed-Solomon Codes, introduced in 1960, are based on Galois Fields, Cyclic Groups, Language Automata and Coding Theory. These codes impacted multiple industries such as space telecommunication.
Session 2.0
8:35 to 9:20
9-219
Stephen Jennings
MathGPT.ai
MathGPT.ai: An AI-Powered Platform Built for Math
Learn how MathGPT.ai provides curriculum-aligned, instructor-led AI tutoring that is accurate, cheat-proof, and infinitely patient—built within a complete course and assignment management system. This session will highlight how MathGPT.ai supports student understanding, reduces math anxiety, and maintains academic integrity while offering an affordable solution for departments. Faculty will also learn how to explore the platform and participate in Summer or Fall 2026 pilots.
Session 2.0
9:00 to 9:20
9-201
Calvin Rose*
Eckerd College
Creating a Model for Mangrove Population Dynamics with Python Script
Within ecology, given the rise in sea levels and the subsequent intrusion of salt water, it is important to see how mangroves respond to these environmental changes and stressors. Invasive species can also encroach on natural mangrove habitats causing them to behave irregularly. After the introduction of Brazilian Peppertrees (BP) into Florida in the 1950s, the mangrove population has suffered critical losses. So far there has not been a publicly available computer model to try and represent mangrove populations, with or without invasive species like the Brazilian Peppertree. This project seeks to create models that accurately represents mangrove population dynamics with the possibility of rule changes for mangroves in different regions and climates. The research project culminated in two python based 2D cellular automata that took into account salinity, survivability, birth rates, aging, storm events, and species interaction. These parameters can be modified to emulate mangroves in different regions and climates, changing the resulting behavior of the species in the model. One model simulates mangrove dynamics in an island setting while the other simulates dynamics for a coastline ecosystem. This project has potential for new editions to the original code, improving the accuracy of the model. Improvements could include fluctuating species’ survival, growth, and chance of death based on age or salt table changes due to hurricanes. With python, these additions can add a new layer of complexity to more accurately model how real mangroves behave in the wild.
Session 2.0
9:00 to 9:20
9-202
Furio Gerwitz*
University of North Florida
Error Correcting Codes
Error correcting codes are structures which recover transmitted messages even in the case of errors, provided the number of errors remains within a threshold. We introduce error correcting codes, describe perfect error correcting codes and linear codes, and discuss their properties. Finally, we introduce binary and ternary Golay codes, verify they are perfect error-correcting codes, and note their prominent usage in the Voyager missions.
Session 2.0
9:00 to 9:20
9-203
Angela Angeleska
The University of Tampa
Balanced Complexes in Metabolic Networks
The talk presents an analysis of metabolic networks from structural perspective. A metabolic network can be viewed as a directed graph with vertices denoting complexes (of reactants) and edges representing reactions. In addition, the reaction fluxes within a network can be represented by edge weights (functions) in the graph. If N is the stoichiometric matrix of the metabolic network, then the reaction fluxes are vectors v with the property vN=0 when the network is in a steady state. Next, we study multi-reaction dependences over the set of steady states and how they affect balancing in specific areas of a metabolic network, defined by the complexes of the network. In particular, we look at the effect of balanced complexes, concordant complexes and forcedly balanced complexes including their relationship to each other. The study utilizes matrix theory and linear programming.
Session 2.0
9:00 to 9:45
9-210
Robin Zide
Indian River State College
Equations of the Mind: Linking Algebra, Psychology, and Authentic Life for Student Wellness
This interactive session explores Equations of the Mind, a linked learning model connecting College Algebra, Introduction to Psychology, and Authentic Life. Participants will experience how the family of functions and the Absolute Value Theorem serve as metaphors for personal growth and post-traumatic transformation—illustrating that positive inputs yield positive outcomes, while setbacks can still produce strength and insight. Rooted in cognitive psychology and student wellness, this approach blends quantitative reasoning, emotional intelligence, and reflective practice to enhance engagement, resilience, and purpose in both mathematics education and life learning.
Session 2.0
9:00 to 10:45
9-212
Bernhard Klingenberg
New College Florida
What does a Master's in Applied Data Science Look Like
What is Data Science and what do data scientists do? What tools are they using? Learn about Data Science in general and about the structure of the Applied Data Science master’s program at New College Florida in particular. I will present recent student projects ranging from solar flare identification to pistachio crop pest management. I’ll also discuss the necessary mathematical and computational background required to enter a master’s program.
Session 2.0
9:00 to 10:45
9-215
Anurag Katyal
Palm Beach State College
Creating AI-Resistant Interactive Activities to Facilitate Active Learning
Do you want to create AI-resistant, engaging, interactive activities to facilitate active learning for your students? This hands-on workshop will introduce participants to the core features of Doenet, a free and open source platform, including answer checking, graphing, and randomization. Participants will work on designing their own classroom-ready learning activity, with opportunities for feedback. Bring a laptop. No prior programming experience necessary, but experience with LaTeX will be helpful.
Session 2.0
9:00 to 9:20
9-218
Christian Corbett*
Florida Atlantic University
Nuclei and d-elements in algebraic frames without FIP
A frame is algebraic if each element is the supremum of the compacts below it. Algebraic frames have been studied extensively, often with the additional criterion that the compact elements possess the finite intersection property (FIP). In this talk, we will explore classes of algebraic frames without FIP. In particular, we will investigate inductive closure operators, focusing on the $d$-operator, and its corresponding fixed points (the $d$-elements). Without FIP, some familiar properties like nuclearity can fail.
Session 2.0
9:25 to 9:45
9-201
Kaitlyn Dunn*
Florida Institute of Technology
Spectral Clustering of Survival–Radiomic Graphs Reveals Hidden Structure in Lung Cancer
Prognosis in lung cancer varies substantially among patients with the same TNM stage, indicating limitations of purely anatomical staging. We construct a survival–similarity graph integrating CT-derived radiomic features with survival time to uncover latent biological structure in a lung cancer cohort. Patients are represented as nodes, with edge weights defined by the product of radiomic similarity (Gaussian kernel on standardized features) and survival similarity (exponential decay of survival differences). A k-nearest-neighbor graph (k = 10) preserves local structure, and spectral clustering of the graph Laplacian to identify three distinct risk groups corresponding to poor, intermediate, and long survival.
Session 2.0
9:25 to 9:45
9-202
Anne Howell*
University of North Florida
Ramsey Theory for Finite Graphs: Complete disorder is impossible.
Ramsey theory formalizes the principle that sufficiently large structures must contain highly ordered substructures. The theory is introduced through the classical result that any group of six people necessarily contains either three mutual acquaintances or three mutual strangers. We discuss this in the context of edge-colored complete subgraphs. Following the inductive proof, a non-trivial example illustrates how Ramsey numbers arise naturally and why determining exact values is difficult.
Session 2.0
9:25 to 9:45
9-203
Austin Anderson
Florida Polytechnic University
Extremal Combinatorics with Sums of Squares
We discuss the behavior of optimizers for the following discrete optimization problem: Given a set of positive integers $S_n=\{1,2,\ldots n-1\},$ what is the \textit{smallest} number of subsets, $M(n),$ partitioning $S_n$ with the property that the sum of the squares of the elements in each subset is at most $n^2?$ \par We present numerical evidence supporting the conjecture that $M_n$ is as large as possible: I.e. $M_n=\left\lceil(\sum_{j=1}^{n}j^2)/n^2\right\rceil.$ We further connect this problem to hypergraph matching theory.
Session 2.0
9:25 to 9:45
9-211
Andrew Murphy*
Embry-Riddle Aeronautical University
A Comparative Classical and Data-driven Facial Analysis of Wide-Field-of-View Lens Captures
WFOV lenses are becoming popular in facial recognition due to the fact that they enhance subject coverage and improve the chances of detecting target faces. However, wide-angle optics introduce nonlinear distortion around the image periphery, which degrades the performance of recognition pipelines. In this talk, we use WFOV lens captures to analyze facial recognition using classical low-complexity algorithms based on the discrete Fourier transform (DFT), discrete cosine transform (DCT), principal component analysis (PCA), and data-driven learning with convolutional neural networks. Finally, we present computational efficiency, compression, accuracy, and precision of recognizing distorted images with qualitative and quantitative measures. Acknowledgment: This is a joint work with Max E. Raabe, Giovanni C. DeCapua, Anthony M. Cafiso, Kaden E. Van Leuven, and Sirani M. Perera.
Session 2.0
9:25 to 9:45
9-218
Donald McGinn
University of West Florida
Prime Producing Polynomials, Pell-type Equations, and the Near-square Prime Conjecture
An outstanding conjecture in number theory is that there are infinitely many near-square primes, which are primes of the form x^2+1. In this talk, we analyze the factorizations of near-square integers and make a connection to Pell-type equations. Also, we show multiple conjectures that are equivalent to the near-square prime conjecture.
Session 2.0
9:25 to 10:20
9-219
Peng Feng
Florida Gulf Coast University
Boundedness, stability and turing patterns in a quasilinear three-species model with prey-taxis and predator-repulsion
This study provides a rigorous mathematical analysis of a quasilinear reaction-diffusion system modeling a one-prey, two-predator ecosystem subject to attractive prey-taxis and mutual predator-repulsion. The primary results include establishing global existence and uniform boundedness of classical solutions for spatial dimensions $d\leq 2$ by deriving uniform-in-time a priori estimates based on energy methods, maximal regularity, and a bootstrapping procedure. The study employs Lyapunov functional analysis to derive sufficient conditions for the global asymptotic stability of both the prey-only equilibrium and the interior coexistence equilibrium. Crucially, Turing instability analysis demonstrates that the sole mechanism of predator-predator repulsion can induce diffusion-driven instability in the system, leading to the formation of non-constant positive steady states characterized by spatial segregation and anti-phase patterns in the competing predator densities, thereby acting as a mechanism for predator coexistence. Numerical simulations are also carried out to complement the theoretical results.
Session 2.0
10:00 to 10:20
9-201
Jonathan Bartik*
University of North Florida
A Mathematical Model for Coupled Rocket Trajectory and Passive Stability
Sounding rockets are simple-bodied aerospace vehicles consisting of a nosecone, fuselage, and stabilizing fins, used to study atmospheric and flight behavior. Rocket trajectory is governed by position, velocity, and fuel mass, while stability is described by nose angle and roll, with \emph{passive stability} implying sole reliance on aerodynamic design. Although small changes in orientation can strongly influence overall motion, trajectory and stability are typically modeled separately. In this paper, we develop a coupled mathematical model using a system of ODEs and analyze the system through trajectory plots, phase-plane diagrams, and a compounded static margin formulation to illustrate stability behavior.
Session 2.0
10:00 to 10:20
9-202
Anne Howell*
University of North Florida
Frucht's Theorem
A deep and surprising connection between group theory and graph theory exists: every finite group arises as an automorphism group of a finite graph. Algebraic and graph-theoretic foundations underlying the theorem are introduced, including group actions, generators, and graph automorphisms. An interesting construction employing pendant subgraphs is examined, through which directed Cayley graph structure is replaced by an equivalent undirected representation. Examples, accompanied by detailed diagrams, are provided to illustrate explicit constructions of graphs whose automorphism groups are isomorphic to prescribed finite groups.
Session 2.0
10:00 to 10:20
9-203
Binod Rimal
University of Tampa
Neural Signatures of Meditation Expertise: EEG-Based Unsupervised Modeling
As mental health and stress management are growing concerns, the demand for effective mental wellness and overall well-being continues to rise. Meditation is increasingly recognized as an effective approach for managing mental health. This study aims to determine whether an individual is an expert meditator based on Electroencephalography (EEG) signals using unsupervised machine learning models. The comparative study examines whether core EEG signals alone are sufficient or if external sensory information is required to identify meditation expertise. These findings strengthen the scientific credibility of meditation and support its broader adoption in both clinical and everyday settings.
Collaborators: Ola A. Abdelnaby, University of Tampa; Rohit Ramesh, Tampa Preparatory School
Session 2.0
10:00 to 10:45
9-210
David House
University of North Florida
Calculus as the Engine of Large Language Models
Large language models such as ChatGPT now shape how our students write, study, and interact with information. But what mathematics actually powers these systems? This talk reveals that at their core, modern AI models are trained using ideas familiar from undergraduate calculus: derivatives, gradients, and the chain rule. We will frame language-model training as a large-scale optimization problem, beginning with a simple notion of “loss” and building intuitive geometric pictures of error landscapes, gradients, and gradient descent. Visual metaphors will be used throughout to show how partial derivatives guide learning and how backpropagation is nothing more than the chain rule applied at massive scale. Designed for math educators, this talk emphasizes conceptual understanding over technical detail and highlights concrete ways these ideas can be used to motivate calculus topics in the classroom. No background in machine learning is assumed.
Session 2.0
10:00 to 10:20
9-211
Ken Mulzet
Florida State College at Jacksonville
Pythagorean Quadruples (and beyond!)
A \textbf{Pythagorean triple} is defined to be a set of positive integers $(a, b, c)$ that solves the Pythagorean equation $$a^2 + b^2 = c^2$$ We define a \textbf{Pythagorean quadruple} to be a set of positive integers $(a, b, c, d)$ that solves the equation $$a^2 + b^2 + c^2 = d^2$$ In this talk, I will present various methods for finding Pythagorean triples and Pythagorean quadruples, as well as similar equations. This will be a fun and interactive talk, so be sure to bring pencil and paper!
Session 2.0
10:00 to 10:20
9-218
Mohamed Jaber
Florida Institute of Technology
Interpretable Radiomics for Survival Prediction in Non–Small Cell Lung Cancer
Anatomic staging incompletely captures tumor biology in non–small cell lung cancer (NSCLC). Using 398 NSCLC patients from TCIA, we evaluated whether CT radiomics provides a compact, interpretable prognostic signal beyond stage. One hundred seven features were grouped into biologically motivated families and analyzed with a multivariate sparse group lasso Cox model (MSGL Cox), with cross-validation and stability selection. A subset of radiomic features was identified as the dominant predictor of survival. This subset stratified the patients across different subgroups and revealed risk heterogeneity that was not explained by stage alone.
Session 2.0
10:25 to 10:45
9-201
Jay Nulph*
University of Central Florida
Spatial Autoregression Model: Dependent Errors
Asymptotic results are given for testing $H_0:\alpha=\beta=1$ for the doubly geometric model $Z_{ij} = \alpha Z_{i-1,j} + \beta Z_{i,j-1} - \alpha\beta Z_{i-1,j-1}+\delta_{ij}$, where $\delta_{ij}$ is a dependent error structure. The Gauss-Newton estimation procedure is used.
Session 2.0
10:25 to 10:45
9-202
Raymond Clines*
University of North Florida
Generalizing Pascal’s Triangle
Pascals’ Triangle and its many properties have been highly studied by mathematicians. In this presentation, we will explore its extension into 3 dimensions with Pascals’ Pyramid. First, we will establish an indexing system for the pyramid and then use this to generalize the properties of the triangle into higher dimensions. We will also introduce and prove several theorems about the pyramid’s structure and show its application to other areas of combinatorics and probability.
Session 2.0
10:25 to 10:45
9-203
Mariya Ivanova
University of Tampa
Teaching Smarter, Not Harder - 10 Practical Ways AI Can Transform the Classroom
This session explores how Artificial Intelligence can serve as a powerful "co-pilot" for educators, moving beyond the hype to focus on ten practical, high-impact applications for the modern classroom. From streamlining lesson planning and administrative tasks to providing instant student feedback and supporting differentiated instruction for diverse learners, participants will discover how AI tools can significantly reduce burnout while enhancing personalized learning. The presentation balances innovation with responsibility, addressing essential ethical considerations such as data privacy and academic integrity.
Session 2.0
10:25 to 10:45
9-219
Jared Bunn
Florida Polytechnic University
The Putnam at Florida Poly - My Experience
In this talk, I will discuss my experience in training a small group of students at Florida Polytechnic University to prepare for the most recent MAA Putnam Competition. I will share my approach to the training sessions and my experience supervising the competition. In addition, I will share my thoughts on why I think more students should participate in the Putnam competition.
Session 2.0
11:00 to 11:20
9-201
Hayden Tyler*
University of North Florida
P-adic Numbers and the Hasse Principle
In this paper, we discuss the $p$-adic numbers and the Hasse Principle. We begin by defining absolute values, but with more detail than usual. Of interest to us is the $p$-adic absolute value. Using this notion, we construct the $p$-adic numbers as an extension field of the rational numbers using Cauchy sequences of rationals. However, we will use the $p$-adic absolute value rather than the usual absolute value. We then provide basic properties of the $p$-adic numbers and define common arithmetic operations on them. Finally, we discuss the Hasse Principle, which suggests that we can learn about the field of rationals by studying the real numbers and $p$-Adic numbers.
Session 2.0
11:00 to 11:20
9-202
Raymond Clines*
University of North Florida
An Introduction to the Mathematics of Juggling
In addition to its entertainment and visual appeal, the art of juggling offers substantial opportunities for mathematical analysis. In this presentation, we will formalize juggling into a notation system called siteswap, and provide examples and a live juggling demonstration of how siteswaps correspond to real juggling patterns. We will also define and prove the necessary conditions for a siteswap to be a valid pattern. Additionally, we will discuss the enumeration of siteswaps and more advanced juggling techniques.
Session 2.0
11:00 to 11:20
9-203
Erin Griesenauer
Eckerd College
Leveraging Trauma-Informed Pedagogy to Support Students Through a Hurricane
Experiencing a hurricane can by traumatic for students and faculty alike. By taking steps to acknowledge this trauma, we can help our students stay focused and motivated in the event of an evacuation. In this talk, I will provide an introduction to trauma-informed pedagogy. We will discuss how the principles of trauma-informed pedagogy can be translated into concrete course policies and activities in a mathematics class. We will focus on how these considerations can be used to help support students during a semester with an emergency evacuation, including ideas for what to do before, during, and after an evacuation.
Session 2.0
11:00 to 11:20
9-212
James Young*
Florida Polytechnic University
Integer factorizations and exact zero-divisor graphs of the integers modulo n
In the integers modulo n, a pair of zero-divisors are exact if they generate each other’s annihilators. We will explore the relationship between the structure of exact zero-divisor graphs and integer factorizations. In particular, an algorithm is presented that efficiently computes these graphs, which are then stored in an interactive database. Computational properties are considered with a view toward potential cryptographical applications.
Session 2.0
11:00 to 11:45
9-219
Gayathri Krishnan
University of Central Florida
Self Advection of a Thin Vortex Filament in Incompressible Fluid
A thin vortex filament in an incompressible fluid, experiences self-induced motion. The self-advection of the filament is explored by working with three models: • Da Rios-Betchov • Hasimoto • Shivamoggi-van Heijst formulations. These models were derived using the Local Induction Approximation for the velocity of the filament. Numerical solutions to these formulations using Optimal Homotopy Analysis Method are presented. The viscous effects in the fluid cause a slipping motion of the filament. The effects of slipping motion on the kinematical and dynamical properties of the filament are investigated.
Session 2.0
11:25 to 11:45
9-211
Cindy Ceijas*
Florida Polytechnic University
Combinatorial Approach to Course Scheduling at Florida Polytechnic
School operations, such as the timetabling problem, become a difficult optimization model as school enrollment increases. Allocating resources such as educators, classrooms, and time slots, under criteria like course level and course sequencing, is an integer NP-hard problem. This presentation will cover our ongoing work on two approaches to the timetabling problem. The first being a genetic algorithm and our analysis of different crossovers and mutation strategies, the second being the construction of a combinatorial model.
Collaborators: Alexander Joyce, Florida Polytechnic University
Session 2.0
11:25 to 11:45
9-212
Ranadeep Daw
University of West Florida
Causal Effects of Urban Amenities on airbnb Prices: A Hybrid Spatial Filtering Approach
We study the effects of urban amenities on nightly prices in short-term rental platforms such as airbnb. Prices are determined both by property characteristics and by their spatial location, which introduces complex local and neighborhood-level variations. We analyze airbnb listings in Broward County, Florida, using a two-stage semiparametric framework with explicit spatial tuning. A generalized additive model captures nonlinear effects of property attributes and broad geographic trends, while a low-rank Moran eigenvector basis filters residual fine-scale spatial dependence. This approach provides a data-driven framework to assess the spatially heterogeneous influence of amenities and neighborhood features, and offers interpretable insights into pricing strategies in densely distributed urban rental markets.