Session Index
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Undergraduate Session 1
1:40PM--2:55PM, DHC 102
Speakers: Dean Andreadis, Alexis Rainis, Ranim Abdelrazek, Mariam Mahmoud, Miki Lu
Undergraduate Session 2
1:40PM--2:55PM, DHC 108
Speakers: Jayna Penn, Jaclyn Troutman, Benjamin McDowell, Andrew Moody, Leah Miller, John Seibert
Undergraduate Session 3
1:40PM--2:55PM, DHC 110
Speakers: Kaden Hunter, Alexandra Ziegler, Peyton Haroldson, Juniper Manges, Dillon Stavarski, Emery Curry, Caleb Rice, Jack Raley, Howra Amirshokoohi
Undergraduate Session 4
1:40PM--2:55PM, DHC 210
Speakers: Noah West, Cole Pearson, Ethan Baratz, Alexander Glatfelter
Undergraduate Session 1
DHC 102
1:40PM, Dean Andreadis (Saint Josephs)
Archimedes
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Archimedes was a Greek mathematician and inventor who made major contributions to science and engineering. He is known for discovering buoyancy, creating the Archimedes screw, and advancing math, with lasting influence today.
Close Abstract1:55PM, Alexis Rainis (Saint Joseph's University )
Solving Proteins Puzzle: How Humans Outsmart Computers
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Protein structure prediction is a major challenge due to the complexity of protein folding. This work examines Foldit, a gamified platform that leverages human intuition to optimize protein conformations. By combining human strategies with computational methods, Foldit demonstrates how crowdsourcing can enhance prediction accuracy and inform hybrid optimization approaches when solving some of the most complex protein puzzles.
Close Abstract2:10PM, Ranim Abdelrazek, Mariam Mahmoud, Miki Lu (Saint Joseph's University)
Analyzing Neuron Action Potentials Through Calculus
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Neurons transmit information through action potentials, marked by rapid changes in membrane voltage. This work explores how calculus, particularly derivatives and graphical analysis, can model and interpret these signals, highlighting the connection between mathematical principles and neural processes.
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Undergraduate Session 2
DHC 108
1:40PM, Jayna Penn, Jaclyn Troutman (Kutztown University)
The Class Equation
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How are the elements of a group related to each other? The class equation is a powerful statement in group theory that highlights the importance of conjugacy classes. Conjugacy classes partition a group. Thus, the sum of the cardinalities of the conjugacy classes is equal to the order of the group. While determining the order of a group is not always difficult, the conjugacy class representation of the order gives insight into how elements of a group interact with each other. In this presentation, we will explore the components of the class equation and its implications.
Close Abstract1:55PM, Benjamin McDowell, Andrew Moody (Kutztown University)
Incremental Graph Game Unlike Any Neighbors at All
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In IGGUANA, a graph's vertices are all initially labeled 0, and players take turns incrementing labels. However, players must take care to never allow two identical (non-zero) labels to be adjacent The last player to make a legal move wins. We will examine which player has the winning strategy on simple graphs, e.g. book graphs, cycles, paths, and bipartite graphs. We then will show tools to analyze winning strategies for more complicated graphs.
Close Abstract2:10PM, Leah Miller (Dickinson College)
$T_r$-Colorings of Digraphs
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In this talk, we consider $T_r$-colorings of digraphs, where all color differences are forbidden except $r$. We focus on minimizing the maximum color used and we determine exact values for directed paths and cycles. We then extend these results to annular and wheel digraphs. For annular digraphs, we identify structural conditions under which optimal colorings with maximum color $r+1$ exist, as well as cases that limit such colorings. We also establish general bounds for wheel digraphs.
Close Abstract2:25PM, John Seibert (Commonwealth University of Pennsylvania - Bloomsburg)
Generalizing Negative Latin Square-Type Partial Difference Set Constructions via Abelian Techniques
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In 2009, Dr. John Polhill introduced product constructions to build new families of negative Latin square-type partial difference sets (PDSs). However, these constructions were initially restricted to abelian 2-groups that admit a specific partition by (16, 5, 0, 2) PDSs. Recent theoretical advancements, specifically a 2025 theorem by Davis et al., have shown that the validity of these product constructions depends solely on the parameters of the PDS partition. Hence, the dependency on the commutativity possessed by the searched groups is eliminated.
This talk reports on a successful computational search of the eight candidate groups of order 16 identified by Brady in 2025 that contain $(16, 5, 0, 2)$ partial difference sets. We confirm that exactly two non-abelian groups of order 16, $\mathbb{Z}_{2} \times D_{4}$ and $(\mathbb{Z}_{2} \times \mathbb{Z}_{2}) \rtimes \mathbb{Z}_{4}$, possess the required partition. By applying the generalization theorem, we extend Polhill’s 2009 constructions to these non-abelian groups for the first time. This result demonstrates that these combinatorial structures are more general than previously known and produces a new family of negative Latin square-type PDSs in larger non-abelian product groups.
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Undergraduate Session 3
DHC 110
1:40PM, Kaden Hunter, Alexandra Ziegler, Peyton Haroldson (Millersville University of Pennsylvania)
Charged Particle Transport in Electric and Magnetic Fields
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The motion of a single charged particle moving in an electromagnetic field can be modeled using Newton's second law and the Lorentz force. Given some initial parameters, the trajectory of any particular particle in an electromagnetic field can be illustrated using ordinary differential equations. However, in systems where it is necessary to consider an enormous number of particles, the individual trajectories of each particle matter less, and instead the dynamics of the population is studied. This project will discuss both types of models, with an emphasis on transport phenomena in charged particle populations using a partial differential equation model. Beginning with simple ordinary differential equations describing how a single particle moves in a linearly damped electromagnetic field system, a lumped population model is then introduced to describe the particle population. Next, the partial differential equation models of diffusion describe how the population of particles spread, drift, and escape from a finite region. Together, these models describe macroscopic transport laws.
Close Abstract1:55PM, Juniper Manges, Dillon Stavarski, Emery Curry (Millersville University)
Mathematical Modeling of Weathering Factors on Stone Stairs
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Since the dawn of civilization, stairs and other stone blocks have been a staple of human architecture. Historians study these structures to better understand many factors of the societies from which they originate. The goal of our research is to mathematically model and quantify weathering on stone stairs, factoring in rates from multiple causes of weathering. We utilize previously derived weathering rates for surface physical weathering by human traffic and internal chemical weathering by water, and propose a rate which models these factors in tandem. We then discuss the applications of our model and other stone weathering models. Lastly we provide further clarification on quantities, and how one might employ the model within field research.
Close Abstract2:10PM, Caleb Rice, Jack Raley (Messiah University)
When Corrections Don’t Cut It: Multiple Testing in Microbiome Analyses
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Microbiomes are complex collections of interrelated microscopic organisms that exist in our lungs, in our guts, on our skin, and elsewhere on our bodies, impacting health outcomes. Detecting associations between microbiomes and health is difficult to accomplish using traditional statistics due to the high sparsity, pairwise microbe correlations, and high dimensionality of microbiome data. One commonly used approach is to test each individual microbial specie’s association with a health outcome using linear regression, but high dimensionality leads to thousands of individual tests and inflated Type I Error rates. While methods exist for controlling the False Discovery Rate (FDR), the efficacy of these corrections is uncertain for microbiome data. If these corrections are not effective, tests to determine the microbes that are associated with health will result in many false discoveries. Here we simulate known microbiome-human health associations to compare the performance of linear regression tests across three microbiome simulators: Negative Binomial, Dirichlet-Multinomial, and MIDASim. A Bonferroni adjustment is applied to provide a conservative adjustment for multiple testing. Plots of our results, along with summary statistics, show that conservative adjustments do not result in controlled FDR in most simulation scenarios across all three simulators. We conclude with a discussion on the need for alternative testing frameworks designed to incorporate the unique characteristics of microbiome data.
Close Abstract2:25PM , Howra Amirshokoohi (Penn State Berks)
Beyond Euclid and Newton: Contributions of Muslim Scholars to Early Mathematics
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When considering the early pioneers of mathematics, we often think of figures such as Euclid, Newton, Pythagoras, and Archimedes. However, mathematicians from underrepresented groups have frequently remained less visible and are not celebrated to the same extent. For students, understanding the historical context of mathematical concepts can have a meaningful emotional impact and enhance learning motivation and engagement. In particular, exposure to diverse contributors to the field can foster a stronger sense of connection to mathematics. This presentation focuses on the Golden Age of Islam, highlighting the profound and often unrecognized contributions of Muslim scholars and polymaths to the development of mathematics.
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Undergraduate Session 4
DHC 210
1:40PM, Noah West (Widener University)
Computing surface mosaic numbers through computational search
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Knot projections can be represented using a fixed set of mosaic tiles arranged on a square grid. The mosaic number of a knot is the minimum grid size required to represent the knot and serves as a natural knot invariant arising from this construction. This idea can be extended by placing mosaics on other surfaces, such as a cube, torus, cylinder, or Möbius band, leading to corresponding variants of the mosaic number. In this project, we compute cubic, toric, cylindrical, and Möbius mosaic numbers using an exhaustive computational search. We describe the algorithms designed to generate and identify these mosaics, summarize optimizations required to extend the search to larger mosaic sizes, and review the patterns and results obtained from the data. Finally, we discuss potential directions for further exploration using this computational framework.
Close Abstract1:55PM, Cole Pearson (Shippensburg University)
Development of a Computational Tool for the Analysis of Kombucha Titrations
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Kombucha is a fermented tea beverage whose unique, complex flavor profile arises largely from its mixture of organic acids, which often include acetic, gluconic, lactic, and carbonic acids. Kombucha brewers—often small, independent businesses—seek to identify which acids are present and their proportions to track fermentation progress and optimize the flavor profile. High-performance liquid chromatography (HPLC) is the industry standard for this analysis but is cost-prohibitive and time-intensive. A titration of a weak acid mixture with strong base, however, is affordable and widely accessible, but traditionally only provides titratable acidity (TA), a measure of total acid content. This work incorporates charge balance, mass balance, and aqueous electrolyte theory into a modular model that can be solved as an inverse parameter minimization problem via nonlinear least-squares fitting in a MATLAB® program using the lsqcurvefit function and Levenberg–Marquardt algorithm. This protocol is able to determine, from a single titration curve: 1) a sample’s number of acids, 2) their identities (via equilibrium constant extraction), 3) their individual concentrations, and 4) their mechanistic behavior through activity coefficients. This program is being packaged into an open-source tool, increasing accessibility for brewers, analysts, and researchers. The tool is validated against HPLC for kombucha samples from 46 independent brewers, finding excellent agreement.
Close Abstract2:10PM, Ethan Baratz (West Chester University of PA)
Least Squares Monte Carlo (LSMC) Guided Approximate Dynamic Portfolio Optimization
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In modern portfolio theory, classical mean-variance (MV) is myopic, ignoring future downside risk needed in long-term capital preservation. We propose a two-stage Approximate Dynamic Programming (ADP) framework that uses Least Squares Monte Carlo (LSMC) to generate forward-looking risk signals. Empirical backtesting on the 2000 and 2008 stock market crises demonstrates that our model enhances capital floor preservation while delivering lower maximum drawdowns compared to myopic and static benchmarks.
Close Abstract2:25PM, Alexander Glatfelter (York College of Pennsylvania)
Dynamics of Voter Satisfaction and Political Party Polarization: A Mathematical and Simulation Based Approach
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This project analyzes how ideological changes in individuals and political parties affect voter satisfaction and party polarization. We set up a theoretical, simulation-based two-dimensional ideological trait space to represent both voters’ and parties’ ideologies. Within this space, individuals update their positions based on their prior ideology, peer influence, media exposure, party alignment, and random shocks capturing misinformation, biases, and irrationality. Parties adjust their platforms based on their prior ideology, responsiveness to their base, strategic positioning relative to rivals, lobbying, and stochastic shocks capturing the same forces. These update equations jointly determine the evolution of ideological positions over time. Voter satisfaction is calculated as a function of ideological distances between individuals and party platforms and the relative size of each party. We hypothesize that when seat allocation is roughly proportional to voter identification, average satisfaction will rise as the number of viable parties increases, whereas in systems that over-reward large parties, satisfaction will tend to fall as the number of parties increases. Finally, initial conditions strongly influence the system’s evolution, with dynamics either converging toward moderation or diverging toward polarization. Results are preliminary; future work calibrates the model to data and conducts robustness checks.
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