MAA  Mathematical Association of America

Seaway Section

Location: Eben Holden

1. Time:

   3:25 pm – 4:10 pm

   Title:

   WOMEN’S HOCKEY MATTERS: Analyzing Game Outcomes in Women’s Professional Hockey Based on Shot-level Data

   Speaker:

   Matlala Sefale (St. Lawrence University)

   Abstract

   This study analyzes 1,502 shot attempts from all 17 games of the 2021-2022 Premier Hockey Federation season to explore how game outcomes relate to shot and player performance. Using data visualization, hypothesis testing, and logistic regression modeling, the research examines whether the on-ice situation—specifically, even-strength versus power play—affects shot outcomes. A Chi-squared test found no significant association between shot result and on-ice situation with $p = 0.591$, suggesting shot success is not solely determined by player advantage. Additionally, a logistic regression model incorporating home and away shot counts per game failed to significantly predict the probability of a home team win, as indicated by a non-significant likelihood ratio test of $p = 0.2$. By applying these statistical methods to women's professional hockey, this research contributes to the growing field of women’s hockey analytics and highlights opportunities for further exploration in performance evaluation and team strategy.

2. Time:

   3:25 pm – 4:10 pm

   Title:

   Textual Analysis and Historical Interpretation of John Laurens and Alexander Hamilton’s Correspondence

   Speaker:

   Abigail Smith (St. Lawrence University)

   Abstract

   Correspondence is one of the most significant forms of primary historical sources, it can provide insight on people’s lives and ideals during a historical era. The letters exchanged between John Laurens and Alexander Hamilton during the American Revolution offer a crucial window into male friendships during the era of the American Revolution as well as showcase the ideals and beliefs held by young revolutionaries. Hamilton and Laurens met as aide de camps to General George Washington during the war, the two bonded over shared aspirations for the future of the US. Over the course of the war, they were stationed at different locations which led to them exchanging several letters. There is some debate amongst historians about the language of these letters, with some speculating they are romantic in nature. Through historical research on colloquialisms and male friendships in the 18th century some type of conclusion can be drawn. However, performing statistical textual analysis on the letters could potentially provide higher insight on the nature of their relationship. This analysis will be done through compiling a dataset of letters exchanged not only between Hamilton and Laurens themselves but also letters they have written with other figures such as the Marquis de Lafayette and Eliza Hamilton. By comparing the letters, statistical tests can be performed to deduce whether or not there is a significant difference in the language of the letters Laurens and Hamilton wrote to each other versus to others.

3. Time:

   3:25 pm – 4:10 pm

   Title:

   Group Theory Demonstrator

   Speaker:

   Carter Banks (St. Lawrence University)

   Abstract

   This project aims to design and construct a physical three-dimensional model that vividly demonstrates the symmetries of a dihedral group. The rotations and reflections of a regular polygon (for project aims, for example, the various ways to rotate or flip a hexagon). Dihedral groups are essential to group theory, representing how one can rotate or flip an n-sided shape while preserving its form. Creating a Physical 3D dihedral group can showcase every possible rotation and mirror reflection. The project aims to make the abstract comprehensible visually. The model will be created using St. Lawrence University's Maker Space and technology (3D printing, laser cutting, and microelectronics) to represent all possible reflection rotations and symmetric groups. The purpose is to help students and educators better grasp three-dimensional rotations and symmetry by observing and interacting with a physical representation of these transformations. We anticipate that this interactive model will make learning group theory more engaging and accessible. This approach addresses a common difficulty in abstracting and visualizing complex transformations by making them concrete and engaging. This project's results include a fully functional 3D dihedral symmetry model, an accompanying guide for its use in instruction, and insights into how physical models can enhance comprehension of mathematical symmetry and group theory. More broadly, it will demonstrate how modern fabrication technology can be harnessed to improve the teaching of abstract mathematical concepts.

4. Time:

   3:25 pm – 4:10 pm

   Title:

   Creating a Sports-Based Framework for Enhancing Education in Data Science?

   Speaker:

   Phoebe Jones (St. Lawrence University)

   Abstract

   The SCORE network is an NSF-funded national network that aims to create Sports Content for Outreach and Education in statistics and data science. The SLU Score team was tasked with creating the modules that are the core educational units of the network, designed to immerse students in real-world data science problems through sports data. These modules promote case-based learning, where students apply data science techniques to analyze and solve challenges in sports analytics through individual lessons, full courses, and workshops.The goal of this work was to create an accessible and hands-on learning experience that is flexible and prepares students for careers in data science and statistics.

5. Time:

   3:25 pm – 4:10 pm

   Title:

   SCORE at St. Lawrence: Developing Introductory Level Statistics Resources Using Non-Traditional Sports Data

   Speaker:

   Abigail Smith (St. Lawrence University)

   Abstract

   The SCORE Network is a national organization that focuses on developing and distributing Sports Content for Outreach, Research, and Education (SCORE) in data science and statistics. The St. Lawrence chapter of SCORE focuses on the use of non-traditional sports data, like ESports, Motorsports, Golf, and Running to develop introductory level statistics resources to be used by educators. Modules include topics like summary statistics, hypothesis testing, linear regression, and data manipulation to fully cover a variety of courses. SCORE as a whole seeks to implement educational framework based real-world problems and applications students are likely to be interested in to engage them in the classroom. This poster focuses on the development process and the educational framework of materials produced by students in our chapter of SCORE during a semester-long independent study in Statistics. In addition, it will highlight the contributions made to the broader SCORE network, by emphasizing our innovative approach to statistics education through non-traditional sports data.

6. Time:

   3:25 pm – 4:10 pm

   Title:

   Gröbner Basis of Polynomial Rings and Path Algebras

   Speaker:

   Nicholas Pisano (SUNY Brockport)

   Abstract

   This paper focuses on Gr\"{o}bner basis theory and how it pertains to polynomial rings and path algebras. We discuss how Buchberger's algorithm as well as Faug\'{e}re's F4 and F5 algorithms. We define path algebras, and introduce non-commuatitive Gr\"{o}bner basis theory in their context. The Buchberger-Green Algorithm is explained and illustrated, with examples to show how computation within it works. The paper discusses analogues between commutative and non-commutative cases, while discussing how they differ and why algorithms such as Faug\'{e}re's F4 Algorithm fail in non-commutative cases. The paper finishes by introducing a result while introducing open problems regarding both commutative and non-commutative cases.

7. Time:

   3:25 pm – 4:10 pm

   Title:

   Using a statistical modeling approach to quantify the processes driving parallel evolution in populations of bacteria

   Speakers:

   Jasonfred Ngwa (Clarkson University), Susan Bailey (Clarkson University), James Greene (Clarkson University), Chimaroke Onyeaghala (Clarkson University), Uresha Dias (Clarkson University)

   Abstract

   Parallel evolution is the evolution of the same traits in independent populations that share a common ancestor. Because it is rare, it is often assumed to arise from strong natural selection, while stochastic processes such as mutation and genetic drift are considered unlikely causes. However, Bailey et al. showed that parallel evolution can also be driven by heterogeneity in mutation rates across the genome. Their statistical modeling approach, which treats observed mutations as outcomes of a modified Poisson process, can quantify the relative contributions of mutation rate heterogeneity and natural selection to parallel evolution. In this study, we refine that approach to test how spatial structure influences parallel evolution. We analyze genomic data from replicate populations of Pseudomonas aeruginosa experimentally evolved under environments differing in spatial structure. The dataset includes counts of synonymous and nonsynonymous mutations across genes in each evolved genome. Using model parameter estimates, we measure parallel evolution and compare the effects of mutation rate heterogeneity and selection across populations. Preliminary results suggest a higher degree of parallel evolution in more structured environments, likely due to intensified competition among new mutations. These findings enhance our understanding of how environment, mutation, and selection interact to shape evolutionary outcomes. More broadly, the ability to predict evolutionary patterns has far-reaching applications, including the development of drugs and vaccines, improvements in agriculture, and contributions to conservation through better forecasts of how species adapt to changing environments.

8. Time:

   3:25 pm – 4:10 pm

   Title:

   Virtual Reality as a Tool for Studying Environmental Perception and Affect

   Speaker:

   Nela Chestojanova (St. Lawrence University)

   Abstract

   This study investigates differences in affective evaluations of environments when experienced in virtual reality (VR) versus real life, with an emphasis on statistical modeling of subjective responses. Using Meta Quest headsets, participants were exposed to both VR and in-person versions of several locations. Affective responses including pleasantness and stimulation were quantified using the Affective Quality of Place Questionnaire administered via Qualtrics. Data were processed and analyzed in RStudio, with attention to data cleaning, distributional checks, and adherence to research ethics protocols. Statistical procedures included paired-samples comparisons of affective ratings across VR and real-world conditions, as well as estimation of effect sizes and confidence intervals to assess practical significance. Exploratory models examined potential covariates (e.g., order effects). Preliminary analyses show that mean pleasantness ratings for real-world environments exceeded VR ratings; however, this difference was not statistically significant, with confidence intervals spanning zero. These results suggest that immersive VR environments can serve as statistically valid approximations of real-world affective experiences. The study highlights opportunities for the application of inferential methods in evaluating VR as a proxy for real environments and contributes to the broader statistical discussion of measurement validity in emerging technologies.

9. Time:

   3:25 pm – 4:10 pm

   Title:

   A Study of Regular Expression Quality and Correctness

   Speaker:

   Oleg Efimov (St. Lawrence University)

   Abstract

   Regular expressions remain a fundamental tool for pattern matching across computer science, data processing, and software engineering. Yet, poorly designed regexes can be both inefficient and also vulnerable to Regular Expression Denial of Service (REDoS) attacks, where excessive backtracking causes exponential runtime blowups. This project addresses two complementary challenges. First, we are developing a set of practical guidelines for writing regular expressions that are readable, maintainable, and efficient. These guidelines focus on simplifying complex patterns, reducing ambiguity, and avoiding common performance pitfalls. Second, we investigate REDoS vulnerabilities, classifying key attack patterns such as nested quantifiers, overlapping alternations, and catastrophic backtracking. For each class, we explore mathematical transformations designed to preserve the functional behavior of the original regex while mitigating ambiguity and limiting worst-case runtime growth. This work brings together best-practice construction rules and formal mitigation techniques aimed at helping developers, researchers, and tool designers write regular expressions that balance performance, safety, and clarity without sacrificing expressiveness.

10. Time:

    3:25 pm – 4:10 pm

    Title:

    Who’s at the Party? Evaluating In-Host Diversity of Coccidioides Fungal Infections

    Speaker:

    Aurora Sauereisen (St. Lawrence University)

    Abstract

    Antibiotic resistance often evolves during treatment and is shaped by within-host pathogen diversity. While this phenomenon is well documented in bacteria, the dynamics of antifungal resistance remain poorly understood. Fungal pathogens such as Coccidioides immitis and C. posadasii, the causative agents of Valley fever, are understudied despite increasing clinical concern. Acquired by inhaling fungal spores and misdiagnosed in up to 30% of pneumonia cases, understanding within-host genetic diversity in Coccidioides is crucial for improving treatment strategies and anticipating resistance evolution. In this study, we sought to quantify the in-host diversity of Coccidioides within patient infections. We conducted prospective genomic surveillance at a national diagnostic laboratory, ARUP, collecting one or more Coccidioides-positive isolates per patient. Samples were processed through ARUP and sequenced on an Illumina platform at the University of Utah. Sequencing reads were then analyzed using our custom cocci-call pipeline to identify single nucleotide polymorphisms (SNPs), and pairwise comparisons were performed in R to assess isolate similarity. We found significance in the mean SNP difference between isolates from the same patient compared to isolates from different patients. Within-host comparisons revealed lower diversity in C. immitis than in C. posadasii. Across-patient comparisons showed the same trend, with C. immitis averaging 9,455 SNPs and C. posadasii 18,583 SNPs. Visual confirmation of within host diversity was additionally obtained through viewing phylogenetic trees. These results reveal unexpectedly high within-host diversity in both species and underscore the need to better understand how such diversity impacts clinical outcomes, pathogen evolution, and antifungal resistance.

11. Time:

    3:25 pm – 4:10 pm

    Title:

    Pattern Avoidance in Binary lattice and Yamanouchi Words

    Speaker:

    Alanna Pellicane (SUNY Brockport)

    Abstract

    This project focuses on the field of combinatorics, specifically, pattern avoidance in binary lattice and Yamanouchi Words. The field of pattern avoidance has a rich history with modern origins in computer science dating back to Knuth (Knuth, 1969). Many enumerative results and characterizations have followed for specific structures including permutations (B´ona, 2022; Marcus and Tardos, 2004), words (Burstein, 1998; Kitaev, 2011), trees (Dotsenko, 2012), and matrices (F¨uredi and Hajnal, 1992; Bouvel et al., 2025). The study of pattern avoidance has many applications in areas including mathematics, computer science and biology. However, while lattice words were determined to be ascent sequences (Dukes, 2016), there appears to be no formal study of pattern avoidance in lattice words or Yamanouchi words. Until now. For example, we discovered that the number of Yamanouchi words of size $n$ avoiding the pattern $010$ is $\lfloor \frac{n}{2} \rfloor +1$. We also found the number of binary a Yamanouchi words of size $n$ that avoid $101$\begin{equation*} Y_n = \left\{ \begin{array}{lr} 1, & \text{if } n=0\\ Y_{n-1}+\lfloor \frac{n}{2} \rfloor, & \text{if } n \geq 1 \end{array} \right\} = \bigg\lfloor \frac{n^2}{4} \bigg\rfloor +1. \end{equation*}

12. Time:

    3:25 pm – 4:10 pm

    Title:

    Excipient Variability Analysis in Drug Product Development

    Speaker:

    Izzy Schreiner (St. Lawrence University)

    Abstract

    In pharmaceutical development, the variability of excipients—non-active ingredients that typically comprise nearly 80% of a drug product—has gained increasing recognition for its role in product performance and robustness. Excipients serve critical functions such as acting as diluents, binders, and disintegrants, making their consistency essential. Excipient variability analysis is performed to compare the lots used in a drug product to all the historic lots in CoA (Certificate of Analysis) Data from excipient vendors. Two approaches are commonly employed: univariate and multivariate analysis. Univariate analysis, often used in submissions to regulatory agencies, is performed on a singular critical material attribute (CMA) for an excipient with material property coverage calculated to quantify the robustness of excipient selection. For multivariate analysis, PCA is performed with all the meaningful CMAs to observe the interdependencies between them for internal risk assessment. Confidence ellipses and convex hulls are then used to calculate robustness in higher dimensions.