Mathematics and Statistics
Brain Computer Interfaces and the MOABB Study
Presenter: Colleen Alexandria Lombard
Faculty Sponsor: David Degras
School: UMass Boston
Research Area: Mathematics and Statistics
Location: Poster Session 3, 1:15 PM - 2:00 PM: Campus Center Auditorium [A11]

Brain-Computer Interfaces (BCI) are difficult to reproduce and lack benchmarking datasets, which hinders rapid progress and dissemination of ideas and best practices in the domain. The Mother of All BCI Benchmarks, also known as MOABB, constitutes a significant step towards standardization and increased reproducibility in BCI research. MOABB provides benchmarking data sets, algorithms, and code for people to use freely in their own research. It contains 36 open data sets and 30 machine learning pipelines intended to provide easier access to researchers and make starting your BCI research much more efficient. My project is to reproduce the MOABB study to learn about BCI research and reproducible science. I learned basic Python to rerun the code provided by MOABB and assess each algorithm on specific datasets. I also mastered various machine learning (ML) techniques, preprocessing pipelines, and feature extraction methods for EEG data, studying the principles, strengths, and limitations of each approach. BCI approaches I have familiarized myself with involve Raw Signal-Based Pipelines, Riemannian Geometry, and Deep Learning techniques. As an end result of my project, I was able to fully understand and successfully replicate the MOABB study. 


A Comparative Analysis of Acoustic and Non-Linear Sound Theory
Presenter: Sage Teo Arias Hambleton
Faculty Sponsor: Robin Young
School: UMass Amherst
Research Area: Mathematics and Statistics
Location: Poster Session 3, 1:15 PM - 2:00 PM: Campus Center Auditorium [A12]

Throughout the history of the applied mathematical understanding of sound, there has been a disparity between the behavior of linear and non-linear sound theory. Through recent developments, this issue has been addressed by approximating non-linear sound with principles of energy conservation, integrating distortion over space and time. This research looks at the audible and numerical behaviour of non-linear sound waves, analyzing differences in pressure profile data under spatial variation. Modern computational techniques, data visualization using Python and data sampling from MATLAB-based scripts, in addition to classical mathematical tools, time series analysis and fast Fourier transforms, provide this research with a framework for strengthening our understanding of non-linear sound quality degradation through space. This research is ongoing, and aims to analyze both anomalous and expected differences in pressure profiles with the mathematical tools applied to uncover deeper intricacies, such as overtones and behaviour of Fourier coefficients, of sound with spatial variation. 


The Morita Construction for Strict Monoidal Categories
Presenter: Samuel Silver
Faculty Sponsor: Martina Rovelli
School: UMass Amherst
Research Area: Mathematics and Statistics
Location: Poster Session 4, 2:15 PM - 3:00 PM: Campus Center Auditorium [A64]

Rings are structures in mathematics which encapsulate the most general framework in which you can add and multiply. Two rings are "isomorphic" if there is a one-to-one correspondence between them respecting addition/multiplication. In the 1950s, Kiiti Morita defined a weaker notion of equivalence of rings than isomorphism, and proved some powerful structural theorems about it.

Modules are structures on which rings can "act" by multiplication. A category is another mathematical structure, in which one has "objects" and "morphisms" (thought of as arrows between objects) such that consecutive morphisms can be composed, just as we can compose functions. For any ring R, there is a category R-Mod of modules over R. We say two rings R and S are Morita equivalent if their categories of modules R-Mod ≃ S-Mod are equivalent. Part of the structure theorem effectively states that Morita equivalence is equivalence in a certain bicategory (like a category, but with additional structure of "morphisms between morphisms").

Monoidal categories are categories equipped with a "multiplication" for objects and morphisms. Rings are monoids in a certain monoidal category (abelian groups with tensor product), and it turns out we can carry out Morita's construction for any monoidal category (with some higher-categorical complications, which we avoid by working with some mild assumptions). 

We'll begin by providing some background on basic category theory. Then we'll define the basic concepts of monoidal category theory, monoids, and modules. We then display our main result: an explicit construction of the Morita bicategory under our simplifying assumptions.

Modeling Shockwaves With Modified Front Tracking Software
Presenter: Zachary Robert Williams
Faculty Sponsor: Robin Young
School: UMass Amherst
Research Area: Mathematics and Statistics
Location: Poster Session 4, 2:15 PM - 3:00 PM: Campus Center Auditorium [A65]

When a large amount of energy is transmitted to a fluid medium instantaneously, such as an explosion, or an object traveling faster than the speed of sound, a shockwave is created. This is a traveling front of energy, characterized by a discontinuous jump in pressure, density, and velocity. Mathematically modeling their behavior requires evaluating solutions to the nonlinear hyperbolic conservation laws known as Euler equations. My research explores the implementation of a modified front tracking software to model solutions to these nonlinear Euler equations. This is a continuation of the work of Robin Young and Manas Bhatnagar. The code functions as a model for evolving solutions to these equations in a one-dimensional material frame. Given the initial conditions of a group of waves, we can solve the corresponding Riemann problems and evolve the state of each wave. Over time, the waves interact with one another, which can be seen in a clean visual model. The method employed in the software is specialized for discontinuous solutions characteristic of shocks. The software treats vacuums explicitly, and compressions explicitly as waves. Along with having detailed control over residuals, we can guarantee convergence of solutions and accurately solve the nonlinear hyperbolic conservation laws used to model shockwave interactions. This method fundamentally permits solutions of high wave speeds, allowing us to compute models for waves far above the speed of sound.

Exploring Historical Problem Solving Techniques of Islamic and Japanese Mathematicians for a Modern Audience and Integration into Higher Dimensional and Computational Applications.
Presenter: Quintin Lemek
Faculty Sponsor: Catherine Buell
School: Fitchburg State University
Research Area: Mathematics and Statistics
Location: Poster Session 4, 2:15 PM - 3:00 PM: Campus Center Auditorium [A66]

A comprehensive reconsideration of the non-Eurocentric mathematical practices and philosophies spanning
the Eastern world that may have gone overlooked or insufficiently explored, particularly when reflected in a
typical undergraduate mathematics program. These practices may include significant and unique problem-
solving techniques that when applied and cross-examined with modern mathematical subjects or fields can
provide noteworthy insights that would be otherwise neglected under prevailing Western techniques.
Considering the breadth of mathematics, focus will be given to the mathematicians of the Islamic Golden
Age and Edo period in Japan. For the former- the proof work of Al-Khwarizmi and Omar Khayyam on
quadratics and cubics forms will be explored when treated in higher dimensions. For the latter- arithmetic tables applied to root-finding developed by Seki Takakazu will be translated computationally and compared with modern root-finding methods.

Forgetting Where You Started: Convergence to Equilibrium in Markov Chains
Presenter: Xiaoran Fan
Faculty Sponsor: John Pike
School: Bridgewater State University
Research Area: Mathematics and Statistics
Location: Poster Session 4, 2:15 PM - 3:00 PM: Campus Center Auditorium [A67]

Markov chains provide a fundamental framework for modeling stochastic systems that arise in probability theory, statistical physics, computer science, and related fields. A central problem in their study is determining when a process “forgets” its initial state and converges to a stable long-term equilibrium. Understanding this convergence behavior is essential for analyzing both theoretical models and practical algorithms.

This project investigates the structural conditions that guarantee convergence for finite, time-homogeneous Markov chains. The analysis focuses on the roles of irreducibility, aperiodicity, and positive recurrence in ensuring the existence and uniqueness of a stationary distribution. Using coupling methods and spectral analysis of transition matrices, the study establishes convergence in total variation distance and provides quantitative bounds on the rate of mixing. In particular, the relationship between eigenvalues of the transition matrix and long-term behavior is examined in detail.

Random walks on finite graphs and groups illustrate how structural properties such as connectivity, symmetry, and generation directly control convergence to equilibrium in Markov chains.

The results demonstrate that finite, irreducible, and aperiodic chains converge exponentially fast, with the second-largest eigenvalue determining the speed of convergence. This work clarifies the mathematical mechanisms underlying equilibrium formation and provides a unified framework for understanding stochastic dynamics across multiple disciplines.


Analysis of Sex-Dependent Gene Expression in Human Aging
Presenter: Amel Hilmi
Faculty Sponsor: Maryclare Griffin
School: UMass Amherst
Research Area: Mathematics and Statistics
Location: Poster Session 4, 2:15 PM - 3:00 PM: Campus Center Auditorium [A68]

Aging is accompanied by widespread molecular changes throughout the human body. Identifying age-associated biomarkers may provide insight into mechanisms underlying age-related disease. Chronic low-grade inflammation, also known as inflammaging, is a recognized hallmark of aging; however, limitations on human research have made it difficult to directly understand inflammaging processes in humans. While inflammaging is recognized as a systemic feature of aging, it remains unclear how inflammatory gene expression patterns differ between males and females across human tissues. Sex-specific differences in immune regulation have been observed in both human and murine studies, yet the extent to which aging-associated inflammatory pathways exhibit sexually dependent transcriptional signatures in humans is not well defined. Various murine studies have revealed of sex-dependent effects of gene expression changes related to aging, such as elevated levels of IL-6r, IL-18, and CRP in women, all of which are associated with cardiovascular and metabolic risk. Consequently, there is an emergent need for identification of sex-related inflammaging biomarkers. Factors such as ethical constraints and tissue collection pose further barriers in identifying these markers; these restraints can be circumvented through the use of open source gene expression data, such as the GTEx data used in this project. We hypothesize that aging is positively associated with systemic  and tissue-dependent changes in expression, with inflammatory pathways exhibiting sex-dependent transcriptional patterns that contribute to distinct trajectories of aging between males and females.

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Quantitative Analysis of Delays in Cortical Maturation in Patients with Focal Epilepsy
Presenter: Mohan D. Ram
Faculty Sponsor: John Staudenmayer
School: UMass Amherst
Research Area: Mathematics and Statistics
Location: Poster Session 4, 2:15 PM - 3:00 PM: Campus Center Auditorium [A69]

Focal epilepsy is associated with lesions confined to one cerebral hemisphere and may disrupt normal cortical maturation in childhood, though the timing and anatomical specificity of this disruption remain unclear. We examined inter-hemispheric differences in cortical function using resting motor threshold (RMT), the minimum stimulation intensity required to elicit a motor response in a resting muscle and an index of cortical excitability measured via transcranial magnetic stimulation (TMS). 

RMT data were analyzed from 154 individuals with focal epilepsy (ages 1-23 years). Generalized additive models characterized nonlinear age-related trends in RMT, motivating segmented (change-point) regression to estimate the age of maturational stabilization. Within-subject comparisons were performed between epileptic and healthy hemispheres. To assess anatomical specificity, regression models examined lesion-related RMT deviations and compared stabilization ages between corticospinal tract and frontal lobe lesions.

In healthy hemispheres, RMT stabilized at 10.81 years (95% CI [10.49, 11.12]) versus 13.68 years (95% CI [13.45, 13.91]) in epileptic hemispheres, reflecting a mean delay of 2.87 years (95% CI [2.48, 3.26], p < .001). Delays were greater in corticospinal tract lesions (4.16 years, 95% CI [3.98, 4.65], p < .001) than frontal lobe lesions (2.03 years, 95% CI [1.55, 2.52], p < .001). Corticospinal tract lesions were also associated with larger RMT deviations and later stabilization.

These findings demonstrate lesion-specific delays in cortical maturation, with particular vulnerability of the corticospinal tract. Improved characterization of maturation timing may inform earlier, targeted interventions to mitigate long-term motor and neurodevelopmental impairments.

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Comparing Impacts of Lecturing and Collaborative Concept Mapping on Learning Outcomes and Perspectives in a Statistics Classroom
Presenter: Samantha Sheedy
Faculty Sponsor: Qian Zhao
School: UMass Amherst
Research Area: Mathematics and Statistics
Location: Poster Session 6, 4:15 PM - 5:00 PM: Campus Center Auditorium [A73]

Student engagement, active participation, and collaborative thinking are often absent from the traditional college lecture model, especially in a mathematical or technical course. Such one-way lectures also do little to assure students that they are learning at a pace consistent with class expectations, or that their ideas and participation are welcomed and valued. In this study, we compare the traditional lecture model with collaborative concept mapping, an interactive activity where students work together to create a node-link diagram that organizes ideas and visually demonstrates relationships between them. We collected a total of 60 survey responses from 19 UMass students in a statistics course, which included quiz questions about course material and opinion-based questions assessing perceived sense of belonging, self-efficacy, and exerted effort in class. Students were asked to complete the survey after four class sessions, with two taught primarily through lecture and two through a collaborative concept mapping exercise. The data will be analyzed through mixed models to measure the association between concept mapping and higher academic performance, as well as stronger senses of belonging and self-efficacy. The findings will help to improve teaching techniques and course designs of college-level statistics courses, as well as help future students in statistics courses learn more effectively and feel more comfortable and confident in class.

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Affordability and Availability of Healthy Foods in Massachusetts
Presenter: Mari Patrick Cornwall-Brady
Faculty Sponsor: Qian Zhao
School: UMass Amherst
Research Area: Mathematics and Statistics
Location: Poster Session 6, 4:15 PM - 5:00 PM: Campus Center Auditorium [A74]

Food insecurity is a persistent public health concern in the United States, affecting nearly 18 million households in 2023. In Massachusetts, approximately 11.5% of residents faced food insecurity during that year, with every county impacted. While federal programs such as the Supplemental Nutrition Assistance Program (SNAP) provide essential support, access to affordable and nutritionally diverse foods remains uneven across communities. This project investigates the affordability and accessibility of healthy foods in Massachusetts, with a specific focus on the diversity of vegetables available in retail outlets. Using 2023 NielsenIQ scanner data, we evaluate vegetable offerings across thousands of stores in Massachusetts. We employ species richness and Simpson’s Diversity Index to measure vegetable diversity and combine these with price information to assess store level food accessibility. Preliminary results reveal variation in vegetable diversity across store types and counties, highlighting inequities in food availability. Our work demonstrates the potential of combining large-scale retail data with ecological diversity measures to inform future policies and interventions addressing food insecurity.

Strategic Deception and Detection in Multi-Agent Environments: A Game-Theoretic Reinforcement Learning Framework
Presenter: Jineshwar Nariani
Faculty Sponsor: Patrick Flaherty
School: UMass Amherst
Research Area: Mathematics and Statistics
Location: Poster Session 6, 4:15 PM - 5:00 PM: Room 163 [C25]

Autonomous agents operating in shared environments face a fundamental tension between achieving their objectives and concealing their intentions from others who may exploit that knowledge. This research develops a theoretical framework and computational model to study adversarial dynamics in multi-agent systems where agents must balance goal achievement against strategic information management.

We model a sequential game between two classes of agents with asymmetric roles and capabilities. One agent class possesses private objectives and must take observable actions over time to achieve them, while simultaneously minimizing the information revealed through those actions. The opposing agent class observes only the environmental signals generated by these actions and attempts to infer the first agent's hidden objectives to gain competitive advantage. Crucially, the information available for inference is generated endogenously through the goal-directed agent's own behavior, creating a dynamic feedback loop between action selection and information leakage.

Our framework synthesizes insights from classical resource allocation games, signaling theory, and multi-agent reinforcement learning. We introduce temporal constraints requiring agents to achieve objectives within fixed horizons, creating non-trivial strategic tradeoffs.

We validate our theoretical framework through computational experiments using policy gradient methods, demonstrating emergent equilibrium behaviors including strategic timing of actions, adaptive belief formation, and an evolving detection-obfuscation arms race. Our results contribute to understanding strategic behavior in competitive multi-agent systems and demonstrate how reinforcement learning can illuminate complex dynamics arising from information asymmetry and adversarial interaction.