Digital Commons Network^™

Skeletal 2-Groups And Category Theory, Nicholas Small '25, Alexander Stepanov '26, Haley Waiksnis '25

Mathematics & Computer Science Student Scholarship

Nicholas Small ’25, Mathematics and Computer Science major
Alexander Stepanov ’26, Mathematics and Studio Art major
Haley Waiksnis ’25, Mathematics major
Faculty Mentor: Dr. Laura Murray, Mathematics and Computer Science

Autonomous Remote Erosion Monitoring Using Computer Vision, Emily Gelchie '24, Gabriel Benz '25

Mathematics & Computer Science Student Scholarship

Emily Gelchie ’24, Computer Science major
Gabriel Benz ’25, Computer Science major
Faculty Mentor: Dr. Martin Helwig, Mathematics and Computer Science

Media Portrayals Of Mathematics And Mathematicians: An Annotated Bibliography Of Published Journal Articles, Sarah O'Connor '26

Education Student Scholarship

Sarah O'Connor ’26, Mathematics major
Faculty Mentor: Dr. Kevin O’Conner, Secondary Education and Dr. Olga Limnios, English

Avatars Runnin' On Dunkin, Keelin Robbins '26

Mathematics & Computer Science Student Scholarship

Keelin Robbins ’26, Computer Science major, Finance minor
Faculty Mentor: Dr. Martin Helwig, Mathematics and Computer Science

Blueberry Drone Ai: Estimating Crop Yield Using Deep Learning & Smart Drones, Luke Tonon, Brandon Mchenry, Anthony Thompson, Harper Zappone, Jacob Green, Hieu Nguyen, Thanh Nguyen

STEM Student Research Symposium Posters

This project seeks to assist blueberry growers in New Jersey estimate crop yield by developing software that allows autonomous drones to capture aerial images of blueberry bushes in the field, perform berry count, and identify blueberry conditions using deep learning models & computer vision.

Blueberry Drone Ai: Smart Farming Of Blueberries Using Artificial Intelligence And Autonomous Drones, Robert Czarnota, Anthony Segrest, Anthony Thompson, Harper Zappone, Hieu Nguyen, Nguyen Thanh, Ik Jae Lee, Lori Green, Tuan Le

STEM Student Research Symposium Posters

This project seeks to assist blueberry growers in New Jersey with preventing blueberry scorch disease. Plants can’t be cured of scorch, so they have to be removed to prevent the disease from spreading to other bushes. This project aims to use object detection and classifier machine learning models in order to detect scorch disease with photos from intelligent drones. Images are first tiled, then processed through and convolutional neural network that detects scorch symptoms. Lastly, a fully connected neural network is implemented to make a final prediction.

Mathematical Modeling For Dental Decay Prevention In Children And Adolescents, Mahdiyeh Soltaninejad

Dissertations

The high prevalence of dental caries among children and adolescents, especially those from lower socio-economic backgrounds, is a significant nationwide health concern. Early prevention, such as dental sealants and fluoride varnish (FV), is essential, but access to this care remains limited and disparate. In this research, a national dataset is utilized to assess sealants' reach and effectiveness in preventing tooth decay, particularly focusing on 2nd molars that emerge during early adolescence, a current gap in the knowledge base. FV is recommended to be delivered during medical well-child visits to children who are not seeing a dentist. Challenges and facilitators in …

The Effect Of Fixed Time Delays On The Synchronization Phase Transition, Shaizat Bakhytzhan

USF Tampa Graduate Theses and Dissertations

Nature is full of synchronization phenomena, which are essential to many scientific fields like biology, chemistry, physics, and neuroscience. The Kuramoto model is a well-known theoretical model that helps explain the fundamental ideas behind synchronization dynamics [6]. Nevertheless, in practical situations, systems frequently display intrinsic latency, which can greatly impact their behavior during synchronization. This insight inspired our work, which looks at the results of adding temporal delays to the Kuramoto model. In particular, we investigate how the system’s synchronization dynamics are affected by delays. We shed light on the mechanisms underpinning synchronization in the face of temporal delays and …

Green Function In Metric Measure Spaces, Mario Bonk, Luca Capogna, Xiaodan Zhou

Mathematics Sciences: Faculty Publications

We study existence and uniqueness of Green functions for the Cheeger QLaplacian in metric measure spaces that are Ahlfors Q-regular and support a Q-Poincar´e inequality with Q > 1. We prove uniqueness of Green functions both in the case of relatively compact domains, and in the global (unbounded) case. We also prove existence of global Green functions in unbounded spaces, complementing the existing results in relatively compact domains proved recently in [BBL20].

Geometries Gon Wild, Naat Ambrosino

Undergraduate Theses

A circle is mathematically defined as the collection of points a given distance away from a set point. Thus, the appearance of a circle varies dramatically across different metrics—for example, the taxicab metric (as popularized by Krause and Reynolds) has a circle that is a Euclidean square. As such, metrics can be partially defined by the appearance of their unit circles. This paper focuses on creating and analyzing an infinite set of metrics defined by their circles being regular polygons. Additionally, it provides a method of exactly generating a regular n-gon given a center, included point, and specified orientation.

Analyzing The Effect Of Targeted Activities On Linear Concept Understanding, Jenae Rogers

Honors Theses

Despite previously showing mastery of all test topics in ALEKS, Andrews’ remedial math students continue to struggle with some of them on the paper tests. After previous research, additional teaching activities, including one targeting word problems, were implemented to address student misconceptions about linear equations. My current research compares student performance on the paper tests before and after these activities on questions regarding linear relationship word problems. My findings show no statistically significant difference in student performance after these activities. These results will lead to further curriculum changes, in an attempt to increase students’ long-term conceptual understanding and problem-solving skills.

Extending Natural Mates In Euclidean 3-Space And Applications To Bertrand Pairs, Alexander Navarro

Honors Theses

In Euclidean 3-space, a family of curves, the co-successor, is motivated and then introduced in relation to the natural mate. A complete characterization of co-successors is proved, followed by an application of the co-successor towards describing Bertrand curves and their mates.

Solvability And Difficulty Of The Snake Puzzle In The Cube And Its Topological Variants, Jamie Shepard

Honors Theses

A snake cube is a puzzle made by a sequence of n3 straight and turn pieces that can fold into a n x n x n cube. Solving the puzzle is comparable to the problem of finding a Hamiltonian path in the grid graph of the cube. By using computer algorithms, we find and count all sequences that are solutions. Furthermore, we can count the unique folding configurations of each sequence giving us an idea of its difficulty. Finally, we expand on this by exploring the problem in other topological variants of the cube, which sheds insight into the problem …

Rsa Algorithm, Evalisbeth Garcia Diazbarriga

ATU Scholars Symposium

I will be presenting about the RSA method in cryptology which is the coding and decoding of messages. My research will focus on proving that the method works and how it is used to communicate secretly.

Data Analytics Internship At Fastenal, Jacob J. Haines

Research & Creative Achievement Day

The poster will present the results from an analysis of Fastenal's customer base to find characteristics among them that serve as useful predictors of their spending habits. This will allow Fastenal to create more accurate control groups when assessing the effectiveness of various marketing initiatives. This poster acts as the communication of capstone experience outcomes which is required for Data Science majors in addition to the capstone experience.

Using Data Visualizations To Analyze Employee Performance At Xcel Energy, Abby Venz

Research & Creative Achievement Day

Companies often are curious about their employee performance. But how, exactly, do they analyze this? As a Data Analytics Intern for Xcel Energy, I was in charge of doing just this. This poster will walk you through the methods used to analyze and model employee performance, as well as the results found and the different ways managers at Xcel Energy used them

My Experience As An It Data Intern, Annajo V. Vonseth

Research & Creative Achievement Day

This poster presentation is focused on my internship as an IT Data Intern with B’nai B’rith Youth Organization (BBYO). I was able to use the skills already learned through courses here at WSU to help project and produce high-end reports. Additionally, I was in-charge of the creation of the survey all the way to creating the PowerPoint presentation with the results. I will also discuss how Microsoft Suites played a huge role in my day-to-day work, from large, complex data sets to cleaning and refining old data, I will be discussing the skills I learned during my time as an …

Finding Combinatorial Patterns In Real Valued Omics Data, Kenneth Smith

Dissertations

Precision medicine is a healthcare approach which tailors disease prevention and treatment to an individual, based on their genetics, environment, lifestyle, and physiological state. These factors interact to produce biological changes that can be measured to produce data called omics, and include genomics, lipidomics, and proteomics. Despite the abundance of omics data and analysis techniques, researchers still struggle to identify biological findings that replicate across data sets and translate into clinical applications. In this dissertation, we employ combinatorial optimization techniques to improve upon three steps in the precision medicine analysis pipeline: 1) data cleaning, 2) community detection, and 3) feature …

Splines On Cayley Graphs Of The Symmetric Group, Nathan Lesnevich

Arts & Sciences Graduate Student Theses and Dissertations

A spline is an assignment of polynomials to the vertices of a graph whose edges are labeled by ideals, where the difference of two polynomials labeling adjacent vertices must belong to the corresponding ideal. The set of splines forms a ring. We consider spline rings where the underlying graph is the Cayley graph of a symmetric group generated by a collection of transpositions. These rings generalize the GKM construction for equivariant cohomology rings of flag, regular semisimple Hessenberg, and permutohedral varieties. These cohomology rings carry two actions of the symmetric group S_n whose graded characters are both of general interest …

The Lowest Discriminant Ideal Of Cayley-Hamilton Hopf Algebras, Zhongkai Mi

LSU Doctoral Dissertations

Discriminant ideals are defined for an algebra R with central subalgebra C and trace tr : R → C. They are indexed by positive integers and more general than discriminants. Usually R is required to be a finite module over C. Unlike the abundace of work on discriminants, there is hardly any literature on discriminant ideals. The levels of discriminant ideals relate to the sums of squares of dimensions of irreducible modules over maximal ideals of C containing these discriminant ideals. We study the lowest level when R is a Cayley-Hamilton Hopf algebra, i.e. C is also a Hopf subalgebra, …

Statistics For Iwasawa Invariants Of Elliptic Curves, Ii, Debanjana Kundu, Anwesh Ray

School of Mathematical & Statistical Sciences Faculty Publications

We study the average behavior of the Iwasawa invariants for Selmer groups of elliptic curves. These results lie at the intersection of arithmetic statistics and Iwasawa theory. We obtain lower bounds for the density of rational elliptic curves with prescribed Iwasawa invariants.

“Don’T Call On Me!”: Mediating Preservice Elementary Teachers’ Mathematics Anxiety In A Problem-Based Classroom, Christina Koehne, Wenyen Huang, Nataly Chesky

Excelsior: Leadership in Teaching and Learning

This study aims to understand the ways in which problem-based teaching in a mathematics content course can alleviate pre-service elementary school teachers' mathematics anxiety. The significance of this work is to help increase the content and pedagogical knowledge of mathematics education, as outlined in STEM policies. Using a mixed method approach, the teachers-researchers explore what methods, procedures, and other perhaps unknown variables, helped pre-service elementary teachers decrease their mathematics anxiety during two mathematics content courses. The findings illuminate five major themes the authors discuss, which are illustrated by rich descriptions of students’ narratives and interviews. Given the importance of mathematics …

Faithful Representation Of Free Groups And Congruent Subgroups Of 𝑆𝐿3 (𝑍), Julius Kurian

Thesis/ Dissertation Defenses

This thesis is concerned with the matrix representation of a free non-abelian group by matrices of size ≥ 3. We proceed from defining an equivalence classes and then transitioning to free groups. We discuss in details the group 𝐺𝑛(𝑘) which is the group generated by the matrices filled with first, (second, etc.) column, except for the intersection with the diagonal, and we have ones on the diagonal and zeros at the other places. The filled places are occupied by the same parameter 𝑘. An alternative proof for the known fact that 𝐺𝑛(3) is not free is provided. The main objective …

Extensions Of Algebraic Frames, Papiya Bhattacharjee

Mathematics Colloquium Series

A frame is a complete lattice that satisfies a strong distributive law, known as the frame law. Frames are also known as Pointfree Topology, as every topology is a frame. Even though the concept of frames originated from topology, the idea has expanded to many other areas of mathematics and frames are now studied in their own merit. Given two frame L and M, we say M is an extension of L if L is a subframe of M. In this talk we will discuss different types of frames extensions, such as Rigid extension, r-extension, and r*-extension between two frames. …

Extensions Of Algebraic Frames, Papiya Bhattacharjee

Algebra Seminar

A frame is a complete lattice that satisfies a strong distributive law, known as the frame law. Frames are also known as Pointfree Topology, as every topology is a frame. Even though the concept of frames originated from topology, the idea has expanded to many other areas of mathematics and frames are now studied in their own merit. Given two frame L and M, we say M is an extension of L if L is a subframe of M. In this talk we will discuss different types of frames extensions, such as Rigid extension, r-extension, and r*-extension between two frames. …

On The Projections And Unitary Groups Of Unital C*-Algebras, Fouzia Shaheen

Thesis/ Dissertation Defenses

H. Dye proved that the unitary group in a factor determines the algebraic type of that factor. Al-Rawashdeh, Booth and Giordano established that, for a large class of simple unital C*- algebras, an isomorphism between the unitary groups, induces an isomorphism between their K0-ordered group and K1-groups. Then using the results of Dadarlat-Elliot-Gong and KirchbergPhillips, the C*-algebras are isomorphic. Dye introduced special projections P{i,j}(a) of the matrix algebra Mn(A), and he used it as a main tool to establish his results in the case of von Neumann factors. Precisely, in case of von Neumann algebra, he proved that if  …

Pricing Asian Options During Crises With The Impact Of Exogenous Events, Moath Ali Bakour

Thesis/ Dissertation Defenses

Asian options are path-dependent options since their payoff is built on the prices of the underlying asset over a time period. The Asian option pricing problem is primarily subject to the prediction model for asset prices. The pioneer Black Scholes paper suggests a GBM- Geometric Brownian motion. The Black-Scholes formula suffers from several shortcomings. For instance, the GBM does not take into consideration crises. Another problem with the Black-Scholes model is that it does not deal with the impact of external events. This work aims at a suggested model that encompasses the impacts of crises and external events together. It …

On Properties Of Pair Operations, Sarah Jane Poiani

Mathematics & Statistics ETDs

For any closure operation $\cl$ and interior operation $\ri$ on a class of $R$-modules, we develop the theory of $\cl$-prereductions and $\ri$-postexpansions. A pair operation is a generalization of closure and interior operations. Using Epstein, R.G. and Vassilev's duality \cite{ERGV-nonres}, we show that these notions are in fact dual to each other. We discuss the relationship between the core and hull and prereductions and postexpansions. We further the thematic notion of duality and seek to understand how it arises in the context of properties pair operations can be endowed with and focus on inner product spaces and properties demonstrated by …

Generalized Q-Fock Spaces And Structural Identities, Daniel Alpay, Paula Cerejeiras, Uwe Kaehler, Baruch Schneider

Mathematics, Physics, and Computer Science Faculty Articles and Research

Using 𝑞-calculus we study a family of reproducing kernel Hilbert spaces which interpolate between the Hardy space and the Fock space. We give characterizations of these spaces in terms of classical operators such as integration and backward-shift operators, and their 𝑞-calculus counterparts. Furthermore, these new spaces allow us to study intertwining operators between classic backward-shift operators and the q-Jackson derivative.

Hgs-3 The Influence Of A Tandem Cycling Program In The Community On Physical And Functional Health, Therapeutic Bonds, And Quality Of Life For Individuals And Care Partners Coping With Parkinson’S Disease, Leila Djerdjour, Jennifer L. Trilk

SC Upstate Research Symposium

Purpose Statement: Several studies have shown that aerobic exercise can have a positive impact on alleviating symptoms experienced by individuals with Parkinson's disease (PD). Despite this evidence, the potential benefits of exercise for both PD patients and their care partners (PD dyad) remain unexplored. This research project investigates the effectiveness, therapeutic collaborations, and physical outcomes of a virtual reality (VR) tandem cycling program specifically designed for PD dyads.

Methods: Following approval from the Prisma Health Institutional Review Board, individuals with PD were identified and screened by clinical neurologists. The pre-testing measures for PD dyads (N=9) included emotional and cognitive status …