Poster Session
Raymond Clines
University of North Florida
Pascal’s Pyramid: A Visual Analysis
Pascal’s Triangle is a well-known structure in mathematics with many properties that have been thoroughly studied. In this poster, we will take a visual approach to exploring its extension into Pascals’ Pyramid. We will first introduce an indexing system for the pyramid and use it to examine some of the pyramid’s properties. We will also establish and prove several theorems about the pyramid’s structure, including its formation with the generalized Pascal’s Identity.
Poster Session
Brandon Cribbs
University of North Florida
Berlekamp-Massey Algorithm: The Problem of Managing Errors
Brandon Cribbs - University of North Florida Berlekamp-Massey Algorithm: The Problem of Managing Errors Reed-Solomon Error-Correcting Codes are a generalization of Hamming Codes in that they correct multiple bits at a time rather than one but the resulting errors are distortions. The errors increase exponentially, which makes the decoding process difficult if not impossible. The Berlekamp-Massey algorithm ensures that the message will be decodes by allowing the errors to be bounded through an algebraic linear recurrence technique using an Error-Locator Polynomial.
Poster Session
Aishwarya Ganapathy
Valencia College
The Future Of Connected Intelligence: Artificial Intelligence (AI), Cloud Computing, Internet Of Things (IoT) In Modern Software
Modern software systems depend on integrating AI, cloud platforms, and IoT for connected intelligence. This presentation covers how IoT collects data, cloud platforms manage it, and AI enables smarter decisions. These technologies boost efficiency and automation, making their integration vital for secure and scalable applications in industries like healthcare, smart cities, and industry.
Poster Session
Furio Gerwitz
University of North Florida
Coloring Maps and the Five Color Theorem
Map coloring, the problem of finding the minimum number of colors with which you can color a map such that no two neighboring regions share the same color, is a classic practical application of graph theory. In this poster, we will formalize maps as planar graphs and prove the Five Color Theorem, which states any map can be colored with at most five colors. We will additionally discuss the significance of the stronger Four Color Theorem, proved much later with nonstandard techniques.
Poster Session
Furio Gerwitz
University of North Florida
Perfect Codes
Perfect codes are algebraic structures in which every word of length n over a finite alphabet serves as either a codeword, or as a failsafe within correction distance of a codeword. In this poster, we introduce Hamming codes, the most famous family of perfect codes, which have a rich history of use in computing and telecommunications. We will prove their perfection by showing they meet the Hamming bound, the fundamental characteristic of perfect codes. Additionally, we prove Hamming codes’ error correction capabilities, discuss their properties as linear codes, and provide methods for their construction.
Poster Session
Joyce Henriquez
Valencia College
The Paradoxical Nature of Motion and Infinity
Achilles and the Tortoise a story about a race between the two where the tortoise receives a head start. Creating a paradox between motion, infinity, and a finite distance. Achilles must travel infinitely many halfway points in order to reach the tortoise. This creates the paradox between motion and distance. In order to solve we need convergent series. This is because it is an infinite series with a finite solution. That is how motion and infinity can co exist. I will delve into the intricacies of how the paradox can be solved.
Poster Session
Dylan Hewlett
University of North Florida
Mapping the Limits of Computation
Computability theory provides a framework for describing the fundamental limits of algorithmic problem-solving. This poster highlights these limits through several cornerstone results. Beginning with Turing machines and the Church–Turing Thesis, it uses the acceptance problem as a key example to illustrate how diagonalization reveals inherent undecidability. The poster then presents mapping reductions as a systematic tool for transferring undecidability between decision problems. Finally, it features Rice’s Theorem, demonstrating that every nontrivial semantic property of a Turing machine’s language is undecidable. Together, these results outline the broad boundaries that constrain automated reasoning about programs.
Poster Session
Anne Howell
University of North Florida
Why Every Finite Group Appears as a Graph Automorphism Group
Frucht states that every finite group can be realized as the automorphism group of a finite graph. This poster presents the theorem together with a detailed inductive proof, illustrated by explicit graph constructions. An interesting technique using pendant subgraphs is examined, showing how directed behavior can be encoded within undirected graphs while maintaining the desired automorphism group.
Poster Session
Anne Howell
University of North Florida
Why Large Graphs Must Contain Structure: Ramsey Theory for Finite Graphs
Any sufficiently large finite graph must contain a complete subgraph of bounded size. This poster presents the classical six-person problem as a concrete entry point into the general theory. Ramsey’s Theorem for finite graphs is provided together with a detailed inductive proof.
Poster Session
Anthonie Page
Florida Institute of Technology
Determining Material Transport Method for Moon Colony Using Differential Equations
Large-scale lunar construction requires transporting vast quantities of material from Earth to the Moon. Two competing infrastructure concepts are high-cadence reusable rocket launches and a space elevator system (“Galactic Harbour”). While rockets have proven operational feasibility, they suffer from high marginal cost per ton and discrete failure risks. In contrast, a space elevator provides continuous throughput but introduces time-dependent mechanical risks such as sway stabilization, fatigue, and transfer slip at the apex hub. The purpose of this work is to develop a unified mathematical framework that compares both systems under consistent assumptions and evaluates which system achieves a target delivery of 100 million metric tons most efficiently.
Poster Session
Eric Rodarte
Embry-Riddle Aeronautical University, Daytona Beach
Low-Rank Spectral Analysis for the Reddening of the Seven Sisters Star Cluster
The Pleiades, also known as the Seven Sisters, is a stunning star cluster located approximately 440 light-years from Earth. This vibrant assemblage of hot blue stars in the Taurus constellation can be admired with the naked eye or through binoculars during early autumn. In this talk, we utilize spectral theory to measure the reddening in the Pleiades star cluster. To evaluate the impact of interstellar dust on reddening, we employ principal component analysis (PCA) on a matrix representing color indices from various photometric bands linked to the cluster’s photometric data. This dataset was obtained from VIZIER. Our PCA analysis of the photometric band matrix revealed that reddening is notably influenced by the color shift observed predominantly in the BP band. Ultimately, our numerical findings were verified, demonstrating an alignment with the extinction laws utilized by Gaia DR3. This is due to the fact that the PCA-derived reddening vector displayed an angular deviation of only 0.170° from the theoretical reddening vector, resulting in a minimal overall percentage difference of 0.294%. This is a joint work with Angelina Scalice, Madison Warner, Kevin Numbe, and Sirani M. Perera.
Poster Session
Eric Rodarte
Embry-Riddle Aeronautical University, Daytona Beach
Low-Rank Spectral Analysis for the Reddening of the Seven Sisters Star Cluster
The Pleiades, also known as the Seven Sisters, is a stunning star cluster located approximately 440 light-years from Earth. This vibrant assemblage of hot blue stars in the Taurus constellation can be admired with the naked eye or through binoculars during early autumn. In this project, we utilize spectral theory to measure the reddening in the Pleiades star cluster. To evaluate the impact of interstellar dust on reddening, we employ principal component analysis (PCA) on a matrix representing color indices from various photometric bands linked to the cluster’s photometric data. This dataset was obtained from VIZIER. Our PCA analysis of the photometric band matrix revealed that reddening is notably influenced by the color shift observed predominantly in the BP band. Ultimately, our numerical findings were verified, demonstrating an alignment with the extinction laws utilized by Gaia DR3. This is due to the fact that the PCA-derived reddening vector displayed an angular deviation of only 0.170° from the theoretical reddening vector, resulting in a minimal overall percentage difference of 0.294%. This is a joint work with Angelina Scalice, Madison Warner, Kevin Numbe, and Sirani M. Perera.
Poster Session
Lennon Shikhman
Florida Institute of Technology
Manifold Learning for Early Detection of Influenza-like Illness from Wearable Data
We study anomaly detection in high-dimensional time-series data through a manifold learning framework. For each subject, self-supervised representation models are used to learn a latent manifold capturing typical system dynamics. Deviations are characterized as sustained departures from this learned manifold, quantified using geometric and statistical criteria including reconstruction error, latent-space distance, and trajectory-based measures reflecting changes in local structure. Temporal aggregation is used to distinguish structured anomalies from transient noise. The framework is evaluated on physiological data where it enables early detection of regime changes relative to individual baselines, illustrating the utility of manifold-based inference in noisy, heterogeneous systems.
Poster Session
Alice Tesser
Rollins College
Admissions Data as a Window into Students' Perspectives on Food Insecurity
The study was motivated by a broader conversation about using admissions data to address social justice on campus. Specifically, it explores how such data can reveal students’ past experiences and perceptions of food insecurity, guide administrations in policy implementation, and foster a more inclusive academic environment. The results indicate a significant association between the percentage of Free and Reduced-Price Lunch program participation at students’ high schools and their enrollment at a small private liberal arts college. Furthermore, our findings emphasize the value of school-specific data over aggregated county-level statistics, underscoring the importance of school zoning policies versus ZIP codes.
