Undergraduate Speaker Session

Session Index

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Undergraduate Session 1
9:40am--11:20am
Speakers: Rohan Jwaleshan, Rory Kelleher, Christopher Mead, Ray Kress, Bharathi Balaji, Marissa Farrell, Lucas Acosta-Morales, Luke Cossman, Taylor Grabowski, Anna Hanlon, Solomaya Schwab

Undergraduate Session 2
9:40am--11:20am
Speakers: Phillip Hopkins, Luke Tufaro, James Hannigan, Ben Jefferis, Jameson Adgalane, Shon Biju, Jacy Lieberum, Samantha Garber, Ryan Rahim, Gregory Boymel

Undergraduate Session 3
9:40am--11:20am
Speakers: Evan Sabini, Garrison Koch, Kayla Barker, Andrew Clickard, Isaac Reiter

Undergraduate Session 1

9:40am, Rohan Jwaleshan, Rory Kelleher (University of the Sciences)
Set Theory and SQL/ Relational Databases
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In this talk we explain how set theory relates to SQL/ relational databases through set operations used in SQL queries. We will provide a general explanation of sets, Venn diagrams and provide an example of SQL queries in our presentation.
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10:00am, Christopher Mead, Ray Kress (University of the Sciences)
Developing Carbon Dioxide Recycling Catalysts With Machine Learning Algorithm
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For many years, scientists have been trying to develop catalysts that are efficient at reducing carbon dioxide back into carbon fuels. Recently, copper catalysts have yielded some of the best results, but they still have much room for improvement. A new machine learning algorithm was designed that accurately evaluates and predicts efficiency for both new and existing copper catalysts, which will greatly increase the speed of future research.
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10:20am, Bharathi Balaji, Marissa Farrell (University of the Sciences)
The Algorithm Behind TikTok
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The $250 billion app, TikTok, is a global social media for short mobile videos. It encourages its users to be creative and share their passions with the world through their followers. The “For You” page is designed to show videos that are specific to the user and their interests, which continues to keep them engaged. How does the company accomplish this? It’s facilitated through a very powerful algorithm, based on creation, moderation, and interaction. The more people upload videos, the more people watch. It is an endless, yet effective cycle.
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10:40am, Lucas Acosta-Morales, Luke Cossman, Taylor Grabowski, Anna Hanlon (DeSales University)
Research, Analysis & Topological Structures (R.A.T.S)
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The Research, Analysis, and Topological Analysis (R.A.T.S) project is focused on behavioral analysis of mice through machine learning and data analysis processes. The RATS pipeline is split into two main procedures, the first being the feature analysis. This section takes in the positional data of the mouse through a machine learning program and then identifies prominent features in the data through a process known as persistent homology. These features are not physical, like a face or tail, but more of an abstract concept that shows key behavioral features. These features are then narrowed down to the 12 most notable features (or about 30 percent of the sample size) through kernel density estimation (KDE). This feature data is then sent to the second phase of the pipeline, the machine learning phase. Here, we create and train a neural network by incorporating the given information about which mice are in pain and which are not. This produces a model tailored towards detecting mice in pain from their homological features alone, ultimately allowing new mice to be analyzed using this same model.
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11:00am, Solomaya Schwab (Cedar Crest College, Bridgewater College )
An epidemiological study on the spread and treatment of treponemal infection in olive baboons
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The bacteria Treponema pallidum ssp. pertenue causes a chronic infection that was thought to affect only humans. However, it was recently found in primates and monkeys in Tanzania National Parks. We develop a compartmental ODE model for the spread of the infection amongst olive baboons. We solve for disease-free and endemic equilibria. We calibrate the model based on the data from Tanzania. We show that the disease-free equilibrium is globally asymptotically stable when the treatment rate is high enough. We use the model to help the parks devise an effective strategy for treatment.
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Undergraduate Session 2

9:40am, Phillip Hopkins, Luke Tufaro (University of the Sciences of Philadelphia)
Collision Course of Mathematics and Chemistry: Using Graph Theory to Describe Molecular Structures
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At times it may feel as if mathematics and chemistry are tied together at the hip. Mathematical skills are required to solve even simple chemistry problems like balancing a chemical equation, or finding the energy associated with a specific absorbance wavelength. From algebra to geometry to calculus and beyond, different disciplines of mathematics are entwined with nearly every aspect of chemistry. Here, we discuss the relationship between graph theory and chemistry and how it can be used to better our understanding of the molecular structure of a given chemical compound. We provide a brief history of how graph theory was adopted by chemists and demonstrate its descriptive and predictive power.
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10:00am, James Hannigan, Ben Jefferis (University of the Sciences )
The Use of Mean Value Theorem(MVT) to Enforce Traffic Laws
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Mean value theorem (MVT) states that on a continuous closed interval [a,b] and on a differential open interval (a,b) that there exists a value c in (a,b) such that f’(c)=(f(b)-f(a))/(b-a). MVT can be used on the highway as a function of distance over time traveled. The velocity of a car going down the highway (mph) can be estimated for a specific point by knowing the car’s displacement over time. Using timestamps obtained from waypoints including time between specified points on a highway or time between toll booths during a trip, MVT can be used as a way to calculate the average speed of a car between waypoints. Law enforcement is yearning to use this average speed as a way to give out citations, since it is accurate and relatively simple to carry out. Our presentation will explain MVT and outline how it is used in law enforcement in dealing with speeding violations.
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10:20am, Jameson Adgalane, Shon Biju (University of the Sciences)
Intelligent Systems in the Army
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The army, as well as other branches of the military, has a great need for mathematics and mathematical sciences. Mathematical research in the Army is typically categorized into one of six components: applied analysis, computational mathematics, probability and statistics, systems and control, discrete mathematics, or intelligent systems. For the purpose of this presentation we will highlight the importance of intelligent systems in the Army. Intelligent systems is a fairly new area of research centered around satisfactory performance of systems in environments which can often present a wide variety of uncertainties. The systems are programmed and taught to learn about both known and unknown factors in their environment and adapt to them accordingly. Intelligent systems are needed mainly in areas such as: distributed command and control, simulated battlefield environments, intelligence augmentation of human centered systems, automatic/aided target recognition, smart medics, and manufacturing systems. The presentation will dive deeper into the specific needs for these types of mathematical systems as well as ways in which they can be developed to achieve their intended goals.
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10:40am, Jacy Lieberum, Samantha Garber (University of the Sciences)
Traffic Jams Explored by Fundamental Diagrams
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This discussion will explore the nature of traffic jams based on fundamental diagrams. It will specifically discuss the relationship between density of vehicles, ρ, and unique flow rate value, Q, which can generate traffic models that can explain ‘phantom traffic jams’ where there is no external reason for an increase in traffic and ‘stop-and-go waves’. These two types of traffic jams analysis will be discussed utilizing the context of the Payne-Whitham Model under the conditions of regular pressure and singular pressure. The Payne-Whitham Model in this circumstance analyzes the relationship between the vehicle density and flow rate along with the desired velocity function. This relationship will be analyzed through the fundamental phase diagrams to explain phantom traffic jams and stop-and-go waves.
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11:00am, Ryan Rahim, Gregory Boymel (University of The Sciences)
The Area of the Circle
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For our research topic, we have chosen Archimedes Theorem of the Area of A Circle. We have selected this topic because it was a significant finding that influences math to this day. The circle shape is a shape that is seen as expected to the everyday eye; however, to a mathematician, the circle is a very odd shape. It raised questions such as does it have infinite sides or no sides? Can other polygonal properties apply to it? How do you measure the perimeter? And so on. The area of a circle was an easy formula that I did in math classes, but later I realized there is a lot more behind it. Since there was a lot of thinking and thought going into finding the circle area, it was our proper choice as to how the circle area discovered this. We will research this topic and have it be put onto a PowerPoint in which we will present to the conference on zoom. We will have diagrams and pictures and go through Archemides’ thought process on how he found the area of a circle. Overall, we will be taking turns presenting and discussing the different aspects of the circle shape, including the methods and history, and emphasizing Archimedes formula for the area of a circle.
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Undergraduate Session 3

9:40am, Evan Sabini (Villanova University)
Induced-Saturation with Star Graphs
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Using the definition of Tennenhouse, a graph $G$ is $\textit{induced $H$-saturated}$ if there exists no induced subgraph $H$ in $G$, but for every edge $e\in \overline{G}$, $G+e$ has an induced subgraph $H$. Tennenhouse showed the existence of induced $K_{1,3}$-saturated graphs for $n\geq 12$. Inspired by his results for this star graph $K_{1,3}$, we looked at the double star $D_{2,2}$ graph formed by taking two $K_{1,3}$ graphs and connecting them at a single vertex. We show via a constructive proof that there exists an induced $D_{2,2}$-saturated graph on $n$ vertices if and only if $n\geq 12$. We also find sufficient conditions to conclude that a graph is induced $D_{m,m}$-saturated.
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10:00am, Garrison Koch, Kayla Barker (Moravian University)
On the Solvability of a Bipartite Graph Reduction Game
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A $game-labeling$ of a bipartite graph is one in which the vertices have non-negative labels and the label sums of the partite sets are equal. A $reduction$ $across$ $an$ $edge$ is one in which the endpoints are both reduced by the same integral amount. We introduce a single player game on a game-labeled bipartite graph $G$ where each move is a reduction across an edge and no move produces a negative label. The goal of the game is to reduce all labels in $G$ to 0, and if the player succeeds in doing so, the player wins the game. In this presentation, we present a necessary and sufficient sum condition for detecting the solvability of the game. We also demonstrate the connection between this game and Double Choco Puzzles.
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10:20am, Andrew Clickard (Bloomsburg University of Pennsylvania)
On the Symmetric Difference Property in Difference Sets under Product Construction
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A $(v, k, \lambda)$ symmetric design is said to have the symmetric difference property (SDP) if the symmetric difference of any three blocks is either a block or the complement of a block. Symmetric designs fulfilling this property have the nice property of having minimal rank, which then implies maximal distance when viewed as bent functions over Reed-Muller codes. Thus, SDP designs become useful in coding theory applications. We show in this paper that difference sets formed by direct product construction of difference sets whose developments have the SDP also have the SDP. We also establish a few results regarding isomorphisms in product constructed SDP designs.
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10:40am, Isaac Reiter (Kutztown University of Pennsylvania)
The VICCard Cipher: Our Contribution to the Field of Playing Card Cryptography
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Before computers, military tacticians and government agents had to rely on pencil-and-paper methods to encrypt information. For agents that want to use low-tech options in order to minimize their digital footprint, non-computerized ciphers are an essential component of their toolbox. Still, the presence of computers limits the pool of effective hand ciphers. If a cipher is not unpredictable enough, then a computer will easily be able to break it. There are $52! \approx 2^{225.58}$ ways to mix a deck of cards. If each deck order is a key, this means that there are $52! \approx 2 ^{225.58}$ different ways to encrypt a given message. To create some perspective, most computer ciphers feature either $2^{128}$ or $2^{256}$ different ways of encrypting the same message. Hence, a cipher created from a deck of cards has the potential to emulate the security of many computer ciphers. Dr. Landquist and I spent the summer of 2019 examining existing playing card ciphers. This led to the main focus of our paper: the creation of a unique, secure playing card cipher. Because of the inspiration provided by the cipher VIC, I am calling our original cipher VICCard. VICCard has gone through multiple versions, each better than the last. Its security is rooted in its combination of numerous cryptographic principles, including a substitution checkerboard, columnar transpositions, lagged Fibonacci generators, and junk letters. As evidenced by certain randomness tests, VICCard has the potential to extensively randomize an English plaintext. In my talk, I will discuss the workings of our cipher, the inspiration behind it, and the associated randomness tests.
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