Undergraduate Speaker Session

Session Index

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Undergrad/Grad Session 1
10:15am--11:25am
Speakers: Lillian Simmons, Alana Danelski, Dylan Roeder, Jared Chin, Megan Clayton, Justin Sellman, Samuel Urban, Simon Joseph, Shira Michel, Chen Sun

Undergrad/Grad Session 2
10:15am--11:25am
Speakers: Ethan Whitney, Elizabeth Hankins, Jeongsu Kyeong, Nour Hawila

Undergrad/Grad Session 1

10:15am, Lillian Simmons (Shippensburg University)
Math Modeling Anti-VEGF Therapy for Prostate Cancer
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Prostate cancer is one of the most common forms of cancer and the second leading cause of death in men in the United States. There is still lots of discussion and research about which methods are best for diagnosis and treatment. One type of treatment is Anti-VEGF therapy, which inhibits the protein VEGF. Vascular endothelial growth factor (VEGF) is one of the main regulators of angiogenesis, the formation of new blood vessels, which is vital for tumor growth. So, by inhibiting VEGF, the progression of the tumor should be affected. Based on the anti-VEGF drug Bevacizumab, a system of ODEs was developed to explore the response to treatment with anti-VEGF and possible combinations of therapies.
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10:30am, Alana Danelski, Dylan Roeder, Jared Chin, Megan Clayton (Millersville University of Pennsylvania)
Fire risk assessment and analysis in Columbia Borough and the City of Lancaster, Pennsylvania
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This talk is based on a team project which analyzes incidences of fire in Columbia Borough, Pennsylvania (PA) and the City of Lancaster, PA, to assess fire risks. A spatial distribution of fire incidents was created based on the seven districts of the Columbia Borough. Statistical tests were used to determine which of the seven districts have significantly different number of yearly responses. The impact that weather has on the occurrence of a fire is investigated. The Lancaster City Bureau of Fire data of building fires from the years 2016 to 2021 was used to analyze building fires on a month-to-month basis. Statistical tests were run with this data to develop findings on fire rates amongst holidays and weather trends. The results of this study will help assess fire risk and make preventive measures over time and space in the study area.
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10:45am, Justin Sellman, Samuel Urban, Simon Joseph (Millersville University of Pennsylvania)
Temporal patterns of different types of fire incidents: A case of the City of Lancaster, Pennsylvania
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This talk is based on a team project investigating the temporal dynamics of different types of fire incidents and their causes in the City of Lancaster, Pennsylvania. Incident data supplied by the Lancaster City Bureau of Fire for the period of 2012 to 2021 is analyzed. The results help assess fire risk and make preventive measures over time for the City of Lancaster.
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11:00am, Shira Michel (Arcadia University)
Approaches to analyze clustered data
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In statistical analysis, ignoring the clustered structure of data can lead to invalid results and statistical tests to be falsely rejected too often. Through R simulations, we investigated the effect of neglecting data clustering and explored statistical approaches that take data clustering into account. Our results and findings are consistent with the literature.
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11:15am, Chen Sun (Muhlenberg College)
Unbounded expected revenue in sad-loser auction
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Auction theory is the study of the real-world auctions. Often in auction theory, we assume that bidders are risk-neutral, that is, the utility function bidders use to measure their surplus is linear, meaning that a dollar gained has as much positive utility as a dollar lost has negative utility. However, according to Prospect Theory bidders are risk averse when positive gains are possible and risk-loving when negative losses are possible. This behavior can be mathematically modelled with a utility function that is concave for positive inputs and convex for negative inputs. When such a utility function is used in the so-called “sad loser” auction, we can prove that expected revenue to the seller is unbounded.
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Undergrad/Grad Session 2

10:15am, Ethan Whitney (West Chester University)
Homometry: When different structures are the same
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Two chords may contain the same musical intervals, despite being otherwise distinct. Different crystal structures can produce identical X-ray diffraction patterns. Under what conditions will this occur? The study and enumeration of these "homometric", or "same-measured" sets began in the 40s and continues as an emerging area of research today. In this talk, we will introduce the idea of homometry in cyclic groups, give illuminating examples, explore natural questions, and state some basic theorems. We will finish by discussing methods of generalization via group rings and/or discrete Fourier transforms.
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10:30am, Elizabeth Hankins (Bryn Mawr College)
Origami Fractals: Folding Paper Infinitely Many Times
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Generally, mathematical origami is restricted to finitely many folds. When we allow for infinitely many folds, some of the foundational theorems of origami break down. Other theorems still hold, but their form is altered. We will look at some of the bizarre phenomena that arise when we allow paper to be folded infinitely many times, and briefly discuss how to build a theory of origami that can handle infinite folds.
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10:45am, Jeongsu Kyeong (Temple University)
Singular integral operators associated with second order elliptic systems in two dimensions
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The goal of this talk is to investigate coefficient tensors associated with second order elliptic operators in infinite sectors in $\mathbb{R}^{2}$ and properties of the corresponding singular integral operators, using Mellin transform techniques. Specifically the discussion is focused on the relationship between distinguished coefficient tensors (those leading to chord-dot-normal type double layer potentials) and $L^{p}$ spectral and Hardy kernel properties of the associated singular integral operators.
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11:05am, Nour Hawila (Penn State University, Department of Biostatistics & Bioinformatics)
Exact-corrected confidence interval for risk difference in noninferiority binomial trials
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A novel confidence interval estimator is proposed for the risk difference in noninferiority binomial trials. The confidence interval is consistent with an exact unconditional test that preserves the type-I error, and has improved power, particularly for smaller sample sizes, compared to the confidence interval by Chan & Zhang (1999). The improved performance of the proposed confidence interval is theoretically justified and demonstrated with simulations and examples. An R package is also distributed that implements the proposed methods along with other confidence interval estimators.
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