Math & Computer Science Faculty Host NSF Sponsored REU 2022
Through a grant from the National Science Foundation, the Math & Computer Science department, once again, hosted the summer Research Experience for Undergraduates. Students from colleges across the country traveled to Ursinus to participate in this intensive program to learn and implement professional research techniques. In close collaboration with Math & Computer Science faculty, the REU students worked in small groups to research various topics of interest (with a lot of added fun) and, at the end of the program, presented their findings to their peers and mentors. The skills this experience offers provide a strong foundation for success in helping the students more confidently tackle complex issues in the future.
Summer 2022 REU Research Projects
Sam Gregory and Kacey La
Automated Approaches to Bowhead Whale Identification
Math and Computer Science
Mentor: Christopher Tralie and Leslie New
Identifying individual bowhead whales plays a vital role in understanding their migration patterns and population. However, the process of manually matching known individuals can be especially time-consuming. With the advancement of modern image processing techniques, this project aims to automate the identification of bowhead whales using convolutional neural networks. The initial neural network identifies key points to outline each whale and uses these points to divide each whale into three sub-sections: the fluke, the back, and the head. Given the limited amount of publicly available bowhead whale pictures, this project uses data from the 2015 Kaggle right whale competition to supplement training data used to outline the bowhead whales. Upon segmenting the whale, each sub-section was used to identify individual bowhead whales though the white patterns and scarring on their backs. The results from each segment were then combined into a final classifier to confidently identify bowhead whales.
Ed Coleman, Jhavon Innocent, Sarah Kircher, and McKade Trauger
COVID-19 Pandemic Response and Overall Health
Math and Computer Science
Mentor: Hugo Montesinos-Yufa
The direct impact of the COVID-19 pandemic and the indirect impact of the ensuing economic and political response have affected the United States on a large scale. Measuring both the direct and indirect effects of COVID-19 allows for better comprehension and analysis of individual states’ pandemic responses. During this NSF-sponsored REU, the indirect impact of COVID-19 on overall health is analyzed through the stringency of individual states’ pandemic policies. Our research utilizes difference-in-difference, linear regression, and correlation matrices to quantify individual state responses’ effect on overall health, particularly mental health. The quantitative results and time-specific political-economic analysis enhance our understanding of the direct and indirect effects of the COVID-19 pandemic on public health. Our results indicate a wide variation in mental health-related issues by age group, with a higher prevalence in younger age categories. While we observe a slight decline in the share of the population experiencing anxiety and depression through January 2021- June 2022, the effects of the stringency index on other areas of health are complex and vary by state. We document a potential surge in employment-related anxiety, a reduction in overall quality of life, and a significant increase in unexplained mass shootings (by quarter/year) since the pandemic started. This research aims to add to the breadth of ongoing COVID-19 research and emphasize the importance of overall health in a large-scale health crisis.
Kasey Cooper, Ava Dreher, Caroline McCrorey
Dynamics of a Stage-Structured Predator-Prey Model with Cannibalism
Math & Computer Science
Mentor: Eric M. Takyi
Cannibalism, or intraspecific predation, is the act of an organism consuming another organism of the same species and is universally found among different living organisms. Examples observed in nature include cannibalism in polar bears (Ursus maritimus), chimpanzees (Pan troglodytes), brook trout (Salvelinus fontinalis), etc. In real life, living organisms grow in stages. Therefore, in this work, we study the effects of cannibalism in a stage-structured predator-prey model. The system is analytically studied and is found to exhibit various dynamics including limit cycles and a Hopf bifurcation. We perform various numerical experiments to support our theoretical findings and discuss the ecological implications of our results. This is a Research Experience for Undergraduates and is supported by the National Science Foundation via grant number 1851948 at Ursinus College.
Zach Schlamowitz, Charley Kirk, Antonio Delgado, Jose Arbelo
Math & Computer Science
Mentor: Christopher Tralie
When analyzing data, it is often of interest to categorize subsets based on similarity. In the case of time series, similarity can be found in key features like the placement and heights of prominent extrema. In this work, we develop a notion of distance between time series to enable such classification. Some approaches we’ve looked at for building this notion have involved representing time series via merge trees and triangulations of convex polygons, which capture the aforementioned key features. Additionally, such representations abstract away from “time-warping,” or reparameterization, allowing reparametrized time-series to be classified together. More recently we have looked at a notion of distance involving persistence pairs and we are looking at a more direct way of visualizing time series. In particular, we seek a distance metric that is robust to noise, as or more discerning than previously proposed distances, and efficiently computable. We show proof of the existence or nonexistence of such a distance metric. While previous work has satisfied the majority of these constraints, no proposed distance metric has simultaneously met them all.