The tropical cyclone diurnal cycle is a regular, daily cycle in hurricanes that may have implications for the structure and intensity of hurricanes. This pattern can be seen in a cooling ring forming in the inner core of the storm near sunset and propagating away from the storm center overnight, followed by warmer clouds on its inside edge. The current state of the art for diurnal cycle measurement has a limited ability to analyze the behavior beyond qualitative observations.
We developed a more mathematically advanced method for quantifying the TC diurnal cycle using tools from Topological Data Analysis. Using 1-dimensional persistent homology to analyze geostationary operational environmental satellite (GOES) IR imagery data from Hurricane Felix in 2007, we are able to detect an approximately daily cycle. These results can be found here.
At College of the Holy Cross, I worked under Dr. David Damiano for my undergraduate senior thesis project. The goal of this project was to detect tortuosity of retinal vasculature. Tortosity, or curving of the vessels, is an indicator for many diseases. Using tools from topological data analysis, specifically 0-dimensional persistent homology, we created a novel method for quantifying tortuosity. (Images from here)
During the summer of 2016 I participated in a research project at Kansas State University studying concepts in graph theory including the spanning tree modulus. This was in collaboration with Derek Hoare and Brandon Sit under the supervision of Dr. Nathan Albin. You can find the paper on this work here.
During the summer of 2015 and through the following academic year, I worked in collaboration with another undergraduate, Brian Toner, at College of the Holy Cross under the supervision of Dr. David Damiano on a continuation of a project started by Melissa McGuirl. We used Damiano & McGuirl's novel techniques developed in this paper with our own modifications to study heterogeneity of antibody uptake values in a new data set of SPECT images of murine tumors. Using this method we were able to distinguish uptake behavior of the antibodies in three different tumor cell lines with varying antigen expression.