I work under the supervision
Sandstede. We are
interested in combining dynamical systems and topological data
analysis to study biological phenomena.
I collaborate with Devon Humphreys and Michael Miyagi under the
of Andrew Blumberg. Briefly, we apply TDA to
evolutionary data and then use techniques from machine
learning methods to classify popylations simulated under different parameter
Research with Undergraduates
Comparing Songs without Listening
In the Summer@ICERM 2017 program I worked with Dr. Katherine Kinnaird,
Erin Bugbee, and Claire Savard on the cover song task. The goal for
this project was to develope a flexible and computationally efficient method for
completing the cover song task. We used methods inspired from topological data analysis to correctly match songs
which are remakes of the same original piece.
Professor Sandstede's research group participates in weekly meetings
semester where we discuss topics in dynamical systems and related
fields. Below is an overview of our meetings along with the presentations I have presented.
A Topological Analysis of Targeted In-111 Uptake in SPECT Images
of Murine Tumors
I worked under the supervision of David Damiano for my
undergraduate thesis at The College of the Holy Cross. We developed a
novel topological method of analyzing Targeted In-111 Uptake in
SPECT Images of Mouse Tumors. The motivation for this method is illustrated in the videos below.
These videos show the super levelsets of images of murine tumors as
we descend through a filtration of tumor uptake values. The video
on the left corresponds to the mouse tumor at hour 24 in the study,
and the video on the right is the same tumor at hour 72. Our method
captures the topological information of these filtrations of the
tumors across a time series of images and surpasses standard
techniques in their ability to capture tumoar heterogenity. You can
find our paper here.
Assimilating Eulerian and Lagrangian data in traffic-flow models
During the summer of 2014 I participated in a research
project on data assimilation for traffic flow through a
Research Training Grant on “Integrating Dynamics and Stochastics.”
worked under the supervision
Sandstede and collaborated with Courtney Cochrane, Joey DeGuire,
Bridget Fan, Emma Holmes, Patrick Murphy, and Jenna
Palmer. Our graduate mentors were Paul Carter, Laura Slivinsky,
and Chao Xia. You can find our paper here.