Time Series Forecasting
I participated in the 2014 session of RIPS at UCLA's Institute for Pure and Applied Mathematics. Our four-student team was contracted by the Los Angeles Police Department to design crime rate forecasting algorithms and implement them in a GUI. I served as the project manager, working alongside Anthony Gusman, Sarah Verros, and Stephanie Sanchez. Our academic mentors were Yoon-Sik Cho and Jeffrey Brantingham.
Mathematical neuroscience (with electroencephalography data)
In the summer of 2013, I participated in a mathematical neuroscience project as part of the Indiana University Mathematics REU, funded by the NSF. My REU partners were Kate Coppess and Ben Seitzman, and our advisor was Evie Malaia. Our report is titled, "EEG time series analysis and functional connectivity network measures of TD and ASD youths."
Stochastically switching dynamical systems
During the summer of 2012, I studied a class of dynamical systems modeled after the Buridan's Ass paradox, as part of the SURIEM REU, funded by the NSA and the NSF, at the Lyman Briggs College of MSU. My REU partners were Blake Chamberlain and Rachel Gettinger, and our advisor was Dan Dougherty. Our report is titled, "Inverse modeling of dynamical systems: multi-dimensional extensions of a stochastic switching problem."
Discrete inverse Fourier approximations
In the summer of 2011, I was a participant in a Summer Learning Institute at Arizona State University, which introduced undergraduate research to the NSF-funded Focused Research Group: Integrated Mathematical Methods in Medical Imaging. Under the mentorship of Anne Gelb, I tested a "back-and-forth" algorithm designed to reconstruct a function from Fourier samples concentrated near the origin. I returned for a portion of the 2012 Summer Learning Institute, studying the regularization of convex minimization problems.
From fall of 2010 to spring of 2012, I worked at Michigan State as a research assistant of Jeffrey Schenker. Alongside fellow undergraduate Trevor Steil, I studied maximally expansive self-avoiding random walks, as well as abelian sandpiles.