Research
"Problems worthy of attack prove their worth by fighting back."
~Paul Erdos
A comparison of the Linearized Optimal Transport and 2-Wasserstein distance
August 2020 - June 2022
The classical optimal transport problem seeks to determine how to rearrange one pile of dirt to look like a different pile of dirt using the least amount of effort. By interpreting piles of dirt as pixel intensities, discrete optimal transport has desirable properties for machine learning algorithms but often times is an impractical method for processing large-scale data sets of images. To offset computational cost, Wang et al. introduced a linearized optimal transport (LOT) approximation scheme which significantly reduces the computational complexity associated with the image comparison task. This project investigates the relationship between linearized optimal transport and discrete optimal transport by proving inequalities relating the metrics and numerically investigating their sharpness.
Throttling for standard zero forcing on directed graphs
June 2020 - August 2020
In many settings, such as electrical network monitoring and quantum systems, it is desired to optimize resources and time among connected objects in a network. This type of optimization motivates the throttling parameter, in which SMALL 2020 extended this parameter to directed graphs. In our work, we explored how graph operations impact the throttling number to give an interval of throttling values for specific graph families.
Modeling Opinion Dynamics using the Affine Boomerang Model
2019 EUREKA Scholars Program
I joined Mechanical Engineering Professor Francesco Bullo's lab as a EUREKA scholar, studying how different social network structures and people's relationships (antagonistic or friendly) can influence the evolution of their opinions. I coded the Affine Boomerang model in MATLAB and observed trends in the updated opinions for star graphs and cycle graphs. The simulations suggest that people's relationships influence whether they will come to agreement or polarize, as well as how fast they will reach one of these states, if at all.