I have taken several approaches to different topics of emergent phenomena in biology. I am
interested in how fine-grain details inform macroscale behavior of biological systems, especially
when stochasticity is involved.
Spatial Constraints on Reaction Rates
Many biological, chemical, and physical processes are characterized by two objects interacting with
each other, such as a protein finding a receptor on a cell membrane. In many cases,these interactions
only occur at localized areas of the particles, planes, or both. We developed mathematical models of
three of these types of systems and then used perturbation theory to calculate simplified models that
capture the key behaviors of these localized areas of reactivity.
In addition to the mathematical analysis, we developed simulation code to confirm the results of
our analysis as well as calculate the value of some parameters that have no known analyical formula.
These simulations are kinetic Monte Carlo simulations of diffusing particles, which break the diffusive
process into two simple stages that can be simulated exactly, allowing for greater efficiency and accuracy.
Dragonflies are excellent hunters that
perform aerial interception to capture their prey. In order to do this, dragonflies must transform sensory input
from the dragonfly eye's frame of reference to the body's frame of reference. We developed a model of the dragonfly
nervous system to study how the dragonfly performs these calculations. This model dragonfly successfully computes
the turns required for interception and indicates testable predictions for how these calculations occur in the
biological dragonfly. By understanding the dragonfly nervous system, neural-inspired neuromorphic implementations
of coordinate transformations can be developed in future work.
Subtle Patterns in Communication
I have used machine learning techniques
to study subtle patterns in human communication for two internship projects. Available information, such as typing
dynamics or word choice, can be used to indicate hidden mental states or intents that we may not be able to
consciously recognize. These interedisciplinary projects stretched both my understanding of machine learning and
applied mathematics as well as my understanding of human cognition.
At Sandia National Laboratories, I worked on a project on natural language processing to categorize
documents of interest using spaCy.
With the CoNECt Lab at University of Illinois Chicago, I developed 3 hidden Markov models in Pyro to identify
the underlying mental state of a user based on their anonymized typing dynamics. This was part of the BiAffect
project, focusing on using typing dynamics to understand mood and cognition.