Alexa Aucoin

Ph. D Candidate, Program in Applied Mathematics at University of Arizona

Research interests: Data driven modeling, statistical machine learning, dynamical systems and computation with applications to neuroscience

Current Research - University of Arizona

“Interpretable feature selection for classifying context-dependent subnetworks in amygdala”
Advisor: Kevin Lin and Kati Gothard

Currently, I am interested in data-driven modeling and interpretable machine learning with applications to neuroscience. The big picture goal of this project is to design an interpretable neural network capable of detecting long-term state changes in experimental electrophysiological data from primate amygdala. The interpretability (or explainability) of network decision making is necessary to inform our understanding of the crucial biological mechanisms involved in encoding and decoding context in the brain. The data is courtesy of the Gothard Lab at the University of Arizona.

"Robustness and consistency of neural networks for statistical machine learning"
Advisor: Kevin Lin

Previously, I have worked on statistical machine learning algorithms with applications to neuroscience. In particular, I designed LSTM networks to classify spike experimental spike-time data recordings from primate amygdala. In addition, I explored how we might leverage dynamical systems techniques for developing networks that are robust against variability in data representations. The data was courtesy of the Gothard Lab at the University of Arizona.

Past Research - Montclair State University

Preferential clustering of aerosol (light) particles in a quasi-geostrophic flow with slow sloshing (top). Corresponding FTLE field (bottom). Regions of high FTLE repel aerosol particles.

Master's Thesis: "Inertial particle transport and coherent structures in geophysical fluid flows"

Advisor: Eric Forgoston

Supported by NSF Award DMS#1418956: ”Transport of Inertial Particles in Time-Dependent and

Stochastic Flows”.

• Utilized finite-time Lyapunov exponents (FTLE) to characterize the attracting and repelling behavior

of inertial particles with respect to Lagrangian coherent structures for varied density ratios and Stokes numbers

• Conducted experiments in a fluid flow tank using particle imaging velocimetry (PIV)

• Developed numerical solver for Maxey-Riley equations with added Coriolis force to compute inertial FTLE used to study various geophysical flow models and experimental data

Undergraduate Research: "The Ping-Pong Effect: Extinction dynamics in stochastic populations coupled through migration"

Advisors: Eric Forgoston and Laura Billings

Supported by NSF Award CMMI#1233397: ”Understanding the Dynamics of Stochastic Disease Spread in Metapopulations”.

• Studied a variety of stochastic population models

• Utilized Master Equation and WKB approximation to analytically determine the mean time to extinction and the optimal path to extinction

• Developed numerical Monte Carlo simulations to compute numerical mean times to extinction.

• Developed numerical iterative scheme to compute optimal extinction paths

Migration allows for local extinction events to be reversed. Coupled populations exhibit "ping-ponging" of local extinctions and revival leading to longer mean time to global extinction.

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