Current/Past Interests
Information Theory / Entropy
I am interested in quantification and characterization of high dimensional data using geometric partition entropy and kernel-based spectral clustering for the purposes of quantifying data quality for various purposes. In addition, I am interested in the flow of information between coupled dynamical systems far from equilibrium and synchronization as a process of information transfer and exchange.
Synchronization of Chaos
Information flows and the process of synchronization of dynamical systems.
Hierarchical Networks
My main current interest centers on understanding the source of hierarchy in real-world networks and modeling biological growth. I believe that hierarchy emerges as the result of all network models being a course-graining of some more complex network of systems of systems. For example, in a social network, nodes are people, but really each person could be modeled (whether correctly or not) as a complex network of neurons. The conductance, or limit on information flow, of these sub-networks should lead to restrictions on the flow through each node in the course-grained model, which may manifest as degree limits. Hierarchy then naturally emerges to allow for efficient dissemination across the network.
Wildlife Conservation
Beginning with a school project in 6th grade at the Atlanta Zoo, I have had a desire to use my skills to help develop better tools for wildlife conservation. Currently, I am interested in the network theory aspects of fractured habitats of endangered species
Picture from: https://nationalzoo.si.edu/animals/
Symmetry Analysis and Numerical Solutions for Semi-linear Elliptic PDE
Using modifications of the Gradient Newton Galerkin Algorithm (GNGA), numerical symmetry breaking bifurcation analysis was done to find solutions of all symmetry types for a two-parameter family of coupled PDE. A cusp catastrophe was found along the main diagonal in the parameter space due to symmetry in the equations.
Machine Learning for Controlled Chaos
Reservoir computing can be used to learn a controller that pushes a chaotic orbit toward a desired orbit