Current/Past Interests
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.
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.
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