Current Interests
Power Grid & Supply-and-Demand Network Systems Modeling
Modeling and simulation for resilient SDN systems combines my love of hierarchical flow structures and a fundamental interest in quantifying information flows in continuous dynamics.
Hierarchical Networks
My main interest centers on understanding the source of hierarchy in real-world networks and modeling growing systems. I believe that hierarchy emerges as the result of all network models being a coarse-graining of a more complex network of systems of systems, e.g., 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 coarse-grained model. Hierarchy then naturally emerges to allow for efficient dissemination of information (or control) 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.
Ecological Dynamics
Perhaps the embodiment of Bonini’s Paradox, no model of complex interacting species can be made complete, but viewing ecological webs as multi-layer networks of flowing resources provides an endless number of interesting modeling questions.
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/
Synchronization of Chaos
Information flows and the process of synchronization of dynamical systems.
Chaos-based Encryption
As traditional encryption protocols become increasingly threatened by both increased computational power and quantum algorithms, I believe there is more to explore in leveraging chaos for real-time E2EE.
Social Organization
Although sad to happen upon this scene, I chose to be amazed at the efficiency and organization of the ants rather than be disgusted by the destruction.
Aggregated Growth
In the cold upstate NY air, crystals form out of the air and melt within hours.
Symmetry and Numerical Analysis of 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.