### Publications

My publications and preprints along with short descriptions and links to where they can be found.

My publications and preprints along with short descriptions and links to where they can be found.

Some of the published works are accompanied by software to either implement or better explain the concepts laid forth.

The regular structure of lattice graphs make them expecially useful structures on which to develop analytic tools. In particular, we compute expressions for the control energy of lattice type systems. The closed form expressions for individual elements of the controllability Gramian of lattice graphs provide insight into the control energy of complex networks.

The analysis of graph's with symmetry is a mature area within the larger fields of abstract algebra and graph theory. Despite this, the ability to create graphs with symmetry was not understood beyond some very simple cases. An algorithm to create general graphs with any symmetry pattern has been submitted for publication in two different versions.

Optimal control of complex systems continues to receive a large amount of attention throughout the systems and controls literature. Typically, complex networks are large with many state variables. On the other hand, there are many applications where one is only interested in a particular subset of the state variables, or a local region of the complex network. Target control provides the expression for the control input to drive a subset of the state variables to desired values.

With the accelerating improvements made in mathematical models of biological systems, the ability to use controls techniques, originally created for engineering applications, as potential drug development tools may soon be realized. Traditional drug development tends to require specialized knowledge to choose the proper experiments to conduct as each experiment can be very expensive. Using numerical tools to limit the number of needed physical experiments by determining a set of most probable drug target combinations has the potential for increasing the pace of drug development and reducing its cost.