Theoretical and computational approach for characterizing and analyzing complexity in nonlinear interaction networks with Markovian dynamics.
Many natural and man-made systems of interest to scientists and engineers are composed of groups of individual elements interacting with each other, through specific channels, to produce and regulate appropriate responses. Examples include chemical reaction networks, cellular (signaling, transcriptional, and metabolic) networks, pharmacokinetic networks, epidemiological networks, ecological networks, social networks, neural networks, multi-agent networks, etc. Understanding the fundamental properties and design principles of such networks is an exciting and challenging research problem whose solution requires development of new theoretical and computational approaches.
The aim of this project is to develop a general theoretical and computational approach for characterizing and analyzing complexity in nonlinear interaction networks with Markovian dynamics. Our work is based on a potential energy landscape perspective that relates topographic features of the landscape to fundamental network properties delineating complexity, such as self-organization, functional stability, robustness, and long-term evolutionary behavior. To achieve feasibility and computational efficiency, we are developing new tools for computing the time evolution of the probability distribution of the underlying stochastic population dynamics.
The overall project is founded on fundamental principles drawn from a number of diverse disciplines, such as computational biochemistry, nonlinear population dynamics, statistical mechanics/thermodynamics, statistical signal processing, and information theory.