This INSPIRE award is partially funded by the Networking Technology and Systems Program in the Division of Computer and Network Systems in the Directorate for Computer Information Science and Engineering; the Mathematical Physics Program in the Division of Physics in the Directorate for Mathematical and Physical Sciences; and the Office of Multidisciplinary Activities in the Directorate for Mathematical and Physical Sciences.
Two grand challenges in two disjoint fields of science are network dynamics prediction and quantum gravity theory. The lack of understanding of fundamental laws driving the dynamics of many complex networks, and consequently our inability to predict and control their behavior, are among the reasons why many practical problems of great significance remain unsolved for decades. The lack of a complete theory of quantum gravity, unifying all the fundamental interactions, is perhaps the most fundamental problem in physics after Einstein. Motivated by the recent results suggesting that the two problems might in fact be intimately related via a geometric duality between hyperbolic and de Sitter spaces---the former reflecting the latent geometry of complex networks, the latter representing the asymptotic geometry of spacetime in the universe---this project addresses both grand challenges and advances science in both fields by deriving fundamental laws of network dynamics.
The main hypothesis that the project investigates is that one can extend and apply the canonical approach in physics used to study all the fundamental interactions in nature to a wide class of physical systems---complex networks. One part of the project focuses on finding Hamiltonians defining Hamilton's equations of network dynamics, and validating the derived equations against the dynamics of real networks. These equations are expected to be simpler than the corresponding equations in gravitational theories. Other parts of the project focus on building tools to predict this dynamics based on the derived equations, and investigating connections between this dynamics, its conformal invariance in the de Sitter/conformal field theory correspondence (dS/CFT) context, and network navigability that may lead to a different interpretation of the dark energy problem in cosmology. This interdisciplinary project combines concepts and methods from mathematical physics and network research by extending the canonical approach in physics to complex networks to advance our understanding of their dynamics, and to explore whether applying theoretical concepts in network science will advance our understanding of dark energy. This project thus opens exciting new research directions by hypothesizing a fundamental connection between Hamiltonian dynamics and network dynamics that until now have been considered completely unrelated. The transformative project thus challenges the conventional wisdom that neither the canonical approach in physics can be useful in studying complex networks, nor network science has anything to offer theoretical physics.
Broader Impact: Many problems of broader impacts in science and society are blocked on network dynamics prediction. Examples include disease treatment, drug design, and a variety of link-prediction problems, which are sub-problems of network dynamics prediction. In general, connections between systems as different as the brain, the Internet, and the universe, appeal to general public, foster creative thinking, and attract wider and more diverse circles of students to science and engineering.
