Ji Liu of Department of Electrical and Computer Engineering, Stony Brook University

Synchronization is a ubiquitous form of distributed coordination in networked dynamical systems spanning biology, climatology, ecology, sociology, and technology. The capacity of a networked system to synchronize is largely shaped by the structure of the underlying interaction network. Yet, unlike the special undirected case, where synchronizability can be characterized by a Laplacian eigenvalue ratio, general directed networks may have complex-valued Laplacian eigenvalues and thus still lack a complete theory for quantifying synchronizability and network design principles for optimal synchronization. Nishikawa and Motter (PNAS 2010) proposed a quantity, called the normalized spread of Laplacian eigenvalues, to measure synchronizability in directed networks and conjectured, based on numerical evidence and without theoretical validation, that its optimal value over all directed graphs with fixed numbers of vertices and arcs is attained when the Laplacian eigenvalues satisfy a distinctive integer-valued pattern. This work proves this conjecture and further shows that the conjectured spectral condition is not only sufficient but also necessary. Moreover, it is established that the optimal integer-valued Laplacian spectrum is always achievable by a class of almost regular directed graphs, which can be constructed through an efficient inductive algorithm. This work is a collaboration with Susie Lu and John Urschel from the Department of Mathematics at MIT.

Biography:

Dr. Ji Liu is an Associate Professor in the Department of Electrical and Computer Engineering at Stony Brook University. He received his B.S. in information engineering from Shanghai Jiao Tong University in 2006 and his Ph.D. in electrical engineering from Yale University in 2013. He was a postdoc at University of Illinois at Urbana-Champaign and Arizona State University. He is an Associate Editor for IEEE Transactions on Control of Network Systems. His current research interests include distributed control and optimization, distributed reinforcement learning, and resiliency of distributed algorithms. His coauthored work has received the 2023 IEEE Control Systems Society Roberto Tempo Best CDC Paper Award and a Distinguished Paper Award at 2024 IEEE International Conference on Distributed Computing Systems.

Email:

Address:United States