Dr Yilun Shang

I have an interdisciplinary interest in complex system, which refers to a system composed of many interacting parts, such that the collective behaviour of those parts together is more than sum of their individual behaviour.

I am currently an Associate Professor in Computer and Information Sciences at Northumbria. Prior to this I have been an Associate Professor at Tongji University leading the Complex Network group in School of Mathematical Sciences for four years (2014-2018). Before this I held various postdoctoral appointments with Institute for Cyber Security and Department of Computer Science at University of Texas at San Antonio, SUTD-MIT International Design Centre at Singapore University of Technology and Design, and Einstein Institute of Mathematics at Hebrew University of Jerusalem (2010-2014). In 2017, I visited Department of Mathematical Sciences at University of Essex as a short stay Essex International Visiting Fellow. I received my PhD degree in Applied Mathematics in 2010 and BSc degree in Mathematics in 2005, both from Shanghai Jiao Tong University. I received the 2016 Dimitrie Pompeiu Prize from the Romanian Academy in recognition of my work in network synchronization and presented a 15min short communication in the 2018 International Congress of Mathematicians in Rio de Janeiro under the auspices of Open Arms Grants.

In the framework of complex networks and systems, my current research activities can roughly be grouped into three categories as follows.

1. Physical and functional properties of complex networks.

Robustness and resilience of complex networks using percolation theory, probabilistic analysis, master equations, network-theoretic methods, and numerical simulations; Information diffusion and epidemic disease models using graph theory, ordinary/partial/stochastic differential equations, stochastic processes, stability theory, Lie algebra method, and numerical simulations.

2. Mathematical properties of complex network models and random graphs.

Combinatorial study of various random graph models, including E-R random graph, Chung-Lu model, random regular graphs, random intersection graphs, random geometric graphs, inhomogeneous random graphs, stochastic block models, networks of networks;  Topological and geometric properties including degree distribution, distance, Hamiltonian path, cycles, connectivity, connected components, clustering coefficient, chromatic number, clique number, independence number, hierarchical self-similarity, expander properties, Gromov hyperbolicity, random walks, graphon, and various algebraic graph indices.

3. Nonlinear dynamical systems and collective behaviours in complex systems.

Social/biological dynamics over complex networks (including opinion evolutions, information diffusion, and swarm dynamics); Synchronization phenomenon and consensus problems in multi-agent systems with applications in system engineering using control theory, matrix theory, optimization methods, and numerical simulations.

Opportunities to carry out postgraduate research towards a PhD/MSc by research exist in all the areas of interest identified above. I’m always open to suggestions for PhD/MSc topics in my research area of complex networks and systems.