RIEB Seminar (Jointly supported by:Grant-in-Aid for Scientific Research (S))
|会場||神戸大学経済経営研究所 兼松記念館1F 調査室|
|報告者||Michael M. DANZIGER|
|論題||Understanding heterogeneous complex systems with percolation|
|概要||We will begin this talk by explaining how percolation theory forms a bridge between statistical physics and the new problems posed by complex systems. We will then show two new examples of how percolation theory can be generalized to systems where it cannot be simply applied due to heterogeneity: either because they have multiple interdependent layers or different classes of nodes which share a common vulnerability.
For interdependent multiplex networks, we consider a system composed of two sets of links, where the links are of variable but constrained geographic length. This network topology has two striking features: random-like and lattice-like behavior depending on the length-scale measured (in each layer) and a nucleation-driven first-order transition (when both layers are combined interdependently). We will discuss why this is an important topological model for real-world systems like infrastructure networks, and some of the surprising implications of our findings. 
For nodes with a common vulnerability, we present a newly developed percolation approach called "color-avoiding percolation". This theory was developed to describe networks in which classes of nodes share a vulnerability to a common adversary or failure. For instance, nodes in a supply chain network that are owned by the same conglomerate or communications routers controlled by the same country. In such a case, it may be desirable or even necessary to have connectivity on enough paths that no single vulnerability can disconnect the network, or no single adversary can intercept the communication (in the security case). The solution of this problem requires a new type of percolation which has a number of interesting theoretical properties, including different critical exponents, nodes required for connectivity but not connected themselves and the ability to provide unique structural insight into the autonomous-systems level internet.
 M.M. Danziger, L.M. Shekhtman, Y. Berezin, S. Havlin, "The effect of spatiality on multiplex networks" Europhysics Letters (in press, 2016) arXiv:1505.01688
 S.M. Krause, M.M. Danziger, V. Zlatic "Hidden connectivity in networks with vulnerable classes of nodes" arXiv:1503.04058