Levich Institute Seminar Announcement, 04/10/2018
Steinman Hall, Room #312
(Chemical Engineering Conference Room)
Dr. Flaviano Morone
City College of CUNY
"Ubiquity of K-core Percolation in Complex Networks"
K-core percolation in complex networks is an extension of percolation, where a giant k-core cluster usually emerges discontinuously when the density of links increases. Here I show that k-core percolation provides a very simple model to describe critical phenomena in networks that nevertheless retains enough realism to make its predictions relevant in several applications. I present our findings showing that k-core percolation is a general mechanism underlying critical phase transitions in ecological communities, brain networks, and jammed matter. Specifically:
i) In ecological communities, I show that the condition for stability of species networks is expressed as a constraint on the strength of dynamical interactions between species and the k-core of the network. This condition predicts the tipping point of the ecosystem's collapse when the species located at the innermost k-core of the network go extinct.
ii) In brain networks, I shown evidence that the conscious/unconscious (CON/UNC) transition is consistent with a k-core percolation model: the UNC state is the maximum core of the CON state. The maximum k-core of the brain in the CON state is composed of V1, V2 and the left middle frontal gyrus (LMFG). These brain regions are the modules that are active in the unconscious state suggesting that the most robust component of the conscious network is the unconscious network and that indeed the transition between the two states is dominated by k-core percolation.
iii) In jammed matter, I show that the structural origin of the jamming transition can be explained as the sudden appearance of k-cores at precise coordination numbers which are related not to the isostatic point, but to the sudden emergence of the 3- and 4-cores as given by k-core percolation theory. At the transition, the k-core variables freeze and the k-core determines the appearance of rigidity. As a key variable involved in critical phenomena, monitoring of the k-core of the network may prove a powerful method to anticipate catastrophic events, understand the global neuronal workspace, and explain the formation of non-crystalline solids, in the vast context that stretches across biology and physics.