Resilience and Cascading Failures in Large-Scale Networks

Abstract:

Many cascading phenomena in social, financial, and technological networks can be studied using epidemic models. 
This talk focuses on the linear threshold model, whereby an initially healthy node in the network gets infected when more than a certain threshold of its neighbors are infected. 
We analyze this model in large directed random networks with heterogeneous agents.
The locally tree-like structure of those large networks allows for an efficient approximation of the infection process in terms of a one-dimensional recursive equation, that describes the evolution of the expected fraction of infected nodes on a infinite tree. 
We show that, for a generic instance of the network and initial condition, the infection process behavior on the original random network is close to the solution of such recursive equation, with probability converging to one exponentially fast in the network size.
Similar results continue to hold in a variant of the model where the thresholds are dynamically adjusted, making the approach amenable to the design of control strategies.

Biography:http://calvino.polito.it/~wilbert/