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# Josh Socolar : Exhaustive Percolation and Random Boolean Networks

The nature of dynamical processes occuring on a directed network can depend qualitatively on the logic implemented at each node. In large random networks where nodes act as Boolean gates, there is a phase transition from quiescent to chaotic behavior as the average degree and/or the probabilities of assigning the different logic functions are varied. To understand the behavior at the transition, we are led to a special type of percolation problem in which the relevant question is not whether a cascade spans the system, but whether it covers the entire system. I will introduce the problem of exhaustive percolation, outline a method for solving it, and describe its application to random Boolean networks.

**Category**: Probability**Duration**: 01:44:54**Date**: December 2, 2010 at 4:10 PM**Views**: 110-
**Tags:**seminar, Probability Seminar

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