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Message passing theory for percolation models on multiplex networks

Presented by: 
Ginestra Bianconi Queen Mary University of London
Thursday 14th July 2016 - 16:00 to 16:30
INI Seminar Room 1
 Multiplex networks describe a large variety of complex systems including infrastructures, transportation networks and biological systems.In presence of interdepedencies between the nodes the robustness of the system to random failures is determined by the mutually connected giant component (MCGC). Much progress on the emergence of the MCGC has been achieved  so far but  the characterization of the emergence of the MCGC is multiplex networks with link overlap in an arbitrary large number of layers has remained elusive. Here I will present a  message passing algorithm for characterizing the percolation transition in multiplex networks with link overlap and an arbitrary number of layers M and I will derive the equation for the order parameter in an ensembles of random multiplex networks. Specifically I will propose and compare two message passing algorithms, that generalize the algorithm widely used to study the percolation transition in multiplex networks without link overlap. The first algorithm describes a directed percolation transition and admits an epidemic spreading interpretation. The second algorithm describes the emergence of the mutually connected giant component, that is the percolation transition, but does not preserve the epidemic spreading interpretation. The phase diagrams for the percolation and directed percolation transition is obtained in simple representative cases. For the same multiplex network structure, in which the directed percolation transition has non-trivial tricritical points, the percolation transition has a discontinuous phase transition, with the exception of the trivial case in which all the layers completely overlap.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons