Structure, phase transitions, and message passing in networks

Many systems of interest to science and engineering can be thought of as networks, including the Internet, the web, transport networks, social networks, neural networks, metabolic networks and ecological networks. The answers to many of our questions about these systems boil down to solving for the behaviour of some process taking place on such a network, such as the flow of traffic on a road network or the spread of a disease across a network of contacts between people.  Message passing methods are a powerful class of mathematical and computational techniques for solving such problems.  This talk will introduce the message passing method through a series of examples and illustrate how it can be used for a wide range of calculations concerning network structure and function.  Amongst other things, the talk will touch upon the calculation of percolation properties, graph spectra and community structure, the deep connections between message-passing fixed points and structural phase transitions in networks, and a new solution to the long-standing problem of message passing on networks with a high density of short loops.

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