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Mathematical Physics Seminar

Webinar: Mark Newman - Structure, phase transitions, and message passing in sparse networks

Date & time: Wednesday, 14 February 2024 at 10:45AM - 11:45AM


Mark Newman– University of Michigan

Wednesday, February 14th, 10:45AM EST (Zoom meeting starts at 10:30 EDT) 

Structure, phase transitions, and message passing in sparse networks

Networks (or graphs) are widely used as a compact and convenient mathematical representation of the structure of many systems of scientific interest, including the Internet, transportation networks, biochemical networks, ecological networks, information networks, and social networks both on- and off-line.  Most networks encountered in empirical studies are very sparse, and standard spectral and linear algebra methods perform poorly when applied to such networks.  Message passing methods, such as belief propagation, offer an alternative which works well in the sparse limit and which can also provide new analytic insights.  This talk will introduce the message passing method through a series of examples and illustrate how the method can be used for a wide range of calculations of network structure and function.  Among other things, the talk will touch upon the calculation of percolation properties, graph spectra, and community structure, the deep connection 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.