Over the last decade, one of the driving problems in systems biology has been to find ``modules" in biological networks. A bewildering variety of definitions of modules have ensued, along with a corresponding multitude of methods for finding these modules and quantifying the modularity either of a biological network or of a particular partitioning of a network. In this talk I'll discuss how two very old ideas --- statistical inference and rate-distortion theory --- can be used to infer modules (along with inferring the true number of modules in a network) and to reveal the modules as an optimal encoding (suggesting an order parameter for modularity which makes reference to no fixed partition or scale). I hope also to illustrate how this driving systems biology problem relates to an older literature in "community detection" (from the social sciences) and "graph partitioning" (from computer science and discrete mathematics).
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