# 2014.10.22 Statistical mechanics for real biological networks

**Title： **Statistical mechanics for real biological networks

**Speaker：** Dr. William Bialek

Professor of Physics, Princeton University

**Time：** 1:00pm Oct 22nd 2014

**Address：** Rm 102, East wing of Old Chemistry Building, Peking Unversity

**Chair： ** Prof. Chao Tang, Center for Quantitative Biology

Abstract：

It is an old dream that ideas from statistical physics could help us understand the phenomena that emerge from biological networks, be they networks of genes, networks of neurons, or networks of organisms. In recent years, it has become possible to make increasingly accurate, simultaneous measurements on the states of (almost) all the nodes in such networks. I’ll discuss the efforts that my colleagues and I are making to connect these data to statistical physics models. The key idea is the (quite old) maximum entropy principle: we try to build models that are consistent with some measured properties of the network (e.g., the correlations among the states of pairs of elements) but otherwise have as little structure as possible. I will use the example of a flock of birds to explain how this works, and to explain our surprise that it works so well. Statistical mechanics teaches us that, as systems become large, the parameter space breaks up into phases, and this also is true for families of maximum entropy models. Thus, we can ask where real networks are in the phase diagram of possible networks. For the flock, we’ll see that the system is poised very close to a critical surface. We can go through a similar (but much more complex) analysis for a network of neurons in the vertebrate retina, and surprisingly we find the same answer – the system seems to be close to criticality, and we can detect hints of criticality in other systems as well. It seems that we are either seeing signs of something general, or we are fooling ourselves, and I’ll outline a path to telling the difference.