(105a) Coarse Graining the Dynamics of (and on) Networks

One can think of large evolving networks as complex dynamical systems. They can be fixed, in which case the states of the nodes could be evolving

in time (e.g. chemical or biochemical reaction networks); alternatively, the nodes may have no distinguishable states, in which case what evolves

is the connectivity/topology of the network (connections are formed and break); finally, one can have both effects occurring (dynamics both on the network

and of the network). I will discuss our group's recent efforts in coarse-graining the dynamic behavior of such complex evolving networks. I will also discuss

the use of modern data-mining techniques in discovering good coarse-grained collective observables that can describe the network state. The

techniques/algorithms I will present are reasonable general, and I will illustrate them through several examples.