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In many systems we can describe emergent macroscopic behaviors,quantitatively, using models that are much simpler than the underlyingmicroscopic interactions; we understand the success of this simplificationthrough the renormalization group. Could similar simplifications succeed incomplex biological systems? We develop explicit coarse-graining procedures thatwe apply to experimental data on the electrical activity in large populationsof neurons in the mouse hippocampus. Probability distributions ofcoarse-grained variables seem to approach a fixed non-Gaussian form, and we seeevidence of power-law dependencies in both static and dynamic quantities as wevary the coarse-graining scale over two decades. Taken together, these resultssuggest that the collective behavior of the network is described by anon-trivial fixed point.

Coarse--graining and hints of scaling in a population of 1000+ neurons