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