If the brain is critical, what is the phase transition?

Neuronal avalanches were experimentally observed in vitro a decade
ago, lending support to a long-held conjecture that the brain as a
dynamical system might be operating near a second-order phase
transition. Nontrivial statistics, such as power law distributions and
other scale-invariant properties, have been the essential connection
between the theory of critical phenomena and neurophysiological
data. Many models which have been used to simulate neuronal collective
behavior share common features, displaying a phase transition from an
absorbing (quiescent) to an active (but otherwise unstructured)
phase. Most of these belong to the directed percolation universality
class, which has served as a theoretical workhorse in the field.

I will discuss the strength and limitations of this theoretical
framework in light of experimental results, which have since been
extended to in vivo experimental setups, including both anesthetized
and non-anesthetized animals. More generally, I will highlight the
need of theoretical developments in Neuroscience, which offers
theoretical physicists a fertile ground for interdisciplinary
research. For instance, how can we model the long-range time
correlations and universal scaling functions observed in the brain
activity of freely-behaving animals? Or, given that current recording
techniques severely undersample neuronal activity, is it possible to
come up with a model that yields scale-invariant statistics even under
similar sampling conditions? Can we reconcile these ideas with the
plethora of oscillatory activity which is observed in the brain?