  Complex systems, when poised near a critical point of a phase transition
between order and disorder, exhibit a dynamics comprising a scale-free mixture
of order and disorder which is universal, i.e. system-independent (1-5). It
allows systems at criticality to adapt swiftly to environmental changes (i.e.,
high susceptibility) as well as to flexibly process and store information.
These unique properties prompted the conjecture that the brain might operate at
criticality (1), a view supported by the recent description of neuronal
avalanches in cortex in vitro (6-8), in anesthetized rats (9) and awake
primates (10), and in neuronal models (11-16). Despite the attractiveness of
this idea, its validity is hampered by the fact that its theoretical
underpinning relies solely on the replication of sizes and durations of
avalanches, which reflect only a portion of the rich dynamics found at
criticality. Here we show experimentally five fundamental properties of
avalanches consistent with criticality: (1) a separation of time scales, in
which the power law probability density of avalanches sizes s, P(s) and the
lifetime distribution of avalanches are invariant to slow, external driving;
(2) stationary P(s) over time; (3) the avalanche probabilities preceding and
following main avalanches obey Omori law (17, 18) for earthquakes; (4) the
average size of avalanches following a main avalanche decays as a power law;
(5) the spatial spread of avalanches has a fractal dimension and obeys
finite-size scaling. Thus, neuronal avalanches are a robust manifestation of
criticality in the brain.
