  Recent experiments on cortical neural networks have revealed the existence of
well-defined avalanches of electrical activity. Such avalanches have been
claimed to be generically scale-invariant -- i.e. power-law distributed -- with
many exciting implications in Neuroscience. Recently, a self-organized model
has been proposed by Levina, Herrmann and Geisel to justify such an empirical
finding. Given that (i) neural dynamics is dissipative and (ii) there is a
loading mechanism "charging" progressively the background synaptic strength,
this model/dynamics is very similar in spirit to forest-fire and earthquake
models, archetypical examples of non-conserving self-organization, which have
been recently shown to lack true criticality. Here we show that cortical neural
networks obeying (i) and (ii) are not generically critical; unless parameters
are fine tuned, their dynamics is either sub- or super-critical, even if the
pseudo-critical region is relatively broad. This conclusion seems to be in
agreement with the most recent experimental observations. The main implication
of our work is that, if future experimental research on cortical networks were
to support that truly critical avalanches are the norm and not the exception,
then one should look for more elaborate (adaptive/evolutionary) explanations,
beyond simple self-organization, to account for this.
