  In this overview, we discuss the connections between the observations of
critical dynamics in neuronal networks and the maximum entropy models that are
often used as statistical models of neural activity, focusing in particular on
the relation between "statistical" and "dynamical" criticality. We present
examples of systems that are critical in one way, but not in the other,
exemplifying thus the difference of the two concepts. We then discuss the
emergence of Zipf laws in neural activity, verifying their presence in retinal
activity under a number of different conditions. In the second part of the
chapter we review connections between statistical criticality and the structure
of the parameter space, as described by Fisher information. We note that the
model-based signature of criticality, namely the divergence of specific heat,
emerges independently of the dataset studied; we suggest this is compatible
with previous theoretical findings.
