  Cortical neurons are bistable; as a consequence their local field potentials
can fluctuate between quiescent and active states, generating slow 0.5-2 Hz
oscillations which are widely known as transitions between Up and Down States.
Despite a large number of studies on Up-Down transitions, deciphering its
nature, mechanisms and function are still today challenging tasks. In this
paper we focus on recent experimental evidence, showing that a class of
spontaneous oscillations can emerge within the Up states. In particular, a
non-trivial peak around 20 Hz appears in their associated power-spectra, what
produces an enhancement of the activity power for higher frequencies (in the
30-90 Hz band). Moreover, this rhythm within Ups seems to be an emergent or
collective phenomenon given that individual neurons do not lock to it as they
remain mostly unsynchronized. Remarkably, similar oscillations (and the
concomitant peak in the spectrum) do not appear in the Down states. Here we
shed light on these findings by using different computational models for the
dynamics of cortical networks in presence of different levels of physiological
complexity. Our conclusion, supported by both theory and simulations, is that
the collective phenomenon of "stochastic amplification of fluctuations"
-previously described in other contexts such as Ecology and Epidemiology--
explains in an elegant and parsimonious manner, beyond model-dependent details,
this extra-rhythm emerging only in the Up states but not in the Downs.
