  The $1/f$-like decay observed in the power spectrum of electro-physiological
signals, along with scale-free statistics of the so-called neuronal avalanches,
constitute evidences of criticality in neuronal systems. Recent in vitro
studies have shown that avalanche dynamics at criticality corresponds to some
specific balance of excitation and inhibition, thus suggesting that this is a
basic feature of the critical state of neuronal networks. In particular, a lack
of inhibition significantly alters the temporal structure of the spontaneous
avalanche activity and leads to an anomalous abundance of large avalanches.
Here we study the relationship between network inhibition and the scaling
exponent $\beta$ of the power spectral density (PSD) of avalanche activity in a
neuronal network model inspired in Self-Organized Criticality (SOC). We find
that this scaling exponent depends on the percentage of inhibitory synapses and
tends to the value $\beta = 1$ for a percentage of about 30%. More
specifically, $\beta$ is close to $2$, namely brownian noise, for purely
excitatory networks and decreases towards values in the interval $[1,1.4]$ as
the percentage of inhibitory synapses ranges between 20 and 30%, in agreement
with experimental findings. These results indicate that the level of inhibition
affects the frequency spectrum of resting brain activity and suggest the
analysis of the PSD scaling behavior as a possible tool to study pathological
conditions.
