Each panel includes a raster plot with 20 simulated spike trains generated simultaneously; each row corresponds to one artificial neuron and each small vertical line to a spike. All neurons were set to fire at a mean rate of 27 spikes s−1 and with a CVISI near 1, as for a Poisson process (the CVISI is equal to the standard deviation of the interspike intervals divided by their mean). Red traces show instantaneous firing rate or spike density, obtained by smoothing the spike traces with a Gaussian function (σ = 10 ms for top row; σ = 5 ms for bottom row) and averaging across neurons. Blue histograms show the average cross-correlation between all possible distinct pairs of units. Cross-correlograms were computed from 20-s segments of simulated data, which included the short segments shown. The y axes are proportional to the probability that two spikes from two different neurons are separated in time by the amount indicated in the x axis. The normalization is such that the probability expected by chance, assuming independence, is set to 1. a–c| Each neuron was driven by 1,000 random inputs and, on average, individual pairs of neurons shared 10% (a), 25% (b) or 50% (c) of those inputs. As the fraction of shared inputs rises, neurons tend to fire closer together in time, which produces larger fluctuations in the average spike density. d–f| Here, the neurons fired through independent Poisson processes, but the underlying firing rate was equal to 27(1 + Asin(2π25t)), where t is the time in seconds, and was identical for all units. So, the mean rate was still 27 spikes s−1, but it oscillated with a frequency of 25 Hz. The amplitude of the oscillations was A = 0.25 (d), A = 0.50 (e) or A = 0.75 (f). See REF. for further details.