The discussion whether temporally coordinated spiking activity really exists and whether it is relevant has been heated over the past few years. To investigate this issue, several approaches have been taken to determine whether synchronized events occur significantly above chance, that is, whether they occur more often than expected if the neurons fire independently. Most investigations ignore or destroy the autostructure of the spiking activity of individual cells or assume Poissonian spiking as a model. Such methods that ignore the autostructure can significantly bias the coincidence statistics. Here, we study the influence of the autostructure on the probability distribution of coincident spiking events between tuples of mutually independent non-Poisson renewal processes. In particular, we consider two types of renewal processes that were suggested as appropriate models of experimental spike trains: a gamma and a log-normal process. For a gamma process, we characterize the shape of the distribution analytically with the Fano factor ( FF c ) . In addition, we perform Monte Carlo estimations to derive the full shape of the distribution and the probability for false positives if a different process type is assumed as was actually present. We also determine how manipulations of such spike trains, here dithering, used for the generation of surrogate data change the distribution of coincident events and influence the significance estimation. We find, first, that the width of the coincidence count distribution and its FF c depend critically and in a nontrivial way on the detailed properties of the structure of the spike trains as characterized by the coefficient of variation C V . Second, the dependence of the FF c on the C V is complex and mostly nonmonotonic. Third, spike dithering, even if as small as a fraction of the interspike interval, can falsify the inference on coordinated firing.

The determination of temporal and spatial correlations in neuronal activity is one of the most important neurophysiological tools to gain insight into the mechanisms of information processing in the brain. Its interpretation is complicated by the difficulty of disambiguating the effects of architecture, single-neuron properties, and network dynamics. We present a theory that describes the contribution of the network dynamics in a network of “spiking” neurons. For a simple neuron model including refractory properties, we calculate the temporal cross-correlations in a completely homogeneous, excitatory, fully connected network in a stable, stationary state, for stochastic dynamics in both discrete and continuous time. We show that even for this simple network architecture, the cross-correlations exhibit a large variety of qualitatively different properties, strongly dependent on the level of noise, the decay constant of the refractory function, and the network activity. At the critical point, the cross-correlations oscillate with a frequency that depends on the refractory properties or decay exponentially with a diverging damping constant (for “weak” refractory properties). We also investigate the effect of the synaptic time constants. It is shown that these time constants may, apart from their influence on the asymmetric peak arising from the direct synaptic connection, also affect the long-term properties of the cross-correlations.