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.

There has been a long and lively debate on whether rate covariance and temporal coordination of spikes, regarded as potential origins for correlations in cortical spike signals, fulfill different roles in the cortical code. In this context, studies that report spike coordination have often been criticized for ignoring fast nonstationarities, which would result in wrongly assigned spike coordination. The underlying hypothesis of this critique is that spike coordination is essentially identical to rate covariation, only on a shorter timescale. This study investigates the validity of this critique. We provide a decomposition for the cross-correlation function of doubly stochastic point processes, where each of the components corresponds precisely to the concepts of dependence under investigation. This allows us to correct the correlation function for rate effects, which implies that spike coordination and rate covariation are statistically separable concepts of dependence. Furthermore, we present direct and intuitive model implementations of the discussed concepts and illustrate that their difference is not a matter of timescale. Analysis of data generated by our models and analytical description of the relevant estimators reveals, however, that spike coordination dramatically influences the accuracy of rate covariance estimation. As a consequence, extreme parameter combinations can lead to situations where the concept of dependence cannot be identified empirically. However, for a wide range of parameters, the concept of dependence underlying a given data set can be identified regardless of its timescale.

The snowflake plot is a scatter plot that displays relative timings of three neurons. It has had rather limited use since its introduction by Perkel, Gerstein, Smith, and Tatton (1975), in part because its triangular coordinates are unfamiliar and its theoretical properties are not well studied. In this letter, we study certain quantitative properties of this plot: we use projections to relate the snowflake plot to the cross-correlation histogram and the spike-triggered joint histogram, study the sampling properties of the plot for the null case of independent spike trains, study a simulation of a coincidence detector, and describe the extension of this plot to more than three neurons.

It has been proposed that cortical neurons organize dynamically into functional groups (cell assemblies) by the temporal structure of their joint spiking activity. Here, we describe a novel method to detect conspicuous patterns of coincident joint spike activity among simultaneously recorded single neurons. The statistical significance of these unitary events of coincident joint spike activity is evaluated by the joint-surprise. The method is tested and calibrated on the basis of simulated, stationary spike trains of independently firing neurons, into which coincident joint spike events were inserted under controlled conditions. The sensitivity and specificity of the method are investigated for their dependence on physiological parameters (firing rate, coincidence precision, coincidence pattern complexity) and temporal resolution of the analysis. In the companion article in this issue, we describe an extension of the method, designed to deal with nonstationary firing rates.

In order to detect members of a functional group (cell assembly) in simultaneously recorded neuronal spiking activity, we adopted the widely used operational definition that membership in a common assembly is expressed in near-simultaneous spike activity. Unitary event analysis, a statistical method to detect the significant occurrence of coincident spiking activity in stationary data, was recently developed (see the companion article in this issue). The technique for the detection of unitary events is based on the assumption that the underlying processes are stationary in time. This requirement, however, is usually not fulfilled in neuronal data. Here we describe a method that properly normalizes for changes of rate: the unitary events by moving window analysis (UEMWA). Analysis for unitary events is performed separately in overlapping time segments by sliding a window of constant width along the data. In each window, stationarity is assumed. Performance and sensitivity are demonstrated by use of simulated spike trains of independently firing neurons, into which coincident events are inserted. If cortical neurons organize dynamically into functional groups, the occurrence of near-simultaneous spike activity should be time varying and related to behavior and stimuli. UEMWA also accounts for these potentially interesting nonstationarities and allows locating them in time. The potential of the new method is illustrated by results from multiple single-unit recordings from frontal and motor cortical areas in awake, behaving monkey.