Precise timing of spikes between different neurons has been found to convey reliable information beyond the spike count. In contrast, the role of small and variable spiking delays, as reported, for example, in the visual cortex, remains largely unclear. This issue becomes particularly important considering the high speed of neuronal information processing, which is assumed to be based on only a few milliseconds within each processing step. We investigate the role of small and variable spiking delays with a parsimonious stochastic spiking model that is strongly motivated by experimental observations. The model contains only two parameters for the response of a neuron to one stimulus, describing directly the rate and the delay, or phase. Within the theoretical model, we specifically investigate two quantities, the probability of correct stimulus detection and the probability of correct change point detection, as a function of these parameters and within short periods of time. Optimal combinations of the two parameters across stimuli are derived that maximize these probabilities and enable comparison of pure rate, pure phase, and combined codes. In particular, the gain in correct detection probability when adding small and variable spiking delays to pure rate coding increases with the number of stimuli. More interesting, small and variable spiking delays can considerably improve the process of detecting changes in the stimulus, while also decreasing the probability of false alarms and thus increasing robustness and speed of change point detection. The results are compared to empirical spike train recordings of neurons in the visual cortex reported earlier in response to a number of visual stimuli. The results suggest that near-optimal combinations of rate and phase parameters may be implemented in the brain and that adding phase information could particularly increase the quality of change point detection in cases of highly similar stimuli.

Oscillatory correlograms are widely used to study neuronal activity that shows a joint periodic rhythm. In most cases, the statistical analysis of cross-correlation histograms (CCH) features is based on the null model of independent processes, and the resulting conclusions about the underlying processes remain qualitative. Therefore, we propose a spike train model for synchronous oscillatory firing activity that directly links characteristics of the CCH to parameters of the underlying processes. The model focuses particularly on asymmetric central peaks, which differ in slope and width on the two sides. Asymmetric peaks can be associated with phase offsets in the (sub-) millisecond range. These spatiotemporal firing patterns can be highly consistent across units yet invisible in the underlying processes. The proposed model includes a single temporal parameter that accounts for this peak asymmetry. The model provides approaches for the analysis of oscillatory correlograms, taking into account dependencies and nonstationarities in the underlying processes. In particular, the auto- and the cross-correlogram can be investigated in a joint analysis because they depend on the same spike train parameters. Particular temporal interactions such as the degree to which different units synchronize in a common oscillatory rhythm can also be investigated. The analysis is demonstrated by application to a simulated data set.

The analysis of neuronal information involves the detection of spatiotemporal relations between neuronal discharges. We propose a method that is based on the positions (phase offsets) of the central peaks obtained from pairwise cross-correlation histograms. Data complexity is reduced to a one-dimensional representation by using redundancies in the measured phase offsets such that each unit is assigned a “preferred firing time” relative to the other units in the group. We propose two procedures to examine the applicability of this method to experimental data sets. In addition, we propose methods that help the investigation of dynamical changes in the preferred firing times of the units. All methods are applied to a sample data set obtained from cat visual cortex.