Inferring collective synchrony observing spiking of one or several neurons

We tackle a quantification of synchrony in a large ensemble of interacting neurons from the observation of spiking events. In a simulation study, we efficiently infer the synchrony level in a neuronal population from a point process reflecting spiking of a small number of units and even from a single neuron. We introduce a synchrony measure (order parameter) based on the Bartlett covariance density; this quantity can be easily computed from the recorded point process. This measure is robust concerning missed spikes and, if computed from observing several neurons, does not require spike sorting. We illustrate the approach by modeling populations of spiking or bursting neurons, including the case of sparse synchrony.