Modern Mathematical Tools and Techniques in Capturing Complexity

Abstract

In the nervous system, neurons convey information by means of electric pulses called action potentials or spikes. The information is encoded in sequences of these pulses, called spike trains. In neurophysiological experiments, spike trains are recorded and analyzed statistically. Time intervals between action potentials is the key feature of spike trains. One of the statistical techniques available for studying spike trains is the autocorrelation. In the neuroscientific literature the term autocorrelation is used to denote frequency histograms of time intervals between every pair of the spikes generated by a single neuron for a period of time. The autocorrelation function is very useful for characterizing spike trains. The shape of the autocorrelation indicates the nature of the dependence among time intervals between consecutive spikes for a specified time window. In this work we propose two statistics to test the hypothesis of independence between time intervals. The bootstrap method is used to calibrate the null distribution of these tests. The tests are applied to real spike trains recorded from the primary visual cortex of anesthetized cats, both during spontaneous activity and after electric stimulation-induced activity. © 2011 Springer-Verlag Berlin Heidelberg.