brainpy.measure.cross_correlation(spikes, bin, dt=None)[source]#

Calculate cross correlation index between neurons.

The coherence 1 between two neurons i and j is measured by their cross-correlation of spike trains at zero time lag within a time bin of \(\Delta t = \tau\). More specifically, suppose that a long time interval T is divided into small bins of \(\Delta t\) and that two spike trains are given by \(X(l)=\) 0 or 1, \(Y(l)=\) 0 or 1, \(l=1,2, \ldots, K(T / K=\tau)\). Thus, we define a coherence measure for the pair as:

\[\kappa_{i j}(\tau)=\frac{\sum_{l=1}^{K} X(l) Y(l)} {\sqrt{\sum_{l=1}^{K} X(l) \sum_{l=1}^{K} Y(l)}}\]

The population coherence measure \(\kappa(\tau)\) is defined by the average of \(\kappa_{i j}(\tau)\) over many pairs of neurons in the network.

  • spikes – The history of spike states of the neuron group.

  • bin (float, int) – The time bin to normalize spike states.

  • dt (float, optional) – The time precision.


cc_index – The cross correlation value which represents the synchronization index.

Return type




Wang, Xiao-Jing, and György Buzsáki. “Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model.” Journal of neuroscience 16.20 (1996): 6402-6413.