elephant.spike_train_correlation.spike_train_timescale

elephant.spike_train_correlation.spike_train_timescale(binned_spiketrain, max_tau)[source]

Calculates the auto-correlation time of a binned spike train. Uses the definition of the auto-correlation time proposed in [[1], Eq. (6)]:

\tau_\mathrm{corr} = \int_{-\tau_\mathrm{max}}^{\tau_\mathrm{max}}\
    \left[ \frac{\hat{C}(\tau)}{\hat{C}(0)} \right]^2 d\tau

where \hat{C}(\tau) = C(\tau)-\nu\delta(\tau) denotes the auto-correlation function excluding the Dirac delta at zero timelag.

Parameters:
binned_spiketrainelephant.conversion.BinnedSpikeTrain

A binned spike train containing the spike train to be evaluated.

max_taupq.Quantity

Maximal integration time \tau_{max} of the auto-correlation function. It needs to be a multiple of the bin_size of binned_spiketrain.

Returns:
timescalepq.Quantity

The auto-correlation time of the binned spiketrain with the same units as in the input. If binned_spiketrain has less than 2 spikes, a warning is raised and np.nan is returned.

Notes

  • \tau_\mathrm{max} is a critical parameter: numerical estimates of the auto-correlation functions are inherently noisy. Due to the square in the definition above, this noise is integrated. Thus, it is necessary to introduce a cutoff for the numerical integration - this cutoff should be neither smaller than the true auto-correlation time nor much bigger.
  • The bin size of binned_spiketrain is another critical parameter as it defines the discretization of the integral d\tau. If it is too big, the numerical approximation of the integral is inaccurate.

References

[1]Wieland, S., Bernardi, D., Schwalger, T., & Lindner, B. (2015). Slow fluctuations in recurrent networks of spiking neurons. Physical Review E, 92(4), 040901.