Abstract
This paper presents a theoretical framework for the spike-train power spectrum of colored-noise driven neurons with spike-frequency adaptation and test this theory against stochastic simulation in various cases. The authors also extend and verify the theory for neurons coupled in a random network, in which the correlations of input fluctuations and of the generated spike train are self-consistently related.
Highlights
Sequences of stereotypic events occur in many fields of physics and beyond: the emissions from a radioactive source, the shot noise in a semiconductor diode, the occurrences of avalanches, earthquakes, and floods, crashes in the stock market, and the generations of action potentials in a nerve cell are all excellent examples for events that reoccur at apparently random instances in time
For all these distinct cases, we focus in this paper predominantly on the correlation statistics, i.e., the spike-train power spectrum
II we introduce our generic two-dimensional IF neuron model and the spiketrain statistics of interest
Summary
Sequences of stereotypic events occur in many fields of physics and beyond: the emissions from a radioactive source, the shot noise in a semiconductor diode, the occurrences of avalanches, earthquakes, and floods, crashes in the stock market, and the generations of action potentials in a nerve cell are all excellent examples for events that reoccur at apparently random instances in time. The inspected model class includes the cases of neurons driven by lowpass-filtered noise (as emerges by synaptic filtering [49,52] or due to slow channel noise [67,68]), driven by high-passfiltered noise (as emerges by presynaptic input spikes with a refractory period [53,62]), endowed with spike-triggered adaptation (as emerges from slow calcium dynamics and calcium-dependent ion channels [85]), and endowed with a bursting mechanism [38,40,41] For all these distinct cases, we focus in this paper predominantly on the correlation statistics, i.e., the spike-train power spectrum. Appendices give details on the numerical solution of our key equations (Appendix A) by a finite-difference scheme [86] and on the ambiguity of the Markovian embedding (Appendix B)
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