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Neural mechanism for binaural pitch perception via ghost stochastic resonance
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Image of FIG. 1.
FIG. 1.

Deterministic response to a distributed harmonic complex signal. The membrane potential for the three neurons is shown: (a) and (b) Input neurons, (d) processing neuron. The synaptic current acting on neuron 3, , is shown in plot (c). The two input neurons are fed with two sinusoidal signals of amplitudes , , and periods , , respectively (which gives a ghost resonance of ). The bias current for all three neurons is , the synaptic coupling between input and processing neurons is and . All noise amplitudes are zero, .

Image of FIG. 2.
FIG. 2.

Distribution of inter-spike intervals of the input neurons in two cases: (a) Both neurons with super-threshold modulation ( , ) plus noise ( , ); and (b) both neurons modulated with a sub-threshold harmonic current ( , ) plus optimal noise ( , ), i.e., in the stochastic resonance regime. The bias currents are and .

Image of FIG. 3.
FIG. 3.

Left panels: Response of the processing neuron for increasing noise amplitude: (a) Mean time between spikes , (b) coefficient of variation , and (c) fraction of pulses spaced around , and as a function of the noise amplitude in the processing neuron, . Right panels: Probability distribution functions of the time between spikes for three values of the noise amplitude : (d) , (e) , and (f) . Parameters are and for the synapses and we used , (which gives ). Other parameters are those of Fig. 2(a) , except for the triangles in plot (c), which correspond to Fig. 2(b) .

Image of FIG. 4.
FIG. 4.

Maximum fraction of pulses at the ghost resonance as a function of the timing mismatch between the input modulating currents relative to the period of the current , . Parameters are the same than in Fig. 3 with .

Image of FIG. 5.
FIG. 5.

Left panels: (a) Mean time between spikes, (b) coefficient of variation, and (c) fraction of pulses around and as a function of . Right panels: Probability distribution functions of the inter-spike intervals for three values of : (d) , (e) , and (f) . The value of is different for each value of , chosen so that the processing neuron is below threshold and does not fire in the absence of noise. In particular, for , and for and . The driving frequencies are and (which gives ). Other parameters are those of Fig. 3(e) (in particular, ).

Image of FIG. 6.
FIG. 6.

(Color) Left: Fraction of pulses occurring at intervals equal to the period of the ghost resonance . Right: Coefficient of variation . Both quantities plotted as function of noise amplitude and .

Image of FIG. 7.
FIG. 7.

Probability of observing a spike in the processing neuron with instantaneous rate (in gray scale) as a function of the frequency of one of the input neurons. We can observe a remarkable agreement of the responses following the lines predicted by Eq. (12) for (dashed lines from top to bottom). Parameters: , , , , .


Generic image for table
Table I.

Parameters values of the Morris–Lecar and synapse models used in this work.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Neural mechanism for binaural pitch perception via ghost stochastic resonance