Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2001-11-29
Phys. Rev. E 66 (2002) 21902
Physics
Condensed Matter
Disordered Systems and Neural Networks
20 pages, 4 figures
Scientific paper
10.1103/PhysRevE.66.021902
By using the wavelet transformation (WT), we have analyzed the response of an ensemble of $N$ (=1, 10, 100 and 500) Hodgkin-Huxley (HH) neurons to {\it transient} $M$-pulse spike trains ($M=1-3$) with independent Gaussian noises. The cross-correlation between the input and output signals is expressed in terms of the WT expansion coefficients. The signal-to-noise ratio (SNR) is evaluated by using the {\it denoising} method within the WT, by which the noise contribution is extracted from output signals. Although the response of a single (N=1) neuron to sub-threshold transient signals with noises is quite unreliable, the transmission fidelity assessed by the cross-correlation and SNR is shown to be much improved by increasing the value of $N$: a population of neurons play an indispensable role in the stochastic resonance (SR) for transient spike inputs. It is also shown that in a large-scale ensemble, the transmission fidelity for supra-threshold transient spikes is not significantly degraded by a weak noise which is responsible to SR for sub-threshold inputs.
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