2 research outputs found
Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises
Dynamics of an ensemble of -unit FitzHugh-Nagumo (FN) neurons subject to
white noises has been studied by using a semi-analytical dynamical mean-field
(DMF) theory in which the original -dimensional {\it stochastic}
differential equations are replaced by 8-dimensional {\it deterministic}
differential equations expressed in terms of moments of local and global
variables. Our DMF theory, which assumes weak noises and the Gaussian
distribution of state variables, goes beyond weak couplings among constituent
neurons. By using the expression for the firing probability due to an applied
single spike, we have discussed effects of noises, synaptic couplings and the
size of the ensemble on the spike timing precision, which is shown to be
improved by increasing the size of the neuron ensemble, even when there are no
couplings among neurons. When the coupling is introduced, neurons in ensembles
respond to an input spike with a partial synchronization. DMF theory is
extended to a large cluster which can be divided into multiple sub-clusters
according to their functions. A model calculation has shown that when the noise
intensity is moderate, the spike propagation with a fairly precise timing is
possible among noisy sub-clusters with feed-forward couplings, as in the
synfire chain. Results calculated by our DMF theory are nicely compared to
those obtained by direct simulations. A comparison of DMF theory with the
conventional moment method is also discussed.Comment: 29 pages, 2 figures; augmented the text and added Appendice
Stochastic Resonance of Ensemble Neurons for Transient Spike Trains: A Wavelet Analysis
By using the wavelet transformation (WT), we have analyzed the response of an
ensemble of (=1, 10, 100 and 500) Hodgkin-Huxley (HH) neurons to {\it
transient} -pulse spike trains () 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 : 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.Comment: 20 pages, 4 figure