Recent advances on information transmission and storage assisted by noise

The interplay between nonlinear dynamic systems and noise has proved to be of great relevance in several application areas. In this presentation, we focus on the areas of information transmission and storage. We review some recent results on information transmission through nonlinear channels assisted by noise. We also present recent proposals of memory devices in which noise plays an essential role. Finally, we discuss new results on the influence of noise in memristors.Comment: To be published in "Theory and Applications of Nonlinear Dynamics: Model and Design of Complex Systems", Proceedings of ICAND 2012 (Springer, 2014

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 $N$ (=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.Comment: 20 pages, 4 figure

Weak-periodic stochastic resonance in a parallel array of static nonlinearities

This paper studies the output-input signal-to-noise ratio (SNR) gain of an uncoupled parallel array of static, yet arbitrary, nonlinear elements for transmitting a weak periodic signal in additive white noise. In the small-signal limit, an explicit expression for the SNR gain is derived. It serves to prove that the SNR gain is always a monotonically increasing function of the array size for any given nonlinearity and noisy environment. It also determines the SNR gain maximized by the locally optimal nonlinearity as the upper bound of the SNR gain achieved by an array of static nonlinear elements. With locally optimal nonlinearity, it is demonstrated that stochastic resonance cannot occur, i.e. adding internal noise into the array never improves the SNR gain. However, in an array of suboptimal but easily implemented threshold nonlinearities, we show the feasibility of situations where stochastic resonance occurs, and also the possibility of the SNR gain exceeding unity for a wide range of input noise distributions.Yumei Ma, Fabing Duan, François Chapeau-Blondeau and Derek Abbot

Noise-enhanced transmission of spike trains in the neuron

We consider the transmission of spike trains in a conductance-based neuron model. A superposition of periodic coherent trains impinge on the neuron, but in a number that is too small to trigger an output response. We then show that addition of incoherent noise trains on the input allows a neuron response exhibiting correlation with the coherent input trains. Furthermore, the number of noise inputs can be increased up to an optimal value where the coherent part of the response reaches a maximum. This property of noise-enhanced signal transmission can be related to the phenomenon of stochastic resonance. The present study demonstrates for the first time the possibility of stochastic resonance in a realistic situation of multiple spike train transmission by the neurons, and it assigns a useful role in information processing to spontaneous random neuron spiking

Noise-enhanced transmission of spike trains in the neuron,”

PACS. 87.22Jb -Muscle contraction, nerve conduction, synaptic transmission, memorization, and other neurophysiological processes (excluding perception processes and speech). PACS. 87.10+e -General, theoretical, and mathematical biophysics (including logic of biosystems, quantum biology, and relevant aspects of thermodynamics, information theory, cybernetics, and bionics). PACS. 05.40+j -Fluctuation phenomena, random processes, and Brownian motion. Abstract. -We consider the transmission of spike trains in a conductance-based neuron model. A superposition of periodic coherent trains impinge on the neuron, but in a number that is too small to trigger an output response. We then show that addition of incoherent noise trains on the input allows a neuron response exhibiting correlation with the coherent input trains. Furthermore, the number of noise inputs can be increased up to an optimal value where the coherent part of the response reaches a maximum. This property of noise-enhanced signal transmission can be related to the phenomenon of stochastic resonance. The present study demonstrates for the first time the possibility of stochastic resonance in a realistic situation of multiple spike train transmission by the neurons, and it assigns a useful role in information processing to spontaneous random neuron spiking

Noise-enhanced transmission of spike trains in the neuron

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