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S. BLANCHARD, D. ROUSSEAU, and F. CHAPEAU-BLONDEAU. Noise enhancement of signal transduction by parallel arrays of nonlinear neurons with threshold and saturation. Neurocomputing, vol. 71:333–341, 2007. 95/197
Abstract Neurocomputing 71 (2007) 333–341 Noise enhancement of signal transduction by parallel arrays of nonlinear neurons with threshold and saturation Solenna Blanchard, David Rousseau, Franc-ois Chapeau-Blondeau Laboratoire d’Ingénierie des Systèmes Automatisés (LISA), Université d’Angers, 62 avenue Notre Dame du Lac, 49000 Angers, France Received 2 June 2006; received in revised form 7 November 2006; accepted 7 December 2006 Communicated by V. Jirsa Available online 20 February 2007 A classic model neuron with threshold and saturation is used to form parallel uncoupled neuronal arrays in charge of the transduction of a periodic or aperiodic noisy input signal. The impact on the transduction efficacy of added noises is investigated. In isolated neurons, improvement by noise is possible only in the subthreshold and in the strongly saturating regimes of the neuronal response. In arrays, improvement by noise is always reinforced, and it becomes possible in all regimes of operation, i.e. in the threshold, in the saturation, and also in the intermediate curvilinear part of the neuronal response. All the configurations of improvement by noise apply equally to periodic and to aperiodic signals. These results extend the possible forms of stochastic resonance or improvement by noise accessible in neuronal systems for the processing of information. r 2007 Elsevier B.V. All rights reserved. Keywords: Neuronal transduction; Stochastic resonance; Array; Saturation; Threshold; Noise 1. Introduction Neurons interconnected in networks are very efficient for signal and information processing, through detailed modalities and mechanisms which are still under intense investigation. Neurons are intrinsically nonlinear devices. It is now known that in nonlinear processes, the presence or even the injection of noise, can play a beneficial role for signal and information processing. This type of usefulnoise phenomena have been widely investigated under the denomination of stochastic resonance [15,1]. Many forms of stochastic resonance or improvement by noise have been reported in various nonlinear systems involved in diverse signal processing operations. Several forms of stochastic resonance have been reported in neural processes (see for instance [14,12] for early experimental demonstrations, and [21] for a recent overview). At the level of the nonlinear neuron, many reported instances of stochastic resonance essentially rely on the threshold or excitable dynamics inherent to the neuron. In such situations, there is usually a Corresponding author. E-mail address: chapeau@univ-angers.fr (F. Chapeau-Blondeau). 0925-2312/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.neucom.2006.12.014 ARTICLE IN PRESS www.elsevier.com/locate/neucom small information-carrying signal, which is by itself too weak to elicit an efficient response from the threshold or excitable dynamics. The noise then cooperates constructively with the small signal, in such a way as to elicit a more efficient neuronal response. Recently, a new mechanism of stochastic resonance has been exhibited when threshold or excitable nonlinearities are assembled into an uncoupled parallel array. This new form has been introduced under the name of suprathreshold stochastic resonance in [25,26], because in the array, addition of noise can improve the transmission of an input signal with arbitrary amplitude, not necessarily a small subthreshold signal. A parallel array is a common architecture for neuron assemblies, especially in sensory systems in charge of the transduction of noisy signals from the environment. Stochastic resonance has been shown possible in neuronal parallel arrays, with various models for the threshold or excitable nonlinear dynamics of the neuron. In neuronal arrays, Collins et al. [11], Chialvo et al. [9], and Hoch et al. [18,19] show stochastic resonance essentially with a subthreshold input signal, while Stocks [24], Stocks and Mannella [27], and Hoch et al. [17] show the novel form of suprathreshold stochastic resonance. 96/197
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