Abstract:
We study the statistical properties of a BCM neuron whose synapses are stimulated by inputs described as a stationary Markov process. We characterize the stable equilibria for the average equations of the synaptic weights as the maxima of a cubic function, associated to the third moments of the inputs distribution, constrained on an ellipsoid defined by the inputs covariance matrix. We do this approach to study the selectivity of a BCM neuron when the input signals are perturbed by a random noise as a function of the noise Root Mean Square (RMS) and the dimension of the input space. We prove the existence of critical values for the noise RMS which define the selectivity properties of the BCM neuron.
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