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ItemEmergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. I. Input selectivity-strengthening correlated input pathwaysGilson, M ; Burkitt, AN ; Grayden, DB ; Thomas, DA ; van Hemmen, JL (SPRINGER, 2009-08-01)Spike-timing-dependent plasticity (STDP) determines the evolution of the synaptic weights according to their pre- and post-synaptic activity, which in turn changes the neuronal activity. In this paper, we extend previous studies of input selectivity induced by (STDP) for single neurons to the biologically interesting case of a neuronal network with fixed recurrent connections and plastic connections from external pools of input neurons. We use a theoretical framework based on the Poisson neuron model to analytically describe the network dynamics (firing rates and spike-time correlations) and thus the evolution of the synaptic weights. This framework incorporates the time course of the post-synaptic potentials and synaptic delays. Our analysis focuses on the asymptotic states of a network stimulated by two homogeneous pools of "steady" inputs, namely Poisson spike trains which have fixed firing rates and spike-time correlations. The (STDP) model extends rate-based learning in that it can implement, at the same time, both a stabilization of the individual neuron firing rates and a slower weight specialization depending on the input spike-time correlations. When one input pathway has stronger within-pool correlations, the resulting synaptic dynamics induced by (STDP) are shown to be similar to those arising in the case of a purely feed-forward network: the weights from the more correlated inputs are potentiated at the expense of the remaining input connections.
ItemSpike-timing-dependent plasticity for neurons with recurrent connectionsBurkitt, AN ; Gilson, M ; van Hemmen, JL (SPRINGER, 2007-05-01)The dynamics of the learning equation, which describes the evolution of the synaptic weights, is derived in the situation where the network contains recurrent connections. The derivation is carried out for the Poisson neuron model. The spiking-rates of the recurrently connected neurons and their cross-correlations are determined self- consistently as a function of the external synaptic inputs. The solution of the learning equation is illustrated by the analysis of the particular case in which there is no external synaptic input. The general learning equation and the fixed-point structure of its solutions is discussed.