Recent neurophysiological experiments have revealed the existence of nonrandom connectivity patterns in the cortex of rats. These patterns consist of certain connectivity structures that appear more often than one would expect if neurons were randomly connected. An example of such departure from randomness is the prevalence of pairs of neurons reciprocally connected. Another example is the overrepresentation of certain connectivity patterns involving three or more neurons connected through strong synapses. It is currently unknown how these nontrivial connectivity patterns arise, and what function they serve. The goal of this project is to study, using analytical and numerical techniques, the emergence of these connectivity patterns, and to elucidate the possible function of nonrandom circuits. We will explore the hypothesis that these patterns naturally result from the interplay between the ongoing cortical activity and the synaptic modifications induced by correlated neuronal activity. In particular, we will determine the conditions necessary for the formation of the nonrandom structures observed in experiments, studying how the rule governing synaptic changes and the input statistics determine the emergent connectivity structure. In a second stage, we will investigate the impact of nonrandom connectivities in the dynamics of cortical circuits, emphasizing the consequences for the stability of self-sustained activity patterns (attractors). Finally, we will concentrate on the distribution of synaptic weights seen in experiments, consisting in a large fraction of silent synapses coexisting with a small fraction of functional synapses whose weights are log-normally distributed. Using analytical tools developed in statistical physics, we will compute the distribution of synaptic weights that maximizes the number of attractors sustained by the cortical circuit, and we will assess whether the distribution measured in the cortex agrees with the optimal distribution.
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