Percolation and Frustration in Neural Networks
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There are reasons to believe that the theoretical and computational techniques of solid state physics can be used to get an understanding of the dynamics of the brain. Here I shall approach along similar lines a related, but less ambitious set of problems stemming from tissue-culture experiments with foetal rat cortex neurons . Starting from a planar array of disconnected cells, dendrites and axons grow out slowly, leading via the formation of clusters of connected cells to a percolating network. After a week, synapses develop at the contacts, allowing the cells to transmit spike-signals by a discrete stochastic process. Growth of the network is much slower than spike-propagation. Two main cell types exist: excitatory cells that increase the spike rate of their target cells, and inhibitory cells that decrease it.
KeywordsCritical Exponent Universality Class Inhibitory Cell Spike Rate Spacetime Structure
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