2_26_09_ExcitatoryInhibitoryNetworks

2_26_09_ExcitatoryInhibitoryNetworks - A recurrent network...

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Unformatted text preview: A recurrent network is a feedforward network with a recurrent synaptic weight matrix. For symmetric M, the eigenvectors are orthonormal, i.e. , and general solutions have time constants r /(1- r ) : r d v dt = M I ( ) v + h v t ( ) = c t ( ) e = 1 N c t ( ) = e h 1 1 e t 1 ( ) r + c ( ) e t 1 ( ) r e e = For a feedforward network: For a recurrent network: r dv a dt = v a + F W ab b = 1 N a u b r d v dt = v + F W u ( ) r d v dt = v + F W u + M v ( ) An important example using a non- symmetric recurrent matrix is the excitatory-inhibitory network: E d v E dt = v E + F E h E + M EE v E + M EI v I ( ) I d v I dt = v I + F I h I + M IE v E + M II v I ( ) where elements of M EE and M IE 0 and those of M II and M EI 0: The first analysis in this lecture uses...
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2_26_09_ExcitatoryInhibitoryNetworks - A recurrent network...

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