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2_26_09_ExcitatoryInhibitoryNetworks

2_26_09_ExcitatoryInhibitoryNetworks - A recurrent network...

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