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Unformatted text preview: Outline of the Lecture Outline of the Lecture Excitatoryinhibitory Network Models Excitatoryinhibitory Network Models Nonsymmetric Matrices Phase Plane Olfactory Nonsymmetric Matrices Phase Plane Olfactory Bulb Bulb Recurrent Networks with Recurrent Networks with Nonsymmetric Matrices Nonsymmetric Matrices May Exhibit Oscillations May Exhibit Oscillations 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 τ r /(1 λ r ) : τ r d v d t = M I ( ) × v + h v t ( 29 = χ μ τ ( 29 ε μ μ = 1 Ν μ ∑ χ υ τ ( 29 = ε υ ⋅ η 1  λ υ 1  ε τ 1  λ υ ( 29 τ ρ + χ υ ( 29 ε τ 1  λ υ ( 29 τ ρ r e μ ⋅ ρ ε υ = δ μ υ For a feedforward network: For a recurrent network: τ r d v a d t =  v a + F W a b b = 1 N a å u b ae è ç ö ø ÷ ae è ç ö ø ÷ τ r d r v d t =  r v + F W × r u ( ) τ r d r v d t =  r v + F W × r u + M × r v ( ) An important example using a non...
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This note was uploaded on 06/08/2009 for the course BME 575L taught by Professor Grzywacz during the Spring '09 term at USC.
 Spring '09
 Grzywacz

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