2_26_09_ExcitatoryInhibitoryNetworks

2_26_09_ExcitatoryInhibitoryNetworks - Outline of the...

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Unformatted text preview: Outline of the Lecture Outline of the Lecture Excitatory-inhibitory Network Models Excitatory-inhibitory Network Models Non-symmetric Matrices Phase Plane Olfactory Non-symmetric Matrices Phase Plane Olfactory Bulb Bulb Recurrent Networks with Recurrent Networks with Non-symmetric Matrices Non-symmetric 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.

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2_26_09_ExcitatoryInhibitoryNetworks - Outline of the...

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