Lab: Efficient balanced networks

Lecturer: Lyudmila Kushnir

Link of the associated Jupyter notebook

Problem 1

1. Implementation of the integrate-and-fire (IF) neuron

\[\dot{V} = -λ V + F c(t)\]

where \(\frac{⟨\dot{C}⟩}{⟨C⟩} << λ\)

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\[\begin{align*} & \frac{ ΔV}{ Δt} = -λ V(t) + Fc(t)\\ ⟺ & V(t+Δt) - V(t) = (-λ V(t) + Fc(t)) Δt\\ ⟺ & V(t+Δt) = (1-λ Δt) V(t) + Fc(t)Δt\\ \end{align*}\]

Time-varying signal:

\[\dot{x} = -λx + c\]

So that if $c$ varies slowly:

\[0 ≃ \dot{x} = -λx + c ⟹ x ≃ c/λ\]