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
\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
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