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:

$$0 ≃ \dot{x} = -λx + c ⟹ x ≃ c/λ$$