Fig. 2: Dynamical regime for optimal information transmission depends on the readout integration timescale.

Discriminating input rates from a noisy output (cf. Fig. 1), we observe that a the number of discriminable inputs, as well as b the dynamic range, are maximal for sub-critical networks (λ < 1). With increasing timescale T (differently colored lines), the maximum locations λ^* (specific to the observables, see insets) move closer to the critical point. Analytic solutions for the limits T → 0 and T → ∞ are shown as black dotted and solid lines, respectively. Parameters: N = 10⁴, K = 10², μ = 0.2, ν = 0.2, σ = 10⁻², ε = 10⁻¹.