In this paper, we investigate the propagation of perturbations in Boolean networks by evaluating the Derrida plot and its modifications. We show that even small random Boolean networks agree well with the predictions of the annealed approximation, but nonrandom networks show a very different behaviour. We focus on networks that were evolved for high dynamical robustness. The most important conc...

Abstract. We consider the weakly asymmetric exclusion process on a bounded interval with particles reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by the viscous Burgers equation with Dirichlet boundary conditions. In the case in which the bulk asymmetry is in the same direction as the drift due to the boundary reservoir...

Let {Eσ(N)}σ∈ΣN be a family of |ΣN | = 2N centered unit Gaussian random variables defined by the covariance matrix CN of elements cN (σ, τ) := Av (Eσ(N)Eτ (N)), and HN (σ) = − √ NEσ(N) the corresponding random Hamiltonian. Then the quenched thermodynamical limit exists if, for every decomposition N = N1 + N2, and all pairs (σ, τ) ∈ ΣN × ΣN : cN (σ, τ) ≤ N1 N cN1(π1(σ), π1(τ)) + N2 N cN2(π2(σ), ...