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We calculate analytically the critical connectivity $K_c$ of Random Threshold Networks (RTN) for homogeneous and inhomogeneous thresholds, and confirm the results by numerical simulations. We find a super-linear increase of $K_c$ with the (average) absolute threshold $|h|$, which approaches $K_c(|h|) sim h^2/(2ln{|h|})$ for large $|h|$, and show that this asymptotic scaling is universal for RTN with Poissonian distributed connectivity and threshold distributions with a variance that grows slower than $h^2$. Interestingly, we find that inhomogeneous distribution of thresholds leads to increased propagation of perturbations for sparsely connected networks, while for densely connected networks damage is reduced; the cross-over point yields a novel, characteristic connectivity $K_d$, that has no counterpart in Boolean networks. Last, local correlations between node thresholds and in-degree are introduced. Here, numerical simulations show that even weak (anti-)correlations can lead to a transition from ordered to chaotic dynamics, and vice versa. It is shown that the naive mean-field assumption typical for the annealed approximation leads to false predictions in this case, since correlations between thresholds and out-degree that emerge as a side-effect strongly modify damage propagation behavior.
The inclusion of a macroscopic adaptive threshold is studied for the retrieval dynamics of both layered feedforward and fully connected neural network models with synaptic noise. These two types of architectures require a different method to be solve
The inclusion of a macroscopic adaptive threshold is studied for the retrieval dynamics of layered feedforward neural network models with synaptic noise. It is shown that if the threshold is chosen appropriately as a function of the cross-talk noise
We systematically study and compare damage spreading at the sparse percolation (SP) limit for random boolean and threshold networks with perturbations that are independent of the network size $N$. This limit is relevant to information and damage prop
We study a model for a random walk of two classes of particles (A and B). Where both species are present in the same site, the motion of As takes precedence over that of Bs. The model was originally proposed and analyzed in Maragakis et al., Phys. Re
Monte Carlo techniques are used to investigate the equilibrium threshold concentration, xe, in the dilute anisotropic antiferromagnet Fe(x)Zn(1-x)F2 in an applied magnetic field, considered to be an ideal random-field Ising model system. Above xe equ