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Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this review, synchronization is analyzed in one of the(More)
A two-time scale asymptotic method has been introduced to analyze the mul-timodal mean-field Kuramoto-Sakaguchi model of oscillator synchronization in the high-frequency limit. The method allows to uncouple the probability density in different components corresponding to the different peaks of the oscillator frequency distribution. Each component evolves(More)
Many natural and artificial two-states signaling devices are connected forming networks. The information-processing potential of these systems is usually related to the response to weak external signals. Here, using a network of overdamped bistable elements, we study the effect of a heterogeneous complex topology on the signal response. The analysis of the(More)
Domain decomposition of two-dimensional domains on which boundary-value elliptic problems are formulated, is accomplished by probabilistic (Monte Carlo) as well as by quasi-Monte Carlo methods, generating only few interfacial values and interpolating on them. Continuous approximations for the trace of solution are thus obtained, to be used as boundary data(More)
Monte Carlo as well as quasi-Monte Carlo methods are used to generate only few in-terfacial values in two-dimensional domains where boundary-value elliptic problems are formulated. This allows for a domain decomposition of the domain. A continuous approximation of the solution is obtained interpolating on such interfaces, and then used as boundary data to(More)
Present and future supercomputers offer many opportunities and advantages to attack complex and demanding industrial and applied mathematical problems, but provide also new challenges. In the Peta-Flops regime, these concern both, the way to exploit the increasingly available power and the need of designing algorithms which are scalable and fault-tolerant(More)
It is well known that overdamped unforced dynamical systems do not oscillate. However, well-designed coupling schemes, together with the appropriate choice of initial conditions, can induce oscillations when a control parameter exceeds a threshold value. In a recent publication [Phys. Rev. E 68, 045102 (2003)]], we demonstrated this behavior in a specific(More)
A domain decomposition method is developed for the numerical solution of non-linear parabolic partial differential equations in any space dimension, based on the probabilistic representation of solutions as an average of suitable multiplicative func-tionals. Such a direct probabilistic representation requires generating a number of random trees, whose role(More)
A comparison is made between the probabilistic domain decomposition (DD) method and a certain deterministic DD method for solving linear elliptic boundary-value problems. Since in the determin-istic approach the CPU time is affected by intercommunications among the processors, it turns out that the probabilistic method performs better , especially when the(More)