We analyze the Fleming-Viot process. The system is confined in a box, whose boundaries act as a sink of Brownian particles. The death rate at the boundaries is matched by the branching (birth) rate in the system and thus the number of particles is kept constant. We show that such a process is described by the Renyi entropy whose production is minimized in the stationary state. The entropy produ...

We revisit the problem of estimating Renyi Entropy from samples, focusing on the important case of collision entropy. With n samples we approximate the collision entropy of X within an additive factor of O ( 2 log 1 2 (1/ ) ) with probability 1− , where ∆ is a known (a priori) upper bound on the difference between Renyi entropies of X of order 2 and 3 respectively. In particular, we simplify an...

Recent improvements in the method of estimating Renyi entropies from measurements of coincidences between the events observed in high energy collisions are reviewed. A new, more precise, formulation of the method is presented and its accuracy analyzed.

This paper reports a new reading for wavelets, which is based on the classical ’De Broglie’ principle. The waveparticle duality principle is adapted to wavelets. Every continuous basic wavelet is associated with a proper probability density, allowing defining the Shannon entropy of a wavelet. Further entropy definitions are considered, such as Jumarie or Renyi entropy of wavelets. We proved tha...

Mapping a complex network of Ncoupled identical oscillators to a quantum system, the nearest neighbor level spacing (NNLS) distribution is used to identify collective chaos in the corresponding classical dynamics on the complex network. The classical dynamics on an Erdos-Renyi network with the wiring probability pER ≤ 1 N is in the state of collective order, while that on an Erdos-Renyi network...

The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for sources with independent (but not iid) outputs, generalizing and improving the result of Holenstein and Renner (IEEE Trans. Inform. Theory, 2011). (a) we charac...