Recent studies of correlations of intensity in databases of natural images revealed a remarkable property. The two point correlations are described in terms of power law behavior, with an exponent which seems to be robust. In the present Letter we consider the statistical meaning of that result. We study many individual images of one of the databases considered. We find that the same law charac...

In this article we study atomic and molecular decompositions in 2-microlocal Besov and Triebel–Lizorkin spaces with variable integrability. We show that, in most cases, the convergence implied in such decompositions holds not only in the distributions sense, but also in the function spaces themselves. As an application, we give a simple proof for the denseness of the Schwartz class in such spac...

In this Letter, we derive exponent inequalities relating the dynamic exponent z to the steady state exponent Γ for a general class of stochastically driven dynamical systems. We begin by deriving a general exact inequality, relating the response function and the correlation function, from which the various exponent inequalities emanate. We then distinguish between two classes of dynamical syste...

We study the dynamic critical behavior of the local bond-update (Sweeny) dynamics for the Fortuin–Kasteleyn random-cluster model in dimensions d = 2, 3, by Monte Carlo simulation. We show that, for a suitable range of q values, the global observable S2 exhibits “critical speeding-up”: it decorrelates well on time scales much less than one sweep, so that the integrated autocorrelation time tends...

This paper investigates the best achievable performance by a hypothesis test satisfying a structural constraint: two functions are computed at two different terminals and the detector consists of a simple comparator checking if the functions agree. Such tests arise as part of study of fundamental limits of channel coding, and hypothesis testing with communication (rate) constraints. A simple ex...

One of the most popular scale exponent estimation algorithms is the Rescaled Range (R/S) analysis. The algorithm estimates the ratio of a range and standard deviation statistics in a window with increasing length. Firstly, through simulations with generated noise we analyze estimation precision of the algorithm and find that the algorithm overestimates and underestimates at lower and higher bou...

We investigate propagating fronts in disordered media that belong to the universality class of wetting contact lines and planar tensile crack fronts. We derive from first principles their nonlinear equations of motion, using the generalized Griffith criterion for crack fronts and three standard mobility laws for contact lines. Then we study their roughness using the self-consistent expansion. W...

The likelihood decoder is a stochastic decoder that selects the decoded message at random, using the posterior distribution of the true underlying message given the channel output. In this work, we study a generalized version of this decoder where the posterior is proportional to a general function that depends only on the joint empirical distribution of the output vector and the codeword. This...