Solutions of conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time. This paper investigates this property from a numerical standpoint. We introduce a class of fully discrete in space and time, high order accurate, diierenceschemes, called generalized monotone...

Relations between Shannon entropy and Rényi entropies of integer order are discussed. For any N–point discrete probability distribution for which the Rényi entropies of order two and three are known, we provide an lower and an upper bound for the Shannon entropy. The average of both bounds provide an explicit extrapolation for this quantity. These results imply relations between the von Neumann...

A hidden Markov process (HMP) is a discrete-time finite-state homogeneous Markov chain observed through a discrete-time memoryless invariant channel. The non-asymptotic equipartition property (NEP) is a bound on the probability of the sample entropy deviating from the entropy rate of a stochastic process, so it can be viewed as a refinement of Shannon-McMillan-Breiman theorem. In this report, w...

A lot of well-balanced schemes have been proposed for discretizing the classical Saint-Venant system for shallow water flows with non-flat bottom. Among them, the hydrostatic reconstruction scheme is a simple and efficient one. It involves the knowledge of an arbitrary solver for the homogeneous problem (for example Godunov, Roe, kinetic. . . ). If this solver is entropy satisfying, then the hy...

We establish the convergence of the nite volume method applied to multidimensional hyperbolic conservation laws, and based on monotone numerical ux-functions. Our technique applies under a fairly unrestrictive assumption on the triangulations (\\at elements" are allowed), and to Lipschitz continuous ux-functions. We treat the initial and boundary value problem, and obtain the strong convergence...

Rényi entropy and Rényi divergence evidence a long track record of usefulness in information theory and its applications. Alfred Rényi never got around to generalizing mutual information in a similar way. In fact, in the literature there are several possible ways to accomplish such generalization, most notably those suggested by Suguru Arimoto, Imre Csiszár, and Robin Sibson. We collect several...

We present new theoretical convergence results on the Cross-Entropy method for discrete optimization. Our primary contribution is to show that a popular implementation of the Cross-Entropy method converges, and finds an optimal solution with probability arbitrarily close to 1. We also give necessary conditions and sufficient conditions under which an optimal solution is generated eventually wit...

Introduction In recent years methods based on radio frequency waves have been used for detecting breast cancer. Using theses waves leads to better results in early detection of breast cancer comparing with conventional mammography which has been used during several years. Materials and Methods In this paper, a new method is introduced for detection of backscattered signals which are received by...

Permutation entropy quantifies the diversity of possible orderings of the values a random or deterministic system can take, as Shannon entropy quantifies the diversity of values. We show that the metric and permutation entropy rates—measures of new disorder per new observed value—are equal for ergodic finite-alphabet information sources (discrete-time stationary stochastic processes). With this...