In this paper, we propose an entropy satisfying conservative method to solve the Fokker-Planck equation of FENE dumbbell model for polymers, subject to homogeneous fluids. Both semi-discrete and fully discrete schemes satisfy all three desired properties: i) mass conservation, ii) positivity preserving, and iii) entropy satisfying in the sense that these schemes satisfy discrete entropy inequal...

An axiomatization of the concept of entropy of a discrete Choquet capacity is given. It is based on three axioms: the symmetry property, a boundary condition for which the entropy reduces to the classical Shannon entropy, and a generalized version of the well-known recursivity property. This entropy, recently introduced to extend the Shannon entropy to nonadditive measures, fulfills several pro...

3 Basics of information theory 3 3.1 Entropy and uncertainty . . . . . . . . . . . . . . . . . . . . . . . 4 3.2 Joint and conditional entropy . . . . . . . . . . . . . . . . . . . . 4 3.3 Mutual information and relative entropy . . . . . . . . . . . . . . 5 3.4 Some inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.5 Entropy of discrete distributions . . . . . . . . . . . ...

We consider semidiscrete and fully discrete conservative finite volume schemes approximating the solution to one dimensional scalar conservation law. We show that all E-schemes are associated with a discrete kinetic formulation with a nonnegative kinetic defect measure. This construction provides an alternative proof of the discrete local entropy inequalities with simple expressions of the disc...

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...

In this paper we present a novel methodology based on a topological entropy, the so-called persistent entropy, for addressing the comparison between discrete piecewise linear functions. The comparison is certified by the stability theorem for persistent entropy. The theorem is used in the implementation of a new algorithm. The algorithm transforms a discrete piecewise linear function into a fil...

The discrete Shannon entropy H was formulated only to measure indeterminacy effected through a set of probabilities, but the indeterminacy in a real-valued discrete variable depends on both the allowed outcomes x and the corresponding probabilities p. A fundamental measure that is sensitive to both x and p is derived here from the total differential entropy of a continuous real variable and its...

The notion of utility maximising entropy (u-entropy) of a probability density, which was introduced and studied in [SZ04], is extended in two directions. First, the relative u-entropy of two probability measures in arbitrary probability spaces is defined. Then, specialising to discrete probability spaces, we also introduce the absolute u-entropy of a probability measure. Both notions are based ...