We present a relaxation scheme for approximating the entropy dissipating weak solutions of the BaerNunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in [16] for the isentropic Baer-Nunziato model and consequently inherits its main properties. Up to our knowledge, this is the only existing scheme for which the ap...

In Liu and Yu (SIAM J Numer Anal 50(3):1207–1239, 2012), we developed a finite volume method for Fokker–Planck equations with an application to finitely extensible nonlinear elastic dumbbell model for polymers subject to homogeneous fluids. The method preserves positivity and satisfies the discrete entropy inequalities, but has only first order accuracy in general cases. In this paper, we overc...

The Minimum-Entropy Clustering (MEC) algorithm proposed in this paper provides an optimal method for addressing the non-stationarity of a source with respect to entropy coding. This algorithm clusters a set of vectors (where each vector consists of a xed number of contiguous samples from a discrete source) using a minimum entropy criterion. In a manner similar to Classi ed Vector Quantization (...

The VQ-style clustering algorithm proposed in this paper provides an optimal method for addressing the non-stationarity of a source with respect to entropy coding. This algorithm which is named Minimum-Entropy Clustering (MEC), clusters a set of vectors (where each vector consists of a fixed number of contiguous samples from a discrete source) using a minimum entropy criterion. In a manner simi...

The inequality containing Csiszár divergence on time scales is generalized for 2n2n-convex functions by using Lidstone interpolating polnomial. As an application, new entropic bounds are also computed. Several inequalities in quantum calculus and hh-discrete established. relationship between Shannon entropy, Kullback-Leibler Jeffreys distance with Zipf-Mandelbrot entropy

Networks used in biological applications at different scales (molecule, cell and population) are of different types: neuronal, genetic, and social, but they share the same dynamical concepts, in their continuous differential versions (e.g., non-linear Wilson-Cowan system) as well as in their discrete Boolean versions (e.g., non-linear Hopfield system); in both cases, the notion of interaction g...

There have been active discussions on how to derive a consistent cryptographic key from noisy data such as biometric templates, with the help of some extra information called a sketch. It is desirable that the sketch reveals little information about the biometric templates even in the worst case (i.e., the entropy loss should be low). The main difficulty is that many biometric templates are rep...

We consider the problem of approximating the entropy of a discrete distribution under several different models of oracle access to the distribution. In the evaluation oracle model, the algorithm is given access to the explicit array of probabilities specifying the distribution. In this model, linear time in the size of the domain is both necessary and sufficient for approximating the entropy. I...

In the case of ergodicity much of the structure of a one-dimensional time-discrete dynamical system is already determined by its ordinal structure. We generally discuss this phenomenon by considering the distribution of ordinal patterns, which describe the up and down in the orbits of a Borel measurable map on a subset of the real numbers. In particular, we give a natural ordinal description of...

The finiteness of black hole entropy suggest that spacetime is fundamentally discrete, and hints at an underlying relationship between geometry and ”information”. The foundation of this relationship is yet to be uncovered, but should manifest itself in a theory of quantum gravity. We review recent attempts to define a microscopic measure for black hole entropy and for the maximum entropy of sph...