Computation of Fokker-Planck equations with satisfying long time behavior is important in many applications and difficult in resolving solution structures induced by non-standard forces. Entropy satisfying conservative methods are proven to be powerful to ensure both equilibrium preserving and mass conservation properties at the discrete level. Following [H. Liu and H. Yu, SIAM Journal on Numer...

Proper design and operation of monitoring systems for water resources management is one of themost important issues of water quality and quantity and accuracy and adequacy of data. The properevaluation of these data has a determining role in the correctand consistent decisions in the areacovered by the system. Therefore, determining proper distribution and number of monitoringnetwork stations a...

A finite volume scheme for the (Patlak-) Keller-Segel model in two space dimensions with an additional cross-diffusion term in the elliptic equation for the chemical signal is analyzed. The main feature of the model is that there exists a new entropy functional yielding gradient estimates for the cell density and chemical concentration. The main features of the numerical scheme are positivity p...

The relative entropy rate is a natural and useful measure of distance between two stochastic processes. In this paper we study the relative entropy rate between two Hidden Markov Processes (HMPs), which is of both theoretical and practical importance. We give new results showing analyticity, representation using Lyapunov exponents, and Taylor expansion for the relative entropy rate of two discr...

We present a numerical method for computing transitional flows as described by the BGK equation of gas kinetic theory. Using the minimum entropy principle to define a discrete equilibrium function, a discrete velocity model of this equation is proposed. This model, like the continuous one, ensures positivity of solutions, conservation of moments, and dissipation of entropy. The discrete velocit...

This paper motivates and interprets entropy centrality, the measure understood as the entropy of flow destination in a network. The paper defines a variation of this measure based on a discrete, random

In almost every engineering and technology fields, information channel capacity is the tightest upper bound on the amount of information that can be reliably transmitted over a communications channel. Brijpaul and Sharma [1] gave a direct method of computing the performance function of a discrete memoryless communication channels. They obtained the performance function for discrete channels by ...

In recent years, the cross-entropy method has been successfully applied to a wide range of discrete optimization tasks. In this paper we consider the cross-entropy method in the context of continuous optimization. We demonstrate the effectiveness of the cross-entropy method for solving difficult continuous multi-extremal optimization problems, including those with nonlinear constraints.

Abstract. The present work deals with the establishment of stability conditions of finite volume methods to approximate weak solutions of the general Euler equations to simulate compressible flows. In oder to ensure discrete entropy inequalities, we derive a new technique based on a local minimum principle to be satisfied by the specific entropy. Sufficient conditions are exhibited to satisfy t...

We consider numerical schemes which combine non-uniform, adaptively redefined spatial meshes with entropy conservative schemes for the evolution step for shock computations. We observe that the resulting adaptive schemes yield approximations free of oscillations in contrast to known fully discrete entropy conservative schemes on uniform meshes. We conclude that entropy conservative schemes are ...