A comprehensive research of Electroencephalography (EEG) is carried out on Empirical Mode Decomposition (EMD) and Discrete Wavelet Transform (DWT) domains. In this scenario, the hybrid feature extraction is performed by utilizing entropy features like Shannon entropy, log-energy entropy and Renyi entropy. Generally, the entropy measures are effective in evaluation of non-linear interrelation an...

Shannon’s entropy power inequality characterizes the minimum differential entropy achievable by the sum of two independent random variables with fixed differential entropies. Since the pioneering work of Shannon, there has been a steady stream of results over the years, trying to understand the structure of Shannon’s entropy power inequality, as well as trying to develop similar entropy power i...

We develop a fine-scale local analysis of measure entropy and measure sequence entropy based on combinatorial independence. The concepts of measure IE-tuples and measure IN-tuples are introduced and studied in analogy with their counterparts in topological dynamics. Local characterizations of the Pinsker von Neumann algebra and its sequence entropy analogue are given in terms of combinatorial i...

Structure-preserving numerical schemes for a nonlinear parabolic fourthorder equation, modeling the electron transport in quantum semiconductors, with periodic boundary conditions are analyzed. First, a two-step backward differentiation formula (BDF) semi-discretization in time is investigated. The scheme preserves the nonnegativity of the solution, is entropy stable and dissipates a modified e...

We consider the problem of finite sample corrections for entropy estimation. New estimates of the Shannon entropy are proposed and their systematic error (the bias) is computed analytically. We find that our results cover correction formulas of current entropy estimates recently discussed in literature. The trade-off between bias reduction and the increase of the corresponding statistical error...

We present a discontinuous Galerkin (DG) scheme with suitable quadrature rules [15] for ideal compressible magnetohydrodynamic (MHD) equations on structural meshes. The semi-discrete scheme is analyzed to be entropy stable by using the symmetrizable version of the equations as introduced by Godunov [32], the entropy stable DG framework with suitable quadrature rules [15], the entropy conservati...

Discrete approximations to hyperbolic systems of conservation laws are studied. We quantify the amount of numerical viscosity present in such schemes, and relate it to their entropy stability by means of comparison. To this end, conservative schemes which are also entropy conservative are constructed. These entropy conservative schemes enjoy second-order accuracy; moreover, they can be interpre...

Transfer entropy has been used to quantify the directed flow of information between source and target variables in many complex systems. While transfer entropy was originally formulated in discrete time, in this paper we provide a framework for considering transfer entropy in continuous time systems, based on Radon-Nikodym derivatives between measures of complete path realizations. To describe ...

A perturbed multi-agent system is a scheme self-possessed of multiple networking agents within a location. This scheme can be used to discuss problems that are impossible or difficult for a specific agent to solve. Intelligence cloud entropy management systems involve functions, methods, procedural approaches, and algorithms. In this study, we introduce a new perturbed algorithm based on the fr...

In this work, we extend a variable-length source coding theorem for discrete memoryless sources to ergodic time-invariant Markov sources of arbitrary order. To accomplish this extension, we establish a formula for the R enyi entropy rate limn!1 H(n)=n. The main tool used to obtain the R enyi entropy rate result is Perron-Frobenius theory. We also examine the expression of the R enyi en-tropy ra...