A variational method for the classical Liouville equation is introduced that facilitates the development of theories for non-equilibrium classical systems. The method is based on the introduction of a complex-valued auxiliary quantity Ψ that is related to the classical position-momentum...

Mastering the underlying characteristics of carbon price changes can help governments formulate correct policies to keep efficient operation of carbon markets, and investors take effective measures to evade their investment risks. Empirical mode decomposition (EMD), a self-adaption data analysis...

Environmental assessment needs of Decision Support Systems (DSSs) able to consider several aspects in a unique analysis framework. The complexity of interaction among ecological, economic and political variables and a widespread lack of data availability lead to difficulty in bringing together...

This paper presents a novel approach for the local analysis of the contour of a planar real world shape. The 1D representation of that contour is a very complicated signal with several non isolated and oscillating singularities, which represent the micro-structure of the shape. The analysis of...

Spatial scales and methods for dealing with scale have been widely discussed in the water resources literature. Different spatial processes operate at different scales so interpretations based on data from one scale may not apply to another. Understanding the behavior of phenomena at...

An entropic measure for the analysis of grey level inhomogeneity (GLI) is proposed as a function of length scale. It allows us to quantify the statistical dissimilarity of the actual macrostate and the maximizing entropy of the reference one. The maximums (minimums) of the measure indicate those...

The statistical measure of spatial inhomogeneity for n points placed in χ cells each of size k×k is generalized to incorporate finite size objects like black pixels for binary patterns of size L×L. As a function of length scale k, the measure is modified in such a way that it relates to...

To quantify the degree of spatial inhomogeneity for multiphase materials we adapt the entropic descriptor (ED) of a pillar model developed to greyscale images. To uncover the contribution of each phase we introduce the suitable “phase splitting” of the adapted descriptor. As a result, each...

On the basis of a model system of pillars built of unit cubes, a two-component entropic measure for the multiscale analysis of spatio-compositional inhomogeneity is proposed. It quantifies the statistical dissimilarity per cell of the actual configurational macrostate and the theoretical...

Multifractal behavior is found in traffic speed time series and mostly measured around the concept of Legendre singularity spectrum. As one of the multifractal spectra, which is the probability distribution of roughness grain exponent, Legendre spectrum is structurally blind to subtle features...