We show that the von Neumann entropy (from herein referred to as the von Neumann index) of a graph’s trace normalized combinatorial Laplacian provides structural information about the level of centralization across a graph. This is done by considering the Theil index, which is an established statistical measure used to determine levels of inequality across a system of ‘agents’, e.g., income lev...

Information entropy has been proved to be an effective tool to quantify the structural importance of complex networks. In the previous work (Xu et al, 2016 [31]), we measure the contribution of a path in link prediction with information entropy. In this paper, we further quantify the contribution of a path with both path entropy and path weight, and propose a weighted prediction index based on ...

For a topological dynamical system (X, f), consisting of a continuous map f : X → X, and a (not necessarily compact) set Z ⊂ X, Bowen [2] defined a dimension-like version of entropy, hX(f, Z). In the same work, he introduced a notion of entropyconjugacy for pairs of invertible compact systems: the systems (X, f) and (Y, g) are entropy-conjugate if there exist invariant Borel sets X ′ ⊂ X and Y ...

The connection between Tsallis entropy for a multifractal distribution and Jackson’s q-derivative is established. Based on this derivation and definition of a homogeneous function, a q-analogue of Shannon’s entropy is discussed. q-additivity of this entropy is shown. We also define q-analogue of Kullback relative entropy. The implications of lattice structure beneath q-calculus are highlighted ...

The structure entropy is an important index to illuminate the structure property of the complex network. Most of the existing structure entropies are based on the degree distribution of the complex network. But the structure entropy based on the degree can not illustrate the structure property of the weighted networks. In order to study the structure property of the weighted networks, a new str...

With the fast development of wearable medical device in recent years, it becomes critical to conduct research on continuously measured physiological signals. Entropy is a key metric for quantifying the irregularity and/or complexity contained in human physiological signals. In this review, we focus on exploring how entropy changes in various physiological signals in cardiovascular diseases. Our...

This study presents an empirical evidence concerning the comparison of  the dynamics of competitiveness in the creative and manufacturing industries. It investigated the impact of the economic crisis in the behavior of the competitiveness of those industries. The samples were 42 firms taken from 3 sub-sectors of the creative industries and 3 sub-sectors of the manufacturing industries listed in...

Based on the analysis of ε − entropy, information in continuous time linear multivariable stochastic systems is discussed. To describe time average information variation after a process transmitted through a continuous time system, the concept of system variety defined by the difference between ε − entropy rates of system input and output is proposed. Furthermore, an equivalent relation between...