A new correlation measure, the product of the Shannon entropy power and the Fisher information of the electron density, is introduced by analyzing the Fisher-Shannon information plane of some two-electron systems (He-like ions, Hooke's atoms). The uncertainty and scaling properties of this information product are pointed out. In addition, the Fisher and Shannon measures of a finite many-electro...

In the search for robust, accurate, and highly efficient financial option valuation techniques, we here present the SWIFT method (Shannon wavelets inverse Fourier technique), based on Shannon wavelets. SWIFT comes with control over approximation errors made by means of sharp quantitative error bounds. The nature of the local Shannon wavelets basis enables us to adaptively determine the proper s...

In the search for robust, accurate, and highly efficient financial option valuation techniques, we here present the SWIFT method (Shannon wavelets inverse Fourier technique), based on Shannon wavelets. SWIFT comes with control over approximation errors made by means of sharp quantitative error bounds. The nature of the local Shannon wavelets basis enables us to adaptively determine the proper s...

The aim of this paper is to present an axiomatization of a generalization of Shannon’s entropy starting from partitions of finite sets. The proposed axiomatization yields as special cases the Havrda-Charvat entropy, and thus, provides axiomatizations for the Shannon entropy, the Gini index, and for other types of entropy used in classification and data mining. Keywords—Shannon entropy, Gini ind...

In general, Shannon zero-capacity is hard to obtain even for very simple small graphs. Lovasz constructed an upper bound in [4] for Shannon capacity which is well-characterized and relatively easy to compute. In some special cases, it is even equal to the Shannon capacity. However, it has been proven that the Lovasz bound is not always tight and counterexamples are not hard to find.

Current definition of high-entropy alloys (HEAs) is commonly based on the configurational entropy. But this depends only chemical composition a HEA and therefore cannot distinguish information content that encoded in various local atomic arrangements measurable by Shannon entropy theory. Here, inspired finding two-dimensional (2D) Sudoku matrices exhibit higher average than 2D random matrix cou...

Contents 10 Quantum Shannon Theory 1 10.1 Shannon for Dummies 2 10.1.1 Shannon entropy and data compression 2 10.1.2 Joint typicality, conditional entropy, and mutual information 6 10.1.3 Distributed source coding 8 10.1.4 The noisy channel coding theorem 9 10.2 Von Neumann Entropy 16 10.2.1 Mathematical properties of H(ρ) 18 10.2.2 Mixing, measurement, and entropy 20 10.2.3 Strong subadditivit...