Most assertions involving Shannon entropy have their Kolmogorov complexity counterparts. A general theorem of Romashchenko [4] states that every information inequality that is valid in Shannon’s theory is also valid in Kolmogorov’s theory, and vice verse. In this paper we prove that this is no longer true for ∀∃-assertions, exhibiting the first example where the formal analogy between Shannon e...

Abstract— Mammogram analysis usually refers to processing of mammograms with the goal of finding abnormality presented in the mammogram. Mammogram segmentation is one of the most critical tasks in automatic mammogram image analysis. Main purpose of mammogram segmentation is to segment suspicious regions by means of an adaptive threshold. In image processing, one of the most efficient techniques...

The uniequness theorem for the Tsallis entropy by introducing the generalized Faddeev’s axiom is proven. Our result improves the recent result, the uniqueness theorem for Tsallis entropy by the generalized Shannon-Khinchin’s axiom in [7], in the sence that our axiom is simpler than his one, as similar that Faddeev’s axiom is simpler than Shannon-Khinchin’s one.

Shannon information entropy is a natural measure of probability (de)localization and thus (un)predictability in various procedures of data analysis for model systems. We pay particular attention to links between the Shannon entropy and the related Fisher information notion, which jointly account for the shape and extension of continuous probability distributions. Classical, dynamical and random...

We consider spin systems in the $d$-dimensional lattice $Z^d$ satisfying so-called strong spatial mixing condition. show that relative entropy functional of corresponding Gibbs measure satisfies a family inequalities which control on given region $V\subset Z^d$ terms weighted sum entropies blocks $A\subset V$ when each $A$ is an arbitrary nonnegative weight $\alpha_A$. These generalize well kno...

We examine the entropy of stationary nonequilibrium measures of boundary driven symmetric simple exclusion processes. In contrast with the Gibbs–Shannon entropy [1, 10], the entropy of nonequilibrium stationary states differs from the entropy of local equilibrium states.

Kullback-Leibler relative-entropy or KL-entropy of P with respect to R defined as ∫ X ln dP dR dP , where P and R are probability measures on a measurable space (X,M), plays a basic role in the definitions of classical information measures. It overcomes a shortcoming of Shannon entropy – discrete case definition of which cannot be extended to nondiscrete case naturally. Further, entropy and oth...

Chaos is often explained in terms of random behaviour; and having positive Kolmogorov–Sinai entropy (KSE) is taken to be indicative of randomness. Although seemly plausible, the association of positive KSE with random behaviour needs justification since the definition of the KSE does not make reference to any notion that is connected to randomness. A common way of justifying this use of the KSE...

Based on the local Shannon entropy concept in information theory, a new measure of aromaticity is introduced. This index, which describes the probability of electronic charge distribution between atoms in a given ring, is called Shannon aromaticity (SA). Using B3LYP method and different basis sets (6-31G**, 6-31+G** and 6-311++G**), the SA values of some five-membered heterocycles, C(4)H(4)X, a...