相关论文: The use of spatial information in entropy measures

We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…

The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…

Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…

We calculate and analyze various entropy measures and their properties for selected probability distributions. The entropies considered include Shannon, R\'enyi, generalized R\'enyi, Tsallis, Sharma-Mittal, and modified Shannon entropy,…

The general idea of information entropy provided by C.E. Shannon "hangs over everything we do" and can be applied to a great variety of problems once the connection between a distribution and the quantities of interest is found. The Shannon…

The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This…

This article introduces the physics of information in the context of molecular biology and genomics. Entropy and information, the two central concepts of Shannon's theory of information and communication, are often confused with each other…

Information entropy is applied to the state of knowledge of reaction amplitudes in pseudoscalar meson photoproduction, and a scheme is developed that quantifies the information content of a measured set of polarization observables. It is…

We present a general approach to the study of the local distribution of measures on Euclidean spaces, based on local entropy averages. As concrete applications, we unify, generalize, and simplify a number of recent results on local…

Shannon's entropy is one of the building blocks of information theory and an essential aspect of Machine Learning methods (e.g., Random Forests). Yet, it is only finitely defined for distributions with fast decaying tails on a countable…

The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or…

We show how the Shannon entropy function can be used as a basis to set up complexity measures weighting the economic efficiency of countries and the specialization of products beyond bare diversification. This entropy function guarantees…

We pedagogically present the information theory as originally established, explaining its essential ideas and paying attention to the expression employed to measure the amount of information. Also we discussed relationships between…

Shannon's information entropy measures of the uncertainty of an event's outcome. If learning about a system reflects a decrease in uncertainty, then a plausible intuition is that learning should be accompanied by a decrease in the entropy…

The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak…

We provide a stochastic extension of the Baez-Fritz-Leinster characterization of the Shannon information loss associated with a measure-preserving function. This recovers the conditional entropy and a closely related information-theoretic…

Various properties of relative entropy have led to its widespread use in information theory. These properties suggest that relative entropy has a role to play in systems that attempt to perform inference in terms of probability…

Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited…

The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…

A linear transformation f(S) of configurational entropy with length scale dependent coefficients as a measure of spatial inhomogeneity is considered. When a final pattern is formed with periodically repeated initial arrangement of point…