scholarly journals Conditional Rényi Entropy and the Relationships between Rényi Capacities

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 526
Author(s):  
Gautam Aishwarya ◽  
Mokshay Madiman
Keyword(s):  
Mutual Information ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Basic Properties ◽  
Reference Measure ◽  
Definition Of ◽  
Discrete Setting

The analogues of Arimoto’s definition of conditional Rényi entropy and Rényi mutual information are explored for abstract alphabets. These quantities, although dependent on the reference measure, have some useful properties similar to those known in the discrete setting. In addition to laying out some such basic properties and the relations to Rényi divergences, the relationships between the families of mutual informations defined by Sibson, Augustin-Csiszár, and Lapidoth-Pfister, as well as the corresponding capacities, are explored.

scholarly journals A Two-Moment Inequality with Applications to Rényi Entropy and Mutual Information

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1244
Author(s):  
Galen Reeves
Keyword(s):  
Mutual Information ◽  
Upper Bound ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Conditional Density ◽  
Moment Inequality ◽  
Single Moment ◽  
Variance Decompositions ◽  
Moment Constraint ◽  
Maximum Entropy Distributions

This paper explores some applications of a two-moment inequality for the integral of the rth power of a function, where 0<r<1. The first contribution is an upper bound on the Rényi entropy of a random vector in terms of the two different moments. When one of the moments is the zeroth moment, these bounds recover previous results based on maximum entropy distributions under a single moment constraint. More generally, evaluation of the bound with two carefully chosen nonzero moments can lead to significant improvements with a modest increase in complexity. The second contribution is a method for upper bounding mutual information in terms of certain integrals with respect to the variance of the conditional density. The bounds have a number of useful properties arising from the connection with variance decompositions.

Rényi Entropy and Rényi Divergence in Sequential Effect Algebra

2020 ◽  
Vol 27 (02) ◽  
pp. 2050008
Author(s):  
Zahra Eslami Giski
Keyword(s):  
Shannon Entropy ◽  
Effect Algebra ◽  
Sequential Effect ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Numerical Examples ◽  
Basic Properties ◽  
Rényi Divergence ◽  
Leibler Divergence ◽  
Entropy Measures

The aim of this study is to extend the results concerning the Shannon entropy and Kullback–Leibler divergence in sequential effect algebra to the case of Rényi entropy and Rényi divergence. For this purpose, the Rényi entropy of finite partitions in sequential effect algebra and its conditional version are proposed and the basic properties of these entropy measures are derived. In addition, the notion of Rényi divergence of a partition in sequential effect algebra is introduced and the basic properties of this quantity are studied. In particular, it is proved that the Kullback–Leibler divergence and Shannon’s entropy of partitions in a given sequential effect algebra can be obtained as limits of their Rényi divergence and Rényi entropy respectively. Finally, to illustrate the results, some numerical examples are presented.

scholarly journals Induced entanglement entropy of harmonic oscillators in non-commutative phase space

2019 ◽  
Vol 34 (33) ◽  
pp. 1950269
Author(s):  
Bingsheng Lin ◽  
Jian Xu ◽  
Taihua Heng
Keyword(s):  
Phase Space ◽  
Ground State ◽  
Entanglement Entropy ◽  
Harmonic Oscillators ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Wigner Functions ◽  
Definition Of

We study the entanglement entropy of harmonic oscillators in non-commutative phase space (NCPS). We propose a new definition of quantum Rényi entropy based on Wigner functions in NCPS. Using the Rényi entropy, we calculate the entanglement entropy of the ground state of the 2D isotropic harmonic oscillators. We find that for some values of the non-commutative parameters, the harmonic oscillators can be entangled in NCPS. This is a new entanglement-like effect caused by the non-commutativity of the phase space.

ANALYSIS OF THE α-RENYI ENTROPY AND ITS APPLICATION FOR MEDICAL IMAGE REGISTRATION

2017 ◽  
Vol 29 (03) ◽  
pp. 1750020
Author(s):  
Meisen Pan ◽  
Fen Zhang
Keyword(s):  
Image Registration ◽  
Mutual Information ◽  
Parameter Optimization ◽  
Medical Image ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Registration Accuracy ◽  
Computational Load ◽  
Image Registrations ◽  
Parameter Ranges

In this paper, the [Formula: see text]-Renyi entropy and [Formula: see text]-Renyi-based mutual information (RMI) are first introduced. Then the influence of the parameter [Formula: see text] on the curve of the RMI and the computational load of image registration are discussed and analyzed to explore the appropriate parameter ranges. Finally, the RMI with the appropriate parameter [Formula: see text] is viewed as the similarity measure between the reference and floating images. In the experiments, the Simplex method is chosen as the multi-parameter optimization one. The experimental results reveal that the proposed method has low computational load, fast registration and good registration accuracy. It is adapted to both mono-modality and multi-modality image registrations.

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