scholarly journals On Rényi Permutation Entropy

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 37
Author(s):  
Tim Gutjahr ◽  
Karsten Keller
Keyword(s):  
Shannon Entropy ◽  
Permutation Entropy ◽  
Correlation Integral ◽  
System A ◽  
The Family ◽  
Rényi Entropies ◽  
Pattern Distribution ◽  
Ordinal Pattern ◽  
Negative Real Number ◽  
Renyi Entropies

Among various modifications of the permutation entropy defined as the Shannon entropy of the ordinal pattern distribution underlying a system, a variant based on Rényi entropies was considered in a few papers. This paper discusses the relatively new concept of Rényi permutation entropies in dependence of non-negative real number q parameterizing the family of Rényi entropies and providing the Shannon entropy for q=1. Its relationship to Kolmogorov–Sinai entropy and, for q=2, to the recently introduced symbolic correlation integral are touched.

scholarly journals Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 196 ◽  
Author(s):  
Orietta Nicolis ◽  
Jorge Mateu ◽  
Javier E. Contreras-Reyes
Keyword(s):  
Shannon Entropy ◽  
Simulation Study ◽  
Hurst Exponent ◽  
Wavelet Spectrum ◽  
Two Dimensional ◽  
Entropy Measures ◽  
Rényi Entropies ◽  
Self Similar ◽  
Fractional Brownian Field ◽  
Renyi Entropies

The aim of this work was to extend the results of Perez et al. (Physica A (2006), 365 (2), 282–288) to the two-dimensional (2D) fractional Brownian field. In particular, we defined Shannon entropy using the wavelet spectrum from which the Hurst exponent is estimated by the regression of the logarithm of the square coefficients over the levels of resolutions. Using the same methodology. we also defined two other entropies in 2D: Tsallis and the Rényi entropies. A simulation study was performed for showing the ability of the method to characterize 2D (in this case, α = 2 ) self-similar processes.

scholarly journals On some functional equations from additive and non-additive measures-I

1980 ◽  
Vol 23 (2) ◽  
pp. 145-150 ◽  
Author(s):  
PL Kannappan
Keyword(s):  
Functional Equation ◽  
Shannon Entropy ◽  
Functional Equations ◽  
Statistical Thermodynamics ◽  
Rényi Entropies ◽  
Algebraic Properties ◽  
Image Position ◽  
Additive Measures ◽  
Measure Entropy ◽  
Renyi Entropies

It is known that while the Shannon and the Rényi entropies are additive, the measure entropy of degree β proposed by Havrda and Charvat (7) is non-additive. Ever since Chaundy and McLeod (4) considered the following functional equationwhich arose in statistical thermodynamics, (1.1) has been extensively studied (1, 5, 6, 8). From the algebraic properties of symmetry, expansibility and branching of the entropy (viz. Shannon entropy Hn, etc.) one obtains the sum representationwhich with the property of additivity yields the functional equation (1.1), (9, 10).

scholarly journals On the Statistical Properties of Multiscale Permutation Entropy: Characterization of the Estimator’s Variance

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 450 ◽  
Author(s):  
Antonio Dávalos ◽  
Meryem Jabloun ◽  
Philippe Ravier ◽  
Olivier Buttelli
Keyword(s):  
Time Scale ◽  
Real Life ◽  
Theoretical Background ◽  
Quadratic Growth ◽  
Permutation Entropy ◽  
Statistical Comparison ◽  
Pattern Distribution ◽  
Ordinal Pattern ◽  
Analysis Of Time Series

Permutation Entropy (PE) and Multiscale Permutation Entropy (MPE) have been extensively used in the analysis of time series searching for regularities. Although PE has been explored and characterized, there is still a lack of theoretical background regarding MPE. Therefore, we expand the available MPE theory by developing an explicit expression for the estimator’s variance as a function of time scale and ordinal pattern distribution. We derived the MPE Cramér–Rao Lower Bound (CRLB) to test the efficiency of our theoretical result. We also tested our formulation against MPE variance measurements from simulated surrogate signals. We found the MPE variance symmetric around the point of equally probable patterns, showing clear maxima and minima. This implies that the MPE variance is directly linked to the MPE measurement itself, and there is a region where the variance is maximum. This effect arises directly from the pattern distribution, and it is unrelated to the time scale or the signal length. The MPE variance also increases linearly with time scale, except when the MPE measurement is close to its maximum, where the variance presents quadratic growth. The expression approaches the CRLB asymptotically, with fast convergence. The theoretical variance is close to the results from simulations, and appears consistently below the actual measurements. By knowing the MPE variance, it is possible to have a clear precision criterion for statistical comparison in real-life applications.

scholarly journals Rényi Extrapolation of Shannon Entropy

2003 ◽  
Vol 10 (03) ◽  
pp. 297-310 ◽  
Author(s):  
Karol Życzkowski
Keyword(s):  
Probability Distribution ◽  
Quantum State ◽  
Shannon Entropy ◽  
Upper Bound ◽  
Von Neumann Entropy ◽  
Discrete Probability ◽  
Von Neumann ◽  
Integer Order ◽  
Rényi Entropies ◽  
Renyi Entropies

Relations between Shannon entropy and Rényi entropies of integer order are discussed. For any N-point discrete probability distribution for which the Rényi entropies of order two and three are known, we provide a lower and an upper bound for the Shannon entropy. The average of both bounds provide an explicit extrapolation for this quantity. These results imply relations between the von Neumann entropy of a mixed quantum state, its linear entropy and traces.

XV.—The Placoderm Fish Rhachiosteus pterygiatus Gross and its Relationships

1966 ◽  
Vol 66 (15) ◽  
pp. 377-392 ◽  
Author(s):  
Roger S. Miles
Keyword(s):  
Sensory System ◽  
System A ◽  
The Family ◽  
Definition Of

SynopsisThe holotype and only known specimen of Rhachiosteus pterygiatus Gross is partially redescribed and new restorations are given. Attention is drawn to important points in its osteology and the possible development of a cutaneous sensory system. A definition of the family Rhachiosteidsæ Stensiö is given. This family differs from all other described groups of euarthrodires in the lack of posterior lateral and posterior dorsolateral flank plates. Rhachiosteus is a pachyosteomorph brachythoracid, as defined in the text, and may be fairly closely related in some way to the (coccosteomorph) family Coccosteidsæ. There is no indication that it is closely related to any other known pachyosteomorph, or to other groups of arthrodires, such as the Rhenanida and Ptyctodontida, in which there are no posterior flank plates.

scholarly journals Analytic critical points of charged Rényi entropies from hyperbolic black holes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Jie Ren
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Study Phase ◽  
Zero Temperature ◽  
Charged Scalar ◽  
Yang Mills ◽  
Gravitational Systems ◽  
Rényi Entropies ◽  
Zero Entropy ◽  
Renyi Entropies

Abstract We analytically study phase transitions of holographic charged Rényi entropies in two gravitational systems dual to the $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory at finite density and zero temperature. The first system is the Reissner-Nordström-AdS5 black hole, which has finite entropy at zero temperature. The second system is a charged dilatonic black hole in AdS5, which has zero entropy at zero temperature. Hyperbolic black holes are employed to calculate the Rényi entropies with the entangling surface being a sphere. We perturb each system by a charged scalar field, and look for a zero mode signaling the instability of the extremal hyperbolic black hole. Zero modes as well as the leading order of the full retarded Green’s function are analytically solved for both systems, in contrast to previous studies in which only the IR (near horizon) instability was analytically treated.

scholarly journals Effect of dissociation energy on Shannon and Rényi entropies

2018 ◽  
Vol 4 (1) ◽  
pp. 134-142 ◽  
Author(s):  
C.A. Onate ◽  
A.N. Ikot ◽  
M.C. Onyeaju ◽  
O. Ebomwonyi ◽  
J.O.A. Idiodi
Keyword(s):  
Dissociation Energy ◽  
Rényi Entropies ◽  
Renyi Entropies
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