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.

SELF-SIMILAR AND SELF-AFFINE PIONIZATION IN NUCLEAR INTERACTIONS AT A FEW AGeV

2004 ◽  
Vol 13 (06) ◽  
pp. 1179-1189 ◽  
Author(s):  
DIPAK GHOSH ◽  
ARGHA DEB ◽  
KEYA DUTTA (CHATTOPADHYAY) ◽  
RINKU SARKAR ◽  
ISHITA SEN (DUTTA)
Keyword(s):  
Phase Space ◽  
Hurst Exponent ◽  
Factorial Moment ◽  
Two Dimensional ◽  
Nuclear Interactions ◽  
Fluctuation Pattern ◽  
Self Similar

Self-affine multiplicity scaling is investigated in the framework of two-dimensional factorial moment methodology using the concept of the Hurst exponent (H) considering different bins of the phase space. We have investigated the fluctuation pattern of emitted pions in 24 Mg - AgBr interactions at 4.5 AGeV and this study reveals that the fluctuation is self-similar in some bins, whereas it is self-affine in other bins, that is, the multiplicity scaling is bin-dependent.

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 Using the Hurst Exponent and Entropy Measures to Predict Effective Transmissibility in Empirical Series of Malaria Incidence

2022 ◽  
Vol 12 (1) ◽  
pp. 496
Author(s):  
João Sequeira ◽  
Jorge Louçã ◽  
António M. Mendes ◽  
Pedro G. Lind
Keyword(s):  
Shannon Entropy ◽  
Hurst Exponent ◽  
Malaria Incidence ◽  
Hidden Variables ◽  
Data Set ◽  
Agent Model ◽  
Human Host ◽  
A Value ◽  
Entropy Measures

We analyze the empirical series of malaria incidence, using the concepts of autocorrelation, Hurst exponent and Shannon entropy with the aim of uncovering hidden variables in those series. From the simulations of an agent model for malaria spreading, we first derive models of the malaria incidence, the Hurst exponent and the entropy as functions of gametocytemia, measuring the infectious power of a mosquito to a human host. Second, upon estimating the values of three observables—incidence, Hurst exponent and entropy—from the data set of different malaria empirical series we predict a value of the gametocytemia for each observable. Finally, we show that the independent predictions show considerable consistency with only a few exceptions which are discussed in further detail.

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 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.

Plastic Ploughing of a Sinusoidal Asperity on a Rough Surface

2015 ◽  
Vol 82 (7) ◽  
Author(s):  
H. Song ◽  
R. J. Dikken ◽  
L. Nicola ◽  
E. Van der Giessen
Keyword(s):  
Friction Stress ◽  
Dislocation Dynamics ◽  
Two Dimensional ◽  
Unit Process ◽  
Contact Models ◽  
Self Similar ◽  
Dynamics Simulations ◽  
Micrometer Scale ◽  
Edge Dislocations ◽  
Flat Contact

Part of the friction between two rough surfaces is due to the interlocking between asperities on opposite surfaces. In order for the surfaces to slide relative to each other, these interlocking asperities have to deform plastically. Here, we study the unit process of plastic ploughing of a single micrometer-scale asperity by means of two-dimensional dislocation dynamics simulations. Plastic deformation is described through the generation, motion, and annihilation of edge dislocations inside the asperity as well as in the subsurface. We find that the force required to plough an asperity at different ploughing depths follows a Gaussian distribution. For self-similar asperities, the friction stress is found to increase with the inverse of size. Comparison of the friction stress is made with other two contact models to show that interlocking asperities that are larger than ∼2 μm are easier to shear off plastically than asperities with a flat contact.

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.

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