Randomizing nonlinear maps via symbolic dynamics

Pseudo Random Number Generators (PRNG) have attracted intense attention due to their obvious importance for many branches of science and technology. A randomizing technique is a procedure designed to improve the PRNG randomness degree according the specific requirements. It is obviously important to...

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Detalles Bibliográficos
Publicado:	2008
Materias:	Permutation entropy Pseudo random number generators Statistical complexity Symbolic dynamics Chaotic systems Probability distributions Statistical methods Random number generation
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03784371_v387_n14_p3373_DeMicco http://hdl.handle.net/20.500.12110/paper_03784371_v387_n14_p3373_DeMicco
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_03784371_v387_n14_p3373_DeMicco
record_format	dspace
spelling	paper:paper_03784371_v387_n14_p3373_DeMicco2023-06-08T15:40:10Z Randomizing nonlinear maps via symbolic dynamics Permutation entropy Pseudo random number generators Statistical complexity Symbolic dynamics Chaotic systems Probability distributions Statistical methods Permutation entropy Pseudo random number generators Statistical complexity Symbolic dynamics Random number generation Pseudo Random Number Generators (PRNG) have attracted intense attention due to their obvious importance for many branches of science and technology. A randomizing technique is a procedure designed to improve the PRNG randomness degree according the specific requirements. It is obviously important to quantify its effectiveness. In order to classify randomizing techniques based on a symbolic dynamics' approach, we advance a novel, physically motivated representation based on the statistical properties of chaotic systems. Recourse is made to a plane that has as coordinates (i) the Shannon entropy and (ii) a form of the statistical complexity measure. Each statistical quantifier incorporates a different probability distribution function, generating thus a representation that (i) sheds insight into just how each randomizing technique operates and also (ii) quantifies its effectiveness. Using the Logistic Map and the Three Way Bernoulli Map as typical examples of chaotic dynamics it is shown that our methodology allows for choosing the more convenient randomizing technique in each instance. Comparison with measures of complexity based on diagonal lines on the recurrence plots [N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Phys. Rep. 438 (2007) 237] support the main conclusions of this paper. © 2008 Elsevier Ltd. All rights reserved. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03784371_v387_n14_p3373_DeMicco http://hdl.handle.net/20.500.12110/paper_03784371_v387_n14_p3373_DeMicco
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Permutation entropy Pseudo random number generators Statistical complexity Symbolic dynamics Chaotic systems Probability distributions Statistical methods Permutation entropy Pseudo random number generators Statistical complexity Symbolic dynamics Random number generation
spellingShingle	Permutation entropy Pseudo random number generators Statistical complexity Symbolic dynamics Chaotic systems Probability distributions Statistical methods Permutation entropy Pseudo random number generators Statistical complexity Symbolic dynamics Random number generation Randomizing nonlinear maps via symbolic dynamics
topic_facet	Permutation entropy Pseudo random number generators Statistical complexity Symbolic dynamics Chaotic systems Probability distributions Statistical methods Permutation entropy Pseudo random number generators Statistical complexity Symbolic dynamics Random number generation
description	Pseudo Random Number Generators (PRNG) have attracted intense attention due to their obvious importance for many branches of science and technology. A randomizing technique is a procedure designed to improve the PRNG randomness degree according the specific requirements. It is obviously important to quantify its effectiveness. In order to classify randomizing techniques based on a symbolic dynamics' approach, we advance a novel, physically motivated representation based on the statistical properties of chaotic systems. Recourse is made to a plane that has as coordinates (i) the Shannon entropy and (ii) a form of the statistical complexity measure. Each statistical quantifier incorporates a different probability distribution function, generating thus a representation that (i) sheds insight into just how each randomizing technique operates and also (ii) quantifies its effectiveness. Using the Logistic Map and the Three Way Bernoulli Map as typical examples of chaotic dynamics it is shown that our methodology allows for choosing the more convenient randomizing technique in each instance. Comparison with measures of complexity based on diagonal lines on the recurrence plots [N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Phys. Rep. 438 (2007) 237] support the main conclusions of this paper. © 2008 Elsevier Ltd. All rights reserved.
title	Randomizing nonlinear maps via symbolic dynamics
title_short	Randomizing nonlinear maps via symbolic dynamics
title_full	Randomizing nonlinear maps via symbolic dynamics
title_fullStr	Randomizing nonlinear maps via symbolic dynamics
title_full_unstemmed	Randomizing nonlinear maps via symbolic dynamics
title_sort	randomizing nonlinear maps via symbolic dynamics
publishDate	2008
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03784371_v387_n14_p3373_DeMicco http://hdl.handle.net/20.500.12110/paper_03784371_v387_n14_p3373_DeMicco
_version_	1768544184574148608

Randomizing nonlinear maps via symbolic dynamics

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