Characterization of chaotic maps using the permutation Bandt-Pompe probability distribution

Rosso, Osvaldo A.; Olivares, F.; Zunino, Luciano; Micco, Luciana De; Aquino, André L. L.; Plastino, A.; Larrondo, H.A.

doi:10.1140/epjb/e2013-30764-5

Cited by 64 publications

(73 citation statements)

References 54 publications

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“…A closer look reveals that our results are in the chaotic attractors zone, corresponding to the localization of a dissipative chaotic system. As can be appreciated from the contrast of our results with the one being shown in [42], in which the Bandt-Pompe pdf was evaluated considering D = 6 (pattern length), τ = 1 (time lag), our results correspond to the localization of a chaotic dissipative system: the Tinkerbell map X-component [42]. EEGs reflect the electrical activity of the brain, and the problem of analyzing and interpreting the meaning of these signals has received a great deal of attention.…”

Section: Resultscontrasting

confidence: 83%

“…This technique, as opposed to most of those in current practice, takes into account the temporal structure of the time series generated by the physical process under study. This feature allows us to uncover important details concerning the ordinal structure of the time series [19,41,42] and can also yield information about temporal correlation [15,16].…”

Section: The Bandt-pompe Approach To the Pdf Determinationmentioning

confidence: 99%

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Entropy-Complexity Characterization of Brain Development in Chickens

Montani

Rosso

2014

Entropy

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Electroencephalography (EEG) reflects the electrical activity of the brain, which can be considered chaotic and ruled by a nonlinear dynamics. Chickens exhibit a protracted period of maturation, and this temporal separation of the synapse formation and maturation phases is analogous to human neural development, though the changes in chickens occur in weeks compared to years in humans. The development of synaptic networks in the chicken brain can be regarded as occurring in two broadly defined phases. We specifically describe the chicken brain development phases in the causality entropy-complexity plane H × C, showing that the complexity of the electrical activity can be characterized by estimating the intrinsic correlational structure of the EEG signal. This allows us to identify the dynamics of the developing chicken brain within the zone of a chaotic dissipative behavior in the plane H × C.

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Section: Resultscontrasting

confidence: 83%

Section: The Bandt-pompe Approach To the Pdf Determinationmentioning

confidence: 99%

Entropy-Complexity Characterization of Brain Development in Chickens

Montani

Rosso

2014

Entropy

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“…Rosso et al [30] also found that f −k power spectrum correlated stochastic processes with 0 < k ≤ 3 are characterized by intermediate permutation entropy and intermediate statistical complexity values between C min JS and C max JS . Similar planar localization were also found for fractional Brownian motion (fBm) and fractional Gaussian noise (fGn) dynamics [9,10,30].…”

Section: The Causality Entropy-complexity Planesupporting

confidence: 71%

Characterization of vehicle behavior with information theory

et al. 2015

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This work proposes the use of Information Theory for the characterization of vehicles behavior through their velocities. Three public data sets were used: i. Mobile Century data set collected on Highway I-880, near Union City, California; ii. Borlänge GPS data set collected in the Swedish city of Borlänge; and iii. Beijing taxicabs data set collected in Beijing, China, where each vehicle speed is stored as a time series. The Bandt-Pompe methodology combined with the Complexity-Entropy plane were used to identify different regimes and behaviors. The global velocity is compatible with a correlated noise with f −k Power Spectrum with k ≥ 0. With this we identify traffic behaviors as, for instance, random velocities (k ≃ 0) when there is congestion, and more correlated velocities (k ≃ 3) in the presence of free traffic flow.

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“…This technique, as opposed to most of those in current practice, takes into account the temporal structure of the time series generated by the physical process under study. This feature allows us to uncover important details concerning the ordinal structure of the time series [23,33,34] and can also yield information about temporal correlation [35,36].…”

Section: The Bandt Pompe Methods For Pdf Evaluationmentioning

confidence: 99%

A permutation information theory tour through different interest rate maturities: the Libor case

Bariviera

Guercio

Martínez

et al. 2015

Phil. Trans. R. Soc. A.

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This paper analyzes Libor interest rates for seven different maturities and referred to operations in British Pounds, Euro, Swiss Francs and Japanese Yen, during the period years 2001 to 2015. The analysis is performed by means of two quantifiers derived from Information Theory: the permutation Shannon entropy and the permutation Fisher information measure. An anomalous behavior in the Libor is detected in all currencies except Euro during the years 2006-2012. The stochastic switch is more severe in 1, 2 and 3 months maturities. Given the special mechanism of Libor setting, we conjecture that the behavior could have been produced 1 by the manipulation that was uncovered by financial authorities. We argue that our methodology is pertinent as a market overseeing instrument.

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Characterization of chaotic maps using the permutation Bandt-Pompe probability distribution

Cited by 64 publications

References 54 publications

Entropy-Complexity Characterization of Brain Development in Chickens

Entropy-Complexity Characterization of Brain Development in Chickens

Characterization of vehicle behavior with information theory

A permutation information theory tour through different interest rate maturities: the Libor case

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