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Stosic D, Stosic D, Stosic T, Stosic B. Generalized weighted permutation entropy. CHAOS (WOODBURY, N.Y.) 2022; 32:103105. [PMID: 36319309 DOI: 10.1063/5.0107427] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Accepted: 09/12/2022] [Indexed: 06/16/2023]
Abstract
A novel heuristic approach is proposed here for time series data analysis, dubbed Generalized weighted permutation entropy, which amalgamates and generalizes beyond their original scope two well established data analysis methods: Permutation entropy and Weighted permutation entropy. The method introduces a scaling parameter to discern the disorder and complexity of ordinal patterns with small and large fluctuations. Using this scaling parameter, the complexity-entropy causality plane is generalized to the complexity-entropy-scale causality box. Simulations conducted on synthetic series generated by stochastic, chaotic, and random processes, as well as real world data, are shown to produce unique signatures in this three dimensional representation.
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Affiliation(s)
- Darko Stosic
- Centro de Informática, Universidade Federal de Pernambuco, Av. Luiz Freire s/n, 50670-901 Recife, PE, Brazil
| | - Dusan Stosic
- Centro de Informática, Universidade Federal de Pernambuco, Av. Luiz Freire s/n, 50670-901 Recife, PE, Brazil
| | - Tatijana Stosic
- Departamento de Estatística e Informática, Universidade Federal Rural de Pernambuco, Rua Dom Manoel de Medeiros s/n, Dois Irm aos, 52171-900 Recife, PE, Brazil
| | - Borko Stosic
- Departamento de Estatística e Informática, Universidade Federal Rural de Pernambuco, Rua Dom Manoel de Medeiros s/n, Dois Irm aos, 52171-900 Recife, PE, Brazil
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2
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Permutation Entropy and Statistical Complexity Analysis of Brazilian Agricultural Commodities. ENTROPY 2019. [PMCID: PMC7514564 DOI: 10.3390/e21121220] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Agricultural commodities are considered perhaps the most important commodities, as any abrupt increase in food prices has serious consequences on food security and welfare, especially in developing countries. In this work, we analyze predictability of Brazilian agricultural commodity prices during the period after 2007/2008 food crisis. We use information theory based method Complexity/Entropy causality plane (CECP) that was shown to be successful in the analysis of market efficiency and predictability. By estimating information quantifiers permutation entropy and statistical complexity, we associate to each commodity the position in CECP and compare their efficiency (lack of predictability) using the deviation from a random process. Coffee market shows highest efficiency (lowest predictability) while pork market shows lowest efficiency (highest predictability). By analyzing temporal evolution of commodities in the complexity–entropy causality plane, we observe that during the analyzed period (after 2007/2008 crisis) the efficiency of cotton, rice, and cattle markets increases, the soybeans market shows the decrease in efficiency until 2012, followed by the lower predictability and the increase of efficiency, while most commodities (8 out of total 12) exhibit relatively stable efficiency, indicating increased market integration in post-crisis period.
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Wu P, Guo L, Duan Y, Zhou W, He G. Control loop performance monitoring based on weighted permutation entropy and control charts. CAN J CHEM ENG 2018. [DOI: 10.1002/cjce.23366] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Ping Wu
- Faculty of Mechanical Engineering & AutomationZhejiang Sci‐Tech UniversityHangzhou 310018 ZhejiangChina
| | - Lingling Guo
- Faculty of Mechanical Engineering & AutomationZhejiang Sci‐Tech UniversityHangzhou 310018 ZhejiangChina
| | - Yiyong Duan
- Faculty of Mechanical Engineering & AutomationZhejiang Sci‐Tech UniversityHangzhou 310018 ZhejiangChina
| | - Wei Zhou
- Faculty of Mechanical Engineering & AutomationZhejiang Sci‐Tech UniversityHangzhou 310018 ZhejiangChina
| | - Guojun He
- Zhejiang ZHENERGY Natural Gas Operation Co., Ltd.Hangzhou310058ZhejiangChina
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Mao X, Shang P, Wang J, Ma Y. Characterizing time series by extended complexity-entropy curves based on Tsallis, Rényi, and power spectral entropy. CHAOS (WOODBURY, N.Y.) 2018; 28:113106. [PMID: 30501212 PMCID: PMC9984240 DOI: 10.1063/1.5038758] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2018] [Accepted: 10/14/2018] [Indexed: 06/09/2023]
Abstract
In this paper, we create three different entropy curves, Tsallis q-complexity-entropy curve, Rényi r-complexity-entropy curve, and Tsallis-Rényi entropy curve via extending the traditional complexity-entropy causality plane and replacing the permutation entropy into power spectral entropy. This kind of method is free of any parameters and some features that are obscure in the time domain can be extracted in the frequency domain. Results from numerical simulations verify that these three entropy curves can characterize time series efficiently. Chaotic and stochastic time series can be distinguished based on whether the q-complexity-entropy curves are opened or closed. The unrelated stochastic process has a negative curvature associated with the Rényi r-complexity-entropy curve, whereas there are positive curvatures for related cases. In addition, the Tsallis-Rényi entropy curve can display the relationship between two entropies. Finally, we apply this method to sleep electrocardiogram and electroencephalography signals. It is proved that these signals possess similar features with long-range correlated 1/f noise. It is robust enough to exhibit different characteristics for each sleep stage. By using surrogate data sets, the nonlinearity of simulated chaotic time series and sleep data can be identified.
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Affiliation(s)
- Xuegeng Mao
- School of Science, Beijing Jiaotong University, Beijing 100044, People’s Republic of China
| | - Pengjian Shang
- School of Science, Beijing Jiaotong University, Beijing 100044, People’s Republic of China
| | - Jing Wang
- Department of Computer Science and Technology, School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, People’s Republic of China
| | - Yan Ma
- Division of Interdisciplinary Medicine and Biotechnology, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, Massachusetts 02215-5400, USA
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Gleiser M, Sowinski D. Configurational information approach to instantons and false vacuum decay in
D
-dimensional spacetime. Int J Clin Exp Med 2018. [DOI: 10.1103/physrevd.98.056026] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
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Aronis KN, Berger RD, Calkins H, Chrispin J, Marine JE, Spragg DD, Tao S, Tandri H, Ashikaga H. Is human atrial fibrillation stochastic or deterministic?-Insights from missing ordinal patterns and causal entropy-complexity plane analysis. CHAOS (WOODBURY, N.Y.) 2018; 28:063130. [PMID: 29960392 PMCID: PMC6026026 DOI: 10.1063/1.5023588] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2018] [Accepted: 06/11/2018] [Indexed: 06/08/2023]
Abstract
The mechanism of atrial fibrillation (AF) maintenance in humans is yet to be determined. It remains controversial whether cardiac fibrillatory dynamics are the result of a deterministic or a stochastic process. Traditional methods to differentiate deterministic from stochastic processes have several limitations and are not reliably applied to short and noisy data obtained during clinical studies. The appearance of missing ordinal patterns (MOPs) using the Bandt-Pompe (BP) symbolization is indicative of deterministic dynamics and is robust to brief time series and experimental noise. Our aim was to evaluate whether human AF dynamics is the result of a stochastic or a deterministic process. We used 38 intracardiac atrial electrograms during AF from the coronary sinus of 10 patients undergoing catheter ablation of AF. We extracted the intervals between consecutive atrial depolarizations (AA interval) and converted the AA interval time series to their BP symbolic representation (embedding dimension 5, time delay 1). We generated 40 iterative amplitude-adjusted, Fourier-transform (IAAFT) surrogate data for each of the AA time series. IAAFT surrogates have the same frequency spectrum, autocorrelation, and probability distribution with the original time series. Using the BP symbolization, we compared the number of MOPs and the rate of MOP decay in the first 1000 timepoints of the original time series with that of the surrogate data. We calculated permutation entropy and permutation statistical complexity and represented each time series on the causal entropy-complexity plane. We demonstrated that (a) the number of MOPs in human AF is significantly higher compared to the surrogate data (2.7 ± 1.18 vs. 0.39 ± 0.28, p < 0.001); (b) the median rate of MOP decay in human AF was significantly lower compared with the surrogate data (6.58 × 10-3 vs. 7.79 × 10-3, p < 0.001); and (c) 81.6% of the individual recordings had a rate of decay lower than the 95% confidence intervals of their corresponding surrogates. On the causal entropy-complexity plane, human AF lay on the deterministic part of the plane that was located above the trajectory of fractional Brownian motion with different Hurst exponents on the plane. This analysis demonstrates that human AF dynamics does not arise from a rescaled linear stochastic process or a fractional noise, but either a deterministic or a nonlinear stochastic process. Our results justify the development and application of mathematical analysis and modeling tools to enable predictive control of human AF.
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Affiliation(s)
- Konstantinos N. Aronis
- Cardiac Arrhythmia Service, Johns Hopkins University School of Medicine, Baltimore, Maryland 21287, USA
| | - Ronald D. Berger
- Cardiac Arrhythmia Service, Johns Hopkins University School of Medicine, Baltimore, Maryland 21287, USA
| | - Hugh Calkins
- Cardiac Arrhythmia Service, Johns Hopkins University School of Medicine, Baltimore, Maryland 21287, USA
| | - Jonathan Chrispin
- Cardiac Arrhythmia Service, Johns Hopkins University School of Medicine, Baltimore, Maryland 21287, USA
| | - Joseph E. Marine
- Cardiac Arrhythmia Service, Johns Hopkins University School of Medicine, Baltimore, Maryland 21287, USA
| | - David D. Spragg
- Cardiac Arrhythmia Service, Johns Hopkins University School of Medicine, Baltimore, Maryland 21287, USA
| | - Susumu Tao
- Cardiac Arrhythmia Service, Johns Hopkins University School of Medicine, Baltimore, Maryland 21287, USA
| | - Harikrishna Tandri
- Cardiac Arrhythmia Service, Johns Hopkins University School of Medicine, Baltimore, Maryland 21287, USA
| | - Hiroshi Ashikaga
- Author to whom correspondence should be addressed: . Telephone: 410-955-7534. Fax: 443-873-5019
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Zhang W, Liu P, Guo H, Wang J. Detecting the chaotic nature in a transitional boundary layer using symbolic information-theory quantifiers. Phys Rev E 2018; 96:052215. [PMID: 29347703 DOI: 10.1103/physreve.96.052215] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2017] [Indexed: 11/07/2022]
Abstract
The permutation entropy and the statistical complexity are employed to study the boundary-layer transition induced by the surface roughness. The velocity signals measured in the transition process are analyzed with these symbolic quantifiers, as well as the complexity-entropy causality plane, and the chaotic nature of the instability fluctuations is identified. The frequency of the dominant fluctuations has been found according to the time scales corresponding to the extreme values of the symbolic quantifiers. The laminar-turbulent transition process is accompanied by the evolution in the degree of organization of the complex eddy motions, which is also characterized with the growing smaller and flatter circles in the complexity-entropy causality plane. With the help of the permutation entropy and the statistical complexity, the differences between the chaotic fluctuations detected in the experiments and the classical Tollmien-Schlichting wave are shown and discussed. It is also found that the chaotic features of the instability fluctuations can be approximated with a number of regular sine waves superimposed on the fluctuations of the undisturbed laminar boundary layer. This result is related to the physical mechanism in the generation of the instability fluctuations, which is the noise-induced chaos.
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Affiliation(s)
- Wen Zhang
- Key Laboratory of Aero-Acoustics (Beihang University), Ministry of Industry and Information Technology and Key Laboratory of Fluid Mechanics (Beihang University), Ministry of Education, Beijing 100083, People's Republic of China
| | - Peiqing Liu
- Key Laboratory of Aero-Acoustics (Beihang University), Ministry of Industry and Information Technology and Key Laboratory of Fluid Mechanics (Beihang University), Ministry of Education, Beijing 100083, People's Republic of China
| | - Hao Guo
- Key Laboratory of Aero-Acoustics (Beihang University), Ministry of Industry and Information Technology and Key Laboratory of Fluid Mechanics (Beihang University), Ministry of Education, Beijing 100083, People's Republic of China
| | - Jinjun Wang
- Key Laboratory of Aero-Acoustics (Beihang University), Ministry of Industry and Information Technology and Key Laboratory of Fluid Mechanics (Beihang University), Ministry of Education, Beijing 100083, People's Republic of China
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Takagi K, Gotoda H, Tokuda IT, Miyano T. Nonlinear dynamics of a buoyancy-induced turbulent fire. Phys Rev E 2017; 96:052223. [PMID: 29347727 DOI: 10.1103/physreve.96.052223] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2017] [Indexed: 11/07/2022]
Abstract
We conduct a numerical study on the dynamic behavior of a buoyancy-induced turbulent fire from the viewpoints of symbolic dynamics, complex networks, and statistical complexity. Here, we consider two classes of entropies: the permutation entropy and network entropy in ε-recurrence networks, both of which evaluate the degree of randomness in the underlying dynamics. These entropies enable us to capture the significant changes in the dynamic behavior of flow velocity fluctuations. The possible presence of two important dynamics, low-dimensional deterministic chaos in the near field dominated by the motion of large-scale vortices and high-dimensional chaos in the far field forming a well-developed turbulent plume, is clearly identified by the multiscale complexity-entropy causality plane.
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Affiliation(s)
- Kazushi Takagi
- Department of Mechanical Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, Japan
| | - Hiroshi Gotoda
- Department of Mechanical Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, Japan
| | - Isao T Tokuda
- Department of Mechanical Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan
| | - Takaya Miyano
- Department of Mechanical Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan
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10
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Randomness Representation of Turbulence in Canopy Flows Using Kolmogorov Complexity Measures. ENTROPY 2017. [DOI: 10.3390/e19100519] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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11
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Ribeiro HV, Jauregui M, Zunino L, Lenzi EK. Characterizing time series via complexity-entropy curves. Phys Rev E 2017; 95:062106. [PMID: 28709196 DOI: 10.1103/physreve.95.062106] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2017] [Indexed: 06/07/2023]
Abstract
The search for patterns in time series is a very common task when dealing with complex systems. This is usually accomplished by employing a complexity measure such as entropies and fractal dimensions. However, such measures usually only capture a single aspect of the system dynamics. Here, we propose a family of complexity measures for time series based on a generalization of the complexity-entropy causality plane. By replacing the Shannon entropy by a monoparametric entropy (Tsallis q entropy) and after considering the proper generalization of the statistical complexity (q complexity), we build up a parametric curve (the q-complexity-entropy curve) that is used for characterizing and classifying time series. Based on simple exact results and numerical simulations of stochastic processes, we show that these curves can distinguish among different long-range, short-range, and oscillating correlated behaviors. Also, we verify that simulated chaotic and stochastic time series can be distinguished based on whether these curves are open or closed. We further test this technique in experimental scenarios related to chaotic laser intensity, stock price, sunspot, and geomagnetic dynamics, confirming its usefulness. Finally, we prove that these curves enhance the automatic classification of time series with long-range correlations and interbeat intervals of healthy subjects and patients with heart disease.
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Affiliation(s)
- Haroldo V Ribeiro
- Departamento de Física, Universidade Estadual de Maringá, Maringá, PR 87020-900, Brazil
| | - Max Jauregui
- Departamento de Física, Universidade Estadual de Maringá, Maringá, PR 87020-900, Brazil
| | - Luciano Zunino
- Centro de Investigaciones Ópticas (CONICET La Plata - CIC), C.C. 3, 1897 Gonnet, Argentina
- Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP), 1900 La Plata, Argentina
| | - Ervin K Lenzi
- Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa, PR 84030-900, Brazil
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12
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Politi A. Quantifying the Dynamical Complexity of Chaotic Time Series. PHYSICAL REVIEW LETTERS 2017; 118:144101. [PMID: 28430461 DOI: 10.1103/physrevlett.118.144101] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2016] [Indexed: 06/07/2023]
Abstract
A powerful approach is proposed for the characterization of chaotic signals. It is based on the combined use of two classes of indicators: (i) the probability of suitable symbolic sequences (obtained from the ordinal patterns of the corresponding time series); (ii) the width of the corresponding cylinder sets. This way, much information can be extracted and used to quantify the complexity of a given signal. As an example of the potentiality of the method, I introduce a modified permutation entropy which allows for quantitative estimates of the Kolmogorov-Sinai entropy in hyperchaotic models, where other methods would be unpractical. As a by-product, estimates of the fractal dimension of the underlying attractors are possible as well.
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Affiliation(s)
- Antonio Politi
- Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, AB24 3UE, Aberdeen, United Kingdom
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Gotoda H, Kobayashi H, Hayashi K. Chaotic dynamics of a swirling flame front instability generated by a change in gravitational orientation. Phys Rev E 2017; 95:022201. [PMID: 28297884 DOI: 10.1103/physreve.95.022201] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2016] [Indexed: 06/06/2023]
Abstract
We have intensively examined the dynamic behavior of flame front instability in a lean swirling premixed flame generated by a change in gravitational orientation [H. Gotoda, T. Miyano, and I. G. Shepherd, Phys. Rev. E 81, 026211 (2010)PLEEE81539-375510.1103/PhysRevE.81.026211] from the viewpoints of complex networks, symbolic dynamics, and statistical complexity. Here, we considered the permutation entropy in combination with the surrogate data method, the permutation spectrum test, and the multiscale complexity-entropy causality plane incorporating a scale-dependent approach, none of which have been considered in the study of flame front instabilities. Our results clearly show the possible presence of chaos in flame front dynamics induced by the coupling of swirl-buoyancy interaction in inverted gravity. The flame front dynamics also possesses a scale-free structure, which is reasonably shown by the probability distribution of the degree in ε-recurrence networks.
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Affiliation(s)
- Hiroshi Gotoda
- Department of Mechanical Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, Japan
| | - Hiroaki Kobayashi
- Department of Mechanical Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, Japan
| | - Kenta Hayashi
- Department of Mechanical Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan
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