1
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Meinardi VB, López JMD, Fajreldines HD, Boyallian C, Balzarini M. Linear mixed-effect models for correlated response to process electroencephalogram recordings. Cogn Neurodyn 2024; 18:1197-1207. [PMID: 38826650 PMCID: PMC11143122 DOI: 10.1007/s11571-023-09984-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2022] [Revised: 04/06/2023] [Accepted: 05/31/2023] [Indexed: 06/04/2024] Open
Abstract
A data set of clinical studies of electroencephalogram recordings (EEG) following data acquisition protocols in control individuals (Eyes Closed Wakefulness - Eyes Open Wakefulness, Hyperventilation, and Optostimulation) are quantified with information theory metrics, namely permutation Shanon entropy and permutation Lempel Ziv complexity, to identify functional changes. This work implement Linear mixed-effects models (LMEMs) for confirmatory hypothesis testing. The results show that EEGs have high variability for both metrics and there is a positive correlation between them. The mean of permutation Lempel-Ziv complexity and permutation Shanon entropy used simultaneously for each of the four states are distinguishable from each other. However, used separately, the differences between permutation Lempel-Ziv complexity or permutation Shanon entropy of some states were not statistically significant. This shows that the joint use of both metrics provides more information than the separate use of each of them. Despite their wide use in medicine, LMEMs have not been commonly applied to simultaneously model metrics that quantify EEG signals. Modeling EEGs using a model that characterizes more than one response variable and their possible correlations represents a new way of analyzing EEG data in neuroscience.
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Affiliation(s)
- Vanesa B. Meinardi
- I.A.P Ciencias Humanas, Universidad Nacional de Villa María, Arturo Jauretche 1555, 5900 Villa María, Córdoba, Argentina
- Centro de Investigación y Transferencia. UNVM, Arturo Jauretche 1555, 5900 Córdoba, Argentina
| | - Juan M. Díaz López
- Instituto Argentino de Ciencias de la Conducta (IACCo), Entre Ríos 419, 5000 Córdoba, Argentina
- Facultad de Matemática, Física, Astronomía y Computación, Universidad Nacional de Córdoba. Haya de la Torre y Medina Allende, Ciudad Universitaria, 5000 Córdoba, Argentina
- Facultad de Ciencias Químicas, Universidad Nacional de Córdoba. Haya de la Torre y Medina Allende, Ciudad Universitaria, 5000 Córdoba, Argentina
| | - Hugo Diaz Fajreldines
- Departamento de Investigaciones Biomédicas, Instituto Privado de Neurociencias. Felix, Fríaz 129, 5000 Córdoba, Argentina
- Facultad de Ciencias Químicas, Universidad Nacional de Córdoba. Haya de la Torre y Medina Allende, Ciudad Universitaria, 5000 Córdoba, Argentina
| | - Carina Boyallian
- Centro de Investigación y Estudios de Matemática. Famaf, UNC., Haya de la Torre y Medina Allende, Ciudad Universitaria, 5000 Córdoba, Argentina
- Facultad de Matemática, Física, Astronomía y Computación, Universidad Nacional de Córdoba. Haya de la Torre y Medina Allende, Ciudad Universitaria, 5000 Córdoba, Argentina
| | - Monica Balzarini
- Estadística y Biometría, Universidad Nacional de Córdoba, UFYMA INTA-CONICET. Camino 60 cuadras km 5 1/2 s/n, 5020 Córdoba, Argentina
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2
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Correia JP. Multifractal analysis of maize and soybean DNA. Sci Rep 2024; 14:10687. [PMID: 38724570 PMCID: PMC11082218 DOI: 10.1038/s41598-024-60722-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2023] [Accepted: 04/26/2024] [Indexed: 05/12/2024] Open
Abstract
This paper investigates the complexity of DNA sequences in maize and soybean using the multifractal detrended fluctuation analysis (MF-DFA) method, chaos game representation (CGR), and the complexity-entropy plane approach. The study aims to understand the patterns and structures of these DNA sequences, which can provide insights into their genetic makeup and improve crop yield and quality. The results show that maize and soybean DNA sequences exhibit fractal properties, indicating a complex and self-organizing structure. We observe the persistence trend between sequences of base pairs, which indicates long-range correlations between base pairs. We also identified the stochastic nature of the DNA sequences of both species.
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Affiliation(s)
- J P Correia
- Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal, RN, 59072-970, Brasil.
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3
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Voltarelli LGJM, Pessa AAB, Zunino L, Zola RS, Lenzi EK, Perc M, Ribeiro HV. Characterizing unstructured data with the nearest neighbor permutation entropy. CHAOS (WOODBURY, N.Y.) 2024; 34:053130. [PMID: 38780438 DOI: 10.1063/5.0209206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2024] [Accepted: 04/25/2024] [Indexed: 05/25/2024]
Abstract
Permutation entropy and its associated frameworks are remarkable examples of physics-inspired techniques adept at processing complex and extensive datasets. Despite substantial progress in developing and applying these tools, their use has been predominantly limited to structured datasets such as time series or images. Here, we introduce the k-nearest neighbor permutation entropy, an innovative extension of the permutation entropy tailored for unstructured data, irrespective of their spatial or temporal configuration and dimensionality. Our approach builds upon nearest neighbor graphs to establish neighborhood relations and uses random walks to extract ordinal patterns and their distribution, thereby defining the k-nearest neighbor permutation entropy. This tool not only adeptly identifies variations in patterns of unstructured data but also does so with a precision that significantly surpasses conventional measures such as spatial autocorrelation. Additionally, it provides a natural approach for incorporating amplitude information and time gaps when analyzing time series or images, thus significantly enhancing its noise resilience and predictive capabilities compared to the usual permutation entropy. Our research substantially expands the applicability of ordinal methods to more general data types, opening promising research avenues for extending the permutation entropy toolkit for unstructured data.
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Affiliation(s)
| | - Arthur A B Pessa
- Departamento de Física, Universidade Estadual de Maringá, Maringá PR 87020-900, Brazil
| | - Luciano Zunino
- Centro de Investigaciones Ópticas (CONICET La Plata - CIC - UNLP), 1897 Gonnet, La Plata, Argentina
- Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP), 1900 La Plata, Argentina
| | - Rafael S Zola
- Departamento de Física, Universidade Estadual de Maringá, Maringá PR 87020-900, Brazil
- Departamento de Física, Universidade Tecnológica Federal do Paraná, Apucarana PR 86812-460, Brazil
| | - Ervin K Lenzi
- Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa PR 84030-900, Brazil
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
- Community Healthcare Center Dr. Adolf Drolc Maribor, Vošnjakova ulica 2, 2000 Maribor, Slovenia
- Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
- Department of Physics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, Republic of Korea
| | - Haroldo V Ribeiro
- Departamento de Física, Universidade Estadual de Maringá, Maringá PR 87020-900, Brazil
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4
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Szwajka K, Zielińska-Szwajka J, Trzepieciński T. Experimental Analysis of Smart Drilling for the Furniture Industry in the Era of Industry 4.0. MATERIALS (BASEL, SWITZERLAND) 2024; 17:2033. [PMID: 38730844 PMCID: PMC11084552 DOI: 10.3390/ma17092033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2024] [Revised: 04/21/2024] [Accepted: 04/24/2024] [Indexed: 05/13/2024]
Abstract
The fact is that hundreds of holes are drilled in the assembly process of furniture sets, so intelligent drilling is a key element in maximizing efficiency. Increasing the feed rate or the cutting speed in materials characterized by a higher machinability index is necessary. Smart drilling, that is, the real-time adjustment of the cutting parameters, requires the evolution of cutting process variables. In addition, it is necessary to control and adjust the processing parameters in real time. Machinability is one of the most important technological properties in the machining process, enabling the determination of the material's susceptibility to machining. One of the machinability indicators is the unit cutting resistance. This article proposes a method of material identification using the short-time Fourier transform in order to automatically adjust cutting parameters during drilling based on force signals, cutting torque and acceleration signals. In the tests, four types of wood-based materials were used as the processed material: medium-density fiberboard, chipboard, plywood board and high-pressure laminate. Holes with a diameter of 10 mm were drilled in the test materials, with variable feed rate, cutting speed and thickness of cutting layer. An innovative method for determining the value of unit cutting resistance was proposed. The results obtained were used to determine the machinability index. Based on the test results, it was shown that both the selected signal measures in the time and frequency domains and the unit cutting resistance are constant for a given material of a workpiece and do not depend on the drilling process parameters. In this article, the methodology is proposed, which can be used as an intelligent technique to support the drilling process to detect the material being machined using data from sensors installed on the machine tool. The work proposes the fundamentals for material identification based on the analysis of force signals and the magnitude of force derivatives. The proposed methodology shows effectiveness, which proves that it can be used in intelligent drilling processes. Hybrid wood-based material structures consisting of different materials are becoming more and more common in building structures for strength, economic and environmental reasons. Due to the difference in the machinability of interconnected materials, cutting parameters must be optimized in real time during machining. Currently, with the rapid development of Industry 4.0, the on-line identification of parameters is becoming necessary to improve the process flow in industrial reality. The proposed methodology can be used as an intelligent technique to support the drilling process in order to detect the material being processed using data from sensors installed on the machine tool.
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Affiliation(s)
- Krzysztof Szwajka
- Department of Integrated Design and Tribology Systems, Faculty of Mechanics and Technology, Rzeszow University of Technology, ul. Kwiatkowskiego 4, 37-450 Stalowa Wola, Poland
| | - Joanna Zielińska-Szwajka
- Department of Component Manufacturing and Production Organization, Faculty of Mechanics and Technology, Rzeszow University of Technology, ul. Kwiatkowskiego 4, 37-450 Stalowa Wola, Poland;
| | - Tomasz Trzepieciński
- Department of Manufacturing Processes and Production Engineering, Rzeszow University of Technology, al. Powstańców Warszawy 8, 35-959 Rzeszów, Poland;
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5
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Vishnoi N, Gupta V, Saurabh A, Kabiraj L. Effect of correlation time of combustion noise on early warning indicators of thermoacoustic instability. CHAOS (WOODBURY, N.Y.) 2024; 34:033129. [PMID: 38498813 DOI: 10.1063/5.0174468] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2023] [Accepted: 02/23/2024] [Indexed: 03/20/2024]
Abstract
In this paper, we analyze the effects of finite correlation time (noise color) of combustion noise on noise-induced coherence and early warning indicators (EWIs) via numerical and experimental studies. We consider the Rijke tube as a prototypical combustion system and model combustion noise as an additive Ornstein-Uhlenbeck process while varying noise intensity and correlation time. We numerically investigate corresponding effects on coherence resonance and multi-fractal properties of pressure fluctuations. Subsequently, we experimentally validate results and elucidate the influence of noise color and intensity on trends in coherence resonance and multi-fractal measures that can be expected in a practical scenario using an electroacoustic simulator. We find that the coherence factor, which quantifies the relative contribution of coherent oscillations in a noisy signal, increases as the system approaches the thermoacoustic instability-irrespective of the correlation time. It works at most levels of combustion noise (except for too low and too high noise levels). The Hurst exponent reduces as the system approaches thermoacoustic instability only when the correlation time is small. These results have implications on the prediction and monitoring of thermoacoustic instability in practical combustors.
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Affiliation(s)
- Neha Vishnoi
- Department of Mechanical Engineering, Indian Institute of Technology Ropar, Punjab 140001, India
| | - Vikrant Gupta
- Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Aditya Saurabh
- Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India
| | - Lipika Kabiraj
- Department of Mechanical Engineering, Indian Institute of Technology Ropar, Punjab 140001, India
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6
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Jiang R, Shang P. Dispersion complexity-entropy curves: An effective method to characterize the structures of nonlinear time series. CHAOS (WOODBURY, N.Y.) 2024; 34:033137. [PMID: 38526984 DOI: 10.1063/5.0197167] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2024] [Accepted: 02/27/2024] [Indexed: 03/27/2024]
Abstract
The complexity-entropy curve (CEC) is a valuable tool for characterizing the structure of time series and finds broad application across various research fields. Despite its widespread usage, the original permutation complexity-entropy curve (PCEC), which is founded on permutation entropy (PE), exhibits a notable limitation: its inability to take the means and amplitudes of time series into considerations. This oversight can lead to inaccuracies in differentiating time series. In this paper, drawing inspiration from dispersion entropy (DE), we propose the dispersion complexity-entropy curve (DCEC) to enhance the capability of CEC in uncovering the concealed structures within nonlinear time series. Our approach initiates with simulated data including the logistic map, color noises, and various chaotic systems. The outcomes of our simulated experiments consistently showcase the effectiveness of DCEC in distinguishing nonlinear time series with diverse characteristics. Furthermore, we extend the application of DCEC to real-world data, thereby asserting its practical utility. A novel approach is proposed, wherein DCEC-based feature extraction is combined with multivariate support vector machine for the diagnosis of various types of bearing faults. This combination achieved a high accuracy rate in our experiments. Additionally, we employ DCEC to assess stock indices from different countries and periods, thereby facilitating an analysis of the complexity inherent in financial markets. Our findings reveal significant insights into the dynamic regularities and distinct structures of these indices, offering a novel perspective for analyzing financial time series. Collectively, these applications underscore the potential of DCEC as an effective tool for the nonlinear time series analysis.
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Affiliation(s)
- Runze Jiang
- School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China
| | - Pengjian Shang
- School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China
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7
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De Gregorio J, Sánchez D, Toral R. Entropy Estimators for Markovian Sequences: A Comparative Analysis. ENTROPY (BASEL, SWITZERLAND) 2024; 26:79. [PMID: 38248204 PMCID: PMC11154276 DOI: 10.3390/e26010079] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Revised: 12/21/2023] [Accepted: 01/16/2024] [Indexed: 01/23/2024]
Abstract
Entropy estimation is a fundamental problem in information theory that has applications in various fields, including physics, biology, and computer science. Estimating the entropy of discrete sequences can be challenging due to limited data and the lack of unbiased estimators. Most existing entropy estimators are designed for sequences of independent events and their performances vary depending on the system being studied and the available data size. In this work, we compare different entropy estimators and their performance when applied to Markovian sequences. Specifically, we analyze both binary Markovian sequences and Markovian systems in the undersampled regime. We calculate the bias, standard deviation, and mean squared error for some of the most widely employed estimators. We discuss the limitations of entropy estimation as a function of the transition probabilities of the Markov processes and the sample size. Overall, this paper provides a comprehensive comparison of entropy estimators and their performance in estimating entropy for systems with memory, which can be useful for researchers and practitioners in various fields.
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Affiliation(s)
| | - David Sánchez
- Institute for Cross-Disciplinary Physics and Complex Systems IFISC (UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain; (J.D.G.); (R.T.)
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8
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Suriano M, Caram LF, Rosso OA. Daily Streamflow of Argentine Rivers Analysis Using Information Theory Quantifiers. ENTROPY (BASEL, SWITZERLAND) 2024; 26:56. [PMID: 38248181 PMCID: PMC11154540 DOI: 10.3390/e26010056] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2023] [Revised: 01/06/2024] [Accepted: 01/07/2024] [Indexed: 01/23/2024]
Abstract
This paper analyzes the temporal evolution of streamflow for different rivers in Argentina based on information quantifiers such as statistical complexity and permutation entropy. The main objective is to identify key details of the dynamics of the analyzed time series to differentiate the degrees of randomness and chaos. The permutation entropy is used with the probability distribution of ordinal patterns and the Jensen-Shannon divergence to calculate the disequilibrium and the statistical complexity. Daily streamflow series at different river stations were analyzed to classify the different hydrological systems. The complexity-entropy causality plane (CECP) and the representation of the Shannon entropy and Fisher information measure (FIM) show that the daily discharge series could be approximately represented with Gaussian noise, but the variances highlight the difficulty of modeling a series of natural phenomena. An analysis of stations downstream from the Yacyretá dam shows that the operation affects the randomness of the daily discharge series at hydrometric stations near the dam. When the station is further downstream, however, this effect is attenuated. Furthermore, the size of the basin plays a relevant role in modulating the process. Large catchments have smaller values for entropy, and the signal is less noisy due to integration over larger time scales. In contrast, small and mountainous basins present a rapid response that influences the behavior of daily discharge while presenting a higher entropy and lower complexity. The results obtained in the present study characterize the behavior of the daily discharge series in Argentine rivers and provide key information for hydrological modeling.
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Affiliation(s)
- Micaela Suriano
- Departamento de Hidráulica, Facultad de Ingeniería, Universidad de Buenos Aires, Av. Las Heras 2214, Buenos Aires C1127AAR, Argentina
- Laboratorio de Redes y Sistemas Móviles, Departamento de Electrónica, Facultad de Ingeniería, Universidad de Buenos Aires, Buenos Aires C1063ACV, Argentina;
| | - Leonidas Facundo Caram
- Laboratorio de Redes y Sistemas Móviles, Departamento de Electrónica, Facultad de Ingeniería, Universidad de Buenos Aires, Buenos Aires C1063ACV, Argentina;
| | - Osvaldo Anibal Rosso
- Instituto de Física (IFLP), Universidad Nacional de La Plata, CONICET, La Plata B1900AJJ, Argentina;
- Instituto de Física, Universidade Federal de Alagoas (UFAL), Maceió 57072-970, Brazil
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9
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Mamori H, Nabae Y, Fukuda S, Gotoda H. Dynamic state of low-Reynolds-number turbulent channel flow. Phys Rev E 2023; 108:025105. [PMID: 37723692 DOI: 10.1103/physreve.108.025105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2023] [Accepted: 07/25/2023] [Indexed: 09/20/2023]
Abstract
We numerically study the dynamic state of a low-Reynolds-number turbulent channel flow from the viewpoints of symbolic dynamics and nonlinear forecasting. A low-dimensionally (high-dimensionally) chaotic state of the streamwise velocity fluctuations emerges at a viscous sublayer (logarithmic layer). The possible presence of the chaotic states is clearly identified by orbital instability-based nonlinear forecasting and ordinal partition transition network entropy in combination with the surrogate data method.
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Affiliation(s)
- Hiroya Mamori
- Department of Mechanical and Intelligent Systems Engineering, The University of Electro-Communications, 1-5-1, Chofugaoka, Chofu, Tokyo 182-8585, Japan
| | - Yusuke Nabae
- Department of Mechanical Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, Japan
| | - Shingo Fukuda
- 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
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10
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Proverbio D, Skupin A, Gonçalves J. Systematic analysis and optimization of early warning signals for critical transitions using distribution data. iScience 2023; 26:107156. [PMID: 37456849 PMCID: PMC10338236 DOI: 10.1016/j.isci.2023.107156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 04/21/2023] [Accepted: 06/12/2023] [Indexed: 07/18/2023] Open
Abstract
Abrupt shifts between alternative regimes occur in complex systems, from cell regulation to brain functions to ecosystems. Several model-free early warning signals (EWS) have been proposed to detect impending transitions, but failure or poor performance in some systems have called for better investigation of their generic applicability. Notably, there are still ongoing debates whether such signals can be successfully extracted from data in particular from biological experiments. In this work, we systematically investigate properties and performance of dynamical EWS in different deteriorating conditions, and we propose an optimized combination to trigger warnings as early as possible, eventually verified on experimental data from microbiological populations. Our results explain discrepancies observed in the literature between warning signs extracted from simulated models and from real data, provide guidance for EWS selection based on desired systems and suggest an optimized composite indicator to alert for impending critical transitions using distribution data.
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Affiliation(s)
- Daniele Proverbio
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue Du Swing, 4367 Belvaux, Luxembourg
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QL, UK
| | - Alexander Skupin
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue Du Swing, 4367 Belvaux, Luxembourg
- National Center for Microscopy and Imaging Research, University of California San Diego, Gilman Drive, La Jolla, CA 9500, USA
- Department of Physics and Material Science, University of Luxembourg, 162a Avenue de La Faiencerie, 1511 Luxembourg, Luxembourg
| | - Jorge Gonçalves
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue Du Swing, 4367 Belvaux, Luxembourg
- Department of Plant Sciences, University of Cambridge, Cambridge CB2 3EA, UK
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11
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Shahriari Z, Algar SD, Walker DM, Small M. Ordinal Poincaré sections: Reconstructing the first return map from an ordinal segmentation of time series. CHAOS (WOODBURY, N.Y.) 2023; 33:2890082. [PMID: 37163996 DOI: 10.1063/5.0141438] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2023] [Accepted: 04/21/2023] [Indexed: 05/12/2023]
Abstract
We propose a robust algorithm for constructing first return maps of dynamical systems from time series without the need for embedding. A first return map is typically constructed using a convenient heuristic (maxima or zero-crossings of the time series, for example) or a computationally nuanced geometric approach (explicitly constructing a Poincaré section from a hyper-surface normal to the flow and then interpolating to determine intersections with trajectories). Our method is based on ordinal partitions of the time series, and the first return map is constructed from successive intersections with specific ordinal sequences. We can obtain distinct first return maps for each ordinal sequence in general. We define entropy-based measures to guide our selection of the ordinal sequence for a "good" first return map and show that this method can robustly be applied to time series from classical chaotic systems to extract the underlying first return map dynamics. The results are shown for several well-known dynamical systems (Lorenz, Rössler, and Mackey-Glass in chaotic regimes).
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Affiliation(s)
- Zahra Shahriari
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
| | - Shannon D Algar
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
| | - David M Walker
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
| | - Michael Small
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
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12
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Kottlarz I, Parlitz U. Ordinal pattern-based complexity analysis of high-dimensional chaotic time series. CHAOS (WOODBURY, N.Y.) 2023; 33:2888089. [PMID: 37133925 DOI: 10.1063/5.0147219] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 04/04/2023] [Indexed: 05/04/2023]
Abstract
The ordinal pattern-based complexity-entropy plane is a popular tool in nonlinear dynamics for distinguishing stochastic signals (noise) from deterministic chaos. Its performance, however, has mainly been demonstrated for time series from low-dimensional discrete or continuous dynamical systems. In order to evaluate the usefulness and power of the complexity-entropy (CE) plane approach for data representing high-dimensional chaotic dynamics, we applied this method to time series generated by the Lorenz-96 system, the generalized Hénon map, the Mackey-Glass equation, the Kuramoto-Sivashinsky equation, and to phase-randomized surrogates of these data. We find that both the high-dimensional deterministic time series and the stochastic surrogate data may be located in the same region of the complexity-entropy plane, and their representations show very similar behavior with varying lag and pattern lengths. Therefore, the classification of these data by means of their position in the CE plane can be challenging or even misleading, while surrogate data tests based on (entropy, complexity) yield significant results in most cases.
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Affiliation(s)
- Inga Kottlarz
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
- Institute for the Dynamics of Complex Systems, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
- Department of Pharmacology and Toxicology, University Medical Center Göttingen (UMG), Robert-Koch-Str. 40, 37075 Göttingen, Germany
- German Center for Cardiovascular Research (DZHK), partner site Göttingen, Robert-Koch-Str. 42a, 37075 Göttingen, Germany
| | - Ulrich Parlitz
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
- Institute for the Dynamics of Complex Systems, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
- German Center for Cardiovascular Research (DZHK), partner site Göttingen, Robert-Koch-Str. 42a, 37075 Göttingen, Germany
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13
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Martínez N, Deza RR, Montani F. Characterizing the information transmission of inverse stochastic resonance and noise-induced activity amplification in neuronal systems. Phys Rev E 2023; 107:054402. [PMID: 37329070 DOI: 10.1103/physreve.107.054402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Accepted: 04/13/2023] [Indexed: 06/18/2023]
Abstract
Purkinje cells exhibit a reduction of the mean firing rate at intermediate-noise intensities, which is somewhat reminiscent of the response enhancement known as "stochastic resonance" (SR). Although the comparison with the stochastic resonance ends here, the current phenomenon has been given the name "inverse stochastic resonance" (ISR). Recent research has demonstrated that the ISR effect, like its close relative "nonstandard SR" [or, more correctly, noise-induced activity amplification (NIAA)], has been shown to stem from the weak-noise quenching of the initial distribution, in bistable regimes where the metastable state has a larger attraction basin than the global minimum. To understand the underlying mechanism of the ISR and NIAA phenomena, we study the probability distribution function of a one-dimensional system subjected to a bistable potential that has the property of symmetry, i.e., if we change the sign of one of its parameters, we can obtain both phenomena with the same properties in the depth of the wells and the width of their basins of attraction subjected to Gaussian white noise with variable intensity. Previous work has shown that one can theoretically determine the probability distribution function using the convex sum between the behavior at small and high noise intensities. To determine the probability distribution function more precisely, we resort to the "weighted ensemble Brownian dynamics simulation" model, which provides an accurate estimate of the probability distribution function for both low and high noise intensities and, most importantly, for the transition of both behaviors. In this way, on the one hand, we show that both phenomena emerge from a metastable system where, in the case of ISR, the global minimum of the system is in a state of lower activity, while in the case of NIAA, the global minimum is in a state of increased activity, the importance of which does not depend on the width of the basins of attraction. On the other hand, we see that quantifiers such as Fisher information, statistical complexity, and especially Shannon entropy fail to distinguish them, but they show the existence of the mentioned phenomena. Thus, noise management may well be a mechanism by which Purkinje cells find an efficient way to transmit information in the cerebral cortex.
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Affiliation(s)
- Nataniel Martínez
- IFIMAR (CONICET), Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, B7602AYL Mar del Plata, Argentina
| | - Roberto R Deza
- IFIMAR (CONICET), Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, B7602AYL Mar del Plata, Argentina
| | - Fernando Montani
- IFLP (CONICET), Facultad de Ciencias Exactas, Universidad Nacional de La Plata, B1900 La Plata, Argentina
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14
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Haruna T. Complexity of couplings in multivariate time series via ordinal persistent homology. CHAOS (WOODBURY, N.Y.) 2023; 33:043115. [PMID: 37097928 DOI: 10.1063/5.0136772] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 03/22/2023] [Indexed: 06/19/2023]
Abstract
We propose a new measure of the complexity of couplings in multivariate time series by combining the techniques of ordinal pattern analysis and topological data analysis. We construct an increasing sequence of simplicial complexes encoding the information about couplings among the components of a given multivariate time series through the intersection of ordinal patterns. The complexity measure is then defined by making use of the persistent homology groups. We validate the complexity measure both theoretically and numerically.
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Affiliation(s)
- Taichi Haruna
- Department of Information and Sciences, School of Arts and Sciences, Tokyo Woman's Christian University, 2-6-1 Zempukuji, Suginami-ku, Tokyo 167-8585, Japan
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15
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Bandt C, Wittfeld K. Two new parameters for the ordinal analysis of images. CHAOS (WOODBURY, N.Y.) 2023; 33:043124. [PMID: 37097936 DOI: 10.1063/5.0136912] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 03/22/2023] [Indexed: 06/19/2023]
Abstract
Local patterns play an important role in statistical physics as well as in image processing. Two-dimensional ordinal patterns were studied by Ribeiro et al. who determined permutation entropy and complexity in order to classify paintings and images of liquid crystals. Here, we find that the 2 × 2 patterns of neighboring pixels come in three types. The statistics of these types, expressed by two parameters, contains the relevant information to describe and distinguish textures. The parameters are most stable and informative for isotropic structures.
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Affiliation(s)
- Christoph Bandt
- Institute of Mathematics, University of Greifswald, 17489 Greifswald, Germany
| | - Katharina Wittfeld
- Department of Psychiatry and Psychotherapy, University Medicine Greifswald, 17475 Greifswald, Germany
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16
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Guisande N, di Nunzio MP, Martinez N, Rosso OA, Montani F. Chaotic dynamics of the Hénon map and neuronal input-output: A comparison with neurophysiological data. CHAOS (WOODBURY, N.Y.) 2023; 33:043111. [PMID: 37097953 DOI: 10.1063/5.0142773] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2023] [Accepted: 03/10/2023] [Indexed: 06/19/2023]
Abstract
In this study, the Hénon map was analyzed using quantifiers from information theory in order to compare its dynamics to experimental data from brain regions known to exhibit chaotic behavior. The goal was to investigate the potential of the Hénon map as a model for replicating chaotic brain dynamics in the treatment of Parkinson's and epilepsy patients. The dynamic properties of the Hénon map were compared with data from the subthalamic nucleus, the medial frontal cortex, and a q-DG model of neuronal input-output with easy numerical implementation to simulate the local behavior of a population. Using information theory tools, Shannon entropy, statistical complexity, and Fisher's information were analyzed, taking into account the causality of the time series. For this purpose, different windows over the time series were considered. The findings revealed that neither the Hénon map nor the q-DG model could perfectly replicate the dynamics of the brain regions studied. However, with careful consideration of the parameters, scales, and sampling used, they were able to model some characteristics of neural activity. According to these results, normal neural dynamics in the subthalamic nucleus region may present a more complex spectrum within the complexity-entropy causality plane that cannot be represented by chaotic models alone. The dynamic behavior observed in these systems using these tools is highly dependent on the studied temporal scale. As the size of the sample studied increases, the dynamics of the Hénon map become increasingly different from those of biological and artificial neural systems.
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Affiliation(s)
- Natalí Guisande
- Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata, Diagonal 113 entre 63 y 64, La Plata 1900, Buenos Aires, Argentina
| | - Monserrat Pallares di Nunzio
- Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata, Diagonal 113 entre 63 y 64, La Plata 1900, Buenos Aires, Argentina
| | - Nataniel Martinez
- Instituto de Física de Mar del Plata, Universidad Nacional de Mar del Plata & CONICET, Mar del Plata 7600, Buenos Aires, Argentina
| | - Osvaldo A Rosso
- Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata, Diagonal 113 entre 63 y 64, La Plata 1900, Buenos Aires, Argentina
- Instituto de Física, Universidade Federal de Alagoas (UFAL), BR 104 Norte km 97, 57072-970 Maceió, Brazil
| | - Fernando Montani
- Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata, Diagonal 113 entre 63 y 64, La Plata 1900, Buenos Aires, Argentina
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17
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A. Gromov V, Beschastnov YN, Tomashchuk KK. Generalized relational tensors for chaotic time series. PeerJ Comput Sci 2023; 9:e1254. [PMID: 37346716 PMCID: PMC10280504 DOI: 10.7717/peerj-cs.1254] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2022] [Accepted: 01/24/2023] [Indexed: 06/23/2023]
Abstract
The article deals with a generalized relational tensor, a novel discrete structure to store information about a time series, and algorithms (1) to fill the structure, (2) to generate a time series from the structure, and (3) to predict a time series. The algorithms combine the concept of generalized z-vectors with ant colony optimization techniques. To estimate the quality of the storing/re-generating procedure, a difference between the characteristics of the initial and regenerated time series is used. For chaotic time series, a difference between characteristics of the initial time series (the largest Lyapunov exponent, the auto-correlation function) and those of the time series re-generated from a structure is used to assess the effectiveness of the algorithms in question. The approach has shown fairly good results for periodic and benchmark chaotic time series and satisfactory results for real-world chaotic data.
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Affiliation(s)
- Vasilii A. Gromov
- School of Data Analysis and Artificial Intelligence, Higher School Economics University, Moscow, Russia
| | - Yury N. Beschastnov
- School of Data Analysis and Artificial Intelligence, Higher School Economics University, Moscow, Russia
| | - Korney K. Tomashchuk
- School of Data Analysis and Artificial Intelligence, Higher School Economics University, Moscow, Russia
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18
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Gonzalez J, Follmann R, Rosa E, Stein W. Computational and experimental modulation of a noisy chaotic neuronal system. CHAOS (WOODBURY, N.Y.) 2023; 33:033109. [PMID: 37003818 DOI: 10.1063/5.0130874] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2022] [Accepted: 02/13/2023] [Indexed: 06/19/2023]
Abstract
In this work, we study the interplay between chaos and noise in neuronal state transitions involving period doubling cascades. Our approach involves the implementation of a neuronal mathematical model under the action of neuromodulatory input, with and without noise, as well as equivalent experimental work on a biological neuron in the stomatogastric ganglion of the crab Cancer borealis. Our simulations show typical transitions between tonic and bursting regimes that are mediated by chaos and period doubling cascades. While this transition is less evident when intrinsic noise is present in the model, the noisy computational output displays features akin to our experimental results. The differences and similarities observed in the computational and experimental approaches are discussed.
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Affiliation(s)
- Josselyn Gonzalez
- School of Biological Sciences, Illinois State University, Normal, Illinois 61790, USA
| | - Rosangela Follmann
- School of Information Technology, Illinois State University, Normal, Illinois 61790, USA
| | - Epaminondas Rosa
- School of Biological Sciences, Illinois State University, Normal, Illinois 61790, USA
| | - Wolfgang Stein
- School of Biological Sciences, Illinois State University, Normal, Illinois 61790, USA
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19
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Zanin M. Continuous ordinal patterns: Creating a bridge between ordinal analysis and deep learning. CHAOS (WOODBURY, N.Y.) 2023; 33:033114. [PMID: 37003830 DOI: 10.1063/5.0136492] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2022] [Accepted: 02/15/2023] [Indexed: 06/19/2023]
Abstract
We introduce a generalization of the celebrated ordinal pattern approach for the analysis of time series, in which these are evaluated in terms of their distance to ordinal patterns defined in a continuous way. This allows us to naturally incorporate information about the local amplitude of the data and to optimize the ordinal pattern(s) to the problem under study. This last element represents a novel bridge between standard ordinal analysis and deep learning, allowing the achievement of results comparable to the latter in real-world classification problems while also retaining the conceptual simplicity, computational efficiency, and easy interpretability of the former. We test this through the use of synthetic time series, generated by standard chaotic maps and dynamical models, data sets representing brain activity in health and schizophrenia, and the dynamics of delays in the European air transport system. We further show how the continuous ordinal patterns can be used to assess other aspects of the dynamics, like time irreversibility.
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Affiliation(s)
- Massimiliano Zanin
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus UIB, 07122 Palma de Mallorca, Spain
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20
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Berlin L, Galyaev A, Lysenko P. Comparison of Information Criteria for Detection of Useful Signals in Noisy Environments. SENSORS (BASEL, SWITZERLAND) 2023; 23:2133. [PMID: 36850735 PMCID: PMC9966083 DOI: 10.3390/s23042133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/16/2023] [Revised: 02/08/2023] [Accepted: 02/12/2023] [Indexed: 06/18/2023]
Abstract
This paper considers the appearance of indications of useful acoustic signals in the signal/noise mixture. Various information characteristics (information entropy, Jensen-Shannon divergence, spectral information divergence and statistical complexity) are investigated in the context of solving this problem. Both time and frequency domains are studied for the calculation of information entropy. The effectiveness of statistical complexity is shown in comparison with other information metrics for different signal-to-noise ratios. Two different approaches for statistical complexity calculations are also compared. In addition, analytical formulas for complexity and disequilibrium are obtained using entropy variation in the case of signal spectral distribution. The connection between the statistical complexity criterion and the Neyman-Pearson approach for hypothesis testing is discussed. The effectiveness of the proposed approach is shown for different types of acoustic signals and noise models, including colored noises, and different signal-to-noise ratios, especially when the estimation of additional noise characteristics is impossible.
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21
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Lehnertz K. Ordinal methods for a characterization of evolving functional brain networks. CHAOS (WOODBURY, N.Y.) 2023; 33:022101. [PMID: 36859225 DOI: 10.1063/5.0136181] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2022] [Accepted: 01/06/2023] [Indexed: 06/18/2023]
Abstract
Ordinal time series analysis is based on the idea to map time series to ordinal patterns, i.e., order relations between the values of a time series and not the values themselves, as introduced in 2002 by C. Bandt and B. Pompe. Despite a resulting loss of information, this approach captures meaningful information about the temporal structure of the underlying system dynamics as well as about properties of interactions between coupled systems. This-together with its conceptual simplicity and robustness against measurement noise-makes ordinal time series analysis well suited to improve characterization of the still poorly understood spatiotemporal dynamics of the human brain. This minireview briefly summarizes the state-of-the-art of uni- and bivariate ordinal time-series-analysis techniques together with applications in the neurosciences. It will highlight current limitations to stimulate further developments, which would be necessary to advance characterization of evolving functional brain networks.
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Affiliation(s)
- Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Venusberg Campus 1, 53127 Bonn, Germany; Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany; and Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53175 Bonn, Germany
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22
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Daniel de Carvalho Barreto I, Stosic T, Cezar Menezes RS, Alves da Silva AS, Rosso OA, Stosic B. Hydrological changes caused by the construction of dams and reservoirs: The CECP analysis. CHAOS (WOODBURY, N.Y.) 2023; 33:023115. [PMID: 36859196 DOI: 10.1063/5.0135352] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2022] [Accepted: 01/16/2023] [Indexed: 06/18/2023]
Abstract
We investigated the influence of the construction of cascade dams and reservoirs on the predictability and complexity of the streamflow of the São Francisco River, Brazil, by using complexity entropy causality plane (CECP) in its standard and weighted form. We analyzed daily streamflow time series recorded in three fluviometric stations: São Francisco (upstream of cascade dams), Juazeiro (downstream of Sobradinho dam), and Pão de Açúcar station (downstream of Sobradinho and Xingó dams). By comparing the values of CECP information quantifiers (permutation entropy and statistical complexity) for the periods before and after the construction of Sobradinho (1979) and Xingó (1994) dams, we found that the reservoirs' operations changed the temporal variability of streamflow series toward the less predictable regime as indicated by higher entropy (lower complexity) values. Weighted CECP provides some finer details in the predictability of streamflow due to the inclusion of amplitude information in the probability distribution of ordinal patterns. The time evolution of streamflow predictability was analyzed by applying CECP in 2 year sliding windows that revealed the influence of the Paulo Alfonso complex (located between Sobradinho and Xingó dams), construction of which started in the 1950s and was identified through the increased streamflow entropy in the downstream Pão de Açúcar station. The other streamflow alteration unrelated to the construction of the two largest dams was identified in the upstream unimpacted São Francisco station, as an increase in the entropy around 1960s, indicating that some natural factors could also play a role in the decreased predictability of streamflow dynamics.
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Affiliation(s)
- Ikaro Daniel de Carvalho Barreto
- Departamento de Estatística e Informática, Universidade Federal Rural de Pernambuco, Av. Manoel Medeiros S/N, Dois Irmãos, Recife 52171-900, PE, Brazil
| | - Tatijana Stosic
- Departamento de Estatística e Informática, Universidade Federal Rural de Pernambuco, Av. Manoel Medeiros S/N, Dois Irmãos, Recife 52171-900, PE, Brazil
| | - Rômulo Simões Cezar Menezes
- Departamento de Energia Nuclear, Universidade Federal de Pernambuco, Moraes Rego 1235, Cidade Universitária, Recife 50670-901, PE, Brazil
| | - Antonio Samuel Alves da Silva
- Departamento de Estatística e Informática, Universidade Federal Rural de Pernambuco, Av. Manoel Medeiros S/N, Dois Irmãos, Recife 52171-900, PE, Brazil
| | - Osvaldo A Rosso
- Instituto de Física, Universidad Federal de Alagoas (UFAL), Brazil and Instituto de Fisica La Plata (IFLP), La Plata, Maceio 57072-900, AL B1900, Argentina
| | - Borko Stosic
- Departamento de Estatística e Informática, Universidade Federal Rural de Pernambuco, Av. Manoel Medeiros S/N, Dois Irmãos, Recife 52171-900, PE, Brazil
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23
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Muñoz-Guillermo M. Multiscale two-dimensional permutation entropy to analyze encrypted images. CHAOS (WOODBURY, N.Y.) 2023; 33:013112. [PMID: 36725655 DOI: 10.1063/5.0130538] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2022] [Accepted: 11/30/2022] [Indexed: 06/18/2023]
Abstract
Multiscale versions of weighted (and non-weighted) permutation entropy for two dimensions are considered in order to compare and analyze the results when different experiments are conducted. We propose the application of these measures to analyze encrypted images with different security levels and encryption methods.
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Affiliation(s)
- María Muñoz-Guillermo
- Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain
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24
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Huang X, Shang HL, Pitt D. Permutation entropy and its variants for measuring temporal dependence. AUST NZ J STAT 2022. [DOI: 10.1111/anzs.12376] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Xin Huang
- Department of Actuarial Studies and Business Analytics Macquarie University Sydney NSW2109Australia
| | - Han Lin Shang
- Department of Actuarial Studies and Business Analytics Macquarie University Sydney NSW2109Australia
| | - David Pitt
- Department of Economics University of Melbourne Melbourne VIC3053Australia
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25
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Chagas ETC, Frery AC, Gambini J, Lucini MM, Ramos HS, Rey AA. Statistical properties of the entropy from ordinal patterns. CHAOS (WOODBURY, N.Y.) 2022; 32:113118. [PMID: 36456325 DOI: 10.1063/5.0118706] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2022] [Accepted: 09/22/2022] [Indexed: 06/17/2023]
Abstract
The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, knowing the joint distribution of the pair entropy-statistical complexity for a large class of time series models would allow statistical tests that are unavailable to date. Working in this direction, we characterize the asymptotic distribution of the empirical Shannon's entropy for any model under which the true normalized entropy is neither zero nor one. We obtain the asymptotic distribution from the central limit theorem (assuming large time series), the multivariate delta method, and a third-order correction of its mean value. We discuss the applicability of other results (exact, first-, and second-order corrections) regarding their accuracy and numerical stability. Within a general framework for building test statistics about Shannon's entropy, we present a bilateral test that verifies if there is enough evidence to reject the hypothesis that two signals produce ordinal patterns with the same Shannon's entropy. We applied this bilateral test to the daily maximum temperature time series from three cities (Dublin, Edinburgh, and Miami) and obtained sensible results.
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Affiliation(s)
- E T C Chagas
- Departamento de Ciência da Computação, Universidade Federal de Minas Gerais, Belo Horizonte, MG 30123-970, Brazil
| | - A C Frery
- School of Mathematics and Statistics, Victoria University of Wellington, Wellington 6140, New Zealand
| | - J Gambini
- Departamento de Ingeniería Informática, Instituto Tecnológico de Buenos Aires, Av. Madero 399, Buenos Aires C1106ACD, Argentina
| | - M M Lucini
- Facultad de Ciencias Exactas, Naturales y Agrimensura, Universidad Nacional de Nordeste, Av. Libertad 5450-Campus "Deodoro Roca," 3400 Corrientes, Argentina
| | - H S Ramos
- Departamento de Ciência da Computação, Universidade Federal de Minas Gerais, Belo Horizonte, MG 30123-970, Brazil
| | - A A Rey
- Centro de Procesamiento de Se nales e Imágenes, Department of Mathematics, Universidad Tecnológica Nacional Facultad Regional Buenos Aires, Ciudad de Buenos Aires C1179AAQ, Argentina
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26
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Fuentes N, Garcia A, Guevara R, Orofino R, Mateos DM. Complexity of Brain Dynamics as a Correlate of Consciousness in Anaesthetized Monkeys. Neuroinformatics 2022; 20:1041-1054. [PMID: 35511398 DOI: 10.1007/s12021-022-09586-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 04/04/2022] [Indexed: 12/31/2022]
Abstract
The use of anaesthesia is a fundamental tool in the investigation of consciousness. Anesthesia procedures allow to investigate different states of consciousness from sedation to deep anesthesia within controlled scenarios. In this study we use information quantifiers to measure the complexity of electrocorticogram recordings in monkeys. We apply these metrics to compare different stages of general anesthesia for evaluating consciousness in several anesthesia protocols. We find that the complexity of brain activity can be used as a correlate of consciousness. For two of the anaesthetics used, propofol and medetomidine, we find that the anaesthetised state is accompanied by a reduction in the complexity of brain activity. On the other hand we observe that use of ketamine produces an increase in complexity measurements. We relate this observation with increase activity within certain brain regions associated with the ketamine used doses. Our measurements indicate that complexity of brain activity is a good indicator for a general evaluation of different levels of consciousness awareness, both in anesthetized and non anesthetizes states.
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Affiliation(s)
- Nicolas Fuentes
- Facultad de Ciencias Exactas, Físicas y Naturales, Universidad Nacional de Córdoba, Córdoba, Argentina
| | - Alexis Garcia
- Facultad de Ciencias Exactas, Físicas y Naturales, Universidad Nacional de Córdoba, Córdoba, Argentina
| | - Ramón Guevara
- Department of Physics and Astronomy, University of Padua, Padua, Italy
| | - Roberto Orofino
- Hospital de Ninos Pedro de Elizalde, Buenos Aires, Argentina.,Hospital Español, La Plata, Argentina
| | - Diego M Mateos
- Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires, Argentina. .,Facultad de Ciencia y Tecnología. Universidad Autónoma de Entre Ríos (UADER), Oro Verde, Entre Ríos, Argentina. .,Instituto de Matemática Aplicada del Litoral (IMAL-CONICET-UNL), CCT CONICET, Santa Fé, Argentina.
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27
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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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28
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Muñoz-Arias MH. Statistical complexity and the road to equilibrium in many-body chaotic quantum systems. Phys Rev E 2022; 106:044103. [PMID: 36397513 DOI: 10.1103/physreve.106.044103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2022] [Accepted: 09/14/2022] [Indexed: 06/16/2023]
Abstract
In this work we revisit the problem of equilibration in isolated many-body interacting quantum systems. We pay particular attention to quantum chaotic Hamiltonians, and rather than focusing on the properties of the asymptotic states and how they adhere to the predictions of the Eigenstate Thermalization Hypothesis, we focus on the equilibration process itself, i.e., the road to equilibrium. Along the road to equilibrium the diagonal ensembles obey an emergent form of the second law of thermodynamics and we provide an information theoretic proof of this fact. With this proof at hand we show that the road to equilibrium is nothing but a hierarchy in time of diagonal ensembles. Furthermore, introducing the notions of statistical complexity and the entropy-complexity plane, we investigate the uniqueness of the road to equilibrium in a generic many-body system by comparing its trajectories in the entropy-complexity plane to those generated by a random Hamiltonian. Finally, by treating the random Hamiltonian as a perturbation we analyzed the stability of entropy-complexity trajectories associated with the road to equilibrium for a chaotic Hamiltonian and different types of initial states.
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Affiliation(s)
- Manuel H Muñoz-Arias
- Center for Quantum Information and Control, CQuIC, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
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Granado M, Collavini S, Baravalle R, Martinez N, Montemurro MA, Rosso OA, Montani F. High-frequency oscillations in the ripple bands and amplitude information coding: Toward a biomarker of maximum entropy in the preictal signals. CHAOS (WOODBURY, N.Y.) 2022; 32:093151. [PMID: 36182366 DOI: 10.1063/5.0101220] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2022] [Accepted: 08/29/2022] [Indexed: 06/16/2023]
Abstract
Intracranial electroencephalography (iEEG) can directly record local field potentials (LFPs) from a large set of neurons in the vicinity of the electrode. To search for possible epileptic biomarkers and to determine the epileptogenic zone that gives rise to seizures, we investigated the dynamics of basal and preictal signals. For this purpose, we explored the dynamics of the recorded time series for different frequency bands considering high-frequency oscillations (HFO) up to 240 Hz. We apply a Hilbert transform to study the amplitude and phase of the signals. The dynamics of the different frequency bands in the time causal entropy-complexity plane, H × C, is characterized by comparing the dynamical evolution of the basal and preictal time series. As the preictal states evolve closer to the time in which the epileptic seizure starts, the, H × C, dynamics changes for the higher frequency bands. The complexity evolves to very low values and the entropy becomes nearer to its maximal value. These quasi-stable states converge to equiprobable states when the entropy is maximal, and the complexity is zero. We could, therefore, speculate that in this case, it corresponds to the minimization of Gibbs free energy. In this case, the maximum entropy is equivalent to the principle of minimum consumption of resources in the system. We can interpret this as the nature of the system evolving temporally in the preictal state in such a way that the consumption of resources by the system is minimal for the amplitude in frequencies between 220-230 and 230-240 Hz.
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Affiliation(s)
- Mauro Granado
- Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata, Diagonal 113 entre 63 y 64, La Plata 1900, Buenos Aires, Argentina
| | - Santiago Collavini
- Instituto de Electrónica Industrial, Control y Procesamiento de Se nales (LEICI), Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP-CONICET), La Plata 1900, Buenos Aires, Argentina
| | - Roman Baravalle
- Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata, Diagonal 113 entre 63 y 64, La Plata 1900, Buenos Aires, Argentina
| | - Nataniel Martinez
- Instituto de Física de Mar del Plata, Universidad Nacional de Mar del Plata & CONICET, Mar del Plata 7600, Buenos Aires, Argentina
| | - Marcelo A Montemurro
- School of Mathematics & Statistics, Faculty of Science, Technology, Engineering & Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom
| | - Osvaldo A Rosso
- Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata, Diagonal 113 entre 63 y 64, La Plata 1900, Buenos Aires, Argentina
| | - Fernando Montani
- Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata, Diagonal 113 entre 63 y 64, La Plata 1900, Buenos Aires, Argentina
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30
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Ziemkiewicz D. Entropy of timekeeping in a mechanical clock. Phys Rev E 2022; 105:055001. [PMID: 35706227 DOI: 10.1103/physreve.105.055001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Accepted: 04/15/2022] [Indexed: 06/15/2023]
Abstract
The dynamics of a unique type of clock mechanism known as grasshopper escapement is investigated with the aim of evaluating its accuracy in a noisy environment. It is demonstrated that the clock's precision scales linearly with the rate of its entropy production, consistently with recently reported results regarding nanoscale and quantum clocks. Moreover, it is shown that the inevitable force variations present in the mechanism can be modeled with a Maxwell-Boltzmann statistic. Finally, the function of clock error is compared with Brownian motion and its fractal-like properties are discussed. The numerical results are confirmed with experimental data.
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Affiliation(s)
- David Ziemkiewicz
- Institute of Mathematics and Physics, UTP University of Science and Technology, Aleje Prof. S. Kaliskiego 7, 85-789 Bydgoszcz, Poland
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31
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Zanin M, Martínez JH. Analyzing international events through the lens of statistical physics: The case of Ukraine. CHAOS (WOODBURY, N.Y.) 2022; 32:051103. [PMID: 35649977 DOI: 10.1063/5.0091628] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2022] [Accepted: 04/08/2022] [Indexed: 06/15/2023]
Abstract
During the last few years, statistical physics has received increasing attention as a framework for the analysis of real complex systems; yet, this is less clear in the case of international political events, partly due to the complexity in securing relevant quantitative data on them. Here, we analyze a detailed dataset of violent events that took place in Ukraine since January 2021 and analyze their temporal and spatial correlations through entropy and complexity metrics and functional networks. Results depict a complex scenario with events appearing in a non-random fashion but with eastern-most regions functionally disconnected from the remainder of the country-something opposing the widespread "two Ukraines" view. We further draw some lessons and venues for future analyses.
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Affiliation(s)
- M Zanin
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus UIB, 07122 Palma de Mallorca, Spain
| | - J H Martínez
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus UIB, 07122 Palma de Mallorca, Spain
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Ferraz MSA, Kihara AH. Beyond randomness: Evaluating measures of information entropy in binary series. Phys Rev E 2022; 105:044101. [PMID: 35590660 DOI: 10.1103/physreve.105.044101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2021] [Accepted: 03/09/2022] [Indexed: 06/15/2023]
Abstract
The enormous amount of currently available data demands efforts to extract meaningful information. For this purpose, different measurements are applied, including Shannon's entropy, permutation entropy, and the Lempel-Ziv complexity. These methods have been used in many applications, such as pattern recognition, series classification, and several other areas (e.g., physical, financial, and biomedical). Data in these applications are often presented in binary series with temporal correlations. Herein, we compare the measures of information entropy in binary series conveying short- and long-range temporal correlations characterized by the Hurst exponent H. Combining numerical and analytical approaches, we scrutinize different methods that were not efficient in detecting temporal correlations. To surpass this limitation, we propose a measure called the binary permutation index (BPI). We will demonstrate that BPI efficiently discriminates patterns embedded in the series, offering advantages over previous methods. Subsequently, we collect stock market time series and rain precipitation data as well as perform in vivo electrophysiological recordings in the hippocampus of an experimental animal model of temporal lobe epilepsy, in which the BPI application in both public open source and experimental data is demonstrated. An index is proposed to evaluate information entropy, allowing the ability to discriminate randomness and extract meaningful information in binary time series.
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Affiliation(s)
- Mariana Sacrini Ayres Ferraz
- Centro de Matemática, Computação e Cognição (CMCC), Universidade Federal do ABC (UFABC), São Bernardo do Campo, São Paulo, Brazil
| | - Alexandre Hiroaki Kihara
- Centro de Matemática, Computação e Cognição (CMCC), Universidade Federal do ABC (UFABC), São Bernardo do Campo, São Paulo, Brazil
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Zunino L, Olivares F, Ribeiro HV, Rosso OA. Permutation Jensen-Shannon distance: A versatile and fast symbolic tool for complex time-series analysis. Phys Rev E 2022; 105:045310. [PMID: 35590550 DOI: 10.1103/physreve.105.045310] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2021] [Accepted: 03/21/2022] [Indexed: 06/15/2023]
Abstract
The main motivation of this paper is to introduce the permutation Jensen-Shannon distance, a symbolic tool able to quantify the degree of similarity between two arbitrary time series. This quantifier results from the fusion of two concepts, the Jensen-Shannon divergence and the encoding scheme based on the sequential ordering of the elements in the data series. The versatility and robustness of this ordinal symbolic distance for characterizing and discriminating different dynamics are illustrated through several numerical and experimental applications. Results obtained allow us to be optimistic about its usefulness in the field of complex time-series analysis. Moreover, thanks to its simplicity, low computational cost, wide applicability, and less susceptibility to outliers and artifacts, this ordinal measure can efficiently handle large amounts of data and help to tackle the current big data challenges.
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Affiliation(s)
- Luciano Zunino
- Centro de Investigaciones Ópticas (CONICET La Plata-CIC-UNLP), 1897 Gonnet, La Plata, Argentina
- Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP), 1900 La Plata, Argentina
| | - Felipe Olivares
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Haroldo V Ribeiro
- Departamento de Física, Universidade Estadual de Maringá, Maringá, PR 87020-900, Brazil
| | - Osvaldo A Rosso
- Instituto de Física, Universidade Federal de Alagoas, Maceió, Alagoas 57072-970, Brazil
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Wang D, Jin N, Zhai L, Ren Y. Quantitative research of the liquid film characteristics in upward vertical gas, oil and water flows. Chin J Chem Eng 2022. [DOI: 10.1016/j.cjche.2022.03.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Refined Multiscale Entropy Analysis of Wrist Pulse for Gender Difference in Traditional Chinese Medicine among Young Individuals. EVIDENCE-BASED COMPLEMENTARY AND ALTERNATIVE MEDICINE 2022; 2022:7285312. [PMID: 35178107 PMCID: PMC8846990 DOI: 10.1155/2022/7285312] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/17/2021] [Accepted: 12/22/2021] [Indexed: 11/17/2022]
Abstract
Pulse signal analysis plays an important role in promoting the objectification of traditional Chinese medicine (TCM). Like electrocardiogram (ECG) signals, wrist pulse signals are mainly caused by cardiac activities and are valuable in analyzing cardiac diseases. A large number of studies have reported ECG signals can distinguish gender characteristics of normal healthy subjects using entropy complexity measures, consistently showing more complexity in females than males. No research up to date, however, has been found on examining gender differences with wrist pulse signals of healthy subjects on entropy complexity measures. This paper is aimed to fill in the research gap, which could, in turn, provide a deeper insight into the pulse signal and might identify potential differences between ECG signals and pulse signals. In particular, several complementary entropy measures with corresponding refined composite multiscale versions are established to perform the analysis for the filtered TCM pulse signals. Experimental results reveal that regardless of entropy measures used, there is no statistically significant gender difference in terms of entropy complexity, indicating that the pulse signal holds less gender characteristics than the ECG signal. In view of these findings, wrist pulse signals could be likely to provide different pieces of information to ECG signals. The present study is the first to quantitatively evaluate gender differences in healthy pulse signals with measures of entropy complexity and more importantly; we expect this study could make contribution to the ongoing pulse intelligent diagnosis and objective analysis, further facilitating the modernization of TCM pulse diagnosis.
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37
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Katchanov YL, Markova YV. Dynamics of senses of new physics discourse: Co-keywords analysis. J Informetr 2022. [DOI: 10.1016/j.joi.2021.101245] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Zanin M, Olivares F, Pulido-Valdeolivas I, Rausell E, Gomez-Andres D. Gait analysis under the lens of statistical physics. Comput Struct Biotechnol J 2022; 20:3257-3267. [PMID: 35782747 PMCID: PMC9237948 DOI: 10.1016/j.csbj.2022.06.022] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Revised: 06/10/2022] [Accepted: 06/10/2022] [Indexed: 11/29/2022] Open
Abstract
Human gait is a fundamental activity, essential for the survival of the individual, and an emergent property of the interactions between complex physical and cognitive processes. Gait is altered in many situations, due both to external constraints, as e.g. paced walk, and to physical and neurological pathologies. Its study is therefore important as a way of improving the quality of life of patients, but also as a door to understanding the inner working of the human nervous system. In this review we explore how four statistical physics concepts have been used to characterise normal and pathological gait: entropy, maximum Lyapunov exponent, multi-fractal analysis and irreversibility. Beyond some basic definitions, we present the main results that have been obtained in this field, as well as a discussion of the main limitations researchers have dealt and will have to deal with. We finally conclude with some biomedical considerations and avenues for further development.
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Affiliation(s)
- Massimiliano Zanin
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus UIB, Palma de Mallorca 07122, Spain
| | - Felipe Olivares
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus UIB, Palma de Mallorca 07122, Spain
| | - Irene Pulido-Valdeolivas
- Department of Anatomy, Histology and Neuroscience, School of Medicine, Universidad Autónoma de Madrid, Calle del Arzobispo Morcillo 2, Madrid 28029, Spain
| | - Estrella Rausell
- Department of Anatomy, Histology and Neuroscience, School of Medicine, Universidad Autónoma de Madrid, Calle del Arzobispo Morcillo 2, Madrid 28029, Spain
| | - David Gomez-Andres
- Department of Anatomy, Histology and Neuroscience, School of Medicine, Universidad Autónoma de Madrid, Calle del Arzobispo Morcillo 2, Madrid 28029, Spain
- Pediatric Neurology, Vall d'Hebron Institut de Recerca (VHIR), Hospital Universitari Vall d'Hebron, Vall d'Hebron Barcelona Hospital Campus, ERN-RND & EURO-NMD, Pg. de la Vall d'Hebron 119-129, Barcelona 08035, Spain
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39
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Dylewsky D, Kaiser E, Brunton SL, Kutz JN. Principal component trajectories for modeling spectrally continuous dynamics as forced linear systems. Phys Rev E 2022; 105:015312. [PMID: 35193205 DOI: 10.1103/physreve.105.015312] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2021] [Accepted: 01/07/2022] [Indexed: 05/08/2023]
Abstract
Delay embeddings of time series data have emerged as a promising coordinate basis for data-driven estimation of the Koopman operator, which seeks a linear representation for observed nonlinear dynamics. Recent work has demonstrated the efficacy of dynamic mode decomposition (DMD) for obtaining finite-dimensional Koopman approximations in delay coordinates. In this paper we demonstrate how nonlinear dynamics with sparse Fourier spectra can be (i) represented by a superposition of principal component trajectories and (ii) modeled by DMD in this coordinate space. For continuous or mixed (discrete and continuous) spectra, DMD can be augmented with an external forcing term. We present a method for learning linear control models in delay coordinates while simultaneously discovering the corresponding exogenous forcing signal in a fully unsupervised manner. This extends the existing DMD with control (DMDc) algorithm to cases where a control signal is not known a priori. We provide examples to validate the learned forcing against a known ground truth and illustrate their statistical similarity. Finally, we offer a demonstration of this method applied to real-world power grid load data to show its utility for diagnostics and interpretation on systems in which somewhat periodic behavior is strongly forced by unknown and unmeasurable environmental variables.
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Affiliation(s)
- Daniel Dylewsky
- Department of Physics, University of Washington, Seattle, Washington 98195, USA
| | - Eurika Kaiser
- Department of Mechanical Engineering, University of Washington, Seattle, Washington 98195, USA
| | | | - J Nathan Kutz
- Department of Applied Mathematics, University of Washington, Seattle, Washington 98195, USA
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40
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Permutation Entropy of Weakly Noise-Affected Signals. ENTROPY 2021; 24:e24010054. [PMID: 35052080 PMCID: PMC8774944 DOI: 10.3390/e24010054] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/29/2021] [Revised: 12/21/2021] [Accepted: 12/23/2021] [Indexed: 11/30/2022]
Abstract
We analyze the permutation entropy of deterministic chaotic signals affected by a weak observational noise. We investigate the scaling dependence of the entropy increase on both the noise amplitude and the window length used to encode the time series. In order to shed light on the scenario, we perform a multifractal analysis, which allows highlighting the emergence of many poorly populated symbolic sequences generated by the stochastic fluctuations. We finally make use of this information to reconstruct the noiseless permutation entropy. While this approach works quite well for Hénon and tent maps, it is much less effective in the case of hyperchaos. We argue about the underlying motivations.
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Noninvasive Methods for Fault Detection and Isolation in Internal Combustion Engines Based on Chaos Analysis. SENSORS 2021; 21:s21206925. [PMID: 34696138 PMCID: PMC8539936 DOI: 10.3390/s21206925] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/02/2021] [Revised: 10/08/2021] [Accepted: 10/13/2021] [Indexed: 11/16/2022]
Abstract
The classic monitoring methods for detecting faults in automotive vehicles based on on-board diagnostics (OBD) are insufficient when diagnosing several mechanical failures. Other sensing techniques present drawbacks such as high invasiveness and limited physical range. The present work presents a fully noninvasive system for fault detection and isolation in internal combustion engines through sound signals processing. An acquisition system was developed, whose data are transmitted to a smartphone in which the signal is processed, and the user has access to the information. A study of the chaotic behavior of the vehicle was carried out, and the feasibility of using fractal dimensions as a tool to diagnose engine misfire and problems in the alternator belt was verified. An artificial neural network was used for fault classification using the fractal dimension data extracted from the sound of the engine. For comparison purposes, a strategy based on wavelet multiresolution analysis was also implemented. The proposed solution allows a diagnosis without having any contact with the vehicle, with low computational cost, without the need for installing sensors, and in real time. The system and method were validated through experimental tests, with a success rate of 99% for the faults under consideration.
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42
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Valensise CM, Serra A, Galeazzi A, Etta G, Cinelli M, Quattrociocchi W. Entropy and complexity unveil the landscape of memes evolution. Sci Rep 2021; 11:20022. [PMID: 34625623 PMCID: PMC8501102 DOI: 10.1038/s41598-021-99468-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2021] [Accepted: 09/22/2021] [Indexed: 11/15/2022] Open
Abstract
On the Internet, information circulates fast and widely, and the form of content adapts to comply with users’ cognitive abilities. Memes are an emerging aspect of the internet system of signification, and their visual schemes evolve by adapting to a heterogeneous context. A fundamental question is whether they present culturally and temporally transcendent characteristics in their organizing principles. In this work, we study the evolution of 2 million visual memes published on Reddit over ten years, from 2011 to 2020, in terms of their statistical complexity and entropy. A combination of a deep neural network and a clustering algorithm is used to group memes according to the underlying templates. The grouping of memes is the cornerstone to trace the growth curve of these objects. We observe an exponential growth of the number of new created templates with a doubling time of approximately 6 months, and find that long-lasting templates are associated with strong early adoption. Notably, the creation of new memes is accompanied with an increased visual complexity of memes content, in a continuous effort to represent social trends and attitudes, that parallels a trend observed also in painting art.
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Affiliation(s)
- Carlo M Valensise
- Enrico Fermi Research Center, Piazza del Viminale, 1, 00184, Roma, Italy.
| | - Alessandra Serra
- Tuscia University - DISTU Department of Modern Languages and Literatures, History, Philosophy and Law Studies, Via S. Carlo, 32, 01100, Viterbo, Italy
| | | | - Gabriele Etta
- Department of Computer Science, Sapienza University of Rome, Viale Regina Elena, 295, 00161, Roma, Italy
| | - Matteo Cinelli
- Department of Environmental Sciences, Informatics and Statistics, Ca' Foscari, University of Venice, Via Torino 155, 30172, Mestre, Italy.,Institute for Complex Systems, Italian National Research Council, Via dei Taurini 19, 00185, Roma, Italy
| | - Walter Quattrociocchi
- Department of Computer Science, Sapienza University of Rome, Viale Regina Elena, 295, 00161, Roma, Italy
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Fernandes LHS, de Araujo FHA, Tabak BM. Insights from the (in)efficiency of Chinese sectoral indices during COVID-19. PHYSICA A 2021; 578:126063. [PMID: 36569041 PMCID: PMC9758612 DOI: 10.1016/j.physa.2021.126063] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2021] [Revised: 04/26/2021] [Indexed: 05/24/2023]
Abstract
This article evaluates the effects of the crisis caused by the new Coronavirus (COVID-19) on the Chinese sectoral indices. Using the complexity-entropy plane methodology, we find that the COVID-19 crisis caused increased inefficiency in most of China's equity sectors. We also find heterogeneous effects depending on the economic sector. Our results are useful for a better understanding the effect of global shocks on the stock markets and how their effects are distributed across economic sectors.
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Affiliation(s)
- Leonardo H S Fernandes
- Department of Economics and Informatics, Federal Rural University of Pernambuco, Av. Gregório Ferraz Nogueira, S/N - José Tomé de Souza Ramos, 569090-535, PE, Serra Talhada, Brazil
| | - Fernando H A de Araujo
- Department of Statistics and Informatics, Federal Rural University of Pernambuco, Rua Dom Manuel de Medeiros, S/N Dois Irmãos - CEP: 52171-900, PE, Recife, Brazil
| | - Benjamin M Tabak
- School of Public Policy and Government, Getulio Vargas Foundation (EPPG/FGV), Brasilia, DF, Brazil
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Jara JL, Morales-Rojas C, Fernández-Muñoz J, Haunton VJ, Chacón M. Using complexity-entropy planes to detect Parkinson's disease from short segments of haemodynamic signals. Physiol Meas 2021; 42. [PMID: 34256359 DOI: 10.1088/1361-6579/ac13ce] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2021] [Accepted: 07/13/2021] [Indexed: 11/11/2022]
Abstract
Objective. There is emerging evidence that analysing the entropy and complexity of biomedical signals can detect underlying changes in physiology which may be reflective of disease pathology. This approach can be used even when only short recordings of biomedical signals are available. This study aimed to determine whether entropy and complexity measures can detect differences between subjects with Parkinsons disease and healthy controls (HCs).Approach. A method based on a diagram of entropy versus complexity, named complexity-entropy plane, was used to re-analyse a dataset of cerebral haemodynamic signals from subjects with Parkinsons disease and HCs obtained under poikilocapnic conditions. A probability distribution for a set of ordinal patterns, designed to capture regularities in a time series, was computed from each signal under analysis. Four types of entropy and ten types of complexity measures were estimated from these distributions. Mean values of entropy and complexity were compared and their classification power was assessed by evaluating the best linear separator on the corresponding complexity-entropy planes.Main results. Few linear separators obtained significantly better classification, evaluated as the area under the receiver operating characteristic curve, than signal mean values. However, significant differences in both entropy and complexity were detected between the groups of participants.Significance. Measures of entropy and complexity were able to detect differences between healthy volunteers and subjects with Parkinson's disease, in poikilocapnic conditions, even though only short recordings were available for analysis. Further work is needed to refine this promising approach, and to help understand the findings in the context of specific pathophysiological changes.
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Affiliation(s)
- J L Jara
- Departamento de Ingeniería Informática, Universidad de Santiago de Chile, Usach, Santiago, Chile
| | - Catalina Morales-Rojas
- Departamento de Ingeniería Informática, Universidad de Santiago de Chile, Usach, Santiago, Chile
| | - Juan Fernández-Muñoz
- Departamento de Ingeniería Informática, Universidad de Santiago de Chile, Usach, Santiago, Chile
| | - Victoria J Haunton
- Department of Cardiovascular Sciences, University of Leicester, Leicester, United Kingdom
| | - Max Chacón
- Departamento de Ingeniería Informática, Universidad de Santiago de Chile, Usach, Santiago, Chile
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Boaretto BRR, Budzinski RC, Rossi KL, Prado TL, Lopes SR, Masoller C. Evaluating Temporal Correlations in Time Series Using Permutation Entropy, Ordinal Probabilities and Machine Learning. ENTROPY 2021; 23:e23081025. [PMID: 34441165 PMCID: PMC8391825 DOI: 10.3390/e23081025] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/08/2021] [Revised: 07/28/2021] [Accepted: 08/03/2021] [Indexed: 11/16/2022]
Abstract
Time series analysis comprises a wide repertoire of methods for extracting information from data sets. Despite great advances in time series analysis, identifying and quantifying the strength of nonlinear temporal correlations remain a challenge. We have recently proposed a new method based on training a machine learning algorithm to predict the temporal correlation parameter, α, of flicker noise (FN) time series. The algorithm is trained using as input features the probabilities of ordinal patterns computed from FN time series, xαFN(t), generated with different values of α. Then, the ordinal probabilities computed from the time series of interest, x(t), are used as input features to the trained algorithm and that returns a value, αe, that contains meaningful information about the temporal correlations present in x(t). We have also shown that the difference, Ω, of the permutation entropy (PE) of the time series of interest, x(t), and the PE of a FN time series generated with α=αe, xαeFN(t), allows the identification of the underlying determinism in x(t). Here, we apply our methodology to different datasets and analyze how αe and Ω correlate with well-known quantifiers of chaos and complexity. We also discuss the limitations for identifying determinism in highly chaotic time series and in periodic time series contaminated by noise. The open source algorithm is available on Github.
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Affiliation(s)
- Bruno R. R. Boaretto
- Department of Physics, Universidade Federal do Paraná, Curitiba 81531-980, Brazil; (B.R.R.B.); (T.L.P.); (S.R.L.)
| | - Roberto C. Budzinski
- Department of Mathematics, Western University, London, ON N6A 3K7, Canada;
- Brain and Mind Institute, Western University, London, ON N6A 3K7, Canada
| | - Kalel L. Rossi
- Theoretical Physics/Complex Systems, ICBM, Carl von Ossietzky University Oldenburg, 26129 Oldenburg, Germany;
| | - Thiago L. Prado
- Department of Physics, Universidade Federal do Paraná, Curitiba 81531-980, Brazil; (B.R.R.B.); (T.L.P.); (S.R.L.)
| | - Sergio R. Lopes
- Department of Physics, Universidade Federal do Paraná, Curitiba 81531-980, Brazil; (B.R.R.B.); (T.L.P.); (S.R.L.)
| | - Cristina Masoller
- Department of Physics, Universitat Politecnica de Catalunya, 08034 Barcelona, Spain
- Correspondence:
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Boaretto BRR, Budzinski RC, Rossi KL, Prado TL, Lopes SR, Masoller C. Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks. Sci Rep 2021; 11:15789. [PMID: 34349134 PMCID: PMC8338970 DOI: 10.1038/s41598-021-95231-z] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2021] [Accepted: 07/15/2021] [Indexed: 02/07/2023] Open
Abstract
Extracting relevant properties of empirical signals generated by nonlinear, stochastic, and high-dimensional systems is a challenge of complex systems research. Open questions are how to differentiate chaotic signals from stochastic ones, and how to quantify nonlinear and/or high-order temporal correlations. Here we propose a new technique to reliably address both problems. Our approach follows two steps: first, we train an artificial neural network (ANN) with flicker (colored) noise to predict the value of the parameter, [Formula: see text], that determines the strength of the correlation of the noise. To predict [Formula: see text] the ANN input features are a set of probabilities that are extracted from the time series by using symbolic ordinal analysis. Then, we input to the trained ANN the probabilities extracted from the time series of interest, and analyze the ANN output. We find that the [Formula: see text] value returned by the ANN is informative of the temporal correlations present in the time series. To distinguish between stochastic and chaotic signals, we exploit the fact that the difference between the permutation entropy (PE) of a given time series and the PE of flicker noise with the same [Formula: see text] parameter is small when the time series is stochastic, but it is large when the time series is chaotic. We validate our technique by analysing synthetic and empirical time series whose nature is well established. We also demonstrate the robustness of our approach with respect to the length of the time series and to the level of noise. We expect that our algorithm, which is freely available, will be very useful to the community.
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Affiliation(s)
- B R R Boaretto
- Department of Physics, Universidade Federal do Paraná, Curitiba, 81531-980, Brazil
| | - R C Budzinski
- Department of Physics, Universidade Federal do Paraná, Curitiba, 81531-980, Brazil
| | - K L Rossi
- Department of Physics, Universidade Federal do Paraná, Curitiba, 81531-980, Brazil
| | - T L Prado
- Department of Physics, Universidade Federal do Paraná, Curitiba, 81531-980, Brazil
| | - S R Lopes
- Department of Physics, Universidade Federal do Paraná, Curitiba, 81531-980, Brazil
| | - C Masoller
- Department of Physics, Universitat Politecnica de Catalunya, 08222, Barcelona, Spain.
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47
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Kurosaka T, Masuda S, Gotoda H. Attenuation of thermoacoustic combustion oscillations in a swirl-stabilized turbulent combustor. CHAOS (WOODBURY, N.Y.) 2021; 31:073121. [PMID: 34340326 DOI: 10.1063/5.0045127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2021] [Accepted: 05/17/2021] [Indexed: 06/13/2023]
Abstract
We experimentally study the attenuation behavior of thermoacoustic combustion oscillations using causality analysis, multiscale randomness analysis, and a complex network. We supply a steady air jet from the injector rim to suppress combustion oscillations. The directional coupling between pressure and heat release rate fluctuations is significantly weakened during the suppression of combustion oscillations. The loss of the primary hub in the turbulence network plays an important role in the degeneration of combustion oscillations.
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Affiliation(s)
- Takuya Kurosaka
- Department of Mechanical Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, Japan
| | - Shinga Masuda
- 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
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48
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Greco A, Gallitto G, D’Alessandro M, Rastelli C. Increased Entropic Brain Dynamics during DeepDream-Induced Altered Perceptual Phenomenology. ENTROPY (BASEL, SWITZERLAND) 2021; 23:839. [PMID: 34208923 PMCID: PMC8306862 DOI: 10.3390/e23070839] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/28/2021] [Revised: 06/20/2021] [Accepted: 06/23/2021] [Indexed: 01/02/2023]
Abstract
In recent years, the use of psychedelic drugs to study brain dynamics has flourished due to the unique opportunity they offer to investigate the neural mechanisms of conscious perception. Unfortunately, there are many difficulties to conduct experiments on pharmacologically-induced hallucinations, especially regarding ethical and legal issues. In addition, it is difficult to isolate the neural effects of psychedelic states from other physiological effects elicited by the drug ingestion. Here, we used the DeepDream algorithm to create visual stimuli that mimic the perception of hallucinatory states. Participants were first exposed to a regular video, followed by its modified version, while recording electroencephalography (EEG). Results showed that the frontal region's activity was characterized by a higher entropy and lower complexity during the modified video, with respect to the regular one, at different time scales. Moreover, we found an increased undirected connectivity and a greater level of entropy in functional connectivity networks elicited by the modified video. These findings suggest that DeepDream and psychedelic drugs induced similar altered brain patterns and demonstrate the potential of adopting this method to study altered perceptual phenomenology in neuroimaging research.
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Affiliation(s)
- Antonino Greco
- Department of Psychology and Cognitive Science, University of Trento, 38068 Rovereto, Italy;
- Centre for Integrative Neuroscience, University of Tübingen, 72076 Tübingen, Germany
- MEG Center, University of Tübingen, 72076 Tübingen, Germany
| | - Giuseppe Gallitto
- Department of Neurology, University Hospital Essen, 45147 Essen, Germany;
| | - Marco D’Alessandro
- Institute of Cognitive Sciences and Technologies, National Research Council, 00185 Rome, Italy;
| | - Clara Rastelli
- Department of Psychology and Cognitive Science, University of Trento, 38068 Rovereto, Italy;
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49
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Nalos L, Jarkovská D, Švíglerová J, Süß A, Záleský J, Rajdl D, Krejčová M, Kuncová J, Rosenberg J, Štengl M. TdP Incidence in Methoxamine-Sensitized Rabbit Model Is Reduced With Age but Not Influenced by Hypercholesterolemia. Front Physiol 2021; 12:692921. [PMID: 34234694 PMCID: PMC8255784 DOI: 10.3389/fphys.2021.692921] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2021] [Accepted: 05/17/2021] [Indexed: 11/13/2022] Open
Abstract
Metabolic syndrome is associated with hypercholesterolemia, cardiac remodeling, and increased susceptibility to ventricular arrhythmias. Effects of diet-induced hypercholesterolemia on susceptibility to torsades de pointes arrhythmias (TdP) together with potential indicators of arrhythmic risk were investigated in three experimental groups of Carlsson's rabbit model: (1) young rabbits (YC, young control, age 12-16 weeks), older rabbits (AC, adult control, age 20-24 weeks), and older age-matched cholesterol-fed rabbits (CH, cholesterol, age 20-24 weeks). TdP was induced by α-adrenergic stimulation by methoxamine and IKr block in 83% of YC rabbits, 18% of AC rabbits, and 21% of CH rabbits. High incidence of TdP was associated with high incidence of single (SEB) and multiple ectopic beats (MEB), but the QTc prolongation and short-term variability (STV) were similar in all three groups. In TdP-susceptible rabbits, STV was significantly higher compared with arrhythmia-free rabbits but not with rabbits with other than TdP arrhythmias (SEB, MEB). Amplitude-aware permutation entropy analysis of baseline ECG could identify arrhythmia-resistant animals with high sensitivity and specificity. The data indicate that the TdP susceptibility in methoxamine-sensitized rabbits is affected by the age of rabbits but probably not by hypercholesterolemia. Entropy analysis could potentially stratify the arrhythmic risk and identify the low-risk individuals.
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Affiliation(s)
- Lukáš Nalos
- Department of Physiology, Faculty of Medicine in Pilsen, Charles University, Pilsen, Czechia.,Biomedical Center, Faculty of Medicine in Pilsen, Charles University, Pilsen, Czechia
| | - Dagmar Jarkovská
- Department of Physiology, Faculty of Medicine in Pilsen, Charles University, Pilsen, Czechia.,Biomedical Center, Faculty of Medicine in Pilsen, Charles University, Pilsen, Czechia
| | - Jitka Švíglerová
- Department of Physiology, Faculty of Medicine in Pilsen, Charles University, Pilsen, Czechia.,Biomedical Center, Faculty of Medicine in Pilsen, Charles University, Pilsen, Czechia
| | - Annabell Süß
- Department of Physiology, Faculty of Medicine in Pilsen, Charles University, Pilsen, Czechia
| | - Jakub Záleský
- Department of Physiology, Faculty of Medicine in Pilsen, Charles University, Pilsen, Czechia
| | - Daniel Rajdl
- Institute of Clinical Biochemistry and Haematology, Faculty of Medicine in Pilsen, Charles University, Pilsen, Czechia
| | - Milada Krejčová
- New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czechia
| | - Jitka Kuncová
- Department of Physiology, Faculty of Medicine in Pilsen, Charles University, Pilsen, Czechia.,Biomedical Center, Faculty of Medicine in Pilsen, Charles University, Pilsen, Czechia
| | - Josef Rosenberg
- New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czechia
| | - Milan Štengl
- Department of Physiology, Faculty of Medicine in Pilsen, Charles University, Pilsen, Czechia.,Biomedical Center, Faculty of Medicine in Pilsen, Charles University, Pilsen, Czechia
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50
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Orlando M, Dvorzhak A, Bruentgens F, Maglione M, Rost BR, Sigrist SJ, Breustedt J, Schmitz D. Recruitment of release sites underlies chemical presynaptic potentiation at hippocampal mossy fiber boutons. PLoS Biol 2021; 19:e3001149. [PMID: 34153028 PMCID: PMC8216508 DOI: 10.1371/journal.pbio.3001149] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2020] [Accepted: 02/17/2021] [Indexed: 01/14/2023] Open
Abstract
Synaptic plasticity is a cellular model for learning and memory. However, the expression mechanisms underlying presynaptic forms of plasticity are not well understood. Here, we investigate functional and structural correlates of presynaptic potentiation at large hippocampal mossy fiber boutons induced by the adenylyl cyclase activator forskolin. We performed 2-photon imaging of the genetically encoded glutamate sensor iGluu that revealed an increase in the surface area used for glutamate release at potentiated terminals. Time-gated stimulated emission depletion microscopy revealed no change in the coupling distance between P/Q-type calcium channels and release sites mapped by Munc13-1 cluster position. Finally, by high-pressure freezing and transmission electron microscopy analysis, we found a fast remodeling of synaptic ultrastructure at potentiated boutons: Synaptic vesicles dispersed in the terminal and accumulated at the active zones, while active zone density and synaptic complexity increased. We suggest that these rapid and early structural rearrangements might enable long-term increase in synaptic strength.
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Affiliation(s)
- Marta Orlando
- Charité – Universitätsmedizin Berlin, corporate member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Berlin, Germany
- NeuroCure Cluster of Excellence, Berlin, Germany
| | - Anton Dvorzhak
- Charité – Universitätsmedizin Berlin, corporate member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Berlin, Germany
- NeuroCure Cluster of Excellence, Berlin, Germany
| | - Felicitas Bruentgens
- Charité – Universitätsmedizin Berlin, corporate member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Berlin, Germany
- NeuroCure Cluster of Excellence, Berlin, Germany
| | - Marta Maglione
- NeuroCure Cluster of Excellence, Berlin, Germany
- Department of Biology, Chemistry, and Pharmacy, Freie Universität Berlin, Berlin, Germany
| | - Benjamin R. Rost
- Charité – Universitätsmedizin Berlin, corporate member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Berlin, Germany
- German Center for Neurodegenerative Diseases, Berlin, Germany
| | - Stephan J. Sigrist
- NeuroCure Cluster of Excellence, Berlin, Germany
- Department of Biology, Chemistry, and Pharmacy, Freie Universität Berlin, Berlin, Germany
- German Center for Neurodegenerative Diseases, Berlin, Germany
| | - Jörg Breustedt
- Charité – Universitätsmedizin Berlin, corporate member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Berlin, Germany
- NeuroCure Cluster of Excellence, Berlin, Germany
| | - Dietmar Schmitz
- Charité – Universitätsmedizin Berlin, corporate member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Berlin, Germany
- NeuroCure Cluster of Excellence, Berlin, Germany
- German Center for Neurodegenerative Diseases, Berlin, Germany
- Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany
- Einstein Center for Neurosciences Berlin, Berlin, Germany
- Max Delbrück Center for Molecular Medicine, Berlin, Germany
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