Anmerkung: Intro -- Preface -- Contents -- Part I RQA Theory -- Chapter 1 Mathematical and Computational Foundations of Recurrence Quantifications -- 1.1 Phase Space Trajectories -- 1.2 Recurrence Plots -- 1.2.1 Definition of Recurrence Plots -- 1.2.2 Structures in Recurrence Plots -- 1.3 Recurrence Quantifications -- 1.3.1 Classical Recurrence Quantification Analysis -- 1.3.2 Extended Recurrence Quantification Analysis -- 1.3.3 Recurrence Time Based Measures -- 1.3.4 Complex Network Based Quantification -- 1.3.5 Advanced Quantification -- 1.3.6 Windowing Techniques -- 1.3.7 Remark on Significance -- 1.3.8 Example: Rössler System with Regime Transitions -- 1.4 Bivariate Extensions of Recurrence Analysis -- 1.4.1 Cross Recurrence Plot -- 1.4.2 Joint Recurrence Plot -- 1.4.3 Comparison Between CRPs and JRPs -- 1.5 Computational Foundations of Recurrence Quantification Analysis -- 1.5.1 Brief Historical Background -- 1.5.2 Computational Strategies -- 1.5.3 Example Program Runs -- 1.5.3.1 Programs RQD, KRQD and JRQD -- 1.5.3.2 Programs RQS, KRQS and JRQS -- 1.5.3.3 Programs RQE, KRQE and JRQE -- 1.5.4 Advanced Topics -- 1.6 Summary -- Appendix: Mathematical Models -- Auto-Regressive Process of 1st Order -- Lorenz System lorenz63 -- Rössler System roessler1976 -- Mutually Coupled Rössler Systems -- References -- Chapter 2 Estimating Kolmogorov Entropy from Recurrence Plots -- 2.1 Introduction -- 2.1.1 Entropy -- 2.1.2 Recurrence Plots -- 2.2 Discrete-State Signals -- 2.2.1 Messages, Symbolic Sequences and Discrete Sources -- 2.2.2 Entropy Rate of Symbolic Sequences -- 2.2.3 Shannon-McMillan-Breiman Theorem -- 2.2.4 RP-Based Estimation of the Entropy (Per Unit Time) -- 2.3 Continuous-State Dynamics -- 2.3.1 Kolmogorov Entropy for a Continuous State System -- 2.3.2 Grassberger and Procaccia Method for Computing K2 -- 2.3.3 RP-Based Method for Computing K2. , 2.4 Some Factors Influencing Computation of Entropy -- 2.4.1 The Notion of ε-Entropy for Analyzing Noisy Dynamics -- 2.4.2 Non-stationarity -- 2.5 Discussion -- References -- Chapter 3 Identifying Coupling Directions by Recurrences -- 3.1 Part I: Estimation of the Direction of the Coupling by Conditional Probabilities of Recurrence -- 3.1.1 Introduction: Part I -- 3.1.2 Detection of the Coupling Direction by Recurrences -- 3.1.3 Numerical Examples -- 3.1.3.1 Strongly Coupled Systems -- 3.1.3.2 Weakly Coupled Systems -- 3.1.3.3 Structurally Different Systems -- 3.1.4 Choice of the Parameters -- 3.1.5 Influence of Noise -- 3.1.6 Passive Experiments -- 3.1.7 Comparison with Other Methods -- 3.1.8 Conclusions: Part I -- 3.2 Part II: Inferring Indirect Coupling -- 3.2.1 Introduction: Part II -- 3.2.2 First Step: Univariate Analysis -- 3.2.3 Second Step: Pairwise Analysis -- 3.2.4 Third Step: Partial MCR -- 3.2.5 Decision Tree -- 3.2.6 Partial MCR for All Couplings of Fig.3.10 -- 3.2.7 Conclusions: Part II -- References -- Chapter 4 Complex Network Analysis of Recurrences -- 4.1 Introduction -- 4.2 From Recurrence Plots to Recurrence Networks -- 4.2.1 Recurrence Networks from Single Dynamical Systems -- 4.2.1.1 Basic Idea -- 4.2.1.2 Complex Network Characteristics -- 4.2.1.3 Shortest Paths in Recurrence Networks -- 4.2.1.4 Local (Vertex-Based) Measures -- 4.2.1.5 Pairwise Vertex and Edge Measures -- 4.2.1.6 Global Network Measures -- 4.2.2 Inter-System Recurrence Networks -- 4.2.2.1 Cross-Recurrences and Cross-Recurrence Networks -- 4.2.2.2 Combining Single-System and Cross-Recurrence Networks -- 4.2.2.3 Interacting Network Characteristics -- 4.2.2.4 Local Measures -- 4.2.2.5 Global Measures -- 4.2.3 Joint Recurrence Networks -- 4.2.3.1 Basic Idea -- 4.2.3.2 α-Joint Recurrence Networks -- 4.3 Analytical Description of Recurrence Networks. , 4.3.1 Random Geometric Graphs -- 4.3.2 Single-System Recurrence Network Characteristics -- 4.3.2.1 General Setting -- 4.3.2.2 Shortest Paths and Geodesics -- 4.3.2.3 Local (Vertex-Based) Measures -- 4.3.2.4 Pairwise Vertex and Edge Measures -- 4.3.2.5 Global Network Measures -- 4.3.2.6 Further Characteristics -- 4.3.3 Inter-System Recurrence Network Characteristics -- 4.3.3.1 Local Measures -- 4.3.3.2 Global Measures -- 4.4 Recurrence Networks: General Properties and Applications -- 4.4.1 Generic Network Characteristics -- 4.4.1.1 Absence of Small-World Effects -- 4.4.1.2 Emergence of Scale-Free Distributions -- 4.4.1.3 Assortative vs. Disassortative Mixing -- 4.4.2 Characterization of Dynamical Complexity -- 4.4.2.1 Average Path Length -- 4.4.2.2 Network Transitivity -- 4.4.2.3 Other Network Characteristics -- 4.4.2.4 Example: Tracing Bifurcations in the Rössler System -- 4.4.3 Characterization of Local Dimensionality -- 4.4.4 Cross-Transitivity Properties and Coupling Asymmetry -- 4.4.5 Joint Transitivity Properties and Synchronization -- 4.4.6 Real-World Applications -- 4.4.6.1 Applications in Climatology -- 4.4.6.2 Applications in Fluid Dynamics -- 4.4.6.3 Applications in Electrochemistry -- 4.4.6.4 Applications in Medicine -- 4.5 Related Approaches -- 4.6 Summary -- References -- Part II RQA Best Practices -- Chapter 5 From Time to Space Recurrences in Biopolymers -- 5.1 Introduction -- 5.1.1 Generalities -- 5.1.2 Recurrence Plots as Distance Matrices -- 5.2 Results -- 5.2.1 Folding Metrics -- 5.2.2 Chemical Metrics -- 5.2.2.1 Functional Hot-Spots in the P53 Protein -- 5.2.2.2 Thermophylic and Mesophylic Rubredoxins -- 5.3 Mixed Metrics for Complex Behavior -- 5.4 Shifting from Protein to DNA Analysis: A Cryptography Tale -- 5.4.1 Coding and Noncoding Regions in DNA -- 5.4.2 Specific Repeated Words in DNA. , 5.5 Analyzing the Information Content of Biopolymers -- 5.6 Conclusion -- Appendix 1: Cryptography -- Appendix 2: Strings from Human Languages -- (A) Dante Alighieri - Inferno - I Canto (tercets 1-3) - FILTERED -- (B) Dante Alighieri - Inferno - I Canto (tercets 1-3) - NONFILTERED (English Translation by Henry Wadsworth Longfellow)) -- (C) Dr. Suess Poem - NONFILTERED -- Appendix 3: Nucleotidic Strings -- Satellite DNA 1 - GenBank: BI067039.1 Homo Sapiens Genomic Region Containing Hypervariable Minisatellites, mRNA Sequence -- Satellite DNA 2 - GenBank: BM439581.1 Homo Sapiens Genomic Region Containing Hypervariable Minisatellites, mRNA Sequence -- References -- Chapter 6 Dynamic Coupling Between Respiratory and Cardiovascular System -- 6.1 Introduction -- 6.2 Recurrence Plot Analysis for the Interaction Between Two Series -- 6.2.1 Application to Test Data Set -- 6.2.2 Quantification -- 6.3 Quantification of Recurrences of the Van Der Pol Model -- 6.4 Cardiorespiratory Synchronization Experiment -- 6.5 Discussion -- References -- Chapter 7 Analysis of Brain Recurrence -- Abbreviations -- 7.1 Introduction -- 7.2 The Brain -- 7.2.1 Physiological Role -- 7.2.2 The Baseline EEG -- 7.2.3 The Stimulated EEG -- 7.2.4 Uses of EEG -- 7.2.5 Complexity Conjecture -- 7.3 Recurrence Analysis -- 7.3.1 Historical Development -- 7.3.2 General Properties of Recurrence Analysis -- 7.3.3 Recurrence Analysis of Model Systems -- 7.3.3.1 Model Systems -- 7.3.3.2 Detection of Nonlinear Determinism -- 7.3.4 Overview of Recurrence Analysis of Brain Electrical Activity -- 7.4 Application of Recurrence Analysis -- 7.4.1 New Paradigm for Studying the Brain -- 7.4.2 Statistical Basis of Brain Recurrence Analysis -- 7.4.3 Discovery of Human Magnetic Sense -- 7.4.4 Rationalizing Inconsistency -- 7.4.5 Canonical Conditions and ABR Variables -- 7.4.6 Inferring Mechanisms. , 7.4.7 Cell-Phone Effects on the Brain -- 7.4.8 Detecting the Presence Effect -- 7.4.9 Diagnosing Multiple Sclerosis -- 7.4.10 Applications in Sleep Medicine -- 7.5 Summary -- References -- Chapter 8 Recurrence Analysis of Otoacoustic Emissions -- 8.1 Introduction -- 8.2 Ear Morphology and Physiology -- 8.3 Otoacoustic Emissions (OAE) -- 8.4 Hearing Losses -- 8.4.1 Age-Related Hearing Loss (ARHL) -- 8.4.2 Noise Induced Hearing Loss (NIHL) -- 8.5 Clinical Practice -- 8.5.1 Pure Tone Audiometry -- 8.5.2 ILO Test -- 8.6 RQA to Study the Characteristics of Otoacoustic Emissions -- 8.7 RQA and Models of the Ear to Study the Origin of Otoacoustic Emissions -- 8.8 RQA in the Diagnosis of Hearing Losses -- 8.8.1 RQA Applied to the Study of CHL and SHL -- 8.8.2 RQA Applied to the Study of ARHL and NIHL -- 8.9 Conclusions and Future Directions -- References -- Chapter 9 Vibration Analysis in Cutting Materials -- 9.1 Introduction and the Dynamical Model -- 9.2 Simulation Results -- 9.3 Recurrence Plot Analysis -- 9.4 Conclusions -- References -- Chapter 10 Dynamical Patterns in Seismology -- 10.1 Introduction -- 10.2 Elements of Seismology -- 10.2.1 Physics of Earthquakes -- 10.2.2 Stick-Slip as a Physical Model of the Seismic Process -- 10.2.3 Seismic Time Series -- 10.2.4 Scaling Relations -- 10.2.5 Patterns of Seismicity -- 10.2.6 Earthquake Prediction -- 10.2.7 Earthquake "Control" -- 10.3 Methods of Revealing Dynamic Patterns in Acoustic/Seismic Time Series -- 10.4 Triggering and Synchronization of Stick-Slip: Laboratory Model of Seismic Process -- 10.4.1 Electromagnetic Triggering of Slip -- 10.4.2 Electromagnetic Stick-Slip Synchronization -- 10.4.3 Measuring EM Synchronization Strength of Stick-Slip -- 10.4.3.1 High Order EM Synchronization of Stick-Slip -- 10.4.4 Dynamic Mechanical Synchronization of Stick-Slip -- 10.5 Dynamical Patterns in Seismicity. , 10.5.1 Recurrence Patterns in Seismic Catalogs.

Anmerkung: Intro -- Foreword -- Preface -- Acknowledgments -- Contents -- Contributors -- Part IMethodological/Theoretical Recurrences -- 1 Torwards Visual Analytics for the Exploration of Large Sets of Time Series -- 1.1 Introduction -- 1.2 Methodology -- 1.2.1 Recurrence Quantification Analysis -- 1.2.2 VAT and iVAT -- 1.2.3 Definitions -- 1.3 Experiment with Synthetic Signals -- 1.3.1 Experimental Setup -- 1.3.2 Experimental Procedure -- 1.3.3 Discussion -- 1.3.4 Potential of Clustering Algorithms -- 1.3.5 Effect of Noise -- 1.4 Experiment with Real-World Signals -- 1.5 Future Lines of Research -- 1.6 Conclusion -- References -- 2 Applications of Transient Signal Analysis Using the Concept of Recurrence Plot Analysis -- Abstract -- 2.1 Introduction -- 2.2 Signal Analysis Tools Based on the RPA Concept -- 2.2.1 The Time-Distributed Recurrence Measure -- 2.2.2 Multi-lag Phase-Space Analysis -- 2.3 Characterization of Partial Discharges in High Voltage Cables -- 2.4 Electrical Arcs in Photovoltaic Panels -- 2.5 Water Hammer Effect Quantification -- 2.6 Conclusions -- Acknowledgement -- References -- 3 Multi-lag Phase Diagram Analysis for Transient Signal Characterization -- 3.1 Introduction -- 3.2 Mathematical Properties of Lag Diversity in Phase Diagram -- 3.3 Multi-lag Phase Diagram Analysis -- 3.3.1 Ellipse Modeling -- 3.3.2 Trend Modeling -- 3.3.3 Extremum Points/Bounding Box -- 3.3.4 Area Calculation -- 3.3.5 Polar Coordinates Analysis -- 3.4 Application Example -- 3.5 Conclusions and Perspectives -- References -- 4 Analysis of Non-stationary Signals by Recurrence Dissimilarity -- 4.1 Introduction -- 4.2 Investigated Nonlinear Systems -- 4.2.1 Burke--Shaw -- 4.2.2 Duffing--van der Pol Oscillator -- 4.2.3 Windmi -- 4.2.4 Noise Generation -- 4.3 Recurrence Dissimilarity -- 4.4 Examination of the Signal State. , 4.4.1 Detection of Chaotic Windows in the Burke--Shaw System -- 4.4.2 Recurrence Dissimilarity in the Duffing--van der Pol System -- 4.4.3 Detection of Chaotic and Periodic Windows in the Windmi System -- 4.5 Recurrence Dissimilarity in the ECG Signals -- 4.6 Evolution of the Two-Phase Flowing Systems -- 4.7 Recurrence Dissimilarity Versus Periodogram Map -- 4.8 Conclusions -- References -- 5 New Insights for Testing Linearity and Complexity with Surrogates: A Recurrence Plot Approach -- 5.1 Introduction -- 5.2 Surrogate Techniques -- 5.2.1 Surrogates for Testing Non-linearity -- 5.2.2 Pseudo-Periodic Twin Surrogates (PPTS) -- 5.3 Discriminating Non-linearity Tests and Statistics Based on Recurrence Plots -- 5.3.1 Reformulation of the DVV Using RPs -- 5.3.2 RQA Measures as Discriminating Statistics -- 5.3.3 Hypothesis Test -- 5.4 Applications -- 5.5 Conclusions -- References -- 6 Approximate Recurrence Quantification Analysis (aRQA) in Code of Best Practice -- 6.1 Introduction -- 6.2 Background and Notation -- 6.2.1 Recurrence Plots (RPs) -- 6.2.2 Recurrence Rate (RR) -- 6.2.3 Determinism (DET) -- 6.2.4 Average Diagonal Line Length (L) -- 6.2.5 Laminarity (LAM) -- 6.3 Approximate Recurrence Quantification Analysis -- 6.3.1 Reformulation of Recurrence Rate (RR) -- 6.3.2 Reformulation of Determinism (DET) -- 6.3.3 Reformulation of Average Diagonal Line Length (L) -- 6.3.4 Reformulation of Laminarity (LAM) -- 6.4 Approximate Recurrence Quantification Analysis with MATLAB -- 6.4.1 Time Delay Embedding -- 6.4.2 Discretization -- 6.4.3 Pairwise Proximity -- 6.4.4 Stationary States -- 6.4.5 Approximate RQA -- 6.5 Empirical Results -- 6.5.1 Data -- 6.5.2 Experimental Protocol -- 6.5.3 Results on Runtime -- 6.5.4 Results on Correlation -- 6.6 Conclusion and Future Work -- References -- 7 Splayed Recurrence Analysis of Iterated Dynamical Systems. , Abstract -- 7.1 Introduction -- 7.2 Graphical Theory -- 7.3 Algorithmic Implementation -- 7.4 SRA Variables -- 7.5 Test Data Sets -- 7.6 Splayed Recurrence Analysis of Test Data Sets -- 7.7 Splayed Recurrence Intervals -- 7.8 Line Entropy and Recurrence Density -- 7.9 Line Lengths and Slopes -- 7.10 Roulette Wheel Challenge -- 7.11 Discussion -- 7.12 Conclusions -- References -- Part IIPractical/Utilitarian Recurrences -- 8 Assessment of Heart Rate Complexity Recovery from Maximal Exercise Using Recurrence Quantification Analysis -- Abstract -- 8.1 Introduction -- 8.2 Methods -- 8.3 Results -- 8.4 Discussion -- 8.5 Conclusions -- References -- 9 Recurrence Analysis of Cardiac Restitution in Human Ventricle -- Abstract -- 9.1 Introduction -- 9.2 Methods -- 9.2.1 Generation of Time-Series -- 9.2.2 Dynamic Bifurcation Diagrams -- 9.3 Results -- 9.3.1 Dynamic Method -- 9.3.2 The Stationarity Method -- 9.4 Discussion -- Acknowledgment -- References -- 10 The Early Phases of Epileptogenesis Induced by Status Epilepticus Are Characterized by Persistent Dynamical Regime of Intermittency Type -- Abstract -- 10.1 Introduction -- 10.2 Methods -- 10.2.1 Animals -- 10.2.2 Models of Epileptogenesis -- 10.2.2.1 Surgical Procedure and Induction of the SE for the Rat Model of Epileptogenesis -- 10.2.2.2 Surgical Procedure and Induction of the SE for the Mouse Model of Epileptogenesis -- 10.2.3 Selection Criteria of the Time Windows of Epileptogenesis and the Related EEG Epochs, for Nonlinear Analysis -- 10.2.4 The Recurrence Quantification Analysis -- 10.2.5 Surrogates Technique and Test of Significance -- 10.2.6 Computational Resources and Software -- 10.2.7 Statistics -- 10.3 Results -- 10.4 Discussion -- Acknowledgments -- References -- 11 Chromatic and Anisotropic Cross-Recurrence Quantification Analysis of Interpersonal Behavior -- Abstract -- 11.1 Introduction. , 11.2 Cross-Matching and Chromatic Quantification Analysis -- 11.2.1 Cross-Matching Procedure -- 11.2.2 Chromatic CRQA -- 11.2.3 Application of Chromatic CRQA: Children's Dyadic Problem Solving -- 11.3 Anisotropic CRQA -- 11.3.1 Analysis of Anisotropic CRPs -- 11.3.2 Application of Anisotropic CRQA: Asymmetric Gestures-Speech Attunement -- 11.4 Model Example of Anisotropic CRQA -- 11.5 Discussion -- Acknowledgment -- References -- 12 Using Cross-Recurrence Quantification Analysis to Understand Social Motor Coordination in Children with Autism Spectrum Disorder -- Abstract -- 12.1 Introduction -- 12.2 Method -- 12.2.1 Data Analysis -- 12.2.1.1 Distribution of Relative Phase Angles (DRP) -- 12.2.1.2 Cross Recurrence Quantification Analysis (CRQA) -- 12.3 Results -- 12.3.1 Object Tapping Task -- 12.3.2 Interpersonal Hand Clapping Game -- 12.4 Discussion -- Acknowledgments -- References -- 13 Restoring Corrupted Cross-Recurrence Plots Using Matrix Completion: Application on the Time-Synchronization Between Market and Volatility Indexes -- 13.1 Introduction -- 13.2 Market and Volatility Indexes: The S& -- P 500--VIX Case -- 13.3 Time-Synchronization Using CRPs -- 13.3.1 Estimation of Embedding Parameters -- 13.4 Restoring Missing Entries in Unthresholded CRPs Using Matrix Completion -- 13.5 Performance Evaluation -- 13.6 Qualitative Economic Implications and Future Work -- References -- 14 Time-Difference-of-Arrival Estimation Based on Cross Recurrence Plots, with Application to Underwater Acoustic Signals -- 14.1 Introduction -- 14.2 Method -- 14.2.1 About Cross-Recurrence Plots -- 14.2.2 Recurrence Quantification Analysis -- 14.2.3 Time-Difference-of-Arrival Estimated with RQA Measures -- 14.3 Results on Simulated Data -- 14.3.1 Performance Analysis Methodology -- 14.3.2 Performances of the RQA Measures. , 14.3.3 Performances as a Function of the Parameters Used to Build the CRP -- 14.3.4 Comparison with the Classical Cross-Correlation -- 14.4 Validation on Real Data -- 14.4.1 Materials and Methods -- 14.4.2 Methodology to Assess the Results on Real Data -- 14.4.3 Results -- 14.5 Conclusion -- References -- 15 Reservoir-Induced Changes in Dynamics and Synchrony of River Water Temperatures Revealed by RQA and CRQA -- Abstract -- 15.1 Introduction -- 15.2 Study Area and Data Description -- 15.3 Methods -- 15.4 Results and Discussion -- 15.5 Conclusions -- Acknowledgements -- References -- 16 Recurrence Analysis of Eddy Covariance Fluxes -- 16.1 Introduction -- 16.2 Data and Preprocessing -- 16.2.1 High Resolution Data from DE-Bay -- 16.2.2 Fluxnet Data from NL-Loo -- 16.3 Recurrence Analysis of Eddy Covariance Fluxes -- 16.3.1 Embedding -- 16.3.2 Recurrence Analysis -- 16.4 High Resolution Data at DE-Bay -- 16.4.1 Fixing Embedding and RA Parameters -- 16.4.2 Changing the Temporal Resolution -- 16.4.3 Results and Discussion -- 16.5 Fluxes at NL-Loo -- 16.5.1 Fixing Embedding and RA Parameters -- 16.5.2 Results and Discussion -- 16.6 Conclusions -- References -- 17 Recurrence Plots for the Analysis of Combustion Dynamics -- 17.1 Introduction -- 17.2 Case Studies -- 17.2.1 Unveiling the Spatio-Temporal Nature of Combustion Dynamics for Turbulent Flame -- 17.2.2 RP Structures for Thermoacoustic Coupling and a Precursor to Flame Blowout -- 17.3 Conclusions -- References -- 18 Recurrence Analysis of Turbulent Fluctuations in Magnetically Confined Plasmas -- 18.1 Introduction -- 18.2 Electrostatic Potential Fluctuations -- 18.3 Recurrence-Based Analysis of Turbulent Fluctuations -- 18.4 Effects of a Bias Radial Electric Field -- 18.5 Conclusions -- References. , 19 Recurrence Quantification Analysis as an Approach for Ultrasonic Testing of Porous Carbon Fibre Reinforced Polymers.

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