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Contents Part I. General 1. Entrop y, Complexit y , Predictabilit y, and Data Analysis of Time Series and Letter Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 By W. Ebeling, L. Molgedey, J. Kurths, and U. Schwarz (With 9 Figures) 1.1 In trod uct ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Conditio na l Entropi es and Pre dic tability . . . . . . . . . . . . . . . . . . . . 4 1.3 Conce pts of Co mpl exi ty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Appl ications to B ioseq uenc es a nd Othe r In formation Carriers . . 10 1.5 Appl ications of Entrop y Concep ts to Data Analysis . . . . . . . . . . . 12 1.6 App licati ons of Complex it y Concep ts . . . . . . . . . . . . . . . . . . . . . . . 16 1.7 Concl usi on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2. W avelet Based Multifractal F orma lism: Applications to DNA Sequences, Satellite Images of the Cloud Structure, and Stock Market Data . . 27 By A. Arneodo, B. Audit, N. Decoster, J.-F. Muzy, and C. Vaillant (With 22 Figures) 2.1 In troduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2 The W avelet Transf orm Modulus Maxi ma Me thod for the Mult ifra ctal Analysi s of 1D signals . . . . . . . . . . . . . . . . . . . 32 2.3 W avelet Bas ed F ractal Analysis of DNA Sequences . . . . . . . . . . . 46 2.4 The 2 D W av elet T ransform Modulus Maxima Method for the Mult ifra ctal Analysi s of Roug h Surfa ces . . . . . . . . . . . . . . . 59
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XI I Conte nts
2.5 Application of the 2D WTMM Methodto High-Resolution Satellite Images of Cloud Structure . . . . . . . . 75
2.6 Beyond Multifractal Analysiswith Wavelet-Based Space-Scale Correlation Functions:Revealing a Causal Information Cascadein Stock Market Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Part II. Climate Systems
3. Space-Time Variability of the European Climate . . 105
By K. Fraedrich and C.-D. Schonwiese (With 16 Figures)
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1053.2 Time and Space Scales: Peaks, Gaps, and Scaling . . . . . . . . . . . . . 1063.3 Europe’s Climate: Storm Tracks, Grosswetterlagen,
and Climate Zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1133.4 Climate Trends: Europe at the End
of the Twentieth Century . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1293.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4. Is Climate Predictable? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
By K. Hasselmann (With 17 Figures)
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1414.2 Weather and Climate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1424.3 Climate Prediction of the First Kind: ENSO . . . . . . . . . . . . . . . . . 1444.4 Stochastic Climate Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1474.5 Climate Predictions of the Second Kind:
Global Warming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1534.6 Linear Response Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1564.7 Detection and Attribution of Climate Change . . . . . . . . . . . . . . . . 1594.8 Nonlinear Signatures in Linear Response . . . . . . . . . . . . . . . . . . . . 1634.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
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5. Atmospheric Persistence Analysis:Novel Approaches and Applications . . . . . . . . . . . . . . . . . 171
By A. Bunde, S. Havlin, E. Koscielny-Bunde, and H.J. Schellnhuber(With 7 Figures)
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
5.2 Analysis of Meteorological Methods . . . . . . . . . . . . . . . . . . . . . . . . . 173
5.3 The Modeling Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
5.4 Record Analysis: Detrending Techniques . . . . . . . . . . . . . . . . . . . . 176
5.5 Analysis of Temperature Records . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
5.6 Analysis of Simulated Temperature Records . . . . . . . . . . . . . . . . . 184
5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
6. Assessment and Management of Critical Events:The Breakdown of Marine Fisheriesand The North Atlantic Thermohaline Circulation193
By J. Kropp, K. Zickfeld, and K. Eisenack (With 12 Figures)
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
6.2 The Role of Market Mechanisms
in Marine Resource Exploitation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1956.3 Could Europe’s Heating System
be Threatened by Human Interference? . . . . . . . . . . . . . . . . . . . . . 204
6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
Part III. Biodynamics
7. Fractal and Multifractal Approaches
in Physiology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
219
By P.Ch. Ivanov, A.L. Goldberger, and H.E. Stanley (With 22 Figures)
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
7.2 Limitations of Traditional Techniques . . . . . . . . . . . . . . . . . . . . . . . 222
7.3 Monofractal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
7.4 Multifractal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
7.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
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XIV Contents
8. Physiological Relevance of Scalingof Heart Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
By L.S. Liebovitch, T. Penzel, and J.W. Kantelhardt (With 11 Figures)
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2598.2 Methods of Scaling Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2618.3 Heart Rate During Sleep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2678.4 Timing Between Arrhythmic Events . . . . . . . . . . . . . . . . . . . . . . . . 2778.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
9. Local Scaling Properties for Diagnostic Purposes . 283
By W. Bunk, F. Jamitzky, R. Pompl, C. Rath, and G. Morfill(With 16 Figures)
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2839.2 Reductionism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2849.3 Scaling Index Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2869.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2889.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
10. Unstable Periodic Orbitsand Stochastic Synchronizationin Sensory Biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
By F. Moss and H. Braun (With 10 Figures)
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31110.2 Unstable Periodic Orbits in Physical and Biological Systems . . . 31910.3 Synchronization of Stable Periodic Orbits
in the Paddlefish Electroreceptor
with an External Periodic Stimulus . . . . . . . . . . . . . . . . . . . . . . . . . 32410.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
11. Crowd Disasters and Simulationof Panic Situations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
By D. Helbing, I.J. Farkas, and T. Vicsek (With 9 Figures)
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
11.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
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