| Extreme Events: Magic, Mysteries, and Challenges | p. 1 |
| Why Study Xevents? | p. 1 |
| What are Xevents? A First Approach | p. 2 |
| What are Xevents? A Second Approach | p. 3 |
| Statistical Characterisation of Xevents | p. 4 |
| Dynamic Characterisation of Xevents | p. 4 |
| Shaping Evolution | p. 5 |
| Commonalities, Analogies, Universality | p. 5 |
| Prediction, Anticipation and Management | p. 6 |
| Trends | p. 7 |
| Building Models | p. 7 |
| Observations | p. 8 |
| Risk | p. 8 |
| How the Book is Organised | p. 9 |
| Background | p. 9 |
| Rationale | p. 9 |
| The Articles | p. 10 |
| Outlook: Research Programme | p. 17 |
| References | p. 18 |
| General Considerations | |
| Anticipating Extreme Events | p. 21 |
| The Representation of Extreme Events | p. 21 |
| From Signs to Anticipation | p. 23 |
| Descartes Rehabilitated | p. 25 |
| Time, Clocks, Rhythms | p. 26 |
| The Hybrid Solution | p. 28 |
| Can a Computer Simulate Anticipation? | p. 35 |
| A New Equilibrium | p. 36 |
| A Holistic View | p. 40 |
| References | p. 43 |
| Mathematical Methods and Concepts for the Analysis of Extreme Events | p. 47 |
| Introduction | p. 47 |
| Statistical Extreme Value Theory | p. 48 |
| Origins: Classical Univariate Case | p. 48 |
| Dependent Data | p. 50 |
| Extremes in Continuous Time: Stochastic Processes, Random Fields | p. 52 |
| Probabilities of Large Deviations: Exact Behaviour | p. 53 |
| Maxima and Excursions of Gaussian and Related Processes and Fields | p. 56 |
| Relationship Between Continuous and Discrete Time: Prediction of Extremes | p. 58 |
| Other Problems | p. 60 |
| Extremes and Statistical Mechanics | p. 61 |
| Extremes and Dynamical Systems | p. 62 |
| Mapping Singularities and Catastrophe Theory: How Can They Be Related to Xevents? | p. 63 |
| References | p. 65 |
| Dynamical Interpretation of Extreme Events: Predictability and Predictions | p. 69 |
| Introduction | p. 69 |
| Prediction versus Predictability | p. 72 |
| Predictability | p. 74 |
| Prediction Schemes for Determinstic and Stochastic Time Series | p. 80 |
| Predictions Based on Markov Chain Models | p. 82 |
| An Example: Turbulent Wind Gusts | p. 84 |
| Conclusions | p. 90 |
| References | p. 93 |
| Endogenous versus Exogenous Origins of Crises | p. 95 |
| Introduction | p. 95 |
| Exogenous and Endogenous Shocks in Social Networks | p. 97 |
| A Simple Epidemic Cascade Model of Social Interactions | p. 98 |
| Internet Download Shocks | p. 100 |
| Book Sale Shocks | p. 102 |
| Social Shocks | p. 107 |
| Exogenous and Endogenous Shocks in Financial Markets | p. 109 |
| Volatility Shocks | p. 109 |
| Financial Crashes | p. 112 |
| Concluding Remarks | p. 114 |
| References | p. 116 |
| Scenarios | |
| Epilepsy: Extreme Events in the Human Brain | p. 123 |
| Introduction | p. 123 |
| Basic Mechanisms | p. 124 |
| EEG and Epilepsy | p. 126 |
| Nonlinear EEG Analysis | p. 128 |
| State Space Reconstruction | p. 129 |
| Measures Based on the Correlation Sum | p. 130 |
| Lyapunov Exponents | p. 131 |
| Synchronization and Interdependencies | p. 132 |
| Testing for Nonlinearity | p. 134 |
| Can Epileptic Seizures Be Anticipated? | p. 135 |
| Can Epileptic Seizures Be Controlled? | p. 138 |
| Conclusions | p. 140 |
| References | p. 141 |
| Extreme Events in the Geological Past | p. 145 |
| Introduction | p. 145 |
| Extreme Events in the Geological Past | p. 146 |
| Events Driven by Plate Tectonics | p. 146 |
| Changes in the Earth's Magnetic Field | p. 149 |
| Periods and Cycles of Ice Ages | p. 151 |
| Volcanism | p. 153 |
| Earthquakes | p. 154 |
| Meteoritic Impacts | p. 155 |
| Floods | p. 157 |
| Predictions and Forecasts on the Geological Timescale | p. 159 |
| Research Perspectives | p. 161 |
| References | p. 164 |
| Wind and Precipitation Extremes in the Earth's Atmosphere | p. 169 |
| Introduction | p. 169 |
| Atmospheric Scales | p. 170 |
| Wind Extremes | p. 172 |
| Small-Scale Extremes | p. 172 |
| Mesoscale Extremes | p. 175 |
| Tropical Cyclones | p. 177 |
| Extratropical Cyclones | p. 179 |
| Jet Streams | p. 179 |
| Precipitation Extremes | p. 181 |
| Discussion | p. 186 |
| References | p. 187 |
| Freak Ocean Waves and Refraction of Gaussian Seas | p. 189 |
| Introduction | p. 189 |
| Gaussian Seas | p. 192 |
| Refraction | p. 194 |
| Refraction and Gaussian Seas | p. 197 |
| Structure of the Density Fluctuations | p. 200 |
| Phase Space and Real Space | p. 200 |
| Runners and Rooster Tails | p. 202 |
| Diffusion and the Freak Index | p. 203 |
| Implications for Wave Statistics | p. 204 |
| Nonuniform Sampling | p. 204 |
| Freak Wave Events | p. 206 |
| Statistical Evidence | p. 206 |
| Conclusions | p. 208 |
| References | p. 209 |
| Predicting the Lifetime of Steel | p. 211 |
| Introduction | p. 211 |
| The Search for Defects: Positrons in Solids | p. 212 |
| The Bonn Positron Microprobe | p. 217 |
| Detection of Plastic Deformation | p. 217 |
| Damage Prediction | p. 222 |
| Summary | p. 230 |
| References | p. 230 |
| Computer Simulations of Opinions and their Reactions to Extreme Events | p. 233 |
| Introduction | p. 233 |
| General Opinion Dynamics | p. 234 |
| The D Model | p. 235 |
| The KH Model | p. 238 |
| The S Model | p. 240 |
| Damage Spreading | p. 241 |
| Continuous Opinions | p. 243 |
| Discrete Opinions | p. 250 |
| Discussion | p. 255 |
| References | p. 256 |
| Networks of the Extreme: A Search for the Exceptional | p. 259 |
| Extreme Events in Complex Systems and Our Perception of Them | p. 259 |
| A Short Survey of Scale-Free Networks | p. 261 |
| Cameo Graphs | p. 262 |
| How Extremists Determine the Structures of Scale-Free Graphs | p. 266 |
| Spreading of Epidemics in Scale-Free Networks and Robustness Under Random Attack | p. 269 |
| Conclusions and Outlook | p. 271 |
| Appendix | p. 272 |
| References | p. 273 |
| Prevention, Precaution, and Avoidance | |
| Risk Management and Physical Modelling for Mountainous Natural Hazards | p. 277 |
| Introduction | p. 277 |
| Risk Management Example for Mountain Roads | p. 278 |
| Integral Risk Management | p. 278 |
| Cost - Benefit Framework for Traffic Protection against Natural Hazards | p. 278 |
| Case Study: Fluela Pass, Switzerland | p. 280 |
| Physical Modelling of Alpine Surface Processes to Support Natural Hazard Forecasting | p. 284 |
| Summary of Alpine Surface Processes | p. 286 |
| Estimating Snow Cover Development and Snow Stability | p. 287 |
| Improvement in Extreme Runoff Forecasts from Alpine Catchments | p. 289 |
| Conclusions | p. 290 |
| References | p. 292 |
| Prevention of Surprise | p. 295 |
| Introduction | p. 295 |
| Dynamic Model | p. 298 |
| Possible Strategies | p. 300 |
| Numerical Results | p. 301 |
| Conclusions | p. 306 |
| Static Model | p. 306 |
| Set-Up | p. 307 |
| Two Societies Game | p. 307 |
| Erroneous Expectations | p. 311 |
| Discussion | p. 314 |
| References | p. 317 |
| Disasters as Extreme Events and the Importance of Network Interactions for Disaster Response Management | p. 319 |
| Disasters as Extreme Events | p. 319 |
| Examples of Causality Chains and Cascade Effects | p. 321 |
| Earthquakes | p. 321 |
| Power Blackouts | p. 322 |
| Hurricanes, Snowstorms, and Floods | p. 324 |
| Terrorist Attacks | p. 327 |
| Epidemics | p. 328 |
| Other Disasters | p. 330 |
| Secondary and Tertiary Disasters | p. 331 |
| Common Elements of Disasters | p. 332 |
| Modeling Causality Networks of Disaster Spreading | p. 334 |
| Assessment of Disaster Management Methods | p. 337 |
| System Dynamics Treatment of the Spread of a Disaster | p. 343 |
| Summary and Conclusion | p. 345 |
| References | p. 346 |
| Index | p. 349 |
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