• Cover (1)
• Half-title (3)
• Title page (5)
• Copyright information (6)
• Dedication (7)
• Contents (9)
• Acknowledgements (13)
• Nomenclature (15)
• Preface (19)
• I Conceptual Foundation of Complexity Science (23)
  • Introduction to Part I (25)
  • 1 The Science of Emergence (27)
    • 1.1 The Importance of Interaction (31)
    • 1.2 Past Views on Emergence (37)
    • 1.3 Further Reading (40)
    • 1.4 Exercises and Projects (41)
  • 2 Conceptual Framework of Emergence (43)
    • 2.1 Emergence of a Characteristic Scale or Lack of Scale (45)
    • 2.2 Emergence of Collective Robust Degrees of Freedom (48)
    • 2.3 Structural Coherence (50)
    • 2.4 Evolutionary Diffusion (53)
    • 2.5 Breaking of Symmetry (55)
    • 2.6 Emergence of Networks (57)
    • 2.7 Temporal Mode (59)
    • 2.8 Adaptive and Evolutionary Dynamics (61)
    • 2.9 Further Reading (62)
    • 2.10 Exercises and Projects (63)
  • 3 Specific Types of Emergent Behaviour (68)
    • 3.1 Ising-Type Models: Transitions and Criticality (70)
    • 3.2 Network Models and Scale vs. No Scale (74)
    • 3.3 Emergence of Coherence in Time: Synchronisation (79)
    • 3.4 Evolutionary Dynamics: Adaptation (82)
    • 3.5 Mean-Field Modelling: Dimensionality and Forecasting (86)
    • 3.6 Further Reading (91)
    • 3.7 Exercises and Projects (92)
  • 4 The Value of Prototypical Models of Emergence (97)
    • 4.1 The Need for Simplification of Models (98)
    • 4.2 O’Keeffe–Einstein Propositions at Work (100)
    • 4.3 Further Reading (104)
    • 4.4 Exercises and Projects (105)
• II Mathematical Tools of Complexity Science (109)
  • Introduction to Part II (111)
  • 5 Branching Processes (115)
    • 5.1 Generator Functions: Sizes and Lifetimes (119)
      • 5.1.1 Size of the Progeny (121)
      • 5.1.2 Time to Extinction (124)
    • 5.2 Branching Trees and Random Walks (125)
    • 5.3 Further Reading (128)
    • 5.4 Exercises and Projects (129)
  • 6 Statistical Mechanics (132)
    • 6.1 Probabilities and Ensembles (132)
    • 6.2 The Ising Model (141)
    • 6.3 The Peculiar Nature of the Critical Point (147)
    • 6.4 Fluctuations, Response and Correlations (149)
    • 6.5 Examples of Correlation Functions: Brain, Flocks of Birds, Finance (154)
    • 6.6 Diverging Range of Correlations (155)
      • 6.6.1 Correlation Function – Exact Approach (156)
      • 6.6.2 Correlation Function – Intuitive Discussion (161)
    • 6.7 The Two-Dimensional XY Model (165)
      • 6.7.1 2d XY: Some Mathematical Details (170)
      • 6.7.2 Vortex Unbinding (175)
      • 6.7.3 The Vortex Unbinding Transition in Other Systems (176)
    • 6.8 Further Reading (178)
    • 6.9 Exercises and Projects (178)
  • 7 Synchronisation (185)
    • 7.1 The Kuramoto Model: The Onset of Synchronisation (186)
    • 7.2 Chimera States (192)
    • 7.3 Further Reading (196)
    • 7.4 Exercises and Projects (197)
  • 8 Network Theory (199)
    • 8.1 Basic Concepts (200)
    • 8.2 Measures of the Importance of Nodes (201)
      • 8.2.1 Degree Centrality (201)
      • 8.2.2 Eigenvector Centrality (206)
      • 8.2.3 Closeness Centrality (209)
      • 8.2.4 Betweenness Centrality (209)
      • 8.2.5 How Well Does it Work? (210)
    • 8.3 Community Detection (210)
    • 8.4 Spreading on Networks – Giant Cluster (218)
    • 8.5 Analysis of Dynamics of and on Networks (225)
      • 8.5.1 Generating Networks (226)
      • 8.5.2 Random Walk on Networks (234)
      • 8.5.3 Synchronisation on Networks (238)
    • 8.6 Further Reading (246)
    • 8.7 Exercises and Projects (247)
  • 9 Information Theory and Entropy (252)
    • 9.1 Information Theory and Interdependence (254)
    • 9.2 Entropy and Estimates of Causal Relations (259)
    • 9.3 From Time Series to Networks (263)
    • 9.4 From Entropy to Probability Distribution (267)
    • 9.5 Measures of Degrees of Complexity (278)
      • 9.5.1 Lempel–Ziv Complexity Measure (278)
      • 9.5.2 Information-Theoretic Approach to Emergence (281)
      • 9.5.3 Group Entropy Measure of Complexity (294)
    • 9.6 Further Reading (296)
    • 9.7 Exercises and Projects (297)
  • 10 Stochastic Dynamics and Equations for the Probabilities (301)
    • 10.1 Random Walk and Diffusion (302)
    • 10.2 First Passage and First Return Times (315)
    • 10.3 Correlations in Time (319)
    • 10.4 Random Walk with Persistence or Anti-persistence: Hurst Exponent (324)
    • 10.5 Stationary Diffusion: Ornstein–Uhlenbeck Process (329)
    • 10.6 Evolutionary Dynamics and Clustering (331)
    • 10.7 Master Equation, Coarse Graining and Free Energy (335)
    • 10.8 Further Reading (340)
    • 10.9 Exercises and Projects (341)
  • 11 Agent-Based Modelling (346)
    • 11.1 Flocks of Birds or Schools of Fish (347)
    • 11.2 Models of Segregation (350)
    • 11.3 The Tangled Nature Model (359)
    • 11.4 Further Reading (371)
    • 11.5 Exercises and Projects (372)
  • 12 Intermittency (378)
    • 12.1 Self-Organised Criticality (379)
      • 12.1.1 Sandpile Models (380)
      • 12.1.2 Mean-Field Analysis (383)
      • 12.1.3 Lessons from Sandpile Models (386)
      • 12.1.4 Forest Fire Model (389)
    • 12.2 Record Dynamics (392)
      • 12.2.1 Statistics of Records (393)
      • 12.2.2 Spin Glasses, Superconductors, Ants and Evolution (397)
    • 12.3 Tangent Map Intermittency (401)
    • 12.4 Further Reading (404)
    • 12.5 Exercises and Projects (405)
  • 13 Tipping Points, Transitions and Forecasting (409)
    • 13.1 Externally Induced Transitions (409)
    • 13.2 Intrinsic Instability (411)
    • 13.3 Further Reading (417)
    • 13.4 Exercises and Projects (417)
  • 14 Concluding Comments and a Look to the Future (419)
    • 14.1 Further Reading (421)
• Glossary (423)
• References (433)
• Index (458)