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复杂性内在逻辑：从数学到可持续世界(英文版) Grammar of Complexity：From Mathematics to a Sustainable

样章
作者：
Dimitri Volchenkov
定价：
99.00 元
版面字数：
300千字
开本：
16开
装帧形式：
精装
版次：
1
最新版次
印刷时间：
2017年
ISBN：
978-7-04-047940-9
物料号：
47940-00
出版时间：
2017-12-07
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
应用统计数学
暂无
  • 目录
    • 前辅文
      • 1 Perplexity of Complexity
        • 1.1 A Compositional Containment Hierarchy of Complex Systems and Processes
          • 1.2 Top-Down and Bottom-Up Processes Associated to Complex Systems and Processes
            • 1.2.1 The Top-Down Process of Adaptation (Downward Causation)
              • 1.2.2 The Bottom-Up Process of Speciation (Upward Causation)
              • 1.3 Example: A Concept of Evolution by Natural Selection
                • 1.4 Saltatory Temporal Evolution of Complex Systems
                  • 1.5 Prediction, Control and Uncertainty Relations
                    • 1.5.1 Physical Determinism and Probabilistic Causation
                      • 1.5.2 Rare and Extreme Events in Complex Systems
                        • 1.5.3 Uncertainty Relations
                        • 1.6 Uncertainty Relation for Survival Strategies
                          • 1.6.1 Situation of Adaptive Uncertainty
                            • 1.6.2 Coping with Growing Uncertainty
                            • 1.7 Resilient, Fragile and Ephemeral Complex Systems and Processes
                              • 1.7.1 Classification of Complex Systems and Processes According to the Prevalent Information Flows
                              • 1.8 Down the Rabbit-Hole: Simplicial Complexes as the Model for Complex Systems
                                • 1.8.1 Simplexes
                                  • 1.8.2 Simplicial Complexes
                                    • 1.8.3 Connectivity
                                    • 1.9 Conclusion
                                    • 2 Preliminaries: Permutations, Partitions, Probabilities and Information
                                      • 2.1 Permutations and Their Matrix Representations
                                        • 2.2 Permutation Orbits and Fixed Points
                                          • 2.3 Fixed Points and the Inclusion-Exclusion Principle
                                            • 2.4 Probability
                                              • 2.5 Finite Markov Chains
                                                • 2.6 Birkhoff–von Neumann Theorem
                                                  • 2.7 Generating Functions
                                                    • 2.8 Partitions
                                                      • 2.8.1 Compositions
                                                        • 2.8.2 Multi-Set Permutations
                                                          • 2.8.3 Weak Partitions
                                                            • 2.8.4 Integer Partitions
                                                            • 2.9 Information and Entropy
                                                              • 2.10 Conditional Information Measures for Complex Processes
                                                                • 2.11 Information Decomposition for Markov Chains
                                                                  • 2.11.1 Conditional Information Measure for the Downward Causation Process
                                                                    • 2.11.2 Conditional Information Measure for the Upward Causation Process
                                                                      • 2.11.3 Ephemeral Information in Markov Chains
                                                                        • 2.11.4 Graphic Representation of Information Decomposition for Markov Chains
                                                                        • 2.12 Concluding Remarks and Further Reading
                                                                        • 3 TheoryofExtremeEvents
                                                                          • 3.1 Structure of Uncertainty
                                                                            • 3.2 Model of Mass Extinction and Subsistence
                                                                              • 3.3 Probability of Mass Extinction and Subsistence Under Uncertainty
                                                                                • 3.4 Transitory Subsistence and Inevitable Mass Extinction Under Dual Uncertainty
                                                                                  • 3.5 Extraordinary Longevity is Possible Under Singular Uncertainty
                                                                                    • 3.6 Zipfian Longevity in a Land of Plenty
                                                                                      • 3.7 A General Rule of Thumb for Subsistence Under Uncertainty
                                                                                        • 3.8 Exponentially Rapid Extinction after Removal of Austerity
                                                                                          • 3.9 On the Optimal Strategy of Subsistence Under Uncertainty
                                                                                            • 3.10 Entropy of Survival
                                                                                              • 3.11 Infinite Information Divergence Between Survival and Extinction
                                                                                                • 3.12 Principle of Maximum Entropy. Why is Zipf’s Law so Ubiquitous in Nature?
                                                                                                  • 3.13 Uncertainty Relation for Extreme Events
                                                                                                    • 3.14 Fragility of Survival in the Model of Mass Extinction and Subsistence
                                                                                                      • 3.15 Conclusion
                                                                                                      • 4 Statistical Basis of Inequality and Discounting the Future and Inequality
                                                                                                        • 4.1 Divide and Conquer Strategy for Managing Strategic Uncertainty
                                                                                                          • 4.1.1 A Discrete Time Model of Survival with Reproduction
                                                                                                            • 4.1.2 Cues to the ‘Faster’ Versus ‘Slower’ Behavioral Strategies
                                                                                                              • 4.1.3 The Most Probable Partition Strategy
                                                                                                                • 4.1.4 The Most Likely ‘Rate’ of Behavioral Strategy
                                                                                                                  • 4.1.5 Characteristic Time of Adaptation and Evolutionary Traps
                                                                                                                  • 4.2 The Use of Utility Functions for Managing Strategic Uncertainty
                                                                                                                    • 4.3 Logarithmic Utility of Time and Hyperbolic Discounting of the Future
                                                                                                                      • 4.3.1 The Arrow-Pratt Measure of Risk Aversion
                                                                                                                        • 4.3.2 Prudence
                                                                                                                        • 4.4 Would You Prefer a Dollar Today or Three Dollars Tomorrow?
                                                                                                                          • 4.5 Inequality Rising from Risk-Taking Under Uncertainty
                                                                                                                            • 4.6 Accumulated Advantage, Pareto Principle
                                                                                                                              • 4.6.1 A Stochastic Urn Process
                                                                                                                                • 4.6.2 Pareto Principle: 80–20 Rule
                                                                                                                                  • 4.6.3 Uncertainty Relation in the Process of Accumulated Advantage
                                                                                                                                  • 4.7 Achieveing Success by Learning
                                                                                                                                    • 4.8 Conclusion
                                                                                                                                    • 5 Elements of Graph Theory. Adjacency, Walks, and Entropies
                                                                                                                                      • 5.1 Binary Relations and Their Graphs
                                                                                                                                        • 5.2 Background from Linear Algebra
                                                                                                                                          • 5.3 Adjacency Operator and Adjacency Matrix
                                                                                                                                            • 5.4 Adjacency and Walks
                                                                                                                                              • 5.5 Determinant of Adjacency Matrix and Cycle Cover of a Graph
                                                                                                                                                • 5.6 Principal Invariants of a Graph
                                                                                                                                                  • 5.7 Euler Characteristic and Genus of a Graph
                                                                                                                                                    • 5.8 Hyperbolicity of Scale-Free Graphs
                                                                                                                                                      • 5.9 Graph Automorphisms
                                                                                                                                                        • 5.10 Automorphism Invariant Linear Functions of a Graph
                                                                                                                                                          • 5.11 Relations Between Eigenvalues of Automorphism Invariant Linear Functions of a Graph
                                                                                                                                                            • 5.12 The Graph as a Dynamical System
                                                                                                                                                              • 5.13 Locally Anisotropic Random Walks on a Graph
                                                                                                                                                                • 5.14 Stationary Distributions of Locally Anisotropic Random Walks
                                                                                                                                                                  • 5.15 Entropy of Anisotropic Random Walks
                                                                                                                                                                    • 5.16 The Relative Entropy Rate for Locally Anisotropic Random Walks
                                                                                                                                                                      • 5.17 Concluding Remarks and Further Reading
                                                                                                                                                                      • 6 Exploring Graph Structures by Random Walks
                                                                                                                                                                        • 6.1 Mixing Rates of Random Walks
                                                                                                                                                                          • 6.2 Generating Functions of Random Walks
                                                                                                                                                                            • 6.3 Cayley-Hamilton’s Theorem for Random Walks
                                                                                                                                                                              • 6.4 Hyperbolic Embeddings of Graphs by Transition Eigenvectors
                                                                                                                                                                                • 6.5 Exploring the Shape of a Graph by Random Currents
                                                                                                                                                                                  • 6.6 Exterior Algebra of Random Walks
                                                                                                                                                                                    • 6.7 Methods of Generalized Inverses in the Study of Graphs
                                                                                                                                                                                      • 6.8 Affine Probabilistic Geometry of Generzlied Inverses
                                                                                                                                                                                        • 6.9 Reduction of Graph Structures to Euclidean Metric Geometry
                                                                                                                                                                                          • 6.10 Probabilistic Interpretation of Euclidean Geometry by Random Walks
                                                                                                                                                                                            • 6.10.1 Norms of and Distances Between the Pointwise Distributions
                                                                                                                                                                                              • 6.10.2 Projections of the Pointwise Distributions onto Each Other
                                                                                                                                                                                              • 6.11 Group Generalized Inverses for Studying Directed Graphs
                                                                                                                                                                                                • 6.12 Electrical Resistance Networks
                                                                                                                                                                                                  • 6.12.1 Probabilistic Interpretation of the Major Eigenvectors of the Kirchhoff Matrix
                                                                                                                                                                                                    • 6.12.2 Probabilistic Interpretation of Voltages and Currents
                                                                                                                                                                                                    • 6.13 Dissipation and Effective Resistance Distance
                                                                                                                                                                                                      • 6.14 Effective Resistance Bounded by the Shortest Path Distance
                                                                                                                                                                                                        • 6.15 Kirchhoff and Wiener Indexes of a Graph
                                                                                                                                                                                                          • 6.16 Relation Between Effective Resistance and Commute Time Distances
                                                                                                                                                                                                            • 6.17 Summary
                                                                                                                                                                                                            • 7 We Shape Our Buildings; Thereafter They Shape Us
                                                                                                                                                                                                              • 7.1 The City as the Major Editor of Human Interactions
                                                                                                                                                                                                                • 7.2 Build Environments Organizing Spatial Experience in Humans
                                                                                                                                                                                                                  • 7.3 Spatial Graphs of Urban Environments
                                                                                                                                                                                                                    • 7.4 How a City Should Look?
                                                                                                                                                                                                                      • 7.4.1 Labyrinths
                                                                                                                                                                                                                        • 7.4.2 Manhattan’s Grid
                                                                                                                                                                                                                          • 7.4.3 German Organic Cities
                                                                                                                                                                                                                            • 7.4.4 The Diamond Shaped Canal Network of Amsterdam
                                                                                                                                                                                                                              • 7.4.5 The Canal Network of Venice
                                                                                                                                                                                                                                • 7.4.6 A Regional Railway Junction
                                                                                                                                                                                                                                • 7.5 First-Passage Times to Ghettos
                                                                                                                                                                                                                                  • 7.6 Why is Manhattan so Expensive?
                                                                                                                                                                                                                                    • 7.7 First-Passage Times and the Tax Assessment Rate of Land
                                                                                                                                                                                                                                      • 7.8 Mosque and Church in Dialog
                                                                                                                                                                                                                                        • 7.9 Which Place is the Ideal Crime Scene?
                                                                                                                                                                                                                                          • 7.10 To Act Now to Sustain Our Common Future
                                                                                                                                                                                                                                            • 7.11 Conclusion
                                                                                                                                                                                                                                            • 8 Complexity of Musical Harmony
                                                                                                                                                                                                                                              • 8.1 Music as a Communication Process
                                                                                                                                                                                                                                                • 8.2 Musical Dice Game as a Markov Chain
                                                                                                                                                                                                                                                  • 8.2.1 Musical Utility Function
                                                                                                                                                                                                                                                    • 8.2.2 Notes Provide Natural Discretization of Music
                                                                                                                                                                                                                                                    • 8.3 Encoding a Discrete Model of Music (MIDI) into a Markov Chain Transition Matrix
                                                                                                                                                                                                                                                      • 8.4 Musical Dice Game as a Generalized Communication Process
                                                                                                                                                                                                                                                        • 8.4.1 The Density and Recurrence Time to a Note in the MDG
                                                                                                                                                                                                                                                          • 8.4.2 Entropy and Redundancy in Musical Compositions
                                                                                                                                                                                                                                                            • 8.4.3 Downward Causation in Music: Long-Range Structural Correlations (Melody)
                                                                                                                                                                                                                                                            • 8.5 First-Passage Times to Notes Resolve Tonality of the Musical Score
                                                                                                                                                                                                                                                              • 8.6 Analysis of Selected Musical Compositions
                                                                                                                                                                                                                                                                • 8.7 First-Passage Times to Notes Feature a Composer
                                                                                                                                                                                                                                                                  • 8.8 Conclusion
                                                                                                                                                                                                                                                                  • References
                                                                                                                                                                                                                                                                    • Index

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