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复杂性内在逻辑(从数学到可持续世界)(英文版)(精)

  • 定价: ¥99
  • ISBN:9787040479409
  • 开 本:16开 精装
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  • 出版社:高等教育
  • 页数:269页
  • 作者:(德)沃尔琴科夫|...
  • 立即节省:
  • 2017-12-01 第1版
  • 2017-12-01 第1次印刷
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导语

  

内容提要

  

  复杂系统中的关系通常定义在两个以上的事物之间,因此可以用超图和具有更加,复杂的多维数的对象表示。沃尔琴科夫著罗朝俊、伊布拉基莫夫、阿弗莱诺维奇主编的《复杂性内在逻辑(从数学到可持续世界)(英文版)(精)》简要介绍复杂性和复杂系统科学,并且讨论基于比例随机游动信息流分析的多层级复杂系统定量描述的通用信息论方法。本书将回归到A.N.Kolmogorov所强调的从微观到宏观尺度的信息的传递是复杂系统行为的中心的基本思想。  本书内容包括介观复杂系统现代理论、时间序列、超图和图、比例随机游动以及应用于探索和表征复杂系统的现代信息理论,既适合研究生又适合初学者。本书内容自包含,并为一致地讨论诸多应用(如城市结构和音乐创作)提供了必要的基础。
    Dimitri Volchenkov博士是得克萨斯理工大学副教授,也是四川理工学院“****”讲座教授。他的研究兴趣在于复杂性科学和应用数学。他著有13本专著,发表了132篇文章,是4种交叉学科期刊的主编和21种国际期刊的审稿人。

目录

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
    1.5.1Physical 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, Probabilitiesand 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 Conditionallnformation 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 oflnformation Decomposition for Markov Chains
  2.12 Concluding Remarks and Further Reading
3 Theory of Extreme Events
  3.1 Structure of Uncertainty
  3.2 Model of Mass Extinction and Subsistence
  3.3 Probability of Mass Extinction and Subsistence UnderUncertainty
  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 UnderUncertainty
  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