　　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。
　　《复杂性内在逻辑：从数学到可持续世界（英文版）》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。
　　《复杂性内在逻辑：从数学到可持续世界（英文版）》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。
　　《复杂性内在逻辑：从数学到可持续世界（英文版）》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。
　　《复杂性内在逻辑：从数学到可持续世界（英文版）》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“千人计划”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。

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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
……

4 Statistical Basis oflnequality and Discounting the Futureand Inequality
5 Elements of Graph Theory． Adjacency， Walks， andEntropies
6 Exploring Graph Structures by Random Walks
7 We Shape Our Buildings; Thereafter They Shape Us
8 Complexity of Musical Harmony

References
Index
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 World] 下载 mobi epub pdf txt 电子书格式