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  • 複雜性內在邏輯:從數學到可持續世界
  • 點閱:3
  • 並列題名:Grammar of complexity : from mathematics to a sustainable world
  • 作者: (德)沃爾琴科夫(Dimitri Volchenkov)[著]
  • 出版社:高等教育出版社
  • 出版年:2017[民106]
  • 集叢名:非線性物理科學
  • ISBN:9787040479409
  • 格式:JPG
  • 附註:簡體字版 含索引
租期14天 今日租書可閱讀至2022-02-08

複雜系統中的關係通常定義在兩個以上的事物之間,因此可以用超圖和具有更加,複雜的多維數的對象表示。
本書簡要介紹複雜性和複雜系統科學,並且討論基於比例隨機游動信息流分析的多層級複雜系統定量描述的通用信息論方法。
本書將回歸A.N.Kolmogorov所強調的從微觀到宏觀尺度的信息的傳遞是複雜系統行為的中心的基本思想。
本書內容包含介觀複雜系統現在理論、時間序列、超圖和圖、比例隨機游動以及應用於探索和表徵複雜系統的現代信息理論,既適合研究生又適合初學者。
本書內容自包含,並為一致地討論諸多應用(如城市結構和音樂創作)提供了必要的基礎。Dimitri Volchenkov博士是德克薩斯理工大學副教授,也是四川理工學院“千人計畫”講座教授。他的研究興趣在於複雜性科學和應用數學。他著有13本專著,發表了132篇文章,是4種交叉學科期刊的主編和21種國際期刊的審稿人。

  • 1 Perplexity of Complexity(第1頁)
    • 1.1 A Compositional Containment Hierarchy of Complex Systems and Processes(第1頁)
    • 1.2 Top-Down and Bottom-Up Processes Associated to Complex Systems and Processes(第2頁)
    • 1.3 Example: A Concept of Evolution by Natural Selection(第5頁)
    • 1.4 Saltatory Temporal Evolution of Complex Systems(第6頁)
    • 1.5 Prediction, Control and Uncertainty Relations(第7頁)
    • 1.6 Uncertainty Relation for Survival Strategies(第10頁)
    • 1.7 Resilient, Fragile and Ephemeral Complex Systems and Processes(第12頁)
    • 1.8 Down the Rabbit-Hole: Simplicial Complexes as the Model for Complex Systems(第16頁)
    • 1.9 Conclusion(第20頁)
  • 2 Preliminaries: Permutations, Partitions, Probabilities and Information(第23頁)
    • 2.1 Permutations and Their Matrix Representations(第23頁)
    • 2.2 Permutation Orbits and Fixed Points(第26頁)
    • 2.3 Fixed Points and the Inclusion-Exclusion Principle(第28頁)
    • 2.4 Probability(第30頁)
    • 2.5 Finite Markov Chains(第31頁)
    • 2.6 Birkhoff – von Neumann Theorem(第33頁)
    • 2.7 Generating Functions(第34頁)
    • 2.8 Partitions(第36頁)
    • 2.9 Information and Entropy(第40頁)
    • 2.10 Conditional Information Measures for Complex Processes(第42頁)
    • 2.11 Information Decomposition for Markov Chains(第45頁)
    • 2.12 Concluding Remarks and Further Reading(第50頁)
  • 3 Theory of Extreme Events(第53頁)
    • 3.1 Structure of Uncertainty(第53頁)
    • 3.2 Model of Mass Extinction and Subsistence(第54頁)
    • 3.3 Probability of Mass Extinction and Subsistence Under Uncertainty(第57頁)
    • 3.4 Transitory Subsistence and Inevitable Mass Extinction Under Dual Uncertainty(第59頁)
    • 3.5 Extraordinary Longevity is Possible Under Singular Uncertainty(第60頁)
    • 3.6 Zipfian Longevity in a Land of Plenty(第62頁)
    • 3.7 A General Rule of Thumb for Subsistence Under Uncertainty(第64頁)
    • 3.8 Exponentially Rapid Extinction after Removal of Austerity(第65頁)
    • 3.9 On the Optimal Strategy of Subsistence Under Uncertainty(第68頁)
    • 3.10 Entropy of Survival(第70頁)
    • 3.11 Infinite Information Divergence Between Survival and Extinction(第72頁)
    • 3.12 Principle of Maximum EntropyWhy is Zipf’s Law so Ubiquitous in Nature?(第73頁)
    • 3.13 Uncertainty Relation for Extreme Events(第75頁)
    • 3.14 Fragility of Survival in the Model of Mass Extinction and Subsistence(第76頁)
    • 3.15 Conclusion(第78頁)
  • 4 Statistical Basis of Inequality and Discounting the Future and Inequality(第79頁)
    • 4.1 Divide and Conquer Strategy for Managing Strategic Uncertainty(第79頁)
    • 4.2 The Use of Utility Functions for Managing Strategic Uncertainty(第85頁)
    • 4.3 Logarithmic Utility of Time and Hyperbolic Discounting of the Future(第86頁)
    • 4.4 Would You Prefer a Dollar Today or Three Dollars Tomorrow?(第89頁)
    • 4.5 Inequality Rising from Risk-Taking Under Uncertainty(第90頁)
    • 4.6 Accumulated Advantage, Pareto Principle(第92頁)
    • 4.7 Achieveing Success by Learning(第97頁)
    • 4.8 Conclusion(第102頁)
  • 5 Elements of Graph TheoryAdjacency, Walks, and Entropies(第103頁)
    • 5.1 Binary Relations and Their Graphs(第103頁)
    • 5.2 Background from Linear Algebra(第104頁)
    • 5.3 Adjacency Operator and Adjacency Matrix(第105頁)
    • 5.4 Adjacency and Walks(第106頁)
    • 5.5 Determinant of Adjacency Matrix and Cycle Cover of a Graph(第107頁)
    • 5.6 Principal Invariants of a Graph(第108頁)
    • 5.7 Euler Characteristic and Genus of a Graph(第111頁)
    • 5.8 Hyperbolicity of Scale-Free Graphs(第113頁)
    • 5.9 Graph Automorphisms(第114頁)
    • 5.10 Automorphism Invariant Linear Functions of a Graph(第115頁)
    • 5.11 Relations Between Eigenvalues of Automorphism Invariant Linear Functions of a Graph(第118頁)
    • 5.12 The Graph as a Dynamical System(第120頁)
    • 5.13 Locally Anisotropic Random Walks on a Graph(第121頁)
    • 5.14 Stationary Distributions of Locally Anisotropic Random Walks(第123頁)
    • 5.15 Entropy of Anisotropic Random Walks(第126頁)
    • 5.16 The Relative Entropy Rate for Locally Anisotropic Random Walks(第128頁)
    • 5.17 Concluding Remarks and Further Reading(第130頁)
  • 6 Exploring Graph Structures by Random Walks(第131頁)
    • 6.1 Mixing Rates of Random Walks(第131頁)
    • 6.2 Generating Functions of Random Walks(第132頁)
    • 6.3 Cayley-Hamilton’s Theorem for Random Walks(第134頁)
    • 6.4 Hyperbolic Embeddings of Graphs by Transition Eigenvectors(第135頁)
    • 6.5 Exploring the Shape of a Graph by Random Currents(第139頁)
    • 6.6 Exterior Algebra of Random Walks(第141頁)
    • 6.7 Methods of Generalized Inverses in the Study of Graphs(第142頁)
    • 6.8 Affine Probabilistic Geometry of Generzlied Inverses(第144頁)
    • 6.9 Reduction of Graph Structures to Euclidean Metric Geometry(第145頁)
    • 6.10 Probabilistic Interpretation of Euclidean Geometry by Random Walks(第146頁)
    • 6.11 Group Generalized Inverses for Studying Directed Graphs(第149頁)
    • 6.12 Electrical Resistance Networks(第151頁)
    • 6.13 Dissipation and Effective Resistance Distance(第153頁)
    • 6.14 Effective Resistance Bounded by the Shortest Path Distance(第155頁)
    • 6.15 Kirchhoff and Wiener Indexes of a Graph(第156頁)
    • 6.16 Relation Between Effective Resistance and Commute Time Distances(第157頁)
    • 6.17 Summary(第157頁)
  • 7 We Shape Our Buildings; Thereafter They Shape Us(第159頁)
    • 7.1 The City as the Major Editor of Human Interactions(第160頁)
    • 7.2 Build Environments Organizing Spatial Experience in Humans(第160頁)
    • 7.3 Spatial Graphs of Urban Environments(第162頁)
    • 7.4 How a City Should Look?(第163頁)
    • 7.5 First-Passage Times to Ghettos(第178頁)
    • 7.6 Why is Manhattan so Expensive?(第179頁)
    • 7.7 First-Passage Times and the Tax Assessment Rate of Land(第182頁)
    • 7.8 Mosque and Church in Dialog(第183頁)
    • 7.9 Which Place is the Ideal Crime Scene?(第185頁)
    • 7.10 To Act Now to Sustain Our Common Future(第188頁)
    • 7.11 Conclusion(第190頁)
  • 8 Complexity of Musical Harmony(第191頁)
    • 8.1 Music as a Communication Process(第191頁)
    • 8.2 Musical Dice Game as a Markov Chain(第193頁)
    • 8.3 Encoding a Discrete Model of Music (MIDI) into a Markov Chain Transition Matrix(第196頁)
    • 8.4 Musical Dice Game as a Generalized Communication Process(第200頁)
    • 8.5 First-Passage Times to Notes Resolve Tonality of the Musical Score(第204頁)
    • 8.6 Analysis of Selected Musical Compositions(第207頁)
    • 8.7 First-Passage Times to Notes Feature a Composer(第247頁)
    • 8.8 Conclusion(第249頁)
  • References(第251頁)
  • Index(第267頁)
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租期14天
今日租書可閱讀至2022-02-08
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