Muutke küpsiste eelistusi

Grammar Of Complexity: From Mathematics To A Sustainable World [Kõva köide]

(Texas Tech Univ, Usa)
  • Formaat: Hardback, 284 pages
  • Ilmumisaeg: 08-Mar-2018
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9813232498
  • ISBN-13: 9789813232495
Teised raamatud teemal:
Grammar Of Complexity: From Mathematics To A Sustainable WorldSuurem pilt
  • Formaat: Hardback, 284 pages
  • Ilmumisaeg: 08-Mar-2018
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9813232498
  • ISBN-13: 9789813232495
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9789813232495.html
Märksõnad:
The book is an introduction, for both graduate students and newcomers to the field of the modern theory of mesoscopic complex systems, time series, hypergraphs and graphs, scaled random walks, and modern information theory. As these are applied for the exploration and characterization of complex systems. Our self-consistent review provides the necessary basis for consistency. We discuss a number of applications such diverse as urban structures and musical compositions.
1 Perplexity of Complexity
1(22)
1.1 A Compositional Containment Hierarchy of Complex Systems and Processes
1(1)
1.2 Top-Down and Bottom-Up Processes Associated to Complex Systems and Processes
2(3)
1.2.1 The Top-Down Process of Adaptation (Downward Causation)
3(1)
1.2.2 The Bottom-Up Process of Speciation (Upward Causation)
3(2)
1.3 Example: A Concept of Evolution by Natural Selection
5(1)
1.4 Saltatory Temporal Evolution of Complex Systems
6(1)
1.5 Prediction, Control and Uncertainty Relations
7(3)
1.5.1 Physical Determinism and Probabilistic Causation
7(1)
1.5.2 Rare and Extreme Events in Complex Systems
8(1)
1.5.3 Uncertainty Relations
9(1)
1.6 Uncertainty Relation for Survival Strategies
10(2)
1.6.1 Situation of Adaptive Uncertainty
10(1)
1.6.2 Coping with Growing Uncertainty
11(1)
1.7 Resilient, Fragile and Ephemeral Complex Systems and Processes
12(4)
1.7.1 Classification of Complex Systems and Processes According to the Prevalent Information Flows
13(3)
1.8 Down the Rabbit-Hole: Simplicial Complexes as the Model for Complex Systems
16(4)
1.8.1 Simplexes
16(2)
1.8.2 Simplicial Complexes
18(1)
1.8.3 Connectivity
18(2)
1.9 Conclusion
20(3)
2 Preliminaries: Permutations, Partitions, Probabilities and Information
23(30)
2.1 Permutations and Their Matrix Representations
23(3)
2.2 Permutation Orbits and Fixed Points
26(2)
2.3 Fixed Points and the Inclusion-Exclusion Principle
28(2)
2.4 Probability
30(1)
2.5 Finite Markov Chains
31(2)
2.6 Birkhoff--von Neumann Theorem
33(1)
2.7 Generating Functions
34(2)
2.8 Partitions
36(4)
2.8.1 Compositions
36(1)
2.8.2 Multi-Set Permutations
37(1)
2.8.3 Weak Partitions
38(1)
2.8.4 Integer Partitions
39(1)
2.9 Information and Entropy
40(2)
2.10 Conditional Information Measures for Complex Processes
42(3)
2.11 Information Decomposition for Markov Chains
45(5)
2.11.1 Conditional Information Measure for the Downward Causation Process
46(1)
2.11.2 Conditional Information Measure for the Upward Causation Process
47(2)
2.11.3 Ephemeral Information in Markov Chains
49(1)
2.11.4 Graphic Representation of Information Decomposition for Markov Chains
50(1)
2.12 Concluding Remarks and Further Reading
50(3)
3 Theory of Extreme Events
53(26)
3.1 Structure of Uncertainty
53(1)
3.2 Model of Mass Extinction and Subsistence
54(3)
3.3 Probability of Mass Extinction and Subsistence Under Uncertainty
57(2)
3.4 Transitory Subsistence and Inevitable Mass Extinction Under Dual Uncertainty
59(1)
3.5 Extraordinary Longevity is Possible Under Singular Uncertainty
60(2)
3.6 Zipfian Longevity in a Land of Plenty
62(2)
3.7 A General Rule of Thumb for Subsistence Under Uncertainty
64(1)
3.8 Exponentially Rapid Extinction after Removal of Austerity
65(3)
3.9 On the Optimal Strategy of Subsistence Under Uncertainty
68(2)
3.10 Entropy of Survival
70(2)
3.11 Infinite Information Divergence Between Survival and Extinction
72(1)
3.12 Principle of Maximum Entropy. Why is Zipf's Law so Ubiquitous in Nature?
73(2)
3.13 Uncertainty Relation for Extreme Events
75(1)
3.14 Fragility of Survival in the Model of Mass Extinction and Subsistence
76(2)
3.15 Conclusion
78(1)
4 Statistical Basis of Inequality and Discounting the Future and Inequality
79(24)
4.1 Divide and Conquer Strategy for Managing Strategic Uncertainty
79(6)
4.1.1 A Discrete Time Model of Survival with Reproduction
80(1)
4.1.2 Cues to the `Faster' Versus `Slower' Behavioral Strategies
81(1)
4.1.3 The Most Probable Partition Strategy
81(2)
4.1.4 The Most Likely `Rate' of Behavioral Strategy
83(1)
4.1.5 Characteristic Time of Adaptation and Evolutionary Traps
84(1)
4.2 The Use of Utility Functions for Managing Strategic Uncertainty
85(1)
4.3 Logarithmic Utility of Time and Hyperbolic Discounting of the Future
86(3)
4.3.1 The Arrow-Pratt Measure of Risk Aversion
88(1)
4.3.2 Prudence
88(1)
4.4 Would You Prefer a Dollar Today or Three Dollars Tomorrow?
89(1)
4.5 Inequality Rising from Risk-Taking Under Uncertainty
90(2)
4.6 Accumulated Advantage, Pareto Principle
92(5)
4.6.1 A Stochastic Urn Process
92(3)
4.6.2 Pareto Principle: 80-20 Rule
95(1)
4.6.3 Uncertainty Relation in the Process of Accumulated Advantage
96(1)
4.7 Achieveing Success by Learning
97(5)
4.8 Conclusion
102(1)
5 Elements of Graph Theory. Adjacency, Walks, and Entropies
103(28)
5.1 Binary Relations and Their Graphs
103(1)
5.2 Background from Linear Algebra
104(1)
5.3 Adjacency Operator and Adjacency Matrix
105(1)
5.4 Adjacency and Walks
106(1)
5.5 Determinant of Adjacency Matrix and Cycle Cover of a Graph
107(1)
5.6 Principal Invariants of a Graph
108(3)
5.7 Euler Characteristic and Genus of a Graph
111(2)
5.8 Hyperbolicity of Scale-Free Graphs
113(1)
5.9 Graph Automorphisms
114(1)
5.10 Automorphism Invariant Linear Functions of a Graph
115(3)
5.11 Relations Between Eigenvalues of Automorphism Invariant Linear Functions of a Graph
118(2)
5.12 The Graph as a Dynamical System
120(1)
5.13 Locally Anisotropic Random Walks on a Graph
121(2)
5.14 Stationary Distributions of Locally Anisotropic Random Walks
123(3)
5.15 Entropy of Anisotropic Random Walks
126(2)
5.16 The Relative Entropy Rate for Locally Anisotropic Random Walks
128(2)
5.17 Concluding Remarks and Further Reading
130(1)
6 Exploring Graph Structures by Random Walks
131(28)
6.1 Mixing Rates of Random Walks
131(1)
6.2 Generating Functions of Random Walks
132(2)
6.3 Cayley-Hamilton's Theorem for Random Walks
134(1)
6.4 Hyperbolic Embeddings of Graphs by Transition Eigenvectors
135(4)
6.5 Exploring the Shape of a Graph by Random Currents
139(2)
6.6 Exterior Algebra of Random Walks
141(1)
6.7 Methods of Generalized Inverses in the Study of Graphs
142(2)
6.8 Affine Probabilistic Geometry of Generzlied Inverses
144(1)
6.9 Reduction of Graph Structures to Euclidean Metric Geometry
145(1)
6.10 Probabilistic Interpretation of Euclidean Geometry by Random Walks
146(3)
6.10.1 Norms of and Distances Between the Pointwise Distributions
146(1)
6.10.2 Projections of the Pointwise Distributions onto Each Other
147(2)
6.11 Group Generalized Inverses for Studying Directed Graphs
149(2)
6.12 Electrical Resistance Networks
151(2)
6.12.1 Probabilistic Interpretation of the Major Eigenvectors of the Kirchhoff Matrix
152(1)
6.12.2 Probabilistic Interpretation of Voltages and Currents
153(1)
6.13 Dissipation and Effective Resistance Distance
153(2)
6.14 Effective Resistance Bounded by the Shortest Path Distance
155(1)
6.15 Kirchhoff and Wiener Indexes of a Graph
156(1)
6.16 Relation Between Effective Resistance and Commute Time Distances
157(1)
6.17 Summary
157(2)
7 We Shape Our Buildings; Thereafter They Shape Us
159(32)
7.1 The City as the Major Editor of Human Interactions
160(1)
7.2 Build Environments Organizing Spatial Experience in Humans
160(2)
7.3 Spatial Graphs of Urban Environments
162(1)
7.4 How a City Should Look?
163(15)
7.4.1 Labyrinths
164(4)
7.4.2 Manhattan's Grid
168(2)
7.4.3 German Organic Cities
170(2)
7.4.4 The Diamond Shaped Canal Network of Amsterdam
172(2)
7.4.5 The Canal Network of Venice
174(3)
7.4.6 A Regional Railway Junction
177(1)
7.5 First-Passage Times to Ghettos
178(1)
7.6 Why is Manhattan so Expensive?
179(3)
7.7 First-Passage Times and the Tax Assessment Rate of Land
182(1)
7.8 Mosque and Church in Dialog
183(2)
7.9 Which Place is the Ideal Crime Scene?
185(3)
7.10 To Act Now to Sustain Our Common Future
188(2)
7.11 Conclusion
190(1)
8 Complexity of Musical Harmony
191(60)
8.1 Music as a Communication Process
191(2)
8.2 Musical Dice Game as a Markov Chain
193(3)
8.2.1 Musical Utility Function
193(1)
8.2.2 Notes Provide Natural Discretization of Music
194(2)
8.3 Encoding a Discrete Model of Music (MIDI) into a Markov Chain Transition Matrix
196(4)
8.4 Musical Dice Game as a Generalized Communication Process
200(4)
8.4.1 The Density and Recurrence Time to a Note in the MDG
200(1)
8.4.2 Entropy and Redundancy in Musical Compositions
201(2)
8.4.3 Downward Causation in Music: Long-Range Structural Correlations (Melody)
203(1)
8.5 First-Passage Times to Notes Resolve Tonality of the Musical Score
204(3)
8.6 Analysis of Selected Musical Compositions
207(40)
8.7 First-Passage Times to Notes Feature a Composer
247(2)
8.8 Conclusion
249(2)
References 251(16)
Index 267