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|Additional Physical Format:||Print version:
Hypernetworks in the Science of Complex Systems.
Singapore : World Scientific Publishing Company, ©2013
|Document Type:||Book, Computer File|
|All Authors / Contributors:||
|Notes:||Q-transmission and q-percolation.|
|Description:||1 online resource (349 pages).|
|Contents:||Preface; Foreword; Acknowledgments; Contents; 1. Introduction; 1.1 The emergence of hypernetwork theory; Polyhedra and simplices; Simplicial complexes and algebraic topology; Q-analysis; Backcloth and traffic; Hypersimplices, hypernetworks, multilevel systems and structural events; 1.2 Complexity; Complex Systems Science; Computer simulation; 1.3 Complex systems science, design and policy; Complexity and Design; Complexity and Policy; 1.4 Hypernetworks in the science of complex systems; 2. Sets and Relations; 2.1 Elements of set theory; Sets; Set membership. Set definition by intension and extensionOperations on sets; Classes; Partitions; Power Sets; Universal Sets and Complements; Sets and Logic; Products of Sets; 2.2 Mappings and functions; Composition of mappings; Inverses; 2.3 Relations; Incidence matrices and relations; Bipartite relations; Relations and logic; Composition of Relations; Equivalence and Partitions; Example; Order Relations; 3. Hypergraphs and the Galois Lattice; 3.1 Hypergraphs; 3.2 The Hypergraphs of a Bipartite Network; 3.3 The Galois Connection; 3.4 Galois Pairs and Maximal Rectangles; 3.5 The Galois Lattice. 3.6 Weak and Strong Connectivity in Hypergraphs4. Simplicial Complexes and Q-analysis; 4.1 From sets to simplices; Simplices; Examples of simplicies; Vertex parts and polyhedral wholes; 4.2 Simplices, polyhedra and their faces; 4.3 The intersection of simplices; 4.4 Representing social structure by connected simplices; 4.5 Simplicial families and simplicial complexes; Simplicial systems and bipartite relations; 4.6 Multidimensional connectivity in simplicial complexes; 4.7 Q-analysis; 4.8 Structure Vectors; 4.9 The Difference Operator; 4.10 Eccentricity; 4.11 Q-graphs; 4.12 Stars and hubs. 4.13 Galois Families4.14 Simplicial prisms; 4.15 Galois Prisms; 4.16 Descriptor Simplices and Antivertices; 4.17 Networks and Simplicial Complexes; 4.18 Examples; 4.18.1 Example: Sky and Water; 4.18.2 Example: Discriminating textured surfaces; 4.18.3 Example: Random Q-analysis; 4.18.4 Example: the Q-analysis of road intersections; Multidimensional Spaghetti; Magic Roundabouts; 4.18.5 Example: The Wisdom of Crowds; 4.18.6 Example: Multidimensional Structure in Road Networks; 5. Backcloth and traffic: dynamics constrained by topology. 5.1 The space-time backcloth constrains physical and social traffic5.2 Structuring the social backcloth to constrain the traffic; 5.3 The backcloth allows and forbids but does not require; 5.4 Traffic as patterns of numbers on the backcloth simplices; 5.5 Measuring the traffic; Ordinal measurements and order relations; 5.6 Measuring the backcloth; 5.7 Traffic-dependent backcloth dynamics; 5.8 Matrices as backcloth supporting flow traffic; 5.9 Matrices as backcloth supporting descriptor traffic; 5.10 Q-transmission in simplicial complexes; q-transmission fronts.|
|Series Title:||World scientific series on complexity science.|