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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Johnson, Jeffrey. Hypernetworks in the Science of Complex Systems. Singapore : World Scientific Publishing Company, ©2013 |

Material Type: | Document |

Document Type: | Book, Computer File |

All Authors / Contributors: |
Jeffrey Johnson |

ISBN: | 9781860949739 1860949738 |

OCLC Number: | 870245930 |

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. |

### Abstract:

The modern world is complex beyond human understanding and control. The science of complex systems aims to find new ways of thinking about the many interconnected networks of interaction that defy traditional approaches. Thus far, research into networks has largely been restricted to pairwise relationships represented by links between two nodes. This volume marks a major extension of networks to multidimensional hypernetworks for modeling multi-element relationships, such as companies making up the stock market, the neighborhoods forming a city, people making up committees, divisions making up.

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