Epidemics and rumours in complex networks:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Pr.
2010
|
| Series: | London Mathematical Society lecture note series
369 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [117] - 121 |
| Physical Description: | VI, 123 S. graph. Darst. |
| ISBN: | 9780521734431 |
Staff View
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Record in the Search Index
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| adam_text | Titel: Epidemics and rumours in complex networks
Autor: Draief, Moez
Jahr: 2010
Contents
Introduction page 1
PART I SHAPELESS NETWORKS Galton-Watson branching processes 5 7
1.1 Introduction 7
1.2 Depth-first exploration 9
1.3 Breadth-first exploration 10
1.4 One-by-one exploration 12
1.5 Chernoff bounds and total population size 15
1.6 Notes 17
1.7 Problems 17
Reed-Frost epidemics and Erdös-Renyi random graphs 19
2.1 Introduction 19
2.2 Emergence of the giant component 21
2.3 The subcritical regime 23
2.4 The supercritical regime 25
2.5 The critical regime 29
2.6 Notes 33
Connectivity and Poisson approximation 35
3.1 Introduction 35
3.2 Variation distance 35
3.3 The Stein-Chen method 37
3.4 Emergence of Connectivity in E-R graphs 40
3.5 Notes 44
Diameter of Erdös-Renyi graphs 46
4.1 Introduction 46
vi Contents
4.2 Diameter ofE-R graphs 48
4.3 Control of neighbourhood growth 49
4.4 Bounds for the diameter 51
4.5 Notes 53
5 From microscopic to macroscopic dynamics 54
5.1 Introduction 54
5.2 Birth and death processes 55
5.3 Kurtz s theorem 57
5.4 Notes 61
PART II STRUCTURED NETWORKS 63
The small-world phenomenon 65
6.1 Introduction 65
6.2 Small world according to Strogatz and Watts 66
6.3 Small world according to Kleinberg 71
6.4 Notes 76
Power laws via preferential attachment 77
7.1 Introduction 77
7.2 Barabäsi-Albert random graphs 78
7.3 Yule process 83
7.4 Notes 86
Epidemics on general graphs 87
8.1 Introduction 87
8.2 Reed-Frost model 88
8.3 SIS model 90
8.4 Epidemics on specific graphs 100
8.5 Notes 107
Viral marketing and optimised epidemics 108
9.1 Model and motivation 108
9.2 Algorithmic hardness 109
9.3 Submodular structure and its consequences 110
9.4 Viral marketing 112
9.5 Notes 115
References 117
Index 122
|
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| series | London Mathematical Society lecture note series |
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| spelling | Draief, Moez 1978- Verfasser (DE-588)140571132 aut Epidemics and rumours in complex networks Moez Draief ; Laurant Massoulié Cambridge Cambridge Univ. Pr. 2010 VI, 123 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture note series 369 Literaturverz. S. [117] - 121 Epidemiologie (DE-588)4015016-1 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Nächste-Nachbarn-Problem (DE-588)4376579-8 gnd rswk-swf Epidemiologie (DE-588)4015016-1 s Nächste-Nachbarn-Problem (DE-588)4376579-8 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Massoulié, Laurent Verfasser aut London Mathematical Society lecture note series 369 (DE-604)BV000000130 369 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020625291&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Draief, Moez 1978- Massoulié, Laurent Epidemics and rumours in complex networks London Mathematical Society lecture note series Epidemiologie (DE-588)4015016-1 gnd Stochastisches Modell (DE-588)4057633-4 gnd Nächste-Nachbarn-Problem (DE-588)4376579-8 gnd |
| subject_GND | (DE-588)4015016-1 (DE-588)4057633-4 (DE-588)4376579-8 |
| title | Epidemics and rumours in complex networks |
| title_auth | Epidemics and rumours in complex networks |
| title_exact_search | Epidemics and rumours in complex networks |
| title_full | Epidemics and rumours in complex networks Moez Draief ; Laurant Massoulié |
| title_fullStr | Epidemics and rumours in complex networks Moez Draief ; Laurant Massoulié |
| title_full_unstemmed | Epidemics and rumours in complex networks Moez Draief ; Laurant Massoulié |
| title_short | Epidemics and rumours in complex networks |
| title_sort | epidemics and rumours in complex networks |
| topic | Epidemiologie (DE-588)4015016-1 gnd Stochastisches Modell (DE-588)4057633-4 gnd Nächste-Nachbarn-Problem (DE-588)4376579-8 gnd |
| topic_facet | Epidemiologie Stochastisches Modell Nächste-Nachbarn-Problem |
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