Adaptive Networks: Theory, Models and Applications (Google eBook)

Front Cover
Thilo Gross, Hiroki Sayama
Springer Science & Business Media, Jan 1, 2009 - Adaptive computing systems - 332 pages
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With adaptive, complex networks, the evolution of the network topology and the dynamical processes on the network are equally important and often fundamentally entangled. Recent research has shown that such networks can exhibit a plethora of new phenomena which are ultimately required to describe many real-world networks. Some of those phenomena include robust self-organization towards dynamical criticality, formation of complex global topologies based on simple, local rules, and the spontaneous division of 'labor' in which an initially homogenous population of network nodes self-organizes into functionally distinct classes. These are just a few. This book is a state-of-the-art survey of those unique networks. In it, leading researchers set out to define the future scope and direction of some of the most advanced developments in the vast field of complex network science and its applications.
  

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Contents

Adaptive Networks
1
12 The Interplay Between State and Topology
2
13 Timescale Separation and Critical Phenomena
3
14 SelfOrganization of Nontrivial Network Topologies
4
15 Adaptive Networks with Inseparable Timescales
5
16 In this Book
6
References
8
RealWorld Examples of Adaptive Networks
9
921 Continuous Opinions
194
922 TwoValued Choice and Irreversible Discord
195
923 The Influence of Bounded Tolerance
197
924 Asymmetric Insertion of Influence
199
925 Other Approaches
201
931 The Adaptive SIS Model
202
932 Other Approaches
206
94 Summary and Outlook
207

Social Group Dynamics in Networks
11
22 Construction of the Networks
13
23 Finding Communities
15
232 Preferential Attachment at the Level of Communities
16
233 The Static Communities
20
234 Validating the Communities
22
24 Evolving Communities
24
25 Statistical Properties of the Community Dynamics
27
252 Stationarity and Lifetime
29
253 Predicting Community Break Up
30
254 Merging of Communities
32
26 Conclusion
34
References
35
TimeDependent Complex Networks Dynamic Centrality Dynamic Motifs and Cycles of Social Interactions
39
32 Dynamic Centrality in Spatial Proximity Social Networks
44
33 Dynamic Network Motifs and Cycles of Social Interaction
46
34 Summary
48
References
49
Adaptive Biological Networks
51
42 Network Development in Mycelial Fungi
52
43 Predicted Transport Characteristics of the Mycelial Network
54
44 Comparison Between Predicted Transport and Experimental Transport
58
46 Network Robustness
61
48 Universal Features of Biological Networks?
65
References
67
SelfOrganization of Adaptive Networks
71
SelfOrganized Criticality and Adaptation in Discrete Dynamical Networks
72
52 Dynamics of Random Boolean Networks and Random Threshold Networks
77
522 Random Boolean Networks
79
524 Basic Dynamical Properties of RBNs and RTNs
80
53 Network SelfOrganization from Coevolution of Dynamics and Topology
83
532 Adaptive Thresholds Time Scale Separation Leads to Complex Topologies
90
533 Extension to Random Boolean Networks
93
534 CorrelationBased Rewiring in Neural Networks
96
54 Summary and Outlook
101
References
103
SelfOrganization and Complex Networks
107
62 Scale Invariance and SelfOrganization
109
622 SelfOrganized Criticality
111
63 Complex Networks
115
632 Network Models
116
64 A SelfOrganized Network Model
122
641 Motivation
123
642 Definition
124
643 Analytical Solution
125
644 Particular Cases
128
65 Conclusions
132
References
133
SelfOrganization of Network Structure in CoupledMap Systems
137
72 Adaptive Network of LogisticMap Units
138
721 Model Formulation
139
722 Unit Dynamics
140
723 Connection Dynamics
143
724 Network Structure
145
725 Dynamic Networks in the Desynchronized Phase
147
73 Adaptive Network of Bursting Units
153
732 Unit Dynamics
154
733 Connection Dynamics
155
734 Mechanism of Structure Formation
158
75 Summary and Discussion
160
References
162
Dynamical Optimization and Synchronization in Adaptive Complex Networks
164
82 Phase Synchronization in the Kuramoto Model
167
83 Complete Synchronization and Enhanced Synchronizability in Adaptive Complex Networks
175
832 Enhanced Synchronizability in Adaptive Complex Networks
180
84 Conclusions
186
References
187
Contact Processes and Epidemiology on Adaptive Networks
189
Contact Processes and Moment Closure on Adaptive Networks
191
92 Opinion Formation Theme and Variations
193
References
208
Noise Induced Dynamics in Adaptive Networks with Applications to Epidemiology
209
102 Model
212
103 Bifurcation Structure
214
104 Effect of Recovered Class on Fluctuations
216
105 Delayed Outbreaks
221
106 Lifetime of the Endemic Steady State
222
107 Network Geometry
223
108 Conclusions and Discussion
225
References
226
Social Games on Adaptive Networks
228
A Dynamic Model of Social Network Formation
231
A Baseline Model of Uniform Reinforcement
234
Symmetrized Reinforcement
235
113 Making Enemies
237
1131 The Transfer Model
238
1132 The Resistance Model
239
1133 A Better Model?
240
1142 Analysis of Discounting the Past
241
1143 Introduction of Noise
242
1144 Noise and Discounting
243
115 Reinforcement by Games of Nontrivial Strategy
244
1152 Coevolution of Structure and Strategy
246
116 Conclusion
247
References
251
Evolutionary Games in SelfOrganizing Populations
252
122 Active Linking
254
1221 Linking Dynamics
255
1222 Strategy Dynamics
256
1223 Separation of Timescales
258
1224 Effects of Active Linking
260
123 Individual Based Linking Dynamics
261
1232 Numerical Results
263
1233 Graph Structures Under Individual Based Linking Dynamics
264
124 Discussion
265
References
266
The Diplomats Dilemma Maximal Power for Minimal Effort in Social Networks
269
132 Definition of the Model
271
1322 Moves
272
1324 Strategy Updates and Stochastic Rewiring
274
133 Numerical Results
275
1333 Effects of Strategies on the Network Topology
277
1334 Transition Probabilities
282
1335 Dependence on System Size and Noise
283
134 Discussion
284
References
287
GraphRewritingBased Approaches
289
GraphRewriting Automata as a Natural Extension of Cellular Automata
290
142 Formulation
292
1421 Rules of GraphRewriting Automata
293
1422 Update Procedure
294
1423 Simulation of GraphRewriting Automata
295
1424 Examples
296
143 Rule Design by HandCoding
297
1431 Design of Selfreplicating Turing Machine
298
144 Rule Search by Evolutionary Computation
300
1442 Simulation Results
302
145 Exhaustive Trial
303
1451 Rule Representation
304
146 Conclusions
307
References
308
Generative Network Automata A Generalized Framework for Modeling Adaptive Network Dynamics Using Graph Rewritings
311
152 About Graph Rewriting
313
153 Definition of GNA
314
154 Generality of GNA
317
1552 Methods
320
1553 Results
321
156 Conclusion
329
References
330
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