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E-raamat: Guide To Temporal Networks, A (Second Edition)

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  • Formaat: 300 pages
  • Sari: Series On Complexity Science 6
  • Ilmumisaeg: 05-Oct-2020
  • Kirjastus: World Scientific Europe Ltd
  • Keel: eng
  • ISBN-13: 9781786349170
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Guide To Temporal Networks, A (Second Edition)Suurem pilt
  • Formaat: 300 pages
  • Sari: Series On Complexity Science 6
  • Ilmumisaeg: 05-Oct-2020
  • Kirjastus: World Scientific Europe Ltd
  • Keel: eng
  • ISBN-13: 9781786349170
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"Network science offers a powerful language to represent and study complex systems composed of interacting elements - from the Internet to social and biological systems. A Guide to Temporal Networks presents recent theoretical and modelling progress in the emerging field of temporally varying networks and provides connections between the different areas of knowledge required to address this multi-disciplinary subject. After an introduction to key concepts on networks and stochastic dynamics, the authors guide the reader through a coherent selection of mathematical and computational tools for network dynamics. Perfect for students and professionals, this book is a gateway to an active field of research developing between the disciplines of applied mathematics, physics and computer science, with applications in others including social sciences, neuroscience and biology. This second edition extensively expands upon the coverage of the first addition as the authors expertly present recent theoretical and modelling progress in the emerging field of temporal networks, providing the keys to (and connections between) the different areas of knowledge required to address this multi-disciplinary problem"--
Preface to the second edition v
Preface vii
1 Introduction 1(6)
2 Mathematical toolbox 7(30)
2.1 Probability
7(4)
2.1.1 Discrete variables
7(3)
2.1.2 Continuous variables
10(1)
2.2 Renewal processes
11(7)
2.2.1 Poisson processes
11(4)
2.2.2 General renewal processes
15(3)
2.3 Random walks and diffusion
18(3)
2.3.1 Discrete time
18(2)
2.3.2 Continuous time
20(1)
2.4 Power-law distributions
21(4)
2.5 Maximum likelihood
25(2)
2.6 Entropy, information and similarity measures
27(2)
2.7 Matrix algebra
29(2)
2.8 Linear stability
31(1)
2.9 Markov chains
32(3)
2.10 Branching processes
35(2)
3 Static networks 37(38)
3.1 Definition
37(2)
3.2 Degree distribution
39(2)
3.3 Measures derived from walks and paths
41(2)
3.4 Clustering coefficient
43(1)
3.5 Spectral properties
44(3)
3.6 Discrete-time random walks on networks
47(2)
3.7 Centrality
49(5)
3.7.1 Closeness centrality
49(1)
3.7.2 Betweenness centrality
49(1)
3.7.3 Katz centrality
50(1)
3.7.4 Eigenvector centrality
51(1)
3.7.5 PageRank
51(3)
3.8 Models of networks
54(8)
3.8.1 Erdos-Renyi random graph
55(3)
3.8.2 Configuration model
58(2)
3.8.3 Growing network with preferential attachment
60(2)
3.9 Network motifs
62(2)
3.10 Community detection
64(11)
3.10.1 Modularity
65(3)
3.10.2 Markov stability
68(2)
3.10.3 Infomap
70(3)
3.10.4 Overlapping communities
73(2)
4 Analysis of temporal networks 75(88)
4.1 Definition
75(6)
4.1.1 Event-based representation
75(2)
4.1.2 Snapshot representation
77(2)
4.1.3 Other representations
79(2)
4.2 Temporal walks and paths
81(8)
4.2.1 Definition
81(3)
4.2.2 Temporal distances
84(3)
4.2.3 Vector clock
87(2)
4.3 Components
89(2)
4.4 Triangle counts
91(3)
4.4.1 Temporal coherence of a triangle
91(2)
4.4.2 Clustering coefficient
93(1)
4.5 Centrality
94(14)
4.5.1 Time-independent centrality
95(5)
4.5.2 Time-dependent centrality
100(8)
4.6 Statistical properties of event times
108(10)
4.6.1 Distribution of inter-event times
108(1)
4.6.2 Coefficient of variation
109(1)
4.6.3 Local variation
110(1)
4.6.4 Detrending
111(1)
4.6.5 Fano factor
112(3)
4.6.6 Detrended fluctuation analysis
115(3)
4.7 Temporal correlation
118(5)
4.8 Null models and randomization procedures
123(3)
4.9 Temporal motifs
126(4)
4.10 Detection of change points and anomalies
130(7)
4.10.1 Methods based on statistical hypothesis testing and network distance measures
131(3)
4.10.2 Bayesian approach to change-point detection
134(1)
4.10.3 System-state dynamics of temporal networks
135(2)
4.11 Link prediction
137(3)
4.12 Network embedding
140(1)
4.13 Communities in temporal networks
141(18)
4.13.1 Modularity maximization under estrangement constraint
143(1)
4.13.2 Community matching approach
144(3)
4.13.3 Mapping change
147(3)
4.13.4 Model-based approach
150(2)
4.13.5 Multilayer modularity
152(4)
4.13.6 Tensor factorization approach
156(3)
4.14 Temporal networks from multivariate time series
159(4)
5 Models of temporal networks 163(40)
5.1 Models of non-Markovianity
163(2)
5.2 Stochastic temporal networks
165(1)
5.3 Activity-driven model
165(6)
5.4 Priority queue models
171(6)
5.5 Self-exciting processes
177(8)
5.5.1 Hawkes processes
178(3)
5.5.2 Cascading Poisson processes
181(4)
5.6 Markovian log-linear models
185(6)
5.7 Memory networks
191(5)
5.8 Metapopulation model
196(7)
6 Dynamics on temporal networks 203(50)
6.1 Waiting-time paradox
204(5)
6.2 Gillespie algorithms
209(7)
6.2.1 Original Gillespie algorithm
209(1)
6.2.2 Non-Markovian Gillespie algorithm
210(3)
6.2.3 Laplace Gillespie algorithm
213(3)
6.3 Random walks
216(6)
6.3.1 Node-centric random walks
216(4)
6.3.2 Edge-centric random walks
220(2)
6.4 Epidemic processes
222(23)
6.4.1 Models of epidemic processes
222(4)
6.4.2 SIS dynamics on metapopulation models
226(2)
6.4.3 SIS dynamics on switching networks
228(6)
6.4.4 SIR dynamics on the neighbour exchange network model
234(5)
6.4.5 Viral spreading dynamics under bursty interaction
239(5)
6.4.6 SIR dynamics on a tree-like stochastic temporal network
244(1)
6.5 Synchronization
245(5)
6.6 Network controllability
250(3)
Appendix A Discrete-time random walks on the line 253(4)
Appendix B Transient and absorbing states of Markov chains 257(2)
Appendix C Derivation of the degree distribution of the Barabasi-Albett (BA) model 259(4)
Bibliography 263(20)
Index 283
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