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E-raamat: Computational Network Theory: Theoretical Foundations and Applications

(Center for Integrative Bioinformatics, Vienna, Austria), (Stowers Institute of Medical Research, Kansas City, USA),
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Computational Network Theory: Theoretical Foundations and ApplicationsSuurem pilt
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This comprehensive introduction to computational network theory as a branch of network theory builds on the understanding that such networks are a tool to derive or verify hypotheses by applying computational techniques to large scale network data.

The highly experienced team of editors and high-profile authors from around the world present and explain a number of methods that are representative of computational network theory, derived from graph theory, as well as computational and statistical techniques.

With its coherent structure and homogenous style, this reference is equally suitable for courses on computational networks.

Arvustused

"The authors present and explain a number of methods that are representative of computational network theory, derived from graph theory, as well as computational and statistical techniques. With its coherent structure and homogeneous style, this reference is equally suitable for courses on computational networks." (Zentralblatt MATH 2016)

Color Plates xv
Preface xxxi
List Of Contributors xxxiii
1 Model Selection for Neural Network Models: A Statistical Perspective 1(28)
Michele La Rocca
Cira Perna
1.1 Introduction
1(1)
1.2 Feedforward Neural Network Models
2(2)
1.3 Model Selection
4(10)
1.3.1 Feature Selection by Relevance Measures
6(4)
1.3.2 Some Numerical Examples
10(2)
1.3.3 Application to Real Data
12(2)
1.4 The Selection of the Hidden Layer Size
14(12)
1.4.1 A Reality Check Approach
15(1)
1.4.2 Numerical Examples by Using the Reality Check
16(3)
1.4.3 Testing Superior Predictive Ability for Neural Network Modeling
19(2)
1.4.4 Some Numerical Results Using Test of Superior Predictive Ability
21(2)
1.4.5 An Application to Real Data
23(3)
1.5 Concluding Remarks
26(1)
References
26(3)
2 Measuring Structural Correlations in Graphs 29(46)
Ziyu Guan
Xifeng Yan
2.1 Introduction
29(3)
2.1.1 Solutions for Measuring Structural Correlations
31(1)
2.2 Related Work
32(2)
2.3 Self Structural Correlation
34(18)
2.3.1 Problem Formulation
34(1)
2.3.2 The Measure
34(3)
2.3.2.1 Random Walk and Hitting Time
35(1)
2.3.2.2 Decayed Hitting Time
36(1)
2.3.3 Computing Decayed Hitting Time
37(4)
2.3.3.1 Iterative Approximation
37(2)
2.3.3.2 A Sampling Algorithm for h(vi, B)
39(1)
2.3.3.3 Complexity
40(1)
2.3.4 Assessing SSC
41(4)
2.3.4.1 Estimating p(Vq)
41(1)
2.3.4.2 Estimating the Significance of p(Vq)
42(3)
2.3.5 Empirical Studies
45(6)
2.3.5.1 Datasets
45(1)
2.3.5.2 Performance of DHT Approximation
45(2)
2.3.5.3 Effectiveness on Synthetic Events
47(2)
2.3.5.4 SSC of Real Event
49(2)
2.3.5.5 Scalability of Sampling-alg
51(1)
2.3.6 Discussions
51(1)
2.4 Two-Event Structural Correlation
52(20)
2.4.1 Preliminaries and Problem Formulation
52(1)
2.4.2 Measuring TESC
53(3)
2.4.2.1 The Test
54(2)
2.4.2.2 Reference Nodes
56(1)
2.4.3 Reference Node Sampling
56(6)
2.4.3.1 Batch_BFS
57(1)
2.4.3.2 Importance Sampling
58(3)
2.4.3.3 Global Sampling in Whole Graph
61(1)
2.4.3.4 Complexity Analysis
61(1)
2.4.4 Experiments
62(8)
2.4.4.1 Graph Datasets
62(1)
2.4.4.2 Event Simulation Methodology
63(1)
2.4.4.3 Performance Comparison
63(2)
2.4.4.4 Batch Importance Sampling
65(1)
2.4.4.5 Impact of Graph Density
66(1)
2.4.4.6 Efficiency and Scalability
66(2)
2.4.4.7 Real Events
68(2)
2.4.5 Discussions
70(2)
2.5 Conclusions
72(1)
Acknowledgments
72(1)
References
72(3)
3 Spectral Graph Theory and Structural Analysis of Complex Networks: An Introduction 75(22)
Salissou Moutari
Ashraf Ahmed
3.1 Introduction
75(1)
3.2 Graph Theory: Some Basic Concepts
76(5)
3.2.1 Connectivity in Graphs
77(3)
3.2.2 Subgraphs and Special Graphs
80(1)
3.3 Matrix Theory: Some Basic Concepts
81(2)
3.3.1 Trace and Determinant of a Matrix
81(1)
3.3.2 Eigenvalues and Eigenvectors of a Matrix
82(1)
3.4 Graph Matrices
83(3)
3.4.1 Adjacency Matrix
84(1)
3.4.2 Incidence Matrix
84(1)
3.4.3 Degree Matrix and Diffusion Matrix
85(1)
3.4.4 Laplace Matrix
85(1)
3.4.5 Cut-Set Matrix
86(1)
3.4.6 Path Matrix
86(1)
3.5 Spectral Graph Theory: Some Basic Results
86(5)
3.5.1 Spectral Characterization of Graph Connectivity
87(2)
3.5.1.1 Spectral Theory and Walks
88(1)
3.5.2 Spectral Characteristics of some Special Graphs and Subgraphs
89(2)
3.5.2.1 Tree
89(1)
3.5.2.2 Bipartite Graph
89(1)
3.5.2.3 Complete Graph
90(1)
3.5.2.4 Regular Graph
90(1)
3.5.2.5 Line Graph
90(1)
3.5.3 Spectral Theory and Graph Colouring
91(1)
3.5.4 Spectral Theory and Graph Drawing
91(1)
3.6 Computational Challenges for Spectral Graph Analysis
91(3)
3.6.1 Krylov Subspace Methods
91(3)
3.6.2 Constrained Optimization Approach
94(1)
3.7 Conclusion
94(1)
References
95(2)
4 Contagion in Interbank Networks 97(40)
Grzegorz Halaj
Christoffer Kok
4.1 Introduction
97(2)
4.2 Research Context
99(4)
4.3 Models
103(16)
4.3.1 Simulated Networks
104(5)
4.3.1.1 Probability Map
105(1)
4.3.1.2 Interbank Network
105(2)
4.3.1.3 Contagion Mechanism
107(1)
4.3.1.4 Fire sales of Illiquid Portfolio
108(1)
4.3.2 Systemic Probability Index
109(1)
4.3.3 Endogenous Networks
110(9)
4.3.3.1 Banks
113(2)
4.3.3.2 First Round-Optimization of Interbank Assets
115(1)
4.3.3.3 Second Round-Accepting Placements According to Funding Needs
116(1)
4.3.3.4 Third Round-Bargaining Game
117(1)
4.3.3.5 Fourth Round-Price Adjustments
118(1)
4.4 Results
119(8)
4.4.1 Data
119(1)
4.4.2 Simulated Networks
120(3)
4.4.3 Structure of Endogenous Interbank Networks
123(4)
4.5 Stress Testing Applications
127(3)
4.6 Conclusions
130(1)
References
131(6)
5 Detection, Localization, and Tracking of a Single and Multiple Targets with Wireless Sensor Networks 137(36)
Natallia Katenka
5.1 Introduction and Overview
137(1)
5.2 Data Collection and Fusion by WSN
138(3)
5.3 Target Detection
141(8)
5.3.1 Target Detection from Value Fusion (Energies)
142(1)
5.3.2 Target Detection from Ordinary Decision Fusion
143(1)
5.3.3 Target Detection from Local Vote Decision Fusion
144(5)
5.3.3.1 Remark 1: LVDF Fixed Neighbourhood Size
145(1)
5.3.3.2 Remark 2: LVDF Regular Grids
146(2)
5.3.3.3 Remark 3: Quality of Approximation
148(1)
5.3.3.4 Remark 4: Detection Performance
148(1)
5.3.3.5 Concluding Remarks
148(1)
5.4 Single Target Localization and Diagnostic
149(8)
5.4.1 Localization and Diagnostic from Value Fusion (Energies)
150(1)
5.4.2 Localization and Diagnostic from Ordinary Decision Fusion
151(1)
5.4.3 Localization and Diagnostic from Local Vote Decision Fusion
152(1)
5.4.4 Hybrid Maximum Likelihood Estimates
153(1)
5.4.5 Properties of Maximum-Likelihood Estimates
154(3)
5.4.5.1 Remark 1: Accuracy of Target Localization
155(1)
5.4.5.2 Remark 2: Starting Values for Localization
155(1)
5.4.5.3 Remark 3: Robustness to Model Misspecification
156(1)
5.4.5.4 Remark 4: Computational Cost
156(1)
5.4.5.5 Concluding Remarks
157(1)
5.5 Multiple Target Localization and Diagnostic
157(4)
5.5.1 Multiple Target Localization from Energies
158(1)
5.5.2 Multiple Target Localization from Binary Decisions
158(1)
5.5.3 Multiple Target Localization from Corrected Decisions
159(6)
5.5.3.1 Remark 1: Hybrid Estimation
160(1)
5.5.3.2 Remark 2: Starting Values
160(1)
5.5.3.3 Estimating the Number of Targets
160(1)
5.5.3.4 Concluding Remarks
160(1)
5.6 Multiple Target Tracking
161(4)
5.7 Applications and Case Studies
165(5)
5.7.1 The NEST Project
166(2)
5.7.2 The ZebraNet Project
168(2)
5.8 Final Remarks
170(1)
References
171(2)
6 Computing in Dynamic Networks 173(46)
Othon Michail
Ioannis Chatzigiannakis
Paul G. Spirakis
6.1 Introduction
173(4)
6.1.1 Motivation-State of the Art
173(4)
6.1.2 Structure of the
Chapter
177(1)
6.2 Preliminaries
177(3)
6.2.1 The Dynamic Network Model
177(2)
6.2.2 Problem Definitions
179(1)
6.3 Spread of Influence in Dynamic Graphs (Causal Influence)
180(2)
6.4 Naming and Counting in Anonymous Unknown Dynamic Networks
182(14)
6.4.1 Further Related Work
183(1)
6.4.2 Static Networks with Broadcast
183(3)
6.4.3 Dynamic Networks with Broadcast
186(2)
6.4.4 Dynamic Networks with One-to-Each
188(7)
6.4.5 Higher Dynamicity
195(1)
6.5 Causality, Influence, and Computation in Possibly Disconnected Synchronous Dynamic Networks
196(16)
6.5.1 Our Metrics
196(5)
6.5.1.1 The Influence Time
196(3)
6.5.1.2 The Moi (Concurrent Progress)
199(1)
6.5.1.3 The Connectivity Time
200(1)
6.5.2 Fast Propagation of Information under Continuous Disconnectivity
201(2)
6.5.3 Termination and Computation
203(16)
6.5.3.1 Nodes Know an Upper Bound on the ct: An Optimal Termination Criterion
204(1)
6.5.3.2 Known Upper Bound on the oit
205(3)
6.5.3.3 Hearing the Future
208(4)
6.6 Local Communication Windows
212(3)
6.7 Conclusions
215(1)
References
216(3)
7 Visualization and Interactive Analysis for Complex Networks by means of Lossless Network Compression 219(18)
Matthias Reimann
Loic Royer
Simone Daminelli
Michael Schroeder
7.1 Introduction
219(2)
7.1.1 Illustrative Example
221(1)
7.2 Power Graph Algorithm
221(6)
7.2.1 Formal Definition of Power Graphs
221(1)
7.2.2 Semantics of Power Graphs
222(1)
7.2.3 Power Graph Conditions
222(1)
7.2.4 Edge Reduction and Relative Edge Reduction
223(2)
7.2.5 Power Graph Extraction
225(2)
7.3 Validation - Edge Reduction Differs from Random
227(1)
7.4 Graph Comparison with Power Graphs
228(1)
7.5 Excursus: Layout of Power Graphs
229(2)
7.6 Interactive Visual Analytics
231(3)
7.6.1 Power Edge Filtering
232(2)
7.6.1.1 Zooming and Network Expansion
233(1)
7.7 Conclusion
234(1)
References
234(3)
Index 237
Matthias Dehmer studied mathematics at the University of Siegen (Germany) and received his Ph.D. in computer science from the Technical University of Darmstadt (Germany). Afterwards, he was a research fellow at Vienna Bio Center (Austria), Vienna University of Technology, and University of Coimbra (Portugal). He obtained his habilitation in applied discrete mathematics from the Vienna University of Technology. Currently, he is Professor at UMIT - The Health and Life Sciences University (Austria) and also holds a position at the Universität der Bundeswehr München. His research interests are in applied mathematics, bioinformatics, systems biology, graph theory, complexity and information theory. He has written over 180 publications in his research areas.

Frank Emmert-Streib studied physics at the University of Siegen (Germany) gaining his PhD in theoretical physics from the University of Bremen (Germany). He received postdoctoral training from the Stowers Institute for Medical Re- search (Kansas City, USA) and the University of Washington (Seattle, USA). Currently, he is an associate professor at the Queen's University Belfast (UK) at the Center for Cancer Research and Cell Biology heading the Computational Biology and Machine Learning Laboratory. His main research interests are in the field of computational medicine, network biology and statistical genomics.
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