Preface |
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xi | |
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PART 1 MALWARE DIFFUSION MODELING FRAMEWORK |
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Chapter 1 Fundamentals of Complex Communications Networks |
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3 | (24) |
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1.1 Introduction to Communications Networks and Malicious Software |
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3 | (2) |
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1.2 A Brief History of Communications Networks and Malicious Software |
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5 | (10) |
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1.2.1 From Computer to Communications Networks |
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5 | (4) |
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1.2.2 The Emergence and Proliferation of Wireless Networks |
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9 | (3) |
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1.2.3 Malicious Software and the Internet |
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12 | (3) |
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1.3 Complex Networks and Network Science |
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15 | (12) |
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16 | (5) |
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21 | (2) |
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1.3.3 Network Graphs Primer |
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23 | (4) |
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Chapter 2 Malware Diffusion in Wired and Wireless Complex Networks |
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27 | (12) |
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2.1 Diffusion Processes and Malware Diffusion |
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27 | (3) |
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2.1.1 General Diffusion Processes |
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27 | (1) |
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2.1.2 Diffusion of Malware in Communication Networks |
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28 | (2) |
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2.2 Types of Malware Outbreaks in Complex Networks |
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30 | (4) |
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2.3 Node Infection Models |
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34 | (5) |
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Chapter 3 Early Malware Diffusion Modeling Methodologies |
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39 | (24) |
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39 | (1) |
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3.2 Basic Epidemics Models |
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39 | (14) |
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3.2.1 Simple (Classical) Epidemic Model---SI Model |
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41 | (3) |
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3.2.2 General Epidemic Model: Kermack-McKendrick Model |
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44 | (2) |
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46 | (3) |
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49 | (4) |
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3.3 Other Epidemics Models |
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53 | (5) |
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3.3.1 Epidemics Model in Scale-free Networks |
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53 | (2) |
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3.3.2 Generalized Epidemics-Endemics Models |
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55 | (3) |
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3.4 Miscellaneous Malware Modeling Models |
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58 | (1) |
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3.5 Scope and Achievements of Epidemics |
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59 | (4) |
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PART 2 STATE-OF-THE-ART MALWARE MODELING FRAMEWORKS |
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Chapter 4 Queuing-based Malware Diffusion Modeling |
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63 | (44) |
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63 | (1) |
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4.2 Malware Diffusion Behavior and Modeling via Queuing Techniques |
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64 | (3) |
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64 | (2) |
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4.2.2 Mapping of Malware Diffusion to a Queuing Problem |
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66 | (1) |
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4.3 Malware Diffusion Modeling in Nondynamic Networks |
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67 | (24) |
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71 | (1) |
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4.3.2 Steady-state Behavior and Analysis |
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72 | (19) |
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4.4 Malware Diffusion Modeling in Dynamic Networks with Churn |
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91 | (16) |
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4.4.1 Malware Diffusion Models and Network Churn |
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94 | (1) |
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4.4.2 Open Queuing Network Theory for Modeling Malware Spreading in Complex Networks with Churn |
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94 | (4) |
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4.4.3 Analysis of Malware Propagation in Networks with Churn |
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98 | (3) |
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4.4.4 Demonstration of Queuing Framework for Malware Spreading in Complex and Wireless Networks |
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101 | (6) |
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Chapter 5 Malware-Propagative Markov Random Fields |
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107 | (32) |
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107 | (1) |
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5.2 Markov Random Fields Background |
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108 | (7) |
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5.2.1 Markov Random Fields |
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108 | (2) |
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5.2.2 Gibbs Distribution and Relation to MRFs |
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110 | (1) |
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5.2.3 Gibbs Sampling and Simulated Annealing |
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111 | (4) |
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5.3 Malware Diffusion Modeling Based on MRFs |
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115 | (3) |
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118 | (9) |
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119 | (5) |
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5.4.2 Regular Lattices: Finite and Infinite Grids |
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124 | (3) |
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5.5 Complex Networks with Stochastic Topologies |
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127 | (12) |
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129 | (2) |
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5.5.2 Small-world Networks |
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131 | (1) |
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5.5.3 Scale-free Networks |
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132 | (1) |
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5.5.4 Random Geometric Networks |
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133 | (1) |
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5.5.5 Comparison of Malware Diffusion in Complex Topologies |
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134 | (5) |
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Chapter 6 Optimal Control Based Techniques |
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139 | (16) |
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139 | (3) |
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6.2 Example---an Optimal Dynamic Attack: Seek and Destroy |
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142 | (4) |
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6.2.1 Dynamics of State Evolution |
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143 | (2) |
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6.2.2 Objective Functional |
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145 | (1) |
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6.3 Worm's Optimal Control |
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146 | (9) |
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6.3.1 Structure of the Maximum Damage Attack |
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148 | (3) |
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6.3.2 Proof of Theorem 6.1 |
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151 | (1) |
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6.3.3 Proof of Theorem 6.1: Optimal Rate of Killing |
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152 | (2) |
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154 | (1) |
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Chapter 7 Game-Theoretic Techniques |
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155 | (14) |
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155 | (2) |
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157 | (3) |
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7.3 Network-Malware Dynamic Game |
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160 | (9) |
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160 | (1) |
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7.3.2 A Framework for Computation of the Saddle-point Strategies |
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161 | (2) |
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7.3.3 Structural Properties of Saddle-point Defense Strategy |
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163 | (3) |
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7.3.4 Structure of the Saddle-point Attack Strategy |
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166 | (1) |
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167 | (2) |
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Chapter 8 Qualitative Comparison |
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169 | (12) |
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169 | (1) |
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8.2 Computational Complexity Comparison |
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170 | (2) |
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8.3 Implementation Efficiency Comparison |
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172 | (1) |
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8.4 Sensitivity Comparison |
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173 | (1) |
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8.5 Practical Value Comparison |
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174 | (2) |
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176 | (1) |
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177 | (4) |
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PART 3 APPLICATIONS AND THE ROAD AHEAD |
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Chapter 9 Applications of State-of-the-art Malware Modeling Frameworks |
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181 | (34) |
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181 | (11) |
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9.1.1 Introduction and Objectives |
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181 | (1) |
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9.1.2 Queuing Model for the Aggregated Network Behavior under Attack |
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181 | (1) |
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9.1.3 Steady-state Behavior and Analysis |
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182 | (3) |
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9.1.4 Optimal Attack Strategies |
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185 | (2) |
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9.1.5 Robustness Analysis for Wireless Multihop Networks |
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187 | (4) |
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191 | (1) |
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9.2 Dynamics of Information Dissemination |
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192 | (17) |
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9.2.1 Introduction to Information Dissemination |
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192 | (3) |
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9.2.2 Previous Works on Information Dissemination |
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195 | (1) |
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9.2.3 Epidemic-based Modeling Framework for IDD in Wireless Complex Communication Networks |
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196 | (2) |
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9.2.4 Wireless Complex Networks Analyzed and Assessment Metrics |
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198 | (3) |
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9.2.5 Useful-information Dissemination Epidemic Modeling |
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201 | (8) |
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9.3 Malicious-information Propagation Modeling |
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209 | (6) |
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9.3.1 SIS Closed Queuing Network Model |
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210 | (5) |
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Chapter 10 The Road Ahead |
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215 | (8) |
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215 | (1) |
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10.2 Open Problems for Queuing-based Approaches |
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215 | (2) |
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10.3 Open Problems for MRF-based Approaches |
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217 | (1) |
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10.4 Optimal Control and Dynamic Game Frameworks |
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218 | (1) |
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10.5 Open Problems for Applications of Malware Diffusion Modeling Frameworks |
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219 | (1) |
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10.6 General Directions for Future Work |
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220 | (3) |
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223 | (6) |
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223 | (3) |
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226 | (3) |
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APPENDIX A Systems of Ordinary Differential Equations |
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229 | (6) |
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229 | (1) |
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A.2 First-order Differential Equations |
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230 | (1) |
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A.3 Existence and Uniqueness of a Solution |
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231 | (1) |
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A.4 Linear Ordinary Differential Equations |
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232 | (1) |
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233 | (2) |
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APPENDIX B Elements of Queuing Theory and Queuing Networks |
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235 | (20) |
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235 | (1) |
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B.2 Basic Queuing Systems, Notation, and Little's Law |
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235 | (1) |
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B.2.1 Elements of a Queuing System |
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236 | (1) |
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B.2.2 Fundamental Notation and Quantities of Interest |
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237 | (1) |
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B.2.3 Relation Between Arrival-Departure Processes and Little's Law |
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238 | (2) |
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B.3 Markovian Systems in Equilibrium |
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240 | (1) |
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B.3.1 Discrete-time Markov Chains |
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240 | (2) |
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B.3.2 Continuous-time Markov Processes |
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242 | (1) |
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B.3.3 Birth-and-Death Processes |
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242 | (2) |
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B.3.4 The M/M/1 Queuing System |
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244 | (1) |
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B.3.5 The M/M/m System and Other Multiserver Queuing Systems |
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244 | (3) |
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247 | (1) |
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248 | (2) |
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250 | (2) |
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B.6.1 Analytical Solution of Two-queue Closed Queuing Network |
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252 | (3) |
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APPENDIX C Optimal Control Theory and Hamiltonians |
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255 | (28) |
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C.1 Basic Definitions, State Equation Representations, and Basic Types of Optimal Control Problems |
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255 | (4) |
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C.2 Calculus of Variations |
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259 | (2) |
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C.3 Finding Trajectories that Minimize Performance Measures |
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261 | (1) |
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C.3.1 Functionals of a Single Function |
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261 | (1) |
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C.3.2 Functionals of Several Independent Functions |
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262 | (1) |
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C.3.3 Piecewise-smooth Extremals |
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263 | (1) |
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C.3.4 Constrained Extrema |
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263 | (3) |
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C.4 Variational Approach for Optimal Control Problems |
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266 | (1) |
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C.4.1 Necessary Conditions for Optimal Control |
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266 | (1) |
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C.4.2 Pontryagin's Minimum Principle |
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267 | (1) |
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C.4.3 Minimum-time Problems |
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268 | (1) |
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C.4.4 Minimum Control-effort Problems |
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269 | (2) |
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C.4.5 Singular Intervals in Optimal Control Problems |
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271 | (1) |
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C.5 Numerical Determination of Optimal Trajectories |
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272 | (1) |
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273 | (1) |
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C.5.2 Variation of Extremals |
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274 | (1) |
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275 | (1) |
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C.5.4 Gradient Projection |
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276 | (3) |
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C.6 Relationship Between Dynamic Programming (DP) and Minimum Principle |
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279 | (4) |
Bibliography |
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283 | (10) |
Author Index |
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293 | (6) |
Subject Index |
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299 | |