| Foreword | 5 |
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| Contents | 7 |
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| Mathematical Methods in Counterterrorism: Tools and Techniques for a New Challenge | 14 |
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| 1 Introduction | 14 |
| 2 Organization | 15 |
| 3 Conclusion and Acknowledgements | 17 |
| Network Analysis | 19 |
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| Modeling Criminal Activity in Urban Landscapes | 20 |
| 1 Introduction | 20 |
| 2 Background and Motivation | 22 |
| 3 Mastermind Framework | 25 |
| 4 Mastermind: Modeling Criminal Activity | 30 |
| 5 Concluding Remarks | 39 |
| References | 40 |
| Extracting Knowledge from Graph Data in Adversarial Settings | 43 |
| 1 Characteristics of Adversarial Settings | 43 |
| 2 Sources of Graph Data | 44 |
| 3 Eigenvectors and the Global Structure of a Graph | 45 |
| 4 Visualization | 46 |
| 5 Computation of Node Properties | 47 |
| 6 Embedding Graphs in Geometric Space | 49 |
| 7 Summary | 62 |
| References | 63 |
| Mathematically Modeling Terrorist Cells: Examining the Strength of Structures of Small Sizes | 65 |
| 1 Back to Basics : Recap of the Poset Model of Terrorist Cells | 65 |
| 2 Examining the Strength of Terrorist Cell Structures – Questions Involved and Relevance to Counterterrorist Operations | 67 |
| 3 Definition of Strength in Terms of the Poset Model | 68 |
| 4 Posets Addressed | 69 |
| 5 Algorithms Used | 69 |
| 6 Structures of Posets of Size 7: Observations and Patterns | 71 |
| 7 Implications and Applicability | 75 |
| 8 Ideas for Future Research | 76 |
| 9 Conclusion | 77 |
| Acknowledgments | 77 |
| References | 77 |
| Combining Qualitative and Quantitative Temporal Reasoning for Criminal Forensics* | 78 |
| 1 Introduction | 78 |
| 2 Temporal Knowledge Representation and Reasoning | 80 |
| 3 Point-Interval Logic | 81 |
| 4 Using Temper for Criminal Forensics – The London Bombing | 91 |
| 5 Conclusion | 97 |
| Acknowledgements | 98 |
| References | 98 |
| Two Theoretical Research Questions Concerning the Structure of the Perfect Terrorist Cell | 100 |
| Appendix: Cutsets and Minimal Cutsets of All n-Member Posets(n = 5) | 103 |
| References | 111 |
| Forecasting | 113 |
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| Understanding Terrorist Organizations with a Dynamic Model | 114 |
| 1 Introduction | 114 |
| 2 A Mathematical Model | 116 |
| 3 Analysis of the Model | 118 |
| 4 Discussion | 121 |
| 5 Counter-Terrorism Strategies | 124 |
| 6 Conclusions | 127 |
| 7 Appendix | 128 |
| References | 131 |
| Inference Approaches to Constructing Covert Social Network Topologies | 133 |
| 1 Introduction | 133 |
| 2 Network Analysis | 134 |
| 3 A Bayesian Inference Approach | 135 |
| 4 Case 1 Analysis | 137 |
| 5 Case 2 Analysis | 140 |
| 6 Conclusions | 144 |
| References | 145 |
| A Mathematical Analysis of Short-term Responses to Threats of Terrorism | 147 |
| 1 Introduction | 147 |
| 2 Information Model | 151 |
| 3 Defensive Measures | 154 |
| 4 Analysis | 158 |
| 5 Illustrative numerical experiments | 162 |
| 6 Summary | 164 |
| References | 166 |
| Network Detection Theory | 167 |
| 1 Introduction | 167 |
| 2 Random Intersection Graphs | 171 |
| 3 Subgraph Count Variance | 175 |
| 4 Dynamic Random Graphs | 178 |
| 5 Tracking on Networks | 179 |
| 6 Hierarchical Hypothesis Management | 183 |
| 7 Conclusion | 186 |
| Acknowledgments | 186 |
| References | 186 |
| Communication/Interpretation | 188 |
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| Security of Underground Resistance Movements | 189 |
| 1 Introduction | 189 |
| 2 Best defense against optimal subversive strategies | 190 |
| 3 Best defense against random subversive strategies | 194 |
| 4 Maximizing the size of surviving components | 197 |
| 5 Ensuring that the survivor graph remains connected | 200 |
| References | 207 |
| Intelligence Constraints on Terrorist Network Plots | 209 |
| 1 Introduction | 209 |
| 2 Tipping Point in Conspiracy Size | 210 |
| 3 Tipping Point Examples | 213 |
| 4 Stopping Rule for Terrorist Attack Multiplicity | 216 |
| 5 Preventing Spectacular Attacks | 217 |
| References | 218 |
| On Heterogeneous Covert Networks | 219 |
| 1 Introduction | 220 |
| 2 Preliminaries | 221 |
| 3 Secrecy and Communication in Homogeneous Covert Networks | 222 |
| 4 Jemaah Islamiya Bali bombing | 224 |
| 5 A First Approach to Heterogeneity in Covert Networks | 227 |
| References | 232 |
| Two Models for Semi-Supervised Terrorist Group Detection | 233 |
| 1 Introduction | 233 |
| 2 Terrorist Group Detection from Crime and Demographics Data | 234 |
| 3 Offender Group Representation Model (OGRM) | 239 |
| 4 Group Detection Model (GDM) | 240 |
| 5 Offender Group Detection Model (OGDM) | 241 |
| 6 Experiments and Evaluation | 246 |
| 7 Conclusion | 248 |
| References | 251 |
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