Mathematical Methods in Counterterrorism (eBook)

Foreword 5
Contents 7
Mathematical Methods in Counterterrorism: Tools and Techniques for a New Challenge 14
1 Introduction 14
2 Organization 15
3 Conclusion and Acknowledgements 17
Network Analysis 19
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
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
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
Behavior 254
CAPE: Automatically Predicting Changes in Group Behavior 255
1 Introduction 255
2 CAPE Architecture 257
3 SitCAST Predictions 258
4 CONVEX and SitCAST 260
5 The CAPE Algorithm 262
6 Experimental Results 268
7 Related Work 269
8 Conclusions 270
Acknowledgements 270
References 271
Interrogation Methods and Terror Networks 272
1 Introduction 272
2 Model 275
3 The Optimal Network 279
4 The Enforcement Agency 282
5 Extensions and Conclusions 286
Appendix 287
References 291
Terrorists and Sponsors. An Inquiry into Trust and Double- Crossing 292
1 State-Terrorist Coalitions 292
2 The Mathematical Model 296
3 Equilibrium Strategies 298
4 Payoff to T 301
5 The Trust Factor 303
6 Interpretation 304
7 Conclusion. External Shocks 309
References 309
Simulating Terrorist Cells: Experiments and Mathematical Theory 310
1 Introduction 310
2 The Question of Theory versus Real-Life Applications 311
3 Design 312
4 Procedure 313
5 Analysis and Conclusions 314
Appendix 317
References 317
Game Theory 318
A Brinkmanship Game Theory Model of Terrorism 319
1 Introduction 319
2 The Extensive Form of the Brinkmanship Game 322
3 Incentive Compatibility ( Credibility ) Constraints 325
4 Equilibrium Solution and Interpretation of the Results 328
5 Conclusion 330
References 332
Strategic Analysis of Terrorism 333
1 Introduction 333
2 Strategic Substitutes and Strategic Complements in the Study of Terrorism 335
3 Terrorist Signaling: Backlash and Erosion Effects 342
4 Concluding Remarks 347
References 347
Underfunding in Terrorist Organizations 349
1 Introduction 349
2 Motivation 353
3 Model 359
4 Results 361
5 Discussion 370
6 Conclusion 375
Mathematical Appendix 377
References 380
History of the Conference on Mathematical Methods in Counterterrorism 383
Personal Reflections on Beauty and Terror 384
1 Shadows Strike 384
2 The Thinking Man’s Game 384
3 The Elephant: Politics 386
4 Toward a Mathematical Theory of Counterterrorism 388

CAPE: Automatically Predicting Changes in Group Behavior (p. 253-254)

Amy Sliva, V.S. Subrahmanian, Vanina Martinez, and Gerardo Simari

Abstract There is now intense interest in the problem of forecasting what a group will do in the future. Past work [1, 2, 3] has built complex models of a group’s behavior and used this to predict what the group might do in the future. However, almost all past work assumes that the group will not change its past behavior. Whether the group is a group of investors, or a political party, or a terror group, there is much interest in when and how the group will change its behavior. In this paper, we develop an architecture and algorithms called CAPE to forecast the conditions under which a group will change its behavior.We have tested CAPE on social science data about the behaviors of seven terrorist groups and show that CAPE is highly accurate in its predictions—at least in this limited setting.

1 Introduction

Group behavior is a continuously evolving phenomenon. The way in which a group of investors behaves is very different from the way a tribe in Afghanistan might behave, which in turn, might be very different from how a political party in Zimbabwe might behave. Most past work [1, 4, 2, 3, 5] on modeling group behaviors focuses on learning a model of the behavior of the group, and using that to predict what the group might do in the future. In contrast, in this paper, we develop algorithms to learn when a given group will change its behaviors.

As an example, we note that terrorist groups are constantly evolving. When a group establishes a standard operating procedure over an extended period of time, the problem of predicting what that group will do in a given situation (hypothetical or real) is easier than the problem of determining when, if, and how the group will exhibit a significant change in its behavior or standard operating procedure. Systems such as the CONVEX system [1] have developed highly accurate methods of determining what a given group will do in a given situation based on its past behaviors. However, their ability to predict when a group will change its behaviors is yet to be proven.

In this paper, we propose an architecture called CAPE that can be used to effectively predict when and how a terror group will change its behaviors. The CAPE methodology and algorithms have been tested out on about 10 years of real world data on 5 terror groups in two countries and—in those cases at least—have proven to be highly accurate.

The rest of this paper describes how this forecasting has been accomplished with the CAPE methodology. In Section 2, we describe the architecture of the CAPE system. Section3 gives details of an algorithm to estimate what the environmental variables will look like at a future point in time. In Section 4, we briefly describe an existing system called CONVEX [1] for predicting what a group will do in a given situation s and describe how to predict the actions that a group will take at a given time in the future.