| |
| |
Mathematical Methods in Counterterrorism: Tools and Techniques for a New Challenge | |
| |
| |
| |
| |
Introduction | |
| |
| |
| |
Organization | |
| |
| |
| |
Conclusion and Acknowledgements | |
| |
| |
| |
Network Analysis | |
| |
| |
Modeling Criminal Activity in Urban Landscapes | |
| |
| |
| |
| |
Introduction | |
| |
| |
| |
Background and Motivation | |
| |
| |
| |
Computational Criminology | |
| |
| |
| |
Challenges and Needs | |
| |
| |
| |
Modeling Paradigm | |
| |
| |
| |
Mastermind Framework | |
| |
| |
| |
Mathematical Framework | |
| |
| |
| |
Rapid Prototyping with CoreASM | |
| |
| |
| |
Interactive Design with Control State ASMs | |
| |
| |
| |
Mastermind: Modeling Criminal Activity | |
| |
| |
| |
Overview | |
| |
| |
| |
Agent Architecture | |
| |
| |
| |
Urban Landscape Model | |
| |
| |
| |
Space Evolution Module: ASM Model | |
| |
| |
| |
Lessons Learned | |
| |
| |
| |
Concluding Remarks | |
| |
| |
| |
<l>5</l> | |
| |
| |
Extracting Knowledge from Graph Data in Adversarial Settings | |
| |
| |
| |
| |
Characteristics of Adversarial Settings | |
| |
| |
| |
Sources of Graph Data | |
| |
| |
| |
Eigenvectors and the Global Structure of a Graph | |
| |
| |
| |
Visualization | |
| |
| |
| |
Computation of Node Properties | |
| |
| |
| |
Social Network Analysis (SNA) | |
| |
| |
| |
Principal eigenvector of the adjacency matrix | |
| |
| |
| |
Embedding Graphs in Geometric Space | |
| |
| |
| |
The Walk Laplacian of a graph | |
| |
| |
| |
Dimensionality reduction | |
| |
| |
| |
The rightmost eigenvectors | |
| |
| |
| |
The leftmost eigenvectors | |
| |
| |
| |
The 'middle' eigenvectors | |
| |
| |
| |
Working in a lower-dimensional space | |
| |
| |
| |
Overlays of eigenvectors and edges | |
| |
| |
| |
Using con-elation rather than connection | |
| |
| |
| |
Summary | |
| |
| |
References | |
| |
| |
Mathematically Modeling Terrorist Cells: Examining the Strength of Structures of Small Sizes | |
| |
| |
| |
| |
"Back to Basics": Recap of the Poset Model of Terrorist Cells | |
| |
| |
| |
Examining the Strength of Terrorist Cell Structures-Questions Involved and Relevance to Counterterrorist Operations | |
| |
| |
| |
Definition of "Strength" in Terms of the Poset Model | |
| |
| |
| |
Posets Addressed | |
| |
| |
| |
Algorithms Used | |
| |
| |
| |
Structures of Posets of Size 7: Observations and Patterns | |
| |
| |
| |
Implications and Applicability | |
| |
| |
| |
Ideas for Future Research | |
| |
| |
| |
Conclusion | |
| |
| |
References | |
| |
| |
Combining Qualitative and Quantitative Temporal Reasoning for Criminal Forensics | |
| |
| |
| |
| |
Introduction | |
| |
| |
| |
Temporal Knowledge Representation and Reasoning | |
| |
| |
| |
Point-Interval Logic | |
| |
| |
| |
Language and Point Graph Representation | |
| |
| |
| |
Operations on Point Graphs | |
| |
| |
| |
Inference | |
| |
| |
| |
Deciding Consistency | |
| |
| |
| |
Temper | |
| |
| |
| |
Using Temper for Criminal Forensics-The London Bombing | |
| |
| |
| |
Conclusion | |
| |
| |
References | |
| |
| |
Two Theoretical Research Questions Concerning the Structure of the Perfect Terrorist Cell | |
| |
| |
| |
References | |
| |
| |
| |
Forecasting | |
| |
| |
Understanding Terrorist Organizations with a Dynamic Model | |
| |
| |
| |
| |
Introduction | |
| |
| |
| |
A Mathematical Model | |
| |
| |
| |
Analysis of the Model | |
| |
| |
| |
Discussion | |
| |
| |
| |
Nascent terrorist organizations | |
| |
| |
| |
Conditions for Victory | |
| |
| |
| |
Stable Equilibria | |
| |
| |
| |
Counter-Terrorism Strategies117 | |
| |
| |
| |
Targeting the leaders | |
| |
| |
| |
Encouraging desertion | |
| |
| |
| |
Minimization of Strength | |
| |
| |
| |
Conclusions | |
| |
| |
| |
Appendix | |
| |
| |
| |
Proof of the theorem | |
| |
| |
| |
Concrete Example of Strength Minimization | |
| |
| |
References | |
| |
| |
Inference Approaches to Constructing Covert Social Network Topologies | |
| |
| |
| |
| |
Introduction | |
| |
| |
| |
Network Analysis | |
| |
| |
| |
A Bayesian Inference Approach | |
| |
| |
| |
Case 1 Analysis | |
| |
| |
| |
Case 2 Analysis | |
| |
| |
| |
Conclusions | |
| |
| |
References | |
| |
| |
A Mathematical Analysis of Short-term Responses to Threats of Terrorism | |
| |
| |
| |
| |
Introduction | |
| |
| |
| |
Information Model | |
| |
| |
| |
Defensive Measures | |
| |
| |
| |
Analysis | |
| |
| |
| |
Interaction between warnings and physical deployments | |
| |
| |
| |
Effect of intelligence on defensive measures | |
| |
| |
| |
Illustrative numerical experiments | |
| |
| |
| |
Summary | |
| |
| |
References | |
| |
| |
Network Detection Theory | |
| |
| |
| |
| |
Introduction | |
| |
| |
| |
Random Intersection Graphs165 | |
| |
| |
| |
Induced edge clique covers; exact quantities | |
| |
| |
| |
Expected subgraph counts in the constant-?limit | |
| |
| |
| |
Subgraph Count Variance | |
| |
| |
| |
Dynamic Random Graphs | |
| |
| |
| |
The telegraph process | |
| |
| |
| |
The dynamic Erd�s-R�nyi process | |
| |
| |
| |
Tracking on Networks | |
| |
| |
| |
The LRDT Framework for Static Networks | |
| |
| |
| |
Hierarchical Hypothesis Management | |
| |
| |
| |
The Hypothesis Lattice | |
| |
| |
| |
The HHM Algorithm | |
| |
| |
| |
An Example | |
| |
| |
| |
Conclusion | |
| |
| |
References | |
| |
| |
| |
Communication/Interpretation | |
| |
| |
Security of Underground Resistance Movements | |
| |
| |
| |
| |
Introduction | |
| |
| |
| |
Best defense against optimal subversive strategies | |
| |
| |
| |
Best defense against random subversive strategies | |
| |
| |
| |
Maximizing the size of surviving components | |
| |
| |
| |
Ensuring that the survivor graph remains connected | |
| |
| |
References | |
| |
| |
Intelligence Constraints on Terrorist Network Plots | |
| |
| |
| |
| |
Introduction | |
| |
| |
| |
Tipping Point in Conspiracy Size | |
| |
| |
| |
Tipping Point Examples | |
| |
| |
| |
Stopping Rule for Terrorist Attack Multiplicity | |
| |
| |
| |
Preventing Spectacular Attacks | |
| |
| |
References | |
| |
| |
On Heterogeneous Covert Networks | |
| |
| |
| |
| |
Introduction | |
| |
| |
| |
Preliminaries | |
| |
| |
| |
Secrecy and Communication in Homogeneous Covert Networks | |
| |
| |
| |
Jemaah Islamiya Bali bombing | |
| |
| |
| |
A First Approach to Heterogeneity in Covert Networks | |
| |
| |
| |
The Optimal High Risk Interaction Pair | |
| |
| |
| |
Approximating Optimal Heterogeneous Covert Networks | |
| |
| |
References | |
| |
| |
Two Models for Semi-Supervised Terrorist Group Detection | |
| |
| |
| |
| |
Introduction | |
| |
| |
| |
Terrorist Group Detection from Crime and Demographics Data | |
| |
| |
| |
COPLINK CrimeNet Explorer | |
| |
| |
| |
TMODS | |
| |
| |
| |
Offender Group Representation Model (OGRM) | |
| |
| |
| |
Group Detection Model (GDM) | |
| |
| |
| |
Offender Group Detection Model (OGDM) | |
| |
| |
| |
Computing Similarity Score | |
| |
| |
| |
Using Terrorist Modus Operandi Ontology | |
| |
| |
| |
Deciding Threshold | |
| |
| |
| |
Feature Selection | |
| |
| |
| |
Experiments and Evaluation | |
| |
| |
| |
Performance Matrix | |
| |
| |
| |
Testbed: Terrorist Groups Detected in Bursa | |
| |
| |
| |
Conclusion | |
| |
| |
References | |
| |
| |
| |
Behavior | |
| |
| |
CAPE: Automatically Predicting Changes in Group Behavior | |
| |
| |
| |
| |
Introduction | |
| |
| |
| |
CAPE Architecture | |
| |
| |
| |
SitCAST Predictions | |
| |
| |
| |
CONVEX and SitCAST | |
| |
| |
| |
The CAPE Algorithm | |
| |
| |
| |
The Change Table | |
| |
| |
| |
Learning Predictive Conditions from the Change Table | |
| |
| |
| |
The CAPE-Forecast Algorithm | |
| |
| |
| |
Experimental Results | |
| |
| |
| |
Related Work | |
| |
| |
| |
Conclusions | |
| |
| |
References | |
| |
| |
Interrogation Methods and Terror Networks | |
| |
| |
| |
| |
Introduction | |
| |
| |
| |
Related Literature | |
| |
| |
| |
Model | |
| |
| |
| |
Law Enforcement Agency | |
| |
| |
| |
Information Structure | |
| |
| |
| |
Payoffs | |
| |
| |
| |
The Optimal Network | |
| |
| |
| |
The Enforcement Agency | |
| |
| |
| |
Investigation Budget Allocation | |
| |
| |
| |
Legal Environment and Interrogation Methods | |
| |
| |
| |
Extensions and Conclusions | |
| |
| |
References | |
| |
| |
Terrorists and Sponsors. An Inquiry into Trust and Double-Crossing | |
| |
| |
| |
| |
State-Terrorist Coalitions | |
| |
| |
| |
The Mathematical Model | |
| |
| |
| |
Equilibrium Strategies | |
| |
| |
| |
Payoff to T | |
| |
| |
| |
The Trust Factor | |
| |
| |
| |
Interpretation | |
| |
| |
| |
Conclusion. External Shocks | |
| |
| |
References | |
| |
| |
Simulating Terrorist Cells: Experiments and Mathematical Theory | |
| |
| |
| |
| |
Introduction | |
| |
| |
| |
The Question of Theory versus Real-Life Applications | |
| |
| |
| |
Design | |
| |
| |
| |
Procedure312 | |
| |
| |
| |
Analysis and Conclusions | |
| |
| |
References | |
| |
| |
| |
Game Theory | |
| |
| |
A Brinkmanship Game Theory Model of Terrorism | |
| |
| |
| |
| |
The Extensive Form of the Brinkmanship Game | |
| |
| |
| |
Incentive Compatibility ("Credibility") Constraints | |
| |
| |
| |
The Effectiveness Constraint | |
| |
| |
| |
The Acceptability Constraint | |
| |
| |
| |
Equilibrium Solution and Interpretation of the Results | |
| |
| |
| |
Conclusion | |
| |
| |
References | |
| |
| |
Strategic Analysis of Terrorism | |
| |
| |
| |
| |
Introduction | |
| |
| |
| |
Strategic Substitutes and Strategic Complements in the Study of Terrorism | |
| |
| |
| |
Proactive Counterterrorism Measures | |
| |
| |
| |
Defensive Conntermeasures: globalized Threat | |
| |
| |
| |
Defensive Measures: No Collateral Damage | |
| |
| |
| |
Intelligence | |
| |
| |
| |
Other Cases | |
| |
| |
| |
Terrorist Signaling: Backlash and Erosion Effects | |
| |
| |
| |
Concluding Remarks | |
| |
| |
Undeerfunding in Terrorist organizations | |
| |
| |
| |
| |
Introduction | |
| |
| |
| |
Motivation | |
| |
| |
| |
Game | |
| |
| |
| |
Actors | |
| |
| |
| |
Model | |
| |
| |
| |
Game Form | |
| |
| |
| |
Actors | |
| |
| |
| |
Results | |
| |
| |
| |
Equilibrium Strategies | |
| |
| |
| |
Comparative Statics | |
| |
| |
| |
Discussion | |
| |
| |
| |
Conclusion | |
| |
| |
References | |
| |
| |
| |
History of the Conference on Mathematical Methods in Counterterrorism | |
| |
| |
Personal Reflections on Beauty and Terror | |
| |
| |
| |
| |
Shadows Strike | |
| |
| |
| |
The "Thinking Man's Game" | |
| |
| |
| |
The Elephant: Politics | |
| |
| |
| |
Toward a Mathematical Theory of Counterterrorism | |