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2009 | Book

Mathematical Methods in Counterterrorism: Tools and Techniques for a New Challenge Read chapter Read first chapter

Mathematical Methods in Counterterrorism

Editors: Nasrullah Memon, Ph.D, Jonathan David Farley, D.Phil. (Oxon.), David L. Hicks, Ph.D, Torben Rosenorn

Publisher: Springer Vienna

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

Terrorism is one of the serious threats to international peace and security that we face in this decade. No nation can consider itself immune from the dangers it poses, and no society can remain disengaged from the efforts to combat it. The termcounterterrorism refers to the techniques, strategies, and tactics used in the ?ght against terrorism. Counterterrorism efforts involve many segments of so- ety, especially governmental agencies including the police, military, and intelligence agencies (both domestic and international). The goal of counterterrorism efforts is to not only detect and prevent potential future acts but also to assist in the response to events that have already occurred. A terrorist cell usually forms very quietly and then grows in a pattern – sp- ning international borders, oceans, and hemispheres. Surprising to many, an eff- tive “weapon”, just as quiet – mathematics – can serve as a powerful tool to combat terrorism, providing the ability to connect the dots and reveal the organizational pattern of something so sinister. The events of 9/11 instantly changed perceptions of the wordsterrorist andn- work, especially in the United States. The international community was confronted with the need to tackle a threat which was not con?ned to a discreet physical - cation. This is a particular challenge to the standard instruments for projecting the legal authority of states and their power to uphold public safety. As demonstrated by the events of the 9/11 attack, we know that terrorist attacks can happen anywhere.

Table of Contents

Frontmatter

Mathematical Methods in Counterterrorism: Tools and Techniques for a New Challenge

Frontmatter
Mathematical Methods in Counterterrorism: Tools and Techniques for a New Challenge
Throughout the years mathematics has served as the most basic and fundamental tool employed by scientists and researchers to study and describe a wide variety of fields and phenomena. One of the most important practical application areas of mathematics has been for national defense and security purposes. For example, during the Second World War, the mathematical principles underlying game theory and cryptography played a very important role in military planning. Since that time, it has become clear that mathematics has an important role to play in securing victory in any global conflict, including the struggle faced by national security and law enforcement officials in the fight against those engaged in terrorism and other illicit activities.
David L. Hicks, Nasrullah Memon, Jonathan D. Farley, Torben Rosenørn

Network Analysis

Frontmatter
Modeling Criminal Activity in Urban Landscapes
Computational and mathematical methods arguably have an enormous potential for serving practical needs in crime analysis and prevention by offering novel tools for crime investigations and experimental platforms for evidence-based policy making. We present a comprehensive formal framework and tool support for mathematical and computational modeling of criminal behavior to facilitate systematic experimental studies of a wide range of criminal activities in urban environments. The focus is on spatial and temporal aspects of different forms of crime, including opportunistic and serial violent crimes. However, the proposed framework provides a basis to push beyond conventional empirical research and engage the use of computational thinking and social simulations in the analysis of terrorism and counter-terrorism.
Patricia Brantingham, Uwe Glässer, Piper Jackson, Mona Vajihollahi
Extracting Knowledge from Graph Data in Adversarial Settings
Abstract
Graph data captures connections and relationships among individuals, and between individuals and objects, places, and times. Because many of the properties f graphs are emergent, they are resistant to manipulation by adversaries. This robustness comes at the expense of more-complex analysis algorithms. We describe several approaches to analysing graph data, illustrating with examples from the relationships within al Qaeda.
David Skillicorn
Mathematically Modeling Terrorist Cells: Examining the Strength of Structures of Small Sizes
Abstract
This paper aims to discuss the strengths of different terrorist cell structures, using the partially ordered set (“poset”) model of terrorist cells to define the strength of terrorist cell structures.We discuss algorithms implemented in a program examining the structures of posets of seven elements, and the patterns observed in this analysis. We then discuss implications of these findings, and their applicability to government strategic operations - namely, the possibilities for future expansion and use of the algorithms to produce structures fitting certain parameters, and the caution which must be exercised in following previous suggestions that terrorist cell structures can be assumed to be trees, since structures containing “V” structures and more than one leader can be more secure than trees, according to our findings. We end with several questions that require future investigation in order to increase applicability to strategic operations, and suggestions for how such questions may be approached.
Lauren McGough
Combining Qualitative and Quantitative Temporal Reasoning for Criminal Forensics
Abstract
The paper presents an application of temporal knowledge representation and reasoning techniques to forensic analysis, especially in answering certain investigative questions relating to time-sensitive information about a criminal or terrorist activity. A brief introduction to a temporal formalism called Point-Interval Logic is presented. A set of qualitative and quantitative temporal facts is taken from the London bombing incident that took place on July 7, 2005, to illustrate the use of temporal reasoning for criminal forensics. The information used in the illustration is gathered through the online news sites. A hypothetical investigation on the information is carried out to identify certain time intervals of potential interest to counterterrorist investigators. A software tool called Temper that implements Point-Interval Logic is used to run the analysis and reasoning presented in the paper.
Abbas K. Zaidi, Mashhood Ishaque, Alexander H. Levis
Two Theoretical Research Questions Concerning the Structure of the Perfect Terrorist Cell
Abstract
Two questions of theoretical interest regarding the number of cutsets in a poset are presented.
Jonathan David Farley

Forecasting

Frontmatter
Understanding Terrorist Organizations with a Dynamic Model
Abstract
Terrorist organizations change over time because of processes such as recruitment and training as well as counter-terrorism (CT) measures, but the effects of these processes are typically studied qualitatively and in separation from each other. Seeking a more quantitative and integrated understanding, we constructed a simple dynamic model where equations describe how these processes change an organization’s membership. Analysis of the model yields a number of intuitive as well as novel findings. Most importantly it becomes possible to predict whether counter-terrorism measures would be sufficient to defeat the organization. Furthermore, we can prove in general that an organization would collapse if its strength and its pool of foot soldiers decline simultaneously. In contrast, a simultaneous decline in its strength and its pool of leaders is often insufficient and short-termed. These results and other like them demonstrate the great potential of dynamic models for informing terrorism scholarship and counter-terrorism policy making.
Alexander Gutfraind
Inference Approaches to Constructing Covert Social Network Topologies
Abstract
Social network analysis techniques are being increasingly employed in counter-terrorism and counter-insurgency operations to develop an understanding of the organisation, capabilities and vulnerabilities of adversary groups. However, the covert nature of these groups makes the construction of social network topologies very challenging. An additional constraint is that such constructions often have to be made on a fast time-scale using data that has a limited shelf-life. Consequently, developing effective processes for constructing network representations from incomplete and limited data of variable quality is a topic of much current interest. Here we show how Bayesian inference techniques can be used to construct candidate network topologies and predict missing links in two different analysis scenarios. The techniques are illustrated by application to data from open-source publications.
Christopher J. Rhodes
A Mathematical Analysis of Short-term Responses to Threats of Terrorism
Abstract
A terror threat information model capturing the uncertainty in timing and location of terror attacks is developed to create a mathematical framework for analyzing counterterrorism decision making. Using this framework two important defensive mechanisms, warnings and the deployment of physical resources are studied. Warnings are relatively inexpensive to issue but their effectiveness suffers from false alarms. Physical deployments of trained security personnel can directly thwart attacks but are expensive and need to be targeted to specific locations. By structuring the tradeoffs faced by decision makers in a formal way we try to shed light on an important public policy problem. We show that the interaction between the use of warnings and physical defenses is complex and significant.
Edieal J. Pinker
Network Detection Theory
Abstract
Despite the breadth of modern network theory, it can be difficult to apply its results to the task of uncovering terrorist networks: the most useful network analyses are often low-tech, link-following approaches. In the traditional military domain, detection theory has a long history of finding stealthy targets such as submarines. We demonstrate how the detection theory framework leads to a variety of network analysis questions. Some solutions to these leverage existing theory; others require novel techniques – but in each case the solutions contribute to a principled methodology for solving network detection problems. This endeavor is difficult, and the work here represents only a beginning. However, the required mathematics is interesting, being the synthesis of two fields with little common history.
James P. Ferry, Darren Lo, Stephen T Ahearn, Aaron M. Phillips

Communication/Interpretation

Frontmatter
Security of Underground Resistance Movements
Abstract
In an attempt to better understand the possible lines of communication in a terrorist group, we consider a graph theoretic model and the competing demands of the desire for ease of communication versus the danger of betrayal of subverted or captured members. We first examine what the design should be when the attack on the network is optimal as well as when it is random but in both cases with no restriction on the surviving network. Then the question of what the design should be to minimize damage but to ensure that the average size of the surviving components is as large as possible is considered. Finally the restriction that all the survivors are capable of communicating is examined.
Bert Hartnell, Georg Gunther
Intelligence Constraints on Terrorist Network Plots
Abstract
Since 9/11, the western intelligence and law enforcement services have managed to interdict the great majority of planned attacks against their home countries. Network analysis shows that there are important intelligence constraints on the number and complexity of terrorist plots. If two many terrorists are involved in plots at a given time, a tipping point is reached whereby it becomes progressively easier for the dots to be joined and for the conspirators to be arrested, and for the aggregate evidence to secure convictions. Implications of this analysis are presented for the campaign to win hearts and minds.
Gordon Woo
On Heterogeneous Covert Networks
Abstract
Covert organizations are constantly faced with a tradeoff between secrecy and operational efficiency. Lindelauf, Borm and Hamers [13] developed a theoretical framework to determine optimal homogeneous networks taking the above mentioned considerations explicitly into account. In this paper this framework is put to the test by applying it to the 2002 Jemaah Islamiyah Bali bombing. It is found that most aspects of this covert network can be explained by the theoretical framework. Some interactions however provide a higher risk to the network than others. The theoretical framework on covert networks is extended to accommodate for such heterogeneous interactions. Given a network structure the optimal location of one risky interaction is established. It is shown that the pair of individuals in the organization that should conduct the interaction that presents the highest risk to the organization, is the pair that is the least connected to the remainder of the network. Furthermore, optimal networks given a single risky interaction are approximated and compared. When choosing among a path, star and ring graph it is found that for low order graphs the path graph is best. When increasing the order of graphs under consideration a transition occurs such that the star graph becomes best. It is found that the higher the risk a single interaction presents to the covert network the later this transition from path to star graph occurs.
Roy Lindelauf, Peter Borm, Herbert Hamers
Two Models for Semi-Supervised Terrorist Group Detection
Abstract
Since discovery of organization structure of offender groups leads the investigation to terrorist cells or organized crime groups, detecting covert networks from crime data are important to crime investigation. Two models, GDM and OGDM, which are based on another representation model – OGRM are developed and tested on nine terrorist groups. GDM, which is basically depending on police arrest data and “caught together” information and OGDM, which uses a feature matching on year-wise offender components from arrest and demographics data, performed well on terrorist groups, but OGDM produced high precision with low recall values. OGDM uses a terror crime modus operandi ontology which enabled matching of similar crimes.
Fatih Ozgul, Zeki Erdem, Chris Bowerman

Behavior

Frontmatter
CAPE: Automatically Predicting Changes in Group Behavior
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.
Amy Sliva, V.S. Subrahmanian, Vanina Martinez, Gerardo Simari
Interrogation Methods and Terror Networks
Abstract
We examine how the structure of terror networks varies with legal limits on interrogation and the ability of authorities to extract information from detainees. We assume that terrorist networks are designed to respond optimally to a tradeoff caused by information exchange: Diffusing information widely leads to greater internal efficiency, but it leaves the organization more vulnerable to law enforcement. The extent of this vulnerability depends on the law enforcement authority’s resources, strategy and interrogation methods. Recognizing that the structure of a terrorist network responds to the policies of law enforcement authorities allows us to begin to explore the most effective policies from the authorities’ point of view.
Mariagiovanna Baccara, Heski Bar-Isaac
Terrorists and Sponsors. An Inquiry into Trust and Double-Crossing
Abstract
We consider the conditions that lead to the dissolution of state-terrorist coalitions. While such coalitions have well known advantages, they also have structural weaknesses that are largely ignored in the literature on the state sponsorship of terrorism. Each player in the coalition has interests that are only partially shared and, in some cases, at odds with those of its partner. Long term cooperation must be based on mutual advantage and mutual trust, both of which are subject to change over time.We examine the conditions that are needed to begin and maintain a cooperative strategy and the circumstances that lead a state and a terrorist group to leave the coalition and double-cross its partner. Equilibrium strategies for both players are defined and interpreted.
Gordon H. McCormick, Guillermo Owen
Simulating Terrorist Cells: Experiments and Mathematical Theory
Abstract
How well do mathematical models of terrorist cells apply to the reallife struggle against terrorism? Certainly, mathematical models have been useful in the past for military planning and predicting the behavior of U.S. adversaries, but how well do mathematical projections of terrorist behavior actually hold up when tested on living people and real situations? This paper first presents a mathematical model of terrorist cells and their functionality, and then discusses the procedure and results of an experiment conducted to test this model’s theoretical projections by comparing them with experimental results, thus confronting the question of theory versus reality.
Lauren McGough

Game Theory

Frontmatter
A Brinkmanship Game Theory Model of Terrorism
Abstract
This study reveals conditions under which a world leader might credibly issue a brinkmanship threat of preemptive action to deter sovereign states or transnational terrorist organizations from acquiring weapons of mass destruction (WMD). The model consists of two players: the United Nations (UN) “Principal,” and a terrorist organization “Agent.” The challenge in issuing a brinkmanship threat is that it needs to be sufficiently unpleasant to deter terrorists from acquiring WMD, while not being so repugnant to those that must carry it out that they would refuse to do so. Two “credibility constraints” are derived. The first relates to the unknown terrorist type (Hard or Soft), and the second to acceptable risks (“blowback”) to the World community. Graphing the incentive-compatible Nash equilibrium solutions reveals when a brinkmanship threat is credible, and when it is not – either too weak to be effective, or unacceptably dangerous to the World community.
Francois Melese
Strategic Analysis of Terrorism
Abstract
Two areas that are increasingly studied in the game-theoretic literature on terrorism and counterterrorism are collective action and asymmetric information. One contribution of this chapter is a survey and extension of continuous policy models with differentiable payoff functions. In this way, policies can be characterized as strategic substitutes (e. g., proactive measures), or strategic complements (e. g., defensive measures). Mixed substitute–complement models are also introduced. We show that the efficiency of counterterror policy depends upon (i) the strategic substitutes-complements characterization, and (ii) who initiates the action. Surprisingly, in mixed-models the dichotomy between individual and collective action may disappear. A second contribution is the consideration of a signaling model where indiscriminant spectacular terrorist attacks may erode terrorists’ support among its constituency, and proactive government responses can create a backlash effect in favor of terrorists. A novel equilibrium of this model reflects the well-documented ineffectiveness of terrorism in achieving its stated goals.
Daniel G. Arce, Todd Sandler
Underfunding in Terrorist Organizations
Abstract
A review of international terrorist activity reveals a pattern of financially strapped operatives working for organizations that seem to have plenty of money. To explain this observation, and to examine when restricting terrorists’ funds will reduce their lethality, we model a hierarchical terror organization in which leaders delegate financial and logistical tasks to middlemen, but cannot perfectly monitor them for security reasons. These middlemen do not always share their leaders’ interests: the temptation exists to skim funds from financial transactions. When middlemen are sufficiently greedy and organizations suffer from sufficiently strong budget constraints, leaders will not fund attacks because the costs of skimming are too great. Using general functional forms, we find important nonlinearities in terrorists’ responses to government counter-terrorism. Restricting terrorists’ funds may be ineffective until a critical threshold is reached, at which point cooperation within terrorist organizations begins to break down and further government actions have a disproportionately large impact.
Jacob N. Shapiro, David A. Siegel

History of the Conference on Mathematical Methods in Counterterrorism

Personal Reflections on Beauty and Terror
Abstract
The history of the Conference on Mathematical Methods in Counterterrorism is briefly described.
Jonathan David Farley
Metadata
Title
Mathematical Methods in Counterterrorism
Editors
Nasrullah Memon, Ph.D
Jonathan David Farley, D.Phil. (Oxon.)
David L. Hicks, Ph.D
Torben Rosenorn
Copyright Year
2009
Publisher
Springer Vienna
Electronic ISBN
978-3-211-09442-6
Print ISBN
978-3-211-09441-9
DOI
https://doi.org/10.1007/978-3-211-09442-6

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