AAAS Focuses on a World of Counterterrorism Mathematics

April 22, 2009

The case for spurring the development of mathematical and computational techniques quantifying terror threats and gauging the effectiveness of counterterrorism operations here and abroad was the rationale behind the "5th Conference on Mathematical Methods in Counterterrorism," recently held at the American Association for the Advancement of Science, in Washington, D.C.

Twenty experts, from academia, industry, the military, and the Department of Homeland Security, showed that mathematics can play a key role in analyzing and deterring terrorist activity; identifying the formation and growth of terror cells; developing strategies for breaking up cells; reducing, and perhaps eliminating, possibilities of border penetration; and offering the means of emergency planning and response.

The mathematics behind "clique percolation," for instance, could reveal when "too many terrorists spoil the plot," according to one researcher. Diffusion modeling could help predict the chances for violence in a society by weighing the competing forces of provocation and reaction, another researcher claimed. And order theory can help in evaluating the vulnerability of key resources and infrastructure, according to a third investigator.

Jennifer O'Connor (Department of Homeland Security), who spoke about "Knowledge to Action: DHS's Challenge for the Mathematical Community," told the speakers and the gathering, "You're working in an area right now that is huge." Her department, she indicated, "is very interested in moving from ideas in the mathematical community" to security-based applications incorporating concepts such as geospatial pattern understanding and multicamera object recognition.

The speakers had numerous suggestions, proposals, and descriptions of activities.

William Burns (Center for Risk and Economic Analysis of Terrorism Events), in his talk "Responding to Terrorism: Risk Perceptions, Communication and Societal Impacts," emphasized a dynamics model, based on survey and interview data, that predicts how a community might react to a terrorist attack.

Gordon Woo (Risk Management Solutions, London), author of The Mathematics of Natural Catastrophes, offered ideas for "Quantifying Terrorism Risk under the Obama Administration." After noting that only two of dozens of European terror plots—the 2004 Madrid train bombings and the 2005 attack on London's transit system—had not been foiled, he proffered as a solution clique percolation. Because fifty represents the maximum number of "operatives" who could clandestinely be involved in attack planning, networks are susceptible to data mining, he claimed. "It is hard to keep a plot secret," Woo said.

Barry C. Ezell (Old Dominion University), talking about "Bioterrorism Risk Probabilistic Risk Analysis," noted, "Because of the adaptive nature of the terrorist adversary, mathematical tools like decision trees, game theory, and agent-based modeling are needed to assess the risks of terrorist events." The probabilistic approach, he stressed, has a part to play in efforts to "decompose the universe of terrorism scenarios." When representing the actions of enemies "in the form of a decision tree, we have to understand their preferences," he said, but cautioned that no model can represent or envision the nature of every threat.

Roy Lindelauf (Tilburg University and Netherlands Defense Academy), in addressing issues of "Covert Affiliation Networks," stressed the importance of analyzing the activities of networks by deciphering hypergraph structures representing operational data and using game-theoretical power indices in so-called one-mode affiliation analysis.

Col. Steve Horton gave an overview of Network Science activities at the U.S. Military Academy, West Point, which includes the fields of behavioral sciences and leadership; electrical engineering and computer science; mathematical sciences; chemistry and life sciences; and systems engineering.

Georges Grinstein (University of Massachusetts, Lowell) spoke of the Visual Analytics Science and Technology contest math problems and solutions that help to strengthen the skills of counterterrorist analysts, homeland security analysts, and data analysts.

Uffe Kock Wiil (University of Southern Denmark) talked of "CrimeFighter: A Toolbox for Counterterrorism," which is a research lab making use of investigative methods for data mining, mathematical modeling, social network analysis, graph theory, link analysis, knowledge management, and hypertext capabilities. Its activities in criminal investigation include data acquisition tools supporting web harvesting; knowledge structuring tools supporting information analysis; and algorithms for data mining visualization and social network analysis.

Alexander Gutfraind (Cornell University), in "Understanding Terrorist Organizations with a Dynamic Model," had constructed a dynamic model that, he said, could predict whether counterterrorism measures could "defeat" a terror organization. "We can prove in general," he claimed, "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 others like them demonstrate the great potential of dynamic models for informing terrorism scholarship and counterterrorism policy-making."

Vladimir Keilis-Borok (University of California, Los Angeles) had as his topic the "Algorithmic Prediction of Terrorism Surges: Non-linear Dynamics Approach." His methodology, he indicated, "integrates modeling of statistical mechanics kind and pattern recognition of infrequent events," which has been developed by the artificial intelligence school of I. Gelfand. Pilot analysis of real data on terrorism suggests "common types of self-adjusting premonitory patterns," he said, which can be used with other prediction methods.

Jim Ferry (Metron, Inc.) looked at "Bayesian Modeling of Group Structure in Dynamic Networks," the goal of which is to determine the "structure and evolution of relationships between people or other entities based on data about the history of their interactions." Ferry claimed to have developed an "efficient simulation of the Markov process model" in order to track the membership at the "vertices in a network." The results of one scenario demonstrated, he said, how positive information (changes in network structure) and negative information (periods of no change) might reveal a terror group's membership.

Daniel Myers (University of Notre Dame) spoke of "Collective Violence and Repression: Making Use of the Opposing Forces Diffusion Model." This model proposes that the observed frequency of collective political violence is a function of the "diffusion of a provocation ideology and the diffusion of a repression ideology." Simulation and empirical data demonstrated, Myers claimed, that "when modeling a wave using early adopter data," the model allows people to "effectively intervene during the early stages of a violence wave and change the course of the action wave."

Neil Johnson (University of Miami) addressed "Identification of a Common Group Dynamics underlying Recent Wars and Terrorism." Johnson developed a model to predict the duration of attacks, and then "test out the consequences of different intervention strategies." Attacks may follow a power law: The number of attacks in any given year, for instance, is proportional to the number of deaths. Over time, "the process of coalescence and fragmentation eventually reaches a steady-state which is solvable analytically," he posited. "It yields a power law with coefficient of 2.5 that holds true for diverse conflicts."

Georg Gunther (Memorial University of Newfoundland), an expert in "Communications and Security in Terrorist Networks: A Graph-Theoretic Model," noted that a terrorist network could be modeled by setting up a graph whose vertices represent the individuals in the network, and whose edges represent lines of communication. A clearer understanding of structural problems of communication, he said, "might provide for counter-terrorist organizations better insights for effective ways of neutralizing the threat posed by terrorist networks."

Cliff Joslyn (Pacific Northwest National Laboratory), speaking on the subject "The Mathematical Challenges to Knowledge Systems Technologies for the Intelligence Community," observed that "efforts to increase analytical capabilities within the intelligence community face large challenges in the areas of interconnectivity and interoperability of data sources and data bases." There is a need for order morphisms for ontology alignment; lattice metrics for ontology analysis; and path analyses of labeled graphs for knowledge discovery in semantic databases.

Jafar Adibi (PricewaterhouseCoopers, LLP) looked into "Measuring Confidence Intervals in Link Discovery: A Bootstrap Approach." LD algorithms are being used, he said, to develop techniques to find hidden patterns in large amounts of data. Now, because a new LD engine purportedly can find hidden relationships among entities in any "public or private data source," a closer look at a "bootstrap resampling method" might measure its accuracy.

Ed Kaplan (Yale University) took a close look at "Inference and Interdiction in a Terror Queue Model" when he presented a queueing model "relating terror threats and their detection"—with an eye towards understanding how preventive counterterror measures "enable the interdiction of terror suspects."

George Markowsky (University of Maine) tackled "What Order Theory Can Tell You about Comparing Apples and Oranges: The Problem of Selecting the Most Probable Target." The goal of risk assessment, said Markowsky, "is to get a linear order of potential targets so that limited resources can be deployed to protect the most probable targets." Order theory, he noted, can help to come up with a single linear order out of several linear orders that might be unrelated to one another. "The problem of comparing apples and oranges is a real one,” Markowsky declared. "Security is a dynamic process," he said. "I worry when people say this target is worth 390 points and it gets engraved in stone."

William McGill (Pennsylvania State University), focusing on "Regional Capabilities Performance Assessment for Homeland Security," discussed the use of "fuzzy systems" to define the relationship between "region risk mitigation capabilities" (that is, response and recovery) and losses due to "adverse initiating events." He described and demonstrated the details of the model.

Jonathan Farley (Phoenix Mathematics, Inc.), Anthony Harkin (Rochester Institute of Technology), and Benn Tannenbaum (AAAS) organized the math-based conference.

Source: American Association for the Advancement of Science, March 24, 2009.