A mathematical model that tests the durability of terrorist cell structures
by Quaneisha Jenkins
At a time when the threat to national security remains elevated, some turn to mathematical models for strategy-based decision making to counter terrorism. Using math to enhance national security has historical precedent in RAND, a global policy think tank formed after WWII, and since then, has been used to locate landmines and ensure information security. Professor Jonathan Farley, Department of Mathematics and Computer Science at the University of the West Indies, Jamaica, developed a mathematical model to test the durability of terrorist cell structures while he worked as a fellow at Stanford's Center for International Security and Cooperation (CISAC).
The Power of Math
While at Stanford from 2005 to 2006, Farley researched the application of mathematics to problems in homeland security, such as terrorist cell formation, strategies for disrupting these cells and analysis of their activities. In particular, Farley tried to improve upon a commonly used model of terrorist cells after attending a presentation by Dr. Gordon Woo, a catastrophe consultant for Risk Management Solutions Inc, titled Ò Modeling the Al Qaeda". Woo used graph theory to analyze terrorist networks: nodes represent members of terrorist cells and a connecting line between two nodes denotes a relationship. This graph model used ÒThe Connectedness CriterionÓ: if a few nodes are severed, then the likelihood of a cell being deactivated increases. However, according to Farley, this criterion doesn't address issues such as the "impact of rank - the difference between leaders and foot soldiers" within a network. Farley claims that noting the significance of hierarchy within a network is crucial to increasing the probability of deactivating the entire terrorist cell.
Terrorist Lattices
Farley drew upon his expertise in lattice theory to construct a more accurate model of terrorist networks. Lattice theory uses partially ordered sets of terrorists to demonstrate relationships such as hierarchy between nodes. The sets are partially ordered because some of the members have the same rank, e.g., terrorist cells have several foot soldiers. Severing any few nodes by capturing or killing terrorists would not disable the network, unless the specific nodes severed were in a special relationship within the cell.
The link between a topmost node and a bottommost node, denoting high and low ranking individuals, respectively, is termed a maximal chain. Only when enough of these links are cut, such as by preventing communication between leaders and footsoldiers, do nodes become isolated and the cell more likely to be deactivated. The collections of nodes that intersect every maximal chain are cut sets. Lattice theory can be used to calculate the probability that a cell has been destroyed by mapping out cut sets.
By using Farley's research on terrorist lattices, law enforcement would be better able to allocate resources for counterterrorism strategies. Instead of spending enormous amounts of manpower trying to capture as many terrorists as possible, law enforcement could use a strategy of capturing as many as leaders as possible in order to break the chains of command.
Safe Guessing
As with all mathematical models there are to be expected shortcomings. Are terrorist cells hierarchical? What about lone actors? This model, according to Farley, does not Òaccurately describe reality; this is merely better than guessing.Ó It is meant to help those in positions of power make better informed decisions about counter-strategies. It is not a net with which to catch terrorists.The NAACP's Crisis Magazine quotes Farley as saying, ÒWe're creating tools that enable decision makers to make more logical decisions rather than relying on intuition or guess work." The less reliance on guessing, the more lives and money can be saved.
Factbox #1: What is in store for Farley's lattice theory on counterterrorism strategies? For starters, he is organizing a conference on Mathematical Methods in Counterterrorism, where various academics will present talks directed at a broader audience encompassing the general public, policy makers, politicians and members of law enforcement agencies. Farley is also working to establish an Institute for Mathematical Methods in Counter-terrorism at Rochester Institute of Technology. Phoenix Mathematics, Inc., co-founded by Farley, who is also the chief scientist of the company, is creating software for law enforcement agencies using the lattice model of hierarchy to combat terrorism.
Factbox #2: Dr. Jonathan D. Farley graduated summa cum laude from Harvard University in 1991, later receiving the 2004 Harvard Foundation's Distinguished Scientist of the Year Award, and graduated with a doctorate from Oxford University in 1995, where a year earlier he had received its highest mathematics award. From 2001-2002, he was one of only four American Fulbright Distinguished Scholars to the United Kingdom. His accomplishments in the field of lattice theory include solving several problems that have remained unsolved for many decades, including a problem in transversal theory. He is the co-founder of Hollywood Math and Science Consulting and has written and been featured in several major American and British publications such as Time Magazine, The New York Times, The Guardian, Crisis Magazine, and Jet. The City of Cambridge, Massachusetts has officially declared March 19, 2004 to be ÒDr. Jonathan David Farley DayÓ.