New-age tools to fight terror: Mathematical models and science of probability.

After India’s surgical strikes on terror cells across the border in September, militants attacked the Nagrota Army base in November, raising disturbing questions on the ability of security agencies to second guess terror. Perhaps it is time New Delhi took a closer look at new age tools developed by researchers whose computational analyses of extremist organisations have become powerful weapons in the fight against terrorism.

Security agencies across the world currently employ more than 40 math models to stay a step ahead of terrorists. Jonathan Farley, professor at the University of the West Indies, uses the lattice theory — a branch of mathematics that deals with ordered sets — to ascertain the probability of how many members need to be ‘taken out’ before a terrorist cell can be disrupted. This, in turn, helps to determine the structure of an ‘ideal’ terrorist cell which is most resistant to the loss of its members. Mathematicians Stephen Trench and Hannah Fry of the University College, London base their model on the Hawkes process (used in earthquake prediction programmes): It assumes that terror strikes occur in clusters and an attack is likely to be followed soon after by others — like after-shocks following an earthquake.

Neil Johnson of Miami University and his team mix maths and social media to predict terrorist attacks. Their algorithm detects signs of imminent terror strikes by monitoring social media posts used by radical groups. Prof. Johnson says social media serves as a recruitment platform for extremists and even seemingly innocuous online conversations on extremist topics could portend violent terrorist acts.

By studying pro-ISIS posts in various languages, for instance, he found strong linkages between terrorist-inspired posts and the likelihood of terror attacks actually happening. In fact, he says, it’s possible to see people “materialising” around certain social groups to share information in real-time, just like “crystals form in a test-tube”. This technology could help security agencies track sympathisers who get together at random before becoming terrorists themselves. Thus online ‘lone wolf’ actors apparently act on their own only for short periods of time. After a while, a “coalescence process” begins in the online activity of such individuals and they become identifiable with different groups, or “aggregates”. Prof. Johnson calls this the “ecology of aggregates” which allows his algorithm to track the trajectories of individuals through it.

But of especial interest to India would be the Temporal-Probabilistic Rule System developed by Venkatramana Subrahmanian, University of Maryland, which not only predicts terror attacks but also suggests counter strategies. The programme is based on two frameworks: the Stochastic Opponent Modeling Agents (SOMA) and the multiplayer game theory models. Both are built on data reflecting hundreds of variables relevant to terror groups in South Asia like the LeT, JeM, and SIMI. These variables describe both the environment in which a group operates as well as the intensity of the group’s actions.


After India’s surgical strikes on terror cells across the border in September, terrorists attacked the Nagrota Army base in November, raising disturbing questions on the ability of security agencies to second guess terror.

SOMA identifies environment conditions favourable for the group’s actions and predicts the probability ‘P’ that it will carry out action ‘A’ with intensity ‘I’, when some condition is true in the environment. The multiplayer game theory correlates sets of actions that each player can perform and assigns a “payoff” for each combination of actions that a group can take. This yields something called a ‘payoff matrix,’ showing all possible combinations of actions, and the payoffs for each scenario. In the LeT game theory, these actions include covert action or coercive diplomacy that policy makers could use. So in a hypothetical situation with five players (LeT, Pak military, Pak civilian government, US, and India), for each combination of actions these players could take, the model evaluates how good or bad that scenario could be for them. If, for instance, the US increases aid to Pakistan and the LeT carries out major attacks, the payoff for the US would be very low.

Prof. Subrahmanian’s programme derives from Nash equilibria (mathematical techniques for determining action combinations that depend on ‘stable’ situations) and calculates both ‘pure’ equilibria—where each player may or may not take an action, and ‘mixed’ equilibria—where each player can take probabilistic combinations of action (e.g., the Pak military may talk peace for some of the time, while funding and training the LeT for the rest of the time). “We found that of all the Nash equilibria in which LeT behaves well (i.e., does not carry out attacks),” says Prof. Subrahmanian, “the US and India both use covert action against LeT and/or coercive diplomacy with respect to Pakistan, and there is no additional military/development aid to Pakistan.”

During World War II, the US Navy neutralised Germany’s U-boat threat by asking chess grandmaster Reuben Fine to analyse the probability of U-boats surfacing at certain points in the sea. And Britain recruited several chess masters to devise a mathematical model to crack the German Enigma code, which virtually won the war for the Allies. More than six decades later, the free world is again turning to mathematical models and the science of probability to help fight a new enemy: Terrorism.