Mathematics to detect terror

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Can math models of gaming strategies be used to detect terrorism networks? The answer is yes, according to a paper in the SIAM Journal on Discrete Mathematics.

In a paper published in the journal last month, authors Anthony Bonato, Dieter Mitsche, and Pawel Pralat describe a mathematical model to disrupt the flow of information in a complex real-world network, such as a terrorist organization, using minimal resources.

According to Homeland Security News wire a SIAM release reports that terror networks are comparable in their structure of hierarchical organization in companies and certain online social networks, where information flows in one direction from a source, which produces the information or data, downwards to sinks, which consume it. Such networks are called hierarchical social networks.

“In such networks, the flow of information is often one way,” explains author Pawel Pralat. “For example, a celebrity such as Justin Bieber sends out a tweet, which is sent to millions of his followers. These followers send out their own retweets, and so on. We may therefore view hierarchical social networks as directed networks without cycles, or directed acyclic graphs (DAGs).”

Here, there is no requirement for reciprocity (the celebrity does not necessarily follow his or her followers). Similarly, in a terrorist network, the leaders pass plans down to the foot soldiers, and usually only one messenger needs to receive the message for the plan to be executed.

Disruption of the flow of information would correspond to halting the spread of news in an online social network or intercepting messages on a terror network.

The authors propose a generalized stochastic model for the flow and disruption of information based on a two-player outdoor game called “Seepage,” where players who depict agents attempt to block the movement of another player, an intruder, from a source node to a sink. “The game – motivated by the 1973 eruption of the Eldfell volcano in Iceland – displays some similarities to an approach used in mathematical counterterrorism, where special kinds of DAGs are used to model the disruption of terrorist cells,” says Pralat.

The motivating eruption caused a major crisis at the time, as lava flow threatened to close off the harbor, the island’s main source of income. In the game, inhabitants attempt to protect the harbor by pouring water on the volcanic lava to halt its progress. A mathematical model of the game pits two opponents against each other – the sludge, or intruder, against the greens, or agents – forming