May 16, 2013 ? 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 flow of information in a complex real-world network, such as a terrorist organization, using minimal resources.
Terror networks are comparable in their structure to 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 in 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 a directed acyclic graph, with one source (the top of the volcano) and many sinks representing the lake. The parameter, "seepage," represents the amount of contamination, and the "green number" corresponds to the number of agents required to halt it.
A previous study modeled terrorist cells as partially ordered sets (a special kind of DAG), which are often used in mathematics to analyze an ordering, sequencing, or arrangement of distinct objects. In such a system, terrorist plans are formulated by nodes at the top of the hierarchy, which represent the leaders or maximal nodes of the set. The plans are transmitted down to the nodes at the bottom: these represent foot soldiers in a terror network or minimal nodes in the set who would be presumed to carry out these plans. The assumption is that one messenger is sufficient for reception and execution of the plan. Thus, if the partially ordered set represents a courier network for a terrorist organization, the intention would be to block all routes from the maximal node to the minimal nodes by capturing or killing a subset of agents.
In this paper, the authors utilize the similarities in the previous terrorist cell model to Seepage, where greens try to prevent the sludge from moving to the sinks by blocking nodes. A number of different winning strategies employed by both players are explored when played on a DAG. The seepage and green number for disrupting a given hierarchical social network are analyzed.
The primary difference from the previous study's model is that the Seepage model is dynamic: greens can move and choose new sets of nodes over time. The authors determine that Seepage is a more realistic model of counterterrorism, as the agents do not necessarily act all at once, but over time.
The analysis is made in two types of terrorist network structures, as Pralat explains, "We consider two extreme profiles: one where the network is regular, where every agent has about the same number of connections. The second profile is power law, where some agents have many connections, but most have very few." This is analyzed by considering the total degree distribution of nodes in the DAG. In regular DAGs, each level of the DAG would have nodes with about the same out-degree (number of outgoing edges emanating from a node), while power law DAGs would have many more low-degree nodes and a few with high degrees.
Mathematical analysis allows the authors to determine what point in a network would be most effective for disrupting messages. "Our mathematical results reinforce the view that intercepting the information or message in a hierarchical social network following a power law is more difficult close to levels near the source. For regular networks, it does not matter as much where the message is disrupted," says Pralat. "Future work could look at more complex profiles of networks, along with developing effective algorithms for disrupting the flow of information in a DAG using our game-theoretic approach."
Source: http://feeds.sciencedaily.com/~r/sciencedaily/top_news/~3/Adpbt4Zmc_4/130516142656.htm
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Mozilla today launched the latest version of its Firefox browser for Mac, Windows and Linux, and the highlight of Firefox 21 is additional support for Mozilla’s Social API. This API allows social providers to integrated directly with Firefox and the organization launched in cooperation with Facebook at the end of last year. Today, it is adding Cliqz, Mixi and msnNOW to the mix. The new Social API integrations, Mozilla says, “help you stay connected to your social networks, no matter where you go on the Web.” Once installed, users can access these integrations from buttons in the browser toolbar. Cliqz users, for example, will be able to see content recommendations right in the new social sidebar in Firefox, share links across their social networks and preview Twitter commentary, all without actually going to Cliqz. The integration with Japan’s Mixi and Microsoft’s msnNOW works in the same way. The Social API, Mozilla writes, “has endless potential for integrating social networks, e-mail, finance, music, cloud possibilities, services, to-do lists, sports, news and other applications into your Firefox experience.” Now that it has landed in Firefox stable, chances are we will see a number of additional integrations in the near future. Also new in this version is preliminary support for the new Firefox Health Report. Similar to what Microsoft is doing with Internet Explorer, Firefox will now also provide users with suggestions for how to improve the application’s startup time. Firefox For Android The Android version of Firefox was also bumped up to version 21 today and with it, the team has integrated support for two new open source fonts, Charis and Open Sans. The fonts will replace the three Android default fonts to enable “a more visually appealing and clear reading experience on the Web.” The difference is “subtle, but beautiful,” Mozilla says. Also new are the ability to save media files through a long tap and access to your recent browsing history through the back and forward buttons. This new version for Android also includes some HTML5 improvements and the browser now scores 421 out of the 500 possible points on HTML5test.com (plus 14 bonus points).




