to improve our capabilities in counter-WMD. And mathematical science methods of machine learning are necessary for improving our capabilities in autonomy and human-machine interfaces. Computational neuroscience, which relies heavily on the mathematical sciences, is also a promising area for future developments in human-machine interfaces.

The realm of threat detection in general requires a multiplicity of techniques from the mathematical sciences. How can one most quickly detect patterns that might indicate the spread of a pathogen spread by bioterrorism? How does one understand the structure of a terrorist network? Can one design a power grid or a transportation network in such a way that it is maximally resistant to attack? A new threat, cyberwarfare, grows in magnitude. Fighting back will involve a multipronged response: better encryption, optimized design of networks, and the burgeoning mathematics-and statistics-intensive field of anomaly detection.

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