Military scientists at the Defense Advanced Research Projects Agency over a year ago put out a call to get answers to what it called the world's 23 toughest math questions with the idea that major math breakthroughs could greatly enhance the country's security. While it is unclear what DARPA would do with the answers to those questions, the Pentagon today added to the search for mathematical genius by announcing it was looking to more tightly couple advanced math concepts with battlefield tactics.
Specifically, the Department of Defense said it was looking to fully realize the power of sophisticated mathematics and push the frontiers of traditional applied mathematics and to cultivate mathematical ideas that are not represented in typical applications today.
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While a combination of new math with more established approaches for battlefield applications is envisioned, exploration of ideas with potential for ultimately leapfrogging today's techniques is what the DoD said it wants. The idea is to tap world-class mathematical scientists from the academic research community as well as other research organizations to make such work possible.
So what is the DoD looking for? It vaguely outlined these math challenges and requirements:
- - New math techniques for fusing, predicting, visualizing and extracting features and information from disparate sources ranging from sensor data (optical, radio‐frequency, acoustic, and chemical) to human intelligence data to historical database to expert opinion (human, electronic and signal intelligence sources.
- - Developing a global understanding from data that are most often local in nature, requiring the fusion of data acquired from multiple, disparate sources, is one battlefield challenge into which classical tools of applied mathematics have provided only limited inroads (much current research in this area has adopted heuristic approaches due to the intractability of more rigorous ones based in classical applied mathematics).
- The need to quantify uncertainty as it manifests in large‐scale interconnected systems, ultimately achieving descriptions of a battle space that let decision makers understand risk in terms relevant and meaningful to their tasks. Detecting the presence of poorly defined anomalies in large data sets/streams has become recognized as an important capability, particularly in today's battlefield where adversaries are difficult to distinguish from civialians. Post‐analysis of suicide bombings, for example, have revealed hints available in sensor data in the form of unusual events preceding the actual attack. Identifying such cues in sensor data in prognostic fashion rather than after the fact presents a formidable mathematical challenge, the DoD stated.
The DoD went on to say that the battlefield is an increasingly complicated environment that includes a multitude of fixed and moving objects, including people, stationary structures as well as slow moving air and ground vehicles. On the battlefield, myriad sensors of varying types, capabilities, on‐board processing power, coverage patterns, and mechanisms of deployment are available - increasingly in networked configurations, the DoD stated. New math techniques to sort out and make sense of it all for commanders is in part what's needed.
The DoD said its capability to collect data well exceeds its capability to process it into timely and reliable information that can be used by soldiers, sailors, airmen and marines in making decisions at all levels - including crucial shoot/no‐shoot decisions. Furthermore, making the best use of battlefield sensor assets still entails unresolved challenges even at the fundamental levels of sensor placement and management, the DoD stated.
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