Applied Mathematics Seminar

Maximizing the probability of detection of a man-made target using symmetry
vendredi, 24 mars 2017 - 12:00 pm12:30 pm
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SPEAKER: Bao Nyugen (TBA) DATE: Friday, March 24, 2017 TIME: 12:00 pm ROOM: B015 ABSTRACT: e propose a globally optimal strategy to detect a target in a search & rescue mission. We assume that the target exhibits mirror symmetry, i.e., that the left hand side of a target is the mirror image of the right hand side of the same target. In addition, it is assumed that the cross section is maximal at the interface between the left hand side and the right hand side and decreases monotonically as we move away from the interface. The optimal strategy consists of choosing n aspect angles to inspect a target to ensure that the probability of detection is maximal. This is generally an NP-hard problem in the sense that to find the optimal angles in n dimensions normally consumes a lot of computational power. Fortunately, in this problem, we use a combination of variational calculus and symmetry principles to determine analytically the globally optimal angles for a general class of man-made targets. The solutions will help the search & rescue operators plan for an effective strategy in a search and rescue mission. Such a strategy is robust as most targets of interest possess approximate mirror symmetry along one or more axes. For example, a human body or a canoe or a mine when cut in half yield approximately such symmetry. This work could inform the way search and rescue missions are conducted by recognizing the importance of aspect angles.