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This article addresses the problem of allocating devices for localized hazard protection across a region. Each identical device provides only local protection, and the devices serve localities that are exposed to nonidentical intensities of hazard. A method for seeking the optimal allocation Policy Decisions is described, highlighting the potentially competing objectives of maximizing local risk reductions and coverage risk reductions. The metric for local risk reductions is the sum of the local economic risks avoided. The metric for coverage risk reductions is adapted from the p-median problem and equal to the sum of squares of the distances from all unserved localities to their closest associated served locality. Three graphical techniques for interpreting the Policy Decisions are presented. The three linked graphical techniques are applied serially. The first technique identifies Policy Decisions that are nearly Pareto optimal. The second identifies locations where sensor placements are most justified, based on a risk-cost-benefit analysis under uncertainty. The third displays the decision space for any particular policy decision. The method is illustrated in an application to chemical, biological, and/or radiological weapon sensor placement, but has implications for disaster preparedness, transportation safety, and other arenas of public safety.

Phantom limb pain (PLP) is a chronic, intractable condition that affects over 2 million Americans. PLP has been treated by pharmaceuticals, and interventional treatments, as well as psychological strategies including sensory illusions. This work develops a theoretical framework to characterize prior instantiations of sensory illusions. Each instantiation is a particular treatment protocol that consists of three design elements: stimulus modality, volitional movement, and multisensory interaction. Utilizing this framework, we custom-built a haptics-enabled mirror visual feedback (MVF) sensory illusion. The device provides its amputee user with tactile and proprioceptive feedback, specifically the capability to interact with a 1 DOF haptic slider bar. In this way, we sought to incorporate additional sensory modalities into the illusion. In a case study with lower limb amputees (N=3), the realism of the device's seven illusions was evaluated. Preliminary results are that: 1) interaction with the haptic slider bar increased the amputee's sense of presence of the amputated limb, 2) one subject with intractable chronic PLP experienced relief that persisted during use of the device and reported tactile and proprioceptive sensation in the phantom limb, 3) forceful pressure against the slider bar produced asymmetric proprioceptive forces that interrupted the illusion, 4) the specific amputation site affected which illusions were most believable. These preliminary findings indicate that multi-sensory illusions may augment and enhance MVF instantiations, potentially improving the therapeutic value for a wider range of amputation cases.

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