Homological Sensor Networks, Volume 54, Number 1

10 NOTICES OF THE AMS VOLUME 54, NUMBER 1 Sensors and Sense-ability A sensor is a device that measures some feature of a domain or environment and returns a signal from which information may be extracted. Sensors vary in scope, resolution, and ability. The information they return can be as simple as a binary flag, as with a metal detector that beeps to indicate a detection threshold being crossed. A more complex sensor, such as a video camera, can return a signal requiring sophisticated analysis to extract relevant data. An increasingly common application for sensors is to scan a region for a particular object or substance. For example, one might wish to determine the existence and location of an outbreak of fire in a national forest. Questions of more interest to national security involve detection of radiological or biological hazards, hidden mines and munitions, or specific individuals in a crowd. All of these scenarios pose difficult and challenging data management problems. Numerous strategies exist, aided by the fact that sensor technology provides an expansive array of available hardware. A fundamental dichotomy exists in the approach to sensing an environment based on the number and complexity of sensors. For a fixed cost (monetary, or perhaps “total complexity”), one can deploy a small number of sophisticated “global” sensors with high signal complexity and precise readings. In contrast, one can deploy a large number of small, coarse, “local” devices that may have large uncertainties in their readings. Different strategies are appropriate for different tasks. The human body contains examples of sensor systems with a small multiplicity of highly complex devices (for sight) as well as vast networks of local sensors (for touch). Technology promises to push the envelope on both sides of this spectrum, yielding new types of powerful, global sensors, as well as local sensors of surprisingly small size. The relevant question for the mathematician is which types of mathematics will be useful in analyzing sophisticated sensor networks. It may be that the most exciting possibilities lie in the domain of the small. Swarms of local sensors at microor nanoscale have the potential to revolutionize the way that we think about security and surveillance problems [4]. However, this brings with it the difficulty of integration. How does one collect local information and collate it into global environmental data?