Math in the News
Topology Becoming Essential to Real-World Sensor-Network Applications
May 16, 2007
Topologythe piecing together of a space's global structure from local snapshotsis finding a place in today's technological world. One arena of application is in stitching together the enormous amounts of data generated by computerized sensor networks to provide the big picture.
Engineers and technicians, for example, can now deploy complex wireless sensor networks to track the movements of animals in game reserves; to monitor the number of boats in a harbor; and, in military field tests, to determine the trajectories of bullets.
More than a century old, topology focuses on a shape's features that don't change when it is physically altered and its geometry is distorted. Once the topological structure of a set of data (or sensor network) is established, algebraic and numerical tools can then be used to uncover seemingly unknown attributes or piece together disparate data.
These toolssuch as the Euler characteristic and homology algorithmsare "good for finding hidden features inside a space that you can't see very well" and about which "you don't have all the information," mathematician Robert Ghrist, of the University of Illinois at Urbana-Champaign, said in a recent Science News article.
There's more to come. Imagine tiny, sensing computers embedded in buildings, streets, and cell phones to keep us abreast of the weather, changes in light, temperature, noise, traffic, deadly chemicals in the air, and more, with topology providing the glue that makes sense of all the data.
Source: Science News, May 5, 2007