National Science Foundation To Fund Engineering, Math Collaboration

Sept. 14, 2004

by Judy Long

The National Science Foundation has awarded a three-year $300,000 grant to a group of Baylor University professors to fund a study of time scales, research they say could have a variety of practical applications. The professors leading the study are Dr. Ian Gravagne, assistant professor of electrical and computer engineering, Dr. John Davis, assistant professor of mathematics, and Dr. Robert Marks, Distinguished Professor of Electrical and Computer Engineering.

The term time scales refers to the way dynamic systems change over time. In the past, engineers and mathematicians have thought of time as a variable that either sweeps continuously like the hands of an old-fashioned clock, or changes at discrete and uniform intervals, such as what occurs with a digital clock. Time scale theory can describe systems that are "in between," having both analog and digital characteristics.

Gravagne said most engineering applications assume timing is either continuous or uniformly discrete, but a number of applications fall between the two--their timing may have a discrete nature without being divided into equal intervals.

Gravagne and his colleagues are applying time scales to distributed control networks. These are found in the electronic systems that control automobiles, robots, aircraft and certain manufacturing processes. Modern automobiles, for example, are designed with a communication network that functions through wires connected to every operating part of the vehicle. Two kinds of events can occur on the network--recurring and non-recurring. The recurring events occur at regular intervals, such as the signal to the speedometer. Non-recurring events can happen at any time, such as when the driver applies the brakes.

"These non-recurring signals push aside the recurrent signals and throw off the timing of the whole system," Gravagne said.

"We are studying this phenomenon to understand ways to make the recurrent processes more tolerant to non-uniform timing. The end result will save communication bandwidth, keeping down the cost of automation in industries that use sensing and control networks."

Davis is interested in using time scales to model other dynamic systems, such as biological plant populations, financial business cycles and stochastic (or random) time systems.

Marks will apply time scales to improve signal processing techniques that make noisy speech more intelligible or improve the quality of a grainy photograph.

Gravagne said that time scale theory has been studied by mathematicians for more than 10 years, but the Baylor group is the first to publish anything on its engineering applications.

The time scale group's efforts have been recognized in another way, too, with the recent selection of Dr. Jeffrey DaCunha for a prestigious three-year postdoctoral fellowship jointly sponsored by the United States Military Academy at West Point and the Army Research Lab at Aberdeen, Md. A Baylor undergraduate, DaCunha is one of the first Ph.D. recipients in the Baylor mathematics department's new doctoral program. He was also a recipient of the Graduate Student Association's 2004 Outstanding Graduate Student Award for his work.

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