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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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