3 Baylor professors head research group on $300,000 grant
Oct. 14, 2004
By SARAH DIGREGORIO, reporter
It isn't often that mathematical theories change. However, great strides
are being made in a relatively new field of math called time scales.
These strides are being taken with the help of a three-year $300,000
grant from the National Science Foundation to a research group of three
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, are heading
up the research group.
Three years ago, Gravagne was working on robotics in the engineering
department when he came across a problem. Most robots as we know them
today can only function in one of two ways -- discreet or continuous.
According to Gravagne and Davis, discreet robotics work like an elbow,
moving at certain points. Continuous robotics are more like snakes, moving
continuously at multiple and indistinguishable points. Time scales are
a mathematical theory to describe how both discreet and continuous systems
Gravagne wanted to combine these two functions and use a hybrid of the
systems, but didn't have the math in order to complete the operation.
Through an e-mail to the mathematics department, Davis and Gravagne started
working to develop the math theory to do the engineering work. This robotics
question spawned the beginning of the development of the time scales,
or hybrid theories, that can be used for many applications in various
"Time scales are a wide-open field," Davis said. "The
theory has only been around for about 10 years and have never
been used in applications."
Davis and Gravagne worked for a year with two graduate students working
on the theories involved. Marks came to Baylor after that first year
and quickly joined the research group.
"Time scales is mathematics that can be applied to a number of
different disciplines, a tool that can be used in various areas and we
are just beginning to scratch the surface with applications for this
new area of ideas," Marks said.
There is very little research on either the math or engineering functions
of time scales. Baylor is one of the few places nationwide where any
work is being done with the new theory, and the first university to publish
any papers on the subject.
"This research is a cooperative effort, combining both the mathematics
and engineering departments," Davis said. "It really
fits with Baylor's philosophy of interdisciplinary work that
breaks down artificial
boundaries between departments."
Marks agrees with Davis, adding that engineering working with mathematics
is a synergistic relationship that fits very well with the goals of Baylor
2012 in opening a new paradigm in the way people look at engineering
The research group is using the National Science Foundation grant to
explore time scale applications in distributed control networks.
"There is a tiny Internet in every modern car that hooks together
the sensors, actuators, motors, hydraulics and moving parts, and computers.
In certain situations, there becomes so much information in the network
that things start not working," Gravagne said.
According to Gravagne, the best way to control the network from freezing
right now is to control the amount of information trying to go through
the network that can crash the system. Research conducted by the group
will use time scales to help change the timing of the functions so that
manufacturers can put more peripherals on each network. Distributed control
networks also appear in manufacturing and medical technology fields.
According to Marks, time scales can be used to help distributed control
networks because in most cases where computers are being used to control
physical things the computer operates at a steady, pre-defined pace.
"Part of the solution to the distributed control networks problem
is to allow the computer to change its timing. Time scales math can handle
situations with nonuniform timing, such as is involved in the automobile
systems," Marks said.
According to Davis, the money from the National Science Foundation primarily
goes to the graduate students hired to do part of the research. Two engineering
graduate students have been hired to work on building computer simulations
and hardware for communications networks. A mathematics doctoral candidate
will be hired to help work on the theory. Gravagne said he also hopes
to use undergraduates in the research and has applied for an amendment
to their National Science Foundation grant to be used for an undergraduate
The research group meets twice a week during the academic year, and
more frequently during the summer. For the first two years, the work
is highly theoretical. The group will transition to testing and refining
their theories during the third year.
"Baylor is the epicenter for this research in the country, drawing
talent, research money and prestige to Baylor," Davis said. "This
will benefit people from the Army to the general good of
the scientific community."