Researchers find method to separate chaos from noise


MIT researchers have developed a technique that could mean chaos for
many scientists.

In every field from microbiology to astronomy, researchers get erratic
data-strange results that don't fit established patterns. Are those data
simply noise-random, unpredictable signals that are best ignored-or do
they actually follow a subtle structure?

That there is order behind seeming disorder is the essence of chaos, a
phenomenon that has been found in many areas of science, from the
weather (as established by Professor Emeritus Edward N. Lorenz of the
Department of Earth, Atmospheric and Planetary Sciences) to the orbits
of asteroids (as established by Professor Jack Wisdom of the same
department).

Knowing that chaos exists in a system helps scientists learn more about
that system. "Finding chaos in a system implies that there is a
structure behind that system. And that's something you want to know,"
said Dr. Chi-Sang Poon, a principal research scientist in the Harvard-
MIT Division of Health Sciences and Technology. In addition,
understanding the chaotic pattern could in some cases allow scientists
to control the phenomenon.

But first chaos must be detected, and that is quite difficult. "There's
a very fine line between chaos and noise," Dr. Poon said. A new
mathematical technique developed by Dr. Poon and Mauricio Barahona, a
graduate student in physics, may simplify the process.

The technique, which the scientists describe in the May 16 issue of
Nature, is much more sensitive than others in distinguishing chaos from
noise. It also requires an order of magnitude fewer data points, which
means that many more scientists will now be able to analyze their data
for chaos.

Dr. Poon has already received excited queries from a biomedical
scientist and a climatologist. "Both have relatively small data sets
because their data are difficult to get, so none of the existing methods
would work in their cases," Dr. Poon said. "Tens of thousands of data
points are needed for other techniques. We can determine with very high
probability if there's chaos in a data set with just a few hundred data
points."

The new technique grew out of an assignment Dr. Poon gave his class in
1993. "I had an idea for a way to detect chaos, but I hadn't tested it
yet," he explained. Several students did a good job on the assignment,
but "Mauricio [Barahona] did a terrific job," Dr. Poon said. Mr.
Barahona proceeded to extend the study, while at the same time working
toward his PhD in physics (he will receive his degree this month). His
thesis is unrelated to the work reported in Nature.

Dr. Poon notes that the new technique, which is a mathematical
procedure, is adapted from earlier work by the late Norbert Wiener.
Professor Wiener, a member of the MIT faculty for 45 years, was a genius
who among other things founded the field of cybernetics. (Dr. Poon named
one of his computer network nodes "cybernet" in honor of Professor
Wiener.)

In continuing work, Dr. Poon is fine-tuning the technique and working
with other colleagues in applying it to heart disease. The human
heartbeat is thought to be a chaotic system, Dr. Poon explained. Its
irregular rhythm "is actually a symbol of health," he said. With
congestive heart failure, for example, "the heartbeat is seen to get
more and more regular."

So "our long-term hope is to use our technique as a diagnostic tool for
heart disease by detecting changes in the chaotic system," he said. He
is collaborating on the current work with Roger G. Mark, the Grover M.
Hermann Professor of Health Sciences and Technology, and Professor
Richard J. Cohen, both of the Harvard-MIT Division of Health Sciences
and Technology. Christopher K. Merrill, a senior in electrical
engineering and computer science, is also involved through the
Undergraduate Research Opportunities Program.

The work is supported by the NSF, the Office of Naval Research, the
National Heart, Lung, and Blood Institute, and a Spanish MEC-Fulbright
Fellowship. Dr. Poon has applied for a patent on the technique.

A version of this article appeared in MIT Tech Talk on June 5, 1996.


Topics: Mathematics

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