2009 CSL Undergraduate Summer Research Stipend Report
Aram Apyan | Evan Estola | Erik Harpstead | Jae Kwan Lee | Ryan McClure | Jesse Reinhardt | Peter Schemmel | Andrew Yates
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Jae Kwan Lee
Fourth-year undergraduate, Applied Mathematics
Jeffrey Duan
Professor of Applied Mathematics
PERTURBATION ON THE MANIFOLDS WITH APPLICATION TO BIOMEDICAL MODELING
As the life sciences have exploded, with a flood of new information and data, so has the interdisciplinary area of mathematical biology. Mathematical models can help scientists understand why something is happening and what might happen next—such as how molecules in a cell interact, or how a tumor develops—in areas from ecology to epidemiology and more.
Professor Duan is the director of the Laboratory for Stochastics and Dynamics at IIT and a guest faculty fellow at Argonne National Laboratory. His expertise is mathematics to help describe random, dynamic systems, including biomedical systems.
"There are not many first principles in biomedicine that can be put in familiar mathematics models," he said. "We only know a small part of the typical biomedical system or process."
A student from South Korea who transferred to IIT from Ajour University in 2008, Jae Kwan has learned many kinds of mathematics in the classroom. But he never before had the chance to put his knowledge to work in research. This summer, he worked on a model in MATLAB studying the impact of small perturbation on the invariant manifolds for application to biomedical modeling. Perturbations help find an approximate solution based on a solution to a related problem, and invariant manifolds are geometric structures that help us understand dynamical behaviors of complex systems.
"I changed the perturbation so it showed a change in the model," said Jae Kwan. Ultimately, the idea is to help the scientist understand how the biological process changes when some system parameters change.
Besides the software, Jae Kwan also will write a paper and create a poster about his work, and probably present the research at a conference. The experience should help him get into graduate school, and it gave him a different view of his field. "This kind of work is very new," he said. "It makes me creative to try to figure out things no one has before."
Download the 2009 Undergraduate Summer Research Stipend report. (1 MB .pdf)
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