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“That’s why I came here—the reputation of the department. They were doing a lot of interesting work, and that attracted me. We can work with lots of other departments in many different areas,” Herron says.
Earlier this year, Herron spent a six-month sabbatical at Los Alamos National Laboratory, studying the Earth’s core using rotating convector problems.
“We want to understand the origin of the geophysical properties of the Earth—its magnetism, for instance. These things are connected with the ocean, the currents—though it’s not one equation that links them,” he explains.
Herron is still sometimes surprised where math has led him: “In high school, I liked physics and chemistry, but what I liked best was the math in them. Now look what I’m doing.”
Thomas Yu’s work has applications in everything from medical imaging to cartoon animation. He is a de-noiser and a data compressor—mathematical specialties that didn’t even exist in the first half of the century.
“There are not many things that only mathematicians can do, but there are certainly a few important aspects in science and technology that only mathematicians have the capacity to investigate,” says Yu, assistant professor of mathematics.
Yu was invited to the Max Planck Institute of Biochemistry in Germany, where researchers showed him pictures of nerve tissue from a frog’s body, measuring about 50 atoms across and taken with a powerful electron microscope. The image resembled a tangle of yellow yarn.
“There was much noise in it. The picture was not clear. They wanted a picture with less noise and more detailed information,” Yu explains.
By “noise,” Yu means irrelevant, extraneous information—in this case, visual clutter that obscured details in the nerve tissue. He devised a program that dramatically cleaned up the image.
“We call it ‘de-noising.’ Think of white noise. It makes no sense. It’s not helpful. Interesting data has some meaningful structure. With mathematics, we can formalize the concept of ‘meaningful structure’ and devise tools to eliminate noise and bring out the meaning,” he says.
Yu is interested in a quality known to mathematicians as “smoothness”—the visual redundancies possessed by most objects. In other words, most of an apple’s surface appears red, even if its skin is mottled with brown bruises and green, unripe spots. Yu has designed a program that permits a computer graphics designer to capitalize on this redundancy and more quickly and efficiently render a visual facsimile.
Yu displayed photocopies of two roughly similar objects—multi-colored tori, or doughnut-shaped geometric forms. One is smooth and rounded; the other, highly angular, like an artist’s sketch. Using a technique called subdivision, Yu has figured out an efficient way for a cartoon animator to go from the coarse outline to the finished image. Similar techniques, he said, have been employed in such computer-generated animated films as A Bug’s Life.
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