Mathematicians like Stanley Osher, Yves Meyer, Daniel Spielman and Alberto Adrego Pinto are examining areas of life where maths can find applications, including modelling of human behaviour, writes Kalyan Ray

Mathematics can very well trigger a multi-billion dollar spectacle. Ask James Cameron if you don’t believe. The world’s biggest money-grossing movie, Avatar, would not have been a reality without some complicated mathematics.

The same maths that made the Na’vis’ struggle on Pandora so real could also be used to locate a terrorist hide-out and give out a better scan even though the patient had to stay for a few fleeting seconds inside an MRI machine.

Meet Stanley Osher, one of the best-known brains in applied mathematics from the University of California, Los Angeles, who pioneered such mathematics. Over the years, he has researched on a new area of mathematics called ‘level set methods’, which is a way of determining how surfaces such as bubbles move in three dimensions and how they merge and so on. Though on the face of it, LSM appears to be a subject of academic interest, Osher and his graduate students Ron Fedkiw found its utility in computer graphics. The maths also found its way to Hollywood.

Ants was the first movie that used LSM-based graphics, followed by films like Terminator. But computer graphics touched a new height with Cameron’s sci-fi epic, all set for a global re-release with nine minutes of additional footage. “Our method was used extensively to create the graphics for Avatar. It was used to make water, hills and fires in the movie. Most of the Hollywood studios like Disney and Columbia Tristar use our technology,” Osher told Deccan Herald at the International Congress of Mathematicians that ended in Hyderabad on August 27.

In fact, Cameron’s earlier blockbuster Titanic was probably the last well known film that used old-fashioned technologies. The water in Titanic did not come out well, he said, adding that the LSM offered a much more simplified model to mimic the natural world more accurately. Osher – who describes himself as the world’s best analyst among the current lot – doesn’t have much time to look for more innovative applications in the movies, which he describes as the fake world. The real world of military and medical imaging attracts him more.

Maths in real life

For the military, applied mathematics comes handy in detecting IED (improvised explosive device) from space. For the medical community, it means subjecting a patient under less radiation exposure in an MRI or CT machine but still getting an improved scan. The 68-year old mathematician is using maths for practical applications for many years. It began with the infamous Los Angeles riot in 1993 when the city went up in smoke triggered by the Rodney King incident. One of the cases involved a truck driver, Denny, who was at the receiving end of one attack. A video image taken from a helicopter revealed a speck on the arm of a person throwing a brick at Denny. Osher who was doing video image analysis with his colleague L Rudin resolved the speck into a rose tattoo, leading to the conviction of the suspect. But Osher is among a rare breed of mathematicians whose work has a direct and immediate bearing in the real world. Most mathematicians work in esoteric areas with complicated concepts and admit that their work has no immediate practical applications. Actually it can take several decades before new concepts in higher mathematics found an application.

Meyer’s maths

Take the research of Yves Meyer, professor emeritus at Ecole Normale Superieure de Cachan in France for example. Winner of the Gauss prize in the ICM, 2010, Meyer made many fundamental contributions to several areas in mathematics. The applications came over a decade later. Meyer’s work forms the basis of the common photograph standard JPEG-2000 and restoration of satellite imagery.

More recently, one of Meyer’s early work – known as Meyer Sets – was exploited to process the images beamed by European Space Agency’s Herschel space probe that aims to photograph some of the universe’s oldest and coldest stars in the universe. Being some of the coldest stars, they emanate very faint light necessitating the requirement for a new algorithm to process even those faint lights. Meyer’s 1970 work was used to make sense of it.

“Mathematics is an exciting place as there are applications from academics to industry,” said Daniel Spielman of Yale University, USA. Spielman who bagged the 2010 Rolf Nevanlinna prize for outstanding contribution to the mathematical aspect of information sciences, thanked his Grade-4 teacher for fuelling his interest in maths.

While the information sciences offer tremendous opportunities for mathematicians, Spielman whose work on error correcting code has made the online credit card transaction secure, said new opportunities are opening up in system biology, drug development and even in social areas like economy and political science. “Mathematics is used to understand the unpredictable nature of the financial market,” said Alberto Adrego Pinto from the Universidade do Porto in Portugal. Incidentally, Pinto and his colleagues used the same type of mathematical models was to find out distribution of sun spots.

The next big challenge for mathematicians like Pinto is to model human behaviour. “It’s very complicated but we are working on it,” he admitted.

Original Link: http://www.deccanherald.com/content/92587/brains-behind-maths.html