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2009 Newsletter FALL 2009 CommonTHE Denominator UCLA DEPARTMENT OF MATHEMATICS NEWSLETTER Blurred Deblurred Original The blurry image is generated by the convolution of the original image with an average kernel size of 100 X 100 pixels. The deblurred image is obtained by nonlocal total variation (NLTV) regularization with Bregman iterations. Using block by block NLTV denoising, the problem is solved by the Bregmanized Operator Splitting method. Image reconstruction performed by Assistant Adjunct Professor Xiaoqun Zhang UCLA Math Takes a Walk INSIDE UCLA Math on the Applied Side Takes a Walk on These are heady times for the Department’s applied PDEs: framework for applied math Partial differen- the Applied Side 1–3 math group, which recently climbed to a high-water tial equations (PDEs), the governing equations that New Faculty 4 mark third place ranking in the most recent U.S. quantify physical phenomena, are the common Faculty News 4–5 News & World Report survey of graduate school framework for the group’s research which divides Focus on Research 6–7 programs. Individual honors abound as well: Stan into two broad areas: physics-based problems and Osher was newly elected to the American Academy data-driven problems (e.g. imaging). As Professor Events 8–9 of Arts & Sciences and is set to give a plenary ad- Chris Anderson explains, “When I’m asked to talk to Graduate News 10–11 dress on new algorithms in information science at graduate students about the program, I say the one Undergraduate News 12–13 the 2010 International Congress of Mathematicians. thing you’ll learn is PDEs because that’s what we Curtis Center Andrea Bertozzi was honored for her profound contri- do here.” Chris works with applied physicists at HRL (math education) 14 butions to diverse areas of applied mathematics as Laboratories to develop simulation tools for the de- the Society for Industrial and Applied Mathematics’ sign of quantum dots as part of its efforts to build a IPAM 15 (SIAM) youngest Sonia Kovalevsky lecturer. The ap- quantum computer. Russ also shares his research Alumni News 16–17 plied group’s most recent addition, Joey Teran, was interest in materials modeling with additional work Giving 18 named by DISCOVER magazine as one of the bright- in plasma dynamics and fluid dynamics. Our Donors 19 est young scientists for his pioneering work in virtual Whichever side of the applied equation they surgery. And Russ Caflisch, founding member of the fall on, the Department’s applied math faculty are Letter from the California Nanosystems Institute, completes his first distinguished by their outwardly focused nature and Chair 20 year as director of IPAM, the NSF-funded math insti- keen interest in research that impacts and revolution- tute that fosters cutting edge collaborations between izes medicine, biology, criminology, information sci- world-class mathematicians and scientists. ence, robotics, visual effects and materials science. continued on page 2 2 THE COMMON DENOMINATOR | FALL 2009 UCLA Math Takes a Walk on the Applied Side continued from page 1 House of algorithms Veteran image process- Paul Roberts, renowned for his contributions ing guru Stan Osher offers this take on their to problems of magnetohydrodynamics (MHD) success: “We’re the house of algorithms.” of the earth’s core and the dynamo theory, His work in the late 1970s and mid-1980s with Bjorn Engquist, students, and frequent developed courses on fluid mechanics and X-box + math = virtual surgery visitor Ami Harten impacted shock calcula- has a joint appointment with the Institute of http://www.spotlight.ucla.edu/faculty/ tions, culminating in essentially nonoscilla- Geophysics and Planetary Physics. Alan Laub, joseph-teran-virtual-surgery/ founding director of the Institute for Digital Re- tory (ENO) schemes. With Lenny Rudin, Stan search and Education (IDRE) also crosses over applied ideas from shock waves to imaging, age processing, remote sensing and complex departments, carrying a second appointment in advancing the field significantly. As the co-de- fluids. Andrea is particularly excited about electrical engineering. His mathematical focus veloper (with James Sethian) of the level set a new research project on the Atomic Force is numerical linear algebra with emphasis on method in the late 1980s, Stan’s research Microscope (AFM) that melds her research small dense problems and matrix analysis. Re- transformed the visual effects industry with in imaging with her mathematical swarming jecting the practice of “throwing their work over this powerful technique that simulates every models that she has translated into robotic the wall,” the applied group seeks outside col- imaginable component of a digital environ- platforms in the applied math lab. The AFM laborations with scientists, doctors, engineers, ment, including plants, clouds, clothing, hair project forges an interdisciplinary partnership physicists, the military, animators and others and water. On Google, “level set method” with the Lawrence Berkeley National Labora- to help solve real world problems. Fortunately gets 1,850,000 hits with applications in two- tory’s Molecular Foundry. The goal is to design for the group, UCLA’s world-class research en- phase fluid flow, solid mechanics, computer transformative computation-based methods vironment offers a vast pool of onsite scientific vision, nanoscience, control and many other for real-time data acquisition and analysis in customers in the engineering school, medical fields. Most recently, Stan and his “genius” chemical and biological experiments con- center, and the fertile ground of IPAM. graduate student entourage are developing ducted at the nanoscale level. “This is really techniques to solve optimization problems exciting for me because I work on problems in Strong applied/pure faculty bonds The group that arise from compressed sensing, which control and sensing and I work on problems in also harmoniously co-exists with the Depart- allows images and signals to be reconstruct- image processing and I’ve never been able to ment’s talented pure math core, leveraging ed from small amounts of data. The “Split combine the two,” says Andrea. The Defense in-house theoretical expertise to enhance its Bregman” method is one such new promising Threat Reduction Agency through NSF re- applied research. A well-known example is the technique that Stan co-developed with gradu- cently funded her potentially groundbreaking breakthrough results by Terry Tao, Emmanuel ate student Tom Goldstein for image denois- remote sensing project to develop algorithms Candes (Stanford) and Justin Romberg (Geor- ing in magnetic resonance imaging (MRI) for sensor systems for use in the detection of gia Tech) in compressed sensing, which have technology. The method has already attracted chemical and biological materials. Andrea’s had major impact on advancements in image widespread interest. The group’s image pro- work aims to improve techniques for rapidly processing. Honorary applied group member cessing innovators also build on the ideas processing and understanding evolving infor- and IPAM Director Emeritus Mark Green ex- of others, including nonlocal means, a revo- mation from diverse platforms to accurately plains, “The amity between pure and applied lutionary process for image denoising devel- identify and track threats that are critical to math started when Stan Osherj and Bjorn oped by French researcher Jean-Michel Morel, the country’s security. Engquist arrived. They knew how to sell the a frequent visitor and collaborator. Algorithms Addressing more local threats, Andrea rest of the department on applied math and from discrete math, such as graph cuts, are is also part of a high profile interdisciplin- they brought in the rest of the group. When also being creatively employed to efficiently ary team, including UCLA anthropologist Jeff Tony Chan became the first applied chair, that solve certain image science problems. Brantingham and University of California, Ir- again said something. We could have an ap- vine, criminologists, who are working with the Swarms of research Director of Applied Math- plied chair and not worry that this would be Los Angeles Police Department on diverse ematics Andrea Bertozzi’s 2009 SIAM Sonia the end of the world as we knew it. Indeed, crime modeling projects with the goal of bet- Kovalevsky lecture “Swarming by Nature and it marked a new beginning.” Tony continues ter policing through detection and prediction. by Design” could also describe her numer- to take on the world as the new president of The Army Research Office is now looking to ous research interests, which literally swarm Hong Kong University of Science and Technol- apply these models to track insurgent activi- across the scientific community. Her expertise ogy this September after serving as the NSF ties abroad. In the area of fluid flows, Andrea in swarming (large-scale coordinated move- assistant director in charge of its mathemati- and her Lawrence Livermore National Labo- ment, with no centralized control, observed in cal and physical sciences directorate. Tony’s ratory (LLNL) colleague Alice Koniges will be fish schools, locust swarms and bird flocks) ascendancy in global scientific leadership developing numerical simulations of fracture represents one of the many applications of is more evidence of the group’s versatility and multimaterial debris flow for LLNL’s new PDEs she focuses on that also include im- across multiple borders. National Ignition Facility (NIF). The facility UCLA DEPARTMENT OF MATHEMATICS NEWSLETTER 3 uses lasers to create a new energy source by search extends into the virtual worlds of special fusing hydrogen into helium. Andrea has en- effects for the movie industry. Working as math- listed Stan and Joey Teran for their expertise ematical consultants to Disney’s animators, he on solids and fluids modeling to simulate the and his students have made a number of break- blast wave and analyze how debris shoots off throughs in hair simulation and fracturing rigid the component parts. Donning hard hats and objects. Since making the strategic decision to protective gear, Andrea and Joey were recent- develop new technologies in-house, the studio ly treated to a VIP tour of the facility.
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