During the last two decades, fast algorithms have brought a variety of large-scale physical and biophysical modeling tasks within practical reach. This is particularly true of integral equation approaches to electromagnetics, acoustics, gravitation, elasticity, and fluid dynamics. The practical application of these methods, however, requires analytic representations that lead to well-conditioned linear systems, quadrature methods that permit the accurate evaluation of boundary integrals with singular kernels, and techniques for a posteriori error estimation that permit robust mesh refinement. At the 2014 SIAM Annual Meeting Leslie Greengard of the Simons Foundation and Courant Institute of Mathematical Sciences, New York University, gave an overview of recent progress in these areas with a particular emphasis on wave scattering problems in complex geometry via The John von Neumann Lecture. View the video for an overview of his talk:
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How can mathematical models help in the prediction of storms and hurricanes? How do they help determine the uncertainty that underlies extreme weather conditions? Understanding these answers can help reduce the human and monetary costs associated with natural disasters. Lindley Graham of the University of Texas at Austin and Troy Butler of the University of Colorado explain how such models and simulations help us better understand natural disasters in this video:
Jeff Sachs of Merck Research Laboratories explains how mathematical models can make seemingly insurmountable amounts of data in medicine and biotechnology more manageable and informative. How can models be designed to uncover information we need from medical data in order to determine actions to be taken and decisions to be made in drug discovery and development?
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What makes cholesterol good or bad? High-density lipoprotein, or “good cholesterol” is believed to play an important role in lowering cardiovascular disease risk. But how and why does it do so, and does raising the level of good cholesterol reduce one’s risk of heart disease? To answer this and other questions about cholesterol, Norman Mazer of Roche Innovation Center in Basel uses mathematical models to represent the different biological processes involved in cholesterol metabolism. Using this model of lipoprotein metabolism and kinetics, Dr. Mazer’s group is attempting to understand the link between cholesterol and heart disease. Watch the video to learn more!
How do bacteria move? Can we turn to math and physics for answers? Jasmine Nirody, a graduate student at UC-Berkeley, has been fascinated with how organisms move since she was a little kid. Now she is using that passion to study how tiny organisms like bacteria move despite the large frictional and viscous forces acting against them in their environments. Using principles from applied mathematics and theoretical biophysics, Nirody is studying how flagellar forces help bacteria move via mechanistic models of the bacterial flagellar motor.
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How do the basics of what goes on in our tissues during normal development give us a better understanding of what happens when things go awry in the malignant disease state? In this clip, Arthur Lander of the University of California, Irvine, speaks about how biological systems use control and regulation to achieve or maintain desired outcomes in growth and development. Controlled growth is not only essential for biological development, but also plays an important role in preventing the kinds of out-of-control growth we see in certain cancers. Lander’s group builds mathematical models that mimic real tissues in order to understand normal growth control. Using such models, his lab is determining how morphogenesis is achieved by turning growth on and off in certain desired locations via regulated feedback between growing cells and those that produce tissues.
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The extraordinary success of search engines, recommendation systems, and speech and image recognition software suggests that future advances in these technologies could have a major impact in our lives. In this talk, we discuss modern intelligent-algorithmic systems based on sophisticated statistical learning models and powerful optimization techniques. One can envision new algorithms that operate in the stochastic or batch settings, and that take full advantage of parallelism. We review our remarkable understanding of classical stochastic approximation techniques, and pose some open questions. The lecture concludes with a discussion of modern neural nets and the demands they impose on optimization methods.At the 2014 SIAM Annual Meeting Jorge Nocedal talked about all this and more. Watch the video!
We live in an era in which the creation of new data is growing exponentially such that every two days we create as much new data as we did from the beginning of mankind until the year 2003. One of the greatest scientific challenges of the 21st century is to effectively understand and make use of the vast amount of information being produced. Visual data analysis will be among our most important tools to understand such large and often complex data. In this talk at the 2014 SIAM Annual Meeting, Christopher Johnson of the University of Utah presented state-of-the-art visualization techniques, including ways to visually characterize associated error and uncertainty, applied to Big Data problems in science, engineering, and medicine.
The last two decades have seen an exponential increase in genomic and biomedical data, which will soon outstrip advances in computing power to perform current methods of analysis. Extracting new science from these massive datasets will require not only faster computers; it will require smarter algorithms. At the 2014 SIAM Annual Meeting, Bonnie Berger of the Massachusetts Institute of Technology (MIT), showed how ideas from cutting-edge algorithms, including spectral graph theory and modern data structures, can be used to attack challenges in sequencing, medical genomics and biological networks.
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