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Sunday, March 25, 2007

Abel Prize to NYU Professor S.R. Srinivasa Varadhan

The Norwegian Academy of Sciences has awarded the Abel Prize for Mathematics to the Indian-American professor Sathamangalam R. Srinivasa Varadhan (67) of New York University. Varadhan receives the prize “for his fundamental contributions to probability theory and in particular for creating a unified theory of large deviation”.

The Abel prize, worth six million kronor (864,450 dollars), was created by Norway's government in 2002 to mark the 200th anniversary of the birth of the great Norwegian mathematician Niels Henrik Abel. It is viewed as the equivalent of a Nobel prize, which is not awarded for mathematics.

Varadhan hails from Chennai, India. He received his undergraduate degree in 1959 from Presidency College, Chennai (then Madras) and his doctorate in 1963 from the Indian Statistical Institute, Kolkata (then Calcutta). Since 1963, he has worked at the Courant Institute of Mathematical Sciences, New York University, where he is currently Professor of Mathematics and Frank J. Gould Professor of Science.

Probability theory is the mathematical tool for analyzing situations governed by chance. Varadhan's speciality lies in the theory of large deviations or studies of the occurrence of rare events. Over the last four decades, the theory of large deviations has become a cornerstone of modern probability, both pure and applied. Varadhan’s theory of large deviations provides a unifying and efficient method for clarifying a rich variety of phenomena arising in complex stochastic systems, in fields as diverse as quantum field theory, statistical physics, population dynamics, econometrics and finance, and traffic engineering. It has also greatly expanded our ability to use computers to simulate and analyze the occurrence of rare events as is described by the Abel Committee,"Varadhan’s work has great conceptual strength and ageless beauty. His ideas have been hugely influential and will continue to stimulate further research for a long time”.

This marks the second time in three years an NYU mathematician has won the Abel Prize. In 2005, it was given to Professor Peter Lax of the Courant Institute. That's an occurrence of a rare event indeed!

We did not wish to end this posting on a sad note but Mathematicians are also human and unfortunately some of them had to face and survive greatest tragedies in life and then continue their great work. In order to put Prof. Varadhan's achievement in a greater perspective of life that goes beyond Mathematics or any award whatsoever, we thought we should mention to our readers that the elder of Varadhan's two sons, Gopal, was killed in the attacks on the World Trade Center on September 11, 2001.

Monday, March 19, 2007

Mathematicians Could Map E8 Lie Group

Atlas Group14 Team members of the Atlas Project (photo courtesy: American Institute of Mathematics)

The American Institute of Mathematics (AIM) announced today that after four years of intensive collaboration, 18 top mathematicians and computer scientists from the U.S. and Europe have successfully mapped E8, one of the largest and most complicated structures in mathematics.

This achievement is significant both as an advance in basic knowledge and because of the many connections between E8 and other areas, including string theory and advanced geometry, number theory and chemistry.

Sophus LieSophus Lie

E8 is an example of a Lie group. Lie groups were invented by the 19th century Norwegian mathematician Sophus Lie to study symmetry. Underlying any symmetrical object, such as a sphere, is a Lie group. Balls, cylinders or cones are familiar examples of symmetric three-dimensional objects. Mathematicians study symmetries in higher dimensions and this has applications in many conceptual issues in various branches of science. E8 is an extraordinarily complicated group: it is the symmetries of a particular 57-dimensional object, and E8 itself is 248-dimensional!

The magnitude of the E8 calculation invites comparison with the Human Genome Project. The human genome, which contains all the genetic information of a cell, is less than a gigabyte in size. The result of the E8 calculation, which contains all the information about E8 and its representations, is 60 gigabytes in size. That is enough space to store 45 days of continuous music in MP3 format. The answer, if written out in tiny print, would cover an area the size of Manhattan.

The E8 calculation is part of an ambitious project known as the Atlas of Lie Groups and Representations. The goal of the Atlas project is to determine the unitary representations of all the Lie groups. This is one of the great unsolved problems of mathematics, dating from the early 20th century. The Atlas team consists of about 20 researchers from the United States and Europe. The core group consists of Jeffrey Adams (University of Maryland), Dan Barbasch (Cornell), John Stembridge (University of Michigan), Peter Trapa (University of Utah) , Marc van Leeuwen (Poitiers, France), David Vogan (MIT), and (until his death in 2006) Fokko du Cloux (Lyon, France).

Monday, March 12, 2007

PDE2D from Visual Numerics

Visual NumericsVisual Numerics, Inc., celebrating 36 years of producing advanced numerical analysis and visualization software, announced the availability of PDE2D, a partial differential equation (PDE) solver authored by University of Texas-El Paso Mathematics Professor Dr. Granville Sewell.

Dr. Sewell's software package PDE2D solves general nonlinear, time-dependent, steady-state and eigenvalue systems of partial differential equations in 1D intervals, general 2D regions and a wide range of simple 3D regions. The software features an interactive user interface, which makes it very easy-to-use, yet PDE2D users have all the flexibility of Fortran at their disposal. Collocation and Galerkin finite element methods are used, on automatically generated meshes of higher order elements, so that at least fourth order accuracy is available for all problems. PDE2D has extensive built-in graphics, and also provides an interface to MATLAB®'s graphical and post-processing abilities.

The PDE2D is available through Visual Numerics' Affiliated Products and Services (VNIAPS), a brand new channel program for downloadable high-quality software. Through the Visual Numerics Storefront, users purchase and download electronic copies of PDE2D or a trial version, receive technical support from Dr. Sewell through Visual Numerics Forums, and engage in topical discussions about PDEs and PDE2D. The PDE2D interactive driver automatically creates a FORTRAN program that is then compiled using a FORTRAN compiler, and linked with the PDE2D library. A compatible FORTRAN compiler is thus a prerequisite for PDE2D.

Additional product information about PDE2D and a trial version are located at http://www.vni.com/products/affiliated/index.html. Dr. Sewell will provide user support for PDE2D through the PDE2D Forum within the VNI Forum at http://forums.vni.com/.

Sunday, March 04, 2007

Cancer Research Uses Parallel Computing

The National Cancer Institute’s Pediatric Oncology Branch is using parallel computing software to accelerate medical discoveries.

The researchers use a Matlab-based application called CORR4DM to correlate one genomic array against a database of 100,000 parts of a gene, in search of specific DNA components or attributes. The results help them to understand the relationship between the genes, and may even direct future genomic research.

Running a single correlation on a desktop computer could take a week or more to complete. An explosion in the amount of genomic data available to researchers has made their work increasingly difficult. Their tasks require more computing power, more system memory, and - all too often - more time. And in the race to understand how genetics and cancer are linked, time is precious. Thus, once the sample sizes grew to consist of tens of thousands of arrays, it became obvious parallel computing was necessary to provide larger correlations.

Scientists made use of Interactive Supercomputing's (ISC) Star-P software. This allows them to make use of powerful high performance computers to explore vast public databases to have insight into the genetic risk factors for cancer, foster new procedures for testing tumors, or even identify genetic changes resulting from treatment. The software also allowed them to quickly interact with the data. 'Star-P' (as described in our past posting) lets scientists continue to work with their preferred tools, shielding them from the programming complexities of parallel systems. It can automatically connect MATLAB to the server and parallelises the application code.