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Event(s) on January 2005
- Friday, 7th January, 2005
Title: BIG Statistics Speaker: Prof. Dennis KJ Lin, Department of Supply Chian and Information Systems, The Pennsylvania State University, USA Time/Place: 10:30 - 11:30
Abstract: In the past decade, we have witnessed the revolution of information technology. Its impact to statistical research is enormous. This talk attempts to address recent developments and some potential research issues in Business, Industry and Government (BIG) Statistics. An overall introduction and review will be given at the beginning. For each subject the problem will be introduced, some initial results will be presented, and future research problems will be suggested. If time permits, I will also discuss some recent advances in Data Mining.
- Wednesday, 12th January, 2005
Title: From Preferences to Trees: From Social Choice to Biology Speaker: Prof. F.R. McMorris, Department of Applied Mathematics, Illinois Institute of Technology, USA Time/Place: 11:00 - 12:00
Abstract: The problem of aggregating the individual preferences of a group of "voters" into a group consensus preference has been studied for many years. Indeed, mathematical investigations of consensus problems go back to the contributions of Borda (1770), of Condorcet (1785), and of Pareto (1896) and are still frequently cited today. But the origins of this talk are in Kennth Arrow's world-shaking doctoral thesis in 1951, Social Choice and Individual Values, one of several contributions for which he received the Nobel Prize for economics in 1972. This talk will briefly review Arrow's work and then show how Arrow's paradigm of social choice has been applied in classification and clustering - - primarily in the biological sciences.
- Thursday, 13th January, 2005
Title: Multiscale Refinement Subdivision in Geometric and Nonlinear Settings Speaker: Dr. Thomas P.Y. Yu, Department of Mathematical Sciences, Rensselaer Polytechnic Institute, USA Time/Place: 11:30 - 12:30
Abstract: Multiscale refinement subdivision, or subdivision for short, are methods for taking coarsely sampled data and recursively creating very finely sampled data consistent with the coarse-scale data. They have played important roles in the processing of surface data gathered by 3D scanners and for a variety of emerging geometric representation problems, such as representing data which take values in a nonlinear manifold (e.g. the sphere, SO(3), etc..) Such “second generation subdivision methods” allow a kind of multiscale representation of nonlinear data that does for such data what wavelets were able to do for images and signals. The resulted multiscale representations are the key to data compression, feature extraction, noise removal, fast search, and other processing problems that arise in exploiting such data. Subdivision algorithms typically look quite simple, but their simplicity is deceptive --- more often than not it is highly nontrivial to understand their properties. The speaker will present some recent and past results, and some of the challenging analysis problems that remain. Another part of this talk presents a new methodology for multiscale digital geometry known as "Jet Subdivision". Along the way, we shall also have the pleasure to see how the modern intrinsic view of differential geometry happens to be very instrumental for the development of this methodology. Some of the materials of this talk can be found in http://www.rpi.edu/~yut/JetSubdivision
- Tuesday, 18th January, 2005
Title: SCD Methods for Linear Systems Speaker: Prof. Yuan Jin Yun, Department of Mathematics, Univ Federal Do Parana, Brazil Time/Place: 11:30 - 12:30
Abstract: The semi-conjugate direction vectors are introduced to establish the left conjugate direction method for solving general linear systems. Some nice properties of the method are presented. Several techniques are discussed to overcome the break-down problem. Some variant of the method is proposed. The method was generalized to complex case. For the complex case, the method has very nice properties. Finally the method was applied to solve several large scale linear systems arising from numerical methods of partial differential equations. The numerical results illustrate that the method is very competitive. Since the work is preliminary, there are still many open problems to be solved.
- Tuesday, 25th January, 2005
Title: On Numerical Methods for PDEs with Constraints Speaker: Dr. Manuel Torrilhon, ETH Zurich & HKUST Time/Place: 11:30 - 12:30
Abstract: A number of hyperbolic conservation laws have intrinsic constraints like vanishing divergences or constant curl. These constraints do not change the character of the equations and they remain hyperbolic. With the finite speed of propagation finite volume methods are the proper choice for numerical method. Unfortunately, most of the common schemes do not respect the constraint and additional treatment is needed. Guided by multidimensional discretizations of hyperbolic conservation laws a framework is shown how to incorporate the constraints into the flux formulation of a numerical method. This approach keeps well known features like shock capturing and upwinding while introducing an exact preservation of a constraint discretization. Applications of the framework and numerical results will be shown for the case of constrained divergence-free and curl-free advection, magnetohydrodynamics and the wave equation system.