 |
|
Event(s) on January 2005
- 7/1/2005
| 題目: |
BIG Statistics |
| 講員: |
Prof. Dennis KJ Lin, Department of Supply Chian and Information Systems, The Pennsylvania State University, USA |
| 時間/地點: |
10:30 - 11:30
FSC1217
|
| | |
| 摘要: |
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.
|
- 12/1/2005
| 題目: |
From Preferences to Trees: From Social Choice to Biology |
| 講員: |
Prof. F.R. McMorris, Department of Applied Mathematics, Illinois Institute of Technology, USA |
| 時間/地點: |
11:00 - 12:00
RRS905
|
| | |
| 摘要: |
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.
|
- 13/1/2005
| 題目: |
Multiscale Refinement Subdivision in Geometric and Nonlinear Settings |
| 講員: |
Dr. Thomas P.Y. Yu, Department of Mathematical Sciences, Rensselaer Polytechnic Institute, USA |
| 時間/地點: |
11:30 - 12:30
FSC1217
|
| | |
| 摘要: |
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
|
- 18/1/2005
| 題目: |
SCD Methods for Linear Systems |
| 講員: |
Prof. Yuan Jin Yun, Department of Mathematics, Univ Federal Do Parana, Brazil |
| 時間/地點: |
11:30 - 12:30
FSC1217
|
| | |
| 摘要: |
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.
|
- 25/1/2005
| 題目: |
On Numerical Methods for PDEs with Constraints |
| 講員: |
Dr. Manuel Torrilhon, ETH Zurich & HKUST |
| 時間/地點: |
11:30 - 12:30
FSC1217
|
| | |
| 摘要: |
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.
|
|
|
|
|
