 |
|
Event(s) on November 2006
- 14/11/2006
| 題目: |
Optimisation-based Multilevel Methods for Image Restoration |
| 講員: |
Prof. Ke Chen, Department of Mathematical Sciences, University of Liverpool, UK |
| 時間/地點: |
11:30 - 12:30
FSC 1217
|
| | |
| 摘要: |
Development of fast multilevel methods is of fundamental importance
in variational image processing and Computer vision. Digital
images are often of extremely large scale and the usual solution
methods (e.g. the gradient descent approach) can be very slow
to converge. Standard multilevel methods (either the algorithms
or convergence theories) are not immediately applicable to many
variational models that are either associated with either non-smooth
and non-differentiable Functionals or partial differential equations
with discontinuous and highly non-smooth coefficients.
In this talk, we consider the basic ROF(Rudin_Osher_Fatemi 1992)
denoising model in both the primal variable and its dual variable.
Firstly for the primal formulation, previous multilevel work
involved regularizing the non-smooth terms in the models in order
to apply
the standard nonlinear algorithms. Our work aims to solve the
minimisation problem without regularizing the non-smooth term.
Using piecewise constant corrections from local coordinate descent
optimisation in A multilevel setting, we can ensure the locally
stuck solutions to converge to the global minimizer. The convergence
proof involves a detailed study of the otal variation norm and
its hemivariateness. Finally we shall give a brief
introduction to recent work on solving the dual formulation
by Chambolle (2004) and on restoration models for salt-and-pepper
type images. This talk summarises various joint works with T
F Chan (UCLA), J L Carter (UCB), J Savage (Liverpool), R Chan
(CUHK) and X C Tai (Bergen).
|
- 14/11/2006
| 題目: |
On Preconditioned Iterative Methods for Burgers Equations |
| 講員: |
Ms. Yumei Huang, Department of Mathematics, Hong Kong Baptist University, HKSAR, China |
| 時間/地點: |
14:00 - 15:00
FSC 1217
|
| | |
| 摘要: |
We study the Newton method and a fixed-point method for solving
the
system of nonlinear equations arising from the Sinc-Galerkin
discretization of
the Burgers equations are studied. In each step of the Newton
method or
the fixed-point method, a structured sub-system of linear equations
is obtained and needs to be solved numerically.
In this paper, preconditioning techniques are applied to
solve such linear sub-systems.
The bounds for eigenvalues of the preconditioned
matrices are derived and
numerical examples are given to illustrate the effectiveness
of the proposed methods. We also find that a combination of
the
Newton/fixed-point iteration with
the preconditioned GMRES method is quite efficient for the
Sinc-Galerkin discretization of the Burgers equations.
Future work is also proposed in this report.
|
- 21/11/2006
| 題目: |
Dimension Reduction Method for Multivariate Response Data |
| 講員: |
Mr. Songqiao Wen, Department of Mathematics, Hong Kong Baptist University, HKSAR, China |
| 時間/地點: |
14:00 - 15:00
FSC 1217
|
| | |
| 摘要: |
As the focus of dimension reduction is on reducing the
dimensionality of predictors, most of the existing work assume
that
the response variable is univariate. In this paper, we propose
a
general principle that can convert any existing dimension reduction
method for univariate response into an estimator that can be
applied
to dimension reduction problems with multivariate response data.
We
also discuss the root n consistency and the asymptotic distribution
of our new estimator. The simulation studies show that our method
perform well.
|
- 28/11/2006
| 題目: |
Detection of Spaced Motifs |
| 講員: |
Dr. Siu-Ming Yiu, Department of Computer Science, The University of Hong Kong, HKSAR, China |
| 時間/地點: |
11:00 - 12:00
FSC 1217
|
| | |
| 摘要: |
In this talk, we will start with some
background information about motifs,
binding sites, and transcription factors.
Then, we will introduce the motif
finding problem and discuss briefly why
this problem is difficult. In particular,
we will talk about spaced motifs and why
existing approaches may not be appropriate
for locating this type of motifs. Finally, we
will present an approach we proposed
for identifying spaced motifs, followed by
some experimental results. This solution is
a joint work with Dr Ken Sung and Dr Rajaraman
Kanagasabai of the National University of
Singapore.
|
- 29/11/2006
| 題目: |
A Truck Driver's Question, Sharing a Glass of Water, Cantor sets, and an Interesting Probability Distribution |
| 講員: |
Prof. Kevin Iga, Department of Mathematics, Pepperdine University, USA |
| 時間/地點: |
11:30 - 12:30
FSC 1217
|
| | |
| 摘要: |
A professional mover asked my colleague a math question. The
initial math question is a problem relating to moving water
between
two glasses with a straw, which can be solved using fairly simple
techniques. But variations on this question lead to some
surprising connections with some beautiful mathematics, including
Cantor sets, doing infinite series backwards, and a very mysterious
probability distribution that seems to have stumped Erds.
|
|
|
|
|
