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Event(s) on January 2011
- 4/1/2011
| 題目: |
Explicit Estimating Equations for Semiparametric Generalized Linear Latent Variable Models |
| 講員: |
Dr. MA Yanyuan, Department of Statistics, Texas A&M University, USA |
| 時間/地點: |
11:30 - 12:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
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| 摘要: |
We study the generalized linear latent variable models without
requiring a distributional assumption of the latent variables.
Using a geometric approach, we derive consistent semiparametric
estimators.
We demonstrate that these models possess a property similar
to that of a sufficient complete statistic, which enables us
to simplify the estimating procedure and explicitly formulate
the semiparametric estimating equations.
We further show that the explicit estimators have the usual
root-$n$ consistency and asymptotic normality. We explain the
computational implementation of our method and illustrate the
numerical performance of the estimators in finite sample situations
via extensive simulation studies.
The advantage of our estimators over the existing likelihood
approach is also shown via numerical comparison. We employ the
method to analyze a real data example from economics.
This is joint work with Marc Genton.
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- 4/1/2011
| 題目: |
Functional Boxplots for Complex Data Visualization |
| 講員: |
Prof. Marc GENTON, Department of Statistics, Texas A&M University, USA |
| 時間/地點: |
15:00 - 16:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
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| 摘要: |
This paper proposes an informative exploratory tool, the functional
boxplot, for visualizing functional data, as well as its generalization,
the enhanced functional boxplot. Based on the center outwards
ordering induced by band depth for functional data, the descriptive
statistics of a functional boxplot are: the envelope of the 50%
central region, the median curve and the maximum non-outlying
envelope. In addition, outliers can be detected in a functional
boxplot by the 1.5 times the 50% central region empirical rule,
analogous to the rule for classical boxplots.
The construction of a functional boxplot is illustrated on a
series of sea surface temperatures related to the El Nino phenomenon
and its outlier detection performance is explored by simulations.
As applications, the functional boxplot and enhanced functional
boxplot are demonstrated on children growth data and spatio-temporal
U.S. precipitation data for nine climatic regions, respectively.
Further adjustments of the functional boxplot for outlier detection
in spatio-temporal data are discussed as well. The talk is based
on joint work with Ying Sun.
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- 7/1/2011
| 題目: |
ICM Distinguished Computational Mathematics Lecture: Studies on Wilson Nonconforming Finite Element |
| 講員: |
Prof. Zhong-Ci Shi, Institute of Computational Mathematics, Chinese Academy of Sciences, China |
| 時間/地點: |
11:00 - 12:00 (Preceded by Reception at 10:30am)
LT1, Cha Chi-Ming Science Tower, HSH Campus, Hong Kong Baptist University
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| 摘要: |
Wilson nonconforming finite element (1973) is a very useful rectangular
element In practice. it has been shown in many engineering applications
that the convergence behavior of this element is better than
that of the commonly used bilinear element. However, mathematical
studies carried out so far cannot justify it. The results obtained
by use of standard finite element analysis technique are not
satisfied.
Recently (2007-) we tackle this problem from a different view
point, i.e. from Mechanics, where the Wilson element was originated.
We have succeeded in proving both mathematically and numerically
that the Wilson element is free of shear locking for a wide class
of bending dominated plane elasticity problems, while the bilinear
element suffers from the shear locking.
Therefore, we elucidate a long-standing folklore: why Wilson
element does a better job in many practical applications than
the bilinear element.
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- 11/1/2011
| 題目: |
Dimension Reduction in Regression |
| 講員: |
Ms. FENG Zhenghui, Department of Mathematics, Hong Kong Baptist University, HKSAR |
| 時間/地點: |
11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
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| 摘要: |
The appearance of massive data lead statistics to a new time.
Using traditional statistical method could seldom satisfy the
new case. We study some dimension reduction methods in regression.
In the first part, we investigate how to select a parsimonious
dimension reduction semiparametric model (DRSM) that is of the
additive structure with orthogonal projection directions. Different
from the classical sufficient dimension reduction, the problem
for DRSM involves both selecting nonparametric component functions
and estimating projection directions. To implement component
function selection and projection direction estimation simultaneously,
we propose an alternating selection-optimization algorithm to
alternatively search best model fitting and direction estimation.
In the second part, for generalized linear model, when dimension
of predictor is large, or error has heavy tail, classical estimation
method will be unstable. Our two staged method could overcome
this in the meaning of dimension reduction. Simulation studies
are carried out to examine the performance of the new methods
and real data example is also analysed for illustration.
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- 14/1/2011
| 題目: |
CMIV Colloquium: A Fast Algorithm for Euler’s Elastica Model Using Augmented Lagrangian Method |
| 講員: |
Prof. Xue-Cheng Tai, Nanyang Technological University, Singapore |
| 時間/地點: |
11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
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| 摘要: |
Minimization of functionals related to Euler's elastica energy
has a wide range of applications in computer vision and image
processing. An issue is that a high order nonlinear partial differential
equation (PDE) needs to be solved and the conventional algorithm
usually takes high computational cost. In this paper, we propose
a fast and efficient numerical algorithm to solve minimization
problems related to the Euler's elastica energy and show applications
to variational image denoising, image inpainting, and image zooming.
We reformulate the minimization problem as a constrained minimization
problem, followed by an operator splitting method and relaxation.
The proposed constrained minimization problem is solved by using
an augmented Lagrangian approach. Numerical tests on real and
synthetic cases are supplied to demonstrate the efficiency of
our method.
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- 14/1/2011
| 題目: |
Variational Surface reconstruction based on Delaunay triangulation and graph cut |
| 講員: |
Dr. WANG Desheng, Division of Mathematical Sciences, School of Physical & Mathematical Sciences, Nanyang Technological University, Singapore |
| 時間/地點: |
15:00 - 16:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
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| 摘要: |
In this talk, we shall start with a review on surface reconstruction
based on Delaunay triangulation from sectional contours and unoriented
points set. Motivated by addressing the difficulties in surface
reconstruction from noisy, under-sampling, multiphase data input,
we developed a robust and efficient approach which is based on
minimizing a geometrical functional defined on the dual-graph
to the Delaunay tetrahedral mesh constructed using all or part
of the given points set. The application to open surface reconstruction
will be discussed. The issue on how to keep the features involving
ridges and corners will be addressed as well.
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- 18/1/2011
| 題目: |
Perfectly matched layers for the fluid equations |
| 講員: |
Mr. GAO Zhen, Division of Applied Mathematics, Brown University, USA , & School of Mathematical Sciences, Ocean University of China, China |
| 時間/地點: |
11:30 - 12:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
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| 摘要: |
The perfectly matched layer (PML) is to design an artificial layer
surrounding the computational domain so that the outgoing wave
are absorbed in the layer and reflections are only exponentially
small in terms of the layer width. It works as a relatively simple
and efficient tool for truncating a computational domain in an
infinity or semi-infinity spatial domain.
In this talk, we discuss the development of perfectly matched
layers for the fluid equations which are the Boltzmann equation
and the Navier-Stokes equation respectively. First of all, the
discretization of the Boltzmann equation in velocity space via
a Galerkin approach based on Hermite polynomials, is presented.
Secondly, The PML formulation for the Boltzmann equation is constructed
via a modal analysis, that is, to perform Laplace transformation
in time-direction and Fourier transformation in spatial variables.
By properly choosing a set of auxiliary parameters, it is a long
time stable PML model. Last but not least, the PML model for
the Navier-Stokes equation is designed by assigning the Navier-Stokes
equation and the Boltzmann equation in the computational domain
and the artificial layer separately. The results are compared
with reference solutions computed from a larger domain in several
standard test examples, confirming the accuracy and efficiency
of the proposed approaches.
This is a joint work with Prof. Jan S. Hesthaven at Brown University,
USA and Prof. Tim Warburton at Rice University, USA.
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- 19/1/2011
| 題目: |
Parallel Time Integrators |
| 講員: |
Dr. Benjamin ONG, Department of Mathematics, Michigan State University, USA |
| 時間/地點: |
11:30 - 12:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
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| 摘要: |
We discuss a family of parallel time integrators based on defect
correction for multi-core, multi-node or multi-gpgpu systems.
The key idea is to re-write the defect correction framework so
that, after initial startup costs, each correction loop can be
lagged behind the previous correction loop in a manner that facilitates
running the predictor and correctors in parallel.
Time permitting, we will discuss present work in generating
a parallel space-time algorithm for solving Poisson's or Helmholtz's
equation using boundary integral treecode algorithms.
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- 26/1/2011
| 題目: |
CMIV Colloquium: Quantum Error Correction and Generalized Numerical Ranges |
| 講員: |
Professor Chi-Kwong Li, 2011 Fulbright Fellow, Hong Kong University of Science & Technology, Hong Kong |
| 時間/地點: |
11:30 - 12:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
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| 摘要: |
The numerical range is a useful tool for studying matrices and
operators, and there are many generalizations of the concept
motivated by theory and applications. In this talk, we will focus
on the higher rank numerical range, which arises from the study
of quantum error correction. Recent results and open problems
on the topic will be described.
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