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Event(s) on March 2015


  • Tuesday, 3rd March, 2015

    Title: Rate-Optimal Detection of Very Short Signal Segments
    Speaker: Prof. Ming YUAN, Department of Statistics, University of Wisconsin-Madison, USA
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Motivated by a range of applications in engineering and genomics, we consider in this paper detection of very short signal segments in three settings: signals with known shape, arbitrary signals, and smooth signals. Optimal rates of detection are established for the three cases and rate-optimal detectors are constructed. The detectors are easily implementable and are based on scanning with linear and quadratic statistics. Our analysis reveals both similarities and differences in the strategy and fundamental difficulty of detection among these three settings.


  • Friday, 6th March, 2015

    Title: Approximate Versions of the Alternating Direction Method of Multipliers
    Speaker: Prof. Jonathan Eckstein, Department of Management Science & Information Systems, Rutgers University, USA
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The Alternating Direction Method of Multipliers (ADMM) is a decomposition method for convex optimization, currently enjoying some popularity in the solution of machine learning, image processing, and stochastic programming problems. This talk reviews the convergence mechanism of the ADMM and presents three new, provably convergent approximate versions in which one or (in two variants) both optimization subproblems arising at each iteration may be solved inexactly using practically testable approximation criteria. Preliminary computational results applying two of these methods to two different problem classes indicate that in cases in which an iterative method is used for at least one of the ADMM subproblems, these variants can significantly reduce total computational effort. We also discuss the application of these approximation techniques to the Progressive Hedging (PH) algorithm for stochastic programming, which may be viewed as an particular case of the ADMM.


  • Thursday, 12th March, 2015

    Title: Orthogonal Low Rank Tensor Approximation
    Speaker: Prof. Moody CHU, Department of Mathematics, North Carolina State University, USA
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: With the notable exceptions of two cases — that tensors of order 2, namely, matrices, always have best approximations of arbitrary low ranks and that tensors of any order always have the best rank-one approximation, it is known that high-order tensors may fail to have best low rank approximations. When the condition of orthogonality is imposed, even under the modest assumption that only one set of components in the decomposed rank-one tensors is required to be mutually perpendicular, the situation is changed completely — orthogonal low rank approximations always exist. The purpose of this paper is to discuss the best low rank approximation subject to orthogonality. The conventional high-order power method is modified to address the orthogonality via the polar decomposition. Algebraic geometry technique is employed to show that for almost all tensors the orthogonal alternating least squares method converges globally.


  • Thursday, 12th March, 2015

    Title: Time-Frequency Analysis and Signal Decomposition
    Speaker: Prof. Charles K. Chui, Department of Statistics, Stanford University, USA
    Time/Place: 15:00  -  16:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The notion of frequency for nonlinear and non-stationary signals is introduced and discussed. Motivated by the EMD scheme, the adaptive harmonic model is used for instantaneous signal extraction and signal decomposition from a given blind source. Direct application to several clinical problems, including sleep-depth detection and anesthetic-depth detection, will also be discussed.


  • Friday, 13th March, 2015

    Title: Solve one-dimensional FBSDE using Deferred Correction
    Speaker: Mr. Bo GONG, Department of Mathematics, Hong Kong Baptist University, Hong Kong
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The study of forward-backward stochastic differential equation (FBSDE) arises from various problems in finance. After the establishment for the link between Markovian FBSDE and PDE, FBSDE has served as another tool to study PDE. Deferred Correction is a numerical method initially designed for ODE, which computes high-order solution by recursively solving some low-order schemes. This method has been extended to FBSDE. It is important to prove the convergence of the method. In this talk, some preliminary ideas will be presented and discussed.


  • Tuesday, 17th March, 2015

    Title: Valuation of Large Variable Annuity Portfolios under Nested Simulation: A Functional Data Approach
    Speaker: Dr. Guojun Gan, Department of Mathematics, University of Connecticut, USA
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: A variable annuity (VA) is equity-linked annuity product that has rapidly grown in popularity around the world in recent years. Research up to date on VA largely focuses on the valuation of guarantees embedded in a single VA contract. However, methods developed for individual VA contracts based on option pricing theory cannot be extended to large VA portfolios. Insurance companies currently use nested simulation to valuate guarantees for VA portfolios but efficient valuation under nested simulation for a large VA portfolio has been a real challenge. The computation in nested simulation is highly intensive and often prohibitive. In this talk, I will introduce a novel approach that combines a clustering technique with a functional data analysis technique to address the issue.


  • Wednesday, 25th March, 2015

    Title: From a microscopic model to a macroscopic model with cross-diffusion in Population Dynamics
    Speaker: Ms. Ariane TRESCASES, Department of Mathematics, ENS Cachan, France
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: We consider a class of reaction-cross diffusion systems naturally arising in Population Dynamics. In those systems, cross diffusion terms appear only in one of the two equations (triangular case). We present results of existence of weak solutions for these systems. The solutions are obtained as the limit of the solutions of a microscopic model where only standard diffusions appear. The results use Lyapounov-like functionals and duality lemmas. This is a joint work with Laurent Desvillettes.


  • Thursday, 26th March, 2015

    Title: Spectral theory of Neumann-Poincar'e operator and applications
    Speaker: Prof. Hyeonbae KANG, Department of Mathematics, Inha University, Korea
    Time/Place: 16:30  -  17:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The Neumann-Poincar'e (NP) operator is a boundary integral operator which arises naturally when solving boundary value problems using layer potentials. It is not self-adjoint with the usual inner product. But it can symmetrized by introducing a new inner product on $H^{-1/2}$ spaces using Plemelj's symmetrization principle. Recently many interesting properties of the NP operator have been discovered. I will discuss about this development and various applications including solvability of PDEs with complex coefficients and plasmon resonance.