Colloquium/Seminar

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Event(s) on February 2018


  • Thursday, 1st February, 2018

    Title: Stochastic Symplectic Methods and Multi-symplectic Methods for Two Stochastic Hamiltonian Partial Differential Equations
    Speaker: Prof. Jialin Hong, LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathem, Chinese Academy of Sciences, China
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk we review some results on stochastic symplectic methods for stochastic Hamiltonian systems, including stochastic generating functions and stochastic Hamilton-Jacobi theory. We investigate the canonical form and the stochastic symplectic structure of stochastic nonlinear Schroedinger equations (SSEs), and show that the symplectic Runge-Kutta semidiscretization for SSEs in time preserves charge conservation law. We present stochastic multi-symplectic methods for stochastic Maxwell equations, and show that these methods preserve physical properties of equations. 


  • Friday, 2nd February, 2018

    Title: Fluid-structure interactions between rigid bodies and incompressible flow
    Speaker: Dr. Qi TANG, Department of Mathematical Sciences, Rensselaer Polytechnic Institute, U.S.A.
    Time/Place: 10:30  -  11:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Fluid-structure interaction (FSI) problems have drawn significant attention in recent years due to their great practical importance in aeronautical engineering, coastal engineering, and biomedical engineering, among others. In this talk, I will discuss our recent study of the FSI regime involving viscous incompressible flow and rigid bodies. Such FSI problems arise in many applications of science and engineering, including particulate flows and mechanical heart valves. We begin by exposing two types of effects arising from the forces and torques on the rigid body due to fluid, referred to as added-mass and added-damping effects. A novel partitioned algorithm is then developed to handle both effects. The scheme is based on a generalized Robin interface condition for the fluid pressure that includes terms involving the linear and angular accelerations of the body. Added-damping effects are treated with approximate added-damping tensors that are defined by certain integrals over the surface of the body. In simple model geometries we prove that the proposed scheme remains stable, without sub-iterations, for bodies of any mass even when the fluid effects are large. Its extension to general geometry is performed using finite difference methods and overlapping grids. A series of challenging benchmark problems are presented to verify the theoretical results and demonstrate the efficiency of the scheme.


  • Monday, 5th February, 2018

    Title: Statistical Analysis of Correlated Multi-response Data in Bio-medical Applications
    Speaker: Ms Xianghong Hu, Department of Mathematics, Hong Kong Baptist University, HKSAR
    Time/Place: 16:00  -  17:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Correlated data arise in many situations, for example, repeated measurements on the same subject or genetical correlation between some traits or diseases. We will conduct two statical analysis studies of correlated data sets in the biomedical domain. The first is the personalized prediction of the blood pressure(Sbp/Dbp). A framework of multi-response and re-weighted multi-response linear mixed effect model is built. We extended the MM algorithm developed by Zou(2015) to the Multi-response cases. Under this framework, we can also do model selection through regularization.  The other is related to the genome-wide association studies. Through analysis of the GWAS summary statistics of some diseases and metabolites, we found high genetic correlations between some of them. Our goal is to find the causal genetic variants that both affect the correlated traits and metabolites through a multi-trait GWAS analysis. If the causal genetic variants are located, the true correlation between metabolites and diseases are verified, which is important for the medical development.


  • Wednesday, 14th February, 2018

    Title: Error bounds for Structured Convex Programming: Theory and Applications
    Speaker: Dr. Zirui Zhou, Department of Mathematics, Simon Fraser University, Canada
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in practical implementation and convergence analysis of a host of iterative methods for solving optimization problems. In this talk, we present a new framework for establishing error bounds for a class of structured convex optimization problems, in which the objective function is the sum of a smooth convex function and a possibly nonsmooth convex function. Such a class encapsulates not only fairly general constrained minimization problems but also various regularized loss minimization formulations in machine learning, signal processing, and statistics. Using our framework, we show that a number of existing error bound results can be recovered in a unified and transparent manner. To further demonstrate the power of our framework, we apply it to establish new error bounds for nuclear-norm and $ell_{1,p}$-norm regularized loss minimization formulations.


  • Monday, 26th February, 2018

    Title: Multi-domain Networks Association for Biological Data Using Block Signed Graph Clustering
    Speaker: Ms. LIU Ye, Department of Mathematics, Hong Kong Baptist University, HKSAR
    Time/Place: 14:00  -  15:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Multi-domain biological network association and clustering have attracted a lot of attention in biological data integration and understanding, which can provide a more global and accurate understanding of biological phenomenon. In many problems, different domains may have different cluster structures. Due to rapid growth of data collection from different sources, some domains may be strongly or weakly associated with the other domains. A key challenge is how to determine the degree of association among different domains, and to achieve accurate clustering results by data integration. In this paper, we propose an unsupervised learning approach for multi-domain network association by using block signed graph clustering. In particular, with consistency weights calculation, the proposed algorithm automatically identify domains relevant to each other strongly (or weakly) by assigning them larger (or smaller) weights. This approach not only significantly improve clustering accuracy but also understand multi-domain networks association. In each iteration of the proposed algorithm, we update consistency weights based on cluster structure of each domain, and then make use of different sets of eigenvectors to obtain different cluster structures in each domain. Experimental results on both synthetic data sets and real data sets (including neuron activity data and gene expression data) empirically demonstrate the effectiveness of the proposed algorithm in clustering performance and in domain association capability.


  • Monday, 26th February, 2018

    Title: Transformation between OR and RR in the case-control studies for meta-analysis
    Speaker: Mr. Lin Enxuan, Department of Mathematics, Hong Kong Baptist University, HKSAR
    Time/Place: 16:00  -  17:00
    SCT909, Cha Chi-ming Science Tower, HSH Campus, Hong Kong Baptist University
    Abstract: In meta-analysis, how to combine different effect sizes is a common problem for researchers. For categorical data, odds ratio (OR) and relative risk (RR) are both commonly reported. Zhang and Yu proposed a method of transforming RR to OR in the cohort studies in 1998 and this method is widely used nowadays.  However, Zhang and Yu’s method is not good fitted in the case-control studies because of the bias of parameter estimation. In this talk we describe our recent approach which provides a fitted transformation in the case-control studies and demonstrate the utility of this method. Also we will introduce our further work in meta-analysis.


  • Monday, 26th February, 2018

    Title: A Parallelizable Algorithm for Orthogonally Constrained Optimization Problems     
    Speaker: Prof. LIU Xin, Institute of Computational Mathematics, Chinese Academy of Sciences, China
    Time/Place: 16:00  -  17:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: To construct a parallel approach for solving orthogonally constrained optimization problems is usually regarded as an extremely difficult mission, due to the low scalability of orthogonalization procedure. In this talk, we propose an infeasible algorithm for solving optimization problems with orthogonality constraints, in which orthogonalization is no longer needed at each iteration, and hence the algorithm can be parallelized. We also establish a global subsequence convergence and a worst-case complexity for our proposed algorithm. Numerical experiments illustrate that the new algorithm attains a good performance and a high scalability in solving discretized Kohn-Sham total energy minimization problems. 


  • Wednesday, 28th February, 2018

    Title: Order Determination for Large Dimensional Matrices
    Speaker: Mr. Zeng Yicheng, Department of Mathematics, Hong Kong Baptist University, HKSAR
    Time/Place: 10:00  -  11:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk, we investigate order determination for large dimensional matrices where the dimensions of matrices are proportional to the sample sizes. As the asymptotic behaviors of the eigenvalues are completely different from those in fixed dimension scenarios, we then introduce a valley-cliff estimation to attack this challenge. We propose two versions of the estimation: one is based on the original differences of eigenvalues and the other on transformed differences for reducing the effect from the ridge selection in the criterion. This generic methodology can be applied to various matrices. As examples, we apply it to spiked population models, factor models with auto-covariance matrices and spiked Fisher matrices. Numerical studies, including simulations and real data analysis, are conducted to examine the finite sample performances of the method and comparisons with existing methods are also performed. Also we will introduce our further work in order determination.