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Event(s) on June 2015


  • Thursday, 4th June, 2015

    Title: Sub-Riemannian geometry on infinite dimensional manifolds
    Speaker: Prof. Irina Markin, Mathematical Department, University of Bergen, Norway
    Time/Place: 15:30  -  16:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: We start from the definition of an infinite-dimensional manifold with a specific choice of the underlying vector space for developing the smooth calculus. Then we define Riemannian and sub-Riemannian structures, and discuss the choice of a tool for studying geodesics on infinite-dimensional sub-Riemannian manifolds. We show that, similarly to the finite-dimensional case, there are two different, but not mutually disjoint classes of geodesics. We present geodesic equations for those classes of geodesics which is natural generalizations of classical Riemannian geodesics. We indicate possible applications to fluid mechanics and questions of controllability.


  • Thursday, 4th June, 2015

    Title: Euler-Arnold equations in sub-Riemannian geometry on Teichmuller space and curve
    Speaker: Prof Alexander Vasilev, Department of Mathematics, University of Bergen, Norway
    Time/Place: 16:30  -  17:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: We consider the group of orientation-preserving diffeomorphisms of the unit circle and its central extension, the Virasoro-Bott group, with their respective horizontal distributions, which are Ehresmann connections with respect to a projection to the smooth universal Teichmüller space and the universal Teichmüller curve associated to the space of normalized univalent functions. We find equations for the normal sub- Riemannian geodesics with respect to the pullback of the Kählerian metrics, namely, the Velling-Kirillov metric on the class of normalized univalent functions and the Weil- Petersson metric on the universal Teichmüller space. The geodesic equations are sub-Riemannian analogues of the Euler-Arnold equation and they lead to the CLM, KdV and other known non-linear PDEs.


  • Monday, 8th June, 2015

    Title: A new Dirichlet process mixture model for nonparametric Bayesian quantile regression
    Speaker: Dr. Nan LIN, Department of Mathematic, Washington University in St. Louis, USA
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: We propose a new nonparametric Bayesian approach to quantile regression using Dirichlet process mixture of logistic distributions (DPML). Many existing Bayesian quantile regression methods are based on parametric substitution of the error distribution by the asymmetric Laplace distribution, which is inconsistent with the typical nonparametric nature of quantile regression. The logistic distribution has a simple form in its quantile function and hence easily accomodates the quantile constraint. Our proposed DPML model enjoys great model flexibility by mixing over both the location parameter and the scale parameter. We further established the posterior consistency of our proposed model and provided Markov chain Monte Carlo algorithms for posterior inference. The performance of our approaches is evaluated using simulated data and real data.


  • Wednesday, 10th June, 2015

    Title: Novel Models for Recovering High-order Tensors From Highly Incomplete Observations
    Speaker: Dr. Yao Wang, Department of Statistics, Xian Jiaotong University, China
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Various applications, e.g., video surveillance, hyperspectral imaging and dynamic MR image reconstruction, can be formulated as recovering a high-order tensor from highly incomplete observations. Despite an increasingly common interest, high-order tensor recovery remains a challenging problem because of the underlying complex structures of tensors. The existing approaches are developed through unfolding the tensor into different matrix forms and then using conventional matrix recovery techniques. Such matricization fails to effectively exploit the tensor structure and may lead to suboptimal procedure. The focus of the talk is on introducing some novel models to remedy this issue for three tensor related applications, i.e., background subtraction from compressive measurements, hyperspectral/multispectral compressive sensing, and multispectral image completion. As compared with the existing models, our models are capable of characterizing extensive spatial-temporal structures that underlie the high-order tensors, yielding better quality of recovery from generally fewer observations.


  • Thursday, 18th June, 2015

    Title: Hardy Spaces, Elliptic BVPs and Div-Curl Lemmas
    Speaker: Prof. Der-Chen CHANG, Department of Mathematics and Statistics, Georgetown University, USA
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk, I want to discuss a long term joint project with E.M. Stein and G. Dafni. The first part of this talk will discuss estimates of elliptic boundary value problems in Hardy spaces. More precisely, let Omega be a bound domain in R^n with smooth boundary. Consider the following elliptic boundary value problem: Delta u=f in Omega, Xu=g on partial Omega. Here, X is a transversal vector field to the boundary. This includes the regular Dirichlet and Neumann problem. In the first part of this talk, we first introduce suitable Hardy spaces H^p(Omega) on Omega. Then we shall show that ||(partial^2 u)/(partial x_j partial x_k)||_(H^p (Omega)) <= C_p ||f||_(H^p(Omega)) for 0


  • Wednesday, 24th June, 2015

    Title: Differential methylation analysis for whole genome bisulfite sequencing data
    Speaker: Dr. WU Hao , Department of Biostatistics and Bioinformatics, Emory University, USA
    Time/Place: 15:00  -  16:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: DNA methylation is an important epigenetic modification involved in many biological processes and diseases. Recent developments in whole genome bisulfite sequencing (WGBS) technology have enabled genome-wide measurements of DNA methylation at single base pair resolution. An important question in WGBS data analysis is to compare DNA methylation profiles under different biological contexts, and identify differentially methylated regions (DMRs). In this talk I will present our recent works on statistical method development for DMR calling in WGBS data under different scenarios. We have method for two-group comparison, with or without biological replicates, and method for general experimental designs. In these methods, we characterize the WGBS count data using hierarchical model that accounts for the spatial correlation of methylation levels, sequence depth, and biological variation. DMR detection is achieved by testing differential methylation at each CpG site. The methods are implemented in freely available Bioconductor package DSS.


  • Monday, 29th June, 2015

    Title: ICTS Data Assimilation Program: Survey about Global and Regional Numerical Weather Prediction (Lecture 1)
    Speaker: Prof. Roland Potthast, Deutscher Wetterdienst DWD and BMVBS Federal Ministry of Transport, Building and Urban Development, Germany
    Time/Place: 10:00  -  11:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: We provide an introduction into data assimilation for numerical weather prediction. We will provide a survey about the current state of the art in terms of available data types and the general framework of operational centers such as Deutscher Wetterdienst or ECMWF. Today, our numerical schemes for modelling and data assimilation as well as boundary data for the high-resolution regional models are used by around 40 countries world-wide. Measurement data range form conventional direct measurements of temperature, pressure, humidity and wind to various remote sensing measurements with instruments which are ground- or satellite-based. Further, we will describe the framework of operational work on data assimilation and the role of mathematical and meteorological research and development - describing a vision of an intense integration of research with operational developments as it is employed within the German research community.


  • Monday, 29th June, 2015

    Title: ICTS Data Assimilation Program: Ensemble and Particle Filters for Large-Scale Data Assimilation (Lecture 2)
    Speaker: Prof. Roland Potthast, Deutscher Wetterdienst DWD and BMVBS Federal Ministry of Transport, Building and Urban Development, Germany
    Time/Place: 11:15  -  12:15
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In almost all operational centres for numerical weather prediction around the world ensemble data assimilation techniques are of rapidly growing importance. Ensemble techniques allow to describe and forecast uncertainty of the analysis, but they also improve the assimilation result itself, by allowing estimates of the covariance or, more general, the prior and posterior probability distribution of atmospheric states. In our talk, we will first give a survey about methods for data assimilation from the viewpoint of mathematical analysis. In particular, we introduce cycled inversion schemes and use them to introduce the Kalman Filter and its ensemble-based variants such as the Local Ensemble Tranform Kalman Filter LETKF. In the second part of the talk, we present recent work on the further development of the ensemble data assimilation towards a particle filter for large-scale atmospheric systems, which keeps the advantages of the LETKF, but overcomes some of its limitations. We describe a Localized Markov Chain Particle Filter (LMCPF), present its mathematical foundation and show some tests for simple systems. The implementation of the LMCPF in the KENDA framework of DWD is ongoing work.


  • Monday, 29th June, 2015

    Title: EPS: An empirical Bayes approach to integrating pleiotropy and tissue-specific information for prioritizing risk genes
    Speaker: Dr. Jin Liu, Centre for Quantitative Medicine, Duke-NUS Graduate Medical School Singapore, Singapore
    Time/Place: 14:00  -  15:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: World-wide researchers have generated a huge volume of genomic data, including thousands of genome-wide association studies (GWAS) and massive gene expression data from different tissues. How to perform joint analysis of these data to gain new biological insights becomes a critical step to understand the aetiology of complex diseases. Due to the polygenic architecture of complex diseases, identification of risk genes remains challenging. As motivated by genetic correlation among complex diseases (formally known as “pleiotropy”) and tissue-specific gene expression patterns, we proposed EPS, an Empirical Bayes approach to integrating Pleiotropy and Tissue-Specific information for prioritizing risk genes. As demonstrated by extensive simulation study, EPS greatly improved the power of identification of disease risk genes. Rigorous hypothesis testing of pleiotropy and tissue-specific risk gene expression pattern became achievable based on EPS. All the model parameters can be adaptively estimated from the developed expectation maximization (EM) algorithm. We applied EPS to the Bipolar disorder (BPD) and schizophrenia (SCZ) GWAS from Psychiatric Genomics Consortium, along with incorporation of gene expression data of multiple tissues from the Genotype-Tissue Expression project (GTEx).The results of this real data analysis demonstrated many benefits of using EPS.