Colloquium/Seminar

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Event(s) on June 2017


  • Thursday, 1st June, 2017

    Title: Panning for gold: Model-free knockoffs for high-dimensional controlled variable selection
    Speaker: Dr. Jinchi, LV, Business Adminstration, Data Sciences and Operations Department, Marshall School of Business, University of Southern California, U.S.A.
    Time/Place: 15:30  -  16:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Many contemporary large-scale applications involve building interpretable models linking a large set of potential covariates to a response in a nonlinear fashion, such as when the response is binary. Although this modeling problem has been extensively studied, it remains unclear how to effectively control the fraction of false discoveries even in high-dimensional logistic regression, not to mention general high-dimensional nonlinear models. To address such a practical problem, we propose a new framework of textit{model-free} knockoffs, which reads from a different perspective the knockoff procedure (Barber and Candès, 2015) originally designed for controlling the false discovery rate in linear models. The key innovation of our method is to construct knockoff variables probabilistically instead of geometrically. This enables model-free knockoffs to deal with arbitrary (and unknown) conditional models and any dimensions, including when the dimensionality $p$ exceeds the sample size $n$, while the original knockoffs procedure is constrained to homoscedastic linear models with $n ge p$.  Our approach requires the design matrix be random (independent and identically distributed rows) with a covariate distribution that is known, although we show our procedure to be robust to unknown/estimated distributions. To our knowledge, no other procedure solves the textit{controlled} variable selection problem in such generality, but in the restricted settings where competitors exist, we demonstrate the superior power of knockoffs through simulations. Finally, we apply our procedure to data from a case-control study of Crohn's disease in the United Kingdom, making twice as many discoveries as the original analysis of the same data. This is a joint work with Emmanuel Candès, Yingying Fan and Lucas Janson.


  • Friday, 2nd June, 2017

    Title: Interpolation on High Dimensional Point Cloud
    Speaker: Dr. SHI Zuoqiang, Mathematical Sciences Center, Tsinghua University, China
    Time/Place: 16:00  -  17:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Interpolation on high dimensional point cloud provides a fundamental model in many data analysis and machine learning problems. In this talk, we will present some PDE based methods to do interpolation on point cloud. Applications in image processing and data analysis are shown to demonstrate the performance of our methods.


  • Saturday, 3rd June, 2017

    Title: Mathematics of Super-resolution in Wave Imaging
    Speaker: Prof. Habib Ammari, ETH Zürich, Switzerland
    Time/Place: 11:00  -  12:00 (Preceded by Reception at 10:30pm)
    SCT909, Cha Chi-ming Science Tower, HSH Campus, Hong Kong Baptist University
    Abstract: Super-resolution imaging is a collective name for a number of emerging techniques that achieve resolution below the conventional resolution limit, defined as the minimum distance required between two point-like targets to distinguish between them. The main objective of this lecture is to enhance our understanding of the fundamental super-resolution imaging mechanisms and to unify them by using the finest mathematical and computational tools.


  • Saturday, 3rd June, 2017

    Title: Solving semilinear parabolic PDEs by branching diffusion processes.
    Speaker: Dr. Xiaolu Tan, CEREMADE, University of Paris Dauphine, France
    Time/Place: 16:00  -  17:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: We provide a probabilistic representation for a class of semilinear parabolic PDEs, using branching diffusion processes. We then discuss how to use this representation to obtain a numerical algorithm to solve these PDEs.


  • Tuesday, 6th June, 2017

    Title: On Chaos and NP-Hardness in Computational Nonlinear Sciences and Global Optimization
    Speaker: Prof. David Yang Gao, Department of Mathematics, Federation University Australia, Australia
    Time/Place: 11:30  -  12:30
    FSC702, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Chaotic phenomena in complex systems and NP-hard problems in computer science have been studied extensively for more than a half century. However, most people may not know what the chaos really is, which problems are truly NP-hard, and the inner connection of these two concepts. This lecture intends to answer these fundamental questions as well as to present a unified theory for modelling natural phenomena and a powerful methodology for solving challenging problems in multi-scale complex systems. Canonical duality is a breakthrough methodological theory, which can be used not only to model complicated phenomena within a unified framework, but also for solving a wide class of nonconvex/nonsmooth/discrete problems in multidisciplinary fields [1,2,3]. The associated triality theory reveals an interesting multi-scale duality pattern in complex systems, which can be used to identify both global and local extrema and to design powerful algorithms for solving challenging problems. Starting from Yin-Yang duality in I-Jing and traility in DNA and quantum mechanics, the speaker will first present a unified mathematical model for multi-scale complex systems, which lays a foundation for understanding complicated phenomena in nature, including bifurcation, chaos, decision making, game theory, information technology, logistics, manufactures, phase transitions, scheduling, and management science, etc. Based on this model, he will show how a precise mathematical theory of duality was developed and why this theory can be used for solving not only the most challenging problems in chaotic dynamics and post-buckling of nonlinear structures, but also a large class of so-called “NP-hard” problems in global optimization and computer science. The inner connection between this theory and other popular methodologies, such as SDP method in nonconvex/integer programming and HQ regularization in image process, will be discussed. Applications will be illustrated by some well-known benchmark problems in global optimization, sensor networks and bi-level topology optimization of structural design. A very interesting relation between chaos in nonlinear dynamics and NP-Hardness in global optimization will be revealed. This talk will bring some fundamentally new insights into nonconvex analysis, complex systems, and computational science.


  • Friday, 9th June, 2017

    Title: Patterns in Eigenvalues
    Speaker: Prof. Persi Diaconis, Stanford University, USA
    Time/Place: 11:00  -  12:00 (Preceded by Reception at 10:30am)
    LT2, Cha Chi-ming Science Tower, HSH Campus, Hong Kong Baptist University
    Abstract: Typical large matrices show remarkable patterns in their eigenvalue distribution. These same distributions appear in a variety of other real world problems: in the distance between parked cars, the shape of a burning piece of paper, in neutron scattering experiments and the zeros of Riemann's zeta function. I will explain the patterns and tell some of their stories in a talk aimed at a general mathematical and statistical audience.


  • Tuesday, 13th June, 2017

    Title: Goodness-of-fit Testing of Error Distribution in Linear Measurement Error Models¹
    Speaker: Prof. Hira Lal Koul, Department of Statistics & Probability, Michigan State University, U.S.A.
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk we shall discuss a class of goodness-of-fit tests for the error density function in linear measurement errors regression models using a deconvolution kernel density estimators of the regression model error density. The test statistic is an analog of the Bickel and Rosenblatt type test statistic. The asymptotic null distribution of the proposed test statistics is derived for both the ordinary smooth and super smooth cases. The consistency against a fixed alternative and the asymptotic power of the proposed tests against a class of local nonparametric alternatives are also obtained for both cases. A finite sample simulation study shows some superiority of the proposed test compared to very few other existing tests.


  • Tuesday, 27th June, 2017

    Title: Controllability of Some Coupled Stochastic Parabolic Systems by One Control 
    Speaker: Prof. LIU Xu, School of Mathematics and Statistics, Northeast Normal University, Changchun, China
    Time/Place: 10:00  -  11:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk, the null controllability of some coupled stochastic parabolic systems by one control is studied. The method is based on the Lebeau-Robbiano strategy. Compared to deterministic coupled parabolic systems, the coupling appearing in diffusion terms in the stochastic case introduces an interesting new phenomenon. An example is given to show that the controllability is not robust with respect to coupling coefficients in diffusion terms. This indicates that the usual Carleman-type estimate approach does not seem to work for the controllability of coupled stochastic parabolic systems. Also, Kalman-type rank condition does not hold any more.


  • Tuesday, 27th June, 2017

    Title: Stabilization of the damped wave equations 
    Speaker: Prof. FU Xiaoyu, School of Mathematics , Sichuan University, Chengdu, China
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk, we will discuss decay properties of solutions to wave equations with mixed boundary conditions. When the Geometric Control Condition on the dissipative region is not satisfied, we show that sufficiently smooth solutions to the equations decay logarithmically.