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Event(s) on May 2013

  • Monday, 13th May, 2013

    Title: DLS: Mathematical Models of Competing Phytoplankton Species for Light in a Water Column
    Speaker: Prof. Sze-Bi Hsu, National Tsing-Hua University, Taiwan
    Time/Place: 16:00  -  17:00 (Preceded by Reception at 3:30pm)
    RRS905, Sir Run Run Shaw Building, HSH Campus, Hong Kong Baptist University
    Abstract: Phytoplankton are microscopic plant-like organisms that drift in the water column of lakes and oceans. They grow abundantly around the world and are responsible for the consumption of at least 60% carbon dioxide on earth. They are the foundation of the marine food chain. Nutrients and light are the essential resources for the growth of the phytoplankton. In this talk we shall restrict our attentions to eutrophic ecosystems where nutrient supplies are ample, and species compete only for light. First we consider the competition of species in a well-mixing water column. The model takes a form of system of ordinary differential equations. In this case we consider the effect with or without photo-inhibition to the growth of phytoplankton species. We classify the asymptotic behavior of the solutions. Then we consider the competition of species in a poorly mixing water column. The model takes a form of nonlocal reaction-advectiondiffusion system. We first prove the global convergence of the solution for the case of single population growth. Then we apply the global bifurcation theory to obtain the coexistence of two species.

  • Tuesday, 14th May, 2013

    Title: Sufficient Dimension Reduction for Multiple Populations
    Speaker: Dr. WEN Xuerong Meggie, Department of Mathematics and Statistics , Missouri University of Science and Technology, USA
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Two topics in the area of dimension reduction for multiple populations will be explored. We will first propose a link-free test for testing whether two (or more) multi-index models share identical indices via the sufficient dimension reduction approach. Test statistics are developed based upon three different sufficient dimension reduction methods: (i) sliced inverse regression, (ii) sliced average variance estimation and (iii) directional regression. The asymptotic null distributions of our test statistics are derived. Next, we will discuss model-free shrinkage variable selection via sufficient dimension reduction for multiple datasets.

  • Tuesday, 21st May, 2013

    Title: Checking the Adequacy of Regression Models With Complex Data Structure
    Speaker: Mr. GUO Xu, Department of Mathematics, Hong Kong Baptist University, Hong Kong
    Time/Place: 10:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In the first part, we investigate model checking in a class of regression models with a dimension reduction structure when the number of predictors is divergent with the sample size. A test is suggested for generalized linear models against general semi-parametric multi-index models. To benefit from the dimension reduction structure of models, the test statistic is designed to be adaptive to the underlying model such that it is more powerful than existing local smoothing-based tests in an asymptotic sense. The limiting null distribution is chi-square with one degree of freedom. The test can detect local alternatives distinct from the null at a faster rate than that in fixed dimensional cases. As sparsity is commonly assumed and is believed to be reasonable in high dimensional data analysis, we further extend our methodology to sparse multi-index models. In the second part, we aim to study model checking for general linear regression model with non-ignorable missing response. Based on an exponential tilting model, we first propose three estimators for the unknown parameter in the general linear regression model. Three empirical process-based tests are constructed. We discuss the asymptotic properties of the proposed tests under null and local alternative hypothesis with different scenarios. We find that in some situations, these three tests perform the same in asymptotic sense. Simulation studies are also carried out to assess the performance of our proposed test procedure. Finally some real data sets are analyzed to further illustrate our methods.



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