Colloquium/Seminar
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Event(s) on January 2017
- Tuesday, 3rd January, 2017
Title: Small Perturbation of a Semilinear Pseudo-Parabolic Equation Speaker: Prof. Yin Jingxue, South China Normal University , China Time/Place: 14:00 - 15:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: In this talk, we discuss large time behavior of solutions for the Cauchy problem of a semilinear pseudo-parabolic equation with a small nontrivial perturbation $f(x)$, which is assumed to be not identically equal to zero, but it is preferred to be small. - Friday, 6th January, 2017
Title: An introduction of network meta-analysis Speaker: Dr. Shengjie DONG, Yantaishan Hospital, China Time/Place: 15:30 - 16:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: The ever increasing number of alternative treatment options and the plethora of clinical trials have put systematic reviews and meta-analysis under a new perspective by emphasizing the need to make inferences about competing treatments for the same condition. The statistical component in reviews that compare multiple interventions, network meta-analysis, is the next generation evidence synthesis toolkit which, when properly applied, can serve decision-making better than the established pairwise meta-analysis. In this lecture, we will introduce the statistical foundation of network meta-analysis. The assumption of the network meta-analysis twill be explained. Then, we will perform the network meta-analysis in the Bayesian and frequent framework using a classical case. - Friday, 6th January, 2017
Title: On the Numerical Solution of a Nonlinear, Non-Smooth Eigenvalue Problem or when Bingham Meets Bratu: An Operator-Splitting Approach Speaker: Prof. Roland Glowinski, University of Houston, USA Time/Place: 17:15 - 18:15 (Preceded by Reception at 4:45pm)
SCT501, Science Tower, HSH Campus, Hong Kong Baptist UniversityAbstract: Some years ago, we suggested to a colleague looking for nonlinear saddle-point problems with multiple solutions (in order to test mountain-pass based solution methods) to have a look at the following elliptic one:
(BBPV):
Find {u, &lamda;} in H^{1}_{0} (Ω) x R_{+} such that
μ int_{Ω} ∇ u cdot ∇ (v-u)dx + τ_{y}[int_{Ω} |∇ v|dx - int_{Ω} |∇ u| dx] ≥ λ int_{Ω} e^{u}(v-u)dx, for all v in H^{1}_{0}(Ω),
where Ω is a bounded domain of R^{2}, μ and τ_{y} being both > 0.(BBPV) is nothing, but the variational formulation of the following nonlinear, non-smooth Dirichlet problem
(BBPE):
-μ∇^{2}u+τ_{y}&partial; j(u) ∋ λ e^{u} in Ω,
u = 0 on &partial;Ω,
where &partial; j(u) denotes the sub-differential at u of the convex functional j: H^{1}_{0}(Ω) -> R defined by j(v)=int_{Ω} |∇ v|dx. Suppose that τ_{y}=0 in the above formulations, then the above problem reduces to the celebrated Bratu-Gelfand problem
-μ∇^{2}μ=λ e^{u} in Ω,
u=0 on &partial;Ω.On the other hand, if, in (BBPV) and (BBPE), one replaces λ e^{u} by a constant ϖ, the resulting inequalities and equations model the flow of a Bingham visco-plastic medium of viscosity μ and plasticity yield τ_{y} in an infinitely long cylinder of cross-section Ω, with ϖ, and u denoting the (algebraic) pressure drop per unit length and the flow axial velocity, respectively.
Problem (BBPV), (BBPE) has clearly the flavor of a non-smooth nonlinear eigenvalue problem for an elliptic operator. The numerical solution of such problems by minimax (mountain-pass) methods has been investigated by our colleagues Xudong Yao and Jianxin Zhou. Our goal in this lecture is to present a conceptually simpler methodology based on operator-splitting: The resulting algorithms are natural generalizations of the inverse power method for symmetric matrix eigenvalue computation.
The results of numerical experiments performed by our collaborator F. Foss will be presented.
- Tuesday, 10th January, 2017
Title: Introduction to sparse representation, dictionary learning and fast transform optimization Speaker: Prof. Francois Malgouyres , Department of Mathematics, Université paul sabatier, France Time/Place: 16:30 - 17:30
OEE1017, Oen Hall Building (East Wing), HSH Campus, Hong Kong Baptist UniversityAbstract: In this talk I will give the main intuitions and the most comprehensible results underlying the dimensionality reduction performed in Signal, Image processing and statistics. In particular I will highlight the evolution from non-linear approximation, compressed sensing, dictionary learning to deep matrix factorization. - Friday, 13th January, 2017
Title: On the correlation analysis of RNA-seq data Speaker: Prof. Yinglei Lai, Department of Statistics, The George Washington University, USA Time/Place: 10:30 - 11:30
FSC1111, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Genome-wide RNA sequencing (RNA-seq) data have been increasingly collected during the recent years. A correlation analysis of RNA-seq data can be important for us to understand how genes interact with each other. RNA-seq data are generally count-type observations. Furthermore, many genes have multiple isoforms. Therefore, it can be challenging to conduct a correlation analysis of RNA-seq data. We propose a multivariate approach for the correlation analysis of RNA-seq data. Our simulation study demonstrates the advantage of our method. We use the RNA-seq data collected by The Cancer Genome Atlas (TCGA) project to illustrate our method. - Saturday, 14th January, 2017
Title: Dispersion property and high order approximation for the Boltzmann equation Speaker: Prof. HE LingBing, Department of Mathematical Sciences, Tsinghua University, Beijing, China Time/Place: 10:30 - 11:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: In this talk, we will present two recent results on the Boltzmann equation. The first one is to show the dispersion and scattering properties for the Boltzmann equation with angular cut off near vacuum. The second one is to show that by designing a new approximated equation which incorporates the angular cutoff Boltzmann collision operator and Landau collision operator, we get the higher order of accuracy than that of only angular cutoff approximation. - Monday, 16th January, 2017
Title: Some kernel-based methods in data science Speaker: Dr. Jun Fan, Department of Statistics, University of Wisconsin-Madison, USA Time/Place: 10:30 - 11:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Personalized medicine has attracted considerable attention in recent years. The main goal of personalized dose finding is to infer an optimal individualized dose rule from a clinical trial. The problem can be generally formulated as an optimization model that maximizes the so-called value function. Due to its discontinuous nature, we devise approximations to the value function by using density kernels. This talk will present our recent work on a unified kernel approach for personalized dose finding. Some related problems in data science will also be discussed. - Tuesday, 17th January, 2017
Title: Local-in-time well-posedness theory for MHD boundary layer in Sobolev spaces without monotonicity Speaker: Prof. XIE Feng, Department of Mathematics, Shanghai Jiaotong University, China Time/Place: 15:30 - 16:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: In this talk, we will study the well-posedness theory for the MHD boundary layer. The boundary layer equations are governed by the Prandtl type equations that are derived from the incompressible MHD system with non-slip boundary condition on the velocity and perfectly conducting condition on the magnetic field. Under the assumption that the initial tangential magnetic field is not zero, we establish the local-in-time existence, uniqueness of solution for the nonlinear MHD boundary layer equations. Compared with the well-posedness theory of the classical Prandtl equations for which the monotonicity condition of the tangential velocity plays a crucial role, this monotonicity condition is not needed for MHD boundary layer. This justifies the physical understanding that the magnetic field has a stabilizing effect on MHD boundary layer in rigorous mathematics. This talk is based on the joint work with Dr. Chengjie Liu and Professor Tong Yang from CityU of Hong Kong. - Friday, 20th January, 2017
Title: Term Structure of “Skewness” and Option Returns Speaker: Mr Ou Jitao, Department of Mathematics, Hong Kong Baptist University, Hong Kong Time/Place: 15:00 - 16:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Option payoffs are non-negative by design like those from an insurance policy. Therefore, option returns must be positively skewed from zero. Positive return skewness to option holders transcribes to negative return skewness to option writers. Returns from selling an option is positively related to its skewness, a conjecture that has receive support from recent studies. On the other hand, it becomes a fact that there is a significant negative correlation between asset returns and volatility. Extending upon Boyer and Vorkink (2014), this study derive a measure of ex-ante measure of option return skewness which accommodates the negative return-volatility relationship in asset returns. Moreover, the study tests how time-to-expiration and moneyness affect the skewness and return of an option. Last but not the least, the study extends upon research on intraday volatility variations and examines intraday variation in the skewness measure. - Friday, 20th January, 2017
Title: Data assimilation methods in weather forecasting Speaker: Miss Yan Hanjun , Department of Mathematics, Hong Kong Baptist University, Hong Kong Time/Place: 16:00 - 17:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Numerical weather prediction plays an important role in weather forecasting area. The weather research and forecasting (WRF) Model is a numerical weather prediction system and which generates atmospheric simulation by observation and analysis data. There are two essential parts in WRF model which are model forecasting and WRF data assimilation. Model forecasting uses initial state to generate forecast state and WRF data assimilation (WRFDA) uses forecast state to generate analysis state for the next iteration. For a long term forecasting, therefore, the whole procedure is a cycling mode. In the WRF model, the method for WRFDA is three dimensional variational data assimilation (3DVAR). The first term of this model is based on the difference between analysis state and previous model forecast state and the second term is based on the difference between observations and analysis state. In this talk, we introduce a Gradient Matching method for WRFDA, to replaces difference of forecast and analysis of state variables from 3DVAR. This new method avoid the huge computations in matrix-vector multiplication because of the sparsity in gradient matching. We compare two different WRFDA methods and the experimental results show how much more efficient our method works. For the future work, we will propose a new method which will use tensor completion into data assimilation. - Monday, 23rd January, 2017
Title: Exponential integrators for stochastic Schrödinger equations driven by Ito noise Speaker: Prof. David Cohen, Mathematics, Umeå University, Sweden Time/Place: 10:00 - 11:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: We consider the numerical discretisation in time of stochastic Schrödinger equations by exponential integrators. After reviewing some concepts in stochastic analysis, we will present an exponential integrator for a stochastic Schrödinger equation and discuss its convergence as well as its long-time behaviour. Numerical simulations will also be presented in order to confirm the above theoretical results.