Colloquium/Seminar
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Event(s) on December 2015
- Wednesday, 2nd December, 2015
Title: HKBU MATH 45th Anniversary Distinguished Lecture - Bridging the Gap Between Numerical Analysis and Computational Practice: A Case Study Speaker: Prof. Fred J. Hickernell, Department of Applied Mathematics, Illinois Institute of Technology, USA Time/Place: 16:30 - 17:30 (Preceded by Reception at 4:00pm)
RRS905, Sir Run Run Shaw Building, HSH Campus, Hong Kong Baptist UniversityAbstract: Solving complex quantitative problems requires numerical computation. We want numerical algorithms to be rigorously justified so that we can trust their answers. We also want numerical algorithms to adapt their computational effort to match the difficulty of the problem. Sadly, it is rare for numerical algorithms to be both adaptive and guaranteed to succeed. We propose a paradigm for correcting this deficiency.
We begin with a problem familiar to calculus students: integration over a finite interval. We explain why the trapezoidal rule error bounds taught in calculus classes are impractical and why the error estimates taught in computational mathematics classes are flawed. We develop alternative, rigorous, data-based error bounds for cones of integrands.
We then look at (quasi-)Monte Carlo simulation for estimating the mean of a random variable or the value of a multidimensional integral. Again the idea of a cone of inputs allows us to rigorously bound the error. These algorithms are available in our Guaranteed Automatic Integration Library (GAIL), which we demonstrate with examples from computational finance and other areas.
Finally, we suggest computational skills that mathematicians must learn to contribute meaningfully to the computational science and engineering enterprise. These skills go beyond what is now commonly taught.
- Thursday, 3rd December, 2015
Title: Insecticide resistance and its implications for mosquito and malaria control Speaker: Prof. Stepen Gourley, Department of Mathematics, University of Surrey, UK Time/Place: 11:30 - 12:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Mosquitoes can rapidly develop resistance to insecticides, which is a big problem in malaria control. Current insecticides kill rapidly on contact, but this leads to intense selection for resistance because young adults are killed. Of considerable current interest is the possibility of slowing down or even halting the evolution of resistance. Biologists believe that much weaker selection for resistance can be achieved if insecticides target only old mosquitoes that have already laid most of their eggs. This strategy aims to exploit the fact that most mosquitoes do not live long enough to transmit malaria, due to a long latency stage for the malaria parasite in the mosquito. I will present the results of some mathematical work using stage structured population models that can make predictions about the delayed onset of resistance in the mosquito population when they are subjected to an insecticide that only acts late in life. I will also summarise some ongoing work that includes the malaria disease dynamics and also the consequences of mosquito control either at the larval or adult stage. Larvae can become resistant to larvicides, but the evolutionary cost of this acquired resistance may be reduced longevity as adults, which reduces the likelihood of the parasites completing their developmental stages and thus can actually benefit malaria control. This is a joint collaboration with Rongsong Liu, Chuncheng Wang and Jianhong Wu. - Wednesday, 9th December, 2015
Title: Stochastic control for a class of nonlinear kernels and applications Speaker: Dr. ZHOU Chao, Department of Mathematics, National University of Singapore, Singapore Time/Place: 15:00 - 16:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: A stochastic control problem for a class of nonlinear stochastic kernels is studied. We prove a dynamic programming principle (DPP) for the value function by a measurable selection argument and consider several applications of the DPP. This is a joint work with Dylan POSSAMAI and Xiaolu TAN. - Thursday, 10th December, 2015
Title: Dynamic Programming for Generalized State Constraints Speaker: Mr. ZHOU Yulong, Department of Mathematics, Hong Kong Baptist University, Hong Kong Time/Place: 14:30 - 16:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: We prove a dynamic programming principle for stochastic optimal control problems with expectation constraints by measurable selection approach. Since state constraints problems, target problems, quantilehedging and ecient hedging can all be reformulated into expectation constraints, we apply our results to prove the corresponding dynamic programming principle for these four classes of stochastic control problems in a continuous but non-Markovian setting. - Tuesday, 15th December, 2015
Title: HKBU MATH 45th Anniversary Distinguished Lecture - IMEX Time Marching for Discontinuous Galerkin Methods Speaker: Prof. Chi-Wang Shu, Brown University, USA Time/Place: 16:30 - 17:30 (Preceded by Reception at 4:00pm)
SCT909, Science Tower, HSH Campus, Hong Kong Baptist UniversityAbstract: For discontinuous Galerkin methods approximating convection diffusion equations, explicit time marching is expensive since the time step is restricted by the square of the spatial mesh size. Implicit methods, however, would require the solution of non-symmetric, non-positive definite and nonlinear systems, which could be difficult. The high order accurate implicit-explicit (IMEX) Runge-Kutta or multi-step time marching, which treats the diffusion term implicitly (often linear, resulting in a linear positive-definite solver) and the convection term (often nonlinear) explicitly, can greatly improve computational efficiency. We prove that certain IMEX time discretizations, up to third order accuracy, coupled with local discontinuous Galerkin method for the diffusion term treated implicitly, and regular discontinuous Galerkin method for the convection term treated explicitly, are unconditionally stable (the time step is upper bounded only by a constant depending on the diffusion coefficient but not on the spatial mesh size) and optimally convergent. The results also hold for drift-diffusion model in semiconductor device simulations, where a convection diffusion equation is coupled with an electrical potential equation. Numerical experiments confirm the good performance of such schemes. This is a joint work with Haijin Wang, Qiang Zhang and Yunxian Liu. - Wednesday, 16th December, 2015
Title: Fast and accurate numerical methods for FPDEs and related nonlocal models Speaker: Prof. WANG Hong, Department of Mathematics, University of South Carolina, USA Time/Place: 15:00 - 16:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Fractional PDEs and related nonlocal models provide an adequate and accurate description of transport processes that exhibit anomalous diffusion and/or long-range space-time interactions. Computationally, because of the nonlocal property of these models, the numerical methods often generate dense stiffness matrices. Traditionally, direct methods were used to solve these problems, which require O(N3) computations (per time step) and O(N2) mememy, where N is the number of unknowns. We go over the development of accurate and efficient numerical methods for these nonlocal models, which has an optimal order storage and almost linear computational complexity. These methods were developed by utilizing the structure of the stiffness matrices. No lossy compression or approximation was used. Hence, these methods retaining the same accuracy and approximation/conservation property of the underlying numerical methods. We will also discuss the open problems in the development and our future direction of research. - Wednesday, 16th December, 2015
Title: Simultaneous Tomographic Reconstruction and Segmentation with Class Priors Speaker: Dr. DONG Yiqiu, Department of Applied Mathematics and Computer Science, Technical University of Denmark, Denmark Time/Place: 16:00 - 17:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: We consider tomographic imaging problems where the goal is to obtain both a reconstructed image and a corresponding segmentation. A classical approach is to first reconstruct and then segment the image. In this talk, I will introduce a hybrid approach that simultaneously produces both a reconstructed image and a segmentation. We incorporate priors about the desired classes of the segmentation through a Hidden Markov Measure Field Model, and we impose a regularization term for the spatial variation of the classes across neighboring pixels. Simulation experiments with artificial and real data demonstrate that our combined approach can produce better results than the classical two-step approach. - Monday, 21st December, 2015
Title: HKBU MATH 45th Anniversary Distinguished Lecture - Symmetry Breaking and Hopf Bifurcation for Incompressible Viscous Flow in a Symmetric Planar Expansion Channel Speaker: Prof. Roland Glowinski, University of Houston, USA Time/Place: 11:00 - 12:00 (Preceded by Reception at 10:30am)
RRS905, Sir Run Run Shaw Building, HSH Campus, Hong Kong Baptist UniversityAbstract: The main goal of this lecture is to report on some computational investigations concerning symmetry breaking and Hopf bifurcation phenomena for Newtonian incompressible viscous flow in symmetric planar expansion channels as the flow Reynolds number increases (we assume that the channel flow is modelled by the Navier-Stokes equations). A particular attention will be given to the influence of mesh refinement on those critical values of the Reynolds number where symmetry breaking and Hopf bifurcation take place.