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Event(s) on November 2005
- Tuesday, 1st November, 2005
Title: Modeling and Simulations of Dislocations Speaker: Prof. Yang Xiang, Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong Time/Place: 14:30 - 15:30
Abstract: Dislocations are line defects in solids which carry the plastic deformation. We present a three-dimensional level set simulation method for dislocation dynamics. This method easily handles topological changes of the dislocation microstructures, and naturally accounts for the complicated three dimensional motion of dislocations. This method has been applied to the dislocation dynamics in the presence of a particle dispersion, dislocation dynamics in thin films, and the dislocation model of grain boundaries.
- Tuesday, 8th November, 2005
Title: How to Determine our Objective Function? Speaker: Prof. Mila Nikolova, CMLA ENS de Cachan, France Time/Place: 11:30 - 12:30
Abstract: The solutions of various problems in imaging applications, signal processing, inverse problems and other application fields, are defined via the minimization of an objective function. Objective functions must convey mixed desiderata -- that the solution is close to the observation model and that it exhibits specific features. The usual ways to construct objective functions are bayesian statistics and variational formulations for PDEs, as well as other heuristics. In the literature, there are so many objective functions (and especially regularization terms), that it is easy to get lost! Nevertheless, one can observe lapses between desiderata and solutions. A unifying theory is needed to understand the limitations and the properties of these methods. Independently of any interpretation and heuristic, a solution, defined as the minimizer of an objective function, is an implicit function of both the data and the shape of the objective function. This point of view raises the question of how the features of the reconstructed signals and images are determined by the shape of the objective function. Our talk will present a series of analytical results obtained by the author which characterize some essential features exhibited by the minimizers of regularized objective functions, in connection with the shape of the objective function. Points of interest are the recovery of homogeneous regions, textures and edges, and the processing of signals and images containing outliers or spikes, as well as specific applications of the obtained properties. All theoretical results are illustrated using various numerical experiments in signal and image reconstruction. Our point of view allows a real control on the sought-after solutions. But many questions remain to examine thus opening a broad research field.
- Tuesday, 15th November, 2005
Title: Complex Network Models of Disease Transmission Dynamics: Control of SARS Speaker: Prof. Michael Small, Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hong Kong Time/Place: 11:30 - 12:30
Abstract: We describe stochastic small-world and scale-free network model of transmission of the SARS virus. Unlike the standard Susceptible-(Exposed)-Infected-Removed models of disease transmission our model captures both geographically localised outbreaks and ``super-spreaders'' events. Moreover, the combination of localised and long range links allows for the more accurate modelling of partial isolation and various public health policies. From this model, we derive an expression for the probability of a widespread outbreak and a condition to ensure that the epidemic is controlled. Moreover, multiple simulations are used to make predictions of the likelihood of various eventual scenarios for fixed initial conditions. The main conclusions of this study are: (i) ``super-spreaders'' may occur even if the infectiousness of all infected individuals is constant; (ii) consistent with previous reports, extended exposure time beyond $3$--$5$ days (i.e. significant nosocomial transmission) was the key factor in the severity of the SARS outbreak in Hong Kong; and, (iii) the spread of SARS can be effectively controlled by either limiting long range links (imposing a partial quarantine) or to enforce rapid hospitalisation and isolation of symptomatic individuals.
- Tuesday, 22nd November, 2005
Title: SSC Algorithms for Noisy Optimisation Problems Speaker: Prof. Steve Wenbin Liu, Kent Business School, University of Kent, and Department of Mathematics, Hong Kong Baptist University Time/Place: 11:30 - 12:30
Abstract: In this talk we present the overall idea used in constructing a class of optimisation algorithms for the problems with strong noise. Then several applications in OR, Neural-Networks and global optimisation were discussed.
- Tuesday, 29th November, 2005
Title: Flexible Modeling via a Hybrid Estimation Scheme in Generalized Mixed Models for Longitudinal Data Speaker: Prof. Samuel Wong, Department of Statistics, The Chinese University of Hong Kong Time/Place: 11:30 - 12:30
Abstract: To circumvent the computational complexity of likelihood inference in generalized mixed models that assume linear or more general additive regression models of covariate effects, Laplace's approximations to multiple integrals in the likelihood have been commonly used without addressing the issue of adequacy of the approximations for individuals with sparse observations. In this paper, we propose a hybrid estimation scheme to address this issue. The likelihoods for subjects with sparse observations use Monte Carlo approximations involving importance sampling, while Laplace's approximation is used for the likelihoods of other subjects that satisfy a certain diagnostic check on the adequacy of Laplace's approximation. Because of its computational tractability, the proposed approach allows flexible modeling of covariate effects by using regression splines and model selection procedures for knot and variable selection. Its computational and statistical advantages are illustrated by simulation and by application to longitudinal data from a fecundity study of fruit flies, for which overdispersion is modeled via a double exponential family. This is a joint work with Prof. Tze-Leung Lai of the Department of Statistics at Stanford University and Prof. Mei-Chiung Shih of the Department of Biostatistics at Harvard School of Public Health.