Colloquium/Seminar
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Event(s) on December 2006
- Monday, 4th December, 2006
Title: Supervised Texture Classification Using Characteristic Generalized Gaussian Density Speaker: Mr. Siu Kai Choy, Department of Mathematics, Hong Kong Baptist University, HKSAR, China Time/Place: 14:00 - 15:00
FSC 1217Abstract: Generalized Gaussian density (GGD) is a well proven model for high frequency wavelet subbands and has been applied in texture image retrieval with satisfactory results. In this talk, we propose to adopt the GGD model in a supervised learning context for texture classification. Given a training set of GGDs, we define a characteristic GGD (CGGD) that minimizes its Kullback-Leibler distance (KLD) to the training set. We present mathematical analysis that proves the existence of our characteristic GGD and provide a sufficient condition for the uniqueness of CGGD, thus establishing a theoretical basis for its use. Our experimental results show that the proposed CGGD signature together with the use of KLD has a superior recognition performance compared with existing approaches. - Tuesday, 12th December, 2006
Title: Chaos from the Statistical Viewpoint - The Frobenius-Perron Operator and its Approximation Speaker: Prof. Jiu Ding, Department of Mathematics, The University of Southern Mississippi, USA Time/Place: 11:30 - 12:30
FSC 1217Abstract: The ergodic theory of chaotic dynamical systems plays an important role in modern science and technology, such as computational molecular dynamics and wireless communications. In this talk, we look at chaos from the statistical point of view and introduce the concept of Frobenius-Perron operators associated with chaotic transformations. The classic Ulam's method and its modern extensions will be presented too. - Wednesday, 13th December, 2006
Title: Numerical Approximation of Population Balance Equations in Process Engineering Speaker: Prof. Gerald Warnecke, Institut fuer Analysis und Numerik, Universität Magdeburg, Germany Time/Place: 11:30 - 12:30
FSC1217Abstract: Population balance equations are widely used in many chemical and process engineering problems involving crystallization, fluidized bed granulation, aerosol science etc. Analytical solutions are available only for a limited number of simplified problems and therefore numerical solutions are frequently needed to solve a population balance system. A general population balance equation for simultaneous aggregation, breakage, growth and nucleation in a well mixed system is given as an integro-partial differential equation for a particle property distribution function. Sectional methods are well known for their simplicity and conservation properties. Therefore numerical techniques belonging to this category are most commonly used. In these methods, all particles within a computational cell, which in some papers is called a class, section or interval, are supposed to be of the same size. These methods divide the size range into small cells and then apply a balance equation for each cell. The continuous population balance equation is then reduced to a set of ordinary differential equations. However, it is well known that the numerical results by previous sectional methods were inaccurate. Furthermore, there is a lack of numerical schemes in the literature which can be used to solve growth, nucleation, aggregation, and breakage processes, i.e. differential and integral terms, simultaneously. We present a new numerical scheme for solving a general population balance equation which assigns particles within the cells more precisely. The technique follows a two step strategy. The first is to calculate the average size of newborn particles in a cell and the other to assign them to neighboring nodes such that important properties of interest are exactly preserved. The new technique preserves all the advantages of conventional discretized methods and provides a significant improvement in predicting the particle size distributions. The technique allows the convenience of using geometric- or equal-size cells. The numerical results show the ability of the new technique to predict very well the time evolution of the second moment as well as the complete particle size distribution. Moreover, a special way of coupling the different process has been described. It has been demonstrated that the new coupling makes the technique more useful by being not only more accurate but also computationally less expensive. Furthermore, a new idea that considers the growth process as aggregation of existing particle with new small nuclei has been presented. In that way the resulting discretization of the growth process becomes very simple and consistent with first two moments. Additionally, it becomes easy to combine the growth discretization with other processes. Moreover all discretizations including the growth have been made consistent with first two moments. The new discretization of growth is a little diffusive but it predicts the first two moments exactly without any computational difficulties like appearance of negative values or instability etc. The accuracy of the scheme has been assessed partially by numerical analysis and by comparing analytical and numerical solutions of test problems. The numerical results are in excellent agreement with the analytical results and show the ability to predict higher moments very precisely. Additionally, an extension of the proposed technique to higher dimensional problems is discussed. - Monday, 18th December, 2006
Title: Wofoo Distinguished Applied Mathematics Lecture Series: Intersection Between Probability and Other Branches of Mathematics and Sciences Speaker: Prof. Zhi-Ming Ma, Institute of Applied Mathematics, Chinese Academy of Sciences, China Time/Place: 11:00 - 12:00
SCT LT1Abstract: Probability and statistics have brought fruitful achievements intersecting with other branches of mathematics and sciences. In ICM2006, Wendelin Werner received a Fields Medal "for his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory". Andrei Okounkov received a Fields Medal "for his contributions bridging probability, representation theory and algebraic geometry". The founder of Stochastic Analysis, Kiyoshi Ito, received the first Gauss Prize for Applications of Mathematics. Nevanlinna Prize was awarded to Jon Kleinberg for his important contributions to Internet search and stochastic complex networks. In this lecture I shall briefly talk about some active research directions, with the preference of my own interests, of the intersection between Probability and other branches of Mathematics and Sciences. - Monday, 18th December, 2006
Title: Applications of Optimal Design Ideas to Biomedical Problems Speaker: Prof. Weng Kee Wong, Department of Biostatistics, School of Public Health, University of California at Los Angeles, USA Time/Place: 14:30 - 15:30
FSC 1217Abstract: Optimal design theory has been around for a long time but its use in the biomedical arena is quite limited. I will provide a brief overview of work in this field, and discuss applications of optimal design ideas to tackle a few practical problems. The focus will be on modern strategies for designing improved biomedical studies. Specifically, I will discuss how optimal design ideas can be applied to design studies with several objectives and in studies where the response has different variances across treatment groups. I will also discuss how to construct efficient designs that incorporate anticipated missing data information using data from a rheumatoid arthritis trial.