Monday, April 20, 2009 - 13:00 , Location: Skiles 255 , Tiancheng Ouyang , Brigham Young , Organizer: Chongchun Zeng
In this talk, I will show many interesting orbits in 2D and 3D of the N-body problem. Some of them do not have symmetrical property nor with equal masses. Some of them with collision singularity. The methods of our numerical optimization lead to search the initial conditions and properties of preassigned orbits. The variational methods will be used for the prove of the existence.
Friday, April 17, 2009 - 13:00 , Location: Skiles 255 , Gilad Lerman , University of Minnesota , Organizer: Sung Ha Kang
Note special day.
We propose a fast multi-way spectral clustering algorithm for multi-manifold data modeling, i.e., modeling data by mixtures of manifolds (possibly intersecting). We describe the supporting theory as well as the practical choices guided by it. We first develop the case of hybrid linear modeling, i.e., when the underlying manifolds are affine subspaces in a Euclidean space, and then we extend this setting to more general manifolds. We exemplify the practical use of the algorithm by demonstrating its successful application to problems of motion segmentation.
Monday, April 13, 2009 - 13:00 , Location: Skiles 255 , Stacey Levine , Duquesne University , Organizer: Sung Ha Kang
We present new finite difference approximations for solving variational problems using the TV and Besov smoothness penalty functionals. The first approach reduces oversmoothing and anisotropy found in common discrete approximations of the TV functional. The second approach reduces the staircasing effect that arises from TV type smoothing. The algorithms converge and can be sped up using a multiscale algorithm. Numerical examples demonstrate both the qualitative and quantitative behavior of the solutions.
Monday, March 30, 2009 - 13:00 , Location: Skiles 255 , Richardo March , Istituto per le Applicazioni del Calcolo "Mauro Picone" of C.N.R. , Organizer: Haomin Zhou
We consider ordered sequences of digital images. At a given pixel a time course is observed which is related to the time courses at neighbour pixels. Useful information can be extracted from a set of such observations by classifying pixels in groups, according to some features of interest. We assume to observe a noisy version of a positive function depending on space and time, which is parameterized by a vector of unknown functions (depending on space) with discontinuities which separate regions with different features in the image domain. We propose a variational method which allows to estimate the parameter functions, to segment the image domain in regions, and to assign to each region a label according to the values that the parameters assume on the region. Approximation by \Gamma-convergence is used to design a numerical scheme. Numerical results are reported for a dynamic Magnetic Resonance imaging problem.
Wednesday, March 25, 2009 - 13:00 , Location: Skiles 255 , Junping Wang , NSF , Organizer: Haomin Zhou
This talk will first review domain decomposition methods for second order elliptic equations, which should be accessible to graduate students. The second part of the talk will deal with possible extensions to the Stokes equation when discretized by finite element methods. In particular, we shall point out the difficulties in such a generalization, and then discuss ways to overcome the difficulties.
Monday, March 23, 2009 - 13:00 , Location: Skiles 255 , Shigui Ruan , University of Miami , Organizer: Yingfei Yi
Understanding the seasonal/periodic reoccurrence of influenza will be very helpful in designing successful vaccine programs and introducing public health interventions. However, the reasons for seasonal/periodic influenza epidemics are still not clear even though various explanations have been proposed. In this talk, we present an age-structured type evolutionary epidemiological model of influenza A drift, in which the susceptible class is continually replenished because the pathogen changes genetically and immunologically from one epidemic to the next, causing previously immune hosts to become susceptible. Applying our recent established center manifold theory for semilinear equations with non-dense domain, we show that Hopf bifurcation occurs in the model. This demonstrates that the age-structured type evolutionary epidemiological model of influenza A drift has an intrinsic tendency to oscillate due to the evolutionary and/or immunological changes of the influenza viruses. (based on joint work with Pierre Magal).
Monday, March 9, 2009 - 13:05 , Location: Skiles 255 , Zhi J. Wang , Aerospace Engineering, Iowa State University , Organizer: Yingjie Liu
The current breakthrough in computational fluid dynamics (CFD) is the emergence of unstructured grid based high-order (order > 2) methods. The leader is arguably the discontinuous Galerkin method, amongst several other methods including the multi-domain spectral, spectral volume (SV), and spectral difference (SD) methods. All these methods possess the following properties: k-exactness on arbitrary grids, and compactness, which is especially important for parallel computing. In this talk, recent progresses in the DG, SV, SD and a unified formulation called lifting collocation penalty will be presented. Numerical simulations with the SV and the SD methods will be presented. The talk will conclude with several remaining challenges in the research on high-order methods.
Monday, February 23, 2009 - 13:00 , Location: Skiles 255 , Tiejun Li , Peking University , Organizer: Haomin Zhou
The tau-leaping algorithm is proposed by D.T. Gillespie in 2001 for accelerating the simulation for chemical reaction systems. It is faster than the traditional stochastic simulation algorithm (SSA), which is an exact simulation algorithm. In this lecture, I will overview some recent mathematical results on tau-leaping done by our group, which include the rigorous analysis, construction of the new algorithm, and the systematic analysis of the error.
Monday, February 9, 2009 - 13:00 , Location: Skiles 255 , Giuseppe Mastroianni , Dept. of Mathematics and Informatics, Univ. of Basilicata, Italy) , Organizer: Haomin Zhou
In this talk I will show a simple projection method for Fredholm integral equation (FIE) defined on finite intervals and a Nyström method for FIE defined on the real semiaxis. The first method is based the polynomial interpolation of functions in weighted uniform norm. The second one is based on a Gauss truncated quadrature rule. The stability and the convergence of the methods are proved and the error estimates are given.
Monday, January 26, 2009 - 13:00 , Location: Skiles 255 , Ming-Jun Lai , University of Georgia , Organizer: Haomin Zhou
I will first explain why we want to find the sparse solutions of underdetermined linear systems. Then I will explain how to solve the systems using \ell_1, OGA, and \ell_q approaches. There are some sufficient conditions to ensure that these solutions are the sparse one, e.g., some conditions based on restricted isometry property (RIP) by Candes, Romberg, and Tao'06 and Candes'08. These conditions are improved recently in Foucart and Lai'08. Furthermore, usually, Gaussian random matrices satisfy the RIP. I shall explain random matrices with strictly sub-Gaussian random variables also satisfy the RIP.