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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.

Monday, January 12, 2009 - 13:00 ,
Location: Skiles 255 ,
Frank Crosby ,
Naval Surface Warfare Center, Panama City ,
Organizer: Haomin Zhou

Several imaging innovations have been designed to find hidden objects in coastal areas of entry, such as beaches and ports. Each imaging device is designed to exploit particular distinguishing characteristics. This talk with cover using a tunable multi-spectral camera for polarization based detection and object identification with a flash LIDAR camera that produces three-dimensional imagery.

Monday, November 17, 2008 - 13:00 ,
Location: Skiles 255 ,
Maoan Han ,
Shanghai Normal University ,
Organizer: Haomin Zhou

Let H(m) denote the maximal number of limit cycles of polynomial systems of degree m. It is called the Hilbert number. The main part of Hilbert's 16th problem posed in 1902 is to find its value. The problem is still open even for m=2. However, there have been many interesting results on the lower bound of it for m\geq 2. In this paper, we give some new lower bounds of this number. The results obtained in this paper improve all existing results for all m\geq 7 based on some known results for m=3,4,5,6. In particular, we confirm the conjecture H(2k+1) \geq (2k+1)^2-1 and obtain that H(m) grows at least as rapidly as \frac{1}{2\ln2}(m+2)^2\ln(m+2) for all large m.