Seminars and Colloquia by Series

Grain boundary motion in thin films

Series
Applied and Computational Mathematics Seminar
Time
Wednesday, September 9, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Amy Novick-CohenTechnion
Grain boundaries within polycrystalline materials are known to be governed by motion by mean curvature. However, when the polycrystalline specimen is thin, such as in thin films, then the effects of the exterior surfaces start to play an important role. We consider two particularly simple geometries, an axi-symmetric geometry, and a half loop geometry which is often employed in making measurements of the kinetic coefficient in the motion by mean curvature equation, obtaining corrective terms which arise due to the coupling of grain boundaries to the exterior surface.   Joint work with Anna Rotman, Arkady Vilenkin & Olga Zelekman-Smirin

The joint spectral radius of a set of matrices: theoretical and computational aspects.

Series
Applied and Computational Mathematics Seminar
Time
Monday, August 31, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Nicola Guglielmi Università di L'Aquila
In this talk I will address the problem of the computation of the jointspectral radius (j.s.r.) of a set of matrices.This tool is useful to determine uniform stability properties of non-autonomous discrete linear systems. After explaining how to extend the spectral radius from a single matrixto a set of matrices and illustrate some applications where such conceptplays an important role I will consider the problem of the computation ofthe j.s.r. and illustrate some possible strategies. A basic tool I willuse to this purpose consists of polytope norms, both real and complex.I will illustrate a possible algorithm for the computation of the j.s.r. ofa family of matrices which is based on the use of these classes of norms.Some examples will be shown to illustrate the behaviour of the algorithm.Finally I will address the problem of the finite computability of the j.s.r.and state some recent results, open problems and conjectures connected withthis issue.

Rigid and Nonrigid Registration Models for Medical Images

Series
Applied and Computational Mathematics Seminar
Time
Tuesday, August 18, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Justin W. L. WanComputer Science, University of Waterloo
In image guided procedures such as radiation therapies and computer-assisted surgeries, physicians often need to align images that are taken at different times and by different modalities. Typically, a rigid registration is performed first, followed by a nonrigid registration. We are interested in efficient registrations methods which are robust (numerical solution procedure will not get stuck at local minima) and fast (ideally real time). We will present a robust continuous mutual information model for multimodality regisration and explore the new emerging parallel hardware for fast computation. Nonrigid registration is then applied afterwards to further enhance the results. Elastic and fluid models were usually used but edges and small details often appear smeared in the transformed templates. We will propose a new inviscid model formulated in a particle framework, and derive the corresponding nonlinear partial differential equations for computing the spatial transformation. The idea is to simulate the template image as a set of free particles moving toward the target positions under applied forces. Our model can accommodate both small and large deformations, with sharper edges and clear texture achieved at less computational cost. We demonstrate the performance of our model on a variety of images including 2D and 3D, mono-modal and multi-modal, synthetic and clinical data.

Fast numerical methods for solving linear PDEs

Series
Applied and Computational Mathematics Seminar
Time
Thursday, April 23, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Per-Gunnar MartinssonDept of Applied Mathematics, University of Colorado

Please Note: Note special day

Linear boundary value problems occur ubiquitously in many areas of science and engineering, and the cost of computing approximate solutions to such equations is often what determines which problems can, and which cannot, be modelled computationally. Due to advances in the last few decades (multigrid, FFT, fast multipole methods, etc), we today have at our disposal numerical methods for most linear boundary value problems that are "fast" in the sense that their computational cost grows almost linearly with problem size. Most existing "fast" schemes are based on iterative techniques in which a sequence of incrementally more accurate solutions is constructed. In contrast, we propose the use of recently developed methods that are capable of directly inverting large systems of linear equations in almost linear time. Such "fast direct methods" have several advantages over existing iterative methods: (1) Dramatic speed-ups in applications involving the repeated solution of similar problems (e.g. optimal design, molecular dynamics). (2) The ability to solve inherently ill-conditioned problems (such as scattering problems) without the use of custom designed preconditioners. (3) The ability to construct spectral decompositions of differential and integral operators. (4) Improved robustness and stability. In the talk, we will also describe how randomized sampling can be used to rapidly and accurately construct low rank approximations to matrices. The cost of constructing a rank k approximation to an m x n matrix A for which an O(m+n) matrix-vector multiplication scheme is available is O((m+n)*k). This cost is the same as that of the well-established Lanczos scheme, but the randomized scheme is significantly more robust. For a general matrix A, the cost of the randomized scheme is O(m*n*log(k)), which should be compared to the O(m*n*k) cost of existing deterministic methods.

Periodic orbits of the N-body problem in celestial mechanics

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 20, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Tiancheng OuyangBrigham Young
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.

Multi-manifold data modeling via spectral curvature clustering

Series
Applied and Computational Mathematics Seminar
Time
Friday, April 17, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Gilad LermanUniversity of Minnesota

Please Note: 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.

Numerical Methods for Total Variation and Besov Smoothing

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 13, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Stacey LevineDuquesne University
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.

A variational method for the classification, segmentation and denoising of a time series field

Series
Applied and Computational Mathematics Seminar
Time
Monday, March 30, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Richardo MarchIstituto per le Applicazioni del Calcolo "Mauro Picone" of C.N.R.
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.

Domain Decompostion Methods for Stokes Equations

Series
Applied and Computational Mathematics Seminar
Time
Wednesday, March 25, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Junping WangNSF
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.

Hopf Bifurcation in Age Structured Models with Application to Influenza A Drift

Series
Applied and Computational Mathematics Seminar
Time
Monday, March 23, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Shigui RuanUniversity of Miami
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).

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