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2017-07-25 〜 08-01 Justin Wan博士による連続講演会(2017.07.25, 27 and 08.01)

投稿者:  速水 謙(国立情報学研究所)
会場: 国立情報学研究所
概要: 科学計算(画像処理、マルチグリッド法、金融工学)に関する話題です。

日程 2017年 7月25,27日, 8月1日
会場 国立情報学研究所
National Institute of Informatics (NII)
access
本文 Lectures on Scientific Computing by Dr. Justin Wan

Speaker: Dr. Justin W.L. Wan
Canada Research Chair in Scientific Computing,
Associate Professor, SciCom group in the David R. Cheriton School of Computer Science at University of Waterloo, Canada,
Director of the Centre for Computational Mathematics in Industry and Commerce (CCMIC).


Talk 1:
Date: July 25th (Tuesday), 11:00-12:00am
Room: 12F, 1208
Title: Graph Cut and Linear Algebra Approach to Cell Image Segmentation
Abstract:
Segmentation of cells in time-lapse bright-field microscopic images is crucial in understanding cell behaviors for medical research. However, the complex nature of the cells, together with poor contrast, broken cell boundaries and the halo artifact, pose nontrivial challenges to this problem. In this talk, we present robust mathematical models based on linear algebra techniques to segment bright-field cells automatically. One approach is to formulate image segmentation as graph cut problems. We combine the techniques of graph cut, multiresolution, and Bhattacharyya measure, performed in a multiscale framework, to locate multiple cells in bright-field images. Another approach is to treat cell image segmentation as a background subtraction problem. It can be formulated as a robust Principal Component Pursuit (PCP) problem which minimizes the rank of the image matrix. In this approach, we exploit the sparse component of the PCP solution for identifying the cell pixels. However, the spar
se component and the nonzero entries can scatter all over the image, resulting in a noisy segmentation. We improve the model by combining PCP with spectral clustering. Spectral clustering makes use of the eigenvectors of the graph Laplacian matrix to classify data. Seemingly unrelated approaches, we combine the two techniques by incorporating normalized-cut in the PCP as a measure for the quality of the segmentation. Experimental results demonstrate that the proposed models are effective in segmenting cells obtained from bright-field images.

Talk 2:
Date: July 27th (Thursday), 11:00-12:00 am
Room: 12F, 1212
Title: Multigrid Methods: from Elliptic, Hyperbolic to Nonlinear Partial Differential Equations
Abstract:
Multigrid methods have been well known solvers for their mesh independent convergence. They are efficient for Poisson-type problems as well as smooth coefficient elliptic partial differential equations (PDEs). However, when the coefficients exhibit jumps, for instance, in interface problems, the convergence can be slow. For non-elliptic problems such as hyperbolic equations as well as nonlinear PDEs, standard multigrid methods do not work well. In this talk, we will present efficient and robust multigrid methods for solving different types of PDEs. We explore different techniques for constructing interpolation, restriction, and coarse grid operators. They are so designed to capture the properties of the underlying PDE problems so that they will result in fast convergence. We will present numerical results to demonstrate the effectiveness of the multigrid methods.

Talk 3:
Date: August 1st (Tuesday), 11:00-12:00 am
Room: 19F, 1901
Title:
Numerical Methods for PDE Problems arising from Option Pricing, Asset Allocation, and Dynamic Bertrand Oligopolies
Abstract:
Black-Scholes modeling is central in computational finance. It also leads to PDEs with challenging numerical issues. In this talk, we will present accurate and efficient numerical methods for solving different types of PDEs that arise from option pricing, asset allocation, regime switching and Bertrand oligopolies. In particular, we present an accurate finite difference method for solving partial integro-differential equations arising from pricing European and American options when the underlying asset is driven by a CGMY process. We will then present numerical methods and fast solvers for solving Hamilton-Jacobi-Bellman (HJB) equations as well as the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations, which arise in asset allocation and stochastic optimal control problems. When there are multiple value functions, for instance, regime switching models in option pricing, or nonzero sum stochastic differential games in dynamic Bertrand oligopoly, the resulting model will result in a syste
m of coupled HJB PDEs. We will discuss the discretization of the nonlinear systems, the issues of viscosity solutions, monotone finite difference schemes, and fast solvers for solving the systems of discrete HJB equations. We demonstrate numerically the performance of the numerical methods by examples of various computational finance problems.
問い合わせ先 速水 謙
Ken Hayami
e-mail: hayamiseparatornii.ac.jp
詳細 web talk on 2017.07.25,
talk on 2017.07.27,
talk on 2017.08.01 .