応用数理

This paper presents some resent achievements of earthquake simutation, which is divided into the seismic wave propagation simulation and the seismic structure response simulation. These achievements are based on new mathematical treatment of continuum mechanics problems, and numerical algorithms of solving the problems are developed. A multi-scale analysis method is developed for the seismic wave propagation simulation; numerical dispersion is reduced by introducing a new discretization scheme. A smart treatment of crack initiation and propagation is developed for the seismic structure response simulation, so that a numerical experiment is made failure processes by using numerous samples for one structure.

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By the development of information and communication technology in recent years, a lot of quick and detailed socioeconomic data can be collected. In order to understand a mechanism behind a socioeconomic phenomenon using the extensive and large-scale real data, a social and group simulation becomes still more important as analytical tools. This paper introduces researches of social and group simulation based on analysis of real data, and real data analysis based on simulation results. First, about financial markets, traffics, and pedestrian dynamics, researches of the integration were introduced. Next, a movement to establish the theory and the methodology of the integration of a social simulation and real data as general technique or research approach was explained.

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マウスの全身のマルチスライスX線CT(Computed Tomography)画像から,2種類の脂肪組織(皮下脂肪組織と内臓脂肪組織)の体内での分布状態を自動的に量的形質として定量するための手法について紹介する.一枚のX線CT画像は,体軸に垂直な断面上でのX線吸収率(CT値)の分布を表したものである.脂肪組織に特異的なCT値をもつ領域の抽出によって,脂肪組織の体内での分布状態を再構築できる.しかしながら,皮下脂肪組織と内臓脂肪組織は同一のCT値の範囲に含まれるため,CT値の比較のみでは分類できない.そのため,両者を空間的に隔てる体腔(胸腔と腹腔)の形状を認識し,脂肪組織がその内外のいずれに存在するかに基づいて分類することが必要になる.骨格や筋肉,肺,皮膚などの形状を標識点として用い,体腔を含めたマウス全身の形状を数値的に認識する手法の可能性を,実際に脂肪組織の分類と定量を行った結果を示しながら紹介する.

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In this paper, we present the MPACK, a multiple precision version of BLAS and LAPACK, which I have been developing since 2007. The aim of the MPACK library is provding better very accurate linear algebra environment for everyone. Some features of the MPACK are: (i) providing reference implementation and/or API, based on BLAS and LPACK, (ii) currently 76 MBLAS routines and 100 MLPACK routines are available. Complex number is supported. The MBLAS part is completed, and the MLPACK part includes LU, Cholesky decompostion, condition number estimation, solves eigenvalue problems, (iii) works on many different OSes like Linux, Mac, Windows, FreeBSD, etc, (iv) supported by four multiple precision arithmetic libraries, MPFR, MPC, GMP and QD, (v) written in C++ and very easy to use, via C++ binding, (vi) licensed under 2-clause BSD license, therefore everyone can use it without restriction. The newest version 0.6.7 is released on 2010/8/20, and can be obtained at http://mplapack.sourceforge.net/.

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