著者
一森 哲男
出版者
一般社団法人日本応用数理学会
雑誌
日本応用数理学会論文誌 = Transactions of the Japan Society for Industrial and Applied Mathematics (ISSN:09172246)
巻号頁・発行日
vol.16, no.3, pp.265-276, 2006-09-25
被引用文献数
2

This paper discusses two apportionment methods taking account of dispersion. The first one minimizes the variance of per capita shares of a representative of 47 prefectures. And the second one minimizes the coeffcient of variation of those shares of a representative of 47 prefectures. We observe that these methods give reasonable allocations of 300 seats to 47 prefectures and also reasonable allocations of 180 to 11 blocks in Japan.
著者
岩見 真吾 佐藤 佳 小柳 義夫
出版者
一般社団法人日本応用数理学会
雑誌
応用数理 (ISSN:09172270)
巻号頁・発行日
vol.22, no.2, pp.85-94, 2012-06-26

Recently, in order to investigate the fundamental phenomena in immunology and virology such as maintenance of immune memory, T-cell homeostasis, the relationship between aging and immunosenescence, the regulation of the adaptive immune response during viral infection, the pathogenesis of CD4^+ depletion in HIV infection, and the underlying mechanisms of leukemia, we successfully quantied lymphocyte kinetics in humanized mice through BrdUlabeling experiment. It is worth noting that our findings are the first to assess lymphocyte dynamics utilizing this technique. At first, we will briefly give an outline of the "Quantification system of lymphocyte kinetics in humanized mice" and then we will discuss about properties of the lymphocyte kinetics and utilities of our established system.
著者
杉原 厚吉
出版者
一般社団法人日本応用数理学会
雑誌
応用数理 (ISSN:09172270)
巻号頁・発行日
vol.1, no.4, pp.280-299, 1991-12-16
被引用文献数
12

New approaches are presented to the problem of topological inconsistency caused by geometric algorithms implemented in finite-precision arithmetic. In geometric computation numerical errors often create inconsistency in topological structures and thus cause theoretically correct algorithms to fail. To overcome this problem two approaches are considered for the case of constructing the Voronoi diagram as an example. In the first approach, higher-precision arithmetic is used to construct a closed world in which topological structures are judged always precisely, and the symbolic perturbation technique is employed to avoid complicated branches of processing for degenerate cases. In the second approach, the highest priority is placed on the maintenance of topological consistency and numerical results are used as lower-priority information; the resultant algorithm is robust in the sense that inconsistency never arises and is correct in the sense that the output converges to the true solution as the precision becomes higher.
著者
永持 仁
出版者
一般社団法人日本応用数理学会
雑誌
応用数理 (ISSN:09172270)
巻号頁・発行日
vol.8, no.1, pp.20-29, 1998-03-16

The connectivity augmentation problem asks to add to a given graph the smallest number of new edges so that the edge- (or vertex-) connectivity of the graph increases up to a specified value k. The problem is first studied by K. P. Eswaran and R. E. Tarjan in 1976, and both type of connectivity augmentation problems for k=2 are shown to be polynomially solvable. Afterwards, in 1987 T. Watanabe and A. Nakamura proved that the problem of making a given graph k-edge-connected by adding the smallest number of edges can be solved in O(k^2(kn+m)n^4) time for general k, where n and m are the number of vertices and edges in the input graph, respectively. Recently, a significantly faster O(nm log n+n^2 log^2 n) time algorithm for solving this problem is proposed by H. Nagamochi and T. Ibaraki by applying L. Lovasz's edge-splitting theorem. This note first reviews this alogorithm and then shows how to modify the algorithm to solve the edgeconnectivity augmentation problem for a graph with real-weighted edges.
著者
武田 利浩 田中 昭吉 丹野 州宣
出版者
一般社団法人日本応用数理学会
雑誌
日本応用数理学会論文誌 (ISSN:09172246)
巻号頁・発行日
vol.5, no.4, pp.399-409, 1995-12-15

Various types of neural networks have been proposed, and many applications of the technology have also been vigorously promoted in the wide range of the fields. However, simulations of large scale neural networks require quite high speed computation ability because of an enormous of time in learning. Then, many studies have been reported on efficient parallel simulation of neural networks. This paper proposes parallel computing algorithm allowing the back-propagation model to be simulated upon an 8-neighbor processor array. Taking account of the parallelism intrinsically imbedded in the neural networks, the algorithm realizes high speed neural network computation. The time complexities of the algorithm are only O(NLp/P)for communications and O(N^2L/P)for computation in one step learning processing, where N is the number of the neurons in a layer, P(pxp)is the number of processors, and L is the number of the layers.
著者
塩出 亮 阿部 邦美 藤野 清次
出版者
一般社団法人日本応用数理学会
雑誌
日本応用数理学会論文誌 (ISSN:09172246)
巻号頁・発行日
vol.17, no.1, pp.27-42, 2007-03-25
被引用文献数
2

The MRTR method has been recognized as an effective iterative method for singular systems of linear equations. The MRTR method is based on the three-term recurrence formula of the CG method and the algorithm is proven to be mathematically equivalent to the CR method. In this paper, we extend the MRTR method to solve complex symmetric linear systems. We describe this extended cs_MRTR method and prove that this method is mathematically equivalent to the COCR method. Numerical examples show that the cs_MRTR method shows a more stable convergence behavior than the COCR method.(Theory)

1 0 0 0 OA 準結晶の数理

著者
藤原 毅夫
出版者
一般社団法人日本応用数理学会
雑誌
応用数理 (ISSN:09172270)
巻号頁・発行日
vol.1, no.2, pp.117-134, 1991-06-14

Quasicrystals are newly discovered equiliblate systems, showing diffraction patterns of the sharp and densely distributed spots with the crystallographically disallowed symmetry. These materials open a new field of condensed matter physics. Mathematical aspects of quasicrystals are briefly reviewed, including several general methods constructing quasiperiodic systems, generalized crystallography and fractal character of electronic structures.
著者
相島 健助 松尾 宇泰 室田 一雄 杉原 正顕
出版者
一般社団法人日本応用数理学会
雑誌
日本応用数理学会論文誌 (ISSN:09172246)
巻号頁・発行日
vol.17, no.2, pp.97-131, 2007-06-25
被引用文献数
3

Convergence theorems are established with mathematical rigour for two algorithms for the computation of singular values of bidiogonal matrices: the differential quotient difference with shift (dqds) and the modified discrete Lotka-Volterra with shift (mdLVs). Global convergence is guaranteed under a fairly general assumption on the shift, and the asymptotic rate of convergence is 1.5 for the Johnson bound shift. This result for the mdLVs algorithm is a substantial improvement of the convergence analysis by Iwasaki and Nakamura. Numerical examples support these theoretical results.
著者
平山 弘 小宮 聖司 佐藤 創太郎
出版者
一般社団法人日本応用数理学会
雑誌
日本応用数理学会論文誌 (ISSN:09172246)
巻号頁・発行日
vol.12, no.1, pp.1-8, 2002-03-15
被引用文献数
11

The arithmetic operations and functions of Taylor series can be defined by C++ language. The functions which consist of arithmetic operations, pre-defined functions and conditional statements can be expanded in Taylor series. Using this, the solution of an ordinary differential equation can be expanded in Taylor series. The solution can be expanded up to arbitrary order, so the calculation formula of arbitrary order can be used instead of Runge-Kutta formula. Taylor series can be used for the evaluations of the errors and the optimal step size within given error allowance easily. In addition, we can transform Taylor series into Pade series, which give arbitrary order, high precision and A-stable formula for solving ordinary differential equation numerically.
著者
増田 直紀 巳波 弘佳 今野 紀雄
出版者
一般社団法人日本応用数理学会
雑誌
応用数理 (ISSN:09172270)
巻号頁・発行日
vol.16, no.1, pp.2-16, 2006-03-28
被引用文献数
3

Recently, complex networks have drawn increasing interests. It is often convenient to regard this research area to be composed of studies of network structure and network functions. Studies of network structure are concerned about topological characteristics of complex networks such as the small-world and scale-free properties. Studies of network functions deal with processes and phenomena on complex networks such as virus propagation. This article is a minireview of complex networks from these dual viewpoints.
著者
片山 幹基 木村 欣司 高田 雅美 坪井 洋明 岩崎 雅史 中村 佳正
出版者
一般社団法人日本応用数理学会
雑誌
日本応用数理学会論文誌 (ISSN:09172246)
巻号頁・発行日
vol.18, no.3, pp.389-407, 2008-09-25
被引用文献数
1

本論文では,上2重対角行列の高速特異値分解法1-SVDにおける左特異ベクトル計算部を改善し,直交性の優れた精度のよい左特異ベクトルを高速に求める新たな手法を定式化する.さらに,その有効性を数値実験により評価する.
著者
山本 有作
出版者
一般社団法人日本応用数理学会
雑誌
日本応用数理学会論文誌 (ISSN:09172246)
巻号頁・発行日
vol.16, no.4, pp.507-534, 2006-12-25
被引用文献数
1

The QR algorithm is one of the most reliable and widely used methods to compute the eigenvalues of symmetric and nonsymmetric matrices. However, it is not straightforward to execute the QR algorithm efficiently on modern architectures such as processors with hierarchical memory or parallel computers because of its inherent sequential nature and low data reference locality. To overcome this difficulty, Bai & Demmel proposed the multishift QR algorithm in 1989 and this idea has been greatly expanded since then. In this paper, we introduce the basic theory of the multishift QR algorithm and review recent developments to improve its efficiency, such as the two-tone QR algorithm, aggressive early deflation and the fully-pipelined multishift QR algorithm. Directions for future research are also discussed.
著者
山本 有作
出版者
一般社団法人日本応用数理学会
雑誌
日本応用数理学会論文誌 (ISSN:09172246)
巻号頁・発行日
vol.15, no.2, pp.181-208, 2005-06-25
被引用文献数
6

The Algorithm of Multiple Relatively Robust Representations (MR^3) is a new algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem proposed by I. Dhillon in 1997. It has attracted much attention because it can compute all the eigenvectors of an n×n matrix in only O(n^2) work and is easy to parallelize. In this article, we survey the papers related to the MR^3 algorithm and try to present a simple and easily understandable picture of the algorithm by explaining, one by one, its key ingredients such as the relatively robust representations of a symmetric tridiagonal matrix, the dqds algorithm for computing accurate eigenvalues and the twisted factorization for computing accurate eigenvectors. Limitations of the algorithm and directions for future research are also discussed.