著者

田端 正久

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.15, no.3, pp.259-268, 2005-09-27

著者

曽 道智 茨木 俊秀

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.9, no.1, pp.12-27, 1999-03-15

被引用文献数

1

---

We survey the recent research in the field of cake divisions and their procedures. The question is how to divide a cake among n players, so that a certain fairness is achieved, where players have individual measures on the cake, and each player only knows his own measure. The model has very wide applications, such as dividing up the property in an estate, and even in determining the border in an international dispute. We first review mathematical definitions of various concepts of fairness. Although the existence of fair divisions is proved under some mathematical conditions, their dividing procedures are not known for all cases. We summarize several existing division procedures and classify them according to their methods and purposes. Finally, we mention some related topics and describe possible future research directions.

著者

齊藤 宣一

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.17, no.2, pp.186-187, 2007-06-26

著者

今野 浩

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.1, pp.36-50, 1991-03-15

---

Recently, a remarkable progress has been made in the field of the global minimization of nonconvex functions over a polytope. The purpose of this article is to survey one of the most successful approaches in this field, namely parametric programming approaches to quasilinear nonconvex minimization problems. The problems to be discussed are: linear multiplicative programming problems, i. e., the minimization of the product of two affine functions; minimization of the sum of two linear fractional functions; minimization of concave quadratic functions and bilinear programming problems. It will be shown that a global minimum of a fairly large scale problems can be obtained efficiently by applying parametric simplex algorithms. Further, it will be shown that a convex multiplicative programming problems, i. e., the minimization of the product of two convex functions, can be solved by parametrizatioh and branch and bound techniques.

著者

岩田 覚

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.20, no.2, 2010-06-25

著者

平田 祥人

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.105-114, 2012

---

In this paper, we review our recent developments of mathematical models for prostate cancer under intermittent androgen suppression. In the intermittent androgen suppression, androgen suppression, which is hormone therapy for prostate cancer, is intermittently stopped to delay the relapse of cancer. To optimize the protocol to each patient, we have proposed some mathematical models including ordinary differential equation models and partial differential equation models. Our most recent model is a three-dimensional piecewise linear model. One of the three variables of the model is for androgen dependent cancer cells and the other two variables are for androgen independent cancer cells. This piecewise linear model can not only fit clinical datasets of tumor marker called prostate specific antigen very well but also classify patients based on past time series of the tumor in a manner similar to medical doctors' classifications. We also discuss the future developments of mathematical methods for mathematical medicine including personalized treatment scheduling.

著者

薩摩 順吉 時弘 哲治

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.9, no.3, pp.236-246, 1999-09-16

---

Cellular automata exhibiting solitonical behavior are discussed. Then it is shown that such cellular automata are directly related to a class of nonlinear wave equations by means of the technique of "ultradiscretization". Mathematical meaning and applications to other equations of the technique are also mentioned.

著者

徳永 隆治 松本 隆 徳田 功

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.7, no.4, pp.271-282, 1997-12-15

被引用文献数

1

---

This paper reports a simple algorithm for reconstructing bifurcation diagrams only from time-wave forms of a parameterized family of dynamical systems, without knowing an explicit form of the dynamics and its dependence on the parameters. The algorithm consists of two steps. First, nonlinear predictors are sought using a particular class of nonlinear functions with a lot of model parameters. Second, significant parameters contributing the bifurcation are found by the principal component analysis. Using the parameterized family of nonlinear predictors, it is possible to obtain bifurcation diagram qualitatively similar to that of the original systems. The algorithm is tested against Henon equation and Rossler equation.

著者

安藤 英俊 藤木 史朗 鳥山 孝司

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.20, no.2, pp.107-116, 2010-06-25

---

Many Preconditioning algorithms for Krylov subspace methods are developed and well tested on parallel computing environment like PC clusters, but performance of those methods on GPU differs from those on clusters. Although incomplete LU decomposition is the most popular preconditioner for Krylov subspace methods on CPU, its implementation on GPU was never successful because of the sequential nature of the algorithm. By using C for CUDA environment, we have efficiently implemented ILU(0) on GPU. We have also implemented and evaluated various kinds of preconditioning methods for Krylov subspace solvers on GPU, including Jacobi, Red-Black Gauss-Seidel, Line-by-Line and ILU(0). ILU(0) preconditioner turned out to be most efficient and fastest among these preconditioners when solving Poisson equation.

著者

恩田 智彦

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.5, no.1, pp.73-74, 1995-03-15

著者

深畑 幸俊

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.19, no.2, pp.84-96, 2009-06-25

被引用文献数

1

---

粘弾性の問題を取り扱う際に対応原理がよく用いられる.本稿では,対応原理にラプラス変換の最終値定理を併せて用いることで,粘性緩和完了後の解などが煩雑な粘弾性の計算を経ずに,弾性問題の解から直接に得られることを示す.

著者

甘利 俊一 川鍋 元明

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.6, no.2, pp.96-109, 1996

参考文献数

19

被引用文献数

10

---

The present paper studies estimation of the coefficient θ of a linear dependence relation y=θx between two variables x and y from n pairs (y_i, x_i), i=1, …, n, of noise-contaminated observations. This is an old problem where the maximum likelihood estimator or the least square estimator is known not to be a,symptotically optimal. A simple estimator which improves the above one is explicitly given. This is a typical example of semiparametric statistical estimation. The method of estimating functions is used to solve the problem. Information geometry is used for elucidating the set of all the estimating functions and the asymptotic efficiency of the related estimators. A fibre structure is composed on the manifold of a semiparametric model and a dual couple of parallel transports are introduced on the fibres.

著者

赤木 久眞 中野 時衛 土肥 博 吉田 献一

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.4, pp.254-259, 2012

参考文献数

8

著者

下山 武司 伊豆 哲也 小暮 淳

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.19, no.1, pp.28-32, 2009-03-25

参考文献数

17

著者

須田 礼仁

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.21, no.2, 2011-06-24

著者

野島 武敏

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.18, no.4, pp.271-284, 2008

参考文献数

35

---

The present author proposed 'Origami Technology', and envisages the formation of a new discipline; mathematical analysis of Origami and its development in academic applications especially in engineering use. Origami structures consisting of zigzagged faces have foldable/deployable functions as well as solidification characters. Models presented in this paper include typical foldable/deployable thin cylinders, conical-shaped membranes, circular sheets which may be folded or wrapped. These shape-changeable origami models are analytically designed by folding or creasing a flat sheet or a thin plate into a 3-dimentional shape. New types of ultra-light 3-D honeycomb core models and a newly developed core panel named "dia-core" (consisting of 2 periodically dimpled panel pieces) are also presented for use in building such as aerospace structures. The former models are designed by analyzing the helical patterns or structures often found in living organisms, because such helical structures are easily deployed due to the presence of fewer dynamic restraints. The latter are developed on purely geometrical basis. As for academic applications of Origami modeling, two examples are shown; the phyllotaxis of leaves or flowers showing helical patterns, and axial buckling and torsional buckling of cylindrical tubes and conical shells are explained by using origami modeling.

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

宮本 雅彦

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.17, no.1, pp.65-68, 2007-03-26

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.