著者

赤池 弘次

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.9, no.4, pp.342-344, 1999-12-15 (Released:2017-04-08)

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:24321982)

巻号頁・発行日

vol.31, no.3, pp.15-22, 2021-09-22 (Released:2021-12-26)

参考文献数

19

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This paper reviews some counterexamples in numerical analysis for solving partial differential equations. We point out the danger of having a preconception regarding the fact that a numerical solution is correct. Counterexamples, on the other hand, are interesting research subjects by themselves and could give new insights.

著者

宇田 智紀 横山 知郎 坂上 貴之

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:24240982)

巻号頁・発行日

vol.29, no.2, pp.187-224, 2019 (Released:2019-06-25)

参考文献数

22

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概要. 坂上・横山による2 次元ハミルトンベクトル場の流線トポロジーの文字列分類理論を大量のデータに対して適用するには,その計算機実装が不可欠である.本稿ではパーシステントホモロジーを用いた離散的定式化によりハミルトニアンのレーブグラフを得る安定かつ適合な手法を得た.これに基づき,ハミルトニアンデータから文字列表現を自動計算するアルゴリズムを構成し,その2次元非圧縮流体への適用例を示す.

著者

甘利 俊一

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.2, no.1, pp.37-56, 1992

参考文献数

26

被引用文献数

3

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Information geometry is a new theoretical method to elucidate intrinsic geometrical structures underlying information systems. It is applicable to wide areas of information sciences including statistics, information theory, systems theory, etc. More concretely, information geometry studies the intrinsic geometrical structure of the manifold of probability distributions. It is found that the manifold of probability distributions leads us to a new and rich differential geometrical theory. Since most of information sciences are closely related to probability distributions, it gives a powerful method to study their intrinsic structures. A manifold consisting of a smooth family of probability distributions has a unique invariant Riemannian metric given by the Fisher information. It admits a one-parameter family of invariant affine connections, called the α-connection, where α and-α-connections are dually coupled with the Riemannian metric. The duality in affine connections is a new concept in differential geometry. When a manifold is dually flat, it admits an invariant divergence measure for which a generalized Pythagorian theorem and a projection theorem hold. The dual structure of such manifolds can be applied to statistical inference, multiterminal information theory, control systems theory, neural networks manifolds, etc. It has potential ability to be applied to general disciplines including physical and engineering sciences.

著者

高島 克幸

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:24240982)

巻号頁・発行日

vol.25, no.2, pp.117-133, 2015-06-25 (Released:2017-04-08)

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楕円曲線暗号は,Koblitz,Millerによって独立に1985年に提案されて以来,新たな応用を生み出しながら,現在まで発展している.本稿では,私が関わったトピックを中心にして,誕生30年を迎える楕円曲線暗号の進展を,数論アルゴリズム的な側面から振り返る.特に,スカラー倍算,ペアリング演算,同種写像計算という3つの一方向性関数と,それらに基づくDiffie-Hellman型鍵共有法に焦点を当てながらサーベイを行う.

著者

斉藤 一哉

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.26, no.1, pp.9-14, 2016 (Released:2016-07-27)

参考文献数

18

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This study presents a new method for designing self-deploying origami using the geometrically misaligned creases. In this method, some facets are replaced by “holes” such that the systems become a 1-DOF mechanism. These perforated origami models can be folded and unfolded similar to rigidfoldable(without misalignment) models because of their DOF despite the existence of the misalignment. Focusing on the removed facets, the holes will deform according to the motion of the frame of the remaining parts. In the proposed method, these holes are filled with elastic parts and store elastic energy for self-deployment. First, a new extended rigid-folding simulation technique is proposed to estimate the deformation of the holes. Next by using the above technique, the proposed method is applied on arbitrary-size quadrilateral mesh origami. Finally, by using the finite-element method, the authors conduct numerical simulations and confirm the deployment capabilities of the models.

著者

甘利 俊一

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.11, no.1, pp.73-76, 2001-03-15 (Released:2017-04-08)

著者

稲葉 寿

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.12, no.3, pp.294-307, 2002-09-25 (Released:2017-04-08)

参考文献数

37

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In this paper, we introduce recent developments in mathematical models for demography and epidemics. During last two decades, functional analytic approach for structured population dynamics has been rapidly developed, which was a result of fruitful interaction between applied mathematics and theoretical biology. First, we sketch some developments of idea of asynchronous exponential growth for age-structured populations, which is a modern refinement of traditional idea of Malthusian growth. Next general approach to non-linear structured population models is reviewed with special attention to pair formation models. Finally we consider a Kermack's and McKendrick's epidemic model and an age-structured SIR epidemic model to clear the crucial role of the basic reproduction number in the threshold phenomena. Though we know that many deterministic structured population models have been successfully examined as infinite dimensional dynamical system, even after efforts of two decades, building a universal framework to describe time evolution of structured populations under complex environments has been still an open problem.

著者

杉山 将

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:24240982)

巻号頁・発行日

vol.23, no.3, pp.439-452, 2013-09-25 (Released:2017-04-08)

被引用文献数

2

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確率分布間の距離の推定は機械学習における基礎的な研究課題の一つであり,二標本検定,変化点検知,クラスバランス推定など様々な目的に応用することができる.本稿では,確率分布の推定を介さない直接距離近似法,特に,カルバック・ライブラー距離,ピアソン距離,相対ピアソン距離,L^2距離の直接近似法を概観する.

著者

江口 真透

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.30, no.3, pp.40-42, 2020-09-24 (Released:2020-12-26)

参考文献数

10

著者

松田 孟留

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.31, no.4, pp.7-14, 2021-12-22 (Released:2022-03-31)

参考文献数

32

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In this paper, we review the theory of shrinkage estimation and superharmonicity. First, we introduce Steinʼs paradox on estimation of the normal mean vector and explain its relationship with superharmonicity. Next, we investigate the extension to matrices, in which the shrinkage of singular values plays a key role for exploiting low-rankness. Finally, we illustrate recent developments on shrinkage predictive densities, empirical Bayes marix completion and matrix superharmonicity.

著者

緒方 秀教 平山 弘

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:24240982)

巻号頁・発行日

vol.26, no.1, pp.33-43, 2016 (Released:2016-08-19)

参考文献数

6

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概要. 本論文では,平山が提案した有限区間積分に対する数値積分法 —本論文では「超函数法」と呼ぶ —について解析を行う.超函数法では,問題とする積分を閉積分路上の複素積分に変換して,周期関数に対して性能の良い台形公式で近似計算する.数値実験により,超函数法は積分区間端点の特異性が強い積分に対して有効であることがわかる.また,超函数法と佐藤超函数論との関係についても触れる.

著者

畔上 秀幸

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.30, no.1, pp.34-37, 2020-03-25 (Released:2020-06-30)

参考文献数

2

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 (ISSN:24240982)

巻号頁・発行日

vol.23, no.1, pp.15-35, 2013-03-25 (Released:2017-04-08)

参考文献数

16

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本論文では下記の内容を含む.(1)すべての除数方式の配分結果が,あるタイプの離散最適化問題の最適解として表現できることを示した.(2)ある基本特性を満たす除数方式のサブクラス(人口比例型除数方式)を提案し,人口比例型除数方式を離散最適化問題として表現した.この基本特性を満たす目的関数の性質についても議論した.(3)最後に,人口比例型除数方式が著者が以前に提案していた緩和除数方式に等価であることを証明した.

著者

二宮 祥一

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.30, no.4, pp.8-15, 2020-12-22 (Released:2021-03-31)

参考文献数

25

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Numerical calculation of E[f(X(1,x))] where {X(t,x)}t≧0 is a diffusion process defined by a stochastic differential equation (SDE) is called weak approximation of the SDE. The author discusses higherorder discretization algorithms based on Kusuokaʼs theory. The fundamental theorem by Kusuoka and three algorithms are explained.

著者

岩本 真裕子

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.26, no.2, pp.14-21, 2016-06-24 (Released:2016-09-30)

参考文献数

16

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This study aim to investigate the mechanism of adhesive locomotion in gastropod. It has been reported by previous study that the significant factors of locomotion mechanism are “propagation of muscular waves” and “interfacial friction against the ground”. Interfacial friction has been considered to be controlled by lifting the pedal up, or dynamic viscoelasticity of mucus. To lift pedal up in appropriate timing, complex signals from the center would be necessary although the mechanism of lifting is simple in kinetics. This study focused on the hypothesis of dynamic viscoelasticity of mucus reported by Denny from the point of view of automatic frictional control similar to the mechanism of locomotion in earthworm. Based on the matter of previous study, a simple mathematical model which captures essential factors obtained by qualitative observations is proposed, and the physical parameters in the model are estimated by quantitative results from careful experiments. It has been verified by numerical calculations with the model that the mutual interaction between flexible muscular contraction waves and nonlinear dynamic viscoelasticity of the mucus can achieve an efficient locomotion. The important result in this study is that two locomotion styles, direct wave and retrograde wave, which has been understood by different mechanism, can be realized by the same mechanism.

著者

渡辺 澄夫

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.31, no.3, pp.7-14, 2021-09-22 (Released:2021-12-26)

参考文献数

15

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Many statistical models and learning machines are not regular but singular, hence the conventional theory using asymptotic normality can not be employed in analysis of such models. This paper explains the new mathematical theory which enables us to clarify the asymptotic behaviors of the generalization loss and the free energy based on algebraic geometry. Also the short history how this theory has been applied to real world problems is introduced.

著者

三中 信宏

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.32, no.2, pp.80-86, 2022-06-24 (Released:2022-09-30)

参考文献数

34

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In the field of statistical data analysis in research, there is considerable discussion about the details of statistical methods and statistical modeling applied to the actual data. However, the fact that philosophical and conceptual issues in statistical science lie behind a variety of practical problems is not often discussed in the open. Meanwhile, this paper discusses the relative comparison of competing hypotheses, model selection by AIC (Akaike’s Information Criterion), and the nature of statistics as “abduction” as nondeductive reasoning, which is based on the statistical criterion of “simplicity.”

著者

宮本 裕一郎

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.23, no.3, pp.129-134, 2013-09-25 (Released:2017-04-08)

著者

清 智也

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.29, no.1, pp.20-26, 2019-03-26 (Released:2019-06-30)

参考文献数

21

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Ranking systems are often based on a weighted sum of several quantitative variables. We discuss how to determine the weight. Anatural weighting method is standardization. Other possibilities are principal component analysis and factor analysis. The author recently proposed an objective general index as a different way of weighting. In this paper, we study a relationship between the objective general index and the existing methods.