46 0 0 0 OA 情報幾何学

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.2, no.1, pp.37-56, 1992-03-16 (Released:2017-04-08)
参考文献数
26

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
池田 思朗 本間 希樹 植村 誠
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.25, no.1, pp.15-19, 2015-03-25 (Released:2017-04-08)

In this paper, we show some examples of sparse modeling in astronomy. In many cases, astronomy data has sparsity. If we can utilize it, we will have better results. What is measured in astronomy is the electromagnetic wave of various wavelength. The technology used for each wavelength is different. We show three examples. For each of them, the sparse modeling plays an important role.
著者
大野 泰生 後藤 丈志
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.16, no.3, pp.187-195, 2006-09-25 (Released:2017-04-08)
参考文献数
20

Jenkins recently showed that an odd perfect number must be divisible by a prime greater than 10^7. The aim of this article is to give a new algorithm to obtain such a lower bound. The theory of cyclotomic numbers plays an important role in the algorithm. We also discuss some relation between cyclotomic numbers and ABC conjecture.
著者
佐藤 寛之
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.27, no.1, pp.21-30, 2017 (Released:2017-06-30)
参考文献数
29

This paper deals with Riemannian optimization, that is, optimization on Riemannian manifolds. Theories of Euclidean optimization and Riemannian manifolds are first briefly reviewed together with some simple and motivating examples, followed by the Riemannian optimization theory. Retractions and vector transports on Riemannian manifolds are introduced according to the literature to describe a general Riemannian optimization algorithm. Recent convergence analysis results of several types of Riemannian conjugate gradient methods, such as Fletcher-Reeves and Dai-Yuan-types, are then given and discussed in detail. Some applications of Riemannian optimization to problems of current interest, such as 1)singular value decomposition in numerical linear algebra; 2)canonical correlation analysis and topographic independent component analysis as statistical methods; 3)low-rank tensor completion for machine learning; 4)optimal model reduction in control theory; and 5)doubly stochastic inverse eigenvalue problem, are also introduced.
著者
石井 晃 太田 奨
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.25, no.2, pp.50-58, 2015-06-25 (Released:2017-04-08)

We apply a mathematical theory for hit phenomenon for prediction of the "general election" of AKB48 which is very popular girls group in Japan.

15 0 0 0 OA 機械学習の概要

著者
鈴木 大慈
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.28, no.1, pp.32-37, 2018 (Released:2018-06-30)
参考文献数
26
被引用文献数
1
著者
玉井 敬一 佐野 雅己
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.2, pp.10-17, 2019 (Released:2019-09-30)
参考文献数
29

In this article, we review recent progress in the understanding of the transition from laminar to turbulent flow in shear flows. We describe why and how the idea of directed percolation can be applied to these transitions in different flows, and how the idea was tested by experiments and simulations.
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

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
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

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
松浦 望
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.3, pp.17-24, 2016 (Released:2016-12-26)
参考文献数
19

This is an overview of the paper[19], which makes a survey of discrete differential geometry of curves and surfaces. We review a few representatives of discrete curves and surfaces, with emphasis on close connections between both the theories of discrete differential geometry and discrete integrable systems.
著者
鈴木 崇文 岩見 真吾 竹内 康博
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.473-486, 2008
参考文献数
18

2005年9月中国で実施された家禽の鳥インフルエンザウイルスに対するワクチン接種政策を例に数理モデルを考える.解析の結果,大変興味深いことに,家禽へのワクチン接種率を上げることが,総感染個体数を増加させうることを発見した.つまり,感染個体数を減少させるための家禽に対するワクチン政策が,感染個体数の増加を引き起こしている.本論文では,こういった「ワクチン政策のパラドックス」について詳しく報告する.