著者
新屋 良磨
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.15-22, 2021-12-22 (Released:2022-03-31)
参考文献数
4

Formal language theory is the field of study of non-commutative objects so-called “languages” (sets of words). While many problems on languages are difficult to solve due to the non-commutativity, the situation could be drastically changed if we consider a commutative invariant of a language. This paper explains some commutative invariants of languages with concrete examples.

48 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
浦川 肇
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.1, pp.29-45, 2002-03-15 (Released:2017-04-08)
参考文献数
48

A brief survey on the spectral geometry of a finite or infinite graph is given. After the adjacency matrix, discrete Laplacian and discrete Green's formula are introduced, the spectral geometry of finite graphs, particularly, estimation of the first positive eigenvalue in terms of the Cheeger constant, examples of isospectral or cospectral graphs and the Faber=Krahn type inequality are discussed. For infinite graphs, spectrum of the discrete Laplacian, the heat kernel and Green kernel are estimated. Finally, a relation between the finite element method for the Dirichlet boundary eigenvalue problem and the eigenvalue problem of the adjacency matrix for a graph is given.
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
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
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.

16 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, 2018-03-23 (Released:2018-06-30)
参考文献数
26
被引用文献数
3
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
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.
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

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.