10 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:09172270)
巻号頁・発行日
vol.2, no.1, pp.37-56, 1992-03-16
被引用文献数
3 or 0

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
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
松谷 茂樹
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.13, no.1, pp.48-60, 2003-03-25
被引用文献数
1 or 0

In 1691, James Bernoulli proposed the following problem called elastica problem : "What shape of elastica, an ideal thin elastic rod in a plane, is allowed ?" Euler essentially solved the problem in 1744 by developing studies of variation problem and elliptic function theory. Their studies are regarded as prototypes of harmonic map theory, nonlinear differential theory, soliton theory, differential geometry, algebraic geometry, theory of moduil of elliptic curves and so on. In this article we mention their mathematical meaning with their historical background from viewpoint of pure and applied mathematics : Their studies started from concreteness to abstractand they applied constructed abstract theory to the concrete problem. We also introduce a current study of statistical mechanics of elasticas, which might be settled by knowledge of hyperelliptic function theory.
著者
菊池 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:09172270)
巻号頁・発行日
vol.12, no.2, pp.104-108, 2002-06-15
被引用文献数
6 or 0

As an introduction to the special topics section of traffic flow problem, a brief history of mathematical researches in this area is described. Some basic concepts, such as a q-k diagram, are introduced at the same time.
著者
蔵本 由紀
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.175-177, 2007-06-26
著者
行木 孝夫
出版者
日本応用数理学会
雑誌
応用数理 (ISSN:09172270)
巻号頁・発行日
vol.13, no.2, pp.125-136, 2003-06

ライフゲームに代表されるセルオートマトンは簡明な定義からなる系であ りながら多様な挙動を示すものとして広く研究されてきた。 本稿では エルゴード理論、力学系のごく簡単な導入を行い、 エントロピーや変分原理など関連する事項を整理するとともに 力学系としてのセルオートマトンの特徴を明らかにする。
著者
神保 秀一
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.11, no.2, pp.152-162, 2001-06-15

本稿ではギンツブルグ・ランダウ方程式(以下GL方程式と呼ぶ)およびボルテクス(vortex)についての偏微分方程式の立場からの近年の研究について述べる.GL方程式は物理において超伝導や超流動の現象で電流や流体の状態を記述する方程式として現れる.ボルテクスはこれらの流れの停留する点であり,また,その近傍にエネルギーが偏在する点でもあり,状態を特徴付ける重要な性質である.一方,ボルテクスは数学的には解の関数(Φ=Φ(x))のゼロ点に対応するが,解としての幾何的な性質を特徴付ける興味ある対象である.また,解の安定性や大域的な性質を調べるうえでも手がかりとなるので重要である.その解析のために非線型解析の方法が華々しく応用される.特にGL方程式のなかの小さいパラメータの極限(特異摂動)において,ボルテクスの挙動を求める研究が注目を集めている.このような事情でGL方程式は近年(90年以降)ホットな研究テーマであり続けている.
著者
村木 尚文
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.13, no.2, pp.137-149, 2003-06-25

One of the main features of quantum probability(=noncommutative probability) is the diversity of notions of 'independence' for noncommutative random variables. Besides the three fundamental examples of universal independence (tensor, free and Boolean independence), there is another example called 'monotone independence' which was introduced and studied by the author. We give a brief review on 'monotone probability' which can be developed based on the notion of monotone independence. Especially we present the monotonic analogue of central limit theorem, law of small numbers, convolution, infinite divisibility and Levy-Hincin formula. Furthermore, we give a classification theorem for universal notions of independence.
著者
牧野 淳一郎
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.8, no.4, pp.277-287, 1998-12-15 (Released:2017-04-08)
参考文献数
18

I overview the Fast Multipole Method (FMM) and the Barnes-Hut tree method. These algorithms evaluate mutual gravitational interaction between N particles in O(N) or O(N log N) times, respectively. I present basic algorithms as well as recent developments, such as Anderson's method of using Poisson's formula, the use of FFT, and other optimization techniques. I also summarize the current states of two algorithms. Though FMM with O(N) scaling is theoretically preferred over O(N log N) tree method, comparisons of existing implementations proved otherwise. This result is not surprizing, since the calculation cost of FMM scales as O(Np^2) where p is the order of expansion, while that of the tree method scales as O(N log Np).
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:09172270)
巻号頁・発行日
vol.25, no.2, pp.50-58, 2015-06-25

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
柳澤 大地 西成 活裕
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.1, pp.2-14, 2012-03-27

Jamology is a new scientific and engineering research, which deals with flow and jam of every self-driven particle in the world. One of the most famous models used in Jamology is Cellular Automaton (CA), where time, space, and state are discrete. In this paper, we introduce the essence and the contribution of CA models in Jamology. Traffic CA models succeed to reproduce meta-stable state, which is an essential phenomenon in real traffic, and show some results which can be applied to ease congestion at junctions and weaving sections. Besides, collaboration of CA and Queueing theory creates a new queueing model which gives us mathematically-exact solution useful for application. Furthermore, two dimensional CA models for pedestrians are extended in many ways to study how the specific characteristics of pedestrians affect on their flow. In the last section of the paper, we also discuss the scope of application of CA models.