40 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
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
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
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
富安(大石) 亮子
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.3, pp.4-16, 2016 (Released:2016-12-26)
参考文献数
23

When P ⊂ ℝ3 is a periodic point set with the period lattice L, an efficient method to determine the quadratic form of L ⊂ ℝ3 (more precisely, its equivalence class over ℤ.) from the average theta series of P has a practical application to the problem known as “powder indexing” in crystallography. By using “topographs” defined in the reduction theory of quadratic forms, we succeeded in developing an algorithm robust against loss and errors of information due to observational problems, suppressing the computation time. We introduce how the topographs were used in the method.
著者
石田 祥子 萩原 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.26, no.1, pp.15-21, 2016 (Released:2016-07-27)
参考文献数
23

Conformal maps are applied for designing foldable forms. This method is able to produce the complicated developed patterns for the geometrical forms such as cones, disks, and tori with different main curvatures from the simple developed patterns for cylinders that are already known, based on the similarity of the quadrilateral elements that determine regular fold lines.
著者
住井 英二郎
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.17, no.4, pp.280-290, 2007-12-26 (Released:2017-04-08)
参考文献数
15

This survey presents Abadi and Gordon's spi-calculus, which is a "process calculus" (i.e., a formal language of concurrent computation) for the verification of "cryptographic protocols" (i.e., procedures for secure communication in computer networks). First, we present process calculi before the spi-calculus (CCS and the pi-calculus), introducing the notion of reaction relation and structural congruence. We then define the spi-calculus and show an example of cryptographic ptotocols, represented as a class of spi-calculus processes. After discussing the formalization of security properties (secrecy and authenticity) and multiple sessions, we conclude by referring to generalizations of the spi-calculus (Abadi and Fournet's applied pi-calculus, and a recent result by Bruno Blanchet).