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

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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

鷲尾 巧

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.20, no.2, pp.154-161, 2010-06-25 (Released:2017-04-08)

参考文献数

7

著者

鷲尾 巧

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.20, no.4, pp.329-337, 2010-12-24 (Released:2017-04-08)

参考文献数

5

著者

鷲尾 巧

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.20, no.3, pp.242-249, 2010-09-24 (Released:2017-04-08)

参考文献数

4

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

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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

園田 翔

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.33, no.1, pp.4-13, 2023-03-24 (Released:2023-06-30)

参考文献数

30

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Characterization of the typical deep learning solutions is crucial to understanding and controlling deep learning. Due to the complex structure of real deep neural networks (NNs), various simplified mathematical models are employed in conventional theoretical analysis. In this study, we describe a mathematical model of a single hidden layer in an NN, which is an integral representation of NNs, and its right inverse operator (or analysis operator), the ridgelet transform. Furthermore, while the classical ridgelet transform was obtained heuristically, we had recently developed a natural technique to derive it. As an application, we succeeded in developing an NN on manifolds (noncompact symmetric spaces) and deriving the associated ridgelet transform.

著者

額田 彰

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.20, no.2, pp.125-131, 2010-06-25 (Released:2017-04-08)

参考文献数

6

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Latest GPUs have not only high computation power but also high memory bandwidth required to accelerate memory intensive computations like FFT. This paper presents a high performance FFT library for CUDA GPUs. It is important to use auto-tuning to exploit the best performance. As a result, the library achieved much higher than other existing libraries.

著者

菊地 文雄 及川 一誠

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.27, no.1, pp.36-41, 2017-03-24 (Released:2017-06-30)

参考文献数

19

被引用文献数

1

著者

高橋 大輔

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.1, pp.35-38, 2013-03-26 (Released:2017-04-08)

参考文献数

5

著者

広田 良吾

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.3, no.1, pp.48-57, 1993-03-15 (Released:2017-04-08)

被引用文献数

1

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.27, no.3, pp.7-14, 2017-09-26 (Released:2017-12-26)

参考文献数

26

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Low rank tensor estimation has a lot of applications such as recommendation system, spatiotemporal data analysis, and multi-task learning. We consider a Bayes estimator for this problem. We give theoretical analyses for the Bayes estimator and show that the Bayes estimator achieves the minimax optimal predictive accuracy. We also consider a nonparametric tensor model and a Bayes estimator for that model. It is also shown that the Bayes estimator of the nonparametric model achieves the minimax optimality. Finally, numerical experiments were conducted on restaurant evaluation data and give comparison with the Bayes estimators and other methods.

著者

吉川 周二

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.2, pp.2-9, 2020-06-24 (Released:2020-09-30)

参考文献数

9

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The energy method to derive various properties of the solution from its energy-structure of the equations is one of the classical methods for partial differential equations. When the numerical scheme also possesses the energy-structure, the energy method can be applied to the scheme in the same way. In this article we introduce an application of energy method for the structure-preserving finite difference schemes through proofs of the existence of the solution and error estimate.

著者

古賀 弘樹

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.8, no.2, pp.152-155, 1998-06-15 (Released:2017-04-08)

参考文献数

2

著者

大鶴 泰輔

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.3, pp.24-27, 2019-09-25 (Released:2019-12-26)

著者

梅野 健

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.4, pp.221-234, 2022-12-23 (Released:2023-03-31)

参考文献数

10

著者

落合 卓四郎

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.2, no.3, pp.269-272, 1992-09-16 (Released:2017-04-08)

著者

楠岡 成雄

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.5, no.2, pp.171, 1995-06-15 (Released:2017-04-08)

著者

紀 一誠

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.5, no.2, pp.145-146, 1995-06-15 (Released:2017-04-08)

著者

石井 一成

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.3, pp.220-235, 1999-09-16 (Released:2017-04-08)

参考文献数

26

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Population genetics theory of molecular evolution under a fluctuating environment was reviewed. Taking the Parity Model (a two allele model under a two state Markov environment) as a prototype model, a comprehensive picture of the stationary evolution under a joint effect of mutation, stochastic selection and random genetic drift due to a finite population size was studied both on the evolution rate and the genetic polymorphism. Besides the neutral mutaion model and the slightly deleterious model as its special cases, this model has a fluctuating evolution case where the evolution rate is approximated by the environment fluctuation rate. General formulas of evolution rate were given for the weak mutation limit and the infinitely large population case. Formula of the index of dispersion of substitution numbers was given for arbitrary jump Markov process model of wild type adaptive state. Power series solution method was developed to calculate the stationary distribution of the replicon frequency for the Parity Model.

著者

池田 正弘

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.2, pp.2-10, 2021-06-24 (Released:2021-09-30)

参考文献数

29

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In the present paper, I review our recent two papers of the joint works with Atsushi Miyauchi (Tokyo Univ.), Yuuki Takai(KIT) and Yuichi Yoshida (NII). I mainly introduce the background of their papers and the fundamental notions for community detection of networks. First I review the notion of Laplacian and Cheegerʼs inequality for the usual undirected graph. After that, I introduce the definition of the (submodular) Laplacian for hypergraphs and the heat on them. Especially, I introduce several properties of the Laplacian and heat such as maximal monotonicity of the Laplacian and well-definedness of the heat and the Personalized PageRank respectively. Moreover, I introduce the application of the properties to the community detection on hypergraphs.