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

大鋳 史男 鈴木 達也 杉本 一臣

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.12, no.1, pp.67-78, 2002-03-15 (Released:2017-04-08)

参考文献数

7

被引用文献数

1

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Several methods that distinguish between a normal and an abnormal time series have been proposed. See Iokibe [3], Kaplan and Glass [4], and Wayland, Bromley, Pickett and Passamante [7]. These methods are algorithmically complicated, and then it is hard to clear the mathematical properties of them. In this paper we propose two simple methods for the problem of classification of time series data, which are called cos analysis method (CAM) and simplified cos analysis method (SCAM). Applying the proposed methods to the artificially produced chaotic time series data and the pressure data of an extruder, we show that we may practically use the methods for checking the strangeness of machines. Furthermore, using ergodic theory, we show that the quantity derived by the simplified cos analysis method equals to -1/2, when the time series data is random.

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

江崎 信行

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.33, no.2, pp.66-79, 2023 (Released:2023-06-25)

参考文献数

13

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概要. コストの問題が大きいが校庭を芝生化する運動が盛んになりつつある.施工方法等の工夫によって低コスト化が実現可能であり,本研究では,その根拠となる芝草の成長過程を数理モデルとして記述し,数値シミュレーションによって有用性を示す.時間依存の成長係数をもつロトカ・ボルテラ方程式に対して,実践に基づくパラメタを定めるとき,低コスト化を説明する数値実験結果が得られ,実践された施工が有効であることが確認できた.

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.

著者

青木 繁 天谷 賢治

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.10, no.2, pp.121-129, 2000-06-15 (Released:2017-04-08)

参考文献数

10

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After a brief description about the ill-posed inverse problems which are discretized with the finite element method etc., a method for solving such problems is presented with a practical example. This method consists of the following procedures. 1. The singular value decomposition of the coefficient matrix is performed, and then the rank is appropriately reduced. 2. A set of solutions is represented by Moore-Penrose's solution and the null space. 3. The solution is obtained by fuzzy reasoning using the set of solutions and sets of fuzzy priori information. Following three studies are presented: a study which the Kalman filtering technique is applied to estimate the material parameters of two nonlinear constitutive equations, A method for obtaining the optimal experimental/measurement procedure for general estimation problems, and a method (GA filter) for non-linear state space estimation using genetic algorithm.

著者

三宅 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:24321982)

巻号頁・発行日

vol.8, no.2, pp.133-146, 1998-06-15 (Released:2017-04-08)

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In most cases treated in information theory, stationary memoryless/ergodic property on the system are assumed. In this paper, source coding theorems on the general information sources, which means neither stationary memoryless nor stationary ergodic property are conditioned, are considered. We clarify the following two issues: 1) What quantity can be essential in source coding problems under the general sources? 2) What are the differences between theorems under conventional stationary memoryless/ergodic condition and ones under the general sources?

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.3, pp.160-169, 2022-09-22 (Released:2022-12-26)

参考文献数

14