研究者総覧

松浦 真也 (マツウラ マサヤ)

  • 大学院理工学研究科 数理物質科学専攻 教授
Last Updated :2020/11/10

研究者情報

学位

  • 博士(工学)(東京大学)

J-Global ID

研究キーワード

  • 実験数学   時系列解析   数理工学   Experimental Mathematics   Time series Analysis   Mathematical Engineering   

研究分野

  • 情報通信 / 計算科学
  • 自然科学一般 / 応用数学、統計数学
  • 自然科学一般 / 数学基礎

学歴

  •         - 2000年   東京大学   工学系研究科   計数工学
  •         - 2000年   東京大学   Graduate School, Division of Engineering

所属学協会

  • 日本応用数理学会   日本数学会   

研究活動情報

論文

  • 髙橋 亮治, 小原 敬士, 松浦 真也
    大学教育実践ジャーナル = Journal of faculty and staff development in higher education 15 141 - 146 愛媛大学教育・学生支援機構 2017年
  • Masaya Matsuura
    Journal of Geometry 106 2 383 - 403 2015年07月 研究論文(学術雑誌) 
    © 2015, Springer Basel AG. Circles, ellipses, squares, rectangles, rhombuses and cross shapes are all special cases of Lamé curves (also known as superellipses). As a further generalization of Lamé curves, the Belgian botanist Johan Gielis introduced the notion of the so-called superformula with a view to the application to modeling and understanding the shapes of plants and animals. Despite the fact that Gielis’ superformula is expressed by a single simple equation, it can describe a wide range of various shapes, including, for example, triangle-like shapes, star-like shapes, flower-like shapes and so on. So far, it seems that most of the studies about Gielis curves (the curves generated by Gielis’ superformula) are application-oriented. In this paper, we examine precisely and analytically the mathematical structure of Gielis curves from a theoretical point of view. The original equation of the superformula has six parameters, which is too many to deal with at once. Therefore, we focus on a restricted case where the number of the parameters is reduced to three. In particular, we analyze the curvature at the “corners” and the midpoint of the “sides” of Gielis curves. We also derive the limit curves of Gielis curves and compare them with regular polygons.
  • Masaya Matsuura
    Journal for Geometry and Graphics 18 45 - 59 2014年01月 
    The curve = 1 for a, b, p > 0 in the xy-plane is called a Lamé curve. It is also known as a superellipse and is one of the symbols of Scandinavian design. For fixed a and b, the above curve expands as p increases and shrinks as p decreases. The curve converges to a rectangle as p ∞, while it converges to a cross shape as p → 0+. In general, if p > 2, Lamé curves have shapes which lie between ellipses and rectangles. From the viewpoint of application, one of the fundamental problems is to detect the "optimal" value of the exponent p which creates the "most refined" shape. With this in mind, we closely examine how the curvature of Lamé curves depends on p. In particular, we derive an explicit expression of the asymptote of the maximum curvature, which is the main result of this paper. © 2014 Heldermann Verlag.
  • Masaya Matsuura
    APPLIED MATHEMATICS AND COMPUTATION 219 3 773 - 780 2012年10月 研究論文(学術雑誌) 
    The CG method (conjugate gradient method) is one of the most important and useful algorithms for the numerical solution of linear equations. On the other hand, Burg's algorithm is an algorithm for estimating the parameters of time series models. Both algorithms are quite popular in the field of numerical calculation and time series analysis, respectively. It is less known, however, that these algorithms have a common mathematical structure. It seems that not so many researchers are familiar with both of these algorithms. Therefore, in this paper, we review these algorithms and see how they are related with each other. This leads to a notion of "anti-stationarity" in time series analysis. (C) 2012 Elsevier Inc. All rights reserved.
  • Masaya Matsuura
    LINEAR ALGEBRA AND ITS APPLICATIONS 436 9 3475 - 3479 2012年05月 研究論文(学術雑誌) 
    In this paper, we slightly generalize the notion of G-matrices, which has been recently introduced. A real nonsingular matrix A is called a G-matrix if there exist nonsingular diagonal matrices D-1 and D-2 such that D(1)A(T)D(2) = A(-1). We generalize this definition to the case where A can be singular. We say that a real matrix A, which is nor necessarily square, is a generalized G-matrix (GG-matrix) if there exist nonsingular diagonal matrices D-1 and D-2 such that D(1)A(T)D(2) is a g-inverse of A. The main purpose of this paper is to show that any generalized Cauchy matrix is a GG-matrix. (C) 2011 Elsevier Inc. All rights reserved
  • Maciej Klimek, Masaya Matsuura, Yasunori Okabe
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 342 2 816 - 829 2008年06月 研究論文(学術雑誌) 
    With the aim of understanding the mathematical structure of the fluctuation-dissipation theorem in non-equilibrium statistical physics and then constructing a mathematical principle in the modeling problem for time series analysis, we have developed the theory of KM2O-Langevin equations for discrete time stochastic processes. In this paper, as a new method for model analysis in the theory of KM2O-Langevin equations, we show that block frames provide a natural mathematical language for dealing with minimum norm expansions of multi-dimensional stochastic processes which do not necessarily satisfy stationarity and non-degeneracy conditions. (C) 2007 Elsevier Inc. All rights reserved.
  • 松浦真也
    シミュレーション 26 2 107 - 111 2007年06月
  • Sho Nakamula, Minoru Takeo, Yasunori Okabe, Masaya Matsuura
    Earth, Planets and Space 59 6 567 - 577 2007年 研究論文(学術雑誌) 
    An automatic detection and a precise picking of the arrival times of seismic waves using digital seismograms are important for earthquake early detection systems. Here we suggest a new method for detecting and picking P- and S-wave signals automatically. Compared to methods currently in use, our method requires fewer assumption with properties of the data time series. We divide a record into intervals of equal lengths and check the "local and weak stationarity" of each interval using the theory of the KM2O-Langevin equations. The intervals are stationary when these include only background noise, but the stationarity breaks abruptly when a seismic signal arrives and the intervals include both the background noise and the P-wave. This break of stationarity makes us possible to detect P-wave arrival. We expand the method for picking of S-waves. We applied our method to earthquake data from Hi-net Japan, and 90% of P-wave auto-picks were found to be within 0.1 s of the corresponding manual picks, and 70% of S-wave picks were within 0.1 s of the manual picks. This means that our method is accurate enough to use as a part of the seismic early detection systems. Copyright © The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS) The Seismological Society of Japan The Volcanological Society of Japan The Geodetic Society of Japan The Japanese Society for Planetary Sciences TERRAPUB.
  • Minoru Takeo, Hiroko Ueda, Yasunori Okabe, Masaya Matsuura
    Geophysical Journal International 165 1 87 - 107 2006年04月 研究論文(学術雑誌) 
    Since the 1970s, deep low-frequency earthquakes (DLF) with depths ranging 20-40 km have been observed just beneath the Japan Island Arc. Almost all of these earthquakes are recognized up to now have had magnitudes less than 2.5, so that we have little information concerning IDLE Employing the theory of KM2O-Langevin equations, we develop a new method to represent the characteristics of the coda parts of DLF, and propose a new concept of 'average dissipation spectrum'. The new averaging algorithm for the KM2O-Langevin matrix function was applied in the analysis of DLF (M: 1.0), which occurred in Akita prefecture on 2001 July 11, and we succeeded in separating the characteristics of the source vibration system and the source excitation process into the averaged dissipation term and the fluctuation term, respectively. The gaps between the arrival times of the fluctuation term's peaks at three stations near the epicentre are slightly different than the gaps between the S-wave arrival times. Assuming a homogenous crust structure with an S-wave velocity of 4.3 km s(-1) and assuming the depth of the second source to be the same as that of the hypocentre, the second source lies about 1.5 km, N 56 degrees E of the hypocentre. We estimate the common characteristics of this DLF successfully by using the 'average dissipation spectrum', which is made up of typical frequencies, theta(k), attenuation factors, Q(k) and amplitude factors, A(k). The common elements of (theta(k) similar to 1.5, Q(k) similar to -0.3) an (theta(k) similar to 3.25, Q(k) similar to -0.45) among all stations indicate the characteristics of the source dynamics of the Akita DLF. The major parts of the coda waves of DLF satisfy the stationary property, and the causality values for the linear and odd-degree non-linear transformations are relatively higher than those for the even-degree non-linear transformations. These characteristics are quite different from the characteristics of tectonic earthquakes. This quantitative property is common among all DLF.
  • Minoru Takeo, Hiroko Ueda, Yasunori Okabe, Masaya Matsuura
    GEOPHYSICAL JOURNAL INTERNATIONAL 165 1 87 - 107 2006年04月 研究論文(学術雑誌) 
    Since the 1970s, deep low-frequency earthquakes (DLF) with depths ranging 20-40 km have been observed just beneath the Japan Island Arc. Almost all of these earthquakes are recognized up to now have had magnitudes less than 2.5, so that we have little information concerning IDLE Employing the theory of KM2O-Langevin equations, we develop a new method to represent the characteristics of the coda parts of DLF, and propose a new concept of 'average dissipation spectrum'. The new averaging algorithm for the KM2O-Langevin matrix function was applied in the analysis of DLF (M: 1.0), which occurred in Akita prefecture on 2001 July 11, and we succeeded in separating the characteristics of the source vibration system and the source excitation process into the averaged dissipation term and the fluctuation term, respectively. The gaps between the arrival times of the fluctuation term's peaks at three stations near the epicentre are slightly different than the gaps between the S-wave arrival times. Assuming a homogenous crust structure with an S-wave velocity of 4.3 km s(-1) and assuming the depth of the second source to be the same as that of the hypocentre, the second source lies about 1.5 km, N 56 degrees E of the hypocentre. We estimate the common characteristics of this DLF successfully by using the 'average dissipation spectrum', which is made up of typical frequencies, theta(k), attenuation factors, Q(k) and amplitude factors, A(k). The common elements of (theta(k) similar to 1.5, Q(k) similar to -0.3) an (theta(k) similar to 3.25, Q(k) similar to -0.45) among all stations indicate the characteristics of the source dynamics of the Akita DLF. The major parts of the coda waves of DLF satisfy the stationary property, and the causality values for the linear and odd-degree non-linear transformations are relatively higher than those for the even-degree non-linear transformations. These characteristics are quite different from the characteristics of tectonic earthquakes. This quantitative property is common among all DLF.
  • Y Okabe, M Matsuura
    Journal of the Mathematical Society of Japan 57 4 1067 - 1076 2005年10月 研究論文(学術雑誌) 
    In this paper, we shall develop the linear causal analysis for the system consisting of two flows in a real inner product space and give an algorithm for calculating the non-linear filter for a discrete stochastic system which is given by two discrete time stochastic processes, to be called a signal process and an observation process, based upon the theory of KM2O-Langevin equations.
  • Y Okabe, M Matsuura
    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN 57 4 1067 - 1076 2005年10月 研究論文(学術雑誌) 
    In this paper, we shall develop the linear causal analysis for the system consisting of two flows in a real inner product space and give an algorithm for calculating the non-linear filter for a discrete stochastic system which is given by two discrete time stochastic processes, to be called a signal process and an observation process, based upon the theory of KM2O-Langevin equations.
  • M Matsuura
    JOURNAL OF ALGEBRA 284 2 578 - 592 2005年02月 研究論文(学術雑誌) 
    In calculations with matrices, block calculations play an important role. To elucidate the essential structures of block decompositions, we shall in this paper introduce a simple system of axioms which guarantees block calculations of rings. The axioms can be interpreted as rules of some kind of information filters. We shall also give another system of axioms in terms of idempotents which is equivalent to the above mentioned system and is similar to the Kolmogorov axioms of probability spaces. (C) 2004 Elsevier Inc. All rights reserved.
  • Chaos and KM2O-Langevin equations(共著)
    Bulletin of Informatics and Cybernetics 37 73 - 107 2005年
  • M Matsuura
    SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 27 3 654 - 664 2005年 研究論文(学術雑誌) 
    In previous papers, we have investigated degenerate stochastic processes (or more generally, degenerate flows in inner product spaces), which is important in the analysis of time series obtained from deterministic dynamical systems. In this paper, we shall generalize the results in [M. Matsuura, Methodol. Comput. Appl. Probab., 5 (2003), pp. 369 - 387] and derive recursive relations for the minimum norm coefficients of the equations which describe the time evolutions of degenerate nonstationary flows. The obtained results can be considered as recursive relations among the minimum norm least squares solutions of matrix equations.
  • Masaya Matsuura
    Electoronic Journal of Linear Algebra 10,146-154 146 - 154 2003年06月 
    In this paper, the notion of Moore-Penrose biorthogonal systems is generalized. In [Fiedler, Moore-Penrose biorthogonal systems in Euclidean spaces, Lin. Alg. Appl. 362 (2003), pp. 137-143], transformations of generating systems of Euclidean spaces are examined in connection with the Moore-Penrose inverses of their Gram matrices. In this paper, g-inverses are used instead of the Moore-Penrose inverses and, in particular, the details of transformations derived from reflexive g-inverses are studied. Furthermore, the characterization theorem of Moore-Penrose inverses in [Fiedler and Markham, A characterization of the Moore-Penrose inverse, Lin. Alg. Appl. 179 (1993), pp. 129-133] is extended to any reflexive g-inverse.
  • M Matsuura
    LINEAR ALGEBRA AND ITS APPLICATIONS 364 321 - 323 2003年05月 研究論文(学術雑誌) 
    Let A and B be any n x n real symmetric matrices. The following fact is well known: If \I-n - alphaA - betaB\ = \I-n - alphaA\\I-n - betaB\ for any alpha, beta is an element of R, then AB = 0. There exist various proofs. In this paper, we refine Olkin's method [Linear Algebra Appl. 264 (1997) 217]. Furthermore, his determinantal result is generalized. (C) 2003 Elsevier Science Inc. All rights reserved.
  • M Matsuura, Y Okabe
    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN 55 2 523 - 563 2003年04月 研究論文(学術雑誌) 
    We have developed the theory of KM2O-Langevin equations for stationary and non-degenerate flow in an inner product space. As its generalization and refinement of the results in [14], [15], [16], we shall treat in this paper a general flow in an inner product space without both the stationarity property and the non-degeneracy property. At first, we shall derive the KM2O-Langevin equation describing the time evolution of the flow and prove the fluctuation-dissipation theorem which states that there exists a relation between the fluctuation part and the dissipation part of the above KM2O-Langevin equation. Next we shall prove the characterization theorem of stationarity property, the construction theorem of a flow with any given nonnegative definite matrix function as its two-point covariance matrix function and the extension theorem of a stationary flow without losing stationarity property.
  • On a method for detecting certain signs of stock market crashes by non-linear stationarity tests(共著)
    International Journal of Pure and Applied Mathematics 3 4 443 - 484 2003年
  • On a new fluctuation-dissipation theorem for degenerate stationary flows
    Methodology and Computing in Applied Probability 5,369-387 2003年
  • On the theory of KM2-Langerin equations for non-stationary degenerate flows(共著)
    Journal of the Mathematical Society of Japan 55 2 523 - 563 2003年
  • Maciej Klimek, Erlendur Karlsson, Masaya Matsuura, Yasunori Okabe
    Hokkaido Mathematical Journal 31 3 615 - 628 2002年 研究論文(学術雑誌) 
    We give a short proof, based on the geometry of inner product spaces, of the fluctuation-dissipation theorem that asserts applicability of the Whittle-Wiggins-Robinson algorithm in the context of the KM2O-Langevin equations also in degenerate and non-stationary cases. © 2002 by the University of Notre Dame. All rights reserved.
  • Masaya Matsuura, Yasunori Okabe
    Japanese Journal of Mathematics 27 1 51 - 112 2001年 研究論文(学術雑誌)
  • Yasunori Okabe, Masaya Matsuura
    Hokkaido Mathematical Journal 29 2 369 - 382 2000年 研究論文(学術雑誌) 
    In this paper, we prove an extension theorem for a given stationary flow from the pointview of the fluctuation-dissipation theorem and apply it to an extension problem for a given positive definite matrix function with Toeplitz condition defined on a finite set. © 2000 by the University of Notre Dame. All rights reserved.

講演・口頭発表等

MISC

  • Minoru Takeo, Hiroko Ueda, Yasunori Okabe, Masaya Matsuura Geophysical Journal International 165 (1) 87 -107 2006年04月 
    Since the 1970s, deep low-frequency earthquakes (DLF) with depths ranging 20-40 km have been observed just beneath the Japan Island Arc. Almost all of these earthquakes are recognized up to nowhave had magnitudes less than 2.5, so that we have little information concerning DLF. Employing the theory of KM2O-Langevin equations, we develop a new method to represent the characteristics of the cod a parts of DLF, and propose a new concept of 'average dissipation spectrum'. Th e new averaging algorithm for the KM2O-Langevin matrix function was applied in the analysis of DLF (M: 1.0), which occurred in Akita prefecture on 2001 July 11, and we succeeded in separating the characteristics of the source vibration system and the source excitation process into the averaged dissipation term and the fluctuation term, respectively. The gaps between the arrival times of the fluctuation term's peaks at three stations near the epicentre are slightly different than the gaps between the S-wave arrival times. Assuming a homogenous crust structure with an S-wave velocity of 4.3 km s-1 and assuming the depth of the second source to be the same as that of the hypocentre, the second source lies about 1.5 km, N 56°E of the hypocentre. We estimate the common characteristics of this DLF successfully by using the 'average dissipation spectrum', which is made up of typical frequencies, θk, attenuation factors, Qkk and amplitude factors, Ak. The common elements of (θk ∼ 1.5, Qk ∼ -0.3) and (θk ∼ 3.25, Qk ∼-0.45) among all stations indicate the characteristics of the source dynamics of the Akita DLF. The major parts of the cod a waves of DLF satisfy the stationary property, and the causality values for the linear and odd-degree non-linear transformations are relatively higher than those for the even-degree non-linear transformations. These characteristics are quite different from the characteristics of tectonic earthquakes. This quantitative property is common among all DLF. © 2006 The Authors Journal compilation © 2006 RAS.
  • Yasunori Okabe, Masaya Matsuura Journal of the Mathematical Society of Japan 57 (4) 1067 -1076 2005年10月 
    In this paper, we shall develop the linear causal analysis for the system consisting of two flows in a real inner product space and give an algorithm for calculating the non-linear filter for a discrete stochastic system which is given by two discrete time stochastic processes, to be called a signal process and an observation process, based upon the theory of KM2O-Langevin equations.
  • Chaos and KM2O-Langevin equations(jointly worked)
    Bulletin of Informatics and Cybernetics 37 73 -107 2005年
  • On a method for detecting certain signs of stock market crashes by non-linear stationarity tests(jointly worked)
    International Journal of Pure and Applied Mathematics 3 (4) 443 -484 2003年
  • On the theory of KM2O-Langerin equations for non-stationary degenerate flows(jointly worked)
    Journal of the Mathematical Society of Japan 55 (2) 523 -563 2003年
  • A geometric proof of the fluctuation-dissipation theorem for the KM2O-Langevin equation(jointly worked)
    Hokkaido Mathematical Journal 31 (3) 615 -628 2002年
  • On a non-linear prediction problem for one-dimensional stochastic processes(jointly worked)
    Japanese Journal of Mathematics 27 (1) 51 -112 2001年
  • On the theory of KM2O-Langevin equations for stationary flows(3) : extension theorem(jointly worked)
    Hokkaido Mathematical Journal 29 (2) 369 -382 2000年

共同研究・競争的資金等の研究課題

  • 数理閉曲線・曲面を用いたデザイン支援システムの開発
    日本学術振興会:科学研究費助成事業 基盤研究(C)
    研究期間 : 2015年04月 -2019年03月 
    代表者 : 松浦 真也
  • Mathematical Finance
    Cooperative Research
  • Non-linear Time Series Analysis
    Cooperative Research
  • The theory of KM2O-Langevin Equations
    Cooperative Research

社会貢献活動

  • 愛媛県高等学校教育研究会数学部会顧問
    期間 : 2015年04月 - 現在
    役割 : 助言・指導
  • 出張講義「パズルの数理」
    期間 : 2017年11月06日
    役割 : 講師
    主催者・発行元 : 新田青雲中等教育学校
  • 松山東高校SGH課題研究「スウェーデンと日本の比較分析」
    期間 : 2016年04月 - 2017年09月
    役割 : 助言・指導
    主催者・発行元 : 松山東高校
  • 出張講義「パズルの数理」
    期間 : 2016年12月12日
    役割 : 講師
    主催者・発行元 : 宇和島南中等教育学校
  • 松山東高校SGH課題研究「データで比べるスウェーデンと日本」
    期間 : 2015年09月 - 2016年03月
    役割 : 助言・指導
    主催者・発行元 : 松山東高校

愛媛大学教員活動実績

教育活動(B)

担当授業科目(B01)

  • 2019, 前期, 学部, 微積分
  • 2019, 前期, 学部, 卒業研究Ⅰ
  • 2019, 前期, 学部, 数理情報の基礎
  • 2019, 前期, 学部, 数理情報の基礎
  • 2019, 前期, 博士, 数理科学特論ⅩⅡ


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