Updated on 2024/02/02

写真a

 
TAKAMATSU Mizuyo
 
Organization
Faculty of Science and Engineering Professor
Other responsible organization
Information and System Engineering Course of Graduate School of Science and Engineering, Master's Program
Electrical Engineering and Information Systems Course of Graduate School of Science and Engineering, Doctoral Program
Contact information
The inquiry by e-mail is 《here
External link

Degree

  • 博士(情報理工学) ( 東京大学 )

  • 修士(情報理工学) ( 東京大学 )

Education

  • 2010.3
     

    The University of Tokyo   Graduate School of Information Science and Technology   doctor course   completed

  • 2007.3
     

    The University of Tokyo   Graduate School of Information Science and Technology   master course   completed

  • 2005.3
     

    The University of Tokyo   Faculty of Engineering   graduated

  • 2001.3
     

    女子学院高等学校   graduated

Research History

  • 2022.4 -  

    中央大学理工学部教授

  • 2013.4 - 2022.3

    中央大学理工学部情報工学科准教授

  • 2010.4 - 2013.3

    中央大学理工学部情報工学科助教

Professional Memberships

  • 日本オペレーションズ・リサーチ学会

  • 日本応用数理学会

  • 日本都市計画学会

Research Interests

  • オペレーションズ・リサーチ

  • 数理工学

  • 最適化

Research Areas

  • Informatics / Mathematical informatics  / Mathematical Informatics

Papers

  • Optimizing train stopping patterns for congestion management

    Tatsuki Yamauchi, Mizuyo Takamatsu, Shinji Imahori

    Public Transport   15 ( 1 )   1 - 29   2023.3

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    Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

    DOI: 10.1007/s12469-021-00286-w

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    Other Link: https://link.springer.com/article/10.1007/s12469-021-00286-w/fulltext.html

  • Bus timetable design to ensure smooth transfers in areas with low-frequency public transportation services Reviewed

    M. Takamatsu, A. Taguchi

    Transportation Science   54   1238 - 1250   2020

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1287/trsc.2019.0918

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  • Index reduction for differential-algebraic equations with mixed matrices Reviewed

    S. Iwata, T. Oki, M. Takamatsu

    Journal of the ACM   66 ( 5 )   35:1 - 35:34   2019.8

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1145/3341499

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  • Index reduction via unimodular transformations Reviewed

    S. Iwata, M. Takamatsu

    SIAM Journal on Matrix Analysis and Applications   39 ( 3 )   1135 - 1151   2018.7

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1137/17M111794X

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  • 交通状況による遅延を考慮し円滑な乗換を保証するバス時刻表の設計―静岡県富士市の公共交通設計への最適化技術の活用 Reviewed

    田中健裕, 高松瑞代, 菅原宏明, 田口 東

    都市計画論文集   52 ( 3 )   1320 - 1326   2017.10

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    Language:Japanese   Publishing type:Research paper (scientific journal)   Publisher:The City Planning Institute of Japan  

    Trains and buses are the most important means of transportation in suburban cities in Japan. It is common for passengers to change buses and/or trains to get to their destination, but buses usually do not arrive at bus stops on time because of traffic congestion. In this paper, we design bus timetables which ensure smooth transfer and avoid delay propagation in Fuji city. Since the train and bus network in Fuji City is intricate, we need to determine arrival/departure time of each bus with the aim of optimizing the whole of the network. We construct a time-space network from the train and bus timetables in Fuji City, and present a mathematical optimization model to design bus timetables with delay scenarios generated based on site investigation and data analysis.

    DOI: 10.11361/journalcpij.52.1320

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  • Optimizing train stopping patterns for congestion management Reviewed

    Tatsuki Yamauchi, Mizuyo Takamatsu, Shinji Imahori

    OpenAccess Series in Informatics   59 ( 13 )   2017.9

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing  

    In this paper, we optimize train stopping patterns during morning rush hour in Japan. Since trains are extremely crowded, we need to determine stopping patterns based not only on travel time but also on congestion rates of trains. We exploit a Wardrop equilibrium model to compute passenger flows subject to congestion phenomena and present an efficient local search algorithm to optimize stopping patterns which iteratively computes a Wardrop equilibrium. We apply our algorithm to railway lines in Tokyo including Keio Line with six types of trains and succeed in relaxing congestion with a small effect on travel time.

    DOI: 10.4230/OASIcs.ATMOS.2017.13

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  • 通勤時間帯の駅構内における購買行動の数理モデル Reviewed

    田口東, 高松瑞代

    日本応用数理学会論文誌   27 ( 2 )   147 - 161   2017.6

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  • Index reduction via unimodular transformations Reviewed

    S. Iwata, M. Takamatsu

    Proceedings of the 10th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications   39 ( 3 )   257 - 266   2017.5

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    DOI: 10.1137/17M111794X

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  • ON THE KRONECKER CANONICAL FORM OF SINGULAR MIXED MATRIX PENCILS Reviewed

    Satoru Iwata, Mizuyo Takamatsu

    SIAM JOURNAL ON CONTROL AND OPTIMIZATION   55 ( 3 )   2134 - 2150   2017

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SIAM PUBLICATIONS  

    Consider a linear time-invariant dynamical system that can be described as Fx(t) = Ax(t) + Bu(t), where A, B, and F are mixed matrices, i.e., matrices having two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. The controllable subspace of the system is closely related to the Kronecker canonical form of the mixed matrix pencil (A - sF | B). Under a physically meaningful assumption justi fied by the dimensional analysis, we provide a combinatorial characterization of the sums of the minimal row/column indices of the Kronecker canonical form of mixed matrix pencils. The characterization leads to a matroid-theoretic algorithm for efficiently computing the dimension of the controllable subspace for the system with nonsingular F.

    DOI: 10.1137/16M1057516

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  • Train and bus timetable design to ensure smooth transfer in areas with low-frequency public transportation services Reviewed

    M. Takamatsu, A. Taguchi

    Proceedings of the 6th International Conference on Railway Operations Modelling and Analysis   ( 34 )   034 - 1-034-20   2015.3

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  • Structural characterization of hybrid equations with tractability index at most two Reviewed

    Mizuyo Takamatsu

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS   411 ( 2 )   639 - 651   2014.3

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    In circuit simulation, differential-algebraic equations (DAEs) to be solved numerically are obtained through circuit analysis methods. While the modified nodal analysis (MNA) is the most popular method, the hybrid analysis has been shown to have inherent advantage over MNA in terms of index, which is a measure of the numerical difficulty of DAEs. A recent paper of Iwata, Takamatsu, and Tischendorf (2012) has characterized the network structure that leads to DAEs with tractability index zero and one in the hybrid analysis. As a sequel, this paper gives a necessary condition for the hybrid equations to have tractability index at most two. Moreover, we show that this condition is also sufficient for linear time-invariant circuits if dependent sources satisfy a genericity assumption. Since commonly-used circuits fulfill the condition, it is ensured that the hybrid analysis results in a DAE with tractability index at most two in most cases. By combining our results with the previous one, we obtain criteria for tractability index zero/one/two. (C) 2013 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jmaa.2013.10.018

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  • MATCHING PROBLEMS WITH DELTA-MATROID CONSTRAINTS Reviewed

    Naonori Kakimura, Mizuyo Takamatsu

    SIAM JOURNAL ON DISCRETE MATHEMATICS   28 ( 2 )   942 - 961   2014

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SIAM PUBLICATIONS  

    Given an undirected graph G = (V, E) and a delta-matroid (V, F), the delta-matroid matching problem is to find a maximum cardinality matching M such that the set of the end vertices of M belongs to F. This problem is a natural generalization of the matroid matching problem to delta-matroids, and thus it cannot be solved in polynomial time in general. This paper introduces a class of the delta-matroid matching problem, where the given delta-matroid is a projection of a linear delta-matroid. We first show that it can be solved in polynomial time if the given linear delta-matroid is generic. This result enlarges a polynomially solvable class of matching problems with precedence constraints on vertices such as the 2-master/slave matching. In addition, we design a polynomial-time algorithm when the graph is bipartite and the delta-matroid is defined on one vertex side. This result is extended to the case where a linear matroid constraint is additionally imposed on the other vertex side.

    DOI: 10.1137/110860070

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  • Computing the Maximum Degree of Minors in Mixed Polynomial Matrices via Combinatorial Relaxation Reviewed

    Satoru Iwata, Mizuyo Takamatsu

    ALGORITHMICA   66 ( 2 )   346 - 368   2013.6

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER  

    Mixed polynomial matrices are polynomial matrices with two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. The computation of their maximum degrees of minors is known to be reducible to valuated independent assignment problems, which can be solved by polynomial numbers of additions, subtractions, and multiplications of rational functions. However, these arithmetic operations on rational functions are much more expensive than those on constants.
    In this paper, we present a new algorithm of combinatorial relaxation type. The algorithm finds a combinatorial estimate of the maximum degree by solving a weighted bipartite matching problem, and checks if the estimate is equal to the true value by solving independent matching problems. The algorithm mainly relies on fast combinatorial algorithms and performs numerical computation only when necessary. In addition, it requires no arithmetic operations on rational functions. As a byproduct, this method yields a new algorithm for solving a linear valuated independent assignment problem.

    DOI: 10.1007/s00453-012-9640-8

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  • On the Kronecker canonical form of singular mixed matrix pencils Reviewed

    S. Iwata, M. Takamatsu

    Proceedings of the 8th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications   261 - 270   2013.6

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  • PASMOデータを用いた鉄道利用者の購買行動分析 Reviewed

    高松瑞代, 田口東, 服部優奈, 太田雅文, 末松孝司

    オペレーションズ・リサーチ   58 ( 1 )   37 - 46   2013.1

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  • 低頻度な公共交通網を有する地域の移動利便性の評価手法に関する研究 ―時空間ネットワークを用いた公共交通網と都市構造の関連分析 Reviewed

    赤星健太郎, 高松瑞代, 田口東, 石井儀光, 小坂知義

    都市計画論文集   47 ( 3 )   847 - 852   2012.10

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  • TRACTABILITY INDEX OF HYBRID EQUATIONS FOR CIRCUIT SIMULATION Reviewed

    Satoru Iwata, Mizuyo Takamatsu, Caren Tischendorf

    MATHEMATICS OF COMPUTATION   81 ( 278 )   923 - 939   2012.4

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:AMER MATHEMATICAL SOC  

    Modern modeling approaches for circuit simulation such as the modified nodal analysis (MNA) lead to differential-algebraic equations (DAEs). The index of a DAE is a measure of the degree of numerical difficulty. In general, the higher the index is, the more difficult it is to solve the DAE.
    In this paper, we consider a broader class of analysis methods called the hybrid analysis. For nonlinear time-varying circuits with general dependent sources, we give a structural characterization of the tractability index of DAEs arising from the hybrid analysis. This enables us to determine the tractability index efficiently, which helps to avoid solving higher index DAEs in circuit simulation.

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  • Matching problems with delta-matroid constraints Reviewed

    N. Kakimura, M. Takamatsu

    Proceedings of the 18th Computing: the Australasian Theory Symposium (CATS 2012)   83 - 92   2012.1

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  • Netal: High-performance implementation of network analysis library considering computer memory hierarchy Reviewed

    Yuichiro Yasui, Katsuki Fujisawa, Kazushige Goto, Naoyuki Kamiyama, Mizuyo Takamatsu

    Journal of the Operations Research Society of Japan   54 ( 4 )   259 - 280   2011.12

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    Language:English   Publishing type:Research paper (international conference proceedings)  

    The use of network analysis has increased in various fields. In particular, a lot of attention has been paid to centrality metrics using shortest paths, which require a comparatively smaller amount of computation, and the global characteristic features within the network. While theoretical and experimental progress has enabled greater control over networks, large amounts of computation required for dealing with large-scale networks is a major hurdle. This research is on high-performance network analysis considering the memory hierarchy in a computer; it targets extremely important kernel types called shortest paths and centrality. Our implementation, called NETAL (NETwork Analysis Library), can achieve high efficiency in parallel processing using many-core processors such as the AMD Opteron 6174, which has the NUMA architecture. We demonstrated through tests on real-world networks that NETAL is faster than previous implementations. In the all-pairs shortest paths for the weighted graph USA-road-d. NY. gr (n. -264K, m -734K), our implementatioll solved the shortest path distance labels in 44.4 seconds and the shortest paths with multiple predecessors in 411.2 seconds. Compared with the 9th DJMACS benchmark solver, our implementation is, respectively, 302.7 times and 32.7 times faster. NETAL succeeded in solving the shortest path distance labels for the USA-road-d.IJSA.gr (ii =24M, m =581V1) without preprocessing in 7.75 days. Numerical results showed that our implementation performance was 432.4 times that of the Δ-stepping algorithm and 228.9 times that of the 9th DIMACS benchmark solver. Furthermore, while GraphCT took 18 hours to compute the betweenness of web-BerkStan, our implementation computed multiple centrality metncs (closeness, graph, stress, and betweenness) simultaneously within 1 hour. A performance increase of 2.4-3.7 times compared with R-MAT graph was confirmed for SSCA#2. © The Operations Research Society of Japan.

    DOI: 10.15807/jorsj.54.259

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  • On the Kronecker canonical form of mixed matrix pencils Reviewed

    S. Iwata, M. Takamatsu

    Proceedings of the 7th Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications   427 - 436   2011.5

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  • Computing the Maximum Degree of Minors in Mixed Polynomial Matrices via Combinatorial Relaxation Reviewed

    Satoru Iwata, Mizuyo Takamatsu

    INTEGER PROGRAMMING AND COMBINATORAL OPTIMIZATION, IPCO 2011   6655   274 - 286   2011

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:SPRINGER-VERLAG BERLIN  

    Mixed polynomial matrices are polynomial matrices with two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. The computation of their maximum degrees of minors is known to be reducible to valuated independent assignment problems, which can be solved by polynomial numbers of additions, subtractions, and multiplications of rational functions. However, these arithmetic operations on rational functions are much more expensive than those on constants.
    In this paper, we present a new algorithm of combinatorial relaxation type. The algorithm finds a combinatorial estimate of the maximum degree by solving a weighted bipartite matching problem, and checks if the estimate is equal to the true value by solving independent matching problems. The algorithm mainly relies on fast combinatorial algorithms and performs numerical computation only when necessary. In addition, it requires no arithmetic operations on rational functions. As a byproduct, this method yields a new algorithm for solving a linear valuated independent assignment problem.

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  • ON THE KRONECKER CANONICAL FORM OF MIXED MATRIX PENCILS Reviewed

    Satoru Iwata, Mizuyo Takamatsu

    SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS   32 ( 1 )   44 - 71   2011

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    A mixed matrix pencil is a matrix pencil with two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. In this paper, the indices of nilpotency of the Kronecker canonical form for a mixed matrix pencil are characterized in terms of matroids. As a byproduct, this provides an algorithm for computing the rank of a power product of a square mixed matrix.

    DOI: 10.1137/100783315

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  • Index characterization of differential-algebraic equations in hybrid analysis for circuit simulation Reviewed

    Mizuyo Takamatsu, Satoru Iwata

    INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS   38 ( 4 )   419 - 440   2010.5

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:JOHN WILEY & SONS LTD  

    Modern modeling approaches in circuit simulation naturally lead to differential algebraic equations (DAEs). The index of a DAE is a measure of the degree of numerical difficulty. In general, the higher the index, the more difficult it is to solve the DAE. The modified nodal analysis (MNA) is known to yield a DAE with index at most two in a wide class of nonlinear time-varying electric circuits.
    In this paper, we consider a broader class of analysis method called the hybrid analysis. For linear time-invariant RLC circuits, we prove that the index of the DAE arising from the hybrid analysis is at most one, and give a structural characterization for the index of a DAE in the hybrid analysis. This yields an efficient algorithm for finding an optimal hybrid analysis in which the index of the DAE to be solved attains zero. Finally, for linear time-invariant electric circuits that may contain dependent sources, we prove that the optimal hybrid analysis by no means results in a higher index DAE than MNA. Copyright (C) 2008 John Wiley & Sons, Ltd.

    DOI: 10.1002/cta.577

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  • Index minimization of differential-algebraic equations in hybrid analysis for circuit simulation Reviewed

    Satoru Iwata, Mizuyo Takamatsu

    MATHEMATICAL PROGRAMMING   121 ( 1 )   105 - 121   2010.1

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER  

    Modern modeling approaches for circuit analysis lead to differential-algebraic equations (DAEs). The index of a DAE is a measure of the degree of numerical difficulty. In general, the higher the index is, the more difficult it is to solve the DAE. The index of the DAE arising from the modified nodal analysis (MNA) is determined uniquely by the structure of the circuit. Instead, we consider a broader class of analysis method called the hybrid analysis. For linear time-invariant electric circuits, we devise a combinatorial algorithm for finding an optimal hybrid analysis in which the index of the DAE to be solved attains the minimum. The optimal hybrid analysis often results in a DAE with lower index than MNA.

    DOI: 10.1007/s10107-008-0227-8

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  • Hybrid Analysis of Nonlinear Time-Varying Circuits Providing DAEs with Index at Most One Reviewed

    Satoru Iwata, Mizuyo Takamatsu, Caren Tischendorf

    SCIENTIFIC COMPUTING IN ELECTRICAL ENGINEERING SCEE 2008   14   151 - +   2010

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:SPRINGER-VERLAG BERLIN  

    Commercial packages for transient circuit simulation are often based on the modified nodal analysis (MNA) which allows an automatic setup of model equations and requires a nearly minimal number of variables. However, it may lead to differential-algebraic equations (DAEs) with higher index. Here, we present a hybrid analysis for nonlinear time-varying circuits leading to DAEs with index at most one. This hybrid analysis is based merely on the network topology, which possibly leads to an automatic setup of the hybrid equations from netlists. Moreover, we prove that the minimum index of the DAE arising from the hybrid analysis never exceeds the index from MNA. As a positive side effect, the number of equations from the hybrid analysis is always no greater than that one from MNA. This suggests that the hybrid analysis is superior to MNA in numerical accuracy and computational effort.

    DOI: 10.1007/978-3-642-12294-1_20

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  • Matroidal characterization on index of DAEs in hybrid analysis for general circuits Reviewed

    S. Iwata, M. Takamatsu, C. Tischendorf

    Proceedings of the 6th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications   351 - 360   2009.5

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  • Computing the degrees of al l cofactors in mixed polynomial matrices Reviewed

    Satoru Iwata, Mizuyo Takamatsu

    SIAM Journal on Discrete Mathematics   23 ( 2 )   647 - 660   2009

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    A mixed polynomial matrix is a polynomial matrix which has two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. This paper presents an algorithm for computing the degrees of all cofactors simultaneously in a regular mixed polynomial matrix. The algorithm is based on the valuated matroid intersection and all pair shortest paths. The technique is also used for improving the running time of the algorithm for minimizing the index of the differential-algebraic equation in the hybrid analysis for circuit simulation. © 2009 Society for Industrial and Applied Mathematics.

    DOI: 10.1137/070706021

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  • COMPUTING THE DEGREES OF ALL COFACTORS IN MIXED POLYNOMIAL MATRICES Reviewed

    Satoru Iwata, Mizuyo Takamatsu

    SIAM JOURNAL ON DISCRETE MATHEMATICS   23 ( 2 )   647 - 660   2009

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SIAM PUBLICATIONS  

    A mixed polynomial matrix is a polynomial matrix which has two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. This paper presents an algorithm for computing the degrees of all cofactors simultaneously in a regular mixed polynomial matrix. The algorithm is based on the valuated matroid intersection and all pair shortest paths. The technique is also used for improving the running time of the algorithm for minimizing the index of the differential-algebraic equation in the hybrid analysis for circuit simulation.

    DOI: 10.1137/070706021

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  • Index reduction for differential-algebraic equations by substitution method Reviewed

    Mizuyo Takamatsu, Satoru Iwata

    LINEAR ALGEBRA AND ITS APPLICATIONS   429 ( 8-9 )   2268 - 2277   2008.10

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ELSEVIER SCIENCE INC  

    Differential-algebraic equations (DAEs) naturally arise in many applications, but present numerical and analytical difficulties. The index of a DAE is a measure of the degree of numerical difficulty. In general, the higher the index is, the more difficult it is to solve the DAE. Therefore, it is desirable to transform the original DAE into an equivalent DAE with lower index.
    In this paper, we propose an index reduction method for linear DAEs with constant coefficients. The method is applicable to any DAE having at most one derivative per equality. In contrast to the other existing methods, it does not introduce any additional variables. Exploiting a combinatorial property of degrees of minors in polynomial matrices, we show that the method always reduces the index exactly by one. Thus the paper exhibits an application of combinatorial matrix theory to numerical analysis of DAEs. (C) 2008 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.laa.2008.06.025

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  • Index reduction for differential-algebraic equations in circuit simulation Reviewed

    M. Takamatsu, S. Iwata

    第20回 回路とシステム軽井沢ワークショップ論文集   35 - 40   2007.4

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    Language:Japanese   Publishing type:Research paper (conference, symposium, etc.)   Publisher:電子情報通信学会  

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  • Computing degrees of all cofactors in mixed polynomial matrices Reviewed

    S. Iwata, M. Takamatsu

    Proceedings of the 5th Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications   156 - 165   2007.4

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  • Index minimization of differential-algebraic equations in hybrid analysis for circuit simulation Reviewed

    S. Iwata, M. Takamatsu

    Proceedings of the 5th Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications   128 - 137   2007.4

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  • Analysis of a nonlinear system using interval arithmetic: computation of an output admissible set Reviewed

    M. Takamatsu, Y. Oishi, K. Hirata

    計測自動制御学会論文集   42 ( 12 )   1320 - 1327   2006.12

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:計測自動制御学会  

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▼display all

Books

  • 応用がみえる線形代数

    高松, 瑞代

    岩波書店  2020.2  ( ISBN:9784000051316

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    Total pages:ix, 211p   Language:Japanese  

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  • セジウィック:アルゴリズムC 第5部 グラフアルゴリズム

    田口 東, 高松 瑞代, 高澤 兼二郎( Role: Joint translator ,  Original_author: R.セジウィック)

    2021.11 

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MISC

  • 公共交通の時空間ネットワークと最適化

    高松瑞代

    数理科学   677   7 - 13   2019.11

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    Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (trade magazine, newspaper, online media)  

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  • 線形代数はどこで使われているか

    高松瑞代

    大学数学の質問箱   75 - 79   2019.5

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    Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (trade magazine, newspaper, online media)   Publisher:日本評論社  

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  • 線形代数はどこで使われているか

    高松瑞代

    数学セミナー   55 ( 6 )   35 - 39   2016.6

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    Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (trade magazine, newspaper, online media)  

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  • Discrete Optimization Approach to Index Reduction for Differential-Algebraic Equations

    [O]perations research as a management science [r]esearch   53 ( 1 )   53 - 54   2008.1

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    Language:Japanese   Publisher:The Operations Research Society of Japan  

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Presentations

  • 組合せ緩和を利用した微分代数方程式の指数減少法 Invited

    高松瑞代

    RIMS共同研究「数値解析が拓く次世代情報社会~エッジから富岳まで~」  2022.10 

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  • つながる高知県路線バスネットワークの設計: シュタイナー連結性問題によるモデル化と実験的考察

    荒川兼次, 田口東, 石井儀光, 赤星健太郎

    日本オペレーションズ・リサーチ学会2020年春季研究発表会  2020.3 

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  • バイクシェアリングシステムにおける需要予測とポート配置の最適化

    寺田大樹

    日本オペレーションズ・リサーチ学会2020年春季研究発表会  2020.3 

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  • 利用者均衡配分に基づく時間帯別列車運行計画の最適化

    山内達貴, 高松瑞代, 今堀慎治

    日本オペレーションズ・リサーチ学会2018年秋季研究発表会  2018.9 

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  • 過疎地域における時間依存交通流に基づく公共交通の設計

    小田元, 高松瑞代, 田口東

    日本オペレーションズ・リサーチ学会2018年秋季研究発表会  2018.9 

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  • Index reduction via unimodular transformations

    S. Iwata, M. Takamatsu

    The 23rd International Symposium on Mathematical Programming (ISMP 2018)  2018.7 

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  • Optimizing train stopping patterns for congestion management

    T. Yamauchi, M. Takamatsu, S. Imahori

    The 23rd International Symposium on Mathematical Programming (ISMP 2018)  2018.7 

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  • Index reduction for differential-algebraic equations with mixed matrices

    S. Iwata, T. Oki, M. Takamatsu

    SIAM Workshop on Combinatorial Scientific Computing (CSC18)  2018.6 

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  • 数学を使って社会問題を解決する-バス時刻表の最適化

    第25回JST数学キャラバン 拡がりゆく数学 in 水戸 2018  2018.1 

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  • 交通状況による遅延を考慮し円滑な乗換を保証するバス時刻表の設計

    田中健裕, 菅原宏明, 田口 東

    第52回日本都市計画学会学術研究論文発表会  2017.11 

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  • 数学を使って社会問題を解決する-バス時刻表の最適化

    第22回JST数学キャラバン 拡がりゆく数学 in 気仙沼 ~数学で世界を素敵に~  2017.10 

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  • 混合行列を係数とする微分代数方程式の指数減少法

    岩田 覚, 大城 泰平, 高松 瑞代

    日本応用数理学会2017年度年会  2017.9 

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  • 利用者均衡配分に基づく優等列車停車駅の最適化

    山内達貴, 高松瑞代, 今堀慎治

    日本オペレーションズ・リサーチ学会2017年秋季研究発表会  2017.9 

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  • 電力需要予測への機械学習法の適用

    武田朗子, 岩田覚

    日本オペレーションズ・リサーチ学会2017年春季研究発表会  2017.3 

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  • 遅延に頑健な路線バスの時刻表設計

    田中健裕, 菅原宏明, 田口東

    日本オペレーションズ・リサーチ学会2017年春季研究発表会  2017.3 

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  • 東京都における自転車走行環境の評価と最適経路の探索

    茗荷魁斗

    地理情報システム学会第25回学術研究発表大会  2016.10 

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  • ユニモジュラ変換による微分代数方程式の指数減少法

    岩田覚

    日本応用数理学会2016年度年会  2016.9 

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  • 構造可制御部分空間のマトロイド理論的解析

    岩田覚

    日本応用数理学会2016年研究部会連合発表会  2016.3 

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  • 混合行列束のKronecker標準形に関する組合せ論的解析とシステム制御への応用

    日本オペレーションズ・リサーチ学会「最適化の基盤とフロンティア」研究部会第6回研究会  2016.3 

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  • 非正則混合行列束のKronecker標準形に関する組合せ論的解析

    岩田覚

    日本応用数理学会2015年度年会  2015.9 

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  • 駅の乗降者数に基づく駅構内売店の取扱商品最適化

    田口東

    日本オペレーションズ・リサーチ学会2015年秋季研究発表会  2015.9 

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  • Bus timetable design in areas with low-frequency public transportation services

    A. Taguchi

    The 22nd International Symposium on Mathematical Programming (ISMP 2015)  2015.7 

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  • 時空間ネットワークを用いた低頻度運行バスの時刻表設計

    田口東

    日本オペレーションズ・リサーチ学会研究部会「公共的社会システムとOR」  2014.5 

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  • PASMOデータを用いた駅構内売店のコンビニ化による|rn|購買行動変化の分析

    田口東, 太田雅文

    日本オペレーションズ・リサーチ学会2013年春季研究発表会  2013.3 

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  • 回路シミュレーションにおける微分代数方程式の最適モデリング

    「文部科学省委託事業 数学協働プログラム」最適化ワークショップ: 拡がっていく最適化  2013.2 

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  • 鉄道・バス乗換保証のための数理計画モデル

    田口東, 赤星健太郎, 石井儀光, 小坂知義

    日本オペレーションズ・リサーチ学会2012年秋季研究発表会  2012.9 

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  • 鉄道・バスの円滑な乗換を目指した時空間ネットワーク設計

    田口東

    第24回RAMPシンポジウム  2012.9 

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  • Matching problems with delta-matroid constraints

    N. Kakimura

    The 21st International Symposium on Mathematical Programming (ISMP 2012)  2012.8 

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  • 指数2の混合方程式を導く回路の構造的特徴付け

    日本応用数理学会2012年研究部会連合発表会  2012.3 

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  • デルタマトロイド制約付きマッチング

    垣村尚徳

    日本オペレーションズ・リサーチ学会2012年春季研究発表会  2012.3 

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  • PASMOデータを用いた鉄道利用と駅ナカ購買行動の関連分析

    田口東, 服部優奈, 太田雅文, 末松孝司

    日本オペレーションズ・リサーチ学会2011年秋季研究発表会  2011.9 

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  • On Kronecker canonical form of mixed matrix pencils

    S. Iwata

    SIAM Workshop on Combinatorial Scientific Computing (CSC11)  2011.5 

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  • 防犯センサを利用したオフィス内の人数推定

    田口東

    日本オペレーションズ・リサーチ学会2011年春季研究発表会  2011.3 

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  • 混合多項式行列の小行列式の最大次数を計算する組合せ緩和法

    岩田覚

    日本オペレーションズ・リサーチ学会2010年秋季研究発表会  2010.9 

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  • 混合行列束のKronecker標準形の組合せ論的解析

    岩田覚

    情報処理学会アルゴリズム研究会  2009.9 

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  • 混合行列束のKronecker標準形の組合せ論的解析

    岩田覚

    情報処理学会アルゴリズム研究会  2009.9 

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  • 非線形時変回路に対する混合方程式の組合せ論的解析-グラフ構造による順良指数の特徴付け-

    岩田覚, Caren Tischendorf

    京都大学数理解析研究所共同研究集会  2009.7 

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  • 非線形時変RLC回路における混合方程式の指数の解析

    岩田覚, Caren Tischendorf

    日本応用数理学会2008年度年会  2008.9 

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  • 電気回路の混合解析における微分代数方程式の指数最小化

    岩田覚

    京都大学数理解析研究所共同研究集会  2008.7 

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  • RLC回路の混合解析における冪零指数の構造的特徴付け

    岩田覚

    日本応用数理学会2007年度年会  2007.9 

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  • Index reduction for differential-algebraic equations by discrete optimization techniques

    S. Iwata

    京都大学数理解析研究所共同研究集会  2006.11 

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  • 電気回路の混合解析における冪零指数最小化

    岩田覚

    日本応用数理学会2006年度年会  2006.9 

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Awards

  • 日本オペレーションズ・リサーチ学会 第8回研究賞奨励賞

    2018.9  

  • 日本応用数理学会 2018年度論文賞(実用部門)

    2018.9   通勤時間帯の駅構内における購買行動の数理モデル

    田口東, 高松瑞代

  • 日本都市計画学会 2012年年間優秀論文賞受賞

    2013.5   日本都市計画学会   低頻度な公共交通網を有する地域の移動利便性の評価手法に関する研究

    赤星健太郎, 高松瑞代, 田口東, 石井儀光, 小坂知義

  • 日本オペレーションズ・リサーチ学会 第25回学生論文賞

    2007.9   日本オペレーションズ・リサーチ学会   Discrete Optimization Approach to Index Reduction for Differential-Algebraic Equations

Research Projects

  • 時空間ネットワークを用いた人の流れの最適化

    Grant number:22K11925  2022.4 - 2026.3

    日本学術振興会  科学研究費助成事業 基盤研究(C)  基盤研究(C)  中央大学

    高松 瑞代

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    Grant amount: \4030000 ( Direct Cost: \3100000 、 Indirect Cost: \930000 )

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  • 公共交通の時空間ネットワークと最適化

    Grant number:16K16356  2016.4 - 2022.3

    文部科学省  科学研究費補助金(日本学術振興会・文部科学省)-若手研究(B) 

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    Grant type:Competitive

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  • Combinatorial Methods for Matrix Computation in Dynamical Systems Analysis

    Grant number:25730009  2013.4 - 2017.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)  Grant-in-Aid for Young Scientists (B)  Chuo University

    TAKAMATSU Mizuyo

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    Grant amount: \3770000 ( Direct Cost: \2900000 、 Indirect Cost: \870000 )

    Many modeling and simulation tools for dynamical systems adopt algorithms based on the structural approach. An advantage of the structural approach is that it is supported by efficient combinatorial algorithms that are free from errors in numerical computation. On the other hand, however, algorithms based on the structural approach sometimes fail because they discard numerical information.
    Combinatorial matrix theory is a branch of mathematics that combines combinatorial optimization techniques and matrix computation. In this research, we develop algorithms to analyze dynamical systems based on combinatorial matrix theory.

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  • 都市内の災害時の流動に関する総合的研究―効率性と頑健性を備えた都市実現に向けて―

    2013.4 - 2016.3

    文部科学省  科学研究費補助金(日本学術振興会・文部科学省) 

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  • Combinatorial Optimization Approach to Optimal Differential-Algebraic Equations Modeling

    Grant number:22860057  2010 - 2011

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Research Activity Start-up  Grant-in-Aid for Research Activity Start-up  Chuo University

    TAKAMATSU Mizuyo

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    Grant amount: \3146000 ( Direct Cost: \2420000 、 Indirect Cost: \726000 )

    Dynamical systems which appear in numerical simulation are often described by differential-algebraic equations(DAEs). In order to improve accuracy of numerical simulation, a great deal of research has been made on numerical solution methods. However, accuracy depends not only on how to solve but also on what to solve. This research has developed methods to obtain DAEs which are easy to solve numerically.

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  • Index Reduction Methods for Differential-Algebraic Equation Models by Discrete Optimization Techniques

    Grant number:20560057  2008 - 2010

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)  Kyoto University

    IWATA Satoru, TAKAMATSU Mizuyo, TISCHENDORF Caren

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    Grant amount: \4160000 ( Direct Cost: \3200000 、 Indirect Cost: \960000 )

    Large-scale dynamical systems, such as integrated circuits and chemical plants, are naturally described by differential-algebraic equations (DAEs). However, numerical solution of DAEs is often much more difficult than that of ODEs. This research focuses on DAEs arising in circuit simulation and establishes an efficient method to obtain a differential-algebraic equation model that is the easiest to solve numerically.

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  • 組合せ最適化手法の行列束と微分代数方程式への応用

    Grant number:09J06729  2009    

    日本学術振興会  科学研究費助成事業 特別研究員奨励費  特別研究員奨励費  東京大学

    高松 瑞代

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    Grant amount: \700000 ( Direct Cost: \700000 )

    本研究では,古典的な回路解析法である混合解析を非線形時変回路に適用して得られる微分代数方程式を解析し,指数0/1に対する回路の構造的特徴づけを与えた.微分代数方程式の指数は数値的難しさの指標であり,指数が大きいほど数値計算が困難になる.特に,指数2以上の微分代数方程式は,指数0/1の場合に比べて数値計算がはるかに難しいことが知られている.本研究で得られた特徴づけを利用することで,指数が0/1/2以上のいずれになるかを高速に判定することができる.また,素子を追加することで,指数1以下の回路設計が可能になる.この特徴づけは,昨年度に提案した非線形時変RLC回路に対する結果の拡張になっている.拡張に成功したことで,より現実の回路を対象に含めることができる.今後は,この特徴づけが混合解析における指数最小化アルゴリズムの構築に役立つことが期待される.さらに本研究では,物理システムを記述する有用な道具である混合行列束のクロネッカー標準形の計算法を提案し,微分代数方程式の指数を計算する新たなアルゴリズムを導出した.これまで得られていた結果は,行列のすべての係数が独立パラメータであるという仮定を課していた.本研究ではこの結果を,独立パラメータと正確な数値を持つ混合行列束に拡張することで,現実に現れるモデルへの適用を可能にした.本研究の特徴は,回路や数値解析の分野に現れる問題に対し,最適化の視点に立ち,マトロイド理論を利用して取り組んでいる点にある.

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Allotted class

  • 2023   卒業研究Ⅰ   Department

  • 2023   卒業研究Ⅱ   Department

  • 2023   基盤系オブジェクト指向プログラミング演習   Department

  • 2023   情報総合演習   Department

  • 2023   最適化   Department

  • 2023   空間数学   Department

  • 2023   情報工学論文研修第一   Graduate school

  • 2023   情報工学論文研修第三   Graduate school

  • 2023   情報工学論文研修第二   Graduate school

  • 2023   情報工学論文研修第四   Graduate school

  • 2023   数理構造論   Graduate school

  • 2023   組合せ最適化特論   Graduate school

  • 2023   電気・情報系特殊論文研修Ⅰ   Graduate school

  • 2023   電気・情報系特殊論文研修Ⅱ   Graduate school

  • 2023   電気・情報系特殊論文研修Ⅲ   Graduate school

  • 2023   電気・情報系特殊論文研修Ⅳ   Graduate school

  • 2023   電気・情報系特殊論文研修Ⅴ   Graduate school

  • 2023   電気・情報系特殊論文研修Ⅵ   Graduate school

  • 2023   電気・情報系特論   Graduate school

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