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Saiki Yoshitaka  齊木 吉隆

… Alternative Names

SAIKI Yoshitaka  齊木 吉隆

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Researcher Number 20433740
Other IDs
  • ORCIDhttps://orcid.org/0000-0002-3184-0577
Affiliation (Current) 2025: 一橋大学, 大学院経営管理研究科, 教授
Affiliation (based on the past Project Information) *help 2019 – 2025: 一橋大学, 大学院経営管理研究科, 教授
2018 – 2019: 一橋大学, 大学院経営管理研究科, 准教授
2013 – 2017: 一橋大学, 大学院商学研究科, 准教授
2013 – 2014: 一橋大学, 商学研究科, 准教授
2013: 一橋大学大学院, 商学研究科, 准教授
2011 – 2012: 北海道大学, 理学(系)研究科(研究院), 助教
Review Section/Research Field
Principal Investigator
Transformative Research Areas, Section (II) / Medium-sized Section 12:Analysis, applied mathematics, and related fields / Foundations of mathematics/Applied mathematics / Sections That Are Subject to Joint Review: Basic Section12030:Basic mathematics-related , Basic Section12040:Applied mathematics and statistics-related / Basic Section 12030:Basic mathematics-related / Basic Section 12040:Applied mathematics and statistics-related / General mathematics (including Probability theory/Statistical mathematics)
Except Principal Investigator
Medium-sized Section 12:Analysis, applied mathematics, and related fields / Basic Section 61040:Soft computing-related / Basic Section 07030:Economic statistics-related / Foundations of mathematics/Applied mathematics / Economic theory
Keywords
Principal Investigator
力学系 / カオス / データ駆動モデリング / 間欠性 / 流体乱流 / 機械学習 / ヘテロカオス / 準周期軌道 / 数値解析 / 数値計算 … More / 周期軌道 / 不安定周期軌道 / 時間遅れ座標 / 回帰 / 微分方程式 / 分岐 / カオス的サドル / 為替変動 / 時系列解析 / 景気変動 / reservoir computing / turbulence / hetero chaos / nonhyperbolicity / dynamical system / 制御 / リザーバーコンピューティング / 非双曲ダイナミクス / 非双曲力学系 / モンテカルロ法 / 数値解析学 / 凖周期軌道 / フーリエ級数 / 位相共役 / ジーゲル球 / ジーゲル板 / 回転数 / 時間遅れ埋め込み / 重み付きバーコフ平均 / 高速計算 / バーコフ平均 / 非双曲性 / カオス的遍歴 / 大規模数値解析 / 複雑現象の数理 / 応用数学 / 非双曲系 / 多様体 / リアプノフ解析 / リアプノフベクトル … More
Except Principal Investigator
鉱工業生産指数 / 景気循環 / 機械学習 / 乱流 / ランダム力学系理論 / ランダムノイズ / 非線形経済動学 / 非線形結合力学系 / 地域間同期現象 / コンポジット・インデックス / フーリエ・バンドパスフィルター / ヒルベルト変換 / 景気動向指数(CI) / 地域景気循環 / 同期 / 時系列データ解析 / Conley-Morse分解 / 成層圏 / 対流圏 / 時系列解析 / カオス力学系 / データ同化 / 確率微分方程式 / 非線形振動子 / ウェーブレット / マクロ経済学 / カオス的遍歴 / 大域結合写像モデル / 結合振動子系 / ウェーブレット解析 / 同期現象 Less
  • Research Projects

    (13 results)
  • Research Products

    (103 results)
  • Co-Researchers

    (26 People)
  •  回帰を用いたデータ駆動微分方程式モデルの構造解析Principal Investigator

    • Principal Investigator
      齊木 吉隆
    • Project Period (FY)
      2025 – 2026
    • Research Category
      Grant-in-Aid for Transformative Research Areas (A)
    • Review Section
      Transformative Research Areas, Section (II)
    • Research Institution
      Hitotsubashi University
  •  New Developments in Fluid Dynamics Research Based on Dynamical Systems TheoryPrincipal Investigator

    • Principal Investigator
      齊木 吉隆
    • Project Period (FY)
      2024 – 2027
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Review Section
      Basic Section 12040:Applied mathematics and statistics-related
      Basic Section 12030:Basic mathematics-related
      Sections That Are Subject to Joint Review: Basic Section12030:Basic mathematics-related , Basic Section12040:Applied mathematics and statistics-related
    • Research Institution
      Hitotsubashi University
  •  Construction and exploration of nonlinear economic dynamic models with dynamically changing time evolution rules

    • Principal Investigator
      小野崎 保
    • Project Period (FY)
      2024 – 2026
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Review Section
      Basic Section 61040:Soft computing-related
    • Research Institution
      Rissho University
  •  物理と数学の協働による乱流クロージャー問題解決に向けた機械学習理論の創出

    • Principal Investigator
      米田 剛
    • Project Period (FY)
      2024 – 2028
    • Research Category
      Grant-in-Aid for Scientific Research (A)
    • Review Section
      Medium-sized Section 12:Analysis, applied mathematics, and related fields
    • Research Institution
      Hitotsubashi University
  •  Data-driven modeling of ordinary differential equations using regressionPrincipal Investigator

    • Principal Investigator
      齊木 吉隆
    • Project Period (FY)
      2023 – 2024
    • Research Category
      Grant-in-Aid for Transformative Research Areas (A)
    • Review Section
      Transformative Research Areas, Section (II)
    • Research Institution
      Hitotsubashi University
  •  Expediting and Elaborating Business Forecast Using Machine LearningPrincipal Investigator

    • Principal Investigator
      齊木 吉隆
    • Project Period (FY)
      2021 – 2024
    • Research Category
      Grant-in-Aid for Challenging Research (Exploratory)
    • Review Section
      Medium-sized Section 12:Analysis, applied mathematics, and related fields
    • Research Institution
      Hitotsubashi University
  •  Data analysis and large-scale simulation of regional business cycles

    • Principal Investigator
      Onozaki Tamotsu
    • Project Period (FY)
      2019 – 2021
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Review Section
      Basic Section 07030:Economic statistics-related
    • Research Institution
      Rissho University
  •  Intermittency due to hetero-chaotic property and its inferencePrincipal Investigator

    • Principal Investigator
      齊木 吉隆
    • Project Period (FY)
      2019 – 2024
    • Research Category
      Fund for the Promotion of Joint International Research (Fostering Joint International Research (B))
    • Review Section
      Medium-sized Section 12:Analysis, applied mathematics, and related fields
    • Research Institution
      Hitotsubashi University
  •  Fast Computation of Birkhoff Average along a Quasi-periodic Orbit and its ApplicationsPrincipal Investigator

    • Principal Investigator
      SAIKI Yoshitaka
    • Project Period (FY)
      2017 – 2020
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Foundations of mathematics/Applied mathematics
    • Research Institution
      Hitotsubashi University
  •  Mathematical characterization of chaotic itinerancyPrincipal Investigator

    • Principal Investigator
      SAIKI YOSHITAKA
    • Project Period (FY)
      2014 – 2016
    • Research Category
      Grant-in-Aid for Challenging Exploratory Research
    • Research Field
      Foundations of mathematics/Applied mathematics
    • Research Institution
      Hitotsubashi University
  •  Construction of mathematical models for long-term forecast of atmospheric variation by climate time-series

    • Principal Investigator
      SAKAJO Takashi
    • Project Period (FY)
      2013 – 2014
    • Research Category
      Grant-in-Aid for Challenging Exploratory Research
    • Research Field
      Foundations of mathematics/Applied mathematics
    • Research Institution
      Kyoto University
  •  Understanding Synchronization of Business Cycles Using Wavelet Analysis and Nonlinear Coupled Oscillator Models

    • Principal Investigator
      ONOZAKI Tamotsu
    • Project Period (FY)
      2012 – 2013
    • Research Category
      Grant-in-Aid for Challenging Exploratory Research
    • Research Field
      Economic theory
    • Research Institution
      Rissho University
  •  Analysis of non-hyperbolic systems through unstable periodic orbitsPrincipal Investigator

    • Principal Investigator
      SAIKI Yoshitaka
    • Project Period (FY)
      2011 – 2013
    • Research Category
      Grant-in-Aid for Young Scientists (B)
    • Research Field
      General mathematics (including Probability theory/Statistical mathematics)
    • Research Institution
      Hitotsubashi University
      Hokkaido University

All 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 Other

All Journal Article Presentation

  • [Journal Article] Constructing low-dimensional ordinary differential equations from chaotic time series of high- or infinite-dimensional systems using radial-function-based regression2023

    • Author(s)
      Tsutsumi Natsuki、Nakai Kengo、Saiki Yoshitaka
    • Journal Title

      Physical Review E

      Volume: 108 Issue: 5 Pages: 054220-054220

    • DOI

      10.1103/physreve.108.054220

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21K18584, KAKENHI-PROJECT-22K17965, KAKENHI-PROJECT-19KK0067, KAKENHI-PUBLICLY-23H04465
  • [Journal Article] Hausdorff Dimension of Cantor Intersections and Robust Heterodimensional Cycles for Heterochaos Horseshoe Maps2023

    • Author(s)
      Saiki Yoshitaka、Takahasi Hiroki、Yorke James A.
    • Journal Title

      SIAM Journal on Applied Dynamical Systems

      Volume: 22 Issue: 3 Pages: 1852-1876

    • DOI

      10.1137/22m1504986

    • Peer Reviewed / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-19KK0067, KAKENHI-PUBLICLY-23H04465
  • [Journal Article] Can the Flap of a Butterfly’s Wings Shift a Tornado into Texas Without Chaos?2023

    • Author(s)
      Saiki Yoshitaka、Yorke James A.
    • Journal Title

      Atmosphere

      Volume: 14 Issue: 5 Pages: 821-821

    • DOI

      10.3390/atmos14050821

    • Peer Reviewed / Open Access
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Journal Article] Characterizing Small-Scale Dynamics of Navier-Stokes Turbulence with Transverse Lyapunov Exponents: A Data Assimilation Approach2023

    • Author(s)
      Inubushi Masanobu、Saiki Yoshitaka、Kobayashi Miki U.、Goto Susumu
    • Journal Title

      Physical Review Letters

      Volume: 131 Issue: 25 Pages: 254001-254001

    • DOI

      10.1103/physrevlett.131.254001

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19KK0067, KAKENHI-PROJECT-22K03420, KAKENHI-PROJECT-20H02068
  • [Journal Article] The twisted baker map2023

    • Author(s)
      Saiki Yoshitaka、Takahasi Hiroki、Yorke James A
    • Journal Title

      Nonlinearity

      Volume: 36 Issue: 3 Pages: 1776-1788

    • DOI

      10.1088/1361-6544/acb4d3

    • Peer Reviewed / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Journal Article] Hausdorff dimension of Cantor intersections and robust heterodimensional cycles for heterochaos horseshoe maps2023

    • Author(s)
      Saiki Yoshitaka、Takahasi Hiroki、Yorke James A
    • Journal Title

      SIAM Journal on Applied Dynamical Systems, 印刷中

      Volume: -

    • Peer Reviewed / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Journal Article] Constructing differential equations using only a scalar time-series about continuous time chaotic dynamics2022

    • Author(s)
      Tsutsumi Natsuki、Nakai Kengo、Saiki Yoshitaka
    • Journal Title

      Chaos: An Interdisciplinary Journal of Nonlinear Science

      Volume: 32 Issue: 9 Pages: 091101-091101

    • DOI

      10.1063/5.0100166

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21K18584, KAKENHI-PROJECT-22K17965, KAKENHI-PROJECT-19KK0067
  • [Journal Article] Regional Synchronization during Economic Contraction: The Case of the U.S. and Japan2022

    • Author(s)
      Muto Makoto、Onozaki Tamotsu、Saiki Yoshitaka
    • Journal Title

      Applied Economics

      Volume: 55 Issue: 30 Pages: 3472-3486

    • DOI

      10.1080/00036846.2022.2115450

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21K18584, KAKENHI-PROJECT-19KK0067
  • [Journal Article] Dynamical system analysis of a data-driven model constructed by reservoir computing2021

    • Author(s)
      M. U. Kobayashi, K. Nakai, Y. Saiki, N. Tsutsumi
    • Journal Title

      Physical Review E

      Volume: 104 Issue: 4 Pages: 044215-044215

    • DOI

      10.1103/physreve.104.044215

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18K03433, KAKENHI-PROJECT-19KK0067
  • [Journal Article] Piecewise-linear maps with heterogeneous chaos2021

    • Author(s)
      Y. Saiki, H. Takahasi and J. A. Yorke
    • Journal Title

      Nonlinearity

      Volume: 34 Issue: 8 Pages: 5744-5761

    • DOI

      10.1088/1361-6544/ac0d45

    • Peer Reviewed / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Journal Article] Machine-learning construction of a model for a macroscopic fluid variable using the delay-coordinate of a scalar observable2020

    • Author(s)
      K. Nakai and Y. Saiki
    • Journal Title

      Discrete and Continuous Dynamical Systems Series S

      Volume: -

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Journal Article] Machine-learning construction of a model for a macroscopic fluid variable using the delay-coordinate of a scalar observable2020

    • Author(s)
      Nakai Kengo, Saiki Yoshitaka
    • Journal Title

      Discrete & Continuous Dynamical Systems - S

      Volume: - Issue: 3 Pages: 1079-1092

    • DOI

      10.3934/dcdss.2020352

    • Peer Reviewed / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-19J12482, KAKENHI-PROJECT-17K05360
  • [Journal Article] Machine-learning construction of a model for a macroscopic fluid variable using the delay-coordinate of a scalar observable2020

    • Author(s)
      K. Nakai and Y. Saiki
    • Journal Title

      Discrete and Continuous Dynamical Systems Series S

      Volume: -

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17K05360
  • [Journal Article] Solving the Babylonian Problem of quasiperiodic rotation rates2019

    • Author(s)
      S. Das, Y. Saiki, E. Sander and J. A. Yorke
    • Journal Title

      Discrete and Continuous Dynamical Systems Series S

      Volume: 12 Pages: 2279-2305

    • Peer Reviewed / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-17K05360
  • [Journal Article] Intermittent transition between synchronization and desynchronization in multi-regional business cycles2018

    • Author(s)
      K. Esashi, T. Onozaki, Y. Saiki and Y. Sato
    • Journal Title

      Structural Change and Economic Dynamics

      Volume: 44 Pages: 68-76

    • DOI

      10.1016/j.strueco.2017.10.005

    • Peer Reviewed / Open Access
    • Data Source
      KAKENHI-PROJECT-17K05360, KAKENHI-PROJECT-18K03441
  • [Journal Article] Empirical evaluated SDE modelling for dimensionality reduction systems and its predictability estimates2018

    • Author(s)
      N. Nakano, M. Inatsu, S. Kusuoka and Y. Saiki
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 印刷中 Issue: 2 Pages: 553-589

    • DOI

      10.1007/s13160-017-0296-2

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17K05360
  • [Journal Article] Low-dimensional paradigms for high-dimensional hetero-chaos2018

    • Author(s)
      Y. Saiki, M. F. Sanjuan and J. A. Yorke
    • Journal Title

      Chaos

      Volume: 28

    • Peer Reviewed / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-17K05360
  • [Journal Article] Machine-learning inference of fluid variables from data using reservoir computing2018

    • Author(s)
      K. Nakai and Y. Saiki
    • Journal Title

      Physical Review E

      Volume: 98

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17K05360
  • [Journal Article] Quasiperiodic orbits in Siegel disks/balls and the Babylonian problem2018

    • Author(s)
      Y. Saiki and J. A. Yorke
    • Journal Title

      Regular and Chaotic Dynamics

      Volume: 23 Pages: 735-750

    • Peer Reviewed / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-17K05360
  • [Journal Article] Generalized Lorenz Equations on a Three-Sphere2017

    • Author(s)
      Y. Saiki, E. Sander and J. A. Yorke
    • Journal Title

      European Physical Journal Special Topics

      Volume: 226 Issue: 9 Pages: 1751-1764

    • DOI

      10.1140/epjst/e2017-70055-y

    • Peer Reviewed / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-17K05360
  • [Journal Article] Generalized Lorenz Equations on a Three-Sphere2017

    • Author(s)
      Y. Saiki, E. Sander and J. A. Yorke
    • Journal Title

      Eurpean Physical Journal Special Topics

      Volume: 印刷中

    • Peer Reviewed / Acknowledgement Compliant / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Journal Article] Network analyses of chaotic systems through unstable periodic orbits2017

    • Author(s)
      M. U. Kobayashi and Y. Saiki
    • Journal Title

      Chaos

      Volume: 27 Issue: 8 Pages: 081103-081103

    • DOI

      10.1063/1.4995043

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17K05360
  • [Journal Article] Quantitative quasiperiodicity2017

    • Author(s)
      S. Das, Y. Saiki, E. Sander and J. A. Yorke
    • Journal Title

      Nonlinearity

      Volume: 30 Issue: 11 Pages: 4111-4140

    • DOI

      10.1088/1361-6544/aa84c2

    • Peer Reviewed / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-17K05360
  • [Journal Article] Measuring quasiperiodicity2016

    • Author(s)
      S. Das, C. B. Dock, Y. Saiki, M. Salgado-Flores, E. Sander, J. Wu and J. A. Yorke
    • Journal Title

      Europhysics Letters

      Volume: 114 Pages: 40005-40005

    • Peer Reviewed / Acknowledgement Compliant / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Journal Article] Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation2015

    • Author(s)
      Yoshitaka Saiki, Michio Yamada, Abraham C.-L. Chian, Rodrigo A. Miranda and Erico L. Rempel
    • Journal Title

      Chaos

      Volume: 25 Issue: 10 Pages: 103123-103123

    • DOI

      10.1063/1.4933267

    • Peer Reviewed / Acknowledgement Compliant / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-15K13458, KAKENHI-PROJECT-26610034, KAKENHI-PROJECT-25610139, KAKENHI-PROJECT-24340016
  • [Journal Article] 非双曲力学系の不安定周期軌道解析 : エノン写像の周期軌道展開2014

    • Author(s)
      斉木吉隆
    • Journal Title

      九州大学応用力学研究所研究集会報告「非線形波動現象の拡がり」

      Volume: 25AO-S2 Pages: 91-100

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Journal Article] Manifold structures of Unstable Periodic Orbits and the Appearance of a Periodic Window in Chaotic Systems2014

    • Author(s)
      M. U. Kobayashi and Y. Saiki
    • Journal Title

      Physical Review

      Volume: E 89

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Journal Article] Manifold structures of Unstable Periodic Orbits and the Appearance of a Periodic Window in Chaotic Systems2014

    • Author(s)
      M. U. Kobayashi and Y. Saiki
    • Journal Title

      Physical Review E

      Volume: 89 Pages: 1-6

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25610028
  • [Journal Article] Manifold structures of Unstable Periodic Orbits and the Appearance of a Periodic Window in Chaotic Systems2014

    • Author(s)
      Miki U Kobayashi, Yoshitaka Saiki
    • Journal Title

      Physical Review E

      Volume: Vol.89

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Journal Article] 非双曲力学系の不安定周期軌道解析:エノン写像の周期軌道展開2014

    • Author(s)
      斉木吉隆
    • Journal Title

      九州大学応用力学研究所 研究集会報告「非線形波動現象の拡がり」

      Volume: 25AO-S2 Pages: 91-100

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25610028
  • [Journal Article] 非双曲力学系の不安定周期軌道解析:エノン写像の周期軌道展開2014

    • Author(s)
      斉木吉隆
    • Journal Title

      九州大学応用力学研究所 研究集会報告「非線形波動現象の拡がり」

      Volume: 25AO-S2 Pages: 91-100

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Journal Article] Time Averaged Properties Along Unstable Periodic Orbits of the Kuramoto-Sivashinsky Equation, Nankai Series in Pure2013

    • Author(s)
      Y. Saiki and M. Yamada
    • Journal Title

      Applied Mathematics and Theoretical Physics, World Scientific

      Volume: Volume 10 Pages: 145-154

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Journal Article] Time Averaged Properties Along Unstable Periodic Orbits of the Kuramoto-Sivashinsky Equation2013

    • Author(s)
      Yoshitaka Saiki and Michio Yamada
    • Journal Title

      Nankai Series in Pure, Applied Mathematics and Theoretical Physics

      Volume: 10 Pages: 145-154

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Journal Article] Recognition of transition patterns in a business cycle model by unstable periodic orbits2011

    • Author(s)
      Y. Saiki and K. Ishiyama
    • Journal Title

      International Journal of Bifurcation and Chaos

      Volume: 21 Pages: 1-21

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Journal Article] Economic intermittency in a two-country model of business cycles coupled by investment2011

    • Author(s)
      Y. Saiki, A. Chian and H. Yoshida
    • Journal Title

      Chaos, Solitons and Fractals

      Volume: 44 Pages: 418-428

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] Construction of differential equations from scalar chaotic time series2023

    • Author(s)
      Natsuki Tsutsumi, Kengo Nakai, Yoshitaka Saiki
    • Organizer
      ICIAM 2023
    • Int'l Joint Research
    • Data Source
      KAKENHI-PUBLICLY-23H04465
  • [Presentation] 高次元カオスのミニマルモデルについて2023

    • Author(s)
      齊木吉隆
    • Organizer
      第62回MCMEセミナー
    • Invited
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Presentation] On some small models to understand high dimensional dynamics2023

    • Author(s)
      Yoshitaka Saiki
    • Organizer
      International Workshop on Ergodic Theory, Dynamical Systems, and Climate Sciences
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Presentation] カオス的時系列データに基づく微分方程式推定2022

    • Author(s)
      齊木 吉隆
    • Organizer
      RIMS研究集会「力学系の理論と諸分野への応用」
    • Data Source
      KAKENHI-PROJECT-21K18584
  • [Presentation] カオス的時系列データに基づく微分方程式推定2022

    • Author(s)
      齊木 吉隆
    • Organizer
      RIMS研究集会「力学系の理論と諸分野への応用」
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Presentation] Simple examples of heterochaotic dynamics2022

    • Author(s)
      齊木 吉隆
    • Organizer
      RIMS研究集会「ランダム力学系・非自励力学系研究の展望:理論と応用」
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Presentation] 機械学習による気象現象のデータ駆動型時間発展モデルの構築2022

    • Author(s)
      神野 拓哉, 三浦 裕亮, 中井 拳吾, 齊木 吉隆, 末松 環, 高須賀 大輔, 米田 剛
    • Organizer
      応用数学合同研究集会
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Presentation] 機械学習による気象現象のデータ駆動型時間発展モデルの構築2022

    • Author(s)
      神野 拓哉, 三浦 裕亮, 中井 拳吾, 齊木 吉隆, 末松 環, 高須賀 大輔, 米田 剛
    • Organizer
      応用数学合同研究集会
    • Data Source
      KAKENHI-PROJECT-21K18584
  • [Presentation] いくつかの低次元次元力学系トイモデルについて2022

    • Author(s)
      齊木 吉隆
    • Organizer
      研究集会「現象と数理モデル 2022」
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Presentation] 流体マクロ時系列のデータ駆動型微分方程式モデリング2022

    • Author(s)
      堤 夏輝, 中井 拳吾, 齊木 吉隆
    • Organizer
      応用数学合同研究集会
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Presentation] Heterochaos baker map and twisted baker map2022

    • Author(s)
      齊木 吉隆
    • Organizer
      京都力学系セミナー
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Presentation] 機械学習モデルによる各種力学系的性質の再現性2022

    • Author(s)
      小林幹 ,中井拳吾,齊木吉隆,堤夏輝
    • Organizer
      冬の力学系研究集会
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Presentation] Low-dimensional paradigms for high-dimensional chaos2021

    • Author(s)
      Yoshitaka Saiki
    • Organizer
      Jim A. Yorke's 80th Birthday Celebration Workshop
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Presentation] カオス的時系列データに基づく微分方程式推定2021

    • Author(s)
      中井拳吾,齊木吉隆,堤夏輝
    • Organizer
      応用数学合同研究集会
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Presentation] 機械学習モデルの力学系構造の再現性と流体統計量の予測2021

    • Author(s)
      小林幹 ,中井拳吾,齊木吉隆,堤夏輝
    • Organizer
      応用数学合同研究集会
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Presentation] Machine-learning inference of variables of a chaotic fluid flow from data using reservoir computing2019

    • Author(s)
      K. Nakai and Y. Saiki
    • Organizer
      NOLTA2019
    • Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-17K05360
  • [Presentation] ヘテロカオス2019

    • Author(s)
      齊木吉隆
    • Organizer
      Advancing Interaction among mathematical concepts and methods towards practical problems 2019
    • Invited
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Presentation] Machine-learning inference of variables of a chaotic fluid flow from data using reservoir computing2019

    • Author(s)
      K. Nakai and Y. Saiki
    • Organizer
      Nonlinear Theory and Its Applications (NOLTA2019)
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Presentation] 流体マクロ変数に関する数理モデルの機械学習に基づく構築2019

    • Author(s)
      齊木吉隆
    • Organizer
      Prometech Simulation Conference
    • Invited
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Presentation] Machine-learning construction of a model for a macroscopic fluid variable using the delay-coordinate of a scalar observable2019

    • Author(s)
      K. Nakai and Y. Saiki
    • Organizer
      George Mason University Applied and Computational Mathematics Seminar
    • Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-17K05360
  • [Presentation] ヘテロカオスと間欠性2019

    • Author(s)
      齊木吉隆
    • Organizer
      現象と数理モデル2019
    • Data Source
      KAKENHI-PROJECT-17K05360
  • [Presentation] 流体マクロ変数に関する数理モデルの機械学習に基づく構築2019

    • Author(s)
      K. Nakai and Y. Saiki
    • Organizer
      Prometech Simulation Conference
    • Invited
    • Data Source
      KAKENHI-PROJECT-17K05360
  • [Presentation] ヘテロカオスと同期2019

    • Author(s)
      齊木吉隆
    • Organizer
      現象と数理モデル2019
    • Data Source
      KAKENHI-PROJECT-19KK0067
  • [Presentation] 機械学習に基づいた流体マクロ変数に関する数理モデル構築ならびに時間発展予測2019

    • Author(s)
      K. Nakai and Y. Saiki
    • Organizer
      理論応用力学講演会  AIMaP 数学応用セッション
    • Invited
    • Data Source
      KAKENHI-PROJECT-17K05360
  • [Presentation] ヘテロカオス2019

    • Author(s)
      齊木吉隆
    • Organizer
      Advancing Interaction among mathematical concepts and methods towards practical problems 2019
    • Invited
    • Data Source
      KAKENHI-PROJECT-17K05360
  • [Presentation] Machine-learning prediction of fluid variables2018

    • Author(s)
      K. Nakai and Y. Saiki
    • Organizer
      Boston University/ Keio University Workshop 2018 Dynamical systems
    • Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-17K05360
  • [Presentation] 複雑現象における同期2016

    • Author(s)
      齊木吉隆
    • Organizer
      現象と数理モデル 2016
    • Place of Presentation
      富山第一ホテル(富山県富山市)
    • Year and Date
      2016-12-27
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Presentation] 高次元空間における準周期軌道の回転数の計算方法2016

    • Author(s)
      齊木吉隆
    • Organizer
      RIMS研究集会 力学系とその関連分野の連携探索
    • Place of Presentation
      京都大学数学教室(京都府京都市)
    • Year and Date
      2016-06-09
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Presentation] 準周期軌道にまつわるバーコフ平均の高速計算とその応用2016

    • Author(s)
      齊木吉隆
    • Organizer
      第14回 ダイナミクス研究会中野
    • Place of Presentation
      明治大学中野キャンパス(東京都中野区)
    • Year and Date
      2016-04-16
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Presentation] 力学系が生み出す準周期軌道の同定手法について2016

    • Author(s)
      齊木吉隆
    • Organizer
      Perspectives in Mathematical Sciences
    • Place of Presentation
      岡山大学(岡山県・岡山市)
    • Year and Date
      2016-01-06
    • Invited
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Presentation] Weighted Birkhoff Average and Quasiperiodicity2016

    • Author(s)
      Yoshitaka Saiki
    • Organizer
      日本応用数理学会年会 JSIAM-ANZIAM 特別OS
    • Place of Presentation
      北九州国際会議場(福岡県北九州市)
    • Year and Date
      2016-09-13
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Presentation] Numerical identification of quasiperiodicity2016

    • Author(s)
      齊木吉隆
    • Organizer
      冬の力学系研究集会
    • Place of Presentation
      日本大学軽井沢研修所(長野県・軽井沢町)
    • Year and Date
      2016-01-10
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Presentation] Weighted Bihkhoff average and quasiperiodicity2016

    • Author(s)
      齊木吉隆
    • Organizer
      力学系セミナー
    • Place of Presentation
      北海道大学(北海道・札幌市)
    • Year and Date
      2016-03-22
    • Invited
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Presentation] Multi-chaos: A Low Dimensional Paradigm for High Dimensional Chaos2016

    • Author(s)
      齊木吉隆
    • Organizer
      研究集会「現象と数理モデル」
    • Place of Presentation
      姫路キャッスルグランヴィリオホテル(兵庫県・姫路市)
    • Year and Date
      2016-03-08
    • Invited
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Presentation] Unstable periodic orbits in a coupled intermittent map2015

    • Author(s)
      齊木吉隆
    • Organizer
      RIMS研究集会「ランダム力学系理論とその応用」
    • Place of Presentation
      京都大学(京都府・京都市)
    • Year and Date
      2015-09-30
    • Invited
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Presentation] 確率微分方程式モデルを用いたベクトル時系列データ解析におけるアンサンブル予測可能性評価2015

    • Author(s)
      中野直人・稲津將・楠岡誠一郎・齊木吉隆
    • Organizer
      日本数学会2015年会
    • Place of Presentation
      明治大学(東京)
    • Year and Date
      2015-03-23
    • Data Source
      KAKENHI-PROJECT-25610028
  • [Presentation] 双曲性が崩れた状況における不安定周期軌道展開の試み2015

    • Author(s)
      齊木吉隆
    • Organizer
      数学協働プログラム研究集会 「大自由度分子系における化学反応機序の理解と制御」
    • Place of Presentation
      北海道大学(北海道・札幌市)
    • Year and Date
      2015-11-01
    • Invited
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Presentation] データ同化手法に関する数理科学的諸相と今後の展望2015

    • Author(s)
      齊木吉隆
    • Organizer
      日本応用数理学会
    • Place of Presentation
      金沢大学(石川県・金沢市)
    • Year and Date
      2015-09-10
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Presentation] Chaotic Itineracy in Regional Business Cycle Synchronization2015

    • Author(s)
      齊木吉隆
    • Organizer
      NED2015
    • Place of Presentation
      中央大学(東京都・八王子市)
    • Year and Date
      2015-06-27
    • Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Presentation] 多地域景気変動モデルにおけるカオス的遍歴:数理的側面2015

    • Author(s)
      齊木吉隆
    • Organizer
      RIMS共同研究「マクロ経済動学の非線形数理」
    • Place of Presentation
      京都大学(京都府・京都市)
    • Year and Date
      2015-09-14
    • Invited
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Presentation] 多地域景気変動における同期現象2015

    • Author(s)
      齊木吉隆
    • Organizer
      MIMS共同研究集会「可積分系が拓く現象数理モデル」
    • Place of Presentation
      明治大学(東京都・中野区)
    • Year and Date
      2015-11-06
    • Invited
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Presentation] Unstable periodic orbits in intermittent dynamics2014

    • Author(s)
      Y. Saiki
    • Organizer
      Workshop on Lagrangian Coherent Structures and Dynamical Systems
    • Place of Presentation
      Hokkaido University,北海道
    • Year and Date
      2014-03-07
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] 非双曲力学系の不安定周期軌道解析2014

    • Author(s)
      齊木吉隆
    • Organizer
      関東力学系セミナー
    • Place of Presentation
      東京大学
    • Year and Date
      2014-11-19
    • Invited
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Presentation] 同期現象の不安定周期軌道解析2014

    • Author(s)
      齊木吉隆
    • Organizer
      金融研究会
    • Place of Presentation
      一橋大学
    • Year and Date
      2014-04-10
    • Invited
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Presentation] 確率微分方程式モデルを用いたベクトル時系列データ解析における予測可能性評価2014

    • Author(s)
      中野直人・稲津將・楠岡誠一郎・齊木吉隆
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      龍谷大学(大津市)
    • Year and Date
      2014-12-20
    • Data Source
      KAKENHI-PROJECT-25610028
  • [Presentation] 非双曲力学系の不安定周期軌道解析2013

    • Author(s)
      斉木吉隆
    • Organizer
      九州大学応用力学研究所共同利用研究集会「非線形波動研究の拡がり」
    • Place of Presentation
      九州大学,福岡県
    • Year and Date
      2013-11-02
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] 確率微分方程式を用いた時系列解析における統計的係数決定公式と軌道の予測可能性2013

    • Author(s)
      中野 直人・斉木 吉隆・稲津 將・楠岡 誠一郎
    • Organizer
      日本数学会2013年度秋期総合分科会
    • Place of Presentation
      松山市,愛媛県(愛媛大学)
    • Data Source
      KAKENHI-PROJECT-25610028
  • [Presentation] 非双曲力学系の解析2013

    • Author(s)
      斉木吉隆
    • Organizer
      Hayama meeting
    • Place of Presentation
      IPC生産性国際交流センター,神奈川県
    • Year and Date
      2013-09-01
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] Characterization of tangencies between stable and unstable manifolds through unstable periodic orbits2013

    • Author(s)
      Y. Saiki and M. U. Kobayashi
    • Organizer
      The 3rd International Symposium on Innovative Mathematical Modelling
    • Place of Presentation
      The University ofTokyo,東京都
    • Year and Date
      2013-11-15
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] カオス的景気循環モデルの不安定周期軌道解析2012

    • Author(s)
      斉木吉隆
    • Organizer
      数理科学セミナー
    • Place of Presentation
      一橋大学,東京都
    • Year and Date
      2012-06-27
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] カオス力学系の共変リアプノフ解析2012

    • Author(s)
      斉木吉隆
    • Organizer
      研究会「流体乱流の力学と統計-複雑系化学からのアプローチ」
    • Place of Presentation
      しこつ湖鶴雅リゾートスパ水の謌,北海道
    • Year and Date
      2012-03-06
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] Covatiant Lyapunov vectors and unstable periodic orbits in the '63 Lorenz system2012

    • Author(s)
      Y. Saiki
    • Organizer
      Weather-Chaos Seminar
    • Place of Presentation
      University of Maryland, U.S.A
    • Year and Date
      2012-08-27
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] Numerical study of unstable periodic orbits in some chaotic systems2012

    • Author(s)
      Y. Saiki
    • Organizer
      International Conference : 100 years after Poincare
    • Place of Presentation
      Spain
    • Year and Date
      2012-09-09
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] 離散時間カルドアモデルのトーラスとその制御2012

    • Author(s)
      江刺邦彦,斉木吉隆
    • Organizer
      日本地域学会
    • Place of Presentation
      立正大学,東京都
    • Year and Date
      2012-10-07
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] Reconstruction of chaotic saddles and classification of unstable periodic orbits of the Kuramoto-Sivashinsky system2011

    • Author(s)
      Yoshitaka Saiki, Michio Yamada, Abraham C.-L. Chian, Miki U. Kobayashi
    • Organizer
      Dynamics Days Europe 2011
    • Place of Presentation
      Oldenburg University (Germany)
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] Relations between Statistical Values along Unstable Periodic Orbits in Differential Equation Systems2011

    • Author(s)
      Y. Saiki and M. Yamada
    • Organizer
      IUTAM Chaos
    • Place of Presentation
      Kyoto University,京都府
    • Year and Date
      2011-12-01
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] Relations between Statistical Values along Unstable Periodic Orbits in Differential Equation Systems2011

    • Author(s)
      Yoshitaka Saiki., Michio Yamada
    • Organizer
      IUTAM Choas, Kyoto University
    • Place of Presentation
      Kyoto University (京都市)
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] Numerical Study of Unstable Periodic Orbits in the Kuramoto-Sivashinsky system2011

    • Author(s)
      Yoshitaka Saiki
    • Organizer
      Emerging Topics on Differential Equations and their Applications(招待講演)
    • Place of Presentation
      Nankai University (China)
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] Recognition of chaotic saddles and classification of unstable periodic orbits of the Kuramoto-Sivashinsky system2011

    • Author(s)
      Y.Saiki, M. Yamada, A. C.-L Chian, M. U. Kobayashi
    • Organizer
      Dynamics Days Europe
    • Place of Presentation
      Oldenburg University, Germany
    • Year and Date
      2011-09-15
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] Numerical Study of Unstable Periodic Orbits in the Kuramoto-Sivashinsly system2011

    • Author(s)
      Y. Saiki
    • Organizer
      Emerging topics on Differential Equations and their Applications
    • Place of Presentation
      Nankai University, China
    • Year and Date
      2011-12-09
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] Covariant Lyapunov vectors and unstable periodic orbits in the ‘63 Lorenz system

    • Author(s)
      Yoshitaka Saiki
    • Organizer
      Weather-Chaos Seminar
    • Place of Presentation
      University of Maryland (USA)
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] 同期現象の不安定周期軌道解析

    • Author(s)
      齊木吉隆
    • Organizer
      新潟ミニ研究会
    • Place of Presentation
      新潟大学
    • Year and Date
      2014-04-17 – 2014-04-18
    • Data Source
      KAKENHI-PROJECT-26610034
  • [Presentation] Numerical study of unstable periodic orbits in some chaotic systems

    • Author(s)
      Yoshitaka Saiki
    • Organizer
      International Conference: 100 years after Poincare
    • Place of Presentation
      Hotel NH Gijon (Spain)
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] 離散時間カルドアモデルのトーラスとその制御

    • Author(s)
      江刺邦彦、斉木吉隆
    • Organizer
      日本地域学会
    • Place of Presentation
      立正大学 (東京都品川区)
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] Unstable periodic orbits in intermittent dynamics

    • Author(s)
      Yoshitaka Saiki
    • Organizer
      Workshop on Lagrangian Coherent Structures and Dynamical Systems
    • Place of Presentation
      Hokkaido University (北海道)
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] カオス的景気循環モデルの不安定周期軌道解析

    • Author(s)
      斉木吉隆
    • Organizer
      数理科学セミナー
    • Place of Presentation
      一橋大学 (東京都国立市)
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] Characterization of tangencies between stable and unstable manifolds through unstable periodic orbits

    • Author(s)
      Yoshitaka Saiki and Miki U Kobayashi
    • Organizer
      The 3rd International Symposium on Innovative Mathematical Modelling
    • Place of Presentation
      The University of Tokyo (東京)
    • Data Source
      KAKENHI-PROJECT-23740065
  • [Presentation] 非双曲力学系の不安定周期軌道解析

    • Author(s)
      斉木吉隆
    • Organizer
      九州大学応用力学研究所 共同利用研究集会 「非線形波動研究の拡がり」
    • Place of Presentation
      九州大学 (福岡)
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740065
  • 1.  ONOZAKI Tamotsu (10233595)
    # of Collaborated Projects: 5 results
    # of Collaborated Products: 1 results
  • 2.  YANAGITA Tatsuo (80242262)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 3.  高橋 博樹 (00467440)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 4 results
  • 4.  小林 幹 (10547011)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 4 results
  • 5.  犬伏 正信 (20821698)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 1 results
  • 6.  ISHIYAMA Kenichi (30610133)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 7.  SAKAJO Takashi (10303603)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 8.  NAKANO Naoto (30612642)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 3 results
  • 9.  INATSU Masaru (80422450)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 3 results
  • 10.  MIYOSHI Takemasa (90646209)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 11.  武藤 誠 (50898351)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 12.  國府 寛司 (50202057)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 13.  米田 剛 (30619086)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 14.  後藤 晋 (40321616)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 15.  ESASHI Kunihiko
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 16.  SATO Yuzuru
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 17.  YAMADA Michio
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 1 results
  • 18.  Chian Abraham C.-L.
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 19.  Das Suddhasattwa
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 1 results
  • 20.  Dock Chris B.
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 1 results
  • 21.  Miranda Rodrigo A.
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 22.  Salgado-Flores Martin
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 1 results
  • 23.  Rempel Erico L.
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 24.  Sander Evelyn
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 2 results
  • 25.  Wu Jin
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 1 results
  • 26.  Yorke James A.
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 2 results

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