• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Novel time-series analysis for dynamics based on topological-computation

Research Project

Project/Area Number 24654022
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKyoto University

Principal Investigator

KOKUBU Hiroshi  京都大学, 理学(系)研究科(研究院), 教授 (50202057)

Project Period (FY) 2012-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2013: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords力学系 / 時系列 / 不安定性 / 大域的構造 / 位相計算 / Morse分解 / 数理モデル / ノイズ
Research Abstract

Mathematical foundation is given for Morse decomposition of dynamical systems from time-series data using topological-computation method. The theory is successfully applied to time-series data from a biological regulatory network model and global circulation data in meteorology.
For a biological application, our theory on dynamical time-series analysis for Morse decomposition is combined with the Fiedler-Mochizuki theory on regulatory networks, and is tested for a model of a gene regulatory network of circadian rhythm.
Our dynamical time-series analysis for Morse decomposition is also applied to some data on the global circulation in the troposphere and stratosphere, and correctly recovered transition of characteristic pressure patterns which meteorologists empirically observed.

Report

(3 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • Research Products

    (19 results)

All 2014 2013 2012

All Journal Article (4 results) (of which Peer Reviewed: 3 results) Presentation (15 results) (of which Invited: 13 results)

  • [Journal Article] A topological computation approach to the interior crisis bifurcation2013

    • Author(s)
      Hiroshi Kokubu and Hiroe Oka
    • Journal Title

      Nonlinear Theory and Its Applications, IEICE

      Volume: 4 Issue: 1 Pages: 97-103

    • DOI

      10.1587/nolta.4.97

    • NAID

      130003375415

    • ISSN
      2185-4106
    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Capturing the global behavior of dynamical systems with Conley-Morse graphs, "Advances in Cognitive Neurodynamics (III)", Proc2013

    • Author(s)
      Z.Arai, H.Kokubu, I.Obayashi
    • Journal Title

      The Third International Conference on Cognitive Neurodynamics, (Niseko, Japan, June 10-13, 2011), Springer

      Pages: 665-672

    • Related Report
      2013 Final Research Report
  • [Journal Article] Capturing the global behavior of dynamical systems with Conley-Morse graphs,2013

    • Author(s)
      Zin Arai, Hiroshi Kokubu, and Ippei Obayashi,
    • Journal Title

      "Advances in Cognitive Neurodynamics (III)" Proceedings of The Third International Conference on Cognitive Neurodynamics,

      Volume: III Pages: 665-672

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Combinatorial-topological framework for the analysis of global dynamics2012

    • Author(s)
      Justin Bush, Marcio Gameiro, Shaun Harker, Hiroshi Kokubu, Konstantin Mischaikow, Ippei Obayashi, Pawel Pilarczyk
    • Journal Title

      Chaos

      Volume: 22 Issue: 4 Pages: 047508-047508

    • DOI

      10.1063/1.4767672

    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Analysis of Global Dynamics from Time-series Data : Case Studies2014

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      IMA Workshop"Algebraic Topology in Dynamics, Differential Equations, and Experimental Data"
    • Place of Presentation
      U Minnesota, IMA
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Analysis of Global Dynamics from Time-series Data: Case Studies2014

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      IMA Workshop “Topological Structures in Computational Biology”
    • Place of Presentation
      IMA, U Minnesota, USA
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Topological Computation Method for Dynamical Time Series Analysis and its Applications2013

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      The First International Conference on Dynamics of Differential Equations
    • Place of Presentation
      Georgia Institute of Technology, Atlanta, U.S.A
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Dynamical time series analysis using a topological computation method2013

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      2013 Northeastern Asian Symposium on High Performance Computing Methods and Modeling
    • Place of Presentation
      Chengdu, China
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] Detecting Morse Decompositions of the Global Attractor of Regulatory Networks by Time Series Data2013

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      IMA Workshop"Topological Structures in Computational Biology"
    • Place of Presentation
      IMA, U Minnesota
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] 遺伝子ネットワークの新しい捉え方 (2) Fiedler-望月によるFVS理論2013

    • Author(s)
      國府寛司
    • Organizer
      RIMS共同研究「力学系・トポロジーの生命科学・物質科学への応用」
    • Place of Presentation
      アクティプラザ琵琶,滋賀県
    • Related Report
      2013 Annual Research Report
  • [Presentation] 遺伝子ネットワークの力学系理論2013

    • Author(s)
      國府寛司
    • Organizer
      RIMS共同研究「力学系・トポロジーの生命科学・物質科学への応用」
    • Place of Presentation
      アクティプラザ琵琶,滋賀県
    • Related Report
      2013 Annual Research Report
  • [Presentation] Detecting Morse Decompositions of the Global Attractor of Regulatory Networks by Time Series Data2013

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      IMA Workshop “Topological Structures in Computational Biology”
    • Place of Presentation
      IMA, U Minnesota, USA
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Topological Computation Method for Dynamical Time Series Analysis and its Applications2013

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      The First International Conference on Dynamics of Differential Equations
    • Place of Presentation
      Georgia Institute of Technology, Atlanta, U.S.A.
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] ダイナミクス全構造計算による新しい相空間構造解析の方法とその応用2012

    • Author(s)
      國府寛司
    • Organizer
      計測自動制御学会第50回自律分散システム部会研究会
    • Place of Presentation
      京都大学百周年時計台記念館国際交流ホール
    • Year and Date
      2012-06-15
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Topological Computation Methods for Global Dynamics and Bifurcations2012

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      Part 1 : Theory, Part 2: Application, NCTS Workshop on Dynamical Systems
    • Place of Presentation
      National Tsinghua University, Hsinchu, Taiwan
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Topological computation method for global dynamics and its application, Nonlinear Partial Differential Equations, Dynamical Systems and Their Applications2012

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      International Conference in honor of Professor Hiroshi Matano
    • Place of Presentation
      RIMS, Kyoto University
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Topological computation method for global dynamics and its application2012

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      Nonlinear Partial Differential Equations, Dynamical Systems and Their Applications
    • Place of Presentation
      RIMS, Kyoto University
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] ダイナミクス全構造計算による新しい相空間構造解析の方法とその応用2012

    • Author(s)
      國府寛司
    • Organizer
      計測自動制御学会 第50回自律分散システム部会研究会
    • Place of Presentation
      京都大学百周年時計台記念館
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Topological Computation Methods for Global Dynamics and Bifurcations, Part 2: Application2012

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      NCTS Workshop on Dynamical Systems
    • Place of Presentation
      NCTS, National Tsinghua University Hsinchu, Taiwan
    • Related Report
      2012 Research-status Report
    • Invited

URL: 

Published: 2013-05-31   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi