2013 Fiscal Year Final Research Report
Novel time-series analysis for dynamics based on topological-computation
| Project/Area Number |
24654022
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyoto University |
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Principal Investigator |
KOKUBU Hiroshi 京都大学, 理学(系)研究科(研究院), 教授 (50202057)
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| Project Period (FY) |
2012-04-01 – 2014-03-31
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| 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 |
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| 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.
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