| Project/Area Number |
24540222
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Ryukoku University |
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Principal Investigator |
Oka Hiroe 龍谷大学, 理工学部, 教授 (20215221)
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| Co-Investigator(Renkei-kenkyūsha) |
KOKUBU Hiroshi 京都大学, 大学院理学研究科, 教授 (50202057)
ARAI Jin 北海道大学, 理学系研究科, 准教授 (80362432)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 力学系 / モース分解 / 大域的構造 / 時系列 / 全構造計算 / 制御ネットワーク系 / データ解析 / パーシステンス・ホモロジー / 乱流データ / global attractor / dynamical systems / time series / topological / computational / morse decomposition / topology / data analysis / unstable invariant set / rigorous computation / regulatory network / 不変集合 / 分岐 / トポロジー / 厳密計算 |
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| Outline of Final Research Achievements |
Topological-computational method (database schema) is our original approach in order to overcome the weak point of the analysis of real dynamical systems. The theory and an application (2-dim’l discrete dynamical system called Leslie model) is discussed in our paper. Also, boundary crisis, which is typical in the global bifurcations is studied in this methods, and obtain a theorem using a notion of chain orbit.
A switching network is a simple model for gene regulatory network representing the regulation of proteins, and we study the database of such systems. Moreover we treat the time series data of some gene regulatory network, from which we obtain a Morse decomposition, which is same as the one from a different method. We also study the graphical time series obtained by 3-D turbulence and get some computational results wrt persistence homology.
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