Network Theory from Endo-perspective
| Project/Area Number |
18K03423
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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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| Review Section |
Basic Section 12040:Applied mathematics and statistics-related
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| Research Institution | Tokyo Woman's Christian University |
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Principal Investigator |
Haruna Taichi 東京女子大学, 現代教養学部, 准教授 (20518659)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2022: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 圏論 / ネットワーク / 数理モデル / べき乗則 / 記憶容量 / カオスの縁 / ブーリアンネットワーク / 相互情報量 / 応用圏論 / 情報流 |
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| Outline of Final Research Achievements |
Modes of the relations between different levels in complex systems were investigated from the endo-perspective. In particular, we studied the dynamics and information flow on networks and networks open from within. In the former, we mathematically clarified that a kind of critical dynamics is selected from the optimization of local information flow on Boolean networks, which are mathematical models of gene regulatory networks. In the latter, we defined the notion of networks open from within by formulating the idea that nodes in a network are processes in the language of category theory. We proposed measures of the importance of nodes as inputs and outputs using the notion of lateral path derived from this formulation. We applied the measures to biological network analysis.
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| Academic Significance and Societal Importance of the Research Achievements |
ネットワーク上のダイナミクスと情報流に関する結果は単純化された数理モデルに対するものであるが、従来から数値シミュレーションが主な研究手法である複雑系の内在的観点からの理論研究において、数理的結果を得ることができることを示した理論的意義は大きい。内側から開いたネットワークに関する結果は、従来は別々に発展してきた主に統計物理学に基づく複雑ネットワークの科学と数学の圏論に基づくネットワーク理論の橋渡しとなる萌芽的な成果であり、両者の更なる相互作用による今後の発展が期待できるものである。
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Report
(6 results)
Research Products
(36 results)
