Origin of fractality in complex networks and self-organized criticality
| Project/Area Number |
16K05466
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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 |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Hokkaido University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
小布施 秀明 北海道大学, 工学研究院, 助教 (50415121)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | フラクタル / 臨界現象 / 複雑ネットワーク / スモールワールド / 自己組織化 / 数理物理 |
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| Outline of Final Research Achievements |
Studying the origin of fractality found in many real-world complex networks, we have obtained the following results. (1) We proposed a model of fractal complex networks based on an SOC dynamics driven by the antagonistic relationship between the growth of a functional network and its cascading overload failure, (2) we have shown a fractal and small-world structures, and their structural crossover in the process of time development of the SOC model, (3) to clarify the role of a long-range repulsive correlation between hub nodes to the fractal property, long-range degree correlations in a complex network have been formulated in a quite general manner, and (4) we have elucidated that fractality cannot be realized only by nearest-neighbor degree correlations but a long-range hub repulsion is closely related to the origin of fractality.
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| Academic Significance and Societal Importance of the Research Achievements |
現実の複雑ネットワークはスモールワールド性を有する構造とフラクタル性をもつ構造に大別される。この内フラクタル構造の起源は未だ明らかにされていなかったが、本研究でSOCがフラクタル構造の一つの起源であることが解明されらことにより、大域的構造相関の発現がユークリッド距離の有無と無関係に統一的に理解できることが明らかとなった。また、複雑ネットワークにおける長距離次数相関という大域的構造相関が一般的に定式化されたことで、ネットワークの様々な構造的性質やネットワーク上のダイナミクスが長距離次数相関とどのように関係しているかを定量的に研究するための礎が築かれた。
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Report
(4 results)
Research Products
(85 results)
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[Journal Article] Observation of topological edge states in parity-time-symmetric quantum walks2017
Author(s)
L. Xiao, X. Zhan, Z. H. Bian, K. K. Wang, X. Zhang, X. P. Wang, J. Li, K. Mochizuki, D. Kim, N. Kawakami, W. Yi, H. Obuse, B. C. Sanders, P. Xue
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Journal Title
Nature Physics
Volume: 13
Issue: 11
Pages: 1117-1123
DOI
Related Report
Peer Reviewed / Int'l Joint Research
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[Presentation] Observation of edge states of Floquet topological phases in PT symmetric quantum walks2017
Author(s)
Hideaki Obuse, Ken Mochizuki, Dakyeong Kim, Norio Kawakami L. Xiao, X. Zhan, Z.H. Bian, K.K. Wang, X. Zhang, X.P. Wang, J. Li, W. Yi, B. Sanders, P. Xue
Organizer
International Conference on Topological Materials Science 2017 (TopoMat2017)
Place of Presentation
東京工業大学（東京）
Year and Date
2017-05-09
Related Report
Int'l Joint Research
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[Presentation] 散逸を伴うPT対称な量子ウォークにおけるフロッケトポロジカル相の理論とエッジ状態の実験による観測2017
Author(s)
小布施秀明, 望月健, 金多景, 川上則雄, A.L. Xiao, B.X. Zhan, Z.H. Bian, K.K. Wang, X. Zhang, X.P. Wang, J.Li, W. Yi, P. Xue
Organizer
日本物理学会 第72回年次大会
Place of Presentation
大阪大学（大阪市）
Year and Date
2017-03-17
Related Report
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[Presentation] PT symmetric non-unitary quantum walks2016
Author(s)
Hideaki Obuse
Organizer
Workshop of Quantum Simulation and Quantum Walks 2016
Place of Presentation
Czech Technical University in Prague, Prague, Czech
Year and Date
2016-11-17
Related Report
Int'l Joint Research / Invited
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[Presentation] Sensitivity of a quantum walk to boundary2016
Author(s)
Etsuo Segawa, Hideaki Obuse
Organizer
Workshop of Quantum Simulation and Quantum Walks 2016
Place of Presentation
Czech Technical University in Prague, Prague, Czech
Year and Date
2016-11-17
Related Report
Int'l Joint Research / Invited
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