動的変化するネットワークと結合力学系との相互作用が生む秩序化へのダイナミクス

2015 Fiscal Year Annual Research Report

• Project/Area Number: 24740266
• Research Institution: Kagawa University
• Principal Investigator: 青木 高明 香川大学, 教育学部, 准教授 (30553284)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: adaptive network / complex nework / temporal network

Outline of Annual Research Achievements

本年度は，ネットワークの時間変化情報として、イベント時系列データに注目した，多くの社会ネットワークにおいて，相互作用データはイベント時系列として得られる．メール、メーセッジ，通話の発生時刻がその例である．ネットワーク構造はデータを時間的に積分することで得られるが、結果的に時間パターンに関する情報が欠落する．しかし実際、多くの社会活動パターンに共通する特徴として、イベント活動はバースト的(時間的不均一性)であるとの報告がある(Barabasi, A. L. , Nature, 2005)．一方で積分化ネットワークは社会的関係性に関する情報を提供し、多数事例でリンク数(次数)が冪分布に従うことが知られている(構造的不均一性)．これらの時間的・構造的不均一性は、ソーシャル時系列データの両面であるが，従来は別々のモデルを用いて説明が為されてきた．これに対して本課題では、相互作用するポアソン過程の集団現象として、２つの不均一性を統一的に説明する確率モデルの構築を行った(Aoki, Rocha & Gross, PRE, 2016)．特定の条件で積分化ネットワークは次数がべき分布(スケールフリー性)を再現すると共に，各ノードのメッセージイベント時系列からはバースト性が観測された．さらにモデルのマスター方程式を導出し，これを母関数解析することでメッセージ送信のパラメータに応じて，次数分布の分散が発散し転移が生じることを確認した．同時にメッセージイベントの時間間隔がべき分布となることを導出した．

Research Products

• [Int'l Joint Research] University of Naples Federico II/University of Bristol(イタリア，イギリス)
  • Country Name: イタリア，イギリス
  • Counterpart Institution: University of Naples Federico II/University of Bristol
• [Int'l Joint Research] University of Namur/University of Bristol(ベルギー，イギリス)
  • Country Name: ベルギー，イギリス
  • Counterpart Institution: University of Namur/University of Bristol
• [Journal Article] Temporal and structural heterogeneities emerging in adaptive temporal networks (2016)
  • Author(s): Takaaki Aoki, Luis E. C. Rocha, and Thilo Gross
  • Journal Title: Physical Review E Volume: 93 Pages: 040301(R)
  • DOI: 10.1103/PhysRevE.93.040301
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Heterogeneity induces emergent functional networks for synchronization (2015)
  • Author(s): Francesco Scafuti, Takaaki Aoki, and Mario di Bernardo
  • Journal Title: Physical Review E Volume: 91 Pages: 062913
  • DOI: 10.1103/PhysRevE.91.062913
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Presentation] Self-Organization of Temporal Network (2015)
  • Author(s): Takaaki Aoki, Luis E C Rocha, Thilo Gross
  • Organizer: International Symposium on Nonlinear Theory and its Applications (NOLTA2015)
  • Place of Presentation: HongKong, China
  • Year and Date: 2015-12-03 – 2015-12-03
  • Int'l Joint Research / Invited
• [Presentation] A model of adaptive temporal networks (2015)
  • Author(s): Takaaki Aoki
  • Organizer: The 3rd East Asia Joint Seminar on Statistical Physics
  • Place of Presentation: Korea Institute of Advanced Study (KIAS), Seoul, Korea
  • Year and Date: 2015-10-15 – 2015-10-15
  • Int'l Joint Research / Invited
• [Presentation] Hodge-Kodaira Decomposition of Evolving Neural Networks (2015)
  • Author(s): Keiji Miura and Takaaki Aoki
  • Organizer: The 4th IFAC Conference on Analysis and Control of Chaotic Systems
  • Place of Presentation: Tokyo Metropolitan Univ. , Tokyo
  • Year and Date: 2015-08-28 – 2015-08-28
  • Int'l Joint Research / Invited
• [Presentation] Network organization as a dynamical system (2015)
  • Author(s): Takaaki Aoki
  • Organizer: The 4th IFAC Conference on Analysis and Control of Chaotic Systems
  • Place of Presentation: Tokyo Metropolitan Univ. , Tokyo
  • Year and Date: 2015-08-28 – 2015-08-28
  • Int'l Joint Research / Invited
• [Presentation] An evolutionary strategy for network control and synchronization with application to neural systems (2015)
  • Author(s): rancesco Scafuti, Takaaki Aoki, and Mario di Bernardo
  • Organizer: The 4th IFAC Conference on Analysis and Control of Chaotic Systems
  • Place of Presentation: Tokyo Metropolitan Univ. , Tokyo
  • Year and Date: 2015-08-28 – 2015-08-28
  • Int'l Joint Research / Invited
• [Presentation] Scaling of Hodge-Kodaira decomposition distinguishes learning rules of neural networks (2015)
  • Author(s): Keiji Miura and Takaaki Aoki
  • Organizer: The 8th International congress on Industrial and Applied mathematics
  • Place of Presentation: China National Convention Center, Beijing, China
  • Year and Date: 2015-08-10 – 2015-08-10
  • Int'l Joint Research / Invited
• [Presentation] Network organization as a dynamical system (2015)
  • Author(s): Takaaki Aoki
  • Organizer: The 8th International congress on Industrial and Applied mathematics
  • Place of Presentation: China National Convention Center, Beijing, China
  • Year and Date: 2015-08-10 – 2015-08-10
  • Int'l Joint Research / Invited
• [Presentation] Evolution of heterogeneous networks of oscillators for network control and synchronization (2015)
  • Author(s): Takaaki Aoki, Francesco Scafuti, Mario di Bernardo
  • Organizer: Dynamics of Coupled Oscillators: 40 years of the Kuramoto Model
  • Place of Presentation: Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
  • Year and Date: 2015-07-28 – 2015-07-28
  • Int'l Joint Research
• [Presentation] Two kinds of heterogeneities emerging in adaptive temporal networks (2015)
  • Author(s): Takaaki Aoki, Luis E. C. Rocha, and Thilo Gross
  • Organizer: Netsci 2015 (International school and conference on network science)
  • Place of Presentation: World Trade Center, Zaragoza, Spain
  • Year and Date: 2015-06-04 – 2015-06-04
  • Int'l Joint Research
• [Presentation] Heterogeneities in temporal networks emerging from adaptive social interactions (2015)
  • Author(s): Takaaki Aoki, Luis E. C. Rocha, and Thilo Gross
  • Organizer: SIAM Conference on Applications of Dynamical Systems
  • Place of Presentation: Snowbird Ski and Summer Resort, Snowbird, USA
  • Year and Date: 2015-05-17 – 2015-05-17
  • Int'l Joint Research
• [Remarks] Adaptive network: ネットワーク構造とダイナミクスとの相互作用
  • URL: http://www.ed.kagawa-u.ac.jp/~aoki/Research.htm