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Spectral analysis of complex networks and modeling methods by statistics

Research Project

Project/Area Number 23654046
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionTohoku University

Principal Investigator

OBATA Nobuaki  東北大学, 情報科学研究科, 教授 (10169360)

Co-Investigator(Renkei-kenkyūsha) HORA Akihito  北海道大学, 大学院・理学研究院, 教授 (10212200)
KONNO Norio  横浜国立大学, 大学院・工学研究院, 教授 (80205575)
Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywordsネットワーク / 量子確率 / 量子ウォーク / ランダムグラフ / スペクトル / 局在化 / 有向グラフ / 固有値分布
Research Abstract

(1) Spectral analysis of networks: The asymptotic spectral distribution of the distance-k graph of the cartesian product graph is derived as a combinatorial central limit theorem. The asymptotic spectral distribution of weighted hypercubes are described in terms of q-deformed Hermite polynomials. The spectral distribution is completely determined for the Manhattan product of directed paths of small orders, and thier asymptotic behaviors are obtained in the infinite length.
(2) Statistical and asymptotic behaviors of dynamics for the modeling methods: A quantum probabilistic method is applied to classical random walks for reconstructing transition probability and recurrence probability. A necessary and sufficient condition is obtained for a quantum walk (Grover walk) on a spidernet in order to exhibit the localization.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (44 results)

All 2014 2013 2012 2011 Other

All Journal Article (13 results) (of which Peer Reviewed: 12 results) Presentation (28 results) (of which Invited: 2 results) Book (1 results) Remarks (2 results)

  • [Journal Article] The Karlin-McGregor formula for paths connected with a clique2013

    • Author(s)
      Nobuaki Obata
    • Journal Title

      Prob. Math. Stat

      Volume: 33(2) Pages: 451-466

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic spectral distributions of distance-k graphs of Cartesian product graphs2013

    • Author(s)
      Yuji Hibino, Hun Hee Lee, and Nobuaki Obata
    • Journal Title

      Colloq. Math.

      Volume: 132 Issue: 1 Pages: 35-51

    • DOI

      10.4064/cm132-1-4

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Distance-k graphs of hypercube and q-Hermite polynomials2013

    • Author(s)
      Hun Hee Lee and Nobuaki Obata
    • Journal Title

      Infin. Dimens. Anal. Quantum Probab. Relat. Top.

      Volume: 16 Issue: 02 Pages: 1350011-1350011

    • DOI

      10.1142/s0219025713500112

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Localization of the Grover walks on spidernets and free Meixner laws2013

    • Author(s)
      Norio Konno, Nobuaki Obata, and Etsuo Segawa
    • Journal Title

      Comm. Math. Phys.

      Volume: 322 Issue: 3 Pages: 667-695

    • DOI

      10.1007/s00220-013-1742-x

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Spectra of Manhattan Products of Directed Paths <i>P</i><sub><i>n</i></sub>#<i>P</i><sub>2</sub>2012

    • Author(s)
      Nobuaki Obata
    • Journal Title

      Interdisciplinary Information Sciences

      Volume: 18 Issue: 1 Pages: 43-54

    • DOI

      10.4036/iis.2012.43

    • NAID

      130001916189

    • ISSN
      1340-9050, 1347-6157
    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] One-mode interacting Fock spaces and random walks on graphs2012

    • Author(s)
      Nobuaki Obata
    • Journal Title

      Stochastics

      Volume: 84 Issue: 2-3 Pages: 383-392

    • DOI

      10.1080/17442508.2010.550919

    • Related Report
      2013 Final Research Report 2012 Research-status Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Manhattan products of digraphs : characteristic polynomials and examples2012

    • Author(s)
      Nobuaki Obata
    • Journal Title

      Ann. Funct. Anal

      Volume: 3(2) Pages: 135-143

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic spectral distributions of distance k-graphs of large-dimensional hypercubes2012

    • Author(s)
      Nobuaki Obata
    • Journal Title

      Banach Center Publications

      Volume: 96 Pages: 287-292

    • DOI

      10.4064/bc96-0-20

    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Manhattan Products of Digraphs: Characteristic polynomials and examples2012

    • Author(s)
      Nobuaki Obata
    • Journal Title

      Ann. Funct. Anal.

      Volume: 3 Pages: 135-143

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Asymptotic spectral distributions of distance ...2012

    • Author(s)
      Nobuaki Obata
    • Journal Title

      to appear in Banach Center Publications

      Volume: 未定

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Manhattan product of digraphs2012

    • Author(s)
      Nobuaki Obata
    • Journal Title

      to appear in RIMS Kokyuroku

      Volume: 未定

    • Related Report
      2011 Research-status Report
  • [Journal Article] Markov product of positive definite kernels and applications to Q-matrices of graph products2011

    • Author(s)
      Nobuaki Obata
    • Journal Title

      Colloq. Math

      Volume: 122(2) Pages: 177-184

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Markov product of positive definite kernels ...2011

    • Author(s)
      Nobuaki Obata
    • Journal Title

      Colloq. Math.

      Volume: 122 Pages: 177-184

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Free Meixner laws and localization of quantum walks on spidernets2014

    • Author(s)
      Nobuaki Obata
    • Organizer
      Non-commutative and infinite dimensional harmonic analysis : representation theory and probability theory
    • Place of Presentation
      九州大学
    • Year and Date
      2014-02-17
    • Related Report
      2013 Final Research Report
  • [Presentation] Coupled oscillators on digraphs with self-adaptive dynamics2014

    • Author(s)
      Nobuaki Obata
    • Organizer
      International Joint Research Week on Non-Commutative Stochastic Systems : Analysis, Modelling, and Applications
    • Place of Presentation
      東北大学
    • Year and Date
      2014-02-07
    • Related Report
      2013 Final Research Report
  • [Presentation] Spectral analysis of digraphs and coupled oscillators2013

    • Author(s)
      Nobuaki Obata
    • Organizer
      3rd Tunisian-Japanese Conference : Geometric and Harmonic Analysis on Homogeneous Spaces and Applications
    • Place of Presentation
      Yasmine Hammamet, Tunisia
    • Year and Date
      2013-12-19
    • Related Report
      2013 Final Research Report
  • [Presentation] Spectral analysis of Manhattan street networks2013

    • Author(s)
      Nobuaki Obata
    • Organizer
      Tunisian -Japanese Symposium on Science, Society and Technology (TJASSST 2013)
    • Place of Presentation
      Yasmine Hammamet, Tunisia
    • Year and Date
      2013-11-15
    • Related Report
      2013 Final Research Report
  • [Presentation] Spectra of Manhattan street digraphs for synchronization of coupled oscillators2013

    • Author(s)
      Nobuaki Obata
    • Organizer
      NIMS Hot Topics Workshops on The 8th Jikji workshop : Infinite Dimensional Analysis and Quantum Probability
    • Place of Presentation
      Daejeon, Korea
    • Year and Date
      2013-08-19
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] Asymptotic spectral distributions of distance k-graphs of Cartesian product graphs2012

    • Author(s)
      Nobuaki Obata
    • Organizer
      International Conference in Honour of Sixtieth Birthday of Rajendra Bhatia : Matrices and Operators Indian Institute of Science
    • Place of Presentation
      Bangalore, India
    • Year and Date
      2012-12-29
    • Related Report
      2013 Final Research Report
  • [Presentation] Quantum probability and asymptotic spectral analysis of growing graphs2012

    • Author(s)
      Nobuaki Obata
    • Organizer
      International Conference on mathematical modeling and its aplications (ICMMA 2012)
    • Place of Presentation
      Annamalainagar, India
    • Year and Date
      2012-12-23
    • Related Report
      2013 Final Research Report
  • [Presentation] Asymptotic spectral analysis of growing graphs : A quantum probabilistic approach2012

    • Author(s)
      Nobuaki Obata
    • Organizer
      International Conference on Frontiers of Statistics and its Applications
    • Place of Presentation
      Puducherry, India
    • Year and Date
      2012-12-22
    • Related Report
      2013 Final Research Report
  • [Presentation] Quantum probability and asymptotic spectral analysis of growing graphs2012

    • Author(s)
      Nobuaki Obata
    • Organizer
      International Conference on Stochastic Modelling and Simulation (ICSMS2012)
    • Place of Presentation
      Chennai, India
    • Year and Date
      2012-12-17
    • Related Report
      2013 Final Research Report
  • [Presentation] Distance k-graphs of direct product graphs and their asymptotic spectral distributions2012

    • Author(s)
      Nobuaki Obata
    • Organizer
      QP 33 "Quantum Probabilities and Related Fields" Centre International de Rencontres Mathematiques (CIRM)
    • Place of Presentation
      Luminy, France
    • Year and Date
      2012-10-05
    • Related Report
      2013 Final Research Report
  • [Presentation] Localization of quantum walks on spidernets2012

    • Author(s)
      Nobuaki Obata
    • Organizer
      15th Workshop on Non-Commutative Harmonic Analysis : Random Matrices, representation theory and free probability
    • Place of Presentation
      with applications Mathematical Research and Conference Center (MRCC), Bedlewo, Poland
    • Year and Date
      2012-09-24
    • Related Report
      2013 Final Research Report
  • [Presentation] Random walk, quantum walk, and quantum probability2012

    • Author(s)
      Nobuaki Obata
    • Organizer
      6th KMS Probability Workshop
    • Place of Presentation
      Seoul, Korea
    • Year and Date
      2012-06-01
    • Related Report
      2013 Final Research Report
  • [Presentation] Spectral analysis of digraphs2012

    • Author(s)
      Nobuaki Obata
    • Organizer
      Workshop on Non-Commutative Harmonic Analysis with Applications to Real World Complex Phenomena
    • Place of Presentation
      Hanyang University, Korea
    • Year and Date
      2012-01-16
    • Related Report
      2013 Final Research Report
  • [Presentation] Random walk, quantum walk, and quantum probability2012

    • Author(s)
      Nobuaki Obata
    • Organizer
      6th Korean Mathenatical Society Probability Workshop
    • Place of Presentation
      Seoul, Korea
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Localization of quantum walks on spidernets2012

    • Author(s)
      Nobuaki Obata
    • Organizer
      15th Workshop on Non-Commutative Harmonic Analysis: Random Matrices, representation theory and free probability, with applications
    • Place of Presentation
      Bedlewo, Poland
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Distance k-graphs of direct product graphs and their asymptotic spectral distributions2012

    • Author(s)
      Nobuaki Obata
    • Organizer
      QP 33: Quantum Probabilities and Related Fields
    • Place of Presentation
      Luminy, France
    • Related Report
      2012 Research-status Report
  • [Presentation] Asymptotic spectral analysis of growing graphs: A quantum probabilistic approach2012

    • Author(s)
      Nobuaki Obata
    • Organizer
      International Conference on Frontiers of Statistics and its Applications
    • Place of Presentation
      Puducherry, India
    • Related Report
      2012 Research-status Report
  • [Presentation] Spectral analysis of digraphs2012

    • Author(s)
      Nobuaki Obata
    • Organizer
      Workshop on Non-Commutative Harmonic Analysis ...(招待講演)
    • Place of Presentation
      Seoul, Korea
    • Related Report
      2011 Research-status Report
  • [Presentation] Quantum probabilistic spectral analysis of graphs2011

    • Author(s)
      Nobuaki Obata
    • Organizer
      数理解析研究所研究集会「独立性と従属性の数理 -- 代数と確率の出会い --」
    • Place of Presentation
      京都
    • Year and Date
      2011-12-19
    • Related Report
      2013 Final Research Report 2011 Research-status Report
  • [Presentation] Quantum probabilistic spectral analysis of large graphs2011

    • Author(s)
      Nobuaki Obata
    • Organizer
      The 2nd Tunisian--Japanese Conference : Geometric and Harmonic Analysis on Homogeneous Spaces and Applications
    • Place of Presentation
      Sousse, Tunisia
    • Year and Date
      2011-12-14
    • Related Report
      2013 Final Research Report
  • [Presentation] Spectral analysis of product graphs2011

    • Author(s)
      Nobuaki Obata
    • Organizer
      3rd Conference of Settat on Operator Algebras and Applications Marrakesh
    • Place of Presentation
      Morocco
    • Year and Date
      2011-11-01
    • Related Report
      2013 Final Research Report
  • [Presentation] Quantum probabilistic spectral analysis of networks and applications2011

    • Author(s)
      Nobuaki Obata
    • Organizer
      International Conference on Stochastic Analysis and Applications Hammamet
    • Place of Presentation
      Tunisia
    • Year and Date
      2011-10-11
    • Related Report
      2013 Final Research Report
  • [Presentation] Spectral analysis of Manhattan products of digraphs2011

    • Author(s)
      Nobuaki Obata
    • Organizer
      14th Workshop : Non-commutative Harmonic Analysis
    • Place of Presentation
      Bedlewo, Poland
    • Year and Date
      2011-09-25
    • Related Report
      2013 Final Research Report
  • [Presentation] Spectral analysis of Manhattan products of ...2011

    • Author(s)
      Nobuaki Obata
    • Organizer
      14th Workshop: Non-commutative Harmonic Analysis(招待講演)
    • Place of Presentation
      Bedlewo, Poland
    • Related Report
      2011 Research-status Report
  • [Presentation] Quantum probabilistic spectral analysis of ...2011

    • Author(s)
      Nobuaki Obata
    • Organizer
      Internat. Conf. Stochastic Anal. Appl.(招待講演)
    • Place of Presentation
      Hammamet, Tunisia
    • Related Report
      2011 Research-status Report
  • [Presentation] Spectral analysis of product graphs2011

    • Author(s)
      Nobuaki Obata
    • Organizer
      3rd Settat Conf. Operator Algebras and Appl.
    • Place of Presentation
      Marrakesh, Morocco
    • Related Report
      2011 Research-status Report
  • [Presentation] Quantum probabilistic spectral analysis of ...2011

    • Author(s)
      Nobuaki Obata
    • Organizer
      2nd Tunisian-Japanese Conf. Geo. Harm. Anal.
    • Place of Presentation
      Sousse, Tunisia
    • Related Report
      2011 Research-status Report
  • [Presentation] Free Meixner laws and localization of quantum walks on spidernets

    • Author(s)
      Nobuaki Obata
    • Organizer
      Non-commutative and infinite dimensional harmonic analysis: representation theory and probability theory
    • Place of Presentation
      九州大学
    • Related Report
      2013 Annual Research Report
  • [Book] 確率モデル要論2012

    • Author(s)
      尾畑伸明
    • Publisher
      牧野書店
    • Related Report
      2012 Research-status Report
  • [Remarks]

    • URL

      http://www.math.is.tohoku.ac.jp

    • Related Report
      2013 Final Research Report
  • [Remarks] 研究室ウェッブページ

    • URL

      http://www.math.is.tohoku.ac.jp/~obata/

    • Related Report
      2012 Research-status Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

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