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Graph bisection problem: approaches from statistical mechanics and theoretical computer science

Research Project

Project/Area Number 22300003
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Fundamental theory of informatics
Research InstitutionTokyo Institute of Technology

Principal Investigator

KABASHIMA Yoshiyuki  東京工業大学, 総合理工学研究科(研究院), 教授 (80260652)

Co-Investigator(Kenkyū-buntansha) WATANABE Osamu  東京工業大学, 大学院情報理工学研究科, 教授 (80158617)
Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥18,200,000 (Direct Cost: ¥14,000,000、Indirect Cost: ¥4,200,000)
Fiscal Year 2013: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2012: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2010: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Keywordsキャビティ法 / グラフ分割問題 / スペクトラル法 / ランダム行列 / レプリカ法 / 評価表現辞書構築 / 自然言語処理
Research Abstract

Statistical mechanics has developed various techniques for analyzing large scale and complicated statistical models through research on complex physical systems such as spin glasses. Recently, much attention has been paid for such methodologies as foundations of efficient approximate algorithms and powerful analytical techniques in information sciences. The main objective of this research project is to deepen the understanding of the effectiveness of such methodologies by collaboration of a physicist and a theoretical computer scientist on a concrete problem. The problem that we focused on was graph bisection problems. We particularly examined the origin of the effectiveness of the ``spectral method'', which is known as a dominant approximate solver for the bisection problem. As a practical application of the graph bisection problem, we also improved an exiting method for the extraction of polarity lexicon from word networks utilizing the knowledge of statistical mechanics.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (56 results)

All 2014 2013 2012 2011 2010 Other

All Journal Article (30 results) (of which Peer Reviewed: 30 results) Presentation (23 results) (of which Invited: 3 results) Book (3 results)

  • [Journal Article] Cavity-based robustness analysis of interdependent networks : Influences of intranetwork and internetwork degree-degree correlations2014

    • Author(s)
      S.Watanabe and Y.Kabashima
    • Journal Title

      Phys. Rev

      Volume: E 89 Issue: 1

    • DOI

      10.1103/physreve.89.012808

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Cavity approach to complex networks2014

    • Author(s)
      Y. Kabashima and S. Watanabe
    • Journal Title

      Topologica

      Volume: 未定

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The query complexity of witness finding2014

    • Author(s)
      A. Kawachi, B. Rossmany and O. Watanabe
    • Journal Title

      Proc. of the 9th International Computer Science Symposium in Russia

      Volume: 未定

    • NAID

      120006582539

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Message passing algorithms for MLS-3LIN problem2013

    • Author(s)
      O.Watanabe
    • Journal Title

      Algorithmica

      Volume: 66 Issue: 4 Pages: 848-868

    • DOI

      10.1007/s00453-013-9762-7

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Is Valiant-Vazirani's isolation probabilityimprovable?2013

    • Author(s)
      Holger Dell, Valentine Kabanets,Dieter van Melkebeek, Osamu Watanabe
    • Journal Title

      Computational Complexity

      Volume: 22(2) Issue: 2 Pages: 345-383

    • DOI

      10.1007/s00037-013-0059-7

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] The first eigenvalues of (c,d)-regular graph, IEICE Trans2013

    • Author(s)
      N.Nakagawa and H.Yamaguchi
    • Journal Title

      Information Systems

      Volume: E96-D(3) Pages: 433-442

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Statistical mechanics approach to 1-bit compressed sensing2013

    • Author(s)
      Yingying Xu and Yoshiyuki Kabashima
    • Journal Title

      Journal of Statistical Mechanics

      Volume: 2013 Issue: 02 Pages: P02041-P02041

    • DOI

      10.1088/1742-5468/2013/02/p02041

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The first eigenvalue of (c, d)-regular graph2013

    • Author(s)
      K. Nakagawa and H. Yamaguchi
    • Journal Title

      IEICE Trans. Information Systems

      Volume: E96-D(3) Pages: 433-442

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Statistical Mechanical Analysis of Semantic Orientations on Lexical Network2012

    • Author(s)
      T.Goto, Y.Kabashima and H.Takamura
    • Journal Title

      Proceedings of the 24^<th> International Conference on Computational Linguistics (COLING2012)

      Pages: 977-993

    • URL

      http://aclweb.org/anthology//C/C12/C12-1060.pdf

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] First eigenvalue/eigenvector in sparse random symmetric matrices : Influences of degree fluctuation2012

    • Author(s)
      Y.Kabashima and H.Takahasi
    • Journal Title

      J. Phys. A : Math. Theor

      Volume: 45 Issue: 32 Pages: 325001-325001

    • DOI

      10.1088/1751-8113/45/32/325001

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sparse-Matrix-Based Compressed Sensing for Spectrum Sensing in Flexible Wireless2012

    • Author(s)
      D.Lee, Y.Kabashima, K.Takeda, T.Yamada, K.Akabane and K.Uehara
    • Journal Title

      Proceedings of the 18^<th> Asia-Pacific Conference on Communications (APCC2012)

      Pages: 418-422

    • URL

      http://www.mlab.t.u-tokyo.ac.jp/attachent/file/256/20120528APCC_final.pdf

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Propagation connectivity of random hypergraphs2012

    • Author(s)
      A.Coja-Oghlan, M.Onjo and O.Watanabe
    • Journal Title

      The Electronic Journal of Combinatorics

      Volume: 19 Pages: 1-25

    • URL

      http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i1p17

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Compressed sensing with sparse, structured matrices2012

    • Author(s)
      M.C.Angelini, F.Ricci-Tersenghi and Y.Kabashima
    • Journal Title

      Proc. Fiftieth Annual Allerton Conference (Allerton House, UIUC, Illinois, USA October 1 - 5, 2012)

      Pages: 808-814

    • DOI

      10.1109/allerton.2012.6483301

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Typical l1-reconstruction limit of sparse vectors represented by concatenations of random orthogonal matrices2012

    • Author(s)
      Yoshiyuki Kabashima, Mikko Vehkaperae and Saikat Chatterjee
    • Journal Title

      Journal of Statistical Mechanics

      Volume: 2012 Issue: 12 Pages: P12003-P12003

    • DOI

      10.1088/1742-5468/2012/12/p12003

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Mean-field Approach for an Intercarrier Interference Canceller for OFDM2012

    • Author(s)
      A. Sakata, Y. Kabashima and Y Peleg
    • Journal Title

      Journal of Statistical Mechanics

      Volume: 2012 Issue: 07 Pages: P07006-P07006

    • DOI

      10.1088/1742-5468/2012/07/p07006

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Replica Plefka expansion of Ising systems2012

    • Author(s)
      Muneki Yasuda, Yoshiyuki Kabashima and Kazuyuki Tanaka
    • Journal Title

      Journal of Statistical Mechanics

      Volume: (2012) Issue: 04 Pages: 1-16

    • DOI

      10.1088/1742-5468/2012/04/p04002

    • Related Report
      2012 Annual Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the optimality of lattices for the Coppersmith technique2012

    • Author(s)
      Y. Aono, M. Agrawal, T. Satoh, and O. Watanabe
    • Journal Title

      Proc. 17th Australasian Conference on Information Security and Privacy (ACISP 2012) LNCS

      Volume: 7372 Pages: 376-389

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Estimating the Gowers norm of modulo functions over prime fields2012

    • Author(s)
      A. Kawachi, H. Tanaka, and O. Watanabe
    • Journal Title

      IEICE Transactions on Information and Systems

      Volume: E95-D(3) Pages: 755-762

    • NAID

      10030611565

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Statistical Mechanical Analysis of Semantic Orientations on Lexical Network2012

    • Author(s)
      Takuma Goto, Yoshiyuki Kabashima and Hiroya Takamura
    • Journal Title

      Proceedings of the 24th International Conference on Computational Linguistics (COLING2012)

      Pages: 977-994

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Average Growth Rate of Low-Density Generator-Matrix Codes Ensembles2012

    • Author(s)
      Kazushi Mimura, Tadashi Wadayama, Yoshiyuki Kabashima
    • Journal Title

      Proceedings of the 2012 IEEE International Symposium on Information Theory and its Applications (ISITA2012, Honolulu, US)

      Pages: 322-326

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sparse-Matrix-Based Compressed Sensing for Spectrum Sensing in Flexible Wireless2012

    • Author(s)
      D. Lee, Y. Kabashima, K. Takeda, T. Yamada, K. Akabane, and K. Uehara
    • Journal Title

      Proceedings of the 18th Asia-Pacific Conference on Comunications (APCC2012)

      Pages: 418-422

    • DOI

      10.1109/apcc.2012.6388172

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analysis of Sparse Representations Using Bi-Orthogonal Dictionaries2012

    • Author(s)
      Mikko Vehkaperae, Yoshiyuki Kabashima, Saikat Chatterjee, Erik Aurell, Mikael Skoglund and Lars K. Rasmussen
    • Journal Title

      Proceedings of Information Theory Workshop 2012 (ITW2012)

      Pages: 652-656

    • DOI

      10.1109/itw.2012.6404757

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Estimating the Gowers Norm of Modulo Functions over Prime Fields2012

    • Author(s)
      A.Kawachi, H.Tanaka, O.Watanabe
    • Journal Title

      IEICE Transactions on Information and Systems

      Volume: E95-D Issue: 3 Pages: 755-762

    • DOI

      10.1587/transinf.E95.D.755

    • NAID

      10030611565

    • ISSN
      0916-8532, 1745-1361
    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spectral Analysis of Random Sparse Matrices2011

    • Author(s)
      T.Ando, Y.Kabashima, H.Takahashi, O.Watanabe and M.Yamamoto
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

      Volume: E94-A Issue: 6 Pages: 1247-1256

    • DOI

      10.1587/transfun.E94.A.1247

    • NAID

      10029802201

    • ISSN
      0916-8508, 1745-1337
    • Related Report
      2013 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Statistical mechanical assessment of a reconstruction limit of compressed sensing : Toward theoretical analysis of correlated signals2011

    • Author(s)
      K.Takeda, Y.Kabashima
    • Journal Title

      EPL (Europhysics Letters)

      Volume: 95 Issue: 1 Pages: 18006-18006

    • DOI

      10.1209/0295-5075/95/18006

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cavity approach to first eigenvalue problem in a family of symmetric random sparse matrices2010

    • Author(s)
      Y.Kabashima, H.Takahashi, O.Watanabe
    • Journal Title

      J.Phys.Conf.Ser.

      Volume: 233 Pages: 0120011-11

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cavity analysis on the robustness of random networks against targeted attacks : Influences of degree-degree correlations2010

    • Author(s)
      Y.Shiraki, Y.Kabshima
    • Journal Title

      Phys.Rev.E

      Volume: 82 Pages: 0361011-10

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Average-case analysis for the MAX-2SAT problem2010

    • Author(s)
      O.Watanale, M.Yamamoto
    • Journal Title

      Theoretical Computer Science

      Volume: 411(16-18) Pages: 1685-1697

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Propagation connectivity of random hypergraphs2010

    • Author(s)
      A.Coja-Oghlan, M.Onsjo, O.Watanabe
    • Journal Title

      Lecture Notes on Computer Science

      Volume: 6302 Pages: 490-503

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spectral Analysis of Random Sparse Matrices

    • Author(s)
      T.Ando, Y.Kabashima, H.Takahashi, O.Watanabe, M.Yamamoto
    • Journal Title

      IEICE TRANS. ED

      Volume: (to appear)

    • NAID

      10029802201

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Cavity-based robustness analysis of complex networks2013

    • Author(s)
      Y.Kabashima and S.Watanabe
    • Organizer
      East Asia Joint Seminars on Statistical Physics
    • Place of Presentation
      Kyoto, Japan
    • Year and Date
      2013-10-22
    • Related Report
      2013 Final Research Report
  • [Presentation] Cavity approach to complex networks2013

    • Author(s)
      Y.Kabashima and S.Watanabe
    • Organizer
      International Workshop on Phase Transition, Critical Phenomena and Related Topics on Complex Networks
    • Place of Presentation
      Sapporo, Japan
    • Year and Date
      2013-09-09
    • Related Report
      2013 Final Research Report
  • [Presentation] Cavity-based robustness analysis of intra- and inter-correlated network2013

    • Author(s)
      Shunsuke Watanabe and Yoshiyuki Kabashima
    • Organizer
      STATPHYS25, Seoul
    • Place of Presentation
      Seoul, Korea
    • Related Report
      2013 Annual Research Report
  • [Presentation] Cavity approach to complex networks2013

    • Author(s)
      Y. Kabashima and S. Watanabe
    • Organizer
      International Workshop on Phase Transition, Critical Phenomena and Related Topics on Complex Networks
    • Place of Presentation
      北海道大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Cavity-based robustness analysis of complex networks2013

    • Author(s)
      Yoshiyuki Kabashima and Shunsuke Watanabe
    • Organizer
      East Asia Joint Seminars on Statistical Physics
    • Place of Presentation
      京都大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Statistical mechanics approach to the first eigenvalue problem in symmetric random sparse matrices2012

    • Author(s)
      Y.Kabashima
    • Organizer
      The 5^<th> International Conference of IMBIC on Mathematical Sciences for Advancement of Science and Technology (MSAST2011)
    • Place of Presentation
      Kolkata, India
    • Year and Date
      2012-12-18
    • Related Report
      2013 Final Research Report
  • [Presentation] ランダム行列とスピングラス理論2012

    • Author(s)
      樺島祥介
    • Organizer
      日本物理学会2012年秋季大会シンポジウム「ランダム行列の過去・現在・未来」
    • Place of Presentation
      横浜国立大学
    • Year and Date
      2012-09-21
    • Related Report
      2013 Final Research Report
  • [Presentation] On the first eigenvalue/eigenvector in sparse random symmetric matrices2012

    • Author(s)
      Y.Kabashima
    • Organizer
      School on Large Scale Problems in Machine Learning and Workshop on Common Concepts in Machine Learning and Statistical Physics
    • Place of Presentation
      Trieste, Italy
    • Year and Date
      2012-08-29
    • Related Report
      2013 Final Research Report 2012 Annual Research Report
  • [Presentation] A Study of the Universal Threshold in the L1 Recovery by Statistical Mechanics2012

    • Author(s)
      K.Takeda, Y.Kabashima
    • Organizer
      The 46th Conference on Information Sciences and Systems
    • Place of Presentation
      Princeton, USA(招待講演)
    • Year and Date
      2012-03-23
    • Related Report
      2011 Annual Research Report
  • [Presentation] Message passing algorithms for MLS-3LIN problem2012

    • Author(s)
      O.Watanabe
    • Organizer
      The 9^<th> Meeting on Analytic Algorithms and Combinatorics (ANALCO'12)
    • Place of Presentation
      Kyoto Japan
    • Year and Date
      2012-01-16
    • Related Report
      2013 Final Research Report
  • [Presentation] Message passing algorithms for MLS-3LIN problem2012

    • Author(s)
      Osamu Watanabe
    • Organizer
      The 9th Meeting on Analytic Algorithmics and Combinatrics (ANALCO'12)
    • Place of Presentation
      Kyoto, Japan
    • Year and Date
      2012-01-16
    • Related Report
      2011 Annual Research Report
  • [Presentation] Statistical Mechanical Analysis of Semantic Orientations on Lexical Network2012

    • Author(s)
      Takuma Goto, Yoshiyuki Kabashima and Hiroya Takamura
    • Organizer
      The 24th International Conference on Computational Linguistics (COLING2012)
    • Place of Presentation
      IIT Bombay, Mumbai, India
    • Related Report
      2012 Annual Research Report
  • [Presentation] Average Growth Rate of Low-Density Generator-Matrix Codes Ensembles2012

    • Author(s)
      Kazushi Mimura, Tadashi Wadayama, Yoshiyuki Kabashima
    • Organizer
      The 2012 IEEE International Symposium on Information Theory and its Applications (ISITA2012)
    • Place of Presentation
      Honolulu, USA
    • Related Report
      2012 Annual Research Report
  • [Presentation] Sparse-Matrix-Based Compressed Sensing for Spectrum Sensing in Flexible Wireless2012

    • Author(s)
      D. Lee, Y. Kabashima, K. Takeda, T. Yamada, K. Akabane, and K. Uehara
    • Organizer
      The 18th Asia-Pacific Conference on Comunications (APCC2012)
    • Place of Presentation
      Jeju, Korea
    • Related Report
      2012 Annual Research Report
  • [Presentation] Compressed sensing with sparse, structured matrices2012

    • Author(s)
      Maria Chiara Angelini, Federico Ricci-Tersenghi and Yoshiyuki Kabashima
    • Organizer
      The Fiftieth Annual Allerton Conference (Allerton2012)
    • Place of Presentation
      Allerton House, UIUC, Illinois, USA
    • Related Report
      2012 Annual Research Report
  • [Presentation] ランダム行列とスピングラス理論2012

    • Author(s)
      樺島祥介
    • Organizer
      日本物理学会2012年秋季大会シンポジウム「ランダム行列の過去・現在・未来」
    • Place of Presentation
      横浜国立大学(神奈川県)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Analysis of Sparse Representations Using Bi-Orthogonal Dictionaries2012

    • Author(s)
      Mikko Vehkaperae, Yoshiyuki Kabashima, Saikat Chatterjee, Erik Aurell, Mikael Skoglund and Lars K. Rasmussen
    • Organizer
      Information Theory Workshop 2012 (ITW2012)
    • Place of Presentation
      Lausanne, Switzerland
    • Related Report
      2012 Annual Research Report
  • [Presentation] Statistical mechanics approach to the first eigenvalue problem in symmetric random sparse matrices2011

    • Author(s)
      Yoshiyuki Kabashima
    • Organizer
      The 5th International Conference of IMBIC on Mathematical Sciences for Advancement of Science and Technology (MSAST2011)
    • Place of Presentation
      Kolkata, India
    • Year and Date
      2011-12-18
    • Related Report
      2011 Annual Research Report
  • [Presentation] Evaluations of hash distributed A^* in optimal sequence alignment2011

    • Author(s)
      Y.Kobayashi, A.Kishimoto, O.Watanabe
    • Organizer
      The 22th International Joint Conference on Artificial Intelligence (IJCAI'11)
    • Place of Presentation
      Barcelona, Spain
    • Year and Date
      2011-07-22
    • Related Report
      2011 Annual Research Report
  • [Presentation] Finding most-likely solution of the perturbed k-linear-equation problem2011

    • Author(s)
      Osamu Watanabe
    • Organizer
      Interdisciplinary Applications of Statistical Physics & Complex Networks
    • Place of Presentation
      Beijing, China
    • Year and Date
      2011-03-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] Statistical mechanics approach to compressive sensing2010

    • Author(s)
      Y.Kabashima
    • Organizer
      Statistical Physics and Computer Science (Beijing Satellite Meeting of STATPHYS-24)
    • Place of Presentation
      Beijing, China
    • Year and Date
      2010-07-09
    • Related Report
      2010 Annual Research Report
  • [Presentation] Statistical Mechanical Analysis of a Typical Reconstruction Limit of Compressed Sensing2010

    • Author(s)
      Y.Kabashima, T.Wadayama, T.Tanaka
    • Organizer
      IEEE International Symposium on Information Theory 2010
    • Place of Presentation
      Austin, Texas, USA
    • Year and Date
      2010-06-17
    • Related Report
      2010 Annual Research Report
  • [Presentation] Statistical Mechanical Analysis of a Compressed Sensing Utilizing Correlated Compression Matrix2010

    • Author(s)
      K.Takeda, Y.Kabashima
    • Organizer
      IEEE International Symposium on Information Theory 2010
    • Place of Presentation
      Austin, Texas, USA
    • Year and Date
      2010-06-17
    • Related Report
      2010 Annual Research Report
  • [Book] ランダム行列の数理と科学,第3章2014

    • Author(s)
      樺島祥介(分担執筆)
    • Publisher
      森北出版
    • Related Report
      2013 Final Research Report
  • [Book] Randomness through Computation (H. Zenil ed.), Chapter 242011

    • Author(s)
      O.Watanabe(分担執筆)
    • Publisher
      World Scientific
    • Related Report
      2013 Final Research Report
  • [Book] Randomness through ComputationのChapter 24(H.Zenil ed.)2011

    • Author(s)
      O.Watanabe(分担執筆)
    • Publisher
      World Scientific
    • Related Report
      2011 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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