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Research on replica symmetry breaking in sparsely connected spin glass models

Research Project

Project/Area Number 17340116
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionTokyo Institute of Technology

Principal Investigator

KABASHIMA Yoshiyuki  Tokyo Institute of Technology, Dept. of Comput Intell. & Syst. Sci., Professor (80260652)

Co-Investigator(Kenkyū-buntansha) HUKUSHIMA Koji  University of Tokyo, Dept. of Basic Science, Associate Professor (80282606)
INOUE Masato  Waseda University, Dept. of Elect. Eng. & Bioscience, Associate Professor (70376953)
Project Period (FY) 2005 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥12,770,000 (Direct Cost: ¥11,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2007: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2006: ¥5,100,000 (Direct Cost: ¥5,100,000)
Fiscal Year 2005: ¥3,900,000 (Direct Cost: ¥3,900,000)
Keywordsspin glasses / sparsely connected models / replica symmetry breaking / de Almeida-Thouless instability / spin glass susceptibility / survey propagation / AT解析 / 信念伝搬 / レプリカ法 / モンテカルロ法 / 低密度パリティ検査符号
Research Abstract

The objective of this research is to explore the replica symmetry breaking (RSB) phenomena observed in sparsely connected spin glass models of Ising spins. In particular, we seek for a general expression of the de Almeida-Thouless (AT) condition which signals the local instability for RSB and examine properties of the RSB phase of the sparsely-connected models. The obtained results are summarized as follows.
1. A general expression of the AT condition was obtained by evaluation of the spin glass susceptibility utilizing the belief propagation algorithm. We also found that the AT condition is determined by a stochastic process that is subject to a large deviation statistics, and developed a methodology to assess the large deviation rate function that characterizes the stochastic process.
2. An algorithm to efficiently search Bethe approximation solutions is developed. We performed the Hessian analysis of the Bethe free energy using this algorithm and found that an expected finite size scaling relation is likely to hold for solutions of the Bethe approximation when the external field is relatively small although numerical determination of the critical point is difficult.
3. For Markov Chain Monte Carlo-based assessment of the critical point, we examined properties of three measures, the principal eigen value of the susceptibility matrix A, that of the spin glass susceptibility matrix ASG and the spin glass susceptibility XSG. We found that for A and ASG, certain bias corrections are indispensable due to finite-size effect although ASG is most preferred in terms of accuracy of data.
4. Properties in the limit of vanishing temperature was examined by using the replica method. The analysis indicates that the ground states are characterized by the one step RSB solution. This property is in contrast with that of the fully connected models, the zero temperature states of which are generally described by the full RSB solution.

Report

(4 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (56 results)

All 2008 2007 2006 2005 Other

All Journal Article (37 results) (of which Peer Reviewed: 13 results) Presentation (18 results) Book (1 results)

  • [Journal Article] Perceptron capacity revisited: classification ability for correlated patterns2008

    • Author(s)
      Y. Shinzato and Y. Kabashima
    • Journal Title

      J. Phys. A: Math. Theor. (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Inference from correlated patterns: a unified theory for perceptron learning and linear vector channels2008

    • Author(s)
      Y. Kabashima
    • Journal Title

      J. Phys. Conf. Ser. 95

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Inference from correlated patterns : a unified theory for perceptron learning and linear vector channels2008

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

      J. Phys. Conf. Ser. 95 012001

      Pages: 13-13

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Statistical mechanical analysis of the linear vector channel in digital communication2007

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

      J. Phys. A: Math. Theor. 40

      Pages: 14085-14098

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Sequential minimization of the Bethe Free Energy of Ising Spin Systems2007

    • Author(s)
      Y. Tonosaki and Y. Kabashima
    • Journal Title

      Interdisciplinary Information Sciences 13

      Pages: 57-64

    • NAID

      110006279749

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] LDPC Decoding Dynamics from a PCA Viewpoint2007

    • Author(s)
      S. Hara, Y. Akira, E. Ishii, M. Inoue and M. Okada
    • Journal Title

      Interdisciplinary Information Sciences 13

      Pages: 43-48

    • NAID

      110006274938

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Numerical study of Thouless-Anderson-Palmer metastable states in three-body Ising spin glasses2007

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

      Physical Review B 75

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Statistical mechanical analysis of the linear vector channels in digital communication2007

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

      J. Phys. A : Math. Theor. 40

      Pages: 14085-14098

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Sequential Minimization of the Bethe Free Energy of Ising Spin Systems2007

    • Author(s)
      Y., Tonosaki, Y., Kabashima
    • Journal Title

      Interdisciplinary Information Sciences Vol. 13, No. 1

      Pages: 57-64

    • NAID

      110006279749

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] LDPC Decoding Dynamics from a PCA Viewpoint2007

    • Author(s)
      S., Hara, Y., Akira, E., Ishii, M., Inoue, M., Okada
    • Journal Title

      Interdisciplinary Information Sciences Vol. 13, No. 1

      Pages: 43-48

    • NAID

      110006274938

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Numerical study of Thouless-Anderson-Palmer metastable states in three-body Ising spin glasses2007

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

      Phys. Rev. B 75 094405

      Pages: 6-6

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Akaike Information Criterion AIC- Modeling, Prediction and Knowledge Discovery-(in Japanese)2007

    • Author(s)
      H., Akaike, S-i., Amari, G., Kitagawa, Y., Kabashima, H., Shimodaira, (K., Murota, T> Tsuchiya, eds.)
    • Journal Title

      Kyoritu Shuppan

      Pages: 160-160

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Sequential Minimization of the Bethe Free Energy of Ising Spin Systems2007

    • Author(s)
      Y. Tonosaki and Y. Kabashima
    • Journal Title

      Interdisciplinary Information Sciences 13

      Pages: 57-64

    • NAID

      110006279749

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] LDPC Decoding Dynamics from a PCA Viewpoint2007

    • Author(s)
      S. Hara, Y. Akiba, E. Ishii, M. Inoue and M. Okada
    • Journal Title

      Interdisciplinary Information Sciences 13

      Pages: 43-48

    • NAID

      110006274938

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical study of Thouless-Anderson-Palmer metastable states in three-body Ising spin glasses2007

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

      Physical Review B 75

    • Related Report
      2006 Annual Research Report
  • [Journal Article] LDPC decoding dynamics from a PCA viewpoint2007

    • Author(s)
      S.Hara, Y.Akira, E.Ishii, M.Inoue, M.Okada
    • Journal Title

      Interdisciplinary Information Sciences (in Press)

    • NAID

      110006274938

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Analysis of CDMA systems that are characterized by eigenvalue spectrum2006

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

      Europhysics Letters 76

      Pages: 1193-1196

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Tutorial on Brain-Inspired Computing Part 5: Statistical Mechanics of Communication and Computation2006

    • Author(s)
      Y. Kabashima
    • Journal Title

      New Generation Computing 24

      Pages: 403-420

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Survey propagation for the cascading Sourlas code2006

    • Author(s)
      JPL Hatchet and Y. Kabashima
    • Journal Title

      J. Phys. A: Math. Gen. 39

      Pages: 10659-10672

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Statistical Mechanical Approach to Lossy Data Compression: Theory and Practice2006

    • Author(s)
      T. Hosaka and Y. Kabashima
    • Journal Title

      Physica A 365

      Pages: 113-119

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Analysis Method Combining Monte Carlo Simulation and Principal Component Analysis-Application to Sourlas code-2006

    • Author(s)
      M. Inoue, K. Hukushima and M. Okada
    • Journal Title

      J. Phys. Soc. Jpn. 75

    • NAID

      110004799201

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Analysis of CDMA systems that are characterized by eigenvalue spectrum2006

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

      Europhysics Letters 76

      Pages: 1193-1199

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Tutorial on Brain-Inspired Computing Part 5 : Statistical Mechanics of Communication and Computation2006

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

      New Generation Computing 24

      Pages: 403-420

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Survey propagation for the cascading Sourlas code2006

    • Author(s)
      JPL., Hatchet, Y., Kabashima
    • Journal Title

      JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 39

      Pages: 10659-10672

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Statistical Mechanical Approach to Lossy Data Compression : Theory and Practice2006

    • Author(s)
      T., Hosaka, Y., Kabashima
    • Journal Title

      Physica A 365, Issue 1

      Pages: 113-119

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Analysis Method Combining Monte Carlo Simulation and Principal Component Analysis- Application to Sourlas Code2006

    • Author(s)
      M., Inoue, K., Hukushima, M., Okada
    • Journal Title

      J. Phys. Soc. Jpn. 75 084003

      Pages: 6-6

    • NAID

      110004799201

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Survey propagation for cascading Sourlas code2006

    • Author(s)
      JPL.Hatchett, Y.Kabashima
    • Journal Title

      Journal of Physics A : Mathematical and General 39

      Pages: 10659-10672

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Tutorial on Brain-Inspired Computing Part 5 : Statistical Mechanics of Communication and Computation2006

    • Author(s)
      Y.Kabashima
    • Journal Title

      New Generation Computing 25

      Pages: 403-420

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Analysis of CDMA systems that are characterized by eigenvalue spectrum2006

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

      Europhysics Letters 76

      Pages: 1193-1199

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Extended scaling scheme for critically divergent quantities in ferromagnets and spin glasses2006

    • Author(s)
      I.A.Campbell, K.Hukushima, H.Takayama
    • Journal Title

      Phys. Rev. Lett. 97

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Statistical Mechanical Development of a Sparse Bayesian Classifier2005

    • Author(s)
      S.Uda, Y.Kabashima
    • Journal Title

      Journal of the Physical Society of Japan 74

      Pages: 2233-2242

    • NAID

      110001979698

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Replicated Bethe Free Energy : A Variational Principle behind Survey Propagation2005

    • Author(s)
      Y.Kabashima
    • Journal Title

      Journal of the Physical Society of Japan 74

      Pages: 2133-2136

    • NAID

      110001979674

    • Related Report
      2005 Annual Research Report
  • [Journal Article] An Exact Analytic Continuation to Complex Replica Number in the Discrete Random Energy Model of Finite System Size2005

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

      Progress of Theoretical Physics Supplement 157

      Pages: 103-106

    • NAID

      110001275990

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Monte Carlo simulations of the phase transition of the three-dimensional isotropic Heisenberg spin glass2005

    • Author(s)
      H.Hukushima, H.Kawamura
    • Journal Title

      Physical Review B 72

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Temperature Chaos and Bond Chaos in Edwards-Anderson Ising Spin Glasses : Domain-Wall Free-Energy Measurements2005

    • Author(s)
      M.Sasaki, K.Hukushima, H.Yoshino, H.Takayama
    • Journal Title

      Physical Review Letters 95

    • NAID

      120000775175

    • Related Report
      2005 Annual Research Report
  • [Journal Article] An LDPCC decoding algorithm based on Bowman-Levin approximation-- Comparison with BP and CCCP --2005

    • Author(s)
      M Inoue, M Komiya, Y Kabashima
    • Journal Title

      Proceedings of 2005 IEEE International Symposium on Information Theory

      Pages: 444-448

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Perceptron capacity revisited ; classification ability for correlated patterns

    • Author(s)
      T., Shinzato, Y., Kabashima
    • Journal Title

      J. Phys. A : Math. Theor. (To appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] An integral formula for large random rectangular matrices and its application to analysis of linear vector channels2008

    • Author(s)
      Y. Kabashima
    • Organizer
      PHYSCOMNET2008
    • Place of Presentation
      Berlin, Germany
    • Year and Date
      2008-04-04
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] An integral formula for large random rectangular matrices and its application to analysis of linear vector channels2008

    • Author(s)
      Y., Kabashima
    • Organizer
      PHYSCOMNET 2008
    • Place of Presentation
      Berlin,Germany
    • Year and Date
      2008-04-04
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 複素レプリカ平面における分配関数の零点の性質-RSBを伴う場合-2008

    • Author(s)
      小渕智之, 西森秀稔, 樺島祥介
    • Organizer
      日本物理学会第63回年次大会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-26
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Zeros of the replicated partition function on the complex replica pane-in the presence of the RSB (in Japanese)2008

    • Author(s)
      T., Obuchi, H., Nishimori, Y., Kabashima
    • Organizer
      The 63rd annual meeting of the Japanese Physical Society
    • Place of Presentation
      Kinki University, Japan
    • Year and Date
      2008-03-26
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 磁場あり疎結合スピングラス模型におけるBethe近似を用いたAT解析2007

    • Author(s)
      原慎平, 井上真郷, 高橋久尚, 福島孝治, 樺島祥介
    • Organizer
      日本物理学会第62回年次大会
    • Place of Presentation
      北海道大学
    • Year and Date
      2007-09-21
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] AT analysis with Bethe approximation in sparsely-connected spin-glass model with magnetic field (in Japanese)2007

    • Author(s)
      S., Hara, M., Inoue, H., Takahashi, K., Hukushima, Y., Kabashima
    • Organizer
      The 62nd annual meeting of the Japanese Physical Society
    • Place of Presentation
      Hokkaido University, Japan
    • Year and Date
      2007-09-21
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 結合された温度の異なる2つのランジュバン方程式で記述される系の定常状態の研究2007

    • Author(s)
      金子勇治, 樺島祥介
    • Organizer
      日本物理学会春季大会
    • Place of Presentation
      鹿児島大学
    • Year and Date
      2007-03-21
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] A study of stationary state which is described by coupled two Langevin equations that have different temperatures (in Japanese)2007

    • Author(s)
      Y., Kaneko, Y., Kabashima
    • Organizer
      The 2007 spring meeting of the Japanese Physical Society
    • Place of Presentation
      Kagoshima University, Japan
    • Year and Date
      2007-03-21
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] イジングスピン系のべーテ自由エネルギー逐次的最小化2007

    • Author(s)
      外崎幸則, 樺島祥介
    • Organizer
      日本物理学会春季大会
    • Place of Presentation
      鹿児島大学
    • Year and Date
      2007-03-20
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Sequential minimization of the Bethe free energy of Ising spin systems (in Japanese)2007

    • Author(s)
      Y., Tonosaki, Y., Kabashima
    • Organizer
      The 2007 spring meeting of the Japanese Physical Society
    • Place of Presentation
      Kagoshima University, Japan
    • Year and Date
      2007-03-20
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] レプリカ拡張に基づくAT線のモード解析2006

    • Author(s)
      樺島祥介, 福島孝治
    • Organizer
      日本物理学会秋季大会
    • Place of Presentation
      千葉大学
    • Year and Date
      2006-09-23
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Mode analysis of the AT line in the replica extension framework (in Japanese)2006

    • Author(s)
      Y., Kabashima, K., Hukushima
    • Organizer
      The 2006 autumn meeting of the Japanese Physical Society
    • Place of Presentation
      Chiba University, Japan
    • Year and Date
      2006-09-23
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 単一サンプル系に関するレプリカ法とレプリカ対称性の破れについて2006

    • Author(s)
      樺島祥介
    • Organizer
      情報物理学の数理的構造
    • Place of Presentation
      京都大学数理解析学研究所
    • Year and Date
      2006-06-30
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the replica method for single sample systems and replica symmetry breaking (in Japanese)2006

    • Author(s)
      Y., Kabashima
    • Organizer
      Mathematical Structure of Information Physics, RIMS
    • Place of Presentation
      Kyoto University, Japan
    • Year and Date
      2006-06-30
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] レプリカ拡張に基づいたAT条件の考察2006

    • Author(s)
      樺島祥介, 福島孝治
    • Organizer
      日本物理学第61回年次大会
    • Place of Presentation
      愛媛大学
    • Year and Date
      2006-03-27
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 自由エネルギー降下原理に基づくTAP方程式の解法2006

    • Author(s)
      外崎幸徳, 樺島祥介
    • Organizer
      日本物理学第61回年次大会
    • Place of Presentation
      愛媛大学
    • Year and Date
      2006-03-27
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Review on the AT line in the replica extension framework (in Japanese)2006

    • Author(s)
      Y., Kabashima, K., Hukushima
    • Organizer
      The 61st annual meeting of the Japanese Physical Society
    • Place of Presentation
      Ehime University, Japan
    • Year and Date
      2006-03-27
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Solving TAP equation based on free energy descent principle (in Japanese)2006

    • Author(s)
      Y., Tonosaki, Y., Kabashima
    • Organizer
      The 61st annual meeting of the Japanese Physical Society
    • Place of Presentation
      Ehime University, Japan
    • Year and Date
      2006-03-27
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] 赤池情報量基準AIC-モデリング・予測・知識発見-2007

    • Author(s)
      赤池弘次・甘利俊一・北川源四郎・樺島祥介・下平英寿著, 室田一雄・土谷隆編
    • Total Pages
      160
    • Publisher
      共立出版
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary

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Published: 2005-04-01   Modified: 2016-04-21  

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