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Stochastic formulation of sampling dynamics in generalized ensemble methods

Jae Gil Kim1,*, Yoshifumi Fukunishi2, Akinori Kidera3, and Haruki Nakamura4

  • 1Japan Biological Information Research Center (JBIRC), Japan Biological Informatics Consortium, Aomi 2-41-6, Koto-ku, Tokyo 135-0064, Japan
  • 2Biological Information Research Center (BIRC), National Institute of Advanced Industrial Science and Technology, Aomi 2-41-6, Koto-ku, Tokyo 135-0064, Japan
  • 3Graduate School of Integrated Science, Yokohama City University, Yokohama 230-0045, Japan
  • 4Laboratory of Protein Informatics, Research Center for Structural Biology Institute for Protein Research, Osaka University 3-2 Yamadaoka, Suita, Osaka 565-0871, Japan

  • *Corresponding author. Email address: jgkim@jbirc.aist.go.jp
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Phys. Rev. E 69, 021101 – Published 10 February, 2004

DOI: https://doi.org/10.1103/PhysRevE.69.021101

Abstract

The fundamental relations of the sampling process in the multicanonical ensemble and simulated tempering have been studied in the expanded ensembles formalism. The simulated tempering is identified as the multicanonical sampling with the generalized weight determined by a Laplace transform of the temperature weight. The characteristic dynamics of both sampling methods has been verified in the stochastic formulation of the sampling process. Our study gives a necessary and sufficient condition for the weights to realize a uniform sampling in the energy and temperature spaces. Based on the stochastic model, robust force biased iteration schemes have been proposed to allow automatic determinations of uniform sampling weights.

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References (30)

  1. M. Karplus and G.A. Petsko, Nature (London) 347, 631 (1990).
  2. J.P.K. Doye, D.J. Wales, and M.A. Miller, J. Chem. Phys. 109, 8143 (1998).
  3. C. Maranas and C. Floudas, J. Chem. Phys. 97, 7667 (1992).
  4. D.D. Frantz, D.L. Freeman, and J.D. Doll, J. Chem. Phys. 93, 2769 (1990); K. Hukushima and K. Nemoto, J. Phys. Soc. Jpn. 65, 1604 (1996).
  5. J.P. Valleau, J. Chem. Phys. 99, 4718 (1993).
  6. B.A. Berg and T. Neuhaus, Phys. Lett. B 267, 249 (1991).
  7. J. Lee, Phys. Rev. Lett. 71, 211 (1993).
  8. E. Marinari and G. Parisi, Europhys. Lett. 19, 451 (1992).
  9. A.P. Lyubartsev, A.A. Martsinovski, S.V. Shevkunov, and P.N. Vorontsov-Velyaminov, J. Chem. Phys. 96, 1776 (1992).
  10. F. Wang and D.P. Landau, Phys. Rev. Lett. 86, 2050 (2001).
  11. U.H.E. Hansmann, Comp. Sci. Eng. 5, 64 (2003).
  12. B.A. Berg and T. Celik, Phys. Rev. Lett. 69, 2292 (1992).
  13. U.H.E. Hansmann and Y. Okamoto, J. Comput. Chem. 14, 1333 (1993); N.A. Alves and U.H.E. Hansmann, J. Chem. Phys. 117, 2337 (2002).
  14. U.H.E. Hansmann and Y. Okamoto, Phys. Rev. E 54, 5863 (1996).
  15. S. Kumar, P. Payne, and M. Vasquez, J. Comput. Chem. 17, 1269 (1996).
  16. C. Tsallis, J. Stat. Phys. 52, 479 (1988).
  17. I. Andricioaei and J.E. Straub, Phys. Rev. E 53, 3055 (1996); J. Chem. Phys. 107, 9117 (1997).
  18. U.H.E. Hansmann and Y. Okamoto, Phys. Rev. E 56, 2228 (1997).
  19. Y. Pak and S. Wang, J. Chem. Phys. 111, 4359 (1999).
  20. I. Fukuda and H. Nakamura, Phys. Rev. E 65, 026105 (2002).
  21. C. Beck, Phys. Rev. Lett. 87, 180601 (2001).
  22. N. Nakajima, H. Nakamura, and A. Kidera, J. Phys. Chem. B 101, 817 (1997); U.H.E. Hansman, Y. Okamoto, and F. Eisenmenger, Chem. Phys. Lett. 259, 321 (1996).
  23. J.G. Kim, Y. Fukunishi, and H. Nakamura, Phys. Rev. E 67, 011105 (2003).
  24. J.G. Kim, Y. Fukunishi, A. Kidera, and H. Nakamura, Phys. Rev. E 68, 021110 (2003).
  25. T. Terada, Y. Matsuo, and A. Kidera, J. Chem. Phys. 118, 4306 (2003).
  26. N. Rathore, T.A. Knotts IV, and J.J. de Pablo, J. Chem. Phys. 118, 4285 (2003).
  27. K. Morikami, T. Nakai, A. Kidera, M. Saito, and H. Nakamura, J. Comput. Chem. 16, 243 (1992).
  28. W.D. Cornell, P. Cieplak, C.I. Bayly, I.R. Gould, K.M. Merz, Jr., D.M. Ferguson, D.C. Spellmeyer, T. Fox, J.W. Caldwell, and P.A. Kollman, J. Am. Chem. Soc. 117, 5179 (1995).
  29. F. Yasar, T. Celik, B.A. Berg, and H. Meirovitch, J. Comput. Chem. 21, 1251 (2000); ibid.23, 1127 (2002).
  30. A.M. Ferrenberg and R.H. Swendsen, Phys. Rev. Lett. 61, 2635 (1988); ibid.63, 1195 (1989).

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Phys. Rev. E 69, 021101– Published 10 February, 2004
  • Received 11 July 2003

© 2004 American Physical Society

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