Efficient Pseudorandom number generators for biomolecular simulations on graphics processors

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List of references:

  1. A. G. Anderson, W. A. Goddard III, P. Schröder. Quantum Monte Carlo on graphical processing units // Comput. Phys. Commun. — 2007. — V. 177. — P. 298–306. — DOI: 10.1016/j.cpc.2007.03.004. — ads: 2007CoPhC.177..298A.
  2. J. A. Anderson, C. D. Lorentz, A. Travesset. General purpose molecular dynamics simulations fully implemented on graphics processing units // J. Comput. Phys. — 2008. — V. 227. — DOI: 10.1016/j.jcp.2008.01.047.
  3. L. Barreira. Poincar´e recurrence: old and new / XIVth International Congress on Mathematical Physics. — World Scientific, 2006. — P. 415–422. — MathSciNet: MR2227854. — ads: 2006maph.conf..415B.
  4. V. Barsegov, D. Klimov, D. Thirumalai. Mapping the energy landscape of biomolecules using single molecule force correlation spectroscopy: Theory and applications // Biophys. J. — 2006. — V. 90. — P. 3827–3841. — DOI: 10.1529/biophysj.105.075937.
  5. G. E. P. Box, M. E. Miller. A note on the generation of normal random deviates // Ann. Math. Statist. — 1958. — V. 29. — P. 610–611. — DOI: 10.1214/aoms/1177706645.
  6. R. P. Brent. Uniform random number generators for supercomputers / Proc. Fifth Australian Supercomputer Conference. — 1992. — P. 95–104.
  7. R. P. Brent, S. Larvala, P. Zimmermann. A fast algorithm for testing reducibility of trinomials mod 2 and some new primitive trinomials of degree 3021377 // Math. of Comput. — 2003. — V. 72. — P. 1443–1452. — DOI: 10.1090/S0025-5718-02-01478-3. — MathSciNet: MR1972745. — ads: 2003MaCom..72.1443B.
  8. B. R. Brooks, R. E. Bruccoleri, B. D. Olafson, D. J. States, S. Swaminathan, M. Karplus. CHARMM: A programm for macromolecular energy, minimization, and dynamics calculations // J. Comput. Chem. — 1983. — V. 4. — P. 187–217. — DOI: 10.1002/jcc.540040211.
  9. C. Clementi. Coarse-grained models of protein folding: toy models or predictive tools? // Curr. Opin. Struct. Biol. — 2008. — V. 18. — P. 10–15. — DOI: 10.1016/j.sbi.2007.10.005.
  10. J. E. Davis, A. Ozsoy, S. Patel, M. Taufer. Towards large-scale molecular dynamics simulations on graphics processors / BICoB’09: Proceedings of the 1st International Conference on Bioinformatics and Computational Biology. — Berlin, Heidelberg: Springer-Verlag, 2009. — P. 176–186.
  11. R. I. Dima, H. Joshi. Probing the origin of tubulin rigidity with molecular simulations // Proc. Natl. Acad. Sci. USA. — 2008. — V. 105. — P. 15743–15748. — DOI: 10.1073/pnas.0806113105. — ads: 2008PNAS..10515743D.
  12. M. Doi, S. Edwards. The Theory of Polymer Dynamics / International Series of Monographs on Physics. — Oxford Science Publications, 1988.
  13. D. L. Ermak, J. A. McCammon. Brownian dynamics with hydrodynamic interactions // J. Chem. Phys. — 1978. — V. 69. — P. 1352–1360. — DOI: 10.1063/1.436761. — ads: 1978JChPh..69.1352E.
  14. A. M. Ferrenberg, D. P. Landau, Y. J. Wong. Monte Carlo simulations: Hidden errors from “good” random number generators // Phys. Rev. Lett. — 1992. — V. 69. — P. 3382–3384. — DOI: 10.1103/PhysRevLett.69.3382. — ads: 1992PhRvL..69.3382F.
  15. M. S. Friedrichs, P. Eastman, V. Vaidyanathan, M. Houston, S. Legrand, A. L. Beberg, D. L. Ensign, C. M. Bruins, V. S. Pande. Accelerating molecular dynamic simulation on graphics processing units // J. Comput. Chem. — 2009. — V. 30. — P. 864–872. — DOI: 10.1002/jcc.21209.
  16. P. Grassberger. On correlations in “good” random number generators // Phys. Lett. A. — 1993. — V. 181. — P. 43–46. — DOI: 10.1016/0375-9601(93)91122-L. — ads: 1993PhLA..181...43G.
  17. U. Haberthür, A. Caflisch. FACTS: Fast analytical continuum treatment of salvation // J. Comput. Chem. — 2008. — V. 29. — P. 701–715. — DOI: 10.1002/jcc.20832.
  18. M. J. Harvey, G. D. Fabritilis. An implementation of the smooth Particle Mesh Ewald method on GPU hardware // J. Chem. Theory Comput. — 2009. — V. 5. — P. 2371–2377. — DOI: 10.1021/ct900275y.
  19. G. Hummer, A. Szabo. Kinetics from nonequilibrium single-molecule pulling experiments // Biophys. J. — 2003. — V. 85. — P. 5–15. — DOI: 10.1016/S0006-3495(03)74449-X.
  20. C. Hyeon, R. I. Dima, D. Thirumalai. Pathways and kinetic barriers in mechanical unfolding and refolding of RNA and proteins // Structure. — 2006. — V. 14. — P. 1633–1645. — DOI: 10.1016/j.str.2006.09.002.
  21. P. L’Ecuyer. Maximally equidistributed combined Tausworthe generators // Math. Comput. — 1996. — V. 65. — P. 203–213. — DOI: 10.1090/S0025-5718-96-00696-5. — MathSciNet: MR1325871. — ads: 1996MaCom..65..203L.
  22. P. L’Ecuyer, F. Blouin, R. Couture. A search for good multiple recursive random number generators // ACM Trans. Model. Comput. Simul. — 1993. — V. 3. — P. 87–98. — DOI: 10.1145/169702.169698.
  23. P. L’Ecuyer, R. Simard. TestU01: A C library for empirical testing of random number generators // ACM Trans. Math. Softw. — 2007. — V. 33. — P. 22. — DOI: 10.1145/1268776.1268777. — MathSciNet: MR2404400.
  24. G. Marsaglia. DIEHARD: A battery of tests of randomness. — 1996. — http://stat.fsu.edu/geo/diehard.html.
  25. G. Marsaglia. Random numbers for C: The END?. — 1999. — Published on sci.crypt. — https://groups.google.com/forum/#!topic/sci.crypt/yoaCpGWKEk0.
  26. G. Marsaglia, T. A. Bray. A convenient method for generating normal variables // SIAM Rev. — 1964. — V. 6. — P. 260–264. — DOI: 10.1137/1006063. — MathSciNet: MR0172441. — ads: 1964SIAMR...6..260M.
  27. M. Mascagni, A. Srinivasan. Algorithm 806: SPRNG: A scalable library for pseudorandom number generation // ACM Trans. Math. Softw. — 2000. — V. 26. — P. 436–461. — DOI: 10.1145/358407.358427. — MathSciNet: MR1821052.
  28. M. Mascagni, A. Srinivasan. Parameterizing parallel multiplicative lagged-Fibonacci generators // Parallel Comput. — 2004. — V. 30. — P. 899–916. — DOI: 10.1016/j.parco.2004.06.001. — MathSciNet: MR2078624.
  29. M. Matsumoto, Y. Kurita. Twisted GFSR generators // ACM Trans. Model. Comput. Simul. — 1992. — V. 2. — P. 179–194. — DOI: 10.1145/146382.146383.
  30. M. Matsumoto, Y. Kurita. Twisted GFSR generators II // ACM Trans. Model. Comput. Simul. — 1994. — V. 4. — P. 254–266. — DOI: 10.1145/189443.189445.
  31. M. Matsumoto, T. Nishimura. Mersenne Twister: A 623-dimensionally equidistributed uniform pseudo-random number generator // ACM Trans. Model. Comput. Simul. — 1998. — V. 8. — P. 3–30. — DOI: 10.1145/272991.272995.
  32. J. A. van Meel, A. Arnold, D. Frenkel, S. F. P. Zwart, R. Belleman. Harvesting graphics power for MD simulations // Mol. Simul. — 2008. — V. 34. — P. 259–266. — DOI: 10.1080/08927020701744295.
  33. M. Mickler, R. I. Dima, H. Dietz, C. Hyeon, D. Thirumalai, M. Rief. Revealing the bifurcation in the unfolding pathways of GFP by using single-molecule experiments and simulations // Proc. Natl. Acad. Sci. USA. — 2007. — V. 104. — P. 20268–20273. — DOI: 10.1073/pnas.0705458104. — ads: 2007PNAS..10420268M.
  34. GPU Gems 3. — Addison-Wesley, 2008. — Nguyen H. (Ed.).
  35. NVIDIA CUDA C Programming Best Practices Guide. — NVIDIA, 2009. — 2.3 edition.
  36. NVIDIA CUDA Programming Guide. — NVIDIA, 2009. — 2.3.1 edition.
  37. NVIDIA’s Next generation CUDA Compute Architecture: Fermi. — NVIDIA, 2009. — 1.1 edition.
  38. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery. Numerical Recipes in C, The Art of Scientific Computing. — Cambridge University Press, 1992. — second edition. — MathSciNet: MR1201159.
  39. H. Risken. The Fokker-Planck Equation. — Springer-Verlag, 1989. — second edition. — MathSciNet: MR0987631.
  40. W. Selke, A. L. Talapov, L. N. Shchur. Cluster-flipping Monte Carlo algorithm and correlations in “good” random number generators // JETP Lett. — 1993. — V. 58. — P. 665–668. — MathSciNet: MR1249656. — ads: 1993JETPL..58..665S.
  41. J. Soto. Statistical testing of random number generators. — 1999. — https://csrc.nist.gov/csrc/media/publications/conference-paper/1999/10/21/proceedings-of-the-22nd-nissc-1999/documents/papers/p24.pdf.
  42. J. E. Stone, J. C. Phillips, P. L. Freddolino, D. J. Hardy, L. G. Trabuco, K. Schulten. Accelerating molecular modeling applications with graphical processors // J. Comput. Chem. — V. 28. — P. 2618–2640. — DOI: 10.1002/jcc.20829.
  43. R. C. Tausworthe. Random numbers generated by linear recurrence modulo two // Math. Comput. — 1965. — V. 19. — P. 201–209. — DOI: 10.1090/S0025-5718-1965-0184406-1. — MathSciNet: MR0184406.
  44. V. Tozzini. Coarse-grained models for proteins // Curr. Opin. Struct. Biol. — 2005. — V. 15. — P. 144–150. — DOI: 10.1016/j.sbi.2005.02.005.
  45. W. W. Tsang, G. Marsaglia. The Ziggurat method for generating random variables // J. Stat. Softw. — 2000. — V. 5.
  46. T. Veitshans, D. Klimov, D. Thirumalai. Protein folding kinetics: timescales, pathways and energy landscapes in terms of sequence-dependent properties // Fold. Des. — 1997. — V. 2. — P. 1–22. — DOI: 10.1016/S1359-0278(97)00002-3.
  47. J. Yang, Y. Wang, Y. Chen. GPU accelerated molecular dynamics simulations of thermal conductivities // J. Comput. Phys. — 2007. — V. 221. — P. 799–804. — DOI: 10.1016/j.jcp.2006.06.039. — ads: 2007JCoPh.221..799Y.
  48. A. Zhmurov, R.I. Dima, Y.A. Kholodov, V. Barsegov. SOP-GPU: Accelerating biomolecular simulations in the centisecond timescale using graphics processors // Proteins: Structure, Function, and Bioinformatics. — 2010. — V. 78, no. 14. — P. 2984–2999. — DOI: 10.1002/prot.22824.

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