Efficient sampling methods for combinations of signs, phases, hyperphases, and molecular orientations

Methods in Enzymology

Volumn 276, Issue , 1997, Pages 424-448

  Bricogne, Gérard ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

BAYES THEOREM; CRYSTAL STRUCTURE; FOURIER TRANSFORMATION; GEOMETRY; MATHEMATICAL COMPUTING; MOLECULAR MODEL; PRIORITY JOURNAL; REVIEW; SAMPLING; STATISTICAL ANALYSIS; X RAY CRYSTALLOGRAPHY;

EID: 0031045642     PISSN: 00766879     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0076-6879(97)76070-1     Document Type: Article

References (69)

1. G. Bricogne, Methods Enzymol. 276, [23], 1997 (this volume).
2. G. Bricogne, Acta Cryst. A47, 803-829 (1991).
3. G. Bricogne, in "The Molecular Replacement Method. Proceedings of the CCP4 Study Weekend 31 January-1st February 1992," (W. Wolf, E. J. Dodson, and S. Gover, eds.), pp. 62-75. Daresbury Laboratory, Warrington, 1992.
4. W. W. Rouse Ball and H. S. M. Coxeter, "Mathematical Recreations and Essays," 13th edition. Dover Publications, New York, 1987.
5. W. Cochran and A. S. Douglas, Nature 171, 1112-1113 (1953).
6. W. Cochran and A. S. Douglas, Proc. R. Soc. Lond. A227, 486-500 (1955).
7. W. Cochran and A. S. Douglas, Proc. R. Soc. Lond. A243, 281-288 (1957).
8. V. Vand and R. Pepinsky, Z. Krist. 107, 202-224 (1956).
9. M. M. Woolfson, Acta Cryst. 7, 65-67 (1954).
10. I. J. Good, Acta Cryst. 7, 603-604 (1954).
11. G. Bricogne, Acta Cryst. D49, 37-60 (1993).
12. R. A. Fisher, Ann. Eugenics 11, 341-353 (1942).
13. R. A. Fisher, Ann. Eugenics 12, 283-290 (1945).
14. F. J. MacWilliams and N. J. A. Sloane, "The Theory of Error-Correcting Codes," North-Holland, Amsterdam, 1977.
15. J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups." Springer-Verlag, New York, 1988.
16. O. Taussky and J. Todd, Ann. Soc. Polon. Math. 21, 303-308 (1949).
17. S. K. Zaremba, J. Lond. Math. Soc. 26, 70-71 (1950).
18. S. K. Zaremba, J. Lond. Math. Soc. 27, 242-246 (1952).
19. T. M. Thompson, "From Error-Correcting Codes through Sphere Packings to Simple Groups," The Carus Mathematical Monographs, vol. 21. The Mathematical Association of America, 1983.
20. H. L. J. Kamps and J. H. van Lint, J. Comb. Theory 3, 315-325 (1967).
21. R. G. Stanton, in "Recent Progress in Combinatorics" (W. T. Tutte, ed.), pp. 21-36. Academic Press, New York, 1969.
22. C. E. Shannon and W. Weaver, "The Mathematical Theory of Communication." University of Illinois Press, Urbana, 1949.
23. P. S. White and M. M. Woolfson, Acta Cryst. A31, 53-56 (1975).
24. C. Riche, Acta Cryst. A29, 133-137 (1973).
25. P. Main, Acta Cryst. A33, 750-757 (1977).
26. P. Main, Acta Cryst. A34, 31-38 (1978).
27. N. M. Korobov, Doklady Akademii Nauk SSSR 124, 1207-1210 (Russian) (1959).
28. N. M. Korobov, Doklady Akademii Nauk SSSR 132, 1207-1210 (Russian).
29. English translation: Soviet Mathematics Doklady 1, 696-700 (1960).
30. N. M. Korobov, "Number-Theoretic Methods in Approximate Analysis." Fizmatgiz, Moscow, 1963 (Russian).
31. E. Hlawka, Annali di Matematica Pura ed Applicata 54, 325-334 (1961).
32. E. Hlawka, Monatshefte für Mathematik 66, 140-151 (1962).
33. E. Hlawka, Compositio Math. 16, 92-105 (1964).
34. L. K. Hua and Y. Wang, Scientia Sinica 14, 964-978 (1965).
35. S. K. Zaremba, Annali di Matematica Pura ed Applicata 73, 293-317 (1966).
36. N. S. Bahvalov, Vestnik Moskov. Univ. Ser. Mat. Meh. Astr. Fiz. Him. 4, 3-18 (1959).
37. S. K. Zaremba, ed., "Applications of Number Theory to Numerical Analysis." Academic Press, New York, 1972.
38. L. K. Hua and Y. Wang, "Applications of Number Theory to Numerical Analysis." Springer-Verlag, Berlin, 1981.
39. I. H. Sloan and S. Joe, "Lattice Methods for Multiple Integration." Clarendon Press, Oxford, 1994.
40. G. Bricogne, in "International Tables for Crystallography," Vol. B (U. Shmueli, ed.), pp. 23-106. Kluwer Academic Publishers, Dordrecht, 1993.
41. G. D. Cohen, M. R. Karpovsky, H. F. Mattson, Jr., and J. R. Schatz, IEEE Trans. Inform. Theory IT-31, 328-343 (1985).
42. R. L. Graham and N. J. A. Sloane, IEEE Trans. Inform. Theory IT-31, 385-401 (1985).
43. N. J. A. Sloane, J. Comb. Theory A42, 61-86 (1986).
44. R. E. A. C. Paley, J. Math. and Physics 12, 311-320 (1933).
45. A. Hedayat and W. D. Wallis, Ann. Stat. 6, 1184-1238 (1978).
46. R. L. Plackett and J. P. Burman, Biometrika 33, 305-325 (1946).
47. J. Leech and N. J. A. Sloane, Can. J. Math. 23, 718-745 (1971).
48. N. J. A. Sloane, in "Combinatorial Surveys" (P. J. Cameron, ed.), pp. 117-164. Academic Press, London, 1977.
49. N. Ja. Vilenkin, "Special Functions and the Theory of Group Representations." American Mathematical Society, Providence, RI, 1968.
50. C. Müller, "Spherical Harmonics," Lecture Notes in Mathematics, Vol. 178. Springer-Verlag, Berlin, 1966.
51. E. M. Stein and G. Weiss, "Introduction to Fourier Analysis on Euclidean Spaces." Princeton University Press, Princeton, NJ, 1971.
52. P. Delsarte, J. M. Goethals, and J. J. Seidel, Geometriae Dedicata 6, 363-388 (1977).
53. J. M. Goethals and J. J. Seidel, in "Relations between Combinatorics and Other Parts of Mathematics" (D. K. Ray-Chaudhuri, ed.), pp. 255-272. Proc. Symp. Pure Math. 34.
54. J. M. Goethals and J. J. Seidel, in "Relations between Combinatorics and Other Parts of Mathematics" (D. K. Ray-Chaudhuri, ed.), pp. 255-272. Proc. Symp. Pure Math. 34.
55. J. M. Goethals and J. J. Seidel, in "The Geometric Vein" (C. Davis, B. Grünbaum, and R. Mathon, eds.), pp. 203-218. Springer-Verlag, Berlin, 1981.
56. J. M. Goethals and J. J. Seidel, Nieuw Archief voor Wiskunde 29, 50-58.
57. M. Hamermesh, "Group Theory and Its Application to Physical Problems." Addison-Wesley, Reading, MA, 1962.
58. H. S. M. Coxeter, "Non-Euclidean Geometry," 5th edition. University of Toronto Press, Toronto, 1965.
59. H. S. M. Coxeter, "Introduction to Geometry," 2nd edition. Wiley, New York, 1980.
60. D. Hilbert and S. Cohn-Vossen, "Geometry and the Imagination," translated by P. Nemenyi. Chelsea Publishing Co., New York, 1952.
61. O. Rodrigues, J. de Mathématiques Pures et Appliquées 5, 380-440 (1840).
62. P. Du Val, "Homographies, Quaternions and Rotations." Clarendon Press, Oxford, 1964.
63. J. M. Montesinos, "Classical Tessellations and Three-Manifolds." Springer-Verlag, Berlin, 1987.
64. S. L. Altmann, "Rotations, Quaternions, and Double Groups." Clarendon Press, Oxford, 1986.
65. S. L. Altmann, Mathematics Magazine 62, 291-308 (1989).
66. R. A. Crowther, in "The Molecular Replacement Method" (M. G. Rossmann, ed.), pp. 173-178. Gordon and Breach, New York, 1972.
67. H. S. M. Coxeter, "Regular Polytopes," 3rd edition. Dover Publications, New York, 1973.
68. G. N. Salihov, Dokl. Akad. Nauk SSSR 223, 1075-1078. English translation: Soviet Math. Dokl. 16, 1046-1049 (1975).
69. G. N. Salihov, Dokl. Akad. Nauk SSSR 223, 1075-1078. English translation: Soviet Math. Dokl. 16, 1046-1049 (1975).