By David M. Ferguson, J. Ilja Siepmann, Donald G. Truhlar, Ilya Prigogine, Stuart A. Rice
In Monte Carlo tools in Chemical Physics: An advent to the Monte Carlo procedure for Particle Simulations J. Ilja Siepmann Random quantity turbines for Parallel purposes Ashok Srinivasan, David M. Ceperley and Michael Mascagni among Classical and Quantum Monte Carlo tools: "Variational" QMC Dario Bressanini and Peter J. Reynolds Monte Carlo Eigenvalue tools in Quantum Mechanics and Statistical Mechanics M. P. Nightingale and C.J. Umrigar Adaptive Path-Integral Monte Carlo equipment for exact Computation of Molecular Thermodynamic homes Robert Q. Topper Monte Carlo Sampling for Classical Trajectory Simulations Gilles H. Peslherbe Haobin Wang and William L. Hase Monte Carlo ways to the Protein Folding challenge Jeffrey Skolnick and Andrzej Kolinski Entropy Sampling Monte Carlo for Polypeptides and Proteins Harold A. Scheraga and Minh-Hong Hao Macrostate Dissection of Thermodynamic Monte Carlo Integrals Bruce W. Church, Alex Ulitsky, and David Shalloway Simulated Annealing-Optimal Histogram equipment David M. Ferguson and David G. Garrett Monte Carlo equipment for Polymeric structures Juan J. de Pablo and Fernando A. Escobedo Thermodynamic-Scaling equipment in Monte Carlo and Their software to section Equilibria John Valleau Semigrand Canonical Monte Carlo Simulation: Integration alongside Coexistence traces David A. Kofke Monte Carlo equipment for Simulating part Equilibria of complicated Fluids J. Ilja Siepmann Reactive Canonical Monte Carlo J. Karl Johnson New Monte Carlo Algorithms for Classical Spin structures G. T. Barkema and M.E.J. NewmanContent:
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The exponential sum (Fourier transform of the density) of a sequence uo , . . , uk is For a random sequence, (I C,(k) 1)’ = k (for g # 0). This fact can be used to test correlation within, and between, random number sequences [13,16]. Consider two random sequences X and Y and 30 ASHOK SRINIVASAN, DAVID M. 2) In each term of this sum, we find the difference between an element of each sequence at a fixed offset apart. If this difference were uniformly distributed, then we should have (I C( j, 1, k) 1)' = k.
Mod. Phys. C 7(3), 295-303 (1996). 38. E. Hlwaka, “Funktionen von Beschrankter Variation in der Theorie der Gleichverteiling,” Ann. Mat. Pura Appl. 54,325-333 (1961). 39. K. F. Roth, “On Irregularities of Distribution,” Mathematika 1,73-79 (1954). 40. J. H. Halton, “On the Efficiency of Certain Quasi-Random Sequences of Points in Evaluating Multi-dimensional Integrals,” Num. Math. 2,84-90 (1960). 41. H. Faure, “Using Permutations to Reduce Discrepancy,” J. Comp. Appl. Math. 31, 97-103 (1990). 42.
ACM 31, 1192-1201 (1988). 10. P. L’Ecuyer, “Random Numbers for Simulation,” Commun. ACM 33,85-97 (1990). 11. G. Marsaglia, “A Current View of Random Number Generators,” in Computing Science and Statistics: Proceedings of the X V I t h Symposium on the Interface, 1985, pp. 3-10. 12. P. ps. 13. M. Mascagni, S. A. Cuccaro, D. V. Pryor, and M. L. Robinson, “Recent Developments in Parallel Pseudorandom Number Generation,” in Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, Vol.