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 approach for Particle Simulations J. Ilja Siepmann Random quantity turbines for Parallel functions Ashok Srinivasan, David M. Ceperley and Michael Mascagni among Classical and Quantum Monte Carlo equipment: "Variational" QMC Dario Bressanini and Peter J. Reynolds Monte Carlo Eigenvalue equipment in Quantum Mechanics and Statistical Mechanics M. P. Nightingale and C.J. Umrigar Adaptive Path-Integral Monte Carlo tools for actual 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 methods 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 platforms Juan J. de Pablo and Fernando A. Escobedo Thermodynamic-Scaling tools in Monte Carlo and Their software to part Equilibria John Valleau Semigrand Canonical Monte Carlo Simulation: Integration alongside Coexistence strains David A. Kofke Monte Carlo equipment for Simulating part Equilibria of advanced Fluids J. Ilja Siepmann Reactive Canonical Monte Carlo J. Karl Johnson New Monte Carlo Algorithms for Classical Spin platforms G. T. Barkema and M.E.J. Newman.

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Payne, “Generalized Feedback Shift Register Pseudorandom Number Algorithms,” J . ACM 20,456-468 (1973). 22. R. C. Tausworthe, “Random Numbers Generated by Linear Recurrence Modulo Two,” Math. Comp. 19,201-209 (1965). 23. S. W. Golomb, Shift Register Sequences, rev. , Aegean Park Press, Laguna Hills, CA, 1982. 24. J. L. Massey, “Shift-Register Synthesis and bch Decoding,” I E E E Trans. Inform. Theory 15,122-127 (1969). 25. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992.

As with Metropolis, this path is also a Markov chain. One can see that the function F(R) acts as a drift, pushing the walkers toward regions of configuration space where the trial wavefunction is large. This increases the efficiency of the simulation, in contrast to the standard Metropolis move where the walker has the same probability of moving in every direction. There is, however, a minor point that needs to be addressed: the time discretization of the Langevin equation, exact only for z + 0, has introduced a time step bias absent in Metropolis sampling.

15,211-219 (1995). 29. M. Mascagni, “A Parallel Non-Linear Fibonacci Pseudorandom Number Generator,” Abstract, 45th SIAM Annual Meeting, 1997. 30. J. Eichenauer and J. Lehn, “A Nonlinear Congruential Pseudorandom Number Generator,” Stat. Hefte 37, 315-326 (1986). 31. H. Niederreiter, “Statistical Independence of Nonlinear Congruential Pseudorandom Numbers,” Montash. Math. 106, 149-159 (1988). 32. H. Niederreiter, “On a New Class of Pseudorandom Numbers for Simulation Methods,” J. Comput. Appl. Math.