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The weighted stochastic simulation algorithm (wSSA) recently introduced by Kuwahara and Mura [J. Chem. Phys. 129, 165101 (2008)] is an innovative variation on the stochastic simulation algorithm (SSA). It enables one to estimate, with much less computational effort than was previously thought possible using a Monte Carlo simulation procedure, the probability that a specified event will occur in a chemically reacting system within a specified time when that probability is very small. This paper presents some procedural extensions to the wSSA that enhance its effectiveness in practical applications. The paper also attempts to clarify some theoretical issues connected with the wSSA, including its connection to first passage time theory and its relation to the SSA. [ABSTRACT FROM AUTHOR]

The thermodynamic stability of a folded RNA is intricately tied to the counterions and the free energy of this interaction must be accounted for in any realistic RNA simulations. Extending a tight-binding model published previously, in this paper we investigate the fundamental structure of charges arising from the interaction between small functional RNA molecules and divalent ions such as Mg2+ that are especially conducive to stabilizing folded conformations. The characteristic nature of these charges is utilized to construct a discretely connected energy landscape that is then traversed via a novel application of a deterministic graph search technique. This search method can be incorporated into larger simulations of small RNA molecules and provides a fast and accurate way to calculate the free energy arising from the interactions between an RNA and divalent counterions. The utility of this algorithm is demonstrated within a fully atomistic Monte Carlo simulation of the P4-P6 domain of the Tetrahymena group I intron, in which it is shown that the counterionmediated free energy conclusively directs folding into a compact structure. [ABSTRACT FROM AUTHOR]

Mathematical and computational modeling are key tools in analyzing important biological processes in cells and living organisms. In particular, stochastic models are essential to accurately describe the cellular dynamics, when the assumption of the thermodynamic limit can no longer be applied. However, stochastic models are computationally much more challenging than the traditional deterministic models. Moreover, many biochemical systems arising in applications have multiple time-scales, which lead to mathematical stiffness. In this paper we investigate the numerical solution of a stochastic continuous model of well-stirred biochemical systems, the chemical Langevin equation. The chemical Langevin equation is a stochastic differential equation with multiplicative, non-commutative noise. We propose an adaptive stepsize algorithm for approximating the solution of models of biochemical systems in the Langevin regime, with small noise, based on estimates of the local error. The underlying numerical method is the Milstein scheme. The proposed adaptive method is tested on several examples arising in applications and it is shown to have improved efficiency and accuracy compared to the existing fixed stepsize schemes. [ABSTRACT FROM AUTHOR]

Using computer simulations to model the folding of proteins into their native states is computationally expensive due to the extraordinarily low degeneracy of the ground state. In this paper, we develop an efficient way to sample these folded conformations using Wang Landau sampling coupled with the configurational bias method (which uses an unphysical 'temperature' that lies between the collapse and folding transition temperatures of the protein). This method speeds up the folding process by roughly an order of magnitude over existing algorithms for the sequences studied. We apply this method to study the adsorption of intrinsically disordered hydrophobic polar protein fragments on a hydrophobic surface. We find that these fragments, which are unstructured in the bulk, acquire secondary structure upon adsorption onto a strong hydrophobic surface. Apparently, the presence of a hydrophobic surface allows these random coil fragments to fold by providing hydrophobic contacts that were lost in protein fragmentation. [ABSTRACT FROM AUTHOR]

In recent years, computer simulations have become increasingly useful when trying to understand the complex dynamics of biochemical networks, particularly in stochastic systems. In such situations stochastic simulation is vital in gaining an understanding of the inherent stochasticity present, as these models are rarely analytically tractable. However, a stochastic approach can be computationally prohibitive for many models. A number of approximations have been proposed that aim to speed up stochastic simulations. However, the majority of these approaches are fundamentally serial in terms of central processing unit (CPU) usage. In this paper, we propose a novel simulation algorithm that utilises the potential of multi-core machines. This algorithm partitions the model into smaller sub-models. These sub-models are then simulated, in parallel, on separate CPUs. We demonstrate that this method is accurate and can speed-up the simulation by a factor proportional to the number of processors available. [ABSTRACT FROM AUTHOR]

This paper describes a new Monte Carlo method based on a novel stochastic potential switching algorithm. This algorithm enables the equilibrium properties of a system with potential V to be computed using a Monte Carlo simulation for a system with a possibly less complex stochastically altered potential V. By proper choices of the stochastic switching and transition probabilities, it is shown that detailed balance can be strictly maintained with respect to the original potential V. The validity of the method is illustrated with a simple one-dimensional example. The method is then generalized to multidimensional systems with any additive potential, providing a framework for the design of more efficient algorithms to simulate complex systems. A near-critical Lennard-Jones fluid with more than 20 000 particles is used to illustrate the method. The new algorithm produced a much smaller dynamic scaling exponent compared to the Metropolis method and improved sampling efficiency by over an order of magnitude. [ABSTRACT FROM AUTHOR]

We propose an algorithm for accurate, systematic, and scalable computation of interatomic forces within the auxiliary-field quantum Monte Carlo (AFQMC) method. The algorithm relies on the Hellmann-Feynman theorem and incorporates Pulay corrections in the presence of atomic orbital basis sets. We benchmark the method for small molecules by comparing the computed forces with the derivatives of the AFQMC potential energy surface and by direct comparison with other quantum chemistry methods. We then perform geometry optimizations using the steepest descent algorithm in larger molecules. With realistic basis sets, we obtain equilibrium geometries in agreement, within statistical error bars, with experimental values. The increase in computational cost for computing forces in this approach is only a small prefactor over that of calculating the total energy. This paves the way for a general and efficient approach for geometry optimization and molecular dynamics within AFQMC. [ABSTRACT FROM AUTHOR]

In this paper a new algorithm is presented that improves the efficiency of Wang and Landau algorithm or density of states (DOS) Monte Carlo simulations by employing rejected states. The algorithm is shown to have a performance superior to that of the original Wang-Landau [F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001)] algorithm and the more recent configurational temperature DOS algorithm. The performance of the method is illustrated in the context of results for the Lennard-Jones fluid. [ABSTRACT FROM AUTHOR]

This paper formulates a hybrid Monte Carlo implementation of the Fourier path integral (FPI-HMC) approach with partial averaging. Such a hybrid Monte Carlo approach allows one to generate collective moves through configuration space using molecular dynamics while retaining the computational advantages associated with the Fourier path integral Monte Carlo method. In comparison with the earlier Metropolis Monte Carlo implementations of the FPI algorithm, the present HMC method is shown to be significantly more efficient for quantum Lennard-Jones solids and suggests that such algorithms may prove useful for efficient simulations of a range of atomic and molecular systems. [ABSTRACT FROM AUTHOR]

Calculation of the effective diffusion coefficient D(x), depending on the longitudinal coordinate x in 2D channels with periodically corrugated walls, is revisited. Instead of scaling the transverse lengths and applying the standard homogenization techniques, we propose an algorithm based on formulation of the problem in the complex plane. A simple model is solved to explain the behavior of D(x) in the channels with short periods L, observed by Brownian simulations of Dagdug et al. [J. Chem. Phys. 133, 034707 (2010)]. [ABSTRACT FROM AUTHOR]

We discuss how the Phase Integration Method (PIM), recently developed to compute symmetrized time correlation functions [M. Monteferrante, S. Bonella, and G. Ciccotti, Mol. Phys. 109, 3015 (2011)], can be adapted to sampling/generating the thermal Wigner density, a key ingredient, for example, in many approximate schemes for simulating quantum time dependent properties. PIM combines a path integral representation of the density with a cumulant expansion to represent the Wigner function in a form calculable via existing Monte Carlo algorithms for sampling noisy probability densities. The method is able to capture highly non-classical effects such as correlation among the momenta and coordinates parts of the density, or correlations among the momenta themselves. By using alternatives to cumulants, it can also indicate the presence of negative parts of the Wigner density. Both properties are demonstrated by comparing PIM results to those of reference quantum calculations on a set of model problems. [ABSTRACT FROM AUTHOR]

We calculate the corrections to the thermodynamic limit of the critical density for jamming in the Kob-Andersen and Fredrickson-Andersen kinetically-constrained models, and find them to be finitedensity corrections, and not finite-size corrections. We do this by introducing a new numerical algorithm, which requires negligible computer memory since contrary to alternative approaches, it generates at each point only the necessary data. The algorithm starts from a single unfrozen site and at each step randomly generates the neighbors of the unfrozen region and checks whether they are frozen or not. Our results correspond to systems of size greater than 107 x 107, much larger than any simulated before, and are consistent with the rigorous bounds on the asymptotic corrections. We also find that the average number of sites that seed a critical droplet is greater than 1. [ABSTRACT FROM AUTHOR]

Metadynamics is an efficient method for simulation of the free energy of many-particle systems. Over the last several years it has been applied to study a wide variety of systems, ranging from simple fluids to biological macromolecules. The method relies on uniform sampling along specified collective variables or order parameters. Such order parameters, however, are often bounded, and metadynamics algorithms as originally developed suffer from systematic errors at the corresponding boundaries. While several approaches have been proposed in the past to correct these errors for unidimensional systems, no method exists to fully correct these errors in multi-dimensional systems at points where multiple boundaries meet. Here we present a correction scheme that circumvents this limitation. [ABSTRACT FROM AUTHOR]

Configurational-bias Monte Carlo has been incorporated into the Wang-Landau method. Although the Wang-Landau algorithm enables the calculation of the complete density of states, its applicability to continuous molecular systems has been limited to simple models. With the inclusion of more advanced sampling techniques, such as configurational-bias, the Wang-Landau method can be used to simulate complex chemical systems. The accuracy and efficiency of the method is assessed using as a test case systems of linear alkanes represented by a united-atom model. With strict convergence criteria, the density of states derived from the Wang-Landau algorithm yields the correct heat capacity when compared to conventional Boltzmann sampling simulations. [ABSTRACT FROM AUTHOR]

We propose an efficient algorithm to perform Monte Carlo simulations of dense systems using multiple particle moves. The method is intended to be used in the atomistic simulation of complex systems, where the computing requirements for a single simulation run make advisable the use of parallel computing. The algorithm is based on the use of steps in which all the particle positions of the system are perturbed simultaneously. A division of the system in clusters of particles is performed, using a bonding criterion which makes feasible that the acceptance or rejection of the new particle coordinates can be carried out independently for each cluster. [ABSTRACT FROM AUTHOR]

We have developed a box length search algorithm to efficiently find the appropriate box dimensions for constant-volume molecular simulation of periodic structures. The algorithm works by finding the box lengths that equalize the pressure in each direction while maintaining constant total volume. Maintaining the volume at a fixed value ensures that quantitative comparisons can be made between simulation and experimental, theoretical or other simulation results for systems that are incompressible or nearly incompressible. We test the algorithm on a system of phase-separated block copolymers that has a preferred box length in one dimension. We also describe and test a Monte Carlo algorithm that allows the box lengths to change while maintaining constant volume. We find that the box length search algorithm converges at least two orders of magnitude more quickly than the variable box length Monte Carlo method. Although the box length search algorithm is not ergodic, it successfully finds the box length that minimizes the free energy of the system. We verify this by examining the free energy as determined by the Monte Carlo simulation. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Using feedback and an evolutionary algorithm (EA), the weak field pump–probe photoionization signal at a single time delay is optimized in Li[sub 2]. A single launch state is prepared via excitation with a cw laser, from which a pump pulse excites a superposition of two rotational states on an excited electronic potential energy curve: E [sup 1]Σ[sub g][sup +](v[sub E]=9, J[sub E]=27 and 29). The EA modifies the phase pattern versus wavelength of the ultrafast pump pulses using a pulse shaper with a 128 pixel liquid crystal spatial light modulator. Limitations of frequency resolution for the pulse shaper create an effective temporal window in which pulses can be shaped. Optimization of the photoionization signal at pump–probe time delays outside of this temporal pulse shaping window involves phase shifts of only the two frequencies resonant with the transition of the wave packet states, effectively introducing a phase shift in the wave packet recurrences. For pump–probe time delays inside the pulse shaping window, optimization of the photoionization shows the influence of not only resonant but also nonresonant wavelengths. In this regime, the phase shift of wave packet recurrences as well as the time-dependent wave packet amplitude coefficients are optimized. First order time dependent perturbation theory is used to explain the mechanism by which the photoionization is maximized. These experiments are the first to use an optimization routine as a tool to identify a variety of simultaneous mechanisms that underlie the maximization of a process. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Markov state models (MSMs) have become a popular approach for investigating the conformational dynamics of proteins and other biomolecules. MSMs are typically built from numerous molecular dynamics simulations by dividing the sampled configurations into a large number of microstates based on geometric criteria. The resulting microstate model can then be coarse-grained into a more understandable macrostate model by lumping together rapidly mixing microstates into larger, metastable aggregates. However, finite sampling often results in the creation of many poorly sampled microstates. During coarse-graining, these states are mistakenly identified as being kinetically important because transitions to/from them appear to be slow. In this paper, we propose a formalism based on an algebraic principle for matrix approximation, i.e., the Nyström method, to deal with such poorly sampled microstates. Our scheme builds a hierarchy of microstates from high to low populations and progressively applies spectral clustering on sets of microstates within each level of the hierarchy. It helps spectral clustering identify metastable aggregates with highly populated microstates rather than being distracted by lowly populated states. We demonstrate the ability of this algorithm to discover the major metastable states on two model systems, the alanine dipeptide and trpzip2 peptide. [ABSTRACT FROM AUTHOR]

Fewest-switches surface hopping is one of the simplest and most popular methods for the computational study of nonadiabatic processes. Recently, a very simple phase correction was introduced to the traditional surface hopping algorithm, substantially improving its accuracy with essentially no associated computational cost [N. Shenvi, J. E. Subotnik, and W. Yang, J. Chem. Phys. 135, 024101 (2011)]. In this paper, we show that we can modify our phase-corrected algorithm slightly such that it takes into account one type of decoherence, again with no additional computational cost. We apply our algorithm to two existing model problems, demonstrating that it can indeed capture one particular type of decoherence without any of the sophisticated machinery of alternative algorithms. [ABSTRACT FROM AUTHOR]

The Davydov D1 ansatz, which assigns individual bosonic trajectories to each spin state, is an efficient, yet extremely accurate trial state for time-dependent variation of the sub-Ohmic spin-boson model [N. Wu, L. Duan, X. Li, and Y. Zhao, J. Chem. Phys. 138, 084111 (2013)]. A surface hopping algorithm is developed employing the Davydov D1 ansatz to study the spin dynamics with a sub-Ohmic bosonic bath. The algorithm takes into account both coherent and incoherent dynamics of the population evolution in a unified manner, and compared with semiclassical surface hopping algorithms, hopping rates calculated in this work follow more closely the Marcus formula. [ABSTRACT FROM AUTHOR]

The stochastic simulation algorithm (SSA) was introduced by Gillespie and in a different form by Kurtz. Since its original formulation there have been several attempts at improving the efficiency and hence the speed of the algorithm. We briefly discuss some of these methods before outlining our own simple improvement, the recycling direct method (RDM), and demonstrating that it is capable of increasing the speed of most stochastic simulations. The RDM involves the statistically acceptable recycling of random numbers in order to reduce the computational cost associated with their generation and is compatible with several of the pre-existing improvements on the original SSA. Our improvement is also sufficiently simple (one additional line of code) that we hope will be adopted by both trained mathematical modelers and experimentalists wishing to simulate their model systems. [ABSTRACT FROM AUTHOR]