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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 control strategy of multi-stroke repetitive driving is often required in the micro–nano-system. However, the current research only focuses on the modeling algorithm of a single stroke; thus, it is difficult to realize the hysteresis compensation at any stroke of the piezoelectric actuator. This paper proposes a multi-stroke compensation algorithm combined with the inverse model: through the analysis of the hysteresis model, the rising trajectory with better linearity is defined as the target line to find a mathematical expression with fewer parameters to describe the falling trajectory, then to find the relationship between maximum stroke voltage and the above parameters to establish a mathematical model that can describe any stroke, and finally, to verify that the above model applies to any unknown stroke, thereby realizing multi-stroke compensation. The experimental results show that the hysteresis corrected rate after the above algorithm compensation is mostly over 85%, of which the maximum hysteresis corrected rate is 93.81% and the hysteresis error is less than 2.5%. Experiments prove the effectiveness of the above multi-stroke compensation algorithm based on the inverse model and extend the research on piezoelectric hysteresis characteristics to multi-stroke compensation. [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 the use of a Monte Carlo model incorporating a finite-element method computing the electrostatic fields inside and outside a semiconductor, plus a ray-tracing algorithm for determining the doping contrast observed in a scanning electron microscope (SEM). This combined numerical method also enables the effects on the doping contrast of surface band-bending to be distinguished from those of external patch fields outside the specimen, as well as any applied macroscopic external fields from the detection system in the SEM. Good agreement of our new theory with experiment is obtained. The contrast characteristics in energy-filtered secondary electron images are also explained. The results of this work lead to a more advanced understanding of the doping contrast mechanisms, thereby enabling quantitative dopant profiling using the SEM. [ABSTRACT FROM AUTHOR]

This paper reports on a method which allows a decrease in the minimal detectable temperature in visible and near infrared thermography. This original method permits an increase in the thermal sensitivity without loss of good spatial resolution. It is based on a binning operation and a super-resolution algorithm. The radiometric model and super-resolution method are presented. Measurements on two different samples show the enhancement of the thermal sensitivity and the capability of the method. Finally, the authors propose different ways in which the method can be applied. [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]

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]

In this paper, a method for numerical simulation of the shape of a ferrofluid under external magnetic fields and the gravitational field is presented. The final shape is determined by an equilibrium condition of energy in a coupled system of electromagnetic fields and ferrofluid in the presence of gravity. The shape of the ferrofluid is captured by using the level set technique. The velocity field is calculated using continuum shape sensitivity analysis based on the material derivative concept. The numerical algorithm is implemented with a standard finite element procedure and tested on a shaping problem of ferrofluid located under an electromagnet. The numerical results showed that the proposed algorithm and numerical techniques are feasible and effective means of calculating ferrofluid shape variation under magnetic fields and the gravitational force. [ABSTRACT FROM AUTHOR]

Thermal asperity (TA) causes a major problem in data detection process. Without the TA detection and correction algorithm, the system performance (even with perfect synchronization) can be unacceptable, depending on how severe the TA effect is. This paper proposes a new method to suppress the TA effects in perpendicular magnetic recording channels. The TA detection is a threshold-based approach, while the TA correction is done by averaging the readback signal and applying a least-squares fitting technique to estimate the TA signal. Then, the corrected readback signal is obtained by subtracting the TA-affected readback signal by the reconstructed TA signal. Results indicate that the proposed method performs better than the existing one in terms of bit-error rate and is robust to changes in the peak TA amplitude. [ABSTRACT FROM AUTHOR]

In active noise control (ANC) systems, virtual microphones provide a means of projecting the zone of quiet away from the physical microphone to a remote location. To date, linear ANC algorithms, such as the filtered-x least mean square (FXLMS) algorithm, have been used with virtual sensing techniques. In this paper, a nonlinear ANC algorithm is developed for a virtual microphone by integrating the remote microphone technique with the filtered-s least mean square (FSLMS) algorithm. The proposed algorithm is evaluated experimentally in the cancellation of chaotic noise in a one-dimensional duct. The secondary paths evaluated experimentally exhibit non-minimum phase response and hence poor performance is obtained with the conventional FXLMS algorithm compared to the proposed FSLMS based algorithm. This is because the latter is capable of predicting the chaotic signal found in many physical processes responsible for noise. In addition, the proposed algorithm is shown to outperform the FXLMS based remote microphone technique under the causality constraint (when the propagation delay of the secondary path is greater than the primary path). A number of experimental results are presented in this paper to compare the performance of the FSLMS algorithm based virtual ANC algorithm with the FXLMS based virtual ANC algorithm. [ABSTRACT FROM AUTHOR]

The first aim of this paper is to give emphasis to the importance of assessing phase information when reconstructing and mapping a sound field. In fact, in acoustic analysis phase distribution is frequently simply either not considered or ignored, even though it can supply very useful information for the understanding of the mapping itself or for further analyses. In this paper a procedure to carry out phase mapping of acoustic sources in beamforming measurement is illustrated. The second aim of this paper is to propose a straightforward iterative optimization algorithm based on the monopole substitution starting from beamforming results. It allows for the reconstruction of sound field without the use of any matrix inversion. Both numerical and experimental validations of the method are presented. Results shown hereafter prove the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

Community structure can naturally emerge in paths to synchronization, and scratching it from the paths is a tough issue that accounts for the diverse dynamics of synchronization. In this paper, with assumption that the synchronization on complex networks is made up of local and collective processes, we proposed a scheme to lock the local synchronization (phase locking) at a stable state, meanwhile, suppress the collective synchronization based on Kuramoto model. Through this scheme, the network dynamics only contains the local synchronization, which suggests that the nodes in the same community synchronize together and these synchronization clusters well reveal the community structure of network. Furthermore, by analyzing the paths to synchronization, the relations or overlaps among different communities are also obtained. Thus, the community detection based on the scheme is performed on five real networks and the observed community structures are much more apparent than modularity-based fast algorithm. Our results not only provide a deep insight to understand the synchronization dynamics on complex network but also enlarge the research scope of community detection. [ABSTRACT FROM AUTHOR]

Recently, a computational algorithm based on Bayesian data analysis was presented to invert the linear rheology of branched polymers [Shanbhag, S., Rheol. Acta 49, 411-422 (2010)]. When rheological data of an unknown polymer mixture are supplied, the algorithm produces an exhaustive distribution of structures and compositions, consistent with the rheology. Frequently, it identifies multiple or degenerate structures. In this proof-of-concept paper, a resolution of the degeneracy is sought by appealing to the concept of combinatorial rheology [Larson, R. G., Macromolecules 34, 4556-4571 (2001)], where the unknown sample is strategically blended with a well-characterized fraction. Experimental load is alleviated by identifying the optimal type, molecular weight, and composition of the polymer fraction to blend with the unknown sample, to discriminate between the degenerate structures, most conclusively. Two methods are proposed and tested on a particular mixture that is characterized by severe degeneracy. Both proposed methods are able to correctly identify the structure and composition of the original mixture by requiring two additional rheological experiments. [ABSTRACT FROM AUTHOR]

Landscape paradigm is ubiquitous in physics and other natural sciences, but it has to be supplemented with both quantitative and qualitatively meaningful tools for analyzing the topography of a given landscape. We here consider dynamic explorations of the relief and introduce as basic topographic features “wells of duration T and altitude y.” We determine an intrinsic exploration mechanism governing the evolutions from an initial state in the well up to its rim in a prescribed time, whose finite-difference approximations on finite grids yield a constructive algorithm for determining the wells. Our main results are thus (i) a quantitative characterization of landscape topography rooted in a dynamic exploration of the landscape, (ii) an alternative to stochastic gradient dynamics for performing such an exploration, (iii) a constructive access to the wells, and (iv) the determination of some bare dynamic features inherent to the landscape. The mathematical tools used here are not familiar in physics: They come from set-valued analysis (differential calculus of set-valued maps and differential inclusions) and viability theory (capture basins of targets under evolutionary systems) that have been developed during the last two decades; we therefore propose a minimal Appendix exposing them at the end of this paper to bridge the possible gap. [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]

As a three-dimensional measuring instrument, the laser tracker is widely used in industrial measurement. To avoid the influence of angle measurement error on the overall measurement accuracy, the multi-station and time-sharing measurement with a laser tracker is introduced on the basis of the global positioning system (GPS) principle in this paper. For the proposed method, how to accurately determine the coordinates of each measuring point by using a large amount of measured data is a critical issue. Taking detecting motion error of a numerical control machine tool, for example, the corresponding measurement algorithms are investigated thoroughly. By establishing the mathematical model of detecting motion error of a machine tool with this method, the analytical algorithm concerning on base station calibration and measuring point determination is deduced without selecting the initial iterative value in calculation. However, when the motion area of the machine tool is in a 2D plane, the coefficient matrix of base station calibration is singular, which generates a distortion result. In order to overcome the limitation of the original algorithm, an improved analytical algorithm is also derived. Meanwhile, the calibration accuracy of the base station with the improved algorithm is compared with that with the original analytical algorithm and some iterative algorithms, such as the Gauss-Newton algorithm and Levenberg-Marquardt algorithm. The experiment further verifies the feasibility and effectiveness of the improved algorithm. In addition, the different motion areas of the machine tool have certain influence on the calibration accuracy of the base station, and the corresponding influence of measurement error on the calibration result of the base station depending on the condition number of coefficient matrix are analyzed. [ABSTRACT FROM AUTHOR]