Wolf Method Research Articles

Effect of truncating electrostatic interactions on predicting thermodynamic properties of water–methanol systems

ABSTRACTThe combination of the TraPPE and OPLS/2016 force fields with five water models, TIP3P, SPC/E, OPC, TIP4P/2005 and TIP4P/EW was used to compute mixing enthalpies, excess chemical potentials and activity coefficients of water and methanol. Excess chemical potentials and activity coefficients were computed in an expanded version of the NPT ensemble. We found the best agreement between experimental data for all the computed properties of water–methanol mixtures for the TIP4P/2005-TraPPE force fields. The performance of the spherical cutoff methods in MC and MD simulations was compared to the Ewald summation. The radial distribution functions obtained from the Ewald summation and the Damped-Shifted Force (DSF) method were in excellent agreement. Numerical artifacts appeared at the cutoff radius when the original Wolf method was used to calculate the electrostatic interactions. The calculated excess mixing enthalpies, excess chemical potentials, and activity coefficients of water and methanol obtained from the Wolf method were in good agreement with the DSF method. Our simulation results show that the numerical artifacts of the original Wolf method have little effect for energy calculations in aqueous methanol mixtures.

A Modified Shifted Force Approach to the Wolf Summation.

The Wolf method for calculation of electrostatic interactions in molecular simulations is known to describe the energy well, whereas the forces have discontinuities. For a more reliable description of the forces this method can be extended with a shifted force approach. This leads to a good description of the forces and precise molecular dynamics simulation, but the description of the energy becomes poorer. In this study we propose a modification of a shifted force extension to describe the energy as well as the forces in better agreement to reference data as determined from the Ewald summation. We show that vapor-liquid phase equilibria (VLE) calculated with Monte Carlo simulations in the grand canonical ensemble and dynamic properties calculated with molecular dynamics simulations can be calculated reliably using this modification to describe the electrostatic interactions.

Trasfugen: Traffic assignment of urban network by an approximation fuzzy genetic algorithm

This paper proposes the Trasfugen method for traffic assignment aimed at solving the user equilibrium problem. To this end, the method makes use of a genetic algorithm. A fuzzy system is proposed for controlling the mutation and crossover rates of the genetic algorithm, and the corrective strategy is exploited for handling the equilibrium problem constraints. In the model, an approximation algorithm is proposed for obtaining the paths between the origin–destination pairs in the demand matrix. Unlike the traditional deterministic algorithm that has exponential time complexity, this approximation algorithm has polynomial time complexity and is executed much faster. Afterward, the Trasfugen method is applied to the urban network of Tehran metropolitan and the efficiency is investigated. Upon comparing the results obtained from the proposed model with those obtained from the conventional traffic assignment method, namely, the Frank–Wolfe method; it is shown that the proposed algorithm, while acting worse during the initial iterations, achieves better results in the subsequent iterations. Moreover, it prevents the occurrence of local optimal points as well as early/premature convergence, thus producing better results than the Frank–Wolfe algorithm.

Nonlinear dynamics of contact interaction of a size-dependent plate supported by a size-dependent beam.

A mathematical model of complex vibrations exhibited by contact dynamics of size-dependent beam-plate constructions was derived by taking the account of constraints between these structural members. The governing equations were yielded by variational principles based on the moment theory of elasticity. The centre of the investigated plate was supported by a beam. The plate and the beam satisfied the Kirchhoff/Euler-Bernoulli hypotheses. The derived partial differential equations (PDEs) were reduced to the Cauchy problems by the Faedo-Galerkin method in higher approximations, whereas the Cauchy problem was solved using a few Runge-Kutta methods. Reliability of results was validated by comparing the solutions obtained by qualitatively different methods. Complex vibrations were investigated with the help of methods of nonlinear dynamics such as vibration signals, phase portraits, Fourier power spectra, wavelet analysis, and estimation of the largest Lyapunov exponents based on the Rosenstein, Kantz, and Wolf methods. The effect of size-dependent parameters of the beam and plate on their contact interaction was investigated. It was detected and illustrated that the first contact between the size-dependent structural members implies chaotic vibrations. In addition, problems of chaotic synchronization between a nanoplate and a nanobeam were addressed.

Quantifying Chaos by Various Computational Methods. Part 1: Simple Systems.

The aim of the paper was to analyze the given nonlinear problem by different methods of computation of the Lyapunov exponents (Wolf method, Rosenstein method, Kantz method, the method based on the modification of a neural network, and the synchronization method) for the classical problems governed by difference and differential equations (Hénon map, hyperchaotic Hénon map, logistic map, Rössler attractor, Lorenz attractor) and with the use of both Fourier spectra and Gauss wavelets. It has been shown that a modification of the neural network method makes it possible to compute a spectrum of Lyapunov exponents, and then to detect a transition of the system regular dynamics into chaos, hyperchaos, and others. The aim of the comparison was to evaluate the considered algorithms, study their convergence, and also identify the most suitable algorithms for specific system types and objectives. Moreover, an algorithm of calculation of the spectrum of Lyapunov exponents based on a trained neural network has been proposed. It has been proven that the developed method yields good results for different types of systems and does not require a priori knowledge of the system equations.

Modification of the Wolf Method and Evaluation for Molecular Simulation of Vapor–Liquid Equilibria

A modification of the Wolf method [ Wolf et al. J. Chem. Phys. 1999 , 110 , 8254 - 8282 ], a spherically truncated pairwise summation to evaluate electrostatic interactions efficiently, is proposed. This method achieves better results for the energy, and the approach is used for determining phase equilibria in the grand canonical ensemble. To assess optimal parameters for the Wolf summation we propose a simple iterative approach using the Ewald summation as a reference. We show that phase equilibrium properties for pure components as well as mixtures can be calculated accurately using the Wolf summation. Our study considers molecular fluids with partial charges but without net charge.

Real-space pairwise electrostatic summation in a uniform neutralizing background

Evaluating the total energy of an extended distribution of point charges, which interact through the Coulomb potential, is central to the study of condensed matter. With near ubiquity, the summation required is carried out using Ewald's method, which splits the problem into two separately convergent sums; one in real space and the other in reciprocal space. Density functional based electronic structure methods require the evaluation of the ion-ion repulsive energy, neutralised by a uniform background charge. Here a purely real-space approach is described. It is straightforward to implement, computationally efficient and offers linear scaling. When applied to the evaluation of the electrostatic energy of neutral ionic crystals, it is shown to be closely related to Wolf's method.

Combining Progressive Hedging with a Frank--Wolfe Method to Compute Lagrangian Dual Bounds in Stochastic Mixed-Integer Programming

We present a new primal-dual algorithm for computing the value of the Lagrangian dual of a stochastic mixed-integer program (SMIP) formed by relaxing its nonanticipativity constraints. This dual is widely used in decomposition methods for the solution of SMIPs. The algorithm relies on the well-known progressive hedging method, but unlike previous progressive hedging approaches for SMIP, our algorithm can be shown to converge to the optimal Lagrangian dual value. The key improvement in the new algorithm is an inner loop of optimized linearization steps, similar to those taken in the classical Frank--Wolfe method. Numerical results demonstrate that our new algorithm empirically outperforms the standard implementation of progressive hedging for obtaining bounds in SMIP.

Molecular Simulation of Vapor-Liquid Equilibria Using the Wolf Method for Electrostatic Interactions.

The applicability of the Wolf method for calculating electrostatic interactions is verified for simulating vapor–liquid equilibria of hydrogen sulfide, methanol, and carbon dioxide. Densities, chemical potentials, and critical properties are obtained with Monte Carlo simulations using the Continuous Fractional Component version of the Gibbs Ensemble. Saturated vapor pressures are obtained from NPT simulations. Excellent agreement is found between simulation results and data from literature (simulations using the Ewald summation). It is also shown how to choose the optimal parameters for the Wolf method. Even though the Wolf method requires a large simulation box in the gas phase, due to the lack of screening of electrostatics, one can consider the Wolf method as a suitable alternative to the Ewald summation in VLE calculations.

Multi-label regularized quadratic programming feature selection algorithm with Frank–Wolfe method

Feature selection is an effective pre-processing step to remove possible redundant and irrelevant features for various machine learning paradigms, which can help build a more understandable machine learning based component in hybrid expert systems. Single-label quadratic programming feature selection (QPFS) model is formulated as a QP problem with a unit simplex constraint to both minimize feature-feature redundancy and maximize feature-label relevance simultaneously. Since its redundancy matrix is desired not to be positive semi-definite and then estimated by Nystrom low-rank approximation method, its performance depends greatly on under-sampling rate and random permutation. In this paper, without any approximation, we extend this model to construct a regularized version (rQPFS), resulting in a strictly convex QP problem, to achieve a globally optimal subset of features. To reduce the increment of computational time for entire redundancy matrix, Frank–Wolfe method with a sub-linear convergence rate and its special cases for strictly convex function and unit simplex constraint are applied to solve our rQPFS efficiently. Furthermore, to tackle multi-label FS paradigm, pruned problem transformation trick is used to evaluate feature-label relevance to describe label correlations sufficiently. The detailed experimental study on eight data sets shows that our proposed method performs the best, compared with six state-of-the-art multi-label FS methods, according to six instance-based performance evaluation measures.

Mathematical modelling of physically/geometrically non-linear micro-shells with account of coupling of temperature and deformation fields

A mathematical model of flexible physically non-linear micro-shells is presented in this paper, taking into account the coupling of temperature and deformation fields. The geometric non-linearity is introduced by means of the von Kármán shell theory and the shells are assumed to be shallow. The Kirchhoff-Love hypothesis is employed, whereas the physical non-linearity is yielded by the theory of plastic deformations. The coupling of fields is governed by the variational Biot principle. The derived partial differential equations are reduced to ordinary differential equations by means of both the finite difference method of the second order and the Faedo-Galerkin method. The Cauchy problem is solved with methods of the Runge-Kutta type, i.e. the Runge-Kutta methods of the 4th (RK4) and the 2nd (RK2) order, the Runge-Kutta-Fehlberg method of the 4th order (rkf45), the Cash-Karp method of the 4th order (RKCK), the Runge-Kutta-Dormand-Prince (RKDP) method of the 8th order (rk8pd), the implicit 2nd-order (rk2imp) and 4th-order (rk4imp) methods. Each of the employed approaches is investigated with respect to time and spatial coordinates. Analysis of stability and nature (type) of vibrations is carried out with the help of the Largest Lyapunov Exponent (LLE) using the Wolf, Rosenstein and Kantz methods as well as the modified method of neural networks.The existence of a solution of the Faedo-Galerkin method for geometrically non-linear problems of thermoelasticity is formulated and proved.A priori estimates of the convergence of the Faedo-Galerkin method are reported. Examples of calculation of vibrations and loss of stability of square shells are illustrated and discussed.

Similar to Adiponectin, Serum Levels of Osteocalcin are Associated with Mammographic Breast Density in Postmenopausal Women.

Breast cancer is the most common type of cancer in Canadian women and worldwide. Mammographic density is a well-established breast cancer risk. Recent evidence suggested inverse correlations among adiponectin, osteocalcin, and the risk developing breast cancer. The objective of the study was to evaluate the relationship between breast density and adiponectin and osteocalcin concentrations. A cross-sectional study was performed in 239 women, age range 40 to 60. Mammographic density, serum adiponectin, and osteocalcin levels were measured. According to the Wolfe method, participants were divided into those with low-risk and high-risk pattern mammograms. The study population included 107 premenopausal and 132 postmenopausal women. Parameters were no different between women with low-risk and high-risk patterns. In obese postmenopausal women, the high-risk pattern mammogram group had significantly higher values of adiponectin and osteocalcin compared with the low-risk pattern group. Multiple linear regression analyses showed that adiponectin and osteocalcin levels were associated with high-risk pattern mammograms. Adiponectin and osteocalcin levels were directly associated with high-risk pattern mammograms in obese postmenopausal women. These results do not support the use of adipokines as biomarkers; nevertheless, the most important factor is to assess the risk through breast density.

An Extended Frank--Wolfe Method with “In-Face” Directions, and Its Application to Low-Rank Matrix Completion

Motivated principally by the low-rank matrix completion problem, we present an extension of the Frank--Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. This is accomplished by a new approach to generating “in-face” directions at each iteration, as well as through new choice rules for selecting between in-face and “regular” Frank--Wolfe steps. Our framework for generating in-face directions generalizes the notion of away steps introduced by Wolfe. In particular, the in-face directions always keep the next iterate within the minimal face containing the current iterate. We present computational guarantees for the new method that trade off efficiency in computing near-optimal solutions with upper bounds on the dimension of minimal faces of iterates. We apply the new method to the matrix completion problem, where low-dimensional faces correspond to low-rank matrices. We present computational results that demonstrate the effectiveness of our methodological approach at producing nearly optimal solutions of very low rank. On both artificial and real datasets, we demonstrate significant speedups in computing very low rank nearly optimal solutions as compared to the Frank--Wolfe method (as well as several of its significant variants).

Extension of Wolfe Method for Solving Quadratic Programming with Interval Coefficients

Quadratic programming with interval coefficients developed to overcome cases in classic quadratic programming where the coefficient value is unknown and must be estimated. This paper discusses the extension of Wolfe method. The extended Wolfe method can be used to solve quadratic programming with interval coefficients. The extension process of Wolfe method involves the transformation of the quadratic programming with interval coefficients model into linear programming with interval coefficients model. The next step is transforming linear programming with interval coefficients model into two classic linear programming models with special characteristics, namely, the optimum best and the worst optimum problem.

Polarisation of polar dumbbell fluids in thermal gradients: the importance of the treatment of electrostatic interactions

ABSTRACTWe use non-equilibrium molecular dynamics simulations to study dipolar dumbbell fluids in a thermal gradient. We study the relative orientation of size asymmetric molecules with respect to the thermal gradient, and the sensitivity of the orientation to whether the Wolf method or Ewald summation is employed to compute the electrostatic interactions. For these systems, we find that the Wolf method overestimates the degree of molecular orientation. We also present new data on fluids with very small dipole moments which give novel insight into how the molecular asymmetry influences the polarisation response in the thermal gradient.

Fast and scalable Lasso via stochastic Frank–Wolfe methods with a convergence guarantee

Frank---Wolfe (FW) algorithms have been often proposed over the last few years as efficient solvers for a variety of optimization problems arising in the field of machine learning. The ability to work with cheap projection-free iterations and the incremental nature of the method make FW a very effective choice for many large-scale problems where computing a sparse model is desirable. In this paper, we present a high-performance implementation of the FW method tailored to solve large-scale Lasso regression problems, based on a randomized iteration, and prove that the convergence guarantees of the standard FW method are preserved in the stochastic setting. We show experimentally that our algorithm outperforms several existing state of the art methods, including the Coordinate Descent algorithm by Friedman et al. (one of the fastest known Lasso solvers), on several benchmark datasets with a very large number of features, without sacrificing the accuracy of the model. Our results illustrate that the algorithm is able to generate the complete regularization path on problems of size up to four million variables in <1?min.

Non-equilibrium simulations of thermally induced electric fields in water.

Using non-equilibrium molecular dynamics simulations, it has been recently demonstrated that water molecules align in response to an imposed temperature gradient, resulting in an effective electric field. Here, we investigate how thermally induced fields depend on the underlying treatment of long-ranged interactions. For the short-ranged Wolf method and Ewald summation, we find the peak strength of the field to range between 2 × 10(7) and 5 × 10(7) V/m for a temperature gradient of 5.2 K/Å. Our value for the Wolf method is therefore an order of magnitude lower than the literature value [J. A. Armstrong and F. Bresme, J. Chem. Phys. 139, 014504 (2013); J. Armstrong et al., J. Chem. Phys. 143, 036101 (2015)]. We show that this discrepancy can be traced back to the use of an incorrect kernel in the calculation of the electrostatic field. More seriously, we find that the Wolf method fails to predict correct molecular orientations, resulting in dipole densities with opposite sign to those computed using Ewald summation. By considering two different multipole expansions, we show that, for inhomogeneous polarisations, the quadrupole contribution can be significant and even outweigh the dipole contribution to the field. Finally, we propose a more accurate way of calculating the electrostatic potential and the field. In particular, we show that averaging the microscopic field analytically to obtain the macroscopic Maxwell field reduces the error bars by up to an order of magnitude. As a consequence, the simulation times required to reach a given statistical accuracy decrease by up to two orders of magnitude.

Integrating congestion pricing and transit investment planning

This paper develops a mathematical model and solution procedure to identify an optimal zonal pricing scheme for automobile traffic to incentivize the expanded use of transit as a mechanism to stem congestion and the social costs that arise from that congestion. The optimization model assumes that there is a homogenous collection of users whose behavior can be described as utility maximizers and for which their utility function is driven by monetary costs. These monetary costs are assumed to be the tolls in place, the per mile cost to drive, and the value of their time. We assume that there is a system owner who sets the toll prices, collects the proceeds from the tolls, and invests those funds in transit system improvements in the form of headway reductions. This yields a bi-level optimization model which we solve using an iterative procedure that is an integration of a genetic algorithm and the Frank–Wolfe method. The method and solution procedure is applied to an illustrative example.

Predicting Traffic Flow in Local Area Networks by the Largest Lyapunov Exponent

The dynamics of network traffic are complex and nonlinear, and chaotic behaviors and their prediction, which play an important role in local area networks (LANs), are studied in detail, using the largest Lyapunov exponent. With the introduction of phase space reconstruction based on the time sequence, the high-dimensional traffic is projected onto the low dimension reconstructed phase space, and a reduced dynamic system is obtained from the dynamic system viewpoint. Then, a numerical method for computing the largest Lyapunov exponent of the low-dimensional dynamic system is presented. Further, the longest predictable time, which is related to chaotic behaviors in the system, is studied using the largest Lyapunov exponent, and the Wolf method is used to predict the evolution of the traffic in a local area network by both Dot and Interval predictions, and a reliable result is obtained by the presented method. As the conclusion, the results show that the largest Lyapunov exponent can be used to describe the sensitivity of the trajectory in the reconstructed phase space to the initial values. Moreover, Dot Prediction can effectively predict the flow burst. The numerical simulation also shows that the presented method is feasible and efficient for predicting the complex dynamic behaviors in LAN traffic, especially for congestion and attack in networks, which are the main two complex phenomena behaving as chaos in networks.

Long Range Dependence Prognostics for Bearing Vibration Intensity Chaotic Time Series

According to the chaotic features and typical fractional order characteristics of the bearing vibration intensity time series, a forecasting approach based on long range dependence (LRD) is proposed. In order to reveal the internal chaotic properties, vibration intensity time series are reconstructed based on chaos theory in phase-space, the delay time is computed with C-C method and the optimal embedding dimension and saturated correlation dimension are calculated via the Grassberger–Procaccia (G-P) method, respectively, so that the chaotic characteristics of vibration intensity time series can be jointly determined by the largest Lyapunov exponent and phase plane trajectory of vibration intensity time series, meanwhile, the largest Lyapunov exponent is calculated by the Wolf method and phase plane trajectory is illustrated using Duffing-Holmes Oscillator (DHO). The Hurst exponent and long range dependence prediction method are proposed to verify the typical fractional order features and improve the prediction accuracy of bearing vibration intensity time series, respectively. Experience shows that the vibration intensity time series have chaotic properties and the LRD prediction method is better than the other prediction methods (largest Lyapunov, auto regressive moving average (ARMA) and BP neural network (BPNN) model) in prediction accuracy and prediction performance, which provides a new approach for running tendency predictions for rotating machinery and provide some guidance value to the engineering practice.