Free Energy Level Correction by Monte Carlo Resampling with Weighted Histogram Analysis Method

Free energy calculations may provide vital information for studying various chemical and biological processes. Quantum mechanical methods are required to accurately describe interaction energies, but their computations are often too demanding for conformational sampling. As a remedy, level correction schemes that allow calculating high level free energies based on conformations from lower level simulations have been developed. Here, we present a variation of a Monte Carlo (MC) resampling approach in relation to the weighted histogram analysis method (WHAM). We show that our scheme can generate free energy surfaces that can practically converge to the exact one with sufficient sampling, and that it treats cases with insufficient sampling in a more stable manner than the conventional WHAM-based level correction scheme. It can also provide a guide for checking the uncertainty of the level-corrected surface and a well-defined criterion for deciding the extent of smoothing on the free energy surface for its visual improvement. We demonstrate these aspects by obtaining the free energy maps associated with the alanine dipeptide and proton transfer network of the KillerRed protein in explicit water, and exemplify that the MC resampled WHAM scheme can be a practical tool for producing free energy surfaces of realistic systems.     

单通道实现三级Clipped模型的光学神经网络系统

提出并采用单通道光学系统实现了三级Clipped模型的神经网络,并用统计方法计算了三级Clipped模型的存储容量,和Clipped模型相比,三级Clippdd模型有更强的存储与寻址能力.     

光学焦距测量误差分布的实验研究

为解决光学检测中的误差分布问题 ,提出了用实验方法验证其分布 ,而不是简单地依据经验估计其分布为均匀分布、三角分布或正态分布。通过人眼目视测量与CCD光电测试 ,分析比较大量的采样数据 ,通常人为操作因素及仪器机械精度是目视光学检测中的一个主要误差源 ,进而得到目视测焦距的误差分布 ,并进行拟合性检验     

Histogram equalization of vibration fringes in holography

Common reconstructed fringes in holographic interferometry of vibration show rapidly diminishing intensity with extended amplitude limiting the measurement range. Using computer-simulated fringe patterns, linear histogram equalization is applied to redistribute the intensity for significant enhancement in the higher amplitude range. The cases of time-average and real-time single-frequency sinusoidal vibration are described.     

Sampling free energy surfaces as slices by combining umbrella sampling and metadynamics

Metadynamics (MTD) is a very powerful technique to sample high‐dimensional free energy landscapes, and due to its self‐guiding property, the method has been successful in studying complex reactions and conformational changes. MTD sampling is based on filling the free energy basins by biasing potentials and thus for cases with flat, broad, and unbound free energy wells, the computational time to sample them becomes very large. To alleviate this problem, we combine the standard Umbrella Sampling (US) technique with MTD to sample orthogonal collective variables (CVs) in a simultaneous way. Within this scheme, we construct the equilibrium distribution of CVs from biased distributions obtained from independent MTD simulations with umbrella potentials. Reweighting is carried out by a procedure that combines US reweighting and Tiwary–Parrinello MTD reweighting within the Weighted Histogram Analysis Method (WHAM). The approach is ideal for a controlled sampling of a CV in a MTD simulation, making it computationally efficient in sampling flat, broad, and unbound free energy surfaces. This technique also allows for a distributed sampling of a high‐dimensional free energy surface, further increasing the computational efficiency in sampling. We demonstrate the application of this technique in sampling high‐dimensional surface for various chemical reactions using ab initio and QM/MM hybrid molecular dynamics simulations. Further, to carry out MTD bias reweighting for computing forward reaction barriers in ab initio or QM/MM simulations, we propose a computationally affordable approach that does not require recrossing trajectories. © 2016 Wiley Periodicals, Inc.     

Molecular dynamics simulations of LiCl association and NaCl association in water by means of ABEEM/MM

Constrained molecular dynamics simulations have been used to investigate the LiCl and NaCl ionic association in water in terms of atom-bond electronegativity equalization method fused into molecular mechanics (ABEEM/MM). The simulations make use of the seven-site fluctuating charge and flexible ABEEM-7P water model, based on which an ion-water interaction potential has been constructed. The mean force and the potential of mean force for LiCl and NaCl in water, the charge distributions, as well as the structural and dynamical properties of contact ion pair dissociation have been investigated. The results are reasonable and informative. For LiCl ion pair in water, the solvent-separated ion pair configurations are more stable than contact ion pair configurations. The calculated PMF for NaCl in water indicates that contact ion pair and solvent-separated ion pair configurations are of comparable stability.     

Improved Approach for the Maximum Entropy Deconvolution Problem

The probability density function (pdf) valid for the Gaussian case is often applied for describing the convolutional noise pdf in the blind adaptive deconvolution problem, although it is known that it can be applied only at the latter stages of the deconvolution process, where the convolutional noise pdf tends to be approximately Gaussian. Recently, the deconvolutional noise pdf was approximated with the Edgeworth Expansion and with the Maximum Entropy density function for the 16 Quadrature Amplitude Modulation (QAM) input but no equalization performance improvement was seen for the hard channel case with the equalization algorithm based on the Maximum Entropy density function approach for the convolutional noise pdf compared with the original Maximum Entropy algorithm, while for the Edgeworth Expansion approximation technique, additional predefined parameters were needed in the algorithm. In this paper, the Generalized Gaussian density (GGD) function and the Edgeworth Expansion are applied for approximating the convolutional noise pdf for the 16 QAM input case, with no need for additional predefined parameters in the obtained equalization method. Simulation results indicate that improved equalization performance is obtained from the convergence time point of view of approximately 15,000 symbols for the hard channel case with our new proposed equalization method based on the new model for the convolutional noise pdf compared to the original Maximum Entropy algorithm. By convergence time, we mean the number of symbols required to reach a residual inter-symbol-interference (ISI) for which reliable decisions can be made on the equalized output sequence.     

BayesWHAM: A Bayesian approach for free energy estimation,reweighting, and uncertainty quantification in the weighted histogram analysis method

The weighted histogram analysis method (WHAM) is a powerful approach to estimate molecular free energy surfaces (FES) from biased simulation data. Bayesian reformulations of WHAM are valuable in proving statistically optimal use of the data and providing a transparent means to incorporate regularizing priors and estimate statistical uncertainties. In this work, we develop a fully Bayesian treatment of WHAM to generate statistically optimal FES estimates in any number of biasing dimensions under arbitrary choices of the Bayes prior. Rigorous uncertainty estimates are generated by Metropolis‐Hastings sampling from the Bayes posterior. We also report a means to project the FES and its uncertainties into arbitrary auxiliary order parameters beyond those in which biased sampling was conducted. We demonstrate the approaches in applications of alanine dipeptide and the unthreading of a synthetic mimic of the astexin‐3 lasso peptide. Open‐source MATLAB and Python implementations of our codes are available for free public download. © 2017 Wiley Periodicals, Inc.     

Mass Transport Based Multi-Model Color Transfer

Image editing is a hot research topic in the image processing region, and one of the most basic problems in this field is the color transfer. It modifies the color style of the target image to match the color palette of the source while preserving the content of the target. Although there exist many algorithms to deal with this problem, none of existing methods can handle all kinds of images, especially complex landscape images. In this paper, we propose a Mass Transport based color transfer method in the CIELab color space, which can generate natural transfer results for different kinds of images including landscapes. Different from previous methods using the same transfer model for all the channels, we adopt different models for the luminance channel and color channels. For the luminance channel, a global transfer method is adopted for keeping the consistence in the visual perception. For the color channels, we construct a model based on histogram and Mass Transport, which perfectly transfers the colors of all the pixels from the source to the target and simultaneously preserves the content. What is more, experiments on real images demonstrate that our approach performs favorably against most of the existing methods.