A hierarchic collision detection algorithm for simple Brownian dynamics

We describe an algorithm to avoid steric violation (bumps) between bodies arranged in a hierarchy. The algorithm recursively directs the focus of a bump-detector towards the interactions of children whose parents are in collision. This has the effect of concentrating available computer resources towards maintaining good steric interactions in the region where bodies are colliding. The algorithm was implemented and tested under two programming environments: a graphical environment, OpenGL under Java3D, and a non-graphical environment in “C”. The former used a built-in collision detection system whereas the latter used a simple algorithm devised previously for the interaction of “soft” bodies. This simpler system was found to run much faster (by 50-fold) even after allowing for time spent on graphical activity and was also better at preventing steric violations. With a hierarchy of three levels of 100, the non-graphical implementation was able to simulate a million atomic bodies for 100,000 steps in 12 h on a laptop computer.     

Empirical valence bond models for reactive potential energy surfaces: a parallel multilevel genetic program approach

We describe a new method for constructing empirical valence bond potential energy surfaces using a parallel multilevel genetic program (PMLGP). Genetic programs can be used to perform an efficient search through function space and parameter space to find the best functions and sets of parameters that fit energies obtained by ab initio electronic structure calculations. Building on the traditional genetic program approach, the PMLGP utilizes a hierarchy of genetic programming on two different levels. The lower level genetic programs are used to optimize coevolving populations in parallel while the higher level genetic program (HLGP) is used to optimize the genetic operator probabilities of the lower level genetic programs. The HLGP allows the algorithm to dynamically learn the mutation or combination of mutations that most effectively increase the fitness of the populations, causing a significant increase in the algorithm's accuracy and efficiency. The algorithm's accuracy and efficiency is tested against a standard parallel genetic program with a variety of one-dimensional test cases. Subsequently, the PMLGP is utilized to obtain an accurate empirical valence bond model for proton transfer in 3-hydroxy-gamma-pyrone in gas phase and protic solvent.     

Controlled backwashing in a membrane sequencing batch reactor used for toxic wastewater treatment

A new control algorithm for performing filtration in a membrane sequencing batch reactor (MSBR) to prevent fouling is presented. Based on continuous measurements of the transmembrane pressure (TMP) and the permeate flux, the algorithm decides when to initiate backwashing. The algorithm was tested on a laboratory scale bioreactor treating synthetic wastewater containing 4-chlorophenol (4CP) as model toxic compound and filtration was carried out using a submerged tubular membrane module and a diaphragm pump. Several controller configurations were tested for different MSBR cycles. The results showed that the proposed algorithm was robust against the highly varying mixed liquor characteristics and was able to keep the TMP below critical values and maintain the flux at a maximum for most of the filtration time. Therefore, despite possible frequent backwashes, the total filtration time was minimized.     

Rationalizing nuclear overhauser effect data for compounds adopting multiple-solution conformations

An algorithm is described for refining the populations of a set of multiple-solution conformers using experimental nuclear Overhauser effects (nOes). The method is based upon representing the effective relaxation matrix for the set of interconverting proposed conformers as a linear combination of relaxation matrices (LCORMs) due to each conformer. The conformer population derivative of the nOe is derived from a Taylor series expression for the calculated nOe. This derivative may then be used in a standard nonlinear least-squares refinement procedure. The LCORM nOe procedure is tested using a monosaccharide system, 1-O-methyl-α-L -iduronate, that is known to exhibit conformational variability. The measured nOes for this system are used to refine the populations of a set of three static conformers, namely, the ¹C₄, ⁴C₁, and ²S₀ ring conformers. The populations thus derived are compared to those previously obtained using nuclear magnetic resonance proton-proton coupling constant information. Two possible extensions to the method are discussed: The first uses combined nOe and coupling constant data while the second removes the restrictions that the conformers used for fitting be rigid entities. © 1994 by John Wiley & Sons, Inc.     

Hybrid stochastic simulations of intracellular reaction–diffusion systems

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction–diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction–diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.     

A fast parallel clustering algorithm for molecular simulation trajectories

We implemented a GPU‐powered parallel k‐centers algorithm to perform clustering on the conformations of molecular dynamics (MD) simulations. The algorithm is up to two orders of magnitude faster than the CPU implementation. We tested our algorithm on four protein MD simulation datasets ranging from the small Alanine Dipeptide to a 370‐residue Maltose Binding Protein (MBP). It is capable of grouping 250,000 conformations of the MBP into 4000 clusters within 40 seconds. To achieve this, we effectively parallelized the code on the GPU and utilize the triangle inequality of metric spaces. Furthermore, the algorithm's running time is linear with respect to the number of cluster centers. In addition, we found the triangle inequality to be less effective in higher dimensions and provide a mathematical rationale. Finally, using Alanine Dipeptide as an example, we show a strong correlation between cluster populations resulting from the k‐centers algorithm and the underlying density. © 2012 Wiley Periodicals, Inc.     

Algorithm for calculating the dissociation constants of weak electrolytes and ampholites in water solutions

An algorithm for calculating the dissociation constants of weak organic acids and bases in water solutions is developed on the basis of spectrophotometric data on the UV and visible regions without measuring the рН of the medium or using buffer solutions. The proposed algorithm is tested experimentally for six single-base acids and single-acid bases of different strengths. The relative error in determining the dissociation constants does not exceed 5% and is in agreement with the literature data.     

Geometrically feasible binding modes of a flexible ligand molecule at the receptor site

A very efficient algorithm for determining the geometrically feasible binding modes of a flexible ligand molecule at the receptor site is presented. It is based on distance geometry but maintains the requirements of three dimensions. The distance geometry manipulation can superimpose two bodies without explicitly calculating the necessary rigid rotation and translation. The whole conformation space of a flexible molecule can be efficiently examined by considering only a finite number of conformational points. The method is suitable only when the criterion for superposition is some minimum distance limit. It cannot, however, give the exact distance between two points in two different bodies.     

Comprehensive two-dimensional gas chromatography/time-of-flight mass spectrometry peak sorting algorithm

We report a novel peak sorting method for the two-dimensional gas chromatography/time-of-flight mass spectrometry (GC x GC/TOF-MS) system. The objective of peak sorting is to recognize peaks from the same metabolite occurring in different samples from thousands of peaks detected in the analytical procedure. The developed algorithm is based on the fact that the chromatographic peaks for a given analyte have similar retention times in all of the chromatograms. Raw instrument data are first processed by ChromaTOF (Leco) software to provide the peak tables. Our algorithm achieves peak sorting by utilizing the first- and second-dimension retention times in the peak tables and the mass spectra generated during the process of electron impact ionization. The algorithm searches the peak tables for the peaks generated by the same type of metabolite using several search criteria. Our software also includes options to eliminate non-target peaks from the sorting results, e.g., peaks of contaminants. The developed software package has been tested using a mixture of standard metabolites and another mixture of standard metabolites spiked into human serum. Manual validation demonstrates high accuracy of peak sorting with this algorithm.     

Development and validation of an improved algorithm for overlaying flexible molecules

A program for overlaying multiple flexible molecules has been developed. Candidate overlays are generated by a novel fingerprint algorithm, scored on three objective functions (union volume, hydrogen-bond match, and hydrophobic match), and ranked by constrained Pareto ranking. A diverse subset of the best ranked solutions is chosen using an overlay-dissimilarity metric. If necessary, the solutions can be optimised. A multi-objective genetic algorithm can be used to find additional overlays with a given mapping of chemical features but different ligand conformations. The fingerprint algorithm may also be used to produce constrained overlays, in which user-specified chemical groups are forced to be superimposed. The program has been tested on several sets of ligands, for each of which the true overlay is known from protein–ligand crystal structures. Both objective and subjective success criteria indicate that good results are obtained on the majority of these sets.     

Surface hopping simulation of the vibrational relaxation of I2 in liquid xenon using the collective probabilities algorithm

A surface hopping simulation of the vibrational relaxation of highly excited I(2) in liquid xenon is presented. The simulation is performed by using the collective probabilities algorithm which assures the coincidence of the classical and quantum populations. The agreement between the surface hopping simulation results and the experimental measurements for the vibrational energy decay curves at different solvent densities and temperatures is shown to be good. The overlap of the decay curves when the time axis is linearly scaled is explained in terms of the perturbative theory for the rate constants. The contribution of each solvent atom to the change of the quantum populations of the solute molecule is used to analyze the mechanism of the relaxation process     

Optimization of mass spectrometers using the adaptive particle swarm algorithm

Optimization of mass spectrometers using the adaptive particle swarm algorithm (APSA) is described along with implementations for ion optical simulations and various time-of-flight (TOF) instruments. The need for in situ self optimization is addressed through discussion of the reflectron TOF mass spectrometer (RTOF) on the European Space Agency mission Rosetta. In addition, a tool for optimization of laboratory mass spectrometers is presented and tested on two different instruments. After the application of APSA optimization, a substantial increase in performance for mass spectrometers that have manually been tuned for several weeks or months is demonstrated.     

Efficient first-principles electronic dynamics

An efficient first-principles electronic dynamics method is introduced in this article. The approach we put forth relies on incrementally constructing a time-dependent Fock∕Kohn-Sham matrix using active space density screening method that reduces the cost of computing two-electron repulsion integrals. An adaptive stepsize control algorithm is developed to optimize the efficiency of the electronic dynamics while maintaining good energy conservation. A selected set of model dipolar push-pull chromophore molecules are tested and compared with the conventional method of direct formation of the Fock∕Kohn-Sham matrix. While both methods considered herein take on identical dynamical simulation pathways for the molecules tested, the active space density screening algorithm becomes much more computationally efficient. The adaptive stepsize control algorithm, when used in conjunction with the dynamically active space method, yields a factor of ～3 speed-up in computational cost as observed in electronic dynamics using the time dependent density functional theory. The total computational cost scales nearly linear with increasing size of the molecular system.     

Activity coefficients of binary methanol alcohol mixtures from cluster weighting

The hydrogen bond network of different small alcohols is investigated via cluster analysis. Methanol/alcohol mixtures are studied with increasing chain length and branching of the molecule. Those changes can play an important role in different fields, including solvent and metal extraction. The extended tight binding method GFN2-xTB allows the evaluation and geometry optimization of thousands of clusters built via a genetic algorithm. Interaction energies and geometries are evaluated and discussed for the neat systems. Thermodynamic properties, such as vaporization enthalpies and activity coefficients, are calculated with the binary quantum cluster equilibrium (bQCE) approach using our in-house code Peacemaker 2.8. Combined distribution functions of the distances against the angles of the hydrogen bonds are evaluated for neat and mixed clusters and weighted by the equilibrium populations achieved from bQCE calculations.     

基于分步相关成分分析的中药材质量鉴别神经元分类器

提出并构建了一种基于分步相关成分分析的神经元分类器(SCCA-HBP),并将其用于中药材质量模式分类.通过从色谱分析所得到的高维数据集中分步提取分类相关成分,获取化学模式特征向量,使神经元分类器输入模式向量的维数降低.此外,提出用带输出误差死区的混合BP算法训练神经元分类器,提高了网络学习训练速度和分类准确性.以32个当归样品质量等级分类鉴别为例考察本方法,分类正确率为100%,优于PCA-BP(84.4%)和SCCA-BP(90.6%)方法;且训练时间仅为BP算法的54.2%.     

Langevin dynamics for rigid bodies of arbitrary shape

We present an algorithm for carrying out Langevin dynamics simulations on complex rigid bodies by incorporating the hydrodynamic resistance tensors for arbitrary shapes into an advanced rotational integration scheme. The integrator gives quantitative agreement with both analytic and approximate hydrodynamic theories for a number of model rigid bodies and works well at reproducing the solute dynamical properties (diffusion constants and orientational relaxation times) obtained from explicitly solvated simulations.     

Thermal conductivities of molecular liquids by reverse nonequilibrium molecular dynamics

The reverse nonequilibrium molecular dynamics method for thermal conductivities is adapted to the investigation of molecular fluids. The method generates a heat flux through the system by suitably exchanging velocities of particles located in different regions. From the resulting temperature gradient, the thermal conductivity is then calculated. Different variants of the algorithm and their combinations with other system parameters are tested: exchange of atomic velocities versus exchange of molecular center-of-mass velocities, different exchange frequencies, molecular models with bond constraints versus models with flexible bonds, united-atom versus all-atom models, and presence versus absence of a thermostat. To help establish the range of applicability, the algorithm is tested on different models of benzene, cyclohexane, water, and n-hexane. We find that the algorithm is robust and that the calculated thermal conductivities are insensitive to variations in its control parameters. The force field, in contrast, has a major influence on the value of the thermal conductivity. While calculated and experimental thermal conductivities fall into the same order of magnitude, in most cases the calculated values are systematically larger. United-atom force fields seem to do better than all-atom force fields, possibly because they remove high-frequency degrees of freedom from the simulation, which, in nature, are quantum-mechanical oscillators in their ground state and do not contribute to heat conduction.     

A continuous wavelet transform algorithm for peak detection

Contactless conductivity detector technology has unique advantages for microfluidic applications. However, the low S/N and varying baseline makes the signal analysis difficult. In this paper, a continuous wavelet transform-based peak detection algorithm was developed for CE signals from microfluidic chips. The Ridger peak detection algorithm is based on the MassSpecWavelet algorithm by Du et al. [Bioinformatics 2006, 22, 2059-2065], and performs a continuous wavelet transform on data, using a wavelet proportional to the first derivative of a Gaussian function. It forms sequences of local maxima and minima in the continuous wavelet transform, before pairing sequences of maxima to minima to define peaks. The peak detection algorithm was tested against the Cromwell, MassSpecWavelet, and Linear Matrix-assisted laser desorption/ionization-time-of-flight-mass spectrometer Peak Indication and Classification algorithms using experimental data. Its sensitivity to false discovery rate curve is superior to other techniques tested.