A macroion electrokinetics algorithm

A numerical algorithm is presented for the standard model of macroion electrokinetics and certain generalizations of it. The macroion consists of a cylindrical section with identical, hemispheroidal endcaps, each piece having arbitrary length. The system of one macroion and adjoining salt solution is subjected to an arbitrary sequence of pulsed electrical fields and pulsed translational and rotational velocities. Numerical solutions are obtained for the time dependent electrostatic and mobile ion concentration fields and the solvent velocity. From these fields the dielectric response, force, and torque are calculated. Generalizations of the standard model include the diffusive motion of macroion surface charges, partial slip of solvent motion at the macroion surface, and a simple model for the reactive exchange of surface charge with solution ions. The primary illustrative application is to recent measurements of electric birefringence versus applied field frequency for poly-(tetrafluorothylene) colloidal particles, but a few results are presented for the dielectric response of DNA fragments and of spherical colloidal particles. The source code and additional details are provided as supplementary documentation.     

Multiple sequence alignment algorithm based on a dispersion graph and ant colony algorithm

In this article, we describe a representation for the processes of multiple sequences alignment (MSA) and used it to solve the problem of MSA. By this representation, we took every possible aligning result into account by defining the representation of gap insertion, the value of heuristic information in every optional path and scoring rule. On the basis of the proposed multidimensional graph, we used the ant colony algorithm to find the better path that denotes a better aligning result. In our article, we proposed the instance of three‐dimensional graph and four‐dimensional graph and advanced a special ichnographic representation to analyze MSA. It is yet only an experimental software, and we gave an example for finding the best aligning result by three‐dimensional graph and ant colony algorithm. Experimental results show that our method can improve the solution quality on MSA benchmarks. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

FWAVina: A novel optimization algorithm for protein-ligand docking based on the fireworks algorithm

Protein-ligand docking is an essential process that has accelerated drug discovery. How to accurately and effectively optimize the predominant position and orientation of ligands in the binding pocket of a target protein is a major challenge. This paper proposed a novel ligand binding pose search method called FWAVina based on the fireworks algorithm, which combined the fireworks algorithm with the efficient Broyden-Fletcher-Goldfarb-Shannon local search method adopted in AutoDock Vina to address the pose search problem in docking. The FWA was used as a global optimizer to rapidly search promising poses, and the Broyden-Fletcher-Goldfarb-Shannon method was incorporated into FWAVina to perform an exact local search. FWAVina was developed and tested on the PDBbind and DUD-E datasets. The docking performance of FWAVina was compared with the original Vina program. The results showed that FWAVina achieves a remarkable execution time reduction of more than 50 % than Vina without compromising the prediction accuracies in the docking and virtual screening experiments. In addition, the increase in the number of ligand rotatable bonds has almost no effect on the efficiency of FWAVina. The higher accuracy, faster convergence and improved stability make the FWAVina method a better choice of docking tool for computer-aided drug design. The source code is available at https://github.com/eddyblue/FWAVina/.     

The slow-scale stochastic simulation algorithm

Reactions in real chemical systems often take place on vastly different time scales, with "fast" reaction channels firing very much more frequently than "slow" ones. These firings will be interdependent if, as is usually the case, the fast and slow reactions involve some of the same species. An exact stochastic simulation of such a system will necessarily spend most of its time simulating the more numerous fast reaction events. This is a frustratingly inefficient allocation of computational effort when dynamical stiffness is present, since in that case a fast reaction event will be of much less importance to the system's evolution than will a slow reaction event. For such situations, this paper develops a systematic approximate theory that allows one to stochastically advance the system in time by simulating the firings of only the slow reaction events. Developing an effective strategy to implement this theory poses some challenges, but as is illustrated here for two simple systems, when those challenges can be overcome, very substantial increases in simulation speed can be realized.     

A gradient extremal walking algorithm

Gradient extremals define stream beds connecting stationary points on molecular potential energy surfaces. Using this concept we have developed an algorithm to determine transition states. We initiate walks at equilibrium geometries and follow the gradient extremals until a stationary point is reached. As an illustration we have investigated the mechanism for exchange of protons on carbon in methylenimine (H₂C=NH) using a multi-reference self-consistent-field wave function.     

Analytical algorithm for molecular modeling

A molecular modeling procedure, based on internal coordinates and strictly analytical even in the most intricated cases, is described. Internal coordinates, always nonredundant, become mutually independent and can be varied without constraints. Structural refinement from diffraction data (Least-square method, LS) can be done using the classical Gauss-Newton approach and avoiding Lagrange multipliers. A comparative test done using published data has shown that while the new method gives rise to a structural refinement in perfect agreement with the known structure, the traditional methods (z-matrix and constraints based) does not work.     

A FAST pattern matching algorithm

The advent of digital computers has made the routine use of pattern-matching possible in various applications. This has also stimulated the development of many algorithms. In this paper, we propose a new algorithm that offers improved performance compared to those reported in the literature so far. The new algorithm has been evolved after analyzing the well-known algorithms such as Boyer-Moore, Quick-search, Raita, and Horspool. The overall performance of the proposed algorithm has been improved using the shift provided by the Quick-search bad-character and by defining a fixed order of comparison. These result in the reduction of the character comparison effort at each attempt. The best- and the worst- case time complexities are also presented in this paper. Most importantly, the proposed method has been compared with the other widely used algorithms. It is interesting to note that the new algorithm works consistently better for any alphabet size.     

An electron repulsion integral compression algorithm

A data compression algorithm for packing/unpacking floating point numbers is presented. The method has been used to compress large volumes of data commonly generated in ab initio quantum mechanical calculations. To retain an accuracy of 10^?6 Hartree on the final energy, the required file space needed is approximately half its original size whereas the CPU time required to solve the Hartree–Fock self-consistent field equations increases with 30–60%. © 1993 John Wiley & Sons, Inc.     

色谱指纹图谱组合相似度的算法

色谱指纹图谱相似度是评价中药质量稳定性的有效手段之一,其中向量夹角余弦相似度应用最为广泛。但是当色谱峰面积分布范围宽时,夹角余弦对数据的差异响应不灵敏。以土茯苓色谱指纹图谱数据为实例证实了当两样本数据间比例相差较大时,夹角余弦相似度对共有峰和非共有峰响应的灵敏程度相差很大。组合相似度在共有峰的夹角余弦相似度基础上纳入了非共有峰的影响,分别计算非共有峰和共有峰对相似度的贡献,并以最大峰比例同态性为指标,确定非共有峰的合适权重。基于样本峰面积数据建立的组合相似度模型能灵敏地反映待测样本与参照样本内在成分的峰比例变化,适合衡量多个药材样本间的相似程度,已成为评价药材质量相似度的新方法。     

Cluster algorithm for nonadditive hard-core mixtures

In this paper, we present a cluster algorithm for the numerical simulations of nonadditive hard-core mixtures. This algorithm allows one to simulate and equilibrate systems with a number of particles two orders of magnitude larger than previous simulations. The phase separation for symmetric binary mixtures is studied for different nonadditivities as well as for the Widom-Rowlinson model [B. Widom and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970)] in two and three dimensions. The critical densities are determined from finite size scaling. The critical exponents for all the nonadditivities are consistent with the Ising universality class.     

An algorithm for overlapped chromatogram separation

Non-negative matrix factorization (NMF) is a recently developed method for real time data analysis. In the past it has been used for facial recognition and spectral data analysis. Most of the NMF algorithms do not converge to a stable limit point and uniqueness in results is also a problem in NMF. To improve the convergence, a new NMF algorithm with modified multiplicative update (ML-NMFmse) has been proposed in this work for strongly overlapped and embedded chromatograms separation. To get same results for all the runs, instead of random initialization, three different initialization methods have been used namely, ALS–NMF (robust initialization), NNDSVD based initialization and EFA based initializations. The proposed ML-NMFmse algorithm is applied on the simulated and experimental overlapped chromatograms obtained for acetone and acrolein mixture, using Gas Chromatography–Flame Ionization Detector. Before applying NMF, Principal Component Analysis (PCA) was applied to determine number of components in the mixture taken. The result of proposed ML-NMFmse is compared with that of existing Multivariate Curve Resolution-Alternating Least Squares method in optimal conditions for both the algorithms. In the case of embedded chromatogram, the proposed ML-NMFmse with Robust method (ALS-NMF) of initialization performs better than all other methods. For a resolution of severely overlapped chromatograms, the proposed ML-NMFmse with NNDSVD method of initialization outperforms all other methods.     

Evolutionary algorithm based configuration interaction approach

A new evolutionary algorithm for stochastic configuration interaction (CI) method designed as an affordable approximation to full configuration interaction (FCI) has been described here. The key components of the algorithm are initiation, propagation, and termination steps taking inspiration from the genetic algorithm. The propagation step is performed with cloning (retention of a Slater determinant without change), mutation (single excitation/de‐excitation), and crossover (exchange of α and β strings between two Slater determinants) and termination is selection of few Slater determinants based on certain fitness function (measure of importance of a determinant in the CI space) and rejection of the rest. We find that the absolute value of the CI coefficients is a suitable fitness function when combined with a fixed selection scheme. We have tested its accuracy in 1D Hubbard problem and ground state potential energy surface (PES) has also been constructed for symmetric bond breaking of water molecule, where the errors are found to be around 10 mE_h with low non‐parallelity error, when retaining only a small fraction of the total number of Slater determinants in the final population. This shows that this method has the ability to capture both static and dynamic correlation. Performance and convergence properties of the algorithm are also tested for N₂ triple bond breaking problem. The algorithm opens up a promising way for stochastic sampling of the important determinants in the full Hilbert space.     

An algorithm for three-dimensional Voronoi S-network

The paper presents an algorithm for calculating the three-dimensional Voronoi-Delaunay tessellation for an ensemble of spheres of different radii (additively-weighted Voronoi diagram). Data structure and output of the algorithm is oriented toward the exploration of the voids between the spheres. The main geometric construct that we develop is the Voronoi S-network (the network of vertices and edges of the Voronoi regions determined in relation to the surfaces of the spheres). General scheme of the algorithm and the key points of its realization are discussed. The principle of the algorithm is that for each determined site of the network we find its neighbor sites. Thus, starting from a known site of the network, we sequentially find the whole network. The starting site of the network is easily determined based on certain considerations. Geometric properties of ensembles of spheres of different radii are discussed, the conditions of applicability and limitations of the algorithm are indicated. The algorithm is capable of working with a wide variety of physical models, which may be represented as sets of spheres, including computer models of complex molecular systems. Emphasis was placed on the issue of increasing the efficiency of algorithm to work with large models (tens of thousands of atoms). It was demonstrated that the experimental CPU time increases linearly with the number of atoms in the system, O(n).     

Simple algorithm for isothermal-isobaric molecular dynamics

We review principles of non-Hamiltonian statistical mechanics and present a new set of equations and integration algorithm for isothermal-isobaric dynamics. The chief advantage of the present scheme is that it is somewhat simpler than previous methods. We perform numerical simulations to test the accuracy of the algorithm and compare its stability to that of a "gold standard," a symplectic integrator for Hamiltonian dynamics of the same system. The stability of the isothermal-isobaric algorithm is comparable to the stability of the symplectic integrator.     

The prism algorithm for two-electron integrals

A new approach to the evaluation of two-electron repulsion integrals over contracted Gaussian basis functions is developed. The new scheme encompasses 20 distinct, but interrelated, paths from simple shell-quartet parameters to the target integrals, and, for any given integral class, the path requiring the fewest floating-point operations (FLOPS ) is that used. Both theoretical (FLOP counting) and practical (CPU timing) measures indicate that the method represents a substantial improvement over the HGP algorithm.     

Steepest-descent algorithm for vibrational analysis calculations

In this paper we consider problems concerning the effectiveness of iterational calculations on vibrational analysis. Instead of the widespread least-squares method of force field refinement, another method is proposed based on the steepest-descent algorithm for calculation of the functional minimum of many variables. The new method does not require inverting of a large, poorly conditioned matrix or the introduction of experimental damping coefficients for improving the convergency of the calculations. Test calculations performed for several molecules exhibit a significant “elasticity” of the proposed algorithm allowing more precise reproduction of the molecular vibration frequencies than can be found in recently published works.     

A hierarchical transition state search algorithm

A hierarchical transition state search algorithm is developed and its implementation in the density functional theory program deMon2k is described. This search algorithm combines the double ended saddle interpolation method with local uphill trust region optimization. A new formalism for the incorporation of the distance constrain in the saddle interpolation method is derived. The similarities between the constrained optimizations in the local trust region method and the saddle interpolation are highlighted. The saddle interpolation and local uphill trust region optimizations are validated on a test set of 28 representative reactions. The hierarchical transition state search algorithm is applied to an intramolecular Diels-Alder reaction with several internal rotors, which makes automatic transition state search rather challenging. The obtained reaction mechanism is discussed in the context of the experimentally observed product distribution.     

An algorithm for reversal median problem

In this paper, we present an algorithm for reversal median problem whose performance ratio is less than 2.     

An efficient algorithm for chemical fingerprinting

In this paper, we present and analyze a constructive polynomial-time algorithm that helps in solving the problem of comparing FT-ICR data to theoretical compounds. A brute-force approach to solving the problem is exponential in its worst-case. Our algorithm serves as the backbone of a more general interactive software tool for chemical fingerprinting which is to be developed in a subsequent paper. A preliminary algorithm analysis shows that our approach is efficient for most commercial applications involving the general problem of determining combinations of elements that satisfy a set of prescribed constraints.