Numerical analysis of breaking waves using the moving particle semi-implicit method

The numerical method used in this study is the moving particle semi-implicit (MPS) method, which is based on particles and their interactions. The particle number density is implicitly required to be constant to satisfy incompressibility. A semi-implicit algorithm is used for two-dimensional incompressible non-viscous flow analysis. The particles whose particle number densities are below a set point are considered as on the free surface. Grids are not necessary in any calculation steps. It is estimated that most of computation time is used in generation of the list of neighboring particles in a large problem. An algorithm to enhance the computation speed is proposed. The MPS method is applied to numerical simulation of breaking waves on slopes. Two types of breaking waves, plunging and spilling breakers, are observed in the calculation results. The breaker types are classified by using the minimum angular momentum at the wave front. The surf similarity parameter which separates the types agrees well with references. Breaking waves are also calculated with a passively moving float which is modelled by particles. Artificial friction due to the disturbed motion of particles causes errors in the flow velocity distribution which is shown in comparison with the theoretical solution of a cnoidal wave. © 1998 John Wiley & Sons, Ltd.     

Theoretical approach to the pharmacophoric pattern of GABAB analogs

In order to determine the structural requirements that are important for GABA_B binding affinity, a quantum-chemical-based conformational study has been performed, followed by a similarity analysis which includes 12 GABA_B analogs. Due to the flexibility of the structures, a semigrid GABA_B analog [2RS-(5,5-dimethyl) morpholinyl-acetic acid] has been used as a template for the amonium moiety in order to help to identify the active conformation. Both in vacuo, and solvent-simulated calculations, for the physiological media modeled as water molecules, have been compared, for this analog, at ab initio (G94, 6-31+G(d,p)) and semiempirical (PM3) levels, respectively. On the basis of this comparison, the results of in vacuo PM3 calculations have been chosen for the similarity analysis. We have included, in the calculations, a group of molecules heterogeneous enough to become representative of the different families that can bind to the GABA_B receptor site. Following their comparison we report the leading characteristics that can be related to their binding capability and define a pharmacophoric pattern for GABA_B analogs. The latter is compared with the one previously found for the binding affinity at the GABA_A receptor site. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 1195–1208, 1998     

ELECT++: Faster conformational search method for docking flexible molecules using molecular similarity

We have developed a program, ELECT++ (Effective LEssening of Conformations by Template molecules in C++), to speed up the conformational search for small flexible molecules using the similar property principle. We apply this principle to molecular shape and, importantly, to molecular flexibility. After molecules in a database are clustered according to flexibility and shape (FCLUST++), additional reagents are generated to screen the conformational space of molecules in each cluster (TEMPLATE++). We call these representative reagents of each cluster template reagents. Template reagents and clustered reagents produce, after reaction, template molecules and clustered molecules, respectively (tREACT++). The conformations of a template molecule are searched in the context of a macromolecular target. Acceptable conformational choices are then applied to all molecules in its cluster, thus effectively biasing conformational space to speed up conformational searches (tSEARCH++). In our incremental search method, it is necessary to calculate the root-mean-square deviations (RMSD) matrix of distances between different conformations of the same molecule to reduce the number of conformations. Instead of calculating the RMSD matrix for all molecules in a cluster, the RMSD matrix of a template molecule is chosen as a reference and applied to all the molecules in its cluster. We demonstrate that FCLUST++ clusters the primary amine reagents from the Available Chemicals Directory (ACD) successfully. The program tSEARCH++ was applied to dihydrofolate reductase with virtual molecules generated by tREACT++ using clustered primary amine reagents. The conformational search by the program tSEARCH++ was about 4.8 times faster than by SEARCH++, with an acceptable range of errors. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1834–1852, 1998     

Quantum similarity measures under atomic shell approximation: First order density fitting using elementary Jacobi rotations

The elementary Jacobi rotations technique is proposed as a useful tool to obtain fitted electronic density functions expressed as linear combinations of atomic spherical shells, with the additional constraint that all coefficients are kept positive. Moreover, a Newton algorithm has been implemented to optimize atomic shell exponents, minimizing the quadratic error integral function between ab initio and fitted electronic density functions. Although the procedure is completely general, as an application example both techniques have been used to compute a 1S-type Gaussian basis for atoms H through Kr, fitted from a 3-21G basis set. Subsequently, molecular electronic densities are modeled in a promolecular approximation, as a simple sum of parameterized atomic contributions. This simple molecular approximation has been employed to show, in practice, its usefulness to some computational examples in the field of molecular quantum similarity measures. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 2023–2039, 1997     

Fast computation,rotation, and comparison of low resolution spherical harmonic molecular surfaces

A procedure that rapidly generates an approximate parametric representation of macromolecular surface shapes is described. The parametrization is expressed as an expansion of real spherical harmonic basis functions. The advantage of using a parametric representation is that a pair of surfaces can be matched by using a quasi-Newton algorithm to minimize a suitably chosen objective function. Spherical harmonics are a natural and convenient choice of basis function when the task is one of search in a rotational search space. In particular, rotations of a molecular surface can be simulated by rotating only the harmonic expansion coefficients. This rotational property is applied for the first time to the 3-dimensional molecular similarity problem in which a pair of similar macromolecular surfaces are to be maximally superposed. The method is demonstrated with the superposition of antibody heavy chain variable domains. Special attention is given to computational efficiency. The spherical harmonic expansion coefficients are determined using fast surface sampling and integration schemes based on the tessellation of a regular icosahedron. Low resolution surfaces can be generated and displayed in under 10 s and a pair of surfaces can be maximally superposed in under 3 s on a contemporary workstation. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 383–395, 1999     

A time-series approach to measuring node similarity in networks and its application to community detection

A central concept in network analysis is that of similarity between nodes. In this paper, we introduce a dynamic time-series approach to quantifying the similarity between nodes in networks. The problem of measuring node similarity is exquisitely embedded into the framework of time series for state evolution of nodes. We develop a deterministic parameter-free diffusion model to drive the dynamic evolution of node states, and produce a unique time series for each source node. Then we introduce a measure quantifying how far all the other nodes are located from each source one. Following this measure, a quantity called dissimilarity index is proposed to signify the extent of similarity between nodes. Thereof, our dissimilarity index gives a deep and natural integration between the local and global perspectives of topological structure of networks. Furthermore, we apply our dissimilarity index to unveil community structure in networks, which verifies the proposed dissimilarity index.     

Nonlinear Exact Solutions of the 2-Dimensional Rotational Euler Equations for the Incompressible Fluid

In this paper, the Clarkson–Kruskal direct approach is employed to investigate the exact solutions of the2-dimensional rotational Euler equations for the incompressible fluid. The application of the method leads to a system of completely solvable ordinary differential equations. Several special cases are discussed and novel nonlinear exact solutions with respect to variables x and y are obtained. It is of interest to notice that the pressure p is obtained by the second kind of curvilinear integral and the coefficients of the nonlinear solutions are solitary wave type functions like tanh(kt/2)and sech(kt/2) due to the rotational parameter k = 0. Such phenomenon never appear in the classical Euler equations wherein the Coriolis force arising from the gravity and Earth's rotation is ignored. Finally, illustrative numerical figures are attached to show the behaviors that the exact solutions may exhibit.     

关于幂等阵的相似与线性组合

证明了数域上两个同阶幂等阵相似的充要条件是它们有相同的秩;给出了幂等阵的相似标准型;讨论了两个幂等阵的线性组合仍是幂等阵的充要条件.     

A spectral similarity measure using Bayesian statistics

A spectral similarity measure was developed that can differentiate subtle differences between two spectra. The spectra are digitalized into a vector. The difference between the two spectra is defined by a difference vector, which is one spectrum minus the other. The spectral similarity measure is transformed into a hypothesis test of the similarities and differences between the two spectra. The scalar mean of the difference vector is used as the statistical variable for the hypothesis test. A threshold for the hypothesis that the spectra are different was proposed. The Bayesian prior odds ratio was estimated from multiple spectra of the same sample. The posterior odds ratio was used to quantity the spectral similarity measure of the two spectra. Diffuse reflectance near-infrared spectra of tobacco samples of two formulations were used to demonstrate this method. The results show that this new method can detect subtle differences between the spectra.