The equivalent potential of water for electronic structure of aspartic acid

The equivalent potential of water for the electronic structure of aspartic acid (Asp(-)) in solution is constructed by the first-principles, all-electrons, ab initio calculations. Aspartic acid is a hydrophilic amino acid which is negatively charged in neutral water solution. The main process of calculation consists of three steps. Firstly, the geometric structure of the cluster containing Asp(-) and water molecules is calculated by the free cluster calculation. Then, based on the obtained geometric structure, the electronic structure of Asp(-) with the potential of water molecules is calculated using the self-consistent cluster-embedding method. Finally, the electronic structure of Asp(-) with the potential of dipoles is calculated. The results show that the major effect of water on Asp(-)'s electronic structure is lowering the occupied molecular orbitals by about 0.02 Ry on average, and narrowing energy gap by 10.8%. The effect of water on the electronic structure of Asp(-) can be simulated by dipoles potential.     

Functionals for multilinear fractional embedding

A novel representation is developed as a measure for multilinear fractional embedding.Corresponding extensions are given for the Bourgain–Brezis–Mironescu theorem and Pitt's inequality. New results are obtained for diagonal trace restriction on submanifolds as an application of the Hardy–Littlewood–Sobolev inequality. Smoothing estimates are used to provide new structural understanding for density functional theory, the Coulomb interaction energy and quantum mechanics of phase space. Intriguing connections are drawn that illustrate interplay among classical inequalities in Fourier analysis.     

Vertex centrality of complex networks based on joint nonnegative matrix factorization and graph embedding

Finding crucial vertices is a key problem for improving the reliability and ensuring the effective operation of networks, solved by approaches based on multiple attribute decision that suffer from ignoring the correlation among each attribute or the heterogeneity between attribute and structure. To overcome these problems, a novel vertex centrality approach, called VCJG, is proposed based on joint nonnegative matrix factorization and graph embedding. The potential attributes with linearly independent and the structure information are captured automatically in light of nonnegative matrix factorization for factorizing the weighted adjacent matrix and the structure matrix, which is generated by graph embedding. And the smoothness strategy is applied to eliminate the heterogeneity between attributes and structure by joint nonnegative matrix factorization. Then VCJG integrates the above steps to formulate an overall objective function, and obtain the ultimately potential attributes fused the structure information of network through optimizing the objective function. Finally, the attributes are combined with neighborhood rules to evaluate vertex's importance. Through comparative analyses with experiments on nine real-world networks, we demonstrate that the proposed approach outperforms nine state-of-the-art algorithms for identification of vital vertices with respect to correlation, monotonicity and accuracy of top-10 vertices ranking.     

ScGSLC: An unsupervised graph similarity learning framework for single-cell RNA-seq data clustering

Accurate clustering of cells from single-cell RNA sequencing (scRNA-seq) data is an essential step for biological analysis such as putative cell type identification. However, scRNA-seq data has high dimension and high sparsity, which makes traditional clustering methods less effective to reflect the similarity between cells. Since genetic network fundamentally defines the functions of cell and deep learning shows strong advantages in network representation learning, we propose a novel scRNA-seq clustering framework ScGSLC based on graph similarity learning. ScGSLC effectively integrates scRNA-seq data and protein-protein interaction network to a graph. Then graph convolution network is employed by ScGSLC to embedding graph and clustering the cells by the calculated similarity between graphs. Unsupervised clustering results of nine public data sets demonstrate that ScGSLC shows better performance than the state-of-the-art methods.     

Investigation of the Second Harmonic Generation at the Water–Vacuum Interface by Using Multi-Scale Modeling Methods

The Sequential Quantum Mechanics/Molecular Mechanics scheme has been enacted to perform a systematic investigation of the polarizability (α) and first hyperpolarizability (β) responses at the water–vacuum interface. After performing classical molecular dynamics simulations to provide snapshots of the structures, quantum chemistry calculations of the linear and nonlinear optical responses have been performed for clusters of five water molecules at the time-dependent DFT level in combination with different embedding schemes, ranging from point charges to polarizable point charges, with and without local field effects. When going from the bulk to the interface, the main observations of these calculations encompass i) a modest increase of the average polarizability but an increase by about a factor of two of its anisotropy, ii) an increase by about 20 % of the β_HRS response, accompanied by a small increase of its depolarization ratio, and iii) a net increase of the component of the β tensor normal to the interface (β_zzz) as well as of β_//. Globally, the interfacial effects on β are localized at the first molecular layer while they are observed up to the fourth molecular layer on α.     

路的积图的边平衡性质

2009年, Kwong和Lee考虑了一个图论中新的标号问题—图的边平衡指标集.在本文中,通过利用嵌入标号图的方法,考察了路的积图的边平衡性质.     

Analytical nuclear excited‐state gradients for the Tamm–Dancoff approximation using uncoupled frozen‐density embedding

We report the derivation and implementation of analytical nuclear gradients for excited states using time‐dependent density functional theory using the Tamm–Dancoff approximation combined with uncoupled frozen‐density embedding using density fitting. Explicit equations are presented and discussed. The implementation is able to treat singlet as well as triplet states and functionals using the local density approximation, the generalized gradient approximation, combinations with Hartree–Fock exchange (hybrids), and range‐separated functionals such as CAM‐B3LYP. The new method is benchmarked against supermolecule calculations in two case studies: The solvatochromic shift of the (vertical) fluorescence energy of 4‐aminophthalimide on solvation, and the first local excitation of the benzonitrile dimer. Whereas for the 4‐aminophthalimide–water complex deviations of about 0.2 eV are obtained to supermolecular calculations, for the benzonitrile dimer the maximum error for adiabatic excitation energies is below 0.01 eV due to a weak coupling of the subsystems. © 2017 Wiley Periodicals, Inc.     

On the upper embedding of symmetric configurations with block size 3

We consider the problem of embedding a symmetric configuration with block size 3 in an orientable surface in such a way that the blocks of the configuration form triangular faces and there is only one extra large face. We develop a sufficient condition for such an embedding to exist given any orientation of the configuration, and show that this condition is satisfied for all configurations on up to 19 points. We also show that there exists a configuration on 21 points which is not embeddable in any orientation. As a by-product, we give a revised table of numbers of configurations, correcting the published figure for 19 points. We give a number of open questions about embeddability of configurations on larger numbers of points.     

流形学习在运动声源声特征提取方面的研究*

运动声源因声信号时变性、叠加性和空时耦合性强,声数据呈现高维、非线性等特点,使得关键声特征提取困难,声特征提取方法复杂度高、数值计算量大、有效性差。因此,如何有效提取声特征并降低提取方法复杂度成为目前多源声场声源精准识别需迫切解决的关键科学问题。由此,该文提出短时傅里叶变换(STFT)和局部线性嵌入算法(LLE)联合的STFT-LLE流形学习声特征提取方法,并将此方法应用于运动声特征提取,且通过仿真实验测试对其进行了验证。该方法为运动声目标的分类识别提供了技术支撑。