Numerical Convergence of the Sinc Discrete Variable Representation for Solving Molecular Vibrational States with a Conical Intersection in Adiabatic Representation

Within the Born-Oppenheimer (BO) approximation, nuclear motions of a molecule are often envisioned to occur on an adiabatic potential energy surface (PES). However, this single PES picture should be reconsidered if a conical intersection (CI) is present, although the energy is well below the CI. The presence of the CI results in two additional terms in the nuclear Hamiltonian in the adiabatic presentation, i.e., the diagonal BO correction (DBOC) and the geometric phase (GP), which are divergent at the CI. At the same time, there are cusps in the adiabatic PESs. Thus usually it is regarded that there is numerical difficulty in a quantum dynamics calculation for treating CI in the adiabatic representation. A popular numerical method in nuclear quantum dynamics calculations is the Sinc discrete variable representation (DVR) method. We examine the numerical accuracy of the Sinc DVR method for solving the Schr?dinger equation of a two dimensional model of two electronic states with a CI in both the adiabatic and diabatic representation. The results suggest that the Sinc DVR method is capable of giving reliable results in the adiabatic representation with usual density of the grid points, without special treatment of the divergence of the DBOC and the GP. The numerical uncertainty is not worse than that after the introduction of an arbitrary vector potential for accounting the GP, whose accurate form usually is not easy to obtain.     

A visual representation for RNA secondary structure and its application

The graphical representation of biological sequences is an important subject in the area of genome studies. We propose a novel visual representation for RNA secondary structures. Some symmetric properties and information on the base distribution and compositions can be intuitively reflected by the projection graphs of the points corresponding to the RNA secondary structures. Then our method is applied to compute the similarity of 12 classical samples and 11 real RNA secondary structures. The results indicate that our method can not only effectively analyze the similarity between RNA secondary structures but also show a high consistency with other literatures. Moreover, our method only needs the geometrical center of the characteristic curve of the RNA secondary structure to compute the similarity matrix, which means a low computational complexity. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Using Huffman coding method to visualize and analyze DNA sequences

On the basis of the Huffman coding method, we propose a new graphical representation of DNA sequence. The representation can avoid degeneracy and loss of information in the transfer of data from a DNA sequence to its graphical representation. Then a multicomponent vector from the representation is introduced to characterize quantitatively DNA sequences. The components of the vector are derived from the graphical representation of DNA primary sequence. The examination of similarities and dissimilarities among the complete coding sequences of β-globin gene of 11 species and six ND6 proteins shows the utility of the scheme.     

Novel numerical and graphical representation of DNA sequences and proteins

We have introduced novel numerical and graphical representations of DNA, which offer a simple and unique characterization of DNA sequences. The numerical representation of a DNA sequence is given as a sequence of real numbers derived from a unique graphical representation of the standard genetic code. There is no loss of information on the primary structure of a DNA sequence associated with this numerical representation. The novel representations are illustrated with the coding sequences of the first exon of β-globin gene of half a dozen species in addition to human. The method can be extended to proteins as is exemplified by humanin, a 24-aa peptide that has recently been identified as a specific inhibitor of neuronal cell death induced by familial Alzheimer's disease mutant genes.     

视觉表征视角下中学化学教科书编排的“三序”结合*——以“物质结构”相关内容为例

教科书的编排有其内在的逻辑结构,视觉表征是教科书的重要组成部分,因此视觉表征的选用也应遵循一定的原则。研究借鉴Gkitzia等人的分析框架对人教版初、高中化学教科书中“物质结构”相关内容的视觉表征进行编码分析。在对表征类型及功能分布分析的基础上,结合教科书中物质结构相关知识内容的编排及学生认知、心理发展规律展开讨论。研究发现,人教版教科书中视觉表征的分布与教科书编排的“三序”原则较为契合,能够针对不同学段、学生特点选用视觉表征。最后,依据研究结论,针对教科书中视觉表征的编选和使用提出建议。     

中学生对“溶液”概念理解的可视化表征及启示

学生概念理解的可视化表征可以通过学生的作图来展示,分析图示可以获取学生概念理解的更加深入的信息。梳理了国内外有关中学生对“溶液”概念理解的研究,集中对学生的作图进行分析,呈现了中学生对“溶液”概念理解的可视化表征。针对作图发现的学生概念理解的结果,提出了促进中学生“溶液”概念理解的教学启示。     

Sparse Representation Classification of Tobacco Leaves Using Near-Infrared Spectroscopy and a Deep Learning Algorithm

A spare representation classification method for tobacco leaves based on near-infrared spectroscopy and deep learning algorithm is reported in this paper. All training samples were used to make up a data dictionary of the sparse representation and the test samples were represented by the sparsest linear combinations of the dictionary by sparse coding. The regression residual of the test sample to each class was computed and finally assigned to the class with the minimum residual. The effectiveness of spare representation classification method was compared with K-nearest neighbor and particle swarm optimization–support vector machine algorithms. The results show that the classification accuracy of the proposed method is higher and it is more efficient. The results suggest that near-infrared spectroscopy with spare representation classification algorithm may be an alternative method to traditional methods for discriminating classes of tobacco leaves.     

对称群标准表示矩阵计算新方法

在多体问题的对称群方法中,群表示矩阵的计算是关键性问题。Young-Yamanouchi规则给出了标准正交表示的计算方法,然而该法相当繁琐,颇难使用,本文将2列Young表标准表示的计算方法[1]推广到任意不可约表示,给出对称群标准表示矩阵计算新方法.     

实验论文中“实验用品”表达的几个问题

指出了目前化学实验论文及实验教科书中“实验用品”表述中存在的没有“实验用品”表述,表述时仪器、试剂、材料、试样不加区分和缺少主要仪器与试剂的问题,分析了问题原因,提出了改进建议,旨在为完善实验论文及实验教科书提供参考。     

New Poisson Sum Formula Derived by Squeezing Transformation in Quantum Optics

Using squeezing transform in the context of quantum optics and based on the Fourier series expansion we rigorously derive a new Poisson sum formula. Application of this new formula to the representation transformation of kq-wave function for describing electrons in periodic lattice is demonstrated. In so doing, the transition matrix element of harmonic oscillator in kq representation is derived.