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.     

中成药质量稳定性的原子吸收光谱鉴别分析

对全国各地用原子吸收光谱仪测定10批次大活络丸中12种无机元素及建立的指纹图谱,尝试用成分数据分析法、向量相似法和模糊聚类法建立全国无机元素的指纹图谱和中药质量控制标准方法,获得较满意的结果。研究表明,建立无机元素指纹图谱控制中成药中无机元素的质量,具有很好的实用性和可操作性,用于全国各地不同厂家生产的大活络丸无机元素的质量控制是切实可行的。     

Numerical characterization of DNA sequences based on the k-step Markov chain transition probability

A DNA sequence can be regarded as a discrete-time Markov chain. Based on k-step transition probabilities, we construct a series of 4 x 4 k-step transition matrices to characterize the DNA primary sequences. According to the properties of Markov chains, we obtain distributions of A, T, C and G, and analyze the changes among them from yesterday to tomorrow. We can calculate the probabilities of nucleotide triples of DNA primary sequences. Finally, we introduce a correlation of this kind of transition matrices and consider it as an invariant to analyze the similarities/dissimilarities of DNA sequences.     

基于关键词的对等网络节点群相似性度量模型研究

为了进一步提高基于P2P的内容分发网CDN（content delivery network）的搜索效率,对用户就近组成的节点群（peer group）进行了研究,提出了节点群相似的概念和基于关键词的节点群相似性度量模型.当一个需求在本节点群不能满足时,优先到相似性高的节点群中查找,以较快地满足跨节点群的需求.度量模型对任意两个节点群首先根据节点中各文档关键词的一致程度判断对应两个节点的相似度,然后根据相似节点对的数量和相似度来判断两个节点群相似度.实验表明,使用所提出的度量模型得出的计算结果比传统的基于VSM的算法更接近于实际情况.     

Symmetries and Exact Solutions of the Breaking Soliton Equation

With the aid of the classical Lie group method and nonclassical Lie group method, we derive the classical Lie point symmetry and the nonclassical Lie point symmetry of (2+1)-dimensional breaking soliton (BS) equation. Using the symmetries, we find six classical similarity reductions and two nonclassical similarity reductions of the BS equation. Varieties of exact solutions of the BS equation are obtained by solving the reduced equations.     

基于归一化割的主题划分算法研究

为了保证抽取信息的全面性,主题划分成了不可或缺的工作。借助同义词词林,从词语的语义角度计算文本中各个段落间的相似度,建立段落文本关系图。基于文本关系图对归一化割分割准则中权值矩阵的构建做出调整,使之更能体现出段落间的相似程度,并使用该准则对文本进行主题划分。结果表明,该方法无论是对连续段落还是跨段落表达同一主题的主题划分均较为有效。