Spectral analysis of phylogenetic data

The spectral analysis of sequence and distance data is a new approach to phylogenetic analysis. For two-state character sequences, the character values at a given site split the set of taxa into two subsets, a bipartition of the taxa set. The vector which counts the relative numbers of each of these bipartitions over all sites is called a sequence spectrum. Applying a transformation called a Hadamard conjugation, the sequence spectrum is transformed to the conjugate spectrum. This conjugation corrects for unobserved changes in the data, independently from the choice of phylogenetic tree. For any given phylogenetic tree with edge weights (probabilities of state change), we define a corresponding tree spectrum. The selection of a weighted phylogenetic tree from the given sequence data is made by matching the conjugate spectrum with a tree spectrum. We develop an optimality selection procedure using a least squares best fit, to find the phylogenetic tree whose tree spectrum most closely matches the conjugate spectrum. An inferred sequence spectrum can be derived from the selected tree spectrum using the inverse Hadamard conjugation to allow a comparison with the original sequence spectrum. A possible adaptation for the analysis of four-state character sequences with unequal frequencies is considered. A corresponding spectral analysis for distance data is also introduced. These analyses are illustrated with biological examples for both distance and sequence data. Spectral analysis using the Fast Hadamard transform allows optimal trees to be found for at least 20 taxa and perhaps for up to 30 taxa. The development presented here is self contained, although some mathematical proofs available elsewhere have been omitted. The analysis of sequence data is based on methods reported earlier, but the terminology and the application to distance data are new.     

“铅树”生成条件的研究

提出了生成“铅树”反应成功的关键是硅酸凝胶的坚固性,找到了较好的硅酸凝胶的制备条件,使该氧化还原平衡移动的反应成功率提高了９０ ％ 以上．     

计算一类递归方程的增广Petri网模型

递归方程的计算一直是一个较为复杂的问题,为更好的解决这一问题,建立各种模型是十分必要的.斐波那契数列是一个著名的递归方程,在这个方程的基础上,针对同类的递归方程建立了增广Petri网模型,并对模型的运行进行了分析.     

复变函数f（z）在∞点的留数及其应用

对有理函数ｆ（ｚ）在∞点的留数提供了一个非常简捷的方法，并且利用ｆ（ｚ）在∞点的留数来计算孤立奇点ｚ０的留数。     

韶关地区乡镇移动通信网络覆盖的优化

探讨了如何优化和延伸基站覆盖信号,降低网络优化成本,改善道路遮挡覆盖和农村信号覆盖弱的延伸系统.使基站覆盖系统的下行信号增强超过10 dB,上行信号增强超过8 dB,有效地加大了基站的覆盖半径.     

基于扩展有效的逆DEA模型

为了克服决策单元在有效性的评价和排序方面占主导地位的缺陷,在扩展DEA模型的基础上,对于输出减少时的逆DEA问题进行了讨论.通过求解相应的多目标规划问题(VP),得到了多目标规划(VP)的Pareto弱有效解与评价减少了输出的决策单元的规划问题的最优值之间的一些相关性质.对于决策单元为弱DEA有效的情形,也进行了类似的讨论.最后用数值实例加以说明.     

一类广义Petersen图的邻强边染色

研究了一类广义Petersen图G(n,k)的邻强边染色,构造性地证明了:若n≡0(mod3),k≡/0(mod3),则χ_(as)~′(G(n,k))=4.其中χa′s(G(n,k))表示G(n,k)的邻强边色数.     

树图及其顶点数的计算

文章从生成树之间的距离出发,定义了连通图的树图概念并证明了若干个简单性质,然后根据基本关联矩阵的性质,讨论了用行列式计算给定连通图的树图的顶点数。     

高维增广相空间中广义完整非保守力学系统的Lie对称定理及其逆定理

依据广义增广相空间中完整非保守力学系统的运动微分方程在无限小变换下的不变性,建立系统的确定方程,给出结构方程和守恒量的形式及有关结论的逆命题。