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.     

Implications of ancient DNA for phylogenetic studies

The utility of DNA sequence characters from fossil specimens is examined from a phylogenetic perspective. Four ways that fossil characters can alter phylogenetic hypotheses are discussed. Two empirical examples and a third hypothetical example concerning amber-preserved insects are presented to illustrate these phenomena. Fossil DNA sequences as characters will be affected by the problem of missing data and missing taxa. In general, cladogram accuracy will be more greatly affected by missing taxa and cladogram resolution will be affected more acutely by missing data. Due to these points, an examination of the importance of the phylogenetic question being addressed, the utility of the fossil DNA sequences and the rarity of the fossil should be considered before damage of a fossil is undertaken.     

DNA in wheat seeds from European archaeological sites

We have used hybridization analysis to detect ancient DNA in wheat seeds collected from three archaeological sites in Europe and the Middle East. One of these samples, carbonizedT. spelta dated to the first millennium BC, has yielded PCR products after amplification with primers directed at the leader regions of the HMW (high molecular weight) glutenin alleles. Sequences obtained from these products suggest that the DNA present in the Danebury seeds is chemically damaged, as expected for ancient DNA, and also indicate that it should be possible to study the genetic variability of archaeological wheat by ancient DNA analysis. Finally, we describe a PCR-based system that enables tetraploid and hexaploid wheats to be distinguished.     

Blaschke积的系数

本文研究了Blaschke积族β_c-{B(Z)-∏((r_k-Z)/(1-r_kZ)) from k=1 to m}的系数,并得到了一些结果。     

基于DNA序列的信息隐藏

研究了以DNA序列为载体的信息隐藏,提出了一个信息隐藏算法.该算法首先将秘密信息经预处理、编码、调制变成一维随机DNA序列;然后由一个随机数序列决定隐藏信息在载体的高复杂性区域的位置;最后在隐藏信息的位置,秘密信息字符替代载体字符.由该算法实现的信息隐藏既具有一定的稳健性和安全性,又符合生物学意义.实验结果也证明了该算法的有效性.     

增强型步长值预测器研究

研究了增强型步长值预测器.通过对传统步长值预测器的改进,可对部分重复型非等步长数据序列作出正确预测,提升性能.文中讨论了增强型步长值预测器的诸设计因素,如信心系统机制和公共子数据存储等.模拟结果表明,增强型步长值预测器能够对绝大部分适于值预测的数据序列作出正确预测.     

二重序列空间l_(q)的对偶空间

证明了当1≤p,q<+∞时,{eij}∞i,j=1是空间lpq的连续线性泛函的表示,证明了空间lpq的对偶空间为(lpq)=luw,其中,1相似文献   

Iterative Method for Constructing Complete Complementary Sequences with Lengths of 2^mN

Complete complementary sequences are widely used in spectrum spread communications because of their ideal correlation functions. A previous method generates complete complementary sequences with lengths of N^nN （n,N ∈ Z^＋）. This paper presents a new iterative method to construct complete complementary sequences with lengths of 2^mN （m,N ∈ Z^＋）. The analysis proves that this method can produce many sequence sets that do not appear in sequence sets generated by the former method, especially shorter sequence sets. The result will certainly increase the application of complete complementary sequences in communication engineering and related fields.     

Banach空间中的1阶Bessel序列

在Banach空间X中引入了1阶Bessel序列与Bessel算子的概念,证明了X上的全体1阶Bessel序列构成一个Banach空间;对X上的任意1阶Bessel序列f={fn}n∈Λ,引入了算子Tf:X*→l1,给出一个序列成为1阶Bessel序列的若干充分必要条件;引入(1,∞)阶对偶对的概念,证明了(f,g*)成为X×X*中的(1,∞)阶对偶对当且仅当Tf*Tg*|X=IX.     

两类矩阵环上的短正合列

文章讨论了两类二阶矩阵环上的模及其短正合列,得到环R上的短正合列在两类矩阵环的自然推广形式.