In [1] various strange identities involving summations over partitions were proposed by using Faa di Bruno formula. In this paper, some other strange identities are got in an analogous way and a corollary is obtained by using inversion formulas of Lagrange.
In this paper, Jabotinsky matrices in [4, 5] are modified and a type of infinite lower triangular matrices T(f) is discussed. Some algebraic properties of T(f) are obtained and proved. Additionally, some inverse pairs and combinatorial identities associated with derivatives are obtained.
单核苷酸多态性(Single nucleotide polymorphism—SNP)被认为是揭示遗传变异理想的分子标记,近几年来一系列针对高通量测序平台的技术如RAD,GBS,RRLs,2b-RAD等成为非模式生物尤其是水生动物的de novo SNP标记规模开发和大样本群体遗传研究的有利途径。本文从理论上讨论了测序错误和重复序列因素对de novo SNP分型的影响,并利用模式生物拟南芥RAD模拟数据对理论分析进行了验证。通过理论推导和模拟验证发现测序数据量在15～20X左右时单拷贝区域内SNP被检测的概率大于95%,等位基因的支持度不小于2时能够有效屏蔽掉测序错误对SNP分型的影响(假阳性低于2%),这些为实际数据的de novo SNP分型提供了理论上的指导。
