In number theory, a prime k-tuple is a finite collection of values representing a repeatable pattern of differences between prime numbers. For a k-tuple (a, b, …), the positions where the k-tuple matches a pattern in the prime numbers are given by the set of integers n for which all of the values (n + a, n + b, …) are prime.

通常情况下，较短的K-tuple能够更好地捕捉序列中的局部相似性，但可能会在比对过程中产生误配。 而较长的K-tuple则能够更好地区分序列的差异，但可能会错过一些相似性区域。

2020年8月11日 · 也被称为 k-tuple 方法，是一种启发式算法(heuristic)，不追求最优比对但是比动态规划效率高很多，尤其适用于在大规模数据库搜索匹配序列，大名鼎鼎的 BLAST 就是用此方法。

Alignment method比对方法，通常可选Quick (快速比对)或Smith&Waterman (最佳比对)，当选择快速比对时，设置较小的k-tuple值，可以提高精确度，当序列较长时，一般要设置较大的k-tuple值。 （dna序列：k-tuple值可选范围2-6；蛋白质序列：k-tuple值可选范围1-3。 如果在前一对话框选择的是Fastalignment,则在此对话框中选择Quickalignment,否则选择Dynamicalignment即可。 其它参数不必改变，点击对话框中间的“DefaultParameters” 使其它参数取原始默认值。 点击“下一 …

2024年1月11日 · 本文介绍了BLAST算法，一种用于数据库搜索的局部比对方法，通过K-tuple或K-mer减少比对时间。BLAST利用动态规划找到高得分联配对（HSP），并通过E-value评估序列相似性，降低假阳性的可能性。

In this chapter, we review the work of Gallagher [6] in the direction of the Hardy–Littlewood k -tuples conjecture, a vast (and quantitative) generalization of the twin primes conjecture. Let H denote a k -tuple of distinct integers. What does one expect about the distribution of the integers n such that n + h is prime for each ? h ∈ H?

4 天之前 · The k-tuple conjecture states that the asymptotic number of prime constellations can be computed explicitly. In particular, unless there is a trivial divisibility condition that stops p, p+a_1, ..., p+a_k from consisting of primes infinitely often, then such prime constellations will occur with an asymptotic density which is computable in terms ...

文章在基因组 K -tuple分布的基础上, 给出了一种推测生物序列差异大小的非序列比对方法。 该方法可用于衡量真实DNA序列和随机重排序列在 K -tuple分布上的差异。将此方法用于构建含有26种胎盘哺乳动物线粒体全基因组的系统树时, 随着 K 的增大, 系统树的分类效果与生物学一致公认的结果愈加匹配。结果表明, 用此方法构建的系统进化树比用其他非序列比对分析方法构建的更加合理。 关键词: K -tuple, 非序列比对, DNA序列, 线粒体全基因组, 系统树. Abstract:

In mathematics, a k-tuple is an ordered set of k values (a vector of degree k): ( a 1 , a 2 , ..., a k ). When working in the context of prime numbers a k -tuple usually refers to a k -tuple of distinct integers which are used as the constant terms in a k -tuple of linear polynomials:

1 The Hardy-Littlewood k-tuples conjecture Let H denote a k-tuple of distinct integers. What does one expect about the distribution of the integers n such that n+h is prime for each h 2 H? Here is a rather simple-minded guess. The prime number theorem suggests that if one chooses a random integer of size x, it will be prime with probability 1 ...