标题： 纠正纳米孔测序读段中的多次替换错误 显示英文标题

标题： Correcting Multiple Substitutions in Nanopore-Sequencing Reads

摘要： 尽管与竞争技术相比，纳米孔测序仪具有显著优势，但由于纳米孔的物理特性和生物过程固有的噪声，它们面临着高错误率的问题。 因此，不仅制定高效的纠错构造对于这些信道至关重要，而且建立此类编码方案所需的最小冗余度界限也是必不可少的。 在此背景下，我们采用了一种简化的纳米孔测序模型，该模型受到毛的启发\emph{等}的工作，考虑了符号间干扰和测量噪声的影响。 对于长度为$n$的输入序列，生成的向量，称为 \emph{读取向量}，可能还会遭受最多\(t\)次替换错误。 我们使用著名的图论 clique 覆盖技术来证明至少需要\(t\log n -O(1)\)位冗余才能纠正多次（\(t \geq 2\)）替换。 虽然这与单次替换的情况相比令人惊讶，后者最多需要\(\log \log n - O(1)\)位冗余，但根据读取向量的特性，立即可以得到一个最优到常数因子的纠错码。 显示英文摘要

摘要： Despite their significant advantages over competing technologies, nanopore sequencers are plagued by high error rates, due to physical characteristics of the nanopore and inherent noise in the biological processes. It is thus paramount not only to formulate efficient error-correcting constructions for these channels, but also to establish bounds on the minimum redundancy required by such coding schemes. In this context, we adopt a simplified model of nanopore sequencing inspired by the work of Mao \emph{et al.}, accounting for the effects of intersymbol interference and measurement noise. For an input sequence of length $n$, the vector that is produced, designated as the \emph{read vector}, may additionally suffer at most \(t\) substitution errors. We employ the well-known graph-theoretic clique-cover technique to establish that at least \(t\log n -O(1)\) bits of redundancy are required to correct multiple (\(t \geq 2\)) substitutions. While this is surprising in comparison to the case of a single substitution, that necessitates at most \(\log \log n - O(1)\) bits of redundancy, a suitable error-correcting code that is optimal up to a constant follows immediately from the properties of read vectors.