Related papers: Estimating phylogenetic distances between genomic …
In order to conduct a statistical analysis on a given set of phylogenetic gene trees, we often use a distance measure between two trees. In a statistical distance-based method to analyze discordance between gene trees, it is a key to decide…
Ancestral sequence reconstruction is a key task in computational biology. It consists in inferring a molecular sequence at an ancestral species of a known phylogeny, given descendant sequences at the tip of the tree. In addition to its many…
Given two random finite sequences from $[k]^n$ such that a prefix of the first sequence is a suffix of the second, we examine the length of their longest common subsequence. If $\ell$ is the length of the overlap, we prove that the expected…
Sequencing by synthesis is used in many next-generation DNA sequencing technologies. Some of the technologies, especially those exploring the principle of single-molecule sequencing, allow incomplete nucleotide incorporation in each cycle.…
We study the problem of aligning multiple sequences with the goal of finding an alignment that either maximizes the number of aligned symbols (the longest common subsequence (LCS)), or minimizes the number of unaligned symbols (the…
Unbalanced translocations are among the most frequent chromosomal alterations, accounted for 30\% of all losses of heterozygosity, a major genetic event causing inactivation of tumor suppressor genes. Despite of their central role in…
We determine the distribution of the number of saddle connections on a random translation surface of large genus. More specifically, for genus $g$ tending to infinity, the number of saddle connections with lengths in a given interval…
The discrete distribution of the length of longest increasing subsequences in random permutations of $n$ integers is deeply related to random matrix theory. In a seminal work, Baik, Deift and Johansson provided an asymptotics in terms of…
DNA sequence alignment is important today as it is usually the first step in finding gene mutation, evolutionary similarities, protein structure, drug development and cancer treatment. Covid-19 is one recent example. There are many…
This study aims to publish a novel similarity metric to increase the speed of comparison operations. Also the new metric is suitable for distance-based operations among strings. Most of the simple calculation methods, such as string length…
We determine the average number of distinct subsequences in a random binary string, and derive an estimate for the average number of distinct subsequences of a particular length.
The normalized edit distance is one of the distances derived from the edit distance. It is useful in some applications because it takes into account the lengths of the two strings compared. The normalized edit distance is not defined in…
We show that the cophylogenetic distance, k-interval cospeciation, is distinct from other metrics and accounts for global congruence between locally incongruent trees. The growth of the neighborhood of trees which satisfy the largest…
The frequency distributions of DNA k-mers are shaped by fundamental biological processes and offer a window into genome structure and evolution. Inspired by analogies to natural language, prior studies have attempted to model genomic k-mer…
We study the effects of the sequence on the propagation of nonlinear excitations in simple models of DNA in which we incorporate actual DNA sequences obtained from human genome data. We show that kink propagation requires forces over a…
Breakpoint graphs are ubiquitous structures in the field of genome rearrangements. Their cycle decomposition has proved useful in computing and bounding many measures of (dis)similarity between genomes, and studying the distribution of…
The equidistant subsequence pattern matching problem is considered. Given a pattern string $P$ and a text string $T$, we say that $P$ is an \emph{equidistant subsequence} of $T$ if $P$ is a subsequence of the text such that consecutive…
A fundamental notion of distance between train and test distributions from the field of domain adaptation is discrepancy distance. While in general hard to compute, here we provide the first set of provably efficient algorithms for testing…
Genome and metagenome comparisons based on large amounts of next-generation sequencing (NGS) data pose significant challenges for alignment-based approaches due to the huge data size and the relatively short length of the reads.…
We revisit the complexity of approximate pattern matching in an elastic-degenerate string. Such a string is a sequence of $n$ finite sets of strings of total length $N$, and compactly describes a collection of strings obtained by first…