Related papers: Estimating phylogenetic distances between genomic …
We investigate the order of the variance of the optimal alignments score of two independent iid binary random words having the same length. The letters are equiprobable, but the scoring function is such that one letter has a larger score…
A classical problem in comparative genomics is to compute the rearrangement distance, that is the minimum number of large-scale rearrangements required to transform a given genome into another given genome. While the most traditional…
We study here the so called subsequence pattern matching also known as hidden pattern matching in which one searches for a given pattern $w$ of length $m$ as a subsequence in a random text of length $n$. The quantity of interest is the…
The number of the non-shared edges of two phylogenies is a basic measure of the dissimilarity between the phylogenies. The non-shared edges are also the building block for approximating a more sophisticated metric called the nearest…
Genome rearrangements are events where large blocks of DNA exchange places during evolution. The analysis of these events is a promising tool for understanding evolutionary genomics, providing data for phylogenetic reconstruction based on…
Extreme deformations of the DNA double helix attracted a lot of attention during the past decades. Particularly, the determination of the persistence length of DNA with extreme local disruptions, or kinks, has become a crucial problem in…
In recent years, a number of methods have been developed to infer complex demographic histories, especially historical population size changes, from genomic sequence data. Coalescent Hidden Markov Models have proven to be particularly…
We propose a computational method to measure and visualize interrelationships among any number of DNA sequences allowing, for example, the examination of hundreds or thousands of complete mitochondrial genomes. An "image distance" is…
The goal of this paper is to study the similarity between sequences using a distance between the \emph{context} trees associated to the sequences. These trees are defined in the framework of \emph{Sparse Probabilistic Suffix Trees} (SPST),…
We prove a conjecture of Drew Armstrong on the average maximal length of $k$-alternating subsequence of permutations. The $k=1$ case is a well-known result of Richard Stanley.
Motivation: Spliced alignment refers to the alignment of messenger RNA (mRNA) or protein sequences to eukaryotic genomes. It plays a critical role in gene annotation and the study of gene functions. Accurate spliced alignment demands…
We introduce a model of DNA sequence evolution which can account for biases in mutation rates that depend on the identity of the neighboring bases. An analytic solution for this class of non-equilibrium models is developed by adopting…
A tandem duplication denotes the process of inserting a copy of a segment of DNA adjacent to its original position. More formally, a tandem duplication can be thought of as an operation that converts a string $S = AXB$ into a string $T =…
Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…
Motivated by mutation processes occurring in in-vivo DNA-storage applications, a channel that mutates stored strings by duplicating substrings as well as substituting symbols is studied. Two models of such a channel are considered: one in…
Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…
In this paper, we consider a tree inference problem motivated by the critical problem in single-cell genomics of reconstructing dynamic cellular processes from sequencing data. In particular, given a population of cells sampled from such a…
A rapid and low-cost method to sequence DNA would usher in a revolution in medicine. We propose and theoretically show the feasibility of a protocol for sequencing based on the distributions of transverse electrical currents of…
A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to…
A classical measure of string comparison is given by the longest common subsequence (LCS) problem on a pair of strings. We consider its generalisation, called the semi-local LCS problem, which arises naturally in many string-related…