Related papers: Probabilistic Models of k-mer Frequencies (Extende…
Background: With the fast development of next generation sequencing technologies, increasing numbers of genomes are being de novo sequenced and assembled. However, most are in fragmental and incomplete draft status, and thus it is often…
The analysis of biological sequencing data has been one of the biggest applications of string algorithms. The approaches used in many such applications are based on the analysis of k-mers, which are short fixed-length strings present in a…
k-mers (nucleotide strings of length k) form the basis of several algorithms in computational genomics. In particular, k-mer abundance information in sequence data is useful in read error correction, parameter estimation for genome…
The wide array of currently available genomes display a wonderful diversity in size, composition and structure with many more to come thanks to several global biodiversity genomics initiatives starting in recent years. However, sequencing…
Frequencies of $k$-mers in sequences are sometimes used as a basis for inferring phylogenetic trees without first obtaining a multiple sequence alignment. We show that a standard approach of using the squared-Euclidean distance between…
Genomic evolution can be viewed as string-editing processes driven by mutations. An understanding of the statistical properties resulting from these mutation processes is of value in a variety of tasks related to biological sequence data,…
Distances between sequences based on their $k$-mer frequency counts can be used to reconstruct phylogenies without first computing a sequence alignment. Past work has shown that effective use of k-mer methods depends on 1) model-based…
Recently, ultra high-throughput sequencing of RNA (RNA-Seq) has been developed as an approach for analysis of gene expression. By obtaining tens or even hundreds of millions of reads of transcribed sequences, an RNA-Seq experiment can offer…
Genome assembly tools based on the de Bruijn graph framework rely on a parameter k, which represents a trade-off between several competing effects that are difficult to quantify. There is currently a lack of tools that would automatically…
The amount of non-unique sequence (non-singletons) in a genome directly affects the difficulty of read alignment to a reference assembly for high throughput-sequencing data. Although a greater length increases the chance for reads being…
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…
This paper presents a probabilistic approach for DNA sequence analysis. A DNA sequence consists of an arrangement of the four nucleotides A, C, T and G and different representation schemes are presented according to a probability measure…
We consider phylogeny estimation under a two-state model of sequence evolution by site substitution on a tree. In the asymptotic regime where the sequence lengths tend to infinity, we show that for any fixed $k$ no statistically consistent…
RNA-Seq is rapidly becoming the standard technology for transcriptome analysis. Fundamental to many of the applications of RNA-Seq is the quantification problem, which is the accurate measurement of relative transcript abundances from the…
Various approaches to alignment-free sequence comparison are based on the length of exact or inexact word matches between two input sequences. Haubold {\em et al.} (2009) showed how the average number of substitutions between two DNA…
Estimating the abundances of all $k$-mers in a set of biological sequences is a fundamental and challenging problem with many applications in biological analysis. While several methods have been designed for the exact or approximate…
Motivated by empirical observations of algebraic duplicated sequence length distributions in a broad range of natural genomes, we analytically formulate and solve a class of simple discrete duplication/substitution models that generate…
This paper provides a comprehensive review of recent advancements in k-mer-based data structures representing collections of several samples (sometimes called colored de Bruijn graphs) and their applications in large-scale sequence indexing…
The utility of DNA sequence substrings (k-mers) in alignment-free phylogenetic classification, including that of bacteria and viruses, is increasingly recognized. However, its biological basis eludes many twenty-first century practitioners.…
Many commonly studied species now have more than one chromosome-scale genome assembly, revealing a large amount of genetic diversity previously missed by approaches that map short reads to a single reference. However, many species still…