Related papers: Zimin patterns in genomes
DNA sequences encode critical genetic information, yet their variable length and discrete nature impede direct utilization in deep learning models. Existing DNA representation schemes convert sequences into numerical vectors but fail to…
In a recent article, Behrens and Vingron (JCB 17, 12, 2010) compute waiting times for k-mers to appear during DNA evolution under the assumption that the considered k-mers do not occur in the initial DNA sequence, an issue arising when…
The length of coding sequence series in microbial genomes were regarded as a fluctuating system and characterized by the methods of statistical physics. The distribution and the correlatin properties of 50 genomes including bacteria and…
Finding maximal exact matches (MEMs) between strings is an important task in bioinformatics, but it is becoming increasingly challenging as geneticists switch to pangenomic references. Fortunately, we are usually interested only in the…
We find finite-state recurrences to enumerate the words on the alphabet $[n]^r$ which avoid the patterns 123 and $1k(k-1)\dots2$, and, separately, the words which avoid the patterns 1234 and $1k(k-1)\dots2$.
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.…
We consider avoiding mesosomes -- that is, words of the form $xx'$ with $x'$ a conjugate of $x$ that is different from $x$ -- over a binary alphabet. We give a structure theorem for mesosome-avoiding words, count how many there are,…
We introduce the $k$-bonacci polyominoes, a new family of polyominoes associated with the binary words avoiding $k$ consecutive $1$'s, also called generalized $k$-bonacci words. The polyominoes are very entrancing objects, considered in…
Sequence organizations are viewed from two points: one is from informational redundancy or informational correlation (IC) and another is from k-mer frequency statistics. Two problems are investigated. The first is how the ICs exceed the…
In this work we study reverse complementary genomic word pairs in the human DNA, by comparing both the distance distribution and the frequency of a word to those of its reverse complement. Several measures of dissimilarity between distance…
Counting the frequencies of k-mers in read libraries is often a first step in the analysis of high-throughput sequencing experiments. Infrequent k-mers are assumed to be a result of sequencing errors. The frequent k-mers constitute a…
Identifying palindromes in sequences has been an interesting line of research in combinatorics on words and also in computational biology, after the discovery of the relation of palindromes in the DNA sequence with the HIV virus. Efficient…
We analyzed the periodic patterns in E. coli promoters and compared the distributions of the corresponding patterns in promoters and in the complete genome to elucidate their function. Except the three-base periodicity, coincident with that…
We study the primary DNA structure of four of the most completely sequenced human chromosomes (including chromosome 19 which is the most dense in coding), using Non-extensive Statistics. We show that the exponents governing the decay of the…
Advances in DNA sequencing technology will soon result in databases of thousands of genomes. Within a species, individuals' genomes are almost exact copies of each other; e.g., any two human genomes are 99.9% the same. Relative Lempel-Ziv…
Statistical analysis of bacteria genomes texts has been performed on the basis of 20 complete genomes origin from Genebank. It has been revealed that the word ranked distributions are quite well approximated by logarithmic law. Results…
In this article, we review existing probabilistic models for modeling abundance of fixed-length strings (k-mers) in DNA sequencing data. These models capture dependence of the abundance on various phenomena, such as the size and repeat…
Dokos et. al. studied the distribution of two statistics over permutations $\mathfrak{S}_n$ of $\{1,2,\dots, n\}$ that avoid one or more length three patterns. A permutation $\sigma\in\mathfrak{S}_n$ contains a pattern…
Compositional spectra (CS) analysis based on k-mer scoring of DNA sequences was employed in this study for dot-plot comparison of human and primate genomes. The detection of extended conserved synteny regions was based on continuous fuzzy…
Languages across the world exhibit Zipf's law of abbreviation, namely more frequent words tend to be shorter. The generalized version of the law - an inverse relationship between the frequency of a unit and its magnitude - holds also for…