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Tandem duplication is an evolutionary process whereby a segment of DNA is replicated and proximally inserted. The different configurations that can arise from this process give rise to some interesting combinatorial questions. Firstly, we…
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…
Sequencing a genome to determine an individual's DNA produces an enormous number of short nucleotide subsequences known as reads, which must be reassembled to reconstruct the full genome. We present a method for analyzing this type of data…
Genome assembly, the process of reconstructing a long genetic sequence by aligning and merging short fragments, or reads, is known to be NP-hard, either as a version of the shortest common superstring problem or in a Hamiltonian-cycle…
Biclustering is the task of simultaneously clustering the rows and columns of the data matrix into different subgroups such that the rows and columns within a subgroup exhibit similar patterns. In this paper, we consider the case of…
Motivated by recent experiments probing shape, size and dynamics of bacterial chromosomes in growing cells, we consider a polymer model consisting of a circular backbone to which side-loops are attached, confined to a cylindrical cell. Such…
The problem of reconstructing a sequence from the set of its length-$k$ substrings has received considerable attention due to its various applications in genomics. We study an uncoded version of this problem where multiple random sources…
Establishing cutoff, an abrupt transition from "not mixed" to "well mixed", is a classical topic in the theory of mixing times for Markov chains. Interest has grown recently in determining not only the existence of cutoff and the order of…
How long threadlike eukaryotic chromosomes fit tidily in the small volume of the nucleus without significant entanglement is just beginning to be understood, thanks to major advances in experimental techniques. Several polymer models, which…
The huge amount of data acquired by high-throughput sequencing requires data reduction for effective analysis. Here we give a clustering algorithm for genome-wide open chromatin data using a new data reduction method. This method regards…
The problem of efficiently characterizing degree sequences of simple hypergraphs is a fundamental long-standing open problem in Graph Theory. Several results are known for restricted versions of this problem. This paper adds to the list of…
The concept of k-spectrum for genomes is here investigated as a basic tool to analyze genomes. Related spectral notions based on k-mers are introduced with some related mathematical properties which are relevant for informational analysis…
Active loop extrusion - the process of formation of dynamically growing chromatin loops due to the motor activity of DNA-binding protein complexes - is firmly established mechanism responsible for chromatin spatial organization at different…
A constructive method is provided that outputs a directed graph which is named a broken crown graph, containing $5n-9$ vertices and $k$ Hamiltonian cycles for any choice of integers $n \geq k \geq 4$. The construction is not designed to be…
Recently, Marcus et al. (Bioinformatics 2014) proposed to use a compressed de Bruijn graph to describe the relationship between the genomes of many individuals/strains of the same or closely related species. They devised an $O(n \log g)$…
We generalize the notion of linear chord diagrams to the case of matched sets of size $k$, which we call $k$-chord diagrams. We provide formal generating functions and recurrence relations enumerating these $k$-chord diagrams by the number…
In comparative genomics, the rearrangement distance between two genomes (equal the minimal number of genome rearrangements required to transform them into a single genome) is often used for measuring their evolutionary remoteness.…
An amino acid sequence of a protein may be decomposed into consecutive overlapping strings of length K. How unique is the converse, i.e., reconstruction of amino acid sequences using the set of K-strings obtained in the decomposition? This…
We examine the number of cycles of length k in a permutation, as a function on the symmetric group. We write it explicitly as a combination of characters of irreducible representations. This allows to study formation of long cycles in the…
In this article, we investigate different parsimony-based approaches towards finding recombination breakpoints in a multiple sequence alignment. This recombination detection task is crucial in order to avoid errors in evolutionary analyses…