Related papers: Extending the Overlap Graph for Gene Assembly in C…
A variety of modeling frameworks have been proposed and utilized in complex systems studies, including dynamical systems models that describe state transitions on a system of fixed topology, and self-organizing network models that describe…
Genome assembly is a fundamental problem in Bioinformatics, where for a given set of overlapping substrings of a genome, the aim is to reconstruct the source genome. The classical approaches to solving this problem use assembly graphs, such…
Graphs are naturally used to describe the structures of various real-world systems in biology, society, computer science etc., where subgraphs or motifs as basic blocks play an important role in function expression and information…
Earlier formulations of the DNA assembly problem were all in the context of perfect assembly; i.e., given a set of reads from a long genome sequence, is it possible to perfectly reconstruct the original sequence? In practice, however, it is…
Convergent rewriting systems on algebraic structures give methods to solve decision problems, to prove coherence results, and to compute homological invariants. These methods are based on higher-dimensional extensions of the critical…
Reverse engineering of gene regulatory networks presents one of the big challenges in systems biology. Gene regulatory networks are usually inferred from a set of single-gene over-expressions and/or knockout experiments. Functional…
A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and…
Within biology, it is of interest to construct DNA complexes of a certain shape. These complexes can be represented through graph theory, using edges to model strands of DNA joined at junctions, represented by vertices. Because guided…
Understanding genetic variation, e.g., through mutations, in organisms is crucial to unravel their effects on the environment and human health. A fundamental characterization can be obtained by solving the haplotype assembly problem, which…
Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However,…
The classical attenuation regulation of gene expression in bacteria is considered. We propose to represent the secondary RNA structure in the leader region of a gene or an operon by a term, and we give a probabilistic term rewriting system…
The ongoing explosion of genome sequence data is transforming how we reconstruct and understand the histories of biological systems. Across biological scales, from individual cells to populations and species, trees-based models provide a…
In this paper we show how string rewriting methods can be applied to give a new method of computing double cosets. Previous methods for double cosets were enumerative and thus restricted to finite examples. Our rewriting methods do not…
Repetitive DNA (repeats) poses significant challenges for accurate and efficient genome assembly and sequence alignment. This is particularly true for metagenomic data, where genome dynamics such as horizontal gene transfer, gene…
Motivated by the question of how macromolecules assemble, the notion of an {\it assembly tree} of a graph is introduced. Given a graph $G$, the paper is concerned with enumerating the number of assembly trees of $G$, a problem that applies…
An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs.…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric…
Hypergraphs, a generalization of graphs, naturally represent groupwise relationships among multiple individuals or objects, which are common in many application areas, including web, bioinformatics, and social networks. The flexibility in…
Inspired by RNA-editing as occurs in transcriptional processes in the living cell, we introduce an abstract notion of string adjustment, called guided rewriting. This formalism allows simultaneously inserting and deleting elements. We prove…
The effort to understand network systems in increasing detail has resulted in a diversity of methods designed to extract their large-scale structure from data. Unfortunately, many of these methods yield diverging descriptions of the same…