Genus Ranges of Chord Diagrams

A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thickening the backbone to an annulus and attaching bands to the inner boundary circle at the ends of each chord. Variations of this construction are considered here, where bands are possibly attached to the outer boundary circle of the annulus. The genus range of a chord diagram is the genus values over all such variations of surfaces thus obtained from a given chord diagram. Genus ranges of chord diagrams for a fixed number of chords are studied. Integer intervals that can, and cannot, be realized as genus ranges are investigated. Computer calculations are presented, and play a key role in discovering and proving the properties of genus ranges.Comment: 12 pages, 8 figure

DSBplot: Indels in DNA Double-strand Break Repair Experiments

Double-strand breaks (DSBs) in DNA are naturally occurring destructive events in all organisms that may lead to genome instability. Cells employ various repair methods known as non-homologous end joining (NHEJ), microhomology mediated end joining (MMEJ), and homology-directed recombination (HDR). These repair processes may lead to DNA sequence variations (e.g., nucleotide insertions, deletions, and substitutions) at the location of the break. Studying DNA DSB repair processes often involves the use of high throughput sequencing assays to precisely quantify the sequence variations near the break with software tools. Often methods of assessing and visualizing these data have not taken into account the full complexity of the sequencing data, such as the frequency, type, and position of the sequence variations in a single comprehensive representation. Here we present a method that allows visualization of the overall variation pattern as well as comparison of these patterns among experimental setups.Comment: 10 pages, 3 figure

DNA splicing: computing by observing

Motivated by several techniques for observing molecular processes in real-time we introduce a computing device that stresses the role of the observer in biological computations and that is based on the observed behavior of a splicing system. The basic idea is to introduce a marked DNA strand into a test tube with other DNA strands and restriction enzymes. Under the action of these enzymes the DNA starts to splice. An external observer monitors and registers the evolution of the marked DNA strand. The input marked DNA strand is then accepted if its observed evolution follows a certain expected pattern. We prove that using simple observers (finite automata), applied on finite splicing systems (finite set of rules and finite set of axioms), the class of recursively enumerable languages can be recognized. © Springer Science+Business Media B.V. 2007

Sofic shifts with synchronizing presentations

AbstractA sofic shift S is a symbolic dynamical system that can be viewed as a set of all bi-infinite sequences obtained by reading the labels of all bi-infinite paths in a finite directed labeled graph G. The presentation G is synchronizing if for every vertex v there is a word xv such that every path in G labeled with xv has v as a terminal vertex. We present an example of a subshift of finite type that has no unique minimal deterministic presentation and we show that if a sofic shift has a synchronizing, deterministic presentation (sdp), then it has a unique minimal one. Irreducible sofic shifts, subshifts of finite type and nonwandering systems have synchronizing, deterministic presentations. We give an intrinsic characterization of a sofic shift S that has an sdp in terms of the syntactic monoid M(S) of the factor language F(S) of S. Another characterization of sofic shifts with sdp's is given in terms of the predecessor sets. We show that a sofic shift can have at most one bi-synchronizing presentation

Forbidding and enforcing on graphs

We define classes of graphs based on forbidding and enforcing boundary conditions. Forbidding conditions prevent a graph to have certain combinations of subgraphs and enforcing conditions impose certain subgraph structures. We say that a class of graphs is an fe-class if the class can be defined through forbidding and enforcing conditions (fe-system). We investigate properties of fe-systems and characterize familiar classes of graphs such as paths and cycles, trees, bi-partite, complete, Eulerian, and k-regular graphs as fe-classes. © 2012 Elsevier B.V. All rights reserved

Int. J. Natural Computing 13(2), special issue on Unconventional Computation and Natural Computation (UCNC '12)

International audienc