261 research outputs found

### Polyominoes Simulating Arbitrary-Neighborhood Zippers and Tilings

This paper provides a bridge between the classical tiling theory and the
complex neighborhood self-assembling situations that exist in practice. The
neighborhood of a position in the plane is the set of coordinates which are
considered adjacent to it. This includes classical neighborhoods of size four,
as well as arbitrarily complex neighborhoods. A generalized tile system
consists of a set of tiles, a neighborhood, and a relation which dictates which
are the "admissible" neighboring tiles of a given tile. Thus, in correctly
formed assemblies, tiles are assigned positions of the plane in accordance to
this relation. We prove that any validly tiled path defined in a given but
arbitrary neighborhood (a zipper) can be simulated by a simple "ribbon" of
microtiles. A ribbon is a special kind of polyomino, consisting of a
non-self-crossing sequence of tiles on the plane, in which successive tiles
stick along their adjacent edge. Finally, we extend this construction to the
case of traditional tilings, proving that we can simulate
arbitrary-neighborhood tilings by simple-neighborhood tilings, while preserving
some of their essential properties.Comment: Submitted to Theoretical Computer Scienc

### Ciliate Gene Unscrambling with Fewer Templates

One of the theoretical models proposed for the mechanism of gene unscrambling
in some species of ciliates is the template-guided recombination (TGR) system
by Prescott, Ehrenfeucht and Rozenberg which has been generalized by Daley and
McQuillan from a formal language theory perspective. In this paper, we propose
a refinement of this model that generates regular languages using the iterated
TGR system with a finite initial language and a finite set of templates, using
fewer templates and a smaller alphabet compared to that of the Daley-McQuillan
model. To achieve Turing completeness using only finite components, i.e., a
finite initial language and a finite set of templates, we also propose an
extension of the contextual template-guided recombination system (CTGR system)
by Daley and McQuillan, by adding an extra control called permitting contexts
on the usage of templates.Comment: In Proceedings DCFS 2010, arXiv:1008.127

### Properties of Pseudo-Primitive Words and their Applications

A pseudo-primitive word with respect to an antimorphic involution \theta is a
word which cannot be written as a catenation of occurrences of a strictly
shorter word t and \theta(t). Properties of pseudo-primitive words are
investigated in this paper. These properties link pseudo-primitive words with
essential notions in combinatorics on words such as primitive words,
(pseudo)-palindromes, and (pseudo)-commutativity. Their applications include an
improved solution to the extended Lyndon-Sch\"utzenberger equation u_1 u_2 ...
u_l = v_1 ... v_n w_1 ... w_m, where u_1, ..., u_l \in {u, \theta(u)}, v_1,
..., v_n \in {v, \theta(v)}, and w_1, ..., w_m \in {w, \theata(w)} for some
words u, v, w, integers l, n, m \ge 2, and an antimorphic involution \theta. We
prove that for l \ge 4, n,m \ge 3, this equation implies that u, v, w can be
expressed in terms of a common word t and its image \theta(t). Moreover,
several cases of this equation where l = 3 are examined.Comment: Submitted to International Journal of Foundations of Computer Scienc

### An investigation into inter- and intragenomic variations of graphic genomic signatures

We provide, on an extensive dataset and using several different distances,
confirmation of the hypothesis that CGR patterns are preserved along a genomic
DNA sequence, and are different for DNA sequences originating from genomes of
different species. This finding lends support to the theory that CGRs of
genomic sequences can act as graphic genomic signatures. In particular, we
compare the CGR patterns of over five hundred different 150,000 bp genomic
sequences originating from the genomes of six organisms, each belonging to one
of the kingdoms of life: H. sapiens, S. cerevisiae, A. thaliana, P. falciparum,
E. coli, and P. furiosus. We also provide preliminary evidence of this method's
applicability to closely related species by comparing H. sapiens (chromosome
21) sequences and over one hundred and fifty genomic sequences, also 150,000 bp
long, from P. troglodytes (Animalia; chromosome Y), for a total length of more
than 101 million basepairs analyzed. We compute pairwise distances between CGRs
of these genomic sequences using six different distances, and construct
Molecular Distance Maps that visualize all sequences as points in a
two-dimensional or three-dimensional space, to simultaneously display their
interrelationships. Our analysis confirms that CGR patterns of DNA sequences
from the same genome are in general quantitatively similar, while being
different for DNA sequences from genomes of different species. Our analysis of
the performance of the assessed distances uses three different quality measures
and suggests that several distances outperform the Euclidean distance, which
has so far been almost exclusively used for such studies. In particular we show
that, for this dataset, DSSIM (Structural Dissimilarity Index) and the
descriptor distance (introduced here) are best able to classify genomic
sequences.Comment: 14 pages, 6 figures, 5 table

- …