18 research outputs found
On the uniform generation of modular diagrams
In this paper we present an algorithm that generates -noncrossing,
-modular diagrams with uniform probability. A diagram is a labeled
graph of degree over vertices drawn in a horizontal line with arcs
in the upper half-plane. A -crossing in a diagram is a set of
distinct arcs with the property . A diagram without any
-crossings is called a -noncrossing diagram and a stack of length
is a maximal sequence
. A diagram is
-modular if any arc is contained in a stack of length at least
. Our algorithm generates after preprocessing time,
-noncrossing, -modular diagrams in time and space
complexity.Comment: 21 pages, 7 figure
Shapes of topological RNA structures
A topological RNA structure is derived from a diagram and its shape is
obtained by collapsing the stacks of the structure into single arcs and by
removing any arcs of length one. Shapes contain key topological, information
and for fixed topological genus there exist only finitely many such shapes. We
shall express topological RNA structures as unicellular maps, i.e. graphs
together with a cyclic ordering of their half-edges. In this paper we prove a
bijection of shapes of topological RNA structures. We furthermore derive a
linear time algorithm generating shapes of fixed topological genus. We derive
explicit expressions for the coefficients of the generating polynomial of these
shapes and the generating function of RNA structures of genus . Furthermore
we outline how shapes can be used in order to extract essential information of
RNA structure databases.Comment: 27 pages, 11 figures, 2 tables. arXiv admin note: text overlap with
arXiv:1304.739
Topology of RNA-RNA interaction structures
The topological filtration of interacting RNA complexes is studied and the
role is analyzed of certain diagrams called irreducible shadows, which form
suitable building blocks for more general structures. We prove that for two
interacting RNAs, called interaction structures, there exist for fixed genus
only finitely many irreducible shadows. This implies that for fixed genus there
are only finitely many classes of interaction structures. In particular the
simplest case of genus zero already provides the formalism for certain types of
structures that occur in nature and are not covered by other filtrations. This
case of genus zero interaction structures is already of practical interest, is
studied here in detail and found to be expressed by a multiple context-free
grammar extending the usual one for RNA secondary structures. We show that in
time and space complexity, this grammar for genus zero
interaction structures provides not only minimum free energy solutions but also
the complete partition function and base pairing probabilities.Comment: 40 pages 15 figure
Target prediction and a statistical sampling algorithm for RNA-RNA interaction
It has been proven that the accessibility of the target sites has a critical
influence for miRNA and siRNA. In this paper, we present a program, rip2.0, not
only the energetically most favorable targets site based on the
hybrid-probability, but also a statistical sampling structure to illustrate the
statistical characterization and representation of the Boltzmann ensemble of
RNA-RNA interaction structures. The outputs are retrieved via backtracing an
improved dynamic programming solution for the partition function based on the
approach of Huang et al. (Bioinformatics). The time and space
algorithm is implemented in C (available from
\url{http://www.combinatorics.cn/cbpc/rip2.html})Comment: 7 pages, 10 figure
Uniform generation of RNA pseudoknot structures with genus filtration
Huang FWD, Nebel M, Reidys CM. Uniform generation of RNA pseudoknot structures with genus filtration. 2013