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DESCRIPTION VARNA is a tool for the automated drawing, visualization and annotation of the secondary structure of RNA, designed as a companion software for web servers and databases. FEATURES VARNA implements four drawing algorithms, supports input/output using the classic formats dbn, ct, bpseq and RNAML and exports the drawing as five picture formats,(More)
The recursive method formalized by Nijenhuis and Wilf [15] and systematized by Flajolet, Van Cutsem and Zimmermann [8], is extended here to oating-point arithmetic. The resulting ADZ method enables one to generate decomposable data structures | both labelled or unlabelled | uniformly at random, in expected O(n ) time and space, after a preprocessing phase(More)
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the object. Generating trees lead to a fast computation of enumeration sequences (sometimes, to explicit formulae as well) and(More)
This paper presents several randomised algorithms for generating paths in large models according to a given coverage criterion. Using methods for counting combinatorial structures, these algorithms can efficiently explore very large models, based on a graphical representation by an automaton or by a product of several automata. This new approach can be(More)
Two combinatorial statistics, the pyramid weight and the number of exterior pairs, are investigated on the set of Dyck paths. Explicit formulae are given for the generating functions of Dyck paths of prescribed pyramid weight and prescribed number of exterior pairs. The proofs are combinatorial and rely on the method of q-grammars as well as on two new(More)
Some strings -the textsare assumed to be randomly generated, according to a probability model that is either a Bernoulli model or a Markov model. A rare event is the over or under-representation of a word or a set of words. The aim of this paper is twofold. First, a single word is given. We study the tail distribution of the number of its occurrences. Sharp(More)
This paper addresses the problem of selecting finite test sets and automating this selection. Among these methods, some are deterministic and some are statistical. The kind of statistical testing we consider has been inspired by the work of Thevenod-Fosse and Waeselynck. There, the choice of the distribution on the input domain is guided by the structure of(More)
We present a new alignment algorithm for pairwise comparison of RNA secondary structures represented as arc-annotated sequences. This allows to perform biologically relevant operations on RNA structures (as pairing or unpairing nucleotides) in a natural and realistic way. We describe three variants of the algorithm: global alignment, local alignment, and(More)
In this paper we rst show that the permutation-path coloring problem is NP-hard even for very restrictive instances like involutions, which are permutations that contain only cycles of length at most two, on both binary trees and on trees having only two vertices with degree greater than two, and for circular permutations which are permutations that contain(More)