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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 $g$. Furthermore we outline how shapes can be used in order to extract essential information of RNA structure databases.
In this paper we study properties of topological RNA structures, i.e.~RNA contact structures with cross-serial interactions that are filtered by their topological genus. RNA secondary structures within this framework are topological structures having
Given a random RNA secondary structure, $S$, we study RNA sequences having fixed ratios of nuclotides that are compatible with $S$. We perform this analysis for RNA secondary structures subject to various base pairing rules and minimum arc- and stack
In this paper we introduce a novel, context-free grammar, {it RNAFeatures$^*$}, capable of generating any RNA structure including pseudoknot structures (pk-structure). We represent pk-structures as orientable fatgraphs, which naturally leads to a fil
Recently several minimum free energy (MFE) folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Their folding targets are interaction structures, that can be represented as diagrams with two backb
The effect of polyvalent molecular cations, such as spermine, on the condensation of DNA into very well-defined toroidal shapes have been well studied and understood. However, a great effort has been made trying to obtain similar condensed structures