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Conjugacy invariant pseudo-norms, representability and RNA secondary structures

Gadgil, Siddhartha (2011) Conjugacy invariant pseudo-norms, representability and RNA secondary structures. In: Indian Journal of Pure and Applied Mathematics, 42 (4). pp. 225-237.

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To a reasonable approximation, a secondary structures of RNA is determined by Watson-Crick pairing without pseudo-knots in such a way as to minimise the number of unpaired bases: We show that this minimal number is determined by the maximal conjugacy-invariant pseudo-norm on the free group on two generators subject to bounds on the generators. This allows us to construct lower bounds on the minimal number of unpaired bases by constructing conjugacy invariant pseudo-norms. We show that one such construction, based on isometric actions on metric spaces, gives a sharp lower bound. A major goal here is to formulate a purely mathematical question, based on considering orthogonal representations, which we believe is of some interest independent of its biological roots.

Item Type: Journal Article
Publication: Indian Journal of Pure and Applied Mathematics
Publisher: Indian National Science Academy
Keywords: RNA secondary structure; stem-loop; free groups; Milnor invariants; lower central series
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 09 Nov 2011 05:51
Last Modified: 09 Nov 2011 05:51
URI: http://eprints.iisc.ac.in/id/eprint/41942

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