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arXiv · 1203.3248

Planar diagrams from optimization

S. K. Nechaev·A. N. Sobolevski·O. V. Valba
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Abstract

We propose a new toy model of a heteropolymer chain capable of forming planar secondary structures typical for RNA molecules. In this model the sequential intervals between neighboring monomers along a chain are considered as quenched random variables. Using the optimization procedure for a special class of concave--type potentials, borrowed from optimal transport analysis, we derive the local difference equation for the ground state free energy of the chain with the planar (RNA--like) architecture of paired links. We consider various distribution functions of intervals between neighboring monomers (truncated Gaussian and scale--free) and demonstrate the existence of a topological crossover from sequential to essentially embedded (nested) configurations of paired links.

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S. K. Nechaev, A. N. Sobolevski, O. V. Valba. 2012-09-24. Planar diagrams from optimization. https://doi.org/10.1103/physreve.87.012102

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