Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Loop Homology of Bi-secondary Structures   In this paper we compute the loop homology of bi-secondary structures.
Bi-secondary structures were introduced by Haslinger and Stadler and are pairs
of RNA secondary structures, i.e. diagrams having non-crossing arcs in the
upper half-plane. A bi-secondary structure is represented by drawing its
respective secondary structures in the upper and lower half-plane. An RNA
secondary structure has a loop decomposition, where a loop corresponds to a
boundary component, regarding the secondary structure as an orientable
fatgraph. The loop-decomposition of secondary structures facilitates the
computation of its free energy and any two loops intersect either trivially or
in exactly two vertices. In bi-secondary structures the intersection of loops
is more complex and is of importance in current algorithmic work in
bio-informatics and evolutionary optimization. We shall construct a simplicial
complex capturing the intersections of loops and compute its homology. We prove
that only the zeroth and second homology groups are nontrivial and furthermore
show that the second homology group is free. Finally, we provide evidence that
the generators of the second homology group have a bio-physical interpretation:
they correspond to pairs of mutually exclusive substructures.

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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th