Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Canonical RNA pseudoknot structures   In this paper we study $k$-noncrossing, canonical RNA pseudoknot structures
with minimum arc-length $\ge 4$. Let ${\sf T}_{k,\sigma}^{[4]} (n)$ denote the
number of these structures. We derive exact enumeration results by computing
the generating function ${\bf T}_{k,\sigma}^{[4]}(z)= \sum_n{\sf
T}_{k,\sigma}^{[4]}(n)z^n$ and derive the asymptotic formulas ${\sf
T}_{k,3}^{[4]}(n)^{}\sim c_k n^{-(k-1)^2-\frac{k-1}{2}}
(\gamma_{k,3}^{[4]})^{-n}$ for $k=3,...,9$. In particular we have for $k=3$,
${\sf T}_{3,3}^{[4]}(n)^{}\sim c_3 n^{-5} 2.0348^n$. Our results prove that the
set of biophysically relevant RNA pseudoknot structures is surprisingly small
and suggest a new structure class as target for prediction algorithms.

29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom