Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: On the Validity of Effective Potentials in Crowded Solutions of Linear
  and Ring Polymers with Reversible Bonds
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex