Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Probability distribution function for a solid with vacancies
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th