Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Piezoelectric softening in ferroelectrics: ferroelectric versus
  antiferroelectric PbZr$_{1-x}$Ti$_{x}$O$_{3}$
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex