Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Inverse problems for locally perturbed lattices -- Discrete Hamiltonian
  and quantum graph
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg