Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On discrete loop signatures and Markov loops topology   Our purpose is to explore, in the context of loop ensembles on finite graphs,
the relations between combinatorial group theory, loops topology, loop
measures, and signatures of discrete paths. We determine the distributions of
the loop homotopy class, and of the first and second homologies, defined by the
lower central series of the fundamental group.

23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys