Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the relative bicentralizer flows and the relative flow of weights of
  inclusions of factors of type III$_1$   We show the relative bicentralizer flow and the relative flow of weights are
isomorphic for an inclusion of injective factors of type III$_1$ with finite
index, or an irreducible discrete inclusion whose small algebra is an injective
factor of type III$_1$.

22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex