Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on global Markov properties for mixed graphs   Global Markov properties in mixed graphs are usually formulated in terms of
the path-oriented m-separation or by use of augmented graphs (similar to moral
graphs in the case of directed acyclic graphs). We provide an alternative
characterization that can be easily implemented.

2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci