Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The statistics of wide-separation lenses   The probability that high-redshift sources are gravitationally-lensed with
large image separations (i.e., greater than can be produced by galactic
deflectors) is determined by the cosmological population of group- and
cluster-sized halos. Thus the observed frequency of wide-separation lensed
quasars can be used to constrain not only the halo distribution, but also a
number of cosmological parameters. A calculation of the optical depth due to
collapsed, isothermal halos is a useful guide to the lens statistics, and
illustrates that the number of wide-separation lenses is a sensitive probe of
the mean density of the universe and the present day density variance whilst
being nearly independent of the cosmological constant.

16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph