Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting faces of randomly-projected polytopes when the projection
  radically lowers dimension   This paper develops asymptotic methods to count faces of random
high-dimensional polytopes. Beyond its intrinsic interest, our conclusions have
surprising implications - in statistics, probability, information theory, and
signal processing - with potential impacts in practical subjects like medical
imaging and digital communications. Three such implications concern: convex
hulls of Gaussian point clouds, signal recovery from random projections, and
how many gross errors can be efficiently corrected from Gaussian error
correcting codes.

14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph