Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A constructive proof of the Assouad embedding theorem with bounds on the
  dimension   We give a constructive proof of a theorem of Naor and Neiman, (to appear,
Revista Matematica Iberoamercana), which asserts that if $(E,d)$ is a doubling
metric space, there is an integer $N > 0$, that depends only on the metric
doubling constant, such that for each exponent $\alpha \in (1/2,1)$, we can
find a bilipschitz mapping $F = (E,d^{\alpha}) \to \R^N$.

21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci