Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharper bounds on the Fourier concentration of DNFs   In 1992 Mansour proved that every size-$s$ DNF formula is
Fourier-concentrated on $s^{O(\log\log s)}$ coefficients. We improve this to
$s^{O(\log\log k)}$ where $k$ is the read number of the DNF. Since $k$ is
always at most $s$, our bound matches Mansour's for all DNFs and strengthens it
for small-read ones. The previous best bound for read-$k$ DNFs was
$s^{O(k^{3/2})}$. For $k$ up to $\tilde{\Theta}(\log\log s)$, we further
improve our bound to the optimal $\mathrm{poly}(s)$; previously no such bound
was known for any $k = \omega_s(1)$.
  Our techniques involve new connections between the term structure of a DNF,
viewed as a set system, and its Fourier spectrum.

24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an