  The paper re-analyzes a version of the celebrated Johnson-Lindenstrauss
Lemma, in which matrices are subjected to constraints that naturally emerge
from neuroscience applications: a) sparsity and b) sign-consistency. This
particular variant was studied first by Allen-Zhu, Gelashvili, Micali, Shavit
and more recently by Jagadeesan (RANDOM'19).
  The contribution of this work is a novel proof, which in contrast to previous
works a) uses the modern probability toolkit, particularly basics of
sub-gaussian and sub-gamma estimates b) is self-contained, with no dependencies
on subtle third-party results c) offers explicit constants.
  At the heart of our proof is a novel variant of Hanson-Wright Lemma (on
concentration of quadratic forms). Of independent interest are also auxiliary
facts on sub-gaussian random variables.
