Revised our 'why' statement to 100 words.

1 files changed, 9 insertions, 21 deletions

diff --git a/why_prl.txt b/why_prl.txt
index 48d3544..8c0eef1 100644
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@@ -1,21 +1,9 @@
-   In our paper we study the extension to complex variables of the
-paradigmatic
-model of "complex landscape". We believe it is the first paper to study
-such complex
-"rugged landscapes", a subject of very high interest whose applications
-range from deep networks
-to optimization. In particular, we introduce and study a matrix model that
-has not, to the best of our knowledge
-studied previously, and which plays for the fluctuations around complex
-saddles
-in disordered systems the role played by the well-known semicircle law in
-the real ones.
-Our work is in line with the beautiful
-E *Bogomolny*, O Bohigas, P *Leboeuf* - Physical Review Letters,  1992
-which concerns the roots  one random polynomial of high degree, while ours
-many of low degree.
-We are very sure that sooner or later many new applications of this problem
-will appear, as always
-has been the case of extending into the complex plane the vision of a  real
-problem.
-
+We extend the paradigmatic model of "complex" landscapes to complex variables.
+We believe it is the first such study, a subject of interest with applications
+from deep networks to optimization. In particular, we introduce an apparently
+new matrix model that generalizes the well-known semicircle law for
+fluctuations around real saddles in disordered systems. Our work is in line
+with Bogomolny, Bohigas & Leboeuf (PRL 1992) concerning roots of one random
+polynomial of high degree, while ours many of low degree. Many applications of
+this problem will surely appear, as always occurs when extending a real problem
+into the complex plane.