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authorJaron Kent-Dobias <jaron@kent-dobias.com>2021-03-24 16:00:04 +0100
committerJaron Kent-Dobias <jaron@kent-dobias.com>2021-03-24 16:00:04 +0100
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Paragraph massaging.
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diff --git a/bezout.tex b/bezout.tex
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@@ -88,17 +88,17 @@ sign problem \cite{Cristoforetti_2012_New, Tanizaki_2017_Gradient,
Scorzato_2016_The}. In order to do this correctly, features of landscape of
the action in complex space---such as the relative position of saddles and the
existence of Stokes lines joining them---must be understood. This is typically
-done for simple actions with few critical points, or with a target
-phenomenology that possesses symmetries that restrict the set of critical
+done for simple actions with few critical points, or for a target
+phenomenology with symmetries that restrict the set of critical
points to few candidates. Given the recent proliferation of `glassiness' in
condensed matter and high energy physics, it is inevitable that someone will
-study a complex landscape with these methods, and will find old heuristic
-approaches unsuitable. Such landscapes may in general not be random: here we
+want to apply these methods to a system with a complex landscape, and will find
+they cannot use approaches that rely on such assumptions. Their landscape may not be random: here we
follow the standard strategy of computer science by understanding the generic
features of random instances of a simple case, expecting that this sheds light
-on practical, nonrandom problems. While in this paper we do not address
-analytic continuation of configuration space integrals, understanding the
-distribution and spectra of critical points is an essential first step.
+on practical, nonrandom problems. While in this paper we do not yet address
+analytic continuation of integrals, understanding the distribution and spectra
+of critical points is an essential first step.
Returning to our problem, the spherical constraint is enforced using the method
of Lagrange multipliers: introducing $\epsilon\in\mathbb C$, our constrained