From 3aa483b31c12d6a3afb1215ce6188aca8c314e72 Mon Sep 17 00:00:00 2001 From: "kurchan.jorge" Date: Wed, 30 Dec 2020 11:03:54 +0000 Subject: Update on Overleaf. --- bezout.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) (limited to 'bezout.tex') diff --git a/bezout.tex b/bezout.tex index 9dffe65..96ad257 100644 --- a/bezout.tex +++ b/bezout.tex @@ -44,7 +44,7 @@ Spin-glasses have long been considered the paradigm of many variable `complex landscapes,' a subject that includes neural networks and optimization problems, -most notably constraint satisfaction. The most tractable family of these +most notably constraint satisfaction \cite{mezard2009information}. The most tractable family of these are the mean-field spherical $p$-spin models \cite{Crisanti_1992_The} (for a review see \cite{Castellani_2005_Spin-glass}) defined by the energy \begin{equation} \label{eq:bare.hamiltonian} @@ -447,8 +447,8 @@ dynamics, are a problem we hope to address in future work. This paper provides a first step towards the study of a complex landscape with complex variables. The next obvious one is to study the topology of the - critical points, their basins of attraction following gradient ascent (the - Lefschetz thimbles), and descent (the anti-thimbles) \cite{Witten_2010_A, + critical points, the sets reached following gradient descent (the + Lefschetz thimbles), and ascent (the anti-thimbles) \cite{Witten_2010_A, Witten_2011_Analytic, Cristoforetti_2012_New, Behtash_2017_Toward, Scorzato_2016_The}, which act as constant-phase integrating `contours.' Locating and counting the saddles that are joined by gradient lines---the -- cgit v1.2.3-54-g00ecf