From 875f996cd76d1c534beca1beb2e0e821e3ea84c6 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Fri, 12 Mar 2021 16:58:08 +0100 Subject: Added draft of appeal letter. --- appeal.tex | 74 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 74 insertions(+) create mode 100644 appeal.tex (limited to 'appeal.tex') diff --git a/appeal.tex b/appeal.tex new file mode 100644 index 0000000..d1df16c --- /dev/null +++ b/appeal.tex @@ -0,0 +1,74 @@ +\documentclass[a4paper]{letter} + +\usepackage[utf8]{inputenc} % why not type "Bézout" with unicode? +\usepackage[T1]{fontenc} % vector fonts plz +\usepackage{newtxtext,newtxmath} % Times for PR +\usepackage[ + colorlinks=true, + urlcolor=purple, + linkcolor=black, + citecolor=black, + filecolor=black +]{hyperref} % ref and cite links with pretty colors +\usepackage{xcolor} +\usepackage[style=phys]{biblatex} + +\addbibresource{bezout.bib} + +\signature{ + \vspace{-6\medskipamount} + \smallskip + Jaron Kent-Dobias \& Jorge Kurchan +} + +\address{ + Laboratoire de Physique\\ + Ecole Normale Sup\'erieure\\ + 24 rue Lhomond\\ + 75005 Paris +} + +\begin{document} +\begin{letter}{ + Editorial Office\\ + Physical Review Letters\\ + 1 Research Road\\ + Ridge, NY 11961 +} + +\opening{To the editors of Physical Review,} + +We wish to appeal your decision on our manuscript LZ16835, \emph{Complex +complex landscapes}, which received a single referee report. + + +We believe that the criticisms that the referee addresses to our paper are +not entirely justified (and above all, difficult to answer). We have, however, +clarified as much as possible the parts that the referee found trying. + +The referee is particularly worried that we have cited articles that are not +themselves sufficiently cited, so we thought that it may be useful at this +point to propose a set of referees that are beyond suspicion of incompetence or +uncitedness: + +\begin{tabular}{ll} + G Ben Arous & Courant \\ + M Berry & Bristol\\ + Daniel Fisher& Stanford\\ + T Lubensky & Penn\\ + M Moore & Manchester \\ + E Witten & IAS Princeton +\end{tabular} + +We have also added some very first results of the geometric implications for a +random complex landscape of our calculation, something we plan to expend on in +a future full article. + + +\closing{Sincerely,} + +\vspace{1em} + +\end{letter} + +\end{document} -- cgit v1.2.3-54-g00ecf From 720776cd65074b3eb5edb6a16e672022523bb81c Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Fri, 12 Mar 2021 17:07:11 +0100 Subject: Appeal wording. --- appeal.tex | 18 ++++++++---------- 1 file changed, 8 insertions(+), 10 deletions(-) (limited to 'appeal.tex') diff --git a/appeal.tex b/appeal.tex index d1df16c..2cf4757 100644 --- a/appeal.tex +++ b/appeal.tex @@ -38,18 +38,16 @@ \opening{To the editors of Physical Review,} -We wish to appeal your decision on our manuscript LZ16835, \emph{Complex -complex landscapes}, which received a single referee report. +We wish to appeal your decision on our manuscript \emph{Complex complex +landscapes}, which received a single referee report. +We believe that the referee's overall criticisms of our paper are not entirely +justified (and above all, difficult to answer). We have, however, submitted a +revised manuscript clarifying the specific aspects that the referee found trying. -We believe that the criticisms that the referee addresses to our paper are -not entirely justified (and above all, difficult to answer). We have, however, -clarified as much as possible the parts that the referee found trying. - -The referee is particularly worried that we have cited articles that are not -themselves sufficiently cited, so we thought that it may be useful at this -point to propose a set of referees that are beyond suspicion of incompetence or -uncitedness: +The referee seems particularly worried that we have cited articles that are not +themselves sufficiently cited, so we thought it may be useful propose a set of +referees that are beyond suspicion of incompetence or uncitedness: \begin{tabular}{ll} G Ben Arous & Courant \\ -- cgit v1.2.3-54-g00ecf From c038175a92d5773809f9d0928ba3c9f70b7056a9 Mon Sep 17 00:00:00 2001 From: "kurchan.jorge" Date: Thu, 18 Mar 2021 09:58:50 +0000 Subject: Update on Overleaf. --- appeal.tex | 9 +++++++-- bezout.tex | 32 ++++++++++++++------------------ 2 files changed, 21 insertions(+), 20 deletions(-) (limited to 'appeal.tex') diff --git a/appeal.tex b/appeal.tex index 2cf4757..04c8c96 100644 --- a/appeal.tex +++ b/appeal.tex @@ -52,16 +52,21 @@ referees that are beyond suspicion of incompetence or uncitedness: \begin{tabular}{ll} G Ben Arous & Courant \\ M Berry & Bristol\\ + Y. Fyodorov & King's College, London \\ Daniel Fisher& Stanford\\ - T Lubensky & Penn\\ + T Lubensky & U Penn\\ M Moore & Manchester \\ E Witten & IAS Princeton \end{tabular} -We have also added some very first results of the geometric implications for a +We have also pointed out some very first results of the geometric implications for a random complex landscape of our calculation, something we plan to expend on in a future full article. +Let us conclude by remarking that, although it is probably true that this paper will not +make more than one hundred citations next year, we are confident that it will still +be considered relevant in ten years time. + \closing{Sincerely,} diff --git a/bezout.tex b/bezout.tex index f050707..f596a89 100644 --- a/bezout.tex +++ b/bezout.tex @@ -69,7 +69,7 @@ $z\in\mathbb C^N$ and $J$ to be a symmetric tensor whose elements are $\overline{J^2}=\kappa\overline{|J|^2}$ for complex parameter $|\kappa|<1$. The constraint remains $z^Tz=N$. -The motivations for this paper are of two types. On the practical side, there +The motivations for this paper are of three types. On the practical side, there are indeed situations in which complex variables appear naturally in disordered problems: such is the case in which the variables are \emph{phases}, as in random laser problems \cite{Antenucci_2015_Complex}. Quiver Hamiltonians---used @@ -80,15 +80,14 @@ plane often uncovers underlying simplicity that is otherwise hidden, shedding light on the original real problem, e.g., as in the radius of convergence of a series. -Deforming an integral in $N$ real variables to a surface of dimension $N$ in +Finally, deforming an integral in $N$ real variables to a surface of dimension $N$ in $2N$-dimensional complex space has turned out to be necessary for correctly defining and analyzing path integrals with complex action (see \cite{Witten_2010_A, Witten_2011_Analytic}), and as a useful palliative for the 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---like the relative position of its -saddles---must be understood. Such landscapes are in general not random: here -we propose to follow the strategy of computer science of understanding the +of the action in complex space--- such as the relative position of saddles and the existence of Stokes lines joining them---must be understood. Such landscapes are in general not random: here +we propose to follow standard the strategy of computer science of understanding the generic features of random instances, expecting that this sheds light on practical, nonrandom problems. @@ -107,9 +106,7 @@ holomorphic functions without any symmetry. Samples of $H_0$ nearly provide this, save for a single anomaly: the value of the energy and its gradient at any point $z$ correlate along the $z$ direction, with $\overline{H_0\partial H_0}\propto \overline{H_0(\partial H_0)^*}\propto z$. This anomalous direction -must be neglected, and the constraint surface $z^Tz=N$ is the unique surface -whose normal is parallel to $z$ and which contains the configuration space of -the real $p$-spin model as a subspace. +thus best be forbidden, and the constraint surface $z^Tz=N$ does precisely this. Second, taking the constraint to be the level set of a holomorphic function means the resulting configuration space is a \emph{bone fide} complex manifold, @@ -118,14 +115,13 @@ referenced above. The same cannot be said for the space defined by $z^\dagger z=N$, which is topologically the $(2N-1)$-sphere and cannot admit a complex structure. -A consequence of the constraint is that the model's configuration space is not -compact, nor is its energy bounded. This is not necessarily problematic, as many -related problems have similar properties but are concerned with subspaces on -which the energy is bounded. (In fact, identifying the appropriate subspace -often requires the study of critical points in the whole space.) Where it might -become problematic, we introduce an additional constraint that bounds the -`radius' per spin $r^2\equiv z^\dagger z/N\leq R^2$. The resulting -configuration space is a complex manifold with boundary. We shall see that the +Imposing the constraint with a holomorphic function +makes the resulting configuration space is a \emph{bone fide} complex manifold, which is, as we mentioned, the +situation we wish to model. The same cannot be said for the space defined by $z^\dagger +z=N$, which is topologically the $(2N-1)$-sphere, does not admit a complex +structure, and thus yields a trivial structure of saddles. +However, we will introduce the domains of +`radius' per spin $r^2\equiv z^\dagger z/N\leq R^2$, as a device to classify saddles. We shall see that the `radius' $r$ and its upper bound $R$ prove to be insightful knobs in our present problem, revealing structure as they are varied. Note that taking $R=1$ reduces the problem to that of the ordinary $p$-spin. @@ -159,9 +155,9 @@ usual Kac--Rice formula applied to $\operatorname{Re}H$: \end{equation} This expression is to be averaged over $J$ to give the complexity $\Sigma$ as $N \Sigma= \overline{\log\mathcal N}$, a calculation that involves the replica -trick. In most of the parameter space that we shall study here, the +trick. Based on the experience from these problems \cite{Castellani_2005_Spin-glass}, the \emph{annealed approximation} $N \Sigma \sim \log \overline{ \mathcal N}$ is -exact. +expected to be exact wherever the complexity is positive. The Cauchy--Riemann equations may be used to write \eqref{eq:real.kac-rice} in a manifestly complex way. With the Wirtinger derivative -- cgit v1.2.3-54-g00ecf From 68ae488545e3acd1ff7b7a795af57c0fa10a3fc6 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Thu, 18 Mar 2021 12:19:49 +0100 Subject: Small formatting change. --- appeal.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'appeal.tex') diff --git a/appeal.tex b/appeal.tex index 04c8c96..6af3109 100644 --- a/appeal.tex +++ b/appeal.tex @@ -52,7 +52,7 @@ referees that are beyond suspicion of incompetence or uncitedness: \begin{tabular}{ll} G Ben Arous & Courant \\ M Berry & Bristol\\ - Y. Fyodorov & King's College, London \\ + Y Fyodorov & King's College London \\ Daniel Fisher& Stanford\\ T Lubensky & U Penn\\ M Moore & Manchester \\ -- cgit v1.2.3-54-g00ecf