From c4182fa022ceebd61cfbfe258fbc0f3294ea72cb Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Mon, 23 Jan 2023 11:56:07 +0100
Subject: Changed file format of response letter.

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+\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}
+
+\renewcommand{\thefootnote}{\fnsymbol{footnote}}
+
+\addbibresource{frsb_kac-rice.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}{
+  Agnese I.~Curatolo, Ph.D.\\
+  Physical Review Letters\\
+  1 Research Road\\
+  Ridge, NY 11961
+}
+
+\opening{Dear Dr.~Curatolo,}
+
+Enclosed please find a revised manuscript.
+Neither referee  criticized  the scientific content of our paper,
+nor substantively addressed its presentation. We have followed their comments
+in the direction of  highlighting the importance of having a full solution. In particular
+we have emphasized that going to the full replica treatment uncovers a phase-space structure that needs to be taken into account, and that is absent in the annealed treatment.
+
+
+We have thus added the paragraph:
+
+{\color{red} 
+Having  a full, exact  (`quenched') solution of the generic problem  is not 
+primarily a matter of {\em accuracy}.
+Very basic structural questions are omitted in the approximate `annealed' solution. What is lost  is  the nature, at any given
+energy (or free energy) level, of the stationary points in a generic energy function: at low energies are they basically all minima, with  an exponentially small number of saddles, or
+-- as we show here -- do they consist of a mixture of saddles whose index -- the number of unstable directions -- is a smoothly distributed number? 
+These questions need to be answered for the understanding of the relevance of more complex objects such as
+barrier crossing (which barriers?) \cite{Ros_2019_Complexity, Ros_2021_Dynamical}, or the fate of long-time dynamics
+(which end in what kind of  target states?). 
+
+}
+
+Both referees find that our paper is clearly written but technical, and
+that its topic of "the different RSB schemes" are not suitable for a
+broad audience. This is surprising to the authors, since a quick
+search on Google Scholar reveals several recent PRLs with heavy use of
+RSB schemes. 
+
+We would also like to submit to the referees  that it is somewhat
+incongruous that the solution to a problem that had remained open for 42 years -- during which it was always present in articles in PRL and PRX -- is rejected
+because  it demands of the readers a slightly longer attention span. 
+
+
+
+
+\begin{enumerate}
+  \item PRL has been publishing articles on precisely this problem in the
+    last 30 years.\footfullcite{Fyodorov_2004_Complexity, Bray_2007_Statistics, Fyodorov_2012_Critical, Wainrib_2013_Topological}
+  \item These works were often limited by the fact that general landscapes (for
+    which an annealed solution is not exact) were inaccessible. It is perhaps
+    true that the final solution of an open problem may often be more technical
+    than the previous ones.
+\end{enumerate}
+
+
+
+Below, we respond to the referees' comments.
+
+{\it Report of Referee A -- LY17256/Kent-Dobias
+ The authors consider spin glass models with mixed p-spin interactions
+ on the N-Sphere and calculate the number of stationary points, the
+ logarithm of which yields the complexity. The disorder average of this
+ logarithm is computed with the replica trick, and for different model
+ variants different replica symmetry breaking (RSB) solutions are
+ obtained. A new feature of the solutions, in contrast to previous
+ replica symmetric calculations, is that RSB must occur in parts of the
+ energy-stability phase diagram.
+
+ The paper is clearly written although the content is rather technical
+ and probably only accessible to experts in mean field spin glass
+ models and the different RSB schemes developed in this field. In
+ connection with the well-studied p=3 spin glass model it is briefly
+ mentioned that the complexity and its transitions as a function of
+ energy and/or stability is relevant for the equilibrium and the
+ dynamical behavior of this model – but such a connection has not been
+ made here.
+
+ Therefore, I feel that the results presented here are only interesting
+ for group of experts and I do not assess the finding that the
+ complexity of mixed p-spin glass models shows RSB as a major
+ breakthrough in the field. Therefore, the manuscript is not suitable
+ for publication in Phys. Rev. Lett., and the publication of the
+ accompanying longer paper, submitted to PRE, is sufficient to
+ disseminate the results summarized in this manuscript.}
+
+
+
+Referee A correctly points out that one new feature of the solutions
+outlined in our manuscript is that RSB must occur in parts of the
+phase diagram for these models. However, they neglect another feature:
+that they are the solutions of the *quenched* complexity, which has
+not been correctly calculated until now. We agree with the referee
+that "the complexity of the mixed p-spin glass models" is not a major
+breakthrough in and of itself, we just
+chose to demonstrate  the problem in simplest toy model. But believe that the technique for
+computing the quenched complexity is a major breakthrough  
+{\bf because it brings in the features of organization of saddles of all
+kinds that are invisible in the annealed scheme}. 
+
+
+Referee A states that a connection between the complexity and the
+equilibrium and dynamical behavior is not made in our paper. Until
+recently, this connection was taken for granted, and the demonstration
+that the standard correspondence does not hold in the mixed p-spin
+spherical models was exciting enough news to be published in PRX 10,
+031045 (2020). It is true that our work doesn't solve the problem that
+paper opened, but it does deepen it by showing definitively that the
+use of RSB and the quenched complexity are not sufficient to
+reestablish a landscape–dynamics connection. 
+{\bf One can hardly expect that the structure of saddles at a given energy may be connected
+with dynamics (for example in Sherrington Kirkpatrick) if it is unknown}.
+%We disagree with the
+%referee's implicit assertion that only clean resolutions, and not the
+%compelling deepening of problems, are worthy of a broad audience.
+
+Report of Referee B -- LY17256/Kent-Dobias
+{\it  The paper presents a computation of the complexity in spherical
+ spin-glass models. Neither the techniques nor the results are
+ sufficiently new and relevant to justify publication on PRL. This is
+ not surprising given that the topic has been studied extensively in
+ the last thirty years and more, the only novelty with respect to
+ previous work is that the results are obtained at zero temperature but
+ this is definitively not enough. Essential open problems in the field
+ involves dynamics and activated processes and some results have
+ appeared recently, instead the analysis of the static landscape, to
+ which the present paper is a variation, failed to deliver answers to
+ these questions up to now.
+
+ }
+
+Concerning the statement of Referee B that "the only novelty
+with respect to previous work is that the results are obtained at zero
+temperature", we do not know what to make of the referee's statement.
+The novelty of the paper is most definitely
+not the fact of treating a zero temperature case. 
+We have added the following phrase, that should clarify the situation:
+
+{\color{blue}
+  For simplicity we have concentrated here on the energy, rather
+than  {\em free-energy} landscape, although the latter is sometimes
+more appropriate. From the technical point of view, this makes no fundamental difference, it suffices 
+to apply the same computation to the Thouless-Andreson-Palmer \cite{Crisanti_1995_Thouless-Anderson-Palmer} (TAP) free energy, instead of the energy. We do not expect new features or technical 
+complications arise.
+
+}
+
+
+%For a system where the quenched and annealed
+%complexities differ, there has not been a correct calculation of the
+%quenched complexity at finite temperature. (and, besides our work,
+%only once or twice at zero temperature, e.g., PRX 9, 011003 (2019).)
+%Rejecting a paper based on a severe misconception of its contents or
+%of the state of the field is not appropriate.
+
+We agree with Referee B's assessment of "essential open problems in
+the field," and agree that our work does not deliver answers. However,
+delivering answers for all essential open problems is not the acceptance
+criterion of PRL. These are
+
+  - Open a new research area, or a new avenue within an established area.
+  - Solve, or make essential steps towards solving, a critical problem.
+  - Introduce techniques or methods with significant impact.
+  - Be of unusual intrinsic interest to PRL's broad audience.
+
+We believe our manuscript makes essential steps toward solving the
+critical problem of connecting analysis of the static landscape to
+dynamics. We believe that its essential step is through the
+introduction of a new technique, calculation of the quenched
+complexity, which we believe will have significant impact as it is
+applied to more complicated models.
+
+\closing{Sincerely,}
+
+\vspace{1em}
+
+\end{letter}
+
+\end{document}
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