New appeal letter for PRL.

2 files changed, 104 insertions, 28 deletions

diff --git a/appeal.tex b/appeal.tex
index 7ae78f4..ae37548 100644
--- a/appeal.tex
+++ b/appeal.tex
@@ -8,12 +8,14 @@
   urlcolor=purple,
   linkcolor=black,
   citecolor=black,
-  filecolor=black
+  filecolor=black,
 ]{hyperref} % ref and cite links with pretty colors
 \usepackage{xcolor}
 \usepackage[style=phys]{biblatex}
 
-\addbibresource{bezout.bib}
+\renewcommand{\thefootnote}{\fnsymbol{footnote}}
+
+\addbibresource{frsb_kac-rice.bib}
 
 \signature{
   \vspace{-6\medskipamount}
@@ -30,36 +32,68 @@
 
 \begin{document}
 \begin{letter}{
-  Editorial Office\\
+  Agnese I.~Curatolo, Ph.D.\\
   Physical Review Letters\\
   1 Research Road\\
   Ridge, NY 11961
 }
 
-\opening{To the editors of Physical Review,}
-
-We wish to appeal the decision on our manuscript \emph{How to count in
-hierarchical landscapes: A ‘full’ solution to mean-field complexity}, which was
-rejected without being sent to referees.
-
-The problem of characterizing the geometry of complex energy and cost
-landscapes is long-standing. Until this work, the correct calculation of the
-complexity has only been made for a small minority of systems, those with
-so-called replica symmetry. We show explicitly how such calculations can be
-made for the vast majority of cases.
-
-Landscape complexity even for the simple models we consider is relevant to a
-broad spectrum of physics disciplines. These models appear explicitly in modern
-research of machine learning, like tensor denoising, and understanding how
-complexity, dynamics, and equilibrium interplay in them provides powerful analogies
-and insights into emergent phenomena in more complicated contexts, from
-realistic machine learning models to the behavior of structural glasses.
-Already in this work, we identify the surprising result that the purported
-algorithmic threshold for optimization on mean-field cost functions lies
-\emph{far above} the geometric threshold traditionally understood as the dynamic limit.
-
-We urge you to allow this paper to go to referees and allow it to
-be judged by other scientists at the forefront of these fields.
+\opening{Dear Dr.~Curatolo,}
+
+We wish to appeal the decision concerning our manuscript,
+and expect to take this to the highest level possible in Physical Review.
+Our motivation is scientific, but also one of principle: {\em there should
+not be an implicit bias in favor of partial or purely numerical solutions,
+and against the actual closure of
+a long standing problem, on the basis that the latter is harder to read.}
+
+Neither of the referees criticize the content of the manuscript. They both
+find the article somewhat technical,
+but it should be born in mind that:
+\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}
+
+The other criticisms are:
+
+Referee A remarks that a full connection with dynamics
+is not presented in our paper. This is true, and such a connection does not
+exist at present. We sincerely hope to
+find it, and if we succeed we firmly believe the resulting  article will also be
+worthy of PRL.
+
+Referee B states that
+\begin{enumerate}
+  \item  ``the topic has been studied extensively in  the last thirty years and
+    more'' as a shortcoming, but fails to realize that the solution to the full
+    problem has been open, in spite of all these efforts.
+  \item The meaning of the related remark: ``the only novelty with respect to
+    previous work is that the results are obtained at zero temperature''
+    completely escapes us. Firstly because temperature is not an issue here --
+    it suffices to replace energy by TAP free-energy to introduce it, with
+    essentially no change. Again, the novelty of the article is that generic
+    models, most notably  the Sherrington Kirkpatrick which motivated the first
+    (pioneering but failed) attempt 42 years ago, are now finally accessible.
+  \item ``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.''
+  One could say that development of higher fidelity $q$-bits has failed to
+  deliver the factorization  of large integers up to now, but this is hardly a
+  barrier to publishing substantial progress about their development.
+\end{enumerate}
+
+Again, PRL has devoted a sustained attention to these problems. The referee
+goes on to remark that what is truly important ``involves dynamics and
+activated processes.'' But one of the reasons that they  have not been fully
+understood, as the referee claims correctly, is that these take place
+between states whose geometrical arrangement were not known (except for the
+pure $p$-spin case, or in general, equilibrium), and our work is, we believe, a
+true breakthrough in this direction.
 
 \closing{Sincerely,}
 
diff --git a/frsb_kac-rice.bib b/frsb_kac-rice.bib
index f8d4265..157c14f 100644
--- a/frsb_kac-rice.bib
+++ b/frsb_kac-rice.bib
@@ -168,7 +168,7 @@
 
 @article{Bray_2007_Statistics,
  author = {Bray, Alan J. and Dean, David S.},
- title = {Statistics of Critical Points of Gaussian Fields on Large-Dimensional Spaces},
+ title = {Statistics of Critical Points of {Gaussian} Fields on Large-Dimensional Spaces},
  journal = {Physical Review Letters},
  publisher = {American Physical Society (APS)},
  year = {2007},
@@ -885,3 +885,45 @@ complexity},
 }
 
 
+@article{Fyodorov_2012_Critical,
+ author = {Fyodorov, Yan V. and Nadal, Celine},
+ title = {Critical Behavior of the Number of Minima of a Random Landscape at the Glass Transition Point and the {Tracy}-{Widom} Distribution},
+ journal = {Physical Review Letters},
+ publisher = {American Physical Society (APS)},
+ year = {2012},
+ month = {10},
+ number = {16},
+ volume = {109},
+ pages = {167203},
+ url = {https://doi.org/10.1103%2Fphysrevlett.109.167203},
+ doi = {10.1103/physrevlett.109.167203}
+}
+
+@article{Fyodorov_2004_Complexity,
+ author = {Fyodorov, Yan V.},
+ title = {Complexity of Random Energy Landscapes, Glass Transition, and Absolute Value of the Spectral Determinant of Random Matrices},
+ journal = {Physical Review Letters},
+ publisher = {American Physical Society (APS)},
+ year = {2004},
+ month = {6},
+ number = {24},
+ volume = {92},
+ pages = {240601},
+ url = {https://doi.org/10.1103%2Fphysrevlett.92.240601},
+ doi = {10.1103/physrevlett.92.240601}
+}
+
+@article{Wainrib_2013_Topological,
+ author = {Wainrib, Gilles and Touboul, Jonathan},
+ title = {Topological and Dynamical Complexity of Random Neural Networks},
+ journal = {Physical Review Letters},
+ publisher = {American Physical Society (APS)},
+ year = {2013},
+ month = {3},
+ number = {11},
+ volume = {110},
+ pages = {118101},
+ url = {https://doi.org/10.1103%2Fphysrevlett.110.118101},
+ doi = {10.1103/physrevlett.110.118101}
+}
+