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authorJaron Kent-Dobias <jaron@kent-dobias.com>2023-03-06 19:44:33 +0100
committerJaron Kent-Dobias <jaron@kent-dobias.com>2023-03-06 19:44:33 +0100
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\begin{document}
\begin{letter}{
- Agnese I.~Curatolo, Ph.D.\\
Physical Review Letters\\
1 Research Road\\
Ridge, NY 11961
}
-\opening{Dear Dr.~Curatolo,}
+\opening{To the editors of PRL,}
-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.}
+We wish to appeal the decision concerning our manuscript \textit{Unveiling the complexity of hierarchical energy landscapes}
+which we submitted to PRL.
-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}
+As we mentioned in the reply to the referees, this is a problem that has
+been open for 42 years,
+and several related contributions have been published since in PRL.
-The other criticisms are:
+Our solution for the first time gives the full picture of the structure
+of valleys in a complex landscape, finally rendering the ``state counting''
+(Kac-Rice) approach -- used in several hundred papers --
+compatible with the Parisi solution of equilibrium. As a byproduct, the
+structure of near-equilibrium saddles is for the first time transparent.
-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.
+The reason we are keen to publish in PRL is clear: PRL gives an
+``official'' sense of closure,
+in a way no other journal does. We believe our article deserves it.
\closing{Sincerely,}