\documentclass[a4paper]{letter}

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\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 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, no correct calculation had been
made for the complexity of systems without a so-called replica symmetric
solution, which represent an small minority of systems. 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.

\closing{Sincerely,}

\vspace{1em}

\end{letter}

\end{document}
