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\signature{
  \vspace{-6\medskipamount}
  \smallskip
  Jaron Kent-Dobias
}

\address{
  Istituto Nazionale di Fisica Nucleare, Sezione di Roma I\\
  Piazzale Aldo Moro, 2\\
  Roma RM, Italia\\
  c/o Sapienza Università di Roma\\
  Dipartimento di Fisica, Edificio Guglielmo Marconi
}

\begin{document}
\begin{letter}{
  European Physical Society\\
  6, rue des Frères Lumière\\
  68200 Mulhouse, France
}

\opening{To the editors of EPL,}

I submit my manuscript \emph{When is the average number of saddle points typical?}\
for your consideration. This work examines a long-held but implicit assumption
in the field of disordered landscapes and finds it is often violated in simple
examples. Specifically, conditions for the possibility of clustering structure
among equilibrium states cannot rule out clustering structure among saddle points.

This work is original in its methods and results. Few works have been published
on quenched complexity in disordered landscapes, and fewer still that explicitly
calculate the complexity. Explicit calculation is challenging because the
variational formulas involved are difficult to evaluate without knowledge of an
existing solution. I develop a novel way to find such a solution, directly
applicable to a large class of models of general interest in the theory of
glasses and statistical inference. Moreover, the result---finding novel clustering
among saddles---has not been previously studied.

The importance of the result will not likely be in its direct implications for dynamics in the spherical models, but instead in its larger
implications for when annealed averages can be considered correct. This work decisively shows
that heuristics for deciding which models will have simple structure and
which will be more complex must be treated with care. In the $3+s$ spherical
models examined within, the models and saddles exhibiting nontrivial
structure makes it unlikely that their presence can explain outstanding problems for asymptotic dynamics, but the same structure appearing in other models might be critical to such behavior. The important lesson of this work is that one must look for it in the first place.

\closing{Sincerely,}

\vspace{1em}

\end{letter}

\end{document}
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