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authorJaron Kent-Dobias <jaron@kent-dobias.com>2022-07-14 14:25:41 +0200
committerJaron Kent-Dobias <jaron@kent-dobias.com>2022-07-14 14:25:41 +0200
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@@ -52,7 +52,7 @@ been open ever since \cite{Parisi_1979_Infinite}. To date, the program of
computing the number of stationary points---minima, saddle points, and
maxima---of mean-field complex landscapes has been only carried out for a small subset of
models, including most notably the (pure) $p$-spin model ($p>2$)
-\cite{Rieger_1992_The, Crisanti_1995_Thouless-Anderson-Palmer} and for similar
+\cite{Rieger_1992_The, Crisanti_1995_Thouless-Anderson-Palmer, Cavagna_1997_An, Cavagna_1998_Stationary} and for similar
energy functions inspired by molecular biology, evolution, and machine learning
\cite{Maillard_2020_Landscape, Ros_2019_Complex, Altieri_2021_Properties}. In
a parallel development, it has evolved into an active field of probability
@@ -609,8 +609,8 @@ The Kac--Rice problem has an approximate supersymmetry, which is found when the
absolute value of the determinant is neglected and the trace of the Hessian is
not fixed. This supersymmetry has been studied in great detail in the
complexity of the Thouless--Anderson--Palmer (TAP) free energy
-\cite{Annibale_2003_The, Annibale_2003_Supersymmetric,
-Annibale_2004_Coexistence}. When the absolute value is dropped, the determinant in \eqref{eq:kac-rice} can be
+\cite{Annibale_2003_The, ,Annibale_2003_Supersymmetric,
+Annibale_2004_Coexistence, Cavagna_2005_Cavity, Giardina_2005_Supersymmetry}. When the absolute value is dropped, the determinant in \eqref{eq:kac-rice} can be
represented by an integral over Grassmann variables, which yields a complexity
depending on `bosons' and `fermions' that share the supersymmetry. The Ward
identities associated with the supersymmetry imply that $D=\hat\beta R$