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| -rw-r--r-- | topology.tex | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/topology.tex b/topology.tex index bbd978a..127b15e 100644 --- a/topology.tex +++ b/topology.tex @@ -78,7 +78,7 @@ out-of-equilibrium dynamics. % This block will be filled during the proof stage, and finilized just before publication. % It exists here only as a placeholder, and should not be modified by authors. \noindent\textcolor{white!90!black}{% -\fbox{\parbox{0.975\linewidth}{% +\fbox{\parbox{0.972\linewidth}{% \textcolor{white!40!black}{\begin{tabular}{lr}% \begin{minipage}{0.6\textwidth}% {\small Copyright attribution to authors. \newline @@ -244,8 +244,8 @@ the sign of the determinant, we arrive at the Euler characteristic, or \chi(\Omega)=\int_\Omega d\mathbf x\,\delta\big(\nabla H(\mathbf x)\big)\det\operatorname{Hess}H(\mathbf x) \end{equation} When the Kac--Rice formula is used to calculate the total number stationary -points one must take pains to eliminate the sign of the determinant -\cite{Fyodorov_2004_Complexity}. Here we are correct to include it. +points, one must take pains to eliminate the sign of the determinant +\cite{Fyodorov_2004_Complexity}. Here it is correct to preserve it. We need to choose a function $H$ for our calculation. Because $\chi$ is a topological invariant, any choice will work so long as it does not share some |