OK with abstract and intro

Manuscript/EPAWTFT.tex

@@ -75,28 +75,6 @@
 \newcommand{\up}{\uparrow}
 \newcommand{\dw}{\downarrow}
 
-\newcommand{\updot}{%
-  \mathrel{\ooalign{\hfil$\vcenter{
-    \hbox{$\scriptscriptstyle\bullet$}}$\hfil\cr$\uparrow$\cr}
-  }%
-}
-\newcommand{\dwdot}{%
-  \mathrel{\ooalign{\hfil$\vcenter{
-    \hbox{$\scriptscriptstyle\bullet$}}$\hfil\cr$\downarrow$\cr}
-  }%
-}
-\newcommand{\vac}{%
-  \mathrel{\ooalign{\hfil$\vcenter{
-    \hbox{$\scriptscriptstyle\bullet$}}$\hfil\cr$ $\cr}
-  }%
-}
-
-\newcommand{\uddot}{%
-  \mathrel{\ooalign{\hfil$\vcenter{
-    \hbox{$\scriptscriptstyle\bullet$}}$\hfil\cr$\uparrow\downarrow$\cr}
-  }%
-}
-
 % Center tabularx columns
 \newcolumntype{Y}{>{\centering\arraybackslash}X}