\( \def\bold#1{{\bf #1}} \newcommand{\X}[2]{#1_{\mathrm{#2}}} \newcommand{\sx}{\X{s}{x}} \newcommand{\sy}{\X{s}{y}} \newcommand{\fmi}{\X{f}{min}} \newcommand{\fma}{\X{f}{max}} \newcommand{\kmi}{\X{k}{min}} \newcommand{\kma}{\X{k}{max}} \newcommand{\kp}{k^{\prime}} \newcommand{\gn}{\X{g}{n}} \newcommand{\gf}{\X{g}{f}} \newcommand{\gh}{\X{g}{hyp}} \newcommand{\bh}{\X{b}{hyp}} \newcommand{\E}{E} \newcommand{\Emi}{\X{E}{min}} \newcommand{\Eh}{\X{E}{hyp}} \newcommand{\En}{\X{E}{n}} \newcommand{\Ef}{\X{E}{f}} \newcommand{\dn}{\X{d}{n}} \newcommand{\df}{\X{d}{f}} \newcommand{\pup}{\beta_{p}} \)