\usepackage{pdfpages}

\usepackage[hidelinks]{hyperref}
%\usepackage[1-32]{pagesel} % subset of pages
%\usepackage[33-]{pagesel} % subset of pages
%\usepackage[40-]{pagesel} % subset of pages

\newcommand{\Yaron}[1]{{\textcolor{blue}{{\textsf{Yaron: #1}}}}}

\newcommand{\Ali}[1]{\noindent\textcolor{green}{$\ll$\textsf{#1}$\gg$\marginpar{\tiny\bf \textcolor{green}{Ali}}}}

\newcommand{\Jingwei}[1]{{\textcolor{red}{{\textsf{Jingwei: #1}}}}}

% \newcommand{\Referee}[1]{{\textcolor{red}{{\textsf{Referee: #1}}}}}


% \usepackage[textsize=tiny,disable]{todonotes}
\usepackage[textsize=tiny]{todonotes}
\PassOptionsToPackage{usenames,dvipsnames}{xcolor} % still Undefined color error
\newcommand{\drg}[2][]{\todo[color=blue!20!white,inline,size=\scriptsize,#1]{Jingwei: #2}} 



% \usepackage{thm-restate}

\newenvironment{myproof}{ \paragraph{Proof: } } {\hfill$\square$}
\newenvironment{myproof2}[1]{ \paragraph{Proof of #1: } } {\hfill$\square$}

\newtheorem{fact}{Fact}
\newtheorem{observation}{Observation}
\usepackage{bbm}
\usepackage{graphicx}
\usepackage{caption}
\usepackage{subcaption}
\usepackage{empheq}
\usepackage{float}
% \usepackage{floatrow}
\usepackage{booktabs}
\usepackage{multirow}


% \usepackage{tabularx}
\usepackage{adjustbox}
\usepackage{thmtools}

% \usepackage{stmaryrd}   % shortrightarrow

\usepackage{soul} % yaron 2020/11/03 strike through



% =======================================================================================




\newcommand{\defeq}{\mathrel{\overset{\mathrm{def}}{=}}}

\newcommand{\eg}{\textit{e.g.}}
\newcommand{\eps}{\epsilon}

\newcommand{\indSi}{\mathbb{S}_i } % with subscript i, without superscript \pi 
\newcommand{\indSitilde}{\widetilde{ \mathbb{S} }_i } 
\newcommand{\indFi}{\mathbb{F}_i } 
\newcommand{\indFitilde}{\widetilde{ \mathbb{F} }_i } 
\newcommand{\indPi}{\mathbb{P}_i } 


\newcommand{\E}[1]{\mathbb{E} \left[ {#1} \right]}
\newcommand{\p}[1]{\mathbf{Pr} \left[ {#1} \right]}
\newcommand{\pr}[1]{\mathbf{Pr} \left[ {#1} \right]}
\newcommand{\one}[1]{\BFI \left[ {#1} \right]}
\newcommand{\paren}[1]{ \left( {#1} \right) }
\newcommand{\bigO}[1]{ O \left( {#1} \right) }
\newcommand{\bigOmega}[1]{ \Omega \left( {#1} \right) }
\newcommand{\abs}[1]{ \left | {#1} \right | }
\newcommand{\brackets}[1]{\left[ {#1} \right]}
\newcommand{\braces}[1]{\left\{{#1}\right\}}

\usepackage{color}              % Need the color package
\usepackage[suppress]{color-edits}
\usepackage{color-edits}
\addauthor{Ali}{red}


\newcommand{\bfu}{\mathbf{u}} 
\newcommand{\bfx}{\mathbf{x}} 
\newcommand{\bfy}{\mathbf{y}} 
\newcommand{\bfX}{\mathbf{X}} 
\newcommand{\bfv}{\mathbf{v}}
\newcommand{\bfV}{\mathbf{V}}
\newcommand{\bfa}{\mathbf{a}} 
\newcommand{\bfA}{\mathbf{A}} 
\newcommand{\bfI}{\mathbf{I}} 
\newcommand{\bfm}{\mathbf{m}} 