deletions | additions       diff --git a/header.tex b/header.tex  index e69de29..e89311a 100644  --- a/header.tex  +++ b/header.tex 
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\usepackage{amsmath, amssymb}  \usepackage{enumerate}  \newcommand{\Words}{{\{ 0, 1 \}^*}}  \newcommand{\WordsLen}[1]{{\{ 0, 1 \}^{#1}}}  \DeclareMathOperator{\Sgn}{sgn}  \DeclareMathOperator{\Supp}{supp}  \DeclareMathOperator{\Stab}{stab}  \DeclareMathOperator{\Img}{Im}  \DeclareMathOperator{\E}{E}  \DeclareMathOperator{\Var}{Var}  \DeclareMathOperator{\Ent}{H}  \DeclareMathOperator{\Hom}{Hom}  \DeclareMathOperator{\End}{End}  \DeclareMathOperator{\Sym}{Sym}  \DeclareMathOperator{\T}{T}  \DeclareMathOperator{\R}{r}  \DeclareMathOperator{\A}{a}  \newcommand{\KL}[2]{\operatorname{D}_{\mathrm{KL}}(#1 \| #2)}  \newcommand{\Argmin}[1]{\underset{#1}{\operatorname{arg\,min}}\,}  \newcommand{\Argmax}[1]{\underset{#1}{\operatorname{arg\,max}}\,}  \newcommand{\Nats}{\mathbb{N}}  \newcommand{\Ints}{\mathbb{Z}}  \newcommand{\Rats}{\mathbb{Q}}  \newcommand{\Reals}{\mathbb{R}}  \newcommand{\Coms}{\mathbb{C}}  \newcommand{\Lim}[1]{\lim_{#1 \rightarrow \infty}}  \newcommand{\LimInf}[1]{\liminf_{#1 \rightarrow \infty}}  \newcommand{\LimSup}[1]{\limsup_{#1 \rightarrow \infty}}  \newcommand{\Abs}[1]{\lvert #1 \rvert}  \newcommand{\Norm}[1]{\lVert #1 \rVert}  \newcommand{\Floor}[1]{\lfloor #1 \rfloor}  \newcommand{\Ceil}[1]{\lceil #1 \rceil}  \newcommand{\Chev}[1]{\langle #1 \rangle}