%% %% General definitions one needs all the time %% %\newlength{\aulen} % USENIX/NSDI \newcommand{\aubox}[3]{\parbox[t]{#1}{\centering#2\\\url{#3}}} % ACM %\newcommand{\aubox}[3]{\parbox[t]{#1}{\centering\aufnt{#2}\\\affaddr{\url{#3}}}} %\newcommand{\auboxs}[2]{\parbox[t]{#1}{\centering\aufnt{#2}}} %\newcommand{\affbox}[3]{\parbox[t]{#1}{\centering\affaddr{#2}\\\url{#3}}} \newcommand{\mypara}[1]{\vspace{\parsep}\noindent\textbf{#1}\quad} \newcommand{\myparaend}[1]{\vspace{\parsep}} \newcommand{\xref}[1]{Section~\ref{#1}} %\newcommand{\xref}[1]{\S\ref{#1}} \newcommand{\cref}[1]{Chapter~\ref{#1}} \newcommand{\pxref}[1]{(\xref{#1})} \newcommand{\fref}[1]{Figure~\ref{#1}} \newcommand{\tref}[1]{Table~\ref{#1}} \newcommand{\first}{\emph{(i)}~} \newcommand{\second}{\emph{(ii)}~} \newcommand{\third}{\emph{(iii)}~} \newcommand{\fourth}{\emph{(iv)}~} \newcommand{\fifth}{\emph{(v)}~} \newcommand{\sixth}{\emph{(vi)}~} \newcommand{\zb}{z.\,B. \@} %\newcommand{\ie}{i.\,e., \@} %\newcommand{\eg}{e.\,g., \@} %\newcommand{\Ie}{I.\,e., \@} %\newcommand{\Eg}{E.\,g., \@} %\newcommand{\cf}{cf. \@} %\newcommand{\Cf}{Cf. \@} %\newcommand{\etal}{et~al.\xspace} \newcommand{\perc}{\,\%\xspace} \newcommand{\pert}{\,\textperthousand\xspace} % requires \usepackage{pifont} \newcommand{\checked}{\ding{52}\xspace} \newcommand{\unchecked}{\ding{56}\xspace} \newcommand{\todo}[1]{\textit{\textcolor{red}{TODO: #1}}} %\renewcommand{\todo}[1]{{\LARGE TODO:#1}} % mark changed wording from first submission \newcommand{\new}[1]{\textcolor{blue}{#1}} % for hints and comments \newcommand{\comment}[1]{\textit{\textcolor{green}{#1}}} % mark text blocks that need to be discussed, that might affect other parts \newcommand{\discuss}[1]{\textit{\textcolor{red}{#1}}} % mark deleted text blocks \usepackage[normalem]{ulem} \newcommand{\del}[1]{\textcolor{red}{\sout{#1}}} \newcounter{fn1} \setcounter{fn1}{1} \newcounter{fn2} \setcounter{fn2}{2} \newcounter{fn3} \setcounter{fn3}{3} \newcounter{fn4} \setcounter{fn4}{4} \newcounter{fn5} \setcounter{fn5}{5} \newcounter{tc} \setcounter{tc}{1} \newcommand{\fnsym}[1]{$^{\fnsymbol{#1}}$} \newcommand{\minisec}[1]{\noindent\textbf{#1}:} \newcommand{\microsecond}{\textmu{}s\xspace} \newcommand{\millisecond}{ms\xspace} \newcommand{\microseconds}{\textmu{}s\xspace} \newcommand{\milliseconds}{ms\xspace} \newcommand\textpi{\ensuremath{\pi}\xspace} \newcommand{\ed}[1]{\textsf{\textbf{[#1]}}} \setlength{\marginparwidth}{0.8in} \let\oldmarginpar\marginpar \renewcommand\marginpar[1]{\-\oldmarginpar[\raggedleft\footnotesize \textcolor{blue}{#1}]% {\raggedright\footnotesize \textcolor{blue}{#1}}} \newcounter{mpc} \setcounter{mpc}{1} \newcommand{\mph}[1]{{\textcolor{blue}{$^{\fnsymbol{mpc}}$\marginpar{\fnsymbol{mpc} #1}\stepcounter{mpc}}}} \newcommand{\ccg}{\cellcolor[gray]{0.9}} % requires \usepackage{colortbl} \newcommand{\tcg}[1]{\textcolor[gray]{0.5}{#1}} \newcommand{\commentout}[1]{} \newcommand{\ba}{{\bf a}} \newcommand{\bA}{{\bf A}} \newcommand{\bb}{{\bf b}} \newcommand{\bB}{{\bf B}} \newcommand{\bc}{{\bf c}} \newcommand{\bC}{{\bf C}} \newcommand{\bd}{{\bf d}} \newcommand{\bD}{{\bf D}} \newcommand{\be}{{\bf e}} \newcommand{\bE}{{\bf E}} \newcommand{\bh}{{\bf h}} \newcommand{\bH}{{\bf H}} \newcommand{\bi}{{\bf i}} \newcommand{\bI}{{\bf I}} \newcommand{\bM}{{\bf M}} \newcommand{\bs}{{\bf s}} \newcommand{\bS}{{\bf S}} \newcommand{\bu}{{\bf u}} \newcommand{\bU}{{\bf U}} \newcommand{\bv}{{\bf v}} \newcommand{\bV}{{\bf V}} \newcommand{\bw}{{\bf w}} \newcommand{\bwbar}{\overline{\bw}} \newcommand{\bwhat}{\widehat{\bw}} \newcommand{\bwstar}{\bw^\ast} \newcommand{\bwtilde}{\widetilde{\bw}} \newcommand{\bW}{{\bf W}} \newcommand{\bx}{{\bf x}} \newcommand{\bX}{{\bf X}} \newcommand{\by}{{\bf y}} \newcommand{\bY}{{\bf Y}} \newcommand{\bz}{{\bf z}} \newcommand{\bZ}{{\bf Z}} \newcommand{\balpha}{{\bm \alpha}} \newcommand{\bell}{{\bm \ell}} \newcommand{\cA}{\mathcal{A}} \newcommand{\cC}{\mathcal{C}} \newcommand{\cD}{\mathcal{D}} \newcommand{\cE}{\mathcal{E}} \newcommand{\cF}{\mathcal{F}} \newcommand{\cG}{\mathcal{G}} \newcommand{\cH}{\mathcal{H}} \newcommand{\cL}{\mathcal{L}} \newcommand{\cM}{\mathcal{M}} \newcommand{\cN}{\mathcal{N}} \newcommand{\cO}{\mathcal{O}} \newcommand{\cP}{\mathcal{P}} \newcommand{\cS}{\mathcal{S}} \newcommand{\cT}{\mathcal{T}} \newcommand{\cU}{\mathcal{U}} \newcommand{\cX}{\mathcal{X}} \newcommand{\cY}{\mathcal{Y}} \newcommand{\cZ}{\mathcal{Z}} \newcommand{\eps}{\varepsilon} \newcommand{\pistar}{\pi^\ast} \newcommand{\Qpi}{Q^\pi} \newcommand{\Qstar}{Q^\ast} \newcommand{\Vhat}{\widehat{V}} \newcommand{\Vpi}{V^\pi} \newcommand{\Vbw}{V^\bw} \newcommand{\Vbwbar}{V^{\bwbar}} \newcommand{\Vbwhat}{V^{\bwhat}} \newcommand{\Vbwstar}{V^{\bwstar}} \newcommand{\Vbwtilde}{V^{\bwtilde}} \newcommand{\Vstar}{V^\ast} \newcommand{\wbar}{\overline{w}} \newcommand{\what}{\widehat{w}} \newcommand{\wstar}{w^\ast} \newcommand{\wtilde}{\widetilde{w}} \newcommand{\integerset}{\mathbb{Z}} \newcommand{\naturalset}{\mathbb{N}} \newcommand{\realset}{\mathbb{R}} \newcommand{\betapdf}{P_{\mathrm{beta}}} \newcommand{\betacdf}{F_{\mathrm{beta}}} \newcommand{\gammapdf}{P_{\mathrm{gamma}}} \newcommand{\gammacdf}{F_{\mathrm{gamma}}} \newcommand{\normalpdf}{\cN} \newcommand{\normalcdf}{F_{\cN}} \newcommand{\unifpdf}[2]{\mathrm{U}_{[#1, #2]}} \newcommand{\unifcdf}[2]{F_{\mathrm{U}_{[#1, #2]}}} \newcommand{\convexhull}[1]{\mathrm{Conv\left[#1\right]}} \newcommand{\domain}[1]{\mathrm{Dom\left[#1\right]}} \newcommand{\range}[1]{\mathrm{Rng\left[#1\right]}} \newcommand{\Parents}{\mathsf{Par}} \newcommand{\lyapunov}{L} \newcommand{\lyapunovfactor}{\kappa} \newcommand{\abs}[1]{\left|#1\right|} \newcommand{\ceils}[1]{\left\lceil#1\right\rceil} \newcommand{\E}[2]{\mathbb{E}_{#1} \! \left[#2\right]} \newcommand{\Eabs}[2]{\mathbb{E}_{#1} \! \abs{#2}} \newcommand{\floors}[1]{\left\lfloor#1\right\rfloor} \newcommand{\I}[1]{\mathds{1} \! \left\{#1\right\}} \newcommand{\intin}[2]{\int_{#1} \! \! \! #2 \ud #1} \newcommand{\maxnorm}[1]{\left\|#1\right\|_\infty} \newcommand{\maxnormw}[2]{\left\|#1\right\|_{\infty, #2}} \newcommand{\mode}[1]{\widehat{#1}} \renewcommand{\neg}[1]{\overline{#1}} \newcommand{\negpart}[1]{\left[#1\right]^-} \newcommand{\normw}[2]{\left\|#1\right\|_{#2}} \newcommand{\pospart}[1]{\left[#1\right]^+} \newcommand{\set}[1]{\left\{#1\right\}} \newcommand{\sgn}{\mathrm{sgn}} \newcommand{\subst}[2]{\left\{#1 = #2\right\}} \newcommand{\transpose}{^\mathsf{\scriptscriptstyle T}} \newcommand{\ud}{\, \mathrm{d}} \newcommand{\var}[2]{\mathrm{var}_{#1} \! \left[#2\right]}