\RequirePackage{graphicx}
\RequirePackage{amsmath}
\RequirePackage{amssymb}
\RequirePackage{amsthm}
\RequirePackage{url}
\RequirePackage{pstricks}
\RequirePackage{pst-node}
\RequirePackage{pst-plot}

% Macros which don't take arguments

\newenvironment{itemize-compact}{\begin{itemize}\itemsep=0pt\topsep=0pt\partopsep=0pt\parskip=0pt\parsep=0pt}{\end{itemize}}
\newenvironment{enumerate-compact}{\begin{enumerate}\itemsep=0pt\topsep=0pt\partopsep=0pt\parskip=0pt\parsep=0pt}{\end{enumerate}}
\newenvironment{optimization}{\begin{array}{cll}}{\end{array}}
\newcommand{\minimize}{\displaystyle\operatornamewithlimits{minimize}}
\newcommand{\maximize}{\displaystyle\operatornamewithlimits{maximize}}
\newcommand{\subjectto}{\operatorname{subject\ to}}
\newcommand{\grad}{\nabla}

% Macros which take arguments

\newcommand{\at}[1]{^{({#1})}}
\newcommand{\parens}[1]{{\left({#1}\right)}}
\newcommand{\brackets}[1]{{\left[{#1}\right]}}
\newcommand{\anglebrackets}[1]{{\left\langle{#1}\right\rangle}}
\newcommand{\inner}[2]{\anglebrackets{{#1},{#2}}}
\newcommand{\ind}[1]{{\mathbf{I}\set{{#1}}}}
\newcommand{\zero}{{\mathbf{0}}}
\newcommand{\one}{{\mathbf{1}}}
\newcommand{\kronecker}[2]{{\delta_{{#1}{#2}}}}
\newcommand{\set}[1]{{\left\{{#1}\right\}}}
\newcommand{\abs}[1]{{\left|{#1}\right|}}
\newcommand{\reals}{{\mathbb{R}}}
\newcommand{\complex}{{\mathbb{C}}}
\newcommand{\norm}[1]{\left|\left|{#1}\right|\right|}
\newcommand{\deriv}[1]{{\frac{d}{d{#1}}}}
\newcommand{\pd}[1]{{\frac{\partial}{\partial {#1}}}}
\newcommand{\pdfrac}[2]{{\frac{\partial {#1}}{\partial {#2}}}}
\newcommand{\ppd}[1]{{\frac{\partial^2}{\partial {#1}^2}}}
\newcommand{\pdpd}[2]{{\frac{\partial^2}{\partial {#1}\partial {#2}}}}
\newcommand{\commentout}[1]{}
\newcommand{\nullspace}[1]{{\mathcal{N}({#1})}}
\newcommand{\range}[1]{{\mathcal{R}({#1})}}
\newcommand{\floor}[1]{{\left\lfloor {#1} \right\rfloor}}
\newcommand{\ceil}[1]{{\left\lceil {#1} \right\rceil}}
\newcommand{\remark}[1]{{\red \textbf{[[#1]]}}}
\newcommand{\draft}[1]{\title{#1 \\ \textbf{\normalsize [[Draft: Do not circulate.]]}}}
\newcommand{\mathbi}[1]{\textbf{\em #1}}

% Operators

\newcommand{\argmin}{\operatornamewithlimits{arg\,min}}
\newcommand{\argmax}{\operatornamewithlimits{arg\,max}}
\newcommand{\rank}{\operatorname{rank}}
\newcommand{\sign}{\operatorname{sign}}
\newcommand{\dom}{\operatorname{dom}}
\newcommand{\diag}{\operatorname{diag}}
\newcommand{\trace}{\operatorname{tr}}

% The alphabet!

\newcommand{\cA}{{\mathcal{A}}}
\newcommand{\cB}{{\mathcal{B}}}
\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{\cI}{{\mathcal{I}}}
\newcommand{\cJ}{{\mathcal{J}}}
\newcommand{\cK}{{\mathcal{K}}}
\newcommand{\cL}{{\mathcal{L}}}
\newcommand{\cM}{{\mathcal{M}}}
\newcommand{\cN}{{\mathcal{N}}}
\newcommand{\cO}{{\mathcal{O}}}
\newcommand{\cP}{{\mathcal{P}}}
\newcommand{\cQ}{{\mathcal{Q}}}
\newcommand{\cR}{{\mathcal{R}}}
\newcommand{\cS}{{\mathcal{S}}}
\newcommand{\cT}{{\mathcal{T}}}
\newcommand{\cU}{{\mathcal{U}}}
\newcommand{\cV}{{\mathcal{V}}}
\newcommand{\cW}{{\mathcal{W}}}
\newcommand{\cX}{{\mathcal{X}}}
\newcommand{\cY}{{\mathcal{Y}}}
\newcommand{\cZ}{{\mathcal{Z}}}

\newcommand{\bA}{{\mathbf{A}}}
\newcommand{\bB}{{\mathbf{B}}}
\newcommand{\bC}{{\mathbf{C}}}
\newcommand{\bD}{{\mathbf{D}}}
\newcommand{\bE}{{\mathbf{E}}}
\newcommand{\bF}{{\mathbf{F}}}
\newcommand{\bG}{{\mathbf{G}}}
\newcommand{\bH}{{\mathbf{H}}}
\newcommand{\bI}{{\mathbf{I}}}
\newcommand{\bJ}{{\mathbf{J}}}
\newcommand{\bK}{{\mathbf{K}}}
\newcommand{\bL}{{\mathbf{L}}}
\newcommand{\bM}{{\mathbf{M}}}
\newcommand{\bN}{{\mathbf{N}}}
\newcommand{\bO}{{\mathbf{O}}}
\newcommand{\bP}{{\mathbf{P}}}
\newcommand{\bQ}{{\mathbf{Q}}}
\newcommand{\bR}{{\mathbf{R}}}
\newcommand{\bS}{{\mathbf{S}}}
\newcommand{\bT}{{\mathbf{T}}}
\newcommand{\bU}{{\mathbf{U}}}
\newcommand{\bV}{{\mathbf{V}}}
\newcommand{\bW}{{\mathbf{W}}}
\newcommand{\bX}{{\mathbf{X}}}
\newcommand{\bY}{{\mathbf{Y}}}
\newcommand{\bZ}{{\mathbf{Z}}}

\newcommand{\bbA}{{\mathbb{A}}}
\newcommand{\bbB}{{\mathbb{B}}}
\newcommand{\bbC}{{\mathbb{C}}}
\newcommand{\bbD}{{\mathbb{D}}}
\newcommand{\bbE}{{\mathbb{E}}}
\newcommand{\bbF}{{\mathbb{F}}}
\newcommand{\bbG}{{\mathbb{G}}}
\newcommand{\bbH}{{\mathbb{H}}}
\newcommand{\bbI}{{\mathbb{I}}}
\newcommand{\bbJ}{{\mathbb{J}}}
\newcommand{\bbK}{{\mathbb{K}}}
\newcommand{\bbL}{{\mathbb{L}}}
\newcommand{\bbM}{{\mathbb{M}}}
\newcommand{\bbN}{{\mathbb{N}}}
\newcommand{\bbO}{{\mathbb{O}}}
\newcommand{\bbP}{{\mathbb{P}}}
\newcommand{\bbQ}{{\mathbb{Q}}}
\newcommand{\bbR}{{\mathbb{R}}}
\newcommand{\bbS}{{\mathbb{S}}}
\newcommand{\bbT}{{\mathbb{T}}}
\newcommand{\bbU}{{\mathbb{U}}}
\newcommand{\bbV}{{\mathbb{V}}}
\newcommand{\bbW}{{\mathbb{W}}}
\newcommand{\bbX}{{\mathbb{X}}}
\newcommand{\bbY}{{\mathbb{Y}}}
\newcommand{\bbZ}{{\mathbb{Z}}}

\newcommand{\fA}{{\mathfrak{A}}}
\newcommand{\fB}{{\mathfrak{B}}}
\newcommand{\fC}{{\mathfrak{C}}}
\newcommand{\fD}{{\mathfrak{D}}}
\newcommand{\fE}{{\mathfrak{E}}}
\newcommand{\fF}{{\mathfrak{F}}}
\newcommand{\fG}{{\mathfrak{G}}}
\newcommand{\fH}{{\mathfrak{H}}}
\newcommand{\fI}{{\mathfrak{I}}}
\newcommand{\fJ}{{\mathfrak{J}}}
\newcommand{\fK}{{\mathfrak{K}}}
\newcommand{\fL}{{\mathfrak{L}}}
\newcommand{\fM}{{\mathfrak{M}}}
\newcommand{\fN}{{\mathfrak{N}}}
\newcommand{\fO}{{\mathfrak{O}}}
\newcommand{\fP}{{\mathfrak{P}}}
\newcommand{\fQ}{{\mathfrak{Q}}}
\newcommand{\fR}{{\mathfrak{R}}}
\newcommand{\fS}{{\mathfrak{S}}}
\newcommand{\fT}{{\mathfrak{T}}}
\newcommand{\fU}{{\mathfrak{U}}}
\newcommand{\fV}{{\mathfrak{V}}}
\newcommand{\fW}{{\mathfrak{W}}}
\newcommand{\fX}{{\mathfrak{X}}}
\newcommand{\fY}{{\mathfrak{Y}}}
\newcommand{\fZ}{{\mathfrak{Z}}}

\newcommand{\vA}{{\vec{A}}}
\newcommand{\vB}{{\vec{B}}}
\newcommand{\vC}{{\vec{C}}}
\newcommand{\vD}{{\vec{D}}}
\newcommand{\vE}{{\vec{E}}}
\newcommand{\vF}{{\vec{F}}}
\newcommand{\vG}{{\vec{G}}}
\newcommand{\vH}{{\vec{H}}}
\newcommand{\vI}{{\vec{I}}}
\newcommand{\vJ}{{\vec{J}}}
\newcommand{\vK}{{\vec{K}}}
\newcommand{\vL}{{\vec{L}}}
\newcommand{\vM}{{\vec{M}}}
\newcommand{\vN}{{\vec{N}}}
\newcommand{\vO}{{\vec{O}}}
\newcommand{\vP}{{\vec{P}}}
\newcommand{\vQ}{{\vec{Q}}}
\newcommand{\vR}{{\vec{R}}}
\newcommand{\vS}{{\vec{S}}}
\newcommand{\vT}{{\vec{T}}}
\newcommand{\vU}{{\vec{U}}}
\newcommand{\vV}{{\vec{V}}}
\newcommand{\vW}{{\vec{W}}}
\newcommand{\vX}{{\vec{X}}}
\newcommand{\vY}{{\vec{Y}}}
\newcommand{\vZ}{{\vec{Z}}}

\newcommand{\ba}{{\mathbi{a}}}
\newcommand{\bb}{{\mathbi{b}}}
\newcommand{\bc}{{\mathbi{c}}}
\newcommand{\bd}{{\mathbi{d}}}
\newcommand{\be}{{\mathbi{e}}}
\newcommand{\boldf}{{\mathbi{f}}}
\newcommand{\bg}{{\mathbi{g}}}
\newcommand{\bh}{{\mathbi{h}}}
\newcommand{\bi}{{\mathbi{i}}}
\newcommand{\bj}{{\mathbi{j}}}
\newcommand{\bk}{{\mathbi{k}}}
\newcommand{\bl}{{\mathbi{l}}}
\newcommand{\bm}{{\mathbi{m}}}
\newcommand{\bn}{{\mathbi{n}}}
\newcommand{\bo}{{\mathbi{o}}}
\newcommand{\bp}{{\mathbi{p}}}
\newcommand{\bq}{{\mathbi{q}}}
\newcommand{\br}{{\mathbi{r}}}
\newcommand{\bs}{{\mathbi{s}}}
\newcommand{\bt}{{\mathbi{t}}}
\newcommand{\bu}{{\mathbi{u}}}
\newcommand{\bv}{{\mathbi{v}}}
\newcommand{\bw}{{\mathbi{w}}}
\newcommand{\bx}{{\mathbi{x}}}
\newcommand{\by}{{\mathbi{y}}}
\newcommand{\bz}{{\mathbi{z}}}

\newcommand{\va}{{\vec{a}}}
\newcommand{\vb}{{\vec{b}}}
\newcommand{\vc}{{\vec{c}}}
\newcommand{\vd}{{\vec{d}}}
\newcommand{\ve}{{\vec{e}}}
\newcommand{\vf}{{\vec{f}}}
\newcommand{\vg}{{\vec{g}}}
\newcommand{\vh}{{\vec{h}}}
\newcommand{\vi}{{\vec{i}}}
\newcommand{\vj}{{\vec{j}}}
\newcommand{\vk}{{\vec{k}}}
\newcommand{\vl}{{\vec{l}}}
\newcommand{\vm}{{\vec{m}}}
\newcommand{\vn}{{\vec{n}}}
\newcommand{\vo}{{\vec{o}}}
\newcommand{\vp}{{\vec{p}}}
\newcommand{\vq}{{\vec{q}}}
\newcommand{\vr}{{\vec{r}}}
\newcommand{\vs}{{\vec{s}}}
\newcommand{\vt}{{\vec{t}}}
\newcommand{\vu}{{\vec{u}}}
\newcommand{\vv}{{\vec{v}}}
\newcommand{\vw}{{\vec{w}}}
\newcommand{\vx}{{\vec{x}}}
\newcommand{\vy}{{\vec{y}}}
\newcommand{\vz}{{\vec{z}}}

\newcommand{\valpha}{{\vec{\alpha}}}
\newcommand{\vbeta}{{\vec{\beta}}}
\newcommand{\vgamma}{{\vec{\gamma}}}
\newcommand{\vdelta}{{\vec{\delta}}}
\newcommand{\vepsilon}{{\vec{\epsilon}}}
\newcommand{\vvarepsilon}{{\vec{\varepslion}}}
\newcommand{\vzeta}{{\vec{\zeta}}}
\newcommand{\veta}{{\vec{\eta}}}
\newcommand{\vtheta}{{\vec{\theta}}}
\newcommand{\vvartheta}{{\vec{\vartheta}}}
\newcommand{\viota}{{\vec{\iota}}}
\newcommand{\vkappa}{{\vec{\kappa}}}
\newcommand{\vlambda}{{\vec{\lambda}}}
\newcommand{\vmu}{{\vec{\mu}}}
\newcommand{\vnu}{{\vec{\nu}}}
\newcommand{\vxi}{{\vec{\xi}}}
\newcommand{\vpi}{{\vec{\pi}}}
\newcommand{\vvarpi}{{\vec{\varpi}}}
\newcommand{\vrho}{{\vec{\rho}}}
\newcommand{\vvarrho}{{\vec{\varrho}}}
\newcommand{\vsigma}{{\vec{\sigma}}}
\newcommand{\vvarsigma}{{\vec{\varsigma}}}
\newcommand{\vtau}{{\vec{\tau}}}
\newcommand{\vupsilon}{{\vec{\upsilon}}}
\newcommand{\vphi}{{\vec{\phi}}}
\newcommand{\vvarphi}{{\vec{\varphi}}}
\newcommand{\vchi}{{\vec{\chi}}}
\newcommand{\vpsi}{{\vec{\psi}}}
\newcommand{\vomega}{{\vec{\omega}}}

\newcommand{\balpha}{{\boldsymbol{\alpha}}}
\newcommand{\bbeta}{{\boldsymbol{\beta}}}
\newcommand{\bgamma}{{\boldsymbol{\gamma}}}
\newcommand{\bdelta}{{\boldsymbol{\delta}}}
\newcommand{\bepsilon}{{\boldsymbol{\epsilon}}}
\newcommand{\bvarepsilon}{{\boldsymbol{\barepslion}}}
\newcommand{\bzeta}{{\boldsymbol{\zeta}}}
\newcommand{\boldeta}{{\boldsymbol{\eta}}}
\newcommand{\btheta}{{\boldsymbol{\theta}}}
\newcommand{\bvartheta}{{\boldsymbol{\bartheta}}}
\newcommand{\biota}{{\boldsymbol{\iota}}}
\newcommand{\bkappa}{{\boldsymbol{\kappa}}}
\newcommand{\blambda}{{\boldsymbol{\lambda}}}
\newcommand{\bmu}{{\boldsymbol{\mu}}}
\newcommand{\bnu}{{\boldsymbol{\nu}}}
\newcommand{\bxi}{{\boldsymbol{\xi}}}
\newcommand{\bpi}{{\boldsymbol{\pi}}}
\newcommand{\bvarpi}{{\boldsymbol{\barpi}}}
\newcommand{\brho}{{\boldsymbol{\rho}}}
\newcommand{\bvarrho}{{\boldsymbol{\barrho}}}
\newcommand{\bsigma}{{\boldsymbol{\sigma}}}
\newcommand{\bvarsigma}{{\boldsymbol{\barsigma}}}
\newcommand{\btau}{{\boldsymbol{\tau}}}
\newcommand{\bupsilon}{{\boldsymbol{\upsilon}}}
\newcommand{\bphi}{{\boldsymbol{\phi}}}
\newcommand{\bvarphi}{{\boldsymbol{\varphi}}}
\newcommand{\bchi}{{\boldsymbol{\chi}}}
\newcommand{\bpsi}{{\boldsymbol{\psi}}}
\newcommand{\bomega}{{\boldsymbol{\omega}}}

\newcommand{\vGamma}{{\vec{\Gamma}}}
\newcommand{\vDelta}{{\vec{\Delta}}}
\newcommand{\vTheta}{{\vec{\Theta}}}
\newcommand{\vLambda}{{\vec{\Lambda}}}
\newcommand{\vXi}{{\vec{\Xi}}}
\newcommand{\vPi}{{\vec{\Pi}}}
\newcommand{\vSigma}{{\vec{\Sigma}}}
\newcommand{\vUpsilon}{{\vec{\Upsilon}}}
\newcommand{\vPhi}{{\vec{\Phi}}}
\newcommand{\vPsi}{{\vec{\Psi}}}
\newcommand{\vOmega}{{\vec{\Omega}}}

\newcommand{\bGamma}{{\boldsymbol{\Gamma}}}
\newcommand{\bDelta}{{\boldsymbol{\Delta}}}
\newcommand{\bTheta}{{\boldsymbol{\Theta}}}
\newcommand{\bLambda}{{\boldsymbol{\Lambda}}}
\newcommand{\bXi}{{\boldsymbol{\Xi}}}
\newcommand{\bPi}{{\boldsymbol{\Pi}}}
\newcommand{\bSigma}{{\boldsymbol{\Sigma}}}
\newcommand{\bUpsilon}{{\boldsymbol{\Upsilon}}}
\newcommand{\bPhi}{{\boldsymbol{\Phi}}}
\newcommand{\bPsi}{{\boldsymbol{\Psi}}}
\newcommand{\bOmega}{{\boldsymbol{\Omega}}}