\newcommand{\comment}[1]{}

\newcommand{\bmath}[1]{\mbox{$\mathbf{#1}$}}
\newcommand{\rank}{\textrm{rank}}

\newcommand{\nrsfm}[0] {{\sc nrs{\rm\em f}\sc m }}
\newcommand{\nrsfmS}[0] {{\sc nrs{\rm\em f}\sc m}}
\newcommand{\sfm}[0] {{\sc s{\rm\em f}\sc m }}
\newcommand{\sfmS}[0] {{\sc s{\rm\em f}\sc m}}
\newcommand{\etal}{\emph{et al. }}
\newcommand{\etals}{\emph{et al.}}
\newcommand{\timescomp}{\hspace{-1mm}\times\hspace{-0.5mm}}
\newcommand{\minuscomp}{\hspace{-1mm}-\hspace{-1mm}}
\newcommand{\minusc}{\hspace{-0.5mm}-\hspace{-0.5mm}}
\newcommand{\plusc}{\hspace{-0.5mm}+\hspace{-0.5mm}}


%lowercase--------------------------------
\newcommand{\bzero}{\textbf{0}}
\newcommand{\bone}{\textbf{1}}
\newcommand{\ba}{\mathbf{a}}
\newcommand{\bb}{\mathbf{b}}
\newcommand{\bc}{\mathbf{c}}
\newcommand{\bd}{\mathbf{d}}
\newcommand{\be}{\mathbf{e}}
\newcommand{\bff}{\mathbf{f}}
\newcommand{\bg}{\mathbf{g}}
\newcommand{\bh}{\mathbf{h}}
\newcommand{\bi}{\mathbf{i}}
\newcommand{\bm}{\mathbf{m}}
\newcommand{\bn}{\mathbf{n}}
\newcommand{\bl}{\mathbf{l}}
\newcommand{\bp}{\mathbf{p}}
\newcommand{\btp}{\tilde{\mathbf{p}}}
\newcommand{\bq}{\mathbf{q}}
\newcommand{\br}{\mathbf{r}}
\newcommand{\bs}{\mathbf{s}}
\newcommand{\bts}{\tilde{\mathbf{s}}}
\newcommand{\bt}{\mathbf{t}}
\newcommand{\bu}{\mathbf{u}}
\newcommand{\btu}{\tilde{\mathbf{u}}}
\newcommand{\bv}{\mathbf{v}}
\newcommand{\bw}{\mathbf{w}}
\newcommand{\bx}{\mathbf{x}}
\newcommand{\btx}{\tilde{\mathbf{x}}}
\newcommand{\by}{\mathbf{y}}
\newcommand{\bz}{\mathbf{z}}

%uppercase--------------------------------
\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{\btF}{\tilde{\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{\btbS}{\breve{\mathbf{S}}}
\newcommand{\btS}{\tilde{\mathbf{S}}}
\newcommand{\bS}{\mathbf{S}}
\newcommand{\bT}{\mathbf{T}}
\newcommand{\btT}{\tilde{\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{\1}{\bmath{1}}
\newcommand{\0}{\bmath{0}}

%hat--------------------------------
\newcommand{\bhc}{\hat{\mathbf{c}}}
\newcommand{\bhd}{\hat{\mathbf{d}}}
\newcommand{\bhF}{\hat{\mathbf{F}}}
\newcommand{\bhG}{\hat{\mathbf{G}}}
\newcommand{\bhH}{\hat{\mathbf{H}}}
\newcommand{\bhJ}{\hat{\mathbf{J}}}
\newcommand{\bhK}{\hat{\mathbf{K}}}
\newcommand{\bhp}{\hat{\mathbf{p}}}



%mathcal--------------------------------
\newcommand{\mA}{\mathcal{A}}
\newcommand{\mB}{\mathcal{B}}
\newcommand{\mC}{\mathcal{C}}
\newcommand{\mD}{\mathcal{D}}
\newcommand{\mE}{\mathcal{E}}
\newcommand{\mF}{\mathcal{F}}
\newcommand{\mI}{\mathcal{I}}
\newcommand{\mK}{\mathcal{K}}
\newcommand{\mM}{\mathcal{M}}
\newcommand{\mN}{\mathcal{N}}
\newcommand{\mL}{\mathcal{L}}
\newcommand{\mP}{\mathcal{P}}
\newcommand{\mR}{\mathcal{R}}
\newcommand{\mS}{\mathcal{S}}
\newcommand{\mT}{\mathcal{T}}
\newcommand{\mmt}{\mathcal{t}}
\newcommand{\mU}{\mathcal{U}}
\newcommand{\mW}{\mathcal{W}}
\newcommand{\mmx}{\mathcal{x}}
\newcommand{\mX}{\mathcal{X}}
\newcommand{\mZ}{\mathcal{Z}}




%mathbb--------------------------------
\newcommand{\mbR}{\mathbb{R}} %symbol for the Real numbers


%symmbols--------------------------------
\newcommand{\Avvo}{\mathcal{A}}
\newcommand{\Tvvo}{\mathcal{T}}
\newcommand{\balpha}{\boldsymbol{\alpha}}
\newcommand{\bdelta}{\boldsymbol{\delta}}
\newcommand{\bDelta}{\boldsymbol{\Delta}}
\newcommand{\blambda}{\boldsymbol{\lambda}}
\newcommand{\bLambda}{\boldsymbol{\Lambda}}
\newcommand{\bmu}{\boldsymbol{\mu}}
\newcommand{\bgamma}{\boldsymbol{\gamma}}
\newcommand{\bGamma}{\boldsymbol{\Gamma}}
\newcommand{\bSigma}{\boldsymbol{\Sigma}}
\newcommand{\btheta}{\boldsymbol{\theta}}
\newcommand{\bzeta}{\boldsymbol{\zeta}}
\newcommand{\bTheta}{\boldsymbol{\Theta}}
\newcommand{\brho}{\boldsymbol{\rho}}
\newcommand{\bphi}{\boldsymbol{\phi}}
\newcommand{\bPhi}{\boldsymbol{\Phi}}
\newcommand{\bpsi}{\boldsymbol{\psi}}
\newcommand{\bPsi}{\boldsymbol{\Psi}}
\newcommand{\bxi}{\boldsymbol{\xi}}
\newcommand{\bUpsilon}{\boldsymbol{\Upsilon}}
\newcommand{\bomega}{\boldsymbol{\omega}}
\newcommand{\bbeta}{\boldsymbol{\beta}}
\newcommand{\bOmega}{\boldsymbol{\Omega}}
\newcommand{\bvarphi}{\boldsymbol{\varphi}}
\newcommand{\bpi}{\boldsymbol{\pi}}


\newcommand{\mo}{\boldsymbol{o}}

\newcommand{\berror}{\boldsymbol{\varepsilon}}

\newcommand{\st}{{\;t}}
\newcommand{\sk}{{\;k}}
\newcommand{\tms}{\hspace{-1mm}\times{\hspace{-1mm}}}
\newcommand{\hh}{\hspace{-1mm}}



\newcommand{\argmin}{\operatornamewithlimits{arg\,min}}
\newcommand{\argmax}{\operatornamewithlimits{arg\,max}}




\newcommand{\Err}{\textrm{Err}}
\newcommand{\Rot}{\textrm{rot}}
\newcommand{\Trans}{\textrm{trans}}


\renewcommand{\labelitemi}{-}
%\renewcommand{\labelitemii}{\Radioactivity}
%\renewcommand{\labelitemiii}{\Biohazard}
