%
%	Macros for 
%
\newcommand{\dmatrix}{{M}}
\newcommand{\vdmatrix}[1]{{\bar{\dmatrix}_{#1}}}

\newcommand{\mcal}[1]{{\mathcal{#1}}}

\newcommand{\half}{\frac{1}{2}}

\newcommand{\costallb}{\epsilon_S}
\newcommand{\costalla}{\costallb(M)}

\newcommand{\rowM}[1]{\bar{M}_{#1}}
\newcommand{\mr}{\rowM{r}}

\newcommand{\M}{{\bf M}}
\newcommand{\HM}{H_{_\M}}

\newcommand{\ispace}{{\cal{X}}}
\newcommand{\lspace}{{\cal{Y}}}

\newcommand{\comdots}{, \ldots ,}

\newfont{\msym}{msbm10}
\newcommand{\reals}{{\Bbb{R}}} 
%{\mbox{\msym {R}}}}
\newcommand{\D}{{\cal D}}
\newcommand{\Z}{{\cal Z}}
\newcommand{\X}{{\cal X}}
\newcommand{\Y}{{\cal Y}}

\newcommand{\vw}{{\bar{w}}}
\newcommand{\vx}{{\bar{x}}}
\newcommand{\ve}{{\bar{1}}}
\newcommand{\vh}{{\bar{h}}}
\newcommand{\veta}{{\bar{\eta}}}
\newcommand{\vzero}{{\bar{0}}}
\newcommand{\vtau}{{\bar{\tau}}}
\newcommand{\vnu}{{\bar{\nu}}}
\newcommand{\vD}{{\bar{D}}}
\newcommand{\vB}{{\bar{B}}}
\newcommand{\vepsilon}{{\bar{\epsilon}}}
\newcommand{\sample}{{\{(\vx_1,y_1),\ldots,(\vx_m,y_m)\}}}

\newcommand{\pseudocodefont}{\normalsize}
\newcommand{\nolineskips}{
\setlength{\parskip}{0pt}
\setlength{\parsep}{0pt}
\setlength{\topsep}{0pt}
\setlength{\partopsep}{0pt}
\setlength{\itemsep}{0pt}}



\newcommand{\figline}{\rule{0.90\textwidth}{0.5pt}}

\newcommand{\QED}{\hfill$\;\;\;\rule[0.1mm]{2mm}{2mm}$}

\newcommand{\eqdef}{\stackrel{\rm def}{=}}