%\usepackage{algorithmic}
%\usepackage{algpseudocode}
%\usepackage{epsfig}		% This package allows encapsulated postscript
%\usepackage{subfigure}		% This package allows subfigures
\usepackage{amsmath}
\usepackage{amssymb}

\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\argmin}{arg\,min}

\newcommand{\subdiv}[2]{#1\!\!\parallel_#2\,}

\def\seqmember{q}   % member of example sequence
\def\seqnmember{\acute{\seqmember}} % member of second example sequence
\def\seqindex{n} % index
%\def\subseq{M}
\def\seqdiv{\lambda} % sequence division
\def\subseqiter{\theta} %iteration of subsequence elements
\def\seqalpha{\Theta} % number of elements per subsequence
\def\seqiter{a} % index for subsequences in super sequence
\def\seqdef{Q} % example sequence
\def\seqndef{\acute{\seqdef}} % example sequence 2
%\def\seqdeflength{K} %
\def\demoa{\vartriangle} % example elements
\def\demob{\blacktriangledown} % example elements

\def\ssep{\,:\,} % set builder separator symbol

\newcommand{\seqlength}[1]{|#1|}


%General symbols
\def\time{t}
\def\timeorigin{\time_\textrm{org}}
\def\timeend{\time_\textrm{end}}
\def\timespan{\time_\textrm{span}}
\def\delt{\Delta \time}
\def\duration{\textrm{d}}		% duration of a note
\def\start{\textrm{s}}		% onset time of a note
\def\starttime{{\time_{\start}}}
\def\durationtime{{\time_{\duration}}}
\def\velocity{\nu}		% velocity/dynamic of a note
\def\dist{d}			% distance function 
\def\sync{\textsf{\emph{S}}}			% total syncopation value for a model (subscripted with model name e.g. \sync_\textrm{LHL}
\def\sequence{Y}		% for a sequence of notes
\def\note{y}			% a note
\def\sequenceindex{n}		% for a sequence of notes
\def\sequencelength{{|\sequence|}}%N

%\def\metricset{XXX}
\def\metricvector{H}
\def\metricmember{h}
\def\metricweight{w}
\def\metricweightset{W}
\def\metriclevel{L}
\def\levelmax{\metriclevel_\textrm{max}}
\def\metricindex{j}
\def\metrictotal{I}
\def\subdivision{\lambda}
\def\subdivisionset{\Lambda}
\def\allseqs{\mathbb{S}}
\def\repnum{\alpha}


\def\conitersum{\bigodot}

\newcommand{\dsum}[2]{
\hspace{-0.1cm}
\begin{array}{c}
_{{#1}}%
%\vspace{-0.2cm}
\\ \conitersum% \vspace{-0.2cm}
 \\ ^{{#2}}\\
\end{array} \hspace{-0.2cm}
}

\def\concatplus{\ast}
\def\concatmul{\otimes}

%time-span symbols
\def\timespansequence{T}
\def\spanlength{\time_\textrm{span}}  	% length of a timespan
\def\spanvector{V}  	% timespan vector
\def\binaryspanvector{B}
\def\binaryspanmember{b}
\def\spanmember{v} 		% member of a timespan vector
\def\spanindex{m} 		% index of timespan vector
\def\spandim{{|\spanvector|}}%M			% dimension of a timespan vector
\def\binaryspandim{{|\binaryspanvector|}}%B

\def\true{\textrm{True}}

\def\dontcare{\textrm{X}}

%LHL specific
\def\lhl{LHL}
%\def\lhlsumfunc{\varphi}
\def\lhlfunc{\kappa}
\def\lhlnode{\psi}
\def\lhliter{a}
%\def\terminals{\mathcal{S}}	% the set of all terminal nodes
\def\NoteNode{\textsf{\small{N}}}	% node type N (note)
\def\RestNode{\textsf{\small{R}}}	% node type R (rest)
\def\NoteNodeIndex{j}	% node type N (note)
\def\RestNodeIndex{i}	% node type R (rest)
%\def\lhlnr{f(\lhlnode_\RestNodeIndex)}		% local syncopation value in LHL


\def\NodeType{\eta}	% a node
%\def\NRpairs{P}
\def\lhlindex{a}
\def\lhlseq{\Psi}


%Keith specific
\def\keith{KTH}
\def\keithD{c}			% keith's D value (highest power of 2 that is less than the note duration)
\def\keithk{k}			% keith local syncopation score for a note
\def\keithostart{\mathfrak{o}}
\def\keithoend{\mathfrak{e}}
\def\keithd{g}
\def\keitha{\xi}

% Pressing specific
\def\pressing{PRS}
\def\prssubdiv{\mathcal{L}}
\def\prstotalfunc{f}
\def\prstypefunc{g}
\def\prssumfunc{q}


% metrical
\def\metrical{TMC} %tousaint's metrical complexity
\def\metricity{\varphi}
\def\binaryspanvectorhat{\hat{\binaryspanvector}}
\def\binaryspanmemberhat{\hat{\binaryspanmember}}

%off-beatness
\def\offbeat{TOB}
\def\tobweight{\varsigma}


\def\sioros{SG}
\def\levelsrange{\beta}
\def\previousweight{\gamma}
\def\sgdif{\vartheta}
\def\sgaverage{u}
\def\sgpotential{\phi}
\def\sgscore{s}
%\def\sgx{{1}}
%\def\sgy{{2}}
\def\sgnext{{\rho}}
\def\sgprev{{\varrho}}
\def\sghhat{\ell}%{\hat{\metricweight}}}
\def\sgmhat{{\hat{\spanindex}}}
\def\maxmetricweight{\metricmember_\textrm{max}}


% WNBD specific
\def\wnbd{WNBD}
\def\wnbdD{\mathcal{W}}
\def\wnbdT{\mathcal{T}}
\def\strongbeat{\mu}
\def\strongbeatindex{i}

%Keller-Schubert Autocorrelation
\def\ksa{KSA}


\def\pvalue{p}
\def\regression{r}

% Best-Single Combined
\def\bsingle{\textrm{BSC}}
\def\bsingletwo{\bsingle_2}
\def\bsinglethree{\bsingle_3}

%Weighted-Multiple Combined
\def\wmultiple{\textrm{WMC}}

% Tempo-Dependent 
\def\tempo{\Upsilon}
\def\td{\textsf{T}}
\def\tdmodel{\textrm{M}}
\def\bigtild{\hspace{-0.12cm}\sim\hspace{-0.12cm}}
\def\littletild{\sim}


\def\scalingfunction{F}

% rhythm categories
\def\binary{4/4 monorhythms}
\def\ternary{6/8 monorhythms}
\def\polyrhythms{polyrhythms}

\newcommand{\refFig}[1] {Figure~\ref{#1}}
\newcommand{\shortCap}[2] {\caption[#1]{#1 #2}}
%\newcommand{\url}[1] {\texttt{#1}}

% Quadratic function
\def\parameterA{a}
\def\parameterB{b}
\def\parameterC{c}

\def\sigp{0.001}