$$
\newcommand{\yt}{\dot{y}}
\newcommand{\yo}{\tilde{y}}
\newcommand{\vect}[1]{{\boldsymbol{{#1}}}}
\newcommand{\x}{\vect{x}}
\newcommand{\thres}{\vect{t}}
\newcommand{\X}{\vect{X}}
\newcommand{\Xt}{\dot{\X}}
\newcommand{\Xc}{{\X}}
\newcommand{\model}{{\vect{\phi}}}
\newcommand{\C}{{\vect{C}}}
\newcommand{\Ccheck}{\check{\vect{C}}}
\newcommand{\pt}{\dot{p}}
\newcommand{\pc}{p}
\newcommand{\pyix}[2]{\pc_{\yo={#1}}({#2})}
\newcommand{\pyx}[1]{\pyix{i}{#1}}
\newcommand{\ec}{{e}}
\newcommand{\Qt}{\dot{\vect{Q}}}
\newcommand{\Qc}{\vect{Q}}
\newcommand{\amax}{\mathop{\arg\max}\limits}
\newcommand{\defined}{≔}
$$