text:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Twenty Seconds Resume/CV
% LaTeX Template
% Version 1.0 (14/7/16)
%
% Original author:
% Carmine Spagnuolo (cspagnuolo@unisa.it) with major modifications by
% Vel (vel@LaTeXTemplates.com) and Harsh (harsh.gadgil@gmail.com)
%
% License:
% The MIT License (see included LICENSE file)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%----------------------------------------------------------------------------------------
%	PACKAGES AND OTHER DOCUMENT CONFIGURATIONS
%----------------------------------------------------------------------------------------

\documentclass[letterpaper]{twentysecondcv} % a4paper for A4

% Command for printing skill overview bubbles
\newcommand\skills{
~
	\smartdiagram[bubble diagram]{
        \textbf{Ingeniería de}\\\textbf{Sistemas},
        \textbf{Full Stack}\\\textbf{Web Dev},
        \textbf{~~~~~OOP~~~~~~},
        \textbf{Hybrid}\\\textbf{Mobile Dev},
        \textbf{Angular}\\\textbf{4},
        \textbf{Pruebas}\\\textbf{~~Unitarias~~},
        \textbf{ORM}\\\textbf{Database}
    }
}

% Programming skill bars
\programming{{C $\textbullet$ C++  $\textbullet$ R / 3}, {Java $\textbullet$ SQL $\textbullet$ \large \LaTeX / 3.5}, {HTML5 $\textbullet$ JS $\textbullet$ Python / 5}}

% interest bars
\interest{{Desarrollo Back-End / 5.8}, {Desarrollo Front-End / 5.8}, {Planeación y Diagramación / 5.5}, {Experiencia de usuario / 5.7}}

% Projects text
\projects{
\textbf{DecAR} - An augmented reality interior decoration app for Android \\
        \textbf{CIS*6320} - An implementation of the Bicubic interpolation algorithm in C++
        \textbf{CIS*6650} - A comparative statistical study of SVM kernels, and number of hidden layers in ANN, on 5 UCI datasets
        \textbf{CIS*6660} - A data linkage project to integrate Canada's WWI casualties and 1901 Canadian census using an SVM
        \textbf{CIS*6650} - A statistical study of spurious correlations, such as correlating beer production with election outcome
}
\aboutmesidebar{
La presente es mi hoja de vida, en la cual, plasmo mi perfil académico, experiencia laboral, mis referencias personales y las competencias que considero hacen de mi perfil el indicado para desempeñarme como Desarrollador FullStack.
}
%----------------------------------------------------------------------------------------
%	 PERSONAL INFORMATION
%----------------------------------------------------------------------------------------
% If you don't need one or more of the below, just remove the content leaving the command, e.g. \cvnumberphone{}

\cvname{BRAYAN RONALDO MOJICA BARRIOS} % Your name
\cvjobtitle{ \large{Desarrollador Web \textbf{FullStack}}  } % Job
% title/career

\cvlinkedin{}
\cvgithub{ronaldomb98}
\cvfacebook{ronaldo.mojica.12}
\cvnumberphone{(+57) 311 236 6178} % Phone number
\cvphone{(8) 269 6764} % Phone number
\cvsite{} % Personal website
\cvmail{ronaldomb98@gmail.com} % Email address

%----------------------------------------------------------------------------------------

\begin{document}

%-------------------------- Personal Info ---------------------------------------
\makepersonalinfo
\begin{center}
\section{DATOS PERSONALES}
%\huge{\textbf{DATOS PERSONALES}}
\end{center}
\noindent\rule{1\textwidth}{1.4pt}

  \begin{center}

        \LeftBox{NOMBRES}{BRAYAN RONALDO}  \\
        \LeftBox{APELLIDOS}{MOJICA BARRIOS}       \\
        \LeftBox{FECHA DE NACIMIENTO}{MAYO 12 DE 1998}     \\
        \LeftBox{LUGAR DE NACIMIENTO}{IBAGUÉ - TOLIMA}  \\
        \LeftBox{EDAD}{19 AÑOS}  \\
        \LeftBox{CÉDULA}{1.110.590.392 DE IBAGUÉ}  \\
        \LeftBox{ESTADO CIVIL}{SOLTERO}  \\
        \LeftBox{DIRECCIÓN DE RESIDENCIA}{SMZ 5 MZ 3 CASA 16, BARRIO TUNJOS 1}  \\
        \LeftBox{TELEFONO FIJO}{2696764}  \\
        \LeftBox{CELULAR}{3112366178}  \\
        \LeftBox{CORREO ELECTRÓNICO}{ronaldomb98@gmail.com}  \\
        \LeftBox{NOMBRE DEL PADRE}{EFREY MOJICA CANIZALES}  \\
        \LeftBox{NOMBRE DE LA MADRE}{DORIS NIDYA BARRIOS HERNANDEZ}  \\
  \end{center}

%\begin{center}
%  \huge{\textbf{FORMACIÓN ACADÉMICA}}
%\end{center}

\begin{center}
\vspace{2cm}
\section{FORMACIÓN ACADÉMICA}
%\huge{\textbf{DATOS PERSONALES}}
\end{center}
\noindent\rule{1\textwidth}{1.4pt}

% Primaria ----------------------------------------
\subsection{EDUCACIÓN BÁSICA PRIMARIA}
\begin{center}
  \LeftBox{COLEGIO}{JOSÉ JOAQUÍN FLOREZ HERNÁNDEZ}  \\
  \LeftBox{FECHA DE GRADUACIÓN}{25 DE NOVIEMBRE DEL 2008}       \\
\end{center}
\vspace{.5cm}
% Secundaria ----------------------------------------
\subsection{EDUCACIÓN BÁSICA SECUNDARIA Y MEDIA}
\begin{center}
  \LeftBox{COLEGIO}{ESCUELA NORMAL SUPERIOR DE IBAGUÉ}  \\
  \LeftBox{TITULO OBTENIDO}{BACHILLER ACADÉMICO CON}  \\
  \LeftBoxWthoutSep{}{PROFUNDIZACIÓN EN EDUCACIÓN}  \\
  \LeftBox{FECHA DE GRADUACIÓN}{25 DE NOVIEMBRE DEL 2008}       \\
\end{center}
\vspace{.5cm}
% Universidad ----------------------------------------
\subsection{ESTUDIOS SUPERIORES}
\textbf{\normalsize{TECNOLOGÍA}}
\begin{center}
  \LeftBox{INSTITUCIÓN}{UNIVERSIDAD DEL TOLIMA}  \\
  \LeftBox{TITULO OBTENIDO}{TECNOLOGÍA EN GESTIÓN}  \\
  \LeftBoxWthoutSep{}{DE BASES DE DATOS}  \\
  \LeftBox{FECHA DE GRADUACIÓN}{3 DE AGOSTO DEL 2017}       \\
\end{center}
\textbf{\normalsize{INGENIERÍA}}
\begin{center}
  \LeftBox{INSTITUCIÓN}{UNIVERSIDAD DEL TOLIMA}  \\
  \LeftBox{PROGRAMA ACADÉMICO}{INGENIERÍA DE SISTEMAS}  \\
  \LeftBox{ESTADO}{EN CURSO}       \\
\end{center}
\vspace{.5cm}
\begin{flushleft}
\textbf{NOTA:} ACTUALMENTE ESTOY CURSANDO SÉPTIMO SEMESTRE DEL PROGRAMA ACADÉMICO.
\end{flushleft}

\newpage
\makeabilities % Print the sidebar
% Secundaria ----------------------------------------
\subsection{TALLERES Y CURSOS}
\begin{twenty} % Environment for a list with descriptions
	\twentyitem
    	{2016}
        {TALLER}
        {DISEÑAR UNA APLICACIÓN WEB DE SOPORTE QR PARA DAR INFORMACIÓN NUTRICIONAL DE LAS PRINCIPALES FRUTAS CULTIVADAS EN IBAGUÉ}
        {
        	\href
        		{http://www.sena.edu.co/es-co/Paginas/default.aspx}
        		{Universidad del Tolima, Colombia}}
        {}
        {Expositor del proyecto en el iv foro de investigación formativa, efectuado el dia sábado 31 de octubre de 2015, organizado por el programa de ingeniería de sistemas de la universidad del tolima.\\}
	\twentyitem
    	{2017}
        {CURSO}
        {DESARROLLO DE APLICACIONES WEB CON PHP}
        {
        	\href
        		{http://www.sena.edu.co/es-co/Paginas/default.aspx}
        		{SENA, Colombia}}
        {}
        {Se trabajó con el Framework Laravel\\}
	\twentyitem
    	{2017}
		{CURSO}
        {DESARROLLO DE APLICACIONES WEB \\UTILIZANDO API’S DE HTML5 }
        {
        	\href
        		{http://www.sena.edu.co/es-co/Paginas/default.aspx}
        		{SENA, Colombia}}
        {}
        {HTML5 - CSS3}
	\twentyitem
    	{2017}
        {CURSO}
        {DISEÑO DE SITIOS WEB}
        {
        	\href
        		{http://www.sena.edu.co/es-co/Paginas/default.aspx}
        		{SENA, Colombia}}
        {}
        {HTML5 - CSS3\\}
	%\twentyitem{<dates>}{<title>}{<organization>}{<location>}{<description>}
\end{twenty}
\vspace{.5cm}
\subsection{OTROS}
\begin{twenty} % Environment for a list with descriptions
	\twentyitem
    	{2015 - 2016}
        {}
        {INGLÉS}
        {
        	\href
        	{http://www.sena.edu.co/es-co/Paginas/default.aspx}
        	{Universidad Del Tolima, Colombia}
       	}
        {}
        {Cursé y Aprové 7 niveles de Ingles}
	%\twentyitem{<dates>}{<title>}{<organization>}{<location>}{<description>}
\end{twenty}
%----------------------------------------------------------------------------------------
%	 EXPERIENCE
%----------------------------------------------------------------------------------------
\begin{center}
\vspace{2cm}
\section{EXPERIENCIA}
\end{center}
\noindent\rule{1\textwidth}{1.4pt}

\begin{twenty} % Environment for a list with descriptions
\twentyitem
    	{Enero 2016}
		{Julio 2016}
        {Desarrollador Fullstack}
        {Planeación y desarrollo}
        {
        \begin{center}
  			\LeftBox{JEFE INMEDIATO}{David Carvajal Bonilla}       \\
  			\LeftBox{TELEFONO}{+1 - 514 292 9371 de Canadá}       \\
		\end{center}
        \vspace{.5cm}
        A continuación, hago mención de los proyectos:
        }
        {\begin{itemize}
        \item {
        	\textbf{GanaGana App} - Desarrollo de una aplicación movil híbrida. Herramientas principales:
        	\begin{itemize}
        		\item ANGULAR 2
        		\item IONIC 2
        		\item FIREBASE
        	\end{itemize}
        }
        \item {
        	\textbf{4Home} - Desarrollo de una \textit{single page application}. Herramientas principales:
        	\begin{itemize}
        		\item ANGULAR 2
        		\item FIREBASE
        	\end{itemize}
        } \begin{flushleft}
\vspace{.5cm}
\textbf{NOTA:} Es importante recalcar que el control de versiones de ambos proyectos se llevaron a cabo con git.
\end{flushleft}
        \end{itemize}}

        \\

	%\twentyitem{<dates>}{<title>}{<location>}{<description>}
\end{twenty}
\vspace{.5cm}

\newpage
\makesidebarcommon % Print the sidebar
%----------------------------------------------------------------------------------------
%	 REF. PERSONALES
%----------------------------------------------------------------------------------------
\begin{center}
\section{REFERENCIAS PERSONALES}
\end{center}
\noindent\rule{1\textwidth}{1.4pt}
\subsection{PRIMERA REFERENCIA}
\begin{center}
  \LeftBox{NOMBRES Y APELLIDOS}{MAURICIO LOZANO MONROY}  \\
  \LeftBox{CÉDULA}{93369808}       \\
  \LeftBox{PROFESIÓN}{ESPECIALISTA EN ADMINISTRACIÓN}       \\
  \LeftBoxWthoutSep{}{DE LA
SEGURIDAD}  \\
  \LeftBox{OCUPACIÓN}{GERENTE DE SEGURIDAD}       \\
  \LeftBox{TELEFONO}{3217997863}       \\
\end{center}
\subsection{SEGUNDA REFERENCIA}
\begin{center}
  \LeftBox{NOMBRES Y APELLIDOS}{DAVID CARVAJAL BONILLA}  \\
  \LeftBox{CÉDULA}{1110479192}       \\
  \LeftBox{PROFESIÓN}{INGENIERO EN SISTEMAS}       \\
  \LeftBox{OCUPACIÓN}{DESARROLLADOR}       \\
  \LeftBox{TELEFONO}{3004340472}       \\
\end{center}

\subsection{TERCERA REFERENCIA}
\begin{center}
  \LeftBox{NOMBRES Y APELLIDOS}{HENRY GIOVANNY GONZALEZ WALTERO}  \\
  \LeftBox{CÉDULA}{1110517520}       \\
  \LeftBox{PROFESIÓN}{INGENIERO EN SISTEMAS}       \\
  \LeftBox{OCUPACIÓN}{INSTRUCTOR SENA}       \\
  \LeftBox{TELEFONO}{3162456035}       \\
\end{center}
%----------------------------------------------------------------------------------------
%	 REF. FAMILIARES
%----------------------------------------------------------------------------------------
\vspace{2cm}
\begin{center}
\section{REFERENCIAS FAMILIARES}
\end{center}
\noindent\rule{1\textwidth}{1.4pt}
\subsection{PRIMERA REFERENCIA}
\begin{center}
  \LeftBox{NOMBRES Y APELLIDOS}{EFREY MOJICA CANIZALES}  \\
  \LeftBox{CÉDULA}{93356869 DE IBAGUÉ}       \\
  \LeftBox{OCUPACIÓN}{SUPERVISOR DE ALMACEN}       \\
  \LeftBox{TELEFONO}{3177647531}       \\
  \LeftBox{PARENTESCO}{PADRE}       \\
\end{center}
\subsection{SEGUNDA REFERENCIA}
\begin{center}
  \LeftBox{NOMBRES Y APELLIDOS}{DORIS NIDYA BARRIOS HERNANDEZ}  \\
  \LeftBox{CÉDULA}{52112053 DE BOGOTÁ}       \\
  \LeftBox{OCUPACIÓN}{AMA DE CASA}       \\
  \LeftBox{TELEFONO}{2696764}       \\
  \LeftBox{PARENTESCO}{MADRE}       \\
\end{center}

\subsection{TERCERA REFERENCIA}
\begin{center}
  \LeftBox{NOMBRES Y APELLIDOS}{FREDY FABIAN MOJICA BARRIOS}  \\
  \LeftBox{CÉDULA}{1110590392}       \\
  \LeftBox{OCUPACIÓN}{DOCENTE MAGISTER}       \\
  \LeftBox{TELEFONO}{3214139992}       \\
  \LeftBox{PARENTESCO}{HERMANO}       \\
\end{center}
\newpage
\makesidebarcommon % Print the sidebar
%----------------------------------------------------------------------------------------
%	 ANEXOS
%----------------------------------------------------------------------------------------
\begin{center}
\section{ANEXOS}
\end{center}
\noindent\rule{1\textwidth}{1.4pt}
\includegraphics[width=\textwidth]{img/diplomatecnologo.jpg}
\newpage
\makesidebarcommon
\includegraphics[width=\textwidth]{img/actadegradotecnologo.jpg}
\newpage
\makesidebarcommon
\includegraphics[width=\textwidth]{img/diseñositiosweb.jpg}
\includegraphics[width=\textwidth]{img/laravel.jpg}
\newpage
\makesidebarcommon
\includegraphics[width=\textwidth]{img/appwebhtml5.jpg}
\vspace{2cm}
\includegraphics[width=\textwidth]{img/libretamil.png}
\newpage
%----------------------------------------------------------------------------------------
%	 PORTAFOLIO
%----------------------------------------------------------------------------------------
\makesidebarcommon
\begin{center}
\section{PORTAFOLIO}
\end{center}
\noindent\rule{1\textwidth}{1.4pt}
\subsection{4Home}
\begin{flushleft}
El objetivo del sistema de información es permitirle al usuario hacer reserva del servicio de profesional de oficios domésticos a través de la aplicación web. Por otro lado, un sistema de para el administrador que le permitiera re-asignar reservas, y brindar bonos de descuento para los pagos que se efectuarán con PayU.
\end{flushleft}
\begin{center}
\includegraphics[width=.9\textwidth]{img/4home1.png}
\end{center}
\vspace{1cm}
\begin{center}
\includegraphics[width=.9\textwidth]{img/4home2.png}
\end{center}

\newpage
\makesidebarcommon % Print the sidebar
\begin{center}
\includegraphics[width=.9\textwidth]{img/4home3.png}
\end{center}

\newpage
\makesidebarcommon % Print the sidebar
\subsection{GanaGana App}
\begin{flushleft}
La aplicación cuenta con las siguientes características
\begin{itemize}
\item Un sistema de autenticación y almacenamiento de información en firebase
\item Primera interfaz de usuario con accesos rápidos, sidebar, slides publicitarios.
\end{itemize}
\end{flushleft}
\begin{center}
\includegraphics[width=.3\textwidth]{img/ganagana1.png}
\includegraphics[width=.3\textwidth]{img/ganagana2.png}
\end{center}
\vspace{1cm}
\begin{itemize}
\item Juego de arma parejas para entretención y publicidad
\item Kit de la suerte que consistía en recorrer toda la ciudad en busca de códigos QR, esto a fin de premiar a quien consiguiera todos.
\end{itemize}
\begin{center}
\includegraphics[width=.3\textwidth]{img/ganagana3.png}
\includegraphics[width=.3\textwidth]{img/ganagana4.png}
\includegraphics[width=.3\textwidth]{img/ganagana5.png}
\end{center}
\newpage
\makesidebarcommon % Print the sidebar
\begin{itemize}
\item Portafolio de servicios que brinda la empresa.
\item Generador de numero de la suerte
\item Simulador de Giros
\end{itemize}
\begin{center}
\includegraphics[width=.3\textwidth]{img/ganagana6.png}
\includegraphics[width=.3\textwidth]{img/ganagana7.png}
\end{center}
\end{document}


text:
\chapter{New Beerpint Book}

IT'S ALWAYS AN exciting moment when Dennis Beerpint publishes a new opus. The poet of the beatnik and the twee has a new book out next week, and what a very fat book it is! Those of you expecting a magisterial collection of epic Beerpintian versifying are likely to be disappointed, however. There is but a single poem nestled within its six hundred pages, and it is a very short poem. One might even call it gnomic. The rest of the book is given over to what Beerpint's long-suffering publishers dub 'hefty apparatus'. This sounds like something you might find in a well-appointed gymnasium, but is in fact a collection of what we literary types prefer to call 'weird hot-headed ravings from Dennis Beerpint'.

There is an 'introductory essay', of over two hundred pages, which is neither introductory of anything nor, really, an essay as such. If one were to be kind, one might say it was an example of surrealist 'automatic writing'. If one were to be unkind, but honest, one would say it resembles the disjointed drivellings of an untethered brain gone to seed. This farrago of nonsense is accompanied by so many footnotes that, taken together, they are longer than the 'essay' itself. If we are to believe the preface (forty-nine pages in total), the footnotes were penned not by the poet, but by his all-too-real Doppelg\"{a}nger, a sort of shadow Beerpint who dogs his every step, like the familiar in the story by J Sheridan Le Fanu.

Now listen. I have been following Dennis Beerpint's career from its foetal stages, and this is the first I have heard tell of a Doppelg\"{a}nger. I am assuming the poet is not referring to one of those fanatical acolytes who express their devotion by dressing like him, adopting the same hairstyles, eating and drinking an identical diet, and languishing upon municipal park benches clutching one of his flimsy poetry pamphlets to their bosoms, pretending to be morbidly ill. It pains me to say it, but I used to be one of their number. My bench was situated near the duckpond in the park, and I feigned tuberculosis. The point is that we were akin to the bodyguards employed by the film director George Lucas, who all look alarmingly like him, but we never pretended to \emph{be} him, and we would certainly never have threatened Beerpint's immortal, and poetic, soul. Yet these are the charges laid at the Doppelg\"{a}nger's door in the preface, and, indeed, by its own admission, in those interminable and frankly ill-written footnotes.

I have actually read the footnotes, in my review copy, with the aid of a magnifying glass. They are printed in very, very tiny type, in a font called Uber-Ornate Near-Illegible High German Blunkett Gothic. I have needed daily eye-drops ever since, and spend much of my time lying down in a darkened room. All I am willing to say is that the footnotes, far from casting any light on the imbecilic ravings of Beerpint's essay, are themselves bereft of any sense whatsoever. It is like reading the prose of the more impenetrable Gallic postmodernists while being repeatedly beaten about the ears with a farmer's shovel - an experience, by the way, I have undergone on more than one occasion, after accepting an offer to write a critique of Lacan or Derrida or one of those old frauds for the weekly magazine \emph{Farmers With Shovels Consider The Left Bank Intellectual Ferment}. Despite my suffering, I recommend this publication, a sort of \emph{Reader's Digest} for the shovelling farmers community, and one which contains in each issue a goodly number of illustrations by the noted hyperrealist linocutter Rex Hyper.

But we are getting away from Beerpint, which will never do. In addition to the preface and the introductory essay with its voluminous footnotes, there is a lengthy section entitled 'Mental Pudding'. I have read this half a dozen times and still have no idea what it is meant to be about, or what connection it has to the poem. Then there is a bibliography, supposedly of books consulted by the poet during the writing of his new work. This actually has some interest, giving us a valuable insight into Beerpint's preoccupations and influences. He has read widely, if haphazardly, in almost as many languages as Anthony Burgess could babble in. No doubt the preposterous Mancunian polymath will be rolling in his grave that not a single one of his works appears in this bibliography. But Ayn Rand is there (\emph{Why I Like Stamp Collecting}), and Pebblehead, and Robert Ludlum, and Dick Van Dyke (\emph{Faith, Hope and Hilarity: A Child's Eye View of Religion}). Beerpint seems also to know his onions when it comes to books about onions, birdseed, the Boxer Rising, lobsters, Futurist boy scouts, dirigibles and hot air balloons, fish entrails, Ruby and Oswald, the Scharnhorst, inexplicable flapping noises, the life and death of Karen Carpenter, bobsleigh, flumes, pigeons, gutta percha, tectonic plates, anteaters, William Betty 'the Young Roscius', tarpaulin, the Symmesian Hollow Earth Theory, gloves, infections of the pituitary gland, Bird's custard (but, oddly, no other custard), greenfly, hobnails, spiders, vinegar, Chumpot patent soap, the 1648 Peace of Westphalia, various paps and slops and gruels, gaslight, heists, H L Mencken, fruit, pips, sledgehammer wit, the Cottingley Fairies, other fairies, non-fairy life-forms, Geoff Hurst, Belshazzar's Feast, oil rigs, Shoeburyness, herons, space travel, chrestomathies, car jacking, toilet tissue, bales of hay, bales of straw, bales, bales, Baxter's Invigorating Fluid, and other bales.

It is important to acknowledge the breadth of knowledge Beerpint is bringing to the table, as it were, when one reads the poem. In the past, he has been accused - not least by me - of treating his readers with contempt and knocking out verses willy nilly, without care or thought, or even a proper pencil. I was particularly harsh in my review of his collection \emph{The Assassination Of Andrew Motion}, which I described as 'vindictive, contemptuous, and written without care or thought or even a proper pencil'. Beerpint has not spoken to me since, but I retain my superbly aloof critical detachment, and can therefore, with a foppish wave of my hand, announce, with due objectivity, that in spite of the ridiculous 'apparatus' with which this new book is padded out, the poem itself is a masterpiece. Indeed, I would go so far as to say that it guarantees his place in the pantheon, for all time. I am so damned impressed with it that I am going to thumb my nose at the copyright laws and publish the poem here. That will save you from having to buy the book, and if as a result Beerpint or his publishers get upset then I am perfectly willing to meet them in a field, at dawn, with pistols.

So here it is then, the new poem from Dennis Beerpint, in its entirety:

\begin{verse}
\begin{emph}
Where oh where

Is the troglodyte Voltaire?
\end{emph}
\end{verse}

domain: tex


text:
\def\qtr{Summer 2020}
\def\due{Monday, August 10 at 11:59 pm}
\def\latedue{Thursday, May 13 at 11:59 pm}
\def\piazza{\url{ https://piazza.com/stanford/summer2020/cs229}}
\def\psetnum{3 }

%%% Change the following flag to toggle between questions or solutions
\ifdefined\solutions {} \else \def\solutions{1} \fi

\input{macros.tex}

\def\shownotes{1}  %set 1 to show author notes
\ifnum\shownotes=1
\newcommand{\authnote}[2]{[#1: #2]}
\else
\newcommand{\authnote}[2]{}
\fi

\newcommand{\tnote}[1]{{\color{blue}\authnote{TM}{#1}}}
\newcommand{\fk}[1]{{\color{purple}{[FK:#1]}}}
\newcommand{\notes}[1]{{\color{blue} Note:} \textit{#1} \newline}

\usepackage{dsfont}

\begin{document}

\pagestyle{myheadings} \markboth{}{CS229 Problem Set \#\psetnum}

\ifnum\solutions=1{
{\huge\noindent CS 229, \qtr\\
Problem Set \#\psetnum Solutions}\\\\
YOUR NAME HERE (\texttt{YOUR SUNET HERE})
} \else {\huge
\noindent CS 229, \qtr\\
Problem Set \#\psetnum
} \fi

\ruleskip

{\bf Due {\due } on Gradescope.}

\medskip

\input{00-instructions/00-main}

\begin{enumerate}[wide, labelwidth=!, labelindent=0pt]

\clearpage
\input{cartpole/00-main}

\clearpage
\input{kl_divergence/00-main}

\clearpage
\input{k_means/00-main}

\clearpage
\input{semi_supervised_em/00-main}

\clearpage
\input{pca/00-main}

\clearpage
\input{ica/00-main}

\end{enumerate}

\end{document}


text:
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{listings}
\newcommand\tab[1][0.5cm]{\hspace*{#1}}

\title{E04 - ANN}
\author{Vinicius Gasparini}
\date{17 de Setembro de 2019}

\begin{document}

\maketitle

\section{Jacobi - Implementação}
\begin{lstlisting}[frame=single]
from pprint import pprint
from numpy import array, diag, diagflat, dot, linalg

def jacobi(A,b,N,x):
    D_ = diagflat(diag(A))
    L_U  = A - D_
    D_ = linalg.inv(D_)

    for i in range(N-1):
        x = dot(dot(-D_,L_U) , x)+dot(D_,b)
        print('X(%d) = '%(i+1),end='')
        print(x)
    return x

A = array([ [ 7.6 ,-0.2 ,-0.6 , 2   ,-1.3 , 1.2 , 2.3 ],
            [-2.4 , 18  ,-0.9 , 2.7 , 2.1 ,-2   , 0.4],
            [ 0.3 , 0.9 ,16.8 ,-1.9 , 1.3 , 2.2 ,-1.5],
            [-2   ,-1.2 , 2.4 ,11.8 ,-1.6 ,-1.6 ,-1.1],
            [-1.8 ,-2.5 , 2.4 ,-1.4 ,13.1 , 1.7 ,-2.7],
            [-2.2 , 1.8 , 1.9 ,-0.6 ,-0.1 , 10  , 1.3],
            [-1.5 ,-2   , 2.5 , 1.8 , 0.7 , 1.2 , 12.1]])

b = array([-0.8,-1.6,-4.6,0.8,0.8,4.6,4.0])
chute = array([-4.9,1.8,3.8,-2.8,-2.6,0.2,-2])

sol = jacobi(A,b,N=10,x=chute)
\end{lstlisting}
\newpage
\section{Resposta}
\begin{lstlisting}[frame=single]
A: array([[ 7.6, -0.2, -0.6,  2. , -1.3,  1.2,  2.3],
       [-2.4, 18. , -0.9,  2.7,  2.1, -2. ,  0.4],
       [ 0.3,  0.9, 16.8, -1.9,  1.3,  2.2, -1.5],
       [-2. , -1.2,  2.4, 11.8, -1.6, -1.6, -1.1],
       [-1.8, -2.5,  2.4, -1.4, 13.1,  1.7, -2.7],
       [-2.2,  1.8,  1.9, -0.6, -0.1, 10. ,  1.3],
       [-1.5, -2. ,  2.5,  1.8,  0.7,  1.2, 12.1]])

b: [-0.8 -1.6 -4.6  0.8  0.8  4.6  4. ]

x: [-0.30957065 -0.13108813 -0.28340396
    0.15146424  0.05709781  0.44505971
    0.25836421]
\end{lstlisting}
Pontando, a resposta correta é o \textit{\textbf{item c}}
\end{document}


text:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                   Einstellungen
%
% Hier können alle relevanten Einstellungen für diese Arbeit gesetzt werden.
% Dazu gehören Angaben u.a. über den Autor sowie Formatierungen.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Angaben  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Die meisten der folgenden Daten werden auf dem
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%% des Dokuments.
\setzemartrikelnr{4815162342}
\setzekurs{TINF13B3}
\setzetitel{Autonome Navigation (im Indoor-Bereich) der selbstbalancierenden Plattform RobStep}
\setzedatumAbgabe{Mai 2016}
\setzefirma{Firma GmbH}
\setzefirmenort{Firmenort}
\setzeabgabeort{Karlsruhe}
\setzeabschluss{Bachelor of Engineering}
\setzestudiengang{Informationstechnik}
\setzedhbw{Karlsruhe}
\setzebetreuer{Prof. Dr. Markus Strand}
\setzegutachter{-}
\setzezeitraum{5tes \& 6tes Semester}
\setzearbeit{Studienarbeit}
\setzeautor{Philip Hug \& Simon Simon}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%% Literaturverzeichnis %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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text:
\documentclass[oneside,10pt,A4]{scrartcl}

%%% Load packages
%\usepackage{amsthm,amsmath}
%\RequirePackage{natbib}
%\RequirePackage[authoryear]{natbib}% uncomment this for author-year bibliography
\RequirePackage{hyperref}
\usepackage[utf8]{inputenc} %unicode support
%\usepackage[applemac]{inputenc} %applemac support if unicode package fails
%\usepackage[latin1]{inputenc} %UNIX support if unicode package fails
\usepackage{graphicx}

\usepackage{tabularx}
\usepackage{booktabs}

\usepackage[noabbrev]{cleveref}
\usepackage{siunitx}
\DeclareSIUnit \basepair{bp}
\DeclareSIUnit \byte{B}
\DeclareSIPrefix\mebi{Mi}{10}
\DeclareSIPrefix\gibi{Gi}{10}

\input{biocon-stuff.tex}
\input{docker-stuff.tex}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                                             %%
%%  If you wish to display your graphics for   %%
%%  your own use using includegraphic or       %%
%%  includegraphics, then comment out the      %%
%%  following two lines of code.               %%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\def\includegraphic{}
%\def\includegraphics{}

\usepackage{todonotes}
\setlength{\marginparwidth}{3cm}

\newcounter{todocounter}
\newcommand{\ff}[1]
{\stepcounter{todocounter}
 \todo[color=blue!40,author=For Frank]{\thetodocounter: #1}
 }
\newcommand{\ak}[1]
{\stepcounter{todocounter}
 \todo[color=green!40,author=Arthur]{\thetodocounter: #1}
 }

%%% Put your definitions there:
\newcommand{\formatprogramnames}[1]{\texttt{#1}}
\newcommand{\ce}{\formatprogramnames{chloroExtractor}}
\newcommand{\oa}{\formatprogramnames{ORG.Asm}}
\newcommand{\fp}{\formatprogramnames{Fast-Plast}}
\newcommand{\ioga}{\formatprogramnames{IOGA}}
\newcommand{\np}{\formatprogramnames{NOVOPlasty}}
\newcommand{\go}{\formatprogramnames{GetOrganelle}}
\newcommand{\cassp}{\formatprogramnames{Chloroplast assembly protocol}}

\newcommand{\zenododataset}{\cite{zenododataset}}
\newcommand{\zenodorepo}{\cite{zenodorepo}}

\newcommand{\genename}[1]{\textit{#1}}

% Niklas table
%\newcommand{\ok}{\textcolor[rgb]{0.7,0.7,0}{\textsc{\bfseries{}OKAY}}}
%\newcommand{\bad}{\textcolor{red}{\textsc{\bfseries{}BAD}}}
%\newcommand{\good}{\textcolor[rgb]{0,0.6,0}{\textsc{\bfseries{}GOOD}}}
\newcommand{\ok}{\textsc{Okay}}
\newcommand{\bad}{\textsc{Bad}}
\newcommand{\good}{\textsc{Good}}

\usepackage{longtable}
\usepackage{pdflscape}
\usepackage{capt-of}

\renewcommand{\thetable}{S\arabic{table}}%
\renewcommand{\thefigure}{S\arabic{figure}}
%%% Begin ...
\begin{document}

\title{A systematic comparison of  chloroplast genome assembly tools}
\subtitle{Supplemental material}
\author{\parbox{\textwidth}{\centering{}Jan A Freudenthal, Simon Pfaff, Niklas Terhoeven, Arthur Korte, Markus J Ankenbrand and Frank Förster}}
\date{}
\maketitle
\listoftables

\begin{landscape}
\setlength{\LTcapwidth}{1.5\textwidth}
\begin{table}[ht]
\caption{Sequencing Read Archive and Genbank accessions for novel chloroplast genomes}
\label{tab:accessions_suppl}
\centering
\begin{tabular}{lcccc}\toprule
Species & SRA-Accession & Assembler & Uses & Genbank-Accession \\\midrule
\emph{Antirrhinum majus \emph{subsp.} Striatum} & ERR2744402 & \go{} & ornamental plant & - \\
\emph{Antirrhinum majus \emph{var.} pseudomajus} & ERR2744401 & \go{} & ornamental plant & - \\
\emph{Arachis magna} & SRR8481359 & \go{} & - & - \\
\emph{Boechera stricta} & SRR6821984 & \np{} & - & - \\
\emph{Buddleja globosa} & SRR6331521 & \go{} & folk medicine & - \\
\emph{Congea tomentosa} & SRR6940055 & \go{} & - & - \\
\emph{Cucurbita argyrosperma} & SRR2531270 & \go{} & crop plant & - \\
\emph{Cucurbita ecuadorensis} & SRR2531278 & \go{} & - & - \\
\emph{Cucurbita lundelliana} & SRR2531284 & \go{} & - & - \\
\emph{Cucurbita okeechobeensis} & SRR2531280 & \go{} & - & - \\
\emph{Cucurbita pedatifolia} & SRR2531289 & \go{} & - & - \\
\emph{Cuscuta campestris} & ERR1917165 & \go{} & - & - \\
\emph{Erysimum baeticum} & SRR7223704 & \go{} & - & - \\
\emph{Erysimum nevadense} & SRR7223710 & \go{} & - & - \\
\emph{Garrya flavescens} & SRR2401791 & \go{} & - & - \\
\emph{Gerbera hybrid cultivar} & SRR2154064 & \go{} & - & -\\
\emph{Leucanthemum vulgare} & ERR3089127 & \go{} & ornamental plant & - \\
\emph{Petraeovitex bambusetorum} & SRR6940081 & \go{} & - & - \\
\emph{Pityopsis graminifolia \emph{var.} Graminifolia} & SRR4457826 & \go{} & ornamental plant & - \\
\emph{Pityopsis graminifolia \emph{var.} tenuifolia} & SRR4457835 & \go{} & ornamental plant & - \\
\bottomrule
\end{tabular}
\end{table}
\end{landscape}

\begin{landscape}
\setlength{\LTcapwidth}{1.5\textwidth}
\begin{longtable}{cccrrcc}
\caption[Summary real data set]{\textbf{Summary real data set.} List of real data sets used during our benchmark study. The tables was sorted by species name. Additionally, the table contains the accession for the Sequencing Read Archive (SRA Acc) and the accession of the used reference (Ref Acc). Moreover, the original number of read pairs (read pairs), the overall number of sequenced nucleotides (base pairs), and the mean read length (read len.) is given. Finally, the last column contains the information, if that data set was used for the check of the consistency.}\label{tab:real_dataset_details} \\
\toprule
Taxon & SRA Acc & Ref Acc & read pairs & base pairs (bp) & read len. (bp) & Consistency check \\\midrule
\endfirsthead
\multicolumn{7}{c}{\tablename\ \thetable\ -- \textit{Continued from previous page}}\\[0.5em]
Taxon & SRA Acc & Ref Acc & read pairs & base pairs (bp) & read len. (bp) & Consistency check \\ \midrule
\endhead
\bottomrule
\multicolumn{7}{r}{Continued on next page}\\
\endfoot
\endlastfoot
\input{sra_ref.tex}
\end{longtable}

\newpage
{\tiny
\captionof{table}{Docker images used in our benchmark setup.}
\label{tab:dockerimages_suppl}
\centering
\begin{tabular}{ccc}
        \toprule
          Tool & Image name and tag & SHA256 Checksum   \\ \midrule
          \ce & \dockerce & \dockercesha \\
          \cassp & \dockercassp & \dockercasspsha \\
          \fp & \dockerfp & \dockerfpsha \\
          \go & \dockergo & \dockergosha \\
          \ioga & \dockerioga & \dockeriogasha \\
          \np & \dockernp & \dockernpsha \\
          \oa & \dockeroa & \dockeroasha \\ \bottomrule
      \end{tabular}
}
\end{landscape}

\begin{table}[ht]
\caption{Performance metrics input size 25K}
\label{tab:perform25K_suppl}
\centering
\begin{tabular}{rlrrrr}
  \toprule
 & program & threads & Peak CPU usage & Peak memory & Peak disk usage (GB) \\
  \midrule
1 & CAP &   1 & 113.32 & 0.31 & 0.06 \\
  2 & CAP &   2 & 166.60 & 0.26 & 0.05 \\
  3 & CAP &   4 & 305.99 & 0.26 & 0.05 \\
  4 & CAP &   8 & 569.12 & 0.37 & 0.06 \\
  5 & CE &   1 & 111.49 & 3.41 & 0.07 \\
  6 & CE &   2 & 199.12 & 3.41 & 0.07 \\
  7 & CE &   4 & 343.22 & 3.41 & 0.07 \\
  8 & CE &   8 & 509.51 & 3.41 & 0.07 \\
  9 & Fast-Plast &   1 & 118.31 & 0.77 & 0.30 \\
  10 & Fast-Plast &   2 & 213.57 & 0.77 & 0.31 \\
  11 & Fast-Plast &   4 & 379.27 & 0.77 & 0.32 \\
  12 & Fast-Plast &   8 & 657.20 & 0.77 & 0.35 \\
  13 & GetOrganelle &   1 & 111.39 & 0.38 & 0.05 \\
  14 & GetOrganelle &   2 & 170.30 & 0.32 & 0.05 \\
  15 & GetOrganelle &   4 & 242.27 & 0.31 & 0.06 \\
  16 & GetOrganelle &   8 & 346.98 & 0.31 & 0.07 \\
  17 & IOGA &   1 & 118.12 & 18.61 & 6.25 \\
  18 & IOGA &   2 & 224.74 & 17.88 & 6.26 \\
  19 & IOGA &   4 & 394.98 & 16.62 & 5.60 \\
  20 & IOGA &   8 & 733.11 & 21.76 & 11.13 \\
  21 & NOVOPlasty &   1 & 78.38 & 0.04 & 0.00 \\
  22 & NOVOPlasty &   2 & 86.64 & 0.04 & 0.00 \\
  23 & NOVOPlasty &   4 & 86.50 & 0.04 & 0.00 \\
  24 & NOVOPlasty &   8 & 87.32 & 0.04 & 0.00 \\
  25 & org.ASM &   1 & 112.08 & 0.79 & 0.03 \\
  26 & org.ASM &   2 & 115.44 & 0.79 & 0.03 \\
  27 & org.ASM &   4 & 105.09 & 0.79 & 0.03 \\
  28 & org.ASM &   8 & 105.78 & 0.79 & 0.03 \\
   \bottomrule
\end{tabular}
\end{table}

\begin{table}[ht]
\caption{Performance metrics input size 250K}
\label{tab:perform250K_suppl}
\centering
\begin{tabular}{rlrrrr}
  \toprule
 & program & threads & Peak CPU usage & Peak memory & Peak disk usage (GB) \\
  \midrule
1 & CAP &   1 & 114.38 & 0.90 & 0.65 \\
  2 & CAP &   2 & 204.39 & 0.93 & 0.65 \\
  3 & CAP &   4 & 337.09 & 0.97 & 0.65 \\
  4 & CAP &   8 & 652.75 & 1.08 & 0.65 \\
  5 & CE &   1 & 117.57 & 3.96 & 0.63 \\
  6 & CE &   2 & 230.35 & 3.96 & 0.63 \\
  7 & CE &   4 & 414.25 & 3.96 & 0.63 \\
  8 & CE &   8 & 755.76 & 3.97 & 0.63 \\
  9 & Fast-Plast &   1 & 118.81 & 1.40 & 0.78 \\
  10 & Fast-Plast &   2 & 234.12 & 2.25 & 0.78 \\
  11 & Fast-Plast &   4 & 425.89 & 2.32 & 0.79 \\
  12 & Fast-Plast &   8 & 845.94 & 2.52 & 0.79 \\
  13 & GetOrganelle &   1 & 117.94 & 1.07 & 0.40 \\
  14 & GetOrganelle &   2 & 227.05 & 1.13 & 0.40 \\
  15 & GetOrganelle &   4 & 403.35 & 1.08 & 0.40 \\
  16 & GetOrganelle &   8 & 747.20 & 1.03 & 0.39 \\
  17 & IOGA &   1 & 118.62 & 12.03 & 4.01 \\
  18 & IOGA &   2 & 234.09 & 9.71 & 4.01 \\
  19 & IOGA &   4 & 420.77 & 10.09 & 3.48 \\
  20 & IOGA &   8 & 842.57 & 19.21 & 9.45 \\
  21 & NOVOPlasty &   1 & 111.97 & 0.32 & 0.00 \\
  22 & NOVOPlasty &   2 & 115.07 & 0.32 & 0.00 \\
  23 & NOVOPlasty &   4 & 116.42 & 0.31 & 0.00 \\
  24 & NOVOPlasty &   8 & 115.86 & 0.31 & 0.00 \\
  25 & org.ASM &   1 & 118.10 & 0.93 & 0.06 \\
  26 & org.ASM &   2 & 161.76 & 0.93 & 0.06 \\
  27 & org.ASM &   4 & 163.01 & 0.93 & 0.06 \\
  28 & org.ASM &   8 & 160.74 & 0.93 & 0.06 \\
   \bottomrule
\end{tabular}
\end{table}

\begin{table}[ht]
\caption{Performance metrics input size 2.5M}
\label{tab:perform2.5M_suppl}
\centering
\begin{tabular}{rlrrrr}
  \toprule
 & program & threads & Peak CPU usage & Peak memory & Peak disk usage (GB) \\
 \midrule
1 & CAP &   1 & 118.80 & 6.83 & 6.59 \\
  2 & CAP &   2 & 209.22 & 7.58 & 6.59 \\
  3 & CAP &   4 & 357.36 & 7.25 & 6.59 \\
  4 & CAP &   8 & 683.71 & 6.99 & 6.59 \\
  5 & CE &   1 & 118.78 & 5.34 & 2.01 \\
  6 & CE &   2 & 234.82 & 5.34 & 2.01 \\
  7 & CE &   4 & 415.74 & 5.28 & 2.09 \\
  8 & CE &   8 & 844.95 & 5.34 & 2.01 \\
  9 & Fast-Plast &   1 & 119.24 & 6.80 & 5.80 \\
  10 & Fast-Plast &   2 & 237.34 & 6.98 & 5.82 \\
  11 & Fast-Plast &   4 & 443.27 & 8.02 & 5.69 \\
  12 & Fast-Plast &   8 & 872.07 & 8.87 & 5.69 \\
  13 & GetOrganelle &   1 & 118.91 & 5.25 & 3.31 \\
  14 & GetOrganelle &   2 & 235.18 & 5.26 & 3.31 \\
  15 & GetOrganelle &   4 & 420.10 & 5.44 & 3.31 \\
  16 & GetOrganelle &   8 & 845.13 & 6.07 & 3.31 \\
  17 & IOGA &   1 & 119.46 & 18.64 & 8.83 \\
  18 & IOGA &   2 & 237.22 & 21.24 & 10.19 \\
  19 & IOGA &   4 & 425.50 & 18.71 & 10.56 \\
  20 & IOGA &   8 & 857.29 & 25.23 & 16.51 \\
  21 & NOVOPlasty &   1 & 112.67 & 2.69 & 0.00 \\
  22 & NOVOPlasty &   2 & 117.77 & 2.58 & 0.00 \\
  23 & NOVOPlasty &   4 & 117.40 & 2.74 & 0.00 \\
  24 & NOVOPlasty &   8 & 117.28 & 2.74 & 0.00 \\
  25 & org.ASM &   1 & 118.73 & 2.63 & 0.37 \\
  26 & org.ASM &   2 & 184.53 & 2.63 & 0.37 \\
  27 & org.ASM &   4 & 177.03 & 2.63 & 0.37 \\
  28 & org.ASM &   8 & 176.25 & 2.63 & 0.37 \\
   \bottomrule
\end{tabular}
\end{table}

\begin{landscape}
\begin{longtable}{lcccp{7cm}c}
\caption[Novel data set]{\textbf{Novel data set.}}\label{tab:novels_supp} \\
  \toprule
 SRA Accession & Depth & TaxID & Rank & Related References with Depth & Status \\
 \midrule
\endfirsthead
\multicolumn{6}{c}{\tablename\ \thetable\ -- \textit{Continued from previous page}}\\[0.5em]
 SRA Accession & Depth & TaxID & Rank & Related References with Depth & Status \\
 \midrule
\endhead
\bottomrule
\multicolumn{6}{r}{Continued on next page}\\
\endfoot
\endlastfoot
DRR053713 & 3 & 71243 & order & NC\_033350(3) & success \\
DRR057122 & 3 & 3650 & family & NC\_007144(3) NC\_023544(3) NC\_029484(3) NC\_031834(3) NC\_032008(3) NC\_033899(3) NC\_015983(4) & success \\
DRR106816 & 5 & 2231393 & no rank & NC\_009259(5) NC\_013843(5) NC\_016708(5) NC\_018051(5) NC\_021091(5) NC\_023090(5) NC\_025909(5) NC\_027677(5) NC\_029406(5) NC\_031429(5) NC\_034742(5) NC\_034743(5) NC\_034774(5) NC\_002694(6) NC\_003119(6) NC\_007942(6) NC\_011163(6) NC\_011828(6) NC\_014057(6) NC\_014063(6) NC\_021636(6) NC\_021645(6) NC\_021646(6) NC\_021647(6) NC\_021648(6) NC\_021649(6) NC\_021650(6) NC\_022868(6) NC\_024034(6) NC\_024035(6) NC\_024036(6) NC\_024038(6) NC\_024166(6) NC\_025743(6) NC\_025744(6) NC\_025745(6) NC\_027073(6) NC\_027074(6) NC\_027075(6) NC\_027076(6) NC\_027077(6) NC\_027078(6) NC\_027079(6) NC\_027080(6) NC\_027148(6) NC\_027149(6) NC\_027150(6) NC\_027151(6) NC\_027152(6) NC\_027153(6) NC\_027154(6) NC\_027155(6) NC\_029828(6) NC\_030329(6) NC\_032066(6) NC\_032691(6) NC\_034229(6) NC\_035228(6) NC\_035229(6) NC\_028171(7) & success \\
ERR1917165 & 5 & 4118 & family & NC\_009808(3) NC\_026703(3) NC\_031159(3) NC\_034670(3) & success \\
ERR2003066 & 3 & 721789 & tribe & NC\_018767(3) NC\_019601(3) NC\_019602(3) NC\_034347(3) NC\_015206(4) NC\_018766(4) & success \\
ERR2744401 & 5 & 156152 & family & NC\_028519(3) NC\_028520(3) NC\_031345(3) NC\_034688(3) NC\_031153(4) NC\_031344(4) & success \\
ERR2744402 & 4 & 156152 & family & NC\_028519(3) NC\_028520(3) NC\_031345(3) NC\_034688(3) NC\_031153(4) NC\_031344(4) & success \\
ERR3089127 & 4 & 102810 & tribe & NC\_020092(3) NC\_020320(3) NC\_020607(3) NC\_025910(3) NC\_030785(3) NC\_031399(3) NC\_031400(3) NC\_034683(3) NC\_034851(3) & success \\
SRR2154064 & 4 & 4210 & family & NC\_027835(4) NC\_034648(4) NC\_007578(5) NC\_007977(5) NC\_010601(5) NC\_013553(5) NC\_015543(5) NC\_015621(5) NC\_020092(5) NC\_020320(5) NC\_020607(5) NC\_023107(5) NC\_023108(5) NC\_023109(5) NC\_023110(5) NC\_023111(5) NC\_023112(5) NC\_023113(5) NC\_023114(5) NC\_023833(5) NC\_024286(5) NC\_025910(5) NC\_027113(5) NC\_027434(5) NC\_028005(5) NC\_028006(5) NC\_028027(5) NC\_029465(5) NC\_030173(5) NC\_030275(5) NC\_030772(5) NC\_030773(5) NC\_030783(5) NC\_030785(5) NC\_031395(5) NC\_031396(5) NC\_031399(5) NC\_031400(5) NC\_031815(5) NC\_031816(5) NC\_031833(5) NC\_031853(5) NC\_031898(5) NC\_032056(5) NC\_032057(5) NC\_034320(5) NC\_034321(5) NC\_034322(5) NC\_034323(5) NC\_034324(5) NC\_034325(5) NC\_034326(5) NC\_034327(5) NC\_034328(5) NC\_034683(5) NC\_034810(5) NC\_034811(5) NC\_034812(5) NC\_034813(5) NC\_034814(5) NC\_034815(5) NC\_034816(5) NC\_034817(5) NC\_034818(5) NC\_034819(5) NC\_034820(5) NC\_034821(5) NC\_034822(5) NC\_034823(5) NC\_034824(5) NC\_034825(5) NC\_034827(5) NC\_034828(5) NC\_034829(5) NC\_034830(5) NC\_034831(5) NC\_034832(5) NC\_034847(5) NC\_034848(5) NC\_034849(5) NC\_034850(5) NC\_034851(5) NC\_034852(5) NC\_034853(5) NC\_034854(5) NC\_034856(5) NC\_034857(5) NC\_034858(5) NC\_034859(5) NC\_034860(5) NC\_034861(5) NC\_034862(5) NC\_034864(5) NC\_034865(5) NC\_034866(5) NC\_034867(5) NC\_034868(5) NC\_034869(5) NC\_034870(5) NC\_034871(5) NC\_034872(5) NC\_034873(5) NC\_034874(5) NC\_034875(5) NC\_034876(5) NC\_034877(5) NC\_034878(5) NC\_034879(5) NC\_034880(5) NC\_034881(5) NC\_034882(5) NC\_034883(5) NC\_034884(5) NC\_034885(5) NC\_034886(5) NC\_034887(5) NC\_034888(5) NC\_034889(5) NC\_034891(5) NC\_034892(5) NC\_034893(5) NC\_034894(5) NC\_034895(5) NC\_034896(5) NC\_034897(5) NC\_034898(5) NC\_034899(5) NC\_034900(5) NC\_034901(5) NC\_034902(5) NC\_034903(5) NC\_034996(5) & success \\
SRR2176133 & 3 & 40550 & order & NC\_026786(3) NC\_027659(3) & success \\
SRR2401791 & 4 & 91888 & no rank & NC\_016433(4) NC\_021449(4) NC\_023463(4) NC\_025652(4) NC\_025653(4) NC\_029719(4) NC\_030212(4) NC\_031435(4) NC\_031436(4) NC\_008407(5) NC\_009808(5) NC\_013707(5) NC\_020098(5) NC\_021111(5) NC\_022859(5) NC\_023102(5) NC\_023115(5) NC\_023131(5) NC\_023132(5) NC\_023464(5) NC\_023465(5) NC\_024845(5) NC\_025641(5) NC\_025642(5) NC\_025651(5) NC\_025787(5) NC\_026202(5) NC\_026291(5) NC\_026703(5) NC\_027262(5) NC\_027838(5) NC\_027955(5) NC\_028519(5) NC\_028520(5) NC\_028533(5) NC\_029700(5) NC\_031159(5) NC\_031345(5) NC\_031437(5) NC\_031441(5) NC\_031442(5) NC\_031443(5) NC\_031444(5) NC\_031445(5) NC\_033534(5) NC\_034308(5) NC\_034309(5) NC\_034310(5) NC\_034311(5) NC\_034312(5) NC\_034670(5) NC\_034688(5) NC\_034691(5) NC\_034693(5) NC\_034694(5) NC\_034695(5) NC\_035000(5) NC\_001879(6) NC\_004561(6) NC\_007500(6) NC\_007602(6) NC\_007943(6) NC\_008096(6) NC\_015401(6) NC\_015604(6) NC\_015608(6) NC\_015623(6) NC\_016068(6) NC\_018117(6) NC\_018552(6) NC\_022451(6) NC\_024261(6) NC\_024292(6) NC\_025657(6) NC\_026551(6) NC\_026563(6) NC\_026567(6) NC\_026570(6) NC\_026574(6) NC\_026694(6) NC\_026726(6) NC\_026906(6) NC\_027099(6) NC\_027177(6) NC\_027441(6) NC\_027442(6) NC\_028007(6) NC\_028009(6) NC\_028069(6) NC\_028070(6) NC\_028614(6) NC\_029370(6) NC\_029746(6) NC\_029817(6) NC\_029818(6) NC\_029819(6) NC\_029820(6) NC\_029821(6) NC\_029822(6) NC\_029823(6) NC\_029824(6) NC\_029825(6) NC\_029833(6) NC\_030044(6) NC\_030056(6) NC\_030167(6) NC\_030168(6) NC\_030171(6) NC\_030177(6) NC\_030178(6) NC\_030185(6) NC\_030207(6) NC\_030282(6) NC\_030319(6) NC\_030543(6) NC\_030755(6) NC\_030756(6) NC\_030757(6) NC\_031153(6) NC\_031155(6) NC\_031344(6) NC\_031433(6) NC\_031434(6) NC\_031805(6) NC\_031874(6) NC\_032054(6) NC\_032724(6) NC\_033354(6) NC\_033524(6) NC\_033525(6) NC\_033526(6) NC\_033527(6) NC\_034698(6) NC\_034951(6) NC\_035143(6) AC\_000188(7) NC\_007898(7) NC\_016468(7) NC\_020431(7) NC\_021423(7) NC\_022431(7) NC\_022432(7) NC\_025655(7) NC\_025656(7) NC\_025658(7) NC\_026876(7) NC\_026877(7) NC\_026878(7) NC\_026879(7) NC\_026880(7) NC\_026881(7) NC\_026882(7) NC\_027259(7) NC\_029459(7) NC\_029460(7) NC\_031852(7) NC\_034660(7) NC\_035233(7) NC\_008535(8) NC\_030053(8) & success \\
SRR2531270 & 3 & 3650 & family & NC\_007144(3) NC\_023544(3) NC\_029484(3) NC\_031834(3) NC\_032008(3) NC\_033899(3) NC\_015983(4) & success \\
SRR2531276 & 4 & 3650 & family & NC\_007144(3) NC\_023544(3) NC\_029484(3) NC\_031834(3) NC\_032008(3) NC\_033899(3) NC\_015983(4) & success \\
SRR2531278 & 3 & 3650 & family & NC\_007144(3) NC\_023544(3) NC\_029484(3) NC\_031834(3) NC\_032008(3) NC\_033899(3) NC\_015983(4) & success \\
SRR2531280 & 3 & 3650 & family & NC\_007144(3) NC\_023544(3) NC\_029484(3) NC\_031834(3) NC\_032008(3) NC\_033899(3) NC\_015983(4) & success \\
SRR2531284 & 3 & 3650 & family & NC\_007144(3) NC\_023544(3) NC\_029484(3) NC\_031834(3) NC\_032008(3) NC\_033899(3) NC\_015983(4) & success \\
SRR2531289 & 3 & 3650 & family & NC\_007144(3) NC\_023544(3) NC\_029484(3) NC\_031834(3) NC\_032008(3) NC\_033899(3) NC\_015983(4) & success \\
SRR4124062 & 7 & 2231393 & no rank & NC\_009259(5) NC\_013843(5) NC\_016708(5) NC\_018051(5) NC\_021091(5) NC\_023090(5) NC\_025909(5) NC\_027677(5) NC\_029406(5) NC\_031429(5) NC\_034742(5) NC\_034743(5) NC\_034774(5) NC\_002694(6) NC\_003119(6) NC\_007942(6) NC\_011163(6) NC\_011828(6) NC\_014057(6) NC\_014063(6) NC\_021636(6) NC\_021645(6) NC\_021646(6) NC\_021647(6) NC\_021648(6) NC\_021649(6) NC\_021650(6) NC\_022868(6) NC\_024034(6) NC\_024035(6) NC\_024036(6) NC\_024038(6) NC\_024166(6) NC\_025743(6) NC\_025744(6) NC\_025745(6) NC\_027073(6) NC\_027074(6) NC\_027075(6) NC\_027076(6) NC\_027077(6) NC\_027078(6) NC\_027079(6) NC\_027080(6) NC\_027148(6) NC\_027149(6) NC\_027150(6) NC\_027151(6) NC\_027152(6) NC\_027153(6) NC\_027154(6) NC\_027155(6) NC\_029828(6) NC\_030329(6) NC\_032066(6) NC\_032691(6) NC\_034229(6) NC\_035228(6) NC\_035229(6) NC\_028171(7) & success \\
SRR4124063 & 6 & 2231393 & no rank & NC\_009259(5) NC\_013843(5) NC\_016708(5) NC\_018051(5) NC\_021091(5) NC\_023090(5) NC\_025909(5) NC\_027677(5) NC\_029406(5) NC\_031429(5) NC\_034742(5) NC\_034743(5) NC\_034774(5) NC\_002694(6) NC\_003119(6) NC\_007942(6) NC\_011163(6) NC\_011828(6) NC\_014057(6) NC\_014063(6) NC\_021636(6) NC\_021645(6) NC\_021646(6) NC\_021647(6) NC\_021648(6) NC\_021649(6) NC\_021650(6) NC\_022868(6) NC\_024034(6) NC\_024035(6) NC\_024036(6) NC\_024038(6) NC\_024166(6) NC\_025743(6) NC\_025744(6) NC\_025745(6) NC\_027073(6) NC\_027074(6) NC\_027075(6) NC\_027076(6) NC\_027077(6) NC\_027078(6) NC\_027079(6) NC\_027080(6) NC\_027148(6) NC\_027149(6) NC\_027150(6) NC\_027151(6) NC\_027152(6) NC\_027153(6) NC\_027154(6) NC\_027155(6) NC\_029828(6) NC\_030329(6) NC\_032066(6) NC\_032691(6) NC\_034229(6) NC\_035228(6) NC\_035229(6) NC\_028171(7) & success \\


text:
Algorytm \textsc{ece} charakteryzuje się wysoką parametryzacją. Jednostkowy ekspozer opisywany jest przez jego głębię przestrzenną (liczbę cech użytych do jego konstrukcji), promień oddziaływania próbek oraz ziarno kwantyzacji. Dobór ekspozerów do budowy komitetu może być prowadzony na jeden z trzech sposobów:
	\begin{itemize}
		\item kosztowny czasowo przegląd zupełny,
		\item nie dająca gwarancji poprawnej selekcji, ale szybka metoda losowych podzbiorów z limitem, oraz
		\item kompromis w postaci heurystycznej metody z parametrem puli analizowanych ekspozerów oraz limitu członków końcowego komitetu.
	\end{itemize}

Dodatkowo zaimplementowano w nim pięć rodzajów wag, wpływających na udział pojedynczego ekspozera w klasyfikatorze. Zakładając, że każdy składowy ekspozer jest określony przez takie same parametry wewnętrzne (co jest jedynie najprostszą jego odmianą), w obrębie eksperymentu mamy aż pięć zmiennych do przebadania, co w wypadku danych wielowymiarowych jest bardzo czasochłonne i zużywa bardzo duże ilości zasobów.

W związku z tym, poniższe eksperymenty mają za zadanie określić, jak algorytm radzi sobie w warunkach ograniczonej parametryzacji. We wszystkich z nich została więc przyjęta metoda doboru klasyfikatorów do komitetu, oparta na losowych podzbiorach z limitem, a głosowanie odbywa się przy użyciu najprostszej metody, gdzie każdy klasyfikator bazowy ma taki sam wpływ na rezultat klasyfikacji. W oparciu o to założenie, zaproponowane zostały trzy eksperymenty:

\begin{itemize}
	\item Badanie wpływu na jakość klasyfikacji wartości promienia --- przy stałym ziarnie i limicie o wartości \verb|15|,
	\item Badanie wpływu na jakość klasyfikacji wartości ziarna --- przy stałym promieniu o wartości \verb|9|\% i limicie o wartości \verb|15|,
	\item Badanie wpływu na jakość klasyfikacji wartości limitu --- przy wartościach promienia i ziarna, które dały najlepsze rezultaty w poprzednich eksperymentach.
\end{itemize}


text:
\hypertarget{stm32f4xx__hal_8h}{}\section{Dynamixel-\/\+M\+X106/mbed/\+T\+A\+R\+G\+E\+T\+\_\+\+N\+U\+C\+L\+E\+O\+\_\+\+F446\+R\+E/stm32f4xx\+\_\+hal.h File Reference}
\label{stm32f4xx__hal_8h}\index{Dynamixel-\/\+M\+X106/mbed/\+T\+A\+R\+G\+E\+T\+\_\+\+N\+U\+C\+L\+E\+O\+\_\+\+F446\+R\+E/stm32f4xx\+\_\+hal.\+h@{Dynamixel-\/\+M\+X106/mbed/\+T\+A\+R\+G\+E\+T\+\_\+\+N\+U\+C\+L\+E\+O\+\_\+\+F446\+R\+E/stm32f4xx\+\_\+hal.\+h}}

This file contains all the functions prototypes for the H\+AL module driver.

{\ttfamily \#include \char`\"{}stm32f4xx\+\_\+hal\+\_\+conf.\+h\char`\"{}}\\*
\subsection*{Macros}
\begin{DoxyCompactItemize}
\item
\#define \hyperlink{group___h_a_l___exported___macros_ga4a466905a367266e7c23417248dc741d}{\+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M2}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M2\+\_\+\+S\+T\+OP))
\begin{DoxyCompactList}\small\item\em Freeze/\+Unfreeze Peripherals in Debug mode. \end{DoxyCompactList}\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M3}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M3\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M4}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M4\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M5}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M5\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M6}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M6\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M7}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M7\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M12}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M12\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M13}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M13\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M14}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M14\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+R\+TC}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+R\+T\+C\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+W\+W\+DG}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+W\+W\+D\+G\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+I\+W\+DG}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+I\+W\+D\+G\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+I2\+C1\+\_\+\+T\+I\+M\+E\+O\+UT}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+I2\+C1\+\_\+\+S\+M\+B\+U\+S\+\_\+\+T\+I\+M\+E\+O\+UT))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+I2\+C2\+\_\+\+T\+I\+M\+E\+O\+UT}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+I2\+C2\+\_\+\+S\+M\+B\+U\+S\+\_\+\+T\+I\+M\+E\+O\+UT))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+I2\+C3\+\_\+\+T\+I\+M\+E\+O\+UT}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+I2\+C3\+\_\+\+S\+M\+B\+U\+S\+\_\+\+T\+I\+M\+E\+O\+UT))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+C\+A\+N1}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+C\+A\+N1\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+C\+A\+N2}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+C\+A\+N2\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M1}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B2\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B2\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M1\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M8}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B2\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B2\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M8\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M9}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B2\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B2\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M9\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M10}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B2\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B2\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M10\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M11}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B2\+FZ $\vert$= (D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B2\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M11\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M2}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M2\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M3}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M3\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M4}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M4\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M5}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M5\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M6}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M6\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M7}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M7\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M12}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M12\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M13}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M13\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M14}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M14\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+R\+TC}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+R\+T\+C\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+W\+W\+DG}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+W\+W\+D\+G\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+I\+W\+DG}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+I\+W\+D\+G\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+I2\+C1\+\_\+\+T\+I\+M\+E\+O\+UT}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+I2\+C1\+\_\+\+S\+M\+B\+U\+S\+\_\+\+T\+I\+M\+E\+O\+UT))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+I2\+C2\+\_\+\+T\+I\+M\+E\+O\+UT}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+I2\+C2\+\_\+\+S\+M\+B\+U\+S\+\_\+\+T\+I\+M\+E\+O\+UT))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+I2\+C3\+\_\+\+T\+I\+M\+E\+O\+UT}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+I2\+C3\+\_\+\+S\+M\+B\+U\+S\+\_\+\+T\+I\+M\+E\+O\+UT))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+C\+A\+N1}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+C\+A\+N1\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+C\+A\+N2}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B1\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B1\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+C\+A\+N2\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M1}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B2\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B2\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M1\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M8}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B2\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B2\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M8\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M9}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B2\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B2\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M9\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M10}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B2\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B2\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M10\+\_\+\+S\+T\+OP))
\item
\#define {\bfseries \+\_\+\+\_\+\+H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+U\+N\+F\+R\+E\+E\+Z\+E\+\_\+\+T\+I\+M11}()~(D\+B\+G\+M\+CU-\/$>$A\+P\+B2\+FZ \&= $\sim$(D\+B\+G\+M\+C\+U\+\_\+\+A\+P\+B2\+\_\+\+F\+Z\+\_\+\+D\+B\+G\+\_\+\+T\+I\+M11\+\_\+\+S\+T\+OP))
\item
\#define \hyperlink{group___h_a_l___exported___macros_ga9500619e1ec21659bd32b1dfecd5afc1}{\+\_\+\+\_\+\+H\+A\+L\+\_\+\+S\+Y\+S\+C\+F\+G\+\_\+\+R\+E\+M\+A\+P\+M\+E\+M\+O\+R\+Y\+\_\+\+F\+L\+A\+SH}()~(S\+Y\+S\+C\+FG-\/$>$M\+E\+M\+R\+MP \&= $\sim$(\hyperlink{group___peripheral___registers___bits___definition_ga3c05039ec67573c00da29f58b914f258}{S\+Y\+S\+C\+F\+G\+\_\+\+M\+E\+M\+R\+M\+P\+\_\+\+M\+E\+M\+\_\+\+M\+O\+DE}))
\begin{DoxyCompactList}\small\item\em Main Flash memory mapped at 0x00000000. \end{DoxyCompactList}\item
\#define \hyperlink{group___h_a_l___exported___macros_ga59782d94690fd538b25def536c81c3ed}{\+\_\+\+\_\+\+H\+A\+L\+\_\+\+S\+Y\+S\+C\+F\+G\+\_\+\+R\+E\+M\+A\+P\+M\+E\+M\+O\+R\+Y\+\_\+\+S\+Y\+S\+T\+E\+M\+F\+L\+A\+SH}()
\begin{DoxyCompactList}\small\item\em System Flash memory mapped at 0x00000000. \end{DoxyCompactList}\item
\#define \hyperlink{group___h_a_l___exported___macros_ga86d36fdb1571fd56ffeecfaed80c6805}{\+\_\+\+\_\+\+H\+A\+L\+\_\+\+S\+Y\+S\+C\+F\+G\+\_\+\+R\+E\+M\+A\+P\+M\+E\+M\+O\+R\+Y\+\_\+\+S\+R\+AM}()
\begin{DoxyCompactList}\small\item\em Embedded S\+R\+AM mapped at 0x00000000. \end{DoxyCompactList}\end{DoxyCompactItemize}
\subsection*{Functions}
\begin{DoxyCompactItemize}
\item
\hyperlink{stm32f4xx__hal__def_8h_a63c0679d1cb8b8c684fbb0632743478f}{H\+A\+L\+\_\+\+Status\+Type\+Def} {\bfseries H\+A\+L\+\_\+\+Init} (void)
\item
\hyperlink{stm32f4xx__hal__def_8h_a63c0679d1cb8b8c684fbb0632743478f}{H\+A\+L\+\_\+\+Status\+Type\+Def} {\bfseries H\+A\+L\+\_\+\+De\+Init} (void)
\item
void {\bfseries H\+A\+L\+\_\+\+Msp\+Init} (void)
\item
void {\bfseries H\+A\+L\+\_\+\+Msp\+De\+Init} (void)
\item
\hyperlink{stm32f4xx__hal__def_8h_a63c0679d1cb8b8c684fbb0632743478f}{H\+A\+L\+\_\+\+Status\+Type\+Def} {\bfseries H\+A\+L\+\_\+\+Init\+Tick} (uint32\+\_\+t Tick\+Priority)
\item
void {\bfseries H\+A\+L\+\_\+\+Inc\+Tick} (void)
\item
void {\bfseries H\+A\+L\+\_\+\+Delay} (\hyperlink{core__sc300_8h_aec43007d9998a0a0e01faede4133d6be}{\+\_\+\+\_\+\+IO} uint32\+\_\+t Delay)
\item
uint32\+\_\+t {\bfseries H\+A\+L\+\_\+\+Get\+Tick} (void)
\item
void {\bfseries H\+A\+L\+\_\+\+Suspend\+Tick} (void)
\item
void {\bfseries H\+A\+L\+\_\+\+Resume\+Tick} (void)
\item
uint32\+\_\+t {\bfseries H\+A\+L\+\_\+\+Get\+Hal\+Version} (void)
\item
uint32\+\_\+t {\bfseries H\+A\+L\+\_\+\+Get\+R\+E\+V\+ID} (void)
\item
uint32\+\_\+t {\bfseries H\+A\+L\+\_\+\+Get\+D\+E\+V\+ID} (void)
\item
void {\bfseries H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+Enable\+D\+B\+G\+Sleep\+Mode} (void)
\item
void {\bfseries H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+Disable\+D\+B\+G\+Sleep\+Mode} (void)
\item
void {\bfseries H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+Enable\+D\+B\+G\+Stop\+Mode} (void)
\item
void {\bfseries H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+Disable\+D\+B\+G\+Stop\+Mode} (void)
\item
void {\bfseries H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+Enable\+D\+B\+G\+Standby\+Mode} (void)
\item
void {\bfseries H\+A\+L\+\_\+\+D\+B\+G\+M\+C\+U\+\_\+\+Disable\+D\+B\+G\+Standby\+Mode} (void)
\item
void {\bfseries H\+A\+L\+\_\+\+Enable\+Compensation\+Cell} (void)
\item
void {\bfseries H\+A\+L\+\_\+\+Disable\+Compensation\+Cell} (void)
\end{DoxyCompactItemize}

\subsection{Detailed Description}
This file contains all the functions prototypes for the H\+AL module driver.

\begin{DoxyAuthor}{Author}
M\+CD Application Team
\end{DoxyAuthor}
\begin{DoxyVersion}{Version}
V1.\+4.\+1
\end{DoxyVersion}
\begin{DoxyDate}{Date}
09-\/\+October-\/2015
\end{DoxyDate}
\begin{DoxyAttention}{Attention}

\end{DoxyAttention}
\subsubsection*{\begin{center}\copyright{} C\+O\+P\+Y\+R\+I\+G\+H\+T(c) 2015 S\+T\+Microelectronics\end{center} }

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met\+:
\begin{DoxyEnumerate}
\item Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
\item Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
\item Neither the name of S\+T\+Microelectronics nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
\end{DoxyEnumerate}

T\+H\+IS S\+O\+F\+T\+W\+A\+RE IS P\+R\+O\+V\+I\+D\+ED BY T\+HE C\+O\+P\+Y\+R\+I\+G\+HT H\+O\+L\+D\+E\+RS A\+ND C\+O\+N\+T\+R\+I\+B\+U\+T\+O\+RS \char`\"{}\+A\+S I\+S\char`\"{} A\+ND A\+NY E\+X\+P\+R\+E\+SS OR I\+M\+P\+L\+I\+ED W\+A\+R\+R\+A\+N\+T\+I\+ES, I\+N\+C\+L\+U\+D\+I\+NG, B\+UT N\+OT L\+I\+M\+I\+T\+ED TO, T\+HE I\+M\+P\+L\+I\+ED W\+A\+R\+R\+A\+N\+T\+I\+ES OF M\+E\+R\+C\+H\+A\+N\+T\+A\+B\+I\+L\+I\+TY A\+ND F\+I\+T\+N\+E\+SS F\+OR A P\+A\+R\+T\+I\+C\+U\+L\+AR P\+U\+R\+P\+O\+SE A\+RE D\+I\+S\+C\+L\+A\+I\+M\+ED. IN NO E\+V\+E\+NT S\+H\+A\+LL T\+HE C\+O\+P\+Y\+R\+I\+G\+HT H\+O\+L\+D\+ER OR C\+O\+N\+T\+R\+I\+B\+U\+T\+O\+RS BE L\+I\+A\+B\+LE F\+OR A\+NY D\+I\+R\+E\+CT, I\+N\+D\+I\+R\+E\+CT, I\+N\+C\+I\+D\+E\+N\+T\+AL, S\+P\+E\+C\+I\+AL, E\+X\+E\+M\+P\+L\+A\+RY, OR C\+O\+N\+S\+E\+Q\+U\+E\+N\+T\+I\+AL D\+A\+M\+A\+G\+ES (I\+N\+C\+L\+U\+D\+I\+NG, B\+UT N\+OT L\+I\+M\+I\+T\+ED TO, P\+R\+O\+C\+U\+R\+E\+M\+E\+NT OF S\+U\+B\+S\+T\+I\+T\+U\+TE G\+O\+O\+DS OR S\+E\+R\+V\+I\+C\+ES; L\+O\+SS OF U\+SE, D\+A\+TA, OR P\+R\+O\+F\+I\+TS; OR B\+U\+S\+I\+N\+E\+SS I\+N\+T\+E\+R\+R\+U\+P\+T\+I\+ON) H\+O\+W\+E\+V\+ER C\+A\+U\+S\+ED A\+ND ON A\+NY T\+H\+E\+O\+RY OF L\+I\+A\+B\+I\+L\+I\+TY, W\+H\+E\+T\+H\+ER IN C\+O\+N\+T\+R\+A\+CT, S\+T\+R\+I\+CT L\+I\+A\+B\+I\+L\+I\+TY, OR T\+O\+RT (I\+N\+C\+L\+U\+D\+I\+NG N\+E\+G\+L\+I\+G\+E\+N\+CE OR O\+T\+H\+E\+R\+W\+I\+SE) A\+R\+I\+S\+I\+NG IN A\+NY W\+AY O\+UT OF T\+HE U\+SE OF T\+H\+IS S\+O\+F\+T\+W\+A\+RE, E\+V\+EN IF A\+D\+V\+I\+S\+ED OF T\+HE P\+O\+S\+S\+I\+B\+I\+L\+I\+TY OF S\+U\+CH D\+A\+M\+A\+GE.


text:
\documentclass{scrartcl}

\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}

%from a lecture by Badiou (November 18, 2006), Miguel Abreu Gallery, New York

\begin{document}

	\hspace{-3cm}
	\begin{tikzpicture}[very thick]
	\draw (0,6)--(19,6);
	\draw (0,-6)--(19,-6);

	%diagonal lines
	\draw (0.25,5.75)--(16.25,0);
	\draw (0.25,-5.75)--(16.25,0);

	%boxes
	\fill[white] (14.85,0.75) rectangle (15,-0.75);
	\filldraw[draw=black,fill=white] (15,0.75) rectangle (18,-0.75);
	\node at (16.5,0) {\Huge \textsc{event}};
	\draw[->,>=stealth] (16.5,1)--(16.5,2);
	\node at (16.5,2.35) {\Large \textsc{disappearance}};
	\draw[->,>=stealth] (16.5,-1)--(16.5,-2);
	\node at (16.5,-2.4) {\Large \textsc{consequences}};
	%
	\filldraw[draw=black,fill=white] (0.75,1) rectangle (4.5,-1);
	\node at (2.35,0) {\LARGE \textsc{There is}};
	%
	\filldraw[draw=black,fill=white] (12,5) rectangle (14.25,4);
	\node at (13.1,4.5) {\huge \textsc{being}};
	%
	\filldraw[draw=black,fill=white] (12,-5) rectangle (15,-4);
	\node at (13.5,-4.5) {\huge \textsc{subject}};

	%dots
	\filldraw (2,5.12) circle (2pt) node[above right] {Appearance, Being-there};
	\filldraw (5,4.05) circle (2pt) node[above right] {Logical consistency};
	\filldraw (7.5,3.15) circle (2pt) node[above right] {Transcendental};
	\filldraw (10,2.25) circle (2pt) node[above right] {Inexistent};
	\filldraw (12.5,1.35) circle (2pt) node[above right] {Points};
	%
	\filldraw (2,-5.12) circle (2pt) node[below right] {Creative present};
	\filldraw (5,-4.05) circle (2pt) node[below right] {New body};
	\filldraw (7.5,-3.15) circle (2pt) node[below right] {Conditions};
	\filldraw (10,-2.25) circle (2pt) node[below right] {Trace};
	\filldraw (12.5,-1.35) circle (2pt) node[below right] {Organs};

	%labels
	\node at (4.25,6.5) {\LARGE \textsc{indifferent multiplicities}};
	\node at (2.75,-6.5) {\LARGE \textsc{eternal truths}};

	%\draw[help lines] (0,-6) grid (19,6);
	\end{tikzpicture}

\end{document}


text:
\usepackage{beamerarticle}

\chapter{Approximation de problèmes mixtes}
\label{cha:appr-de-probl-1}

\section{Model Problems}
\label{sec:model-problems}

  We consider now model problems as systems of PDEs where several functions are
  unknowns and which don't play the same roles \emph{mathematically} and
  \emph{physically}.
  \begin{problem}{Stokes}
    \begin{equation}
      \label{eq:chmixte:98}
      \left\{\begin{array}[c]{rl}
          -\Delta u + \nabla p & = f\ \mbox{ in } \Omega\\
          \nabla \cdot u & = 0\ \mbox{ in } \Omega
        \end{array}\right.
    \end{equation}
    where $u: \Omega \mapsto \R{d}$ is a velocity and $p: \Omega \mapsto \R{}$
    is a pressure.
  \end{problem}
  \begin{problem}{Darcy}
    \begin{equation}
      \label{eq:chmixte:99}
      \left\{\begin{array}[c]{rl}
          \sigma + \nabla u & = f\ \mbox{ in } \Omega\\
          \nabla \cdot \sigma & = g\ \mbox{ in } \Omega
        \end{array}\right.
    \end{equation}
    where $\sigma: \Omega \mapsto \R{d}$ is a velocity and $u: \Omega \mapsto \R{}$
    is a hydraulic charge(pressure).

  \end{problem}

\section{Applications}

  We shall focus on Stokes, but the abstract setting of the next section is
  the same for Stokes and Darcy.

\begin{block}{Stokes and incompressible Navier-Stokes for Newtonian fluids}
  The Stokes model is the basis for fluid mechanics models and is a
  simplication of the Navier-Stokes equations where the viscous effects/terms
  are much bigger than the convective ones
  \begin{equation}
    \label{eq:chmixte:3}
    \left\{\begin{array}[c]{rl}
           \rho( \frac{\partial u}{\partial t} + u \cdot \nabla u) - \nu \Delta u + \nabla p & = f\ \mbox{ in } \Omega\\
           \nabla \cdot u & = 0\ \mbox{ in } \Omega
         \end{array}\right.
     \end{equation}
     The first equation results from the conservation of momentum and the second
     from the conservation of mass.
   \end{block}

  \begin{remark}{}
    The well-posedness of these problems results from a so-called \alert{inf-suf
    condition} which is not automatically transfered at the \emph{discrete level}.
  \end{remark}

  \begin{remark}{In practice}
    In order to ensure that the finite element approximation is well-posed, we
    will need to choose approximation spaces that satisfy a \emph{compatibility
    condition} that ensures that a \emph{discrete inf-sup condition} is satisfied.
  \end{remark}

\section{Saddle point problems}
\label{sec:saddle-point-probl}

\subsection{Abstract Continuous Setting}
  Denote
  \begin{itemize}
  \item $X$ and $M$ two Hilbert spaces\footnote{An euclidian space which is
  complete for the norm induced by the scalar product}
  \item two linear forms $f \in X'=\mathcal{L}(X, \R{})$ and $g \in
    M'=\mathcal{L}(M, \R{})$
  \item $a \in \mathcal{L}(X\times X, \R{})$ and $b \in \mathcal{L}(X\times M,
    \R{})$ two bilinear forms
  \end{itemize}
  We are interested in the following abstract problem:
  \begin{problem}[Abstract formulation]
    \label{prob:chmixte:1}
    Look for $(u,p) \in X \times M$ such that
    \begin{equation}
      \label{eq:chmixte:4}
      \left\{
        \begin{array}[c]{rl}
          a(u,v) + b(v,p) & = f(v), \quad \forall v \in X\\
          b(u,q) & = g(q), \quad \forall q \in M
        \end{array}
      \right.
    \end{equation}
  \end{problem}

\subsection{Definition of a saddle point problem}
  \begin{definition}[Saddle point problem]
    \label{def:chmixte:1}
    If the bilinear form $a$ is \emph{symmetric} and positive on $X\times X$, we
    say that problem~\ref{prob:chmixte:1} is a \emph{saddle point problem}.
  \end{definition}

  \begin{remark}{Structure of the problem}
    \begin{itemize}
    \item the space of solution is the same of the test space
    \item the unknown $p$ does not appear in the second equation
    \item the unknown functions $u$ and $p$ are coupled via the same bilinear
      form $b$ is the first and second equation.
    \end{itemize}
    The next question is : \alert{is the problem~\ref{prob:chmixte:1} well-posed?}
  \end{remark}

\section{Well posed problem}
\label{sec:well-posed-problemframe}

\subsection{Reformulation}
  Let's rewrite Problem~\ref{prob:chmixte:1}. Denote $V=X\times M$ and introduce $c
  \in \mathcal{L}(V\times V, \R{})$ such that
  \begin{equation}
    \label{eq:chmixte:5}
    c((u,p),(v,q)) = a(u,v)+b(v,p)+b(u,q)
  \end{equation}
  and $h\in \mathcal{L}(V,\R{})$ such that
  \begin{equation}
    \label{eq:chmixte:6}
    h(v,q) = f(v)+g(q)
  \end{equation}
  then problem~\ref{prob:chmixte:1} reads
  \begin{problem}
    \label{prob:chmixte:2}
    Look for $(u,p) \in V$ such that
    \begin{equation}
      \label{eq:chmixte:7}
        \begin{array}[c]{rl}
          c((u,p), (v,q)) & = h(v,q), \quad \forall (v,q) \in V
        \end{array}
      \end{equation}
  \end{problem}

  \begin{theorem}[Well posedness of the Saddle-Point problem]
    \label{thr:chmixte:1}
    We suppose that $a$ is coercive over $X$, the problem~\ref{prob:chmixte:2} is
    \emph{well-posed} if and only if the bilinear form $b$ satisfies the
    following inf-sup condition: there exists $\beta > 0$ such that
    \begin{equation}
      \label{eq:chmixte:8}
      \inf_{q \in M} \sup_{v \in X} \frac{b(v,q)}{||v||_X ||q||_M} \geq \beta
    \end{equation}
  \end{theorem}
  \begin{remark}
    \begin{itemize}
    \item Lax-Milgram provides only a sufficient condition for well-posedness
    \item the form $c$ in Problem~\ref{prob:chmixte:2} does not satisfy Lax-Milgram.
    \end{itemize}
  \end{remark}

  Let's introduce the so-called \emph{Lagrangian} $l \in \mathcal{L}(X\times M,
  \R{})$ defined by
  \begin{equation}
    \label{eq:chmixte:9}
    l(v,q) =  \frac{1}{2} a(v,v) + b(v,q) - f(v) - g(q)
  \end{equation}
  \begin{definition}[Saddle point]
    \label{def:chmixte:2}
    We say that the point $(u,p)\in X\times M$ is a saddle point of $l$ if
    \begin{equation}
      \label{eq:chmixte:10}
      \forall (v,q) \in X\times M, \quad l(u,q) \leq l(u,p) \leq l(v,p)
    \end{equation}
  \end{definition}
  \begin{proposition}[Unicity of the saddle point]
    \label{prop:chmixte:1}
    Under the hypothesys of theorem~\ref{thr:chmixte:1}, the Lagrangian $l$ defined
    by~\eqref{eq:chmixte:9} has a \emph{unique} saddle point. Moreover this saddle point
    is the the unique solution of problem~\ref{prob:chmixte:1}.
  \end{proposition}

\section{Finite element approximation}
\label{sec:finite-elem-appr}

\subsection{Abstract Discrete Problem}
  We now turn to the approximation of the problem~\ref{prob:chmixte:1} by a \emph{standard
  Galerkin method} in a \emph{conforming} way.

  Denote the two spaces $X_h \subset X$ and $M_h \subset M$, we consider the
  following problem:
  \begin{problem}
    \label{prob:chmixte:3}
    Look for $(u_h,p_h) \in X_h \times M_h$ such that
    \begin{equation}
      \label{eq:chmixte:11}
      \left\{
        \begin{array}[c]{rl}
          a(u_h,v_h) + b(v_h,p_h) & = f(v_h), \quad \forall v_h \in X_h\\
          b(u_h,q_h) & = g(q_h), \quad \forall q_h \in M_h
        \end{array}
      \right.
    \end{equation}
  \end{problem}

  \begin{theorem}[Well-posedness of the discrete problem]
    \label{thr:chmixte:2}
    We suppose that $a$ is coercive over $X$ and that $X_h \subset X$ and $M_h
    \subset M$. Then the problem~\ref{prob:chmixte:3} is \emph{well-posed} if and only
    if the following \emph{discrete inf-sup condition}  is satisfied: there
    exists $\beta_h  > 0$ such that
    \begin{equation}
      \label{eq:chmixte:12}
      \inf_{q_h \in M_h} \sup_{v_h \in X_h} \frac{b(v_h,q_h)}{||v_h||_{X_h} ||q_h||_{M_h}} \geq \beta_h
    \end{equation}
  \end{theorem}

  \begin{remark}{Compatibility condition}
    Problem~\ref{prob:chmixte:3} to be well posed, requires that the spaces $X_h$ and
    $M_h$ satisfy the condition~\eqref{eq:chmixte:12}. This is known as the
    Babuska-Brezzi (BB) or Ladyhenskaya-Babuska-Brezzi (LBB).
  \end{remark}

  Regarding error analysis, we have the following lemma
  \begin{lemma}
    \label{lem:1}
      Thanks to the Lemma of Céa applied to Saddle-Point Problems, the unique
      solution $(u,p)$ of problem~\ref{prob:chmixte:3}  satisfy
      \begin{equation}
        \label{eq:chmixte:13}
        \begin{array}[c]{rl}
          ||u-u_h||_X & \leq c_{1h} \inf_{v_h \in X_h}  ||u-v_h||_X + c_{2}
          \inf_{q_h \in M_h}  ||q-q_h||_M\\
          ||p-p_h||_X & \leq c_{3h} \inf_{v_h \in X_h}  ||u-v_h||_X + c_{4h} \inf_{q_h \in M_h}  ||q-q_h||_M
        \end{array}
      \end{equation}
      where
      \begin{itemize}
      \item $c_{1h} =
        (1+\frac{||a||_{X,X}}{\alpha})(1+\frac{||b||_{X,M}}{\beta_h})$ where
        $\alpha$ is the coercivity constant of $a$ over X.
      \item $c_{2} = \frac{||b||_{X,M}}{\alpha}$
      \item $c_{3h} = c_{1h} \frac{||a||_{X,X}}{\beta_h}$, $c_{4h} = 1+ \frac{||b||_{X,M}}{\beta_h}+\frac{||a||_{X,X}}{\beta_h}$
      \end{itemize}
  \end{lemma}
  \begin{remark}
    The constants $c_{1h}, c_{3h}, c_{4h}$ are as large as $\beta_h$ is small.
  \end{remark}

\subsection{Linear system associated}
\label{sec:linear-system}

The discretisation process leads to a linear system. We denote
  \begin{itemize}
  \item $N_u = \dim {X_h}$
  \item $N_p = \dim {M_h}$
  \item $\{\phi_i\}_{i=1,...,N_u}$ a basis of $X_h$
  \item $\{\psi_k\}_{k=1,...,N_p}$ a basis of $M_h$
  \item for all $u_h = \sum_{i=1}^{N_u} u_i \phi_i$, we associate $U \in
    \R{N_u}$, $U=(u_1,\ldots,u_{N_u})^T$, the component vector of $u_h$ is
    $\{\phi_i\}_{i=1,\ldots,N_u}$
  \item for all $p_h = \sum_{k=1}^{N_p} u_k \psi_k$, we associate $P \in
    \R{N_p}$, $P=(p_1,\ldots,p_{N_p})^T$, the component vector of $p_h$ is $\{\psi_k\}_{k=1,\ldots,N_p}$
  \end{itemize}

  \begin{block}{}
    The matricial form of problem ~\ref{prob:chmixte:3} reads
    \begin{equation}
      \label{eq:chmixte:15}
      \begin{bmatrix}
        \mathcal{A} & \mathcal{B}^T\\
        \mathcal{B} & 0
      \end{bmatrix}
      \begin{bmatrix}
        U \\
        P
      \end{bmatrix}
      =
      \begin{bmatrix}
        F\\
        G
      \end{bmatrix}
    \end{equation}
    where the matrix $\mathcal{A} \in \R{N_u,N_u}$ and $\mathcal{B} \in
    \R{N_p,N_u}$ have the coefficients
    \begin{equation}
      \label{eq:chmixte:16}
      \mathcal{A}_{ij} = a(\phi_j,\phi_i), \quad \mathcal{B}_{ki} = b(\phi_i,\psi_k)
    \end{equation}
    and the vectors $\mathcal{F} \in \R{N_u}$ and $\mathcal{G} \in \R{N_p}$
    have the coefficients
    \begin{itemize}
    \item $F_i=f(\phi_i)$
    \item $G_k=g(\psi_k)$
    \end{itemize}
  \end{block}

  \begin{remark}[Remarks on the linear system]
    \label{rem:2}
    \begin{enumerate}
    \item Since $a$ is symmetric and coercive, $\mathcal{A}$ is \emph{symmetric
       positive definite}
     \item The matrix of the system \eqref{eq:chmixte:15} is symmetric but not positive
     \item The inf-sup condition~\eqref{eq:chmixte:12} is equivalent to the fact that
       $\mathcal{B}$ is of \emph{maximum rank}, \emph{i.e.} $\ker(\mathcal{B}^T)
       = \{0 \}$.
     \item From theorem~\ref{thr:chmixte:2}, the matrix of the system~\eqref{eq:chmixte:15} is
       invertible
    \end{enumerate}
  \end{remark}

  \begin{block}{When the Inf-sup condition is not satisfied}
    The counter examples when the inf-sup condition~\eqref{eq:chmixte:12} is not
    satisfied(e.g. $\mathcal{B}$ is not maximum rank ) occur usually in two
    cases:
    \begin{enumerate}
    \item $\dim {M_h} > \dim {X_h}$: the space of pressure is too large for the
      matrix $\mathcal{B}$ to be maximum rank. In that case $\mathcal{B}$ is
      injective ($\ker(\mathcal{B}) = \{0\})$. We call this \emph{locking}.
    \item there exists a vector $Q^* \neq 0$ in $\ker(\mathcal{B}^T)$. The
      discrete field $q^*_h$ in $M_h$, $q^*_h=\sum_{k=1}^{N_p} Q^*_k \psi_k$,
      associated is called a \emph{spurious mode}. $q^*_H$ is such that
      \begin{equation}
        \label{eq:chmixte:14}
        b(v_h,q^*_h)=0.
      \end{equation}

    \end{enumerate}
  \end{block}

We now introduce the Uzawa matrix.
\begin{block}{Uzawa}
  The matrix
    \begin{equation}
      \label{eq:chmixte:17}
      \mathcal{U} = \mathcal{B} \mathcal{A}^{-1} \mathcal{B}^T
    \end{equation}
    is called the \emph{Uzawa matrix}. It is \emph{symmetric positive definite}
    from the properties of $\mathcal{A}$, $\mathcal{B}$
  \end{block}
  \begin{block}{Applications}
    The Uzawa matrix occurs when eliminating the velocity in
    system~\eqref{eq:chmixte:15} and get a linear system on $P$:
    \begin{equation}
      \label{eq:chmixte:18}
      \mathcal{U} P = \mathcal{B} \mathcal{A}^{-1} F - G
    \end{equation}
    then one application is to solve \eqref{eq:chmixte:15} by solving \eqref{eq:chmixte:18}
    iteratively and compute the velocity afterwards.
  \end{block}

\section{Mixed finite element for Stokes}
\label{sec:mixed-finite-element}

\subsection{Variational formulation }
\label{sec:vari-form-}

We start with the Well-posedness at the continuous level
  \begin{itemize}
  \item   We consider the model problem~\eqref{eq:chmixte:1} with homogeneous Dirichlet
  condition on velocity $u = 0$ on $\partial \Omega$
  \item   We suppose the $f \in [L^2(\Omega)]^d$ and $g \in L^2(\Omega)$ with
  \begin{equation}
    \label{eq:chmixte:20}
    \int_\Omega g = 0
  \end{equation}
    Introduce
  \begin{equation}
    \label{eq:chmixte:19}
    L^2_0(\Omega) = \Big\{ q \in L^2(\Omega): \int_\Omega q = 0 \Big\}
  \end{equation}

  \end{itemize}

  \begin{remark}{The condition~\eqref{eq:chmixte:20}}
    The condition~\eqref{eq:chmixte:20} comes from the divergence theorem applied to the
    divergence equation and the fact that $u=0$ on the boundary
    \begin{equation}
      \label{eq:chmixte:21}
      \int_\Omega g = \int_\Omega \nabla \cdot u = \int_{\partial \Omega} u
      \cdot n = 0
    \end{equation}
    This is a \emph{necessary} condition for the existence of a solution $(u,p)$
    for the Stokes equations with these boundary conditions.
  \end{remark}

We turn now to the variational formulation.  The Stokes problem reads
    \begin{problem}[Stokes Variational Formulation]
      \label{prob:chmixte:4}
      Look for $(u,p) \in [H^1_0(\Omega)]^d \times L^2_0(\Omega)$ such that
      \begin{equation}
        \label{eq:chmixte:25}
      \left\{
        \begin{array}[c]{rl}
          \int_\Omega \nabla u : \nabla v -\int_\Omega p \nabla \cdot v  & =
          \int_\Omega f \cdot v, \quad \forall v \in [H^1_0(\Omega)]^d\\
          \int_\Omega q \nabla \cdot u & = - \int_\Omega g q, \quad \forall q \in L^2_0(\Omega)
        \end{array}
      \right.
    \end{equation}
    \end{problem}
    We retrieve the problem~\ref{prob:chmixte:1} with $X=[H^1_0(\Omega)]^d$ and
    $M=L^2_0(\Omega)$ and
    \begin{equation}
      \label{eq:chmixte:22}
      \begin{array}[c]{rlrl}
      a(u,v) &= \int_\Omega \nabla u : \nabla v,& \quad b(v,p) &= -\int_\Omega p
      \nabla \cdot v,\\
      \quad f(v) &=  \int_\Omega f \cdot v,& \quad g(q) &= - \int_\Omega g q
      \end{array}
    \end{equation}
    \begin{remark}{Pressure up to a constant}
      The pressure is known up to a constant, that's why we look for them in
      $L^2_0(\Omega)$ to ensure uniqueness.
    \end{remark}

% \begin{frame}
%   \frametitle{Well-posedness}

%   \begin{lemma}
%     \label{lem:2}
%     Denote $\Omega$ a domain of $\R{d}, d \geq 2$, Then the operator
%     \begin{equation}
%       \label{eq:chmixte:23}
%       \nabla \cdot : [H^1_0(\Omega)]^d \mapsto L^2_0(\Omega)
%     \end{equation}
%     is surjective.
%   \end{lemma}

%   This lemma and the theorem
%

\subsection{Finite element approximation}
\label{sec:finite-elem-appr-1}

  Denote $X_h \subset [H^1_0(\Omega)]^d$ and $M_h \subset L^2_0(\Omega)$

  \begin{problem}[Discrete Stokes formulation]
    \label{prob:chmixte:5}
    Look for $(u_h,p_h) \in X_h \times M_h$ such that
    \begin{equation}
      \label{eq:chmixte:24}
      \left\{
        \begin{array}[c]{rl}
          \int_\Omega \nabla u_h : \nabla v_h + \int_\Omega p_h \nabla \cdot v_h
          & = \int_\Omega f \cdot v_h, \quad \forall v_h \in X_h\\
          \int_\Omega q_h \nabla \cdot u_h & = -\int_\Omega g q_h, \quad \forall q_h \in M_h
        \end{array}
      \right.
    \end{equation}
  \end{problem}
  \begin{remark}[Well-posedness]
    \label{rem:1}
    This problem, thanks to theorem~\ref{thr:chmixte:2} is well-posed if and only if
    $X_h$ and $M_h$ are such that there exists $\beta_h > 0$
    \begin{equation}
      \label{eq:chmixte:26}
      \inf_{q_h \in M_h} \sup_{v_h \in X_h} \frac{\int_\Omega q_h \nabla \cdot v_h}{||v_h||_{X_h} ||q_h||_{M_h}} \geq \beta_h
    \end{equation}
  \end{remark}

% \lstinputlisting{mystokes.cpp}

\subsection{Some counter examples: bad finite element for Stokes}
\label{sec:counter-examples}

In this section we present two classical bad finite element approximations.

\subsubsection{Finite element $\poly{P}_1/\poly{P}_0$: locking}
    thanks to the Euler relations

    \begin{equation}
      \label{eq:chmixte:28}
      \begin{array}[c]{rl}
        N_{\mathrm{cells}} - N_{\mathrm{edges}} + N_{vertices}  &= 1-I\\
      N^\partial_{\mathrm{vertices}} - N^\partial_{\mathrm{edges}} &= 0
      \end{array}
    \end{equation}
    where $I$ is the number of holes in $\Omega$.  We have that $\dim {M_h} =
    N_{\mathrm{cells}}$, $\dim {X_h} = 2 N^i_{\mathrm{vertices}}$ and so
    \begin{equation}
      \label{eq:chmixte:29}
      \dim {M_h} - \dim {X_h} = N_{\mathrm{cells}} - 2 N^i_{\mathrm{vertices}} =
      N^\partial_{\mathrm{edges}} - 2 > 0
    \end{equation}
    so $M_h$ is too rich for the condition \eqref{eq:chmixte:26} and we have
    $\ker(\mathcal{B}) = \{0\}$ such that the \emph{only} discrete $u_h^*$,
    with components $U^*$, satisfying $\mathcal{B} U^*$ is the nul field, $U^*=0$.

\subsubsection{Finite element $\poly{Q}_1/\poly{P}_0$: spurious mode}

    We can construct in that case a function $q_h^*$ on a uniform grid which is
    equal alternatively -1, +1 (chessboard) in the cells of  the mesh, then
    \begin{equation}
      \label{eq:chmixte:27}
      \forall v_h \in [Q^1_{c,h}]^d, \quad \int_\Omega q^*_h \nabla \cdot v_h = 0
    \end{equation}
    and thus the associated $X_h$, $M_h$ do not satisfy  the condition~\eqref{eq:chmixte:26}.

\subsubsection{Finite element $\poly{P}_1/\poly{P}_1$: spurious mode}
    We can construct in that case a function $q_h^*$ on a uniform grid which is
    equal alternatively -1, 0, +1 at the vertices of the mesh, then
    \begin{equation}
      \label{eq:chmixte:27}
      \forall v_h \in [P^1_{c,h}]^d, \quad \int_\Omega q^*_h \nabla \cdot v_h = 0
    \end{equation}
    and thus the associated $X_h$, $M_h$ do not satisfy  the condition~\eqref{eq:chmixte:26}.

\subsection{Mini-Element}
\label{sec:finite-elem-stok}

  The problem with the $\poly{P}_1/\poly{P}_1$ mixed finite element is that the
  velocity is not \emph{rich} enough. A cure is to add a function $v_h^*$ in the
  velocity approximation space to ensure that
  \begin{equation}
    \label{eq:chmixte:30}
    \int_\Omega q^*_h \nabla \cdot v_h^* \neq 0
  \end{equation}
  where $q_h^*$ is the spurious mode. To do that we add the bubble function to
  the $\poly{P}_1$ velocity space.
  \begin{definition}[Bubble function]
    \label{def:chmixte:3}
    Recall the construction of finite elements on a reference convex $\hat{K}$.
    We say that $\hat{b}: \hat{K} \mapsto \R{}$ is a bubble function if:
    \begin{itemize}
    \item $\hat{b} \in H^1_0(\hat{K})
$
    \item $0 \leq \hat{b}(\hat{x}) \leq 1, \quad \forall \hat{x} \in \hat{K}$
    \item $\hat{b}(\hat{C}) = 1, \quad \mbox{where} \hat{C}$ is the barycenter of $\hat{K}$
    \end{itemize}
  \end{definition}

  \begin{exampleblock}{Example}
    The function
    \begin{equation}
      \label{eq:chmixte:31}
      \hat{b} = (d+1)^{d+1} \Pi_{i=0}^d\ \hat{\lambda}_i
    \end{equation}


text:
\begin{figure}[H]
  \centering
  \includegraphics[width=0.7\linewidth]{./chapters/exp2/methodology2_3.png}
  \caption[Third portion of the flowchart from Figure \ref{fig:method2}]
          {Third portion of the flowchart from Figure \ref{fig:method2} being
           described in this section.}
\end{figure}

The chosen algorithms (\textit{k}-nearest neighbors, decision trees, and
\gls{MLL} calculations) are introduced in Section \ref{sec:algs} and their
implementation details are in Section \ref{sec:statmodel1}.  This section will
therefore only cover the implementation differences from the previous work.
The \gls{MLL} calculations are implemented identically to Chapter
\ref{ch:exp1}.  However, the scikit-learn algorithms in this experiment did
undergo a new round of hyperparameter optimization.

The full list of 22 training sets that undergo training and prediction are as
follows:
\begin{itemize}
  \item 1 set of nuclide masses (29 nuclide masses from Chapter \ref{ch:exp1})
  \item 3 sets of nuclide activities
    \begin{itemize}
      \item 32 nuclide activities (full knowledge scenario for all nuclides,
            whether or not they are present in a quantity able to be detected)
      \item 12 nuclide activities (full knowledge for long energy windows list)
      \item 7 nuclide activities (full knowledge for short energy windows list)
    \end{itemize}
  \item 18 detector-based processed spectra sets
    \begin{itemize}
      \item Auto energy windows lists applied to six detectors (lab-based
            \gls{HPGe}, portable \gls{HPGe}, \gls{CZT}, \gls{SrI2}, \gls{LaBr3},
            \gls{NaI})
      \item Short energy windows lists applied to six detectors above
      \item Long energy windows lists applied to six detectors above
    \end{itemize}
\end{itemize}

\begin{table}[!htb]
  \centering
  \begin{tabular}{@{}llcll@{}}
    \toprule
    \textbf{\begin{tabular}[c]{@{}l@{}}Training Set\\ Description\end{tabular}} &
    \textbf{\begin{tabular}[c]{@{}l@{}}Prediction\\ Parameter\end{tabular}} &
    \textbf{\begin{tabular}[c]{@{}l@{}}\textit{k} \\ (N neighbors)\end{tabular}} &
    \textbf{\begin{tabular}[c]{@{}l@{}}Max \\ Depth\end{tabular}} &
    \textbf{\begin{tabular}[c]{@{}l@{}}Max \\ Features\end{tabular}} \\
    \toprule
    \multirow{4}{*}{\begin{tabular}[c]
    {@{}l@{}}29 \\ Nuclide\\ Masses\end{tabular}}          & Reactor Type & 4 & 56 & 29          \\
                                                           & Burnup       & 1 & 77 & 29          \\
                                                           & Enrichment   & 1 & 73 & 29          \\
                                                           & Cooling Time & 2 & 45 & 29          \\
                                                           \hline
    \multirow{4}{*}{\begin{tabular}[c]
    {@{}l@{}}32\\ Nuclide\\ Activities\end{tabular}}       & Reactor Type & 1 & 41 & 32          \\
                                                           & Burnup       & 1 & 49 & 32          \\
                                                           & Enrichment   & 1 & 67 & 32          \\
                                                           & Cooling Time & 7 & 56 & 32          \\
                                                           \hline
    \multirow{4}{*}{\begin{tabular}[c]
    {@{}l@{}}7 or 12\\ Nuclide \\ Activities\end{tabular}} & Reactor Type & 1 & 67 & 7 or 12     \\
                                                           & Burnup       & 1 & 78 & 7 or 12     \\
                                                           & Enrichment   & 1 & 60 & 7 or 12     \\
                                                           & Cooling Time & 4 & 68 & 7 or 12     \\
                                                           \hline
    \multirow{4}{*}{\begin{tabular}[c]
    {@{}l@{}}Energy \\ Windows:\\ Short\end{tabular}}      & Reactor Type & 1 & 62 & 42          \\
                                                           & Burnup       & 1 & 62 & 42          \\
                                                           & Enrichment   & 4 & 64 & 42          \\
                                                           & Cooling Time & 2 & 54 & 42          \\
                                                           \hline
    \multirow{4}{*}{\begin{tabular}[c]
    {@{}l@{}}Energy \\ Windows:\\ Long\end{tabular}}       & Reactor Type & 4 & 62 & 151         \\
                                                           & Burnup       & 1 & 51 & 151         \\
                                                           & Enrichment   & 5 & 73 & 151         \\
                                                           & Cooling Time & 2 & 64 & 151         \\
                                                           \hline
    \multirow{4}{*}{\begin{tabular}[c]
    {@{}l@{}}Energy \\ Windows:\\ Auto\end{tabular}}       & Reactor Type & 2 & 61 & None or 150 \\
                                                           & Burnup       & 1 & 52 & None or 150 \\
                                                           & Enrichment   & 4 & 67 & None or 150 \\
                                                           & Cooling Time & 2 & 58 & None or 150 \\
    \bottomrule
  \end{tabular}
  \caption[Optimized algorithm hyperparameters for all training sets in second
           experiment]
          {Optimized algorithm hyperparameters; the energy lists took all
           detectors into account.}
  \label{tbl:exp2hypparam}
\end{table}

Table \ref{tbl:exp2hypparam} lists the hyperparameter optimization results for
the 22 training sets. Because the 29 nuclide mass training set is included in
this chapter for comparison, its optimization results are also listed here.
The number of features for decision trees are not limited because the test runs
for optimization provided highly variable results. The only case where this is
not true is with the auto energy windows list for the lab-based \gls{HPGe} with
a length of 206; the maximum features for this one case are limited to 150.
Instead, optimization was carried out only on the maximum depth for decision
trees with keeping the full length of features.  This is an area that could
undergo deeper exploration than what occurs in this work, since the training
sets with large feature sets can become overfit.

The optimization took place in two rounds, where the first round had a coarser
grid of \textit{k} for \textit{k}-nearest neighbors and maximum depth for
decision trees and the second round had a finer grid of parameters. The 7 \& 12
nuclide activity training sets were optimized separately but contain averages
of the two results for the maximum depth, and the higher value of \textit{k}
when the two did not match. The \textit{k} and maximum depths were averaged
across all six detectors for each energy window list length (short, long, and
auto).  There were fairly consistent results from the short and long lists, but
the variable length of the auto-generated energy windows lists (in Table
\ref{tbl:enwindows}) gave a wider range of ideal hyperparameters.