From d02dd9341ff95642ffeaaa78807fbe10acd35184 Mon Sep 17 00:00:00 2001 From: Louis Lacoste Date: Fri, 22 Mar 2024 10:37:16 +0100 Subject: [PATCH] Fixing page number position and removing prez.tex --- prez.Rnw | 5 +- prez.pdf | Bin 1019933 -> 2717413 bytes prez.tex | 633 ------------------------------------------------------- 3 files changed, 3 insertions(+), 635 deletions(-) delete mode 100644 prez.tex diff --git a/prez.Rnw b/prez.Rnw index ff1253d..f4d698b 100644 --- a/prez.Rnw +++ b/prez.Rnw @@ -32,7 +32,7 @@ alsoletter={.} \setbeamertemplate{footline}{ \begin{tikzpicture}[remember picture,overlay] % Utiliser un compteur pour sélectionner différentes images avec modulo 5 - \pgfmathtruncatemacro{\imageindex}{mod(\thepage-1,4)+1} + \pgfmathtruncatemacro{\imageindex}{mod(\thepage-1,10)+1} \node[anchor=south west, inner sep=0pt] at (current page.south west) { % Insérer l'image à gauche \includegraphics[height=0.5cm]{img/footer/image\imageindex} @@ -45,7 +45,8 @@ alsoletter={.} \hfill% 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-\usepackage{booktabs} -\usepackage[scale=2]{ccicons} -\usepackage[style=authoryear-comp,backend=biber]{biblatex} -%== use and define color ==% -\AtEveryCite{\color{blue}} -\addbibresource{references.bib} - -\usepackage{pgfplots} -\usepackage{amsmath} -\usepackage{bm} -\usepackage{listings} -\lstset{frame=tb, -language=R, -keywordstyle=\color{blue}, -alsoletter={.} -} -\usepgfplotslibrary{dateplot} - -% Customize footline to include current and total slide numbers -\makeatletter - -\setbeamertemplate{footline}{ - \begin{tikzpicture}[remember picture,overlay] - % Utiliser un compteur pour sélectionner différentes images avec modulo 5 - \pgfmathtruncatemacro{\imageindex}{mod(\thepage-1,4)+1} - \node[anchor=south west, inner sep=0pt] at (current page.south west) { - % Insérer l'image à gauche - \includegraphics[height=0.5cm]{img/footer/image\imageindex} - }; - \node[anchor=south east, inner sep=0pt] at (current page.south east) { - % Vous pouvez également ajouter d'autres éléments à droite du pied de page si nécessaire - }; - \end{tikzpicture} - \ifnum\c@framenumber>1% - \hfill% - {\fontsize{10}{12}\selectfont % Adjust the font size here - \color{gray}% - \insertframenumber/\inserttotalframenumber}% - \fi% -} -\makeatother - -\usepackage{xspace} -\newcommand{\themename}{\textbf{\textsc{metropolis}}\xspace} - -\title{Projet: ANOVA Phylogénétique} -\subtitle{Présentation du Mercredi 10 Jan. 2024} -% \date{\today} -\date{} -\author{Alizée Geffroy, Louis Lacoste, encadrés par Mélina Gallopin et Paul Bastide} -\institute{M2 MathSV Université Paris-Saclay} -% \titlegraphic{\hfill\includegraphics[height=1.5cm]{logo.pdf}} -\IfFileExists{upquote.sty}{\usepackage{upquote}}{} -\begin{document} - -\maketitle -\begin{frame}{Sommaire} - \setbeamertemplate{section in toc}[sections numbered] - \tableofcontents%[hideallsubsections] -\end{frame} - -\section[Rappel du contexte et enjeux du projet]{Rappel du contexte et enjeux du projet} -\begin{frame}[fragile]{Contexte biologique} -\begin{itemize} - \item Un arbre phylo avec plusieurs espèces - \item Un trait quantitatif présent chez ces espèces - \item Représenté par un paramètre $\mu$ -\end{itemize} -Typiquement un gène dont on mesure l'expression. -Dans \textbf{\textcite{gomez-mestrePhylogeneticAnalysesReveal2012}} ces méthodes sont utilisées pour répondre à des questions d'évolution et d'ordre d'apparition de caractères chez les \emph{Anoures}. -\end{frame} -\begin{frame}{ANOVA vs ANOVA phylogénétique} - \begin{equation*} - \bm{Y} = \bm{X}\beta+ \bm{\sigma} \bm{E} \text{ où } \bm{X}=(1,1_2, ..., 1_K) \text{ et }\beta = (\mu _1, \beta _2, ..., \beta _K)^T - \end{equation*} - \begin{columns} - - \column{0.5\textwidth} - \begin{center} - Anova - \end{center} - \begin{equation*} - \bm{E} \sim \mathcal{N}(0_n, \bm{Id}) - \end{equation*} - - \column{0.5\textwidth} - \begin{center} - Anova phylogénétique - \end{center} - \begin{equation*} - \bm{E} \sim \mathcal{N}(0_n, \bm{V}) - \end{equation*} - \end{columns} - \begin{center} - Estimateur du max. de vraisemblance - \end{center} - \begin{columns} - \column{0.5\textwidth} - \centering - $\hat{\beta} = (\bm{X}^{T}\bm{X})^{-1}\bm{X}^{T}\bm{Y}$\\ - $\hat{\sigma}^2 = \frac{1}{n-p} (\bm{Y} - \bm{X}\hat{\beta})^T(\bm{Y} - \bm{X}\hat{\beta})$ - % Finir - \column{0.5\textwidth} - \centering - $\hat{\beta}_{phylo} = (\bm{X}^{T}\bm{V}^{-1}\bm{X})^{-1}\bm{X}^{T}\bm{V}^{-1}\bm{Y}$\\ - $\hat{\sigma}_{phylo}^2 = \frac{1}{n-p} (\bm{Y} - \bm{X}\hat{\beta})^T\bm{V}^{-1}(\bm{Y} - \bm{X}\hat{\beta})$ - \end{columns} - - - \footnotetext{Pour l'ANOVA Phylogénétique, nos références sont \cite{bastideContinuousTraitEvolution} et \cite{bastideModelesEvolutionCaracteres2022} et pour l'ANOVA, \cite{belModeleLineaireSes}.} -Objectif : Comparer les méthodes Anova et Anova phylogénétique -\end{frame} -\begin{frame}{Différents types de groupes} -\begin{columns} - \begin{column}{0.5\textwidth} - \begin{figure} - \centering - On forme des groupes \textbf{en lien avec la phylogénie}. - \includegraphics[scale=0.32]{img/group_phylo_tree.png} - \caption{Arbre phylogénétique et groupes concordants} - \label{fig:phylo_matching} - \end{figure} - \end{column} - \begin{column}{0.5\textwidth} - \begin{figure} - \centering - On forme des groupes qui ne sont \textbf{pas phylogénétiques}. - \includegraphics[scale=0.32]{img/group_nonphylo_tree.png} - \caption{Arbre phylogénétique et groupes non concordants} - \label{fig:phylo-non-matching} - \end{figure} - \end{column} -\end{columns} - -\end{frame} - -% \begin{frame}[fragile]{Cas 1} -% Anova classique VS Anova phylogénétique -% \newline -% Voir les impacts de leur utilisation dans 2 cas: -% \begin{itemize} -% \item 1) On attribue des groupes au hasard -> les groupes ne sont pas liés à l'info phylogénétique -% \item 2) Les groupes sont définis en lien avec la phylogénie (des espèces proches ont un trait identique ou proche) -> la phylogénie donne une information sur les groupes -% \end{itemize} -% #METTRE LES IMAGES - -% Objectifs : Comparer les méthodes Anova et Anova phylogénétique -% \end{frame} -% \begin{frame}[fragile]{Nos hypothèses} -% \newline -% \begin{itemize} -% \item 1) Groupes non liés à l'info phylogénétique -> l'Anova phylogénétique sera égale voir moins bonne que l'Anova classique -% \item 2) Phylogénie donne une information sur les groupes -> l'Anova phylogénétique va donner de meilleurs résultats que la classique en prenant en compte la structure de l'arbre -% \end{itemize} -% \end{frame} - -\begin{frame}[fragile]{Les résultats, 1} -\begin{figure} - \centering - \includegraphics[scale=0.32]{img/simulation_power_pure_BM.png} - \caption{Avec de la variabilité purement phylogénétique} - \label{fig:only_phylo_error} -\end{figure} -\end{frame} - -\begin{frame}[fragile]{Les résultats, 2} -\begin{figure} - \centering - \includegraphics[scale=0.32]{img/simulation_power_pure_both_error.png} - \caption{Avec de la variabilité phylogénétique et d'erreur de mesure} - \label{fig:with_phylo_and_measure_error} -\end{figure} -\end{frame} - -\begin{frame}[fragile]{Ce qu'il se passe vraiment} -L'observation se présente sous la forme suivante si réécrite en tant que modèle à effets mixtes : -$$\bm{Y} = \bm{X}\beta + \underbrace{\bm{E}}_{\bm{Z} u + \epsilon} $$ -avec $\bm{Z} u \sim \mathcal{N}(0,\sigma^2_{phylo}V)$, $\epsilon \sim \mathcal{N}(0,\sigma^2_{mesure}\bm{Id})$ et $Var(\bm{E})=\sigma^2_{phylo} (V + \lambda\bm{Id})$ où $\lambda=\frac{\sigma^2_{mesure}}{\sigma^2_{phylo}}$ - -Les méthodes d'ANOVA phylogénétique telles qu'implémentées dans \texttt{phylolm} estiment les paramètres $\sigma^2_{mesure}$ d'erreur de mesure et $\sigma^2_{phylo}$ de variabilité dûe à la phylogénie.\\ -\emph{Mais} une fois estimé, lors du test de Fisher les paramètres sont considérés comme si non estimés. - - -Le but ici est donc d'utiliser l'approximation de \textcite{satterthwaiteApproximateDistributionEstimates1946} afin de calculer les degrés de libertés du test de loi de Fisher à réaliser. -\end{frame} - -\section{Conclusions et perspectives} -\begin{frame}{Avec des données individuelles} -\begin{center} -\usetikzlibrary{trees} -\scalebox{0.75}{ -\begin{tikzpicture}[level distance=2cm, - level 1/.style={sibling distance=4cm}, - level 2/.style={sibling distance=2cm}, - level 3/.style={sibling distance=1cm}] - \node {Root} - child { - node {A} - child {node {A1} - child {node {}} - child {node {}} - child {node {}} - } - child {node {A2} - child {node {}} - child {node {}} - child {node {}} - } - } - child { - node {B} - child {node {B1} - child {node {}} - child {node {}} - child {node {}} - } - child {node {B2} - child {node {}} - child {node {}} - child {node {}} - } - } - child { - node {C} - child {node {C1} - child {node {}} - child {node {}} - child {node {}} - } - child {node {C2} - child {node {}} - child {node {}} - child {node {}} - } - }; -\end{tikzpicture} -}\\ -\end{center} -Le package \texttt{phylolimma}\footnote{Disponible sur \url{https://github.com/pbastide/phylolimma/}} permet de compléter un arbre existant en ajoutant les sous-branches au bout.\\ -Nous voulons obtenir une méthode d'estimation des paramètres et l'implémenter sur ce type d'arbre. -\end{frame} -\begin{frame}{Perspectives} - \begin{itemize} - \item Implémenter le test statistique correspondant à l'approximation de Satterthwaite. - \item Implémenter le test de ratio de log-vraisemblance. - \item Implémenter avec plusieurs individus par espèces - \end{itemize} - \begin{block}{Objectif principal} - Trouver un test robuste et rapide, applicable à des milliers de données d'expressions de gènes mesurées dans une expérience RNAseq typique. - \end{block} - -\end{frame} - -\section{Références et appendices} -\begin{frame}[allowframebreaks]{References} - - \printbibliography - % \bibliographystyle{abbrv} - -\end{frame} - -\appendix - -\begin{frame}[allowframebreaks]{Code pour les simulations} - Le code pour les simulations est disponible sur notre 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