Adding translation in english

.gitignore

@@ -24,6 +24,8 @@
 ## Generated if empty string is given at "Please type another file name for output:"
 .pdf
 
+*.pdf
+
 ## Bibliography auxiliary files (bibtex/biblatex/biber):
 *.bbl
 *.bbl-SAVE-ERROR

annexe.tex

@@ -1,7 +1,7 @@
 \section{VEM}
 
 \begin{frame}
-    \frametitle{Pourquoi VE minimise KL ?}
+    \frametitle{Why does VE minimizes KL ?}
     \begin{align*}
         \ell_c(\bY,\bZ,\bW;\theta)                               & = \log \Prob(\bZ, \bW|\bY;\theta) + \ell(\bY;\theta)                                    \\
         \Leftrightarrow            \ell(\bY;\theta)              & = \ell_c(\bY,\bZ,\bW;\theta) - \log \Prob(\bZ, \bW|\bY;\theta)                          \\
@@ -9,14 +9,14 @@
         \Leftrightarrow            \ell(\bY;\theta)              & = \Esp_{\Ryt}[\ell_c(\bY,\bZ,\bW;\theta)] - \Esp_{\Ryt}[\log \Prob(\bZ,\bW|\bY;\theta)] \\
     \end{align*}
     \begin{align*}
-        \text{Or }\KL{\Ryt}{\log \Prob(\bZ,\bW|\bY;\theta)}                         & = - \Esp_{\Ryt} [\log \frac{\Prob(\bZ,\bW|\bY;\theta)}{\Ryt}] \\
+        \text{But }\KL{\Ryt}{\log \Prob(\bZ,\bW|\bY;\theta)}                        & = - \Esp_{\Ryt} [\log \frac{\Prob(\bZ,\bW|\bY;\theta)}{\Ryt}] \\
         = - \Esp_{\Ryt} [\log \Prob(\bZ,\bW|\bY;\theta)] +                          & \underbrace{\Esp_{\Ryt[\log \Ryt]}}_{-\Hshannon(\Ryt)}        \\
         \Leftrightarrow \KL{\Ryt}{\log \Prob(\bZ,\bW|\bY;\theta)} + \Hshannon(\Ryt) & = - \Esp_{\Ryt} [\log \Prob(\bZ,\bW|\bY;\theta)]
     \end{align*}
-    D'où $\ell(\bY;\theta) - \KL{\Ryt}{\log \Prob(\bZ,\bW|\bY;\theta)} = \mathcal{J}(\tau;\theta) \qed$
+    Thus $\ell(\bY;\theta) - \KL{\Ryt}{\log \Prob(\bZ,\bW|\bY;\theta)} = \mathcal{J}(\tau;\theta) \qed$
 \end{frame}
 
-\section{Résultats~\cite{baldockSystemsApproachReveals2019a,baldockDailyTemporalStructure2011}}
+\section{Résultats~\cite{baldockSystemsApproachReveals2019,baldockDailyTemporalStructure2011}}
 \begin{frame}[allowframebreaks]
     \begin{figure}[ht]
         \centering
@@ -28,7 +28,7 @@
         \begin{subfigure}[t]{0.5\textwidth}
             \centering
             \includegraphics[width=0.45\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Bristol.pdf}
-            \caption{Réordonnée}
+            \caption{Reordered}
         \end{subfigure}
         \caption{Bristol}
     \end{figure}
@@ -43,7 +43,7 @@
         \begin{subfigure}[t]{0.5\textwidth}
             \centering
             \includegraphics[width=0.5\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Edinburgh.pdf}
-            \caption{Réordonnée}
+            \caption{Reordered}
         \end{subfigure}
         \caption{Edinburgh}
     \end{figure}

presentation.tex

@@ -2,7 +2,7 @@
 \usetheme{Boadilla}
 
 % importations
-\usepackage[french]{babel} % pour dire que le texte est en francais
+% \usepackage[french]{babel} % pour dire que le texte est en francais
 \usepackage{csquotes}
 \usepackage[T1]{fontenc} % pour les font postscript
 \usepackage[cyr]{aeguill} % Police vectorielle TrueType, guillemets francais
@@ -111,9 +111,8 @@
 
 
 \subtitle{Présentation LSD}
-\title[Collections de réseaux bipartites]{Analyse jointe de collections de 
+\title[Bipartite networks collection]{Joint analysis of bipartite networks collection}
-réseaux bipartites}
+\author[L. Lacoste]{Louis \textsc{Lacoste}, under the supervision of Pierre Barbillon and
-\author[L. Lacoste]{Louis \textsc{Lacoste}, encadré par Pierre Barbillon et 
 Sophie Donnet\newline Laboratoire MIA Paris-Saclay} % Sous la supervision de Pierre
 \date{}
 
@@ -129,7 +128,7 @@ Sophie Donnet\newline Laboratoire MIA Paris-Saclay} % Sous la supervision de Pie
 
     \renewcommand{\pgfuseimage}[1]{\scalebox{.75}{\includegraphics{#1}}}
     \begin{frame}[noframenumbering,plain,allowframebreaks]
-        \frametitle{Bibliographie}
+        \frametitle{References}
         \printbibliography
     \end{frame}
 \end{refsection}
@@ -139,9 +138,9 @@ Sophie Donnet\newline Laboratoire MIA Paris-Saclay} % Sous la supervision de Pie
 \begin{refsection}
     \include{annexe}
     \renewcommand{\pgfuseimage}[1]{\scalebox{.75}{\includegraphics{#1}}}
-    \section{Références annexes}
+    \section{Appendices references}
     \begin{frame}[noframenumbering,plain,allowframebreaks]
-        \frametitle{Bibliographie des annexes}
+        \frametitle{Appendices references}
         \printbibliography
     \end{frame}
 \end{refsection}

principal.tex

@@ -1,8 +1,8 @@
-\section{Contexte du modèle}
+\section{Model Context}
-\label{sec:contexte-du-modele}
+\label{sec:context-of-the-model}
 
 \begin{frame}
-    \frametitle{Pourquoi un réseau ?}
+    \frametitle{Why a network?}
     \begin{columns}
         \begin{column}{0.5\textwidth}
             \begin{columns}
@@ -12,8 +12,8 @@
                         \begin{tikzpicture}[scale=.6,rotate=270]
                             \input{tikz/plantpollinatornetwork.tex}
                         \end{tikzpicture}
-                        \caption{Exemple d'un réseau}
+                        \caption{Example of a network}
-                        \label{fig:plantes-pollin}
+                        \label{fig:plants-pollin}
                     \end{figure}
                 \end{column}
                 \begin{column}{0.3\textwidth}
@@ -27,34 +27,34 @@
                         \end{pmatrix}
                     \end{align*}
                     \footnotesize
-                    Matrice d'adjacence associée
+                    Associated adjacency matrix
                 \end{column}
             \end{columns}
             \begin{figure}[ht]
                 \centering
-                \includestandalone[width=0.7\textwidth]{tikz/applications/baldock/graph-Baldock2019_Bristol}
+                \includegraphics[width=0.7\textwidth]{tikz/applications/baldock/graph-Baldock2019_Bristol.pdf}
-                \caption{Réseau plante-pollinisateur de
+                \caption{Plant-pollinator network of
-                    Bristol\newline\cite{baldockSystemsApproachReveals2019a}}
+                    Bristol\newline\cite{baldockSystemsApproachReveals2019}}
                 \label{fig:label}
             \end{figure}
         \end{column}
         \begin{column}{0.5\textwidth}
             \begin{itemize}
-                \item Modélisation d'interactions variées, ici d'écosystèmes
+                \item Modeling of various interactions, here ecosystems
-                \item Structure nécessaire pour~: suivi biodiversité, robustesse, risque
+                \item Structure necessary for: biodiversity monitoring, robustness, risk
-                      d'effondrement
+                      of collapse
-                \item De plus en plus disponibles
+                \item Increasingly available
             \end{itemize}
         \end{column}
     \end{columns}
 \end{frame}
 
-\begin{frame}{Méthodes d'analyse pour un réseau}
+\begin{frame}{Analysis methods for a network}
-    Plusieurs méthodes~:
+    Several methods~:
     \begin{itemize}
-        \item Métriques~: degré, centralité, emboîtement \dots
+        \item Metrics~: degree, centrality, nesting \dots
-        \item Plongement des réseaux avec GNN
+        \item Network embedding with GNN
-        \item \textbf<2>{\emph{Clustering} des n\oe uds avec modèles à variables latentes}
+        \item \textbf<2>{\emph{Clustering} of nodes with latent variable models}
     \end{itemize}
 \end{frame}
 
@@ -70,32 +70,32 @@
                 \begin{tikzpicture}[scale=0.35]
                     \input{tikz/lbm.tex}
                 \end{tikzpicture}
-                \caption{Exemple de LBM\footnotemark[\thefootnote]}
+                \caption{Example of LBM\footnotemark[\thefootnote]}
                 \label{fig:LBMvisu}
             \end{figure}
         \end{column}
         \only<1>{
             \begin{column}{0.51\linewidth}
-                \begin{block}{Modèle hiérarchique}
+                \begin{block}{Hierarchical model}
                     \vspace{-\baselineskip}
                     \begin{align*}
                         \forall q\in[\![ 1, Q_1]\!],~ & \mathbb{P}(Z_i = q) = \pi_q                          \\
                         \forall r\in[\![ 1, Q_2]\!],~ & \mathbb{P}(W_j = r) =  \rho_r                        \\
                                                       & Y_{ij} | Z_i, W_j \sim \mathcal{F}(\alpha_{Z_i,W_j})
                     \end{align*}
-                    où $|\pi| = Q_1, |\rho| = Q_2, |\alpha| = Q_1 \times Q_2$
+                    where $|\pi| = Q_1, |\rho| = Q_2, |\alpha| = Q_1 \times Q_2$
                 \end{block}
-                \begin{block}{Formule concise LBM}
+                \begin{block}{Concise LBM formula}
                     $Y \sim \mathcal{F}\text{-BiSBM}_{n_1,n_2}(Q_1, Q_2, \pi, \rho, \alpha)$
                 \end{block}
             \end{column}}
         \only<2>{
             \begin{column}{0.51\linewidth}
-                Avec \begin{itemize}
+                With \begin{itemize}
-                    \item $Q_1 = |\{{\color{blueind}\bullet},{\color{cyanind}\bullet},{\color{electricblue}\bullet}\}|$ blocs fixés en ligne
+                    \item $Q_1 = |\{{\color{blueind}\bullet},{\color{cyanind}\bullet},{\color{electricblue}\bullet}\}|$ fixed row blocks
-                    \item $Q_2 = |\{{\color{burntorange}\bullet},{\color{goldenyellow}\bullet},{\color{peach}\bullet}\}|$ blocs fixés en colonne
+                    \item $Q_2 = |\{{\color{burntorange}\bullet},{\color{goldenyellow}\bullet},{\color{peach}\bullet}\}|$ fixed column blocks
                 \end{itemize}
-                \begin{block}{Paramètres}
+                \begin{block}{Parameters}
                     \begin{itemize}
                         \item $\pi_{{\color{blueind}\bullet}} = \mathbb{P}(Z_i = {\color{blueind}\bullet})$
                         \item $\rho_{{\color{burntorange}\bullet}} = \mathbb{P}(W_j = {\color{burntorange}\bullet})$
@@ -105,11 +105,11 @@
             \end{column}}
     \end{columns}
 
-    \footnotetext[\thefootnote]{Que j'appellerai par la suite BiSBM}
+    \footnotetext[\thefootnote]{Which I will henceforth call BiSBM}
 \end{frame}
 
 \begin{frame}
-    \frametitle{Plusieurs réseaux}
+    \frametitle{Multiple networks}
     \begin{figure}[ht]
         \centering
         \begin{subfigure}[ht]{0.3\textwidth}
@@ -124,15 +124,15 @@
             \includegraphics[width=1.1\textwidth]{tikz/applications/baldock/mat-Baldock2019_Leeds.pdf}
             \caption{Leeds}
         \end{subfigure}
-        \caption{Matrices d'adjacence,~\cite{baldockSystemsApproachReveals2019a}}
+        \caption{Adjacency matrices,~\cite{baldockSystemsApproachReveals2019}}
         \label{fig:adj}
     \end{figure}
 \end{frame}
 
-\section[Modèles collection bipartites]{Modèles de collection de réseaux bipartites}
+\section[Bipartite collection models]{Bipartite network collection models}
-\label{sec:extension-de-colsbm-aux-reseaux-bipartites}
+\label{sec:extension-of-colsbm-to-bipartite-networks}
 \begin{frame}
-    \frametitle{Collections bipartites}
+    \frametitle{Bipartite collections}
     \[
         \forall m \in \{1\dots M\}, Y^m \overset{ind}{\sim} \mathcal{F}\text{-BiSBM}_{n_1^m,n_2^m}(Q_1^m, Q_2^m, \pi^m, \rho^m, \alpha^m)
     \]
@@ -144,28 +144,28 @@
                 \caption{Bristol}
             \end{subfigure}
             \begin{subfigure}[ht]{0.3\textwidth}
-                \includestandalone[width=1.1\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Edinburgh}
+                \includegraphics[width=1.1\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Edinburgh.pdf}
                 \caption{Edinburgh}
             \end{subfigure}
             \begin{subfigure}[ht]{0.3\textwidth}
-                \includestandalone[width=1.1\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Leeds}
+                \includegraphics[width=1.1\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Leeds.pdf}
                 \caption{Leeds}
             \end{subfigure}
-            \caption{Matrices d'adjacence réordonnées, grâce au LBM}
+            \caption{Reordered adjacency matrices, thanks to LBM}
             \label{fig:adj-reord}
         \end{figure}
     }
 \end{frame}
 
 \begin{frame}
-    \frametitle{Différents modèles}
+    \frametitle{Different models}
     \onslide<1->{    \begin{block}{\emph{iid}-colBiSBM}
             \[
                 \forall m \in \{1\dots M\}, Y^m \overset{iid}{\sim}
                 \mathcal{F}\text{-BiSBM}_{n_1^m,n_2^m}(Q_1, Q_2, \pi, \rho, \alpha)
             \]
 
-            avec $\theta = (\pi, \rho, \alpha)$.
+            with $\theta = (\pi, \rho, \alpha)$.
         \end{block}}
     \onslide<2>{    \begin{block}{$\pi\rho$-colBiSBM}
             \[
@@ -173,53 +173,53 @@
                 \mathcal{F}\text{-BiSBM}_{n_1^m,n_2^m}(Q_1, Q_2, \pi^m, \rho^m, \alpha)
             \]
 
-            avec $\theta = ((\pi^m)_{m=1,\dots, M}, (\rho^m)_{m=1,\dots, M}, \alpha)$.
+            with $\theta = ((\pi^m)_{m=1,\dots, M}, (\rho^m)_{m=1,\dots, M}, \alpha)$.
         \end{block}
     }
 \end{frame}
 \begin{frame}
-    \frametitle{Estimation des paramètres}
+    \frametitle{Parameter estimation}
-    % DONE dire que tau i q m c' est la proba que Zim = q, approximation de la proba variationnelle. Parce qu on impose lindependance
+    % DONE say that tau i q m c' is the probability that Zim = q, approximation of the variational probability. Because we impose independence
-    % Par maximisation d'une borne inférieure variationnelle de la
+    % By maximizing a variational lower bound of the
-    % log-vraisemblance des données observées.
+    % log-likelihood of the observed data.
-    Maximisation de la log-vraisemblance ?
+    Maximizing the log-likelihood?
-    \begin{block}{log-vraisemblance et log-vraisemblance complète}
+    \begin{block}{log-likelihood and complete log-likelihood}
         \[
             \ell(\bm{Y};\theta) = \sum_{\bm{Z,W}\in \bm{\mathcal{Z}\times\mathcal{W}}} \ell_c(\bm{Y}, \bm{Z}, \bm{W};\theta)
         \]
 
-        avec $\bm{\mathcal{Z}} = \{1,\dots,\alert<2>{Q_1}\}^{\alert<2>{n}},
+        with $\bm{\mathcal{Z}} = \{1,\dots,\alert<2>{Q_1}\}^{\alert<2>{n}},
             \bm{\mathcal{W}} = \{1,\dots,\alert<2>{Q_2}\}^{\alert<2>{n}}$
     \end{block}
-    \uncover<3>{Donc, algorithme classique $\Rightarrow$
+    \uncover<3>{So, classic algorithm $\Rightarrow$
         \emph{Expectation-Maximization} (EM).}
 \end{frame}
 
 \begin{frame}
-    \frametitle{Par EM classique}
+    \frametitle{By classic EM}
-    A l'itération $(t)$ :
+    At iteration $(t)$:
     \begin{itemize}
-        \item[$\bullet$]\textbf{Étape E}: calculer
+        \item[$\bullet$]\textbf{E Step}: calculate
               $$ \mathcal{Q}(\theta | \theta^{(t-1)}) =   \mathbb E_{\alert<2>{\bm Z, \bm W | \bm Y, \theta^{(t-1)}} } \left[\ell_c(\bm Y, \bm W, \bm Z; \theta)  \right] $$
-        \item[$\bullet$]\textbf{Étape M}:
+        \item[$\bullet$]\textbf{M Step}:
               $$ \theta^{(t)} = \arg \max_{\theta} \mathcal{Q}(\theta | \theta^{(t-1)})$$
     \end{itemize}
     \uncover<2>{
-        \begin{alertblock}{Problème pour l'EM classique}
+        \begin{alertblock}{Problem for classic EM}
-            Loi de $\bm{Z,W|Y},\theta^{(t-1)}$ inaccessible
+            Law of $\bm{Z,W|Y},\theta^{(t-1)}$ inaccessible
         \end{alertblock}}
 
 \end{frame}
 
 \begin{frame}
-    Par \emph{Variational EM}, comme proposé
+    By \emph{Variational EM}, as proposed
-    par~\cite{daudinMixtureModelRandom2008,
+    by~\cite{daudinMixtureModelRandom2008,
-        chabert-liddellLearningCommonStructures2024a}.
+        chabert-liddellLearningCommonStructures2024}.
-    \begin{block}{Approximation variationnelle de $\bm{Z,W|Y},\theta^{(t-1)}$}
+    \begin{block}{Variational approximation of $\bm{Z,W|Y},\theta^{(t-1)}$}
         $\mathcal{R}_{Y^m,\tau}(\mathbf{Z}^m, \mathbf{W}^m) =
             \mathcal{R}^1_{Y^m,\tau}(\mathbf{Z}^m)
             {\color{red}\times}
-            \mathcal{R}^2_{Y^m,\tau}(\mathbf{W}^m) \Rightarrow$ indépendance lignes, colonnes.
+            \mathcal{R}^2_{Y^m,\tau}(\mathbf{W}^m) \Rightarrow$ independence rows, columns.
     \end{block}
     \begin{multline*}
         \ell (\bm{Y};\theta) \geq \color{red}\sum_{m=1}^{M} \bigg(
@@ -229,13 +229,13 @@
         \color{red}\bigg) \color{black}
         \eqcolon \mathcal{J}(\tau;\theta)
     \end{multline*}
-    où $\mathcal{Q}^m(\theta\mid\theta^{(t)}) =
+    where $\mathcal{Q}^m(\theta\mid\theta^{(t)}) =
         \mathbb{E}_{\mathbf{Z}^m,\mathbf{W}^m
         \sim \mathcal{R}_{Y^m,\tau}(.)}
         \left[ \ell_c(Y^m,\mathbf{Z}^m,\mathbf{W}^m | \theta) \right] \,$
 \end{frame}
 
-\begin{frame}{Formule développée de l'EM variationnel}
+\begin{frame}{Developed formula of variational EM}
     \begin{multline*}
         \ell (\bm{Y};\theta) \geq \color{red}\sum_{m=1}^{M} \bigg( \color{black} \sum_{i = 1}^{n_1^m}\sum_{j=1}^{n_2^m}\sum_{q \in \mathcal{Q}_{1,m}} \sum_{r \in \mathcal{Q}_{2,m}} \tau^{1,m}_{i,q} \tau^{2,m}_{j,r} \log f(Y^{m}_{ij}; \alpha_{qr}) \\
         + \sum_{i=1}^{n_1^m} \sum_{q \in \mathcal{Q}_{1,m}} \tau^{1,m}_{i,q} \log \pi_{\color{black}q}^{\color{gray}m} + \sum_{j=1}^{n_2^m} \sum_{r \in \mathcal{Q}_{2,m}} \tau^{2,m}_{j,r} \log \rho_{\color{black}r}^{\color{gray}m} \\
@@ -243,13 +243,13 @@
         \mathcal{J}(\tau;\theta),
     \end{multline*}
 
-    \begin{block}{Approximation variationnelle}
+    \begin{block}{Variational approximation}
         $\tau_{iq}^{1,m} = \mathcal{R}^1_{Y^m,\tau}(Z_{iq}^m = 1)$
-        et $\tau_{jr}^{2,m} = \mathcal{R}^2_{Y^m,\tau}(W_{jr}^m = 1)$
+        and $\tau_{jr}^{2,m} = \mathcal{R}^2_{Y^m,\tau}(W_{jr}^m = 1)$
     \end{block}
 \end{frame}
 
-\begin{frame}{Étape \emph{Variational Expectation}}
+\begin{frame}{\emph{Variational Expectation} Step}
     \[
         \widehat{\tau}^{(t+1)} = \arg \max_{\tau}
         \mathcal{J}(\mathcal{\tau},\bm{\widehat{\theta}}^{(t)})
@@ -262,22 +262,22 @@
             \widehat{\tau}_{jr}^{2,m} \propto \widehat{\rho}_{r}^{m(t)} \prod_{i=1}^{n_1^m}\prod_{q\in\mathcal{Q}_1^m} f(Y_{ij}^m;\widehat{\alpha}_{qr}^{(t)})^{\widehat{\tau}_{iq}^{1,m(t+1)}} & \forall j = 1, \dots , n_2^m, r \in \mathcal{Q}_2^m
         \end{cases}
     \end{equation*}
-    \footnotetext[2]{Initialisation des $\widehat{\tau}$ avec un
+    \footnotetext[2]{Initialization of $\widehat{\tau}$ with a
-        \emph{spectral clustering} sur les réseaux.}
+        \emph{spectral clustering} on the networks.}
 \end{frame}
 
-\begin{frame}{Étape \emph{Maximization}}
+\begin{frame}{\emph{Maximization} Step}
     \[
         \widehat{\theta}^{(t+1)} = \arg \max_{\theta} \mathcal{J}(\mathcal{\bm{\widehat{\tau}}}^{(t+1)},\theta)
     \]
 
-    \begin{block}{Paramètres de connectivité}
+    \begin{block}{Connectivity parameters}
         \begin{align*}
             \widehat{\alpha}_{qr} = \frac{\sum_{m=1}^{M} \sum_{i=1}^{n_1^m} \sum_{j=1}^{n_2^m} \tau_{iq}^{1,m} \tau_{jr}^{2,m} \alert<2>{Y_{ij}^m}}{\sum_{m=1}^{M} \sum_{i=1}^{n_1^m} \sum_{j=1}^{n_2^m} \tau_{iq}^{1,m} \tau_{jr}^{2,m}}
         \end{align*}
     \end{block}
     \only<1>{
-        \begin{block}{Proportions pour \emph{iid}}
+        \begin{block}{Proportions for \emph{iid}}
             \begin{align*}
                 \widehat{\pi}_q = \frac{\sum_{m=1}^{M} \sum_{i=1}^{n_1^m} \tau_{iq}^{1,m}}{\sum_{m=1}^{M} n_1^m} &  &
                 \widehat{\rho}_r = \frac{\sum_{m=1}^{M} \sum_{j=1}^{n_2^m} \tau_{jr}^{2,m}}{\sum_{m=1}^{M} n_2^m}
@@ -285,7 +285,7 @@
         \end{block}
     }
     \only<2>{
-        \begin{block}{Proportions pour $\pi\rho$}
+        \begin{block}{Proportions for $\pi\rho$}
             \begin{align*}
                 \widehat{\pi}^{\color{red}m}_q = \frac{\sum_{i=1}^{n_1^m} \tau_{iq}^{1,m}}{n_1^m} &  &
                 \widehat{\rho}^{\color{red}m}_r = \frac{\sum_{j=1}^{n_2^m} \tau_{jr}^{2,m}}{n_2^m}
@@ -295,26 +295,26 @@
 
 \end{frame}
 
-\section{Sélection de modèle}
+\section{Model selection}
 \begin{frame}
-    \frametitle{Problème choix de $(Q_1, Q_2)$}
+    \frametitle{Problem of choosing $(Q_1, Q_2)$}
-    Besoin sélectionner $Q_1$ et $Q_2$. Critère BIC-Like\footnote{ICL + Entropie + pénalité}
+    Need to select $Q_1$ and $Q_2$. BIC-Like criterion\footnote{ICL + Entropy + penalty}
 
     \begin{align*}
         \text{BIC-L}(\bm{Y}, Q_1, Q_2) & = \max_{\theta} \mathbb{E}_{\mathcal{R}_{\mathbf{Y},\hat{\tau}}} [\ell_c(\bm{Y,Z,W};\theta)] + \mathcal{H(\mathcal{R}_{\mathbf{Y},\hat{\tau}})} - \frac{1}{2}\text{pen}(\theta, Q_1, Q_2) \\
                                        & = \max_{\theta} \mathcal{J(\mathcal{R}_{\mathbf{Y},\hat{\tau}}, \theta)} - \frac{1}{2}\text{pen}(\theta, Q_1, Q_2)
     \end{align*}
 
-    \begin{alertblock}{Problèmes de l'exploration}
+    \begin{alertblock}{Exploration problems}
         \begin{itemize}
-            \item Exploration de $\mathbb{N}^2$ coûteux.
+            \item Exploration of $\mathbb{N}^2$ costly.
-            \item Sensibilité initialisations.
+            \item Sensitivity to initializations.
         \end{itemize}
     \end{alertblock}
 \end{frame}
 
 \begin{frame}
-    \frametitle{Choix de $(Q_1,Q_2)$ - Approche gloutonne}
+    \frametitle{Choice of $(Q_1,Q_2)$ - Greedy approach}
     \begin{columns}
         \begin{column}{0.5\linewidth}
             \begin{tikzpicture}
@@ -323,22 +323,22 @@
         \end{column}
         \begin{column}{0.35\linewidth}
             \begin{itemize}
-                \item Modèle initialisé~:\\
+                \item Initial model~:\\
                       \begin{tikzpicture}
                           \draw[fill=gray, draw=gray] circle [radius=0.225cm];
                       \end{tikzpicture}
                       \onslide<2->{
-                \item Modèle après \emph{split}~:
+                \item Model after \emph{split}~:
                       \begin{tikzpicture}
                           \draw[fill=blueind, draw=blueind] circle [radius=0.225cm];
                       \end{tikzpicture}
-                \item Modèle maximisant le critère~:\\
+                \item Model maximizing the criterion~:\\
                       \begin{tikzpicture}
                           \draw[fill=white, draw=green, very thick] circle [radius=0.225cm];
                       \end{tikzpicture}
                       }
                       \onslide<3->{
-                \item Modèle après \emph{merge}~:
+                \item Model after \emph{merge}~:
                       \begin{tikzpicture}
                           \draw[fill=red, draw=red] circle [radius=0.225cm];
                       \end{tikzpicture}
@@ -348,23 +348,23 @@
     \end{columns}
 \end{frame}
 \begin{frame}
-    \frametitle{Choix de $(Q_1,Q_2)$ - Fenêtre glissante}
+    \frametitle{Choice of $(Q_1,Q_2)$ - Sliding window}
     \begin{columns}
         \begin{column}{0.6\textwidth}
             \begin{figure}
                 \input{tikz/moving-window}
-                \caption{Fenêtre glissante}
+                \caption{Sliding window}
             \end{figure}
         \end{column}
         \begin{column}{0.4\textwidth}
             \only<3>{\begin{block}{}
-                    Initialisation du modèle si nécessaire
+                    Initialization of the model if necessary
                 \end{block}}
             \only<9>{\begin{block}{}
-                    Localisation du nouveau mode
+                    Localization of the new mode
                 \end{block}}
             \only<10>{\begin{block}{}
-                    Déplacement sur le nouveau mode puis itération
+                    Move to the new mode then iterate
                 \end{block}}
         \end{column}
     \end{columns}
@@ -374,7 +374,7 @@
 \label{sec:application}
 
 \begin{frame}
-    \frametitle{Résultats~\cite{baldockSystemsApproachReveals2019a}}
+    \frametitle{Results~\cite{baldockSystemsApproachReveals2019}}
 
     \only<1>{
         \begin{figure}[ht]
@@ -386,21 +386,21 @@
             \end{subfigure}\hfil
             \begin{subfigure}[t]{0.5\textwidth}
                 \centering
-                \includestandalone[width=0.45\textwidth]{tikz/applications/baldock/mat-Baldock2019_Edinburgh}
+                \includegraphics[width=0.45\textwidth]{tikz/applications/baldock/mat-Baldock2019_Edinburgh.pdf}
                 \caption{Edinburgh}
             \end{subfigure}
             \newline
             \begin{subfigure}[ht]{0.5\textwidth}
                 \centering
-                \includestandalone[width=0.5\textwidth]{tikz/applications/baldock/mat-Baldock2019_Leeds}
+                \includegraphics[width=0.5\textwidth]{tikz/applications/baldock/mat-Baldock2019_Leeds.pdf}
                 \caption{Leeds}
             \end{subfigure}\hfil
             \begin{subfigure}[ht]{0.5\textwidth}
                 \centering
-                \includestandalone[width=0.5\textwidth]{tikz/applications/baldock/mat-Baldock2019_Reading}
+                \includegraphics[width=0.5\textwidth]{tikz/applications/baldock/mat-Baldock2019_Reading.pdf}
                 \caption{Reading}
             \end{subfigure}
-            \caption{Matrices d'adjacence,~\cite{baldockSystemsApproachReveals2019a}}
+            \caption{Adjacency matrices,~\cite{baldockSystemsApproachReveals2019}}
         \end{figure}
     }
     \only<2>{
@@ -408,57 +408,57 @@
             \centering
             \begin{subfigure}[t]{0.5\textwidth}
                 \centering
-                \includestandalone[width=0.45\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Bristol}
+                \includegraphics[width=0.45\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Bristol.pdf}
                 \caption{Bristol}
             \end{subfigure}\hfil
             \begin{subfigure}[t]{0.5\textwidth}
                 \centering
-                \includestandalone[width=0.45\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Edinburgh}
+                \includegraphics[width=0.45\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Edinburgh.pdf}
                 \caption{Edinburgh}
             \end{subfigure}
             \newline
             \begin{subfigure}[ht]{0.5\textwidth}
                 \centering
-                \includestandalone[width=0.5\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Leeds}
+                \includegraphics[width=0.5\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Leeds.pdf}
                 \caption{Leeds}
             \end{subfigure}\hfil
             \begin{subfigure}[ht]{0.5\textwidth}
                 \centering
-                \includestandalone[width=0.5\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Reading}
+                \includegraphics[width=0.5\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Reading.pdf}
                 \caption{Reading}
             \end{subfigure}
-            \caption{Matrices d'adjacence réordonnée par \emph{iid}-colBiSBM,~\cite{baldockSystemsApproachReveals2019a}}
+            \caption{Reordered adjacency matrices by \emph{iid}-colBiSBM,~\cite{baldockSystemsApproachReveals2019}}
         \end{figure}
     }
 \end{frame}
 
 \begin{frame}
-    \frametitle{Clustering de réseaux}
+    \frametitle{Network clustering}
     \begin{figure}[ht]
-        \includestandalone[width=0.45\textwidth]{tikz/applications/baldock/mat-Baldock2011_TB+Baldock2011_JN}
+        \includegraphics[width=0.45\textwidth]{tikz/applications/baldock/mat-Baldock2011_TB+Baldock2011_JN.pdf}
-        \caption{Matrice d'adjacence,~\cite{baldockDailyTemporalStructure2011}}
+        \caption{Adjacency matrix,~\cite{baldockDailyTemporalStructure2011}}
     \end{figure}
 \end{frame}
 
 \begin{frame}[allowframebreaks]
-    \frametitle{Application à~\cite{baldockDailyTemporalStructure2011,
+    \frametitle{Application to~\cite{baldockDailyTemporalStructure2011,
-            baldockSystemsApproachReveals2019a}}
+            baldockSystemsApproachReveals2019}}
     \begin{figure}[t]
         \centering
         \begin{subfigure}{0.5\textwidth}
             \centering
             \includegraphics[scale=0.2,angle=-90]{backup-app-iid.png}
-            \caption{Modèle $iid$}
+            \caption{Model $iid$}
         \end{subfigure}%
         ~
         \begin{subfigure}{0.5\textwidth}
             \centering
             \includegraphics[scale=0.2,angle=-90]{backup-app-pirho.png}
-            \caption{Modèle $\pi\rho$}
+            \caption{Model $\pi\rho$}
         \end{subfigure}%
-        \caption{Partitionnement des réseaux
+        \caption{Partitioning of networks
-            de~\cite{baldockDailyTemporalStructure2011,
+            of~\cite{baldockDailyTemporalStructure2011,
-                baldockSystemsApproachReveals2019a}}
+                baldockSystemsApproachReveals2019}}
     \end{figure}
 
     \begin{figure}[t]
@@ -467,23 +467,23 @@
             \centering
             \includegraphics[scale=0.1]{backup-app-iid-struct1.png}
             \includegraphics[scale=0.2]{backup-app-iid-struct2.png}
-            \caption{Modèle $iid$,\\
+            \caption{Model $iid$,\\
-                séparent réseau africain et réseaux anglais}
+                separate African network and English networks}
         \end{subfigure}%
         ~
         \begin{subfigure}{0.5\textwidth}
             \centering
             \includegraphics[scale=0.2]{backup-app-pirho-struct.png}
-            \caption{Modèle $\pi\rho$,\\
+            \caption{Model $\pi\rho$,\\
-                fusionnent réseaux africain et anglais}
+                merge African and English networks}
         \end{subfigure}%
-        \caption{Structures détectées pour les réseaux
+        \caption{Structures detected for networks
-            de~\cite{baldockDailyTemporalStructure2011,
+            of~\cite{baldockDailyTemporalStructure2011,
-                baldockSystemsApproachReveals2019a}}
+                baldockSystemsApproachReveals2019}}
     \end{figure}
 \end{frame}
 
-\begin{frame}{Algorithme du clustering}
+\begin{frame}{Clustering algorithm}
     \centering
     \vspace{0.25\baselineskip}
     \begin{tikzpicture}[scale=0.85]
@@ -494,38 +494,38 @@
     \]
 \end{frame}
 
-\begin{frame}{Résultats}
+\begin{frame}{Results}
     \begin{figure}[ht]
         \centering
         \begin{subfigure}{0.5\textwidth}
             \centering
-            \includestandalone[width=1\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2011_TB+Baldock2011_JN}
+            \includegraphics[width=1\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2011_TB+Baldock2011_JN.pdf}
-            \caption{Réordonnée par LBM}
+            \caption{Reordered by LBM}
         \end{subfigure}\hfil
         \begin{subfigure}{0.5\textwidth}
             \centering
-            \includestandalone[width=1\textwidth]{tikz/applications/baldock/pirho-colbisbm-mat-Baldock2011_TB+Baldock2011_JN}
+            \includegraphics[width=1\textwidth]{tikz/applications/baldock/pirho-colbisbm-mat-Baldock2011_TB+Baldock2011_JN.pdf}
-            \caption{Réordonnée par $\pi\rho$-colBiSBM}
+            \caption{Reordered by $\pi\rho$-colBiSBM}
         \end{subfigure}
 
-        \caption{Matrice d'adjacence réordonnée par $\pi\rho$-colBiSBM,~\cite{baldockDailyTemporalStructure2011}}
+        \caption{Reordered adjacency matrix by $\pi\rho$-colBiSBM,~\cite{baldockDailyTemporalStructure2011}}
     \end{figure}
 \end{frame}
 
 \section{Conclusion}
 \label{sec:conclusion}
 \begin{frame}
-    \frametitle{Conclusion et perspectives}
+    \frametitle{Conclusion and perspectives}
-    % DONE Ajouter une slide conclusion perspective
+    % DONE Add a conclusion perspective slide
-    % Rappeler les modeles avec clustering
+    % Recall models with clustering
-    % Evoquer l'analyse de reseaux corrigés pour l'échantillonnage
+    % Mention analysis of corrected networks for sampling
-    % Lien vers le package
+    % Link to the package
-    \begin{block}{Capacités}
+    \begin{block}{Capabilities}
         \begin{itemize}
-            \item 4 modèles dont 3 qui ont une flexibilité sur au moins une des
+            \item 4 models including 3 with flexibility on at least one of
-                  dimensions (adaptabilité aux données).
+                  the dimensions (adaptability to data).
-            \item Détecter structures classiques et moins classique de façon agnostique.
+            \item Detect classic and less classic structures in an agnostic way.
-            \item Partitionner un ensemble de réseaux selon leurs structures.
+            \item Partition a set of networks according to their structures.
         \end{itemize}
     \end{block}
 
@@ -533,22 +533,22 @@
 
 \begin{frame}{Perspectives}
     \begin{itemize}
-        \item Investiguer stabilité face à l'aléatoire et aux \emph{optima} locaux.
+        \item Investigate stability against randomness and local \emph{optima}.
-        \item Preuve d'identifiabilité du modèle $\pi\rho$.
+        \item Proof of identifiability of the $\pi\rho$ model.
     \end{itemize}
 
-    \begin{block}{Package et applications}
+    \begin{block}{Package and applications}
         \begin{itemize}
-            \item Intégration au package \texttt{colSBM}, amélioration interface utilisateur et
+            \item Integration into the \texttt{colSBM} package, improvement of user interface and
-                  ajout retours écologues
+                  addition of ecologists' feedback
-            \item Publication CRAN
+            \item CRAN publication
-            \item Intégrer possibilité d'un critère supplémentaire pour le clustering
+            \item Integrate the possibility of an additional criterion for clustering
-            \item Appliquer clustering données de
+            \item Apply clustering to data from
                   \cite{pichonTellingMutualisticAntagonistic2024,doreRelativeEffectsAnthropogenic2021}
         \end{itemize}
 
     \end{block}
     \bigskip
     \centering
-    Merci pour votre attention~!
+    Thank you for your attention~!
 \end{frame}