Verified Commit 745f0f8f authored by Laurent Modolo's avatar Laurent Modolo
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update pseudo_time.Rmd

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......@@ -216,9 +216,9 @@ x_{2,i} \\
## Real dimension of count data
\begin{center}
\includegraphics[height=4cm]{./img/wadington_landscape.png}
\end{center}
\href{https://doi.org/10.1016/j.tibtech.2020.05.003}{
\includegraphics[height=4cm]{img/wadington_landscape.png}
}
\begin{center}
There are multiple factors that define the transcription landscape
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......@@ -42,6 +42,15 @@ classoption: aspectratio=169
6. Differential expression analysis (Monday 11 July 2022 - 15:30)
## Waddington landscape
\begin{center}
\href{https://doi.org/10.1016/j.tibtech.2020.05.003}{
\includegraphics[width=\textwidth]{img/wadington_landscape.png}
}
\end{center}
# Continuous clustering
## Pseudo-time
......@@ -79,6 +88,41 @@ one RNA-Seq experiment constitutes a {\bf time series}, with each {\bf cell repr
## Topology
\begin{center}
\begin{tikzpicture}
\fill
(0.5,3.5) node {\bf $\text{gene}_1$}
-- (0.5,2.5) node {\bf $\text{gene}_2$}
-- (0.5,1.5) node {\bf $\vdots$}
-- (0.5,0.5) node {\bf $\text{gene}_n$};
\fill
(1.5,4.5) node {\bf $\text{cell}_1$}
-- (1.5,3.5) node {mRNA}
-- (1.5,2.5) node {mRNA}
-- (1.5,1.5) node {$\vdots$}
-- (1.5,0.5) node {mRNA};
\fill
(2.5,4.5) node {\bf $\text{2 cells}_2$}
-- (2.5,3.5) node {mRNA}
-- (2.5,2.5) node {mRNA}
-- (2.5,1.5) node {$\vdots$}
-- (2.5,0.5) node {mRNA};
\fill
(3.5,4.5) node {\bf $\cdots$}
-- (3.5,3.5) node {$\cdots$}
-- (3.5,2.5) node {$\cdots$}
-- (3.5,1.5) node {$\ddots$}
-- (3.5,0.5) node {$\cdots$};
\fill
(4.5,4.5) node {\bf $\text{cell}_c$}
-- (4.5,3.5) node {mRNA}
-- (4.5,2.5) node {mRNA}
-- (4.5,1.5) node {$\vdots$}
-- (4.5,0.5) node {mRNA};
\draw (1,0) grid (5,4);
\end{tikzpicture}
\vspace{1em}
\href{http://www.nature.com/doifinder/10.1038/nbt.2859}{
\includegraphics[width=0.8\textwidth]{img/types_of_topology.png}
}
......@@ -88,7 +132,7 @@ one RNA-Seq experiment constitutes a {\bf time series}, with each {\bf cell repr
\begin{center}
\href{http://www.nature.com/doifinder/10.1038/nbt.2859}{
\includegraphics[width=0.8\textwidth]{img/monocle_1.png}
\includegraphics[width=\textwidth]{img/monocle_1.png}
}
{\bf MST}: Minimum Spanning Tree
\end{center}
......@@ -97,7 +141,7 @@ one RNA-Seq experiment constitutes a {\bf time series}, with each {\bf cell repr
\begin{center}
\href{http://www.nature.com/doifinder/10.1038/nbt.2859}{
\includegraphics[width=0.7\textwidth]{img/monocle_2.png}
\includegraphics[width=0.6\textwidth]{img/monocle_2.png}
}
\end{center}
......@@ -147,6 +191,28 @@ traveling salesman problem (TSP)
## Slinshot
### Principal curve
\begin{center}
\begin{columns}
\column{0.6\textwidth}
\begin{center}
\href{https://www.semanticscholar.org/paper/Principal-Curves-Hastie-Stuetzle/c2ebc4e4c5b421ab7b70ab6076f78c3220c54bfe}{
\includegraphics[width=\textwidth]{img/principal_curve.png}
}
\end{center}
\column{0.4\textwidth}
\begin{itemize}
\item a. The linear regression line
\item b. The principal-component
\item c. The smooth regression curve
\item d. The principal curve minimizes
\end{itemize}
\end{columns}
\end{center}
## Slinshot
### Clustering followed by MST and principal curve
\begin{center}
......@@ -159,6 +225,8 @@ traveling salesman problem (TSP)
## reCAT
### We know the shape of the cell graph
\begin{center}
\href{https://www.nature.com/articles/s41467-017-00039-z}{
\includegraphics[width=0.8\textwidth]{img/recat.png}
......@@ -338,6 +406,7 @@ The counts are smoothed by average pooling over $k$ neighbors (5-30)
## Velocity
\vspace{-1em}
\begin{center}
\href{https://doi.org/10.1101/2022.02.12.480214}{
\includegraphics[width=\textwidth]{img/velocity_model.png}
......@@ -345,9 +414,43 @@ The counts are smoothed by average pooling over $k$ neighbors (5-30)
\end{center}
\vspace{-1em}
the velocity $v_i$ may be computed for each cell $i$:
\vspace{-1em}
\[v_i = \frac{\delta s_i}{\delta t} = \left(\beta u_i - \gamma s_i\right) \propto u_i - \frac{\gamma}{\beta}s_i\]
## Velocity
### The velocity estimation relyies heavilly on the k-NN graph
\begin{center}
\href{https://doi.org/10.1101/2022.06.19.494717}{
\includegraphics[width=\textwidth]{img/velocity_estimation.png}
}
\end{center}
## Velocity
### The velocity projection for non-linear methods in not reliable
\begin{center}
\href{https://doi.org/10.1101/2022.06.19.494717}{
\includegraphics[width=\textwidth]{img/velocity_dim_red_1.png}
}
\end{center}
## Velocity
### The velocity projection for non-linear methods in not reliable
\begin{center}
\href{https://doi.org/10.1101/2022.06.19.494717}{
\includegraphics[width=\textwidth]{img/velocity_dim_red_2.png}
}
simulation on a dataset of 10 genes
\end{center}
## VeloViz
\begin{center}
......
......@@ -46,17 +46,17 @@ classoption: aspectratio=169
## Hypothesis testing
\begin{itemize*}
\begin{itemize}
\item $H_0$: the gene pression is the same between the $2$ groups
\item $H_1$: the gene pression is not the same between the $2$ groups
\end{itemize*}
\end{itemize}
## Hypothesis testing
\begin{itemize*}
\begin{itemize}
\item $H_0$: the gene pression is the same between the $2$ groups
\item $H_1$: the gene pression is not the same between the $2$ groups
\end{itemize*}
\end{itemize}
\begin{center}
\bf We reject $H_0$ with a given risk $\alpha$ and a power $\beta$
......
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