Verified Commit ade75b26 authored by Laurent Modolo's avatar Laurent Modolo
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update pseudo_time.Rmd

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......@@ -267,23 +267,54 @@ When we have a scRNASeq time serie we want:
\begin{center}
\href{https://doi.org/10.1016/j.cell.2019.01.006}{
\includegraphics[width=\textwidth]{img/OT_1.png}
\includegraphics[width=0.9\textwidth]{img/OT_1.png}
}
\end{center}
## Waddington OT
\begin{center}
\href{https://doi.org/10.1016/j.cell.2019.01.006}{
\includegraphics[width=\textwidth]{img/OT_2.png}
\href{olivier gandrillon}{
\includegraphics[width=\textwidth]{img/OT_eq.png}
\includegraphics[width=\textwidth]{img/OT_ex.png}
}
\end{center}
## Waddington OT
\begin{center}
\href{olivier gandrillon}{
\includegraphics[width=0.5\textwidth]{img/coupling_1.png}
}
\end{center}
## Waddington OT
\begin{center}
\href{olivier gandrillon}{
\includegraphics[width=0.5\textwidth]{img/coupling_2.png}
}
\end{center}
We can find the optime coupling between time $t_i$ and $t_{i+1}$
## Waddington OT
\begin{center}
\href{olivier gandrillon}{
\includegraphics[width=0.5\textwidth]{img/coupling_3.png}
}
\end{center}
## Waddington OT
\begin{center}
\href{https://doi.org/10.1016/j.cell.2019.01.006}{
\includegraphics[width=\textwidth]{img/OT_2.png}
}
\end{center}
We can find the optime coupling between time $t_i$ and $t_{i+1}$ accounting for cell death and birth
## Waddington OT
### iPSCs reprogramming
\begin{center}
......@@ -294,6 +325,38 @@ We can find the optime coupling between time $t_i$ and $t_{i+1}$
259,155 cells collected at 39 time points across 18 days
## Velocity
\begin{center}
\href{https://doi.org/10.1101/2022.02.12.480214}{
\includegraphics[width=\textwidth]{img/velocity.png}
}
\end{center}
The counts are smoothed by average pooling over $k$ neighbors (5-30)
## Velocity
\begin{center}
\href{https://doi.org/10.1101/2022.02.12.480214}{
\includegraphics[width=\textwidth]{img/velocity_model.png}
}
\end{center}
\vspace{-1em}
the velocity $v_i$ may be computed for each cell $i$:
\vspace{-1em}
\[v_i = \frac{\delta s_i}{\delta t} = \left(\beta u_i - \gamma s_i\right) \propto u_i - \frac{\gamma}{\beta}s_i\]
## VeloViz
\begin{center}
\href{https://jef.works/veloviz/}{
\includegraphics[width=0.7\textwidth]{img/veloviz.png}
}
\end{center}
# single-cell RNA-Seq Differential expression analysis *Monday 11 July 2022*
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