diff --git a/.zed/tasks.json b/.zed/tasks.json
deleted file mode 100644
index 7500c78..0000000
--- a/.zed/tasks.json
+++ /dev/null
@@ -1,25 +0,0 @@
-// Static tasks configuration.
-//
-[
-    {
-        "label": "forward_search",
-        "command": "/Applications/Skim.app/Contents/SharedSupport/displayline -r -z -b $ZED_ROW $ZED_DIRNAME/$ZED_STEM.pdf",
-        "allow_concurrent_runs": false,
-        "reveal": "never",
-        "hide": "always"
-    },
-    {
-        "label": "pdflatex_view",
-        "command": "cd \"$ZED_DIRNAME\" && pdflatex -shell-escape -synctex=-1 \"$ZED_STEM\" && /Applications/Skim.app/Contents/SharedSupport/displayline -r -z -b $ZED_ROW \"$ZED_STEM\".pdf",
-        "allow_concurrent_runs": false,
-        "reveal": "no_focus",
-        "hide": "on_success"
-    },
-    {
-        "label": "latexmk_view",
-        "command": "cd \"$ZED_DIRNAME\" && latexmk -pdf \"$ZED_STEM\" && /Applications/Skim.app/Contents/SharedSupport/displayline -r -z -b $ZED_ROW \"$ZED_STEM\".pdf",
-        "allow_concurrent_runs": false,
-        "reveal": "no_focus",
-        "hide": "on_success"
-    }
-]
\ No newline at end of file
diff --git a/main.tex b/main.tex
index 7254219..7120e39 100644
--- a/main.tex
+++ b/main.tex
@@ -97,16 +97,27 @@ Given the same input as connectivity interdiction, find
 \end{problem}
 
 \p
-First considered in [Chalermsook \etal{}, ICALP'22] as a subproblem in MWU framework when solving minimum $k$-edge connected spanning subgraph (ECSS) problem.
+... first appear in [Chalermsook \etal{}, ICALP'22] as a subproblem in MWU framework when solving some positive covering LP\footnote{minimum $k$-edge connected spanning subgraph}.
 \end{frame}
 
 \begin{frame}{Method in [Huang \etal{}, IPCO'24]}
-Let $\tau$ be a $(1+\e)$-approximation to the normalized min-cut and let $C^*$ be the optimal $B$-free cut.
-\begin{lemma}
-$C^*$ is a $(2+2\e)$-approximate min-cut in $(G,w_\tau)$, 
+$\tau$ is a $(1+\e)$-approximation to the normalized min-cut\\
+$C^*$ is the optimal $B$-free cut.
 
+\p
+\begin{lemma}
+There is an edge weight $w_\tau$ such that\\
+$C^*$ is a $(2+2\e)$-approximate min-cut in $(G,w_\tau)$,
 where $w_\tau(e)=\min(\tau c(e),w(e))$ is the truncated edge weight.
 \end{lemma}
+
+\p
+\begin{algo}
+enumerate approx solutions to normalized min-cut \quad  \textcolor{gray}{$\log_{1+\e}(Bnw_{\max})$}\\
+\quad   reweight the graph \quad \textcolor{gray}{$O(m)$}\\
+\quad   enumerate all $2+2\e$ min-cuts \quad \textcolor{gray}{$\tilde O(n^4)$}\\
+\quad\quad  run FPTAS for knapsack on the cut
+\end{algo}
 \end{frame}
 
 \begin{frame}{LP method}
@@ -139,7 +150,7 @@ Let $C^*$ be the optimal $B$-free mincut and let $\lambda^*$ be the optimal solu
 
 \section{Cogirth of perturbed graphic matroids}
 \begin{frame}{Matroid}
-A matroid $M=(E,\mathcal B)$ is a structure on set $E$.
+A \emph{matroid} $M=(E,\mathcal B)$ is a structure on set $E$.
 
 ``Bases'' $\mathcal B$ is a collection of subsets with the following properties:
 \begin{itemize}
@@ -150,15 +161,15 @@ then there exists $b\in B-A$ such that $A-a+b\in \mathcal B$.
 \end{itemize}
 
 \p
-$X\subset E$ is a cocycle if $X\cap B$ is not empty for all $B\in \mathcal B$.
+$X\subset E$ is a \emph{cocycle} if $X\cap B$ is not empty for all $B\in \mathcal B$.
 
-The size of minimum cocycle is the cogirth.
+The size of minimum cocycle is the \emph{cogirth}.
 \end{frame}
 
 \begin{frame}{Examples}
 \begin{itemize}
 \item Graphic matroids. $E$ is the edge set. $\mathcal B$ is the collection of all spanning forests. Cogirth is the size of min-cut.
-\item Uniform matroids. $E$ is a set. $\mathcal B$ is the collection of all subsets of $E$ with $5$ elements. Cogirth is $|E|-4$.
+\item Uniform matroids. $E$ is a large set. $\mathcal B$ is the collection of all subsets of $E$ with $5$ elements. Cogirth is $|E|-4$.
 \item Binary matroids. $E$ is a set of binary vectors. $\mathcal B$ is the collection of maximum linearly independent sets. What is the cogirth?
 \item ...
 \end{itemize}
@@ -253,10 +264,10 @@ If $M$ and deletion minors of $M$ have constant gap, then $M(A')/\tau$ has const
 \end{frame}
 
 % \section{Conclusion}
-\begin{frame}{Takeaways}
-\begin{itemize}
-\item try LP methods whenever possible \pause
-\item Look at the easy cases/minors first: many theorems want to generalize
-\end{itemize}
-\end{frame}
+% \begin{frame}{Takeaways}
+% \begin{itemize}
+% \item try LP methods whenever possible \pause
+% \item Look at the easy cases/minors first: many theorems want to generalize
+% \end{itemize}
+% \end{frame}
 \end{document}
\ No newline at end of file