diff --git a/main.pdf b/main.pdf
index 10bb5bd..a0b0299 100644
Binary files a/main.pdf and b/main.pdf differ
diff --git a/main.tex b/main.tex
index eaf0de5..3a887cf 100644
--- a/main.tex
+++ b/main.tex
@@ -131,7 +131,7 @@ How to derive normalized min cut for connectivity interdiction?
 \begin{aligned}
 \max&   &                   z&          &   & \\
 s.t.&   &   \sum_{e} y_e c(e) &\leq B   &   &\text{(budget for $F$)}\\
-&       &   \sum_{e\in T} x_e&\geq 1   &   &\forall T\quad \text{($x$ forms a cut)}\\
+&       &   \sum_{e\in T} x_e&\geq 1   &   &\forall T\quad \text{($x$ is a cut)}\\
 &       &   \sum_{e} \min(0,x_e-y_e) w(e)&\geq z   &   &\\
 &       &   y_e,x_e&\in\{0,1\}      &   &\forall e
 \end{aligned}
@@ -143,7 +143,7 @@ we can assume that $y_e\leq x_e$.
 \begin{aligned}
 \min&   &                   \sum_{e} (x_e&-y_e) w(e)          &   & \\
 % s.t.&   &   \sum_{e} (x_e-y_e) w(e)&\geq z   &   &\\
-s.t.&       &   \sum_{e\in T} x_e&\geq 1   &   &\forall T\quad \text{($x$ forms a cut)}\\
+s.t.&       &   \sum_{e\in T} x_e&\geq 1   &   &\forall T\quad \text{($x$ is a cut)}\\
 &       &   \sum_{e} y_e c(e) &\leq B   &   &\text{(budget for $F$)}\\
 &       &   x_e&\geq y_e   &   &\forall e\quad(F\subset C)\\
 &       &   y_e,x_e&\in\{0,1\}      &   &\forall e
@@ -157,7 +157,7 @@ A further reformulation (the new $x$ is $x-y$) gives us the following,
 \begin{equation*}
 \begin{aligned}
 \min&   &                   \sum_{e} x_e w(e)          &   & \\
-s.t.&       &   \sum_{e\in T} x_e+y_e&\geq 1   &   &\forall T\quad \text{($x$ forms a cut)}\\
+s.t.&       &   \sum_{e\in T} x_e+y_e&\geq 1   &   &\forall T\quad \text{($x+y$ is a cut)}\\
 &       &   \sum_{e} y_e c(e) &\leq B   &   &\text{(budget for $F$)}\\
 % &       &   x_e&\geq y_e   &   &\forall e\quad(F\subset C)\\
 &       &   y_e,x_e&\in\{0,1\}      &   &\forall e