gen

1 files changed, 4 insertions, 4 deletions

diff --git a/general.tex b/general.tex
index 6e56577..75b87ad 100644
--- a/general.tex
+++ b/general.tex
@@ -32,8 +32,8 @@ a covariance $\sigma^2 I_d$, and the experimenter is solving a ridge regression
 problem with penalty term $\norm{x}_2^2$. 
 
 Moreover, our results can be extended to the general Bayesian case, by
-replacing $I_d$ with the positive semidefinite matrix $R$. First, we set the
-origin of the value function so that $V(\emptyset) = 0$; we define:
+replacing $I_d$ with the positive semidefinite matrix $R$. First, we re-set the
+origin of the value function so that $V(\emptyset) = 0$:
 \begin{align}\label{eq:normalized}
     \tilde{V}(S)
     & = \frac{1}{2}\log\det(R + \T{X_S}X_S) - \frac{1}{2}\log\det R\\
@@ -42,11 +42,11 @@ origin of the value function so that $V(\emptyset) = 0$; we define:
 
 Applying the mechanism described in algorithm~\ref{mechanism} and adapting the
 analysis of the approximation ratio, we get the following result which extends
-theorem~\ref{thm:main}:
+Theorem~\ref{thm:main}:
 
 \begin{theorem}
  There exists a truthful and budget feasible mechanism for the objective
- function $\tilde{V}$ \eqref{eq:normalized}. Furthermore, for any $\varepsilon
+ function $\tilde{V}$ given by \eqref{eq:normalized}. Furthermore, for any $\varepsilon
  > 0$, in time $O(\text{poly}(|\mathcal{N}|, d, \log\log \varepsilon^{-1}))$,
  the algorithm computes a set $S^*$ such that:
  \begin{displaymath}