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+
+\subsection{D-Optimality Criterion}
+\begin{lemma}
+For any $M>0$, there is no truthful, budget feasible, individionally rational mechanism for optimal mechanism design with value fuction $V(S) = \det{\T{X_S}X_S}$.
+\end{lemma}
+\begin{proof}
+\input{proof_of_lower_bound1}
+\end{proof}
+
+This motivates us to look at $$V(S) = \log\det(I_d+\T{X_S}X_S).$$ Interesting for many reasons. Experiment with basis points $e_1$,\ldots,$e_d$, already given for free. Connections to Baysian optimal experiment design: we explore this more in Section~\ref{...}. Close to $D$-optimality criterion when number of experiments is large. Important properties $V(\emptyset)=0$, $V$ is submodular, allows us to exploit the arsenal in our disposal to deal with budget feasible mechanism design for submodular functions.
+
+\subsection{Truthful, Constant Approximation Mechanism}
+
+
 In this section we present a mechanism for the problem described in
 section~\ref{sec:auction}. Previous works on maximizing submodular functions
 \cite{nemhauser, sviridenko-submodular} and desiging auction mechanisms for