Decreased length of caption for Lower Bounds table; capitalized the title; adjusted spacing of captions on figures.

introduction.tex

@@ -92,7 +92,8 @@ $\omega\inparen{\inparen{\qruntime{\optquery{\qhard}, \tupset, \bound}}^{C_0}}$
 $\Omega\inparen{\inparen{\qruntime{\optquery{\qhard}, \tupset, \bound}}^{c_0\cdot k}}$ for {\em some} $c_0>0$ & Multiple & \Cref{conj:known-algo-kmatch}\\
 \hline
 \end{tabular}
-\caption{Our lower bounds for $\qhard$, any query from a class of hard queries  parameterized by $k$.  For $\pdb = \inset{\worlds, \bpd}$ those with `Multiple' in the second column need the algorithm to be able to handle multiple $\bpd$, i.e. probability distributions (for a given $\tupset$). The last column states the hardness assumptions that imply the lower bounds in the first column ($\eps_o,C_0,c_0$ are constants that are independent of $k$).}
+\caption{Our lower bounds for $\qhard$ parameterized by $k$ $\inparen{\Cref{sec:hard:sub:pre}}$ over \abbrCTIDB $\pdb$.  % = \inset{\worlds, \bpd}$.
+Those with `Multiple' in the second column need the algorithm to be able to handle multiple $\bpd$.  See~\Cref{sec:hard} for further details.}%, i.e. probability distributions (for a given $\tupset$). The last column states the hardness assumptions that imply the lower bounds in the first column ($\eps_o,C_0,c_0$ are constants that are independent of $k$).}
 \label{tab:lbs}
 \vspace{-0.73cm}
 \end{table*}

main.tex

@@ -106,7 +106,7 @@ sensitive=true
 
 \begin{document}
 
-\title{Computing expected multiplicities for bag-TIDBs with bounded multiplicities}
+\title{Computing Expected Multiplicities for Bag-TIDBs with Bounded Multiplicities}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \author{Su Feng}\email{sfeng14@hawk.iit.edu}

prob-def.tex

@@ -50,9 +50,10 @@ The circuits $\inparen{1}$ and $\inparen{2}$ in column $\poly$ of \Cref{fig:two-
 			\draw[->] (b3) -- (a4);
 			\draw[->] (a4) -- (2.25, 2.75);
 		\end{tikzpicture}
+		\setlength{\abovecaptionskip}{-0.025cm}
 		\caption{Circuit encoding of $(X + 2Y)(2X - Y)$}
 		\label{fig:circuit}
-		\vspace{-0.53cm}
+		\vspace{-0.58cm}
 	\end{figure}
 
 

two-step-model.tex

@@ -132,7 +132,9 @@
 		\node[below=0.2cm of rrect]{{\LARGE $\expct\pbox{\poly(\vct{X})}$}};
 	\end{tikzpicture}
 	}
+	\setlength{\abovecaptionskip}{-0.35cm}
 	\caption{Intensional Query Evaluation Model $(\query_2 = \project_{\text{Point}}$ $\inparen{T\join_{\text{Point} = \text{Point}_1}R}$ where, for table $R,~\bound = 2$, while for $T,~\bound = 1.)$}
 	\label{fig:two-step}
+	\vspace{-0.43cm}
 \end{figure*}