deletions | additions       diff --git a/subsection_Shape_Indexing_and_Similarity__.tex b/subsection_Shape_Indexing_and_Similarity__.tex  index c1dfabe..50c4773 100644  --- a/subsection_Shape_Indexing_and_Similarity__.tex  +++ b/subsection_Shape_Indexing_and_Similarity__.tex 
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where a larger score indicates a greater degree of similarity.  We consider both similarities with a single query ligand and similarities with shape constraints. The similarity of a shape, $A$, with the minimum, $MIN$, and maximum, $MAX$, shape constraints is computed by averaging their shape Tanimotos:  \begin{equation*}  \begin{aligned}  \delta(A,MIN,MAX) &  = \frac{\delta(A,MIN) + \delta(A,MAX)}{2} \\  &  = \frac{1}{2}\left(\frac{A \cap MIN}{A \cup MIN} + \frac{A \cap MAX}{A \cup MAX }\right) \end{aligned}  \end{equation*}  The average ranges from zero to one, where a value of one is only achieved when all three shapes are identical.