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Abstract  Molecular shape is a useful tool for identifying small-molecules for therapeutics. Shape similarity can be computed using either alignment methods, a computationally demanding approach, or feature vector methods, which are computationally less demanding but less accurate. The computational cost of alignment can be reduced by pre-aligning shapes, as is done with the Volumetric-Aligned Molecular Shapes (VAMS) method. Here we introduce and evaluate Fragment Oriented Molecular Shapes (FOMS), where shapes are aligned based on molecular fragments. FOMS performs equivalently or better than both VAMS and an optimizing alignment method. More significantly, FOMS enables the use of \textit{shape constraints}, a novel method for precisely specifying molecular shape queries that provides the ability to perform partial shape matching and supports search algorithms that function on an interactive time scale.