However, when examining the growth of shape space per unit volume for a maximum count of reference shapes [15], shape space was shown to grow gradually and smoothly as a function of ST.
The small and shared unique shapes completely dominate in Figure 8(a), being nearly the same as the total count of unique shapes across the entire volume; however, the small unique shapes in Figure 8(b) show a very shallow minimum at about volume 200 Å3 prior to significantly increasing as a function of volume.
The diversity of shape space was investigated by determining the shape similarity threshold to achieve a maximum on the count of reference shapes per unit of conformer volume.
This was achieved by leveraging our recent study on the diversity of shape space [15], where shape space was shown to grow gradually as a function of conformer volume and a dynamic shape similarity threshold for a relatively constant count of reference shapes.
This is not completely desirable as the computational cost of clustering effectively increases as the square (or worse) of the total count of reference shapes (especially when this count is large), when considering N reference shapes must be compared against K conformers and N
The volume range 433-999 is the largest in both volume spanned and count of reference shapes.
One also sees that keeping the count of reference shapes at a maximum for a given volume as an approach and analysis can allow one to achieve an understanding as to how diverse shape space is as a function of shape similarity.
Most studies of inattentional blindness manipulate attention using videos or simple computer displays; people focus attention on an arbitrary task counting passes of basketballs, counting bounces of shapes, judging lengths of lines, etc.—and fail to notice unexpected objects or shapes passing through the display (e.g., Mack & Rock, 1998; Most et al., 2001; Simons & Chabris, 1999).
This growth was linear when considering the logarithm of the count of reference shape and chemical structures, whether using a single conformer or multiple conformers per structure.
Another interesting observation in Figure 8(a), one can see that the absolute count of large unique shapes stays relatively constant in the volume range, with an average count and standard deviation of 22.2 +/- 7.8 and a mode of 24.
Frequency plot of the total count of fingerprint reference shapes set per conformer for the first ten conformers of the 26,157,365 PubCompoundompound records in the Search set, corresponding to 246,874,949 conformers.
