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(A) KDS, (B) DNP and (C) enumerated set.
Furthermore, the module selections formed by these modules belong to superior solutions in the enumerated set (top 15%).
In this manner, 95,522 different assemblies were identified from the enumerated set.
Figure 10 Sampling of ring assemblies without alpha atoms common to the enumerated set and either KDS or the DNP. Figure 11 Sampling of structurally unique ring assemblies without alpha atoms from the complement of the enumerated set.
Similarly, the average molecular weight over time does not change as the enumerated set grows from 10,000 to 250,000 members (Figure 5B).
A sampling of intersecting ring systems appears in Figure 10 and a sampling of unique ring systems from the complement of the enumerated set appears in Figure 11.
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Multi-fusion similarity analyses [21] of compounds in the KDS, DNP and enumerated sets further substantiate the conclusion that the virtual compounds resemble both of the former sets in terms of physicochemical properties (Figure 6A).
Molecular Complexity MC score = log 10 nBridgeAtoms + 1 + log 10 nSpiroAtoms + 1 + log 10 nStereoCenters + 1 + log 10 nMidLargeRings + 1 + log 10 nNonAromaticDoubleBonds + 1 + nHeavyAtoms 1.005 - nHeavyAtoms Figure 14 Molecular complexity (MC) score distribution for the KDS, DNP and enumerated sets.
As expected, analysis of the KDS, Dictionary of Natural Products (DNP) and enumerated sets indicate that the collection of randomly generated virtual compounds resembles that of the DNP with respect to the ratio of carbon, nitrogen and oxygen atoms present in each molecule, but with a narrower molecular weight range (Figure 1).
We then focus on the more general problem of enumerating sets of compatible paths.
To enumerate sets of entities, a canonical approach is to start with the empty set and then iteratively form larger sets by adding one element at a time; if it is evident that no further solutions can be derived from a certain set, the process of extension is stopped, i.e. unnecessary parts of the search space are pruned.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com