Poset-averaging

This posetic approach thence provides a novel approach to struc-ture/property and structure/bioactivity correlations, with focus in some sense beyond simple molecular structure, in that this approach attends to how a structure fits into a systematic (reaction) network of structures. Different manners for fitting and prediction of properties are noted, with illustration of an especially simple poset-average scheme. Some numerical evidence indicates that such approaches are quite reasonable. It is emphasized that such directed reaction graphs admitting posetic treatment are widespread. 

This scheme is notably rather like the neighbour-averaging scheme originally used by Mendeleev to make predictions for selected properties of (then) missing elements (e g. eka-silicon, later named germanium). Indeed this scheme in application to Mendeleev s periodic table is often described in texts for introductory chemistry courses. Notably Mendeleev s scheme evidently appears to have even more in common with our present work when Mendeleev s periodic table is viewed as a poset (such as indeed has been suggested). Errors (as BP(A)-BP(A)) for the so predicted boiling points of the methylbenzenes are exhibited in Fig. 7. 

A priori this is fine as the first attribute definitely should compensate the second one. However, the sites, which belong to (1,0),(0,1) on the one side and (1,0), (0,5) on the other side will get the same averaged rank Thus, the analysis by linear extensions alone should be carried out with appropriate care. We continue the analysis of the poset and discuss the attribute profiles. 

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