Weighted paths

The notation ( ) a used in the last equality of the above equation indicates that this expression can be viewed as the average work in the so-called work-weighted path ensemble... 

In the work-weighted path ensemble the statistical weight of a particular trajectory z 3 ) explicitly depends on the work performed on the system along that trajectory. The work distribution in the work-weighted path ensemble for a particular value of... 

Randic M, Basak SC (1999) Optimal molecular descriptors based on weighted path numbers. J. Chem. Inf. Comput. Sci. 39 261-266. 

Amic, D., Lucic, B., Nikolic, S., and Trinajstic, N. (2001) Predicting inhibition of microsomal p-hydroxylation of aniline by aliphatic alcohols a QSAR approach based on the weighted path numbers. Croat. Chem. Acta 74, 237-250. 

Molecular BO numbers (MID) are molecular descriptors defined as - weighted path counts or weighted - walk counts, mainly proposed to uniquivocally identify a molecule by a single real number, the aim being to obtain highly discriminatory power [Randic, 1984b Szymanski et al, 1986a],... 

These indices are usually calculated by assigning a weighting factor Wy to each - path or - walk of the - molecular graph with v, and Vy as endpoints. By summing all weighted paths (or walks) starting from the ith vertex, atomic ID numbers (AID) are obtained as -> local vertex invariants characterizing the atomic environment. 

A molecular weighted path number obtained by weighting graph edges with -> conventional bond order [Randic and Jurs, 1989] ... 

Randic, M. and Basak, S.C. (1999c). Optimal Molecular Descriptors Based on Weighted Path Numbers. J.Chem.InfComput.ScL, 39, 261-266. 

Other graph invariants derived from the Hosoya Z matrix are the eigenvalues and the coefficients of the —> characteristic polynomial. Moreover, sequences of weighted paths and the weighted path counts were defined using as the path weights the magnitude of the Z... 

Weighted path counts and Randic connectivity ID numbers for 2-methyl-2-pentene. 

Other variable topological indices are variable path counts, which are weighted path counts obtained by weighting the graph edges involving heteroatoms with one or more variable parameters [Randic and Basak, 1999,2000b Randicand Pompe, 1999 Amic, Basak et al, 2002],... 

A fragment approach to structure-activity correlations, based on the characterization of fragments by suitably weighted paths [377],... 

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