## 3 Results
Inspection of the bottom left corner of Figure 3 shows that the situation is broadly the same regarding the molecules whose repellent activity is poorly predicted by both categories of models. More generally, the comparison of Figures 2 and 3 shows that the cloud of points is less dispersed in the former than the latter. This is due not only to the learning process used by the three-layer perceptron, but also to the great structural diversity of the 2171 molecules. In any case, what is the most important to study are molecules whose repellent activities are always or very often correctly predicted by one category of model, whereas they are not or only poorly predicted by the other category of model. Figure 2 clearly shows that the largest differences in predictions between the ML and MH models concern non-repellent molecules. Thus, for example, the training set molecules #1976 (salicylic acid, allyl ester), #1985 (salicylic acid, ethyl ester), and #1990 (salicylic acid, _iso_-propyl ester), located in the bottom right of Figure 2, are non-repellents always correctly predicted as such by the MH models, while their activity is correctly predicted in only 25%, 17.44%, and 19.81% of cases by the ML models, respectively (Table S2). The situation is broadly the same when these molecules belong to the test sets of the models (Figure 3, Table S2). There exist significant differences in the MlogP and MHlogP descriptor values for these three compounds. Indeed, the MlogP vs. MHlogP values of chemicals #1976, #1985, and #1990 equal 2.00 vs. 4.23, 1.78 vs. 3.87, and 2.09 vs. 4.29, respectively (Table S2). It is interesting to note that an experimental log \(P\) value of 2.95 is given for chemical #1985 in VEGA 1.1.4 and the reliability of the MlogP and MHlogP values for chemical #1976 was estimated as low and moderate, respectively. The same difference of ranking was also provided for chemical #1990. Nevertheless, these differences in log \(P\) values cannot explain the behavior of the three molecules with the two types of models. Indeed, for example, salicylic acid, menthyl ester (#1987), is a non-repellent always predicted as such by both types of models, whatever its belonging to the training and test sets, while its MlogP value equals 3.55 and its MHlogP value is 7.39 (Tables S1 and S2). The MH models always correctly predict the non-repellent activity of salicylic acid, \(n\)-butyl ester (#1982), as a member of the different training and test sets (located vertically to the 100% unit of the abscissa axis in Figures 2 and 3). In contrast, only 67.96% and 53.12% of good predictions are obtained with the ML models, respectively (Table S2, Figures 2 and 3). Well predicted by the ML1 and MH1 models as a training set member, the MlogP, MHlogP, and experimental log \(P\) values of chemical #1982 equal 2.38, 4.85 (Table S2), and 4.63, respectively. The five chemicals located just below chemical #1982 in Figure 2 also have their activity better predicted by the MH models than the ML models. Thus, the non-repellents #1088 (\(p\)-ethoxyproiophenone), #955 (5,9-dimethyldecanoic acid), #2123 (2,4,6-trimethyl-1,2,5,6-tetrahydrobenzaldehyde oxime), #1058 (dodecylenic acid), and #1282 (o-hydroxy-_iso_-butylrophenone) are predicted as such by the MH models from about 92% to 97% as training set members and from 85% to 100% when they belong to the test sets (Table S2). With the ML models, the ranges are from about 53% to 60% and from 21% to 43% when they are training and test set members, respectively (Table S2). The MH1 model also outperforms the ML1 model regarding these five non-repellents. The MHlogP values of these chemicals are greater than the corresponding MlogP values of at least one log unit except chemical #1088, for which the MlogP value equals 2.13, while the MHlogP value is 2.74 (Table S2), a good reliability being attributed to the former predicted log \(P\) and moderate for the latter.