## 5 Discussion  
For the ease of discussion and interpretation the most important and detailed statistical results collected through Tables 4-7 are summarized in Table 9. Table 8 shows a special case that will be discussed later on. While Tables 4-7 collect the detailed information about the modeling of the eleven properties, and especially about the type of indices, valence deltas, and structure of the ANN computations, Table 9 gives direct information about the different models. Looking for MMCI indices (letter M), in MLS, they are optimal for three properties: refractive index RI, flashpoints FP, and cutoff UV. In ANN computations with one hidden neuron, (ANN 1 HN, Table 5), these are instead important descriptors for cutoff UV, flashpoints FP, and elutropic values EI. It seems that properties with less training points are better modelled by MMCIs. Concerning the statistical results for the training compounds, ANN 1 HN (Table 9, 1 st line) improves over MLS for T\({}_{\text{b}}\), and El properties, while it lays behind for \(-\chi\)\(\cdot\)10\({}^{6}\), otherwise results are rather similar. With the whole set of compounds (Table 9, second line); i.e., with training (and test with ANN)--plus evaluated compound ANN 1 HN calculations improve again over MLS for T\({}_{\text{b}}\), and El, while they stay behind with \(\varepsilon\), \(\gamma\), UV, and \(-\chi\)\(\cdot\)10\({}^{6}\). As soon as the number of hidden neurons grows either by external choice, enHN (Table 6), or by software choice, snHN (Table 7), MMCIs are optimal descriptors only for Elutropic values (silica) El, which is the property with the lowest number of points. The multiple hidden neuron case shows that, at the training level ANN enHN (Table 9), things improve consistently over the two previous cases (MLS and ANN 1 HN) for T\({}_{\text{b}}\), \(\varepsilon\), d, RI, \(\gamma\), FP, \(\mu\), and UV. For \(-\chi\)\(\cdot\)10\({}^{6}\), ANN with several hidden neurons improves with respect to ANN 1 HN, and for El there is an improvement only in relation to MLS (Table 4). Results for viscosity, \(\eta\), are rather similar throughout the three cases. Mostly, improvement concerns both the \(r^{2}\) and the s statistics. Concerning the whole set of compounds (TR, TE and EV) statistics improve in relation to the two previous cases (MLS and ANN 1 HN) for T\({}_{\text{b}}\), \(\varepsilon\), \(\gamma\), FP, \(\mu\), and UV. The advantage of the ANN over the MLS procedure in general is not striking in the eleven properties. In fact, with the only exception of the training plus test for the \(-\chi\)\(\cdot\)10\({}^{6}\) property it does not achieve any useful improvement. Normally, for an optimal modeling the number of hidden neurons that are externally chosen (ANN enHN, Table 9) is smaller than the number of hidden neurons chosen by the software (ANN snHN, Table 9). In some cases, it is much smaller, like for T\({}_{\text{b}}\) (an extreme case), d, and \(\gamma\). Furthermore, ANN snHN statistics are either worse or similar to the ANN enHN ones. This means that if you intend to let the software choose the number of hidden neurons then it is better that you stick to the MLS modeling. Could that depend on the ANN initial weights considered? Probably even if it seems a general trend; i.e., it shows up with nearly all properties. The MLS results compare rather well with the ANN 1 HN results even if the ANN computations have a number of weights bigger (by two) than the number of regression coefficients of the corresponding MLS computations. Thus, we decided to perform ANN calculations by deleting the two indices with the lowest sensibility values in Table 5. In those cases where deletion of two indices gives rise to poor modeling, we deleted only one index. In this last case, the number of weights is no longer equal (actually it is bigger by one) to the number of regression coefficients or weights of the MLS case.