## 3 Results and Discussion
### Estimation of the Detection Limits of the Adopted Optical Devices
To support the comparison with statistics data, the KORA, AirVisual Pro, and EPLI+ stages 7-11 and 8-11 datasets were reduced to the same data dimension by averaging the concentrations measured in the corresponding day time over one minute. Statistical evaluation of the reduced pattern superposition was performed by applying the ordinary least square method to the whole sampling campaign dataset (see Supplementary Materials Table S3). The results confirmed that the best superposition with KORA was achieved with EPLI+ stages 8-11, whereas AirVisual Pro better superposed with fractions 7-11, with the former sum about one-third of the latter, probably due to what was previously observed for the garage environment. The hypothesis was verified for the days with higher concentrations (all the indoor busy, outdoor, and garage) with one exception on 20 March for the AirVisual Pro. The principal component analysis (PCA) confirmed and did not give additional information to the least square method (see Supplementary Materials Figure S7). The statistical significance of the applied methods was not sufficient to drive a general conclusion for the LODs and a more complex model, called PARAFAC, was applied to the whole dataset. Different pre-processing methods were considered before applying PARAFAC (data not shown), and the best result was obtained by scaling across the mode of the PM concentrations and mean centering across the instruments mode. An unconstrained PARAFAC model with one to four components was fitted to explore the data structure. The choice of the number of components was considered a crucial step of the data analysis. Different criteria were evaluated, such as core consistency [46], percent error of explained variance, and sum of squared errors, to determine the right number of components. The sum of squares was evaluated in terms of the loss function given relative to the loss function value of the one-component model. The following results are shown for each number of components in Table 4. It can be seen that a two-component PARAFAC model was appropriate, having core consistency of 100%, whereas three- and four-component models showed a core consistency of 7.65% and 17.99%, respectively. This result indicates that the two-component model is more stable than the other two. The explained variance suggests that two components are optimal because the increase obtained with more than two components is small relative to the increase in explained variance obtained using up to two components. The score plot of component 1 vs. component 2 (F1 vs. F2) is reported for the first mode (instruments mode, see Supplementary Materials Figure S8). They accounted for 81.17% of the total variability, F1 for 66.15%, and F2 for 15.02%. In detail, along F1 a systematic variation seems to exist, based on the inclusion of the finest fraction of the EPLI+ (see Table 1). Indeed, the sum of fractions starting from 8 and 1 were opposite to each other, and in between there were those starting from 7 and 6. The scores started from very negative values and reached high positive values, from stage 8 to stage 1. Along F2 there was discrimination between the coarser fractions (11 and 12) included in the sum. All data including fraction 12 were located at positive F2 score values, on the opposite side of all data up to 11 lying \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Components** & **Loss** & **\% Explained Variance** & **Core Consistency** \\ \hline
1 & 1.00 & 66.15 & 100 \\
2 & 0.56 & 81.17 & 100 \\
3 & 0.30 & 89.72 & 7.65 \\
4 & 0.21 & 92.89 & 17.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Loss function values relative to the value for a one-component model, explained variance (expressed as percentage), and core consistency with respect to the number of components calculated by the PARAFAC model. together with both KORA and AirVisual Pro at negative score values. The formation of the couples most correlated to each other is evidenced: KORA with S8-11 and AirVisual Pro with S7-11.