## 3 Results
### Adaptive Learning Integration with ABMS
Having said that, the recorded high skewness value exhibits a significant positive asymmetry. Simultaneously, the kurtosis figure displays a slight tendency of greater deviations to the mean that conforms with previous findings. In summary, computed metrics agree that density values are not homogeneous and that outliers' demeanor is meaningful. Along with it, a histogram of densities is plotted in Figure 6 according to [PERSON]'s criteria. As expected, the histogram in Figure 6 provides further details on the distribution of the density figures. For instance, around 60% of the measurements are lower than the 0.1 people per square meter mark, while only 0.9 percent of the values are actually larger than the social distancing measure. In simpler terms, results show that potentially dangerous situations happen less than 1% of the time. For good measure, Figure 6 could raise some doubts about the densities' distribution, since the graphic may lead to thinking that these could be drawn from a mixing of two random variables. One way of making sure that results are legitimate is by means of an analysis of independence. By this study's standards, the densities should follow some foreseeable structure, given that gatherings are based upon the academic schedule. Due to this, an overlapped scatter plot should evince non-random patterns, and an autocorrelation plot is likely to exhibit substantial correlations for some lag values. Figure 7 conveys the previously mentioned diagrams. \begin{table}
\begin{tabular}{c c} \hline \hline
**Statistic** & **Value** \\ \hline Mean & 0.1053 \\ Median & 0.0112 \\ Std. dev. & 0.1436 \\ Minimum & 0 \\ Maximum & 0.5597 \\ Skewness & 1.1383 \\ Kurtosis & 3.0050 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Base densities’ basic statistics. Figure 6: Histogram of base densities. Unsurprisingly, Figure 7 clearly demonstrates that the data densities are not random. Specifically, Figure 7 visually depicts the sequential arrangement of data points and illustrates the relationships between each data point and its neighboring point. Therefore, as the data exhibits a linear tendency, this plot effectively highlights the non-random nature of the data densities. Similarly, in Figure 7, the autocorrelation between each data point and its preceding data points is visually represented. Autocorrelation values span from \(1\) to \(-1\), denoting positive or negative correlations, respectively. Notably, the figure displays autocorrelation values approaching either extreme, indicating the existence of autocorrelation within the dataset and confirming the non-random nature of the data densities. To continue with the analysis, two box-plots are brought into the examination to browse how densities behave in various temporal groupings. Figure 8 presents the above-stated charts. A closer inspection of Figure 8 shows noticeable differences between the examined temporal partitions. For instance, it is apparent from the figure on the left that weekends' densities are almost negligible. Additionally, Friday's quantities do not exceed the 0.35 bar, implying that unfavorable gatherings are not likely to occur from Friday to Sunday. At the same time, Monday to Thursday's maximum measurements are close to the 0.5 benchmark, with the highest values being recorded on Tuesdays. Setting aside, the figure on the right shows that bigger congregations happen close to lunchtime, where most agents look for a place to eat in one of the few available. Other distinctive top figures are seen near common arrival and departure times, suggesting that agents crowd in places near the entrances and exits at these time frames. Altogether, the evidence suggests that Tuesdays close to lunchtime deliver the utmost risk of clustering. For a proper validation of the last statement, Table 7 presents the mean confidence intervals for the densities each day and in the whole week. The evidence in Table 7 supports that Tuesdays hold noticeably larger gatherings than any other day of the week.