## 4 Case Study
The features of the investigated buildings, including building height, volume, and area for each building shape (A to G), are summarized in Table 4. This table also reports the number of floors, the number of apartments per floor, and the window area. Table 5 shows the number of buildings per each type considered. According to data from the Italian Institute of Statistics (ISTAT) for the year 2020, the considered building stock houses 948,850 people. To define user habits, the following assumptions are considered: all adults go to work every weekday, and children and young people attend school or university. Occupation profiles are created for each category of people (elderly, adults, children, teenagers, and young adults), considering different habits for weekdays (Monday to Friday), Saturdays, and Sundays. Based on these occupation profiles, the total daily occupancy profile of building users is calculated as the average occupancy profile. An example of the occupancy profile for weekdays (Monday to Friday) is shown in Figure 2, whereas Table 6 shows the distribution of people inside the apartments. It is important to mention that the occupancy profiles developed for this study represent typical usage patterns of residential buildings. Specifically, three distinct occupancy profiles based on national statistical data and standard occupancy schedules outlined in ref. [10] are considered. These occupancy profiles are modeled by accounting for variables such as the number of occupants, their daily schedules, internal heat gains from occupants and appliances, and ventilation rates. This approach only includes residential buildings; therefore, it does not account for the energy usage in other buildings where residents may spend time when they are not at home, such as workplaces, schools, or commercial spaces. As a result, any potential increase in energy consumption in these non-residential buildings due to occupant presence has not been included in the analysis, which is strictly limited to the residential building stock. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **A** & **B** & **C** & **D** & **E** & **F** & **G** \\ \hline Height [m] & 18 & 15 & 15 & 12 & 18 & 24 & 30 \\ Volume [m\({}^{3}\)] & 4608 & 16,500 & 16,005 & 11,340 & 11,520 & 4080 & 17,280 \\ Area [m\({}^{2}\)] & 256 & 1100 & 1067 & 945 & 640 & 170 & 576 \\ Number of floors & 6 & 5 & 5 & 4 & 6 & 8 & 10 \\ Number of apartments per floor & 3 & 14 & 10 & 10 & 7 & 2 & 5 \\ Window area [m\({}^{2}\)] & 210.54 & 311.40 & 539.72 & 141.12 & 320.16 & 241.92 & 355.20 \\ Shape & block & closed courtyard & open courtyard & line & line & tower & tower \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Features of investigated buildings. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Layer** & **Thickness [m]** & **Conductivity** & **Specific Heat** \\  & **[kj/hmk]** & **Capacity [kj/kgk]** & **Density [kg/m\({}^{3}\)]** & **U [w/m\({}^{2}\)k]** \\ \hline lime and gypsum plaster & 0.020 & 2.520 & 1.000 & 1400 \\ hollow bricks & 0.080 & 1.476 & 0.840 & 1600 \\ air cavity & \multicolumn{3}{c}{R = 0.05 \(\mathrm{hm}^{2}\mathrm{K}/\mathrm{k}\mathrm{J}\)} \\ hollow bricks & 0.120 & 1.476 & 0.840 & 1600 \\ cement, sand, lime plaster & 0.020 & 3.240 & 0.910 & 1800 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Stratigraphy of the empty box walls. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Type** & **A1** & **B1** & **C2** & **D1** & **D2** & **E1** & **E2** & **F1** & **F2** & **G1** & **G2** & **TOT** \\ \hline Number & 876 & 512 & 374 & 54 & 158 & 125 & 420 & 59 & 212 & 24 & 126 & 2940 \\ Percentage & 30\% & 17\% & 13\% & 2\% & 5\% & 4\% & 14\% & 2\% & 7\% & 1\% & 4\% & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Number of buildings per each constructive type. The heat gains due to the diverse appliances considered are reported in Table 7. Each heat gain has a specific schedule that varies on weekdays, Saturdays, and Sundays.