## 3 Case Studies
### Air Transportation Between World Regions and Communication Space  
When analyzing time series that describe processes in a system, which in our case, is a communication space based on air transportation, the task of analyzing a set of regional subsystems as a single whole arises, which reflects the properties of the global communication space. In this example, an analysis of passenger transport flows between different regions of the world was performed, which allowed us to evaluate the dynamic properties of the world communication space. The following statistical regions of the world according to ICAO were selected: Eastern and Southern Africa, Western and Central Africa, the Arab world, Central Europe and the Baltic, East Asia and the Pacific, Europe and Central Asia, the European Union, Latin America and the Caribbean, Middle East and North Africa, North America, South Asia, and Sub-Saharan Africa [35]. The integrating indicator was the total registered indicator of global passenger transportation volumes. Figure 10 shows the geography of these regions. Figure 11 shows curves describing the change in the flow of air passenger traffic within regions and between regions of the world for the period 1970-2021. The data were divided into decades, which allowed us to assess the changes in the influence of regions on communication directions over these years. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Y**} & \multicolumn{6}{c}{**X**} \\ \cline{2-7}  & **Yekaterinburg** & **Chelyabinsk** & **Ufa** & \begin{tabular}{c} **Moscow** \\ **(Vnukovo)** \\ \end{tabular} & **Moscow** & \
\begin{tabular}{c} **Moscow** \\ **(Domodedovo)** \\ \end{tabular} &
\begin{tabular}{c} **Moscow** \\ **(Sheremetyevo)** \\ \end{tabular} \\ \hline Yekaterinburg & 0 & 0 & 0.4/0 & 0 & 0 & 0 \\ Chelyabinsk & 0 & 0 & 0.1/0 & 0 & 0 & 0 \\ Ufa & 0/0.2 & 0/0.3 & 0 & 0.3/0.53 & 0.3/0.56 & 0.5/0.2 \\ Moscow (Vnuukovo) & 0 & 0 & 0 & 0 & 0 & 0 \\ Moscow (Domodedovo) & 0 & 0 & 0 & 0 & 0 & 0 \\ Moscow (Sheremetyevo) & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Transfer entropy from \(Y\) to \(X\) based on regional transportation statistics. Figure 9: Graph \(G_{\text{TE}}\) for total movements and air transport movements: (**a**) terminal passengers; (**b**) freight. Figure 11: Plot describing the change in the flows of passenger air traffic in the world for the period 1970–2021 [37]. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c} \hline \hline  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** \\ \hline Africa Eastern and Southern & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.18 & 0 & 0 \\ Africa Western and Central & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.18 & 0 & 0 \\ Arab World & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.18 & 0 & 0 \\ Central Europe and the Baltics & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.18 & 0 & 0 \\ East Asia and Pacific & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.18 & 0 & 0 \\ Europe and Central Asia & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.18 & 0 & 0 \\ European Union & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.18 & 0 & 0 \\ Latin America and Caribbean & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.18 & 0 & 0 \\ Middle East and North Africa & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.18 & 0 & 0 \\ North America & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.18 & 0 & 0 \\ South Asia & 0.04 & 0.04 & 0.04 & 0.04 & 0.04 & 0.04 & 0.04 & 0.04 & 0 & 0.04 & 0 \\ Sub-Saharan Africa & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.18 & 0 & 0 \\ World & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.18 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Transfer entropy values for 1970–2021. Figure 10: ICAO statistical regions [36]. Figure 11: Plot describing the change in the flows of passenger air traffic in the world for the period 1970–2021 [37].