## 4 Results
### Density Characteristics of Spatiotemporal Distribution  
Leveraging the capabilities of ArcGIS 10.2 software, we undertook a sophisticated examination of the spatiotemporal distribution of smart healthcare and geriatric care facilities across China for the five-year period spanning from 2017 to 2021. Employing advanced statistical methodologies, including kernel density estimation and the standard deviation ellipse analysis, we unravelled the intricate patterns and trends within the dataset.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Year**} & \multirow{2}{*}{\begin{tabular}{c} **Number of Elderly** \\ **Care Centers** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Theoretical** \\ **Nearest Neighbour** \\ **Distance/km** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Actual Nearest** \\ **Neighbour** \\ **Index** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Nearest** \\ **Neighbour** \\ **Index** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Type of Space** \\ **Structure** \\ \end{tabular} } \\  & & & & & & \\
2017 & 19 & 316.174 & 293.515 & 0.928 & \(-0.598\) & Random \\
2018 & 29 & 255.920 & 214.589 & 0.839 & \(-1.664\) & Clustered \\
2019 & 52 & 201.043 & 135.521 & 0.674 & \(-4.496\) & Clustered \\
2020 & 68 & 176.294 & 103.908 & 0.589 & \(-6.477\) & Clustered \\
2021 & 85 & 157.683 & 79.855 & 0.506 & \(-8.705\) & Clustered \\ \hline \hline \end{tabular}
\end{table}
Table 1: The nearest neighbour index of the smart healthy aging center.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Year**} & \multirow{2}{*}{\begin{tabular}{c} **Number of Elderly** \\ **Centers** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Number of Provincial** \\ **Administrations** \\ \end{tabular} } & \multicolumn{2}{c}{\
\begin{tabular}{c} **Imbalance Index** \\ **(S)** \\ \end{tabular} } & \multicolumn{2}{c}{
\begin{tabular}{c} **Geographical Concentration** \\ **Index (G)** \\ \end{tabular} } \\ \hline
2017 & 19 & 12 & 0.263 & 32.015 \\
2018 & 29 & 13 & 0.385 & 33.610 \\
2019 & 52 & 19 & 0.442 & 30.285 \\
2020 & 68 & 19 & 0.475 & 30.987 \\
2021 & 85 & 19 & 0.492 & 31.282 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The imbalance index and geographical concentration index of the smart healthy aging center.  
The fruit of this analytical labor is meticulously laid out in the sequence of graphical representations, as depicted in Figure 3a through Figure 3e.  
Through comparison, it was found that in 2017, there was no obvious density core in the study area. However, as the number and coverage of smart health and elderly care bases continue to increase, the spatial aggregation characteristics of the bases have become more and more obvious. In 2018 and 2019, the density growth of the three provinces of  
Figure 3: Kernel density and standard deviation elliptic of the smart healthy aging center: 2017–2021 corresponds to (**a–e**).  
Sichuan, Zhejiang, and Shandong changed significantly, and the base overall showed a three-pole concentration spatial pattern. In 2020 and 2021, while the three provinces of Sichuan, Zhejiang, and Shandong remain in the lead, the four provinces of Henan, Anhui, Guangdong, and Hubei have also begun to show agglomeration characteristics, and the base as a whole shows a three-pole concentration-multi-core surround type spatial pattern.