## 2 Materials and Methods
### The Implementation Process of PDC-RA  
We will introduce the implementation of PDC-RA based on Tencent LBS data. Considering that the research area's population size changes over the course of a day, we should select a representative moment. We calculate the PDC-RA value by the Thiessen polygon spatial subdivision method.  
(1) Choosing a representative moment  
Population size data at different hours in multi-days were obtained from Tencent's location-based big data platform. We analyze the temporal and spatial variation and pick a representative moment Tencent LBS data as the data for calculating PDC-RA. Through 24 hours of group summation statistics, the temporal change characteristics of the population quantity in the experimental area during multiple days (weekdays and weekends) are shown in Figure 3. Weekdays and weekends show the same trend of change. The lowest population was at approximately 05:00, and the peak population occurred at about 21:00. What's more, 94% of people are at home according to a national time-use survey [34]. We select the 21:00 population points data as the research area's actual carrying population. The 21:00 population points data are processed to a 21:00 population points layer: 21 PPL for short.  
2. Thiessen polygon spatial subdivision  
Each point object population value of 21 PPL represents the statistical aggregation degree of its circumjacent coverage, which is calculated from Tencent's location-based big data platform. If we intersect points of 21 PPL with residential areas, there will be a great spatial error. So, studying the method for mapping discrete points into continuous space is the basis for counting the population of residential areas. We adopt the characteristics of \"any position in the polygon is closest to the sample point\" in the Thiessen polygon, construct the population distribution statistical point data using the Thiessen polygon on Tencent LBS data, and apply the spatial association rules by intersecting with plots, as shown in Figure 4. Thiessen polygons are a type of partition of the space plane. The method is characterized by any position within the polygon being the closest to potential points. Each polygon contains only one sample point. In considering of the equal division characteristics of the Thiessen polygon in spatial segmentation, the method can be used to solve problems such as nearest points, minimum closed circles, spatial analyses, adjacency, proximity, and reachability analyses.  
After the points of 21 PPL are allocated to each residential area, the population size of the residential area is calculated. The calculation equation of the population in each residential area is as shown in Equation (7):  
\[V^{\prime}_{PDC-RA}(i)=\sum_{r=1}^{u}\big{(}\frac{A_{c}(r)}{A(r)}\times P(r) \big{)}(r=1,2\ldots,u) \tag{7}\]  
\(V^{\prime}_{PDC-RA}(i)\) is the PDC-RA value of residential area \(i\). \(u\) indicates the number of Thiessen polygons that are superimposed on residential area \(i\), \(A_{c}(r)\) indicates that the sub-block area of residential area \(i\) intersects with the Thiessen polygon \(r\), \(A(r)\) indicates the area of the Thiessen polygon \(r\), and \(P(r)\) indicates the population value of the Thiessen polygon \(r\). The PDC-RA results are shown in Table A1.  
Figure 3: Comparison diagram of population size changes over a weekday and weekend.  
The normalization Equation (8) gains the values of PDC-RA that have been max normalized. \(\mathrm{V}^{\prime}_{PDC-RA}(max)\) indicates the maximum value of \(V^{\prime}_{PDC-RA}(i)\). The purpose of max normalization is to prevent PDC-RA values from reaching zero and not being applied to SARSF-RA calculations.  
\[V_{PDC-RA}(i)=\frac{V^{\prime}_{PDC-RA}(i)}{V^{\prime}_{PDC-RA}(max)} \tag{8}\]