Figure 3
From: Understanding the mesoscopic scaling patterns within cities
Interactions and sub-linear scaling. (a) Illustration of the localized connection between AP and infrastructure. We assume that an AP connects to its n nearest neighbors by the infrastructure network, and n is a constant number. For simplicity, we draw a two-dimensional schematic. In fact, the population distribution and infrastructure connections are three-dimensional. (b) \(\ell \sim \rho ^{-\alpha }\) of road network data (\(\alpha\) = 0.562, \(R^2\) = 0.985). (c) Scatter plot between the observed and predicted infrastructure volumes obtained from Eq. (3). (d) Illustration of the global interaction between people and people. (e) Scatter plots of \(\langle 1-\alpha \rangle\) and \(\langle \alpha \rangle\), which are the exponents of P and A in the regression \(\log _{10} V_i = C_i + (1-\alpha ) \log _{10} P_i + \alpha \log _{10} A_i\), respectively. The red line is the prediction of the Cobb–Douglas function with constant returns to scale. (f) \(R^2\)s of the ten studied cities. The average \(R^2\) obtained from Eq. (4) is 0.927 (red dots), and we also put the results of Fig. 2c here (black dots) for comparison.
