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Urban Scaling and Its Deviations: Revealing the Structure of Wealth, Innovation and Crime across Cities
Figure 3
Relationships between local urban performance measured by personal income, patents and violent crime and their spatial distributions.
A) normalized SAMIs for income versus patents are shown in polar coordinates, see SI, together with best-fit linear relation capturing overall average correlation (solid line, gradient = 0.38
0.04, 
= 0.20). The color and size of circles both denote the magnitude of the combined SAMIs for each city; b) similar representation for income versus violent crime with best-fit linear relation (gradient = −0.19
0.07, 
= 0.05), and c) similar representation for patents versus violent crime with best-fit linear relation (gradient = −0.34
0.05, 
= 0.12). Note that B) and C) show a small amount of anti-correlation between SAMIs, which contrasts with the positive correlations for the per capita quantities due to their size dependence. d) Spatial distribution of income residuals (SAMIs) in 2006 (created with Google maps, see online (http://www.santafe.edu/urban_observatory/).). Red (blue) dots correspond to deviations above (below) expectation for city size. The size of the circle denotes the magnitude of the SAMIs. e) Average cross-correlation between SAMIs versus spatial separation distance, showing short-range spatial correlation. Averages shown are subject to large variation for distances 
200 km (124 miles) with standard deviation 
0.6.
doi: https://doi.org/10.1371/journal.pone.0013541.g003