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1: Two interpretations of scaling laws for urban dynamics
2: Scaling laws in complex systems
3: An ontology for urban systems
4: Urban systems as multilevel organisation
5: Morphological intuition of urban systems
6: Multilevel interactions in systems of cities
7: Zipf law as universal emerging property of urban systems
8: Why transfering the scaling law model?
9: Case studies: 3 types of urban systems
10: Data for case studies
11: Scaling of urban activity sectors
12: Scaling parameter > 1: leading economic sectors FIRE (Finance, Insurance, Real Estate)
13: Scaling parameter ≈ 1: Common Sectors
14: Scaling parameter < 1: mature sectors
15: Interpretation: Scaling laws and Innovation cycles
16: Interpretation of scaling parameters
17: Theory of innovation in urban systems (1)
18: Theory of innovation in urban systems (2)
19: Theory of innovation in urban systems (3)
20: Main innovation cycles having generated urban specialisation
21: Stages in innovation cycle
22: Theory of innovation in urban systems (4)
23: Connexion with scaling
24: Innovation cycles and substitution process
25: Theory testing 1: Economic diversity and city size
26: Scaling and diversity of urban functions
27: Economic diversity of French “aires urbaines” in 1999
28: Economic diversity of US Metropolitan Areas in 2000
29: Economic diversity of South African urban agglomerations in 2001
30: City size and economic diversity
31: Theory testing 2: Evolution of scaling parameters
32: Increasing and Stable β exponents over 1
33: Decreasing β exponents : hierarchical diffusion of innovation
34: Theory testing 3: Occupational groups
35: French survey: occupational groups
36: French survey: occupational groups
37: French survey: occupational groups
38: French survey: occupational groups
39: French survey: occupational groups
40: US survey: occupational groups
41: US survey: occupational groups
42: US survey: occupational groups
43: A physical interpretation of scaling laws
44: A « physical » interpretation of urban scaling laws
45: Scaling parameters and growth trajectories
46: Growth trajectories according to scaling exponent
47: Urban trajectory (Bettencourt et al., 2009)
48: Interpretation of scaling exponent (Bettencourt et al. 2009)
49: Geographical theory of dynamics in urban systems
50: Cities trajectories in innovation space
51: Theory testing 4: urban growth
52: Defining cities and urban systems for comparison
53: Results: a formal contradiction
54: Reformulating Gibrat’s model
55: Estimated β values (France)
56: Estimated β values (USA)
57: Annualised β values (France and USA)
58: Getting more information about growth process with reformulated Gibrat’s model
59: Factor analysis of estimation residuals (France)
60: Correlations between urban growth cycles (France)
61: Factor analysis of residuals (US)
62: Spatial pattern of F1 coordinates
63: Correlation of F1 coordinates with distance to North-Eastern coast =0.65
64: Innovation diffusion and spatial integration of urban systems
65: Matching classes of urban growth trajectories (residual) and Kondratiev cycles (France)
66: A geographical model for simulating urban growth
67: Modelling innovation cycles diffusion through spatial interaction
68: Consequences of the rules
69: Main parameters in the model
70: Waves of growth linked to innovations
71: Simulated trajectories of individual cities
72: Evolution of beta (size effect) according to innovation cycles
73: PCA pattern of simulated growth residuals
74: Evolution of city size inequalities in Gibrat (blue line) and geographical model (black line)
75: The geographical growth model
76: Conclusion: why is Gibrat’s model « more or less » valid?
77: Linking scaling laws to a geographical model of urban growth with spatial interaction and innovation cycles
78: More research