Rank clocks

Nature

Volumn 444, Issue 7119, 2006, Pages 592-596

  Batty, Michael ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

GRAPHIC METHODS; INTERNET; MATHEMATICAL MODELS; MOLECULAR DYNAMICS;

GRAPHICAL REPRESENTATION; INTERNET HUBS; RANK-SIZE SCALING; TURBULENT MICRO-DYNAMICS;

CLOCKS;

FIRM SIZE; RANKING; SIZE DISTRIBUTION; TIMESCALE; URBAN GROWTH;

ARTICLE; CALCULATION; CITY; CIVILIZATION; DATA ANALYSIS; DYNAMICS; ENTROPY; GROWTH RATE; INTERNET; MATHEMATICAL ANALYSIS; MODEL; PRIORITY JOURNAL; RANK CLOCK; TIME; UNITED KINGDOM; UNITED STATES;

EURASIA; EUROPE; NORTH AMERICA; UNITED KINGDOM; UNITED STATES; WESTERN EUROPE;

EID: 33845256049     PISSN: 00280836     EISSN: 14764687     Source Type: Journal    
DOI: 10.1038/nature05302     Document Type: Article

References (25)

1. Blank, A. & Solomon, S. Power laws in cities population, financial markets and internet sites: Scaling and systems with a variable number of components. Physica A 287, 279-288 (2000).
2. Gabaix, X. & Ioannides, Y. M. in Handbook of Regional and Urban Economics Vol. 4 (eds Henderson, V. & Thisse, J-F.) 2341-2378 (North-Holland, Amsterdam, 2004).
3. Axtell, R. L. Zipf distribution of U.S. firm sizes. Science 293, 1818-1820 (2001).
4. Adamic, L. A. & Huberman, B. A. Zipf's law and the internet. Glottometrics 3, 143-150 (2002).
5. Stanley, M. H. R. et al. Scaling behavior in the growth of companies. Nature 379, 804-806 (1996).
6. White, D. R., Kejzar, N., Tsallis, C. & Rozenblat, C. Generative Historical Model of City-Size Hierarchies: 430BCE-2005 (ISCOM Working Paper, Institute of Mathematical Behavioral Sciences, University of California, Irvine, CA, 2005).
7. Barabasi, A-L. The origin of bursts and heavy tails in human dynamics. Nature 435, 207-211 (2005).
8. Gibson, C. Population of the 100 Largest Cities and Other Urban Places in the United States: 1790 to 1990 (Population Division Paper 27, US Bureau of the Census, Washington DC, 1998).
9. Zipf, G. K. Human Behavior and the Principle of Least Effort (Addison-Wesley, Cambridge, Massachusetts, 1949).
10. CDU census website. 〈http://census.ac.uk/cdu/〉 (accessed 8 August, 2006).
11. Chandler, T. Four Thousand Years of Urban Growth: An Historical Census (Edward Mellon, Lampeter, UK, 1987).
12. Ioannides, Y. M. & Overman, H. G. Zipf's law for cities: An empirical examination. Reg. Sci. Urban Econ. 33, 127-137 (2003).
13. Havlin, S. The distance between Zipf plots. Physica A 216, 148-150 (1995).
14. Guerin-Pace, F. Rank-size distribution and the process of urban growth. Urban Stud. 32, 551-562 (1995).
15. Robson, B. T. Urban Growth: An Approach (Methuen, London, 1972).
16. Theil, H. Statistical Decomposition Analysis (North-Holland, Amsterdam, 1972).
17. Batty, M. Entropy in spatial aggregation. Geogr. Anal. 8, 1-21 (1976).
18. Gell-Mann, M. & Tsallis, C. (eds) Nonextensive Entropy- Interdisciplinary Applications (Oxford Univ. Press, New York, 2004).
19. Turchin, P. Historical Dynamics: Why States Rise and Fall (Princeton Univ. Press, Princeton, New Jersey, 2003).
20. Gabaix, X. Zipf's law for cities: An explanation. Q. J. Econ. 114, 739-767 (1999).
21. Sornette, D. & Cont, R. Convergent multiplicative processes repelled from zero: Power laws and truncated power laws. J. Phys. I (Paris) 7, 431-444 (1997).
22. Pumain, D. in Hierarchy in Natural and Social Sciences (ed. Pumain, D.) 169-222 (Springer, Dordrecht, 2006).
23. Gibrat, R. Les Inégalités Économiques (Librarie du Recueil, Sirey, Paris, 1931).
24. Malcai, O., Biham, O. & Solomon, S. Power-law distributions and Levy-stable intermittent fluctuations in stochastic systems of many autocatalytic elements. Phys. Rev. E 60, 1299-1303 (1999).
25. Krapivsky, P. L. & Redner, S. Statistics of changes in lead node in connectivitydriven networks. Phys. Rev. Lett. 89, 258703 (2002).