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Tomography of scaling.

Marc Barthelemy1,2

  • 1Institut de Physique Théorique, CEA-CNRS, Gif-sur-Yvette, 91191, France.

Journal of the Royal Society, Interface
|November 28, 2019
PubMed
Summary

This study introduces a new method to analyze scaling in complex systems, overcoming noise-induced fitting issues. The local scaling exponent provides a

Area of Science:

  • Complex systems analysis
  • Statistical physics
  • Urban studies

Background:

  • Scaling laws describe how system properties change with size, often using a power-law form Y ~ P^β.
  • Noise in data can obscure true nonlinear scaling behavior (β ≠ 1) and complicate standard regression analysis.
  • Accurate scaling exponent determination is crucial for understanding and predicting system behavior.

Purpose of the Study:

  • To develop a robust method for analyzing scaling in complex systems, particularly when noise interferes with traditional regression.
  • To introduce a 'local scaling exponent' (β_loc) as a tool to probe scaling behavior across different system size ratios.
  • To assess the relevance of nonlinearity and identify effective scaling exponents even in the presence of noise or complex scaling forms.

Main Methods:

Keywords:
citiescomplex systemsnonlinearityscaling

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  • Defining a local scaling exponent (β_loc) based on the relationship between two systems of different sizes (P1 and P2).
  • Analyzing β_loc as a function of the size ratio (P2/P1), akin to a 'tomography scan' of scaling.
  • Applying the method to real-world urban datasets to validate its effectiveness.

Main Results:

  • The local scaling exponent method effectively assesses nonlinearity and identifies optimal scaling exponents.
  • The approach provides new insights in cases where standard analysis is inconclusive due to noise or complex scaling.
  • The method successfully detected issues like the absence of a single scaling exponent and the presence of threshold effects in urban data.

Conclusions:

  • The local scaling exponent offers a powerful alternative for analyzing scaling in complex systems, especially under noisy conditions.
  • This 'tomographic' approach enhances the reliability of scaling exponent estimation and reveals nuanced system dynamics.
  • The method has practical applications in urban studies and can identify limitations in simple scaling models.