README.md

Statistical Laws in Complex Systems

This repository contains the data and code used in:

• E. G. Altmann, "Statistical Laws in Complex Systems: Combining Mechanistic Models and Data Analysis",
  

monograph (expected Dec. 2024) part of the Springer series ”Understanding Complex Systems”, pre-print available at arXiv:2407.19874 (Jul. 2024).

Folders:

• data/
  datasets us in the analysis of the different Statistical Laws:

  • Allometric laws
  • Cities
  • Income (Pareto's law)
  • Linguistic laws Large datasets, needs to be downloaded from https://doi.org/10.5281/zenodo.13119897

• notebooks/
  jupyter notebooks used to generate the figures and tables of the paper:

  • allometric.ipynb contains the analysis of Kleiber’s law and allometric scaling laws – Sec. 2.2.3 – including Figs. 2.7 and 2.8.
  • bibliometric-data.ipynb contains the analysis of the bibliometric data shown in Fig. 4.2.
  • burstinessWords.ipynb contains the analysis of the inter-event time between words – Sec. 2.3.1 – including Figs. 2.11 and 3.1.
  • [cities.ipynb contains the analysis of all urban data, including the ALZ law – Sec. 2.1.2 –, urban scaling laws – Sec. 2.2.1 –, Figs. 1.1, 2.2, 2.5, 3.2, 3.3, 3.5, and 3.7, and Tab. 3.4.3.
  • constrained-powerlaw.ipynb contains the code to generate constrained surrogates – Sec. 3.4.2 – including Fig. 3.12.
  • heaps.ipynb contains the analysis of Herdan-Heaps’ law – Sec. 2.2.2 – including Fig. 2.6.
  • pareto.ipynb contains the analysis of Pareto’s law of inequality – Sec. 2.1.1 – including Fig. 2.1
  • synthetic-powerlaw.ipynb contains the generation and analysis of synthetic power-law datasets with correlation – Sec. 3.3.4 – including Figs. 3.8 and 3.9.
  • zipf.ipynb Contains the analysis of Zipf’s law of word frequencies – Sec. 2.1.3 – including Figs. 2.3-3.6 and Tab. 3.3-3.4

• src/
  source code used in the data analysis.

Credit:

This repository builds on the ideas, code, and data from:

• Urban Scaling laws:

  • Paper: J. C. Leitao, J.M. Miotto, M. Gerlach, and E. G. Altmann, "Is this scaling nonlinear?", Royal Society Open Science 3, 150649 (2016)
  • Paper: E. G. Altmann, "Spatial interactions in urban scaling laws", PLOS ONE 15, e0243390 (2020)
  • Code: https://github.com/edugalt/scaling

• Fitting frequency distributions and rank-frequency distributions:

  • Paper: M. Gerlach and E. G. Altmann, "Stochastic model for the vocabulary growth in natural languages", Phys. Rev. X 3, 021006 (2013)
  • Paper: H. H. Chen, T. J. Alexander, D. F.M. Oliveira, E. G. Altmann, "Scaling laws and dynamics of hashtags on Twitter", Chaos 30, 063112 (2020) or arXiv
  • Code: https://github.com/edugalt/TwitterHashtags

• Effect of correlation

  • Paper: M. Gerlach and E. G. Altmann, "Testing statistical laws in complex systems", Phys. Rev. Lett. 122, 168301 (2019) or arXiv
  • Code: https://github.com/martingerlach/testing-statistical-laws-in-complex-systems

• Constrained surrogates

  • Paper: J. M. Moore, G. Yan, E. G Altmann, "Nonparametric Power-Law Surrogates", Phys. Rev. X 12, 021056 (2022)
  • Code: https://github.com/JackMurdochMoore/power-law/