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# Statistical Laws in Complex Systems

This repository contains the data and code used in the manuscript "Statistical Laws in Complex Systems", [arXiv:2407.19874](https://arxiv.org/abs/2407.19874) (2024).
This repository contains the data and code used in:
- [E. G. Altmann](https://www.maths.usyd.edu.au/u/ega/), "Statistical Laws in Complex Systems: Combining Mechanistic Models and Data Analysis", <br>

## Folders:

- data/ <br>
datasets used in the analysis. The data on linguistic laws is large and needs to be downloaded from https://doi.org/10.5281/zenodo.13119897
[monograph (expected Dec. 2024)](https://link.springer.com/book/9783031731631) part of the Springer series [”Understanding Complex Systems”](https://www.springer.com/series/5394), pre-print available at [arXiv:2407.19874](https://arxiv.org/abs/2407.19874) (Jul. 2024).

- notebooks/ <br>
jupyter notebooks used to generate the figures of the paper.
## Folders:

- src/ <br>
- [data/](https://github.com/edugalt/StatisticalLaws/blob/main/data/) <br>
datasets us in the analysis of the different Statistical Laws:
- [Allometric laws](https://github.com/edugalt/StatisticalLaws/tree/main/data/allometric)
- [Cities](https://github.com/edugalt/StatisticalLaws/tree/main/data/cities)
- [Income (Pareto's law)](https://github.com/edugalt/StatisticalLaws/tree/main/data/income)
- [Linguistic laws](https://github.com/edugalt/StatisticalLaws/tree/main/data/language) Large datasets, needs to be downloaded from https://doi.org/10.5281/zenodo.13119897

- [notebooks/](https://github.com/edugalt/StatisticalLaws/blob/main/notebooks/) <br>
jupyter notebooks used to generate the figures and tables of the [paper](https://arxiv.org/abs/2407.19874):

- [allometric.ipynb](https://github.com/edugalt/StatisticalLaws/blob/main/notebooks/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](https://github.com/edugalt/StatisticalLaws/blob/main/notebooks/bibliometric-data.ipynb) contains the analysis of the bibliometric data shown in Fig. 4.2.
- [burstinessWords.ipynb](https://github.com/edugalt/StatisticalLaws/blob/main/notebooks/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](https://github.com/edugalt/StatisticalLaws/blob/main/notebooks/constrained-powerlaw.ipynb) contains the code to generate constrained surrogates – Sec. 3.4.2 – including Fig. 3.12.
- [heaps.ipynb](https://github.com/edugalt/StatisticalLaws/blob/main/notebooks/heaps.ipynb) contains the analysis of Herdan-Heaps’ law – Sec. 2.2.2 – including Fig. 2.6.
- [pareto.ipynb](https://github.com/edugalt/StatisticalLaws/blob/main/notebooks/) contains the analysis of Pareto’s law of inequality – Sec. 2.1.1 – including Fig. 2.1
- [synthetic-powerlaw.ipynb](https://github.com/edugalt/StatisticalLaws/blob/main/notebooks/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](https://github.com/edugalt/StatisticalLaws/blob/main/notebooks/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/](https://github.com/edugalt/StatisticalLaws/blob/main/src/) <br>
source code used in the data analysis.


## Credit:

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