Tree networks of real-world data: analysis of efficiency and spatiotemporal scales

Figure from Cipollini et. al., Phys. Rev. Research 2025.

This repository contains the code used in the paper Cipollini and Schomaker, Tree networks of real-world data: analysis of efficiency and spatiotemporal scales, Phys. Rev. Research, 2025, https://doi.org/10.1103/ztmk-glc4.

To replicate the results, run: bash run_pipeline.sh

The bash file calls the following scripts: - Workspace/gridsearch.py or depending on your choice Workspace/gridsearch_nist.py - create_network_dataset.py - Portegys.py

Before running the bash file: - from the Zenodo download, take the folder data and place it in ./Workspace - from the Zenodo download, take the files data\nist\train.dat and data\nist\test.dat and place them in Workspace\boom-nist-k=5-nc=0,1,2,3,4,5,6,7,8,9-f=2000,2000-s=1 - uncomment the corresponding lines to a desired dataset (MNIST, NIST, FASHIONMNIST) and the seed to select a specific subset of the dataset. - Set the number of independent tree formation processes and the parameter r range at line 22 (or 23). - Select the maximum iterations, e.g. max_iter=100, over which you want to compute the averaged quantities with the call to Portegys.py

To generate the tree structures for the NIST dataset, uncomment line 23 in run_pipeline.sh. The seed is irrelevant for the NIST case.

The script: - dataset_complexity_estimation.py plots figure 2. - Portegys_plot_over_all_r.py produces the same figure and analysis as Portegys.py, but addresses the full range of r for panel (a) in figure 5. - hierarchical_phase_transition.py plots panels (d) and (e) in figure 5. - grid_of_spectral_entropy.sh calls grid_of_spectral_entropy.py: takes as input the path of a directory and plots the .jpg files contained in a tabular structure. - plot_network_over_r.py produces panel (b) in figure 5. - run_overDatasets.sh only runs Portegys.py the analysis and produces the plots. - clean.sh and move.sh are helper scripts to erase and move files in Workspace and Dataset (the folder that will contain the generated trees after you run run_pipeline.sh)

Dataset

https://zenodo.org/records/13883206

Acknowledgments

The script boom.c is provided by Prof. Dr. L. Schomaker. The authors gratefully acknowledge Jos van Goor for providing the scripts contained in the directory ./Workspace that enabled efficient grid-search across parameters. Methods for measuring thermodynamic efficiency - thermo_spectrum and thermo_trajectory - are imported from the script reported in Ghavasieh, A., De Domenico, M. Diversity of information pathways drives sparsity in real-world networks. Nat. Phys. 20, 512–519 (2024).