Timeliness criticality

This repository contains the code necessary to reproduce the simulations shown in https://arxiv.org/abs/2309.15070 and discussed in https://arxiv.org/pdf/2307.03546.

This code was generated by three authors:

- José Moran (Julia code)
- Deb Panja (C code)
- Matthijs Romijnders (Python code)

Julia code (used to determine critical buffers)

To run this in julia, you need to instantiate the project environment in your REPL. Change directories to julia_temp_criticality and run

] activate .

You can then run the simulations in the jupyter notebook julia_nb.ipynb, or you can run the example script example.jl from the command line.

julia --project example.jl

This will save a file example.png in the directory with a simulation run, which should look like this:

C code (used to determine avalanche statistics)

To compile the C code, used for more heavy computations and in particular the avalanche simulations, cd into the C directory and run

 gcc temporal_avalanches.c -o temporal_avalanches -lm -O2

this will create an executable temporal_avalanches which you can run with

./temporal_avalanches

which will then store files called out (containing the time-series), avalanches (containing avalanche sizes), persistence (containing the persistence times) and correlations (containing the time-series autocorrelation functions) in your working directory, from which probability distributions are determined.

Once we have data on probability distributions (such as avalanches and persistence), we can post-process them by pooling into logarithmic bins and doing an exponential smoothing (for plotting purposes) by running the following awk script:

awk '{obin=bin;bin=int(20*log($1));a[bin]+=$2;n[bin]++; if (obin!=bin) print exp(bin*0.05),a[bin]/n[bin];}' < datafile > datafile.smoothed

note that the 20 in the awk script is the number of bins per decade, and the 0.05 is the bin width in the original data. These scale factors can be freely chosen, but their product must equal 1. This was used to produce e.g. Figure 5 in the "Timeliness Criticality" paper.

Python code (used for temporal networks)

To be added.