Criticality

Simulate bifurcating dynamical systems, record time series and run hctsa to produce features that characterize the dynamical system and its control parameter; then, run analyses to determine which features are most useful for predicting this parameter.

Reproducing figures

This repository accompanies the paper "Tracking the distance to criticality in systems with unknown noise". The two new features we introduce in the paper are CR_RAD_1, available in RAD.m, and fitSupercriticalHopfRadius_1, available in fitSupercriticalHopfRadius.m. The bulk of this repository is concerned with simulating dynamical systems with varying control parameters and noise strengths then analyzing hctsa features of the resulting time series; we provide a guide to this workflow in the following sections. First, in this section, we describe a procedure for reproducing the figures from the paper using code contained in the paper/ directory.

To add this repository to the Matlab path, download hctsa v0.98 and run startup() in the hctsa directory, then run add_all_subfolders.m in the top-level Criticality directory. To reproduce figures 1 to 5, first download the main dataset (produced with the workflow described below or hosted on figshare). Place the time_series_data.mat file at papers/time_series_data.mat, navigate to paper/, and run the script figures.m.

Supplemental figure 2 can be reproduced by running the following scripts (in order, in their respective directories):

1. paper/other_systems/gensystem.m: individually for the five systems specified in the script, to generate simulated data for various normal forms,
2. paper/measurement_noise/measurement_noise_generator.m: individually for the two input files specified in the script, to generate simulated data for various measurement noise strengths,
3. paper/other_systems/plot_systems.m and paper/measurement_noise/plot_measurement_noise.m: to plot the results.

Figure 6, describing our case study on tracking the visual cortical hierarchy from Neuropixels data, can be reproduced in Julia by activating and instantiating the project located at paper/Criticality.jl/ then running the following scripts (in order):

1. SessionSelection.jl: filter recording sessions based on quality metrics and save the resulting session table,
2. DownloadData.jl (optional; requires hpc): download all data files (~1 TB) for the selected sessions,
3. DistributeCriticality (optional; requires hpc): compute feature values for all sessions in parallel. The results of this script are provided in paper/Criticality.jl/data/,
4. plot_DistributedCriticality.jl: plot all analyses from the paper.
5. HierarchyPlot.jl: plot the schematic of the mouse visual cortical hierarchy.

Setup

In addition to cloning this repository, hctsa v0.98 should be installed in a convenient location and the following modifications performed:

• Add the -v7.3 flag to the save function on line 144 of TS_init.m (allowing for larger .mat files)
• Change the maximum time series length to 10000000 on line 101 of SQL_add.m (allowing for longer time series)
• Use strcmp to compare time series labels on line 207 of TS_combine
• Comment out line 194 of TS_Compute.m

A workflow begins by adding files to the Matlab path; run startup() in the hctsa directory and add_all_subfolders() in the Criticality directory.

To reproduce the main analyses, refer to the files testTimeseries.m, testHCTSA.md and testAnalysis.m in ./test/. Below is an outline of a typical workflow: simulating dynamical systems, running hctsa and analyzing feature values.

Time Series

Stochastic dynamical systems are simulated by the ./Time_Series_Generation/time_series_generator/time_series_generator.m function using the Euler-Maruyama method. For an example time series with the default parameters:

x = time_series_generator();

More complex simulations are defined by name-value pairs or an inputs structure which specify a dynamical system, any relevant options and the structure of the output. See time_series_generator.m for a full description of input options and their defaults or TSG_systems.m for a list of available dynamical systems:

x = time_series_generator('cp_range', [-1, 0], 'etarange', [0.1, 1], 'system_type', 'quadratic_potential');
x = time_series_generator('input_struct', inputs);
x = time_series_generator('input_file', 'inputs.mat');

To construct an inputs structure, run the function make_input_struct. This can be done by directly providing name-value pairs, or by opening a GUI:

inputs = make_input_struct();

Alternatively, a blank structure can be created and then filled using Matlab's variable editor:

inputs = make_input_struct(false);

hctsa

If the foldername option is provided to time_series_generator then the time series will be saved into a hctsa compatible .mat file (e.g. timeseries.mat). This can be directly transformed into an HCTSA.mat file, usually utilising all operations, with:

TS_init('timeseries.mat', [], [], 0);

Serial hctsa calculation can then be initiated with:

TS_compute(0, [], [], [], [], 1);

Which will fill the TS_DataMat array in the HCTSA.mat file with time series feature values.

Distributed Calculations

For massive dynamical system simulations feature calculation can be performed on an HPC cluster; this repository allows distributed computation to be accomplished in three ways.

distributed_hctsa

If the time series array is not intractably large it can simply be transferred to a cluster and distributed_hctsa (or the slightly modified version at ./PBS/Distributed_hctsa/modified/) can be used to subset timeseries, calculate features and recombine the results (as detailed in ./docs/USydPhysicsHPC.md). In this repository the hctsa install directory is assumed to be ~/hctsa_v098/ and the self location is ~/Criticality/.

PBS Array jobs

For larger datasets the process of saving, loading and dividing a single HCTSA.mat file becomes extremely slow, so the save_cp_split option of time_series_generator can be used to directly subset the timeseries at simulation. This option can be set to the number of jobs intended to run on the cluster, as long as this is smaller than the number of different control parameters represented in the dataset. Copying all the subdirectories produced to the cluster, following the same initialisation of Matlab and hctsa before running PBS_array_TS_compute.sh (in the same directory as the time series subdirectories) fills the HCTSA.mat subset files with feature values.

Additionally, time_series_generator can itself be run on a cluster; parameter_sweep.m takes a template input structure and produces subdirectories that each contain an input file varying in the specified option. PBS_generate_time_series.sh can then be run on the cluster, in the folder containing these subdirectories, to fill them with a timeseries.mat file, after which PBS_array_TS_compute.sh can be used to calculate feature values.

Integrated hctsa

A (very) small number of analyses required datasets too large to save to disk; modified versions of TS_init (./Modified_hctsa/light_TS_init.m) and TS_compute (./Modified_hctsa/light_TS_compute.m) bypasses the usual save procedure and do not save time series. These can be used in combination with the parameter_sweep.m and PBS_generate_time_series.sh files by setting the integrated_hctsa option of time_series_generator to non-default values (i.e each subdirectory with its own input file will simulate timeseries and calculate feature values, saving only HCTSA.mat subset files to disk-- without timeseries).

Feature Analysis

The majority of functions contained in this repository are for analyzing the feature array-- TS_DataMat-- produced using hctsa from time series datasets formatted by time_series_generator. Most operate on a time_series_data structure which is produced from an HCTSA.mat; many peripheral functions are unimportant but the central analyses are here outlined.

Analysis begins with ./Feature_Analysis/save_data.m; the working directory should contain an HCTSA.mat and an inputs.mat file. Then:

save_data('./time_series_data.mat', 'keyword1,keyword2', 'timeseries_source', 'HCTSA.mat', 'inputs.mat');

Produces a time_series_data.mat file in the current directory keywords, a source annotation, analysis pre-allocations and only the critical portions of the two earlier files-- the TS_DataMat array, Operations table and inputs structure. For distributed calculations, the working directory would instead contain subdirectories each with an HCTSA.mat time series subset file and an inputs_out.mat options subset file-- save_data() options can be used to combine these subsets.

All further analyses now operate on time_series_data.mat; some modify the structure it contains, others simply read from or plot it. ./Feature_Analysis/Modify_data/ contains the former; the most crucial are the following, which should be run in order:

group_by_noise('time_series_data.mat', 'time_series_data.mat')
find_correlation('time_series_data.mat', 'Pearson', [-1, 0], 'time_series_data.mat');

group_by_noise observes the Inputs field of the time_series_data structure and organises the data such that each row represents one noise parameter (eta) and the rows are arranged by increasing control parameter (cp). find_correlation calculates the correlation for each set of timeseries (each at one eta value) against the range of cp values they represent; in the above example, the Pearson linear correlation between control parameters -1 and 0. In both functions the first and last arguments are the source and destination of the data, respectively.

./Feature_Analysis/Analyse_data/ holds functions to score and rank features; the most useful are get_feature_stats, which accepts a row (and therefore one eta value) of time_series_data, and get_combined_feature_stats, which accepts the entire structure:

tbl1 = get_feature_stats(time_series_data(1, :), {'Absolute_Correlation'})
tbl2 = get_combined_feature_stats(time_series_data, {'Absolute_Correlation'}, {'Absolute_Correlation_Mean'}, [], true);

tbl1 will rank the hctsa features by the magnitude of their correlation to the control parameter, for the noise value represented in the first time_series_data row. tbl2 will average the Absolute_Correlation between rows and therefore noise parameters; features will be ranked by their Absolute_Correlation_Mean, and Absolute_Correlation will be excluded from the table (4th argument).

Finally, ./Feature_Analysis/Plot_Data/ functions help to visualise the time_series_data; for instance, the distribution of the statistic Aggregated_Absolute_Correlation over all features can be plotted and compared to how it evaluates a single feature-- autocorrelation at lag 1, with ID 93 as recorded in the Operations field of time_series_data:

histogramStat(time_series_data, 'Aggregated_Absolute_Correlation')
plot_feature_vals(93, time_series_data, 'noise', true, [1, 25, 50, 75, 100], true)