This is a repository of MATLAB codes accompanying the paper:

• Cifre I, Miller Flores MT, Penalba L, Ochab JK and Chialvo DR (2021) Revisiting Nonlinear Functional Brain Co-activations: Directed, Dynamic, and Delayed. Front. Neurosci. 15:700171. doi: 10.3389/fnins.2021.700171

See also how this meethod can be adapted to experiments in the task paradigm (not just resting-state):

• Ceglarek A, Ochab JK, Cifre I, Fafrowicz M, Sikora-Wachowicz B, Lewandowska K, Bohaterewicz B, Marek T and Chialvo DR (2021) Non-linear Functional Brain Co-activations in Short-Term Memory Distortion Tasks. Front. Neurosci. 15:778242. doi: 10.3389/fnins.2021.778242

Corresponding author: [email protected] (see also: http://www.chialvo.net)
Repository manager: [email protected] (see also: http://cs.if.uj.edu.pl/jeremi)

• rbeta_events finds events in the source/seed signal (e.g., mean signal from a selected Region of Interest) and returns the segments of the source and target time series around the time of the event occurrence
• rbeta_corrs computes linear correlations between the source and target segments
• rbeta_delays computes delays between the estimated source event peak and the closest estimated peak in the target time series
• pear_delays computes delays by finding a shift maximising the covariance between the source and target time series

For a single source time series of length T and an array of target time series of the same length, the general call is:

 [target_segments, source_segments, event_times] = rbeta_events(target, source, thr, past, future)

where thr can be usually set to 1 (which defines events as points crossing one standard deviation threshold), and past and future define the size of the segments around the event to be extracted (in total it has past + future + 1 points).

The general call is:

[corrs_mean, corrs] = rbeta_corrs(events,events_seed,pastD,futureD)

corrs gives the correlations between source/target segments that occurred around individual events;
corrs_mean gives the correlations between average shapes (i.e., segments averaged over all the events identified).
If you only need average correlations, skip the output (which is much faster):

[corrs_mean] = rbeta_corrs(events,events_seed)

The order of averaging and correlating matters (i.e., the average of corrs will in general produce a slightly different result than corrs_mean).

Use pastD and futureD if the segments provided by rbeta_events turn out to be larger than you need, and you do not wish to recompute them (although it is fast). For instance, pastD=-2; futureD=-2; will shorten the segments computed with past=6; future=8; to past=4;future=6;.

[corrs_mean, corrs]=rbeta_corrs(events,events_seed,pastD,futureD)

If you do not want to change past/future parameters, skip them:

[corrs_mean, corrs]=rbeta_corrs(events,events_seed)

These Pearson correlations are uncorrected. If you wish to Fisher transform them, remember to do atanh(corrs_mean).

You can use either

[delays_mean, delays] = rbeta_delays(events,events_seed,pastD,futureD)

which computes delays for each event and delays_mean for averaged events or only the average event delays

[delays_mean] = rbeta_delays(events,events_seed,pastD,futureD)

which skips computing individual events, making it much faster.

By default, the script looks for the closest peaks, which can be set explicitly:

[delays_mean] = rbeta_delays(events,events_seed,pastD,futureD,'closest')

but it can also look for the largest peaks in the vicinity (defined by the size of the provided segments):

[delays_mean] = rbeta_delays(events,events_seed,pastD,futureD,'largest')

The function pear_delays can also take the closest'/'largest' setting.

Checked for Matlab versions:

• R2022a
• TBA

For Python implementation, possibly faster, see https://github.com/gdbassett/rbeta.