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Finally, thanks to all the people who were involved with and supported me through this project: @thosvarley.bsky.social, @fasky.bsky.social , Maria Grazia Puxeddu, and Olaf Sporns. I'm always grateful for your friendship and guidance.

So to summarize: time-localized O-information shows different things than time-averaged O-information. Some subsets (those corresponding to canonical RSNs) are just information-rich. Both synergistic and redundant subsets are highly recurrent. And momentary z-score sign can help predict syn/red.

This is cool also because it can provide a computational heuristic for finding these subsets. Got a subset that’s all the same sign at a time point, but looking for synergy? Don't calculate O, just pick another subset. (HUGE caveat: may not generalize to non-Gaussian or even non-fMRI datasets.)

Finally: if it's the same subsets... what is it about their activity that is different? At all subset sizes, synergistic subsets split the natural bipartition that is formed by binarizing the data: they have positive and negative z-scores. Redundant subsets prefer to have much more of one sign.

We repeated this flavor of analysis for even larger subsets (up to size 75) by optimizing for the most synergistic and most redundant subset on each time point independently. We found very similar temporal structure marked by good recurrence.

But the triads have great recurrence structure. Synergistic and redundant triads both recur long periods of time after their initial occurrence—these may represent states that the brain is meaningfully returning to.

We exhaustively calculated the local O-information for all triads at each time point, to find the maximally synergistic and maximally redundant triads (one for each time point). As expected from the previous result, the same triads dominate both time series.

But interesting things happen in smaller subsets. The subsets with the most redundant, time-averaged O-information have BOTH the most redundant AND the most synergistic time points! They are just information-rich. This is highly unexpected—but will continue to be confirmed throughout the results.

First, we treated the whole brain as one large interaction. It’s essentially awash in redundancy all the time. Most participants never experience a whole-brain synergistic moments… and if they do, those moments are mostly noise.

The local O-information gives a temporally resolved measure of synergy/redundancy dominance: one value per time point. So for each set of brain regions, you can now obtain a time series instead of a single value. But, of course, how you choose to sample the interactions matters. So what did we do?