To conclude, massive thanks to my supervisor Luc @lucberthouze.bsky.social for (list is too long for the character limit), and Pedro for pushing me to test these intuitions on more complex systems

If these questions sound interesting to you, do contact me!

I will post a much longer blog-like thread later here and on my website, I really want to share some graph-theory tricks that I think are very useful to study multivariate IT quantities.

For now: enricocaprioglio.github.io/Lucciole/blo...

2 - synergy from low-order interactions does seem less mysterious now! But, how do these antibalanced interaction motifs came to be?

3 - SBT and multivariate IT thus seem very similar (especially when you assume Gaussianity). What can we learn from combining these two lines of work?

Some final thoughts/questions:

1 - Interesting things happen at the pairwise level, which need to be taken into account. Negative/inhibitory interactions are very important in many biological systems (and maybe in social systems as well? idk)

Is there any reason to believe that this intuition works for other complex systems? And does it work using real data (our proofs do require the correlation matrices to have a spectral radius < 2)?

Surprisingly, yeah it works!

Theo. 2: if a OU process with N=3 is synergistic, then interactions must be antibalanced

Theo. 3: antibalanced interaction motifs are necessary for OU processes to be synergy-dominated

For any strength of interactions, here are some numerical results when N = 8 (using every possible sign pattern):

To get some analytical results, we studied Ornstein–Uhlenbeck (OU) processes for which we have a simple expression for the stationary Σ (symmetric interactions). Using this, we get to two more theorems, one for systems of size 3, and the other for any size in the limit of weak interactions:

Basically, in diffusive systems with +ve couplings, we expect triadic closure in the correlations. In other words, it's weird when two nodes are (anti)uncorrelated, but both are correlated with a third node.

The intuition being there must be a negative underlying interaction between the two nodes.

Then we asked: how do we get here? What kind of interactions are needed to obtain these correlational structures?

Note: the structures above are all made of "forbidden triads" (see e.g., "the strength of weak ties")

First, we used the O-information and (social) structural balanced theory to show that the O-information can be expanded in terms of closed walks in the correlation matrix Σ.

The terms that contribute synergistically are exactly the kind of walks that you would find in antibalanced graphs!

Importantly, thanks to @sussexcogs.bsky.social, @anilseth.bsky.social and @sussex.ac.uk!

Organized by @simoncbowes.bsky.social, Ben White and I

Around Falmer, photo taken by Simon Bowes

Between Brighton and Clayton, on the A23

Below you can find a short thread of road signs that say emerge.

Feel free to add your photos!

Panelists/respondents include:
@neuromorphicboki.bsky.social
@cdj.bsky.social
@pessoabrain.bsky.social

Let me know if anyone else is here on Bluesky!