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Enrico @enricocaprioglio.bsky.social · 20d

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

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Enrico @enricocaprioglio.bsky.social · 20d

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...

Synergistic Motifs Tutorials | Enrico Caprioglio

A quick collection of tutorials I made

enricocaprioglio.github.io

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Enrico @enricocaprioglio.bsky.social · 20d

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?

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Enrico @enricocaprioglio.bsky.social · 20d

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)

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Enrico @enricocaprioglio.bsky.social · 20d

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!

(LEFT) Antibalanced interaction motifs characterize synergy-dominated complex systems with pairwise coupling. Plots show Ω versus the number of antibalanced triangles in the pairwise coupling matrix. (a) For the Ising model we compute Ω exactly for each possible coupling configuration (β = 0.25). (b) For the SL network of oscillators we report the mean Ω (circle) over 100 initial conditions and the minimum Ω (star) found (lower bound) across configurations with a specific no. of antibalanced triangles.

The curves in both (a) and (b) are similar to the one for the OU process. With no antibalanced triangles, the system is displaying the highest redundancy. While for the largest number of antibalanced triangles, the system show the lowest Ω(X) (most synergistic)

(RIGHT) Structural balance-energy predicts synergy: the most synergistic N-plets maximise U and positive U guarantees synergy-dominance. (a) N-plets from a multivariate time-series of 9 foreign-exchange (FX) rate logarithmic returns. (b) N-plets from resting-state fMRI functional-connectivity matrices (229 brain regions).
Here we see that Ω(X) and a measure of balanced U behave very similarly (strongly anticorrelated). Near zero however, interesting stuff happens.

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Enrico @enricocaprioglio.bsky.social · 20d

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):

Antibalanced interaction motifs are necessary for synergy-dominance in dynamical Gaussian systems. Mean Ω(X) as a function of the number of antibalanced triangles in the interaction matrix. Lower bounds indicate the lowest Ω(X) encountered in our numerical exploration across all configurations with a specific no. of antibalanced triangles. Each mean Ω(X) is coloured according to its mean balance-energy value U.

Here, Ω(X) is anticorrelated with the number of antibalanced triangle motifs in the interaction matrix of the OU process. When all triangles are balanced, the system is very redundant. When all triangles are antibalanced, the system displays the highest synergy (i.e., lowest Ω(X))

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Enrico @enricocaprioglio.bsky.social · 20d

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:

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Enrico @enricocaprioglio.bsky.social · 20d

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.

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Enrico @enricocaprioglio.bsky.social · 20d

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")

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Enrico @enricocaprioglio.bsky.social · 20d

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!

LEFT: if the graph G is antibalanced, every closed walk in G contributes negatively in the expansion of the O-information.

RIGHT: examples of synergistic (correlation) motifs that ensure synergy-dominance

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Enrico @enricocaprioglio.bsky.social · 20d

🚨 How do collective behaviours (high-order interdependencies) *emerge*❓

Can systems with low-order interactions do it?
What do these minimal synergistic systems look like?

In arxiv.org/abs/2505.246... we show when and how synergies emerge when no high-order mechanisms are involved.

Short 🧵: 1/N

Synergistic Motifs in Gaussian Systems

High-order interdependencies are central features of complex systems, yet a mechanistic explanation for their emergence remains elusive. Currently, it is unknown under what conditions high-order inter...

arxiv.org

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Reposted by Enrico

Giovanni Petri @lordgrilo.bsky.social · 29d

Next week (on the 15th and 16th), with @yasserroudi.bsky.social and Federico Turkheimer we will organize a workshop on the "The Topology of Human and Synthetic Minds"

Please do join us!
(Registration is free but required for access/catering!)

lordgrilo.github.io/topology-nat...

The Topology of Human and Synthetic Minds - Workshop

lordgrilo.github.io

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Enrico @enricocaprioglio.bsky.social · Aug 19

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

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

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Enrico @enricocaprioglio.bsky.social · Aug 19

Around Falmer, photo taken by Simon Bowes

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Enrico @enricocaprioglio.bsky.social · Aug 19

Between Brighton and Clayton, on the A23

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Enrico @enricocaprioglio.bsky.social · Aug 19

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

Feel free to add your photos!

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Enrico @enricocaprioglio.bsky.social · Aug 19

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

Let me know if anyone else is here on Bluesky!

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Enrico @enricocaprioglio.bsky.social · Aug 19

Third edition of the emergence workshop is almost here!

You can register using the QR code on the poster

Any questions, you can message me here or send an email!

sussexcogs.bsky.social @sussexcogs.bsky.social · Aug 18

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Reposted by Enrico

Jonathan Eisen @phylogenomics.bsky.social · Jan 3

Murmurations of birds near #DavisCA. I recorded for like 20 minutes. This is a selection of some of the best bits. It was stunning. Awe insirpingly stunning. #Birds

www.youtube.com/watch?v=cvrv...

Murmurations near Davis, CA

YouTube video by Jonathan Eisen

www.youtube.com

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Enrico @enricocaprioglio.bsky.social · Dec 28

Like it’s just as silly as most celebrity drama don’t get me wrong (maybe FIDE should realize that), but the interviews are really funny

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Enrico @enricocaprioglio.bsky.social · Dec 28

I’m usually allergic to celebrity drama and gossip, but there’s something different about chess drama

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Enrico @enricocaprioglio.bsky.social · Nov 29

Highly recommend! Great Christmas gift

Btw, I’m still annoyed von Nuemann wasn’t included in Nolan’s Oppenheimer. I think a scene depicting an annoyed Einstein complaining about von Neumann blasting music in the office was a huge miss

ananyo.bsky.social @ananyo.bsky.social · Nov 28

Less than four weeks to Xmas Day! This year, why not give your nearest and dearest the gift of unrivaled genius? 😜
'The Man from the Future' is available in a dozen languages.
AND those crazy folk at Amazon Italia have cut the price of the Kindle edition to €3.99! 😅 www.amazon.it/Luomo-venuto...

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Reposted by Enrico

Manlio De Domenico @manlius.bsky.social · Nov 27

#NeuroSky friends, can you point to a freely reusable image showing, to some extent, the pipeline for how to build a connectome from Diffusion Tensor Imaging?

If tailored to students or non-specialistic audience, even better. Any format would be fine (even a paper figure with open license). 🙏

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Reposted by Enrico

Mark A. Hanson @hansonmark.bsky.social · Nov 19

The strain on scientific publishing: we set out to characterise the remarkable growth of the scientific literature in the last few years, in spite of declining growth in total scientists. What is going on?

direct.mit.edu/qss/article/...

A 🧵 1/n
#AcademicSky #PhDchat #ScientificPublishing #SciPub

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Reposted by Enrico

Katelyn E. Knox @katelynknox.bsky.social · Oct 21

I've experimented with various writing schedules & productivity strategies, always wondering what variables really matter in publishing more academic writing.

Read what I discovered in my blog post:
katelynknox.com/academic-wri...
#academicpublishing #academicsuccess #academicsky

The 2 Biggest Factors of my Most Successful Writing Semesters (drawn from 4 years of writing session data!)

Over the years, my schedule and responsibilities have led me to experiment with various writing schedules and productivity strategies. I’ve always wondered what variables really matter in publishing m...

katelynknox.com

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