George Cantwell

The perplexing “connected cluster axiom” – Inverse Complexity Lab Research group on inverse problems in complex systems and network science.

I wrote a blog post about the often stated but never explained assumption that communities in graphs should always be connected.

This is inconsistent with statistical significance and null models that underlie the most widely employed methods.

skewed.de/lab/posts/co...

Maybe a partial answer to your question of where this idea comes from: a network is sometimes *defined* to be the largest component, e.g., the internet is the largest component of connected computers. In those cases specifically it could be sensible starting point.

Embedding networks with the random walk first return time distribution We propose the first return time distribution (FRTD) of a random walk as an interpretable and mathematically grounded node embedding. The FRTD assigns a probability mass function to each node, allowin...

A principled graph embedding that also appears to work well in practice: arxiv.org/abs/2512.02694

Multilayer network science: theory, methods, and applications Multilayer network science has emerged as a central framework for analysing interconnected and interdependent complex systems. Its relevance has grown substantially with the increasing availability of...

Our review on multilayer network science is out on the arXiv. Thanks to all collaborators of the AccelNet MultiNet project, great working with you all 🙏 @alexvespi.bsky.social @ymoreno.bsky.social @lordgrilo.bsky.social @anduviera.bsky.social @baronca.bsky.social
arxiv.org/abs/2511.23371

Whoever created OpenReview looked at online anonymous forums and thought "yes, this is the platform to foster productive debate"

Ah yes, Ramanujan's famous proof that pi^2 is rational

Very good post. I very much agree with the overall position.

I suspect saying if an array is "really" a vector, or a linear transform, or a photo, or a graph, or ..., is up to us as humans

Do you mean like: you have a (d x n) data matrix, hidden representations are, e.g., (4d x n), and the final output is say (2 x n). If so, isn't this the prototypical use case?

Excited to introduce Vibes from Meta. Eat your slop, piggies!

Message passing for epidemiological interventions on networks with loops
https://arxiv.org/abs/2509.21596

Our fall seminar series begins this Thursday, Oct. 2 (4pm UTC+1/11am EDT) with a talk by Elena Candellone. She’ll be speaking about “Mapping extreme users through negative ties in online social interactions”, followed by a discussion on “the joy of planning scientific events”.

Robustness of 'small' networks Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component ...

arXiv alert! 📄🚨
Robustness of small networks
arxiv.org/abs/2509.23670
Great to dust off one of my favorite topics and get to collaborate with the legendary
@aliceschwarze.bsky.social and Peter Mucha

Graduate Program * Complexity Science Hub Courses are offered both by CSH and by our partner universities, one of which will serve as the degree-granting entity. Students will be guided to the

#SpreadtheWord
We are looking for #PhD candidates passionate about using large-scale data analysis, quantitative models, and complexity science to study the complex interactions within #epidemiology, #OneHealth, and #publichealthsystems.
More info: csh.ac.at/education/gr...

The Probabilistic Systems, Information, and Inference group at the University of Cambridge is seeking applicants for funded PhD positions.

Anyone who wants to study networks/complex systems/statistical physics/inference can email me at gtc31@cam.ac.uk

Right, we solved directly for the stationary state, but one could also integrate for the transient. I'll look into it... thanks!

Oh, you have some nice calculations for the cluster expansion! But I think this reinfection counting has the same equilibrium prediction as the regular pair-approx

The threshold and quasi-stationary distribution for the SIS model on networks We study the Susceptible-Infectious-Susceptible (SIS) model on arbitrary networks. The well-established pair approximation treats neighboring pairs of nodes exactly while making a mean field approxima...

We found a nice way to accurately solve the SIS model. Rather than expanding in space with ever larger moment closures (pairs, triples, ...), we expand in time. No more difficult than pair-approximations yet much more accurate.
arxiv.org/abs/2509.11706

Strong emergence

Postdoc job! I expect to have an opening at Johns Hopkins for a postdoctoral researcher working somewhere in the broad realms of physics, philosophy, and complexity. Apply at Academic Jobs Online:

academicjobsonline.org/ajo/jobs/30496

Not sure how many scientists here have tried Claude Code or similar command line coding assistants. I had a complicated family property tax problem that was best solved by a brute force Monte Carlo simulation approach, so I spent a few days coding up and analyzing a model with Claude Code.

Applications are open for SFI's 2026 Complexity Postdoctoral Fellowships

If you’ve recently earned a Ph.D. in any scientific field and want to pursue independent, transdisciplinary research, consider applying.

Deadline: October 1, 2025
Apply here: santafe.edu/sfifellowship

beautiful location for statphys

YouTube video by Biocontrol Seminars Eric De Giuli: Noise equals endogenous control

My talk from
@bioctrl.bsky.social
about the physical origin of agency is uploaded here:
youtube.com/watch?v=YY21...
TLDR: noise equals control. Nature is constantly sampling control trajectories via noise

sign for "Probabilistic Systems, Information and Inference lab"

New group name! We are now the "probabilistic systems, information and inference" aka Ψ²

collaboration with friends @oxfordmathematics.bsky.social Erik Hormann and @lambiotte.bsky.social

The Kac formula says the average return time for a random walker is a wonderfully simple combination of global and local structure: 2m/k_i. Inspired by this result we characterize the full distribution in a similar manner. doi.org/10.1103/Phys...

Approximation for return time distributions of random walks on sparse networks link.aps.org/doi/10.1103/...

The quiet before the storm.

Good morning #NetSci2025

A reader of Free Agents sent me this lovely poem by Jared Anderson... 😊