Ramón Nartallo-Kaluarachchi

Oxford Mathematician @alaingoriely.bsky.social awarded the 2025 LMS/IMA David Crighton Medal for his deep and influential insights into mechanical and biological processes, support of early career mathematicians, and commitment to the public understanding of maths.

www.maths.ox.ac.uk/node/72714

Explosive neural networks via higher-order interactions in curved statistical manifolds - Nature Communications Higher-order interactions shape complex neural dynamics but are hard to model. Here, authors use a generalization of the maximum entropy principle to introduce a family of curved neural networks, reve...

Our paper just out in Nature Communications!
www.nature.com/articles/s41...

We introduce curved neural networks naturally introducing high-order interactions showing:
• explosive phase transitions
• enhanced memory retrieval via self-annealing
• increased memory capacity through geometric curvature

YouTube video by Workshop on stochastic thermodynamics (WOST) Ramón Nartallo-Kaluarachchi: A structural perspective on nonequilibrium brain network dynamics

This year’s Workshop on Stochastic Thermodynamics (WOST VI) talks are now online!

I was very grateful to give a short talk about my work on nonequilibrium brain network dynamics:

youtu.be/-z38f0fVMs4?...

Today, the Tour de France begins 3 gruelling weeks of sun, scenery & summits, but what's the key to winning in this elite world of small margins? How about appetite for risk? @imgoxford.bsky.social & @javichico.bsky.social lead the breakaway.

Read more: www.maths.ox.ac.uk/node/72427

#TDF2025

Core-shell microcapsules compatible with routine injection enable prime/boost immunization against malaria with a single shot Engineered injectable microcapsules loaded with the R21 malaria vaccine enable delayed release, potentially removing the need for booster injections.

Tremendously proud of my dear friend Romain Guyon who has just published this amazing paper on the cover of Science Translational Medicine!

He has invented revolutionary new technology for the delivery of booster vaccine doses in a single shot.

www.science.org/doi/10.1126/...

Final shift at @netsciconf.bsky.social presenting my poster on nonequilibrium brain network dynamics.

Also got to see our fearless leader, Renaud Lambiotte, collect his well-deserved Fellowship.

#NetSci2025

Speaking at NetSci2025 about our recent Learning on Graphs paper.

We build up a theoretical and applied approach to use Hodge theory on graphs to study stochastic systems!

arxiv.org/pdf/2409.07479

#NetSci2025

You won't believe your eyes!

I posted about this paper this a while ago on another website, but figured I'd post it here now that I have a few followers. (Joint with @haharrington.bsky.social, Jacob Leygonie, @uzulim.bsky.social, and Louis Theran).

arxiv.org/abs/2411.08201

1/10

Me and Leonardo recently sat down to talk to Dyrol about our recent project, and more generally about collaboration in the mathematical and applied sciences. We hope you enjoy!
You can read the paper here: www.pnas.org/doi/abs/10.1...
Or the case study on the Maths site
www.maths.ox.ac.uk/node/70955

YouTube video by Fresh from the ArXiv Ramon Nartallo-Kaluarachchi: Non-equilibrium steady-states, from diffusion to digraphs

Last week, I gave the Networks seminar here at Oxford on:

'Nonequilibrium steady-states: from diffusion to digraphs',

talking about some of my recent work on discrete approximations of nonequilibrium diffusions. It is available online:
www.youtube.com/watch?v=ezep...

:)

🚨REVIEW
We have written a review on the emerging topic of nonequilibrium, irreversible dynamics in the brain.

Now out on the arXiv: arxiv.org/abs/2504.12188

We introduce the relevant mathematical frameworks, discuss recent interesting results, and look to the future of this research direction!

May we introduce to you @lambiotte.bsky.social, Professor of Mathematics here in the University (and cathedral city) of Oxford, well-connected across all networks (hint to watch the film) and great family guy. Except when he's talking to them about maths.

How do axons “choose” their path during neurodevelopment?
Besides chemical cues, axons can respond to the mechanical stiffness of their environment.
This behavior is called durotaxis.
In this paper, we develop a full multiscale model of axon durotaxis.

doi.org/10.1016/j.jm...

Modelling cerebrovascular pathology and the spread of amyloid beta in Alzheimer’s disease: royalsocietypublishing.org/doi/10.1098/... #ProcA #Alzheimers #biophysics

In this paper, we connect local damage to brain vasculature to global progression of toxic proteins leading to neurodegenerative diseases.
royalsocietypublishing.org/doi/epdf/10....
We identify situations where disease initiation can be caused by focal hypoperfusion following vascular injury.

If we are to develop a mathematical framework that makes progress towards empirical use in biology, it must embrace complexity, data and simulation. We hope that our perspective acts as a roadmap to guide some future research directions in mathematical biology and complexity!

Finally, holistic modelling is not at odds with theoretical biophysics, and we maintain that the ultimate goal of theoretical biology is the discovery of fundamental, translational principles. We point in promising directions

Biological systems can be monitored with new data collection techniques to extract huge amounts of information. This can help construct data-driven dynamical models which learn approximate forms of dynamics directly from observations. This switches the focus to the inverse-problem of modelling

Complex systems can be difficult to model with simple equations. Agent-based models can allow modellers to design heterogeneous and detailed interactions at the microscopic scale. With sufficient computational power and data, this can lead to so-called digital twins

In addition to structural complexity, biological systems also evolve with different spatial and temporal scales, which often cannot be separated. We consider Alzheimer's as an example and indicate how such scales can be integrated into a single model

Whilst complex systems scientists and network scientists have developed rich representation for complex interactions, such research remains largely theoretical. We call for a more applied approach, utilising these structures for predictive modelling in biology

Biological systems are often complex, making them difficult to model with the typical frameworks of theoretical physics

From reductionism to realism: Holistic mathematical modelling for complex biological systems At its core, the physics paradigm adopts a reductionist approach to modelling, aiming to understand fundamental phenomena by decomposing them into simpler, elementary processes. While this strategy ha...

🚨PERSPECTIVE

We have written a perspective calling for a holistic approach to mathematical modelling for biological systems - it now out on the arXiv: arxiv.org/abs/2503.20511

A thread 🧵

Time-irreversibility reveals hidden structure in neural dynamics Why do some memories last a lifetime while others fade away?

We have also been featured on the Oxford Psychiatry page: www.psych.ox.ac.uk/news/time-ir...

🚨 New paper out in PNAS! 🚨

We introduce a method to pinpoint which neural interactions are far from equilibrium by mapping time-irreversible dynamics onto directed multilayer graphs.

Check out this feature on the @oxfordmathematics.bsky.social website regarding our recent paper:

www.maths.ox.ac.uk/node/70955

Thanks to @oxfordmathematics.bsky.social, Centre for Eudaimonia and Human Flourishing, Centre for Brain and Cognition UPF, and @musicinthebrain.bsky.social!!

We then apply this to MEG data recorded during an auditory recognition task. We are able to identify which higher-order interactions are significantly irreversible which we hypothesise results from a causal, nonequilibrium interaction.

In this paper, we present the DiMViGI framework for measuring the irreversibility of higher order interactions in neural recordings.
Our method builds directed, multiplex visibility graphs from which we calculate degree distributions and measure irreversibility with divergence.