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We're super excited to use these models to understand how shifts in neuronal physiology, for example induced by neuromodulators and neuropeptides, can give rise to changes in population dynamics. Stay tuned for follow-up work in the coming weeks! arxiv.org/abs/2607.09516

A multi-ensemble mean-field reduction method for networks of globally coupled phase oscillators with arbitrary parameter distributionsUnderstanding the dynamical properties of coupled phase oscillator systems with heterogeneous oscillator frequencies has been a long-standing challenge of complex systems theory. While the seminal wor...arxiv.org

Now, we introduce Lorentzian-Mixture Mean Field models: a method to fit a low-d set of ODEs to neural pops w/ arbitrary distributions of physiological parameters. LMMFs let us simulate and do bifurcation analysis on ODE equivalents of actual spiking populations, like these from @alleninstitute.org

@rgast.bsky.social previously extended this work to explore how introducing physiological heterogeneity into mean-field models of neural populations changes their dynamics. However, the models still assume 1) infinitely large populations and 2) Cauchy-distributed spike thresholds.

But in the past 20 years, better methods have emerged. Ott and Antonsen's ansatz gives exact, low-d solutions for collective dynamics of populations of coupled oscillators, and Montbrió, Pazó, and Roxin adapted this to QIF spiking neurons, giving next-gen mean-field models of neural firing rates.

On top of this, W&C had to introduce temporal coarse-graining of their firing rate units to get a clean solution for their dynamics. This kills many phenomena that exist in spiking neurons, like transient peaks in spiking at stimulus onset. Nevertheless, W&C rate units are widely used to this day.

What is a firing rate unit? A neuron in an RNN sums its inputs, passes this through a sigmoid-like nonlinearity, & sends this back to the network. It dates to Wilson & Cowan: the sigmoid is the fraction of spiking neurons that pass threshold, assuming neurons are 1) independent and 2) unconnected.

These are all done in Illustrator with a Wacom Bamboo pen tablet. I've used one for about two decades now- requires you to be able to draw without looking at your hand, but once you develop that motor skill it's great.

This was a fun opinion article to write (and I had a great time making the illustrations) - I hope it inspires folks to join us in exploring jellyfish as a model system to study the physics of nervous system-muscle-body-environment interactions!

Jellyfish medusae also grow and change their body shape over their lifespan, in ways that dramatically alter the physics of their body-fluid interactions. So a fun open question is how their nervous system (which is adding new neurons throughout the lifespan) adapts itself to these body changes.

The jellyfish's nerve net orchestrates these whole-body maneuvers despite lacking any central organizing brain, a beautiful example of distributed, collective activity can give rise to coherent function.

Awesome to see this out, congrats Josh!

Mindstorms was great! That's so kind of you to share, pepperoni dogfart

Precisely articulated research plans that are formulated in terms of exactly three conceptually linked but methodologically independent specific aims

Bird scientists definitely win for most memeable model organism

I think this is ultimately what is driving the current push on virtual organisms/digital twins- bite the bullet and simulate ALL the things and hope you'll be able to make sense of the result.

Pop bio dealing with frustrations that are very familiar to neurotheorists. If I want to study X, I must fix Y and Z to idealized values and pretend they don't matter (take X, Y, Z = plasticity, physiology, connectivity, neuromodulation, behavior...) or lose both tractability and interpretability.

Agreed re the cortical column Markram targeted, but I think connectomics could be hugely beneficial to study of areas like hypothalamus, where we have evolutionarily wired "artisanal" circuits implementing very specific rules for how different drives interact with each other :)