14 - The Kuramoto model

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Murmuration of starlings.

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In this edition

The Kuramoto model
Events
Vacancies

The Kuramoto model

"The guiding motto in the life of every natural philosopher should be, 'Seek simplicity and distrust it.’ " - Alfred North Whitehead (1919).

Building on the work of Norbert Wiener (1961) and Art Winfree (1967), Yoshiki Kuramoto (1975, 1984) developed a simple and elegant model of synchronization in systems of phase-coupled oscillators.

I really like this model, because it is a very intuitive way to understand how oscillations spontaneously emerge from their underlying units, and how they, in turn, affect the activity of those units.

Imagine you have a group of oscillators, for example fireflies flashing their lights, a flock of starlings in flight, or neurons in a nervous system. In each of these groups, the individual oscillators are connected to each other in some way.

In the Kuramoto model, the behavior of each oscillator is influenced not only by its own natural speed or frequency, but also by the average frequency of the other oscillators it is connected to. Each oscillator adjusts its frequency based on the average frequency of the others.

If the strength of the connections between the individual oscillators (coupling strength) exceeds a certain threshold, something like a phase transition can be observed. Just like vapor turns to water at a certain temperature, the oscillators spontaneously start to synchronize. Instead of cycling in a chaotic and disorganized way, they coalesce into a “pack” and cycle together.

Click on the image below to play around with the model! (Opens a new window.)

“Ride my Kuramotocycle!” Explorable made by Dirk Brockman and Steven Strogatz (2018).

As I mentioned, different parameters affect how the oscillators synchronize, if at all. One is the variability in the intrinsic frequency of the oscillators. The broader this distribution, the more difficult it is to synchronize the whole population. The other key parameter is coupling strength; how much influence the oscillators exert over one another. The higher the coupling strength, the tighter the synchronization will be.

As you can see, the Kuramoto model implies circular causality. The causal relationship between variables forms a feedback loop. As the system synchronizes, the stronger the pull on other neurons to join the pack becomes. As predicted by the model, brain oscillations are not just driven by underlying spiking activity, but also shape the timing of that spiking activity (e.g. Jacobs et al., 2007, Anastassiou et al., 2011).

The Kuramoto model has been used to study a wide range of phenomena, from the synchronization of biological rhythms in the human body to the coordinated flashing of fireflies in a forest. If you are interested to learn more, the video below gives a beautiful overview. Steven Strogatz, who is a physicist, also wrote one of my all-time favorite books: “Sync”.

Events

September 14-15, 2023 mbt Conference 2.0 , Belgrade, RS
Methods in Mobile EEG

September 27-29, Multimodal EEG Workshop (TMS-EEG), Milan, IT
Integrating EEG and neuronavigated TMS techniques

October 16-19, 2023 Cutting Gardens 2023 (M)EEG methods conference
This multi-hub meeting is all about cutting edge (M)EEG methods. Hubs (gardens) are sprouting in Ghent (BE), Berlin (DE), Donostia (San Sebastián, ES), Belgrade (CS), Nijmegen (NL), Bornemouth (UK), Lyon (FR), Paraná (AR), Santiago (CL), San Diego (US), Montréal (CA), La Habana (CU), Dundee (SC), Caen (FR), Genova (IT), Roma (IT), Regensburg (DE), Chengdu (CN).

Vacancies

PhD

• Tilburg University, NL - Everyday memory in younger and older adults.

• Coventry University, UK - Nonlinear system identification and deep learning for neurodegenerative disease detection.

• Tilburg University, NL - Neurocognitive foundations of individual language learning abilities.

• Ghent University, BE - Early vision and selective attention.

• Max Planck Institute, Frankfürt, DE - Categorization of vocal sounds.

• INSERM, Grenoble, FR - Perceptual consciousness and hallucinations.

Post-Doc

• University of Essex, UK - Motor control decline in healthy older adults.

• Leibniz Research Centre for Working Environment and Human Factors, DE - Computational Neuroscience / Biostatistics / Data Analysis.

• University of Missouri-Columbia, US - Covert visual attention.

• Western University, CA - Music and Neuroscience.

• Universität Bielefeld, DE - Auditory and cognitive neuroscience.

• INSERM, Grenoble, FR - Perceptual consciousness with computational modeling and invasive electrophysiology in humans.

• Université de Montréal, CA - From Inter-Brain Connectivity to Inter-Personal Psychiatry.

• State University of New York (SUNY), US - Multiscale brain circuit models, low-dimensional neural manifolds and BMIs.

• Texas A&M University, US - Human states predictions (e.g., stress, learning, fatigue) and closed-loop technological mitigations in controlled and field environments using wearable neuro/physiological/behavioral sensors.

• Texas A&M University, US - Multimodal brain-behavior mappings of human-autonomy teaming across increasing contextual complexities. 

• Duke University, Durham, US - Neurocognitive mechanisms underpinning the regulation of cognitive stability and flexibility.

• Institute of Psychiatry and Neuroscience of Paris, FR - Memory and Perception.

• Heinrich Heine University Düsseldorf, DE - Decision making and learning.

• UC Berkeley, US - Cognition and Action lab.

• Centre de Recherche de Cerveau et Cognition, Toulouse, FR - The role of travelling waves in cognition.

RA’s

• Royal Holloway University of London, UK - Manos Tsakiris lab.

• Junior Specialist (RA) - UC Davis, US - Neuroprosthetics Lab

• Research engineer (Ingenieur d’étude) - CNRS, Brain and Cognition Research Centre, Toulouse, FR.

• Research Assistant - Trinity College Dublin

• Associate in research - Duke University, Durham, US.

• RA - Ernst Strüngman Institute, Frankfurt, DE.

Senior positions

• Senior Lecturer - University of Glasgow, SC

• Assistant Professor - Durham University, UK

• Assistant Professor - University of Leiden, NL

• Associate Director - Brainworks, Yale University, US

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