14 papers
Synchronization of higher-dimensional Kuramoto oscillators on networks: from scalar to matrix-weighted couplings
Anna Gallo, Renaud Lambiotte, Timoteo Carletti
The Kuramoto model is the paradigmatic model to study synchronization in coupled oscillator systems. In its classical formulation, the oscillators move on the unit circle, each cha…
Drift-Diffusion Matching: Embedding dynamics in latent manifolds of asymmetric neural networks
Ramón Nartallo-Kaluarachchi, Renaud Lambiotte, Alain Goriely
Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of ass…
The nestedness of higher-order networks
Timothy LaRock, Yanting Zhang, Jean-Gabriel Young +3
In contrast to dyadic interactions, higher-order interactions may contain one another, with subgroups naturally embedded within larger groups. These containment patterns arise empi…
Coarse-graining nonequilibrium diffusions with Markov chains
Ramón Nartallo-Kaluarachchi, Renaud Lambiotte, Alain Goriely
We investigate nonequilibrium steady-state dynamics in both continuous- and discrete-state stochastic processes. Our analysis focuses on planar diffusion dynamics and their coarse-…
Structure-aware divergences for comparing probability distributions
Rohit Sahasrabuddhe, Renaud Lambiotte
Many natural and social science systems are described using probability distributions over elements that are related to each other: for instance, occupations with shared skills or…
Global Synchronization in Matrix-Weighted Networks
Anna Gallo, Yu Tian, Renaud Lambiotte +1
Synchronization phenomena in complex systems are fundamental to understanding collective behavior across disciplines. While classical approaches model such systems by using scalar-…