Topological Signals

This research explores how higher-order interactions in complex systems influence the dynamics of topological signals, revealing new insights into the interplay between topology and dynamics.

This research introduces Global Topological Dirac Synchronization, a state where oscillators associated with simplices and cells of arbitrary dimension, coupled by the Topological Dirac operator, operate in unison. The study combines algebraic topology, non-linear dynamics, and machine learning to derive the conditions for the existence and stability of this synchronization state.

This research explores Turing patterns on discrete topologies, extending the classical theory of pattern formation to networks and higher-order structures. The study highlights the potential of this approach to transcend the conventional boundaries of PDE-based methods, offering insights into self-organization phenomena across various disciplines.

This research explores the global synchronization of topological signals on higher-order networks, revealing that topological constraints impact synchronization differently across various network structures.

This research examines reaction-diffusion processes on networks, particularly focusing on topological signals across nodes, links, and cells. It uses the Dirac operator to study interactions and reveals conditions for Turing pattern emergence, validating the findings on network models and square lattices.