A groundbreaking study led by Professor Ginestra Bianconi from Queen Mary University of London, in collaboration with international researchers, has unveiled a transformative framework for understanding complex systems. Published in Nature Physics, this pioneering study establishes the new field of higher-order topological dynamics, revealing how the hidden topology of networks shapes everything from brain activity to artificial intelligence.
"Complex systems like the brain, climate, and next-generation artificial intelligence rely on interactions that extend beyond simple pairwise relationships. Our study reveals the critical role of higher-order networks, structures that capture multi-body interactions, in shaping the dynamics of such systems," said Professor Bianconi.
By integrating discrete topology with non-linear dynamics, the research highlights how topological signals, dynamical variables defined on nodes, edges, triangles, and other higher-order structures, drive phenomena such as topological synchronization, pattern formation, and triadic percolation. These findings not only advance the understanding of the underlying mechanisms in neuroscience and climate science but also pave the way for revolutionary machine learning algorithms inspired by theoretical physics.
"The surprising result that emerges from this research" Professor Bianconi added, is that topological operators including the Topological Dirac operator, offer a common language for treating complexity, AI algorithms, and quantum physics. "
From the synchronised rhythms of brain activity to the dynamic patterns of the climate system, the study establishes a connection between topological structures and emergent behaviour. For instance, researchers demonstrate how higher-order holes in networks can localise dynamical states, offering potential applications in information storage and neural control. In artificial intelligence, this approach may lead to the development of algorithms that mimic the adaptability and efficiency of natural systems.
"The ability of topology to both structure and drive dynamics is a game-changer," Professor Bianconi added. This research sets the stage for further exploration of dynamic topological systems and their applications, from understanding brain research to formulate new AI algorithms. "
This study brings together leading minds from institutions across Europe, the United States, and Japan, showcasing the power of interdisciplinary research. "Our work demonstrates that the fusion of topology, higher-order networks, and non-linear dynamics can provide answers to some of the most pressing questions in science today," Professor Bianconi remarked.
