Researchers led by Queen Mary University have proposed a new way to understand complex systems like brains or climate, with many parts working together. This study is published in Nature Physics.

This study wants to start a new field called higher-order topological dynamics. Topology is all about studying shapes and spaces, like how objects connect or form patterns, even if they bend or stretch. Dynamics focuses on how things change over time, like how water flows in a river or how a crowd moves together. Together, higher-order topological dynamics looks at how complex shapes in networks influence the way systems evolve and behave.

The researchers show how hidden network shapes affect brain activity, climate patterns, and artificial intelligence (AI).

“Complex systems like the brain, climate, and next-generation artificial intelligence rely on interactions that extend beyond simple pairwise relationships,” says research leader Ginestra Bianconi in a Queen Mary University press release. “Our study reveals the critical role of higher-order networks, structures that capture multi-body interactions, in shaping the dynamics of such systems,”

The study mixes topology with the non-linear dynamics of things that move in tricky patterns. They found topological signals, tied to points, lines, and shapes in networks, control things like synchronization, pattern formation, and percolation.

New AI tools based on physics

This work could help understand brains and climate better. It could also lead to new AI tools based on physics. Bianconi says a big surprise is that topological operators connect complexity, AI, and quantum physics. For example, the study shows how holes in networks can trap energy states. This might help store data or control brain-like systems. In AI, it could make smarter, nature-like algorithms.

Bianconi calls this a game-changer because topology both builds and drives how systems act. This research could improve brain science and create fresh AI ideas. Blending topology, higher-order networks, and non-linear dynamics could provide answers to big science questions.

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