A significant shift is underway in the realm of complex systems analysis: the evolution of network science to encompass higher-order interactions. For decades, networks have been instrumental in modeling intricate relationships within diverse domains, from neuroscience to ecology. However, these structures have proven limited in capturing simultaneous multi-unit interactions, a behavior prevalent across numerous phenomena.
To bridge this gap, researchers are turning to higher-order structures such as simplicial complexes and hypergraphs, which account for multi-agent dynamics. One notable figure driving this advancement is Professor Bianconi, whose work on topological signals and the Dirac-Bianconi operator has garnered attention. This operator, inspired by quantum mechanics and differential geometry, encodes both local and global interactions across various topological dimensions, making it a potent tool for studying higher-order diffusion, synchronization, and pattern formation.
The implications of this research extend to fields like neuroscience, where brain activity unfolds across interconnected regions, and climate science, where edge variables offer more accurate descriptions than traditional models. Furthermore, the team behind this work, comprising scholars from eight countries, has highlighted the interplay between topology and dynamics in the context of synchronization and Dirac-Turing pattern formation.
The research, published in Nature Physics as a perspective article, also delves into triadic interactions, a common higher-order effect in neuroscience and ecology, which can cause time-varying network behavior, including chaos and periodicity. This work underscores the importance of interdisciplinary cooperation in advancing scientific knowledge and addressing global challenges.
The Institute of Science Tokyo (Science Tokyo) is at the forefront of this cutting-edge research, with Professor Hiroya Nakao’s group involved in several related projects. In May 2025, Professor Bianconi will visit Science Tokyo to further strengthen collaboration between institutions, thanks to a generous grant from the World Research Hub of Science Tokyo. This collaboration promises to yield valuable insights for researchers within the institution and the broader Japanese community of complex systems.
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