Research database

Higher-Order Networks and their Dynamics is an emerging field of research that relates to different efforts running in parallel1,2. Three themes stand out. First, dynamical questions about higher-order networks relevant in physics are often out of reach for mathematical dynamical systems theory: Higher-order network dynamical systems are special (nongeneric), and the foundations for a comprehensive theory are still in their infancy. Second, the structure of the higher-order interactions is typically captured by hypergraphs and simplicial complexes. While progress has been made to characterize properties of hypergraphs, how they relate to the dynamics of higher-order networks remains elusive. Third, higher-order structures have been instrumental in the analysis of data: For example, topological data analysis captures higher-order relations in data and has opened new avenues for analysing data from brain recordings. However, these developments and perspectives have evolved separately from one another, which obstructs breakthroughs from a unified perspective: As only demonstrated very recently, a dynamical perspective allows to explain critical transitions in complex system induced by higher-order interactions3. To identify the role of nonpairwise ‘higher-order’ interactions in the emergence of complex dynamical behaviour, BeyondTheEdge will consolidate the emergent research themes of foundations, structure into a new field of Higher- Order Network Dynamics. To this end, BeyondTheEdge brings together key researchers in the different themes of higher-order network dynamics (foundations, structure, data) from all corners of Europe—including Widening Countries4 in Southern and Eastern Europe—building on recent individual efforts. The network is interdisciplinary (including mathematics, physics, computer science, neuroscience) and intersectorial (including academia, private research institutes, and industry) to develop new mathematical insights and apply them to real-world problems, such as bibliometric analysis with SME partner CWTS. BeyondTheEdge will train a cohort of 10 PhD students at the interface of the three emergent themes to become a new generation of mathematicians and scientists, who will be truly native to the emergent field of Higher-Order Network Dynamics. The training program—based on research, education, and complementary skills training—will enable the PhD students to innovate, collaborate, and become the next generation of leading professionals in academia, industry, or the public sector: The innovative training activities will ensure that all PhD students can apply their skills beyond the academic context and put them in perspective of the wider (developing) world. Supervisor training activities are included so that the more junior project partners can shape the PhD education of the future. Thus, BeyondTheEdge will make a lasting contribution that will far outlive the duration of this doctoral training network.