Now showing items 1-6 of 6
Nonlinear Analogue of the May-Wigner Instability Transition
We study a system of $N\gg 1$ degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing ...
Network Geometry and Complexity
(Springer Verlag, 2018-07-18)
Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order ...
Large deviation theory of percolation on multiplex networks
Recently increasing attention has been addressed to the fluctuations observed in percolation defined in single and multiplex networks. These fluctuations are extremely important to characterize the robustness of real finite ...
Simplicial complexes: higher-order spectral dimension and dynamics
Simplicial complexes constitute the underlying topology of interacting complex systems including among the others brain and social interaction networks. They are generalized network structures that allow to go beyond the ...
Explosive higher-order Kuramoto dynamics on simplicial complexes
(American Physical Society, 2020)
The higher-order interactions of complex systems, such as the brain, are captured by their simplicial complex structure and have a significant effect on dynamics. However the existing dynamical models defined on simplicial ...
The higher-order spectrum of simplicial complexes: a renormalization group approach
Network topology is a flourishing interdisciplinary subject that is relevant for different disciplines including quantum gravity and brain research. The discrete topological objects that are investigated in network topology ...