Reconstructing higher-order interactions in coupled dynamical systems.

Higher-order interactions play a key role for the operation and function of a complex system. However, how to identify them is still an open problem. Here, we propose a method to fully reconstruct the structural connectivity of a system of coupled dynamical units, identifying both pairwise and higher-order interactions from the system time evolution. Our method works for any dynamics, and allows the reconstruction of both hypergraphs and simplicial complexes, either undirected or directed, unweighted or weighted. With two concrete applications, we show how the method can help understanding the complexity of bacterial systems, or the microscopic mechanisms of interaction underlying coupled chaotic oscillators.

Synchronizing network systems in the presence of limited resources via edge snapping.

In this work, we propose a multilayer control protocol for the synchronization of network dynamical systems under limited resources. In addition to the layer where the interactions of the system take place, i.e., the backbone network, we propose a second, adaptive layer, where the edges are added or removed according to the edge snapping mechanism. Different from classic edge snapping, the inputs to the edge dynamics are modified to cap the number of edges that can be activated. After studying the local stability of the overall network dynamics, we illustrate the effectiveness of the approach on a network of Rössler oscillators and then show its robustness in a more general setting, exemplified with a model of the Italian high-voltage power grid.

Persistence of information flow: A multiscale characterization of human brain.

Information exchange in the human brain is crucial for vital tasks and to drive diseases. Neuroimaging techniques allow for the indirect measurement of information flows among brain areas and, consequently, for reconstructing connectomes analyzed through the lens of network science. However, standard analyses usually focus on a small set of network indicators and their joint probability distribution. Here, we propose an information-theoretic approach for the analysis of synthetic brain networks (based on generative models) and empirical brain networks, and to assess connectome's information capacity at different stages of dementia. Remarkably, our framework accounts for the whole network state, overcoming limitations due to limited sets of descriptors, and is used to probe human connectomes at different scales. We find that the spectral entropy of empirical data lies between two generative models, indicating an interpolation between modular and geometry-driven structural features. In fact, we show that the mesoscale is suitable for characterizing the differences between brain networks and their generative models. Finally, from the analysis of connectomes obtained from healthy and unhealthy subjects, we demonstrate that significant differences between healthy individuals and the ones affected by Alzheimer's disease arise at the microscale (max. posterior probability smaller than 1%) and at the mesoscale (max. posterior probability smaller than 10%).