New paper!
We know that, in systems of phase oscillators, solitary states can appear as the system undergoes a transition from disordered behaviour to synchronous motion. But did you know that, in models of spiking neurons, they can appear in both directions of the transition? In this work, we show you how this happens.

https://journals.aps.org/pre/abstract/10.1103/xtgc-f766

#physics #mathematics #dynamics #oscillators #neurons #synchronization #networks #higherorder

New paper!
How can we detect the presence of communities in networks with higher-order interactions? For instance, by maximizing hypermodularity! Also, this formulation will allow you to leverage tensor spectral methods to do it. Additionally, the paper also argues that the "overfitting" of modularity methods is actually just people applying them where they are not supposed to be used. And, as a byproduct, there is an explanation of why higher-order SVD works so well in classification tasks in machine learning. Oh, the code is available to use in your own projects (link in the first comment). And moreover, the code includes an efficient data structure for higher-order networks that is independent from the community detection method and that you can also use in your own work. 😎

https://journals.aps.org/prresearch/abstract/10.1103/58dr-wktc

#networks #complexity #physics #maths #CompSci #graphs #higherorder #hypergraphs #community #detection #algorithm #communitystructure #modularity #hypermodularity

New paper, just out.

Often, in real-world situations, one does not know the full structure of a network. However, at the same time, one can often observe some interactions that take place on it, and may be interested in knowing its full structure. For example, one may be detecting some partial criminal activity and may want to determine the whole organization. We consider higher-order networks, which are structures with many-body interactions, and specifically simplicial complexes, and show that one can reconstruct a whole network almost perfectly simply by observing the transient of the dynamics that takes place on it. In fact, we give 3 different algorithms to do it, with different complexities and accuracies, so you can choose which one suits you best.

#physics #mathematics #networks #reconstruction #higherorder #simplicialcomplex #hypergraphs #evolutionarygames #transient #dynamics #algorithm