New paper!

If you want to assess the stability of the synchronization of a system of identical oscillators, you can use the Master Stability Function. However, what do you do in a real-world case, when the elements of the system are not exactly identical? We show how to extend the formalism and use it also when there are many-body interactions, such as in a simplicial complex.

https://journals.aps.org/prresearch/abstract/10.1103/ml7b-r35h

#mathematics #physics #science #synchronization #stability #chaos #MSF #simplicialcomplex #complexity #nonlinear #dynamics

If you don't have access to the journal, you can download it from here

https://charodelgenio.weebly.com/recon.html

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

The paper is on Physical Review E

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.044304

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

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

#simplicialcomplex + #Causality +#Reservoircomputing:
"Higher-order Granger reservoir computing: simultaneously achieving scalable complex structures inference and accurate dynamics prediction" https://www.nature.com/articles/s41467-024-46852-1

#dynamicalsystem #ML #AI

It would be interesting if someone used simplicial complex techniques from topology to analyze Wikipedia, or even developed tools for end users to
apply simplicial complexes to Wikipedia queries. The following papers illustrate what you can do with them.

"Co-occurrence simplicial complexes in mathematics: identifying the holes of knowledge"
https://appliednetsci.springeropen.com/articles/10.1007/s41109-018-0074-3

"The shape of collaborations"
https://www.semanticscholar.org/paper/The-shape-of-collaborations-Patania-Petri/e00b3707885b94647619d66147dda40363fd090e

#Wikipedia #TDA #simplicialCOmplex