Conrad J. Pérez-Vicente

TL;DR: P perturbative analysis is used to reveal analytically the structure of eigenvectors and eigenvalues of the complete network in terms of the spectral properties of the individual layers of the multiplex network, and allows us to understand the physics of diffusionlike processes on top of multiplex networks.

TL;DR: The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators and provides a useful connection between synchronization dynamics, complex networks topology, and spectral graph analysis.

TL;DR: An extended analysis, based on the dynamics towards synchronization of a system of coupled oscillators, of the hierarchy of communities in complex networks, provides a useful connection between synchronization dynamics, complex networks topology and spectral graph analysis.

TL;DR: The results show that GMWP method is the one attaining the best performance, providing reliable estimates which can be improved when the statistics is increased, and some of them are affected by problems such as the linearization of the right tail of the spectrum.

TL;DR: In this article, the authors discuss the multifractal microcanonical formalism in a comprehensive, unified way, including new theoretical proofs and validation tests on real signals, so completing some known gaps in the foundations of this theory.