arXiv subjects

Conrad J. Perez-Vicente

Publications and source records attributed to Conrad J. Perez-Vicente.

4 recordsLinked to original sources

arXiv2012

Diffusion dynamics on multiplex networks

We study the time scales associated to diffusion processes that take place on multiplex networks, i.e. on a set of networks linked through interconnected layers. To this end, we propose the construction of a supra-Laplacian matrix, which consists of a dimensional lifting of the Laplacian matrix of each layer of the multiplex network. We use perturbative analysis to reveal analytically the structure of eigenvectors and eigenvalues of the complete network in terms of the spectral properties of the individual layers. The spectrum of the supra-Laplacian allows us to understand the physics of diffusion-like processes on top of multiplex networks.

physics.soc-ph↗

arXiv2008

On optimal wavelet bases for the realization of microcanonical cascade processes

Multiplicative cascades are often used to represent the structure of multiscaling variables in many physical systems, specially turbulent flows. In processes of this kind, these variables can be understood as the result of a successive tranfer in cascade from large to small scales. For a given signal, only its optimal wavelet basis can represent it in such a way that the cascade relation between scales becomes explicit, i.e., it is geometrically achieved at each point of the system. Finding such a basis is a data-demanding, highly-complex task. In this paper we propose a formalism that allows to find the optimal wavelet in an efficient, less data-demanding way. We confirm the appropriateness of this approach by analyzing the results on synthetic signals constructed with prescribed optimal bases. Although we show the validity of our approach constrainted to given families of wavelets, it can be generalized for a continuous unconstrainted search scheme.

cond-mat.stat-mech↗

arXiv2006

Synchronization processes in complex networks

We present an extended analysis, based on the dynamics towards synchronization of a system of coupled oscillators, of the hierarchy of communities in complex networks. In the synchronization process, different structures corresponding to well defined communities of nodes appear in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology and spectral graph analysis.

nlin.AO↗

arXiv2005

Synchronization reveals topological scales in complex networks

We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular structures corresponding to well defined communities of nodes emerge in different time scales, ordered in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology and spectral graph analysis.

cond-mat.dis-nn↗