Frequency-based brain networks: From a multiplex framework to a full multilayer description

We explore how to study dynamical interactions between brain regions using functional multilayer networks whose layers represent the different frequency bands at which a brain operates. Specifically, we investigate the consequences of considering the brain as a multilayer network in which all brain regions can interact with each other at different frequency bands, instead of as a multiplex network, in which interactions between different frequency bands are only allowed within each brain region and not between them. We study the second smallest eigenvalue of the combinatorial supra-Laplacian matrix of the multilayer network in detail, and we thereby show that the heterogeneity of interlayer edges and, especially, the fraction of missing edges crucially modify the spectral properties of the multilayer network. We illustrate our results with both synthetic network models and real data sets obtained from resting state magnetoencephalography. Our work demonstrates an important issue in the construction of frequency-based multilayer brain networks.Comment: 13 pages, 8 figure

Beware of the Small-World neuroscientist!

The SW has undeniably been one of the most popular network descriptors in the neuroscience literature. Two main reasons for its lasting popularity are its apparent ease of computation and the intuitions it is thought to provide on how networked systems operate. Over the last few years, some pitfalls of the SW construct and, more generally, of network summary measures, have widely been acknowledged

The Topology of Music Recommendation Networks

We study the topology of several music recommendation networks, which rise from relationships between artist, co-occurrence of songs in playlists or experts' recommendation. The analysis uncovers the emergence of complex network phenomena in this kind of recommendation networks, built considering artists as nodes and their resemblance as links. We observe structural properties that provide some hints on navigation and possible optimizations on the design of music recommendation systems. Finally, the analysis derived from existing music knowledge sources provides a deeper understanding of the human music similarity perceptions.Comment: 15 pages, 3 figure

Taming out-of-equilibrium dynamics on interconnected networks

A wide variety of social, biological or technological systems can be described as processes taking place on networked structures in continuous interaction with other networks. We propose here a new methodology to describe, anticipate and manage, in real time, the out-of-equilibrium dynamics of processes that evolve on interconnected networks. This goal is achieved through the full analytical treatment of the phenomenology and its reduction to a two-dimensional flux diagram, allowing us to predict at every time step the dynamical consequences of modifying the links between the different ensembles. Our results are consistent with real data and the methodology can be translated to clustered networks and/or interconnected networks of any size, topology or origin, from the struggle for knowledge on innovation structures to international economic relations or disease spreading on social groups.Ministerio de Economía y Competitividad; Comunidad de Madri

Bistable phase control via rocking in a nonlinear electronic oscillator

We experimentally demonstrate the effective rocking of a nonlinear electronic circuit operating in a periodic regime. Namely, we show that driving a Chua circuit with a periodic signal, whose phase alternates (also periodically) in time, we lock the oscillation frequency of the circuit to that of the driving signal, and its phase to one of two possible values shifted by pi, and lying between the alternating phases of the input signal. In this way, we show that a rocked nonlinear oscillator displays phase bistability. We interpret the experimental results via a theoretical analysis of rocking on a simple oscillator model, based on a normal form description (complex Landau equation) of the rocked Hopf bifurcationComment: 7 pages, 10 figure

The Social Network of Contemporary Popular Musicians

In this paper we analyze two social network datasets of contemporary musicians constructed from allmusic.com (AMG), a music and artists' information database: one is the collaboration network in which two musicians are connected if they have performed in or produced an album together, and the other is the similarity network in which they are connected if they where musically similar according to music experts. We find that, while both networks exhibit typical features of social networks such as high transitivity, several key network features, such as degree as well as betweenness distributions suggest fundamental differences in music collaborations and music similarity networks are created.Comment: 7 pages, 2 figure