Functional brain networks: great expectations, hard times and the big leap forward

Many physical and biological systems can be studied using complex network theory, a new statistical physics understanding of graph theory. The recent application of complex network theory to the study of functional brain networks has generated great enthusiasm as it allows addressing hitherto non-standard issues in the field, such as efficiency of brain functioning or vulnerability to damage. However, in spite of its high degree of generality, the theory was originally designed to describe systems profoundly different from the brain. We discuss some important caveats in the wholesale application of existing tools and concepts to a field they were not originally designed to describe. At the same time, we argue that complex network theory has not yet been taken full advantage of, as many of its important aspects are yet to make their appearance in the neuroscience literature. Finally, we propose that, rather than simply borrowing from an existing theory, functional neural networks can inspire a fundamental reformulation of complex network theory, to account for its exquisitely complex functioning mode

Functional Brain Networks: beyond the small-world paradigm

This contribution reviews the current state of art comprising the application of Complex Networks Theory to the analysis of functional brain networks. We briefly overview the main advances in this field during the last decade and we explain how graph analysis has increased our knowledge about how the brain behaves when performing a specific task or how it fails when a certain pathology arises. We also show the limitations of this kind of analysis, which have been a source of confusion and misunderstanding when interpreting the results obtained. Finally, we discuss about a possible direction to follow in the next years

Editorial

In fact, much of the attraction of network theory initially stemmed from the fact that many networks seem to exhibit some sort of universality, as most of them belong to one of three classes: random, scale-free and small-world networks. Structural properties have been shown to translate into different important properties of a given system, including efficiency, speed of information processing, vulnerability to various forms of stress, and robustness. For example, scale-free and random topologies were shown to be..

Nonlocal analysis of modular roles

We introduce a new methodology to characterize the role that a given node plays inside the community structure of a complex network. Our method relies on the ability of the links to reduce the number of steps between two nodes in the network, which is measured by the number of shortest paths crossing each link, and its impact on the node proximity. In this way, we use node closeness to quantify the importance of a node inside its community. At the same time, we define a participation coefficient that depends on the shortest paths contained in the links that connect two communities. The combination of both parameters allows to identify the role played by the nodes in the network, following the same guidelines introduced by Guimerà et al. [Guimerà & Amaral, 2005] but, in this case, considering global information about the network. Finally, we give some examples of the hub characterization in real networks and compare our results with the parameters most used in the literature

Inferring the connectivity of coupled oscillators from time-series statistical similarity analysis

A system composed by interacting dynamical elements can be represented by a network, where the nodes represent the elements that constitute the system, and the links account for their interactions, which arise due to a variety of mechanisms, and which are often unknown. A popular method for inferring the system connectivity (i.e., the set of links among pairs of nodes) is by performing a statistical similarity analysis of the time-series collected from the dynamics of the nodes. Here, by considering two systems of coupled oscillators (Kuramoto phase oscillators and Rossler chaotic electronic oscillators) with known and controllable coupling conditions, we aim at testing the performance of this inference method, by using linear and non linear statistical similarity measures. We find that, under adequate conditions, the network links can be perfectly inferred, i.e., no mistakes are made regarding the presence or absence of links. These conditions for perfect inference require: i) an appropriated choice of the observed variable to be analysed, ii) an appropriated interaction strength, and iii) an adequate thresholding of the similarity matrix. For the dynamical units considered here we find that the linear statistical similarity measure performs, in general, better than the non-linear ones.Peer ReviewedPostprint (published version

Synchronization-based computation through networks of coupled oscillators

The mesoscopic activity of the brain is strongly dynamical, while at the same time exhibits remarkable computational capabilities. In order to examine how these two features coexist, here we show that the patterns of synchronized oscillations displayed by networks of neural mass models, representing cortical columns, can be used as substrates for Boolean-like computations. Our results reveal that the same neural mass network may process different combinations of dynamical inputs as different logical operations or combinations of them. This dynamical feature of the network allows it to process complex inputs in a very sophisticated manner. The results are reproduced experimentally with electronic circuits of coupled Chua oscillators, showing the robustness of this kind of computation to the intrinsic noise and parameter mismatch of the coupled oscillators. We also show that the information-processing capabilities of coupled oscillations go beyond the simple juxtaposition of logic gates.Peer ReviewedPostprint (published version

Generalized synchronization in relay systems with instantaneous coupling

We demonstrate the existence of generalized synchronization in systems that act as mediators between two dynamical units that, in turn, show complete synchronization with each other. These are the so-called relay systems. Specifically, we analyze the Lyapunov spectrum of the full system to elucidate when complete and generalized synchronization appear. We show that once a critical coupling strength is achieved, complete synchronization emerges between the systems to be synchronized, and at the same point, generalized synchronization with the relay system also arises. Next, we use two nonlinear measures based on the distance between phase-space neighbors to quantify the generalized synchronization in discretized time series. Finally, we experimentally show the robustness of the phenomenon and of the theoretical tools here proposed to characterize it

Libro Blanco de los Sistemas Complejos Socio-tecnológicos

La Red SocioComplex está formada por la Universitat de Barcelona (coordinación), Fundación IMDEA Networks, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-Universitat Illes Balears), Universidad de Burgos, Universidad Carlos III de Madrid, Universitat Rovira i Virgili, Universitat de València y Universidad de Zaragoza - Instituto de Biocomputación y Física de los Sistemas Complejos.Este libro blanco analiza por primera vez las principales fuerzas de la investigación española en ciencias de la complejidad en el contexto de los sistemas socio-tecnológicos.El Libro Blanco de los Sistemas Complejos Socio-tecnológicos forma parte del conjunto de acciones realizadas por la red temática SocioComplex FIS2015-71795-REDT financiada por parte del Ministerio de Economía, Industria y Competitividad – Agencia Estatal de Investigación y del Fondo Europeo de Desarrollo Regional (FEDER)

Entrainment of semiconductor lasers : noise, modulation and synchronization

El objetivo de esta tesis es el estudio de la dinámica de los láseres de semiconductor (LS) con realimentación óptica, tanto desde el punto de vista experimental como numérico. La reflexión de la luz emitida por el láser, debida a la presencia de un espejo externo, es capaz de inducir una dinámica caótica en su intensidad de salida. Concretamente, cuando el láser es bombeado cerca de su corriente umbral, puede entrar en el régimen de fluctuaciones de baja frecuencia (LFF), caracterizado por repentinas caídas de su intensidad a tiempos irregulares. El comportamiento pulsado, y caótico, en este régimen es de especial interés desde el punto de vista de la dinámica de sistemas no-lineales, pero también por sus aplicaciones en comunicaciones ópticas.Si queremos resumir los resultados de esta tesis ordenados cronológicamente,debemos empezar hablando de ruido. El efecto de el ruido en un sistema no-lineal puede ser de gran ayuda en la obtención de una respuesta más regular, efectos como la resonancia coherente o la resonancia estocástica han dado buena prueba de ello. Con el objetivo de observar ambos fenómenos en el comportamiento pulsado de un láser en régimen de LFF, se realizan simulaciones numéricas a partir del modelo de Lang-Kobayashi (LK), que describe la evolución del campo eléctrico y los portadores en un LS. Los resultados obtenidos demuestran que añadiendo cierta cantidad de ruido externo a través de la corriente de bombeo, los pulsos observados en la intensidad de salida se vuelven más regulares, que es la característica típica de la resonancia de coherencia (RC). Si la corriente de bombeo está modulada con una señal periódica de cierta frecuencia, se puede observar cómo el ruido externo ayuda al sistema a seguir dicha frecuencia, lo que se refleja en la intensidad de salida con unas caídas no sólo más regulares, sino también a la frecuencia de forzamiento. Este fenómeno, observado en diversos sistemas no-lineales, se conoce como resonancia estocástica (SR). Los estudios realizados permiten observar que no sólo la amplitud del ruido es importante, sino también su tiempo de correlación, debiéndose ajustar ambos parámetros para poder observar dichas resonancias. En relación con el efecto del ruido en estos sistemas, se estudia (experimental y numéricamente) el caso de un láser en LFF cuando es modulado con dos frecuencias, observando resonancia a frecuencias no presentes en el sistema. Estos resultados son la primera evidencia experimental de este fenómeno, bautizado como resonancia fantasma (GR), el cual sólo habia sido predicho teóricamente hasta el momento.Paralelamente, se analizan los efectos del acoplamiento de dos sistemas caóticos, en nuestro caso dos láseres en régimen de LFF. Los resultados demostran que el acoplamiento puede incrementar la respuesta de un sistema no lineal a un señal periódica externa.Se profundiza también en el estudio del comportamiento multimodo de los láseres de semiconductor con realimentación óptica. Se presentan resultados experimentales y numéricos del comportamiento de los modos longitudinales en el régimen de LFF, observándose como, cuando la intensidad total cae, se activan modos laterales que hasta el momento permanecian apagados. Finalmente, y continuando con el estudio de la dinámica multimodo, se analiza la sincronización de dos láseres multimodo mediante una extensión del modelo de LK, observándose sincronización generalizada y anticipada, tanto de la intensidad total, como entre los modos longitudinales de cada láser. Estos resultados sugieren la utilización de este tipo de láseres para la transmisión de mensajes multiplexados.Postprint (published version

Competition among networks highlights the power of the weak

The unpreventable connections between real networked systems have recently called for an examination of percolation, diffusion or synchronization phenomena in multilayer networks. Here we use network science and game theory to explore interactions in networks-of-networks and model these as a game for gaining importance. We propose a viewpoint where networks choose the connection strategies, in contrast with classical approaches where nodes are the active players. Specifically, we investigate how creating paths between networks leads to different Nash equilibria that determine their structural and dynamical properties. In a wide variety of cases, selecting adequate connections leads to a cooperative solution that allows weak networks to overcome the strongest opponent. Counterintuitively, each weak network can induce a global transition to such cooperative configuration regardless of the actions of the strongest network. This power of the weak reveals a critical dominance of the underdogs in the fate of networks-of-networks