Showing papers by "Stefano Boccaletti published in 2013"

Emergence of network features from multiplexity

Abstract: Many biological and man-made networked systems are characterized by the simultaneous presence of different sub-networks organized in separate layers, with links and nodes of qualitatively different types. While during the past few years theoretical studies have examined a variety of structural features of complex networks, the outstanding question is whether such features are characterizing all single layers, or rather emerge as a result of coarse-graining, i.e. when going from the multilayered to the aggregate network representation. Here we address this issue with the help of real data. We analyze the structural properties of an intrinsically multilayered real network, the European Air Transportation Multiplex Network in which each commercial airline defines a network layer. We examine how several structural measures evolve as layers are progressively merged together. In particular, we discuss how the topology of each layer affects the emergence of structural properties in the aggregate network.

Modeling the multi-layer nature of the European Air Transport Network: Resilience and passengers re-scheduling under random failures

Abstract: We study the dynamics of the European Air Transport Network by using a multiplex network formalism. We will consider the set of flights of each airline as an interdependent network and we analyze the resilience of the system against random flight failures in the passenger's rescheduling problem. A comparison between the single-plex approach and the corresponding multiplex one is presented illustrating that the multiplexity strongly affects the robustness of the European Air Network.

Eigenvector centrality of nodes in multiplex networks

Abstract: We extend the concept of eigenvector centrality to multiplex networks, and introduce several alternative parameters that quantify the importance of nodes in a multi-layered networked system, including the definition of vectorial-type centralities. In addition, we rigorously show that, under reasonable conditions, such centrality measures exist and are unique. Computer experiments and simulations demonstrate that the proposed measures provide substantially different results when applied to the same multiplex structure, and highlight the non-trivial relationships between the different measures of centrality introduced.

Eigenvector centrality of nodes in multiplex networks

Abstract: We extend the concept of eigenvector centrality to multiplex networks, and introduce several alternative parameters that quantify the importance of nodes in a multi-layered networked system, including the definition of vectorial-type centralities. In addition, we rigorously show that, under reasonable conditions, such centrality measures exist and are unique. Computer experiments and simulations demonstrate that the proposed measures provide substantially different results when applied to the same multiplex structure, and highlight the non-trivial relationships between the different measures of centrality introduced.

Explosive transitions to synchronization in networks of phase oscillators

Abstract: The emergence of dynamical abrupt transitions in the macroscopic state of a system is currently a subject of the utmost interest. The occurrence of a first-order phase transition to synchronization of an ensemble of networked phase oscillators was reported, so far, for very particular network architectures. Here, we show how a sharp, discontinuous transition can occur, instead, as a generic feature of networks of phase oscillators. Precisely, we set conditions for the transition from unsynchronized to synchronized states to be first-order, and demonstrate how these conditions can be attained in a very wide spectrum of situations. We then show how the occurrence of such transitions is always accompanied by the spontaneous setting of frequency-degree correlation features. Third, we show that the conditions for abrupt transitions can be even softened in several cases. Finally, we discuss, as a possible application, the use of this phenomenon to express magnetic-like states of synchronization.

Explosive synchronization in weighted complex networks.

Abstract: The emergence of dynamical abrupt transitions in the macroscopic state of a system is currently a subject of the utmost interest. Given a set of phase oscillators networking with a generic wiring of connections and displaying a generic frequency distribution, we show how combining dynamical local information on frequency mismatches and global information on the graph topology suggests a judicious and yet practical weighting procedure which is able to induce and enhance explosive, irreversible, transitions to synchronization. We report extensive numerical and analytical evidence of the validity and scalability of such a procedure for different initial frequency distributions, for both homogeneous and heterogeneous networks, as well as for both linear and nonlinear weighting functions. We furthermore report on the possibility of parametrically controlling the width and extent of the hysteretic region of coexistence of the unsynchronized and synchronized states.

Generalized synchronization in relay systems with instantaneous coupling.

Abstract: 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.

Synchronization in networks of slightly nonidentical elements

Abstract: We study synchronization processes in networks of slightly non identical chaotic systems, for which a complete invariant synchronization manifold does not rigorously exist. We show and quantify how a slightly dispersed distribution in parameters can be properly modelled by a noise term affecting the stability of the synchronous invariant solution emerging for identical systems when the parameter is set at the mean value of the original distribution.

Feature Selection in the Reconstruction of Complex Network Representations of Spectral Data

Abstract: Complex networks have been extensively used in the last decade to characterize and analyze complex systems, and they have been recently proposed as a novel instrument for the analysis of spectra extracted from biological samples Yet, the high number of measurements composing spectra, and the consequent high computational cost, make a direct network analysis unfeasible We here present a comparative analysis of three customary feature selection algorithms, including the binning of spectral data and the use of information theory metrics Such algorithms are compared by assessing the score obtained in a classification task, where healthy subjects and people suffering from different types of cancers should be discriminated Results indicate that a feature selection strategy based on Mutual Information outperforms the more classical data binning, while allowing a reduction of the dimensionality of the data set in two orders of magnitude

Knowledge Discovery in Spectral Data by Means of Complex Networks

Abstract: In the last decade, complex networks have widely been applied to the study of many natural and man-made systems, and to the extraction of meaningful information from the interaction structures created by genes and proteins. Nevertheless, less attention has been devoted to metabonomics, due to the lack of a natural network representation of spectral data. Here we define a technique for reconstructing networks from spectral data sets, where nodes represent spectral bins, and pairs of them are connected when their intensities follow a pattern associated with a disease. The structural analysis of the resulting network can then be used to feed standard data-mining algorithms, for instance for the classification of new (unlabeled) subjects. Furthermore, we show how the structure of the network is resilient to the presence of external additive noise, and how it can be used to extract relevant knowledge about the development of the disease.

Collective stochastic coherence and synchronizability in weighted scale-free networks

Abstract: Coupling frequently enhances noise-induced coherence and synchronization in interacting nonlinear systems, but it does so separately. In principle collective stochastic coherence and synchronizability are incompatible phenomena, since strongly synchronized elements behave identically and thus their response to noise is indistinguishable to that of a single element. Therefore one can expect systems that synchronize well to have a poor collective response to noise. Here we show that, in spite of this apparent conflict, a certain coupling architecture is able to reconcile the two properties. Specifically, our results reveal that weighted scale-free networks of diffusively coupled excitable elements exhibit both high synchronizability of their subthreshold dynamics and a good collective response to noise of their pulsed dynamics. This is established by comparing the behavior of this system to that of random, regular, and unweighted scale-free networks. We attribute the optimal response of weighted scale-free networks to the link homogeneity (with respect to node degree) provided by the weighting procedure, which balances the degree heterogeneity typical of SFNs.

Emergence of network features from

Abstract: Many biological and man-made networked systems are characterized by the simultaneous presence of different sub-networks organized in separate layers, with links and nodes of qualitatively different types. While during the past few years theoretical studies have examined a variety of structural features of complex networks, the outstanding question is whether such features are characterizing all single layers, or rather emerge as a result of coarse-graining, i.e. when going from the multilayered to the aggregate network representation. Here we address this issue with the help of real data. We analyze the structural properties of an intrinsically multilayered real network, the European Air Transportation Multiplex Network in which each commercial airline defines a network layer. We examine how several structural measures evolve as layers are progressively merged together. In particular, we discuss how the topology of each layer affects the emergence of structural properties in the aggregate network.

Parenclitic networks: a multilayer description of heterogeneous and static data-sets

Abstract: Describing a complex system is in many ways a problem akin to identifying an object, in that it involves defining boundaries, constituent parts and their relationships by the use of grouping laws. Here we propose a novel method which extends the use of complex networks theory to a generalized class of non-Gestaltic systems, taking the form of collections of isolated, possibly heterogeneous, scalars, e.g. sets of biomedical tests. The ability of the method to unveil relevant information is illustrated for the case of gene expression in the response to osmotic stress of {\it Arabidopsis thaliana}. The most important genes turn out to be the nodes with highest centrality in appropriately reconstructed networks. The method allows predicting a set of 15 genes whose relationship with such stress was previously unknown in the literature. The validity of such predictions is demonstrated by means of a target experiment, in which the predicted genes are one by one artificially induced, and the growth of the corresponding phenotypes turns out to feature statistically significant differences when compared to that of the wild-type.

Centrality of nodes in multiplex networks

Abstract: We extend the concept of eigenvector centrality to multiplex networks, and introduce several alternative parameters that quantify the importance of nodes in a multi-layered networked system, including the definition of vectorial-type centralities. In addition, we rigorously show that, under reasonable conditions, such centrality measures exist and are unique. Computer experiments and simulations demonstrate that the proposed measures provide substantially different results when applied to the same multiplex structure, and highlight the non-trivial relationships between the different measures of centrality introduced.

Parenclitic networks' representation of data sets

Abstract: Describing a complex system is in many ways a problem akin to identifying an object, in that it involves defining boundaries, constituent parts and their relationships by the use of grouping laws. Here we propose a novel method which extends the use of complex networks theory to a generalized class of non-Gestaltic systems, taking the form of collections of isolated, possibly heterogeneous, scalars, e.g. sets of biomedical tests. The ability of the method to unveil relevant information is illustrated for the case of gene expression in the response to osmotic stress of {\it Arabidopsis thaliana}. The most important genes turn out to be the nodes with highest centrality in appropriately reconstructed networks. The method allows predicting a set of 15 genes whose relationship with such stress was previously unknown in the literature. The validity of such predictions is demonstrated by means of a target experiment, in which the predicted genes are one by one artificially induced, and the growth of the corresponding phenotypes turns out to feature statistically significant differences when compared to that of the wild-type.

Computing with complex-valued networks of phase oscillators

Abstract: A computational paradigm based on phase-locked states of oscillators embedded in a complex-valued weighted network is introduced, and its efficiency and scalability in performing single- and multiple-input Boolean and non-Boolean operations are demonstrated. The paradigm introduces phase rotation mechanisms in each link of the network, without the need for external control loops, or adaptive mechanisms. We show that the proposed computation allows outperforming standard implementations of Boolean logic, by reducing the computational cost of operations, and permitting the construction of memory elements with single dynamical units.

Functional Hubs in Mild Cognitive Impairment

Abstract: We investigate how hubs of functional brain networks are modified as a result of mild cognitive impairment (MCI), a condition causing a slight but noticeable decline in cognitive abilities, which sometimes precedes the onset of Alzheimer's disease. We used magnetoencephalography (MEG) to investigate the functional brain networks of a group of patients suffering from MCI and a control group of healthy subjects, during the execution of a short-term memory task. Couplings between brain sites were evaluated using synchronization likelihood, from which a network of functional interdependencies was constructed and the centrality, i.e. importance, of their nodes quantified. The results showed that, with respect to healthy controls, MCI patients were associated with decreases and increases in hub centrality respectively in occipital and central scalp regions, supporting the hypothesis that MCI modifies functional brain network topology, leading to more random structures.