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Register a new userEmergent explosive synchronization in adaptive complex networks
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Adaptation plays a fundamental role in shaping the structure of a complex network and improving its functional fitting. Even when increasing the level of synchronization in a biological system is considered as the main driving force for adaptation, there is evidence of negative effects induced by excessive synchronization. This indicates that coherence alone can not be enough to explain all the structural features observed in many real-world networks. In this work, we propose an adaptive network model where the dynamical evolution of the node states towards synchronization is coupled with an evolution of the link weights based on an anti-Hebbian adaptive rule, which accounts for the presence of inhibitory effects in the system. We found that the emergent networks spontaneously develop the structural conditions to sustain explosive synchronization. Our results can enlighten the shaping mechanisms at the heart of the structural and dynamical organization of some relevant biological systems, namely brain networks, for which the emergence of explosive synchronization has been observed.
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Networks of chaotic units with static couplings can synchronize to a common chaotic trajectory. The effect of dynamic adaptive couplings on the cooperative behavior of chaotic networks is investigated. The couplings adjust to the activities of its two units by two competing mechanisms: An exponential decrease of the coupling strength is compensated by an increase due to de-synchronized activity. This mechanism prevents the network from reaching a steady state. Numerical simulations of a coupled map lattice show chaotic trajectories of de-synchronized units interrupted by pulses of mutually synchronized clusters. These pulses occur on all scales, sometimes extending to the entire network. Clusters of synchronized units can be triggered by a small group of synchronized units.
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the mathematical tools of statistical physics have proven to be particularly suitable for studying and understanding complex networks. Nevertheless, an important obstacle to this theoretical approach is still represented by the difficulties to draw parallelisms between network science and more traditional aspects of statistical physics. In this paper, we explore the relation between complex networks and a well known topic of statistical physics: renormalization. A general method to analyze renormalization flows of complex networks is introduced. The method can be applied to study any suitable renormalization transformation. Finite-size scaling can be performed on computer-generated networks in order to classify them in universality classes. We also present applications of the method on real networks.
In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and nonequilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer, and social scientists share a common interest in studying epidemic spreading and rely on similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while focusing on the main results and the paradigmatic models in infectious disease modeling, the major results concerning generalized social contagion processes are also presented. Finally, the research activity at the forefront in the study of epidemic spreading in coevolving, coupled, and time-varying networks is reported.
Large multipartite quantum systems tend to rapidly reach extraordinary levels of complexity as their number of constituents and entanglement links grow. Here we use complex network theory to study a class of continuous variables quantum states that present both multipartite entanglement and non-Gaussian statistics. In particular, the states are built from an initial imprinted cluster state created via Gaussian entangling operations according to a complex network structure. To go beyond states that can be easily simulated via classical computers we engender non-Gaussian statistics via multiple photon subtraction operations. We then use typical networks measures, the degree and clustering, to characterize the emergent complex network of photon-number correlations after photon subtractions. We show that, in contrast to regular clusters, in the case of imprinted complex network structures the emergent correlations are strongly affected by photon subtraction. On the one hand, we unveil that photon subtraction universally increases the average photon-number correlations, regardless of the imprinted network structure. On the other hand, we show that the shape of the distributions in the emergent networks after subtraction is greatly influenced by the structure of the imprinted network, as witnessed by their higher-moments. Thus for the field of network theory, we introduce a new class of networks to study. At the same time for the field of continuous variable quantum states, this work presents a new set of practical tools to benchmark systems of increasing complexity.
The availability of data from many different sources and fields of science has made it possible to map out an increasing number of networks of contacts and interactions. However, quantifying how reliable these data are remains an open problem. From Biology to Sociology and Economy, the identification of false and missing positives has become a problem that calls for a solution. In this work we extend one of newest, best performing models -due to Guimera and Sales-Pardo in 2009- to directed networks. The new methodology is able to identify missing and spurious directed interactions, which renders it particularly useful to analyze data reliability in systems like trophic webs, gene regulatory networks, communication patterns and social systems. We also show, using real-world networks, how the method can be employed to help searching for new interactions in an efficient way.
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