Thomas

Because diffusion typically involves symmetric interactions, scant attention has been focused on studying asymmetric cases. However, important networked systems underlain by diffusion (e.g. cortical networks and WWW) are inherently directed. In the case of undirected diffusion, it can be shown that the steady-state probability of the random walk dynamics is fully correlated with the degree, which no longer holds for directed networks. We investigate the relationship between such probability and the inward node degree, which we call efficiency , in modular networks. Our findings show that the efficiency of a given community depends mostly on the balance between its ingoing and outgoing connections. In addition, we derive analytical expressions to show that the internal degree of the nodes does not play a crucial role in their efficiency, when considering the Erdős–Rényi and Barabási–Albert models. The results are illustrated with respect to the macaque cortical network, prov...

Random Geometric Graphs (RGG) can be cast within the formalism of hidden-variables models. For RGG, the hidden-variables coincide with the coordinates of the nodes. We develop a general approach to extrapolate the typical configurations of a generic hidden-variable model and apply it to RGG. For any RGG, defined through a rigid or a soft geometric rule, the method allows to face a non trivial optimization problem: Given $N$ nodes, a domain $\mathcal{D}$, and a desired average connectivity $<k>$, find - if any - the distribution of nodes having support in $\mathcal{D}$ and average connectivity $<k>$. However, we find out that, in the thermodynamic limit, nodes can be only either uniformly distributed, or highly condensed, the two regimes being separated by a first order phase transition characterized by a finite jump of $<k>$. Other intermediate values of $<k>$ correspond to very rare graph realizations. The phase transition is triggered by the underlying geometry whose strength can be tuned by a parameter $a\in[0,1]$, with $a=1$ for rigid geometry (only close nodes are connected) and $a=0$ for rigid anti-geometry (only distant nodes are connected). Consistently, when $a=1/2$ there is no geometry and no phase transition. After discussing the numerical analysis, we provide a combinatorial argument to fully explain the mechanism inducing this phase transition and recognize it as an easy-hard-easy transition. Our result shows that, in general, ad hoc optimized networks can hardly be designed, unless to rely to specific heterogeneous constructions, not necessarily scale free.

For a globally coupled network of semiconductor lasers with delayed optical feedback, we demonstrate the existence of chimera states. The domains of coherence and incoherence that are typical for chimera states are found to exist for the amplitude, phase, and inversion of the coupled lasers. These chimera states defy several of the previously established existence criteria. While chimera states in phase oscillators generally demand nonlocal coupling, large system sizes, and specially prepared initial conditions, we find chimera states that are stable for global coupling in a network of only four coupled lasers for random initial conditions. The existence is linked to a regime of multistability between the synchronous steady state and asynchronous periodic solutions. We show that amplitude-phase coupling, a concept common in different fields, is necessary for the formation of the chimera states.

Axelrod's model in the square lattice with nearest-neighbors interactions exhibits culturally homogeneous as well as culturally fragmented absorbing configurations. In the case the agents are characterized by $F=2$ cultural features and each feature assumes $k$ states drawn from a Poisson distribution of parameter $q$ these regimes are separated by a continuous transition at $q_c = 3.10 \pm 0.02$. Using Monte Carlo simulations and finite size scaling we show that the mean density of cultural domains $\mu$ is an order parameter of the model that vanishes as $\mu \sim \left ( q - q_c \right)^\beta$ with $\beta = 0.67 \pm 0.01$ at the critical point. In addition, for the correlation length critical exponent we find $\nu = 1.63 \pm 0.04$ and for Fisher's exponent, $\tau = 1.76 \pm 0.01$. This set of critical exponents places the continuous phase transition of Axelrod's model apart from the known universality classes of nonequilibrium lattice models.

To analyse the relationship between stability against large perturbations and topological properties of a power transmission grid, we employ a statistical analysis of a large ensemble of synthetic power grids, looking for significant statistical relationships between the single-node basin stability measure and classical as well as tailormade weighted network characteristics. This method enables us to predict poor values of single-node basin stability for a large extent of the nodes, offering a node-wise stability estimation at low computational cost. Further, we analyse the particular function of certain network motifs to promote or degrade the stability of the system. Here we uncover the impact of so-called detour motifs on the appearance of nodes with a poor stability score and discuss the implications for power grid design.

Author(s): N. Bastas, K. Kosmidis, P. Giazitzidis, and M. Maragakis

In phase-transition phenomena, the estimation of the critical point is crucial for the calculation of the various critical exponents and the determination of the universality class they belong to. However, this is not an easy task, since a large amount of realizations is needed to eliminate the nois...

[Phys. Rev. E 90, 062101] Published Mon Dec 01, 2014

Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. In this letter we show the potential of selected recurrence plot measures for the investigation of even high-dimensional dynamics. We apply this method on spatially extended chaos, such as derived from the Lorenz96 model and show that the recurrence plot based measures can qualitatively characterize typical dynamical properties such as chaotic or periodic dynamics. Moreover, we demonstrate its power by analyzing satellite image time series of vegetation cover with contrasting dynamics as a spatially extended and potentially high-dimensional example from the real world.

Author(s): Tobias Kuhn, Matjaž Perc, and Dirk Helbing

An automated analysis of the words in 117 years worth of the Physical Review selects scientific memes—significant ideas that emerge and spread through the literature.

[Phys. Rev. X 4, 041036] Published Fri Nov 21, 2014

Many complex natural and physical systems exhibit patterns of interconnection that conform, approximately, to a network structure referred to as scale-free. Preferential attachment is one of many algorithms that have been introduced to model the growth and structure of scale-free networks. With so many different models of scale-free networks it is unclear what properties of scale-free networks are typical, and what properties are peculiarities of a particular growth or construction process. We propose a simple maximum entropy process which provides the best representation of what are typical properties of scale-free networks, and provides a standard against which real and algorithmically generated networks can be compared. As an example we consider preferential attachment and find that this particular growth model does not yield typical realizations of scale-free networks. In particular, the widely discussed "fragility" of scale-free networks is actually found to be due to the peculiar "hub-centric" structure of preferential attachment networks. We provide a method to generate or remove this latent hub-centric bias --- thereby demonstrating exactly which features of preferential attachment networks are atypical of the broader class of scale-free networks. We are also able to statistically demonstrate whether real networks are typical realizations of scale-free networks, or networks with that particular degree distribution; using a new surrogate generation method for complex networks, exactly analogous the the widely used surrogate tests of nonlinear time series analysis.

We consider robustness and percolation properties of the networks of networks, in which random nodes in different individual networks (layers) can be interdependent. We explore the emergence of the giant mutually connected component, generalizing the percolation cluster in a single network to interdependent networks, and observe the strong effect of loops of interdependencies. In particular, we find that the giant mutual component does not emerge in a loop formed by any number of layers. In contrast, we observe multiple hybrid transitions in networks of networks formed by infinite number of randomly connected layers, corresponding to the percolation of layers with different number of interdependencies. In particular we find that layers with many interdependencies are more fragile than layers with less interdependencies. These hybrid transitions, combining a discontinuity and a singularity, are responsible for joining a finite fraction of nodes in different layers to the giant mutually connected component. In the case of partial interdependence, when only a fraction of interlinks between layers provide interdependence, some of these transitions can become continuous.

Author(s): Ameerah Jabr-Hamdan, Jie Sun, and Daniel ben-Avraham

We study the Krapivsky-Redner (KR) network growth model, but where new nodes can connect to any number of existing nodes, m, picked from a power-law distribution p(m)∼m−α. Each of the m new connections is still carried out as in the KR model with probability redirection r (corresponding to degree ex...

[Phys. Rev. E 90, 052812] Published Mon Nov 17, 2014

Author(s): Yohsuke Murase, János Török, Hang-Hyun Jo, Kimmo Kaski, and János Kertész

Recent empirical studies using large-scale data sets have validated the Granovetter hypothesis on the structure of the society in that there are strongly wired communities connected by weak ties. However, as interaction between individuals takes place in diverse contexts, these communities turn out ...

[Phys. Rev. E 90, 052810] Published Mon Nov 17, 2014

Author(s): N. Azimi-Tafreshi, S. N. Dorogovtsev, and J. F. F. Mendes

We describe the complex global structure of giant components in directed multiplex networks that generalizes the well-known bow-tie structure, generic for ordinary directed networks. By definition, a directed multiplex network contains vertices of one type and directed edges of m different types. In...

[Phys. Rev. E 90, 052809] Published Mon Nov 17, 2014

Author(s): Vijay Singh, C. T. Brunson, and Stefan Boettcher

We analyze the phase transitions that emerge from the recursive design of certain hyperbolic networks that includes, for instance, a discontinuous (“explosive”) transition in ordinary percolation. To this end, we solve the q-state Potts model in the analytic continuation for noninteger q with the re...

[Phys. Rev. E 90, 052119] Published Thu Nov 13, 2014

We describe synchronization transitions in an ensemble of globally coupled phase oscillators with a bi-harmonic coupling function, and two sources of disorder - diversity of intrinsic oscillatory frequencies and external independent noise. Based on the self-consistent formulation, we derive analytic solutions for different synchronous states. We report on various non-trivial transitions from incoherence to synchrony where possible scenarios include: simple supercritical transition (similar to classical Kuramoto model), subcritical transition with large area of bistability of incoherent and synchronous solutions, and also appearance of symmetric two-cluster solution which can coexist with regular synchronous state. Remarkably, we show that the interplay between relatively small white noise and finite-size fluctuations can lead to metastable asynchronous solution.

Author(s): Brian Karrer, M. E. J. Newman, and Lenka Zdeborová

We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate percolation as a message passing process and demonstrate how the resu...

[Phys. Rev. Lett. 113, 208702] Published Wed Nov 12, 2014

Author(s): Kathleen E. Hamilton and Leonid P. Pryadko

We construct a tight lower bound for the site percolation threshold on an infinite graph, which becomes exact for an infinite tree. The bound is given by the inverse of the maximal eigenvalue of the Hashimoto matrix used to count nonbacktracking walks on the original graph. Our bound always exceeds ...

[Phys. Rev. Lett. 113, 208701] Published Wed Nov 12, 2014

Author(s): Travis Martin, Xiao Zhang, and M. E. J. Newman

Eigenvector centrality is a common measure of the importance of nodes in a network. Here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to concentrate on a small number of nodes in the network. In th...

[Phys. Rev. E 90, 052808] Published Wed Nov 12, 2014

Here we consider the download statistics of EPL publications. We find that papers in the journal are characterised by fast accumulations of downloads during the first couple of months after publication, followed by slower rates thereafter, behaviour which can be represented by a model with predictive power. We also find that individual papers can be classified in various ways, allowing us to compare categories for open-access and non-open-access papers. For example, for the latter publications, which comprise the bulk of EPL papers, a small proportion (2%) display intense bursts of download activity, possibly following an extended period of less remarkable behaviour. About 18% have an especially high degree of attractiveness over and above what is typical for the journal. One can also classify the ageing of attractiveness by examining download half-lives. Approximately 18% have strong interest initially, waning in time. A further 20% exhibit "delayed recognition" with relatively late spurs in download activity. Although open-access papers enjoy more downloads on average, the proportions falling into each category are similar.

Author(s): P. Rattana, L. Berthouze, and I. Z. Kiss

In this paper, we study an adaptive spatial network. We consider a susceptible-infected-susceptible (SIS) epidemic on the network, with a link or contact rewiring process constrained by spatial proximity. In particular, we assume that susceptible nodes break links with infected nodes independently o...

[Phys. Rev. E 90, 052806] Published Tue Nov 11, 2014

Author(s): Anatol E. Wegner

Many complex systems can be represented as networks of interacting elements. A new theoretical method identifies characteristics of the connectivity patterns of networks.

[Phys. Rev. X 4, 041026] Published Mon Nov 10, 2014

Author(s): Guadalupe C. Garcia, Annick Lesne, Claus C. Hilgetag, and Marc-Thorsten Hütt

Topological cycles in excitable networks can play an important role in maintaining the network activity. When properly activated, cycles act as dynamic pacemakers, sustaining the activity of the whole network. Most previous research has focused on the contributions of short cycles to network dynamic...

[Phys. Rev. E 90, 052805] Published Mon Nov 10, 2014

Author(s): F. L. Metz, G. Parisi, and L. Leuzzi

We develop a thorough analytical study of the O(1/N) correction to the spectrum of regular random graphs with N→∞ nodes. The finite-size fluctuations of the resolvent are given in terms of a weighted series over the contributions coming from loops of all possible lengths, from which we obtain the is...

[Phys. Rev. E 90, 052109] Published Mon Nov 10, 2014

Interacting epidemics on diverse multilayer networks are increasingly important in modeling and analyzing the diffusion processes of real complex systems. A viral agent spreading on one layer of a multilayer network can interact with its counterparts by promoting (cooperative interaction), suppressi...

Author(s): O. V. Usatenko, S. S. Melnik, S. S. Apostolov, N. M. Makarov, and A. A. Krokhin

We propose an efficient iterative method for generating random correlated binary sequences with a prescribed correlation function. The method is based on consecutive linear modulations of an initially uncorrelated sequence into a correlated one. Each step of modulation increases the correlations unt...

[Phys. Rev. E 90, 053305] Published Thu Nov 06, 2014

Author(s): Pan Zhang, Cristopher Moore, and Lenka Zdeborová

Predicting labels of nodes in a network, such as community memberships or demographic variables, is an important problem with applications in social and biological networks. A recently discovered phase transition puts fundamental limits on the accuracy of these predictions if we have access only to ...

[Phys. Rev. E 90, 052802] Published Wed Nov 05, 2014

We analyze the phase transitions that emerge from the recursive design of certain hyperbolic networks that includes, for instance, a discontinuous ("explosive") transition in ordinary percolation. To this end, we solve the $q$-state Potts model in the analytic continuation for non-integer $q$ with t...

We describe the complex global structure of giant components in directed multiplex networks which generalizes the well-known bow-tie structure, generic for ordinary directed networks. By definition, a directed multiplex network contains vertices of one type and directed edges of $m$ different types....

We study the self-avoiding walk on complex fractal networks called the $(u,v)$-flower by mapping it to the $N$-vector model in a generating function formalism. First, we analytically calculate the critical exponent $\nu$ and the connective constant by a renormalization-group analysis in arbitrary fr...

Author(s): Ignacio Hermoso de Mendoza, Leonardo A. Pachón, Jesús Gómez-Gardeñes, and David Zueco

Synchronization is a ubiquitous phenomenon occurring in social, biological, and technological systems when the internal rythms of their constituents are adapted to be in unison as a result of their coupling. This natural tendency towards dynamical consensus has spurred a large body of theoretical an...

[Phys. Rev. E 90, 052904] Published Tue Nov 04, 2014