Edmilson Roque

Discontinuous transition is observed in the equilibrium cluster properties of a percolation model with suppressed cluster growth as the growth parameter g0 is tuned to the critical threshold at sufficiently low initial seed concentration rho in contrast to the previously reported results on non- equilibrium growth models. In the present model, the growth process follows all the criteria of the original percolation model except continuously updated occupation probability of the lattice sites that suppresses the growth of a cluster according to its size. As rho varied from higher values to smaller values, a line of continuous transition points encounters a coexistence region of spanning and non- spanning large clusters. At sufficiently small values of rho (less equal 0.05), the growth parameter g0 exceeds the usual percolation threshold and generates compact spanning clusters leading to discontinuous transitions.

When dealing with the dissemination of epidemics, one important question that can be asked is the location where the contamination began. In this paper, we analyze three spreading schemes and propose and validate an effective methodology for the identification of the source nodes. The method is based on the calculation of the centrality of the nodes on the sampled network, expressed here by degree, betweenness, closeness and eigenvector centrality. We show that the source node tends to have the highest measurement values. The potential of the methodology is illustrated with respect to three theoretical complex network models as well as a real-world network, the email network of the University Rovira i Virgili.

We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of edges are governed by continuous-time Markov processes with rate parameters that can depend on properties of the nodes. In addition to computing equilibrium properties of these models, we demonstrate their use in data analysis and statistical inference, giving efficient algorithms for fitting them to observed network data. This allows us, for instance, to estimate the time constants of network evolution or infer community structure from temporal network data using cues embedded both in the probabilities over time that node pairs are connected by edges and in the characteristic dynamics of edge appearance and disappearance. We illustrate our methods with a selection of applications, both to computer-generated test networks and real-world examples.

Author(s): Amitava Banerjee and Muktish Acharyya

We have studied the dynamics of the paradigmatic Kuramoto-Sakaguchi model of identical coupled phase oscillators with various kinds of time-dependent connectivity using Eulerian discretization. We first explore the parameter spaces for various types of collective states using the phase plots of the …

[Phys. Rev. E] Published Mon Jul 25, 2016

Author(s): Ivan Kryven

The weak component generalizes the idea of connected components to directed graphs. In this paper, an exact criterion for the existence of the giant weak component is derived for directed graphs with arbitrary bivariate degree distributions. In addition, we consider a random process for evolving dir…

[Phys. Rev. E 94, 012315] Published Wed Jul 27, 2016

Time to remodel the journal impact factor

Nature 535, 7613 (2016). doi:10.1038/535466a

Nature and the Nature journals are diversifying their presentation of performance indicators.

Author(s): Takashi Nishikawa and Adilson E. Motter

Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the complete synchronization of the entire network is the state inheri…

[Phys. Rev. Lett.] Published Wed Jul 27, 2016

Abstract

Globally coupled doubling maps are studied in this paper. In this setting and for finitely many sites, two distinct bifurcation values of the coupling strength have been identified in the literature, corresponding to the emergence of contracting directions (Koiller and Young in Nonlinearity, 23(5):1121, 2010) and, specifically for \(N=3\) sites, to the loss of ergodicity (Fernandez in Journal of Statistical Physics, 154(4):999–1029, 2014). On the one hand, we reconsider these results and provide an interpretation of the observed dynamical phenomena in terms of the synchronization of the sites. On the other hand, we initiate a new point of view which focuses on the evolution of distributions and allows to incorporate the investigation of a continuum of sites. In particular, we observe phenomena that is analogous to the limit states of the contracting regime of \(N=3\) sites.

Topological techniques are powerful tools for characterizing the complexity of many dynamical systems, including the commonly studied area-preserving maps of the plane. However, the extension of many topological techniques to higher dimensions is filled with roadblocks preventing their application. This article shows how to extend the homotopic lobe dynamics (HLD) technique, previously developed for 2D maps, to volume-preserving maps of a three-dimensional phase space. Such maps are physically relevant to particle transport by incompressible fluid flows or by magnetic field lines. Specifically, this manuscript shows how to utilize two-dimensional stable and unstable invariant manifolds, intersecting in a heteroclinic tangle, to construct a symbolic representation of the topological dynamics of the map. This symbolic representation can be used to classify system trajectories and to compute topological entropy. We illustrate the salient ideas through a series of examples with increasing complexity. These examples highlight new features of the HLD technique in 3D. Ultimately, in the final example, our technique detects a difference between the 2D stretching rate of surfaces and the 1D stretching rate of curves, illustrating the truly 3D nature of our approach.

We show that self-consistent partial synchrony in globally coupled oscillatory ensembles is a general phenomenon. We analyze in detail appearance and stability properties of this state in possibly the simplest setup of a biharmonic Kuramoto-Daido phase model as well as demonstrate the effect in limit-cycle relaxational Rayleigh oscillators. Such a regime extends the notion of splay state from a uniform to distribution of phases to an oscillating one. Suitable collective observables such as the Kuramoto order parameter allow detecting the presence of a inhomogeneous distribution. The characteristic and most peculiar property of partial synchrony is the difference between the frequencies of single units and that of the macroscopic field.

Author(s): Miguel A. Rodríguez

We obtain graphicality conditions for general types of scale-free networks. The same conditions obtained for uncorrelated networks are obtained in the general case. Then an upper bound relating γ, the exponent of the degree distribution, with the cutoff exponent κ, as κ<1/γ is established. This b…

[Phys. Rev. E 94, 012314] Published Tue Jul 26, 2016

Recently, some studies started to unveil the wealthy of interactions that occur between groups of nodes when looking at the small scale of interactions taking place in complex networks. Such findings claim for a new systematic methodology to quantify, at node level, how a dynamics is being influenced (or differentiated) by the structure of the underlying system. Here we define a new measure that, based on dynamical characteristics obtained for a large set of initial conditions, compares the dynamical behavior of the nodes present in the system. Through this measure we find that the geographic and Barab\'asi-Albert models have high capacity for generating networks that exhibit groups of nodes with distinct dynamics compared to the rest of the network. The application of our methodology is illustrated with respect of two real systems. In the first we use the neuronal network of the nematode Caenorhabditis elegans to show that the interneurons of the ventral cord of the nematode presents a very large dynamical differentiation when compared to the rest of the network. The second application concerns the SIS epidemic model on an airport network, where we quantify how different the distribution of infection times of high and low degree nodes can be, when compared to the expected value for the network.

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 do not play a crucial role in their efficiency, when considering the Erd\H{o}s-R\'enyi and Barab\'asi-Albert models. The results are illustrated with respect to the macaque cortical network, providing subsidies for improving transportation and communication systems.

We investigate q-voter model with stochastic noise arising from independence on complex networks. Using the pair approximation, we provide comprehensive, mathematical description of its behavior and derive formula for the critical point. The analytical results are validated by carrying out Monte Carlo experiments. The pair approximation prediction exhibits substantial agreement with simulations, especially for networks with weak clustering and large average degree. Nonetheless, for the average degree close to q, some discrepancies originate. It is the first time the presented approach has been applied to the nonlinear voter dynamics with noise. Up till now, the analytical results have been obtained only for a complete graph. We show that in the limiting case the prediction of pair approximation coincides with the known solution on a fully connected network.

We consider the observability model in networks with arbitrary topologies. We introduce a system of coupled nonlinear equations, valid under the locally tree-like ansatz, to describe the size of the largest observable cluster as a function of the fraction of directly observable nodes present in the network. We perform a systematic analysis on 95 real-world graphs and compare our theoretical predictions with numerical simulations of the observability model. Our method provides almost perfect predictions in the majority of the cases, even for networks with very large values of the clustering coefficient. Potential applications of our theory include the development of efficient and scalable algorithms for real-time surveillance of social networks, and monitoring of technological networks.

The access to an ever increasing amount of information in the modern world gave rise to the development of many quantitative indicators about urban regions in the globe. Therefore, there is a growing need for a precise definition of how to delimit urban regions, so as to allow proper respective characterization and modeling. Here we present a straightforward methodology to automatically detect urban region borders around a single seed point. The method is based on a diffusion process having street crossings and terminations as source points. We exemplify the potential of the methodology by characterizing the geometry and topology of 21 urban regions obtained from 8 distinct countries. The geometry is studied by employing the lacunarity measurement, which is associated to the regularity of holes contained in a pattern. The topology is analyzed by associating the betweenness centrality of the streets with their respective class, such as motorway or residential, obtained from a database.

Recently, some studies started to unveil the wealthy of interactions that occur between groups of nodes when looking at the small scale of interactions taking place in complex networks. Such findings claim for a new systematic methodology to quantify, at node level, how a dynamics is being influenced (or differentiated) by the structure of the underlying system. Here we define a new measure that, based on dynamical characteristics obtained for a large set of initial conditions, compares the dynamical behavior of the nodes present in the system. Through this measure we find that the geographic and Barab\'asi-Albert models have high capacity for generating networks that exhibit groups of nodes with distinct dynamics compared to the rest of the network. The application of our methodology is illustrated with respect of two real systems. In the first we use the neuronal network of the nematode Caenorhabditis elegans to show that the interneurons of the ventral cord of the nematode presents a very large dynamical differentiation when compared to the rest of the network. The second application concerns the SIS epidemic model on an airport network, where we quantify how different the distribution of infection times of high and low degree nodes can be, when compared to the expected value for the network.

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 do not play a crucial role in their efficiency, when considering the Erd\H{o}s-R\'enyi and Barab\'asi-Albert models. The results are illustrated with respect to the macaque cortical network, providing subsidies for improving transportation and communication systems.

We investigate the q-voter model with stochastic noise arising from independence on complex networks. Using the pair approximation, we provide a comprehensive, mathematical description of its behavior and derive a formula for the critical point. The analytical results are validated by carrying out Monte Carlo experiments. The pair approximation prediction exhibits substantial agreement with simulations, especially for networks with weak clustering and large average degree. Nonetheless, for the average degree close to q, some discrepancies originate. It is the first time we are aware of that the presented approach has been applied to the nonlinear voter dynamics with noise. Up till now, the analytical results have been obtained only for a complete graph. We show that in the limiting case the prediction of pair approximation coincides with the known solution on a fully connected network.

Social Networks allow users to self-present by sharing personal contents with others which may add comments. Recent studies highlighted how the emotions expressed in a post affect others' posts, eliciting a congruent emotion. So far, no studies have yet investigated the emotional coherence between wall posts and its comments. This research evaluated posts and comments mood of Facebook profiles, analyzing their linguistic features, and a measure to assess an excessive self-presentation was introduced. Two new experimental measures were built, describing the emotional loading (positive and negative) of posts and comments, and the mood correspondence between them was evaluated. The profiles "empathy", the mood coherence between post and comments, was used to investigate the relation between an excessive self-presentation and the emotional coherence of a profile. Participants publish a higher average number of posts with positive mood. To publish an emotional post corresponds to get more likes, comments and receive a coherent mood of comments, confirming the emotional contagion effect reported in literature. Finally, the more empathetic profiles are characterized by an excessive self-presentation, having more posts, and receiving more comments and likes. To publish emotional contents appears to be functional to receive more comments and likes, fulfilling needs of attention-seeking.

We consider the observability model in networks with arbitrary topologies. We introduce a system of coupled nonlinear equations, valid under the locally tree-like ansatz, to describe the size of the largest observable cluster as a function of the fraction of directly observable nodes present in the network. We perform a systematic analysis on 95 real-world graphs and compare our theoretical predictions with numerical simulations of the observability model. Our method provides almost perfect predictions in the majority of the cases, even for networks with very large values of the clustering coefficient. Potential applications of our theory include the development of efficient and scalable algorithms for real-time surveillance of social networks, and monitoring of technological networks.

We introduce a new matrix function for studying graphs and real-world networks based on a double-factorial penalization of walks between nodes in a graph. This new matrix function is based on the matrix error function. We find a very good approximation of this function using a matrix hyperbolic tangent function. We derive a communicability function, a subgraph centrality and a double-factorial Estrada index based on this new matrix function. We obtain upper and lower bounds for the double-factorial Estrada index of graphs, showing that they are similar to those of the single-factorial Estrada index. We then compare these indices with the single-factorial one for simple graphs and real-world networks. We conclude that for networks containing chordless cycles---holes---the two penalization schemes produce significantly different results. In particular, we study two series of real-world networks representing urban street networks, and protein residue networks. We observe that the subgraph centrality based on both indices produce significantly different ranking of the nodes. The use of the double factorial penalization of walks opens new possibilities for studying important structural properties of real-world networks where long-walks play a fundamental role, such as the cases of networks containing chordless cycles.

We introduce a new, and quite general variational model for opinion dynamics based on pairwise interaction potentials and a range of opinion evolution protocols ranging from random interactions to global synchronous flows in the opinion state space. The model supports the concept of topic "coupling", allowing opinions held by individuals to be changed via indirect interaction with others on different subjects. Interaction topology is governed by a graph that determines interactions. Our model, which is really a family of variational models, has, as special cases, many of the previously established models for the opinion dynamics. After introducing the model, we study the dynamics of the special case in which the potential is either a tent function or a constructed bell-like curve. We find that even in these relatively simple potential function examples there emerges interesting behavior. We also present results of preliminary numerical explorations of the behavior of the model to motivate questions that can be explored analytically.

Author(s): K. Kang, S. H. Piao, and H. J. Choi

Micron-sized colloidal spheres that are dispersed in an isotropic-nematic bi-phasic host suspension of charged rods (fd-virus particles) are shown to spontaneously form dimers, which exhibit a synchronized oscillatory motion. Dimer formation is not observed in mono-phase of isotropic and nematic sus…

[Phys. Rev. E] Published Mon Jul 25, 2016

We examine the correlations between rings in random network glasses in two dimensions as a function of their separation. Initially, we use the topological separation (measured by the number of intervening rings), but this lead to pseudo-long-range correlations due to a lack of topological charge neutrality in the shells surrounding a central ring. This effect is associated with the non-circular nature of the shells. It is ,therefore, necessary to use the geometrical distance between ring centers. Hence we find a generalization of the Aboav-Weaire law out to larger distances, with the correlations between rings decaying away when two rings are more than about 3 rings apart.

We investigate the influence of the contact network structure on the spread of epidemics over an heterogeneous population. In our model, the epidemic process spreads over a directed weighted graph. A continuous-time individual-based susceptible-infected-susceptible (SIS) is analyzed using a first-order mean-field approximation.

First, we consider a network with general topology in order to investigate the epidemic threshold and the stability properties of the system. Then, we analyze the case of a community network relying on the graph-theoretical notion of equitable partition. We show that, in this case, the epidemic threshold can be computed using a lower-dimensional dynamical system. Moreover we prove that the positive steady-state of the original system, that appears above the threshold, can be computed using this lower-dimensional system.

In the second part of the work, we leverage on our model to derive a cost-optimal curing policy, in order to prevent the disease from persisting indefinitely within the population. The solution of this optimization problem is obtained by formulating a convex minimization problem on a general but symmetric network structure. Finally, in the case of a two-level optimal curing problem, an algorithm is designed with a polynomial time complexity in the network size.

Social media have great potential to support diverse information sharing, but there is widespread concern that platforms like Twitter do not result in communication between those who hold contradictory viewpoints. Because users can choose whom to follow, prior research suggests that social media users exist in 'echo chambers' or become polarized. We seek evidence of this in a complete cross section of hyperlinks posted on Twitter, using previously validated measures of the political slant of news sources to study information diversity. Contrary to prediction, we find that the average account posts links to more politically moderate news sources than the ones they receive in their own feed. However, members of a tiny network core do exhibit cross-sectional evidence of polarization and are responsible for the majority of tweets received overall due to their popularity and activity, which could explain the widespread perception of polarization on social media.

Author(s): M. E. J. Newman and Gesine Reinert

Community detection, the division of a network into dense subnetworks with only sparse connections between them, has been a topic of vigorous study in recent years. However, while there exist a range of effective methods for dividing a network into a specified number of communities, it is an open qu…

[Phys. Rev. Lett.] Published Fri Jul 22, 2016

Author(s): P. Kómár, T. Topcu, E. M. Kessler, A. Derevianko, V. Vuletić, J. Ye, and M. D. Lukin

We propose a protocol for creating a fully entangled GHZ-type state of neutral atoms in spatially separated optical atomic clocks. In our scheme, local operations make use of the strong dipole-dipole interaction between Rydberg excitations, which give rise to fast and reliable quantum operations inv…

[Phys. Rev. Lett.] Published Fri Jul 22, 2016