Edmilson Roque

Among the consequences of the disordered interaction topology underlying many social, techno- logical and biological systems, a particularly important one is that some nodes, just because of their position in the network, may have a disproportionate effect on dynamical processes mediated by the complex interaction pattern. For example, the early adoption by an opinion leader in a social network may change the fate of a commercial product, or just a few super-spreaders may determine the virality of a meme in social media. Despite many recent efforts, the formulation of an accurate method to optimally identify influential nodes in complex network topologies remains an unsolved challenge. Here, we present the exact solution of the problem for the specific, but highly relevant, case of the Susceptible-Infected-Removed (SIR) model for epidemic spreading at criticality. By exploiting the mapping between bond percolation and the static properties of SIR, we prove that the recently introduced Non-Backtracking centrality is the optimal criterion for the identification of influential spreaders in locally tree-like networks at criticality. By means of simulations on synthetic networks and on a very extensive set of real-world networks, we show that the Non-Backtracking centrality is a highly reliable metric to identify top influential spreaders also in generic graphs not embedded in space, and for noncritical spreading.

Complex systems are usually illustrated by networks which captures the topology of the interactions between the entities. To better understand the roles played by the entities in the system one needs to uncover the underlying community structure of the system. In recent years, systems with interactions that have various types or can change over time between the entities have attracted an increasing research attention. However, algorithms aiming to solve the key problem - community detection - in multilayer networks are still limited. In this work, we first introduce the multilayer network model representation with multiple aspects, which is flexible to a variety of networks. Then based on this model, we naturally derive the multilayer modularity - a widely adopted objective function of community detection in networks - from a static perspective as an evaluation metric to evaluate the quality of the communities detected in multilayer networks. It enables us to better understand the essence of the modularity by pointing out the specific kind of communities that will lead to a high modularity score. We also propose a spectral method called mSpec for the optimization of the proposed modularity function based on the supra-adjacency representation of the multilayer networks. Experiments on the electroencephalograph network and the comparison results on several empirical multilayer networks demonstrate the feasibility and reliable performance of the proposed method.

Author(s): Mor Nitzan, Eytan Katzav, Reimer Kühn, and Ofer Biham

We present analytical results for the distribution of shortest path lengths between random pairs of nodes in configuration model networks. The results, which are based on recursion equations, are shown to be in good agreement with numerical simulations for networks with degenerate, binomial and powe…

[Phys. Rev. E] Published Wed May 18, 2016

Author(s): Changyao Chen, Damián H. Zanette, Jeffrey R. Guest, David A. Czaplewski, and Daniel Lopez

Autonomous oscillators, such as clocks and lasers, produce periodic signals \emph{without} any external frequency reference. In order to sustain stable periodic motions, there needs to be external energy supply as well as nonlinearity built into the oscillator to regulate the amplitude. Usually, non…

[Phys. Rev. Lett.] Published Mon May 23, 2016

Author(s): Paul Schultz, Thomas Peron, Deniz Eroglu, Thomas Stemler, Gonzalo Marcelo Ramírez Ávila, Francisco A. Rodrigues, and Jürgen Kurths

Natural and man--made networks often possess locally tree-like sub-structures. Taking such tree networks as our starting point, we show how the addition of links changes the synchronization properties of the network. We focus on two different methods of link addition. The first method adds single li…

[Phys. Rev. E] Published Fri May 20, 2016

Author(s): Sasibhusan Mahata, Swetamber Das, and Neelima Gupte

The problem of synchronization of coupled Hamiltonian systems presents interesting features due to the mixed nature (regular and chaotic) of the phase space. We study these features by examining the synchronization of unidirectionally coupled area-preserving maps coupled by the Pecora-Caroll method.…

[Phys. Rev. E] Published Fri May 20, 2016

Author(s): Pedro D. Pinto, Fernando A. Oliveira, and André L. A. Penna

In this article, we present an approach for the thermodynamics of phase oscillators induced by an internal multiplicative noise. We analytically derive the free energy, entropy, internal energy, and specific heat. In this framework, the formulation of the first law of thermodynamics requires the def…

[Phys. Rev. E 93, 052220] Published Mon May 23, 2016

Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in an ensemble of random geometric graphs. Here we identify structural properties of networks that guarantee that random graphs having these properties are geometric. Specifically we show that random graphs in which expected degree and clustering of every node are fixed to some constants are equivalent to random geometric graphs on the real line, if clustering is sufficiently strong. Large numbers of triangles, homogeneously distributed across all nodes as in real networks, are thus a consequence of network geometricity. The methods we use to prove this are quite general and applicable to other network ensembles, geometric or not, and to certain problems in quantum gravity.

Author(s): Simeon Bird, Ilias Cholis, Julian B. Muñoz, Yacine Ali-Haïmoud, Marc Kamionkowski, Ely D. Kovetz, Alvise Raccanelli, and Adam G. Riess

A theoretical analysis examines the possibility that the black holes detected by LIGO serve as dark matter.

[Phys. Rev. Lett. 116, 201301] Published Thu May 19, 2016

Author(s): Dmitri Krioukov

Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in an ensemble of random geometric graphs. Here we identify str…

[Phys. Rev. Lett. 116, 208302] Published Thu May 19, 2016

The increasing power of computer technology does not dispense with the need to extract meaningful in- formation out of data sets of ever growing size, and indeed typically exacerbates the complexity of this task. To tackle this general problem, two methods have emerged, at chronologically different times, that are now commonly used in the scientific community: data mining and complex network theory. Not only do complex network analysis and data mining share the same general goal, that of extracting information from complex systems to ultimately create a new compact quantifiable representation, but they also often address similar problems too. In the face of that, a surprisingly low number of researchers turn out to resort to both methodologies. One may then be tempted to conclude that these two fields are either largely redundant or totally antithetic. The starting point of this review is that this state of affairs should be put down to contingent rather than conceptual differences, and that these two fields can in fact advantageously be used in a synergistic manner. An overview of both fields is first provided, some fundamental concepts of which are illustrated. A variety of contexts in which complex network theory and data mining have been used in a synergistic manner are then presented. Contexts in which the appropriate integration of complex network metrics can lead to improved classification rates with respect to classical data mining algorithms and, conversely, contexts in which data mining can be used to tackle important issues in complex network theory applications are illustrated. Finally, ways to achieve a tighter integration between complex networks and data mining, and open lines of research are discussed.

We discuss the distribution of commuting distances and its relation to income. Using data from Denmark, the UK, and the US, we show that the commuting distance is (i) broadly distributed with a slow decaying tail that can be fitted by a power law with exponent $\gamma \approx 3$ and (ii) an average growing slowly as a power law with an exponent less than one that depends on the country considered. The classical theory for job search is based on the idea that workers evaluate the wage of potential jobs as they arrive sequentially through time, and extending this model with space, we obtain predictions that are strongly contradicted by our empirical findings. We propose an alternative model that is based on the idea that workers evaluate potential jobs based on a quality aspect and that workers search for jobs sequentially across space. We also assume that the density of potential jobs depends on the skills of the worker and decreases with the wage. The predicted distribution of commuting distances decays as $1/r^{3}$ and is independent of the distribution of the quality of jobs. We find our alternative model to be in agreement with our data. This type of approach opens new perspectives for the modeling of mobility.

Exploiting the information about members of a Social Network (SN) represents one of the most attractive and dwelling subjects for both academic and applied scientists. The community of Complexity Science and especially those researchers working on multiplex social systems are devoting increasing efforts to outline general laws, models, and theories, to the purpose of predicting emergent phenomena in SN's (e.g. success of a product). On the other side the semantic web community aims at engineering a new generation of advanced services tailored to specific people needs. This implies defining constructs, models and methods for handling the semantic layer of SNs. We combined models and techniques from both the former fields to provide a hybrid approach to understand a basic (yet complex) phenomenon: the propagation of individual interests along the social networks. Since information may move along different social networks, one should take into account a multiplex structure. Therefore we introduced the notion of "Semantic Multiplex". In this paper we analyse two different semantic social networks represented by authors publishing in the Computer Science and those in the American Physical Society Journals. The comparison allows to outline common and specific features

Scientists pursue collective knowledge, but they also seek personal recognition from their peers. When scientists decide whether or not to work on a big new problem, they weigh the potential rewards of a major discovery against the costs of setting aside other projects. These self-interested choices can potentially spread researchers across problems in an efficient manner, but efficiency is not guaranteed. We use simple economic models to understand such decisions and their collective consequences. Academic science differs from industrial R&D in that academics often share partial solutions to gain reputation. This convention of Open Science is thought to accelerate collective discovery, but we find that it need not do so. The ability to share partial results influences which scientists work on a particular problem; consequently, Open Science can slow down the solution of a problem if it deters entry by important actors.

For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation is split into an initial decrease characterized by the maximal Lyapunov exponent and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. The time scales of both processes can be either of the same or of very different orders of magnitude. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall size of the attractor) for exceedingly long times and therefore remain partially predictable. We introduce a 0-1 indicator for chaos capable of describing this scenario, arguing, in addition, that the chaotic closed braids found close to a period-doubling transition are generically partially predictable.

We propose real-space renormalized dynamical mean field theory (rr-DMFT) to deal with large clusters in the framework of a cluster extension of the DMFT. In the rr-DMFT, large clusters are decomposed into multiple smaller clusters through a real-space renormalization. In this work, the renormalization effect is taken into account only at the lowest order with respect to the intercluster coupling, which nonetheless reproduces exactly both the noninteracting and atomic limits. Our method allows us large cluster-size calculations which are intractable with the conventional cluster extensions of the DMFT with impurity solvers, such as the continuous-time quantum Monte Carlo and exact diagonalization methods. We benchmark the rr-DMFT for the two-dimensional Hubbard model on a square lattice at and away from half filling, where the spatial correlations play important roles. Our results on the spin structure factor indicate that the growth of the antiferromagnetic spin correlation is taken into account beyond the decomposed cluster size. We also show that the self-energy obtained from the large-cluster solver is reproduced by our method better than the solution obtained directly for the smaller cluster. When applied to the Mott metal-insulator transition, the rr-DMFT is able to reproduce the reduced critical value for the Coulomb interaction comparable to the large cluster result.

Author(s): Chiu Fan Lee and Gunnar Pruessner

This paper aims to provide a theoretical framework for the recent experimental observation that actomyosin networks exhibit a scale-free, power-law structure reminiscent of self-organized criticality. The authors explain this phenomenon by invoking the notion of percolation with trapping, in which clusters of voids can develop and persist. This approach also provides additional predictions that will stimulate more experimental work.

[Phys. Rev. E 93, 052414] Published Fri May 20, 2016

Abstract

Synchronization phenomenon is ubiquitous in our complex systems, and many phenomenological models have been proposed and studied analytically and numerically. Among them, the Kuramoto model serves as a prototype model for the phase synchronization of weakly coupled oscillators. In this paper, we study the finiteness of collisions (crossings) among Kuramoto oscillators in the relaxation process toward the phase-locked states and the total number of phase-locked states with positive (Kuramoto) order parameters. For identical oscillators, it is well known that collisions between distinct oscillators cannot occur in finite-time, and we show that there are only a finite number of phase-locked states with positive order parameters. However, for non-identical oscillators, oscillators with different natural frequencies can cross each other in their relaxation process, and estimating the total number of phase-locked states is a nontrivial matter. We show that, for the non-identical case, asymptotic phase-locking is equivalent to the finiteness of collisions, and the total number of phase-locked states with positive order parameters is bounded above by \(2^N\) , where N is the number of oscillators.

We analyse various properties of stochastic Markov processes with multiplicative white noise. We take a single-variable problem as a simple example, and we later extend the analysis to the Landau–Lifshitz–Gilbert equation for the stochastic dynamics of a magnetic moment. In particular, we focus on the non-equilibrium transfer of angular momentum to the magnetization from a spin-polarised current of electrons, a technique which is widely used in the context of spintronics to manipulate magnetic moments. We unveil two hidden dynamical symmetries of the generating functionals of these Markovian multiplicative white-noise processes. One symmetry only holds in equilibrium and we use it to prove generic relations such as the fluctuation-dissipation theorems. Out of equilibrium, we take profit of the symmetry-breaking terms to prove fluctuation theorems. The other symmetry yields strong dynamical relations between correlation and response functions which can notably simplify the numeri...

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 dat...

The interaction topology among the constituents of a complex network plays a crucial role in the network’s evolutionary mechanisms and functional behaviors. However, some network topologies are usually unknown or uncertain. Meanwhile, coupling delays are ubiquitous in various man-made and natural networks. Hence, it is necessary to gain knowledge of the whole or partial topology of a complex dynamical network by taking into consideration communication delay. In this paper, topology identification of complex dynamical networks is investigated via generalized synchronization of a two-layer network. Particularly, based on the LaSalle-type invariance principle of stochastic differential delay equations, an adaptive control technique is proposed by constructing an auxiliary layer and designing proper control input and updating laws so that the unknown topology can be recovered upon successful generalized synchronization. Numerical simulations are provided to illustrate the effectiven...

We present the pedagogical interest for the teaching of special relativity of the 1895 Lorentz transformations, which are a simple modification of the Galilean ones, satisfying the invariance of light velocity at first order in ##IMG## [http://ej.iop.org/images/0143-0807/37/4/045601/ejpaa227fieqn1.gif] {$V/c.$} Since they are also the infinitesimal version of the better known but more complicated 1904 Lorentz ones, they allow us to address the main topics of this teaching (time dilatation, length contraction, relativistic dynamics, invariance of electromagnetism) and to recover standard results through simple integrations or the use of invariants. In addition, they are directly related to important historical issues, including Einstein’s 1911 relativistic approach to gravitation.

Collective chaos is shown to emerge, via a period-doubling cascade, from quasiperiodic partial synchronization in a population of identical inhibitory neurons with delayed global coupling. This system is thoroughly investigated by means of an exact model of the macroscopic dynamics, valid in the thermodynamic limit. The collective chaotic state is reproduced numerically with a finite population, and persists in the presence of weak heterogeneities. Finally, the relationship of the model's dynamics with fast neuronal oscillations is discussed.

For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation may split into an initial exponential decrease, characterized by the maximal Lyapunov exponent, and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. The time scales of both processes can be either of the same or of very different orders of magnitude. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall extent of the attractor) for exceedingly long times and therefore remain partially predictable.

Tests for distinguishing chaos from laminar flow widely use the time evolution of inter-orbital correlations as an indicator. Standard tests however yield mostly ambiguous results when it comes to distinguish partially predictable chaos and laminar flow, which are characterized respectively by attractors of fractally broadened braids and limit cycles. For a resolution we introduce a novel 0-1 indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories, showing that this test robustly discriminates chaos, including partially predictable chaos, from laminar flow. One can use furthermore the finite time cross-correlation of pairs of initially close trajectories to distinguish, for a complete classification, also between strong and partially predictable chaos. We are thus able to identify laminar flow as well as strong and partially predictable chaos in a 0-1 manner solely from the properties of pairs of trajectories.

In this study, we investigate the resilience of duplex networked layers ($\alpha$ and $\beta$) coupled with antagonistic interlinks, each layer of which inhibits its counterpart at the microscopic level, changing the following factors: whether the influence of the initial failures in $\alpha$ remains (quenched (Case Q)) or not (free (Case F)); the effect of intralayer degree-degree correlations in each layer and interlayer degree-degree correlations; and the type of the initial failures, such as random failures (RFs) or targeted attacks (TAs). We illustrate that the percolation processes repeat in both Cases Q and F, although only in Case F are nodes that initially failed reactivated. To analytically evaluate the resilience of each layer, we develop a methodology based on the cavity method for deriving the size of a giant component (GC). Strong hysteresis, which is ignored in the standard cavity analysis, is observed in the repetition of the percolation processes particularly in Case F. To handle this, we heuristically modify interlayer messages for macroscopic analysis, the utility of which is verified by numerical experiments. The percolation transition in each layer is continuous in both Cases Q and F. We also analyze the influences of degree-degree correlations on the robustness of layer $\alpha$, in particular for the case of TAs. The analysis indicates that the critical fraction of initial failures that makes the GC size in layer $\alpha$ vanish depends only on its intralayer degree-degree correlations. Although our model is defined in a somewhat abstract manner, it may have relevance to ecological systems that are composed of endangered species (layer $\alpha$) and invaders (layer $\beta$), the former of which are damaged by the latter whereas the latter are exterminated in the areas where the former are active.

When two pedestrians travelling in opposite directions approach one another, each must decide on which side (the left or the right) they will attempt to pass. If both make the same choice then passing can be completed with ease, while if they make opposite choices an embarrassing stand-off or collision can occur. Pedestrians who encounter each other frequently can establish "social norms" that bias this decision. In this study we investigate the effect of binary decision-making by pedestrians when passing on the dynamics of pedestrian flows in order to study the emergence of a social norm in crowds with a mixture of individual biases. Such a situation may arise, for instance, when individuals from different communities mix at a large sporting event or at transport hubs. We construct a phase diagram that shows that a social norm can still emerge provided pedestrians are sufficiently attentive to the choices of others in the crowd. We show that this collective behaviour has the potential to greatly influence the dynamics of pedestrians, including the breaking of symmetry by the formation of lanes.

Community detection can be considered as a variant of cluster analysis applied to complex networks. For this reason, all existing studies have been using tools derived from this field when evaluating community detection algorithms. However, those are not completely relevant in the context of network analysis, because they ignore an essential part of the available information: the network structure. Therefore, they can lead to incorrect interpretations. In this article, we review these measures, and illustrate this limitation. We propose a modification to solve this problem, and apply it to the three most widespread measures: purity, Rand index and normalized mutual information (NMI). We then perform an experimental evaluation on artificially generated networks with realistic community structure. We assess the relevance of the modified measures by comparison with their traditional counterparts, and also relatively to the topological properties of the community structures. On these data, the modified NMI turns out to provide the most relevant results.

To well understand crowd behavior, microscopic models have been developed in recent decades, in which an individual's behavioral/psychological status can be modeled and simulated. A well-known model is the social-force model innovated by physical scientists (Helbing and Molnar, 1995; Helbing, Farkas and Vicsek, 2000; Helbing et al., 2002). This model has been widely accepted and mainly used in simulation of crowd evacuation in the past decade. A problem, however, is that the testing results of the model were not explained in consistency with the psychological findings, resulting in misunderstanding of the model by psychologists. This paper will bridge the gap between psychological studies and physical explanation about this model. We reinterpret this physics-based model from a psychological perspective, clarifying that the model is consistent with psychological theories on stress, including time-related stress and interpersonal stress. Based on the conception of stress, we renew the model at both micro-and-macro level. Existing simulation results such as faster-is-slower effect will be reinterpreted by Yerkes-Dodson law, and herding and grouping effect are further discussed by integrating attraction into the social force. In brief the social-force model exhibits a bridge between the physics laws and psychological principles regarding crowd motion, and this paper will renew and reinterpret the model on the foundation of psychological studies.

Author(s): Diego Pazó and Ernest Montbrió

Collective chaos is shown to emerge, via a period-doubling cascade, from quasiperiodic partial synchronization in a population of identical inhibitory neurons with delayed global coupling. This system is thoroughly investigated by means of an exact model of the macroscopic dynamics, valid in the the…

[Phys. Rev. Lett.] Published Wed May 11, 2016