Edmilson Roque

What do societies, the Internet, and the human brain have in common? They are all examples of complex relational systems, whose emerging behaviours are largely determined by the non-trivial networks of interactions among their constituents, namely individuals, computers, or neurons, rather than the properties of the units themselves. In the last two decades, network scientists have proposed models of increasing complexity to better understand real-world systems. Only recently we have realised that multiplexity, i.e. the coexistence of several types of interactions among the constituents of a complex system, is responsible for substantial qualitative and quantitative differences in the type and variety of behaviours that a complex system can exhibit. As a consequence, multilayer and multiplex networks have become a hot topic in complexity science. Here we provide an overview of some of the measures proposed so far to characterise the structure of multiplex networks, and a selection of models aiming at reproducing those structural properties and quantifying their statistical significance. Focusing on a subset of relevant topics, this brief review is a quite comprehensive introduction to the most basic tools for the analysis of multiplex networks observed in the real-world. The wide applicability of multiplex networks as a framework to model complex systems in different fields, from biology to social sciences, and the colloquial tone of the paper will make it an interesting read for researchers working on both theoretical and experimental analysis of networked systems.

Superparamagnetic tunnel junctions are nanostructures that auto-oscillate stochastically under the effect of thermal noise. Recent works showed that despite their stochasticity, such junctions possess a capability to synchronize to subthreshold voltage drives, in a way that can be enhanced or controlled by adding noise. In this work, we investigate a system composed of two electrically coupled junctions, connected in series to a periodic voltage source. We make use of numerical simulations and of an analytical model to demonstrate that both junctions can be phase-locked to the drive, in phase or in anti-phase. This synchronization phenomenon can be controlled by both thermal and electrical noises, although the two types of noises induce qualitatively different behaviors. Namely, thermal noise can stabilize a regime where one junction is phase-locked to the drive voltage while the other is blocked in one state. On the contrary, electrical noise causes the junctions to have highly correlated behaviors and thus cannot induce the latter. These results open the way for the design of superparamagnetic tunnel junctions that can perform computation through synchronization, and which harvest the largest part of their energy consumption from thermal noise.

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In the last decade network science has shed new light on the anatomical connectivity and on correlations in the activity of different areas of the human brain. The study of brain networks has made possible in fact to detect the central areas of a neural system, and to identify its building blocks by looking at overabundant small subgraphs, known as motifs. However, network analysis of the brain has so far mainly focused on structural and functional networks as separate entities. The recently developed mathematical framework of multi-layer networks allows to perform a multiplex analysis of the human brain where the structural and functional layers are considered at the same time. In this work we describe how to classify subgraphs in multiplex networks, and we extend motif analysis to networks with many layers. We then extract multi-layer motifs in brain networks of healthy subjects by considering networks with two layers, respectively obtained from diffusion and functional magnetic resonance imaging. Results indicate the statistically significance of subgraphs where the presence of a physical connection between two areas (link at the structural layer) coexists with positive correlations in their activity (positive link in the functional layer). Finally, we investigate the existence of a reinforcement mechanism between the two layers by looking at how the presence of a link in one layer depends on the intensity of the connection in the other one. Showing that functional connectivity is non-trivially constrained by the underlying anatomical network, our work contributes to a better understanding of the interplay between structure and function in the human brain.

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Clustering algorithms for large networks typically use the modularity score to compare which partitions better represent modular structure in the data. Given a network, the modularity of a partition of the vertex set is a number in [0, 1) which measures the extent to which edge density is higher within parts than between parts; and the modularity of the network is the maximum modularity of any partition. We show that random cubic graphs usually have modularity in the interval (0.666, 0.804); and random r-regular graphs for large r usually have modularity ${\Theta}(1/\sqrt{r})$. Our results can give thresholds for the statistical significance of clustering found in large regular networks.

The modularity of cycles and low degree trees is known to be asymptotically 1. We extend these results to all graphs whose product of treewidth and maximum degree is much less than the number of edges. This shows for example that random planar graphs typically have modularity close to 1.

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What do societies, the Internet, and the human brain have in common? They are all examples of complex relational systems, whose emerging behaviours are largely determined by the non-trivial networks of interactions among their constituents, namely individuals, computers, or neurons, rather than the properties of the units themselves. In the last two decades, network scientists have proposed models of increasing complexity to better understand real-world systems. Only recently we have realised that multiplexity, i.e. the coexistence of several types of interactions among the constituents of a complex system, is responsible for substantial qualitative and quantitative differences in the type and variety of behaviours that a complex system can exhibit. As a consequence, multilayer and multiplex networks have become a hot topic in complexity science. Here we provide an overview of some of the measures proposed so far to characterise the structure of multiplex networks, and a selection of models aiming at reproducing those structural properties and quantifying their statistical significance. Focusing on a subset of relevant topics, this brief review is a quite comprehensive introduction to the most basic tools for the analysis of multiplex networks observed in the real-world. The wide applicability of multiplex networks as a framework to model complex systems in different fields, from biology to social sciences, and the colloquial tone of the paper will make it an interesting read for researchers working on both theoretical and experimental analysis of networked systems.

We introduce a new Self-Organized Criticality (SOC) model for simulating price evolution in an artificial financial market, based on a multilayer network of traders. The model also implements, in a quite realistic way with respect to previous studies, the order book dy- namics, by considering two assets with variable fundamental prices. Fat tails in the probability distributions of normalized returns are observed, together with other features of real financial markets.

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In the last decade, network science has shed new light both on the structural (anatomical) and on the functional (correlations in the activity) connectivity among the different areas of the human brain. The analysis of brain networks has made possible to detect the central areas of a neural system, and to identify its building blocks by looking at overabundant small subgraphs, known as motifs. However, network analysis of the brain has so far mainly focused on anatomical and functional networks as separate entities. The recently developed mathematical framework of multi-layer networks allows to perform an analysis of the human brain where the structural and functional layers are considered together. In this work we describe how to classify the subgraphs of a multiplex network, and we extend motif analysis to networks with an arbitrary number of layers. We then extract multi-layer motifs in brain networks of healthy subjects by considering networks with two layers, anatomical and functional, respectively obtained from diffusion and functional magnetic resonance imaging. Results indicate that subgraphs in which the presence of a physical connection between brain areas (links at the structural layer) coexists with a non-trivial positive correlation in their activities are statistically overabundant. Finally, we investigate the existence of a reinforcement mechanism between the two layers by looking at how the probability to find a link in one layer depends on the intensity of the connection in the other one. Showing that functional connectivity is non-trivially constrained by the underlying anatomical network, our work contributes to a better understanding of the interplay between structure and function in the human brain.

ArXiv preprint server plans multimillion-dollar overhaul

Nature 534, 7609 (2016). http://www.nature.com/doifinder/10.1038/534602a

Author: Richard Van Noorden

Users urge caution in revamp of service at the heart of physics.

Meet the challenge of interdisciplinary science

Nature 534, 7609 (2016). doi:10.1038/534589b

Problems of modern society demand collaborative research.

We analyse the possible dynamical states emerging for two symmetrically pulse coupled populations of leaky integrate-and-fire neurons. In particular, we observe broken symmetry states in this set-up: namely, breathing chimeras, where one population is fully synchronized and the other is in a state of partial synchronization (PS) as well as generalized chimera states, where both populations are in PS, but with different levels of synchronization. Symmetric macroscopic states are also present, ranging from quasi-periodic motions, to collective chaos, from splay states to population anti-phase partial synchronization. We then investigate the influence disorder, random link removal or noise, on the dynamics of collective solutions in this model. As a result, we observe that broken symmetry chimera-like states, with both populations partially synchronized, persist up to 80 \% of broken links and up to noise amplitudes 8 \% of threshold-reset distance. Furthermore, the introduction of disorder on symmetric chaotic state has a constructive effect, namely to induce the emergence of chimera-like states at intermediate dilution or noise level.

Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial distribution of time delays with regard to synchronization, by decomposing it into patterns and therefore reducing the stability analysis into the tractable problem of a finite set of delay-coupled differential equations. We analyse delay-structured networks of phase oscillators and we find that, depending on the heterogeneity of the delays, the oscillators group in phase-shifted, anti-phase, steady, and non-stationary clusters, and analytically compute their stability boundaries. These results find direct application in the study of brain oscillations.

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For a network formed by nodes and undirected links between pairs of nodes, the network optimal attack problem aims at deleting a minimum number of target nodes to break the network down into many small components. This problem is intrinsically related to the feedback vertex set problem that was successfully tackled by spin glass theory and an associated belief propagation-guided decimation (BPD) algorithm [H.-J. Zhou, Eur. Phys. J. B 86 (2013) 455]. In the present work we apply the BPD alrogithm (which has approximately linear time complexity) to the network optimal attack problem, and demonstrate that it has much better performance than a recently proposed Collective Information algorithm [F. Morone and H. A. Makse, Nature 524 (2015) 63--68] for different types of random networks and real-world network instances. The BPD-guided attack scheme often induces an abrupt collapse of the whole network, which may make it very difficult to defend.

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Collective motion of large human crowds often depends on their density. In extreme cases like heavy metal concerts and Black Friday sales events, motion is dominated by physical interactions instead of conventional social norms. Here, we study an active matter model inspired by situations when large groups of people gather at a point of common interest. Our analysis takes an approach developed for jammed granular media and identifies Goldstone modes, soft spots, and stochastic resonance as structurally-driven mechanisms for potentially dangerous emergent collective motion.

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We analyse the possible dynamical states emerging for two symmetrically pulse coupled populations of leaky integrate-and-fire neurons. In particular, we observe broken symmetry states in this set-up: namely, breathing chimeras, where one population is fully synchronized and the other is in a state of partial synchronization (PS) as well as generalized chimera states, where both populations are in PS, but with different levels of synchronization. Symmetric macroscopic states are also present, ranging from quasi-periodic motions, to collective chaos, from splay states to population anti-phase partial synchronization. We then investigate the influence disorder, random link removal or noise, on the dynamics of collective solutions in this model. As a result, we observe that broken symmetry chimera-like states, with both populations partially synchronized, persist up to 80 \% of broken links and up to noise amplitudes 8 \% of threshold-reset distance. Furthermore, the introduction of disorder on symmetric chaotic state has a constructive effect, namely to induce the emergence of chimera-like states at intermediate dilution or noise level.

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Author(s): Salomon Mugisha and Hai-Jun Zhou

For a network formed by nodes and undirected links between pairs of nodes, the network optimal attack problem aims at deleting a minimum number of target nodes to break the network down into many small components. This problem is intrinsically related to the feedback vertex set problem that was succ…

[Phys. Rev. E] Published Mon Jun 27, 2016

Author(s): M. A. Lopes, E. M. Lopes, S. Yoon, J. F. F. Mendes, and A. V. Goltsev

We study the impact of random pinning fields on the emergence of synchrony in the Kuramoto model on complete graphs and uncorrelated random complex networks. We consider random fields with uniformly distributed directions and homogeneous and heterogeneous (Gaussian) field magnitude distribution. In …

[Phys. Rev. E] Published Tue Jun 28, 2016

We study a nonlocal diffusion equation approximating the dynamics of coupled phase oscillators on large graphs. Under appropriate assumptions, the model has a family of steady state solutions called twisted states. We prove a sufficient condition for stability of twisted states with respect to perturbations in the Sobolev and BV spaces. As an application, we study stability of twisted states in the Kuramoto model on small-world graphs.

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In this article, we present a systematic study of the critical behavior of phase oscillators with multiplicative noise from a thermodynamic equilibrium approach. We have already presented the thermodynamics of phase noise oscillators and mapped out in detail the behavior of free energy, entropy, and specific heat in a previous work [P. D. Pinto, F.A. Oliveira, A.L.A. Penna, Phys. Rev. E 93, 052220 (2016)], in which we also introduced the concept of synchronization field. This proved to be important in order to understand the effect of multiplicative noise in the synchronization of the system. Using this approach, our aim is now to study analytically the critical behavior of this system from which we derive a fluctuation-dissipation relation as well as the critical exponents associated with the order parameter, specific heat, and susceptibility. We show that the exponents obey the Rushbrooke and Widom scaling laws.

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Author(s): Roberto Franzosi, Domenico Felice, Stefano Mancini, and Marco Pettini

A central issue in the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate with a—in principle, any—network a differentiable object (a Rieman…

[Phys. Rev. E 93, 062317] Published Mon Jun 27, 2016

Author(s): Markus Brede and Alexander C. Kalloniatis

We present an analysis of conditions under which the dynamics of a frustrated Kuramoto—or Kuramoto-Sakaguchi—model on sparse networks can be tuned to enhance synchronization. Using numerical optimization techniques, linear stability, and dimensional reduction analysis, a simple tuning scheme for set…

[Phys. Rev. E 93, 062315] Published Thu Jun 23, 2016

That any two persons are separated by a relatively small number of intermediary contacts -- the "small-world" phenomenon -- is a surprising but well established regularity in human social networks. To date, network science has ignored the question of whether the small world phenomenon manifests itself in similar ways across dyadic classes defined by individual traits, such as age or sex. To address this gap in the literature, we explore the phenomenon of "age-specific small worlds" by employing a mobile phone network built from billions of communication events approximating interaction patterns at a societal scale. We observe the average distance between any pair of users is 9.52, corresponding to nine-and-a-half degrees of separation. More importantly, we show that there is a systematic relationship between age and the average distance connecting that person to others, with some age groups falling below this average quantity while others falling above. Young people live in the "smallest world," being separated from other young people and their parent's generation via a comparatively small number of intermediaries. Older people live in the "least small world," being separated from their same age peers and their younger counterparts by a relatively large number of intermediaries. Middle age-people fall in between, being sociometrically close to both younger and older generations. However, there exists no significant difference of this age-effect on small world size between men and women. In all these results demonstrate that age-group heterogeneity of the small world can be traced to well-known social mechanisms affecting the way that age interacts with overall volume of connectivity and the relative prevalence of kin ties and non-kin ties, and may have important implications for our understanding of information cascades, diffusion phenomena, and the localized spread of fads and fashions.

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Self-rotation occurs in an exciton-polariton condensate in a two-dimensional semiconductor microcavity pumped by a nonresonant Gaussian laser beam. A wave packet of the condensate spontaneously rotates around the center of the pumped region at a constant frequency breaking the rotation symmetry of the system. When two self-rotating condensates are created with an appropriate distance, synchronization occurs between the dynamics of the self-rotating condensates.

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Author(s): Diego Pazó, Juan M. López, and Antonio Politi

We show that in generic one-dimensional Hamiltonian lattices the diffusion coefficient of the maximum Lyapunov exponent diverges in the thermodynamic limit. We trace this back to the long-range correlations associated with the evolution of the hydrodynamic modes. In the case of normal heat transport…

[Phys. Rev. Lett.] Published Thu Jun 23, 2016

Author(s): Gareth J. Baxter, Ginestra Bianconi, Rui A. da Costa, Sergey N. Dorogovtsev, and José F. F. Mendes

We develop the theory of sparse multiplex networks with partially overlapping links based on their local tree-likeness. This theory enables us to find the giant mutually connected component in a two-layer multiplex network with arbitrary correlations between connections of different types. We find t…

[Phys. Rev. E] Published Tue Jun 21, 2016

Author(s): V. K. Chandrasekar, R. Gopal, D. V. Senthilkumar, and M. Lakshmanan

We report the emergence of a new collective dynamical state, namely phase-flip chimera, from an ensemble of identical nonlinear oscillators that are coupled indirectly via the dynamical variables from a common environment, which in turn are nonlocally coupled. The phase-flip chimera is characterized…

[Phys. Rev. E] Published Tue Jun 21, 2016

Author(s): Hideaki Yamamoto, Shigeru Kubota, Yudai Chida, Mayu Morita, Satoshi Moriya, Hisanao Akima, Shigeo Sato, Ayumi Hirano-Iwata, Takashi Tanii, and Michio Niwano

We study the effect of network size on synchronized activity in living neuronal networks. Dissociated cortical neurons form synaptic connections in culture and generate synchronized spontaneous activity by 10 days in vitro. Using micropatterned surfaces to extrinsically control the size of neuronal …

[Phys. Rev. E] Published Wed Jun 22, 2016

Author(s): V. Pérez-Muñuzuri, D. Garaboa-Paz, and A. P. Muñuzuri

The problem of synchronization of finite-size chemical oscillators described by active inertial particles is addressed for situations in which they are immersed in a reacting non-stationary chaotic flow. Active substances in the fluid will be modeled by Lagrangian particles closely following the flu…

[Phys. Rev. E] Published Wed Jun 22, 2016