Edmilson Roque

We propose a unified approach to nonlinear modal analysis in dissipative oscillatory systems. This approach eliminates conflicting definitions, covers both autonomous and time-dependent systems, and provides exact mathematical existence, uniqueness and robustness results. In this setting, a nonlinear normal mode (NNM) is a set filled with small-amplitude recurrent motions: a fixed point, a periodic orbit or the closure of a quasiperiodic orbit. In contrast, a spectral submanifold (SSM) is an invariant manifold asymptotic to a NNM, serving as the smoothest nonlinear continuation of a spectral subspace of the linearized system along the NNM. The existence and uniqueness of SSMs turns out to depend on a spectral quotient computed from the real part of the spectrum of the linearized system. This quotient may well be large even for small dissipation, thus the inclusion of damping is essential for firm conclusions about NNMs, SSMs and the reduced-order models they yield.

Abstract

Biology achieves novel functions like error correction, ultra-sensitivity and accurate concentration measurement at the expense of free energy through Maxwell Demon-like mechanisms. The design principles and free energy trade-offs have been studied for a variety of such mechanisms. In this review, we emphasize a perspective based on dynamical phases that can explain commonalities shared by these mechanisms. Dynamical phases are defined by typical trajectories executed by non-equilibrium systems in the space of internal states. We find that coexistence of dynamical phases can have dramatic consequences for function vs free energy cost trade-offs. Dynamical phases can also provide an intuitive picture of the design principles behind such biological Maxwell Demons.

Notable recent works have focused on the multi-layer properties of coevolving diseases. We point out that very similar systems play an important role in population ecology. Specifically we study a meta food-web model that was recently proposed by Pillai et al. This model describes a network of species connected by feeding interactions, which spread over a network of spatial patches. Focusing on the essential case, where the network of feeding interactions is a chain, we develop an analytical approach for the computation of the degree distributions of colonized spatial patches for the different species in the chain. This framework allows us to address ecologically relevant questions. Considering configuration model ensembles of spatial networks, we find that there is an upper bound for the fraction of patches that a given species can occupy, which depends only on the networks mean degree. For a given mean degree there is then an optimal degree distribution that comes closest to the upper bound. Notably scale-free degree distributions perform worse than more homogeneous degree distributions if the mean degree is sufficiently high. Because species experience the underlying network differently the optimal degree distribution for one particular species is generally not the optimal distribution for the other species in the same food web. These results are of interest for conservation ecology, where, for instance, the task of selecting areas of old-growth forest to preserve in an agricultural landscape, amounts to the design of a patch network.

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Many online collaboration networks struggle to gain user activity and become self-sustaining due to the ramp-up problem or dwindling activity within the system. Prominent examples include online encyclopedias such as (Semantic) MediaWikis, Question and Answering portals such as StackOverflow, and many others. Only a small fraction of these systems manage to reach self-sustaining activity, a level of activity that prevents the system from reverting to a non-active state. In this paper, we model and analyze activity dynamics in synthetic and empirical collaboration networks. Our approach is based on two opposing and well-studied principles: (i) without incentives, users tend to lose interest to contribute and thus, systems become inactive, and (ii) people are susceptible to actions taken by their peers (social or peer influence). With the activity dynamics model that we introduce in this paper we can represent typical situations of such collaboration networks. For example, activity in a collaborative network, without external impulses or investments, will vanish over time, eventually rendering the system inactive. However, by appropriately manipulating the activity dynamics and/or the underlying collaboration networks, we can jump-start a previously inactive system and advance it towards an active state. To be able to do so, we first describe our model and its underlying mechanisms. We then provide illustrative examples of empirical datasets and characterize the barrier that has to be breached by a system before it can become self-sustaining in terms of critical mass and activity dynamics. Additionally, we expand on this empirical illustration and introduce a new metric p---the Activity Momentum---to assess the activity robustness of collaboration networks.

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Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades. Here we study the dynamics of networks evolving according to preferential attachment, known to approximate well the large-scale growth dynamics of a variety of real networks. We show that this dynamics is Hamiltonian, thus casting the study of complex networks dynamics to the powerful canonical formalism, in which the time evolution of a dynamical system is described by Hamilton's equations. We derive the explicit form of the Hamiltonian that governs network growth in preferential attachment. This Hamiltonian turns out to be nearly identical to graph energy in the configuration model, which shows that the ensemble of random graphs generated by preferential attachment is nearly identical to the ensemble of random graphs with scale-free degree distributions. In other words, preferential attachment generates nothing but random graphs with power-law degree distribution. The extension of the developed canonical formalism for network analysis to richer geometric network models with non-degenerate groups of symmetries may eventually lead to a system of equations describing network dynamics at small scales.

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Identifying a set of influential spreaders in complex networks plays a crucial role in effective information spreading. A simple strategy is to choose top-$r$ ranked nodes as spreaders according to influence ranking method such as PageRank, ClusterRank and $k$-shell decomposition. Besides, some heuristic methods such as hill-climbing, SPIN, degree discount and independent set based are also proposed. However, these approaches suffer from a possibility that some spreaders are so close together that they overlap sphere of influence or time consuming. In this report, we present a simply yet effectively iterative method named VoteRank to identify a set of decentralized spreaders with the best spreading ability. In this approach, all nodes vote in a spreader in each turn, and the voting ability of neighbors of elected spreader will be decreased in subsequent turn. Experimental results on four real networks show that under Susceptible-Infected-Recovered (SIR) model, VoteRank outperforms the traditional benchmark methods on both spreading speed and final affected scale. What's more, VoteRank is also superior to other group-spreader identifying methods on computational time.

In renormalized field theories there are in general one or few fixed points which are accessible by the renormalization-group flow. They can be identified from the fixed-point equations. Exceptionally, an infinite family of fixed points exists, parameterized by a scaling exponent $\zeta$, itself function of a non-renormalizing parameter. Here we report a different scenario with an infinite family of fixed points of which seemingly only one is chosen by the renormalization-group flow. This dynamical selection takes place in systems with an attractive interaction ${\cal V}(\phi)$, as in standard $\phi^4$ theory, but where the potential $\cal V$ at large $\phi$ goes to zero, as e.g. the attraction by a defect.

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Author(s): Bogdan Danila

A simple but efficient spectral approach for analyzing the community structure of complex networks is introduced. It works the same way for all types of networks, by spectrally splitting the adjacency matrix into a “unipartite” and a “multipartite” component. These two matrices reveal the structure …

[Phys. Rev. E 93, 022301] Published Mon Feb 01, 2016

Author(s): Moira L. Steyn-Ross and D. A. Steyn-Ross

Mean-field models of the brain approximate spiking dynamics by assuming that each neuron responds to its neighbors via a naive spatial average that neglects local fluctuations and correlations in firing activity. In this paper we address this issue by introducing a rigorous formalism to enable spati…

[Phys. Rev. E 93, 022402] Published Mon Feb 01, 2016

Author(s): Hidetsugu Sakaguchi and Takayuki Okita

We propose a coupled system of fast and slow phase oscillators. We observe two-step transitions to quasi-periodic motions by direct numerical simulations of this coupled oscillator system. A low-dimensional equation for order parameters is derived using the Ott-Antonsen ansatz. The applicability of …

[Phys. Rev. E] Published Fri Jan 29, 2016

Author(s): Oliver Mülken, Maxim Dolgushev, and Mircea Galiceanu

We study the transport efficiency of excitations on complex quantum networks with loops. For this we consider sequentially growing networks with different topologies of the sequential subgraphs. This can lead either to a universal complete breakdown of transport for complete-graph-like sequential su…

[Phys. Rev. E] Published Thu Jan 28, 2016

Author(s): Wes Viles, Cedric E. Ginestet, Ariana Tang, Mark A. Kramer, and Eric D. Kolaczyk

We consider the problem of distinguishing between different rates of percolation under noise. A statistical model of percolation is constructed allowing for the birth and death of edges as well as the presence of noise in the observations. This graph-valued stochastic process is composed of a latent…

[Phys. Rev. E] Published Fri Jan 29, 2016

We address the issue of the reducibility of the dynamics on a multilayer network to an equivalent process on an aggregated single-layer network. As a typical example of models for opinion formation in social networks, we implement the voter model on a two-layer multiplex network, and we study its dynamics as a function of two control parameters, namely the fraction of edges simultaneously existing in both layers of the network (edge overlap), and the fraction of nodes participating in both layers (interlayer connectivity or degree of multiplexity). We compute the asymptotic value of the number of active links (interface density) in the thermodynamic limit, and the time to reach an absorbing state for finite systems, and we compare the numerical results with the analytical predictions on equivalent single-layer networks obtained through various possible aggregation procedures. We find a large region of parameters where the interface density of large multiplexes gives systematic d...

Many models and real complex systems possess critical thresholds at which the systems shift from one sate to another. The discovery of the early warnings of the systems in the vicinity of critical point are of great importance to estimate how far a system is from a critical threshold. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the fluctuation and geometrical structures of magnetization time series of two-dimensional Ising model around critical point. The Hurst exponent has been confirmed to be a good indicator of phase transition. Increase of the multifractality of the time series have been observed from generalized Hurst exponents and singularity spectrum. Both Long-term correlation and broad probability density function are identified to be the sources of multifractality of time series near critical regime. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties of magnetization time series from complex network perspective. Evolution of the topology quantities such as clustering coefficient, average degree, average shortest path length, density, assortativity and heterogeneity serve as early warnings of phase transition. Those methods and results can provide new insights about analysis of phase transition problems and can be used as early warnings for various complex systems.

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Author(s): Thomas Erneux, Lionel Weicker, Larissa Bauer, and Philipp Hövel

We analyze the FitzHugh-Nagumo equations subject to time-delayed self-feedback in the activator variable. Parameters are chosen such that the steady state is stable independent of the feedback gain and delay t. We demonstrate that stable large amplitude t-periodic oscillations can, however, coexist …

[Phys. Rev. E] Published Tue Jan 26, 2016

A broad range of complex physical and biological systems exhibits scaling laws. The human language is a complex system of words organization. Studies of written texts have revealed intriguing scaling laws that characterize the frequency of words occurrence, rank of words, and growth in the number of distinct words with text length. While studies have predominantly focused on the language system in its written form, such as books, little attention is given to the structure of spoken language. Here we investigate a database of spoken language transcripts and written texts, and we uncover that words organization in both spoken language and written texts exhibits scaling laws, although with different crossover regimes and scaling exponents. We propose a model that provides insight into words organization in spoken language and written texts, and successfully accounts for all scaling laws empirically observed in both language forms.

Author(s): Yan Zhang, Antonios Garas, and Frank Schweitzer

We analyze the controllability of a two-layer network, where driver nodes can be chosen randomly only from one layer. Each layer contains a scale-free network with directed links and the node dynamics depends on the incoming links from other nodes. We combine the in-degree and out-degree values to a…

[Phys. Rev. E 93, 012309] Published Wed Jan 27, 2016

Author(s): Mark J. Panaggio, Daniel M. Abrams, Peter Ashwin, and Carlo R. Laing

Chimera states are dynamical patterns in networks of coupled oscillators in which regions of synchronous and asynchronous oscillation coexist. Although these states are typically observed in large ensembles of oscillators and analyzed in the continuum limit, chimeras may also occur in systems with f…

[Phys. Rev. E 93, 012218] Published Thu Jan 28, 2016

Human impacts on the planet, including anthropogenic climate change, are reshaping ecosystems in unprecedented ways. To meet the challenge of conserving biodiversity in this rapidly changing world, we must understand how ecological assemblages respond to novel conditions (1). However, species in ecosystems are not fixed entities, even without human-induced change. All ecosystems experience natural turnover in species presence and abundance. Taking account of this baseline turnover in conservation planning could play an important role in protecting biodiversity. Author: Anne E. Magurran

As has been shown by Watanabe and Strogatz (WS) [Phys. Rev. Lett., 70, 2391 (1993)], a population of identical phase oscillators, sine-coupled to a common field, is a partially integrable system for any size: its dynamics reduces to equations for several collective variables. Here we develop a perturbation approach for weakly nonidentical ensembles. We calculate corrections to the WS dynamics for two types of perturbations: due to a distribution of natural frequencies and of forcing terms, and due to small white noise. We demonstrate, that in both cases the complex mean field for which the dynamical equations are written, is close up to the leading order in the perturbation to the Kuramoto order parameter. This supports validity of the dynamical reduction suggested by Ott and Antonsen [Chaos, 18, 037113 (2008)] for weakly inhomogeneous populations.

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As has been shown by Watanabe and Strogatz (WS) [Phys. Rev. Lett., 70, 2391 (1993)], a population of identical phase oscillators, sine-coupled to a common field, is a partially integrable system for any size: its dynamics reduces to equations for several collective variables. Here we develop a perturbation approach for weakly nonidentical ensembles. We calculate corrections to the WS dynamics for two types of perturbations: due to a distribution of natural frequencies and of forcing terms, and due to small white noise. We demonstrate, that in both cases the complex mean field for which the dynamical equations are written, is close up to the leading order in the perturbation to the Kuramoto order parameter. This supports validity of the dynamical reduction suggested by Ott and Antonsen [Chaos, 18, 037113 (2008)] for weakly inhomogeneous populations.

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Mastering the game of Go with deep neural networks and tree search

Nature 529, 7587 (2016). doi:10.1038/nature16961

Authors: David Silver, Aja Huang, Chris J. Maddison, Arthur Guez, Laurent Sifre, George van den Driessche, Julian Schrittwieser, Ioannis Antonoglou, Veda Panneershelvam, Marc Lanctot, Sander Dieleman, Dominik Grewe, John Nham, Nal Kalchbrenner, Ilya Sutskever, Timothy Lillicrap, Madeleine Leach, Koray Kavukcuoglu, Thore Graepel & Demis Hassabis

The game of Go has long been viewed as the most challenging of classic games for artificial intelligence owing to its enormous search space and the difficulty of evaluating board positions and moves. Here we introduce a new approach to computer Go that uses ‘value

Google AI algorithm masters ancient game of Go

Nature 529, 7587 (2016). http://www.nature.com/doifinder/10.1038/529445a

Author: Elizabeth Gibney

Deep-learning software defeats human professional for first time.

Propelled by the increasing availability of large-scale high-quality data, advanced data modeling and analysis techniques are enabling many novel and significant scientific understanding of a wide range of complex social, natural, and technological systems. These developments also provide opportunities for studying cultural systems and phenomena -- which can be said to refer to all products of human creativity and way of life. An important characteristic of a cultural product is that it does not exist in isolation from others, but forms an intricate web of connections on many levels. In the creation and dissemination of cultural products and artworks in particular, collaboration and communication of ideas play an essential role, which can be captured in the heterogeneous network of the creators and practitioners of art. In this paper we propose novel methods to analyze and uncover meaningful patterns from such a network using the network of western classical musicians constructed from a large-scale comprehensive Compact Disc recordings data. We characterize the complex patterns in the network landscape of collaboration between musicians across multiple scales ranging from the macroscopic to the mesoscopic and microscopic that represent the diversity of cultural styles and the individuality of the artists.

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Understanding the network structure, and finding out the influential nodes is a challenging issue in the large networks. Identifying the most influential nodes in the network can be useful in many applications like immunization of nodes in case of epidemic spreading, during intentional attacks on complex networks. A lot of research is done to devise centrality measures which could efficiently identify the most influential nodes in the network. There are two major approaches to the problem: On one hand, deterministic strategies that exploit knowledge about the overall network topology in order to find the influential nodes, while on the other end, random strategies are completely agnostic about the network structure. Centrality measures that can deal with a limited knowledge of the network structure are required. Indeed, in practice, information about the global structure of the overall network is rarely available or hard to acquire. Even if available, the structure of the network might be too large that it is too much computationally expensive to calculate global centrality measures. To that end, a centrality measure is proposed that requires information only at the community level to identify the influential nodes in the network. Indeed, most of the real-world networks exhibit a community structure that can be exploited efficiently to discover the influential nodes. We performed a comparative evaluation of prominent global deterministic strategies together with stochastic strategies with an available and the proposed deterministic community-based strategy. Effectiveness of the proposed method is evaluated by performing experiments on synthetic and real-world networks with community structure in the case of immunization of nodes for epidemic control.

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Stability is a desirable property of complex ecosystems. If a community of interacting species is at a stable equilibrium point then it is able to withstand small perturbations to component species' abundances without suffering adverse effects. In ecology, the Jacobian matrix evaluated at an equilibrium point is known as the community matrix, which describes the population dynamics of interacting species. A system's asymptotic short- and long-term behaviour can be determined from eigenvalues derived from the community matrix. Here we use results from the theory of pseudospectra to describe intermediate, transient dynamics. We first recover the established result that the transition from stable to unstable dynamics includes a region of `transient instability', where the effect of a small perturbation to species' abundances---to the population vector---is amplified before ultimately decaying. Then we show that the shift from stability to transient instability can be affected by uncertainty in, or small changes to, entries in the community matrix, and determine lower and upper bounds to the maximum amplitude of perturbations to the population vector. Of five different types of community matrix, we find that amplification is least severe when predator-prey interactions dominate. This analysis is relevant to other systems whose dynamics can be expressed in terms of the Jacobian matrix. Our results will lead to improved understanding of how multiple perturbations to a complex system may irrecoverably break stability.

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We have studied effects of perturbations on the cat cerebral cortex. According to the literature, this cortex structure can be described by a clustered network. This way, we construct a clustered network with the same number of areas as in the cat matrix, where each area is described as a sub-network with small-world property. We focus on the suppression of neuronal phase synchronisation considering different kinds of perturbations. Among the various controlling interventions, we choose three methods: delayed feedback control, external time-periodic driving, and activation of selected neurons. We simulate these interventions to provide a procedure to suppress undesired and pathological abnormal rhythms that can be associated with many forms of synchronisation. In our simulations, we have verified that the efficiency of synchronisation suppression by delayed feedback control is higher than external time-periodic driving and activation of selected neurons for the cat cerebral cortex with the same coupling strengths.

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We have developed a simple cellular automata model for nonlinearly coupled phase oscillators which can exhibit many important collective dynamical states found in other synchronizing systems. The state of our system is specified by a set of integers chosen from a finite set and defined on a lattice with periodic boundary conditions. The integers undergo coupled dynamics over discrete time steps. Depending on the values of coupling strength and range of coupling, we observed interesting collective dynamical phases namely: asynchronous, where all the integers oscillate incoherently; synchronized, where all integers oscillate coherently and also other states of intermediate and time-dependent ordering. We have adapted conventional order parameters used in coupled oscillator systems to measure the amount of synchrony in our system. We have plotted phase diagrams of these order parameters in the plane of strength of coupling and the radius of coupling. The phase diagrams reveal interesting properties about the nature of the synchronizing transition. There are partially ordered states, where there are synchronized clusters which are shown to have a power law distribution of their sizes. The power law exponent is found to be independent of the system parameters. We also discuss the possibility of chimera states in this model. A criterion of persistence of chimera is developed analytically and compared with numerical simulation.

Author(s): Carlo Cafaro, Sean Alan Ali, and Adom Giffin

From the Horowitz-Esposito stochastic thermodynamical description of information flows in dynamical systems [J. M. Horowitz and M. Esposito, Phys. Rev. X4, 031015 (2014)], it is known that while the second law of thermodynamics is satisfied by a joint system, the entropic balance for the subsystems …

[Phys. Rev. E] Published Tue Jan 26, 2016

We have developed a simple cellular automata model for nonlinearly coupled phase oscillators which can exhibit all important collective dynamical states found in other synchronizing systems. Depending on the values of coupling strength and radius of coupling, we observed four phases namely: asynchronous, where all the oscillators oscillate incoherently, chimera, where a single group of connecting oscillators oscillates coherently and rest oscillate incoherently, the multichimera and synchronized, where all oscillators oscillate coherently. We have plotted the phase diagram in the plane described by strength of coupling and the radius of coupling using the strength of incoherence. Furthermore, the chimera and multichimera were distinguished by discontinuity measure. The phase diagrams reveal interesting properties about the nature of the synchronizing transition. The multichimera state is shown to have a power law distribution of synchronized cluster sizes, whose exponent is found to be independent of the system parameters.

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