Thomas

Given their importance in shaping social networks and determining how information or diseases propagate in a population, human interactions are the subject of many data collection efforts. To this aim, different methods are commonly used, from diaries and surveys to wearable sensors. These methods show advantages and limitations but are rarely compared in a given setting. As surveys targeting friendship relations might suffer less from memory biases than contact diaries, it is also interesting to explore how daily contact patterns compare with friendship relations and with online social links. Here we make progresses in these directions by leveraging data from a French high school: face-to-face contacts measured by two concurrent methods, sensors and diaries; self-reported friendship surveys; Facebook links. We compare the data sets and find that most short contacts are not reported in diaries while long contacts have larger reporting probability, with a general tendency to overestimate durations. Measured contacts corresponding to reported friendship can have durations of any length but all long contacts correspond to reported friendships. Online links not associated to reported friendships correspond to short face-to-face contacts, highlighting the different nature of reported friendships and online links. Diaries and surveys suffer from a low sampling rate, showing the higher acceptability of sensor-based platform. Despite the biases, we found that the overall structure of the contact network, i.e., the mixing patterns between classes, is correctly captured by both self-reported contacts and friendships networks. Overall, diaries and surveys tend to yield a correct picture of the structural organization of the contact network, albeit with much less links, and give access to a sort of backbone of the contact network corresponding to the strongest links in terms of cumulative durations.

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

We show that coexisting domains of coherent and incoherent oscillations can be induced in an ensemble of any identical nonlinear dynamical systems using the nonlocal rotational matrix coupling with an asymmetry parameter. Further, chimera is shown to emerge in a wide range of the asymmetry parameter...

[Phys. Rev. E] Published Mon Jun 08, 2015

Author(s): Per Sebastian Skardal, Juan G. Restrepo, and Edward Ott

We investigate the effect of preferentially connecting oscillators with similar frequency to each other in networks of coupled phase oscillators (i.e., frequency assortativity). Using the network Kuramoto model as an example, we find that frequency assortativity can induce chaos in the macroscopic d...

[Phys. Rev. E] Published Mon Jun 08, 2015

Very often, when studying topological or dynamical properties of random scale-free networks, it is tacitly assumed that degree-degree correlations are not present. However, simple constraints, such as the absence of multiple edges and self-loops, can give rise to intrinsic correlations in these structures. In the same way that Fermionic correlations in thermodynamic systems are relevant only in the limit of low temperature, the intrinsic correlations in scale-free networks are relevant only when the extreme values for the degrees grow faster than the square-root of the network size. In this situation, these correlations can significantly affect the dependence of the average degree of the nearest neighbors of a given vertice on this vertices's degree. Here, we introduce an analytical approach that is capable to predict the functional form of this property. Moreover, our results indicate that random scale-free networks models are not self-averaging, that is, the second moment of their degree distribution may vary orders of magnitude among different realizations. Finally, we argue that the intrinsic correlations investigated here may have profound impact on the critical properties of random scale-free networks.

We address here the problem of generating random graphs uniformly from the set of simple connected graphs having a prescribed degree sequence. Our goal is to provide an algorithm designed for practical use both because of its ability to generate very large graphs (efficiency) and because it is easy to implement (simplicity). We focus on a family of heuristics for which we introduce optimality conditions, and show how this optimality can be reached in practice. We then propose a different approach, specifically designed for real-world degree distributions, which outperforms the first one. Based on a conjecture which we argue rigorously and which was confirmed by strong empirical evidence, we finally reduce the best asymptotic complexity bound known so far.

Author(s): Pawan Kumar, Dinesh Kumar Verma, P. Parmananda, and S. Boccaletti

We report experimental evidence of explosive synchronization in coupled chemo-mechanical systems, namely in mercury beating-heart (MBH) oscillators. Connecting four MBH oscillators in a star network configuration and setting natural frequencies of each oscillator in proportion to the number of its l...

[Phys. Rev. E 91, 062909] Published Tue Jun 09, 2015

Publication date: 2 August 2015
Source:Physics Reports, Volume 588
Author(s): Prabir K. Mukherjee
Although the rotator phases of the normal alkanes have been studied for the greater part of the century, it is only in the last two decades that the experimental and theoretical investigations of the structures and phase transitions of these systems have been advanced. This review article presents a comprehensive overview until this date of the theoretical developments and experimental studies in this subject. This article discusses the unified picture of the symmetry, structure and types of rotator phases of normal alkanes. This is followed by a discussion of the order parameters involved in the phase transitions. The application of the various theories to the description of the rotator phase transitions are reviewed comprehensively. The basic ideas of Landau theory and renormalization group theory and its applications to study these transitions are discussed. The current status of the study of the rotator phase transitions in the binary mixtures of alkanes including the nanoparticles and liquid crystal is outlined. A survey is given of existing computer simulation studies of the rotator phase transitions of the normal alkanes. A critical assessment of the experimental and theoretical investigations concerning the elastic properties of the rotator phases is made.

Author(s): Ibrahim Ozken, Deniz Eroglu, Thomas Stemler, Norbert Marwan, G. Baris Bagci, and Jürgen Kurths

Irregular sampling of data sets is one of the challenges often encountered in time series analysis, since traditional methods cannot be applied and the frequently used interpolation approach can corrupt the data and bias the subsequence analysis. Here we present the TrAnsformation-Cost Time-Series (...

[Phys. Rev. E] Published Wed Jun 03, 2015

Author(s): Bernard Sonnenschein, Thomas K. DM. Peron, Francisco A. Rodrigues, Jürgen Kurths, and Lutz Schimansky-Geier

We study two intertwined globally coupled networks of noisy Kuramoto phase oscillators that have the same natural frequency, but differ in their perception of the mean field and their contribution to it. Such a give-and-take mechanism is given by asymmetric in- and out-coupling strengths which can b...

[Phys. Rev. E] Published Wed Jun 03, 2015

The notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny region. In this paper we define the notion of survivability: Given a random initial condition, what is the likelihood that the transient behaviour of a deterministic system does not leave a region of desirable states. We demonstrate the utility of this novel stability measure by considering models from climate science, neuronal networks and power grids. We also show that a semi-analytic lower bound for the survivability of linear systems allows a numerically very efficient survivability analysis in realistic models of power grids. Our numerical and semi-analytic work underlines that the type of stability measured by survivability is not captured by common asymptotic stability measures.

Publication date: 26 July 2015
Source:Physics Reports, Volume 587
Author(s): V.S. Anishchenko, Ya.I. Boev, N.I. Semenova, G.I. Strelkova
We review rigorous and numerical results on the statistics of Poincaré recurrences which are related to the modern development of the Poincaré recurrence problem. We analyze and describe the rigorous results which are achieved both in the classical (local) approach and in the recently developed global approach. These results are illustrated by numerical simulation data for simple chaotic and ergodic systems. It is shown that the basic theoretical laws can be applied to noisy systems if the probability measure is ergodic and stationary. Poincaré recurrences are studied numerically in nonautonomous systems. Statistical characteristics of recurrences are analyzed in the framework of the global approach for the cases of positive and zero topological entropy. We show that for the positive entropy, there is a relationship between the Afraimovich–Pesin dimension, Lyapunov exponents and the Kolmogorov–Sinai entropy either without and in the presence of external noise. The case of zero topological entropy is exemplified by numerical results for the Poincare recurrence statistics in the circle map. We show and prove that the dependence of minimal recurrence times on the return region size demonstrates universal properties for the golden and the silver ratio. The behavior of Poincaré recurrences is analyzed at the critical point of Feigenbaum attractor birth. We explore Poincaré recurrences for an ergodic set which is generated in the stroboscopic section of a nonautonomous oscillator and is similar to a circle shift. Based on the obtained results we show how the Poincaré recurrence statistics can be applied for solving a number of nonlinear dynamics issues. We propose and illustrate alternative methods for diagnosing effects of external and mutual synchronization of chaotic systems in the context of the local and global approaches. The properties of the recurrence time probability density can be used to detect the stochastic resonance phenomenon. We also discuss how the fractal dimension of chaotic attractors can be estimated using the Poincaré recurrence statistics.

Author(s): P. G. Kevrekidis, D. E. Pelinovsky, and A. Saxena

We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. This instability is due to the nonlinearity-induced coupling of the linearization’s internal modes of negative energy with the continuous spectrum....

[Phys. Rev. Lett. 114, 214101] Published Fri May 29, 2015

Author(s): Carsten Grabow, Stefan Grosskinsky, Jürgen Kurths, and Marc Timme

Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph Laplacian, or a similar linear operator. The structure of networks ...

[Phys. Rev. E 91, 052815] Published Wed May 27, 2015

Nature Methods 12, 481 (2015). doi:10.1038/nmeth.3392

Authors: Tobias Pietzsch, Stephan Saalfeld, Stephan Preibisch & Pavel Tomancak

In the case of graph partitioning, the emergence of localized eigenvectors can cause the standard spectral method to fail. To overcome this problem, the spectral method using a non-backtracking matrix was proposed. Based on numerical experiments on several examples of real networks, it is clear that the non-backtracking matrix does not exhibit localization of eigenvectors. However, we show that localized eigenvectors of the non-backtracking matrix can exist outside the spectral band, which may lead to deterioration in the performance of graph partitioning.

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Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the $dk$-series, a complete set of basic characteristics of the network structure, to study the statistical dependencies between different network properties. We consider six real networks---the Internet, US airport network, human protein interactions, technosocial web of trust, English word network, and an fMRI map of the human brain---and find that many important local and global structural properties of these networks are closely reproduced by $dk$-random graphs whose degree distributions, degree correlations, and clustering are as in the corresponding real network. We discuss important conceptual, methodological, and practical implications of this evaluation of network randomness, and release software to generate $dk$-random graphs.

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A substantial volume of research has been devoted to studies of community structure in networks, but communities are not the only possible form of large-scale network structure. Here we describe a broad extension of community structure that encompasses traditional communities but includes a wide range of generalized structural patterns as well. We describe a principled method for detecting this generalized structure in empirical network data and demonstrate with real-world examples how it can be used to learn new things about the shape and meaning of networks.

Many natural, complex systems are remarkably stable thanks to an absence of feedback acting on their elements. When described as networks, these exhibit few or no cycles, and associated matrices have small leading eigenvalues. It has been suggested that this architecture can confer advantages to the system as a whole, such as `qualitative stability', but this observation does not in itself explain how a loopless structure might arise. We show here that the number of feedback loops in a network, as well as the eigenvalues of associated matrices, are determined by a structural property called trophic coherence, a measure of how neatly nodes fall into distinct levels. Our theory correctly classifies a variety of networks -- including those derived from genes, metabolites, species, neurons, words, computers and trading nations -- into two distinct regimes of high and low feedback, and provides a null model to gauge the significance of related magnitudes. Since trophic coherence suppresses feedback, whereas an absence of feedback alone does not lead to coherence, our work suggests that the reasons for `looplessness' in nature should be sought in coherence-inducing mechanisms.

Publication date: 20 July 2015
Source:Physics Reports, Volume 586
Author(s): D. Hennig, C. Mulhern, L. Schimansky-Geier, G.P. Tsironis, P. Hänggi
The physics of activated escape of objects out of a metastable state plays a key role in diverse scientific areas involving chemical kinetics, diffusion and dislocation motion in solids, nucleation, electrical transport, motion of flux lines superconductors, charge density waves, and transport processes of macromolecules and astrophysics, to name but a few. The underlying activated processes present the multidimensional extension of the Kramers problem of a single Brownian particle. In comparison to the latter case, however, the dynamics ensuing from the interactions of many coupled units can lead to intriguing novel phenomena that are not present when only a single degree of freedom is involved. In this review we report on a variety of such phenomena that are exhibited by systems consisting of chains of interacting units in the presence of potential barriers. In the first part we consider recent developments in the case of a deterministic dynamics driving cooperative escape processes of coupled nonlinear units out of metastable states. The ability of chains of coupled units to undergo spontaneous conformational transitions can lead to a self-organised escape. The mechanism at work is that the energies of the units become re-arranged, while keeping the total energy conserved, in forming localised energy modes that in turn trigger the cooperative escape. We present scenarios of significantly enhanced noise-free escape rates if compared to the noise-assisted case. The second part of the review deals with the collective directed transport of systems of interacting particles overcoming energetic barriers in periodic potential landscapes. Escape processes in both time-homogeneous and time-dependent driven systems are considered for the emergence of directed motion. It is shown that ballistic channels immersed in the associated mixed high-dimensional phase space are at the source for the directed long-range transport. Open problems and future directions are discussed in order to invigorate readers to engage in their own research.

The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their topological structure can be diverse, resulting from different mechanisms including multiplicative processes and optimization. In spatial networks or in graphs where cost constraints are at work, as it occurs in a plethora of situations from power grids to the wiring of neurons in the brain, optimization plays an important part in shaping their organization. In this paper we study network designs resulting from a Pareto optimization process, where different simultaneous constraints are the targets of selection. We analyze three variations on a problem finding phase transitions of different kinds. Distinct phases are associated to different arrangements of the connections; but the need of drastic topological changes does not determine the presence, nor the nature of the phase transitions encountered. Instead, the functions under optimization do play a determinant role. This reinforces the view that phase transitions do not arise from intrinsic properties of a system alone, but from the interplay of that system with its external constraints.

Our ability to control complex systems is a fundamental challenge of contemporary science. Recently introduced tools to identify the driver nodes, nodes through which we can achieve full control, predict the existence of multiple control configurations, prompting us to classify each node in a network based on their role in control. Accordingly a node is critical, intermittent or redundant if it acts as a driver node in all, some or none of the control configurations. Here we develop an analytical framework to identify the category of each node, leading to the discovery of two distinct control modes in complex systems: centralized vs distributed control. We predict the control mode for an arbitrary network and show that one can alter it through small structural perturbations. The uncovered bimodality has implications from network security to organizational research and offers new insights into the dynamics and control of complex systems.

A Sleeping Beauty (SB) in science refers to a paper whose importance is not recognized for several years after publication. Its citation history exhibits a long hibernation period followed by a sudden spike of popularity. Previous studies suggest a relative scarcity of SBs. The reliability of this conclusion is, however, heavily dependent on identification methods based on arbitrary threshold parameters for sleeping time and number of citations, applied to small or monodisciplinary bibliographic datasets. Here we present a systematic, large-scale, and multidisciplinary analysis of the SB phenomenon in science. We introduce a parameter-free measure that quantifies the extent to which a specific paper can be considered an SB. We apply our method to 22 million scientific papers published in all disciplines of natural and social sciences over a time span longer than a century. Our results reveal that the SB phenomenon is not exceptional. There is a continuous spectrum of delayed recognition where both the hibernation period and the awakening intensity are taken into account. Although many cases of SBs can be identified by looking at monodisciplinary bibliographic data, the SB phenomenon becomes much more apparent with the analysis of multidisciplinary datasets, where we can observe many examples of papers achieving delayed yet exceptional importance in disciplines different from those where they were originally published. Our analysis emphasizes a complex feature of citation dynamics that so far has received little attention, and also provides empirical evidence against the use of short-term citation metrics in the quantification of scientific impact.

Cascading failures are one of the main reasons for blackouts in electrical power grids. Stable power supply requires a robust design of the power grid topology. Currently, the impact of the grid structure on the grid robustness is mainly assessed by purely topological metrics, that fail to capture the fundamental properties of the electrical power grids such as power flow allocation according to Kirchhoff's laws. This paper deploys the effective graph resistance as a metric to relate the topology of a grid to its robustness against cascading failures. Specifically, the effective graph resistance is deployed as a metric for network expansions (by means of transmission line additions) of an existing power grid. Four strategies based on network properties are investigated to optimize the effective graph resistance, accordingly to improve the robustness, of a given power grid at a low computational complexity. Experimental results suggest the existence of Braess's paradox in power grids: bringing an additional line into the system occasionally results in decrease of the grid robustness. This paper further investigates the impact of the topology on the Braess's paradox, and identifies specific sub-structures whose existence results in Braess's paradox. Careful assessment of the design and expansion choices of grid topologies incorporating the insights provided by this paper optimizes the robustness of a power grid, while avoiding the Braess's paradox in the system.

The spectral properties of the adjacency matrix provide a trove of information about the structure and function of complex networks. In particular, the largest eigenvalue and its associated principal eigenvector are crucial in the understanding of nodes centrality and the unfolding of dynamical processes. Here we show that two distinct types of localization of the principal eigenvector may occur in heterogeneous networks. For synthetic networks with degree distribution $P(q) \sim q^{-\gamma}$, localization occurs on the largest hub if $\gamma>5/2$; for $\gamma<5/2$ a new type of localization arises on a mesoscopic subgraph associated with the shell with the largest index in the $K$-core decomposition. Similar evidence for the existence of distinct localization modes is found in the analysis of real-world networks. Our results open a new perspective on dynamical processes on networks and on a recently proposed alternative measure of node centrality based on the non-backtracking matrix.

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Degree correlation is an important topological property common to many real-world networks. In this paper, the statistical measures for characterizing the degree correlation in networks are investigated analytically. We give an exact proof of the consistency for the statistical measures, reveal the general linear relation in the degree correlation, which provide a simple and interesting perspective on the analysis of the degree correlation in complex networks. By using the general linear analysis, we investigate the perturbation of the degree correlation in complex networks caused by the addition of few nodes and the rich club. The results show that the assortativity of homogeneous networks such as the ER graphs is easily to be affected strongly by the simple structural changes, while it has only slight variation for heterogeneous networks with broad degree distribution such as the scale-free networks. Clearly, the homogeneous networks are more sensitive for the perturbation than the heterogeneous networks.

Author(s): Ali Faqeeh, Sergey Melnik, and James P. Gleeson

We introduce network L-cloning, a technique for creating ensembles of random networks from any given real-world or artificial network. Each member of the ensemble is an L-cloned network constructed from L copies of the original network. The degree distribution of an L-cloned network and, more import...

[Phys. Rev. E 91, 052807] Published Thu May 14, 2015

The cluster synchronization (CS) is a very important characteristic for the higher harmonic cou- pling Kuramoto system. A novel method from the symmetry transformation is provided, and it gives CS a profoundly mathematical explanation and clear physical annotation. Detailed numerical studies for the order parameters in various conditions confirm the theoretical predictions from this new view of the symmetry transformation. The work is very beneficial to the further study on CS in various systems.

We consider non-Gaussian ensembles of random normal matrices with the constraint that the ensembles are invariant under unitary transformations. We show that the level density of eigenvalues exhibits disk or ring structure in the complex plane. We also show that the n -eigenvalue correlation and the spacing distribution are universal and identical to that of complex (Gaussian) Ginibre ensemble. Our results are confirmed by Monte Carlo calculations. We verify the universality for dissipative quantum kicked rotor systems.

Markov chains (MCs) are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution (DD), since they simply require a procedure for rewiring edges. The major challenge is to find the right number of steps to run such a chain, so that we generate truly independent samples. Theoretical bounds for mixing times of these MCs are too large to be practically useful. Practitioners have no useful guide for choosing the length, and tend to pick numbers fairly arbitrarily. We give a principled mathematical argument showing that it suffices for the length to be proportional to the number of the desired number of edges. We also prescribe a method for choosing this proportionality constant. We run a series of experiments showing that the distributions of common graph properties converge in this time, providing empirical evidence for our claims.

Multilayer relationships among entities and information about entities must be accompanied by the means to analyse, visualize and obtain insights from such data. We present open-source software (muxViz) that contains a collection of algorithms for the analysis of multilayer networks, which are an important way to represent a large variety of complex systems throughout science and engineering. We demonstrate the ability of muxViz to analyse and interactively visualize multilayer data using empirical genetic, neuronal and transportation networks. Our software is available at https://github.com/manlius/muxViz.