Thomas

Based on the basin of attraction, the basin stability is quantified to measure a system's ability to regain an equilibrium state subjected to even large perturbations. In this letter, we demonstrate a novel phenomenon uncovered by the basin stability that in complex networks of second-order Kuramoto models successively undergoes two first-order transitions: an onset transition from an unstable to a locally stable synchronous state, and a suffusing transition from a locally stable to a globally stable synchronous state; we call this sequence onset-suffusing transitions . We provide an analytical treatment of basin stability by a mean-field analysis. Our findings are in good agreement with simulations and fundamentally deepen the understanding of stability of microscopic mechanisms towards synchronization.

Cooperative behavior, which pervades nature, can be significantly enhanced when agents interact in a structured rather than random way; however, the key structural factors that affect cooperation are not well understood. Moreover, the role structure plays with cooperation has largely been studied through observing overall cooperation rather than the underlying components that together shape cooperative behavior. In this paper we address these two problems by first applying evolutionary games to a wide range of networks, where agents play the Prisoner's Dilemma with a three-component stochastic strategy, and then analyzing agent-based simulation results using principal component analysis. With these methods we study the evolution of trust, reciprocity and forgiveness as a function of several structural parameters. This work demonstrates that community structure, represented by network modularity, among all the tested structural parameters, has the most significant impact on the emergence of cooperative behavior, with forgiveness showing the largest sensitivity to community structure. We also show that increased community structure reduces the dispersion of trust and forgiveness, thereby reducing the network-level uncertainties for these two components; graph transitivity and degree also significantly influence the evolutionary dynamics of the population and the diversity of strategies at equilibrium.

Scientific Reports 5 doi: 10.1038/srep09340

Author(s): Michael Small, Yingying Li, Thomas Stemler, and Kevin Judd

Preferential attachment, by which new nodes attach to existing nodes with probability proportional to the existing nodes' degree, has become the standard growth model for scale-free networks, where the asymptotic probability of a node having degree k is proportional to k^−γ. However, the motivation f...

[Phys. Rev. E 91, 042801] Published Tue Apr 07, 2015

Preferential attachment --- by which new nodes attach to existing nodes with probability proportional to the existing nodes' degree --- has become the standard growth model for scale-free networks, where the asymptotic probability of a node having degree $k$ is proportional to $k^{-\gamma}$. However...

We introduce network $L$-cloning, a novel 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...

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

We study the impact of network heterogeneity on relaxation dynamics of the Kuramoto model on uncorrelated complex networks with scale-free degree distributions. Using the Ott-Antonsen method and the annealed-network approach, we find that the critical behavior of the relaxation rate near the synchro...

[Phys. Rev. E 91, 032814] Published Mon Mar 30, 2015

Author(s): P. Van Mieghem and R. van de Bovenkamp

Mean-field approximations (MFAs) are frequently used in physics. When a process (such as an epidemic or a synchronization) on a network is approximated by MFA, a major hurdle is the determination of those graphs for which MFA is reasonably accurate. Here, we present an accuracy criterion for Markovi...

[Phys. Rev. E 91, 032812] Published Mon Mar 30, 2015

Network motifs are generally studied to characterize the local interaction patterns of networks. Here, we apply the concept of a motif profile to a synchronous Boolean network model of the formation of mutualistic ecological communities, focusing on four-node subgraphs. We consider the process by which networks dynamically progress from a random initial condition to an attractor (steady state or limit cycle, collectively viewed in this context as a stable community). While the subgraphs are not classified as motifs in the usual sense of the term, we show that subgraphs with predominantly stabilizing (i.e. beneficial for species persistence) interactions are generally composed of species that are present in the attractor. The converse also holds: subgraphs with predominantly destabilizing (i.e. detrimental for species persistence) interactions are more commonly composed of species that are present in the community only transiently. We discuss our findings in the context of mutualistic ecological networks, and argue that the dynamic motif profile may provide a valuable analytical tool in other networks representing complex dynamic systems.

We survey the concept of assortativity, starting from its original definition by Newman in 2002. Degree assortativity is the most commonly used form of assortativity. Degree assortativity is extensively used in network science. Since degree assortativity alone is not sufficient as a graph analysis tool, assortativity is usually combined with other graph metrics. Much of the research on assortativity considers undirected, non-weighted networks. The research on assortativity needs to be extended to encompass also directed links and weighted links. In addition, the relation between assortativity and line graphs, complementary graphs and graph spectra needs further work, to incorporate directed graphs and weighted links. The present survey paper aims to summarize the work in this area and provides a new scope of research.

Author(s): A. V. Ivlev, J. Bartnick, M. Heinen, C.-R. Du, V. Nosenko, and H. Löwen

A tenet of classical physics—Newton’s third law—can in fact be violated when the interacting particles are embedded in a nonequilibrium environment. Researchers present the statistical foundations of many-body systems with such interactions.

[Phys. Rev. X 5, 011035] Published Thu Mar 26, 2015

Author(s): I. Sendiña-Nadal, I. Leyva, A. Navas, J. A. Villacorta-Atienza, J. A. Almendral, Z. Wang, and S. Boccaletti

We study the organization of finite-size, large ensembles of phase oscillators networking via scale-free topologies in the presence of a positive correlation between the oscillators' natural frequencies and the network's degrees. Under those circumstances, abrupt transitions to synchronization are k...

[Phys. Rev. E 91, 032811] Published Thu Mar 26, 2015

Author(s): Tiago P. Peixoto

Modeling a network with too many parameters is likely to lead to overfitting. The minimum description length principle is used to reliably model networks and robustly differentiate models on the basis of confidence levels.

[Phys. Rev. X 5, 011033] Published Wed Mar 25, 2015

Music performance by professional musicians involves a wide-spectrum of cognitive and multi-sensory motor skills, whose biological basis is unknown. Several neuroscientific studies have demonstrated that the brains of professional musicians and non-musicians differ structurally and functionally and that musical training enhances cognition. However, the molecules and molecular mechanisms involved in music performance remain largely unexplored. Here, we investigated the effect of music performance on the genome-wide peripheral blood transcriptome of professional musicians by analyzing the transcriptional responses after a 2-hr concert performance and after a ‘music-free’ control session. The up-regulated genes were found to affect dopaminergic neurotransmission, motor behavior, neuronal plasticity, and neurocognitive functions including learning and memory. Particularly, candidate genes such as SNCA, FOS and DUSP1 that are involved in song perception and production in songbirds, were identified, suggesting an evolutionary conservation in biological processes related to sound perception/production. Additionally, modulation of genes related to calcium ion homeostasis, iron ion homeostasis, glutathione metabolism, and several neuropsychiatric and neurodegenerative diseases implied that music performance may affect the biological pathways that are otherwise essential for the proper maintenance of neuronal function and survival. For the first time, this study provides evidence for the candidate genes and molecular mechanisms underlying music performance.

Scientific Reports 5 doi: 10.1038/srep09506

Author(s): Emily S. C. Ching, Pik-Yin Lai, and C. Y. Leung

We present a method that reconstructs both the links and their relative coupling strength of bidirectional weighted networks. Our method requires only measurements of node dynamics as input. Using several examples, we demonstrate that our method can give accurate results for weighted random and weig...

[Phys. Rev. E 91, 030801] Published Tue Mar 24, 2015

In many real-world complex systems, the time-evolution of the network's structure and the dynamic state of its nodes are closely entangled. Here, we study opinion formation and imitation on an adaptive complex network which is dependent on the individual dynamic state of each node and vice versa to model the co-evolution of renewable resources with the dynamics of harvesting agents on a social network. The adaptive voter model is coupled to a set of identical logistic growth models and we show that in such systems, the rate of interactions between nodes as well as the adaptive rewiring probability play a crucial role for the sustainability of the system's equilibrium state. We derive a macroscopic description of the system which provides a general framework to model and quantify the influence of single node dynamics on the macroscopic state of the network and is applicable to many fields of study, such as epidemic spreading or social modeling.

Author(s): Wenchao Yang, Weijie Lin, Xingang Wang, and Liang Huang

The dynamical responses of a complex system to external perturbations are of both fundamental interest and practical significance. Here, by the model of networked chaotic oscillators, we investigate how the synchronization behavior of a complex network is influenced by an externally added periodic d...

[Phys. Rev. E 91, 032912] Published Thu Mar 19, 2015

In many countries poker is one of the most popular card games. Although each variant of poker has its own rules, all involve the use of money to make the challenge meaningful. Nowadays, in the collective consciousness, some variants of poker are referred to as games of skill, others as gambling. A poker table can be viewed as a psychology lab, where human behavior can be observed and quantified. This work provides a preliminary analysis of the role of rationality in poker games, using a stylized version of Texas Hold'em. In particular, we compare the performance of two different kinds of players, i.e. rational versus irrational players, during a poker tournament. Results show that these behaviors (i.e. rationality and irrationality) affect both the outcomes of challenges and the way poker should be classified.

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 be both positive and negative. We uncover in this minimal network of networks intriguing patterns of discordance, where the ensemble splits into two clusters separated by a constant phase lag. If it differs from $\pi$, then traveling wave solutions emerge. We observe a second route to traveling waves via traditional one-cluster states. Bistability is found between the various collective states. Analytical results and bifurcation diagrams are derived with a reduced system.

The Hamiltonian Mean Field (HMF) model of coupled inertial, Hamiltonian rotors is a prototype for conservative dynamics in systems with long-range interactions. We consider the case where the interactions between the rotors are governed by a network described by a weighted adjacency matrix. By studying the linear stability of the incoherent state, we find that the transition to synchrony occurs at a coupling constant $K$ inversely proportional to the largest eigenvalue of the adjacency matrix. We derive a closed system of equations for a set of local order parameters and use these equations to study the effect of network heterogeneity on the synchronization of the rotors. We find that for values of $K$ just beyond the transition to synchronization the degree of synchronization is highly dependent on the network's heterogeneity, but that for large values of $K$ the degree of synchronization is robust to changes in the heterogeneity of the network's degree distribution. Our results are illustrated with numerical simulations on Erd\"os-Renyi networks and networks with power-law degree distributions.

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 dynamics. By applying a mean-field approximation in combination with the dimension reduction method of Ott and Antonsen, we show that the dynamics can be described by a low dimensional system of equations. We use the reduced system to characterize the macroscopic chaos using Lyapunov exponents, bifurcation diagrams, and time-delay embeddings. Finally, we show that the emergence of chaos stems from the formation of multiple groups of synchronized oscillators, i.e., meta-oscillators.

It is well known that the length of a syntactic dependency determines its online memory cost. Thus, the problem of the placement of a head and its dependents (complements or modifiers) that minimizes online memory is equivalent to the problem of the minimum linear arrangement of a star tree. However, how that length is translated into cognitive cost is not known. This study shows that the online memory cost is minimized when the head is placed at the center, regardless of the function that transforms length into cost, provided only that this function is strictly monotonically increasing. Online memory defines a quasi-convex adaptive landscape with a single central minimum if the number of elements is odd and two central minima if that number is even. We discuss various aspects of the dynamics of word order of subject (S), verb (V) and object (O) from a complex systems perspective and suggest that word orders tend to evolve by swapping adjacent constituents from an initial or early SOV configuration that is attracted towards a central word order by online memory minimization. We also suggest that the stability of SVO is due to at least two factors, the quasi-convex shape of the adaptive landscape in the online memory dimension and online memory adaptations that avoid regression to SOV. Although OVS is also optimal for placing the verb at the center, its low frequency is explained by its long distance to the seminal SOV in the permutation space.

Data describing human interactions often suffer from incomplete sampling of the underlying population. As a consequence, the study of contagion processes using data-driven models can lead to a severe underestimation of the epidemic risk. Here we present a systematic method to alleviate this issue and obtain a better estimation of the risk in the context of epidemic models informed by high-resolution time-resolved contact data. We consider several such data sets collected in various contexts and perform controlled resampling experiments. We show how the statistical information contained in the resampled data can be used to build a series of surrogate versions of the unknown contacts. We simulate epidemic processes on the resulting reconstructed data sets and show that it is possible to obtain good estimates of the outcome of simulations performed using the complete data set. We discuss limitations and potential improvements of our method.

Author(s): J. A. Méndez-Bermúdez, A. Alcazar-López, A. J. Martínez-Mendoza, Francisco A. Rodrigues, and Thomas K. DM. Peron

By the use of extensive numerical simulations, we show that the nearest-neighbor energy-level spacing distribution P(s) and the entropic eigenfunction localization length of the adjacency matrices of Erdős-Rényi (ER) fully random networks are universal for fixed average degree ξ≡αN (α and N being th...

[Phys. Rev. E 91, 032122] Published Fri Mar 13, 2015

Chimera states are complex spatio-temporal patterns in which domains of synchronous and asynchronous dynamics coexist in coupled systems of oscillators. We examine how the character of the individual elements influences chimera states by studying networks of nonlocally coupled Van der Pol oscillators. Varying the bifurcation parameter of the Van der Pol system, we can interpolate between regular sinusoidal and strongly nonlinear relaxation oscillations, and demonstrate that more pronounced nonlinearity induces multi-chimera states with multiple incoherent domains. We show that the stability regimes for multi-chimera states and the mean phase velocity profiles of the oscillators change significantly as the nonlinearity becomes stronger. Furthermore, we reveal the influence of time delay on chimera patterns.

We find chimera states with respect to amplitude dynamics in a network of Stuart-Landau oscillators. These partially coherent and partially incoherent spatio-temporal patterns appear due to the interplay of nonlocal network topology and symmetry-breaking coupling. As the coupling range is increased, the oscillations are quenched, amplitude chimeras disappear and the network enters a symmetry-breaking stationary state. This particular regime is a novel pattern which we call chimera death. It is characterized by the coexistence of spatially coherent and incoherent inhomogeneous steady states and therefore combines the features of chimera state and oscillation death. Additionally, we show two different transition scenarios from amplitude chimera to chimera death. Moreover, for amplitude chimeras we uncover the mechanism of transition towards in-phase synchronized regime and discuss the role of initial conditions.

Author(s): Manlio De Domenico, Andrea Lancichinetti, Alex Arenas, and Martin Rosvall

Ensembles of people, research ideas, and cells all represent complex interacting networks. Scientists use a community-detection method to trace the interconnectedness of networks.

[Phys. Rev. X 5, 011027] Published Fri Mar 06, 2015

Ellipsoidal micron-sized colloidal particles can oscillate spontaneously when trapped in a focused laser beam. If two oscillating particles are held in proximity their oscillations synchronize through hydrodynamic interactions. The degree of synchronization depends on the distance between the oscill...

We describe the effect of power-law initial distributions of clusters on ordinary percolation and its generalizations, specifically, models of explosive percolation processes based on local optimization. These aggregation processes were shown to exhibit continuous phase transitions if the evolution ...

Observing and controlling complex networks are of paramount interest for understanding complex physical, biological and technological systems. Recent studies have made important advances in identifying sensor or driver nodes, through which we can observe or control a complex system. Yet, the observational uncertainty induced by measurement noise and the energy required for control continue to be significant challenges in practical applications. Here we show that the variability of control energy and observational uncertainty for different directions of the state space depend strongly on the number of driver nodes. In particular, we find that if all nodes are directly driven, control is energetically feasible, as the maximum energy increases sublinearly with the system size. If, however, we aim to control a system through a single node, control in some directions is energetically prohibitive, increasing exponentially with the system size. For the cases in between, the maximum energy decays exponentially when the number of driver nodes increases. We validate our findings in several model and real networks, arriving to a series of fundamental laws to describe the control energy that together deepen our understanding of complex systems.