Thomas

Authors: Guadalupe Cascallares and Pablo M. Gleiser.
The European Physical Journal B Vol. 88 , page 254
Published online: 12/10/2015
Keywords: Statistical and Nonlinear Physics.

The idea of a collective intelligence behind the complex natural structures built by organisms suggests that the organization of social networks is selected so as to optimize problem-solving competence at the group-level. Here we study the influence of the social network topology on the performance of a group of agents whose task is to locate the global maxima of NK fitness landscapes. Agents cooperate by broadcasting messages informing on their fitness and use this information to imitate the fittest agent in their influence networks. In the case those messages convey accurate information on the proximity of the solution (i.e., for smooth fitness landscapes) we find that high connectivity as well as centralization boost the group performance. For rugged landscapes, however, these characteristics are beneficial for small groups only. For large groups, it is advantageous to slow down the information transmission through the network to avoid local maximum traps. Long-range links and modularity have marginal effects on the performance of the group, except for a very narrow region of the model parameters.

Author(s): Tiago P. Peixoto

Many network systems are composed of interdependent but distinct types of interactions, which cannot be fully understood in isolation. These different types of interactions are often represented as layers, attributes on the edges, or as a time dependence of the network structure. Although they are c…

[Phys. Rev. E 92, 042807] Published Fri Oct 09, 2015

Explosive synchronization (ES) on heterogenous networks is a hot topic in the study of complex networks in recent years. In this paper, we introduce an analytical framework to study the ES of Kuramoto oscillators on a star configuration, which is a simple and special heterogenous network. By using the Ott–Antonsen ansatz, we obtain a reduced set of low-dimensional equations for the macroscopic evolution of the system considered. Analysis of this reduced system theoretically confirms that the phase transition of the order parameter is indeed discontinuous. We also extend the problem studied to a general case with frequencies perturbation. The results show the phase transition is still discontinuous when the perturbations are small, and it degenerates to a continuous transition while the perturbation width exceeds a critical value. Numerical simulations show good agreement with the theoretical predictions. Our work provides an insightful perspective to understand the ES phenomena i...

A wide range of natural and engineered phenomena rely on large networks of interacting units to reach a dynamical consensus state where the system collectively operates. Here we study the dynamics of self-organizing systems and show that for generic directed networks the collective frequency of the ensemble is {\it not} the same as the mean of the individuals' natural frequencies. Specifically, we show that the collective frequency equals a weighted average of the natural frequencies, where the weights are given by an out-flow centrality measure that is equivalent to a reverse PageRank centrality. Our findings uncover an intricate dependence of the collective frequency on both the structural directedness and dynamical heterogeneity of the network, and also reveal an unexplored connection between synchronization and PageRank, which opens the possibility of applying PageRank optimization to synchronization. Finally, we demonstrate the presence of collective frequency variation in real-world networks by considering the UK and Scandinavian power grids.

Author(s): Ming Li, Youjin Deng, and Bing-Hong Wang

As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two k cliques means that they share at least l<k vertices. In this paper we develop a theoretical approach to study clique percolation in Erdős-Rényi graphs, w…

[Phys. Rev. E 92, 042116] Published Wed Oct 07, 2015

Salmon represented a critical resource for prehistoric foragers along the North Pacific Rim, and continue to be economically and culturally important; however, the origins of salmon exploitation remain unresolved. Here we report 11,500-y-old salmon associated with a cooking hearth and human burials from the Upward Sun River Site, near the...

Brazilian science paralysed by economic slump

Nature 526, 7571 (2015). http://www.nature.com/doifinder/10.1038/526016a

Author: Elizabeth Gibney

From unpaid electricity bills to delayed participation in a telescope project, funding cuts bite.

Quantifying the similarity between symbolic sequences is a traditional problem in Information Theory which requires comparing the frequencies of symbols in different sequences. In numerous modern applications, ranging from DNA over music to texts, the distribution of symbol frequencies is characterized by heavy-tailed distributions (e.g., Zipf's law). The large number of low-frequency symbols in these distributions poses major difficulties to the estimation of the similarity between sequences, e.g., they hinder an accurate finite-size estimation of entropies. Here we show analytically how the systematic (bias) and statistical (fluctuations) errors in these estimations depend on the sample size~$N$ and on the exponent~$\gamma$ of the heavy-tailed distribution. Our results are valid for the Shannon entropy $(\alpha=1)$, its corresponding similarity measures (e.g., the Jensen-Shanon divergence), and also for measures based on the generalized entropy of order $\alpha$. For small $\alpha$'s, including $\alpha=1$, the errors decay slower than the $1/N$-decay observed in short-tailed distributions. For $\alpha$ larger than a critical value $\alpha^* = 1+1/\gamma \leq 2$, the $1/N$-decay is recovered. We show the practical significance of our results by quantifying the evolution of the English language over the last two centuries using a complete $\alpha$-spectrum of measures. We find that frequent words change more slowly than less frequent words and that $\alpha=2$ provides the most robust measure to quantify language change.

We introduce a model of adaptive temporal networks whose evolution is regulated by an interplay between node activity and dynamic exchange of information through links. We study the model by using a master equation approach. Starting from a homogeneous initial configuration, we show that temporal and structural heterogeneities, characteristic of real-world networks, spontaneously emerge. This theoretically tractable model thus contributes to the understanding of the dynamics of human activity and interaction networks.

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Nature Physics 11, 791 (2015). doi:10.1038/nphys3494

Authors: Roberta Sinatra, Pierre Deville, Michael Szell, Dashun Wang & Albert-László Barabási

An analysis of Web of Science data spanning more than 100 years reveals the rapid growth and increasing multidisciplinarity of physics — as well its internal map of subdisciplines.

Nature Physics 11, 848 (2015). doi:10.1038/nphys3402

Authors: Marco Tulio Angulo, Yang-Yu Liu & Jean-Jacques Slotine

The microscopic principles organizing dynamic units in complex networks—from proteins to power generators—can be understood in terms of network ‘motifs’: small interconnection patterns that appear much more frequently in real networks than expected in random networks. When considered as small subgraphs isolated from a large network, these motifs are more robust to parameter variations, easier to synchronize than other possible subgraphs, and can provide specific functionalities. But one can isolate these subgraphs only by assuming, for example, a significant separation of timescales, and the origin of network motifs and their functionalities when embedded in larger networks remain unclear. Here we show that most motifs emerge from interconnection patterns that best exploit the intrinsic stability characteristics at different scales of interconnection, from simple nodes to whole modules. This functionality suggests an efficient mechanism to stably build complex systems by recursively interconnecting nodes and modules as motifs. We present direct evidence of this mechanism in several biological networks.

Author(s): Yoshiki Sugitani, Keiji Konishi, and Naoyuki Hara

We present a procedure to systematically design the connection parameters that will induce amplitude death in oscillator networks with time-varying delay connections. The parameters designed by the procedure are valid in oscillator networks with any network topology and with any connection delay. Th…

[Phys. Rev. E] Published Tue Sep 29, 2015

Author(s): Christophe Schülke and Federico Ricci-Tersenghi

Detecting communities in a network, based only on the adjacency matrix, is a problem of interest to several scientific disciplines. Recently, Zhang and Moore have introduced an algorithm in [P. Zhang and C. Moore, Proceedings of the National Academy of Sciences {\bf{111}}, 18144 (2014)], called \mod…

[Phys. Rev. E] Published Wed Sep 23, 2015

Griffiths phases and localization in hierarchical modular networks

Scientific Reports, Published online: 24 September 2015; doi:10.1038/srep14451

We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the SIS and SIR dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasi-stationary state method we numerically show the existence of disease localization and the emergence of two or more susceptibility peaks, which are characterized analytically and numerically through the inverse participation ratio. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe a characteristic transition in the eigenvalue spectra of the supra-contact tensor as a function of the ratio of two spreading rates: if the rate at which the disease spreads within a layer is comparable to the spreading rate across layers, the individual spectra of each layer merge with the coupling between layers. Finally, we verified the barrier effect, i.e., for three-layer configuration, when the layer with the largest eigenvalue is located at the center of the line, it can effectively act as a barrier to the disease. The formalism introduced here provides a unifying mathematical approach to disease contagion in multiplex systems opening new possibilities for the study of spreading processes.

Author(s): Luís F. Seoane and Ricard Solé

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 mechan…

[Phys. Rev. E 92, 032807] Published Mon Sep 21, 2015

Author(s): Dirk Witthaut and Marc Timme

We study the propagation of cascading failures in complex supply networks with a focus on nonlocal effects occurring far away from the initial failure. It is shown that a high clustering and a small average path length of a network generally suppress nonlocal overloads. These properties are typical …

[Phys. Rev. E 92, 032809] Published Wed Sep 23, 2015

Author(s): Oleg V. Maslennikov, Vladimir I. Nekorkin, and Jürgen Kurths

The impact of connectivity and individual dynamics on the basin stability of the burst synchronization regime in small-world networks consisting of chaotic slow-fast oscillators {is studied}. It is shown that there are rewiring probabilities corresponding to the largest basin stabilities which uncov…

[Phys. Rev. E] Published Thu Sep 17, 2015

Author(s): Faryad Darabi Sahneh, Caterina Scoglio, and Piet Van Mieghem

An interconnected network features a structural transition between two regimes \cite{radicchi2013NP}: one where the network components are structurally distinguishable and one where the interconnected network functions as a whole. Our exact solution for the coupling threshold uncovers network topolo…

[Phys. Rev. E] Published Fri Sep 18, 2015

Author(s): Franco Bagnoli and Raúl Rechtman

We study models of a society composed of a mixture of conformist and reasonable contrarian agents that at any instant hold one of two opinions. Conformists tend to agree with the average opinion of their neighbors and reasonable contrarians to disagree, but revert to a conformist behavior in the pre…

[Phys. Rev. E] Published Fri Sep 18, 2015

Authors: Petter Holme and Petter Holme.
The European Physical Journal B Vol. 88 , page 234
Published online: 21/9/2015

We show that the mathematical structure of Tsallis entropy underlies an important and ubiquitous problem in nonlinear science related to an efficient synchronization of weakly forced nonlinear oscillators. The maximization of the locking range of oscillators with the use of phase models is analyzed with general constraints that encompass forcing waveform power, magnitude, or area. The optimization problem is then recasted as a general form of Tsallis entropy maximization. The solution of these optimization problems is shown to be a direct consequence from Hölder's inequality. The resulting new maximization principle is confirmed in numerical simulations and experiments with chemical oscillations with nickel electrodissolution. While weakly nonlinear oscillators have generic optimal waveforms (sinusoidal, 50% duty cycle square wave, and equally paced bipolar pulses for power-, area-, and magnitude-constraints, respectively), strongly nonlinear oscillators require more complex wav...

Coupled phase-oscillators are important models related to synchronization. Recently, Ott-Antonsen(OA) ansatz is developed and used to get low-dimensional collective behaviors in coupled oscillator systems. In this paper, we develop a simple and concise approach based on the equations of order parameters, namely, order parameter analysis, with which we point out that the OA ansatz is rooted in the dynamical symmetry of the order parameters. With our approach the scope of the OA ansatz is identified as two conditions, i.e., infinite size of the system and only three nonzero Fourier coefficients of the coupling function. Coinciding with each of the conditions, a distinctive system out of the scope is taken into account and discussed with the order parameter analysis. Two approximation methods are introduced respectively, namely the ensemble approach and the dominating-term assumption.

Author(s): Nikolaj Kulvelis, Maxim Dolgushev, and Oliver Mülken

We consider single-particle quantum transport on parametrized complex networks. Based on general arguments regarding the spectrum of the corresponding Hamiltonian, we derive bounds for a measure of the global transport efficiency defined by the time-averaged return probability. For treelike networks…

[Phys. Rev. Lett. 115, 120602] Published Thu Sep 17, 2015

In evolving complex systems such as air traffic and social organizations, collective effects emerge from their many components' dynamic interactions. While the dynamic interactions can be represented by temporal networks with nodes and links that change over time, they remain highly complex. It is therefore often necessary to use methods that extract the temporal networks' large-scale dynamic community structure. However, such methods are subject to overfitting or suffer from effects of arbitrary, a priori imposed timescales, which should instead be extracted from data. Here we simultaneously address both problems and develop a principled data-driven method that determines relevant timescales and identifies patterns of dynamics that take place on networks as well as shape the networks themselves. We base our method on an arbitrary-order Markov chain model with community structure, and develop a nonparametric Bayesian inference framework that identifies the simplest such model that can explain temporal interaction data.

Author(s): Alexander A. Alemi, Matthew Bierbaum, Christopher R. Myers, and James P. Sethna

We use a popular fictional disease, zombies, in order to introduce techniques used in modern epidemiology modeling, and ideas and techniques used in the numerical study of critical phenomena. We consider variants of zombie models, from fully connected continuous time dynamics to a full scale exact s…

[Phys. Rev. E] Published Tue Sep 15, 2015

Roads and cities of 18th century France

Scientific Data, Published online: 15 September 2015; doi:10.1038/sdata.2015.48