Thomas

The effect of population size on patterns and rates of language evolution is controversial. Do languages with larger speaker populations change faster due to a greater capacity for innovation, or do smaller populations change faster due to more efficient diffusion of innovations? Do smaller populations suffer greater loss of language...

Author(s): Yang Chen, Zhoujian Cao, Shihong Wang, and Gang Hu

Very recently, a first-order phase transition, named explosive synchronization (ES), has attracted great attention due to its remarkable novelty in theory and significant impact in applications. However, so far, all observations of ES have been associated with various correlation constraints on syst...

[Phys. Rev. E 91, 022810] Published Tue Feb 17, 2015

Author(s): Winnie Poel, Anna Zakharova, and Eckehard Schöll

We study the interplay between network topology and complex space-time patterns and introduce a concept to analytically predict complex patterns in networks of Stuart-Landau oscillators with linear symmetric and instantaneous coupling based solely on the network topology. These patterns consist of p...

[Phys. Rev. E 91, 022915] Published Tue Feb 17, 2015

We deduce and discuss the implications of self-similarity for the stability in terms of robustness to failure of multiplexes, depending on interlayer degree correlations. First, we define self-similarity of multiplexes and we illustrate the concept in practice using the configuration model ensemble. Circumscribing robustness to survival of the mutually percolated state, we find a new explanation based on self-similarity both for the observed fragility of interconnected systems of networks and for their robustness to failure when interlayer degree correlations are present. Extending the self-similarity arguments, we show that interlayer degree correlations can change completely the stability properties of self-similar multiplexes, so that they can even recover a zero percolation threshold and a continuous transition in the thermodynamic limit, qualitatively exhibiting thus the ordinary stability attributes of noninteracting networks. We confirm these results with numerical simulations.

Most methods proposed to uncover communities in complex networks rely on combinatorial graph properties. Usually an edge-counting quality function, such as modularity, is optimized over all partitions of the graph compared against a null random graph model. Here we introduce a systematic dynamical framework to design and analyze a wide variety of quality functions for community detection. The quality of a partition is measured by its Markov Stability, a time-parametrized function defined in terms of the statistical properties of a Markov process taking place on the graph. The Markov process provides a dynamical sweeping across all scales in the graph, and the time scale is an intrinsic parameter that uncovers communities at different resolutions.

This dynamic-based community detection leads to a compound optimization, which favours communities of comparable centrality (as defined by the stationary distribution), and provides a unifying framework for spectral algorithms, as well as different heuristics for community detection, including versions of modularity and Potts model. Our dynamic framework creates a systematic link between different stochastic dynamics and their corresponding notions of optimal communities under distinct (node and edge) centralities. We show that the Markov Stability can be computed efficiently to find multi-scale community structure in large networks.

Many real-world complex systems are best modeled by multiplex networks of interacting network layers. The multiplex network study is one of the newest and hottest themes in the statistical physics of complex networks. Pioneering studies have proven that the multiplexity has broad impact on the system's structure and function. In this Colloquium paper, we present an organized review of the growing body of current literature on multiplex networks by categorizing existing studies broadly according to the type of layer coupling in the problem. Major recent advances in the ?field are surveyed and some outstanding open challenges and future perspectives will be proposed.

To understand the effect of generalized infection processes, we suggest and study the core contact process (CCP) on complex networks. In CCP an uninfected node is infected when at least k different infected neighbors of the node select the node for the infection. The healing process is the same as that of the normal CP. It is analytically and numerically shown that discontinuous transitions occur in CCP on random networks and scale-free networks depending on infection rate and initial density of infected nodes. The discontinuous transitions include hybrid transitions with β = 1/2 and β = 1. The asymptotic behavior of the phase boundary related to the initial density is found analytically and numerically. The mapping between CCP with k and static ( k +1)-core percolation is supposed from the ( k +1)-core structure in the active phase and the hybrid transition with β = 1/2. From these properties of CCP one can see that CCP is one of the ...

We describe synchronization transitions in an ensemble of globally coupled phase oscillators with a bi-harmonic coupling function, and two sources of disorder—diversity of the intrinsic oscillators’ frequencies, and external independent noise forces. Based on the self-consistent formulation, we derive analytic solutions for different synchronous states. We report on various non-trivial transitions from incoherence to synchrony, with the following possible scenarios: simple supercritical transition (similar to classical Kuramoto model); subcritical transition with large area of bistability of incoherent and synchronous solutions; appearance of a symmetric two-cluster solution which can coexist with the regular synchronous state. We show that the interplay between relatively small white noise and finite-size fluctuations can lead to metastability of the asynchronous solution.

Zipf's law is just one out of many universal laws proposed to describe statistical regularities in language. Here we review and critically discuss how these laws can be statistically interpreted, fitted, and tested (falsified). The modern availability of large databases of written text allows for tests with an unprecedent statistical accuracy and also a characterization of the fluctuations around the typical behavior. We find that fluctuations are usually much larger than expected based on simplifying statistical assumptions (e.g., independence and lack of correlations between observations).These simplifications appear also in usual statistical tests so that the large fluctuations can be erroneously interpreted as a falsification of the law. Instead, here we argue that linguistic laws are only meaningful (falsifiable) if accompanied by a model for which the fluctuations can be computed (e.g., a generative model of the text). The large fluctuations we report show that the constraints imposed by linguistic laws on the creativity process of text generation are not as tight as one could expect.

Author(s): Patrycja Jaros, Yuri Maistrenko, and Tomasz Kapitaniak

We report different types of chimera states in the Kuramoto model with inertia. They arise on the route from coherence, via so-called solitary states, to the rotating waves. We identify the wide region in parameter space, in which a different type of chimera state, i.e., the imperfect chimera state,...

[Phys. Rev. E 91, 022907] Published Tue Feb 10, 2015

In this study we offer an approach to network physiology, which proceeds from transcriptomic data and uses gene ontology analysis to identify the biological processes most enriched in several critical time points of wound healing process (days 0, 3 and 7). The top-ranking differentially expressed genes for each process were used to build two networks: one with all proteins regulating the transcription of selected genes, and a second one involving the proteins from the signaling pathways that activate the transcription factors. The information from these networks is used to build a network of the most enriched processes with undirected links weighted proportionally to the count of shared genes between the pair of processes, and directed links weighted by the count of relationships connecting genes from one process to genes from the other. In analyzing the network thus built we used an approach based on random walks and accounting for the temporal aspects of the spread of a signal ...

Author(s): Sarika Jalan, Aradhana Singh, Suman Acharyya, and Jürgen Kurths

We study the mechanisms of frequency-synchronized cluster formation in coupled nonidentical oscillators and investigate the impact of presence of a leader on the cluster synchronization. We find that the introduction of a leader, a node having large parameter mismatch, induces a profound change in t...

[Phys. Rev. E 91, 022901] Published Mon Feb 02, 2015

Cities are characterized by concentrating population, economic activity and services. However, not all cities are equal and a natural hierarchy at local, regional or global scales spontaneously emerges. In this work, we introduce a method to quantify city influence using geolocated tweets to characterize human mobility. Rome and Paris appear consistently as the cities attracting most diverse visitors. The ratio between locals and non-local visitors turns out to be fundamental for a city to truly be global. Focusing only on urban residents' mobility flows, a city to city network can be constructed. This network allows us to analyze centrality measures at different scales. New York and London play a predominant role at the global scale, while urban rankings suffer substantial changes if the focus is set at a regional level.

In this paper we propose, discuss and illustrate a computationally feasible definition of chaos which can be applied very generally to situations that are commonly encountered, including attractors, repellers and non-periodically forced systems. This definition is based on an entropy-like quantity, which we call "expansion entropy", and we define chaos as occurring when this quantity is positive. We relate and compare expansion entropy to the well-known concept of topological entropy, to which it is equivalent under appropriate conditions. We also present example illustrations, discuss computational implementations, and point out issues arising from attempts at giving definitions of chaos that are not entropy-based.

Author(s): Lucas Wardil and Christoph Hauert

Research collaboration occurs more frequently today than in the past. As a consequence, cooperation and competition are crucial determinants of academic success. In multiauthored publications, not all authors contribute evenly. Hence, some authors end up with less time or resources to work on parall...

[Phys. Rev. E 91, 012825] Published Fri Jan 30, 2015

Author(s): Andrea Lancichinetti, M. Irmak Sirer, Jane X. Wang, Daniel Acuna, Konrad Körding, and Luís A. Nunes Amaral

Digital, text-based data are being created at a high rate in today’s electronic society. A new algorithm accurately and efficiently assigns topic tags to unstructured text.

[Phys. Rev. X 5, 011007] Published Thu Jan 29, 2015

Author(s): Y. Gandica, J. Carvalho, and F. Sampaio dos Aidos

A model for the probabilistic function followed in editing Wikipedia is presented and compared with simulations and real data. It is argued that the probability of editing is proportional to the editor's number of previous edits (preferential attachment), to the editor's fitness, and to an aging fac...

[Phys. Rev. E 91, 012824] Published Thu Jan 29, 2015

Chimera states are complex spatio-temporal patterns that consist of coexisting domains of spatially coherent and incoherent dynamics. This counterintuitive phenomenon was first observed in systems of identical oscillators with symmetric coupling topology. Can one overcome these limitations? To addre...

We study the interplay between network topology and complex space-time patterns and introduce a concept to analytically predict complex patterns in networks of Stuart--Landau oscillators with linear symmetric and instantaneous coupling based solely on the network topology. These patterns consist of ...

In this work we study a peculiar example of social organization on Facebook: the Occupy Movement -- i.e., an international protest movement against social and economic inequality organized online at a city level. We consider 179 US Facebook public pages during the time period between September 2011 and February 2013. The dataset includes 618K active users and 753K posts that received about 5.2M likes and 1.1M comments. By labeling user according to their interaction patterns on pages -- e.g., a user is considered to be polarized if she has at least the 95% of her likes on a specific page -- we find that activities are not locally coordinated by geographically close pages, but are driven by pages linked to major US cities that act as hubs within the various groups. Such a pattern is verified even by extracting the backbone structure -- i.e., filtering statistically relevant weight heterogeneities -- for both the pages-reshares and the pages-common users networks.

The dynamics of power-grid networks is becoming an increasingly active area of research within the physics and network science communities. The results from such studies are typically insightful and illustrative, but are often based on simplifying assumptions that can be either difficult to assess or not fully justified for realistic applications. Here we perform a comprehensive comparative analysis of three leading models recently used to study synchronization dynamics in power-grid networks -- a fundamental problem of practical significance given that frequency synchronization of all power generators in the same interconnection is a necessary condition for a power grid to operate. We show that each of these models can be derived from first principles within a common framework based on the classical model of a generator, thereby clarifying all assumptions involved. This framework allows us to view power grids as complex networks of coupled second-order phase oscillators with both forcing and damping terms. Using simple illustrative examples, test systems, and real power-grid datasets, we study the inherent frequencies of the oscillators as well as their coupling structure, comparing across the different models. We demonstrate, in particular, that if the network structure is not homogeneous, generators with identical parameters need to be modeled as non-identical oscillators in general. We also discuss an approach to estimate the required (dynamical) parameters that are unavailable in typical power-grid datasets, their use for computing the constants of each of the three models, and an open-source MATLAB toolbox that we provide for these computations.

In this paper we propose a quantum algorithm to measure the similarity between a pair of unattributed graphs. We design an experiment where the two graphs are merged by establishing a complete set of connections between their nodes and the resulting structure is probed through the evolution of conti...

Author(s): Hangmo Yi

I investigate the quantum phase transition of the transverse-field quantum Ising model in which nearest neighbors are defined according to the connectivity of scale-free networks. Using a continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, I identify the quant...

[Phys. Rev. E 91, 012146] Published Wed Jan 28, 2015

Author(s): Quantong Guo, Xin Jiang, Yanjun Lei, Meng Li, Yifang Ma, and Zhiming Zheng

Human awareness plays an important role in the spread of infectious diseases and the control of propagation patterns. The dynamic process with human awareness is called awareness cascade, during which individuals exhibit herd-like behavior because they are making decisions based on the actions of ot...

[Phys. Rev. E 91, 012822] Published Wed Jan 28, 2015

Author(s): Hiroaki Daido

This paper studies how the degree of synchronization in a large population of coupled oscillators responds to a periodic external force. After introducing the concept of susceptibility for the response to the external force, the author finds that in the case of uniform coupling, this susceptibility diverges at the phase transition to macroscopic synchronization. For the case of random coupling, the susceptibility exhibits a cusp when the system enters a glasslike phase.

[Phys. Rev. E 91, 012925] Published Wed Jan 28, 2015

Author(s): Per Sebastian Skardal, Dane Taylor, Jie Sun, and Alex Arenas

We report erosion of synchronization in networks of coupled phase oscillators, a phenomenon where perfect phase synchronization is unattainable in steady state, even in the limit of infinite coupling. An analysis reveals that the total erosion is separable into the product of terms characterizing co...

[Phys. Rev. E 91, 010802] Published Wed Jan 28, 2015

The dynamics of power-grid networks is becoming an increasingly active area of research within the physics and network science communities. The results from such studies are typically insightful and illustrative, but are often based on simplifying assumptions that can be either difficult to assess or not fully justified for realistic applications. Here we perform a comprehensive comparative analysis of three leading models recently used to study synchronization dynamics in power-grid networks—a fundamental problem of practical significance given that frequency synchronization of all power generators in the same interconnection is a necessary condition for a power grid to operate. We show that each of these models can be derived from first principles within a common framework based on the classical model of a generator, thereby clarifying all assumptions involved. This framework allows us to view power grids as complex networks of coupled second-order phase oscillators with...

Locating the source that triggers a dynamical process is a fundamental but challenging problem in complex networks, ranging from epidemic spreading in society and on the Internet to cancer metastasis in the human body. An accurate localization of the source is inherently limited by our ability to simultaneously access the information of all nodes in a large-scale complex network. This thus raises two critical questions: how do we locate the source from incomplete information and can we achieve full localization of sources at any possible location from a given set of observable nodes. Here we develop a time-reversal backward spreading algorithm to locate the source of a diffusion-like process efficiently and propose a general locatability condition. We test the algorithm by employing epidemic spreading and consensus dynamics as typical dynamical processes and apply it to the H1N1 pandemic in China. We find that the sources can be precisely located in arbitrary networks insofar as the locatability condition is assured. Our tools greatly improve our ability to locate the source of diffusion in complex networks based on limited accessibility of nodal information. Moreover, they have implications for controlling a variety of dynamical processes taking place on complex networks, such as inhibiting epidemics, slowing the spread of rumors, pollution control and environmental protection.

Author(s): Yashar Ahmadian, Francesco Fumarola, and Kenneth D. Miller

Networks studied in many disciplines, including neuroscience and mathematical biology, have connectivity that may be stochastic about some underlying mean connectivity represented by a non-normal matrix. Furthermore, the stochasticity may not be independent and identically distributed (iid) across e...

[Phys. Rev. E 91, 012820] Published Mon Jan 26, 2015

Author(s): Loukas Skarpalezos, Aristotelis Kittas, Panos Argyrakis, Reuven Cohen, and Shlomo Havlin

We study the problem of a particle or message that travels as a biased random walk towards a target node in a network in the presence of traps. The bias is represented as the probability p of the particle to travel along the shortest path to the target node. The efficiency of the transmission proces...

[Phys. Rev. E 91, 012817] Published Mon Jan 26, 2015