Thomas

Hubs are network components that hold positions of high importance for network function. Previous research has identified hubs in human brain networks derived from neuroimaging data; however, there is little consensus on the localization of such hubs. Moreover, direct evidence regarding the role of various proposed hubs in network function...

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

We study optimal synchronization in networks of heterogeneous phase oscillators. Our main result is the derivation of a synchrony alignment function that encodes the interplay between network structure and oscillators’ frequencies and that can be readily optimized. We highlight its utility in two ge...

[Phys. Rev. Lett. 113, 144101] Published Tue Sep 30, 2014

Nature Physics 10, 712 (2014). doi:10.1038/nphys3097

Author: Ginestra Bianconi

Many networks interact with one another by forming multilayer networks, but these structures can lead to large cascading failures. The secret that guarantees the robustness of multilayer networks seems to be in their correlations.

Nature Physics 10, 762 (2014). doi:10.1038/nphys3081

Authors: Saulo D. S. Reis, Yanqing Hu, Andrés Babino, José S. Andrade Jr, Santiago Canals, Mariano Sigman & Hernán A. Makse

Networks in nature do not act in isolation, but instead exchange information and depend on one another to function properly. Theory has shown that connecting random networks may very easily result in abrupt failures. This finding reveals an intriguing paradox: if natural systems organize in interconnected networks, how can they be so stable? Here we provide a solution to this conundrum, showing that the stability of a system of networks relies on the relation between the internal structure of a network and its pattern of connections to other networks. Specifically, we demonstrate that if interconnections are provided by network hubs, and the connections between networks are moderately convergent, the system of networks is stable and robust to failure. We test this theoretical prediction on two independent experiments of functional brain networks (in task and resting states), which show that brain networks are connected with a topology that maximizes stability according to the theory.

Author(s): Tue Herlau, Mikkel N. Schmidt, and Morten Mørup

In stochastic block models, which are among the most prominent statistical models for cluster analysis of complex networks, clusters are defined as groups of nodes with statistically similar link probabilities within and between groups. A recent extension by Karrer and Newman [Karrer and Newman, Phy...

[Phys. Rev. E 90, 032819] Published Mon Sep 29, 2014

Author(s): N. Azimi-Tafreshi, J. Gómez-Gardeñes, and S. N. Dorogovtsev

We generalize the theory of k-core percolation on complex networks to k-core percolation on multiplex networks, where k≡(k1,k2,...,kM). Multiplex networks can be defined as networks with vertices of one kind but M different types of edges, representing different types of interactions. For such netwo...

[Phys. Rev. E 90, 032816] Published Mon Sep 29, 2014

A basic problem in the analysis of social networks is missing data. When a network model does not accurately capture all the actors or relationships in the social system under study, measures computed on the network and ultimately the final outcomes of the analysis can be severely distorted. For this reason, researchers in social network analysis have characterised the impact of different types of missing data on existing network measures. Recently a lot of attention has been devoted to the study of multiple-network systems, e.g., multiplex networks. In these systems missing data has an even more significant impact on the outcomes of the analyses. However, to the best of our knowledge, no study has focused on this problem yet. This work is a first step in the direction of understanding the impact of missing data in multiple networks. We first discuss the main reasons for missingness in these systems, then we explore the relation between various types of missing information and their effect on network properties. We provide initial experimental evidence based on both real and synthetic data.

We consider pulse-coupled Leaky Integrate-and-Fire neural networks with randomly distributed synaptic couplings. This random dilution induces fluctuations in the evolution of the macroscopic variables and deterministic chaos at the microscopic level. Our main aim is to mimic the effect of the dilution as a noise source acting on the dynamics of a globally coupled non-chaotic system. Indeed, the evolution of a diluted neural network can be well approximated as a fully pulse coupled network, where each neuron is driven by a mean synaptic current plus additive noise. These terms represent the average and the fluctuations of the synaptic currents acting on the single neurons in the diluted system. The main microscopic and macroscopic dynamical features can be retrieved with this stochastic approximation. Furthermore, the microscopic stability of the diluted network can be also reproduced, as demonstrated from the almost coincidence of the measured Lyapunov exponents in the deterministic and stochastic cases for an ample range of system sizes. Our results strongly suggest that the fluctuations in the synaptic currents are responsible for the emergence of chaos in this class of pulse coupled networks.

Author(s): Robert S. Farr, John L. Harer, and Thomas M. A. Fink

A new class of network models are introduced, which are easily repairable and able to withstand multiple attacks. Optimization rules are given for the design of square and triangular lattice repairable networks.

[Phys. Rev. Lett. 113, 138701] Published Fri Sep 26, 2014

We investigate the influence of time delayed coupling on the nature of the aging transition in a system of coupled oscillators that have a mix of active and inactive oscillators, where the aging transition is defined as the gradual loss of collective synchrony as the proportion of inactive oscillato...

Author(s): Adam Lipowski and Dorota Lipowska

We examine a community structure in random graphs of size n and link probability p/n determined with the Newman greedy optimization of modularity. Calculations show that for p<1 communities are nearly identical with clusters. For p=1 the average sizes of a community sav and of the giant community...

[Phys. Rev. E 90, 032815] Published Thu Sep 25, 2014

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 vs 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 focused on how repeat collaborations in projects for inventions affect performance. Repeat collaborations have two contradictory aspects. A positive aspect is team development or experience, and a negative aspect is team degeneration or decline. Since both contradicting phenomena are observed, inventors have a dilemma as to whether they should keep collaborating in a team or not. The dilemma has not previously been quantitatively analyzed.

We provide quantitative and extensive analyses of the dilemma in creative projects by using patent data from Japan and the United States. We confirm three predictions to quantitatively validate the existence of the dilemma. The first prediction is that the greater the patent a team achieves, the longer the team will work together. The second prediction is that the impact of consecutive patents decreases after a team makes a remarkable invention, which is measured by the impact of patents. The third prediction is that the expectation of impact with new teams is greater than that with the same teams successful in the past. We find these predictions are validated in patents published in Japan and the United States. On the basis of these three predictions, we can quantitatively validate the dilemma in creative projects. We also propose preventive strategies for degeneration. One is developing technological diversity, and another is developing inventor diversity in teams.We find the two strategies are both effective by validating with the data.

In the aftermath of the publication of the “emotional contagion” study conducted by Facebook researchers working with Cornell University scholars (1, 2), many observers weighed in about everything from the acceptability of undertaking the research at all, to how it was conducted, the rules and regulations that applied to it,...

Employing the Kuramoto model as an illustrative example, we show how the use of the mean-field approximation can be applied to large networks of phase oscillators with assortativity. We then use the ansatz of Ott and Antonsen ( Chaos , 19 (2008) 037113) to reduce the mean-field kinetic equations to a system of ordinary differential equations. The resulting formulation is illustrated by application to a network Kuramoto problem with degree assortativity and correlation between the node degrees and the natural oscillation frequencies. Good agreement is found between the solutions of the reduced set of ordinary differential equations obtained from our theory and full simulations of the system. These results highlight the ability of our method to capture all the phase transitions (bifurcations) and system attractors. One interesting result is that degree assortativity can induce transitions from a steady macroscopic state to a temporally oscillating macroscopic state thro...

Nonlinear oscillators exhibit synchronization (injection-locking) to external periodic forcings, which underlies the mutual synchronization in networks of nonlinear oscillators. Despite its history of synchronization and the practical importance of injection-locking to date, there are many important open problems of an efficient injection-locking for a given oscillator. In this work, I elucidate a hidden mechanism governing the synchronization limit under weak forcings, which is related to a widely known inequality; Hölderʼs inequality. This mechanism enables us to understand how and why the efficient injection-locking is realized; a general theory of synchronization limit is constructed where the maximization of the synchronization range or the stability of synchronization for general forcings including pulse trains, and a fundamental limit of general m : n phase locking, are clarified systematically. These synchronization limits and their utility are systematicall...

Networks often represent systems that do not have a long history of study in traditional fields of physics; albeit, there are some notable exceptions, such as energy landscapes and quantum gravity. Here, we consider networks that naturally arise in cosmology. Nodes in these networks are stationary observers uniformly distributed in an expanding open Friedmann–Lemaître–Robertson–Walker universe with any scale factor and two observers are connected if one can causally influence the other. We show that these networks are growing Lorentz-invariant graphs with power-law distributions of node degrees. These networks encode maximum information about the observable universe available to a given observer.

In recent decades, a number of centrality metrics describing network properties of nodes have been proposed to rank the importance of nodes. In order to understand the correlations between centrality metrics and to approximate a high-complexity centrality metric by a strongly correlated low-complexity metric, we ?first study the correlation between centrality metrics in terms of their Pearson correlation coefficient and their similarity in ranking of nodes. In addition to considering the widely used centrality metrics, we introduce a new centrality measure, the degree mass. The m order degree mass of a node is the sum of the weighted degree of the node and its neighbors no further than m hops away. We find that the B_{n}, the closeness, and the components of x_{1} are strongly correlated with the degree, the 1st-order degree mass and the 2nd-order degree mass, respectively, in both network models and real-world networks. We then theoretically prove that the Pearson correlation coefficient between x_{1} and the 2nd-order degree mass is larger than that between x_{1} and a lower order degree mass. Finally, we investigate the effect of the inflexible antagonists selected based on different centrality metrics in helping one opinion to compete with another in the inflexible antagonists opinion model. Interestingly, we find that selecting the inflexible antagonists based on the leverage, the B_{n}, or the degree is more effective in opinion-competition than using other centrality metrics in all types of networks. This observation is supported by our previous observations, i.e., that there is a strong linear correlation between the degree and the B_{n}, as well as a high centrality similarity between the leverage and the degree.

Author(s): Guilherme Ferraz de Arruda, André Luiz Barbieri, Pablo Martín Rodríguez, Francisco A. Rodrigues, Yamir Moreno, and Luciano da Fontoura Costa

The identification of the most influential spreaders in networks is important to control and understand the spreading capabilities of the system as well as to ensure an efficient information diffusion such as in rumorlike dynamics. Recent works have suggested that the identification of influential s...

[Phys. Rev. E 90, 032812] Published Mon Sep 22, 2014

Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in abrupt failures. This theoretical finding bares an intrinsic paradox: If natural systems organize in interconnected networks, how can they be so stable? Here we provide a solution to this conundrum, showing that the stability of a system of networks relies on the relation between the internal structure of a network and its pattern of connections to other networks. Specifically, we demonstrate that if network inter-connections are provided by hubs of the network and if there is a moderate degree of convergence of inter-network connection the systems of network are stable and robust to failure. We test this theoretical prediction in two independent experiments of functional brain networks (in task- and resting states) which show that brain networks are connected with a topology that maximizes stability according to the theory.

Publication date: 15 December 2014
Source:Physica A: Statistical Mechanics and its Applications, Volume 416
Author(s): Jiawei Luo , Guanghui Li , Dan Song , Cheng Liang
Discovering motifs in protein–protein interaction networks is becoming a current major challenge in computational biology, since the distribution of the number of network motifs can reveal significant systemic differences among species. However, this task can be computationally expensive because of the involvement of graph isomorphic detection. In this paper, we present a new algorithm (CombiMotif) that incorporates combinatorial techniques to count non-induced occurrences of subgraph topologies in the form of trees. The efficiency of our algorithm is demonstrated by comparing the obtained results with the current state-of-the art subgraph counting algorithms. We also show major differences between unicellular and multicellular organisms. The datasets and source code of CombiMotif are freely available upon request.

Author(s): Otti D'Huys, Thomas Jüngling, and Wolfgang Kinzel

A delay is known to induce multistability in periodic systems. Under influence of noise, coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns. For coupled phase oscillators we reduce the delay system to a nondelayed Langevin equation,...

[Phys. Rev. E 90, 032918] Published Fri Sep 19, 2014

Author(s): Dirk Witthaut and Marc Timme

The Kuramoto model constitutes a paradigmatic model for the dissipative collective dynamics of coupled oscillators, characterizing in particular the emergence of synchrony (phase locking). Here we present a classical Hamiltonian (and thus conservative) system with 2N state variables that in its acti...

[Phys. Rev. E 90, 032917] Published Fri Sep 19, 2014

The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability distribution of these degrees over the whole network. Therefore, the degree is very important structural parameter of network topology. However, given the number of nodes and the degree of each node in a network, the topology of the network cannot be determined. Therefore, we propose the degree-layer theory of network topology to describe deeply the network topology. First, we propose the concept of degree-tree with the breadth-first search tree. The degrees of all nodes are layered and have a hierarchical structure. Second,the degree-layer theory is described in detail. Two new concepts are defined in the theory. An index is proposed to quantitatively distinguish the two network topologies. It also can quantitatively measure the stability of network topology built by a model mechanism. One theorem is given and proved, furthermore, and one corollary is derived directly from the theorem. Third, the applications of the degree-layer theory are discussed in the ER random network, WS small world network and BA scale-free network, and the influences of the degree distribution on the stability of network topology are studied in the three networks. In conclusion, the degree-layer theory is helpful for accurately describing the network topology, and provides a new starting point for researching the similarity and isomorphism between two network topologies.

Several real-world systems can be represented as multi-layer complex networks, i.e. in terms of a superposition of various graphs, each related to a different mode of connection between nodes. Hence, the definition of proper mathematical quantities aiming at capturing the level of complexity of those systems is required. Various attempts have been made to measure the empirical dependencies between the layers of a multiplex, for both binary and weighted networks. In the simplest case, such dependencies are measured via correlation-based metrics: we show that this is equivalent to the use of completely homogeneous benchmarks specifying only global constraints, such as the total number of links in each layer. However, these approaches do not take into account the heterogeneity in the degree and strength distributions, which are instead a fundamental feature of real-world multiplexes. In this work, we compare the observed dependencies between layers with the expected values obtained from reference models that appropriately control for the observed heterogeneity in the degree and strength distributions. This leads to novel multiplexity measures that we test on different datasets, i.e. the International Trade Network (ITN) and the European Airport Network (EAN). Our findings confirm that the use of homogeneous benchmarks can lead to misleading results, and furthermore highlight the important role played by the distribution of hubs across layers.

Identifying the most influential spreaders is an important issue in understanding and controlling spreading processes on complex networks. Recent studies showed that nodes located in the core of a network as identified by the k-shell decomposition are the most influential spreaders. However, through a great deal of numerical simulations, we observe that not in all real networks do nodes in high shells are very influential: in some networks the core nodes are the most influential which we call true core, while in others nodes in high shells, even the innermost core, are not good spreaders which we call core-like group. By analyzing the k-core structure of the networks, we find that the true core of a network links diversely to the shells of the network, while the core-like group links very locally within the group. For nodes in the core-like group, the k-shell index cannot reflect their location importance in the network. We further introduce a measure based on the link diversity of shells to effectively distinguish the true core and core-like group, and identify core-like groups throughout the networks. Our findings help to better understand the structural features of real networks and influential nodes.

We derive a two-layer multiplex Kuramoto model from weakly coupled Wilson-Cowan oscillators on a cortical network with inhibitory synaptic time delays. Depending on the coupling strength and a phase shift parameter, related to cerebral blood flow and GABA concentration, respectively, we numerically identify three macroscopic phases: unsynchronized, synchronized, and chaotic dynamics. These correspond to physiological background-, epileptic seizure-, and resting-state cortical activity, respectively. We also observe frequency suppression at the transition from resting-state to seizure activity.

Many networks can be usefully decomposed into a dense core plus an outlying, loosely-connected periphery. Here we propose an algorithm for performing such a decomposition on empirical network data using methods of statistical inference. Our method fits a generative model of core-periphery structure to observed data using a combination of an expectation--maximization algorithm for calculating the parameters of the model and a belief propagation algorithm for calculating the decomposition itself. We find the method to be efficient, scaling easily to networks with a million or more nodes and we test it on a range of networks, including real-world examples as well as computer-generated benchmarks, for which it successfully identifies known core-periphery structure with low error rate. We also demonstrate that the method is immune from the detectability transition observed in the related community detection problem, which prevents the detection of community structure when that structure is too weak. There is no such transition for core-periphery structure, which is detectable, albeit with some statistical error, no matter how weak it is.

The sum of independent Wishart matrices, taken from distributions with unequal covariance matrices, plays a crucial role in multivariate statistics, and has applications in the fields of quantitative finance and telecommunication. However, analytical results concerning the corresponding eigenvalue statistics have remained unavailable, even for the sum of two Wishart matrices. This can be attributed to the complicated and rotationally noninvariant nature of the matrix distribution that makes extracting the information about eigenvalues a nontrivial task. Using a generalization of the Harish-Chandra-Itzykson-Zuber integral, we find exact solution to this problem for the complex Wishart case when one of the covariance matrices is proportional to the identity matrix, while the other is arbitrary. We derive exact and compact expressions for the joint probability density and marginal density of eigenvalues. The analytical results are compared with numerical simulations and we find perf...