Bootstrap percolation is a well-known model to study the spreading of rumors, new products or innovations on social networks. The empirical studies show that the community structure is ubiquitous among various social ...
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Bootstrap percolation is a well-known model to study the spreading of rumors, new products or innovations on social networks. The empirical studies show that the community structure is ubiquitous among various social networks. Thus, studying the bootstrap percolation on the complex networks with communities can bring us new and important insights into the spreading dynamics in social networks. This has attracted a lot of scientists' attention recently. In this letter, we study the bootstrap percolation on Erdos-Renyi networks with communities and observed second-order, hybrid (both second and first order) and multiple hybrid phase transitions, which is rare in natural system. Moreover, we have analytically solved this system and obtained the phase diagram, which is further justified well by the corresponding simulations. Copyright (C) EPLA, 2014
In this work we study a simple evolutionary model of bipartite networks whose evolution is based on the duplication of nodes. Using analytical results along with numerical simulation of the model, we show that the abo...
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In this work we study a simple evolutionary model of bipartite networks whose evolution is based on the duplication of nodes. Using analytical results along with numerical simulation of the model, we show that the above evolutionary model results in weighted scale-free networks. Indeed we find that in the one-mode picture we have weighted networks with scale-free distributions for interesting quantities like the weights, the degrees and the weighted degrees of the nodes and the weights of the edges.
The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggeste...
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The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional form contains important clues as to underlying evolutionary processes that have shaped the network. Generally, the functional form for the degree distribution has been determined in an ad hoc fashion, with clear power-law-like behaviour often only extending over a limited range of connectivities. Here we apply formal model selection techniques to decide which probability distribution best describes the degree distributions of protein interaction networks. Contrary to previous studies, this well-defined approach suggests that the degree distribution of many molecular networks is often better described by distributions other than the popular power-law distribution. This, in turn, suggests that simple, if elegant, models may not necessarily help in the quantitative understanding of complex biological processes.
Signaling pathways and networks determine the ability to communicate in systems ranging from living cells to human society. We investigate how the network structure constrains communication in social, man-made and bio...
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Signaling pathways and networks determine the ability to communicate in systems ranging from living cells to human society. We investigate how the network structure constrains communication in social, man-made and biological networks. We find that human networks of governance and collaboration have predictable communication on tete-a-tete level, reflecting well-defined pathways. In contrast, communication pathways in the Internet are more distributed. For molecular networks, the communication ability in the single-celled yeast resembles the one of human networks, whereas the more complicated Drosophila is closer to the Internet. For all investigated networks, the global communication is worse than for their random counterparts, reflecting the fact that long-distance communication is disfavored.
Using a steady-state process of node duplication and deletion, relevant to biological and ecological systems, we produce networks with 1/k scale-free degree distributions in the limit of vanishing connectance. The pro...
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Using a steady-state process of node duplication and deletion, relevant to biological and ecological systems, we produce networks with 1/k scale-free degree distributions in the limit of vanishing connectance. The process involves no growth in nodes and inherent preferential attachment is counterbalanced by preferential detachment. The mean-field evolution is considered and the 1/k law is verified under certain approximations. An ansatz for the degree distribution is proposed on the basis of symmetry considerations and is shown to coincide well with the simulation data. Distributional forms other than power law also arise when the duplication fidelity is relaxed.
Statistical physics is used to investigate independent component analysis with polynomial contrast functions. While the replica method fails, an adapted cavity approach yields valid results. The learning curves, obtai...
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Statistical physics is used to investigate independent component analysis with polynomial contrast functions. While the replica method fails, an adapted cavity approach yields valid results. The learning curves, obtained in a suitable thermodynamic limit, display a first-order phase transition from poor to perfect generalization.
In human societies the probability of strategy adoption from a given person may be affected by the personal features. Now we investigate how an artificially imposed restricted ability to reproduce, overruling ones fit...
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In human societies the probability of strategy adoption from a given person may be affected by the personal features. Now we investigate how an artificially imposed restricted ability to reproduce, overruling ones fitness, affects an evolutionary process. For this purpose we employ the evolutionary prisoner's dilemma game on different complex graphs. Reproduction restrictions can have a facilitative effect on the evolution of cooperation that sets in irrespective of particularities of the interaction network. Indeed, an appropriate fraction of less fertile individuals may lead to full supremacy of cooperators where otherwise defection would be widespread. By studying cooperation levels within the group of individuals having full reproduction capabilities, we reveal that the recent mechanism for the promotion of cooperation is conceptually similar to the one reported previously for scale-free networks. Our results suggest that the diversity in the reproduction capability, related to inherently different attitudes of individuals, can enforce the emergence of cooperative behavior among selfish competitors.
We investigate the evolution of cooperative behaviors of small-world networking agents in a snowdrift game mode, where two agents (nodes) are connected with probability depending on their spatial Euclidean lattice dis...
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We investigate the evolution of cooperative behaviors of small-world networking agents in a snowdrift game mode, where two agents (nodes) are connected with probability depending on their spatial Euclidean lattice distance in the power-law form controlled by an exponent alpha. Extensive numerical simulations indicate that the game dynamics crucially depends on the spatial topological structure of underlying networks with different values of the exponent alpha. Especially, in the distance-independent case of alpha=0, the small-world connectivity pattern contributes to an enhancement of cooperation compared with that in regular lattices, even for the case of having a high cost-to-benefit ratio r. However, with the increment of alpha > 0, when r >= 0.4, the spatial distance-dependent small-world (SDSW) structure tends to inhibit the evolution of cooperation in the snowdrift game.
We present a renormalization approach to solve the Sznajd opinion formation model on complex networks. For the case of two opinions, we present an expression of the probability of reaching consensus for a given opinio...
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We present a renormalization approach to solve the Sznajd opinion formation model on complex networks. For the case of two opinions, we present an expression of the probability of reaching consensus for a given opinion as a function of the initial fraction of agents with that opinion. The calculations reproduce the sharp transition of the model on a fixed network, as well as the recently observed smooth function for the model when simulated on a growing complex networks.
World currency network constitutes one of the most complexstructures that is associated with the contemporary civilization. On a way towards quantifying its characteristics we study the cross correlations in changes ...
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World currency network constitutes one of the most complexstructures that is associated with the contemporary civilization. On a way towards quantifying its characteristics we study the cross correlations in changes of the daily foreign exchange rates within the basket of 60 currencies in the period December 1998-May 2005. Such a dynamics turns out to predominantly involve one outstanding eigenvalue of the correlation matrix. The magnitude of this eigenvalue depends however crucially on which currency is used as a base currency for the remaining ones. Most prominent it looks from the perspective of a peripheral currency. This largest eigenvalue is seen to systematically decrease and thus the structure of correlations becomes more heterogeneous, when more significant currencies are used as reference. An extreme case in this later respect is the USD in the period considered. Besides providing further insight into subtle nature of complexity, these observations point to a formal procedure that in general can be used for practical purposes of measuring the relative currencies significance on various time horizons.
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