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  • Physical Review E  (15)
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  • 1
    Language: English
    In: Physical review. E, Statistical, nonlinear, and soft matter physics, July 2011, Vol.84(1 Pt 2), pp.016104
    Description: We introduce a broad class of analytically solvable processes on networks. In the special case, they reduce to random walk and consensus process, the two most basic processes on networks. Our class differs from previous models of interactions (such as the stochastic Ising model, cellular automata, infinite particle systems, and the voter model) in several ways, the two most important being (i) the model is analytically solvable even when the dynamical equation for each node may be different and the network may have an arbitrary finite graph and influence structure and (ii) when local dynamics is described by the same evolution equation, the model is decomposable, with the equilibrium behavior of the system expressed as an explicit function of network topology and node dynamics.
    Keywords: Models, Theoretical
    E-ISSN: 1550-2376
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  • 2
    Language: English
    In: Physical review. E, Statistical, nonlinear, and soft matter physics, January 2012, Vol.85(1 Pt 2), pp.016114
    Description: The influence of the network's structure on the dynamics of spreading processes has been extensively studied in the last decade. Important results that partially answer this question show a weak connection between the macroscopic behavior of these processes and specific structural properties in the network, such as the largest eigenvalue of a topology related matrix. However, little is known about the direct influence of the network topology on the microscopic level, such as the influence of the (neighboring) network on the probability of a particular node's infection. To answer this question, we derive both an upper and a lower bound for the probability that a particular node is infective in a susceptible-infective-susceptible model for two cases of spreading processes: reactive and contact processes. The bounds are derived by considering the n-hop neighborhood of the node; the bounds are tighter as one uses a larger n-hop neighborhood to calculate them. Consequently, using local information for different neighborhood sizes, we assess the extent to which the topology influences the spreading process, thus providing also a strong macroscopic connection between the former and the latter. Our findings are complemented by numerical results for a real-world email network. A very good estimate for the infection density ρ is obtained using only two-hop neighborhoods, which account for 0.4% of the entire network topology on average.
    Keywords: Models, Theoretical ; Communicable Diseases -- Epidemiology
    E-ISSN: 1550-2376
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  • 3
    Language: English
    In: Physical review. E, Statistical, nonlinear, and soft matter physics, October 2011, Vol.84(4 Pt 2), pp.046102
    Description: Communities are not static; they evolve, split and merge, appear and disappear, i.e., they are the product of dynamical processes that govern the evolution of a network. A good algorithm for community detection should not only quantify the topology of the network but incorporate the dynamical processes that take place on the network. We present an algorithm for community detection that combines network structure with processes that support the creation and/or evolution of communities. The algorithm does not embrace the universal approach but instead tries to focus on social networks and model dynamic social interactions that occur on those networks. It identifies leaders and communities that form around those leaders. It naturally supports overlapping communities by associating each node with a membership vector that describes the node's involvement in each community. This way, in addition to the overlapping communities, we can identify nodes that are good followers of their leader and also nodes with no clear community involvement that serve as proxies between several communities and that are equally as important. We run the algorithm for several real social networks which we believe represent a good fraction of the wide body of social networks and discuss the results, including other possible applications.
    Keywords: Physics - Physics And Society ; Condensed Matter - Statistical Mechanics ; Computer Science - Social And Information Networks;
    E-ISSN: 1550-2376
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  • 4
    Language: English
    In: Physical review. E, Statistical, nonlinear, and soft matter physics, May 2010, Vol.81(5 Pt 2), pp.056102
    Description: An alternate model for rumor spreading over networks is suggested, in which two rumors (termed rumor 1 and rumor 2) with different probabilities of acceptance may propagate among nodes. The propagation is not symmetric in the sense that when deciding which rumor to adopt, nodes always consider rumor 1 first. The model is a natural generalization of the well-known epidemic SIS (susceptible-infective-susceptible) model and reduces to it when some of the parameters of this model are zero. We find that preferred rumor 1 is dominant in the network when the degree of nodes is high enough and/or when the network contains large clustered groups of nodes, expelling rumor 2. However, numerical simulations on synthetic networks show that it is possible for rumor 2 to occupy a nonzero fraction of the nodes in many cases as well. Specifically, in the Watts-Strogatz small-world model a moderate level of clustering supports its adoption, while increasing randomness reduces it. For Erdos-Renyi networks, a low average degree allows the coexistence of the two types of rumors. In Barabasi-Albert networks generated with a low m , where m is the number of links when a new node is added, it is also possible for rumor 2 to spread over the network.
    ISSN: 15393755
    E-ISSN: 1550-2376
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  • 5
    Language: English
    In: Physical review. E, Statistical, nonlinear, and soft matter physics, October 2009, Vol.80(4 Pt 1), pp.041102
    Description: We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a complete graph, a cycle graph, and a path graph. An accurate approximation for the cover time distribution, with computational complexity of O(2n) , is also presented. The approximation is numerically tested only for graphs with n〈or=1000 nodes.
    Keywords: Stochastic Processes
    ISSN: 15393755
    E-ISSN: 1550-2376
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  • 6
    Language: English
    In: Physical review. E, May 2018, Vol.97(5-1), pp.052305
    Description: We introduce a framework for studying social dilemmas in networked societies where individuals follow a simple state-based behavioral mechanism based on generalized reciprocity, which is rooted in the principle "help anyone if helped by someone." Within this general framework, which applies to a wide range of social dilemmas including, among others, public goods, donation, and snowdrift games, we study the cooperation dynamics on a variety of complex network examples. By interpreting the studied model through the lenses of nonlinear dynamical systems, we show that cooperation through generalized reciprocity always emerges as the unique attractor in which the overall level of cooperation is maximized, while simultaneously exploitation of the participating individuals is prevented. The analysis elucidates the role of the network structure, here captured by a local centrality measure which uniquely quantifies the propensity of the network structure to cooperation by dictating the degree of cooperation displayed both at the microscopic and macroscopic level. We demonstrate the applicability of the analysis on a practical example by considering an interaction structure that couples a donation process with a public goods game.
    Keywords: Cooperative Behavior ; Game Theory
    ISSN: 24700045
    E-ISSN: 2470-0053
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  • 7
    Language: English
    In: Physical review. E, August 2017, Vol.96(2-1), pp.022315
    Description: A growing body of empirical evidence indicates that social and cooperative behavior can be affected by cognitive and neurological factors, suggesting the existence of state-based decision-making mechanisms that may have emerged by evolution. Motivated by these observations, we propose a simple mechanism of anonymous network interactions identified as a form of generalized reciprocity-a concept organized around the premise "help anyone if helped by someone'-and study its dynamics on random graphs. In the presence of such a mechanism, the evolution of cooperation is related to the dynamics of the levels of investments (i.e., probabilities of cooperation) of the individual nodes engaging in interactions. We demonstrate that the propensity for cooperation is determined by a network centrality measure here referred to as neighborhood importance index and discuss relevant implications to natural and artificial systems. To address the robustness of the state-based strategies to an invasion of defectors, we additionally provide an analysis which redefines the results for the case when a fraction of the nodes behave as unconditional defectors.
    Keywords: Quantitative Biology - Populations And Evolution;
    ISSN: 24700045
    E-ISSN: 2470-0053
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  • 8
    Language: English
    In: Physical review. E, Statistical, nonlinear, and soft matter physics, April 2002, Vol.65(4 Pt 2A), pp.046215
    Description: We show that Lyapunov exponents of a stochastic system, when computed for a specific realization of the noise process, are related to conditional Lyapunov exponents in deterministic systems. We propose to use the term stochastically induced regularity instead of noise-induced synchronization and explain the reason why. The nature of stochastically induced regularity is discussed: in some instances, it is a dynamical analog of Parrondo's paradox.
    ISSN: 1539-3755
    E-ISSN: 15502376
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  • 9
    Language: English
    In: Physical review. E, Statistical, nonlinear, and soft matter physics, April 2006, Vol.73(4 Pt 2), pp.046102
    Description: Node betweenness has been studied recently by a number of authors, but until now less attention has been paid to edge betweenness. In this paper, we present an exact analytic study of edge betweenness in evolving scale-free and non-scale-free trees. We aim at the probability distribution of edge betweenness under the condition that a local property, the in-degree of the "younger" node of a randomly selected edge, is known. En route to the conditional distribution of edge betweenness the exact joint distribution of cluster size and in-degree, and its one-dimensional marginal distributions have been presented in the paper as well. From the derived probability distributions the expectation values of different quantities have been calculated. Our results provide an exact solution not only for infinite, but for finite networks as well.
    Keywords: Computer Science - Networking And Internet Architecture ; Condensed Matter - Other Condensed Matter ; G.2.2;
    ISSN: 1539-3755
    E-ISSN: 15502376
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  • 10
    Language: English
    In: Physical review. E, Statistical, nonlinear, and soft matter physics, September 2002, Vol.66(3 Pt 2A), pp.036229
    Description: We address the question of bounds on the synchronization error for the case of nearly identical nonlinear systems. It is pointed out that negative largest conditional Lyapunov exponents of the synchronization manifold are not sufficient to guarantee a small synchronization error and that one has to find bounds for the deformation of the manifold due to perturbations. We present an analytic bound for a simple subclass of systems, which includes the Lur'e systems, showing that the bound for the deformation grows as the largest singular value of the linearized system gets larger. Then, the Lorenz system is taken as an example to demonstrate that the phenomenon is not restricted to Lur'e systems.
    Keywords: Physics;
    ISSN: 1539-3755
    E-ISSN: 15502376
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