Response of complex networks to stimuli

Bar‐Yam, Yaneer; Epstein, Irving R.

doi:10.1073/pnas.0400673101

Cited by 93 publications

(95 citation statements)

References 19 publications

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“…And the robustness is important for understanding evolutionary processes and homeostasis of gene regulatory networks [18,19,20,21,22]. However, in this report we investigated only robustness to the single site inversion.…”

Section: Summary and Discussionmentioning

confidence: 91%

Robustness of Attractor States in Complex Networks

Kinoshita¹,

Iguchi²,

Yamada³

2008

AIP Conference Proceedings

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Abstract. We study the intrinsic properties of attractors in the Boolean dynamics in complex network with scale-free topology, comparing with those of the so-called random Kauffman networks. We have numerically investigated the frozen and relevant nodes for each attractor, and the robustness of the attractors to the perturbation that flips the state of a single node of attractors in the relatively small network (N = 30 ∼ 200). It is shown that the rate of frozen nodes in the complex networks with scale-free topology is larger than that in the random Kauffman model. Furthermore, we have found that in the complex scale-free networks with fluctuations of in-degree number the attractors are more sensitive to the state flip of a highly connected node than to the state flip of a less connected node.

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Section: Summary and Discussionmentioning

confidence: 91%

Robustness of Attractor States in Complex Networks

Kinoshita¹,

Iguchi²,

Yamada³

2008

AIP Conference Proceedings

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“…These local majority rules are equivalent to Glauber dynamics (20) at zero temperature as studied, e.g., on d-dimensional hypercubic networks (30) and on random Poissonian networks (31). Recently, similar dynamic models were also used in the context of opinion spreading (28), network robustness and sensitivity (25), and the yeast cell-cycle regulation system (26). In general, the graph of a random scale-free network may be disconnected and consist of several components.…”

Section: Models and Methodsmentioning

confidence: 99%

“…This sensitivity of ordered spin patterns to selective spin flips has been independently observed in ref. 25. In contrast to the behavior of the decay time for strongly disordered patterns, the minimal fraction varies smoothly with the decay exponent ␥ in the vicinity of ␥ ϭ 5͞2.…”

mentioning

confidence: 95%

“…This sensitivity of ordered spin patterns to selective spin flips has been independently observed in ref. 25. Thus, a scale-free network with a decay exponent ␥ that is close to ␥ ϭ 2 has the additional property that one needs to selectively flip only a very small fraction of the spins to induce a transition from one ordered pattern to the other.…”

Section: [14]mentioning

confidence: 99%

“…2, whereas analogous processes on scale-free networks have only been addressed rather recently (24)(25)(26).…”

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confidence: 99%

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Dynamic pattern evolution on scale-free networks

Zhou

Lipowsky

2005

Proc. Natl. Acad. Sci. U.S.A.

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A general class of dynamic models on scale-free networks is studied by analytical methods and computer simulations. Each network consists of N vertices and is characterized by its degree distribution, P(k), which represents the probability that a randomly chosen vertex is connected to k nearest neighbors. Each vertex can attain two internal states described by binary variables or Ising-like spins that evolve in time according to local majority rules. Scalefree networks, for which the degree distribution has a power law tail P(k) ϳ k ؊␥ , are shown to exhibit qualitatively different dynamic behavior for ␥ < 5͞2 and ␥ > 5͞2, shedding light on the empirical observation that many real-world networks are scale-free with 2 < ␥ < 5͞2. For 2 < ␥ < 5͞2, strongly disordered patterns decay within a finite decay time even in the limit of infinite networks. For ␥ > 5͞2, on the other hand, this decay time diverges as ln(N) with the network size N. An analogous distinction is found for a variety of more complex models including Hopfield models for associative memory networks. In the latter case, the storage capacity is found, within mean field theory, to be independent of N in the limit of large N for ␥ > 5͞2 but to grow as N ␣ with ␣ ‫؍‬ (5 ؊ 2␥)͞(␥ ؊ 1) for 2 < ␥ < 5͞2.random network ͉ Boolean dynamics ͉ cellular automata ͉ associative memory

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From centrality to temporary fame: Dynamic centrality in complex networks

2006

Self Cite

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We develop a new approach to the study of the dynamics of link utilization in complex networks using records of communication in a large social network. Counter to the perspective that nodes have particular rolesKey Words: social networks, time-based networks, dynamic hubs, multiscale networks, turbulent networks R ecent advances have demonstrated that the study of universal properties in physical systems may be extended to complex networks in biological and social systems [1][2][3][4][5]. This has opened the study of such networks to experimental and theoretical characterization of properties and mechanisms of formation. In this article we extend the study of complex networks by considering the dynamics of the activity of network connections. Our analysis suggests that fundamentally new insights can be obtained from the dynamical behavior, including a dramatic time dependence of the role of nodes that is not apparent from static (time aggregated) analysis of node connectivity and network topology.We study the communication between 57,158 e-mail users based on data sampled over a period of 113 days from log files maintained by the e-mail server at a large university [6]. The time when an e-mail link is established between any pair of e-mail addresses is routinely registered in a server, enabling the analysis of the temporal dynamics of the interactions within the network. To consider only e-mails that reflect the flow of valuable information, spam and bulk mailings were excluded using a prefilter. There were 447,543 messages exchanged by the users during a 113-day observation. We report results obtained by treating the communications as an undirected network, where e-mail addresses are regarded as nodes and two nodes are linked if there is an e-mail communication between them. Analysis based on treating the network with asymmetric links (where a distinction is made between out-going links and incoming links) gave essentially equivalent results. From the temporal Correspondence to: Yaneer Bar-Yam,

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Response of complex networks to stimuli

Cited by 93 publications

References 19 publications

Robustness of Attractor States in Complex Networks

Robustness of Attractor States in Complex Networks

Dynamic pattern evolution on scale-free networks

From centrality to temporary fame: Dynamic centrality in complex networks

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