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Browsing Mathematics & Statistics by Author "Melnik, Sergey"

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Browsing Mathematics & Statistics by Author "Melnik, Sergey"

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  • Gleeson, James P.; Melnik, Sergey; Ward, Jonathan A; Porter, Mason A; Murcha, Peter J (American Physical Society, 2012)
    Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is ...
  • Gleeson, James P.; Melnik, Sergey (American Physical Society, 2009)
    An analytical approach to calculating bond percolation thresholds, sizes of k-cores, and sizes of giant connected components on structured random networks with nonzero clustering is presented. The networks are generated ...
  • Hackett, Adam W.; Melnik, Sergey; Gleeson, James P. (American Physical Society, 2011)
    We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of random networks with arbitrary degree distribution and nonzero clustering introduced previously ...
  • Melnik, Sergey; Porter, Mason A; Mucha, Peter J; Gleeson, James P. (American Institute of Physics, 2014)
    We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module, and the inter-module connections are defined by the joint degree-degree distribution of nodes for each ...
  • Gleeson, James P.; Melnik, Sergey; Hackett, Adam W. (American Physical Society, 2010)
    The question of how clustering (nonzero density of triangles) in networks affects their bond percolation threshold has important applications in a variety of disciplines. Recent advances in modeling highly clustered networks ...
  • Melnik, Sergey; Ward, Jonathan A; Gleeson, James P.; Porter, Mason A (American Institute of Physics, 2013)
    The spread of ideas across a social network can be studied using complex contagion models, in which agents are activated by contact with multiple activated neighbors. The investigation of complex contagions can provide ...
  • Melnik, Sergey; Hackett, Adam W.; Porter, Mason A; Mucha, Peter J; Gleeson, James P. (American Physical Society, 2011)
    We demonstrate that a tree-based theory for various dynamical processes operating on static, undirected networks yields extremely accurate results for several networks with high levels of clustering. We find that such a ...

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