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Exhaustive percolation on random networks

Samuelsson, Björn LU and Socolar, Joshua E. S. (2006) In Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 74(3).
Abstract
We consider propagation models that describe the spreading of an attribute, called “damage,” through the nodes of a random network. In some systems, the average fraction of nodes that remain undamaged vanishes in the large system limit, a phenomenon we refer to as exhaustive percolation. We derive scaling law exponents and exact results for the distribution of the number of undamaged nodes, valid for a broad class of random networks at the exhaustive percolation transition and in the exhaustive percolation regime. This class includes processes that determine the set of frozen nodes in random Boolean networks with indegree distributions that decay sufficiently rapidly with the number of inputs. Connections between our calculational methods... (More)
We consider propagation models that describe the spreading of an attribute, called “damage,” through the nodes of a random network. In some systems, the average fraction of nodes that remain undamaged vanishes in the large system limit, a phenomenon we refer to as exhaustive percolation. We derive scaling law exponents and exact results for the distribution of the number of undamaged nodes, valid for a broad class of random networks at the exhaustive percolation transition and in the exhaustive percolation regime. This class includes processes that determine the set of frozen nodes in random Boolean networks with indegree distributions that decay sufficiently rapidly with the number of inputs. Connections between our calculational methods and previous studies of percolation beginning from a single initial node are also pointed out. Central to our approach is the observation that key aspects of damage spreading on a random network are fully characterized by a single function specifying the probability that a given node will be damaged as a function of the fraction of damaged nodes. In addition to our analytical investigations of random networks, we present a numerical example of exhaustive percolation on a directed lattice. (Less)
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author
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
volume
74
issue
3
publisher
American Physical Society
external identifiers
  • scopus:33749244629
ISSN
1539-3755
DOI
10.1103/PhysRevE.74.036113
language
English
LU publication?
no
id
5c8050c0-8dd5-4d36-bed7-bc130725be1f (old id 1260848)
alternative location
http://link.aps.org/abstract/PRE/v74/e036113
date added to LUP
2008-10-31 09:02:57
date last changed
2019-07-30 01:49:51
@article{5c8050c0-8dd5-4d36-bed7-bc130725be1f,
  abstract     = {We consider propagation models that describe the spreading of an attribute, called “damage,” through the nodes of a random network. In some systems, the average fraction of nodes that remain undamaged vanishes in the large system limit, a phenomenon we refer to as exhaustive percolation. We derive scaling law exponents and exact results for the distribution of the number of undamaged nodes, valid for a broad class of random networks at the exhaustive percolation transition and in the exhaustive percolation regime. This class includes processes that determine the set of frozen nodes in random Boolean networks with indegree distributions that decay sufficiently rapidly with the number of inputs. Connections between our calculational methods and previous studies of percolation beginning from a single initial node are also pointed out. Central to our approach is the observation that key aspects of damage spreading on a random network are fully characterized by a single function specifying the probability that a given node will be damaged as a function of the fraction of damaged nodes. In addition to our analytical investigations of random networks, we present a numerical example of exhaustive percolation on a directed lattice.},
  articleno    = {036113},
  author       = {Samuelsson, Björn and Socolar, Joshua E. S.},
  issn         = {1539-3755},
  language     = {eng},
  number       = {3},
  publisher    = {American Physical Society},
  series       = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)},
  title        = {Exhaustive percolation on random networks},
  url          = {http://dx.doi.org/10.1103/PhysRevE.74.036113},
  volume       = {74},
  year         = {2006},
}