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The emergence of connectivity in neuronal networks: From bootstrap percolation to auto-associative memory

Turova, Tatyana LU (2012) In Brain Research 1434. p.277-284
Abstract
We consider a random synaptic pruning in an initially highly interconnected network. It is proved that a random network can maintain a self-sustained activity level for some parameters. For such a set of parameters a pruning is constructed so that in the resulting network each neuron/node has almost equal numbers of in- and out-connections. It is also shown that the set of parameters which admits a self-sustained activity level is rather small within the whole space of possible parameters. It is pointed out here that the threshold of connectivity for an auto-associative memory in a Hopfield model on a random graph coincides with the threshold for the bootstrap percolation on the same random graph. It is argued that this coincidence... (More)
We consider a random synaptic pruning in an initially highly interconnected network. It is proved that a random network can maintain a self-sustained activity level for some parameters. For such a set of parameters a pruning is constructed so that in the resulting network each neuron/node has almost equal numbers of in- and out-connections. It is also shown that the set of parameters which admits a self-sustained activity level is rather small within the whole space of possible parameters. It is pointed out here that the threshold of connectivity for an auto-associative memory in a Hopfield model on a random graph coincides with the threshold for the bootstrap percolation on the same random graph. It is argued that this coincidence reflects the relations between the auto-associative memory mechanism and the properties of the underlying random network structure. This article is part of a Special Issue entitled "Neural Coding". (C) 2011 Elsevier B.V. All rights reserved. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Integrate-and-fire network, Random graph, Storage capacity, Percolation
in
Brain Research
volume
1434
pages
277 - 284
publisher
Elsevier
external identifiers
  • wos:000301559700025
  • scopus:84856609728
ISSN
1872-6240
DOI
10.1016/j.brainres.2011.07.050
language
English
LU publication?
yes
id
73d84fcb-6818-42f6-b310-d8858ae1d051 (old id 2515255)
date added to LUP
2012-05-07 12:37:02
date last changed
2017-11-05 03:18:51
@article{73d84fcb-6818-42f6-b310-d8858ae1d051,
  abstract     = {We consider a random synaptic pruning in an initially highly interconnected network. It is proved that a random network can maintain a self-sustained activity level for some parameters. For such a set of parameters a pruning is constructed so that in the resulting network each neuron/node has almost equal numbers of in- and out-connections. It is also shown that the set of parameters which admits a self-sustained activity level is rather small within the whole space of possible parameters. It is pointed out here that the threshold of connectivity for an auto-associative memory in a Hopfield model on a random graph coincides with the threshold for the bootstrap percolation on the same random graph. It is argued that this coincidence reflects the relations between the auto-associative memory mechanism and the properties of the underlying random network structure. This article is part of a Special Issue entitled "Neural Coding". (C) 2011 Elsevier B.V. All rights reserved.},
  author       = {Turova, Tatyana},
  issn         = {1872-6240},
  keyword      = {Integrate-and-fire network,Random graph,Storage capacity,Percolation},
  language     = {eng},
  pages        = {277--284},
  publisher    = {Elsevier},
  series       = {Brain Research},
  title        = {The emergence of connectivity in neuronal networks: From bootstrap percolation to auto-associative memory},
  url          = {http://dx.doi.org/10.1016/j.brainres.2011.07.050},
  volume       = {1434},
  year         = {2012},
}