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Networks of random trees as a model of neuronal connectivity

Ajazi, Fioralba LU ; Chavez–Demoulin, Valérie and Turova, Tatyana LU (2019) In Journal of Mathematical Biology
Abstract

We provide an analysis of a randomly grown 2-d network which models the morphological growth of dendritic and axonal arbors. From the stochastic geometry of this model we derive a dynamic graph of potential synaptic connections. We estimate standard network parameters such as degree distribution, average shortest path length and clustering coefficient, considering all these parameters as functions of time. Our results show that even a simple model with just a few parameters is capable of representing a wide spectra of architecture, capturing properties of well-known models, such as random graphs or small world networks, depending on the time of the network development. The introduced model allows not only rather straightforward... (More)

We provide an analysis of a randomly grown 2-d network which models the morphological growth of dendritic and axonal arbors. From the stochastic geometry of this model we derive a dynamic graph of potential synaptic connections. We estimate standard network parameters such as degree distribution, average shortest path length and clustering coefficient, considering all these parameters as functions of time. Our results show that even a simple model with just a few parameters is capable of representing a wide spectra of architecture, capturing properties of well-known models, such as random graphs or small world networks, depending on the time of the network development. The introduced model allows not only rather straightforward simulations but it is also amenable to a rigorous analysis. This provides a base for further study of formation of synaptic connections on such networks and their dynamics due to plasticity.

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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
Branching process, Neuronal network, Random graph
in
Journal of Mathematical Biology
publisher
Springer
external identifiers
  • scopus:85069708377
ISSN
0303-6812
DOI
10.1007/s00285-019-01406-8
language
English
LU publication?
yes
id
c29c4864-bee1-41d9-82f5-41cdbeb38bf8
date added to LUP
2019-08-09 15:29:01
date last changed
2019-10-15 07:11:57
@article{c29c4864-bee1-41d9-82f5-41cdbeb38bf8,
  abstract     = {<p>We provide an analysis of a randomly grown 2-d network which models the morphological growth of dendritic and axonal arbors. From the stochastic geometry of this model we derive a dynamic graph of potential synaptic connections. We estimate standard network parameters such as degree distribution, average shortest path length and clustering coefficient, considering all these parameters as functions of time. Our results show that even a simple model with just a few parameters is capable of representing a wide spectra of architecture, capturing properties of well-known models, such as random graphs or small world networks, depending on the time of the network development. The introduced model allows not only rather straightforward simulations but it is also amenable to a rigorous analysis. This provides a base for further study of formation of synaptic connections on such networks and their dynamics due to plasticity.</p>},
  author       = {Ajazi, Fioralba and Chavez–Demoulin, Valérie and Turova, Tatyana},
  issn         = {0303-6812},
  keyword      = {Branching process,Neuronal network,Random graph},
  language     = {eng},
  month        = {07},
  publisher    = {Springer},
  series       = {Journal of Mathematical Biology},
  title        = {Networks of random trees as a model of neuronal connectivity},
  url          = {http://dx.doi.org/10.1007/s00285-019-01406-8},
  year         = {2019},
}