On full-connectivity properties of locally connected oscillatory networks

Fernando Corinto, Marco Gilli, T. Roska

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The latest many-core chip technology advances foster highly parallel computing systems. Consequently, it is crucial to conceive hardware oriented architectures and to realize VLSI platforms, with kilo- or mega-processors, that are able to process and recognize spatial-temporal patterns without breaking them into frames. Oscillatory networks, their archetype being the Turing morphogenesis model, represent a suitable paradigm for processing spatial-temporal time-periodic patterns. In this manuscript we aim at pointing out full-connectivity properties of locally connected oscillatory networks (LCONs) with linear memoryless and space-invariant interactions. In particular, it is analytically shown that LCONs can implement any operators of globally connected networks with linear dynamical interactions, if some suitable components of the oscillator state vector are coupled. The key issue of our results is that the inverse of a banded matrix is almost always full, i.e., almost all of its entries are nonzero. Space-invariant local connectivity allows for hardware realizations with straightforward architectures.

Original languageEnglish
Article number5688202
Pages (from-to)1063-1075
Number of pages13
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Volume58
Issue number5
DOIs
Publication statusPublished - 2011

Fingerprint

Hardware
Parallel processing systems
Processing

Keywords

  • Cellular nonlinear networks
  • fully connected networks
  • oscillatory patterns

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

On full-connectivity properties of locally connected oscillatory networks. / Corinto, Fernando; Gilli, Marco; Roska, T.

In: IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 58, No. 5, 5688202, 2011, p. 1063-1075.

Research output: Contribution to journalArticle

@article{50f88a5726bf4f809fc561fe2099bda1,
title = "On full-connectivity properties of locally connected oscillatory networks",
abstract = "The latest many-core chip technology advances foster highly parallel computing systems. Consequently, it is crucial to conceive hardware oriented architectures and to realize VLSI platforms, with kilo- or mega-processors, that are able to process and recognize spatial-temporal patterns without breaking them into frames. Oscillatory networks, their archetype being the Turing morphogenesis model, represent a suitable paradigm for processing spatial-temporal time-periodic patterns. In this manuscript we aim at pointing out full-connectivity properties of locally connected oscillatory networks (LCONs) with linear memoryless and space-invariant interactions. In particular, it is analytically shown that LCONs can implement any operators of globally connected networks with linear dynamical interactions, if some suitable components of the oscillator state vector are coupled. The key issue of our results is that the inverse of a banded matrix is almost always full, i.e., almost all of its entries are nonzero. Space-invariant local connectivity allows for hardware realizations with straightforward architectures.",
keywords = "Cellular nonlinear networks, fully connected networks, oscillatory patterns",
author = "Fernando Corinto and Marco Gilli and T. Roska",
year = "2011",
doi = "10.1109/TCSI.2010.2092050",
language = "English",
volume = "58",
pages = "1063--1075",
journal = "IEEE Transactions on Circuits and Systems II: Express Briefs",
issn = "1057-7122",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "5",

}

TY - JOUR

T1 - On full-connectivity properties of locally connected oscillatory networks

AU - Corinto, Fernando

AU - Gilli, Marco

AU - Roska, T.

PY - 2011

Y1 - 2011

N2 - The latest many-core chip technology advances foster highly parallel computing systems. Consequently, it is crucial to conceive hardware oriented architectures and to realize VLSI platforms, with kilo- or mega-processors, that are able to process and recognize spatial-temporal patterns without breaking them into frames. Oscillatory networks, their archetype being the Turing morphogenesis model, represent a suitable paradigm for processing spatial-temporal time-periodic patterns. In this manuscript we aim at pointing out full-connectivity properties of locally connected oscillatory networks (LCONs) with linear memoryless and space-invariant interactions. In particular, it is analytically shown that LCONs can implement any operators of globally connected networks with linear dynamical interactions, if some suitable components of the oscillator state vector are coupled. The key issue of our results is that the inverse of a banded matrix is almost always full, i.e., almost all of its entries are nonzero. Space-invariant local connectivity allows for hardware realizations with straightforward architectures.

AB - The latest many-core chip technology advances foster highly parallel computing systems. Consequently, it is crucial to conceive hardware oriented architectures and to realize VLSI platforms, with kilo- or mega-processors, that are able to process and recognize spatial-temporal patterns without breaking them into frames. Oscillatory networks, their archetype being the Turing morphogenesis model, represent a suitable paradigm for processing spatial-temporal time-periodic patterns. In this manuscript we aim at pointing out full-connectivity properties of locally connected oscillatory networks (LCONs) with linear memoryless and space-invariant interactions. In particular, it is analytically shown that LCONs can implement any operators of globally connected networks with linear dynamical interactions, if some suitable components of the oscillator state vector are coupled. The key issue of our results is that the inverse of a banded matrix is almost always full, i.e., almost all of its entries are nonzero. Space-invariant local connectivity allows for hardware realizations with straightforward architectures.

KW - Cellular nonlinear networks

KW - fully connected networks

KW - oscillatory patterns

UR - http://www.scopus.com/inward/record.url?scp=79955522399&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955522399&partnerID=8YFLogxK

U2 - 10.1109/TCSI.2010.2092050

DO - 10.1109/TCSI.2010.2092050

M3 - Article

AN - SCOPUS:79955522399

VL - 58

SP - 1063

EP - 1075

JO - IEEE Transactions on Circuits and Systems II: Express Briefs

JF - IEEE Transactions on Circuits and Systems II: Express Briefs

SN - 1057-7122

IS - 5

M1 - 5688202

ER -