Scalability of Asynchronous Networks Is Limited by One-to-One Mapping between Effective Connectivity and Correlations

PLoS Computational Biology
Sacha Jennifer van AlbadaMarkus Diesmann

Abstract

Network models are routinely downscaled compared to nature in terms of numbers of nodes or edges because of a lack of computational resources, often without explicit mention of the limitations this entails. While reliable methods have long existed to adjust parameters such that the first-order statistics of network dynamics are conserved, here we show that limitations already arise if also second-order statistics are to be maintained. The temporal structure of pairwise averaged correlations in the activity of recurrent networks is determined by the effective population-level connectivity. We first show that in general the converse is also true and explicitly mention degenerate cases when this one-to-one relationship does not hold. The one-to-one correspondence between effective connectivity and the temporal structure of pairwise averaged correlations implies that network scalings should preserve the effective connectivity if pairwise averaged correlations are to be held constant. Changes in effective connectivity can even push a network from a linearly stable to an unstable, oscillatory regime and vice versa. On this basis, we derive conditions for the preservation of both mean population-averaged activities and pairwise averag...Continue Reading

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Citations

Nov 1, 2016·Cerebral Cortex·Espen HagenGaute T Einevoll
Mar 6, 2018·Frontiers in Neuroinformatics·Jakob JordanSusanne Kunkel
Oct 21, 2017·PloS One·Benedict J LünsmannMarc Timme
Jul 25, 2019·PLoS Computational Biology·Madhura R JoglekarLai-Sang Young
Oct 20, 2018·PLoS Computational Biology·Maximilian SchmidtSacha Jennifer van Albada
Feb 2, 2017·PLoS Computational Biology·Jannis SchueckerMoritz Helias
Jun 10, 2017·Frontiers in Neuroinformatics·Jan HahneMarkus Diesmann
Nov 24, 2018·Frontiers in Neuroinformatics·Johanna SenkBenjamin Weyers
Oct 24, 2018·Frontiers in Neuroinformatics·Inga BlundellAbigail Morrison
May 21, 2020·Frontiers in Neuroinformatics·Jakob JordanSusanne Kunkel
Feb 23, 2017·Frontiers in Neuroinformatics·Francisco NaverosNiceto R Luque
Jun 1, 2017·Frontiers in Neuroinformatics·Tammo IppenMarkus Diesmann
Mar 7, 2021·Scientific Reports·Anar AmgalanHava T Siegelmann
Aug 20, 2021·Neural Computation·Cecilia RomaroSalvador Dura-Bernal

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Software Mentioned

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Python
PyNN

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