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

This title appears in the Scientific Report : 2015

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

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 stati...

Personal Name(s):	van Albada, Sacha (Corresponding author)
	Helias, Moritz / Diesmann, Markus
Contributing Institute:	Theoretical Neuroscience; IAS-6 Computational and Systems Neuroscience; INM-6
Published in:	PLoS Computational Biology, 11 (2015) 9, S. e1004490 -
Imprint:	San Francisco, Calif. Public Library of Science 2015
PubMed ID:	26325661
DOI:	10.1371/journal.pcbi.1004490
Document Type:	Journal Article
Research Program:	Supercomputing and Modelling for the Human Brain Theory of multi-scale neuronal networks Brain-inspired multiscale computation in neuromorphic hybrid systems The Human Brain Project Theory, modelling and simulation
Link:	OpenAccess OpenAccess
	Publikationsportal JuSER

Please use the identifier: http://dx.doi.org/10.1371/journal.pcbi.1004490 in citations.
Please use the identifier: http://hdl.handle.net/2128/9319 in citations.

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 averaged correlations under a change in numbers of neurons or synapses in the asynchronous regime typical of cortical networks. We find that mean activities and correlation structure can be maintained by an appropriate scaling of the synaptic weights, but only over a range of numbers of synapses that is limited by the variance of external inputs to the network. Our results therefore show that the reducibility of asynchronous networks is fundamentally limited.