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Neural Systems Under Change of Scale

Fagerholm, ED; Foulkes, WMC; Gallero-Salas, Y; Helmchen, F; Friston, KJ; Leech, R; Moran, RJ; (2021) Neural Systems Under Change of Scale. Frontiers in Computational Neuroscience , 15 , Article ARTN 643. 10.3389/fncom.2021.643148. Green open access

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Abstract

We derive a theoretical construct that allows for the characterisation of both scalable and scale free systems within the dynamic causal modelling (DCM) framework. We define a dynamical system to be “scalable” if the same equation of motion continues to apply as the system changes in size. As an example of such a system, we simulate planetary orbits varying in size and show that our proposed methodology can be used to recover Kepler’s third law from the timeseries. In contrast, a “scale free” system is one in which there is no characteristic length scale, meaning that images of such a system are statistically unchanged at different levels of magnification. As an example of such a system, we use calcium imaging collected in murine cortex and show that the dynamical critical exponent, as defined in renormalization group theory, can be estimated in an empirical biological setting. We find that a task-relevant region of the cortex is associated with higher dynamical critical exponents in task vs. spontaneous states and vice versa for a task-irrelevant region.

Type: Article
Title: Neural Systems Under Change of Scale
Open access status: An open access version is available from UCL Discovery
DOI: 10.3389/fncom.2021.643148
Publisher version: https://doi.org/10.3389/fncom.2021.643148
Language: English
Additional information: © 2021 Fagerholm, Foulkes, Gallero-Salas, Helmchen, Friston, Leech and Moran. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
Keywords: scalable neural systems, scale free neural systems, mechanical similarity, dynamic causal modeling (DCM), computational neuroscience, theoretical neuroscience, renormalisation group theory
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences > UCL Queen Square Institute of Neurology
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences > UCL Queen Square Institute of Neurology > Imaging Neuroscience
URI: https://discovery.ucl.ac.uk/id/eprint/10128543
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