Imperial College London
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Matthew Foulkes

Faculty of Natural Sciences, Department of Physics

Professor of Physics
 
 
 
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Contact

 

wmc.foulkes Website

 
 
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Location

 

810Blackett LaboratorySouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Fagerholm:2021:10.1186/s13408-021-00108-0,
author = {Fagerholm, ED and Foulkes, W and Friston, KJ and Moran, RJ and Leech, R},
doi = {10.1186/s13408-021-00108-0},
journal = {Journal of Mathematical Neuroscience},
pages = {1--15},
title = {Rendering neuronal state equations compatiblewith the principle of stationary action},
url = {http://dx.doi.org/10.1186/s13408-021-00108-0},
volume = {11},
year = {2021}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - The principle of stationary action is a cornerstone of modern physics, providing a powerful framework for investigating dynamical systems found in classical mechanics through to quantum field theory. However, computational neuroscience, despite its heavy reliance on concepts in physics, is anomalous in this regard as its main equations of motion are not compatible with a Lagrangian formulation and hence with the principle of stationary action. Taking the Dynamic Causal Modelling (DCM) neuronal state equation as an instructive archetype of the first-order linear differential equations commonly found in computational neuroscience, we show that it is possible to make certain modifications to this equation to render it compatible with the principle of stationary action. Specifically, we show that a Lagrangian formulation of the DCM neuronal state equation is facilitated using a complex dependent variable, an oscillatory solution, anc a Hermitian intrinsic connectivity matrix. We first demonstrate proof of principle by using Bayesian model inversion to show that both the original and modified models can be correctly identified via in silico data generated directly from their respective equations of motion. We then provide motivation for adopting the modified models in neuroscience by using three different types of publicly available in vivo neuroimaging datasets, together with open source MATLAB code, to show that the modified (oscillatory) model provides a more parsimonious explanation for some of these empirical timeseries. It is our hope that this work will, in combination with existing techniques, allow people to explore the symmetries and associated conservation laws within neural systems – and to exploit the computational expediency facilitated by direct variational techniques.
AU  - Fagerholm,ED
AU  - Foulkes,W
AU  - Friston,KJ
AU  - Moran,RJ
AU  - Leech,R
DO  - 10.1186/s13408-021-00108-0
EP  - 15
PY  - 2021///
SN  - 2190-8567
SP  - 1
TI  - Rendering neuronal state equations compatiblewith the principle of stationary action
T2  - Journal of Mathematical Neuroscience
UR  - http://dx.doi.org/10.1186/s13408-021-00108-0
UR  - https://mathematical-neuroscience.springeropen.com/articles/10.1186/s13408-021-00108-0
UR  - http://hdl.handle.net/10044/1/90599
VL  - 11
ER  -
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