Accessibility navigation


Kernel reconstruction for delayed neural field equations

Alswaihli, J., Potthast, R., Bojak, I., Saddy, D. and Hutt, A. (2018) Kernel reconstruction for delayed neural field equations. The Journal of Mathematical Neuroscience, 8. 3. ISSN 2190-8567

[img]
Preview
Text (Open Access) - Published Version
· Available under License Creative Commons Attribution.
· Please see our End User Agreement before downloading.

3MB
[img] Text - Accepted Version
· Restricted to Repository staff only

3MB

To link to this item DOI: 10.1186/s13408-018-0058-8

Abstract/Summary

Understanding the neural field activity for realistic living systems is a challenging task in contemporary neuroscience. Neural fields have been studied and developed theoretically and numerically with considerable success over the past four decades. However, to make effective use of such models, we need to identify their constituents in practical systems. This includes the determination of model parameters and in particular the reconstruction of the underlying effective connectivity in biological tissues. In this work, we provide an integral equation approach to the reconstruction of the neural connectivity in the case where the neural activity is governed by a delay neural field equation. As preparation, we study the solution of the direct problem based on the Banach fixed point theorem. Then we reformulate the inverse problem into a family of integral equations of the first kind. This equation will be vector valued when several neural activity trajectories are taken as input for the inverse problem. We employ spectral regularization techniques for its stable solution. A sensitivity analysis of the regularized kernel reconstruction with respect to the input signal u is carried out, investigating the Frechet differentiability of the kernel with respect to the signal. Finally, we use numerical examples to show the feasibility of the approach for kernel reconstruction, including numerical sensitivity tests, which show that the integral equation approach is a very stable and promising approach for practical computational neuroscience.

Item Type:Article
Refereed:Yes
Divisions:Interdisciplinary centres and themes > Centre for Integrative Neuroscience and Neurodynamics (CINN)
Faculty of Life Sciences > School of Psychology and Clinical Language Sciences > Department of Psychology
Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:75097
Uncontrolled Keywords:Neural fields; Integral equations; Fixed point theorem; Inverse problems; Regularization
Publisher:Springer

Downloads

Downloads per month over past year

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation