Papers by Jehan Alswaihli
Journal of mathematical neuroscience, Jan 5, 2018
Understanding the neural field activity for realistic living systems is a challenging task in con... more 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 t...
Journal of mathematical neuroscience, Jan 5, 2018
Understanding the neural field activity for realistic living systems is a challenging task in con... more 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 t...
The need to understand the neural field activity for realistic living systems is a current challe... more The need to understand the neural field activity for realistic living systems is a current challenging task in neuroscience. For several decades, neural fields have been studied and developed theoretically and numerically. However, to make practical use of the equations, we need to determine their constituents in practical systems. This includes the determination of parameters or the reconstruction of the underlying connectivity in biological tissue. The thesis is part of the fields of inverse problems and data assimilation applied to neural field theory. Inverse problems deals with the reconstruction of structural information or characteristics of some natural system and data assimilation deals with the repeated estimation of the dynamical state of a system. Dealing with medical systems, both tasks are strongly related due to the fact that often structural information is missing or strongly incomplete, such that the state estimation needs to reconstruct the structural information a...
The Journal of Mathematical Neuroscience, 2018
Understanding the neural field activity for realistic living systems is a challenging task in con... more 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 em-ploy 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 Fréchet 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.
Uploads
Papers by Jehan Alswaihli
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 em-ploy 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 Fréchet 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.