16 citations · 32 across the 8 of their papers we have counts for
8 papers
Numerical Periodic Normalization at Codim 1 Bifurcations of Limit Cycles in DDEs
M. M. Bosschaert, B. Lentjes, L. Spek +1
Recent work in [53, 54] by the authors on periodic center manifolds and normal forms for bifurcations of limit cycles in delay differential equations (DDEs) motivates the derivatio…
Deep Networks are Reproducing Kernel Chains
Tjeerd Jan Heeringa, Len Spek, Christoph Brune
Identifying an appropriate function space for deep neural networks remains a key open question. While shallow neural networks are naturally associated with Reproducing Kernel Banac…
Embeddings between Barron spaces with higher order activation functions
Tjeerd Jan Heeringa, Len Spek, Felix Schwenninger +1
The approximation properties of infinitely wide shallow neural networks heavily depend on the choice of the activation function. To understand this influence, we study embeddings b…
Bifurcations of Neural Fields on the Sphere
Len Spek, Stephan A. van Gils, Yuri A. Kuznetsov +1
A common model to study pattern formation in large groups of neurons is the neural field. We investigate a neural field with excitatory and inhibitory neurons, like Wilson and Cowa…
Duality for Neural Networks through Reproducing Kernel Banach Spaces
Len Spek, Tjeerd Jan Heeringa, Felix Schwenninger +1
Reproducing Kernel Hilbert spaces (RKHS) have been a very successful tool in various areas of machine learning. Recently, Barron spaces have been used to prove bounds on the genera…
Periodic Center Manifolds for DDEs in the Light of Suns and Stars
B. Lentjes, L. Spek, M. M. Bosschaert +1
In this paper we prove the existence of a periodic smooth finite-dimensional center manifold near a nonhyperbolic cycle in classical delay differential equations by using the Lyapu…
Dynamics of delayed neural field models in two-dimensional spatial domains
L. Spek, M. Polner, K. Dijkstra +1
Delayed neural field models can be viewed as a dynamical system in an appropriate functional analytic setting. On two dimensional rectangular space domains, and for a special class…
Neural Field Models with Transmission Delays and Diffusion
Len Spek, Yuri A. Kuznetsov, Stephan A. van Gils
A neural field models the large scale behaviour of large groups of neurons. We extend results of van Gils et al. [2013] and Dijkstra et al. [2015] by including a diffusion term int…