Kuramoto-Sivashinsky dynamics on the center-unstable manifold
SIAM Journal on Applied Mathematics
Introduction to the theory of neural computation
Introduction to the theory of neural computation
Reconstructing phase space from PDE simulations
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Lending direction to neural networks
Neural Networks
Neural Networks in Non-Euclidean Spaces
Neural Processing Letters
Learning to walk through imitation
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Analysing periodic phenomena by circular PCA
BIRD'07 Proceedings of the 1st international conference on Bioinformatics research and development
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In the usual construction of a neural network, the individual nodes store and transmit real numbers that lie in an interval on the real line; the values are often envisioned as amplitudes. In this article we present a design for a circular node, which is capable of storing and transmitting angular information. We develop the forward and backward propagation formulas for a network containing circular nodes. We show how the use of circular nodes may facilitate the characterization and parameterization of periodic phenomena in general. We describe applications to constructing circular self-maps, periodic compression, and one-dimensional manifold decomposition. We show that a circular node may be used to construct a homeomorphism between a trefoil knot in â聞聺3 and a unit circle. We give an application with a network that encodes the dynamic system on the limit cycle of the Kuramoto-Sivashinsky equation. This is achieved by incorporating a circular node in the bottleneck layer of a three-hidden-layer bottleneck network architecture. Exploiting circular nodes systematically offers a neural network alternative to Fourier series decomposition in approximating periodic or almost periodic functions.