We study a variational model for transition layers with an underlying functional that combines an Allen-Cahn type structure with an additional nonlocal interaction term. A transition layer is represented by a map from R to S...
We study a variational model for transition layers with an underlying functional that combines an Allen-Cahn type structure with an additional nonlocal interaction term. A transition layer is represented by a map from R to S...
This paper shows that the celebrated embedding theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an...
We consider the wave equation ε2(-∂t2+Δ)u+f(u)=0 for 0 < ε≪ 1 , where f is the derivative of a balanced, double-well potential, the model case being f(u) = u- u3. For equations of this form, we construct...
Echo State Networks (ESNs) are a class of single-layer recurrent neural networks that have enjoyed recent attention. In this paper we prove that a suitable ESN, trained on a series of measurements of an invertible dynamical...
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