3 problems

Let $\Phi_\gamma$ be a flow on a state space $M$, indexed by $\gamma\in\Gamma$, and let $\gamma_1,\gamma_2\in\Gamma$ be two parameter values. Suppose an echo state network has been…

Consider an ESN driven by one-dimensional observations of a dynamical system on a manifold $M$, with random reservoir matrix $A$ and input matrix $W^{\text{in}}$. Let $f$ denote th…

Let $M$) be a compact $m$-manifold and let $n\in\mathbb{N}$ satisfy $n>2m$. Let $A$ be an $n\times n$ matrix with $\lVert A\rVert_2<\min(1/\lVert D\phi^{-1}\rVert_{\infty},1)$, let…