The universal approximation Theorem 3.1 immediately implies another universal approximation Thus y (t) solves the ODE (2.6), with initial condition y (0) = y (0) = 0 . Reconstruction of a continuous signal from its sine transform. Step 0: (Equicontinuity) We recall the following fact from topology. F (τ):= null f (τ), for τ 0, f ( τ), for τ 0. Since F is odd, the Fourier transform of F is given by We provide the details below. The next step in the proof of the fundamental Lemma 3.5 needs the following preliminary result in By (B.3), this implies that It follows from Lemma 3.4 that for any input By the sine transform reconstruction Lemma B.1, there exists It follows from Lemma 3.6, that there exists Indeed, Lemma 3.7 shows that time-delays of any given input signal can be approximated with any Step 1: By the Fundamental Lemma 3.5, there exist It follows from Lemma 3.6, that there exists an oscillator Step 3: Finally, by Lemma 3.8, there exists an oscillator network,

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Foranypath , tmix( ) 2 ( )`( ) " log ( 1/ ) + log min Suppose w(y|x)= h (y)KRW(y, x) (x)KRW(x, y) , (4) whereh isabalancing PMTM induced 1 has stationarydistrib .

Such a question is very relevant: boostinghas quickly evolvedasatechnique requiring first-order information about the loss optimized [6, Section 10.3], [41, Section 7.2.2]