We introduce a new method for proving explicit upper bounds on the VC Dimension of general functional basis networks, and prove as an application, for the first time, the VC Dimension of analogâ€¦ (More)

We introduce a new method for proving explicit upper bounds on the VC Dimension of general functional basis networks, and prove as an application, for the rst time, that the VC Dimension of analogâ€¦ (More)

Using relativizations of results of Goncharov and Peretyat'kin on decidable homogeneous models, we prove that if M is S-saturated for some Scott set S, and F is an enumeration of S, then M has aâ€¦ (More)

The possible boundary conditions consistent with the integrability of the classical sine-Gordon equation are studied. A boundary value problem on the half-line x â‰¤ 0 with local boundary condition atâ€¦ (More)

We give axiomatizations and prove quantifier elimination theorems for first-order theories of unramified valued fields with an automorphism having a close interaction with the valuation. We achieveâ€¦ (More)

Techniques from diierential topology are used to give polynomial bounds for the VC-dimension of sigmoidal neural networks. The bounds are quadratic in w, the dimension of the space of weights.â€¦ (More)