Recovering a function from its gram determinants

Recovering a Function from a Dini Derivative

Recovering a function from its spherical mean values in two and three dimensions

The problem of determining a function from a subset of its spherical means has a rich history in pure and applied mathematics. Its connection with photoacoustic imaging has already been made abundantly clear in earlier chapters in this volume: when the sound speed νs in a medium is constant the pressure at time t and point r is expressed in terms of spherical means of the pressure, and its time...

Recovering a Logic from Its Fragments by Meta-Fibring

In this paper we address the question of recovering a logic system by combining two or more fragments of it. We show that, in general, by fibring two or more fragments of a given logic the resulting logic is weaker than the original one, because some meta-properties of the connectives are lost after the combination process. In order to overcome this problem, the categoriesMcon and Seq of multip...

Recovering a Feed-Forward Net From Its Output

We study feed-forward nets with arbitrarily many layers, using the standard sigmoid, tanh x. Aside from technicalities, our theorems are: 1. Complete knowledge of the output of a neural net for arbitrary inputs uniquely specifies the architecture, weights and thresholds; and 2. There are only finitely many critical points on the error surface for a generic training problem. Neural nets were ori...

On Recovering a Bounded Distributive Lattice from Its Endomorphism Monoid

The sub algebra functor Sub A is faithful for Boolean algebras (Sub A •Sub B implies A • B, see D. Sachs [7] ), but it is not faithful for bounded distributive lattices or unbounded distributive lattices. The automorphism functor Aut A is highly unfaithful even for Boolean algebras. The endomorphism functor End A is the most faithful of all three. B. M. Schein [8] and K. D.' Magill [5] establis...