In this paper we use a “uniformity” property of Riemann integration to obtain a single-hidden-layer neural network of fixed translates of a (not necessarily radial) basis function with a fixed “width” that approximates a (possibly infinite) set of target functions arbitrarily well in the supremum norm over a compact set. The conditions on the set of target functions are simple and intuitive: un...

Given a bipartite graph G = (X ∪̇ D, E ⊆ X × D), an X-perfect matching is a matching in G that covers every node in X. In this paper we study the following generalisation of the X-perfect matching problem, which has applications in constraint programming: Given a bipartite graph as above and a collection F ⊆ 2 of k subsets of X, find a subset M ⊆ E of the edges such that for each C ∈ F , the edg...

We establish several new measures of simultaneous algebraic approximations for families of complex numbers (θ1, . . . , θn) related to the classical exponential and elliptic functions. These measures are completely explicit in terms of the degree and height of the algebraic approximations. In some instances, they imply that the fieldQ(θ1, . . . , θn) has transcendance degree≥2 overQ. This appro...