Abstract This paper investigates four classes of functions with a single discontinuous point. We give the sufficient and necessary conditions under which the second order iterates are continuous ...

However, these methods may not be optimal to encode the dynamical behaviors on the interaction graphs in that they can not generate “fully”-temporal embeddings and do not consider information ...

In the space of continuous functions of a real variable, the set of nowhere differentiable functions has long been known to be topologically "generic". In this paper it is shown further that in a ...

Atsuji has internally characterized those metric spaces X for which each real-valued continuous function on X is uniformly continuous as follows: (1) the set X' of limit points of X is compact, and (2 ...

We propose a notion of universality for graph neural networks (GNNs) in the large random graphs limit, tailored for node-level tasks. When graphs are drawn from a latent space model, or from a graphon ...