Federated learning has emerged recently as a promising solution for distributing machine tasks through modern networks of mobile devices. Recent studies have obtained lower bounds on the expected decrease in model loss that is achieved each round federated learning. However, convergence generally requires large number communication rounds, which induces delay training and costly terms network r...

Riemann’s theorems on the rearrangement of absolutely convergent and conditionally convergent series of real numbers are analysed within Bishop-style constructive mathematics. The constructive proof that every rearrangement of an absolutely convergent series has the same sum is relatively straightforward; but the proof that a conditionally convergent series can be rearranged to converge to what...

In this paper we extend the notion of convergent systems defined by B.P. Demidovich and introduce the notions of uniformly, exponentially convergent and input-to-state convergent systems. Basic (interconnection) properties of such systems are established. Sufficient conditions for input-to-state convergence are presented. For a class of nonlinear systems we design (output) feedback controllers ...

BACKGROUND Convergence extension movements are conserved tissue rearrangements implicated in multiple morphogenetic events. While many of the cell behaviors involved in convergent extension are known, the molecular interactions required for this process remain elusive. However, past evidence suggests that regulation of cell adhesion molecule function is a key step in the progression of these be...