Federated learning (FL), as an emerging edge artificial intelligence paradigm, enables many devices to collaboratively train a global model without sharing their private data. To enhance the training efficiency of FL, various algorithms have been proposed, ranging from first-order second-order methods. However, these cannot be applied in scenarios where gradient information is not available, e....

The present note is devoted to establish some extremal results for the zerothorder general Randić index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.

Let G = (V, E), V {v1, v2,..., vn}, be a simple connected graph of order n and size m, without isolated vertices. Denote by d1 ? d2 ?... dn, di d(vi) sequence vertex degrees G. The general zeroth-order Randic index is defined as 0R?(G) ?ni =1 d?i, where an arbitrary real number. corresponding coindex via 0R??(G) ?ni=1(n?1?di)d?i. Some new bounds for the relationship between 0R??(G?) 0R???1(G?) ...

We study a class of cooperative multi-agent optimization problems, where each agent is associated with local action vector and cost, the goal to cooperatively find joint profile that minimizes average costs. consider setting gradient information not readily available, agents only observe their costs incurred by actions as feedback determine new actions. propose zeroth-order scheme provide expli...

Large-N multi-matrix loop equations are formulated as quadratic difference equations in concatenation of gluon correlations. Though non-linear, they involve highest rank correlations linearly. They are underdetermined in many cases. Additional linear equations for gluon correlations, associated to symmetries of action and measure are found. Loop equations aren’t differential equations as they i...