We give two pathological phenomena for non-separable AF-algebras which do not occur for separable AF-algebras. One is that non-separable AFalgebras are not determined by their Bratteli diagrams, and the other is that there exists a non-separable AF-algebra which is prime but not primitive.

This paper formulates a distributed computation problem, where master asks ${\mathsf N}$ workers to compute linearly separable function. The task function can be expressed as K}_{\mathrm{ c}}$ linear combinations of K}$ messages, each message is one dataset. Our objective find the optimal tradeoff between cost (number unco...