The polarizability operator plays a central role in density functional perturbation theory and other perturbative treatment of first principle electronic structure theories. cost computing the generally scales as $${\mathcal {O}}(N_{e}^4)$$ where $$N_e$$ is number electrons system. recently developed adaptively compressed (ACP) formulation [L. Lin, Z. Xu L. Ying, Multiscale Model. Simul. 2017] ...

A broadcast protocol allows a sender to distribute a message through a point-to-point network to a set of parties, such that (i) all parties receive the same message, even if the sender is corrupted, and (ii) this is the sender’s message, if he is honest. Broadcast protocols satisfying these properties are known to exist if and only if t < n/3, where n denotes the total number of parties, and t...