In this paper, we propose a first-order distributed optimization algorithm that is provably robust to Byzantine failures-arbitrary and potentially adversarial behavior, where all the participating agents are prone failure. We model each agent's state over time as two-state Markov chain indicates or trustworthy behaviors at different instants. set no restrictions on maximum number of any given t...

Abstract A hybrid Potts model where a random concentration p of the spins assume q 0 states and 1 − > is introduced. It known that when system homogeneous, with an integer spin number or , it undergoes second first order transition, respectively. argued there * such transition nature changed at *. This idea demonstrated analytically by simulations for two different types interaction: usual s...