We investigate the application of line-graph operator to one-dimensional spin models with periodic boundary conditions. The spins (or interactions) in original structure become interactions spins) resulting structure. identify conditions which ensure that each new is stable, is, its configuration minimises internal energy. Then, making a correspondence between configurations and binary sequence...

Uncertainty quantification plays an important role in problems that involve inferring a parameter of initial value problem from observations the solution. Conrad et al.\ (\textit{Stat.\ Comput.}, 2017) proposed randomisation deterministic time integration methods as strategy for quantifying uncertainty due to unknown discretisation error. We consider this systems are described by deterministic,...