au ▁algorithm ▁can ▁be ▁applied ▁to ▁any ▁system ▁which ▁is ▁character ized ▁by ▁a ▁cost ▁( or ▁energy ) ▁function . ▁For ▁instance , ▁it ▁has ▁been ▁applied ▁to ▁the ▁solution ▁of ▁numerical ▁integr als ▁and ▁the ▁fol ding ▁of ▁prote ins . ▁The ▁Wang – Land au ▁sampling ▁is ▁related ▁to ▁the ▁met ad ynam ics ▁algorithm . ▁ ▁Over view ▁ ▁The ▁Wang ▁and ▁Land au ▁algorithm ▁is ▁used ▁to ▁obtain ▁an ▁estimate ▁for ▁the ▁density ▁of ▁states ▁of ▁a ▁system ▁character ized ▁by ▁a ▁cost ▁function . ▁It ▁uses ▁a ▁non - Mark ov ian ▁st ochastic ▁process ▁which ▁asympt ot ically ▁converges ▁to ▁a ▁mult ican on ical ▁ensemble . ▁( I . e . ▁to ▁a ▁Metropol is – H ast ings ▁algorithm ▁with ▁sampling ▁distribution ▁inverse ▁to ▁the ▁density ▁of ▁states .) ▁The ▁major ▁consequence ▁is ▁that ▁this ▁sampling ▁distribution ▁leads ▁to ▁a ▁simulation ▁where ▁the ▁energy ▁bar riers ▁are ▁invisible . ▁This ▁means ▁that ▁the ▁algorithm ▁vis its ▁all ▁the ▁accessible ▁states ▁( f avor able ▁and ▁less ▁favor able ) ▁much ▁faster ▁than ▁a ▁Metropol is ▁algorithm . ▁ ▁Algorithm ▁ ▁Consider ▁a ▁system ▁defined ▁on ▁a ▁phase ▁space ▁, ▁and ▁a ▁cost ▁function , ▁E , ▁( e . g . ▁the ▁energy ), ▁bounded ▁on ▁a ▁spectrum ▁, ▁which ▁has ▁an ▁associated ▁density ▁of ▁states ▁, ▁which ▁is ▁to ▁be ▁estimated . ▁The ▁estim ator ▁is ▁. ▁Because ▁Wang ▁and ▁Land au ▁algorithm ▁works ▁in ▁discrete ▁spect ra , ▁the ▁spectrum ▁ ▁is