▁extended ▁by ▁the ▁same ▁method ▁as ▁in ▁the ▁original ▁version ▁of ▁B LA ST , ▁and ▁the ▁H SP s ' ▁( High - sc oring ▁segment ▁pair ) ▁scores ▁of ▁the ▁extended ▁regions ▁are ▁then ▁created ▁by ▁using ▁a ▁substitution ▁matrix ▁as ▁before . ▁ ▁List ▁all ▁of ▁the ▁H SP s ▁in ▁the ▁database ▁whose ▁score ▁is ▁high ▁enough ▁to ▁be ▁considered . ▁ ▁We ▁list ▁the ▁H SP s ▁whose ▁scores ▁are ▁greater ▁than ▁the ▁empir ically ▁determined ▁cut off ▁score ▁S . ▁By ▁exam ining ▁the ▁distribution ▁of ▁the ▁alignment ▁scores ▁mode led ▁by ▁comparing ▁random ▁sequences , ▁a ▁cut off ▁score ▁S ▁can ▁be ▁determined ▁such ▁that ▁its ▁value ▁is ▁large ▁enough ▁to ▁guarantee ▁the ▁significance ▁of ▁the ▁remaining ▁H SP s . ▁ ▁E valu ate ▁the ▁significance ▁of ▁the ▁H SP ▁score . ▁ ▁B LA ST ▁next ▁ass esses ▁the ▁statistical ▁significance ▁of ▁each ▁H SP ▁score ▁by ▁explo iting ▁the ▁G umb el ▁extreme ▁value ▁distribution ▁( E VD ). ▁( It ▁is ▁proved ▁that ▁the ▁distribution ▁of ▁Smith - W at erman ▁local ▁alignment ▁scores ▁between ▁two ▁random ▁sequences ▁follows ▁the ▁G umb el ▁E VD . ▁For ▁local ▁align ments ▁containing ▁g aps ▁it ▁is ▁not ▁proved .). ▁In ▁accord ance ▁with ▁the ▁G umb el ▁E VD , ▁the ▁probability ▁p ▁of ▁obser ving ▁a ▁score ▁S ▁equal ▁to ▁or ▁greater ▁than ▁x ▁is ▁given ▁by ▁the ▁equation ▁▁ ▁where ▁▁▁ ▁The ▁statistical ▁parameters ▁ ▁and ▁ ▁are ▁estimated ▁by ▁fitting