♦t❤❡r s✉❝❤ ✈❛r✐❛❜❧❡s✳ ✷ ❛♥❞ ✭✐❞❡❛❧❧②✮ tr✐❡s t♦ ✜♥❞ ♦✉t t❤❡ ✐♠♣♦rt❛♥t ❧✐♥❣✉✐st✐❝ ❢❡❛t✉r❡s✳ ❈❛♥ ✇❡ ❛♣♣❧② t❤✐s t❡❝❤♥✐q✉❡ t♦ ❧❡❛r♥❡r ❞❛t❛❄ ✶ ❈❛♥ ✇❡ ❛✉t♦♠❛t✐❝❛❧❧② ✏❞❡t❡❝t✑ t❤❡ ❧❡❛r♥❡rs ▲ ✶ ❢r♦♠ ✐ts t❡①ts❄ ✷ ❲❤❛t ❦✐♥❞ ♦❢ ✈❛r✐❛❜❧❡s ♣❧❛② ❛ ✭❝♦♥❢♦✉♥❞✐♥❣✮ r♦❧❡❄ ✸ ❈❛♥ ✇❡ ✐s♦❧❛t❡ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ ❞✐✛❡r❡♥t ✈❛r✐❛❜❧❡s❄ ❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ❈♦♠✐♥❣ ❢r♦♠ st②❧♦♠❡tr② ❙t②❧♦♠❡tr②✳ ✳ ✳ ✶ ❝❧❛ss✐✜❡s t❡①ts ❛❝❝♦r❞✐♥❣ t♦ ♥♦♥✲❧✐♥❣✉✐st✐❝ ✈❛r✐❛❜❧❡s✿ ◮ ❛✉t❤♦rs❤✐♣ ✭✇❤♦ ✇r♦t❡ ❛ ♣✐❡❝❡❄✮ ◮ ❣❡♥❞❡r ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹ ✴ ✺✷
✷ ❛♥❞ ✭✐❞❡❛❧❧②✮ tr✐❡s t♦ ✜♥❞ ♦✉t t❤❡ ✐♠♣♦rt❛♥t ❧✐♥❣✉✐st✐❝ ❢❡❛t✉r❡s✳ ❈❛♥ ✇❡ ❛♣♣❧② t❤✐s t❡❝❤♥✐q✉❡ t♦ ❧❡❛r♥❡r ❞❛t❛❄ ✶ ❈❛♥ ✇❡ ❛✉t♦♠❛t✐❝❛❧❧② ✏❞❡t❡❝t✑ t❤❡ ❧❡❛r♥❡rs ▲ ✶ ❢r♦♠ ✐ts t❡①ts❄ ✷ ❲❤❛t ❦✐♥❞ ♦❢ ✈❛r✐❛❜❧❡s ♣❧❛② ❛ ✭❝♦♥❢♦✉♥❞✐♥❣✮ r♦❧❡❄ ✸ ❈❛♥ ✇❡ ✐s♦❧❛t❡ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ ❞✐✛❡r❡♥t ✈❛r✐❛❜❧❡s❄ ❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ❈♦♠✐♥❣ ❢r♦♠ st②❧♦♠❡tr② ❙t②❧♦♠❡tr②✳ ✳ ✳ ✶ ❝❧❛ss✐✜❡s t❡①ts ❛❝❝♦r❞✐♥❣ t♦ ♥♦♥✲❧✐♥❣✉✐st✐❝ ✈❛r✐❛❜❧❡s✿ ◮ ❛✉t❤♦rs❤✐♣ ✭✇❤♦ ✇r♦t❡ ❛ ♣✐❡❝❡❄✮ ◮ ❣❡♥❞❡r ◮ ♦t❤❡r s✉❝❤ ✈❛r✐❛❜❧❡s✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹ ✴ ✺✷
❈❛♥ ✇❡ ❛♣♣❧② t❤✐s t❡❝❤♥✐q✉❡ t♦ ❧❡❛r♥❡r ❞❛t❛❄ ✶ ❈❛♥ ✇❡ ❛✉t♦♠❛t✐❝❛❧❧② ✏❞❡t❡❝t✑ t❤❡ ❧❡❛r♥❡rs ▲ ✶ ❢r♦♠ ✐ts t❡①ts❄ ✷ ❲❤❛t ❦✐♥❞ ♦❢ ✈❛r✐❛❜❧❡s ♣❧❛② ❛ ✭❝♦♥❢♦✉♥❞✐♥❣✮ r♦❧❡❄ ✸ ❈❛♥ ✇❡ ✐s♦❧❛t❡ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ ❞✐✛❡r❡♥t ✈❛r✐❛❜❧❡s❄ ❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ❈♦♠✐♥❣ ❢r♦♠ st②❧♦♠❡tr② ❙t②❧♦♠❡tr②✳ ✳ ✳ ✶ ❝❧❛ss✐✜❡s t❡①ts ❛❝❝♦r❞✐♥❣ t♦ ♥♦♥✲❧✐♥❣✉✐st✐❝ ✈❛r✐❛❜❧❡s✿ ◮ ❛✉t❤♦rs❤✐♣ ✭✇❤♦ ✇r♦t❡ ❛ ♣✐❡❝❡❄✮ ◮ ❣❡♥❞❡r ◮ ♦t❤❡r s✉❝❤ ✈❛r✐❛❜❧❡s✳ ✷ ❛♥❞ ✭✐❞❡❛❧❧②✮ tr✐❡s t♦ ✜♥❞ ♦✉t t❤❡ ✐♠♣♦rt❛♥t ❧✐♥❣✉✐st✐❝ ❢❡❛t✉r❡s✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹ ✴ ✺✷
❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ❈♦♠✐♥❣ ❢r♦♠ st②❧♦♠❡tr② ❙t②❧♦♠❡tr②✳ ✳ ✳ ✶ ❝❧❛ss✐✜❡s t❡①ts ❛❝❝♦r❞✐♥❣ t♦ ♥♦♥✲❧✐♥❣✉✐st✐❝ ✈❛r✐❛❜❧❡s✿ ◮ ❛✉t❤♦rs❤✐♣ ✭✇❤♦ ✇r♦t❡ ❛ ♣✐❡❝❡❄✮ ◮ ❣❡♥❞❡r ◮ ♦t❤❡r s✉❝❤ ✈❛r✐❛❜❧❡s✳ ✷ ❛♥❞ ✭✐❞❡❛❧❧②✮ tr✐❡s t♦ ✜♥❞ ♦✉t t❤❡ ✐♠♣♦rt❛♥t ❧✐♥❣✉✐st✐❝ ❢❡❛t✉r❡s✳ ❈❛♥ ✇❡ ❛♣♣❧② t❤✐s t❡❝❤♥✐q✉❡ t♦ ❧❡❛r♥❡r ❞❛t❛❄ ✶ ❈❛♥ ✇❡ ❛✉t♦♠❛t✐❝❛❧❧② ✏❞❡t❡❝t✑ t❤❡ ❧❡❛r♥❡rs ▲ ✶ ❢r♦♠ ✐ts t❡①ts❄ ✷ ❲❤❛t ❦✐♥❞ ♦❢ ✈❛r✐❛❜❧❡s ♣❧❛② ❛ ✭❝♦♥❢♦✉♥❞✐♥❣✮ r♦❧❡❄ ✸ ❈❛♥ ✇❡ ✐s♦❧❛t❡ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ ❞✐✛❡r❡♥t ✈❛r✐❛❜❧❡s❄ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹ ✴ ✺✷
❧❡①✐s s②♥t❛① ♠♦r♣❤♦❧♦❣② ✷ ❍♦✇ ❞♦ ▲ ✶ ❡✛❡❝ts s❤♦✇ ♦♥ ❞✐✛❡r❡♥t ❧✐♥❣✉✐st✐❝ ❧❡✈❡❧s❄ ✸ ❚♦ ✇❤❛t ❡①t❡♥t ❞♦ ▲ ✶ ❡✛❡❝ts ❧❡❛❞ t♦ ✉♥❣r❛♠♠❛t✐❝❛❧ str✉❝t✉r❡s ✐♥ t❤❡ ❧❡❛r♥❡r ❧❛♥❣✉❛❣❡❄ ✹ ❍♦✇ str♦♥❣ ✐s t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ s❡❝♦♥❞❛r② ✈❛r✐❛❜❧❡s ✭❡✳❣✳ ❝♦♥t❡♥t✮❄ ❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ❈♦♥✈❡r❣✐♥❣ r❡s❡❛r❝❤ q✉❡st✐♦♥s ✶ ❈❛♥ ✇❡ q✉❛♥t✐❢② t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤❡ ❧❡❛r♥❡r✬s ▲✶ ♦♥ ❤✐s✴❤❡r ❧❛♥❣✉❛❣❡ ✉s❡❄ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✺ ✴ ✺✷
✸ ❚♦ ✇❤❛t ❡①t❡♥t ❞♦ ▲ ✶ ❡✛❡❝ts ❧❡❛❞ t♦ ✉♥❣r❛♠♠❛t✐❝❛❧ str✉❝t✉r❡s ✐♥ t❤❡ ❧❡❛r♥❡r ❧❛♥❣✉❛❣❡❄ ✹ ❍♦✇ str♦♥❣ ✐s t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ s❡❝♦♥❞❛r② ✈❛r✐❛❜❧❡s ✭❡✳❣✳ ❝♦♥t❡♥t✮❄ ❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ❈♦♥✈❡r❣✐♥❣ r❡s❡❛r❝❤ q✉❡st✐♦♥s ✶ ❈❛♥ ✇❡ q✉❛♥t✐❢② t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤❡ ❧❡❛r♥❡r✬s ▲✶ ♦♥ ❤✐s✴❤❡r ❧❛♥❣✉❛❣❡ ✉s❡❄ ✷ ❍♦✇ ❞♦ ▲ ✶ ❡✛❡❝ts s❤♦✇ ♦♥ ❞✐✛❡r❡♥t ❧✐♥❣✉✐st✐❝ ❧❡✈❡❧s❄ ◮ ❧❡①✐s ◮ s②♥t❛① ◮ ♠♦r♣❤♦❧♦❣② ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✺ ✴ ✺✷
✹ ❍♦✇ str♦♥❣ ✐s t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ s❡❝♦♥❞❛r② ✈❛r✐❛❜❧❡s ✭❡✳❣✳ ❝♦♥t❡♥t✮❄ ❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ❈♦♥✈❡r❣✐♥❣ r❡s❡❛r❝❤ q✉❡st✐♦♥s ✶ ❈❛♥ ✇❡ q✉❛♥t✐❢② t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤❡ ❧❡❛r♥❡r✬s ▲✶ ♦♥ ❤✐s✴❤❡r ❧❛♥❣✉❛❣❡ ✉s❡❄ ✷ ❍♦✇ ❞♦ ▲ ✶ ❡✛❡❝ts s❤♦✇ ♦♥ ❞✐✛❡r❡♥t ❧✐♥❣✉✐st✐❝ ❧❡✈❡❧s❄ ◮ ❧❡①✐s ◮ s②♥t❛① ◮ ♠♦r♣❤♦❧♦❣② ✸ ❚♦ ✇❤❛t ❡①t❡♥t ❞♦ ▲ ✶ ❡✛❡❝ts ❧❡❛❞ t♦ ✉♥❣r❛♠♠❛t✐❝❛❧ str✉❝t✉r❡s ✐♥ t❤❡ ❧❡❛r♥❡r ❧❛♥❣✉❛❣❡❄ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✺ ✴ ✺✷
❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ❈♦♥✈❡r❣✐♥❣ r❡s❡❛r❝❤ q✉❡st✐♦♥s ✶ ❈❛♥ ✇❡ q✉❛♥t✐❢② t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤❡ ❧❡❛r♥❡r✬s ▲✶ ♦♥ ❤✐s✴❤❡r ❧❛♥❣✉❛❣❡ ✉s❡❄ ✷ ❍♦✇ ❞♦ ▲ ✶ ❡✛❡❝ts s❤♦✇ ♦♥ ❞✐✛❡r❡♥t ❧✐♥❣✉✐st✐❝ ❧❡✈❡❧s❄ ◮ ❧❡①✐s ◮ s②♥t❛① ◮ ♠♦r♣❤♦❧♦❣② ✸ ❚♦ ✇❤❛t ❡①t❡♥t ❞♦ ▲ ✶ ❡✛❡❝ts ❧❡❛❞ t♦ ✉♥❣r❛♠♠❛t✐❝❛❧ str✉❝t✉r❡s ✐♥ t❤❡ ❧❡❛r♥❡r ❧❛♥❣✉❛❣❡❄ ✹ ❍♦✇ str♦♥❣ ✐s t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ s❡❝♦♥❞❛r② ✈❛r✐❛❜❧❡s ✭❡✳❣✳ ❝♦♥t❡♥t✮❄ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✺ ✴ ✺✷
❚r❛♥s❢❡r ❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ✶ ❚r❛♥s❢❡r ✷ ❘♦❛❞ ♠❛♣ ✸ ❖✉r ❞❛t❛ ✲ t❤❡ ❋❛❧❦♦ ❝♦r♣✉s ✹ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ✺ Pr❡❧✐♠✐♥❛r② r❡s✉❧ts ✻ ❚✇♦ ✐ss✉❡s ✼ ❚❛❦✐♥❣ t❤❡ ❡ss❛② t♦♣✐❝ ✐♥t♦ ❛❝❝♦✉♥t ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❘❡s✉❧ts ✽ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ✾ ✶✵ ❈♦♥❝❧✉s✐♦♥ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✻ ✴ ✺✷
▼❛♥② st✉❞✐❡s ❤❛✈❡ ❧♦♦❦❡❞ ❛t ❡❛❝❤ ❧❡✈❡❧ ✐♥❞❡♣❡♥❞❡♥t❧②✳ r❡❧❛t✐✈❡ ❝♦♥tr✐❜✉t✐♦♥s ♦❢ ▲✶ ♦♥ ❧✐♥❣✉✐st✐❝ ❧❡✈❡❧s ❬❲❡ ♥❡❡❞❪ ✏ ❛ r❡❧✐❛❜❧❡ ✇❛② t♦ ♠❡❛s✉r❡ t❤❡ r❡❧❛t✐✈❡ ❝♦♥tr✐❜✉t✐♦♥s ♦❢ t❤❡ ♥❛t✐✈❡ ❧❛♥❣✉❛❣❡ t♦ t❤❡ ❡❛s❡ ♦r ❞✐✣❝✉❧t② ❧❡❛r♥❡rs ❤❛✈❡ ✇✐t❤ ❡❛❝❤ s✉❜s②st❡♠ ❛♥❞✱ ❜② ✐♠♣❧✐❝❛t✐♦♥✱ t❤❡ t♦t❛❧ ❝♦♥tr✐❜✉t✐♦♥ ♦❢ tr❛♥s❢❡r t♦ t❤❡ ♣r♦❝❡ss ♦❢ s❡❝♦♥❞ ❧❛♥❣✉❛❣❡ ❛❝q✉✐s✐t✐♦♥✳✏ ✭❖❞❧✐♥ ✷✵✵✸✱ ♣✳ ✹✸✾✮ ❚r❛♥s❢❡r ❚r❛♥s❢❡r ❛s ❝r♦ss✲❧✐♥❣✉✐st✐❝ ✐♥✢✉❡♥❝❡ ❚r❛♥s❢❡r ✲ ✇♦r❦✐♥❣ ❞❡✜♥✐t✐♦♥ ▲❛♥❣✉❛❣❡ tr❛♥s❢❡r r❡❢❡rs t♦ ❛♥② ✐♥st❛♥❝❡ ♦❢ ❧❡❛r♥❡r ❞❛t❛ ✇❤❡r❡ ❛ st❛t✐st✐❝❛❧❧② s✐❣♥✐✜❝❛♥t ❝♦rr❡❧❛t✐♦♥ ✭♦r ♣r♦❜❛❜✐❧✐t②✲❜❛s❡❞ r❡❧❛t✐♦♥✮ ✐s s❤♦✇♥ t♦ ❡①✐st ❜❡t✇❡❡♥ s♦♠❡ ❢❡❛t✉r❡ ♦❢ t❤❡ ✐♥t❡r❧❛♥❣✉❛❣❡ ❛♥❞ ❛♥② ♦t❤❡r ❧❛♥❣✉❛❣❡ t❤❛t ❤❛s ❜❡❡♥ ♣r❡✈✐♦✉s❧② ❛❝q✉✐r❡❞ ✭s❡❡ ❊❧❧✐s ✷✵✵✾✮ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✼ ✴ ✺✷
r❡❧❛t✐✈❡ ❝♦♥tr✐❜✉t✐♦♥s ♦❢ ▲✶ ♦♥ ❧✐♥❣✉✐st✐❝ ❧❡✈❡❧s ❬❲❡ ♥❡❡❞❪ ✏ ❛ r❡❧✐❛❜❧❡ ✇❛② t♦ ♠❡❛s✉r❡ t❤❡ r❡❧❛t✐✈❡ ❝♦♥tr✐❜✉t✐♦♥s ♦❢ t❤❡ ♥❛t✐✈❡ ❧❛♥❣✉❛❣❡ t♦ t❤❡ ❡❛s❡ ♦r ❞✐✣❝✉❧t② ❧❡❛r♥❡rs ❤❛✈❡ ✇✐t❤ ❡❛❝❤ s✉❜s②st❡♠ ❛♥❞✱ ❜② ✐♠♣❧✐❝❛t✐♦♥✱ t❤❡ t♦t❛❧ ❝♦♥tr✐❜✉t✐♦♥ ♦❢ tr❛♥s❢❡r t♦ t❤❡ ♣r♦❝❡ss ♦❢ s❡❝♦♥❞ ❧❛♥❣✉❛❣❡ ❛❝q✉✐s✐t✐♦♥✳✏ ✭❖❞❧✐♥ ✷✵✵✸✱ ♣✳ ✹✸✾✮ ❚r❛♥s❢❡r ❚r❛♥s❢❡r ❛s ❝r♦ss✲❧✐♥❣✉✐st✐❝ ✐♥✢✉❡♥❝❡ ❚r❛♥s❢❡r ✲ ✇♦r❦✐♥❣ ❞❡✜♥✐t✐♦♥ ▲❛♥❣✉❛❣❡ tr❛♥s❢❡r r❡❢❡rs t♦ ❛♥② ✐♥st❛♥❝❡ ♦❢ ❧❡❛r♥❡r ❞❛t❛ ✇❤❡r❡ ❛ st❛t✐st✐❝❛❧❧② s✐❣♥✐✜❝❛♥t ❝♦rr❡❧❛t✐♦♥ ✭♦r ♣r♦❜❛❜✐❧✐t②✲❜❛s❡❞ r❡❧❛t✐♦♥✮ ✐s s❤♦✇♥ t♦ ❡①✐st ❜❡t✇❡❡♥ s♦♠❡ ❢❡❛t✉r❡ ♦❢ t❤❡ ✐♥t❡r❧❛♥❣✉❛❣❡ ❛♥❞ ❛♥② ♦t❤❡r ❧❛♥❣✉❛❣❡ t❤❛t ❤❛s ❜❡❡♥ ♣r❡✈✐♦✉s❧② ❛❝q✉✐r❡❞ ✭s❡❡ ❊❧❧✐s ✷✵✵✾✮ ▼❛♥② st✉❞✐❡s ❤❛✈❡ ❧♦♦❦❡❞ ❛t ❡❛❝❤ ❧❡✈❡❧ ✐♥❞❡♣❡♥❞❡♥t❧②✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✼ ✴ ✺✷
❚r❛♥s❢❡r ❚r❛♥s❢❡r ❛s ❝r♦ss✲❧✐♥❣✉✐st✐❝ ✐♥✢✉❡♥❝❡ ❚r❛♥s❢❡r ✲ ✇♦r❦✐♥❣ ❞❡✜♥✐t✐♦♥ ▲❛♥❣✉❛❣❡ tr❛♥s❢❡r r❡❢❡rs t♦ ❛♥② ✐♥st❛♥❝❡ ♦❢ ❧❡❛r♥❡r ❞❛t❛ ✇❤❡r❡ ❛ st❛t✐st✐❝❛❧❧② s✐❣♥✐✜❝❛♥t ❝♦rr❡❧❛t✐♦♥ ✭♦r ♣r♦❜❛❜✐❧✐t②✲❜❛s❡❞ r❡❧❛t✐♦♥✮ ✐s s❤♦✇♥ t♦ ❡①✐st ❜❡t✇❡❡♥ s♦♠❡ ❢❡❛t✉r❡ ♦❢ t❤❡ ✐♥t❡r❧❛♥❣✉❛❣❡ ❛♥❞ ❛♥② ♦t❤❡r ❧❛♥❣✉❛❣❡ t❤❛t ❤❛s ❜❡❡♥ ♣r❡✈✐♦✉s❧② ❛❝q✉✐r❡❞ ✭s❡❡ ❊❧❧✐s ✷✵✵✾✮ ▼❛♥② st✉❞✐❡s ❤❛✈❡ ❧♦♦❦❡❞ ❛t ❡❛❝❤ ❧❡✈❡❧ ✐♥❞❡♣❡♥❞❡♥t❧②✳ r❡❧❛t✐✈❡ ❝♦♥tr✐❜✉t✐♦♥s ♦❢ ▲✶ ♦♥ ❧✐♥❣✉✐st✐❝ ❧❡✈❡❧s ❬❲❡ ♥❡❡❞❪ ✏ ❛ r❡❧✐❛❜❧❡ ✇❛② t♦ ♠❡❛s✉r❡ t❤❡ r❡❧❛t✐✈❡ ❝♦♥tr✐❜✉t✐♦♥s ♦❢ t❤❡ ♥❛t✐✈❡ ❧❛♥❣✉❛❣❡ t♦ t❤❡ ❡❛s❡ ♦r ❞✐✣❝✉❧t② ❧❡❛r♥❡rs ❤❛✈❡ ✇✐t❤ ❡❛❝❤ s✉❜s②st❡♠ ❛♥❞✱ ❜② ✐♠♣❧✐❝❛t✐♦♥✱ t❤❡ t♦t❛❧ ❝♦♥tr✐❜✉t✐♦♥ ♦❢ tr❛♥s❢❡r t♦ t❤❡ ♣r♦❝❡ss ♦❢ s❡❝♦♥❞ ❧❛♥❣✉❛❣❡ ❛❝q✉✐s✐t✐♦♥✳✏ ✭❖❞❧✐♥ ✷✵✵✸✱ ♣✳ ✹✸✾✮ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✼ ✴ ✺✷
❘♦❛❞ ♠❛♣ ❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ✶ ❚r❛♥s❢❡r ✷ ❘♦❛❞ ♠❛♣ ✸ ❖✉r ❞❛t❛ ✲ t❤❡ ❋❛❧❦♦ ❝♦r♣✉s ✹ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ✺ Pr❡❧✐♠✐♥❛r② r❡s✉❧ts ✻ ❚✇♦ ✐ss✉❡s ✼ ❚❛❦✐♥❣ t❤❡ ❡ss❛② t♦♣✐❝ ✐♥t♦ ❛❝❝♦✉♥t ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❘❡s✉❧ts ✽ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ✾ ✶✵ ❈♦♥❝❧✉s✐♦♥ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✽ ✴ ✺✷
❘♦❛❞ ♠❛♣ ❋r♦♠ s✐♠✐❧❛r✐t② t♦ tr❛♥s❢❡r ❲❡ ✇❛♥t t♦ ❝❧❛ss✐❢② ■▲✲t❡①ts ❢♦r ❛✉t❤♦r✬s ▲✶✿ ❲❡ ❞❡✜♥❡ ❛ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❢♦r t❡①ts✿ ◮ ❆ t❡①t ✐s ❛ str✐♥❣ ♦❢ ❝❤❛r❛❝t❡rs✳ ◮ ❚❛❦❡ t✇♦ t❡①ts ❆ ❛♥❞ ❇ ✱ ❝♦♠♣✉t❡ ❛ ♥✉♠❜❡r ❙ ❢r♦♠ t❤❡♠✳ ◮ ■♥t❡r♣r❡t❡ t❤✐s ♥✉♠❜❡r ❛s ❛♥ ✐♥❞✐❝❛t♦r ❢♦r s✐♠✐❧❛r✐t②✳ ❆ss✐❣♥ ❛ t❡①t t♦ t❤❡ ✏♠♦st s✐♠✐❧❛r✑ ▲✶ ✭❞❡t❛✐❧s ❧❛t❡r✦✮ ❛ ♣♦st❡r✐♦r✐ ❥✉st✐✜❝❛t✐♦♥ ■❢ t❤❡ ❛ss✐❣♥♠❡♥ts ❛r❡ ❝♦rr❡❝t✱ ⇒ t❤❡♥ ❙ ✐s ❛ r❡✢❡❝t✐♦♥ ♦❢ ▲✶ s♣❡❝✐✜❝ str✉❝t✉r❡s ✐♥ ■▲ ✭ ⇐ tr❛♥s❢❡r✮✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✾ ✴ ✺✷
✭❛✮ t❤❡ ❧❡❛r♥❡r t❡①t ✭❜✮ ❛ ❣r❛♠♠❛t✐❝❛❧❧② ❝♦rr❡❝t❡❞ ✈❡rs✐♦♥ ♦❢ ✐t ✭t❛r❣❡t ❤②♣♦t❤❡s✐s✮ ■❢ t❤❡r❡ ✐s ❛ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤♦s❡ r❡s✉❧ts ❢♦r t❤❡♥ t❤✐s r❡✢❡❝ts tr❛♥s❢❡r ❧❡❛❞✐♥❣ t♦ ✉♥❣r❛♠♠❛t✐❝❛❧ ■▲✲str✉❝t✉r❡s✳ ❚r❛♥s❢❡r ❛♥❞ ❣r❛♠♠❛t✐❝❛❧ ❡rr♦rs ❘♦❛❞ ♠❛♣ ❋r♦♠ s✐♠✐❧❛r✐t② t♦ tr❛♥s❢❡r ❚r❛♥s❢❡r ♦♥ ❞✐✛❡r❡♥t ❧✐♥❣✉✐st✐❝ ❧❡✈❡❧s ▲✶ ❝❧❛ss✐✜❝❛t✐♦♥ r❡s✉❧ts ❜❛s❡❞ ♦♥ ❞✐✛❡r❡♥t ❧✐♥❣✉✐st✐❝ ❧❡✈❡❧s r❡✢❡❝t tr❛♥s❢❡r ♦♥ t❤❛t s♣❡❝✐✜❝ ❧❡✈❡❧ ◮ ❧❡♠♠❛ ⇒ ✭♠❛✐♥❧②✮ tr❛♥s❢❡r ♦♥ ❧❡①✐❝❛❧ ❝❤♦✐❝❡ ◮ ♣❛rt✲♦❢✲s♣❡❡❝❤ ⇒ ✭♠❛✐♥❧②✮ s②♥t❛❝t✐❝ tr❛♥s❢❡r ◮ ❧❡♠♠❛✲t♦❦✲❞✐✛❡r❡♥❝❡ ⇒ ✐♥✢❡❝t✐♦♥❛❧ ♠♦r♣❤♦❧♦❣②❄ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✵ ✴ ✺✷
❘♦❛❞ ♠❛♣ ❋r♦♠ s✐♠✐❧❛r✐t② t♦ tr❛♥s❢❡r ❚r❛♥s❢❡r ♦♥ ❞✐✛❡r❡♥t ❧✐♥❣✉✐st✐❝ ❧❡✈❡❧s ▲✶ ❝❧❛ss✐✜❝❛t✐♦♥ r❡s✉❧ts ❜❛s❡❞ ♦♥ ❞✐✛❡r❡♥t ❧✐♥❣✉✐st✐❝ ❧❡✈❡❧s r❡✢❡❝t tr❛♥s❢❡r ♦♥ t❤❛t s♣❡❝✐✜❝ ❧❡✈❡❧ ◮ ❧❡♠♠❛ ⇒ ✭♠❛✐♥❧②✮ tr❛♥s❢❡r ♦♥ ❧❡①✐❝❛❧ ❝❤♦✐❝❡ ◮ ♣❛rt✲♦❢✲s♣❡❡❝❤ ⇒ ✭♠❛✐♥❧②✮ s②♥t❛❝t✐❝ tr❛♥s❢❡r ◮ ❧❡♠♠❛✲t♦❦✲❞✐✛❡r❡♥❝❡ ⇒ ✐♥✢❡❝t✐♦♥❛❧ ♠♦r♣❤♦❧♦❣②❄ ❚r❛♥s❢❡r ❛♥❞ ❣r❛♠♠❛t✐❝❛❧ ❡rr♦rs ■❢ t❤❡r❡ ✐s ❛ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤♦s❡ r❡s✉❧ts ❢♦r ✭❛✮ t❤❡ ❧❡❛r♥❡r t❡①t ✭❜✮ ❛ ❣r❛♠♠❛t✐❝❛❧❧② ❝♦rr❡❝t❡❞ ✈❡rs✐♦♥ ♦❢ ✐t ✭t❛r❣❡t ❤②♣♦t❤❡s✐s✮ t❤❡♥ t❤✐s r❡✢❡❝ts tr❛♥s❢❡r ❧❡❛❞✐♥❣ t♦ ✉♥❣r❛♠♠❛t✐❝❛❧ ■▲✲str✉❝t✉r❡s✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✵ ✴ ✺✷
❖✉r ❞❛t❛ ✲ t❤❡ ❋❛❧❦♦ ❝♦r♣✉s ❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ✶ ❚r❛♥s❢❡r ✷ ❘♦❛❞ ♠❛♣ ✸ ❖✉r ❞❛t❛ ✲ t❤❡ ❋❛❧❦♦ ❝♦r♣✉s ✹ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ✺ Pr❡❧✐♠✐♥❛r② r❡s✉❧ts ✻ ❚✇♦ ✐ss✉❡s ✼ ❚❛❦✐♥❣ t❤❡ ❡ss❛② t♦♣✐❝ ✐♥t♦ ❛❝❝♦✉♥t ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❘❡s✉❧ts ✽ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ✾ ✶✵ ❈♦♥❝❧✉s✐♦♥ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✶ ✴ ✺✷
❖✉r ❞❛t❛ ✲ t❤❡ ❋❛❧❦♦ ❝♦r♣✉s ❋❛❧❦♦ ✭▲ü❞❡❧✐♥❣ ❡t ❛❧✳ ✷✵✵✽✮ ❝♦r♣✉s s✉❜s❡t ▲✶ ★ ♦❢ t❡①ts ❚❡①ts ✐♥❝❧✉❞❡❞ ✭❞❡✉✮ ❛ ●❡r♠❛♥ ✶✵ ❧❛♥❣✉❛❣❡s ✇✐t❤ ❛t ❧❡❛st ✶✵ t❡①ts ❊♥❣❧✐s❤ ✭❡♥❣✮ ✹✷ ❉❛♥✐s❤ ✭❞❛♥✮ ✸✼ ❧❡❛r♥❡rs ✇✐t❤ ♦♥❧② ♦♥❡ ▲✶ ❋r❡♥❝❤ ✭❢r❛✮ ✶✹ ❘✉ss✐❛♥ ✭r✉s✮ ✶✵ ❱❡r② s♠❛❧❧ ❞❛t❛ s❛♠♣❧❡ ❚✉r❦✐s❤ ✭t✉r✮ ✶✵ ❲❡ ✉s❡ ♦♥❧② ≈ ✻✻ . ✵✵✵ t♦❦❡♥s✳ t♦t❛❧ ✶✷✻ t❡①ts ❚❤✐s ✐s ✸✹✪ ♦❢ ❋❛❧❦♦✳ ❛ ❝♦♥tr♦❧ ❣r♦✉♣✱ ❡①❝❧✉❞❡❞ ✐❢ s❡♥s✐❜❧❡ t✐t❧❡ t❡①ts ✏❝r✐♠❡✑ ✶✶ ❑r✐♠✐♥❛❧✐tät ③❛❤❧t s✐❝❤ ♥✐❝❤t ❛✉s✳ ✏❢❡♠✐♥✐s♠✑ ✷✸ ❉❡r ❋❡♠✐♥✐s♠✉s ❤❛t ❞❡♥ ■♥t❡r❡ss❡♥ ❞❡r ❋r❛✉❡♥ ♠❡❤r ❣❡s❝❤❛❞❡t ❛❧s ❣❡♥üt③t✳ ✏✇❛❣❡s✑ ✻✵ ❉✐❡ ✜♥❛♥③✐❡❧❧❡ ❊♥t❧♦❤♥✉♥❣ ❡✐♥❡s ▼❡♥s❝❤❡♥ s♦❧❧t❡ ❞❡♠ ❇❡✐tr❛❣ ❡♥ts♣r❡❝❤❡♥✱ ❞❡♥ ❡r✴ s✐❡ ❢ür ❞✐❡ ●❡s❡❧❧s❝❤❛❢t ❣❡❧❡✐st❡t ❤❛t✳ ✏st✉❞✐❡s✑ ✸✷ ❉✐❡ ♠❡✐st❡♥ ❯♥✐✈❡rs✐täts❛❜s❝❤❧üss❡ s✐♥❞ ♥✐❝❤t ♣r❛①✐s♦r✐❡♥t✐❡rt ✉♥❞ ❜❡r❡✐t❡♥ ❞✐❡ ❙t✉❞❡♥t❡♥ ♥✐❝❤t ❛✉❢ ❞✐❡ ✇✐r❦❧✐❝❤❡ ❲❡❧t ✈♦r✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✷ ✴ ✺✷
t♦❦❡♥ ♦r✐❣✐♥❛❧ t❡①ts✿ ▼❛♥ ❞❡♥❦❡ ❛♥ ❞❡♥ ✉♥t❡rs❝❤✐❡❞❧✐❝❤❡♥ ●r✉♣♣❡♥✱ ❞✐❡ s✐❝❤ ❢ür ❞❡♥ ❯♠✇❡❧tss❝❤✉t③ ❡✐♥s❡t③❡♥✳ P❖❙ P❛rt✲♦❢✲❙♣❡❡❝❤ t❛❣ s❡q✉❡♥❝❡ ✭❚r❡❡t❛❣❣❡r ✶ ✮✿ P■❙ ❱❱❋■◆ ❆PP❘ ❆❘❚ ❆❉❏❆ ◆◆ ✩✱ P❘❊▲❙ P❘❋ ❆PP❘ ❆❘❚ ◆◆ ❱❱■◆❋ ✩✳ ❧❡♠♠❛ ❧❡♠♠❛ s❡q✉❡♥❝❡✿ ♠❛♥ ❞❡♥❦❡♥ ❛♥ ❞ ✉♥t❡rs❝❤✐❡❞❧✐❝❤ ●r✉♣♣❡ ✱ ❞ ❡r⑤❡s⑤s✐❡ ❢ür ❞ ❯♠✇❡❧tss❝❤✉t③ ❡✐♥s❡t③❡♥ ✳ ❧❡❛r♥❡r ❚❤❡ r❛✇ ❧❡❛r♥❡r t❡①ts✿ ▼❛♥ ❞❡♥❦❡ ❛♥ ❞❡♥ ✉♥t❡rs❝❤✐❡❞❧✐❝❤❡♥ ●r✉♣♣❡♥✱ ❞✐❡ ❬✳ ✳ ✳ ❪ ❚❛r❣❡t ❤②♣♦t❤❡s✐s ✭❩❍✶✮ t❤❡ ❣r❛♠♠❛t✐❝❛❧✐③❡❞ ✈❡rs✐♦♥✭❘❡③♥✐❝❡❦ ❡t ❛❧✳ ✷✵✶✵✮✿ ▼❛♥ ❞❡♥❦❡ ❛♥ ❞✐❡ ✉♥t❡rs❝❤✐❡❞❧✐❝❤❡♥ ●r✉♣♣❡♥✱ ❞✐❡ ❬✳ ✳ ✳ ❪ ▲❡✈❡❧ ♦❢ ❧✐♥❣✉✐st✐❝ r❡♣r❡s❡♥t❛t✐♦♥✿ ✶ ▲❡✈❡❧ ♦❢ ❡rr♦r ❝♦♥t❛♠✐♥❛t✐♦♥✿ ✷ ❖✉r ❞❛t❛ ✲ t❤❡ ❋❛❧❦♦ ❝♦r♣✉s ❋❛❧❦♦ ✲ ✻ r❡♣r❡s❡♥t❛t✐♦♥s ❲❡ ❤❛✈❡ ✻ r❡♣r❡s❡♥t❛t✐♦♥s ♦❢ ❡❛❝❤ t❡①t✳ ❊❛❝❤ r❡♣r❡s❡♥t❛t✐♦♥ ✐s ❞❡✜♥❡❞ ❜② t✇♦ ✈❛r✐❛❜❧❡s✿ ✶ ❙❝❤♠✐❞ ✶✾✾✹✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✸ ✴ ✺✷
❧❡❛r♥❡r ❚❤❡ r❛✇ ❧❡❛r♥❡r t❡①ts✿ ▼❛♥ ❞❡♥❦❡ ❛♥ ❞❡♥ ✉♥t❡rs❝❤✐❡❞❧✐❝❤❡♥ ●r✉♣♣❡♥✱ ❞✐❡ ❬✳ ✳ ✳ ❪ ❚❛r❣❡t ❤②♣♦t❤❡s✐s ✭❩❍✶✮ t❤❡ ❣r❛♠♠❛t✐❝❛❧✐③❡❞ ✈❡rs✐♦♥✭❘❡③♥✐❝❡❦ ❡t ❛❧✳ ✷✵✶✵✮✿ ▼❛♥ ❞❡♥❦❡ ❛♥ ❞✐❡ ✉♥t❡rs❝❤✐❡❞❧✐❝❤❡♥ ●r✉♣♣❡♥✱ ❞✐❡ ❬✳ ✳ ✳ ❪ ▲❡✈❡❧ ♦❢ ❡rr♦r ❝♦♥t❛♠✐♥❛t✐♦♥✿ ✷ ❖✉r ❞❛t❛ ✲ t❤❡ ❋❛❧❦♦ ❝♦r♣✉s ❋❛❧❦♦ ✲ ✻ r❡♣r❡s❡♥t❛t✐♦♥s ❲❡ ❤❛✈❡ ✻ r❡♣r❡s❡♥t❛t✐♦♥s ♦❢ ❡❛❝❤ t❡①t✳ ❊❛❝❤ r❡♣r❡s❡♥t❛t✐♦♥ ✐s ❞❡✜♥❡❞ ❜② t✇♦ ✈❛r✐❛❜❧❡s✿ ▲❡✈❡❧ ♦❢ ❧✐♥❣✉✐st✐❝ r❡♣r❡s❡♥t❛t✐♦♥✿ ✶ t♦❦❡♥ ♦r✐❣✐♥❛❧ t❡①ts✿ ▼❛♥ ❞❡♥❦❡ ❛♥ ❞❡♥ ✉♥t❡rs❝❤✐❡❞❧✐❝❤❡♥ ●r✉♣♣❡♥✱ ❞✐❡ s✐❝❤ ❢ür ❞❡♥ ❯♠✇❡❧tss❝❤✉t③ ❡✐♥s❡t③❡♥✳ P❖❙ P❛rt✲♦❢✲❙♣❡❡❝❤ t❛❣ s❡q✉❡♥❝❡ ✭❚r❡❡t❛❣❣❡r ✶ ✮✿ P■❙ ❱❱❋■◆ ❆PP❘ ❆❘❚ ❆❉❏❆ ◆◆ ✩✱ P❘❊▲❙ P❘❋ ❆PP❘ ❆❘❚ ◆◆ ❱❱■◆❋ ✩✳ ❧❡♠♠❛ ❧❡♠♠❛ s❡q✉❡♥❝❡✿ ♠❛♥ ❞❡♥❦❡♥ ❛♥ ❞ ✉♥t❡rs❝❤✐❡❞❧✐❝❤ ●r✉♣♣❡ ✱ ❞ ❡r⑤❡s⑤s✐❡ ❢ür ❞ ❯♠✇❡❧tss❝❤✉t③ ❡✐♥s❡t③❡♥ ✳ ✶ ❙❝❤♠✐❞ ✶✾✾✹✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✸ ✴ ✺✷
❖✉r ❞❛t❛ ✲ t❤❡ ❋❛❧❦♦ ❝♦r♣✉s ❋❛❧❦♦ ✲ ✻ r❡♣r❡s❡♥t❛t✐♦♥s ❲❡ ❤❛✈❡ ✻ r❡♣r❡s❡♥t❛t✐♦♥s ♦❢ ❡❛❝❤ t❡①t✳ ❊❛❝❤ r❡♣r❡s❡♥t❛t✐♦♥ ✐s ❞❡✜♥❡❞ ❜② t✇♦ ✈❛r✐❛❜❧❡s✿ ▲❡✈❡❧ ♦❢ ❧✐♥❣✉✐st✐❝ r❡♣r❡s❡♥t❛t✐♦♥✿ ✶ t♦❦❡♥ ♦r✐❣✐♥❛❧ t❡①ts✿ ▼❛♥ ❞❡♥❦❡ ❛♥ ❞❡♥ ✉♥t❡rs❝❤✐❡❞❧✐❝❤❡♥ ●r✉♣♣❡♥✱ ❞✐❡ s✐❝❤ ❢ür ❞❡♥ ❯♠✇❡❧tss❝❤✉t③ ❡✐♥s❡t③❡♥✳ P❖❙ P❛rt✲♦❢✲❙♣❡❡❝❤ t❛❣ s❡q✉❡♥❝❡ ✭❚r❡❡t❛❣❣❡r ✶ ✮✿ P■❙ ❱❱❋■◆ ❆PP❘ ❆❘❚ ❆❉❏❆ ◆◆ ✩✱ P❘❊▲❙ P❘❋ ❆PP❘ ❆❘❚ ◆◆ ❱❱■◆❋ ✩✳ ❧❡♠♠❛ ❧❡♠♠❛ s❡q✉❡♥❝❡✿ ♠❛♥ ❞❡♥❦❡♥ ❛♥ ❞ ✉♥t❡rs❝❤✐❡❞❧✐❝❤ ●r✉♣♣❡ ✱ ❞ ❡r⑤❡s⑤s✐❡ ❢ür ❞ ❯♠✇❡❧tss❝❤✉t③ ❡✐♥s❡t③❡♥ ✳ ▲❡✈❡❧ ♦❢ ❡rr♦r ❝♦♥t❛♠✐♥❛t✐♦♥✿ ✷ ❧❡❛r♥❡r ❚❤❡ r❛✇ ❧❡❛r♥❡r t❡①ts✿ ✟ ▼❛♥ ❞❡♥❦❡ ❛♥ ✟ ❞❡♥ ✉♥t❡rs❝❤✐❡❞❧✐❝❤❡♥ ●r✉♣♣❡♥✱ ❞✐❡ ❬✳ ✳ ✳ ❪ ❚❛r❣❡t ❤②♣♦t❤❡s✐s ✭❩❍✶✮ t❤❡ ❣r❛♠♠❛t✐❝❛❧✐③❡❞ ✈❡rs✐♦♥✭❘❡③♥✐❝❡❦ ❡t ❛❧✳ ✷✵✶✵✮✿ ▼❛♥ ❞❡♥❦❡ ❛♥ ❞✐❡ ✉♥t❡rs❝❤✐❡❞❧✐❝❤❡♥ ●r✉♣♣❡♥✱ ❞✐❡ ❬✳ ✳ ✳ ❪ ✶ ❙❝❤♠✐❞ ✶✾✾✹✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✸ ✴ ✺✷
❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ✶ ❚r❛♥s❢❡r ✷ ❘♦❛❞ ♠❛♣ ✸ ❖✉r ❞❛t❛ ✲ t❤❡ ❋❛❧❦♦ ❝♦r♣✉s ✹ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ✺ Pr❡❧✐♠✐♥❛r② r❡s✉❧ts ✻ ❚✇♦ ✐ss✉❡s ✼ ❚❛❦✐♥❣ t❤❡ ❡ss❛② t♦♣✐❝ ✐♥t♦ ❛❝❝♦✉♥t ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❘❡s✉❧ts ✽ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ✾ ✶✵ ❈♦♥❝❧✉s✐♦♥ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✹ ✴ ✺✷
❙ s✉❜str✐♥❣s ❆ ①❛❜❛② ❇ ❜❝❜❛❜❞ ✷ ✶ ❧♦❣ ✷ ✶ ✶ ✶ ✵✾ ❛ ✶ ✶ ❧♦❣ ✶ ✶ ✶ ✵ ✻✾ ❛❜ ✶ ✸ ❧♦❣ ✶ ✸ ✶ ✶ ✸✾ ❜ ✶ ✵ ❧♦❣ ✶ ✵ ✶ ✵ ① ✸ ✶✼ ❛♥ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡ ❆❧❧ s✉❜str✐♥❣s ♦❢ ❛❧❧ ❧❡♥❣t❤s ❝♦♥tr✐❜✉t❡✿ ◆♦ ♠❛①✐♠❛❧ ❧❡♥❣t❤ ✐s s❡t ✭❛s ✐s t❤❡ ✉s✉❛❧ ♣r❛①✐s✮✳ ◆♦ ♦t❤❡r ✐♥❢♦r♠❛t✐♦♥ t❤❛♥ ✭❝❤❛r❛❝t❡r✮ str✐♥❣ r❡♣❡t✐t✐♦♥s ❛r❡ ✉s❡❞✳ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❙ ❡①♣❧❛✐♥❡❞ ❜② ❡①❛♠♣❧❡ ❚✇♦ ✈❡r② s❤♦rt t❡①ts✿ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✺ ✴ ✺✷
❙ s✉❜str✐♥❣s ❇ ❜❝❜❛❜❞ ✷ ✶ ❧♦❣ ✷ ✶ ✶ ✶ ✵✾ ❛ ✶ ✶ ❧♦❣ ✶ ✶ ✶ ✵ ✻✾ ❛❜ ✶ ✸ ❧♦❣ ✶ ✸ ✶ ✶ ✸✾ ❜ ✶ ✵ ❧♦❣ ✶ ✵ ✶ ✵ ① ✸ ✶✼ ❛♥ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡ ❆❧❧ s✉❜str✐♥❣s ♦❢ ❛❧❧ ❧❡♥❣t❤s ❝♦♥tr✐❜✉t❡✿ ◆♦ ♠❛①✐♠❛❧ ❧❡♥❣t❤ ✐s s❡t ✭❛s ✐s t❤❡ ✉s✉❛❧ ♣r❛①✐s✮✳ ◆♦ ♦t❤❡r ✐♥❢♦r♠❛t✐♦♥ t❤❛♥ ✭❝❤❛r❛❝t❡r✮ str✐♥❣ r❡♣❡t✐t✐♦♥s ❛r❡ ✉s❡❞✳ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❙ ❡①♣❧❛✐♥❡❞ ❜② ❡①❛♠♣❧❡ ❚✇♦ ✈❡r② s❤♦rt t❡①ts✿ ❆ = ①❛❜❛② ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✺ ✴ ✺✷
❙ s✉❜str✐♥❣s ✷ ✶ ❧♦❣ ✷ ✶ ✶ ✶ ✵✾ ❛ ✶ ✶ ❧♦❣ ✶ ✶ ✶ ✵ ✻✾ ❛❜ ✶ ✸ ❧♦❣ ✶ ✸ ✶ ✶ ✸✾ ❜ ✶ ✵ ❧♦❣ ✶ ✵ ✶ ✵ ① ✸ ✶✼ ❛♥ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡ ❆❧❧ s✉❜str✐♥❣s ♦❢ ❛❧❧ ❧❡♥❣t❤s ❝♦♥tr✐❜✉t❡✿ ◆♦ ♠❛①✐♠❛❧ ❧❡♥❣t❤ ✐s s❡t ✭❛s ✐s t❤❡ ✉s✉❛❧ ♣r❛①✐s✮✳ ◆♦ ♦t❤❡r ✐♥❢♦r♠❛t✐♦♥ t❤❛♥ ✭❝❤❛r❛❝t❡r✮ str✐♥❣ r❡♣❡t✐t✐♦♥s ❛r❡ ✉s❡❞✳ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❙ ❡①♣❧❛✐♥❡❞ ❜② ❡①❛♠♣❧❡ ❚✇♦ ✈❡r② s❤♦rt t❡①ts✿ ❆ = ①❛❜❛② ❇ = ❜❝❜❛❜❞ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✺ ✴ ✺✷
❙ ✷ ✶ ❧♦❣ ✷ ✶ ✶ ✶ ✵✾ ❛ ✶ ✶ ❧♦❣ ✶ ✶ ✶ ✵ ✻✾ ❛❜ ✶ ✸ ❧♦❣ ✶ ✸ ✶ ✶ ✸✾ ❜ ✶ ✵ ❧♦❣ ✶ ✵ ✶ ✵ ① ✸ ✶✼ ❛♥ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡ ❆❧❧ s✉❜str✐♥❣s ♦❢ ❛❧❧ ❧❡♥❣t❤s ❝♦♥tr✐❜✉t❡✿ ◆♦ ♠❛①✐♠❛❧ ❧❡♥❣t❤ ✐s s❡t ✭❛s ✐s t❤❡ ✉s✉❛❧ ♣r❛①✐s✮✳ ◆♦ ♦t❤❡r ✐♥❢♦r♠❛t✐♦♥ t❤❛♥ ✭❝❤❛r❛❝t❡r✮ str✐♥❣ r❡♣❡t✐t✐♦♥s ❛r❡ ✉s❡❞✳ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❙ ❡①♣❧❛✐♥❡❞ ❜② ❡①❛♠♣❧❡ ❚✇♦ ✈❡r② s❤♦rt t❡①ts✿ s✉❜str✐♥❣s ❆ = ①❛❜❛② ❇ = ❜❝❜❛❜❞ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✺ ✴ ✺✷
❙ ❧♦❣ ✷ ✶ ✶ ✶ ✵✾ ✶ ✶ ❧♦❣ ✶ ✶ ✶ ✵ ✻✾ ❛❜ ✶ ✸ ❧♦❣ ✶ ✸ ✶ ✶ ✸✾ ❜ ✶ ✵ ❧♦❣ ✶ ✵ ✶ ✵ ① ✸ ✶✼ ❛♥ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡ ❆❧❧ s✉❜str✐♥❣s ♦❢ ❛❧❧ ❧❡♥❣t❤s ❝♦♥tr✐❜✉t❡✿ ◆♦ ♠❛①✐♠❛❧ ❧❡♥❣t❤ ✐s s❡t ✭❛s ✐s t❤❡ ✉s✉❛❧ ♣r❛①✐s✮✳ ◆♦ ♦t❤❡r ✐♥❢♦r♠❛t✐♦♥ t❤❛♥ ✭❝❤❛r❛❝t❡r✮ str✐♥❣ r❡♣❡t✐t✐♦♥s ❛r❡ ✉s❡❞✳ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❙ ❡①♣❧❛✐♥❡❞ ❜② ❡①❛♠♣❧❡ ❚✇♦ ✈❡r② s❤♦rt t❡①ts✿ s✉❜str✐♥❣s ❆ = ①❛❜❛② ❇ = ❜❝❜❛❜❞ ✷ ✶ ❛ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✺ ✴ ✺✷
❙ ❧♦❣ ✷ ✶ ✶ ✶ ✵✾ ❧♦❣ ✶ ✶ ✶ ✵ ✻✾ ✶ ✸ ❧♦❣ ✶ ✸ ✶ ✶ ✸✾ ❜ ✶ ✵ ❧♦❣ ✶ ✵ ✶ ✵ ① ✸ ✶✼ ❛♥ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡ ❆❧❧ s✉❜str✐♥❣s ♦❢ ❛❧❧ ❧❡♥❣t❤s ❝♦♥tr✐❜✉t❡✿ ◆♦ ♠❛①✐♠❛❧ ❧❡♥❣t❤ ✐s s❡t ✭❛s ✐s t❤❡ ✉s✉❛❧ ♣r❛①✐s✮✳ ◆♦ ♦t❤❡r ✐♥❢♦r♠❛t✐♦♥ t❤❛♥ ✭❝❤❛r❛❝t❡r✮ str✐♥❣ r❡♣❡t✐t✐♦♥s ❛r❡ ✉s❡❞✳ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❙ ❡①♣❧❛✐♥❡❞ ❜② ❡①❛♠♣❧❡ ❚✇♦ ✈❡r② s❤♦rt t❡①ts✿ s✉❜str✐♥❣s ❆ = ①❛❜❛② ❇ = ❜❝❜❛❜❞ ✷ ✶ ❛ ✶ ✶ ❛❜ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✺ ✴ ✺✷
❙ ❧♦❣ ✷ ✶ ✶ ✶ ✵✾ ❧♦❣ ✶ ✶ ✶ ✵ ✻✾ ❧♦❣ ✶ ✸ ✶ ✶ ✸✾ ✶ ✵ ❧♦❣ ✶ ✵ ✶ ✵ ① ✸ ✶✼ ❛♥ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡ ❆❧❧ s✉❜str✐♥❣s ♦❢ ❛❧❧ ❧❡♥❣t❤s ❝♦♥tr✐❜✉t❡✿ ◆♦ ♠❛①✐♠❛❧ ❧❡♥❣t❤ ✐s s❡t ✭❛s ✐s t❤❡ ✉s✉❛❧ ♣r❛①✐s✮✳ ◆♦ ♦t❤❡r ✐♥❢♦r♠❛t✐♦♥ t❤❛♥ ✭❝❤❛r❛❝t❡r✮ str✐♥❣ r❡♣❡t✐t✐♦♥s ❛r❡ ✉s❡❞✳ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❙ ❡①♣❧❛✐♥❡❞ ❜② ❡①❛♠♣❧❡ ❚✇♦ ✈❡r② s❤♦rt t❡①ts✿ s✉❜str✐♥❣s ❆ = ①❛❜❛② ❇ = ❜❝❜❛❜❞ ✷ ✶ ❛ ✶ ✶ ❛❜ ❜ ✶ ✸ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✺ ✴ ✺✷
❙ ❧♦❣ ✷ ✶ ✶ ✶ ✵✾ ❧♦❣ ✶ ✶ ✶ ✵ ✻✾ ❧♦❣ ✶ ✸ ✶ ✶ ✸✾ ❧♦❣ ✶ ✵ ✶ ✵ ✸ ✶✼ ❛♥ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡ ❆❧❧ s✉❜str✐♥❣s ♦❢ ❛❧❧ ❧❡♥❣t❤s ❝♦♥tr✐❜✉t❡✿ ◆♦ ♠❛①✐♠❛❧ ❧❡♥❣t❤ ✐s s❡t ✭❛s ✐s t❤❡ ✉s✉❛❧ ♣r❛①✐s✮✳ ◆♦ ♦t❤❡r ✐♥❢♦r♠❛t✐♦♥ t❤❛♥ ✭❝❤❛r❛❝t❡r✮ str✐♥❣ r❡♣❡t✐t✐♦♥s ❛r❡ ✉s❡❞✳ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❙ ❡①♣❧❛✐♥❡❞ ❜② ❡①❛♠♣❧❡ ❚✇♦ ✈❡r② s❤♦rt t❡①ts✿ s✉❜str✐♥❣s ❆ = ①❛❜❛② ❇ = ❜❝❜❛❜❞ ✷ ✶ ❛ ✶ ✶ ❛❜ ❜ ✶ ✸ ✶ ✵ ① ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✺ ✴ ✺✷
❙ ❧♦❣ ✶ ✶ ✵✾ ❧♦❣ ✶ ✵ ✻✾ ❧♦❣ ✶ ✶ ✸✾ ❧♦❣ ✶ ✵ ✸ ✶✼ ❛♥ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡ ❆❧❧ s✉❜str✐♥❣s ♦❢ ❛❧❧ ❧❡♥❣t❤s ❝♦♥tr✐❜✉t❡✿ ◆♦ ♠❛①✐♠❛❧ ❧❡♥❣t❤ ✐s s❡t ✭❛s ✐s t❤❡ ✉s✉❛❧ ♣r❛①✐s✮✳ ◆♦ ♦t❤❡r ✐♥❢♦r♠❛t✐♦♥ t❤❛♥ ✭❝❤❛r❛❝t❡r✮ str✐♥❣ r❡♣❡t✐t✐♦♥s ❛r❡ ✉s❡❞✳ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❙ ❡①♣❧❛✐♥❡❞ ❜② ❡①❛♠♣❧❡ ❚✇♦ ✈❡r② s❤♦rt t❡①ts✿ s✉❜str✐♥❣s ❆ = ①❛❜❛② ❇ = ❜❝❜❛❜❞ ✷ ✶ ✷ · ✶ ❛ ✶ ✶ ✶ · ✶ ❛❜ ❜ ✶ ✸ ✶ · ✸ ✶ ✵ ✶ · ✵ ① ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✺ ✴ ✺✷
❙ ✶ ✶ ✵✾ ✶ ✵ ✻✾ ✶ ✶ ✸✾ ✶ ✵ ✸ ✶✼ ❛♥ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡ ❆❧❧ s✉❜str✐♥❣s ♦❢ ❛❧❧ ❧❡♥❣t❤s ❝♦♥tr✐❜✉t❡✿ ◆♦ ♠❛①✐♠❛❧ ❧❡♥❣t❤ ✐s s❡t ✭❛s ✐s t❤❡ ✉s✉❛❧ ♣r❛①✐s✮✳ ◆♦ ♦t❤❡r ✐♥❢♦r♠❛t✐♦♥ t❤❛♥ ✭❝❤❛r❛❝t❡r✮ str✐♥❣ r❡♣❡t✐t✐♦♥s ❛r❡ ✉s❡❞✳ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❙ ❡①♣❧❛✐♥❡❞ ❜② ❡①❛♠♣❧❡ ❚✇♦ ✈❡r② s❤♦rt t❡①ts✿ s✉❜str✐♥❣s ❆ = ①❛❜❛② ❇ = ❜❝❜❛❜❞ ✷ ✶ ❧♦❣ ( ✷ · ✶ ) ❛ ✶ ✶ ❧♦❣ ( ✶ · ✶ ) ❛❜ ❧♦❣ ( ✶ · ✸ ) ❜ ✶ ✸ ✶ ✵ ❧♦❣ ( ✶ · ✵ ) ① ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✺ ✴ ✺✷
❙ ✶ ✵✾ ✵ ✻✾ ✶ ✸✾ ✵ ✸ ✶✼ ❛♥ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡ ❆❧❧ s✉❜str✐♥❣s ♦❢ ❛❧❧ ❧❡♥❣t❤s ❝♦♥tr✐❜✉t❡✿ ◆♦ ♠❛①✐♠❛❧ ❧❡♥❣t❤ ✐s s❡t ✭❛s ✐s t❤❡ ✉s✉❛❧ ♣r❛①✐s✮✳ ◆♦ ♦t❤❡r ✐♥❢♦r♠❛t✐♦♥ t❤❛♥ ✭❝❤❛r❛❝t❡r✮ str✐♥❣ r❡♣❡t✐t✐♦♥s ❛r❡ ✉s❡❞✳ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❙ ❡①♣❧❛✐♥❡❞ ❜② ❡①❛♠♣❧❡ ❚✇♦ ✈❡r② s❤♦rt t❡①ts✿ s✉❜str✐♥❣s ❆ = ①❛❜❛② ❇ = ❜❝❜❛❜❞ ✷ ✶ ❧♦❣ ( ✷ · ✶ + ✶ ) ❛ ✶ ✶ ❧♦❣ ( ✶ · ✶ + ✶ ) ❛❜ ❧♦❣ ( ✶ · ✸ + ✶ ) ❜ ✶ ✸ ✶ ✵ ❧♦❣ ( ✶ · ✵ + ✶ ) ① ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✺ ✴ ✺✷
❙ ✸ ✶✼ ❛♥ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡ ❆❧❧ s✉❜str✐♥❣s ♦❢ ❛❧❧ ❧❡♥❣t❤s ❝♦♥tr✐❜✉t❡✿ ◆♦ ♠❛①✐♠❛❧ ❧❡♥❣t❤ ✐s s❡t ✭❛s ✐s t❤❡ ✉s✉❛❧ ♣r❛①✐s✮✳ ◆♦ ♦t❤❡r ✐♥❢♦r♠❛t✐♦♥ t❤❛♥ ✭❝❤❛r❛❝t❡r✮ str✐♥❣ r❡♣❡t✐t✐♦♥s ❛r❡ ✉s❡❞✳ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❙ ❡①♣❧❛✐♥❡❞ ❜② ❡①❛♠♣❧❡ ❚✇♦ ✈❡r② s❤♦rt t❡①ts✿ s✉❜str✐♥❣s ❆ = ①❛❜❛② ❇ = ❜❝❜❛❜❞ ✷ ✶ ❧♦❣ ( ✷ · ✶ + ✶ ) = ✶ . ✵✾ ❛ ✶ ✶ ❧♦❣ ( ✶ · ✶ + ✶ ) = ✵ . ✻✾ ❛❜ ❧♦❣ ( ✶ · ✸ + ✶ ) = ✶ . ✸✾ ❜ ✶ ✸ ✶ ✵ ❧♦❣ ( ✶ · ✵ + ✶ ) = ✵ ① ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✺ ✴ ✺✷
❙ ❛♥ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡ ❆❧❧ s✉❜str✐♥❣s ♦❢ ❛❧❧ ❧❡♥❣t❤s ❝♦♥tr✐❜✉t❡✿ ◆♦ ♠❛①✐♠❛❧ ❧❡♥❣t❤ ✐s s❡t ✭❛s ✐s t❤❡ ✉s✉❛❧ ♣r❛①✐s✮✳ ◆♦ ♦t❤❡r ✐♥❢♦r♠❛t✐♦♥ t❤❛♥ ✭❝❤❛r❛❝t❡r✮ str✐♥❣ r❡♣❡t✐t✐♦♥s ❛r❡ ✉s❡❞✳ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❙ ❡①♣❧❛✐♥❡❞ ❜② ❡①❛♠♣❧❡ ❚✇♦ ✈❡r② s❤♦rt t❡①ts✿ s✉❜str✐♥❣s ❆ = ①❛❜❛② ❇ = ❜❝❜❛❜❞ ✷ ✶ ❧♦❣ ( ✷ · ✶ + ✶ ) = ✶ . ✵✾ ❛ ✶ ✶ ❧♦❣ ( ✶ · ✶ + ✶ ) = ✵ . ✻✾ ❛❜ ❧♦❣ ( ✶ · ✸ + ✶ ) = ✶ . ✸✾ ❜ ✶ ✸ ✶ ✵ ❧♦❣ ( ✶ · ✵ + ✶ ) = ✵ ① � = ✸ . ✶✼ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✺ ✴ ✺✷
❛♥ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡ ❆❧❧ s✉❜str✐♥❣s ♦❢ ❛❧❧ ❧❡♥❣t❤s ❝♦♥tr✐❜✉t❡✿ ◆♦ ♠❛①✐♠❛❧ ❧❡♥❣t❤ ✐s s❡t ✭❛s ✐s t❤❡ ✉s✉❛❧ ♣r❛①✐s✮✳ ◆♦ ♦t❤❡r ✐♥❢♦r♠❛t✐♦♥ t❤❛♥ ✭❝❤❛r❛❝t❡r✮ str✐♥❣ r❡♣❡t✐t✐♦♥s ❛r❡ ✉s❡❞✳ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❙ ❡①♣❧❛✐♥❡❞ ❜② ❡①❛♠♣❧❡ ❚✇♦ ✈❡r② s❤♦rt t❡①ts✿ s✉❜str✐♥❣s ❆ = ①❛❜❛② ❇ = ❜❝❜❛❜❞ ✷ ✶ ❧♦❣ ( ✷ · ✶ + ✶ ) = ✶ . ✵✾ ❛ ✶ ✶ ❧♦❣ ( ✶ · ✶ + ✶ ) = ✵ . ✻✾ ❛❜ ❧♦❣ ( ✶ · ✸ + ✶ ) = ✶ . ✸✾ ❜ ✶ ✸ ✶ ✵ ❧♦❣ ( ✶ · ✵ + ✶ ) = ✵ ① ❙ = � = ✸ . ✶✼ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✺ ✴ ✺✷
❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❙ ❡①♣❧❛✐♥❡❞ ❜② ❡①❛♠♣❧❡ ❚✇♦ ✈❡r② s❤♦rt t❡①ts✿ s✉❜str✐♥❣s ❆ = ①❛❜❛② ❇ = ❜❝❜❛❜❞ ✷ ✶ ❧♦❣ ( ✷ · ✶ + ✶ ) = ✶ . ✵✾ ❛ ✶ ✶ ❧♦❣ ( ✶ · ✶ + ✶ ) = ✵ . ✻✾ ❛❜ ❧♦❣ ( ✶ · ✸ + ✶ ) = ✶ . ✸✾ ❜ ✶ ✸ ✶ ✵ ❧♦❣ ( ✶ · ✵ + ✶ ) = ✵ ① ❙ = � = ✸ . ✶✼ ❛♥ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡ ❆❧❧ s✉❜str✐♥❣s ♦❢ ❛❧❧ ❧❡♥❣t❤s ❝♦♥tr✐❜✉t❡✿ ⇒ ◆♦ ♠❛①✐♠❛❧ ❧❡♥❣t❤ ✐s s❡t ✭❛s ✐s t❤❡ ✉s✉❛❧ ♣r❛①✐s✮✳ ◆♦ ♦t❤❡r ✐♥❢♦r♠❛t✐♦♥ t❤❛♥ ✭❝❤❛r❛❝t❡r✮ str✐♥❣ r❡♣❡t✐t✐♦♥s ❛r❡ ✉s❡❞✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✺ ✴ ✺✷
❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❱❛r✐♦✉s st②❧♦♠❡tr✐❝ t❛s❦s ❤❛✈❡ ❜❡❡♥ ✐♥✈❡st✐❣❛t❡❞ ✇✐t❤ ❙ ✿ ❋❡❧✐① ●♦❧❝❤❡r ✭✷✵✵✼✮✳ ✏❆ ♥❡✇ t❡①t st❛t✐st✐❝❛❧ ♠❡❛s✉r❡ ❛♥❞ ✐ts ❛♣♣❧✐❝❛t✐♦♥ t♦ st②❧♦♠❡tr②✑✳ ■♥✿ ❈♦r♣✉s ▲✐♥❣✉✐st✐❝s ✷✵✵✼ ✳ ❯♥✐✈❡rs✐t② ♦❢ ❇✐r♠✐♥❣❤❛♠ ❋❡❧✐① ●♦❧❝❤❡r ✭t♦ ❛♣♣❡❛r✮✳ ✏❆♥❛❧②s✐♥❣ ❝♦✉♥t✐♥❣ s✉✣① tr❡❡s ♦❢ ♥❛t✉r❛❧ ❧❛♥❣✉❛❣❡ t❡①ts ✭♣r❡❧✐♠✐♥❛r② t✐t❧❡✮✑✳ P❤❉ t❤❡s✐s✳ ❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✻ ✴ ✺✷
❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ❙♦♠❡ ❞❡t❛✐❧s ♦❢ t❤❡ ❝❧❛ss✐✜❝❛t✐♦♥ ♠❡t❤♦❞ ❚❛❦❡ ♦♥❡ t❡①t ❚ ✐ ❛❢t❡r ❛♥♦t❤❡r ❛s t❡st t❡①t ✭✶✷✻ t❡①ts✮✳ ❢♦❧❧♦✇✐♥❣ st❡♣s✿ ❈♦♠♣✉t❡ ❙ ( ❚ ✐ , ❚ ❥ ) ❢♦r t❤❡ r❡♠❛✐♥✐♥❣ ✶✷✺ tr❛✐♥✐♥❣ t❡①ts ✭ ✐ � = ❥ ✮ ✶ ●r♦✉♣ t❤♦s❡ ❙ ✈❛❧✉❡s ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ▲✶ ♦❢ t❤♦s❡ tr❛✐♥✐♥❣ t❡①ts✳ ✷ ❈♦♠♣✉t❡ t❤❡ ♠❡❛♥ ❙ ✈❛❧✉❡ ❙ ▲ ✶ ❢♦r ❡❛❝❤ ▲✶ ❣r♦✉♣✳ ✸ ❆ss✐❣♥ t❤❡ t❡st t❡①t ❚ ✐ t♦ t❤❡ ▲✶ ❣r♦✉♣ ✇✐t❤ t❤❡ ❤✐❣❤❡st ❙ ▲ ✶ ✳ ✹ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✼ ✴ ✺✷
Pr❡❧✐♠✐♥❛r② r❡s✉❧ts ❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ✶ ❚r❛♥s❢❡r ✷ ❘♦❛❞ ♠❛♣ ✸ ❖✉r ❞❛t❛ ✲ t❤❡ ❋❛❧❦♦ ❝♦r♣✉s ✹ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ✺ Pr❡❧✐♠✐♥❛r② r❡s✉❧ts ✻ ❚✇♦ ✐ss✉❡s ✼ ❚❛❦✐♥❣ t❤❡ ❡ss❛② t♦♣✐❝ ✐♥t♦ ❛❝❝♦✉♥t ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❘❡s✉❧ts ✽ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ✾ ✶✵ ❈♦♥❝❧✉s✐♦♥ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✽ ✴ ✺✷
Pr❡❧✐♠✐♥❛r② r❡s✉❧ts ▲✶ ❝❧❛ss✐✜❝❛t✐♦♥ ✕ Pr♦♦❢ ♦❢ ❝♦♥❝❡♣t baseline tok POS Lemma 1.0 ❙❡♥s✐❜❧❡ ✜rst r❡s✉❧ts✿ 0.8 ❆❜♦✈❡ ❜❛s❡❧✐♥❡ ✭✸✶ . ✷ = ✷✽ % ✮✳ Classification accuracy ◮ ❘❡♣r♦❞✉❝✐♥❣ s✐♠✐❧❛r r❡s✉❧ts ❛ ✳ 0.6 60 60 t♦❦ ❛♥❞ ❧❡♠♠❛ ♥❡❛r❧② ✐❞❡♥t✐❝❛❧✳ 59 54 48 P❖❙ ❧♦✇❡r✳ 44 0.4 ❚❛r❣❡t ❍②♣♦t❤❡s✐s s❡❡♠s ❧♦✇❡r✳ 0.2 ❛ ❑♦♣♣❡❧ ❡t ❛❧✳ ✷✵✵✸❀ ❑♦♣♣❡❧ ❡t ❛❧✳ ✷✵✵✺❀ ❚s✉r ❡t ❛❧✳ ✷✵✵✼❀ ❏♦❥♦❲♦♥❣ ❡t ❛❧✳ ✷✵✵✾❀ ●♦❧❝❤❡r t♦ ❛♣♣❡❛r 0.0 Text Target Hypothesis ❋✐❣✉r❡✿ ❞✐sr❡❣❛r❞✐♥❣ ●❡r♠❛♥ ▲✶ t❡①ts✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶✾ ✴ ✺✷
❚✇♦ ✐ss✉❡s ❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ✶ ❚r❛♥s❢❡r ✷ ❘♦❛❞ ♠❛♣ ✸ ❖✉r ❞❛t❛ ✲ t❤❡ ❋❛❧❦♦ ❝♦r♣✉s ✹ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ✺ Pr❡❧✐♠✐♥❛r② r❡s✉❧ts ✻ ❚✇♦ ✐ss✉❡s ✼ ❚❛❦✐♥❣ t❤❡ ❡ss❛② t♦♣✐❝ ✐♥t♦ ❛❝❝♦✉♥t ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❘❡s✉❧ts ✽ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ✾ ✶✵ ❈♦♥❝❧✉s✐♦♥ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✷✵ ✴ ✺✷
❚✇♦ ✐ss✉❡s ❚❛❦✐♥❣ t❤❡ ❡ss❛② t♦♣✐❝ ✐♥t♦ ❛❝❝♦✉♥t ❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ✶ ❚r❛♥s❢❡r ✷ ❘♦❛❞ ♠❛♣ ✸ ❖✉r ❞❛t❛ ✲ t❤❡ ❋❛❧❦♦ ❝♦r♣✉s ✹ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ✺ Pr❡❧✐♠✐♥❛r② r❡s✉❧ts ✻ ❚✇♦ ✐ss✉❡s ✼ ❚❛❦✐♥❣ t❤❡ ❡ss❛② t♦♣✐❝ ✐♥t♦ ❛❝❝♦✉♥t ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❘❡s✉❧ts ✽ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ✾ ✶✵ ❈♦♥❝❧✉s✐♦♥ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✷✶ ✴ ✺✷
❚✇♦ ✐ss✉❡s ❚❛❦✐♥❣ t❤❡ ❡ss❛② t♦♣✐❝ ✐♥t♦ ❛❝❝♦✉♥t ❆♥♦t❤❡r ♣♦ss✐❜❧❡ ✐♥✢✉❡♥❝❡✿ ❈♦♥t❡♥t ❯♥t✐❧ ♥♦✇ ✇❡ ✐❣♥♦r❡❞ t❤❡ ❡ss❛② t♦♣✐❝ ♣❡♦♣❧❡ ✇r♦t❡ ❛❜♦✉t✳ ❖❜✈✐♦✉s❧②✱ t❡①ts ❛❜♦✉t ✏❝r✐♠❡✑ ✇✐❧❧ s❤❛r❡ ✇♦r❞s✳ ❚❤✐s ♦❢ ❝♦✉rs❡ ❧❡❛❞s t♦ ❤✐❣❤❡r ❙ ✈❛❧✉❡s✳ ■❢ t❤✐s t♦♣✐❝ ❡✛❡❝t ✐s ❧❛r❣❡r t❤❛♥ t❤❡ ▲✶ ❡✛❡❝t✱ t❤❡ ❧❛tt❡r ✇✐❧❧ ❜❡ ♠❛s❦❡❞✳ ■♥ st②❧♦♠❡tr②✱ t❤✐s ✐s ❛ ✇❡❧❧ ❦♥♦✇♥ ♣r♦❜❧❡♠✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✷✷ ✴ ✺✷
❚✇♦ ✐ss✉❡s ❚❛❦✐♥❣ t❤❡ ❡ss❛② t♦♣✐❝ ✐♥t♦ ❛❝❝♦✉♥t ❝❧❛ss✐✜❝❛t✐♦♥ ❛❝❝♦r❞✐♥❣ t♦ t♦♣✐❝ baseline tok POS Lemma 112 1.0 111 111 111 0.8 t♦❦ ❛♥❞ ❧❡♠♠❛ ✈❡r② ❤✐❣❤ Classification accuracy ✭ > ✾✽ % ✮✳ 0.6 56 55 P❖❙ ♠✉❝❤ ❧♦✇❡r✳ 0.4 ◮ ❜✉t ❛❜♦✈❡ ❜❛s❡❧✐♥❡✦ ❂❃ t♦♣✐❝ ❡✛❡❝t ✈❡r② str♦♥❣✳ 0.2 0.0 Text Target Hypothesis ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✷✸ ✴ ✺✷
❚✇♦ ✐ss✉❡s ❚❛❦✐♥❣ t❤❡ ❡ss❛② t♦♣✐❝ ✐♥t♦ ❛❝❝♦✉♥t ❆ s✐♠♣❧❡ ❤❡✉r✐st✐❝ ❢♦r ✜❧t❡r✐♥❣ ♦✉t ❡ss❛② t♦♣✐❝ ❲❡ ❞✐✈✐❞❡ ❛❧❧ ❙ ( ❆ , ❇ ) ✐♥ t✇♦ ❣r♦✉♣s✿ ❆ ❛♥❞ ❇ ❤❛✈❡ t❤❡ s❛♠❡ t♦♣✐❝ ✳ ✶ ❚❤❡② ❤❛✈❡ ♥♦t✳ ✷ ❲❡ ❝♦♠♣✉t❡ t❤❡ ♠❡❛♥ ♦❢ ❡❛❝❤ ❣r♦✉♣✳ ❊❛❝❤ ❙ ✈❛❧✉❡ ✐s ❞✐✈✐❞❡❞ ❜② t❤❡ ♠❡❛♥ ♦❢ ✐ts ❣r♦✉♣✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✷✹ ✴ ✺✷
❚✇♦ ✐ss✉❡s ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ✶ ❚r❛♥s❢❡r ✷ ❘♦❛❞ ♠❛♣ ✸ ❖✉r ❞❛t❛ ✲ t❤❡ ❋❛❧❦♦ ❝♦r♣✉s ✹ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ✺ Pr❡❧✐♠✐♥❛r② r❡s✉❧ts ✻ ❚✇♦ ✐ss✉❡s ✼ ❚❛❦✐♥❣ t❤❡ ❡ss❛② t♦♣✐❝ ✐♥t♦ ❛❝❝♦✉♥t ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❘❡s✉❧ts ✽ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ✾ ✶✵ ❈♦♥❝❧✉s✐♦♥ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✷✺ ✴ ✺✷
❚✇♦ ✐ss✉❡s ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❈♦♣✐❡❞ ♠❛t❡r✐❛❧ ❡①♣❧♦s✐♦♥ ♦❢ s✉❜str✐♥❣s ❚❤❡ ♥✉♠❜❡r ♦❢ s✉❜str✐♥❣s ♦❢ ❛ str✐♥❣ ❣r♦✇s q✉❛❞r❛t✐❝❛❧❧② ✇✐t❤ ✐ts ❧❡♥❣t❤✳ ❚❡①ts ❛❜♦✉t t❤❡ s❛♠❡ s✉❜❥❡❝t ✇✐❧❧ ♥♦r♠❛❧❧② s❤❛r❡ ❧❡①✐❝❛❧ ♠❛t❡r✐❛❧✳ ❲❡ ❤❛✈❡ ❛♥ ❛❞❞✐t✐♦♥❛❧ ♣r♦❜❧❡♠✿ ❚❤❡ ❢✉❧❧ t♦♣✐❝ ✇❡ ❝❛❧❧ ✏❢❡♠✐♥✐s♠✑ r❡❛❞s ❛s ❉❡r ❋❡♠✐♥✐s♠✉s ❤❛t ❞❡♥ ■♥t❡r❡ss❡♥ ❞❡r ❋r❛✉❡♥ ♠❡❤r ❣❡s❝❤❛❞❡t ❛❧s ❣❡♥üt③t✳ ❋❡♠✐♥✐s♠ ❞❛♠❛❣❡❞ t❤❡ ✐♥t❡r❡sts ♦❢ t❤❡ ✇♦♠❡♥ r❛t❤❡r t❤❛♥ ✐t ❤❡❧♣❡❞ t❤❡♠✳ ❊s♣❡❝✐❛❧❧② ❧❡❛r♥❡rs t❡♥❞ t♦ ❝♦♣② ♣❤r❛s❡s ❧✐❦❡ ✏❞❡♥ ■♥t❡r❡ss❡♥ ❞❡r ❋r❛✉❡♥✑✳ ❚❤❡s❡ ❧♦♥❣ s❤❛r❡❞ s✉❜str✐♥❣s ♠❛❦❡ ✉♥♣r♦♣♦rt✐♦♥❛❧ ❝♦♥tr✐❜✉t✐♦♥s t♦ ❙ ✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✷✻ ✴ ✺✷
❚✇♦ ✐ss✉❡s ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❉❡✜♥✐t✐♦♥ ♦❢ ✏❝♦♣✐❡❞ ♠❛t❡r✐❛❧✑ ❲❡ ✉s❡ ❛ s✐♠♣❧❡ ❤❡✉r✐st✐❝ t♦ ✐❞❡♥t✐❢② ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❉❡✜♥✐t✐♦♥ ✭❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ♦❢ ♦r❞❡r ♥ ✮ ❆ str✐♥❣ ✐♥ t❡①t ❚ ✐s ❝♦♣✐❡❞ ❢r♦♠ s♦✉r❝❡ t❡①t ❙ ✱ ✐❢ ✳ ✳ ✳ ✐t ♦❝❝✉rs ♦♥❧② ♦♥❝❡ ✐♥ t❤❡ s♦✉r❝❡ t❡①t ❙ ✳ ✳ ✳ ✳ t❤✐s ✐s tr✉❡ ❡✈❡♥ ✐❢ ✇❡ str✐♣ ♥ ❝❤❛r❛❝t❡rs ❛t ❜♦t❤ s✐❞❡s✳ ❊①❛♠♣❧❡ ✭s❡t ♥ t♦ ✶✮ s♦✉r❝❡ ❙ ❉♦ ✇❡ ❤❛✈❡ ❜❡❡r ♦r ❞♦ ✇❡ ❤❛✈❡ ✇✐♥❡✱ ❏♦s❡❢❄ t❡①t ❚ ❙♦♠❡♦♥❡ ♠✉st ❤❛✈❡ ❜❡❡♥ t❡❧❧✐♥❣ ❧✐❡s ❛❜♦✉t ❏♦s❡❢ ❑✳ ❛♣♣❧②✐♥❣ t❤❡ ❞❡✜♥✐t✐♦♥✿ ✏ ❏♦s❡❢✑ ✐s ❝♦♣✐❡❞✳ ✏ ❤❛✈❡ ❜✑ ✐s ♥♦t ✭✏❤❛✈❡✑ ♦❝❝✉rs t✇✐❝❡ ✐♥ s♦✉r❝❡ t❡①t ❙ ✮ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✷✼ ✴ ✺✷
❚✇♦ ✐ss✉❡s ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❉❡✜♥✐t✐♦♥ ♦❢ ✏❝♦♣✐❡❞ ♠❛t❡r✐❛❧✑ ❲❡ ✉s❡ ❛ s✐♠♣❧❡ ❤❡✉r✐st✐❝ t♦ ✐❞❡♥t✐❢② ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❉❡✜♥✐t✐♦♥ ✭❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ♦❢ ♦r❞❡r ♥ ✮ ❆ str✐♥❣ ✐♥ t❡①t ❚ ✐s ❝♦♣✐❡❞ ❢r♦♠ s♦✉r❝❡ t❡①t ❙ ✱ ✐❢ ✳ ✳ ✳ ✐t ♦❝❝✉rs ♦♥❧② ♦♥❝❡ ✐♥ t❤❡ s♦✉r❝❡ t❡①t ❙ ✳ ✳ ✳ ✳ t❤✐s ✐s tr✉❡ ❡✈❡♥ ✐❢ ✇❡ str✐♣ ♥ ❝❤❛r❛❝t❡rs ❛t ❜♦t❤ s✐❞❡s✳ ❊①❛♠♣❧❡ ✭s❡t ♥ t♦ ✶✮ s♦✉r❝❡ ❙ ❉♦ ✇❡ ❤❛✈❡ ❜❡❡r ♦r ❞♦ ✇❡ ❤❛✈❡ ✇✐♥❡✱ ❏♦s❡❢❄ t❡①t ❚ ❙♦♠❡♦♥❡ ♠✉st ❤❛✈❡ ❜❡❡♥ t❡❧❧✐♥❣ ❧✐❡s ❛❜♦✉t ❏♦s❡❢ ❑✳ ❛♣♣❧②✐♥❣ t❤❡ ❞❡✜♥✐t✐♦♥✿ ✏ ❏♦s❡❢✑ ✐s ❝♦♣✐❡❞✳ ✏ ❤❛✈❡ ❜✑ ✐s ♥♦t ✭✏❤❛✈❡✑ ♦❝❝✉rs t✇✐❝❡ ✐♥ s♦✉r❝❡ t❡①t ❙ ✮ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✷✼ ✴ ✺✷
❚✇♦ ✐ss✉❡s ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❉❡✜♥✐t✐♦♥ ♦❢ ✏❝♦♣✐❡❞ ♠❛t❡r✐❛❧✑ ❲❡ ✉s❡ ❛ s✐♠♣❧❡ ❤❡✉r✐st✐❝ t♦ ✐❞❡♥t✐❢② ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❉❡✜♥✐t✐♦♥ ✭❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ♦❢ ♦r❞❡r ♥ ✮ ❆ str✐♥❣ ✐♥ t❡①t ❚ ✐s ❝♦♣✐❡❞ ❢r♦♠ s♦✉r❝❡ t❡①t ❙ ✱ ✐❢ ✳ ✳ ✳ ✐t ♦❝❝✉rs ♦♥❧② ♦♥❝❡ ✐♥ t❤❡ s♦✉r❝❡ t❡①t ❙ ✳ ✳ ✳ ✳ t❤✐s ✐s tr✉❡ ❡✈❡♥ ✐❢ ✇❡ str✐♣ ♥ ❝❤❛r❛❝t❡rs ❛t ❜♦t❤ s✐❞❡s✳ ❊①❛♠♣❧❡ ✭s❡t ♥ t♦ ✶✮ s♦✉r❝❡ ❙ ❉♦ ✇❡ ❤❛✈❡ ❜❡❡r ♦r ❞♦ ✇❡ ❤❛✈❡ ✇✐♥❡✱ ❏♦s❡❢❄ t❡①t ❚ ❙♦♠❡♦♥❡ ♠✉st ❤❛✈❡ ❜❡❡♥ t❡❧❧✐♥❣ ❧✐❡s ❛❜♦✉t ❏♦s❡❢ ❑✳ ❛♣♣❧②✐♥❣ t❤❡ ❞❡✜♥✐t✐♦♥✿ ✏ ❏♦s❡❢✑ ✐s ❝♦♣✐❡❞✳ ✏ ❤❛✈❡ ❜✑ ✐s ♥♦t ✭✏❤❛✈❡✑ ♦❝❝✉rs t✇✐❝❡ ✐♥ s♦✉r❝❡ t❡①t ❙ ✮ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✷✼ ✴ ✺✷
❚✇♦ ✐ss✉❡s ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❉❡✜♥✐t✐♦♥ ♦❢ ✏❝♦♣✐❡❞ ♠❛t❡r✐❛❧✑ ❲❡ ✉s❡ ❛ s✐♠♣❧❡ ❤❡✉r✐st✐❝ t♦ ✐❞❡♥t✐❢② ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❉❡✜♥✐t✐♦♥ ✭❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ♦❢ ♦r❞❡r ♥ ✮ ❆ str✐♥❣ ✐♥ t❡①t ❚ ✐s ❝♦♣✐❡❞ ❢r♦♠ s♦✉r❝❡ t❡①t ❙ ✱ ✐❢ ✳ ✳ ✳ ✐t ♦❝❝✉rs ♦♥❧② ♦♥❝❡ ✐♥ t❤❡ s♦✉r❝❡ t❡①t ❙ ✳ ✳ ✳ ✳ t❤✐s ✐s tr✉❡ ❡✈❡♥ ✐❢ ✇❡ str✐♣ ♥ ❝❤❛r❛❝t❡rs ❛t ❜♦t❤ s✐❞❡s✳ ❊①❛♠♣❧❡ ✭s❡t ♥ t♦ ✶✮ s♦✉r❝❡ ❙ ❉♦ ✇❡ ❤❛✈❡ ❜❡❡r ♦r ❞♦ ✇❡ ❤❛✈❡ ✇✐♥❡✱ ❏♦s❡❢❄ t❡①t ❚ ❙♦♠❡♦♥❡ ♠✉st ❤❛✈❡ ❜❡❡♥ t❡❧❧✐♥❣ ❧✐❡s ❛❜♦✉t ❏♦s❡❢ ❑✳ ❛♣♣❧②✐♥❣ t❤❡ ❞❡✜♥✐t✐♦♥✿ ✏ ❏♦s❡❢✑ ✐s ❝♦♣✐❡❞✳ ✏ ❤❛✈❡ ❜✑ ✐s ♥♦t ✭✏❤❛✈❡✑ ♦❝❝✉rs t✇✐❝❡ ✐♥ s♦✉r❝❡ t❡①t ❙ ✮ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✷✼ ✴ ✺✷
❚✇♦ ✐ss✉❡s ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❊①❛♠♣❧❡ ♥ = ✷ ❩✉♠ ❙❝❤❧✉ss ❣❧❛✉❜❡ ✐❝❤✱ ❞❛ss ❞❡r ❋❡♠✐♥✐s♠✉s ❞❡♥ ■♥t❡r❡ss❡♥ ❞❡r ❋r❛✉❡♥ s❡❤r ✈✐❡❧ ♥üt③❡♥ ❦ö♥♥❡✱ ❛❜❡r ❡s ❣✐❜t ③✉ ✈✐❡❧❡ ▲❡✉t❡✱ ❞✐❡ ❞✐❡ ❑♦♥③❡♣t❡ ❞❡s ❋❡♠✐♥✐s♠✉s s❝❤❛❞❡♥✱ ✇❡♥♥ s✐❡ ❞❡♠ ❋❡♠✐♥✐s✉♠✉s ❢ür ❢❛❧s❝❤❡♥ ●rü♥❞❡♥ ♦❞❡r ✐♥ ❞❡♥ ❢❛❧s❝❤❡♥ ❙✐t✉❛t✐♦♥❡♥ ♥üt③❡♥✳ ❆t t❤❡ ❡♥❞ ■ t❤✐♥❦✱ t❤❛t ❢❡♠✐♥✐s♠ ❝♦✉❧❞ ❤❡❧♣ t❤❡ ✐♥t❡r❡sts ♦❢ t❤❡ ✇♦♠❡♥ ✈❡r② ♠✉❝❤✱ ❜✉t t❤❡r❡ ❛r❡ t♦♦ ♠❛♥② ♣❡♦♣❧❡✱ ✇❤✐❝❤ ❤❛r♠ t❤❡♠ ❝♦♥❝❡♣ts ♦❢ ❢❡♠✐♥✐s♠✱ ✐❢ t❤❡② ❤❡❧♣ ❢❡♠✐♥✐♥✐s♠ ❢♦r ✇r♦♥❣s r❡❛s♦♥s ♦r ✐♥ ✇r♦♥❣ s✐t✉❛t✐♦♥s✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✷✽ ✴ ✺✷
❚✇♦ ✐ss✉❡s ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❊①❛♠♣❧❡ ♥ = ✺ ❩✉♠ ❙❝❤❧✉ss ❣❧❛✉❜❡ ✐❝❤✱ ❞❛ss ❞❡r ❋❡♠✐♥✐s♠✉s ❞❡♥ ■♥t❡r❡ss❡♥ ❞❡r ❋r❛✉❡♥ s❡❤r ✈✐❡❧ ♥üt③❡♥ ❦ö♥♥❡✱ ❛❜❡r ❡s ❣✐❜t ③✉ ✈✐❡❧❡ ▲❡✉t❡✱ ❞✐❡ ❞✐❡ ❑♦♥③❡♣t❡ ❞❡s ❋❡♠✐♥✐s♠✉s s❝❤❛❞❡♥✱ ✇❡♥♥ s✐❡ ❞❡♠ ❋❡♠✐♥✐s✉♠✉s ❢ür ❢❛❧s❝❤❡♥ ●rü♥❞❡♥ ♦❞❡r ✐♥ ❞❡♥ ❢❛❧s❝❤❡♥ ❙✐t✉❛t✐♦♥❡♥ ♥üt③❡♥✳ ❆t t❤❡ ❡♥❞ ■ t❤✐♥❦✱ t❤❛t ❢❡♠✐♥✐s♠ ❝♦✉❧❞ ❤❡❧♣ t❤❡ ✐♥t❡r❡sts ♦❢ t❤❡ ✇♦♠❡♥ ✈❡r② ♠✉❝❤✱ ❜✉t t❤❡r❡ ❛r❡ t♦♦ ♠❛♥② ♣❡♦♣❧❡✱ ✇❤✐❝❤ ❤❛r♠ t❤❡♠ ❝♦♥❝❡♣ts ♦❢ ❢❡♠✐♥✐s♠✱ ✐❢ t❤❡② ❤❡❧♣ ❢❡♠✐♥✐♥✐s♠ ❢♦r ✇r♦♥❣s r❡❛s♦♥s ♦r ✐♥ ✇r♦♥❣ s✐t✉❛t✐♦♥s✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✷✽ ✴ ✺✷
❚✇♦ ✐ss✉❡s ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❊①❛♠♣❧❡ ♥ = ✶✵ ❩✉♠ ❙❝❤❧✉ss ❣❧❛✉❜❡ ✐❝❤✱ ❞❛ss ❞❡r ❋❡♠✐♥✐s♠✉s ❞❡♥ ■♥t❡r❡ss❡♥ ❞❡r ❋r❛✉❡♥ s❡❤r ✈✐❡❧ ♥üt③❡♥ ❦ö♥♥❡✱ ❛❜❡r ❡s ❣✐❜t ③✉ ✈✐❡❧❡ ▲❡✉t❡✱ ❞✐❡ ❞✐❡ ❑♦♥③❡♣t❡ ❞❡s ❋❡♠✐♥✐s♠✉s s❝❤❛❞❡♥✱ ✇❡♥♥ s✐❡ ❞❡♠ ❋❡♠✐♥✐s✉♠✉s ❢ür ❢❛❧s❝❤❡♥ ●rü♥❞❡♥ ♦❞❡r ✐♥ ❞❡♥ ❢❛❧s❝❤❡♥ ❙✐t✉❛t✐♦♥❡♥ ♥üt③❡♥✳ ❆t t❤❡ ❡♥❞ ■ t❤✐♥❦✱ t❤❛t ❢❡♠✐♥✐s♠ ❝♦✉❧❞ ❤❡❧♣ t❤❡ ✐♥t❡r❡sts ♦❢ t❤❡ ✇♦♠❡♥ ✈❡r② ♠✉❝❤✱ ❜✉t t❤❡r❡ ❛r❡ t♦♦ ♠❛♥② ♣❡♦♣❧❡✱ ✇❤✐❝❤ ❤❛r♠ t❤❡♠ ❝♦♥❝❡♣ts ♦❢ ❢❡♠✐♥✐s♠✱ ✐❢ t❤❡② ❤❡❧♣ ❢❡♠✐♥✐♥✐s♠ ❢♦r ✇r♦♥❣s r❡❛s♦♥s ♦r ✐♥ ✇r♦♥❣ s✐t✉❛t✐♦♥s✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✷✽ ✴ ✺✷
❘❡s✉❧ts ❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ✶ ❚r❛♥s❢❡r ✷ ❘♦❛❞ ♠❛♣ ✸ ❖✉r ❞❛t❛ ✲ t❤❡ ❋❛❧❦♦ ❝♦r♣✉s ✹ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ✺ Pr❡❧✐♠✐♥❛r② r❡s✉❧ts ✻ ❚✇♦ ✐ss✉❡s ✼ ❚❛❦✐♥❣ t❤❡ ❡ss❛② t♦♣✐❝ ✐♥t♦ ❛❝❝♦✉♥t ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❘❡s✉❧ts ✽ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ✾ ✶✵ ❈♦♥❝❧✉s✐♦♥ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✷✾ ✴ ✺✷
❘❡s✉❧ts ❘❡s✉❧ts ❢♦r ▲ ✶ ❝❧❛ss✐✜❝❛t✐♦♥ solely normed topic averaged ❈❧❛ss✐✜❝❛t✐♦♥ ◗✉❛❧✐t② 80 ling. repr. 70 lemma pos correctly assigned L1's tok 60 text level learner ZH1 Filesize 50 200000 250000 300000 40 ♥♦t ✜❧t❡r❡❞ 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 ❤❡❛✈② ✜❧t❡r✐♥❣ 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲ ✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲ ✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷
❘❡s✉❧ts ❘❡s✉❧ts ❢♦r ▲ ✶ ❝❧❛ss✐✜❝❛t✐♦♥ solely normed topic averaged 80 ✟✟✟ ling. repr. 70 lemma ✟✟✟✟✟ pos correctly assigned L1's tok 60 text level learner ZH1 Filesize 50 200000 250000 300000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲ ✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲ ✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ♦❜s❡r✈❛t✐♦♥ ✶ ❋✐❧t❡r✐♥❣ ♦✉t ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❤❡❧♣s ❛ ❧♦t ❢♦r t♦❦ ❛♥❞ ❧❡♠♠❛ ✳ ⇒ ❈♦♣✐❡❞ ♠❛t❡r✐❛❧ ❤❛♠♣❡rs ▲ ✶ ❝❧❛ss✐✜❝❛t✐♦♥✳ ❖♣t✐♠✉♠ ❜❡t✇❡❡♥ ♥ = ✺ ❛♥❞ ♥ = ✶✵✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷
❘❡s✉❧ts ❘❡s✉❧ts ❢♦r ▲ ✶ ❝❧❛ss✐✜❝❛t✐♦♥ solely normed topic averaged 80 ling. repr. 70 lemma pos correctly assigned L1's tok 60 text level learner ZH1 Filesize 50 200000 250000 300000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲ ✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲ ✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷
❘❡s✉❧ts ❘❡s✉❧ts ❢♦r ▲ ✶ ❝❧❛ss✐✜❝❛t✐♦♥ solely normed topic averaged 80 ling. repr. 70 lemma pos correctly assigned L1's tok 60 text level learner ZH1 Filesize 50 200000 250000 300000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲ ✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲ ✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ♦❜s❡r✈❛t✐♦♥ ✷ ❋✐❧t❡r✐♥❣ ♦✉t ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❞♦❡s ♥♦t ❝❤❛♥❣❡ ♠✉❝❤ ❢♦r P❖❙ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷
❘❡s✉❧ts ❘❡s✉❧ts ❢♦r ▲ ✶ ❝❧❛ss✐✜❝❛t✐♦♥ solely normed topic averaged 80 ling. repr. 70 lemma pos correctly assigned L1's tok 60 text level learner ZH1 Filesize 50 200000 250000 300000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲ ✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲ ✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷
❘❡s✉❧ts ❘❡s✉❧ts ❢♦r ▲ ✶ ❝❧❛ss✐✜❝❛t✐♦♥ solely normed topic averaged 80 ling. repr. 70 lemma pos correctly assigned L1's tok 60 text level learner ZH1 Filesize 50 200000 250000 300000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲ ✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲ ✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ♦❜s❡r✈❛t✐♦♥ ✸ t♦❦ > ❧❡♠♠❛ ≫ P❖❙ P❖❙ ✐s ❛ ✈❡r② r❡❞✉❝❡❞ t❡①t ✈❡rs✐♦♥✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷
❘❡s✉❧ts ❘❡s✉❧ts ❢♦r ▲ ✶ ❝❧❛ss✐✜❝❛t✐♦♥ solely normed topic averaged 80 ling. repr. 70 lemma pos correctly assigned L1's tok 60 text level learner ZH1 Filesize 50 200000 250000 300000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲ ✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲ ✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷
❘❡s✉❧ts ❘❡s✉❧ts ❢♦r ▲ ✶ ❝❧❛ss✐✜❝❛t✐♦♥ solely normed topic averaged 80 ling. repr. 70 lemma pos correctly assigned L1's tok 60 text level learner ZH1 Filesize 50 200000 250000 300000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲ ✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲ ✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ♦❜s❡r✈❛t✐♦♥ ✹ ❚♦ ❛✈❡r❛❣❡ ♦✉t t♦♣✐❝ ❤❡❧♣s ❢♦r t♦❦ ❛♥❞ ❧❡♠♠❛ ✳ ⇒ ■❣♥♦r✐♥❣ t♦♣✐❝ ❤❛♠♣❡rs ▲ ✶ ❝❧❛ss✐✜❝❛t✐♦♥✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷
❘❡s✉❧ts ❘❡s✉❧ts ❢♦r ▲ ✶ ❝❧❛ss✐✜❝❛t✐♦♥ solely normed topic averaged 80 ling. repr. 70 lemma pos correctly assigned L1's tok 60 text level learner ZH1 Filesize 50 200000 250000 300000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲ ✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲ ✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷
❘❡s✉❧ts ❘❡s✉❧ts ❢♦r ▲ ✶ ❝❧❛ss✐✜❝❛t✐♦♥ solely normed topic averaged 80 ling. repr. 70 lemma pos correctly assigned L1's tok 60 text level learner ZH1 Filesize 50 200000 250000 300000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲ ✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲ ✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ♦❜s❡r✈❛t✐♦♥ ✺ ❆❣❛✐♥✱ ♥♦ s✉❝❤ ❡✛❡❝t ❢♦r P❖❙ ✳ ⇒ ♠✉❝❤ ❧❡ss ✐♥t❡r❛❝t✐♦♥ ❜❡t✇❡❡♥ t♦♣✐❝ ❛♥❞ ▲ ✶✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷
❘❡s✉❧ts ❘❡s✉❧ts ❢♦r ▲ ✶ ❝❧❛ss✐✜❝❛t✐♦♥ solely normed topic averaged 80 ling. repr. 70 lemma pos correctly assigned L1's tok 60 text level learner ZH1 Filesize 50 200000 250000 300000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲ ✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲ ✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷
❘❡s✉❧ts ❘❡s✉❧ts ❢♦r ▲ ✶ ❝❧❛ss✐✜❝❛t✐♦♥ solely normed topic averaged 80 ling. repr. 70 lemma pos correctly assigned L1's tok 60 text level learner ZH1 Filesize 50 200000 250000 300000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲ ✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲ ✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ♦❜s❡r✈❛t✐♦♥ ✻ ❧❡❛r♥❡r t❡①t > ❩❍✶ ❈♦rr❡❝t✐♦♥ r❡❞✉❝❡s ▲ ✶ ❡✛❡❝t✳ ◆♦t s♦ ❝❧❡❛r ❢♦r ❧❡♠♠❛ ✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷
❘❡s✉❧ts ❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥ solely normed topic averaged 120 ling. repr. 100 lemma correctly assigned text topics pos tok text level 80 learner ZH1 Filesize 60 250000 300000 350000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝ ✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷
❘❡s✉❧ts solely normed topic averaged ❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥ 80 ling. repr. 70 lemma correctly assigned L1's pos tok 60 text level learner ZH1 50 Filesize solely normed topic averaged 200000 250000 300000 40 120 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ling. repr. 100 lemma correctly assigned text topics pos tok text level 80 learner ZH1 Filesize 60 250000 300000 350000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝ ✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷
❘❡s✉❧ts solely normed topic averaged ❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥ 80 ling. repr. 70 lemma correctly assigned L1's pos tok 60 text level learner ZH1 50 Filesize solely normed topic averaged 200000 250000 300000 40 120 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ling. repr. 100 lemma correctly assigned text topics pos tok text level 80 learner ZH1 Filesize 60 250000 300000 350000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝ ✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ♦❜s❡r✈❛t✐♦♥ ✶ ❋✐❧t❡r✐♥❣ ♦✉t ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ✇✐t❤ ❤✐❣❤ ♥ ❞♦❡s ♥♦t ✐♥✢✉❡♥❝❡ t♦❦ ❛♥❞ ❧❡♠♠❛ ✳ ⇒ ❈♦♣✐❡❞ ♠❛t❡r✐❛❧ ✐s ♥♦t ✐❞❡♥t✐❝❛❧ ✇✐t❤ t❡①t t♦♣✐❝ ✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷
❘❡s✉❧ts solely normed topic averaged ❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥ 80 ling. repr. 70 lemma correctly assigned L1's pos tok 60 text level learner ZH1 50 Filesize solely normed topic averaged 200000 250000 300000 40 120 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ling. repr. 100 lemma correctly assigned text topics pos tok text level 80 learner ZH1 Filesize 60 250000 300000 350000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝ ✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷
❘❡s✉❧ts solely normed topic averaged ❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥ 80 ling. repr. 70 lemma correctly assigned L1's pos tok 60 text level learner ZH1 50 Filesize solely normed topic averaged 200000 250000 300000 40 120 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ling. repr. 100 lemma correctly assigned text topics pos tok text level 80 learner ZH1 Filesize 60 250000 300000 350000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝ ✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ♦❜s❡r✈❛t✐♦♥ ✷ ❆❣❛✐♥✱ ❜❡t✇❡❡♥ ♥ = ✺ ❛♥❞ ♥ = ✶✵ ✐s t❤❡ ♠♦st ✐♥t❡r❡st✐♥❣ str❡❝❤✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷
❘❡s✉❧ts solely normed topic averaged ❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥ 80 ling. repr. 70 lemma correctly assigned L1's pos tok 60 text level learner ZH1 50 Filesize solely normed topic averaged 200000 250000 300000 40 120 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ling. repr. 100 lemma correctly assigned text topics pos tok text level 80 learner ZH1 Filesize 60 250000 300000 350000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝ ✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷
❘❡s✉❧ts solely normed topic averaged ❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥ 80 ling. repr. 70 lemma correctly assigned L1's pos tok 60 text level learner ZH1 50 Filesize solely normed topic averaged 200000 250000 300000 40 120 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ling. repr. 100 lemma correctly assigned text topics pos tok text level 80 learner ZH1 Filesize 60 250000 300000 350000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝ ✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ♦❜s❡r✈❛t✐♦♥ ✸ ❲❤❡♥ ♠♦r❡ ❛♥❞ ♠♦r❡ ✐s ✜❧t❡r❡❞ ♦✉t P❖❙ ♥❡❛r❧② ❤✐ts t❤❡ ❜❛s❡ ❧✐♥❡✳ ⇒ ▼✉❝❤ ♦❢ ▲ ✶ ✐♥✢✉❡♥❝❡ ✐♥ t♦♣✐❝ ❞✉❡ t♦ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ✳ ❆▲▲❄ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷
❘❡s✉❧ts solely normed topic averaged ❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥ 80 ling. repr. 70 lemma correctly assigned L1's pos tok 60 text level learner ZH1 50 Filesize solely normed topic averaged 200000 250000 300000 40 120 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ling. repr. 100 lemma correctly assigned text topics pos tok text level 80 learner ZH1 Filesize 60 250000 300000 350000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝ ✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ♦❜s❡r✈❛t✐♦♥ ✸ ❲❤❡♥ ♠♦r❡ ❛♥❞ ♠♦r❡ ✐s ✜❧t❡r❡❞ ♦✉t P❖❙ ♥❡❛r❧② ❤✐ts t❤❡ ❜❛s❡ ❧✐♥❡✳ ⇒ ▼✉❝❤ ♦❢ ▲ ✶ ✐♥✢✉❡♥❝❡ ✐♥ t♦♣✐❝ ❞✉❡ t♦ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ✳ ❆▲▲❄ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷
❘❡s✉❧ts solely normed topic averaged ❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥ 80 ling. repr. 70 lemma correctly assigned L1's pos tok 60 text level learner ZH1 50 Filesize solely normed topic averaged 200000 250000 300000 40 120 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ling. repr. 100 lemma correctly assigned text topics pos tok text level 80 learner ZH1 Filesize 60 250000 300000 350000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝ ✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷
❘❡s✉❧ts solely normed topic averaged ❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥ 80 ling. repr. 70 lemma correctly assigned L1's pos tok 60 text level learner ZH1 50 Filesize solely normed topic averaged 200000 250000 300000 40 120 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ling. repr. 100 lemma correctly assigned text topics pos tok text level 80 learner ZH1 Filesize 60 250000 300000 350000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝ ✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ♦❜s❡r✈❛t✐♦♥ ✹ ❧❡♠♠❛ > t♦❦ ( ≫ P❖❙ ) ⇒ ❧❡♠♠❛ ❜❡tt❡r ❢♦r t♦♣✐❝ ✱ t♦❦ ❜❡tt❡r ❢♦r ▲ ✶ ❝❧❛ss✐✜❝❛t✐♦♥✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷
❘❡s✉❧ts solely normed topic averaged ❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥ 80 ling. repr. 70 lemma correctly assigned L1's pos tok 60 text level learner ZH1 50 Filesize solely normed topic averaged 200000 250000 300000 40 120 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ling. repr. 100 lemma correctly assigned text topics pos tok text level 80 learner ZH1 Filesize 60 250000 300000 350000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝ ✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷
❘❡s✉❧ts solely normed topic averaged ❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥ 80 ling. repr. 70 lemma correctly assigned L1's pos tok 60 text level learner ZH1 50 Filesize solely normed topic averaged 200000 250000 300000 40 120 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ling. repr. 100 lemma correctly assigned text topics pos tok text level 80 learner ZH1 Filesize 60 250000 300000 350000 40 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 1/n ❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝ ✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳ ♦❜s❡r✈❛t✐♦♥ ✺ ❖✉r ❤❡✉r✐st✐❝ ❢♦r t♦♣✐❝ ✐♥✢✉❡♥❝❡ r❡❞✉❝t✐♦♥ ✇♦r❦s ✈❡r② ✇❡❧❧✿ P❡r❢♦r♠❛♥❝❡ ❞r♦♣s t♦ ❡st✐♠❛t❡❞ ❜❛s❡ ❧✐♥❡✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷
❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇ ✶ ❚r❛♥s❢❡r ✷ ❘♦❛❞ ♠❛♣ ✸ ❖✉r ❞❛t❛ ✲ t❤❡ ❋❛❧❦♦ ❝♦r♣✉s ✹ ❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ✕ ❜❛s✐❝ ❝♦♥❝❡♣t ✺ Pr❡❧✐♠✐♥❛r② r❡s✉❧ts ✻ ❚✇♦ ✐ss✉❡s ✼ ❚❛❦✐♥❣ t❤❡ ❡ss❛② t♦♣✐❝ ✐♥t♦ ❛❝❝♦✉♥t ●❡tt✐♥❣ r✐❞ ♦❢ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❘❡s✉❧ts ✽ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ✾ ✶✵ ❈♦♥❝❧✉s✐♦♥ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✷ ✴ ✺✷
❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ❲❤❡r❡ t♦ ❣♦ ❢r♦♠ ❤❡r❡❄ ❙✉❝❝❡ss❢✉❧ ❝❧❛ss✐✜❝❛t✐♦♥ ✐s ❛ r❡❧✐❛❜❧❡ ✐♥❞✐❝❛t♦r ❢♦r ❡①✐st✐♥❣ tr❛♥s❢❡r✳ ❜✉t ❡✛❡❝t s✐③❡s ❝❛♥✬t ❜❡ r❡❛❞✐❧② q✉❛♥t✐✜❡❞✳ ❚❤❡ t♦♣✐❝ ❡✛❡❝t s❡❡♠s t♦ ❜❡ ✏str♦♥❣❡r✑ t❤❛♥ ▲✶✳ ❜✉t ❤♦✇ ♠✉❝❤❄ ⇒ ❝♦♠♣❛r✐s♦♥ ♦❢ ❝❧❛ss✐✜❝❛t✐♦♥ ❛❝❝✉r❛❝✐❡s ✐s r❛t❤❡r ✐♥❞✐r❡❝t✳ ❈❛♥ ✇❡ s✉r♣❛ss t❤❡ st②❧♦♠❡tr✐❝ ❝❧❛ss✐✜❝❛t✐♦♥❛❧ ✈✐❡✇❄ ✶ ❈❛♥ ✇❡ ❞✐r❡❝t❧② q✉❛♥t✐❢② t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t♦♣✐❝ ❛♥❞ ▲✶❄ ✷ ❈❛♥ ✇❡ ❞✐r❡❝t❧② ❝♦♠♣❛r❡ t❤❡♠❄ ❋♦r ❞✐✛❡r❡♥t ❧❡✈❡❧s ♦❢ r❡♣r❡s❡♥t❛t✐♦♥❄ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✸ ✴ ✺✷
❚❤✐s ✭❧✐♥❡❛r ♠✐①❡❞✮ ♠♦❞❡❧ ✐s ✜tt❡❞✳ ❚❤❡ ♣❛r❛♠❡t❡rs ❛♥❞ ❝❛♥ ❜❡ ❝♦♠♣❛r❡❞✳ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ❇✉✐❧❞✐♥❣ ❛ ✭❧✐♥❡❛r ♠✐①❡❞✮ ♠♦❞❡❧ ❋♦r ❡❛❝❤ ❙ ( ❆ , ❇ ) ✇❡ ❝♦♥str✉❝t t✇♦ ✈❛r✐❛❜❧❡s✿ s❛♠❡❚♦♣✐❝ ✶ ✐❢ ❆ ❛♥❞ ❇ s❤❛r❡ ✐ts t♦♣✐❝✱ ✵ ♦t❤❡r✇✐s❡✳ s❛♠❡▲✶ ✶ ✐❢ ❛✉t❤♦rs ♦❢ ❆ ❛♥❞ ❇ s❤❛r❡ ▲✶✱ ✵ ♦t❤❡r✇✐s❡✳ ◆♦✇ ✇❡ s❡t ✉♣ ❛ ♠♦❞❡❧ ❙ = α · s❛♠❡❚♦♣✐❝ + β · s❛♠❡▲ ✶ + ❁t❡①t s♣❡❝✐✜❝ ❝♦♥tr✐❜✉t✐♦♥s❃ + ǫ ✇❤❡r❡ ◮ ǫ ✐s ❛ ♥♦r♠❛❧❧② ❞✐str✐❜✉t❡❞ ❡rr♦r t❡r♠✳ ◮ t❤❡ ❁t❡①t s♣❡❝✐✜❝ ❝♦♥tr✐❜✉t✐♦♥s❃ ❛r❡ ❛ss✉♠❡❞ ♥♦r♠❛❧❧② ❞✐str✐❜✉t❡❞ t♦♦✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✹ ✴ ✺✷
❚❤✐s ✭❧✐♥❡❛r ♠✐①❡❞✮ ♠♦❞❡❧ ✐s ✜tt❡❞✳ ❚❤❡ ♣❛r❛♠❡t❡rs ❛♥❞ ❝❛♥ ❜❡ ❝♦♠♣❛r❡❞✳ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ❇✉✐❧❞✐♥❣ ❛ ✭❧✐♥❡❛r ♠✐①❡❞✮ ♠♦❞❡❧ ❋♦r ❡❛❝❤ ❙ ( ❆ , ❇ ) ✇❡ ❝♦♥str✉❝t t✇♦ ✈❛r✐❛❜❧❡s✿ s❛♠❡❚♦♣✐❝ ✶ ✐❢ ❆ ❛♥❞ ❇ s❤❛r❡ ✐ts t♦♣✐❝✱ ✵ ♦t❤❡r✇✐s❡✳ s❛♠❡▲✶ ✶ ✐❢ ❛✉t❤♦rs ♦❢ ❆ ❛♥❞ ❇ s❤❛r❡ ▲✶✱ ✵ ♦t❤❡r✇✐s❡✳ ◆♦✇ ✇❡ s❡t ✉♣ ❛ ♠♦❞❡❧ ❙ = α · s❛♠❡❚♦♣✐❝ + β · s❛♠❡▲ ✶ + ❁t❡①t s♣❡❝✐✜❝ ❝♦♥tr✐❜✉t✐♦♥s❃ + ǫ ✇❤❡r❡ ◮ ǫ ✐s ❛ ♥♦r♠❛❧❧② ❞✐str✐❜✉t❡❞ ❡rr♦r t❡r♠✳ ◮ t❤❡ ❁t❡①t s♣❡❝✐✜❝ ❝♦♥tr✐❜✉t✐♦♥s❃ ❛r❡ ❛ss✉♠❡❞ ♥♦r♠❛❧❧② ❞✐str✐❜✉t❡❞ t♦♦✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✹ ✴ ✺✷
❚❤✐s ✭❧✐♥❡❛r ♠✐①❡❞✮ ♠♦❞❡❧ ✐s ✜tt❡❞✳ ❚❤❡ ♣❛r❛♠❡t❡rs ❛♥❞ ❝❛♥ ❜❡ ❝♦♠♣❛r❡❞✳ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ❇✉✐❧❞✐♥❣ ❛ ✭❧✐♥❡❛r ♠✐①❡❞✮ ♠♦❞❡❧ ❋♦r ❡❛❝❤ ❙ ( ❆ , ❇ ) ✇❡ ❝♦♥str✉❝t t✇♦ ✈❛r✐❛❜❧❡s✿ s❛♠❡❚♦♣✐❝ ✶ ✐❢ ❆ ❛♥❞ ❇ s❤❛r❡ ✐ts t♦♣✐❝✱ ✵ ♦t❤❡r✇✐s❡✳ s❛♠❡▲✶ ✶ ✐❢ ❛✉t❤♦rs ♦❢ ❆ ❛♥❞ ❇ s❤❛r❡ ▲✶✱ ✵ ♦t❤❡r✇✐s❡✳ ◆♦✇ ✇❡ s❡t ✉♣ ❛ ♠♦❞❡❧ ❙ = α · s❛♠❡❚♦♣✐❝ + β · s❛♠❡▲ ✶ + ❁t❡①t s♣❡❝✐✜❝ ❝♦♥tr✐❜✉t✐♦♥s❃ + ǫ ✇❤❡r❡ ◮ ǫ ✐s ❛ ♥♦r♠❛❧❧② ❞✐str✐❜✉t❡❞ ❡rr♦r t❡r♠✳ ◮ t❤❡ ❁t❡①t s♣❡❝✐✜❝ ❝♦♥tr✐❜✉t✐♦♥s❃ ❛r❡ ❛ss✉♠❡❞ ♥♦r♠❛❧❧② ❞✐str✐❜✉t❡❞ t♦♦✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✹ ✴ ✺✷
❚❤✐s ✭❧✐♥❡❛r ♠✐①❡❞✮ ♠♦❞❡❧ ✐s ✜tt❡❞✳ ❚❤❡ ♣❛r❛♠❡t❡rs ❛♥❞ ❝❛♥ ❜❡ ❝♦♠♣❛r❡❞✳ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ❇✉✐❧❞✐♥❣ ❛ ✭❧✐♥❡❛r ♠✐①❡❞✮ ♠♦❞❡❧ ❋♦r ❡❛❝❤ ❙ ( ❆ , ❇ ) ✇❡ ❝♦♥str✉❝t t✇♦ ✈❛r✐❛❜❧❡s✿ s❛♠❡❚♦♣✐❝ ✶ ✐❢ ❆ ❛♥❞ ❇ s❤❛r❡ ✐ts t♦♣✐❝✱ ✵ ♦t❤❡r✇✐s❡✳ s❛♠❡▲✶ ✶ ✐❢ ❛✉t❤♦rs ♦❢ ❆ ❛♥❞ ❇ s❤❛r❡ ▲✶✱ ✵ ♦t❤❡r✇✐s❡✳ ◆♦✇ ✇❡ s❡t ✉♣ ❛ ♠♦❞❡❧ ❙ = α · s❛♠❡❚♦♣✐❝ + β · s❛♠❡▲ ✶ + ❁t❡①t s♣❡❝✐✜❝ ❝♦♥tr✐❜✉t✐♦♥s❃ + ǫ ✇❤❡r❡ ◮ ǫ ✐s ❛ ♥♦r♠❛❧❧② ❞✐str✐❜✉t❡❞ ❡rr♦r t❡r♠✳ ◮ t❤❡ ❁t❡①t s♣❡❝✐✜❝ ❝♦♥tr✐❜✉t✐♦♥s❃ ❛r❡ ❛ss✉♠❡❞ ♥♦r♠❛❧❧② ❞✐str✐❜✉t❡❞ t♦♦✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✹ ✴ ✺✷
❚❤✐s ✭❧✐♥❡❛r ♠✐①❡❞✮ ♠♦❞❡❧ ✐s ✜tt❡❞✳ ❚❤❡ ♣❛r❛♠❡t❡rs ❛♥❞ ❝❛♥ ❜❡ ❝♦♠♣❛r❡❞✳ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ❇✉✐❧❞✐♥❣ ❛ ✭❧✐♥❡❛r ♠✐①❡❞✮ ♠♦❞❡❧ ❋♦r ❡❛❝❤ ❙ ( ❆ , ❇ ) ✇❡ ❝♦♥str✉❝t t✇♦ ✈❛r✐❛❜❧❡s✿ s❛♠❡❚♦♣✐❝ ✶ ✐❢ ❆ ❛♥❞ ❇ s❤❛r❡ ✐ts t♦♣✐❝✱ ✵ ♦t❤❡r✇✐s❡✳ s❛♠❡▲✶ ✶ ✐❢ ❛✉t❤♦rs ♦❢ ❆ ❛♥❞ ❇ s❤❛r❡ ▲✶✱ ✵ ♦t❤❡r✇✐s❡✳ ◆♦✇ ✇❡ s❡t ✉♣ ❛ ♠♦❞❡❧ ❙ = α · s❛♠❡❚♦♣✐❝ + β · s❛♠❡▲ ✶ + ❁t❡①t s♣❡❝✐✜❝ ❝♦♥tr✐❜✉t✐♦♥s❃ + ǫ ✇❤❡r❡ ◮ ǫ ✐s ❛ ♥♦r♠❛❧❧② ❞✐str✐❜✉t❡❞ ❡rr♦r t❡r♠✳ ◮ t❤❡ ❁t❡①t s♣❡❝✐✜❝ ❝♦♥tr✐❜✉t✐♦♥s❃ ❛r❡ ❛ss✉♠❡❞ ♥♦r♠❛❧❧② ❞✐str✐❜✉t❡❞ t♦♦✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✹ ✴ ✺✷
❚❤❡ ♣❛r❛♠❡t❡rs ❛♥❞ ❝❛♥ ❜❡ ❝♦♠♣❛r❡❞✳ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ❇✉✐❧❞✐♥❣ ❛ ✭❧✐♥❡❛r ♠✐①❡❞✮ ♠♦❞❡❧ ❋♦r ❡❛❝❤ ❙ ( ❆ , ❇ ) ✇❡ ❝♦♥str✉❝t t✇♦ ✈❛r✐❛❜❧❡s✿ s❛♠❡❚♦♣✐❝ ✶ ✐❢ ❆ ❛♥❞ ❇ s❤❛r❡ ✐ts t♦♣✐❝✱ ✵ ♦t❤❡r✇✐s❡✳ s❛♠❡▲✶ ✶ ✐❢ ❛✉t❤♦rs ♦❢ ❆ ❛♥❞ ❇ s❤❛r❡ ▲✶✱ ✵ ♦t❤❡r✇✐s❡✳ ◆♦✇ ✇❡ s❡t ✉♣ ❛ ♠♦❞❡❧ ❙ = α · s❛♠❡❚♦♣✐❝ + β · s❛♠❡▲ ✶ + ❁t❡①t s♣❡❝✐✜❝ ❝♦♥tr✐❜✉t✐♦♥s❃ + ǫ ✇❤❡r❡ ◮ ǫ ✐s ❛ ♥♦r♠❛❧❧② ❞✐str✐❜✉t❡❞ ❡rr♦r t❡r♠✳ ◮ t❤❡ ❁t❡①t s♣❡❝✐✜❝ ❝♦♥tr✐❜✉t✐♦♥s❃ ❛r❡ ❛ss✉♠❡❞ ♥♦r♠❛❧❧② ❞✐str✐❜✉t❡❞ t♦♦✳ ❚❤✐s ✭❧✐♥❡❛r ♠✐①❡❞✮ ♠♦❞❡❧ ✐s ✜tt❡❞✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✹ ✴ ✺✷
❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ❇✉✐❧❞✐♥❣ ❛ ✭❧✐♥❡❛r ♠✐①❡❞✮ ♠♦❞❡❧ ❋♦r ❡❛❝❤ ❙ ( ❆ , ❇ ) ✇❡ ❝♦♥str✉❝t t✇♦ ✈❛r✐❛❜❧❡s✿ s❛♠❡❚♦♣✐❝ ✶ ✐❢ ❆ ❛♥❞ ❇ s❤❛r❡ ✐ts t♦♣✐❝✱ ✵ ♦t❤❡r✇✐s❡✳ s❛♠❡▲✶ ✶ ✐❢ ❛✉t❤♦rs ♦❢ ❆ ❛♥❞ ❇ s❤❛r❡ ▲✶✱ ✵ ♦t❤❡r✇✐s❡✳ ◆♦✇ ✇❡ s❡t ✉♣ ❛ ♠♦❞❡❧ ❙ = α · s❛♠❡❚♦♣✐❝ + β · s❛♠❡▲ ✶ + ❁t❡①t s♣❡❝✐✜❝ ❝♦♥tr✐❜✉t✐♦♥s❃ + ǫ ✇❤❡r❡ ◮ ǫ ✐s ❛ ♥♦r♠❛❧❧② ❞✐str✐❜✉t❡❞ ❡rr♦r t❡r♠✳ ◮ t❤❡ ❁t❡①t s♣❡❝✐✜❝ ❝♦♥tr✐❜✉t✐♦♥s❃ ❛r❡ ❛ss✉♠❡❞ ♥♦r♠❛❧❧② ❞✐str✐❜✉t❡❞ t♦♦✳ ❚❤✐s ✭❧✐♥❡❛r ♠✐①❡❞✮ ♠♦❞❡❧ ✐s ✜tt❡❞✳ ❚❤❡ ♣❛r❛♠❡t❡rs α ❛♥❞ β ❝❛♥ ❜❡ ❝♦♠♣❛r❡❞✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✹ ✴ ✺✷
✷ ▼✉❝❤ str♦♥❣❡r t❤❛♥ ▲✶ ❢♦r t♦❦❡♥ ❛♥❞ ❧❡♠♠❛ ✳ ✸ ◆♦ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t♦❦❡♥ ❛♥❞ ❧❡♠♠❛ ✹ t❤❡ ▲✶ ✐♥✢✉❡♥❝❡ ✐♥ P❖❙ ✐s ♠✉❝❤ ♠♦r❡ ♣r♦♥♦✉♥❝❡❞✳ ✺ ❘❡♠♦✈✐♥❣ ❡rr♦rs ✭s❧✐❣❤t❧②✮ ✇❡❛❦❡♥s ▲✶ ✐♥✢✉❡♥❝❡✳ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ❚❤❡ r❡s✉❧ts n=10 1.2 lemma ♦❜s❡r✈❛t✐♦♥s pos Relative influence of L1 and topic tok ✶ ❡ss❛② t♦♣✐❝ ✈❡r② str♦♥❣✳ 0.8 0.6 0.4 0.2 learner ZH1 Layer ❋✐❣✉r❡✿ ▲✶ ✭ β ✮ ❡✛❡❝t ❞✐✈✐❞❡❞ ❜② t♦♣✐❝ ✭ α ✮ ❡✛❡❝t✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✺ ✴ ✺✷
✸ ◆♦ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t♦❦❡♥ ❛♥❞ ❧❡♠♠❛ ✹ t❤❡ ▲✶ ✐♥✢✉❡♥❝❡ ✐♥ P❖❙ ✐s ♠✉❝❤ ♠♦r❡ ♣r♦♥♦✉♥❝❡❞✳ ✺ ❘❡♠♦✈✐♥❣ ❡rr♦rs ✭s❧✐❣❤t❧②✮ ✇❡❛❦❡♥s ▲✶ ✐♥✢✉❡♥❝❡✳ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ❚❤❡ r❡s✉❧ts n=10 1.2 lemma ♦❜s❡r✈❛t✐♦♥s pos Relative influence of L1 and topic tok ✶ ❡ss❛② t♦♣✐❝ ✈❡r② str♦♥❣✳ 0.8 0.6 ✷ ▼✉❝❤ str♦♥❣❡r t❤❛♥ ▲✶ ❢♦r t♦❦❡♥ ❛♥❞ ❧❡♠♠❛ ✳ 0.4 0.2 learner ZH1 Layer ❋✐❣✉r❡✿ ▲✶ ✭ β ✮ ❡✛❡❝t ❞✐✈✐❞❡❞ ❜② t♦♣✐❝ ✭ α ✮ ❡✛❡❝t✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✺ ✴ ✺✷
✹ t❤❡ ▲✶ ✐♥✢✉❡♥❝❡ ✐♥ P❖❙ ✐s ♠✉❝❤ ♠♦r❡ ♣r♦♥♦✉♥❝❡❞✳ ✺ ❘❡♠♦✈✐♥❣ ❡rr♦rs ✭s❧✐❣❤t❧②✮ ✇❡❛❦❡♥s ▲✶ ✐♥✢✉❡♥❝❡✳ ❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ❚❤❡ r❡s✉❧ts n=10 1.2 lemma ♦❜s❡r✈❛t✐♦♥s pos Relative influence of L1 and topic tok ✶ ❡ss❛② t♦♣✐❝ ✈❡r② str♦♥❣✳ 0.8 0.6 ✷ ▼✉❝❤ str♦♥❣❡r t❤❛♥ ▲✶ ❢♦r t♦❦❡♥ ❛♥❞ ❧❡♠♠❛ ✳ 0.4 ✸ ◆♦ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t♦❦❡♥ ❛♥❞ ❧❡♠♠❛ 0.2 learner ZH1 Layer ❋✐❣✉r❡✿ ▲✶ ✭ β ✮ ❡✛❡❝t ❞✐✈✐❞❡❞ ❜② t♦♣✐❝ ✭ α ✮ ❡✛❡❝t✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✺ ✴ ✺✷
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