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❲❤❛t s✐♠✐❧❛r✐t② t❡❧❧s ✉s ❛❜♦✉t tr❛♥s❢❡r✳ ❘❡tr✐❡✈✐♥❣ ▲✶ ❢r♦♠ ❧❡❛r♥❡r t❡①ts ✐♥ ❋❛❧❦♦

▼❛r❝ ❘❡③♥✐❝❡❦ ✫ ❋❡❧✐① ●♦❧❝❤❡r

❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥

❩✇❡✐t❡r ❚ü❜✐♥❣❡♥✲❇❡r❧✐♥ ❲♦r❦s❤♦♣ ③✉r ❆♥❛❧②s❡ ✈♦♥ ▲❡r♥❡rs♣r❛❝❤❡ ✵✺✳✶✷✳✷✵✶✶

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✶ ✴ ✺✷

❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥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❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇

❈♦♠✐♥❣ ❢r♦♠ s❡❝♦♥❞ ❧❛♥❣✉❛❣❡ ❛❝q✉✐s✐t✐♦♥ r❡s❡❛r❝❤

▲❡❛r♥❡r ❈♦r♣✉s ❘❡s❡❛r❝❤

✶ st✉❞② ♦❢ ❧❡❛r♥❡r ❧❛♥❣✉❛❣❡ ◮ ♣❛tt❡r♥s ◮ ❝♦♥tr♦❧❧✐♥❣ ✈❛r✐❛❜❧❡s ✷ ❛♥❞ ❞❡s❝r✐❜❡ t❤❡ ✈❛r✐❛❜✐❧✐t② ❜❡t✇❡❡♥ ❧❡❛r♥❡rs ❛♥❞ ❧❡❛r♥❡r s✉❜❣r♦✉♣s

❲❤❛t ♠❡❛s✉r❡s ❝❛♥ ❤❡❧♣ ✉s ✉♥❝♦✈❡r ❤✐❞❞❡♥ ♣❛tt❡r♥s ✐♥ ❧❡❛r♥❡r ❞❛t❛❄

✶ ❆r❡ ❧❡❛r♥❡r ❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡s ❞❡t❡❝t❛❜❧❡ ✐♥ ❧❡❛r♥❡r t❡①ts❄ ✷ ❍♦✇ ❞♦ t❤♦s❡ ✈❛r✐❛❜❧❡s ❛✛❡❝t t❤❡ ❧❡❛r♥❡r ❧❛♥❣✉❛❣❡❄ ✸ ❍♦✇ str♦♥❣ ✐s t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤♦s❡ ✈❛r✐❛❜❧❡s❄ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸ ✴ ✺✷

❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇

❈♦♠✐♥❣ ❢r♦♠ s❡❝♦♥❞ ❧❛♥❣✉❛❣❡ ❛❝q✉✐s✐t✐♦♥ r❡s❡❛r❝❤

▲❡❛r♥❡r ❈♦r♣✉s ❘❡s❡❛r❝❤

✶ st✉❞② ♦❢ ❧❡❛r♥❡r ❧❛♥❣✉❛❣❡ ◮ ♣❛tt❡r♥s ◮ ❝♦♥tr♦❧❧✐♥❣ ✈❛r✐❛❜❧❡s ✷ ❛♥❞ ❞❡s❝r✐❜❡ t❤❡ ✈❛r✐❛❜✐❧✐t② ❜❡t✇❡❡♥ ❧❡❛r♥❡rs ❛♥❞ ❧❡❛r♥❡r s✉❜❣r♦✉♣s

❲❤❛t ♠❡❛s✉r❡s ❝❛♥ ❤❡❧♣ ✉s ✉♥❝♦✈❡r ❤✐❞❞❡♥ ♣❛tt❡r♥s ✐♥ ❧❡❛r♥❡r ❞❛t❛❄

✶ ❆r❡ ❧❡❛r♥❡r ❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡s ❞❡t❡❝t❛❜❧❡ ✐♥ ❧❡❛r♥❡r t❡①ts❄ ✷ ❍♦✇ ❞♦ t❤♦s❡ ✈❛r✐❛❜❧❡s ❛✛❡❝t t❤❡ ❧❡❛r♥❡r ❧❛♥❣✉❛❣❡❄ ✸ ❍♦✇ str♦♥❣ ✐s t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤♦s❡ ✈❛r✐❛❜❧❡s❄ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸ ✴ ✺✷

❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s✿ ❏♦✐♥✐♥❣ t✇♦ ♣♦✐♥ts ♦❢ ✈✐❡✇

❈♦♠✐♥❣ ❢r♦♠ s❡❝♦♥❞ ❧❛♥❣✉❛❣❡ ❛❝q✉✐s✐t✐♦♥ r❡s❡❛r❝❤

▲❡❛r♥❡r ❈♦r♣✉s ❘❡s❡❛r❝❤

✶ st✉❞② ♦❢ ❧❡❛r♥❡r ❧❛♥❣✉❛❣❡ ◮ ♣❛tt❡r♥s ◮ ❝♦♥tr♦❧❧✐♥❣ ✈❛r✐❛❜❧❡s ✷ ❛♥❞ ❞❡s❝r✐❜❡ t❤❡ ✈❛r✐❛❜✐❧✐t② ❜❡t✇❡❡♥ ❧❡❛r♥❡rs ❛♥❞ ❧❡❛r♥❡r s✉❜❣r♦✉♣s

❲❤❛t ♠❡❛s✉r❡s ❝❛♥ ❤❡❧♣ ✉s ✉♥❝♦✈❡r ❤✐❞❞❡♥ ♣❛tt❡r♥s ✐♥ ❧❡❛r♥❡r ❞❛t❛❄

✶ ❆r❡ ❧❡❛r♥❡r ❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡s ❞❡t❡❝t❛❜❧❡ ✐♥ ❧❡❛r♥❡r t❡①ts❄ ✷ ❍♦✇ ❞♦ t❤♦s❡ ✈❛r✐❛❜❧❡s ❛✛❡❝t t❤❡ ❧❡❛r♥❡r ❧❛♥❣✉❛❣❡❄ ✸ ❍♦✇ str♦♥❣ ✐s t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤♦s❡ ✈❛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❧✐♥ ■■ ✷✵✶✶ ✹ ✴ ✺✷

❘❡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❧✐♥ ■■ ✷✵✶✶ ✹ ✴ ✺✷

❘❡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❧✐♥ ■■ ✷✵✶✶ ✹ ✴ ✺✷

❘❡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❧✐♥ ■■ ✷✵✶✶ ✹ ✴ ✺✷

❘❡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❧✐♥ ■■ ✷✵✶✶ ✹ ✴ ✺✷

❘❡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❧✐♥ ■■ ✷✵✶✶ ✹ ✴ ✺✷

❘❡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❧✐♥ ■■ ✷✵✶✶ ✹ ✴ ✺✷

❘❡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❧✐♥ ■■ ✷✵✶✶ ✺ ✴ ✺✷

❘❡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❧✐♥ ■■ ✷✵✶✶ ✺ ✴ ✺✷

❘❡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❧✐♥ ■■ ✷✵✶✶ ✺ ✴ ✺✷

❘❡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❧✐♥ ■■ ✷✵✶✶ ✻ ✴ ✺✷

❚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❧✐♥ ■■ ✷✵✶✶ ✼ ✴ ✺✷

❚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❧✐♥ ■■ ✷✵✶✶ ✼ ✴ ✺✷

❚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❧✐♥ ■■ ✷✵✶✶ ✾ ✴ ✺✷

❘♦❛❞ ♠❛♣

❋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♦♠ 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

❚❡①ts ✐♥❝❧✉❞❡❞

❧❛♥❣✉❛❣❡s ✇✐t❤ ❛t ❧❡❛st ✶✵ t❡①ts ❧❡❛r♥❡rs ✇✐t❤ ♦♥❧② ♦♥❡ ▲✶

❱❡r② s♠❛❧❧ ❞❛t❛ s❛♠♣❧❡

❲❡ ✉s❡ ♦♥❧② ≈ ✻✻.✵✵✵ t♦❦❡♥s✳ ❚❤✐s ✐s ✸✹✪ ♦❢ ❋❛❧❦♦✳ ▲✶ ★ ♦❢ t❡①ts

• ❡r♠❛♥

✭❞❡✉✮❛ ✶✵ ❊♥❣❧✐s❤ ✭❡♥❣✮ ✹✷ ❉❛♥✐s❤ ✭❞❛♥✮ ✸✼ ❋r❡♥❝❤ ✭❢r❛✮ ✶✹ ❘✉ss✐❛♥ ✭r✉s✮ ✶✵ ❚✉r❦✐s❤ ✭t✉r✮ ✶✵ t♦t❛❧ ✶✷✻ t❡①ts

❛❝♦♥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❧✐♥ ■■ ✷✵✶✶ ✶✷ ✴ ✺✷

❖✉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❧✐♥ ■■ ✷✵✶✶ ✶✸ ✴ ✺✷

❖✉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❧✐♥ ■■ ✷✵✶✶ ✶✸ ✴ ✺✷

❖✉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✐♠✐❧❛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

❙ ❡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

❙ ❡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

❙ ❡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

❙ ❡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

❙ ❡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

❙ ❡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

❙ ❡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

❙ ❡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

❙ ❡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

❙ ❡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

❙ ❡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

❙ ❡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

❙ ❡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

❙ ❡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

Text Target Hypothesis tok POS Lemma Classification accuracy 0.0 0.2 0.4 0.6 0.8 1.0 baseline 59 48 60 54 44 60

❋✐❣✉r❡✿ ❞✐sr❡❣❛r❞✐♥❣ ●❡r♠❛♥ ▲✶ t❡①ts✳

❙❡♥s✐❜❧❡ ✜rst r❡s✉❧ts✿ ❆❜♦✈❡ ❜❛s❡❧✐♥❡ ✭✸✶.✷ = ✷✽%✮✳

◮ ❘❡♣r♦❞✉❝✐♥❣ s✐♠✐❧❛r r❡s✉❧ts❛✳

t♦❦ ❛♥❞ ❧❡♠♠❛ ♥❡❛r❧② ✐❞❡♥t✐❝❛❧✳ P❖❙ ❧♦✇❡r✳ ❚❛r❣❡t ❍②♣♦t❤❡s✐s s❡❡♠s ❧♦✇❡r✳

❛❑♦♣♣❡❧ ❡t ❛❧✳ ✷✵✵✸❀ ❑♦♣♣❡❧ ❡t ❛❧✳ ✷✵✵✺❀ ❚s✉r ❡t ❛❧✳ ✷✵✵✼❀ ❏♦❥♦❲♦♥❣ ❡t ❛❧✳

✷✵✵✾❀ ●♦❧❝❤❡r t♦ ❛♣♣❡❛r

✭❍✉♠❜♦❧❞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♦♣✐❝

Text Target Hypothesis tok POS Lemma Classification accuracy 0.0 0.2 0.4 0.6 0.8 1.0 baseline 111 56 111 111 55 112

t♦❦ ❛♥❞ ❧❡♠♠❛ ✈❡r② ❤✐❣❤ ✭> ✾✽%✮✳ P❖❙ ♠✉❝❤ ❧♦✇❡r✳

◮ ❜✉t ❛❜♦✈❡ ❜❛s❡❧✐♥❡✦

❂❃ t♦♣✐❝ ❡✛❡❝t ✈❡r② str♦♥❣✳

✭❍✉♠❜♦❧❞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✐❛❧

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✷✻ ✴ ✺✷

❚❡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♦ ❙✳

❡①♣❧♦s✐♦♥ ♦❢ s✉❜str✐♥❣s

❚❤❡ ♥✉♠❜❡r ♦❢ s✉❜str✐♥❣s ♦❢ ❛ str✐♥❣ ❣r♦✇s q✉❛❞r❛t✐❝❛❧❧② ✇✐t❤ ✐ts ❧❡♥❣t❤✳

❚✇♦ ✐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✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷

1/n correctly assigned L1's

40 50 60 70 80 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 200000 250000 300000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

♥♦t ✜❧t❡r❡❞ ❤❡❛✈② ✜❧t❡r✐♥❣ ❈❧❛ss✐✜❝❛t✐♦♥ ◗✉❛❧✐t②

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r ▲✶ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷

1/n correctly assigned L1's

40 50 60 70 80 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 200000 250000 300000

❋✐❣✉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✇❡❡♥ ♥ = ✺ ❛♥❞ ♥ = ✶✵✳

✟✟✟✟✟ ✟✟✟

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r ▲✶ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷

1/n correctly assigned L1's

40 50 60 70 80 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 200000 250000 300000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r ▲✶ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷

1/n correctly assigned L1's

40 50 60 70 80 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 200000 250000 300000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

♦❜s❡r✈❛t✐♦♥ ✷

❋✐❧t❡r✐♥❣ ♦✉t ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ❞♦❡s ♥♦t ❝❤❛♥❣❡ ♠✉❝❤ ❢♦r P❖❙

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r ▲✶ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷

1/n correctly assigned L1's

40 50 60 70 80 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 200000 250000 300000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r ▲✶ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷

1/n correctly assigned L1's

40 50 60 70 80 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 200000 250000 300000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

♦❜s❡r✈❛t✐♦♥ ✸

t♦❦ > ❧❡♠♠❛ ≫ P❖❙ P❖❙ ✐s ❛ ✈❡r② r❡❞✉❝❡❞ t❡①t ✈❡rs✐♦♥✳

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r ▲✶ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷

1/n correctly assigned L1's

40 50 60 70 80 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 200000 250000 300000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r ▲✶ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷

1/n correctly assigned L1's

40 50 60 70 80 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 200000 250000 300000

❋✐❣✉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✐♦♥✳

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r ▲✶ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷

1/n correctly assigned L1's

40 50 60 70 80 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 200000 250000 300000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r ▲✶ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷

1/n correctly assigned L1's

40 50 60 70 80 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 200000 250000 300000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

♦❜s❡r✈❛t✐♦♥ ✺

❆❣❛✐♥✱ ♥♦ s✉❝❤ ❡✛❡❝t ❢♦r P❖❙ ✳ ⇒ ♠✉❝❤ ❧❡ss ✐♥t❡r❛❝t✐♦♥ ❜❡t✇❡❡♥ t♦♣✐❝ ❛♥❞ ▲✶✳

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r ▲✶ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷

1/n correctly assigned L1's

40 50 60 70 80 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 200000 250000 300000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② ▲✶✳ ❲✐t❤♦✉t ●❡r♠❛♥ ▲✶✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r ▲✶ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✵ ✴ ✺✷

1/n correctly assigned L1's

40 50 60 70 80 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 200000 250000 300000

❋✐❣✉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 ❧❡♠♠❛✳

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷

1/n correctly assigned text topics

40 60 80 100 120 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 250000 300000 350000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷

1/n correctly assigned text topics

40 60 80 100 120 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 250000 300000 350000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

• ling. repr.

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷

1/n correctly assigned text topics

40 60 80 100 120 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 250000 300000 350000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

• ling. repr.

♦❜s❡r✈❛t✐♦♥ ✶

❋✐❧t❡r✐♥❣ ♦✉t ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ ✇✐t❤ ❤✐❣❤ ♥ ❞♦❡s ♥♦t ✐♥✢✉❡♥❝❡ t♦❦ ❛♥❞ ❧❡♠♠❛✳ ⇒ ❈♦♣✐❡❞ ♠❛t❡r✐❛❧ ✐s ♥♦t ✐❞❡♥t✐❝❛❧ ✇✐t❤ t❡①t t♦♣✐❝✳

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷

1/n correctly assigned text topics

40 60 80 100 120 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 250000 300000 350000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

• ling. repr.

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷

1/n correctly assigned text topics

40 60 80 100 120 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 250000 300000 350000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

• ling. repr.

♦❜s❡r✈❛t✐♦♥ ✷

❆❣❛✐♥✱ ❜❡t✇❡❡♥ ♥ = ✺ ❛♥❞ ♥ = ✶✵ ✐s t❤❡ ♠♦st ✐♥t❡r❡st✐♥❣ str❡❝❤✳

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷

1/n correctly assigned text topics

40 60 80 100 120 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 250000 300000 350000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

• ling. repr.

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷

1/n correctly assigned text topics

40 60 80 100 120 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 250000 300000 350000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

• ling. repr.

♦❜s❡r✈❛t✐♦♥ ✸

❲❤❡♥ ♠♦r❡ ❛♥❞ ♠♦r❡ ✐s ✜❧t❡r❡❞ ♦✉t P❖❙ ♥❡❛r❧② ❤✐ts t❤❡ ❜❛s❡ ❧✐♥❡✳ ⇒ ▼✉❝❤ ♦❢ ▲✶ ✐♥✢✉❡♥❝❡ ✐♥ t♦♣✐❝ ❞✉❡ t♦ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧✳ ❆▲▲❄

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷

1/n correctly assigned text topics

40 60 80 100 120 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 250000 300000 350000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

• ling. repr.

♦❜s❡r✈❛t✐♦♥ ✸

❲❤❡♥ ♠♦r❡ ❛♥❞ ♠♦r❡ ✐s ✜❧t❡r❡❞ ♦✉t P❖❙ ♥❡❛r❧② ❤✐ts t❤❡ ❜❛s❡ ❧✐♥❡✳ ⇒ ▼✉❝❤ ♦❢ ▲✶ ✐♥✢✉❡♥❝❡ ✐♥ t♦♣✐❝ ❞✉❡ t♦ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧✳ ❆▲▲❄

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷

1/n correctly assigned text topics

40 60 80 100 120 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 250000 300000 350000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

• ling. repr.

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷

1/n correctly assigned text topics

40 60 80 100 120 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 250000 300000 350000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

• ling. repr.

♦❜s❡r✈❛t✐♦♥ ✹

❧❡♠♠❛ > t♦❦ (≫ P❖❙ ) ⇒ ❧❡♠♠❛ ❜❡tt❡r ❢♦r t♦♣✐❝✱ t♦❦ ❜❡tt❡r ❢♦r ▲✶ ❝❧❛ss✐✜❝❛t✐♦♥✳

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷

1/n correctly assigned text topics

40 60 80 100 120 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 250000 300000 350000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

• ling. repr.

❘❡s✉❧ts

❘❡s✉❧ts ❢♦r t♦♣✐❝ ❝❧❛ss✐✜❝❛t✐♦♥

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✶ ✴ ✺✷

1/n correctly assigned text topics

40 60 80 100 120 solely normed 0.0 0.1 0.2 0.3 0.4 0.5 topic averaged 0.0 0.1 0.2 0.3 0.4 0.5

• ling. repr.

lemma pos tok text level learner ZH1 Filesize 250000 300000 350000

❋✐❣✉r❡✿ ❈❧❛ss✐✜❡❞ ❜② t❡①t t♦♣✐❝✳ ❲✐t❤ ●❡r♠❛♥ ✜❧❡s✳ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ✐s ❜❛s❡ ❧✐♥❡✳

• ling. repr.

♦❜s❡r✈❛t✐♦♥ ✺

❖✉r ❤❡✉r✐st✐❝ ❢♦r t♦♣✐❝ ✐♥✢✉❡♥❝❡ r❡❞✉❝t✐♦♥ ✇♦r❦s ✈❡r② ✇❡❧❧✿ P❡r❢♦r♠❛♥❝❡ ❞r♦♣s t♦ ❡st✐♠❛t❡❞ ❜❛s❡ ❧✐♥❡✳

❇❡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❧✐♥ ■■ ✷✵✶✶ ✸✸ ✴ ✺✷

❇❡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 ❛♥❞ ❝❛♥ ❜❡ ❝♦♠♣❛r❡❞✳

✭❍✉♠❜♦❧❞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 ❛♥❞ ❝❛♥ ❜❡ ❝♦♠♣❛r❡❞✳

✭❍✉♠❜♦❧❞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 ❛♥❞ ❝❛♥ ❜❡ ❝♦♠♣❛r❡❞✳

✭❍✉♠❜♦❧❞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 ❛♥❞ ❝❛♥ ❜❡ ❝♦♠♣❛r❡❞✳

✭❍✉♠❜♦❧❞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 ❛♥❞ ❝❛♥ ❜❡ ❝♦♠♣❛r❡❞✳

✭❍✉♠❜♦❧❞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 ❛♥❞ ❝❛♥ ❜❡ ❝♦♠♣❛r❡❞✳

✭❍✉♠❜♦❧❞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❧✐♥ ■■ ✷✵✶✶ ✸✹ ✴ ✺✷

❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥

❚❤❡ r❡s✉❧ts

0.2 0.4 0.6 0.8 1.2

n=10

Layer Relative influence of L1 and topic learner ZH1 lemma pos tok

❋✐❣✉r❡✿ ▲✶ ✭β✮ ❡✛❡❝t ❞✐✈✐❞❡❞ ❜② t♦♣✐❝ ✭α✮ ❡✛❡❝t✳

♦❜s❡r✈❛t✐♦♥s

✶ ❡ss❛② t♦♣✐❝ ✈❡r② str♦♥❣✳ ✷ ▼✉❝❤ str♦♥❣❡r t❤❛♥ ▲✶ ❢♦r

t♦❦❡♥ ❛♥❞ ❧❡♠♠❛✳

✸ ◆♦ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥

t♦❦❡♥ ❛♥❞ ❧❡♠♠❛

✹ t❤❡ ▲✶ ✐♥✢✉❡♥❝❡ ✐♥ P❖❙ ✐s

♠✉❝❤ ♠♦r❡ ♣r♦♥♦✉♥❝❡❞✳

✺ ❘❡♠♦✈✐♥❣ ❡rr♦rs ✭s❧✐❣❤t❧②✮

✇❡❛❦❡♥s ▲✶ ✐♥✢✉❡♥❝❡✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✺ ✴ ✺✷

❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥

❚❤❡ r❡s✉❧ts

0.2 0.4 0.6 0.8 1.2

n=10

Layer Relative influence of L1 and topic learner ZH1 lemma pos tok

❋✐❣✉r❡✿ ▲✶ ✭β✮ ❡✛❡❝t ❞✐✈✐❞❡❞ ❜② t♦♣✐❝ ✭α✮ ❡✛❡❝t✳

♦❜s❡r✈❛t✐♦♥s

✶ ❡ss❛② t♦♣✐❝ ✈❡r② str♦♥❣✳ ✷ ▼✉❝❤ str♦♥❣❡r t❤❛♥ ▲✶ ❢♦r

t♦❦❡♥ ❛♥❞ ❧❡♠♠❛✳

✸ ◆♦ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥

t♦❦❡♥ ❛♥❞ ❧❡♠♠❛

✹ t❤❡ ▲✶ ✐♥✢✉❡♥❝❡ ✐♥ P❖❙ ✐s

♠✉❝❤ ♠♦r❡ ♣r♦♥♦✉♥❝❡❞✳

✺ ❘❡♠♦✈✐♥❣ ❡rr♦rs ✭s❧✐❣❤t❧②✮

✇❡❛❦❡♥s ▲✶ ✐♥✢✉❡♥❝❡✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✺ ✴ ✺✷

❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥

❚❤❡ r❡s✉❧ts

0.2 0.4 0.6 0.8 1.2

n=10

Layer Relative influence of L1 and topic learner ZH1 lemma pos tok

❋✐❣✉r❡✿ ▲✶ ✭β✮ ❡✛❡❝t ❞✐✈✐❞❡❞ ❜② t♦♣✐❝ ✭α✮ ❡✛❡❝t✳

♦❜s❡r✈❛t✐♦♥s

✶ ❡ss❛② t♦♣✐❝ ✈❡r② str♦♥❣✳ ✷ ▼✉❝❤ str♦♥❣❡r t❤❛♥ ▲✶ ❢♦r

t♦❦❡♥ ❛♥❞ ❧❡♠♠❛✳

✸ ◆♦ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥

t♦❦❡♥ ❛♥❞ ❧❡♠♠❛

✹ t❤❡ ▲✶ ✐♥✢✉❡♥❝❡ ✐♥ P❖❙ ✐s

♠✉❝❤ ♠♦r❡ ♣r♦♥♦✉♥❝❡❞✳

✺ ❘❡♠♦✈✐♥❣ ❡rr♦rs ✭s❧✐❣❤t❧②✮

✇❡❛❦❡♥s ▲✶ ✐♥✢✉❡♥❝❡✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✺ ✴ ✺✷

❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥

❚❤❡ r❡s✉❧ts

0.2 0.4 0.6 0.8 1.2

n=10

Layer Relative influence of L1 and topic learner ZH1 lemma pos tok

❋✐❣✉r❡✿ ▲✶ ✭β✮ ❡✛❡❝t ❞✐✈✐❞❡❞ ❜② t♦♣✐❝ ✭α✮ ❡✛❡❝t✳

♦❜s❡r✈❛t✐♦♥s

✶ ❡ss❛② t♦♣✐❝ ✈❡r② str♦♥❣✳ ✷ ▼✉❝❤ str♦♥❣❡r t❤❛♥ ▲✶ ❢♦r

t♦❦❡♥ ❛♥❞ ❧❡♠♠❛✳

✸ ◆♦ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥

t♦❦❡♥ ❛♥❞ ❧❡♠♠❛

✹ t❤❡ ▲✶ ✐♥✢✉❡♥❝❡ ✐♥ P❖❙ ✐s

♠✉❝❤ ♠♦r❡ ♣r♦♥♦✉♥❝❡❞✳

✺ ❘❡♠♦✈✐♥❣ ❡rr♦rs ✭s❧✐❣❤t❧②✮

✇❡❛❦❡♥s ▲✶ ✐♥✢✉❡♥❝❡✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✺ ✴ ✺✷

❇❡②♦♥❞ ❝❧❛ss✐✜❝❛t✐♦♥

❚❤❡ r❡s✉❧ts

0.2 0.4 0.6 0.8 1.2

n=10

Layer Relative influence of L1 and topic learner ZH1 lemma pos tok

❋✐❣✉r❡✿ ▲✶ ✭β✮ ❡✛❡❝t ❞✐✈✐❞❡❞ ❜② t♦♣✐❝ ✭α✮ ❡✛❡❝t✳

♦❜s❡r✈❛t✐♦♥s

✶ ❡ss❛② t♦♣✐❝ ✈❡r② str♦♥❣✳ ✷ ▼✉❝❤ str♦♥❣❡r t❤❛♥ ▲✶ ❢♦r

t♦❦❡♥ ❛♥❞ ❧❡♠♠❛✳

✸ ◆♦ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥

t♦❦❡♥ ❛♥❞ ❧❡♠♠❛

✹ t❤❡ ▲✶ ✐♥✢✉❡♥❝❡ ✐♥ P❖❙ ✐s

♠✉❝❤ ♠♦r❡ ♣r♦♥♦✉♥❝❡❞✳

✺ ❘❡♠♦✈✐♥❣ ❡rr♦rs ✭s❧✐❣❤t❧②✮

✇❡❛❦❡♥s ▲✶ ✐♥✢✉❡♥❝❡✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡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❧✐♥ ■■ ✷✵✶✶ ✸✻ ✴ ✺✷

❈♦♥❝❧✉s✐♦♥

▼❛✐♥ r❡s✉❧ts

✶ ▲✶ ❤❛s ❛ ❤✐❣❤ ❛♥❞ q✉❛♥t✐✜❛❜❧❡ ✐♥✢✉❡♥❝❡ ♦♥ ♦✉r s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙✳ ✷ ❙❡♥s✐❜❧❡ r❡❧❛t✐♦♥s ❜❡t✇❡❡♥ ❧❡❛r♥❡r t❡①t ❛♥ ❚❛r❣❡t ❍②♣♦t❤❡s✐s✳ ✸ ❙❡♥s✐❜❧❡ r❡❧❛t✐♦♥s ❜❡t✇❡❡♥ t♦❦✱ ❧❡♠♠❛ ❛♥❞ P❖❙ ✳ ✹ ❲❡ s❡❡ ❛ ✈✐✈✐❞ ✐♥t❡r♣❧❛② ❜❡t✇❡❡♥ ▲✶ ❛♥❞ t♦♣✐❝✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✼ ✴ ✺✷

❈♦♥❝❧✉s✐♦♥

▼❛✐♥ r❡s✉❧ts

✶ ▲✶ ❤❛s ❛ ❤✐❣❤ ❛♥❞ q✉❛♥t✐✜❛❜❧❡ ✐♥✢✉❡♥❝❡ ♦♥ ♦✉r s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙✳ ✷ ❙❡♥s✐❜❧❡ r❡❧❛t✐♦♥s ❜❡t✇❡❡♥ ❧❡❛r♥❡r t❡①t ❛♥ ❚❛r❣❡t ❍②♣♦t❤❡s✐s✳ ✸ ❙❡♥s✐❜❧❡ r❡❧❛t✐♦♥s ❜❡t✇❡❡♥ t♦❦✱ ❧❡♠♠❛ ❛♥❞ P❖❙ ✳ ✹ ❲❡ s❡❡ ❛ ✈✐✈✐❞ ✐♥t❡r♣❧❛② ❜❡t✇❡❡♥ ▲✶ ❛♥❞ t♦♣✐❝✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✼ ✴ ✺✷

❈♦♥❝❧✉s✐♦♥

▼❛✐♥ r❡s✉❧ts

✶ ▲✶ ❤❛s ❛ ❤✐❣❤ ❛♥❞ q✉❛♥t✐✜❛❜❧❡ ✐♥✢✉❡♥❝❡ ♦♥ ♦✉r s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙✳ ✷ ❙❡♥s✐❜❧❡ r❡❧❛t✐♦♥s ❜❡t✇❡❡♥ ❧❡❛r♥❡r t❡①t ❛♥ ❚❛r❣❡t ❍②♣♦t❤❡s✐s✳ ✸ ❙❡♥s✐❜❧❡ r❡❧❛t✐♦♥s ❜❡t✇❡❡♥ t♦❦✱ ❧❡♠♠❛ ❛♥❞ P❖❙ ✳ ✹ ❲❡ s❡❡ ❛ ✈✐✈✐❞ ✐♥t❡r♣❧❛② ❜❡t✇❡❡♥ ▲✶ ❛♥❞ t♦♣✐❝✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✼ ✴ ✺✷

❈♦♥❝❧✉s✐♦♥

▼❛✐♥ r❡s✉❧ts

✶ ▲✶ ❤❛s ❛ ❤✐❣❤ ❛♥❞ q✉❛♥t✐✜❛❜❧❡ ✐♥✢✉❡♥❝❡ ♦♥ ♦✉r s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙✳ ✷ ❙❡♥s✐❜❧❡ r❡❧❛t✐♦♥s ❜❡t✇❡❡♥ ❧❡❛r♥❡r t❡①t ❛♥ ❚❛r❣❡t ❍②♣♦t❤❡s✐s✳ ✸ ❙❡♥s✐❜❧❡ r❡❧❛t✐♦♥s ❜❡t✇❡❡♥ t♦❦✱ ❧❡♠♠❛ ❛♥❞ P❖❙ ✳ ✹ ❲❡ s❡❡ ❛ ✈✐✈✐❞ ✐♥t❡r♣❧❛② ❜❡t✇❡❡♥ ▲✶ ❛♥❞ t♦♣✐❝✳ ✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✼ ✴ ✺✷

❈♦♥❝❧✉s✐♦♥

❲❤❛t ❢♦❧❧♦✇s ✐♥ ♣r❛❝t✐❝❛❧ t❡r♠s❄

t♦♣✐❝

◆♦t t♦ t❛❦❡ t♦♣✐❝ ✐♥t♦ ❛❝❝♦✉♥t ♠✐❣❤t ✐❣♥♦r❡ ❛ str♦♥❣ s♦✉r❝❡ ♦❢ ✈❛r✐❛♥❝❡✳

❝♦♣✐❡❞ ♠❛t❡r✐❛❧

❈♦♣✐❡❞ ♠❛t❡r✐❛❧ ❝❛♥ ❞✐st♦rt r❡s✉❧ts✳ ⇒ ❚❤✐s ❝❛♥ ❛♥❞ s❤♦✉❧❞ ❜❡ ❤❛♥❞❧❡❞ ✐♥❞❡♣❡♥❞❡♥t❧②✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✽ ✴ ✺✷

❈♦♥❝❧✉s✐♦♥

❚❖❉❖s

❧♦♦❦✐♥❣ ❞❡❡♣❡r

❲❤✐❝❤ ❢❡❛t✉r❡s ♦❢ t❤❡ ❧❡❛r♥❡r t❡①ts ❝♦♥t❛✐♥ t❤❡ ▲✶ ❞❡♣❡♥❞❡♥❝❡❄

P❖❙ ❛♥❞ t♦♣✐❝

❍♦✇ str♦♥❣ ✐s t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❡①t t♦♣✐❝ ♦♥ t❤❡ P❖❙ r❡♣r❡s❡♥t❛t✐♦♥❄ ■s ✐t s♣✉r✐♦✉s ♦r ❧✐♥❣✉✐st✐❝❛❧❧② ✐♥t❡r❡st✐♥❣❄

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✸✾ ✴ ✺✷

❈♦♥❝❧✉s✐♦♥

❚❤❛♥❦ ②♦✉

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✵ ✴ ✺✷

▲✐t❡r❛t✉r ■

❈♦♦❦✱ ❱✐✈✐❛♥ ❏❛♠❡s ✭✷✵✵✸✮✳ ❊✛❡❝ts ♦❢ t❤❡ s❡❝♦♥❞ ❧❛♥❣✉❛❣❡ ♦♥ t❤❡ ✜rst✳ ❱♦❧✳ ✸✳ ❙❡❝♦♥❞ ❧❛♥❣✉❛❣❡ ❛❝q✉✐s✐t✐♦♥✳ ❈❧❡✈❡❞♦♥✿ ▼✉❧t✐❧✐♥❣✉❛❧ ▼❛tt❡rs✳ ■❙❇◆✿ ✶✽✺✸✺✾✻✸✸✼✳ ❯❘▲✿ ❤tt♣✿✴✴✇✇✇✳❣❜✈✳❞❡✴❞♠s✴❜s✴t♦❝✴✸✺✼✵✹✶✽✼✾✳♣❞❢✳ ❊❧❧✐s✱ ❘♦❞✱ ❡❞✳ ✭✷✵✵✾✮✳ ❚❤❡ st✉❞② ♦❢ s❡❝♦♥❞ ❧❛♥❣✉❛❣❡ ❛❝q✉✐s✐t✐♦♥✳ ❖①❢♦r❞ ❛♣♣❧✐❡❞ ❧✐♥❣✉✐st✐❝s✳ ❖①❢♦r❞ ❬✉✳❛✳❪✿ ❖①❢♦r❞ ❯♥✐✈✳ Pr❡ss✳ ■❙❇◆✿ ✾✼✽ ✵ ✶✾ ✹✹✷✷✺✼ ✹✳

• ♦❧❝❤❡r✱ ❋❡❧✐① ✭✷✵✵✼✮✳ ✏❆ ♥❡✇ t❡①t st❛t✐st✐❝❛❧ ♠❡❛s✉r❡ ❛♥❞ ✐ts ❛♣♣❧✐❝❛t✐♦♥ t♦

st②❧♦♠❡tr②✑✳ ■♥✿ ❈♦r♣✉s ▲✐♥❣✉✐st✐❝s ✷✵✵✼✳ ❯♥✐✈❡rs✐t② ♦❢ ❇✐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❧✐♥✳

• r❛♥❣❡r✱ ❙②❧✈✐❛♥❡ ✭✷✵✵✽✮✳ ✏▲❡❛r♥❡r ❝♦r♣♦r❛✑✳ ■♥✿ ❈♦r♣✉s ❧✐♥❣✉✐st✐❝s✳ ❊❞✳ ❜②

❆♥❦❡ ▲ü❞❡❧✐♥❣ ❡t ❛❧✳ ❱♦❧✳ ✶✳ ❍❛♥❞❜ü❝❤❡r ③✉r ❙♣r❛❝❤✲ ✉♥❞ ❑♦♠♠✉♥✐❦❛t✐♦♥s✇✐ss❡♥s❝❤❛❢t ✴ ❍❛♥❞❜♦♦❦s ♦❢ ▲✐♥❣✉✐st✐❝s ❛♥❞ ❈♦♠♠✉♥✐❝❛t✐♦♥ ❙❝✐❡♥❝❡✳ ❇❡r❧✐♥✱ ◆❡✇ ❨♦r❦✿ ▼♦✉t♦♥ ❞❡ ●r✉②t❡r✱ ♣♣✳ ✷✺✾✕✷✼✺✳ ■❙❇◆✿ ✾✼✽✲✸✲✶✶✲✵✶✽✵✹✸✲✺✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✶ ✴ ✺✷

▲✐t❡r❛t✉r ■■

❏♦❥♦❲♦♥❣✱ ❙③❡✲▼❡♥❣ ❡t ❛❧✳ ✭✷✵✵✾✮✳ ✏❈♦♥tr❛st✐✈❡ ❆♥❛❧②s✐s ❛♥❞ ◆❛t✐✈❡ ▲❛♥❣✉❛❣❡ ■❞❡♥t✐✜❝❛t✐♦♥✑✳ ■♥✿ ❆✉str❛❧❛s✐❛♥ ▲❛♥❣✉❛❣❡ ❚❡❝❤♥♦❧♦❣② ❆ss♦❝✐❛t✐♦♥ ❲♦r❦s❤♦♣ ✷✵✵✾✳ ❊❞✳ ❜② ▲✉✐③ ❆✉❣✉st♦ P✐③③❛t♦ ❡t ❛❧✳✱ ♣♣✳ ✺✸✕✻✶✳ ❏✉♦❧❛✱ P❛tr✐❝❦ ✭✷✵✵✹✮✳ ❆❞✲❤♦❝ ❆✉t❤♦rs❤✐♣ ❆ttr✐❜✉t✐♦♥ ❈♦♠♣❡t✐t✐♦♥✳ ❯❘▲✿ ❤tt♣✿✴✴✇✇✇✳♠❛t❤❝s✳❞✉q✳❡❞✉✴⑦❥✉♦❧❛✴❛✉t❤♦rs❤✐♣❴❝♦♥t❡st✳❤t♠❧ ✭✈✐s✐t❡❞ ♦♥ ✵✸✴✷✹✴✷✵✶✶✮✳ ❑♦♣♣❡❧✱ ▼♦s❤❡ ❡t ❛❧✳ ✭✷✵✵✸✮✳ ✏❊①♣❧♦✐t✐♥❣ ❙t②❧✐st✐❝ ■❞✐♦s②♥❝r❛s✐❡s ❢♦r ❆✉t❤♦rs❤✐♣ ❆ttr✐❜✉t✐♦♥✑✳ ■♥✿ Pr♦❝❡❡❞✐♥❣s ♦❢ ■❏❈❆■✬✵✸ ❲♦r❦s❤♦♣ ♦♥ ❈♦♠♣✉t❛t✐♦♥❛❧ ❆♣♣r♦❛❝❤❡s t♦ ❙t②❧❡ ❆♥❛❧②s✐s ❛♥❞ ❙②♥t❤❡s✐s✱ ♣♣✳ ✻✾✕✼✷✳ ❑♦♣♣❡❧✱ ▼♦s❤❡ ❡t ❛❧✳ ✭✷✵✵✺✮✳ ✏❆✉t♦♠❛t✐❝❛❧❧② ❉❡t❡r♠✐♥✐♥❣ ❛♥ ❆♥♦♥②♠♦✉s ❆✉t❤♦r✬s ◆❛t✐✈❡ ▲❛♥❣✉❛❣❡✑✳ ■♥✿ ■♥t❡❧❧✐❣❡♥❝❡ ❛♥❞ ❙❡❝✉r✐t② ■♥❢♦r♠❛t✐❝s✳ ▲❡❝t✉r❡ ◆♦t❡s ✐♥ ❈♦♠♣✉t❡r ❙❝✐❡♥❝❡✳ ❙♣r✐♥❣❡r✱ ♣♣✳ ✷✵✾✕✷✶✼✳ ❯❘▲✿ ❤tt♣✿✴✴✇✇✇✳s♣r✐♥❣❡r❧✐♥❦✳❝♦♠✴❝♦♥t❡♥t✴r❡♠✻✈♥❣✽r✷✵❡❜❦✸q✴✳ ▲ü❞❡❧✐♥❣✱ ❆♥❦❡ ❡t ❛❧✳ ✭✷✵✵✽✮✳ ✏❉❛s ▲❡r♥❡r❦♦r♣✉s ❋❛❧❦♦✑✳ ■♥✿ ❉❡✉ts❝❤ ❛❧s ❋r❡♠❞s♣r❛❝❤❡ ✹✺✳✷✱ ♣♣✳ ✻✼✕✼✸✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✷ ✴ ✺✷

▲✐t❡r❛t✉r ■■■

❖❞❧✐♥✱ ❚❡r❡♥❝❡ ✭✷✵✵✸✮✳ ✏❈r♦ss✲❧✐♥❣✉✐st✐❝ ■♥✢✉❡♥❝❡✑✳ ■♥✿ ❍❛♥❞❜♦♦❦ ♦♥ ❙❡❝♦♥❞ ▲❛♥❣✉❛❣❡ ❆❝q✉✐s✐t✐♦♥✳ ❊❞✳ ❜② ❈❛t❤❡r✐♥❡ ❉♦✉❣❤t② ❡t ❛❧✳ ❇❧❛❝❦✇❡❧❧✱ ♣♣✳ ✹✸✻✕✹✽✻✳ ❘ ❉❡✈❡❧♦♣♠❡♥t ❈♦r❡ ❚❡❛♠ ✭✷✵✶✶✮✳ ❘✿ ❆ ▲❛♥❣✉❛❣❡ ❛♥❞ ❊♥✈✐r♦♥♠❡♥t ❢♦r ❙t❛t✐st✐❝❛❧ ❈♦♠♣✉t✐♥❣✳ ■❙❇◆ ✸✲✾✵✵✵✺✶✲✵✼✲✵✳ ❘ ❋♦✉♥❞❛t✐♦♥ ❢♦r ❙t❛t✐st✐❝❛❧ ❈♦♠♣✉t✐♥❣✳ ❱✐❡♥♥❛✱ ❆✉str✐❛✳ ❯❘▲✿ ❤tt♣✿✴✴✇✇✇✳❘✲♣r♦❥❡❝t✳♦r❣✴✳ ❘❡③♥✐❝❡❦✱ ▼❛r❝ ❡t ❛❧✳ ✭✷✵✶✵✮✳ ❉❛s ❋❛❧❦♦✲❍❛♥❞❜✉❝❤✿ ❑♦r♣✉s❛✉❢❜❛✉ ✉♥❞ ❆♥♥♦t❛t✐♦♥❡♥✿ ❱❡rs✐♦♥ ✶✳✵✳ ❇❡r❧✐♥✳ ❯❘▲✿ ❤tt♣✿✴✴✇✇✇✳❧✐♥❣✉✐st✐❦✳❤✉✲❜❡r❧✐♥✳❞❡✴✐♥st✐t✉t✴♣r♦❢❡ss✉r❡♥✴❦♦ r♣✉s❧✐♥❣✉✐st✐❦✴❢♦rs❝❤✉♥❣✴❢❛❧❦♦✳ ❘♦♠❛✐♥❡✱ ❙✉③❛♥♥❡ ✭✷✵✵✸✮✳ ✏❱❛r✐❛t✐♦♥✑✳ ■♥✿ ❚❤❡ ❤❛♥❞❜♦♦❦ ♦❢ s❡❝♦♥❞ ❧❛♥❣✉❛❣❡ ❛❝q✉✐s✐t✐♦♥✳ ❊❞✳ ❜② ❈❛t❤❡r✐♥❡ ❉♦✉❣❤t②✳ ❱♦❧✳ ✶✹✳ ❇❧❛❝❦✇❡❧❧ ❤❛♥❞❜♦♦❦s ✐♥ ❧✐♥❣✉✐st✐❝s✳ ▼❛❧❞❡♥✱ ▼❆ ❬✉✳❛✳❪✿ ❇❧❛❝❦✇❡❧❧✱ ♣♣✳ ✹✵✾✕✹✸✺✳ ■❙❇◆✿ ✵✲✻✸✶✲✷✶✼✺✹✲✶✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✸ ✴ ✺✷

▲✐t❡r❛t✉r ■❱

❙❝❤♠✐❞✱ ❍❡❧♠✉t ✭✶✾✾✹✮✳ ✏Pr♦❜❛❜✐❧✐st✐❝ P❛rt✲♦❢✲❙♣❡❡❝❤ ❚❛❣❣✐♥❣ ❯s✐♥❣ ❉❡❝✐s✐♦♥ ❚r❡❡s✑✳ ■♥✿ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ◆❡✇ ▼❡t❤♦❞s ✐♥ ▲❛♥❣✉❛❣❡ Pr♦❝❡ss✐♥❣✱ ♣♣✳ ✹✹✕✹✾✳ ❯❘▲✿ ❤tt♣✿ ✴✴✇✇✇✳✐♠s✳✉♥✐✲st✉tt❣❛rt✳❞❡✴❢t♣✴♣✉❜✴❝♦r♣♦r❛✴tr❡❡✲t❛❣❣❡r ✶✳♣❞❢✳ ❚s✉r✱ ❖r❡♥ ❡t ❛❧✳ ✭✷✵✵✼✮✳ ✏❯s✐♥❣ ❈❧❛ss✐✜❡r ❋❡❛t✉r❡s ❢♦r ❙t✉❞②✐♥❣ t❤❡ ❊✛❡❝t ♦❢ ◆❛t✐✈❡ ▲❛♥❣✉❛❣❡ ❈❤♦✐❝❡ ♦❢ ❲r✐tt❡♥ ❙❡❝♦♥❞ ▲❛♥❣✉❛❣❡ ❲♦r❞s✑✳ ■♥✿ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ❲♦r❦s❤♦♣ ♦♥ ❈♦❣♥✐t✐✈❡ ❆s♣❡❝ts ♦❢ ❈♦♠♣✉t❛t✐♦♥❛❧ ▲❛♥❣✉❛❣❡ ❆❝q✉✐s✐t✐♦♥✳ ❆❈▲✱ ♣♣✳ ✾✕✶✻✳ ❲❛❧t❡r✱ ▼❛✐❦ ❡t ❛❧✳✱ ❡❞s✳ ✭✷✵✵✽✮✳ ❋♦rt❣❡s❝❤r✐tt❡♥❡ ▲❡r♥❡r✈❛r✐❡tät❡♥✿ ❑♦r♣✉s❧✐♥❣✉✐st✐❦ ✉♥❞ ❩✇❡✐ts♣r❛❝❤❡r✇❡r❜s❢♦rs❝❤✉♥❣✳ ❱♦❧✳ ✺✷✵✳ ▲✐♥❣✉✐st✐s❝❤❡ ❆r❜❡✐t❡♥✳ ❚ü❜✐♥❣❡♥✿ ▼❛① ◆✐❡♠❡②❡r ❱❡r❧❛❣✳ ■❙❇◆✿ ✾✼✽✸✹✽✹✸✵✺✷✵✺✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✹ ✴ ✺✷

❆♥♦t❤❡r ✈✐❡✇ ♦♥ t❤❡ r❡s✉❧ts

German files excluded

level of representation correctly classified files (L1)

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lemma pos copies removed

• tok

lemma pos topic averaged solely normed ebene

• learner

ZH1

❋✐❣✉r❡✿ ▲✶ ❈❧❛ss✐✜❝❛t✐♦♥✳ ▼❛①✐♠✉♠ ❛t ✽✷/✶✶✸ = ✵.✼✷ ± ✵.✵✾✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✺ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 22

24 17 18 25 20 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 19 4 3 2 9 12 1 2 6 11 8 6 9 1 1 2 8 1 1 1 7 2 2 8

❋✐❣✉r❡✿ ❘❛✇ t❡①t✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡ ♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤ ▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳

❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st ✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✻ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 24

22 24 15 19 22 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 22 3 8 1 3 13 1 4 13 6 7 11 1 1 3 8 1 9 1 1 9

❋✐❣✉r❡✿ t✐t❧❡ ❛✈❡r❛❣❡❞ ♦✉t✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡ ♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤ ▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳

❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st ✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✻ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 23

22 29 15 16 21 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 22 5 6 4 13 1 3 21 4 4 9 1 1 11 1 8 2 1 9

❋✐❣✉r❡✿ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ r❡♠♦✈❡❞✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡ ♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤ ▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳

❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st ✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✻ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 23

22 29 15 16 21 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 22 5 6 4 13 1 3 21 4 4 9 1 1 11 1 8 2 1 9

❋✐❣✉r❡✿ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ r❡♠♦✈❡❞✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡ ♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤ ▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳

❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st ✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✻ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 23

22 29 15 16 21 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 22 5 6 4 13 1 3 21 4 4 9 1 1 11 1 8 2 1 9

❋✐❣✉r❡✿ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ r❡♠♦✈❡❞✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

◮ ■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡

♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤ ▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳

❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st ✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✻ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 23

22 29 15 16 21 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 22 5 6 4 13 1 3 21 4 4 9 1 1 11 1 8 2 1 9

❋✐❣✉r❡✿ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ r❡♠♦✈❡❞✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

◮ ■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡

♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤ ▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳

❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st ✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✻ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 23

22 29 15 16 21 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 22 5 6 4 13 1 3 21 4 4 9 1 1 11 1 8 2 1 9

❋✐❣✉r❡✿ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ r❡♠♦✈❡❞✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

◮ ■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡

♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

◮ ■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤

▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳

❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st ✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✻ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 23

22 29 15 16 21 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 22 5 6 4 13 1 3 21 4 4 9 1 1 11 1 8 2 1 9

❋✐❣✉r❡✿ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ r❡♠♦✈❡❞✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

◮ ■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡

♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

◮ ■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤

▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳

❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st ✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✻ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 23

22 29 15 16 21 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 22 5 6 4 13 1 3 21 4 4 9 1 1 11 1 8 2 1 9

❋✐❣✉r❡✿ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ r❡♠♦✈❡❞✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

◮ ■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡

♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

◮ ■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤

▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳ ◮ ❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st

✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✻ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 22

24 17 18 25 20 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 19 4 3 2 9 12 1 2 6 11 8 6 9 1 1 2 8 1 1 1 7 2 2 8

❋✐❣✉r❡✿ ❘❛✇ t❡①t✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡ ♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤ ▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳

❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st ✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✼ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 24

22 24 15 19 22 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 22 3 8 1 3 13 1 4 13 6 7 11 1 1 3 8 1 9 1 1 9

❋✐❣✉r❡✿ t✐t❧❡ ❛✈❡r❛❣❡❞ ♦✉t✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡ ♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤ ▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳

❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st ✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✼ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 23

22 29 15 16 21 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 22 5 6 4 13 1 3 21 4 4 9 1 1 11 1 8 2 1 9

❋✐❣✉r❡✿ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ r❡♠♦✈❡❞✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡ ♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤ ▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳

❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st ✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✼ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 23

22 29 15 16 21 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 22 5 6 4 13 1 3 21 4 4 9 1 1 11 1 8 2 1 9

❋✐❣✉r❡✿ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ r❡♠♦✈❡❞✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡ ♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤ ▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳

❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st ✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✼ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 23

22 29 15 16 21 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 22 5 6 4 13 1 3 21 4 4 9 1 1 11 1 8 2 1 9

❋✐❣✉r❡✿ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ r❡♠♦✈❡❞✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

◮ ■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡

♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤ ▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳

❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st ✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✼ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 23

22 29 15 16 21 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 22 5 6 4 13 1 3 21 4 4 9 1 1 11 1 8 2 1 9

❋✐❣✉r❡✿ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ r❡♠♦✈❡❞✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

◮ ■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡

♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤ ▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳

❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st ✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✼ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 23

22 29 15 16 21 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 22 5 6 4 13 1 3 21 4 4 9 1 1 11 1 8 2 1 9

❋✐❣✉r❡✿ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ r❡♠♦✈❡❞✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

◮ ■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡

♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

◮ ■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤

▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳

❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st ✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✼ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 23

22 29 15 16 21 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 22 5 6 4 13 1 3 21 4 4 9 1 1 11 1 8 2 1 9

❋✐❣✉r❡✿ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ r❡♠♦✈❡❞✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

◮ ■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡

♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

◮ ■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤

▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳

❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st ✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✼ ✴ ✺✷

❉✐str✐❜✉t✐♦♥ ♦❢ r✐❣❤t ❛♥❞ ✇r♦♥❣ ❝❧❛ss✐✜❝❛t✐♦♥s

• 23

22 29 15 16 21 37 13 42 14 10 10 126 dan deu eng fra rus tur dan deu eng fra rus tur real L1 classified as 22 5 6 4 13 1 3 21 4 4 9 1 1 11 1 8 2 1 9

❋✐❣✉r❡✿ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧ r❡♠♦✈❡❞✳

✶ ●❡r♠❛♥ ✐s ❞❡t❡❝t❡❞ ✇✐t❤ ✶✵✵✪

❛❝❝✉r❛❝②✳

◮ ■▲ ❤❛s ❜❡❡♥ ❝❧❛✐♠❡❞ t♦ ❜❡

♠♦r❡ ✈❛r✐❛❜❧❡✳ ✭s❡❡ ❘♦♠❛✐♥❡ ✷✵✵✸✮

✷ ▼♦st ❝❧❛ss✐✜❝❛t✐♦♥ ❡rr♦rs ♦❝❝✉r

❢♦r ❊♥❣❧✐s❤ ❧❡❛r♥❡rs✳

◮ ■♥✢✉❡♥❝❡ ♦❢ ❝♦♠♠♦♥ ❊♥❣❧✐s❤

▲✷ ♦♥ ●❡r♠❛♥ ▲✸❄ ✭s❡❡ ❈♦♦❦ ✷✵✵✸✮

✸ ❚✉r❦✐s❤ ❜❡❤❛✈❡s ❛ ❜✐t ❡rr❛t✐❝✳ ◮ ❚❤♦s❡ ✇❡r❡ t❤❡ ♠♦st

✉♥❣r❛♠♠❛t✐❝❛❧ t❡①ts✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✼ ✴ ✺✷

◆♦r♠✐♥❣ ❙

✶✶ ◆♦r♠✐♥❣ ❙ ✶✷ ❉❡♥s✐t② ♣❧♦ts

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✽ ✴ ✺✷

◆♦r♠✐♥❣ ❙

❆♥ ♦❜✈✐♦✉s ♣r♦❜❧❡♠

❚❤❡ s✐♠✐❧❛r✐t② ♠❡❛s✉r❡ ❙ ❛s ❛ ❢♦r♠✉❧❛ ❙(❆, ❇) =

• ❛❧❧ s✉❜str✐♥❣s s

❧♦❣(❋❆(s)❋❇(s) + ✶) ❋❆(s) ✕ ❋r❡q✉❡♥❝② ♦❢ s✉❜str✐♥❣ s ✐♥ ❚❡①t ❆ ▲♦♥❣❡r t❡①ts ⇒ ♠♦r❡ ❛♥❞ ♠♦r❡ ❢r❡q✉❡♥t s✉❜str✐♥❣s✳ ❙ ❣r♦✇s ✇✐t❤ t❡①t ❧❡♥❣t❤✦ ▲❡♥❣t❤ ❞❡♣❡♥❞❡♥❝② ♥♦t ❡❛s② t♦ ♣❛r❛♠❡tr✐③❡✳ ❛♥❞ t❤❛t ✇♦✉❧❞ ♥♦t ❜❡ t❤❡ ❢✉❧❧ st♦r②✳✳✳ ❆♥ ✇♦r❦✐♥❣ ❤❡✉r✐st✐❝ ✐s ❛♣♣❧✐❡❞✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✹✾ ✴ ✺✷

◆♦r♠✐♥❣ ❙

❆ ❧✐❢❡ ❡①❛♠♣❧❡

Ti tj 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

❋✐❣✉r❡✿ ❉❛r❦✿ ❧♦✇ ❙✲✈❛❧✉❡s❀ ▲✐❣❤t✿ ❤✐❣❤ ❙✲✈❛❧✉❡s✳

❊✐❣❤t ❉✉t❝❤ ❛✉t❤♦rs❛✳ ❖♥❡ tr❛✐♥✐♥❣ ✜❧❡ ✴ ♦♥❡ t❡st ✜❧❡✳ ❊❛❝❤ tr❛✐♥✐♥❣ ✜❧❡ ❝♦♠♣❛r❡❞ ✇✐t❤ ❡❛❝❤ t❡st ✜❧❡✳ ❂❃ ❚r❛✐♥✐♥❣ ❋✐❧❡ ✽ ✐s t❤❡ s❤♦rt❡st ♦♥❡✳ ❂❃ ❉❛r❦❡st ❝♦❧✉♠♥✳ ❂❃ ❧♦✇❡st ❙ ✈❛❧✉❡s✳

❛❏✉♦❧❛ ✷✵✵✹✳

❙✐♠♣❧❡✿ ❉✐✈✐❞✐♥❣ ❈♦❧✉♠♥s ❜② t❤❡✐r ♠❡❛♥✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✺✵ ✴ ✺✷

◆♦r♠✐♥❣ ❙

❆✈❡r❛❣✐♥❣ ♦✉t s✐♥❣❧❡ t❡①t ❞❡♣❡♥❞❡♥❝✐❡s

Ti tj 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Ti tj 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

❚❤✐s ♥♦r♠❡❞ ✈❡rs✐♦♥ ♦❢ ❙ ✐s ✇❤❛t ✇❡ r❡❛❧❧② ✉s❡❞✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✺✶ ✴ ✺✷

❉❡♥s✐t② ♣❧♦ts

✶✶ ◆♦r♠✐♥❣ ❙ ✶✷ ❉❡♥s✐t② ♣❧♦ts

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✺✷ ✴ ✺✷

❉❡♥s✐t② ♣❧♦ts

❉✐str✐❜✉t✐♦♥ ♦❢ ❙(❆, ❇) ✈❛❧✉❡s

• r❡❡♥✿ ❆ ❛♥❞ ❇ s❤❛r❡ t✐t❧❡ ♦r ▲✶

❘❡❞✿ ❉✐✛❡r❡♥t t✐t❧❡ ♦r ▲✶✳ ❙❛♠❡ t✐t❧❡ ♦r ♥♦t❄ ❙❛♠❡ ▲✶ ♦r ♥♦t❄

S in arbitrary units Density same title not same title S in arbitrary units Density same L1 not same L1

t✐t❧❡ ♠✉❝❤ str♦♥❣❡r t❤❛♥ ▲✶✳ ❇✉t s✐♠✐❧❛r✐t② ❞✉❡ t♦ ▲✶ ✐s ✇❤❛t ✇❡ ❛r❡ ✐♥t❡r❡st❡❞ ✐♥✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✺✸ ✴ ✺✷

❉❡♥s✐t② ♣❧♦ts

❉✐str✐❜✉t✐♦♥ ♦❢ ❙(❆, ❇) ✈❛❧✉❡s ❛❢t❡r ❛✈❡r❛❣✐♥❣ ♦✉t t✐t❧❡

❆❣❛✐♥✿ ●r❡❡♥✿ ❆ ❛♥❞ ❇ s❤❛r❡ ▲✶❀ ❘❡❞✿ ❉✐✛❡r❡♥t ▲✶✳ ✇✐t❤ t✐t❧❡✿ t✐t❧❡ ❡✛❡❝t r❡♠♦✈❡❞✿

S in arbitrary units Density same L1 not same L1 S in arbitrary units Density same L1 not same L1

❚❤❡ ❞✐✛❡r❡♥❝❡ ✐s ♠✉❝❤ ❝❧❡❛r❡r ♥♦✇✳ ❈❧❛ss✐✜❝❛t✐♦♥ ❥✉♠♣s ❢r♦♠ ✻✺ t♦ ✼✹ ❝♦rr❡❝t ❞❡❝✐s✐♦♥s ✭♦✉t ♦❢ ✶✷✻✮✳ ❙✉s♣✐❝✐♦✉s❧② str❡t❝❤❡❞ r✐❣❤t t❛✐❧✳ ❚♦ t❤✐s ✇❡ t✉r♥ ♥♦✇✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✺✹ ✴ ✺✷

❉❡♥s✐t② ♣❧♦ts

❉✐str✐❜✉t✐♦♥ ♦❢ ❙(❆, ❇) ✈❛❧✉❡s ❛❢t❡r ❛✈❡r❛❣✐♥❣ ♦✉t t✐t❧❡

❆❣❛✐♥✿ ●r❡❡♥✿ ❆ ❛♥❞ ❇ s❤❛r❡ ▲✶❀ ❘❡❞✿ ❉✐✛❡r❡♥t ▲✶✳ ✇✐t❤ t✐t❧❡✿ t✐t❧❡ ❡✛❡❝t r❡♠♦✈❡❞✿

S in arbitrary units Density same L1 not same L1 S in arbitrary units Density same L1 not same L1

❚❤❡ ❞✐✛❡r❡♥❝❡ ✐s ♠✉❝❤ ❝❧❡❛r❡r ♥♦✇✳ ❈❧❛ss✐✜❝❛t✐♦♥ ❥✉♠♣s ❢r♦♠ ✻✺ t♦ ✼✹ ❝♦rr❡❝t ❞❡❝✐s✐♦♥s ✭♦✉t ♦❢ ✶✷✻✮✳ ❙✉s♣✐❝✐♦✉s❧② str❡t❝❤❡❞ r✐❣❤t t❛✐❧✳ ❚♦ t❤✐s ✇❡ t✉r♥ ♥♦✇✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✺✹ ✴ ✺✷

❉❡♥s✐t② ♣❧♦ts

❉✐str✐❜✉t✐♦♥ ♦❢ ❙(❆, ❇) ✈❛❧✉❡s ❛❢t❡r ❛✈❡r❛❣✐♥❣ ♦✉t t✐t❧❡

❆❣❛✐♥✿ ●r❡❡♥✿ ❆ ❛♥❞ ❇ s❤❛r❡ ▲✶❀ ❘❡❞✿ ❉✐✛❡r❡♥t ▲✶✳ ✇✐t❤ t✐t❧❡✿ t✐t❧❡ ❡✛❡❝t r❡♠♦✈❡❞✿

S in arbitrary units Density same L1 not same L1 S in arbitrary units Density same L1 not same L1

❚❤❡ ❞✐✛❡r❡♥❝❡ ✐s ♠✉❝❤ ❝❧❡❛r❡r ♥♦✇✳ ❈❧❛ss✐✜❝❛t✐♦♥ ❥✉♠♣s ❢r♦♠ ✻✺ t♦ ✼✹ ❝♦rr❡❝t ❞❡❝✐s✐♦♥s ✭♦✉t ♦❢ ✶✷✻✮✳ ❙✉s♣✐❝✐♦✉s❧② str❡t❝❤❡❞ r✐❣❤t t❛✐❧✳ ⇒ ❚♦ t❤✐s ✇❡ t✉r♥ ♥♦✇✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✺✹ ✴ ✺✷

❉❡♥s✐t② ♣❧♦ts

❉❡♥s✐t② ♣❧♦ts ❛❢t❡r r❡♠♦✈✐♥❣ ❝♦♣✐❡❞ ♠❛t❡r✐❛❧

S in arbitrary units Density same L1 not same L1 S in arbitrary units Density same L1 not same L1

❚❤❡ r✐❣❤t t❛✐❧ ✐s ❣r❡❛t❧② r❡❞✉❝❡❞✳ ❈❧❛ss✐✜❝❛t✐♦♥ r❡s✉❧ts ❛❣❛✐♥ ❥✉♠♣ ❢r♦♠ ✼✹ t♦ ✽✹ ❝♦rr❡❝t ✭❢r♦♠ ✶✷✻✮✳

✭❍✉♠❜♦❧❞t✲❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥✮ ❙t②❧♦♠❡tr② ✫ tr❛♥s❢❡r ✐♥ ❋❛❧❦♦ ❚ü❜❡r❧✐♥ ■■ ✷✵✶✶ ✺✺ ✴ ✺✷