Ph.D. Dissertation

■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ P❤✳❉✳ ❉✐ss❡rt❛t✐♦♥ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❆❞✈✐s♦r✿ ❉r✳ P❛♦❧♦ ❘♦ss♦ ❉♣t♦✳ ❙✐st❡♠❛s ■♥❢♦r♠át✐❝♦s ② ❈♦♠♣✉t❛❝✐ó♥ ❯♥✐✈❡rs✐❞❛❞ P♦❧✐té❝♥✐❝❛ ❞❡ ❱❛❧❡♥❝✐❛ ✷✾✴✶✵✴✷✵✶✵ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❖✉t❧✐♥❡ ✶ ❙✉♠♠❛r② ■♥tr♦❞✉❝t✐♦♥ ▼♦t✐✈❛t✐♦♥ ❖❜❥❡❝t✐✈❡s ♦❢ t❤❡ P❤✳❉✳ ❚❤❡s✐s ✷ ❘❡s♦✉r❝❡s ●❡♦✲❲♦r❞◆❡t ✸ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ✹ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ✺ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ✻ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ▼♦t✐✈❛t✐♦♥ ❚❤❡s✐s ❖❜❥❡❝t✐✈❡s ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❖✉t❧✐♥❡ ✶ ❙✉♠♠❛r② ■♥tr♦❞✉❝t✐♦♥ ▼♦t✐✈❛t✐♦♥ ❖❜❥❡❝t✐✈❡s ♦❢ t❤❡ P❤✳❉✳ ❚❤❡s✐s ✷ ❘❡s♦✉r❝❡s ●❡♦✲❲♦r❞◆❡t ✸ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ✹ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ✺ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ✻ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ▼♦t✐✈❛t✐♦♥ ❚❤❡s✐s ❖❜❥❡❝t✐✈❡s ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ▼♦t✐✈❛t✐♦♥ ❙✉♠♠❛r② ❯s❡rs s❡❛r❝❤ ❢♦r ❣❡♦❣r❛♣❤✐❝❛❧❧② ❝♦♥str❛✐♥❡❞ ✐♥❢♦r♠❛t✐♦♥✿ ●❛♥ ❡t ❛❧✳ ✭✷✵✵✽✮ ❡st✐♠❛t❡❞ t❤❛t ✶✷.✾✹% ♦❢ q✉❡r✐❡s s✉❜♠✐tt❡❞ t♦ t❤❡ ❆❖▲ s❡❛r❝❤ ❡♥❣✐♥❡ ❡①♣r❡ss❡❞ ❛ ❣❡♦❣r❛♣❤✐❝❛❧❧② ❝♦♥str❛✐♥❡❞ ✐♥❢♦r♠❛t✐♦♥ ♥❡❡❞ ✭❡✳❣✳ ✏❍♦t❡❧s ✐♥ ◆❡✇ ❨♦r❦✧✮ ❙❛♥❞❡rs♦♥ ❛♥❞ ❑♦❤❧❡r ✭✷✵✵✹✮ ❢♦✉♥❞ t❤❛t ✶✽.✻% ♦❢ t❤❡ q✉❡r✐❡s s✉❜♠✐tt❡❞ t♦ t❤❡ ❊①❝✐t❡ s❡❛r❝❤ ❡♥❣✐♥❡ ❝♦♥t❛✐♥❡❞ ❛t ❧❡❛st ❛ ❣❡♦❣r❛♣❤✐❝ t❡r♠ ✶ ●❡♦❈▲❊❋ ✱ t❤❡ ❈▲❊❋ ❡✈❛❧✉❛t✐♦♥ ❝❛♠♣❛✐❣♥ ❢♦r ❣❡♦❣r❛♣❤✐❝❛❧ ■❘ . % ✷✺ ✻ ♦❢ ❈▲❊❋ ◗❆ q✉❡st✐♦♥s ❝♦♥t❛✐♥❡❞ ❛ ❣❡♦❣r❛♣❤✐❝❛❧ ❝♦♥str❛✐♥t ♦r ❢♦❝✉s✱ ♦r ❜♦t❤ ✶ ❤tt♣✿✴✴✐r✳s❤❡❢✳❛❝✳✉❦✴❣❡♦❝❧❡❢✴ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ▼♦t✐✈❛t✐♦♥ ❚❤❡s✐s ❖❜❥❡❝t✐✈❡s ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❚♦♣♦♥②♠s ❆ ❚♦♣♦♥②♠ ✐s ❛ ♣❧❛❝❡ ♥❛♠❡ ✭❢r♦♠ t❤❡ ●r❡❡❦ t´♦♣♦❝ ✭♣❧❛❝❡✮ ❛♥❞ ´♦♥✉♠❛ ✭♥❛♠❡✮✮ ❚♦♣♦♥②♠s ❛r❡ ✭♦❢t❡♥✮ t❤❡ ♦♥❧② ❣❡♦❣r❛♣❤✐❝ ✐♥❢♦r♠❛t✐♦♥ s♦✉r❝❡s ✐♥ ✉♥str✉❝t✉r❡❞ t❡①ts ❑❡② ❢♦r t❤❡ ●■❘ ✭✉♥str✉❝t✉r❡❞ ✐♥❢♦r♠❛t✐♦♥✮ → ●■❙ ✭str✉❝t✉r❡❞ ♠❛♣✲❜❛s❡❞ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ s♣❛❝❡✮ ❜r✐❞❣❡ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ▼♦t✐✈❛t✐♦♥ ❚❤❡s✐s ❖❜❥❡❝t✐✈❡s ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠s ❛r❡ ❛♠❜✐❣✉♦✉s ❊①❛♠♣❧❡s P❛r✐s✱ ❋r❛♥❝❡ ✈s✳ P❛r✐s✱ ❚❡①❛s ❈❛♠❜r✐❞❣❡✱ ▼❆ ✈s✳ ❈❛♠❜r✐❞❣❡✱ ❯❑ ✈s✳ ❈❛♠❜r✐❞❣❡✱ ◆❩ ... ✸✹ ✏❙♣r✐♥❣✜❡❧❞s✧ ✐♥ t❤❡ ❯❙❆ ●❛r❜✐♥ ❛♥❞ ▼❛♥✐ ✭✷✵✵✺✮✿ ✹✵.✶% ♦❢ t♦♣♦♥②♠s ✐♥ ❆❋P ♥❡✇s ❙♠✐t❤ ❛♥❞ ❈r❛♥❡ ✭✷✵✵✶✮✿ ✺✼.✶% ♦❢ ◆♦rt❤ ❆♠❡r✐❝❛♥ t♦♣♦♥②♠s ✉s❡❞ ✐♥ ♥❡✇s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐s t❤❡ t❛s❦ ♦❢ ❛ss✐❣♥✐♥❣ t♦ ❛♥ ❛♠❜✐❣✉♦✉s ♣❧❛❝❡ ♥❛♠❡ ✐ts ❝♦rr❡❝t r❡❢❡r❡♥t ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ▼♦t✐✈❛t✐♦♥ ❚❤❡s✐s ❖❜❥❡❝t✐✈❡s ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❖✉t❧✐♥❡ ✶ ❙✉♠♠❛r② ■♥tr♦❞✉❝t✐♦♥ ▼♦t✐✈❛t✐♦♥ ❖❜❥❡❝t✐✈❡s ♦❢ t❤❡ P❤✳❉✳ ❚❤❡s✐s ✷ ❘❡s♦✉r❝❡s ●❡♦✲❲♦r❞◆❡t ✸ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ✹ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ✺ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ✻ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ▼♦t✐✈❛t✐♦♥ ❚❤❡s✐s ❖❜❥❡❝t✐✈❡s ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s ❙✉♠♠❛r② ❯♥❞❡r ✇❤✐❝❤ ❝♦♥❞✐t✐♦♥s ✐s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✉s❡❢✉❧ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧❄ ■♥ ❞❡t❛✐❧✿ ■s t❤❡ ❝❤♦✐❝❡ ♦❢ ❛ s♣❡❝✐✜❝ ♠❡t❤♦❞✴t♦♣♦♥②♠ r❡s♦✉r❝❡ r❡❧❡✈❛♥t❄ ❲❤✐❝❤ ❢❡❛t✉r❡s ♦❢ t❤❡ t❛r❣❡t ❝♦❧❧❡❝t✐♦♥ ♠❛② ❛✛❡❝t t❤❡ r❡s✉❧ts❄ ❍♦✇ ❞♦❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ s❝❛❧❡ ✇✐t❤ r❡s♣❡❝t t♦ t❤❡ ❣r❛♥✉❧❛r✐t② ♦❢ t❤❡ t❛s❦❄ ❲❤✐❝❤ ❧❡✈❡❧ ♦❢ ❡rr♦rs ✐♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐s r❡q✉✐r❡❞ ✐♥ ♦r❞❡r t♦ ❞❡t❡r✐♦r❛t❡ t❤❡ ♣❡r❢♦r♠❛♥❝❡ ✐♥ ■❘ t❛s❦s❄ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ▼♦t✐✈❛t✐♦♥ ❚❤❡s✐s ❖❜❥❡❝t✐✈❡s ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ▼❡t❤♦❞♦❧♦❣② ❙✉♠♠❛r② ❉❡✈❡❧♦♣ ❛♥❞ ❡✈❛❧✉❛t❡ ❞✐✛❡r❡♥t ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ♠❡t❤♦❞s P✐❝❦ ❛ t♦♣♦♥②♠ r❡s♦✉r❝❡ P✐❝❦ ❛ ❧❛❜❡❧❧❡❞ t❡st ❝♦❧❧❡❝t✐♦♥ ■♥t❡❣r❛t❡ ❚❉ ✐♥t♦ ●■❘ ❛♥❞ ◗❆ s②st❡♠s ❊✈❛❧✉❛t❡ t❤❡ ♣❡r❢♦r♠❛♥❝❡ ♦❢ t❤❡s❡ s②st❡♠s ✇✐t❤ ❛♥❞ ✇✐t❤♦✉t ❚❉ ❊✈❛❧✉❛t❡ t❤❡ ♣❡r❢♦r♠❛♥❝❡ ♦❢ t❤❡s❡ s②st❡♠s ✇✐t❤ t❤❡ ✐♥tr♦❞✉❝t✐♦♥ ♦❢ ❛rt✐✜❝✐❛❧ ❡rr♦rs ■♥s♣✐r❡❞ ❜② t❤❡ ✇♦r❦ ♦❢ ▼✳❙❛♥❞❡rs♦♥ ✭✶✾✾✹✮ ♦♥ ❲❙❉ ❢♦r ■❘ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ▼♦t✐✈❛t✐♦♥ ❚❤❡s✐s ❖❜❥❡❝t✐✈❡s ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❈❛rr✐❡❞ ♦✉t ❲♦r❦ ❉❡✈❡❧♦♣♠❡♥t ❛♥❞ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♦❢ t✇♦ ❚❉ ♠❡t❤♦❞s✿ ❲♦r❞◆❡t✲❜❛s❡❞ ❈♦♥❝❡♣t✉❛❧ ❉❡♥s✐t② ❛♥❞ ♠❛♣✲❜❛s❡❞ ❊✈❛❧✉❛t✐♦♥ ♦❢ t❤❡s❡ ♠❡t❤♦❞s ❉❡✈❡❧♦♣♠❡♥t ♦❢ t✇♦ r❡s♦✉r❝❡s ♥❡❡❞❡❞ ❢♦r t❤❡ ❡✈❛❧✉❛t✐♦♥ ●❡♦✲❲♦r❞◆❡t✿ ❲♦r❞◆❡t ✇✐t❤ ❣❡♦❣r❛♣❤✐❝❛❧ ❝♦♦r❞✐♥❛t❡s ●❡♦❙❡♠❈♦r✿ ❧❛❜❡❧❧✐♥❣ ♦❢ t♦♣♦♥②♠s ✐♥ ❙❡♠❈♦r ❆♣♣❧✐❝❛t✐♦♥ ♦❢ ❚❉ ♦♥ ❛ ✏r❡❛❧ ✇♦r❧❞✧ s❝❡♥❛r✐♦ ✭✏▲✬❆❞✐❣❡✧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥✮ ❉❡✈❡❧♦♣♠❡♥t ♦❢ ❛ ●■❘ s❡❛r❝❤ ❡♥❣✐♥❡ ✭●❡♦❲♦r❙❊✮ ❊①♣❡r✐♠❡♥ts ✇✐t❤ ●■❘ ❛♥❞ ❚❉ ❉❡✈❡❧♦♣♠❡♥t ♦❢ ❛ ◗❆ s②st❡♠ ✭❙❡♠✲◗✉❛s❛r✮ ❊①♣❡r✐♠❡♥ts ✇✐t❤ ◗❆ ❛♥❞ ❚❉ ●❡♦♦r❡❦❛✦ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ●❡♦✲❲♦r❞◆❡t ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❚♦♣♦♥②♠ ❆♠❜✐❣✉✐t② ❙✉♠♠❛r② ❚♦♣♦♥②♠ ❛♠❜✐❣✉✐t② ❝❛♥ ♠✐s❧❡❛❞ s❡❛r❝❤ ❡♥❣✐♥❡s✳✳✳ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ●❡♦✲❲♦r❞◆❡t ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❚♦♣♦♥②♠ ❆♠❜✐❣✉✐t② ❙✉♠♠❛r② ✳✳✳❛♥❞ ❡✈❡♥ ❤✉♠❛♥s✱ s♦♠❡t✐♠❡s✳✳✳ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ●❡♦✲❲♦r❞◆❡t ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❚♦♣♦♥②♠ ❘❡s♦✉r❝❡s ❏✉❞❣✐♥❣ t❤❡ ♣♦❧②s❡♠② ♦❢ ❛ t♦♣♦♥②♠ ❞❡♣❡♥❞s ♦♥ ✇♦r❧❞ ❦♥♦✇❧❡❞❣❡ ❲♦r❧❞ ❦♥♦✇❧❡❞❣❡ ✐s ❞❡t❡r♠✐♥❡❞ ❜② t❤❡ r❡s♦✉r❝❡ ✉s❡❞ ❈❧❛ss✐✜❡❞ ❛❝❝♦r❞✐♥❣ t♦✿ ✿ ❛r❡❛ ❝♦✈❡r❡❞ ✭❧♦❝❛❧ ✈s✳ ❣❧♦❜❛❧ ❢♦❝✉s✮ ❝♦✈❡r❛❣❡ ✿ ★ ♦❢ ❧✐st❡❞ t♦♣♦♥②♠s ❞❡t❛✐❧ ✿ ❝♦✈❡r❛❣❡ s❝♦♣❡ s❝♦♣❡ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ●❡♦✲❲♦r❞◆❡t ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❊①❛♠♣❧❡ ❊♥❣❧✐s❤ ❲✐❦✐♣❡❞✐❛ ●❡♦◆❛♠❡s ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ●❡♦✲❲♦r❞◆❡t ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ●❛③❡tt❡❡rs ●❛③❡tt❡❡rs ❧✐st t♦♣♦♥②♠s t♦❣❡t❤❡r ✇✐t❤ t❤❡ ♣❧❛❝❡s t❤❡② ❛r❡ r❡❢❡rr✐♥❣ t♦✱ ✉s✉❛❧❧② ✐❞❡♥t✐✜❡❞ ❜② ♠❡❛♥s ♦❢ ❣❡♦❣r❛♣❤✐❝❛❧ ❝♦♦r❞✐♥❛t❡s ❊①❛♠♣❧❡✿ P❛r✐s✱ ❚❡①❛s → ✸✸♦ ✸✾′ ◆ ✾✺♦ ✸✷′ ❲ P❛r✐s✱ ❋r❛♥❝❡ → ✹✽♦ ✺✶′ ◆ , ✷♦ ✷✶′ ❊ ... ❚❤❡② ❛r❡ ❧✐❦❡ ❝♦♠♠♦♥ ❞✐❝t✐♦♥❛r✐❡s ❧✐st✐♥❣ ✇♦r❞ ♠❡❛♥✐♥❣s ●❡♦♥❛♠❡s✱ ❲✐❦✐♣❡❞✐❛✲❲♦r❧❞ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ●❡♦✲❲♦r❞◆❡t ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ●❡♦❣r❛♣❤✐❝❛❧ ❖♥t♦❧♦❣✐❡s ❖♥t♦❧♦❣✐❡s ❛r❡ str✉❝t✉r❡❞ r❡s♦✉r❝❡s ✐♥ ✇❤✐❝❤ ♣❧❛❝❡s ❛r❡ r❡❧❛t❡❞ ❤✐❡r❛r❝❤✐❝❛❧❧②✱ ❜② ♠❡❛♥s ♦❢ ❝♦♥t❛✐♥♠❡♥t r❡❧❛t✐♦♥s❀ ❊①❛♠♣❧❡✿ P❛r✐s ∈ ❚❡①❛s ∈ ❯❙❆ ∈ ❆♠❡r✐❝❛ ∈ ❲♦r❧❞ P❛r✐s ∈ ❋r❛♥❝❡ ∈ ❊✉r♦♣❡ ∈ ❲♦r❧❞ ●❡tt② ❚●◆✱ ❨❛❤♦♦✦ ●❡♦P❧❛♥❡t✱ ✭●❡♦✲✮❲♦r❞◆❡t ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ●❡♦✲❲♦r❞◆❡t ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❈♦✈❡r❛❣❡ ❈♦♠♣❛r✐s♦♥ ❚②♣❡ ●❛③❡tt❡❡r ❖♥t♦❧♦❣✐❡s ◆❛♠❡ ❈♦♦r❞✐♥❛t❡s ●❡♦♥❛♠❡s ② ❲✐❦✐♣❡❞✐❛✲❲♦r❧❞ ② ●❡tt② ❚●◆ ② ❨❛❤♦♦✦ ●❡♦P❧❛♥❡t ♥ ❲♦r❞◆❡t ② ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ∗ ❈♦✈❡r❛❣❡ ∼ ✼, ✵✵✵, ✵✵✵ ✷✻✹, ✷✽✽ ✶, ✶✶✺, ✵✵✵ ∼ ✻, ✵✵✵, ✵✵✵ ✷, ✶✽✽ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ●❡♦✲❲♦r❞◆❡t ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❆✈❡r❛❣❡ ❆♠❜✐❣✉✐t② ❘❡s♦✉r❝❡ ❲✐❦✐♣❡❞✐❛ ✭●❡♦✮ ●❡♦♥❛♠❡s ❲♦r❞◆❡t✷✳✵ ❙✉♠♠❛r② ❯♥✐q✉❡ ♥❛♠❡s ❘❡❢❡r❡♥ts ❆♠❜✐❣✉✐t② ✶✽✵, ✵✽✻ ✷✻✹, ✷✽✽ ✶.✹✼ ✷, ✾✺✹, ✻✾✺ ✸, ✾✽✽, ✸✻✵ ✶.✸✺ ✷, ✵✻✾ ✷, ✶✽✽ ✶.✵✻ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ●❡♦✲❲♦r❞◆❡t ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ▼♦st P♦❧②s❡♠♦✉s ❚♦♣♦♥②♠s ❜② ❘❡s♦✉r❝❡ ❙✉♠♠❛r② ●❡♦♥❛♠❡s ❚♦♣♦♥②♠ ★ ♦❢ P❧❛❝❡s ❙❛♥ ❆♥t♦♥✐♦ ✶✱✺✸✻ ▼✐❧❧ ❈r❡❡❦ ✶✱✺✷✾ ❙♣r✐♥❣ ❈r❡❡❦ ✶✱✹✽✸ ❙❛♥ ❏♦sé ✶✱✸✻✵ ❉r② ❈r❡❡❦ ✶✱✷✻✾ ❙❛♥t❛ ❘♦s❛ ✶✱✶✽✺ ❇❡❛r ❈r❡❡❦ ✶✱✵✽✻ ▼✉❞ ▲❛❦❡ ✶✱✵✼✸ ❑r❛❥❛♥ ✶✱✵✸✵ ❙❛♥ ❋r❛♥❝✐s❝♦ ✾✷✾ ❲♦r❞◆❡t ❚♦♣♦♥②♠ ★ ♦❢ P❧❛❝❡s ❱✐❝t♦r✐❛ ✺ ❆❜❡r❞❡❡♥ ✹ ❈♦❧✉♠❜✐❛ ✹ ❏❛❝❦s♦♥ ✹ ❆✈♦♥ ✸ ❈♦❧✉♠❜✉s ✸ ●r❡❡♥✈✐❧❧❡ ✸ ❇❛♥❣♦r ✸ ❙❛❧❡♠ ✸ ❑✐♥❣st♦♥ ✸ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ●❡♦✲❲♦r❞◆❡t ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❖✉t❧✐♥❡ ✶ ❙✉♠♠❛r② ■♥tr♦❞✉❝t✐♦♥ ▼♦t✐✈❛t✐♦♥ ❖❜❥❡❝t✐✈❡s ♦❢ t❤❡ P❤✳❉✳ ❚❤❡s✐s ✷ ❘❡s♦✉r❝❡s ●❡♦✲❲♦r❞◆❡t ✸ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ✹ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ✺ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ✻ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ●❡♦✲❲♦r❞◆❡t ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ●❡♦✲❲♦r❞◆❡t ❲♦r❞◆❡t ❧♦❝❛t✐♦♥s ♠❛♣♣❡❞ t♦ ❧♦❝❛t✐♦♥s ✐♥ t❤❡ ❲✐❦✐♣❡❞✐❛✲❲♦r❧❞ ❣❛③❡tt❡❡r ❈♦♠♣❡♥s❛t❡s t❤❡ ❧❛❝❦ ♦❢ ❣❡♦❣r❛♣❤✐❝❛❧ ❝♦♦r❞✐♥❛t❡s ✐♥ ❲♦r❞◆❡t ▼❛♣♣✐♥❣ ❤❡✉r✐st✐❝ ❜❛s❡❞ ♦♥ ❲♦r❞◆❡t ❤♦❧♦♥②♠s ❛♥❞ ❤②♣❡r♥②♠s ❤♦❧♦♥②♠② ♣❛rt✲♦❢ ♦r ♠❡♠❜❡rs❤✐♣ ❊①❛♠♣❧❡✿ ✏❊✉r♦♣❡❵✧ ✐s ❛♥ ❤♦❧♦♥②♠ ♦❢ ✏■t❛❧②✧✱ ✏❋r❛♥❝❡✧✱ ✏❙♣❛✐♥✧✱ ❡t❝✳✳✳ ❤②♣❡r♥②♠② ✐s✲❛ r❡❧❛t✐♦♥s❤✐♣ ❊①❛♠♣❧❡✿ ✏❝✐t②✧ ✐s ❤②♣❡r♥②♠ ♦❢ ✏❘♦♠❡✧ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ●❡♦✲❲♦r❞◆❡t ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ▼❛♣♣✐♥❣ ❊①❛♠♣❧❡ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ●❡♦✲❲♦r❞◆❡t ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❆✈❛✐❧❛❜✐❧✐t② ❚❤❡ r❡s✉❧t✐♥❣ r❡s♦✉r❝❡ ✐s ❝♦♥st✐t✉t❡❞ ❜② ✷, ✵✶✷ ❧❛❜❡❧❧❡❞ s②♥❡ts ▲✐st❡❞ ❛s ❛♥ ✏♦✣❝✐❛❧✧ ❲♦r❞◆❡t ❡①♣❛♥s✐♦♥ ❤tt♣✿✴✴✇♦r❞♥❡t✳♣r✐♥❝❡t♦♥✳❡❞✉✴✇♦r❞♥❡t✴r❡❧❛t❡❞✲♣r♦❥❡❝ts✴ t❤ ✷✵✶✵✮ ❞✐✛❡r❡♥t ■t ❤❛s ❜❡❡♥ ❞♦✇♥❧♦❛❞❡❞ ❛t ✷✻✼ ✭❛s ♦❢ ❖❝t✳ ✶✾ ✐♥st✐t✉t✐♦♥s✱ ♦r❣❛♥✐③❛t✐♦♥s ❛♥❞ ♣r✐✈❛t❡ ❡♥t❡r♣r✐s❡s✱ s✉❝❤ ❛s✿ Pr❡ss✿ ◆❡✇ ❨♦r❦ ❚✐♠❡s✱ ❇❇❈ ❯♥✐✈❡rs✐t✐❡s✿ ❙t❛♥❢♦r❞✱ ❇♦st♦♥ ❯♥✐✈❡rs✐t②✱ ■♠♣❡r✐❛❧ ❈♦❧❧❡❣❡✱ ❯♥✐✈❡rs✐t② ♦❢ ❙❤❡✣❡❧❞✱ ❯◆❊❉✱ P❛r✐s ✶✵✱ P♦❧✐t❡❝♥✐❝♦ ❞✐ ▼✐❧❛♥♦✱ ❇❡r❦❡❧❡②✳✳✳ ●♦✈❡r♥♠❡♥t ❛❣❡♥❝✐❡s✿ ❯✳❙✳ ●❡♦❧♦❣✐❝❛❧ ❙✉r✈❡②✱ ❯✳❙✳ ❆r♠② ❚♦♣♦❣r❛♣❤✐❝ ❊♥❣✐♥❡❡r✐♥❣ ❈❡♥tr❡ ✳✳✳ Pr✐✈❛t❡ ❡♥t❡r♣r✐s❡s✿ ❊◆■✱ ❖r❛♥❣❡ ✳✳✳ ❋r❡❡❧② ❞✐str✐❜✉t❡❞ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❜② ♠❡❛♥s ♦❢ ❈♦♥❝❡♣t✉❛❧ ❉❡♥s✐t② ▼❡t❤♦❞ ♦r✐❣✐♥❛❧❧② ❞❡✈❡❧♦♣❡❞ ❢♦r ♥♦✉♥ s❡♥s❡ ❞✐s❛♠❜✐❣✉❛t✐♦♥ ✉s✐♥❣ s✉❜✲❤✐❡r❛r❝❤✐❡s ♦❢ ❤②♣❡r♥②♠s ❜② ❆❣✐rr❡ ❛♥❞ ❘✐❣❛✉ ✭✶✾✾✻✮ ❚♦♣♦♥②♠ ❛❞❛♣t❛t✐♦♥✿ s✉❜✲❤✐❡r❛r❝❤✐❡s ♦❢ ❤♦❧♦♥②♠s ✇ ✱ ✇✐t❤ |✇ | s❡♥s❡s❀ ✇❀ ❇✉✐❧❞ |✇ | s✉❜❤✐❡r❛r❝❤✐❡s✱ ♦♥❡ ❢♦r ❡❛❝❤ s❡♥s❡ ♦❢ ✇ ❀ ❋♦r ❡❛❝❤ s❡♥s❡ s ♦❢ ✇ ✱ ❝❛❧❝✉❧❛t❡ ❈❉s ❀ ❆ss✐❣♥ t♦ ✇ t❤❡ s❡♥s❡ ✇❤✐❝❤ ♠❛①✐♠✐s❡s ❈❉s ✳ ✶ ❙❡❧❡❝t t❤❡ ♥❡①t ❛♠❜✐❣✉♦✉s ✇♦r❞ ✷ ❙❡❧❡❝t t❤❡ ❝♦♥t❡①t ✸ ✹ ✺ ❝¯✇ ✱ ✐✳❡✳ ❛ s❡q✉❡♥❝❡ ♦❢ ✇♦r❞s✱ ❢♦r ❈❉ ❢♦r♠✉❧❛ ❈❉ (♠, ❢ , ♥) = ♠α ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐  ♠ ❧♦❣ ❢ ♥ ✭✶✮ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❈♦♥❝❡♣t✉❛❧ ❉❡♥s✐t②✿ ❊①❛♠♣❧❡ ❙♦✉r❝❡ t❡①t ❍❛rts✜❡❧❞ ❤❛s ❜❡❡♥ ♠❛②♦r ♦❢ ❆t❧❛♥t❛✱ ✇✐t❤ ❡①❝❡♣t✐♦♥ ♦❢ ♦♥❡ ❜r✐❡❢ ✐♥t❡r❧✉❞❡✱ s✐♥❝❡ ✶✾✸✼ ✳ ✳ ✳ ●❡♦r❣✐❛ ❘❡♣✉❜❧✐❝❛♥s ❛r❡ ❣❡tt✐♥❣ str♦♥❣ ❡♥❝♦✉r❛❣❡♠❡♥t t♦ ❡♥t❡r ❛ ❝❛♥❞✐❞❛t❡ ✳ ✳ ✳ ❙t❛t❡ P❛rt② ❈❤❛✐r♠❛♥ ❏❛♠❡s ❲✳ ❉♦rs❡② ❛❞❞❡❞ t❤❛t ❡♥t❤✉s✐❛s♠ ✇❛s ♣✐❝❦✐♥❣ ✉♣ ❢♦r ❛ st❛t❡ r❛❧❧② t♦ ❜❡ ❤❡❧❞ ❙❡♣t✳ ✽ ✐♥ ❙❛✈❛♥♥❛❤ ❛t ✇❤✐❝❤ ♥❡✇❧② ❡❧❡❝t❡❞ ❚❡①❛s ❙❡♥✳ ❏♦❤♥ ❚♦✇❡r ✇✐❧❧ ❜❡ t❤❡ ❢❡❛t✉r❡❞ s♣❡❛❦❡r✳ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❈♦♥❝❡♣t✉❛❧ ❉❡♥s✐t②✿ ❊①❛♠♣❧❡ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❈♦♥❝❡♣t✉❛❧ ❉❡♥s✐t②✿ ❊✈❛❧✉❛t✐♦♥ ❊✈❛❧✉❛t✐♦♥ ❝♦r♣✉s✿ ●❡♦❙❡♠❈♦r ❙❡♠❛♥t✐❝❛❧❧② ❧❛❜❡❧❡❞ ❝♦r♣✉s ❢♦r ❲❙❉ ❲❡ ❛❞❞❡❞ ❛ t❛❣ ❢♦r t♦♣♦♥②♠s ❚♦♣♦♥②♠s ✐❞❡♥t✐✜❡❞ ❜② ♠❡❛♥s ♦❢ ❤②♣❡r♥②♠② ❯s❡❞ ❢♦r ❚❉ ❡✈❛❧✉❛t✐♦♥ ✐♥ ♦t❤❡r r❡❧❛t❡❞ ✇♦r❦s✱ ❜② ❖✈❡r❡❧❧ ✭✷✵✵✾✮ ❛♥❞ ❇❡♥s❛❧❡♠ ❛♥❞ ❑❤♦❧❧❛❞✐ ✭✷✵✶✵✮ ❈✉rr❡♥t❧② t❤✐s ✐s t❤❡ ♦♥❧② ♣✉❜❧✐❝❧② ❛✈❛✐❧❛❜❧❡ ❝♦r♣✉s ❢♦r ❚❉ ❡✈❛❧✉❛t✐♦♥ ❝♦♥t❡①t s✐③❡ ♣r❡❝✐s✐♦♥ r❡❝❛❧❧ ❝♦✈❡r❛❣❡ s❡♥t❡♥❝❡ ✾✷.✷% ✼✽.✾% ✽✺.✻% ✵.✽✺✵ ♣❛r❛❣r❛♣❤ ✾✶.✼% ✼✻.✹% ✽✸.✹% ✵.✽✸✸ ❞♦❝✉♠❡♥t ✽✾.✾% ✼✼.✺% ✽✻.✷% ✵.✽✸✷ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❋✲♠❡❛s✉r❡ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❈♦♠♣❛r❛t✐✈❡ ❊✈❛❧✉❛t✐♦♥ ❈♦♠♣❛r❡❞ t♦ ❛ ♠❛♣✲❜❛s❡❞ ♠❡t❤♦❞ ♦r✐❣✐♥❛❧❧② ✐♥tr♦❞✉❝❡❞ ❜② ❙♠✐t❤ ❛♥❞ ▼❛♥♥ ✭✷✵✵✶✮✿ ▲❡t t ❜❡ ❛♥ ❛♠❜✐❣✉♦✉s t♦♣♦♥②♠ ✇✐t❤ ❝♦♥t❡①t ♦❢ s✐③❡ ♥ ❦ ♣♦ss✐❜❧❡ r❡❢❡r❡♥ts✱ ❋✐♥❞ ✐♥ ●❡♦✲❲♦r❞◆❡t t❤❡ ❝♦♦r❞✐♥❛t❡s ♦❢ ❡❛❝❤ ❝✐ ✳ ❛♠❜✐❣✉♦✉s✱ ❝♦♥s✐❞❡r ❛❧❧ ✐ts ♣♦ss✐❜❧❡ ❧♦❝❛t✐♦♥s✳ ▲❡t s❡t ♦❢ t❤❡ r❡tr✐❡✈❡❞ ♣♦✐♥ts❀ P❝ ❝ ❝ ❝ ❝ ♥ ❝ ■❢ ✐ ✐s ❝ ❜❡ t❤❡ P P ˆ = ( ✵ + ✶ + . . . + ♥ )/ ♦❢ ❝ ❀ ❛❧❧ t❤❡ ♣♦✐♥ts ❜❡✐♥❣ ♠♦r❡ t❤❛♥ ✷σ ❛✇❛② ❢r♦♠ ❈❛❧❝✉❧❛t❡ t❤❡ ❝❡♥tr♦✐❞ ❘❡♠♦✈❡ ❢r♦♠ ❈ ❝ˆ✱ ❛♥❞ r❡❝❛❧❝✉❧❛t❡ ❝ˆ ♦✈❡r t❤❡ ♥❡✇ s❡t ♦❢ ♣♦✐♥ts ✭P̄❝ ✮❀ ❈❛❧❝✉❧❛t❡ t❤❡ ❞✐st❛♥❝❡s ❢r♦♠ ❝ ˆ ♦❢ t✵ , t✶ , . . . , t❦ ❀ ❙❡❧❡❝t t❤❡ ❧♦❝❛t✐♦♥ t❥ ❤❛✈✐♥❣ ♠✐♥✐♠✉♠ ❞✐st❛♥❝❡ ❢r♦♠ ❝ ˆ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ▼❛♣✲❜❛s❡❞ ♠❡t❤♦❞✿ ❊①❛♠♣❧❡ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❘❡s✉❧ts ♦♥ ●❡♦❙❡♠❈♦r ❝♦♥t❡①t ❙❡♥t❡♥❝❡ P❛r❛❣r❛♣❤ ❉♦❝✉♠❡♥t s②st❡♠ ♣ r ❝ ❈❉ ✾✷.✷% ✼✽.✾% ✽✺.✻% ✵.✽✺✵ ▼❛♣ ✽✸.✷% ✷✼.✽% ✸✸.✺% ✵.✹✶✼ ▼❛♣✲✷σ ✽✸.✷% ✷✼.✽% ✸✸.✺% ✵.✹✶✼ ❈❉ ✾✶.✼% ✼✻.✹% ✽✸.✹% ✵.✽✸✸ ▼❛♣ ✽✹.✵% ✹✶.✻% ✹✾.✻% ✵.✺✺✼ ▼❛♣✲✷σ ✽✹.✵% ✹✶.✻% ✹✾.✻% ✵.✺✺✼ ❈❉ ✽✾.✾% ✼✼.✺% ✽✻.✷% ✵.✽✸✷ ▼❛♣ ✽✼.✾% ✼✵.✷% ✼✾.✾% ✵.✼✽✶ ▼❛♣✲✷σ ✽✻.✺% ✻✾.✷% ✼✾.✾% ✵.✼✻✽ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❋ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❖✉t❧✐♥❡ ✶ ❙✉♠♠❛r② ■♥tr♦❞✉❝t✐♦♥ ▼♦t✐✈❛t✐♦♥ ❖❜❥❡❝t✐✈❡s ♦❢ t❤❡ P❤✳❉✳ ❚❤❡s✐s ✷ ❘❡s♦✉r❝❡s ●❡♦✲❲♦r❞◆❡t ✸ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ✹ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ✺ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ✻ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❙❡t✲✉♣ ❍♦✇ ❞♦ ❚❉ ♠❡t❤♦❞s ✇♦r❦ ✐♥ ✏r❡❛❧ ✇♦r❧❞✧ ♣r♦❜❧❡♠s❄ ▲✐✈❡▼❡♠♦r✐❡s ♣r♦❥❡❝t ✭✸ ♠♦♥t❤s ✐♥t❡r♥s❤✐♣ ❛t ❋❇❑✲■❘❙❚ ✉♥❞❡r t❤❡ s✉♣❡r✈✐s✐♦♥ ♦❢ ❇❡r♥❛r❞♦ ▼❛❣♥✐♥✐✮ ❉✐s❛♠❜✐❣✉❛t❡ t♦♣♦♥②♠s ✐♥ ❛♥ ■t❛❧✐❛♥ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ✻✵✵✱✵✵✵ ♥❡✇s ❛rt✐❝❧❡s ❢r♦♠ ✏▲✬❆❞✐❣❡✧ ✷✵✵✷✲✷✵✵✻ ❈♦❧❧❡❝t✐♦♥ ♣r❡✈✐♦✉s❧② ♣r♦❝❡ss❡❞ ✇✐t❤ ❛ P❖❙ t❛❣❣❡r ❛♥❞ ❛ ◆❊❘ ✼✵, ✵✷✺ ❞✐✛❡r❡♥t t♦♣♦♥②♠s ✭✺✽.✾% ♦❝❝✉rr✐♥❣ ♦♥❧② ♦♥❝❡✮ P✉r♣♦s❡✿ s❤♦✇ ♦♥ ❛ ♠❛♣ ✇❤✐❝❤ ♣❧❛❝❡s ❛r❡ ♠❡♥t✐♦♥❡❞ ✐♥ ❛♥ ❛rt✐❝❧❡ ●r❛♥✉❧❛r✐t②✿ str❡❡t ♥❛♠❡s ❙tr❡❡t ♥❛♠❡s r❡♣r❡s❡♥t ✾.✷✻% ♦❢ ❛❧❧ t♦♣♦♥②♠s ✐♥ t❤❡ ❝♦❧❧❡❝t✐♦♥ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ▲♦❝❛❧✐t② ♦❢ t❤❡ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ▲♦❝❛❧✐t② ♦❢ t❤❡ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❆s ❛ ❝♦♠♣❛r✐s♦♥✿ ❞✐st❛♥❝❡s ❢r♦♠ ✏▲♦s ❆♥❣❡❧❡s✧ ✐♥ t❤❡ ●❡♦❈▲❊❋ ❝♦❧❧❡❝t✐♦♥ ✭▲❆ ❚✐♠❡s ✶✾✾✹ ✰ ●❧❛s❣♦✇ ❍❡r❛❧❞ ✶✾✾✺✮ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ▼♦st ❢r❡q✉❡♥t t♦♣♦♥②♠s ❙✉♠♠❛r② ●r♦✉♣❡❞ ❜② ♥❡✇s♣❛♣❡r s❡❝t✐♦♥✿ t♦♣♦♥②♠ ❚r❡♥t♦ ♣r♦✈✐♥❝✐❛ ❚r❡♥t✐♥♦ ❘♦✈❡r❡t♦ ■t❛❧✐❛ ❘♦♠❛ ❇♦❧③❛♥♦ ❝♦♠✉♥❡ ❆r❝♦ P❡r❣✐♥❡ ❛❧❧ ❢r❡q✉❡♥❝② ✷✻✵, ✽✻✸ ✶✵✾, ✷✶✷ ✾✾, ✺✺✺ ✽✽, ✾✾✺ ✽✻, ✹✻✽ ✼✵, ✽✹✸ ✺✷, ✻✺✷ ✺✷, ✵✶✺ ✸✾, ✷✶✹ ✸✺, ✾✻✶ ✐♥t❡r♥❛t✐♦♥❛❧ t♦♣♦♥②♠ ❢r❡q✉❡♥❝② ❘♦♠❛ ✸✷, ✺✹✼ ■t❛❧✐❛ ✶✾, ✾✷✸ ▼✐❧❛♥♦ ✾, ✾✼✽ ■r❛q ✾, ✵✶✵ ❯❙❆ ✽, ✽✸✸ ❚r❡♥t♦ ✽, ✷✻✾ ❊✉r♦♣❛ ✼, ✻✶✻ ■sr❛❡❧❡ ✹, ✾✵✽ ❙t❛t✐ ❯♥✐t✐ ✹, ✻✻✼ ❚r❡♥t✐♥♦ ✹, ✻✹✸ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❘✐✈❛ ❞❡❧ ●❛r❞❛ t♦♣♦♥②♠ ❢r❡q✉❡♥❝② ❆r❝♦ ✷✺, ✷✺✻ ❘✐✈❛ ✷✶, ✵✸✶ ♣r♦✈✐♥❝✐❛ ✻, ✽✾✾ ❉r♦ ✻, ✷✻✺ ❚r❡♥t♦ ✻, ✷✺✶ ❝♦♠✉♥❡ ✺, ✼✸✸ ❘✐✈❛ ❞❡❧ ●❛r❞❛ ✺, ✹✹✽ ❘♦✈❡r❡t♦ ✹, ✷✹✶ ❚♦r❜♦❧❡ ✸, ✽✼✸ ●❛r❞❛ ✸, ✽✹✵ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❇✉✐❧❞✐♥❣ ❛ ❘❡s♦✉r❝❡ Pr♦❜❧❡♠✿ str❡❡t ♥❛♠❡s ♥♦t ❝♦✈❡r❡❞ ❜② ❣❛③❡tt❡❡rs ❛♥❞ ❝✉rr❡♥t❧② ❛✈❛✐❧❛❜❧❡ r❡s♦✉r❝❡s ❙♦❧✉t✐♦♥✿ ❝♦♠❜✐♥❡ ❛ ❣❡♥❡r❛❧ ❣❛③❡tt❡❡r ✭❲✐❦✐♣❡❞✐❛✲❲♦r❧❞✮ ✇✐t❤ ❞❛t❛ ❢r♦♠ ❛ ✇❡❜✲❜❛s❡❞ s❡r✈✐❝❡ ✭●♦♦❣❧❡ ▼❛♣s ❣❡♦❝♦❞✐♥❣✮ ▲✬❆❞✐❣❡ r❡♣♦s✐t♦r② ❲✐❦✐♣❡❞✐❛✲❲♦r❧❞ ●❡♦♥❛♠❡s ❲♦r❞◆❡t✷✳✵ ❯♥✐q✉❡ ♥❛♠❡s ❘❡❢❡r❡♥ts ❛✈❣✳ ❛♠❜✐❣✉✐t② , ✶✽✵, ✵✽✻ ✷, ✾✺✹, ✻✾✺ ✷, ✵✻✾ , ✷✻✹, ✷✽✽ ✸, ✾✽✽, ✸✻✵ ✷, ✶✽✽ ✹ ✻✽ ✶✸ ✸✷✹ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ✻✷ ✹✵✽ . ✶.✹✼ ✶.✸✺ ✶.✵✻ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❙tr❡❡t ♥❛♠❡s ❛♠❜✐❣✉✐t② ❍✐❣❤❡r ❛♠❜✐❣✉✐t② ❞✉❡ t♦ str❡❡t ♥❛♠❡s✿ P (❋ ) ♣r♦❜❛❜✐❧✐t② ♦❢ ✜♥❞✐♥❣ ❛♥ ❛♠❜✐❣✉♦✉s t♦♣♦♥②♠ ❛t ❢r❡q✉❡♥❝② ❋ ✿ P (❋ ) = ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ |❚❛♠❜❋ | |❚❋ | ✭✷✮ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❙tr❡❡t ♥❛♠❡s ❛♠❜✐❣✉✐t② ❘❡❛s♦♥s✿ ◆❛♠✐♥❣ ❛❢t❡r ❢❛♠♦✉s ♣❡♦♣❧❡ ♦r ❤✐st♦r✐❝❛❧ ❞❛t❡s✿ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❙tr❡❡t ♥❛♠❡s ❛♠❜✐❣✉✐t② ◆❛♠✐♥❣ ❛❢t❡r ❛ ❝✐t② t❤❡ r♦❛❞ ✐s ♣♦✐♥t✐♥❣ t♦✿ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❙tr❡❡t ♥❛♠❡s ❛♠❜✐❣✉✐t② ▲❛r❣❡ r♦❛❞ ❝r♦ss✐♥❣ ❛❞♠✐♥✐str❛t✐✈❡ ❜♦✉♥❞❛r✐❡s✿ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❉✐s❛♠❜✐❣✉❛t✐♥❣ str❡❡t ♥❛♠❡s ❈❛♥♥♦t ✉s❡ s✐❜❧✐♥❣s✿ ❊①❛♠♣❧❡ ✏❱✐❛ ▼❛♥t♦✈❛✧✿ ✹ ♣♦ss✐❜✐❧✐t✐❡s ✐♥ t❤❡ ❚r❡♥t♦ ♣r♦✈✐♥❝❡ ♦♥❧② ✿ ❱✐❛ ▼❛♥t♦✈❛✱ ❆r❝♦ ✭❚◆✮✱ ❚r❡♥t✐♥♦✲❆❧t♦ ❆❞✐❣❡✱ ■t❛❧✐❛ ❱✐❛ ▼❛♥t♦✈❛✱ ❇r❡♥t♦♥✐❝♦ ✭❚◆✮✱ ❚r❡♥t✐♥♦✲❆❧t♦ ❆❞✐❣❡✱ ■t❛❧✐❛ ❱✐❛ ▼❛♥t♦✈❛✱ ❈❛❞❡r③♦♥❡ ✭❚◆✮✱ ❚r❡♥t✐♥♦✲❆❧t♦ ❆❞✐❣❡✱ ■t❛❧✐❛ ❱✐❛ ▼❛♥t♦✈❛✱ ✸✽✶✵✵ ❚r❡♥t♦ ✭❚◆✮✱ ❚r❡♥t✐♥♦✲❆❧t♦ ❆❞✐❣❡✱ ■t❛❧✐❛ ⇒ ❈♦♥❝❡♣t✉❛❧ ❉❡♥s✐t② ♥♦t ♣♦ss✐❜❧❡ ⇒ ❯s❡ t❤❡ ♠❛♣✲❜❛s❡❞ ♠❡t❤♦❞ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❆ ❝❛s❡ st✉❞②✿ ❚❉ ✐♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❉✐s❛♠❜✐❣✉❛t✐♥❣ str❡❡t ♥❛♠❡s ■❞❡❛✿ t♦ t❛❦❡ ✐♥t♦ ❛❝❝♦✉♥t ❧♦❝❛❧✐t② ❛♥❞ ✏❛✉t❤♦r✐t②✧ ♦❢ ♠♦st ❢r❡q✉❡♥t t♦♣♦♥②♠s ✏❚r❡♥t♦✧ ❛❞❞❡❞ t♦ ❝♦♥t❡①t ❈❡♥tr♦✐❞ ♣♦s✐t✐♦♥ ♠♦❞✐✜❡❞ ❜② ❢r❡q✉❡♥❝✐❡s✿ ❋ (❝ ) ✐ ( ❥ ) = ∑❝ ∈❈ (❞ (❝ ,s ))✷ ❀ ✐ ▼ ✐ ❥ ❘❡s♦❧✈❡ ✇✐t❤ s = ❛r❣s ∈❙ ♠❛① ❋✐ (s❥ )✳ ❥ ❋ s ✐ ❊✈❛❧✉❛t✐♦♥ ♦✈❡r ❛ s❡t ♦❢ ✶, ✵✷✹ ♠❛♥✉❛❧❧② ❧❛❜❡❧❧❡❞ t♦♣♦♥②♠s ❡①tr❛❝t❡❞ ❢r♦♠ ❛ s❡t ♦❢ ✶✺✵ r❛♥❞♦♠❧② s❡❧❡❝t❡❞ ❞♦❝✉♠❡♥ts ♠❡t❤♦❞ ♣r❡❝✐s✐♦♥ r❡❝❛❧❧ ❋✲♠❡❛s✉r❡ ♠❛♣✰❢r❡q✰❧♦❝❛❧ ✽✽.✽✶% ✽✽.✼✸% ✵.✽✽✽ ♠❛♣✰❧♦❝❛❧ ✼✾.✸✻% ✼✾.✷✽% ✵.✼✾✸ ❜❛s❡❧✐♥❡ ✭♦♥❧② ♠❛♣✮ ✼✽.✾✼% ✼✽.✾✵% ✵.✼✽✾ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❊①♣❡r✐♠❡♥t❛❧ s❡t✲✉♣ ●❡♦❲♦r❙❊✭●❊❖❣r❛♣❤✐❝❛❧ ❲❖❘❞♥❡t ❙❡❛r❝❤ ❊♥❣✐♥❡✮ ❑❡②✇♦r❞✲❜❛s❡❞ r❛♥❦✐♥❣ ✇✐t❤ ♦r ✇✐t❤♦✉t t♦♣♦♥②♠ ❞✐s❛♠❜✐❣✉❛t✐♦♥ ●❡♦❣r❛♣❤✐❝❛❧❧② ❆❞❥✉st❡❞ ❘❛♥❦✐♥❣ ✭●❆❘✮ ✇✐t❤ ♦r ✇✐t❤♦✉t t♦♣♦♥②♠ ❞✐s❛♠❜✐❣✉❛t✐♦♥ ❆rt✐✜❝✐❛❧ ❚❉ ❡rr♦rs ♦♥ ❈▲■❘✲❲❙❉ ❝♦❧❧❡❝t✐♦♥ ❚♦♣♦♥②♠ r❡s♦✉r❝❡s✿ ✭●❡♦✲✮❲♦r❞◆❡t✱ ●❡♦♥❛♠❡s ■❘ ❝♦❧❧❡❝t✐♦♥✿ ●❡♦❈▲❊❋✱ ❈▲■❘✲❲❙❉ ❚♦♣✐❝s ❢r♦♠ ●❡♦❈▲❊❋ ✷✵✵✺✲✷✵✵✽ ❝♦♥❢✳ ❚✐t❧❡ ❖♥❧② ❚✐t❧❡ ❉❡s❝ ❆❧❧ ❋✐❡❧❞s ❛✈❣✳ q✉❡r② ❧❡♥❣t❤ . ✶✼.✾✻ ✺✷.✹✻ ✺ ✼✹ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ # t♦♣♦♥②♠s ✾✵ # ❛♠❜✳ t♦♣♦♥②♠s ✷✺ ✶✸✷ ✹✷ ✺✸✽ ✶✸✺ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ●❡♦❲♦r❙❊✿ ■♥❞❡①✐♥❣ ♠♦❞✉❧❡ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ●❡♦❲♦r❙❊✿ ❙❡❛r❝❤ ♠♦❞✉❧❡ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ●❡♦❲♦r❙❊✿ ❙❡❛r❝❤ ♣❤❛s❡ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✈s✳ ♥♦ ❞✐s❛♠❜✐❣✉❛t✐♦♥ ❆❧❧ ✜❡❧❞s✿ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✈s✳ ♥♦ ❞✐s❛♠❜✐❣✉❛t✐♦♥ ❚✐t❧❡ ❛♥❞ ❉❡s❝r✐♣t✐♦♥✿ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✈s✳ ♥♦ ❞✐s❛♠❜✐❣✉❛t✐♦♥ ❚✐t❧❡ ♦♥❧②✿ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✈s✳ ♥♦ ❞✐s❛♠❜✐❣✉❛t✐♦♥ ▼❆P ❝♦♠♣❛r✐s♦♥✿ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✈s✳ ♥♦ ❞✐s❛♠❜✐❣✉❛t✐♦♥ ❯s✐♥❣ ●❆❘✿ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❙✐♠✉❧❛t❡❞ ❡rr♦rs ❚❛r❣❡t ❝♦❧❧❡❝t✐♦♥✿ ❈▲■❘✲❲❙❉✱ ❛✉t♦♠❛t✐❝❛❧❧② ❧❛❜❡❧❧❡❞ ✇✐t❤ ❲◆✶✳✻ s❡♥s❡s ✭❆❣✐rr❡✱ ✷✵✵✽✮ ⇒ ♥♦t ❛ ✶✵✵% ❛❝❝✉r❛t❡ ❧❛❜❡❧❧✐♥❣ ❆ ♣❡r❝❡♥t❛❣❡ ♦❢ ♠♦♥♦s❡♠✐❝ t♦♣♦♥②♠s ✇❡r❡ ❛ss✐❣♥❡❞ ❛♥ ❤♦❧♦♥②♠ t❤❛t ✐s ♥♦t t❤❡✐r ❛❝t✉❛❧ ❤♦❧♦♥②♠ ❙✐♠✉❧❛t❡❞ ❡rr♦r ❧❡✈❡❧s✿ ✶✵%, ✷✵%, ✸✵%, ✹✵%, ✺✵%, ✻✵% ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❙✐♠✉❧❛t❡❞ ❡rr♦rs✿ r❡s✉❧ts ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❊①♣❡r✐♠❡♥t❛❧ s❡t✲✉♣ ◗❆ s②st❡♠✿ ❙❡♠◗✉❛s❛r ✭❈▲❊❋ ❘♦❜✉st ❲❙❉✲◗❆ ✷✵✵✾ ♣❛rt✐❝✐♣❛t✐♦♥✮ ◗✉❡st✐♦♥s✿ ✼✼ q✉❡st✐♦♥s ❢r♦♠ t❤❡ ❈▲❊❋✲◗❆ ✷✵✵✺ ❛♥❞ ✷✵✵✻ ❝r♦ss✲❧✐♥❣✉❛❧ ❊♥❣❧✐s❤✲❙♣❛♥✐s❤ t❡st s❡ts ❚❡st ❝♦❧❧❡❝t✐♦♥✿ ❈▲■❘✲❲❙❉ ✇✐t❤ s✐♠✉❧❛t❡❞ ❡rr♦rs ✭s❛♠❡ ❛s ●■❘ ❡①♣❡r✐♠❡♥ts✮ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙❡♠◗✉❛s❛r ❙✉♠♠❛r② ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❚❉ ✐♥ ◗❆✿ r❡s✉❧ts ✭s✐♠✉❧❛t❡❞ ❡rr♦rs✮ r✉♥ ❈▲■❘✲❲❙❉ ✶✵✪ ❡rr♦r ✷✵✪ ❡rr♦r ✸✵✪ ❡rr♦r ✹✵✪ ❡rr♦r ✺✵✪ ❡rr♦r ✻✵✪ ❡rr♦r ❘ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❳ ✷ ✵ ✵ ✵ ✵ ✵ ✵ ❯ ❆❝❝✉r❛❝② ✵ ✶✸✳✷✶✪ ✶ ✶✸✳✷✶✪ ✵ ✶✸✳✷✶✪ ✵ ✶✸✳✷✶✪ ✵ ✶✸✳✷✶✪ ✵ ✶✸✳✷✶✪ ✵ ✶✸✳✷✶✪ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❊✈❛❧✉❛t✐♦♥ ♦❢ ♣❛ss❛❣❡ r❡tr✐❡✈❛❧ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ●❡♦♦r❡❦❛✦ ❆ ❣❡♦❣r❛♣❤✐❝❛❧❧② ❝♦♥str❛✐♥❡❞ ✐♥❢♦r♠❛t✐♦♥ ♥❡❡❞ ♠❛② ❜❡ ❡①♣r❡ss❡❞ ✐♥ ❛ ❜❡tt❡r ✇❛② ✇✐t❤ ❛ ♠❛♣✲❜❛s❡❞ ✉s❡r ✐♥t❡r❢❛❝❡ ◆❛t✉r❛❧ ❧❛♥❣✉❛❣❡✿ ✐♠♣r❡❝✐s❡ ❜✉t s❤♦rt ❛♥❞ ❞❡s❝r✐♣t✐✈❡ ●❡♦❣r❛♣❤②✿ ♣r❡❝✐s❡ ❜✉t ❝♦♠♣❧❡① ❙P■❘■❚ Pr♦❥❡❝t ✭❈✳❇✳ ❏♦♥❡s ❡t ❛❧ ✭✷✵✵✷✮✮ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ●❡♦♦r❡❦❛✦ ▼❛✐♥ ♣❛❣❡ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ●❡♦♦r❡❦❛✦ ❆r❝❤✐t❡❝t✉r❡ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❙❡❧❡❝t✐♦♥ ♦❢ r❡❧❡✈❛♥t q✉❡r✐❡s ❚ ˆ(❚ ∩ ● ) = ♣ (● )♣ (❚ ) ✭✐♥❞❡♣❡♥❞❡♥❝❡ ❛ss✉♠♣t✐♦♥✮✿ ♣ ♣(❳ ) = ❢r❡q (❳ )/ ♠❛①❢r❡q(✇ ) ✇ ∈ Ω ▼✉t✉❛❧ ✐♥❢♦r♠❛t✐♦♥ ♦❢ ● ❛♥❞ ❚ ✿ ■ (❚ ; ● ) = ♣(❚ ∩ ● ) ❧♦❣ ♣♣((❚❚)∩♣(●●)) ❊①♣❡❝t❡❞ ❝♦✲♦❝❝✉rr❡♥❝❡ ♦❢ ♣❧❛❝❡ ● ❛♥❞ t❤❡♠❡ ❊①❛♠♣❧❡ ❢ (“♣❡st♦ ”) = ✷✾, ✼✵✵, ✵✵✵ ⇒ ♣(“♣❡st♦ ”) = ✷✾, ✼✵✵, ✵✵✵/✷, ✶✹✼, ✹✸✻, ✷✹✹ = ✵.✵✶✹ ❢ (“●❡♥♦✈❛”) = ✹✷✵, ✽✶✼ ⇒ ♣(“●❡♥♦✈❛”) = ✹✷✵, ✽✶✼/✷, ✶✹✼, ✹✸✻, ✷✹✹ = ✵.✵✵✵✷ ♣(“♣❡st♦ ” ∩ “●❡♥♦✈❛”) = ✵.✵✵✵✷ · ✵.✵✶✹ = ✵.✵✵✵✵✵✷✽ ■ (“♣❡st♦ ”; “●❡♥♦✈❛”) = ✵.✵✵✶✶ ✭■ (“♣❡st♦ ”; “❚♦r✐♥♦ ”) = ✵.✵✵✵✵✷✮ ❊①♣❡❝t❡❞ ♣❛❣❡ ❝♦✉♥t ✻, ✵✶✸❀ ❛❝t✉❛❧✿ ✶✵✸, ✵✵✵ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❊①❛♠♣❧❡ r❡s✉❧ts ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❊✈❛❧✉❛t✐♦♥ ♦♥ ●❡♦❈▲❊❋ ●❡♦❈▲❊❋ ✷✵✵✺ t❡st s❡t ●❡♦❲♦r❙❊ ✭❦❡②✇♦r❞✲❜❛s❡❞✮ ●❡♦♦r❡❦❛✦ ✭♠❛♣✲❜❛s❡❞✮ ✇✐t❤ ❢✉s✐♦♥ ♦r ♥♦t t♦♣✐❝ ❛✈❣✳ ▼❘❘ ●❡♦♦r❡❦❛✦ ●❡♦♦r❡❦❛✦ ●❡♦❲◆ ✭◆♦ ❋✉s✐♦♥✮ ✭✰ ❇♦r❞❛ ❋✉s✐♦♥✮ ✵✳✻✶✷ ✵✳✼✺✻ ✵✳✹✾✼ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ●❡♦❣r❛♣❤✐❝❛❧ ❉✐✈❡rs✐t② ✐♥ ❘❡s✉❧ts ▼❘❘ ❢♦r ❡❛❝❤ ❞✐✛❡r❡♥t ❧♦❝❛t✐♦♥ r❡tr✐❡✈❡❞ t♦♣✐❝ ✶st ✷♥❞ ✸r❞ ✹t❤ ✶✳✵✵✵ ✵✳✵✵✵ ✵✳✺✵✵ ✶✳✵✵✵ ●❈✲✵✵✷ ▲♦♥❞♦♥ ■t❛❧② ▼♦s❝♦✇ ❇❡❧❣✐✉♠ ✶✳✵✵✵ ✶✳✵✵✵ ✵✳✵✵✵ ✶✳✵✵✵ ●❈✲✵✵✸ ❍❛✐t✐ ▼❡①✐❝♦ ●✉❛t❡♠❛❧❛ ❇r❛③✐❧ ✶✳✵✵✵ ✶✳✵✵✵ ●❈✲✵✵✺ ❏❛♣❛♥ ❚♦❦②♦ ✶✳✵✵✵ ✵✳✷✵✵ ✶✳✵✵✵ ✶✳✵✵✵ ●❈✲✵✵✼ ❯❑ ■r❡❧❛♥❞ ❊✉r♦♣❡ ❇❡❧❣✐✉♠ ✺t❤ ✶✳✵✵✵ ●❡r♠❛♥② ✵✳✵✵✵ ❈❤✐❧❡ ✵✳✵✵✵ ❋r❛♥❝❡ ... ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❚♦♣♦♥②♠ ❛♠❜✐❣✉✐t② ✐♥ ♣❧❛❝❡ ♣r♦❜❛❜✐❧✐t② ❡st✐♠❛t✐♦♥ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❈♦♥tr✐❜✉t✐♦♥s ●❡♦✲❲♦r❞◆❡t ❛♥❞ ●❡♦❙❡♠❈♦r❀ ❚❤❡ st✉❞② ♦♥ t❤❡ ✏▲✬❆❞✐❣❡✧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥ ❤✐❣❤❧✐❣❤t❡❞ t❤❡ ♣r♦❜❧❡♠s t❤❛t ❝♦✉❧❞ ❜❡ ❢♦✉♥❞ ✇❤✐❧❡ ✇♦r❦✐♥❣ ♦♥ ❛ ❧♦❝❛❧ ♥❡✇s ❝♦❧❧❡❝t✐♦♥✱ ✇✐t❤ ❛ str❡❡t ❧❡✈❡❧ ❣r❛♥✉❧❛r✐t②❀ ❚❤❡ ❞❡s✐❣♥ ❛♥❞ t❤❡ ❡✈❛❧✉❛t✐♦♥ ♦❢ t❤❡ ❈❉ ❛♥❞ ♠❛♣✲❜❛s❡❞ ❞✐s❛♠❜✐❣✉❛t✐♦♥ ♠❡t❤♦❞s❀ ❊①♣❡r✐♠❡♥ts t♦ ❞❡t❡r♠✐♥❡ ✉♥❞❡r ✇❤✐❝❤ ❝♦♥❞✐t✐♦♥s ❚❉ ♠❛② ❜❡ ✉s❡❞ t♦ ✐♠♣r♦✈❡ t❤❡ ♣❡r❢♦r♠❛♥❝❡ ✐♥ ●■❘ ❛♥❞ ◗❆❀ ❊①♣❡r✐♠❡♥ts t♦ ❞❡t❡r♠✐♥❡ t❤❡ r❡❧❛t✐♦♥ ❜❡t✇❡❡♥ ❡rr♦r ❧❡✈❡❧s ✐♥ ❚❉ ❛♥❞ r❡s✉❧ts ✐♥ ●■❘ ❛♥❞ ◗❆❀ ■♠♣❧❡♠❡♥t❛t✐♦♥ ♦❢ ❛ ♣r♦t♦t②♣❡ s❡❛r❝❤ ❡♥❣✐♥❡ ✭●❡♦♦r❡❦❛✦✮ t❤❛t ❡①♣❧♦✐ts ❝♦✲♦❝❝✉rr❡♥❝❡s ♦❢ t♦♣♦♥②♠s ❛♥❞ ❝♦♥❝❡♣ts✳ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❆♥❛❧②s✐s ❙✉♠♠❛r② ❚♦♣♦♥②♠ ❞✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ✐s ✉s❡❢✉❧ ♦♥❧② ✐❢ t❤❡ r❡s♦✉r❝❡ ✐s ❤✐❣❤❧② ❞❡t❛✐❧❡❞ ❛♥❞ t♦♣✐❝s ❛r❡ s❤♦rt ❍♦✇❡✈❡r✿ s♠❛❧❧ ✐♠♣r♦✈❡♠❡♥ts✱ ✐rr❡❧❡✈❛♥t ❞✐✛❡r❡♥❝❡s ❡✈❡♥ ✇❤❡♥ ✻✵% ❡rr♦rs ❛r❡ ✐♥tr♦❞✉❝❡❞ ❚❉ ❞♦❡s ♥♦t r❡♣r❡s❡♥t ❛♥ ✐ss✉❡ ❢♦r ◗❆ ❚♦♦ ♠❛♥② ❡rr♦rs ❞❡r✐✈❡❞ ❢r♦♠ ♦t❤❡r ❝r✐t✐❝❛❧ ❝♦♠♣♦♥❡♥ts ✐♥ ◗❆ s②st❡♠s ■t✬s ❞✐✣❝✉❧t t♦ ❝♦rr❡❝t❧② ❡st✐♠❛t❡ t❤❡ ♣r♦❜❛❜✐❧✐t✐❡s ❢♦r t❤❡ ❝♦✲♦❝❝✉rr❡♥❝❡s ♦❢ ♣❧❛❝❡ ❛♥❞ ❡✈❡♥ts s✐♥❝❡ ♣❧❛❝❡ ♥❛♠❡s ✐♥ t❤❡ ✇❡❜ ❛r❡ ♥♦t ❞✐s❛♠❜✐❣✉❛t❡❞ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ❋✉t✉r❡ ❲♦r❦s ❊①♣❡r✐♠❡♥ts ✇✐t❤ ▲●▲ ❝♦❧❧❡❝t✐♦♥ ❜② ❉✳▲✐❡❜❡r♠❛♥♥ ❈♦♠♣❛r✐s♦♥ ✇✐t❤ ♦✛✲t❤❡✲s❤❡❧❢ ♠❡t❤♦❞s ✭❨❛❤♦♦✦ ♣❧❛❝❡♠❛❦❡r✮ ❉✐✛❡r❡♥t ■❘ ♠♦❞❡❧s❄ ●❡♦♦r❡❦❛✦ ✐♥t❡r❢❛❝❡ t♦ ❜❡ ✐♠♣r♦✈❡❞ ❯s❡r✲❜❛s❡❞ ❡✈❛❧✉❛t✐♦♥ ♦❢ ●❡♦♦r❡❦❛✦ ❞✐✈❡rs✐✜❡❞ r❡s✉❧ts ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧ ■♥tr♦❞✉❝t✐♦♥ ❘❡s♦✉r❝❡s ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ●■❘ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ◗❆ ❚❉ ✐♥ t❤❡ ❲❡❜✿ ●❡♦♦r❡❦❛✦ ❙✉♠♠❛r② ■♠♣❛❝t ♦❢ ❘❡s❡❛r❝❤ ●❡♦✲❲♦r❞◆❡t✱ ●❡♦❙❡♠❈♦r ✉s❡❞ ❜② ♦t❤❡r r❡s❡❛r❝❤❡rs ❆♣♣r♦①✳ ✻✵ r❡❧❛t❡❞ ♣✉❜❧✐❝❛t✐♦♥s ❇✉s❝❛❧❞✐ ❉✳✱ ❘♦ss♦ P✳✱ ●ó♠❡③ ❏✳▼✳✱ ❙❛♥❝❤✐s ❊✳ ✭✷✵✵✾✮ ❆♥s✇❡r✐♥❣ ◗✉❡st✐♦♥s ✇✐t❤ ❛♥ ♥✲❣r❛♠ ❜❛s❡❞ P❛ss❛❣❡ ❘❡tr✐❡✈❛❧ ❊♥❣✐♥❡✳ ■♥✿ ❏♦✉r♥❛❧ ♦❢ ■♥t❡❧❧✐❣❡♥t ■♥❢♦r♠❛t✐♦♥ ❙②st❡♠s✱ ✈♦❧✳ ✸✹✱ ♣♣✳ ✶✶✸✲✶✸✹✳ ❙♣r✐♥❣❡r✳ ❇✉s❝❛❧❞✐ ❉✳✱ ❘♦ss♦ P✳ ✭✷✵✵✽✮ ❆ ❝♦♥❝❡♣t✉❛❧ ❞❡♥s✐t②✲❜❛s❡❞ ❛♣♣r♦❛❝❤ ❢♦r t❤❡ ❞✐s❛♠❜✐❣✉❛t✐♦♥ ♦❢ t♦♣♦♥②♠s✳ ■♥✿ ■♥t❡r♥❛t✐♦♥❛❧ ❏♦✉r♥❛❧ ♦❢ ●❡♦❣r❛♣❤✐❝❛❧ ■♥❢♦r♠❛t✐♦♥ ❙❝✐❡♥❝❡✱ ✷✷ ✭✸✮✿ ✶✹✸✲✶✺✸✳ ❚❛②❧♦r ❛♥❞ ❋r❛♥❝✐s✳ ❙♣❡❝✐❛❧ ■ss✉❡ ♦♥ ●❡♦❣r❛♣❤✐❝❛❧ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧✳ ❊❞✐t♦rs✿ ❈❤r✐s ❏♦♥❡s ❛♥❞ ❘♦ss P✉r✈❡s✳ ❤✲✐♥❞❡①✿ ✶✶✱ ❣✲✐♥❞❡①✿ ✶✺ ❉❛✈✐❞❡ ❇✉s❝❛❧❞✐ ❚♦♣♦♥②♠ ❉✐s❛♠❜✐❣✉❛t✐♦♥ ✐♥ ■♥❢♦r♠❛t✐♦♥ ❘❡tr✐❡✈❛❧