Chapter P♦r♦✉s s✐❧✐❝♦♥ ❉✐str✐❜✉t❡❞ ❇r❛❣❣ r❡✌❡❝t♦rs ❚❤✐s ❈❤❛♣t❡r ❞❡s❝r✐❜❡s t❤❡ ❢❛❜r✐❝❛t✐♦♥ ♦❢ ❉✐str✐❜✉t❡❞ ❇r❛❣❣ ❘❡✌❡❝t♦r ✇✐t❤ P❙✐ ❛♥❞ t❤❡ ❡☛❡❝t ♦❢ ✐♦♥ ✐rr❛❞✐❛t✐♦♥ ♦♥ t❤❡✐r ❢♦r♠❛t✐♦♥✳ ❆❢t❡r ❝❤❛r❛❝t❡r✐③❛t✐♦♥ ❛♥❞ ♦♣t✐♠✐③❛t✐♦♥✱ ✈❛r✲ ✐♦✉s ♥♦✈❡❧ P❙✐ ❜❛s❡❞ ❉❇❘ str✉❝t✉r❡s ✇❡r❡ ❢❛❜r✐❝❛t❡❞✳ ■♥ ❛❞❞✐t✐♦♥✱ ❈❤❛♣t❡r ✺✳✺ ❞❡s❝r✐❜❡s t❤❡ ✉s❡ ♦❢ t❤❡ ❧❛r❣❡ ❛r❡❛ ✐rr❛❞✐❛t✐♦♥ ❢❛❝✐❧✐t② t♦❣❡t❤❡r ✇✐t❤ ❯❱ ❧✐t❤♦❣r❛♣❤② t♦ ♣r♦❞✉❝❡ ❧❛r❣❡ ❛rr❛②s ♦❢ ✐rr❛❞✐❛t❡❞ P❙✐ ❉❇❘s✱ ❞❡♠♦♥str❛t✐♥❣ t❤❡ ♠❛ss ♣r♦❞✉❝t✐♦♥✴✉♣s❝❛❧✐♥❣ ❝❛♣❛❜✐❧✐t✐❡s ♦❢ ♦✉r ♠❛❝❤✐♥✐♥❣ t❡❝❤♥✐q✉❡✳ ✺✳✶ ❉✐str✐❜✉t❡❞ ❇r❛❣❣ r❡✌❡❝t♦rs ❆ ❞✐❡❧❡❝tr✐❝ ♠✐rr♦r✱ ❛❧s♦ ❝❛❧❧❡❞ ❛ ❉✐str✐❜✉t❡❞ ❇r❛❣❣ r❡✌❡❝t♦r ✭❉❇❘✮ ✐s ❛ str✉❝t✉r❡ ❢♦r♠❡❞ ❢r♦♠ ❛ ♣❡r✐♦❞✐❝ ♠✉❧t✐❧❛②❡r ❝♦♠♣r✐s✐♥❣ ❛❧t❡r♥❛t✐♥❣ ❤✐❣❤ ❛♥❞ ❧♦✇ r❡❢r❛❝t✐✈❡ ✐♥❞❡① ❧❛②❡rs ✭❋✐❣ ✺✳✶✮✳ ❚❤✐s ❞❡s✐❣♥ ❝r❡❛t❡s ❛ r❡❣✐♦♥ ♦❢ ❤✐❣❤ r❡✌❡❝t✐✈✐t② ✇❤❡r❡ ❛ r❛♥❣❡ ♦❢ ✇❛✈❡❧❡♥❣t❤s ♦❢ ✇✐❞t❤ ✹✕ t❤❛t ✐s ❝❡♥t❡r❡❞ ♦♥ t❤❡ ❞❡s✐❣♥❡❞ r❡s♦♥❛♥t ✇❛✈❡❧❡♥❣t❤ ✕ ✇✐❧❧ ❜❡ r❡✌❡❝t❡❞✳ ❊❛❝❤ ❧❛②❡r ✇✐t❤✐♥ t❤❡ ♠✉❧t✐❧❛②❡r ❤❛s ❛ t❤✐❝❦♥❡ss ❞ ❛♥❞ r❡❢r❛❝t✐✈❡ ✐♥❞❡① ♥✳ ❚❤✐s ❣✐✈❡s ❡❛❝❤ ❧❛②❡r ❛♥ ♦♣t✐❝❛❧ t❤✐❝❦♥❡ss ♦❢ ♥❞✱ ✇❤✐❝❤ s❤♦✉❧❞ ❡q✉❛❧ ✕✴✹✳ ❈♦♠♣♦♥❡♥ts ♦❢ ❛♥ ✐♥❝✐❞❡♥t ✇❤✐t❡ ❧✐❣❤t ♦♥ t❤❡ s✉r❢❛❝❡ ♦❢ ❛ ❉❇❘ ❛r❡ r❡✌❡❝t❡❞ ❛t s✉❝❝❡ss✐✈❡ ❜♦✉♥❞❛r✐❡s ✭❋✐❣ ✺✳✶✮ t❤r♦✉❣❤♦✉t t❤❡ ❛ss❡♠❜❧② ❛♥❞ r❡❛♣♣❡❛r ❛t t❤❡ s✉r❢❛❝❡ ❛❧❧ ✐♥ ♣❤❛s❡✳ ❚❤❡s❡ ❝♦♠♣♦♥❡♥ts t❤❡♥ r❡❝♦♠❜✐♥❡ ❝♦♥str✉❝t✐✈❡❧② r❡s✉❧t✐♥❣ ✐♥ ❛ r❡✌❡❝t❡❞ ♣❡❛❦ ♦❢ ✇✐❞t❤ ✹✕ ❝❡♥t❡r❡❞ ♦♥ ✕✳ ❈♦♥s❡q✉❡♥t❧②✱ t❤❡ ❡☛❡❝t✐✈❡ r❡✌❡❝t❛♥❝❡ ❝❛♥ ❜❡ ♠❛❞❡ ✈❡r② ❤✐❣❤ ❜② ✐♥❝r❡❛s✐♥❣ t❤❡ ♥✉♠❜❡r ♦❢ t❤❡ ❧❛②❡rs ✭❋✐❣ ✺✷ ✺✺ ✸✳ ❚❤❡ r❡❢r❛❝t✐✈❡ ✐♥❞❡① ♦❢ P❙✐✱ ♥✱ ❞❡♣❡♥❞s ♦♥ ✐ts ♣♦r♦s✐t②✳ ❚❤❡r❡❢♦r❡✱ ❜② ✈❛r②✐♥❣ t❤❡ ❝✉rr❡♥t ❞❡♥s✐t② ❞✉r✐♥❣ t❤❡ ❡❧❡❝tr♦❝❤❡♠✐❝❛❧ ❛♥♦❞✐③❛t✐♦♥ ♣r♦✲ ❝❡ss✱ ✐t ✐s ♣♦ss✐❜❧❡ t♦ ✈❛r② t❤❡ ♣♦r♦s✐t②✴r❡❢r❛❝t✐✈❡ ✐♥❞✐❝❡s ✐♥ t❤❡ ❛♥♦❞✐③❛t✐♦♥ ❞✐r❡❝t✐♦♥✳ ■♥ t❤✐s ✇❛②✱ ❛♥ ❛❧t❡r♥❛t✐♥❣ ♥ ✈❡rs✉s ❞❡♣t❤ ♣r♦☞❧❡ ♠❛② ❜❡ ❛❝❤✐❡✈❡❞✳ P❙✐ ❧❛②❡rs ♦❢ ❛❧t❡r♥❛t✲ ✐♥❣ ♣♦r♦s✐t②✴r❡❢r❛❝t✐✈❡ ✐♥❞✐❝❡s ❛r❡ ❡ss❡♥t✐❛❧❧② ❉❇❘ str✉❝t✉r❡s ✇❤✐❝❤ ❜❡❤❛✈❡ ❧✐❦❡ ♦♣t✐❝❛❧ ✐♥t❡r❢❡r❡♥❝❡ ☞❧t❡rs✳ ❚❤❡s❡ str✉❝t✉r❡s ❛r❡ ❛❜❧❡ t♦ ❢✉♥❝t✐♦♥ ✐♥ ❜♦t❤ t❤❡ ✐♥❢r❛r❡❞ ❛♥❞ ✈✐s✐❜❧❡ ✇❛✈❡❧❡♥❣t❤ r❡❣✐♠❡s ❛s ✐t ✐s ❞❡♣❡♥❞❡♥t ♣r✐♠❛r✐❧② ♦♥ t❤❡ t❤✐❝❦♥❡ss ❞ ♦❢ t❤❡ ♦♣t✐❝❛❧ t❤✐❝❦♥❡ss ♥❞✳ ❚❤❡ ✐♠♣♦rt❛♥❝❡ ♦❢ t❤❡ ❝❤❛r❛❝t❡r✐③❛t✐♦♥s ✐♥ ❈❤❛♣t❡r ✸✳✷✳✶ ❛♥❞ ❈❤❛♣t❡r ✸✳✷✳✷ ❢♦r t❤❡ P❙✐ ❢♦r♠❛t✐♦♥ r❛t❡ ❛♥❞ t❤❡ P❙✐ r❡❢r❛❝t✐✈❡ ✐♥❞❡① r❡s♣❡❝t✐✈❡❧②✱ ✐s ❛♣♣❛r❡♥t✳ ❚❤❡ ❝❤❛r❛❝t❡r✐③❡❞ ❞❛t❛ ♣r❡s❡♥t❡❞ ✐♥ ❋✐❣ ✸✳✷ ❛♥❞ ❋✐❣ ✸✳✺ ♣r♦✈✐❞❡s t❤❡ P❙✐ ❢♦r♠❛t✐♦♥ r❛t❡ ❛♥❞ t❤❡ P❙✐ r❡❢r❛❝t✐✈❡ ✐♥❞❡① r❡s♣❡❝t✐✈❡❧② ❛r❡ ✉s❡❞ ❡①t❡♥s✐✈❡❧② ❢♦r ❛❧❧ t❤❡ ✇♦r❦ ❞♦♥❡ ✐♥ t❤✐s ❝❤❛♣t❡r✳ ✺✳✷✳✶ P❙✐ ❉❇❘ ❋✐❣✉r❡ ✺✳✸✿ ❈r♦ss s❡❝t✐♦♥❛❧ ❙❊▼ ✐♠❛❣❡ ♦❢ ❛ ♠✉❧t✐❧❛②❡r P❙✐ str✉❝t✉r❡✳ ❚❤✐s str✉❝t✉r❡ ✇❛s ❢❛❜r✐❝❛t❡❞ ✉s✐♥❣ t✇♦ ❞✐☛❡r❡♥t ❝✉rr❡♥t ❞❡♥s✐t✐❡s s✉❝❝❡ss✐✈❡❧② ❛♣♣❧✐❡❞ ♦♥❡ ❛❢t❡r ❛♥♦t❤❡r✱ ❝r❡❛t✐♥❣ ❧❛②❡rs ✇✐t❤ ❛❧t❡r♥❛t✐♥❣ ❤✐❣❤ ❛♥❞ ❧♦✇ ♣♦r♦s✐t②✳ ❚❤❡ ❞❛r❦❡r ❧❛②❡rs ❛r❡ ♦❢ ❧♦✇❡r ♣♦r♦s✐t②✳ ❋✐❣ ✺✳✸ s❤♦✇s t❤❡ ❝r♦ss s❡❝t✐♦♥s ♦❢ s✉❝❝❡ss❢✉❧❧② ❢❛❜r✐❝❛t❡❞ ♠✉❧t✐❧❛②❡r P❙✐ str✉❝t✉r❡s✳ ❲✐t❤ t❤❡ ❦♥♦✇❧❡❞❣❡ ♦❢ t❤❡ P❙✐ ❢♦r♠❛t✐♦♥ r❛t❡s ✭❋✐❣ ✸✳✷✮ ❛t ❞✐☛❡r❡♥t ❝✉rr❡♥t ❞❡♥s✐t✐❡s✱ ✺✾ ✐rr❛❞✐❛t❡❞ r❡❣✐♦♥s✱ t❤❡ ♦♣t✐❝❛❧ t❤✐❝❦♥❡ss ♥❞✬ ❛t t❤❡ ✐rr❛❞✐❛t❡❞ r❡❣✐♦♥ ✇✐❧❧ r❡✌❡❝t ❛ s♠❛❧❧❡r ✐♥❝r❡❛s✐♥❣ ✐♦♥ ✌✉❡♥❝❡✱ ❞ ❁ ♥❞ ✕ ✳ ❚❤✐s ❡☛❡❝t✐✈❡❧② ♠❡❛♥s t❤❛t t❤❡ ❉❇❘ ✱ s✐♥❝❡ ❣❡ts s♠❛❧❧❡r✱ t❤❡ r❡✌❡❝t❡❞ ✕ ♥❞ ❂ ✕✴✹ ❢♦r t❤❡s❡ ❉❇❘s✳ ❚❤✉s ✇✐t❤ ❞❡❝r❡❛s❡s ❛s ✇❡❧❧ ❛♥❞ t❤✐s ✐s s❡❡♥ ❛s ❛ ❜❧✉❡ s❤✐❢t ✐♥ t❤❡ r❡✌❡❝t❛♥❝❡✳ ❆❧s♦ ♦❜s❡r✈❡❞ ✐s t❤❡ r❡✌❡❝t❡❞ ♣❡❛❦ ✇✐❞t❤ ✹✕ r❡❞✉❝❡s ✇✐t❤ ✌✉❡♥❝❡s✳ ❛♥❞ ✹✕ ✈❡rs✉s ❞♦s❡✳ ❱❛❧✉❡s ♦❢ ✕ ❛r❡ ♠✉❧t✐♣❧✐❡❞ ❜② ✵✳✷ t♦ ♥♦r♠❛❧✐③❡ ✹✕ ❢♦r ❝♦♠♣❛r✐s♦♥ ♦❢ t❤❡✐r r❡❧❛t✐✈❡ r❛t❡s ♦❢ ❝❤❛♥❣❡✳ ✭❜✮✿ ♥ ✈❡rs✉s ❏ ❢♦r ✶✺ ✷ ✶✺ ✷ ❛♥ ✉♥✐rr❛❞✐❛t❡❞ ✇❛❢❡r ❛♥❞ ❢♦r ✌✉❡♥❝❡s ♦❢ ✶ ✂ ✶✵ ✴❝♠ ❛♥❞ ✷ ✂ ✶✵ ✴❝♠ ✳ ✭❝✮✿ ❆✈❡r❛❣❡ t❤✐❝❦♥❡ss ♦❢ ❛♥ ❡t❝❤❡❞ ❜✐❧❛②❡r ♣❡r✐♦❞ ❢r♦♠ ❋✐❣ ✸✳✶✸✳ ❆❧s♦ s❤♦✇♥ ❛r❡ ♥❤ ❛♥❞ ♥❧ ✭♠✉❧t✐♣❧✐❡❞ ❜② ✶✵✵✮ ❛♥❞ t❤❡ ❛✈❡r❛❣❡ ♦♣t✐❝❛❧ ❜✐❧❛②❡r t❤✐❝❦♥❡ss ✈❡rs✉s ✌✉❡♥❝❡✳ ✭❞✮✿ ❘❛t✐♦ ✹♥✴♥ ❋✐❣✉r❡ ✺✳✽✿ ✭❛✮✿ ❱❛r✐❛t✐♦♥ ♦❢ ✕ t❤❡ ✉♥✐rr❛❞✐❛t❡❞ r❡s✉❧t t♦ t❤❛t ♦❢ ❚❤❡ ❛ss✉♠♣t✐♦♥ t❤❛t t❤❡ r❡❢r❛❝t✐✈❡ ✐♥❞❡① r❡♠❛✐♥s ✉♥❝❤❛♥❣❡❞ ✇✐t❤ ✐♦♥ ✐rr❛❞✐❛t✐♦♥ ✐s ✻✵ ❛❝t✉❛❧❧② ♥♦t tr✉❡✳ ❋✐❣ ✺✳✽✭❜✮ s❤♦✇s ♥ ✈❡rs✉s ❏ ♠❡❛s✉r❡❞ ❛t ❛ ✇❛✈❡❧❡♥❣t❤ ♦❢ ✻✵✵ ♥♠ ✐♥ ❛♥ ✉♥✐rr❛❞✐❛t❡❞ s❛♠♣❧❡ t♦❣❡t❤❡r ✇✐t❤ ♥ ✈❡rs✉s ❏ ♣❧♦ts ❢♦r P❙✐ s❛♠♣❧❡s ✐rr❛❞✐❛t❡❞ ✇✐t❤ ✌✉❡♥❝❡s ♦❢ ✶ ✂ ✶✵✶✺ ✴❝♠✷ ❛♥❞ ✷ ✂ ✶✵✶✺ ✴❝♠✷ ✳ ❆❧❧ t❤r❡❡ s❛♠♣❧❡s ❤❛✈❡ ❧❛②❡rs ✇✐t❤ ❛❧t❡r♥❛t✐♥❣ r❡❢r❛❝t✐✈❡ ✐♥❞✐❝❡s ❛♥♦❞✐③❡❞ ✇✐t❤ ❏ ❂ ✷✺ ♠❆✴❝♠✷ ❛♥❞ ✽✺ ♠❆✴❝♠✷ ✳ ❆❧❧ r❡❢r❛❝t✐✈❡ ✐♥❞✐❝❡s ❤❡r❡ ✇❡r❡ ❞❡t❡r♠✐♥❡❞ ❜② t❤❡ ♠❡t❤♦❞s ❛♥❞ ♣r♦❝❡❞✉r❡s ❞❡s❝r✐❜❡❞ ✐♥ ❈❤❛♣t❡r ✸✳✷✳ ❆s ❝❛♥ ❜❡ ♦❜s❡r✈❡❞ ❢r♦♠ ✺✳✽✭❜✮✱ t❤❡ ❞✐☛❡r❡♥❝❡ ✐♥ r❡❢r❛❝t✐✈❡ ✐♥❞❡①✱ ✹♥ ❂ ♥❤ ✲ ♥❧ ✱ ✐s ❛♣♣r♦①✐♠❛t❡❧② s❛♠❡ ❢♦r ❛❧❧ t❤❡ ✐rr❛❞✐❛t❡❞ ❛♥❞ ✉♥✐rr❛❞✐❛t❡❞ s❛♠♣❧❡s ✭❣r❛❞✐❡♥t ♦❢ ♣❧♦ts✮✳ ❚❤❡ ❛✈❡r❛❣❡ ✈❛❧✉❡ ♦❢ r❡❢r❛❝t✐✈❡ ✐♥❞❡① ♥ ✖ ❂ ✭♥❤ ✰ ♥❧ ✮✴✷ ❤♦✇❡✈❡r✱ ✐♥❝r❡❛s❡s ✇✐t❤ ✌✉❡♥❝❡✳ ❋✐❣ ✺✳✽✭❝✮ s❤♦✇s t❤❡ ♠❡❛s✉r❡❞ t❤✐❝❦♥❡ss ✭✉s✐♥❣ ❙❊▼✮ ♦❢ ❛ s✐♥❣❧❡ ♣♦r♦✉s ❜✐❧❛②❡r ✭♦❢ ❤✐❣❤ ❛♥❞ ❧♦✇ r❡❢r❛❝t✐✈❡ ✐♥❞❡①✮ ✈❡rs✉s ✌✉❡♥❝❡✳ ❚❤❡ ♠❡❛s✉r❡❞ ✈❛❧✉❡s ♦❢ ♥ ✭❢r♦♠ t❤❡ s❛♠❡ s❛♠♣❧❡s ✐♥ ❋✐❣ ✺✳✽✭❜✮✮ ❛t ❏ ❂ ✷✺ ❛♥❞ ✽✺ ♠❆✴❝♠✷ ❛r❡ ♣❧♦tt❡❞ ❛❣❛✐♥st ✌✉❡♥❝❡✳ ■♥ ❛❞❞✐t✐♦♥s✱ ❛ ♥❡✇ ♣❛r❛♠❡t❡r✱ t❤❡ ❛✈❡r❛❣❡ ♦♣t✐❝❛❧ ❜✐❧❛②❡r t❤✐❝❦♥❡ss✱ ❞❡☞♥❡❞ ❛s t❤❡ ♣r♦❞✉❝t ♦❢ t❤❡ ♠❡❛s✉r❡❞ ❜✐❧❛②❡r t❤✐❝❦♥❡ss ✇✐t❤ t❤❡ ❛✈❡r❛❣❡ r❡❢r❛❝t✐✈❡ ✐♥❞❡① ♥ ✖ ❞✱ ✐s ❛❧s♦ ♣❧♦tt❡❞ ❛❣❛✐♥st ✌✉❡♥❝❡✳ ❚❤❡ ❜❧✉❡ s❤✐❢t❡❞ r❡✌❡❝t✐✈✐t② ♠❛② ♥♦✇ ❜❡ ✉♥❞❡rst♦♦❞ ♠♦r❡ ❝♦♠♣r❡❤❡♥s✐✈❡❧②✳ ❚❤♦✉❣❤ t❤❡ r❡❢r❛❝t✐✈❡ ✐♥❞❡① ✐♥❝r❡❛s❡s ✇✐t❤ ✌✉❡♥❝❡ ✐♥ ❋✐❣ ✺✳✽✭❜✮✱ t❤❡ ❛✈❡r❛❣❡ ♦♣t✐❝❛❧ t❤✐❝❦♥❡ss ♥ ✖ ❞ r❡❞✉❝❡s ✇✐t❤ ✌✉❡♥❝❡ ❜❡❝❛✉s❡ t❤❡ r❡❞✉❝t✐♦♥ ✐♥ ❧❛②❡r t❤✐❝❦♥❡ss ♦✉t✇❡✐❣❤s t❤❡ ✐♥❝r❡❛s❡❞ r❡❢r❛❝t✐✈❡ ✐♥❞❡①✱ ❤❡♥❝❡ ✕ ✐s ❜❧✉❡✲s❤✐❢t❡❞✳ ❋✐❣ ✺✳✽✭❛✮ s❤♦✇s t❤❡ ♣❧♦t ♦❢ r❡✌❡❝t❡❞ ♣❡❛❦ ❚❤❡ r❡✌❡❝t❡❞ ♣❡❛❦ ❤❛❞ ❜❧✉❡ s❤✐❢t❡❞ ❢r♦♠ ✕ ❛♥❞ t❤❡ ♣❡❛❦ ✇✐❞t❤ ✹✕ ✈❡rs✉s ✌✉❡♥❝❡✳ ✕ ❂ ✼✹✵ ♥♠ ♦❢ t❤❡ ✉♥✐rr❛❞✐❛t❡❞ s❛♠♣❧❡ t♦ ✕ ❂ ✹✾✵ ♥♠ ♦❢ t❤❡ s❛♠♣❧❡ ✐rr❛❞✐❛t❡❞ ✇✐t❤ ❛ ✌✉❡♥❝❡ ♦❢ ✷ ✂ ✶✵✶✺✴❝♠✷✳ ❇♦t❤ ✕ ❛♥❞ ✹✕ ✹✕ r❡❞✉❝❡s s✐❣♥✐☞❝❛♥t❧② ❢❛st❡r✳ ✹✕ t❤❡ r❡✌❡❝t❡❞ r❡s♦♥❛♥t ♣❡❛❦ ❢r♦♠ ❛ ❉❇❘ ✐s r❡❧❛t❡❞ t♦ t❤❡ ❧❛②❡r r❡❢r❛❝t✐✈❡ ✐♥❞✐❝❡s ❜② ✹✕✕ ✙ ✙✷ ✹♥✖♥ ✳ ■♥ ❋✐❣ ✺✳✽✭❞✮✱ ✹♥✴ ♥ ✐s ❧❡ss ❛t ✐rr❛❞✐❛t❡❞ t❤❛♥ ✉♥✐rr❛❞✐❛t❡❞ r❡❣✐♦♥s ❜❡❝❛✉s❡ ✇❤✐❧❡ ♥ ✖ ✐♥❝r❡❛s❡s ✇✐t❤ ✌✉❡♥❝❡✱ ✹♥ r❡♠❛✐♥s r❡❧❛t✐✈❡❧② ❝♦♥st❛♥t✳ ❍❡♥❝❡✱ ✹✕✴✕ ❞❡❝r❡❛s❡s ❛❝❝♦r❞✐♥❣❧② ❛s ✇❡❧❧✳ ❚❤✐s ❡①♣❧❛✐♥s ✇❤② ✇✐❞t❤ ♦❢ t❤❡ r❡✌❡❝t✐✈✐t② ♣❡❛❦ ✹✕ ✐♥ ❋✐❣ ✺✳✼ ❜❡❝♦♠❡s ♥❛rr♦✇❡r ✇✐t❤ r❡❞✉❝❡ ✇✐t❤ ✐♥❝r❡❛s✐♥❣ ✌✉❡♥❝❡✱ ❤♦✇❡✈❡r✱ ✐♥❝r❡❛s✐♥❣ ✌✉❡♥❝❡✳ ❚❤❡ ♠♦st ✐♠♣♦rt❛♥t r❡s✉❧t t♦ t❛❦❡ ❢r♦♠ t❤❡s❡ ✐s ❤♦✇ ♠✉❝❤ ❜❧✉❡ s❤✐❢t ♠❛② ❜❡ ❛❝❤✐❡✈❡❞ ❢r♦♠ ❛ ♣❛rt✐❝✉❧❛r ✇❛✈❡❧❡♥❣t❤ ✇✐t❤ ✐♦♥ ✐rr❛❞✐❛t✐♦♥✳ ❲✐t❤ t❤✐s ❦♥♦✇❧❡❞❣❡✱ ❝♦♥tr♦❧❧❛❜❧❡ ✻✺ st❛❣❡✱ t❤❡ s❛♠♣❧❡s ✇❡r❡ ❝❧❡❛✈❡❞ ♣❡r♣❡♥❞✐❝✉❧❛r t♦ t❤❡ ✐rr❛❞✐❛t❡❞ ❧✐♥❡ ❛♥❞ ❤❛❞ t❤❡✐r ❝r♦ss s❡❝t✐♦♥s ✐♠❛❣❡❞ ✇✐t❤ ❛ ❙❊▼ t♦ s❤♦✇ ❤♦✇ t❤❡ s❤❛♣❡ ♦❢ t❤❡ ❧❛②❡rs ❝❤❛♥❣❡s ♣r♦❣r❡ss✐✈❡❧② ✇✐t❤ ❛♥♦❞✐③❛t✐♦♥ ❞❡♣t❤✳ ■♥ t❤❡ ☞rst st❛❣❡ ✭❋✐❣ ✺✳✶✷✭❛✮✮ ❢♦r t❤❡ ❧♦✇❡r ✌✉❡♥❝❡ ♦❢ ✷ ✂ ✶✵✶✺✴❝♠✷✱ t❤❡ ♠✉❧t✐❧❛②❡r st❛❝❦ ❛t t❤❡ ❝❡♥t❡r ♦❢ t❤❡ ✐rr❛❞✐❛t❡❞ ❧✐♥❡ ❛r❡ t❤✐♥♥❡r t❤❛♥ ❛t t❤❡ ✉♥✐rr❛❞✐❛t❡❞ ❜❛❝❦❣r♦✉♥❞ ❢♦r r❡❛s♦♥s ❞✐s❝✉ss❡❞ ✐♥ t❤❡ ♣r❡✈✐♦✉s s❡❝t✐♦♥ ✭✺✳✸✮ ♦❢ t❤✐s ❝❤❛♣t❡r✳ ❚❤❡ ♠✉❧t✐❧❛②❡r✬s t❤✐❝❦♥❡ss ✐♥❝r❡❛s❡s ❢r♦♠ t❤❡ ✐rr❛❞✐❛t❡❞ t♦ t❤❡ ✉♥✐rr❛❞✐❛t❡❞ ❜♦✉♥❞❛r② ❛t ❜♦t❤ s✐❞❡s ❛♥❞ ❜❡❝♦♠❡s ♣r♦❣r❡ss✐✈❡❧② t✐❧t❡❞ ❛t ❛♥ ❛♥❣❧❡ ❞❡☞♥❡❞ ❛s ✥ ✇✐t❤ ❛♥♦❞✐③❡❞ ❞❡♣t❤✳ ❚❤❡s❡ ❛♥♦❞✐③❡❞ ❧❛②❡rs ✇❡r❡ t❤❡♥ r❡♠♦✈❡❞ ❛♥❞ t❤❡ ✇❛❢❡r ❣♦❡s t❤r♦✉❣❤ ❛♥♦t❤❡r ❛♥♦❞✐③❛t✐♦♥ ♣r♦❞✉❝❡ t❤❡ ✷♥❞ st❛❣❡ ❉❇❘ ✭❋✐❣ ✺✳✶✷✭❜✮✮✳ ■♥ t❤❡ ✷♥❞ st❛❣❡✱ t❤❡ s❛♠♣❧❡✬s t✐❧t❡❞ s✉r❢❛❝❡ ♣r♦☞❧❡ ❛t t❤❡ ❜♦✉♥❞❛r✐❡s ✐s ❛❝t✉❛❧❧② t❤❛t ♦❢ t❤❡ ☞♥❛❧ ♣♦r♦✉s ❧❛②❡r ♦❢ t❤❡ ✶st st❛❣❡ ❉❇❘✳ ❍❡r❡✱ ❛s ✇✐t❤ t❤❡ st❛❣❡ ✶ ❉❇❘✱ t❤❡ t✐❧t ❛♥❣❧❡ ✥ ✐♥❝r❡❛s❡s ✇✐t❤ ❢✉rt❤❡r ❛♥♦❞✐③❡❞ ❞❡♣t❤✳ ❚❤✐s ♣r♦❝❡ss ✇❛s t❤❡♥ r❡♣❡❛t❡❞ t♦ ❣✐✈❡ ❛ ✸r❞ st❛❣❡ ❉❇❘ ❛s s❤♦✇♥ ✐♥ ❋✐❣ ✺✳✶✷✭❝✮✳ ❇② ♥♦✇✱ t❤❡ t✐❧t ❛♥❣❧❡ ❤❡r❡ ❤❛s r❡❛❝❤❡❞ ❛ ❝♦♥st❛♥t ✈❛❧✉❡ ❛♥❞ ❞♦ ♥♦t ✐♥❝r❡❛s❡ ❢✉rt❤❡r ❞❡s♣✐t❡ ❝♦♥t✐♥✉❡❞ ❛♥♦❞✐③❛t✐♦♥ ✉♥❧✐❦❡ t❤❡ ❝❛s❡ ❢♦r st❛❣❡ ✶ ❛♥❞ ✷✳ ❚❤✐s ✐s ❡✈✐❞❡♥t ❢r♦♠ t❤❡ ♦❜s❡r✈❛t✐♦♥ t❤❛t t❤❡ ❉❇❘ ❜♦✉♥❞❛r② ❛t t❤❡ s✉r❢❛❝❡ ✐s ♣❛r❛❧❧❡❧ t♦ t❤❡ ✉♥❞❡r❧②✐♥❣ s✐❧✐❝♦♥ s✉r❢❛❝❡ ❢♦r t❤❡ ✸r❞ st❛❣❡ ❉❇❘ ✐♥ ❋✐❣ ✺✳✶✷✭❝✮✳ ❋✐❣ ✺✳✶✸✭❛✮ s❤♦✇s ❛ ♣❧♦t ♦❢ ❞✐☛❡r❡♥t ✌✉❡♥❝❡s✳ ✥ r❡❛❝❤ ❛ ♣♦✐♥t ✇❤❡r❡ ✥ ✈❡rs✉s ❛♥♦❞✐③❛t✐♦♥ ❞❡♣t❤ ❢♦r ❉❇❘s ✐rr❛❞✐❛t❡❞ ✇✐t❤ ✐♥❝r❡❛s❡s ❛♣♣r♦①✐♠❛t❡❧② ❧✐♥❡❛r❧② ✇✐t❤ ❞❡♣t❤ ❢♦r ❛❧❧ ✌✉❡♥❝❡s ❛♥❞ ✥ ❜❡❝♦♠❡s ❝♦♥st❛♥t✳ ❚❤✐s ♠❛② ❜❡ ❛ttr✐❜✉t❡❞ t♦ t❤❡ ❞❡❝♦✉♣❧✐♥❣ ❜❡t✇❡❡♥ t❤❡ ❧♦✇❡r✴❤✐❣❤❡r ❤♦❧❡ ❝✉rr❡♥t ✌♦✇✐♥❣ t❤r♦✉❣❤ t❤❡ ✐rr❛❞✐❛t❡❞✴✉♥✐rr❛❞✐❛t❡❞ r❡❣✐♦♥s ❞✉r✐♥❣ t❤❡ ❡❧❡❝tr♦❝❤❡♠✐❝❛❧ ❛♥♦❞✐③❛t✐♦♥ ❛s t❤❡ ✉♥❞❡r❧②✐♥❣ s✉r❢❛❝❡✲r❡❧✐❡❢ ♣r♦☞❧❡ ❡✈♦❧✈❡s✳ ❉✐☛❡r❡♥t ✌✉❡♥❝❡s ♣r♦❞✉❝❡ s✐♠✐❧❛r ❜❡❤❛✈✐♦r ❛♥❞ ❞✐☛❡rs ♦♥❧② ✐♥ t❤❡ ❛♥♦❞✐③❡❞ ❞❡♣t❤s ❢♦r ✥ t♦ ❜❡❝♦♠❡ ❝♦♥st❛♥t✳ ❋❧✉❡♥❝❡ ✐♥❝r❡❛s❡s ✥ s✐♠♣❧② ❜❡❝❛✉s❡ t❤❡ ♠♦r❡ ✐rr❛❞✐❛t❡❞ ❉❇❘ ❧❛②❡rs ❛r❡ t❤✐♥♥❡r ❛s ❛ r❡s✉❧t ♦❢ ❣r❡❛t❡r r❡❞✉❝t✐♦♥ ✐♥ t❤❡ P❙✐ ❢♦r♠❛t✐♦♥ ✭s❡❡ ❈❤❛♣t❡r ✸✳✻✮✱ ❣✐✈✐♥❣ r✐s❡ t♦ ❛ ❜✐❣❣❡r ❞✐☛❡r❡♥❝❡ ✐♥ t❤❡ P❙✐ t❤✐❝❦♥❡ss ❛❝r♦ss t❤❡ ✐rr❛❞✐❛t❡❞ ❛♥❞ ✉♥✐rr❛❞✐❛t❡❞ ❜♦✉♥❞❛r✐❡s ✇✐t❤ ❛♥♦❞✐③❡❞ ❞❡♣t❤✳ ■♥s❡t ♦❢ ❋✐❣ ✺✳✶✸✭❛✮ ✐s ❛ ♣❧♦t ✇❤✐❝❤ s❤♦✇s t❤❛t ✥ ❝❤❛♥❣❡s ❛♣♣r♦①✐♠❛t❡❧② ❧✐♥❡❛r❧② ✇✐t❤ ✌✉❡♥❝❡✳ ❍❡♥❝❡✱ ❉❇❘s ✇✐t❤ ❞✐☛❡r❡♥t ❜♦✉♥❞❛r② ❧❛②❡r t✐❧ts ♠❛② ✻✼ ❧❡❢t✱ r❡✌❡❝t❡❞ ✇❛✈❡❧❡♥❣t❤s ✐s s❡♥s✐t✐✈❡ t♦ ❝❤❛♥❣❡s ✐♥ ❧❛②❡r t❤✐❝❦♥❡ss s✐♥❝❡ ✕ ✈❛r✐❡s s❧♦✇❧② ✇✐t❤ s✐♥ ✒✳ t♦ ❞✱ ❜✉t ❧❡ss s♦ t♦ ❝❤❛♥❣❡s ✐♥ ❧❛②❡r t✐❧t s✐♥❝❡ ✕ ✐s ♣r♦♣♦rt✐♦♥❛❧ ❆t ❛♥② ♣♦s✐t✐♦♥ ✐♥ t❤❡ t✐❧t❡❞ ❜♦✉♥❞❛r② ❜❡t✇❡❡♥ t❤❡ ✐rr❛❞✐❛t❡❞ ❛♥❞ ✉♥✐rr❛❞✐❛t❡❞ r❡❣✐♦♥s✱ t❤❡ ❧❛②❡r t❤✐❝❦♥❡ss ✐s ❝♦♥st❛♥t ✇✐t❤ ❞❡♣t❤ ❛♥❞ ❤❡♥❝❡ ❝♦❤❡r❡♥t❧② r❡✌❡❝ts ❛ ♣❛rt✐❝✉❧❛r ✇❛✈❡❧❡♥❣t❤✳ ❍♦✇❡✈❡r✱ ❜❡❝❛✉s❡ t❤❡ ❧❛②❡r t❤✐❝❦♥❡ss ❛r❡ ❞✐☛❡r❡♥t ❛❝r♦ss t❤❡ t✐❧t❡❞ ❜♦✉♥❞❛r②✱ ❧♦♥❣❡r✴s❤♦rt❡r r❡❞✴❜❧✉❡ ✇❛✈❡❧❡♥❣t❤s ❛r❡ r❡✌❡❝t❡❞ ❝❧♦s❡r t♦ t❤❡ ✉♥✐rr❛❞✐❛t❡❞✴✐rr❛❞✐❛t❡❞ s✐❞❡s✱ r❡s✉❧t✐♥❣ ✐♥ ❞✐☛❡r❡♥t ✇❛✈❡❧❡♥❣t❤s ❜❡✐♥❣ r❡✌❡❝t❡❞ ✇❤✐❝❤ r❡❝♦♠❜✐♥❡ t♦ ❛♣♣❡❛r ✇❤✐t❡ ✇❤❡♥ ✈✐❡✇❡❞ ❢r♦♠ t❤❡ t♦♣✳ ❚❤✐s s❛♠❡ ♣r♦❝❡ss ♦❝❝✉rs ✐♥ t❤❡ ♠♦r❡ t✐❧t❡❞ ❧❛②❡rs ❜❡♥❡❛t❤✱ ✇❤✐❝❤ ❛❧s♦ r❡✌❡❝t ❛ ✇✐❞❡ r❛♥❣❡ ♦❢ ✇❛✈❡❧❡♥❣t❤s t❤r♦✉❣❤ ❞✐☛❡r❡♥t ❛♥❣❧❡s✳ ❘❡✌❡❝t✐♦♥s ❢r♦♠ t❤❡ r✐❣❤t s✐❞❡ ♦❢ t❤❡ t✐❧t❡❞ ❜♦✉♥❞❛r② r❡✌❡❝ts ❧✐❣❤t t❤r♦✉❣❤ ❛ ❝♦♠♣❧❡♠❡♥t❛r② r❛♥❣❡ ♦❢ ❛♥❣❧❡s s✐♥❝❡ t❤❡ ❧❛②❡rs ❛r❡ t✐❧t❡❞ ✐♥ t❤❡ ♦♣♣♦s✐t❡ s❡♥s❡✳ ❚❤❡ ❝♦♠❜✐♥❡❞ ❡☛❡❝t ❣✐✈❡s ❛ ✇✐❞❡ ❛♥❣❧❡ ♦❢ r❡✌❡❝t❡❞ ❧✐❣❤t✳ ❈♦♠♣❛r❛t✐✈❡❧②✱ ✐❧❧✉♠✐♥❛t✐♦♥ ❛t t❤❡ st❡❡♣ ♣❛r❛❧❧❡❧ ✭❝♦♥st❛♥t ✥✮ t✐❧t❡❞ ❧❛②❡rs ❞❡❡♣ ✇✐t❤✐♥ t❤❡ ❜♦✉♥❞❛r② ✇♦✉❧❞ ♣r♦❞✉❝❡ ❛ ♠♦r❡ ♠♦♥♦❝❤r♦♠❛t✐❝ r❡✌❡❝t✐♦♥ s✐♥❝❡ t❤❡ ❧❛②❡r t❤✐❝❦♥❡ss ❝❡❛s❡s t♦ ❝❤❛♥❣❡ ❛❝r♦ss t❤❡ t✐❧t❡❞ ❜♦✉♥❞❛r②✳ ❚♦ ♣r♦❞✉❝❡ s✉❝❤ ❉❇❘s ✇✐t❤ ♣❛r❛❧❧❡❧ t✐❧t❡❞ ❜♦✉♥❞❛r② ❧❛②❡rs✱ ❛ t❤✐❝❦ P❙✐ ✐s ☞rst ❛♥♦❞✐③❡❞ ❛♥❞ r❡♠♦✈❡❞✱ ❜❡❢♦r❡ t❤❡ ☞♥❛❧ ❛♥♦❞✐③❛t✐♦♥ ♦❢ t❤❡ ☞♥❛❧ ❉❇❘✳ ❋✐❣ ✺✳✶✹ ❞❡♠♦♥str❛t❡s t❤❡ ❦✐♥❞ ♦❢ r❡✌❡❝t✐♦♥s t❤❛t ♠❛② ❜❡ ♦❜t❛✐♥❡❞ ❢r♦♠ ✇❤✐t❡ ❧✐❣❤t ✐❧❧✉♠✐♥❛t✐♦♥ ♦♥ t❤❡s❡ ❉❇❘s ❛t ❞✐☛❡r❡♥t st❛❣❡s ❛♥❞ ❣❡♦♠❡tr✐❡s✳ r♦✇s ✇❡r❡ ✐rr❛❞✐❛t❡❞ ✇✐t❤ ❛ ✌✉❡♥❝❡ ♦❢ ✷ ✐rr❛❞✐❛t❡❞ ✇✐t❤ ✌✉❡♥❝❡s ♦❢ ✶ ✂ ✶✵ ✂ ✶✺ ✴❝♠✷ ✳ ✶✵ ✶✺ ✴❝♠✷ ❆❧❧ ❉❇❘s ✐♥ t❤❡ ✉♣♣❡r ✇❤✐❧❡ t❤♦s❡ ✐♥ t❤❡ ❧♦✇❡r r♦✇s ✇❡r❡ ❚❤❡ ❉❇❘s ✐♥ ❋✐❣ ✺✳✶✹✭❛✮✲✭❞✮ ❛r❡ ✸r❞ st❛❣❡ ❉❇❘s ✇❤✐❧❡ t❤❡ ❉❇❘s ✐♥ ✺✳✶✹✭❡✮ ✇❡r❡ ✷♥❞ st❛❣❡ ❉❇❘s✳ ❚❤❡ ♦♣t✐❝❛❧ ✐♠❛❣❡s ♦❢ t❤❡ ❉❇❘s ✐♥ ❋✐❣ ✺✳✶✹✭❜✮ ✇❡r❡ t❛❦❡♥ ✉♥❞❡r ♥♦r♠❛❧ ✐❧❧✉♠✐♥❛t✐♦♥ ✭ ✒ ✵ ❂ ✾✵ ✮✳ ❚❤❡ t♦♣✱ ✌❛t ❉❇❘ s✉r❢❛❝❡s r❡✌❡❝t r❡❞ ♦r ❜❧✉❡✱ ❞❡♣❡♥❞✐♥❣ ♦♥ t❤❡ ✌✉❡♥❝❡✱ ✇❤✐❧❡ ♥♦ ✈✐s✐❜❧❡ r❡✌❡❝t✐♦♥s ✇❛s ♦❜s❡r✈❡❞ ❢r♦♠ t❤❡ t✐❧t❡❞ ❜♦✉♥❞❛r✐❡s✳ ■♥ ❋✐❣ ✺✳✶✹✭❝✮✱ t❤❡ ❉❇❘s ✇❡r❡ ✐❧❧✉♠✐♥❛t❡❞ ❛t ❛♥ ❛♥❣❧❡ ✭s♠❛❧❧ ✒✮✳ ❚❤❡ t✐❧t❡❞ ❜♦✉♥❞❛r✐❡s ✐♥ t❤❡ ❧♦✇❡r r♦✇ ♥♦✇ r❡✌❡❝t ❣r❡❡♥✱ ❜❧✉❡s❤✐❢t❡❞ ❢r♦♠ t❤❡ r❡✌❡❝t✐♦♥ ♦❢ t❤❡ t♦♣ ❉❇❘ s✉r❢❛❝❡✱ ❝♦♥s✐st❡♥t ✇✐t❤ t❤❡ ❇r❛❣❣ ❡q✉❛t✐♦♥✳ ❙✐♥❣❧❡ ❝♦❧♦r ✐s ❜❡✐♥❣ r❡✌❡❝t❡❞ ❢r♦♠ t❤❡ ❉❇❘s ✐♥ t❤❡ ❧♦✇❡r r♦✇ ❜❡❝❛✉s❡ t❤❡s❡ ❛r❡ ✸r❞ st❛❣❡ ❉❇❘s ✇❤❡r❡ t❤❡ t✐❧t❡❞ ❧❛②❡rs ❛r❡ ♣❛r❛❧❧❡❧ ✭❝♦♥st❛♥t ✥ ✮✱ ❛♥❞ ❤❡♥❝❡ t❤❡ ❇r❛❣❣ ❝♦♥❞✐t✐♦♥ ❤♦❧❞s ❢♦r ♦♥❧② ♦♥❡ ♣❛rt✐❝✉❧❛r ✼✶ ✐♥❝✐❞❡♥❝❡✳ ❍✐❣❤❧② ✐♥❝❧✐♥❡❞ ✐❧❧✉♠✐♥❛t✐♦♥s ✭s♠❛❧❧ ✒✮ ♦♥ t❤❡ ♦t❤❡r ❤❛♥❞ ❛❧❧♦✇s ❢♦r r❡✌❡❝t✐♦♥ ❢r♦♠ t❤❡s❡ s✐❞❡s ❛♥❞ ♥♦t t❤❡ t♦♣ ✌❛t ❤❡①❛❣♦♥❛❧ s❤❛♣❡✳ ❯s✐♥❣ t❤✐s ❛s ❛ st❛rt✐♥❣ ♠❛t❡r✐❛❧✱ t❤✐s str✉❝t✉r❡ ❝♦✉❧❞ ❡❛s✐❧② ❜❡ ❢❛❜r✐❝❛t❡❞ ✐♥t♦ ❛ ✷♥❞ ♦r ✸r❞ st❛❣❡ ✸❉ ❉❇❘s✳ ❚♦ s✉♠♠❛r✐③❡ t❤✐s s❡❝t✐♦♥✱ ✇❡ ❤❛✈❡ ✉s❡ ✐♦♥ ✐rr❛❞✐❛t❡❞ ♠✐❝r♦♠❛❝❤✐♥❡❞ ✸❉ P❙✐ ❉❇❘ t♦ ✎ ❚✉♥❡ t❤❡ r❛♥❣❡ ♦❢ t❤❡ t✐❧t❡❞ ❛♥❣❧❡ ✥ t♦ ♣r♦❞✉❝❡ ❡✐t❤❡r ✇✐❞❡✲❜❛♥❞ ✇❤✐t❡ r❡✌❡❝t✐✈✐t② ♦r s✐♥❣❧❡ ❝♦❧♦r r❡✌❡❝t✐✈✐t② ✎ ❈♦♥tr♦❧ t❤❡ r❛♥❣❡ ♦❢ ❛♥❣❧❡s ♦✈❡r ✇❤✐❝❤ ✐♥❝✐❞❡♥t ❧✐❣❤t ✐s r❡✌❡❝t❡❞ ♦r ♥♦t ■♥ ❛❞❞✐t✐♦♥ t❤❡ ✉s❡ t❤❡ ❧❛r❣❡ ❛r❡❛ ✐rr❛❞✐❛t✐♦♥ ❢❛❝✐❧✐t✐❡s ❢♦r r❛♣✐❞ ♣r♦❞✉❝t✐♦♥ ✸❉ ❉❇❘s ❤❛s ❜❡❡♥ ❞❡♠♦♥str❛t❡❞✳ ❚❤✐s s❡❝t✐♦♥ s❤♦✇s ❤♦✇ ❇r❛❣❣ r❡✌❡❝t✐♦♥ t❤r♦✉❣❤ ❛ r❛♥❣❡ ♦❢ ❛♥❣❧❡s ❢♦r ❛ s✐♥❣❧❡ ❜❡❛♠ ✐♥❝✐❞❡♥t ❛♥❣❧❡ ♠❛② ❛❝❤✐❡✈❡❞ ✉s✐♥❣ ✸❉✱ t✉♥❛❜❧❡ P❙✐ ❉❇❘s ❛♥❞ ♣❛tt❡r♥❡❞ ♦✈❡r ❧❛r❣❡ ❛r❡❛s ✇✐t❤ ♠✐❝r♦♠❡t❡r r❡s♦❧✉t✐♦♥✳ ❚❤♦✉❣❤ t❤✐s ✇♦r❦ ♦♥❧② ❞❡s❝r✐❜❡s ❛♣♣❧✐❝❛t✐♦♥s ✐♥ r❡✌❡❝t✐✈❡ ❞✐s♣❧❛②s✱ ✐t ♦♣❡♥s ✉♣ ♦t❤❡r ♣♦t❡♥t✐❛❧ ✉s❡s ✐♥ ❝♦♥tr♦❧❧✐♥❣ t❤❡ ❛♥❣❧❡ ❛♥❞ ✇❛✈❡❧❡♥❣t❤ ♦❢ ❡♠✐tt❡❞ ❧✐❣❤t ❢♦r ♣r♦❞✉❝✐♥❣ ✇❤✐t❡ r❡✌❡❝t✐✈❡ s✉r❢❛❝❡s ❢♦r r❡s♦♥❛♥t ✇❤✐t❡ ❧✐❣❤t ❡♠✐ss✐♦♥ ❢r♦♠ s❡♠✐❝♦♥❞✉❝t♦r ♥❛♥♦❝r②st❛❧s✱ ✸❉ ✐♥❞✐✈✐❞✉❛❧ ❛♥❞ ❝♦✉♣❧❡❞ ♦♣t✐❝❛❧ ♠✐❝r♦✲ ❝❛✈✐t✐❡s✱ s✐❧✐❝♦♥✲❜❛s❡❞ ❧❛s❡rs✱ ❛♥❞ t✉♥❛❜❧❡ s✐❧✐❝♦♥✲❜❛s❡❞ ♣❤♦t♦♥✐❝ ❜❛♥❞ ❣❛♣ str✉❝t✉r❡s ❢♦r ♦♣t✐❝❛❧ ♠♦❞✉❧❛t✐♦♥✳ ✺✳✺ ▲❛r❣❡ ❛r❡❛ ❉❇❘ ❚❤❡ ✇♦r❦ ♣r❡s❡♥t❡❞ ✐♥ t❤❡ ♣r❡✈✐♦✉s s❡❝t✐♦♥s ♦♥ P❙✐ ❉❇❘s ♦♣❡♥s ♥❡✇ ❛✈❡♥✉❡s ✐♥ ♣r♦❞✉❝✐♥❣ ❤✐❣❤ ❞❡♥s✐t② P❙✐ ♣❛tt❡r♥❡❞ ❉❇❘s ❢♦r ❞✐s♣❧❛②s ❛♥❞ ❛rr❛②s ♦❢ ♠✐❝r♦❝❛✈✐t✐❡s t✉♥❡❞ t♦ ❞✐❢✲ ❢❡r❡♥t ✇❛✈❡❧❡♥❣t❤s✱ ❝♦✉♣❧❡❞ ♠✐❝r♦❝❛✈✐t✐❡s✱ s✐❧✐❝♦♥✲❜❛s❡❞ ❧❛s❡rs ❛♥❞ t✉♥❛❜❧❡ s✐❧✐❝♦♥✲❜❛s❡❞ ♣❤♦t♦♥✐❝ ❜❛♥❞ ❣❛♣ str✉❝t✉r❡s ❢♦r ♦♣t✐❝❛❧ ♠♦❞✉❧❛t✐♦♥✳ ❍♦✇❡✈❡r✱ ✇✐❞❡r ❛♣♣❧✐❝❛t✐♦♥ r❡q✉✐r❡s r❛♣✐❞✱ ♠❛ss ♣❛tt❡r♥✐♥❣ ♦✈❡r ❧❛r❣❡ ✇❛❢❡rs s✉r❢❛❝❡s✳ ■♥ t❤✐s ✇♦r❦✱ s✐♠♣❧❡ ♠♦❞✐☞❝❛t✐♦♥s ✇❡r❡ ♠❛❞❡ t♦ ❛ ♠❡❣❛✈♦❧t ❛❝❝❡❧❡r❛t♦r ❛♥❞ ♥✉❝❧❡❛r ♠✐❝r♦♣r♦❜❡ t♦ ❣✐✈❡ ❛ ❢❛❝✐❧✐t② ❝❛♣❛❜❧❡ ♦❢ ❧❛r❣❡ ❛r❡❛ ✐rr❛❞✐❛t✐♦♥ ✭s❡❡ ❈❤❛♣t❡r ✷✳✹✳✷ ❢♦r t❤❡ ❢❛❝✐❧✐t② s❡t✉♣✮ ❛t ▼❡❱ ✐♦♥ ❡♥❡r❣✐❡s✱ ✇✐t❤ t❤❡ ♣❛tt❡r♥✐♥❣ ❛❝❤✐❡✈❡❞ ✉s✐♥❣ ❛ ♠✉❧t✐❧❡✈❡❧ ♣❤♦t♦r❡s✐st ♠❛s❦✳ ✼✸ ❞✐☛❡r❡♥t ❝♦❧♦rs✳ ❚❤❡ ✇❛❢❡rs ✇❡r❡ t❤❡♥ ✇❛s❤❡❞ ✐♥ ❡t❤❛♥♦❧ ❛♥❞ ❞r✐❡❞ ✐♥ ❛✐r✳ ❋♦✉r ❞✐☛❡r❡♥t s❛♠♣❧❡s ✇❡r❡ ✐rr❛❞✐❛t❡❞ ❛♥❞ ❛♥♦❞✐③❡❞ ✭❋✐❣ ✺✳✶✼✮✳ ❋♦r t❤❡ s❛♠♣❧❡s ✐♥ ❋✐❣ ✺✳✶✼✭❛✮✲✭❝✮✱ t✇♦ r❡✌❡❝t✐✈❡ ❝♦❧♦rs ❛r❡ ♣r♦❞✉❝❡❞✱ ✇✐t❤ t❤❡ ✐rr❛❞✐❛t❡❞ r❡❣✐♦♥s ❝♦rr❡s♣♦♥❞✐♥❣ t♦ t❤❡ ❣r✐❞ ❤♦❧❡s ❜❧✉❡✲s❤✐❢t❡❞ ✇✐t❤ r❡s♣❡❝t t♦ t❤❡ ✉♥✐rr❛❞✐❛t❡❞ r❡❣✐♦♥s ❝♦rr❡s♣♦♥❞✐♥❣ t♦ t❤❡ ❣r✐❞ ❜❛rs✳ ■♥ ❋✐❣ ✺✳✶✼✭❞✮✱ ❛♥ ❛❞❞✐t✐♦♥❛❧ ❣r✐❞ ✇✐t❤ ❛ ✶✷✳✼ ✖♠ ♣❡r✐♦❞ ✇❛s ♣❧❛❝❡❞ ♦♥ t❤❡ ✇❛❢❡r s✉r❢❛❝❡✱ r❡s✉❧t✐♥❣ ✐♥ t❤r❡❡ r❡✌❡❝t✐✈❡ ❝♦❧♦rs✳ ❚❤❡ ☞♥❡r ♠❡s❤ ❣r✐❞ ✐rr❛❞✐❛t✐♦♥ ♣❛tt❡r♥ ❝❛♥ ❜❡ s❡❡♥✱ ✇✐t❤ t❤❡ ♠♦st ❜❧✉❡s❤✐❢t❡❞ r❡❣✐♦♥s ❜❡✐♥❣ t❤♦s❡ ✇❤❡r❡ t❤❡ ❜❡❛♠ ❤❛s ♣❛ss❡❞ t❤r♦✉❣❤ ❜♦t❤ s❡ts ♦❢ ❤♦❧❡s✳ ✺✳✺✳✷ P❛tt❡r♥❡❞ ❧❛r❣❡ ❛r❡❛ ✐rr❛❞✐❛t✐♦♥ ✇✐t❤ ♣❤♦t♦r❡s✐st ♠❛s❦s ❚❤❡ ❞❡♠♦♥str❛t✐♦♥ t♦ r❛♣✐❞❧② ❢❛❜r✐❝❛t❡ ❧❛r❣❡ ❛rr❛②s ♦❢ ❉❇❘s ✇✐t❤ t❤❡ ❣r✐❞s s❤♦✇s t❤❡ ✈✐❛❜✐❧✐t② ♦❢ t❤✐s t❡❝❤♥✐q✉❡✳ ❍♦✇❡✈❡r✱ ❛ s✉r❢❛❝❡ ♠❛s❦ str✉❝t✉r❡ ✐s r❡q✉✐r❡❞ t♦ ♣r♦❞✉❝❡ r❡✌❡❝t✐✈❡ ❝♦❧♦rs ♦❢ ❛r❜✐tr❛r② s❤❛♣❡s ❛♥❞ s✐③❡s✳ ❚❤❡ ❢❛❜r✐❝❛t✐♦♥ ❛♥❞ ✉s❡ ♦❢ ❛ ♣❤♦t♦r❡s✐st ✭P❘✮ ♠❛s❦ str✉❝t✉r❡ ✐s ♥♦✇ ❞❡s❝r✐❜❡❞ ✇❤✐❝❤ ❣✐✈❡s t❤❡ ❝❛♣❛❜✐❧✐t② ♦❢ ❝r❡❛t✐♥❣ ❧❛r❣❡✲❛r❡❛ ♣❛tt❡r♥❡❞ ❉❇❘s ✐♥ ❝♦♥❥✉♥❝t✐♦♥ ✇✐t❤ t❤✐s ❧❛r❣❡ ❛r❡❛ ✐rr❛❞✐❛t✐♦♥ s②st❡♠✳ ❚❤❡ P❘ ✉s❡❞ ❢♦r t❤✐s ✇♦r❦ ✐s ❆❩✹✻✷✵ ❛♥❞ ✐s ♣❛tt❡r♥❡❞ ✉s✐♥❣ ❯❱ ❧✐t❤♦❣r❛♣❤② ❢❛❝✐❧✐t✐❡s ❛t ■▼❘❊ ✭❢♦r ♠♦r❡ ✐♥❢♦r♠❛t✐♦♥ ❛♥❞ ❝❤❛r❛❝t❡r✐③❛t✐♦♥ ♦❢ t❤✐s r❡s✐st r❡❢❡r t♦ ❈❤❛♣t❡r ✷✳✹✳✷✮✳ ❚♦ t❡st t❤❡ ❡☛❡❝t✐✈❡♥❡ss ♦❢ ❆❩✹✻✷✵ ❛s ❛ ♠❛s❦ t♦ st♦♣ t❤❡ ✐♥❝✐❞❡♥t ✐♦♥s✱ ❞✐☛❡r❡♥t s✐♥❣❧❡ ❧❛②❡r❡❞ ♣❛tt❡r♥❡❞ P❘ ✇❡r❡ ✐rr❛❞✐❛t❡❞ ✇✐t❤ ✈❛r✐♦✉s ✌✉❡♥❝❡s ❛♥❞ s✉❜s❡q✉❡♥t❧② ❛♥♦❞✐③❡❞ ✐♥t♦ ❉❇❘s r❡✌❡❝t✐♥❣ ❞✐☛❡r❡♥t ❝♦❧♦rs✳ ❚❤❡ r❡s✉❧ts ❢♦r t❤✐s t❡st ❛r❡ s✉♠♠❛r✐③❡❞ ✐♥ ❋✐❣ ✺✳✶✽✳ ❆❩✹✻✷✵ ♣r♦✈❡s t♦ ❜❡ ❡☛❡❝t✐✈❡ ✐♥ st♦♣♣✐♥❣ ✐♥❝♦♠✐♥❣ ✐♦♥s ❢r♦♠ ❞❛♠❛❣✐♥❣ t❤❡ ✉♥❞❡r❧②✐♥❣ s✐❧✐❝♦♥✳ ❆❩✹✻✷✵ ✇❛s ❛❧s♦ ❝❤♦s❡♥ ❜❡❝❛✉s❡ ❛ t❤✐❝❦ ❧❛②❡r ♦❢ ✼✖♠ ♠❛② ❜❡ s♣✐♥ ❝♦❛t❡❞ ♦♥t♦ s✐❧✐✲ ❝♦♥✳ ■♥ ❛❞❞✐t✐♦♥✱ ♠✉❧t✐❧❡✈❡❧❡❞ P❘ st❡♣s ♠❛② ❜❡ ❢❛❜r✐❝❛t❡❞ ❜② ❝♦♥tr♦❧❧✐♥❣ t❤❡ ❯❱ ❡①♣♦s✉r❡ t✐♠❡✳ ❙✉❝❤ ❛ ♠✉❧t✐❧❡✈❡❧ ♠❛s❦ ✐s ♥❡❝❡ss❛r② t♦ ✐rr❛❞✐❛t❡ ❞✐☛❡r❡♥t ❛♠♦✉♥ts ♦❢ ❞❛♠❛❣❡✴✌✉❡♥❝❡ t♦ t❤❡ ✉♥❞❡r❧②✐♥❣ s✐❧✐❝♦♥ ❢♦r ♣r♦❞✉❝✐♥❣ s❡✈❡r❛❧ r❡✌❡❝t✐✈❡ ❝♦❧♦rs ♦❢ t❤❡ r❡s✉❧t❛♥t ❉❇❘✳ ■♦♥s ♦❢ t✇♦ ♦r t❤r❡❡ ❞✐☛❡r❡♥t ❡♥❡r❣✐❡s ❛r❡ ✉s❡❞ t♦ ✐rr❛❞✐❛t❡ t❤❡ s❛♠❡ ❛r❡❛ ✇✐t❤ ♦♥❧② t❤♦s❡ ❛❜♦✈❡ ❛ ❝❡rt❛✐♥ ❡♥❡r❣② ❞❡t❡r♠✐♥❡❞ ❜② t❤❡ P❘ ♠❛s❦ t❤✐❝❦♥❡ss ♠❛② ♣❡♥❡tr❛t❡ t❤❡ ✇❛❢❡r✳ ❙❘■▼ ❬✸✵❪ s✐♠✉❧❛t✐♦♥ ♦❢ ✷✵✵ ❛♥❞ ✸✺✵ ❦❡❱ ♣r♦t♦♥ ✐♦♥s ✐♥❝✐❞❡♥t ♦♥ ❞✐☛❡r❡♥t t❤✐❝❦♥❡ss❡s ♦❢ P❘ ♦♥ ✼✼ ❙✐♠✐❧❛r❧②✱ t♦ ❢❛❜r✐❝❛t❡ ❘❡❞✱ ❨❡❧❧♦✇✱ ●r❡❡♥ ❛♥❞ ❇❧✉❡ ✭❘❨●❇✮ ❝♦❧♦r ♣✐①❡❧s✱ ❛ P❘ ✇✐t❤ ❢♦✉r ❞✐☛❡r❡♥t t❤✐❝❦♥❡ss ✇❛s ♣r♦❞✉❝❡❞ ❜② ❞♦✉❜❧❡ ❡①♣♦s✐♥❣ t❤❡ P❘ ✇✐t❤ ❛ ❝❤r♦♠❡ P▼ ♦❢ ❣r❛t✐♥❣ str✉❝t✉r❡ ♦❢ ✷✵ ✖♠ ♣❡r✐♦❞ ✭✶✵✴✶✵✖♠ ✇✐❞❡ ♦♣❛q✉❡✴❝❧❡❛r r❡❣✐♦♥s✮ ✐♥ ♣❛r❛❧❧❡❧ ❛♥❞ ♣❡r♣❡♥❞✐❝✉❧❛r ❞✐r❡❝t✐♦♥s ✭❋✐❣ ✺✳✷✷✮ ❆❢t❡r ❡①♣♦s✉r❡s t♦ ❛ ❝❡rt❛✐♥ ❞♦s❡s ♦❢ ❯❱✱ t❤❡ P❘ ❧❛②❡r ✇❛s ❞❡✈❡❧♦♣❡❞ ✐♥t♦ ❛ ♣❛tt❡r♥ ♦❢ sq✉❛r❡ ♣✐①❡❧s✳ ❋✐❣ ✺✳✷✷ s❤♦✇s ❛ s❝❤❡♠❛t✐❝ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ❢❛❜r✐❝❛t✐♦♥ ♣r♦❝❡❞✉r❡✱ ✇❤❡r❡ ❡①♣♦s✉r❡ ♦❢ ❣r❛t✐♥❣ ✐♥ ✵ ❛♥❞ ✾✵ ❞❡❣r❡❡s ♣r♦❞✉❝❡s ❢♦✉r ❧❡✈❡❧ sq✉❛r❡ ♣✐①❡❧s ✐♥ t❤❡ P❘✳ ❚❤❡ ❡☛❡❝t✐✈❡ ❯❱ ❡①♣♦s✉r❡ t✐♠❡✴❞♦s❡ t♦ ❝r❡❛t❡ sq✉❛r❡ ♣✐①❡❧s ♣❛tt❡r♥❡❞ ♣❡r✐♦❞✐❝❛❧❧② ✇✐t❤ ❢♦✉r ❞✐☛❡r❡♥t ❞❡♣t❤s ✐♥ P❘ ✐s ❛❧s♦ s❤♦✇♥ ✐♥ ❋✐❣ ✺✳✷✷✳ ■rr❛❞✐❛t✐♥❣ t❤❡ ❢♦✉r ❧❡✈❡❧ P❘ ✇❛s ❝❛rr✐❡❞ ♦✉t ✉s✐♥❣ t❤r❡❡ ♣r♦t♦♥ ❡♥❡r❣✐❡s ♦❢ ✸✼✺ ❦❡❱✱ ✷✺✵ ❦❡❱ ❛♥❞ ✶✺✵ ❦❡❱ ❛♥❞ t❤✐s r❡s✉❧ts ✐♥ ❢♦✉r ❞✐☛❡r❡♥t ✌✉❡♥❝❡s ✐♥ t❤❡ ✉♥❞❡r❧②✐♥❣ s✐❧✐❝♦♥✳ ❚❤❡ s❛♠♣❧❡ ✇❛s t❤❡♥ ❛♥♦❞✐③❡❞ ✇✐t❤ t✇❡❧✈❡ ❜✐❧❛②❡rs ✇✐t❤ ❛❧t❡r♥❛t✐♥❣ ❝✉rr❡♥t ❞❡♥s✐t✐❡s t♦ ❢♦r♠ P❙✐ ❉❇❘s✳ ❋✐❣ ✺✳✷✸✭❛✮ ❛♥❞ ✭❜✮ ❛r❡ ♦♣t✐❝❛❧ ✐♠❛❣❡s ♦❢ t❤❡ P❙✐ ❉❇❘s ✐♥ t❤❡ ❢♦r♠ ♦❢ ❘❨●❇ r❡✌❡❝t✐✈❡ ❝♦❧♦rs ♣✐①❡❧s ❡❛❝❤ ✶✵ ✖♠ ✂ ✶✵ ✖♠ ✐♥ ❞✐♠❡♥s✐♦♥✳ ■♥ ♣r❡✈✐♦✉s s❡❝t✐♦♥ ♦♥ t❤❡ ❢♦r♠❛t✐♦♥ ♦❢ ♣❛tt❡r♥❡❞ ❉❇❘s ✉s✐♥❣ ✷ ▼❡❱ ♣r♦t♦♥s ✭❈❤❛♣t❡r ✺✳✸✮✱ t❤❡ r❡s✉❧t❛♥t ❞❡❢❡❝t ♣r♦☞❧❡ ✐s ❛❧♠♦st ❝♦♥st❛♥t ✇✐t❤ ❞❡♣t❤✳ ❚❤✐s r❡s✉❧t❡❞ ✐♥ ❛ ❧✐♥❡❛r ❜❧✉❡ s❤✐❢t ✈❡rs✉s ✌✉❡♥❝❡ ♦✇✐♥❣ t♦ t❤❡ ❧✐♥❡❛r ❝❤❛♥❣❡ ✐♥ P❙✐ ❢♦r♠❛t✐♦♥ r❛t❡ ❝❛✉s❡❞ ❜② t❤❡ r❡❞✉❝t✐♦♥ ✐♥ ❤♦❧❡ ❝✉rr❡♥t ❞❡♥s✐t② ✌♦✇✐♥❣ t❤r♦✉❣❤ t❤❡ ✐rr❛❞✐❛t❡❞ ❛r❡❛s✳ ❍❡r❡✱ t❤❡ ❞❡❢❡❝t ❞❡♣t❤ ♣r♦☞❧❡ ❝❧♦s❡ t♦ t❤❡ s✉r❢❛❝❡ ❜❡❝✉❛s❡ ♦❢ t❤❡ ❧♦✇ ❡♥❡r❣✐❡s ✉s❡❞ ✐s ❤✐❣❤❧② ♥♦♥✲✉♥✐❢♦r♠✳ ❆s ❛ r❡s✉❧t✱ t❤❡ r❡❧❛t✐♦♥s❤✐♣ ❜❡t✇❡❡♥ ♣❡❛❦ r❡✌❡❝t❡❞ ✇❛✈❡❧❡♥❣t❤ ❛♥❞ ✌✉❡♥❝❡ ✐s ♥♦t s♦ ❝❧❡❛r❧② ❞❡☞♥❡❞✳ ❆ ❞❡❣r❡❡ ♦❢ ❡①♣❡r✐♠❡♥t❛t✐♦♥ ❢♦r t❤❡ ✌✉❡♥❝❡ ❛♥❞ ❛♥♦❞✐③❛t✐♦♥ ❝♦♥❞✐t✐♦♥s ✇❛s r❡q✉✐r❡❞ t♦ ❝♦♥tr♦❧❧❛❜❧② ♣r♦❞✉❝❡ ❛ ❣✐✈❡♥ r❡✌❡❝t❡❞ ❝♦❧♦r ❝♦♠❜✐♥❛t✐♦♥✳ ❋✐❣ ✺✳✷✸ s❤♦✇s ♣❛tt❡r♥❡❞ ❉❇❘s ♣r♦❞✉❝❡❞ ✐♥ t❤❡ ❢♦r♠ ♦❢ ❘❨●❇ ❝♦❧♦r ♣✐①❡❧s ❛r❡ t❤❡ r❡s✉❧t ♦❢ ❝❛r❡❢✉❧ ♦♣t✐♠✐③❛t✐♦♥✳ ❆ ❧✐♥❡ s❝❛♥ ✐♥ ❋✐❣ ✺✳✷✸❝ s❤♦✇s ❣♦♦❞ ✉♥✐❢♦r♠✐t②✳ ■♥ ❛❞❞✐t✐♦♥✱ t❤✐s ✉♥✐❢♦r♠✐t② ❡①t❡♥❞s ♦✈❡r t❤❡ ❢✉❧❧✲✐rr❛❞✐❛t❡❞ ❛r❡❛ ♦❢ s❡✈❡r❛❧ sq✉❛r❡ ❝❡♥t✐♠❡t❡rs✳ ✺✳✻ ❙✉♠♠❛r② ❚♦ s✉♠♠❛r✐③❡ t❤✐s ❝❤❛♣t❡r✿ ✎ P❙✐ ❜❛s❡❞ ❉❇❘s ❤❛s ❜❡❡♥ s✉❝❝❡ss❢✉❧❧② ❢❛❜r✐❝❛t❡❞✳ ✼✽ ✎ ❈♦♥tr♦❧❧❛❜❧❡ ❜❧✉❡ s❤✐❢t✐♥❣ ♦❢ t❤❡ P❙✐ ❉❇❘s ✇✐t❤ ✐♦♥ ✐rr❛❞✐❛t✐♦♥ ❤❛s ❜❡❡♥ s✉❝❝❡ss❢✉❧❧② ❞❡♠♦♥str❛t❡❞ ❛♥❞ ❝❤❛r❛❝t❡r✐③❡❞✳ ✎ ❚❤r❡❡ ❞✐♠❡♥s✐♦♥❛❧ P❙✐ ❜❛s❡❞ ❉❇❘ ✇✐t❤ t❤❡ ❛❜✐❧✐t② t♦ r❡✌❡❝t ❛❧❧ ✐♥❝✐❞❡♥t ✇❛✈❡❧❡♥❣t❤s t❤r♦✉❣❤ ❛ ✇✐❞❡ ❛♥❣✉❧❛r r❛♥❣❡✱ r❡s✉❧t✐♥❣ ✐♥ ✇❤✐t❡ r❡✌❡❝t✐✈❡ r❡❣✐♦♥s ❤❛s ❜❡❡♥ ❞❡♠♦♥✲ str❛t❡❞✳ ❆♥❞ ❝r❡❛t✐✈❡ ✉s❡ ♦❢ t❤✐s ✇❛s s❤♦✇♥ ✐♥ t❤❡ ❢♦r♠ ♦❢ ❛❧♣❤❛♥✉♠❡r✐❝ ✐♠❛❣❡s ✇❤✐❝❤ ❞✐s♣❧❛②s ❞✐☛❡r❡♥t ♥✉♠❜❡rs ✇❤❡♥ ✐❧❧✉♠✐♥❛t❡❞ ❞✐☛❡r❡♥t❧②✳ ✎ ❆ ✐rr❛❞✐❛t✐♦♥ ❢❛❝✐❧✐t② ❤❛s ❜❡❡♥ ❝♦♥str✉❝t❡❞ ✇❤✐❝❤ ♣r♦❥❡❝ts ❛ ❢♦❝✉s❡❞✱ ❤✐❣❤❧② ❝♦♥✲ ✈❡r❣❡♥t ▼❡❱ ✐♦♥ ❜❡❛♠ ♦✈❡r ❛ ✇❛❢❡r ❛r❡❛ ♦❢ s❡✈❡r❛❧ sq✉❛r❡ ❝❡♥t✐♠❡t❡rs✱ s✉✐t❛❜❧❡ ❢♦r ♣❛tt❡r♥✐♥❣ ✇❛❢❡rs t♦ ❞❡♣t❤s ♦❢ s❡✈❡r❛❧ ♠✐❝r♦♠❡t❡rs✳ ❚❤✐s ❢❛❝✐❧✐t② ✇❛s ✉s❡❞ t♦ ♣r♦❞✉❝❡ ❧❛r❣❡✲❛r❡❛ ♣❛tt❡r♥❡❞ ❉❇❘s ❞❡☞♥❡❞ ❜② ❛ ❧❛②❡r ♦❢ ♠✉❧t✐❧❡✈❡❧ P❘✳ ❚❤❡ ♣r♦❞✉❝t✐♦♥ ♦❢ ❤✐❣❤ ❞❡♥s✐t② P❙✐ ♣❛tt❡r♥❡❞ ❉❇❘s ❤❛s ♣♦t❡♥t✐❛❧ ✐♥ ♠❛♥② ❞✐☛❡r❡♥t ❛♣♣❧✐❝❛t✐♦♥s ❧✐❦❡ ❞✐s♣❧❛②s ♦r ❛rr❛②s ♦❢ ♠✐❝r♦❝❛✈✐t✐❡s t✉♥❡❞ t♦ ❞✐☛❡r❡♥t ✇❛✈❡❧❡♥❣t❤s✱ ❝♦✉♣❧❡❞ ♠✐❝r♦❝❛✈✐t✐❡s✱ s✐❧✐❝♦♥✲❜❛s❡❞ ❧❛s❡rs ❛♥❞ t✉♥❛❜❧❡ s✐❧✐❝♦♥✲❜❛s❡❞ ♣❤♦t♦♥✐❝ ❜❛♥❞ ❣❛♣ str✉❝t✉r❡s ❢♦r ♦♣t✐❝❛❧ ♠♦❞✉❧❛t✐♦♥✳ [...]... mesh grid irradiation pattern can be seen, with the most blueshifted regions being those where the beam has passed through both sets of holes 5.5.2 Patterned large area irradiation with photoresist masks The demonstration to rapidly fabricate large arrays of DBRs with the grids shows the viability of this technique However, a surface mask structure is required to produce re ective colors of arbitrary... fabricated into a 2nd or 3rd stage 3D DBRs To summarize this section, we have use ion irradiated micromachined 3D PSi DBR to Tune the range of the tilted angle to produce either wide-band white re ectivity or single color re ectivity Control the range of angles over which incident light is re ected or not In addition the use the large area irradiation facilities for rapid production 3D DBRs has been demonstrated... fabrication and use of a photoresist (PR) mask structure is now described which gives the capability of creating large-area patterned DBRs in conjunction with this large area irradiation system The PR used for this work is AZ4620 and is patterned using UV lithography facilities at IMRE (for more information and characterization of this resist refer to Chapter 2.4.2) To test the e ectiveness of AZ4620... irradiate di erent amounts of damage/ uence to the underlying silicon for producing several re ective colors of the resultant DBR Ions of two or three di erent energies are used to irradiate the same area with only those above a certain energy determined by the PR mask thickness may penetrate the wafer SRIM [30 ] simulation of 200 and 35 0 keV proton ions incident on di erent thicknesses of PR on ... unirradiated regions because while n increases with uence, Rn remains relatively constant Hence, R/ decreases accordingly as well This explains why width of the re ectivity peak R in Fig 5.7 becomes narrower with reduce with increasing uence, however, increasing uence The most important result to take from these is how much blue shift may be achieved from a particular wavelength with ion irradiation With. .. microcavities, silicon- based lasers and tunable silicon- based photonic band gap structures for optical modulation However, wider application requires rapid, mass patterning over large wafers surfaces In this work, simple modi cations were made to a megavolt accelerator and nuclear microprobe to give a facility capable of large area irradiation (see Chapter 2.4.2 for the facility setup) at MeV ion energies, with. .. irradiated line and had their cross sections imaged with a SEM to show how the shape of the layers changes progressively with anodization depth In the rst stage (Fig 5.12(a)) for the lower uence of 2 ¢ 1015/cm2, the multilayer stack at the center of the irradiated line are thinner than at the unirradiated background for reasons discussed in the previous section (5 .3) of this chapter The multilayer's thickness... because the more irradiated DBR layers are thinner as a result of greater reduction in the PSi formation (see Chapter 3. 6), giving rise to a bigger di erence in the PSi thickness across the irradiated and unirradiated boundaries with anodized depth Inset of Fig 5. 13( a) is a plot which shows that changes approximately linearly with uence Hence, DBRs with di erent boundary layer tilts may 67 left, re ected... tilted boundary To produce such DBRs with parallel tilted boundary layers, a thick PSi is rst anodized and removed, before the nal anodization of the nal DBR Fig 5.14 demonstrates the kind of re ections that may be obtained from white light illumination on these DBRs at di erent stages and geometries rows were irradiated with a uence of 2 irradiated with uences of 1 ¢ 10 ¢ 15 /cm2 10 15 /cm2 All DBRs... unirradiated samples (gradient of plots) The average value of refractive index n = (nh + nl )/2 however, increases with uence Fig 5.8(c) shows the measured thickness (using SEM) of a single porous bilayer (of high and low refractive index) versus uence The measured values of n (from the same samples in Fig 5.8(b)) at J = 25 and 85 mA/cm2 are plotted against uence In additions, a new parameter, the average . Chapter 5