Chapter ❙✐❧✐❝♦♥ ❇❛s❡❞ ❈♦♠♣✉t❡r ●❡♥❡r❛t❡❞ ❍♦❧♦❣r❛♣❤② ❚❤✐s ❝❤❛♣t❡r ❞❡s❝r✐❜❡s ❛❜♦✉t ✉s✐♥❣ t❤❡ ✐♦♥ ✐rr❛❞✐❛t❡❞ s✐❧✐❝♦♥ ♠✐❝r♦♠❛❝❤✐♥✐♥❣ t❡❝❤♥✐q✉❡ t♦ tr❛♥s❢❡r ❝♦♠♣✉t❡r ❣❡♥❡r❛t❡❞ ❤♦❧♦❣r❛♠ ✭❈●❍✮ ♣❛tt❡r♥s ♦♥t♦ t❤❡ s✐❧✐❝♦♥ s✉r❢❛❝❡✳ Pr✐♦r t♦ t❤❡ ❛❝t✉❛❧ ❢❛❜r✐❝❛t✐♦♥ ♦❢ ❛ s✐❧✐❝♦♥ ❜❛s❡❞ ❈●❍✱ P❇❲ ✇❛s ✉s❡❞ t♦ ❞✐r❡❝t ✇r✐t❡ ❈●❍ ♣❛tt❡r♥s ♦♥ P▼▼❆ ❢♦r t❤❡ ♣✉r♣♦s❡ ♦❢ ❢❛❜r✐❝❛t✐♥❣ s✇✐t❝❤❛❜❧❡ ❈●❍ ✭❈❤❛♣t❡r ✻✳✷✮✳ ✻✳✶ ■♥tr♦❞✉❝t✐♦♥ ✻✳✶✳✶ ❍♦❧♦❣r❛♣❤② ❍♦❧♦❣r❛♣❤② ✐s ❛ ♠❡t❤♦❞ t❤❛t ❛❧❧♦✇s ❢♦r t❤❡ st♦r❛❣❡✱ r❡tr✐❡✈❛❧ ❛♥❞ ♣r♦❝❡ss✐♥❣ ♦❢ ✐♥❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❢♦r♠ ♦❢ ❧✐❣❤t ✐♥✈❡♥t❡❞ ❜② ❉❡♥♥✐s ●❛❜♦r ✐♥ ✶✾✹✼✳ ❚❤❡ t❡r♠ ❤♦❧♦❣r❛♠ ✐s ❞❡r✐✈❡❞ ❢r♦♠ t❤❡ ●r❡❡❦ ✇♦r❞ ❤♦❧♦s ✇❤✐❝❤ ♠❡❛♥s ✇❤♦❧❡✳ ❚❤✐s ❛♣♣r♦♣r✐❛t❡❧② ❞❡s❝r✐❜❡s t❤❡ ❤♦❧♦❣r❛♣❤② ❛s ✐t r❡❝♦r❞s t❤❡ ✇❛✈❡✲❢r♦♥t ✐♥❢♦r♠❛t✐♦♥ ❜❛s❡❞ ♦♥ ❧✐❣❤t ✇❤✐❝❤ ✐s s❝❛tt❡r❡❞ ❢r♦♠ ❛♥ ♦❜❥❡❝t ✐♥t♦ ❛ ❤♦❧♦❣r❛♠ ❛♥❞ ♣r♦❞✉❝❡s ❛ r❡❝♦♥str✉❝t❡❞ ✐♠❛❣❡ ❢r♦♠ ✐t✳ ❯♥❧✐❦❡ ❝♦♥✈❡♥t✐♦♥❛❧ ♣❤♦t♦❣r❛♣❤② ✐♥ ✇❤✐❝❤ ♦♥❧② ❧✐❣❤t✲✐♥t❡♥s✐t② ✐♥❢♦r♠❛t✐♦♥ ✐s r❡❝♦r❞❡❞✱ ❛ ❤♦❧♦❣r❛♠ r❡❝♦r❞s ❜♦t❤ ✐♥t❡♥s✐t② ❛♥❞ ♣❤❛s❡ ✐♥❢♦r♠❛t✐♦♥✱ t❤✉s ❤❛s t❤❡ ❛❜✐❧✐t② t♦ r❡❝♦♥str✉❝t t❤r❡❡ ❞✐♠❡♥s✐♦♥❛❧ ✐♠❛❣❡s✳ ❆s t❤❡ ♣♦s✐t✐♦♥ ♦❢ t❤❡ ✈✐❡✇❡r ❝❤❛♥❣❡s✱ t❤❡ r❡❝♦♥str✉❝t❡❞ ✐♠❛❣❡ ❢r♦♠ ❛ ❤♦❧♦❣r❛♠ ❝❤❛♥❣❡s ✼✾ ✽✷ ❋✐❣✉r❡ ✻✳✸✿ ✭❛✮ ✐♥s❡t s❤♦✇s ◆❯❙ ✐♥♣✉t ☞❧❡✱ ❝♦♠♣r✐s✐♥❣ ✸✵ ❜② ✶✺ ♣✐①❡❧s✳ ✭❛✮✱ ✭❜✮ ❝♦rr❡s♣♦♥❞✐♥❣ ❈●❍ ♣❛tt❡r♥ ❆❢t❡r ❛ ❈●❍ ❤♦❧♦❣r❛♠ ✐s ❝♦♠♣✉t❡❞✱ ✐t ❤❛s t♦ ❜❡ r❡❝♦r❞❡❞ ♦♥t♦ ❛ ♠❡❞✐✉♠ t❤❛t ✐s ❛❜❧❡ t♦ ♠♦❞✉❧❛t❡ t❤❡ ✐♥t❡r❢❡r❡♥❝❡ ♣❛tt❡r♥ ❢r♦♠ ❛ ❝♦❤❡r❡♥t ❧✐❣❤t s♦✉r❝❡ t♦ ♣r♦❞✉❝❡ ❛ r❡❝♦♥str✉❝t❡❞ ✐♠❛❣❡✳ ▼❛♥② ❞✐☛❡r❡♥t ♠❛t❡r✐❛❧s ❤❛✈❡ ❜❡❡♥ ✉s❡❞ t♦ r❡❝♦r❞ ❈●❍s✱ ❡✳❣✳ ♣❤♦t♦r❡❢r❛❝t✐✈❡ ♠❛t❡r✐❛❧s ❧✐❦❡ ❇❛❚✐❖✸ ❬✼✷❪✱ ♣❤♦t♦♣♦❧②♠❡rs ❬✼✸❪ ❛♥❞ t❤❡r♠♦✲♣❧❛st✐❝s ❬✼✹❪✳ ●❡♥❡r❛❧❧②✱ t❤❡s❡ ♠❛t❡r✐❛❧s ❤❛✈❡ ♣❤②s✐❝❛❧ ♣r♦♣❡rt✐❡s ✇❤✐❝❤ ❡♥❛❜❧❡ t❤❡♠ t♦ ♠♦❞✉❧❛t❡ ❡✐t❤❡r t❤❡ ♣❤❛s❡ ♦r t❤❡ ❛♠♣❧✐t✉❞❡ ♦❢ t❤❡ ✐♥❝♦♠✐♥❣ ❧✐❣❤t✱ ❜✉t ♥♦t ❜♦t❤✳ P❤❛s❡ ♠♦❞✉❧❛t✐♦♥ ✐s ✉s✉❛❧❧② ❞♦♥❡ ❜② ❝❤❛♥❣✐♥❣ t❤❡ ♦♣t✐❝❛❧ t❤✐❝❦♥❡ss t❤r♦✉❣❤ ✇❤✐❝❤ ❧✐❣❤t ❤❛s t♦ tr❛✈❡❧✱ ✇❤✐❧❡ ❛♠♣❧✐t✉❞❡ ♠♦❞✲ ✉❧❛t✐♦♥ ✐s ❝❛rr✐❡❞ ❜② ❤❛✈✐♥❣ ✈❛r②✐♥❣ ✐♥t❡♥s✐t✐❡s ♦❢ ❧✐❣❤t t♦ ♣❛ss t❤r♦✉❣❤ ❢♦r tr❛♥s♠✐ss✐♦♥ ❈●❍✱ ♦r r❡✌❡❝t❡❞ ❢♦r r❡✌❡❝t✐✈❡ ❈●❍✳ ❈●❍ ❞❡✈✐❝❡s ❜❛s❡❞ ♦♥ ❧✐q✉✐❞ ❝r②st❛❧ s♣❛t✐❛❧ ❧✐❣❤t ♠♦❞✉❧❛t♦rs ❤❛✈❡ ❛❧s♦ ❜❡❡♥ r❡♣♦rt❡❞ ❬✼✺❪✳ ❚♦ ❞❛t❡✱ t❤❡② ❛r❡ t❤❡ ♦♥❧② ❞❡✈✐❝❡s ✇❤✐❝❤ ❛r❡ ❛❜❧❡ t♦ ♠♦❞✉❧❛t❡ ❜♦t❤ ♣❤❛s❡ ❛♥❞ ❛♠♣❧✐t✉❞❡ ❬✼✻❪✳ ❍♦✇❡✈❡r✱ t❤❡✐r ♣✐①❡❧ r❡s♦❧✉t✐♦♥ ✐s ✉s✉❛❧❧② ✐♥ t❤❡ r❛♥❣❡ ♦❢ t❡♥s ♦❢ ♠✐❝r♦♥s✳ ✻✳✷ ❙✇✐t❝❤❛❜❧❡ ❈●❍ ❆ ❣r♦✉♣ ✐♥ t❤❡ ◆❛♥②❛♥❣ ❚❡❝❤♥♦❧♦❣✐❝❛❧ ❯♥✐✈❡rs✐t② ♦❢ ❙✐♥❣❛♣♦r❡ ✭◆❚❯✮ ❙❝❤♦♦❧ ♦❢ ❊❧❡❝tr✐✲ ❝❛❧ ❛♥❞ ❊❧❡❝tr♦♥✐❝ ❊♥❣✐♥❡❡r✐♥❣ r❡❝❡♥t❧② r❡♣♦rt❡❞ ❛ s✇✐t❝❤❛❜❧❡ ♣❤❛s❡ ♠♦❞✉❧❛t❡❞✱ ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ ❝❛❧❝✉❧❛t❡❞ ❈●❍ ❢❛❜r✐❝❛t❡❞ ✉s✐♥❣ ♣♦❧②♠❡r✲❞✐s♣❡rs❡❞ ❧✐q✉✐❞ ❝r②st❛❧s ✭P❉▲❈✮ ❛♥❞ ❧✐q✉✐❞ ❝r②st❛❧ ✭▲❈✮ ❝❡❧❧ ✇✐t❤ ♣❛tt❡r♥❡❞ ❡❧❡❝tr♦❞❡ ❬✼✵❪✳ P❤❛s❡ ♠♦❞✉❧❛t✐♦♥ ✐s ❛❝❤✐❡✈❡❞ ❜② ❤❛✈✐♥❣ ❛♥ ♦♣t✐❝❛❧ ♣❛t❤ ❧❡♥❣t❤ ❞✐☛❡r❡♥❝❡ ✇❤✐❝❤ ❡①✐st ❜❡❝❛✉s❡ ♦❢ t❤❡ ❞✐☛❡r❡♥❝❡ ✐♥ r❡❢r❛❝t✐✈❡ ✐♥❞✐❝❡s ✐♥ t❤❡ ♣♦❧②♠❡r✲r✐❝❤ ❛♥❞ ▲❈✲r✐❝❤ r❡❣✐♦♥s✳ ❯♣♦♥ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ❛♥ ❡①t❡r♥❛❧ ✈♦❧t❛❣❡✱ ✽✹ ❆ ✺ ✖♠ t❤✐❝❦ ❧❛②❡r ♦❢ ♣♦❧②♠❡t❤②❧♠❡t❤❛❝r②❧❛t❡ ✭P▼▼❆✮ ✇❛s ☞rst ♣r❡♣❛r❡❞ ♦♥ ❛ ✶ ♠♠ t❤✐❝❦ ❣❧❛ss s❧✐❞❡ ❜② s♣✐♥ ❝♦❛t✐♥❣✳ ❆s ❛ ☞rst ❛tt❡♠♣t✱ t❤❡ ❈●❍ ♣❛tt❡r♥ ❝♦♠♣✉t❡❞ ❜② t❤❡ r❛② tr❛❝✐♥❣ ♠❡t❤♦❞ ❬✼✼❪ ✐♥ ❋✐❣ ✻✳✸ ✇❛s ♣r♦t♦♥ ❜❡❛♠ ✇r✐tt❡♥ ♦♥ P▼▼❆✳ ■t ✇❛s ❝♦♥✈❡rt❡❞ ✐♥t♦ ❛ ❢♦r♠❛t ✇❤✐❝❤ ❢✉❧❧② s♣❡❝✐☞❡s t❤❡ ♣❛tt❡r♥ ✐♥ t❡r♠s ♦❢ ❝♦♦r❞✐♥❛t❡s ✇❤✐❝❤ ❝❛♥ t❤❡♥ ❜❡ r❡❛❞ ❜② ■❖◆❙❈❆◆ ✭❈❤❛♣t❡r ✷✳✹✳✶✮ ❛♥❞ tr❛♥s❢❡r t❤❡ ❈●❍ ❞✐☛r❛❝t✐♦♥ ♣❛tt❡r♥ t♦ t❤❡ P▼▼❆✳ ❚❤✐s ❢♦r♠ ♦❢ P❇❲ ✐s ❞❡♠❛♥❞✐♥❣ s✐♥❝❡ ✐t r❡q✉✐r❡s ❢r❡q✉❡♥t ❜❡❛♠ ❜❧❛♥❦✐♥❣ ❞✉❡ t♦ t❤❡ ♠❛♥② ❝❤❛♥❣❡s ❢r♦♠ ❜❧❛❝❦ t♦ ✇❤✐t❡ ♣✐①❡❧s t②♣✐❝❛❧❧② ❢♦✉♥❞ ✐♥ ❈●❍ ♣❛tt❡r♥s✳ ❚❤❡ ❈●❍ ♣❛tt❡r♥ ✐s tr❛♥s❢❡rr❡❞ t♦ P▼▼❆ ❜② ✐rr❛❞✐❛t✐♥❣ ♦✈❡r ❛♥ ❛r❡❛ ♦❢ ✷ ✂ ✷ ♠♠✷ ❝♦♥t❛✐♥✐♥❣ ✶✵✷✹ ✂ ✶✵✷✹ ♣✐①❡❧s✱ ❣✐✈✐♥❣ ❛ ♣✐①❡❧ s✐③❡ ❛♥❞ r❡s♦❧✉t✐♦♥ ♦❢ ❛♣♣r♦①✐♠❛t❡❧② ✷ ✂ ✷ ✖♠✳ ❚❤❡ ♣r♦t♦♥ ❜❡❛♠ ❝✉rr❡♥t ♦❢ ✼✵ ♣❆ ✇❛s ❢♦❝✉s❡❞ t♦ ❛ s♣♦t s✐③❡ t♦ ♠❛t❝❤ t❤❛t ♦❢ ❡❛❝❤ ♣✐①❡❧✳ ❚❤❡ ✌✉❡♥❝❡ r❡q✉✐r❡❞ ❢♦r P▼▼❆ t♦ ❜❡ r❡♠♦✈❡❞ ❢♦r s✉❜s❡q✉❡♥t ❞❡✈❡❧♦♣♠❡♥t ✐s ✶✹✵ ♥❈✴♠♠✷ ✭✽✳✼✻ ✂ ✶✵✶✸ ✐♦♥s✴❝♠✷ ✮ ❢♦r ✷ ▼❡❱ ♣r♦t♦♥s ❬✼✽❪ ✇❤✐❝❤ ❣✐✈❡s ❛ t♦t❛❧ ✐rr❛❞✐❛t✐♦♥ t✐♠❡ ♦❢ ❛♣♣r♦①✐♠❛t❡❧② ✷✳✷ ❤♦✉rs✳ ❘❡♠♦✈❛❧ ♦❢ ✐rr❛❞✐❛t❡❞ P▼▼❆ ✇❛s ❞♦♥❡ ✉s✐♥❣ ❛ s♦❧✉t✐♦♥ ♦❢ ✐s♦♣r♦♣❛♥♦❧ ❛♥❞ ✇❛t❡r ✐♥ t❤❡ ✈♦❧✉♠❡ r❛t✐♦ ♦❢ ✼✿✸ ❢♦r ✶✵ ♠✐♥ ❛t r♦♦♠ t❡♠♣❡r❛t✉r❡✳ ❚❤❡ ■P❆ ❜❛s❡❞ s♦❧✉t✐♦♥ ✇❛s ✉s❡❞ ❛s ❛ ❞❡✈❡❧♦♣❡r ❛s ✐ts ❡☛❡❝t ♦♥ ✉♥❡①♣♦s❡❞✴✉♥✲✐rr❛❞✐❛t❡❞ P▼▼❆ r❡s✐st ✐s ❧❡ss ❛❣❣r❡ss✐✈❡ ❬✼✽❪ t❤❛♥ t❤❛t ♦❢ t❤❡ ❝♦♥✈❡♥t✐♦♥❛❧ ●● ❞❡✈❡❧♦♣❡r✳ ❚❤✐s ❡♥s✉r❡s t❤❛t t❤❡ str✉❝t✉r❛❧ ♣r❡❝✐s✐♦♥ ♦❢ t❤❡ str✉❝t✉r❡s ✐s ❞❡t❡r♠✐♥❡❞ ❜② t❤❡ s✐③❡ ♦❢ t❤❡ ❢♦❝✉s❡❞ ♣r♦t♦♥ ❜❡❛♠✱ r❛t❤❡r t❤❛♥ ❛r✐s✐♥❣ ❢r♦♠ t❤❡ ❡t❝❤✐♥❣ ♦❢ ✉♥✲✐rr❛❞✐❛t❡❞ r❡s✐st✳ ❚❤❡ ❞❡✈❡❧♦♣❡❞ P▼▼❆ ♣❛tt❡r♥s ❝♦♥t❛✐♥ t❤❡ ❈●❍ ❞✐☛r❛❝t✐♦♥ ♣❛tt❡r♥ ❛♥❞ ❛r❡ s❤♦✇♥ ✐♥ ❋✐❣ ✻✳✹✭❝✮ ❛♥❞ ✭❞✮ ❛t t❤❡ s❛♠❡ ♠❛❣♥✐☞❝❛t✐♦♥ ❛s t❤❡ ♦r✐❣✐♥❛❧ ❣❡♥❡r❛t❡❞ ❈●❍ ✐♠❛❣❡s ✐♥ ❋✐❣ ✻✳✹✭❛✮ ❛♥❞ ✭❜✮ ❢♦r ❛ ❞✐r❡❝t ❝♦♠♣❛r✐s♦♥✳ ●♦♦❞ ♣❛tt❡r♥ tr❛♥s❢❡r ❢r♦♠ t❤❡ ✐♠❛❣❡ ☞❧❡ ✐♥t♦ t❤❡ P▼▼❆ ❧❛②❡r ✐s ❛❝❤✐❡✈❡❞✳ ❚❤❡ r❡❝♦♥str✉❝t✐♦♥ ♣r♦❝❡ss ❢♦r ❈●❍ ❣❡♥❡r❛t❡❞ ❜② t❤❡ r❛② tr❛❝✐♥❣ ♠❡t❤♦❞s ✐s ❝❛rr✐❡❞ ❛s s❤♦✇♥ ✐♥ ❋✐❣ ✻✳✷✳ ❋✐❣ ✻✳✺✭❛✮ s❤♦✇s ❛ ❞✐☛r❛❝t✐♦♥ ♣❛tt❡r♥ ❢♦r♠❡❞ ❜② s❤✐♥✐♥❣ ❛ ❜❧✉❡ ❧❛s❡r ✭✹✼✸ ♥♠✮ t❤r♦✉❣❤ t❤❡ ❞❡✈❡❧♦♣❡❞ P▼▼❆ ❈●❍ ♣❛tt❡r♥✱ ✇✐t❤ ♥♦ ❧❡♥s❡s ♣r❡s❡♥t✳ ❆ ❜❧✉❡ ❧❛s❡r ✐s ✉s❡❞ ❤❡r❡ ❛s ✐t ✐s ♠♦r❡ ✐♥t❡♥s❡ t❤❛♥ t❤❡ ❛✈❛✐❧❛❜❧❡ r❡❞ ❧❛s❡r✱ s♦ ♣r♦❞✉❝✐♥❣ ❛ ✇✐❞❡r r❛♥❣❡ ♦❢ ✈✐s✐❜❧❡ ❞✐☛r❛❝t✐♦♥ s♣♦ts✳ ❚❤❡ ❜r✐❣❤t s♣♦ts ❛r❡ ♣r♦❞✉❝❡❞ ❜② t❤❡ ♠❛♥② ♦r❞❡rs ♦❢ ❞✐☛r❛❝t✐♦♥ ❢r♦♠ t❤❡ ❤✐❣❤ r❡s♦❧✉t✐♦♥ ❈●❍ ♣❛tt❡r♥✳ ❋✐❣ ✻✳✺✭❜✮ s❤♦✇s t❤❡ ❈●❍ ✐♠❛❣❡ r❡❝♦♥str✉❝t❡❞ ✉s✐♥❣ ❛ r❡❞ ❧❛s❡r ♣♦✐♥t❡r ✭✻✺✵ ♥♠✱ ✺ ♠❲ ♣♦✇❡r✮✳ ❲❤❡♥ ✐❧❧✉♠✐♥❛t❡❞ ✇✐t❤ t❤❡ ❧❛s❡r✱ t❤❡ ✽✼ ✻✳✸ ❙✐❧✐❝♦♥ ❛s ❛ r❡❝♦r❞✐♥❣ ♠❡❞✐✉♠ ❢♦r ❈●❍ ❯♣♦♥ t❤❡ s✉❝❝❡ss❢✉❧ ❞❡♠♦♥str❛t✐♦♥ t❤❛t P❇❲ ❝♦✉❧❞ ❜❡ ✉s❡❞ t♦ ❞✐r❡❝t ✇r✐t❡ ❈●❍ ♣❛tt❡r♥s ✐♥t♦ P▼▼❆✱ t❤❡ ♥❛t✉r❛❧ ♥❡①t st❡♣ ✇❛s t♦ ❛tt❡♠♣t t♦ ♠❛❝❤✐♥❡ ❈●❍ ♣❛tt❡r♥s ♦♥t♦ s✐❧✐❝♦♥ ✉s✐♥❣ ♦✉r ♠❛❝❤✐♥✐♥❣ t❡❝❤♥✐q✉❡ t♦❣❡t❤❡r ✇✐t❤ t❤❡ ❧❛r❣❡ ❛r❡❛ ✐rr❛❞✐❛t✐♦♥ ❢❛❝✐❧✐t②✳ ■t ✐s ❞✐✍❝✉❧t t♦ r❡❝♦r❞ ❈●❍ ♣❛tt❡r♥s ✇✐t❤ ✈❛r✐❛❜❧❡ ♣✐①❡❧ ♠♦❞✉❧❛t✐♦♥ t♦ ❛♠♣❧✐t✉❞❡ ❛♥❞ ♣❤❛s❡✱ s♦ ❡①✐st✐♥❣ r❡❝♦r❞✐♥❣ t❡❝❤♥✐q✉❡s✱ ✉s✐♥❣ ♣❤♦t♦❧✐t❤♦❣r❛♣❤② ❢♦r ❡①❛♠♣❧❡✱ ✉s✉❛❧❧② ♠♦❞✉❧❛t❡ ✐♥ ❛♥ ♦♥✴♦☛ ❜✐♥❛r② ♠❛♥♥❡r✳ ❲❤✐❧❡ ✐t ✐s ♣♦ss✐❜❧❡ t♦ ♠❛❦❡ ❈●❍ ♣❛tt❡r♥s ✇✐t❤ ❡❧❡❝tr♦♥ ❜❡❛♠ ❧✐t❤♦❣r❛♣❤② ❛t ✈❡r② ❤✐❣❤ s♣❛t✐❛❧ r❡s♦❧✉t✐♦♥s ♦❢ ✶✵ ♥♠✱ t❤✐s ✐s ❛❧s♦ ❧✐♠✐t❡❞ t♦ ❛ ❜✐♥❛r② ❢❛s❤✐♦♥ r❛t❤❡r t❤❛♥ ❞✐☛❡r✐♥❣ ❞❡❣r❡❡s ♦❢ r❡s♣♦♥s❡ ♦❢ ✐♥❞✐✈✐❞✉❛❧ ♣✐①❡❧s✳ ▼♦r❡♦✈❡r✱ ♠♦st ❡①✐st✐♥❣ ❈●❍ r❡❝♦r❞✐♥❣ ♠❡❞✐❛ ❛r❡ ✉s✉❛❧❧② ♦♥❧② ❛❜❧❡ t♦ ♠♦❞✉❧❛t❡ ❡✐t❤❡r t❤❡ ♣❤❛s❡ ♦r t❤❡ ❛♠♣❧✐t✉❞❡ ❜✉t ♥♦t ❜♦t❤✳ ■♥ t❤✐s s❡❝t✐♦♥✱ ✇❡ ❞❡♠♦♥str❛t❡ t❤❡ ❛❜✐❧✐t② t♦ ♠♦❞✉❧❛t❡ ❜♦t❤ t❤❡ ❛♠♣❧✐t✉❞❡ ❛♥❞ ♣❤❛s❡ ✉s✐♥❣ ♠✐❝r♦♠❛❝❤✐♥❡❞ s✐❧✐❝♦♥ s✉r❢❛❝❡s✳ ■♥ ❛❞❞✐t✐♦♥✱ ✇❡ ❞❡♠♦♥str❛t❡ t❤❡ ♣♦ss✐❜✐❧✐t② ♦❢ t❤✐s ❛♣♣r♦❛❝❤ ❢♦r ✈❛r✐❛❜❧❡ ♣❤❛s❡ ❛♥❞ ❛♠♣❧✐t✉❞❡ ♠♦❞✉❧❛t✐♦♥✳ ✵✳✵✷ ✡✳❝♠ ♣✲t②♣❡ s✐❧✐❝♦♥ ✇❛❢❡rs ❛r❡ ✉s❡❞ ❤❡r❡ ❛s ✐t ✇❛s ♣r❡✈✐♦✉s❧② s❤♦✇♥ t❤❛t t❤❡ r❛t❡ ♦❢ ❛♥♦❞✐③❛t✐♦♥ ✐♥ t❤✐s ♠❛t❡r✐❛❧ ❝❛♥ ❜❡ ❝♦♥tr♦❧❧❡❞ ♦✈❡r ❛ ✇✐❞❡r r❛♥❣❡ ❜② ✈❛r②✐♥❣ t❤❡ ✐rr❛❞✐❛t✐♦♥ ✌✉❡♥❝❡ ✭❈❤❛♣t❡r ✸✳✻✮✳ ❲❛❢❡rs ✇❡r❡ ❝♦❛t❡❞ ✇✐t❤ ❍▼❉❙ ✭❤❡①❛♠❡t❤②❧❞✐s✐❧❛③❛♥❡✮ ❜② ✈❛♣♦r ♣r✐♠✐♥❣ t♦ ❝r❡❛t❡ ❛❞❤❡s✐♦♥ ❜❡t✇❡❡♥ t❤❡ s❛♠♣❧❡ ❛♥❞ ♣❤♦t♦r❡s✐st ✭P❘✮✳ ❆ ✼ ✖♠ t❤✐❝❦ P❘✱ ❆❩✹✻✷✵ ✭❈❤❛♣t❡r ✷✳✹✳✷✮✱ ✇❛s s♣✐♥✲❝♦❛t❡❞ ♦♥t♦ t❤❡ ✇❛❢❡r ❛♥❞ t❤❡♥ ♣r❡✲❜❛❦❡❞ t♦ ✾✺✍ ❈ ❢♦r ✹ ♠✐♥✉t❡s✳ ❆ ❝❤r♦♠❡ ♠❛s❦ ❝♦♥t❛✐♥✐♥❣ t❤❡ ❈●❍ ♣❛tt❡r♥s ❝♦♠♣✉t❡❞ ❜② t❤❡ ❋♦✉r✐❡r tr❛♥s❢♦r♠ ♠❡t❤♦❞ ✇❛s ❢❛❜r✐❝❛t❡❞ ❜② ❧❛s❡r ❧✐t❤♦❣r❛♣❤②✳ ❚❤❡ ♣❛tt❡r♥ ✇❛s t❤❡♥ tr❛♥s❢❡rr❡❞ t♦ t❤❡ P❘ ❜② st❛♥❞❛r❞ ❯❱ ♣❤♦t♦❧✐t❤♦❣r❛♣❤② r❡s✉❧t✐♥❣ ✐♥ ✷✲st❡♣ ✭r❡s✐st ❛♥❞ s✐❧✐❝♦♥ st❡♣✮ ❜✐♥❛r② ❈●❍ ♣❛tt❡r♥ ♦♥ t❤❡ ♣❤♦t♦r❡s✐st✳ ❚❤❡ s❛♠♣❧❡ ✇❛s t❤❡♥ ❡①♣♦s❡❞ t♦ ❛ ✻✵✵ ❦❡❱ ❤❡❧✐✉♠ ✐♦♥ ❜❡❛♠ ✇❤✐❝❤ ✇❛s ✉♥✐❢♦r♠❧② ❞✐str✐❜✉t❡❞ ♦✈❡r ❛♥ ❛r❡❛ ♦❢ ✶✳✺ ✂ ✶✳✺ ❝♠✳ ❍❡❧✐✉♠ ✐♦♥s ✇❡r❡ ✉s❡❞ ♦✇✐♥❣ t♦ t❤❡✐r ❣r❡❛t❡r ❞❡❢❡❝ts ❣❡♥❡r❛t✐♦♥ r❛t❡ ♦❢ ❝♦♠♣❛r❡❞ ✇✐t❤ ♣r♦t♦♥s✱ ❤❡♥❝❡ ❛ s❤♦rt❡r ✐rr❛❞✐❛t✐♦♥ t✐♠❡ ✐s ♥❡❡❞❡❞✳ ✻✵✵ ❦❡❱ ❤❡❧✐✉♠ ✐♦♥s ❤❛✈❡ ❛ r❛♥❣❡ ♦❢ ✹✳✵✴✷✳✸ ✖♠ ✐♥ ♣❤♦t♦r❡s✐st✴s✐❧✐❝♦♥ r❡s♣❡❝t✐✈❡❧②✱ s♦ t❤❡ P❘ ✐s t❤✐❝❦ ❡♥♦✉❣❤ t♦ ♣r❡✈❡♥t ✐rr❛❞✐❛t✐♦♥ ✐♥❞✉❝❡❞✲❞❛♠❛❣❡ t♦ t❤❡ ✉♥❞❡r❧②✐♥❣ s✐❧✐❝♦♥✳ ❚❤❡ ✌✉❡♥❝❡ ✇❛s s❡t ❛t ✺ ✂ ✶✵✶✹ ✐♦♥s✴❝♠✷ ✱ ✇❤✐❝❤ ✐s ❤✐❣❤ ❡♥♦✉❣❤ t♦ ❣r❡❛t❧② r❡❞✉❝❡ t❤❡ s✉❜s❡q✉❡♥t r❛t❡ ♦❢ P❙✐ ❢♦r♠❛t✐♦♥ ✽✽ ✐♥ s✐❧✐❝♦♥✳ ■♥ t❤✐s ✇❛②✱ ♥♦ ❞❡❢❡❝ts ❛r❡ ✐♥tr♦❞✉❝❡❞ t♦ t❤❡ ✉♥✲❡①♣♦s❡❞✴✉♥✲✐rr❛❞✐❛t❡❞ ❛r❡❛s ❛♥❞ ❞✉r✐♥❣ t❤❡ s✉❜s❡q✉❡♥t ❛♥♦❞✐③❛t✐♦♥ st❡♣ ❛♥❞ P❙✐ ❢♦r♠❛t✐♦♥ r❛t❡ ✇✐❧❧ ♥♦t ❜❡ r❡❞✉❝❡❞ ✐♥ t❤❡s❡ ❛r❡❛s ❝♦♠♣❛r❡❞ t♦ t❤❡ ✐rr❛❞✐❛t❡❞ r❡❣✐♦♥s✳ ❋♦r ❛ t②♣✐❝❛❧ ❜❡❛♠ ❝✉rr❡♥t ♦❢ ✶✵✵ ♥❆ t❤❡ ✐rr❛❞✐❛t✐♦♥ t✐♠❡ ❢♦r ❡❛❝❤ s❛♠♣❧❡ ✇❛s ❛❜♦✉t ✸✵ ♠✐♥✉t❡s✳ ❆❢t❡r ✐rr❛❞✐❛t✐♦♥✱ t❤❡ P❘ ❧❛②❡r ✇❛s r❡♠♦✈❡❞ ✉s✐♥❣ ♥❛♥♦str✐♣♣❡r ❚▼ ✭❈②❛♥t❡❦ ■♥❝✮ ❛♥❞ t❤❡ ✇❛❢❡r ❛♥♦❞✐③❡❞ ❛t ❛ ❝✉rr❡♥t ❞❡♥s✐t② ✷ ♦❢ ✼✵ ♠❆✴❝♠ ✳ ❋✐♥❛❧❧②✱ t❤❡ ✇❛❢❡r ✇❛s ✐♠♠❡rs❡❞ ✐♥ ❑❖❍ s♦❧✉t✐♦♥ t♦ r❡♠♦✈❡ t❤❡ P❙✐ ❧❛②❡r✱ ❧❡❛✈✐♥❣ ❜❡❤✐♥❞ ❛ ♠✐❝r♦♠❛❝❤✐♥❡❞ ✷✲st❡♣ s✐❧✐❝♦♥ ❜✐♥❛r② s✉r❢❛❝❡ r❡❧✐❡❢ ❈●❍ ♣❛tt❡r♥✳ ■♠❛❣❡ r❡❝♦♥str✉❝t✐♦♥ ✇❛s ❝❛rr✐❡❞ ♦✉t ❜② s✐♠♣❧② r❡✌❡❝t✐♥❣ ❛ ✺♠❲ r❡❞ ✭✻✺✵ ♥♠✮ ❧❛s❡r ♦☛ t❤❡ ❈●❍ ♣❛tt❡r♥s ♦♥t♦ ❛ ✈✐❡✇✐♥❣ s❝r❡❡♥✳ ✻✳✸✳✶ ❇✐♥❛r② ♣❤❛s❡ ❛♥❞ ❛♠♣❧✐t✉❞❡ ❈●❍ ♣❛tt❡r♥s ❋✐❣ ✻✳✾✭❛✮ s❤♦✇s ❛ ❜✐♥❛r② ♣❤❛s❡ ❈●❍ ♣❛tt❡r♥ ♦❢ t❤❡ ❧❡tt❡rs ◆❚❯ ♠❛❞❡ ✉♣ ♦❢ ✶✵✷✹ ✂ ✶✵✷✹ ❜❧❛❝❦ ❛♥❞ ✇❤✐t❡ ♣✐①❡❧s✳ ❋✐❣ ✻✳✾✭❜✮ s❤♦✇s ❛♥ ♦♣t✐❝❛❧ ✐♠❛❣❡ ♦❢ t❤❡ ❜✐♥❛r② ♣❤❛s❡ ❈●❍ ♣❛tt❡r♥ ✐♥ tr❛♥s❢❡rr❡❞ ♦♥t♦ s✐❧✐❝♦♥ ❜② t❤❡ ♣r♦❝❡❞✉r❡s ❞❡s❝r✐❜❡❞ ❛❜♦✈❡✳ ❇✐♥❛r② ♣❤❛s❡ ♠♦❞✉❧❛t✐♦♥ ✐s ❛❝❤✐❡✈❡❞ ❜② t❤❡ t✇♦ ♠✐❝r♦♠❛❝❤✐♥❡❞ st❡♣ ❤❡✐❣❤ts❀ t❤❡ ❤✐❣❤❡r st❡♣s ❛r❡ t❤❡ ✐rr❛❞✐❛t❡❞ r❡❣✐♦♥s ✇❤✐❧❡ t❤❡ ❧♦✇❡r st❡♣s ❛r❡ t❤❡ ✉♥✐rr❛❞✐❛t❡❞ r❡❣✐♦♥s ✇❤❡r❡ t❤❡ ❛♥♦❞✐③❛t✐♦♥ r❛t❡ ✐s ❤✐❣❤❡r✳ ❚❤❡s❡ ✐rr❛❞✐❛t❡❞ ❛♥❞ ✉♥✐rr❛❞✐❛t❡❞ r❡❣✐♦♥s ❝♦rr❡s♣♦♥❞ t♦ t❤❡ ❜❧❛❝❦ ❛♥❞ ✇❤✐t❡ ♣✐①✲ ❡❧s ✐♥ ❋✐❣ ✻✳✾✭❛✮ r❡s♣❡❝t✐✈❡❧②✳ ❋r♦♠ ❆❋▼ ♠❡❛s✉r❡♠❡♥ts✱ t❤❡ ❞✐☛❡r❡♥❝❡ ✐♥ st❡♣ ❤❡✐❣❤t ✐s ❛♣♣r♦①✐♠❛t❡❧② ✼✵✵ ♥♠✳ ❚❤✐s ❝❛✉s❡s ✐♥❝♦♠✐♥❣ ❧✐❣❤t t♦ tr❛✈❡❧ t❤r♦✉❣❤ ❞✐☛❡r❡♥t ♦♣t✐❝❛❧ ♣❛t❤ ❧❡♥❣t❤s✱ ❤❡♥❝❡ ♠♦❞✉❧❛t✐♥❣ t❤❡ ♣❤❛s❡✳ ❋✐❣ ✻✳✾✭❝✮ ❛♥❞ ✭❞✮ ❛r❡ ❡♥❧❛r❣❡❞ ✐♠❛❣❡s ♦❢ t❤❡ ❣❡♥❡r✲ ❛t❡❞ ❈●❍ ❛♥❞ t❤❡ ♦♣t✐❝❛❧ ✐♠❛❣❡ ♦❢ t❤❡ ❈●❍ ♣❛tt❡r♥ ♦♥ s✐❧✐❝♦♥ r❡s♣❡❝t✐✈❡❧②✳ ❚❤❡ s♠❛❧❧❡st ❢❡❛t✉r❡ s✐③❡ ♦♥ t❤❡ s❛♠♣❧❡ ✐s ✹ ✂ ✹ ✖♠✳ ●♦♦❞ ♣❛tt❡r♥ tr❛♥s❢❡r ✐s ❛❝❤✐❡✈❡❞✱ ❞❡♠♦♥str❛t✐♥❣ t❤❡ ♣r❡❝✐s✐♦♥ ❛♥❞ ❛❝❝✉r❛❝② t❤❛t ♠❛② ❜❡ ❛❝❤✐❡✈❡❞✱ r❡s✉❧t✐♥❣ ✐♥ ❛ ❣♦♦❞ r❡❝♦♥str✉❝t❡❞ ❜✐♥❛r② ✐♠❛❣❡ ✐♥ ❋✐❣ ✻✳✶✵✳ ❋✐❣ ✻✳✶✶✭❛✮ s❤♦✇s ❛ ❜✐♥❛r② ❛♠♣❧✐t✉❞❡ ❈●❍ ♠❛❞❡ ✉♣ ♦❢ ✸✵✵ ♣✐①❡❧s✳ ✂ ✸✵✵ ❜❧❛❝❦ ❛♥❞ ✇❤✐t❡ ❚❤❡ ❈●❍ ♣❛tt❡r♥ ✇❛s tr❛♥s❢❡rr❡❞ ✐♥t♦ s✐❧✐❝♦♥ ♦✈❡r ❛♥ ❛r❡❛ ♦❢ ✶✳✺ ✇✐t❤ ❛ ♣✐①❡❧ s✐③❡ ♦❢ ✺ ✂ ✺ ✖♠✳ ✂ ✶✳✺ ♠♠✱ ❚❤❡r❡ ❛r❡ t✇♦ ❞✐st✐♥❝t ✐♥t❡♥s✐t✐❡s ♦❢ r❡✌❡❝t❡❞ ❧✐❣❤t ✇❤✐❝❤ ❞✐☛❡r ✐♥ ✐♥t❡♥s✐t② ❜② ✸✵✪ ❛s ♠❡❛s✉r❡❞ ❢r♦♠ ❛ ❧✐♥❡ ♣r♦☞❧❡ ✉s✐♥❣ ❛ ♠✐❝r♦s❝♦♣❡✱ r❡s✉❧t✐♥❣ ✾✵ ❋✐❣✉r❡ ✻✳✶✶✿ ✭❛✮ ❇✐♥❛r② ❛♠♣❧✐t✉❞❡ ❈●❍ ♣❛tt❡r♥ ❝♦♥s✐st✐♥❣ ♦❢ ✸✵✵ ✂ ✸✵✵ ♣✐①❡❧s✳ ✭❜✮✱✭❝✮ r❡s♣❡❝t✐✈❡❧② s❤♦✇ ❛♥ ♦♣t✐❝❛❧ ❛♥❞ ❙❊▼ ✐♠❛❣❡ ♦❢ ♣❛rt ♦❢ t❤❡ tr❛♥s❢❡rr❡❞ ❈●❍ ♣❛tt❡r♥ ✐♥ s✐❧✐❝♦♥✳ ✭❞✮ ❘❡❝♦♥str✉❝t❡❞ ✐♠❛❣❡ ♦❢ ❛ ♣❤❛s❡ ❈●❍✳ ■♥s❡t s❤♦✇s t❤❡ ♦r✐❣✐♥❛❧ ❡♥❝♦❞❡❞ ✐♠❛❣❡✳ ✐♥ ♠♦❞✉❧❛t✐♦♥ ♦❢ t❤❡ ❛♠♣❧✐t✉❞❡ ♦❢ ✐♥❝♦♠✐♥❣ ❧✐❣❤t✳ ❚❤❡ ✐rr❛❞✐❛t❡❞ r❡❣✐♦♥s ✭❜❧❛❝❦ ♣✐①❡❧s✮ ❛r❡ ❧❡ss r❡✌❡❝t✐✈❡ ✇❤✐❧❡ t❤❡ ✉♥✐rr❛❞✐❛t❡❞ r❡❣✐♦♥s ✭✇❤✐t❡ ♣✐①❡❧s✮ ❛r❡ ♠♦r❡ r❡✌❡❝t✐✈❡ ♦✇✐♥❣ t♦ ❛ ✈❛r✐❡t② ♦❢ ❢❛❝t♦rs ✇❤✐❝❤ ✇✐❧❧ ❜❡ ❞✐s❝✉ss❡❞ ❧❛t❡r ✐♥ t❤✐s s❡❝t✐♦♥✳ ●♦♦❞ ♣❛tt❡r♥ tr❛♥s❢❡r ✐s ❛❣❛✐♥ ♦❜s❡r✈❡❞ ✐♥ ❋✐❣ ✻✳✶✶✭❜✮ ❛♥❞ ✭❝✮✱ r❡s✉❧t✐♥❣ ✐♥ ❛ ❣♦♦❞ r❡❝♦♥str✉❝t❡❞ ✐♠❛❣❡ ✐♥ ❋✐❣ ✻✳✶✶✭❞✮✳ ❚❤❡ ♦r✐❣✐♥❛❧ ❡♥❝♦❞❡❞ ✐♠❛❣❡ ❜❡❛r✐♥❣ t❤❡ ❧❡tt❡rs ❵♥✉s ♣❤②s✐❝s✬ ✐s s❤♦✇♥ ✐♥ t❤❡ ✐♥s❡t ♦❢ ❋✐❣ ✻✳✶✶✭❞✮✳ ❚❤❡ s❛♠♣❧❡ ✐♥ ❋✐❣ ✻✳✶✶ ❞❡♠♦♥str❛t❡s t❤❛t s✐❧✐❝♦♥ ♠❛② ❜❡ ✉s❡❞ ❢♦r ❜✐♥❛r② t②♣❡ ❛♠♣❧✐✲ t✉❞❡ ❈●❍ t♦ ♣r♦❞✉❝❡ ❜✐♥❛r② t②♣❡ r❡❝♦♥str✉❝t❡❞ ✐♠❛❣❡s✳ ❲❡ ❤❛✈❡ ❛❧s♦ ❢❛❜r✐❝❛t❡❞ ❜✐♥❛r② ❛♠♣❧✐t✉❞❡ r❡✌❡❝t✐✈❡ ❈●❍ ♣❛tt❡r♥s ❝❛♣❛❜❧❡ ♦❢ ♣r♦❞✉❝✐♥❣ ❣r❡② s❝❛❧❡ r❡❝♦♥str✉❝t❡❞ ✐♠❛❣❡s✳ ❋✐❣ ✻✳✶✷✭❛✮ ✐♥s❡t s❤♦✇s t❤❡ ❡♥❝♦❞❡❞ ✐♠❛❣❡ ✐♥ ✇❤✐❝❤ ❡❛❝❤ ❧❡tt❡r ✐♥ t❤❡ ✇♦r❞s ❵❣r❡② s❝❛❧❡✬ ❤❛s ✾✶ ❋✐❣✉r❡ ✻✳✶✷✿ ●r❛②s❝❛❧❡ r❡❝♦♥str✉❝t❡❞ ❤♦❧♦❣r❛♠s ❢r♦♠ ❜✐♥❛r② ❛♠♣❧✐t✉❞❡ ❈●❍ ♣❛tt❡r♥s ♦♥ s✐❧✐❝♦♥✱ ✇✐t❤ t❤❡ ♦r✐❣✐♥❛❧ ❡♥❝♦❞❡❞ ✐♠❛❣❡s s❤♦✇♥ ✐♥ t❤❡ ✐♥s❡ts✳ ✭❛✮ ❚❤❡ ❧❡tt❡rs ✧❣r❡②✧ ❤❛s t❤❡ ❧❡tt❡rs ✧❣✧✱ ✧r✧✱ ✧❡✧ ❛♥❞ ✧②✧ ✐♥ ✶✵✵✪✱ ✷✺✪✱ ✺✵✪ ❛♥❞ ✼✺✪ ✐♥t❡♥s✐t② r❡s♣❡❝t✐✈❡❧②✳ ✭❜✮✱ ✭❝✮✱ ✭❞✮ ●r❡② s❝❛❧❡ r❡❝♦♥str✉❝t❡❞ ✐♠❛❣❡s ♦❢ ❆❧❜❡rt ❊✐♥st❡✐♥✱ t❤❡ ▼♦♥❛ ▲✐s❛ ❛♥❞ ❧♦❣♦ ♦❢ t❤❡ ◆❛t✐♦♥❛❧ ❯♥✐✈❡rs✐t② ♦❢ ❙✐♥❣❛♣♦r❡ ❞✐☛❡r✐♥❣ ✐♥t❡♥s✐t②✳ ❚❤❡ r❡❝♦♥str✉❝t❡❞ ✐♠❛❣❡ ✐♥ ❋✐❣ ✻✳✶✷✭❛✮ ❡①❤✐❜✐ts t❤❡ ❞✐☛❡r✐♥❣ ✐♥t❡♥s✐t✐❡s r❡❛s♦♥❛❜❧② ✇❡❧❧✱ ❛s ❞♦ t❤❡ ♦t❤❡r r❡❝♦♥str✉❝t❡❞ ❣r❡② s❝❛❧❡ ✐♠❛❣❡s ✐♥ ❋✐❣ ✻✳✶✷✳ ✻✳✸✳✷ ❈♦♥t✐♥✉♦✉s❧② ✈❛r✐❛❜❧❡ ❛♠♣❧✐t✉❞❡ ❛♥❞ ♣❤❛s❡ ❈●❍ ❲❤❛t ✇❛s ❞❡♠♦♥str❛t❡❞ s♦ ❢❛r ✐s t❤❛t s✐❧✐❝♦♥ ❝❛♥ ❜❡ ♠❛❝❤✐♥❡❞ t♦ ❣✐✈❡ s✉✍❝✐❡♥t ❞✐☛❡r❡♥❝❡s ✐♥ r❡✌❡❝t✐✈❡ ✐♥t❡♥s✐t② ❛♥❞ ♣❤❛s❡ t♦ ♣r♦❞✉❝❡ ❜✐♥❛r② r❡❝♦♥str✉❝t❡❞ ❈●❍ ✐♠❛❣❡s✳ ❍❡r❡ ✇❡ ❢✉rt❤❡r s❤♦✇ t❤❛t s✐❧✐❝♦♥ ❝❛♥ ❜❡ ❝♦♥t✐♥✉♦✉s❧② ♠❛❝❤✐♥❡❞ ✐♥ ❜♦t❤ ♣✐①❡❧ ❤❡✐❣❤t ❛♥❞ r❡✌❡❝t✐✈✐t②✱ ❛❧❧♦✇✐♥❣ t❤❡ ❣❡♥❡r❛t✐♦♥ ♦❢ ❜❡tt❡r q✉❛❧✐t② r❡❝♦♥str✉❝t❡❞ ❤♦❧♦❣r❛♠s ❬✼✾❪ ✐♥ ❝♦♥❥✉♥❝t✐♦♥ ✇✐t❤ s✉✐t❛❜❧❡ ❈●❍ ♣❛tt❡r♥s✳ ❋✐✈❡ ✶✵ ✖♠ ✇✐❞❡ ❧✐♥❡s ✇❡r❡ ✐rr❛❞✐❛t❡❞ ✐♥ ❛ s✐❧✐❝♦♥ ✇❛❢❡r ❜② P❇❲ ✇✐t❤ ✷ ▼❡❱ ♣r♦t♦♥ ✾✷ ❋✐❣✉r❡ ✻✳✶✸✿ ✭❛✮ ❖♣t✐❝❛❧ ✐♠❛❣❡ ♦❢ s✉r❢❛❝❡ r❡❧✐❡❢ s✐❧✐❝♦♥ ✇✐t❤ ☞✈❡ ❧✐♥❡s ✶✵✖♠ ✐♥ ✇✐❞t❤ ✐rr❛❞✐❛t❡❞ ✇✐t❤ ✶✺ ✷ ✶✺ ✷ ✶✵ ✴❝♠ ✱ ✐♥ ✐♥❝r❡♠❡♥ts ♦❢ ✶ ✶✵ ✴❝♠ ❆❋▼ ♠❡❛s✉r❡♠❡♥ts ♦❢ t❤❡ ✐♥❝r❡❛s✐♥❣ ✌✉❡♥❝❡ ❢r♦♠ ✶ t♦ ✺ ✂ ✂ r♦✉❣❤♥❡ss ♦❢ ❡❛❝❤ ❧✐♥❡ ✐s ✐♥❞✐❝❛t❡❞✳ ✭❜✮ ❍♦r✐③♦♥t❛❧ ❧✐♥❡ ♣r♦☞❧❡ ❛❝r♦ss t❤❡ ✐rr❛❞✐❛t❡❞ ❧✐♥❡s ❛t t❤❡ ❧♦❝❛t✐♦♥ ✐♥❞✐❝❛t❡❞ ✐♥ ❜② t❤❡ r❡❞ ❧✐♥❡ ✐♥ ✭❛✮ s❤♦✇✐♥❣ ❧❛r❣❡ ✈❛r✐❛t✐♦♥s ✐♥ r❡✌❡❝t❡❞ ✐♥t❡♥s✐t② ❢r♦♠ ✇❤✐t❡ ❧✐❣❤t ✌✉❡♥❝❡s ❢r♦♠ ✶ t♦ ✺ ✂ ✶✵✶✺ ✴❝♠✷ ✱ ✐♥ ✐♥❝r❡♠❡♥ts ♦❢ ✶ ✂ ✶✵✶✺ ✴❝♠✷ ❢r♦♠ r✐❣❤t t♦ ❧❡❢t✳ ❚❤❡ ✇❛❢❡r ✇❛s t❤❡♥ ❛♥♦❞✐③❡❞ t♦ ❛ ❞❡♣t❤ ♦❢ ✼✵✵ ♥♠ ❛♥❞ t❤❡ P❙✐ r❡♠♦✈❡❞✳ ❋✐❣ ✻✳✶✸❛ s❤♦✇s t❤❡ r❡✌❡❝t✐✈✐t② t❤❡ r❡♠❛✐♥✐♥❣ s✐❧✐❝♦♥ s✉r❢❛❝❡✱ ✇✐t❤ r❡✌❡❝t✐✈✐t② ❝❧❡❛r❧② ✐♥❝r❡❛s✐♥❣ ✇✐t❤ ✌✉❡♥❝❡✳ ❆ ❧✐♥❡ ♣r♦☞❧❡ ❛❝r♦ss t❤❡ ☞✈❡ ❧✐♥❡s ✐s s❤♦✇♥ ✐♥ ❋✐❣ ✻✳✶✸✭❜✮ ❛♥❞ s❤♦✇s ❞✐st✐♥❝t ❧❡✈❡❧s ♦❢ r❡✌❡❝✲ t✐✈✐t② ❢♦r ❡❛❝❤ ✌✉❡♥❝❡✱ ✇✐t❤ t❤❡ r❡✌❡❝t❡❞ ✐♥t❡♥s✐t② ✈❛r②✐♥❣ ✉♣ t♦ ✺✵ ✪✳ ❆❋▼ ♠❡❛s✉r❡♠❡♥ts ❢♦r t❤❡ r♦✉❣❤♥❡ss ♦❢ ❡❛❝❤ ❧✐♥❡ ❞❡♠♦♥str❛t❡ t❤❛t ✐t ❞❡❝r❡❛s❡s ✇✐t❤ ✌✉❡♥❝❡✳ ❍♦✇❡✈❡r✱ t❤❡ r♦✉❣❤♥❡ss ✈❛r✐❛t✐♦♥ ✇♦✉❧❞ ♦♥❧② r❡s✉❧t ❛ ❝❤❛♥❣❡ ✐♥ r❡✌❡❝t✐✈✐t② ♦❢ ✶✲✷✪✳ ■rr❛❞✐❛t❡❞ ❛r❡❛s ❤❛s ❧❡ss ❝✉rr❡♥t ✌♦✇✐♥❣ t❤r♦✉❣❤ ❞✉r✐♥❣ ❛♥♦❞✐③❛t✐♦♥✱ ❝♦♥s❡q✉❡♥t❧②✱ t❤❡ ♣♦r♦s✐t② ♦❢ t❤❡ P❙✐ ❢♦r♠ ✐♥ t❤❡s❡ r❡❣✐♦♥s ❛r❡ ♠✉❝❤ ❧♦✇❡r✳ ❍❡♥❝❡✱ ✇❡ ❛ttr✐❜✉t❡ t❤❡ ❧❛r❣❡ ♦❜s❡r✈❡❞ ✈❛r✐❛t✐♦♥ ✐♥ r❡✌❡❝t✐✈✐t② t♦ ❣r❡❛t❡r ❞✐✍❝✉❧t② ✐♥ r❡♠♦✈✐♥❣ t❤❡ P❙✐ ♦❢ ❧♦✇❡r ♣♦r♦s✐t② ❢r♦♠ t❤❡ ✐rr❛❞✐✲ ❛t❡❞ s✉r❢❛❝❡s ❛♥❞ ♣r❡❢❡r❡♥t✐❛❧ ❛♠❜✐❡♥t ♦①✐❞❛t✐♦♥ ♦❢ t❤❡ r♦✉❣❤❡r s✉r❢❛❝❡s✱ ❤❡♥❝❡ ❛ ❧♦✇❡r r❡✌❡❝t✐✈✐t②✳ ❚❤✐s ❞❡♠♦♥str❛t❡s t❤❛t ♦✉r s✐❧✐❝♦♥ ♠✐❝r♦♠❛❝❤✐♥✐♥❣ ♣r♦❝❡ss ✐s ♥♦t ❧✐♠✐t❡❞ t♦ ♠♦❞✉❧❛t✐♥❣ t❤❡ ❛♠♣❧✐t✉❞❡ ♦❢ ❧✐❣❤t ✐♥ ❛ ❜✐♥❛r② ❢❛s❤✐♦♥✱ ❜✉t ✐s ❛❜❧❡ t♦ ✈❛r✐❛❜❧② ♠♦❞✉❧❛t❡ t❤❡ ❛♠♣❧✐t✉❞❡ ♦❢ ✐♥❝♦♠✐♥❣ ❧✐❣❤t ♦✈❡r ❛ ✇✐❞❡ r❛♥❣❡✳ ❋✐✈❡ ✈❡rt✐❝❛❧ ❜❛rs ✇❡r❡ ✐rr❛❞✐❛t❡❞ ✉s✐♥❣ P❇❲ ✉s✐♥❣ ✷ ▼❡❱ ♣r♦t♦♥s✳ ❊❛❝❤ ❜❛r ✇❛s ✶✵ ✂ ✶✵✵ ✖♠✱ ✇✐t❤ ✌✉❡♥❝❡s ✐♥❝r❡❛s✐♥❣ ❢r♦♠ ✷✱ ✹✱ ✻✱ ✽✱ ❛♥❞ ✶✵ ✂ ✶✵✶✺ ♣r♦t♦♥s✴❝♠✷ ✳ ❚❤❡ ❛r❡❛ ✇❛s ♦✈❡r❧❛♣♣❡❞ ✇✐t❤ s✐♠✐❧❛r❧② ✐rr❛❞✐❛t❡❞ ❤♦r✐③♦♥t❛❧ ❜❛rs✱ r❡s✉❧t✐♥❣ ✐♥ ❛ ❝❤❡❝❦❡r ❜♦❛r❞ ✐♠❛❣❡✳ ✾✸ ❋✐❣✉r❡ ✻✳✶✹✿ ✭❛✮ ❙❊▼ ✐♠❛❣❡ ♦❢ t❤❡ s✉r❢❛❝❡ r❡❧✐❡❢ ♦❢ ❛ s✐❧✐❝♦♥ ✇❛❢❡r ✇❤✐❝❤ ✇❛s ✐rr❛❞✐❛t❡❞ ✐♥ ❛ ❝r♦ss ❤❛t❝❤❡❞ ♠❛♥♥❡r✱ ♣r♦❞✉❝✐♥❣ st❡♣s ♦❢ ♠❛♥② ❞✐☛❡r❡♥t ❤❡✐❣❤ts✳ ❚❤✐s ✐s t❤❡ s❛♠❡ ❢❛❜r✐❝❛t❡❞ str✉❝t✉r❡ s❤♦✇♥ ✐♥ ❋✐❣ ✹✳✺✳ ✡ ✭❜✮ P❧♦t ♦❢ t❤❡ r❡❧❛t✐♦♥s❤✐♣ ❜❡t✇❡❡♥ t❤❡ ❛♥♦❞✐③❛t✐♦♥ r❛t❡ ❛♥❞ ✌✉❡♥❝❡ ❢♦r ✵✳✵✷ ✳❝♠ s✐❧✐❝♦♥ ✇❛❢❡rs✳ ❚❤✐s ✐s t❤❡ s❛♠❡ ♣❧♦t s❤♦✇♥ ✐♥ ❋✐❣ ✸✳✻ ❚❤❡ s❛♠♣❧❡ ✇❛s t❤❡♥ ❡t❝❤❡❞ ❛t ✶✷ ♠❆✴❝♠✷ ❢♦r ✹ ♠✐♥✉t❡s ❛♥❞ t❤❡ P❙✐ r❡♠♦✈❡❞✳ ❚❤❡ ❛♥♦❞✐③❛t✐♦♥ r❛t❡ r❡❞✉❝❡s ✇✐t❤ ✌✉❡♥❝❡✱ ❛s s❤♦✇♥ ✐♥ ❋✐❣ ✻✳✶✹✭❜✮✱ ♣r♦❞✉❝✐♥❣ ✐♥❝r❡❛s✐♥❣ st❡♣ ❤❡✐❣❤t ♦❢ t❤❡ s✉r❢❛❝❡ r❡❧✐❡❢ ♣❛tt❡r♥✳ ■♥❝♦♠✐♥❣ ❧✐❣❤t ✐s r❡✌❡❝t❡❞ t❤r♦✉❣❤ ❞✐☛❡r❡♥t ♦♣t✐❝❛❧ ♣❛t❤ ❧❡♥❣t❤s ❞✉❡ t♦ t❤❡ ❞✐☛❡r✐♥❣ ❤❡✐❣❤ts✱ ❤❡♥❝❡ ✈❛r✐❛❜❧② ♠♦❞✉❧❛t✐♥❣ t❤❡ ♣❤❛s❡ r❛t❤❡r t❤❛♥ ❥✉st ✐♥ ❛ ❜✐♥❛r② ❢❛s❤✐♦♥✳ ✻✳✹ ❙✉♠♠❛r② P❇❲ ✇❛s ✉s❡❞ t♦ ❢❛❜r✐❝❛t❡ ♣❤❛s❡ ♠♦❞✉❧❛t❡❞ ❈●❍ ♣❛tt❡r♥s ✇❤✐❝❤ ✇❡r❡ ☞♥❛❧❧② ✉s❡❞ t♦ ♠❛❦❡ ❛ ❧✐q✉✐❞ ❝r②st❛❧ ❜❛s❡❞ s✇✐t❝❤❛❜❧❡ ❈●❍ ❝❡❧❧✳ ❚❤❡ ❛❜✐❧✐t② t♦ ❢❛❜r✐❝❛t❡ ❜✐♥❛r② ♣❤❛s❡ ❛♥❞ ❛♠♣❧✐t✉❞❡ ❈●❍ ♣❛tt❡r♥s ♦♥ s✐❧✐❝♦♥ ✇❤✐❝❤ ❣✐✈❡ r✐s❡ t♦ ❣♦♦❞ r❡❝♦♥str✉❝t❡❞ ✐♠❛❣❡s ✇❛s ❛❧s♦ ❞❡♠♦♥str❛t❡❞✳ ■♥ ❛❞❞✐t✐♦♥✱ t❤❡s❡ ❜✐♥❛r② ❈●❍ ❛r❡ ❛❜❧❡ t♦ ♣r♦❞✉❝❡ ❣♦♦❞ ❣r❛②s❝❛❧❡ r❡❝♦♥str✉❝t❡❞ ✐♠❛❣❡s✳ ❚❤❡ ❡①✐st✐♥❣ ❈●❍ ❣❡♥❡r❛t✐♥❣ s♦❢t✇❛r❡ ✇❤✐❝❤ ✇❡ ✉s❡ t♦ ❣❡♥❡r❛t❡ ♦✉r ❈●❍ ♣❛tt❡r♥s ✐s ♦♥❧② ❛❜❧❡ t♦ ♣r♦❞✉❝❡ ❜✐♥❛r② t②♣❡ ♣❤❛s❡ ❛♥❞ ❜✐♥❛r② ❈●❍✳ ◆❡✈❡rt❤❡❧❡ss✱ t♦❣❡t❤❡r ✇✐t❤ ❛♥ ❛♣♣r♦♣r✐❛t❡ ❈●❍ ❣❡♥❡r❛t✐♥❣ s♦❢t✇❛r❡✱ t❤✐s ✇♦r❦ s❤♦✇s t❤❛t ✐t ✐s ♣♦ss✐❜❧❡ t♦ ✉s❡ s✐❧✐❝♦♥ ❛s ❛ r❡❝♦r❞✐♥❣ ♠❡❞✐✉♠ t♦ ✈❛r✐❛❜❧② ♠♦❞✉❧❛t❡ ❛♠♣❧✐t✉❞❡ ❛♥❞ ♣❤❛s❡ ❜② ❤❛✈✐♥❣ ✈❛r②✐♥❣ r❡✌❡❝t✐✈✐t② ❛♥❞ st❡♣ ❤❡✐❣❤ts r❡s♣❡❝t✐✈❡❧②✳ Chapter ❙✐❧✐❝♦♥ ❈♦♥❝❛✈❡ ▼✐❝r♦ ▼✐rr♦rs ✼✳✶ ■♥tr♦❞✉❝t✐♦♥ ❆ ❝♦♥❝❛✈❡ ♣r♦☞❧❡ ✐♥ t❤❡ ♠✐❝r♦♥ r❡❣✐♠❡ ✐s ♦❢ ✐♥t❡r❡st ❜❡❝❛✉s❡ ♦❢ ✐ts ❛❜✐❧✐t② t♦ ❢♦❝✉s ✐♥❝♦♠✐♥❣ ❧✐❣❤t ✐♥t♦ ❛ s♣♦t✳ ■♥ ❜✐♦s❡♥s✐♥❣ ♦r ❝❡❧❧ tr❛♣♣✐♥❣ ❞❡✈✐❝❡s✱ ❛♥ ✐♥❝♦♠✐♥❣ ❧❛s❡r t❤❛t ✐s ❢♦❝✉s❡❞ ❜② s✉❝❤ ❛ ❝♦♥❝❛✈❡ ♠✐rr♦r ❛❝ts ❧✐❦❡ ♦♣t✐❝❛❧ t✇❡❡③❡rs t♦ tr❛♣✴♣✉s❤ ♣❛rt✐❝❧❡s ✇✐t❤ t❤❡ ♦♣t✐❝❛❧ ❣r❛❞✐❡♥t✴s❝❛tt❡r✐♥❣ ❢♦r❝❡ ❬✽✵✱ ✽✶❪✳ ■♥ t❤❡ ☞❡❧❞ ♦❢ ▼❊▼❙ ❛♥❞ ♦♣t♦❡❧❡❝tr♦♥✐❝s✱ ✐t ♠❛② ❜❡ ✉s❡❞ t♦ ❛s ❛ ✈❛r✐❛❜❧❡ ♦♣t✐❝❛❧ ❛tt❡♥✉❛t♦r ❬✽✷❪ ♦r t♦ ♣r♦❞✉❝❡ ❛♥ ❡♥❤❛♥❝❡❞ ❛♥❞ ❧♦❝❛❧✐③❡❞ ❧✐❣❤t s✐❣♥❛❧ ❢♦r ♣❛r❛❧❧❡❧ ❧♦✇ ❧♦ss ♦♣t✐❝❛❧ ✐♥t❡r❝♦♥♥❡❝t s②st❡♠s ❬✽✸❪✳ ❋r♦♠ t❤❡s❡ ❝♦♥❝❛✈❡ ♣r♦☞❧❡s✱ ✐t ✐s ❡❛s② t♦ ❢✉rt❤❡r ❢❛❜r✐❝❛t❡ ❝♦♥❝❛✈❡ ♦♣t✐❝❛❧ ❝❛✈✐t✐❡s s✐♠♣❧② ❜② ❝♦✉♣❧✐♥❣ t✇♦ s✉❝❤ ♠✐rr♦rs t♦❣❡t❤❡r ♦r ✇✐t❤ ❛♥ ♦♣t✐❝❛❧ ☞❜❡r ❬✽✹❪✳ ❚❤❡s❡ ❦✐♥❞ ♦❢ ❝♦♥❝❛✈❡ ❝❛✈✐t✐❡s ❛r❡ ♦❢ ✐♥t❡r❡st ✐♥ q✉❛♥t✉♠ ✐♥❢♦r♠❛t✐♦♥ s❝✐❡♥❝❡✱ ♣❛rt✐❝✉❧❛r❧② ✐♥ t❤❡ ❢❛❜r✐❝❛t✐♦♥ ♦❢ ❛t♦♠ ❝❤✐♣s ❬✹✾✱ ✽✹❪ ♦r ❢♦r s♠❛❧❧ ♣❛rt✐❝❧❡s ❞❡t❡❝t✐♦♥s ❬✽✺❪✳ ❙✐♥❣❧❡ ♣❤♦t♦♥s ♠❛② ❜❡ ♣r♦❞✉❝❡❞ ♦♥ ❞❡♠❛♥❞ ✉s✐♥❣ ❛t♦♠s ✐♥ s✉❝❤ ❛ ❝♦♥❝❛✈❡ ❝❛✈✐t② t♦ ❤❛✈❡ ❡♥t❛♥❣❧❡♠❡♥t ❡☛❡❝ts ✇✐t❤ ❛ s❤❛r❡❞ ❝❛✈✐t② ♣❤♦t♦♥ ❬✽✻✱ ✽✼❪✳ ❊✈✐❞❡♥t❧② t❤❡♥✱ t❤❡r❡ ❡①✐st ❛ ❞❡♠❛♥❞ ❢♦r t❤❡ ❛❜✐❧✐t② t♦ r❡❧✐❛❜❧② ❛♥❞ ❝♦♥tr♦❧❧❛❜❧② ♣r♦❞✉❝❡ s✉❝❤ ❝♦♥❝❛✈❡ ♣r♦☞❧❡s✳ ✼✳✶✳✶ ❉✐☛❡r❡♥t ❛♣♣r♦❛❝❤❡s ❢♦r ❢❛❜r✐❝❛t✐♥❣ ❝♦♥❝❛✈❡ ♠✐rr♦rs ❚❤❡r❡ ❤❛✈❡ ❜❡❡♥ s❡✈❡r❛❧ t❡❝❤♥✐q✉❡s r❡♣♦rt❡❞ t♦ ❢❛❜r✐❝❛t❡ ❝♦♥❝❛✈❡ ♠✐rr♦rs ♦♥ ❞✐☛❡r❡♥t ♠❛t❡r✐❛❧s✳ ❚❤❡s❡ ✐♥❝❧✉❞❡ ❞✐☛✉s✐♦♥ ♦❢ ✐♦♥ ❞♦♣❛♥ts ♦♥ ❣❧❛ss ❬✽✸❪✱ ♠❡❧t✐♥❣ ♣❤♦t♦r❡s✐st ❞✐s❦s ✾✹ ✾✺ t♦ ♦❜t❛✐♥ ❛ s♣❤❡r✐❝❛❧ s❤❛♣❡ ❢♦❧❧♦✇❡❞ ❜② ❞r② ❡t❝❤✐♥❣ ♦♥ ●❛❆s ❬✽✽❪ ❛♥❞ tr❛♣♣✐♥❣ ♦❢ ❛✐r ❜✉❜❜❧❡s ✐♥ ❜♦r♦s✐❧✐❝❛t❡ ❣❧❛ss ❬✹✾❪✳ ❋❛❜r✐❝❛t✐♥❣ ❝♦♥❝❛✈❡ ♠✐rr♦rs ♦♥ s✐❧✐❝♦♥ ❛r❡ ❡s♣❡❝✐❛❧❧② ✐♠♣♦rt❛♥t t♦ ❛❧❧♦✇ ❢♦r ❡❛s② ✐♥t❡❣r❛t✐♦♥ ♦❢ ♣❤♦t♦♥✐❝s ✐♥t♦ t❤❡ ✇❡❧❧✲❞❡✈❡❧♦♣❡❞ s✐❧✐❝♦♥ ♠✐❝r♦❡❧❡❝tr♦♥✐❝s ✐♥❢r❛str✉❝t✉r❡✱ ❛s ✇❡❧❧ ❛s ❢♦r ❣♦♦❞ r❡♣r♦❞✉❝✐❜✐❧✐t② ❛♥❞ ✉♣✲s❝❛❧✐♥❣ ♣✉r♣♦s❡s✳ ❋✉♥❝t✐♦♥❛❧ ♦♣t✐❝❛❧ tr❛♣♣✐♥❣ t❡❝❤♥✐q✉❡s ♦♥ s✐❧✐❝♦♥ s✉r❢❛❝❡s ❛♥❞ ❡♥✈✐r♦♥♠❡♥t ❛r❡ ❛❧s♦ ✈❡r② ✐♠♣♦rt❛♥t ❬✽✾❪✳ ❚❤❡ ❢❛❜r✐❝❛t✐♦♥ ♦❢ ❝♦♥❝❛✈❡ ♠✐rr♦rs ✐♥ s✐❧✐❝♦♥ ✐s ♥♦t tr✐✈✐❛❧✱ ♥❡✈❡rt❤❡❧❡ss✱ ✐t ✇❛s r❡♣♦rt❡❞ ✐♥ ❘❡❢ ❬✽✹❪✳ ❈♦♥❝❛✈❡ ♣r♦☞❧❡s ✇❡r❡ ❝r❡❛t❡❞ ❜② ✐s♦tr♦♣✐❝ ✇❡t ❡t❝❤✐♥❣ ♦❢ s✐❧✐❝♦♥ t❤r♦✉❣❤ ❝✐r❝✉❧❛r ❛♣❡rt✉r❡s ✐♥ ❛ ❧✐t❤♦❣r❛♣❤✐❝ ♠❛s❦ ✉s✐♥❣ ❛ ♠✐①t✉r❡ ♦❢ ❍❋ ❛♥❞ ❍◆❖✸ ✉♥❞❡r ❝♦♥t✐♥✉♦✉s ❛❣✐t❛t✐♦♥✳ ❋❛❜r✐❝❛t✐♦♥ ♦❢ ❝♦♥❝❛✈❡ s✐❧✐❝♦♥ ♠✐rr♦rs ✐♥ t❤✐s r❡❢❡r❡♥❝❡ ✇❛s ♣r✐♠❛r✐❧② ♠♦t✐✈❛t❡❞ ❜② ♣♦t❡♥t✐❛❧ ❛♣♣❧✐❝❛t✐♦♥s ✐♥ q✉❛♥t✉♠ ✐♥❢♦r♠❛t✐♦♥ s❝✐❡♥❝❡s✱ ♣❛rt✐❝✉❧❛r❧② ❢♦r t❤❡ st✉❞✐❡s ♦❢ ❝❛✈✐t② ◗❊❉ st✉❞✐❡s ❛♥❞ t❤❡ ❢❛❜r✐❝❛t✐♦♥ ♦❢ ❛t♦♠ tr❛♣s✳ ❋♦r ❢❛❜r✐❝❛t✐♦♥ ♦❢ s✉❝❤ ❞❡✈✐❝❡s✱ ❛ ❧♦✇ r♦✉❣❤♥❡ss ✐s ✈❡r② ✐♠♣♦rt❛♥t s♦ ❛s t♦ ♠✐♥✐♠✐③❡ ❧♦ss✳ ❉❡s♣✐t❡ ❛ r❡❧❛t✐✈❡❧② ❧❛r❣❡ s✉r❢❛❝❡ r♦✉❣❤♥❡ss ♦❢ ✻♥♠ ♦❢ t❤❡ ❛s✲❢❛❜r✐❝❛t❡❞ ❝♦♥❝❛✈❡ ♠✐rr♦r✱ t❤❡② ♠❛♥❛❣❡❞ t♦ ❛❝❤✐❡✈❡ ❛ ☞♥❛❧ r♦✉❣❤♥❡ss ♦❢ ✷♥♠ ❛❢t❡r ❤✐❣❤ q✉❛❧✐t② ❝♦❛t✐♥❣s✳ ❆ s✐♠✐❧❛r ♠❡t❤♦❞ t♦ ❢❛❜r✐❝❛t❡ ❝♦♥❝❛✈❡ ♣r♦☞❧❡s ♦♥ s✐❧✐❝♦♥ ✐s r❡♣♦rt❡❞ ✐♥ ❘❡❢ ❬✾✵❪✳ ❚❤❡ ✉s❡ ♦❢ t❤❡r♠❛❧ ♦①✐❞❡ ✭❙✐❖✷ ✮ ❛♥❞ ❧♦✇✲str❡ss s✐❧✐❝♦♥ ♥✐tr✐❞❡ ✭❙✐✸ ◆✹ ✮ ❛s ❛ ❤❛r❞ ♠❛s❦ t♦❣❡t❤❡r ✇✐t❤ ✐s♦tr♦♣✐❝ ✇❡t ❡t❝❤✐♥❣ ♦❢ s✐❧✐❝♦♥ ✐♥ ❛♥ ❡t❝❤ s♦❧✉t✐♦♥ ❝♦♥t❛✐♥✐♥❣ ❡t❝❤ s♦❧✉t✐♦♥ ❝♦♥s✐sts ♦❢ ❍❋ ❛♥❞ ❍◆❖✸ ✇❛s ✉s❡❞ t♦ ❝r❡❛t❡ ❝♦♥❝❛✈❡ ♣r♦☞❧❡s ♦♥ s✐❧✐❝♦♥ ✇❤✐❝❤ ✇❡r❡ ✉s❡❞ s✉❜s❡q✉❡♥t❧② ❛s ♠♦❧❞s t♦ ❢♦r♠ ♠✐❝r♦❧❡♥s❡s ♦♥ ♣♦❧②♠❡rs✳ ●✐✈❡♥ t❤❡ r❛♥❣❡ ♦❢ ❛♣♣❧✐❝❛t✐♦♥s ❢♦r ❝♦♥tr♦❧❧❛❜❧② ❢❛❜r✐❝❛t❡❞ ❝♦♥❝❛✈❡✱ ♠✐❝r♦♠❡t❡r✲s❝❛❧❡ ♠✐rr♦rs ❛♥❞ ♠✐❝r♦❝❛✈✐t✐❡s✱ ❤❡r❡ ✇❡ ❞✐s❝✉ss ❛ ♥❡✇ ♣r♦❝❡ss ❢♦r ♠❛❦✐♥❣ s✉❝❤ str✉❝t✉r❡s ✐♥ s✐❧✐❝♦♥ ✉s✐♥❣ ❛ ♣r♦❝❡ss ♦❢ ✐♦♥ ✐rr❛❞✐❛t✐♦♥ ❛♥❞ ❡❧❡❝tr♦❝❤❡♠✐❝❛❧ ❛♥♦❞✐③❛t✐♦♥✳ ❚❤✐s ♣r♦❝❡ss ❤❛s ❜❡❡♥ ✉s❡❞ t♦ ❢❛❜r✐❝❛t❡ s♣❤❡r✐❝❛❧ ❝♦♥❝❛✈❡ ♣r♦☞❧❡s ✇❤✐❝❤ ♣r♦❞✉❝❡ ❛ ♣♦✐♥t ❢♦❝✉s✳ ■♥ ❛❞❞✐t✐♦♥✱ ❝♦♥❝❛✈❡ ❝②❧✐♥❞r✐❝❛❧ ♣r♦☞❧❡s ✇❤✐❝❤ ♣r♦❞✉❝❡ ❧✐♥❡ ❢♦❝✉s ❤❛✈❡ ❛❧s♦ ❜❡❡♥ ❢❛❜r✐❝❛t❡❞✳ ❚❤✐s s❛♠❡ ♣r♦❝❡ss ♠❛② ❜❡ ✉s❡❞ t♦ ❢❛❜r✐❝❛t❡ ❛♥② ❡❧❧✐♣t✐❝❛❧ ♣r♦☞❧❡ ❜❡t✇❡❡♥ t❤❡s❡ ❣❡♦♠❡tr✐❡s ❛s ✇❡❧❧✳ ✾✻ ❋✐❣✉r❡ ✼✳✶✿ ✭❛✮✱ ✭❜✮ ❛♥❞ ✭❝✮ s❤♦✇s t❤❡ ❝r♦ss s❡❝t✐♦♥❛❧ s❝❤❡♠❛t✐❝ ♣r♦❝❡ss ✌♦✇ ❢♦r t❤❡ ❢❛❜r✐❝❛t✐♦♥ ♦❢ t❤❡ ❝♦♥❝❛✈❡ ♠✐rr♦rs ❛♥❞ ❝♦♥❝❛✈❡ ❝②❧✐♥❞❡rs✳ ✭❞✮ ❞❡☞♥❡s t❤❡ ♣❛r❛♠❡t❡rs ❆✱ ❈ ❛♥❞ ❉ ❛s t❤❡ ✇✐❞t❤ ♦❢ t❤❡ ✐rr❛❞✐❛t❡❞ ❛♥♥✉❧✉s✴❧✐♥❡s✱ ❞✐❛♠❡t❡r ♦❢ t❤❡ ❝❡♥tr❛❧ ❛♣❡rt✉r❡ ❛♥❞ t❤❡ ☞♥❛❧ ❞✐❛♠❡t❡r ♦❢ t❤❡ ♠✐rr♦r✴❝②❧✐♥❞❡r r❡s♣❡❝t✐✈❡❧②✳ ✭❡✮ ❛♥❞ ✭❢✮ s❤♦✇ t❤❡ ♣❤♦t♦r❡s✐sts ♣❛tt❡r♥s ✉s❡❞ ❢♦r ❢❛❜r✐❝❛t✐♥❣ t❤❡ ❝♦♥❝❛✈❡ ♠✐rr♦rs ❛♥❞ ❝②❧✐♥❞❡rs r❡s♣❡❝t✐✈❡❧② ❛♥❞ t❤❡ ❡q✉✐✈❛❧❡♥t ♣❛r❛♠❡t❡rs ❆✱ ❈ ❛♥❞ ❉ ♦❢ t❤❡ ❝②❧✐♥❞❡rs ❛♥❞ ♠✐rr♦rs ✐♥ ♣❧❛♥❛r ✈✐❡✇✳ ✼✳✷ ❋❛❜r✐❝❛t✐♦♥ ♦❢ ❝♦♥❝❛✈❡ ♣r♦☞❧❡s ✈✐❛ ✐♦♥ ✐rr❛❞✐❛t✐♦♥ ❛♥❞ s❛❝r✐☞❝✐❛❧ P❙✐ ❆ s❝❤❡♠❛t✐❝ ♦❢ t❤❡ ❢❛❜r✐❝❛t✐♦♥ ♣r♦❝❡ss ✐s s❤♦✇♥ ✐♥ ❋✐❣ ✼✳✶✭❛✮✲✭❝✮✳ ❆♥♥✉❧✐ ♣❛tt❡r♥s ✇❡r❡ ♣❛tt❡r♥❡❞ ✉s✐♥❣ st❛♥❞❛r❞ ❯❱ ❧✐t❤♦❣r❛♣❤② ♦♥ ❛ ✼✖♠ t❤✐❝❦ ❆❩ ✹✻✷✵ ♣❤♦t♦r❡s✐st s♣✐♥ ✭❈❤❛♣✲ t❡r ✷✳✹✳✷✮ ❝♦❛t❡❞ ♦♥ ✵✳✵✷ ✡✳❝♠ ♣✲t②♣❡ ✇❛❢❡rs ✭❋✐❣ ✼✳✶✭❡✮✳ ❚❤❡ ❛♥♥✉❧✐ ❛r❡ t❤❡♥ ✐rr❛❞✐❛t❡❞ ✾✼ ✇✐t❤ ❛ ❧❛r❣❡ ❛r❡❛ ❜❡❛♠ ♦❢ ✻✵✵ ❦❡❱ ❤❡❧✐✉♠ ✐♦♥s✱ ✇❤✐❝❤ ❤❛s ❛ r❛♥❣❡ ♦❢ ❛♣♣r♦①✐♠❛t❡❧② ✷✳✸✖♠ ✐♥ s✐❧✐❝♦♥✳ ❚❤❡ ✇❛❢❡rs ✇❡r❡ ✐rr❛❞✐❛t❡❞ ✇✐t❤ ❛ ✌✉❡♥❝❡ ♦❢ ✸ ✂ ✶✵✶✹ ✐♦♥s✴❝♠✷ ✱ ❤✐❣❤ ❡♥♦✉❣❤ t♦ st♦♣ P❙✐ ❢r♦♠ ❢♦r♠✐♥❣✳ ❚❤❡ ❤❡❧✐✉♠ ✐♦♥s ❛r❡ ❝♦♠♣❧❡t❡❧② s❤✐❡❧❞❡❞ ✐♥ ❛r❡❛s ♦♥ t❤❡ s❛♠✲ ♣❧❡ ❝♦✈❡r❡❞ ✇✐t❤ ♣❤♦t♦r❡s✐st ❛♥❞ ❝r❡❛t❡ ❞❡❢❡❝ts ♦♥❧② ✐♥ t❤❡ ❡①♣♦s❡❞ ✇❛❢❡r r❡❣✐♦♥s✳ ❚❤✐s ❡☛❡❝t✐✈❡❧② ♠❡❛♥s ✇❡ ❛r❡ ❝r❡❛t✐♥❣ ❛ ❤❛r❞ ❍❋ r❡s✐st❛♥t ♠❛s❦ ❛♥❞ P❙✐ ♦♥❧② ❢♦r♠s ❢r♦♠ t❤❡ s♠❛❧❧ ❝❡♥tr❛❧ ❛♣❡rt✉r❡ ❛t t❤❡ s✉r❢❛❝❡✳ ❆s P❙✐ ❢♦r♠❛t✐♦♥ ✐s ✐s♦tr♦♣✐❝ ❢♦r ✵✳✵✷ ✡✳❝♠ ♣✲t②♣❡ ✇❛❢❡rs ❬✶✻❪✱ ❝✉r✈❡❞ str✉❝t✉r❡s ♥❛t✉r❛❧❧② ❢♦r♠s ❛❢t❡r t❤❡ t♦♣ ✐rr❛❞✐❛t❡❞ r❡❣✐♦♥s ❛r❡ ✉♥❞❡r✲ ❝✉t✳ ▼♦r❡♦✈❡r✱ ❤✐❣❤❧② ❞♦♣❡❞ ✇❛❢❡rs ❧✐❦❡ t❤❡s❡ ❛r❡ ❦♥♦✇♥ t♦ ❤❛✈❡ ❛ s♠♦♦t❤ ☞♥❛❧ r❡❧✐❡✈❡❞ s✉r❢❛❝❡ ❛❢t❡r t❤❡ r❡♠♦✈❛❧ ♦❢ P❙✐ ❬✺✵❪✳ ❋r♦♠ t❤❡ s❝❤❡♠❛t✐❝s ✐♥ ❋✐❣ ✼✳✶✭❞✮✱ ✐t ❝❛♥ ❜❡ s❡❡♥ t❤❛t t❤❡ r❛❞✐✉s ♦❢ ❡❛❝❤ ❝♦♥❝❛✈❡ ♠✐rr♦r ✐s ❞❡t❡r♠✐♥❡❞ ❜② t❤❡ r❛❞✐✉s ♦❢ t❤❡ ❝❡♥tr❛❧ ❛♣❡rt✉r❡ ♣❧✉s ❤❛❧❢ t❤❡ ✇✐❞t❤ ♦❢ t❤❡ ❛♥♥✉❧✉s✳ ❚❤❡ ❞✐❛♠❡t❡r ♦❢ t❤❡ ❝♦♥❝❛✈❡ ♠✐rr♦r ✇♦✉❧❞ ♥♦t ✐♥❝r❡❛s❡ ❢✉rt❤❡r ♦♥❝❡ t❤❡ t✇♦ ❢r♦♥ts ♦❢ t❤❡ P❙✐ ❢♦r♠❛t✐♦♥ ♠❡❡t ❤❛❧❢✇❛② ✉♥❞❡r♥❡❛t❤ ❡❛❝❤ ✐rr❛❞✐❛t❡❞ ❛♥♥✉❧✉s✳ ❈♦♥❝❛✈❡ ♣r♦☞❧❡s ✇✐t❤ t✇♦ ❞✐☛❡r❡♥t ❞✐❛♠❡t❡rs✱ ❉ ❂ ✷✵✖♠ ❛♥❞ ❉ ❂ ✶✵✵ ✖♠✱ ✇❡r❡ ❢❛❜r✐❝❛t❡❞ ❤❡r❡✳ ❆❢t❡r t❤❡ ✐rr❛❞✐❛t✐♦♥✱ t❤❡ ♣❤♦t♦r❡s✐st ✇❛s r❡♠♦✈❡❞ ✇✐t❤ ♥❛♥♦str✐♣♣❡r ❛♥❞ t❤❡ ✇❛❢❡r ❡❧❡❝tr♦❝❤❡♠✐❝❛❧❧② ❛♥♦❞✐③❡❞ ❛t ✼✵♠❆✴❝♠✷ ❢♦r ❞✐☛❡r❡♥t ❛♠♦✉♥t ♦❢ t✐♠❡ ❞❡♣❡♥❞✐♥❣ ♦♥ t❤❡ ❞✐♠❡♥s✐♦♥s ♦❢ t❤❡ ❛♥♥✉❧✐✳ ❋♦r ❡①❛♠♣❧❡✱ ❛ ❝♦♥❝❛✈❡ ♠✐rr♦r ✇✐t❤ ❛ ❞✐❛♠❡t❡r ♦❢ ❉ ❂ ✶✵✵✖♠ ❤❛s ❛ ❝❡♥tr❛❧ ❛♣❡rt✉r❡ ❞✐❛♠❡t❡r ♦❢ ✺ ✖♠ ❛♥❞ ❛♥ ✾✺✖♠ ✇✐❞❡ ❛♥♥✉❧✉s✳ ❚❤❡ ❛♥♦❞✐③❡❞ ❞❡♣t❤ ✇♦✉❧❞ ❤❛✈❡ t♦ ❜❡ ❛t ❧❡❛st ✹✼✳✺✖♠✱ ❤❛❧❢ t❤❡ ✇✐❞t❤ ♦❢ t❤❡ ❛♥♥✉❧✉s s♦ t❤❛t t❤❡ ✐rr❛❞✐❛t❡❞ ❛♥♥✉❧✉s ✐s ❝♦♠♣❧❡t❡❧② ✉♥❞❡r❝✉t✳ ❆t t❤❡ ❡♥❞ ♦❢ t❤❡ ❛♥♦❞✐③❛t✐♦♥✱ ❛ ❧❛r❣❡ ❡❧❡❝tr♦♣♦❧✐s❤✐♥❣ ❝✉rr❡♥t ♣✉❧s❡ ✐s ❛♣♣❧✐❡❞ t♦ ❞❡t❛❝❤ t❤❡ P❙✐ ❛♥❞ t❤❡ ✐rr❛❞✐❛t❡❞ s✐❧✐❝♦♥ ❢r♦♠ t❤❡ ✉♥❞❡r❧②✐♥❣ ❝♦♥❝❛✈❡ s✐❧✐❝♦♥ s✉r❢❛❝❡✳ ❑❖❍ ✇❛s ♥♦t ✉s❡❞ t♦ r❡♠♦✈❡ t❤❡ P❙✐ ✐♥ t❤✐s ✇♦r❦ s✐♥❝❡ ✐t ✐s ❛♥ ❛♥✐s♦tr♦♣✐❝ ❡t❝❤❛♥t ❛♥❞ ✐s ♣❧❛♥❡ ❞❡♣❡♥❞❡♥t✳ ■♥ t❤❡ ❝❛s❡ ♦❢ ❛ ❝♦♥❝❛✈❡ s✐❧✐❝♦♥ s✉r❢❛❝❡✱ t❤❡ ❡☛❡❝t ♦❢ ❛♥② ❑❖❍ ❡①♣♦s✉r❡ ✐s ✐♠♠❡❞✐❛t❡❧② ❛♣♣❛r❡♥t s✐♥❝❡ s✉❝❤ ❛ ✇✐❞❡ ❛♥❣✉❧❛r r❛♥❣❡ ♦❢ ❝r②st❛❧❧✐♥❡ ♣❧❛♥❡s ❛r❡ ❡①♣♦s❡❞✱ ❛s s❤♦✇♥ ✐♥ ❋✐❣ ✼✳✼✭❛✮✳ ❚❤✐s ❵❜❧♦ss♦♠✬ ♣❛tt❡r♥ r❡s✉❧t✐♥❣ ❢r♦♠ ❑❖❍ ❡t❝❤✐♥❣ ✇❛s r❡♣♦rt❡❞ ♣r❡✈✐♦✉s❧② ✐♥ ❘❡❢ ❬✾✶❪✳ ❙❛♠♣❧❡s ✇❡r❡ t❤❡♥ ❝❧❡❛♥❡❞ ✉s✐♥❣ ❛ ♠❡❣❛s♦♥✐❝ ❝❧❡❛♥❡r ❬✺✸❪ t♦ r❡♠♦✈❡ ❛♥② s✐❧✐❝♦♥ ❞❡❜r✐s ❧❡❢t ❜❡❤✐♥❞ ❢r♦♠ t❤❡ ❛♥♦❞✐③❛t✐♦♥✳ ❚❤❡ s✉r❢❛❝❡ r♦✉❣❤♥❡ss ✇❛s ❢✉rt❤❡r r❡❞✉❝❡❞ ❜② ✐t❡r❛t✐✈❡❧② ✶✵✵ t❤❡ s✐❧✐❝♦♥ ❜✉❧❦ ❛♥❞ ❛s ❝❛♥ ❜❡ s❡❡♥ ✐♥ ❋✐❣ ✼✳✸✳ ❚❤❡s❡ ✐rr❛❞✐❛t❡❞ ❧✐♥❡s ❛r❡ ❜❛s✐❝❛❧❧② ❢r❡❡ st❛♥❞✐♥❣ ♠✉❧t✐❧❛②❡r P❙✐ str✉❝t✉r❡s✱ ❛♥❞ s♣❡❝t❛❝✉❧❛r r❡✌❡❝t✐✈❡ ❝♦❧♦rs ♠❛② ❜❡ ♦❜s❡r✈❡❞ ❢r♦♠ t❤❡♠✳ ❆❧t❤♦✉❣❤ t❤❡s❡ t❡sts ❞✐❞ ♥♦t ❢♦r♠ ♥✐❝❡ ❝♦♥❝❛✈❡ s✐❧✐❝♦♥ ♠✐rr♦rs✱ ✐t ❤❛s s❤♦✇♥ ✉s t❤❡ ♣♦ss✐❜✐❧✐t✐❡s ♦❢ ❢❛❜r✐❝❛t✐♦♥ ❢r❡❡st❛♥❞✐♥❣ P❙✐ str✉❝t✉r❡s ✉s✐♥❣ ✐♦♥ ✐rr❛❞✐❛t✐♦♥ t♦❣❡t❤❡r ✇✐t❤ ❛♥ ❡❧❡❝tr♦♣♦❧✐s❤✐♥❣ st❡♣✳ ❈♦♥❝❛✈❡ s✐❧✐❝♦♥ ♠✐rr♦rs ❋✐❣✉r❡ ✼✳✹✿ ✭❛✮ ❛♥❞ ✭❜✮ s❤♦✇s ❝♦♥❝❛✈❡ ❝②❧✐♥❞r✐❝❛❧ ♠✐rr♦rs✳ ✭❝✮ ❛♥❞ ✭❞✮ s❤♦✇ ❝♦♥❝❛✈❡ ♠✐rr♦rs✳ ✭❛✮ ✐s ❛♥ ✖♠ ❝♦♥❝❛✈❡ ❝②❧✐♥❞❡r✳ ✭❜✮ s❤♦✇s ❛ ❝r♦ss s❡❝t✐♦♥ ♦❢ ❛ ❝♦♥❝❛✈❡ ❝②❧✐♥❞❡r ✇✐t❤ ❉ ✖♠✱ ✇❤✐❝❤ ♠❛② ❛❧s♦ r❡♣r❡s❡♥t t❤❡ ❝r♦ss s❡❝t✐♦♥s ♦❢ ❉ ❂ ✶✵✵ ✖♠ ❝♦♥❝❛✈❡ ♠✐rr♦rs✳ ✭❝✮ ✐s ❛♥ ♦♣t✐❝❛❧ ✐♠❛❣❡ ♦❢ ❛ ❧❛r❣❡ ❛rr❛② ♦❢ ❉ ❂ ✷✵ ✖♠ ❝♦♥❝❛✈❡ ♠✐rr♦rs✳ ✭❞✮ ✐s ❛♥ ❙❊▼ ✐♠❛❣❡ ♦❢ ❛ s✐♥❣❧❡ ❉ ❂ ✶✵✵ ✖♠ ❝♦♥❝❛✈❡ ♦♣t✐❝❛❧ ✐♠❛❣❡ ♦❢ ❛ ❉ ❂ ✷✵ ❂ ✶✵✵ ♠✐rr♦r✳ ❚❤❡ ✐♦♥ ✐rr❛❞✐❛t✐♦♥ ♣r♦❝❡ss ✇❛s ❝❛rr✐❡❞ ♦✉t ✉s✐♥❣ ❛ ❧❛r❣❡ ❛r❡❛✱ ✉♥✐❢♦r♠ ✐♦♥ ❜❡❛♠ ✇✐t❤ ❛ ♣❛tt❡r♥❡❞ ♣❤♦t♦r❡s✐st ♠❛s❦✳ ❚❤✐s ♠❡❛♥s t❤❛t ❧❛r❣❡ ❛rr❛②s ♦❢ ❝♦♥❝❛✈❡ ♠✐rr♦rs ♠❛② ❜❡ ❢❛❜r✐❝❛t❡❞ s✐♠✉❧t❛♥❡♦✉s❧② ❛s s❤♦✇♥ ✐♥ ❋✐❣ ✼✳✹✭❝✮✳ ❚❤❡ ❢❛❜r✐❝❛t❡❞ ❛rr❛②s ♦❢ ❝♦♥❝❛✈❡ ♣r♦☞❧❡s ♠❛② ✈❡r② ✇❡❧❧ ❜❡ ✉s❡❞ ❛s ♠♦❧❞s ♦r t❡♠♣❧❛t❡s t♦ ♣r♦❞✉❝❡ ♠✐❝r♦❧❡♥s❡s ✐♥ ♣♦❧②♠❡rs ❬✾✵❪✳ ❆♥ ❛❞❞✐t✐♦♥❛❧ ❢❡❛t✉r❡ ✐s t❤❛t t❤❡ ❧♦❝❛t✐♦♥ ♦❢ ❡❛❝❤ ♠✐rr♦r ♠❛② ❜❡ ♣r❡❝✐s❡❧② ❝♦♥tr♦❧❧❡❞✱ ✉♥❧✐❦❡ ✶✵✶ ❋✐❣✉r❡ ✼✳✺✿ ✭❛✮ ✐s ❛ ❙❊▼ ❝r♦ss s❡❝t✐♦♥ ✐♠❛❣❡ ♦❢ ❛ ❝♦♥❝❛✈❡ ❝②❧✐♥❞❡r ✇✐t❤ ❉ ❂ ✷✵ ✖♠ ❢❛❜r✐❝❛t❡❞ ✇✐t❤ ❛ P❙✐ ♠✉❧t✐❧❛②❡r ❛❜♦✈❡ t❤❡ ❝♦♥❝❛✈❡ s✐❧✐❝♦♥ s✉r❢❛❝❡✳ ✭❜✮ s❤♦✇s ❛ ❙❊▼ ❝r♦ss s❡❝t✐♦♥ ♦❢ ❛ ❝♦♥❝❛✈❡ ❝②❧✐♥❞❡r ❛♥♦❞✐③❡❞ s✉❝❤ t❤❛t t❤❡ ✐rr❛❞✐❛t❡❞ r❡❣✐♦♥s ❛r❡ ♥♦t ❢✉❧❧② ✉♥❞❡r❝✉t ❛♥❞ t❤❡ P❙✐ r❡♠♦✈❡❞ ✇✐t❤ ❞✐❧✉t❡❞ ❑❖❍✳ t❤❡ r❛♥❞♦♠ ♠✐rr♦r ❢❛❜r✐❝❛t✐♦♥ ❜② tr❛♣♣✐♥❣ ❜✉❜❜❧❡s ✐♥ ❜♦r♦s✐❧✐❝❛t❡ ❬✹✾❪✳ ❋✐❣ ✼✳✼✭❝✮ s❤♦✇s ❛♥ ♦♣t✐❝❛❧ ✐♠❛❣❡ ♦❢ ♦♥❡ s✉❝❤ ❝♦♥❝❛✈❡ ♠✐rr♦r ✇❤❡r❡ t❤❡ ♠✐❝r♦s❝♦♣❡ st❛❣❡ ✇❛s ♣♦s✐t✐♦♥❡❞ s♦ ❛s t♦ ❝❛♣t✉r❡ t❤❡ ❢♦❝❛❧ ♣♦✐♥t ♦❢ t❤❡ ♠✐rr♦r ✇❤❡r❡ ✐♥❝♦♠✐♥❣ ❧✐❣❤t ✇❛s ❢♦❝✉s❡❞ ✐♥t♦ ❛ s✐♥❣❧❡ ❜r✐❣❤t s♣♦t ✐♥ t❤❡ ❝❡♥t❡r ♦❢ t❤❡ ♠✐rr♦r✳ ❚❤❡ ♦♣t✐❝❛❧ ✐♠❛❣❡ ♦❢ t❤❡ ❝r♦ss s❡❝t✐♦♥s ♦❢ t❤❡ ♠✐rr♦rs ✐s s❤♦✇♥ ✐♥ ❋✐❣ ✼✳✹✭❜✮✳ ■♥ ❋✐❣ ✼✳✺✭❛✮✱ ❉ ❂ ✷✵✖♠ ❝♦♥❝❛✈❡ ♠✐rr♦rs ✇❡r❡ ❢♦r♠❡❞ ❜② ❝r❡❛t✐♥❣ ♠✉❧t✐❧❛②❡r❡❞ P❙✐ ✇✐t❤ ❛❧t❡r♥❛t✐♥❣ ♣♦r♦s✐t② ❛♥❞ ❝❧❡❛✈❡❞ t♦ s❤♦✇ t❤❡✐r ❝r♦ss s❡❝t✐♦♥s✳ ❚❤❡ ❢♦r♠❛t✐♦♥ ♦❢ t❤❡ ♠✉❧t✐❧❛②❡r s❡r✈❡s t❤❡ ♣✉r♣♦s❡ ♦❢ tr❛❝❦✐♥❣ t❤❡ ♣r♦❣r❡ss✐♦♥ ♦❢ t❤❡ P❙✐ ❢♦r♠❛t✐♦♥ t❤r♦✉❣❤ t❤❡ ❝❡♥tr❛❧ ❛♣❡rt✉r❡s✳ P❙✐ ❧❛②❡rs ❢♦r♠❡❞ ❛r❡ ✐♥✐t✐❛❧❧② ♣❛r❛❧❧❡❧ t♦ t❤❡ s✉r❢❛❝❡✱ ❤♦✇❡✈❡r✱ ♦♥❝❡ t❤❡ ❢♦r♠❛t✐♦♥ ❣♦❡s ♣❛st t❤❡ ❡♥❞ ♦❢ r❛♥❣❡ ♦❢ t❤❡ ❤❡❧✐✉♠ ✐rr❛❞✐❛t✐♦♥✱ ❝✉r✈❡ ♣r♦☞❧❡s ❜❡❣✐♥s t♦ ❢♦r♠✳ ■t ♠❛② ❛❧s♦ ❜❡ s❡❡♥ ❤❡r❡ t❤❛t t❤❡ ❞✐❛♠❡t❡r ♦❢ ❡❛❝❤ ♠✐rr♦r ✐s ✐♥❝r❡❛s✐♥❣ ✉♥t✐❧ t❤❡ ♣♦✐♥t ✇❤❡♥ t❤❡ t✇♦ ❢r♦♥ts ♦❢ P❙✐ ❢♦r♠❛t✐♦♥ ♠❡❡t ✉♥❞❡r♥❡❛t❤ t❤❡ ✐rr❛❞✐❛t❡❞ ❛♥♥✉❧✉s✳ ❚❤❡ r♦✉❣❤♥❡ss r❡❞✉❝t✐♦♥ ❜② ✐t❡r❛t✐✈❡ t❤❡r♠❛❧ ♦①✐❞❛t✐♦♥ ✇❛s st✉❞✐❡❞ ❛♥❞ ❆❋▼ ♠❡❛✲ s✉r❡♠❡♥ts ✇❡r❡ ❝❛rr✐❡❞ ♦✉t ♣❡r✐♦❞✐❝❛❧❧② ❛❢t❡r ❡✈❡r② ❢♦✉r ❤♦✉rs ♦❢ ♦①✐❞❛t✐♦♥ ❛♥❞ r❡♠♦✈❛❧ ♦❢ ♦①✐❞❡ ♦♥ t❤r❡❡ ❞✐☛❡r❡♥t s❛♠♣❧❡s✳ ❚❤❡ r❡s✉❧ts ❛r❡ ♣❧♦tt❡❞ ✐♥ ❋✐❣ ✼✳✻✭❜✮✳ ■♥ ♦♥❡ s❛♠♣❧❡✱ t❤❡ r♦✉❣❤♥❡ss ♦❢ t❤❡ ♠✐rr♦r ✇❛s r❡❞✉❝❡❞ ❢r♦♠ ✸✳✹♥♠ t♦ ✶✳✼♥♠✱ ✇❤✐❧❡ ✐♥ t❤❡ t✇♦ ♦t❤❡r s❛♠♣❧❡s t❤❡✐r r♦✉❣❤♥❡ss ✇❡r❡ r❡❞✉❝❡❞ t♦ ❛❜♦✉t ✷✳✺ ♥♠✳ ❚❤✐s ✐s ❝♦♥s✐st❡♥t ✇✐t❤ t❤❡ ✇♦r❦ ❜② ▲❛✐ ❬✺✶❪ ✇❤♦ r❡♣♦rt❡❞ t❤❛t t❤❡ ☞♥❛❧ r♦✉❣❤♥❡ss ❛❝❤✐❡✈❛❜❧❡ ❢r♦♠ t❤✐s ♠❡t❤♦❞ ✐s ❞❡t❡r♠✐♥❡❞ ❜② ✐ts ✐♥✐t✐❛❧ r♦✉❣❤♥❡ss ✳ ✶✵✷ ❋✐❣✉r❡ ✼✳✻✿ ✭❛✮ ✐s ❛ ♣❧♦t s❤♦✇✐♥❣ t❤❡ r✳♠✳s✳ r♦✉❣❤♥❡ss ✈❡rs✉s ♦①✐❞✐③❛t✐♦♥ t✐♠❡ ❢♦r t❤r❡❡ ❞✐☛❡r❡♥t s❛♠♣❧❡s ❋✐❣✉r❡ ✼✳✼✿ ✭❛✮ s❤♦✇s t❤❡ ❵❜❧♦ss♦♠✬ ♣❛tt❡r♥ ♦♥ ❛ ❝♦♥❝❛✈❡ ♠✐rr♦r r❡s✉❧t✐♥❣ ❢r♦♠ t❤❡ ❛♥✐s♦tr♦♣✐❝ ❑❖❍ s✶✱ s✷ ❛♥❞ s✸✳ ✭❜✮ s❤♦✇s t❤❡ ❆❋▼ ✐♠❛❣❡ ♦❢ t❤❡ s❛♠♣❧❡ ✇✐t❤ t❤❡ ❧♦✇❡st r✳♠✳s✳ r♦✉❣❤♥❡ss ♦❢ ✶✳✼ ♥♠✳ r❡♠♦✈❛❧ ♦❢ P❙✐✳ ■♥ ✭❜✮ t❤❡ P❙✐ ✇❛s r❡♠♦✈❡❞ ❜② ❡❧❡❝tr♦♣♦❧✐s❤✐♥❣ ❛♥❞ t❤❡ ❜♦tt♦♠ ♦❢ ❝♦♥❝❛✈❡ ♠✐rr♦r ✐s ✐♥ ❢♦❝✉s✳ ✭❝✮ t❤❡ ♠✐❝r♦s❝♦♣❡ st❛❣❡ ✇❛s ♠♦✈❡❞ ✉♥t✐❧ t❤❡ ✐♥❝♦♠✐♥❣ ❧✐❣❤t ✐s ❢♦❝✉s❡❞ ✐♥t♦ ❛ s✐♥❣❧❡ ❜r✐❣❤t s♣♦t ❜② t❤❡ ❝♦♥❝❛✈❡ s✐❧✐❝♦♥ ♠✐rr♦r✳ ✭❞✮ ✐s ❛ ♣❧♦t ♦❢ t❤❡ ✐♥t❡♥s✐t② ♦❢ t❤❡ ❜r✐❣❤t s♣♦t ✐♥ t❤❡ ❝❡♥t❡r ♦❢ ❛ ❝♦♥❝❛✈❡ ♠✐rr♦r ✈❡rs✉s t❤❡ ♠✐❝r♦s❝♦♣❡ st❛❣❡ ✈❡rt✐❝❛❧ ♣♦s✐t✐♦♥ ♠❡❛s✉r❡❞ ❢r♦♠ t❤❡ ❜♦tt♦♠ ♦❢ t❤❡ ❝♦♥❝❛✈❡ ♠✐rr♦r✳ ❚❤❡ ❤✐❣❤❡st ✐♥t❡♥s✐t② ✐s ♠❡❛s✉r❡❞ t♦ ❜❡ ✷✺ ❢♦❝❛❧ ❧❡♥❣t❤ ♦❢ t❤❡ ♠✐rr♦r✳ ✖♠ ❢r♦♠ t❤❡ ❜♦tt♦♠ ♦❢ t❤❡ ♠✐rr♦r ❛♥❞ t❤✐s ♠❛② ❜❡ t❛❦❡♥ t♦ ❜❡ t❤❡ ✶✵✸ ✖ ■♥ ❋✐❣ ✼✳✼✭❜✮✱ ✭❝✮ ❛♥❞ ✭❞✮✱ t❤❡ ❢♦❝❛❧ ❧❡♥❣t❤ ♦❢ ❛ ❉ ❂ ✶✵✵ ♠ ♠✐rr♦r ✇❛s ❝❤❛r❛❝t❡r✐③❡❞ ✇✐t❤ t❤❡ ❛✐❞ ♦❢ ❛ ♠✐❝r♦s❝♦♣❡✳ ■♥ ❋✐❣ ✼✳✼✭❜✮✱ t❤❡ ♠✐❝r♦s❝♦♣❡ ✇❛s ☞rst ♣♦s✐t✐♦♥❡❞ t♦ ❤❛✈❡ t❤❡ ❜♦tt♦♠ ♦❢ t❤❡ ♠✐rr♦r ✐♥ ❢♦❝✉s✳ ❚❤❡ ♠✐❝r♦s❝♦♣❡ ✇❛s t❤❡♥ ♠♦✈❡❞ ✈❡rt✐❝❛❧❧② ❞♦✇♥✇❛r❞s ✐♥ st❡♣s ✉♥t✐❧ t❤❡ ❝❡♥t❡r r❡❣✐♦♥ ♦❢ t❤❡ ♠✐rr♦r ❢♦❝✉s❡s ✐♥t♦ ❛ s✐♥❣❧❡ ❜r✐❣❤t s♣♦t✳ ■♥t❡♥s✐t② ♠❡❛s✉r❡♠❡♥ts ✇❛s ♠❛❞❡ ✐♥t❡r♠✐tt❡❞❧② ❛♥❞ ♣❧♦tt❡❞ ✐♥ ❋✐❣ ✼✳✼✭❞✮✳ ❚❤❡ ❢♦❝❛❧ ❧❡♥❣t❤ ✐s t❛❦❡♥ t♦ ❜❡ ❛♣♣r♦①✐♠❛t❡❧② ✷✺ ✖♠ ✇❤❡r❡ t❤❡ ✐♥t❡♥s✐t② ♦❢ t❤❡ ❝❡♥tr❛❧ s♣♦t ✐s t❤❡ ❤✐❣❤❡st✳ ❚❤✐s ❢✉rt❤❡r ♣r♦✈❡s t❤❛t t❤❡ ❝♦♥❝❛✈❡ ♠✐rr♦rs ❛r❡ s♣❤❡r✐❝❛❧ ✐♥ ♥❛t✉r❡ s✐♥❝❡ t❤❡ ♣❧❛♥❛r r❛❞✐✉s ✐s ✺✵ ✖♠ ❛♥❞ s♣❤❡r✐❝❛❧ ♠✐rr♦rs ❤❛✈❡ ❢♦❝❛❧ ❧❡♥❣t❤ ❛t ❤❛❧❢ t❤❡✐r r❛❞✐✉s✳ ✼✳✸ ❈♦♥❝❛✈❡ ♠✉❧t✐❧❛②❡r ❉❇❘ ❋✐❣✉r❡ ✼✳✽✿ ✭❛✮✱ ✭❜✮ ❛♥❞ ✭❝✮ ❛r❡ ♦♣t✐❝❛❧ ✐♠❛❣❡s ♦❢ ❝♦♥❝❛✈❡ ❉✐str✐❜✉t❡❞ ❇r❛❣❣ ♠✐rr♦rs ❞❡s✐❣♥❡❞ t♦ ❢♦❝✉s❡❞ ❛♥❞ r❡✌❡❝t ❜❧✉❡✱ ❣r❡❡♥ ❛♥❞ r❡❞ r❡s♣❡❝t✐✈❡❧②✳ ❚❤❡s❡ ❝♦♥❝❛✈❡ ❇r❛❣❣ ♠✐rr♦rs ❛r❡ ✐❧❧✉♠✐♥❛t❡❞ ✇✐t❤ ✇❤✐t❡ ❧✐❣❤t ❛♥❞ t❤❡② ❝♦rr❡❝t❧② s❡❧❡❝t ❛♥❞ ❢♦❝✉s❡❞ t❤❡✐r r❡s♣❡❝t✐✈❡ ❝♦❧♦rs✳ ❆ ❧✐♥❡ s❝❛♥ ✇❛s t❛❦❡♥ ❛❝r♦ss t❤❡ r❡❞ ❝♦♥❝❛✈❡ ❇r❛❣❣ ♠✐rr♦r ❛s s❤♦✇♥ ✐♥ ✭❝✮ ❛♥❞ ✐s ♣❧♦tt❡❞ ✐♥ ✭❞✮✳ ❚❤❡ ♣❧♦t ❝♦rr❡❝t❧② s❤♦✇ t❤❛t r❡❞ ✐s t❤❡ ❞♦♠✐♥❛♥t ❝♦❧♦r ❢♦❝✉s❡❞ t♦ ❛ ♣♦✐♥t✳ ✶✵✹ ❙✐❧✐❝♦♥ ✇❛s ❞❡♠♦♥str❛t❡❞ t♦ ❜❡ ❛ ❣♦♦❞ ♠❛t❡r✐❛❧ ❢♦r t❤❡ ❢❛❜r✐❝❛t✐♦♥ ♦❢ ♠✉❧t✐❧❛②❡r❡❞ str✉❝t✉r❡s ✭❈❤❛♣t❡r ✺✮✳ ❚❤❡ r❡❢r❛❝t✐✈❡ ✐♥❞❡① ♥ ♦❢ ❛ s✐♥❣❧❡ P❙✐ ❧❛②❡r ✐s ❞❡♣❡♥❞❡♥t ♦♥ t❤❡ ♣♦r♦s✐t② ✇❤✐❝❤ ✐s ✐♥ t✉r♥ ❞❡♣❡♥❞❡♥t ♦♥ t❤❡ ❝✉rr❡♥t ❞❡♥s✐t② ✉s❡❞ ❞✉r✐♥❣ t❤❡ ❛♥♦❞✐③❛t✐♦♥ ♣r♦❝❡ss✳ ❚❤❡ ❢♦r♠❛t✐♦♥ ♦❢ P❙✐ ✐s s❡❧❢✲❧✐♠✐t✐♥❣✱ ❤❡♥❝❡✱ t♦ ❝r❡❛t❡ ❛ P❙✐ ❜❛s❡❞ ❇r❛❣❣ r❡✌❡❝t♦r✱ ♦♥❡ ❥✉st ❛❧t❡r♥❛t❡s t❤❡ ❝✉rr❡♥t ❞❡♥s✐t✐❡s ❞✉r✐♥❣ ❛♥♦❞✐③❛t✐♦♥ t♦ ❝r❡❛t❡ ❧❛②❡rs ✇✐t❤ ❛❧t❡r♥❛t✲ ✐♥❣ ❤✐❣❤✴❧♦✇ r❡❢r❛❝t✐✈❡ ✐♥❞✐❝❡s ❛s ✐♥ ❋✐❣ ✼✳✺✭❛✮✳ ❚❤❡ ✉s❡ ♦❢ ✐♦♥ ✐rr❛❞✐❛t✐♦♥ t♦ s❧♦✇ ❞♦✇♥ P❙✐ ❢♦r♠❛t✐♦♥ ✇❛s s✉❝❝❡ss❢✉❧❧② ✉s❡❞ t♦ t✉♥❡ t❤❡ r❡✌❡❝t✐✈✐t② ♦❢ s✉❝❤ ❇r❛❣❣ r❡✌❡❝t♦rs ✭❈❤❛♣t❡r ✺✳✸✮ ❛s ✇❡❧❧ ❛s t♦ ❢❛❜r✐❝❛t❡ t❤r❡❡ ❞✐♠❡♥s✐♦♥❛❧ ❇r❛❣❣ r❡✌❡❝t♦rs ✭❈❤❛♣t❡r ✺✳✹✮✳ ❍❡r❡ ✇❡ ❞❡✲ s❝r✐❜❡ t❤❡ ❢❛❜r✐❝❛t✐♦♥ ♦❢ P❙✐ ♠✉❧t✐❧❛②❡r ❇r❛❣❣ r❡✌❡❝t♦rs ❢r♦♠ t❤❡ ❝♦♥❝❛✈❡ s✐❧✐❝♦♥ s✉r❢❛❝❡s✱ ❣✐✈✐♥❣ t❤❡ ❛❜✐❧✐t② t♦ s❡❧❡❝t✐✈❡❧② r❡✌❡❝t ❛♥❞ ❢♦❝✉s ♣❛rt✐❝✉❧❛r ✇❛✈❡❧❡♥❣t❤s✳ ❚❤❡ ❝♦♥❝❛✈❡ s✐❧✐❝♦♥ ♠✐rr♦rs ✇❡r❡ ✉s❡❞ t♦ ❢♦r♠ ❝♦♥❝❛✈❡ ♠✉❧t✐❧❛②❡r P❙✐ ❇r❛❣❣ r❡✌❡❝t♦rs✳ ❚❤r❡❡ s❛♠♣❧❡s ✇❡r❡ ❛♥♦❞✐③❡❞ t♦ s❡❧❡❝t ❛♥❞ ❢♦❝✉s r❡❞✱ ❣r❡❡♥ ❛♥❞ ❜❧✉❡ ❛t ✻✸✵♥♠✱ ✺✸✵♥♠ ❛♥❞ ✹✺✵♥♠ r❡s♣❡❝t✐✈❡❧② ❢r♦♠ ❛ ✇❤✐t❡ ✐♥❝✐❞❡♥t ❧✐❣❤t✳ ❚❤❡② ✇❡r❡ ❢❛❜r✐❝❛t❡❞ t♦ ❤❛✈❡ ✷✵ s❡ts ♦❢ ❜✐❧❛②❡rs ✇✐t❤ ❛❧t❡r♥❛t✐♥❣ ❝✉rr❡♥t ❞❡♥s✐t✐❡s ♦❢ ✶✵♠❆✴❝♠✷ ❛♥❞ ✼✵♠❆✴❝♠✷ ✳ ❚❤❡ ❛♥♦❞✐③❡❞ t❤✐❝❦♥❡ss ♦❢ ❡❛❝❤ ❧❛②❡r ✇❛s ✈❛r✐❡❞ t♦ ❤❛✈❡ ❞✐☛❡r❡♥t ♦♣t✐❝❛❧ t❤✐❝❦♥❡ss ♥❞ ❝♦rr❡s♣♦♥❞✐♥❣ t♦ ♦♥❡ q✉❛rt❡r ♦❢ t❤❡✐r r❡s♣❡❝t✐✈❡ ✇❛✈❡❧❡♥❣t❤✳ ❋✐❣ ✼✳✽✭❛✮✱ ✭❜✮ ❛♥❞ ✭❝✮ s❤♦✇s t❤❡ ♦♣t✐❝❛❧ ✐♠❛❣❡s ♦❢ s✉❝❝❡ss❢✉❧❧② ❢❛❜r✐❝❛t❡❞ ❝♦♥❝❛✈❡ ❉ ❂ ✶✵✵✖♠ P❙✐ ❇r❛❣❣ r❡✌❡❝t♦rs ❞❡s✐❣♥❡❞ t♦ r❡✌❡❝t ❜❧✉❡✱ ❣r❡❡♥ ❛♥❞ r❡❞✳ ❚❤❡s❡ ❝♦♥❝❛✈❡ ❇r❛❣❣ r❡✌❡❝t♦rs ✇❡r❡ ✐❧❧✉♠✐♥❛t❡❞ ✇✐t❤ ❛ ✇❤✐t❡ ❧✐❣❤t s♦✉r❝❡ ❛♥❞ t❤❡ ❝♦♥❝❛✈❡ ❇r❛❣❣ r❡✌❡❝t♦rs t❤❡♥ s❡❧❡❝t t❤❡ r❡s♣❡❝t✐✈❡ ✇❛✈❡❧❡♥❣t❤s ❛♥❞ ❢♦❝✉s t❤❡♠ ✐♥t♦ ❛ s✐♥❣❧❡ s♣♦t✳ ❲✐t❤ t❤❡ ❛✐❞ ♦❢ ❛ ♠✐❝r♦s❝♦♣❡✱ ❛ ❧✐♥❡ s❝❛♥ ♠❡❛s✉r✐♥❣ t❤❡ ✐♥t❡♥s✐t② ♦❢ t❤❡ r❡❞✱ ❣r❡❡♥ ❛♥❞ ❜❧✉❡ s♣❡❝tr❛❧ ❝♦♠♣♦♥❡♥ts ✇❛s ♠❡❛s✉r❡❞ ❛❝r♦ss t❤❡ ❢♦❝✉s❡❞ ♣♦✐♥t ✭❋✐❣ ✼✳✽✭❝✮ ❛♥❞ ♣❧♦tt❡❞ ✐♥ ❋✐❣ ✼✳✽✭❞✮✳ ❚❤❡ ❧✐♥❡ s❝❛♥ s❤♦✇s t❤❡ ❞♦♠✐♥❛♥t r❡❞ ❝♦❧♦r t❤❛t t❤✐s ♠✐rr♦r ✇❛s ❞❡s✐❣♥❡❞ t♦ r❡✌❡❝t ❛♥❞ ❢♦❝✉s✳ ■t ❛❧s♦ s❤♦✇s t❤❛t t❤❡ ♠✐rr♦r ❢♦❝✉s❡s t❤❡ ✐♥❝♦♠✐♥❣ ❧✐❣❤t ❞♦✇♥ t♦ ❛ ❜❡❛♠ s♣♦t ♦❢ ❛♣♣r♦①✐♠❛t❡❧② ✶✖♠ ✭❋❲❍▼ ❢r♦♠ ❋✐❣ ✼✳✽✭❞✮✮✳ ❚❤✐s ❧✐♥❡ s❝❛♥ ♣❧♦t ✈❡r② ❛♣♣r♦♣r✐❛t❡❧② s❤♦✇s ❜♦t❤ t❤❡ ❢♦❝✉s✐♥❣ ❛♥❞ ✇❛✈❡❧❡♥❣t❤ s❡❧❡❝t✐✈❡ ♣r♦♣❡rt✐❡s ♦❢ t❤❡s❡ ❝✉r✈❡❞ P❙✐ ❇r❛❣❣ r❡✌❡❝t♦rs ❝♦♥❝✉rr❡♥t❧②✳ ❚❤✐s ✇♦r❦ ❛❧s♦ ❞❡♠♦♥str❛t❡s t❤❡ ❛❜✐❧✐t② t♦ ❢♦r♠ ❝✉r✈❡❞ P❙✐ ❞✐str✐❜✉t❡❞ ❇r❛❣❣ r❡✌❡❝t♦rs✱ ✐♥ ✇❤✐❝❤ ❡❛❝❤ ❧❛②❡r r❡♠❛✐♥s ♣❛r❛❧❧❡❧ t♦ t❤♦s❡ ❛❜♦✈❡ ❛♥❞ ❜❡❧♦✇ ✐t✳ ❲❤✐❧❡ ✶✵✺ t❤❡s❡ ❇r❛❣❣ ❘❡✌❡❝t♦rs ❤❛✈❡ ❜❡❡♥ ❞❡♠♦♥str❛t❡❞ ❢♦r ✈✐s✐❜❧❡ ✇❛✈❡❧❡♥❣t❤s✱ ✐t ❝❛♥ ❡❛s✐❧② ❜❡ ❡①t❡♥❞❡❞ t♦ t❤❡ ✐♥❢r❛✲r❡❞ s✐♠♣❧② ❜② ✐♥❝r❡❛s✐♥❣ t❤❡ t❤✐❝❦♥❡ss ♦❢ ❡❛❝❤ ❧❛②❡r ✐♥ t❤❡ ♠✉❧t✐❧❛②❡r✳ ✼✳✹ ❙✉♠♠❛r② ❲❡ ❤❛✈❡ ❢❛❜r✐❝❛t❡❞ s✐❧✐❝♦♥ ❝♦♥❝❛✈❡ s♣❤❡r✐❝❛❧ ♠✐rr♦rs ❛♥❞ ❝♦♥❝❛✈❡ ❝②❧✐♥❞❡rs ✇✐t❤ ❧♦✇ r♦✉❣❤✲ ♥❡ss ❛♥❞ ❞❡♠♦♥str❛t❡❞ t❤❡ ❛❜✐❧✐t② t♦ ❞♦ s♦ r❡♣❡❛t❡❞❧② ❛♥❞ ❝♦♥tr♦❧❧❛❜❧②✳ ❚❤❡ ❧♦❝❛t✐♦♥✱ ❞✐❛♠❡t❡rs ❛♥❞ t❤❡ ❤❡✐❣❤t ♦❢ t❤❡ ❝♦♥❝❛✈❡ ♠✐rr♦rs ❛♥❞ ❝♦♥❝❛✈❡ ❝②❧✐♥❞❡rs ♠❛② ❜❡ ❝♦♥tr♦❧❧❡❞ ❛♥❞ ❛r❡ ❧✐♠✐t❡❞ ♣r✐♠❛r✐❧② ❜② t❤❡ ♣❛tt❡r♥✐♥❣ ♦❢ t❤❡ P❘ ♣❛tt❡r♥s ❞✉r✐♥❣ t❤❡ ❯❱ ❧✐t❤♦❣r❛♣❤② st❡♣✳ ❚❤❡s❡ ❝♦♥❝❛✈❡ str✉❝t✉r❡s ❤❛✈❡ ❛ ✈❛r✐❡t② ♦❢ ❛♣♣❧✐❝❛t✐♦♥s r❛♥❣✐♥❣ ❢r♦♠ ▼❊▼❙ ❛♥❞ ♦♣t♦❡❧❡❝tr♦♥✐❝s t♦ ❧❛❜✲♦♥✲❛✲❝❤✐♣ ❞❡✈✐❝❡s✳ ❚❤❡② ♠❛② ❛❧s♦ ❜❡ ✉s❡❞ ❛s t❡♠♣❧❛t❡s ♦r ♠♦❧❞s t♦ ♣r♦❞✉❝❡ ♠✐❝r♦❧❡♥s❡s ♦♥ ♣♦❧②♠❡rs✳ ❇② ✉s✐♥❣ t❤❡s❡ ❝♦♥❝❛✈❡ ♠✐rr♦rs ✐♥ ❝♦♥❥✉♥❝t✐♦♥ ✇✐t❤ ♣❧❛♥❡ ♠✐rr♦rs✱ s♠❛❧❧ ♦♣t✐❝❛❧ ❝❛✈✐t✐❡s ❝❛♥ ❜❡ ❜✉✐❧t ❢♦r s✐♥❣❧❡ ❛t♦♠ ❞❡t❡❝t✐♦♥ ♦r q✉❛♥t✉♠ ✐♥❢♦r♠❛t✐♦♥ ❝♦♥tr♦❧ t❤r♦✉❣❤ ❝❛✈✐t② ◗❊❉ ❡☛❡❝ts✳ ■♥ ❛❞❞✐t✐♦♥✱ ✉s✐♥❣ t❤❡s❡ ❝♦♥❝❛✈❡ ♠✐rr♦rs ❛s ❛ st❛rt✐♥❣ ♠❛t❡r✐❛❧✱ ✇❡ ❤❛✈❡ ❛❧s♦ ❢❛❜r✐❝❛t❡❞ ❝♦♥❝❛✈❡ P❙✐ ❜❛s❡❞ ❇r❛❣❣ r❡✌❡❝t♦rs ✇❤✐❝❤ ❛r❡ ❛❜❧❡ t♦ ❤❛✈❡ ✇❛✈❡❧❡♥❣t❤ s❡❧❡❝t✐✈❡ ❢♦❝✉s✳ ❚❤✐s ✇✐❧❧ ❜❡ ✉s❡❢✉❧ ❢♦r t❡❧❡❝♦♠♠✉♥✐❝❛t✐♦♥s ♦r t♦ ❜❡ ✉s❡❞ ❛s ♦♣t✐❝❛❧ ✐♥t❡r❝♦♥♥❡❝t✳ [...]... over an area of 1.5 ¢ 1.5 cm Helium ions were used owing to their greater defects generation rate of compared with protons, hence a shorter irradiation time is needed 600 keV helium ions have a range of 4. 0/2.3 m in photoresist /silicon respectively, so the PR is thick enough to prevent irradiation induced-damage to the underlying silicon The uence was set at 5 ¢ 10 14 ions/cm2 , which is high enough to... Functional optical trapping techniques on silicon surfaces and environment are also very important [89] The fabrication of concave mirrors in silicon is not trivial, nevertheless, it was reported in Ref [ 84] Concave pro les were created by isotropic wet etching of silicon through circular apertures in a lithographic mask using a mixture of HF and HNO3 under continuous agitation Fabrication of concave silicon. .. reduce the subsequent rate of PSi formation 88 in silicon In this way, no defects are introduced to the un-exposed/un-irradiated areas and during the subsequent anodization step and PSi formation rate will not be reduced in these areas compared to the irradiated regions For a typical beam current of 100 nA the irradiation time for each sample was about 30 minutes After irradiation, the PR layer was removed... consisting of 300 ¢ 300 pixels (b),(c) respectively show an optical and SEM image of part of the transferred CGH pattern in silicon (d) Reconstructed image of a phase CGH Inset shows the original encoded image in modulation of the amplitude of incoming light The irradiated regions (black pixels) are less re ective while the unirradiated regions (white pixels) are more re ective owing to a variety of factors... further show that silicon can be continuously machined in both pixel height and re ectivity, allowing the generation of better quality reconstructed holograms [79] in conjunction with suitable CGH patterns Five 10 m wide lines were irradiated in a silicon wafer by PBW with 2 MeV proton 92 Figure 6.13: (a) Optical image of surface relief silicon with ve lines 10m in width irradiated with 15 2 15 2 10... coupling two such mirrors together or with an optical ber [ 84] These kind of concave cavities are of interest in quantum information science, particularly in the fabrication of atom chips [49 , 84] or for small particles detections [85] Single photons may be produced on demand using atoms in such a concave cavity to have entanglement e ects with a shared cavity photon [86, 87] Evidently then, there exist... pattern consisting of 10 24 10 24 pixels (b) Optical image of the 2 silicon surface relief pattern The total area of the CGH on the Si is 1 1 mm while the smallest features 2 are about 4 4 m (c),(d) are enlarged images of the CGH pattern the corresponding optical image on silicon ¢ Figure 6.10: ¢ Reconstructed image from the binary phase CGH in Fig 6.9 The inset shows the encoded image of the letters "NTU"... motivated by potential applications in quantum information sciences, particularly for the studies of cavity QED studies and the fabrication of atom traps For fabrication of such devices, a low roughness is very important so as to minimize loss Despite a relatively large surface roughness of 6nm of the as-fabricated concave mirror, they managed to achieve a nal roughness of 2nm after high quality coatings... mirrors on di erent materials These include di usion of ion dopants on glass [83], melting photoresist disks 94 95 to obtain a spherical shape followed by dry etching on GaAs [88] and trapping of air bubbles in borosilicate glass [49 ] Fabricating concave mirrors on silicon are especially important to allow for easy integration of photonics into the well-developed silicon microelectronics infrastructure, as... 6. 14: (a) SEM image of the surface relief of a silicon wafer which was irradiated in a cross hatched manner, producing steps of many di erent heights This is the same fabricated structure shown in Fig 4. 5 (b) Plot of the relationship between the anodization rate and uence for 0.02 cm silicon wafers This is the same plot shown in Fig 3.6 The sample was then etched at 12 mA/cm2 for 4 minutes and the PSi . Chapter 6