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❯s❡r✲❞❡✜♥❡❞ t②♣❡s

◮ ❲❡ ❧❡❛r♥❡❞ ❤♦✇ t♦ ✉s❡

◮ ✈❡❝t♦r❁❞♦✉❜❧❡❃✱ ◮ str✐♥❣✱ ◮ ❢str❡❛♠✱ ◮ str✐♥❣str❡❛♠✳

❯s✐♥❣ t❤❡s❡ ♥❡✇ t②♣❡s ❤❛s ♠❛❞❡ ❛s ♠✉❝❤ ♠♦r❡ ♣r♦❞✉❝t✐✈❡ ❈✰✰ ♣r♦❣r❛♠♠❡rs✳

◮ ❲r✐t✐♥❣ ♦✉r ♦✇♥ t②♣❡s ✐s t❤❡ ♥❡①t st❡♣✳ ◮ ❚❤❡ ♠❛✐♥ ❥♦❜ ♦❢ ❛ ♣r♦❣r❛♠♠❡r ✐♥ ❛♥ ♦❜❥❡❝t✲♦r✐❡♥t❡❞ ❧❛♥❣✉❛❣❡

✐s ✇r✐t✐♥❣ t❤❡✐r ♦✇♥ t②♣❡s✳

❈❧❛ss✱ ♦❜❥❡❝t✱ ✐♥st❛♥❝❡

❲❡ ❛❧r❡❛❞② ❦♥♦✇ t❤❡ ❢♦❧❧♦✇✐♥❣✿

◮ ❊✈❡r② ✈❛r✐❛❜❧❡ ✐♥ ❈✰✰ ❤❛s ❛ t②♣❡✳ ◮ ❨♦✉ ❝❛♥ ❤❛✈❡ ❧♦ts ♦❢ ✈❛r✐❛❜❧❡s ♦❢ ❛ ❣✐✈❡♥ t②♣❡✳

■♥ t❤❡ ❧❛♥❣✉❛❣❡ ♦❢ ♦❜❥❡❝t✲♦r✐❡♥t❡❞ ♣r♦❣r❛♠♠✐♥❣ ✇❡ s❛②✿

◮ ❊✈❡r② ♦❜❥❡❝t ✐♥ ❈✰✰ ❤❛s ❛ ❝❧❛ss✳ ◮ ❨♦✉ ❝❛♥ ❤❛✈❡ ❧♦ts ♦❢ ✐♥st❛♥❝❡s ♦❢ t❤❡ s❛♠❡ ❝❧❛ss✳

❊①❛♠♣❧❡

str✐♥❣✥s✭✧❚♦✥❜❡✱✥♦r✥♥♦t✥t♦✥❜❡❄✧✮❀ ■♥ t❤❡ ❝♦❞❡ ❛❜♦✈❡ s ✐s ❛♥ ♦❜❥❡❝t ♦❢ t②♣❡ str✐♥❣✳ ■t ✐s ❛♥ ✐♥st❛♥❝❡ ♦❢ t❤❡ ❝❧❛ss str✐♥❣✳

❲❤❛t ✐s ❛♥ ♦❜❥❡❝t❄

◮ ❆♥ ♦❜❥❡❝t ✐s ❛ ❜✉♥❞❧❡ ♦❢ ❞❛t❛ ❛♥❞ ❢✉♥❝t✐♦♥s t♦ ❤❡❧♣ ✇✐t❤

✇♦r❦✐♥❣ ✇✐t❤ t❤❛t ❞❛t❛✳

◮ ❚❤❡ t②♣❡ ♦❢ ❞❛t❛ ❛♥❞ ❢✉♥❝t✐♦♥s s✉♣♣♦rt❡❞ ❜② ❛♥ ♦❜❥❡❝t ❞❡♣❡♥❞

♦♥❧② ♦♥ ✐ts ❝❧❛ss✳ ❆❧❧ ✐♥st❛♥❝❡s ♦❢ t❤❡ s❛♠❡ ❝❧❛ss ❤❛✈❡ t❤❡ s❛♠❡ ❢✉♥❝t✐♦♥s ❛♥❞ t❤❡ s❛♠❡ t②♣❡s ♦❢ ❞❛t❛✳

❊①❛♠♣❧❡

❆♥ ✐♥st❛♥❝❡ ♦❢ t❤❡ ❝❧❛ss str✐♥❣ ❝♦♥s✐sts ♦❢✿

◮ ❉❛t❛ ❝♦♥s✐st✐♥❣ ♦❢ ❛ s❡q✉❡♥❝❡ ♦❢ ❝❤❛r❛❝t❡rs✳ ◮ ❋✉♥❝t✐♦♥s s✉❝❤ ❛s s✐③❡✱ ✐♥s❡rt✱ ❡r❛s❡ ❢♦r ✇♦r❦✐♥❣ ✇✐t❤ t❤✐s

❞❛t❛✳

◮ ❚❤❡ ❝❧❛ss str✐♥❣ ✐s ✇❤❡r❡ ❛❧❧ t❤❡s❡ ❢✉♥❝t✐♦♥s ❛♥❞ ❞❛t❛ t②♣❡s

❛r❡ ❞❡✜♥❡❞✳

❆♥ ❡①❛♠♣❧❡ ❝❧❛ss

▲❡t ✉s r❡♣r❡s❡♥t ❛ ♣♦✐♥t ✐♥ t✇♦ ❞✐♠❡♥s✐♦♥s ✉s✐♥❣ ❛ ❝❧❛ss✳

❝❧❛ss✥❈❛rt❡s✐❛♥P♦✐♥t✥④ ♣✉❜❧✐❝✿ ✥✥✥✥❞♦✉❜❧❡✥①❀ ✥✥✥✥❞♦✉❜❧❡✥②❀ ⑥❀

◮ ❚❤✐s ✐s ❝❛❧❧❡❞ ❛ ❝❧❛ss ❞❡❝❧❛r❛t✐♦♥✳ ◮ ❲❡ ✇❛♥t t❤✐s ❝❧❛ss t♦ ❜❡ ❛✈❛✐❧❛❜❧❡ t♦ ✉s❡rs ♦❢ ♦✉r ❧✐❜r❛r② s♦ ✐t

✐s ❞❡❝❧❛r❡❞ ✐♥ t❤❡ ✳❤ ✜❧❡✳

◮ ❚❤❡ ♥❛♠❡ ♦❢ ♦✉r ❝❧❛ss ✐s ❈❛rt❡s✐❛♥P♦✐♥t ◮ ❆ ❈❛rt❡s✐❛♥ ♣♦✐♥t ❝♦♥t❛✐♥s t✇♦ ❞♦✉❜❧❡ ✈❛❧✉❡s ❝❛❧❧❡❞ ① ❛♥❞ ②✳ ◮ ❯s❡rs ♦❢ t❤❡ ❧✐❜r❛r② ❛r❡ ❛❧❧♦✇❡❞ t♦ ✉s❡ t❤❡ ✈❛❧✉❡s ♦❢ ① ❛♥❞ ② ✐♥

t❤❡✐r ♦✇♥ ❝♦❞❡✱ s♦ t❤❡s❡ ❛r❡ ♠❛r❦❡❞ ❛s ♣✉❜❧✐❝✳

❯s✐♥❣ t❤❡ ❝❧❛ss

✥✥✥✥❈❛rt❡s✐❛♥P♦✐♥t✥♣❀ ✥✥✥✥♣✳①✥❂✥✶✵✵❀ ✥✥✥✥♣✳②✥❂✥✶✺✵❀ ✥✥✥✥❝♦✉t✥❁❁✥✧❈♦♦r❞✐♥❛t❡s✥✭✧❀ ✥✥✥✥❝♦✉t✥❁❁✥♣✳①✥❀ ✥✥✥✥❝♦✉t✥❁❁✥✧✱✥✧❀ ✥✥✥✥❝♦✉t✥❁❁✥♣✳②✥❀ ✥✥✥✥❝♦✉t✥❁❁✥✧✮❭♥✧❀ ✥✥✥✥♣✳①✥✯❂✥✷❀ ✥✥✥✥♣✳②✥✯❂✥✷❀ ✥✥✥✥❝♦✉t✥❁❁✥✧❘❡s❝❛❧❡❞✥❝♦r❞✐♥❛t❡s✥✭✧❀ ✥✥✥✥❝♦✉t✥❁❁✥♣✳①✥❀ ✥✥✥✥❝♦✉t✥❁❁✥✧✱✥✧❀ ✥✥✥✥❝♦✉t✥❁❁✥♣✳②✥❀ ✥✥✥✥❝♦✉t✥❁❁✥✧✮❭♥✧❀

◮ ❚❤❡ ♥❛♠❡ ♦❢ t❤❡ ❝❧❛ss ✐s t❤❡ ♥❛♠❡ ✉s❡❞ ✇❤❡♥ ②♦✉ ✇❛♥t t♦

❝r❡❛t❡ ♦❜❥❡❝ts ♦❢ t❤❡ ❝❧❛ss✳

◮ ❨♦✉ ✉s❡ ❛ ❞♦t ✳ t♦ ❛❝❝❡ss t❤❡ ❞❛t❛ ✐♥s✐❞❡ ②♦✉r ❝❧❛ss✳ ◮ ❨♦✉ ❝❛♥ ♦♥❧② ❛❝❝❡ss t❤❡ ✈❛r✐❛❜❧❡s ❜❡❝❛✉s❡ t❤❡② ❛r❡ ♣✉❜❧✐❝✿✳

❉❡❧❡t❡ t❤❡ ✇♦r❞ ♣✉❜❧✐❝✿ ❛♥❞ s❡❡ ✇❤❛t ❤❛♣♣❡♥s✳

❚❤❡ s②♥t❛① ❢♦r ❞❡❝❧❛r✐♥❣ ❝❧❛ss❡s

❝❧❛ss ❈▲❆❙❙❴◆❆▼❊ ④ ♣✉❜❧✐❝✿ ❉❆❚❆ ❆◆❉ ❋❯◆❈❚■❖◆ ❉❊❈▲❆❘❆❚■❖◆❙ ♣r✐✈❛t❡✿ ❉❆❚❆ ❆◆❉ ❋❯◆❈❚■❖◆ ❉❊❈▲❆❘❆❚■❖◆❙ ⑥❀

◮ ❨♦✉ ❝❛♥ ❞❡✜♥❡ ❝❧❛ss❡s ✐♥ ❤❡❛❞❡r ✜❧❡s ♦r ❝♣♣ ✜❧❡s✳ ❯s❡ ❤❡❛❞❡r

✜❧❡s ✐❢ ②♦✉ ✇❛♥t ✉s❡rs ♦❢ t❤❡ ❧✐❜r❛r② t♦ ✉s❡ ②♦✉r ❝❧❛ss✳

◮ ❨♦✉ ♠✉st r❡♠❡♠❜❡r t❤❡ s❡♠✐✲❝♦❧♦♥ ❛t t❤❡ ❡♥❞✳ ❨♦✉✬❧❧ ♦❢t❡♥

❣❡t ✈❡r② ❝♦♥❢✉s✐♥❣ ❡rr♦rs ✐❢ ②♦✉ ♦♠✐t ✐t✳

◮ ▲✐❦❡ ✈❛r✐❛❜❧❡ ♥❛♠❡s✱ ❝❧❛ss ♥❛♠❡s s❤♦✉❧❞ ❝♦♥t❛✐♥ ♥♦ s♣❛❝❡s ♦r

str❛♥❣❡ ❝❤❛r❛❝t❡rs ❛♥❞ s❤♦✉❧❞ st❛rt ✇✐t❤ ❛ ❧❡tt❡r✳ ■ r❡❝♦♠♠❡♥❞ ✉s✐♥❣ ❝❛♠❡❧ ❝❛s❡ st❛rt✐♥❣ ✇✐t❤ ❛ ❝❛♣✐t❛❧ ❧❡tt❡r✳

◮ ❲❡✬❧❧ ❞✐s❝✉ss ♣✉❜❧✐❝ ❛♥❞ ♣r✐✈❛t❡ ❧❛t❡r✳

❆♥♦t❤❡r ❡①❛♠♣❧❡ ❝❧❛ss

❝❧❛ss✥P♦❧❛rP♦✐♥t✥④ ♣✉❜❧✐❝✿ ✥✥✥✥❞♦✉❜❧❡✥r❀ ✥✥✥✥❞♦✉❜❧❡✥t❤❡t❛❀ ⑥❀

❲r✐t✐♥❣ ❛ ❢✉♥❝t✐♦♥ t❤❛t ✉s❡s ♦✉r ❝❧❛ss❡s✿

❈❛rt❡s✐❛♥P♦✐♥t✥♣♦❧❛r❚♦❈❛rt❡s✐❛♥✭✥❝♦♥st✥P♦❧❛rP♦✐♥t✫✥♣✥✮✥④ ✥✥✥✥❈❛rt❡s✐❛♥P♦✐♥t✥❝❀ ✥✥✥✥❝✳①✥❂✥♣✳r✯❝♦s✭✥♣✳t❤❡t❛✥✮❀ ✥✥✥✥❝✳②✥❂✥♣✳r✯s✐♥✭✥♣✳t❤❡t❛✥✮❀ ✥✥✥✥r❡t✉r♥✥❝❀ ⑥

◮ ❈❛rt❡s✐❛♥P♦✐♥ts ❛r❡ ❝♦♥s✐❞❡r❡❞ ❜✐❣ ♦❜❥❡❝ts✱ s♦ ✇❡ ♣❛ss t❤❡♠ ❜②

r❡❢❡r❡♥❝❡ ❢♦r ❡✣❝✐❡♥❝②✳

◮ ❲❡ ✉s❡ t❤❡ ❝♦♥st ❦❡②✇♦r❞ t♦ ❡♥s✉r❡ t❤❛t t❤❡ ❢✉♥❝t✐♦♥ ✐s♥✬t

❛❧❧♦✇❡❞ t♦ ❝❤❛♥❣❡ t❤❡ r ❛♥❞ t❤❡t❛ ❝♦♦r❞✐♥❛t❡s✳

❆ t❡st ❢♦r ❜♦t❤ ❢✉♥❝t✐♦♥s

st❛t✐❝✥✈♦✐❞✥t❡stP♦❧❛r❚♦❈❛rt❡s✐❛♥✭✮✥④ ✥✥✥✥P♦❧❛rP♦✐♥t✥♣❀ ✥✥✥✥♣✳r✥❂✥✷✳✵❀ ✥✥✥✥♣✳t❤❡t❛✥❂✥P■✴✷❀ ✥✥✥✥❈❛rt❡s✐❛♥P♦✐♥t✥❝✥❂✥♣♦❧❛r❚♦❈❛rt❡s✐❛♥✭✥♣✥✮❀ ✥✥✥✥❆❙❙❊❘❚❴❆PP❘❖❳❴❊◗❯❆▲✭✥❝✳①✱✵✳✵✱✵✳✵✵✶✥✮❀ ✥✥✥✥❆❙❙❊❘❚❴❆PP❘❖❳❴❊◗❯❆▲✭✥❝✳②✱✷✳✵✱✵✳✵✵✶✥✮❀ ⑥

◮ ■❢ ②♦✉ ❝♦♠♣❛r❡ t❤✐s ❛❣❛✐♥st ♦✉r ♣r❡✈✐♦✉s t❡st ❝♦❞❡✱ ②♦✉ ✇✐❧❧ s❡❡

t❤❛t ✐t ✐s ♠❛r❣✐♥❛❧❧② s✐♠♣❧❡r✳

◮ ❆❣❛✐♥st t❤✐s t❤❡ ❝♦❞❡ ❢♦r t❤❡ ❢✉♥❝t✐♦♥s ✐s ♠❛r❣✐♥❛❧❧② ❧♦♥❣❡r✳ ◮ ❲❤❡♥ ❞❡s✐❣♥✐♥❣ ❧✐❜r❛r✐❡s✱ ❝❤♦♦s❡ ✇❤❛t ✐s ❜❡st ❢♦r t❤❡ ✉s❡r ♦❢

t❤❡ ❧✐❜r❛r②✱ ♥♦t t❤❡ ❛✉t❤♦r ♦❢ t❤❡ ❧✐❜r❛r②✳

◮ ■♥ t❤✐s ❝❛s❡✱ t❤❡ ✈❡rs✐♦♥ ✇✐t❤ ❝❧❛ss❡s ✐s ❜❡tt❡r✳

❲❤❛t ❤❛✈❡ ❝❧❛ss❡s ❣✐✈❡♥ ✉s ❤❡r❡❄

◮ ❲❡ ❤❛✈❡ ❡st❛❜❧✐s❤❡❞ ❛ ❝❧❡❛r ❝♦♥✈❡♥t✐♦♥ t❤❛t x✲❝♦♦r❞✐♥❛t❡s ❛r❡

❝❛❧❧❡❞ ① ❛♥❞ y✲❝♦♦r❞✐♥❛t❡s ❛r❡ ❝❛❧❧❡❞ ②✳ ❚❤✐s ✇✐❧❧ ♠❛❦❡ ❝♦❞❡ ✇r✐tt❡♥ ✉s✐♥❣ ❈❛rt❡s✐❛♥P♦✐♥t ❝❧❡❛r❡r t❤❛♥ ❝♦❞❡ t❤❛t ✉s❡s ① s♦♠❡ ♦❢ t❤❡ t✐♠❡✱ ❳ s♦♠❡ ♦❢ t❤❡ t✐♠❡✱ ❛♥❞ ①❝♦♦r❞ t❤❡ r❡st ♦❢ t❤❡ t✐♠❡✳

◮ ❲❡✬✈❡ ❡st❛❜❧✐s❤❡❞ s✐♠✐❧❛r ❝♦♥✈❡♥t✐♦♥s ❢♦r ♣♦❧❛r ❝♦♦r❞✐♥❛t❡s✳ ◮ ❲❡ ❛r❡ ❛❜❧❡ t♦ r❡t✉r♥ ♠✉❧t✐♣❧❡ ✈❛❧✉❡s ✇✐t❤♦✉t ✉s✐♥❣ ♣❛ss ❜②

r❡❢❡r❡♥❝❡✳

◮ ❲❡ ❤❛✈❡ ♠❛❞❡ ✐t ❡❛s✐❡r ❢♦r ✉s❡rs ♦❢ ♦✉r ❧✐❜r❛r② t♦ ✇♦r❦ ✇✐t❤

❈❛rt❡s✐❛♥ ❛♥❞ ♣♦❧❛r ❝♦♦r❞✐♥❛t❡s✳ ▼❛❦✐♥❣ ❧✐❢❡ ❡❛s✐❡r ❢♦r ♦✉r ✉s❡rs ✐s ♦✉r ♠❛✐♥ ❛✐♠ ✇❤❡♥ ✇r✐t✐♥❣ ❛ ❧✐❜r❛r②✳

❆❞❞✐♥❣ ❢✉♥❝t✐♦♥s t♦ ❝❧❛ss❡s

❝❧❛ss✥❈✐r❝❧❡✥④ ♣✉❜❧✐❝✿ ✥✥✥✥❞♦✉❜❧❡✥r❛❞✐✉s❀ ✥✥✥✥❞♦✉❜❧❡✥❛r❡❛✭✮❀ ✥✥✥✥❞♦✉❜❧❡✥❝✐r❝✉♠❢❡r❡♥❝❡✭✮❀ ⑥❀

◮ ❚❤❡ ❝✐r❝❧❡ ❝❧❛ss ❝♦♠❡s ✇✐t❤ t✇♦ ❢✉♥❝t✐♦♥s ②♦✉ ❝❛♥ ❝❛❧❧✿ ◮ ❛r❡❛✭✮ r❡t✉r♥s t❤❡ ❛r❡❛ ♦❢ t❤❡ ❝✐r❝❧❡✱ ◮ ❝✐r❝✉♠❢❡r❡♥❝❡✭✮ r❡t✉r♥s t❤❡ ❝✐r❝✉♠❢❡r❡♥❝❡ ♦❢ t❤❡ ❝✐r❝❧❡✳ ◮ ❚❤✐s ❞❡❝❧❛r❡s t❤❡ ❢✉♥❝t✐♦♥s✱ ✇❡✬❧❧ ❤❛✈❡ t♦ ❞❡✜♥❡ t❤❡♠ ✐♥ ❛

❈✰✰ ✜❧❡✳

❯s✐♥❣ t❤❡ ❢✉♥❝t✐♦♥s

❇❡❢♦r❡ ✇❡ ✐♠♣❧❡♠❡♥t t❤❡s❡ ❢✉♥❝t✐♦♥s✱ ❧❡t✬s ❜❡ t❡st✲❞r✐✈❡♥ ❞❡✈❡❧♦♣❡rs ❛♥❞ ✇r✐t❡ t❡sts ❢♦r t❤❡♠✳

st❛t✐❝✥✈♦✐❞✥t❡st❆r❡❛❖❢❈✐r❝❧❡✭✮✥④ ✥✥✥✥❈✐r❝❧❡✥❝❀ ✥✥✥✥❝✳r❛❞✐✉s✥❂✥✹❀ ✥✥✥✥❆❙❙❊❘❚❴❆PP❘❖❳❴❊◗❯❆▲✭✥❝✳❛r❡❛✭✮✱✥✶✻✯P■✱✥✵✳✵✶✥✮❀ ⑥ st❛t✐❝✥✈♦✐❞✥t❡st❈✐r❝✉♠❢❡r❡♥❝❡❖❢❈✐r❝❧❡✭✮✥④ ✥✥✥✥❈✐r❝❧❡✥❝❀ ✥✥✥✥❝✳r❛❞✐✉s✥❂✥✷❀ ✥✥✥✥❆❙❙❊❘❚❴❆PP❘❖❳❴❊◗❯❆▲✭✥❝✳❝✐r❝✉♠❢❡r❡♥❝❡✭✮✱✥✹✯P■✱✥✵✳✵✶✥✮❀ ⑥

◮ ❨♦✉ ✉s❡ ❛ ❞♦t t♦ ❝❛❧❧ ❛ ❢✉♥❝t✐♦♥ ♦♥ ❛ ♣❛rt✐❝✉❧❛r ♦❜❥❡❝t ✐♥st❛♥❝❡✳

❋♦r ❡①❛♠♣❧❡ ❝✳❛r❡❛✭✮ ❝♦♠♣✉t❡s t❤❡ ❛r❡❛ ♦❢ t❤❡ ❝✐r❝❧❡ ❝✳

◮ ❨♦✉ ❞♦♥✬t ♥❡❡❞ t♦ ♣❛ss t❤❡ r❛❞✐✉s t♦ t❤❡ ❢✉♥❝t✐♦♥ ❛r❡❛ t❤❡

❝✐r❝❧❡ ✐♥st❛♥❝❡ ✏❦♥♦✇s✑ ✐ts ♦✇♥ ❛r❡❛✳

❉❡✜♥✐♥❣ t❤❡ ❢✉♥❝t✐♦♥s

❆s ✉s✉❛❧ ❢♦r ❈✰✰ ❢✉♥❝t✐♦♥s✱ ✇❡ ✇r✐t❡ t❤❡ ❞❡✜♥✐t✐♦♥s ✐♥ ❛ ✳❝♣♣ ✜❧❡✳

❞♦✉❜❧❡✥❈✐r❝❧❡✿✿❛r❡❛✭✮✥④ ✥✥✥✥r❡t✉r♥✥P■✯r❛❞✐✉s✯r❛❞✐✉s❀ ⑥ ❞♦✉❜❧❡✥❈✐r❝❧❡✿✿❝✐r❝✉♠❢❡r❡♥❝❡✭✮✥④ ✥✥✥✥r❡t✉r♥✥✷✯P■✯r❛❞✐✉s❀ ⑥

◮ ❲❤❡♥ ②♦✉ ❞❡✜♥❡ ❛ ❢✉♥❝t✐♦♥ ❢♦r ❛ ❝❧❛ss✱ ②♦✉ ♠✉st ❛❧✇❛②s

s♣❡❝✐❢② t❤❡ ♥❛♠❡ ♦❢ t❤❡ ❝❧❛ss ✐♥ t❤❡ ❞❡✜♥✐t✐♦♥✳ ❚❤❡ s②♥t❛① ✐s✿ ❈▲❆❙❙❴◆❆▼❊✿✿❋❯◆❈❚■❖◆❴◆❆▼❊✳ ■❢ ②♦✉ ❢♦r❣❡t t♦ ❞♦ t❤✐s ②♦✉✬❧❧ ❣❡t ❧✐♥❦❡r ❡rr♦rs s❛②✐♥❣ ②♦✉✬✈❡ ❢♦r❣♦tt❡♥ t♦ ❞❡✜♥❡ t❤❡ ❢✉♥❝t✐♦♥✳

◮ ❚❤❡ ❈✐r❝❧❡ ❢✉♥❝t✐♦♥s ❛r❡ ❛❜❧❡ t♦ ❛❝❝❡ss t❤❡ ♠❡♠❜❡r ✈❛r✐❛❜❧❡

r❛❞✐✉s ❛♥❞ t❤❡ ❣❧♦❜❛❧ ✈❛r✐❛❜❧❡ P■✳

▼❡♠❜❡r ✈❛r✐❛❜❧❡s ❛♥❞ ❢✉♥❝t✐♦♥s

◮ ❆ ♠❡♠❜❡r ✈❛r✐❛❜❧❡ ♦❢ ❛ ❝❧❛ss ✐s ❛ ✈❛r✐❛❜❧❡ ❞❡✜♥❡❞ ✐♥ t❤❡ ❝❧❛ss✳ ◮ ❆ ♠❡♠❜❡r ❢✉♥❝t✐♦♥ ♦❢ ❛ ❝❧❛ss ✐s ❛ ❢✉♥❝t✐♦♥ ❞❡✜♥❡❞ ✐♥ t❤❡ ❝❧❛ss✳ ◮ ❨♦✉ ❝❛♥ ❛❝❝❡ss ♠❡♠❜❡r ✈❛r✐❛❜❧❡s ❛♥❞ ❢✉♥❝t✐♦♥s ✇❤❡♥ ✇r✐t✐♥❣

❢✉♥❝t✐♦♥ ❞❡✜♥✐t✐♦♥s✳

◮ ❨♦✉ ♠✉st s♣❡❝✐❢② t❤❡ ❝❧❛ss ♥❛♠❡ ✉s✐♥❣ ✿✿ ✇❤❡♥ ✇r✐t✐♥❣ t❤❡

❞❡✜♥✐t✐♦♥ ♦❢ ❛ ♠❡♠❜❡r ❢✉♥❝t✐♦♥✳

❚❤❡ ❝♦♥st ❦❡②✇♦r❞

■❢ ❛ ♠❡♠❜❡r ❢✉♥❝t✐♦♥ ❞♦❡s♥✬t ❝❤❛♥❣❡ t❤❡ ♦❜❥❡❝t✱ ②♦✉ s❤♦✉❧❞ ♠❛r❦ ✐t ❛s ❝♦♥st✳ ❨♦✉ ❞♦ t❤✐s ❜② ✇r✐t✐♥❣ ❝♦♥st ❛t t❤❡ ❡♥❞ ♦❢ t❤❡ ❞❡❝❧❛r❛t✐♦♥ ❛♥❞ ❞❡✜♥✐t✐♦♥✳

❝❧❛ss✥❈✐r❝❧❡✥④ ♣✉❜❧✐❝✿ ✥✥✥✥❞♦✉❜❧❡✥r❛❞✐✉s❀ ✥✥✥✥❞♦✉❜❧❡✥❛r❡❛✭✮✥❝♦♥st❀ ✥✥✥✥❞♦✉❜❧❡✥❝✐r❝✉♠❢❡r❡♥❝❡✭✮✥❝♦♥st❀ ⑥❀ ✴✯ ✥✯✥✥✥❈♦♠♣✉t❡s✥t❤❡✥❛r❡❛✥♦❢✥❛✥❝✐r❝❧❡ ✥✯✴ ❞♦✉❜❧❡✥❈✐r❝❧❡✿✿❛r❡❛✭✮✥❝♦♥st✥④ ✥✥✥✥r❡t✉r♥✥P■✯r❛❞✐✉s✯r❛❞✐✉s❀ ⑥

❆ ❇❧❛❝❦✕❙❝❤♦❧❡s ▼♦❞❡❧ ❝❧❛ss

❝❧❛ss✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✥④ ♣✉❜❧✐❝✿ ✥✥✥✥❞♦✉❜❧❡✥st♦❝❦Pr✐❝❡❀ ✥✥✥✥❞♦✉❜❧❡✥✈♦❧❛t✐❧✐t②❀ ✥✥✥✥❞♦✉❜❧❡✥r✐s❦❋r❡❡❘❛t❡❀ ✥✥✥✥❞♦✉❜❧❡✥❞❛t❡❀ ⑥❀

◮ ◆♦t✐❝❡ t❤❛t t❤✐s ❝❧❛ss ♦♥❧② ❝♦♥t❛✐♥s t❤❡ ✈❛r✐❛❜❧❡s ❛ss♦❝✐❛t❡❞

✇✐t❤ t❤❡ ♠♦❞❡❧✳

◮ ❲❡✬❧❧ s♣❡❝✐❢② ❞✐✛❡r❡♥t ♦♣t✐♦♥ ❝♦♥tr❛❝ts ✐♥ ❞✐✛❡r❡♥t ❝❧❛ss❡s ◮ ❲❡ ♠✐❣❤t ❛❞❞ ❢✉♥❝t✐♦♥s t♦ ❞♦ t❤✐♥❣s ❧✐❦❡ ❣❡♥❡r❛t❡ s✐♠✉❧❛t❡❞

♦♣t✐♦♥ ♣r✐❝❡s✳

◮ ❲❡✬r❡ s♣❡❝✐❢②✐♥❣ t❤❡ ❞❛t❡ ❛s ❛ ❞♦✉❜❧❡✳ ❨♦✉ ✇♦✉❧❞♥✬t ❞♦ t❤✐s

✐♥ r❡❛❧ ❝♦❞❡✱ ❜✉t ■ ❞♦♥✬t ✇❛♥t t♦ ✇❛st❡ t✐♠❡ ♦♥ t❤✐♥❦✐♥❣ ❛❜♦✉t ❝❛❧❡♥❞❛rs✳ ❲❡✬❧❧ ♠❡❛s✉r❡ ❞❛t❡s ✐♥ ②❡❛rs s✐♥❝❡ ✵ ❆✳❉✳✳ ❙♦ ❏❛♥✉❛r② t❤❡ ✜rst ✷✵✶✹ ✇♦✉❧❞ ❜❡ r❡♣r❡s❡♥t❡❞ ❛s ✷✵✶✹.✵✳

❆ ❈❛❧❧ ❖♣t✐♦♥ ❝❧❛ss

❝❧❛ss✥❈❛❧❧❖♣t✐♦♥✥④ ♣✉❜❧✐❝✿ ✥✥✥✥❞♦✉❜❧❡✥str✐❦❡❀ ✥✥✥✥❞♦✉❜❧❡✥♠❛t✉r✐t②❀ ✥✥✥✥❞♦✉❜❧❡✥♣❛②♦❢❢✭✥❞♦✉❜❧❡✥st♦❝❦❆t▼❛t✉r✐t②✥✮✥❝♦♥st❀ ✥✥✥✥❞♦✉❜❧❡✥♣r✐❝❡✭✥❝♦♥st✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✫✥❜s♠✥✮ ✥✥✥✥✥✥✥✥❝♦♥st❀ ⑥❀

◮ ❚❤❡ ❝❛❧❧ ♦♣t✐♦♥ ❤❛s ❛ str✐❦❡ ❛♥❞ ♠❛t✉r✐t②✱ ❜✉t ❦♥♦✇s ♥♦t❤✐♥❣

❛❜♦✉t t❤❡ ❝✉rr❡♥t ♠❛r❦❡t ❞❛t❛✳ ❚❤✐s ♠❡❛♥s ❛ ❈❛❧❧❖♣t✐♦♥ ♦❜❥❡❝t ✇✐❧❧ r❡♠❛✐♥ ✉♥❝❤❛♥❣❡❞ ❛s t❤❡ ♠❛r❦❡t ❝❤❛♥❣❡s✳

◮ ■t ❤❛s ❛ ❢✉♥❝t✐♦♥ t♦ ❝♦♠♣✉t❡ t❤❡ ♣❛②♦✛ ❛t ♠❛t✉r✐t②✳ ◮ ■t ❤❛s ❛ ❢✉♥❝t✐♦♥ t♦ ❝♦♠♣✉t❡ t❤❡ ♣r✐❝❡ ❣✐✈❡♥ s♦♠❡ ❤②♣♦t❤❡t✐❝❛❧

♠❛r❦❡t ❞❛t❛ ✐♥ t❤❡ ❢♦r♠ ♦❢ ❛ ❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✳

◮ ◆♦t❡ t❤❡ ❝♦♥st st❛t❡♠❡♥ts✳

❚❤❡ ❞❡✜♥✐t✐♦♥ ♦❢ ♣❛②♦❢❢

❞♦✉❜❧❡✥❈❛❧❧❖♣t✐♦♥✿✿♣❛②♦❢❢✭ ✥✥✥✥✥✥✥✥❞♦✉❜❧❡✥st♦❝❦❆t▼❛t✉r✐t②✥✮✥❝♦♥st✥④ ✥✥✥✥✐❢✥✭st♦❝❦❆t▼❛t✉r✐t②❃str✐❦❡✮✥④ ✥✥✥✥✥✥✥✥r❡t✉r♥✥st♦❝❦❆t▼❛t✉r✐t②✲str✐❦❡❀ ✥✥✥✥⑥✥❡❧s❡✥④ ✥✥✥✥✥✥✥✥r❡t✉r♥✥✵✳✵❀ ✥✥✥✥⑥ ⑥

◮ ❆❧❧ t❤❡ ❝♦♥st ❦❡②✇♦r❞s ❡①❛❝t❧② ♠❛t❝❤ t❤❡ ❞❡❝❧❛r❛t✐♦♥✳ ◮ ❈❛❧❧✐♥❣ ♣❛②♦❢❢ ❞♦❡s♥✬t ❝❤❛♥❣❡ t❤❡ ♦♣t✐♦♥ ✐♥ ❛♥②✇❛②✳ ❚❤✐s ✐s

✇❤② ✐t ✐s ❞❡❝❧❛r❡❞ ❝♦♥st✳

❚❤❡ ❞❡✜♥✐t✐♦♥ ♦❢ ♣r✐❝❡

❚❤✐s ❝♦♠♣✉t❡s t❤❡ ♣r✐❝❡ ✉s✐♥❣ t❤❡ ❇❧❛❝❦✕❙❝❤♦❧❡s ❢♦r♠✉❧❛✳

❞♦✉❜❧❡✥❈❛❧❧❖♣t✐♦♥✿✿♣r✐❝❡✭ ✥✥✥✥✥✥✥✥❝♦♥st✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✫✥❜s♠✥✮✥❝♦♥st✥④ ✥✥✥✥❞♦✉❜❧❡✥❙✥❂✥❜s♠✳st♦❝❦Pr✐❝❡❀ ✥✥✥✥❞♦✉❜❧❡✥❑✥❂✥str✐❦❡❀ ✥✥✥✥❞♦✉❜❧❡✥s✐❣♠❛✥❂✥❜s♠✳✈♦❧❛t✐❧✐t②❀ ✥✥✥✥❞♦✉❜❧❡✥r✥❂✥❜s♠✳r✐s❦❋r❡❡❘❛t❡❀ ✥✥✥✥❞♦✉❜❧❡✥❚✥❂✥♠❛t✉r✐t②✥✲✥❜s♠✳❞❛t❡❀ ✥✥✥✥❞♦✉❜❧❡✥♥✉♠❡r❛t♦r✥❂ ✥✥✥✥✥✥✥✥❧♦❣✭✥❙✴❑✥✮✥✰✥✭✥r✥✰✥s✐❣♠❛✯s✐❣♠❛✯✵✳✺✮✯❚❀ ✥✥✥✥❞♦✉❜❧❡✥❞❡♥♦♠✐♥❛t♦r✥❂✥s✐❣♠❛✥✯✥sqrt✭❚✥✮❀ ✥✥✥✥❞♦✉❜❧❡✥❞✶✥❂✥♥✉♠❡r❛t♦r✴❞❡♥♦♠✐♥❛t♦r❀ ✥✥✥✥❞♦✉❜❧❡✥❞✷✥❂✥❞✶✥✲✥❞❡♥♦♠✐♥❛t♦r❀ ✥✥✥✥r❡t✉r♥✥❙✯♥♦r♠❝❞❢✭❞✶✮✥✲✥❡①♣✭✲r✯❚✮✯❑✯♥♦r♠❝❞❢✭❞✷✮❀ ⑥

◮ ♣r✐❝❡ t❛❦❡s ❛s ♣❛r❛♠❡t❡r ❛ ❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧ ❝❛❧❧❡❞ ♠✳

❚❤✐s ✐s ♣❛ss❡❞ ❜② ❝♦♥st❛♥t r❡❢❡r❡♥❝❡✳ ■t ✐s ♣❛ss❡❞ ❜② r❡❢❡r❡♥❝❡ ❜❡❝❛✉s❡ t❤✐s ✐s ♠♦r❡ ❡✣❝✐❡♥t t❤❛♥ ♣❛ss ❜② ✈❛❧✉❡✳ ■t ✐s ♣❛ss❡❞ ❛s ❛ ❝♦♥st r❡❢❡r❡♥❝❡ ❜❡❝❛✉s❡ ♣r✐❝❡ ❞♦❡s♥✬t ❝❤❛♥❣❡ ✐ts ✈❛❧✉❡✳

◮ ❈❛❧❧✐♥❣ ♣r✐❝❡ ❞♦❡s♥✬t ❝❤❛♥❣❡ t❤❡ ♦♣t✐♦♥ ❝♦♥tr❛❝t✱ s♦ t❤❡

❢✉♥❝t✐♦♥ ❞❡❝❧❛r❛t✐♦♥ ❡♥❞s ✇✐t❤ ❝♦♥st❀✳ ❈♦rr❡s♣♦♥❞✐♥❣❧② ✇❡ ❤❛✈❡ t❤❡ ❝♦♥st ❛♣♣❡❛r✐♥❣ ❜❡❢♦r❡ ④ ✐♥ t❤❡ ❞❡✜♥✐t✐♦♥✳

◮ ❚❤❡ ✉s❡ ♦❢ ❝♦♥st ❛♥❞ ♣❛ss ❜② r❡❢❡r❡♥❝❡ ♠✉st ❡①❛❝t❧② ♠❛t❝❤ ✐♥

t❤❡ ❞❡❝❧❛r❛t✐♦♥ ❛♥❞ ❞❡✜♥✐t✐♦♥✳

❯s✐♥❣ t❤❡ ❈❛❧❧❖♣t✐♦♥ ❝❧❛ss

❖✉r ✉♥✐t t❡sts ♣r♦✈✐❞❡s ❛ ❤❡❧♣❢✉❧ ❡①❛♠♣❧❡ ♦❢ ✉s❛❣❡✿

st❛t✐❝✥✈♦✐❞✥t❡st❈❛❧❧❖♣t✐♦♥Pr✐❝❡✭✮✥④ ✥✥✥✥❈❛❧❧❖♣t✐♦♥✥❝❛❧❧❖♣t✐♦♥❀ ✥✥✥✥❝❛❧❧❖♣t✐♦♥✳str✐❦❡✥❂✥✶✵✺✳✵❀ ✥✥✥✥❝❛❧❧❖♣t✐♦♥✳♠❛t✉r✐t②✥❂✥✷✳✵❀ ✥✥✥✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✥❜s♠❀ ✥✥✥✥❜s♠✳❞❛t❡✥❂✥✶✳✵❀ ✥✥✥✥❜s♠✳✈♦❧❛t✐❧✐t②✥❂✥✵✳✶❀ ✥✥✥✥❜s♠✳r✐s❦❋r❡❡❘❛t❡✥❂✥✵✳✵✺❀ ✥✥✥✥❜s♠✳st♦❝❦Pr✐❝❡✥❂✥✶✵✵✳✵❀ ✥✥✥✥❞♦✉❜❧❡✥♣r✐❝❡✥❂✥❝❛❧❧❖♣t✐♦♥✳♣r✐❝❡✭✥❜s♠✥✮❀ ✥✥✥✥❆❙❙❊❘❚❴❆PP❘❖❳❴❊◗❯❆▲✭✥♣r✐❝❡✱✥✹✳✵✹✻✱✥✵✳✵✶✮❀ ⑥

❲❤❛t ❤❛s ✉s✐♥❣ ❝❧❛ss❡s ❜♦✉❣❤t ✉s ✭s♦ ❢❛r✮❄

◮ ❊❛s✐❡r ♣r♦❣r❛♠♠✐♥❣✳ ■❢ ✇❡ ❤❛✈❡ ❛ s✐♥❣❧❡ ❢✉♥❝t✐♦♥

❜❧❛❝❦❙❝❤♦❧❡sPr✐❝❡ t❤❛t t❛❦❡s ✺ ❞♦✉❜❧❡ ♣❛r❛♠❡t❡rs✱ ✐t ✐s ❛❧♠♦st ✐♠♣♦ss✐❜❧❡ t♦ r❡♠❡♠❜❡r ✇❤❛t t❤❡ ❝♦rr❡❝t ♦r❞❡r ❢♦r t❤❡ ♣❛r❛♠❡t❡rs ✐s✳

◮ ❊❛s✐❡r ❞❡❜✉❣❣✐♥❣✳ ■❢ ②♦✉ ❤❛✈❡ ❛ ❢✉♥❝t✐♦♥ t❤❛t t❛❦❡s ✺ ❞♦✉❜❧❡

♣❛r❛♠❡t❡rs✱ ✐ts ❛❧♠♦st ✐♠♣♦ss✐❜❧❡ t♦ s♣♦t ✐❢ s♦♠❡♦♥❡ ❤❛s ❛❝❝✐❞❡♥t❛❧❧② ♣✉t t❤❡ ♣❛r❛♠❡t❡rs ✐♥ t❤❡ ✇r♦♥❣ ♦r❞❡r✳

◮ ❈♦♥s✐st❡♥❝②✳ ■❢ ✇❡ ✉s❡ t❤❡ s❛♠❡ ❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧ ❝❧❛ss t♦

♣r✐❝❡ ♣✉t ♦♣t✐♦♥s✱ ❆s✐❛♥ ♦♣t✐♦♥s✱ ❦♥♦❝❦✲♦✉t ♦♣t✐♦♥s ❡t❝✳ ✇❡✬❧❧ ❤❛✈❡ ❛ ❧✐❜r❛r② t❤❛t ✐s ♠✉❝❤ ❡❛s✐❡r t♦ ✉s❡✳

❘❡❝♦♠♠❡♥❞❡❞ ♣r♦❣r❛♠♠✐♥❣ ❝♦♥✈❡♥t✐♦♥s

◮ ❲❤❡♥❡✈❡r ♣♦ss✐❜❧❡✱ ❞♦♥✬t ♣✉t ❝❧❛ss ❞❡❝❧❛r❛t✐♦♥s ✐♥ ❤❡❛❞❡r ✜❧❡s✳

P✉t t❤❡♠ ✐♥ ❝♣♣ ✜❧❡s✳ ❨♦✉ s❤♦✉❧❞ tr② t♦ ❤✐❞❡ ✐♥❢♦r♠❛t✐♦♥ ✐❢ ♣♦ss✐❜❧❡✳

◮ ■❢ ②♦✉ ❞❡❝✐❞❡ t♦ ♣✉t ❛ ❝❧❛ss ✐♥ ❛ ❤❡❛❞❡r ✜❧❡✱ ❞❡✜♥❡ ♦♥❧② ♦♥❡

❝❧❛ss ✐♥ ❡❛❝❤ ❤❡❛❞❡r ✜❧❡✳

◮ ◆❛♠❡ t❤❛t ❝❧❛ss t❤❡ s❛♠❡ ❛s t❤❡ ❤❡❛❞❡r ✜❧❡✳ ◮ ●✐✈❡ ❝❧❛ss❡s ♥❛♠❡s t❤❛t ❛r❡ ♥♦✉♥s✿ ❢♦r ❡①❛♠♣❧❡

❈❛rt❡s✐❛♥P♦✐♥t ♦r ❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✳

◮ ❯s❡ ✉♣♣❡r ❝❛s❡ ❢♦r t❤❡ ✜rst ❧❡tt❡r ♦❢ ❛ ❝❧❛ss ♥❛♠❡✳

❚❤❡ ✜❧❡s ❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✳❤ ❛♥❞ ❈❛❧❧❖♣t✐♦♥✳❤ ❞❡♠♦♥str❛t❡ t❤❡s❡ ❝♦♥✈❡♥t✐♦♥s✳ ❚❤❡ ✜❧❡ ❣❡♦♠❡tr②✳❤ ❜r❡❛❦s t❤❡♠✳

❚❤❡ ❝♦♥st ❦❡②✇♦r❞

◮ ❚❤❡ ❝♦♥st ❦❡②✇♦r❞ ✐s ❛♥ ♦♣t✐♦♥❛❧ ❢❡❛t✉r❡ ✐♥ ❈✰✰✳ ❨♦✉ ❝❛♥

❝❤♦♦s❡ t♦ ✉s❡ ✐t ✐❢ ②♦✉ ✇❛♥t t❤❡ ❝♦♠♣✐❧❡r t♦ ❣✉❛r❛♥t❡❡ t❤❛t ②♦✉ ♥❡✈❡r ❛❝❝✐❞❡♥t❛❧❧② ❝❤❛♥❣❡ ❛♥ ♦❜❥❡❝t ✇❤❡♥ ②♦✉ ❞✐❞♥✬t ♠❡❛♥ t♦✳

◮ ❚♦ ✉s❡ t❤❡ ❝♦♥st ❦❡②✇♦r❞ ❛t ❛❧❧✱ ②♦✉ ♥❡❡❞ t♦ ✉s❡ ✐t

❡✈❡r②✇❤❡r❡✳

◮ ❉❡❝✐❞✐♥❣ ✇❤❡t❤❡r t♦ ✉s❡ ✐t ✐s ❛ s♦❢t✇❛r❡ ❛r❝❤✐t❡❝t✉r❡ q✉❡st✐♦♥✿

✐t ❛✛❡❝ts t❤❡ ✇❤♦❧❡ ♣r♦❥❡❝t✳ ■♥ ♣r❛❝t✐❝❡✱ t❤✐s ♠❡❛♥s ②♦✉✬❧❧ ♥❡❡❞ t♦ ❛s❦ ②♦✉r ❜♦ss ✇❤❡t❤❡r s❤❡ ✇❛♥ts ②♦✉ t♦ ✉s❡ ✐t ♦r ♥♦t✳

◮ ■❢ ②♦✉ ❛r❡ ✇r✐t✐♥❣ ❛ ❧✐❜r❛r②✱ ②♦✉✬❧❧ ♥❡❡❞ t♦ ✉s❡ t❤❡ ❝♦♥st

❦❡②✇♦r❞ ✐❢ ②♦✉r ❧✐❜r❛r② ✉s❡rs ✇❛♥t t♦ ✉s❡ t❤❡ ❝♦♥st ❦❡②✇♦r❞✳

❆ ♠♦r❡ s♦♣❤✐st✐❝❛t❡❞ ❡①❛♠♣❧❡

❝❧❛ss✥P✐❡❈❤❛rt✥④ ♣✉❜❧✐❝✿ ✥✥✥✥✈♦✐❞✥s❡t❚✐t❧❡✭✥❝♦♥st✥st❞✿✿str✐♥❣✫✥t✐t❧❡✥✮❀ ✥✥✥✥✈♦✐❞✥❛❞❞❊♥tr②✭✥❝♦♥st✥st❞✿✿str✐♥❣✫✥❧❛❜❡❧✱ ✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥❞♦✉❜❧❡✥✈❛❧✉❡✥✮❀ ✥✥✥✥✈♦✐❞✥✇r✐t❡❆s❍❚▼▲✭✥st❞✿✿♦str❡❛♠✫✥♦✉t✥✮✥❝♦♥st❀ ✥✥✥✥✈♦✐❞✥✇r✐t❡❆s❍❚▼▲✭✥❝♦♥st✥st❞✿✿str✐♥❣✫✥❢✐❧❡✥✮✥❝♦♥st❀ ♣r✐✈❛t❡✿ ✥✥✥✥st❞✿✿str✐♥❣✥t✐t❧❡❀ ✥✥✥✥st❞✿✿✈❡❝t♦r❁st❞✿✿str✐♥❣❃✥❧❛❜❡❧s❀ ✥✥✥✥st❞✿✿✈❡❝t♦r❁❞♦✉❜❧❡❃✥✈❛❧✉❡s❀ ⑥❀

Pr✐✈❛t❡ ♠❡♠❜❡rs

◮ ❚❤❡ ❞❛t❛ ✈❛r✐❛❜❧❡s ❛r❡ ❞❡❝❧❛r❡❞ ❛s ♣r✐✈❛t❡✳ ❚❤✐s ♠❡❛♥s ♦♥❧②

♠❡♠❜❡r ❢✉♥❝t✐♦♥s ♦❢ P✐❡❈❤❛rt ❝❛♥ s❡❡ t❤♦s❡ ✈❛r✐❛❜❧❡s✳

◮ ❚❤✐s ✐s ❝♦♥s✐❞❡r❡❞ ❣♦♦❞ ♣r♦❣r❛♠♠✐♥❣ st②❧❡✳

◮ ■t ♠❡❛♥s ✐t ✐s ✐♠♣♦ss✐❜❧❡ ❢♦r ❧❛❜❡❧s ❛♥❞ ✈❛❧✉❡s t♦ ❝♦♥t❛✐♥ ❛

❞✐✛❡r❡♥t ♥✉♠❜❡r ♦❢ ❡❧❡♠❡♥ts✳

◮ ■t ♠❡❛♥s ②♦✉ ❝❛♥ ❝❤❛♥❣❡ t❤❡ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ❞❡t❛✐❧s ✭✐✳❡✳ ❤♦✇

❞❛t❛ ✐s st♦r❡❞✮ ✇✐t❤♦✉t ✉s❡rs ♦❢ ②♦✉r ❝❧❛ss ❜❡✐♥❣ ❛✛❡❝t❡❞ ✐♥ ❛♥②✇❛②✳

◮ ❚❤❡ ♣r✐✈❛t❡ ❦❡②✇♦r❞ ❛❧❧♦✇s ②♦✉ t♦ ♣❡r❢♦r♠ ♠♦r❡

s♦♣❤✐st✐❝❛t❡❞ ✐♥❢♦r♠❛t✐♦♥ ❤✐❞✐♥❣ t❤❛♥ ❥✉st ❝❤♦♦s✐♥❣ ✇❤❛t t♦ ♣✉t ✐♥ t❤❡ ❤❡❛❞❡r ✜❧❡✳

◮ ◆♦t ♣✉tt✐♥❣ ❛ ❝❧❛ss ✐♥ ❛ ❤❡❛❞❡r ✜❧❡ ❣✐✈❡s ❡✈❡♥ ♠♦r❡

✐♥❢♦r♠❛t✐♦♥ ❤✐❞✐♥❣ t❤❛♥ ♠❛❦✐♥❣ t❤✐♥❣s ♣r✐✈❛t❡✳

◮ ❨♦✉ ❝❛♥ ♠❛❦❡ ❤❡❧♣❡r ❢✉♥❝t✐♦♥s ♣r✐✈❛t❡✱ ❛s ✇❡❧❧ ❛s ♠❛❦✐♥❣

❞❛t❛ ♣r✐✈❛t❡✳

❊♥❝❛♣s✉❧❛t✐♦♥

◮ ❊♥❝❛♣s✉❧❛t✐♦♥ r❡❢❡rs t♦ t✇♦ t❤✐♥❣s✿

◮ ❚❤❡ ❜✉♥❞❧✐♥❣ t♦❣❡t❤❡r ♦❢ r❡❧❛t❡❞ ✐t❡♠s ✐♥t♦ ❛ s✐♥❣❧❡ ♦❜❥❡❝t✳ ◮ Pr❡✈❡♥t✐♥❣ ❞✐r❡❝t ♠❡ss✐♥❣ ✇✐t❤ t❤❡ ✐♥t❡r♥❛❧ ❞❛t❛ ♦❢ ❛♥ ♦❜❥❡❝t✳

◮ ❊♥❝❛♣s✉❧❛t✐♦♥ ✐s ❝♦♠♠♦♥ ✐♥ r❡❛❧ ✇♦r❧❞ ❞❡s✐❣♥✳

◮ ❆❧❧ t❤❡ ❧✐❣❤t✐♥❣ ❝♦♥tr♦❧s ♦❢ ❛ ❝❛r ❛r❡ ♣✉t ♦♥ t❤❡ ❞❛s❤❜♦❛r❞ ❛♥❞

❛r❡ ❝❧❡❛r❧② s❡♣❛r❛t❡❞ ❢r♦♠ t❤❡ ❝♦♥tr♦❧s ❢♦r t❤❡ ✇✐♥❞♦✇s ❛♥❞ t❤❡ s❡❛ts✳

◮ ❨♦✉ ❝❛♥ ❝♦♥tr♦❧ ❛ ❝❛r t❤r♦✉❣❤ st❛♥❞❛r❞ ❢✉♥❝t✐♦♥s ✭t✉r♥ ❧❡❢t✱

t✉r♥ r✐❣❤t ❡t❝✳✮✳ ❚❤❡ ✐♥t❡r♥❛❧ ✇♦r❦✐♥❣s ❛r❡ ❤✐❞❞❡♥ ❢r♦♠ t❤❡ ✉s❡r ❝♦♠♣❧❡t❡❧②✳

◮ ❏✉st ❛s t❤❡s❡ ❞❡s✐❣♥ ♣r✐♥❝✐♣❧❡s ♠❛❦❡ ❝❛rs ❡❛s✐❡r t♦ ✉s❡✱ s♦ t❤❡

s❛♠❡ ♣r✐♥❝✐♣❧❡s ♠❛❦❡ ♦❜❥❡❝ts ✐♥ ♦❜❥❡❝t✲♦r✐❡♥t❡❞ ♣r♦❣r❛♠s ❡❛s② t♦ ✉s❡✳

❊♥❝❛♣s✉❧❛t✐♦♥ ❊①❛♠♣❧❡

❊①❛♠♣❧❡

❍♦✇ ❞♦❡s t❤❡ ✈❡❝t♦r❁❞♦✉❜❧❡❃ ❝❧❛ss st♦r❡ ✐t✬s ❞❛t❛✱ ❣✐✈❡♥ t❤❛t ✐t ❝❛♥✬t ❜❡ ✉s✐♥❣ ❛ ✈❡❝t♦r❁❞♦✉❜❧❡❃ ✐ts❡❧❢❄

❙♦❧✉t✐♦♥

❨♦✉ ❞♦♥✬t ♥❡❡❞ t♦ ❦♥♦✇✦ ▼♦st ♦❢ t❤❡ t✐♠❡ ②♦✉ ❞♦♥✬t ❝❛r❡ ❛♥❞ ②♦✉r ❧✐❢❡ ✐s ❡❛s✐❡r ❢♦r ♥♦t ❤❛✈✐♥❣ t♦ t❤✐♥❦ ❛❜♦✉t t❤✐s✳

❊①❛♠♣❧❡

❲❤❛t ❛r❡ t❤❡ ✐♥t❡r♥❛❧ ❞❛t❛ ♠❡♠❜❡rs ♦❢ ❛♥ ❢♦str❡❛♠❄

❙♦❧✉t✐♦♥

❲❤♦ ❝❛r❡s❄

❯s✐♥❣ ❛ P✐❡ ❈❤❛rt

st❛t✐❝✥✈♦✐❞✥t❡stP✐❡❈❤❛rt❈❧❛ss✭✮✥④ ✥✥✥✥✴✴✥❥✉st✥❝❤❡❝❦s✥t❤❛t✥t❤❡✥❝❧❛ss✥❝♦♠♣✐❧❡s✥❡t❝✳ ✥✥✥✥P✐❡❈❤❛rt✥♣✐❡❈❤❛rt❀ ✥✥✥✥♣✐❡❈❤❛rt✳❛❞❞❊♥tr②✭✧▼✉s❤r♦♦♠s✧✱✷✵✵✮❀ ✥✥✥✥♣✐❡❈❤❛rt✳❛❞❞❊♥tr②✭✧❙❛❧❛♠✐✧✱✶✵✵✮❀ ✥✥✥✥♣✐❡❈❤❛rt✳❛❞❞❊♥tr②✭✧❙♣✐♥❛❝❤✧✱✶✺✵✮❀ ✥✥✥✥♣✐❡❈❤❛rt✳s❡t❚✐t❧❡✭✧P✐③③❛✥❚♦♣♣✐♥❣s✧✮❀ ✥✥✥✥♣✐❡❈❤❛rt✳✇r✐t❡❆s❍❚▼▲✭✥✧P✐③③❛P✐❡✳❤t♠❧✧✥✮❀ ⑥

◮ ❆ ❦❡② ❜❡❧✐❡❢ ❜❡❤✐♥❞ ♦❜❥❡❝t ♦r✐❡♥t❛t✐♦♥ ✐s t❤❛t ②♦✉ s❤♦✉❧❞ ✜♥❞

t❤✐s ❝♦❞❡ ✈❡r② ❡❛s② t♦ ✉♥❞❡rst❛♥❞✳

❲r✐t✐♥❣ t❤❡ P✐❡ ❈❤❛rt ✐♠♣❧❡♠❡♥t❛t✐♦♥

❚❤❡ ❝♦❞❡ t♦ ❞❡✜♥❡ t❤❡ ❢✉♥❝t✐♦♥s ✐s ✈❡r② s✐♠✐❧❛r t♦ t❤❡ ❝♦❞❡ ✇❡ ✇r♦t❡ ❜❡❢♦r❡ ✇❡ ✐♥tr♦❞✉❝❡❞ ♦❜❥❡❝ts✳ ❨♦✉ ❝❛♥ s❡❡ t❤❡ ❢✉❧❧ ❧✐st✐♥❣s ✐♥ ❋▼▲✐❜✳ ❍❡r❡ ✐s ❛♥ ❡①❝❡r♣t✿

✈♦✐❞✥P✐❡❈❤❛rt✿✿s❡t❚✐t❧❡✭✥❝♦♥st✥st❞✿✿str✐♥❣✫✥t✥✮✥④ ✥✥✥✥t✐t❧❡✥❂✥t❀ ⑥ ✈♦✐❞✥P✐❡❈❤❛rt✿✿❛❞❞❊♥tr②✭✥❝♦♥st✥str✐♥❣✫✥❧❛❜❡❧✱ ✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥❞♦✉❜❧❡✥✈❛❧✉❡✥✮✥④ ✥✥✥✥❧❛❜❡❧s✳♣✉s❤❴❜❛❝❦✭✥❧❛❜❡❧✥✮❀ ✥✥✥✥✈❛❧✉❡s✳♣✉s❤❴❜❛❝❦✭✥✈❛❧✉❡✥✮❀ ⑥

◮ ❋✉♥❝t✐♦♥s ❧✐❦❡ ✇r✐t❡❚♦♣❇♦✐❧❡rP❧❛t❡❖❢P✐❡❈❤❛rt ❛r❡ ❧❡❢t

❛❧♠♦st ✉♥❝❤❛♥❣❡❞✳ ❚❤❡②✬r❡ ✇r✐tt❡♥ ❛s ♦r❞✐♥❛r② ❢✉♥❝t✐♦♥s✳ ❲❡✬✈❡ ❥✉st ❛❞❞❡❞ ❛ t✐t❧❡ ♣❛r❛♠❡t❡r✳

◮ ◆♦t✐❝❡ t❤❛t ✇❤❡♥ ②♦✉ ✇r✐t❡ ❛ ♠❡♠❜❡r ❢✉♥❝t✐♦♥✬s ❞❡✜♥✐t✐♦♥✱

②♦✉ ❤❛✈❡ ❝♦♥✈❡♥✐❡♥t ❛❝❝❡ss t♦ ❛❧❧ t❤❡ ♠❡♠❜❡r ✈❛r✐❛❜❧❡s ❛♥❞ ♠❡♠❜❡r ❢✉♥❝t✐♦♥s✳

❈♦♥str✉❝t♦rs

■♥✐t✐❛❧✐③❛t✐♦♥ ♦❢ ❧♦❝❛❧ ✈❛r✐❛❜❧❡s

◮ ■❢ ②♦✉ ❞❡❝❧❛r❡ ❛ ❞♦✉❜❧❡ ✐♥ ❈✰✰ ❜✉t ❞♦ ♥♦t s❡t ✐ts ✈❛❧✉❡✱ ❈✰✰

❞♦❡s ♥♦t ❣✉❛r❛♥t❡❡ t❤❡ ✈❛❧✉❡✳

◮ ■♥ ♣r❛❝t✐❝❡✱ t❤❡ ❝♦♠♣✉t❡r ✇✐❧❧ ❥✉st ❣r❛❜ s♦♠❡ ❢r❡❡ ♠❡♠♦r② ❛♥❞

✉s❡ ✇❤❛t❡✈❡r ✈❛❧✉❡s ❤❛♣♣❡♥ t♦ ❜❡ t❤❡r❡✳ ✐♥t✥♠❛✐♥✭✮✥④ ✥✥✥❞♦✉❜❧❡✥❞❀ ✥✥✥❝♦✉t✥❁❁✥✧❲❤❛t✥✐s✥t❤❡✥✈❛❧✉❡✥♦❢✥❞❄❭♥✧❀ ✥✥✥❝♦✉t✥❁❁✥❞❀ ⑥

◮ ❚❤❡ ❈✰✰ st❛♥❞❛r❞ ❞♦❡s♥✬t s❛② ✇❤❛t t❤✐s ♣r♦❣r❛♠ s❤♦✉❧❞ ❞♦✳ ◮ ■❢ ✇❡ ❝♦♠♣✐❧❡ ✇✐t❤ ✇❛r♥✐♥❣s ❛s ❡rr♦rs✱ ✇❡ ❣❡t ❛♥ ❡rr♦r ♠❡ss❛❣❡✳

■♥✐t✐❛❧✐③❛t✐♦♥ ♦❢ ♠❡♠❜❡r ✈❛r✐❛❜❧❡s

❚❤✐s ✇✐❧❧ ❢❛✐❧ ❢♦r s✐♠✐❧❛r r❡❛s♦♥s✳ ❝❧❛ss✥P♦✐♥t✥④ ♣✉❜❧✐❝✿ ✥✥✥✥❞♦✉❜❧❡✥①❀ ✥✥✥✥❞♦✉❜❧❡✥②❀ ⑥❀ ✐♥t✥♠❛✐♥✭✮✥④ ✥✥✥P♦✐♥t✥♣❀ ✥✥✥❝♦✉t✥❁❁✥✧❲❤❛t✥✐s✥t❤❡✥✈❛❧✉❡✥♦❢✥①❄❭♥✧❀ ✥✥✥❝♦✉t✥❁❁✥♣✳①❀ ✥✥✥r❡t✉r♥✥✵❀ ⑥

❈♦♥str✉❝t♦rs

◮ ❨♦✉ ❝❛♥ ❣✐✈❡ ②♦✉r ❈✰✰ ❝❧❛ss❡s ❝♦♥str✉❝t♦rs✳ ◮ ❆ ❝♦♥str✉❝t♦r ♣❡r❢♦r♠s t❤❡ ✐♥✐t✐❛❧✐③❛t✐♦♥ ♦❢ ❛♥ ♦❜❥❡❝t t♦ ❧❡❛✈❡

✐t ✐♥ ❛ s❡♥s✐❜❧❡ st❛t❡✳

◮ ❚♦ ❝♦♥str✉❝t ❛ ✈❡❝t♦r ♦❢ ❧❡♥❣t❤ ✶✵✵ ✐♥✐t✐❛❧✐③❡❞ ✇✐t❤ ③❡r♦s✿

✈❡❝t♦r❁❞♦✉❜❧❡❃✥✈✭✶✵✵✱✵✳✵✮❀

◮ ❚♦ ❝♦♥str✉❝t ❛ str✐♥❣ ✇✐t❤ ❝❤❛r❛❝t❡rs ❙♦♠❡✥t❡①t✳

str✐♥❣✥s✭✧❙♦♠❡✥t❡①t✧✮❀

❉❡❢❛✉❧t ❈♦♥str✉❝t♦r

◮ ▼♦st ❝❧❛ss❡s ❤❛✈❡ ❛ ❞❡❢❛✉❧t ❝♦♥str✉❝t♦r t❤❛t ✐♥✐t✐❛❧✐③❡s t❤❡

♦❜❥❡❝t ✐♥ ❛ s❡♥s✐❜❧❡ ❞❡❢❛✉❧t st❛t❡✳

◮ ❚♦ ❝r❡❛t❡ ❛♥ ❡♠♣t② ✈❡❝t♦r✿

✈❡❝t♦r❁❞♦✉❜❧❡❃✥✈❀ ❚❤❡ ❞❡❢❛✉❧t ❝♦♥str✉❝t♦r ✐s ❛✉t♦♠❛t✐❝❛❧❧② ❝❛❧❧❡❞✳

◮ ❚♦ ❝r❡❛t❡ ❛♥ ❡♠♣t② str✐♥❣✿

str✐♥❣✥s❀

❚♦ ✇r✐t❡ ❛ ❞❡❢❛✉❧t ❝♦♥str✉❝t♦r

❝❧❛ss✥P♦✐♥t✥④ ♣✉❜❧✐❝✿ ✥✥✥✥P♦✐♥t✭✮❀✥✴✴✥❞❡❝❧❛r❡✥❞❡❢❛✉❧t✥❝♦♥str✉❝t♦r ✥✥✥✥❞♦✉❜❧❡✥①❀ ✥✥✥✥❞♦✉❜❧❡✥②❀ ⑥❀ P♦✐♥t✿✿P♦✐♥t✭✮✥④ ✥✥✥✥①❂✵✳✵❀ ✥✥✥✥②❂✵✳✵❀ ⑥ ✐♥t✥♠❛✐♥✭✮✥④ ✥✥✥P♦✐♥t✥♣❀ ✥✥✥❝♦✉t✥❁❁✥✧❲❤❛t✥✐s✥t❤❡✥✈❛❧✉❡✥♦❢✥①❄❭♥✧❀ ✥✥✥❝♦✉t✥❁❁✥♣✳①❀ ✥✥✥r❡t✉r♥✥✵❀ ⑥

❘✉❧❡s ❢♦r ✇r✐t✐♥❣ ❛ ❞❡❢❛✉❧t ❝♦♥str✉❝t♦r

◮ ❚❤❡ ❝♦♥str✉❝t♦r ❞❡❝❧❛r❛t✐♦♥ ❧♦♦❦s ❧✐❦❡ ❛ ❢✉♥❝t✐♦♥ ❞❡❝❧❛r❛t✐♦♥

❡①❝❡♣t✿

◮ ❚❤❡r❡ ✐s ♥♦ r❡t✉r♥ t②♣❡✳ ◮ ❚❤❡r❡ ❛r❡ ♥♦ ♣❛r❛♠❡t❡rs✳ ◮ ■♥st❡❛❞ ♦❢ t❤❡ ❢✉♥❝t✐♦♥ ♥❛♠❡ ②♦✉ ❤❛✈❡ t❤❡ ♥❛♠❡ ♦❢ t❤❡ ❝❧❛ss✳

◮ ❚❤❡ ❝♦♥str✉❝t♦r ❞❡✜♥✐t✐♦♥ ❧♦♦❦s ❧✐❦❡ ❛ ❢✉♥❝t✐♦♥ ❞❡✜♥✐t✐♦♥

❡①❝❡♣t✿

◮ ❚❤❡r❡ ✐s ♥♦ r❡t✉r♥ t②♣❡✳ ◮ ❚❤❡r❡ ❛r❡ ♥♦ ♣❛r❛♠❡t❡rs✳ ◮ ■♥st❡❛❞ ♦❢ t❤❡ ❢✉♥❝t✐♦♥ ♥❛♠❡ ②♦✉ ❤❛✈❡ t❤❡ ♥❛♠❡ ♦❢ t❤❡ ❝❧❛ss✳

❍♦✇ ❝♦♥str✉❝t♦rs ✇♦r❦

◮ ❚❤✐♥❦ ♦❢ ❛ ❝♦♥str✉❝t♦r ❛s ❛ ❢✉♥❝t✐♦♥ t❤❛t ✐s ❛✉t♦♠❛t✐❝❛❧❧②

❝❛❧❧❡❞ ❜❡❢♦r❡ ❛♥②♦♥❡ ✐s ❛❧❧♦✇❡❞ t♦ s❡❡ t❤❡ ♦❜❥❡❝t✳

◮ ❙❡t ❛❧❧ ✐♥t✱ ❞♦✉❜❧❡ ❡t❝✳ ✜❡❧❞s t♦ s❡♥s✐❜❧❡ ❞❡❢❛✉❧t ✈❛❧✉❡s✳ ◮ ❨♦✉ s❤♦✉❧❞ ❡♥s✉r❡ t❤❛t t❤❡ ♦❜❥❡❝t ✐s ✐♥ ❛ ❝♦♥s✐st❡♥t st❛t❡

❜❡❢♦r❡ ❛♥②♦♥❡ ❡✈❡r s❡❡s ✐t✳ P❡r❢♦r♠ ✇❤❛t❡✈❡r ♣r♦❝❡ss✐♥❣ ✐s r❡q✉✐r❡❞ t♦ ❛❝❤✐❡✈❡ t❤✐s✳

❆❧t❡r♥❛t✐✈❡ s②♥t❛①

❝❧❛ss✥P♦✐♥t✥④ ♣✉❜❧✐❝✿ ✥✥✥✥P♦✐♥t✭✮❀✥✴✴✥❞❡❝❧❛r❡✥❞❡❢❛✉❧t✥❝♦♥str✉❝t♦r ✥✥✥✥❞♦✉❜❧❡✥①❀ ✥✥✥✥❞♦✉❜❧❡✥②❀ ⑥❀ P♦✐♥t✿✿P♦✐♥t✭✮✥✿ ✥✥✥✥①✭✵✳✵✮✱ ✥✥✥✥②✭✵✳✵✮✥④ ⑥ ✐♥t✥♠❛✐♥✭✮✥④ ✥✥✥P♦✐♥t✥♣❀ ✥✥✥❝♦✉t✥❁❁✥✧❲❤❛t✥✐s✥t❤❡✥✈❛❧✉❡✥♦❢✥①❄❭♥✧❀ ✥✥✥❝♦✉t✥❁❁✥♣✳①❀ ✥✥✥r❡t✉r♥✥✵❀ ⑥

◆♦t❡s ♦♥ t❤❡ ❛❧t❡r♥❛t✐✈❡ s②♥t❛①

P♦✐♥t✿✿P♦✐♥t✭✮✥✿ ✥✥✥✥①✭✵✳✵✮✱ ✥✥✥✥②✭✵✳✵✮✥④ ⑥

◮ ❚❤❡ ❧✐st ♦❢ st❛t❡♠❡♥ts x(✵.✵), y(✵.✵) ✐s ❝❛❧❧❡❞ ❛♥ ✐♥✐t✐❛❧✐③❛t✐♦♥

❧✐st✳

◮ ◆♦t❡ t❤❛t t❤✐s ❝♦♠❡s ❛❢t❡r ❛ ❝♦❧♦♥ ❝❤❛r❛❝t❡r ✿ ❛♥❞ ❜❡❢♦r❡ t❤❡

④✳

◮ ❯s❡ t❤✐s t♦ ❝❛❧❧ ❝♦♥str✉❝t♦rs ♦❢ ❛❧❧ t❤❡ ✜❡❧❞s ✐♥s✐❞❡ ②♦✉r ♦❜❥❡❝t✳

❲❤✐❝❤ s②♥t❛① s❤♦✉❧❞ ②♦✉ ✉s❡❄

◮ ❊①♣❡r✐❡♥❝❡❞ ❈✰✰ ♣r♦❣r❛♠♠❡rs ♣r❡❢❡r ❛♥ ✐♥✐t✐❛❧✐③❛t✐♦♥ ❧✐st

❜❡❝❛✉s❡ ✐t ✐s ❢❛st❡r✳

◮ ❚❤✐s ✐s ❜❡❝❛✉s❡ ❝❛❧❧✐♥❣ t❤❡ ❞❡❢❛✉❧t ❝♦♥str✉❝t♦r ❛♥❞ t❤❡♥

♣❡r❢♦r♠✐♥❣ ❛ss✐❣♥♠❡♥t ✇✐❧❧ ❜❡ s❧♦✇❡r t❤❛♥ ✉s✐♥❣ t❤❡ r✐❣❤t ✈❛❧✉❡ ✜rst t✐♠❡✳ str✐♥❣✥♠②❙tr✐♥❣❀ ♠②❙tr✐♥❣❂✧❙♦♠❡✥t❡①t✧❀ ✐s s❧♦✇❡r t❤❛♥ str✐♥❣✥♠②❙tr✐♥❣✭✧❙♦♠❡✥t❡①t✧✮❀

❖t❤❡r ❝♦♥str✉❝t♦rs

❝❧❛ss✥❈❛❧❧❖♣t✐♦♥✥④ ♣✉❜❧✐❝✿ ✥✥✥✥❞♦✉❜❧❡✥str✐❦❡❀ ✥✥✥✥❞♦✉❜❧❡✥♠❛t✉r✐t②❀ ✥✥✥✥❈❛❧❧❖♣t✐♦♥✭✮❀✥✴✴✥❞❡❢❛✉❧t✥❝♦♥str✉❝t♦r ✥✥✥✥❈❛❧❧❖♣t✐♦♥✭❞♦✉❜❧❡✥str✐❦❡✱✥❞♦✉❜❧❡✥♠❛t✉r✐t②✮❀✴✴❛❧t❡r♥❛t✐✈❡ ⑥❀ ✴✴✥❞❡❢❛✉❧t✥❝♦♥str✉❝t♦r✥✐♠♣❧❡♠❡♥t❛t✐♦♥ ❈❛❧❧❖♣t✐♦♥✿✿❈❛❧❧❖♣t✐♦♥✭✮✥✿ ✥✥✥✥str✐❦❡✭✵✳✵✮✱ ✥✥✥✥♠❛t✉r✐t②✭✵✳✵✮✥④ ⑥ ✴✴✥❛❧t❡r♥❛t✐✈❡✥❝♦♥str✉❝t♦r✥✐♠♣❧❡♠❡♥t❛t✐♦♥ ❈❛❧❧❖♣t✐♦♥✿✿❈❛❧❧❖♣t✐♦♥✭ ✥✥✥✥✥✥✥✥❞♦✉❜❧❡✥s✱ ✥✥✥✥✥✥✥✥❞♦✉❜❧❡✥♠✥✮✥✿ ✥✥✥✥str✐❦❡✭s✮✱ ✥✥✥✥♠❛t✉r✐t②✭♠✮✥④ ⑥

❉❡s✐❣♥✐♥❣ ✇✐t❤ ❝♦♥str✉❝t♦rs

◮ ❚♦ ❝r❡❛t❡ ❛♥ ♦♣t✐♦♥ ✇✐t❤ str✐❦❡ ✶✵✵ ❛♥❞ ♠❛t✉r✐t② ✷.✵✿

❈❛❧❧❖♣t✐♦♥✥♠②❖♣t✐♦♥✭✥✶✵✵✱✥✷✳✵✥✮❀

◮ ❚❤✐s s❡❡♠s ❝♦♥✈❡♥✐❡♥t✱ ❜✉t t❤✐s ✐s ♣r♦❜❛❜❧② ♥♦t ❛ ✈❡r② ❣♦♦❞

❞❡s✐❣♥✿

◮ ❇② ✐♥tr♦❞✉❝✐♥❣ ❝❧❛ss❡s ✇❡ ❣♦t r✐❞ ♦❢ t❤❡ ♣r♦❜❧❡♠ ♦❢ ❤❛✈✐♥❣ t♦

r❡♠❡♠❜❡r ✇❤❛t ♦r❞❡r t♦ ♣✉t ♣❛r❛♠❡t❡rs ✇❤❡♥ ❝❛❧❧✐♥❣ ❢✉♥❝t✐♦♥s✳

◮ ❇② ❤❛✈✐♥❣ ❛ ❝♦♥str✉❝t♦r ✇✐t❤ ♠✉❧t✐♣❧❡ ♣❛r❛♠❡t❡rs✱ ✇❡✬✈❡

r❡✐♥tr♦❞✉❝❡❞ t❤✐s ♣r♦❜❧❡♠✦

◮ ❇② ❝♦♥tr❛st✿

◮ ❇❡✐♥❣ ❛❜❧❡ t♦ ❝♦♥str✉❝t ❛ ✈❡❝t♦r ♦❢ ❣✐✈❡♥ s✐③❡ ❛♥❞ ❞❡❢❛✉❧t

✈❛❧✉❡ ✐s ❛ ❣♦♦❞ ✉s❡ ♦❢ ❝♦♥str✉❝t♦rs✳

◮ ❇❡✐♥❣ ❛❜❧❡ t♦ ❝♦♥str✉❝t ❛ str✐♥❣ ✇✐t❤ t❤❡ ❞❡s✐r❡❞ t❡①t ✐s ❛❧s♦

❛ ❣♦♦❞ ✉s❡ ♦❢ ❝♦♥str✉❝t♦rs✳

❙✐♥❣❧❡ ♣❛r❛♠❡t❡r ❝♦♥str✉❝t♦rs

◮ str✐♥❣ ❤❛s ❛ ❝♦♥str✉❝t♦r t❤❛t t❛❦❡s r❛✇ t❡①t ❞❛t❛✳

str✐♥❣✥s✭✧❙♦♠❡✥r❛✇✥t❡①t✧✮❀

◮ ❈✰✰ ✇✐❧❧ ❛✉t♦♠❛t✐❝❛❧❧② ❝♦♥✈❡rt r❛✇ t❡①t ❞❛t❛ t♦ str✐♥❣s✳

♣❧♦t✭✥✧♠②P❧♦t✳t①t✧✱✥①❱❡❝✱✥②❱❡❝✥✮❀

◮ ❚❤✐s ✇♦r❦s ❡✈❡♥ t❤♦✉❣❤ t❤❡ ✜rst ♣❛r❛♠❡t❡r ♦❢ ❛ ♣❧♦t ✐s

❞❡❝❧❛r❡❞ t♦ ❜❡ ❛ ❝♦♥st✥str✐♥❣✫✳

◮ ■❢ ②♦✉ ✇r✐t❡ ❛ s✐♥❣❧❡ ♣❛r❛♠❡t❡r ❝♦♥str✉❝t♦r✱ ❈✰✰ ✇✐❧❧ ♣❡r❢♦r♠

s✐♠✐❧❛r ❛✉t♦♠❛t✐❝ ❝♦♥✈❡rs✐♦♥s✳

❙♦✉♥❞s ❝♦♦❧✱ ❜✉t ✐t✬s ❛ t❡rr✐❜❧❡ ✐❞❡❛

◮ ❙✉♣♣♦s❡ ②♦✉ ❤❛❞ ❛❞❞❡❞ ❛ ❝♦♥str✉❝t♦r t♦ ❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧

✇❤❡r❡ ②♦✉ ♣r♦✈✐❞❡ ❥✉st t❤❡ st♦❝❦ ♣r✐❝❡✿

❝❧❛ss✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✥④ ♣✉❜❧✐❝✿ ✥✥✥✥❞♦✉❜❧❡✥st♦❝❦Pr✐❝❡❀ ✥✥✥✥❞♦✉❜❧❡✥❞❛t❛❀ ✥✥✥✥❞♦✉❜❧❡✥✈♦❧❛t✐❧✐t②❀ ✥✥✥✥❞♦✉❜❧❡✥r✐s❦❋r❡❡❘❛t❡❀ ✥✥✥✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✭✮❀ ✥✥✥✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✭✥❞♦✉❜❧❡✥st♦❝❦Pr✐❝❡✥✮❀✥✴✴✥❦❡②✥❧✐♥❡ ⑥❀

◮ ❈✰✰ ✇✐❧❧ ♥♦✇ ❛✉t♦♠❛t✐❝❛❧❧② ❝♦♥✈❡rt ❞♦✉❜❧❡s ✐♥t♦

❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧ ✐♥st❛♥❝❡s✳

◮ ❚❤✐s ✐s ✇❡✐r❞ ❛♥❞ ✉♥❞❡s✐r❛❜❧❡✳

❚❤❡ ❡①♣❧✐❝✐t ❦❡②✇♦r❞

◮ ▼❛r❦ ❝♦♥str✉❝t♦rs t❤❛t t❛❦❡ ♦♥❡ ♣❛r❛♠❡t❡r ❛s ❡①♣❧✐❝✐t✳

❝❧❛ss✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✥④ ♣✉❜❧✐❝✿ ✥✥✥✥❞♦✉❜❧❡✥st♦❝❦Pr✐❝❡❀ ✥✥✥✥❞♦✉❜❧❡✥❞❛t❛❀ ✥✥✥✥❞♦✉❜❧❡✥✈♦❧❛t✐❧✐t②❀ ✥✥✥✥❞♦✉❜❧❡✥r✐s❦❋r❡❡❘❛t❡❀ ✥✥✥✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✭✮❀ ✥✥✥✥❡①♣❧✐❝✐t✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✭✥❞♦✉❜❧❡✥st♦❝❦Pr✐❝❡✥✮❀ ⑥❀

◮ ❚❤✐s ♣r❡✈❡♥ts ❛✉t♦♠❛t✐❝ ❝♦♥✈❡rs✐♦♥✳ ◮ ■♥ t❤❡ ✈❡r② r❛r❡ ❡✈❡♥t t❤❛t ❛✉t♦♠❛t✐❝ ❝♦♥✈❡rs✐♦♥ ✐s ✉s❡❢✉❧ ✭❛s

❢♦r str✐♥❣s✮ ②♦✉ ❝❛♥ ❞r♦♣ t❤❡ ❡①♣❧✐❝✐t✳

◮ ■❢ ②♦✉ ❢♦r❣❡t t❤❡ ❡①♣❧✐❝✐t ✐t ✐s♥✬t t❤❡ ❡♥❞ ♦❢ t❤❡ ✇♦r❧❞✳

❙✉♠♠❛r②

◮ ❲❡✬✈❡ ❧❡❛r♥❡❞ ❤♦✇ t♦ ✇r✐t❡ ❝❧❛ss❡s t❤❛t ❣r♦✉♣ ❞❛t❛ t♦❣❡t❤❡r✳ ◮ ❲❡✬✈❡ ❧❡❛r♥❡❞ ❤♦✇ t♦ ❛❞❞ ❢✉♥❝t✐♦♥s t♦ ♦✉r ❝❧❛ss❡s✳ ◮ ❲❡✬✈❡ s❡❡♥ t❤❛t ✉s✐♥❣ ❝❧❛ss❡s ♠❛❦❡s ❧✐❢❡ ❡❛s✐❡r ❢♦r ✉s❡rs ♦❢ ♦✉r

❧✐❜r❛r②✳

◮ ❲❡✬✈❡ ❧❡❛r♥❡❞ ❤♦✇ t♦ ✉s❡ t❤❡ ❦❡②✇♦r❞s ♣✉❜❧✐❝ ❛♥❞ ♣r✐✈❛t❡

t♦ ❤✐❞❡ ❞❛t❛ ❢r♦♠ ✉s❡rs ♦❢ ♦✉r ❧✐❜r❛r②✳

◮ ❲❡✬✈❡ ❧❡❛r♥❡❞ t❤❡ ❜✉③③✇♦r❞ ✏❡♥❝❛♣s✉❧❛t✐♦♥✑✳ ◮ ❲❡✬✈❡ ❧❡❛r♥❡❞ ❤♦✇ t♦ ✉s❡ t❤❡ ❝♦♥st ❦❡②✇♦r❞ t♦ ✐♥❞✐❝❛t❡

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

◮ ❲❡✬✈❡ ❧❡❛r♥❡❞ ❤♦✇ t♦ ❣✐✈❡ ❝❧❛ss❡s ❝♦♥str✉❝t♦rs✳