Prr s Prrs - - PowerPoint PPT Presentation

pr r s pr r s
SMART_READER_LITE
LIVE PREVIEW

Prr s Prrs - - PowerPoint PPT Presentation

Prr s Prrs tt r t t tr tst


slide-1
SLIDE 1

Pr♦❣r❛♠♠✐♥❣ ▲❛♥❣✉❛❣❡s ❛♥❞ Pr♦❣r❛♠s

◗✉♦t❛t✐♦♥ ❢r♦♠ ❉♦♥❛❧❞ ❑♥✉t❤✱ ❛♥ ❡♠✐♥❡♥t ❈♦♠♣✉t❡r ❙❝✐❡♥t✐st ❛♥❞ ✇✐♥♥❡r ♦❢ t❤❡ ✶✾✼✹ ❚✉r✐♥❣ ❆✇❛r❞✳ ❚❤❡ ❜❡st ♣r♦❣r❛♠s ❛r❡ ✇r✐tt❡♥ s♦ t❤❛t ❝♦♠♣✉t✐♥❣ ♠❛❝❤✐♥❡s ❝❛♥ ♣❡r❢♦r♠ t❤❡♠ q✉✐❝❦❧② ❛♥❞ s♦ t❤❛t ❤✉♠❛♥ ❜❡✐♥❣s ❝❛♥ ✉♥❞❡rst❛♥❞ t❤❡♠ ❝❧❡❛r❧②✳ ❆ ♣r♦❣r❛♠♠❡r ✐s ✐❞❡❛❧❧② ❛♥ ❡ss❛②✐st ✇❤♦ ✇♦r❦s ✇✐t❤ tr❛❞✐t✐♦♥❛❧ ❛❡st❤❡t✐❝ ❛♥❞ ❧✐t❡r❛r② ❢♦r♠s ❛s ✇❡❧❧ ❛s ♠❛t❤❡♠❛t✐❝❛❧ ❝♦♥❝❡♣ts✱ t♦ ❝♦♠♠✉♥✐❝❛t❡ t❤❡ ✇❛② t❤❛t ❛♥ ❛❧❣♦r✐t❤♠ ✇♦r❦s ❛♥❞ t♦ ❝♦♥✈✐♥❝❡ ❛ r❡❛❞❡r t❤❛t t❤❡ r❡s✉❧ts ✇✐❧❧ ❜❡ ❝♦rr❡❝t✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-2
SLIDE 2

❈ ▼✐❧❡st♦♥❡s

✶ ❖r✐❣✐♥❛❧❧② ❞❡✈❡❧♦♣❡❞ ❜② ❉❡♥♥✐s ❘✐t❝❤✐❡ ✐♥ ❡❛r❧② ✼✵s ❢♦r ✉s❡ ✇✐t❤

❯♥✐① ❛s ❛ ❣❡♥❡r❛❧ s②st❡♠ ♣r♦❣r❛♠♠✐♥❣ ❧❛♥❣✉❛❣❡✳

✷ ■♥ ✶✾✼✽✱ ❑❡r♥✐❣❤❛♥ ❛♥❞ ❘✐t❝❤✐❡ ♣✉❜❧✐s❤ ❚❤❡ ❈ Pr♦❣r❛♠♠✐♥❣

▲❛♥❣✉❛❣❡✱ ♣♦♣✉❧❛r❧② ❦♥♦✇♥ ❛s ❑✫❘✶✳ ❈ ✐♠♣❧❡♠❡♥t❛t✐♦♥s ❜❛s❡❞ ♦♥ ❜♦♦❦ s♣❡❝✐✜❝❛t✐♦♥ ❦♥♦✇♥ ❛s ❑✫❘✶ ❈✳

✸ ✶✾✽✵ st❛♥❞❛r❞✐③❛t✐♦♥ ❜② ❆◆❙■ ❛♥❞ ■❙❖❀ ❝❤❛♥❣❡s ✐♥❝❧✉❞❡

❢✉♥❝t✐♦♥ ♣r♦t♦t②♣❡s✳ ❑♥♦✇♥ ❛s ❈✽✾ ♦r ❈✾✵✳ ❑✫❘✷ ❞❡s❝r✐❜❡s ❈✽✾✳

✹ ✶✾✾✵s st❛♥❞❛r❞✐③❛t✐♦♥ ❡✛♦rts ❧❡❞ t♦ ❈✾✾❀ ❝❤❛♥❣❡s ✐♥❝❧✉❞❡

✈❛r✐❛❜❧❡✲❧❡♥❣t❤ ❛rr❛②s✱ ✐♥❧✐♥❡ ❢✉♥❝t✐♦♥s✳

✺ ✷✵✵✵✬s st❛♥❞❛r❞✐③❛t✐♦♥ ❡✛♦rts ❧❡❞ t♦ ❈✶✶❀ ❝❤❛♥❣❡s ✐♥❝❧✉❞❡

♠✉❧t✐t❤r❡❛❞✐♥❣ s✉♣♣♦rt✱ ❛♥♦♥②♠♦✉s str✉❝t✉r❡s ❛♥❞ ✉♥✐♦♥s✱ ♥♦r❡t✉r♥ ❢✉♥❝t✐♦♥s✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-3
SLIDE 3

❉✐st✐♥❣✉✐s❤✐♥❣ ❋❡❛t✉r❡s

❆ t②♣❡ ❞❡s❝r✐❜❡s ❤♦✇ ❛ s❡q✉❡♥❝❡ ♦❢ ❜②t❡s s❤♦✉❧❞ ❜❡ ✐♥t❡r♣r❡t❡❞✳ ❈ ✐s st❛t✐❝❛❧❧② t②♣❡❞❀ ✐✳❡✳ t❤❡ ❝♦♠♣✐❧❡r ❝❤❡❝❦s t②♣❡ ❝♦♠♣❛t✐❜✐❧✐t②✳ ❍♦✇❡✈❡r✱ ❈ ❛❧❧♦✇s ❛ ♣r♦❣r❛♠♠❡r t♦ s❡❧❡❝t✐✈❡❧② ♦✈❡rr✐❞❡ t②♣❡ ❝❤❡❝❦✐♥❣✳ ❆❧❧♦✇s ♣r♦❣r❛♠♠❡r t♦ ♠❛♥✐♣✉❧❛t❡ ❞❛t❛ ❛t t❤❡ ❜✐t✲❧❡✈❡❧✳ ▲♦✇ ❧❡✈❡❧✿ ❙✉♣♣♦rt ❢♦r ❞✐r❡❝t❧② ♠❛♥✐♣✉❧❛t✐♥❣ ♠❡♠♦r② ❛❞❞r❡ss❡s✳ ❚❤✐s ❞✐st✐♥❣✉✐s❤❡s ❈ ❢r♦♠ ❤✐❣❤❡r✲❧❡✈❡❧ ♣r♦❣r❛♠♠✐♥❣ ❧❛♥❣✉❛❣❡s ✇❤❡r❡ ♠❡♠♦r② ✐s ❛❜str❛❝t❡❞ ♦✉t✳ ❆❧❧♦✇s ♣r♦❣r❛♠♠❡r t♦t❛❧ ❝♦♥tr♦❧ ♦✈❡r ♠❡♠♦r② ❛❧❧♦❝❛t✐♦♥✳ ❯s❡s ❛ ✈❡r② ❧✐♠✐t❡❞ ♠❛❝r♦ s②st❡♠ ✭❝♦♠♣✐❧❡✲t✐♠❡ t❡①t s✉❜st✐t✉t✐♦♥✮✳ ❲✐❞❡❧② ❛✈❛✐❧❛❜❧❡✿ ❤✐❣❤❡r ❧❡✈❡❧ ♣r♦❣r❛♠♠✐♥❣ ❧❛♥❣✉❛❣❡s ❛r❡ ♦❢t❡♥ ✐♠♣❧❡♠❡♥t❡❞ ❜② ❜❡✐♥❣ tr❛♥s❧❛t❡❞ ✐♥t♦ ❈✱ ❛t ❧❡❛st ✐♥✐t✐❛❧❧②✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-4
SLIDE 4

❈ ❊①♣r❡ss✐♦♥s

❊①♣r❡ss✐♦♥s r❡t✉r♥ ❛ ✈❛❧✉❡ ✇❤✐❝❤ ❝❛♥ ❜❡ st♦r❡❞ ✐♥ ❛ ✈❛r✐❛❜❧❡✳ ❊①♣r❡ss✐♦♥ t②♣❡s ✐♥❝❧✉❞❡✿ ❆r✐t❤♠❡t✐❝ ❡①♣r❡ss✐♦♥s ✉s❡ ♦♣❡r❛t♦rs ❧✐❦❡ ✰✱ ✲✱ ✯✱ ✴✱ ✪✳ ✲❛ ✰ ①✪② ✲ ③ ❈♦♠♣❛r✐s♦♥ ❡①♣r❡ss✐♦♥s ✉s❡ ♦♣❡r❛t♦rs ❧✐❦❡ ❂❂✱ ✦❂✱ ❁✱ ❁❂✱ ❃✱ ❃❂✳ ① <❂ ✸ ▲♦❣✐❝❛❧ ❡①♣r❡ss✐♦♥s ✉s❡ ♦♣❡r❛t♦rs ❧✐❦❡ ✫✫✱ ⑤⑤✱ ✦ ✇✐t❤ ✵ ✐♥t❡r♣r❡t❡❞ ❛s ❢❛❧s❡✱ ♥♦♥✲✵ ❛s tr✉❡✳ ❙❤♦rt✲❝✐r❝✉✐t ❡✈❛❧✉❛t✐♦♥✳ ✭❧♦ <❂ ✐✮ ✫✫ ✭✐ < ❤✐✮ ✴✴❝♦♠♣❛r✐s♦♥ s✉❜✲❡①♣r❡ss✐♦♥s ✴✴✐❢ ❧♦ > ✐✱ ✐ < ❤✐ ♥♦t ❡✈❛❧✉❛t❡❞

❈ ■♥tr♦❞✉❝t✐♦♥

slide-5
SLIDE 5

❈ ❊①♣r❡ss✐♦♥s ❈♦♥t✐♥✉❡❞

❇✐t ❡①♣r❡ss✐♦♥s ✉s❡ ♦♣❡r❛t♦rs ❧✐❦❡ ✫✱ ⑤✱ ⑦✱ ❃❃✱ ❁❁✳ ✇♦r❞ ⑤ ✶ ✴✴r❡s✉❧t ✇✐❧❧ ❛❧✇❛②s ❤❛✈❡ ▲❙❇ ✶ ✇♦r❞ ✫ ♠❛s❦ ✴✴r❡s✉❧t ❤❛s ✵✲❜✐ts ✐♥ ♠❛s❦ ❛ << ✶ ✴✴s❤✐❢t t♦ ❧❡❢t ❆ss✐❣♥♠❡♥t ❡①♣r❡ss✐♦♥s ✉s❡ ♦♣❡r❛t♦rs ❧✐❦❡ ❂✱ ✰❂✱ ✯❂✱ ❡t❝✳ ❛ ❂ ❜ ❂ ① < ② ✴✴✭❜ ❂ ① ✫✫ ②✮ ✐s ❛♥ ❡①♣r❡ss✐♦♥ ✴✴✇✐t❤ ✈❛❧✉❡ ① < ② ✇❤✐❝❤ ✐s ✴✴❛ss✐❣♥❡❞ t♦ ❛ ✐ ✰❂ ❥ ❂ ✐♥❝ ✴✴❛❧♠♦st ❧✐❦❡ ✐ ❂ ✭❥ ❂ ✐ ✰ ✐♥❝✮

❈ ■♥tr♦❞✉❝t✐♦♥

slide-6
SLIDE 6

❖♣❡r❛t♦r Pr❡❝❡❞❡♥❝❡

❆r♦✉♥❞ ✶✺ ❧❡✈❡❧s ♦❢ ♦♣❡r❛t♦r ♣r❡❝❡❞❡♥❝❡✳ ❆❧❧ ♦♣❡r❛t♦rs ❡①❝❡♣t ❛ss✐❣♥♠❡♥t ♦♣❡r❛t♦rs ❛r❡ ❧❡❢t✲❛ss♦❝✐❛t✐✈❡❀ ❆♥ ♦♣❡r❛t♦r ⊕ ✐s ❧❡❢t✲❛ss♦❝✐❛t✐✈❡ ✐❢ ❆ ⊕ ❇ ⊕ ❈ = (❆ ⊕ ❇) ⊕ ❈✳ Pr❡❝❡❞❡♥❝❡ ❢♦r ♠♦st ♦♣❡r❛t♦rs ❡①❝❡♣t ❜✐t✇✐s❡ ♦♣❡r❛t♦rs ✐s ♣r❡tt② ♥❛t✉r❛❧✱ ❜✉t ✇❤❡♥ ✐♥ ❞♦✉❜t ✉s❡ ♣❛r❡♥t❤❡s❡s t♦ ❞✐s❛♠❜✐❣✉❛t❡✳ ❛ ✰ ❢✭❜✮✯❝ ✲❞ ✴✴✭❛ ✰ ✭❢✭❜✮✯❝✮✮ ✲ ❞ ❛ < ❜ ✫✫ ❜ ❂❂ ❝ ✴✴✭❛ < ❜✮ ✫✫ ✭❜ ❂❂ ❝✮ ❛ ❂ ❜ << ♥ ✰ ✶ ✴✴❛ ❂ ✭❜ << ✭♥ ✰ ✶✮✮ ❛ ✰ ❜ << ♥ ✴✴✭❛ ✰ ❜✮ << ♥ ❛ ❂❂ ❜ ✫ ❝ ✴✴✭❛ ❂❂ ❜✮ ✫ ❝

❈ ■♥tr♦❞✉❝t✐♦♥

slide-7
SLIDE 7

❈ ❙t❛t❡♠❡♥ts

❙t❛t❡♠❡♥ts ❞♦ ♥♦t ❤❛✈❡ ❛ ✈❛❧✉❡ ✭♥♦t❡ t❤❛t s♦♠❡ ♣r♦❣r❛♠♠✐♥❣ ❧❛♥❣✉❛❣❡s ❞♦ ♥♦t ❤❛✈❡ st❛t❡♠❡♥ts✮✳ ❙t❛t❡♠❡♥ts ✐♥❝❧✉❞❡✿ ❉❡❝❧❛r❛t✐♦♥ st❛t❡♠❡♥t ❛ss♦❝✐❛t❡s ❛ t②♣❡ ✇✐t❤ ❛ ✈❛r✐❛❜❧❡✳ ❆ ✈❛r✐❛❜❧❡ ✐s ❛ ♥❛♠❡ ❢♦r ❛ ❜❧♦❝❦ ♦❢ ♠❡♠♦r②✳ ✐♥t s✉♠ ❂ ✵❀ ✴✴✐♥✐t✐❛❧✐③❡r ❡①♣r❡ss✐♦♥ ❞♦✉❜❧❡ ❛❝❝❀ ✴✴♥♦ ✐♥✐t✐❛❧✐③❡r❀ ❞✐s❝♦✉r❛❣❡❞ ❆ss✐❣♥♠❡♥t st❛t❡♠❡♥t ✐s ❛♥ ❛ss✐❣♥♠❡♥t ❡①♣r❡ss✐♦♥ t❡r♠✐♥❛t❡❞ ❜② ❛ s❡♠✐✲❝♦❧♦♥✳ ❛ ❂ ❜ ❂ ① < ②❀ ✐ ✰❂ ❥ ❂ ✐♥❝❀

❈ ■♥tr♦❞✉❝t✐♦♥

slide-8
SLIDE 8

❈ ❙t❛t❡♠❡♥ts ❈♦♥t✐♥✉❡❞

❈♦♥❞✐t✐♦♥❛❧ ✐❢ st❛t❡♠❡♥ts✳ ✐❢ ✭❛ < ❜✮ ④ ① ✰❂ ✷❀ ② ✯❂ ✸❀ ⑥ ❡❧s❡ ④ ① ❂ ② ❂ ✵❀ ⑥ ✐❢ ✭❝♦♥❞✮ ① ✰❂ ✶❀ ✴✴♥♦ ❡❧s❡ ■♥st❡❛❞ ♦❢ ✐❢ ✭❝♦♥❞✮ ① ❂ ❡①♣r✶ ❡❧s❡ ① ❂ ❡①♣r✷❀ ✉s❡ ❄✿ t❡r♥❛r② ♦♣❡r❛t♦r ❡①♣r❡ss✐♦♥ ① ❂ ✭❝♦♥❞✮ ❄ ❡①♣r✶ ✿ ❡①♣r✷❀

❈ ■♥tr♦❞✉❝t✐♦♥

slide-9
SLIDE 9

❈ ❙t❛t❡♠❡♥ts ❈♦♥t✐♥✉❡❞

▼✉❧t✐✇❛② ❜r❛♥❝❤ ✉s✐♥❣ ❛ s✇✐t❝❤ st❛t❡♠❡♥t✳ ❯s✉❛❧❧② ♠✉st ❤❛✈❡ ❛ ❜r❡❛❦ ❢♦r ❡❛❝❤ ❝❛s❡✳ s✇✐t❝❤ ✭① ✪ ✶✺✮ ④ ✴✴❧♦♦❦ ❛t ❧❛st ✹ ❜✐ts ♦❢ ① ❝❛s❡ ✵✿ s✉♠ ✰❂ ✷✵❀ ❜r❡❛❦❀ ❝❛s❡ ✹✿ s✉♠ ✰❂ ✷✷❀ ✴✴♥♦ ❜r❡❛❦✿ ✇✐❧❧ ❢❛❧❧ t❤r✉ t♦ ♥❡①t ❝❛s❡ ❝❛s❡ ✼✿ ♣r♦❞ ✯❂ ✸❀ ❞❡❢❛✉❧t✿ s✉♠ ✰❂ ✸❀ ♣r♦❞ ✯❂ ✷❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-10
SLIDE 10

❈ ❙t❛t❡♠❡♥ts ❈♦♥t✐♥✉❡❞

■t❡r❛t✐✈❡✱ ✐✳❡✳ ❧♦♦♣✐♥❣ st❛t❡♠❡♥ts ✐♥❝❧✉❞❡ ✭✐♥ ❞❡❝r❡❛s✐♥❣ ♦r❞❡r ♦❢ ♣r❡❢❡r❡♥❝❡✮✿ ❢♦r ❧♦♦♣✿ ❜♦❞② ♥♦t ❡①❡❝✉t❡❞ ❛t ❛❧❧ ✐❢ ❝♦♥❞✐t✐♦♥ ✐♥✐t✐❛❧❧② ❢❛❧s❡✳ ✴✴s✉♠ ❡❧❡♠❡♥ts ♦❢ ❛rr❛② ❛❬♥❪ ❢♦r ✭✐♥t ✐ ❂ ✵❀ ✐ < ♥❀ ✐✰✰✮ s✉♠ ✰❂ ❛❬✐❪❀ ❞♦✲ ✇❤✐❧❡ ❧♦♦♣❀ ❜♦❞② ❡①❡❝✉t❡❞ ❛t ❧❡❛st ♦♥❝❡✳ ◆♦t ✇✐❞❡❧② ✉s❡❞✳ ✴✴❢✭✮ ❝❛❧❧❡❞ ❛t ❧❡❛st ♦♥❝❡ ❞♦ ④ s ✰❂ ❢✭①✮❀ ⑥ ✇❤✐❧❡ ✭s < ❧✐♠✐t✮❀ ✇❤✐❧❡ ❧♦♦♣✿ ❜♦❞② ♥♦t ❡①❡❝✉t❡❞ ❛t ❛❧❧ ✐❢ ❝♦♥❞✐t✐♦♥ ✐♥✐t✐❛❧❧② ❢❛❧s❡✳ ✴✴✜♥❞ ✜①❡❞ ♣♦✐♥t ♦❢ ❢✉♥❝t✐♦♥ ❢✭✮ ✇❤✐❧❡ ✭❢✭❛✮ ✦❂ ❛✮ ❛ ❂ ❢✭❛✮❀

❈ ■♥tr♦❞✉❝t✐♦♥

slide-11
SLIDE 11

❉❛t❛

■♥ ❛♥② ♣r♦❣r❛♠♠✐♥❣ ❧❛♥❣✉❛❣❡ t❤❡r❡ ❛r❡ t✇♦ ❦✐♥❞s ♦❢ ❞❛t❛✿ Pr✐♠✐t✐✈❡ ❉❛t❛ ❉❛t❛ ✇❤✐❝❤ ❤❛s ♥♦ ✐♥t❡r♥❛❧ str✉❝t✉r❡ ❛❞✈❡rt✐③❡❞ ❜② t❤❡ ❧❛♥❣✉❛❣❡✳ ■♥ ❈✱ t❤✐s ✐♥❝❧✉❞❡s ✈❛r✐♦✉s ✢❛✈♦rs ♦❢ ✐♥t❡❣❡rs ❛♥❞ r❡❛❧ ♥✉♠❜❡rs ❛s ✇❡❧❧ ❛s ♣♦✐♥t❡rs ✭❈ ❞♦❡s ❛❧s♦ ❛❧❧♦✇ ❣❡tt✐♥❣ ❛t t❤❡ ✐♥t❡r♥❛❧ str✉❝t✉r❡✱ ❜✉t t❤✐s ✐s ❛ ❧♦✇✲❧❡✈❡❧ ❢❡❛t✉r❡✮✳ ❈♦♠♣♦s✐t❡ ❉❛t❛ ❉❛t❛ ✇❤✐❝❤ ✐s ❛ ❝♦❧❧❡❝t✐♦♥ ♦❢ ♦t❤❡r ❞❛t❛✳ ■♥ ❈✱ t❤✐s ✐♥❝❧✉❞❡s ❛rr❛②s ✭s❡q✉❡♥❝❡ ♦❢ ❞❛t❛ ♦❢ t❤❡ s❛♠❡ t②♣❡✮ ❛♥❞ str✉❝t✉r❡s✴✉♥✐♦♥s ✭❝♦❧❧❡❝t✐♦♥s ♦❢ ❞❛t❛ ♦❢ ♣♦ss✐❜❧② ❞✐✛❡r❡♥t t②♣❡s✮✳ ❯❧t✐♠❛t❡❧②✱ ❛❧❧ ❞❛t❛ ❡♥t✐t✐❡s ❛r❡ r❡♣r❡s❡♥t❡❞ ❛s ❛ s❡q✉❡♥❝❡ ♦❢ ❜②t❡s✳ ■♥ ❈✱ t❤❡ ♥✉♠❜❡r ♦❢ ❜②t❡s t❛❦❡♥ ✉♣ ❜② ❛♥② ❞❛t❛ ❡♥t✐t② ① ✐s ❣✐✈❡♥ ❜② t❤❡ ❡①♣r❡ss✐♦♥ s✐③❡♦❢✭①✮✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-12
SLIDE 12

❈ ■♥t❡❣❡rs

❱❛r✐♦✉s ✢❛✈♦rs ♦❢ ✐♥t❡❣❡rs ✭✐♥ ♦r❞❡r ♦❢ ♥♦♥✲❞❡❝r❡❛s✐♥❣ s✐③❡✮✿ s❤♦rt ❆t ❧❡❛st ✷ ❜②t❡s✳ ✐♥t ❆t ❧❡❛st ✷ ❜②t❡s✱ ❝❛♥ ❜❡ ✹ ♦r ✽ ❞❡♣❡♥❞✐♥❣ ♦♥ ♠❛❝❤✐♥❡✳ ❧♦♥❣ ❆t ❧❡❛st ✹ ❜②t❡s✱ ❝❛♥ ❜❡ ✽ ❞❡♣❡♥❞✐♥❣ ♦♥ ♠❛❝❤✐♥❡✳ ❧♦♥❣ ❧♦♥❣ ❆t ❧❡❛st ✽ ❜②t❡s✳ ❈❛♥ ❤❛✈❡ ♠♦❞✐✜❡r s✐❣♥❡❞ ♦r ✉♥s✐❣♥❡❞✳ ❉❡❢❛✉❧t ✐s s✐❣♥❡❞✳ ■❢ ✉♥s✐❣♥❡❞ ✉s❡❞ ✇✐t❤♦✉t ❛ t②♣❡✱ t❤❡♥ t②♣❡ ✐s ✐♥t✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-13
SLIDE 13

■♥t❡❣❡r ❉❡❝❧❛r❛t✐♦♥s ✇✐t❤ ■♥✐t✐❛❧✐③❡rs

✴✴s✐❣♥❡❞ ❜② ❞❡❢❛✉❧t s❤♦rt ❛♥s✇❡r ❂ ✹✷❀ ✴✴s✐❣♥❡❞✿ ✉s✉❛❧❧② ✷ ❜②t❡s ✐♥t ♥❡①t ❂ ❛♥s✇❡r ✰ ✶❀ ✴✴s✐❣♥❡❞✿ ♦❢t❡♥ ✹ ❜②t❡s ❧♦♥❣ t✇✐❝❡ ❂ ✷ ✯ ❛♥s✇❡r❀ ✴✴✹ ♦r ✽ ❜②t❡s ❧♦♥❣ ❧♦♥❣ ❤❛❧❢ ❂ ❛♥s✇❡r✴✷❀ ✴✴❛t ❧❡❛st ✽ ❜②t❡s ❧♦♥❣ ✈❛❧✉❡ ❂ ✾✾▲❀ ✴✴✉s❡ ♦❢ ❛ ❧♦♥❣ ❧✐t❡r❛❧ ✴✴❡①♣❧✐❝✐t❧② ❞❡❝❧❛r❡❞ ✉♥s✐❣♥❡❞ ✉♥s✐❣♥❡❞ s❤♦rt s✶ ❂ ✷✷❀ ✉♥s✐❣♥❡❞ s❤♦rt s✷ ❂ ✶ << ✶✺❀ ✴✴♦❦ ✉♥s✐❣♥❡❞ s❤♦rt s✸ ❂ ✶ << ✶✻❀ ✴✴♠❛② ♦✈❡r✢♦✇ ✉♥s✐❣♥❡❞ ✉ ❂ ✾✾❀ ✴✴t②♣❡ ❞❡❢❛✉❧ts t♦ ✐♥t s❤♦rt s✹ ❂ ✶ << ✶✺❀ ✴✴s✐❣♥❡❞✿ ♠❛② ♦✈❡r✢♦✇ ✴✴t♦ ♥❡❣❛t✐✈❡

❈ ■♥tr♦❞✉❝t✐♦♥

slide-14
SLIDE 14

❈❤❛r❛❝t❡rs ✐♥ ❈

❈ ❞♦❡s ♥♦t r❡❛❧❧② s✉♣♣♦rt ❝❤❛r❛❝t❡rs ♦r str✐♥❣s✳ ❆ ✈❛r✐❛❜❧❡ ❞❡❝❧❛r❡❞ ✇✐t❤ t②♣❡ ❝❤❛r✱ ✐s ❞❡❝❧❛r✐♥❣ ❛ ✶✲❜②t❡ ✐♥t❡❣❡r✳ ■❢ ❛ ✈❛r✐❛❜❧❡ ✐s ❞❡❝❧❛r❡❞ ❛s ❛ ❝❤❛r✱ ✇✐t❤♦✉t ❛ s✐❣♥❡❞ ♦r ✉♥s✐❣♥❡❞ ♠♦❞✐✜❡r✱ t❤❡♥ ✐t✬s s✐❣♥❡❞✲♥❡ss ✐s ✉♥❞❡✜♥❡❞✳ ❈ ❞♦❡s s✉♣♣♦rt ❝❤❛r❛❝t❡r ❧✐t❡r❛❧s ❡♥❝❧♦s❡❞ ✇✐t❤✐♥ s✐♥❣❧❡ q✉♦t❡s✳ ❚❤❡s❡ ✐♥t❡❣❡r ✈❛❧✉❡ ❡q✉❛❧ t♦ ❝♦❞❡ ♦❢ ❝❤❛r❛❝t❡r ✐♥ t❤❡ ❧♦❝❛❧ ❝❤❛r❛❝t❡r ❡♥❝♦❞✐♥❣ ✭❢♦r ❡①❛♠♣❧❡✱ ✬❆✬ ❤❛s ✐♥t❡❣❡r ✈❛❧✉❡ ✻✺ ✐♥ t❤❡ ❆❙❈■■ ❡♥❝♦❞✐♥❣✮✳ ❈❤❛r❛❝t❡r ❧✐t❡r❛❧s s✉♣♣♦rt ❡s❝❛♣❡s ❛s ✐♥ ✬❭♥✬ ♥❡✇❧✐♥❡✱ ✬❭t✬ t❛❜ ❛♥❞ ✬❭✵✬ ◆❯▲ ❝❤❛r❛❝t❡r✳ ❙✐♥❝❡ ❝❤❛r❛❝t❡rs ❛r❡ ♠❡r❡❧② ✐♥t❡❣❡rs✱ ❛r✐t❤♠❡t✐❝ ❝❛♥ ❜❡ ♣❡r❢♦r♠❡❞ ✇✐t❤ t❤❡♠ ❛s ✐♥ ❝❤❛r ❝❀ ✳✳✳ ❝ ✲ ✬✵✬✱ ❜✉t t❤❡ r❡s✉❧ts ❛r❡ ♥♦t ♣♦rt❛❜❧❡ ✐♥ t❤❛t t❤❡② ♠❛② ✈❛r② ✇✐t❤ ❞✐✛❡r❡♥t ❝❤❛r❛❝t❡r ❡♥❝♦❞✐♥❣s✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-15
SLIDE 15

❈❤❛r ❉❡❝❧❛r❛t✐♦♥s

❈❤❛rs ❛r❡ ❛❧✇❛②s ✶ ❜②t❡✳ ❝❤❛r ❝✶ ❂ ✬❆✬❀ ✴✴✻✺ ✐♥ ❆❙❈■■ ❝❤❛r ❝✷ ❂ ✬❇✬❀ ✴✴✻✻ ✐♥ ❆❙❈■■ ❝❤❛r ❝✸ ❂ ❝✶ ✰ ✶❀ ✴✴s❛♠❡ ✈❛❧✉❡ ❛s ❝✷✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-16
SLIDE 16

❈ ❆rr❛②s

❆rr❛②s ❛r❡ ❛ ❢✉♥❞❛♠❡♥t❛❧ ❛❜str❛❝t✐♦♥ ✐♥ ♠❛♥② ♣r♦❣r❛♠♠✐♥❣ ❧❛♥❣✉❛❣❡s ✇❤✐❝❤ ❛❜str❛❝t ♦✉t t❤❡ r❛♥❞♦♠✲❛❝❝❡ss ♣r♦♣❡rt② ♦❢ t❤❡ ♠❛✐♥ ♠❡♠♦r② ✐♥ ❝✉rr❡♥t ❝♦♠♣✉t❡r t❡❝❤♥♦❧♦❣②✳ ■♥ ❈✱ ❛rr❛②s ❛r❡ ❞❡❝❧❛r❡❞ ✉s✐♥❣ sq✉❛r❡ ❜r❛❝❦❡ts ❛❢t❡r t❤❡ ♥❛♠❡ ♦❢ t❤❡ ❛rr❛②✳ ✐♥t ❛❬✸❪❀ ✐♥t ❜❬❪ ❂ ④ ✶✱ ✷✱ ✸ ⑥❀ ❊♠♣❧♦②❡❡ ❡♠♣❧♦②❡❡s❬♥✉♠❊♠♣❧♦②❡❡s❪❀ ❆ ❈ str✐♥❣ ✐s ❛♥ ❛rr❛② ♦❢ ❝❤❛r❛❝t❡rs t❡r♠✐♥❛t❡❞ ❜② ❛ ◆❯▲ ❝❤❛r❛❝t❡r ✬❭✵✬✳ ❝❤❛r ❤❡❧❧♦❬❪ ❂ ✧❤❡❧❧♦✧❀ ✴✴❛rr❛② ♦❢ ✻ ❝❤❛r✬s ❈ ❛rr❛②s ❛r❡ ❝❧♦s❡❧② r❡❧❛t❡❞ t♦ ♣♦✐♥t❡rs ✭♠♦r❡ ❛❜♦✉t t❤❛t ❧❛t❡r✮✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-17
SLIDE 17

■♥t❡❣❡r ❙✉♠ Pr♦❣r❛♠

■♥ s✉♠✳❝✿ ★✐♥❝❧✉❞❡ <st❞✐♦✳❤> st❛t✐❝ ✐♥t ❛❝❝ ❂ ✶✷✸❀ ✐♥t ♠❛✐♥✭✮ ④ ✐♥t ✈❛❧✉❡s❬❪ ❂ ④ ✷✱ ✺✱ ✲✾✱ ⑥❀ ❢♦r ✭✉♥s✐❣♥❡❞ ✐ ❂ ✵❀ ✐ < s✐③❡♦❢✭✈❛❧✉❡s✮✴s✐③❡♦❢✭✈❛❧✉❡s❬✵❪✮❀ ✐✰✰✮ ④ ✐♥t ✈❛❧✉❡ ❂ ✈❛❧✉❡s❬✐❪❀ ❛❝❝ ✰❂ ✈❛❧✉❡❀ ⑥ ♣r✐♥t❢✭✧✪❞\♥✧✱ ❛❝❝✮❀ r❡t✉r♥ ✵❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-18
SLIDE 18

■♥t❡❣❡r ❙✉♠ Pr♦❣r❛♠ ▲♦❣

❈♦♠♣✐❧✐♥❣✿ ✩ ❣❝❝ ✲❣ ✲❲❛❧❧ ✲st❞❂❝✶✶ s✉♠✳❝ ✲♦ s✉♠ ✲❣ ❛❧❧♦✇s ❞❡❜✉❣❣✐♥❣ ❝♦♠♣✐❧❡❞ ♣r♦❣r❛♠✳ ✲❲❛❧❧ ✉s❡❞ ❢♦r t✉r♥✐♥❣ ♦♥ r❡❛s♦♥❛❜❧❡ ✇❛r♥✐♥❣s✳ ✲st❞❂❝✶✶ ❛❧❧♦✇s ✉s❡ ♦❢ ❈✶✶ ❢❡❛t✉r❡s✳ ✲♦ s✉♠ ❝r❡❛t❡s ❡①❡❝✉t❛❜❧❡ ✐♥ ✜❧❡ s✉♠ ✭❞❡❢❛✉❧t ✐s ❛✳♦✉t✮✳ ❘✉♥ ✉s✐♥❣✿ ✩ ✳✴s✉♠ ✶✷✶ ✩

❈ ■♥tr♦❞✉❝t✐♦♥

slide-19
SLIDE 19

■♥t❡❣❡r ❙✉♠ Pr♦❣r❛♠ ❉✐s❝✉ss✐♦♥

❛❝❝ ✐s ❞❡❝❧❛r❡❞ ♦✉ts✐❞❡ ♦❢ ❛♥② ❢✉♥❝t✐♦♥✳ ■t ✐s ❧♦♦s❡❧② r❡❢❡rr❡❞ t♦ ❛s ❛ ❣❧♦❜❛❧ ✈❛r✐❛❜❧❡✳ ❱❛r✐❛❜❧❡s ❞❡❝❧❛r❡❞ ♦✉ts✐❞❡ ❛♥② ❢✉♥❝t✐♦♥ ❤❛✈❡ ❧✐❢❡t✐♠❡ ❡q✉❛❧ t♦ t❤❛t ♦❢ t❤❡ ❡♥t✐r❡ ♣r♦❣r❛♠✳ ■❢ ❛ ✈❛r✐❛❜❧❡ ✐s ❞❡❝❧❛r❡❞ ✇✐t❤ t❤❡ st❛t✐❝ q✉❛❧✐✜❡r✱ t❤❡♥ ✐t ❤❛s ❧✐❢❡t✐♠❡ ❡q✉❛❧ t♦ t❤❛t ♦❢ t❤❡ ❡♥t✐r❡ ♣r♦❣r❛♠ ❜✉t ✐s ✈✐s✐❜❧❡ ♦♥❧② t♦ t❤❡ s✉❜s❡q✉❡♥t ❝♦❞❡ ✐♥ t❤❡ s❛♠❡ ❝♦♠♣✐❧❛t✐♦♥ ✉♥✐t ✭✜❧❡✮✳ ■❢ ❛ ✈❛r✐❛❜❧❡ ✐s ❞❡❝❧❛r❡❞ ✇✐t❤ t❤❡ ❡①t❡r♥ q✉❛❧✐✜❡r✱ t❤❡♥ ✐t ❤❛s ❧✐❢❡t✐♠❡ ❡q✉❛❧ t♦ t❤❛t ♦❢ t❤❡ ❡♥t✐r❡ ♣r♦❣r❛♠ ❛♥❞ ✐s ✈✐s✐❜❧❡ t♦ t❤❡ ❡♥t✐r❡ ♣r♦❣r❛♠✳ ■❢ t❤❡r❡ ✐s ♥♦ st❛t✐❝ s♣❡❝✐✜❡r✱ t❤❡♥ t❤❡ ❞❡❝❧❛r❛t✐♦♥ ❞❡❢❛✉❧ts t♦ ❜❡ ❡①t❡r♥✳ ■♥ ❝✉rr❡♥t ♣r♦❣r❛♠♠✐♥❣ ♣r❛❝t✐❝❡✱ ❣❧♦❜❛❧ ✈❛r✐❛❜❧❡s ❛r❡ r❡❣❛r❞❡❞ ❛s ❡✈✐❧ ❛♥❞ s❤♦✉❧❞ ❜❡ ❛✈♦✐❞❡❞ ❛s ❢❛r ❛s ♣♦ss✐❜❧❡✳ ❘❡❛❞✲♦♥❧② ❣❧♦❜❛❧s ❛r❡ ♥♦t ❛s ❜❛❞ ❛s r❡❛❞✲✇r✐t❡ ❣❧♦❜❛❧s✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-20
SLIDE 20

■♥t❡❣❡r ❙✉♠ Pr♦❣r❛♠ ❉✐s❝✉ss✐♦♥ ❈♦♥t✐♥✉❡❞

❱❛r✐❛❜❧❡s ❞❡❝❧❛r❡❞ ✇✐t❤✐♥ ❛ ❜r❛❝❡✲❞❡❧✐♠✐t❡❞ ❜❧♦❝❦ ❛r❡ ✈✐s✐❜❧❡ ♦♥❧② ✇✐t❤✐♥ t❤❛t ❜❧♦❝❦ ❛♥❞ ✭✐❢ t❤❡r❡ ✐s ♥♦ st❛t✐❝ q✉❛❧✐✜❡r✮ r❡t❛✐♥ t❤❡✐r ✈❛❧✉❡ ♦♥❧② ❞✉r✐♥❣ ❛ s✐♥❣❧❡ ❡①❡❝✉t✐♦♥ ♦❢ t❤❛t ❜❧♦❝❦✳ ❙♣❡❝✐✜❝❛❧❧②✱ ✈❛r✐❛❜❧❡s ❞❡❝❧❛r❡❞ ✇✐t❤✐♥ ❛ ❢✉♥❝t✐♦♥ ❛r❡ ✈✐s✐❜❧❡ ♦♥❧② ✇✐t❤✐♥ t❤❛t ❢✉♥❝t✐♦♥ ❛♥❞ ✭✐❢ t❤❡r❡ ✐s ♥♦ st❛t✐❝ q✉❛❧✐✜❡r✮ r❡t❛✐♥ t❤❡✐r ✈❛❧✉❡ ♦♥❧② ❞✉r✐♥❣ ❛ s✐♥❣❧❡ ❛❝t✐✈❛t✐♦♥ ♦❢ t❤❛t ❢✉♥❝t✐♦♥✳ ❚❤❡s❡ ❦✐♥❞ ♦❢ ❛✉t♦✲✈❛r✐❛❜❧❡s ❛r❡ ✐♥✈❛❧✉❛❜❧❡ ✐♥ ✐♠♣❧❡♠❡♥t✐♥❣ r❡❝✉rs✐✈❡ ❢✉♥❝t✐♦♥s ✇❤❡r❡ ♠✉❧t✐♣❧❡ ❛❝t✐✈❛t✐♦♥s ♦❢ ❛ ❢✉♥❝t✐♦♥ ❛r❡ ❛❧✐✈❡ s✐♠✉❧t❛♥❡♦✉s❧②✳ ✐♥t ❢❛❝t♦r✐❛❧✭✐♥t ♥✮ ④ r❡t✉r♥ ✭♥ <❂ ✵✮ ❄ ✶ ✿ ♥ ✯ ❢❛❝t♦r✐❛❧✭♥ ✲ ✶✮❀ ⑥ ✴✴❢❛❝t♦r✐❛❧✭✹✮✿ ♥ ❤❛s ✈❛❧✉❡s ✹✱ ✸✱ ✷✱ ✶✱ ✵✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-21
SLIDE 21

■♥t❡❣❡r ❙✉♠ Pr♦❣r❛♠ ❉✐s❝✉ss✐♦♥ ❈♦♥t✐♥✉❡❞

❯s✉❛❧❧②✱ ❜❡st ♣r❛❝t✐❝❡ ✐s t♦ ❛❧✇❛②s ♣r♦✈✐❞❡ ❛♥ ✐♥✐t✐❛❧ ✈❛❧✉❡ ❢♦r ❛ ✈❛r✐❛❜❧❡ ✇❤❡♥ ✐t ✐s ❞❡❝❧❛r❡❞✳ ❆rr❛② ✈❛❧✉❡s❬❪ ✐s ✐♥✐t✐❛❧✐③❡❞ ✇✐t❤ ✐♥✐t✐❛❧ ✈❛❧✉❡s ❡♥❝❧♦s❡❞ ✇✐t❤✐♥ ❜r❛❝❡s✳ ❈♦✉❧❞ ❛❧s♦ ❜❡ ❞❡❝❧❛r❡❞ ❛s ✐♥t ✈❛❧✉❡s❬✸❪ ❂ ④ ✷✱ ✺✱ ✲✾ ⑥❀ ❜✉t t❤❡ s✐③❡ ✇♦✉❧❞ ❜❡ r❡❞✉♥❞❛♥t✳ ❇❡st ♣r❛❝t✐❝❡ ✐s t♦ ♦♠✐t t❤❡ s✐③❡ ♦❢ t❤❡ ❛rr❛② ❛♥❞ ❧❡t ✐t ❜❡ ❞❡t❡r♠✐♥❡❞ ❜② t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ✐♥✐t✐❛❧✐③❡r✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-22
SLIDE 22

■♥t❡❣❡r ❙✉♠ Pr♦❣r❛♠ ❉✐s❝✉ss✐♦♥ ❈♦♥t✐♥✉❡❞

❙✐♥❝❡ t❤❡ ❛rr❛② ✈❛❧✉❡s❬❪ ❤❛s ✸ ❡❧❡♠❡♥ts✱ ✇❡ ❝♦✉❧❞ ❤❛✈❡ ❝♦❞❡❞ t❤❡ ❢♦r✲❧♦♦♣ ❛s✿ ❢♦r ✭✐♥t ✐ ❂ ✵❀ ✐ < ✸❀ ✐✰✰✮ ④ ✳✳✳ ⑥ ■❢ ✇❡ ❞❡❝✐❞❡❞ t♦ ❛❞❞ ❛♥♦t❤❡r ❡❧❡♠❡♥t t♦ ✈❛❧✉❡s❬❪✱ ✇❡ ✇♦✉❧❞ ❛❧s♦ ♥❡❡❞ t♦ ❝❤❛♥❣❡ t❤❡ ❧♦♦♣ ❜♦✉♥❞ t♦ ✹✳ ❆ ✈❡r② ✐♠♣♦rt❛♥t r✉❧❡ ✐♥ ♣r♦❣r❛♠♠✐♥❣ ✐s ❉♦♥✬t ❘❡♣❡❛t ❨♦✉rs❡❧❢ ✭❉❘❨✮✳ ❙♣❡❝✐✜❝❛❧❧②✱ ②♦✉ s❤♦✉❧❞ ❛✈♦✐❞ s✐t✉❛t✐♦♥s ✇❤❡r❡ ❝❤❛♥❣✐♥❣ ♦♥❡ ♣❛rt ♦❢ ❛ ♣r♦❣r❛♠ ♥❡❝❡ss❛r✐❧② r❡q✉✐r❡s ❝❤❛♥❣✐♥❣ ❛♥♦t❤❡r ♣❛rt ❜❡❝❛✉s❡ t❤❡ s❡❝♦♥❞ ♣❛rt ❞❡♣❡♥❞s ♦♥ t❤❡ ✜rst ♣❛rt✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-23
SLIDE 23

■♥t❡❣❡r ❙✉♠ Pr♦❣r❛♠ ❉✐s❝✉ss✐♦♥ ❈♦♥t✐♥✉❡❞

❚❤❡ ✉s❡ ♦❢ t❤❡ ❝♦♠♣❧❡① ❡①♣r❡ss✐♦♥ s✐③❡♦❢✭✈❛❧✉❡s✮✴s✐③❡♦❢✭✈❛❧✉❡s❬✵❪✮ ❛✈♦✐❞s ❛ ❉❘❨ ✈✐♦❧❛t✐♦♥✳ ❚❤❡ ❡①♣r❡ss✐♦♥ s✐③❡♦❢✭✈❛❧✉❡s✮ ❣✐✈❡s t❤❡ t♦t❛❧ ♥✉♠❜❡r ♦❢ ❜②t❡s ♦❝❝✉♣✐❡❞ ❜② t❤❡ ✈❛❧✉❡s❬❪ ❛rr❛② ❛♥❞ s✐③❡♦❢✭✈❛❧✉❡s❬✵❪✮ ❣✐✈❡s t❤❡ t♦t❛❧ ♥✉♠❜❡r ♦❢ ❜②t❡s ♦❝❝✉♣✐❡❞ ❜② t❤❡ ✈❛❧✉❡s❬✵❪ ❡❧❡♠❡♥t✳ ❍❡♥❝❡ t❤❡ q✉♦t✐❡♥t ❣✐✈❡s t❤❡ ♥✉♠❜❡r ♦❢ ❡❧❡♠❡♥ts ✐♥ t❤❡ ✈❛❧✉❡s❬❪ ❛rr❛②✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-24
SLIDE 24

■♥t❡❣❡r ❘❡♣r❡s❡♥t❛t✐♦♥

❚❤❡ ❈ ✐♥t❡❣❡r t②♣❡s ❝❛♥ ❜❡ r❡❣❛r❞❡❞ ❛s ❛❜str❛❝t t②♣❡s ✇❤✐❝❤ ♠♦❞❡❧ ❛ ✜♥✐t❡ s✉❜s❡t ♦❢ t❤❡ ✐♥✜♥✐t❡ s❡t ♦❢ ❛❧❧ ✐♥t❡❣❡rs✳ ❚❤❡s❡ ❛❜str❛❝t t②♣❡s ♣❡r♠✐ts t❤❡ ✉s✉❛❧ ❛r✐t❤♠❡t✐❝ ♦♣❡r❛t✐♦♥s ✰✱ ✲✱ ✯✱ ✴✱ ✪✱ ✇✐t❤ r❡s✉❧ts ❝♦♥s✐st❡♥t ✇✐t❤ ✉s✉❛❧ ❛r✐t❤♠❡t✐❝ ✭s✉❜❥❡❝t t♦ s✐③❡ r❡str✐❝t✐♦♥s✮✳ ❍♦✇❡✈❡r✱ ❈ ❤❛s ♦♣❡r❛t♦rs ❧✐❦❡ ❜✐t✇✐s❡✲❛♥❞ ✫✱ ❜✐t✇✐s❡✲♦r ⑤✱ ❧❡❢t✲s❤✐❢t ❁❁ ❛♥❞ r✐❣❤t✲s❤✐❢t ❃❃ ✐♥ ✇❤✐❝❤ t❤❡ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ✐♥t❡❣❡rs ✐s ♥♦ ❧♦♥❣❡r ❛❜str❛❝t✳ ❙♦ ✐t ✐s ♥❡❝❡ss❛r② t♦ ✉♥❞❡rst❛♥❞ t❤❡ ✐♥t❡r♥❛❧ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ✐♥t❡❣❡rs✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-25
SLIDE 25

❉❡❝✐♠❛❧ P♦s✐t✐♦♥❛❧ ◆♦t❛t✐♦♥

■♥ ♣♦s✐t✐♦♥❛❧ ♥♦t❛t✐♦♥✱ t❤❡ ✈❛❧✉❡ ♦❢ ❛ ❞✐❣✐t ❞❡♣❡♥❞s ♦♥ ✐ts ♣♦s✐t✐♦♥ ✐♥ t❤❡ ♥✉♠❜❡r✳ ❙♣❡❝✐✜❝❛❧❧②✱ ❛ ❞❡❝✐♠❛❧ ✐♥t❡❣❡r ❞♥−✶❞♥−✷ . . . ❞✶❞✵ r❡♣r❡s❡♥ts t❤❡ ♥✉♠❜❡r✿ ✶✵♥−✶ × ❞♥−✶ + ✶✵♥−✷ × ❞♥−✷ + . . . + ✶✵✶ × ❞✶ + ✶✵✵ × ❞✵ ❋♦r ❡①❛♠♣❧❡✱ ✶✷✸ == ✶ × ✶✵✷ + ✷ × ✶✵✶ + ✸ × ✶✵✵ P♦s✐t✐♦♥❛❧ ♥♦t❛t✐♦♥ ✐s ❛ ❜✐❣ ✇✐♥ ♦✈❡r ❛❞❞✐t✐✈❡ ♥♦t❛t✐♦♥s ❧✐❦❡ ❘♦♠❛♥ ♥✉♠❡r❛❧s ❛s t❤❡ ✈❛❧✉❡ ♦❢ ❛ r❡♣r❡s❡♥t❡❞ ♥✉♠❜❡r ✐♥❝r❡❛s❡s ❡①♣♦♥❡♥t✐❛❧❧② ✇✐t❤ t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ r❡♣r❡s❡♥t❛t✐♦♥✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-26
SLIDE 26

P♦s✐t✐♦♥❛❧ ◆♦t❛t✐♦♥ ❢♦r ❛ ●❡♥❡r❛❧ ❇❛s❡

❋♦r ❛ ❣❡♥❡r❛❧ ❜❛s❡ ❇ ❛♥❞ ❞✐❣✐ts ✵, ✶, . . . ❇ − ✶ ✐♥ ❜❛s❡✲❇✱ t❤❡ ✈❛❧✉❡ ♦❢ ❛♥ ♥✲❞✐❣✐t ✐♥t❡❣❡r ❜♥−✶❜♥−✷ . . . ❜✶❜✵ ✐♥ ❜❛s❡✲❇ ✐s ❣✐✈❡♥ ❜②✿ ❇♥−✶ × ❜♥−✶ + ❇♥−✷ × ❜♥−✷ + . . . + ❇✶ × ❜✶ + ❇✵ × ❜✵ ❊①❛♠♣❧❡s✿ ❇❛s❡ ✷ ❜✐♥❛r② ✶✵✶✵ = ✶ × ✷✸ + ✵ × ✷✷ + ✶ × ✷✶ + ✵ × ✷✵ = ✻✳ ❇❛s❡ ✶✻ ❤❡①❛❞❡❝✐♠❛❧ ✼✼ = ✼ × ✶✻✶ + ✼ × ✶✻✵ = ✶✶✾✳ ❇❛s❡ ✽ ♦❝t❛❧ ✼✼ = ✼ × ✽✶ + ✼ × ✽✵ = ✻✸✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-27
SLIDE 27

❈♦♠♠♦♥ ❇❛s❡s ✉s❡❞ ✐♥ Pr♦❣r❛♠♠✐♥❣

❉❡❝✐♠❛❧ ❜❛s❡ ✐s ❛❧♠♦st ❛❧✇❛②s t❤❡ ❞❡❢❛✉❧t✳ ❊①❛♠♣❧❡✿ ✼✺ ❇❛s❡✲✷ ❜✐♥❛r② ♥✉♠❜❡rs ❛r❡ ❝♦♠♠♦♥❧② ✉s❡❞ ✇✐t❤✐♥ ❝♦♠♣✉t❡rs ❜✉t ✉s✉❛❧❧② t♦♦ ✈❡r❜♦s❡ ❢♦r ❤✉♠❛♥ ✉s❡✳ ❊①❛♠♣❧❡✿ ✵✶✵✵✶✵✶✶ ❜✐♥❛r② ✇❤✐❝❤ ✐s ✼✺ ❞❡❝✐♠❛❧✳ ◆♦t ✐♥ st❛♥❞❛r❞ ❈✱ ❛✈❛✐❧❛❜❧❡ ❛s ❣❝❝ ❡①t❡♥s✐♦♥ ✵❜✵✶✵✵❴✶✵✶✶✳ ❇❛s❡✲✶✻ ❝♦♠♠♦♥❧② ✉s❡❞ ❛s ✐t ✐s ❡❛s② t♦ ❝♦♥✈❡rt t♦✴❢r♦♠ ❜✐♥❛r②✳ ❉✐❣✐ts ✵ ✳✳ ✾ ❤❛✈❡ ✉s✉❛❧ ♠❡❛♥✐♥❣s✱ ❆ ✳✳ ❋ ✭❝❛♥ ❛❧s♦ ❜❡ ❧♦✇❡r✲❝❛s❡✮ r❡♣r❡s❡♥t ✈❛❧✉❡s ✶✵ ✳✳ ✶✺✳ ❆♥ ❡①❛♠♣❧❡ ♦❢ ❛ ❈ ❤❡①❛❞❡❝✐♠❛❧ ❧✐t❡r❛❧ ✐s ✵①✹❇ ✭♦r ✵①✹❜✮ ❡q✉❛❧ t♦ ❞❡❝✐♠❛❧ ✼✺✳ ❇❛s❡✲✽ ✇❛s ✉s❡❞ ❡❛r❧✐❡r ✇❤❡♥ ✇♦r❞✲❧❡♥❣t❤s ✇❡r❡ ♠✉❧t✐♣❧❡s ♦❢ ✸ ❜✐ts ✭P❉P✲✽✿ ✶✷✲❜✐ts✮ ❜✉t ♥♦t ♣♦♣✉❧❛r ❝✉rr❡♥t❧②✳ ■♥ ❈✱ ❛♥② ✐♥t❡❣❡r st❛rt✐♥❣ ✇✐t❤ ❛ ❧❡❛❞✐♥❣ ✵ ✐s ♦❝t❛❧✳ ❋♦r ❡①❛♠♣❧❡✱ ❈ ✐♥t❡r♣r❡ts ✵✶✶✸ ❛s ❛♥ ♦❝t❛❧ ❧✐t❡r❛❧ ❡q✉❛❧ t♦ ❞❡❝✐♠❛❧ ✼✺✳ ❚❤✐s ❝❛♥ ❜❡ ❛ ❣♦t❝❤❛ ❢♦r t❤❡ ✉♥✇❛r②✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-28
SLIDE 28

❘❡♣r❡s❡♥t❛t✐♦♥s

❇✐♥❛r② ❉❡❝✐♠❛❧ ❍❡① ❖❝t ✵✵✵✵ ✵ ✵①✵ ✵✵ ✵✵✵✶ ✶ ✵①✶ ✵✶ ✵✵✶✵ ✷ ✵①✷ ✵✷ ✵✵✶✶ ✸ ✵①✸ ✵✸ ✵✶✵✵ ✹ ✵①✹ ✵✹ ✵✶✵✶ ✺ ✵①✺ ✵✺ ✵✶✶✵ ✻ ✵①✻ ✵✻ ✵✶✶✶ ✼ ✵①✼ ✵✼

❈ ■♥tr♦❞✉❝t✐♦♥

slide-29
SLIDE 29

❘❡♣r❡s❡♥t❛t✐♦♥s ❈♦♥t✐♥✉❡❞

❇✐♥❛r② ❉❡❝✐♠❛❧ ❍❡① ❖❝t ✶✵✵✵ ✽ ✵①✽ ✵✶✵ ✶✵✵✶ ✾ ✵①✾ ✵✶✶ ✶✵✶✵ ✶✵ ✵①❆ ✵✶✷ ✶✵✶✶ ✶✶ ✵①❇ ✵✶✸ ✶✶✵✵ ✶✷ ✵①❈ ✵✶✹ ✶✶✵✶ ✶✸ ✵①❉ ✵✶✺ ✶✶✶✵ ✶✹ ✵①❊ ✵✶✻ ✶✶✶✶ ✶✺ ✵①❋ ✵✶✼

❈ ■♥tr♦❞✉❝t✐♦♥

slide-30
SLIDE 30

❖❝t❛❧✱ ❍❡①❛❞❡❝✐♠❛❧ ❈♦♥✈❡rs✐♦♥s ✐♥ ❈

■♥ ❜❛s❡s✳❝✿ st❛t✐❝ ✈♦✐❞ ❜❛s❡s✭❧♦♥❣ ✈❛❧✉❡s❬❪✱ ✐♥t ♥❱❛❧✉❡s✮ ④ ❢♦r ✭✐♥t ✐ ❂ ✵❀ ✐ < ♥❱❛❧✉❡s❀ ✐✰✰✮ ④ ❧♦♥❣ ✈ ❂ ✈❛❧✉❡s❬✐❪❀ ♣r✐♥t❢✭✧♥✉♠❜❡r✿ ✪❧❞ ❂❂ ✵✪❧♦ ❂❂ ✵❳✪❧❳ ❂❂ ✵①✪❧①\♥✧✱ ✈✱ ✈✱ ✈✱ ✈✮❀ ⑥ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-31
SLIDE 31

❖❝t❛❧✱ ❍❡①❛❞❡❝✐♠❛❧ ❈♦♥✈❡rs✐♦♥s ✐♥ ❈✿ ♠❛✐♥✭✮

■♥ ❜❛s❡s✳❝✿ ✐♥t ♠❛✐♥✭✮ ④ ❧♦♥❣ ✈❛❧✉❡s✶❬❪ ❂ ④ ✼✺✱ ✶✷✸✱ ✾✾ ⑥❀ ❧♦♥❣ ✈❛❧✉❡s✷❬❪ ❂ ④ ✵✼✺✱ ✵①✶✷✸✱ ✵①✾✾ ⑥❀ ❜❛s❡s✭✈❛❧✉❡s✶✱ s✐③❡♦❢✭✈❛❧✉❡s✶✮✴s✐③❡♦❢✭✈❛❧✉❡s✶❬✵❪✮✮❀ ❜❛s❡s✭✈❛❧✉❡s✷✱ s✐③❡♦❢✭✈❛❧✉❡s✷✮✴s✐③❡♦❢✭✈❛❧✉❡s✷❬✵❪✮✮❀ r❡t✉r♥ ✵❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-32
SLIDE 32

❖❝t❛❧✱ ❍❡①❛❞❡❝✐♠❛❧ ❈♦♥✈❡rs✐♦♥s ✐♥ ❈ ▲♦❣

✩ ✳✴❜❛s❡s ♥✉♠❜❡r✿ ✼✺ ❂❂ ✵✶✶✸ ❂❂ ✵❳✹❇ ❂❂ ✵①✹❜ ♥✉♠❜❡r✿ ✶✷✸ ❂❂ ✵✶✼✸ ❂❂ ✵❳✼❇ ❂❂ ✵①✼❜ ♥✉♠❜❡r✿ ✾✾ ❂❂ ✵✶✹✸ ❂❂ ✵❳✻✸ ❂❂ ✵①✻✸ ♥✉♠❜❡r✿ ✻✶ ❂❂ ✵✼✺ ❂❂ ✵❳✸❉ ❂❂ ✵①✸❞ ♥✉♠❜❡r✿ ✷✾✶ ❂❂ ✵✹✹✸ ❂❂ ✵❳✶✷✸ ❂❂ ✵①✶✷✸ ♥✉♠❜❡r✿ ✶✺✸ ❂❂ ✵✷✸✶ ❂❂ ✵❳✾✾ ❂❂ ✵①✾✾ ✩

❈ ■♥tr♦❞✉❝t✐♦♥

slide-33
SLIDE 33

❇✐♥❛r② ❆r✐t❤♠❡t✐❝

❇✐♥❛r② ❛r✐t❤♠❡t✐❝ ✇♦r❦s ❥✉st ❧✐❦❡ ❞❡❝✐♠❛❧ ❛r✐t❤♠❡t✐❝ ❡①❝❡♣t ❢♦r ✉s✐♥❣ ✷ ❛s t❤❡ ❜❛s❡✳ ❊①❛♠♣❧❡s ♦❢ ❛❞❞✐t✐♦♥ ❛♥❞ s✉❜tr❛❝t✐♦♥✳ ✵ ✶ ✵ ✶ ❴ ✶ ✵ ✵ ✵ ❂ ✵①✺✽ ❂ ✽✽ ✰ ✵ ✶ ✵ ✵ ❴ ✵ ✵ ✵ ✶ ❂ ✵①✹✶ ❂ ✻✺ ✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲ ✶ ✵ ✵ ✶ ❴ ✶ ✵ ✵ ✶ ❂ ✵①✾✾ ❂ ✶✺✸ ✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲ ✵ ✶ ✵ ✶ ❴ ✶ ✵ ✵ ✵ ❂ ✵①✺✽ ❂ ✽✽ ✲ ✵ ✶ ✵ ✵ ❴ ✵ ✵ ✵ ✶ ❂ ✵①✹✶ ❂ ✻✺ ✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲ ✵ ✵ ✵ ✶ ❴ ✵ ✶ ✶ ✶ ❂ ✵①✶✼ ❂ ✷✸ ✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲

❈ ■♥tr♦❞✉❝t✐♦♥

slide-34
SLIDE 34

❈ ■♥t❡❣❡r ▲✐t❡r❛❧s

❆s ❞✐s❝✉ss❡❞ ♣r❡✈✐♦✉s❧②✱ ✐♥t❡❣❡r ✈❛❧✉❡s ❝❛♥ ❜❡ s♣❡❝✐✜❡❞ ✐♥ ♦❝t❛❧ ✭❧❡❛❞✐♥❣ ✵✮✱ ❤❡①❛❞❡❝✐♠❛❧ ✭❧❡❛❞✐♥❣ ✵① ♦r ✵❳✮ ♦r ❞❡❝✐♠❛❧ ✭❞❡❢❛✉❧t✮✳ ❍♦✇❡✈❡r✱ t❤❛t ❞♦❡s ♥♦t s❛② ❛♥②t❤✐♥❣ ❛❜♦✉t ✇❤✐❝❤ ✐♥t❡❣❡r t②♣❡ t❤❛t ❧✐t❡r❛❧ ❝♦rr❡s♣♦♥❞s t♦✳ s❤♦rt ❛♥❞ ❝❤❛r ✐♥t❡❣❡rs ❛❧✇❛②s ♣r♦♠♦t❡❞ t♦ ✐♥t ✐♥t❡❣❡rs ✇✐t❤✐♥ ❡①♣r❡ss✐♦♥s✳ ❍❡♥❝❡ s❤♦rt✱ ❝❤❛r ❛r❡ ♣r✐♠❛r✐❧② st♦r❛❣❡ t②♣❡s✳ ❆ ❧✐t❡r❛❧ ✇✐t❤ ❧ ♦r ▲ s✉✣① ✐s ❛ ❧♦♥❣✳ Pr❡s❡♥❝❡ ♦❢ ❛ ❧♦♥❣ ❧✐t❡r❛❧ ✇✐t❤✐♥ ❛♥ ❡①♣r❡ss✐♦♥ ✇✐❧❧ ❢♦r❝❡ ❡①♣r❡ss✐♦♥ t♦ ❜❡ ❡✈❛❧✉❛t❡❞ ❛s ❛ ❧♦♥❣✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-35
SLIDE 35

❈ ■♥t❡❣❡r ▲✐t❡r❛❧s ❈♦♥t✐♥✉❡❞

❆ ✐♥t❡❣❡r ❧✐t❡r❛❧ ✇✐t❤ ❛ ✉ ♦r ❯ s✉✣① ✐s ✉♥s✐❣♥❡❞✳ ❊①❛♠♣❧❡ ✶✵✷✹❯✳ ❆ ✐♥t❡❣❡r ❧✐t❡r❛❧ ✇✐t❤ ❛ ❧❧ ♦r ▲▲ s✉✣① ✐s ❧♦♥❣ ❧♦♥❣✳ ❊①❛♠♣❧❡✿ ✶✵✷✹▲▲✳ ❚❤❡ s✐③❡ ❛♥❞ ✉♥s✐❣♥❡❞ s✉✣①❡s ❝❛♥ ❜❡ ❝♦♠❜✐♥❡❞ ✐♥ ❡✐t❤❡r ♦r❞❡r✿ ✶✵✷✹❯▲ ♦r ✶✵✷✹▲✉ ❛r❡ t❤❡ s❛♠❡✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-36
SLIDE 36

❇✐t ❖♣❡r❛t♦rs

✫ ❇✐t✇✐s❡✲❛♥❞ ♦❢ t✇♦ ✐♥t❡❣❡rs✳ ✵①✶✷✸✹ ✫ ✵①❢✵❢✵ r❡s✉❧ts ✐♥ ✵①✶✵✸✵✳ ⑤ ❇✐t✇✐s❡✲♦r ♦❢ t✇♦ ✐♥t❡❣❡rs✳ ✵①✶✷✸✹ ⑤ ✵①❢✵❢✵ r❡s✉❧ts ✐♥ ✵①❢✷❢✹✳ ❫ ❇✐t✇✐s❡✲①♦r ♦❢ t✇♦ ✐♥t❡❣❡rs✳ ✵①✶✷✸✹ ❫ ✵①❢✵❢✵ r❡s✉❧ts ✐♥ ✵①❡✷❝✹✳ ⑦ ❇✐t✇✐s❡ ❝♦♠♣❧❡♠❡♥t✳ ⑦✵①✶✷✸✹ r❡s✉❧ts ✐♥ ✵①❡❞❝❜✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-37
SLIDE 37

❙❤✐❢t ❖♣❡r❛t♦rs

❁❁ ✐ ❁❁ ♥ ✐s t❤❡ ✈❛❧✉❡ ♦❢ ✐ s❤✐❢t❡❞ t♦ t❤❡ ❧❡❢t ❜② ♥ ❜✐ts ✇✐t❤ ✵ ❜❡✐♥❣ s❤✐❢t❡❞ ✐♥ ❢r♦♠ t❤❡ r✐❣❤t✳ ✵①✸ ❁❁ ✷ ✐s ✵①❝✳ ❈❛♥ ❜❡ ✉s❡❞ ❢♦r ♠✉❧t✐♣❧②✐♥❣ ❜② ♣♦✇❡rs✲♦❢✲✷✳ ❃❃ ✐ ❃❃ ♥ ✐s t❤❡ ✈❛❧✉❡ ♦❢ ✐ s❤✐❢t❡❞ t♦ t❤❡ r✐❣❤t ❜② ♥ ❜✐ts✳ ■❢ ✐ ✐s ✉♥s✐❣♥❡❞✱ t❤❡♥ ✵ ✐s s❤✐❢t❡❞ ✐♥ ❢r♦♠ t❤❡ ❧❡❢t❀ ♦t❤❡r✇✐s❡ t❤❡ s✐❣♥ ❜✐t ✐s s❤✐❢t❡❞ ✐♥✳ ❊①❛♠♣❧❡✿ ✵①❝ ❃❃ ✷ ✐s ✵①✸✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-38
SLIDE 38

❇✐t ❛♥❞ ❙❤✐❢t ❖♣❡r❛t♦r ❊①❛♠♣❧❡s

❆ss✉♠❡ ✉♥s✐❣♥❡❞ ✐♥t ✉ ❛♥❞ ❜✐ts ❛r❡ ♥✉♠❜❡r❡❞ st❛rt✐♥❣ ✇✐t❤ ▲❙❇ ❜❡✐♥❣ ❜✐t ✵✱ ♥❡①t ❜✐t ❜❡✐♥❣ ✶✱ ❡t❝✳ ❇✐t✇✐s❡ ♦♣❡r❛t♦rs ❤❛✈❡ ✉♥✐♥t✉✐t✐✈❡ ♣r❡❝❡❞❡♥❝❡❀ ❛❧✇❛②s ♣❛r❡♥t❤❡s✐③❡ t♦ ❛✈♦✐❞ ❛♠❜✐❣✉✐t②✳ ◆♦♥✲③❡r♦ ✐✛ ❜✐t ✵ ♦❢ ✉ ✐s ✵✿ ✭✭✉ ✫ ✵①✶✮ ❂❂ ✵✮✳ ◆♦♥✲③❡r♦ ✐✛ ❜✐t ✷ ♦❢ ✉ ✐s ✶✿ ✭✭✉ ✫ ✵①✹✮ ✦❂ ✵✮✳ ❙❡t ▲❙❇ ♦❢ ✉ t♦ ✶ ✇✐t❤♦✉t ❝❤❛♥❣✐♥❣ ♦t❤❡r ❜✐ts✿ ✉ ⑤❂ ✵①✶✳ ❙❡t ▲❙❇ ♦❢ ✉ t♦ ✵ ✇✐t❤♦✉t ❝❤❛♥❣✐♥❣ ♦t❤❡r ❜✐ts✿ ✉ ✫❂ ⑦✵①✶✳ ❱❛❧✉❡ ♦❢ ✷♥❞ ❤❡①❡t ✭❜✐ts ✹ ✲ ✼✮ ♦❢ ✉✿ ✭✉ ✫ ✵①❢✵✮ ❃❃ ✹ ♦r ✭✉ ❃❃ ✹✮ ✫ ✵①✵❢✳ ◆♦♥✲③❡r♦ ✐✛ ▼❙❇ ♦❢ ✉ ✐s ✶✿ ✭✉ ✫ ⑦✭⑦✵✉ ❃❃ ✶✮✮ ✦❂ ✵✳ ◆♦t❡ ✉ s✉✣① ✐♥ ✵✉ ❛❜s♦❧✉t❡❧② ♥❡❝❡ss❛r②✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-39
SLIDE 39

❈♦✉♥t✐♥❣ ★ ♦❢ ✶s ✐♥ ❛♥ ✐♥t

■♥ ❝♦✉♥t✲✶s✲✶✳❝✿ ✐♥t ❝♦✉♥t❴♦♥❡s✭✉♥s✐❣♥❡❞ ✈✮ ④ ✐♥t ♦♥❡s ❂ ✵❀ ❢♦r ✭✉♥s✐❣♥❡❞ ✐ ❂ ✈❀ ✐ > ✵❀ ✐ >>❂ ✶✮ ④ ✐❢ ✭✐ ✫ ✶✮ ♦♥❡s✰✰❀ ⑥ r❡t✉r♥ ♦♥❡s❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-40
SLIDE 40

❈♦✉♥t✐♥❣ ★ ♦❢ ✶s ✐♥ ❛♥ ✐♥t ❈♦♥t✐♥✉❡❞

■♥ ❝♦✉♥t✲✶s✲✶✳❝✿ ✐♥t ♠❛✐♥✭✮ ④ ✉♥s✐❣♥❡❞ ✈❛❧✉❡s❬❪ ❂ ④ ✶✷✸✱ ✸✷✱ ✷✺✺ ⑥❀ ❢♦r ✭✐♥t ✐ ❂ ✵❀ ✐ < s✐③❡♦❢✭✈❛❧✉❡s✮✴s✐③❡♦❢✭✈❛❧✉❡s❬✵❪✮❀ ✐✰✰✮ ④ ✉♥s✐❣♥❡❞ ✈ ❂ ✈❛❧✉❡s❬✐❪❀ ♣r✐♥t❢✭✧★ ♦❢ ♦♥❡s ✐♥ ✪✉ ✭✵①✪①✮ ✐s ✪❞\♥✧✱ ✈✱ ✈✱ ❝♦✉♥t❴♦♥❡s✭✈✮✮❀ ⑥ r❡t✉r♥ ✵❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-41
SLIDE 41

❈♦✉♥t✐♥❣ ★ ♦❢ ✶s ✐♥ ❛♥ ✐♥t ▲♦❣

✩ ✳✴❝♦✉♥t✲✶s✲✶ ★ ♦❢ ♦♥❡s ✐♥ ✶✷✸ ✭✵①✼❜✮ ✐s ✻ ★ ♦❢ ♦♥❡s ✐♥ ✸✷ ✭✵①✷✵✮ ✐s ✶ ★ ♦❢ ♦♥❡s ✐♥ ✷✺✺ ✭✵①❢❢✮ ✐s ✽ ✩

❈ ■♥tr♦❞✉❝t✐♦♥

slide-42
SLIDE 42

❈♦✉♥t✐♥❣ ★ ♦❢ ✶s ✐♥ ❛♥ ✐♥t ❉✐s❝✉ss✐♦♥

❚❤❡ ❧♦♦♣ st❛rts ✇✐t❤ ✐ s❡t t♦ t❤❡ ✈❛❧✉❡ ✈ ✇✐t❤✐♥ ✇❤✐❝❤ ✇❡ ✇❛♥t t♦ ❝♦✉♥t t❤❡ ♥✉♠❜❡r ♦❢ ✶✲❜✐ts✳ ❇❛s✐❝ ❈ ❞♦❡s ♥♦t ❤❛✈❡ ❜♦♦❧❡❛♥ t②♣❡❀ t❤❡ ✈❛❧✉❡ ✵ ✐s tr❡❛t❡❞ ❛s ❢❛❧s❡✱ ❛♥② ♥♦♥✲③❡r♦ ✈❛❧✉❡ ✐s tr❡❛t❡❞ ❛s tr✉❡✳ ❍❡♥❝❡ ♦♥❡s ✐s ✐♥❝r❡♠❡♥t❡❞ ✐❢ ✐ ✫ ✶ ✐s ♥♦♥✲③❡r♦❀ ✐✳❡✳✱ ♦♥❡s ✐s ✐♥❝r❡♠❡♥t❡❞ ✐✛ t❤❡ ❧❡❛st✲s✐❣♥✐✜❝❛♥t ❜✐t ✭▲❙❇✮ ♦❢ ✐ ✐s ✶✳ ❆❢t❡r ❡❛❝❤ ✐t❡r❛t✐♦♥ ♦❢ t❤❡ ❧♦♦♣✱ ✐ ✐s s❤✐❢t❡❞ t♦ t❤❡ r✐❣❤t ❜② ✶ ♣♦s✐t✐♦♥✳ ❚❤✉s t❤❡ ✶✬s ✐♥ ✐ ♠❛❦❡ t❤❡✐r ✇❛② t♦✇❛r❞s t❤❡ ▲❙❇✳ ❚❤❡ ❧♦♦♣ t❡r♠✐♥❛t❡s ✇❤❡♥ ✐ ✐s ✵❀ ✐✳❡✳✱ t❤❡r❡ ❛r❡ ♥♦ ♠♦r❡ ✶✬s t♦ ❝♦✉♥t ❛♥❞ ♦♥❡s ❝♦♥t❛✐♥s t❤❡ ❝♦✉♥t ♦❢ ✶✬s ✐♥ t❤❡ ♦r✐❣✐♥❛❧ ✈❛❧✉❡ ✈✳ ❚❤❡ ♥✉♠❜❡r ♦❢ ✐t❡r❛t✐♦♥s ✐♥ t❤❡ ❧♦♦♣ ✇✐❧❧ ❞❡♣❡♥❞ ♦♥ t❤❡ ♣♦s✐t✐♦♥ ♦❢ t❤❡ ❧❡❢t♠♦st ✶ ✐♥ t❤❡ ♦r✐❣✐♥❛❧ ✈❛❧✉❡ ✈✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-43
SLIDE 43

❈♦✉♥t✐♥❣ ★ ♦❢ ✶s ✐♥ ❛♥ ✐♥t✿ ✷♥❞ ❆tt❡♠♣t

■♥ ❝♦✉♥t✲✶s✲✷✳❝ ✇❡ r❡❞✉❝❡ ♥✉♠❜❡r ♦❢ ❧♦♦♣ ✐t❡r❛t✐♦♥s t♦ ♥✉♠❜❡r ♦❢ ✶✬s ✐♥ ♦r✐❣✐♥❛❧ ✈❛❧✉❡✿ ✐♥t ❝♦✉♥t❴♦♥❡s✭✉♥s✐❣♥❡❞ ✈✮ ④ ✐♥t ♦♥❡s ❂ ✵❀ ✇❤✐❧❡ ✭✈ > ✵✮ ④ ✈ ✫❂ ✈ ✲ ✶❀ ♦♥❡s✰✰❀ ⑥ r❡t✉r♥ ♦♥❡s❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-44
SLIDE 44

❈♦✉♥t✐♥❣ ★ ♦❢ ✶s ✐♥ ❛♥ ✐♥t✿ ✷♥❞ ❆tt❡♠♣t ❉✐s❝✉ss✐♦♥

■❢ ✈ ✐s ✶✵✶✵✵✵✱ t❤❡♥ ✈ ✲ ✶ ✐s ✶✵✵✶✶✶✳ ❍❡♥❝❡ ✈ ✫ ✭✈ ✲ ✶✮ ✐s ✶✵✵✵✵✵✳ ❇② ❛ss✐❣♥✐♥❣ t❤✐s ❜❛❝❦ t♦ ✈✱ ✇❡ ❦♥♦❝❦✲♦✉t t❤❡ r✐❣❤t♠♦st ✶ ✐♥ ✈ ✐♥ ❡❛❝❤ ❧♦♦♣ ✐t❡r❛t✐♦♥✳ ❙✐♥❝❡ ✇❡ ❦♥♦❝❦✲♦✉t t❤❡ r✐❣t❤♠♦st ✶ ✐♥ ❡❛❝❤ ❧♦♦♣ ✐t❡r❛t✐♦♥ ❛♥❞ ✐♥❝r❡♠❡♥t ♦♥❡s ♦♥ ❡❛❝❤ ❧♦♦♣ ✐t❡r❛t✐♦♥ ❛♥❞ t❡r♠✐♥❛t❡ t❤❡ ❧♦♦♣ ✇❤❡♥ ♥♦ ✶✬s r❡♠❛✐♥ ✐♥ ✈✱ ❛t ❧♦♦♣ t❡r♠✐♥❛t✐♦♥ ♦♥❡s ✇✐❧❧ ❝♦♥t❛✐♥ t❤❡ ♥✉♠❜❡r ♦❢ ✶✬s ✐♥ t❤❡ ♦r✐❣✐♥❛❧ ✈❛❧✉❡ ♦❢ ✈✳ ◆♦t❡ t❤❛t ❡✈❡♥ t❤♦✉❣❤ t❤❡ ♣❛r❛♠❡t❡r ✈❛❧✉❡ ✈ ✐s ❜❡✐♥❣ ❝❤❛♥❣❡❞ ✇✐t❤✐♥ ❝♦✉♥t❴♦♥❡s✭✮✱ t❤❛t ❝❤❛♥❣❡ ✇✐❧❧ ♥♦t ❜❡ r❡✢❡❝t❡❞ ✐♥ t❤❡ ❝❛❧❧❡r ♦❢ ❝♦✉♥t❴♦♥❡s✭✮✳ ❚❤❛t ✐s ❜❡❝❛✉s❡ ✇❤❡♥ ♣❛r❛♠❡t❡rs ❛r❡ ♣❛ss❡❞ ✐♥ ❈✱ ❛ ❝♦♣② ♦❢ t❤❡ ❛❝t✉❛❧ ♣❛r❛♠❡t❡r ✐s ♣❛ss❡❞✳ ❚❤✐s ✐s r❡❢❡rr❡❞ t♦ ❛s ❝❛❧❧✲❜②✲✈❛❧✉❡✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-45
SLIDE 45

❇✐❣ ❊♥❞✐❛♥ ✈❡rs✉s ▲✐tt❧❡ ❊♥❞✐❛♥

■♥ ✇❤❛t ♦r❞❡r ❛r❡ ♠✉❧t✐✲❜②t❡ q✉❛♥t✐t✐❡s ✭❧✐❦❡ ✐♥t❡❣❡rs ♦r ✢♦❛ts✮ st♦r❡❞ ✐♥ ♠❡♠♦r②❄ ❚✇♦ ❝♦♠♠♦♥ s♦❧✉t✐♦♥s✿ ❧✐tt❡ ❡♥❞✐❛♥ ✈❡rs✉s ❜✐❣ ❡♥❞✐❛♥ ✭❞❡t❛✐❧s ❢♦❧❧♦✇✮✳ ❙♦♠❡ ♠❛❝❤✐♥❡s ❝❛♥ ❝❤♦♦s❡ ❞②♥❛♠✐❝❛❧❧② ✭✧❜✐✲❡♥❞✐❛♥✧✮✳ ❯s✉❛❧❧② ♥♦t ✈✐s✐❜❧❡ t♦ ♣r♦❣r❛♠♠❡r ♦♥ ❛♥ ✐♥❞✐✈✐❞✉❛❧ ♠❛❝❤✐♥❡ ❜✉t ✐s ❛♥ ✐ss✉❡ ✇❤❡♥ s❡♥❞✐♥❣ ❜✐♥❛r② ❞❛t❛ ❜❡t✇❡❡♥ ♠❛❝❤✐♥❡s✳ ▼❛♥② ❝✉rr❡♥t ♥❡t✇♦r❦s ♠❛♥❞❛t❡ ❜✐❣✲❡♥❞✐❛♥✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-46
SLIDE 46

▲✐tt❧❡ ❊♥❞✐❛♥

▲✐tt❧❡ ❊♥❞✐❛♥ ▲❡❛st s✐❣♥✐✜❝❛♥t ❜②t❡ st♦r❡❞ ✐♥ ❧♦✇ ❛❞❞r❡ss✱ ♥❡①t ❧❡❛st s✐❣♥✐✜❝❛♥t ❜②t❡ st♦r❡❞ ✐♥ ♥❡①t ❤✐❣❤❡r ❛❞❞r❡ss✱ ✳✳✱ ♠♦st s✐❣♥✐✜❝❛♥t ❜②t❡ st♦r❡❞ ✐♥ ❤✐❣❤ ❛❞❞r❡ss✳ ❋♦r ❡①❛♠♣❧❡✱ ✐❢ ✵①✵✶✷✸✹✺✻✼ st♦r❡❞ ❛t ✵①✶✵✵✿ ❆❞❞r❡ss✿ ✵①✶✵✵ ✵①✶✵✶ ✵①✶✵✷ ✵①✶✵✸ ❱❛❧✉❡✿ ✵①✻✼ ✵①✹✺ ✵①✷✸ ✵①✵✶ ■♥t❡❧ ♠❛❝❤✐♥❡s ❧✐tt❧❡ ❡♥❞✐❛♥✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-47
SLIDE 47

❇✐❣ ❊♥❞✐❛♥

❇✐❣ ❊♥❞✐❛♥ ▼♦st s✐❣♥✐✜❝❛♥t ❜②t❡ st♦r❡❞ ✐♥ ❧♦✇ ❛❞❞r❡ss✱ ♥❡①t ♠♦st s✐❣♥✐✜❝❛♥t ❜②t❡ st♦r❡❞ ✐♥ ♥❡①t ❤✐❣❤❡r ❛❞❞r❡ss✱ ✳✳✱ ❧❡❛st s✐❣♥✐✜❝❛♥t ❜②t❡ st♦r❡❞ ✐♥ ❤✐❣❤ ❛❞❞r❡ss✳ ❋♦r ❡①❛♠♣❧❡✱ ✐❢ ✵①✵✶✷✸✹✺✻✼ st♦r❡❞ ❛t ✵①✶✵✵✿ ❆❞❞r❡ss✿ ✵①✶✵✵ ✵①✶✵✶ ✵①✶✵✷ ✵①✶✵✸ ❱❛❧✉❡✿ ✵①✵✶ ✵①✷✸ ✵①✹✺ ✵①✻✼ ■❇▼✱ ❙✉♥ ❜✐❣ ❡♥❞✐❛♥✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-48
SLIDE 48

❊♥❞✐❛♥ Pr♦❣r❛♠

■♥ ❡♥❞✐❛♥✳❝✿ ✐♥t ♠❛✐♥✭✮ ④ ✉♥✐♦♥ ④ ✴✴♠❡♠♦r② ❢♦r ✐ ❛♥❞ ❜②t❡s ♦✈❡r❧❛♣ ✐♥t ✐❀ ❝❤❛r ❜②t❡s❬s✐③❡♦❢✭✐♥t✮❪❀ ⑥ ✉ ❂ ④ ✵①✶✷✸✹✺✻ ⑥❀ ♣r✐♥t❢✭✧✐♥t ❂ ✵①✪①\♥✧✱ ✉✳✐✮❀ ❢♦r ✭✐♥t ✐ ❂ ✵❀ ✐ < s✐③❡♦❢✭✐♥t✮❀ ✐✰✰✮ ④ ♣r✐♥t❢✭✧❜②t❡s❬✪❞❪ ❛t ✪♣ ✐s ✵①✪✵✷①\♥✧✱ ✐✱ ✫✉✳❜②t❡s❬✐❪✱ ✉✳❜②t❡s❬✐❪✮❀ ⑥ r❡t✉r♥ ✵❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-49
SLIDE 49

❊♥❞✐❛♥ Pr♦❣r❛♠ ▲♦❣ ♦♥ ①✽✻

✩ ✳✴❡♥❞✐❛♥ ✐♥t ❂ ✵①✶✷✸✹✺✻ ❜②t❡s❬✵❪ ❛t ✵①✼❢❢❢✺✻✺❝❢❡✵✵ ✐s ✵①✺✻ ❜②t❡s❬✶❪ ❛t ✵①✼❢❢❢✺✻✺❝❢❡✵✶ ✐s ✵①✸✹ ❜②t❡s❬✷❪ ❛t ✵①✼❢❢❢✺✻✺❝❢❡✵✷ ✐s ✵①✶✷ ❜②t❡s❬✸❪ ❛t ✵①✼❢❢❢✺✻✺❝❢❡✵✸ ✐s ✵①✵✵ ✩

❈ ■♥tr♦❞✉❝t✐♦♥

slide-50
SLIDE 50

❊♥❞✐❛♥ Pr♦❣r❛♠ ▲♦❣ ♦♥ ❙♣❛r❝

❜✐♥❣s✉♥s✷✪ ✳✴❡♥❞✐❛♥ ✐♥t ❂ ✵①✶✷✸✹✺✻ ❜②t❡s❬✵❪ ❛t ❢❢❜❢❢✾✵✵ ✐s ✵①✵✵ ❜②t❡s❬✶❪ ❛t ❢❢❜❢❢✾✵✶ ✐s ✵①✶✷ ❜②t❡s❬✷❪ ❛t ❢❢❜❢❢✾✵✷ ✐s ✵①✸✹ ❜②t❡s❬✸❪ ❛t ❢❢❜❢❢✾✵✸ ✐s ✵①✺✻ ❜✐♥❣s✉♥s✷✪

❈ ■♥tr♦❞✉❝t✐♦♥

slide-51
SLIDE 51

❊♥❞✐❛♥ Pr♦❣r❛♠ ❉✐s❝✉ss✐♦♥

❚❤❡ ♠❡♠❜❡rs ♦❢ ❛ ✉♥✐♦♥ ❛r❡ ❛ss✐❣♥❡❞ ❛t t❤❡ s❛♠❡ ♠❡♠♦r② ❧♦❝❛t✐♦♥✳ ❍❡♥❝❡ ✉✳✐ ❛♥❞ ✉✳❜②t❡s ♦❝❝✉♣② t❤❡ s❛♠❡ ♠❡♠♦r② ❧♦❝❛t✐♦♥✳ ❚❤✐s ❛❧❧♦✇s ✉s t♦ ❧♦♦❦ ❛t t❤❡ ✐♥❞✐✈✐❞✉❛❧ ❜②t❡s ✐♥ ✐♥t ✐✳ ❚❤❡ ✫ ✉♥❛r② ♦♣❡r❛t♦r r❡t✉r♥s t❤❡ ❛❞❞r❡ss ♦❢ ✐ts ♦♣❡r❛♥❞✳ ❍❡♥❝❡ ✫✉✳❜②t❡s❬✐❪ r❡t✉r♥s t❤❡ ❛❞❞r❡ss ♦❢ t❤❡ ✐✬t❤ ❜②t❡✳ ◆♦t❡ t❤❛t ❢♦r ①✽✻✱ t❤❡ ♠♦st s✐❣♥✐✜❝❛♥t ❜②t❡ ✐s st♦r❡❞ ❛t ❛ ❤✐❣❤❡r ❛❞❞r❡ss t❤❛♥ t❤❡ ❧❡❛st s✐❣♥✐✜❝❛♥t ❜②t❡✳ ❍❡♥❝❡ ①✽✻ ✐s ❛ ❧✐tt❧❡✲❡♥❞✐❛♥ ❛r❝❤✐t❡❝t✉r❡✳ ◆♦t❡ t❤❛t ❢♦r s♣❛r❝✱ t❤❡ ❧❡❛st s✐❣♥✐✜❝❛♥t ❜②t❡ ✐s st♦r❡❞ ❛t ❛ ❤✐❣❤❡r ❛❞❞r❡ss t❤❛♥ t❤❡ ❧❡❛st s✐❣♥✐✜❝❛♥t ❜②t❡✳ ❍❡♥❝❡ s♣❛r❝ ✐s ❛ ❜✐❣✲❡♥❞✐❛♥ ❛r❝❤✐t❡❝t✉r❡✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-52
SLIDE 52

❙✐❣♥❡❞ ▼❛❣♥✐t✉❞❡ ❘❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ❙✐❣♥❡❞ ■♥t❡❣❡rs

❙✐❣♥❡❞ ♠❛❣♥✐t✉❞❡ r❡♣r❡s❡♥t❛t✐♦♥✿ ■♥t❡❣❡r r❡♣r❡s❡♥t❡❞ ✉s✐♥❣ ❛ s✐♥❣❧❡ s✐❣♥ ❜✐t ✭✵ ♣♦s✐t✐✈❡✱ ✶ ♥❡❣❛t✐✈❡✮ ❛♥❞ ❛♥ ✉♥s✐❣♥❡❞ ♠❛❣♥✐t✉❞❡✳ ✰✼✺ ❤❛s ✽✲❜✐t s✐❣♥❡❞ ♠❛❣♥✐t✉❞❡ r❡♣r❡s❡♥t❛t✐♦♥ ✵✶✵✵❴✶✵✶✶❀ ✲✼✺ ❤❛s ✽✲❜✐t s✐❣♥❡❞ ♠❛❣♥✐t✉❞❡ r❡♣r❡s❡♥t❛t✐♦♥ ✶✶✵✵❴✶✵✶✶❀ ✵ ❤❛s t✇♦ r❡♣r❡s❡♥t❛t✐♦♥s✿ ✰✵✿ ✵✵✵✵❴✵✵✵✵ ❛♥❞ ✲✵✿ ✶✵✵✵❴✵✵✵✵✳ ◆♦t ✉s❡❞ ✐♥ ♣r❛❝t✐❝❡✱ ❜✉t ✉s❡❢✉❧ ✇❤❡♥ ✐♥t❡r♣r❡t✐♥❣ ✢♦❛t✐♥❣ ♣♦✐♥t r❡♣r❡s❡♥t❛t✐♦♥ ❛s ✐♥t❡❣❡rs✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-53
SLIDE 53

❚✇♦✬s ❈♦♠♣❧❡♠❡♥t ❘❡♣r❡s❡♥t❛t✐♦♥

❚✇♦✬s ❝♦♠♣❧❡♠❡♥t ✐s t❤❡ r❡♣r❡s❡♥t❛t✐♦♥ ✉s❡❞ ❝✉rr❡♥t❧② ❢♦r r❡♣r❡s❡♥t✐♥❣ s✐❣♥❡❞ ✐♥t❡❣❡rs✳ ●✐✈❡♥ ❜✐ts ❜♥−✶❜♥−✷ . . . ❜✶❜✵✱ t❤❡ ▼❙❇ ✐s ✉s❡❞ ❛s ❛ s✐❣♥ ❜✐t ✇✐t❤ ✇❡✐❣❤t −✷♥−✶✳ ❚❤❡ ♦✈❡r❛❧❧ ✈❛❧✉❡ ✐s✿ ❜♥−✶ × −✷♥−✶ + ❜♥−✷ × ✷♥−✷ . . . ❜✶ × ✷✶ + ❜✵ × ✷✵ ✰✼✺ ❤❛s ✽✲❜✐t ✷✬s ❝♦♠♣❧❡♠❡♥t r❡♣r❡s❡♥t❛t✐♦♥ ✵✶✵✵❴✶✵✶✶❀ ✲✼✺ ❤❛s ✽✲❜✐t ✷✬s ❝♦♠♣❧❡♠❡♥t r❡♣r❡s❡♥t❛t✐♦♥ ✶✵✶✶❴✵✶✵✶ ✇❤✐❝❤ ✐s ✲✶✷✽ ✰ ✺✸✳ ❚♦ ♥❡❣❛t❡ ❛ ✷✬s ❝♦♠♣❧❡♠❡♥t ♥✉♠❜❡r✱ ❢♦r♠ ✐ts ❜✐t✲❝♦♠♣❧❡♠❡♥t ❛♥❞ ❛❞❞ ✶ t♦ t❤❡ r❡s✉❧t✳ ❋♦r ❡①❛♠♣❧❡✱ ✲✼✺ ❂❂ ✭⑦✵✶✵✵❴✶✵✶✶ ✰ ✶✮ ❂❂ ✭✶✵✶✶❴✵✶✵✵ ✰ ✶✮ ❂❂ ✶✵✶✶❴✵✶✵✶ ✭✲✶✷✽ ✰ ✺✸ ❂❂ ✲✼✺✮✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-54
SLIDE 54

❚✇♦✬s ❈♦♠♣❧❡♠❡♥t ❊①❛♠♣❧❡s

❊①❛♠♣❧❡s ♦❢ ✽✲❜✐t ✷✬s ❝♦♠♣❧❡♠❡♥t ♥✉♠❜❡rs✿ ✶✵✵✵ ✵✵✵✵ ❂❂ ✲✶✷✽ ✶✵✵✵ ✵✵✵✶ ❂❂ ✲✶✷✼ ✶✵✵✵ ✵✵✶✵ ❂❂ ✲✶✷✻ ✶✵✵✵ ✵✵✶✶ ❂❂ ✲✶✷✺ ✳✳✳ ✶✶✶✶ ✶✶✶✶ ❂❂ ✲✶ ✵✵✵✵ ✵✵✵✵ ❂❂ ✵ ✵✵✵✵ ✵✵✵✶ ❂❂ ✶ ✳✳✳ ✵✶✶✶ ✶✶✶✶ ❂❂ ✶✷✼

❈ ■♥tr♦❞✉❝t✐♦♥

slide-55
SLIDE 55

❚✇♦✬s ❈♦♠♣❧❡♠❡♥t ❋❡❛t✉r❡s

❆s②♠♠❡tr✐❝✳ ❲✐t❤ ♥✲❜✐ts✱ ♥♦♥✲♥❡❣❛t✐✈❡ ♥✉♠❜❡rs r❛♥❣❡ ❢r♦♠ ✵ . . . ✷♥−✶ − ✶ ❜✉t t❤❡ ♥❡❣❛t✐✈❡ ♥✉♠❜❡rs r❛♥❣❡ ❢r♦♠ −✶ . . . − ✷♥−✶✳ ❚❤❡r❡ ✐s ♥♦ ♣♦s✐t✐✈❡ ❝♦✉♥t❡r♣❛rt t♦ −✷♥−✶✳ ❚❤✐s ❝❛♥ r❡s✉❧t ✐♥ s✉❜t❧❡ ❜✉❣s✳ ❊❛❝❤ r❡♣r❡s❡♥t❛❜❧❡ ♥✉♠❜❡r ❤❛s ❛ ✉♥✐q✉❡ r❡♣r❡s❡♥t❛t✐♦♥✳ ◆♦ ♠✉❧t✐♣❧❡ r❡♣r❡s❡♥t❛t✐♦♥s ❢♦r ✵✳ ✲✵ ❂❂ ✭✵①❋❋❋❋❋❋❋❋ ✰ ✶✮ ❂❂ ✵①✵✵✵✵✵✵✵✵❵✳ ◆♦t❡ t❤❛t ❛♥ ✉♥s✐❣♥❡❞ ♥✲❜✐t ♥✉♠❜❡r ❝❛♥ r❡♣r❡s❡♥t ✈❛❧✉❡s ✐♥ t❤❡ r❛♥❣❡ ✵ . . . ✷♥ − ✶✳ ❙♦ t❤❡ ❧❛r❣❡st ✉♥s✐❣♥❡❞ ♥✉♠❜❡r ✐s ✶ ♠♦r❡ t❤❛♥ t✇✐❝❡ t❤❡ ❧❛r❣❡st ♣♦s✐t✐✈❡ ✷✬s ❝♦♠♣❧❡♠❡♥t ♥✉♠❜❡r✳ ❚❤✐s ✐s s♦♠❡t❤✐♥❣ t♦ ❦❡❡♣ ✐♥ ♠✐♥❞ ✇❤❡♥ ❝♦♥✈❡rt✐♥❣ ❜❡t✇❡❡♥ s✐❣♥❡❞ ❛♥❞ ✉♥s✐❣♥❡❞ r❡♣r❡s❡♥t❛t✐♦♥✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-56
SLIDE 56

❖✉t♣✉t ❇✐♥❛r② ❘❡♣r❡s❡♥t❛t✐♦♥

■♥ ♦✉t✲❜✐ts✳❝✿ st❛t✐❝ ✈♦✐❞ ♦✉t❴❜✐ts✭s❤♦rt ✈❛❧✉❡✱ ❋■▲❊ ✯♦✉t✮ ④ ❢♣r✐♥t❢✭♦✉t✱ ✧✪❞ ❂❂ ✵①✪① ❂❂ ✵✪♦ ❂❂ ✵❜✧✱ ✈❛❧✉❡✱ ✈❛❧✉❡✱ ✈❛❧✉❡✮❀ ✐♥t ♥❇✐ts ❂ ❈❍❆❘❴❇■❚ ✯ s✐③❡♦❢✭✈❛❧✉❡✮❀ ✉♥s✐❣♥❡❞ ♠❛s❦ ❂ ✵①✶ << ✭♥❇✐ts ✲ ✶✮❀ ❢♦r ✭✐♥t ✐ ❂ ♥❇✐ts ✲ ✶❀ ✐ >❂ ✵❀ ✐✲✲✮ ④ ❝❤❛r ❝ ❂ ✭♠❛s❦ ✫ ✈❛❧✉❡✮ ❄ ✬✶✬ ✿ ✬✵✬❀ ♠❛s❦ >>❂ ✶❀ ❢♣r✐♥t❢✭♦✉t✱ ✧✪❝✧✱ ❝✮❀ ✐❢ ✭✐ ✪ ✹ ❂❂ ✵ ✫✫ ♠❛s❦ > ✵✮ ❢♣r✐♥t❢✭♦✉t✱ ✧❴✧✮❀ ⑥ ❢♣r✐♥t❢✭♦✉t✱ ✧\♥✧✮❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-57
SLIDE 57

❖✉t♣✉t ❇✐♥❛r② ❘❡♣r❡s❡♥t❛t✐♦♥✿ ♠❛✐♥✭✮

■♥ ♦✉t✲❜✐ts✳❝✿ ✐♥t ♠❛✐♥✭✮ ④ s❤♦rt ✈❛❧✉❡s❬❪ ❂ ④ ✵✱ ✶✻✱ ✷✺✺✱ ✶<<✭s✐③❡♦❢✭s❤♦rt✮✯❈❍❆❘❴❇■❚ ✲ ✷✮✱ ✲✶✱ ✲✹✱ ✲✺✱ ⑥❀ ❢♦r ✭✐♥t ✐ ❂ ✵❀ ✐ < s✐③❡♦❢✭✈❛❧✉❡s✮✴s✐③❡♦❢✭✈❛❧✉❡s❬✵❪✮❀ ✐✰✰✮ ④ ♦✉t❴❜✐ts✭✈❛❧✉❡s❬✐❪✱ st❞♦✉t✮❀ ⑥ r❡t✉r♥ ✵❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-58
SLIDE 58

❖✉t♣✉t ❇✐♥❛r② ❘❡♣r❡s❡♥t❛t✐♦♥✿ ▲♦❣

✳✴♦✉t✲❜✐ts ✵ ❂❂ ✵①✵ ❂❂ ✵✵ ❂❂ ✵❜✵✵✵✵❴✵✵✵✵❴✵✵✵✵❴✵✵✵✵ ✶✻ ❂❂ ✵①✶✵ ❂❂ ✵✷✵ ❂❂ ✵❜✵✵✵✵❴✵✵✵✵❴✵✵✵✶❴✵✵✵✵ ✷✺✺ ❂❂ ✵①❢❢ ❂❂ ✵✸✼✼ ❂❂ ✵❜✵✵✵✵❴✵✵✵✵❴✶✶✶✶❴✶✶✶✶ ✶✻✸✽✹ ❂❂ ✵①✹✵✵✵ ❂❂ ✵✹✵✵✵✵ ❂❂ ✵❜✵✶✵✵❴✵✵✵✵❴✵✵✵✵❴✵✵✵✵ ✲✶ ❂❂ ✵①❢❢❢❢❢❢❢❢ ❂❂ ✵✸✼✼✼✼✼✼✼✼✼✼ ❂❂ ✵❜✶✶✶✶❴✶✶✶✶❴✶✶✶✶❴✶✶✶✶ ✲✹ ❂❂ ✵①❢❢❢❢❢❢❢❝ ❂❂ ✵✸✼✼✼✼✼✼✼✼✼✹ ❂❂ ✵❜✶✶✶✶❴✶✶✶✶❴✶✶✶✶❴✶✶✵✵ ✲✺ ❂❂ ✵①❢❢❢❢❢❢❢❜ ❂❂ ✵✸✼✼✼✼✼✼✼✼✼✸ ❂❂ ✵❜✶✶✶✶❴✶✶✶✶❴✶✶✶✶❴✶✵✶✶

❈ ■♥tr♦❞✉❝t✐♦♥

slide-59
SLIDE 59

❙✐❣♥❡❞✱ ❯♥s✐❣♥❡❞ ❆❞❞✐t✐♦♥

❚❤❡ ♦♣❡r❛t✐♦♥ ♦❢ ❛❞❞✐t✐♦♥ ✐s t❤❡ s❛♠❡ ❢♦r ❜♦t❤ s✐❣♥❡❞ ❛♥❞ ✉♥s✐❣♥❡❞ ♥✉♠❜❡rs ✇✐t❤ ✷✬s ❝♦♠♣❧❡♠❡♥t✳ ❈♦♥s✐❞❡r ✸ ❜✐ts ♥✉♠❜❡rs✿ ❯♥s✐❣♥❡❞✿ ✵ t♦ ✼❀ ❙✐❣♥❡❞ ✲✹ t♦ ✸✳ ❊❛❝❤ ❢♦❧❧♦✇✐♥❣ t❛❜❧❡ s❤♦✇s ❛❞❞✐t✐♦♥ ♦❢ ❛❧❧ ❝♦♠❜✐♥❛t✐♦♥s ♦❢ ❛ ❧❡❢t ♦♣❡r❛♥❞ ✇✐t❤ t✇♦ r✐❣❤t ♦♣❡r❛♥❞s✳ ❙✐❣♥❡❞ r❡s✉❧t ✐♥❞✐❝❛t❡❞ ❜② ❛ s✐❣♥❡❞ r❡s✉❧t ✐♥ ♣❛r❡♥t❤❡s❡s✳ ❖✈❡r✢♦✇ ✐♥❞✐❝❛t❡❞ ❜② ❛ ✯✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-60
SLIDE 60

❙✐❣♥❡❞✱ ❯♥s✐❣♥❡❞ ❆❞❞✐t✐♦♥ ❚❛❜❧❡s

❆❞❞✐t✐♦♥ t❛❜❧❡ ❢♦r ♦♣❡❘❛♥❞ ◆ ❛♥❞ ♦♣❡❘❛♥❞ ✵❜✵✵✵ ❛s ✇❡❧❧ ❛s ♦♣❡❘❛♥❞ ◆ ❛♥❞ ♦♣❡❘❛♥❞ ✵❜✵✵✶✿ ❘❛♥❞✶/❘❛♥❞✷ ✵✵✵ = ✵ ( ✵) ✵✵✶ = ✶ (+✶) ✵✵✵ = ✵ ( ✵) ✵✵✵ = ✵ ( ✵) ✵✵✶ = ✶ (+✶) ✵✵✶ = ✶ (+✶) ✵✵✶ = ✶ (+✶) ✵✶✵ = ✷ (+✷) ✵✶✵ = ✷ (+✷) ✵✶✵ = ✷ (+✷) ✵✶✶ = ✸ (+✸) ✵✶✶ = ✸ (+✸) ✵✶✶ = ✸ (+✸) ✶✵✵ = ✹ (−✹∗) ✶✵✵ = ✹ (−✹) ✶✵✵ = ✹ (−✹) ✶✵✶ = ✺ (−✸) ✶✵✶ = ✺ (−✸) ✶✵✶ = ✺ (−✸) ✶✶✵ = ✻ (−✷) ✶✶✵ = ✻ (−✷) ✶✶✵ = ✻ (−✷) ✶✶✶ = ✼ (−✶) ✶✶✶ = ✼ (−✶) ✶✶✶ = ✼ (−✶) ✵✵✵ = ✵∗ ( ✵)

❈ ■♥tr♦❞✉❝t✐♦♥

slide-61
SLIDE 61

❙✐❣♥❡❞✱ ❯♥s✐❣♥❡❞ ❆❞❞✐t✐♦♥ ❚❛❜❧❡s ❈♦♥t✐♥✉❡❞

❆❞❞✐t✐♦♥ t❛❜❧❡ ❢♦r ♦♣❡❘❛♥❞ ◆ ❛♥❞ ♦♣❡❘❛♥❞ ✵❜✵✶✵ ❛s ✇❡❧❧ ❛s ♦♣❡❘❛♥❞ ◆ ❛♥❞ ♦♣❡❘❛♥❞ ✵❜✵✶✶✿ ❘❛♥❞✶/❘❛♥❞✷ ✵✶✵ = ✷ (+✷) ✵✶✶ = ✸ (+✸) ✵✵✵ = ✵ ( ✵) ✵✶✵ = ✷ (+✷) ✵✶✶ = ✸ (+✸) ✵✵✶ = ✶ (+✶) ✵✶✶ = ✸ (+✸) ✶✵✵ = ✹ (−✹∗) ✵✶✵ = ✷ (+✷) ✶✵✵ = ✹ (−✹∗) ✶✵✶ = ✺ (−✸∗) ✵✶✶ = ✸ (+✸) ✶✵✶ = ✺ (−✸∗) ✶✶✵ = ✻ (−✷∗) ✶✵✵ = ✹ (−✹) ✶✶✵ = ✻ (−✷) ✶✶✶ = ✼ (−✶) ✶✵✶ = ✺ (−✸) ✶✶✶ = ✼ (−✶) ✵✵✵ = ✵∗ ( ✵) ✶✶✵ = ✻ (−✷) ✵✵✵ = ✵∗ ( ✵) ✵✵✶ = ✶∗ (+✶) ✶✶✶ = ✼ (−✶) ✵✵✶ = ✶∗ (+✶) ✵✶✵ = ✷∗ (+✷)

❈ ■♥tr♦❞✉❝t✐♦♥

slide-62
SLIDE 62

❙✐❣♥❡❞✱ ❯♥s✐❣♥❡❞ ❆❞❞✐t✐♦♥ ❚❛❜❧❡s ❈♦♥t✐♥✉❡❞

❆❞❞✐t✐♦♥ t❛❜❧❡ ❢♦r ♦♣❡❘❛♥❞ ◆ ❛♥❞ ♦♣❡❘❛♥❞ ✵❜✶✵✵ ❛s ✇❡❧❧ ❛s ♦♣❡❘❛♥❞ ◆ ❛♥❞ ♦♣❡❘❛♥❞ ✵❜✶✵✶✿ ❘❛♥❞✶/❘❛♥❞✷ ✶✵✵ = ✹ (−✹) ✶✵✶ = ✺ (−✸) ✵✵✵ = ✵ ( ✵) ✶✵✵ = ✹ (−✹) ✶✵✶ = ✺ (−✸) ✵✵✶ = ✶ (+✶) ✶✵✶ = ✺ (−✸) ✶✶✵ = ✻ (−✷) ✵✶✵ = ✷ (+✷) ✶✶✵ = ✻ (−✷) ✶✶✶ = ✼ (−✶) ✵✶✶ = ✸ (+✸) ✶✶✶ = ✼ (−✶) ✵✵✵ = ✵∗ ( ✵) ✶✵✵ = ✹ (−✹) ✵✵✵ = ✵∗ ( ✵∗) ✵✵✶ = ✶∗ (+✶∗) ✶✵✶ = ✺ (−✸) ✵✵✶ = ✶∗ (+✶∗) ✵✶✵ = ✷∗ (+✷∗) ✶✶✵ = ✻ (−✷) ✵✶✵ = ✷∗ (+✷∗) ✵✶✶ = ✸∗ (+✸∗) ✶✶✶ = ✼ (−✶) ✵✶✶ = ✸∗ (+✸∗) ✶✵✵ = ✹∗ (−✹)

❈ ■♥tr♦❞✉❝t✐♦♥

slide-63
SLIDE 63

❙✐❣♥❡❞✱ ❯♥s✐❣♥❡❞ ❆❞❞✐t✐♦♥ ❚❛❜❧❡s ❈♦♥t✐♥✉❡❞

❆❞❞✐t✐♦♥ t❛❜❧❡ ❢♦r ♦♣❡❘❛♥❞ ◆ ❛♥❞ ♦♣❡❘❛♥❞ ✵❜✶✶✵ ❛s ✇❡❧❧ ❛s ♦♣❡❘❛♥❞ ◆ ❛♥❞ ♦♣❡❘❛♥❞ ✵❜✶✶✶✿ ❘❛♥❞✶/❘❛♥❞✷ ✶✶✵ = ✻ (−✷) ✶✶✶ = ✼ (−✶) ✵✵✵ = ✵ ( ✵) ✶✶✵ = ✻ (−✷) ✶✶✶ = ✼ (−✶) ✵✵✶ = ✶ (+✶) ✶✶✶ = ✼ (−✶) ✵✵✵ = ✵∗ ( ✵) ✵✶✵ = ✷ (+✷) ✵✵✵ = ✵∗ ( ✵) ✵✵✶ = ✶∗ (+✶) ✵✶✶ = ✸ (+✸) ✵✵✶ = ✶∗ (+✶) ✵✶✵ = ✷∗ (+✷) ✶✵✵ = ✹ (−✹) ✵✶✵ = ✷∗ (+✷∗) ✵✶✶ = ✸∗ (+✸∗) ✶✵✶ = ✺ (−✸) ✵✶✶ = ✸∗ (+✸∗) ✶✵✵ = ✹∗ (−✹) ✶✶✵ = ✻ (−✷) ✶✵✵ = ✹∗ (−✹) ✶✵✶ = ✺∗ (−✸) ✶✶✶ = ✼ (−✶) ✶✵✶ = ✺∗ (−✸) ✶✶✵ = ✻∗ (−✷)

❈ ■♥tr♦❞✉❝t✐♦♥

slide-64
SLIDE 64

❚②♣✐❝❛❧ ❘❛♥❣❡s ❢♦r ❯♥s✐❣♥❡❞ ❚②♣❡s

✲✲✲✲✲✲✲✲✲✲✰✲✲✲✲✲✲✲✲✰✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲ ⑤ ★ ❜✐ts ⑤ ▼✐♥✳ ⑤ ▼❛① ❱❛❧✉❡ ⑤ ✰✲✲✲✲✲✲✲✲✲✰✲✲✲✲✲✲✲✲✰✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✰ ⑤ ✽ ⑤ ✵ ⑤ ✷✺✺⑤ ⑤ ✶✻ ⑤ ✵ ⑤ ✻✺✱✺✸✺⑤ ⑤ ✸✷ ⑤ ✵ ⑤ ✹✱✷✾✹✱✾✻✼✱✷✾✺⑤ ⑤ ✻✹ ⑤ ✵ ⑤✶✽✱✹✹✻✱✼✹✹✱✵✼✸✱✼✵✾✱✺✺✶✱✻✶✺⑤ ✲✲✲✲✲✲✲✲✲✲✰✲✲✲✲✲✲✲✲✰✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲

❈ ■♥tr♦❞✉❝t✐♦♥

slide-65
SLIDE 65

❚②♣✐❝❛❧ ❘❛♥❣❡s ❢♦r ❙✐❣♥❡❞ ❚②♣❡s

✰✲✲✲✲✲✰✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✰✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✰ ⑤★❜✐ts⑤ ▼✐♥✳ ❱❛❧✉❡ ⑤ ▼❛① ❱❛❧✉❡ ⑤ ✰✲✲✲✲✲✰✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✰✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✰ ⑤ ✽ ⑤ ✲✶✷✽⑤ ✶✷✼⑤ ⑤ ✶✻ ⑤ ✲✸✷✱✼✻✽⑤ ✸✷✱✼✻✼⑤ ⑤ ✸✷ ⑤ ✲✷✱✶✹✼✱✹✽✸✱✻✹✽⑤ ✷✱✶✹✼✱✹✽✸✱✻✹✼⑤ ⑤ ✻✹ ⑤✲✾✱✷✷✸✱✸✼✷✱✵✸✻✱✽✺✹✱✼✼✺✱✽✵✽⑤ ✾✱✷✷✸✱✸✼✷✱✵✸✻✱✽✺✹✱⑤ ⑤ ⑤ ⑤ ✼✼✺✱✽✵✼ ⑤ ✰✲✲✲✲✲✰✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✰✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✰

❈ ■♥tr♦❞✉❝t✐♦♥

slide-66
SLIDE 66

❋✐♥❞✐♥❣ ■♥t❡❣❡r ❙✐③❡s ✐♥ ❈

■♥ ✐♥t❡❣❡r✲s✐③❡s✳❝✿ ★✐♥❝❧✉❞❡ <st❞✐♦✳❤> ✐♥t ♠❛✐♥✭✮ ④ ✴✴❝♦♥❝❛t❡♥❛t✐♦♥ ♦❢ ❛❞❥❛❝❡♥t str✐♥❣ ❧✐t❡r❛❧s ✴✴✪❧❞ ♥♦t ♣♦rt❛❜❧❡❀ ♠♦❞❡r♥ ❈ ❛❧❧♦✇s ✪③✉ ❢♦r s✐③❡♦❢✭✮ ♣r✐♥t❢✭✧s✐③❡♦❢✭❝❤❛r✮ ❂ ✪❧❞✱ s✐③❡♦❢✭s❤♦rt✮ ❂ ✪❧❞✱ ✧ ✧s✐③❡♦❢✭✐♥t✮ ❂ ✪❧❞ s✐③❡♦❢✭❧♦♥❣✮ ❂ ✪❧❞✱ ✧ ✧s✐③❡♦❢✭❧♦♥❣ ❧♦♥❣✮ ❂ ✪❧❞\♥✧✱ s✐③❡♦❢✭❝❤❛r✮✱ s✐③❡♦❢✭s❤♦rt✮✱ s✐③❡♦❢✭✐♥t✮✱ s✐③❡♦❢✭❧♦♥❣✮✱ s✐③❡♦❢✭❧♦♥❣ ❧♦♥❣✮✮❀ r❡t✉r♥ ✵❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-67
SLIDE 67

■♥t❡❣❡r ❙✐③❡s✿ ❊❞✐t❡❞ ▲♦❣

s✐③❡♦❢✭❝❤❛r✮ ❂ ✶✱ s✐③❡♦❢✭s❤♦rt✮ ❂ ✷✱ s✐③❡♦❢✭✐♥t✮ ❂ ✹ s✐③❡♦❢✭❧♦♥❣✮ ❂ ✽✱ s✐③❡♦❢✭❧♦♥❣ ❧♦♥❣✮ ❂ ✽

❈ ■♥tr♦❞✉❝t✐♦♥

slide-68
SLIDE 68

P♦✇❡rs ♦❢ ∼ ✶✵✵✵

❙✐♥❝❡ ✷✶✵ = ✶✵✷✹ ✇❤✐❝❤ ✐s ❝❧♦s❡ t♦ ✶✵✵✵✱ ✷✷✵ = ✶✱✵✹✽✱✺✼✻ ✇❤✐❝❤ ✐s ❝❧♦s❡ t♦ ✶✱✵✵✵✱✵✵✵✱ ✇❡ ❝❛♥ ✉s❡ ❦✐❧♦ ❛♥❞ ♠❡❣❛ ♥♦t❛t✐♦♥✱ ❜✉t ♥❡❡❞ t♦ ❞✐st✐♥❣✉✐s❤ ❜❡t✇❡❡♥ ♣♦✇❡rs ♦❢ ✶✵✵✵ ❛♥❞ ♣♦✇❡rs ♦❢ ✶✵✷✹✳ P♦✇❡rs ♦❢ ✶✵✵✵✿ ♥♦r♠❛❧ ♠❡tr✐❝ ♥♦t❛t✐♦♥✿ ❦❇✱ ▼❇✱ ●❇✱ ❡t❝✳ P♦✇❡rs ♦❢ ✶✵✷✹✿ ■❊❈ ✉♥✐ts✿ ❑✐❇✱ ▼✐❇✱ ●✐❇✱ ❡t❝✳ ❲r✐t❡ ♣r♦❣r❛♠ t♦ s❤♦✇ q✉❛♥t✐t✐❡s ❛ss♦❝✐❛t❡❞ ✇✐t❤ ❞✐✛❡r❡♥t ✉♥✐ts✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-69
SLIDE 69

❑✐❧♦ P♦✇❡rs Pr♦❣r❛♠ ▲♦❣

◆♦t❡ ♦✈❡r✢♦✇ ❢♦r ③❡tt❛ ❛♥❞ ②♦tt❛✳ ★♠❡tr✐❝ ✉♥✐ts ✩ ✳✴❦✐❧♦✲♣♦✇❡rs ✶✵✵✵✯✯✶ ❂ ✶ ❦✐❧♦❜②t❡ ✭❦❇✮ ✇❤✐❝❤ ✐s ✶✵✵✵ ❜②t❡s ✶✵✵✵✯✯✷ ❂ ✶ ♠❡❣❛❜②t❡ ✭▼❇✮ ✇❤✐❝❤ ✐s ✶✵✵✵✵✵✵ ❜②t❡s ✶✵✵✵✯✯✸ ❂ ✶ ❣✐❣❛❜②t❡ ✭●❇✮ ✇❤✐❝❤ ✐s ✶✵✵✵✵✵✵✵✵✵ ❜②t❡s ✶✵✵✵✯✯✹ ❂ ✶ t❡r❛❜②t❡ ✭❚❇✮ ✇❤✐❝❤ ✐s ✶✵✵✵✵✵✵✵✵✵✵✵✵ ❜②t❡s ✶✵✵✵✯✯✺ ❂ ✶ ♣❡t❛❜②t❡ ✭P❇✮ ✇❤✐❝❤ ✐s ✶✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵ ❜②t❡s ✶✵✵✵✯✯✻ ❂ ✶ ❡①❛❜②t❡ ✭❊❇✮ ✇❤✐❝❤ ✐s ✶✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵ ❜②t❡s ✶✵✵✵✯✯✼ ❂ ✶ ③❡tt❛❜②t❡ ✭❩❇✮ ✇❤✐❝❤ ✐s ✸✽✼✺✽✷✵✵✶✾✻✽✹✷✶✷✼✸✻ ❜②t❡s ✶✵✵✵✯✯✽ ❂ ✶ ②♦tt❛❜②t❡ ✭❨❇✮ ✇❤✐❝❤ ✐s ✷✵✵✸✼✻✹✷✵✺✷✵✻✽✾✻✻✹✵ ❜②t❡s

❈ ■♥tr♦❞✉❝t✐♦♥

slide-70
SLIDE 70

❑✐❧♦ P♦✇❡rs Pr♦❣r❛♠ ▲♦❣ ❈♦♥t✐♥✉❡❞

★✐❡❝ ✉♥✐ts ✶✵✷✹✯✯✶ ❂ ✶ ❦✐❜✐❜②t❡ ✭❑✐❇✮ ✇❤✐❝❤ ✐s ✶✵✷✹ ❜②t❡s ✶✵✷✹✯✯✷ ❂ ✶ ♠❡❜✐❜②t❡ ✭▼✐❇✮ ✇❤✐❝❤ ✐s ✶✵✹✽✺✼✻ ❜②t❡s ✶✵✷✹✯✯✸ ❂ ✶ ❣✐❜✐❜②t❡ ✭●✐❇✮ ✇❤✐❝❤ ✐s ✶✵✼✸✼✹✶✽✷✹ ❜②t❡s ✶✵✷✹✯✯✹ ❂ ✶ t❡❜✐❜②t❡ ✭❚✐❇✮ ✇❤✐❝❤ ✐s ✶✵✾✾✺✶✶✻✷✼✼✼✻ ❜②t❡s ✶✵✷✹✯✯✺ ❂ ✶ ♣❡❜✐❜②t❡ ✭P✐❇✮ ✇❤✐❝❤ ✐s ✶✶✷✺✽✾✾✾✵✻✽✹✷✻✷✹ ❜②t❡s ✶✵✷✹✯✯✻ ❂ ✶ ❡①❜✐❜②t❡ ✭❊✐❇✮ ✇❤✐❝❤ ✐s ✶✶✺✷✾✷✶✺✵✹✻✵✻✽✹✻✾✼✻ ❜②t❡s ✶✵✷✹✯✯✼ ❂ ✶ ③❡❜✐❜②t❡ ✭❩✐❇✮ ✇❤✐❝❤ ✐s ✵ ❜②t❡s ✶✵✷✹✯✯✽ ❂ ✶ ②♦❜✐❜②t❡ ✭❨✐❇✮ ✇❤✐❝❤ ✐s ✵ ❜②t❡s ✩

❈ ■♥tr♦❞✉❝t✐♦♥

slide-71
SLIDE 71

❑✐❧♦ P♦✇❡rs Pr♦❣r❛♠✿ ❚②♣❡ ❉❡❝❧❛r❛t✐♦♥

■♥ ❦✐❧♦✲♣♦✇❡rs✳❝✿ ✴✯✯ P❛❝❦❛❣❡ ✉♥✐t✲♥❛♠❡ ❛♥❞ ✐ts ❛❜❜r❡✈✐❛t✐♦♥✳ ✯✴ t②♣❡❞❡❢ str✉❝t ④ ❝♦♥st ❝❤❛r ✯♥❛♠❡❀ ❝♦♥st ❝❤❛r ✯❛❜❜r❀ ⑥ ❯♥✐t❀

❈ ■♥tr♦❞✉❝t✐♦♥

slide-72
SLIDE 72

❑✐❧♦ P♦✇❡rs Pr♦❣r❛♠✿ ▼❡tr✐❝ ❉❛t❛

st❛t✐❝ ❯♥✐t ♠❡tr✐❝❯♥✐ts❬❪ ❂ ④ ④ ✧❦✐❧♦❜②t❡✧✱ ✧❦❇✧ ⑥✱ ④ ✧♠❡❣❛❜②t❡✧✱ ✧▼❇✧ ⑥✱ ④ ✧❣✐❣❛❜②t❡✧✱ ✧●❇✧ ⑥✱ ④ ✧t❡r❛❜②t❡✧✱ ✧❚❇✧ ⑥✱ ④ ✧♣❡t❛❜②t❡✧✱ ✧P❇✧ ⑥✱ ④ ✧❡①❛❜②t❡✧✱ ✧❊❇✧ ⑥✱ ④ ✧③❡tt❛❜②t❡✧✱ ✧❩❇✧ ⑥✱ ④ ✧②♦tt❛❜②t❡✧✱ ✧❨❇✧ ⑥✱ ⑥❀

❈ ■♥tr♦❞✉❝t✐♦♥

slide-73
SLIDE 73

❑✐❧♦ P♦✇❡rs Pr♦❣r❛♠✿ ■❊❈ ❉❛t❛

st❛t✐❝ ❯♥✐t ✐❡❝❯♥✐ts❬❪ ❂ ④ ④ ✧❦✐❜✐❜②t❡✧✱ ✧❑✐❇✧ ⑥✱ ④ ✧♠❡❜✐❜②t❡✧✱ ✧▼✐❇✧ ⑥✱ ④ ✧❣✐❜✐❜②t❡✧✱ ✧●✐❇✧ ⑥✱ ④ ✧t❡❜✐❜②t❡✧✱ ✧❚✐❇✧ ⑥✱ ④ ✧♣❡❜✐❜②t❡✧✱ ✧P✐❇✧ ⑥✱ ④ ✧❡①❜✐❜②t❡✧✱ ✧❊✐❇✧ ⑥✱ ④ ✧③❡❜✐❜②t❡✧✱ ✧❩✐❇✧ ⑥✱ ④ ✧②♦❜✐❜②t❡✧✱ ✧❨✐❇✧ ⑥✱ ⑥❀

❈ ■♥tr♦❞✉❝t✐♦♥

slide-74
SLIDE 74

❑✐❧♦ P♦✇❡rs Pr♦❣r❛♠✿ ●✉ts

st❛t✐❝ ✈♦✐❞ ♦✉t❯♥✐ts✭✉♥s✐❣♥❡❞ ❜❛s❡✱ ❯♥✐t ✉♥✐ts❬❪✱ ✐♥t ♥❯♥✐ts✱ ❋■▲❊ ✯♦✉t✮ ④ ✉♥s✐❣♥❡❞ ❧♦♥❣ ❧♦♥❣ ✈ ❂ ✶❀ ❢♦r ✭✐♥t ✐ ❂ ✵❀ ✐ < ♥❯♥✐ts❀ ✐✰✰✮ ④ ✈ ✯❂ ❜❛s❡❀ ❢♣r✐♥t❢✭♦✉t✱ ✧✪❞✯✯✪❞ ❂ ✶ ✪s ✭✪s✮ ✧ ✧✇❤✐❝❤ ✐s ✪❧❧✉ ❜②t❡s\♥✧✱ ❜❛s❡✱ ✐ ✰ ✶✱ ✉♥✐ts❬✐❪✳♥❛♠❡✱ ✉♥✐ts❬✐❪✳❛❜❜r✱ ✈✮❀ ⑥ ❢♣r✐♥t❢✭♦✉t✱ ✧\♥✧✮❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-75
SLIDE 75

❑✐❧♦ P♦✇❡rs Pr♦❣r❛♠ ♠❛✐♥✭✮ ❋✉♥❝t✐♦♥

✐♥t ♠❛✐♥✭✮ ④ ♦✉t❯♥✐ts✭✶✵✵✵✉✱ ♠❡tr✐❝❯♥✐ts✱ s✐③❡♦❢✭♠❡tr✐❝❯♥✐ts✮✴s✐③❡♦❢✭♠❡tr✐❝❯♥✐ts❬✵❪✮✱ st❞♦✉t✮❀ ♦✉t❯♥✐ts✭✶✵✷✹✉✱ ✐❡❝❯♥✐ts✱ s✐③❡♦❢✭✐❡❝❯♥✐ts✮✴s✐③❡♦❢✭✐❡❝❯♥✐ts❬✵❪✮✱ st❞♦✉t✮❀ r❡t✉r♥ ✵❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-76
SLIDE 76

❑✐❧♦ P♦✇❡rs Pr♦❣r❛♠ ❉✐s❝✉ss✐♦♥

❆ ❈ str✉❝t ❛❧❧♦✇s ♣❛❝❦❛❣✐♥❣ r❡❧❛t❡❞ ❞❛t❛ t♦❣❡t❤❡r✳ ■♥ ❈✱ t②♣❡❞❡❢ ❞❡✜♥❡s ❛ ♥❛♠❡ ❢♦r s♦♠❡ t②♣❡✳ ❙♦ t❤❡ ♣r♦❣r❛♠ ✉s❡s t❤❡ ♥❛♠❡ ❯♥✐t t♦ r❡❢❡r t♦ ❛ ♣❛rt✐❝✉❧❛r str✉❝t t②♣❡✳ ◆♦t❡ t❤❡ ✉s❡ ♦❢ t❤❡ ✉ s✉✣① ♦♥ ✶✵✵✵✉ ❛♥❞ ✶✵✷✹✉ t♦ ♣❛ss ❛♥ ✉♥s✐❣♥❡❞ ❜❛s❡ ✈❛❧✉❡ t♦ ♦✉t❯♥✐ts✭✮✳ ■❊❈ ✉♥✐ts ❤❛✈❡ ♥♦t r❡❛❧❧② ❝❛✉❣❤t ♦♥✳ ■♥ ♣r❛❝t✐❝❡✱ ●❇ ♠❛② ♠❡❛♥ ✧❣✐❣❛❜②t❡✧ ♦r ✧❣✐❜✐❜②t❡✧✱ ❞❡♣❡♥❞✐♥❣ ♦♥ ❝♦♥t❡①t✳ ■♥ ❝♦♠♠❡r❝✐❛❧ ❝♦♥t❡①ts✱ ♠❡♠♦r② s✐③❡s ❛r❡ ♦❢t❡♥ st❛t❡❞ ✐♥ ■❊❈ ✉♥✐ts✱ ❞✐s❦ s✐③❡s ✐♥ ♠❡tr✐❝ ✉♥✐ts ❜✉t ♥♦ ❣✉❛r❛♥t❡❡s✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-77
SLIDE 77

❇♦♦❧❡❛♥s

❇❛s✐❝ ❈ ❞♦❡s ♥♦t ❤❛✈❡ ❛♥② ❜♦♦❧❡❛♥ t②♣❡✳ ❈✾✾ ✐♥tr♦❞✉❝❡❞ st❞❜♦♦❧✳❤ ❤❡❛❞❡r ✇✐t❤ s✉✐t❛❜❧❡ ❞❡✜♥✐t✐♦♥s ❢♦r tr✉❡ ❛♥❞ ❢❛❧s❡✳ ❈♦♠♣❛r✐s♦♥ ♦♣❡r❛t♦rs ❁✱ ❁❂✱ ❃✱ ❃❂✱ ❂❂✱ ✦❂ r❡t✉r♥ r❡s✉❧t ✶ ❢♦r tr✉❡ ❛♥❞ ✵ ❢♦r ❢❛❧s❡✳ ▲♦❣✐❝❛❧ ♦♣❡r❛t♦rs ✫✫✱ ⑤⑤✱ ✦ tr❡❛t ✵ ❛s ❢❛❧s❡✱ ❛❧❧ ♥♦♥✲✵ ✈❛❧✉❡s ❛s tr✉❡✳ ❈ ❤❛s ❛ s✐♥❣❧❡ ❢❛❧s② ✈❛❧✉❡✿ ✵✳ ❆❧❧ ✈❛❧✉❡s ♦t❤❡r t❤❛♥ ✵ ❛r❡ tr✉t❤②✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-78
SLIDE 78

❈♦♠♣❛r✐♥❣ ◆✉♠❡r✐❝ ❊①♣r❡ss✐♦♥s ✐♥ ❈

❆♥ ❡①♣r❡ss✐♦♥ ✇❤✐❝❤ ❝♦♠♣❛r❡s t✇♦ ♥✉♠❡r✐❝ ❡①♣r❡ss✐♦♥s ✐s ❦♥♦✇♥ ❛s ❛ r❡❧❛t✐♦♥❛❧ ❡①♣r❡ss✐♦♥✳ ❂❂✱ ✭✦❂✮ ❘❡t✉r♥s ✶ ✐✛ t✇♦ ❡①♣r❡ss✐♦♥s ❛r❡ ❡q✉❛❧ ✭♥♦t✲❡q✉❛❧✮✱ ✵ ♦t❤❡r✇✐s❡✳ ❉♦ ♥♦t ✉s❡ ✇✐t❤ ✢♦❛t✐♥❣ ♣♦✐♥t t②♣❡s✿ ❊①❛♠♣❧❡✿ ✐❢ ✭✐ ✦❂ ✵✮ ❜ ❂ ①✴✐❀✳ ❲❛t❝❤ ♦✉t ❢♦r ✐♥❝♦rr❡❝t ✉s❡ ♦❢ ❂✳ ❋♦r ❡①❛♠♣❧❡✱ ✐❢ ✭✐ ❂ ✵✮ ❜ ❂ ✶ ❡❧s❡ ❜ ❂ ①✴✐❀ ✇✐❧❧ ❛❧✇❛②s ❞✐✈✐❞❡ ❜② ✐ ❜❡❝❛✉s❡ ♦❢ ✉s❡ ♦❢ ❂ ✐♥st❡❛❞ ♦❢ ❂❂ ✐♥ ❝♦♠♣❛r✐s♦♥✳ ❙♦♠❡ ♣r♦❣r❛♠♠❡rs ♣r♦t❡❝t ❢♦r t❤✐s ❝❛s❡ ❜② ✇r✐t✐♥❣ ✐❢ ✭✵ ❂❂ ✐✮ ✇❤✐❝❤ ✇✐❧❧ ❝❛✉s❡ ❛ ❝♦♠♣✐❧❛t✐♦♥ ❡rr♦r ✐❢ ✇r✐tt❡♥ ✐♥❝♦rr❡❝t❧② ❛s ✐❢ ✭✵ ❂ ✐✮✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-79
SLIDE 79

❈♦♠♣❛r✐♥❣ ◆✉♠❡r✐❝ ❊①♣r❡ss✐♦♥s ✐♥ ❈ ❈♦♥t✐♥✉❡❞

❁✱ ✭❃✮ ❘❡t✉r♥s ✶ ✐✛ t❤❡ ❧❡❢t✲❤❛♥❞ ❡①♣r❡ss✐♦♥ ✐s ❧❡ss✲t❤❛♥ ✭❣r❡❛t❡r✲t❤❛♥✮ t❤❡ r✐❣❤t✲❤❛♥❞ ❡①♣r❡ss✐♦♥✱ ✵ ♦t❤❡r✇✐s❡✳ ❊①❛♠♣❧❡✿ ❢♦r ✭✐♥t ✐ ❂ ✵❀ ✐ < ✶✵❀ ✐✰✰✮ ④ ✳✳✳ ⑥✳ ❁❂✱ ✭❃❂✮ ❘❡t✉r♥s ✶ ✐✛ t❤❡ ❧❡❢t✲❤❛♥❞ ❡①♣r❡ss✐♦♥ ✐s ❧❡ss✲t❤❛♥✲♦r✲❡q✉❛❧✲t♦ ✭❣r❡❛t❡r✲t❤❛♥✲♦r✲❡q✉❛❧✲t♦✮ t❤❡ r✐❣❤t✲❤❛♥❞ ❡①♣r❡ss✐♦♥✱ ✵ ♦t❤❡r✇✐s❡✳ ❊①❛♠♣❧❡✿ ❢♦r ✭✐♥t ✐ ❂ ✾❀ ✐ >❂ ✵❀ ✐✲✲✮ ④ ✳✳✳ ⑥✳ ❈❛♥ ❛❧s♦ ✉s❡ ♦♥ r✐❣❤t✲❤❛♥❞✲s✐❞❡ ♦❢ ❛ss✐❣♥♠❡♥t ❛s ✐♥✿ ✐♥t ❛▲❚✶✵ ❂ ✭❛ < ✶✵✮❀✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-80
SLIDE 80

❙❤♦rt✲❈✐r❝✉✐t ▲♦❣✐❝❛❧ ❖♣❡r❛t♦rs

❚❤❡ ♦♣❡r❛t♦rs ⑤⑤ ✭❧♦❣✐❝❛❧✲♦r✮ ❛♥❞ ✫✫ ✭❧♦❣✐❝❛❧✲❛♥❞✮ ❡✈❛❧✉❛t❡ ♦♣❡r❛♥❞s ❢r♦♠ ❧❡❢t✲t♦✲r✐❣❤t✱ ❜✉t st♦♣ ✭✧s❤♦rt✲❝✐r❝✉✐t✧✮ t❤❡ ❡✈❛❧✉❛t✐♦♥ ✐♠♠❡❞✐❛t❡❧② ♦♥❝❡ t❤❡ r❡s✉❧t ✐s ❦♥♦✇♥ ❢♦r s✉r❡❀ ✐✳❡✳ t❤❡② ♠❛② ♥♦t ❡✈❛❧✉❛t❡ t❤❡✐r ✷♥❞ ♦♣❡r❛♥❞ ✐❢ t❤❡ r❡s✉❧t ✐s ❞❡t❡r♠✐♥❡❞ ❜② t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ ✜rst ♦♣❡r❛♥❞✳ ❆ ⑤⑤ ❇ ■❢ ❡①♣r❡ss✐♦♥ ❆ ❡✈❛❧✉❛t❡s t♦ ♥♦♥✲③❡r♦✱ t❤❡♥ r❡t✉r♥ ✶ ✇✐t❤♦✉t ❡✈❡r ❡✈❛❧✉❛t✐♥❣ ❡①♣r❡ss✐♦♥ ❇✳ ❖t❤❡r✇✐s❡ r❡t✉r♥ ✵ ✐❢ ❇ t♦♦ ❡✈❛❧✉❛t❡s t♦ ✵✱ ♦t❤❡r✇✐s❡ r❡t✉r♥ ✶✳ ❊①❛♠♣❧❡✿ ■♥ ✐❢ ✭① ❂❂ ✵ ⑤⑤ ②✴① > ✶✵✮ ④ ⑥✱ s❤♦rt✲❝✐r❝✉✐t ♣r♦♣❡rt② ♦❢ ⑤⑤ ❛✈♦✐❞s ❞✐✈✐s✐♦♥✲❜②✲✵ ❡rr♦r✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-81
SLIDE 81

❙❤♦rt✲❈✐r❝✉✐t ▲♦❣✐❝❛❧ ❖♣❡r❛t♦rs ❈♦♥t✐♥✉❡❞

❆ ✫✫ ❇ ■❢ ❡①♣r❡ss✐♦♥ ❆ ❡✈❛❧✉❛t❡s t♦ ✵✱ t❤❡♥ r❡t✉r♥ ✵ ✇✐t❤♦✉t ❡✈❡r ❡✈❛❧✉❛t✐♥❣ ❡①♣r❡ss✐♦♥ ❇✳ ❖t❤❡r✇✐s❡ r❡t✉r♥ ✶ ✐❢ ❇ t♦♦ ❡✈❛❧✉❛t❡s t♦ ♥♦♥✲③❡r♦✱ ♦t❤❡r✇✐s❡ r❡t✉r♥ ✵✳ ❊①❛♠♣❧❡✿ ❙❡❛r❝❤ ❢♦r ✜rst ❡❧❡♠❡♥t ♦❢ ❛❬♥❪ ✇❤✐❝❤ ✐s ❡q✉❛❧ t♦ ❦❡②✿ ❢♦r ✭✐♥t ✐ ❂ ✵❀ ✐ < ♥ ✫✫ ❛❬✐❪ ✦❂ ❦❡②❀ ✐✰✰✮ ④ ✳✳✳ ⑥ ◆♦t❡ t❤❛t ❜❡❝❛✉s❡ ♦❢ s❤♦rt✲❝✐r❝✉✐t ❡✈❛❧✉❛t✐♦♥✱ ✇❤❡♥ ✐ ❂❂ ♥ ❝♦❞❡ ❞♦❡s ♥♦t ❡①❛♠✐♥❡ ❛❬✐❪ ❛t ❛❧❧✱ t❤✉s ❛✈♦✐❞✐♥❣ ❛♥ ✐♥❞❡①✲♦✉t✲♦❢✲❜♦✉♥❞s ❡rr♦r✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-82
SLIDE 82

▲♦❣✐❝❛❧ ◆♦t

✦ ❆ ❘❡t✉r♥ ✵ ✐❢ ❆ ✐s ♥♦♥✲③❡r♦✱ ✶ ✇❤❡♥ ❆ ✐s ✵✳ ❈❛♥ ❛✈♦✐❞ ✉s✐♥❣ ✦ ❜② ❛♣♣❧②✐♥❣ ❉❡▼♦r❣❛♥✬s ❧❛✇✿ ❡①❛♠♣❧❡✱ ✐♥st❡❛❞ ♦❢ ✦✭① <❂ ✶✵ ⑤⑤ ② ❂❂ ✺✮ ✉s❡ ✭① > ✶✵ ✫✫ ② ✦❂ ✺✮✱ ❜✉t ✉s❡ ✦ ✐❢ ✐t ✐s ❝❧❡❛r❡r ✐♥ ❛ ♣❛rt✐❝✉❧❛r ❝♦♥t❡①t✳ ■❞✐♦♠ ✦✦① ❝❛♥ ❜❡ ✉s❡❞ t♦ ❝♦♥✈❡rt ❢r♦♠ ① ✇❤✐❝❤ ♠❛② ♥♦t ❜❡ str✐❝t❧② ✵ ♦r ✶ t♦ ❛ str✐❝t ✵ ♦r ✶ ✈❛❧✉❡✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-83
SLIDE 83

▲♦❣✐❝❛❧ ❖♣❡r❛t♦rs ✈❡rs✉s ❇✐t✇✐s❡ ❖♣❡r❛t♦rs

❉♦ ♥♦t ❝♦♥❢✉s❡ ❜✐t✲✇✐s❡ ♦♣❡r❛t♦rs ✫✱ ⑤✱ ❫✱ ⑦ ✇✐t❤ ❧♦❣✐❝❛❧ ♦♣❡r❛t♦rs ✫✫✱ ⑤⑤✱ ✦ ✇❤✐❝❤ ♦♣❡r❛t❡ ♦♥ ♣s❡✉❞♦✲❜♦♦❧❡❛♥ ✈❛❧✉❡s✳ ▲♦❣✐❝❛❧ ♦♣❡r❛t♦rs ✫✫ ❛♥❞ ⑤⑤ ❤❛✈❡ s❤♦rt✲❝✐r❝✉✐t s❡♠❛♥t✐❝s ❛♥❞ ♠❛② ♥♦t ❡✈❛❧✉❛t❡ t❤❡✐r ✷♥❞ ♦♣❡r❛♥❞❀ ❜✐t✇✐s❡✲♦♣❡r❛t♦rs ✫ ❛♥❞ ⑤ ❛❧✇❛②s ❡✈❛❧✉❛t❡ ❜♦t❤ ♦♣❡r❛♥❞s✳ ❆ss✐❣♥♠❡♥t ♦♣❡r❛t♦rs ✫❂✱ ⑤❂ ❛♥❞ ❫❂ r❡❢❡r t♦ t❤❡ ❜✐t✇✐s❡ ♦♣❡r❛t♦rs✳ ◆♦ ❛ss✐❣♥♠❡♥t ♦♣❡r❛t♦rs ❢♦r ❧♦❣✐❝❛❧ ♦♣❡r❛t♦rs ✫✫ ❛♥❞ ⑤⑤✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-84
SLIDE 84

■❢✲t❤❡♥✲❡❧s❡ ❊①♣r❡ss✐♦♥s

① ❂ ✭❝♦♥❞✮ ❄ ❡①♣r✶ ✿ ❡①♣r✷ ❡q✉✐✈❛❧❡♥t t♦ ✐❢ ✭❝♦♥❞✮ ① ❂ ❡①♣r✶ ❡❧s❡ ① ❂ ❡①♣r✷❀ ◆♦t❡ ✐t ✐s ♣♦ss✐❜❧❡ t♦ ❝❤❛✐♥ ❝♦♥❞✐t✐♦♥s t♦❣❡t❤❡r ❛s ✐♥ ① ❂ ✭❝♦♥❞✶✮ ❄ ❡①♣r✶ ✿ ✭❝♦♥❞✷✮ ❄ ❡①♣r✷ ✿ ❡①♣r✸ ✇❤✐❝❤ ✐s ❡q✉✐✈❛❧❡♥t t♦ ① ❂ ✭❝♦♥❞✶✮ ❄ ❡①♣r✶ ✿ ✭✭❝♦♥❞✷✮ ❄ ❡①♣r✷ ✿ ❡①♣r✸✮✱ ❜✉t ❝❛♥ ❡❛s✐❧② t✉r♥ ✉❣❧②✳ ■ t❡♥❞ t♦ ♦✈❡r✉s❡ t❤✐s ✐♥ ♠② ❝♦❞❡ ❝♦♠♣❛r❡❞ t♦ ♥♦r♠❛❧ ♣r❛❝t✐❝❡✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-85
SLIDE 85

▼❡♠♦r② ❆❞❞r❡ss❡s ❛♥❞ P♦✐♥t❡rs

❯♥❧✐❦❡ ❤✐❣❤❡r✲❧❡✈❡❧ ❧❛♥❣✉❛❣❡s✱ ❈ ❡①♣♦s❡s ♠❡♠♦r② ❛❞❞r❡ss❡s t♦ t❤❡ ♣r♦❣r❛♠♠❡r✳ ❚❤❡ ❛❞❞r❡ss ♦❢ ❛ ✈❛❧✉❡ ❝❛♥ ❜❡ ♦❜t❛✐♥❡❞ ❜② ✉s✐♥❣ t❤❡ ✫ ♣r❡✜① ♦♣❡r❛t♦r✳ ❆ ♣♦✐♥t❡r ✐s ❛ ✈❛r✐❛❜❧❡ ✇❤✐❝❤ ❤♦❧❞s ❛♥ ❛❞❞r❡ss✳ ✐♥t ✐ ❂ ✾✾❀ ✐♥t ✯♣✐ ❂ ✫✐❀ ✴✴❞❡❝❧❛r❡ ♣✐ ❛s ♣♦✐♥t❡r t♦ ✐ ❝❤❛r ❝ ❂ ✬❳✬❀ ❝❤❛r ✯♣❝ ❂ ✫❝❀ ✴✴❞❡❝❧❛r❡ ♣❝ ❛s ♣♦✐♥t❡r t♦ ❝ ✐♥t ✯♣ ❂ ✫✭✐ ✰ ✶✮❀ ✴✴❡rr♦r✿ ✐ ✰ ✶ ❞♦❡s ♥♦t ❤❛✈❡ ❛❞❞r❡ss ◆❯▲▲ ✐s ❛ s♣❡❝✐❛❧ ♣♦✐♥t❡r ✈❛❧✉❡ ✇❤✐❝❤ ❞♦❡s ♥♦t ♣♦✐♥t ❛♥②✇❤❡r❡✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-86
SLIDE 86

❉❡r❡❢❡r❡♥❝✐♥❣

❉❡r❡❢❡r❡♥❝✐♥❣ ❛ ♣♦✐♥t❡r ♠❡❛♥s t♦ ❛❝❝❡ss t❤❡ ♠❡♠♦r② ✐t ♣♦✐♥ts t♦✳ ❉♦♥❡ ✉s✐♥❣ ✯ ❛s ❛ ♣r❡✜① ♦♣❡r❛t♦r✳ ◆❯▲▲ ❝❛♥♥♦t ❜❡ ❞❡r❡❢❡r❡♥❝❡❞✳ ✐♥t ✐ ❂ ✾✾❀ ✐♥t ✯♣✐ ❂ ✫✐❀ ✐♥t ❥ ❂ ✯♣✐ ✰ ✶❀ ✴✴❞❡r❡❢❡r❡♥❝❡ ♣✐❀ ❥ ❂❂ ✶✵✵ ✯♣✐ ❂ ✯♣✐ ✰ ✷❀ ✴✴❜♦t❤ ▲❍❙ ❛♥❞ ❘❍❙ ❞❡r❡❢❡r❡♥❝❡ ✴✴✐ ❂❂ ✶✵✶ ❝❤❛r ❝ ❂ ✬❳✬❀ ❝❤❛r ✯♣❝ ❂ ✫❝❀ ❝❤❛r ❝✶ ❂ ✯♣❝ ✲ ✷❀ ✴✴❞❡r❡❢❡r❡♥❝❡ ♣❝❀ ✴✴❝✶ ❂ ✬❱✬ ✇✐t❤ ❝♦♥t✐❣✉♦✉s ❡♥❝♦❞✐♥❣ ✯♣❝ ✰❂ ✶❀ ✴✴❝ ❂❂ ✬❨✬ ✇✐t❤ ❝♦♥t✐❣✉♦✉s ❡♥❝♦❞✐♥❣

❈ ■♥tr♦❞✉❝t✐♦♥

slide-87
SLIDE 87

❆rr❛②s

❆ ❈ ❛rr❛② ❜❛s✐❝❛❧❧② ❥✉st r❡♣r❡s❡♥ts t❤❡ ❛❞❞r❡ss ♦❢ ❛♥ ❛r❡❛ ♦❢ ♠❡♠♦r②❀ ✐✳❡✳✱ ❛ ❈ ❛rr❛② ✐s ❜❛s✐❝❛❧❧② ❛ ♣♦✐♥t❡r✳ ■t ❢♦❧❧♦✇s t❤❛t ❛ ❈ ❛rr❛② ❞♦❡s ♥♦t tr❛❝❦ t❤❡ ♥✉♠❜❡r ♦❢ ❡❧❡♠❡♥ts ✐t ❤❛s✳ ❚❤❡ ♣r♦❣r❛♠♠❡r ♥❡❡❞s t♦ tr❛❝❦ t❤❡ ♥✉♠❜❡r ♦❢ ❡❧❡♠❡♥ts ✐♥ t❤❡ ❛rr❛②✳ ❙♦♠❡ ❛❧t❡r♥❛t✐✈❡s✿

❍❛✈❡ ❛♥♦t❤❡r ✈❛r✐❛❜❧❡ ✇❤✐❝❤ ❡①♣❧✐❝✐t❧② st♦r❡s t❤❡ ♥✉♠❜❡r ♦❢ ❡❧❡♠❡♥ts ✐♥ t❤❡ ❛rr❛②✳ ▼❛r❦ t❤❡ ❡♥❞ ♦❢ t❤❡ ❛rr❛② ✉s✐♥❣ s♦♠❡ ❦✐♥❞ ♦❢ s❡♥t✐♥❡❧ ✈❛❧✉❡❀ ✐✳❡✳ ❛ ✈❛❧✉❡ ✇❤✐❝❤ ❝❛♥♥♦t ♦❝❝✉r ❛s ❛ ❧❡❣❛❧ ✈❛❧✉❡ ✐♥ t❤❡ ❞❛t❛ st♦r❡❞ ✐♥ t❤❡ ❛rr❛②✳ ❋♦r ❡①❛♠♣❧❡✱ ✐❢ ❛♥ ❛rr❛② st♦r❡s ♦♥❧② ♥♦♥✲♥❡❣❛t✐✈❡ ✐♥t❡❣❡rs✱ t❤❡♥ ✲✶ ❝♦✉❧❞ ❜❡ ✉s❡❞ ❛s ❛ s❡♥t✐♥❡❧✳ ❚❤❡ ♥✉♠❜❡r ♦❢ ❡❧❡♠❡♥ts ✐♥ t❤❡ ❛rr❛② ✐s ❦♥♦✇♥ ❛❤❡❛❞ ♦❢ t✐♠❡ ❛s s♦♠❡ ✜①❡❞ ✈❛❧✉❡ ✭❧✐❦❡ s❛② ✷✼✮ ❛♥❞ ❛❧❧ ❝♦❞❡ ✐s ✇r✐tt❡♥ ❛ss✉♠✐♥❣ t❤❛t s✐③❡✳ ❯s✉❛❧❧② ❛ ❜❛❞ ✐❞❡❛✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-88
SLIDE 88

❲❤❡♥ ❆rr❛②s ❛r❡ P♦✐♥t❡rs

P❡t❡r ❱❛♥ ❉❡r ▲✐♥❞❡♥ ✐♥ ❉❡❡♣ ❈ ❙❡❝r❡ts✿ ❚❤❡ ✉s❡ ♦❢ ❛♥ ❛rr❛② ♥❛♠❡ ✐♥ ❛♥ ❡①♣r❡ss✐♦♥ ✭♥♦t ❞❡❝❧❛r❛t✐♦♥✮ ✇❤✐❝❤ ✐s ♥♦t ❛♥ ♦♣❡r❛♥❞ ♦❢ s✐③❡♦❢✭✮ ✐s tr❡❛t❡❞ ❜② t❤❡ ❝♦♠♣✐❧❡r ❛s ❛ ♣♦✐♥t❡r t♦ t❤❡ ✜rst ❡❧❡♠❡♥t ♦❢ t❤❡ ❛rr❛②✳ ❆ s✉❜s❝r✐♣t ✐s ❛❧✇❛②s ❡q✉✐✈❛❧❡♥t t♦ ❛♥ ♦✛s❡t ❢r♦♠ ❛ ♣♦✐♥t❡r✳ ❆♥ ❛rr❛② ♥❛♠❡ ✐♥ t❤❡ ❞❡❝❧❛r❛t✐♦♥ ♦❢ ❛ ❢✉♥❝t✐♦♥ ♣❛r❛♠❡t❡r ✐s tr❡❛t❡❞ ❜② t❤❡ ❝♦♠♣✐❧❡r ❛s ❛ ♣♦✐♥t❡r t♦ t❤❡ ✜rst ❡❧❡♠❡♥t ♦❢ t❤❡ ❛rr❛②✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ ❛rr❛②s ❛r❡ ♣❛ss❡❞ ❜② r❡❢❡r❡♥❝❡ ❢♦r ❡✣❝✐❡♥❝② r❡❛s♦♥s ✭❛❧❧ ♥♦♥✲❛rr❛② ❞❛t❛ ❛r❡ ♣❛ss❡❞ ❜② ✈❛❧✉❡✮✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-89
SLIDE 89

P♦✐♥t❡rs ❛♥❞ ❆rr❛②s

❖♥❧② ♦♣❡r❛t✐♦♥s ❢♦r ❛♥ ❛rr❛② ❛r❡ ❣❡tt✐♥❣ ✐ts s✐③❡ ✉s✐♥❣ s✐③❡♦❢✭✮ ♦r ♦❜t❛✐♥✐♥❣ ❛ ♣♦✐♥t❡r t♦ ❡❧❡♠❡♥t ✵ ♦❢ t❤❡ ❛rr❛②✳ ❆❧❧ ♦t❤❡r ❛rr❛② ♦♣s ❛r❡ r❡❛❧❧② ♣♦✐♥t❡r ♦♣s✳ ❛❬✐❪ ✐s ❡q✉✐✈❛❧❡♥t t♦ ✯✭❛ ✰ ✐✮ ✇❤✐❝❤ ✐s ❡q✉✐✈❛❧❡♥t t♦ ✯✭✐ ✰ ❛✮ ✇❤✐❝❤ ✐s ❡q✉✐✈❛❧❡♥t t♦ ✐❬❛❪✳ ❲❤❡♥ ✉s❡❞ ✇✐t❤✐♥ ❛♥ ❡①♣r❡ss✐♦♥✱ ❛♥ ❛rr❛② ✐s ❡q✉✐✈❛❧❡♥t t♦ ❛ ♣♦✐♥t❡r t♦ ✐ts ✜rst ❡❧❡♠❡♥t✳ ✐♥t ❛❬✶✵❪✱ ✐❀ ✴✴❛ ✐s ❛rr❛② ♦❢ ✶✵ ✐♥t✬s❀ ✐ ✐s ✐♥t✳ ❛❬✐❪❀ ✴✴✐✬t❤ ❡❧❡♠❡♥t ♦❢ ❛✳ ✯✭❛ ✰ ✐✮❀ ✴✴❛❧s♦ ✐✬t❤ ❡❧❡♠❡♥t ♦❢ ❛✳ ✯✭✐ ✰ ❛✮❀ ✴✴❛❧s♦ ✐✬t❤ ❡❧❡♠❡♥t ♦❢ ❛✳ ✐❬❛❪❀ ✴✴❛❧s♦ ✐✬t❤ ❡❧❡♠❡♥t ♦❢ ❛✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-90
SLIDE 90

❆rr❛② ♦❢ ❝❤❛r ❛♥❞ P♦✐♥t❡r t♦ ❝❤❛r ❆r❡ ❉✐✛❡r❡♥t

❝❤❛r ✯♠s❣ ❂ ✧❤❡❧❧♦✧❀✿ ♠s❣✿ ❬ ✳✳✳ ❪ ✲✲✲✲❃ ❬✬❤✬⑤✬❡✬⑤✬❧✬⑤✬❧✬⑤✬♦✬⑤✬❭✵✬❪

s✐③❡♦❢✭♠s❣✮ ✇✐❧❧ ❜❡ t❤❡ s✐③❡ ♦❢ ❛ ♣♦✐♥t❡r ✭✐✳❡✳ ❛ ♠❡♠♦r②

❛❞❞r❡ss✮✳ ❚②♣✐❝❛❧❧②✱ t❤✐s ✐s ✹ ♦r ✽✳ ❚♦ ❝♦♠♣✉t❡ t❤❡ ❛❞❞r❡ss ♦❢ ♠s❣❬✐❪✱ t❤❡ ❝♦♠♣✐❧❡r ✇✐❧❧ ♥❡❡❞ t♦ ♣r♦❞✉❝❡ ❝♦❞❡ t♦ ❛❞❞ t❤❡ ✈❛❧✉❡ ♦❢ ✐ t♦ t❤❡ ✈❛❧✉❡ st♦r❡❞ ❛t ♠❡♠♦r② ❧♦❝❛t✐♦♥ ♠s❣✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-91
SLIDE 91

❆rr❛② ♦❢ ❝❤❛r ❛♥❞ P♦✐♥t❡r t♦ ❝❤❛r ❆r❡ ❉✐✛❡r❡♥t ❈♦♥t✐♥✉❡❞

❝❤❛r ♠s❣❬❪ ❂ ✧❤❡❧❧♦✧❀ ♠s❣✿ ❬✬❤✬⑤✬❡✬⑤✬❧✬⑤✬❧✬⑤✬♦✬⑤✬❭✵✬❪

s✐③❡♦❢✭♠s❣✮ ✇✐❧❧ ❜❡ ✻✳

❚♦ ❝♦♠♣✉t❡ t❤❡ ❛❞❞r❡ss ♦❢ ♠s❣❬✐❪✱ t❤❡ ❝♦♠♣✐❧❡r ✇✐❧❧ ♥❡❡❞ t♦ ♣r♦❞✉❝❡ ❝♦❞❡ t♦ ❛❞❞ t❤❡ ✈❛❧✉❡ ♦❢ ✐ t♦ t❤❡ ❛❞❞r❡ss ♦❢ ♠s❣✳ ■t ✐s ✇r♦♥❣ t♦ ❤❛✈❡ ♦♥❡ ✜❧❡ ❞❡✜♥❡ ❝❤❛r ♠s❣❬❪ ❂ ✧❤❡❧❧♦✧❀ ❛♥❞ ❛♥♦t❤❡r ✜❧❡ ❞❡❝❧❛r❡ ❡①t❡r♥ ❝❤❛r ✯♠s❣❀ ❛s t❤❡ ❝♦♠♣✐❧❡r ✇✐❧❧ ❣❡♥❡r❛t❡ ❞✐✛❡r❡♥t ❛❝❝❡ss ❝♦❞❡✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-92
SLIDE 92

▼✉❧t✐✲❉✐♠❡♥s✐♦♥❛❧ ❆rr❛②s

❈ ❤❛s ♦♥❧② ✶✲❞✐♠❡♥s✐♦♥❛❧ ❛rr❛②s✳ ❊❧❡♠❡♥ts ♦❢ ❛rr❛②s ❝❛♥ t❤❡♠s❡❧✈❡s ❜❡ ❛rr❛②s✱ ✇❤✐❝❤ ♣❡r♠✐ts ❛rr❛② ♥♦t❛t✐♦♥ ❧✐❦❡ ❛❬✐❪❬❥❪ ❢♦r ♠✉❧t✐♣❧❡ ❞✐♠❡♥s✐♦♥s ❢♦r st❛t✐❝ ❛♥❞ ❛✉t♦ ✭❜✉t ♥♦t ❞②♥❛♠✐❝❛❧❧② ♠❛❧❧♦❝✭✮✬❞✮ ❛rr❛②s✳ ❲❤❡♥ ❞❡❝❧❛r✐♥❣ ✭♥♦t ❞❡✜♥✐♥❣✮ ❛ ♠✉❧t✐✲❞✐♠❡♥s✐♦♥❛❧ ❛rr❛②✱ ✜rst ✭❧❡❢t♠♦st✮ ❞✐♠❡♥s✐♦♥ ❝❛♥ ❜❡ ✉♥s♣❡❝✐✜❡❞ ❛s ✐♥ ❛❬❪❬✶✵❪❬✸❪✳ ■♠♣♦ss✐❜❧❡ t♦ ❤❛✈❡ ♠✉❧t✐✲❞✐♠❡♥s✐♦♥❛❧ ❛rr❛② ❛s ❢✉♥❝t✐♦♥ ♣❛r❛♠❡t❡rs ✇✐t❤♦✉t ❛❧❧ ❜✉t t❤❡ ❧❡❢t♠♦st ❞✐♠❡♥s✐♦♥ s♣❡❝✐✜❡❞✳ ❙♦ ✐♥t ❛❬❪❬❪ ✐s ♥♦t ❛❧❧♦✇❡❞ ❛s ❛ ❢✉♥❝t✐♦♥ ♣❛r❛♠❡t❡r✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-93
SLIDE 93

❉❡❝❧❛r❛t✐♦♥s ✈❡rs✉s ❉❡✜♥✐t✐♦♥s

❆ ❞❡❝❧❛r❛t✐♦♥ ♣r♦✈✐❞❡s ✐♥❢♦r♠❛t✐♦♥ ❛❜♦✉t ❛♥ ❡♥t✐t② ❧✐❦❡ ❛ ✈❛r✐❛❜❧❡ ♦r ❢✉♥❝t✐♦♥✳ ❆ ❞❡✜♥✐t✐♦♥ ♣r♦✈✐❞❡s ❛ ❞❡✜♥✐t❡ ✈❛❧✉❡ ❢♦r t❤❛t ❡♥t✐t②✳ ❆♥ ❡♥t✐t② ❝❛♥ ❤❛✈❡ ♠✉❧t✐♣❧❡ ❞❡❝❧❛r❛t✐♦♥s ❛s ❧♦♥❣ ❛s t❤❡② ❛r❡ ❝♦♥s✐st❡♥t✳ ❚❤❡r❡ ❝❛♥ ♦♥❧② ❜❡ ❛ s✐♥❣❧❡ ❞❡✜♥✐t✐♦♥ ❢♦r ❛♥ ❡♥t✐t②✳ ❖❢t❡♥ t❤❡r❡ ✐s ♦♥❧② ❛ s✐♥❣❧❡ st❛t❡♠❡♥t ✇❤✐❝❤ ❝♦♠❜✐♥❡s ❜♦t❤ ❛ ❞❡❝❧❛r❛t✐♦♥ ✇✐t❤ ❛ ❞❡✜♥✐t✐♦♥✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-94
SLIDE 94

❉❡❝❧❛r❛t✐♦♥s ✈s ❉❡✜♥✐t✐♦♥s ❊①❛♠♣❧❡

✴✴❞❡❝❧❛r❡ ❢✉♥❝t✐♦♥ ✇❤✐❝❤ t❛❦❡s ✉♥s♣❡❝✐✜❡❞ ♣❛r❛♠❡t❡rs ✈♦✐❞ q✉❛❞r❛t✐❝❴r♦♦ts✭✮❀ ✴✴s❡❝♦♥❞ ❝♦♥s✐st❡♥t ❞❡❝❧❛r❛t✐♦♥ ✴✴♣❛r❛♠❡t❡r ♥❛♠❡s ♦♣t✐♦♥❛❧ ✐♥ ❞❡❝❧❛r❛t✐♦♥ ✈♦✐❞ q✉❛❞r❛t✐❝❴r♦♦ts✭❞♦✉❜❧❡✱ ❞♦✉❜❧❡ ❜✱ ❞♦✉❜❧❡ ❝✱ ❞♦✉❜❧❡ ✯✱ ❞♦✉❜❧❡ ✯✮❀

❈ ■♥tr♦❞✉❝t✐♦♥

slide-95
SLIDE 95

❉❡❝❧❛r❛t✐♦♥s ✈s ❉❡✜♥✐t✐♦♥s ❊①❛♠♣❧❡

✴✴❢✉♥❝t✐♦♥ ❞❡✜♥✐t✐♦♥ ✈♦✐❞ q✉❛❞r❛t✐❝❴r♦♦ts✭ ✴✴♣❛r❛♠❡t❡r ❞❡✜♥✐t✐♦♥s✴❞❡❝❧❛r❛t✐♦♥s ❞♦✉❜❧❡ ❛✱ ❞♦✉❜❧❡ ❜✱ ❞♦✉❜❧❡ ❝✱ ❞♦✉❜❧❡ ✯r♦♦t✶✱ ❞♦✉❜❧❡ ✯r♦♦t✷✮ ④ ❞♦✉❜❧❡ ❞✐s❝r❀ ✴✴✉♥✐♥✐t✐❛❧✐③❡❞ ✈❛r✐❛❜❧❡ ❞❡✜♥✐t✐♦♥ ❞✐s❝r ❂ ❜✯❜ ✲ ✹✯❛✯❝❀ ❛ss❡rt✭❞✐s❝r >❂ ✵✮❀ ❞♦✉❜❧❡ sqr♦♦t ❂ sqrt✭❞✐s❝r✮❀ ✴✴❞❡✜♥✐t✐♦♥ ✇✐t❤ ✐♥✐t ✯r♦♦t✶ ❂ ✭✲❜ ✰ sqr♦♦t✮ ✴ ✭✷ ✯ ❛✮❀ ✯r♦♦t✷ ❂ ✭✲❜ ✲ sqr♦♦t✮ ✴ ✭✷ ✯ ❛✮❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-96
SLIDE 96

❙✉♠ ♦❢ ■♥t❡❣❡r ❈♦♠♠❛♥❞✲▲✐♥❡ ❆r❣✉♠❡♥ts ▲♦❣

◆♦t ♣❛rt✐❝✉❧❛r❧② r♦❜✉st ✐♥ ❝❤❡❝❦✐♥❣ ❢♦r ❡rr♦rs✿ ✩ ❣❝❝ ✲❣ ✲❲❛❧❧ ✲❲❡①tr❛ ✲st❞❂❝✶✶ s✉♠✲❛r❣s✳❝ ✲♦ s✉♠✲❛r❣s ✩ ✳✴s✉♠✲❛r❣s ✷✷ ✲✸ ✺ ✷✹ ★s✐❧❡♥t❧② ✐❣♥♦r❡ ❣❛r❜❛❣❡ ❛t ❡♥❞ ♦❢ ✈❛❧✉❡s ✩ ✳✴s✉♠✲❛r❣s ✷✷ ✲✸① ✺ ✷✹ ★s✐❧❡♥t❧② ✐❣♥♦r❡ t♦t❛❧❧② ❣❛r❜❛❣❡ ✈❛❧✉❡s ✩ ✳✴s✉♠✲❛r❣s ✷✷ ✲✸① ✺ ❣❛r❜❛❣❡ ✸ ✷✼ ✩

❈ ■♥tr♦❞✉❝t✐♦♥

slide-97
SLIDE 97

❙✉♠ ♦❢ ■♥t❡❣❡r ❈♦♠♠❛♥❞✲▲✐♥❡ ❆r❣✉♠❡♥ts

■♥ s✉♠✲❛r❣s✳❝✿ ✴✯✯ ❖✉t♣✉t s✉♠ ♦❢ ✐♥t❡❣❡r ❝♦♠♠❛♥❞✲❧✐♥❡ ❛r❣✉♠❡♥ts ♦♥ st❞♦✉t✳ ✯✴ ✐♥t ♠❛✐♥✭✐♥t ❛r❣❝✱ ❝♦♥st ❝❤❛r ✯❛r❣✈❬❪✮ ④ ✐♥t s✉♠ ❂ ✵❀ ❢♦r ✭✐♥t ✐ ❂ ✶❀ ✐ < ❛r❣❝❀ ✐✰✰✮ ④ s✉♠ ✰❂ ❛t♦✐✭❛r❣✈❬✐❪✮❀ ⑥ ♣r✐♥t❢✭✧✪❞\♥✧✱ s✉♠✮❀ r❡t✉r♥ ✵❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-98
SLIDE 98

❙✉♠ ♦❢ ■♥t❡❣❡r ❈♦♠♠❛♥❞✲▲✐♥❡ ❆r❣✉♠❡♥ts ❉✐s❝✉ss✐♦♥

❘❡❝♦❧❧❡❝t t❤❛t ❛ ❈ str✐♥❣ ✐s ❛ ❛rr❛② ♦❢ ❝❤❛r t❡r♠✐♥❛t❡❞ ❜② ❛ ◆❯▲ ❝❤❛r❛❝t❡r ✬❭✵✬✳ ❋✐rst ❛r❣✉♠❡♥t t♦ ♠❛✐♥✭✮ ❛r❣❝ ❣✐✈❡s t❤❡ ♥✉♠❜❡r ♦❢ ❝♦♠♠❛♥❞✲❧✐♥❡ ❛r❣✉♠❡♥ts ✐♥❝❧✉❞✐♥❣ t❤❡ ♥❛♠❡ ♦❢ t❤❡ ♣r♦❣r❛♠✳ ❚❤❡ ♥♦t❛t✐♦♥ ❝❤❛r ✯str ❝❛♥ ❜❡ r❡❣❛r❞❡❞ ❛s ❞❡❝❧❛r✐♥❣ str t♦ ❜❡ ❛ str✐♥❣ ✭str✐❝t❧② s♣❡❛❦✐♥❣✱ ✐s ✐s ❞❡❝❧❛r✐♥❣ str t♦ ❜❡ ❛ ♣♦✐♥t❡r t♦ ❛ ❝❤❛r✮✳ ❍❡♥❝❡ ❝♦♥st ❝❤❛r ✯❛r❣✈❬❪ ❞❡❝❧❛r❡s ❛r❣✈ t♦ ❜❡ ❛♥ ❛rr❛② ♦❢ str✐♥❣s❀ t❤❡ ❝♦♥st ♠❡❛♥s t❤❛t t❤❡ str✐♥❣s ❝❛♥♥♦t ❜❡ ❝❤❛♥❣❡❞✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-99
SLIDE 99

❙✉♠ ♦❢ ■♥t❡❣❡r ❈♦♠♠❛♥❞✲▲✐♥❡ ❆r❣✉♠❡♥ts ❉✐s❝✉ss✐♦♥ ❈♦♥t✐♥✉❡❞

❛t♦✐✭✮ ✐s ❛ ❢✉♥❝t✐♦♥ ❞❡❝❧❛r❡❞ ✐♥ ✐♥❝❧✉❞❡❞ ✜❧❡ ❁st❞❧✐❜✳❤❃ ✇❤✐❝❤ ❝♦♥✈❡rts ❛ str✐♥❣ ✭✇❤✐❝❤ s❤♦✉❧❞ ❝♦♥t❛✐♥ ♦♥❧② ❝❤❛r❛❝t❡rs ❝♦rr❡s♣♦♥❞✐♥❣ t♦ ❞❡❝✐♠❛❧ ❞✐❣✐ts✮ t♦ t❤❡ ✐♥t❡r♥❛❧ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ❛ ❈ ✐♥t❡❣❡r✳ ❭♥ ✐s ❛♥ ❡s❝❛♣❡ s❡q✉❡♥❝❡ ✉s❡❞ ✇✐t❤✐♥ ❈✲str✐♥❣s t♦ ❞❡♥♦t❡ ❛ ♥❡✇❧✐♥❡ ❝❤❛r❛❝t❡r✳ ❚❤❡ ✜rst ❛r❣✉♠❡♥t ❢♦r ♣r✐♥t❢✭✮ s❤♦✉❧❞ ❜❡ ❛ ❈✲str✐♥❣ ❞❡♥♦t✐♥❣ ❛ ❈ str✐♥❣✳ ✪ ❝❤❛r❛❝t❡rs ❛r❡ ✉s❡❞ ❛s ❡s❝❛♣❡ s❡q✉❡♥❝❡s ✇✐t❤✐♥ ❛ ❢♦r♠❛t str✐♥❣ t♦ ✐♥tr♦❞✉❝❡ ❢♦r♠❛t s♣❡❝✐✜❡rs ✉s❡❞ t♦ ♣r✐♥t t❤❡ ♥❡①t ❝♦rr❡s♣♦♥❞✐♥❣ ❛r❣✉♠❡♥t✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-100
SLIDE 100

❉❡❝❧❛r❛t✐♦♥s ❲✐t❤ ❝♦♥st ▼♦❞✐✜❡r

❉❡❝❧❛r✐♥❣ ❛ ✈❛r✐❛❜❧❡ ❝♦♥st ♠❡❛♥s t❤❛t ✐t ❝❛♥♥♦t ❜❡ ❞✐r❡❝t❧② ❛ss✐❣♥❡❞ t♦✳ ❝♦♥st ✐♥t ✐ ❂ ✷✷❀ ✐ ❂ ✹✷❀ ✴✴❝♦♠♣✐❧❡r ❡rr♦r ❱❛r✐❛❜❧❡ ❝❛♥ st✐❧❧ ❜❡ ❝❤❛♥❣❡❞ ✈✐❛ ❛❧✐❛s✐♥❣✳ ■❢ t❤❡ ✈❛r✐❛❜❧❡ ❞❡❝❧❛r❡s ❛ str✉❝t ♦r ✉♥✐♦♥✱ t❤❡♥ ♠❡♠❜❡rs ❝❛♥ st✐❧❧ ❜❡ ❝❤❛♥❣❡❞✳ t②♣❡❞❡❢ str✉❝t ④ ✐♥t ①❀ ✐♥t ②❀ ⑥ ❙❀ ❝♦♥st ❙ s ❂ ④ ✶✱ ✷ ⑥❀ ❙ t❀ t ❂ s❀ ✴✴❜✐t✇✐s❡ ❝♦♣② t✳① ❂ ✾✾❀ ✴✴♦❦ s ❂ t❀ ✴✴❡rr♦r s✳① ❂ ✷✷❀ ✴✴♦❦

❈ ■♥tr♦❞✉❝t✐♦♥

slide-101
SLIDE 101

❝♦♥st ✇✐t❤ P♦✐♥t❡r ❊①❛♠♣❧❡s

❝♦♥st ✐♥t ✐ ❂ ✷✷❀ ❝♦♥st ✐♥t ✯♣✶ ❂ ✫✐❀ ✴✴♣♦✐♥t❡r t♦ ❝♦♥st ✐♥t ✯♣✶ ❂ ✹✷❀ ✴✴❝♦♠♣✐❧❡r ❡rr♦r ✐♥t ✯♣✷ ❂ ✫✭✭✐♥t✮✐✮❀ ✴✴✭✐♥t✮ r❡♠♦✈❡s ❝♦♥st ✯♣✷ ❂ ✹✷❀ ✴✴♦❦✿ ✐ ❝❤❛♥❣❡❞✦✦ ✐♥t ❥ ❂ ✐❀ ✐♥t ✯❝♦♥st ♣✸ ❂ ✫❥❀ ✴✴❝♦♥st ♣♦✐♥t❡r t♦ ✐♥t ✯♣✸ ❂ ✹✷❀ ✴✴♦❦ ♣✸ ❂ ♣✷❀ ✴✴❡rr♦r ❝♦♥st ✐♥t ✯❝♦♥st ♣✹ ❂ ✫❥❀ ✴✴❝♦♥st ♣♦✐♥t❡r t♦ ❝♦♥st ✐♥t ✯♣✹ ❂ ✹✷❀ ✴✴❡rr♦r ♣✹ ❂ ♣✷❀ ✴✴❡rr♦r

❈ ■♥tr♦❞✉❝t✐♦♥

slide-102
SLIDE 102

❉❡❝❧❛r❛t✐♦♥ ♦❢ ❈♦♠♠❛♥❞✲▲✐♥❡ ❆r❣✉♠❡♥ts ✐♥ ♠❛✐♥✭✮

❚②♣✐❝❛❧ ❞❡❝❧❛r❛t✐♦♥ ❝♦♥st ❝❤❛r ✯❛r❣✈❬❪ ❢♦r s❡❝♦♥❞ ❛r❣✉♠❡♥t ♦❢ ♠❛✐♥✭✮✱ ❞❡❝❧❛r❡s ❛r❣✈ t♦ ❜❡ ❛♥ ❛rr❛② ♦❢ ♣♦✐♥t❡rs t♦ ❝♦♥st❛♥t ❝❤❛r ✭t②♣✐❝❛❧❧②✱ ❝♦♥st❛♥t str✐♥❣s✮ ✇✐t❤ ❡❛❝❤ ❡❧❡♠❡♥t ❝♦♥t❛✐♥✐♥❣ ❛ ❝♦♠♠❛♥❞✲❧✐♥❡ ❛r❣✉♠❡♥t str✐♥❣✳ ❛r❣✈❬✶❪✱ ❛r❣✈❬✷❪ ❡t❝✳ ❤❛✈❡ t②♣❡ ♦❢ t❤❡ ❛rr❛② ❡❧❡♠❡♥t✿ ♥❛♠❡❧② ♣♦✐♥t❡r t♦ ❝♦♥st ❝❤❛r✱ ✐✳❡✳ ❝♦♥st ❝❤❛r ✯❀ ❍❡♥❝❡ ✫❛r❣✈❬✶❪ ❛♥❞ ✫❛r❣✈❬✷❪ ❤❛✈❡ t②♣❡ ♣♦✐♥t❡r t♦ ♣♦✐♥t❡r t♦ ❝♦♥st ❝❤❛r✱ ✐✳❡✳ ❝♦♥st ❝❤❛r ✯✯✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-103
SLIDE 103

❘❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ❈♦♠♠❛♥❞✲▲✐♥❡ ❆r❣✉♠❡♥ts

  • ✐✈❡♥ ❝♦♠♠❛♥❞✲❧✐♥❡ ✳✴s✉♠✲❛r❣s ✷✷ ✲✸ ✺✱ ✇❡ ❤❛✈❡ ❛r❣✈ ❛rr❛② ❛s

❢♦❧❧♦✇s✿ ❛r❣✈❬✵❪✿ ❬ ❪ ✲✲✲✲✲❃ ❬ ✬✳✬ ✬✴✬ ✬s✬ ✬✉✬ ✳✳✳ ✬❣✬ ✬s✬ ✬❭✵✬ ❪ ❛r❣✈❬✶❪✿ ❬ ❪ ✲✲✲✲✲❃ ❬ ✬✷✬ ✬✷✬ ✬❭✵✬ ❪ ❛r❣✈❬✷❪✿ ❬ ❪ ✲✲✲✲✲❃ ❬ ✬✲✬ ✬✸✬ ✬❭✵✬ ❪ ❛r❣✈❬✸❪✿ ❬ ❪ ✲✲✲✲✲❃ ❬ ✬✺✬ ✬❭✵✬ ❪ ❛r❣✈❬✹❪✿ ❬ ◆❯▲▲ ❪ ★✉s✉❛❧❧②

❈ ■♥tr♦❞✉❝t✐♦♥

slide-104
SLIDE 104

▼♦r❡ ❘♦❜✉st ❙✉♠ Pr♦❣r❛♠✿ ▲♦❣

✩ ❣❝❝ ✲❣ ✲❲❛❧❧ ✲❲❡①tr❛ ✲st❞❂❝✶✶ r♦❜✉st✲s✉♠✳❝ ❭ ✲♦ r♦❜✉st✲s✉♠ ✩ ✳✴r♦❜✉st✲s✉♠ ✷✷ ✲✸ ✺ ✷✹ ★♣r♦❞✉❝❡ ❡rr♦r ♠❡ss❛❣❡ ❢♦r ❜❛❞ ❛r❣✉♠❡♥ts ✩ ✳✴r♦❜✉st✲s✉♠ ✷✷ ✲✸① ✺ ❜❛❞ ❛r❣✉♠❡♥t ✲✸① ♥♦t ✐♥t❡❣❡r✿ ✐❣♥♦r❡❞ ✷✼ ★♣r♦❞✉❝❡ ❡rr♦r ♠❡ss❛❣❡ ❢♦r ❜❛❞ ❛r❣✉♠❡♥ts ✩ ✳✴r♦❜✉st✲s✉♠ ✷✷ ✲✸① ✺ ❣❛r❜❛❣❡ ✸ ❜❛❞ ❛r❣✉♠❡♥t ✲✸① ♥♦t ✐♥t❡❣❡r✿ ✐❣♥♦r❡❞ ❜❛❞ ❛r❣✉♠❡♥t ❣❛r❜❛❣❡ ♥♦t ✐♥t❡❣❡r✿ ✐❣♥♦r❡❞ ✸✵ ✩

❈ ■♥tr♦❞✉❝t✐♦♥

slide-105
SLIDE 105

❆ ▼♦r❡ ❘♦❜✉st Pr♦❣r❛♠ t♦ ❙✉♠ ❆r❣✉♠❡♥ts

■♥ r♦❜✉st✲s✉♠✳❝✿ ✴✯✯ ❖✉t♣✉t s✉♠ ♦❢ ✐♥t❡❣❡r ❝♦♠♠❛♥❞✲❧✐♥❡ ❛r❣✉♠❡♥ts ♦♥ st❞♦✉t✳ ✯✴ ✐♥t ♠❛✐♥✭✐♥t ❛r❣❝✱ ❝♦♥st ❝❤❛r ✯❛r❣✈❬❪✮ ④ ✐♥t s✉♠ ❂ ✵❀ ❢♦r ✭✐♥t ✐ ❂ ✶❀ ✐ < ❛r❣❝❀ ✐✰✰✮ ④ ❝❤❛r ✯♣❀ ✐♥t ♥ ❂ strt♦❧✭❛r❣✈❬✐❪✱ ✫♣✱ ✶✵✮❀ ✐❢ ✭✯♣ ❂❂ ✬\✵✬✮ ④ s✉♠ ✰❂ ♥❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-106
SLIDE 106

❆ ▼♦r❡ ❘♦❜✉st Pr♦❣r❛♠ t♦ ❙✉♠ ❆r❣✉♠❡♥ts ❈♦♥t✐♥✉❡❞

❡❧s❡ ④ ❢♣r✐♥t❢✭st❞❡rr✱ ✧❜❛❞ ❛r❣✉♠❡♥t ✪s ♥♦t ✐♥t❡❣❡r✿ ✐❣♥♦r❡❞\♥✧✱ ❛r❣✈❬✐❪✮❀ ⑥ ⑥ ♣r✐♥t❢✭✧✪❞\♥✧✱ s✉♠✮❀ r❡t✉r♥ ✵❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-107
SLIDE 107

P♦✐♥t❡r ❙✉♠ ❆♥♥♦t❛t❡❞ ▲♦❣

★ ✶✷ ✰ ✶✸ ✰ ✲✶✷ ✩ ✳✴♣tr✲s✉♠ ✶✷ ✶✸ ✲✵①❝ ✶✸ ✩ ✳✴♣tr✲s✉♠ ✵ ★▲❛st ✷ ♥✉♠❜❡rs ❛r❡ ✐♥ ❡rr♦r ❛♥❞ ✐❣♥♦r❡❞ ★ ✻✹ ✰ ✲✶✼✶ ✰ ✯✯ ✰ ✯✯ ✩ ✳✴♣tr✲s✉♠ ✵✶✵✵ ✲✵①❆❜ ✶✷❈ ✵✾✾ ✲✶✵✼ ✩

❈ ■♥tr♦❞✉❝t✐♦♥

slide-108
SLIDE 108

P♦✐♥t❡r ❙✉♠

■♥ ♣tr✲s✉♠✳❝✿ ✴✯✯ ❙✉♠ ♥✉♠❡r✐❝ str✐♥❣s ❬✯st❛rt✱ ✯❡♥❞✮✱ s✐❧❡♥t❧② ✐❣♥♦r✐♥❣ ✯ ❛♥② str✐♥❣s ✇❤✐❝❤ ❛r❡ ♥♦t ✈❛❧✐❞ ❈ ✐♥t❡❣❡r ❧✐t❡r❛❧s✳ ✯✴ ❧♦♥❣ ♣tr❴s✉♠✭❝♦♥st ❝❤❛r ✯✯st❛rt✱ ❝♦♥st ❝❤❛r ✯✯❡♥❞✮ ④ ❧♦♥❣ s✉♠ ❂ ✵❀ ❢♦r ✭❝♦♥st ❝❤❛r ✯✯♣ ❂ st❛rt❀ ♣ ✦❂ ❡♥❞❀ ♣✰✰✮ ④ ❝❤❛r ✯❡♥❞P❀ ❧♦♥❣ ✈ ❂ strt♦❧✭✯♣✱ ✫❡♥❞P✱ ✵✮❀✴✴✵✿ ❝✲s②♥t❛① ✐♥ts ✐❢ ✭✯❡♥❞P ❂❂ ✬\✵✬✮ s✉♠ ✰❂ ✈❀ ⑥ r❡t✉r♥ s✉♠❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-109
SLIDE 109

P♦✐♥t❡r ❙✉♠ ❈♦♥t✐♥✉❡❞

✐♥t ♠❛✐♥✭✐♥t ❛r❣❝✱ ❝♦♥st ❝❤❛r ✯❛r❣✈❬❪✮ ④ ♣r✐♥t❢✭✧✪❧❞\♥✧✱ ♣tr❴s✉♠✭✫❛r❣✈❬✶❪✱ ✫❛r❣✈❬❛r❣❝❪✮✮❀ r❡t✉r♥ ✵❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-110
SLIDE 110

P♦✐♥t❡r ❙✉♠ ❉✐s❝✉ss✐♦♥

strt♦❧✭✮ ♥❡❡❞s t♦ r❡t✉r♥ ❛ ♣♦✐♥t❡r t♦ t❤❡ ✜rst ♥♦♥✲❧❡❣❛❧ ❝❤❛r❛❝t❡r ❢♦✉♥❞ ✐♥ t❤❡ ✐♥t❡❣❡r str✐♥❣ ♣♦✐♥t❡❞ t♦ ❜② ✐ts ✜rst ❛r❣✉♠❡♥t✳ ❙✐♥❝❡ r❡t✉r♥ ✈❛❧✉❡ ✐s ❜❡✐♥❣ ✉s❡❞ t♦ r❡t✉r♥ t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ ✐♥t❡❣❡r✱ t❤✐s ♣♦✐♥t❡r ♠✉st ❜❡ r❡t✉r♥❡❞ ✉s✐♥❣ ❛ ❢✉♥❝t✐♦♥ ♣❛r❛♠❡t❡r✳ ❙✐♥❝❡ t❤❡ ❛❝t✉❛❧ ❛r❣✉♠❡♥ts ♣❛ss❡❞ t♦ ❛ ❢✉♥❝t✐♦♥ ❛r❡ ❝♦♣✐❡s ♦❢ t❤❡ ✈❛❧✉❡ ♣❛ss❡❞ ❜② t❤❡ ❝❛❧❧❡r ❛ ❢✉♥❝t✐♦♥ ❝❛♥♥♦t ❛✛❡❝t t❤❡ ✈❛❧✉❡ ♦❢ ❛ ♣❛r❛♠❡t❡r ✐♥ ✐ts ❝❛❧❧❡r✳ ❚❤❡ ♦♥❧② ✇❛② t♦ ❤❛✈❡ ❛ ❢✉♥❝t✐♦♥ r❡t✉r♥ ❛ ✈❛❧✉❡ ✈✐❛ ❛♥ ❛r❣✉♠❡♥t ✐s t♦ ❤❛✈❡ t❤❡ ❝❛❧❧❡r ♣❛ss ❛ ♣♦✐♥t❡r t♦ t❤❛t ✈❛❧✉❡ ❛♥❞ ❤❛✈❡ t❤❡ ❢✉♥❝t✐♦♥ r❡t✉r♥ t❤❡ ✈❛❧✉❡ ✉s✐♥❣ t❤❡ ♣♦✐♥t❡r✳ ❙✐♥❝❡ strt♦❧✭✮ ♥❡❡❞s t♦ r❡t✉r♥ ❛ ♣♦✐♥t❡r ✈✐❛ ✐ts ❛r❣✉♠❡♥t✱ t❤❡ s❡❝♦♥❞ ♣❛r❛♠❡t❡r ✐s ♣❛ss❡❞ ❛s ♣♦✐♥t❡r t♦ ❛ ♣♦✐♥t❡r✱ ✐✳❡✳ ✫❡♥❞P✳ ❉❡❝❧❛r❛t✐♦♥ ♦❢ strt♦❧✭✮ ✐s ❧♦♥❣ strt♦❧✭❝♦♥st ❝❤❛r ✯str✱ ❝❤❛r ✯✯❡♥❞✱ ✐♥t ❜❛s❡✮✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-111
SLIDE 111

P♦✐♥t❡r ❙✉♠ ❉✐s❝✉ss✐♦♥ ❈♦♥t✐♥✉❡❞

■♥ ♣tr❴s✉♠✭✮✱ st❛rt ✐s ❛❞❞r❡ss ♦❢ ✜rst str✐♥❣✳ ❙✐♥❝❡ ❛ str✐♥❣ ❤❛s t②♣❡ ❝❤❛r ✯✱ st❛rt ✐s ❞❡❝❧❛r❡❞ ❝❤❛r ✯✯✳ ❡♥❞ ✐s ❛❞❞r❡ss ♦♥❡ ♣❛st t❤❛t ♦❢ t❤❡ ❧❛st str✐♥❣❀ ✐✳❡✳ ❡♥❞ ✐s ❛♥ ❡①❝❧✉s✐✈❡ ❧✐♠✐t✳ ♣ ✐s ✐♥✐t✐❛❧✐③❡❞ t♦ st❛rt ♦❢ t②♣❡ ❝♦♥st ❝❤❛r ✯✯✳ ❍❡♥❝❡ ✯♣ ❤❛s t②♣❡ ❝♦♥st ❝❤❛r ✯ ✇❤✐❝❤ ✐s t❤❡ str✐♥❣ ❜❡✐♥❣ s❡♥t ❛s t❤❡ ✜rst ❛r❣✉♠❡♥t t♦ strt♦❧✭✮ ♣✰✰ ✇✐❧❧ ♣♦✐♥t t♦ ♥❡①t str✐♥❣✳ ❙✐♥❝❡ ❡♥❞ ✐s ❛♥ ❡①❝❧✉s✐✈❡ ❧✐♠✐t✱ t❤❡ ❧♦♦♣ q✉✐ts ✇❤❡♥ ♣ ❂❂ ❡♥❞✳ ✫❛r❣✈❬❛r❣❝❪ ✐s t❤❡ ❛❞❞r❡ss ♦❢ ❛ ♣♦ss✐❜❧② ♥♦♥✲❡①✐st✐♥❣ ❡❧❡♠❡♥t ♦❢ ❛r❣✈❬❪✳ ❚❤✐s ❛♣♣❡❛rs t♦ ❜❡ ❛❧❧♦✇❡❞ ❜② t❤❡ ❧❛♥❣✉❛❣❡ st❛♥❞❛r❞✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-112
SLIDE 112

❋r❛❝t✐♦♥❛❧ ❇✐♥❛r② ◆✉♠❜❡rs

  • ✐✈❡♥ ❛ ❢r❛❝t✐♦♥❛❧ ❜✐♥❛r② ♥✉♠❜❡r

❜♠❜♠−✶ . . . ❜✶❜✵.❜−✶❜−✷ . . . ❜−♥−✶❜−♥ ❇② ❛♥❛❧♦❣② ✇✐t❤ ❞❡❝✐♠❛❧ ♥♦t❛t✐♦♥✱ ✐ts ✈❛❧✉❡ ✇✐❧❧ ❜❡ ❣✐✈❡♥ ❜②

  • ✐=−♥

✷✐ × ❜✐ ❙♦ ✇❡ ✇♦✉❧❞ ❤❛✈❡✿ ❜✐♥❛r② ✵✳✶ r❡♣r❡s❡♥t✐♥❣ ❞❡❝✐♠❛❧ ✵✳✺✱ ❜✐♥❛r② ✵✳✵✶ r❡♣r❡s❡♥t✐♥❣ ❞❡❝✐♠❛❧ ✵✳✷✺ ❛♥❞ ❜✐♥❛r② ✶✶✳✶✵✶ r❡♣r❡s❡♥t✐♥❣ ❞❡❝✐♠❛❧ ✸✳✻✷✺✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-113
SLIDE 113

■❊❊❊ ❋❧♦❛t✐♥❣ P♦✐♥t ❘❡♣r❡s❡♥t❛t✐♦♥

❙✐♠✐❧❛r t♦ s❝✐❡♥t✐✜❝ ♥♦t❛t✐♦♥ ✇❤❡r❡ ❛ ♥✉♠❜❡r ✐s r❡♣r❡s❡♥t❡❞ ✉s✐♥❣ ❛ ♠❛♥t✐ss❛ ❛♥❞ ❛♥ ❡①♣♦♥❡♥t✳ ■❊❊❊ ✢♦❛ts ✉s✐♥❣ ❜✐♥❛r② ❢♦r ❜♦t❤ t❤❡ ♠❛♥t✐ss❛ ❛♥❞ t❤❡ ❡①♣♦♥❡♥t✳ ❋❧♦❛t✐♥❣ ♣♦✐♥t r❡♣r❡s❡♥t❛t✐♦♥ ❝♦♥t❛✐♥s ❛ s✐♥❣❧❡ s✐❣♥ ❜✐t✱ ❛ ❦✲❜✐t ❡①♣♦♥❡♥t ✜❡❧❞ ❛♥❞ ❛♥ ♥✲❜✐t ♠❛♥t✐ss❛ ♦r s✐❣♥✐✜❝❛♥❞ ❢r❛❝t✐♦♥ ✜❡❧❞✳ ❯s✉❛❧❧②✱ t❤❡ ❡①♣♦♥❡♥t ✐s ❛❞❥✉st❡❞ s♦ t❤❛t t❤❡ ❢r❛❝t✐♦♥ ✜❡❧❞ ✐s ❛❧✇❛②s ♦❢ t❤❡ ❢♦r♠ ✶. . . .✱ ✐✳❡✳ t❤❡r❡ ✐s ❛❧✇❛②s ❛ ✶ ❜❡❢♦r❡ t❤❡ ❜✐♥❛r② ♣♦✐♥t✳ ❍❡♥❝❡ t❤❡r❡ ✐s ♥♦ ♣♦✐♥t ✐♥ st♦r✐♥❣ ✐t ❛♥❞ ✇❡ s❛② t❤❛t t❤❡ ❢r❛❝t✐♦♥ ✜❡❧❞ ✐s ♥♦r♠❛❧✐③❡❞✳ ❊①♣♦♥❡♥t ✐s st♦r❡❞ ✇✐t❤ ❛ ❜✐❛s✳ ❘❡s❡r✈❡ ❡①♣♦♥❡♥t ♦❢ ❛❧❧ ✵✬s ❛♥❞ ❛❧❧ ✶✬s ❢♦r ❡①❝❡♣t✐♦♥❛❧ ❝❛s❡s✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-114
SLIDE 114

❋❧♦❛t✐♥❣ P♦✐♥t ❋♦r♠❛ts

❇❡❝❛✉s❡ ♦❢ ♥♦r♠❛❧✐③❛t✐♦♥✱ s✐♥❣❧❡ ♣r❡❝✐s✐♦♥ ✭✉s✉❛❧❧② ❈ ✢♦❛t✬s✮ ♦♥❧② st♦r❡ ❛ ✷✸✲❜✐t ❢r❛❝t✐♦♥ ✇❤✐❝❤ ❛❝t✉❛❧❧② r❡♣r❡s❡♥ts ✷✹✲❜✐ts✳ ❆❣❛✐♥✱ ❞✉❡ t♦ ♥♦r♠❛❧✐③❛t✐♦♥ ❞♦✉❜❧❡ ♣r❡❝✐s✐♦♥ ✭✉s✉❛❧❧② ❈ ❞♦✉❜❧❡✬s✮ ♦♥❧② st♦r❡ ❛ ✺✷✲❜✐t ❢r❛❝t✐♦♥ ✇❤✐❝❤ ❛❝t✉❛❧❧② r❡♣r❡s❡♥ts ✺✸ ❜✐ts✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-115
SLIDE 115

❋❧♦❛t✐♥❣ P♦✐♥t ❈❛s❡s

❉❡♥♦r♠❛❧✐③❡❞ ♥✉♠❜❡rs ❛❧❧♦✇ ❣r❛❝❡❢✉❧ ✉♥❞❡r✢♦✇✳ ❙♣❡❝✐❛❧ ✈❛❧✉❡s ♦❢ ±∞ ❛❧❧♦✇s s❛t✉r❛t✐♥❣ ❛r✐t❤♠❡t✐❝✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-116
SLIDE 116

◆♦t✲❛✲◆✉♠❜❡r ✭❵◆❛◆❵✮

❲❤❡♥ ❡①♣♦♥❡♥t ✐s ❛❧❧ ✶✬s ❛♥❞ ❢r❛❝t✐♦♥ ♥♦♥✲③❡r♦✱ ✇❡ ❤❛✈❡ ❛ ◆❛◆✳ ◆❛◆ ✐♥❞✐❝❛t❡s ❛♥ ✐♥✈❛❧✐❞ r❡s✉❧t ❧✐❦❡ ✵✴✵✳ ❈❛♥ ❝❛✉s❡ ❛♥ ❡①❝❡♣t✐♦♥ ✭✧s✐❣♥❛❧❧✐♥❣✧ ◆❛◆✮ ♦r s✐♠♣❧② ♣r♦♣❛❣❛t❡s ❛s ◆❛◆ ✭✧q✉✐❡t✧ ◆❛◆✮✳ ◆❛◆ ❝♦♠♣❛r❡s ❢❛❧s❡ ✇✐t❤ ❛♥②t❤✐♥❣✱ ✐♥❝❧✉❞✐♥❣ ✐ts❡❧❢✳ ❞♦✉❜❧❡ ① ❂ ✵✴✵❀ ① ❂❂ ①❀ ✴✴❡✈❛❧✉❛t❡s t♦ ✵✳ ① ✦❂ ①❀ ✴✴❡✈❛❧✉❛t❡s t♦ ✶✳ ① ❁ ②❀ ✴✴❡✈❛❧✉❛t❡s t♦ ✵ ❢♦r ❛♥② ②✳ ② ❁ ①❀ ✴✴❡✈❛❧✉❛t❡s t♦ ✵ ❢♦r ❛♥② ②✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-117
SLIDE 117

❋❧♦❛t✐♥❣ P♦✐♥t ▼✐s❝❡❧❧❛♥❡❛

❈❛♥ ❜❡ s♦rt❡❞ ❜② tr❡❛t✐♥❣ ❜✐t r❡♣r❡s❡♥t❛t✐♦♥ ❧❡①✐❝♦❣r❛♣❤✐❝❛❧❧② ♦r ❛s s✐❣♥❡❞✲♠❛❣♥✐t✉❞❡ ✐♥t❡❣❡rs✳ ■♥ ❈✱ ✢♦❛t ❧✐t❡r❛❧s ♠✉st ❤❛✈❡ tr❛✐❧✐♥❣ ❢ ♦r ❋❀ ♦t❤❡r✇✐s❡ t❤❡ ❧✐t❡r❛❧ ✐s tr❡❛t❡❞ ❛s ❛ ❞♦✉❜❧❡✳ ❚❤❡ ✈❛❧✉❡ ❝♦♥tr✐❜✉t❡❞ ❜② t❤❡ ❧❛st ❜✐t ✐♥ t❤❡ ♠❛♥t✐ss❛ ✭✧✉♥✐t ✐♥ ❧❛st ♣❧❛❝❡✧✮ ❞❡♣❡♥❞s ♦♥ t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ ❡①♣♦♥❡♥t✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-118
SLIDE 118

❋❧♦❛t✐♥❣ P♦✐♥t P❛r❛♠❡t❡rs

❋❧♦❛t✐♥❣ ♣♦✐♥t ❢♦r♠❛t ❝❤❛r❛❝t❡r✐③❡❞ ❜② ✷ ♣❛r❛♠❡t❡rs✿ ◆ t♦t❛❧ ♥✉♠❜❡r ♦❢ ❜✐ts✳ ❦ ♥✉♠❜❡r ♦❢ ❡①♣♦♥❡♥t ❜✐ts✳ ❇✐❛s❡❞ ❜② ✷❦−✶ − ✶✳ ■t ❢♦❧❧♦✇s t❤❛t ♥✉♠❜❡r ♦❢ ❜✐ts ❛✈❛✐❧❛❜❧❡ ❢♦r st♦r✐♥❣ ♠❛♥t✐ss❛ ✐s ♠ = ◆ − ❦ − ✶✳ ■❊❊❊ s✐♥❣❧❡ ♣r❡❝✐s✐♦♥✿ ◆ = ✸✷✱ ❦ = ✽✱ ♠ = ✸✷ − ✽ − ✶ = ✷✸✳ ❚❤❡ ❡①♣♦♥❡♥t ❜✐❛s ✐s ✷✽−✶ − ✶ = ✶✷✼✳ ◆♦r♠❛❧✐③❡❞ ❡①♣♦♥❡♥ts ✐♥ ✐♥❝❧✉s✐✈❡✲r❛♥❣❡ [−✶✷✻, ✶✷✼]✳ ■❊❊❊ ❞♦✉❜❧❡ ♣r❡❝✐s✐♦♥✿ ◆ = ✻✹✱ ❦ = ✶✶✱ ♠ = ✻✹−✶✶−✶ = ✺✷✳ ❚❤❡ ❡①♣♦♥❡♥t ❜✐❛s ✐s ✷✶✶−✶ −✶ = ✶✵✷✸✳ ◆♦r♠❛❧✐③❡❞ ❡①♣♦♥❡♥ts ✐♥ ✐♥❝❧✉s✐✈❡✲r❛♥❣❡ [−✶✵✷✷, ✶✵✷✸]✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-119
SLIDE 119

❋❧♦❛t✐♥❣ P♦✐♥t ❱❛❧✉❡s

  • ✐✈❡♥ ❛ ♥♦♥✲❡①❝❡♣t✐♦♥❛❧ ✢♦❛t✐♥❣ ♣♦✐♥t ♥✉♠❜❡r ✭❡①♣♦♥❡♥t ✜❡❧❞

✐s ♥♦t ❛❧❧ ✵✬s ❛♥❞ ♥♦t ❛❧❧ ✶✬s✮✱ ✐t✬s ✈❛❧✉❡ ✐s✿ (−✶)s × ▼ × ✷❡ ✇❤❡r❡ s ✐s t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ s✐❣♥✲❜✐t✱ ▼ ✐s t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ ♠❛♥t✐ss❛ ❛♥❞ ❡ ✐s t❤❡ ❡①♣♦♥❡♥t ✈❛❧✉❡ ✭❛❢t❡r ❛❞❥✉st✐♥❣ ❜② t❤❡ ❜✐❛s✮✳ ❆ss✉♠✐♥❣ t❤❛t t❤❡ ✈❛❧✉❡ ❛s ❛♥ ✉♥s✐❣♥❡❞ ❜✐♥❛r② ✐♥t❡❣❡r ♦❢ t❤❡ ♠❛♥t✐ss❛ ✜❡❧❞ ✐s ♠′✱ ❢♦r ♥♦r♠❛❧✐③❡❞ ♥✉♠❜❡rs ▼ = ✶ + ♠′/✷♠❀ ❢♦r ❞❡♥♦r♠❛❧✐③❡❞ ♥✉♠❜❡rs ▼ = ♠′/✷♠✳ ❆ss✉♠✐♥❣ t❤❛t t❤❡ ✈❛❧✉❡ ❛s ❛♥ ✉♥s✐❣♥❡❞ ❜✐♥❛r② ✐♥t❡❣❡r ♦❢ t❤❡ ❡①♣♦♥❡♥t ✜❡❧❞ ✐s ❡′✱ ❢♦r ♥♦r♠❛❧✐③❡❞ ♥✉♠❜❡rs ❡ = ❡′ − (✷❦−✶ − ✶)❀ ❢♦r ❞❡♥♦r♠❛❧✐③❡❞ ♥✉♠❜❡rs ❡ = −(✷❦−✶ − ✷)✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-120
SLIDE 120

❋❧♦❛t✐♥❣ P♦✐♥t ❱❛❧✉❡s ❈♦♥t✐♥✉❡❞

◆♦r♠❛❧✐③❡❞ ✈❛❧✉❡s ❲❤❡♥ ✵ < ❡′ < ✷❦ − ✶✿ ▼ = ✶ + ♠′/✷♠ ❛♥❞ ❡ = ❡′ − (✷❦−✶ − ✶) ✭✇❤❡♥ ❦ = ✽✱ s♠❛❧❧❡st ❡①♣♦♥❡♥t ❢♦r ♥♦r♠❛❧✐③❡❞ ♥✉♠❜❡rs ✐s −✶✷✻✮✳ ❍❡♥❝❡ ✈❛❧✉❡ ✐s (−✶)s × (✶ + ♠′/✷♠) × ✷❡′−(✷❦−✶−✶)✳ ❉❡♥♦r♠❛❧✐③❡❞ ✈❛❧✉❡s ❲❤❡♥ ❡′ = ✵✿ ▼ = ♠′/✷♠ ❛♥❞ ❡ = −(✷❦−✶ − ✷) ✭✇❤❡♥ ❦ = ✽✱ s♠❛❧❧❡st ❡①♣♦♥❡♥t ❢♦r ❞❡♥♦r♠❛❧✐③❡❞ ♥✉♠❜❡rs r❡♠❛✐♥s st✉❝❦ ❛t −✶✷✻✮✳ ❍❡♥❝❡ ✈❛❧✉❡ ✐s (−✶)s × (♠′/✷♠) × ✷−(✷❦−✶−✷)✳ ■♥✜♥✐t✐❡s ❡′ = ✷❦ − ✶, ♠′ = ✵✳ ❱❛❧✉❡ ✐s (−✶)s × ∞✳ ◆❛◆✬s ❡′ = ✷❦ − ✶, ♠′ = ✵✳ ❱❛❧✉❡ ✐s ◆❛◆✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-121
SLIDE 121

✽✲❇✐t ❋❧♦❛t ❱❛❧✉❡s

❋♦❧❧♦✇✐♥❣ s❧✐❞❡s ❧✐st ❛❧❧ ✈❛❧✉❡s ❢♦r ❛ ✼✲❜✐t ✢♦❛t✳ ❋✐❡❧❞s ❢r♦♠ ▼❙❇ t♦ ▲❙❇✿ ✶✲❜✐t s✐❣♥ ✸✲❜✐t ❡①♣♦♥❡♥t ❜✐❛s❡❞ ❜② ✸✳

❋✐❡❧❞ ✈❛❧✉❡ ✐♥ ❬✶✱ ✻❪✿ ❡①♣♦♥❡♥t ✈❛❧✉❡ ❬✲✷✱ ✸❪✳ ❋✐❡❧❞ ✈❛❧✉❡ ✵✿ ❞❡♥♦r♠❛❧✐③❡❞✿ ❡①♣♦♥❡♥t ✈❛❧✉❡ ✲✷✳ ❋✐❡❧❞ ✈❛❧✉❡ ✼✿ ❊①❝❡♣t✐♦♥❛❧ ❝❛s❡s✿ ■♥✜♥✐t✐❡s ✰ ◆❛◆✳

✸✲❜✐t ❢r❛❝t✐♦♥❀ ❢♦r ♥♦r♠❛❧✐③❡❞ ♥✉♠❜❡rs✱ ✐♠♣❧✐❝✐t ✶ t♦ ❧❡❢t ♦❢ ❜✐♥❛r② ♣♦✐♥t✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-122
SLIDE 122

✭✼✲✸✮✲❇✐t ❋❧♦❛t ❱❛❧✉❡s ❈♦♥t✐♥✉❡❞

❇✐ts ❊①♣ ❋r❛❝t✐♦♥ ❱❛❧✉❡ ✵ ✵✵✵ ✵✵✵ ✵ ✵ +✵.✵✵✵✵✵✵(✷−✷ × (✵ + ✵/✽)) ✵ ✵✵✵ ✵✵✶ ✵ ✶ +✵.✵✸✶✷✺✵(✷−✷ × (✵ + ✶/✽)) ✵ ✵✵✵ ✵✶✵ ✵ ✷ +✵.✵✻✷✺✵✵(✷−✷ × (✵ + ✷/✽)) ✵ ✵✵✵ ✵✶✶ ✵ ✸ +✵.✵✾✸✼✺✵(✷−✷ × (✵ + ✸/✽)) ✵ ✵✵✵ ✶✵✵ ✵ ✹ +✵.✶✷✺✵✵✵(✷−✷ × (✵ + ✹/✽)) ✵ ✵✵✵ ✶✵✶ ✵ ✺ +✵.✶✺✻✷✺✵(✷−✷ × (✵ + ✺/✽)) ✵ ✵✵✵ ✶✶✵ ✵ ✻ +✵.✶✽✼✺✵✵(✷−✷ × (✵ + ✻/✽)) ✵ ✵✵✵ ✶✶✶ ✵ ✼ +✵.✷✶✽✼✺✵(✷−✷ × (✵ + ✼/✽))

❈ ■♥tr♦❞✉❝t✐♦♥

slide-123
SLIDE 123

✭✼✲✸✮✲❇✐t ❋❧♦❛t ❱❛❧✉❡s ❈♦♥t✐♥✉❡❞

❇✐ts ❊①♣ ❋r❛❝t✐♦♥ ❱❛❧✉❡ ✵ ✵✵✶ ✵✵✵ ✶ ✵ +✵.✷✺✵✵✵✵(✷−✷ × (✶ + ✵/✽)) ✵ ✵✵✶ ✵✵✶ ✶ ✶ +✵.✷✽✶✷✺✵(✷−✷ × (✶ + ✶/✽)) ✵ ✵✵✶ ✵✶✵ ✶ ✷ +✵.✸✶✷✺✵✵(✷−✷ × (✶ + ✷/✽)) ✵ ✵✵✶ ✵✶✶ ✶ ✸ +✵.✸✹✸✼✺✵(✷−✷ × (✶ + ✸/✽)) ✵ ✵✵✶ ✶✵✵ ✶ ✹ +✵.✸✼✺✵✵✵(✷−✷ × (✶ + ✹/✽)) ✵ ✵✵✶ ✶✵✶ ✶ ✺ +✵.✹✵✻✷✺✵(✷−✷ × (✶ + ✺/✽)) ✵ ✵✵✶ ✶✶✵ ✶ ✻ +✵.✹✸✼✺✵✵(✷−✷ × (✶ + ✻/✽)) ✵ ✵✵✶ ✶✶✶ ✶ ✼ +✵.✹✻✽✼✺✵(✷−✷ × (✶ + ✼/✽))

❈ ■♥tr♦❞✉❝t✐♦♥

slide-124
SLIDE 124

✭✼✲✸✮✲❇✐t ❋❧♦❛t ❱❛❧✉❡s ❈♦♥t✐♥✉❡❞

❇✐ts ❊①♣ ❋r❛❝t✐♦♥ ❱❛❧✉❡ ✵ ✵✶✵ ✵✵✵ ✷ ✵ +✵.✺✵✵✵✵✵(✷−✶ × (✶ + ✵/✽)) ✵ ✵✶✵ ✵✵✶ ✷ ✶ +✵.✺✻✷✺✵✵(✷−✶ × (✶ + ✶/✽)) ✵ ✵✶✵ ✵✶✵ ✷ ✷ +✵.✻✷✺✵✵✵(✷−✶ × (✶ + ✷/✽)) ✵ ✵✶✵ ✵✶✶ ✷ ✸ +✵.✻✽✼✺✵✵(✷−✶ × (✶ + ✸/✽)) ✵ ✵✶✵ ✶✵✵ ✷ ✹ +✵.✼✺✵✵✵✵(✷−✶ × (✶ + ✹/✽)) ✵ ✵✶✵ ✶✵✶ ✷ ✺ +✵.✽✶✷✺✵✵(✷−✶ × (✶ + ✺/✽)) ✵ ✵✶✵ ✶✶✵ ✷ ✻ +✵.✽✼✺✵✵✵(✷−✶ × (✶ + ✻/✽)) ✵ ✵✶✵ ✶✶✶ ✷ ✼ +✵.✾✸✼✺✵✵(✷−✶ × (✶ + ✼/✽))

❈ ■♥tr♦❞✉❝t✐♦♥

slide-125
SLIDE 125

✭✼✲✸✮✲❇✐t ❋❧♦❛t ❱❛❧✉❡s ❈♦♥t✐♥✉❡❞

❇✐ts ❊①♣ ❋r❛❝t✐♦♥ ❱❛❧✉❡ ✵ ✵✶✶ ✵✵✵ ✸ ✵ +✶.✵✵✵✵✵✵(✷✵ × (✶ + ✵/✽)) ✵ ✵✶✶ ✵✵✶ ✸ ✶ +✶.✶✷✺✵✵✵(✷✵ × (✶ + ✶/✽)) ✵ ✵✶✶ ✵✶✵ ✸ ✷ +✶.✷✺✵✵✵✵(✷✵ × (✶ + ✷/✽)) ✵ ✵✶✶ ✵✶✶ ✸ ✸ +✶.✸✼✺✵✵✵(✷✵ × (✶ + ✸/✽)) ✵ ✵✶✶ ✶✵✵ ✸ ✹ +✶.✺✵✵✵✵✵(✷✵ × (✶ + ✹/✽)) ✵ ✵✶✶ ✶✵✶ ✸ ✺ +✶.✻✷✺✵✵✵(✷✵ × (✶ + ✺/✽)) ✵ ✵✶✶ ✶✶✵ ✸ ✻ +✶.✼✺✵✵✵✵(✷✵ × (✶ + ✻/✽)) ✵ ✵✶✶ ✶✶✶ ✸ ✼ +✶.✽✼✺✵✵✵(✷✵ × (✶ + ✼/✽))

❈ ■♥tr♦❞✉❝t✐♦♥

slide-126
SLIDE 126

✭✼✲✸✮✲❇✐t ❋❧♦❛t ❱❛❧✉❡s ❈♦♥t✐♥✉❡❞

❇✐ts ❊①♣ ❋r❛❝t✐♦♥ ❱❛❧✉❡ ✵ ✶✵✵ ✵✵✵ ✹ ✵ +✷.✵✵✵✵✵✵(✷✶ × (✶ + ✵/✽)) ✵ ✶✵✵ ✵✵✶ ✹ ✶ +✷.✷✺✵✵✵✵(✷✶ × (✶ + ✶/✽)) ✵ ✶✵✵ ✵✶✵ ✹ ✷ +✷.✺✵✵✵✵✵(✷✶ × (✶ + ✷/✽)) ✵ ✶✵✵ ✵✶✶ ✹ ✸ +✷.✼✺✵✵✵✵(✷✶ × (✶ + ✸/✽)) ✵ ✶✵✵ ✶✵✵ ✹ ✹ +✸.✵✵✵✵✵✵(✷✶ × (✶ + ✹/✽)) ✵ ✶✵✵ ✶✵✶ ✹ ✺ +✸.✷✺✵✵✵✵(✷✶ × (✶ + ✺/✽)) ✵ ✶✵✵ ✶✶✵ ✹ ✻ +✸.✺✵✵✵✵✵(✷✶ × (✶ + ✻/✽)) ✵ ✶✵✵ ✶✶✶ ✹ ✼ +✸.✼✺✵✵✵✵(✷✶ × (✶ + ✼/✽))

❈ ■♥tr♦❞✉❝t✐♦♥

slide-127
SLIDE 127

✭✼✲✸✮✲❇✐t ❋❧♦❛t ❱❛❧✉❡s ❈♦♥t✐♥✉❡❞

❇✐ts ❊①♣ ❋r❛❝t✐♦♥ ❱❛❧✉❡ ✵ ✶✵✶ ✵✵✵ ✺ ✵ +✹.✵✵✵✵✵✵(✷✷ × (✶ + ✵/✽)) ✵ ✶✵✶ ✵✵✶ ✺ ✶ +✹.✺✵✵✵✵✵(✷✷ × (✶ + ✶/✽)) ✵ ✶✵✶ ✵✶✵ ✺ ✷ +✺.✵✵✵✵✵✵(✷✷ × (✶ + ✷/✽)) ✵ ✶✵✶ ✵✶✶ ✺ ✸ +✺.✺✵✵✵✵✵(✷✷ × (✶ + ✸/✽)) ✵ ✶✵✶ ✶✵✵ ✺ ✹ +✻.✵✵✵✵✵✵(✷✷ × (✶ + ✹/✽)) ✵ ✶✵✶ ✶✵✶ ✺ ✺ +✻.✺✵✵✵✵✵(✷✷ × (✶ + ✺/✽)) ✵ ✶✵✶ ✶✶✵ ✺ ✻ +✼.✵✵✵✵✵✵(✷✷ × (✶ + ✻/✽)) ✵ ✶✵✶ ✶✶✶ ✺ ✼ +✼.✺✵✵✵✵✵(✷✷ × (✶ + ✼/✽))

❈ ■♥tr♦❞✉❝t✐♦♥

slide-128
SLIDE 128

✭✼✲✸✮✲❇✐t ❋❧♦❛t ❱❛❧✉❡s ❈♦♥t✐♥✉❡❞

❇✐ts ❊①♣ ❋r❛❝t✐♦♥ ❱❛❧✉❡ ✵ ✶✶✵ ✵✵✵ ✻ ✵ +✽.✵✵✵✵✵✵(✷✸ × (✶ + ✵/✽)) ✵ ✶✶✵ ✵✵✶ ✻ ✶ +✾.✵✵✵✵✵✵(✷✸ × (✶ + ✶/✽)) ✵ ✶✶✵ ✵✶✵ ✻ ✷ +✶✵.✵✵✵✵✵✵(✷✸ × (✶ + ✷/✽)) ✵ ✶✶✵ ✵✶✶ ✻ ✸ +✶✶.✵✵✵✵✵✵(✷✸ × (✶ + ✸/✽)) ✵ ✶✶✵ ✶✵✵ ✻ ✹ +✶✷.✵✵✵✵✵✵(✷✸ × (✶ + ✹/✽)) ✵ ✶✶✵ ✶✵✶ ✻ ✺ +✶✸.✵✵✵✵✵✵(✷✸ × (✶ + ✺/✽)) ✵ ✶✶✵ ✶✶✵ ✻ ✻ +✶✹.✵✵✵✵✵✵(✷✸ × (✶ + ✻/✽)) ✵ ✶✶✵ ✶✶✶ ✻ ✼ +✶✺.✵✵✵✵✵✵(✷✸ × (✶ + ✼/✽))

❈ ■♥tr♦❞✉❝t✐♦♥

slide-129
SLIDE 129

✭✼✲✸✮✲❇✐t ❋❧♦❛t ❱❛❧✉❡s ❈♦♥t✐♥✉❡❞

❇✐ts ❊①♣ ❋r❛❝t✐♦♥ ❱❛❧✉❡ ✵ ✶✶✶ ✵✵✵ ✼ ✵ +✐♥✜♥✐t② ✵ ✶✶✶ ✵✵✶ ✼ ✶ +♥❛♥ ✵ ✶✶✶ ✵✶✵ ✼ ✷ +♥❛♥ ✵ ✶✶✶ ✵✶✶ ✼ ✸ +♥❛♥ ✵ ✶✶✶ ✶✵✵ ✼ ✹ +♥❛♥ ✵ ✶✶✶ ✶✵✶ ✼ ✺ +♥❛♥ ✵ ✶✶✶ ✶✶✵ ✼ ✻ +♥❛♥ ✵ ✶✶✶ ✶✶✶ ✼ ✼ +♥❛♥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-130
SLIDE 130

✭✼✲✸✮✲❇✐t ❋❧♦❛t ❱❛❧✉❡s ❈♦♥t✐♥✉❡❞

❇✐ts ❊①♣ ❋r❛❝t✐♦♥ ❱❛❧✉❡ ✶ ✵✵✵ ✵✵✵ ✵ ✵ −✵.✵✵✵✵✵✵(−✷−✷ × (✵ + ✵/✽)) ✶ ✵✵✵ ✵✵✶ ✵ ✶ −✵.✵✸✶✷✺✵(−✷−✷ × (✵ + ✶/✽)) ✶ ✵✵✵ ✵✶✵ ✵ ✷ −✵.✵✻✷✺✵✵(−✷−✷ × (✵ + ✷/✽)) ✶ ✵✵✵ ✵✶✶ ✵ ✸ −✵.✵✾✸✼✺✵(−✷−✷ × (✵ + ✸/✽)) ✶ ✵✵✵ ✶✵✵ ✵ ✹ −✵.✶✷✺✵✵✵(−✷−✷ × (✵ + ✹/✽)) ✶ ✵✵✵ ✶✵✶ ✵ ✺ −✵.✶✺✻✷✺✵(−✷−✷ × (✵ + ✺/✽)) ✶ ✵✵✵ ✶✶✵ ✵ ✻ −✵.✶✽✼✺✵✵(−✷−✷ × (✵ + ✻/✽)) ✶ ✵✵✵ ✶✶✶ ✵ ✼ −✵.✷✶✽✼✺✵(−✷−✷ × (✵ + ✼/✽))

❈ ■♥tr♦❞✉❝t✐♦♥

slide-131
SLIDE 131

✭✼✲✸✮✲❇✐t ❋❧♦❛t ❱❛❧✉❡s ❈♦♥t✐♥✉❡❞

❇✐ts ❊①♣ ❋r❛❝t✐♦♥ ❱❛❧✉❡ ✶ ✵✵✶ ✵✵✵ ✶ ✵ −✵.✷✺✵✵✵✵(−✷−✷ × (✶ + ✵/✽)) ✶ ✵✵✶ ✵✵✶ ✶ ✶ −✵.✷✽✶✷✺✵(−✷−✷ × (✶ + ✶/✽)) ✶ ✵✵✶ ✵✶✵ ✶ ✷ −✵.✸✶✷✺✵✵(−✷−✷ × (✶ + ✷/✽)) ✶ ✵✵✶ ✵✶✶ ✶ ✸ −✵.✸✹✸✼✺✵(−✷−✷ × (✶ + ✸/✽)) ✶ ✵✵✶ ✶✵✵ ✶ ✹ −✵.✸✼✺✵✵✵(−✷−✷ × (✶ + ✹/✽)) ✶ ✵✵✶ ✶✵✶ ✶ ✺ −✵.✹✵✻✷✺✵(−✷−✷ × (✶ + ✺/✽)) ✶ ✵✵✶ ✶✶✵ ✶ ✻ −✵.✹✸✼✺✵✵(−✷−✷ × (✶ + ✻/✽)) ✶ ✵✵✶ ✶✶✶ ✶ ✼ −✵.✹✻✽✼✺✵(−✷−✷ × (✶ + ✼/✽))

❈ ■♥tr♦❞✉❝t✐♦♥

slide-132
SLIDE 132

✭✼✲✸✮✲❇✐t ❋❧♦❛t ❱❛❧✉❡s ❈♦♥t✐♥✉❡❞

❇✐ts ❊①♣ ❋r❛❝t✐♦♥ ❱❛❧✉❡ ✶ ✵✶✵ ✵✵✵ ✷ ✵ −✵.✺✵✵✵✵✵(−✷−✶ × (✶ + ✵/✽)) ✶ ✵✶✵ ✵✵✶ ✷ ✶ −✵.✺✻✷✺✵✵(−✷−✶ × (✶ + ✶/✽)) ✶ ✵✶✵ ✵✶✵ ✷ ✷ −✵.✻✷✺✵✵✵(−✷−✶ × (✶ + ✷/✽)) ✶ ✵✶✵ ✵✶✶ ✷ ✸ −✵.✻✽✼✺✵✵(−✷−✶ × (✶ + ✸/✽)) ✶ ✵✶✵ ✶✵✵ ✷ ✹ −✵.✼✺✵✵✵✵(−✷−✶ × (✶ + ✹/✽)) ✶ ✵✶✵ ✶✵✶ ✷ ✺ −✵.✽✶✷✺✵✵(−✷−✶ × (✶ + ✺/✽)) ✶ ✵✶✵ ✶✶✵ ✷ ✻ −✵.✽✼✺✵✵✵(−✷−✶ × (✶ + ✻/✽)) ✶ ✵✶✵ ✶✶✶ ✷ ✼ −✵.✾✸✼✺✵✵(−✷−✶ × (✶ + ✼/✽))

❈ ■♥tr♦❞✉❝t✐♦♥

slide-133
SLIDE 133

✭✼✲✸✮✲❇✐t ❋❧♦❛t ❱❛❧✉❡s ❈♦♥t✐♥✉❡❞

❇✐ts ❊①♣ ❋r❛❝t✐♦♥ ❱❛❧✉❡ ✶ ✵✶✶ ✵✵✵ ✸ ✵ −✶.✵✵✵✵✵✵(−✷✵ × (✶ + ✵/✽)) ✶ ✵✶✶ ✵✵✶ ✸ ✶ −✶.✶✷✺✵✵✵(−✷✵ × (✶ + ✶/✽)) ✶ ✵✶✶ ✵✶✵ ✸ ✷ −✶.✷✺✵✵✵✵(−✷✵ × (✶ + ✷/✽)) ✶ ✵✶✶ ✵✶✶ ✸ ✸ −✶.✸✼✺✵✵✵(−✷✵ × (✶ + ✸/✽)) ✶ ✵✶✶ ✶✵✵ ✸ ✹ −✶.✺✵✵✵✵✵(−✷✵ × (✶ + ✹/✽)) ✶ ✵✶✶ ✶✵✶ ✸ ✺ −✶.✻✷✺✵✵✵(−✷✵ × (✶ + ✺/✽)) ✶ ✵✶✶ ✶✶✵ ✸ ✻ −✶.✼✺✵✵✵✵(−✷✵ × (✶ + ✻/✽)) ✶ ✵✶✶ ✶✶✶ ✸ ✼ −✶.✽✼✺✵✵✵(−✷✵ × (✶ + ✼/✽))

❈ ■♥tr♦❞✉❝t✐♦♥

slide-134
SLIDE 134

✭✼✲✸✮✲❇✐t ❋❧♦❛t ❱❛❧✉❡s ❈♦♥t✐♥✉❡❞

❇✐ts ❊①♣ ❋r❛❝t✐♦♥ ❱❛❧✉❡ ✶ ✶✵✵ ✵✵✵ ✹ ✵ −✷.✵✵✵✵✵✵(−✷✶ × (✶ + ✵/✽)) ✶ ✶✵✵ ✵✵✶ ✹ ✶ −✷.✷✺✵✵✵✵(−✷✶ × (✶ + ✶/✽)) ✶ ✶✵✵ ✵✶✵ ✹ ✷ −✷.✺✵✵✵✵✵(−✷✶ × (✶ + ✷/✽)) ✶ ✶✵✵ ✵✶✶ ✹ ✸ −✷.✼✺✵✵✵✵(−✷✶ × (✶ + ✸/✽)) ✶ ✶✵✵ ✶✵✵ ✹ ✹ −✸.✵✵✵✵✵✵(−✷✶ × (✶ + ✹/✽)) ✶ ✶✵✵ ✶✵✶ ✹ ✺ −✸.✷✺✵✵✵✵(−✷✶ × (✶ + ✺/✽)) ✶ ✶✵✵ ✶✶✵ ✹ ✻ −✸.✺✵✵✵✵✵(−✷✶ × (✶ + ✻/✽)) ✶ ✶✵✵ ✶✶✶ ✹ ✼ −✸.✼✺✵✵✵✵(−✷✶ × (✶ + ✼/✽))

❈ ■♥tr♦❞✉❝t✐♦♥

slide-135
SLIDE 135

✭✼✲✸✮✲❇✐t ❋❧♦❛t ❱❛❧✉❡s ❈♦♥t✐♥✉❡❞

❇✐ts ❊①♣ ❋r❛❝t✐♦♥ ❱❛❧✉❡ ✶ ✶✵✶ ✵✵✵ ✺ ✵ −✹.✵✵✵✵✵✵(−✷✷ × (✶ + ✵/✽)) ✶ ✶✵✶ ✵✵✶ ✺ ✶ −✹.✺✵✵✵✵✵(−✷✷ × (✶ + ✶/✽)) ✶ ✶✵✶ ✵✶✵ ✺ ✷ −✺.✵✵✵✵✵✵(−✷✷ × (✶ + ✷/✽)) ✶ ✶✵✶ ✵✶✶ ✺ ✸ −✺.✺✵✵✵✵✵(−✷✷ × (✶ + ✸/✽)) ✶ ✶✵✶ ✶✵✵ ✺ ✹ −✻.✵✵✵✵✵✵(−✷✷ × (✶ + ✹/✽)) ✶ ✶✵✶ ✶✵✶ ✺ ✺ −✻.✺✵✵✵✵✵(−✷✷ × (✶ + ✺/✽)) ✶ ✶✵✶ ✶✶✵ ✺ ✻ −✼.✵✵✵✵✵✵(−✷✷ × (✶ + ✻/✽)) ✶ ✶✵✶ ✶✶✶ ✺ ✼ −✼.✺✵✵✵✵✵(−✷✷ × (✶ + ✼/✽))

❈ ■♥tr♦❞✉❝t✐♦♥

slide-136
SLIDE 136

✭✼✲✸✮✲❇✐t ❋❧♦❛t ❱❛❧✉❡s ❈♦♥t✐♥✉❡❞

❇✐ts ❊①♣ ❋r❛❝t✐♦♥ ❱❛❧✉❡ ✶ ✶✶✵ ✵✵✵ ✻ ✵ −✽.✵✵✵✵✵✵(−✷✸ × (✶ + ✵/✽)) ✶ ✶✶✵ ✵✵✶ ✻ ✶ −✾.✵✵✵✵✵✵(−✷✸ × (✶ + ✶/✽)) ✶ ✶✶✵ ✵✶✵ ✻ ✷ −✶✵.✵✵✵✵✵✵(−✷✸ × (✶ + ✷/✽)) ✶ ✶✶✵ ✵✶✶ ✻ ✸ −✶✶.✵✵✵✵✵✵(−✷✸ × (✶ + ✸/✽)) ✶ ✶✶✵ ✶✵✵ ✻ ✹ −✶✷.✵✵✵✵✵✵(−✷✸ × (✶ + ✹/✽)) ✶ ✶✶✵ ✶✵✶ ✻ ✺ −✶✸.✵✵✵✵✵✵(−✷✸ × (✶ + ✺/✽)) ✶ ✶✶✵ ✶✶✵ ✻ ✻ −✶✹.✵✵✵✵✵✵(−✷✸ × (✶ + ✻/✽)) ✶ ✶✶✵ ✶✶✶ ✻ ✼ −✶✺.✵✵✵✵✵✵(−✷✸ × (✶ + ✼/✽))

❈ ■♥tr♦❞✉❝t✐♦♥

slide-137
SLIDE 137

✭✼✲✸✮✲❇✐t ❋❧♦❛t ❱❛❧✉❡s ❈♦♥t✐♥✉❡❞

❇✐ts ❊①♣ ❋r❛❝t✐♦♥ ❱❛❧✉❡ ✶ ✶✶✶ ✵✵✵ ✼ ✵ −✐♥✜♥✐t② ✶ ✶✶✶ ✵✵✶ ✼ ✶ −♥❛♥ ✶ ✶✶✶ ✵✶✵ ✼ ✷ −♥❛♥ ✶ ✶✶✶ ✵✶✶ ✼ ✸ −♥❛♥ ✶ ✶✶✶ ✶✵✵ ✼ ✹ −♥❛♥ ✶ ✶✶✶ ✶✵✶ ✼ ✺ −♥❛♥ ✶ ✶✶✶ ✶✶✵ ✼ ✻ −♥❛♥ ✶ ✶✶✶ ✶✶✶ ✼ ✼ −♥❛♥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-138
SLIDE 138

❈❤❛r❛❝t❡r ❙❡ts

❆ ❝❤❛r❛❝t❡r ✐s ❛♥ ❛❜str❛❝t ❡♥t✐t② r❡♣r❡s❡♥t✐♥❣ ❛ s②♠❜♦❧ ✉s❡❞ ✐♥ ✇r✐t✐♥❣ s♦♠❡ ❤✉♠❛♥ ❧❛♥❣✉❛❣❡✳ Pr✐♥t❡❞ r❡♣r❡s❡♥t❛t✐♦♥ ✐s ❛ ❣❧②♣❤✳ ❘❡♣r❡s❡♥t❡❞ ❜② ❛♥ ✐♥t❡❣❡r ❝♦❞❡ ✇✐t❤✐♥ ❝♦♠♣✉t❡rs✳ ❆ ❝❤❛r❛❝t❡r s❡t ❝♦✉❧❞ r❡❢❡r t♦ ❛♥ ❛❜str❛❝t s❡t ♦❢ ❝❤❛r❛❝t❡rs✱ ♦r ❛ ♠♦r❡ ❝♦♥❝r❡t❡ ♠❛♣♣✐♥❣ ❢r♦♠ s♦♠❡ ❝❤❛r❛❝t❡r ❝♦❞❡s t♦ ❣❧②♣❤s✳ ▼❛♥② ❞✐✛❡r❡♥t ❝❤❛r❛❝t❡r s❡ts✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-139
SLIDE 139

❆❙❈■■

✶✾✻✵s✿ ❆❙❈■■ ✐s ❛ ✼✲❜✐t ❝♦❞❡ ✵①✵✵ ✲ ✵①✼❋ ❡✈♦❧✈❡❞ ❢r♦♠ ❝♦❞❡s ✉s❡❞ ❢♦r t❡❧❡❣r❛♣❤✳ ✾✺ ♣r✐♥t❛❜❧❡ ❝❤❛r❛❝t❡rs✱ ✸✸ ❝♦♥tr♦❧ ❝❤❛r❛❝t❡rs✳ ✵①✵✵ ✲ ✵①✶❋ ❈♦♥tr♦❧ ❝♦❞❡s✿ ✵①✵❛ ❫❏✱ ✬❭♥✬ ❧✐♥❡ ❢❡❡❞❀ ✵①✵❞ ❫▼✱ ✬❭r✬ ❝❛rr✐❛❣❡ r❡t✉r♥❀ ✵①✵✼ ❫●✱ ✬❭❛✬ ❜❡❧❧❀ ✵①✵✾✱ ❫■✬✱ ✬❭t✬❵ ❤♦r✐③♦♥t❛❧ t❛❜❀ ✵①✵✽✱ ❫❍✱ ✬❭❜✬❵ ❜❛❝❦s♣❛❝❡❀ ✵①✵❝ ❫▲✱ ✬❭❢✬ ❢♦r♠ ❢❡❡❞❀ ✵①✶❇ ❫❬ ❡s❝❛♣❡✳ ✵①✷✵ ✭✸✷✮✿ s♣❛❝❡ ❝❤❛r❛❝t❡r✳ ✵①✸✵ ✲ ✵①✸✾ ✭✹✽ ✲ ✺✼✮✿ ❞✐❣✐ts✳ ✵①✹✶ ✲ ✵①✺❛ ✭✻✺ ✲ ✾✵✮✿ ✉♣♣❡r✲❝❛s❡ ❛❧♣❤❛❜❡t ❆ ✲ ❩✳ ●❡t ❝♦rr❡s♣♦♥❞✐♥❣ ❝♦♥tr♦❧✲❝♦❞❡ ❜② str✐♣♣✐♥❣ ♦✛ ❤✐❣❤ ❜✐t ❜✻✳ ✵①✻✶ ✲ ✵①✼❛ ✭✾✼ ✲ ✶✷✷✮✿ ❧♦✇❡r✲❝❛s❡ ❛❧♣❤❛❜❡t ❛ ✲ ③✳ ✵①✼❢✿ ❞❡❧❡t❡ ❝❤❛r❛❝t❡r✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-140
SLIDE 140

❆❙❈■■ ❈♦♥t✐♥✉❡❞

❈♦❞❡s ♥♦t ❧✐st❡❞ ❛❜♦✈❡ ❛r❡ s②♠❜♦❧ ♦r ♣✉♥❝t✉❛t✐♦♥ ❝❤❛r❛❝t❡rs✳ Pr♦❜❧❡♠s ✇✐t❤ ❝❤❛r❛❝t❡rs ❧✐❦❡ ❜r❛❝❦❡ts ❬ ❛♥❞ ❪✱ ❛♥❞ ❜r❛❝❡s ④ ❛♥❞ ⑥✱ ✇❤✐❝❤ ✇❡r❡ ❞✐✣❝✉❧t t♦ t②♣❡ ♦♥ s♦♠❡ ❦❡②❜♦❛r❞s ✭❝✉rr❡♥t❧② r❛r❡✮✳ ▲❡❞ t♦ ❈ tr✐❣r❛♣❤s✿ ❄❄① ❢♦r ❛❧t❡r♥❛t❡ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ♣r♦❜❧❡♠❛t✐❝ ❝❤❛r❛❝t❡rs✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-141
SLIDE 141

✽✲❇✐t ❈❤❛r❛❝t❡r ❙❡ts

■❇▼ ❊❇❈❉■❈ ❯s❡❞ ❜② ■❇▼ ♠❛✐♥❢r❛♠❡s✳ ◆♦♥✲❝♦♥t✐❣✉♦✉s ❛❧♣❤❛❜❡t✐❝ ❝❤❛r❛❝t❡rs✳ ▼✉❧t✐♣❧❡ ❝♦❞❡ ♣❛❣❡s✳ ❊①t❡♥❞❡❞ ❆❙❈■■ ✶✾✽✵s✱ ✶✾✾✵s✳ ▼✐❝r♦s♦❢t ❝♦❞❡ ♣❛❣❡s ❢♦r ❞✐✛❡r❡♥t ❧❛♥❣✉❛❣❡s❀ ■❙❖✲✽✽✺✾✲✯ ❢♦r ❞✐✛❡r❡♥t ❧❛♥❣✉❛❣❡s✳ ✽✽✺✾✲✶ ▲❛t✐♥✲✶ ❢♦r ❲❡st❡r♥ ❊✉r♦♣❡❛♥ ❧❛♥❣✉❛❣❡s✱ ✽✽✺✾✲✷ ▲❛t✐♥✲✷ ❢♦r ❈❡♥tr❛❧ ❊✉r♦♣❡❛♥ ❧❛♥❣✉❛❣❡s✱ ✳✳✱ ✽✽✺✾✲✾ ▲❛t✐♥✲✺ ❢♦r ❚✉r❦✐s❤✳ ❖t❤❡r ✽✽✺✾✲✯ ✈❛r✐❛♥ts ❝♦✈❡r ♠♦st ❊✉r♦♣❡❛♥ ❧❛♥❣✉❛❣❡s✱ ❆r❛❜✐❝✱ ❍❡❜r❡✇✱ ❚❤❛✐✳ ❱❛r✐♦✉s ✐♥❝♦♠♣❛t✐❜✐❧✐t❡s✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-142
SLIDE 142

❈❏❑ ▲❛♥❣✉❛❣❡s

❈❏❑✿ ❈❤✐♥❡s❡✱ ❏❛♣❛♥❡s❡ ❛♥❞ ❑♦r❡❛♥✳ ❈❏❑❱✿ ✰ ❱✐❡t♥❛♠❡s❡✳ ❈♦✈❡r ♠❛✐♥ ❊❛st ❆s✐❛♥ ▲❛♥❣✉❛❣❡s✳ ❚❤♦✉s❛♥❞s ♦❢ ❝❤❛r❛❝t❡rs r❡q✉✐r❡❞✳ ✽ ❜✐ts ✐♥s✉✣❝✐❡♥t✳ ❚✇♦ ♠❛❥♦r ❛♣♣r♦❛❝❤❡s✿ ❲✐❞❡ ❈❤❛r❛❝t❡rs ❊♥❝♦❞❡ ❝❤❛r❛❝t❡rs ✉s✐♥❣ ✶✻✲❜✐ts ✭♦r ✇✐❞❡r✮✳ ▼✉❧t✲❇②t❡ ❱❛r✐❛❜❧❡ ▲❡♥❣t❤ ❊♥❝♦❞✐♥❣ ◆❡❡❞ ❡s❝❛♣❡ s❡q✉❡♥❝❡s t♦ s❤✐❢t ✐♥t❡r♣r❡t❛t✐♦♥s✳ ◆❡❡❞ t♦ s❝❛♥ str✐♥❣ s❡q✉❡♥t✐❛❧❧② t♦ ✐♥t❡r♣r❡t ❡s❝❛♣❡ s❡q✉❡♥❝❡s ❝♦rr❡❝t❧②✳ ❊♥t✐r❡ str✐♥❣ ❝♦rr✉♣t❡❞ ✐❢ ❛ s✐♥❣❧❡ ❜✐t ✐s ❝♦rr✉♣t❡❞✳ ❊①❛♠♣❧❡✿ ❙❤✐❢t ❏■❙✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-143
SLIDE 143

❯♥✐❝♦❞❡

❯♥✐❝♦❞❡ ✉♥✐✈❡rs❛❧ ❝❤❛r❛❝t❡r s❡t ✇✐❞❡❧② ✉s❡❞ ❜② ❛❧❧ ♠♦❞❡r♥ ❝♦♠♣✉t❡r s②st❡♠s t♦ r❡♣r❡s❡♥t ✐♥t❡r♥❛t✐♦♥❛❧ ❝❤❛r❛❝t❡rs✳ ❖✈❡r ✶ ♠✐❧❧✐♦♥ ❝♦❞❡ ♣♦✐♥ts ❢r♦♠ ✵①✵✵✵✵✵✵ t♦ ✵①✶✵❋❋❋❋✳ ❇❛s✐❝ ▼✉❧t✐❧✐♥❣✉❛❧ P❧❛♥❡ ✭❇▼P✮✿ ❝♦❞❡ ♣♦✐♥ts ❧❡ss t❤❛♥ ✵①✶✵✵✵✵✳ ❈❤❛r❛❝t❡rs ♦❢t❡♥ s♣❡❝✐✜❡❞ ❜② ♥❛♠❡ ♦r ❜② ❝♦❞❡✲♣♦✐♥t ❛s ❯✰①①①①✳ ❈♦♠❜✐♥✐♥❣ ❝❤❛r❛❝t❡rs✳ ❈❛♥ ❜❡ ❡♥❝♦❞❡❞ ✉s✐♥❣ ❛ ✜①❡❞ ✇✐❞t❤ ✭❯❚❋✲✸✷✮ ♦r ✈❛r✐❛❜❧❡ ✇✐❞t❤ ❡♥❝♦❞✐♥❣ ✭❯❚❋✲✶✻ ♦♥ ✇✐♥❞♦✇s✱ ❯❚❋✲✽ ♦♥ ✉♥✐① ❛♥❞ ✇✇✇✮✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-144
SLIDE 144

❯❚❋✲✽ ❊♥❝♦❞✐♥❣ ❢♦r ❯♥✐❝♦❞❡

❯❚❋✲✽ ✐s ❛ ♣♦♣✉❧❛r ✈❛r✐❛❜❧❡ ✇✐❞t❤ ❡♥❝♦❞✐♥❣ ❢♦r ❯♥✐❝♦❞❡ ✇❤✐❝❤ ✐s ❝♦♠♣❛t✐❜❧❡ ✇✐t❤ ❆❙❈■■✳ ❯s❡❞ ✇✐❞❡❧② ♦♥ ❲❲❲✳ ✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✰✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲ ❯♥✐❝♦❞❡ ❘❛♥❣❡ ⑤ ❊♥❝♦❞✐♥❣ ✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✰✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲ ❯✰✵✵✵✵✵✵✵✵✵ ✲ ❯✰✵✵✵✵✵✵✼❋ ⑤ ✵①①①①①①① ❯✰✵✵✵✵✵✵✵✽✵ ✲ ❯✰✵✵✵✵✵✼❋❋ ⑤ ✶✶✵①①①①① ✶✵①①①①①① ❯✰✵✵✵✵✵✵✽✵✵ ✲ ❯✰✵✵✵✵❋❋❋❋ ⑤ ✶✶✶✵①①①① ✶✵①①①①①① ✶✵①①①①①① ❯✰✵✵✵✵✶✵✵✵✵ ✲ ❯✰✵✵✶❋❋❋❋❋ ⑤ ✶✶✶✶✵①①① ✶✵①①①①①① ✶✵①①①①①① ⑤ ✶✵①①①①①① ❯✰✵✵✵✷✵✵✵✵✵ ✲ ❯✰✵✸❋❋❋❋❋❋ ⑤ ✶✶✶✶✶✵①① ✶✵①①①①①① ✶✵①①①①①① ⑤ ✶✵①①①①①① ✶✵①①①①①① ❯✰✵✹✵✵✵✵✵✵✵ ✲ ❯✰✼❋❋❋❋❋❋❋ ⑤ ✶✶✶✶✶✶✵① ✶✵①①①①①① ✶✵①①①①①① ⑤ ✶✵①①①①①① ✶✵①①①①①① ⑤ ✶✵①①①①①① ✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✰✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲

❈ ■♥tr♦❞✉❝t✐♦♥

slide-145
SLIDE 145

❯❚❋✲✽ ❊♥❝♦❞✐♥❣ ❢♦r ❯♥✐❝♦❞❡ ❈♦♥t✐♥✉❡❞

❙✐♥❣❧❡ ❜②t❡ ❡♥❝♦❞✐♥❣s ❝♦♠♣❛t✐❜❧❡ ✇✐t❤ ❆❙❈■■✳ ▲❡❛❞✐♥❣ ♥✉♠❜❡r ♦❢ ✶s ✐♥ ✜rst ❜②t❡ ❣✐✈❡s ★ ♦❢ ❜②t❡s ✐♥ ♠✉❧t✐✲❜②t❡ s❡q✉❡♥❝❡s✳ ✹✲❜②t❡ ❡♥❝♦❞✐♥❣ s✉✣❝✐❡♥t t♦ r❡♣r❡s❡♥t ❛❧❧ ❯♥✐❝♦❞❡ ❝❤❛r❛❝t❡rs ✉♣ t♦ ❯✰✶✵❋❋❋❋✳ ❊❛s② t♦ s②♥❝❤r♦♥✐③❡ ❢r♦♠ ♠✐❞❞❧❡ ♦❢ str✐♥❣ ❜② s❦✐♣♣✐♥❣ ✶✵①①①①①① ❜②t❡s✳ ❉❡s✐❣♥❡❞ ✐♥ ✶✾✾✷ ❜② ❑❡♥ ❚❤♦♠♣s♦♥ ♦♥ ❛ ♣❧❛❝❡♠❛t ❛t ❛ ◆❡✇ ❏❡rs❡② ❞✐♥❡r✦

❈ ■♥tr♦❞✉❝t✐♦♥

slide-146
SLIDE 146

❯❚❋✲✽ ✇✐t❤ ❈

▼✉st s❡t ❧♦❝❛❧❡ ❛♣♣r♦♣r✐❛t❡❧②✳ str❧❡♥✭✮ ❣✐✈❡s ♥✉♠❜❡r ♦❢ ❜②t❡s✱ ♥♦t ♥✉♠❜❡r ♦❢ ❝❤❛r❛❝t❡rs✳ ❘♦✉t✐♥❡s ✐♥ st❛♥❞❛r❞ ❧✐❜r❛r② ❛✈❛✐❧❛❜❧❡✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-147
SLIDE 147

❙t❛♥❞❛r❞ ■✴❖ ❊①❛♠♣❧❡✿ ✇❝✭✶✮ ▲♦❣

✇❝✳❝ ❝♦♥t❛✐♥s ❛ s✐♠♣❧❡ ✇♦r❞✲❝♦✉♥t ✭✇❝✭✶✮✮ ♣r♦❣r❛♠✿ ✩ ✇❤✐❝❤ ✇❝ ✴✉sr✴❜✐♥✴✇❝ ✩ ✇❝ ✇❝✳❝ ✻✷ ✶✽✸ ✶✶✺✹ ✇❝✳❝ ✩ ✳✴✇❝ ✇❝✳❝ ✻✷ ✶✽✸ ✶✶✺✹ ✇❝✳❝ ✩ ✳✴✇❝ ✇❝✳❝ ❜✉❢❢❡r✳❝ ✻✷ ✶✽✸ ✶✶✺✹ ✇❝✳❝ ✶✹ ✹✶ ✷✼✽ ❜✉❢❢❡r✳❝ ✼✻ ✷✷✹ ✶✹✸✷ t♦t❛❧ ✩ ✇❝ ❁✇❝✳❝ ✻✷ ✶✽✸ ✶✶✺✹ ✩ ✳✴✇❝ ❁✇❝✳❝ ✻✷ ✶✽✸ ✶✶✺✹ ✩

❈ ■♥tr♦❞✉❝t✐♦♥

slide-148
SLIDE 148

❙t❛♥❞❛r❞ ■✴❖ ❊①❛♠♣❧❡✿ ✇❝✭✶✮ Pr♦❣r❛♠

❡♥✉♠ ④ ❈❖❯◆❚❴❈❍❆❘❙ ❂ ✼ ⑥❀ st❛t✐❝ ✐♥t ♥❈❚♦t❛❧ ❂ ✵❀ ✴✯ t♦t❛❧ ★ ♦❢ ❝❤❛rs ✯✴ st❛t✐❝ ✐♥t ♥❲❚♦t❛❧ ❂ ✵❀ ✴✯ t♦t❛❧ ★ ♦❢ ✇♦r❞s ✯✴ st❛t✐❝ ✐♥t ♥▲❚♦t❛❧ ❂ ✵❀ ✴✯ t♦t❛❧ ★ ♦❢ ❧✐♥❡s ✯✴

❈ ■♥tr♦❞✉❝t✐♦♥

slide-149
SLIDE 149

❙t❛♥❞❛r❞ ■✴❖ ❊①❛♠♣❧❡✿ ✇❝✭✶✮ ♠❛✐♥✭✮ Pr♦❣r❛♠

✐♥t ♠❛✐♥✭✐♥t ❛r❣❝✱ ❝♦♥st ❝❤❛r ✯❛r❣✈❬❪✮ ④ ✐♥t ✐❀ ✐❢ ✭❛r❣❝ ❂❂ ✶✮ ④ ✇❝✭✧✧✱ st❞✐♥✮❀ ⑥ ❡❧s❡ ④ ❢♦r ✭✐ ❂ ✶❀ ✐ < ❛r❣❝❀ ✐✰✰✮ ④ ❋■▲❊ ✯✐♥ ❂ ❢♦♣❡♥✭❛r❣✈❬✐❪✱ ✧r✧✮❀ ✐❢ ✭✦✐♥✮ ④ ❢♣r✐♥t❢✭st❞❡rr✱ ✧❝♦✉❧❞ ♥♦t r❡❛❞ ✪s✿ ✪s\♥✧✱ ❛r❣✈❬✐❪✱ str❡rr♦r✭❡rr♥♦✮✮❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-150
SLIDE 150

❙t❛♥❞❛r❞ ■✴❖ ❊①❛♠♣❧❡✿ ✇❝✭✶✮ ♠❛✐♥✭✮ Pr♦❣r❛♠ ❈♦♥t✐♥✉❡❞

❡❧s❡ ④ ✇❝✭❛r❣✈❬✐❪✱ ✐♥✮❀ ❢❝❧♦s❡✭✐♥✮❀ ⑥ ⑥ ✴✴❢♦r ✭✐ ❂ ✶❀ ✐ < ❛r❣❝❀ ✐✰✰✮ ✐❢ ✭❛r❣❝ > ✷✮ ④ ♣r✐♥t❢✭✧✪✯❞ ✪✯❞ ✪✯❞ t♦t❛❧\♥✧✱ ❈❖❯◆❚❴❈❍❆❘❙✱ ♥▲❚♦t❛❧✱ ❈❖❯◆❚❴❈❍❆❘❙✱ ♥❲❚♦t❛❧✱ ❈❖❯◆❚❴❈❍❆❘❙✱ ♥❈❚♦t❛❧✮❀ ⑥ ⑥ ✴✴❡❧s❡ ✐❢ ❛r❣❝ ✦❂ ✶ r❡t✉r♥ ✵❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-151
SLIDE 151

❙t❛♥❞❛r❞ ■✴❖ ❊①❛♠♣❧❡✿ ✇❝✭✶✮ Pr♦❣r❛♠

✈♦✐❞ ✇❝✭❝♦♥st ❝❤❛r ✯❢◆❛♠❡✱ ❋■▲❊ ✯❢✮ ④ ✐♥t ✐♥❲♦r❞ ❂ ✵❀ ✐♥t ♥❈ ❂ ✵✱ ♥❲ ❂ ✵✱ ♥▲ ❂ ✵❀ ✐♥t ❝❀ ✴✴st❛♥❞❛r❞ ❈ ✐❞✐♦♠ ❢♦r r❡❛❞✐♥❣ ✜❧❡ ✇❤✐❧❡ ❝❤❡❝❦✐♥❣ ❊❖❋ ✇❤✐❧❡ ✭✭❝ ❂ ❢❣❡t❝✭❢✮✮ ✦❂ ❊❖❋✮ ④ ♥❈✰✰❀ ✐❢ ✭❝ ❂❂ ✬\♥✬✮ ♥▲✰✰❀ ✐❢ ✭✐ss♣❛❝❡✭❝✮✮ ④ ✐♥❲♦r❞ ❂ ✵❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-152
SLIDE 152

❙t❛♥❞❛r❞ ■✴❖ ❊①❛♠♣❧❡✿ ✇❝✭✶✮ Pr♦❣r❛♠

❡❧s❡ ④ ✐❢ ✭✦✐♥❲♦r❞✮ ♥❲✰✰❀ ✐♥❲♦r❞ ❂ ✶❀ ⑥ ⑥ ✐❢ ✭❢❡rr♦r✭❢✮✮ ④ ❢♣r✐♥t❢✭st❞❡rr✱ ✧✐✴♦ ❡rr♦r✿ ✪s\♥✧✱ str❡rr♦r✭❡rr♥♦✮✮❀ ⑥ ♣r✐♥t❢✭✧✪✯❞ ✪✯❞ ✪✯❞ ✪s\♥✧✱ ❈❖❯◆❚❴❈❍❆❘❙✱ ♥▲✱ ❈❖❯◆❚❴❈❍❆❘❙✱ ♥❲✱ ❈❖❯◆❚❴❈❍❆❘❙✱ ♥❈✱ ❢◆❛♠❡✮❀ ♥❈❚♦t❛❧ ✰❂ ♥❈❀ ♥❲❚♦t❛❧ ✰❂ ♥❲❀ ♥▲❚♦t❛❧ ✰❂ ♥▲❀ ⑥

❈ ■♥tr♦❞✉❝t✐♦♥

slide-153
SLIDE 153

❈ ❈❤❛r❛❝t❡r ■✴❖

✐♥t ❢❣❡t❝✭❋■▲❊ ✯str❡❛♠✮❀ ✐♥t ❣❡t❝✭❋■▲❊ ✯str❡❛♠✮❀ ✴✴❧✐❦❡ ❢❣❡t❝✭✮ ❜✉t ♠❛② ❜❡ ♠❛❝r♦ ✐♥t ❣❡t❝❤❛r✭✈♦✐❞✮❀ ✴✴❣❡t❝✭st❞✐♥✮ ✐♥t ❢♣✉t❝✭✐♥t ❝✱ ❋■▲❊ ✯str❡❛♠✮❀ ✐♥t ♣✉t❝✭✐♥t ❝✱ ❋■▲❊ ✯str❡❛♠✮❀ ✴✴❧✐❦❡ ❢♣✉t❝✭✮ ✴✴❜✉t ♠❛② ❜❡ ♠❛❝r♦ ✐♥t ♣✉t❝❤❛r✭✐♥t ❝✮❀ ✴✴♣✉t❝✭❝✱ st❞♦✉t✮

❈ ■♥tr♦❞✉❝t✐♦♥

slide-154
SLIDE 154

❈ ❈❤❛r❛❝t❡r ■✴❖

❲❤② ❞♦ ❢✉♥❝t✐♦♥s ♦♥ ♣r❡✈✐♦✉s s❧✐❞❡ tr❡❛t ❝❤❛r❛❝t❡rs ❛s ✐♥t✬s r❛t❤❡r t❤❛♥ ❝❤❛r❄ ❋♦r t❤❡ ♦✉t♣✉t ♣✉t✯✭✮ ❢✉♥❝t✐♦♥s✱ t❤❡ r❡❛s♦♥ ✐s t♦ ❞♦ ✇✐t❤ ❝♦♠♣❛t✐❜✐❧✐t② ✇✐t❤ ♣r❡✲■❙❖ ❈ ✇❤❡r❡ ❛❧❧ ❝❤❛r✴s❤♦rt ❛r❣✉♠❡♥ts ✇❡r❡ ♣❛ss❡❞ ❛s ✐♥t✬s✳ ❇✉t ✇❤② ❢♦r ✐♥♣✉t❄ ❈♦✉❧❞♥✬t ❣❡t✯✭✮ s✐♠♣❧② r❡t✉r♥ ❛ ❝❤❛r❄

❈ ■♥tr♦❞✉❝t✐♦♥

slide-155
SLIDE 155

❙✐❣♥❡❞♥❡ss ♦❢ ❝❤❛r

■♥ ❈✱ t❤❡ s✐❣♥❡❞♥❡ss ♦❢ ❛ ♣❧❛✐♥ ❝❤❛r ✐s ✉♥❞❡✜♥❡❞ ❛s ♦♥ s♦♠❡ ♣❧❛t❢♦r♠s ❝❤❛r ♠❛② ❜❡ s✐❣♥❡❞✱ ♦♥ ♦t❤❡rs ✐t ♠❛② ❜❡ ✉♥s✐❣♥❡❞✳ ❈❛♥ ❜❡ ❡①♣❧✐❝✐t ❜② ❞❡❝❧❛r✐♥❣ s✐❣♥❡❞ ❝❤❛r ♦r ✉♥s✐❣♥❡❞ ❝❤❛r✳ ❣❡t✯✭✮ ❢✉♥❝t✐♦♥s r❡t✉r♥ ❊❖❋ ♦♥ ❡♥❞✲♦❢✲✜❧❡ ♦r ❡rr♦r✳ ❊❖❋ ✐s t②♣✐❝❛❧❧② ❛ ♥❡❣❛t✐✈❡ ♥✉♠❜❡r✱ ✉s✉❛❧❧② ✲✶✳ ❍❡♥❝❡ ❣❡t✯✭✮ ❢✉♥❝t✐♦♥s r❡t✉r♥ ✐♥t✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-156
SLIDE 156

❘❡❝♦r❞ ■✴❖

s✐③❡❴t ❢r❡❛❞✭✈♦✐❞ ✯❜✉❢✱ s✐③❡❴t r❡❝❙✐③❡✱ s✐③❡❴t ♥❘❡❝s✱ ❋■▲❊ ✯✐♥♣✉t✮❀ s✐③❡❴t ❢✇r✐t❡✭❝♦♥st ✈♦✐❞ ✯❜✉❢✱ s✐③❡❴t r❡❝❙✐③❡✱ s✐③❡❴t ♥❘❡❝s✱ ❋■▲❊ ✯♦✉t♣✉t✮❀ ❈❛♥ r❡❛❞✴✇r✐t❡ ♥❘❡❝s r❡❝♦r❞s ❡❛❝❤ ❤❛✈✐♥❣ s✐③❡ ♦❢ r❡❝❙✐③❡ ❜②t❡s✳ ❈❛♥ ❜❡ ✉s❡❞ ❢♦r s❡r✐❛❧✐③✐♥❣ ❜✐♥❛r② ❞❛t❛ ❧✐❦❡ str✉❝t✬s✳ ❙✐♠♣❧❡✲♠✐♥❞❡❞ s❡r✐❛❧✐③❛t✐♦♥ ❧✐❦❡❧② ♣r♦❜❧❡♠❛t✐❝✿ ❜✐♥❛r② ❞❛t❛ ✐s ✐♥❤❡r❡♥t❧② ✉♥♣♦rt❛❜❧❡ ✭❡♥❞✐❛♥ ❛♥❞ s✐③❡ ✐ss✉❡s✮✳ ❙❡r✐❛❧✐③❡❞ ♣♦✐♥t❡rs ❛r❡ ♠❡❛♥✐♥❣❧❡ss✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-157
SLIDE 157

❋♦r♠❛tt❡❞ ■✴❖

♣r✐♥t❢✭✮✱ ❢♣r✐♥t❢✭✮✱ s❝❛♥❢✭✮✱ ❢s❝❛♥❢✭✮ ❛♥❞ ❢r✐❡♥❞s✳ ❙✐♥❝❡ ❈ ❝❛♥♥♦t ❝❤❛♥❣❡ ❛❝t✉❛❧ ♣❛r❛♠❡t❡rs✱ ✐t ✐s ♥❡❝❡ss❛r② t❤❛t s❝❛♥❢✭✮ r❡❝❡✐✈❡ ♣♦✐♥t❡rs t♦ ✈❛r✐❛❜❧❡s t♦ ❜❡ ❝❤❛♥❣❡❞✳ ✐♥t ✈❛❧❀ s❝❛♥❢✭✧✪❞✧✱ ✈❛❧✮❀ ✴✴❲❘❖◆● s❝❛♥❢✭✧✪❞✧✱ ✫✈❛❧✮❀ ✴✴❝♦rr❡❝t ❋♦r♠❛t s♣❡❝✐✜❡rs ❢♦r ♣r✐♥t❢✭✮ ❛♥❞ s❝❛♥❢✭✮ ❜❡❛r s✉♣❡r✜❝✐❛❧ r❡s❡♠❜❧❛♥❝❡ ❜✉t ❛r❡ ❞✐✛❡r❡♥t✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-158
SLIDE 158

❘❡❢❡r❡♥❝❡s

❚❡①t✱ ❈❤ ✷✳ ❑✫❘✷✳ ❙t❡✈❡ ❙✉♠♠✐t✱ ❈ Pr♦❣r❛♠♠✐♥❣ ❋❆◗s✱ ❆❞❞✐s♦♥✲❲❡s❧❡②✱ ◆♦✈✳ ✶✾✾✺✳ P❛rt✐❛❧❧② ♦♥❧✐♥❡✳ P❡t❡r ❱❛♥ ❉❡r ▲✐♥❞❡♥✱ ❊①♣❡rt ❈ Pr♦❣r❛♠♠✐♥❣✿ ❉❡❡♣ ❈ ❙❡❝r❡ts✱ Pr❡♥t✐❝❡✲❍❛❧❧✱ ✶✾✾✹✳ ❍❡♥r② ❙✳ ❲❛rr❡♥✱ ❏r✳ ❍❛❝❦❡r✬s ❉❡❧✐❣❤t✱ ❆❞❞✐s♦♥✲❲❡s❧❡②✱ ✷✵✵✸✳ ❈♦♥t❛✐♥s ❧♦ts ♦❢ ❜✐t✲t✇✐❞❞❧✐♥❣ tr✐❝❦s✳ ❆■ ▼❡♠♦ ✷✸✾✱ ❚❡❝❤♥✐❝❛❧ ❘❡♣♦rt ▼■❚ ❆■ ▲❛❜✱ ✶✾✼✷✳ ♦♥❧✐♥❡ ❝♦♣②✳ ❯s✉❛❧❧② r❡❢❡rr❡❞ t♦ ❛s ❍❆❑▼❊▼ ❜❡❝❛✉s❡ ♦❢ ✻✲❝❤❛r❛❝t❡r ✜❧❡ ❧✐♠✐t✳

❈ ■♥tr♦❞✉❝t✐♦♥

slide-159
SLIDE 159

❘❡❢❡r❡♥❝❡s ❈♦♥t✐♥✉❡❞

❉❛♥♥② ❈♦❤❡♥✱ ❖♥ ❍♦❧② ❲❛rs ❛♥❞ ❛ P❧❡❛ ❢♦r P❡❛❝❡✱ ❈♦♠♣✉t❡r✱ ❖❝t ✶✾✽✶✳ ❊❧❡❝tr♦♥✐❝ ❝♦♣② ❛✈❛✐❧❛❜❧❡ ✈✐❛ ❇❯ ▲✐❜r❛r✐❡s✳ ❆♥ ❡❛r❧✐❡r t❡①t ✈❡rs✐♦♥ ✐s ♦♥❧✐♥❡✳ ❏✳ ❈♦r♣❡❧❛✱ ❆ ❚✉t♦r✐❛❧ ♦♥ ❈❤❛r❛❝t❡r ❙❡t ■ss✉❡s ❛t ❁❤tt♣✿✴✴✇✇✇✳❝s✳t✉t✳✜✴⑦❥❦♦r♣❡❧❛✴❝❤❛rs✳❤t♠❧❃✳ ❖❧✈❡ ▼❛✉❞❛❧✱ ❏♦♥ ❏❛✉❣❡r✱ ❉❡❡♣ ❈✱ ❉✐st✐♥❣✉✐s❤❡s ❜❡t✇❡❡♥ s✉♣❡r✜❝✐❛❧ ❛♥❞ ❞❡❡♣ ✉♥❞❡rst❛♥❞✐♥❣ ♦❢ ♣r♦❣r❛♠♠✐♥❣ ❧❛♥❣✉❛❣❡s✳

❈ ■♥tr♦❞✉❝t✐♦♥