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May 31, 2023 549 likes •783 views

trs r trs r r t t r r

SLIDE 1

■♥t❡r❢❛❝❡s

SLIDE 2

❚❤❡ ♥❡❡❞ ❢♦r ✐♥t❡r❢❛❝❡s

◮ ❚❤❡ ❝♦❞❡ ❢♦r ♣r✐❝✐♥❣ ❛ ❈❛❧❧❖♣t✐♦♥ ❛♥❞ t❤❡ ❝♦❞❡ ❢♦r ♣r✐❝✐♥❣ ❛

P✉t❖♣t✐♦♥ ❜② ▼♦♥t❡ ❈❛r❧♦ ✐s ✐❞❡♥t✐❝❛❧ ❛♣❛rt ❢r♦♠ t❤❡ s♣❡❝✐✜❝❛t✐♦♥ ♦❢ t❤❡ t②♣❡ ♦❢ t❤❡ ♦♣t✐♦♥✳

SLIDE 3

❚❤❡ ❢❛♥t❛s② ❝♦❞❡

❞♦✉❜❧❡✥▼♦♥t❡❈❛r❧♦Pr✐❝❡r✿✿♣r✐❝❡✭ ✥✥✥✥✥✥✥✥❝♦♥st✥P❛t❤■♥❞❡♣❡♥❞❡♥t❖♣t✐♦♥✫✥♦♣t✐♦♥✱ ✥✥✥✥✥✥✥✥❝♦♥st✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✫✥♠♦❞❡❧✥✮✥④ ✥✥✥✥❞♦✉❜❧❡✥t♦t❛❧✥❂✥✵✳✵❀ ✥✥✥✥❢♦r✥✭✐♥t✥✐❂✵❀✥✐❁♥❙❝❡♥❛r✐♦s❀✥✐✰✰✮✥④ ✥✥✥✥✥✥✥✥✈❡❝t♦r❁❞♦✉❜❧❡❃✥♣❛t❤❂✥♠♦❞❡❧✳ ✥✥✥✥✥✥✥✥✥✥✥✥❣❡♥❡r❛t❡❘✐s❦◆❡✉tr❛❧Pr✐❝❡P❛t❤✭ ✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥♦♣t✐♦♥✳❣❡t▼❛t✉r✐t②✭✮✱ ✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✶✥✮❀ ✥✥✥✥✥✥✥✥❞♦✉❜❧❡✥st♦❝❦Pr✐❝❡✥❂✥♣❛t❤✳❜❛❝❦✭✮❀ ✥✥✥✥✥✥✥✥❞♦✉❜❧❡✥♣❛②♦❢❢✥❂✥♦♣t✐♦♥✳♣❛②♦❢❢✭✥st♦❝❦Pr✐❝❡✥✮❀ ✥✥✥✥✥✥✥✥t♦t❛❧✰❂✥♣❛②♦❢❢❀ ✥✥✥✥⑥ ✥✥✥✥❞♦✉❜❧❡✥♠❡❛♥✥❂✥t♦t❛❧✴♥❙❝❡♥❛r✐♦s❀ ✥✥✥✥❞♦✉❜❧❡✥r✥❂✥♠♦❞❡❧✳r✐s❦❋r❡❡❘❛t❡❀ ✥✥✥✥❞♦✉❜❧❡✥❚✥❂✥♦♣t✐♦♥✳❣❡t▼❛t✉r✐t②✭✮✥✲✥♠♦❞❡❧✳❞❛t❡❀ ✥✥✥✥r❡t✉r♥✥❡①♣✭✲r✯❚✮✯♠❡❛♥❀ ⑥

SLIDE 4

❊①♣❧❛♥❛t✐♦♥ ♦❢ t❤❡ ❝♦♥❝❡♣ts

◮ ❖✉r ❝♦❞❡ t♦ ♣r✐❝❡ ❛ ❈❛❧❧❖♣t✐♦♥ ♦♥❧② ❣❡♥❡r❛t❡s ♣r✐❝❡s ✇✐t❤

♦♥❡ t✐♠❡ st❡♣✱ s♦ ✐t ✐s ♦♥❧② ✈❛❧✐❞ ❢♦r ♣❛t❤✲✐♥❞❡♣❡♥❞❡♥t ♦♣t✐♦♥s✳

◮ ❲♦✉❧❞♥✬t ✐t ❜❡ ♥✐❝❡ ✐❢ ✇❡ ❝♦✉❧❞ ♣r✐❝❡ ❛❧❧ ♣❛t❤✲✐♥❞❡♣❡♥❞❡♥t

♦♣t✐♦♥s ✇✐t❤ t❤❡ s❛♠❡ ❝♦❞❡❄

◮ ●✐✈❡♥ t❤❛t ❈✰✰ r❡q✉✐r❡s ✉s t♦ s♣❡❝✐❢② t❤❡ t②♣❡ ♦❢ ❛❧❧

♣❛r❛♠❡t❡rs✱ ✇❡ ♥❡❡❞ t♦ ❞❡✜♥❡ ❛ t②♣❡ t❤❛t r❡♣r❡s❡♥ts ❛ ❣❡♥❡r❛❧ ♣❛t❤✲✐♥❞❡♣❡♥❞❡♥t ♦♣t✐♦♥✳

SLIDE 5

❖t❤❡r ❡①❛♠♣❧❡s

◮ ❆♥ ♦str❡❛♠ ✐s ❛ ❣❡♥❡r❛❧ t②♣❡✳

◮ ❲❡ ❝❛♥ ✇r✐t❡ t♦ ❛ ❣❡♥❡r❛❧ ♦str❡❛♠✳ ◮ ❆♥ ♦str❡❛♠ ♠✐❣❤t ❜❡ ❛ ✜❧❡✱ ❛ ♣r✐♥t❡r ♦r t❤❡ ■♥t❡r♥❡t✳

◮ ■♥ t❤❡ r❡❛❧ ✇♦r❧❞✱ ❛ ❝❛r ✐s ❛ ❣❡♥❡r❛❧ t②♣❡✳

◮ ❲❡ ❝❛♥ st❡❡r t♦ t❤❡ r✐❣❤t✱ ✇❡ ❝❛♥ st❡❡r t♦ t❤❡ ❧❡❢t✳ ◮ ❚❤❡r❡ ❛r❡ ❧♦ts ♦❢ ♠❛❦❡s ♦❢ ❝❛r✱ ❜✉t ✇❡ ✉s❡ t❤❡♠ ❛❧❧ t❤❡ s❛♠❡

✇❛②✳

◮ ■♥ ❛ ❝♦♠♣✉t❡r ❣❛♠❡ ❛ ♠♦♥st❡r ✐s ❛ ❣❡♥❡r❛❧ t②♣❡✳

◮ ❲❡ ❝❛♥ ❞r❛✇ ❛ ♠♦♥st❡r ♦♥ s❝r❡❡♥✳ ◮ ❲❡ ❝❛♥ ❛s❦ ✐t ✇❤❡r❡ ✐t ✇✐❧❧ ♠♦✈❡ ♥❡①t✳ ◮ ●♦❜❧✐♥s ❛♥❞ ❡❧✈❡s ❜❡❤❛✈❡ q✉✐t❡ ❞✐✛❡r❡♥t❧②✱ ❜✉t ✇❡ ❝❛❧❧ t❤❡ s❛♠❡

❢✉♥❝t✐♦♥s t♦ ♣❛✐♥t t❤❡♠ ♦♥ t❤❡ s❝r❡❡♥ ❛♥❞ t♦ ❞❡❝✐❞❡ t❤❡✐r ♥❡①t ♠♦✈❡s✳

◮ ■♥ ❛ tr❛❞✐♥❣ s✐♠✉❧❛t✐♦♥✱ ❛ str❛t❡❣② ✐s ❛ ❣❡♥❡r❛❧ t②♣❡✳

◮ ❲❡ ❝❛♥ ✉s❡ t❤❡ str❛t❡❣② t♦ ❞❡t❡r♠✐♥❡ ✇❤❛t t♦ ❜✉②✳ ◮ ❚❤❡r❡ ❛r❡ ❧♦ts ♦❢ str❛t❡❣✐❡s✱ ❜✉t ❛ s✐♠✉❧❛t♦r s❤♦✉❧❞ ❝♦♣❡ ✇✐t❤

❛❧❧ str❛t❡❣✐❡s✳

SLIDE 6

❚❤❡ ✐❞❡❛ ♦❢ ❛♥ ✐♥t❡r❢❛❝❡

◮ ❲❡ ♥❡❡❞ t♦ s❡♣❛r❛t❡ ✐♥t❡r❢❛❝❡ ❢r♦♠ ✐♠♣❧❡♠❡♥t❛t✐♦♥✳ ◮ ❚❤❡ ✐♥t❡r❢❛❝❡ ❞❡✜♥❡s ❤♦✇ ②♦✉ ❝❛♥ ✐♥t❡r❛❝t ✇✐t❤ ❛♥ ♦❜❥❡❝t✳ ◮ ■t ❞❡✜♥❡s ❛ ❝♦♥tr❛❝t t❤❛t ♠✉st ❜❡ ❢✉❧✜❧❧❡❞ ❜② t❤❡ ❢✉♥❝t✐♦♥

❊①❛♠♣❧❡

❆ ♣❛t❤✲✐♥❞❡♣❡♥❞❡♥t ♦♣t✐♦♥ ♠✉st ✐♠♣❧❡♠❡♥t t✇♦ ❢✉♥❝t✐♦♥s✿

◮ ❞♦✉❜❧❡✥♣❛②♦❢❢✭✥❞♦✉❜❧❡✥❢✐♥❛❧❙t♦❝❦Pr✐❝❡✥✮❀ ◮ ❞♦✉❜❧❡✥❣❡t▼❛t✉r✐t②✭✮❀ ❚❤✐s ❞❡✜♥❡s t❤❡ ✐♥t❡r❢❛❝❡ ♦❢ ❛

♣❛t❤✲✐♥❞❡♣❡♥❞❡♥t ♦♣t✐♦♥✳

SLIDE 7

❆♥ ✐♥t❡r❢❛❝❡ ❝❧❛ss ✐♥ ❈✰✰

❊①❛♠♣❧❡

❆ ♣❛t❤✲✐♥❞❡♣❡♥❞❡♥t ♦♣t✐♦♥ ♠✉st ✐♠♣❧❡♠❡♥t t✇♦ ❢✉♥❝t✐♦♥s✿

◮ ❞♦✉❜❧❡✥♣❛②♦❢❢✭✥❞♦✉❜❧❡✥❢✐♥❛❧❙t♦❝❦Pr✐❝❡✥✮❀ ◮ ❞♦✉❜❧❡✥❣❡t▼❛t✉r✐t②✭✮❀

❈✰✰ ❡q✉✐✈❛❧❡♥t ✐s✿

❝❧❛ss✥P❛t❤■♥❞❡♣❡♥❞❡♥t❖♣t✐♦♥✥④ ♣✉❜❧✐❝✿ ✥✥✥✥✴✯✥✥❆✥✈✐rt✉❛❧✥❞❡str✉❝t♦r✥✯✴ ✥✥✥✥✈✐rt✉❛❧✥⑦P❛t❤■♥❞❡♣❡♥❞❡♥t❖♣t✐♦♥✭✮✥④⑥ ✥✥✥✥✴✯✥✥❘❡t✉r♥s✥t❤❡✥♣❛②♦❢❢✥❛t✥♠❛t✉r✐t②✥✯✴ ✥✥✥✥✈✐rt✉❛❧✥❞♦✉❜❧❡✥♣❛②♦❢❢✭ ✥✥✥✥✥✥✥✥❞♦✉❜❧❡✥❢✐♥❛❧❙t♦❝❦Pr✐❝❡✮✥❝♦♥st✥❂✥✵❀ ✥✥✥✥✴✯✥✥❘❡t✉r♥s✥t❤❡✥♠❛t✉r✐t②✥♦❢✥t❤❡✥♦♣t✐♦♥✥✯✴ ✥✥✥✥✈✐rt✉❛❧✥❞♦✉❜❧❡✥❣❡t▼❛t✉r✐t②✭✮✥❝♦♥st ✥✥✥✥✥✥✥✥❂✥✵❀ ⑥❀

SLIDE 8

❍♦✇ t♦ ✇r✐t❡ ❛♥ ✐♥t❡r❢❛❝❡

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

✐♥t❡r❢❛❝❡ ❝❧❡❛r❧②✳ ❋♦r ❡①❛♠♣❧❡ P❛t❤■♥❞❡♣❡♥❞❡♥t❖♣t✐♦♥✱ ▼♦♥st❡r ♦r ♦str❡❛♠✳

◮ ❲r✐t❡ ❛ ❝❧❛ss ❞❡❝❧❛r❛t✐♦♥ t❤❛t ❝♦♥t❛✐♥s ❛❧❧ t❤❡ ❢✉♥❝t✐♦♥s ②♦✉

✇♦✉❧❞ ❧✐❦❡ t♦ ♣r❡s❡♥t ✐♥ t❤❡ ❝❧❛ss✳

◮ ❆❞❞ t❤❡ ❦❡②✇♦r❞ ✈✐rt✉❛❧ ❛t t❤❡ ❢r♦♥t ♦❢ ❡✈❡r② ❢✉♥❝t✐♦♥

❞❡❝❧❛r❛t✐♦♥✳

◮ ❆❞❞ t❤❡ t❡①t ❂✵ ❜❡❢♦r❡ t❤❡ s❡♠✐✲❝♦❧♦♥ ❛t t❤❡ ❡♥❞ ♦❢ t❤❡

❞❡❝❧❛r❛t✐♦♥✳

◮ ❆❞❞ t❤❡ ♠②st✐❝❛❧ t❡①t

✥✥✥✥✈✐rt✉❛❧✥⑦❈▲❆❙❙❴◆❆▼❊✭✮✥④⑥ t♦ t❤❡ ❧✐st ♦❢ ❞❡❝❧❛r❛t✐♦♥s✳

SLIDE 9

❲❤❛t ✐s t❤✐s ✈♦♦❞♦♦❄

◮ ❚❤❡ ❂✵ ♠❡❛♥s ✏t❤✐s ❢✉♥❝t✐♦♥ ✐s ♥♦t ✐♠♣❧❡♠❡♥t❡❞ ❞✐r❡❝t❧②✑✳ ❚❤✐s

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

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

✉s❡ t❤❡ ✇♦r❞ ✈✐rt✉❛❧ ♠♦r❡ ❣❡♥❡r❛❧❧②✳ ❚❤✐s ✇✐❧❧ ❡①♣❧❛✐♥ ✇❤② ✇❡ ♥❡❡❞ t♦ ✉s❡ ✐t ❤❡r❡✳

◮ ❚❤❡ ♠②st✐❝❛❧ t❡①t✿

✈✐rt✉❛❧ ⑦❈▲❆❙❙❴◆❆▼❊✭✮ ④⑥ ✐s ❝❛❧❧❡❞ ❛ ✈✐rt✉❛❧ ❞❡str✉❝t♦r✳ ❲❡✬❧❧ ❡①♣❧❛✐♥ t❤❡ ♥❡❡❞ ❢♦r t❤✐s ✇❤❡♥ ✇❡ ❞✐s❝✉ss ❞❡str✉❝t♦rs ❧❛t❡r ✐♥ t❤❡ ❝♦✉rs❡✳

◮ ■✬♠ t❡❛❝❤✐♥❣ ②♦✉ ❤♦✇ t♦ ❞♦ t❤❡ r✐❣❤t t❤✐♥❣ ✇✐t❤♦✉t ❡①♣❧❛✐♥✐♥❣

✐t ❢✉❧❧②✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ ✐t✬s ♠✉❝❤ ❡❛s✐❡r t♦ ❧❡❛r♥ ✇❤❛t ②♦✉ s❤♦✉❧❞ t②♣❡ t❤❛♥ ✇❤② ②♦✉ s❤♦✉❧❞ t②♣❡ ✐t✦

SLIDE 10

❍♦✇ t♦ ✐♠♣❧❡♠❡♥t ❛♥ ✐♥t❡r❢❛❝❡

◮ ❚♦ s♣❡❝✐❢② t❤❛t ②♦✉ ✐♠♣❧❡♠❡♥t ❛♥ ✐♥t❡r❢❛❝❡ ✉s❡ t❤❡ ❢♦❧❧♦✇✐♥❣

❝♦♥str✉❝t✐♦♥✿

❝❧❛ss✥❈❛❧❧❖♣t✐♦♥✥✿✥♣✉❜❧✐❝✥P❛t❤■♥❞❡♣❡♥❞❡♥t❖♣t✐♦♥✥④

◮ ❚❤✐s ♠❡❛♥s t❤❛t ❛ ❈❛❧❧❖♣t✐♦♥ ✐s ❛

P❛t❤■♥❞❡♣❡♥❞❡♥t❖♣t✐♦♥✳ ❨♦✉ ❝❛♥ ♥♦✇ ♣❛ss ❛ r❡❢❡r❡♥❝❡ t♦ ❛ ❈❛❧❧❖♣t✐♦♥ t♦ ❛♥② ❢✉♥❝t✐♦♥ t❤❛t s✐♠♣❧② r❡q✉✐r❡s ❛ r❡❢❡r❡♥❝❡ t♦ ❛ P❛t❤■♥❞❡♣❞❡♥❞❡♥t❖♣t✐♦♥✳

◮ ❆ P✉t❖♣t✐♦♥ ✐s ❛ ♣❛t❤✲✐♥❞❡♣❡♥❞❡♥t ♦♣t✐♦♥ t♦♦✱ s♦ ✇❡ ❝❤❛♥❣❡

t❤❡ ❞❡❝❧❛r❛t✐♦♥ ♦❢ P✉t❖♣t✐♦♥ t♦♦✳

◮ ❖✉r ▼♦♥t❡❈❛r❧♦Pr✐❝❡r ♥♦✇ ✇♦r❦s ❡q✉❛❧❧② ✇❡❧❧ ✇✐t❤ ♣✉t

♦♣t✐♦♥s ❛♥❞ ❝❛❧❧ ♦♣t✐♦♥s✳

SLIDE 11

❚❤❡ ❣❡♥❡r❛❧ s②♥t❛①

❝❧❛ss ❈▲❆❙❙❴◆❆▼❊ ✿ ♣✉❜❧✐❝ ■◆❚❊❘❋❆❈❊❴◆❆▼❊ ④ ✳✳✳ ❞❡❝❧❛r❛t✐♦♥s ❢♦r ❈▲❆❙❙❴◆❆▼❊ ✳✳✳ ⑥❀

◮ ❨♦✉ ✇✐❧❧ ♥❡❡❞ t♦ ♣r♦✈✐❞❡ ❛ ♥❡✇ ❞❡❝❧❛r❛t✐♦♥ ❛♥❞ ❞❡✜♥✐t✐♦♥ ❢♦r

❡✈❡r② ❢✉♥❝t✐♦♥ ❞❡✜♥❡❞ ✐♥ t❤❡ ✐♥t❡r❢❛❝❡ ■◆❚❊❘❋❆❈❊❴◆❆▼❊✳

◮ ❚❤❡② ♠✉st ❤❛✈❡ ❡①❛❝t❧② t❤❡ s❛♠❡ t②♣❡s✱ ❝♦♥st ❞❡❝❧❛r❛t✐♦♥s

❛♥❞ s♦ ❢♦rt❤✳

SLIDE 12

❲❤❛t ❤❛s t❤✐s ❜♦✉❣❤t ✉s❄

◮ ❨♦✉ ❝❛♥ ♥♦✇ ♣r✐❝❡ ❆◆❨ ♣❛t❤✲✐♥❞❡♣❡♥❞❡♥t ♦♣t✐♦♥ ✉s✐♥❣ t❤❡

▼♦♥t❡❈❛r❧♦Pr✐❝❡r✳ ❚❤✐s ✐♥❝❧✉❞❡s ♦♣t✐♦♥s ②♦✉✬✈❡ ♥❡✈❡r t❤♦✉❣❤t ♦❢ ❜❡❢♦r❡✳

◮ ❚❤❡ ▼♦♥t❡❈❛r❧♦Pr✐❝❡r ❝♦❞❡ ✇✐❧❧ r❡♠❛✐♥ ✉♥❝❤❛♥❣❡❞ ❡✈❡♥

✇❤❡♥ ②♦✉ t❤✐♥❦ ♦❢ ❛ ♥❡✇ ♦♣t✐♦♥ ②♦✉ ✇❛♥t t♦ ♣r✐❝❡✳

◮ ❚❤✐s ♠❛❦❡s t❤❡ ▼♦♥t❡❈❛r❧♦Pr✐❝❡r ♣❧✉❣❣❛❜❧❡✳ ❨♦✉ ❝❛♥

❡①t❡♥❞ ✐ts ❢✉♥❝t✐♦♥❛❧✐t② ❜② s✐♠♣❧② ♣❧✉❣❣✐♥❣ ✐♥ ♥❡✇ ♦♣t✐♦♥s✳ ❨♦✉ ❞♦♥✬t ♥❡❡❞ t♦ r❡✇r✐t❡ t❤❡ ❝♦❞❡✳

◮ ▼♦r❡ ❣❡♥❡r❛❧❧②✱ t❤❡ ✉s❡ ♦❢ ✐♥t❡r❢❛❝❡s ♠❡❛♥s ②♦✉ ❝❛♥ ❡①t❡♥❞ ❛

tr❛❞✐♥❣ s②st❡♠ ✇✐t❤ ♥❡✇ t②♣❡s ♦❢ ✜♥❛♥❝✐❛❧ ❝♦♥tr❛❝t✱ ✇✐t❤♦✉t ❤❛✈✐♥❣ t♦ r❡t❡st t❤❡ ✇❤♦❧❡ t❤✐♥❣✳

◮ ◆♦t✐❝❡ t❤❛t ❡❧❡❝tr✐❝❛❧ ♣❧✉❣s ❛r❡ ✏♣❧✉❣❣❛❜❧❡✑ ♣r❡❝✐s❡❧② ❜❡❝❛✉s❡

t❤❡② ❤❛✈❡ ❛ ✇❡❧❧✲❞❡✜♥❡❞ ✐♥t❡r❢❛❝❡✳ ❨♦✉ ❝❛♥ ✉s❡ t❤❡ s❛♠❡ ❡❧❡❝tr✐❝✐t② ❢♦r ❞✐s❤✇❛s❤❡rs✱ ❧❛♠♣s ❛♥❞ t❡❧❡✈✐s✐♦♥s✦

SLIDE 13

❆♥♦t❤❡r ❡①❛♠♣❧❡

◮ ■t ✐s ❡❛s② t♦ ✇r✐t❡ ❛ ❢✉♥❝t✐♦♥ t❤❛t ✐♥t❡❣r❛t❡s ❡①♣ −x✷ ❢r♦♠ a t♦

b ✉s✐♥❣ t❤❡ r❡❝t❛♥❣❧❡ r✉❧❡✳ ❇✉t ❤♦✇ ❝❛♥ ✇❡ ✇r✐t❡ ❛ ❢✉♥❝t✐♦♥ t❤❛t ❝❛♥ ✐♥t❡❣r❛t❡ ❛♥② r❡❛❧✲✈❛❧✉❡❞ ❢✉♥❝t✐♦♥ ❢r♦♠ a t♦ b ✉s✐♥❣ t❤❡ r❡❝t❛♥❣❧❡ r✉❧❡❄

◮ ❍❡r❡ ✐s ♦✉r ❢❛♥t❛s② ❝♦❞❡✿

❞♦✉❜❧❡✥✐♥t❡❣r❛❧✭✥❘❡❛❧❋✉♥❝t✐♦♥✫✥❢✱ ✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥❞♦✉❜❧❡✥❛✱ ✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥❞♦✉❜❧❡✥❜✱ ✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✥✐♥t✥♥P♦✐♥ts✥✮✥④ ✥✥✥✥❞♦✉❜❧❡✥❤✥❂✥✭❜✲❛✮✴♥P♦✐♥ts❀ ✥✥✥✥❞♦✉❜❧❡✥①✥❂✥❛✥✰✥✵✳✺✯❤❀ ✥✥✥✥❞♦✉❜❧❡✥t♦t❛❧✥❂✥✵✳✵❀ ✥✥✥✥❢♦r✥✭✐♥t✥✐❂✵❀✥✐❁♥P♦✐♥ts❀✥✐✰✰✮✥④ ✥✥✥✥✥✥✥✥❞♦✉❜❧❡✥②✥❂✥❢✳❡✈❛❧✉❛t❡✭①✮❀ ✥✥✥✥✥✥✥✥t♦t❛❧✰❂②❀ ✥✥✥✥✥✥✥✥①✰❂❤❀ ✥✥✥✥⑥ ✥✥✥✥r❡t✉r♥✥❤✯t♦t❛❧❀ ⑥

SLIDE 14

❘❡❛❧❋✉♥❝t✐♦♥

◮ ■✬✈❡ ✐♥tr♦❞✉❝❡❞ ❛ t②♣❡ ❝❛❧❧❡❞ ❘❡❛❧❋✉♥❝t✐♦♥✳ ❚❤✐s ♥❛♠❡

❞❡s❝r✐❜❡s t❤❡ ❦✐♥❞s ♦❢ ♦❜❥❡❝t ■ ❝❛♥ ✐♥t❡❣r❛t❡✳

◮ ❆❧❧ ✇❡ ♥❡❡❞ ❢r♦♠ ❛ ❘❡❛❧❋✉♥❝t✐♦♥ ✐s t❤❛t ✐t ❝❛♥ ❝♦♠♣✉t❡ ❛

✈❛❧✉❡ ❛t ❛ ❣✐✈❡♥ ♣♦✐♥t x ∈ R✳ ❲❡ ❞❡✜♥❡ t❤❡ ✐♥t❡r❢❛❝❡ ❜② r❡q✉✐r✐♥❣ t❤❛t ✐t ❤❛s ❛ ❢✉♥❝t✐♦♥ ❡✈❛❧✉❛t❡ t❤❛t ❝♦♠♣✉t❡s t❤❡ ❞❡s✐r❡❞ ✈❛❧✉❡✳

❝❧❛ss✥❘❡❛❧❋✉♥❝t✐♦♥✥④ ♣✉❜❧✐❝✿ ✥✥✥✥✴✯✥✥❆✥✈✐rt✉❛❧✥❞❡str✉❝t♦r✥✯✴ ✥✥✥✥✈✐rt✉❛❧✥⑦❘❡❛❧❋✉♥❝t✐♦♥✭✮✥④⑥❀ ✥✥✥✥✴✯✥✥❚❤✐s✥♠❡t❤♦❞✥✐s✥❛❜str❛❝t✱✥t❤❡r❡✥✐s ✥✥✥✥✥✥✥✥♥♦✥❞❡❢✐♥✐t✐♦♥✥✯✴ ✥✥✥✥✈✐rt✉❛❧✥❞♦✉❜❧❡✥❡✈❛❧✉❛t❡✭✥❞♦✉❜❧❡✥①✥✮✥❂✥✵❀ ⑥❀

◮ ❲❡✬✈❡ ❢♦❧❧♦✇❡❞ ❛❧❧ t❤❡ ✈♦♦❞♦♦ r✉❧❡s ❛❜♦✉t ✈✐rt✉❛❧ ❛♥❞ ❂✵✳

SLIDE 15

■♠♣❧❡♠❡♥t ❘❡❛❧❋✉♥❝t✐♦♥

◮ ❊✈❡r② t✐♠❡ ✇❡ ✇❛♥t t♦ ✐♥t❡❣r❛t❡ ❛ r❡❛❧✲✈❛❧✉❡❞ ❢✉♥❝t✐♦♥ ✇❡

♥❡❡❞ t♦ ✇r✐t❡ ❛♥ ❛♣♣r♦♣r✐❛t❡ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ❝❧❛ss✳

❝❧❛ss✥❙✐♥❋✉♥❝t✐♦♥✥✿✥♣✉❜❧✐❝✥❘❡❛❧❋✉♥❝t✐♦♥✥④ ✥✥✥✥❞♦✉❜❧❡✥❡✈❛❧✉❛t❡✭✥❞♦✉❜❧❡✥①✥✮❀ ⑥❀ ❞♦✉❜❧❡✥❙✐♥❋✉♥❝t✐♦♥✿✿❡✈❛❧✉❛t❡✭✥❞♦✉❜❧❡✥①✥✮✥④ ✥✥✥✥r❡t✉r♥✥s✐♥✭①✮❀ ⑥ st❛t✐❝✥✈♦✐❞✥t❡st■♥t❡❣r❛❧✭✮✥④ ✥✥✥✥❙✐♥❋✉♥❝t✐♦♥✥✐♥t❡❣r❛♥❞❀ ✥✥✥✥❞♦✉❜❧❡✥❛❝t✉❛❧✥❂✥✐♥t❡❣r❛❧✭✥✐♥t❡❣r❛♥❞✱✥✶✱✥✸✱✥✶✵✵✵✥✮❀ ✥✥✥✥❞♦✉❜❧❡✥❡①♣❡❝t❡❞✥❂✥✲❝♦s✭✸✳✵✮✰❝♦s✭✶✳✵✮❀ ✥✥✥✥❆❙❙❊❘❚❴❆PP❘❖❳❴❊◗❯❆▲✭✥❛❝t✉❛❧✱✥❡①♣❡❝t❡❞✱✥✵✳✵✵✵✵✵✶✮❀ ⑥

SLIDE 16

▲♦❝❛❧ ❝❧❛ss❡s

st❛t✐❝✥✈♦✐❞✥t❡st■♥t❡❣r❛❧❱❡rs✐♦♥✷✭✮✥④ ✥✥✥✥❝❧❛ss✥❙✐♥✥✿✥♣✉❜❧✐❝✥❘❡❛❧❋✉♥❝t✐♦♥✥④ ✥✥✥✥♣✉❜❧✐❝✿ ✥✥✥✥✥✥✥✥❞♦✉❜❧❡✥❡✈❛❧✉❛t❡✭✥❞♦✉❜❧❡✥①✥✮✥④ ✥✥✥✥✥✥✥✥✥✥✥✥r❡t✉r♥✥s✐♥✭①✮❀ ✥✥✥✥✥✥✥✥⑥ ✥✥✥✥⑥❀ ✥✥✥✥❙✐♥✥✐♥t❡❣r❛♥❞❀ ✥✥✥✥❞♦✉❜❧❡✥❛❝t✉❛❧✥❂✥✐♥t❡❣r❛❧✭✐♥t❡❣r❛♥❞✱✥✶✱✥✸✱✥✶✵✵✵✥✮❀ ✥✥✥✥❞♦✉❜❧❡✥❡①♣❡❝t❡❞✥❂✥✲❝♦s✭✸✳✵✮✰❝♦s✭✶✳✵✮❀ ✥✥✥✥❆❙❙❊❘❚❴❆PP❘❖❳❴❊◗❯❆▲✭❛❝t✉❛❧✱✥❡①♣❡❝t❡❞✱✥✵✳✵✵✵✵✵✶✮❀ ⑥

SLIDE 17

▲♦❝❛❧ ❝❧❛ss❡s

◮ ❨♦✉ ❝❛♥ ❞❡✜♥❡ ❛ ✏t❤r♦✇❛✇❛②✑ ❝❧❛ss ✐♥s✐❞❡ ❛ ❢✉♥❝t✐♦♥✳ ◮ ◆♦t✐❝❡ t❤❛t t❤❡ ❞❡✜♥✐t✐♦♥ ✐s ♣r♦✈✐❞❡❞ ❢♦r ❡❛❝❤ ♠❡♠❜❡r

❢✉♥❝t✐♦♥ ♥♦t ❥✉st t❤❡ ❞❡❝❧❛r❛t✐♦♥✳

◮ ❏❛✈❛ ❛♥❞ ❈★ ❢❛♥s ✇✐❧❧ ❜❡ ❞✐s❛♣♣♦✐♥t❡❞ t♦ ❧❡❛r♥ t❤❛t ②♦✉ ❝❛♥✬t

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

SLIDE 18

❍♦✇ t♦ s♣♦t ✇❤❡♥ ❛♥ ✐♥t❡r❢❛❝❡ ✐s ♥❡❡❞❡❞ ✶

❉♦ ②♦✉ ❤❛✈❡ ❛♥ ❡✈❡r ❣r♦✇✐♥❣ ❧✐st ♦❢ ♣❛r❛♠❡t❡rs t♦ ②♦✉r ❢✉♥❝t✐♦♥ t♦ ❤❛♥❞❧❡ ❞✐✛❡r❡♥t ❝❛s❡s✳ ❋♦r ❡①❛♠♣❧❡ ✐❢ ②♦✉r ❢✉♥❝t✐♦♥ t❛❦❡s✿

◮ ❆ str✐❦❡✱ ◮ ❆ ♠❛t✉r✐t②✱ ◮ ❆ ❜❛rr✐❡r ❧❡✈❡❧✱ ◮ ❆ ❜♦♦❧ s♣❡❝✐❢②✐♥❣ ✇❤❡t❤❡r t❤✐s ✐s ❛ ❦♥♦❝❦✲♦✉t ♦r ❛ ❦♥♦❝❦✲✐♥

♦♣t✐♦♥✱

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

♦♣t✐♦♥

◮ ✳ ✳ ✳

t❤✐s ✐s ❛ ❝❧✉❡ t❤❛t ②♦✉ ❛r❡ ♠✐ss✐♥❣ ❛♥ ✐♥t❡r❢❛❝❡✳ ▲♦ts ♦❢ ❜♦♦❧ ♣❛r❛♠❡t❡rs ❛r❡ ❛ ♣❛rt✐❝✉❧❛r❧② str♦♥❣ ❝❧✉❡✳

SLIDE 19

❍♦✇ t♦ s♣♦t ✇❤❡♥ ❛♥ ✐♥t❡r❢❛❝❡ ✐s ♥❡❡❞❡❞ ✷

❉♦ ②♦✉ ❦❡❡♣ ❝❤❛♥❣✐♥❣ t❤❡ s❛♠❡ ❢✉♥❝t✐♦♥❄ ❋♦r ❡①❛♠♣❧❡✱ ✐❢ ❡✈❡r② t✐♠❡ ❛ tr❛❞❡r ❝♦♠❡s ✉♣ ✇✐t❤ ❛ ♥❡✇ ✐♥✈❡st♠❡♥t str❛t❡❣② ②♦✉ ✜♥❞ ②♦✉ ❤❛✈❡ t♦ r❡✇r✐t❡ t❤❡ ❢✉♥❝t✐♦♥ ❜❛❝❦❚❡st■♥✈❡st♠❡♥t❙tr❛t❡❣② t❤✐s ✐s ❛ s✐❣♥ t❤❛t ②♦✉ s❤♦✉❧❞ ✐♥tr♦❞✉❝❡ ❛♥ ✐♥ ✐♥t❡r❢❛❝❡✳ P❡r❤❛♣s ②♦✉ ♥❡❡❞ t♦ ❞❡s✐❣♥ ❝❧❛ss❡s ▼❛r❦❡t❉❛t❛ ❛♥❞ P♦rt❢♦❧✐♦ ❛♥❞ ❛ ❣❡♥❡r❛❧ ✐♥t❡r❢❛❝❡ ❢♦r str❛t❡❣✐❡s ❧✐❦❡ t❤✐s✿ ❝❧❛ss✥■♥✈❡st♠❡♥t❙tr❛t❡❣②✥④ ✥✥✥✥✈✐rt✉❛❧✥⑦■♥✈❡st♠❡♥t❙tr❛t❡❣②✭✮✥④⑥❀ ✥✥✥✥✈✐rt✉❛❧✥P♦rt❢♦❧✐♦✥r❡❜❛❧❛♥❝❡P♦rt❢♦❧✐♦✭ ✥✥✥✥✥✥✥✥❝♦♥st✥▼❛r❦❡t❉❛t❛✫✥♠❛r❦❡t❉❛t❛✱ ✥✥✥✥✥✥✥✥❝♦♥st✥P♦rt❢♦❧✐♦✫✥♦❧❞P♦rt❢♦❧✐♦✥✮✥❂✵❀ ⑥❀

SLIDE 20

❍♦✇ t♦ s♣♦t ✇❤❡♥ ❛♥ ✐♥t❡r❢❛❝❡ ✐s ♥❡❡❞❡❞ ✸

◮ ❲❤❡♥❡✈❡r ②♦✉ ♥❡❡❞ t♦ ❦♥♦✇ t❤❡ t②♣❡ ♦❢ t❤❡ ❞❛t❛ t♦ s♦❧✈❡ t❤❡

♣r♦❜❧❡♠✳ ❊✳❣✳✱ ■ ❝❛♥ ♦♥❧② ♣r✐❝❡ ❛♥ ♦♣t✐♦♥ ✐❢ ■ ❦♥♦✇ ✇❤❛t t②♣❡ ♦❢ ♦♣t✐♦♥ ✐t ✐s✳

◮ ❚❤✐s ✐s ✇❤② ❈✰✰ ♠❛❦❡s s✉❝❤ ❛ ❜✐❣ ❞❡❛❧ ♦❢ t❤❡ t②♣❡ ♦❢ ❛❧❧

♣❛r❛♠❡t❡rs✳ ❇② s♣❡❝✐❢②✐♥❣ t②♣❡s✱ ✇❡ ❛r❡ ❛❧s♦ s♣❡❝✐❢②✐♥❣ ❜❡❤❛✈✐♦✉r✳

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

❡♥♦r♠♦✉s ✐❢✱ ❡❧s❡✥✐❢✱ ❡❧s❡✥✐❢ ✳ ✳ ✳ st❛t❡♠❡♥t✳

◮ ❲❤❡♥❡✈❡r ②♦✉ ❢❡❡❧ ②♦✉ ✇❛♥t t♦ ♣❛ss ❢✉♥❝t✐♦♥❛❧✐t② ❛r♦✉♥❞✳ ❋♦r

❡①❛♠♣❧❡ ✐❢ ②♦✉ ✇❛♥t t❤❡ ✉s❡r t♦ ❜❡ ❛❜❧❡ t♦ s❡❧❡❝t✿

◮ ❚❤❡ ❛❧❣♦r✐t❤♠ t♦ ✉s❡✖❢♦r ❡①❛♠♣❧❡ t❤❡ r❛♥❞♦♠✲♥✉♠❜❡r

❣❡♥❡r❛t✐♦♥ ❛❧❣♦r✐t❤♠✳

◮ ❚❤❡ ♠❡t❤♦❞♦❧♦❣② t♦ ✉s❡ t♦ s♦❧✈❡ ❛ ♣r♦❜❧❡♠✖❢♦r ❡①❛♠♣❧❡✱

s❤♦✉❧❞ ✇❡ ♠❡❛s✉r❡ r✐s❦ ✉s✐♥❣ ❱❆❘ ♦r ❈❱❆❘❄

◮ ❚❤❡ ❛❝t✐♦♥ t♦ ♣❡r❢♦r♠✖❢♦r ❡①❛♠♣❧❡✱ ✇❤❛t s❤♦✉❧❞ ✇❡ ❞♦ ✇❤❡♥

✇❡ ❞✐s❝♦✈❡r ❛♥ ❛r❜✐tr❛❣❡ ♦♣♣♦rt✉♥✐t②✱ ❛❧❡rt t❤❡ tr❛❞❡r ♦r ❥✉st ❣♦ ❛❤❡❛❞ ❛♥❞ tr❛❞❡❄

SLIDE 21

❍♦✇ t♦ s♣♦t ✇❤❡♥ ❛♥ ✐♥t❡r❢❛❝❡ ✐s ♥❡❡❞❡❞ ✹

◮ ❊①♣❡r✐❡♥❝❡✦

◮ ❚❤❡r❡ ❛r❡ ♠❛♥② ❜♦♦❦s ❛✈❛✐❧❛❜❧❡ ♦♥ ♦❜❥❡❝t✲♦r✐❡♥t❡❞ ❞❡s✐❣♥

♣❛tt❡r♥s✳

◮ ❆ ❞❡s✐❣♥ ♣❛tt❡r♥ ✐s ❛ t❡❝❤♥✐q✉❡ s♦♠❡♦♥❡ ❤❛s ✉s❡❞ ✐♥ t❤❡ ♣❛st

t♦ s✉❝❝❡ss❢✉❧❧② s♦❧✈❡ ❛ ♣r♦❜❧❡♠✳

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

s❛♠❡ ✐❞❡❛s ✐♥ ②♦✉r ♦✇♥ ❝♦❞❡✳

◮ ❋♦r ❡①❛♠♣❧❡✱ ✇❡ ❤❛✈❡ s❡❡♥ ❛ ❞❡s✐❣♥ ♣❛tt❡r♥ t♦ ✇r✐t❡ ❛ ❣❡♥❡r✐❝

✐♥t❡❣r❛❧ ❢✉♥❝t✐♦♥✳ ❈♦✉❧❞ ②♦✉ ✇r✐t❡ ❛ ❣❡♥❡r✐❝ ❞✐❢❢❡r❡♥t✐❛t❡ ❢✉♥❝t✐♦♥❄

◮ ▲❡❛r♥✐♥❣ ❞❡s✐❣♥ ♣❛tt❡r♥s ✐s ❛ ✇❛② ♦❢ ❝♦♥s❝✐♦✉s❧② ❧❡❛r♥✐♥❣ ❢r♦♠

♦t❤❡r ♣❡♦♣❧❡✬s ❡①♣❡r✐❡♥❝❡✳

SLIDE 22