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Aug 18, 2022 198 likes •493 views

r sstt sss r ts t s t r

SLIDE 1

▼♦r❡ s♦♣❤✐st✐❝❛t❡❞ ❝❧❛ss❡s

SLIDE 2

■♥❧✐♥✐♥❣ ♠❡♠❜❡r ❢✉♥❝t✐♦♥s

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

❝❛❧❧❡❞✳

◮ ■♥❧✐♥❡ ❛ ♠❡♠❜❡r ❢✉♥❝t✐♦♥ ❜② ✐♥❝❧✉❞✐♥❣ t❤❡ ❞❡✜♥✐t✐♦♥ ✐♥ t❤❡

❝❧❛ss ❞❡❝❧❛r❛t✐♦♥✳

◮ ❙❛✈❡s t②♣✐♥❣✱ ❜✉t ♦♥❧② ✉s❡ ✐t ✇❤❡♥ ②♦✉ r❡❛❧❧② ✇❛♥t t♦ ✐♥❧✐♥❡✳

❝❧❛ss✥P♦✐♥t✥④ ♣✉❜❧✐❝✿ ✥✥✥✥❞♦✉❜❧❡✥❣❡t❳✭✮✥❝♦♥st✥④ ✥✥✥✥✥✥✥✥r❡t✉r♥✥①❀ ✥✥✥✥⑥ ✥✥✥✥✴✴✥♦t❤❡r✥♠❡♠❜❡rs✥♦❢✥P♦✐♥t ♣r✐✈❛t❡✿ ✥✥✥✥❞♦✉❜❧❡✥①❀ ✥✥✥✥❞♦✉❜❧❡✥②❀ ⑥❀

SLIDE 3

❚❤❡ t❤✐s ❦❡②✇♦r❞

◮ ♣r✐✈❛t❡ ✈❛r✐❛❜❧❡s ❛r❡ ❣♦♦❞ ❢♦r ✐♥❢♦r♠❛t✐♦♥ ❤✐❞✐♥❣✳ ◮ ❲r✐t❡ ❣❡tt❡rs ❛♥❞ s❡tt❡rs ❛s s❤♦✇♥✳ ◮ t❤✐s ✐s ❛ ♣♦✐♥t❡r t♦ t❤❡ ❝✉rr❡♥t ✐♥st❛♥❝❡ ♦❢ t❤❡ ♦❜❥❡❝t✳

❝❧❛ss✥P♦✐♥t✥④ ♣✉❜❧✐❝✿ ✥✥✥✥❞♦✉❜❧❡✥❣❡t❳✭✮✥❝♦♥st✥④ ✥✥✥✥✥✥✥✥r❡t✉r♥✥①❀ ✥✥✥✥⑥ ✥✥✥✥✈♦✐❞✥s❡t❳✭✥❞♦✉❜❧❡✥①✥✮✥④ ✥✥✥✥✥✥✥✥t❤✐s✲❃①✥❂✥①❀ ✥✥✥✥⑥ ✥✥✥✥✴✴✥♦t❤❡r✥♠❡♠❜❡rs✥♦❢✥P♦✐♥t ♣r✐✈❛t❡✿ ✥✥✥✥❞♦✉❜❧❡✥①❀ ✥✥✥✥❞♦✉❜❧❡✥②❀ ⑥❀

SLIDE 4

❆♥♦t❤❡r ✉s❡ ♦❢ t❤✐s

◮ ♣r✐❝❡ ♠❡t❤♦❞ ♥❡❡❞s ❛ r❡❢❡r❡♥❝❡ t♦ ❛♥ ♦♣t✐♦♥✳ ◮ ✯t❤✐s ✐s ❛ r❡❢❡r❡♥❝❡ t♦ ❛♥ ♦♣t✐♦♥✳

❞♦✉❜❧❡✥❯♣❆♥❞❖✉t❖♣t✐♦♥✿✿♣r✐❝❡✭ ✥✥✥✥✥✥✥✥❝♦♥st✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✫✥♠♦❞❡❧✥✮✥❝♦♥st✥④ ✥✥✥✥▼♦♥t❡❈❛r❧♦Pr✐❝❡r✥♣r✐❝❡r❀ ✥✥✥✥r❡t✉r♥✥♣r✐❝❡r✳♣r✐❝❡✭✥✯t❤✐s✱✥♠♦❞❡❧✥✮❀ ⑥

SLIDE 5

■♥❤❡r✐t❛♥❝❡

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

❝❧❛ss✥❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥✥④ ♣✉❜❧✐❝✿ ✥✥✥✥✴✯✥✥❱✐rt✉❛❧✥❞❡str✉❝t♦r✥✯✴ ✥✥✥✥✈✐rt✉❛❧✥⑦❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥✭✮✥④⑥❀ ✥✥✥✥✴✯✥✥❚❤❡✥♠❛t✉r✐t②✥♦❢✥t❤❡✥♦♣t✐♦♥✥✯✴ ✥✥✥✥✈✐rt✉❛❧✥❞♦✉❜❧❡✥❣❡t▼❛t✉r✐t②✭✮✥❝♦♥st✥❂✥✵❀ ✥✥✥✥✴✯✥✥❈❛❧❝✉❧❛t❡✥t❤❡✥♣❛②♦❢❢✥♦❢✥t❤❡✥♦♣t✐♦♥✥❣✐✈❡♥ ✥✥✥✥✥✥✥✥❛✥❤✐st♦r②✥♦❢✥♣r✐❝❡s✥✯✴ ✥✥✥✥✈✐rt✉❛❧✥❞♦✉❜❧❡✥♣❛②♦❢❢✭ ✥✥✥✥✥✥✥✥❝♦♥st✥st❞✿✿✈❡❝t♦r❁❞♦✉❜❧❡❃✫✥st♦❝❦Pr✐❝❡s ✥✥✥✥✥✥✥✥✮✥❝♦♥st✥❂✥✵❀ ✥✥✥✥✴✯✥✥■s✥t❤❡✥♦♣t✐♦♥✥♣❛t❤✥❞❡♣❡♥❞❡♥t✥✯✴ ✥✥✥✥✈✐rt✉❛❧✥❜♦♦❧✥✐sP❛t❤❉❡♣❡♥❞❡♥t✭✮✥❝♦♥st✥❂✥✵❀ ⑥❀

SLIDE 6

❆ ❜❛s❡ ❝❧❛ss

❝❧❛ss✥❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥❇❛s❡✥✿ ✥✥✥✥✥✥✥✥♣✉❜❧✐❝✥❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥✥④ ♣✉❜❧✐❝✿ ✥✥✥✥✈✐rt✉❛❧✥⑦❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥❇❛s❡✭✮✥④⑥ ✥✥✥✥❞♦✉❜❧❡✥❣❡t▼❛t✉r✐t②✭✮✥❝♦♥st✥④ ✥✥✥✥✥✥✥✥r❡t✉r♥✥♠❛t✉r✐t②❀ ✥✥✥✥⑥ ✥✥✥✥✈♦✐❞✥s❡t▼❛t✉r✐t②✭✥❞♦✉❜❧❡✥♠❛t✉r✐t②✥✮✥④ ✥✥✥✥✥✥✥✥t❤✐s✲❃♠❛t✉r✐t②✥❂✥♠❛t✉r✐t②❀ ✥✥✥✥⑥ ✥✥✥✥❞♦✉❜❧❡✥❣❡t❙tr✐❦❡✭✮✥❝♦♥st✥④ ✥✥✥✥✥✥✥✥r❡t✉r♥✥str✐❦❡❀ ✥✥✥✥⑥ ✥✥✥✥✈♦✐❞✥s❡t❙tr✐❦❡✭✥❞♦✉❜❧❡✥str✐❦❡✥✮✥④ ✥✥✥✥✥✥✥✥t❤✐s✲❃str✐❦❡✥❂✥str✐❦❡❀ ✥✥✥✥⑥ ✥✥✥✥✴✴✳✳✳✥♠♦r❡✥♠❡t❤♦❞s✥✳✳✳ ♣r✐✈❛t❡✿ ✥✥✥✥❞♦✉❜❧❡✥♠❛t✉r✐t②❀ ✥✥✥✥❞♦✉❜❧❡✥str✐❦❡❀ ⑥❀

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

❝♦♠♠♦♥ t♦ ♠♦st ♦♣t✐♦♥s✳

◮ ❚❤❡ ❜❛s❡ ❝❧❛ss ❤❛s ❛ ✈✐rt✉❛❧ ❞❡str✉❝t♦r✳ ❆♥② ❝❧❛ss ✉s❡❞ ❛s ❛

❜❛s❡ ❝❧❛ss ♠✉st ❤❛✈❡ ❛ ✈✐rt✉❛❧ ❞❡str✉❝t♦r✳

SLIDE 7

❊①t❡♥❞✐♥❣ t❤❡ ❜❛s❡ ❝❧❛ss

❝❧❛ss✥P✉t❖♣t✐♦♥✥✿✥♣✉❜❧✐❝✥❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥❇❛s❡✥④ ♣✉❜❧✐❝✿ ✥✥✥✥✴✯✥✥❈❛❧❝✉❧❛t❡✥t❤❡✥♣❛②♦❢❢✥♦❢✥t❤❡✥♦♣t✐♦♥✥❣✐✈❡♥ ✥✥✥✥✥✥✥✥❛✥❤✐st♦r②✥♦❢✥♣r✐❝❡s✥✯✴ ✥✥✥✥❞♦✉❜❧❡✥♣❛②♦❢❢✭ ✥✥✥✥✥✥✥✥❝♦♥st✥st❞✿✿✈❡❝t♦r❁❞♦✉❜❧❡❃✫✥st♦❝❦Pr✐❝❡s ✥✥✥✥✥✥✥✥✮✥❝♦♥st❀ ✥✥✥✥❞♦✉❜❧❡✥♣r✐❝❡✭✥❝♦♥st✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✫✥❜s♠✥✮ ✥✥✥✥✥✥✥✥❝♦♥st❀ ✥✥✥✥❜♦♦❧✥✐sP❛t❤❉❡♣❡♥❞❡♥t✭✮✥❝♦♥st✥④ ✥✥✥✥✥✥✥✥r❡t✉r♥✥❢❛❧s❡❀ ✥✥✥✥⑥❀ ⑥❀

SLIDE 8

◮ ❚❤❡ P✉t❖♣t✐♦♥ ❡①t❡♥❞s t❤❡ ❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥❇❛s❡✳

❙❛♠❡ ♥♦t❛t✐♦♥ ❛s ✉s❡❞ t♦ ✐♠♣❧❡♠❡♥t ❛♥ ✐♥t❡r❢❛❝❡✳

◮ ■t ✐♥❤❡r✐ts t❤❡ ❢✉♥❝t✐♦♥s ❞❡✜♥❡❞ ❜② t❤✐s ❝❧❛ss✳ ◮ ■t ✐♥❤❡r✐ts t❤❡ ✈❛r✐❛❜❧❡s str✐❦❡ ❛♥❞ ♠❛t✉r✐t②✳ ◮ ■t ✐♥❤❡r✐ts t❤❡ ✐♥t❡r❢❛❝❡ ❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥✳ ◮ ❚❤❡r❡ ✐s ♥♦ ♥❡❡❞ t♦ ✇r✐t❡ ♥❡✇ ❣❡t▼❛t✉r✐t② ❛♥❞ ❣❡t❙tr✐❦❡

❢✉♥❝t✐♦♥s✳ ❚❤❡ ♣❛②♦✛ ✐s t❤❛t ✐t ✐s ♥♦✇ ❡❛s② t♦ ✇r✐t❡✿

◮ ❈❛❧❧❖♣t✐♦♥✱ ◮ ❉✐❣✐t❛❧❈❛❧❧❖♣t✐♦♥✱ ◮ ❉✐❣✐t❛❧P✉t❖♣t✐♦♥✱ ◮ ❯♣❆♥❞❖✉t❖♣t✐♦♥✳

SLIDE 9

❚❡r♠✐♥♦❧♦❣②

◮ ❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥❇❛s❡ ✐s t❡r♠❡❞ ❛ s✉♣❡r❝❧❛ss ♦r ❛

♣❛r❡♥t ❝❧❛ss ♦❢ P✉t❖♣t✐♦♥✳

◮ P✉t❖♣t✐♦♥ ✐s t❡r♠❡❞ ❛ s✉❜❝❧❛ss ♦r ❛ ❝❤✐❧❞ ❝❧❛ss ♦❢

❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥❇❛s❡✳

◮ P✉t❖♣t✐♦♥ ❡①t❡♥❞s ❢r♦♠ ❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥❇❛s❡✳ ◮ P✉t❖♣t✐♦♥ ✐♥❤❡r✐ts ❢r♦♠ ❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥❇❛s❡✳

SLIDE 10

❖✈❡rr✐❞✐♥❣ ♠❡t❤♦❞s

❲❡ ❣✐✈❡ ♦✉r ❜❛s❡ ❝❧❛ss ❛ ♠❡t❤♦❞ t♦ ♣r✐❝❡ t❤❡ ♦♣t✐♦♥✿

❝❧❛ss✥❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥❇❛s❡ ✥✥✥✿✥♣✉❜❧✐❝✥❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥✥④ ♣✉❜❧✐❝✿ ✥✥✥✥✴✯✥✥Pr✐❝❡✥t❤❡✥♦♣t✐♦♥✱✥❜②✥▼♦♥t❡✥❈❛r❧♦✥♦r✥♦t❤❡r✇✐s❡✥✯✴ ✥✥✥✥❞♦✉❜❧❡✥♣r✐❝❡✭ ✥✥✥✥✥✥✥✥❝♦♥st✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✫✥♠♦❞❡❧✥✮✥❝♦♥st❀ ✥✥✥✥✴✴✥✳✳✳✥♦t❤❡r✥♠❡♠❜❡rs✥✳✳✳ ⑥❀

■♠♣❧❡♠❡♥t ✐t ✉s✐♥❣ ▼♦♥t❡ ❈❛r❧♦✿

❞♦✉❜❧❡✥❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥❇❛s❡✿✿♣r✐❝❡✭ ✥✥✥✥✥✥✥✥❝♦♥st✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✫✥♠♦❞❡❧✥✮✥❝♦♥st✥④ ✥✥✥✥▼♦♥t❡❈❛r❧♦Pr✐❝❡r✥♣r✐❝❡r❀ ✥✥✥✥r❡t✉r♥✥♣r✐❝❡r✳♣r✐❝❡✭✥✯t❤✐s✱✥♠♦❞❡❧✥✮❀ ⑥

SLIDE 11

❖✈❡rr✐❞✐♥❣ ♠❡t❤♦❞s ❝♦♥t✐♥✉❡❞

❲❡ ❞♦♥✬t ✇❛♥t t♦ ✉s❡ ▼♦♥t❡ ❈❛r❧♦ ❢♦r ♣✉t ♦♣t✐♦♥s✳ ❆❞❞ t❤❡ ❦❡②✇♦r❞ ✈✐rt✉❛❧ t♦ t❤❡ ❞❡❝❧❛r❛t✐♦♥ ♦❢ ♣r✐❝❡✳

❝❧❛ss✥❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥❇❛s❡ ✥✥✥✿✥♣✉❜❧✐❝✥❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥✥④ ♣✉❜❧✐❝✿ ✥✥✥✥✴✯✥✥Pr✐❝❡✥t❤❡✥♦♣t✐♦♥✱✥❜②✥▼♦♥t❡✥❈❛r❧♦✥♦r✥♦t❤❡r✇✐s❡✥✯✴ ✥✥✥✥✈✐rt✉❛❧✥❞♦✉❜❧❡✥♣r✐❝❡✭ ✥✥✥✥✥✥✥✥❝♦♥st✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✫✥♠♦❞❡❧✥✮✥❝♦♥st❀ ✥✥✥✥✴✴✥✳✳✳✥♦t❤❡r✥♠❡♠❜❡rs✥✳✳✳ ⑥❀

SLIDE 12

❖✈❡rr✐❞✐♥❣ ♠❡t❤♦❞s ❝♦♥t✐♥✉❡❞

❲❡ ❝❛♥ ♥♦✇ ♦✈❡rr✐❞❡ t❤❡ ♠❡t❤♦❞ ✐♥ ❛ s✉❜❝❧❛ss✳

❝❧❛ss✥P✉t❖♣t✐♦♥✥✿✥♣✉❜❧✐❝✥❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥❇❛s❡✥④ ♣✉❜❧✐❝✿ ✥✥✥✥❞♦✉❜❧❡✥♣r✐❝❡✭✥❝♦♥st✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✫✥❜s♠✥✮ ✥✥✥✥✥✥✥✥❝♦♥st✥♦✈❡rr✐❞❡❀ ✥✥✥✥✴✴✥✳✳✳✥♦t❤❡r✥♠❡♠❜❡rs✥✳✳✳ ⑥❀

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

t❤❡ ❝♦♥st ❛♥❞ ✫ ❝❤❛r❛❝t❡rs✳

SLIDE 13

❚❤❡ ❦❡②✇♦r❞ ✈✐rt✉❛❧

◮ ✈✐rt✉❛❧ ♠❡❛♥s ♠❛② ❜❡ ♦✈❡rr✐❞❞❡♥✳ ◮ ✐♥ ❛♥ ✐♥t❡r❢❛❝❡ ♥♦ ❢✉♥❝t✐♦♥s ❤❛✈❡ ❞❡✜♥✐t✐♦♥s s♦ ❛❧❧ ♠✉st ❜❡

♦✈❡r✐❞❞❡♥✳ ❚❤❡r❡❢♦r❡ t❤❡② ♠✉st ❜❡ ✈✐rt✉❛❧✳

◮ ❆❧❧ ❝❧❛ss❡s ❤❛✈❡ ❛ ❞❡str✉❝t♦r✳ ❚❤✐s ♠✉st ❜❡ ❞❡❝❧❛r❡❞ ❛s

✈✐rt✉❛❧ ✐♥ ❝❧❛ss❡s t❤❛t ❛r❡ s✉❜❝❧❛ss❡❞ s♦ t❤❛t t❤❡ ❝♦rr❡❝t ❞❡str✉❝t♦r ✐s ❝❛❧❧❡❞✳

◮ ❆♥② ❝❧❛ss t❤❛t ✐s ❞❡s✐❣♥❡❞ t♦ ❜❡ s✉❜❝❧❛ss❡❞ ♠✉st ❤❛✈❡ ❛ ✈✐rt✉❛❧

❞❡str✉❝t♦r✳

SLIDE 14

❆❜str❛❝t ❋✉♥❝t✐♦♥s

◮ ❲❡ s❛② t❤❛t ❛ ❢✉♥❝t✐♦♥ ❤❛s ♥♦ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ❜② ✇r✐t✐♥❣ ❂✵✳ ◮ ❙✉❝❤ ❛ ❢✉♥❝t✐♦♥ ♠✉st ❜❡ ✈✐rt✉❛❧✳ ◮ ❚❤✐s ✐s ❝❛❧❧❡❞ ❛♥ ❛❜str❛❝t ❢✉♥❝t✐♦♥✳ ◮ ■♥t❡r❢❛❝❡s ❛r❡ ❝❧❛ss❡s ✇❤❡r❡ ❛❧❧ ❢✉♥❝t✐♦♥s ❛r❡ ❛❜str❛❝t✳ ◮ ❆♥ ❛❜str❛❝t ❝❧❛ss ✐s ❛ ❝❧❛ss ✇✐t❤ ❛t ❧❡❛st ♦♥❡ ❛❜str❛❝t ❢✉♥❝t✐♦♥✳

❋♦r ❡①❛♠♣❧❡ ❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥❇❛s❡ ❤❛s ❛♥ ❛❜str❛❝t ♣❛②♦❢❢ ❢✉♥❝t✐♦♥✳

SLIDE 15

▼✉❧t✐♣❧❡ ❧❛②❡rs

◮ ❨♦✉ ❝❛♥ ❜✉✐❧❞ ❝♦♠♣❧❡① ❤✐❡r❛r❝❤✐❡s ♦❢ ❝❧❛ss❡s✳ ◮ P✉t❖♣t✐♦♥ ❤❛s ♣❛r❡♥t ❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥❇❛s❡ ❛♥❞

❣r❛♥❞♣❛r❡♥t ❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥✳

◮ ❲❡ s❤♦✉❧❞ ✐♥s❡rt ❛

P❛t❤■♥❞❡♣❡♥❞❡♥t❖♣t✐♦♥✥✐♥t♦✥♦✉r✥❤✐❡r❛r❝❤②✿

❝❧❛ss✥P❛t❤■♥❞❡♣❡♥❞❡♥t❖♣t✐♦♥✥✿ ✥✥✥✥✥✥✥✥♣✉❜❧✐❝✥❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥❇❛s❡✥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❡✥t❤❡✥♣❛②♦❢❢✥❢r♦♠✥❛✥♣r✐❝❡✥♣❛t❤✥✯✴ ✥✥✥✥❞♦✉❜❧❡✥♣❛②♦❢❢✭ ✥✥✥✥✥✥✥✥✥✥✥✥❝♦♥st✥st❞✿✿✈❡❝t♦r❁❞♦✉❜❧❡❃✫✥st♦❝❦Pr✐❝❡s✥✮✥❝♦♥st✥④ ✥✥✥✥✥✥✥✥r❡t✉r♥✥♣❛②♦❢❢✭st♦❝❦Pr✐❝❡s✳❜❛❝❦✭✮✮❀ ✥✥✥✥⑥ ✥✥✥✥✴✯✥✥■s✥t❤❡✥♦♣t✐♦♥✥♣❛t❤✲❞❡♣❡♥❞❡♥t❄✥✯✴ ✥✥✥✥❜♦♦❧✥✐sP❛t❤❉❡♣❡♥❞❡♥t✭✮✥❝♦♥st✥④ ✥✥✥✥✥✥✥✥r❡t✉r♥✥❢❛❧s❡❀ ✥✥✥✥⑥❀ ⑥❀

SLIDE 16

P❛t❤■♥❞❡♣❞❡♥❞❡♥t❖♣t✐♦♥

P❛t❤■♥❞❡♣❡♥❞❡♥t❖♣t✐♦♥ ❞♦❡s t❤❡ ❢♦❧❧♦✇✐♥❣✳

◮ ■t ♣r♦✈✐❞❡s ❛♥ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♦❢ ✐sP❛t❤❉❡♣❡♥❞❡♥t✳ ◮ ■t ❤❛s ❛♥ ❛❜str❛❝t ❢✉♥❝t✐♦♥ t♦ ❝♦♠♣✉t❡ t❤❡ ♣❛②♦✛ ❣✐✈❡♥ ♦♥❧②

t❤❡ ✜♥❛❧ st♦❝❦ ♣r✐❝❡✳

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

❛♥ ❡♥t✐r❡ ♣❛t❤ ♦❢ st♦❝❦ ♣r✐❝❡s✳

SLIDE 17

❊①t❡♥❞✐♥❣ P❛t❤■♥❞❡♣❡♥❞❡♥t❖♣t✐♦♥

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

◮ ❲❡ ♠✉st ♦✈❡rr✐❞❡ t❤❡ ❛❜str❛❝t ❢✉♥❝t✐♦♥ ♣❛②♦❢❢✳ ◮ ❲❡ ❝❤♦♦s❡ t♦ ♦✈❡rr✐❞❡ t❤❡ ❢✉♥❝t✐♦♥ ♣r✐❝❡ ✇✐t❤ ❛ ♠♦r❡

❡✣❝✐❡♥t ✈❡rs✐♦♥✳

SLIDE 18

❯▼▲

❆ ❯▼▲ ❞✐❛❣r❛♠ s❤♦✇s ♦✉r ♦♣t✐♦♥ ❤✐❡r❛r❝❤②✿

SLIDE 19

❆♥♦t❤❡r ❤✐❡r❛r❝❤②

◮ ❆ ❝❧❛ss ❙❤❛♣❡ t❤❛t r❡♣r❡s❡♥ts ❛♥② ✜♥✐t❡ s❤❛♣❡ ✐♥ t❤❡ ♣❧❛♥❡✳ ■t

❤❛s t❤❡ ❢♦❧❧♦✇✐♥❣ ♠❡t❤♦❞s✿

◮ ❆ ♠❡t❤♦❞ ❛r❡❛ t♦ ❝♦♠♣✉t❡ t❤❡ ❛r❡❛✳ ◮ ❆ ♠❡t❤♦❞ ❝♦♥t❛✐♥s t♦ t❡st ✐❢ ❛ ♣♦✐♥t ✐s ✐♥ t❤❡ s❤❛♣❡✳ ◮ ❆ ♠❡t❤♦❞ ❜♦✉♥❞✐♥❣❘❡❝t❛♥❣❧❡ t❤❛t r❡t✉r♥s ❛ ❘❡❝t❛♥❣❧❡

❝♦♥t❛✐♥✐♥❣ t❤❡ ❡♥t✐r❡ s❤❛♣❡✳

◮ ❚❤❡ ❝❧❛ss ❈✐r❝❧❡ ✐s ♦♥❡ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♦❢ ❙❤❛♣❡✳ ◮ ❚❤❡ ❝❧❛ss ❘❡❝t❛♥❣❧❡ ✐s ❛♥♦t❤❡r ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♦❢ ❙❤❛♣❡✳ ◮ ❚❤❡ ❝❧❛ss ❍②♣❡r❈✐r❝❧❡ ✭t❤❡ s❤❛♣❡ x✹ + y✹ < ✶✮ ✐s ❛♥♦t❤❡r

✐♠♣❧❡♠❡♥t❛t✐♦♥ ♦❢ ❙❤❛♣❡✳

◮ ❚❤❡ ❝❧❛ss ❙❤❛♣❡ ❤❛s ❛ ❞❡❢❛✉❧t ✐♠♣❧❡♠❡♥t❛t✐♦♥ ❢♦r ❛r❡❛ t❤❛t

✉s❡s ▼♦♥t❡ ❈❛r❧♦✳

◮ ❈✐r❝❧❡ ❛♥❞ ❘❡❝t❛♥❣❧❡ ♦✈❡rr✐❞❡ ❛r❡❛✳

SLIDE 20

❉✐s❝✉ss✐♦♥

◮ ❆ ❣r❛♣❤✐❝s ❧✐❜r❛r② ✇❤❡r❡ ②♦✉ ❝♦✉❧❞♥✬t ✇r✐t❡ ②♦✉r ♦✇♥ ❙❤❛♣❡

❝❧❛ss❡s ✇♦✉❧❞ ❜❡ ♣r❡tt② ✉s❡❧❡ss

◮ ❆ ♣r✐❝✐♥❣ ❧✐❜r❛r② ✇❤❡r❡ ②♦✉ ❝❛♥✬t ✇r✐t❡ ②♦✉r ♦✇♥ ♦♣t✐♦♥s ✇♦✉❧❞

s✐♠✐❧❛r❧② ❜❡ ✉s❡❧❡ss

◮ ❖❜❥❡❝t✲♦r✐❡♥t❡❞ ♣r♦❣r❛♠♠✐♥❣ ♠❛❦❡s ♦✉r ❧✐❜r❛r② ♣❧✉❣❣❛❜❧❡✳

SLIDE 21

▼✉❧t✐♣❧✐❡ ✐♥❤❡r✐t❛♥❝❡

◮ ■t ✐s ♣♦ss✐❜❧❡ t♦ ❡①t❡♥❞ ♠♦r❡ t❤❛♥ ♦♥❡ ❝❧❛ss✱ ❜✉t t❤❡ r✉❧❡s ❛r❡

❝♦♠♣❧❡①✳

◮ ❘❡❝♦♠♠❡♥❞❡❞ t❤❛t ②♦✉ ♦♥❧② ❡①t❡♥❞ ♦♥❡ ♥♦r♠❛❧ ❝❧❛ss✱ ❜✉t ②♦✉

♠❛② ❡①t❡♥❞ ♠✉❧t✐♣❧❡ ✐♥t❡r❢❛❝❡s✳

✥✥✥✥❝❧❛ss✥❉❡r✐✈❛t✐✈❡❲✐t❤❙tr✐❦❡✥④ ✥✥✥✥♣✉❜❧✐❝✿ ✥✥✥✥✥✥✥✥⑦❉❡r✐✈❛t✐✈❡❲✐t❤❙tr✐❦❡✭✮❀ ✥✥✥✥✥✥✥✥✈✐rt✉❛❧✥❞♦✉❜❧❡✥❣❡t❙tr✐❦❡✭✮✥❝♦♥st✥❂✥✵❀ ✥✥✥✥⑥❀

■♥❤❡r✐t✐♥❣ ❢r♦♠ t✇♦ ♣❛r❡♥ts

❝❧❛ss✥❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥❇❛s❡✥✿ ✥✥✥✥♣✉❜❧✐❝✥❈♦♥t✐♥✉♦✉s❚✐♠❡❖♣t✐♦♥✱ ✥✥✥✥♣✉❜❧✐❝✥❉❡r✐✈❛t✐✈❡❲✐t❤❙tr✐❦❡✥④

SLIDE 22

❈❛❧❧✐♥❣ s✉♣❡r❝❧❛ss ♠❡t❤♦❞s

◮ ❙♦♠❡t✐♠❡s ②♦✉ ✇❛♥t t♦ ❝❛❧❧ ❛ s✉♣❡r❝❧❛ss✬s ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♦❢ ❛

❢✉♥❝t✐♦♥

◮ ❡✳❣✳ ❛♥ ❯♣❆♥❞❖✉t❖♣t✐♦♥ ♦✈❡rr✐❞❡s ♣r✐❝❡ t♦ ❝❤❡❝❦ ✐❢ t❤❡

st♦❝❦ ♣r✐❝❡ ✐s ♦✈❡r t❤❡ ❜❛rr✐❡r✳ ■❢ ✐t ✐s✱ r❡t✉r♥❀ ♦t❤❡r✇✐s❡✱ ✉s❡ s✉♣❡r❝❧❛ss✬s ♠❡t❤♦❞✳

✥✥✥✥❞♦✉❜❧❡✥♣r✐❝❡✭ ✥✥✥✥✥✥✥✥❝♦♥st✥❇❧❛❝❦❙❝❤♦❧❡s▼♦❞❡❧✫✥♠♦❞❡❧✮✥❝♦♥st✥④ ✥✥✥✥✥✥✥✥✐❢✥✭♠♦❞❡❧✳st♦❝❦Pr✐❝❡✥❃❂✥❣❡t❇❛rr✐❡r✭✮✮ ✥✥✥✥✥✥✥✥✥✥✥✥r❡t✉r♥✥✵❀ ✥✥✥✥✥✥✥✥r❡t✉r♥✥❑♥♦❝❦♦✉t❖♣t✐♦♥✿✿♣r✐❝❡✭♠♦❞❡❧✮❀ ✥✥✥✥⑥

SLIDE 23

❋♦r✇❛r❞ ❞❡❝❧❛r❛t✐♦♥s

◮ ❆ ❙❤❛♣❡ ❤❛s ❛ ❢✉♥❝t✐♦♥ ✇❤✐❝❤ r❡t✉r♥s ❛ ❘❡❝t❛♥❣❧❡✳ ◮ ❇✉t ❘❡❝t❛♥❣❧❡ ❡①t❡♥❞s ❙❤❛♣❡✳ ◮ ❙♦❧✉t✐♦♥ ✐s ❝❛❧❧❡❞ ❛ ❢♦r✇❛r❞ ❞❡❝❧❛r❛t✐♦♥✳

❝❧❛ss✥❈❛rt❡s✐❛♥P♦✐♥t❀ ❝❧❛ss✥❘❡❝t❛♥❣❧❡❀ ❝❧❛ss✥❙❤❛♣❡✥④ ♣✉❜❧✐❝✿ ✥✥✥✥✴✯✥✥❉♦❡s✥t❤❡✥♣♦✐♥t✥❧✐❡✥✐♥✥t❤❡✥s❤❛♣❡✥✯✴ ✥✥✥✥✈✐rt✉❛❧✥❜♦♦❧✥❝♦♥t❛✐♥s✭✥❝♦♥st✥❈❛rt❡s✐❛♥P♦✐♥t✫✥♣♦✐♥t✥✮ ✥✥✥✥✥✥✥✥❝♦♥st✥❂✥✵❀ ✥✥✥✥✴✯✥✥❆✥r❡❝t❛♥❣❧❡✥❜♦✉♥❞✐♥❣✥t❤❡✥s❤❛♣❡✥✯✴ ✥✥✥✥✈✐rt✉❛❧✥❘❡❝t❛♥❣❧❡✥❜♦✉♥❞✐♥❣❘❡❝t❛♥❣❧❡✭✮✥❝♦♥st✥❂✥✵❀ ✥✥✥✥✴✯✥✥❇②✥❞❡❢❛✉❧t✥❛r❡❛✥✐s✥❝♦♠♣✉t❡❞✥❜②✥▼♦♥t❡✥❈❛r❧♦✥✯✴ ✥✥✥✥✈✐rt✉❛❧✥❞♦✉❜❧❡✥❛r❡❛✭✮✥❝♦♥st❀ ⑥❀

SLIDE 24

❙t❛t✐❝ ✈❛r✐❛❜❧❡s ❛♥❞ ❢✉♥❝t✐♦♥s

❝❧❛ss✥❈❛❧❧❈♦✉♥t❡❞❙✐♥✥✿✥♣✉❜❧✐❝✥❘❡❛❧❋✉♥❝t✐♦♥✥④ ♣✉❜❧✐❝✿ ✥✥✥✥st❛t✐❝✥✐♥t✥❣❡t◆✉♠❜❡r❖❢❈❛❧❧s✭✮❀ ✥✥✥✥❞♦✉❜❧❡✥❡✈❛❧✉❛t❡✭✥❞♦✉❜❧❡✥①✥✮✥④ ✥✥✥✥✥✥✥✥♥✉♠❈❛❧❧s✰✰❀ ✥✥✥✥✥✥✥✥r❡t✉r♥✥s✐♥✭①✮❀ ✥✥✥✥⑥ ♣r✐✈❛t❡✿ ✥✥✥✥st❛t✐❝✥✐♥t✥♥✉♠❈❛❧❧s❀ ⑥❀

◆❡❡❞ t♦ ✐♥✐t✐❛❧✐③❡ t❤❡ st❛t✐❝ ✈❛r✐❛❜❧❡✳

✐♥t✥❈❛❧❧❈♦✉♥t❡❞❙✐♥✿✿♥✉♠❈❛❧❧s✥❂✥✵❀

SLIDE 25

◮ ❙t❛t✐❝ ✈❛r✐❛❜❧❡s ❛r❡ ❣❧♦❜❛❧ ✈❛r✐❛❜❧❡s s❤❛r❡❞ ❜② ❛❧❧ ✐♥st❛♥❝❡s✳ ◮ ❚♦ ✇♦r❦ ✇✐t❤ st❛t✐❝ ✈❛r✐❛❜❧❡s ②♦✉ ♦❢t❡♥ ✉s❡ st❛t✐❝ ❢✉♥❝t✐♦♥s✳

✐♥t✥❈❛❧❧❈♦✉♥t❡❞❙✐♥✿✿❣❡t◆✉♠❜❡r❖❢❈❛❧❧s✭✮✥④ ✥✥✥✥r❡t✉r♥✥♥✉♠❈❛❧❧s❀ ⑥

SLIDE 26

❲❡✬✈❡ s❡❡♥ ❛ st❛t✐❝ ✈❛r✐❛❜❧❡ ✐♥ ♠t✶✾✸✸✼✳

♠❡rs❡♥♥❡❚✇✐st❡r✳s❡❡❞✭♠t✶✾✾✸✼✿✿❞❡❢❛✉❧t❴s❡❡❞✮❀

❆❞✈❛♥t❛❣❡s ♦✈❡r ❣❧♦❜❛❧ ✈❛r✐❛❜❧❡s ❛♥❞ ❢✉♥❝t✐♦♥s✿

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

SLIDE 27

Pr♦t❡❝t❡❞

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

SLIDE 28