Pr t ss t - - PowerPoint PPT Presentation

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Pr t ss t - - PowerPoint PPT Presentation

Oct 29, 2023 431 likes •1.26k views

Pr t ss t trtr trs s s r tr tr

SLIDE 1

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ✇✐t❤ ❙tr✉❝t✉r❡❞ ❋❛❝t♦rs

❨❛s❤ ❉❡s❤♣❛♥❞❡ ❛♥❞ ❆♥❞r❡❛ ▼♦♥t❛♥❛r✐

❙t❛♥❢♦r❞ ❯♥✐✈❡rs✐t②

▼❛② ✷✽✱ ✷✵✶✹

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✶ ✴ ✺✶

SLIDE 2

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s

❉❛t❛ ♠❛tr✐① ❳ ✷ R♥✂♣ ❋✐♥❞ ❯❀ ❱ s✉❝❤ t❤❛t ❳ ✙ ❯❱❚ ❀ ❯ ✷ R♥✂r ❀ ❱ ✷ R♣✂r ❉✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥✿ r ✜ ♥❀ ♣ ❲❤❛t ❤❛♣♣❡♥s ✐❢ ❯❀ ❱ ❤❛✈❡ s♣❡❝✐❛❧ str✉❝t✉r❡❄

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷ ✴ ✺✶

SLIDE 3

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s

❉❛t❛ ♠❛tr✐① ❳ ✷ R♥✂♣ ❋✐♥❞ ❯❀ ❱ s✉❝❤ t❤❛t ❳ ✙ ❯❱❚ ❀ ❯ ✷ R♥✂r ❀ ❱ ✷ R♣✂r ❉✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥✿ r ✜ ♥❀ ♣ ❲❤❛t ❤❛♣♣❡♥s ✐❢ ❯❀ ❱ ❤❛✈❡ s♣❡❝✐❛❧ str✉❝t✉r❡❄

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷ ✴ ✺✶

SLIDE 4

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s

❉❛t❛ ♠❛tr✐① ❳ ✷ R♥✂♣ ❋✐♥❞ ❯❀ ❱ s✉❝❤ t❤❛t ❳ ✙ ❯❱❚ ❀ ❯ ✷ R♥✂r ❀ ❱ ✷ R♣✂r ❉✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥✿ r ✜ ♥❀ ♣ ❲❤❛t ❤❛♣♣❡♥s ✐❢ ❯❀ ❱ ❤❛✈❡ s♣❡❝✐❛❧ str✉❝t✉r❡❄

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷ ✴ ✺✶

SLIDE 5

■ ✇✐❧❧ t❛❧❦ ♦♥❧② ❛❜♦✉t ♦♥❡ t②♣❡ ♦❢ str✉❝t✉r❡✳ ✳ ✳

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✸ ✴ ✺✶

SLIDE 6

❙♣❛rs❡ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s

❉❛t❛ ♠❛tr✐① ❳ ✷ R♥✂♣ ❋✐♥❞ ❯❀ ❱ s✉❝❤ t❤❛t ❳ ✙ ❯❱❚ ❀ ❯ ✷ R♥✂r ❀ ❱ ✷ R♣✂r s♣❛rs❡ ❉✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥✿ r ✜ ♥❀ ♣ ❲❤❛t ❤❛♣♣❡♥s ✐❢ ❯❀ ❱ ❤❛✈❡ s♣❡❝✐❛❧ str✉❝t✉r❡❄

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹ ✴ ✺✶

SLIDE 7

❊q✉✐✈❛❧❡♥t❧②✿ ❙✉♣❡r♣♦s✐t✐♦♥ ♦❢ s♣❛rs❡ ✈❡❝t♦rs

◮ ❘♦✇s ♦❢ ❳✿

①✶✱ ①✷✱✳ ✳ ✳ ✳ ✳ ✳ ①♥ ✷ R♣✳

◮ ❘♦✇s ♦❢ ❱❚✿

✈✶✱✳ ✳ ✳ ✈r ✷ R♣✳ ①✐ ✙

r

❳

❵❂✶

✉✐❵ ✈❵ ✈✶❀ ✈✷❀ ✿ ✿ ✿ ❀ ✈r s♣❛rs❡

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✺ ✴ ✺✶

SLIDE 8

❊①❛♠♣❧❡✿ ❚♦♣✐❝ ♠♦❞❡❧s

①✐ ✙

r

❳

❵❂✶

✉❵❀✐ ✈❵ ①✐✿ ❉♦❝✉♠❡♥t ✐ ✈❵✿ ❚♦♣✐❝ ❵ ❉♦❝✉♠❡♥t ❂ ❙✉♣❡r♣♦s✐t✐♦♥ ♦❢ t♦♣✐❝s✳ ❚♦♣✐❝ ❂ ❙♣❛rs❡ ❞✐str✐❜✉t✐♦♥ ♦✈❡r ✇♦r❞s

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✻ ✴ ✺✶

SLIDE 9

❊①❛♠♣❧❡✿ ❚♦♣✐❝ ♠♦❞❡❧s

①✐ ✙

r

❳

❵❂✶

✉❵❀✐ ✈❵ ①✐✿ ❉♦❝✉♠❡♥t ✐ ✈❵✿ ❚♦♣✐❝ ❵ ❉♦❝✉♠❡♥t ❂ ❙✉♣❡r♣♦s✐t✐♦♥ ♦❢ t♦♣✐❝s✳ ❚♦♣✐❝ ❂ ❙♣❛rs❡ ❞✐str✐❜✉t✐♦♥ ♦✈❡r ✇♦r❞s

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✻ ✴ ✺✶

SLIDE 10

❊①❛♠♣❧❡✿ ❚♦♣✐❝ ♠♦❞❡❧s

❬❩❤❛♥❣✱ ❊❧ ●❤❛♦✉✐✱ ✷✵✶✶❪

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✼ ✴ ✺✶

SLIDE 11

❖t❤❡r ❛♣♣❧✐❝❛t✐♦♥s

◮ ❉✐❝t✐♦♥❛r② ❧❡❛r♥✐♥❣ ◮ ❈♦♠♣✉t❡r ✈✐s✐♦♥ ◮ ❉✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥ ◮ ✳ ✳ ✳

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✽ ✴ ✺✶

SLIDE 12

❖✉t❧✐♥❡

✶

▼♦❞❡❧

✷

❙t❛t❡ ♦❢ t❤❡ ❛rt

✸

❆❧❣♦r✐t❤♠ ❛♥❞ ♠♦t✐✈❛t✐♦♥

✹

❆♥❛❧②s✐s ❛♥❞ s✐♠✉❧❛t✐♦♥s ❬❛r❳✐✈✿✶✸✶✶✳✺✶✼✾❪

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✾ ✴ ✺✶

SLIDE 13

▼♦❞❡❧

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✶✵ ✴ ✺✶

SLIDE 14

❙♣✐❦❡❞ ❝♦✈❛r✐❛♥❝❡ ♠♦❞❡❧

❳ ❂

r

❳

❵❂✶

♣

☞❵ ✉❵✈❚

❵ ✰ ❩ ◮ ❩✐❥ ✘✐✿✐✿❞✿ ◆✭✵❀ ✶✮✱

✉❵ ✘ ◆✭✵❀ ■♥✂♥✮

◮ ♣ ❂ ✂✭♥✮✳ ◮ ❦✈❵❦✵ ✔ ❦✱ ♠✐♥✐✷s✉♣♣✭✈❵✮ ❥✈❵❀✐❥ ✕ ✈♠✐♥❂

♣ ❦

◮ r✱ ☞❵ ❜♦✉♥❞❡❞ ◮ ❙❡♣❛r❛t✐♦♥ ☞✶ ❃ ☞✷ ❃ ✁ ✁ ✁ ❃ ☞r ❃ ✵

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✶✶ ✴ ✺✶

SLIDE 15

❙♣✐❦❡❞ ❝♦✈❛r✐❛♥❝❡ ♠♦❞❡❧

❳ ❂

r

❳

❵❂✶

♣

☞❵ ✉❵✈❚

❵ ✰ ❩ ◮ ❩✐❥ ✘✐✿✐✿❞✿ ◆✭✵❀ ✶✮✱

✉❵ ✘ ◆✭✵❀ ■♥✂♥✮

◮ ♣ ❂ ✂✭♥✮✳ ◮ ❦✈❵❦✵ ✔ ❦✱ ♠✐♥✐✷s✉♣♣✭✈❵✮ ❥✈❵❀✐❥ ✕ ✈♠✐♥❂

♣ ❦

◮ r✱ ☞❵ ❜♦✉♥❞❡❞ ◮ ❙❡♣❛r❛t✐♦♥ ☞✶ ❃ ☞✷ ❃ ✁ ✁ ✁ ❃ ☞r ❃ ✵

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✶✷ ✴ ✺✶

SLIDE 16

❊q✉✐✈❛❧❡♥t❧②

①✶❀ ①✷❀ ✿ ✿ ✿ ❀ ①♥ ✘✐✿✐✿❞✿ ◆✭✵❀ ✝✮ ✝ ❂

r

❳

❵❂✶

☞❵✈❵✈❚

❵ ✰ ■ ✿

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✶✸ ✴ ✺✶

SLIDE 17

❊q✉✐✈❛❧❡♥t❧②

①✶❀ ①✷❀ ✿ ✿ ✿ ❀ ①♥ ✘✐✿✐✿❞✿ ◆✭✵❀ ✝✮ ✝ ❂

r

❳

❵❂✶

☞❵✈❵✈❚

❵ ✰ ■ ✿

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✶✸ ✴ ✺✶

SLIDE 18

❋♦r ❡❛s❡ ♦❢ ❡①♣♦s✐t✐♦♥✿ r ❂ ✶

❳ ❂

♣

☞ ✉✈❚ ✰ ❩

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✶✹ ✴ ✺✶

SLIDE 19

❆ ❞❡✜♥✐t✐♦♥✿ ❙❛♠♣❧❡ ❝♦✈❛r✐❛♥❝❡

❜

✝ ✑ ✶ ♥ ❳❚❳ ❂ ✶ ♥

♥

❳

✐❂✶

①✐①❚

✐

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✶✺ ✴ ✺✶

SLIDE 20

❙t❛t❡ ♦❢ t❤❡ ❛rt

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✶✻ ✴ ✺✶

SLIDE 21

❖❜❥❡❝t✐✈❡✿ ❙✉♣♣♦rt r❡❝♦✈❡r②

❲❛♥t t♦ r❡❝♦♥str✉❝t s✉♣♣✭✈✮

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✶✼ ✴ ✺✶

SLIDE 22

❙✐♠♣❧❡ P❈❆

Pr✐♥❝✐♣❛❧ ✈❡❝t♦r ♦❢ ❳✿ ✈✶✭❳✮

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✶✽ ✴ ✺✶

SLIDE 23

❙✐♠♣❧❡ P❈❆✿ ❙♣❡❝tr❛❧ ♣❤❛s❡ tr❛♥s✐t✐♦♥

4 Limiting Spectral Density 4 Limiting Spectral Density

♥ ❁ ❈✭☞✮♣ ♥ ❃ ❈✭☞✮♣ ☞ ✰ ✷ ✰ ☞✶ ❤✈✶✭❳✮❀ ✈✐ ✙ ✵ ❤✈✶✭❳✮❀ ✈✐ ❜❞❞ ❛✇❛② ❢r♦♠ ✵

Pr✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥t ✐s ♦rt❤♦❣♦♥❛❧ t♦ t❤❡ s✐❣♥❛❧ ✉♥❧❡ss ♥ ❃ ❈✭☞✮♣

❬❇❛✐❦✱ ❇❡♥ ❆r♦✉s✱ P❡❝❤❡✱ ✷✵✵✺❀ ❇❛✐❦ ❙✐❧✈❡rst❡✐♥✱ ✷✵✵✻❀ P❛✉❧✱ ✷✵✵✼❪

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✶✾ ✴ ✺✶

SLIDE 24

■♥❢♦r♠❛t✐♦♥ t❤❡♦r② ❧♦✇❡r ❜♦✉♥❞

❋♦r ✐ ✷ ❢✶❀ ✿ ✿ ✿ ❀ ♥❣ ①✐ ❂

♣

☞✉✐✈ ✰ ③✐

◮ ❊❛❝❤ s❛♠♣❧❡ ②✐❡❧❞s ✂✭✶✮ ❜✐ts ◮ ◆❡❡❞

✭❦ ❧♦❣ ♣✮ ❜✐ts

◮ ❉♦❛❜❧❡ ✐❢ ♥ ✕ ❈✭☞✮❦ ❧♦❣ ♣

✭❡①❤❛✉st✐✈❡ s❡❛r❝❤✮

❬❆♠✐♥✐✱ ❲❛✐♥✇r✐❣❤t✱ ✷✵✵✾❪

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷✵ ✴ ✺✶

SLIDE 25

■♥❢♦r♠❛t✐♦♥ t❤❡♦r② ❧♦✇❡r ❜♦✉♥❞

❋♦r ✐ ✷ ❢✶❀ ✿ ✿ ✿ ❀ ♥❣ ①✐ ❂

♣

☞✉✐✈ ✰ ③✐

◮ ❊❛❝❤ s❛♠♣❧❡ ②✐❡❧❞s ✂✭✶✮ ❜✐ts ◮ ◆❡❡❞

✭❦ ❧♦❣ ♣✮ ❜✐ts

◮ ❉♦❛❜❧❡ ✐❢ ♥ ✕ ❈✭☞✮❦ ❧♦❣ ♣

✭❡①❤❛✉st✐✈❡ s❡❛r❝❤✮

❬❆♠✐♥✐✱ ❲❛✐♥✇r✐❣❤t✱ ✷✵✵✾❪

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷✵ ✴ ✺✶

SLIDE 26

❈❛♥ ✇❡ ❛❝❤✐❡✈❡ t❤✐s ✐♥ ♣♦❧②t✐♠❡❄ ❲❤❛t ❛❜♦✉t ❧✐♥❡❛r t✐♠❡❄

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷✶ ✴ ✺✶

SLIDE 27

❉✐❛❣♦♥❛❧ t❤r❡s❤♦❧❞✐♥❣ ❬❏♦❤♥st♦♥❡✱ ▲✉✱ ✷✵✵✹❪

■❞❡❛ ✝✐✐ ❂ ✶ ✰ ☞ ✈ ✷

✐

❜

✝✐✐ ❂ ✶ ✰ ☞ ✈ ✷

✐ ✰

✶ ♣♥ ❲✐ ❲✐ ✙ ◆✭✵❀ ✶✮ ❙✉♣♣♦rt ❡st✐♠❛t❡

❜

◗ ❂

♥

✐ ✷ ❬♣❪ ✿

❜

✝✐✐ ✕ ✕

♦

✿

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷✷ ✴ ✺✶

SLIDE 28

❉✐❛❣♦♥❛❧ t❤r❡s❤♦❧❞✐♥❣ ❬❏♦❤♥st♦♥❡✱ ▲✉✱ ✷✵✵✹❪

■❞❡❛ ✝✐✐ ❂ ✶ ✰ ☞ ✈ ✷

✐

❜

✝✐✐ ❂ ✶ ✰ ☞ ✈ ✷

✐ ✰

✶ ♣♥ ❲✐ ❲✐ ✙ ◆✭✵❀ ✶✮ ❙✉♣♣♦rt ❡st✐♠❛t❡

❜

◗ ❂

♥

✐ ✷ ❬♣❪ ✿

❜

✝✐✐ ✕ ✕

♦

✿

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷✷ ✴ ✺✶

SLIDE 29

❊①❛♠♣❧❡✿ ☞ ❂ ✶✱ ♣ ❂ ✹✵✵✱ ♥ ❂ ✸✵✵

−0.4

−0.2 0.0 0.2 0.4 Diag−1

❦ ❂ ✶✵✵

−0.4

−0.2 0.0 0.2 0.4 Diag−1

❦ ❂ ✺✵

−0.4

−0.2 0.0 0.2 0.4 Diag−1

❦ ❂ ✶✺ ♥♦✐s❡ ❧❡✈❡❧ ✙

q

✭✷ ❧♦❣ ♣✮❂♥❀ s✐❣♥❛❧ ✙ ☞❂❦

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷✸ ✴ ✺✶

SLIDE 30

❊①❛♠♣❧❡✿ ☞ ❂ ✶✱ ♣ ❂ ✹✵✵✱ ♥ ❂ ✸✵✵

−0.4

−0.2 0.0 0.2 0.4 Diag−1

❦ ❂ ✶✵✵

−0.4

−0.2 0.0 0.2 0.4 Diag−1

❦ ❂ ✺✵

−0.4

−0.2 0.0 0.2 0.4 Diag−1

❦ ❂ ✶✺

♥♦✐s❡ ❧❡✈❡❧ ✙

q

✭✷ ❧♦❣ ♣✮❂♥❀ s✐❣♥❛❧ ✙ ☞❂❦

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷✹ ✴ ✺✶

SLIDE 31

❉✐❛❣♦♥❛❧ t❤r❡s❤♦❧❞✐♥❣

♥♦✐s❡ ❧❡✈❡❧ ✙

s

✷ ❧♦❣ ♣ ♥ ❀ s✐❣♥❛❧ ✙ ☞ ❦ ❲♦r❦s ✐❢ ☞ ❦ ✕ ✶✵

s

❧♦❣ ♣ ♥ ❦ ✔ ❈✭☞✮

s

♥ ❧♦❣ ♣

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷✺ ✴ ✺✶

SLIDE 32

❉✐❛❣♦♥❛❧ t❤r❡s❤♦❧❞✐♥❣

♥♦✐s❡ ❧❡✈❡❧ ✙

s

✷ ❧♦❣ ♣ ♥ ❀ s✐❣♥❛❧ ✙ ☞ ❦ ❲♦r❦s ✐❢ ☞ ❦ ✕ ✶✵

s

❧♦❣ ♣ ♥ ❦ ✔ ❈✭☞✮

s

♥ ❧♦❣ ♣

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷✺ ✴ ✺✶

SLIDE 33

❉✐❛❣♦♥❛❧ t❤r❡s❤♦❧❞✐♥❣

♥♦✐s❡ ❧❡✈❡❧ ✙

s

✷ ❧♦❣ ♣ ♥ ❀ s✐❣♥❛❧ ✙ ☞ ❦ ❲♦r❦s ✐❢ ☞ ❦ ✕ ✶✵

s

❧♦❣ ♣ ♥ ❦ ✔ ❈✭☞✮

s

♥ ❧♦❣ ♣

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷✺ ✴ ✺✶

SLIDE 34

❊①❡❝✉t✐✈❡ s✉♠♠❛r②

r ❂ ✶✱ ❦ ❂ ❦✈❦✵ ✭s♠❛❧❧❡r ❦ ✮ ❡❛s✐❡r✮ ❦

♥ ❧♦❣ ♣

q

♥ ❧♦❣ ♣

■♥❢♦r♠✳✲t❤❡♦r✳ ✉♥❢❡❛s✐❜❧❡ ❬❆♠✐♥✐✱ ❲❛✐♥✇r✐❣❤t✱ ✷✵✵✾❪ ❉✐❛❣♦♥❛❧ t❤r❡s❤♦❧❞✐♥❣ ❬❏♦❤♥st♦♥❡✱ ▲✉✱ ✷✵✵✹❪

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷✻ ✴ ✺✶

SLIDE 35

❈♦♠♣❧❛✐♥ts ❛❜♦✉t ❞✐❛❣♦♥❛❧ t❤r❡s❤♦❧❞✐♥❣

◮ ❙✉♣✲♦♣t✐♠❛❧ s❛♠♣❧❡ s✐③❡ ◮ ❙❡♥s✐t✐✈❡ t♦ t❤❡ ✐✳✐✳❞✳ ♥♦✐s❡ ❛ss✉♠♣t✐♦♥

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷✼ ✴ ✺✶

SLIDE 36

❆♥②t❤✐♥❣ ❜❡tt❡r❄

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷✽ ✴ ✺✶

SLIDE 37

❙❉P r❡❧❛①❛t✐♦♥ ✭❞✬❆s♣r❡♠♦♥t✱ ❊❧ ●❤❛♦✉✐✱ ❏♦r❞❛♥✱ ▲❛♥❝❦r✐❡t✱ ✷✵✵✹✮

♠❛①✐♠✐③❡ ❚r✭❜ ✝❲✮ ❀ s✉❜❥❡❝tt♦ ❲ ✗ ✵ ❀ ❚r✭❲✮ ❂ ✶ ❀

♣

❳

✐❀❥ ❂✶

❥❲✐❥ ❥ ✔ ✘ ✿

◮ ❆♠✐♥✐✱ ❲❛✐♥✇r✐❣❤t ✷✵✵✾✿

❈♦♥❞✐t✐♦♥❛❧❧② ♣♦s✐t✐✈❡ r❡s✉❧ts

◮ ❑r❛✉t❤❣❛♠❡r✱ ◆❛❞❧❡r✱ ❱✐❧❡❝❤♥✐❦✱ ✷✵✶✸✿

❋❛✐❧s ❢♦r ❦ ♣♥

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷✾ ✴ ✺✶

SLIDE 38

❙❉P r❡❧❛①❛t✐♦♥ ✭❞✬❆s♣r❡♠♦♥t✱ ❊❧ ●❤❛♦✉✐✱ ❏♦r❞❛♥✱ ▲❛♥❝❦r✐❡t✱ ✷✵✵✹✮

♠❛①✐♠✐③❡ ❚r✭❜ ✝❲✮ ❀ s✉❜❥❡❝tt♦ ❲ ✗ ✵ ❀ ❚r✭❲✮ ❂ ✶ ❀

♣

❳

✐❀❥ ❂✶

❥❲✐❥ ❥ ✔ ✘ ✿

◮ ❆♠✐♥✐✱ ❲❛✐♥✇r✐❣❤t ✷✵✵✾✿

❈♦♥❞✐t✐♦♥❛❧❧② ♣♦s✐t✐✈❡ r❡s✉❧ts

◮ ❑r❛✉t❤❣❛♠❡r✱ ◆❛❞❧❡r✱ ❱✐❧❡❝❤♥✐❦✱ ✷✵✶✸✿

❋❛✐❧s ❢♦r ❦ ♣♥

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✷✾ ✴ ✺✶

SLIDE 39

❊①❡❝✉t✐✈❡ s✉♠♠❛r②

r ❂ ✶✱ ❦ ❂ ❦✈❦✵ ✭s♠❛❧❧❡r ❦ ✮ ❡❛s✐❡r✮ ❦

♥ ❧♦❣ ♣

♣♥

q

♥ ❧♦❣ ♣

■♥❢♦r♠✳✲t❤❡♦r✳ ✉♥❢❡❛s✐❜❧❡ ❬❆♠✐♥✐✱ ❲❛✐♥✇r✐❣❤t✱ ✷✵✵✾❪ ❈♦♠♣✉t✳ ❢❡❛s✐❜❧❡❄ ❬❑r❛✉t❤❣❛♠❡r ❡t ❛❧✳ ✷✵✶✸❪ ❉✐❛❣♦♥❛❧ t❤r❡s❤♦❧❞✐♥❣ ❬❏♦❤♥st♦♥❡✱ ▲✉✱ ✷✵✵✹❪

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✸✵ ✴ ✺✶

SLIDE 40

❆ ❝♦♠♣✉t❛t✐♦♥❛❧ ❜❛rr✐❡r❄

❚❤❡♦r❡♠ ✭❇❡rt❤❡t✱ ❘✐❣♦❧❧❡t✱ ✷✵✶✸✮

❆ss✉♠❡ t❤❛t P❧❛♥t❡❞❈❧✐q✉❡ ❝❛♥♥♦t ❜❡ s♦❧✈❡❞ ✐♥ ♣♦❧②♥♦♠✐❛❧ t✐♠❡ ❢♦r ❝❧✐q✉❡ s✐③❡ ♥✵✿✵✵✶ ✔ ❥❈❧✐q✉❡❥ ✔ ♥✵✿✹✾✾✳ ❚❤❡♥❛ s✉♣♣✭✈✮ ❝❛♥♥♦t ❜❡ ❢♦✉♥❞ ✐♥ ♣♦❧②♥♦♠✐❛❧ t✐♠❡ ❢♦r ❦ ✔ ♥✵✿✹✾✾✳

❛❙❧✐❣❤t❧② ❞✐✛❡r❡♥t ♠♦❞❡❧

❬❙❡❡ ❛❧s♦ ▼❛✱ ❲✉ ✷✵✶✸❪

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✸✶ ✴ ✺✶

SLIDE 41

❊①❡❝✉t✐✈❡ s✉♠♠❛r②

r ❂ ✶✱ ❦ ❂ ❦✈❦✵ ✭s♠❛❧❧❡r ❦ ✮ ❡❛s✐❡r✮ ❦

♥ ❧♦❣ ♣

♣♥

q

♥ ❧♦❣ ♣

■♥❢♦r♠✳✲t❤❡♦r✳ ✉♥❢❡❛s✐❜❧❡ ❬❆♠✐♥✐✱ ❲❛✐♥✇r✐❣❤t✱ ✷✵✵✾❪ ❈♦♠♣✉t✳ ✉♥❢❡❛s✐❜❧❡❄ ❬❑r❛✉t❤❣❛♠❡r ❡t ❛❧✳ ✷✵✶✸❪ ❬❇❡rt❤❡t✱ ❘✐❣♦❧❧❡t ✷✵✶✸❀ ▼❛✱ ❲✉ ✷✵✶✸❪ ❉✐❛❣♦♥❛❧ t❤r❡s❤♦❧❞✐♥❣ ❬❏♦❤♥st♦♥❡✱ ▲✉✱ ✷✵✵✹❪

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✸✷ ✴ ✺✶

SLIDE 42

❊①❡❝✉t✐✈❡ s✉♠♠❛r②✿ ❚❤✐s ♣❛♣❡r

r ❂ ✶✱ ❦ ❂ ❦✈❦✵ ✭s♠❛❧❧❡r ❦ ✮ ❡❛s✐❡r✮ ❦

♥ ❧♦❣ ♣

♣♥

q

♥ ❧♦❣ ♣

■♥❢♦r♠✳✲t❤❡♦r✳ ✉♥❢❡❛s✐❜❧❡ ❬❆♠✐♥✐✱ ❲❛✐♥✇r✐❣❤t✱ ✷✵✵✾❪ ❈♦♠♣✉t✳ ✉♥❢❡❛s✐❜❧❡❄ ❬❑r❛✉t❤❣❛♠❡r ❡t ❛❧✳ ✷✵✶✸❪ ❬❇❡rt❤❡t✱ ❘✐❣♦❧❧❡t ✷✵✶✸❀ ▼❛✱ ❲✉ ✷✵✶✸❪ ❈♦✈❛r✐❛♥❝❡ t❤r❡s❤✳ ❉✐❛❣♦♥❛❧ t❤r❡s❤♦❧❞✐♥❣ ❬❏♦❤♥st♦♥❡✱ ▲✉✱ ✷✵✵✹❪

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✸✸ ✴ ✺✶

SLIDE 43

❆❧❣♦r✐t❤♠ ❛♥❞ ♠♦t✐✈❛t✐♦♥

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✸✹ ✴ ✺✶

SLIDE 44

❙❛♠♣❧❡ ❝♦✈❛r✐❛♥❝❡

P♦♣✉❧❛t✐♦♥ ❝♦✈❛r✐❛♥❝❡ ✝ ❂ ☞✈✈❚ ✰ ■ ❙❛♠♣❧❡ ❝♦✈❛r✐❛♥❝❡

❜

✝ ✑ ✶ ♥ ❳❚❳ ❂ ✶ ♥

♥

❳

✐❂✶

①✐①❚

✐

❜

✝ ❂ ☞ ✈✈❚ ✰ ■ ✰ ♥♦✐s❡

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✸✺ ✴ ✺✶

SLIDE 45

❙❛♠♣❧❡ ❝♦✈❛r✐❛♥❝❡

P♦♣✉❧❛t✐♦♥ ❝♦✈❛r✐❛♥❝❡ ✝ ❂ ☞✈✈❚ ✰ ■ ❙❛♠♣❧❡ ❝♦✈❛r✐❛♥❝❡

❜

✝ ✑ ✶ ♥ ❳❚❳ ❂ ✶ ♥

♥

❳

✐❂✶

①✐①❚

✐

❜

✝ ❂ ☞ ✈✈❚ ✰ ■ ✰ ♥♦✐s❡

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✸✺ ✴ ✺✶

SLIDE 46

❈♦✈❛r✐❛♥❝❡ t❤r❡s❤♦❧❞✐♥❣

◮ ❇✐❝❦❡❧✱ ▲❡✈✐♥❛ ✷✵✵✾ ◮ Pr♦♣♦s❡❞ ❢♦r ❙P❈❆ ❜② ❑r❛✉t❤❣❛♠❡r✱ ◆❛❞❧❡r✱ ❱✐❧❡❝❤♥✐❦ ✷✵✶✸

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✸✻ ✴ ✺✶

SLIDE 47

❈♦✈❛r✐❛♥❝❡ t❤r❡s❤♦❧❞✐♥❣

❜

✝ ■ ❂☞ ✈ ✈❚ ❙♣❛rs❡✱ ◆♦r♠ ❂ ☞ ✰ ♥♦✐s❡ ❉❡♥s❡✱ ◆♦r♠ ❂ ❝

♣

♣❂♥ ❚❤r❡s❤♦❧❞ ❡♥tr✐❡s ❛t ❧❡✈❡❧ ✕ ❂ ✜❂♣♥ ❙❚✕✭❜ ✝✮ ❝■ ✙ ❙❚✕✭☞ ✈ ✈❚✮ ◆♦r♠ ✙ ☞ ✰ ♥♦✐s❡ ◆♦r♠ ✙ ✧✭✜✮

♣

♣❂♥ ❙❚✕ ✑ s♦❢t t❤r❡s❤♦❧❞✐♥❣ ❛t ❧❡✈❡❧ ✕

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✸✼ ✴ ✺✶

SLIDE 48

❈♦✈❛r✐❛♥❝❡ t❤r❡s❤♦❧❞✐♥❣

❜

✝ ■ ❂☞ ✈ ✈❚ ❙♣❛rs❡✱ ◆♦r♠ ❂ ☞ ✰ ♥♦✐s❡ ❉❡♥s❡✱ ◆♦r♠ ❂ ❝

♣

♣❂♥ ❚❤r❡s❤♦❧❞ ❡♥tr✐❡s ❛t ❧❡✈❡❧ ✕ ❂ ✜❂♣♥ ❙❚✕✭❜ ✝✮ ❝■ ✙ ❙❚✕✭☞ ✈ ✈❚✮ ◆♦r♠ ✙ ☞ ✰ ♥♦✐s❡ ◆♦r♠ ✙ ✧✭✜✮

♣

♣❂♥ ❙❚✕ ✑ s♦❢t t❤r❡s❤♦❧❞✐♥❣ ❛t ❧❡✈❡❧ ✕

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✸✼ ✴ ✺✶

SLIDE 49

❈♦✈❛r✐❛♥❝❡ t❤r❡s❤♦❧❞✐♥❣

❜

✝ ■ ❂☞ ✈ ✈❚ ❙♣❛rs❡✱ ◆♦r♠ ❂ ☞ ✰ ♥♦✐s❡ ❉❡♥s❡✱ ◆♦r♠ ❂ ❝

♣

♣❂♥ ❚❤r❡s❤♦❧❞ ❡♥tr✐❡s ❛t ❧❡✈❡❧ ✕ ❂ ✜❂♣♥ ❙❚✕✭❜ ✝✮ ❝■ ✙ ❙❚✕✭☞ ✈ ✈❚✮ ◆♦r♠ ✙ ☞ ✰ ♥♦✐s❡ ◆♦r♠ ✙ ✧✭✜✮

♣

♣❂♥ ❙❚✕ ✑ s♦❢t t❤r❡s❤♦❧❞✐♥❣ ❛t ❧❡✈❡❧ ✕

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✸✼ ✴ ✺✶

SLIDE 50

❙❚

② ❙❚✜❂♣♥✭②✮ ✰✜❂♣♥ ✜❂♣♥

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✸✽ ✴ ✺✶

SLIDE 51

❈♦✈❛r✐❛♥❝❡ t❤r❡s❤♦❧❞✐♥❣

✶✿ ■♥♣✉t✿ ❉❛t❛ ✭①✐✮✶✔✐✔✷♥✱ ♣❛r❛♠❡t❡r ✜ ✷ R✕✵❀ ✷✿ ❈♦♠♣✉t❡ ❜

✝❀

✸✿ ❙❡t ❙❚✜❂♣♥✭❜

✝✮✐✐ ❂ ✵ ❛♥❞ ✭❢♦r ✐ ✻❂ ❥ ✮✿ ❙❚✜❂♣♥✭❜ ✝✮✐❥ ❂

✽ ❃ ❃ ❁ ❃ ❃ ✿ ❜

✝✐❥

✜ ♣♥

✐❢ ❜ ✝✐❥ ✕ ✜❂♣♥✱ ✵ ✐❢ ✜❂♣♥ ❁ ❜ ✝✐❥ ❁ ✜❂♣♥✱

❜

✝✐❥ ✰

✜ ♣♥

✐❢ ❜ ✝✐❥ ✔ ✜❂♣♥✱

✹✿ ✈✄ ❂ Pr✐♥❝✐♣❛❧ ❡✐❣❡♥✈❡❝t♦r ♦❢ ❙❚✜❂♣♥✭❜

✝✮❀

✺✿ ❵❈❧❡❛♥✬ ✈✄ t♦ ❡st✐♠❛t❡ s✉♣♣♦rt ❜

◗✳

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✸✾ ✴ ✺✶

SLIDE 52

❝

✝

20 40 60 80 20 40 60 80 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✵ ✴ ✺✶

SLIDE 53

❙❚✶✿✺❂♣♥✭❝ ✝✮

20 40 60 80 20 40 60 80 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✶ ✴ ✺✶

SLIDE 54

❆♥❛❧②s✐s ❛♥❞ s✐♠✉❧❛t✐♦♥s

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✷ ✴ ✺✶

SLIDE 55

❆ t❤❡♦r❡♠

❚❤❡♦r❡♠ ✭❉❡s❤♣❛♥❞❡✱ ▼♦♥t❛♥❛r✐✱ ✷✵✶✸✮

❋♦r ❛♥② ☛❀ ☞❀ ✧ ❃ ✵✱ t❤❡r❡ ❡①✐sts ❈ ❂ ❈✭☛❀ ☞❀ ✧✮ ❃ ✵ s✉❝❤ t❤❛t t❤❡ ❢♦❧❧♦✇✐♥❣ ❤❛♣♣❡♥s ❢♦r s✐❣♥❛❧ t♦ ♥♦✐s❡ r❛t✐♦ ☞✱ ❛♥❞ ♣❂♥ ❂ ☛✳ ■❢ ❦ ✔ ❈♣♥✱ t❤❡♥✱ ✇✐t❤ ❤✐❣❤ ♣r♦❜❛❜✐❧✐t②✱

◮ ❦✈✄ ✈❦✷ ✔ ✧ ◮ ❜

◗ ❂ s✉♣♣✭✈✮

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✸ ✴ ✺✶

SLIDE 56

❆ t❤❡♦r❡♠

❚❤❡♦r❡♠ ✭❉❡s❤♣❛♥❞❡✱ ▼♦♥t❛♥❛r✐✱ ✷✵✶✸✮

❋♦r ❛♥② ☛❀ ☞❀ ✧ ❃ ✵✱ t❤❡r❡ ❡①✐sts ❈ ❂ ❈✭☛❀ ☞❀ ✧✮ ❃ ✵ s✉❝❤ t❤❛t t❤❡ ❢♦❧❧♦✇✐♥❣ ❤❛♣♣❡♥s ❢♦r s✐❣♥❛❧ t♦ ♥♦✐s❡ r❛t✐♦ ☞✱ ❛♥❞ ♣❂♥ ❂ ☛✳ ■❢ ❦ ✔ ❈♣♥✱ t❤❡♥✱ ✇✐t❤ ❤✐❣❤ ♣r♦❜❛❜✐❧✐t②✱

◮ ❦✈✄ ✈❦✷ ✔ ✧ ◮ ❜

◗ ❂ s✉♣♣✭✈✮

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✸ ✴ ✺✶

SLIDE 57

❆ t❤❡♦r❡♠

❚❤❡♦r❡♠ ✭❉❡s❤♣❛♥❞❡✱ ▼♦♥t❛♥❛r✐✱ ✷✵✶✸✮

❋♦r ❛♥② ☛❀ ☞❀ ✧ ❃ ✵✱ t❤❡r❡ ❡①✐sts ❈ ❂ ❈✭☛❀ ☞❀ ✧✮ ❃ ✵ s✉❝❤ t❤❛t t❤❡ ❢♦❧❧♦✇✐♥❣ ❤❛♣♣❡♥s ❢♦r s✐❣♥❛❧ t♦ ♥♦✐s❡ r❛t✐♦ ☞✱ ❛♥❞ ♣❂♥ ❂ ☛✳ ■❢ ❦ ✔ ❈♣♥✱ t❤❡♥✱ ✇✐t❤ ❤✐❣❤ ♣r♦❜❛❜✐❧✐t②✱

◮ ❦✈✄ ✈❦✷ ✔ ✧ ◮ ❜

◗ ❂ s✉♣♣✭✈✮

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✸ ✴ ✺✶

SLIDE 58

❈r✉❝✐❛❧ ❧❡♠♠❛✿ ❑❡r♥❡❧ r❛♥❞♦♠ ♠❛tr✐❝❡s

▲❡♠♠❛ ✭❉❡s❤♣❛♥❞❡✱ ▼♦♥t❛♥❛r✐✱ ✷✵✶✸✮

❆ss✉♠❡ ❩ ❂ ✭❩✐❥ ✮✐✔♥❀❥ ✔♣ ✇✐t❤ ❩✐❥ ✘✐✳✐✳❞✳ ◆✭✵❀ ✶❂♥✮✱ ♣❂♥ ✦ ☛✳ ❚❤❡♥✱ ✇✐t❤ ❤✐❣❤ ♣r♦❜❛❜✐❧✐t②

✌ ✌ ✌❙❚✜❂♣♥ ✏

❩❩❚ ❞✐❛❣✭❩❩❚✮

✑✌ ✌ ✌

✷ ✔ ❈✭☛✮ ✜ ✵✿✹✾ ✿

✔ ❈✭☛❀ ✜✮ ✐s ❡❛s②

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✹ ✴ ✺✶

SLIDE 59

❈r✉❝✐❛❧ ❧❡♠♠❛✿ ❑❡r♥❡❧ r❛♥❞♦♠ ♠❛tr✐❝❡s

▲❡♠♠❛ ✭❉❡s❤♣❛♥❞❡✱ ▼♦♥t❛♥❛r✐✱ ✷✵✶✸✮

❆ss✉♠❡ ❩ ❂ ✭❩✐❥ ✮✐✔♥❀❥ ✔♣ ✇✐t❤ ❩✐❥ ✘✐✳✐✳❞✳ ◆✭✵❀ ✶❂♥✮✱ ♣❂♥ ✦ ☛✳ ❚❤❡♥✱ ✇✐t❤ ❤✐❣❤ ♣r♦❜❛❜✐❧✐t②

✌ ✌ ✌❙❚✜❂♣♥ ✏

❩❩❚ ❞✐❛❣✭❩❩❚✮

✑✌ ✌ ✌

✷ ✔ ❈✭☛✮ ✜ ✵✿✹✾ ✿

✔ ❈✭☛❀ ✜✮ ✐s ❡❛s②

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✹ ✴ ✺✶

SLIDE 60

Pr♦♦❢

◮ ❙✭ ✁ ✮ ✑ ❙❚✜❂♣♥✭ ✁ ✮ ◮ ◆ ❂ ❙✭❩❩❚ ❞✐❛❣✭❩❩❚✮✮ ◮ ❚✧ ✒ ❙♣✶ ✒ R♣ ❛♥ ✧✲♥❡t✱ ❥❚✧❥ ✔ ✭✶✵❂✧✮♣✳

P

♥

s✉♣

②✷❙♣✶

❤②❀ ◆②✐ ✕ ✁

♦

✔ ❥❚✧❥ s✉♣

②✷❚✧

P

♥

❤②❀ ◆②✐ ✕ ✭✶ ✷✧✮✁

♦

❙✉✣❝✐❡♥t t♦ ♣r♦✈❡ t❤❛t s✉♣

②✷❚✧

P

♥

❤②❀ ◆②✐ ✕ ❈✜ ✵✿✹✾♦ ✔ ✷ ❡❝♥ ■♥ s✐♠♣❧❡ r❛♥❞♦♠ ♠❛tr✐① ❡♥s❡♠❜❧❡s✿ ❤②❀ ◆②✐ ✐s ▲✐♣s❝❤✐t③ ✐♥ ❩ ✮ ●❛✉ss✐❛♥ ✐s♦♣❡r✐♠❡tr②

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✺ ✴ ✺✶

SLIDE 61

Pr♦♦❢

◮ ❙✭ ✁ ✮ ✑ ❙❚✜❂♣♥✭ ✁ ✮ ◮ ◆ ❂ ❙✭❩❩❚ ❞✐❛❣✭❩❩❚✮✮ ◮ ❚✧ ✒ ❙♣✶ ✒ R♣ ❛♥ ✧✲♥❡t✱ ❥❚✧❥ ✔ ✭✶✵❂✧✮♣✳

P

♥

s✉♣

②✷❙♣✶

❤②❀ ◆②✐ ✕ ✁

♦

✔ ❥❚✧❥ s✉♣

②✷❚✧

P

♥

❤②❀ ◆②✐ ✕ ✭✶ ✷✧✮✁

♦

❙✉✣❝✐❡♥t t♦ ♣r♦✈❡ t❤❛t s✉♣

②✷❚✧

P

♥

❤②❀ ◆②✐ ✕ ❈✜ ✵✿✹✾♦ ✔ ✷ ❡❝♥ ■♥ s✐♠♣❧❡ r❛♥❞♦♠ ♠❛tr✐① ❡♥s❡♠❜❧❡s✿ ❤②❀ ◆②✐ ✐s ▲✐♣s❝❤✐t③ ✐♥ ❩ ✮ ●❛✉ss✐❛♥ ✐s♦♣❡r✐♠❡tr②

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✺ ✴ ✺✶

SLIDE 62

Pr♦♦❢

◮ ❙✭ ✁ ✮ ✑ ❙❚✜❂♣♥✭ ✁ ✮ ◮ ◆ ❂ ❙✭❩❩❚ ❞✐❛❣✭❩❩❚✮✮ ◮ ❚✧ ✒ ❙♣✶ ✒ R♣ ❛♥ ✧✲♥❡t✱ ❥❚✧❥ ✔ ✭✶✵❂✧✮♣✳

P

♥

s✉♣

②✷❙♣✶

❤②❀ ◆②✐ ✕ ✁

♦

✔ ❥❚✧❥ s✉♣

②✷❚✧

P

♥

❤②❀ ◆②✐ ✕ ✭✶ ✷✧✮✁

♦

❙✉✣❝✐❡♥t t♦ ♣r♦✈❡ t❤❛t s✉♣

②✷❚✧

P

♥

❤②❀ ◆②✐ ✕ ❈✜ ✵✿✹✾♦ ✔ ✷ ❡❝♥ ■♥ s✐♠♣❧❡ r❛♥❞♦♠ ♠❛tr✐① ❡♥s❡♠❜❧❡s✿ ❤②❀ ◆②✐ ✐s ▲✐♣s❝❤✐t③ ✐♥ ❩ ✮ ●❛✉ss✐❛♥ ✐s♦♣❡r✐♠❡tr②

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✺ ✴ ✺✶

SLIDE 63

▲❡t✬s tr② t❤❡ s❛♠❡ ❛♣♣r♦❛❝❤

❈♦❧✉♠♥s ♦❢ ❩✿ ❣✶❀ ❣✷❀ ✿ ✿ ✿ ❀ ❣♣ ✘ ◆✭✵❀ ■♥✂♥✮ ❤②❀ ◆②✐ ❂

❳

✐✻❂❥

②✐❙

✏❤❣✐❀ ❣❥ ✐

♥

✑

②❥ r❣✐❤②❀ ◆②✐ ❂ ✷②✐ ♥

❳

❥ ✷❬♣❪♥✐

❙✵✏❤❣✐❀ ❣❥ ✐ ♥

✑

❣❥ ②❥ Pr♦❜❧❡♠s✿

◮ ◆❡❡❞ ❦r❣✐❤②❀ ◆②✐❦✷ ✔ ❈✜ ✵✿✹✾ ◮ ❣❥ ✉♥❜♦✉♥❞❡❞ ◮ ②✐ ❝❛♥ ❜❡ ♣♣ t✐♠❡s ✐ts t②♣✐❝❛❧ ✈❛❧✉❡ ◮ ■❢ ✇❡ ✉s❡ ❥❙✵✭ ✁ ✮❥ ✔ ✶✱ ✇❡ ❧♦♦s❡ t❤❡ ❞❡♣❡♥❞❡♥❝❡ ✐♥ ✜

▲♦♦❦s ❤♦♣❡❧❡ss✦

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✻ ✴ ✺✶

SLIDE 64

▲❡t✬s tr② t❤❡ s❛♠❡ ❛♣♣r♦❛❝❤

❈♦❧✉♠♥s ♦❢ ❩✿ ❣✶❀ ❣✷❀ ✿ ✿ ✿ ❀ ❣♣ ✘ ◆✭✵❀ ■♥✂♥✮ ❤②❀ ◆②✐ ❂

❳

✐✻❂❥

②✐❙

✏❤❣✐❀ ❣❥ ✐

♥

✑

②❥ r❣✐❤②❀ ◆②✐ ❂ ✷②✐ ♥

❳

❥ ✷❬♣❪♥✐

❙✵✏❤❣✐❀ ❣❥ ✐ ♥

✑

❣❥ ②❥ Pr♦❜❧❡♠s✿

◮ ◆❡❡❞ ❦r❣✐❤②❀ ◆②✐❦✷ ✔ ❈✜ ✵✿✹✾ ◮ ❣❥ ✉♥❜♦✉♥❞❡❞ ◮ ②✐ ❝❛♥ ❜❡ ♣♣ t✐♠❡s ✐ts t②♣✐❝❛❧ ✈❛❧✉❡ ◮ ■❢ ✇❡ ✉s❡ ❥❙✵✭ ✁ ✮❥ ✔ ✶✱ ✇❡ ❧♦♦s❡ t❤❡ ❞❡♣❡♥❞❡♥❝❡ ✐♥ ✜

▲♦♦❦s ❤♦♣❡❧❡ss✦

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✻ ✴ ✺✶

SLIDE 65

▲❡t✬s tr② t❤❡ s❛♠❡ ❛♣♣r♦❛❝❤

❈♦❧✉♠♥s ♦❢ ❩✿ ❣✶❀ ❣✷❀ ✿ ✿ ✿ ❀ ❣♣ ✘ ◆✭✵❀ ■♥✂♥✮ ❤②❀ ◆②✐ ❂

❳

✐✻❂❥

②✐❙

✏❤❣✐❀ ❣❥ ✐

♥

✑

②❥ r❣✐❤②❀ ◆②✐ ❂ ✷②✐ ♥

❳

❥ ✷❬♣❪♥✐

❙✵✏❤❣✐❀ ❣❥ ✐ ♥

✑

❣❥ ②❥ Pr♦❜❧❡♠s✿

◮ ◆❡❡❞ ❦r❣✐❤②❀ ◆②✐❦✷ ✔ ❈✜ ✵✿✹✾ ◮ ❣❥ ✉♥❜♦✉♥❞❡❞ ◮ ②✐ ❝❛♥ ❜❡ ♣♣ t✐♠❡s ✐ts t②♣✐❝❛❧ ✈❛❧✉❡ ◮ ■❢ ✇❡ ✉s❡ ❥❙✵✭ ✁ ✮❥ ✔ ✶✱ ✇❡ ❧♦♦s❡ t❤❡ ❞❡♣❡♥❞❡♥❝❡ ✐♥ ✜

▲♦♦❦s ❤♦♣❡❧❡ss✦

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✻ ✴ ✺✶

SLIDE 66

▲❡t✬s tr② t❤❡ s❛♠❡ ❛♣♣r♦❛❝❤

❈♦❧✉♠♥s ♦❢ ❩✿ ❣✶❀ ❣✷❀ ✿ ✿ ✿ ❀ ❣♣ ✘ ◆✭✵❀ ■♥✂♥✮ ❤②❀ ◆②✐ ❂

❳

✐✻❂❥

②✐❙

✏❤❣✐❀ ❣❥ ✐

♥

✑

②❥ r❣✐❤②❀ ◆②✐ ❂ ✷②✐ ♥

❳

❥ ✷❬♣❪♥✐

❙✵✏❤❣✐❀ ❣❥ ✐ ♥

✑

❣❥ ②❥ Pr♦❜❧❡♠s✿

◮ ◆❡❡❞ ❦r❣✐❤②❀ ◆②✐❦✷ ✔ ❈✜ ✵✿✹✾ ◮ ❣❥ ✉♥❜♦✉♥❞❡❞ ◮ ②✐ ❝❛♥ ❜❡ ♣♣ t✐♠❡s ✐ts t②♣✐❝❛❧ ✈❛❧✉❡ ◮ ■❢ ✇❡ ✉s❡ ❥❙✵✭ ✁ ✮❥ ✔ ✶✱ ✇❡ ❧♦♦s❡ t❤❡ ❞❡♣❡♥❞❡♥❝❡ ✐♥ ✜

▲♦♦❦s ❤♦♣❡❧❡ss✦

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✻ ✴ ✺✶

SLIDE 67

▲❡t✬s tr② t❤❡ s❛♠❡ ❛♣♣r♦❛❝❤

❈♦❧✉♠♥s ♦❢ ❩✿ ❣✶❀ ❣✷❀ ✿ ✿ ✿ ❀ ❣♣ ✘ ◆✭✵❀ ■♥✂♥✮ ❤②❀ ◆②✐ ❂

❳

✐✻❂❥

②✐❙

✏❤❣✐❀ ❣❥ ✐

♥

✑

②❥ r❣✐❤②❀ ◆②✐ ❂ ✷②✐ ♥

❳

❥ ✷❬♣❪♥✐

❙✵✏❤❣✐❀ ❣❥ ✐ ♥

✑

❣❥ ②❥ Pr♦❜❧❡♠s✿

◮ ◆❡❡❞ ❦r❣✐❤②❀ ◆②✐❦✷ ✔ ❈✜ ✵✿✹✾ ◮ ❣❥ ✉♥❜♦✉♥❞❡❞ ◮ ②✐ ❝❛♥ ❜❡ ♣♣ t✐♠❡s ✐ts t②♣✐❝❛❧ ✈❛❧✉❡ ◮ ■❢ ✇❡ ✉s❡ ❥❙✵✭ ✁ ✮❥ ✔ ✶✱ ✇❡ ❧♦♦s❡ t❤❡ ❞❡♣❡♥❞❡♥❝❡ ✐♥ ✜

▲♦♦❦s ❤♦♣❡❧❡ss✦

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✻ ✴ ✺✶

SLIDE 68

▲❡t✬s tr② t❤❡ s❛♠❡ ❛♣♣r♦❛❝❤

❈♦❧✉♠♥s ♦❢ ❩✿ ❣✶❀ ❣✷❀ ✿ ✿ ✿ ❀ ❣♣ ✘ ◆✭✵❀ ■♥✂♥✮ ❤②❀ ◆②✐ ❂

❳

✐✻❂❥

②✐❙

✏❤❣✐❀ ❣❥ ✐

♥

✑

②❥ r❣✐❤②❀ ◆②✐ ❂ ✷②✐ ♥

❳

❥ ✷❬♣❪♥✐

❙✵✏❤❣✐❀ ❣❥ ✐ ♥

✑

❣❥ ②❥ Pr♦❜❧❡♠s✿

◮ ◆❡❡❞ ❦r❣✐❤②❀ ◆②✐❦✷ ✔ ❈✜ ✵✿✹✾ ◮ ❣❥ ✉♥❜♦✉♥❞❡❞ ◮ ②✐ ❝❛♥ ❜❡ ♣♣ t✐♠❡s ✐ts t②♣✐❝❛❧ ✈❛❧✉❡ ◮ ■❢ ✇❡ ✉s❡ ❥❙✵✭ ✁ ✮❥ ✔ ✶✱ ✇❡ ❧♦♦s❡ t❤❡ ❞❡♣❡♥❞❡♥❝❡ ✐♥ ✜

▲♦♦❦s ❤♦♣❡❧❡ss✦

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✻ ✴ ✺✶

SLIDE 69

▲❡t✬s tr② t❤❡ s❛♠❡ ❛♣♣r♦❛❝❤

❈♦❧✉♠♥s ♦❢ ❩✿ ❣✶❀ ❣✷❀ ✿ ✿ ✿ ❀ ❣♣ ✘ ◆✭✵❀ ■♥✂♥✮ ❤②❀ ◆②✐ ❂

❳

✐✻❂❥

②✐❙

✏❤❣✐❀ ❣❥ ✐

♥

✑

②❥ r❣✐❤②❀ ◆②✐ ❂ ✷②✐ ♥

❳

❥ ✷❬♣❪♥✐

❙✵✏❤❣✐❀ ❣❥ ✐ ♥

✑

❣❥ ②❥ Pr♦❜❧❡♠s✿

◮ ◆❡❡❞ ❦r❣✐❤②❀ ◆②✐❦✷ ✔ ❈✜ ✵✿✹✾ ◮ ❣❥ ✉♥❜♦✉♥❞❡❞ ◮ ②✐ ❝❛♥ ❜❡ ♣♣ t✐♠❡s ✐ts t②♣✐❝❛❧ ✈❛❧✉❡ ◮ ■❢ ✇❡ ✉s❡ ❥❙✵✭ ✁ ✮❥ ✔ ✶✱ ✇❡ ❧♦♦s❡ t❤❡ ❞❡♣❡♥❞❡♥❝❡ ✐♥ ✜

▲♦♦❦s ❤♦♣❡❧❡ss✦

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✻ ✴ ✺✶

SLIDE 70

▲❡t✬s tr② t❤❡ s❛♠❡ ❛♣♣r♦❛❝❤

❈♦❧✉♠♥s ♦❢ ❩✿ ❣✶❀ ❣✷❀ ✿ ✿ ✿ ❀ ❣♣ ✘ ◆✭✵❀ ■♥✂♥✮ ❤②❀ ◆②✐ ❂

❳

✐✻❂❥

②✐❙

✏❤❣✐❀ ❣❥ ✐

♥

✑

②❥ r❣✐❤②❀ ◆②✐ ❂ ✷②✐ ♥

❳

❥ ✷❬♣❪♥✐

❙✵✏❤❣✐❀ ❣❥ ✐ ♥

✑

❣❥ ②❥ Pr♦❜❧❡♠s✿

◮ ◆❡❡❞ ❦r❣✐❤②❀ ◆②✐❦✷ ✔ ❈✜ ✵✿✹✾ ◮ ❣❥ ✉♥❜♦✉♥❞❡❞ ◮ ②✐ ❝❛♥ ❜❡ ♣♣ t✐♠❡s ✐ts t②♣✐❝❛❧ ✈❛❧✉❡ ◮ ■❢ ✇❡ ✉s❡ ❥❙✵✭ ✁ ✮❥ ✔ ✶✱ ✇❡ ❧♦♦s❡ t❤❡ ❞❡♣❡♥❞❡♥❝❡ ✐♥ ✜

▲♦♦❦s ❤♦♣❡❧❡ss✦

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✻ ✴ ✺✶

SLIDE 71

■❞❡❛s ✭✶✮

②✐ ❝❛♥ ❜❡ ♣♥ t✐♠❡s ✐ts t②♣✐❝❛❧ ✈❛❧✉❡

◮ ❙❡♣❛r❛t❡ ❜✐❣ ❡♥tr✐❡s ♦❢ ② ✭❛❜♦✈❡ ❈❂♣♣✮ ◮ ❚❤❡r❡ ❛r❡ ❛t ♠♦st ♣❂❈ ❜✐❣ ❡♥tr✐❡s ◮ ❈♦♥tr♦❧ ♥♦r♠ ♦❢ ❛❧❧ ✭♣❂❈✮ ✂ ✭♣❂❈✮ s✉❜♠❛tr✐❝❡s

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✼ ✴ ✺✶

SLIDE 72

■❞❡❛s ✭✶✮

②✐ ❝❛♥ ❜❡ ♣♥ t✐♠❡s ✐ts t②♣✐❝❛❧ ✈❛❧✉❡

◮ ❙❡♣❛r❛t❡ ❜✐❣ ❡♥tr✐❡s ♦❢ ② ✭❛❜♦✈❡ ❈❂♣♣✮ ◮ ❚❤❡r❡ ❛r❡ ❛t ♠♦st ♣❂❈ ❜✐❣ ❡♥tr✐❡s ◮ ❈♦♥tr♦❧ ♥♦r♠ ♦❢ ❛❧❧ ✭♣❂❈✮ ✂ ✭♣❂❈✮ s✉❜♠❛tr✐❝❡s

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✼ ✴ ✺✶

SLIDE 73

■❞❡❛s ✭✷✮

r❣✐❤②❀ ◆②✐ ❂ ✷②✐ ♥

❳

❥ ✷❬♣❪♥✐

❙✵✏❤❣✐❀ ❣❥ ✐ ♥

✑

❣❥ ②❥ ❂ ❩❚σ✐✭②✮ ✇❤❡r❡ ❬σ✐✭②✮❪❥ ❂ ✷②✐ ♥ ❙✵✏❤❣✐❀ ❣❥ ✐ ♥

✑

②❥ Pr♦✈❡ t❤❛t✱ ✇✐t❤ ♦✈❡r✇❤❡❧♠✐♥❣ ♣r♦❜❛❜✐❧✐t②

◮ ❦❩❦✷ ✔❝♦♥st✳

✭❦♥♦✇♥✮

◮ ❦σ✐✭②✮❦✷ ✔ ❛✜ ✵✿✹✾

✭✇♦r❦✮

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✽ ✴ ✺✶

SLIDE 74

■❞❡❛s ✭✷✮

r❣✐❤②❀ ◆②✐ ❂ ✷②✐ ♥

❳

❥ ✷❬♣❪♥✐

❙✵✏❤❣✐❀ ❣❥ ✐ ♥

✑

❣❥ ②❥ ❂ ❩❚σ✐✭②✮ ✇❤❡r❡ ❬σ✐✭②✮❪❥ ❂ ✷②✐ ♥ ❙✵✏❤❣✐❀ ❣❥ ✐ ♥

✑

②❥ Pr♦✈❡ t❤❛t✱ ✇✐t❤ ♦✈❡r✇❤❡❧♠✐♥❣ ♣r♦❜❛❜✐❧✐t②

◮ ❦❩❦✷ ✔❝♦♥st✳

✭❦♥♦✇♥✮

◮ ❦σ✐✭②✮❦✷ ✔ ❛✜ ✵✿✹✾

✭✇♦r❦✮

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✽ ✴ ✺✶

SLIDE 75

❚❤r❡s❤♦❧❞ ❜❡❤❛✈✐♦r

0.5 1 1.5 2 0.2 0.4 0.6 0.8 1 k/√n Fraction of support recovered p = 625 p = 1250 p = 2500 p = 5000 0.5 1 1.5 2 0.2 0.4 0.6 0.8 1 k/√n Fraction of support recovered p = 625 p = 1250 p = 2500 p = 5000

❉✐❛❣♦♥❛❧ t❤r❡s❤♦❧❞✐♥❣ ❈♦✈❛r✐❛♥❝❡ t❤r❡s❤♦❧❞✐♥❣

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✹✾ ✴ ✺✶

SLIDE 76

❙♣❛rs✐t② ✐♥ ✇❛✈❡❧❡t ❞♦♠❛✐♥

1,000 2,000 3,000 4,000 −5 · 10−2 5 · 10−2 0.1 1,000 2,000 3,000 4,000 0.1 0.2 0.3 1,000 2,000 3,000 4,000 5 · 10−2 0.1 1,000 2,000 3,000 4,000 −5 · 10−2 5 · 10−2 0.1 1,000 2,000 3,000 4,000 5 · 10−2 0.1 1,000 2,000 3,000 4,000 5 · 10−2 0.1 1,000 2,000 3,000 4,000 −5 · 10−2 5 · 10−2 0.1 1,000 2,000 3,000 4,000 5 · 10−2 0.1 1,000 2,000 3,000 4,000 5 · 10−2 0.1 0 1 n = 1024 n = 1625 n = 2580 PCA DT CT

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✺✵ ✴ ✺✶

SLIDE 77

❈♦♥❝❧✉s✐♦♥✴❖♣❡♥ ♣r♦❜❧❡♠s

◮ ■t ✇♦✉❧❞ ❜❡ ♥✐❝❡ t♦ ✉♥❞❡rst❛♥❞ ❜❡tt❡r ❦❡r♥❡❧ r❛♥❞♦♠ ♠❛tr✐❝❡s✳ ◮ ❦ ❂ ✂✭♣♥✮✿ ❙tr♦♥❣❡r ❧♦✇❡r ❜♦✉♥❞s❄ ◮ ❯s❡ s♣❛rs✐✜❝❛t✐♦♥ t♦ ❛❝❝❡❧❡r❛t❡ t❤✐s ◮ ❖t❤❡r ❛❧❣♦r✐t❤♠s ❢♦r s♣❛rs❡ P❈❆✿ ❛s❦ ♠❡✳ ✳ ✳

❚❤❛♥❦s✦

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✺✶ ✴ ✺✶

SLIDE 78

❈♦♥❝❧✉s✐♦♥✴❖♣❡♥ ♣r♦❜❧❡♠s

◮ ■t ✇♦✉❧❞ ❜❡ ♥✐❝❡ t♦ ✉♥❞❡rst❛♥❞ ❜❡tt❡r ❦❡r♥❡❧ r❛♥❞♦♠ ♠❛tr✐❝❡s✳ ◮ ❦ ❂ ✂✭♣♥✮✿ ❙tr♦♥❣❡r ❧♦✇❡r ❜♦✉♥❞s❄ ◮ ❯s❡ s♣❛rs✐✜❝❛t✐♦♥ t♦ ❛❝❝❡❧❡r❛t❡ t❤✐s ◮ ❖t❤❡r ❛❧❣♦r✐t❤♠s ❢♦r s♣❛rs❡ P❈❆✿ ❛s❦ ♠❡✳ ✳ ✳

❚❤❛♥❦s✦

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✺✶ ✴ ✺✶

SLIDE 79

❈♦♥❝❧✉s✐♦♥✴❖♣❡♥ ♣r♦❜❧❡♠s

◮ ■t ✇♦✉❧❞ ❜❡ ♥✐❝❡ t♦ ✉♥❞❡rst❛♥❞ ❜❡tt❡r ❦❡r♥❡❧ r❛♥❞♦♠ ♠❛tr✐❝❡s✳ ◮ ❦ ❂ ✂✭♣♥✮✿ ❙tr♦♥❣❡r ❧♦✇❡r ❜♦✉♥❞s❄ ◮ ❯s❡ s♣❛rs✐✜❝❛t✐♦♥ t♦ ❛❝❝❡❧❡r❛t❡ t❤✐s ◮ ❖t❤❡r ❛❧❣♦r✐t❤♠s ❢♦r s♣❛rs❡ P❈❆✿ ❛s❦ ♠❡✳ ✳ ✳

❚❤❛♥❦s✦

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✺✶ ✴ ✺✶

SLIDE 80

❈♦♥❝❧✉s✐♦♥✴❖♣❡♥ ♣r♦❜❧❡♠s

◮ ■t ✇♦✉❧❞ ❜❡ ♥✐❝❡ t♦ ✉♥❞❡rst❛♥❞ ❜❡tt❡r ❦❡r♥❡❧ r❛♥❞♦♠ ♠❛tr✐❝❡s✳ ◮ ❦ ❂ ✂✭♣♥✮✿ ❙tr♦♥❣❡r ❧♦✇❡r ❜♦✉♥❞s❄ ◮ ❯s❡ s♣❛rs✐✜❝❛t✐♦♥ t♦ ❛❝❝❡❧❡r❛t❡ t❤✐s ◮ ❖t❤❡r ❛❧❣♦r✐t❤♠s ❢♦r s♣❛rs❡ P❈❆✿ ❛s❦ ♠❡✳ ✳ ✳

❚❤❛♥❦s✦

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✺✶ ✴ ✺✶

SLIDE 81

❈♦♥❝❧✉s✐♦♥✴❖♣❡♥ ♣r♦❜❧❡♠s

◮ ■t ✇♦✉❧❞ ❜❡ ♥✐❝❡ t♦ ✉♥❞❡rst❛♥❞ ❜❡tt❡r ❦❡r♥❡❧ r❛♥❞♦♠ ♠❛tr✐❝❡s✳ ◮ ❦ ❂ ✂✭♣♥✮✿ ❙tr♦♥❣❡r ❧♦✇❡r ❜♦✉♥❞s❄ ◮ ❯s❡ s♣❛rs✐✜❝❛t✐♦♥ t♦ ❛❝❝❡❧❡r❛t❡ t❤✐s ◮ ❖t❤❡r ❛❧❣♦r✐t❤♠s ❢♦r s♣❛rs❡ P❈❆✿ ❛s❦ ♠❡✳ ✳ ✳

❚❤❛♥❦s✦

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✺✶ ✴ ✺✶

SLIDE 82

❈♦♥❝❧✉s✐♦♥✴❖♣❡♥ ♣r♦❜❧❡♠s

◮ ■t ✇♦✉❧❞ ❜❡ ♥✐❝❡ t♦ ✉♥❞❡rst❛♥❞ ❜❡tt❡r ❦❡r♥❡❧ r❛♥❞♦♠ ♠❛tr✐❝❡s✳ ◮ ❦ ❂ ✂✭♣♥✮✿ ❙tr♦♥❣❡r ❧♦✇❡r ❜♦✉♥❞s❄ ◮ ❯s❡ s♣❛rs✐✜❝❛t✐♦♥ t♦ ❛❝❝❡❧❡r❛t❡ t❤✐s ◮ ❖t❤❡r ❛❧❣♦r✐t❤♠s ❢♦r s♣❛rs❡ P❈❆✿ ❛s❦ ♠❡✳ ✳ ✳

❚❤❛♥❦s✦

❆♥❞r❡❛ ▼♦♥t❛♥❛r✐ ✭❙t❛♥❢♦r❞✮ ❙♣❛rs❡ P❈❆ ▼❛② ✷✽✱ ✷✵✶✹ ✺✶ ✴ ✺✶