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SLIDE 1

❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts

❖✳ ❇❧❛③②✱ ●✳ ❋✉❝❤s❜❛✉❡r✱ ❉✳ P♦✐♥t❝❤❡✈❛❧✱ ❉✳ ❱❡r❣♥❛✉❞

❊◆❙ ✴ ❈◆❘❙ ✴ ■◆❘■❆

P❑❈ ✷✵✶✶

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✶ ✴ ✷✹

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SLIDE 2

❇r✐❡❢ ❖✈❡r✈✐❡✇

❈r②♣t♦❣r❛♣❤✐❝ ❚♦♦❧s

❖✉r ■♥st❛♥t✐❛t✐♦♥

❆♣♣❧✐❝❛t✐♦♥s

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✷ ✴ ✷✹

slide-3
SLIDE 3

❇r✐❡❢ ❖✈❡r✈✐❡✇

❈r②♣t♦❣r❛♣❤✐❝ ❚♦♦❧s

❖✉r ■♥st❛♥t✐❛t✐♦♥

❆♣♣❧✐❝❛t✐♦♥s

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✸ ✴ ✷✹

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SLIDE 4

❋♦r ❞❡ss❡rt✱ ✇❡ ❧❡t ♣❡♦♣❧❡ ✈♦t❡ ❈❤♦❝♦❧❛t❡ ❈❛❦❡ ❈❤❡❡s❡ ❈❛❦❡ ❋r✉✐t ❙❛❧❛❞ ❇r✉ss❡❧s ❙♣r♦✉t ❆❢t❡r ❝♦❧❧❡❝t✐♦♥✱ ✇❡ ❝♦✉♥t t❤❡ ♥✉♠❜❡r ♦❢ ❜❛❧❧♦ts✿ ❈❤♦❝♦❧❛t❡ ❈❛❦❡ ✶✷✸ ❈❤❡❡s❡ ❈❛❦❡ ✼✾ ❋r✉✐t ❙❛❧❛❞ ✹✷ ❇r✉ss❡❧s ❙♣r♦✉t ✶

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✹ ✴ ✷✹

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SLIDE 5

❆✉t❤❡♥t✐❝❛t✐♦♥

❖♥❧② ♣❡♦♣❧❡ ❛✉t❤♦r✐③❡❞ t♦ ✈♦t❡ s❤♦✉❧❞ ❜❡ ❛❜❧❡ t♦ ✈♦t❡ P❡♦♣❧❡ s❤♦✉❧❞ ❜❡ ❛❜❧❡ t♦ ✈♦t❡ ♦♥❧② ♦♥❝❡

❆♥♦♥②♠✐t②

❱♦t❡s s❤♦✉❧❞ ❜❡ ❛♥♦♥②♠♦✉s △ ❘❡❝❡✐♣t ❢r❡❡♥❡ss✿ Pr❡✈❡♥t ❱♦t❡ ❙❡❧❧✐♥❣

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✺ ✴ ✷✹

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SLIDE 6

❍♦♠♦♠♦r♣❤✐❝ ❊♥❝r②♣t✐♦♥ ❛♥❞ ❙✐❣♥❛t✉r❡ ❛♣♣r♦❛❝❤

❚❤❡ ✈♦t❡r ❣❡♥❡r❛t❡s ❤✐s ✈♦t❡ ✈✳ ❚❤❡ ✈♦t❡r ❡♥❝r②♣ts ✈ t♦ t❤❡ s❡r✈❡r ✐♥ ❝✳ ❚❤❡ ✈♦t❡r s✐❣♥s ❝ ❛♥❞ ♦✉t♣✉ts σ✳ (❝, σ) ✐s ❛ ❜❛❧❧♦t ✉♥✐q✉❡ ♣❡r ✈♦t❡r✱ ❛♥❞ ❛♥♦♥②♠♦✉s ❈♦✉♥t✐♥❣✿ ❣r❛♥t❡❞ ❤♦♠♦♠♦r♣❤✐❝ ❡♥❝r②♣t✐♦♥ ❈ = ❝✳ ❚❤❡ s❡r✈❡r ❞❡❝r②♣ts ❈✳

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✻ ✴ ✷✹

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SLIDE 7

❱♦t❡ ✈ ❝(✈) − − − − − − − − − − − → σ(❝; s) − − − − − − − − − − − →

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✼ ✴ ✷✹

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SLIDE 8

❱♦t❡ ✈ ❝(✈) − − − − − − − − − − − → ⇋ ❝′ ≡ ❝ ← − − − − − − − − − − −⇋ σ′(❝′; s′) − − − − − − − − − − − →

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✼ ✴ ✷✹

slide-9
SLIDE 9

❊✲❈❛s❤

W i t h d r a w D e p

  • s

i t Spend Seller User ❇❛♥❦

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✽ ✴ ✷✹

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SLIDE 10

❆♥♦♥②♠✐t②

❚❤❡ ❜❛♥❦ ❝❛♥♥♦t ❧✐♥❦ ❛ ✇✐t❤❞r❛✇❛❧ t♦ ❛ ❞❡♣♦s✐t

◆♦ ❞♦✉❜❧❡✲s♣❡♥❞✐♥❣

❆ ❝♦✐♥ s❤♦✉❧❞ ♥♦t ❜❡ ✉s❡❞ t✇✐❝❡

❉❡✜♥✐t✐♦♥ ✭❇❧✐♥❞ ❙✐❣♥❛t✉r❡✮

❆ ❜❧✐♥❞ s✐❣♥❛t✉r❡ ❛❧❧♦✇s ❛ ✉s❡r t♦ ❣❡t ❛ ♠❡ss❛❣❡ ♠ s✐❣♥❡❞ ❜② ❛♥ ❛✉t❤♦r✐t② ✐♥t♦ σ s♦ t❤❛t ✐t ❝❛♥♥♦t r❡❝♦❣♥✐③❡ ❧❛t❡r t❤❡ ♣❛✐r (♠, σ)✳

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✾ ✴ ✷✹

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SLIDE 11

❱♦t❡

❆ ✉s❡r s❤♦✉❧❞ ❜❡ ❛❜❧❡ t♦ ❡♥❝r②♣t ❛ ❜❛❧❧♦t✳ ❍❡ s❤♦✉❧❞ ❜❡ ❛❜❧❡ t♦ s✐❣♥ t❤✐s ❡♥❝r②♣t✐♦♥✳ ❘❡❝❡✐✈✐♥❣ t❤✐s ✈♦t❡✱ ♦♥❡ s❤♦✉❧❞ ❜❡ ❛❜❧❡ t♦ r❛♥❞♦♠✐③❡ ❢♦r ❘❡❝❡✐♣t✲❋r❡❡♥❡ss✳

❊✲❈❛s❤

❆ ✉s❡r s❤♦✉❧❞ ❜❡ ❛❜❧❡ t♦ ❡♥❝r②♣t ❛ t♦❦❡♥ ❚❤❡ ❜❛♥❦ s❤♦✉❧❞ ❜❡ ❛❜❧❡ t♦ s✐❣♥ ✐t ♣r♦✈✐❞✐♥❣ ❯♥❢♦r❣❡❛❜✐❧✐t② ❚❤✐s s✐❣♥❛t✉r❡ s❤♦✉❧❞ ♥♦✇ ❜❡ ❛❜❧❡ t♦ ❜❡ r❛♥❞♦♠✐③❡❞ t♦ ♣r♦✈✐❞❡ ❆♥♦♥②♠✐t②

❖✉r ❙♦❧✉t✐♦♥

❙❛♠❡ ✉♥❞❡r❧②✐♥❣ r❡q✉✐r❡♠❡♥ts❀ ❆❞✈❛♥❝❡ s❡❝✉r✐t② ♥♦t✐♦♥s ✐♥ ❜♦t❤ s❝❤❡♠❡s r❡q✉✐r❡s t♦ ❡①tr❛❝t s♦♠❡ ❦✐♥❞ ♦❢ s✐❣♥❛t✉r❡ ♦♥ t❤❡ ❛ss♦❝✐❛t❡❞ ♣❧❛✐♥t❡①t❀

  • ❡♥❡r❛❧ ❋r❛♠❡✇♦r❦ ❢♦r ❙✐❣♥❛t✉r❡ ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts✳

❈♦♠♠✉t❛t✐✈❡ ❡♥❝r②♣t✐♦♥ ✴ s✐❣♥❛t✉r❡✳

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✶✵ ✴ ✷✹

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SLIDE 12

❊①tr❛❝t❛❜❧❡ ❘❛♥❞♦♠✐③❛❜❧❡ ❙✐❣♥❛t✉r❡ ♦♥ ❈✐♣❤❡rt❡①ts

s′ ❞❦ r ♣❦, r ❞❦ s❦, ♣❦, ❝; s s❦; s r

, s

σ(❈) σ(▼) ❈ ▼ ❊♥❝r②♣tSE ❉❡❝r②♣tE r ❙✐❣❊①tSE ❙✐❣♥S ❙✐❣♥SE r′ ❘❛♥❞♦♠E ❘❛♥❞♦♠S ❘ ❛ ♥ ❞ ♦ ♠

S E

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✶✶ ✴ ✷✹

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SLIDE 13

❇r✐❡❢ ❖✈❡r✈✐❡✇

❈r②♣t♦❣r❛♣❤✐❝ ❚♦♦❧s

❖✉r ■♥st❛♥t✐❛t✐♦♥

❆♣♣❧✐❝❛t✐♦♥s

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✶✷ ✴ ✷✹

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SLIDE 14

❉❡✜♥✐t✐♦♥ ✭❈❉❍✮

  • ✐✈❡♥ ❣, ❣ ❛, ❤ ∈ G✸✱ ✐t ✐s ❤❛r❞ t♦ ❝♦♠♣✉t❡ ❤❛✳

❉❡✜♥✐t✐♦♥ ✭❉▲✐♥✮

  • ✐✈❡♥ ✉, ✈, ✇, ✉❛, ✈ ❜, ✇ ❝ ∈ G✻✱ ✐t ✐s ❤❛r❞ t♦ ❞❡❝✐❞❡ ✇❤❡t❤❡r ❝ = ❛ + ❜✳

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✶✸ ✴ ✷✹

slide-15
SLIDE 15

❉❡✜♥✐t✐♦♥ ✭❊♥❝r②♣t✐♦♥ ❙❝❤❡♠❡✿ ▲✐♥❡❛r ❊♥❝r②♣t✐♦♥✮

❙❡t✉♣(✶❦)✿ G, ✇ ∈ G❀ ❊❑❡②●❡♥✿ ♣❦ = (✉ = ✇ α, ✈ = ✇ β)✱ ❞❦ = (α, β)❀ ❊♥❝r②♣t(♣❦, ❳; r)✿ ❈ = (✉r✶, ✈ r✷, ❳ · ✇ r✶+r✷)❀ ❉❡❝r②♣t(❞❦, ❝)✿ ❳ = ❈✸/(❈ ✶/α

· ❈ ✶/β

)✳

r ♣❦, r ❞❦ ❈ F(▼) ❊♥❝r②♣tSE ❉❡❝r②♣tE r ′ ❘❛♥❞♦♠E

❯♥❧✐♥❦❛❜✐❧✐t② ♦♥ t❤❡ r❛♥❞♦♠✐③❛t✐♦♥✳

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✶✹ ✴ ✷✹

slide-16
SLIDE 16

s′ s❦; s σ(F) F(▼) ❙✐❣♥S ❘❛♥❞♦♠S

❉❡✜♥✐t✐♦♥ ✭❙✐❣♥❛t✉r❡ ❙❝❤❡♠❡✿ ❲❛t❡rs ❙✐❣♥❛t✉r❡✮

❙❡t✉♣(✶❦)✿ G, ❣, ❤ ∈ G, F❀ ❙❑❡②●❡♥✿ ✈❦ = ❣ ①✱ s❦ = ❤①❀ ❙✐❣♥(s❦, ♠; s)✿ σ = (s❦ · F(♠)s, ❣ s)❀ ❱❡r✐❢(✈❦, ♠, σ)✿ ❡(σ✶, ❣) = ❡(F(♠), σ✷) · ❡(❤, ✈❦)✳ s ❝❛♥ ❜❡ r❛♥❞♦♠✐③❡❞✳

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✶✺ ✴ ✷✹

slide-17
SLIDE 17

❉❡✜♥✐t✐♦♥ ✭●r♦t❤ ❙❛❤❛✐ ❈♦♠♠✐t♠❡♥ts✮

❙❡t✉♣(G)✿ ❝❦ = ✉✶, ✉✷, ✉✸ ❈♦♠✭❝❦✱ ❳❀ s✮✿ (✉s✶

✶,✶ · ✉s✸ ✸,✶, ✉s✷ ✷,✷ · ✉s✸ ✸,✷, ❳ · ❣ s✶+s✷ · ✉s✸ ✸,✸)❀

Pr♦✈❡✭❝❦✱ (❳, s)✱ (❊)✮✿ ♣r♦♦❢ φ❀ ❱❡r✐❢②✭❝❦✱ ❝❳✱ (❊)✱ φ✮✿ ❝❤❡❝❦s ✇❤❡t❤❡r φ ✐s ✈❛❧✐❞✳ Pr♦♣❡rt✐❡s✿ s♦✉♥❞♥❡ss ✇✐t♥❡ss✲✐♥❞✐st✐♥❣✉✐s❤❛❜✐❧✐t② ❘❛♥❞♦♠✐③❛❜✐❧✐t②✿ ❈♦♠♠✐t♠❡♥ts ❛♥❞ ♣r♦♦❢s ❛r❡ ♣✉❜❧✐❝❧② r❛♥❞♦♠✐③❛❜❧❡ ❛♥❞ ✉♥❧✐♥❦❛❜❧❡✳

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✶✻ ✴ ✷✹

slide-18
SLIDE 18

❉❡✜♥✐t✐♦♥ ✭●r♦t❤ ❙❛❤❛✐ ❈♦♠♠✐t♠❡♥ts✮

❙❡t✉♣(G)✿ ❝❦ = ✉✶, ✉✷, ✉✸ ❈♦♠✭❝❦✱ ❳❀ s✮✿ (✉s✶

✶,✶ · ✉s✸ ✸,✶, ✉s✷ ✷,✷ · ✉s✸ ✸,✷, ❳ · ❣ s✶+s✷ · ✉s✸ ✸,✸)❀

Pr♦✈❡✭❝❦✱ (❳, s)✱ (❊)✮✿ ♣r♦♦❢ φ❀ ❱❡r✐❢②✭❝❦✱ ❝❳✱ (❊)✱ φ✮✿ ❝❤❡❝❦s ✇❤❡t❤❡r φ ✐s ✈❛❧✐❞✳ Pr♦♣❡rt✐❡s✿ s♦✉♥❞♥❡ss ✇✐t♥❡ss✲✐♥❞✐st✐♥❣✉✐s❤❛❜✐❧✐t② ❘❛♥❞♦♠✐③❛❜✐❧✐t②✿ ❈♦♠♠✐t♠❡♥ts ❛♥❞ ♣r♦♦❢s ❛r❡ ♣✉❜❧✐❝❧② r❛♥❞♦♠✐③❛❜❧❡ ❛♥❞ ✉♥❧✐♥❦❛❜❧❡✳

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✶✻ ✴ ✷✹

slide-19
SLIDE 19

❉❡✜♥✐t✐♦♥ ✭●r♦t❤ ❙❛❤❛✐ ❈♦♠♠✐t♠❡♥ts✮

❙❡t✉♣(G)✿ ❝❦ = ✉✶, ✉✷, ✉✸ ❈♦♠✭❝❦✱ ❳❀ s✮✿ (✉s✶

✶,✶ · ✉s✸ ✸,✶, ✉s✷ ✷,✷ · ✉s✸ ✸,✷, ❳ · ❣ s✶+s✷ · ✉s✸ ✸,✸)❀

Pr♦✈❡✭❝❦✱ (❳, s)✱ (❊)✮✿ ♣r♦♦❢ φ❀ ❱❡r✐❢②✭❝❦✱ ❝❳✱ (❊)✱ φ✮✿ ❝❤❡❝❦s ✇❤❡t❤❡r φ ✐s ✈❛❧✐❞✳ Pr♦♣❡rt✐❡s✿ s♦✉♥❞♥❡ss ✇✐t♥❡ss✲✐♥❞✐st✐♥❣✉✐s❤❛❜✐❧✐t② ❘❛♥❞♦♠✐③❛❜✐❧✐t②✿ ❈♦♠♠✐t♠❡♥ts ❛♥❞ ♣r♦♦❢s ❛r❡ ♣✉❜❧✐❝❧② r❛♥❞♦♠✐③❛❜❧❡ ❛♥❞ ✉♥❧✐♥❦❛❜❧❡✳

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✶✻ ✴ ✷✹

slide-20
SLIDE 20

❇r✐❡❢ ❖✈❡r✈✐❡✇

❈r②♣t♦❣r❛♣❤✐❝ ❚♦♦❧s

❖✉r ■♥st❛♥t✐❛t✐♦♥

❆♣♣❧✐❝❛t✐♦♥s

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✶✼ ✴ ✷✹

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SLIDE 21

❉❡✜♥✐t✐♦♥ ✭❙✐❣♥❛t✉r❡ ❙❝❤❡♠❡✿❘❡✈✐s✐t❡❞ ❲❛t❡rs ❙✐❣♥❛t✉r❡✮

❙❡t✉♣(✶❦)✿ G, ❣, ❤ ∈ G❀ ❙❑❡②●❡♥✿ ✈❦ = ❣ ①✱ s❦ = ❤①❀ ❙✐❣♥(s❦, ♠, ❘✶, ❘✷, ❚; s)✿ ❖♥ ❛ ✈❛❧✐❞ t✉♣❧❡✿ (❡(❘✶❘✷, ✈❦) = ❡(❣, ❚)) ✿ (σ = (s❦(F(♠)❘✶❘✷)s, ❘s

✶, ❘s ✷, ❣ s)❀

❱❡r✐❢(✈❦, ♠, σ) ✿ ❡(σ✶, ❣) = ❡(F(♠)❘✶❘✷, σ✷).❡(❤, ✈❦), ❡(σ✸, ❣) = ❡(❘✶, σ✺), ❡(σ✹, ❣) = ❡(❘✷, σ✺)✳ ❆✈♦✐❞ s♦♠❡ ❜✐t ♣❡r ❜✐t ♣r♦♦❢s✳ ❙❛♠❡ s❡❝✉r✐t② ❛ss✉♠♣t✐♦♥ ❛s st❛♥❞❛r❞ ❲❛t❡rs ❙✐❣♥❛t✉r❡✳

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✶✽ ✴ ✷✹

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SLIDE 22

❈♦♠♠✉t❛t✐✈❡ ♣r♦♣❡rt✐❡s

❊♥❝r②♣t

❚♦ ❡♥❝r②♣t ❛ ♠❡ss❛❣❡ ♠✿ ❝ = (♣❦✶

r✶, ♣❦✷ r✷, F(♠) · ❣ r✶+r✷)

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✶✾ ✴ ✷✹

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SLIDE 23

❈♦♠♠✉t❛t✐✈❡ ♣r♦♣❡rt✐❡s

❊♥❝r②♣t

❚♦ ❡♥❝r②♣t ❛ ♠❡ss❛❣❡ ♠✿ ❝ = (♣❦✶

r✶, ♣❦✷ r✷, F(♠) · ❣ r✶+r✷)

❙✐❣♥ ◦ ❊♥❝r②♣t

❚♦ s✐❣♥ ❛ ✈❛❧✐❞ ❝✐♣❤❡rt❡①t ❝✶, ❝✷, ❝✸✱ ♦♥❡ ❤❛s s✐♠♣❧② t♦ ♣r♦❞✉❝❡✳ σ = (❝✶

s, ❝✷ s, s❦ · ❝✸ s, ♣❦✶ s, ♣❦✷ s, ❣ s) .

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✶✾ ✴ ✷✹

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SLIDE 24

❈♦♠♠✉t❛t✐✈❡ ♣r♦♣❡rt✐❡s

❊♥❝r②♣t

❚♦ ❡♥❝r②♣t ❛ ♠❡ss❛❣❡ ♠✿ ❝ = (♣❦✶

r✶, ♣❦✷ r✷, F(♠) · ❣ r✶+r✷)

❙✐❣♥ ◦ ❊♥❝r②♣t

❚♦ s✐❣♥ ❛ ✈❛❧✐❞ ❝✐♣❤❡rt❡①t ❝✶, ❝✷, ❝✸✱ ♦♥❡ ❤❛s s✐♠♣❧② t♦ ♣r♦❞✉❝❡✳ σ = (❝✶

s, ❝✷ s, s❦ · ❝✸ s, ♣❦✶ s, ♣❦✷ s, ❣ s) .

❉❡❝r②♣t ◦ ❙✐❣♥ ◦ ❊♥❝r②♣t

❯s✐♥❣ ❞❦✳ σ = (σ✸/σ❞❦✶

· σ❞❦✷

, σ✻) = (s❦ · F(♠)s, ❣ s) .

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✶✾ ✴ ✷✹

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SLIDE 25

❇r✐❡❢ ❖✈❡r✈✐❡✇

❈r②♣t♦❣r❛♣❤✐❝ ❚♦♦❧s

❖✉r ■♥st❛♥t✐❛t✐♦♥

❆♣♣❧✐❝❛t✐♦♥s

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✷✵ ✴ ✷✹

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SLIDE 26

❊✲❱♦t✐♥❣

r ♣❦, r s❦, ♣❦, ❝; s r

σ(❈) ❈ F(▼) ❊♥❝r②♣tSE ❙✐❣♥SE ❘ ❛ ♥ ❞ ♦ ♠

S E

❆✉t❤♦r✐t② ❯s❡r

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✷✶ ✴ ✷✹

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SLIDE 27

❇❧✐♥❞ ❙✐❣♥❛t✉r❡

s′ ❞❦ r ♣❦, r ❞❦ s❦, ♣❦, ❝; s σ(❈) σ(F) ❈ F(▼) ❊♥❝r②♣tSE ❉❡❝r②♣tE r ❙✐❣❊①tSE ❙✐❣♥SE ❘❛♥❞♦♠S ❙✐❣♥❡r ❯s❡r

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✷✷ ✴ ✷✹

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SLIDE 28

s′ ❞❦ r ♣❦, r ❞❦ s❦, ♣❦, ❝; s s❦; s r

, s

σ(❈) σ(▼) ❈ ▼ ❊♥❝r②♣tSE ❉❡❝r②♣tE r ❙✐❣❊①tSE ❙✐❣♥S ❙✐❣♥SE r′ ❘❛♥❞♦♠E ❘❛♥❞♦♠S ❘ ❛ ♥ ❞ ♦ ♠

S E

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✷✸ ✴ ✷✹

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SLIDE 29

◆❡✇ ♣r✐♠✐t✐✈❡ ✉♥❞❡r st❛♥❞❛r❞ ❛ss✉♠♣t✐♦♥✿ ❈♦♠♠✉t❛t✐✈❡ ♣r♦♣❡rt② ❜❡t✇❡❡♥ ❙✐❣♥❛t✉r❡ ❛♥❞ ❊♥❝r②♣t✐♦♥ ❖♥❡ ❘♦✉♥❞ ❇❧✐♥❞ ❙✐❣♥❛t✉r❡ ❖♥❡ ❘♦✉♥❞ ❘❡❝❡✐♣t ❋r❡❡ ❊✲❱♦t✐♥❣

❊✣❝✐❡♥❝②

❉▲✐♥ + ❈❉❍ : ✾ℓ + ✸✸ ●r♦✉♣ ❡❧❡♠❡♥ts✳ ❙❳❉❍ + ❈❉❍+ : ✻ℓ + ✶✺, ✻ℓ + ✼ ●r♦✉♣ ❡❧❡♠❡♥ts✳

❖✳ ❇❧❛③② ✭❊◆❙✮ ❙✐❣♥❛t✉r❡s ♦♥ ❘❛♥❞♦♠✐③❛❜❧❡ ❈✐♣❤❡rt❡①ts P❑❈ ✷✵✶✶ ✷✹ ✴ ✷✹