rrsr rsr - - PowerPoint PPT Presentation

SLIDE 1

❉②♥❛♠✐❝ ❇✉rr♦✇s✲❲❤❡❡❧❡r ❚r❛♥s❢♦r♠

▼✐❦❛ë❧ ❙❛❧s♦♥✱ ❚❤✐❡rr② ▲❡❝r♦q✱ ▼❛rt✐♥❡ ▲é♦♥❛r❞ ❛♥❞ ▲❛✉r❡♥t ▼♦✉❝❤❛r❞

❋✉♥❝t✐♦♥❛❧ ▼❡❞✐❝❛❧ ■♠❛❣✐♥❣ ❆❧❣♦r✐t❤♠ ❉❡s✐❣♥ ●r♦✉♣ ❇✐♦■♥❢♦r♠❛t✐❝s ●r♦✉♣ ▲■❚■❙ ❉♣t ❈♦♠♣✉t❡r ❙❝✐❡♥❝❡ ❯♥✐✈❡rs✐t② ♦❢ ❘♦✉❡♥ ❑✐♥❣✬s ❈♦❧❧❡❣❡ ▲♦♥❞♦♥ ❋r❛♥❝❡ ❊♥❣❧❛♥❞

❙tr✐♥❣♦❧♦❣② ✷✵✵✾ ❆ r❡s❡❛r❝❤ ✇♦r❦s❤♦♣ ♦❢ t❤❡ ■sr❛❡❧ ❙❝✐❡♥❝❡ ❋♦✉♥❞❛t✐♦♥

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✶✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 2

▼♦t✐✈❛t✐♦♥

❘❡❝❡♥t ❆❞✈❛♥❝❡s ✐♥ ❉❡❡♣ ❙❡q✉❡♥❝✐♥❣

■♥❞❡① ❧❛r❣❡ ❞②♥❛♠✐❝ t❡①ts ✭❣❡♥♦♠❡s✮ t♦ s♣❡❡❞ ✉♣ ❛♣♣r♦①✐♠❛t❡ ♣❛tt❡r♥ ♠❛t❝❤✐♥❣ ✭♠②r✐❛❞s ♦❢ s❤♦rt ♣❛tt❡r♥s✱ ❛t ♠♦st t✇♦ ❡rr♦rs✱ ✉♥✐q✉❡ ♦❝❝✉rr❡♥❝❡✮✳

❚✇♦ ♣♦ss✐❜❧❡ ❡✣❝✐❡♥t s♦❧✉t✐♦♥s

✭❙❛❧③❜❡r❣✱ ✷✵✵✾✮

❋▼✲■♥❞❡① ▲❩✲■♥❞❡①

❇❲❚ ✰ ❙✉✣① ❆rr❛② ▲❩✲❢❛❝t♦r✐s❛t✐♦♥ ❋❡rr❛❣✐♥❛✲▼❛♥③✐♥✐ ❋❖❈❙✬✵✵ ◆❛✈❛rr♦ ❙P■❘❊✬✵✹

❆❞✈❛♥t❛❣❡s ❈♦♠♣r❡ss❡❞ ✐♥❞❡①❡s ❆♣♣r♦①✐♠❛t❡ str✐♥❣ ♠❛t❝❤✐♥❣ ❉◆❆✱ ✺✵ ▼❜ ✶✾ t♦ ✸✹ ▼❇ ✹✹ ▼❇ ❖✉r ♠❛✐♥ ♠♦t✐✈❛t✐♦♥✿ ✐♥❞❡① ❧❛r❣❡ ❞②♥❛♠✐❝ t❡①ts

❙✐♥❣❧❡ ♠♦❞✐✜❝❛t✐♦♥ ✐♥ t❤❡ t❡①t ❈r❡❛t✐♦♥ ♦❢ ❛ ♥❡✇ ✐♥❞❡① ❢r♦♠ s❝r❛t❝❤❄

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✷✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 3

▼♦t✐✈❛t✐♦♥

❘❡❝❡♥t ❆❞✈❛♥❝❡s ✐♥ ❉❡❡♣ ❙❡q✉❡♥❝✐♥❣

■♥❞❡① ❧❛r❣❡ ❞②♥❛♠✐❝ t❡①ts ✭❣❡♥♦♠❡s✮ t♦ s♣❡❡❞ ✉♣ ❛♣♣r♦①✐♠❛t❡ ♣❛tt❡r♥ ♠❛t❝❤✐♥❣ ✭♠②r✐❛❞s ♦❢ s❤♦rt ♣❛tt❡r♥s✱ ❛t ♠♦st t✇♦ ❡rr♦rs✱ ✉♥✐q✉❡ ♦❝❝✉rr❡♥❝❡✮✳

❚✇♦ ♣♦ss✐❜❧❡ ❡✣❝✐❡♥t s♦❧✉t✐♦♥s

✭❙❛❧③❜❡r❣✱ ✷✵✵✾✮ →

❋▼✲■♥❞❡① ▲❩✲■♥❞❡①

❇❲❚ ✰ ❙✉✣① ❆rr❛② ▲❩✲❢❛❝t♦r✐s❛t✐♦♥ ❋❡rr❛❣✐♥❛✲▼❛♥③✐♥✐ ❋❖❈❙✬✵✵ ◆❛✈❛rr♦ ❙P■❘❊✬✵✹

❆❞✈❛♥t❛❣❡s ❈♦♠♣r❡ss❡❞ ✐♥❞❡①❡s ❆♣♣r♦①✐♠❛t❡ str✐♥❣ ♠❛t❝❤✐♥❣ ❉◆❆✱ ✺✵ ▼❜ ✶✾ t♦ ✸✹ ▼❇ ✹✹ ▼❇ ❖✉r ♠❛✐♥ ♠♦t✐✈❛t✐♦♥✿ ✐♥❞❡① ❧❛r❣❡ ❞②♥❛♠✐❝ t❡①ts

❙✐♥❣❧❡ ♠♦❞✐✜❝❛t✐♦♥ ✐♥ t❤❡ t❡①t ❈r❡❛t✐♦♥ ♦❢ ❛ ♥❡✇ ✐♥❞❡① ❢r♦♠ s❝r❛t❝❤❄

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✷✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 4

▼♦t✐✈❛t✐♦♥

❘❡❝❡♥t ❆❞✈❛♥❝❡s ✐♥ ❉❡❡♣ ❙❡q✉❡♥❝✐♥❣

■♥❞❡① ❧❛r❣❡ ❞②♥❛♠✐❝ t❡①ts ✭❣❡♥♦♠❡s✮ t♦ s♣❡❡❞ ✉♣ ❛♣♣r♦①✐♠❛t❡ ♣❛tt❡r♥ ♠❛t❝❤✐♥❣ ✭♠②r✐❛❞s ♦❢ s❤♦rt ♣❛tt❡r♥s✱ ❛t ♠♦st t✇♦ ❡rr♦rs✱ ✉♥✐q✉❡ ♦❝❝✉rr❡♥❝❡✮✳

❚✇♦ ♣♦ss✐❜❧❡ ❡✣❝✐❡♥t s♦❧✉t✐♦♥s

✭❙❛❧③❜❡r❣✱ ✷✵✵✾✮ →

❋▼✲■♥❞❡① ▲❩✲■♥❞❡①

❇❲❚ ✰ ❙✉✣① ❆rr❛② ▲❩✲❢❛❝t♦r✐s❛t✐♦♥ ❋❡rr❛❣✐♥❛✲▼❛♥③✐♥✐ ❋❖❈❙✬✵✵ ◆❛✈❛rr♦ ❙P■❘❊✬✵✹

❆❞✈❛♥t❛❣❡s ❈♦♠♣r❡ss❡❞ ✐♥❞❡①❡s ❆♣♣r♦①✐♠❛t❡ str✐♥❣ ♠❛t❝❤✐♥❣ ❉◆❆✱ ✺✵ ▼❜ ✶✾ t♦ ✸✹ ▼❇ ✹✹ ▼❇ ❖✉r ♠❛✐♥ ♠♦t✐✈❛t✐♦♥✿ ✐♥❞❡① ❧❛r❣❡ ❞②♥❛♠✐❝ t❡①ts

❙✐♥❣❧❡ ♠♦❞✐✜❝❛t✐♦♥ ✐♥ t❤❡ t❡①t → ❈r❡❛t✐♦♥ ♦❢ ❛ ♥❡✇ ✐♥❞❡① ❢r♦♠ s❝r❛t❝❤❄

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✷✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 5

❖✉r ❝❤♦✐❝❡

❋▼✲■♥❞❡①✿ ♠♦r❡ ❡✣❝✐❡♥t ❛♥❞ ♣r♦❜❛❜❧② ✭❄✮ ❡❛s✐❡r t♦ ✉♣❞❛t❡ ❇✉rr♦✇s✲❲❤❡❡❧❡r ❚r❛♥s❢♦r♠ ❙❛♠♣❧❡s ♦❢ t❤❡ s✉✣① ❛rr❛②

❇❲❚ ✐s ✉s❡❞ t♦ q✉✐❝❦❧②✿ r❡tr✐❡✈❡ t❤❡ ♦r✐❣✐♥❛❧ t❡①t❀ s❡❛r❝❤ ❢♦r ♣❛tt❡r♥s✳ ❲❡ ♥❡❡❞ t❤❡ ✇❤♦❧❡ str✉❝t✉r❡❀ ❙❆ ✐s ✉s❡❞ t♦ q✉✐❝❦❧②✿ ✜♥❞ t❤❡ ♣♦s✐t✐♦♥ ♦❢ ❡❛❝❤ ♦❝❝✉rr❡♥❝❡ ♦❢ ❛ ♣❛tt❡r♥✳ ❲❡ ❝❛♥ s❛♠♣❧❡ t❤❡ ❙❆ ❛♥❞ r❡❝♦✈❡r t❤❡ ♠✐ss✐♥❣ ✈❛❧✉❡s✳

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✸✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 6

❇✉rr♦✇s✲❲❤❡❡❧❡r ❚r❛♥s❢♦r♠ ♦❢ ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❚❤❡ ❜✐❣ ♣✐❝t✉r❡ ❚❤❡ ❇✉rr♦✇s✲❲❤❡❡❧❡r ❚r❛♥s❢♦r♠ ✐s ❛ ♣❡r♠✉t❛t✐♦♥ ♦❢ ❛ t❡①t ❚ t❤❛t ❡❛s❡s t❤❡ ❝♦♠♣r❡ss✐♦♥ ♦❢ ❚✳

✉♥s♦rt❡❞ ❝②❝❧✐❝ s❤✐❢ts ✵ ❈ ❚ ❈ ❚ ● ❈ ✩ ✶ ❚ ❈ ❚ ● ❈ ✩ ❈ ✷ ❈ ❚ ● ❈ ✩ ❈ ❚ ✸ ❚ ● ❈ ✩ ❈ ❚ ❈ ✹ ● ❈ ✩ ❈ ❚ ❈ ❚ ✺ ❈ ✩ ❈ ❚ ❈ ❚ ● ✻ ✩ ❈ ❚ ❈ ❚ ● ❈ s♦rt❡❞ ❝②❝❧✐❝ s❤✐❢ts✱ ❇❲❚ ❋ ▲ ✵ ✩ ❈ ❚ ❈ ❚ ● ❈ ✶ ❈ ✩ ❈ ❚ ❈ ❚ ● ✷ ❈ ❚ ❈ ❚ ● ❈ ✩ ✸ ❈ ❚ ● ❈ ✩ ❈ ❚ ✹ ● ❈ ✩ ❈ ❚ ❈ ❚ ✺ ❚ ❈ ❚ ● ❈ ✩ ❈ ✻ ❚ ● ❈ ✩ ❈ ❚ ❈

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✹✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 7

❇✉rr♦✇s✲❲❤❡❡❧❡r ❚r❛♥s❢♦r♠ ♦❢ ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❚❤❡ ❜✐❣ ♣✐❝t✉r❡ ❚❤❡ ❇✉rr♦✇s✲❲❤❡❡❧❡r ❚r❛♥s❢♦r♠ ✐s ❛ ♣❡r♠✉t❛t✐♦♥ ♦❢ ❛ t❡①t ❚ t❤❛t ❡❛s❡s t❤❡ ❝♦♠♣r❡ss✐♦♥ ♦❢ ❚✳

✉♥s♦rt❡❞ ❝②❝❧✐❝ s❤✐❢ts ✵ ❈ ❚ ❈ ❚ ● ❈ ✩ ✶ ❚ ❈ ❚ ● ❈ ✩ ❈ ✷ ❈ ❚ ● ❈ ✩ ❈ ❚ ✸ ❚ ● ❈ ✩ ❈ ❚ ❈ ✹ ● ❈ ✩ ❈ ❚ ❈ ❚ ✺ ❈ ✩ ❈ ❚ ❈ ❚ ● ✻ ✩ ❈ ❚ ❈ ❚ ● ❈ s♦rt❡❞ ❝②❝❧✐❝ s❤✐❢ts✱ ❇❲❚ ❋ ▲ ✵ ✩ ❈ ❚ ❈ ❚ ● ❈ ✶ ❈ ✩ ❈ ❚ ❈ ❚ ● ✷ ❈ ❚ ❈ ❚ ● ❈ ✩ ✸ ❈ ❚ ● ❈ ✩ ❈ ❚ ✹ ● ❈ ✩ ❈ ❚ ❈ ❚ ✺ ❚ ❈ ❚ ● ❈ ✩ ❈ ✻ ❚ ● ❈ ✩ ❈ ❚ ❈

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✹✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 8

❇✉rr♦✇s✲❲❤❡❡❧❡r ❚r❛♥s❢♦r♠ ♦❢ ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❚❤❡ ❜✐❣ ♣✐❝t✉r❡ ❚❤❡ ❇✉rr♦✇s✲❲❤❡❡❧❡r ❚r❛♥s❢♦r♠ ✐s ❛ ♣❡r♠✉t❛t✐♦♥ ♦❢ ❛ t❡①t ❚ t❤❛t ❡❛s❡s t❤❡ ❝♦♠♣r❡ss✐♦♥ ♦❢ ❚✳

✉♥s♦rt❡❞ ❝②❝❧✐❝ s❤✐❢ts ✵ ❈ ❚ ❈ ❚ ● ❈ ✩ ✶ ❚ ❈ ❚ ● ❈ ✩ ❈ ✷ ❈ ❚ ● ❈ ✩ ❈ ❚ ✸ ❚ ● ❈ ✩ ❈ ❚ ❈ ✹ ● ❈ ✩ ❈ ❚ ❈ ❚ ✺ ❈ ✩ ❈ ❚ ❈ ❚ ● ✻ ✩ ❈ ❚ ❈ ❚ ● ❈ s♦rt❡❞ ❝②❝❧✐❝ s❤✐❢ts✱ ❇❲❚ ❋ ▲ ✵ ✩ ❈ ❚ ❈ ❚ ● ❈ ✶ ❈ ✩ ❈ ❚ ❈ ❚ ● ✷ ❈ ❚ ❈ ❚ ● ❈ ✩ ✸ ❈ ❚ ● ❈ ✩ ❈ ❚ ✹ ● ❈ ✩ ❈ ❚ ❈ ❚ ✺ ❚ ❈ ❚ ● ❈ ✩ ❈ ✻ ❚ ● ❈ ✩ ❈ ❚ ❈

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✹✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 9

❇✉rr♦✇s✲❲❤❡❡❧❡r ❚r❛♥s❢♦r♠ ♦❢ ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❚❤❡ ❜✐❣ ♣✐❝t✉r❡ ❚❤❡ ❇✉rr♦✇s✲❲❤❡❡❧❡r ❚r❛♥s❢♦r♠ ✐s ❛ ♣❡r♠✉t❛t✐♦♥ ♦❢ ❛ t❡①t ❚ t❤❛t ❡❛s❡s t❤❡ ❝♦♠♣r❡ss✐♦♥ ♦❢ ❚✳

✉♥s♦rt❡❞ ❝②❝❧✐❝ s❤✐❢ts ✵ ❈ ❚ ❈ ❚ ● ❈ ✩ ✶ ❚ ❈ ❚ ● ❈ ✩ ❈ ✷ ❈ ❚ ● ❈ ✩ ❈ ❚ ✸ ❚ ● ❈ ✩ ❈ ❚ ❈ ✹

• ❈ ✩ ❈ ❚ ❈ ❚

✺ ❈ ✩ ❈ ❚ ❈ ❚ ● ✻ ✩ ❈ ❚ ❈ ❚ ● ❈ s♦rt❡❞ ❝②❝❧✐❝ s❤✐❢ts✱ ❇❲❚ ❛♥❞ s✉✣① ❛rr❛② ❋ ▲ ✵ ✩ ❈ ❚ ❈ ❚ ● ❈ ✶ ❈ ✩ ❈ ❚ ❈ ❚ ● ✷ ❈ ❚ ❈ ❚ ● ❈ ✩ ✸ ❈ ❚ ● ❈ ✩ ❈ ❚ ✹ ● ❈ ✩ ❈ ❚ ❈ ❚ ✺ ❚ ❈ ❚ ● ❈ ✩ ❈ ✻ ❚ ● ❈ ✩ ❈ ❚ ❈ ❙❆ ✻ ✺ ✵ ✷ ✹ ✶ ✸

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✹✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 10

❇✉rr♦✇s✲❲❤❡❡❧❡r ❚r❛♥s❢♦r♠ ♦❢ ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❚❤❡ ❜✐❣ ♣✐❝t✉r❡ ❚❤❡ ❇✉rr♦✇s✲❲❤❡❡❧❡r ❚r❛♥s❢♦r♠ ✐s ❛ ♣❡r♠✉t❛t✐♦♥ ♦❢ ❛ t❡①t ❚ t❤❛t ❡❛s❡s t❤❡ ❝♦♠♣r❡ss✐♦♥ ♦❢ ❚✳

✉♥s♦rt❡❞ ❝②❝❧✐❝ s❤✐❢ts ✵ ❈ ❚ ❈ ❚ ● ❈ ✩ ✶ ❚ ❈ ❚ ● ❈ ✩ ❈ ✷ ❈ ❚ ● ❈ ✩ ❈ ❚ ✸ ❚ ● ❈ ✩ ❈ ❚ ❈ ✹

• ❈ ✩ ❈ ❚ ❈ ❚

✺ ❈ ✩ ❈ ❚ ❈ ❚ ● ✻ ✩ ❈ ❚ ❈ ❚ ● ❈ s♦rt❡❞ ❝②❝❧✐❝ s❤✐❢ts✱ ❇❲❚ ❛♥❞ s✉✣① ❛rr❛② ❋ ▲ ✵ ✩ ❈ ❚ ❈ ❚ ● ❈ ✶ ❈ ✩ ❈ ❚ ❈ ❚ ● ✷ ❈ ❚ ❈ ❚ ● ❈ ✩ ✸ ❈ ❚ ● ❈ ✩ ❈ ❚ ✹ ● ❈ ✩ ❈ ❚ ❈ ❚ ✺ ❚ ❈ ❚ ● ❈ ✩ ❈ ✻ ❚ ● ❈ ✩ ❈ ❚ ❈ ❙❆ ■❙❆ ✻ ✷ ✺ ✺ ✵ ✸ ✷ ✻ ✹ ✹ ✶ ✶ ✸ ✵

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✹✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 11

❲❤✐❝❤ ❝♦❧✉♠♥ ❞♦ ✇❡ ❤❛✈❡ t♦ ❝♦♥s✐❞❡r❄

❋✐rst ❝♦❧✉♠♥ ❋ = ✩ ❈ ❈ ❈ ● ❚ ❚ ❣❛t❤❡rs ✐❞❡♥t✐❝❛❧ s②♠❜♦❧s❀ ❡❛s② t♦ ❝♦♠♣r❡ss → ✩r✸❈●r✷❚ ✭♥❛✐✈❡❧②✮❀ r❡❝♦✈❡r✐♥❣ ❚ ❢r♦♠ ❋ ✐s ✐♠♣♦ss✐❜❧❡✳ ▲❛st ❝♦❧✉♠♥ ▲ ❈ ● ✩ ❚ ❚ ❈ ❈ ❤❛s ❛ t❡♥❞❛♥❝② t♦ ❝r❡❛t❡ ♣❛❝❦❡ts ♦❢ ✐❞❡♥t✐❝❛❧ s②♠❜♦❧s✿ ❡❛s❡s ❝♦♠♣r❡ss✐♦♥❀ ✐s r❡❝♦✈❡r✐♥❣ ❚ ❢r♦♠ ▲ ♣♦ss✐❜❧❡❄ ❲❡ ✇✐❧❧ s❡❡ t❤❛t ❧❛t❡r ♦♥✳✳✳

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✺✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 12

❲❤✐❝❤ ❝♦❧✉♠♥ ❞♦ ✇❡ ❤❛✈❡ t♦ ❝♦♥s✐❞❡r❄

❋✐rst ❝♦❧✉♠♥ ❋ = ✩ ❈ ❈ ❈ ● ❚ ❚ ✭♥♦ s♦rr②✮ ❣❛t❤❡rs ✐❞❡♥t✐❝❛❧ s②♠❜♦❧s❀ ❡❛s② t♦ ❝♦♠♣r❡ss → ✩r✸❈●r✷❚ ✭♥❛✐✈❡❧②✮❀ r❡❝♦✈❡r✐♥❣ ❚ ❢r♦♠ ❋ ✐s ✐♠♣♦ss✐❜❧❡✳ ▲❛st ❝♦❧✉♠♥ ▲ = ❈ ● ✩ ❚ ❚ ❈ ❈ ❤❛s ❛ t❡♥❞❛♥❝② t♦ ❝r❡❛t❡ ♣❛❝❦❡ts ♦❢ ✐❞❡♥t✐❝❛❧ s②♠❜♦❧s✿ ❡❛s❡s ❝♦♠♣r❡ss✐♦♥❀ ✐s r❡❝♦✈❡r✐♥❣ ❚ ❢r♦♠ ▲ ♣♦ss✐❜❧❡❄ ❲❡ ✇✐❧❧ s❡❡ t❤❛t ❧❛t❡r ♦♥✳✳✳

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✺✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 13

❋▼✲✐♥❞❡①✿ ❛ ❞②♥❛♠✐❝ ❞❛t❛ str✉❝t✉r❡❄

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❇❲❚ ❊❛s② ✭▲❛✉r❡♥t✦✮ ❇❲❚✭❈❚❈❚●❈✩✮ = ❈ ● ✩ ❚ ❚ ❈ ❈ ❇❲❚✭❈❚●❈❚●❈✩✮ = ❈ ● ● ✩ ❚ ❚ ❈ ❈ ❙✉✣① ❆rr❛② ❍❛r❞ ✭▼✐❦❛ë❧✦✮ ❙❆✭❈❚❈❚●❈✩✮ ✻ ✺ ✵ ✷ ✹ ✶ ✸ ❙❆✭❈❚●❈❚●❈✩✮ ✼ ✻ ✸ ✵ ✺ ✷ ✹ ✶ ❇❲❚ ✉♣❞❛t❡ ❧♦♦❦s ❡❛s✐❡r t❤❛♥ ❙❆ ✉♣❞❛t❡ ❇❲❚ ❛♥❞ ❙❆ ❛r❡ str♦♥❣❧② r❡❧❛t❡❞❀ ❇❲❚ ✉♣❞❛t❡ ✇✐❧❧ ❤❡❧♣ ❢♦r ❙❆ ✉♣❞❛t❡✳

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✻✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 14

❋▼✲✐♥❞❡①✿ ❛ ❞②♥❛♠✐❝ ❞❛t❛ str✉❝t✉r❡❄

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❇❲❚ ❊❛s② ✭▲❛✉r❡♥t✦✮ ❇❲❚✭❈❚❈❚●❈✩✮ = ❈ ● ✩ ❚ ❚ ❈ ❈ ❇❲❚✭❈❚●❈❚●❈✩✮ = ❈ ● ● ✩ ❚ ❚ ❈ ❈ ❙✉✣① ❆rr❛② ❍❛r❞ ✭▼✐❦❛ë❧✦✮ ❙❆✭❈❚❈❚●❈✩✮ = ✻ ✺ ✵ ✷ ✹ ✶ ✸ ❙❆✭❈❚●❈❚●❈✩✮ = ✼ ✻ ✸ ✵ ✺ ✷ ✹ ✶ ❇❲❚ ✉♣❞❛t❡ ❧♦♦❦s ❡❛s✐❡r t❤❛♥ ❙❆ ✉♣❞❛t❡ ❇❲❚ ❛♥❞ ❙❆ ❛r❡ str♦♥❣❧② r❡❧❛t❡❞❀ ❇❲❚ ✉♣❞❛t❡ ✇✐❧❧ ❤❡❧♣ ❢♦r ❙❆ ✉♣❞❛t❡✳

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✻✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 15

❋▼✲✐♥❞❡①✿ ❛ ❞②♥❛♠✐❝ ❞❛t❛ str✉❝t✉r❡❄

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❇❲❚ ❊❛s② ✭▲❛✉r❡♥t✦✮ ❇❲❚✭❈❚❈❚●❈✩✮ = ❈ ● ✩ ❚ ❚ ❈ ❈ ❇❲❚✭❈❚●❈❚●❈✩✮ = ❈ ● ● ✩ ❚ ❚ ❈ ❈ ❙✉✣① ❆rr❛② ❍❛r❞ ✭▼✐❦❛ë❧✦✮ ❙❆✭❈❚❈❚●❈✩✮ = ✻ ✺ ✵ ✷ ✹ ✶ ✸ ❙❆✭❈❚●❈❚●❈✩✮ = ✼ ✻ ✸ ✵ ✺ ✷ ✹ ✶ ❇❲❚ ✉♣❞❛t❡ ❧♦♦❦s ❡❛s✐❡r t❤❛♥ ❙❆ ✉♣❞❛t❡ ❇❲❚ ❛♥❞ ❙❆ ❛r❡ str♦♥❣❧② r❡❧❛t❡❞❀ ❇❲❚ ✉♣❞❛t❡ ✇✐❧❧ ❤❡❧♣ ❢♦r ❙❆ ✉♣❞❛t❡✳

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✻✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 16

❋▼✲✐♥❞❡①✿ ❛ ❞②♥❛♠✐❝ ❞❛t❛ str✉❝t✉r❡❄

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❇❲❚ ❊❛s② ✭❍✉♠✱ ❧❡t ♠❡ t❤✐♥❦ ❛❜♦✉t ✐t✦✮ ❇❲❚✭❈❚❈❚●❈✩✮ = ❈ ● ✩ ❚ ❚ ❈ ❈ ❇❲❚✭❈❚●❈❚●❈✩✮ = ❈ ● ● ✩ ❚ ❚ ❈ ❈ ❈♦♥❝❡♣t✉❛❧ ♠❛tr✐❝❡s

❋ ▲ ✵ ✩ ❈ ❚ ❈ ❚ ● ❈ ✶ ❈ ✩ ❈ ❚ ❈ ❚ ● ✷ ❈ ❚ ❈ ❚ ● ❈ ✩ ✸ ❈ ❚ ● ❈ ✩ ❈ ❚ ✹ ● ❈ ✩ ❈ ❚ ❈ ❚ ✺ ❚ ❈ ❚ ● ❈ ✩ ❈ ✻ ❚ ● ❈ ✩ ❈ ❚ ❈ ❋ ▲ ✵ ✩ ❈ ❚ ● ❈ ❚ ● ❈ ✶ ❈ ✩ ❈ ❚ ● ❈ ❚

• ✷ ❈ ❚ ● ❈

✩ ❈ ❚ ● ✸ ❈ ❚ ● ❈ ❚ ● ❈ ✩ ✹ ● ❈ ✩ ❈ ❚ ● ❈ ❚ ✺ ● ❈ ❚ ● ❈ ✩ ❈ ❚ ✻ ❚ ● ❈ ✩ ❈ ❚ ● ❈ ✼ ❚ ● ❈ ❚ ● ❈ ✩ ❈

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✼✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 17

❋▼✲✐♥❞❡①✿ ❛ ❞②♥❛♠✐❝ ❞❛t❛ str✉❝t✉r❡❄

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❇❲❚ ❊❛s② ✭❍✉♠✱ ❧❡t ♠❡ t❤✐♥❦ ❛❜♦✉t ✐t✦✮ ❇❲❚✭❈❚❈❚●❈✩✮ = ❈ ● ✩ ❚ ❚ ❈ ❈ ❇❲❚✭❈❚●❈❚●❈✩✮ = ❈ ● ● ✩ ❚ ❚ ❈ ❈ ❈♦♥❝❡♣t✉❛❧ ♠❛tr✐❝❡s

❋ ▲ ✵ ✩ ❈ ❚ ❈ ❚ ● ❈ ✶ ❈ ✩ ❈ ❚ ❈ ❚ ● ✷ ❈ ❚ ❈ ❚ ● ❈ ✩ ✸ ❈ ❚ ● ❈ ✩ ❈ ❚ ✹ ● ❈ ✩ ❈ ❚ ❈ ❚ ✺ ❚ ❈ ❚ ● ❈ ✩ ❈ ✻ ❚ ● ❈ ✩ ❈ ❚ ❈ ❋ ▲ ✵ ✩ ❈ ❚ ● ❈ ❚ ● ❈ ✶ ❈ ✩ ❈ ❚ ● ❈ ❚

• ✷ ❈ ❚ ● ❈

✩ ❈ ❚ ● ✸ ❈ ❚ ● ❈ ❚ ● ❈ ✩ ✹ ● ❈ ✩ ❈ ❚ ● ❈ ❚ ✺ ● ❈ ❚ ● ❈ ✩ ❈ ❚ ✻ ❚ ● ❈ ✩ ❈ ❚ ● ❈ ✼ ❚ ● ❈ ❚ ● ❈ ✩ ❈

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✼✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 18

❋r♦♠ ❇❲❚(❚)❂❈●✩❚❚❈❈ ❜❛❝❦ t♦ ❚❂❈❚❈❚●❈✩ ❘✐❣❤t✲t♦✲❧❡❢t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❚ ❢r♦♠ ▲✿ ▲❋ ❢✉♥❝t✐♦♥ ✐ ▲ ✵ ❈ ✶

• ✷

✩ ✸ ❚ ✹ ❚ ✺ ❈ ✻ ❈

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✽✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 19

❋r♦♠ ❇❲❚(❚)❂❈●✩❚❚❈❈ ❜❛❝❦ t♦ ❚❂❈❚❈❚●❈✩ ❘✐❣❤t✲t♦✲❧❡❢t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❚ ❢r♦♠ ▲✿ ▲❋ ❢✉♥❝t✐♦♥ ✐ ❋ ▲ ✵ ✩ ❈ ✶ ❈

• ✷

❈ ✩ ✸ ❈ ❚ ✹

• ❚

✺ ❚ ❈ ✻ ❚ ❈ ❉❡❞✉❝❡ s♦rt❡❞ ❋ ❢r♦♠ ✉♥s♦rt❡❞ ▲

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✽✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 20

❋r♦♠ ❇❲❚(❚)❂❈●✩❚❚❈❈ ❜❛❝❦ t♦ ❚❂❈❚❈❚●❈✩ ❘✐❣❤t✲t♦✲❧❡❢t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❚ ❢r♦♠ ▲✿ ▲❋ ❢✉♥❝t✐♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ❈

• ✷

❈ ✩ ✸ ❈ ❚ ✹

• ❚

✺ ❚ ❈ ✻ ❚ ❈ ❘✐❣❤t✲t♦✲❧❡❢t s✉✣①❡s ♦❢ ❚ ✩

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✽✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 21

❋r♦♠ ❇❲❚(❚)❂❈●✩❚❚❈❈ ❜❛❝❦ t♦ ❚❂❈❚❈❚●❈✩ ❘✐❣❤t✲t♦✲❧❡❢t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❚ ❢r♦♠ ▲✿ ▲❋ ❢✉♥❝t✐♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ❈

• ✷

❈ ✩ ✸ ❈ ❚ ✹

• ❚

✺ ❚ ❈ ✻ ❚ ❈ ❘✐❣❤t✲t♦✲❧❡❢t s✉✣①❡s ♦❢ ❚ ✩

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✽✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 22

❋r♦♠ ❇❲❚(❚)❂❈●✩❚❚❈❈ ❜❛❝❦ t♦ ❚❂❈❚❈❚●❈✩ ❘✐❣❤t✲t♦✲❧❡❢t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❚ ❢r♦♠ ▲✿ ▲❋ ❢✉♥❝t✐♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ❈

• ✷

❈ ✩ ✸ ❈ ❚ ✹

• ❚

✺ ❚ ❈ ✻ ❚ ❈ ❘✐❣❤t✲t♦✲❧❡❢t s✉✣①❡s ♦❢ ❚ ✩

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✽✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 23

❋r♦♠ ❇❲❚(❚)❂❈●✩❚❚❈❈ ❜❛❝❦ t♦ ❚❂❈❚❈❚●❈✩ ❘✐❣❤t✲t♦✲❧❡❢t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❚ ❢r♦♠ ▲✿ ▲❋ ❢✉♥❝t✐♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ❈

• ✷

❈ ✩ ✸ ❈ ❚ ✹

• ❚

✺ ❚ ❈ ✻ ❚ ❈ ❘✐❣❤t✲t♦✲❧❡❢t s✉✣①❡s ♦❢ ❚ ✩ ✵

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✽✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 24

❋r♦♠ ❇❲❚(❚)❂❈●✩❚❚❈❈ ❜❛❝❦ t♦ ❚❂❈❚❈❚●❈✩ ❘✐❣❤t✲t♦✲❧❡❢t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❚ ❢r♦♠ ▲✿ ▲❋ ❢✉♥❝t✐♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ❈

• ✷

❈ ✩ ✸ ❈ ❚ ✹

• ❚

✺ ❚ ❈ ✻ ❚ ❈ ❘✐❣❤t✲t♦✲❧❡❢t s✉✣①❡s ♦❢ ❚ ✩ ✵

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✽✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 25

❋r♦♠ ❇❲❚(❚)❂❈●✩❚❚❈❈ ❜❛❝❦ t♦ ❚❂❈❚❈❚●❈✩ ❘✐❣❤t✲t♦✲❧❡❢t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❚ ❢r♦♠ ▲✿ ▲❋ ❢✉♥❝t✐♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ❈

• ✷

❈ ✩ ✸ ❈ ❚ ✹

• ❚

✺ ❚ ❈ ✻ ❚ ❈ ❘✐❣❤t✲t♦✲❧❡❢t s✉✣①❡s ♦❢ ❚ ✩ ✵ ❈

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✽✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 26

❋r♦♠ ❇❲❚(❚)❂❈●✩❚❚❈❈ ❜❛❝❦ t♦ ❚❂❈❚❈❚●❈✩ ❘✐❣❤t✲t♦✲❧❡❢t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❚ ❢r♦♠ ▲✿ ▲❋ ❢✉♥❝t✐♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ❈

• ✷

❈ ✩ ✸ ❈ ❚ ✹

• ❚

✺ ❚ ❈ ✻ ❚ ❈ ❘✐❣❤t✲t♦✲❧❡❢t s✉✣①❡s ♦❢ ❚ ✩ ✵ ❈

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✽✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 27

❋r♦♠ ❇❲❚(❚)❂❈●✩❚❚❈❈ ❜❛❝❦ t♦ ❚❂❈❚❈❚●❈✩ ❘✐❣❤t✲t♦✲❧❡❢t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❚ ❢r♦♠ ▲✿ ▲❋ ❢✉♥❝t✐♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ❈

• ✷

❈ ✩ ✸ ❈ ❚ ✹

• ❚

✺ ❚ ❈ ✻ ❚ ❈ ❘✐❣❤t✲t♦✲❧❡❢t s✉✣①❡s ♦❢ ❚ ✩ ✵ ❈

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✽✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 28

❋r♦♠ ❇❲❚(❚)❂❈●✩❚❚❈❈ ❜❛❝❦ t♦ ❚❂❈❚❈❚●❈✩ ❘✐❣❤t✲t♦✲❧❡❢t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❚ ❢r♦♠ ▲✿ ▲❋ ❢✉♥❝t✐♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ❈

• ✷

❈ ✩ ✸ ❈ ❚ ✹

• ❚

✺ ❚ ❈ ✻ ❚ ❈ ❘✐❣❤t✲t♦✲❧❡❢t s✉✣①❡s ♦❢ ❚ ✩ ✵ ❈ ✶

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✽✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 29

❋r♦♠ ❇❲❚(❚)❂❈●✩❚❚❈❈ ❜❛❝❦ t♦ ❚❂❈❚❈❚●❈✩ ❘✐❣❤t✲t♦✲❧❡❢t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❚ ❢r♦♠ ▲✿ ▲❋ ❢✉♥❝t✐♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ❈

• ✷

❈ ✩ ✸ ❈ ❚ ✹

• ❚

✺ ❚ ❈ ✻ ❚ ❈ ❘✐❣❤t✲t♦✲❧❡❢t s✉✣①❡s ♦❢ ❚ ✩ ✵ ❈ ✶

• ▲❛✉r❡♥t ▼♦✉❝❤❛r❞

❉②♥❛♠✐❝ ❇❲❚ ✽✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 30

❋r♦♠ ❇❲❚(❚)❂❈●✩❚❚❈❈ ❜❛❝❦ t♦ ❚❂❈❚❈❚●❈✩ ❘✐❣❤t✲t♦✲❧❡❢t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❚ ❢r♦♠ ▲✿ ▲❋ ❢✉♥❝t✐♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ❈

• ✷

❈ ✩ ✸ ❈ ❚ ✹

• ❚

✺ ❚ ❈ ✻ ❚ ❈ ❘❡❝♦♥str✉❝t❡❞ t❡①t ❚ ✩ ✵ ❈ ✶

• ▲❛✉r❡♥t ▼♦✉❝❤❛r❞

❉②♥❛♠✐❝ ❇❲❚ ✽✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 31

❋r♦♠ ❇❲❚(❚)❂❈●✩❚❚❈❈ ❜❛❝❦ t♦ ❚❂❈❚❈❚●❈✩ ❘✐❣❤t✲t♦✲❧❡❢t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❚ ❢r♦♠ ▲✿ ▲❋ ❢✉♥❝t✐♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ❈

• ✷

❈ ✩ ✸ ❈ ❚ ✹

• ❚

✺ ❚ ❈ ✻ ❚ ❈ ❘❡❝♦♥str✉❝t❡❞ t❡①t ❚ ✩ ✵ ❈ ✶

• ✹

❚ ✻ ❈ ✸ ❚ ✺ ❈ ✷

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✽✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 32

❆ ✈✐s✉❛❧ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ▲❋ ❢♦r ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❈♦♥s✐❞❡r✐♥❣ ▲❋ ❛s ❛♥ ❛✉t♦♠❛t♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ✶ ❈ ● ✹ ✷ ❈ ✩ ✵ ✸ ❈ ❚ ✺ ✹ ● ❚ ✻ ✺ ❚ ❈ ✷ ✻ ❚ ❈ ✸

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✾✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 33

❆ ✈✐s✉❛❧ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ▲❋ ❢♦r ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❈♦♥s✐❞❡r✐♥❣ ▲❋ ❛s ❛♥ ❛✉t♦♠❛t♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ✶ ❈ ● ✹ ✷ ❈ ✩ ✵ ✸ ❈ ❚ ✺ ✹ ● ❚ ✻ ✺ ❚ ❈ ✷ ✻ ❚ ❈ ✸ ✵ ✶

❈

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✾✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 34

❆ ✈✐s✉❛❧ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ▲❋ ❢♦r ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❈♦♥s✐❞❡r✐♥❣ ▲❋ ❛s ❛♥ ❛✉t♦♠❛t♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ✶ ❈ ● ✹ ✷ ❈ ✩ ✵ ✸ ❈ ❚ ✺ ✹ ● ❚ ✻ ✺ ❚ ❈ ✷ ✻ ❚ ❈ ✸ ✵ ✶

❈

✹

• ▲❛✉r❡♥t ▼♦✉❝❤❛r❞

❉②♥❛♠✐❝ ❇❲❚ ✾✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 35

❆ ✈✐s✉❛❧ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ▲❋ ❢♦r ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❈♦♥s✐❞❡r✐♥❣ ▲❋ ❛s ❛♥ ❛✉t♦♠❛t♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ✶ ❈ ● ✹ ✷ ❈ ✩ ✵ ✸ ❈ ❚ ✺ ✹ ● ❚ ✻ ✺ ❚ ❈ ✷ ✻ ❚ ❈ ✸ ✵ ✶

❈

✹

• ✻

❚

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✾✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 36

❆ ✈✐s✉❛❧ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ▲❋ ❢♦r ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❈♦♥s✐❞❡r✐♥❣ ▲❋ ❛s ❛♥ ❛✉t♦♠❛t♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ✶ ❈ ● ✹ ✷ ❈ ✩ ✵ ✸ ❈ ❚ ✺ ✹ ● ❚ ✻ ✺ ❚ ❈ ✷ ✻ ❚ ❈ ✸ ✵ ✶

❈

✹

• ✻

❚

✸

❈

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✾✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 37

❆ ✈✐s✉❛❧ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ▲❋ ❢♦r ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❈♦♥s✐❞❡r✐♥❣ ▲❋ ❛s ❛♥ ❛✉t♦♠❛t♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ✶ ❈ ● ✹ ✷ ❈ ✩ ✵ ✸ ❈ ❚ ✺ ✹ ● ❚ ✻ ✺ ❚ ❈ ✷ ✻ ❚ ❈ ✸ ✵ ✶

❈

✹

• ✻

❚

✸

❈

✺

❚

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✾✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 38

❆ ✈✐s✉❛❧ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ▲❋ ❢♦r ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❈♦♥s✐❞❡r✐♥❣ ▲❋ ❛s ❛♥ ❛✉t♦♠❛t♦♥ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ✶ ❈ ● ✹ ✷ ❈ ✩ ✵ ✸ ❈ ❚ ✺ ✹ ● ❚ ✻ ✺ ❚ ❈ ✷ ✻ ❚ ❈ ✸ ✵ ✶

❈

✹

• ✻

❚

✸

❈

✺

❚

✷

❈

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✾✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 39

❆ ✈✐s✉❛❧ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ▲❋ ❢♦r ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❈♦♥s✐❞❡r✐♥❣ ▲❋ ❛s ❛♥ ❛✉t♦♠❛t♦♥ ✵ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ✶ ❈ ● ✹ ✷ ❈ ✩ ✵ ✸ ❈ ❚ ✺ ✹ ● ❚ ✻ ✺ ❚ ❈ ✷ ✻ ❚ ❈ ✸ ✵ ✶

❈

✹

• ✻

❚

✸

❈

✺

❚

✷

❈

✵

✩

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✾✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 40

❆ ✈✐s✉❛❧ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ▲❋ ❢♦r ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❈♦♥s✐❞❡r✐♥❣ ▲❋ ❛s ❛♥ ❛✉t♦♠❛t♦♥ ✵ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ✶ ❈ ● ✹ ✷ ❈ ✩ ✵ ✸ ❈ ❚ ✺ ✹ ● ❚ ✻ ✺ ❚ ❈ ✷ ✻ ❚ ❈ ✸ ✵ ✶

❈

✹

• ✻

❚

✸

❈

✺

❚

✷

❈

✵

✩

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✾✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 41

❆ ✈✐s✉❛❧ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ▲❋ ❢♦r ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❈♦♥s✐❞❡r✐♥❣ ▲❋ ❛s ❛♥ ❛✉t♦♠❛t♦♥ ✵ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ✶ ❈ ● ✹ ✷ ❈ ✩ ✵ ✸ ❈ ❚ ✺ ✹ ● ❚ ✻ ✺ ❚ ❈ ✷ ✻ ❚ ❈ ✸ ✵ ✶

❈

✹

• ✻

❚

✸

❈

✺

❚

✷

❈

✵

✩

✵ ✶ ✻ ✸ ✺ ✷ ▲ ❋

❈ ❈ ❈

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✾✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 42

❆ ✈✐s✉❛❧ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ▲❋ ❢♦r ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❈♦♥s✐❞❡r✐♥❣ ▲❋ ❛s ❛♥ ❛✉t♦♠❛t♦♥ ✵ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ✶ ❈ ● ✹ ✷ ❈ ✩ ✵ ✸ ❈ ❚ ✺ ✹ ● ❚ ✻ ✺ ❚ ❈ ✷ ✻ ❚ ❈ ✸ ✵ ✶

❈

✹

• ✻

❚

✸

❈

✺

❚

✷

❈

✵

✩

✵ ✶ ✻ ✸ ✺ ✷ ▲ ❋

❈ ❈ ❈

✵ ✶ ✺ ✷ ✻ ✸ ▲ ❋

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✾✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 43

❆ ✈✐s✉❛❧ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ▲❋ ❢♦r ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❈♦♥s✐❞❡r✐♥❣ ▲❋ ❛s ❛♥ ❛✉t♦♠❛t♦♥ ✵ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ✶ ❈ ● ✹ ✷ ❈ ✩ ✵ ✸ ❈ ❚ ✺ ✹ ● ❚ ✻ ✺ ❚ ❈ ✷ ✻ ❚ ❈ ✸ ✵ ✶

❈

✹

• ✻

❚

✸

❈

✺

❚

✷

❈

✵

✩

✵ ✶ ✻ ✸ ✺ ✷ ▲ ❋ ✵ ✶ ✺ ✷ ✻ ✸ ▲ ❋ ✵ ✺ ✻

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✾✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 44

❆ ✈✐s✉❛❧ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ▲❋ ❢♦r ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❈♦♥s✐❞❡r✐♥❣ ▲❋ ❛s ❛♥ ❛✉t♦♠❛t♦♥ ✵ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ✶ ❈ ● ✹ ✷ ❈ ✩ ✵ ✸ ❈ ❚ ✺ ✹ ● ❚ ✻ ✺ ❚ ❈ ✷ ✻ ❚ ❈ ✸ ✵ ✶

❈

✹

• ✻

❚

✸

❈

✺

❚

✷

❈

✵

✩

✵ ✶ ✻ ✸ ✺ ✷ ▲ ❋ ✵ ✶ ✺ ✷ ✻ ✸ ▲ ❋

✰✶ ✰✶

✶ ✷ ✸ ✶ ✷ ✸

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✾✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 45

❆ ✈✐s✉❛❧ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ▲❋ ❢♦r ❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

❈♦♥s✐❞❡r✐♥❣ ▲❋ ❛s ❛♥ ❛✉t♦♠❛t♦♥ ✵ ✐ ❋ ▲ ▲❋ ✵ ✩ ❈ ✶ ✶ ❈ ● ✹ ✷ ❈ ✩ ✵ ✸ ❈ ❚ ✺ ✹ ● ❚ ✻ ✺ ❚ ❈ ✷ ✻ ❚ ❈ ✸ ✵ ✶

❈

✹

• ✻

❚

✸

❈

✺

❚

✷

❈

✵

✩

✵ ✶ ✻ ✸ ✺ ✷ ▲ ❋ ✵ ✶ ✺ ✷ ✻ ✸ ▲ ❋

❈ ❈ ❈

Pr♦♣❡rt② ✐✶ ■❢ ✐✷

❝

❥✶ ❥✷

❝

t❤❡♥ ✐✶ < ❥✶ ⇐ ⇒ ✐✷ < ❥✷

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✾✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 46

❯♣❞❛t✐♥❣ ▲❋ ❛♥❞ t❤❡ ❇❲❚

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❙t❛❣❡ ✶✿ ✐♥s❡rt❡❞ ❧❡tt❡r ● ✐s ❜❡t✇❡❡♥ ✩ ❛♥❞ ▲ ✭♥♦t ✐♥ ▲✮

✐ ❋ ▲ ✵ ✩ ❈ ✶ ❈ ● ✷ ❈ ✩ ✸ ❈ ❚ ✹ ● ❚ ✺ ❚ ❈ ✻ ❚ ❈

✵ ✶

❈

✹

• ✻

❚

✸

❈

✺

❚

✷

❈

✵

✩

❋ ▲ ✩ ❈ ❚ ● ❈ ❚

• ❈

❈ ✩ ❈ ❚ ● ❈ ❚ ●

• ❈

✩ ❈ ❚ ● ❈ ❚ ❚ ● ❈ ✩ ❈ ❚ ● ❈

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✶✵✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 47

❯♣❞❛t✐♥❣ ▲❋ ❛♥❞ t❤❡ ❇❲❚

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❙t❛❣❡ ✶✿ ✐♥s❡rt❡❞ ❧❡tt❡r ● ✐s ❜❡t✇❡❡♥ ✩ ❛♥❞ ▲ ✭♥♦t ✐♥ ▲✮

✐ ❋ ▲ ✵ ✩ ❈ ✶ ❈ ● ✷ ❈ ✩ ✸ ❈ ❚ ✹ ● ❚ ✺ ❚ ❈ ✻ ❚ ❈

✵ ✶

❈

✹

• ✻

❚

✸

❈

✺

❚

✷

❈

✵

✩

❋ ▲ ✩ ❈ ❚ ● ❈ ❚

• ❈

❈ ✩ ❈ ❚ ● ❈ ❚ ●

• ❈

✩ ❈ ❚ ● ❈ ❚ ❚ ● ❈ ✩ ❈ ❚ ● ❈

❈

✸

❚

✹

• ✺

❈

✻

✩

✼ ▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✶✵✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 48

❯♣❞❛t✐♥❣ ▲❋ ❛♥❞ t❤❡ ❇❲❚

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❙t❛❣❡ ✶✿ ✐♥s❡rt❡❞ ❧❡tt❡r ● ✐s ❜❡t✇❡❡♥ ✩ ❛♥❞ ▲ ✭♥♦t ✐♥ ▲✮

✐ ❋ ▲ ✵ ✩ ❈ ✶ ❈ ● ✷ ❈ ✩ ✸ ❈ ❚ ✹ ● ❚ ✺ ❚ ❈ ✻ ❚ ❈

✵ ✶

❈

✹

• ✻

❚

✸

❈

✺

❚

✷

❈

✵

✩

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

Pr❡s❡r✈❡❞ ③♦♥❡

❇❡st ♣♦ss✐❜❧❡ s✐t✉❛t✐♦♥✿ → ✐♥s❡rt✐♦♥ ❛t ♣♦s✐t✐♦♥ ✶✳ ❖♥❡ ❝❛❧❧ t❤❡ r❡♦r❞❡r ❢✉♥❝t✐♦♥✳ ❖♥ ❛✈❡r❛❣❡✿ → ✐♥s❡rt✐♦♥ ❛t ♣♦s✐t✐♦♥ ♥/✷✳ ♥/✷ ❝❛❧❧s t♦ t❤❡ r❡♦r❞❡r ❢✉♥❝t✐♦♥✳ ❲♦rst✲❝❛s❡ s✐t✉❛t✐♦♥✿ → ✐♥s❡rt✐♦♥ ❛t ♣♦s✐t✐♦♥ ♥✳ ♥ ❝❛❧❧s t♦ t❤❡ r❡♦r❞❡r ❢✉♥❝t✐♦♥✳

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✶✵✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 49

❯♣❞❛t✐♥❣ ▲❋ ❛♥❞ t❤❡ ❇❲❚

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❙t❛❣❡ ✷✿ ✐♥s❡rt❡❞ ❧❡tt❡r ● ✐s ✐♥ ▲ ❢r♦♠ ✸ t♦ ✳✳✳

✐ ❋ ▲ ✵ ✩ ❈ ✶ ❈ ● ✷ ❈ ✩ ✸ ❈ ❚ ✹ ● ❚ ✺ ❚ ❈ ✻ ❚ ❈

✵ ✶

❈

✹

• ✻

❚

✸

❈

✺ ✷

❈

✵

✩

❋ ▲ ❈ ❚ ● ❈ ✩ ❈ ❚ ●

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❄

• ❲❡ ❤❛✈❡ t♦ ❝♦♥s✐❞❡r ❛❧❧ tr❛♥s✐t✐♦♥s

❧❛❜❡❧❡❞ ✇✐t❤ ●✳

❚

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✶✵✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 50

❯♣❞❛t✐♥❣ ▲❋ ❛♥❞ t❤❡ ❇❲❚

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❙t❛❣❡ ✷✿ ✐♥s❡rt❡❞ ❧❡tt❡r ● ✐s ✐♥ ▲ ❢r♦♠ ✸ t♦ ✳✳✳

✐ ❋ ▲ ✵ ✩ ❈ ✶ ❈

• ✷ ❈

✩ ✸ ❈ ● ✹ ● ❚ ✺ ❚ ❈ ✻ ❚ ❈

✵ ✶

❈

✹

• ✻

❚

✸

❈

✺ ✷

❈

✵

✩

❄

• ❚

✶ ✹

• ✸

❄

• ▲❛✉r❡♥t ▼♦✉❝❤❛r❞

❉②♥❛♠✐❝ ❇❲❚ ✶✵✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 51

❯♣❞❛t✐♥❣ ▲❋ ❛♥❞ t❤❡ ❇❲❚

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❙t❛❣❡ ✷✿ ✐♥s❡rt❡❞ ❧❡tt❡r ● ✐s ✐♥ ▲ ❢r♦♠ ✸ t♦ ✳✳✳

✐ ❋ ▲ ✵ ✩ ❈ ✶ ❈

• ✷ ❈

✩ ✸ ❈ ● ✹ ● ❚ ✺ ❚ ❈ ✻ ❚ ❈

✵ ✶

❈

✹

• ✻

❚

✸

❈

✺ ✷

❈

✵

✩

✺

• ❚

✶ ✹

• ✸

✺

• ✰✶

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✶✵✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 52

❯♣❞❛t✐♥❣ ▲❋ ❛♥❞ t❤❡ ❇❲❚

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❙t❛❣❡ ✷✿ ✐♥s❡rt❡❞ ❧❡tt❡r ● ✐s ✐♥ ▲ ❢r♦♠ ✸ t♦ ✳✳✳

✐ ❋ ▲ ✵ ✩ ❈ ✶ ❈

• ✷ ❈

✩ ✸ ❈

• ✹ ●

❚ ✺ ● ❚ ✻ ❚ ❈ ✼ ❚ ❈

✵ ✶

❈

✹

• ✼

❚

✸

❈

✻ ✷

❈

✵

✩

✺

• ❚

◆❡✇ r♦✇ ✇✐❧❧ ❜❡ ✐♥s❡rt❡❞ ❛t ♣♦s✐t✐♦♥ ✺✳ ❋♦r♠❡r st❛t❡s ❣r❡❛t❡r t❤❛♥ ♦r ❡q✉❛❧ t♦ ✺ s❤♦✉❧❞ ❜❡ ✐♥❝r❡♠❡♥t❡❞ ✭r♦✇s s❤♦✉❧❞ ♠♦✈❡ ♦♥❡ st❡♣ ❞♦✇♥✮✳ ✻ ✼

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✶✵✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 53

❯♣❞❛t✐♥❣ ▲❋ ❛♥❞ t❤❡ ❇❲❚

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❙t❛❣❡ ✸✿ ✐♥s❡rt❡❞ ❧❡tt❡r ● ✐s ✐♥ ❋✿ ❢r♦♠ ✺ t♦ ✳✳✳

✐ ❋ ▲ ✵ ✩ ❈ ✶ ❈

• ✷ ❈

✩ ✸ ❈

• ✹ ●

❚ ✺ ● ❚ ✻ ❚ ❈ ✼ ❚ ❈

✵ ✶

❈

✹

• ✼

❚

✸

❈

✻ ✷

❈

✵

✩

✺

• ❚

❋ ▲

• ❈ ❚ ● ❈ ✩ ❈ ❚

❚❤❡ ♥❡✇ r♦✇ t❤❛t ✐s ❛❞❞❡❞ ✐s ❡♥❞✐♥❣ ✇✐t❤ ❚✳ ❲❡ ❤❛✈❡ t♦ ❝♦♥s✐❞❡r ❛❧❧ tr❛♥s✐✲ t✐♦♥s ❧❛❜❡❧❡❞ ✇✐t❤ ❚✳

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✶✵✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 54

❯♣❞❛t✐♥❣ ▲❋ ❛♥❞ t❤❡ ❇❲❚

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❙t❛❣❡ ✸✿ ✐♥s❡rt❡❞ ❧❡tt❡r ● ✐s ✐♥ ❋✿ ❢r♦♠ ✺ t♦ ✳✳✳

✐ ❋ ▲ ✵ ✩ ❈ ✶ ❈

• ✷ ❈

✩ ✸ ❈

• ✹ ●

❚ ✺ ● ❚ ✻ ❚ ❈ ✼ ❚ ❈

✵ ✶

❈

✹

• ✼

❚

✸

❈

✻ ✷

❈

✵

✩

✺

• ❚

✹ ✼

❚

✺ ✻

❚

✲✶✦

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✶✵✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 55

❯♣❞❛t✐♥❣ ▲❋ ❛♥❞ t❤❡ ❇❲❚

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❙t❛❣❡ ✸✿ ✐♥s❡rt❡❞ ❧❡tt❡r ● ✐s ✐♥ ❋✿ ❢r♦♠ ✺ t♦ ✳✳✳

✐ ❋ ▲ ✵ ✩ ❈ ✶ ❈

• ✷ ❈

✩ ✸ ❈

• ✹ ●

❚ ✺ ● ❚ ✻ ❚ ❈ ✼ ❚ ❈

✵ ✶

❈

✹

• ✼

❚

✸

❈

✻ ✷

❈

✵

✩

✺

• ❚

▲[✺] ❂ ✷♥❞ ❚ → ❋[✻] ❂ ✶st ❚✳ ⇒ ♠♦✈❡ r♦✇❬✻❪ t♦ ♣♦s✐t✐♦♥ ✼✳ ✹ ✻

❚

✺ ✼

❚ ✰✶

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✶✵✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 56

❯♣❞❛t✐♥❣ ▲❋ ❛♥❞ t❤❡ ❇❲❚

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❙t❛❣❡ ✸✿ ✐♥s❡rt❡❞ ❧❡tt❡r ● ✐s ✐♥ ❋✿ ❢r♦♠ ✺ t♦ ✳✳✳

✐ ❋ ▲ ✵ ✩ ❈ ✶ ❈

• ✷ ❈

✩ ✸ ❈

• ✹ ●

❚ ✺ ● ❚ ✻ ❚ ❈ ✼ ❚ ❈

✵ ✶

❈

✹

• ✻

❚

✸

❈

✼ ✷

❈

✵

✩

✺

• ❚

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✶✵✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 57

❯♣❞❛t✐♥❣ ▲❋ ❛♥❞ t❤❡ ❇❲❚

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❙t❛❣❡ ✹✿ ✐♥s❡rt❡❞ ❧❡tt❡r ● ✐s ❜❡t✇❡❡♥ ❋ ❛♥❞ ✩ ✭♥♦t ✐♥ ❋✮

✐ ❋ ▲ ✵ ✩ ❈ ✶ ❈

• ✷ ❈

✩ ✸ ❈

• ✹ ●

❚ ✺ ● ❚ ✻ ❚ ❈ ✼ ❚ ❈

✵ ✶

❈

✹

• ✻

❚

✸

❈

✼ ✷

❈

✵

✩

✺

• ❚

❋ ▲ ❈ ❚ ● ❈ ❚ ● ❈ ✩ ❚ ● ❈ ❚ ● ❈ ✩ ❈

❲❡ ❤❛✈❡ t♦ ❝♦♥s✐❞❡r ❛❧❧ tr❛♥s✐t✐♦♥s ❧❛❜❡❧❡❞ ✇✐t❤ ❈✳

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✶✵✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 58

❯♣❞❛t✐♥❣ ▲❋ ❛♥❞ t❤❡ ❇❲❚

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❙t❛❣❡ ✹✿ ✐♥s❡rt❡❞ ❧❡tt❡r ● ✐s ❜❡t✇❡❡♥ ❋ ❛♥❞ ✩ ✭♥♦t ✐♥ ❋✮

✐ ❋ ▲ ✵ ✩ ❈ ✶ ❈

• ✷ ❈

✩ ✸ ❈

• ✹ ●

❚ ✺ ● ❚ ✻ ❚ ❈ ✼ ❚ ❈

✵ ✶

❈

✹

• ✻

❚

✸

❈

✼ ✷

❈

✵

✩

✺

• ❚

✵ ✶

❈

✻ ✸

❈

✰✷✦

✼ ✷

❈

✲✶✦

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✶✵✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 59

❯♣❞❛t✐♥❣ ▲❋ ❛♥❞ t❤❡ ❇❲❚

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❙t❛❣❡ ✹✿ ✐♥s❡rt❡❞ ❧❡tt❡r ● ✐s ❜❡t✇❡❡♥ ❋ ❛♥❞ ✩ ✭♥♦t ✐♥ ❋✮

✐ ❋ ▲ ✵ ✩ ❈ ✶ ❈

• ✷ ❈

✩ ✸ ❈

• ✹ ●

❚ ✺ ● ❚ ✻ ❚ ❈ ✼ ❚ ❈

✵ ✶

❈

✹

• ✻

❚

✸

❈

✼ ✷

❈

✵

✩

✺

• ❚

▲[✼] ❂ ✸r❞ ❈ → ❋[✷] ❂ ✷♥❞ ❈✳ ⇒ ♠♦✈❡ r♦✇❬✷❪ t♦ ♣♦s✐t✐♦♥ ✸✳ ✵ ✶

❈

✻ ✷

❈ ✰✶

✼ ✸

❈ ✰✶

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✶✵✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 60

❯♣❞❛t✐♥❣ ▲❋ ❛♥❞ t❤❡ ❇❲❚

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❙t❛❣❡ ✹✿ ✐♥s❡rt❡❞ ❧❡tt❡r ● ✐s ❜❡t✇❡❡♥ ❋ ❛♥❞ ✩ ✭♥♦t ✐♥ ❋✮

✐ ❋ ▲ ✵ ✩ ❈ ✶ ❈

• ✷ ❈
• ✸ ❈

✩ ✹ ● ❚ ✺ ● ❚ ✻ ❚ ❈ ✼ ❚ ❈

✵ ✶

❈

✹

• ✻

❚

✷

❈

✼ ✸

❈

✵

✩

✺

• ❚

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✶✵✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 61

❯♣❞❛t✐♥❣ ▲❋ ❛♥❞ t❤❡ ❇❲❚

❚ = ❈

✵

❚

✶

❈

✷

❚

✸

• ✹

❈

✺

✩

✻

→ ❚ ′ = ❈

✵

❚

✶

• ✷

❈

✸

❚

✹

• ✺

❈

✻

✩

✼

❙t❛❣❡ ✹✿ ✐♥s❡rt❡❞ ❧❡tt❡r ● ✐s ❜❡t✇❡❡♥ ❋ ❛♥❞ ✩ ✭♥♦t ✐♥ ❋✮

✐ ❋ ▲ ✵ ✩ ❈ ✶ ❈

• ✷ ❈
• ✸ ❈

✩ ✹ ● ❚ ✺ ● ❚ ✻ ❚ ❈ ✼ ❚ ❈

✵ ✶

❈

✹

• ✻

❚

✷

❈

✼ ✸

❈

✵

✩

✺

• ❚

❲❡ ❤❛✈❡ t♦ ❝♦♥s✐❞❡r ❛❧❧ tr❛♥s✐t✐♦♥s ❧❛❜❡❧❡❞ ✇✐t❤ ✩✳ ❖♥❧② ♦♥❡ tr❛♥s✐t✐♦♥ ♣♦✐♥ts t♦ ✵✱ ❜✐♥❣♦✦ ✇❡ ❛r❡ ❞♦♥❡✳

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✶✵✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷

SLIDE 62

❈♦♥❝❧✉s✐♦♥ ❛♥❞ ♣❡rs♣❡❝t✐✈❡s

❖✉r ♠❛✐♥ r❡s✉❧t ❝❛♥ ❜❡ ❡❛s✐❧② ❛❞❛♣t❡❞ ❢♦r ❞❡❧❡t✐♦♥✱ s✉❜st✐t✉t✐♦♥ ❛♥❞ ❢❛❝t♦rs❀ ❞②♥❛♠✐❝ ❇✉rr♦✇s✲❲❤❡❡❧❡r ❚r❛♥s❢♦r♠❀ ❛t ♠♦st ❖(♥) ❝❛❧❧s t♦ r❡♦r❞❡r ❢✉♥❝t✐♦♥ → ❖(♥ ❧♦❣ ♥)❀ ❝❛♥ ❜❡ ❛♥ ❤❡❧♣ ❢♦r ❜✉✐❧❞✐♥❣ ❛ ❞②♥❛♠✐❝ s✉✣① ❛rr❛②❀ P✉❜❧✐❝❛t✐♦♥s ▼✳ ❙❛❧s♦♥✱ ❚✳ ▲❡❝r♦q✱ ▼✳ ▲é♦♥❛r❞✱ ❛♥❞ ▲✳ ▼♦✉❝❤❛r❞ ✭✷✵✵✾✮✳ ❆ ❢♦✉r st❛❣❡ ❛❧❣♦r✐t❤♠ ❢♦r ✉♣❞❛t✐♥❣ ❛ ❇✉rr♦✇s ❲❤❡❡❧❡r ❚r❛♥s❢♦r♠✳ ❚❈❙✳ ❆❝❝❡♣t❡❞✳ ❈✉rr❡♥t ✇♦r❦ ❞②♥❛♠✐❝ ❊①t❡♥❞❡❞ ❙✉✣① ❆rr❛②❀

▲❛✉r❡♥t ▼♦✉❝❤❛r❞ ❉②♥❛♠✐❝ ❇❲❚ ✶✶✴✶✶ ❙tr✐♥❣♦❧♦❣② ✷✵✵✾✱ ❇❛r ■❧❛♥✱ ❆♣r✐❧ ✷