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trt Pr s r rt Pr Prrts r t

  1. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❆ Pr♦t♦❝♦❧ ❉❡s✐❣♥ ❲♦r❦✢♦✇ ❉❡s✐❣♥ ♣r♦t♦❝♦❧ P✉❜❧✐s❤ ✐t ❋✐① ✐t ❲❛✐t ❢♦r ❛♥ ❛tt❛❝❦ ❲❛✐t❡❞ ❧♦♥❣ ❡♥♦✉❣❤ ❉❡❝❧❛r❡ ♣r♦t♦❝♦❧ s❡❝✉r❡ ❍♦✇ ❧♦♥❣ ✐s ❧♦♥❣ ❡♥♦✉❣❤❄ ■t t♦♦❦ ✶✼ ②❡❛rs t♦ ❜r❡❛❦ ◆❡❡❞❤❛♠✲❙❝❤r♦❡❞❡r✦ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  2. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❆ Pr♦t♦❝♦❧ ❉❡s✐❣♥ ❲♦r❦✢♦✇ ❉❡s✐❣♥ ♣r♦t♦❝♦❧ P✉❜❧✐s❤ ✐t ❋✐① ✐t ❲❛✐t ❢♦r ❛♥ ❛tt❛❝❦ ❲❛✐t❡❞ ❧♦♥❣ ❡♥♦✉❣❤ ❉❡❝❧❛r❡ ♣r♦t♦❝♦❧ s❡❝✉r❡ ❍♦✇ ❧♦♥❣ ✐s ❧♦♥❣ ❡♥♦✉❣❤❄ ■t t♦♦❦ ✶✼ ②❡❛rs t♦ ❜r❡❛❦ ◆❡❡❞❤❛♠✲❙❝❤r♦❡❞❡r✦ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  3. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❆ Pr♦t♦❝♦❧ ❉❡s✐❣♥ ❲♦r❦✢♦✇ ❉❡s✐❣♥ ♣r♦t♦❝♦❧ P✉❜❧✐s❤ ✐t ❋✐① ✐t ❲❛✐t ❢♦r ❛♥ ❛tt❛❝❦ ❲❛✐t❡❞ ❧♦♥❣ ❡♥♦✉❣❤ ❉❡❝❧❛r❡ ♣r♦t♦❝♦❧ s❡❝✉r❡ ❍♦✇ ❧♦♥❣ ✐s ❧♦♥❣ ❡♥♦✉❣❤❄ ■t t♦♦❦ ✶✼ ②❡❛rs t♦ ❜r❡❛❦ ◆❡❡❞❤❛♠✲❙❝❤r♦❡❞❡r✦ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  4. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❆ Pr♦t♦❝♦❧ ❉❡s✐❣♥ ❲♦r❦✢♦✇ ❉❡s✐❣♥ ♣r♦t♦❝♦❧ P✉❜❧✐s❤ ✐t ❋✐① ✐t ❲❛✐t ❢♦r ❛♥ ❛tt❛❝❦ ❲❛✐t❡❞ ❧♦♥❣ ❡♥♦✉❣❤ ❉❡❝❧❛r❡ ♣r♦t♦❝♦❧ s❡❝✉r❡ ❍♦✇ ❧♦♥❣ ✐s ❧♦♥❣ ❡♥♦✉❣❤❄ ■t t♦♦❦ ✶✼ ②❡❛rs t♦ ❜r❡❛❦ ◆❡❡❞❤❛♠✲❙❝❤r♦❡❞❡r✦ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  5. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ P❧❛♥ ✶ ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ✷ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊①❛♠♣❧❡✿ ❋❖❖ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❡✲❆✉❝t✐♦♥s ✸ ❈♦♥❝❧✉s✐♦♥ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  6. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❱♦t✐♥❣ ♠❛❝❤✐♥❡s ❛r❡ ♥♦t ❛ r❡❝❡♥t t❡❝❤♥♦❧♦❣② ❚❤❡② ❤❛✈❡ ❜❡❡♥ ✐♥ ✉s❡ ✐♥ t❤❡ ❯❙ ❢♦r ♦✈❡r ✶✵✵ ②❡❛rs✦ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  7. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❊❧❡❝tr♦♥✐❝ ✈♦t✐♥❣ ♠❛❝❤✐♥❡s✳ ✳ ✳ ✳ ✳ ✳ ❛r❡ ✉s❡❞ ❛❧❧ ♦✈❡r t❤❡ ✇♦r❧❞ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  8. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ■♥t❡r♥❡t ✈♦t✐♥❣ ❆✈❛✐❧❛❜❧❡ ✐♥ ❊st♦♥✐❛ ❋r❛♥❝❡ ❙✇✐t③❡r❧❛♥❞ ✳ ✳ ✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  9. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❙❡❝✉r✐t② ❘❡q✉✐r❡♠❡♥ts ❋❛✐r♥❡ss ■♥❞✐✈✐❞✉❛❧ ❱❡r✐✜❛❜✐❧✐t② ❊❧✐❣✐❜✐❧✐t② ❯♥✐✈❡rs❛❧ ❱❡r✐✜❛❜✐❧✐t② ❙❡❝✉r✐t② ❘❡q✉✐r❡♠❡♥ts Pr✐✈❛❝② ❈♦rr❡❝t♥❡ss ❱♦t❡✲■♥❞❡♣❡♥❞❡♥❝❡ ❘❡❝❡✐♣t✲❋r❡❡♥❡ss ❘♦❜✉st♥❡ss ❈♦❡r❝✐♦♥✲❘❡s✐st❛♥❝❡ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  10. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❙❡❝✉r✐t② ❘❡q✉✐r❡♠❡♥ts ❋❛✐r♥❡ss ■♥❞✐✈✐❞✉❛❧ ❱❡r✐✜❛❜✐❧✐t② ❊❧✐❣✐❜✐❧✐t② ❯♥✐✈❡rs❛❧ ❱❡r✐✜❛❜✐❧✐t② ❙❡❝✉r✐t② ❘❡q✉✐r❡♠❡♥ts Pr✐✈❛❝② ❈♦rr❡❝t♥❡ss ❱♦t❡✲■♥❞❡♣❡♥❞❡♥❝❡ ❘❡❝❡✐♣t✲❋r❡❡♥❡ss ❘♦❜✉st♥❡ss ❈♦❡r❝✐♦♥✲❘❡s✐st❛♥❝❡ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  11. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❆tt❛❝❦ ♦♥ Pr✐✈❛❝② ✐♥ ❍❡❧✐♦s ❬❙❈✶✵❪ ❍❡❧✐♦s ❬❆❉▼P◗✵✾❪ ✐s ❛ ✇❡❜ ❜❛s❡❞ ♦♣❡♥✲s♦✉r❝❡ ✈♦t✐♥❣ s②st❡♠ ❜❛s❡❞ ♦♥ ❤♦♠♦♠♦r♣❤✐❝ ❡♥❝r②♣t✐♦♥✳ ❙❡r✈❡r ❆ ❆❧✐❝❡ ❇♦❜ ❇ ❂❆✱❇ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  12. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❆tt❛❝❦ ♦♥ Pr✐✈❛❝② ✐♥ ❍❡❧✐♦s ❬❙❈✶✵❪ ❍❡❧✐♦s ❬❆❉▼P◗✵✾❪ ✐s ❛ ✇❡❜ ❜❛s❡❞ ♦♣❡♥✲s♦✉r❝❡ ✈♦t✐♥❣ s②st❡♠ ❜❛s❡❞ ♦♥ ❤♦♠♦♠♦r♣❤✐❝ ❡♥❝r②♣t✐♦♥✳ ❙❡r✈❡r ❆ ❆ ❆❧✐❝❡ ❇♦❜ ❇ ❂❆✱❇ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  13. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❆tt❛❝❦ ♦♥ Pr✐✈❛❝② ✐♥ ❍❡❧✐♦s ❬❙❈✶✵❪ ❍❡❧✐♦s ❬❆❉▼P◗✵✾❪ ✐s ❛ ✇❡❜ ❜❛s❡❞ ♦♣❡♥✲s♦✉r❝❡ ✈♦t✐♥❣ s②st❡♠ ❜❛s❡❞ ♦♥ ❤♦♠♦♠♦r♣❤✐❝ ❡♥❝r②♣t✐♦♥✳ ❙❡r✈❡r ❆ ❆ ❆❧✐❝❡ ❇♦❜ ❇ ❇ ❂❆✱❇ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  14. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❆tt❛❝❦ ♦♥ Pr✐✈❛❝② ✐♥ ❍❡❧✐♦s ❬❙❈✶✵❪ ❍❡❧✐♦s ❬❆❉▼P◗✵✾❪ ✐s ❛ ✇❡❜ ❜❛s❡❞ ♦♣❡♥✲s♦✉r❝❡ ✈♦t✐♥❣ s②st❡♠ ❜❛s❡❞ ♦♥ ❤♦♠♦♠♦r♣❤✐❝ ❡♥❝r②♣t✐♦♥✳ ❙❡r✈❡r ❆ ❆ ❆❧✐❝❡ ✰ ❇♦❜ ❇ ❇ ❂❆✱❇ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  15. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❆tt❛❝❦ ♦♥ Pr✐✈❛❝② ✐♥ ❍❡❧✐♦s ❬❙❈✶✵❪ ❊✈❡ ❝❛♥ ❛tt❛❝❦ ❆❧✐❝❡✬s ♣r✐✈❛❝② ❜② ❝♦♣②✐♥❣ ❤❡r ✈♦t❡✿ ❙❡r✈❡r ❆❧✐❝❡ ❆ ❊✈❡ ❇ ❇♦❜ ❂❆✱❆✱❇ ❚♦ ♣r❡✈❡♥t t❤✐s ❛tt❛❝❦✱ ✇❡ ❤❛✈❡ t♦ ❡♥❢♦r❝❡ ❱♦t❡✲■♥❞❡♣❡♥❞❡♥❝❡ ✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  16. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❆tt❛❝❦ ♦♥ Pr✐✈❛❝② ✐♥ ❍❡❧✐♦s ❬❙❈✶✵❪ ❊✈❡ ❝❛♥ ❛tt❛❝❦ ❆❧✐❝❡✬s ♣r✐✈❛❝② ❜② ❝♦♣②✐♥❣ ❤❡r ✈♦t❡✿ ❙❡r✈❡r ❆❧✐❝❡ ❆ ❆ ❊✈❡ ❇ ❇♦❜ ❂❆✱❆✱❇ ❚♦ ♣r❡✈❡♥t t❤✐s ❛tt❛❝❦✱ ✇❡ ❤❛✈❡ t♦ ❡♥❢♦r❝❡ ❱♦t❡✲■♥❞❡♣❡♥❞❡♥❝❡ ✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  17. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❆tt❛❝❦ ♦♥ Pr✐✈❛❝② ✐♥ ❍❡❧✐♦s ❬❙❈✶✵❪ ❊✈❡ ❝❛♥ ❛tt❛❝❦ ❆❧✐❝❡✬s ♣r✐✈❛❝② ❜② ❝♦♣②✐♥❣ ❤❡r ✈♦t❡✿ ❙❡r✈❡r ❆❧✐❝❡ ❆ ❆ ❊✈❡ ❇ ❇ ❇♦❜ ❂❆✱❆✱❇ ❚♦ ♣r❡✈❡♥t t❤✐s ❛tt❛❝❦✱ ✇❡ ❤❛✈❡ t♦ ❡♥❢♦r❝❡ ❱♦t❡✲■♥❞❡♣❡♥❞❡♥❝❡ ✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  18. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❆tt❛❝❦ ♦♥ Pr✐✈❛❝② ✐♥ ❍❡❧✐♦s ❬❙❈✶✵❪ ❊✈❡ ❝❛♥ ❛tt❛❝❦ ❆❧✐❝❡✬s ♣r✐✈❛❝② ❜② ❝♦♣②✐♥❣ ❤❡r ✈♦t❡✿ ❙❡r✈❡r ❆❧✐❝❡ ❆ ❆ ❆ ❊✈❡ ❇ ❇ ❇♦❜ ❂❆✱❆✱❇ ❚♦ ♣r❡✈❡♥t t❤✐s ❛tt❛❝❦✱ ✇❡ ❤❛✈❡ t♦ ❡♥❢♦r❝❡ ❱♦t❡✲■♥❞❡♣❡♥❞❡♥❝❡ ✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  19. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❆tt❛❝❦ ♦♥ Pr✐✈❛❝② ✐♥ ❍❡❧✐♦s ❬❙❈✶✵❪ ❊✈❡ ❝❛♥ ❛tt❛❝❦ ❆❧✐❝❡✬s ♣r✐✈❛❝② ❜② ❝♦♣②✐♥❣ ❤❡r ✈♦t❡✿ ❙❡r✈❡r ❆❧✐❝❡ ❆ ❆ ❆ ❊✈❡ ❇ ❇ ❇♦❜ ❆ ❂❆✱❆✱❇ ❚♦ ♣r❡✈❡♥t t❤✐s ❛tt❛❝❦✱ ✇❡ ❤❛✈❡ t♦ ❡♥❢♦r❝❡ ❱♦t❡✲■♥❞❡♣❡♥❞❡♥❝❡ ✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  20. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❆tt❛❝❦ ♦♥ Pr✐✈❛❝② ✐♥ ❍❡❧✐♦s ❬❙❈✶✵❪ ❊✈❡ ❝❛♥ ❛tt❛❝❦ ❆❧✐❝❡✬s ♣r✐✈❛❝② ❜② ❝♦♣②✐♥❣ ❤❡r ✈♦t❡✿ ❙❡r✈❡r ❆❧✐❝❡ ❆ ❆ ✰ ❆ ❊✈❡ ❇ ❇ ❇♦❜ ✰ ❆ ❂❆✱❆✱❇ ❚♦ ♣r❡✈❡♥t t❤✐s ❛tt❛❝❦✱ ✇❡ ❤❛✈❡ t♦ ❡♥❢♦r❝❡ ❱♦t❡✲■♥❞❡♣❡♥❞❡♥❝❡ ✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  21. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ❊①✐st✐♥❣ ❞❡✜♥✐t✐♦♥s ❬❏❈❏✵✺✱ ❇❍▼✵✽❪✿ ❚❛✐❧♦r❡❞ t♦ ❛ s♣❡❝✐✜❝ ♣r♦t♦❝♦❧ ❬❉❑❘✵✾✱ ❉❑❘✶✵❪✿ ❯♥s✉✐t❛❜❧❡ ❢♦r ♣r♦t♦❝♦❧ ❜② ❏✉❡❧s✴❈✐✈✐t❛s ❬❉▲▲✶✶❛✱ ❉▲▲✶✶❜❪✿ ❱♦t❡✲■♥❞❡♣❡♥❞❡♥❝❡ ❜❛s❡❞ ♦♥ ❞❡✜♥✐t✐♦♥s ❜② ❬❉❑❘✵✾✱ ❉❑❘✶✵❪ ❬❑❚✵✾❪✿ ❈♦❡r❝✐♦♥ ❘❡s✐st❛♥❝❡✱ ✈❡r② ✜♥❡✲❣r❛✐♥❡❞ → ❞✐✣❝✉❧t t♦ ❝♦♠♣❛r❡ ❬▲❏P✶✵❪✿ Pr✐✈❛❝② ❛s ✉♥❧✐♥❦❛❜✐❧✐t② ✳ ✳ ✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  22. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ❈♦♥❝❧✉s✐♦♥ ■♥ ❛♥ ✐❞❡❛❧ ✇♦r❧❞✳✳✳ ❲❡ ♥❡❡❞ ❞❡✜♥✐t✐♦♥s t❤❛t ❝❛♥ ❜❡ ❛♣♣❧✐❡❞ ♦♥ ❛♥② ♣r♦t♦❝♦❧ ❛r❡ ❝♦♠♣❛r❛❜❧❡ ✐♥❝❧✉❞❡ ❛❧❧ ❦♥♦✇♥ t❤r❡❛ts✿ ❝♦❡r❝✐♦♥✱ ✈♦t❡✲❜✉②✐♥❣✱ ✈♦t❡✲❝♦♣②✐♥❣✱ ❢♦r❝❡❞ ❛❜st❡♥t✐♦♥ ❛r❡ s✉✐t❛❜❧❡ ❢♦r ❛✉t♦♠❛t✐♦♥ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  23. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s P❧❛♥ ✶ ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ✷ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊①❛♠♣❧❡✿ ❋❖❖ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❡✲❆✉❝t✐♦♥s ✸ ❈♦♥❝❧✉s✐♦♥ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  24. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s P❧❛♥ ✶ ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ✷ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊①❛♠♣❧❡✿ ❋❖❖ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❡✲❆✉❝t✐♦♥s ✸ ❈♦♥❝❧✉s✐♦♥ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  25. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s Pr♦t♦❝♦❧ ❜② ❋✉❥✐♦❦❛✱ ❖❦❛♠♦t♦ ❛♥❞ ❖❤t❛ ❬❋❖❖✾✷❪ ❚❤❡ ♣r♦t♦❝♦❧ ✐s s♣❧✐t ✐♥t♦ t❤r❡❡ ♣❤❛s❡s✿ ❊❧✐❣✐❜✐❧✐t② ❈❤❡❝❦ ❱♦t✐♥❣ ❈♦✉♥t✐♥❣ ❆✉t❤♦r✐t✐❡s✿ ❆❞♠✐♥✐str❛t♦r ❈♦❧❧❡❝t♦r ❆ss✉♠♣t✐♦♥s✿ ❆♥♦♥②♠♦✉s ❝❤❛♥♥❡❧ t♦ t❤❡ ❝♦❧❧❡❝t♦r ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  26. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❈r②♣t♦❣r❛♣❤✐❝ Pr✐♠✐t✐✈❡s✿ ❈♦♠♠✐t♠❡♥t ❆ ✈♦t❡r ❝♦♠♠✐ts t♦ ❤✐s ✈♦t❡ ✉s✐♥❣ ❛ r❛♥❞♦♠ ✈❛❧✉❡✳ ❍✐s ✈♦t❡ ✐s ❤✐❞❞❡♥ ✉♥t✐❧ ❤❡ r❡✈❡❛❧s t❤❡ r❛♥❞♦♠ ✈❛❧✉❡✳ ✭❍✐❞✐♥❣✮ ❍❡ ❝❛♥♥♦t ❝❤❛♥❣❡ ❤✐s ❝♦♠♠✐t♠❡♥t✳ ✭❇✐♥❞✐♥❣✮ ❊q✉❛t✐♦♥❛❧ t❤❡♦r②✿ ♦♣❡♥✭❝♦♠♠✐t✭✈✱ r✮✱ r✮ ❂ ✈ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  27. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❈r②♣t♦❣r❛♣❤✐❝ Pr✐♠✐t✐✈❡s✿ ❙✐❣♥❛t✉r❡ ❚❤❡ ❡❧✐❣✐❜❧❡ ✈♦t❡s ❛r❡ s✐❣♥❡❞ ❜② t❤❡ ❛❞♠✐♥✐str❛t♦r✳ ❆❧❧♦✇s t❤❡ ❝♦❧❧❡❝t♦r t♦ ✈❡r✐❢② t❤❛t t❤❡ ❜❛❧❧♦t ✇❛s ❝❤❡❝❦❡❞ ❜② t❤❡ ❛❞♠✐♥✐str❛t♦r ❛♥❞ t❤✉s ❜❡❧♦♥❣s t♦ ❛ ❧❡❣✐t✐♠❛t❡ ✈♦t❡r✳ ✭❆✉t❤❡♥t✐❝✐t②✮ ❊q✉❛t✐♦♥❛❧ t❤❡♦r②✿ ❝❤❡❝❦s✐❣♥✭s✐❣♥✭①✱ s❦✭❨✮✮✱ ♣❦✭❨✮✮ ❂ ♦❦ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  28. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❈r②♣t♦❣r❛♣❤✐❝ Pr✐♠✐t✐✈❡s✿ ❇❧✐♥❞ s✐❣♥❛t✉r❡ ❚❤❡ ❜❛❧❧♦ts ❛r❡ ❜❧✐♥❞❧② s✐❣♥❡❞ ❜② t❤❡ ❛❞♠✐♥✐str❛t♦r t♦ ❡♥s✉r❡ ♣r✐✈❛❝②✳ ❚❤❡ ✈♦t❡r ❜❧✐♥❞s ❤✐s ❜❛❧❧♦t ❜❡❢♦r❡ s❡♥❞✐♥❣ ✐t t♦ t❤❡ ❛❞♠✐♥✐str❛t♦r✳ ❆❢t❡r ✉♥❜❧✐♥❞✐♥❣ ❤❡ ♦❜t❛✐♥s ❛ s✐❣♥❛t✉r❡ ♦♥ ❤✐s ❜❛❧❧♦t✳ ❊q✉❛t✐♦♥❛❧ t❤❡♦r②✿ ✉♥❜❧✐♥❞✭s✐❣♥✭❜❧✐♥❞✭①✱ r✮✱ ❦❡②✮✱ r✮ ❂ s✐❣♥✭①✱ ❦❡②✮ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  29. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❊❧✐❣✐❜✐❧✐t② ❈❤❡❝❦ ❇♦❜ ❆❞♠✐♥✐str❛t♦r s✐❣♥✭❜❧✐♥❞✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ r B ✷ ✮✱ s❦✭❇♦❜✮✮✱ ■❞❡♥t✐t②✭❇♦❜✮ s✐❣♥✭❜❧✐♥❞✭❝♦♠♠✐t✭ V ✱ r B ✶ ✮✱ r B ✷ ✮✱ s❦✭❆❞✮✮ s✐❣♥✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ s❦✭❆❞✮✮ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  30. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❊❧✐❣✐❜✐❧✐t② ❈❤❡❝❦ ❇♦❜ ❆❞♠✐♥✐str❛t♦r s✐❣♥✭❜❧✐♥❞✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ r B ✷ ✮✱ s❦✭❇♦❜✮✮✱ ■❞❡♥t✐t②✭❇♦❜✮ s✐❣♥✭❜❧✐♥❞✭❝♦♠♠✐t✭ V ✱ r B ✶ ✮✱ r B ✷ ✮✱ s❦✭❆❞✮✮ s✐❣♥✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ s❦✭❆❞✮✮ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  31. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❊❧✐❣✐❜✐❧✐t② ❈❤❡❝❦ ❇♦❜ ❆❞♠✐♥✐str❛t♦r s✐❣♥✭❜❧✐♥❞✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ r B ✷ ✮✱ s❦✭❇♦❜✮✮✱ ■❞❡♥t✐t②✭❇♦❜✮ s✐❣♥✭❜❧✐♥❞✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ r B ✷ ✮✱ s❦✭❆❞✮✮ s✐❣♥✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ s❦✭❆❞✮✮ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  32. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❊❧✐❣✐❜✐❧✐t② ❈❤❡❝❦ ❇♦❜ ❆❞♠✐♥✐str❛t♦r s✐❣♥✭❜❧✐♥❞✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ r B ✷ ✮✱ s❦✭❇♦❜✮✮✱ ■❞❡♥t✐t②✭❇♦❜✮ s✐❣♥✭❜❧✐♥❞✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ r B ✷ ✮✱ s❦✭❆❞✮✮ s✐❣♥✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ s❦✭❆❞✮✮ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  33. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❱♦t✐♥❣ P❤❛s❡ s✐❣♥✭❝♦♠♠✐t✭ A ✱ r A ❆❧✐❝❡ ✶ ✮✱ s❦✭❆❞✮✮ ❈♦❧❧❡❝t♦r s✐❣♥✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ s❦✭❆❞✮✮ ❇♦❜ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  34. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❱♦t✐♥❣ P❤❛s❡ s✐❣♥✭❝♦♠♠✐t✭ A ✱ r A ❆❧✐❝❡ ✶ ✮✱ s❦✭❆❞✮✮ ❈♦❧❧❡❝t♦r s✐❣♥✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ s❦✭❆❞✮✮ ❇♦❜ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  35. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❱♦t✐♥❣ P❤❛s❡ s✐❣♥✭❝♦♠♠✐t✭ A ✱ r A ❆❧✐❝❡ ✶ ✮✱ s❦✭❆❞✮✮ ❈♦❧❧❡❝t♦r s✐❣♥✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ s❦✭❆❞✮✮ ❇♦❜ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  36. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❈♦✉t✐♥❣ P❤❛s❡ ✷✿ r A ❆❧✐❝❡ ❈♦❧❧❡❝t♦r ✶ ✶✿ r B ✶✿ ❝♦♠♠✐t✭ B ✱ r B ✶ ✮ ✶ ✷✿ ❝♦♠♠✐t✭ A ✱ r A ❇♦❜ ✶ ✮ A ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  37. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❈♦✉t✐♥❣ P❤❛s❡ ✷✿ r A ❆❧✐❝❡ ❈♦❧❧❡❝t♦r ✶ ✶✿ r B ✶✿ ❝♦♠♠✐t✭ B ✱ r B ✶ ✮ ✶ ✷✿ ❝♦♠♠✐t✭ A ✱ r A ❇♦❜ ✶ ✮ A ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  38. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❈♦✉t✐♥❣ P❤❛s❡ ✷✿ r A ❆❧✐❝❡ ❈♦❧❧❡❝t♦r ✶ ✶✿ r B ✶✿ ❝♦♠♠✐t✭ B ✱ r B ✶ ✮ ✶ ✷✿ ❝♦♠♠✐t✭ A ✱ r A ❇♦❜ ✶ ✮ A ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  39. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❈♦✉t✐♥❣ P❤❛s❡ ✷✿ r A ❆❧✐❝❡ ❈♦❧❧❡❝t♦r ✶ ✶✿ r B ✶✿ ❝♦♠♠✐t✭ B ✱ r B ✶ ✮ ✶ ✷✿ ❝♦♠♠✐t✭ A ✱ r A ❇♦❜ ✶ ✮ B A ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  40. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s P❧❛♥ ✶ ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ✷ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊①❛♠♣❧❡✿ ❋❖❖ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❡✲❆✉❝t✐♦♥s ✸ ❈♦♥❝❧✉s✐♦♥ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  41. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❉✐✛❡r❡♥t ❉✐♠❡♥s✐♦♥s ❬❉▲▲✶✷❜❪ ❈♦♠♠✉♥✐❝❛t✐♦♥✿ ❱♦t❡✲Pr✐✈❛❝② ✭❱P✮✱ ❘❡❝❡✐♣t✲❋r❡❡♥❡ss ✭❘❋✮✱ ❈♦❡r❝✐♦♥✲❘❡s✐st❛♥❝❡ ✭❈❘✮ ❱♦t❡✲■♥❞❡♣❡♥❞❡♥❝❡✿ ❖✉ts✐❞❡r ✭❖✮✱ ■♥s✐❞❡r ✭■✮ ❋♦r❝❡❞ ❆❜st❡♥t✐♦♥ ❆tt❛❝❦s✿ P❛rt✐❝✐♣❛t✐♦♥ ❖♥❧② ✭P❖✮✱ ❙❡❝✉r✐t② ❛❣❛✐♥st ❋♦r❝❡❞✲❆❜st❡♥t✐♦♥✲❆tt❛❝❦s ✭❋❆✮ ❑♥♦✇❧❡❞❣❡ ❛❜♦✉t ❤♦♥❡st ✈♦t❡rs✿ ❊①✐sts ❇❡❤❛✈✐♦r ✭❊❇✮✱ ❆♥② ❇❡❤❛✈✐♦r ✭❆❇✮ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  42. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❱♦t❡✲Pr✐✈❛❝② ✭❱P✮ ▼❛✐♥ ✐❞❡❛✿ ❖❜s❡r✈❛t✐♦♥❛❧ ❡q✉✐✈❛❧❡♥❝❡ ❜❡t✇❡❡♥ t✇♦ s✐t✉❛t✐♦♥s✳ ❆❧✐❝❡ ❇♦❜ ❱♦t❡ ❆ ❇ ≈ l ❱♦t❡ ❇ ❆ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  43. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❚❤❡ ❆♣♣❧✐❡❞ P✐ ❈❛❧❝✉❧✉s ❬❆❋✵✶❪ ❙②♥t❛① P ✱ Q ✱ R ✿❂ ♣r♦❝❡ss❡s ✵ ♥✉❧❧ ♣r♦❝❡ss P | Q ♣❛r❛❧❧❡❧ ❝♦♠♣♦s✐t✐♦♥ ! P r❡♣❧✐❝❛t✐♦♥ ν n . P ♥❛♠❡ r❡str✐❝t✐♦♥ ✭✏♥❡✇✑✮ ✐❢ M = N t❤❡♥ P ❡❧s❡ Q ❝♦♥❞✐t✐♦♥❛❧ ✐♥ ( u , x ) . P ♠❡ss❛❣❡ ✐♥♣✉t ♦✉t ( u , x ) . P ♠❡ss❛❣❡ ♦✉t♣✉t { M / x } s✉❜st✐t✉t✐♦♥ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  44. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❱♦t❡✲Pr✐✈❛❝②✿ ❚❤❡ ❢♦r♠❛❧ ❞❡✜♥✐t✐♦♥ ❉❡✜♥✐t✐♦♥ ✭❱♦t❡✲Pr✐✈❛❝②✮ ❆ ✈♦t✐♥❣ ♣r♦❝❡ss r❡s♣❡❝ts ❱♦t❡✲Pr✐✈❛❝② ✭❱P✮ ✐❢ ❢♦r ❛❧❧ ✈♦t❡s σ v A ❛♥❞ σ v B ✇❡ ❤❛✈❡ VP ′ [ V σ id A σ f A σ v A | V σ id B σ f B σ v B ] ≈ l VP ′ [ V σ id A σ f A σ v B | V σ id B σ f B σ v A ] ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  45. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❆♥❛❧②s✐s ❚❤❡♦r❡♠ ❋❖❖ ❡♥s✉r❡s ❱♦t❡✲Pr✐✈❛❝②✳ ❈❛♥ ❜❡ ♣r♦✈❡❞ ✉s✐♥❣ Pr♦❱❡r✐❢ ❬❇❆❋✵✽❪ ❛♥❞ Pr♦❙✇❛♣♣❡r ❬❉❘❙✵✽❪✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  46. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❘❡❝❡✐♣t✲❋r❡❡♥❡ss ✭❘❋✮ ❆❣❛✐♥✿ ❖❜s❡r✈❛t✐♦♥❛❧ ❡q✉✐✈❛❧❡♥❝❡ ❜❡t✇❡❡♥ t✇♦ s✐t✉❛t✐♦♥s✱ ❜✉t ❆❧✐❝❡ tr✐❡s t♦ ❝r❡❛t❡ ❛ r❡❝❡✐♣t ♦r ❛ ❢❛❦❡✳ ▼❛❧❧♦r② ❆❧✐❝❡ ❇♦❜ ❙❡❝r❡t ❉❛t❛ ❆ ❇ ≈ l ❋❛❦❡ ❉❛t❛ ❇ ❆ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  47. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❘❡❝❡✐♣t✲❋r❡❡♥❡ss ✭❘❋✮ ❆❣❛✐♥✿ ❖❜s❡r✈❛t✐♦♥❛❧ ❡q✉✐✈❛❧❡♥❝❡ ❜❡t✇❡❡♥ t✇♦ s✐t✉❛t✐♦♥s✱ ❜✉t ❆❧✐❝❡ tr✐❡s t♦ ❝r❡❛t❡ ❛ r❡❝❡✐♣t ♦r ❛ ❢❛❦❡✳ ▼❛❧❧♦r② ❆❧✐❝❡ ❇♦❜ ❙❡❝r❡t ❉❛t❛ ❆ ❇ ≈ l ❋❛❦❡ ❉❛t❛ ❇ ❆ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  48. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❋❖❖ ✐s ♥♦t ❘❋ ❇♦❜ ❆❞♠✐♥✐str❛t♦r s✐❣♥✭❜❧✐♥❞✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ r B ✷ ✮✱ s❦✭❇♦❜✮✮✱ ■❞❡♥t✐t②✭❇♦❜✮ ❚❤❡ r❛♥❞♦♠♥❡ss ❝❛♥ ❜❡ ✉s❡❞ ❛s ❛ r❡❝❡✐♣t✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  49. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❋❖❖ ✐s ♥♦t ❘❋ ❇♦❜ ❆❞♠✐♥✐str❛t♦r s✐❣♥✭❜❧✐♥❞✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ r B ✷ ✮✱ s❦✭❇♦❜✮✮✱ ■❞❡♥t✐t②✭❇♦❜✮ ❚❤❡ r❛♥❞♦♠♥❡ss ❝❛♥ ❜❡ ✉s❡❞ ❛s ❛ r❡❝❡✐♣t✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  50. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❋❖❖ ✐s ♥♦t ❘❋ ❇♦❜ ❆❞♠✐♥✐str❛t♦r s✐❣♥✭❜❧✐♥❞✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ r B ✷ ✮✱ s❦✭❇♦❜✮✮✱ ■❞❡♥t✐t②✭❇♦❜✮ ❚❤❡ r❛♥❞♦♠♥❡ss ❝❛♥ ❜❡ ✉s❡❞ ❛s ❛ r❡❝❡✐♣t✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  51. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❈♦❡r❝✐♦♥✲❘❡s✐st❛♥❝❡ ✭❈❘✮ ❖❜s❡r✈❛t✐♦♥❛❧ ❡q✉✐✈❛❧❡♥❝❡ ❜❡t✇❡❡♥ t✇♦ s✐t✉❛t✐♦♥s✱ ❜✉t ❆❧✐❝❡ ✐s ✉♥❞❡r ❝♦♥tr♦❧ ❜② ▼❛❧❧♦r② ♦r ♦♥❧② ♣r❡t❡♥❞s t♦ ❜❡ s♦✳ ❖r❞❡rs ▼❛❧❧♦r② ❆❧✐❝❡ ❇♦❜ ❙❡❝r❡t ❉❛t❛ ❆ ❇ ≈ l ❋❛❦❡ ❉❛t❛ ❇ ❆ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  52. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❈♦❡r❝✐♦♥✲❘❡s✐st❛♥❝❡ ✭❈❘✮ ❖❜s❡r✈❛t✐♦♥❛❧ ❡q✉✐✈❛❧❡♥❝❡ ❜❡t✇❡❡♥ t✇♦ s✐t✉❛t✐♦♥s✱ ❜✉t ❆❧✐❝❡ ✐s ✉♥❞❡r ❝♦♥tr♦❧ ❜② ▼❛❧❧♦r② ♦r ♦♥❧② ♣r❡t❡♥❞s t♦ ❜❡ s♦✳ ❖r❞❡rs ▼❛❧❧♦r② ❆❧✐❝❡ ❇♦❜ ❙❡❝r❡t ❉❛t❛ ❆ ❇ ≈ l ❋❛❦❡ ❉❛t❛ ❇ ❆ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  53. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❋❖❖ ✐s ♥♦t ❈❘ ❇♦❜ ❆❞♠✐♥✐str❛t♦r s✐❣♥✭❜❧✐♥❞✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ r B ✷ ✮✱ s❦✭❇♦❜✮✮✱ ■❞❡♥t✐t②✭❇♦❜✮ ❆s ❋❖❖ ✐s ♥♦t ❘❋✱ ✐t ❝❛♥♥♦t ❜❡ ❈❘✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  54. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❋❖❖ ✐s ♥♦t ❈❘ ❇♦❜ ❆❞♠✐♥✐str❛t♦r s✐❣♥✭❜❧✐♥❞✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ r B ✷ ✮✱ s❦✭❇♦❜✮✮✱ ■❞❡♥t✐t②✭❇♦❜✮ ❆s ❋❖❖ ✐s ♥♦t ❘❋✱ ✐t ❝❛♥♥♦t ❜❡ ❈❘✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  55. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❋❖❖ ✐s ♥♦t ❈❘ ❇♦❜ ❆❞♠✐♥✐str❛t♦r s✐❣♥✭❜❧✐♥❞✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ r B ✷ ✮✱ s❦✭❇♦❜✮✮✱ ■❞❡♥t✐t②✭❇♦❜✮ ❆s ❋❖❖ ✐s ♥♦t ❘❋✱ ✐t ❝❛♥♥♦t ❜❡ ❈❘✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  56. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ■♥s✐❞❡r ✭■✮ ✈s✳ ❖✉ts✐❞❡r ✭❖✮ ▼❛✐♥ ✐❞❡❛✿ Pr✐✈❛❝②✱ ❜✉t ✇✐t❤ ❛ ✈♦t❡r ✉♥❞❡r ❝♦♥tr♦❧ ♦❢ t❤❡ ❛tt❛❝❦❡r✳ ■❢ ❤❡ ❝❛♥ r❡❧❛t❡ ❤✐s ✈♦t❡ t♦ ❡✳❣✳ ❆❧✐❝❡✬s ✈♦t❡✱ ▼❛❧❧♦r② ❝❛♥ ❞✐st✐♥❣✉✐s❤ ❜♦t❤ s✐❞❡s✳ ❖ r ❞ ❡ r s ▼❛❧❧♦r② ❆❧✐❝❡ ❇♦❜ ❈❤✉❝❦ ❱♦t❡ ❆ ❇ ❄ ≈ l ❱♦t❡ ❇ ❆ ❄ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  57. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ■♥s✐❞❡r ✭■✮ ✈s✳ ❖✉ts✐❞❡r ✭❖✮ ▼❛✐♥ ✐❞❡❛✿ Pr✐✈❛❝②✱ ❜✉t ✇✐t❤ ❛ ✈♦t❡r ✉♥❞❡r ❝♦♥tr♦❧ ♦❢ t❤❡ ❛tt❛❝❦❡r✳ ■❢ ❤❡ ❝❛♥ r❡❧❛t❡ ❤✐s ✈♦t❡ t♦ ❡✳❣✳ ❆❧✐❝❡✬s ✈♦t❡✱ ▼❛❧❧♦r② ❝❛♥ ❞✐st✐♥❣✉✐s❤ ❜♦t❤ s✐❞❡s✳ ❖ r ❞ ❡ r s ▼❛❧❧♦r② ❆❧✐❝❡ ❇♦❜ ❈❤✉❝❦ ❱♦t❡ ❆ ❇ ❄ ≈ l ❱♦t❡ ❇ ❆ ❄ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  58. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❆♥❛❧②s✐s ❚❤❡♦r❡♠ ❋❖❖ ❡♥s✉r❡s ❱♦t❡✲Pr✐✈❛❝② ❢♦r ❛♥ ■♥s✐❞❡r✳ ❈❛♥ ❜❡ ♣r♦✈❡❞ ✉s✐♥❣ Pr♦❱❡r✐❢ ❬❇❆❋✵✽❪ ❛♥❞ Pr♦❙✇❛♣♣❡r ❬❉❘❙✵✽❪✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  59. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❈❛♥ ✇❡ ❝♦♠❜✐♥❡ ❱♦t❡✲■♥❞❡♣❡♥❞❡♥❝❡ ✇✐t❤ ❘❡❝❡✐♣t✲❋r❡❡♥❡ss❄ ✏❘❡❝❡✐♣t✲❋r❡❡♥❡ss ✇✐t❤ ❈❤✉❝❦✑✿ ❖ r ❞ ❡ r s ▼❛❧❧♦r② ❆❧✐❝❡ ❇♦❜ ❈❤✉❝❦ ❙❡❝r❡t ❉❛t❛ ❆ ❇ ❄ ≈ l ❋❛❦❡ ❉❛t❛ ❇ ❆ ❄ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  60. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❈❛♥ ✇❡ ❝♦♠❜✐♥❡ ❱♦t❡✲■♥❞❡♣❡♥❞❡♥❝❡ ✇✐t❤ ❘❡❝❡✐♣t✲❋r❡❡♥❡ss❄ ✏❘❡❝❡✐♣t✲❋r❡❡♥❡ss ✇✐t❤ ❈❤✉❝❦✑✿ ❖ r ❞ ❡ r s ▼❛❧❧♦r② ❆❧✐❝❡ ❇♦❜ ❈❤✉❝❦ ❙❡❝r❡t ❉❛t❛ ❆ ❇ ❄ ≈ l ❋❛❦❡ ❉❛t❛ ❇ ❆ ❄ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  61. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❙❡❝✉r✐t② ❛❣❛✐♥st ❋♦r❝❡❞ ❆❜st❡♥t✐♦♥ ❆tt❛❝❦s ✭❋❆✮ ✈s✳ P❛rt✐❝✐♣❛t✐♦♥ ❖♥❧② ✭P❖✮ ❆❧✐❝❡ ❛❜st❛✐♥s ♦r ✈♦t❡s ✐♥ t✉r♥ ✇✐t❤ ❇♦❜✿ ❆❧✐❝❡ ❇♦❜ ❱♦t❡ ❆ ❇ ≈ l ❱♦t❡ ❇ ❆ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  62. ❆ ❆ ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❙❡❝✉r✐t② ❛❣❛✐♥st ❋♦r❝❡❞ ❆❜st❡♥t✐♦♥ ❆tt❛❝❦s ✭❋❆✮ ✈s✳ P❛rt✐❝✐♣❛t✐♦♥ ❖♥❧② ✭P❖✮ ❆❧✐❝❡ ❛❜st❛✐♥s ♦r ✈♦t❡s ✐♥ t✉r♥ ✇✐t❤ ❇♦❜✿ ❆❧✐❝❡ ❇♦❜ ❱♦t❡ ❇ ≈ l ❱♦t❡ ❇ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  63. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❋❖❖ ✐s ♥♦t ❋❆ ❇♦❜ ❆❞♠✐♥✐str❛t♦r s✐❣♥✭❜❧✐♥❞✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ r B ✷ ✮✱ s❦✭❇♦❜✮✮✱ ■❞❡♥t✐t②✭❇♦❜✮ ❚❤❡ ✐❞❡♥t✐t② ♦❢ ❡❛❝❤ ✈♦t❡r ✐s s❡♥❞ ♦✈❡r ❛ ♣✉❜❧✐❝ ❝❤❛♥♥❡❧✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  64. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❋❖❖ ✐s ♥♦t ❋❆ ❇♦❜ ❆❞♠✐♥✐str❛t♦r s✐❣♥✭❜❧✐♥❞✭❝♦♠♠✐t✭ B ✱ r B ✶ ✮✱ r B ✷ ✮✱ s❦✭❇♦❜✮✮✱ ■❞❡♥t✐t②✭❇♦❜✮ ❚❤❡ ✐❞❡♥t✐t② ♦❢ ❡❛❝❤ ✈♦t❡r ✐s s❡♥❞ ♦✈❡r ❛ ♣✉❜❧✐❝ ❝❤❛♥♥❡❧✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  65. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ■♥tr♦❞✉❝✐♥❣ ❋❛❦❡s✿ ❊①✐sts ❇❡❤❛✈✐♦r ✭❊❇✮ ✈s✳ ❆♥② ❇❡❤❛✈✐♦r ✭❆❇✮ ❙♦♠❡ ♣r♦t♦❝♦❧s ✉s❡ ❢❛❦❡ ✈♦t❡s ❬❏❈❏✵✺❪ t♦ ❛❝❤✐❡✈❡ ❘❡❝❡✐♣t✲❋r❡❡♥❡ss ❛♥❞ ❈♦❡r❝✐♦♥✲❘❡st✐st❛♥❝❡✳ ▼❛❧❧♦r② ❆❧✐❝❡ ❇♦❜ ❙❡❝r❡t ❉❛t❛ ❆ ❇ ≈ l ❆ ❇ ❆ ❋❛❦❡ ❉❛t❛ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  66. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ■♥tr♦❞✉❝✐♥❣ ❋❛❦❡s✿ ❊①✐sts ❇❡❤❛✈✐♦r ✭❊❇✮ ✈s✳ ❆♥② ❇❡❤❛✈✐♦r ✭❆❇✮ ❙♦♠❡ ♣r♦t♦❝♦❧s ✉s❡ ❢❛❦❡ ✈♦t❡s ❬❏❈❏✵✺❪ t♦ ❛❝❤✐❡✈❡ ❘❡❝❡✐♣t✲❋r❡❡♥❡ss ❛♥❞ ❈♦❡r❝✐♦♥✲❘❡st✐st❛♥❝❡✳ ▼❛❧❧♦r② ❆❧✐❝❡ ❇♦❜ ❙❡❝r❡t ❉❛t❛ ❆ ❆ ❇ ≈ l ❆ ❇ ❆ ❋❛❦❡ ❉❛t❛ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  67. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❆♣♣❧✐❝❛t✐♦♥✿ ❋❖❖ ◆♦ ❢❛❦❡s ✉s❡❞✱ ❤❡♥❝❡✿ ❚❤❡♦r❡♠ ❋❖❖ ❡♥s✉r❡s ❱♦t❡✲Pr✐✈❛❝② ❢♦r ❛♥ ■♥s✐❞❡r ❢♦r ❛♥② ❜❡❤❛✈✐♦r ♦❢ t❤❡ ♦t❤❡r ✈♦t❡rs ❜✉t ✐s ♥♦t s❡❝✉r❡ ❛❣❛✐♥st ❋♦r❝❡❞ ❆❜st❡♥t✐♦♥ ❆tt❛❝❦s ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  68. � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❘❡❧❛t✐♦♥s ❛♠♦♥❣ t❤❡ ♥♦t✐♦♥s CR O , FA , AB CR I , FA , AB CR O , FA , EB CR I , FA , EB CR O , PO , AB CR I , PO , AB CR O , PO , EB CR I , PO , EB RF O , FA , AB RF I , FA , AB RF O , FA , EB RF I , FA , EB RF O , PO , EB RF I , PO , EB RF O , PO , AB RF I , PO , AB VP O , FA , AB VP I , FA , AB VP O , FA , EB VP I , FA , EB VP O , PO , EB VP I , PO , EB VP O , PO , AB VP I , PO , AB ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  69. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s P❧❛♥ ✶ ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❢♦r♠❛❧ ♠❡t❤♦❞s ✐♥ s❡❝✉r✐t②❄ ❊❧❡❝tr♦♥✐❝ ❱♦t✐♥❣ ✷ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❊①❛♠♣❧❡✿ ❋❖❖ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❡✲❆✉❝t✐♦♥s ✸ ❈♦♥❝❧✉s✐♦♥ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  70. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s Pr♦❜❧❡♠✿ ❲❡✐❣❤t❡❞ ❱♦t❡s ❬❉▲▲✶✷❛❪ ❲❤❛t ❤❛♣♣❡♥s ✐❢ ✈♦t❡s ❛r❡ ✇❡✐❣❤t❡❞ ✭❡✳❣✳ ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ♥✉♠❜❡r ♦❢ s❤❛r❡s ✐♥ ❛ ❝♦♠♣❛♥②✮❄ ❆❧✐❝❡ ❇♦❜ ❘❡s✉❧t ✻✻✪ ✸✹✪ ❱♦t❡ ❆ ❇ ✻✻✪ ❆✱ ✸✹✪ ❇ ≈ l ✸✹✪ ❆✱ ✻✻✪ ❇ ❱♦t❡ ❇ ❆ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  71. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s Pr♦❜❧❡♠✿ ❲❡✐❣❤t❡❞ ❱♦t❡s ❬❉▲▲✶✷❛❪ ❲❤❛t ❤❛♣♣❡♥s ✐❢ ✈♦t❡s ❛r❡ ✇❡✐❣❤t❡❞ ✭❡✳❣✳ ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ♥✉♠❜❡r ♦❢ s❤❛r❡s ✐♥ ❛ ❝♦♠♣❛♥②✮❄ ❆❧✐❝❡ ❇♦❜ ❘❡s✉❧t ✻✻✪ ✸✹✪ ❱♦t❡ ❆ ❇ ✻✻✪ ❆✱ ✸✹✪ ❇ ≈ l ✸✹✪ ❆✱ ✻✻✪ ❇ ❱♦t❡ ❇ ❆ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  72. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s Pr♦❜❧❡♠✿ ❲❡✐❣❤t❡❞ ❱♦t❡s ❬❉▲▲✶✷❛❪ ❲❤❛t ❤❛♣♣❡♥s ✐❢ ✈♦t❡s ❛r❡ ✇❡✐❣❤t❡❞ ✭❡✳❣✳ ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ♥✉♠❜❡r ♦❢ s❤❛r❡s ✐♥ ❛ ❝♦♠♣❛♥②✮❄ ❆❧✐❝❡ ❇♦❜ ❘❡s✉❧t ✻✻✪ ✸✹✪ ❱♦t❡ ❆ ❇ ✻✻✪ ❆✱ ✸✹✪ ❇ ≈ l � = ✸✹✪ ❆✱ ✻✻✪ ❇ ❱♦t❡ ❇ ❆ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  73. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s Pr♦❜❧❡♠✿ ❲❡✐❣❤t❡❞ ❱♦t❡s ❬❉▲▲✶✷❛❪ ❲❤❛t ❤❛♣♣❡♥s ✐❢ ✈♦t❡s ❛r❡ ✇❡✐❣❤t❡❞ ✭❡✳❣✳ ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ♥✉♠❜❡r ♦❢ s❤❛r❡s ✐♥ ❛ ❝♦♠♣❛♥②✮❄ ❆❧✐❝❡ ❇♦❜ ❘❡s✉❧t ✻✻✪ ✸✹✪ ❱♦t❡ ❆ ❇ ✻✻✪ ❆✱ ✸✹✪ ❇ �≈ l � = ✸✹✪ ❆✱ ✻✻✪ ❇ ❱♦t❡ ❇ ❆ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  74. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s Pr♦❜❧❡♠✿ ❲❡✐❣❤t❡❞ ❱♦t❡s ❙t✐❧❧✿ ❙♦♠❡ ♣r✐✈❛❝② ✐s ♣♦ss✐❜❧❡✦ ❆❧✐❝❡ ❇♦❜ ❈❛r♦❧ ❘❡s✉❧t ✺✵✪ ✷✺✪ ✷✺✪ ✺✵✪ ❆✱ ✺✵✪ ❇ ❱♦t❡ ❆ ❇ ❇ ❱♦t❡ ❇ ❆ ❆ ✺✵✪ ❆✱ ✺✵✪ ❇ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  75. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s Pr♦❜❧❡♠✿ ❲❡✐❣❤t❡❞ ❱♦t❡s ❙t✐❧❧✿ ❙♦♠❡ ♣r✐✈❛❝② ✐s ♣♦ss✐❜❧❡✦ ❆❧✐❝❡ ❇♦❜ ❈❛r♦❧ ❘❡s✉❧t ✺✵✪ ✷✺✪ ✷✺✪ ✺✵✪ ❆✱ ✺✵✪ ❇ ❱♦t❡ ❆ ❇ ❇ ❱♦t❡ ❇ ❆ ❆ ✺✵✪ ❆✱ ✺✵✪ ❇ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  76. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s Pr♦❜❧❡♠✿ ❲❡✐❣❤t❡❞ ❱♦t❡s ❙t✐❧❧✿ ❙♦♠❡ ♣r✐✈❛❝② ✐s ♣♦ss✐❜❧❡✦ ❆❧✐❝❡ ❇♦❜ ❈❛r♦❧ ❘❡s✉❧t ✺✵✪ ✷✺✪ ✷✺✪ ✺✵✪ ❆✱ ✺✵✪ ❇ ❱♦t❡ ❆ ❇ ❇ = ❱♦t❡ ❇ ❆ ❆ ✺✵✪ ❆✱ ✺✵✪ ❇ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  77. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s Pr♦❜❧❡♠✿ ❲❡✐❣❤t❡❞ ❱♦t❡s ❙t✐❧❧✿ ❙♦♠❡ ♣r✐✈❛❝② ✐s ♣♦ss✐❜❧❡✦ ❆❧✐❝❡ ❇♦❜ ❈❛r♦❧ ❘❡s✉❧t ✺✵✪ ✷✺✪ ✷✺✪ ✺✵✪ ❆✱ ✺✵✪ ❇ ❱♦t❡ ❆ ❇ ❇ ≈ l = ❱♦t❡ ❇ ❆ ❆ ✺✵✪ ❆✱ ✺✵✪ ❇ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  78. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❙♦❧✉t✐♦♥✿ ❉❡✜♥✐♥❣ ❱♦t❡✲Pr✐✈❛❝② ✭❱P✮ ❢♦r ✇❡✐❣❤t❡❞ ✈♦t❡s ■❞❡❛✿ ■❢ t✇♦ ✐♥st❛♥❝❡s ❣✐✈❡ t❤❡ s❛♠❡ r❡s✉❧t✱ t❤❡② s❤♦✉❧❞ ❜❡ ❜✐s✐♠✐❧❛r✳ ✳ ✳ ✳ ❆❧✐❝❡ ❇♦❜ ❘❡s✉❧t ✳ ✳ ✳ V A V A ❱♦t❡ ❘❡s✉❧t ✶ ✶ ✷ ✳ ✳ ✳ V B V B ❱♦t❡ ❘❡s✉❧t ✷ ✶ ✷ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  79. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❙♦❧✉t✐♦♥✿ ❉❡✜♥✐♥❣ ❱♦t❡✲Pr✐✈❛❝② ✭❱P✮ ❢♦r ✇❡✐❣❤t❡❞ ✈♦t❡s ■❞❡❛✿ ■❢ t✇♦ ✐♥st❛♥❝❡s ❣✐✈❡ t❤❡ s❛♠❡ r❡s✉❧t✱ t❤❡② s❤♦✉❧❞ ❜❡ ❜✐s✐♠✐❧❛r✳ ✳ ✳ ✳ ❆❧✐❝❡ ❇♦❜ ❘❡s✉❧t ✳ ✳ ✳ V A V A ❱♦t❡ ❘❡s✉❧t ✶ ✶ ✷ ? = ✳ ✳ ✳ V B V B ❱♦t❡ ❘❡s✉❧t ✷ ✶ ✷ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  80. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❙♦❧✉t✐♦♥✿ ❉❡✜♥✐♥❣ ❱♦t❡✲Pr✐✈❛❝② ✭❱P✮ ❢♦r ✇❡✐❣❤t❡❞ ✈♦t❡s ■❞❡❛✿ ■❢ t✇♦ ✐♥st❛♥❝❡s ❣✐✈❡ t❤❡ s❛♠❡ r❡s✉❧t✱ t❤❡② s❤♦✉❧❞ ❜❡ ❜✐s✐♠✐❧❛r✳ ✳ ✳ ✳ ❆❧✐❝❡ ❇♦❜ ❘❡s✉❧t ✳ ✳ ✳ V A V A ❱♦t❡ ❘❡s✉❧t ✶ ✶ ✷ ⇐ ? = ✳ ✳ ✳ V B V B ❱♦t❡ ❘❡s✉❧t ✷ ✶ ✷ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  81. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❙♦❧✉t✐♦♥✿ ❉❡✜♥✐♥❣ ❱♦t❡✲Pr✐✈❛❝② ✭❱P✮ ❢♦r ✇❡✐❣❤t❡❞ ✈♦t❡s ■❞❡❛✿ ■❢ t✇♦ ✐♥st❛♥❝❡s ❣✐✈❡ t❤❡ s❛♠❡ r❡s✉❧t✱ t❤❡② s❤♦✉❧❞ ❜❡ ❜✐s✐♠✐❧❛r✳ ✳ ✳ ✳ ❆❧✐❝❡ ❇♦❜ ❘❡s✉❧t ✳ ✳ ✳ V A V A ❱♦t❡ ❘❡s✉❧t ✶ ✶ ✷ ≈ l ⇐ ? = ✳ ✳ ✳ V B V B ❱♦t❡ ❘❡s✉❧t ✷ ✶ ✷ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  82. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ▲✐♥❦ t♦ ❡①✐st✐♥❣ ❞❡✜♥✐t✐♦♥s✿ ❊q✉❛❧✐t② ♦❢ ❱♦t❡s ✭❊◗✮ ✳ ✳ ✳ ❆❧✐❝❡ ❇♦❜ ❘❡s✉❧t ✳ ✳ ✳ V A V A ❱♦t❡ ❘❡s✉❧t ✶ ✶ ✷ ⇔ ∃ π = V B V B ✳ ✳ ✳ ❱♦t❡ ❘❡s✉❧t ✷ π ( ✶ ) π ( ✷ ) ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  83. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ▲✐♥❦ t♦ ❡①✐st✐♥❣ ❞❡✜♥✐t✐♦♥s✱ ❝♦♥t✬❞ ❚❤❡♦r❡♠ ✭❊q✉✐✈❛❧❡♥❝❡ ♦❢ Pr✐✈❛❝② ❉❡✜♥✐t✐♦♥s✮ ■❢ ❛ ♣r♦t♦❝♦❧ r❡s♣❡❝ts ❊q✉❛❧✐t② ♦❢ ❱♦t❡s ✭❊◗✮✱ t❤❡♥ ❱♦t❡✲Pr✐✈❛❝② ✭❱P✮ ❛♥❞ ❙✇❛♣✲Pr✐✈❛❝② ✭❙✇P✮ ❛r❡ ❡q✉✐✈❛❧❡♥t✿ ❊◗ ❙✇P ❱P ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  84. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❈❛s❡ ❙t✉❞②✿ ❊①t❡♥❞✐♥❣ ❋❖❖ ❊❧✐❛ss♦♥ ❛♥❞ ❩úq✉❡t❡ ❬❊❩✵✻❪✿ ❞✐✛❡r❡♥t ✈❡rs✐♦♥s ♦❢ ❋❖❖ ❬❋❖❖✾✷❪ ✐♠♣❧❡♠❡♥t✐♥❣ ✇❡✐❣❤t❡❞ ✈♦t❡s✱ ❢♦r ❡①❛♠♣❧❡ ✉s✐♥❣ ♠✉❧t✐♣❧❡ ❜❛❧❧♦ts ♣❡r ✈♦t❡r✳ ▼❛♥✉❛❧ ♣r♦♦❢ t♦ s❤♦✇ t❤❛t n n � V A � V B VP A | res ≈ l VP B | res ⇒ i ∗ w i = ∗ w i . i i = ✶ i = ✶ Pr♦❱❡r✐❢ ❬❇❆❋✵✽❪ t♦ ❡st❛❜❧✐s❤ t❤❡ ❢♦❧❧♦✇✐♥❣✱ ✇❤✐❝❤ ❣✐✈❡s ✭❱P✮✳ n n � � V A V B i ∗ w i = ∗ w i ⇒ VP A ≈ l VP B i i = ✶ i = ✶ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  85. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❙✐♥❣❧❡✲❱♦t❡r ❘❡❝❡✐♣t ❋r❡❡♥❡ss ✭❙❘❋✮ ✳ ✳ ✳ ▼❛❧❧♦r② ❆❧✐❝❡ ❇♦❜ ❘❡s✉❧t ✳ ✳ ✳ V A V A ❙❡❝r❡t ❉❛t❛ ❘❡s✉❧t ✶ ✶ ✷ ≈ l ⇐ ? = ✳ ✳ ✳ V B V B ❋❛❦❡ ❉❛t❛ ❘❡s✉❧t ✷ ✶ ✷ ■❢ ❛ ♣r♦t♦❝♦❧ r❡s♣❡❝ts ✭❊◗✮✱ t❤❡♥ ✭❙❘❋✮ ❛♥❞ ✭❙✇❘❋✮ ❛r❡ ❡q✉✐✈❛❧❡♥t✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  86. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❙✐♥❣❧❡✲❱♦t❡r ❘❡❝❡✐♣t ❋r❡❡♥❡ss ✭❙❘❋✮ ✳ ✳ ✳ ▼❛❧❧♦r② ❆❧✐❝❡ ❇♦❜ ❘❡s✉❧t ✳ ✳ ✳ V A V A ❙❡❝r❡t ❉❛t❛ ❘❡s✉❧t ✶ ✶ ✷ ≈ l ⇐ ? = ✳ ✳ ✳ V B V B ❋❛❦❡ ❉❛t❛ ❘❡s✉❧t ✷ ✶ ✷ ■❢ ❛ ♣r♦t♦❝♦❧ r❡s♣❡❝ts ✭❊◗✮✱ t❤❡♥ ✭❙❘❋✮ ❛♥❞ ✭❙✇❘❋✮ ❛r❡ ❡q✉✐✈❛❧❡♥t✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  87. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ❙✐♥❣❧❡✲❱♦t❡r ❘❡❝❡✐♣t ❋r❡❡♥❡ss ✭❙❘❋✮ ✳ ✳ ✳ ▼❛❧❧♦r② ❆❧✐❝❡ ❇♦❜ ❘❡s✉❧t ✳ ✳ ✳ V A V A ❙❡❝r❡t ❉❛t❛ ❘❡s✉❧t ✶ ✶ ✷ ≈ l ⇐ ? = ✳ ✳ ✳ V B V B ❋❛❦❡ ❉❛t❛ ❘❡s✉❧t ✷ ✶ ✷ ■❢ ❛ ♣r♦t♦❝♦❧ r❡s♣❡❝ts ✭❊◗✮✱ t❤❡♥ ✭❙❘❋✮ ❛♥❞ ✭❙✇❘❋✮ ❛r❡ ❡q✉✐✈❛❧❡♥t✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  88. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ▼✉❧t✐✲❱♦t❡r ❘❡❝❡✐♣t ❋r❡❡♥❡ss ✭▼❘❋✮ ✳ ✳ ✳ ▼❛❧❧♦r② ❆❧✐❝❡ ❇♦❜ ❘❡s✉❧t ✳ ✳ ✳ V A V A ❙✷ ❙✶ ❘❡s✉❧t ✶ ✶ ✷ ≈ l ⇐ ? = ✳ ✳ ✳ V B V B ❋✷ ❋✶ ❘❡s✉❧t ✷ ✶ ✷ ▼✉❧t✐✲❱♦t❡r ❘❡❝❡✐♣t ❋r❡❡♥❡ss ✭▼❘❋✮ ✐♠♣❧✐❡s ❙✐♥❣❧❡✲❱♦t❡r ❘❡❝❡✐♣t ❋r❡❡♥❡ss ✭❙❘❋✮✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

  89. ❊①❛♠♣❧❡✿ ❋❖❖ ■♥tr♦❞✉❝t✐♦♥ ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❉❡✜♥✐♥❣ Pr✐✈❛❝② ❲❡✐❣❤t❡❞ ❱♦t❡s ✫ ▼✉❧t✐✲❱♦t❡r ❈♦❡r❝✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❡✲❆✉❝t✐♦♥s ▼✉❧t✐✲❱♦t❡r ❘❡❝❡✐♣t ❋r❡❡♥❡ss ✭▼❘❋✮ ✳ ✳ ✳ ▼❛❧❧♦r② ❆❧✐❝❡ ❇♦❜ ❘❡s✉❧t ✳ ✳ ✳ V A V A ❙✷ ❙✶ ❘❡s✉❧t ✶ ✶ ✷ ≈ l ⇐ ? = ✳ ✳ ✳ V B V B ❋✷ ❋✶ ❘❡s✉❧t ✷ ✶ ✷ ▼✉❧t✐✲❱♦t❡r ❘❡❝❡✐♣t ❋r❡❡♥❡ss ✭▼❘❋✮ ✐♠♣❧✐❡s ❙✐♥❣❧❡✲❱♦t❡r ❘❡❝❡✐♣t ❋r❡❡♥❡ss ✭❙❘❋✮✳ ❏❛♥♥✐❦ ❉r❡✐❡r ❋♦r♠❛❧ ❱❡r✐✜❝❛t✐♦♥ ♦❢ Pr✐✈❛❝② Pr♦♣❡rt✐❡s ❢♦r ❡✲❱♦t✐♥❣

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