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  1. ❇♦✉♥❞❡❞ ❚❛♠♣❡r ❘❡s✐❧✐❡♥❝❡✿ ❍♦✇ t♦ ❣♦ ❜❡②♦♥❞ t❤❡ ❆❧❣❡❜r❛✐❝ ❇❛rr✐❡r Pr❛t②❛② ▼✉❦❤❡r❥❡❡ ❆❛r❤✉s ❯♥✐✈❡rs✐t② ❆s✐❛❝r②♣t ✷✵✶✸ ❏♦✐♥t ✇♦r❦ ✇✐t❤ ■✈❛♥ ❉❛♠❣år❞✱ ❙❡❜❛st✐❛♥ ❋❛✉st ✫ ❉❛♥✐❡❧❡ ❱❡♥t✉r✐ P✳ ▼✉❦❤❡r❥❡❡ ✭❆❛r❤✉s ❈r②♣t♦✮ ❇▲❚ ❆s✐❛❝r②♣t ✷✵✶✸ ✶ ✴ ✶✽

  2. ❚❤✐s t❛❧❦ ❘❡❛❧✐t②✿ ❘❡❛❧✐t②✿ ❙t❛♥❞❛r❞ ❆♥❛❧②s✐s✿ P❤②s✐❝❛❧ ❆tt❛❝❦s P❤②s✐❝❛❧ ❆tt❛❝❦s ❇❧❛❝❦❜♦① ✐♠♣❧❡♠❡♥t t❛♠♣❡r❡❞ ✐♥♣✉t ✐♥♣✉t ✐♥♣✉t t❛♠♣❡r✐♥❣ ❧❡❛❦❛❣❡ ❧❡❛❦❛❣❡ ❛❞✈❡rs❛r② ❛❞✈❡rs❛r② ❛❞✈❡rs❛r② t❛♠♣❡r❡❞ ♦✉t♣✉t ♦✉t♣✉t ♦✉t♣✉t ■♥tr♦❞✉❝t✐♦♥ P❤②s✐❝❛❧ ❆tt❛❝❦s✿ ❚❤❡♦r② ✈s ❘❡❛❧✐t② P✳ ▼✉❦❤❡r❥❡❡ ✭❆❛r❤✉s ❈r②♣t♦✮ ❇▲❚ ❆s✐❛❝r②♣t ✷✵✶✸ ✷ ✴ ✶✽

  3. ❚❤✐s t❛❧❦ ❘❡❛❧✐t②✿ ❘❡❛❧✐t②✿ P❤②s✐❝❛❧ ❆tt❛❝❦s P❤②s✐❝❛❧ ❆tt❛❝❦s ✐♠♣❧❡♠❡♥t t❛♠♣❡r❡❞ ✐♥♣✉t ✐♥♣✉t t❛♠♣❡r✐♥❣ ❧❡❛❦❛❣❡ ❧❡❛❦❛❣❡ ❛❞✈❡rs❛r② ❛❞✈❡rs❛r② t❛♠♣❡r❡❞ ♦✉t♣✉t ♦✉t♣✉t ■♥tr♦❞✉❝t✐♦♥ P❤②s✐❝❛❧ ❆tt❛❝❦s✿ ❚❤❡♦r② ✈s ❘❡❛❧✐t② ❙t❛♥❞❛r❞ ❆♥❛❧②s✐s✿ ❇❧❛❝❦❜♦① ✐♥♣✉t F K ( · ) ❛❞✈❡rs❛r② ♦✉t♣✉t P✳ ▼✉❦❤❡r❥❡❡ ✭❆❛r❤✉s ❈r②♣t♦✮ ❇▲❚ ❆s✐❛❝r②♣t ✷✵✶✸ ✷ ✴ ✶✽

  4. ❚❤✐s t❛❧❦ ❘❡❛❧✐t②✿ P❤②s✐❝❛❧ ❆tt❛❝❦s t❛♠♣❡r❡❞ ✐♥♣✉t t❛♠♣❡r✐♥❣ ❧❡❛❦❛❣❡ ❛❞✈❡rs❛r② t❛♠♣❡r❡❞ ♦✉t♣✉t ■♥tr♦❞✉❝t✐♦♥ P❤②s✐❝❛❧ ❆tt❛❝❦s✿ ❚❤❡♦r② ✈s ❘❡❛❧✐t② ❘❡❛❧✐t②✿ ❙t❛♥❞❛r❞ ❆♥❛❧②s✐s✿ P❤②s✐❝❛❧ ❆tt❛❝❦s ❇❧❛❝❦❜♦① ✐♠♣❧❡♠❡♥t ✐♥♣✉t ✐♥♣✉t F K ( · ) F K ( · ) ❧❡❛❦❛❣❡ ❛❞✈❡rs❛r② ❛❞✈❡rs❛r② ♦✉t♣✉t ♦✉t♣✉t P✳ ▼✉❦❤❡r❥❡❡ ✭❆❛r❤✉s ❈r②♣t♦✮ ❇▲❚ ❆s✐❛❝r②♣t ✷✵✶✸ ✷ ✴ ✶✽

  5. ❚❤✐s t❛❧❦ ✐♥♣✉t ♦✉t♣✉t ■♥tr♦❞✉❝t✐♦♥ P❤②s✐❝❛❧ ❆tt❛❝❦s✿ ❚❤❡♦r② ✈s ❘❡❛❧✐t② ❘❡❛❧✐t②✿ ❘❡❛❧✐t②✿ ❙t❛♥❞❛r❞ ❆♥❛❧②s✐s✿ P❤②s✐❝❛❧ ❆tt❛❝❦s P❤②s✐❝❛❧ ❆tt❛❝❦s ❇❧❛❝❦❜♦① ✐♠♣❧❡♠❡♥t t❛♠♣❡r❡❞ ✐♥♣✉t ✐♥♣✉t t❛♠♣❡r✐♥❣ � F K ( · ) F K ( · ) F � K ( · ) ❧❡❛❦❛❣❡ ❧❡❛❦❛❣❡ ❛❞✈❡rs❛r② ❛❞✈❡rs❛r② ❛❞✈❡rs❛r② t❛♠♣❡r❡❞ ♦✉t♣✉t ♦✉t♣✉t P✳ ▼✉❦❤❡r❥❡❡ ✭❆❛r❤✉s ❈r②♣t♦✮ ❇▲❚ ❆s✐❛❝r②♣t ✷✵✶✸ ✷ ✴ ✶✽

  6. ✐♥♣✉t ♦✉t♣✉t ■♥tr♦❞✉❝t✐♦♥ P❤②s✐❝❛❧ ❆tt❛❝❦s✿ ❚❤❡♦r② ✈s ❘❡❛❧✐t② ❚❤✐s t❛❧❦ ❘❡❛❧✐t②✿ ❘❡❛❧✐t②✿ ❙t❛♥❞❛r❞ ❆♥❛❧②s✐s✿ P❤②s✐❝❛❧ ❆tt❛❝❦s P❤②s✐❝❛❧ ❆tt❛❝❦s ❇❧❛❝❦❜♦① ✐♠♣❧❡♠❡♥t t❛♠♣❡r❡❞ ✐♥♣✉t ✐♥♣✉t t❛♠♣❡r✐♥❣ � F K ( · ) F K ( · ) F � K ( · ) ❧❡❛❦❛❣❡ ❧❡❛❦❛❣❡ ❛❞✈❡rs❛r② ❛❞✈❡rs❛r② ❛❞✈❡rs❛r② t❛♠♣❡r❡❞ ♦✉t♣✉t ♦✉t♣✉t P✳ ▼✉❦❤❡r❥❡❡ ✭❆❛r❤✉s ❈r②♣t♦✮ ❇▲❚ ❆s✐❛❝r②♣t ✷✵✶✸ ✷ ✴ ✶✽

  7. ❈❛♣t✉r❡s Pr❛❝t✐❝❛❧ ❆tt❛❝❦s ❋❛✉❧t ❆tt❛❝❦✦ ❊①❛♠♣❧❡ ❇♦♥❡❤ ❡t ❛❧✳ ❬ ❥♦❝✬✵✶ ❪✿ ■♥❥❡❝t s✐♥❣❧❡ ✭r❛♥❞♦♠✮ ❢❛✉❧t t♦ t❤❡ s✐❣♥✐♥❣✲❦❡② ♦❢ s♦♠❡ t②♣❡ ♦❢ ❘❙❆✲s✐❣ ❢❛❝t♦r ❘❙❆✲♠♦❞✉❧✉s ✦ ❉❡✈❛st❛t✐♥❣ ✦ ▼♦r❡ ✳✳✳ ❆♥❞❡rs♦♥ ✫ ❑✉❤♥ ❬ ✉s❡♥✐①✬✾✻ ❪ ❙❦♦r♦❜♦❣❛t♦✈ ❡t ❛❧✳ ❬ ❝❤❡s✬✵✷ ❪ ❈♦r♦♥ ❡t ❛❧✳ ❬ ❝❤❡s✬✵✾ ❪ ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❝❛r❡ ❛❜♦✉t ❚❛♠♣❡r✐♥❣ ❄ P✳ ▼✉❦❤❡r❥❡❡ ✭❆❛r❤✉s ❈r②♣t♦✮ ❇▲❚ ❆s✐❛❝r②♣t ✷✵✶✸ ✸ ✴ ✶✽

  8. ❊①❛♠♣❧❡ ❇♦♥❡❤ ❡t ❛❧✳ ❬ ❥♦❝✬✵✶ ❪✿ ■♥❥❡❝t s✐♥❣❧❡ ✭r❛♥❞♦♠✮ ❢❛✉❧t t♦ t❤❡ s✐❣♥✐♥❣✲❦❡② ♦❢ s♦♠❡ t②♣❡ ♦❢ ❘❙❆✲s✐❣ ❢❛❝t♦r ❘❙❆✲♠♦❞✉❧✉s ✦ ❉❡✈❛st❛t✐♥❣ ✦ ▼♦r❡ ✳✳✳ ❆♥❞❡rs♦♥ ✫ ❑✉❤♥ ❬ ✉s❡♥✐①✬✾✻ ❪ ❙❦♦r♦❜♦❣❛t♦✈ ❡t ❛❧✳ ❬ ❝❤❡s✬✵✷ ❪ ❈♦r♦♥ ❡t ❛❧✳ ❬ ❝❤❡s✬✵✾ ❪ ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❝❛r❡ ❛❜♦✉t ❚❛♠♣❡r✐♥❣ ❄ ❈❛♣t✉r❡s Pr❛❝t✐❝❛❧ ❆tt❛❝❦s ❋❛✉❧t ❆tt❛❝❦✦ P✳ ▼✉❦❤❡r❥❡❡ ✭❆❛r❤✉s ❈r②♣t♦✮ ❇▲❚ ❆s✐❛❝r②♣t ✷✵✶✸ ✸ ✴ ✶✽

  9. ❉❡✈❛st❛t✐♥❣ ✦ ▼♦r❡ ✳✳✳ ❆♥❞❡rs♦♥ ✫ ❑✉❤♥ ❬ ✉s❡♥✐①✬✾✻ ❪ ❙❦♦r♦❜♦❣❛t♦✈ ❡t ❛❧✳ ❬ ❝❤❡s✬✵✷ ❪ ❈♦r♦♥ ❡t ❛❧✳ ❬ ❝❤❡s✬✵✾ ❪ ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❝❛r❡ ❛❜♦✉t ❚❛♠♣❡r✐♥❣ ❄ ❈❛♣t✉r❡s Pr❛❝t✐❝❛❧ ❆tt❛❝❦s ❋❛✉❧t ❆tt❛❝❦✦ ❊①❛♠♣❧❡ ❇♦♥❡❤ ❡t ❛❧✳ ❬ ❥♦❝✬✵✶ ❪✿ ■♥❥❡❝t s✐♥❣❧❡ ✭r❛♥❞♦♠✮ ❢❛✉❧t t♦ t❤❡ s✐❣♥✐♥❣✲❦❡② ♦❢ s♦♠❡ t②♣❡ ♦❢ ❘❙❆✲s✐❣ = ⇒ ❢❛❝t♦r ❘❙❆✲♠♦❞✉❧✉s ✦ P✳ ▼✉❦❤❡r❥❡❡ ✭❆❛r❤✉s ❈r②♣t♦✮ ❇▲❚ ❆s✐❛❝r②♣t ✷✵✶✸ ✸ ✴ ✶✽

  10. ▼♦r❡ ✳✳✳ ❆♥❞❡rs♦♥ ✫ ❑✉❤♥ ❬ ✉s❡♥✐①✬✾✻ ❪ ❙❦♦r♦❜♦❣❛t♦✈ ❡t ❛❧✳ ❬ ❝❤❡s✬✵✷ ❪ ❈♦r♦♥ ❡t ❛❧✳ ❬ ❝❤❡s✬✵✾ ❪ ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❝❛r❡ ❛❜♦✉t ❚❛♠♣❡r✐♥❣ ❄ ❈❛♣t✉r❡s Pr❛❝t✐❝❛❧ ❆tt❛❝❦s ❋❛✉❧t ❆tt❛❝❦✦ ❊①❛♠♣❧❡ ❇♦♥❡❤ ❡t ❛❧✳ ❬ ❥♦❝✬✵✶ ❪✿ ■♥❥❡❝t s✐♥❣❧❡ ✭r❛♥❞♦♠✮ ❢❛✉❧t t♦ t❤❡ s✐❣♥✐♥❣✲❦❡② ♦❢ s♦♠❡ t②♣❡ ♦❢ ❘❙❆✲s✐❣ = ⇒ ❢❛❝t♦r ❘❙❆✲♠♦❞✉❧✉s ✦ ❉❡✈❛st❛t✐♥❣ ✦ P✳ ▼✉❦❤❡r❥❡❡ ✭❆❛r❤✉s ❈r②♣t♦✮ ❇▲❚ ❆s✐❛❝r②♣t ✷✵✶✸ ✸ ✴ ✶✽

  11. ■♥tr♦❞✉❝t✐♦♥ ❲❤② ❝❛r❡ ❛❜♦✉t ❚❛♠♣❡r✐♥❣ ❄ ❈❛♣t✉r❡s Pr❛❝t✐❝❛❧ ❆tt❛❝❦s ❋❛✉❧t ❆tt❛❝❦✦ ❊①❛♠♣❧❡ ❇♦♥❡❤ ❡t ❛❧✳ ❬ ❥♦❝✬✵✶ ❪✿ ■♥❥❡❝t s✐♥❣❧❡ ✭r❛♥❞♦♠✮ ❢❛✉❧t t♦ t❤❡ s✐❣♥✐♥❣✲❦❡② ♦❢ s♦♠❡ t②♣❡ ♦❢ ❘❙❆✲s✐❣ = ⇒ ❢❛❝t♦r ❘❙❆✲♠♦❞✉❧✉s ✦ ❉❡✈❛st❛t✐♥❣ ✦ ▼♦r❡ ✳✳✳ ❆♥❞❡rs♦♥ ✫ ❑✉❤♥ ❬ ✉s❡♥✐①✬✾✻ ❪ ❙❦♦r♦❜♦❣❛t♦✈ ❡t ❛❧✳ ❬ ❝❤❡s✬✵✷ ❪ ❈♦r♦♥ ❡t ❛❧✳ ❬ ❝❤❡s✬✵✾ ❪ · · · P✳ ▼✉❦❤❡r❥❡❡ ✭❆❛r❤✉s ❈r②♣t♦✮ ❇▲❚ ❆s✐❛❝r②♣t ✷✵✶✸ ✸ ✴ ✶✽

  12. ❖✉r ❋♦❝✉s ▼❡♠♦r② ✫ ❈♦♠♣✉t❛t✐♦♥ ❖♥❧② ▼❡♠♦r② ✭■s❤❛✐ ❡t ❛❧✳ ❬ ❡✉r♦❝r②♣t✬✵✻ ❪✮ ✭●❡♥♥❛r♦ ❡t ❛❧✳ ❬ t❝❝✬✵✹ ❪✮ ◆❛t✉r❛❧ ❋✐rst ❙t❡♣✳ ▼✐❣❤t ❜❡ r❡❛s♦♥❛❜❧❡ ✐♥ ♣r❛❝t✐❝❡✿ ▼♦st ❣❡♥❡r❛❧ ♠♦❞❡❧ ✕ ❖♥❧② ✐♠♣❧❡♠❡♥t t❛♠♣❡r✲♣r♦♦❢ ❜✉t s❡✈❡r❛❧ ❧✐♠✐t❛t✐♦♥s✦ ❝✐r❝✉✐ts ❜✉t ♥♦t ♠❡♠♦r②✳ ■♥tr♦❞✉❝t✐♦♥ ▼♦❞❡❧s ♦❢ ❚❛♠♣❡r✐♥❣ P✳ ▼✉❦❤❡r❥❡❡ ✭❆❛r❤✉s ❈r②♣t♦✮ ❇▲❚ ❆s✐❛❝r②♣t ✷✵✶✸ ✹ ✴ ✶✽

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