❉❊❙■●◆■◆● ❆◆❉ ❖P❚■▼■❩■◆● ❘❊P❘❊❙❊◆❚❆❚■❖◆❙ ❋❖❘ ◆❖◆✲❇■◆❆❘❨ ❈❖◆❙❚❘❆■◆❚❙ ❲❊■ ❳■❆ ◆❆❚■❖◆❆▲ ❯◆■❱❊❘❙■❚❨ ❖❋ ❙■◆●❆P❖❘❊ ✷✵✶✹ ❉❊❙■●◆■◆● ❆◆❉ ❖P❚■▼■❩■◆● ❘❊P❘❊❙❊◆❚❆❚■❖◆❙ ❋❖❘ ◆❖◆✲❇■◆❆❘❨ ❈❖◆❙❚❘❆■◆❚❙ ❲❊■ ❳■❆ ❇✳❊♥❣✳✱ ◆♦rt❤❡❛st❡r♥ ❯♥✐✈❡rs✐t② ✭❈❤✐♥❛✮✱ ✷✵✵✾ ❆ ❚❍❊❙■❙ ❙❯❇▼■❚❚❊❉ ❋❖❘ ❚❍❊ ❉❊●❘❊❊ ❖❋ ❉❖❈❚❖❘ ❖❋ P❍■▲❖❙❖P❍❨ ❉❊P❆❘❚▼❊◆❚ ❖❋ ❈❖▼P❯❚❊❘ ❙❈■❊◆❈❊ ◆❆❚■❖◆❆▲ ❯◆■❱❊❘❙■❚❨ ❖❋ ❙■◆●❆P❖❘❊ ✷✵✶✹ ❉❡❝❧❛r❛t✐♦♥ ■ ❤❡r❡❜② ❞❡❝❧❛r❡ t❤❛t t❤✐s t❤❡s✐s ✐s ♠② ♦r✐❣✐♥❛❧ ✇♦r❦ ❛♥❞ ✐t ❤❛s ❜❡❡♥ ✇r✐tt❡♥ ❜② ♠❡ ✐♥ ✐ts ❡♥t✐r❡t②✳ ■ ❤❛✈❡ ❞✉❧② ❛❝❦♥♦✇❧❡❞❣❡❞ ❛❧❧ t❤❡ s♦✉r❝❡s ♦❢ ✐♥❢♦r♠❛t✐♦♥ ✇❤✐❝❤ ❤❛✈❡ ❜❡❡♥ ✉s❡❞ ✐♥ t❤❡ t❤❡s✐s✳ ❚❤✐s t❤❡s✐s ❤❛s ❛❧s♦ ♥♦t ❜❡❡♥ s✉❜♠✐tt❡❞ ❢♦r ❛♥② ❞❡❣r❡❡ ✐♥ ❛♥② ✉♥✐✈❡r✲ s✐t② ♣r❡✈✐♦✉s❧②✳ ❲❡✐ ❳✐❛ ❏✉❧② ✶✻✱ ✷✵✶✹ ❆❝❦♥♦✇❧❡❞❣♠❡♥t ■ ✇♦✉❧❞ ❧✐❦❡ t♦ t❤❛♥❦ ♠② s✉♣❡r✈✐s♦r ❉r✳ ❘♦❧❛♥❞ ❨❛♣ ❢♦r ❣✉✐❞✐♥❣ ♠❡ t♦ r❡s❡❛r❝❤ ❛♥❞ s✉♣♣♦rt✐♥❣ ♠❡ ❞✉r✐♥❣ t❤❡s❡ ②❡❛rs✳ ❍✐s ❡①t❡♥s✐✈❡ ❦♥♦✇❧❡❞❣❡✱ ❜r♦❛❞ r❡s❡❛r❝❤ ✐♥t❡r❡st✱ ❛♥❞ ❤❛r❞ ✇♦r❦ ✇❡r❡ ❛❧✇❛②s ❡♥❝♦✉r❛❣✐♥❣ ♠❡✳ ❍❡ ❣❛✈❡ ♠❡ ♠❛♥② ✐♥t❡r❡st✐♥❣ ✐❞❡❛s ❛♥❞ ❝♦♥str✉❝t✐✈❡ s✉❣❣❡st✐♦♥s t♦ ❞❡✈❡❧♦♣ ❛♥❞ ✐♠♣r♦✈❡ ♠② r❡s❡❛r❝❤ st✉❞✐❡s ❛♥❞ s❦✐❧❧s✳ ■ ❢❡❡❧ ❧✉❝❦② ❢♦r t❤❡ ♦♣♣♦rt✉♥✐t② ♦❢ ❜❡✐♥❣ ❤✐s ♣♦st❣r❛❞✉❛t❡ st✉❞❡♥t✳ ■ ✇♦✉❧❞ ❧✐❦❡ t♦ t❤❛♥❦ ❈❤❛✈❛❧✐t ▲✐❦✐t✈✐✈❛t❛♥❛✈♦♥❣ ❢♦r t❤❡ ✈❛❧✉❛❜❧❡ ❞✐s❝✉ss✐♦♥ ❛♥❞ ❝♦♠♠❡♥ts ♦♥ t❤✐s t❤❡s✐s✳ ■ ✇♦✉❧❞ ❧✐❦❡ t♦ t❤❛♥❦ ♠② ❝♦✲❛✉t❤♦rs ♦❢ t❤❡ r❡s❡❛r❝❤ ♣❛♣❡rs✱ ❑❡♥✐❧ ❈❤❡♥❣ ❛♥❞ ❈❤❛✈❛❧✐t ▲✐❦✐t✈✐✈❛t❛♥❛✈♦♥❣✳ ■t ❤❛s ❜❡❡♥ ❛ ♣❧❡❛s✉r❡ ✇♦r❦✐♥❣ ✇✐t❤ t❤❡♠✳ ■ ✇❛♥t t♦ t❤❛♥❦ ❇❡❤♥❛③ ❇❛ss❛♥s❤❛❤✐ ❢♦r ♣r♦♦❢r❡❛❞✐♥❣ t❤❡ t❤❡s✐s✳ ❋✐♥❛❧❧②✱ ♠② t❤❛♥❦s ❛♥❞ ❧♦✈❡ ❣♦ t♦ ♠② ♣❛r❡♥ts ❛♥❞ s✐st❡r✳ ❏✉❧② ✶✻✱ ✷✵✶✹ ❈♦♥t❡♥ts ❙✉♠♠❛r② ✐① ▲✐st ♦❢ ❚❛❜❧❡s ✐① ▲✐st ♦❢ ❋✐❣✉r❡s ①✐✐ ✶ ■♥tr♦❞✉❝t✐♦♥ ✶ ✷ ❇❛❝❦❣r♦✉♥❞ ✺ ✷✳✶ ❇❛s✐❝ ❉❡✜♥✐t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✷ ▲♦❝❛❧ ❈♦♥s✐st❡♥❝✐❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✸ ❙♦❧✈✐♥❣ ❈❙Ps ✷✳✹ ●❧♦❜❛❧ ❈♦♥str❛✐♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✹✳✶ ❋♦r♠❛❧ ▲❛♥❣✉❛❣❡ ❚❤❡♦r② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✹✳✷ ❋♦r♠❛❧ ▲❛♥❣✉❛❣❡ ❈♦♥str❛✐♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✹✳✸ ❚❛❜❧❡ ❈♦♥str❛✐♥t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✹✳✹ ▼❉❉ ❈♦♥str❛✐♥t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✸ ●❆❈ ❆❧❣♦r✐t❤♠s ❢♦r ❘❡❣✉❧❛r ❈♦♥str❛✐♥ts ✸✳✶ ✶✶ ✶✾ ❖✈❡r✈✐❡✇ ♦❢ t❤❡ ●❆❈ ❆❧❣♦r✐t❤♠s ❢♦r t❤❡ ❘❡❣✉❧❛r ❛♥❞ ▼❉❉ ❝♦♥✲ str❛✐♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✸✳✶✳✶ ❚❤❡ ❋✐❧t❡r✐♥❣ ❆❧❣♦r✐t❤♠ ❢♦r ❘❡❣✉❧❛r ❈♦♥str❛✐♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✸✳✶✳✷ ❚❤❡ ❋✐❧t❡r✐♥❣ ❆❧❣♦r✐t❤♠ ❢♦r ▼❉❉ ❈♦♥str❛✐♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✷ ◆❋❆✲t♦✲▼❉❉ ❈♦♥✈❡rs✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✳✸ ▼❛✐♥t❛✐♥✐♥❣ ●❆❈ ♦♥ ◆❋❆ ❈♦♥str❛✐♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✹ ❊①♣❡r✐♠❡♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✺ ❈♦♥❝❧✉s✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹ ●❆❈ ❆❧❣♦r✐t❤♠s ❢♦r ●r❛♠♠❛r ❈♦♥str❛✐♥ts ✹✳✶ ❖✈❡r✈✐❡✇ ♦❢ ❊①✐st✐♥❣ ●❆❈ ❆❧❣♦r✐t❤♠s ✹✳✶✳✶ ❚❤❡ ❈❨❑✲♣r♦♣ ❆❧❣♦r✐t❤♠ ✐✐✐ ✷✹ ✸✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✹✳✶✳✷ ❚❤❡ ❆◆❉✴❖❘ ❉❡❝♦♠♣♦s✐t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✹✳✶✳✸ ❚❤❡ ❘❡❢♦r♠✉❧❛t✐♦♥ ✹✶ ✹✳✶✳✹ ❚❤❡ ❈❨❑✲✐♥❝ ❆❧❣♦r✐t❤♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✹✳✷ ❊①t❡♥s✐♦♥ ♦❢ ♥❢❛❝ t♦ ●r❛♠♠❛r ❈♦♥str❛✐♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✳✸ ❊①♣❡r✐♠❡♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✹✳✸✳✶ ❚❤❡ ❙❤✐❢t ❙❝❤❡❞✉❧✐♥❣ Pr♦❜❧❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✸✳✷ ❚❤❡ ❋♦r❦❧✐❢t ❙❝❤❡❞✉❧✐♥❣ Pr♦❜❧❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✸✳✸ ❘❛♥❞♦♠ ❈❙Ps ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✹✳✸✳✹ ❙✉♠♠❛r② ♦❢ ❊①♣❡r✐♠❡♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ❈♦♥❝❧✉s✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✹ ✺ ❖♣t✐♠✐③✐♥❣ ❙❚❘ ✇✐t❤ ❈♦♠♣r❡ss❡❞ ❚❛❜❧❡s ✺✳✶ ❖✈❡r✈✐❡✇ ♦❢ ❙❚❘ ❆❧❣♦r✐t❤♠s ✺✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✺✳✶✳✶ ❙❚❘✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✺✳✶✳✷ ❙❚❘✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✺✳✶✳✸ ❙❚❘✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ❖✈❡r✈✐❡✇ ♦❢ ❙❚❘ ❆❧❣♦r✐t❤♠s ♦♥ ❈♦♠♣r❡ss❡❞ ❚❛❜❧❡ ❘❡♣r❡s❡♥t❛t✐♦♥s ✻✷ ✺✳✷✳✶ ❙❚❘m✲❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✺✳✷✳✷ ❙❚❘sl ✲❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✺✳✷✳✸ ❙❚❘sh✲❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✺✳✸ ❈♦♠♣r❡ss✐♥❣ ❚❛❜❧❡ ✇✐t❤ ❈✲❚✉♣❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✺✳✹ ❙❚❘✷✲❈✿ ❙❚❘✷ ♦♥ ❈✲❚✉♣❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✺✳✺ ❙❚❘✸✲❈✿ ❙❚❘✸ ♦♥ ❈✲❚✉♣❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✺✳✻ ❊①♣❡r✐♠❡♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✺✳✻✳✶ ❈♦♠♣❛r❡ ❙❚❘ ♦♥ ❈✲❚✉♣❧❡s ✇✐t❤ ❖t❤❡r ❘❡♣r❡s❡♥t❛t✐♦♥s ✳ ✳ ✳ ✼✻ ❈♦♥❝❧✉s✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✺✳✷ ✺✳✼ ✻ ❋❛❝t♦r ❊♥❝♦❞✐♥❣ ❢♦r ❍✐❣❤❡r✲❖r❞❡r ❈♦♥s✐st❡♥❝✐❡s ✻✳✶ ✻✳✷ ❖✈❡r✈✐❡✇ ♦❢ ❋P❲❈ ❆❧❣♦r✐t❤♠s ✼✾ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ❊♥❝♦❞✐♥❣ ❚❤r♦✉❣❤ ●❆❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ❚❤❡ ❋❛❝t♦r ❊♥❝♦❞✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✻✳✷✳✶ ❊①❛♠♣❧❡ ♦❢ ❋❛❝t♦r ❊♥❝♦❞✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✻✳✷✳✷ ❈♦♠♣❛r❡ ❘❡♣r❡s❡♥t❛t✐♦♥s ❯s❡❞ ✐♥ ❋❊✱ ✻✳✶✳✶ ❚❤❡ ❡❙❚❘ ❛❧❣♦r✐t❤♠ ✻✳✶✳✷ ❚❤❡ k ✲✐♥t❡r❧❡❛✈❡❞ k ✲❘❡❞✉❝❡❞ ❏♦✐♥ ❚❛❜❧❡s k ■▲✱ ❛♥❞ ❡❙❚❘ ✳ ✳ ✳ ✳ ✽✾ ✻✳✸ ❚❤❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ✻✳✹ ❊①♣❡r✐♠❡♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✻✳✺ ❈♦♥❝❧✉s✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶ ✼ ❈♦♥❝❧✉s✐♦♥ ✶✵✸ ✐✈ ❇✐❜❧✐♦❣r❛♣❤② ✶✶✹ ❆♣♣❡♥❞✐❝❡s ✶✶✺ ❆ ✶✶✼ ❆✳✶ ❚❤❡ ❙❚❘✷ ❆❧❣♦r✐t❤♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ❆✳✷ ❚❤❡ ❙❚❘✸ ❆❧❣♦r✐t❤♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶ ✈ ✈✐ ❙✉♠♠❛r② ●❧♦❜❛❧ ❝♦♥str❛✐♥t ♣❧❛②s ❛ ❝❡♥tr❛❧ r♦❧❡ ✐♥ ❝♦♥str❛✐♥t ♣r♦❣r❛♠♠✐♥❣ ❞✉❡ t♦ ✐ts str♦♥❣ ♠♦❞❡❧❧✐♥❣ ❛♥❞ ❡✣❝✐❡♥t ♣r♦♣❛❣❛t✐♦♥✳ ❚❛❜❧❡ ❝♦♥str❛✐♥t ✐s ❛ ❣❡♥❡r❛❧ ❝♦♥str❛✐♥t ❛s ✐t ❝❛♥ ❞❡✜♥❡ ❛♥ ❛r❜✐tr❛r② ❝♦♥str❛✐♥t ❡①t❡♥s✐♦♥❛❧❧②✱ ❡✐t❤❡r ❛s ❛ s❡t ♦❢ s♦❧✉t✐♦♥s ♦r ❛ s❡t ♦❢ ♥♦♥✲s♦❧✉t✐♦♥s✱ t❤✉s ✐s ❛❜❧❡ t♦ r❡♣r❡s❡♥t ❛♥② ✜♥✐t❡ ❞♦♠❛✐♥ ❝♦♥str❛✐♥t✳ ❚❛❜❧❡ ❝♦♥str❛✐♥t ❝❛♥ ❛❧s♦ ❜❡ ❝♦♥✈❡rt❡❞ t♦ ❛♥❞ s♦❧✈❡❞ ♦♥ ♦t❤❡r r❡♣r❡s❡♥t❛t✐♦♥s✱ s✉❝❤ ❛s ♠✉❧t✐✲✈❛❧✉❡❞ ❞❡❝✐s✐♦♥ ❞✐❛❣r❛♠ ✭▼❉❉✮✱ ❛✉t♦♠❛t♦♥ ❛♥❞ ❣r❛♠♠❛r✳ ■♥ t❤✐s t❤❡s✐s✱ ✇❡ ❢♦❝✉s ♦♥ t❤❡ ❞❡s✐❣♥✱ ♦♣t✐♠✐③❛t✐♦♥ ❛♥❞ ❛♥❛❧②s✐s ♦❢ ♣r♦♣❛❣❛t✐♦♥ ❛❧❣♦r✐t❤♠s ❢♦r ♥♦♥✲❜✐♥❛r② ❝♦♥str❛✐♥ts ✇✐t❤ ❞✐✛❡r❡♥t r❡♣r❡s❡♥t❛t✐♦♥s✳ ❙♦♠❡ ♦❢ t❤❡s❡ ❝♦♥str❛✐♥ts✱ ❡✳❣✳ r❡❣✉❧❛r ❛♥❞ ❣r❛♠♠❛r ❝♦♥str❛✐♥ts✱ ❝❛♥ ❛❧s♦ ❜❡ t❤♦✉❣❤t ❛s t❛❜❧❡ ❝♦♥str❛✐♥ts✳ ❲❡ ✜rst ♣r♦♣♦s❡ ❛ ❣❡♥❡r❛❧✐③❡❞ ❛r❝ ❝♦♥s✐st❡♥❝② ✭●❆❈✮ ❛❧❣♦r✐t❤♠ ❢♦r r❡❣✉❧❛r ❝♦♥str❛✐♥t ❞❡✜♥❡❞ ♦♥ ♥♦♥✲❞❡t❡r♠✐♥✐st✐❝ ✜♥✐t❡ ❛✉t♦♠❛t♦♥ ✭◆❋❆✮✱ ❝❛❧❧❡❞ ♥❢❛❝✳ ❚❤❡ ♥❢❛❝ ❝❛♥ ❛❧s♦ ♣r♦♣❛❣❛t❡ t❤❡ ❝♦♥str❛✐♥t r❡♣r❡s❡♥t❡❞ ❜② ❞❡t❡r♠✐♥✐st✐❝ ✜♥✐t❡ t❤❡ ❛✉t♦♠❛t♦♥✭❉❋❆✮ ♦r ▼❉❉✳ ❲❡ ✐♥✈❡st✐❣❛t❡ t❤❡ ❡✛❡❝t ♦❢ ❞✐✛❡r❡♥t r❡♣r❡s❡♥t❛t✐♦♥s ❢♦❝✉s✐♥❣ ♦♥ t❤❡ s♣❛❝❡✲t✐♠❡ tr❛❞❡♦✛s✳ ❖✉r ❡①♣❡r✐♠❡♥t❛❧ r❡s✉❧ts s❤♦✇ t❤❛t ♥❢❛❝ ✐s ❢❛st❡r ✇❤❡♥ t❤❡ ◆❋❆ ✐s ♠✉❝❤ s♠❛❧❧❡r t❤❛♥ ✐ts ❡q✉✐✈❛❧❡♥t ❉❋❆ ♦r ▼❉❉✳ ❲❡ ❛❧s♦ ❡①t❡♥❞ ♥❢❛❝ t♦ ❣r❛♠♠❛r❝ ❢♦r ❣r❛♠♠❛r ❝♦♥str❛✐♥t ❞❡✜♥❡❞ ♦♥ ❝♦♥t❡①t✲❢r❡❡ ❣r❛♠♠❛r ✭❈❋●✮ ✐♥ ●r❡✐❜❛❝❤ ♥♦r♠❛❧ ❢♦r♠ ✭●◆❋✮✳ ❆❣❛✐♥ ✇❡ s❤♦✇ t❤❛t ❣r❛♠♠❛r❝ ✐s ❢❛st❡r ♦♥ ♠♦r❡ ❝♦♠♣❛❝t ❣r❛♠♠❛rs✳ ❙❡❝♦♥❞✱ ✇❡ r❡✈✐s❡ t❤❡ st❛t❡✲♦❢✲t❤❡✲❛rt ●❆❈ ❛❧❣♦r✐t❤♠s✱ ❙❚❘✱ ❢♦r t❛❜❧❡ ❝♦♥✲ str❛✐♥ts✱ s♦ t❤❛t t❤❡② ❝❛♥ ✇♦r❦ ♦♥ ❝♦♠♣r❡ss❡❞ r❡♣r❡s❡♥t❛t✐♦♥s✳ ❚♦ ❜❡ ♠♦r❡ s♣❡✲ ❝✐✜❝✱ t❤❡ t❛❜❧❡s ❛r❡ ❝♦♠♣r❡ss❡❞ ✐♥t♦ t❤❡ ❈❛rt❡s✐❛♥ ♣r♦❞✉❝t✱ ✇❤✐❝❤ ✇❡ ❝❛❧❧ ❝✲t✉♣❧❡s✳ ❲❡ ❡①t❡♥❞ t❤❡ ❙❚❘✷ ❛♥❞ ❙❚❘✸ ❛❧❣♦r✐t❤♠s t♦ ✇♦r❦ ✇✐t❤ ❝✲t✉♣❧❡✳ ❖✉r ❡①♣❡r✐♠❡♥ts s❤♦✇ t❤❛t ❝♦♠♣r❡ss✐♦♥ ❝❛♥ ❜❡ s✐❣♥✐✜❝❛♥t✱ t❤❡ ♠♦r❡ t❤❡ t❛❜❧❡s ❛r❡ ❝♦♠♣r❡ss✐❜❧❡✱ t❤❡ ❢❛st❡r ❛r❡ t❤❡ ❝✲t✉♣❧❡ ❛❧❣♦r✐t❤♠s✳ ❍✐❣❤❡r✲♦r❞❡r ❝♦♥s✐st❡♥❝✐❡s✱ s✉❝❤ ❛s ❢✉❧❧ ♣❛✐r✇✐s❡ ❝♦♥s✐st❡♥❝② ✭❋P❲❈✮✱ ❛r❡ str♦♥❣❡r t❤❛♥ ●❆❈ ❛♥❞ ❤❛✈❡ t❤❡ ♣♦t❡♥t✐❛❧ ♦❢ str♦♥❣❡r s❡❛r❝❤ s♣❛❝❡ r❡❞✉❝t✐♦♥✳ ❍♦✇❡✈❡r✱ ❤✐❣❤❡r✲♦r❞❡r ❝♦♥s✐st❡♥❝✐❡s ❛r❡ ✉s✉❛❧❧② ♠✉❝❤ ♠♦r❡ ❝♦st❧② t❤❛♥ ●❆❈✱ ❛♥❞ t❤✉s ♥♦t ♠❛♥② ♣r❛❝t✐❝❛❧ ♣r♦♣❛❣❛t✐♦♥ ❛❧❣♦r✐t❤♠s ❤❛✈❡ ❜❡❡♥ ❞❡s✐❣♥❡❞ ♦r ✐♠♣❧❡✲ ♠❡♥t❡❞✳ ❋P❲❈ ✐s ❛ ♣r♦♠✐s✐♥❣ ❤✐❣❤❡r ♦r❞❡r ❝♦♥s✐st❡♥❝②✳ ❘❡❝❡♥t❧② t❤❡ ❡❙❚❘ ❛❧❣♦r✐t❤♠ ❛❞❛♣ts t❤❡ ❙❚❘✷ ●❆❈ ❛❧❣♦r✐t❤♠ t♦ ❡♥❢♦r❝❡ ❋P❲❈ ❜✉t ✐t ♥❡❡❞s ❝♦♠✲ ♣❧❡① ❞❛t❛ str✉❝t✉r❡s ✇❤✐❝❤ ❝❛♥ ✐♠♣♦s❡ s✐❣♥✐✜❝❛♥t ♦✈❡r❤❡❛❞s✳ ❚❤❡ k ✲✐♥t❡r❧❡❛✈❡❞ ❡♥❝♦❞✐♥❣ ✐s ♣r♦♣♦s❡❞ t♦ tr❛♥s❢♦r♠ ❈❙Ps ✇✐t❤ ❞✉❛❧ ✈❛r✐❛❜❧❡s ❛♥❞ ❥♦✐♥ t❛❜❧❡s✱ s♦ t❤❛t k ✲✇✐s❡ ❝♦♥s✐st❡♥❝② ✭str♦♥❣❡r t❤❛♥ ●❆❈✮ ❝❛♥ ❜❡ ❛❝❤✐❡✈❡❞ t❤♦✉❣❤ ●❆❈✳ ❍♦✇✲ ❡✈❡r t❤❡ ❥♦✐♥ t❛❜❧❡s ✐♥ k ✲✐♥t❡r❧❡❛✈❡❞ ❡♥❝♦❞✐♥❣ ♠❛② ❜❡ ❧❛r❣❡ ❛♥❞ t❤✉s s❧♦✇ ❞♦✇♥ t❤❡ ♣r♦♣❛❣❛t✐♦♥ ❛❧❣♦r✐t❤♠s✳ ❚♦ ❝♦♥tr❛st✱ ✇❡ ♣r♦♣♦s❡ ❛ ❞✐✛❡r❡♥t ❡♥❝♦❞✐♥❣ t♦ tr❛♥s✲ ❢♦r♠ ♦♥❡ ❈❙P ✐♥t♦ ❛♥♦t❤❡r ✧❡q✉✐✈❛❧❡♥t✧ ♦♥❡✱ s♦ t❤❛t ❋P❲❈ ❝❛♥ ❜❡ ❡♥❢♦r❝❡❞ ♦♥ t❤❡ ♦r✐❣✐♥❛❧ ❈❙P t❤r♦✉❣❤ ●❆❈ ♦♥ t❤❡ tr❛♥s❢♦r♠❡❞ ♦♥❡✳ ❚❤❡ ❦❡② ✐❞❡❛ ✐s t♦ ❢❛❝✲ t♦r ♦✉t t❤❡ ❝♦♠♠♦♥❧② s❤❛r❡❞ ✈❛r✐❛❜❧❡s ❢r♦♠ ❝♦♥str❛✐♥ts✬ s❝♦♣❡s✱ ❢♦r♠ ♥❡✇ ❝♦♠✲ ♣♦✉♥❞ ✈❛r✐❛❜❧❡s✱ ❛♥❞ r❡✲❛tt❛❝❤ t❤❡♠ ❜❛❝❦ t♦ t❤❡ ❝♦♥str❛✐♥ts ✇❤❡r❡ t❤❡② ❝♦♠❡ ❢r♦♠✳ ❚❤❡s❡ ❝♦♠♣♦✉♥❞ ✈❛r✐❛❜❧❡s ❝❛♥ ❜❡ tr❡❛t❡❞ ❛s ❛ ❞✐✛❡r❡♥t r❡♣r❡s❡♥t❛t✐♦♥ ❞❡s✐❣♥❡❞ ❢♦r ❋P❲❈✳ ❊①♣❡r✐♠❡♥ts s❤♦✇ t❤❛t ♦✉r ❡♥❝♦❞✐♥❣ ✇✐t❤ ♠♦r❡ ❝♦♠♣❛❝t r❡♣r❡s❡♥t❛t✐♦♥s ❝❛♥ ♦✉t♣❡r❢♦r♠ t❤❡ ❡❙❚❘ ❛❧❣♦r✐t❤♠ ❛♥❞ t❤❡ k ✲✐♥t❡r❧❡❛✈❡❞ ❡♥❝♦❞✐♥❣✳ ❲❡ ❛❣❛✐♥ ❞❡♠♦♥str❛t❡ t❤❛t ❜♦t❤ t✐♠❡ ❛♥❞ s♣❛❝❡ ❡✣❝✐❡♥❝② ❝❛♥ ❜❡ ❣❛✐♥❡❞ ❢r♦♠ ❛ s♠❛❧❧❡r r❡♣r❡s❡♥t❛t✐♦♥✳ ✈✐✐✐ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ Pr✐♥❝✐♣❧❡s ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P✬✵✽✮✱ ♣❛❣❡s ✺✵✾✕✺✷✸✱ ✷✵✵✽✳ ❬❈❨✶✵❪ ❑❡♥✐❧ ❈✳ ❑✳ ❈❤❡♥❣ ❛♥❞ ❘♦❧❛♥❞ ❍✳ ❈✳ ❨❛♣✳ ❆♥ ▼❉❉✲❜❛s❡❞ ❣❡♥✲ ❡r❛❧✐③❡❞ ❛r❝ ❝♦♥s✐st❡♥❝② ❛❧❣♦r✐t❤♠ ❢♦r ♣♦s✐t✐✈❡ ❛♥❞ ♥❡❣❛t✐✈❡ t❛❜❧❡ ❝♦♥str❛✐♥ts ❛♥❞ s♦♠❡ ❣❧♦❜❛❧ ❝♦♥str❛✐♥ts✳ ❈♦♥str❛✐♥ts✱ ✶✺✿✷✻✺✕✸✵✹✱ ✷✵✶✵✳ ❬❉❇✾✼❪ ❘♦♠✉❛❧❞ ❉❡❜r✉②♥❡ ❛♥❞ ❈❤r✐st✐❛♥ ❇❡ss✐❡r❡✳ ❋r♦♠ r❡str✐❝t❡❞ ♣❛t❤ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✸r❞ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ Pr✐♥❝✐♣❧❡s ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ❈♦♥✲ str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P✬✾✼✮✱ ♣❛❣❡s ✸✶✷✕✸✷✻✱ ✶✾✾✼✳ ❝♦♥s✐st❡♥❝② t♦ ♠❛①✲r❡str✐❝t❡❞ ♣❛t❤ ❝♦♥s✐st❡♥❝②✳ ❬❉❇✵✶❪ ❘♦♠✉❛❧❞ ❉❡❜r✉②♥❡ ❛♥❞ ❈❤r✐st✐❛♥ ❇❡ss✐❡r❡✳ ❉♦♠❛✐♥ ✜❧t❡r✐♥❣ ❝♦♥s✐s✲ t❡♥❝✐❡s✳ ❬❉❞❧❇✶✹❪ ❏♦✉r♥❛❧ ♦❢ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ❘❡s❡❛r❝❤✱ ✶✹✿✷✵✺✕✷✸✵✱ ✷✵✵✶✳ ❇❛rt ❉❡♠♦❡♥ ❛♥❞ ▼❛r✐❛ ●❛r❝✐❛ ❞❡ ❧❛ ❇❛♥❞❛✳ r✉❧❡s✳ ❬❉P❘✵✻❪ ■♥ ❘❡❞✉♥❞❛♥t s✉❞♦❦✉ ❚❤❡♦r② ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ▲♦❣✐❝ Pr♦❣r❛♠♠✐♥❣✱ ✶✹✿✸✻✸✕✸✼✼✱ ✷✵✶✹✳ ❙♦♣❤✐❡ ❉❡♠❛ss❡②✱ ●✐❧❧❡s P❡s❛♥t✱ ❛♥❞ ▲♦✉✐s✲▼❛rt✐♥ ❘♦✉ss❡❛✉✳ ❝♦st✲r❡❣✉❧❛r ❜❛s❡❞ ❤②❜r✐❞ ❝♦❧✉♠♥ ❣❡♥❡r❛t✐♦♥ ❛♣♣r♦❛❝❤✳ ❆ ❈♦♥str❛✐♥ts✱ ✶✶✿✸✶✺✕✸✸✸✱ ✷✵✵✻✳ ❬❋❊✾✻❪ ❊✉❣❡♥❡ ❈✳ ❋r❡✉❞❡r ❛♥❞ ❈❤❛r❧❡s ❉✳ ❊❧❢❡✳ ◆❡✐❣❤❜♦r❤♦♦❞ ✐♥✈❡rs❡ ❝♦♥s✐s✲ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✸t❤ ◆❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ✭❆❆❆■✬✾✻✮✱ ♣❛❣❡s ✷✵✷✕✷✵✽✱ ✶✾✾✻✳ t❡♥❝② ♣r❡♣r♦❝❡ss✐♥❣✳ ■♥ ❬❋▼✵✶❪ ❋✐❧✐♣♣♦ ❋♦❝❛❝❝✐ ❛♥❞ ▼✐❝❤❛❡❧❛ ▼✐❧❛♥♦✳ ●❧♦❜❛❧ ❝✉t ❢r❛♠❡✇♦r❦ ❢♦r r❡✲ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✼t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r✲ ❡♥❝❡ ♦♥ Pr✐♥❝✐♣❧❡s ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P✬✵✶✮✱ ♠♦✈✐♥❣ s②♠♠❡tr✐❡s✳ ■♥ ♣❛❣❡s ✼✼✕✾✷✱ ✷✵✵✶✳ ❬❋r❡✻✵❪ ❊❞✇❛r❞ ❋r❡❞❦✐♥✳ ❚r✐❡ ♠❡♠♦r②✳ ❈♦♠♠✉♥✐❝❛t✐♦♥s ♦❢ t❤❡ ❆❈▼✱ ✸✭✾✮✿✹✾✵✕✹✾✾✱ ✶✾✻✵✳ ❬❋r❡✾✼❪ ❊✉❣❡♥❡ ❈✳ ❋r❡✉❞❡r✳ ■♥ ♣✉rs✉✐t ♦❢ t❤❡ ❤♦❧② ❣r❛✐❧✳ ❈♦♥str❛✐♥ts✱ ✷✭✶✮✿✺✼✕ ✻✶✱ ✶✾✾✼✳ ❬●❡❝❪ ●❡❝♦❞❡ t❡❛♠✳ ●❡❝♦❞❡✿ t♦♦❧❦✐t ❢♦r ❞❡✈❡❧♦♣✐♥❣ ❝♦♥str❛✐♥t✲❜❛s❡❞ s②s✲ t❡♠s ❛♥❞ ❛♣♣❧✐❝❛t✐♦♥s✱ ✷✵✶✹✳ ❆✈❛✐❧❛❜❧❡ ❢r♦♠ ♦r❣✴✳ ✶✵✼ ❤tt♣✿✴✴✇✇✇✳❣❡❝♦❞❡✳ ❬●❍▲❘✶✸❪ ◆❡❜r❛s ●❤❛r❜✐✱ ❋r❡❞ ❍❡♠❡r②✱ ❈❤r✐st♦♣❤❡ ▲❡❝♦✉tr❡✱ ❛♥❞ ❖❧✐✈✐❡r ❘♦✉s✲ ◆❡✉✈✐è♠❡s ❏♦✉r♥é❡s ❋r❛♥❝♦♣❤♦♥❡s ❞❡ Pr♦❣r❛♠♠❛t✐♦♥ ♣❛r ❈♦♥tr❛✐♥t❡s ✭❏❋P❈✬✶✸✮✱ ♣❛❣❡s s❡❧✳ ❙❚❘ ❡t ❝♦♠♣r❡ss✐♦♥ ❞❡ ❝♦♥tr❛✐♥t❡s t❛❜❧❡s✳ ■♥ ✶✹✸✕✶✹✻✱ ✷✵✶✸✳ ❬●❍▲❘✶✹❪ ◆❡❜r❛s ●❤❛r❜✐✱ ❋r❡❞ ❍❡♠❡r②✱ ❈❤r✐st♦♣❤❡ ▲❡❝♦✉tr❡✱ ❛♥❞ ❖❧✐✈✐❡r ❘♦✉s✲ s❡❧✳ ❙❧✐❝❡❞ t❛❜❧❡ ❝♦♥str❛✐♥ts✿ ❈♦♠❜✐♥✐♥❣ ❝♦♠♣r❡ss✐♦♥ ❛♥❞ t❛❜✉❧❛r Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✶t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ■♥t❡❣r❛t✐♦♥ ♦❢ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ❛♥❞ ❖♣❡r❛t✐♦♥s ❘❡s❡❛r❝❤ t❡❝❤✲ ♥✐q✉❡s ✐♥ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P❆■❖❘✬ ✶✹✮✱ ♣❛❣❡s ✶✷✵✕✶✸✺✱ r❡❞✉❝t✐♦♥✳ ■♥ ✷✵✶✹✳ ❬●❏▼◆✵✼❪ ■❛♥ P✳ ●❡♥t✱ ❈❤r✐s ❏❡✛❡rs♦♥✱ ■❛♥ ▼✐❣✉❡❧✱ ❛♥❞ P❡t❡r ◆✐❣❤t✐♥❣❛❧❡✳ ❉❛t❛ str✉❝t✉r❡s ❢♦r ❣❡♥❡r❛❧✐③❡❞ ❛r❝ ❝♦♥s✐st❡♥❝② ❢♦r ❡①t❡♥s✐♦♥❛❧ ❝♦♥str❛✐♥ts✳ Pr♦❝❡❡❞✐♥❣ ♦❢ t❤❡ ✷✷t❤ ◆❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐✲ ❣❡♥❝❡ ✭❆❆❆■✬✵✼✮✱ ♣❛❣❡s ✶✾✶✕✶✾✼✱ ✷✵✵✼✳ ■♥ ❬●r❡✻✺❪ ❙❤❡✐❧❛ ❆✳ ●r❡✐❜❛❝❤✳ ❆ ♥❡✇ ♥♦r♠❛❧✲❢♦r♠ t❤❡♦r❡♠ ❢♦r ❝♦♥t❡①t✲❢r❡❡ ♣❤r❛s❡ str✉❝t✉r❡ ❣r❛♠♠❛rs✳ ❬●❙✶✷❪ ❏♦✉r♥❛❧ ♦❢ t❤❡ ❆❈▼✱ ✶✷✭✶✮✿✹✷✕✺✷✱ ✶✾✻✺✳ ●r❛❡♠❡ ●❛♥❣❡ ❛♥❞ P❡t❡r ❏✳ ❙t✉❝❦❡②✳ ❊①♣❧❛✐♥✐♥❣ ♣r♦♣❛❣❛t♦rs ❢♦r s✲ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✾t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ■♥t❡❣r❛t✐♦♥ ♦❢ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ❛♥❞ ❖♣❡r❛t✐♦♥s ❘❡s❡❛r❝❤ t❡❝❤✲ ♥✐q✉❡s ✐♥ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P❆■❖❘✬ ✶✷✮✱ ♣❛❣❡s ✶✾✺✕✷✶✵✱ ❉◆◆❋ ❝✐r❝✉✐ts✳ ■♥ ✷✵✶✷✳ ❬●②s✽✻❪ ▼❛r❝ ●②ss❡♥s✳ ❖♥ t❤❡ ❝♦♠♣❧❡①✐t② ♦❢ ❥♦✐♥ ❞❡♣❡♥❞❡♥❝✐❡s✳ ❛❝t✐♦♥s ❉❛t❛❜❛s❡ ❙②st❡♠✱ ✶✶✿✽✶✕✶✵✽✱ ✶✾✽✻✳ ❬❍❋P❩✶✸❪ ❆❈▼ ❚r❛♥s✲ ❏✉♥ ❍❡✱ P✐❡rr❡ ❋❧❡♥❡r✱ ❏✉st✐♥ P❡❛rs♦♥✱ ❛♥❞ ❲❡✐ ▼✐♥❣ ❩❤❛♥❣✳ ❙♦❧✈✐♥❣ Pr♦❝❡❡❞✲ ✐♥❣s ♦❢ t❤❡ ✶✾t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ Pr✐♥❝✐♣❧❡s ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P✬✶✸✮✱ ♣❛❣❡s ✸✽✶✕✸✾✼✱ ✷✵✶✸✳ str✐♥❣ ❝♦♥str❛✐♥ts✿ t❤❡ ❝❛s❡ ❢♦r ❝♦♥str❛✐♥t ♣r♦❣r❛♠♠✐♥❣✳ ■♥ ❬❍❍❖❚✵✽❪ ❚❛r✐❦ ❍❛❞③✐❝✱ ❏♦❤♥ ◆✳ ❍♦♦❦❡r✱ ❇❛rr② ❖✬❙✉❧❧✐✈❛♥✱ ❛♥❞ P❡t❡r ❚✐❡❞❡✲ ♠❛♥♥✳ ❆♣♣r♦①✐♠❛t❡ ❝♦♠♣✐❧❛t✐♦♥ ♦❢ ❝♦♥str❛✐♥ts ✐♥t♦ ♠✉❧t✐✈❛❧✉❡❞ ❞❡❝✐✲ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✹t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ Pr✐♥❝✐♣❧❡s ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P✬✵✽✮✱ ♣❛❣❡s s✐♦♥ ❞✐❛❣r❛♠s✳ ■♥ ✹✹✽✕✹✻✷✱ ✷✵✵✽✳ ✶✵✽ ❬❍▼❯✵✻❪ ❬❍P❨✵✵❪ ■♥tr♦✲ ❞✉❝t✐♦♥ t♦ ❆✉t♦♠❛t❛ ❚❤❡♦r②✱ ▲❛♥❣✉❛❣❡s✱ ❛♥❞ ❈♦♠♣✉t❛t✐♦♥ ✭✸r❞ ❊❞✐✲ t✐♦♥✮✳ ❆❞❞✐s♦♥✲❲❡s❧❡②✱ ✷✵✵✻✳ ❏♦❤♥ ❊✳ ❍♦♣❝r♦❢t✱ ❘❛❥❡❡✈ ▼♦t✇❛♥✐✱ ❛♥❞ ❏❡✛r❡② ❉✳ ❯❧❧♠❛♥✳ ❏✐❛✇❡✐ ❍❛♥✱ ❏✐❛♥ P❡✐✱ ❛♥❞ ❨✐✇❡♥ ❨✐♥✳ ▼✐♥✐♥❣ ❢r❡q✉❡♥t ♣❛tt❡r♥s ✇✐t❤✲ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✷✵✵✵ ❆❈▼ ❙■●▼❖❉ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ▼❛♥❛❣❡♠❡♥t ♦❢ ❉❛t❛✱ ♣❛❣❡s ✶✕✶✷✱ ✷✵✵✵✳ ♦✉t ❝❛♥❞✐❞❛t❡ ❣❡♥❡r❛t✐♦♥✳ ■♥ ❬❍❯✼✾❪ ❏♦❤♥ ❊✳ ❍♦♣❝r♦❢t ❛♥❞ ❏❡✛r❡② ❉✳ ❯❧❧♠❛♥✳ t❤❡♦r②✱ ❧❛♥❣✉❛❣❡s✱ ❛♥❞ ❝♦♠♣✉t❛t✐♦♥✳ ❬❍❱❍❍✶✵❪ ■♥tr♦❞✉❝t✐♦♥ t♦ ❛✉t♦♠❛t❛ ❆❞❞✐s♦♥✲❲❡s❧❡②✱ ✶✾✼✾✳ ❙❛♠✐❞ ❍♦❞❛✱ ❲✐❧❧❡♠✲❏❛♥ ❱❛♥ ❍♦❡✈❡✱ ❛♥❞ ❏♦❤♥ ◆✳ ❍♦♦❦❡r✳ ❆ s②st❡♠✲ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✻t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ Pr✐♥❝✐♣❧❡s ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P✬✶✵✮✱ ♣❛❣❡s ✷✻✻✕✷✽✵✱ ✷✵✶✵✳ ❛t✐❝ ❛♣♣r♦❛❝❤ t♦ ♠❞❞✲❜❛s❡❞ ❝♦♥str❛✐♥t ♣r♦❣r❛♠♠✐♥❣✳ ■♥ ❬■❧♦❪ ■❇▼ ■▲❖● t❡❛♠✳ ■▲❖● ❖♣t✐♠✐③❛t✐♦♥ ❙✉✐t❡s✱ ✷✵✶✹✳ ❆✈❛✐❧❛❜❧❡ ❢r♦♠ ❤tt♣✿✴✴✇✇✇✲✵✶✳✐❜♠✳❝♦♠✴s♦❢t✇❛r❡✴✇❡❜s♣❤❡r❡✴✐❧♦❣✴✳ ❬❏❏◆❱✽✾❪ P✳ ❏❛♥ss❡♥✱ P✳ ❏❡❣♦✉✱ ❇✳ ◆♦✉❣✉✐❡r✱ ❛♥❞ ▼✳ ❈✳ ❱✐❧❛r❡♠✳ ✐♥❣ ♣r♦❝❡ss ❢♦r ❣❡♥❡r❛❧ ❝♦♥str❛✐♥t✲s❛t✐s❢❛❝t✐♦♥ ♣r♦❜❧❡♠s✿ ❆ ✜❧t❡r✲ ❛❝❤✐❡✈✐♥❣ ♣❛✐r✇✐s❡✲❝♦♥s✐st❡♥❝② ✉s✐♥❣ ❛♥ ❛ss♦❝✐❛t❡❞ ❜✐♥❛r② r❡♣r❡s❡♥t❛t✐♦♥✳ ■♥ ❚♦♦❧s ❢♦r ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡✱ ✶✾✽✾✳ ❆r❝❤✐t❡❝t✉r❡s✱ ▲❛♥❣✉❛❣❡s ❛♥❞ ❆❧❣♦r✐t❤♠s✱ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❲♦r❦s❤♦♣ ♦♥✱ ♣❛❣❡s ✹✷✵✕✹✷✼✱ ✶✾✽✾✳ ❬❏◆✶✸❪ ❈❤r✐st♦♣❤❡r ❏❡✛❡rs♦♥ ❛♥❞ P❡t❡r ◆✐❣❤t✐♥❣❛❧❡✳ ❊①t❡♥❞✐♥❣ s✐♠♣❧❡ t❛❜✉✲ Pr♦❝❡❡❞✐♥❣ ♦❢ t❤❡ ✷✸t❤ ■♥t❡r♥❛✲ t✐♦♥❛❧ ❏♦✐♥t ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ✭■❏❈❆■✬✶✸✮✱ ♣❛❣❡s ❧❛r r❡❞✉❝t✐♦♥ ✇✐t❤ s❤♦rt s✉♣♣♦rts✳ ■♥ ✺✼✸✕✺✼✾✱ ✷✵✶✸✳ ❬❑❇✵✺❪ ●❡♦r❣❡ ❑❛ts✐r❡❧♦s ❛♥❞ ❋❛❤✐❡♠ ❇❛❝❝❤✉s✳ ●❡♥❡r❛❧✐③❡❞ ♥♦❣♦♦❞s ✐♥ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✷✵t❤ ◆❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ✭❆❆❆■✬✵✺✮✱ ♣❛❣❡s ✸✾✵✕✸✾✻✱ ✷✵✵✺✳ ❈❙Ps✳ ■♥ ❬❑◆❲✵✾❪ ●❡♦r❣❡ ❑❛ts✐r❡❧♦s✱ ◆✐♥❛ ◆❛r♦❞②ts❦❛✱ ❛♥❞ ❚♦❜② ❲❛❧s❤✳ ❘❡❢♦r♠✉❧❛t✲ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✻t❤ ■♥t❡r♥❛✲ t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ■♥t❡❣r❛t✐♦♥ ♦❢ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ❛♥❞ ❖♣❡r❛✲ t✐♦♥s ❘❡s❡❛r❝❤ t❡❝❤♥✐q✉❡s ✐♥ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P❆■❖❘✬✵✾✮✱ ✐♥❣ ❣❧♦❜❛❧ ❣r❛♠♠❛r ❝♦♥str❛✐♥ts✳ ■♥ ♣❛❣❡s ✶✸✷✕✶✹✼✱ ✷✵✵✾✳ ❬❑❙✵✽❪ ❙❡r❞❛r ❑❛❞✐♦❣❧✉ ❛♥❞ ▼❡✐♥♦❧❢ ❙❡❧❧♠❛♥♥✳ ●r❛♠♠❛r ❝♦♥str❛✐♥ts✳ str❛✐♥ts✱ ✶✺✿✶✶✼✕✶✹✹✱ ✷✵✵✽✳ ✶✵✾ ❈♦♥✲ ❬❑❲✵✼❪ ●❡♦r❣❡ ❑❛ts✐r❡❧♦s ❛♥❞ ❚♦❜② ❲❛❧s❤✳ ❆ ❝♦♠♣r❡ss✐♦♥ ❛❧❣♦r✐t❤♠ ❢♦r Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✸t❤ ■♥t❡r✲ ♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ Pr✐♥❝✐♣❧❡s ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ❈♦♥str❛✐♥t Pr♦✲ ❣r❛♠♠✐♥❣ ✭❈P✬✵✼✮✱ ♣❛❣❡s ✸✼✾✕✸✾✸✱ ✷✵✵✼✳ ❧❛r❣❡ ❛r✐t② ❡①t❡♥s✐♦♥❛❧ ❝♦♥str❛✐♥ts✳ ■♥ + ❬❑❲❘ ✶✵❪ ❙❤❛♥t ❑❛r❛❦❛s❤✐❛♥✱ ❘♦❜❡rt ❲♦♦❞✇❛r❞✱ ❇❡rt❤❡ ❨✳ ❈❤♦✉❡✐r②✱ ❛♥❞ ❈❤r✐st✐❛♥ ❇❡ss✐❡r❡✳ ❈❤r✐st♦♣❤❡r ❘❡❡s♦♥✱ ❆ ✜rst ♣r❛❝t✐❝❛❧ ❛❧✲ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✷✹t❤ ◆❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ✭❆❆❆■✬✶✵✮✱ ❣♦r✐t❤♠ ❢♦r ❤✐❣❤ ❧❡✈❡❧s ♦❢ r❡❧❛t✐♦♥❛❧ ❝♦♥s✐st❡♥❝②✳ ■♥ ♣❛❣❡s ✶✵✶✕✶✵✼✱ ✷✵✶✵✳ ❬▲❛✉✼✽❪ ❏❡❛♥✲▲♦✉✐s ▲❛✉r✐èr❡✳ ❆ ❧❛♥❣✉❛❣❡ ❛♥❞ ❛ ♣r♦❣r❛♠ ❢♦r st❛t✐♥❣ ❛♥❞ s♦❧✈✐♥❣ ❝♦♠❜✐♥❛t♦r✐❛❧ ♣r♦❜❧❡♠s✳ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡✱ ✶✵✭✶✮✿✷✾✕✶✷✼✱ ✶✾✼✽✳ ❬▲❇❍✵✸❪ ❈❤r✐st♦♣❤❡ ▲❡❝♦✉tr❡✱ ❋ré❞ér✐❝ ❇♦✉ss❡♠❛rt✱ ❛♥❞ ❋r❡❞ ❍❡♠❡r②✳ ❊①✲ ♣❧♦✐t✐♥❣ ♠✉❧t✐❞✐r❡❝t✐♦♥❛❧✐t② ✐♥ ❝♦❛rs❡✲❣r❛✐♥❡❞ ❛r❝ ❝♦♥s✐st❡♥❝② ❛❧❣♦✲ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✾t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ Pr✐♥✲ ❝✐♣❧❡s ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P✬✵✸✮✱ ♣❛❣❡s ✹✽✵✕ r✐t❤♠s✳ ■♥ ✹✾✹✱ ✷✵✵✸✳ ❬▲❡❝✶✶❪ ❈❤r✐st♦♣❤❡ ▲❡❝♦✉tr❡✳ ❙❚❘✷✿ ❖♣t✐♠✐③❡❞ s✐♠♣❧❡ t❛❜✉❧❛r r❡❞✉❝t✐♦♥ ❢♦r t❛❜❧❡ ❝♦♥str❛✐♥ts✳ ❬▲❡s✾✺❪ ❚❡❞ ▲❡s❧✐❡✳ ❈♦♥str❛✐♥ts✱ ✶✻✿✸✹✶✕✸✼✶✱ ✷✵✶✶✳ ❊✣❝✐❡♥t ❛♣♣r♦❛❝❤❡s t♦ s✉❜s❡t ❝♦♥str✉❝t✐♦♥✳ ▼❛st❡r✬s t❤❡s✐s✱ ❯♥✐✈❡rs✐t② ♦❢ ❲❛t❡r❧♦♦✱ ✶✾✾✺✳ ❬▲▲✵✹❪ ❨❛t ❈❤✐✉ ▲❛✇ ❛♥❞ ❏✐♠♠② ❍✳ ▼✳ ▲❡❡✳ ●❧♦❜❛❧ ❝♦♥str❛✐♥ts ❢♦r ✐♥t❡❣❡r Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✵t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ Pr✐♥❝✐♣❧❡s ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P✬✵✹✮✱ ♣❛❣❡s ✸✻✷✕✸✼✻✱ ✷✵✵✹✳ ❛♥❞ s❡t ✈❛❧✉❡ ♣r❡❝❡❞❡♥❝❡✳ ❬▲▲❨✶✷❪ ■♥ ❈❤r✐st♦♣❤❡ ▲❡❝♦✉tr❡✱ ❈❤❛✈❛❧✐t ▲✐❦✐t✈✐✈❛t❛♥❛✈♦♥❣✱ ❛♥❞ ❘♦❧❛♥❞ ❍✳ ❈✳ Pr♦✲ ❝❡❡❞✐♥❣s ♦❢ t❤❡ ✷✵t❤ ❊✉r♦♣❡❛♥ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ✭❊❈❆■✬✶✷✮✱ ♣❛❣❡s ✺✶✵✕✺✶✺✱ ✷✵✶✷✳ ❨❛♣✳ ❆ ♣❛t❤✲♦♣t✐♠❛❧ ●❆❈ ❛❧❣♦r✐t❤♠ ❢♦r t❛❜❧❡ ❝♦♥str❛✐♥ts✳ ■♥ ❬▲P❘❚✶✷❪ ❈❤r✐st♦♣❤❡ ▲❡❝♦✉tr❡✱ ◆✐❝♦❧❛s P❛r✐s✱ ❖❧✐✈✐❡r ❘♦✉ss❡❧✱ ❛♥❞ ❙é❜❛st✐❡♥ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✽t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ Pr✐♥❝✐♣❧❡s ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P✬✶✷✮✱ ♣❛❣❡s ✸✾✵✕✹✵✺✱ ✷✵✶✷✳ ❚❛❜❛r②✳ Pr♦♣❛❣❛t✐♥❣ s♦❢t t❛❜❧❡ ❝♦♥str❛✐♥ts✳ ■♥ ✶✶✵ ❬▲P❘❚✶✸❪ ❈❤r✐st♦♣❤❡ ▲❡❝♦✉tr❡✱ ◆✐❝♦❧❛s P❛r✐s✱ ❖❧✐✈✐❡r ❘♦✉ss❡❧✱ ❛♥❞ ❙❡❜❛st✐❡♥ ❚❛❜❛r②✳ ❙♦❧✈✐♥❣ ✇❝s♣ ❜② ❡①tr❛❝t✐♦♥ ♦❢ ♠✐♥✐♠❛❧ ✉♥s❛t✐s✜❛❜❧❡ ❝♦r❡s✳ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✷✹t❤ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❚♦♦❧s ✇✐t❤ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ✭■❈❚❆■✬✶✷✮✱ ♣❛❣❡s ✾✶✺✕✾✷✷✱ ✷✵✶✸✳ ■♥ ❬▲P❙✶✸❪ ❈❤r✐st♦♣❤❡ ▲❡❝♦✉tr❡✱ ❆♥❛st❛s✐❛ P❛♣❛rr✐③♦✉②✱ ❛♥❞ ❑♦st❛s ❙t❡r❣✐♦✉✳ Pr♦❝❡❡❞✐♥❣ ♦❢ t❤❡ ✷✼t❤ ◆❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ✭❆❆❆■✬✶✸✮✱ ♣❛❣❡s ❊①t❡♥❞✐♥❣ ❙❚❘ t♦ ❛ ❤✐❣❤❡r✲♦r❞❡r ❝♦♥s✐st❡♥❝②✳ ■♥ ✺✼✻✕✺✽✷✱ ✷✵✶✸✳ ❬▲❙✵✻❪ ❈❤r✐st♦♣❤❡ ▲❡❝♦✉tr❡ ❛♥❞ ❘❛❞♦s❧❛✇ ❙③②♠❛♥❡❦✳ ●❡♥❡r❛❧✐③❡❞ ❛r❝ ❝♦♥✲ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✷t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ Pr✐♥❝✐♣❧❡s ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P✬✵✻✮✱ ♣❛❣❡s ✷✽✹✕✷✾✽✱ ✷✵✵✻✳ s✐st❡♥❝② ❢♦r ♣♦s✐t✐✈❡ t❛❜❧❡ ❝♦♥str❛✐♥ts✳ ❬▼❛❝✼✼❛❪ ■♥ ❆❧❛♥ ❑✳ ▼❛❝❦✇♦rt❤✳ ❈♦♥s✐st❡♥❝② ✐♥ ♥❡t✇♦r❦s ♦❢ r❡❧❛t✐♦♥s✳ ■♥t❡❧❧✐❣❡♥❝❡✱ ✽✭✶✮✿✾✾ ✕ ✶✶✽✱ ✶✾✼✼✳ ❆rt✐✜❝✐❛❧ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✺t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❏♦✐♥t ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ✭■❏✲ ❈❆■✬✼✼✮✱ ♣❛❣❡s ✺✾✽✕✻✵✻✱ ✶✾✼✼✳ ❬▼❛❝✼✼❜❪ ❆❧❛♥ ❑✳ ▼❛❝❦✇♦rt❤✳ ❖♥ r❡❛❞✐♥❣ s❦❡t❝❤ ♠❛♣s✳ ■♥ ❬▼❛❤✵✷❪ ▼✐❝❤❛❡❧ ▼❛❤❡r✳ ❆♥❛❧②s✐s ♦❢ ❛ ❣❧♦❜❛❧ ❝♦♥t✐❣✉✐t② ❝♦♥str❛✐♥t✳ ■♥ ❬▼❉▲✶✹❪ ❏❡❛♥✲❇❛♣t✐st❡ ▼❛✐r②✱ ❨✈❡s ❉❡✈✐❧❧❡✱ ❛♥❞ ❈❤r✐st♦♣❤❡ ▲❡❝♦✉tr❡✳ ❉♦♠❛✐♥ ❚❤❡ ✹t❤ ❲♦r❦s❤♦♣ ♦♥ ❘✉❧❡✲❇❛s❡❞ ❈♦♥str❛✐♥t ❘❡❛s♦♥✐♥❣ ❛♥❞ Pr♦❣r❛♠♠✐♥❣ ✭❘❈♦❘P✬✵✷ ♦❢ ❈P✬✵✷✮✱ ✷✵✵✷✳ ❦✲✇✐s❡ ❝♦♥s✐st❡♥❝② ♠❛❞❡ ❛s s✐♠♣❧❡ ❛s ❣❡♥❡r❛❧✐③❡❞ ❛r❝ ❝♦♥s✐st❡♥❝②✳ ■♥ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✶t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ■♥t❡❣r❛t✐♦♥ ♦❢ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ❛♥❞ ❖♣❡r❛t✐♦♥s ❘❡s❡❛r❝❤ t❡❝❤♥✐q✉❡s ✐♥ ❈♦♥✲ str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P❆■❖❘✬ ✶✹✮✱ ♣❛❣❡s ✷✸✺✕✷✺✵✱ ✷✵✶✹✳ ❬▼❍✽✻❪ ❘♦❣❡r ▼♦❤r ❛♥❞ ❚❤♦♠❛s ❈✳ ❍❡♥❞❡rs♦♥✳ ❆r❝ ❛♥❞ ♣❛t❤ ❝♦♥s✐st❡♥❝② r❡✈✐s✐t❡❞✳ ❬▼❍❉✶✹❪ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡✱ ✷✽✭✷✮✿✷✷✺ ✕ ✷✸✸✱ ✶✾✽✻✳ ❏❡❛♥✲❇❛♣t✐st❡ ▼❛✐r②✱ P❛s❝❛❧ ❍❡♥t❡♥r②❝❦✱ ❛♥❞ ❨✈❡s ❉❡✈✐❧❧❡✳ ❖♣t✐♠❛❧ ❛♥❞ ❡✣❝✐❡♥t ✜❧t❡r✐♥❣ ❛❧❣♦r✐t❤♠s ❢♦r t❛❜❧❡ ❝♦♥str❛✐♥ts✳ ❈♦♥str❛✐♥ts✱ ✶✾✿✼✼✕✶✷✵✱ ✷✵✶✹✳ ❬▼▼✽✽❪ ❘♦❣❡r ▼♦❤r ❛♥❞ ●ér❛❧❞ ▼❛s✐♥✐✳ ●♦♦❞ ♦❧❞ ❞✐s❝r❡t❡ r❡❧❛①❛t✐♦♥✳ ■♥ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✽t❤ ❊✉r♦♣❡❛♥ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ✭❊❈❆■✬✽✽✮✱ ♣❛❣❡s ✻✺✶✕✻✺✻✱ ✶✾✽✽✳ ✶✶✶ ❬▼♦♥✼✹❪ ❯❣♦ ▼♦♥t❛♥❛r✐✳ ◆❡t✇♦r❦s ♦❢ ❝♦♥str❛✐♥ts✿ ❋✉♥❞❛♠❡♥t❛❧ ♣r♦♣❡rt✐❡s ❛♥❞ ❛♣♣❧✐❝❛t✐♦♥s t♦ ♣✐❝t✉r❡ ♣r♦❝❡ss✐♥❣✳ ■♥❢♦r♠❛t✐♦♥ ❙❝✐❡♥❝❡s✱ ✼✭✵✮✿✾✺ ✕ ✶✸✷✱ ✶✾✼✹✳ ❬▼❙✼✷❪ ❆❧❜❡rt ❘✳ ▼❡②❡r ❛♥❞ ▲❛rr② ❏✳ ❙t♦❝❦♠❡②❡r✳ ❚❤❡ ❡q✉✐✈❛❧❡♥❝❡ ♣r♦❜✲ ❧❡♠ ❢♦r r❡❣✉❧❛r ❡①♣r❡ss✐♦♥s ✇✐t❤ sq✉❛r✐♥❣ r❡q✉✐r❡s ❡①♣♦♥❡♥t✐❛❧ s♣❛❝❡✳ Pr♦❝❡❡❞✐♥❣ ♦❢ t❤❡ ✶✸t❤ ❆♥♥✉❛❧ ❙②♠♣♦s✐✉♠ ♦♥ ❙✇✐t❝❤✐♥❣ ❛♥❞ ❆✉✲ t♦♠❛t❛ ❚❤❡♦r②✱ ♣❛❣❡s ✶✷✺✕✶✷✾✱ ✶✾✼✷✳ ■♥ ❬◆❛r✶✶❪ ◆✐♥❛ ◆❛r♦t②ts❦❛✳ ❘❡❢♦r♠✉❧❛t✐♦♥ ♦❢ ●❧♦❜❛❧ ❈♦♥str❛✐♥ts✳ P❤❉ t❤❡s✐s✱ ❚❤❡ ❯♥✐✈❡rs✐t② ♦❢ ◆❡✇ ❙♦✉t❤ ❲❛❧❡s✱ ✷✵✶✶✳ ❬P❡s✵✶❪ ●✐❧❧❡s P❡s❛♥t✳ ❆ ✜❧t❡r✐♥❣ ❛❧❣♦r✐t❤♠ ❢♦r t❤❡ str❡t❝❤ ❝♦♥str❛✐♥t✳ ■♥ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✼t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ Pr✐♥❝✐♣❧❡s ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P✬✵✶✮✱ ♣❛❣❡s ✶✽✸✕✶✾✺✱ ✷✵✵✶✳ ❬P❡s✵✹❪ ●✐❧❧❡s P❡s❛♥t✳ ❆ r❡❣✉❧❛r ❧❛♥❣✉❛❣❡ ♠❡♠❜❡rs❤✐♣ ❝♦♥str❛✐♥t ❢♦r ✜♥✐t❡ s❡✲ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✵t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r✲ ❡♥❝❡ ♦♥ Pr✐♥❝✐♣❧❡s ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P✬✵✹✮✱ q✉❡♥❝❡s ♦❢ ✈❛r✐❛❜❧❡s✳ ■♥ ♣❛❣❡s ✹✽✷✕✹✾✺✱ ✷✵✵✹✳ ❬P❙✶✷❪ ❆♥❛st❛s✐❛ P❛♣❛rr✐③♦✉ ❛♥❞ ❑♦st❛s ❙t❡r❣✐♦✉✳ ❆♥ ❡✣❝✐❡♥t ❤✐❣❤❡r✲♦r❞❡r Pr♦❝❡❡❞✐♥❣ ♦❢ t❤❡ ✷✻t❤ ◆❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ✭❆❆❆■✬✶✷✮✱ ♣❛❣❡s ✺✸✺✕ ❝♦♥s✐st❡♥❝② ❛❧❣♦r✐❤t♠ ❢♦r t❛❜❧❡ ❝♦♥str✐❛♥ts✳ ■♥ ✺✹✶✱ ✷✵✶✷✳ ❬◗❲✵✻❪ ❈❧❛✉❞❡✲●✉② ◗✉✐♠♣❡r ❛♥❞ ❚♦❜② ❲❛❧s❤✳ ●❧♦❜❛❧ ❣r❛♠♠❛r ❝♦♥str❛✐♥ts✳ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✷t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ Pr✐♥❝✐♣❧❡s ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P✬✵✻✮✱ ♣❛❣❡s ✼✺✶✕✼✺✺✱ ✷✵✵✻✳ ■♥ ❬◗❲✵✼❪ ❈❧❛✉❞❡✲●✉② ◗✉✐♠♣❡r ❛♥❞ ❚♦❜② ❲❛❧s❤✳ ❉❡❝♦♠♣♦s✐♥❣ ❣❧♦❜❛❧ ❣r❛♠✲ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✸t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r✲ ❡♥❝❡ ♦♥ Pr✐♥❝✐♣❧❡s ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P✬✵✼✮✱ ♠❛r ❝♦♥str❛✐♥ts✳ ■♥ ♣❛❣❡s ✺✾✵✕✻✵✹✱ ✷✵✵✼✳ ❬❘é❣✾✹❪ ❏❡❛♥✲❈❤❛r❧❡s ❘é❣✐♥✳ ❆ ✜❧t❡r✐♥❣ ❛❧❣♦r✐t❤♠ ❢♦r ❝♦♥str❛✐♥ts ♦❢ ❞✐✛❡r❡♥❝❡ Pr♦❝❡❡❞✐♥❣ ♦❢ t❤❡ ✶✷t❤ ◆❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ✭❆❆❆■✬✾✹✮✱ ♣❛❣❡s ✸✻✷✕✸✻✼✱ ✶✾✾✹✳ ✐♥ ❈❙Ps✳ ■♥ ❬❘é❣✾✻❪ ❏❡❛♥✲❈❤❛r❧❡s ❘é❣✐♥✳ ●❡♥❡r❛❧✐③❡❞ ❛r❝ ❝♦♥s✐st❡♥❝② ❢♦r ❣❧♦❜❛❧ ❝❛r❞✐♥❛❧✲ Pr♦❝❡❡❞✐♥❣ ♦❢ t❤❡ ✶✸t❤ ◆❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ✭❆❆❆■✬✾✻✮✱ ♣❛❣❡s ✷✵✾✕✷✶✺✱ ✶✾✾✻✳ ✐t② ❝♦♥str❛✐♥ts✳ ■♥ ✶✶✷ ❬❘❙✾✼❪ ●r③❡❣♦r③ ❘♦③❡♥❜❡r❣ ❛♥❞ ❆rt♦ ❙❛❧♦♠❛❛✳ ❍❛♥❞❜♦♦❦ ♦❢ ❢♦r♠❛❧ ❧❛♥✲ ❣✉❛❣❡s✱ ✈♦❧✳ ✶✿ ✇♦r❞✱ ❧❛♥❣✉❛❣❡✱ ❣r❛♠♠❛r✳ ❙♣r✐♥❣❡r✲❱❡r❧❛❣ ◆❡✇ ❨♦r❦✱ ■♥❝✳✱ ◆❡✇ ❨♦r❦✱ ◆❨✱ ❯❙❆✱ ✶✾✾✼✳ ❬❙❡❧✵✻❪ ❬❙❋✾✹❪ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✷t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ Pr✐♥❝✐♣❧❡s ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ✭❈P✬✵✻✮✱ ♣❛❣❡s ✺✸✵✕✺✹✹✱ ✷✵✵✻✳ ▼❡✐♥♦❧❢ ❙❡❧❧♠❛♥♥✳ ❚❤❡ t❤❡♦r② ♦❢ ❣r❛♠♠❛r ❝♦♥str❛✐♥ts✳ ■♥ ❉❛♥✐❡❧ ❙❛❜✐♥ ❛♥❞ ❊✉❣❡♥❡ ❈✳ ❋r❡✉❞❡r✳ ❈♦♥tr❛❞✐❝t✐♥❣ ❝♦♥✈❡♥t✐♦♥❛❧ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✷♥❞ ■♥t❡r♥❛✲ t✐♦♥❛❧ ❲♦r❦s❤♦♣ ♦♥ Pr✐♥❝✐♣❧❡s ❛♥❞ Pr❛❝t✐❝❡ ♦❢ ❈♦♥str❛✐♥t Pr♦❣r❛♠✲ ♠✐♥❣ ✭PP❈P✬✾✹✮✱ ♣❛❣❡s ✶✵✕✷✵✱ ✶✾✾✹✳ ✇✐s❞♦♠ ✐♥ ❝♦♥str❛✐♥t s❛t✐s❢❛❝t✐♦♥✳ ■♥ ❬❙❑▼❇✾✵❪ ❆✳ ❙r✐♥✐✈❛s❛♥✱ ❚✳ ❑❛♠✱ ❙✳ ▼❛❧✐❦✱ ❛♥❞ ❘✳ ❇r❛②t♦♥✳ ❞✐s❝r❡t❡ ❢✉♥❝t✐♦♥ ♠❛♥✐♣✉❧❛t✐♦♥✳ ■♥ ❆❧❣♦r✐t❤♠s ❢♦r ❈♦♠♣✉t❡r ❆✐❞❡❞ ❉❡s✐❣♥✱ ♣❛❣❡s ✾✷✕✾✺✱ ✶✾✾✵✳ ❬❙❙✵✺❪ ◆✐❝♦❧❛♦s ❙❛♠❛r❛s ❛♥❞ ❑♦st❛s ❙t❡r❣✐♦✉✳ ❇✐♥❛r② ❡♥❝♦❞✐♥❣s ♦❢ ♥♦♥✲ ❜✐♥❛r② ❝♦♥str❛✐♥t s❛t✐s❢❛❝t✐♦♥ ♣r♦❜❧❡♠s✿ ❆❧❣♦r✐t❤♠s ❛♥❞ ❡①♣❡r✐♠❡♥✲ t❛❧ r❡s✉❧ts✳ ❏♦✉r♥❛❧ ♦❢ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ❘❡s❡❛r❝❤✱ ✷✹✿✻✹✶✕✻✽✹✱ ✷✵✵✺✳ ❬❚❤♦✻✽❪ ❑❡♥ ❚❤♦♠♣s♦♥✳ ❘❡❣✉❧❛r ❡①♣r❡ss✐♦♥ s❡❛r❝❤ ❛❧❣♦r✐t❤♠✳ t✐♦♥s ♦❢ t❤❡ ❆❈▼✱ ✶✶✭✻✮✿✹✶✾✕✹✷✷✱ ✶✾✻✽✳ ❬❯❧❧✵✼❪ ❏✉❧✐❛♥ ❘✳ ❯❧❧♠❛♥♥✳ P❛rt✐t✐♦♥ s❡❛r❝❤ ❢♦r ♥♦♥✲❜✐♥❛r② ❝♦♥str❛✐♥t s❛t✐s✲ ❢❛❝t✐♦♥✳ ❬✈❇❉✾✺❪ ❈♦♠♠✉♥✐❝❛✲ ■♥❢♦r♠❛t✐♦♥ ❙❝✐❡♥❝❡✱ ✶✼✼✿✸✻✸✾✕✸✻✼✽✱ ✷✵✵✼✳ P❡t❡r ✈❛♥ ❇❡❡❦ ❛♥❞ ❘✐♥❛ ❉❡❝❤t❡r✳ ❖♥ t❤❡ ♠✐♥✐♠❛❧✐t② ❛♥❞ ❣❧♦❜❛❧ ❝♦♥s✐st❡♥❝② ♦❢ r♦✇✲❝♦♥✈❡① ❝♦♥str❛✐♥t ♥❡t✇♦r❦s✳ ❏♦✉r♥❛❧ ♦❢ t❤❡ ❆❈▼✱ ✹✷✭✸✮✿✺✹✸✕✺✻✶✱ ▼❛② ✶✾✾✺✳ ❬✈❇❉✾✼❪ P❡t❡r ✈❛♥ ❇❡❡❦ ❛♥❞ ❘✐♥❛ ❉❡❝❤t❡r✳ ❈♦♥str❛✐♥t t✐❣❤t♥❡ss ❛♥❞ ❧♦♦s❡♥❡ss ✈❡rs✉s ❧♦❝❛❧ ❛♥❞ ❣❧♦❜❛❧ ❝♦♥s✐st❡♥❝②✳ ❏♦✉r♥❛❧ ♦❢ ❚❤❡ ❆❈▼✱ ✭✹✮✿✺✹✾✕ ✺✻✻✱ ✶✾✾✼✳ ❬✈◆❪ ●❡rt❥❛♥ ✈❛♥ ◆♦♦r❞✳ ❋❙❆ ❯t✐❧✐t✐❡s t♦♦❧❜♦①✿ ❛ ❝♦❧❧❡❝t✐♦♥ ♦❢ ✉t✐❧✐t✐❡s t♦ ♠❛♥✐♣✉❧❛t❡ r❡❣✉❧❛r ❡①♣r❡ss✐♦♥s✱ ✜♥✐t❡✲st❛t❡ ❛✉t♦♠❛t❛ ❛♥❞ ✜♥✐t❡✲ st❛t❡ tr❛♥s❞✉❝❡rs✱ ✷✵✶✹✳ ❆✈❛✐❧❛❜❧❡ ❢r♦♠ ❤tt♣✿✴✴✇✇✇✳❧❡t✳r✉❣✳♥❧✴ ⑦✈❛♥♥♦♦r❞✴❋s❛✴❢s❛✳❤t♠❧✳ ❬❲✐❦✶✸❪ ❲✐❦✐♣❡❞✐❛✳ ❙✉❞♦❦✉✿ ❛ ❧♦❣✐❝✲❜❛s❡❞ ❝♦♠❜✐♥❛t♦r✐❛❧ ♥✉♠❜❡r✲♣❧❛❝❡♠❡♥t ♣✉③③❧❡✳ ❤tt♣✿✴✴❡♥✳✇✐❦✐♣❡❞✐❛✳♦r❣✴✇✐❦✐✴❙✉❞♦❦✉✱ ✶✶✸ ✷✵✶✸✳ ❬❳❇❍▲✵✺❪ ❑❡ ❳✉✱ ❋ré❞ér✐❝ ❇♦✉ss❡♠❛rt✱ ❋r❡❞ ❍❡♠❡r②✱ ❛♥❞ ❈❤r✐st♦♣❤❡ ▲❡❝♦✉tr❡✳ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✾t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❏♦✐♥t ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡✱ ❆ s✐♠♣❧❡ ♠♦❞❡❧ t♦ ❣❡♥❡r❛t❡ ❤❛r❞ s❛t✐s✜❛❜❧❡ ✐♥st❛♥❝❡s✳ ■♥ ■❏❈❆■✬✵✺✱ ♣❛❣❡s ✸✸✼✕✸✹✷✱ ✷✵✵✺✳ ❬❳▲✵✵❪ ❑❡ ❳✉ ❛♥❞ ❲❡✐ ▲✐✳ ❊①❛❝t ♣❤❛s❡ tr❛♥s✐t✐♦♥s ✐♥ r❛♥❞♦♠ ❝♦♥str❛✐♥t s❛t✲ ✐s❢❛❝t✐♦♥ ♣r♦❜❧❡♠s✳ ❏♦✉r♥❛❧ ♦❢ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ❘❡s❡❛r❝❤✱ ✶✷✿✾✸✕ ✶✵✸✱ ✷✵✵✵✳ ❬❩❨✵✶❪ ❨✉❛♥❧✐♥ ❩❤❛♥❣ ❛♥❞ ❘♦❧❛♥❞ ❍✳ ❈✳ ❨❛♣✳ ▼❛❦✐♥❣ ❆❈✲✸ ❛♥ ♦♣t✐♠❛❧ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✼t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❏♦✐♥t ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ✭■❏❈❆■✬✵✶✮✱ ♣❛❣❡s ✸✶✻✕✸✷✶✱ ✷✵✵✶✳ ❛❧❣♦r✐t❤♠✳ ■♥ ✶✶✹ ❆♣♣❡♥❞✐❝❡s ✶✶✺ ❆♣♣❡♥❞✐① ❆ ✶✶✼ ✶✶✽ ❆✳✶ ❚❤❡ ❙❚❘✷ ❆❧❣♦r✐t❤♠ ❲❡ r❡♣❧✐❝❛t❡ t❤❡ ❙❚❘✷ ❛❧❣♦r✐t❤♠ ❤❡r❡✳ ❋♦r ♠♦r❡ ❞❡t❛✐❧s✱ ♣❧❡❛s❡ s❡❡ ❬▲❡❝✶✶❪✳ str✷✭c✿ ❝♦♥str❛✐♥t✮ ❜❡❣✐♥ S val ← ∅ S sup ← ∅ ✐❢ lastP ast(P ) ∈ scp(c) t❤❡♥ S val ← S val ∪ {lastP ast(P )} ❢♦r ❡❛❝❤ ✈❛r✐❛❜❧❡ xi ∈ scp(c) ❛♥❞ xi ∈/ past(P ) ❞♦ ←∅ S ← S ∪ {x} ✐❢ |D(xi )| = lastSize[c][xi ]| t❤❡♥ S val ← S val ∪ {xi } lastSize[c][xi ] ← |D(xi )| ❣❛❝❱❛❧✉❡s❬xi ❪ sup sup k←1 ✇❤✐❧❡ k ≤ currentLimit[c] ❞♦ index ← position[c][k] τ ← table[c][index] ✐❢ ✐s❱❛❧✐❞✭c✱τ ✱ S val ✮ t❤❡♥ ❢♦r ❡❛❝❤ ✈❛r✐❛❜❧❡ xi ∈ S sup ❞♦ ✐❢ τ [xi ] ∈/ gacV alues[xi ] t❤❡♥ gacV alues[xi ] ← gacV alues[xi ] ∪ {τ [xi ]} ✐❢ |gacV alues[xi ]| = |D(xi )| t❤❡♥ S sup ← S sup \ {xi } k ←k+1 ❡❧s❡ ✴✴s✇✐t❝❤ t❤❡ ✐♥✈❛❧✐❞ t✉♣❧❡ ✇✐t❤ t❤❡ ❧❛st ✈❛❧✐❞ t✉♣❧❡s ❛♥❞ ✉♣❞❛t❡ currentLimit[c] r❡♠♦✈❡❚✉♣❧❡✭c✱ k ✱ |past(P )|✮ ❢♦r ❡❛❝❤ ✈❛r✐❛❜❧❡ xi ∈ S sup ❞♦ D(xi ) ← gacV alues[x] ✐❢ D(x) = ∅ t❤❡♥ r❡t✉r♥ false ❀ ✴✴✉♣❞❛t❡ t❤❡ ❞♦♠❛✐♥ ♦❢ lastSize[c][xi ] ← |D(xi )| r❡t✉r♥ true ❋✐❣✉r❡ ❆✳✶✿ ❙❚❘✷ ❛❧❣♦r✐t❤♠✳ ✶✶✾ xi ✐s❱❛❧✐❞✭c✿ ❝♦♥str❛✐♥t✱ τ✿ t✉♣❧❡✱ S val : variables✮ ❜❡❣✐♥ ❢♦r ❡❛❝❤ ✈❛r✐❛❜❧❡ xi ∈ S val ❞♦ ✐❢ τ [xi ] ∈/ D(xi ) t❤❡♥ r❡t✉r♥ r❡t✉r♥ false true ❀ r❡♠♦✈❡❚✉♣❧❡✭c✿ ❝♦♥str❛✐♥t✱ k ✿ t✉♣❧❡ ♣♦s✐t✐♦♥✱ curLevel✿ ❝✉rr❡♥t s❡❛r❝❤ ❧❡✈❡❧✮ ❜❡❣✐♥ ✐❢ levelLimit[c][curLevel] = −1 t❤❡♥ levelLimit[c][curLevel] ← currentLimit[c] ✻✵ temp ← position[c][k] position[c][k] ← position[c][currentLimit[c]] position[c][currentLimit[c]] ← temp ✻✶ currentLimit[c] ← currentLimit[c] − r❡st♦r❡❚✉♣❧❡✭c✿ ❝♦♥str❛✐♥t✱ l✿ s❡❛r❝❤ ❧❡✈❡❧ t♦ ❜❡ r❡st♦r❡❞✮ ❜❡❣✐♥ ✐❢ levelLimit[c][l] = −1 t❤❡♥ currentLimit[c] ← levelLimit[c][l] levelLimite[c][l] ← −1 ❋✐❣✉r❡ ❆✳✷✿ ❚❤❡ ♣s❡✉❞♦❝♦❞❡ ♦❢ ✐s❱❛❧✐❞✭✮✱ r❡♠♦✈❡❚✉♣❧❡✭✮✱ ❛♥❞ r❡st♦r❡❚✉♣❧❡✭✮✳ ✶✷✵ ❆✳✷ ❚❤❡ ❙❚❘✸ ❆❧❣♦r✐t❤♠ ❲❡ r❡♣❧✐❝❛t❡ t❤❡ ❙❚❘✸ ❛❧❣♦r✐t❤♠ ❤❡r❡✳ ❋♦r ♠♦r❡ ❞❡t❛✐❧s✱ ♣❧❡❛s❡ s❡❡ ❬▲▲❨✶✷❪✳ ●❆❈✐♥✐t✭c✿ ❝♦♥str❛✐♥t✮ ❜❡❣✐♥ r❡♠♦✈❡ ✐♥✈❛❧✐❞ t✉♣❧❡s ❢r♦♠ r❡❧✭❝✮ inv(c) ← ∅ ❢♦r❡❛❝❤ x ∈ scp(c) ❛♥❞ a ∈ D(x) ❞♦ row (c, x , a).curr ← row(c, x, a).size − dep(c)[row (c, x , a)[0 ]] ← {(x, a)} str3(c : constraint, x : variables, a : value) ❜❡❣✐♥ prevMembers ← inv (c).members ❢♦r k ← t♦ row (c, x , a).curr ❞♦ ✐❢ row (c, x , a)[k ] ∈/ inv (c) t❤❡♥ ❛❞❞ row (c, x , a)[k ] t♦ inv (c) ✐❢ prevMembers = inv (c).members t❤❡♥ r❡t✉r♥ true s❛✈❡✭c✱ prevMembers ✱ stateI ✮ ❢♦r❡❛❝❤ i ∈ {prevMembers + 1, ., inv (c).members} ❞♦ k ← inv (c).dense[i ] ❢♦r❡❛❝❤ (y, b) ∈ dep(c)[k ] s✉❝❤ t❤❛t b ∈ D(y) ❞♦ p ← row (c, y, b).curr ✇❤✐❧❡ p ≥ ❛♥❞ row (c, y, b)[p] ∈ inv (c) ❞♦ p ← p − ✐❢ p < t❤❡♥ r❡♠♦✈❡❱❛❧✉❡✭y, b✮ ✐❢ D(y) = ∅ t❤❡♥ r❡t✉r♥ false ❡❧s❡ ✐❢ p = row (c, y, b).curr t❤❡♥ s❛✈❡✭(c, y, b)✱ row (c, y, b).curr ✱ stateR ✮ row (c, y, b).curr ← p ♠♦✈❡ r❡t✉r♥ (y, b) ❢r♦♠ dep(c)[k ] t♦ dep(c)[row (c, y, b)[p]] true ❋✐❣✉r❡ ❆✳✸✿ ❙❚❘✸ ❛❧❣♦r✐t❤♠✳ ✶✷✶ s❛✈❡✭key ✱ newData✱ store✮ ❜❡❣✐♥ ✐❢ (key, oldData) ∈/ top(store) ❢♦r ❛♥② ♦❧❞❉❛t❛ t❤❡♥ ✐♥s❡rt (key, newData) t♦ top(store) r❡st♦r❡❘✭✮ ❜❡❣✐♥ list ← pop(stateR) ❢♦r❡❛❝❤ ((c, x, a), k) ∈ list ❞♦ row (c, x , a).curr ← k r❡st♦r❡■✭✮ ❜❡❣✐♥ list ← pop(stateI) ❢♦r❡❛❝❤ (c, k) ∈ list ❞♦ inv(c).members ← k r❡♠♦✈❡❱❛❧✉❡✭①✿ ✈❛r✐❛❜❧❡✱ ❛✿ ✈❛❧✉❡✮ ❜❡❣✐♥ r❡♠♦✈❡ ❛ ❢r♦♠ ❛❞❞ (x, a) D(x) t♦ t❤❡ ♣r♦♣❛❣❛t✐♦♥ q✉❡✉❡ ❋✐❣✉r❡ ❆✳✹✿ ❚❤❡ ♣s❡✉❞♦❝♦❞❡ ♦❢ s❛✈❡✭✮✱ r❡st♦r❡■✭✮✱ r❡st♦r❡❘✭✮✱ ❛♥❞ r❡♠♦✈❡✭✮✳ ✶✷✷ [...]... algorithm for the table constraints can also be applied to other constraints indirectly However, the transformed table may be large for the global constraint This is why researchers are interested in developing fast propagation algorithms for it Designing and optimizing the propagation algorithms for table constraints is also a concern of this thesis Given a table constraint, suppose we want to enforce... algorithms on non- binary table constraints which are the most general form of nite domain constraints, and the eect of compact representations which can still represent tables A number of ecient generalized arc consistency (GAC) propagation algorithms have been developed, with mddc [CY10] and various STR [Ull07, Lec11, LLY12] being the state-of-the- art ones for table constraints Although mddc and STR... |S ⇒ w If a language L is L(G) for some CFG with the productions of G, then L is a G} context-free language Before ending this subsection, we give two important and useful normal forms of CFG Chomsky normal form A context-free grammar is in Chomsky normal form (CNF) if all of its production rules are of the forms: A → BC or A→a where A, B , and C are all non- terminals and a is a terminal Every CFG can... called a support for (x, a) in c A variable x ∈ X is GAC i every value a ∈ D(x) is GAC A constraint c is GAC i every variable x ∈ scp(c) is GAC A CSP is GAC i every constraint in C Generalized arc consistency A value is GAC GAC is used for non- binary CSP, while specically arc consistency (AC) is used for binary CSP GAC is the most well known and researched local consistency for non- binary CSPs It... and y : D(y) = {0, 1, 2} cannot take the same values at the same time The intentional representation of c(x, y) is x = y and the extensional representation with satisfying tuples is {(0, 1), (0, 2), (1, 0), (1, 2), (2, 0), (2, 1)} A constraint is binary otherwise otherwise it is ci ≡ cj , unary 1 if its arity is one , or A CSP is non- binary binary binary if its arity is two, or non- if all of its constraints. .. (MAC) [SF94] is a complete CSP solving algorithm for binary CSPs It applies systematic search and enforces arc consistency once a variable is instantiated during search and backtracks when a failure occurs We may use MGAC to emphasize the applications to non- binary CSPs and GAC ltering algorithms M(G)AC is one of the most ecient algorithms to solve large and hard CSPs, due to its ecient core (G)AC algorithms... proposed for non- binary CSPs The propagation algorithms of the local consistencies are introduced in the related chapters The local consistencies for non- binary CSPs can be divided into two classes depending on whether the consistencies alter the constraint graph or the relations of the constraints The local consistencies which only lter the inconsistent values from the domains of variables and not... variance in the size of representations, or can be transformed into other equivalent representations with dierent sizes For example, in Chapter 3, we generate several groups of NFAs which then can be converted into DFAs and MDDs with dierent sizes With these 3 CSPs, we can evaluate the space-time tradeos of the GAC algorithms for the constraints represented in automatons and MDDs In Chapter 5, we... we investigate the eect of constraint representations on the space-time tradeos for the ˆ regular constraints In Chapter 4, we give a GAC algorithm for grammar constraints and compare it with existing algorithms ˆ In Chapter 5, we develop two new STR algorithms which take the benets of the compressed table representations ˆ In Chapter 6, we propose to transform a CSP into another one, so that higher-order... 4-tuple G = (V, T, P, S) where V is a set of nonterminal symbols, T is a set of terminal symbols or called the alphabet, P is the set of productions and S is the start symbol A production Context-free grammar is a rule A→α where A A is a nonterminal and α is a sequence or nonterminals and terminals |G| = p∈P |p|, where |p| is the number of terminals and non- terminals in production p We use ⇒ to indicate