❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ▼■◆❆❙ ●❊❘❆■❙
■◆❙❚■❚❯❚❖ ❉❊ ❈■✃◆❈■❆❙ ❊❳❆❚❆❙
❉❊P❆❘❚❆▼❊◆❚❖ ❉❊ ❊❙❚❆❚❮❙❚■❈❆
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❊❙❚❆❚❮❙❚■❈❆
P❆❯▲❖ ❈❊❘◗❯❊■❘❆ ❉❖❙ ❙❆◆❚❖❙ ❏❯◆■❖❘
▼❖❉❊▲❖❙ ❙❊▼■P❆❘❆▼➱❚❘■❈❖❙ P❆❘❆ ❉❆❉❖❙ ❉❊
❙❖❇❘❊❱■❱✃◆❈■❆ ❈❖▼ ❈❊◆❙❯❘❆ ■◆❚❊❘❱❆▲❆❘
P❆❯▲❖ ❈❊❘◗❯❊■❘❆ ❉❖❙ ❙❆◆❚❖❙ ❏❯◆■❖❘
▼❖❉❊▲❖❙ ❙❊▼■P❆❘❆▼➱❚❘■❈❖❙ P❆❘❆ ❉❆❉❖❙ ❉❊
❙❖❇❘❊❱■❱✃◆❈■❆ ❈❖▼ ❈❊◆❙❯❘❆ ■◆❚❊❘❱❆▲❆❘
❚❡s❡ ❞❡ ❞♦✉t♦r❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲❣r❛❞✉❛çã♦ ❡♠ ❊st❛tíst✐❝❛ ❞♦ ❉❡♣❛rt❛✲ ♠❡♥t♦ ❞❡ ❊st❛tíst✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ❉♦✉t♦r ❡♠ ❊st❛tíst✐❝❛✳
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❋á❜✐♦ ◆♦❣✉❡✐r❛ ❉❡✲ ♠❛rq✉✐
❈♦♦r✐❡♥t❛❞♦r❛✿ Pr♦❢❛✳ ❉r❛✳ ▲♦✉r❞❡s ❈♦♥✲ tr❡r❛s ▼♦♥t❡♥❡❣r♦
▼❖❉❊▲❖❙ ❙❊▼■P❆❘❆▼➱❚❘■❈❖❙ P❆❘❆ ❉❆❉❖❙
❉❊ ❙❖❇❘❊❱■❱✃◆❈■❆ ❈❖▼ ❈❊◆❙❯❘❆
■◆❚❊❘❱❆▲❆❘
▼❖❉❊▲❖❙ ❙❊▼■P❆❘❆▼➱❚❘■❈❖❙ P❆❘❆ ❉❆❉❖❙ ❉❊
❙❖❇❘❊❱■❱✃◆❈■❆ ❈❖▼ ❈❊◆❙❯❘❆ ■◆❚❊❘❱❆▲❆❘
❊st❛ t❡s❡ ❝♦♥té♠ ❛s ❝♦rr❡çõ❡s ❡ ❛❧t❡r❛çõ❡s s✉❣❡r✐❞❛s ♣❡❧❛ ❈♦♠✐ssã♦ ❏✉❧❣❛❞♦r❛ ❞✉r❛♥t❡ ❛ ❞❡❢❡s❛ r❡❛❧✐③❛❞❛ ♣♦r P❛✉❧♦ ❈❡rq✉❡✐r❛ ❞♦s ❙❛♥t♦s ❏✉♥✐♦r ❡♠ ✷✺✴✶✶✴✷✵✶✻✳ ❖ ♦r✐❣✐♥❛❧ ❡♥❝♦♥tr❛✲s❡ ❞✐s♣♦♥í✈❡❧ ♥♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❞❡ ❊st❛tíst✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s✳
❈♦♠✐ssã♦ ❏✉❧❣❛❞♦r❛✿
• Pr♦❢✳ ❉r✳ ❋á❜✐♦ ◆♦❣✉❡✐r❛ ❉❡♠❛rq✉✐ ✭❖r✐❡♥t❛❞♦r✮ ✲ ❯❋▼●
• Pr♦❢❛✳ ❉r❛✳ ▲♦✉r❞❡s ❈♦♥tr❡r❛s ▼♦♥t❡♥❡❣r♦ ✲ ❯❋▼● ✭❈♦♦r✐❡♥t❛❞♦r❛✮ • Pr♦❢❛✳ ❉r❛✳ ❘♦s❛♥❣❡❧❛ ❍❡❧❡♥❛ ▲♦s❝❤✐ ✲ ❯❋▼●
• Pr♦❢✳ ❉r✳ ❱✐♥✐❝✐✉s ❉✐♥✐③ ▼❛②r✐♥❦ ✲ ❯❋▼●
❆❣r❛❞❡❝✐♠❡♥t♦s
⋆❆❣r❛❞❡ç♦ ❛♦ ♠❡✉ ❉❡✉s ❡ ◆♦ss❛ ❙❡♥❤♦r❛ ♣❡❧❛s ♦♣♦rt✉♥✐❞❛❞❡s q✉❡ sã♦ ❝♦❧♦❝❛❞❛s ❡♠ ♠✐♥❤❛
✈✐❞❛✱ ♣♦r s❡✉ ✐♠❡♥s♦ ❛♠♦r ❡ ♣♦r s❡♠♣r❡ ❛❜❡♥ç♦❛r✲♠❡ ❡♠ ♠❡✉s ♣❛ss♦s❀
⋆❆♦ ♠❡✉ ❖r✐❡♥t❛❞♦r ❋á❜✐♦ ◆♦❣✉❡✐r❛ ❉❡♠❛rq✉✐ ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ s❡r s❡✉ ♦r✐❡♥t❛♥❞♦ ❞❡
❞♦✉t♦r❛❞♦✳ ❖❜r✐❣❛❞♦ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ ❡ ♣♦r ❝♦♠♣❛rt✐❧❤❛r ♣❛rt❡ ❞❡ s✉❛ ❡①♣❡r✐ê♥❝✐❛ ❞❡ tr❛❜❛❧❤♦✳ ❱❛❧❡✉ ❋á❜✐♦❀
⋆ ➚ ♠✐♥❤❛ ❈♦♦r✐❡♥t❛❞♦r❛ ▲♦✉r❞❡s ▼♦♥t❡♥❡❣r♦ ♣♦r ❛❝❡✐t❛r ♠❡ ♦r✐❡♥t❛r ♥♦ ✐♥í❝✐♦ ♥❡st❡ tr❛✲
❜❛❧❤♦✱ ❞❡ss❛ ❢♦r♠❛✱ ❤♦❥❡ ♥ã♦ t❡rí❛♠♦s ♥❛❞❛✳ ❖❜r✐❣❛❞♦ ▲♦✉r❞❡s❀
⋆ ➚ ♠✐♥❤❛ ❡s♣♦s❛ ❋❛❜rí❝✐❛ ❡ ♠❡✉ ✜❧❤♦ ❇❡♥t♦✱ ♠✐♥❤❛s ❢♦♥t❡s ❞❡ ✐♥s♣✐r❛çã♦ ❡ ♠♦t✐✈❛çã♦✳
❆❣r❛❞❡ç♦ ❛ ❉❡✉s ♣♦r tê✲❧♦s ❡♠ ♠✐♥❤❛ ✈✐❞❛✳ ❚❡ ❛♠♦❀
⋆ ❆♦s ♠❡✉s ♣❛✐s✱ P❛✉❧♦ ❡ ▼❛r✐③❡t❡✱ ♣♦r t♦❞♦ ❝❛r✐♥❤♦✱ ❛♠♦r✱ ✐♥❝❡♥t✐✈♦s ❡ s✉♣♦rt❡ ♣❛r❛ ♠❛✐s
✉♠❛ ❡t❛♣❛ ❡♠ ♠✐♥❤❛ ✈✐❞❛❀
⋆ ❆♦ Pr♦❣❛♠❛ ❞❡ ▼❡❞✐❝✐♥❛ ❚r♦♣✐❝❛❧ ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ❜♦❧s❛ ❡ ♣❡❧❛ ♥♦✈❛ ❡①♣❡r✐ê♥❝✐❛ ❞❡
tr❛❜❛❧❤♦ ♥❛ ♠❡❞✐❝✐♥❛ tr♦♣✐❝❛❧✳
⋆❆♦ ❞❡♣❛rt❛♠❡♥t♦ ❞❡ ❡st❛tíst✐❝❛ ❡ ❛♦ ♣r♦❣r❛♠❛ ❞❡ ❞♦✉t♦r❛❞♦ ❡♠ ❡st❛tíst✐❝❛ ♣❡❧❛ ♦♣♦rt✉♥✐✲
❞❛❞❡ ❞❡ ❜♦❧s❛ ❝♦♠ ✐♥❝❡♥t✐✈♦s ♣❛r❛ ❛ ♣❡sq✉✐s❛ ❡ ❞♦❝ê♥❝✐❛ ❛tr❛✈és ❞❛ ❜♦❧s❛ r❡ú♥❡✳
⋆ ❆♦s ♠❡♠❜r♦s ❛✈❛❧✐❛❞♦r❡s ❞❡st❡ tr❛❜❛❧❤♦ ❞❡ t❡st❡✿ Pr♦❢❛✳ ❘♦s❛♥❣❡❧❛ ▲♦s❝❤✐✱ Pr♦❢✳ ❱✐♥✐❝✐✉s
▼❛②r✐♥❦✱ Pr♦❢✳ ▼ár✐♦ ❞❡ ❈❛str♦ ❡ Pr♦❢✳ ❱✐❝❡♥t❡ ●❛r✐❜❛②✱ ♣❡❧❛s ót✐♠❛s s✉❣❡stõ❡s ❡ ❝♦♠❡♥tá✲ r✐♦s✳
⋆ ❆❣r❛❞❡ç♦ ♣❡❧❛ ♠✐♥❤❛ ❢❛♠í❧✐❛ ❢♦r♠❛❞❛ ❡♠ ❇❍ ♣♦r ❡ss❡s s❡✐s ❛♥♦s✱ ❘♦❞r✐❣♦✱ ▲✉✐s✱ ❲❡❝s❧❡②✱
◆í✈❡❛✱ ▲í✈✐❛✱ ▲❛r✐ss❛✱ ❏✉❧✐❛♥❛✱ ❏✉❧✐❛♥❡✱ ▼ár❝✐♦✱ ❉❡♥✐s❡✱ ♣♦r t♦❞♦s ♦s ♠♦♠❡♥t♦s ♠❛r❛✈✐❧❤♦s♦s q✉❡ ♣✉❞❡ ❞❡s❢r✉t❛r ❡♠ ♠✐♥❤❛ ❡st❛❞✐❛ ❡♠ ❇❍✳ ❆❣r❛❞❡ç♦ t❛♠❜é♠ ❛♦s ❛♠✐❣♦s✱ ♣❡❧♦s ❞✐✈❡rs♦s ❝♦♥s❡❧❤♦s ❡ ♦r✐❡♥t❛çõ❡s q✉❡ s❡r✈✐r❛♠ ❞❡ ❛❧✐❝❡r❝❡ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳
⋆ ◗✉❡r♦ ❛❣r❛❞❡❝❡r à ❘♦❣ér✐❛ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ ❡ ❞❡❧✐❝❛❞❡③❛ ❡♠ ♠❡ ❛❥✉❞❛r ♥♦s ♠♦♠❡♥t♦s ❞❡
❛❣♦♥✐❛❀
✐✐
❊ ♥✉♥❝❛ t❡ ❡sq✉❡❝❡✱ s❡ ❛s ❝♦✐s❛s ❛✐♥❞❛ ♥ã♦ ❞❡r❛♠ ❝❡rt♦✿ ❚r❛❜❛❧❤❛✱ tr❛❜❛❧❤❛ ❡ tr❛❜❛❧❤❛✦
❘❡s✉♠♦
❊♠ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✱ ❞✐③❡♠♦s q✉❡ ❛ ❝❡♥s✉r❛ é ✐♥t❡r✈❛❧❛r q✉❛♥❞♦ s❛❜❡✲s❡ s♦♠❡♥t❡ q✉❡ ♦ t❡♠♣♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦s ✐♥❞✐✈í❞✉♦s ❡♠ ❛♥á❧✐s❡ ♣❡rt❡♥❝❡ ❛ ✉♠ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦✳ ❆ss✐♠✱ ❡st❛ t❡s❡ ❞❡ ❞♦✉t♦r❛❞♦ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ♣r♦♣♦r ❡①t❡♥sõ❡s ❛♦ ♠♦❞❡❧♦ ❡①♣♦♥❡♥❝✐❛❧ ♣♦r ♣❛rt❡s ❝♦♠ ❣r❛❞❡ ❛❧❡❛tór✐❛✱ ✈✐❛ ❡str✉t✉r❛ ❞❡ ❛❣r✉♣❛♠❡♥t♦ ❞♦ ♠♦❞❡❧♦ ♣❛rt✐çã♦ ♣r♦❞✉t♦✱ s♦❜ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞✐♥â♠✐❝❛✱ ♣❛r❛ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ s✉❥❡✐t♦s à ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r✳ Pr♦♣♦♠♦s ♠♦❞❡❧♦s ♣❛r❛ ❞♦✐s t✐♣♦s ❞❡ ♣♦♣✉❧❛çã♦✿ s❡♠ ❡ ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛❞♦s✳ P❛r❛ ❞❛❞♦s s❡♠ ❢r❛çã♦ ❞❡ ❝✉r❛❞♦s✱ ❛♣r❡s❡♥t❛♠♦s três ♣r♦♣♦st❛s ❞❡ ♠♦❞❡❧❛❣❡♠✳ ❆ ♣r✐♠❡✐r❛✱ r❡♣r❡s❡♥✲ t❛♥❞♦ ♦ ▼❊P ❝♦♠ ❣r❛❞❡ ❛❧❡❛tór✐❛ ❝♦♠ ❡❢❡✐t♦ ❞❛ ❝♦✈❛r✐á✈❡❧ ✜①♦ ♥♦ t❡♠♣♦✱ ❡ ❛s s❡❣✉✐♥t❡s r❡♣r❡s❡♥t❛♥❞♦ ❡①t❡♥sõ❡s ❞❡ ❞♦✐s ♠♦❞❡❧♦s ❞✐♥â♠✐❝♦s✱ ✉♠ ❝♦♠ ❣r❛❞❡ ✜①❛ ❡ ♦✉tr♦ ❝♦♠ ❣r❛❞❡ ❛❧❡❛tór✐❛✱ ❡♠ q✉❡ ❛♠❜♦s ♣❡r♠✐t❡♠ q✉❡ ♦ ❡❢❡✐t♦ ❞❛ ❝♦✈❛r✐á✈❡❧ ✈❛r✐❡ ♥♦ t❡♠♣♦✳ P❛r❛ ❡st❡ t✐♣♦ ❞❡ ♣♦♣✉❧❛çã♦✱ ✐❧✉str❛♠♦s ♦s ♠♦❞❡❧♦s ♣r♦♣♦st♦s✱ ❡ ♠♦❞❡❧♦s ❞✐s♣♦♥í✈❡✐s ♥❛ ❧✐t❡r❛t✉r❛✱ ❝♦♠ ❞❛❞♦s ❞❡ ❝â♥❝❡r ❞❡ ♠❛♠❛✱ ❛✈❛❧✐❛♥❞♦ ♦ t❡♠♣♦ ❛té ❛ ❞❡t❡r✐♦r❛çã♦ ❞❛ ♠❛♠❛ ❞❛s ♣❛❝✐❡♥t❡s✳ ❈♦♠♦ r❡s✉❧t❛❞♦ ♣r✐♥❝✐♣❛❧✱ ♦❜s❡r✈❛♠♦s q✉❡ ♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❝♦♠ ❣r❛❞❡ ✜①❛ ❡ ❡❢❡✐t♦ ✈❛r✐✲ ❛♥❞♦ ♥♦ t❡♠♣♦ ♣r♦♣♦st♦ ❛♣r❡s❡♥t♦✉ ♦s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦ ❛♦s ❞❡♠❛✐s✳ ❊♠ s✐t✉❛çõ❡s ❡♠ q✉❡ ❤á ♣r❡s❡♥ç❛ ❞❡ ✉♠❛ ❢r❛çã♦ ❞❡ ❝✉r❛❞♦s ♥❛ ♣♦♣✉❧❛çã♦✱ ❛♣r❡s❡♥t❛♠♦s ❞✉❛s ♣r♦♣♦st❛s ❞❡ ♠♦❞❡❧♦s ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛✳ ❆ ♣r✐♠❡✐r❛ é ✉♠ ▼❊P ❞✐♥â♠✐❝♦ ❝♦♠ ❣r❛❞❡ ✜①❛ ❡ ❛ s❡❣✉♥❞❛ s❡♥❞♦ ❛ ✈❡rsã♦ ❝♦♠ ❣r❛❞❡ ❛❧❡❛tór✐❛ ✈✐❛ ❡str✉t✉r❛ ❞❡ ❛❣r✉♣❛♠❡♥t♦ ❞♦ ♠♦❞❡❧♦ ♣❛rt✐çã♦ ♣r♦❞✉t♦✱ ❝♦♥str✉í❞♦s ❝♦♠ ❜❛s❡ ♥♦ ♠♦❞❡❧♦ ❞❡ t❡♠♣♦s ❞❡ ♣r♦♠♦çã♦✳ ◆❡st❡ ❝❡♥ár✐♦✱ ✐❧✉str❛♠♦s ♦s ♠♦❞❡❧♦s ♣r♦♣♦st♦s ✉t✐❧✐③❛♥❞♦ ❞❛❞♦s ❞❡ t❡♠♣♦s ❞❡ ✐♥❢❡❝çã♦ ♣♦r ❍■❱✲✶ ❡♠ ♣❛❝✐✲ ❡♥t❡s ❤❡♠♦❢í❧✐❝♦s✳ ❖s r❡s✉❧t❛❞♦s ♠♦str❛r❛♠ q✉❡ ♦ ♠♦❞❡❧♦ ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ❞✐♥â♠✐❝♦ ❝♦♠ ❣r❛❞❡ ❛❧❡❛tór✐❛✱ q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦ ❝♦♠ ♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❝♦♠ ❣r❛❞❡ ✜①❛✱ ❛♣r❡s❡♥t♦✉ ❛ ♠❡❧❤♦r ❛❞❡q✉❛çã♦ ❛♦s ❞❛❞♦s✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❈❡♥s✉r❛ ✐♥t❡r✈❛❧❛r✱ ❋r❛çã♦ ❞❡ ❝✉r❛✱ ▼♦❞❡❧❛❣❡♠ ❞✐♥â♠✐❝❛✱ ▼❊P ❝♦♠ ❣r❛❞❡ ❛❧❡❛tór✐❛✳
❆❜str❛❝t
■♥ s✉r✈✐✈❛❧ ❛♥❛❧②s✐s ✇❡ s❛② t❤❛t t❤❡ ❞❛t❛ ✐s s✉❜❡❥❝t t♦ ✐♥t❡r✈❛❧✲❝❡♥s♦r❡❞ ✇❤❡♥ ✐t ✐s ❦♥♦✇♥ t❤❛t t❤❡ s✉r✈✐✈❛❧ t✐♠❡ ♦❢ t❤❡ ✐♥❞✐✈✐❞✉❛❧s ✐s ✐♥ ❛ ✐♥t❡r✈❛❧ t✐♠❡✳ ❚❤✉s✱ t❤✐s t❤❡s✐s ❛✐♠s t♦ ♣r♦♣♦s❡ ❡①t❡♥s✐♦♥s t♦ t❤❡ ♣✐❡❝❡✇✐s❡ ❡①♣♦♥❡♥t✐❛❧ ♠♦❞❡❧ ✇✐t❤ r❛♥❞♦♠ ❣r✐❞✱ ✈✐❛ t❤❡ ♣r♦❞✉❝t ♣❛rt✐t✐♦♥ ♠♦❞❡❧ ❝❧✉st❡r✐♥❣ str✉❝t✉r❡ ✉♥❞❡r ❛ ❞②♥❛♠✐❝ ❛♣♣r♦❛❝❤✱ t♦ s✉r✈✐✈❛❧ ❞❛t❛ s✉❜❥❡❝t t♦ ✐♥t❡r✈❛❧✲❝❡♥s♦r❡❞✳ ❲❡ ♣r♦♣♦s❡ ♠♦❞❡❧s ❢♦r t✇♦ t②♣❡s ♦❢ ♣♦♣✉❧❛t✐♦♥s✿ ✇✐t❤ ❛♥❞ ✇✐t❤♦✉t ❛ ❝✉r❡❞ ❢r❛❝t✐♦♥✳ ❋♦r ♣♦♣✉❧❛t✐♦♥ ✇✐t❤♦✉t ❛ ❝✉r❡❞ ❢r❛❝t✐♦♥✱ ✇❡ ♣r❡s❡♥t t❤r❡❡ ♠♦❞❡❧✐♥❣ ♣r♦✲ ♣♦s❛❧✳ ❚❤❡ ✜rst ♦♥❡ r❡♣r❡s❡♥t✐♥❣ t❤❡ P❊▼ ✇✐t❤ r❛♥❞♦♠ t✐♠❡ ❣r✐❞✱ ✇✐t❤ t✐♠❡✲✐♥❞❡♣❡♥❞❡♥t ❝♦❡✣❝✐❡♥ts✳ ■♥ ❛❞❞✐t✐♦♥ t✇♦ ❞②♥❛♠✐❝ ♠♦❞❡❧s r❡♣r❡s❡♥t✐♥❣ ❡①t❡♥s✐♦♥s✱ ♦♥❡ ✇✐t❤ ✜①❡❞ t✐♠❡ ❣r✐❞ ❛♥❞ ❛♥♦t❤❡r ✇✐t❤ r❛♥❞♦♠ t✐♠❡ ❣r✐❞✱ ❜♦t❤ ❛❧❧♦✇✐♥❣ t✐♠❡✲❞❡♣❡♥❞❡♥t ❝♦❡✣❝✐❡♥ts✳ ❋♦r t❤✐s t②♣❡ ♦❢ ♣♦♣✉❧❛t✐♦♥✱ ✇❡ ✐❧❧✉str❛t❡ t❤❡ ♣r♦♣♦s❡❞ ♠♦❞❡❧s✱ ❛♥❞ t❤♦s❡ ❛✈❛✐❧❛❜❧❡ ✐♥ t❤❡ ❧✐t❡r❛t✉r❡✱ ✉s✐♥❣ ❛ ❜r❡❛st ❝❛♥❝❡r ❞❛t❛✱ ❛♥❛❧②s✐♥❣ t❤❡ ❞❡t❡r✐♦r❛t✐♦♥ t✐♠❡ ♦❢ t❤❡ ♣❛t✐❡♥ts✳ ❚❤❡ ♠❛✐♥ r❡✲ s✉❧t s❤♦✇s t❤❛t t❤❡ ♣r♦♣♦s❡❞ ❞②♥❛♠✐❝ ♠♦❞❡❧ ✇✐t❤ ✜①❡❞ t✐♠❡ ❣r✐❞ ❛♥❞ t✐♠❡✲✐♥❞❡♣❡♥❞❡♥t ❝♦❡✣❝✐❡♥t ❤❛s t❤❡ ❜❡st r❡s✉❧ts ✇❤❡♥ ❝♦♠♣❛r❡❞ t♦ t❤❡ ♦t❤❡rs✳ ❋♦r s✐t✉❛t✐♦♥s ✇✐t❤ ❝✉r❡❞ ❢r❛❝✲ t✐♦♥ ✐♥ t❤❡ ♣♦♣✉❧❛t✐♦♥✱ ✇❡ ♣r❡s❡♥t t✇♦ ♣r♦♣♦s❛❧s ♦❢ ❝✉r❡ r❛t❡ ♠♦❞❡❧s✳ ❚❤❡ ✜rst ♦♥❡✱ ✐s t❤❡ ❞②♥❛♠✐❝ ▼❊P ✇✐t❤ ✜①❡❞ t✐♠❡ ❣r✐❞✱ ❛♥❞ t❤❡ s❡❝♦♥❞ ❜❡✐♥❣ t❤❡ r❛♥❞♦♠ t✐♠❡ ❣r✐❞ ✈❡rs✐♦♥✱ ✉s✐♥❣ t❤❡ ♣r♦❞✉❝t ♣❛rt✐t✐♦♥ ♠♦❞❡❧ ❝❧✉st❡r✐♥❣ str✉❝t✉r❡✱ ❜✉✐❧t ❜❛s❡❞ ♦♥ t❤❡ ♣r♦♠♦t✐♦♥ t✐♠❡ ♠♦❞❡❧✳ ■♥ t❤✐s s❝❡♥❛r✐♦✱ ✇❡ ✐❧❧✉str❛t❡ ❛♥ ♣r♦♣♦s❡❞ ♠♦❞❡❧s✱ ✉s✐♥❣ t❤❡ ✐♥❢❡❝t✐♦♥ t✐♠❡ ❞❛t❛✳ ❚❤❡ r❡s✉❧ts s❤♦✇ t❤❛t t❤❡ ❞②♥❛♠✐❝ ❝✉r❡ r❛t❡ ♠♦❞❡❧ ✇✐t❤ ❛ r❛♥❞♦♠ t✐♠❡ ❣r✐❞✱ s❤♦✇❡❞ t❤❡ ❜❡st ✜t t♦ t❤❡ ❞❛t❛✱ ✇❤❡♥ ❝♦♠♣❛r❡❞ ✇✐t❤ t❤❡ ❞②♥❛♠✐❝ ❝✉r❡ r❛t❡ ♠♦❞❡❧ ✇✐t❤ ❛ ✜①❡❞ ❣r✐❞ t✐♠❡✳
❑❡②✇♦r❞s✿ ■♥t❡r✈❛❧✲❝❡♥s♦r❡❞✱ ❈✉r❡ r❛t❡ ♠♦❞❡❧✱ ❉✐♥❛♠✐❝ ❛♣♣r♦❛❝❤✱ ❘❛♥❞♦♠ ❣r✐❞ P❊▼✳
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s ✈✐✐✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✐
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✶✳✷ ❏✉st✐✜❝❛t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✶✳✸ ❖r❣❛♥✐③❛çã♦ ❞❛ t❡s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻
✷ ❈♦♥❝❡✐t♦s ●❡r❛✐s ✼
✷✳✶ ❈♦♥❝❡✐t♦s ❜ás✐❝♦s ❡♠ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✷ ▼♦❞❡❧♦ ❞❡ r✐s❝♦s ♣r♦♣♦r❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✸ ▼♦❞❡❧♦ ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✸✳✶ ▼♦❞❡❧♦ ❞❡ t❡♠♣♦ ❞❡ ♣r♦♠♦çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✹ ❈❡♥s✉r❛ ■♥t❡r✈❛❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✹✳✶ ❈♦♥❝❡✐t♦s ✐♥✐❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✹✳✷ ❋✉♥çã♦ ❞❡ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❡ ❛♠♣❧✐❛çã♦ ❞❡ ❞❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✹✳✸ ❆❧❣♦r✐t♠♦ ❞❡ ❛♠♣❧✐❛çã♦ ❞❡ ❞❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶
✸ ▼♦❞❡❧♦ ❡①♣♦♥❡♥❝✐❛❧ ♣♦r ♣❛rt❡s ✷✸
✸✳✶ ▼♦❞❡❧♦ ♣❛rt✐çã♦ ♣r♦❞✉t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✶✳✶ ❆❧❣♦r✐t♠♦ ❞❡ ❇❛rr② ✫ ❍❛rt✐❣❛♥ ✭✶✾✾✸✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✷ ▼❊P ❝♦♠ ❣r❛❞❡ ❛❧❡❛tór✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✸ ❉✐str✐❜✉✐çõ❡s ❛ ♣r✐♦r✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✸✳✶ ❉✐str✐❜✉✐çã♦ ❛ ♣♦st❡r✐♦r✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✹ ▼♦❞❡❧♦s s❡♠✐♣❛r❛♠étr✐❝♦s ♣❛r❛ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❝♦♠ ❝❡♥s✉r❛ ✐♥✲
t❡r✈❛❧❛r ✸✸
✹✳✶ ▼♦❞❡❧♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ s❡♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✹✳✶✳✶ ▼♦❞❡❧♦s ❞❡ ❙✐♥❤❛ ❡t ❛❧✳ ✭✶✾✾✾✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✹✳✶✳✷ ❖ ♠♦❞❡❧♦ ❞❡ ❲❛♥❣ ❡t ❛❧✳ ✭✷✵✶✸✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹✳✶✳✸ ▼♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❝♦♠ ❡❢❡✐t♦ ✈❛r✐❛♥❞♦ ♥♦ t❡♠♣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✹✳✶✳✹ ❆♠♦str❛❣❡♠ ❞♦s ♣s❡✉❞♦t❡♠♣♦s ❞❡ ❢❛❧❤❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
❙❯▼➪❘■❖ ✈✐✐
✹✳✷ ▼♦❞❡❧♦ ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✳✷✳✶ ▼♦❞❡❧❛❣❡♠ ❞✐♥â♠✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✹✳✸ ❙❡❧❡çã♦ ❞❡ ♠♦❞❡❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✸✳✶ ❖r❞❡♥❛❞❛ ❞❛ ♣r❡❞✐t✐✈❛ ❝♦♥❞✐❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✸✳✷ ❈r✐tér✐♦ ❞❡ ✐♥❢♦r♠❛çã♦ ❞❛ ❞❡s✈✐â♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✸✳✸ ❈r✐tér✐♦ ❞❡ ✐♥❢♦r♠❛çã♦ ❞❡ ❲❛t❛♥❛❜❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✺ ❆♣❧✐❝❛çõ❡s ✺✸
✺✳✶ ❆♥á❧✐s❡ ❞❡ ❞❛❞♦s s❡♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✺✳✶✳✶ ❉❛❞♦s s✐♠✉❧❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✺✳✶✳✷ ❉❛❞♦s ❞❡ ❝â♥❝❡r ❞❡ ♠❛♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✺✳✷ ❆♥á❧✐s❡ ❞❡ ❞❛❞♦s ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✺✳✷✳✶ ❘❡❡s❝r❡✈❡♥❞♦ ❛ ♣❛rt✐çã♦ ♠❛✐s ✜♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✺✳✷✳✷ ❉❛❞♦s s✐♠✉❧❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✺✳✷✳✸ ❉❛❞♦s ❞❡ ✐♥❢❡❝çã♦ ♣♦r ❍■❱✲✶ ❡♠ ♣❛❝✐❡♥t❡s ❤❡♠♦❢í❧✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹
✻ ❈♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s ❡ tr❛❜❛❧❤♦s ❢✉t✉r♦s ✾✶
❆ ❘❡s✉❧t❛❞♦s ❞❛s ❛♣❧✐❝❛çõ❡s ✾✹
❆✳✶ ❉❛❞♦s r❡❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹
❇ ❈ó❞✐❣♦s ✲ ●❡r❛çã♦ ❞♦s ❞❛❞♦s ❛rt✐✜❝✐❛✐s ✾✾
❇✳✶ ❉❛❞♦s s❡♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾ ❇✳✷ ❉❛❞♦s ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ■❧✉str❛çã♦ ❞❡ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r ❞♦ ❝❛s♦ ■✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✷ ■❧✉str❛çã♦ ❞❡ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r ❞♦ ❝❛s♦ ■■✳ ✳ ✳ ✳ ✶✼ ✷✳✸ ■❧✉str❛çã♦ ❞❡ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r ❞♦ ❝❛s♦ K✳ ✳ ✳ ✳ ✶✽
✸✳✶ ■❧✉str❛çã♦ ❞❛ ❡str✉t✉r❛ ❞❡ ❛❣r✉♣❛♠❡♥t♦ ❞♦ ▼PP ✱ ❝♦♠ m′ = 5 ❡b = 2✳ ✳ ✳ ✳ ✷✾
✹✳✶ ●❡r❛çã♦ ❞♦s ♣s❡✉❞♦t❡♠♣♦s ❞❡ ❢❛❧❤❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✺✳✶ ❊st✐♠❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ ♦ ♠♦❞❡❧♦ M0 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✺✳✷ ❊st✐♠❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ ♦ ♠♦❞❡❧♦ M1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✺✳✸ ❊st✐♠❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ ♦ ♠♦❞❡❧♦ M2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✺✳✹ ❊st✐♠❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ ♦ ♠♦❞❡❧♦ M3 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✺✳✺ ❊st✐♠❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ ♦ ♠♦❞❡❧♦ M4 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✺✳✻ ❊st✐♠❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ ♦ ♠♦❞❡❧♦ M5 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✺✳✼ ▼é❞✐❛ ❛ ♣♦st❡r✐♦r✐ ❞❡ β1 ❝♦♠♣❛r❛❞♦ ❛♦ ❡❢❡✐t♦ r❡❛❧ ♣❛r❛ ♦ ♠♦❞❡❧♦ M1✳ ✳ ✳ ✳ ✳ ✺✾
✺✳✽ ▼é❞✐❛ ❛ ♣♦st❡r✐♦r✐ ❞❡ β1 ❝♦♠♣❛r❛❞♦ ❛♦ ❡❢❡✐t♦ r❡❛❧ ♣❛r❛ ♦ ♠♦❞❡❧♦ M2✳ ✳ ✳ ✳ ✳ ✺✾
✺✳✾ ▼é❞✐❛ ❛ ♣♦st❡r✐♦r✐ ❞❡ β1 ❝♦♠♣❛r❛❞♦ ❛♦ ❡❢❡✐t♦ r❡❛❧ ♣❛r❛ ♦ ♠♦❞❡❧♦ M4✳ ✳ ✳ ✳ ✳ ✻✵
✺✳✶✵ ▼é❞✐❛ ❛ ♣♦st❡r✐♦r✐ ❞❡ β1 ❝♦♠♣❛r❛❞♦ ❛♦ ❡❢❡✐t♦ r❡❛❧ ♣❛r❛ ♦ ♠♦❞❡❧♦ M4✳ ✳ ✳ ✳ ✳ ✻✵
✺✳✶✶ ❈♦♠♣❛r❛çã♦ ❞♦s ♠♦❞❡❧♦s M0✱M1✱ M2 ❡ M3 ✈✐❛ LP M L✱ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡s
✈❛❧♦r❡s ❞❡m′ ❡ t✐♣♦s ❞❡ ❣r❛❞❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸
✺✳✶✷ ❈♦♠♣❛r❛çã♦ ❞♦s ♠♦❞❡❧♦s M0✱ M1✱ M2 ❡ M3✱ ✈✐❛ DIC✱ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡s
✈❛❧♦r❡s ❞❡m′ ❡ t✐♣♦s ❞❡ ❣r❛❞❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸
✺✳✶✸ ❈♦♠♣❛r❛çã♦ ❞♦s ♠♦❞❡❧♦s M4 ❡ M5✱ ✈✐❛ LP M L✱ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s
φ✱ m′s ❡ ❣r❛❞❡ ❚✐♣♦ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✺✳✶✹ ❈♦♠♣❛r❛çã♦ ❞♦s ♠♦❞❡❧♦sM4 ❡M5✱ ✈✐❛W AIC✱ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡sφ✱
m′s ❡ ❣r❛❞❡ ❚✐♣♦ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼
✺✳✶✺ ❈♦♠♣❛r❛çã♦ ❞♦s ♠♦❞❡❧♦s M4 ❡ M5✱ ✈✐❛ DIC✱ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s φ✱
m′s ❡ ❣r❛❞❡ ❚✐♣♦ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽
✺✳✶✻ ❊st✐♠❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ ♦ ♠♦❞❡❧♦ M0 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
✺✳✶✼ ❊st✐♠❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ ♦ ♠♦❞❡❧♦ M1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
✺✳✶✽ ❊st✐♠❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ ♦ ♠♦❞❡❧♦ M2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
✺✳✶✾ ❊st✐♠❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ ♦ ♠♦❞❡❧♦ M3 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ✐①
✺✳✷✵ ❊st✐♠❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ ♦ ♠♦❞❡❧♦ M4 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶
✺✳✷✶ ❊st✐♠❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ ♦ ♠♦❞❡❧♦ M5 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶
✺✳✷✷ ❊st✐♠❛t✐✈❛ ❞♦ ❡❢❡✐t♦ ❞❛ ❝♦✈❛r✐á✈❡❧ r❛❞✐♦t❡r❛♣✐❛ ❡ q✉í♠✐♦t❡r❛♣✐❛ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦ ♣❛r❛ ♦ ♠♦❞❡❧♦M1✳ ✭❆s ❧✐♥❤❛s tr❛❝❡❥❛❞❛s r❡♣r❡s❡♥t❛♠ ♦s ✐♥t❡r✈❛❧♦s ❞❡
❝r❡❞✐❜✐❧✐❞❛❞❡ ❞❡ ✾✺✪✳✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✺✳✷✸ ❊st✐♠❛t✐✈❛ ❞♦ ❡❢❡✐t♦ ❞❛ ❝♦✈❛r✐á✈❡❧ r❛❞✐♦t❡r❛♣✐❛ ❡ q✉í♠✐♦t❡r❛♣✐❛ ❧♦♥❣♦ ❞♦ t❡♠♣♦
♣❛r❛ ♦ ♠♦❞❡❧♦M2✳ ✭❆s ❧✐♥❤❛s tr❛❝❡❥❛❞❛s r❡♣r❡s❡♥t❛♠ ♦s ✐♥t❡r✈❛❧♦s ❞❡ ❝r❡❞✐✲
❜✐❧✐❞❛❞❡ ❞❡ ✾✺✪✳✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✺✳✷✹ ❊st✐♠❛t✐✈❛ ❞♦ ❡❢❡✐t♦ ❞❛ ❝♦✈❛r✐á✈❡❧ r❛❞✐♦t❡r❛♣✐❛ ❡ q✉í♠✐♦t❡r❛♣✐❛ ❧♦♥❣♦ ❞♦ t❡♠♣♦
♣❛r❛ ♦ ♠♦❞❡❧♦M4✳ ✭❆s ❧✐♥❤❛s tr❛❝❡❥❛❞❛s r❡♣r❡s❡♥t❛♠ ♦s ✐♥t❡r✈❛❧♦s ❞❡ ❝r❡❞✐✲
❜✐❧✐❞❛❞❡ ❞❡ ✾✺✪✳✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✺✳✷✺ ❊st✐♠❛t✐✈❛ ❞♦ ❡❢❡✐t♦ ❞❛ ❝♦✈❛r✐á✈❡❧ r❛❞✐♦t❡r❛♣✐❛ ❡ q✉í♠✐♦t❡r❛♣✐❛ ❧♦♥❣♦ ❞♦ t❡♠♣♦
♣❛r❛ ♦ ♠♦❞❡❧♦M5✳ ✭❆s ❧✐♥❤❛s tr❛❝❡❥❛❞❛s r❡♣r❡s❡♥t❛♠ ♦s ✐♥t❡r✈❛❧♦s ❞❡ ❝r❡❞✐✲
❜✐❧✐❞❛❞❡ ❞❡ ✾✺✪✳✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✺✳✷✻ ❊st✐♠❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ ♣❛❝✐❡♥t❡s ❤❡♠♦❢í❧✐❝♦s✱ ✈✐❛ ❡st✐♠❛✲
❞♦r ❚✉r♥❜✉❧❧ ✭❚✉r♥❜✉❧❧✱ ✶✾✼✻✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✺✳✷✼ ❈♦♠♣❛r❛çã♦ ❞♦s ♠♦❞❡❧♦s M0 ❡M1 ✈✐❛ LP M L✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺
✺✳✷✽ ❈♦♠♣❛r❛çã♦ ❞♦s ♠♦❞❡❧♦s M0 ❡M1 ✈✐❛ W AIC✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻
✺✳✷✾ ❈♦♠♣❛r❛çã♦ ❞♦s ♠♦❞❡❧♦s M0 ❡M1 ✈✐❛ DIC✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻
✺✳✸✵ ❆♠♦str❛ ❛ ♣♦st❡r✐♦r✐ ♣❛r❛ φ ♥♦ ♠♦❞❡❧♦ M0 ❡ M0✱ ❝♦♠ ❣r❛❞❡ ❞♦ ❚✐♣♦ ✶✳ ✳ ✳ ✼✼
✺✳✸✶ ❆♠♦str❛ ❛ ♣♦st❡r✐♦r✐ ♣❛r❛ β0 ♥♦ ♠♦❞❡❧♦ M0 ❡ ❣r❛❞❡ ❞♦ ❚✐♣♦ ✶ ✭❱❛❧♦r r❡❛❧
♥❛ ❧✐♥❤❛ ❡s❝✉r❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✺✳✸✷ ❆♠♦str❛ ❛ ♣♦st❡r✐♦r✐ ♣❛r❛ β1 ♥♦ ♠♦❞❡❧♦ M0 ❡ ❣r❛❞❡ ❞♦ ❚✐♣♦ ✶ ✭❱❛❧♦r r❡❛❧
♥❛ ❧✐♥❤❛ ❡s❝✉r❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✺✳✸✸ ❆♠♦str❛ ❛ ♣♦st❡r✐♦r✐ ♣❛r❛ β0 ♥♦ ♠♦❞❡❧♦ M1 ❡ ❣r❛❞❡ ❞♦ ❚✐♣♦ ✶ ✭❱❛❧♦r r❡❛❧
♥❛ ❧✐♥❤❛ ❡s❝✉r❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✺✳✸✹ ❆♠♦str❛ ❛ ♣♦st❡r✐♦r✐ ♣❛r❛ β1 ♥♦ ♠♦❞❡❧♦ M1 ❡ ❣r❛❞❡ ❞♦ ❚✐♣♦ ✶ ✭❱❛❧♦r r❡❛❧
♥❛ ❧✐♥❤❛ ❡s❝✉r❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✺✳✸✺ ❊st✐♠❛t✐✈❛ ❛ ♣♦st❡r✐♦r✐ ♣❛r❛ ❛ ❢✉♥çã♦ r✐s❝♦ ❜❛s❛❧ ♣❛r❛ ♦s t❡♠♣♦s ❞❡ ♣r♦♠♦çã♦✳ ✽✶ ✺✳✸✻ ❊st✐♠❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣♦♣✉❧❛❝✐♦♥❛❧ ♣❛r❛ ♦ ♠♦❞❡❧♦M0 ✭❧✐♥❤❛
❡♠ ✈❡r♠❡❧❤♦✮ ❡ ❝✉r✈❛s r❡❛✐s ✭❧✐♥❤❛ ❡♠ ♣r❡t♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✺✳✸✼ ❊st✐♠❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣♦♣✉❧❛❝✐♦♥❛❧ ♣❛r❛ ♦ ♠♦❞❡❧♦M1 ✭❧✐♥❤❛
❡♠ ✈❡r♠❡❧❤♦✮ ❡ ❝✉r✈❛s r❡❛✐s ✭❧✐♥❤❛ ❡♠ ♣r❡t♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✺✳✸✽ ❱❛❧♦r❡s ❞❡ LP M L ♣❛r❛ ♦s ♠♦❞❡❧♦s ❛❥✉st❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺
✺✳✸✾ ❱❛❧♦r❡s ❞❡ W AIC ♣❛r❛ ♦s ♠♦❞❡❧♦s ❛❥✉st❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻
✺✳✹✵ ❱❛❧♦r❡s ❞❡ DIC ♣❛r❛ ♦s ♠♦❞❡❧♦s ❛❥✉st❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻
✺✳✹✶ ●rá✜❝♦s ❞❡ ❝❛✐①❛ ❞❛s ❛♠♦str❛s ❛ ♣♦st❡r✐♦r✐ ♣❛r❛ ♦ ❢❛t♦r ❞❡ ❞❡s❝♦♥t♦ ♥♦s ♠♦❞❡❧♦s M0 ❡ M1 ♣❛r❛ ❛ ❣r❛❞❡ ❞♦ ❚✐♣♦ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ①
✺✳✹✸ ❊st✐♠❛t✐✈❛ ❛ ♣♦st❡r✐♦r✐ ♣❛r❛ ❛ ❢✉♥çã♦ r✐s❝♦ ❜❛s❛❧ ♣❛r❛ ♦s t❡♠♣♦s ❞❡ ♣r♦♠♦çã♦ ❡ ❣r❛❞❡ ❞♦ ❚✐♣♦ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✺✳✹✹ ❊st✐♠❛t✐✈❛ ❛ ♣♦st❡r✐♦r✐ ♣❛r❛ ❛ ❢✉♥çã♦ r✐s❝♦ ❜❛s❛❧ ♣❛r❛ ♦s t❡♠♣♦s ❞❡ ♣r♦♠♦çã♦
❡ ❣r❛❞❡ ❞♦ ❚✐♣♦ ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✺✳✹✺ ❍✐st♦❣r❛♠❛ r❡♣r❡s❡♥t❛♥❞♦ ❛ ❞✐str✐❜✉✐çã♦ ❛ ♣♦st❡r✐♦r✐ ❞♦ ♥ú♠❡r♦ ❞❡ ✐♥t❡r✈❛❧♦s
♣❛r❛ ♦ ♠♦❞❡❧♦M1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾
✺✳✹✻ ❊st✐♠❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣♦♣✉❧❛❝✐♦♥❛❧ ♣❛r❛ ♦ ♠♦❞❡❧♦M0 ✭❧✐♥❤❛
♠❛✐s s✉❛✈❡✮ ❡ ❡st✐♠❛❞♦r ❞❡ ❚✉r♥❜✉❧❧ ✭❧✐♥❤❛ ♠❡♥♦s s✉❛✈❡✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵ ✺✳✹✼ ❊st✐♠❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣♦♣✉❧❛❝✐♦♥❛❧ ♣❛r❛ ♦ ♠♦❞❡❧♦M1 ✭❧✐♥❤❛
♠❛✐s s✉❛✈❡✮ ❡ ❡st✐♠❛❞♦r ❞❡ ❚✉r♥❜✉❧❧ ✭❧✐♥❤❛ ♠❡♥♦s s✉❛✈❡✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵
❆✳✶ ❈♦♠♣❛r❛çã♦ ❞♦s ♠♦❞❡❧♦s M4 ❡M5✱ ✈✐❛ ▲P▼▲✱ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡sφ✱
m′s ❡ ❣r❛❞❡ t✐♣♦ ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻
❆✳✷ ❈♦♠♣❛r❛çã♦ ❞♦s ♠♦❞❡❧♦s M4 ❡ M5✱ ✈✐❛ ❲❆■❈✱ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡sφ✱
m′s ❡ ❣r❛❞❡ t✐♣♦ ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼
❆✳✸ ❈♦♠♣❛r❛çã♦ ❞♦s ♠♦❞❡❧♦s M4 ❡M5✱ ✈✐❛ ▲P▼▲✱ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡sφ✱
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ ❘❡s✉♠♦ ❞❡ ❝❡♥ár✐♦s ♣❛r❛ ❞❛❞♦s ❝❡♥s✉r❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺
✸✳✶ ❉✐❢❡r❡♥t❡s ❜❧♦❝♦s ❝♦♥tí❣✉♦s ❢♦r♠❛❞♦s ♣❛r❛ T1, T2, T3✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✺✳✶ ❈r✐tér✐♦s LP M L✱W AIC ❡ DIC ♣❛r❛ ♦s ♠♦❞❡❧♦sM0 ❛M3✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
✺✳✷ ❈r✐tér✐♦ LP M L ♣❛r❛ ♦s ♠♦❞❡❧♦s M4 ❡ M5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
✺✳✸ ❈r✐tér✐♦ W AIC ♣❛r❛ ♦s ♠♦❞❡❧♦s M4 ❡ M5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
✺✳✹ ❈r✐tér✐♦ DIC ♣❛r❛ ♦s ♠♦❞❡❧♦sM4 ❡ M5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
✺✳✺ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ♣❛r❛ ❛ ❛♠♦str❛ ❛ ♣♦st❡r✐♦r✐ ❞♦ ♥ú♠❡r♦ ❞❡ ✐♥t❡r✈❛❧♦s✳ ✻✵ ✺✳✻ ❈r✐tér✐♦s LP M L✱W AIC ❡ DIC ♣❛r❛ ♦s ♠♦❞❡❧♦sM0 ❡M1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷
✺✳✼ ❈r✐tér✐♦s LP M L✱W AIC ❡ DIC ♣❛r❛ ♦ ♠♦❞❡❧♦M2✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷
✺✳✽ ❈r✐tér✐♦s LP M L✱DIC ❡ W AIC ♣❛r❛ ♦ ♠♦❞❡❧♦M3 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷
✺✳✾ ❱❛❧♦r❡s ❞♦s ❝r✐tér✐♦s LP M L ♣❛r❛ ♦s ♠♦❞❡❧♦s M4 ❡ M5 ♣❛r❛ ❣r❛❞❡ ❞♦ ❚✐♣♦ ✶✳ ✻✹
✺✳✶✵ ❱❛❧♦r❡s ❞♦s ❝r✐tér✐♦s W AIC ♣❛r❛ ♦s ♠♦❞❡❧♦sM4 ❡ M5 ♣❛r❛ ❣r❛❞❡ ❞♦ ❚✐♣♦ ✶✳ ✻✺
✺✳✶✶ ❱❛❧♦r❡s ❞♦s ❝r✐tér✐♦s DIC ♣❛r❛ ♦s ♠♦❞❡❧♦sM4 ❡M5 ♣❛r❛ ❣r❛❞❡ ❞♦ ❚✐♣♦ ✶✳ ✻✺
✺✳✶✷ ▼♦❞❡❧♦s ❝♦♠ ♠❡♥♦r LP M L✱ DIC ❡ W AIC✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾
✺✳✶✸ ❘❡s✉♠♦s ❛ ♣♦st❡r✐♦r✐ ♣❛r❛ ♦s ♠♦❞❡❧♦s s❡❧❡❝✐♦♥❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✺✳✶✹ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ♣❛r❛ ♦ ♥ú♠❡r♦ ❞❡ ✐♥t❡r✈❛❧♦s ❛ ♣♦st❡r✐♦r✐✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✺✳✶✺ ❈r✐tér✐♦s LP M L✱W AIC ❡ DIC ♣❛r❛ ♦s ♠♦❞❡❧♦sM0 ❡M1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺
✺✳✶✻ ❊st✐♠❛t✐✈❛s ❞❛ ❢r❛çã♦ ❞❡ ❝✉r❛ ♣❛r❛ ♦s ♠♦❞❡❧♦s M0 ❡ M1 ♣❛r❛ x= 1✳ ✳ ✳ ✳ ✳ ✽✷
✺✳✶✼ ❊st✐♠❛t✐✈❛s ❞❛ ❢r❛çã♦ ❞❡ ❝✉r❛ ♣❛r❛ ♦s ♠♦❞❡❧♦s M0 ❡ M1 ♣❛r❛ x= 0✳ ✳ ✳ ✳ ✳ ✽✸
✺✳✶✽ ❘❡s✉♠♦s ❞❡s❝r✐t✐✈♦s ♣❛r❛ ❛ ❛♠♦str❛ ❛ ♣♦st❡r✐♦r✐ ❞♦ ♥ú♠❡r♦ ❞❡ ✐♥t❡r✈❛❧♦s ♣❛r❛ ♦ ♠♦❞❡❧♦M1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸
✺✳✶✾ ❈r✐tér✐♦s ❞❡ s❡❧❡çã♦ ♣❛r❛ ♦s ♠♦❞❡❧♦s M0 ❡ M1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺
✺✳✷✵ ❘❡s✉❧t❛❞♦s ❞❡s❝r✐t✐✈♦s ❞♦s ♠♦❞❡❧♦s ♠❛✐s ❜❡♠ ❛❥✉st❛❞♦s s❡❣✉♥❞♦ ♦s ❝r✐tér✐♦s ❞❡ s❡❧❡çã♦✱ ❝♦♠ m′ = 40 ❡ ❣r❛❞❡ ❞♦ ❚✐♣♦ ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾
✺✳✷✶ ❘❡s✉♠♦s ❞❡s❝r✐t✐✈♦s ♣❛r❛ ❛ ❞✐str✐❜✉✐çã♦ ❛ ♣♦st❡r✐♦r✐ ❞♦ ♥ú♠❡r♦ ❞❡ ✐♥t❡r✈❛❧♦s ♣❛r❛ ♦ ♠♦❞❡❧♦M1✱ ❝♦♠ m
′
= 40✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾
✺✳✷✷ ❘❡s✉❧t❛❞♦s ❞❡s❝r✐t✐✈♦s ❞❛ ❢r❛çã♦ ❞❡ ❝✉r❛ ♣♦r t✐♣♦ ❞❡ tr❛t❛♠❡♥t♦✱ ♣❛r❛ ♦s ♠♦❞❡❧♦s M0 ❡ M1✱ ❝♦♠ m
′
= 40✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵
❆✳✶ ❱❛❧♦r❡s ❞♦s ❝r✐tér✐♦s ▲P▼▲ ♣❛r❛ ♦s ♠♦❞❡❧♦s M4 ❡M5 ♣❛r❛ ❣r❛❞❡ t✐♣♦ ✷✳ ✳ ✳ ✾✹
▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙ ①✐✐
❆✳✷ ❱❛❧♦r❡s ❞♦s ❝r✐tér✐♦s ❲❆■❈ ♣❛r❛ ♦s ♠♦❞❡❧♦s M4 ❡ M5 ♣❛r❛ ❣r❛❞❡ t✐♣♦ ✷✳ ✳ ✳ ✾✺
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
❆♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ é ❛ ❡①♣r❡ssã♦ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❞❡s✐❣♥❛r ❛ ❛♥á❧✐s❡ ❡st❛tíst✐❝❛ ❞❡ ❞❛❞♦s q✉❛♥❞♦ ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❡♠ ❡st✉❞♦ r❡♣r❡s❡♥t❛ ♦ t❡♠♣♦ ❞❡s❞❡ ✉♠ ✐♥st❛♥t❡ ✐♥✐❝✐❛❧ ❛té ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ❞❡t❡r♠✐♥❛❞♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡✳ ❖ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡ ♣♦❞❡ s❡r✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ♠♦rt❡ ❞❡ ✉♠ ♣❛❝✐❡♥t❡✱ ❛ ❝✉r❛ ♦✉ r❡❝✐❞✐✈❛ ❞❡ ✉♠❛ ❞♦❡♥ç❛ ♦✉ ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ✉♠❛ ❢❛❧❤❛ ❡♠ ✉♠ ❡q✉✐♣❛♠❡♥t♦✳
❖ ❡st❛❞♦ ❞❛ ❛rt❡ ❞❛ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ é ♦ ♣r♦❞✉t♦ ❞❡ ✉♠ ❧♦♥❣♦ ♣r♦❝❡ss♦ q✉❡ s♦❢r❡✉ ✉♠ ❣r❛♥❞❡ ❝r❡s❝✐♠❡♥t♦ ♥♦s ú❧t✐♠♦s ✺✵ ❛♥♦s✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ❈♦❧♦s✐♠♦ ✫ ●✐♦❧♦ ✭✷✵✵✻✮✱ ❛ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ é ✉♠❛ ❞❛s ár❡❛s ❞❛ ❡st❛tíst✐❝❛ q✉❡ ♠❛✐s ❝r❡s❝❡✉ ♥❛s ú❧t✐♠❛s ❞é❝❛❞❛s✱ ✐♠♣✉❧s✐♦♥❛❞❛ ♣❡❧♦ ❛♣❡r❢❡✐ç♦❛♠❡♥t♦ ❞❡ ♣r♦❝❡❞✐♠❡♥t♦s ❡st❛tíst✐❝♦s ❡ ❝♦♠♣✉t❛❝✐♦♥❛✐s ♦❜s❡r✈❛❞♦s ♥❡st❡ ♣❡rí♦❞♦✳
❯♠❛ ❝❛r❛❝t❡ríst✐❝❛ ♣❡❝✉❧✐❛r ❞♦s ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ é ❛ ♣r❡s❡♥ç❛ ❞❡ ❝❡♥s✉r❛✱ ❝❛r❛❝t❡✲ r✐③❛❞❛ ♣❡❧❛ ♦❜s❡r✈❛çã♦ ✐♥❝♦♠♣❧❡t❛ ❞❛ ✈❛r✐á✈❡❧ ❞❡ ✐♥t❡r❡ss❡ ♣❛r❛ ❛❧❣✉♥s ✐♥❞✐✈í❞✉♦s ❞♦ ❡st✉❞♦✱ s❡❥❛ ♣♦r ✐♥✐❝✐❛t✐✈❛ ❞♦s ♠❡s♠♦s ❡♠ s❛✐r ❞♦ ❡st✉❞♦✱ ♣❡r❞❛ ❞❡ ❝♦♥t❛t♦ ❞✉r❛♥t❡ ♦ ❛❝♦♠♣❛♥❤❛✲ ♠❡♥t♦✱ tér♠✐♥♦ ❞♦ ❡st✉❞♦ s❡♠ ❛ ♦❝♦rrê♥❝✐❛ ❞♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡✱ ❡t❝✳ ❆ ❝❡♥s✉r❛ ♣♦❞❡ s❡r ❝❧❛ss✐✜❝❛❞❛ ❝♦♠♦✿
• ❈❡♥s✉r❛ à ❞✐r❡✐t❛✿ ♦ t❡♠♣♦ ❞❡ ♦❝♦rrê♥❝✐❛ ❞♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡ é ♠❛✐♦r q✉❡ ♦ t❡♠♣♦
r❡❣✐str❛❞♦✳
• ❈❡♥s✉r❛ à ❡sq✉❡r❞❛✿ ♦ t❡♠♣♦ r❡❣✐str❛❞♦ é ♠❛✐♦r q✉❡ ♦ t❡♠♣♦ ❞❡ ♦❝♦rrê♥❝✐❛ ❞♦ ❡✈❡♥t♦
❞❡ ✐♥t❡r❡ss❡✳
• ❈❡♥s✉r❛ ✐♥t❡r✈❛❧❛r✿ ♦❝♦rr❡ q✉❛♥❞♦ s❡ s❛❜❡ ❛♣❡♥❛s q✉❡ ♦ t❡♠♣♦ ❞❡ ♦❝♦rrê♥❝✐❛ ❞♦ ❡✈❡♥t♦
❞❡ ✐♥t❡r❡ss❡ ❡stá ❡♠ ✉♠ ❝❡rt♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦✳
❙❡❣✉♥❞♦ ❑❛❧❜✢❡✐s❝❤ ✫ Pr❡♥t✐❝❡ ✭✷✵✵✷✮ ❡ ❈♦❧❧❡tt ✭✷✵✶✺✮✱ ❡♥tr❡ ♦✉tr♦s✱ ♦ t✐♣♦ ❞❡ ❝❡♥s✉r❛ à ❞✐r❡✐t❛ é ♦ q✉❡ ♦❝♦rr❡ ❝♦♠ ♠❛✐♦r ❢r❡q✉ê♥❝✐❛ ❡♠ ♣r♦❜❧❡♠❛s ♣rát✐❝♦s✳ ◆♦ ❡♥t❛♥t♦✱ s✐t✉❛çõ❡s ❡♠ q✉❡ ❛ ❝❡♥s✉r❛ é ✐♥t❡r✈❛❧❛r t❛♠❜é♠ ♦❝♦rr❡♠ ❝♦♠ ❜❛st❛♥t❡ ❢r❡q✉ê♥❝✐❛✱ ❡s♣❡❝✐❛❧♠❡♥t❡ ♥❛ ár❡❛ ♠é❞✐❝❛✳ P❡t♦ ✭✶✾✼✸✮✱ ♣♦r ❡①❡♠♣❧♦✱ r❡❧❛t❛ ❞❛❞♦s ❞❡ ❝♦♥s✉❧t❛s ❛♥✉❛✐s ❝♦♠ ✶✾✻ ♠❡♥✐♥❛s✱ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❛✈❛❧✐❛r ♦ t❡♠♣♦ ❛té ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ♠❛t✉r✐❞❛❞❡ s❡①✉❛❧✱ r❡❣✐str❛❞♦
✶ ✷
♥♦ ♠♦♠❡♥t♦ ❞❡ ❝❛❞❛ ❝♦♥s✉❧t❛✳ ❖✉tr♦ ❡①❡♠♣❧♦ é ♦ tr❛t❛♠❡♥t♦ ❞❡ ♠✉❧❤❡r❡s ❝♦♠ ❝â♥❝❡r ❞❡ ♠❛♠❛✱ ❡♠ q✉❡ ♦s r❡t♦r♥♦s ❛♦ ❡s♣❡❝✐❛❧✐st❛ ♦❝♦rr❡♠ ❛ ❝❛❞❛ q✉❛tr♦ ❛ s❡✐s ♠❡s❡s ❡✱ ❞✉r❛♥t❡ ❛s ✈✐s✐t❛s✱ ♦s ♠é❞✐❝♦s ❛✈❛❧✐❛♠ ❛ ❛♣❛rê♥❝✐❛ ❞❛ ♣❛❝✐❡♥t❡✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛ r❡tr❛çã♦ ❞❛ ♠❛♠❛✱ ❛ q✉❛❧ ❛♣r❡s❡♥t❛ ✉♠ ✐♠♣❛❝t♦ ♥❡❣❛t✐✈♦ ♥❛ ❛♣❛rê♥❝✐❛ ❡ ❡stét✐❝❛ ❣❡r❛❧ ❞❛ ♣❛❝✐❡♥t❡✱ r❡♣r❡s❡♥✲ t❛♥❞♦ ♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡ ❛ s❡r ❡st✉❞❛❞♦ ✭❋✐♥❦❡❧st❡✐♥✱ ✶✾✽✻✮✳ ◆♦s ❛rt✐❣♦s ❞❡ ❑♦♥❣❡r✉❞ ✫ ❙❛♠✉❡❧s❡♥ ✭✶✾✾✶✮ ❡ ❙❛♠✉❡❧s❡♥ ✫ ❑♦♥❣❡r✉❞ ✭✶✾✾✸✮ sã♦ r❡❧❛t❛❞♦s ❞♦✐s ❡st✉❞♦s s♦❜r❡ s✐♥t♦♠❛s r❡s♣✐r❛tór✐♦s ❡ ❛s♠át✐❝♦s✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❞❡ ❢✉♥❝✐♦♥ár✐♦s ♥♦r✉❡❣✉❡s❡s ❞❡ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❢á❜r✐❝❛ q✉❡ tr❛❜❛❧❤❛✈❛♠ ❝♦♠ ❛❧✉♠í♥✐♦✳ ❊♠ t❛✐s ❡st✉❞♦s✱ s❛❜❡✲s❡ s♦♠❡♥t❡ q✉❡ ♦ t❡♠♣♦ ❛té ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ♣❛r❛ ❛♠❜♦s s✐♥t♦♠❛s ♦❝♦rr❡ q✉❛♥❞♦ é ❛t❡st❛❞♦ ♦ ❞✐❛❣♥óst✐❝♦ ❛♣ós ✈✐s✐t❛s ♠é❞✐❝❛s✳ ◆♦ ❡st✉❞♦ s♦❜r❡ ❛ ❡①♣♦s✐çã♦ à t✉❜❡r❝✉❧♦s❡ r❡❛❧✐③❛❞♦ ♣♦r ❙♠✐t❤ ❡t ❛❧✳ ✭✶✾✾✼✮✱ ♦s t❡♠✲ ♣♦s ❞❡ ✐♥❢❡❝çã♦ ♣♦r t✉❜❡r❝✉❧♦s❡ ♥ã♦ sã♦ ♦❜s❡r✈❛❞♦s ❞❡ ❢♦r♠❛ ❡①❛t❛✱ ❤❛✈❡♥❞♦ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡ r❡❣✐str❛r ♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ ❞❡✜♥✐❞♦ ♣❡❧❛ ❝♦♥✈❡rsã♦ t✉❜❡r❝✉❧í♥✐❝❛✱ ❝❛r❛❝t❡r✐③❛♥❞♦✲s❡ ❛ss✐♠ ✉♠ ❝❡♥ár✐♦ ❡♠ q✉❡ ❛ ❝❡♥s✉r❛ é ✐♥t❡r✈❛❧❛r✳ ❖✉tr♦ ❡①❡♠♣❧♦ ♣♦❞❡ s❡r ❡♥❝♦♥tr❛❞♦ ❡♠ ❙✉♥ ✭✷✵✵✻✮✱ q✉❡ ❛♣r❡s❡♥t❛ ✉♠ ❡st✉❞♦ ❡♥✈♦❧✈❡♥❞♦ ✶✻ ❝❡♥tr♦s✱ ❛✈❛❧✐❛♥❞♦ ♦s t❡♠♣♦s ❞❡ ✐♥❢❡❝✲ çã♦ ♣♦r ❍■❱ ❡♠ ❤❡♠♦❢í❧✐❝♦s✱ ❞✐✈✐❞✐❞♦s ❡♠ ❣r✉♣♦s tr❛t❛♠❡♥t♦ ❡ ♣❧❛❝❡❜♦✱ q✉❡ sã♦ ❛✈❛❧✐❛❞♦s tr✐♠❡str❛❧♠❡♥t❡✳ ▼❛✐s ❡①❡♠♣❧♦s ♣♦❞❡♠ s❡r ❡♥❝♦♥tr❛❞♦s ❡♠ ❑❧❡✐♥ ✫ ▼♦❡❝❤s❜❡r❣❡r ✭✷✵✵✸✮✱ ●ó♠❡③ ❡t ❛❧✳ ✭✷✵✵✹✮✱ ❙✉♥ ✭✷✵✵✻✮ ❡ ❈♦❧♦s✐♠♦ ✫ ●✐♦❧♦ ✭✷✵✵✻✮✱ ❡♥tr❡ ♦✉tr♦s✳
❊①✐st❡ ✉♠❛ ✈❛st❛ ❧✐t❡r❛t✉r❛ r❡❧❛❝✐♦♥❛❞❛ ❛♦s ♠♦❞❡❧♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ ❞❛❞♦s ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r✳ ❖ ❛rt✐❣♦ ❞❡ ❋✐♥❦❡❧st❡✐♥ ✭✶✾✽✻✮ ❢♦✐ ✉♠ ❞♦s ♣r✐♠❡✐r♦s tr❛❜❛❧❤♦s ♣✉❜❧✐❝❛❞♦s ♣❛r❛ ❞❛❞♦s ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r ✉t✐❧✐③❛♥❞♦ ♦ ♠♦❞❡❧♦ ❞❡ r✐s❝♦s ♣r♦♣♦r❝✐♦♥❛✐s ❞❡ ❈♦① ✭✶✾✼✷✮✳ ❙✉♥ ✭✶✾✾✻✮ ❛♣r❡s❡♥t♦✉ ✉♠❛ ❡①t❡♥sã♦ ❞♦ t❡st❡ ❧♦❣ r❛♥❦✱ ✐❧✉str❛♥❞♦ ❝♦♠ ❞❛❞♦s ❞❡ ♣❛❝✐❡♥t❡s ❝♦♠ ❆■❉❙✳ ▼❛✐s t❛r❞❡✱ ❙✉♥ ✭✶✾✾✼✮ ❛♣r❡s❡♥t❛ ✉♠❛ ♣r♦♣♦st❛ ❞❡ ♠♦❞❡❧❛❣❡♠ ♣❛r❛ ❞❛❞♦s ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r ✉t✐❧✐③❛♥❞♦ r❡❣r❡ssã♦ ❧♦❣íst✐❝❛✳ ❆rt✐❣♦s ❞❡ ❛✉t♦r❡s ❝♦♠♦ ❍✉❛♥❣ ✭✶✾✾✻✮ ❡ ❑✐♠ ✭✷✵✵✸✮ ❛♣r❡s❡♥t❛♠ r❡s✉❧t❛❞♦s ❛ss✐♥tót✐❝♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡ r✐s❝♦s ♣r♦♣♦r❝✐♦♥❛✐s✱ ♣❛r❛ ❞❛❞♦s tr✉♥❝❛❞♦s à ❡sq✉❡r❞❛✳ ❩❤❛♦ ❡t ❛❧✳ ✭✷✵✵✺✮ ❛♣r❡s❡♥t❛♠ ♠ét♦❞♦s ❞❡ ❡q✉❛çã♦ ❞❡ ❡st✐♠❛çã♦ ❝♦♠♦ ♣r♦❝❡❞✐♠❡♥t♦ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ ❞❡ r✐s❝♦s ♣r♦♣♦r❝✐♦♥❛✐s ♣r♦♣♦st♦ ♣♦r ❈♦① ✭✶✾✼✷✮✱ q✉❛♥❞♦ t❛♥t♦ ♦s t❡♠♣♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ q✉❛♥t♦ ❛s ❝♦✈❛r✐á✈❡✐s ❡stã♦ s✉❥❡✐t♦s ❛ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r✳ ❊♠ ❍❡♥s❝❤❡❧ ❡t ❛❧✳ ✭✷✵✵✾✮ é ❛♣r❡s❡♥t❛❞❛ ✉♠❛ ♥♦✈❛ ♣r♦♣♦st❛ ❞❡ ❡①t❡♥sã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ r✐s❝♦s ♣r♦♣♦r❝✐♦♥❛✐s ♣❛r❛ ❛❝♦♠♦❞❛r ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r ❡♠ q✉❡ ❛ ❢✉♥çã♦ ❞❡ r✐s❝♦ ❜❛s❛❧ é ♠♦❞❡❧❛❞❛ ✈✐❛ s♣❧✐♥❡s ❝ú❜✐❝♦s✳ ❊♥tr❡ ♦s ❛rt✐❣♦s ❞❡ r❡✈✐sã♦✱ ♦s tr❛❜❛❧❤♦s ❞❡ ❩❤❛♥❣ ✫ ❙✉♥ ✭✷✵✶✵✮ ❡ ❑❧❡✐♥ ❡t ❛❧✳ ✭✷✵✶✸✮ ❝❛♣ít✉❧♦ ✶✽✱ ❛♣r❡s❡♥t❛♠ ❝♦♥❝❡✐t♦s ❡ ♠ét♦❞♦s s♦❜r❡ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r ❡ r❡❝❡♥t❡s ❛✈❛♥ç♦s ♥❛ ár❡❛✳
❯♠ ♠♦❞❡❧♦ s❡♠✐♣❛r❛♠étr✐❝♦ ❜❛st❛♥t❡ ♣♦♣✉❧❛r ❡♠ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ é ♦ ♠♦❞❡❧♦ ❡①♣♦♥❡♥❝✐❛❧ ♣♦r ♣❛rt❡s ✭▼❊P✮✳ ❊st❡ ♠♦❞❡❧♦✱ ❛♣❡s❛r ❞❡ s❡r ♣❛r❛♠étr✐❝♦ ❡♠ ✉♠ s❡♥s♦ ❡str✐t♦✱ ♥ã♦ r❡q✉❡r s✉♣♦s✐çõ❡s q✉❛♥t♦ à ❢♦r♠❛ ❞❛ ❢✉♥çã♦ r✐s❝♦✱ ♦ q✉❡ é ❝♦♥s✐❞❡r❛❞♦ ✉♠❛ ✈❛♥t❛❣❡♠ q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦ ❛ ✉♠ ♠♦❞❡❧♦ ♣❛r❛♠étr✐❝♦ q✉❡ r❡str✐♥❣❡ ❛ ❢♦r♠❛ ❞❛ ❢✉♥çã♦ r✐s❝♦✳ ❙❡❣✉♥❞♦ ■❜r❛❤✐♠ ❡t ❛❧✳ ✭✷✵✵✶✮✱ ♦ ▼❊P é ❝❛r❛❝t❡r✐③❛❞♦ ♣❡❧❛ ❛♣r♦①✐♠❛çã♦ ❞❛ ❢✉♥çã♦ r✐s❝♦ ♣♦r s❡❣♠❡♥t♦s ❞❡ r❡t❛s ❝♦♥st❛♥t❡s✱ ❝✉❥♦s ❝♦♠♣r✐♠❡♥t♦s sã♦ ❞❡t❡r♠✐♥❛❞♦s ♣♦r ✉♠❛ ❣r❛❞❡ ❞❡ ♣♦♥t♦s τ q✉❡
✶ ✸
♣❛♣❡❧ ❢✉♥❞❛♠❡♥t❛❧ ♥❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ❞❡ ✐♥t❡r❡ss❡✱ ❜❡♠ ❝♦♠♦ ♥❛ q✉❛❧✐❞❛❞❡ ❞♦ ❛❥✉st❡ ❞♦ ♠♦❞❡❧♦✱ ✉♠❛ ✈❡③ q✉❡ τ ❞❡t❡r♠✐♥❛ ♦ ♥ú♠❡r♦ ❞❡ ✐♥t❡r✈❛❧♦s ♣❛r❛ ❛♣r♦①✐♠❛çã♦ ❞❛
❢✉♥çã♦ r✐s❝♦✳
❆ ❧✐t❡r❛t✉r❛ r❡❧❛❝✐♦♥❛❞❛ ❛♦ ▼❊P é ❜❛st❛♥t❡ ❡①t❡♥s❛✳ ❋r✐❡❞♠❛♥ ✭✶✾✽✷✮ ✉t✐❧✐③❛ ♦ ▼❊P ♣❛r❛ ♠♦❞❡❧❛r ❛ ❢✉♥çã♦ r✐s❝♦ ❞❡ ❜❛s❡ ❞♦ ♠♦❞❡❧♦ ❞❡ ❈♦① ✭✶✾✼✷✮✱ ❛♣r❡s❡♥t❛♥❞♦ ❛s ❝♦♥❞✐çõ❡s ❞❡ ❡①✐stê♥❝✐❛ ❡ ❛ ❞✐str✐❜✉✐çã♦ ❛ss✐♥tót✐❝❛ ❞♦s ❡st✐♠❛❞♦r❡s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ♣❛r❛ ❛s t❛①❛s ❞❡ ❢❛❧❤❛ ❡ ❝♦❡✜❝✐❡♥t❡s ❞❡ r❡❣r❡ssã♦✳ ❊♠ ❑✐♠ ✫ Pr♦s❝❤❛♥ ✭✶✾✾✶✮✱ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛❧❣✉♠❛s ✈❛♥t❛❣❡♥s ❞♦ ▼❊P✱ ♥❛ ❛✉sê♥❝✐❛ ❞❡ ❝♦✈❛r✐á✈❡✐s✱ ❝♦♠♣❛r❛t✐✈❛♠❡♥t❡ ❛♦ ❡st✐♠❛❞♦r ❧✐♠✐t❡ ♣r♦❞✉t♦ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣r♦♣♦st♦ ♣♦r ❑❛♣❧❛♥ ✫ ▼❡✐❡r ✭✶✾✺✽✮✳ ◆♦ ❛rt✐❣♦ ❞❡ ❈❤❡♥ ✫ ■❜r❛❤✐♠ ✭✷✵✵✶✮ é ❡♠♣r❡❣❛❞♦ ♦ ♠ét♦❞♦ ❞❛ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ♣❛r❛ ❛❥✉st❛r ❛s t❛①❛s ❞❡ ❢❛❧❤❛ ❞♦ ▼❊P ♥❛ ♣r❡s❡♥ç❛ ❞❡ ❞❛❞♦s ❢❛❧t❛♥t❡s ❡ ❢r❛çã♦ ❞❡ ❝✉r❛❞♦s✳
❙♦❜ ✉♠❛ ♣❡rs♣❡❝t✐✈❛ ❇❛②❡s✐❛♥❛✱ ●❛♠❡r♠❛♥ ✭✶✾✾✶✮ ❡st❡♥❞❡ ♦ ♠♦❞❡❧♦ ❞❡ ❈♦① ♣r♦♣♦♥❞♦ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞✐♥â♠✐❝❛ ♣❛r❛ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡♠ q✉❡ ♦s ❡❢❡✐t♦s ❞❛s ❝♦✈❛r✐á✈❡✐s ♠✉❞❛♠ ❝♦♠ ♦ t❡♠♣♦✳ P♦st❡r✐♦r♠❡♥t❡✱ ●❛♠❡r♠❛♥ ✭✶✾✾✹✮ ❛♣r❡s❡♥t❛ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞✐♥â✲ ♠✐❝❛ ✭♥❛ ❛✉sê♥❝✐❛ ❞❡ ❝♦✈❛r✐á✈❡✐s✮✱ ❛♦ ✐♥tr♦❞✉③✐r ✉♠❛ ❡str✉t✉r❛ ❞❡ ❝♦rr❡❧❛çã♦ ❡♥tr❡ ❛s t❛①❛s ❞❡ ❢❛❧❤❛ ❞♦ ▼❊P✱ ❛ss♦❝✐❛❞❛s ❛♦s s✉❝❡ss✐✈♦s ✐♥t❡r✈❛❧♦s✱ ❛tr❛✈és ❞♦s ❤✐♣❡r♣❛râ♠❡tr♦s ❞❛ ❞✐s✲ tr✐❜✉✐çã♦ ❛ ♣r✐♦r✐ ❞❡ss❛s t❛①❛s✳ ◆♦ ❝♦♥t❡①t♦ ❞❡ ♠♦❞❡❧♦s ❞❡ ❢r❛❣✐❧✐❞❛❞❡✱ ❙❛❤✉ ❡t ❛❧✳ ✭✶✾✾✼✮ ✉t✐❧✐③❛ ✉♠ ♣r♦❝❡ss♦ ❝♦rr❡❧❛❝✐♦♥❛❞♦ ❛ ♣r✐♦r✐ ♣❛r❛ ❛s t❛①❛s ❞❛ ❢❛❧❤❛ ❞♦ ▼❊P ♣❛r❛ ♠♦❞❡❧❛❣❡♠ ❞❡ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✳ ▼❛✐s ❞❡t❛❧❤❡s s♦❜r❡ ♦ ❡♥❢♦q✉❡ ❇❛②❡s✐❛♥♦ ♣❛r❛ ♦ ❛❥✉st❡ ❞❡ ♠♦❞❡❧♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣♦❞❡♠ s❡r ❡♥❝♦♥tr❛❞♦s ❡♠ ■❜r❛❤✐♠ ❡t ❛❧✳ ✭✷✵✵✶✮✳
❊♠❜♦r❛ ❛ ❧✐t❡r❛t✉r❛ r❡❧❛❝✐♦♥❛❞❛ ❛♦ ▼❊P s❡❥❛ ❜❛st❛♥t❡ ❡①t❡♥s❛✱ ♥❛ ♠❛✐♦r✐❛ ❞♦s tr❛❜❛❧❤♦s ❡①✐st❡♥t❡s ❛ ❣r❛❞❡ é ❡s❝♦❧❤✐❞❛ ❞❡ ❢♦r♠❛ ❛r❜✐trár✐❛✳ ◆❛ ♣rát✐❝❛✱ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❡s♣❡❝✐✜❝❛r♠♦s ✉♠❛ ❣r❛❞❡ ❛♣r♦♣r✐❛❞❛ ♣❛r❛ ♦ ❛❥✉st❡ ❞♦ ▼❊P ♣♦❞❡ s❡r r❡s♦❧✈✐❞♦ ❛ss✉♠✐♥❞♦✲s❡ q✉❡ τ é ♠❛✐s
✉♠ ♣❛râ♠❡tr♦ ❛ s❡r ❡st✐♠❛❞♦✳ ❖❜s❡r✈❡ q✉❡ s♦❜ ✉♠ ❡♥❢♦q✉❡ ❇s❛②❡s✐❛♥♦ ❛ ❡①t❡♥sã♦ é ❞✐r❡t❛✱ ✉♠❛ ✈❡③ q✉❡ ❜❛st❛ ✐♥❝❧✉✐r ✉♠❛ ❞✐str✐❜✉✐çã♦ ❛ ♣r✐♦r✐ ♣❛r❛ τ✳ ❖ ♣r✐♠❡✐r♦ ❡s❢♦rç♦ ❡❢❡t✐✈♦
♥❡st❛ ❞✐r❡çã♦ é ❞❡✈✐❞♦ ❛ ❆r❥❛s ✫ ●❛s❜❛rr❛ ✭✶✾✾✹✮✳ ❊st❡s ❛✉t♦r❡s ❛ss✉♠❡♠ q✉❡ ♦s ♣♦♥t♦s ✜♥❛✐s ❞♦s ✐♥t❡r✈❛❧♦s sã♦ ❞❡✜♥✐❞♦s ❞❡ ❛❝♦r❞♦ ❝♦♠ ✉♠ ♣r♦❝❡ss♦ ❞❡ s❛❧t♦s ❜❛s❡❛❞♦s ♥❛ t❡♦r✐❛ ❞❡ ♠❛rt✐♥❣❛✐s✱ ✐♥❝❧✉í❞♦ ♥♦ ♠♦❞❡❧♦ ❛tr❛✈és ❞❡ ❞✐str✐❜✉✐çõ❡s ❛ ♣r✐♦r✐✳ ❊①t❡♥sõ❡s ❞❡st❛ ❛❜♦r❞❛❣❡♠ ♣♦❞❡♠ s❡r ❡♥❝♦♥tr❛❞❛s ❡♠ ▼❝❦❡❛❣✉❡ ✫ ❚✐❣❤✐♦✉❛rt ✭✷✵✵✵✮ ❡ ❑✐♠ ❡t ❛❧✳ ✭✷✵✵✻✮✳
❉❡♠❛rq✉✐ ❡t ❛❧✳ ✭✷✵✵✽✮ ❛♣r❡s❡♥t❛♠ ✉♠❛ ❛❜♦r❞❛❣❡♠✱ t❛♠❜é♠ ❇❛②❡s✐❛♥❛✱ q✉❡ ✉t✐❧✐③❛ ❛ ❡s✲ tr✉t✉r❛ ❞❡ ❛❣r✉♣❛♠❡♥t♦ ❞♦ ♠♦❞❡❧♦ ♣❛rt✐çã♦ ♣r♦❞✉t♦ ✭▼PP✮✱ ♣r♦♣♦st♦ ♣♦r ❇❛rr② ✫ ❍❛rt✐❣❛♥ ✭✶✾✾✷✮✱ ♣❛r❛ ♠♦❞❡❧❛r ❞✐r❡t❛♠❡♥t❡ ❛ ❛❧❡❛t♦r✐❡❞❛❞❡ ❞❡ τ✳ ❙♦❜ t❛❧ ❛❜♦r❞❛❣❡♠✱ ❛ ♠♦❞❡❧❛❣❡♠
❞❛ ❣r❛❞❡ é ❢❡✐t❛ ❧❡✈❛♥❞♦✲s❡ ❡♠ ❝♦♥t❛ ❛ ❞✐s♣♦s✐çã♦ ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ♥♦ ❡✐①♦ ❞♦ t❡♠♣♦✱ ❡ ❛ ❡①✐stê♥❝✐❛ ❞❡ ♣❡❧♦ ♠❡♥♦s ✉♠ t❡♠♣♦ ❞❡ ❢❛❧❤❛ ❡♠ ❝❛❞❛ ✐♥t❡r✈❛❧♦ ✐♥❞✉③✐❞♦ ♣❡❧❛ ❣r❛❞❡ ❛❧❡❛tór✐❛ ❞♦ ▼❊P é ❣❛r❛♥t✐❞❛✳ ❆❧é♠ ❞✐st♦✱ ❛♣❡s❛r ❞❡ ♦ ♥ú♠❡r♦ ❞❡ ♣❛râ♠❡tr♦s ❛ s❡r❡♠ ❡st✐♠❛❞♦s ♣♦❞❡r ✈❛r✐❛r✱ ❡st❛ ❢♦r♠❛ ❞❡ ♠♦❞❡❧❛❣❡♠ ♠❛♥té♠ ✜①❛❞♦ ♦ ♥ú♠❡r♦ ♠á①✐♠♦ ❞❡ ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦✳ ▼❛✐s r❡❝❡♥t❡♠❡♥t❡✱ ❉❡♠❛rq✉✐ ✭✷✵✶✵✮ ❛♣r❡s❡♥t❛♠ ❡①t❡♥sõ❡s ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ♣r♦♣♦st♦ ❡♠ ●❛♠❡r♠❛♥ ✭✶✾✾✹✮ ❡ ●❛♠❡r♠❛♥ ✭✶✾✾✶✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❡♠ q✉❡ τ é ❝♦♥s✐❞❡✲
✶ ✹
❡♠ q✉❡ ♥❡st❡ ❝❛s♦✱ ❛ ❡s♣❡❝✐✜❝❛çã♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❛ ♣r✐♦r✐ ♣❛r❛ ❛s t❛①❛s ❞❡ ❢❛❧❤❛ ❞♦ ▼❊P é ❢❡✐t❛ ❛ss✉♠✐♥❞♦ ✉♠❛ ❡str✉t✉r❛ ❤✐❡rárq✉✐❝❛✳
❆♣❡s❛r ❞❛ ♣♦♣✉❧❛r✐❞❛❞❡ ❞♦ ▼❊P✱ ❛ ❧✐t❡r❛t✉r❛ r❡❧❛❝✐♦♥❛❞❛ ❛ ❡ss❡ ♠♦❞❡❧♦ ♣❛r❛ ♦ ❛❥✉st❡ ❞❡ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ s✉❥❡✐t♦s ❛ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r ❛✐♥❞❛ é r❡❧❛t✐✈❛♠❡♥t❡ ♣❡q✉❡♥❛✱ s❡♥❞♦ ♠❡♥♦r ❛✐♥❞❛✱ q✉❛♥❞♦ ♣❡♥s❛♠♦s ❡♠ tr❛t❛r τ ❝♦♠♦ ♠❛✐s ✉♠ ♣❛râ♠❡tr♦ ❛ s❡r ❡st✐♠❛❞♦✳ ❯♠
tr❛❜❛❧❤♦ ❜❛st❛♥t❡ ❝✐t❛❞♦ é ♦ ❛rt✐❣♦ ❞❡ ▲✐♥❞s❡② ✫ ❘②❛♥ ✭✶✾✾✽✮✱ q✉❡ ❛♣r❡s❡♥t❛♠ ✉♠ t✉t♦r✐❛❧ ❡♥✈♦❧✈❡♥❞♦ ♠♦❞❡❧♦s ❡ ♠ét♦❞♦s ♣❛r❛♠étr✐❝♦s ❡ ♥ã♦ ♣❛r❛♠étr✐❝♦s✱ ❡♠ q✉❡ ♦ ▼❊P é ✉♠ ❞♦s ♠♦❞❡❧♦s ✉t✐❧✐③❛❞♦s ♥❛ ♠♦❞❡❧❛❣❡♠ ❞♦s ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r✳ ◆♦ ❛rt✐❣♦ ❞❡ ❙✐♥❤❛ ❡t ❛❧✳ ✭✶✾✾✾✮ é ❛♣r❡s❡♥t❛❞❛ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❇❛②❡s✐❛♥❛ s❡♠✐♣❛r❛♠étr✐❝❛ ❛ss✉♠✐♥❞♦ ♦ ▼❊P ♣❛r❛ ♠♦❞❡❧❛❣❡♠ ❞❛ ❢✉♥çã♦ ❞❡ r✐s❝♦ ❜❛s❛❧✱ ❡ ❝♦♠ ❡❢❡✐t♦ ❞❛s ❝♦✈❛r✐á✈❡✐s ✈❛r✐❛♥❞♦ ♥♦ t❡♠♣♦✳ ❖ ♠♦❞❡❧♦ ❞❡ ❙✐♥❤❛ ❡t ❛❧✳ ✭✶✾✾✾✮ é ❜❛s❡❛❞♦ ♥❛ ❛♠♣❧✐❛çã♦ ❞❡ ❞❛❞♦s✱ ❡♠ q✉❡ ♣s❡✉❞♦t❡♠♣♦s ❞❡ ❢❛❧❤❛ sã♦ ❣❡r❛❞♦s ❛tr❛✈és ❞❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❝♦♥❞✐❝✐♦♥❛❧ ❜❛s❡❛❞❛ ♥♦s ♣ró♣r✐♦s ✐♥t❡r✈❛❧♦s ♦❜s❡r✈❛❞♦s ❡ ♥♦s ✈❛❧♦r❡s ❞♦s ♣❛râ♠❡tr♦s ❞❡ ✐♥t❡r❡ss❡✳ ❙♦❜ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❝❧áss✐❝❛✱ ❙❡❛♠❛♥ ✫ ❇✐r❞ ✭✷✵✵✶✮ ✉t✐❧✐③❛r❛♠ ♦ ▼❊P ♣❛r❛ ♠♦❞❡❧❛r ♦ r✐s❝♦ ❞❡ ✐♥❢❡❝çã♦ ♣♦r ❍■❱ ♣❡❧♦ ✉s♦ ❞❡ ❞r♦❣❛s ✐♥❥❡tá✈❡✐s ❞❡♥tr♦ ❞❛ ♣r✐sã♦ ❝♦♠ ❝♦✈❛r✐á✈❡✐s ♠✉❞❛♥❞♦ ♥♦ t❡♠♣♦✳
❘❡❝❡♥t❡♠❡♥t❡✱ ❲❛♥❣ ❡t ❛❧✳ ✭✷✵✶✸✮ ❛♣r❡s❡♥t❛♠ ✉♠❛ ♥♦✈❛ ♣r♦♣♦st❛ ❞❡ ♠♦❞❡❧❛❣❡♠ ❇❛②❡✲ s✐❛♥❛ s❡♠✐♣❛r❛♠étr✐❝❛✱ ❜❛s❡❛❞❛ ♥♦ ▼❊P✱ ♣❛r❛ ♠♦❞❡❧❛r ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ s✉❥❡✐t♦s ❛ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r q✉❡ ❝♦♥s✐❞❡r❛ ✉♠❛ ❡str✉t✉r❛ ❞✐♥â♠✐❝❛ ❡♥tr❡ ♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ r❡❣r❡ssã♦✱ ♣❡r♠✐t✐♥❞♦ ❞❡ss❛ ♠❛♥❡✐r❛ ❝❛♣t❛r ♠✉❞❛♥ç❛s ♥♦s ❡❢❡✐t♦s ❞❛s ❝♦✈❛r✐á✈❡✐s ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✳ ❆ss✐♠ ❝♦♠♦ ❡♠ ❙✐♥❤❛ ❡t ❛❧✳ ✭✶✾✾✾✮✱ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❛♠♣❧✐❛çã♦ ❞❡ ❞❛❞♦s t❛♠❜é♠ é ✉t✐❧✐③❛❞♦ ❡♠ ❲❛♥❣ ❡t ❛❧✳ ✭✷✵✶✸✮✱ q✉❡ ✐♠♣✉t❛ ♣s❡✉❞♦t❡♠♣♦s ❞❡ ❢❛❧❤❛ ♣❛r❛ ❝❛❞❛ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ ♦❜s❡r✈❛❞♦✳ ❆❧é♠ ❞✐ss♦✱ ❛ ❣r❛❞❡τ é tr❛t❛❞❛ ❝♦♠♦ ✉♠❛ q✉❛♥t✐❞❛❞❡ ❛❧❡❛tór✐❛✱ ❡ ♦ ❛❧❣♦r✐t♠♦ ❞❡
▼♦♥t❡ ❈❛r❧♦ ✈✐❛ ❝❛❞❡✐❛s ❞❡ ▼❛r❦♦✈ ❝♦♠ s❛❧t♦s r❡✈❡rsí✈❡✐s ✭❘❏▼❈▼❈✮✱ ♣r♦♣♦st♦ ♣♦r ●r❡❡♥ ✭✶✾✾✺✮✱ é ✉t✐❧✐③❛❞♦ ♣❛r❛ ❛♠♦str❛r ❞❛ ❞✐str✐❜✉✐çã♦ ❛ ♣♦st❡r✐♦r✐✳ ■♥❞❡♣❡♥❞❡♥t❡ ❞♦ t✐♣♦ ❞❡ ❝❡♥✲ s✉r❛✱ ❛ ♣r✐♥❝✐♣❛❧ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ❛s ❛❜♦r❞❛❣❡♥s ♣r♦♣♦st❛s ❡♠ ❉❡♠❛rq✉✐ ❡t ❛❧✳ ✭✷✵✵✽✮ ❡ ❲❛♥❣ ❡t ❛❧✳ ✭✷✵✶✸✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❡stá r❡❧❛❝✐♦♥❛❞❛ ❝♦♠ ♦ ❛❧❣♦r✐t♠♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ♠♦❞❡❧❛r ❛ ❣r❛❞❡τ✱ ♣♦✐s ❡♠ ❉❡♠❛rq✉✐ ❡t ❛❧✳ ✭✷✵✵✽✮ é ✉t✐❧✐③❛❞♦ ❛ ❡str✉t✉r❛ ❞❡ ❛❣r✉♣❛♠❡♥t♦ ❞♦ ▼PP ❛♦
✐♥✈és ❞♦ ❘❏▼❈▼❈ q✉❡ é ✉t✐❧✐③❛❞♦ ♣❛r❛ ❛♠♦str❛r ❞❛ ❞✐str✐❜✉✐çã♦ ❛ ♣♦st❡r✐♦r✐✳
✶ ❖❇❏❊❚■❱❖❙ ✺
❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r✱ ❜❛s❡❛❞♦ ♥♦ ♠♦❞❡❧♦ ❞❡ ❞❡ ❈❛str♦ ❡t ❛❧✳ ✭✷✵✵✾✮✳ ❊♠ ✉♠ ❝❡♥ár✐♦ ❇❛②❡s✐❛♥♦✱ ❇❛♥❡r❥❡❡ ✫ ❈❛r❧✐♥ ✭✷✵✵✹✮ ❛♣r❡s❡♥t❛♠ ✉♠❛ ♣r♦♣♦st❛ ❞❡ ♠♦❞❡❧❛❣❡♠ ❝♦♠♣❧❡t❛♠❡♥t❡ ♣❛r❛♠étr✐❝❛✱ ❜❛s❡❛❞❛ ♥♦ ♠♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ♣❛❞rã♦ ✭❇❡r❦s♦♥ ✫ ●❛❣❡✱ ✶✾✺✷✮✱ ❡♠ q✉❡ é ❛ss✉♠✐❞❛ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❲❡✐❜✉❧❧ ♣❛r❛ ♠♦❞❡❧❛r ♦s ✐♥❞✐✈í❞✉♦s ♥ã♦ ❝✉r❛❞♦s✱ ♣❡r✲ ♠✐t✐♥❞♦ ✉♠❛ ❝♦rr❡❧❛çã♦ ❡s♣❛❝✐❛❧ ❡♥tr❡ ♦s t❡♠♣♦s✳ ❚❤♦♠♣s♦♥ ✫ ❈❤❤✐❦❛r❛ ✭✷✵✵✸✮ ❛♣r❡s❡♥t❛♠ ✉♠ ♠♦❞❡❧♦ ❞❡ ❢r❛❣✐❧✐❞❛❞❡ ❇❛②❡s✐❛♥♦ ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ❜❛s❡❛❞♦ ♥♦ ♠♦❞❡❧♦ ❞❡ t❡♠♣♦s ❞❡ ♣r♦♠♦çã♦ ❡♠ q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❧♦❣✲♥♦r♠❛❧ é ✉t✐❧✐③❛❞❛ ♣❛r❛ ♠♦❞❡❧❛r ❛ ❞✐str✐❜✉✐çã♦ ❞♦s t❡♠✲ ♣♦s ❞❡ ♣r♦♠♦çã♦✳ ❙♦❜r❡ ♦ ✉s♦ ❞♦ ▼❊P ❡♠ ❞❛❞♦s ❝♦♠ ✐♥❞✐✈í❞✉♦s s✉❥❡✐t♦s ❛ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r ❡♠ ✉♠❛ ♣♦♣✉❧❛çã♦ ❝♦♠ ❛ ♣r❡s❡♥ç❛ ❞❡ ❢r❛çã♦ ❞❡ ❝✉r❛❞♦s✱ s♦❜ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❢r❡q✉❡♥t✐st❛ ❑✐♠ ✫ ❏❤✉♥ ✭✷✵✵✽✮ ♣r♦♣õ❡♠ ✉♠ ♠♦❞❡❧♦ ❞❡ ❢r❛❣✐❧✐❞❛❞❡ s❡♠✐♣❛r❛♠étr✐❝♦ ❜❛s❡❛❞♦ ♥♦ ♠♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ♣❛❞rã♦✳
✶✳✶ ❖❜❥❡t✐✈♦s
❊st❛ t❡s❡ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ♣r♦♣♦r ♠♦❞❡❧♦s ❇❛②❡s✐❛♥♦s s❡♠✐♣❛r❛♠étr✐❝♦s ♣❛r❛ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ s✉❥❡✐t♦s ❛ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r✳ ❆ ♣r♦♣♦st❛ ❜ás✐❝❛ ❡stá ❡♠ ❞❡s❡♥✈♦❧✈❡r ♠♦❞❡❧♦s ❞✐♥â♠✐❝♦s✱ ❜❛s❡❛♥❞♦✲s❡ ♥♦ ▼❊P ❝♦♠ ❣r❛❞❡ ❛❧❡❛tór✐❛✱ ✉t✐❧✐③❛♥❞♦ ❛ ❡str✉t✉r❛ ❞❡ ❛❣r✉♣❛♠❡♥t♦ ❞♦ ▼PP✱ ♣❛r❛ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r✱ s❡♠ ❡ ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛❞♦s ♥❛ ♣♦♣✉❧❛çã♦ ❡♠ ❡st✉❞♦✳
P❛r❛ ✉♠❛ ♣♦♣✉❧❛çã♦ s❡♠ ❢r❛çã♦ ❞❡ ❝✉r❛❞♦s✱ ❛❞❛♣t❛♠♦s ♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ♣r♦♣♦st♦ ♣♦r ❉❡♠❛rq✉✐ ❡t ❛❧✳ ✭✷✵✶✷✮ ♣❛r❛ ❛❝♦♠♦❞❛r ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r ❝♦♠ ♦ ❡❢❡✐t♦ ❞❛s ❝♦✈❛r✐á✈❡✐s ✈❛r✐❛♥❞♦ ♥♦ t❡♠♣♦✳ ❊♠ s✐t✉❛çõ❡s q✉❡ ❡♥✈♦❧✈❡♠ ✉♠❛ ❢r❛çã♦ ❞❡ ❝✉r❛❞♦s ♥❛ ♣♦♣✉❧❛çã♦✱ ♣r♦♣♦♠♦s ✉♠ ♥♦✈♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ✉t✐❧✐③❛♥❞♦ ❛ ❛❜♦r❞❛❣❡♠ ❞❡ t❡♠♣♦s ❞❡ ♣r♦♠♦çã♦ ✭❨❛❦♦✈❧❡✈ ❡t ❛❧✳✱ ✶✾✾✸✮✱ ❜❛s❡❛❞♦ ♥❛ ❡①t❡♥sã♦ ❞♦ ♠♦❞❡❧♦ ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ♣r♦♣♦st♦ ❡♠ ❉❡♠❛rq✉✐ ❡t ❛❧✳ ✭✷✵✶✹✮✳
✶✳✷ ❏✉st✐✜❝❛t✐✈❛
❯♠❛ ❞❛s ✈❛♥t❛❣❡♥s ❞❡ s❡ tr❛❜❛❧❤❛r ❝♦♠ ♦ ▼❊P é q✉❡ ❡ss❡ ♠♦❞❡❧♦ ❛♣r❡s❡♥t❛ ❛ ✢❡①✐❜✐❧✐❞❛❞❡ ❞♦s ♠♦❞❡❧♦s ♥ã♦ ♣❛r❛♠étr✐❝♦s s❡♠ ♣❡r❞❡r ❛s ✈❛♥t❛❣❡♥s ❛ss♦❝✐❛❞❛s ❛♦s ♠♦❞❡❧♦s ♣❛r❛♠étr✐❝♦s✱ ❛♦ ♥ã♦ ✐♠♣♦r r❡str✐çõ❡s s♦❜r❡ ❛ ❢✉♥çã♦ r✐s❝♦✳ ❆rt✐❣♦s ❝♦♠♦ ♦ ❞❡ ❆r❥❛s ✫ ●❛s❜❛rr❛ ✭✶✾✾✹✮✱ ▼❝❦❡❛❣✉❡ ✫ ❚✐❣❤✐♦✉❛rt ✭✷✵✵✵✮✱ ❑✐♠ ❡t ❛❧✳ ✭✷✵✵✻✮✱ ❉❡♠❛rq✉✐ ❡t ❛❧✳ ✭✷✵✵✽✮ ❡ ❲❛♥❣ ❡t ❛❧✳ ✭✷✵✶✸✮ ❛♣♦♥t❛♠ q✉❡ ♦ ▼❊P ❝♦♠ ❣r❛❞❡ ❛❧❡❛tór✐❛✱ ❡♠ ❣❡r❛❧✱ ❢♦r♥❡❝❡ ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s q✉❡ ♦ ▼❊P ❛❥✉st❛❞♦ ❛tr❛✈és ❞❡ ❡s❝♦❧❤❛s ❛❞✲❤♦❝ ♣❛r❛ ❛ ❣r❛❞❡ τ✳ ❆❧é♠ ❞✐ss♦✱ ♦ ✉s♦ ❞♦ ▼❊P
