Identi cação de outliers em redes
complexas baseada em caminhada aleatória
❙❊❘❱■➬❖ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❉❖ ■❈▼❈✲❯❙P
❉❛t❛ ❞❡ ❉❡♣ós✐t♦✿ ✴ ✴
❆ss✐♥❛t✉r❛✿
Identi cação de outliers em redes complexas baseada em
caminhada aleatória
❇✐❧③ã ▼❛rq✉❡s ❞❡ ❆r❛ú❥♦
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❩❤❛♦ ▲✐❛♥❣
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ▼❛t❡♠át✐✲ ❝❛s ❡ ❞❡ ❈♦♠♣✉t❛çã♦ ✭■❈▼❈✮ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦ ✭❯❙P✮ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛s ❞❡ ❈♦♠♣✉t❛çã♦ ❡ ▼❛t❡♠át✐❝❛ ❈♦♠♣✉✲ t❛❝✐♦♥❛❧✳
✏❈♦♥❤❡ç♦ ✉♠ ❤♦♠❡♠ ❡♠ ❈r✐st♦ q✉❡ ❢♦✐ ❛rr❡❜❛t❛❞♦ ❛té ❛♦ t❡r❝❡✐r♦ ❝é✉✳ ❊ s❡✐ q✉❡ ♦ t❛❧ ❤♦♠❡♠ ❢♦✐ ❛rr❡❜❛t❛❞♦ ❛♦ ♣❛r❛ís♦
❡ ♦✉✈✐✉ ♣❛❧❛✈r❛s ✐♥❡❢á✈❡✐s✱ ❞❡ q✉❡ ❛♦ ❤♦♠❡♠ ♥ã♦ é ❧í❝✐t♦ ❢❛❧❛r✳✑
✭■■ ❈♦rí♥t✐♦s ✶✷✳✷✲✹✮
➚ ♠✐♥❤❛ ♠ã❡✳ ❯♠❛ ▼❛r✐❛ ❧✉t❛❞♦r❛
❡ tr❛❜❛❧❤❛❞♦r❛✳
Agradecimentos
❚♦❞♦ ❛ ❝✐ê♥❝✐❛ q✉❡ t❡♠♦s ♥ã♦ é ♠❛✐s ❞♦ q✉❡ ❣♦t❛s ❞✐❛♥t❡ ❞❡ t♦❞❛ ❛ ✐♠❡♥s✐❞ã♦ ❞❡ á❣✉❛s q✉❡ r❡✢❡t❡♠ t♦❞❛ ❛ s❛❜❡❞♦r✐❛ ✐♠♣❧í❝✐t❛ ♥❛ ♦❜r❛ ❞✐✈✐♥❛✳ P♦r ✐ss♦ ♠❡ s✐♥t♦ ♦❜r✐❣❛❞♦ ❛ ❛❣r❛❞❡❝❡r ❛ t♦❞♦s ♦s q✉❡ ❝♦♥tr✐❜✉ír❛♠ ❞✐r❡t❛ ❡ ✐♥❞✐r❡t❛♠❡♥t❡ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ss❡ tr❛❜❛❧❤♦ ❡ ♣❛r❛ q✉❡ ❡✉ ♣✉❞❡ss❡ ❛❞q✉✐r✐r ✉♠❛ ♥♦✈❛ ❣♦t❛ ❞❡ ❡♥t❡♥❞✐♠❡♥t♦✳
▼ã❡✱ ♠✉✐t♦ ♦❜r✐❣❛❞♦ ♣♦r s❡✉ ❛♠♦r✱ ♣♦r s✉❛ ❢♦rç❛ ❡ ♣♦r t♦❞♦ ♦ s✉♣♦rt❡✳ ◆♦s ❞✐❛s ❡♠ q✉❡ s❡♥t✐✲♠❡ só✱ ✈♦❝ê ❢♦✐ ✉♠ ❡①❡♠♣❧♦ ❞❡ ❢♦rç❛ ♥♦ q✉❛❧ ♠❡ ❡s♣❡❧❤❡✐✳ ❖ ♣❛✐ ❡st❛r✐❛ ♦r❣✉❧❤♦s♦ ♣❡❧♦ q✉❡ ❡st❛♠♦s ❛❧❝❛♥ç❛♥❞♦✳
◆❡❧♠❛✱ ♦❜r✐❣❛❞♦ ♣♦r ♠❡ ❛♠❛r ❡ s✉♣♦rt❛r ♠♦♠❡♥t♦s ❞✐❢í❝❡✐s ❛♦ ♠❡✉ ❧❛❞♦❀ ♣❡❧❛s ✈❡③❡s ❡♠ q✉❡ ❞✐♠✐♥✉íst❡s ♦s s❡✉s ♣r♦❜❧❡♠❛s ♣❛r❛ ❛❥✉❞❛r✲♠❡ ♥♦s ♠❡✉s✳ ❱♦❝ê é ✉♠❛ ❡s♣♦s❛ ♠❛r❛✈✐❧❤♦s❛✳ ❯♠❛ ♠✉❧❤❡r q✉❡ ❡❞✐✜❝❛ ♦ ❧❛r✳
❆❝áss✐❛✱ s❡✐ q✉❡ s♦✉ ✉♠ ♠♦❞❡❧♦ ♣❛r❛ ✈♦❝ê✳ ❱♦❝ê é ✉♠ ❞♦s ♠♦t✐✈♦s q✉❡ ♠❡ ❢❛③❡♠ ❡♥❢r❡♥t❛r ❛ ❞✐✜❝✉❧❞❛❞❡ ❞❡ ❡st❛r tã♦ ❧♦♥❣❡ ❞❡ ❝❛s❛✳
Pr♦❢✳ ❩❤❛♦✱ ❝❡rt❛♠❡♥t❡ ✈♦❝ê é ✉♠❛ ❞❛s ♣❡ss♦❛s ♠❛✐s ❣❡♥✐❛✐s ❝♦♠ q✉❡♠ ❧✐❞❡✐ ❡♠ t♦❞❛ ♠✐♥❤❛ ✈✐❞❛✳ ▼❡ ❞❡s❝✉❧♣❡ ♣♦r ♠✉✐t❛s ✈❡③❡s s❡r ❛q✉é♠ ❡ ✐♥❝❛♣❛③✳ ●♦st❛r✐❛ ❞❡ ❞✐③❡r q✉❡ ❛ ❝❛❞❛ ❞✐s❝✉ssã♦ q✉❡ t❡♠♦s ♠❡ s✐♥t♦ ♠❛✐s ❡s❝❧❛r❡❝✐❞♦✳ ▼❡ ♦r❣✉❧❤♦ ❞❡ tê✲❧♦ ❝♦♠♦ ♦r✐❡♥t❛❞♦r ❡ ❝♦♠♦ ❛♠✐❣♦✳
❙♦✉ ❣r❛t♦ ❛♦s ❣r❛♥❞❡s ♣r♦❢❡ss♦r❡s q✉❡ t✐✈❡ t❛♥t♦ ♥❛ ➪❘❊❆✶ ❝♦♠♦ ♥♦ ■❈▼❈✳ ❊s♣❡✲ ❝✐❛❧♠❡♥t❡ à Pr♦❢✭❛✮✳ ●r❛ç❛ ◆✉♥❡s✱ ❛♦ Pr♦❢✳ ▼❛r❝✉s ❈✐♥❝✐♥❛t♦✱ ❛♦ Pr♦❢✳ ❘♦❞r✐❣♦ ❚❡❥♦✱ à Pr♦❢✭❛✮✳ ❘❡♥❛t❛ ▼❡♥❡❣❤❡tt✐ ❡ ❛♦ Pr♦❢✳ ❘✐❝❛r❞♦ ❈❛♠♣❡❧❧♦✳ ❱♦❝ês sã♦ ♠♦❞❡❧♦s ❞❡ ♣r♦❢❡ss♦r❡s✳
Pr♦❢✳ ❋r❛♥❝✐s❝♦ ❘♦❞r✐❣✉❡s✱ ♠✉✐t♦ ♦❜r✐❣❛❞♦ ♣❡❧❛ ♣❛r❝❡r✐❛ ❡♠ ❛❧❣✉♥s ❞♦s ♠❡✉s tr❛❜❛❧❤♦s✳ ❚❡♥❤♦ ❝❡rt❡③❛ q✉❡ ❛✐♥❞❛ ✐r❡♠♦s tr❛❜❛❧❤❛r ♠✉✐t♦ ❥✉♥t♦s✳
❙♦✉ ❣r❛t♦ t❛♠❜é♠ ❛ ❝❛❞❛ ✉♠ ❞♦s ♠❡✉s ❛♠✐❣♦s ❡ ❝♦❧❡❣❛s ❞❡ ❡st✉❞♦✱ ❞❡ ❧❛❜♦r❛tór✐♦✱ ❞❡ ❢✉t❡❜♦❧ ❡ ❞❛ ✐❣r❡❥❛✳ ❊s♣❡❝✐❛❧♠❡♥t❡ à ▲✐❧✐❛♥ ❇❡rt♦♥ ❡ ❛♦ ❏❡❛♥ ❍✉❡rt❛s✱ ♣❛r❝❡✐r♦s ❞❡ ♣❡rq✉✐s❛✳ ❈❛❞❛ ✉♠ ❞❡ ✈♦❝ês t❡♠ s✐❞♦ ♠✉✐t♦ ✐♠♣♦rt❛♥t❡ ♣❛r❛ ♠✐♥❤❛ ❡st❛❞❛ ❡♠ ❙ã♦ ❈❛r❧♦s✳
●♦st❛r✐❛ ❞❡ ❛❣r❛❞❡❝❡r às ♠❡♥✐♥❛s ❞♦ ❙❡r✈✐ç♦ ❞❡ Pós✲●r❛❞✉❛çã♦ ♣❡❧❛ ❝♦♠♣r❡❡♥sã♦ ♥❛s ♠❛✐s ❞✐✈❡rs❛s s✐t✉❛çõ❡s✳ ❖❜r✐❣❛❞♦ ❛ ❝❛❞❛ ✉♠ ❞♦s ❢✉♥❝✐♦♥ár✐♦s ❞♦ ■❈▼❈✲❯❙P✳ ❚♦❞♦s ✈♦❝ês tê♠ ✉♠❛ ♣❛r❝❡❧❛ ❞❡ ❝♦♥tr✐❜✉✐çã♦ ♥❡ss❡ tr❛❜❛❧❤♦✳
❆❣r❛❞❡ç♦ ❛♦ ❈◆Pq ♣❡❧♦ s✉♣♦rt❡ ✜♥❛♥❝❡✐r♦ ❞✉r❛♥t❡ ❜♦❛ ♣❛rt❡ ❞❡ss❡ ▼❡str❛❞♦✳
P♦r ✜♠✱ ❣♦st❛r✐❛ ❞❡ ❛❣r❛❞❡❝❡r ❛ t✐✱ ❙❡♥❤♦r ♠❡✉ ❉❡✉s ❡ ♠❡✉ P❛✐✱ ♣❡❧♦ ❡♥t❡♥❞✐♠❡♥t♦ q✉❡ t❡♥s ♠❡ ❞❛❞♦✱ ♣♦r ❝❛❞❛ ♣❡ss♦❛ q✉❡ t❡♥s ❝♦❧♦❝❛❞♦ ♥❛ ♠✐♥❤❛ ✈✐❞❛✱ ❡ ♣♦r t♦❞❛ ❛✉t♦r✐❞❛❞❡ q✉❡ t❡♥s ✐♥st✐t✉í❞♦ s♦❜r❡ ♠✐♠✳ ❙❡✐ q✉❡ ♥❛❞❛ ❞♦ q✉❡ ❢❛③❡s é ❡♠ ✈ã♦✳ P❡ç♦✲t❡ q✉❡ ♣❡r❞♦❡s ♠✐♥❤❛s ❢❛❧❤❛s ❡ ♠✐♥❤❛ ✐♥❝♦♠♣❡tê♥❝✐❛✳ ❙❡✐ q✉❡ ❛ t✐ ♥❛❞❛ é ✐♠♣♦ssí✈❡❧✳ ❖❜r✐❣❛❞♦ ♣♦r s✉❛ ●r❛ç❛ ✐♥❢❛❧í✈❡❧✳ ❖❜r✐❣❛❞♦ ❙❡♥❤♦r ❏❡s✉s✱ ♦❜r✐❣❛❞♦ ❊s♣ír✐t♦ ❙❛♥t♦✳ ❖❜r✐❣❛❞♦✦
Resumo
◆❛ ♥❛t✉r❡③❛ ❡ ♥❛ ❝✐ê♥❝✐❛✱ ❞❛❞♦s ❡ ✐♥❢♦r♠❛çõ❡s q✉❡ ❞❡s✈✐❛♠ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ❞❛ ♠é✲ ❞✐❛ ❢r❡q✉❡♥t❡♠❡♥t❡ ♣♦ss✉❡♠ ❣r❛♥❞❡ r❡❧❡✈â♥❝✐❛✳ ❊ss❡s ❞❛❞♦s sã♦ ✉s✉❛❧♠❡♥t❡ ❞❡♥♦♠✐♥❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛ ❝♦♠♦ ♦✉t❧✐❡rs✳ ❆ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ ♦✉t❧✐❡rs é ✐♠♣♦rt❛♥t❡ ❡♠ ♠✉✐t❛s ❛♣❧✐❝❛çõ❡s r❡❛✐s✱ t❛✐s ❝♦♠♦ ❞❡t❡❝çã♦ ❞❡ ❢r❛✉❞❡s✱ ❞✐❛❣♥óst✐❝♦ ❞❡ ❢❛❧❤❛s✱ ❡ ♠♦♥✐t♦r❛♠❡♥t♦ ❞❡ ❝♦♥❞✐çõ❡s ♠é❞✐❝❛s✳ ◆♦s ú❧t✐♠♦s ❛♥♦s t❡♠✲s❡ t❡st❡♠✉♥❤❛❞♦ ✉♠ ❣r❛♥❞❡ ✐♥t❡r❡ss❡ ♥❛ ár❡❛ ❞❡ ❘❡❞❡s ❈♦♠♣❧❡①❛s✳ ❘❡❞❡s ❝♦♠♣❧❡①❛s sã♦ ❣r❛❢♦s ❞❡ ❣r❛♥❞❡ ❡s❝❛❧❛ q✉❡ ♣♦ss✉❡♠ ♣❛❞rõ❡s ❞❡ ❝♦✲ ♥❡①ã♦ ♥ã♦ tr✐✈✐❛❧✱ ♠♦str❛♥❞♦✲s❡ ✉♠❛ ♣♦❞❡r♦s❛ ♠❛♥❡✐r❛ ❞❡ r❡♣r❡s❡♥t❛çã♦ ❡ ❛❜str❛çã♦ ❞❡ ❞❛❞♦s✳ ❊♠❜♦r❛ ✉♠ ❣r❛♥❞❡ ♠♦♥t❛♥t❡ ❞❡ r❡s✉❧t❛❞♦s t❡♥❤❛♠ s✐❞♦ r❡♣♦rt❛❞♦s ♥❡st❛ ár❡❛ ❞❡ ♣❡sq✉✐s❛✱ ♣♦✉❝♦ t❡♠ s✐❞♦ ❡①♣❧♦r❛❞♦ ❛❝❡r❝❛ ❞❡ ❞❡t❡❝çã♦ ❞❡ ♦✉t❧✐❡rs ❡♠ r❡❞❡s ❝♦♠♣❧❡①❛s✳ ❈♦♥s✐❞❡r❛♥❞♦✲s❡ ❛ ❞✐♥â♠✐❝❛ ❞❡ ✉♠❛ ❝❛♠✐♥❤❛❞❛ ❛❧❡❛tór✐❛✱ ❢♦r❛♠ ♣r♦♣♦st♦s ♥❡st❡ tr❛❜❛✲ ❧❤♦ ✉♠❛ ♠❡❞✐❞❛ ❞❡ ❞✐stâ♥❝✐❛ ❡ ✉♠ ♠ét♦❞♦ ❞❡ r❛♥q✉❡❛♠❡♥t♦ ❞❡ ♦✉t❧✐❡rs✳ ❆tr❛✈és ❞❡st❛ té❝♥✐❝❛✱ é ♣♦ssí✈❡❧ ❞❡t❡❝t❛r ❝♦♠♦ ♦✉t❧✐❡r ♥ã♦ s♦♠❡♥t❡ ♥ós ♣❡r✐❢ér✐❝♦s✱ ♠❛s t❛♠❜é♠ ♥ós ❝❡♥tr❛✐s ✭❤✉❜s✮✱ ❞❡♣❡❞❡♥❞♦ ❞❛ ❡str✉t✉r❛ ❞❛ r❡❞❡✳ ❚❛♠❜é♠ ❢♦✐ ✐❞❡♥t✐✜❝❛❞♦ q✉❡ ❡①✐st❡♠ ❝❛r❛❝t❡ríst✐❝❛s ❜❡♠ ❞❡✜♥✐❞❛s ❡♥tr❡ ♦s ♥ós ♦✉t❧✐❡rs✱ r❡❧❛❝✐♦♥❛❞❛s ❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡ ❞♦s ♠❡s✲ ♠♦s ♣❛r❛ ❛ r❡❞❡✳ ❆❧é♠ ❞✐ss♦✱ ❢♦✐ ❞❡s❝♦❜❡rt♦ q✉❡ ♥ós ♦✉t❧✐❡rs tê♠ ♣❛♣❡❧ ✐♠♣♦rt❛♥t❡ ♣❛r❛ ❛ r♦t✉❧❛çã♦ ❛ ♣r✐♦r✐ ♥❛ t❛r❡❢❛ ❞❡ ❞❡t❡❝çã♦ ❞❡ ❝♦♠✉♥✐❞❛❞❡s s❡♠✐✲s✉♣❡r✈✐s✐♦♥❛❞❛✳ ■st♦ ♣♦rq✉❡ ♦s ♥ós ❝❡♥tr❛✐s sã♦ ❜♦♥s ❞✐❢✉s♦r❡s ❞❡ ✐♥❢♦r♠❛çã♦ ❡ ♦s ♥ós ♣❡r✐❢ér✐❝♦s ❡♥❝♦♥tr❛♠✲s❡ ❡♠ r❡❣✐õ❡s ❞❡ ❜♦r❞❛ ❞❡ ❝♦♠✉♥✐❞❛❞❡✳ ❇❛s❡❛❞♦ ♥❡ss❛ ♦❜s❡r✈❛çã♦✱ ❢♦✐ ♣r♦♣♦st♦ ✉♠ ♠ét♦❞♦ ❞❡ ❞❡t❡❝çã♦ ❞❡ ❝♦♠✉♥✐❞❛❞❡s s❡♠✐✲s✉♣❡r✈✐s✐♦♥❛❞♦✳ ❖s r❡s✉❧t❛❞♦s ❞❡ s✐♠✉❧❛çõ❡s ♠♦str❛♠ q✉❡ ❡ss❛ ❛❜♦r❞❛❣❡♠ é ♣r♦♠✐ss♦r❛✳
Abstract
■♥ ♥❛t✉r❡ ❛♥❞ s❝✐❡♥❝❡✱ ✐♥❢♦r♠❛t✐♦♥ ❛♥❞ ❞❛t❛ t❤❛t ❞❡✈✐❛t❡ s✐❣♥✐✜❝❛♥t❧② ❢r♦♠ t❤❡ ❛✈❡r❛❣❡ ✈❛❧✉❡ ♦❢t❡♥ ❤❛✈❡ ❣r❡❛t r❡❧❡✈❛♥❝❡✳ ❚❤❡s❡ ❞❛t❛ ❛r❡ ♦❢t❡♥ ❝❛❧❧❡❞ ✐♥ ❧✐t❡r❛t✉r❡ ❛s ♦✉t❧✐❡rs✳ ❖✉t❧✐❡r ✐❞❡♥t✐✜❝❛t✐♦♥ ✐s ✐♠♣♦rt❛♥t ✐♥ ♠❛♥② r❡❛❧ ❛♣♣❧✐❝❛t✐♦♥s✱ s✉❝❤ ❛s ❢r❛✉❞ ❞❡t❡❝t✐♦♥✱ ❢❛✉❧t ❞✐❛❣♥♦s✐s✱ ♠♦♥✐t♦r✐♥❣ ♦❢ ♠❡❞✐❝❛❧ ❝♦♥❞✐t✐♦♥s✳ ■♥ r❡❝❡♥t ②❡❛rs✱ ✐t ❤❛s ❜❡❡♥ ✇✐t♥❡ss❡❞ ❛ ❣r❡❛t ✐♥t❡r❡st ✐♥ t❤❡ ❛r❡❛ ♦❢ ❈♦♠♣❧❡① ◆❡t✇♦r❦s✳ ❈♦♠♣❧❡① ♥❡t✇♦r❦s ❛r❡ ❧❛r❣❡✲s❝❛❧❡ ❣r❛♣❤s ✇✐t❤ ♥♦♥✲tr✐✈✐❛❧ ❝♦♥♥❡❝t✐♦♥ ♣❛tt❡r♥s✱ ♣r♦✈✐♥❣ t♦ ❜❡ ❛ ♣♦✇❡r❢✉❧ ✇❛② ♦❢ ❞❛t❛ r❡♣r❡s❡♥t❛t✐♦♥ ❛♥❞ ❛❜str❛❝t✐♦♥✳ ❆❧t❤♦✉❣❤ ❛ ❧❛r❣❡ ❛♠♦✉♥t ♦❢ r❡s✉❧ts ❤❛✈❡ ❜❡❡♥ r❡♣♦rt❡❞ ✐♥ t❤✐s r❡s❡❛r❝❤ ❛r❡❛✱ ❧✐tt❧❡ ❤❛s ❜❡❡♥ ❡①♣❧♦r❡❞ ❛❜♦✉t t❤❡ ♦✉t❧✐❡r ❞❡t❡❝t✐♦♥ ✐♥ ❝♦♠♣❧❡① ♥❡t✇♦r❦s✳ ❈♦♥s✐❞❡r✐♥❣ t❤❡ ❞②♥❛♠✐❝s ♦❢ ❛ r❛♥❞♦♠ ✇❛❧❦✱ ✇❡ ♣r♦♣♦s❡❞ ✐♥ t❤✐s ♣❛♣❡r ❛ ❞✐st❛♥❝❡ ♠❡❛s✉r❡ ❛♥❞ ❛ ♦✉t❧✐❡r r❛♥❦✐♥❣ ♠❡t❤♦❞✳ ❇② ✉s✐♥❣ t❤✐s t❡❝❤♥✐q✉❡✱ ✇❡ ❝❛♥ ❞❡t❡❝t ♥♦t ♦♥❧② ♣❡r✐♣❤❡r❛❧ ♥♦❞❡s✱ ❜✉t ❛❧s♦ ❝❡♥tr❛❧ ♥♦❞❡s ✭❤✉❜s✮ ❛s ♦✉t❧✐❡rs✱ ❞❡♣❡♥❞✐♥❣ ♦♥ t❤❡ ♥❡t✇♦r❦ str✉❝t✉r❡✳ ❲❡ ❛❧s♦ ✐❞❡♥t✐✜❡❞ t❤❛t t❤❡r❡ ❛r❡ ✇❡❧❧ ❞❡✜♥❡❞ r❡❧❛t✐♦♥s❤✐♣ ❜❡t✇❡❡♥ t❤❡ ♦✉t❧✐❡r ♥♦❞❡s ❛♥❞ t❤❡ ❢✉♥❝t✐♦♥❛❧✐t② ♦❢ t❤❡ s❛♠❡ ♥♦❞❡s ❢♦r t❤❡ ♥❡t✇♦r❦✳ ❋✉rt❤❡r♠♦r❡✱ ✇❡ ❢♦✉♥❞ t❤❛t ♦✉t❧✐❡rs ♣❧❛② ❛♥ ✐♠♣♦rt❛♥t r♦❧❡ t♦ ❧❛❜❡❧ ❛ ♣r✐♦r✐ ♥♦❞❡s ✐♥ t❤❡ t❛s❦ ♦❢ s❡♠✐✲s✉♣❡r✈✐s❡❞ ❝♦♠♠✉♥✐t② ❞❡t❡❝t✐♦♥✳ ❚❤✐s ✐s ❜❡❝❛✉s❡ t❤❡ ❤✉❜s ❛r❡ ❣♦♦❞ ✐♥❢♦r♠❛t✐♦♥ ❞✐ss❡♠✐♥❛t♦rs ❛♥❞ ♣❡r✐♣❤❡r❛❧ ♥♦❞❡s ❛r❡ ✉s✉❛❧❧② ❧♦❝❛❧✐③❡❞ ✐♥ t❤❡ r❡❣✐♦♥s ♦❢ ❝♦♠♠✉♥✐t② ❡❞❣❡s✳ ❇❛s❡❞ ♦♥ t❤✐s ♦❜s❡r✈❛t✐♦♥✱ ✇❡ ♣r♦♣♦s❡❞ ❛ ♠❡t❤♦❞ ♦❢ s❡♠✐✲s✉♣❡r✈✐s❡❞ ❝♦♠♠✉♥✐t② ❞❡t❡❝t✐♦♥✳ ❚❤❡ s✐♠✉❧❛t✐♦♥ r❡s✉❧ts s❤♦✇ t❤❛t t❤✐s ❛♣♣r♦❛❝❤ ✐s ♣r♦♠✐s✐♥❣✳
Conteúdo
❙✉♠ár✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ①✐ ▲✐st❛ ❞❡ ❋✐❣✉r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ①✐✐✐
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ❈♦♥t❡①t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✷ ❖❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✶✳✸ ❖r❣❛♥✐③❛çã♦ ❞♦ ❉♦❝✉♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹
✷ ❉❡t❡❝çã♦ ❞❡ ❖✉t❧✐❡rs ✺
✷✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✷ ❆s♣❡❝t♦s ●❡r❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✷✳✶ ◆❛t✉r❡③❛ ❞♦ ❈♦♥❥✉♥t♦ ❞❡ ❉❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✷✳✷ ❚✐♣♦s ❞❡ ❖✉t❧✐❡rs ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✷✳✸ ❉✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❞❡ ❘ót✉❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✷✳✹ ❘✐❣✐❞❡③ ❞♦ ▼ét♦❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✸ ❉❡t❡❝çã♦ ❞❡ ❖✉t❧✐❡rs ❡♠ ❉❛❞♦s ❯♥✐✈❛r✐❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✹ ❉❡t❡❝çã♦ ❞❡ ❖✉t❧✐❡rs ❡♠ ❉❛❞♦s ▼✉❧t✐✈❛r✐❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✹✳✶ ▼ét♦❞♦s ❊st❛tíst✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✹✳✷ ▼ét♦❞♦s ❇❛s❡❛❞♦s ❡♠ ▼✐♥❡r❛çã♦ ❞❡ ❉❛❞♦s ❡ ❆♣r❡♥❞✐③❛❞♦ ❞❡ ▼áq✉✐♥❛ ✶✹ ✷✳✺ ❉❡t❡❝çã♦ ❞❡ ❖✉t❧✐❡rs ❊s♣❛❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✻ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼
✸ ❘❡❞❡s ❈♦♠♣❧❡①❛s ❡ ❉❡t❡❝çã♦ ❞❡ ❈♦♠✉♥✐❞❛❞❡s ✷✶ ✸✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✸✳✷ ❉❡✜♥✐çã♦ ❡ Pr♦♣r✐❡❞❛❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✸✳✷✳✶ ❉✐str✐❜✉✐çã♦ ❞❡ ●r❛✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✷✳✷ ❚r❛♥s✐t✐✈✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✷✳✸ ❊❢❡✐t♦ ❞❡ P❡q✉❡♥♦ ▼✉♥❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✷✳✹ ❊str✉t✉r❛s ❞❡ ❈♦♠✉♥✐❞❛❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✸ ▼♦❞❡❧♦s ❞❡ ❘❡❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✸✳✶ ❘❡❞❡s ❘❛♥❞ô♠✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✸✳✸✳✷ ❘❡❞❡s ❞❡ P❡q✉❡♥♦ ▼✉♥❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✸✳✸ ❘❡❞❡s ▲✐✈r❡ ❞❡ ❊s❝❛❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✸✳✹ ❘❡❞❡s ❝♦♠ ❊str✉t✉r❛s ❞❡ ❈♦♠✉♥✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✸✳✸✳✺ ❘❡❞❡s ●❡♦❣rá✜❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✸✳✹ ❉❡t❡❝çã♦ ❞❡ ❈♦♠✉♥✐❞❛❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✸✳✹✳✶ ▼ét♦❞♦ ❇❛s❡❛❞♦ ❡♠ ❇❡t✇❡❡♥♥❡ss ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✹✳✷ ▼ét♦❞♦ ❇❛s❡❛❞♦ ❡♠ ▼♦❞✉❧❛r✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✸✳✹✳✸ ▼ét♦❞♦ ❇❛s❡❛❞♦ ❡♠ ❈❛♠✐♥❤❛❞❛ ❆❧❡❛tór✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✹✳✹ ▼ét♦❞♦ ❇❛s❡❛❞♦ ❡♠ ❈♦♠♣❡t✐çã♦ ❞❡ P❛rtí❝✉❧❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✸✳✺ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶
✹ ■❞❡♥t✐✜❝❛çã♦ ❞❡ ❖✉t❧✐❡rs ❡♠ ❘❡❞❡s ❈♦♠♣❧❡①❛s ❡ ❆♣❧✐❝❛çã♦ à ❉❡t❡❝çã♦
❞❡ ❈♦♠✉♥✐❞❛❞❡s ✹✺
✹✳✶ ▼❡❞✐❞❛ ❞❡ ❉✐stâ♥❝✐❛ ❞❡ ✉♠❛ ❈❛♠✐♥❤❛❞❛ ❆❧❡❛tór✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✹✳✶✳✶ ❈❛♠✐♥❤❛❞❛ ❆❧❡❛tór✐❛ ❡♠ ❘❡❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✹✳✶✳✷ ❈❛❞❡✐❛s ❞❡ ▼❛r❦♦✈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✶✳✸ ▼❡❞✐❞❛ ❞❡ ❉✐stâ♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✷ ▼ét♦❞♦ ❞❡ ❉❡t❡❝çã♦ ❞❡ ❖✉❧t✐❡rs ❡♠ ❘❡❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✸ ❈♦♠♦ ❋✉♥❝✐♦♥❛ ♦ ▼ét♦❞♦ ❞❡ ❉❡t❡❝çã♦ ❞❡ ❖✉t❧✐❡rs ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✹ ❘❡s✉❧t❛❞♦s ❖❜t✐❞♦s ❡♠ ❘❡❞❡s ❘❡❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✹✳✹✳✶ ❘❡❞❡ ❞♦ ❈❧✉❜❡ ❞❡ ❑❛r❛tê ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✹✳✹✳✷ ❘❡❞❡ ❞❡ ❈♦❧❛❜♦r❛çã♦ ❡♥tr❡ ❈✐❡♥t✐st❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✹✳✸ ❘❡❞❡s ❞❡ ■♥t❡r❛çõ❡s ❡♥tr❡ Pr♦t❡í♥❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✺ ❆♣❧✐❝❛çã♦ à ❉❡t❡❝çã♦ ❞❡ ❈♦♠✉♥✐❞❛❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✺✳✶ ▼ét♦❞♦ ❞❡ Pr♦♣❛❣❛çã♦ ❞❡ ❘ót✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✹✳✺✳✷ ❘♦t✉❧❛çã♦ ❞❡ ❉❛❞♦s ●✉✐❛❞❛ ♣♦r ❖✉t❧✐❡rs ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✻ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸
✺ ❈♦♥❝❧✉sã♦ ✻✺
✺✳✶ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
❘❡❢❡rê♥❝✐❛s ✼✹
Lista de Figuras
✷✳✶ ❍✐st♦❣r❛♠❛ ♣r♦❞✉③✐❞♦ ❝♦♠ ❜❛s❡ ❡♠ ✶✸✻✸✹ ♥❛s❝✐♠❡♥t♦s r❡❣✐str❛❞♦s ♣♦r ❈❤❛♠❜❡r❧❛✐♥ ✭✶✾✼✵✮✳ ❆s ♦❜s❡r✈❛çõ❡s ❞♦s ❝❛s♦s ▼✳✲❚✳ ✈s✳ ▼✳✲❚✳ ❡ ❍❛❞❧✉♠ ✈s✳ ❍❛❞❧✉♠ ❞❡s✈✐❛♠✲s❡ ❛❝❡♥t✉❛❞❛♠❡♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦✳ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ✭❇❛r♥❡tt✱ ✶✾✼✽✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✷✳✷ ❖✉t❧✐❡rs ❡♠ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❜✐❞✐♠❡♥s✐♦♥❛❧✳ ❆s ♦❜s❡r✈❛çõ❡so1 ❡o2 ❡
♦ s✉❜❝♦♥❥✉♥t♦ O3 ♣♦❞❡♠ s❡r ✐❞❡♥t✐✜❝❛❞♦s ❝♦♠♦ ♦✉t❧✐❡rs✳ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛
❞❡ ✭❈❤❛♥❞♦❧❛ ❡t ❛❧✳✱ ✷✵✵✾✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✸ ❙ér✐❡ t❡♠♣♦r❛❧ ❞❡ t❡♠♣❡r❛t✉r❛✿ t2 é ✉♠ ♦✉t❧✐❡r ❝♦♥t❡①t✉❛❧✳ ❊♠❜♦r❛ ❛
t❡♠♣❡r❛t✉r❛ s❡❥❛ ❛ ♠❡s♠❛ ❡♠ t1 ❡ ❡♠ t2✱ ❛♣❡♥❛s ♥♦ ❝♦♥t❡①t♦ ❞❡ t2 ❡ss❛
♦❜s❡r✈❛çã♦ é ♦✉t❧✐❡r✳ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ✭❈❤❛♥❞♦❧❛ ❡t ❛❧✳✱ ✷✵✵✾✮✳ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✹ ❖✉t❧✐❡r ❝♦❧❡t✐✈♦ ❞❡st❛❝❛❞♦ ✭❡♠ ✈❡r♠❡❧❤♦✮✱ ❝♦rr❡s♣♦♥❞❡♥❞♦ ❛ ✉♠❛ ❝♦♥tr❛çã♦ ♣r❡♠❛t✉r❛ ❞♦ átr✐♦ ❡♠ ✉♠ ❡❧❡tr♦❝❛r❞✐♦❣r❛♠❛✳ ❋✐❣✉r❛ ♦❜t✐❞❛ ❞❡ ✭❈❤❛♥❞♦❧❛ ❡t ❛❧✳✱ ✷✵✵✾✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✺ ❈♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❜✐❞✐♠❡♥s✐♦♥❛❧ ❝♦♠ ✈❛r✐á✈❡✐s ❝♦rr❡❧❛❝✐♦♥❛❞❛s✳ ❆ ♦❜✲ s❡r✈❛çã♦ o1 é ✉♠❛ ♦❜s❡r✈❛çã♦ ♦✉t❧✐❡r✳ ◆♦ ❡♥t❛♥t♦✱ tr❛t❛♥❞♦ ❛s ✈❛r✐á✈❡✐s
✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡✱ ♥ã♦ é ♣♦ssí✈❡❧ ❞❡t❡❝t❛r o1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷
✷✳✻ ❈♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❜✐❞✐♠❡♥s✐♦♥❛❧ ❝♦♠ ✈❛r✐❛çã♦ ❞❡ ❞❡♥s✐❞❛❞❡✳ ◆❡ss❡ ❝❛s♦✱ ♠ét♦❞♦s ❜❛s❡❛❞♦s ❡♠ ❞❡♥s✐❞❛❞❡ ❧♦❝❛❧ ❛♣r❡s❡♥t❛♠ ♣❡r❢♦r♠❛♥❝❡ ♠❡❧❤♦r q✉❡ ♠ét♦❞♦s ❜❛s❡❛❞♦s ❡♠ ❞❡♥s✐❞❛❞❡ ❣❧♦❜❛❧✳ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ✭❈❤❛♥❞♦❧❛ ❡t ❛❧✳✱ ✷✵✵✾✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✼ ❚✐♣♦s ❞❡ ♦✉t❧✐❡rs ✐❞❡♥t✐✜❝❛❞♦s s❡❣✉♥❞♦ ♦ ♠ét♦❞♦ ♣r♦♣♦st♦ ❡♠ ✭❈♦st❛ ❡t ❛❧✳✱
✷✵✵✾✮✳ ❖ ♦✉t❧✐❡r ❛♣❛r❡❝❡ ❞❡st❛❝❛❞♦ ❡♠ ♣r❡t♦✳ ❖s ❛✉t♦r❡s ✐❞❡♥t✐✜❝❛♠ ✭❛✮ ❝♦♠♦ ❤✉❜ ❞❡ r❡tr❛♥s♠✐ssã♦ ❣❧♦❜❛❧✱ ✭❜✮ ❝♦♠♦ ❤✉❜ ❞❡ r❡tr❛♥s♠✐ssã♦ ❧♦❝❛❧✱ ✭❝✮ ❝♦♠♦ ✐♥t❡❣r❛❞♦r ❧♦❝❛❧✱ ✭❞✮ ❝♦♠♦ ✐♥t❡❣r❛❞♦r✱ ✭❡✮ ❝♦♠♦ ❝❡♥tr♦ ❞❡ ❝♦♠✉✲ ♥✐❞❛❞❡✱ ✭❢✮ ❝♦♠♦ ❡①tr❡♠✐❞❛❞❡✲❝❧✉st❡r✱ ✭❣✮ ❝♦♠♦ ❝❧✉st❡r✲❝❧✉st❡r✱ ❡ ✭❤✮ ❝♦♠♦ ❡①tr❡♠✐❞❛❞❡✳ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ✭❈♦st❛ ❡t ❛❧✳✱ ✷✵✵✾✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽
✸✳✶ Pr♦❜❧❡♠❛ ❞❛s s❡t❡ ♣♦♥t❡s ❞❡ ❑ö♥✐❣s❜❡r❣✳ ✭❛✮ ■❧✉str❛çã♦ ❞❛ ❝✐❞❛❞❡ ❞❡ ❑ö✲ ♥✐❣s❜❡r❣✳ ✭❜✮ ●r❛❢♦ r❡♣r❡s❡♥t❛♥❞♦ ♦ ♣r♦❜❧❡♠❛ ❞❛s s❡t❡ ♣♦♥t❡s ❞❡ ❑ö♥✐❣s✲ ❜❡r❣✳ ❈❛❞❛ ♣♦rçã♦ ❞❡ t❡rr❛ é r❡♣r❡s❡♥t❛❞❛ ♣♦r ✉♠ ♥ó ❡ ❝❛❞❛ ♣♦♥t❡ é r❡♣r❡s❡♥t❛❞❛ ♣♦r ✉♠❛ ❛r❡st❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷
✸✳✷ ❲♦❧❞ ❲✐❞❡ ❲❡❜✳ Pá❣✐♥❛s ❝♦♥❡❝t❛♠✲s❡ ❛ ♦✉tr❛s ♣á❣✐♥❛s ❛tr❛✈és ❞❡ ❧✐❣❛çõ❡s ❞✐r❡❝✐♦♥❛❞❛s✳ Pá❣✐♥❛s ♠✉✐t♦ ❝♦♥❡❝t❛❞❛s ❡♥tr❡ sí ♣♦❞❡♠ ❝❛r❛❝t❡r✐③❛r t❡♠❛s r❡❧❛❝✐♦♥❛❞♦s✳ ❆❧é♠ ❞✐ss♦✱ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❣r❛✉ ✐♥✢✉❡♥❝✐❛ ❞✐r❡t❛♠❡♥t❡ ❡♠ ❝♦♠♦ ❛ ✐♥❢♦r♠❛çã♦ s❡ ♣r♦♣❛❣❛ ♥❛ r❡❞❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✸✳✸ ❘❡❞❡ s♦❝✐❛❧ ❡♥tr❡ ❛❧✉♥♦s ❞❡ ✉♠❛ ❡s❝♦❧❛ ❛♠❡r✐❝❛♥❛✳ ❆s ❝♦r❡s r❡♣r❡s❡♥t❛♠ ❛s ❡t♥✐❛s✳ ◆♦t❡✲s❡ q✉❡ ❡①✐st❡ ✉♠❛ s❡♣❛r❛çã♦ ❜❡♠ ❞❡✜♥✐❞❛ ❝♦♠ r❡❧❛çã♦ ❛ ❡t♥✐❛ ❞♦s ✐♥❞✐✈í❞✉♦s✳ ❆❧é♠ ❞✐ss♦✱ ❡①✐st❡ ✉♠❛ s❡♣❛r❛çã♦ ❜❡♠ ❞❡✜♥✐❞❛ ❡♥tr❡ ♦s ❛❧✉♥♦s q✉❡ ❝✉rs❛♠ ♦ ❤✐❣❤ s❝❤♦♦❧ ❡ ♦s ❛❧✉♥♦s q✉❡ ❝✉rs❛♠ ♦ ♠❡❞✐✉♠ s❝❤♦♦❧✳ ❊ss❛s ❡str✉t✉r❛s sã♦ ❝♦♥❤❡❝✐❞❛s ❝♦♠♦ ❝♦♠✉♥✐❞❛❞❡s✳ ❋✐❣✉r❛ ♦❜t✐❞❛ ❞❡ ✭◆❡✇♠❛♥✱ ✷✵✵✸✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
✸✳✹ ❉✐str✐❜✉✐çã♦ ❝✉♠✉❧❛t✐✈❛ ❞❡ ❣r❛✉ ❞❡ s❡✐s r❡❞❡s r❡❛✐s✿ ✭❛✮ r❡❞❡ ❞❡ ❝♦❧❛❜♦r❛✲ çã♦ ❡♥tr❡ ♠❛t❡♠át✐❝♦s❀ ✭❜✮ r❡❞❡ ❞❡ ❝✐t❛çõ❡s❀ ✭❝✮ ❛ ❲♦r❧❞ ❲✐❞❡ ❲❡❜❀ ✭❞✮ ❛ ■♥t❡r♥❡t❀ ✭❡✮ r❡❞❡ ❞❡ ❡♥❡r❣✐❛ ❞♦ ❧❛❞♦ ♦❡st❡ ❞♦s ❊st❛❞♦s ❯♥✐❞♦s❀ ✭❢✮ r❡❞❡ ❞❡ ✐♥t❡r❛çõ❡s ❡♥tr❡ ♣r♦t❡í♥❛s✳ ❊♠ ❝❛❞❛ ❣rá✜❝♦✱ ♦ ❡✐①♦ ❞❛s ❛❜❝✐ss❛s r❡♣r❡s❡♥t❛ ♦ ❣r❛✉ k ✭♦ ❣r❛✉ ❞❡ ❡♥tr❛❞❛✱ kin✱ ♥♦ ❝❛s♦ ❞❛ r❡❞❡ ❞❡ ❝✐t❛çõ❡s ❡ ❞❛ ❲♦r❧❞
❲✐❞❡ ❲❡❜✮ ❡♥q✉❛♥t♦ q✉❡ ♦ ❡✐①♦ ❞❛s ♦r❞❡♥❛❞❛s r❡♣r❡s❡♥t❛ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ❞✐str✐❜✉✐çã♦✱P(k)✳ ❉❡ss❛s r❡❞❡s✱ ❛s r❡♣r❡s❡♥t❛❞❛s ❡♠ ✭❝✮✱ ✭❞✮ ❡ ✭❢✮✱ ♣♦s✲
s✉❡♠ ❞✐str✐❜✉✐çã♦ ❞❡ ❣r❛✉ q✉❡ s❡❣✉❡ ❛ ❧❡✐ ❞❡ ♣♦tê♥❝✐❛✳ ❈♦♠♦ r❡♣r❡s❡♥t❛❞❛ ❡♠ ❡s❝❛❧❛ ❧♦❣✲❧✐♥❡❛r✱ ✭❡✮ s❡❣✉❡ ✉♠❛ ❧❡✐ ❡①♣♦♥❡♥❝✐❛❧✳ ❊♠❜♦r❛ ✭❛✮ ❡ ✭❜✮ s❡✲ ❥❛♠ r❡♣r❡s❡♥t❛❞❛s ❡♠ ❡s❝❛❧❛ ❧♦❣✲❧♦❣✱ ❛♠❜❛s ❞❡s✈✐❛♠✲s❡ ❛❝❡♥t✉❛❞❛♠❡♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❛❧✈♦✱ ❡s♣❡❝✐❛❧♠❡♥t❡ ❝♦♠ r❡❧❛çã♦ ❛ ♥ós ❝♦♠ ❛❧t♦ ❣r❛✉✳ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ✭◆❡✇♠❛♥✱ ✷✵✵✸✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻
✸✳✺ ❘❡❞❡ ❝♦♠ três ❡str✉t✉r❛s ❞❡ ❝♦♠✉♥✐❞❛❞❡s ❜❡♠ ❞❡✜♥✐❞❛s✳ ◆ós q✉❡ ♣❡r✲ t❡♥❝❡♠ ❛ ♠❡s♠❛ ❝♦♠✉♥✐❞❛❞❡ ❡stã♦ ❞❡♥s❛♠❡♥t❡ ❝♦♥❡❝t❛❞♦s✱ ❡♥q✉❛♥t♦ q✉❡ ❧✐❣❛çõ❡s ❡♥tr❡ ♥ós ❞❡ ❝♦♠✉♥✐❞❛❞❡s ❞✐st✐♥t❛s sã♦ ❡s♣❛rs❛s✳ ❋✐❣✉r❛ ♦❜t✐❞❛ ❞❡ ✭◆❡✇♠❛♥ ✫ ●✐r✈❛♥✱ ✷✵✵✹✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✸✳✻ ❈♦♥✜❣✉r❛çõ❡s ❞❡ r❡❞❡s r❛♥❞ô♠✐❝❛s ❝♦♠ ✽ ✈ért✐❝❡s✿ ✭❛✮ p= 0❀ ✭❜✮ p= 0.1❀
✭❝✮ p= 0.3❀ ✭❞✮ p= 0.8✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✸✳✼ ❉✐str✐❜✉✐çã♦ ❞❡ ❣r❛✉ ♠é❞✐❛ ❞❡ ✶✵ r❡❞❡s r❛♥❞ô♠✐❝❛s ❝♦♠ ✶✵✵✵ ♥ós ❡ ♣r♦❜❛✲ ❜✐❧✐❞❛❞❡ p= 0.1✳ ❯♠❛ ❞✐str✐❜✉✐çã♦ ❞❡ P♦✐ss♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✸✳✽ ▼♦❞❡❧♦ ❞❡ r❡❞❡s ❞❡ ♣❡q✉❡♥♦ ♠✉♥❞♦ ❞❡ ❲❛tts ✫ ❙tr♦❣❛t③ ✭✶✾✾✽✮✳ P❛r❛
p = 0 t❡♠♦s ✉♠❛ r❡❞❡ r❡❣✉❧❛r✳ ◗✉❛♥t♦ ♠❛✐♦r ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ p✱ ♠❛✐s ♦
♠♦❞❡❧♦ s❡ ❛♣r♦①✐♠❛ ❞❡ ✉♠❛ r❡❞❡ r❛♥❞ô♠✐❝❛✳ P❛r❛ 0.01 < p < 0.1 ❛ r❡❞❡
s❡ ❝♦♠♣♦rt❛ ❝♦♠♦ ✉♠❛ r❡❞❡ ❞❡ ♣❡q✉❡♥♦ ♠✉♥❞♦✳ ◆♦t❡✲s❡ q✉❡ ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ♦s ♥ós ✐❞❡♥t✐✜❝❛❞♦s ❡♠ ✈❡r♠❡❧❤♦ ❡ ❡♠ ❛③✉❧ ❞✐♠✐♥✉✐✱ ❡♥q✉❛♥t♦ q✉❡ ♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ❝❧✉st❡r✐♥❣ ♠❛♥t❡♠✲s❡ ❛❧t♦✳ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ✭❲❛tts ✫ ❙tr♦❣❛t③✱ ✶✾✾✽✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵
✸✳✾ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❞✐stâ♥❝✐❛ ♠é❞✐❛ ❡ ❞♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ❝❧✉st❡r✐♥❣ ❡♠ ❢✉♥✲ çã♦ ❞❡p✱ s❡❣✉♥❞♦ ♦ ♠♦❞❡❧♦ ❞❡ ❲❛tts ✫ ❙tr♦❣❛t③ ✭✶✾✾✽✮✳ ❚❛♥t♦ ♦ ❝♦❡✜❝✐❡♥t❡
❞❡ ❝❧✉st❡r✐♥❣ ❝♦♠♦ ❛ ❞✐stâ♥❝✐❛ ♠é❞✐❛ sã♦ ❛♣r❡s❡♥t❛❞♦s ❡♠ r❛③ã♦ ❞♦s r❡s✲ ♣❡❝t✐✈♦s ✈❛❧♦r❡s ♠á①✐♠♦s✳ P❛r❛ 0.01< p < 0.1 t❡♠♦s ♦ ❡❢❡✐t♦ ❞❡ ♣❡q✉❡♥♦
♠✉♥❞♦✳ ❋✐❣✉r❛ ♦❜t✐❞❛ ❞❡ ✭◆❡✇♠❛♥✱ ✷✵✵✸✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✸✳✶✵ ❉✐str✐❜✉✐çã♦ ❞❡ ❣r❛✉ ♠é❞✐❛ ❞❡ ✶✵ r❡❞❡s ❣❡r❛❞❛s s❡❣✉♥❞♦ ♦ ♠♦❞❡❧♦ ❞❡ ❇❛✲ r❛❜ás✐ ✫ ❆❧❜❡rt ✭✶✾✾✾✮ ❝♦♠ ✶✵✵✵ ♥ós ❡ m= 5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷
✸✳✶✶ ❊①❡♠♣❧♦ ❞❡ r❡❞❡ ❝♦♠ ✻✹ ♥ós ❡ ✹ ❡str✉t✉r❛s ❞❡ ❝♦♠✉♥✐❞❛❞❡s ❜❡♠ ❞❡✜♥✐❞❛s ❣❡r❛❞❛ s❡❣✉♥❞♦ ♦ ♠♦❞❡❧♦ ❞❡ ●✐r✈❛♥ ✫ ◆❡✇♠❛♥ ✭✷✵✵✷✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✸✳✶✷ ❆r✈♦r❡ ❤✐❡rárq✉✐❝❛ ✭♦✉ ❞❡♥❞♦❣r❛♠❛✮ ✐❧✉str❛♥❞♦ ♦ r❡s✉❧t❛❞♦ ❞♦ ♠ét♦❞♦ ❞❡ ❞❡t❡❝çã♦ ❞❡ ❝♦♠✉♥✐❞❛❞❡s ❞❡ ◆❡✇♠❛♥ ✫ ●✐r✈❛♥ ✭✷✵✵✹✮ ❛♣❧✐❝❛❞♦ ❛ r❡❞❡ ❞❛ ❋✐❣✉r❛ ✸✳✺✳ ❖s ❝ír❝✉❧♦s ♥❛ ❜❛s❡ ❞❛ ✜❣✉r❛ r❡♣r❡s❡♥t❛♠ ♦s ♥ós ❞❛ r❡❞❡✳ ▼♦✈❡♥❞♦✲s❡ s❡♥t✐❞♦ ❛ r❛✐③ ❞❛ ár✈♦r❡✱ t❡♠♦s ♣❛rt✐çõ❡s ❝❛❞❛ ✈❡③ ♠❛✐♦r❡s✳ ◆♦ ❝❛s♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ◆❡✇♠❛♥ ✫ ●✐r✈❛♥ ✭✷✵✵✹✮✱ tr❛t❛✲s❡ ❞❡ ✉♠ ♠ét♦❞♦ ❞✐✈✐s✐✈♦✳ ◆❡ss❡ ❝❛s♦✱ ❛ ✈✐s✉❛❧✐③❛çã♦ ♠❛✐s ❛❞❡q✉❛❞❛ é ❛ ♣❛rt✐r ❞❛ r❛✐③ s❡♥t✐❞♦ ❛s ❢♦❧❤❛s✳ ❖ ❝♦rt❡ ❤♦r✐③♦♥t❛❧ r❡❢❡r❡✲s❡ ❛ ♣❛rt✐çã♦ ❞❡ ❝♦♠✉♥✐❞❛❞❡s ❝♦♠ ♠❛✐♦r í♥❞✐❝❡ ❞❡ ♠♦❞✉❧❛r✐❞❛❞❡✳ ❋✐❣✉r❛ ♦❜t✐❞❛ ❞❡ ✭◆❡✇♠❛♥ ✫ ●✐r✈❛♥✱ ✷✵✵✹✮✳ ✳ ✳ ✳ ✸✻
✸✳✶✸ ■❧✉str❛çã♦ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❞❡t❡❝çã♦ ❞❡ ❝♦♠✉♥✐❞❛❞❡s s❡❣✉♥❞♦ ♦ ♠ét♦❞♦ ❞❡ ❝♦♠♣❡t✐çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❡ ❝❛♠✐♥❤❛❞❛ ❛❧❡❛tór✐❛✳ ❆ r❡❞❡ ♣♦ss✉✐ ✶✷✽ ✈ért✐❝❡s✱ ✹ ❝♦♠✉♥✐❞❛❞❡s ❜❡♠ ❞❡✜♥✐❞❛s✱ ❣r❛✉ ♠é❞✐♦hki= 16❡ ♣r♦♣♦rçã♦ ❞❡ ❝♦♥❡①õ❡s
❡♥tr❡ ❝♦♠✉♥✐❞❛❞❡ pout = 0.2✳ ✭❛✮ ❈♦♥✜❣✉r❛çã♦ ✐♥✐❝✐❛❧✿ q✉❛tr♦ ♣❛rtí❝✉❧❛s
♥❛s ❝♦r❡s ❛♠❛r❡❧♦✱ ❝✐❛♥♦✱ ❧❛r❛♥❥❛✱ ❡ ❛③✉❧ sã♦ ❝♦❧♦❝❛❞❛s ❡♠ ✈ért✐❝❡s ❛❧❡❛tór✐♦s ❞❛ r❡❞❡❀ ♦s ✈ért✐❝❡s ❡♠ ✈❡r♠❡❧❤♦ ❡stã♦ ❧✐✈r❡s✳ ❊♠ ✭❜✮ ❞♦♠í♥✐♦ ❞❛s ♣❛rtí❝✉❧❛s ♥❛ ✐t❡r❛çã♦ ✷✺✵✳ ❊♠ ✭❝✮ ❞♦♠í♥✐♦ ❞❛s ♣❛rtí❝✉❧❛s ♥❛ ✐t❡r❛çã♦ ✸✺✵✵✳ ❊♠ ✭❞✮ ❞♦♠í♥✐♦ ❞❛s ♣❛rtí❝✉❧❛s ♥❛ ✐t❡r❛çã♦ ✼✵✵✵✳ ❋✐❣✉r❛ ♦❜t✐❞❛ ❞❡ ✭◗✉✐❧❡s ❡t ❛❧✳✱ ✷✵✵✽✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✸✳✶✹ ❋r❛çã♦ ❞❡ ♥ós ✐❞❡♥t✐✜❝❛❞♦s ❝♦rr❡t❛♠❡♥t❡ ❡♠ s✉❛ ❝♦♠✉♥✐❞❛❞❡ s❡❣✉♥❞♦ ♦ ♠ét♦❞♦ ❞❡ ◗✉✐❧❡s ❡t ❛❧✳ ✭✷✵✵✽✮ ❡♠ r❡❧❛çã♦ ❛♦ ♥í✈❡❧ ❞❡ ❞❡t❡r♠✐♥✐s♠♦ ❞❛ ❝❛♠✐♥❤❛❞❛✳ ❈❛❞❛ ♣♦♥t♦ ❞❛ ❝✉r✈❛ r❡♣r❡s❡♥t❛ ❛ ♠é❞✐❛ ❞❡ ✷✵✵ ❡①❡❝✉çõ❡s ❡♠ ✉♠❛ r❡❞❡ ❝♦♠ ✶✷✽ ♥ós✱ hki = 16✱ ❡ pout = 0,5✳ ❆ ❜❛rr❛ ❞❡ ❡rr♦ r❡♣r❡s❡♥t❛
♦ ❞❡s✈✐♦ ♣❛❞rã♦✳ ❋✐❣✉r❛ ♦❜t✐❞❛ ❞❡ ✭◗✉✐❧❡s ❡t ❛❧✳✱ ✷✵✵✽✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✹✳✶ ❈❛♠✐♥❤❛❞❛ ❛❧❡❛tór✐❛ ❡♠ r❡❞❡s✿ ✭❛✮ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ♦ ❝❛♠✐♥❤❛♥t❡ ♠♦✈❡r✲ s❡ ❛ ♣❛rt✐r ❞♦ ♥ó1❛té ♦s ♥ós ✈✐③✐♥❤♦s ❡♠ ✉♠❛ ✐t❡r❛çã♦❀ ✭❜✲❡✮ ♣r♦❜❛❜✐❧✐❞❛❞❡
❞❡ ♦ ❝❛♠✐♥❤❛♥t❡ ♠♦✈❡r✲s❡ ❛ ♣❛rt✐r ❞♦ ♥ó 1 ❛té ♦s ♥ó 1✱ 2✱ 3 ❡ 4 ❡♠ ❞✉❛s
✐t❡r❛çõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✷ ✭❛✮ ❘❡s✉❧t❛❞♦ ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ ❞❡ ❞❡t❡❝çã♦ ❞❡ ♦✉t❧✐❡rs ❡♠ ✉♠❛ r❡❞❡
❝♦♠ ✺ ♥ós✳ ❊stã♦ ✐❞❡♥t✐✜❝❛❞♦s ❡♠ ✈❡r♠❡❧❤♦ ♦s ♥ós ❝♦♠ ♠❛✐♦r ❡s❝♦r❡ ❞❡ ♦✉t❧✐❡r✳ ✭❜✮ ▼❛tr✐③ ❞❡ ❞✐ss✐♠✐❧❛r✐❞❛❞❡ Λ✳ ◗✉❛♥t♦ ♠❛✐s ✈❡r♠❡❧❤♦✱ ♠❛✐♦r ♦
í♥❞✐❝❡Λ(i, j)✳ ✭❝✮ ❘❛♥q✉❡ ❞❡ ♦✉t❧✐❡rs✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵
✹✳✸ ✭❛✮ ❘❡s✉❧t❛❞♦ ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ ❞❡ ❞❡t❡❝çã♦ ❞❡ ♦✉t❧✐❡rs ❡♠ ✉♠❛ r❡❞❡ ❝♦♠ ✾ ♥ós✳ ❊stã♦ ✐❞❡♥t✐✜❝❛❞♦s ❡♠ ✈❡r♠❡❧❤♦ ♦s ♥ós ❝♦♠ ♠❛✐♦r ❡s❝♦r❡ ❞❡ ♦✉t❧✐❡r✳ ✭❜✮ ▼❛tr✐③ ❞❡ ❞✐ss✐♠✐❧❛r✐❞❛❞❡ Λ✳ ◗✉❛♥t♦ ♠❛✐s ✈❡r♠❡❧❤♦✱ ♠❛✐♦r ♦
í♥❞✐❝❡Λ(i, j)✳ ✭❝✮ ❘❛♥q✉❡ ❞❡ ♦✉t❧✐❡rs✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✹✳✹ ✭❛✮ ❘❡s✉❧t❛❞♦ ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ ❞❡ ❞❡t❡❝çã♦ ❞❡ ♦✉t❧✐❡rs ❡♠ ✉♠❛ r❡❞❡ ❝♦♠ ✶✸ ♥ós✳ ❊stã♦ ✐❞❡♥t✐✜❝❛❞♦s ❡♠ ✈❡r♠❡❧❤♦ ♦s ♥ós ❝♦♠ ♠❛✐♦r ❡s❝♦r❡ ❞❡ ♦✉t❧✐❡r✳ ✭❜✮ ▼❛tr✐③ ❞❡ ❞✐ss✐♠✐❧❛r✐❞❛❞❡ Λ✳ ◗✉❛♥t♦ ♠❛✐s ✈❡r♠❡❧❤♦✱ ♠❛✐♦r ♦
í♥❞✐❝❡Λ(i, j)✳ ✭❝✮ ❘❛♥q✉❡ ❞❡ ♦✉t❧✐❡rs✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✹✳✺ ❘❡s✉❧t❛❞♦ ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ ❞❡ ❞❡t❡❝çã♦ ❞❡ ♦✉t❧✐❡rs ♣r♦♣♦st♦ à r❡❞❡ ❞♦ ❝❧✉❜❡ ❞❡ ❦❛r❛tê r❡❣✐str❛❞❛ ♣♦r ❩❛❝❤❛r② ✭✶✾✼✼✮✳ ❖s ❞❡③ ♥ós ❝♦♠ ♠❛✐♦r ❡s❝♦r❡ ❞❡ ♦✉t❧✐❡r ❛♣❛r❡❝❡♠ ❝♦❧♦r✐❞♦s✳ ◗✉❛♥t♦ ♠❛✐s ✈❡r♠❡❧❤♦ ♠❛✐♦r ♦ ❡s❝♦r❡ ❞❡ ♦✉t❧✐❡r ❞♦ ✐♥❞✐✈í❞✉♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✻ ❘❡s✉❧t❛❞♦ ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ ❞❡ ❞❡t❡❝çã♦ ❞❡ ♦✉t❧✐❡rs ♣r♦♣♦st♦ à r❡❞❡
❞❡ ❝♦❧❛❜♦r❛çã♦ ❡♥tr❡ ❝✐❡♥t✐st❛s r❡❣✐str❛❞❛ ♣♦r ◆❡✇♠❛♥ ✭✷✵✵✻✮✳ ❖s ❞❡③ ♥ós ❝♦♠ ♠❛✐♦r ❡s❝♦r❡ ❞❡ ♦✉t❧✐❡r ❛♣❛r❡❝❡♠ ❝♦❧♦r✐❞♦s✳ ◗✉❛♥t♦ ♠❛✐s ✈❡r♠❡❧❤♦ ♠❛✐♦r ♦ ❡s❝♦r❡ ❞❡ ♦✉t❧✐❡r ❞♦ ✐♥❞✐✈í❞✉♦✳ ❖s ✐♥❞✐✈í❞✉♦s ♠❛✐s ❝♦❧❛❜♦r❛t✐✈♦s ❞❛ r❡❞❡ t❛♠❜é♠ ❛♣❛r❡❝❡♠ ❞❡st❛❝❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✼ ❉✐str✐❜✉✐çã♦ ✭P(σ)✮ ❞♦ ❡s❝♦r❡ ❞❡ ♦✉t❧✐❡r ✈❡r✐✜❝❛❞❛ ♥❛ r❡❞❡ ❞❡ ✐♥t❡r❛çõ❡s
❡♥tr❡ ♣r♦t❡í♥❛s ❞♦ ♠❡t❛❜♦❧✐s♠♦ ❞❛ ❧❡✈❡❞✉r❛ ❙❛❝❝❤❛r♦♠②❝❡s ❝❡r❡✈✐s✐❛❡✳ ❊ss❛ ❞✐str✐❜✉✐çã♦ s❡❣✉❡ ❛ ❧❡✐ ❞❡ ♣♦tê♥❝✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✽ ❋r❛çã♦ ✭ϕ✮ ❞❡ ♣r♦t❡í♥❛s r❡❧❛❝✐♦♥❛❞❛s ❛ ❝❛❞❛ ❣r✉♣♦ ❢✉♥❝✐♦♥❛❧ ❡♥tr❡ ♦s ♥ós
❝♦♠ ♠❛✐♦r ❡s❝♦r❡ ❞❡ ♦✉t❧✐❡r✳ ❆s ♣r♦t❡í♥❛s r❡❧❛❝✐♦♥❛❞❛s ❛♦ ❝✐❝❧♦ ❝❡❧✉❧❛r ❡ ♣r♦✲ ❝❡ss❛♠❡♥t♦ ❞❡ ❉◆❆ ❡ ❛s ♣r♦t❡í♥❛s r❡❧❛❝✐♦♥❛❞❛s ❛♦ ♠❡t❛❜♦❧✐s♠♦ ❞❡st❛❝❛♠✲ s❡ ❞❛s ❞❡♠❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✹✳✾ Pr♦t❡í♥❛s ♠❛✐s ♦✉t❧✐❡rs ✭❡♠ ♣r❡t♦✮ ❡ ♦s r❡s♣❡❝t✐✈♦s ❛rr❛♥❥♦s ❧♦❝❛✐s✳ ❆s
♣r♦t❡í♥❛s ❨▼❘✷✵✼❝ ❡ ❨P❘✵✹✽✇ sã♦ ♣r♦t❡í♥❛s r❡❧❛❝✐♦♥❛❞❛s ❛ ❢✉♥çã♦ ❞❡ ♠❡t❛❜♦❧✐s♠♦✱ ❡♥q✉❛♥t♦ q✉❡ ❛s ♣r♦t❡í♥❛s ❨■▲✶✸✺❝✱ ❨❖❘✷✻✺✇ ❡ ❨▲❘✹✶✾✇ ❛t✉❛♠ ♥♦ ❝✐❝❧♦ ❝❡❧✉❧❛r ❡ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ❉◆❆✳ ❆s ♣r♦t❡í♥❛s ❨❏❘✵✾✶❝ ❡ ❨❏▲✶✾✹✇ ❡stã♦ r❡❧❛❝✐♦♥❛❞❛s ❝♦♠ ❛♠❜❛s ❛s ❢✉♥çõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✶✵ ❯♠❛ ♣r♦t❡í♥❛ t✐♣✐❝❛♠❡♥t❡ ♥ã♦ ♦✉t❧✐❡r ✭❡♠ ♣r❡t♦✮✳ ❆ ♣r♦t❡í♥❛ ❝♦♠ ♠❡♥♦r
❡s❝♦r❡ ❞❡ ♦✉t❧✐❡r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✹✳✶✶ ✭❛✮ ❘♦t✉❧❛çã♦ ❞❡ ❞❛❞♦s ✐❞❡❛❧ ❞❡ ✉♠❛ ❜❛s❡ ❞❡ ❞❛❞♦s s✐♥tét✐❝❛ ❞♦ t✐♣♦ ❜❛♥❛♥❛ ❝♦♠ ✷✵✵ ❡①❡♠♣❧♦s✱ s❡♥❞♦ ✶✵✵ ♣❡rt❡♥❝❡♥t❡s ❛ ❝❧❛ss❡ ✈❡r♠❡❧❤❛ ✭❝✐r❝✉❧♦✮ ❡ ✶✵✵ ♣❡rt❡♥❝❡♥t❡s ❛ ❝❧❛ss❡ ❛③✉❧ ✭q✉❛❞r❛❞♦s✮✳ ✭❜✮ ❘❡❞❡ ❣❡♦❣rá✜❝❛ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❡♠ ✭❛✮✱ ❝♦♥str✉í❞❛ s❡❣✉♥❞♦ ♦ ♠ét♦❞♦ ❛♣r❡s❡♥t❛❞♦ ♥❛ ❙❡çã♦ ✸✳✸✳✺✱ ❝♦♠ λ = 1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷
✹✳✶✷ ❘❡s✉❧t❛❞♦ ❞♦ ♠ét♦❞♦ ❞❡ ♣r♦♣❛❣❛çã♦ ❞❡ rót✉❧♦s ♣r♦♣♦st♦ ❛♣❧✐❝❛❞♦ à r❡❞❡ ❝♦♥str✉✐❞❛ ❛ ♣❛rt✐r ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❞❛ ❋✐❣✉r❛ ✹✳✶✶✭❛✮✿ ✭❛✮ ❝♦♠ ❜❛s❡ ❡♠ ✹✵ ❝♦♥✜❣✉r❛çõ❡s ❞❡ ✶✵ ♥ós r♦t✉❧❛❞♦s ❛ ♣r✐♦r✐✱ ❡s❝♦❧❤✐❞♦s r❛♥❞♦♠✐❝❛✲ ♠❡♥t❡✱ s❡♥❞♦ ✺ ❞❡ ❝❛❞❛ ❝♦♠✉♥✐❞❛❞❡❀ ✭❜✮ ❝♦♠ ❜❛s❡ ♥♦s ✺ ♦✉t❧✐❡rs ❝❡♥tr❛✐s ❞❡ ❝❛❞❛ ❝♦♠✉♥✐❞❛❞❡✳ ϕ é ❛ ♣r❡❝✐sã♦ ❞❡ ❞❡t❡❝çã♦ ❞❡ ❝♦♠✉♥✐❞❛❞❡s ❛ ❝❛❞❛
✐t❡r❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✶✸ ❘❡s✉❧t❛❞♦ ❞♦ ♠ét♦❞♦ ❞❡ ♣r♦♣❛❣❛çã♦ ❞❡ rót✉❧♦s ♣r♦♣♦st♦ ❛♣❧✐❝❛❞♦ à r❡❞❡
❞♦ ❝❧✉❜❡ ❞❡ ❦❛r❛tê ✭❋✐❣✉r❛ ✹✳✺✮✿ ✭❛✮ ❝♦♠ ❜❛s❡ ❡♠ ✷✵ ❝♦♥✜❣✉r❛çõ❡s ❞❡ ✹ ♥ós r♦t✉❧❛❞♦s ❛ ♣r✐♦r✐✱ ❡s❝♦❧❤✐❞♦s r❛♥❞♦♠✐❝❛♠❡♥t❡✱ s❡♥❞♦ ❞♦✐s ❞❡ ❝❛❞❛ ❝♦♠✉♥✐❞❛❞❡❀ ✭❜✮ ❝♦♠ ❜❛s❡ ♥♦s ♥ós ✸✹✱ ✶✱ ✸ ❡ ✸✸✱ ❞♦✐s ♦✉t❧✐❡rs ❝❡♥tr❛✐s ❞❡ ❝❛❞❛ ❝♦♠✉♥✐❞❛❞❡✳ ϕé ❛ ♣r❡❝✐sã♦ ❞❡ ❞❡t❡❝çã♦ ❞❡ ❝♦♠✉♥✐❞❛❞❡s ❛ ❝❛❞❛ ✐t❡r❛çã♦✳ ✻✸
Capítulo
1
Introdução
◆❛ ♥❛t✉r❡③❛ ❡ ♥❛ ❝✐ê♥❝✐❛✱ ❞❛❞♦s ❡ ✐♥❢♦r♠❛çõ❡s q✉❡ ❞❡s✈✐❛♠ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ❞❛ ♠é❞✐❛ ❢r❡q✉❡♥t❡♠❡♥t❡ ♣♦ss✉❡♠ ❣r❛♥❞❡ r❡❧❡✈â♥❝✐❛✳ ❙❡ ❝♦♥s✐❞❡r❛r♠♦s✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ❛t❡♥çã♦ ✈✐s✉❛❧ ❞♦s ❛♥✐♠❛✐s✱ ♦s ❡stí♠✉❧♦s ✈✐s✉❛✐s q✉❡ ❢r❡q✉❡♥t❡♠❡♥t❡ ❛tr❛❡♠ s✉❛ ❛t❡♥çã♦ sã♦ ♦s ❝♦♥t♦r♥♦s ❡ ❛r❡st❛s ❞♦s ♦❜❥❡t♦s✱ ✐st♦ é✱ ❛s r❡❣✐õ❡s ♥ã♦ ❤♦♠♦❣ê♥❡❛s ❞❛ ❝❡♥❛✱ ♦♥❞❡ ❡①✐st❡♠ ❢♦rt❡s ✈❛r✐❛çõ❡s ♥❛ ✐♥t❡♥s✐❞❛❞❡ ❞♦s ❡stí♠✉❧♦s ✈✐s✉❛✐s ✭▼❛rr✱ ✶✾✽✷✮✳ ❉❛❞♦s ❡ ✐♥❢♦r♠❛çõ❡s ❞❡ss❡ t✐♣♦✱ sã♦ ❣❡r❛❧♠❡♥t❡ r❡❢❡r✐❞♦s ♥❛ ❧✐t❡r❛t✉r❛ ❝♦♠♦ ♦✉t❧✐❡rs ♦✉ ❛♥♦♠❛❧✐❛s✳ ❊♠ ✉♠ s❡♥t✐❞♦ ❣❡r❛❧✱ ✉♠❛ ♦❜s❡r✈❛çã♦ ✭♦✉ s✉❜❝♦♥❥✉♥t♦ ❞❡ ♦❜s❡r✈❛çõ❡s✮ ♦✉t❧✐❡r ♣❛r❡❝❡ ❞❡s✈✐❛r✲s❡ ❛❝❡♥t✉❛❞❛♠❡♥t❡ ❡♠ r❡❧❛çã♦ ❛♦s ♦✉tr♦s ♠❡♠❜r♦s ❞❛ ❛♠♦str❛ ❡♠ q✉❡ ♦❝♦rr❡✱ ♣❛r❡❝❡♥❞♦ s❡r ✐♥❝♦♥s✐st❡♥t❡ ❡♠ r❡❧❛çã♦ ❛♦ r❡st❛♥t❡ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s✱ ❞❡ t❛❧ ❢♦r♠❛ q✉❡ s❡ s✉s♣❡✐t❡ q✉❡ t❡♥❤❛ s✐❞♦ ❣❡r❛❞❛ ♣♦r ✉♠ ♠❡❝❛♥✐s♠♦ ❞✐❢❡r❡♥❝✐❛❞♦ ✭●r✉❜❜s✱ ✶✾✻✾❀ ❍❛✇❦✐♥s✱ ✶✾✽✵❀ ❇❛r♥❡tt ✫ ▲❡✇✐s✱ ✶✾✾✹✮✳
P♦r ♠✉✐t♦ t❡♠♣♦ ♣❡♥s♦✉✲s❡ q✉❡ ♦❜s❡r✈❛çõ❡s ♦✉t❧✐❡r ❞❡✈✐❛♠✲s❡ ❛ ❡rr♦s ♥ã♦ ❝♦♥t❡♠♣❧❛✲ ❞♦s ♥❛ ❡s♣❡❝✐✜❝❛çã♦ ❞❡ ✉♠ ♠♦❞❡❧♦ ❞❡ ❛q✉✐s✐çã♦ ❞❡ ❞❛❞♦s✱ ♣♦rt❛♥t♦ s❡♥❞♦ ❝♦♥s✐❞❡r❛❞♦s ✐♠♣✉r❡③❛s ♦✉ r✉í❞♦s✳ ❈♦♥s✐❞❡r❛✈❛✲s❡ q✉❡ ❛ ✐♥tr♦❞✉çã♦ ❞❡ss❛s ♦❜s❡r✈❛çõ❡s ♥❛ ✐♥✈❡st✐❣❛çã♦ s❡r✈✐r✐❛ ❛♣❡♥❛s ♣❛r❛ ❛tr❛♣❛❧❤❛r ❡ ❝♦♥❢✉♥❞✐r ✭❇❛r♥❡tt ✫ ▲❡✇✐s✱ ✶✾✾✹✮✳ P♦r ✐ss♦✱ t✐♣✐❝❛✲ ♠❡♥t❡ ♦❜s❡r✈❛çõ❡s ♦✉t❧✐❡rs ❡r❛♠ ❡❧✐♠✐♥❛❞❛s✳ ◆♦ ❡♥t❛♥t♦✱ ❤♦❥❡ ❡♠ ❞✐❛✱ ❡①✐st❡ ✉♠❛ ✈❛r✐✲ ❡❞❛❞❡ ♠✉✐t♦ ❣r❛♥❞❡ ❞❡ ❛♣❧✐❝❛çõ❡s ♥❛s q✉❛✐s ♦❜s❡r✈❛çõ❡s ♦✉t❧✐❡rs sã♦ ❜❛st❛♥t❡ r❡❧❡✈❛♥t❡✳ ❊①❡♠♣❧♦ ❞✐ss♦ sã♦ ❛♣❧✐❝❛çõ❡s ❝♦♠♦✿ ❞❡t❡❝çã♦ ❞❡ ❢r❛✉❞❡s❀ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ♣❡❞✐❞♦s ❞❡ ❡♠♣rést✐♠♦❀ ❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sã♦ ❡♠ s✐st❡♠❛s❀ ❞✐❛❣♥óst✐❝♦ ❞❡ ❢❛❧❤❛s❀ ♠♦♥✐t♦r❛♠❡♥t♦ ❞❡ ❝♦♥❞✐çõ❡s ♠é❞✐❝❛s❀ ❡♥tr❡ ♦✉tr♦s✳ ◆❡ss❛s ❛♣❧✐❝❛çõ❡s✱ ♦❜s❡r✈❛çõ❡s ♦✉t❧✐❡rs ♣r❡❝✐s❛♠ s❡r ❞❡✲ t❡❝t❛❞❛s ♣❛r❛ q✉❡ ♣♦ss❛♠ s❡r tr❛t❛❞❛s ❛❞❡q✉❛❞❛♠❡♥t❡✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❛ ❛♣❧✐❝❛çã♦ ✭❍♦❞❣❡ ✫ ❆✉st✐♥✱ ✷✵✵✹✮✳
1.1 Contexto
◆♦s ú❧t✐♠♦s ❛♥♦s✱ t❡♠✲s❡ t❡st❡♠✉♥❤❛❞♦ ✉♠ ❣r❛♥❞❡ ✐♥t❡r❡ss❡ ♥❛ ár❡❛ ❞❡ ❘❡❞❡s ❈♦♠✲ ♣❧❡①❛s✱ ♠♦t✐✈❛❞♦ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❡❧❛ ❣r❛♥❞❡ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❞❡ r❡❝✉rs♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❡ ❞❡ r❡❞❡s ❞❡ ❝♦♠✉♥✐❝❛çã♦✱ q✉❡ tê♠ ♣❡r♠✐t✐❞♦ ❛ ❛♥á❧✐s❡ ❞❡ ❞❛❞♦s ❞❡ ❣r❛♥❞❡ ❡s❝❛❧❛✳ ❆s r❡❞❡s ❝♦♠♣❧❡①❛s sã♦ ❣r❛❢♦s ❞❡ ❣r❛♥❞❡ ❡s❝❛❧❛ q✉❡ ♣♦ss✉❡♠ ♣❛❞rõ❡s ❞❡ ❝♦♥❡①õ❡s ♥ã♦ tr✐✈✐❛❧✳ ❘❡❞❡s ❝♦♠♦ ❛ ■♥t❡r♥❡t ✭❋❛❧♦✉ts♦s ❡t ❛❧✳✱ ✶✾✾✾✮✱ ❛ ❲♦r❧❞ ❲✐❞❡ ❲❡❜ ✭❆❧❜❡rt ❡t ❛❧✳✱ ✶✾✾✾✮✱ r❡❞❡s ❞❡ ❞✐str✐❜✉✐çã♦ ❞❡ ❡♥❡r❣✐❛ ❡❧étr✐❝❛ ✭❆❧❜❡rt ❡t ❛❧✳✱ ✷✵✵✹✮✱ r❡❞❡s ❞❡ ❝♦❧❛❜♦r❛çã♦ ❡♥tr❡ ❝✐❡♥t✐st❛s ✭◆❡✇♠❛♥✱ ✷✵✵✶✮✱ r❡❞❡s ❞❡ ✐♥t❡r❛çõ❡s s♦❝✐❛✐s ❡♥tr❡ ✐♥❞✐✈í❞✉♦s ✭❙❝♦tt✱ ✷✵✵✵✮✱ r❡✲ ❞❡s ❞❡ ✐♥t❡r❛çõ❡s ❡♥tr❡ ❝♦♠♣❛♥❤✐❛s ❡ ♦r❣❛♥✐③❛çõ❡s ✭▼✐③r✉❝❤✐✱ ✶✾✽✷✮✱ ❝❛❞❡✐❛s ❞❡ ❝♦♥t❛t♦s s❡①✉❛✐s ✭▲✐❧❥❡r♦s ❡t ❛❧✳✱ ✷✵✵✶✮✱ ❝❛❞❡✐❛s ❛❧✐♠❡♥t❛r❡s ✭▼♦♥t♦②❛ ✫ ❙♦❧é✱ ✷✵✵✷✮✱ ❝❛❞❡✐❛s ❞❡ ✐♥t❡r❛çõ❡s ♠❡t❛❜ó❧✐❝❛s ✭❏❡♦♥❣ ❡t ❛❧✳✱ ✷✵✵✵✮✱ ♦ s✐st❡♠❛ ❞❡ ❞✐str✐❜✉✐çã♦ ❞❛ ❝♦rr❡♥t❡ s❛♥❣✉í✲ ♥❡❛ ✭❲❡st ❡t ❛❧✳✱ ✶✾✾✾✮✱ r❡❞❡s ♥❡✉r❛✐s ❜✐♦❧ó❣✐❝❛s ✭❙♣♦♥rs✱ ✷✵✵✷✮✱ ❡♥tr❡ ♦✉tr❛s✱ tê♠ s✐❞♦ ❡st✉❞❛❞❛s s♦❜ ❡ss❛ ❛❜♦r❞❛❣❡♠ ❞✐❢❡r❡♥❝✐❛❞❛✳ Pr♦♣r✐❡❞❛❞❡s tr✐✈✐❛✐s ❡ s♦❧✉çõ❡s ❡①❛t❛s tê♠ ❞❡✐①❛❞♦ ❞❡ s❡r ♦ ❛❧✈♦✱ ♣❛r❛ ❞❛r ❧✉❣❛r ❛ ♣r♦♣r✐❡❞❛❞❡s ❝♦♠♣❧❡①❛s ❡ s♦❧✉çõ❡s ❛♣r♦①✐♠❛❞❛s ✭◆❡✇♠❛♥ ❡t ❛❧✳✱ ✷✵✵✻✮✳ ❆s r❡❞❡s ❝♦♠♣❧❡①❛s tê♠ s❡ ♠♦str❛❞♦ ✉♠❛ ♣♦❞❡r♦s❛ ♠❛♥❡✐r❛ ❞❡ r❡♣r❡s❡♥t❛çã♦ ❡ ❛❜str❛çã♦ ❞❡ ❞❛❞♦s✱ ❝♦♥st✐t✉✐♥❞♦ ✉♠ tó♣✐❝♦ ✉♥✐✜❝❛❞♦r ❡♠ s✐st❡♠❛s ❝♦♠✲ ♣❧❡①♦s✱ ♣r❡s❡♥t❡ ❡♠ ♣r❛t✐❝❛♠❡♥t❡ t♦❞♦s ♦s r❛♠♦s ❞❛ ❝✐ê♥❝✐❛✱ ❡ ♠✉❞❛♥❞♦ ❛ ♠❛♥❡✐r❛ ❝♦♠ q✉❡ ✈ár✐♦s s✐st❡♠❛s ✐♥t❡r❝♦♥❡❝t❛❞♦s sã♦ ♠♦❞❡❧❛❞♦s ✭❇♦r♥❤♦❧❞t ✫ ❙❝❤✉st❡r✱ ✷✵✵✸✮✳
❙❡❣✉♥❞♦ ❈♦st❛ ❡t ❛❧✳ ✭✷✵✵✼✮✱ três tó♣✐❝♦s tê♠ s✐❞♦ ♦s ♣r✐♥❝✐♣❛✐s r❡s♣♦♥sá✈❡✐s ♣❡❧♦ ❛✈❛♥ç♦ ❞♦s ❡st✉❞♦s ❡♠ ❘❡❞❡s ❈♦♠♣❧❡①❛s✿ ♦ ❡❢❡✐t♦ ❞❡ ♣❡q✉❡♥♦ ♠✉♥❞♦ ✭❲❛tts ✫ ❙tr♦❣❛t③✱ ✶✾✾✽✮✱ ❛ ❞✐str✐❜✉✐çã♦ ❧✐✈r❡ ❞❡ ❡s❝❛❧❛ ✭❇❛r❛❜ás✐ ✫ ❆❧❜❡rt✱ ✶✾✾✾✮✱ ❡ ❛s ❡str✉t✉r❛ ❞❡ ❝♦♠✉✲ ♥✐❞❛❞❡s ✭●✐r✈❛♥ ✫ ◆❡✇♠❛♥✱ ✷✵✵✷✮✳ ❚r❛❞✐❝✐♦♥❛❧♠❡♥t❡ ❛s r❡❞❡s ❝♦♠♣❧❡①❛s ❡r❛♠ ❞❡s❝r✐t❛s ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ♠♦❞❡❧♦ ❞❡ ❊r❞ös ✫ ❘é♥②✐ ✭✶✾✺✾✮✱ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ●r❛❢♦s ❘❛♥❞ô♠✐❝♦s ♦✉ ❘❡❞❡s ❘❛♥❞ô♠✐❝❛s✳ ◆♦ ❡♥t❛♥t♦✱ ❲❛tts ✫ ❙tr♦❣❛t③ ✭✶✾✾✽✮ ❞❡s❝♦❜r✐r❛♠ q✉❡ ❛ ♠❡❞✐❛ ❞❡ ❝❛♠✐♥❤♦s ♠❛✐s ❝✉rt♦s ❡♠ ✉♠❛ r❡❞❡ ♣♦❞❡ s❡r ❞r❛st✐❝❛♠❡♥t❡ r❡❞✉③✐❞❛ ♣♦r ❛❧t❡r❛çã♦ ❛❧❡❛✲ tór✐❛ ❞❡ ♣♦✉❝❛s ❧✐❣❛çõ❡s ❡♠ ✉♠❛ r❡❞❡ r❡❣✉❧❛r✳ ❆ r❡❞❡ r❡s✉❧t❛♥t❡ ❢♦✐ ❞❡♥♦♠✐♥❛❞❛ ❘❡❞❡ ❞❡ P❡q✉❡♥♦ ▼✉♥❞♦✳ ❊♠ ✶✾✾✾✱ ❇❛r❛❜ás✐ ✫ ❆❧❜❡rt ✭✶✾✾✾✮ ❞❡s❝♦❜r✐r❛♠ q✉❡ ♠✉✐t❛s ❞❛s r❡❞❡s r❡❛✐s tê♠ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❣r❛✉ ❞♦s ♥ós q✉❡ ♦❜❡❞❡❝❡ ❛ ❧❡✐ ❞❡ ♣♦tê♥❝✐❛✿ P(k)∼kγ✱ ♦♥❞❡k é
♦ ♥ú♠❡r♦ ❞❡ ❝♦♥❡①õ❡s ❞❡ ✉♠ ♥ó ❡s❝♦❧❤✐❞♦ ❛❧❡❛t♦r✐❛♠❡♥t❡ ❡γ ♦ ❡①♣♦❡♥t❡ ❞❡ ❡s❝❛❧❛✳ ❖ q✉❡
s✐❣♥✐✜❝❛ q✉❡ ❡①✐st❡ ✉♠ ♣❡q✉❡♥♦ ❝♦♥❥✉♥t♦ ❞❡ ♥ós q✉❡ ♣♦ss✉✐ ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ ❧✐❣❛çõ❡s ✭❤✉❜s✮ ❡ ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ ♥ós ❝♦♠ ♣♦✉❝❛s ❧✐❣❛çõ❡s✳ ❊st❛s r❡❞❡s sã♦ ❞❡♥♦♠✐♥❛❞❛s ❘❡❞❡s ▲✐✈r❡ ❞❡ ❊s❝❛❧❛✳ ❊♠ ✷✵✵✷✱ ●✐r✈❛♥ ✫ ◆❡✇♠❛♥ ✭✷✵✵✷✮ r❡✈❡❧❛r❛♠ q✉❡ ❡♠ ♠✉✐t❛s r❡❞❡s r❡❛✐s✱ ❡①✐st❡♠ ❝♦♥❥✉♥t♦s ❞❡ ♥ós ❞❡♥s❛♠❡♥t❡ ❝♦♥❡❝t❛❞♦s ❡♥tr❡ s✐✱ ❝✉❥❛s ❧✐❣❛çõ❡s ❝♦♠ ♥ós ❞❡ ❢♦r❛ ❞♦ ❣r✉♣♦ sã♦ ❡s♣❛rs❛s✳ ❊ss❛s ❡str✉t✉r❛s ❢♦r❛♠ ❞❡♥♦♠✐♥❛❞❛s ❝♦♠✉♥✐❞❛❞❡s✳ ❉❡s❞❡ ❡♥tã♦✱ ♠✉✐t❛s ♣❡sq✉✐s❛s tê♠ s✐❞♦ ❝♦♥❞✉③✐❞❛s ❡♠ ❘❡❞❡s ❈♦♠♣❧❡①❛s✱ t♦r♥❛♥❞♦✲♥❛ ✉♠❛ ár❡❛ ❞❡ ♣❡sq✉✐s❛ ❜❡♠ ❞❡✜♥✐❞❛✳ ❈♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛✱ ✉♠ ❣r❛♥❞❡ ♠♦♥t❛♥t❡ ❞❡ r❡✲ s✉❧t❛❞♦s ❞❡ ♣❡sq✉✐s❛ tê♠ s✐❞♦ r❡♣♦rt❛❞♦s✱ ❡s♣❡❝✐❛❧♠❡♥t❡ r❡❧❛❝✐♦♥❛❞♦s às ❡str✉t✉r❛s ❞❡ ❝♦♠✉♥✐❞❛❞❡s✱ ❝r❡s❝✐♠❡♥t♦ ❡ ❛✉t♦✲♦r❣❛♥✐③❛çã♦ ❞❛s r❡❞❡s✱ ❞✐str✐❜✉✐çã♦ ❞❡ ❣r❛✉✱ r❡s✐❧✐ê♥❝✐❛✱ ♣r♦❝❡ss♦s ❡♣✐❞❡♠✐♦❧ó❣✐❝♦s✱ s✐♥❝r♦♥✐③❛çã♦✱ ❡ ♦✉tr♦s ✭❆❧❜❡rt ✫ ❇❛r❛❜ás✐✱ ✷✵✵✷❀ ◆❡✇♠❛♥✱
✷✵✵✸❀ ❈♦st❛ ❡t ❛❧✳✱ ✷✵✵✼✮✳ ❊♥tr❡t❛♥t♦✱ ♣♦✉❝♦ t❡♠ s✐❞♦ ❡st✉❞❛❞♦ ❛❝❡r❝❛ ❞❡ ♦✉t❧✐❡rs ❡♠ r❡❞❡s ❝♦♠♣❧❡①❛s ✭❈♦st❛ ❡t ❛❧✳✱ ✷✵✵✾✮✳
❚r❛❞✐❝✐♦♥❛❧♠❡♥t❡ ❛ss✉♠✐✲s❡ q✉❡ ❞✐str✐❜✉✐çõ❡s ❞❡ ❞❛❞♦s sã♦ t✐♣✐✜❝❛❞❛s ♣♦r ✉♠❛ ❞✐s✲ tr✐❜✉✐çã♦ ♥♦r♠❛❧ ✭❉❛✈✐❡s ✫ ●❛t❤❡r✱ ✶✾✾✸✮✳ ❊♥tr❡t❛♥t♦✱ ❛s r❡❞❡s ❧✐✈r❡s ❞❡ ❡s❝❛❧❛ tê♠ ♠♦str❛❞♦ q✉❡ ❡ss❛ ❛❜♦r❞❛❣❡♠ ♥❡♠ s❡♠♣r❡ é ✈❡r❞❛❞❡✐r❛✳ ❊♠ ✉♠❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧✱ ♦❜s❡r✈❛çõ❡s ♦✉t❧✐❡rs sã♦ ❛q✉❡❧❛s q✉❡ ❞❡s✈✐❛♠✲s❡ ❞❛ ♠é❞✐❛✱ ❡ ❡stã♦ ❡♠ r❡❣✐õ❡s ❝♦♠ ❞❡s✈✐♦ s✉♣❡r✐♦r ❛♦ ❞❡s✈✐♦ ♣❛❞rã♦✳ ❊♠ ✉♠❛ r❡❞❡ ❧✐✈r❡ ❞❡ ❡s❝❛❧❛✱ s❡ ❝♦♥s✐❞❡r❛r♠♦s ❛ ❝♦♥❡❝t✐✈✐❞❛❞❡ ❞♦s ♥ós ❡ ♦ ❞❡s✈✐♦ ♣❛❞rã♦✱ ♦s ❤✉❜s ♣♦❞❡♠ s❡r ❞❡♥♦♠✐♥❛❞♦s ♦✉t❧✐❡rs✱ ✉♠❛ ✈❡③ q✉❡ s✉❛ ❝♦♥❡❝t✐✈✐❞❛❞❡ ❞❡s✈✐❛✲s❡ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ❞❛ ❝♦♥❡❝t✐✈✐❞❛❞❡ ❞♦s ❞❡♠❛✐s ♥ós✳ P♦ré♠✱ ♦ ❢❛t♦r ❞❡t❡r♠✐♥❛♥t❡ ♣❛r❛ ❡ss❛ ❝❧❛ss✐✜❝❛çã♦ é q✉❡ ❡♠ r❡❞❡s ❧✐✈r❡ ❞❡ ❡s❝❛❧❛ ❤✉❜s sã♦ ♠❡♥♦s ❢r❡q✉❡♥t❡s q✉❡ ♦s ❞❡♠❛✐s ♥ós✳
❖ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛ é ✉♠❛ ár❡❛ ❞❛ ❝✐ê♥❝✐❛ ❞❛ ❝♦♠♣✉t❛çã♦ q✉❡ ✈✐s❛ ❞❡s❡♥✲ ✈♦❧✈❡r ♠ét♦❞♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❝❛♣❛③❡s ❞❡ ✏❛♣r❡♥❞❡r✑ ❛tr❛✈és ❞❛ ❡①♣❡r✐❡♥❝✐❛ ✭▼✐t❝❤❡❧❧✱ ✶✾✾✼❀ ❇✐s❤♦♣✱ ✷✵✵✻✮✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❞❡ rót✉❧♦s✱ ♦ ♣r♦❝❡ss♦ ❞❡ ❛♣r❡♥✲ ❞✐③❛❞♦ ♣♦❞❡ s❡r ❝❧❛ss✐✜❝❛❞♦ ❝♦♠♦ s✉♣❡r✈✐s✐♦♥❛❞♦✱ ♥ã♦✲s✉♣❡r✈✐s✐♦♥❛❞♦✱ ♦✉ ❛✐♥❞❛ s❡♠✐✲ s✉♣❡r✈✐s✐♦♥❛❞♦✳ ◆♦ ❛♣r❡♥❞✐③❛❞♦ s✉♣❡r✈✐s✐♦♥❛❞♦✱ ♦ ♦❜❥❡t✐✈♦ é ✐♥❞✉③✐r ❝♦♥❝❡✐t♦s ❛ ♣❛rt✐r ❞❡ ❡①❡♠♣❧♦s r♦t✉❧❛❞♦s ❝♦♠ ✉♠❛ ❝❧❛ss❡ ❝♦♥❤❡❝✐❞❛✳ ❖ ♣r♦❝❡ss♦ ❞❡ ❛♣r❡♥❞✐③❛❣❡♠ ✈✐s❛ ❛ ❝♦♥str✉çã♦ ❞❡ ✉♠❛ ❢✉♥çã♦ ❞❡ ♠❛♣❡❛♠❡♥t♦ ❡♥tr❛❞❛✲s❛í❞❛ ❝♦♠ ❜❛s❡ ♥❛ ♦❜s❡r✈❛çã♦ ❞♦s ❞❛✲ ❞♦s ❞❡ tr❡✐♥❛♠❡♥t♦ ❢♦r♥❡❝✐❞♦s✳ ◆♦ ❛♣r❡♥❞✐③❛❞♦ ♥ã♦✲s✉♣❡r✈✐s✐♦♥❛❞♦✱ ♦ ♦❜❥❡t✐✈♦ é ❛❣r✉♣❛r ♦s ❞❛❞♦s s❡❣✉♥❞♦ ❛❧❣✉♠ ❝r✐tér✐♦ ❞❡ s✐♠✐❧❛r✐❞❛❞❡ ❡♥tr❡ ❡❧❡s✳ ❖ ♣r♦❝❡ss♦ ❞❡ ❛♣r❡♥❞✐③❛❣❡♠ é ❞✐t♦ ❣✉✐❛❞♦ ♣❡❧♦s ❞❛❞♦s✳ ❖ ❛♣r❡♥❞✐③❛❞♦ s❡♠✐✲s✉♣❡r✈✐s✐♦♥❛❞♦ ❝♦♥st✐t✉✐ ✉♠ ♠❡✐♦ t❡r♠♦ ❡♥tr❡ ❛ ❛❜♦r❞❛❣❡♠ s✉♣❡r✈✐s✐♦♥❛❞❛ ❡ ♥ã♦✲s✉♣❡r✈✐s✐♦♥❛❞❛✳ ◆❡ss❡ ❝❛s♦✱ ♣♦✉❝♦s ♥ós sã♦ r♦✲ t✉❧❛❞♦s ❛ ♣r✐♦r✐✱ ❡ ♦ ♦❜❥❡t✐✈♦ é r♦t✉❧❛r ♦s ❞❡♠❛✐s ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ rót✉❧♦ ❞♦s ♣r✐♠❡✐r♦s✳ P♦❞❡✲s❡ ❞✐③❡r q✉❡ ♦s ❡①❡♠♣❧♦s r♦t✉❧❛❞♦s ❛ ♣r✐♦r✐ sã♦ r❡s♣♦♥sá✈❡✐s ♣♦r ❣✉✐❛r ♦ ♣r♦❝❡ss♦ ❞❡ ❛❣r✉♣❛♠❡♥t♦ ❞♦s ❞❛❞♦s ✭❈❤❛♣❡❧❧❡ ❡t ❛❧✳✱ ✷✵✵✻✮✳
❯♠❛ ✈❡③ q✉❡ ❛s ❡str✉t✉r❛s ❞❡ ❝♦♠✉♥✐❞❛❞❡s r❡♣r❡s❡♥t❛♠ ♣❛❞rõ❡s ❞❡ ✐♥t❡r❛çã♦ ❜❡♠ ❞❡✲ ✜♥✐❞♦s ❡♥tr❡ ♥ós ❞❡ ✉♠❛ r❡❞❡✱ s✉❛ ✐❞❡♥t✐✜❝❛çã♦ é ♠✉✐t♦ ✐♠♣♦rt❛♥t❡ ♣❛r❛ ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❝r❡s❝✐♠❡♥t♦ ❡ ❢♦r♠❛çã♦ ❞❛s r❡❞❡s ✭❉❛♥♦♥ ❡t ❛❧✳✱ ✷✵✵✺✮✳ P♦r ✐ss♦✱ ❞✐✈❡r✲ s♦s ♠ét♦❞♦s tê♠ s✐❞♦ ♣r♦♣♦st♦s ♥❡ss❡ s❡♥t✐❞♦ ✭❩❤♦✉✱ ✷✵✵✸❜✱❛❀ ◆❡✇♠❛♥ ✫ ●✐r✈❛♥✱ ✷✵✵✹❀ ◆❡✇♠❛♥✱ ✷✵✵✹❜✱ ✷✵✵✻❀ ◗✉✐❧❡s ❡t ❛❧✳✱ ✷✵✵✽✮✳ ❉♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❞♦ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛✱ ❡ss❡s ♠ét♦❞♦s ♣♦❞❡♠ s❡r ❝❧❛ss✐✜❝❛❞♦s ❝♦♠♦ ♥ã♦✲s✉♣❡r✈✐s✐♦♥❛❞♦s✳ ◆♦ s❡♥t✐❞♦ ❞❡ ❛✉♠❡♥t❛r ❛ ❡✜❝✐ê♥❝✐❛ ❡ ❡✜❝á❝✐❛ ❞❡ss❡s ♠ét♦❞♦s✱ ❛❧❣✉♥s ♠ét♦❞♦s tê♠ s✐❞♦ ♣r♦♣♦st♦s r❡❝❡♥t❡♠❡♥t❡ s♦❜ ♦ ♣❛r❛❞✐❣♠❛ s❡♠✐✲s✉♣❡r✈✐s✐♦♥❛❞♦ ✭❆❧❧❛❤✈❡r❞②❛♥ ❡t ❛❧✳✱ ✷✵✶✵❀ ▼❛ ❡t ❛❧✳✱ ✷✵✶✵❀ ❇r❡✈❡ ❡t ❛❧✳✱ ✷✵✵✾✮✳ ❊ss❛ ❛❜♦r❞❛❣❡♠ é ♠✉✐t♦ ✐♥t❡r❡ss❛♥t❡✱ ♣♦✐s✱ ❡♠❜♦r❛ ♥ã♦ s❡ ❝♦♥❤❡ç❛ ♦ rót✉❧♦ ❞❡ t♦❞♦s ♦s ✐♥❞✐✈í❞✉♦s ❡♠ ✉♠❛ r❡❞❡✱ ❡①✐st❡♠ ✐♥❞✐✈í❞✉♦s ❜❛st❛♥t❡ r❡♣r❡s❡♥t❛t✐✈♦s q✉❡ ♣♦s✲ s✉❡♠ rót✉❧♦ ❜❡♠ ❞❡✜♥✐❞♦✳ ❉♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❞❡ r❡❞❡s ❞❡ ✐♥t❡r❛çõ❡s s♦❝✐❛✐s✱ é ♦ ❝❛s♦ ❞❡ ❧í❞❡r❡s ❝♦♠✉♥✐tár✐♦s✱ r❡s♣♦♥sá✈❡✐s ♣♦r r❡♣r❡s❡♥t❛r s✉❛ ❝♦♠✉♥✐❞❛❞❡✳ ❈♦♥t✉❞♦✱ ♣♦✉❝♦ t❡♠ s✐❞♦ ❡st✉❞❛❞♦ ❛❝❡r❝❛ ❞❛ r❡❧❡✈â♥❝✐❛ ❞♦s ✐♥❞✐✈í❞✉♦s r♦t✉❧❛❞♦s ❛ ♣r✐♦r✐ ♣❛r❛ ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦s ♠ét♦❞♦s ❞❡ ❞❡t❡❝çã♦ ❞❡ ❝♦♠✉♥✐❞❛❞❡s s❡♠✐✲s✉♣❡r✈✐s✐♦♥❛❞♦s✳
1.2 Objetivo
❖ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦✱ t❡♠ ❝♦♠♦ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t✐✈♦ ❡①♣❧♦r❛r ♦ tó♣✐❝♦ ❞❡t❡❝çã♦ ❞❡ ♦✉✲ t❧✐❡rs ❡♠ r❡❞❡s ❝♦♠♣❧❡①❛s✳ ❈♦♥s✐❞❡r❛♥❞♦✲s❡ ❛ ❞✐♥â♠✐❝❛ ❞❡ ✉♠❛ ❝❛♠✐♥❤❛❞❛ ❛❧❡❛tór✐❛✱ ❢♦✐ ♣r♦♣♦st❛ ✉♠❛ ♠❡❞✐❞❛ ❞❡ ❞✐stâ♥❝✐❛✱ ❛tr❛✈és ❞❛ q✉❛❧ ❢♦✐ ♣♦ssí✈❡❧ ✐❞❡♥t✐✜❝❛r ♦s ♥ós ♦✉t❧✐✲ ❡rs ❡♠ ✉♠❛ r❡❞❡✳ ❊ss❛ ♠❡❞✐❞❛ ❢♦✐ ❛♣❧✐❝❛❞❛ ❡♠ ❞✐✈❡rs❛s r❡❞❡s✱ ❞❡ ♠♦❞♦ q✉❡ ❢♦✐ ♣♦ssí✈❡❧ ✐❞❡♥t✐✜❝❛r q✉❡ ❡①✐st❡♠ ❝❛r❛❝t❡ríst✐❝❛s ❜❡♠ ❞❡✜♥✐❞❛s ♥♦s ♥ós ✐❞❡♥t✐✜❝❛❞♦s ❝♦♠♦ ♦✉t❧✐❡r✱ r❡❧❛❝✐♦♥❛❞❛s ♥ã♦ ❛♣❡♥❛s ❛ ❡str✉t✉r❛ ❞♦s ♥ós ❞❛ r❡❞❡✱ ❝♦♠♦ t❛♠❜é♠ ❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡ ❞♦s ♠❡s♠♦s ♣❛r❛ ♦ s✐st❡♠❛ ❝♦♠♣❧❡①♦✳ ❚❛♠❜é♠✱ ❝♦♠ ❜❛s❡ ♥❛ ♠❡❞✐❞❛ ❞❡ ❞✐stâ♥❝✐❛ ❞❡ ✉♠❛ ❝❛♠✐♥❤❛❞❛ ❛❧❡❛tór✐❛✱ ♣✉❞❡♠♦s ✐❞❡♥t✐✜❝❛r q✉❡ ♥ós ♦✉t❧✐❡rs sã♦ ❜♦♥s ❝❛♥❞✐❞❛t♦s ❛ r♦t✉❧❛çã♦ ❛ ♣r✐♦r✐ ♣❛r❛ ❛ t❛r❡❢❛ ❞❡ ❞❡t❡❝çã♦ ❞❡ ❝♦♠✉♥✐❞❛❞❡s s❡♠✐✲s✉♣❡r✈✐s✐♦♥❛❞❛✱ s❡♥❞♦ ❡❧❡♠❡♥t♦s r❡♣r❡s❡♥t❛t✐✈♦s ❞❡ s✉❛s ❝♦♠✉♥✐❞❛❞❡s✳ ❆❞✐❝✐♦♥❛❧♠❡♥t❡✱ s❡rá ❛♣r❡s❡♥t❛❞♦ ✉♠ ♠ét♦❞♦ ❜✐✲ ♦✐♥s♣✐r❛❞♦ ❞❡ ❞❡t❡❝çã♦ ❞❡ ❝♦♠✉♥✐❞❛❞❡s s❡♠✐✲s✉♣❡r✈✐s✐♦♥❛❞❛✳ ❊ss❡ ♠ét♦❞♦ ❢♦✐ ✉t✐❧✐③❛❞♦ ♣❛r❛ ✈❡r✐✜❝❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❞❛ ❞❡t❡❝çã♦ ❞❡ ❝♦♠✉♥✐❞❛❞❡s s❡♠✐✲s✉♣❡r✈✐s✐♦♥❛❞❛ ❝♦♠ r❡❧❛çã♦ ❛♦s ♥ós r♦t✉❧❛❞♦s ❛ ♣r✐♦r✐✳
1.3 Organização do Documento
❖ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ✐rá ♠♦str❛r ❛ ❛♣❧✐❝❛çã♦ ❞❛ ❝❛♠✐♥❤❛❞❛ ❛❧❡❛tór✐❛ ♣❛r❛ ❛ ❞❡t❡❝çã♦ ❞❡ ♦✉t❧✐❡rs ❡♠ r❡❞❡s✱ ❝♦♠♦ t❛♠❜é♠ ♣❛r❛ ❛ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ ❝❛♥❞✐❞❛t♦s ❛ r♦t✉❧❛çã♦ ❛ ♣r✐♦r✐ ♣❛r❛ ❛ ❞❡t❡❝çã♦ ❞❡ ❝♦♠✉♥✐❞❛❞❡s s❡♠✐✲s✉♣❡r✈✐s✐♦♥❛❞❛✳ P❛r❛ ✐ss♦✱ ♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ❡stá ♦r❣❛♥✐③❛❞♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ ❖ ❈❛♣ít✉❧♦ ✷ ❛♣r❡s❡♥t❛ ✉♠❛ r❡✈✐sã♦ s♦❜r❡ ♦ t❡♠❛ ❞❡t❡❝çã♦ ❞❡ ♦✉t❧✐❡rs✳ ❖ ❈❛♣ít✉❧♦ ✸ ❛♣r❡s❡♥t❛ ✉♠❛ r❡✈✐sã♦ s♦❜r❡ ♦s t❡♠❛s r❡❞❡s ❝♦♠♣❧❡①❛s ❡ ❞❡t❡❝çã♦ ❞❡ ❝♦♠✉♥✐❞❛❞❡s✳ ❖ ❈❛♣ít✉❧♦ ✹ ❛♣r❡s❡♥t❛ ✉♠ ♠ét♦❞♦ ❜❛s❡❛❞♦ ❡♠ ❝❛♠✐♥❤❛❞❛ ❛❧❡❛tór✐❛ ♣r♦♣♦st♦ ♣❛r❛ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ ♦✉t❧✐❡rs ❡♠ r❡❞❡s✱ r❡s✉❧t❛❞♦s ♦❜t✐❞♦s✱ ✉♠ ♠ét♦❞♦ s❡♠✐✲ s✉♣❡r✈✐s✐♦♥❛❞♦ ♣r♦♣♦st♦ ♣❛r❛ ❛ ❞❡t❡❝çã♦ ❞❡ ❝♦♠✉♥✐❞❛❞❡s✱ ❡ ✉♠❛ ❛♥á❧✐s❡ s♦❜r❡ ❛ r♦t✉❧❛çã♦ ❛ ♣r✐♦r✐ ❞❡ ♦✉t❧✐❡rs ♣❛r❛ ❛ t❛r❡❢❛ ❞❡ ❞❡t❡❝çã♦ ❞❡ ❝♦♠✉♥✐❞❛❞❡s s❡♠✐✲s✉♣❡r✈✐s✐♦♥❛❞❛✳ P♦r ✜♠✱ é ❛♣r❡s❡♥t❛❞♦ ♥♦ ❈❛♣ít✉❧♦ ✺ ❛s ♣r✐♥❝✐♣❛✐s ❝♦♥❝❧✉sõ❡s ❞♦ tr❛❜❛❧❤♦ ❡ ♣❡rs♣❡❝t✐✈❛s ❞❡ tr❛❜❛❧❤♦s ❢✉t✉r♦s✳
