❯▼❆ ❊❙❚❘❆❚➱●■❆ ❍❮❇❘■❉❆ P❆❘❆ ❖
P❘❖❇▲❊▼❆ ❉❊ ❈▲❆❙❙■❋■❈❆➬➹❖
❚■❆●❖ ❆▼❆❉❖❘ ❈❖❊▲❍❖
❯▼❆ ❊❙❚❘❆❚➱●■❆ ❍❮❇❘■❉❆ P❆❘❆ ❖
P❘❖❇▲❊▼❆ ❉❊ ❈▲❆❙❙■❋■❈❆➬➹❖
▼❯▲❚■❘❘Ó❚❯▲❖
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❞♦ ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❞❛ ❯♥✐✈❡r✲ s✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s ❝♦♠♦ r❡✲ q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳
❖r✐❡♥t❛❞♦r✿ ❲❛❣♥❡r ▼❡✐r❛ ❏ú♥✐♦r
❈♦✲♦r✐❡♥t❛❞♦r✿ ❆❤♠❡❞ ❆❧✐ ❆❜❞❛❧❧❛ ❊s♠✐♥
❝
✷✵✶✶✱ ❚✐❛❣♦ ❆♠❛❞♦r ❈♦❡❧❤♦✳
❚♦❞♦s ♦s ❞✐r❡✐t♦s r❡s❡r✈❛❞♦s✳
❈♦❡❧❤♦✱ ❚✐❛❣♦ ❆♠❛❞♦r
❈✻✼✷❡ ❯♠❛ ❡str❛té❣✐❛ ❤í❜r✐❞❛ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡
❝❧❛ss✐✜❝❛çã♦ ♠✉❧t✐rrót✉❧♦ ✴ ❚✐❛❣♦ ❆♠❛❞♦r ❈♦❡❧❤♦✳ ✖ ❇❡❧♦ ❍♦r✐③♦♥t❡✱ ✷✵✶✶
①✈✐✱ ✺✾ ❢✳ ✿ ✐❧✳ ❀ ✷✾❝♠
❉✐ss❡rt❛çã♦ ✭♠❡str❛❞♦✮ ✖ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s
❖r✐❡♥t❛❞♦r✿ ❲❛❣♥❡r ▼❡✐r❛ ❏ú♥✐♦r
❈♦✲♦r✐❡♥t❛❞♦r✿ ❆❤♠❡❞ ❆❧✐ ❆❜❞❛❧❧❛ ❊s♠✐♥
✶✳ ❈♦♠♣✉t❛çã♦ ✲ ❚❡s❡s✳ ✷✳ ▼✐♥❡r❛çã♦ ❞❡ ❞❛❞♦s ✭❝♦♠♣✉t❛çã♦✮ ✲ ❚❡s❡s✳ ✸✳ ❙✐st❡♠❛s ❞❡ ❘❡❝✉♣❡r❛çã♦ ❞❛ ✐♥❢♦r♠❛çã♦✭❈♦♠♣✉t❛çã♦✮ ✲ ❚❡s❡s✳ ■✳ ❖r✐❡♥t❛❞♦r✳ ■■✳ ❈♦♦r✐❡♥t❛❞♦r✳ ■■■✳ ❚ít✉❧♦✳
❘❡s✉♠♦
❊st❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ ✉♠ ♥♦✈♦ ♠ét♦❞♦ ♣❛r❛ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ♠✉❧✲ t✐rrót✉❧♦✱ ❜❛s❡❛❞♦ ♥♦ ♠ét♦❞♦ ❞❡ ❡♥①❛♠❡ ❞❡ ♣❛rtí❝✉❧❛s✱ ❝❤❛♠❛❞♦ ▼✉❧t✐ ▲❛❜❡❧ ❑✲◆❡❛r❡st ▼✐❝❤✐❣❛♠ P❛rt✐❝❧❡ ❙✇❛r♠ ❖♣t✐♠✐③❛t✐♦♥ ✭▼▲✲❑▼P❙❖✮✱ q✉❡ ❢♦✐ ❛✈❛❧✐❛❞♦ ✉t✐❧✐③❛♥❞♦✲s❡ ❞✉❛s ❜❛s❡s ❞❡ ❞❛❞♦s r❡❛✐s✳ ❆ ❛♣r❡♥❞✐③❛❣❡♠ ♠✉❧t✐rrót✉❧♦ s❡ ♦r✐❣✐♥♦✉ ♥❛ ❝❛t❡❣♦r✐③❛✲ çã♦ ❞❡ t❡①t♦s✱ ♦♥❞❡ ❝❛❞❛ ❞♦❝✉♠❡♥t♦ ♣♦❞❡ ♣❡rt❡♥❝❡r ❛ ✈ár✐❛s ❝❧❛ss❡s s✐♠✉❧t❛♥❡❛♠❡♥t❡✳ ◆❡st❡ tr❛❜❛❧❤♦ é ♣r♦♣♦st❛ ✉♠❛ ♥♦✈❛ ❛❜♦r❞❛❣❡♠ ❤í❜r✐❞❛✱ ♥❛ q✉❛❧ ♦ ▼▲✲❑▼P❙❖ s❡ ❡♥q✉❛❞r❛✳ ❊st❛ ❛❜♦r❞❛❣❡♠ é ❜❛s❡❛❞❛ ❡♠ ❞✉❛s ❡str❛té❣✐❛s✳ ❆ ♣r✐♠❡✐r❛ ❡str❛té❣✐❛ é ❛ ❞✐✈✐sã♦ ❞♦ ♣r♦❜❧❡♠❛ ♠✉❧t✐rrót✉❧♦ ❡♠ ❞✐✈❡rs♦s ♣r♦❜❧❡♠❛s ❜✐♥ár✐♦s✱ s❡♥❞♦ q✉❡ ♣❛r❛ t❛❧ ❢♦✐ ✉t✐❧✐③❛❞♦ ♦ ▼✐❝❤✐❣❛♥ P❛rt✐❝❧❡ ❙✇❛r♠ ❖♣t✐♠✐③❛t✐♦♥ ✭▼P❙❖✮ ♣❛r❛ r❡s♦❧✈ê✲❧♦s✱ ♣♦ré♠✱ ❡st❛ ❡str❛té❣✐❛ ♥ã♦ ❧❡✈❛ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ❛s ❝♦rr❡❧❛çõ❡s ❡①✐st❡♥t❡s ❡♥tr❡ ❛s ❝❧❛ss❡s✳ ❏á ❛ s❡❣✉♥❞❛ ❡str❛té❣✐❛ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❝♦♥s✐❞❡r❛r ❛s ❝♦rr❡❧❛çõ❡s ❡①✐st❡♥t❡s ❡♥tr❡ ❛s ❝❧❛ss❡s ✉t✐❧✐③❛♥❞♦ ♦ ▼✉❧t✐ ▲❛❜❡❧ ❑✲◆❡❛r❡st ◆❡✐❣❤❜♦r ✭▼▲✲❑◆◆✮✳ ❆✈❛❧✐❛♠♦s ❛ ♣❡r❢♦r✲ ♠❛♥❝❡ ❞♦ ▼▲✲❑▼P❙❖ ✉t✐❧✐③❛♥❞♦ ❛ ❜❛s❡ ❨❡❛st ✭❝❧❛ss✐✜❝❛çã♦ ❢✉♥❝✐♦♥❛❧ ❞❡ ❣❡♥❡s✮ ❡ ❛ ❜❛s❡ ❙❝❡♥❡ ✭❝❧❛ss✐✜❝❛çã♦ s❡♠â♥t✐❝❛ ❞❡ ❝❡♥❛s✮✳ ❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❡❧♦ ▼▲✲❑▼P❙❖ s❡ ✐❣✉❛❧❛♠ ♦✉ s✉♣❡r❛♠ ❛❧❣♦r✐t♠♦s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ♠✉❧t✐rrót✉❧♦ ❞♦ ❡st❛❞♦ ❞❛ ❛rt❡✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❈❧❛ss✐✜❝❛çã♦ ▼✉❧t✐rrót✉❧♦✱ ▼ét♦❞♦ ❞❡ ❊♥①❛♠❡ ❞❡ P❛rtí❝✉❧❛s✱ ▼✐♥❡✲ r❛çã♦ ❞❡ ❉❛❞♦s✳
❆❜str❛❝t
❚❤✐s ✇♦r❦ ♣r❡s❡♥ts ❛ ♥❡✇ ♠❡t❤♦❞ ❢♦r ♠✉❧t✐✲❧❛❜❡❧ ❝❧❛ss✐✜❝❛t✐♦♥ ❜❛s❡❞ ♦♥ P❛rt✐❝❧❡ ❙✇❛r♠ ❖♣t✐♠✐③❛t✐♦♥✱ ❝❛❧❧❡❞ ▼✉❧t✐ ▲❛❜❡❧ ❑✲◆❡❛r❡st ▼✐❝❤✐❣❛♥ P❛rt✐❝❧❡ ❙✇❛r♠ ❖♣t✐♠✐③❛t✐♦♥ ✭▼▲✲❑▼P❙❖✮ ❛♥❞ ❡✈❛❧✉❛t❡s ✐t ❡①♣❡r✐♠❡♥t❛❧❧② ✉s✐♥❣ t✇♦ r❡❛❧✲✇♦r❧❞ ❞❛t❛s❡ts✳ ▼✉❧t✐✲ ❧❛❜❡❧ ❧❡❛r♥✐♥❣ ✜rst ❛r♦s❡ ✐♥ t❤❡ ❝♦♥t❡①t ♦❢ t❡①t ❝❛t❡❣♦r✐③❛t✐♦♥✱ ✇❤❡r❡ ❡❛❝❤ ❞♦❝✉♠❡♥t ♠❛② ❜❡❧♦♥❣ t♦ s❡✈❡r❛❧ ❝❧❛ss❡s s✐♠✉❧t❛♥❡♦✉s❧②✳ ■♥ t❤✐s ✇♦r❦✱ ✇❡ ♣r♦♣♦s❡ ❛ ♥❡✇ ❤②❜r✐❞ ❛♣♣r♦❛❝❤✱ ▼▲✲❑▼P❙❖✳ ■t ✐s ❜❛s❡❞ ♦♥ t✇♦ str❛t❡❣✐❡s✳ ❚❤❡ ✜rst str❛t❡❣② ✐s t❤❡ ▼✐❝❤✐✲ ❣❛♥ P❛rt✐❝❧❡ ❙✇❛r♠ ❖♣t✐♠✐③❛t✐♦♥ ✭▼P❙❖✮✱ ✇❤✐❝❤ ❜r❡❛❦s t❤❡ ♠✉❧t✐✲❧❛❜❡❧ ❝❧❛ss✐✜❝❛t✐♦♥ t❛s❦ ✐♥t♦ s❡✈❡r❛❧ ❜✐♥❛r② ❝❧❛ss✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s✱ ❜✉t ✐t ❞♦❡s ♥♦t t❛❦❡ ✐♥t♦ ❛❝❝♦✉♥t t❤❡ ❝♦rr❡❧❛t✐♦♥s ❛♠♦♥❣ t❤❡ ✈❛r✐♦✉s ❝❧❛ss❡s✳ ❚❤❡ s❡❝♦♥❞ str❛t❡❣② ✐s ▼✉❧t✐ ▲❛❜❡❧ ❑✲◆❡❛r❡st ◆❡✐❣❤❜♦r ✭▼▲✲❑◆◆✮✱ ✇❤✐❝❤ ✐s ❝♦♠♣❧❡♠❡♥t❛r② ❛♥❞ t❛❦❡s ✐♥t♦ ❛❝❝♦✉♥t t❤❡ ❝♦rr❡❧❛t✐♦♥s ❛♠♦♥❣ ❝❧❛ss❡s✳ ❲❡ ❡✈❛❧✉❛t❡❞ t❤❡ ♣❡r❢♦r♠❛♥❝❡ ♦❢ ▼▲✲❑▼P❙❖ ✉s✐♥❣ t✇♦ r❡❛❧✲✇♦r❧❞ ❞❛t❛s❡ts✿ ❨❡❛st ❣❡♥❡ ❢✉♥❝t✐♦♥❛❧ ❛♥❛❧②s✐s ❛♥❞ ♥❛t✉r❛❧ s❝❡♥❡ ❝❧❛ss✐✜❝❛t✐♦♥✳ ❚❤❡ ❡①♣❡✲ r✐♠❡♥t❛❧ r❡s✉❧ts s❤♦✇ t❤❛t ▼▲✲❑▼P❙❖ ♣r♦❞✉❝❡❞ r❡s✉❧ts t❤❛t ♠❛t❝❤ ♦r ♦✉t♣❡r❢♦r♠ ✇❡❧❧✲❡st❛❜❧✐s❤❡❞ ♠✉❧t✐✲❧❛❜❡❧ ❧❡❛r♥✐♥❣ ❛❧❣♦r✐t❤♠s✳
❑❡②✇♦r❞s✿ ▼✉❧t✐✲▲❛❜❡❧ ❈❧❛ss✐❝❛t✐♦♥✱ P❛rt✐❝❧❡ ❙✇❛r♠ ❖♣t✐♠✐③❛t✐♦♥✱ ❉❛t❛ ▼✐♥✐♥❣✳
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ❊t❛♣❛s ❞❛ ▼✐♥❡r❛çã♦ ❞❡ ❉❛❞♦s ❛❞❛♣t❛❞♦ ❞❡ ❍❛♥ ✫ ❑❛♠❜❡r ❬✷✵✵✶❪ ✳ ✳ ✳ ✳ ✻ ✷✳✷ ❋♦r♠❛s ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✭❛✮ r❡❣r❛s ❞❡ ❝❧❛ss✐✜✲
❝❛çã♦✱ ✭❜✮ ár✈♦r❡ ❞❡ ❞❡❝✐sã♦✱ ✭❝✮ r❡❞❡ ♥❡✉r❛❧✱ ❛❞❛♣t❛❞♦ ❞❡ ❍❛♥ ✫ ❑❛♠❜❡r ❬✷✵✵✶❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✸ ❚é❝♥✐❝❛s ♣❛r❛ ❈❧❛ss✐✜❝❛çã♦ ▼✉❧t✐rrót✉❧♦ ❛❞❛♣t❛❞♦ ❞❡ ❈❡rr✐ ❬✷✵✶✵❪ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✹ ▼ét♦❞♦ ❞❡ ❡❧✐♠✐♥❛çã♦ ❞♦s rót✉❧♦s ✭❱❛❧❧✐♠ ❬✷✵✵✾❪✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✺ ▼ét♦❞♦ ❛❞✐t✐✈♦ ❞❡ ❞❡❝♦♠♣♦s✐çã♦ ❞♦s rót✉❧♦s ✭❱❛❧❧✐♠ ❬✷✵✵✾❪✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✻ ▼ét♦❞♦ ♠✉❧t✐♣❧✐❝❛t✐✈♦ ❞❡ ❞❡❝♦♠♣♦s✐çã♦ ❞♦s rót✉❧♦s ✭❱❛❧❧✐♠ ❬✷✵✵✾❪✮ ✳ ✳ ✳ ✳ ✶✹ ✷✳✼ ❆❧❣♦r✐t♠♦ ▼▲✲❑◆◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻
✸✳✶ ❆❧❣♦r✐t♠♦ ❊✈♦❧✉❝✐♦♥ár✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵
✹✳✶ ▼❡t♦❞♦ ❞❡ ❊♥①❛♠❡ ❞❡ P❛rtí❝✉❧❛ ✲ P❙❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✹✳✷ Ps❡✉❞♦ ❆❧❣♦r✐t♠♦ ❞♦ ▼P❙❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵
✺✳✶ ◆♦✈❛ ❖r❣❛♥✐③❛çã♦ ❞♦s ▼ét♦❞♦s ♣❛r❛ ❘❡s♦❧✈❡r ♦ Pr♦❜❧❡♠❛ ▼✉❧t✐rrót✉❧♦ ✳ ✳ ✸✻ ✺✳✷ Ps❡✉❞♦ ❛❧❣♦r✐t♠♦ ❞♦ ▼▲✲❑▼P❙❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✻✳✶ ❈❧❛ss❡s ❋✉♥❝✐♦♥❛✐s ❞♦s ●❡♥❡s ❞❛ ▲❡✈❡❞✉r❛ ❙❛❝❝❤❛r♦♠②❝❡s ❝❡r❡✈✐s✐❛❡ ❊❧✐s✲ s❡❡✛ ✫ ❲❡st♦♥ ❬✷✵✵✺❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✻✳✷ ❋✐❣✉r❛s ♠✉❧t✐rrót✉❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✻✳✸ ❍❛♠♠✐♥❣ ▲♦ss ♥❛ ❇❛s❡ ❨❡❛st ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✻✳✹ ❖♥❡✲❊rr♦r ♥❛ ❇❛s❡ ❨❡❛st ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✻✳✺ ❈♦✈❡r❛❣❡ ♥❛ ❇❛s❡ ❨❡❛st ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✻✳✻ ❘❛♥❦✐♥❣ ▲♦ss ♥❛ ❇❛s❡ ❨❡❛st ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✻✳✼ ❆✈❡r❛❣❡ Pr❡❝✐s✐♦♥ ♥❛ ❇❛s❡ ❨❡❛st ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✻✳✽ ❆✈❡r❛❣❡ Pr❡❝✐s✐♦♥ ♥❛ ❇❛s❡ ■♠❛❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✻✳✾ ❖♥❡ ❊rr♦r ♥❛ ❇❛s❡ ■♠❛❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✻✳✶✵ ❈♦✈❡r❛❣❡ ♥❛ ❇❛s❡ ■♠❛❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼
✻✳✶✶ ❘❛♥❦✐♥❣ ▲♦ss ♥❛ ❇❛s❡ ■♠❛❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✻✳✶✷ ❆✈❡r❛❣❡ Pr❡❝✐s✐♦♥ ♥❛ ❇❛s❡ ■♠❛❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ ❊①❡♠♣❧♦ ❞❡ ❜❛s❡ ♠✉❧t✐rrót✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✷ ❚❛❜❡❧❛s ✉♥✐rrót✉❧♦ r❡s✉❧t❛♥t❡s ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ ❇❘ s♦❜r❡ ❛ t❛❜❡❧❛
♠✉❧t✐rrót✉❧♦ ❞❛ ❚❛❜❡❧❛ ✷✳✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✸ ❉❡♠♦♥str❛çã♦ ❞❛ ❡str❛té❣✐❛ ❞❡ ❡❧✐♠✐♥❛çã♦ ❞❡ ❡①❡♠♣❧♦s ♠✉❧t✐rrót✉❧♦s ✳ ✳ ✳ ✶✷ ✷✳✹ ❉❡♠♦♥str❛çã♦ ❞❛ ❡str❛té❣✐❛ ❞❡ ❡❧✐♠✐♥❛çã♦ ❞❡ ❡①❡♠♣❧♦s ♠✉❧t✐rrót✉❧♦s ✳ ✳ ✳ ✶✷
✻✳✶ ■♥❢♦r♠❛çõ❡s s♦❜r❡ ❛ ❜❛s❡ ❞❡ ❞❛❞♦s ❙❝❡♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✻✳✷ P❛râ♠❡tr♦s ✉t✐❧✐③❛❞♦s ❞✉r❛♥t❡ t♦❞♦s ♦s ❡①♣❡r✐♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✻✳✸ ❘❡s✉❧t❛❞♦s ♥❛ ❇❛s❡ ❨❡❛st ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✻✳✹ ❘❡❧❛çã♦ ❞❡ P❡r❢♦r♠❛♥❝❡ ❞♦s ▼ét♦❞♦s ❞❡ ❈❧❛ss✐✜❝❛çã♦ ▼✉❧t✐rrót✉❧♦ ♣❛r❛ ❛
❇❛s❡ ❨❡❛st ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✻✳✺ ❘❡s✉❧t❛❞♦s ♥❛ ❇❛s❡ ■♠❛❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✻✳✻ ❘❡❧❛çã♦ ❞❡ P❡r❢♦r♠❛♥❝❡ ❞♦s ▼ét♦❞♦s ❞❡ ❈❧❛ss✐✜❝❛çã♦ ▼✉❧t✐rrót✉❧♦ ♣❛r❛ ❛
❇❛s❡ ■♠❛❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
❙✉♠ár✐♦
❘❡s✉♠♦ ✈✐✐
❆❜str❛❝t ✐①
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✐✐✐
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ▼♦t✐✈❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✶✳✷ ❖❜❥❡t✐✈♦ ●❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✶✳✷✳✶ ❖❜❥❡t✐✈♦s ❊s♣❡❝í✜❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✶✳✸ ❖r❣❛♥✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸
✷ ❈❧❛ss✐✜❝❛çã♦ ▼✉❧t✐rrót✉❧♦ ✺
✷✳✶ ❈♦♥s✐❞❡r❛çõ❡s ■♥✐❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✷ ▼✐♥❡r❛çã♦ ❞❡ ❉❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✸ ❈❧❛ss✐✜❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✹ ❈❧❛ss✐✜❝❛çã♦ ▼✉❧t✐rrót✉❧♦ ✲ ▼▲❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✹✳✶ ❆❜♦r❞❛❣❡♠ ■♥❞❡♣❡♥❞❡♥t❡ ❞♦ ❆❧❣♦r✐t♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✹✳✷ ❆❜♦r❞❛❣❡♠ ❉❡♣❡♥❞❡♥t❡ ❞♦ ❆❧❣♦r✐t♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✹✳✸ ❉❡♥s✐❞❛❞❡ ❡ ❈❛r❞✐♥❛❧✐❞❛❞❡ ❞❡ ❘ót✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✹✳✹ ▼étr✐❝❛s ❞❡ ❆✈❛❧✐❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✺ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽
✸ ❈♦♠♣✉t❛çã♦ ❊✈♦❧✉t✐✈❛ ✶✾
✸✳✶ ❈♦♥s✐❞❡r❛çõ❡s ■♥✐❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✷ ❆❧❣♦r✐t♠♦s ❊✈♦❧✉❝✐♦♥ár✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✸ ❘❡♣r❡s❡♥t❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵
✸✳✹ P♦♣✉❧❛çã♦ ■♥✐❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✸✳✺ ❋✉♥çã♦ ❋✐t♥❡ss ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✸✳✻ ❙❡❧❡çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✸✳✼ ❖♣❡r❛❞♦r❡s ❞❡ ❘❡♣r♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✽ ❆❜♦r❞❛❣❡♠ P✐tts❜✉r❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✸✳✾ ❆❜♦r❞❛❣❡♠ ▼✐❝❤✐❣❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✸✳✶✵ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✹ ▼ét♦❞♦ ❞❡ ❊♥①❛♠❡ ❞❡ P❛rtí❝✉❧❛s ✷✺
✹✳✶ ❈♦♥s✐❞❡r❛çõ❡s ■♥✐❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✹✳✷ ▼ét♦❞♦ ❞❡ ❊♥①❛♠❡ ❞❡ P❛rtí❝✉❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✹✳✷✳✶ ❖ ❆❧❣♦r✐t♠♦ P❙❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✹✳✸ P❙❖ ❡ ❈❧❛ss✐✜❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✹✳✸✳✶ ▼✐❝❤✐❣❛♥ P❙❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✹✳✹ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✺ ❖ ♠ét♦❞♦ ♣r♦♣♦st♦✿ ▼▲✲❑▼P❙❖ ✸✺
✺✳✶ ❈♦♥s✐❞❡r❛çõ❡s ■♥✐❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✺✳✷ ❯♠❛ ❆❜♦r❞❛❣❡♠ ❍í❜r✐❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✺✳✸ ▼▲✲❑▼P❙❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✺✳✸✳✶ ❋✉♥❝✐♦♥❛♠❡♥t♦ ❞♦ ▼▲✲❑▼P❙❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✺✳✹ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✻ ❊①♣❡r✐♠❡♥t♦s ❡ ❘❡s✉❧t❛❞♦s ✸✾
✻✳✶ ❈♦♥s✐❞❡r❛çõ❡s ■♥✐❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✻✳✷ ❇❛s❡s ❞❡ ❉❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✻✳✷✳✶ ❇❛s❡ ❨❡❛st ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✻✳✷✳✷ ❇❛s❡ ❙❝❡♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✻✳✸ ❆✈❛❧✐❛çã♦ ❞♦s ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✻✳✹ ❘❡s✉❧t❛❞♦s ❞♦s ❊①♣❡r✐♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✻✳✹✳✶ ❘❡s✉❧t❛❞♦s ❞♦s ❊①♣❡r✐♠❡♥t♦s ♥❛ ❇❛s❡ ❨❡❛st ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✻✳✹✳✷ ❘❡s✉❧t❛❞♦s ❞♦s ❊①♣❡r✐♠❡♥t♦s ♥❛ ❇❛s❡ ■♠❛❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✻✳✺ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
✼ ❈♦♥❝❧✉sã♦ ✺✶
❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✺✸
❆♥❡①♦ ❆ ❆rt✐❣♦ P✉❜❧✐❝❛❞♦ ♥♦ ●❊❈❈❖ ✷✵✶✶ ✺✼
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
◆♦s ú❧t✐♠♦s ❛♥♦s ❤♦✉✈❡ ✉♠ ❞❡♠❛s✐❛❞♦ ❛✉♠❡♥t♦ ♥❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❞❛❞♦s ❞✐s♣♦♥í✈❡✐s✳ ❊st❡s ❞❛❞♦s ❝♦♥tê♠ ✈❛❧✐♦s♦s ❝♦♥❤❡❝✐♠❡♥t♦s ♦❝✉❧t♦s q✉❡ ♣♦❞❡r✐❛♠ s❡r ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛♥á❧✐s❡✱ ❞✐❛❣♥óst✐❝♦✱ s✐♠✉❧❛çã♦ ❡✴♦✉ ♣r♦❣♥óst✐❝♦ ❞♦ ♣r♦❝❡ss♦ q✉❡ ❣❡r♦✉ ❛ ❜❛s❡ ❞❡ ❞❛❞♦s ❛ss♦❝✐❛❞❛ ✭❍❛♥ ✫ ❑❛♠❜❡r ❬✷✵✵✶❪ ❯❧ts❝❤ ❬✶✾✾✾❪✮✳ ❙❡❣✉♥❞♦ ❏❛✐♥ ✫ ●❤♦s❤ ❬✷✵✵✺❪✱ ❛ ✉t✐✲ ❧✐③❛çã♦ ❞❡ ✉♠ ❣r❛♥❞❡ ✈♦❧✉♠❡ ❞❡ ❞❛❞♦s ❞❡ ✉♠❛ ♠❛♥❡✐r❛ ❡✜❝✐❡♥t❡ é ✉♠ ❣r❛♥❞❡ ❞❡s❛✜♦✱ ♦ q✉❡ ❧❡✈❛ ❛ ✉♠❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡ ✉t✐❧✐③❛r ♠ét♦❞♦s s❡♠✐❛✉t♦♠át✐❝♦s ❞❡ ❡①tr❛✐r ❝♦♥❤❡✲ ❝✐♠❡♥t♦ ❞❡st❡s ❞❛❞♦s✳ ❊st❛ ♥❡❝❡ss✐❞❛❞❡ ❧❡✈♦✉ ❛♦ s✉r❣✐♠❡♥t♦ ❞❛ ár❡❛ ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ❞❛❞♦s ♦✉ ❞❛t❛ ♠✐♥✐♥❣ ✭❉▼✮✳
❉▼ ✉t✐❧✐③❛ ♠ét♦❞♦s ❞❡ ✈ár✐❛s ♦✉tr❛s ár❡❛s✱ ❡s♣❡❝✐❛❧♠❡♥t❡ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛ ✭▼❛❝❤✐♥❡ ▲❡❛r♥✐♥❣✮ ❡ ❊st❛tíst✐❝❛✱ ♣❛r❛ ❡①tr❛✐r ❝♦♥❤❡❝✐♠❡♥t♦s ❡✴♦✉ ♣❛❞rõ❡s ❛ ♣❛rt✐r ❞❡ ❝♦♥❥✉♥t♦s ❞❡ ❞❛❞♦s ✭❍❛♥ ✫ ❑❛♠❜❡r ❬✷✵✵✶❪✮✳ ❆s té❝♥✐❝❛s ❞❡ ❉▼ ❡stã♦ ❛❣r✉♣❛❞❛s ♥❛s s❡❣✉✐♥t❡s s✉❜ár❡❛s✿ r❡❣r❛s ❞❡ ❛ss♦❝✐❛çã♦✱ ❛❣r✉♣❛♠❡♥t♦✱ ❝❧❛ss✐✜❝❛çã♦ ❡ ♣r❡✈✐sã♦✳
❆s r❡❣r❛s ❞❡ ❛ss♦❝✐❛çã♦ ✐❞❡♥t✐✜❝❛♠ ❣r✉♣♦s ❞❡ ❞❛❞♦s q✉❡ ❛♣r❡s❡♥t❛♠ ❝♦✲♦❝♦rrê♥❝✐❛ ❡♥tr❡ s✐✳ ❚❛♠❜é♠ ❡♥❝♦♥tr❛♠ ✐t❡♥s q✉❡ ❞❡t❡r♠✐♥❛♠ ❛ ♣r❡s❡♥ç❛ ❞❡ ♦✉tr♦s ❡♠ ✉♠❛ ♠❡s♠❛ tr❛♥s❛çã♦ ❡ ❡st❛❜❡❧❡❝❡♠ r❡❣r❛s q✉❡ ❝♦rr❡❧❛❝✐♦♥❛♠ ❛ ♣r❡s❡♥ç❛ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ✐t❡♥s ❝♦♠ ✉♠ ♦✉tr♦ ✐♥t❡r✈❛❧♦ ❞❡ ✈❛❧♦r❡s ♣❛r❛ ✉♠ ♦✉tr♦ ❝♦♥❥✉♥t♦ ❞❡ ✈❛r✐á✈❡✐s✳ ❯♠❛ ❛ss♦❝✐❛çã♦ é ♥♦r♠❛❧♠❡♥t❡ r❡♣r❡s❡♥t❛❞❛ ♣♦r ✉♠❛ r❡❣r❛ ❞❡ ❛ss♦❝✐❛çã♦ ❞♦ t✐♣♦ X ⇒ Y✱
q✉❡ ✐♠♣❧✐❝❛ ♥✉♠❛ r❡❧❛çã♦ ❞❡ ❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ♦s ❝♦♥❥✉♥t♦s ❞❡ ❞❛❞♦s X ❡Y✳ ❆ss✐♠✱
s❡ X ♦❝♦rr❡ ♥❛ ❜❛s❡ ❞❡ ❞❛❞♦s✱ ❡♥tã♦ Y t❛♠❜é♠ ♦❝♦rr❡ ✭❝♦♠ ❛❧❣✉♠❛ r❡❧❛çã♦ ❛ X✮
✭❈✳●♦♥ç❛❧✈❡s ❬✷✵✵✺❪❀ P✐❡rr❛❦♦s ❡t ❛❧✳ ❬✷✵✵✸❪❀ ❍✐♣♣ ❡t ❛❧✳ ❬✷✵✵✵❪✮✳
❆ té❝♥✐❝❛ ❞❡ ❛❣r✉♣❛♠❡♥t♦ ❝♦♥s✐st❡ ❡♠ ✐❞❡♥t✐✜❝❛r ❝❧❛ss❡s ❞❡ ✐t❡♥s ❡♠ ✉♠❛ ❜❛s❡ ❞❡ ❞❛❞♦s ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛❧❣✉♠❛ ♠❡❞✐❞❛ ❞❡ s✐♠✐❧❛r✐❞❛❞❡✳ ❈❛❞❛ ❣r✉♣♦✱ ❝❤❛♠❛❞♦ ❝❧✉st❡r✱ ❝♦♥s✐st❡ ❞❡ ♦❜❥❡t♦s q✉❡ sã♦ s✐♠✐❧❛r❡s ❡♥tr❡ ❡❧❡s ❡ ❞✐❢❡r❡♥t❡s ❞♦s ♦❜❥❡t♦s ❞♦s ♦✉tr♦s ❣r✉♣♦s✳ ❙❡♥❞♦ ❛ss✐♠✱ ❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦s ❣r✉♣♦s é ❞❛❞❛ ♣♦r ✉♠ ✈❛❧♦r✱ ❝♦♠♦ ♠❡❞✐❞❛s ❞❡ ❞✐stâ♥❝✐❛ ♦✉ s✐♠✐❧❛r✐❞❛❞❡✴❞✐ss✐♠✐❧❛r✐❞❛❞❡✳ ❉✐❢❡r❡♥t❡♠❡♥t❡ ❞❛ ❝❧❛ss✐✜❝❛çã♦ ❡ ♣r❡❞✐çã♦✱
✷ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦
❡♠ q✉❡ ♦s ❞❛❞♦s ❡stã♦ ♣r❡✈✐❛♠❡♥t❡ ❝❧❛ss✐✜❝❛❞♦s✱ ❛ ❛♥á❧✐s❡ ❞❡ ❝❧✉st❡rs tr❛❜❛❧❤❛ s♦❜r❡ ❞❛❞♦s ♥♦s q✉❛✐s ❛s ❝❧❛ss❡s ♥ã♦ ❡stã♦ ❞❡✜♥✐❞❛s ✭P✐❡rr❛❦♦s ❡t ❛❧✳ ❬✷✵✵✸❪✮✳
❆♦ ❝♦♥trár✐♦ ❞❛ ❝❧✉st❡r✐③❛çã♦✱ ♦ ♦❜❥❡t✐✈♦ ❞❛ ❝❧❛ss✐✜❝❛çã♦ ❡ ♣r❡✈✐sã♦ é ✐❞❡♥t✐✜❝❛r ❝❛r❛❝t❡ríst✐❝❛s ❞✐st✐♥t❛s ❞❡ ❝❧❛ss❡s ♣ré✲❞❡✜♥✐❞❛s✱ ❜❛s❡❛❞❛s ♥✉♠ ❝♦♥❥✉♥t♦ ❞❡ ✐♥stâ♥❝✐❛s✳ ❊ss❛ ✐♥❢♦r♠❛çã♦ ♣♦❞❡ s❡r ✉s❛❞❛ t❛♥t♦ ♣❛r❛ ❡♥t❡♥❞❡r ❛ ❡①✐stê♥❝✐❛ ❞♦s ❞❛❞♦s✱ q✉❛♥t♦ ♣❛r❛ ♣r❡❞✐③❡r ❝♦♠♦ ♥♦✈❛s ✐♥stâ♥❝✐❛s s❡ ❝♦♠♣♦rt❛rã♦ ✭P❤②✉ ❬✷✵✵✾❪✮✳ ❊♠ ♦✉tr❛s ♣❛✲ ❧❛✈r❛s✱ ❡♠ ✉♠❛ t❛r❡❢❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❞❡✈❡ s❡r ✐❞❡♥t✐✜❝❛❞♦ ♦ ❝♦♥❥✉♥t♦ ♠í♥✐♠♦ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❝♦♥❤❡❝✐❞❛s ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ♦❜❥❡t♦ q✉❡ s❡❥❛♠ s✉✜❝✐❡♥t❡s ♣❛r❛ ♣r❡✈❡r ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ ❞❡s❝♦♥❤❡❝✐❞❛✳
❙❡♥❞♦ ❛ss✐♠✱ ❝r✐❛♠✲s❡ ♠♦❞❡❧♦s ✭❢✉♥çõ❡s✮ q✉❡ ❞❡s❝r❡✈❡♠ ❡ ❞✐st✐♥❣✉❡♠ ❝❧❛ss❡s ♦✉ ❝♦♥❝❡✐t♦s✱ ❜❛s❡❛❞♦s ❡♠ ❞❛❞♦s ❝♦♥❤❡❝✐❞♦s✱ ❝♦♠ ♦ ♣r♦♣ós✐t♦ ❞❡ ✉t✐❧✐③❛r ❡st❡s ♠♦❞❡❧♦s ♣❛r❛ ♣r❡❞✐③❡r ❛ ❝❧❛ss❡ ❞❡ ♦❜❥❡t♦s q✉❡ ❛✐♥❞❛ ♥ã♦ ❢♦r❛♠ ❝❧❛ss✐✜❝❛❞♦s✳ ❈♦♠♦ ❛ ❝❧❛ss✐✜❝❛çã♦ é ✉♠ ♣r♦❝❡ss♦ ❞❡ ❛♣r❡♥❞✐③❛❞♦ s✉♣❡r✈✐s✐♦♥❛❞♦✱ ♦ ♠♦❞❡❧♦ ❝♦♥str✉í❞♦ ❜❛s❡✐❛✲s❡ ♥❛ ❛♥á❧✐s❡ ♣ré✈✐❛ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❞❡ ❛♠♦str❛❣❡♠ ♦✉ ❞❛❞♦s ❞❡ tr❡✐♥❛♠❡♥t♦✱ ❝♦♥t❡♥❞♦ ♦❜❥❡t♦s ❝♦rr❡t❛♠❡♥t❡ ❝❧❛ss✐✜❝❛❞♦s ✭❍❛♥ ✫ ❑❛♠❜❡r ❬✷✵✵✶❪ ✮✳
◆❡st❡ ❝♦♥t❡①t♦✱ ♣❡r❝❡❜❡✲s❡ q✉❡ ♥❛ ❣r❛♥❞❡ ♠❛✐♦r✐❛ ❞♦s ♣r♦❜❧❡♠❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❡♥❝♦♥tr❛❞♦s ♦s ❞❛❞♦s sã♦ ♠✉t✉❛♠❡♥t❡ ❡①❝❧✉s✐✈♦s✱ ♦✉ s❡❥❛✱ ♣❡rt❡♥❝❡♥t❡s ❛ ❛♣❡♥❛s ✉♠❛ ❝❧❛ss❡✳ ❆❧❣✉♥s ♣r♦❜❧❡♠❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ♣♦❞❡♠ ❝♦♥t❡r ❞❛❞♦s ❛♠❜í❣✉♦s✱ s✐❣♥✐✜❝❛♥❞♦ q✉❡ ❛❧❣✉♠❛s ✐♥stâ♥❝✐❛s ❞♦s ❞❛❞♦s ♣♦❞❡♠ ♣❡rt❡♥❝❡r ❛ ♠❛✐s ❞❡ ✉♠❛ ❝❧❛ss❡ ✭rót✉❧♦✮ s✐♠✉❧t❛♥❡❛♠❡♥t❡✱ ♠♦t✐✈❛♥❞♦ ❛ss✐♠ ♦ s✉r❣✐♠❡♥t♦ ❞❛ ❧✐♥❤❛ ❞❡ ♣❡sq✉✐s❛ ❞❡♥♦♠✐♥❛❞❛ ❝❧❛ss✐✜❝❛çã♦ ♠✉❧t✐rrót✉❧♦ ✭❚s♦✉♠❛❦❛s ✫ ❑❛t❛❦✐s ❬✷✵✵✼❪✮✳
❉❡st❛ ❢♦r♠❛✱ ♦❜s❡r✈❛✲s❡ r❡❝❡♥t❡♠❡♥t❡ ✉♠ ❛✉♠❡♥t♦ s✐❣♥✐✜❝❛t✐✈♦✱ ❞❛ ❝♦♠✉♥✐❞❛❞❡ ❝✐❡♥tí✜❝❛✱ ♥♦ ✐♥t❡r❡ss❡ ♣❡❧♦ ✉s♦ ❡ ❛♣❧✐❝❛çã♦ ❞❛ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛ ❡♠ ♣r♦❜❧❡♠❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦✱ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ✭■s❤✐❜✉❝❤✐ ❡t ❛❧✳ ❬✶✾✾✺❪✮✱ r❡❞❡s ♥❡✉r❛✐s ✭❍❛♥s❡♥ ✫ ❙❛❧❛♠♦♥ ❬✶✾✾✵❪✮✱ ❝♦❧ô♥✐❛ ❞❡ ❢♦r♠✐❣❛s ✭❙❤❡❧♦❦❛r ❡t ❛❧✳ ❬✷✵✵✹❪✮✱ ♠ét♦❞♦ ❞❡ ❡♥①❛♠❡ ❞❡ ♣❛rtí❝✉❧❛s ✭P❛rt✐❝❧❡ ❙✇❛r♠ ❖♣t✐♠✐③❛t✐♦♥ ✲ P❙❖✮ ✭❈❡r✈❛♥t❡s ❡t ❛❧✳ ❬✷✵✵✾❛❪✮✱ ❡♥tr❡ ♦✉tr♦s✳
✶✳✶✳ ▼♦t✐✈❛çã♦ ✸
✶✳✶ ▼♦t✐✈❛çã♦
❆t✉❛❧♠❡♥t❡✱ ♣r♦❜❧❡♠❛s r❡❛✐s ✈ê♠ r❡q✉❡r❡♥❞♦ ❝❛❞❛ ✈❡③ ♠❛✐s ❝❧❛ss✐✜❝❛çã♦ ♠✉❧t✐rrót✉❧♦✳ ❙❡♥❞♦ ❛ ❝❧❛ss✐✜❝❛çã♦ ♠✉❧t✐rrót✉❧♦ ✉♠ ♣r♦❜❧❡♠❛ r❡❧❛t✐✈❛♠❡♥t❡ r❡❝❡♥t❡✱ ❞❡st❡ ♠♦❞♦ ♥ã♦ sã♦ ❡♥❝♦♥tr❛❞♦s ♠✉✐t♦s tr❛❜❛❧❤♦s ♥❛ ❧✐t❡r❛t✉r❛ ❛t✉❛❧♠❡♥t❡✳
❖ P❙❖✱ ♣♦r s✉❛ ✈❡③✱ t❡♠ s✐❞♦ ✉t✐❧✐③❛❞♦ ❝♦♠ s✉❝❡ss♦ ♣❛r❛ r❡s♦❧✈❡r ❞✐✈❡rs♦s ♣r♦✲ ❜❧❡♠❛s ✭P✉❣❤ ❡t ❛❧✳ ❬✷✵✵✺❪❀ ❖♠r❛♥ ❡t ❛❧✳ ❬✷✵✵✻❪❀ ❘❡❞❞② ✫ ❑✉♠❛r ❬✷✵✵✼❪✮✳ ❊st❡ ♠ét♦❞♦ ❞❡♠♦str♦✉ s❡r ❜❛st❛♥t❡ ♣r♦♠✐ss♦r ❡ s❡ ♠♦str♦✉ ❝♦♠♣❛rá✈❡❧ ❡♠ ❞❡s❡♠♣❡♥❤♦ ❛ ❙✐♠✉❧❛t❡❞ ❆♥♥❡❛❧✐♥❣ ❡ ❛❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s ✭◆❡❜t✐ ✫ ▼❡s❤♦✉❧ ❬✷✵✵✾❪✱ ❊s♠✐♥ ❡t ❛❧✳ ❬✷✵✵✽❪✮✳
P♦r s❡r❡♠ r❡❝❡♥t❡s ♥❛ ❧✐t❡r❛t✉r❛ ♥ã♦ s❡ t❡♠ ❝♦♥❤❡❝✐♠❡♥t♦ ❞♦ ✉s♦ ❞♦ ♠ét♦❞♦ P❙❖ ❡♠ ♣r♦❜❧❡♠❛ ♠✉❧t✐rrót✉❧♦✱ ♦ q✉❡ ❝♦♥❢❡r❡ ✉♠ ❝❛rát❡r ♦r✐❣✐♥❛❧ ❛ ❡st❛ ❞✐ss❡rt❛çã♦✳
✶✳✷ ❖❜❥❡t✐✈♦ ●❡r❛❧
❖ ♦❜❥❡t✐✈♦ ❣❡r❛❧ ❞❡st❡ tr❛❜❛❧❤♦ é ❡st✉❞❛r ♦ ▼ét♦❞♦ ❞❡ ❊♥①❛♠❡ ❞❡ P❛rtí❝✉❧❛s ✭ P❙❖ ✮✱ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❡ s✉❛ ❛❞❛♣t❛çã♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ♠✉❧t✐rrót✉❧♦✱ ❞❡♠♦♥str❛♥❞♦ q✉❡ ♦ ♠ét♦❞♦ s❡ ❛♣❧✐❝❛ ❛♦ ♣r♦❜❧❡♠❛✱ ❝♦♠ r❡s✉❧t❛❞♦s ❝♦♠♣❛r❛❞♦s ❡①♣❡✲ r✐♠❡♥t❛❧♠❡♥t❡ ❛♦s ♠ét♦❞♦s ❡①✐st❡♥t❡s ♥❛ ❧✐t❡r❛t✉r❛✳
✶✳✷✳✶ ❖❜❥❡t✐✈♦s ❊s♣❡❝í✜❝♦s
❊s♣❡❝✐✜❝❛♠❡♥t❡✱ ♣r❡t❡♥❞❡✲s❡✿
• ❡st✉❞❛r ❛ ❝❧❛ss✐✜❝❛çã♦ ♠✉❧t✐rrót✉❧♦❀
• ❡st✉❞❛r ♦ ♠ét♦❞♦ ❞❡ ❡♥①❛♠❡ ❞❡ ♣❛rtí❝✉❧❛s ✭P❙❖✮ ❡ s❡✉ ✉s♦ ♣❛r❛ ❝❧❛ss✐✜❝❛çã♦❀
• ❛❞❛♣t❛r ♦ P❙❖ ♣❛r❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ♠✉❧t✐rrót✉❧♦❀
• r❡❛❧✐③❛r ❡①♣❡r✐♠❡♥t♦s ❡ ❝♦♠♣❛rá✲❧♦s ❝♦♠ ♦✉tr♦s ♠ét♦❞♦s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ♠✉❧t✐r✲
rót✉❧♦ ❡♥❝♦♥tr❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛✳
✶✳✸ ❖r❣❛♥✐③❛çã♦
✹ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦
❈❛♣ít✉❧♦ ✷
❈❧❛ss✐✜❝❛çã♦ ▼✉❧t✐rrót✉❧♦
✷✳✶ ❈♦♥s✐❞❡r❛çõ❡s ■♥✐❝✐❛✐s
◆❡ss❡ ❝❛♣ít✉❧♦ sã♦ ✐♥tr♦❞✉③✐❞♦s ♦s ❝♦♥❝❡✐t♦s ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ❞❛❞♦s✱ ❝❧❛ss✐✜❝❛çã♦ ❡ ❝❧❛s✲ s✐✜❝❛çã♦ ♠✉❧t✐rrót✉❧♦ ♣❛r❛ ♠❡❧❤♦r ❡♥t❡♥❞✐♠❡♥t♦ ❞♦ ♣r♦❜❧❡♠❛ ❛❜♦r❞❛❞♦ ♥❡st❡ tr❛❜❛❧❤♦✳ ❙ã♦ ❛♣r❡s❡♥t❛❞❛s ❛s ❡str❛té❣✐❛s ❡♥❝♦♥tr❛❞❛s ♥❛ ❧✐t❡r❛t✉r❛ ♣❛r❛ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛✱ ❜❡♠ ❝♦♠♦ ❛ ❛♣r❡s❡♥t❛çã♦ ❡ ❞✐s❝✉ssã♦ ❞❛s ♠étr✐❝❛s ✉t✐❧✐③❛❞❛s ♥❛ ❛✈❛❧✐❛çã♦ ❞♦s ♠ét♦❞♦s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ♠✉❧t✐rrót✉❧♦✳
✷✳✷ ▼✐♥❡r❛çã♦ ❞❡ ❉❛❞♦s
❆ ♣❛rt✐r ❞❛ ❞é❝❛❞❛ ❞❡ ✶✾✻✵✱ ❛ t❡❝♥♦❧♦❣✐❛ ❞❡ ❛r♠❛③❡♥❛♠❡♥t♦ ❞❡ ❞❛❞♦s t❡♠ ♣❛ss❛❞♦ ♣♦r ✉♠❛ ❣r❛♥❞❡ ❡✈♦❧✉çã♦✱ ❞♦s ♣r✐♠✐t✐✈♦s ❛r♠❛③❡♥❛♠❡♥t♦s ❡♠ ❛rq✉✐✈♦s ♣❛r❛ ♣♦❞❡r♦s♦s ❡ s♦✜st✐❝❛❞♦s s✐st❡♠❛s ❞❡ ❜❛♥❝♦ ❞❡ ❞❛❞♦s✱ ♠❛t❡r✐❛❧✐③❛❞♦s ❛tr❛✈és ❞♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦s ❙✐st❡♠❛s ●❡r❡♥❝✐❛❞♦r❡s ❞❡ ❇❛♥❝♦s ❞❡ ❉❛❞♦s ✭❙●❇❉✬s✮ ❏❛✐♥ ✫ ●❤♦s❤ ❬✷✵✵✺❪✳
❆ q✉❛♥t✐❞❛❞❡ ❞❡ ❞❛❞♦s ❛r♠❛③❡♥❛❞♦s ✈❡♠ ❝r❡s❝❡♥❞♦ ❝❛❞❛ ✈❡③ ♠❛✐s ♥♦s ú❧t✐♠♦s ❛♥♦s✳ ❊ss❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ❞❛❞♦s ❛r♠❛③❡♥❛❞♦s ❝♦♥té♠ ✈❛❧✐♦s♦s ❝♦♥❤❡❝✐♠❡♥t♦s ♦❝✉❧t♦s✱ q✉❡ ♣♦❞❡r✐❛♠ s❡r ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛♥á❧✐s❡✱ ❞✐❛❣♥óst✐❝♦✱ s✐♠✉❧❛çã♦ ❡✴♦✉ ♣r♦❣♥ós✲ t✐❝♦ ❞♦ ♣r♦❝❡ss♦ q✉❡ ❣❡r♦✉ ❛ ❜❛s❡ ❞❡ ❞❛❞♦s ❍❛♥ ✫ ❑❛♠❜❡r ❬✷✵✵✶❪ ❯❧ts❝❤ ❬✶✾✾✾❪✳
❙❡❣✉♥❞♦ ❏❛✐♥ ✫ ●❤♦s❤ ❬✷✵✵✺❪✱ ❛ ✉t✐❧✐③❛çã♦ ❞✐r❡t❛ ❡ ❡✜❝✐❡♥t❡ ❞❡ ✉♠ ✉♠ ❣r❛♥❞❡ ✈♦❧✉♠❡ ❞❡ ❞❛❞♦s é ✉♠ ❣r❛♥❞❡ ❞❡s❛✜♦✳ ❊①✐st❡ ❛ss✐♠✱ ✉♠❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡ ✉t✐❧✐③❛r ♠ét♦❞♦s s❡♠✐❛✉t♦♠át✐❝♦s ♣❛r❛ ❡①tr❛✐r ❝♦♥❤❡❝✐♠❡♥t♦ ❞❡st❡s ❞❛❞♦s✳ ❊st❛ ♥❡❝❡ss✐❞❛❞❡ ❧❡✈♦✉ ❛♦ s✉r❣✐♠❡♥t♦ ❞❛ ár❡❛ ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ❞❛❞♦s ♦✉ ❉❛t❛ ▼✐♥✐♥❣ ✭❉▼✮✳
❊♠ s❡✉ tr❛❜❛❧❤♦ ❍❛♥ ✫ ❑❛♠❜❡r ❬✷✵✵✶❪ ❞❡s❝r❡✈❡♠ ❉❛t❛ ▼✐♥✐♥❣ ✭❉▼✮ ❝♦♠♦ ❡①tr❛✲ çã♦ ♦✉ ✧♠✐♥❡r❛çã♦✧❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ ✉♠❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ❞❛❞♦s✳ ❙❡♥❞♦ ✉♠❛
✻ ❈❛♣ít✉❧♦ ✷✳ ❈❧❛ss✐❢✐❝❛çã♦ ▼✉❧t✐rrót✉❧♦
ár❡❛ ♠✉❧t✐❞✐s❝✐♣❧✐♥❛r✱ q✉❡ ✉t✐❧✐③❛ ❞❡ ♠ét♦❞♦s ❞❡ ✈ár✐❛s ♦✉tr❛s ár❡❛s✱ ❡s♣❡❝✐❛❧♠❡♥t❡ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛ ❡ ❊st❛tíst✐❝❛✱ ♣❛r❛ ❡①tr❛✐r ❝♦♥❤❡❝✐♠❡♥t♦s ❛ ♣❛rt✐r ❞❡ ❝♦♥❥✉♥t♦s ❞❡ ❞❛❞♦s✳
❉❡ ❛❝♦r❞♦ ❝♦♠ ❏❛✐♥ ✫ ●❤♦s❤ ❬✷✵✵✺❪✱ ❉❛t❛ ▼✐♥✐♥❣ ✭❉▼✮ é ♦ ♥ú❝❧❡♦ ❞❡ ✉♠ ♣r♦✲ ❝❡ss♦ ♠❛✐s ❛♠♣❧♦✱ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ❑♥♦✇❧❡❞❣❡ ❉✐s❝♦✈❡r② ✐♥ ❉❛t❛❜❛s❡s ✭❑❉❉✮✳ ❆❧é♠ ❞❛ ❡t❛♣❛ ❞❡ ❉▼✱ q✉❡ ❡❢❡t✐✈❛♠❡♥t❡ ❡①tr❛✐ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❛ ♣❛rt✐r ❞❡ ❞❛❞♦s✱ ♦ ♣r♦❝❡ss♦ ❞❡ ❑❉❉ ✐♥❝❧✉✐ ♦✉tr❛s ❡t❛♣❛s ❝♦♠♦ ♣ré✲♣r♦❝❡ss❛♠❡♥t♦ ✭♦✉ ♣r❡♣❛r❛çã♦ ❞❡ ❞❛❞♦s✮ ❡ ♣ós✲ ♣r♦❝❡ss❛♠❡♥t♦ ✭♦✉ r❡✜♥❛♠❡♥t♦ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦✮✱ ❝♦♠♦ ♣♦❞❡ s❡r ♦❜s❡r✈❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✶ ✳ ❖ ♦❜❥❡t✐✈♦ ❞♦ ♣ré✲♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ❞❛❞♦s é tr❛♥s❢♦r♠❛r ♦s ❞❛❞♦s ♣❛r❛ ❢❛❝✐❧✐t❛r ❛ ❛♣❧✐❝❛çã♦ ❞❡ ✉♠❛ ♦✉ ✈ár✐❛s té❝♥✐❝❛s ❞❡ ❉▼✱ ❡♥q✉❛♥t♦ q✉❡ ♦ ♦❜❥❡t✐✈♦ ❞♦s ♠ét♦❞♦s ❞❡ r❡✜♥❛♠❡♥t♦ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ é ✈❛❧✐❞❛r ❡ ❛♣❡r❢❡✐ç♦❛r ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❡s❝♦❜❡rt♦✳ ■❞❡❛❧♠❡♥t❡✱ é ♥❡❝❡ssár✐♦ q✉❡ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❡✈❛ s❡r ♥ã♦ ❛♣❡♥❛s ♣r❡❝✐s♦✱ ♠❛s t❛♠❜é♠ ❝♦♠♣r❡❡♥sí✈❡❧ ❡ ✐♥t❡r❡ss❛♥t❡ ♣❛r❛ ♦ ✉s✉ár✐♦✳
❋✐❣✉r❛ ✷✳✶✳ ❊t❛♣❛s ❞❛ ▼✐♥❡r❛çã♦ ❞❡ ❉❛❞♦s ❛❞❛♣t❛❞♦ ❞❡ ❍❛♥ ✫ ❑❛♠❜❡r ❬✷✵✵✶❪
✷✳✸✳ ❈❧❛ss✐❢✐❝❛çã♦ ✼
♠❛✐♦r✐❛ ❞❛s ✈❡③❡s✱ ♣❛r❛ ♣❡r♠✐t✐r q✉❡ ♦s ❞❛❞♦s s❡❥❛♠ ✉t✐❧✐③❛❞♦s ❛❞❡q✉❛❞❛♠❡♥t❡ ♥♦ ♣r♦❝❡ss♦ ❞❡ ❉▼✳ P❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞❡st❛ ❡t❛♣❛ ❛❧❣✉♥s ♣❛ss♦s ❞❡✈❡♠ s❡r s❡❣✉✐❞♦s✿
• ❧✐♠♣❡③❛ ❞♦s ❞❛❞♦s❀
• ✐♥t❡❣r❛çã♦ ❞♦s ❞❛❞♦s❀
• tr❛♥s❢♦r♠❛çã♦ ❞♦s ❞❛❞♦s❀
• ❞✐s❝r❡t✐③❛çã♦ ❞♦s ❞❛❞♦s❀
• r❡❞✉çã♦ ❞♦s ❞❛❞♦s❀ ❡
• s❡❧❡çã♦ ❞♦s ❞❛❞♦s✳
❆ s❡❣✉♥❞❛ ❡t❛♣❛✱ ❉▼✱ ❡♥✈♦❧✈❡ ❛ ❛♣❧✐❝❛çã♦ ❞❡ ❛❧❣♦r✐t♠♦s ❞❡ ❛ss♦❝✐❛çã♦✱ ❛❣r✉✲ ♣❛♠❡♥t♦✱ ❝❧❛ss✐✜❝❛çã♦ ❡ ♣r❡✈✐sã♦✱ ❞❡♣❡♥❞ê♥❝✐❛✱ ❡♥tr❡ ♦✉tr♦s✱ s♦❜r❡ ♦s ❞❛❞♦s ❥á ♣ré✲ ♣r♦❝❡ss❛❞♦s ♣❛r❛ ❛ ❡①tr❛çã♦ ❞❡ ♣❛❞rõ❡s út❡✐s ✭❏❛✐♥ ✫ ●❤♦s❤ ❬✷✵✵✺❪✮✳
❖ ú❧t✐♠♦ ♣❛ss♦ ❞♦ ❑❉❉✱ s❡❣✉♥❞♦ ❏❛✐♥ ✫ ●❤♦s❤ ❬✷✵✵✺❪✱ é ❛ ✐♥t❡r♣r❡t❛çã♦ ❞♦ ❝♦✲ ♥❤❡❝✐♠❡♥t♦✱ ♦♥❞❡ ♣❛❞rõ❡s ❡①tr❛í❞♦s ❞❡✈❡♠ s❡r ✐♥t❡r♣r❡t❛❞♦s ❛❞❡q✉❛❞❛♠❡♥t❡✱ ❞❡ ♠♦❞♦ q✉❡ ❡❧❡s ♣♦ss❛♠ s❡r ✉s❛❞♦s ♣❛r❛ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦✱ ♦✉ s❡❥❛✱ ♣❛r❛ ✐♥t❡r♣r❡t❛r ♦ ❝♦♥❤❡❝✐✲ ♠❡♥t♦ q✉❡ ♦s ♣❛❞rõ❡s ❡stã♦ ❛r♠❛③❡♥❛♥❞♦✳ P❛❞rõ❡s ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ sã♦ ❛✈❛❧✐❛❞♦s✱ ♦✉ s❡❥❛✱ sã♦ ❝♦rr❡t❛♠❡♥t❡ ✐❞❡♥t✐✜❝❛❞♦s ♣♦r ♠❡❞✐❞❛s ✐♥t❡r❡ss❛♥t❡s✱ t❛✐s ❝♦♠♦✿
• ♥ã♦ ❢❛❝✐❧♠❡♥t❡ ❝♦♠♣r❡❡♥❞✐❞❛s❀
• ✈á❧✐❞❛s ❡♠ ❞❛❞♦s ❞❡ t❡st❡s ❝♦♠ ❛❧❣✉♠ ❣r❛✉ ❞❡ ❝❡rt❡③❛❀
• ♣♦t❡♥❝✐❛❧♠❡♥t❡ út❡✐s❀
• s✐♥❣✉❧❛r❡s❀ ❡
• ✈á❧✐❞❛s ❡♠ t❡r♠♦s ❞❛ ❤✐♣ót❡s❡ ❞❡ q✉❡ ♦ ✉s✉ár✐♦ ♣r♦❝✉r♦✉ ❝♦♥✜r♠❛r✳
✷✳✸ ❈❧❛ss✐✜❝❛çã♦
✽ ❈❛♣ít✉❧♦ ✷✳ ❈❧❛ss✐❢✐❝❛çã♦ ▼✉❧t✐rrót✉❧♦
❍❛♥ ✫ ❑❛♠❜❡r ❬✷✵✵✶❪ ❛✜r♠❛♠ ❛✐♥❞❛ q✉❡ ♦ ♠♦❞❡❧♦ ❣❡r❛❞♦ ♣♦❞❡ s❡r r❡♣r❡s❡♥t❛❞♦ ❞❡ ❞✐✈❡rs❛s ❢♦r♠❛s✱ t❛✐s ❝♦♠♦✿
• r❡❣r❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✭■❋✲❚❍❊◆✮ ✭❋✐❣✉r❛ ✷✳✷ ❛✮❀
• ár✈♦r❡s ❞❡ ❞❡❝✐sã♦ ✭❋✐❣✉r❛ ✷✳✷ ❜✮❀
• ❢ór♠✉❧❛s ♠❛t❡♠át✐❝❛s❀ ❡
• r❡❞❡s ♥❡✉r❛✐s ✭❋✐❣✉r❛ ✷✳✷ ❝✮✳
❋✐❣✉r❛ ✷✳✷✳ ❋♦r♠❛s ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✭❛✮ r❡❣r❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦✱ ✭❜✮ ár✈♦r❡ ❞❡ ❞❡❝✐sã♦✱ ✭❝✮ r❡❞❡ ♥❡✉r❛❧✱ ❛❞❛♣t❛❞♦ ❞❡ ❍❛♥ ✫ ❑❛♠❜❡r ❬✷✵✵✶❪
❍♦❧❞❡♥ ✫ ❋r❡✐t❛s ❬✷✵✵✼❪ ❞❡s❝r❡✈❡♠ q✉❡ ✉♠❛ r❡❣r❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ é ❝♦♠♣♦st❛ ♣♦r ✉♠ ❛♥t❡❝❡❞❡♥t❡ ✭✈❛❧♦r❡s ❞❡ ❛tr✐❜✉t♦s✮ ❡ ✉♠ ❝♦♥s❡q✉❡♥t❡ ✭❝❧❛ss❡✮✱ ❝♦♠♦ ❡①❡♠♣❧✐✜❝❛❞♦ ❛ s❡❣✉✐r✿
IF < atributo=valor > AN D...AN D < atributo=valor > T HEN < classe >
❖ ❛♥t❡❝❡❞❡♥t❡ é ❝♦♠♣♦st♦ ♣♦r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ t❡r♠♦s✱ s❡♥❞♦ ❝❛❞❛ t❡r♠♦ ✉♠❛ tr✐♣❧❛ ❛tr✐❜✉t♦ ✲ ♦♣❡r❛❞♦r ✲ ✈❛❧♦r✱ ♦♥❞❡✿
✷✳✹✳ ❈❧❛ss✐❢✐❝❛çã♦ ▼✉❧t✐rrót✉❧♦ ✲ ▼▲❈ ✾
• ♦♣❡r❛❞♦r ♣♦❞❡ s❡r ✧❂✧❡♠ ❝❛s♦ ❞❡ ❝❛t❡❣♦r✐❛✴❛tr✐❜✉t♦ ♥♦♠✐♥❛❧ ♦✉ ✧>, <,=,≥,≤
✧❡♠ ❝❛s♦ ❞❡ ❛tr✐❜✉t♦ ❝♦♥tí♥✉♦✳
❆ r❡♣r❡s❡♥t❛çã♦ ❞♦ ♣❛❞rã♦ ❡♥❝♦♥tr❛❞♦✱ ❡♠ ❢♦r♠❛t♦ ❞❡ r❡❣r❛✱ t❡♠ ❛ ✈❛♥t❛❣❡♠ ❞❡ s❡r ❢❛❝✐❧♠❡♥t❡ ❝♦♠♣r❡❡♥❞✐❞♦ ♣❡❧♦ ✉s✉ár✐♦✳
❘❡❣r❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ♣♦❞❡♠ s❡r ❝♦♥s✐❞❡r❛❞❛s ❝♦♠♦ ✉♠ t✐♣♦ ♣❛rt✐❝✉❧❛r ❞❡ ♣r❡✲ ✈✐sã♦ ♦♥❞❡ ♦ ❛♥t❡❝❡❞❡♥t❡ ❞❡ r❡❣r❛ ❝♦♥té♠ ❛ ❝♦♠❜✐♥❛çã♦ ❞❡ ❝♦♥❞✐çõ❡s ♣❛r❛ ❛ ♣r❡✈✐sã♦ ❞❡ ❛tr✐❜✉t♦s ❡ ♦ ❝♦♥s❡q✉❡♥t❡ ❞❛ r❡❣r❛ ❝♦♥té♠ ✉♠❛ ♣r❡✈✐sã♦ ❞♦ ✈❛❧♦r ❞♦ ❛tr✐❜✉t♦ ❍❛♥ ✫ ❑❛♠❜❡r ❬✷✵✵✶❪✳
✷✳✹ ❈❧❛ss✐✜❝❛çã♦ ▼✉❧t✐rrót✉❧♦ ✲ ▼▲❈
❊①✐st❡ ✉♠❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ♣r♦❜❧❡♠❛s ❡♠ q✉❡ ❛❧❣✉♥s ❡①❡♠♣❧♦s ❞♦s ❞❛❞♦s ♣♦✲ ❞❡♠ ♣❡rt❡♥❝❡r ❛ ♠❛✐s ❞❡ ✉♠❛ ❝❧❛ss❡ ✭rót✉❧♦✮ s✐♠✉❧t❛♥❡❛♠❡♥t❡✳ ❊ss❡s ♣r♦❜❧❡♠❛s sã♦ ❝♦♥❤❡❝✐❞♦s ❝♦♠♦ ❝❧❛ss✐✜❝❛çã♦ ♠✉❧t✐rrót✉❧♦ ✭❚r♦❤✐❞✐s ❡t ❛❧✳ ❬✷✵✵✽❪✮ ✭❚❛❜❡❧❛ ✷✳✶✮✳
❚❛❜❡❧❛ ✷✳✶✳ ❊①❡♠♣❧♦ ❞❡ ❜❛s❡ ♠✉❧t✐rrót✉❧♦
Pr♦❜❧❡♠❛ ▼✉❧t✐rrót✉❧♦
❊①❡♠♣❧♦ ❈❧❛ss❡
✶ ❇✱❈
✷ ❆✱❇✱❈
✸ ❈
✹ ❇✱❈
❩❤❛♥❣ ✫ ❩❤♦✉ ❬✷✵✵✼❪ ❛✜r♠❛♠ q✉❡ ♣❡sq✉✐s❛s ❡♠ ❝❧❛ss✐✜❝❛çã♦ ♠✉❧t✐rrót✉❧♦ ❢♦r❛♠ ✐♥✐❝✐❛❧♠❡♥t❡ ♠♦t✐✈❛❞❛s ♣❡❧❛s ❞✐✜❝✉❧❞❛❞❡s ❡♥❝♦♥tr❛❞❛s ♣❛r❛ ❝❛t❡❣♦r✐③❛çã♦ ❞❡ t❡①t♦s✱ ❥á q✉❡ ❞✐✈❡rs♦s ❞♦❝✉♠❡♥t♦s ♣❡rt❡♥❝✐❛♠ ❛ ✈ár✐♦s rót✉❧♦s✳
❆t✉❛❧♠❡♥t❡ ❛ ❝❧❛ss✐✜❝❛çã♦ ❞❡ t❡①t♦s é ❛ ♣r✐♥❝✐♣❛❧ ár❡❛ ❞❡ ❛♣❧✐❝❛çã♦ ❞❡ té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ♠✉❧t✐rrót✉❧♦✳ ❙❡✉ ✉s♦ ❡stá ♣r❡s❡♥t❡ t❛♠❜é♠ ❡♠ r❡❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ ♣❛❞rõ❡s ❡ ❜✐♦✐♥❢♦r♠át✐❝❛✳
❊♠ ✉♠ ♣r♦❜❧❡♠❛ ♠✉❧t✐rrót✉❧♦✱ ❝❛❞❛ ❡❧❡♠❡♥t♦ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ tr❡✐♥❛♠❡♥t♦ ❡stá ❛ss♦❝✐❛❞♦ ❛ ✉♠❛ sér✐❡ ❞❡ rót✉❧♦s ❨✱ ♦♥❞❡ ❨ ⊆ ▲✱ s❡♥❞♦ ▲ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ rót✉❧♦s✳
▲✐ ❡t ❛❧✳ ❬✷✵✵✻❪ ❞❡✜♥❡♠ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ ❙❡♥❞♦ X
✉♠ ❝♦♥❥✉♥t♦ ❞❡ tr❡✐♥❛♠❡♥t♦✱Y ={1,2, ..., k}♦ ❝♦♥❥✉♥t♦ ❞❡ rót✉❧♦s✳ ❉❛❞♦ ✉♠ ❝♦♥❥✉♥t♦
❞❡ tr❡✐♥❛♠❡♥t♦ ❞❛ ❢♦r♠❛ hxi, Yii, xi ∈ X, Yi ∈2|Y|✱ ♦♥❞❡ 2|Y| sã♦ t♦❞❛s ❛s ❝♦♠❜✐♥❛çõ❡s
✶✵ ❈❛♣ít✉❧♦ ✷✳ ❈❧❛ss✐❢✐❝❛çã♦ ▼✉❧t✐rrót✉❧♦
❞❡2|Y| ❝♦♠ ♦ ♠❡♥♦r ❡rr♦✳ ❆ ❞✐✜❝✉❧❞❛❞❡ ❞❡ ❞❡✜♥✐r ♦ ❡rr♦ ❡♠ ♠✉❧t✐rrót✉❧♦ é q✉❡ ❞✐✈❡rs❛s
❝♦♠❜✐♥❛çõ❡s ❞❡ rót✉❧♦s sã♦ ♣♦ssí✈❡✐s✳
◆❛ ♠❛✐♦r✐❛ ❞♦s ❝❛s♦s✱ ❛ ❛❜♦r❞❛❣❡♠ ♠✉❧t✐rrót✉❧♦ ✐♥❞✉③ ✉♠❛ ♦r❞❡♥❛çã♦ ❞♦s ♣♦ssí✲ ✈❡✐s rót✉❧♦s ❞❡ ✉♠❛ ❞❛❞❛ ✐♥stâ♥❝✐❛ ❞❡ ❛❝♦r❞♦ ❝♦♠f(x, ln)✳ ❊♥tã♦✱ ❢♦r♠❛❧♠❡♥t❡ ♣♦❞❡✲
♠♦s ❞❡✜♥✐rrankf(x, l)❝♦♠♦rankf ❞♦ rót✉❧♦l♣❛r❛ ❛ ✐♥stâ♥❝✐❛x✱ ❡ s❡f(x, l1)≤f(x, l2)
❡♥tã♦ rankf(x, l1)≤rankf(x, l2)✳
❚❛♥t♦ ❚r♦❤✐❞✐s ❡t ❛❧✳ ❬✷✵✵✽❪ ❝♦♠♦ ❩❤❛♥❣ ✫ ❩❤♦✉ ❬✷✵✵✼❪✱ ❡♠ s❡✉s tr❛❜❛❧❤♦s✱ ❛❣r✉✲ ♣❛♠ ❡♠ ❞✉❛s ❝❛t❡❣♦r✐❛s ♦s ♠ét♦❞♦s ♣❛r❛ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛ ♠✉❧t✐rrót✉❧♦✿
• ❛ ♣r✐♠❡✐r❛ ❝❛t❡❣♦r✐❛ é ♠❛✐s ✐♥t✉✐t✐✈❛✱ s❡♥❞♦ ❛ ❞❡❝♦♠♣♦s✐çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❡♠
♠ú❧t✐♣❧♦s ❡ ✐♥❞❡♣❡♥❞❡♥t❡s ♣r♦❜❧❡♠❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❜✐♥ár✐❛ ♦✉ ✉♥✐rrót✉❧♦✱ ♠❛✐s ♥ã♦ ❧❡✈❛ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ❛s ❝♦rr❡❧❛çõ❡s ❡①✐st❡♥t❡s ❡♥tr❡ ❛s ❝❧❛ss❡s❀
• ❛ s❡❣✉♥❞❛ ❝❛t❡❣♦r✐❛ s❡r✐❛ ❛ r❡❛❧✐③❛çã♦ ❞❡ ❛❧t❡r❛çõ❡s ♥♦s ❛❧❣♦r✐t♠♦s ❞❡ ❝❧❛ss✐✜❝❛çã♦
❡①✐st❡♥t❡s ♣❛r❛ ♣❡r♠✐t✐r ❛ ❝❧❛ss✐✜❝❛çã♦ ♠✉❧t✐rrót✉❧♦✳
P❛r❛ ✐❧✉str❛r ♦s ❞✐❢❡r❡♥t❡s ♠ét♦❞♦s q✉❡ sã♦ ❡♥❝♦♥tr❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛ ♣❛r❛ ♦ ♣r♦✲ ❜❧❡♠❛ ♠ú❧t✐rrót✉❧♦✱ ❞❡ ❈❛r✈❛❧❤♦ ✫ ❋r❡✐t❛s ❬✷✵✵✾❪ ♦r❣❛♥✐③❛r❛♠ ❞❡ ♠❛♥❡✐r❛ ❤✐❡rárq✉✐❝❛ t♦❞♦s ❡ss❡s ♠ét♦❞♦s✱ ❝♦♠♦ ♦❜s❡r✈❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✸✳
Abordagens Multirrótulo Independente do Algoritmo Baseada em Exemplos Eliminação de Exemplos Conversão de Exemplos Eliminação de Rótulos Decomposição de Rótulos Método Multiplicativo Método Aditivo Criação de Rótulos Baseada em Rótulos Dependente do Algoritmo
SVMs AD ML-KNN
✷✳✹✳ ❈❧❛ss✐❢✐❝❛çã♦ ▼✉❧t✐rrót✉❧♦ ✲ ▼▲❈ ✶✶
❆ s❡❣✉✐r s❡rã♦ ❞✐s❝✉t✐❞❛s ❡ss❛s ❛❜♦r❞❛❣❡♥s✳
✷✳✹✳✶ ❆❜♦r❞❛❣❡♠ ■♥❞❡♣❡♥❞❡♥t❡ ❞♦ ❆❧❣♦r✐t♠♦
❆ ❛❜♦r❞❛❣❡♠ ✐♥❞❡♣❡♥❞❡♥t❡ ❞❡ ❛❧❣♦r✐t♠♦ r❡❛❧✐③❛ ❛ ❞❡❝♦♠♣♦s✐çã♦ ❞♦ ♣r♦❜❧❡♠❛ ♠✉❧t✐rró✲ t✉❧♦ ❡♠ ✈ár✐♦s ❡ ✐♥❞❡♣❡♥❞❡♥t❡s ♣r♦❜❧❡♠❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❜✐♥ár✐❛ ♦✉ ✉♥✐rrót✉❧♦✳ ❊ss❛ ❞❡❝♦♠♣♦s✐çã♦ é r❡❛❧✐③❛❞❛ ❜❛s❡❛♥❞♦✲s❡ ❡♠ ❡①❡♠♣❧♦s ♦✉ ❡♠ rót✉❧♦s✳
✷✳✹✳✶✳✶ ❇❛s❡❛❞❛ ❡♠ ❘ót✉❧♦s
❚❛♠❜é♠ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❇✐♥❛r② ❘❡❧❡✈❛♥❝❡ ✲ ❇❘✱ té❝♥✐❝❛ ❜✐♥ár✐❛ ♦✉ ✉♠✲❝♦♥tr❛✲t♦❞♦s ✭❚s♦✉♠❛❦❛s ✫ ❱❧❛❤❛✈❛s ❬✷✵✵✼❪✮✱ ❡❧❛ ❞✐✈✐❞❡ ♦ ♣r♦❜❧❡♠❛ ♠✉❧t✐rrót✉❧♦ ▲ ❡♠ ▼ ♣r♦❜❧❡♠❛s ❜✐♥ár✐♦s✱ ♣❛r❛ ♦s q✉❛✐s sã♦ ❝r✐❛❞♦s ▼ ❝❧❛ss✐✜❝❛❞♦r❡s✱ s❡♥❞♦ ▼ ♦ ♥ú♠❡r♦ ❞❡ ❝❧❛ss❡s ❞♦ ♣r♦❜❧❡♠❛✳ ❈❛❞❛ ❝❧❛ss✐✜❝❛❞♦r ❝r✐❛❞♦ é ❛ss♦❝✐❛❞♦ ❛ ✉♠❛ ❝❧❛ss❡ ❡ tr❡✐♥❛❞♦ ♣❛r❛ r❡s♦❧✈❡r ✉♠ ♣r♦❜❧❡♠❛ ✉♥✐rrót✉❧♦✱ ❝♦♠♦ ♦❜s❡r✈❛❞♦ ♥❛ ❚❛❜❡❧❛ ✷✳✷✳
❚❛❜❡❧❛ ✷✳✷✳ ❚❛❜❡❧❛s ✉♥✐rrót✉❧♦ r❡s✉❧t❛♥t❡s ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ ❇❘ s♦❜r❡ ❛ t❛❜❡❧❛ ♠✉❧t✐rrót✉❧♦ ❞❛ ❚❛❜❡❧❛ ✷✳✶
❈❧❛ss✐✜❝❛❞♦r ❆ ❊①❡♠♣❧♦ ❈❧❛ss❡ ✶ ¬❆ ✷ ❆ ✸ ¬❆ ✹ ¬❆ ❈❧❛ss✐✜❝❛❞♦r ❇ ❊①❡♠♣❧♦ ❈❧❛ss❡ ✶ ❇ ✷ ❇ ✸ ¬❇ ✹ ❇ ❈❧❛ss✐✜❝❛❞♦r ❈ ❊①❡♠♣❧♦ ❈❧❛ss❡ ✶ ❈ ✷ ❈ ✸ ❈ ✹ ❈
✷✳✹✳✶✳✷ ❆❜♦r❞❛❣❡♠ ❇❛s❡❛❞❛ ❡♠ ❊①❡♠♣❧♦s
❈♦♠♦ ✈❡r✐✜❝❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✸✱ ❛ ❞❡❝♦♠♣♦s✐çã♦ ❜❛s❡❛❞❛ ❡♠ ❡①❡♠♣❧♦s é ❞✐✈✐❞✐❞❛ ❡♠ ✸ ❣r✉♣♦s ❞❡ ❡str❛té❣✐❛s✿
• ❡❧✐♠✐♥❛çã♦ ❞❡ ❡①❡♠♣❧♦s ♠✉❧t✐rrót✉❧♦s ❀
• ❝r✐❛çã♦ ❞❡ rót✉❧♦s s✐♠♣❧❡s ❛ ♣❛rt✐r ❞❡ ♠✉❧t✐rrót✉❧♦s❀ ❡
• ❝♦♥✈❡rsã♦ ❞❡ ❡①❡♠♣❧♦s ♠✉❧t✐rrót✉❧♦s ❡♠ ❡①❡♠♣❧♦s ✉♥✐rrót✉❧♦s✳
✶✷ ❈❛♣ít✉❧♦ ✷✳ ❈❧❛ss✐❢✐❝❛çã♦ ▼✉❧t✐rrót✉❧♦
❙❡♥❞♦ ❛ ♠❛✐s s✐♠♣❧❡s ❞❛s ❡str❛té❣✐❛s ❞❡ ❞❡❝♦♠♣♦s✐çã♦ ❜❛s❡❛❞❛ ♥♦s ❡①❡♠♣❧♦s✱ ♣♦✲ ré♠ ❛ ♠❡♥♦s ❡✜❝❛③✱ ❛ ❡str❛té❣✐❛ r❡❛❧✐③❛ ❛ ❡❧✐♠✐♥❛çã♦ ♥♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ♦s ❡①❡♠♣❧♦s q✉❡ ❝♦♥tê♠ ♠❛✐s ❞❡ ✉♠ rót✉❧♦✳ ❈♦♠ ❛ ❡❧✐♠✐♥❛çã♦ ❞❡st❡s ❡①❡♠♣❧♦s✱ ❡ss❛ ❡str❛té❣✐❛ ♠♦❞✐✜❝❛ ♦ ♣r♦❜❧❡♠❛ ♠✉❧t✐rrót✉❧♦✱ tr❛♥s❢♦r♠❛♥❞♦✲♦ ❡♠ ✉♠ ♣r♦❜❧❡♠❛ ♠❛✐s s✐♠♣❧❡s✱ ♦ ✉♥✐rrót✉❧♦ ✭❚❛❜❡❧❛ ✷✳✸✮✳
❚❛❜❡❧❛ ✷✳✸✳ ❉❡♠♦♥str❛çã♦ ❞❛ ❡str❛té❣✐❛ ❞❡ ❡❧✐♠✐♥❛çã♦ ❞❡ ❡①❡♠♣❧♦s ♠✉❧t✐rrót✉❧♦s
Pr♦❜❧❡♠❛ ▼✉❧t✐rrót✉❧♦ ❊①❡♠♣❧♦ ❈❧❛ss❡ ✶ ❇✱❈ ✷ ❆✱❇✱❈ ✸ ❈ ✹ ❇✱❈ / / Pr♦❜❧❡♠❛ ❯♥✐rrót✉❧♦ ❊①❡♠♣❧♦ ❈❧❛ss❡ ✸ ❈
❈r✐❛çã♦ ❞❡ ❘ót✉❧♦s ❙✐♠♣❧❡s ❛ P❛rt✐r ❞❡ ▼✉❧t✐rrót✉❧♦s
❈❤❛♠❛❞❛ ❞❡ ▲❛❜❡❧✲P♦✇❡rs❡t✱ r❡❛❧✐③❛ ❛ ❝r✐❛çã♦ ❞❡ ✉♠ ♥♦✈♦ rót✉❧♦ ♣❛r❛ ❝❛❞❛ ❝♦♠✲ ❜✐♥❛çã♦ ❞❡ ❝❧❛ss❡s ❡①✐st❡♥t❡s ♥♦ ♣r♦❜❧❡♠❛✳ ❈♦♠ ✐ss♦ ♦ ♥ú♠❡r♦ ❞❡ rót✉❧♦s ❞❡ ❝❧❛ss❡s ❡①✐st❡♥t❡s ♣♦❞❡ ❝r❡s❝❡r ❡①♣♦♥❡♥❝✐❛❧♠❡♥t❡ ❡ r❡s✉❧t❛ ❡♠ ❝❧❛ss❡s ❝♦♠ ♣❡q✉❡♥♦s ♥ú♠❡r♦s ❞❡ ✐♥stâ♥❝✐❛s ❞❡ tr❡✐♥♦✳ ❯♠ ❡①❡♠♣❧♦ ❞❛ ❛♣❧✐❝❛çã♦ ❞❡st❛ té❝♥✐❝❛ ♣♦❞❡ s❡r ✈✐st♦ ♥❛ ❚❛❜❡❧❛ ✷✳✹✳
❚❛❜❡❧❛ ✷✳✹✳ ❉❡♠♦♥str❛çã♦ ❞❛ ❡str❛té❣✐❛ ❞❡ ❡❧✐♠✐♥❛çã♦ ❞❡ ❡①❡♠♣❧♦s ♠✉❧t✐rrót✉❧♦s Pr♦❜❧❡♠❛ ▼✉❧t✐rrót✉❧♦ ❊①❡♠♣❧♦ ❈❧❛ss❡ ✶ ❇✱❈ ✷ ❆✱❇✱❈ ✸ ❈ ✹ ❇✱❈ ✺ ❆ ✻ ❇ / / Pr♦❜❧❡♠❛ ❯♥✐rrót✉❧♦ ❊①❡♠♣❧♦ ❈❧❛ss❡ ✶ ❉ ✷ ❊ ✸ ❈ ✹ ❉ ✺ ❆ ✻ ❇
❈♦♥✈❡rsã♦ ❞❡ ❊①❡♠♣❧♦s ▼✉❧t✐rrót✉❧♦s ❡♠ ❊①❡♠♣❧♦s ❯♥✐rrót✉❧♦s
✷✳✹✳ ❈❧❛ss✐❢✐❝❛çã♦ ▼✉❧t✐rrót✉❧♦ ✲ ▼▲❈ ✶✸
çã♦ ❡①❡♠♣❧♦s ♠✉❧t✐rrót✉❧♦s ❡♠ ❡①❡♠♣❧♦s ✉♥✐rrót✉❧♦s✱ ✉t✐❧✐③❛♥❞♦ ❛ ❡s❝♦❧❤❛ ❞❡ ✉♠ ❞♦s rót✉❧♦s q✉❡ ❡stá ❛ss♦❝✐❛❞♦ ❛♦ ❡①❡♠♣❧♦ ❡ ❡❧✐♠✐♥❛♥❞♦ ♦s ❞❡♠❛✐s rót✉❧♦s✳ ❊ss❛ ❡s❝♦❧❤❛ ♣♦❞❡ s❡r ❢❡✐t❛ ❞❡ ♠❛♥❡✐r❛ ❛❧❡❛tór✐❛ ♦✉ ❞❡ ❢♦r♠❛ ❞❡t❡r♠✐♥✐st❛ ✭❋✐❣✉r❛ ✷✳✹✮✳
❋✐❣✉r❛ ✷✳✹✳ ▼ét♦❞♦ ❞❡ ❡❧✐♠✐♥❛çã♦ ❞♦s rót✉❧♦s ✭❱❛❧❧✐♠ ❬✷✵✵✾❪✮
❖ s❡❣✉♥❞♦ ♠ét♦❞♦✱ ❞❡❝♦♠♣♦s✐çã♦ ❞♦s rót✉❧♦s✱ ❞✐✈✐❞❡ ♦ ♣r♦❜❧❡♠❛ ♠✉❧t✐rrót✉❧♦ ❡♠ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣r♦❜❧❡♠❛s ✉♥✐rrót✉❧♦✳ ❖ ♠ét♦❞♦ ❞❡ ❞❡❝♦♠♣♦s✐çã♦ ❞♦s rót✉❧♦s é s✉❜❞✐✈✐❞✐❞♦ ❡♠ ♠ét♦❞♦ ❛❞✐t✐✈♦ ❡ ♠ét♦❞♦ ♠✉❧t✐♣❧✐❝❛t✐✈♦✳
❖ ♠ét♦❞♦ ❛❞✐t✐✈♦✱ ♦✉ ❝r♦ss tr❛✐♥✐♥❣✱ ❢♦✐ ♣r♦♣♦st♦ ♣♦r ❙❤❡♥ ❡t ❛❧✳ ❬✷✵✵✹❪✱ ♦♥❞❡✱ ♣❛r❛ ❝❛❞❛ ❡①❡♠♣❧♦✱ ❝❛❞❛ ✉♠ ❞♦s ♣♦ssí✈❡✐s rót✉❧♦s s❡rá ✜①❛❞♦ ❡♠ s❡q✉ê♥❝✐❛✳ P♦r ❡①❡♠♣❧♦✱ ❞❛❞♦ ✉♠❛ ✐♥stâ♥❝✐❛ ❝♦♠ ♦s rót✉❧♦s ❆✱ ❇ ❡ ❈ é tr❡✐♥❛❞♦ ✉♠ ❝❧❛ss✐✜❝❛❞♦r ♣❛r❛ ❛ ❝❧❛ss❡ ❆ ❡ t♦❞♦s ♦s ❡①❡♠♣❧♦s q✉❡ ❝♦♥tê♠ ♦ rót✉❧♦ ❆ s❡ t♦r♥❛♠ ❡①❡♠♣❧♦s ✉♥✐rrót✉❧♦ ♣❛r❛ ❝❧❛ss❡ ❆ ✭❋✐❣✉r❛ ✷✳✺✮✳
❋✐❣✉r❛ ✷✳✺✳ ▼ét♦❞♦ ❛❞✐t✐✈♦ ❞❡ ❞❡❝♦♠♣♦s✐çã♦ ❞♦s rót✉❧♦s ✭❱❛❧❧✐♠ ❬✷✵✵✾❪✮
✶✹ ❈❛♣ít✉❧♦ ✷✳ ❈❧❛ss✐❢✐❝❛çã♦ ▼✉❧t✐rrót✉❧♦
❞❡ ❝❧❛ss✐✜❝❛❞♦r❡s ❝r❡s❝❡ ❡①♣♦♥❡♥❝✐❛❧♠❡♥t❡ ❝♦♠ ♦ ♥ú♠❡r♦ ❞❡ rót✉❧♦s ❞♦s ❡①❡♠♣❧♦s✱ ❝♦♠♦ ♦❜s❡r✈❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✻✳
❋✐❣✉r❛ ✷✳✻✳ ▼ét♦❞♦ ♠✉❧t✐♣❧✐❝❛t✐✈♦ ❞❡ ❞❡❝♦♠♣♦s✐çã♦ ❞♦s rót✉❧♦s ✭❱❛❧❧✐♠ ❬✷✵✵✾❪✮
✷✳✹✳✷ ❆❜♦r❞❛❣❡♠ ❉❡♣❡♥❞❡♥t❡ ❞♦ ❆❧❣♦r✐t♠♦
❆ ❛❜♦r❞❛❣❡♠ ❞❡♣❡♥❞❡♥t❡ ❞❡ ❛❧❣♦r✐t♠♦ r❡✉♥❡ ♦s ❛❧❣♦r✐t♠♦s q✉❡ ❢♦r❛♠ ❝r✐❛❞♦s ♣❛r❛ tr❛❜❛❧❤❛r ❝♦♠ ❝❧❛ss✐✜❝❛çã♦ ♠✉❧t✐rrót✉❧♦ ❡ ❛q✉❡❧❡s ♦r✐❣✐♥❛❧♠❡♥t❡ ❞❡s❡♥✈♦❧✈✐❞♦s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✉♥✐rrót✉❧♦ q✉❡ ❢♦r❛♠ ♠♦❞✐✜❝❛❞♦s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✳
❯♠ ❞♦s ♠ét♦❞♦s ❡st❛❞♦ ❞❛ ❛rt❡ ♣❛r❛ ❝❧❛ss✐✜❝❛çã♦ ♠✉❧t✐rrót✉❧♦ é ♦ ❇♦♦s❚❡①t❡r✳ Pr♦♣♦st♦ ♣♦r ❙❝❤❛♣✐r❡ ✫ ❙✐♥❣❡r ❬✷✵✵✵❪✱ ♦ ♠ét♦❞♦ ♠❛♥té♠ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣❡s♦s ♣❛r❛ ❝❛❞❛ ♣❛r ❡①❡♠♣❧♦✲rót✉❧♦ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ tr❡✐♥❛♠❡♥t♦✳ ❖s ♣❛r❡s q✉❡ sã♦ ❞✐❢í❝❡✐s ❞❡ s❡ ♣r❡✈❡r ❝♦rr❡t❛♠❡♥t❡ tê♠ ♦s s❡✉s ♣❡s♦s ✐♥❝r❡♠❡♥t❛❞♦s ❡ ♣❛r❛ ♦s ♣❛r❡s ❢❛❝✐❧♠❡♥t❡ ♣r❡✈✐st♦s ♦s s❡✉s ♣❡s♦s sã♦ ❞❡❝r❡♠❡♥t❛❞♦s✳
❊❧✐ss❡❡✛ ✫ ❲❡st♦♥ ❬✷✵✵✶❪ ♣r♦♣✉s❡r❛♠ ♦ ❘❆◆❑✲❙❱▼✱ ✉♠ ♠ét♦❞♦ ❜❛s❡❛❞♦ ❡♠ ❦❡r♥❡❧s ♣❛r❛ ❝❧❛ss✐✜❝❛çã♦✱ q✉❡ ♠❛①✐♠✐③❛ ❛ s♦♠❛ ❞❛s ♠❛r❣❡♥s ❞❡ t♦❞❛s ❛s ❝❛t❡❣♦r✐❛s s✐♠✉❧t❛♥❡❛♠❡♥t❡✱ ♦r❞❡♥❛♥❞♦ ❛s ❝❛t❡❣♦r✐❛s r❡❧❡✈❛♥t❡s ❞❡ ❝❛❞❛ ✐♥stâ♥❝✐❛ ❞❛ ❜❛s❡ ❞❡ tr❡✐✲ ♥❛♠❡♥t♦ ❡ ♣❡♥❛❧✐③❛♥❞♦ ❛s ✐rr❡❧❡✈❛♥t❡s✳ ❏á ❆✐♦❧❧✐ ❡t ❛❧✳ ❬✷✵✵✹❪ ❞❡s❡♥✈♦❧✈❡r❛♠ ✉♠ ♠ét♦❞♦ ❡♠ q✉❡ ♦ ♣r♦❜❧❡♠❛ ♠✉❧t✐rrót✉❧♦ é ❞✐✈✐❞✐❞♦ ❡♠ ✈ár✐❛s ❙❱▼s ❜✐♥ár✐♦s ❡♠ ♣❛r❛❧❡❧♦✱ ❝♦♠✲ ❜✐♥❛♥❞♦ t♦❞♦s ♦s ❝❧❛ss✐✜❝❛❞♦r❡s ♣♦r ♠❡✐♦ ❞♦ ❝♦♠♣❛rt✐❧❤❛♠❡♥t♦ ❞❛ ♠❛tr✐③ ❦❡r♥❡❧ ❡♥tr❡ ♦s ❞✐❢❡r❡♥t❡s ❝❧❛ss✐✜❝❛❞♦r❡s✳
✷✳✹✳✷✳✶ ▼▲✲❑◆◆
✷✳✹✳ ❈❧❛ss✐❢✐❝❛çã♦ ▼✉❧t✐rrót✉❧♦ ✲ ▼▲❈ ✶✺
tr❛❞✐❝✐♦♥❛❧ ❡ ❞✐❢❡r❡♥❝✐❛❞♦ ♣❡❧♦ ✉s♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s ❛ ♣r✐♦r✐ ❡ ❛ ♣♦st❡r✐♦r✐✳
◆♦ ▼▲✲❑◆◆ ✉♠❛ ❞❛❞❛ ✐♥stâ♥❝✐❛ x ❡stá ❛ss♦❝✐❛❞❛ ❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ rót✉❧♦s Y ⊆ Y✱ ❡ k ♦ ♥ú♠❡r♦ ❞❡ ✈✐③✐♥❤♦s ♠❛✐s ♣ró①✐♠♦s✳ ❙❡❥❛ ~yx ♦ ✈❡t♦r ❞❡ ❝❛t❡❣♦r✐❛s
❞❡ x✱ ♦♥❞❡ ♦ ❧✲és✐♠♦ ❝♦♠♣♦♥❡♥t❡ ~yx(l)(l ∈ Y) t❡♠ ✈❛❧♦r ❞❡ ✶ s❡ l ∈ Y ❡ ✵ ❝❛s♦
❝♦♥trár✐♦✳ ❆❞✐❝✐♦♥❛❧♠❡♥t❡✱ N(x) ❞❡♥♦t❛ ♦ ❝♦♥❥✉♥t♦ ❞♦s k ✈✐③✐♥❤♦s ♠❛✐s ♣ró①✐♠♦s ❞❡ x✱ ✐❞❡♥t✐✜❝❛❞♦ ♥♦ ❝♦♥❥✉♥t♦ ❞❡ tr❡✐♥❛♠❡♥t♦✳ ❇❛s❡❛❞♦ ♥♦s rót✉❧♦s ❞♦s ✈✐③✐♥❤♦s ❞❡ x✱ ♦
✈❡t♦r ❞❡ rót✉❧♦s ✈✐③✐♥❤♦s é ❞❡✜♥✐❞♦ ❝♦♠♦✿
~
Cx(l) = X
a∈N(x)
~ya(l), l ∈ Y ✭✷✳✶✮
♦♥❞❡ Cx~ (l) ❝♦♥t❛ ♦ ♥ú♠❡r♦ ❞❡ ✈✐③✐♥❤♦s ❞❡x ❝♦♥t❡♥❞♦ ❛ ❧✲és✐♠❛ rót✉❧♦✳
P❛r❛ ❝❛❞❛ ✐♥stâ♥❝✐❛ t✱ ♦ ▼▲✲❑◆◆ ✐♥✐❝✐❛❧♠❡♥t❡ ✐❞❡♥t✐✜❝❛ ♦s k ✈✐③✐♥❤♦s ♠❛✐s
♣ró①✐♠♦s N(t) ♥♦ ❝♦♥❥✉♥t♦ ❞❡ tr❡✐♥❛♠❡♥t♦✳ ❙❡❥❛ Hl
1 ♦ ❡✈❡♥t♦ ♦♥❞❡ t ❝♦♥té♠ ♦ ró✲
t✉❧♦ l✱ ❡♥q✉❛♥t♦ Hl
0 ♦ ❡✈❡♥t♦ ♥♦ q✉❛❧ t ♥ã♦ ❝♦♥té♠ l✳ ❈♦♠♣❧❡♠❡♥t❛♥❞♦✱ ❝♦♥s✐❞❡r❡
El
j(j ∈ {0,1,2, ..., k}) ♦ ❡✈❡♥t♦ q✉❡✱ ❞❡ t♦❞♦s ♦s k ✈✐③✐♥❤♦s ❞❡ t✱ ♦♥❞❡ ❡①❛t❛♠❡♥t❡ j
✐♥stâ♥❝✐❛s ❝♦♥té♠ ♦ r♦t✉❧♦ l✳ P♦rt❛♥t♦✱ ❜❛s❡❛❞♦ ♥♦ ✈❡t♦r ❞❡ rót✉❧♦s ✈✐③✐♥❤♦sCt~ ✱ ♦ ✈❡t♦r
❞❡ ❝❛t❡❣♦r✐❛s ~yt é ❞❡t❡r♠✐♥❛❞♦ ✉s❛♥❞♦ ♦ s❡❣✉✐♥t❡ ♣r✐♥❝í♣✐♦ ❞♦ ▼❛①✐♠✉♠ ❛ P♦st❡r✐♦r✐✿
~yt(l) =❛r❣ ♠❛①b∈{0,1}P(Hbl|ECl~t(l)), l ∈ Y ✭✷✳✷✮
✉s❛♥❞♦ ❛ r❡❣r❛ ❞❡ ❇❛②❡s ❛ ❡q✉❛çã♦ ❛❝✐♠❛ ♣♦❞❡ s❡r r❡❡s❝r✐t❛ ❝♦♠♦✿
~yt(l) = ❛r❣ ♠❛①b∈{0,1} P(Hl
b)P(ECl~t(l)|Hbl) P(El
~ Ct(l))
= ❛r❣ ♠❛①b∈{0,1}P(Hbl)P(ECl~t(l)|Hbl) ✭✷✳✸✮
❈♦♠♦ ✈❡r✐✜❝❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✼✱ ✐♥✐❝✐❛❧♠❡♥t❡ ♦ ♠ét♦❞♦ ✐❞❡♥t✐✜❝❛✱ ♣❛r❛ ❝❛❞❛ ✐♥s✲ tâ♥❝✐❛ ♥❛ ❜❛s❡ ❞❡ tr❡✐♥❛♠❡♥t♦✱ ♦s s❡✉s ❦ ✈✐③✐♥❤♦s ♠❛✐s ♣ró①✐♠♦s✳ ❊♥tã♦✱ ❜❛s❡❛❞♦ ♥❛ ✐♥❢♦r♠❛çã♦ ❡st❛tíst✐❝❛ ❛ ♣r✐♦r✐ ♦❜t✐❞❛ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ rót✉❧♦s ❞❡st❡s ✈✐③✐♥❤♦s✱ é ✉t✐❧✐✲ ③❛❞♦ ♦ ♣r✐♥❝í♣✐♦ ▼❛①✐♠✉♠ ❛ P♦st❡r✐♦r✐ ✭▼❆P✮ ♣❛r❛ ❞❡t❡r♠✐♥❛r ♦ ❝♦♥❥✉♥t♦ ❞❡ rót✉❧♦s ❞❛ ✐♥stâ♥❝✐❛ ❞❡ t❡st❡✳
✷✳✹✳✸ ❉❡♥s✐❞❛❞❡ ❡ ❈❛r❞✐♥❛❧✐❞❛❞❡ ❞❡ ❘ót✉❧♦
✶✻ ❈❛♣ít✉❧♦ ✷✳ ❈❧❛ss✐❢✐❝❛çã♦ ▼✉❧t✐rrót✉❧♦
[~yt, ~rt] =▼▲✲❑◆◆(T, k, t, s)
✪ ❈❛❧❝✉❧❛ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❛ ♣r✐♦r✐P(Hl b) ♣❛r❛l∈ Y ❢❛ç❛
P(Hl
1) = (s+ Pm
i=1~yxi(l))/(s×2 +m)
P(Hl
0) = 1−P(H1l)
✜♠ ♣❛r❛
✪ ❈❛❧❝✉❧❛ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❛ ♣♦st❡r✐♦r✐ P(El j|Hlb) ■❞❡♥t✐✜q✉❡N(xi), i∈ {1,2, ..., m}
♣❛r❛l∈ Y ❢❛ç❛
♣❛r❛j∈ {0,1, ..., k}❢❛ç❛ c[j] = 0;c′[j] = 0;
✜♠ ♣❛r❛
♣❛r❛i∈ {0,1, ..., m}❢❛ç❛ δ=C~xi(l) =Pa∈N(xi)~ya(l) s❡(~yxi(l) == 1)❡♥tã♦
c[δ] =c[δ] + 1
✜♠ s❡ s❡♥ã♦
c′[δ] =c′[δ] + 1
✜♠ s❡ ✜♠ ♣❛r❛
♣❛r❛j∈ {0,1, ..., k}❢❛ç❛
P(El
j|H1l) = (s+c[j])/(s×(k+ 1) + Pk
p=0c[p]) P(El
j|H0l) = (s+c′[j])/(s×(k+ 1) + Pk
p=0c′[p])
✜♠ ♣❛r❛ ✜♠ ♣❛r❛
✪ ❈♦♠♣✉t❛~yt❡~rt ■❞❡♥t✐✜❝❛N(t)
♣❛r❛l∈ Y ❢❛ç❛ ~
Ct(l) =Pa∈N(t)~ya(l)
~
yt(l) =❛r❣ ♠❛①b∈{0,1}P(Hbl)P(ECtl~(l)|Hbl)
~
rt(l) =P(El Hl
1|Ct~ (l)
) = (P(Hl
1)P(ECtl~ (l)|H1l))/P(ECtl~(l))
= (P(Hl
1)P(ElCt~ (l)|Hl1))/( P
b∈{0,1}P(Hbl)P(ECtl~(l)|Hbl)) ✜♠ ♣❛r❛
❋✐❣✉r❛ ✷✳✼✳ ❆❧❣♦r✐t♠♦ ▼▲✲❑◆◆
✐♥✢✉❡♥❝✐❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❞❡ ❞✐❢❡r❡♥t❡s ♠ét♦❞♦s ❝❧❛ss✐✜❝❛❞♦r❡s ♠✉❧t✐rrót✉❧♦ ✭❚s♦✉♠❛❦❛s ✫ ❑❛t❛❦✐s ❬✷✵✵✼❪✮✳
P❛r❛ ❞✐s❝✉t✐r ♦ ✐♠♣❛❝t♦ ❞❡ss❛s ❝❛r❛❝t❡ríst✐❝❛s✱ ❛♣r❡s❡♥t❛♠♦s ❛ s❡❣✉✐r ♦s ❝♦♥❝❡✐t♦s ❞❡ ❞❡♥s✐❞❛❞❡ ❡ ❝❛r❞✐♥❛❧✐❞❛❞❡ ❞❡ rót✉❧♦ ❡♠ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s✳
❙❡❥❛ D ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ♠✉❧t✐rrót✉❧♦ q✉❡ ♣♦ss✉✐ N ❡①❡♠♣❧♦s (xi, Yi), i = 1...N ❡|L| ♦ ♥ú♠❡r♦ ❞❡ rót✉❧♦s ♣♦ssí✈❡✐s✳
❈❛r❞✐♥❛❧✐❞❛❞❡ ❞❡ ❘ót✉❧♦✿ é ♦ ♥ú♠❡r♦ ♠é❞✐♦ ❞❡ rót✉❧♦s ♥♦s ❡①❡♠♣❧♦s ❡♠ D✿
CR(D) = 1
N N X
i=1
|Yi|
