❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
P❘❊❋❘❊❈✿ ❯▼❆ ▼❊❚❖❉❖▲❖●■❆ P❆❘❆
❉❊❙❊◆❱❖▲❱■▼❊◆❚❖ ❉❊ ❙■❙❚❊▼❆❙ ❉❊ ❘❊❈❖▼❊◆❉❆➬➹❖
❯❚■▲■❩❆◆❉❖ ❆▲●❖❘■❚▼❖❙ ❉❊ ▼■◆❊❘❆➬➹❖ ❉❊
P❘❊❋❊❘✃◆❈■❆❙
❈▲❊■❆◆❊ ●❖◆➬❆▲❱❊❙ ❖▲■❱❊■❘❆
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❈▲❊■❆◆❊ ●❖◆➬❆▲❱❊❙ ❖▲■❱❊■❘❆
P❘❊❋❘❊❈✿ ❯▼❆ ▼❊❚❖❉❖▲❖●■❆ P❆❘❆
❉❊❙❊◆❱❖▲❱■▼❊◆❚❖ ❉❊ ❙■❙❚❊▼❆❙ ❉❊ ❘❊❈❖▼❊◆❉❆➬➹❖
❯❚■▲■❩❆◆❉❖ ❆▲●❖❘■❚▼❖❙ ❉❊ ▼■◆❊❘❆➬➹❖ ❉❊
P❘❊❋❊❘✃◆❈■❆❙
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ❛♣r❡s❡♥t❛❞❛ à ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥✲ ❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥✲ ❞✐❛✱ ▼✐♥❛s ●❡r❛✐s✱ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ❡①✐❣✐❞♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳
➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ❇❛♥❝♦ ❞❡ ❉❛❞♦s✳
❖r✐❡♥t❛❞♦r❛✿
Pr♦❢❛✳ ❉r❛✳ ❙❛♥❞r❛ ❆♣❛r❡❝✐❞❛ ❞❡ ❆♠♦
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❖s ❛❜❛✐①♦ ❛ss✐♥❛❞♦s✱ ♣♦r ♠❡✐♦ ❞❡st❡✱ ❝❡rt✐✜❝❛♠ q✉❡ ❧❡r❛♠ ❡ r❡❝♦♠❡♥❞❛♠ ♣❛r❛ ❛ ❋❛❝✉❧✲ ❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❛ ❛❝❡✐t❛çã♦ ❞❛ ❞✐ss❡rt❛çã♦ ✐♥t✐t✉❧❛❞❛ ✏Pr❡❢❘❡❝✿ ❯♠❛ ▼❡t♦❞♦❧♦❣✐❛ ♣❛r❛ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ✉t✐❧✐③❛♥❞♦ ❆❧❣♦r✐t♠♦s ❞❡ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s✑ ♣♦r ❈❧❡✐❛♥❡ ●♦♥ç❛❧✈❡s ❖❧✐✈❡✐r❛ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ❡①✐❣✐❞♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳
❯❜❡r❧â♥❞✐❛✱ ✼ ❞❡ ❋❡✈❡r❡✐r♦ ❞❡ ✷✵✶✹
❖r✐❡♥t❛❞♦r❛✿
Pr♦❢❛✳ ❉r❛✳ ❙❛♥❞r❛ ❆♣❛r❡❝✐❞❛ ❞❡ ❆♠♦ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛
❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛✿
Pr♦❢✳ ❉r✳ ❍✉♠❜❡rt♦ ▲✉✐③ ❘❛③❡♥t❡ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛
❉❡❞✐❝❛tór✐❛
❆❣r❛❞❡❝✐♠❡♥t♦s
❆❣r❛❞❡ç♦ ❛ ❉❡✉s ♣r✐♠❡✐r❛♠❡♥t❡✳ ❙❡♠ ❛ s✉❛ ♣r❡s❡♥ç❛ ♥ã♦ ❤❛✈❡r✐❛ ♥❛❞❛ ♣❛r❛ ❛q✉✐ ❛❣r❛❞❡❝❡r✳
❆❣r❛❞❡ç♦ ♠✉✐t♦ ❛♦s ♠❡✉s ♣❛✐s q✉❡ s❡♠♣r❡ ♠❡ ✐♥❝❡♥t✐✈❛r❛♠✱ ♠❡ ❞❡r❛♠ ❛♣♦✐♦ ❡ ❧✉t❛r❛♠ ♣❛r❛ q✉❡ ❡✉ ❝♦♥q✉✐st❛ss❡ t✉❞♦ q✉❡ t❡♥❤♦ ❤♦❥❡✳
➚ ♠✐♥❤❛ ✐r♠ã ❆r✐❛♥❡ ♣♦r t❛♥t❛s ✈❡③❡s ❡s❝✉t❛r ♠❡✉s ❧❛♠❡♥t♦s✱ ♠❡ ♠♦t✐✈❛r ❛ s❡❣✉✐r ❛❞✐❛♥t❡ ❡ ❝♦♠♣r❡❡♥❞❡r t❛♥t♦s ♠♦♠❡♥t♦s ❞❡ ❛✉sê♥❝✐❛✳
➚ ♠✐♥❤❛ ✐r♠ã ❘♦s✐❛♥❡ ♣❡❧♦ ❡①❡♠♣❧♦ ❞❡ ❞✐♥❛♠✐s♠♦ ❡ ♣♦r ♠❡ ♠♦str❛r q✉❡ ❛✐♥❞❛ ❤á ♠✉✐t♦ ♦ q✉❡ ❢❛③❡r✳
❆♦ ♠❡✉ ♠❛r✐❞♦ ▲❡❛♥❞r♦ s❡♠ ♦ q✉❛❧ ❡✉ ♥ã♦ s❡r✐❛ ❝❛♣❛③ ❞❡ ❝♦♥❝❧✉✐r ❡ss❡ ♠❡str❛❞♦✳ ❖❜r✐❣❛❞❛ ♣❡❧❛ ❝♦❧❛❜♦r❛çã♦ ❞✉r❛♥t❡ t♦❞♦ ♦ ♣r♦❝❡ss♦✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♥❛ ❝♦❧❡t❛ ❞❡ ❞❛❞♦s ♥♦s sá❜❛❞♦s✱ ❞♦♠✐♥❣♦s ❡ ♠❛❞r✉❣❛❞❛s ♥♦s ❧❛❜♦r❛tór✐♦s ❞♦ ■♥st✐t✉t♦✳
➚ ♠✐♥❤❛ ❛✈ó ❈❧❡♠ê♥❝✐❛ ♣♦r s❡♠♣r❡ s❡r ♠❡✉ ❡①❡♠♣❧♦ ❞❡ ❞❡❞✐❝❛çã♦ ❡ s❡r✈✐ç♦ ❛♦s ♦✉tr♦s✳ ❆ t♦❞♦s ♦s ♠❡✉s t✐♦s✱ t✐❛s✱ ♣r✐♠♦s ❡ ❞❡♠❛✐s ♣❛r❡♥t❡s q✉❡ ♠❡ ❛❝♦♠♣❛♥❤❛r❛♠✳
❆♦s ♠✉✐t♦s ❛♠✐❣♦s q✉❡ t✐✈❡ q✉❡ ♠❡ ❛❢❛st❛r✱ ❛♦s ♥♦✈♦s ❛♠✐❣♦s q✉❡ ❡♥❝♦♥tr❡✐ ❡♠ ❯❜❡r✲ ❧â♥❞✐❛ ❡ q✉❡ ♠❡ ❞❡r❛♠ ♠✉✐t♦ ❛♣♦✐♦ ❞✉r❛♥t❡ t♦❞❛ ❛ ❝❛♠✐♥❤❛❞❛✳
➚s ❛♠✐❣❛s ❏✉❧✐❡t❡ ❡ ●❡②❝② ♣♦r ❝♦♠♣❛rt✐❧❤❛r❡♠ t❛♥t♦s ♠♦♠❡♥t♦s í♠♣❛r❡s ❞✉r❛♥t❡ ❡ss❛ tr❛❥❡tór✐❛✳ ❆♦s ❞❡♠❛✐s ❛♠✐❣♦s ❞♦ ♠❡str❛❞♦ q✉❡ s❡♠♣r❡ r❡❢♦rç❛r❛♠ ♠✐♥❤❛ ❡s♣❡r❛♥ç❛✳
➚ ❢❛♠í❧✐❛ ●PP✲❯❜❡r❧â♥❞✐❛ q✉❡ ❢♦✐ ♣❡ç❛ ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ ❛ ♠✐♥❤❛ ❝❛♠✐♥❤❛❞❛ ❡ ♠❡ ♣❡r♠✐t✐✉ s❡♥t✐r ❛❝♦❧❤✐❞❛ ❡♠ ✉♠❛ t❡rr❛ tã♦ ❞✐st❛♥t❡ ❞❛ ♠✐♥❤❛ ❝❛s❛✳
❆♦ ■♥st✐t✉t♦ ❋❡❞❡r❛❧ ❞♦ ◆♦rt❡ ❞❡ ▼✐♥❛s ●❡r❛✐s ✲ ❈❛♠♣✉s ❏❛♥✉ár✐❛ q✉❡ ♠❡ ♣r♦♣♦r✲ ❝✐♦♥♦✉ ❞❡❞✐❝❛çã♦ ❡①❝❧✉s✐✈❛ ♣♦r ♠❛✐♦r ♣❛rt❡ ❞♦ t❡♠♣♦ ❞❛ ♣❡sq✉✐s❛ ❡ ♣❡❧❛ ❞✐s♣♦♥✐❜✐❧✐③❛çã♦ ❞❡ ❝♦♠♣✉t❛❞♦r❡s ♣❛r❛ t❡st❡s✳
❘❡s✉♠♦
❆ ❡♥♦r♠❡ q✉❛♥t✐❞❛❞❡ ❞❡ ✐♥❢♦r♠❛çã♦ ❞✐s♣♦♥í✈❡❧ ♥❛ ✇❡❜ t❡♠ ❞✐✜❝✉❧t❛❞♦ ♦s ✉s✉ár✐♦s ❛ s❡❧❡❝✐♦♥❛r❡♠ ✐t❡♥s q✉❡ ❛t❡♥❞❛♠ s✉❛s ♥❡❝❡ss✐❞❛❞❡s✳ ❖s ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ s✉r❣❡♠ ❝♦♠♦ ❢❡rr❛♠❡♥t❛s ✐♥❞✐s♣❡♥sá✈❡✐s ♥❡st❡ ❝❡♥ár✐♦ ❞❡ s♦❜r❡❝❛r❣❛ ❞❡ ✐♥❢♦r♠❛çã♦✱ ❛ ✜♠ ❞❡ ✜❧tr❛r ♦ q✉❡ é ❞❡ ✐♥t❡r❡ss❡ ❞♦ ✉s✉ár✐♦ ❡ ♣❡r♠✐t✐r q✉❡ ❡❧❡ t❡♥❤❛ ✉♠❛ ❡①♣❡r✐ê♥❝✐❛ ❞✐❢❡r❡♥❝✐❛❞❛ ❝♦♠ ♦s ❛t✉❛✐s s✐st❡♠❛s ❞❡ ✐♥❢♦r♠❛çã♦✳
❆♣r❡s❡♥t❛♠♦s ♥❡ss❛ ❞✐ss❡rt❛çã♦ ✉♠❛ ♠❡t♦❞♦❧♦❣✐❛ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦✱ ✉t✐❧✐③❛♥❞♦ ❛❧❣♦r✐t♠♦s ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s✿ ❛ Pr❡❢❘❡❝✳ ❖❜❥❡✲ t✐✈❛♠♦s ❝♦♠ ❡ss❛ ♣r♦♣♦st❛ ❛ ❝♦♥str✉çã♦ ❞❡ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ q✉❡ t❡♥❤❛♠ ❜♦♥s ✈❛❧♦r❡s ❞❡ ❛❝✉rá❝✐❛ ❡ q✉❡ ♣❡r♠✐t❛♠ ✉♠❛ ✐♥t❡r❛çã♦ ❝♦♠ ♦ ✉s✉ár✐♦ ♠❛✐s s❛t✐s❢❛tór✐❛✱ ❛ ♣❛rt✐r ❞❛s ♠❡❞✐❞❛s ❞❡ ✈❛❧✐❞❛çã♦ ❞❡ ❛❝✉rá❝✐❛✱ ❝♦❜❡rt✉r❛✱ ♥♦✈✐❞❛❞❡ ❡ s❡r❡♥❞✐♣✐t②✳
❆ ✉t✐❧✐③❛çã♦ ❞❡ ❛❧❣♦r✐t♠♦s ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ♦❜❥❡t✐✈❛ ❝♦♠♣r❡❡♥❞❡r ❛s ♣r❡✲ ❢❡rê♥❝✐❛s ❞♦s ✉s✉ár✐♦s s♦❜r❡ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦s ✐t❡♥s✱ ❛❧❝❛♥ç❛♥❞♦ r❡❝♦♠❡♥❞❛çõ❡s ♠❛✐s ❛❝✉r❛❞❛s✳ ◆♦ ❡st✉❞♦ ❞❡ ❝❛s♦ ✐♠♣❧❡♠❡♥t❛❞♦✱ ♦ ❙✐st❡♠❛ ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ❳Pr❡❢❘❡❝✱ ❛♣❧✐✲ ❝❛♠♦s ✉♠ ❛❧❣♦r✐t♠♦ ♠✐♥❡r❛❞♦r ❞❡ ✉♠ t✐♣♦ ❡s♣❡❝✐❛❧ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❝♦♥t❡①t✉❛✐s✱ ❛ ✜♠ ❞❡ ❞❡✜♥✐r q✉❛❧ ❛ ♣r❡❢❡rê♥❝✐❛ ❞♦ ✉s✉ár✐♦ ❞✐❛♥t❡ ❞❡ ❞❡t❡r♠✐♥❛❞♦ ❝♦♥t❡①t♦✳
❆♥❛❧✐s❛♠♦s ❛✐♥❞❛ q✉❛✐s sã♦ ♦s ❢❛t♦r❡s ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ♣r♦♣♦st❛ q✉❡ ✐♥✢✉❡♥❝✐❛♠ ♥❛ ♣❡r❢♦r♠❛♥❝❡ ❞♦ ❙✐st❡♠❛ ❞❡ ❘❡❝♦♠❡♥❞❛çã♦✱ ❡ r❡❛❧✐③❛♠♦s ❛ ❝♦♠♣❛r❛çã♦ ❞♦ ❞❡s❡♠♣❡♥❤♦ ❞❡ss❡ s✐st❡♠❛ ❝♦♠ ♦ ❡st❛❞♦ ❞❛ ❛rt❡ ❡♠ r❡❧❛çã♦ ❛ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ❤í❜r✐❞♦s✳
❆❜str❛❝t
❚❤❡ ❤✉❣❡ ❛♠♦✉♥t ♦❢ ✐♥❢♦r♠❛t✐♦♥ ❛✈❛✐❧❛❜❧❡ ♦♥ t❤❡ ✇❡❜ ❤❛s ❜♦t❤❡r❡❞ ✉s❡rs t♦ s❡❧❡❝t ✐t❡♠s t❤❛t ♠❡❡t t❤❡✐r ♥❡❡❞s ✳ ❚❤❡ ❘❡❝♦♠♠❡♥❞❡r ❙②st❡♠s ❡♠❡r❣❡❞ ❛s ✐♥❞✐s♣❡♥s❛❜❧❡ t♦♦❧s ✐♥ t❤✐s ✐♥❢♦r♠❛t✐♦♥ ♦✈❡r❧♦❛❞ s❝❡♥❛r✐♦ ✐♥ ♦r❞❡r t♦ ✜❧t❡r ♦✉t ✇❤❛t ✐s ♦❢ ✐♥t❡r❡st t♦ t❤❡ ✉s❡r ❛♥❞ ❛❧❧♦✇ ❤✐♠ t♦ ❤❛✈❡ ❛ ❞✐✛❡r❡♥t✐❛t❡❞ ❡①♣❡r✐❡♥❝❡ ✇✐t❤ ❡①✐st✐♥❣ ✐♥❢♦r♠❛t✐♦♥ s②st❡♠s✳
❲❡ ♣r❡s❡♥t ❛ ♠❡t❤♦❞♦❧♦❣② ❢♦r ❞❡✈❡❧♦♣✐♥❣ r❡❝♦♠♠❡♥❞❛t✐♦♥ s②st❡♠s✱ ✉s✐♥❣ ♠✐♥✐♥❣ ❛❧✲ ❣♦r✐t❤♠s ♣r❡❢❡r❡♥❝❡s✿ Pr❡❢❘❡❝✳ ❲❡ ❛✐♠ ❛t ❜✉✐❧❞✐♥❣ ❘❡❝♦♠♠❡♥❞❡r ❙②st❡♠s t❤❛t ❤❛✈❡ ❣♦♦❞ ✈❛❧✉❡s ♦❢ ❛❝❝✉r❛❝② ❛♥❞ ❛❧❧♦✇✐♥❣ ❛ ♠♦r❡ s❛t✐s❢②✐♥❣ ✐♥t❡r❛❝t✐♦♥ t♦ t❤❡ ✉s❡r✱ ❢r♦♠ t❤❡ ✈❛❧✐❞❛t✐♦♥ ♠❡❛s✉r❡s ♦❢ ❛❝❝✉r❛❝②✱ ❝♦✈❡r❛❣❡✱ ♥♦✈❡❧t② ❛♥❞ s❡r❡♥❞✐♣✐t②✳
❚❤❡ ✉s❡ ♦❢ ❛❧❣♦r✐t❤♠s ❢♦r ♠✐♥✐♥❣ ♣r❡❢❡r❡♥❝❡s ♦❜❥❡❝t✐✈❡❧② ✉♥❞❡rst❛♥❞ t❤❡ ✉s❡r✬s ♣r❡❢❡✲ r❡♥❝❡s ❛❜♦✉t t❤❡ ❝❤❛r❛❝t❡r✐st✐❝s ♦❢ t❤❡ ✐t❡♠s✱ ❛❝❤✐❡✈✐♥❣ ♠♦r❡ ❛❝❝✉r❛t❡ r❡❝♦♠♠❡♥❞❛t✐♦♥s✳ ■♥ t❤❡ ❝❛s❡ st✉❞② ✐♠♣❧❡♠❡♥t❡❞✱ t❤❡ ❘❡❝♦♠♠❡♥❞❛t✐♦♥ ❙②st❡♠ ❳Pr❡❢❘❡❝✱ ✇❡ ❛♣♣❧② ❛ ♠✐✲ ♥✐♥❣ ❛❧❣♦r✐t❤♠ ❢r♦♠ ❛ s♣❡❝✐❛❧ t②♣❡ ♦❢ ❝♦♥t❡①t✉❛❧ ♣r❡❢❡r❡♥❝❡s ✐♥ ♦r❞❡r t♦ ❞❡✜♥❡ t❤❡ ✉s❡r ♣r❡❢❡r❡♥❝❡s ♦♥ ❛ ❝❡rt❛✐♥ ❝♦♥t❡①t✳
❲❡ ❛❧s♦ ❛♥❛❧②③❡❞ ✇❤❛t ❛r❡ t❤❡ ❢❛❝t♦rs t❤❛t ✐♥✢✉❡♥❝❡ t❤❡ ♠❡t❤♦❞♦❧♦❣② ♣r♦♣♦s❡❞ ✐♥ t❤❡ ❘❡❝♦♠♠❡♥❞❛t✐♦♥ ❙②st❡♠ ♣❡r❢♦r♠❛♥❝❡ ❛♥❞ ♣r❡s❡♥ts t❤❡ ❝♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ♣❡r❢♦r♠❛♥❝❡ ♦❢ t❤✐s s②st❡♠ ✇✐t❤ t❤❡ st❛t❡ ♦❢ t❤❡ ❛rt r❡❣❛r❞✐♥❣ ❍②❜r✐❞ ❘❡❝♦♠♠❡♥❞❡r ❙②st❡♠s✳
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✈✐✐
✶ ■♥tr♦❞✉çã♦ ✶✾
✷ ❈♦♥❝❡✐t♦s ♣r❡❧✐♠✐♥❛r❡s ✷✸
✷✳✶ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✶✳✶ ❆❜♦r❞❛❣❡♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✶✳✷ ❉❡s❛✜♦s ❡♠ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✷✳✶✳✸ ▼❡❞✐❞❛s ❞❡ ◗✉❛❧✐❞❛❞❡ ❡♠ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✷ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✳✷✳✶ ▼♦❞❡❧♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ◗✉❛❧✐t❛t✐✈❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✷✳✷✳✷ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ◆ã♦ ❈♦♥t❡①t✉❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✷✳✷✳✸ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ❈♦♥t❡①t✉❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✸ ❚r❛❜❛❧❤♦s ❈♦rr❡❧❛t♦s ✹✺
✸✳✶ ❆❜♦r❞❛❣❡♥s ❞❡ ❋✐❧tr❛❣❡♠ ❈♦❧❛❜♦r❛t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✸✳✷ ❆❜♦r❞❛❣❡♥s ❇❛s❡❛❞❛s ❡♠ ❈♦♥t❡ú❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✸✳✸ ❆❜♦r❞❛❣❡♥s ❍í❜r✐❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✹ ❆❜♦r❞❛❣❡♥s q✉❡ ❯t✐❧✐③❛♠ ▼✐♥❡r❛çã♦ ❞❡ ❉❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✹ ❆ ▼❡t♦❞♦❧♦❣✐❛ Pr❡❢❘❡❝ ♣❛r❛ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ✺✸ ✹✳✶ ❊t❛♣❛ ✶ ✲ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ❯s✉ár✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✷ ❊t❛♣❛ ✷ ✲ ❆❣r✉♣❛♠❡♥t♦ ❞♦s ❯s✉ár✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✸ ❊t❛♣❛ ✸ ✲ ❆❣r❡❣❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ■♥❞✐✈✐❞✉❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✸✳✶ ▼é❞✐❛ ❆r✐t♠ét✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✹✳✸✳✷ ▼é❞✐❛ P♦♥❞❡r❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✹✳✸✳✸ ◗✉❛♥t✐✜❝❛❞♦r❡s ❋✉③③② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✹ ❊t❛♣❛ ✹ ✲ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✺ ❊t❛♣❛ ✺ ✲ ❘❡❝♦♠❡♥❞❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹
✺ ❱❛❧✐❞❛çã♦ ❞❛ ▼❡t♦❞♦❧♦❣✐❛ Pr❡❢❘❡❝ ✻✼
✺✳✶ ❉❛❞♦s ❞❡ ❚❡st❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼
①✈✐ ❙✉♠ár✐♦
✺✳✷ ▼❡❞✐❞❛s ❞❡ ❱❛❧✐❞❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✺✳✷✳✶ ❆❝✉rá❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✺✳✷✳✷ ❈♦❜❡rt✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✺✳✷✳✸ ◆♦✈✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✺✳✷✳✹ ❙❡r❡♥❞✐♣✐t② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✺✳✸ ❋❛t♦r❡s q✉❡ ■♥✢✉❡♥❝✐❛♠ ♥♦ ❉❡s❡♠♣❡♥❤♦ ❞❛ ▼❡t♦❞♦❧♦❣✐❛ Pr❡❢❘❡❝ ✳ ✳ ✳ ✳ ✳ ✼✹ ✺✳✹ ❈♦♠♣❛r❛çã♦ ❝♦♠ ❖✉tr♦s ❚r❛❜❛❧❤♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻
✻ ❘❡s✉❧t❛❞♦s ❊①♣❡r✐♠❡♥t❛✐s ✼✾
✻✳✶ ❋❛t♦r❡s q✉❡ ■♥✢✉❡♥❝✐❛♠ ♥♦ ❉❡s❡♠♣❡♥❤♦ ❞❛ ▼❡t♦❞♦❧♦❣✐❛ Pr❡❢❘❡❝ ✳ ✳ ✳ ✳ ✳ ✼✾ ✻✳✶✳✶ ●r✉♣♦ ❞❡ ❚❡st❡ ✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✻✳✶✳✷ ●r✉♣♦ ❞❡ ❚❡st❡ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✻✳✶✳✸ ●r✉♣♦ ❞❡ ❚❡st❡ ✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✻✳✷ ❈♦♠♣❛r❛çã♦ ❝♦♠ ❖✉tr♦s ❚r❛❜❛❧❤♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✻✳✷✳✶ ❆❝✉rá❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✻✳✷✳✷ ❈♦❜❡rt✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✻✳✷✳✸ ◆♦✈✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✻✳✷✳✹ ❙❡r❡♥❞✐♣✐t② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✻✳✷✳✺ ❚❡♠♣♦ ❞❡ ❊①❡❝✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻
✼ ❈♦♥❝❧✉sõ❡s ❡ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ✽✾
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶✳✶ ❈❛♣ít✉❧♦s ❞❛ ❞✐ss❡rt❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✷✳✶ ❈❛t❡❣♦r✐❛s ❞❛ ❋✐❧tr❛❣❡♠ ❈♦❧❛❜♦r❛t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✷ ✭❛✮ ❯♠❛ ✐♥stâ♥❝✐❛ ■ ❡ ✭❜✮ ✉♠ ❜❛♥❝♦ ❞❡ ❞❛❞♦s ❞❡ ♣r❡❢❡rê♥❝✐❛ P ❬❞❡ ❆♠♦
❡t ❛❧✳ ✷✵✶✷❛❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✷✳✸ ❘❡❞❡ ❞❡ ♣r❡❢❡rê♥❝✐❛ P◆❡t✶ ❬❞❡ ❆♠♦ ❡t ❛❧✳ ✷✵✶✷❛❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✳✶ ❈❧✉st❡r✐③❛çã♦ ❞♦s ✉s✉ár✐♦s ❡♠ ❬●♦❧❞❜❡r❣ ❡t ❛❧✳ ✷✵✵✶❪ ❝♦♠ ✹ ♥í✈❡✐s ❞❡ r❡✲
❝✉rsã♦ ❢♦r♠❛♥❞♦ ✹✵ ❝❧✉st❡rs✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✸✳✷ ●r❛❢♦ ❜❛s❡❛❞♦ ❡♠ ✉s✉ár✐♦s ❡ ✐t❡♥s ❡♠ ❬❍✉❛♥❣ ❡t ❛❧✳ ✷✵✵✹❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✶ ❆rq✉✐t❡t✉r❛ ●❡r❛❧ ❞❛ ▼❡t♦❞♦❧♦❣✐❛ Pr❡❢❘❡❝ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✷ ❆❧❣♦r✐t♠♦ ❈✉r❡ ❝♦♠ ❞✐❢❡r❡♥t❡s ❢❛t♦r❡s ❞❡ r❡tr❛çã♦✳ ❋♦♥t❡✿ ❬●✉❤❛ ❡t ❛❧✳
✷✵✵✶❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✸ ❈❧✉st❡rs ❜❛s❡❛❞♦s ❡♠ ❞❡♥s✐❞❛❞❡✳ ❋♦♥t❡✿ ❬❊st❡r ❡t ❛❧✳ ✶✾✾✻❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✹ ❊①❡♠♣❧♦s ❞❡Mpref′s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵
✹✳✺ ◗✉❛♥t✐✜❝❛❞♦r❡s ❢✉③③② ❡ s❡✉s ♣❛râ♠❡tr♦s✳ ❋♦♥t❡✿ ❬❈❤✐❝❧❛♥❛ ❡t ❛❧✳ ✷✵✵✶❪ ✳ ✳ ✻✶ ✹✳✻ Mpref′s ❝❛❧❝✉❧❛❞❛s ❝♦♠ q✉❛♥t✐✜❝❛❞♦r❡s ❢✉③③② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷
✹✳✼ ❊♥tr❛❞❛ ❡ ❙❛í❞❛ ❞♦ ▼✐♥❡r❛❞♦r ❞❡ Pr❡❢❡rê♥❝✐❛s ♥❛ ♠❡t♦❞♦❧♦❣✐❛ Pr❡❢❘❡❝ ✳ ✳ ✻✸ ✹✳✽ ❆❧❣♦r✐t♠♦ ❖r❞❡r✲❇②✲Pr❡❢❡r❡♥❝❡s ❛❞❛♣t❛❞♦ ❞❡ ❬❈♦❤❡♥ ❡t ❛❧✳ ✶✾✾✾❪ ✳ ✳ ✳ ✻✹ ✺✳✶ ❚r❛♥s❢♦r♠❛çã♦ ❞❡ ❛✈❛❧✐❛çõ❡s ♣❛r❛ ♣❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
❖ ❝r❡s❝✐♠❡♥t♦ ❞❡ ♠❡r❝❛❞♦s ♦♥❧✐♥❡✱ ❛ ✐♥tr♦❞✉çã♦ ❞❡ ♥♦✈♦s s❡r✈✐ç♦s ✈✐rt✉❛✐s✱ ♦ ❝r❡s❝✐✲ ♠❡♥t♦ ❡①♣❧♦s✐✈♦ ❞❛ ✐♥t❡r♥❡t ❡ ❛ ✈❛r✐❡❞❛❞❡ ❞❡ ✐♥❢♦r♠❛çã♦ ❞✐s♣♦♥í✈❡❧ ♥❛ ❲❡❜ t❡♠ t✐❞♦ ✉♠ ✐♠♣❛❝t♦ ❝♦♥s✐❞❡rá✈❡❧ ♥♦s ❤á❜✐t♦s ❞♦s ❝♦♥s✉♠✐❞♦r❡s✱ ♣r♦✈❡♥❞♦ ❛ ❡❧❡s ❛❝❡ss♦ ❛ ✉♠❛ ❡♥♦r♠❡ ✈❛r✐❡❞❛❞❡ ❞❡ ♣r♦❞✉t♦s ❡ ✐♥❢♦r♠❛çõ❡s✳
❊♥q✉❛♥t♦ ❛ ❧✐❜❡r❞❛❞❡ ❞❡ ❝♦♠♣r❛ t❡♠ ❢❡✐t♦ ❞♦ ❝♦♠ér❝✐♦ ♦♥❧✐♥❡ ✉♠❛ ✐♥❞ústr✐❛ ♠✉❧t✐❜✐❧✐✲ ♦♥ár✐❛✱ t❛♠❜é♠ ❢❡③ ❝♦♠ q✉❡ s❡❥❛ ♠❛✐s ❞✐❢í❝✐❧ ♣❛r❛ ♦s ❝♦♥s✉♠✐❞♦r❡s s❡❧❡❝✐♦♥❛r ♣r♦❞✉t♦s q✉❡ ♠❡❧❤♦r ❛t❡♥❞❛♠ s✉❛s ♥❡❝❡ss✐❞❛❞❡s✳ ❆ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ✐♥❢♦r♠❛çã♦ ❢r❡q✉❡♥t❡♠❡♥t❡ s♦❜r❡❝❛rr❡❣❛ ♦s ✉s✉ár✐♦s✱ ❢❛③❡♥❞♦ ❝♦♠ q✉❡ ❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❞❡ ❡s❝♦❧❤❛s✱ ♥♦ ❧✉❣❛r ❞❡ ♣r♦✲ ❞✉③✐r ✉♠ ❜❡♥❡❢í❝✐♦✱ ❝♦♠❡❝❡ ❛ ❞✐♠✐♥✉✐r ♦ ❜❡♠✲❡st❛r ❞♦s ✉s✉ár✐♦s✳ ❖s ✉s✉ár✐♦s ❝♦♠❡ç❛♠ ❛ ❡♥❝♦♥tr❛r ♠✉✐t❛ ❞✐✜❝✉❧❞❛❞❡ ♣❛r❛ ❝❤❡❣❛r às ❡s❝♦❧❤❛s ♠❛✐s ❛♣r♦♣r✐❛❞❛s ❞❡♥tr❡ ❛ ✐♠❡♥s✐❞ã♦ ❞❡ ✈❛r✐❡❞❛❞❡s ❞❡ ✐t❡♥s ✭♣r♦❞✉t♦s ❡ s❡r✈✐ç♦s✮ q✉❡ ❡st❡s ✇❡❜ s✐t❡s ♦❢❡r❡❝❡♠✳
❉✐❛♥t❡ ❞❡st❡ ❝❡♥ár✐♦✱ ♥♦✈♦s s✐st❡♠❛s ❞❡ ✐♥❢♦r♠❛çã♦ ❝♦♠❡ç❛r❛♠ ❛ s✉r❣✐r ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ✜❧tr❛r ✐♥❢♦r♠❛çõ❡s út❡✐s ❛♦s ✉s✉ár✐♦s✳ ❆♦ t❡♥t❛r ❢❛③❡r ❛❧❣✉♠❛ ❡s❝♦❧❤❛✱ ♦ ✉s✉ár✐♦ só r❡❝❡❜❡ ❛s ✐♥❢♦r♠❛çõ❡s q✉❡ ❧❤❡ sã♦ ♣❡rt✐♥❡♥t❡s✳ ❆ ❡st❡s s✐st❡♠❛s ❞á✲s❡ ♦ ♥♦♠❡ ❞❡ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ q✉❡ ♣♦❞❡♠ s❡r ❞❡✜♥✐❞♦s ❝♦♠♦ ❢❡rr❛♠❡♥t❛s ❡ té❝♥✐❝❛s q✉❡ ❢♦r♥❡❝❡♠ s✉❣❡stõ❡s ❞❡ ✐t❡♥s ❛ s❡r❡♠ ✉t✐❧✐③❛❞♦s ♣❡❧♦s ✉s✉ár✐♦s✳
❖s ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ s✉r❣❡♠ ❝♦♠♦ ✉♠❛ ❢❡rr❛♠❡♥t❛ ✐♥❞✐s♣❡♥sá✈❡❧ ♥♦s ❞✐❛s ❛t✉❛✐s ❞❡✈✐❞♦ ❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ✐♥❢♦r♠❛çã♦ ❞✐s♣♦♥✐❜✐❧✐③❛❞❛✳ ❆❧é♠ ❞❡ s❡r✈✐r ❝♦♠♦ ✉♠ ✜❧tr♦ q✉❡ ♣♦❞❡ s❡r ♠✉✐t♦ ❡✜❝✐❡♥t❡✱ ❡❧❡ ♣❡r♠✐t❡ ✉♠❛ ❡①♣❡r✐ê♥❝✐❛ ❞✐❢❡r❡♥❝✐❛❞❛ ❞♦ ✉s✉ár✐♦ ❝♦♠ ♦ s✐st❡♠❛ ❞❡ ✐♥❢♦r♠❛çã♦✱ q✉❡ ♦ ❞❡✐①❛ ♠❛✐s s❛t✐s❢❡✐t♦ ❝♦♠ ❛s tr❛♥s❛çõ❡s q✉❡ ❡❧❡ r❡❛❧✐③❛✳ ◆♦s ú❧t✐♠♦s t❡♠♣♦s✱ t❡♠ s❡ ❝♦♥st❛t❛❞♦ q✉❡✱ q✉❛♥t♦ ♠❛✐s ♣❡rs♦♥❛❧✐③❛❞♦ é ♦ ❛t❡♥❞✐♠❡♥t♦ ❛♦ ❝❧✐❡♥t❡✱ t❛♥t♦ ♠❛✐s ✜❡❧ ❡❧❡ s❡ t♦r♥❛ à ❡♠♣r❡s❛✳ ❆❧é♠ ❞✐ss♦✱ ❛s r❡❝♦♠❡♥❞❛çõ❡s q✉❛♥❞♦ ❜❡♠ ❢❡✐t❛s ♣♦❞❡♠ ❛✉♠❡♥t❛r ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ✐t❡♥s ✈❡♥❞✐❞♦s✱ ❛❧é♠ ❞❡ ❝♦❧❛❜♦r❛r ♥❛ ✈❡♥❞❛ ❞❡ ✉♠❛ ♠❛✐♦r ❞✐✈❡rs✐❞❛❞❡ ❞❡ ♣r♦❞✉t♦s✳ ❊♥✜♠✱ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ tr❛③❡♠ ✈❛♥t❛❣❡♥s ♥ã♦ só ♣❛r❛ ♦ ✉s✉ár✐♦ q✉❡ ❛❧❝❛♥ç❛ ✉♠❛ ❡①♣❡r✐ê♥❝✐❛ ♠❛✐s s❛t✐s❢❛tór✐❛✱ ♠❛s t❛♠❜é♠ ♣❛r❛ ♦s ❡♠♣r❡❡♥❞✐♠❡♥t♦s✱ q✉❡ ❞❡s❝♦❜r❡♠ ♠❛✐s s♦❜r❡ ❛s ♣r❡❢❡rê♥❝✐❛s ❞♦s s❡✉s ❝❧✐❡♥t❡s ❡ ❛ss✐♠ ♣♦❞❡♠ t❡r ♠❛✐s s✉❝❡ss♦✳
✷✵ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦
r❡❝♦♠❡♥❞❛çã♦ ❞❡ ❡♥tr❡t❡♥✐♠❡♥t♦ ✭✇✇✇✳❧❛st✳❢♠❀ ✇✇✇✳②♦✉t✉❜❡✳❝♦♠❀ ✇✇✇✳♥❡t✢✐①✳❝♦♠✮✱ ❝♦♥t❡ú❞♦ ✭✇✇✇✳②❛❤♦♦✳❝♦♠✮✱ ❡✲❝♦♠♠❡r❝❡ ✭✇✇✇✳❛♠❛③♦♥✳❝♦♠❀ ✇✇✇✳s✉❜♠❛r✐♥♦✳❝♦♠✳❜r✮ ❡ s❡r✈✐ç♦s ✭✇✇✇✳tr✐♣❛❞✈✐s♦r✳❝♦♠✮✳ ❚❛♠❜é♠ ❤á tr❛❜❛❧❤♦s ❞❡ r❡❝♦♠❡♥❞❛çã♦ ❞❡ ❝♦❧❛❜♦r❛❞♦r❡s ❞❡ ♣❡sq✉✐s❛ ✭ ❬❇r❛♥❞ã♦ ❡ ▼♦r♦ ✷✵✶✷❪✮✱ ❞❡ ❛♠✐③❛❞❡s ✭✇✇✇✳❢❛❝❡❜♦♦❦✳❝♦♠✮✱ ❡♥tr❡ ♦✉tr❛s t❛♥t❛s ❛♣❧✐❝❛çõ❡s✳
❖s ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ✉t✐❧✐③❛♠✲s❡ ❞❡ ✈ár✐❛s té❝♥✐❝❛s ♣❛r❛ ❝♦♥s❡❣✉✐r r❡❝♦♠❡♥✲ ❞❛r✳ ❆q✉❡❧❡s ❞❡♥♦♠✐♥❛❞♦s ❇❛s❡❛❞♦s ❡♠ ❈♦♥t❡ú❞♦ ❛✈❛❧✐❛♠✱ ♣♦r ❡①❡♠♣❧♦✱ ♦ ❤✐stór✐❝♦ ❞❡ ❝♦♠♣r❛s ❞♦s ✉s✉ár✐♦s ❡ r❡❝♦♠❡♥❞❛♠ ✐t❡♥s s❡♠❡❧❤❛♥t❡s ❛♦ q✉❡ ❡❧❡ ❥á ♠♦str♦✉ ✐♥t❡r❡ss❡✳ ❏á ♦s s✐st❡♠❛s ❞❡ ❋✐❧tr❛❣❡♠ ❈♦❧❛❜♦r❛t✐✈❛ r❡❝♦♠❡♥❞❛♠ ✐t❡♥s ❛♦ ✉s✉ár✐♦ ❛t✐✈♦ ✭✉s✉ár✐♦ ❛♦ q✉❛❧ s❡ ❞❡s❡❥❛ r❡❝♦♠❡♥❞❛r✮ ❛ ♣❛rt✐r ❞❡ ♦✉tr♦s ✉s✉ár✐♦s q✉❡ t❡♥❤❛♠ ♣r❡❢❡rê♥❝✐❛s s❡♠❡❧❤❛♥t❡s✱ ✐st♦ é✱ q✉❡ ♣♦ss✉❛♠ ✉♠ ❤✐stór✐❝♦ ❞❡ ❝♦♠♣r❛s✴❛✈❛❧✐❛çõ❡s s✐♠✐❧❛r❡s✳ ❖s ✐t❡♥s ❥á ❛✈❛❧✐❛❞♦s ♣❡❧♦s ✉s✉ár✐♦s s❡♠❡❧❤❛♥t❡s sã♦ r❡❝♦♠❡♥❞❛❞♦s ❛♦ ✉s✉ár✐♦ ❛t✐✈♦✳ ❊ss❛ ❛❜♦r❞❛❣❡♠ ♣❛rt❡ ❞♦ ♣r✐♥❝í♣✐♦ ❞❡ q✉❡ s❡ ❞✉❛s ♣❡ss♦❛s ❝♦♥❝♦r❞❛r❛♠ ♥♦ ♣❛ss❛❞♦ ✭❝♦♠♣r❛r❛♠ ♦✉ ❛✈❛❧✐❛r❛♠ ✐t❡♥s ❞❡ ❢♦r♠❛ s❡♠❡❧❤❛♥t❡✮✱ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡❧❛s ❝♦♥t✐♥✉❛r❡♠ ❝♦♥❝♦r❞❛♥❞♦ ♥♦ ❢✉t✉r♦ é ❣r❛♥❞❡✳ ❊ss❛ ❛❜♦r❞❛❣❡♠ t❡♠ s❡ t♦r♥❛❞♦ ❛ ♠❛✐s ♣♦♣✉❧❛r ❡♠ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ❛ ♣❛rt✐r ❞♦s ❜♦♥s r❡s✉❧t❛❞♦s q✉❡ ❡❧❛ ♦❜té♠✳
P❛r❛ ❛❧❝❛♥ç❛r ❜♦❛s r❡❝♦♠❡♥❞❛çõ❡s✱ ♦s ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ❡♥❢r❡♥t❛♠ ❞✐✈❡r✲ s♦s ❞❡s❛✜♦s✳ ❈♦♠♦ ❛s r❡❝♦♠❡♥❞❛çõ❡s sã♦ ❡①tr❛í❞❛s ❛ ♣❛rt✐r ❞❡ ❞❛❞♦s ❥á ❡①✐st❡♥t❡s✱ ✉♠ ♣r✐♠❡✐r♦ ❞❡s❛✜♦ é ❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❞❡ss❡s ❞❛❞♦s✳ ◗✉❛♥t♦ ♠❛✐s ✐♥❢♦r♠❛çã♦✱ ♠❛✐s ❛❝✉r❛❞❛ é ❛ r❡❝♦♠❡♥❞❛çã♦✳ P♦✉❝❛ ✐♥❢♦r♠❛çã♦ ❣❡r❛ r❡❝♦♠❡♥❞❛çõ❡s ♣♦❜r❡s✳ P♦ré♠✱ ❛♦ ♠❡s♠♦ t❡♠♣♦ q✉❡ é ♥❡❝❡ssár✐❛ ♠✉✐t❛ ✐♥❢♦r♠❛çã♦ ♣❛r❛ ❜♦❛s r❡❝♦♠❡♥❞❛çõ❡s✱ ♦ ❞❡s❡♠♣❡♥❤♦ ❞❡ q✉❛❧q✉❡r s✐st❡♠❛ ♣♦❞❡ s❡r ❝♦♠♣r♦♠❡t✐❞♦ ♣♦r ❡ss❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❞❛❞♦s✱ ✐st♦ é✱ ♦ s✐st❡♠❛ ♣r❡❝✐s❛ s❡r ❡s❝❛❧á✈❡❧ ❡♠ r❡❧❛çã♦ ❛♦ ❛✉♠❡♥t♦ ❞♦s ❞❛❞♦s ❝♦♠ ♦ t❡♠♣♦✳ ❖✉tr♦s ❞❡s❛✜♦s ❡s✲ ♣❡❝í✜❝♦s sã♦✿ ❝♦♠♦ r❡❝♦♠❡♥❞❛r ♣❛r❛ ✉♠ ✉s✉ár✐♦ q✉❡ ❛❝❛❜♦✉ ❞❡ s❡ ❝❛❞❛str❛r ♥♦ s✐st❡♠❛❄ ❈♦♠♦ r❡❝♦♠❡♥❞❛r ✉♠ ✐t❡♠ q✉❡ ❛❝❛❜♦✉ ❞❡ s❡r ✐♥❝❧✉í❞♦ ♥♦ ❜❛♥❝♦ ❞❡ ❞❛❞♦s❄
❚❡♥t❛♥❞♦ ♠✐♥✐♠✐③❛r ❡st❡s ❞❡s❛✜♦s✱ ♠✉✐t♦s ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ✐♥❝♦r♣♦r❛♠ ❛❜♦r❞❛❣❡♥s ❤í❜r✐❞❛s ❡♥tr❡ ❛s té❝♥✐❝❛s ❇❛s❡❛❞❛s ❡♠ ❈♦♥t❡ú❞♦ ❡ ❞❡ ❋✐❧tr❛❣❡♠ ❈♦❧❛❜♦r❛t✐✈❛✱ ❛❣r❡❣❛♥❞♦ ❛s ✈❛♥t❛❣❡♥s q✉❡ ❝❛❞❛ ✉♠❛ ❛♣r❡s❡♥t❛✳ ❆❧é♠ ❞✐ss♦✱ ♦✉tr♦ r❡❝✉rs♦ é ❝♦♥❤❡❝❡r ❝♦♠ ❞❡t❛❧❤❡ ❛s ♣r❡❢❡rê♥❝✐❛s ❞♦s ✉s✉ár✐♦s ♣❛r❛ ❝♦♥s❡❣✉✐r r❡❝♦♠❡♥❞❛r ✐t❡♥s r❡❛❧♠❡♥t❡ út❡✐s ❛ ❡❧❡✳
◆❡st❡ ❝♦♥t❡①t♦✱ ❛♣r❡s❡♥t❛♠♦s ♥❡st❛ ❞✐ss❡rt❛çã♦ ✉♠❛ ♠❡t♦❞♦❧♦✐❣❛ ♣❛r❛ ❞❡s❡♥✈♦❧✈✐✲ ♠❡♥t♦ ❞❡ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ✉t✐❧✐③❛♥❞♦ ❛❧❣♦r✐t♠♦s ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s✿ ❛ Pr❡❢❘❡❝✳ ❖❜❥❡t✐✈❛♠♦s ❝♦♠ ❡ss❛ ♣r♦♣♦st❛ ❛ ❝♦♥str✉çã♦ ❞❡ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ❤í❜r✐❞♦s✱ ❡♥tr❡ ❛s ❛❜♦r❞❛❣❡♥s ❇❛s❡❛❞❛ ❡♠ ❈♦♥t❡ú❞♦ ❡ ❞❡ ❋✐❧tr❛❣❡♠ ❈♦❧❛❜♦r❛t✐✈❛✱ ❝❛✲ ♣❛③❡s ❞❡ r❡❝♦♠❡♥❞❛r ✐t❡♥s ❛✐♥❞❛ ♥ã♦ ❛✈❛❧✐❛❞♦s✱ q✉❡ t❡♥❤❛♠ ❜♦♥s ✈❛❧♦r❡s ❞❡ ❛❝✉rá❝✐❛ ❡ q✉❡ ♣❡r♠✐t❛♠ ✉♠❛ ✐♥t❡r❛çã♦ ♠❛✐s s❛t✐s❢❛tór✐❛ ❝♦♠ ♦ ✉s✉ár✐♦✳
✷✶
❞❛ ❝♦❧❛❜♦r❛çã♦ ❡♥tr❡ ✉s✉ár✐♦s ❥á ❝❛❞❛str❛❞♦s ♥♦ s✐st❡♠❛✳ ❖s ✉s✉ár✐♦s sã♦ ♦r❣❛♥✐③❛❞♦s ❡♠ ❣r✉♣♦s ♣❛r❛ ❞❡✜♥✐çã♦ ❞❡ ♣❡r✜s ❞❡ ♣r❡❢❡rê♥❝✐❛s✳ ❈❛❞❛ ♣❡r✜❧ é ❞❡✜♥✐❞♦ ❛ ♣❛rt✐r ❞❛ ♠✐♥❡r❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❞♦s ✉s✉ár✐♦s ♣❡rt❡♥❝❡♥t❡s ❛♦ ❣r✉♣♦✳
❆ ✉t✐❧✐③❛çã♦ ❞❡ ❛❧❣♦r✐t♠♦s ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ✈✐s❛ ❛❧❝❛♥ç❛r ✉♠ ❙✐st❡♠❛ ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ♠❛✐s ❛❝✉r❛❞♦ ❛ ♣❛rt✐r ❞♦ ♠❡❧❤♦r ❝♦♥❤❡❝✐♠❡♥t♦ s♦❜r❡ ♦ q✉❡ ♦s ✉s✉ár✐♦s ♣r❡❢❡r❡♠✳ ❆❧é♠ ❞✐ss♦✱ ♦ ♠♦❞❡❧♦ ❞❡ ♣r❡❢❡rê♥❝✐❛ ♠✐♥❡r❛❞♦ ❞❡✈❡ s❡r ❝❛♣❛③ ❞❡ r❡❝♦♠❡♥❞❛r ♦s ✐t❡♥s ❛ ♣❛rt✐r ❞❛s ❝❛r❛❝t❡ríst✐❝❛s q✉❡ ❡❧❡s ❛♣r❡s❡♥t❛♠✱ ♠✐♥✐♠✐③❛♥❞♦ ♦ ♣r♦❜❧❡♠❛ ❞❡ r❡❝♦♠❡♥❞❛çã♦ ❞❡ ✐t❡♥s r❡❝é♠ ✐♥s❡r✐❞♦s ♥♦ s✐st❡♠❛✳
◆♦ ❡st✉❞♦ ❞❡ ❝❛s♦ r❡❛❧✐③❛❞♦ ♥❡st❡ tr❛❜❛❧❤♦✱ ♣r♦♣♦♠♦s ❛ ❛♣❧✐❝❛çã♦ ❞❡ ✉♠❛ ♠❛♥❡✐r❛ ❡s♣❡❝í✜❝❛ ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s✿ ❛s r❡❣r❛s ❞❡ ♣r❡❢❡rê♥❝✐❛s ❝♦♥t❡①t✉❛✐s✳ ❊st❛s r❡❣r❛s ♣❡r♠✐t❡♠ q✉❡✱ ❞❛❞♦s ❞♦✐s ✐t❡♥s✱ s❡❥❛ ♣♦ssí✈❡❧ ✐♥❢❡r✐r q✉❛❧ ❞❡❧❡s é ♣r❡❢❡r✐❞♦ ❛ ♣❛rt✐r ❞❛s ❝❛r❛❝t❡ríst✐❝❛s q✉❡ ❡❧❡s ❛♣r❡s❡♥t❛♠✳ ❆❧é♠ ❞✐ss♦✱ ❡st❛ ❢♦r♠❛ ❞❡ r❡♣r❡s❡♥t❛r ♣r❡❢❡rê♥❝✐❛s ♣❡r♠✐t❡ q✉❡ s❡❥❛ ✐♥❝❧✉í❞♦ ✉♠ ❝♦♥t❡①t♦✱ ✐st♦ é✱ q✉❛✐s ❝❛r❛❝t❡ríst✐❝❛s ❞♦s ✐t❡♥s ❞❡t❡r♠✐♥❛♠ ❛ ♣r❡❢❡rê♥❝✐❛ ❞♦ ✉s✉ár✐♦✳ ❯♠❛ r❡❣r❛ ❞❡ ♣r❡❢❡rê♥❝✐❛ ❝♦♥t❡①t✉❛❧ ♣♦❞❡ s❡r✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ❛✜r♠❛t✐✈❛✿ ✧❡♥tr❡ ❞♦✐s ✜❧♠❡s ❞❡ ❝♦♠é❞✐❛✱ ♣r❡✜r♦ ♦s ✜❧♠❡s ❝♦♠ ♦ ❛t♦r ❏✐♠ ❈❛rr❡② ❛♦s ❝♦♠ ♦ ❛t♦r ❚♦♠ ❍❛♥❦s✧✳ ◆❡st❛ ❛✜r♠❛t✐✈❛✱ ♦ ❣ê♥❡r♦ ❝♦♠é❞✐❛ é ♦ ❝♦♥t❡①t♦ s♦❜r❡ ♦ q✉❛❧ ❛❝♦♥t❡❝❡ ❛ ♣r❡❢❡rê♥❝✐❛ ❞❡ ✜❧♠❡s ❝♦♠ ♦ ❛t♦r ❏✐♠ ❈❛rr❡②✳
❉✐❛♥t❡ ❞❡st❡ ❝❡♥ár✐♦✱ ♦s ♦❜❥❡t✐✈♦s ❞❡st❡ tr❛❜❛❧❤♦ ❞❡ ❞✐ss❡rt❛çã♦ sã♦✿
• ❉❡s❡♥✈♦❧✈❡r ✉♠❛ ♠❡t♦❞♦❧♦❣✐❛ ❞❡ ❙✐st❡♠❛ ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ q✉❡ ✉t✐❧✐③❛ ❛❧❣♦r✐t♠♦s
❞❡ ♠✐♥❡r❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s❀
• ❯t✐❧✐③❛r ❛ ♠❡t♦❞♦❧♦❣✐❛ ♣❛r❛ ✐♠♣❧❡♠❡♥t❛r ♦ s✐st❡♠❛ ❳Pr❡❢❘❡❝ q✉❡ ✉t✐❧✐③❛ ✉♠ ❛❧❣♦✲
r✐t♠♦ ♠✐♥❡r❛❞♦r ❞❡ ✉♠ t✐♣♦ ❡s♣❡❝✐❛❧ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❝♦♥t❡①t✉❛✐s✳ P❡❧♦ q✉❡ s❛❜❡♠♦s✱ ♥ã♦ ❡①✐st❡ s✐st❡♠❛ ❞❡ r❡❝♦♠❡♥❞❛çã♦ ❜❛s❡❛❞♦ ♥❡st❛ r❡♣r❡s❡♥t❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❞♦ ✉s✉ár✐♦❀
• ❊st✉❞❛r ♦s ❢❛t♦r❡s q✉❡ ✐♥✢✉❡♥❝✐❛♠ ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ ❙✐st❡♠❛ ❞❡ ❘❡❝♦♠❡♥❞❛çã♦❀ • ❆♥❛❧✐s❛r ❛ ♣❡r❢♦r♠❛♥❝❡ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ♣r♦♣♦st❛ ❡♠ ❝♦♠♣❛r❛çã♦ ❛♦ ❡st❛❞♦ ❞❛
❛rt❡ ❡♠ r❡❧❛çã♦ ❛ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ❞❡ ❋✐❧tr❛❣❡♠ ❈♦❧❛❜♦r❛t✐✈❛ ❡ ❤í❜r✐❞♦✱ ❛tr❛✈és ❞❡ ❞✐❢❡r❡♥t❡s ♠❡❞✐❞❛s ❞❡ ✈❛❧✐❞❛çã♦✿ ♣r❡❝✐sã♦✱ r❡✈♦❝❛çã♦✱ ❝♦❜❡rt✉r❛✱ ♥♦✈✐❞❛❞❡ ❡ s❡r❡♥❞✐♣✐t② ✭❙❡çã♦ ✺✳✷✮✳
❆s ❝♦♥tr✐❜✉✐çõ❡s q✉❡ tr❛③❡♠♦s ♥❡ss❡ tr❛❜❛❧❤♦ sã♦✿
• ❉❡✜♥✐çã♦ ❞❡ ✉♠❛ ♠❡t♦❞♦❧♦❣✐❛ ♣❛r❛ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ q✉❡ ✉t✐❧✐③❛ ♠✐♥❡✲
r❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❝♦♠ ❞❡s❡♠♣❡♥❤♦ s✉♣❡r✐♦r ❛♦ ❡st❛❞♦ ❞❛ ❛rt❡ ✲ ❈❛♣ít✉❧♦ ✹ ❡ ❈❛♣ít✉❧♦ ✻❀
• ◆♦✈❛ ♠❛♥❡✐r❛ ❞❡ r❡♣r❡s❡♥t❛r ♦s ✉s✉ár✐♦s ❡♠ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ✲ ❈❛♣ít✉❧♦
✹❀
• ❊st✉❞♦ ❞❡ ❛❧t❡r♥❛t✐✈❛s ❞❡ ❛❣r❡❣❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❡♠ ✉♠ ❣r✉♣♦ ❞❡ ✉s✉ár✐♦s✱ ❈❛♣í✲
✷✷ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦
• ❊st✉❞♦ ❞❡ ❢❛t♦r❡s q✉❡ ✐♥✢✉❡♥❝✐❛♠ ♥♦ ❞❡s❡♠♣❡♥❤♦ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ♣r♦♣♦st❛✱ ❈❛♣í✲
t✉❧♦ ✻✳
❊st❛ ❞✐ss❡rt❛çã♦ ❡stá ♦r❣❛♥✐③❛❞❛ ❝♦♠♦ s❡❣✉❡✳ ◆♦ ❈❛♣ít✉❧♦ ✷ ✐♥tr♦❞✉③✐♠♦s ♦s ❝♦♥❝❡✐t♦s ♣r❡❧✐♠✐♥❛r❡s ♥❡❝❡ssár✐♦s ♣❛r❛ ❛ ❝♦♠♣r❡❡♥sã♦ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ Pr❡❢❘❡❝ ❡ ❞♦s tr❛❜❛❧❤♦s ❝♦rr❡❧❛t♦s✳ ❖ ❈❛♣ít✉❧♦ ✸ ❛♣r❡s❡♥t❛ ♦s tr❛❜❛❧❤♦s ❝♦rr❡❧❛t♦s ❡♠ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦✳ ❖ ❈❛♣ít✉❧♦ ✹ ❛♣r❡s❡♥t❛ ❛ ♠❡t♦❞♦❧♦❣✐❛ Pr❡❢❘❡❝ ♣r♦♣♦st❛✳ ◆♦ ❈❛♣ít✉❧♦ ✺ ❞✐s❝✉t✐♠♦s ❛ ✈❛❧✐❞❛çã♦ ❞❛ ♠❡t♦❞♦❧♦❣✐❛✳ ❖ ❈❛♣ít✉❧♦ ✻ ❛♣r❡s❡♥t❛ ♦s r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ♦❜t✐❞♦s✳ ❖ ❈❛♣ít✉❧♦ ✼ ❛♣r❡s❡♥t❛ ❛s ❝♦♥❝❧✉sõ❡s ❡ ♦s tr❛❜❛❧❤♦s ❢✉t✉r♦s✳ ❆ ✜❣✉r❛ ✶✳✶ s✉❣❡r❡ ❛ s❡q✉ê♥❝✐❛ ❞❡ ❧❡✐t✉r❛ ❞❡st❡ tr❛❜❛❧❤♦✳
❈❛♣ít✉❧♦ ✷
❈♦♥❝❡✐t♦s ♣r❡❧✐♠✐♥❛r❡s
◆❡st❡ ❝❛♣ít✉❧♦ sã♦ ❞❡st❛❝❛❞♦s ❛❧❣✉♥s ❝♦♥❝❡✐t♦s ♥❡❝❡ssár✐♦s ♣❛r❛ ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞♦ tr❛❜❛❧❤♦✳ ❚❛♠❜é♠ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛❧❣✉♠❛s ❞❛s té❝♥✐❝❛s q✉❡ sã♦ ✉t✐❧✐③❛❞❛s ♥❛ ✐♠♣❧❡✲ ♠❡♥t❛çã♦ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ Pr❡❢❘❡❝✳ ◆❛ s❡çã♦ ✷✳✶ s✐♥t❡t✐③❛♠♦s ♦s ❝♦♥❝❡✐t♦s s♦❜r❡ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦✱ ❛s ❛❜♦r❞❛❣❡♥s ❡①✐st❡♥t❡s✱ ♦s ❞❡s❛✜♦s ❡♥❢r❡♥t❛❞♦s ❡ ❝♦♠♦ ❡❧❡s sã♦ ❛✈❛❧✐✲ ❛❞♦s✳ ◆❛ s❡çã♦ ✷✳✷ ❞✐s❝✉t✐♠♦s ❝♦♠♦ r❡♣r❡s❡♥t❛r ♣r❡❢❡rê♥❝✐❛s ♣❛r❛✱ ❛ss✐♠✱ ❛♣r❡s❡♥t❛r ♠✐♥❡r❛❞♦r❡s ❝❛♣❛③❡s ❞❡ ♠✐♥❡r❛r ♦ ❢♦r♠❛t♦ ❞❡ ♣r❡❢❡rê♥❝✐❛ ❞❡s❡❥❛❞♦✳
✷✳✶ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦
❬❘✐❝❝✐ ❡t ❛❧✳ ✷✵✶✶❪ ❞❡✜♥❡ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ❝♦♠♦ ❢❡rr❛♠❡♥t❛s ❡ té❝♥✐❝❛s q✉❡ ❢♦r♥❡❝❡♠ s✉❣❡stõ❡s ❞❡ ✐t❡♥s ❛ ✉s✉ár✐♦s✳ ❆s s✉❣❡stõ❡s sã♦ r❡❧❛❝✐♦♥❛❞❛s ❛ ❞✐✈❡rs♦s ♣r♦❝❡ss♦s ❞❡ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦ ❝♦♠♦✿ ✐t❡♥s ❞❡ ❝♦♠♣r❛ ❡♠ ✉♠ s✉♣❡r♠❡r❝❛❞♦✱ ♠ús✐❝❛s ♣❛r❛ ❡s❝✉t❛r ❡♠ ✉♠❛ rá❞✐♦✱ ♥♦tí❝✐❛s ♣❛r❛ ❧❡r ❡♠ ✉♠ s✐t❡ ❥♦r♥❛❧íst✐❝♦✳ ❖s ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ sã♦ ❞✐r❡❝✐♦♥❛❞♦s ♣❛r❛ ❛✉①✐❧✐❛r ♦s ✉s✉ár✐♦s ❛ ❧✐❞❛r❡♠ ❝♦♠ ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ ❛❧t❡r♥❛t✐✈❛s q✉❡ ✉♠❛ ❧♦❥❛ ❞❡ ❞❡♣❛rt❛♠❡♥t♦s✱ ♣♦r ❡①❡♠♣❧♦✱ ♣♦❞❡ ♦❢❡r❡❝❡r✳
❯♠ ❢❛♠♦s♦ ❝❛s♦ r❡❛❧ é ♦ s✐t❡ ❞❛ ❆♠❛③♦♥✳❝♦♠✱ q✉❡ ❡♠♣r❡❣❛ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ♣❛r❛ ♣❡rs♦♥❛❧✐③❛r ❛ ❧♦❥❛ ✈✐rt✉❛❧ ♣❛r❛ ❝❛❞❛ ❝❧✐❡♥t❡ ✭ ❬❏❛♥♥❛❝❤ ✷✵✵✽❪✮✳ ❊st❛ ❡♠♣r❡s❛ t❛♠❜é♠ ❢♦r♥❡❝❡ ♠é❞✐❛s ❞❡ ❛✈❛❧✐❛çõ❡s ❞♦s ✉s✉ár✐♦s ♣❛r❛ ♦s ❧✐✈r♦s ❛♣r❡s❡♥t❛❞♦s ❡ ✉♠❛ ❧✐st❛ ❞❡ ♦✉tr♦s ❧✐✈r♦s q✉❡ sã♦ ❝♦♠♣r❛❞♦s ♣♦r ✉s✉ár✐♦s q✉❡ ❛❞q✉✐r✐r❛♠ ✉♠ ❧✐✈r♦ ❡s♣❡❝í✜❝♦✳ ❖ ◆❡t✢✐① ✭✇✇✇✳◆❡t✢✐①✳❝♦♠✮✱ ❡♠♣r❡s❛ ❞❡ ❛❧✉❣✉é✐s ❞❡ ✜❧♠❡s ♣❡❧❛ ✐♥t❡r♥❡t✱ ❝❛❧❝✉❧❛ r❡❝♦♠❡♥❞❛çõ❡s ♣❛r❛ ❝❛❞❛ ✉s✉ár✐♦✱ ❛❧é♠ ❞❡ ♠♦str❛r ♦s ✐t❡♥s ♠❛✐s ♣♦♣✉❧❛r❡s ❡ ♣r❡♠✐❛❞♦s✳ ❖ s✐t❡ ❞❛ ▼✐❝r♦s♦❢t ❢♦r♥❡❝❡ s✉❣❡stõ❡s ❞❡ ❞♦✇♥❧♦❛❞s ❞❡ ❢❡rr❛♠❡♥t❛s ❛ ♣❛rt✐r ❞♦s ✐t❡♥s ❥á ♣❡sq✉✐s❛❞♦s ♣❡❧♦ ✉s✉ár✐♦ ✭ ❬❙❤❛♥✐ ❡ ●✉♥❛✇❛r❞❛♥❛ ✷✵✶✶❪ ✮✳
❖s ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ s✉r❣❡♠ ❝♦♠♦ ✉♠❛ ❞❛s ♣r✐♥❝✐♣❛✐s s♦❧✉çõ❡s ♣❛r❛ ❛ s♦✲ ❜r❡❝❛r❣❛ ❞❡ ✐♥❢♦r♠❛çã♦ ❡①✐st❡♥t❡✱ ♣❡r♠✐t✐♥❞♦ ❞✐♠✐♥✉✐r ♦ ❡s❢♦rç♦ ❞❡ ❜✉s❝❛ ❞♦s ✉s✉ár✐♦s ✭ ❬❉❡sr♦s✐❡rs ❡ ❑❛r②♣✐s ✷✵✶✶❪ ❡ ❬❙✉ ❡ ❑❤♦s❤❣♦❢t❛❛r ✷✵✵✾❪✮✳ ❆❧é♠ ❞✐ss♦✱ t❛♠❜é♠ ♣r♦♠❡t❡♠ ✉♠❛ ❛❧t❛ ✜❞❡❧✐❞❛❞❡ ♣♦r ♣❛rt❡ ❞♦s ❝❧✐❡♥t❡s✱ ❛✉♠❡♥t♦ ❞❛s ✈❡♥❞❛s✱ ♠❛✐s r❡❝❡✐t❛ ♣✉❜❧✐❝✐tár✐❛ ❡ ❛❧❝❛♥❝❡ ❞❡ ♠❛✐s ❜❡♥❡❢í❝✐♦s ❛ ♣❛rt✐r ❞❡ ♣r♦♠♦çõ❡s ❡s♣❡❝í✜❝❛s ♣❛r❛ ❞❡t❡r♠✐♥❛❞♦s s❡❣♠❡♥t♦s
✷✹ ❈❛♣ít✉❧♦ ✷✳ ❈♦♥❝❡✐t♦s ♣r❡❧✐♠✐♥❛r❡s
❞❡ ❝❧✐❡♥t❡s✳ ❆❧é♠ ❞❡ss❛s ✈❛♥t❛❣❡♥s✱ ❬❘✐❝❝✐ ❡t ❛❧✳ ✷✵✶✶❪ ❡♥✉♠❡r❛ ♦✉tr♦s ❜❡♥❡❢í❝✐♦s q✉❡ ♦s ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ♣♦❞❡♠ tr❛③❡r ♣❛r❛ ✉♠❛ ❡♠♣r❡s❛ ♦✉ ♦r❣❛♥✐③❛çã♦✿
• ❆✉♠❡♥t❛r ♦ ♥ú♠❡r♦ ❞❡ ✐t❡♥s ✈❡♥❞✐❞♦s✿ ♦ ♣r✐♠❡✐r♦ ♦❜❥❡t✐✈♦ ♣❛r❛ ✐♠♣❧❛♥t❛r ✉♠
❙✐st❡♠❛ ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ é ❛✉♠❡♥t❛r ❛ t❛①❛ ❞❡ ❝♦♥✈❡rsã♦✱ ✐st♦ é✱ ♦ ♥ú♠❡r♦ ❞❡ ✉s✉ár✐♦s q✉❡ ❛❝❡✐t❛♠ ❛s r❡❝♦♠❡♥❞❛çõ❡s ❡ ❛s ❝♦♥s♦♠❡♠✱ ❝♦♠♣❛r❛❞❛ ❛♦ ♥ú♠❡r♦ ❞❡ s✐♠♣❧❡s ✈✐s✐t❛♥t❡s q✉❡ s♦♠❡♥t❡ ♥❛✈❡❣❛♠ ♣❡❧❛ ✐♥❢♦r♠❛çã♦ ❞✐s♣♦♥í✈❡❧✳ ❊st❡ ♦❜❥❡t✐✈♦ é ❛❧❝❛♥ç❛❞♦ ♣♦rq✉❡ ♦s ✐t❡♥s r❡❝♦♠❡♥❞❛❞♦s t❡♥❞❡♠ ❛ s❡r❡♠ ❛❞❡q✉❛❞♦s às ♥❡❝❡ss✐❞❛❞❡s ❡ ❞❡s❡❥♦s ❞♦s ✉s✉ár✐♦s✳
• ❱❡♥❞❡r ✐t❡♥s ♠❛✐s ❞✐✈❡rs♦s✿ ♦s ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ♣❡r♠✐t❡♠ ♦ ✉s✉ár✐♦ s❡✲
❧❡❝✐♦♥❛r ✐t❡♥s q✉❡ ♣♦❞❡♠ s❡r ❞✐❢í❝❡✐s ❞❡ ❡♥❝♦♥tr❛r s❡♠ ✉♠❛ r❡❝♦♠❡♥❞❛çã♦ ♣r❡❝✐s❛✳ ❊♠ ✉♠ ❝❡♥ár✐♦ ❞❡ r❡❝♦♠❡♥❞❛çõ❡s ❞❡ ✜❧♠❡✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ❡♠♣r❡s❛ ❡stá ✐♥t❡r❡ss❛❞❛ ❡♠ ❛❧✉❣❛r t♦❞♦s ♦s ❉❱❉s ♥♦ ❝❛tá❧♦❣♦✱ ♥ã♦ s♦♠❡♥t❡ ♦s ♠❛✐s ♣♦♣✉❧❛r❡s✳ ■ss♦ ♣♦❞❡ s❡r ❞✐❢í❝✐❧ s❡♠ ✉♠ ❙✐st❡♠❛ ❞❡ ❘❡❝♦♠❡♥❞❛çã♦✱ ✉♠❛ ✈❡③ q✉❡ ❛ ❡♠♣r❡s❛ ♥ã♦ ♣♦❞❡ ❝♦rr❡r ♦ r✐s❝♦ ❞❡ ❢❛③❡r ♣r♦♣❛❣❛♥❞❛s ❞❡ ✜❧♠❡s q✉❡ ♥ã♦ sã♦ ❞♦ ❣♦st♦ ❞♦ ✉s✉ár✐♦ ❡♠ ♣❛rt✐❝✉❧❛r✳ ❆❧é♠ ❞✐ss♦✱ ✉♠ ❙✐st❡♠❛ ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ s✉❣❡r❡ ♦✉ ❢❛③ ♣r♦♣❛❣❛♥❞❛ ❞❡ ✜❧♠❡s ♥ã♦ ♣♦♣✉❧❛r❡s ♣❛r❛ ♦s ✉s✉ár✐♦s ❝❡rt♦s✳
• ❆✉♠❡♥t❛r ❛ s❛t✐s❢❛çã♦ ❞♦ ✉s✉ár✐♦✿ ♦ ✉s✉ár✐♦ ✐rá ❡♥❝♦♥tr❛r r❡❝♦♠❡♥❞❛çõ❡s ✐♥t❡r❡s✲
s❛♥t❡s ❡ r❡❧❡✈❛♥t❡s✱ ❢❛③❡♥❞♦ ❝♦♠ q✉❡ ❣♦st❡ ❞❡ ✉s❛r ♦ s✐st❡♠❛✳ ❆ ❝♦♠❜✐♥❛çã♦ ❞❡ ❡✜❝✐❡♥t❡s ❡ ❛❝✉r❛❞❛s r❡❝♦♠❡♥❞❛çõ❡s ❝♦♠ ✉♠❛ ✐♥t❡r❢❛❝❡ ❛♣r♦♣r✐❛❞❛ ♣♦❞❡ ❛✉♠❡♥t❛r ❛ ❛✈❛❧✐❛çã♦ s✉❜❥❡t✐✈❛ ❞♦ ✉s✉ár✐♦ ❡♠ r❡❧❛çã♦ ❛♦ s✐st❡♠❛✳ ■st♦ ♣♦❞❡ ❛✉♠❡♥t❛r ♦ ✉s♦ ❞♦ s✐st❡♠❛ ❡ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛s r❡❝♦♠❡♥❞❛çõ❡s s❡r❡♠ ❛❝❡✐t❛s✳
• ❆✉♠❡♥t❛r ❛ ✜❞❡❧✐❞❛❞❡ ❞♦ ✉s✉ár✐♦✿ ✉♠ ✉s✉ár✐♦ t❡♥❞❡ ❛ s❡r ❧❡❛❧ ❛ ✉♠ ✇❡❜ s✐t❡ q✉❡✱
q✉❛♥❞♦ ✈✐s✐t❛❞♦✱ r❡❝♦♥❤❡❝❡ s✉❛s ♣r❡❢❡rê♥❝✐❛s ❡ ♦ tr❛t❛ ❝♦♠♦ ✉♠ ✐♠♣♦rt❛♥t❡ ✈✐s✐✲ t❛♥t❡✳ ❊st❛ é ❛ ❝❛r❛❝t❡ríst✐❝❛ ❝♦♠✉♠ ❞❡ ✉♠ ❙✐st❡♠❛ ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ✉♠❛ ✈❡③ q✉❡ ❝❛❧❝✉❧❛♠ r❡❝♦♠❡♥❞❛çõ❡s ❛♣r♦✈❡✐t❛♥❞♦ ❛s ✐♥❢♦r♠❛çõ❡s ❛❞q✉✐r✐❞❛s ❞♦s ✉s✉ár✐♦s ❡♠ s✉❛s ✐♥t❡r❛çõ❡s ♣ré✈✐❛s✳ ❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱ q✉❛♥t♦ ♠❛✐s ♦ ✉s✉ár✐♦ ✐♥t❡r❛❣❡ ❝♦♠ ♦ s✐st❡♠❛✱ ♠❡❧❤♦r s❡ ❝♦♥s❡❣✉❡ r❡♣r❡s❡♥t❛r ❛s ♣r❡❢❡rê♥❝✐❛s ❞♦ ✉s✉ár✐♦ ❡ ♠❛✐s ❛ r❡✲ ❝♦♠❡♥❞❛çã♦ ❢❡✐t❛ ♣❡❧♦ ❙✐st❡♠❛ ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ♣♦❞❡ s❡r ❡✜❝✐❡♥t❡✱ ❛❝❡rt❛♥❞♦ ❛s ♣r❡❢❡rê♥❝✐❛s ❞♦ ✉s✉ár✐♦✳
• ▼❡❧❤♦r ❡♥t❡♥❞✐♠❡♥t♦ ❞♦ q✉❡ ♦ ✉s✉ár✐♦ q✉❡r✿ ♦ ❙✐st❡♠❛ ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ❝♦♥s❡❣✉❡
❞❡s❝r❡✈❡r ❛s ♣r❡❢❡rê♥❝✐❛s ❞♦s ✉s✉ár✐♦s✱ ♦✉ ❝♦❧❡t❛❞❛ ❡①♣❧✐❝✐t❛♠❡♥t❡ ♦✉ ♣r❡❞✐t❛ ♣❡❧♦ s✐st❡♠❛✳ ❆ ❡♠♣r❡s❛ ♣♦❞❡ ❡♥tã♦ ❞❡❝✐❞✐r r❡✉s❛r ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♣❛r❛ ♦✉tr♦s ♦❜❥❡t✐✈♦s✱ ❝♦♠♦ ♠❡❧❤♦r❛r ♦ ❣❡r❡♥❝✐❛♠❡♥t♦ ❞♦s ✐t❡♥s ❡♠ ❡st♦q✉❡ ♦✉ ❡♠ ♣r♦❞✉çã♦✳
❉✐❛♥t❡ ❞❡ t❛♥t♦s ❜❡♥❡❢í❝✐♦s✱ ♦s ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ✈❡♠ s❡♥❞♦ ❡♠♣r❡❣❛❞♦s ❡♠ ✉♠❛ ❣r❛♥❞❡ ✈❛r✐❡❞❛❞❡ ❞❡ ❛♣❧✐❝❛çõ❡s t❛✐s ❝♦♠♦✿
✷✳✶✳ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ✷✺
• ♠ús✐❝❛s ✭✇✇✇✳❧❛st✳❢♠✱ ❬❙❤❛r❞❛♥❛♥❞ ❡ ▼❛❡s ✶✾✾✺❪✮✱ • ✜❧♠❡s ✭ ❬▼✐❧❧❡r ❡t ❛❧✳ ✷✵✵✸❪✱ ❬◆❈❇■ ✷✵✵✾❪ ✮✱
• ♥♦tí❝✐❛s ✭ ❬❇✐❧❧s✉s ❡t ❛❧✳ ✷✵✵✷❪ ✮✱
• ♣á❣✐♥❛s ✇❡❜ ✭ ❬▼♦❜❛s❤❡r ❡t ❛❧✳ ✷✵✵✷❪ ✮✱ • ♣✐❛❞❛s ✭ ❬●♦❧❞❜❡r❣ ❡t ❛❧✳ ✷✵✵✶❪ ✮✱
• s❡r✈✐ç♦s✿ ♣❛❝♦t❡s ❞❡ ✈✐❛❣❡♥s ✭✇✇✇✳tr✐♣❛❞✈✐s♦r✳❝♦♠✮✱ ❝♦♥s✉❧t♦r✐❛s✱ ✈❡♥❞❛s ❡ ❛❧✉❣✉é✐s
❞❡ ✐♠ó✈❡✐s✱
• ❡✲❝♦♠♠❡r❝❡ ✭ ❬▲✐♥❞❡♥ ❡t ❛❧✳ ✷✵✵✸❪✮✱
• t❡❧❡✈✐sã♦ ❞✐❣✐t❛❧ ✭ ❬❇❧❛♥❝♦✲❋❡r♥á♥❞❡③ ❡t ❛❧✳ ✷✵✵✽❪✮✱
• ❝♦❧❛❜♦r❛çõ❡s ❡♥tr❡ ♣❡sq✉✐s❛❞♦r❡s ♣❛r❛ ❢♦r♠❛çã♦ ❞❡ ♥♦✈♦s ❣r✉♣♦s ❡ ❝♦❧❛❜♦r❛çõ❡s ❡♠
♣❡sq✉✐s❛s ✭ ❬❇r❛♥❞ã♦ ❡ ▼♦r♦ ✷✵✶✷❪✮✳
✷✳✶✳✶ ❆❜♦r❞❛❣❡♥s
❖s ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ sã♦ ❞❡s❡♥✈♦❧✈✐❞♦s s♦❜ ❞✐✈❡rs❛s ❛❜♦r❞❛❣❡♥s✳ ❆ s❡❣✉✐r ❛♣r❡s❡♥t❛♠♦s ❛s ♠❛✐s ❝♦♠✉♥s ❡ ❛s s✉♣♦s✐çõ❡s q✉❡ ❡❧❛s ❛ss✉♠❡♠ ♣❛r❛ ♣r♦✈❡r r❡❝♦♠❡♥❞❛çã♦✳ ◆♦ ❝❛♣ít✉❧♦ ✸ ❛♣r❡s❡♥t❛♠♦s tr❛❜❛❧❤♦s q✉❡ ❡①♣❧♦r❛♠ ❡ss❛s ❛❜♦r❞❛❣❡♥s✳
❋✐❧tr❛❣❡♠ ❈♦❧❛❜♦r❛t✐✈❛
❆ ❛❜♦r❞❛❣❡♠ ❞❡ ❙✐st❡♠❛ ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ❞❡♥♦♠✐♥❛❞❛ ❋✐❧tr❛❣❡♠ ❈♦❧❛❜♦r❛t✐✈❛ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞❛ ❛ ♣❛rt✐r ❞❡ ✉♠❛ s✐♠♣❧❡s ♦❜s❡r✈❛çã♦✿ ❛s ♣❡ss♦❛s ❢r❡q✉❡♥t❡♠❡♥t❡ ✉s❛♠ r❡✲ ❝♦♠❡♥❞❛çõ❡s ❞❛❞❛s ♣♦r ♦✉tr❛s ♣❡ss♦❛s ❡♠ s✉❛s ❛t✐✈✐❞❛❞❡s r♦t✐♥❡✐r❛s✳ P♦r ❡①❡♠♣❧♦✿ ❛♦ s❡❧❡❝✐♦♥❛r ✉♠ ❧✐✈r♦ ♣❛r❛ ❧❡r✱ ♣r♦❝✉r❛✲s❡ r❡❝♦♠❡♥❞❛çõ❡s ❞❡ q✉❡♠ ❥á ❧❡✉ ❛q✉❡❧❡ ❧✐✈r♦❀ ❡♠✲ ♣r❡❣❛❞♦r❡s ❝♦♥t❛♠ ❝♦♠ ❝❛rt❛s ❞❡ r❡❝♦♠❡♥❞❛çõ❡s ♣❛r❛ ❡s❝♦❧❤❡r ♥♦✈♦s ❢✉♥❝✐♦♥ár✐♦s❀ ❛♦ ❡s❝♦❧❤❡r ✉♠ ✜❧♠❡ ♣❛r❛ ❛ss✐st✐r ❛s ♣❡ss♦❛s t❡♥❞❡♠ ❛ ❧❡r ❝♦♠❡♥tár✐♦s ❡ ❝rít✐❝❛s ❡♠ ❥♦r♥❛✐s ♦✉ s✐t❡s ✭ ❬❘✐❝❝✐ ❡t ❛❧✳ ✷✵✶✶❪✮✳
❆ té❝♥✐❝❛ ❞❡ ❋✐❧tr❛❣❡♠ ❈♦❧❛❜♦r❛t✐✈❛ r❡❝♦♠❡♥❞❛ ♣❛r❛ ✉♠ ✉s✉ár✐♦ ❛t✐✈♦ ✭❛ q✉❡♠ s❡ ❞❡s❡❥❛ r❡❝♦♠❡♥❞❛r✮ ♦s ✐t❡♥s q✉❡ ♦✉tr♦s ✉s✉ár✐♦s✱ ❝♦♠ ❣♦st♦s s✐♠✐❧❛r❡s ❛ ❡❧❡✱ ❣♦st❛r❛♠ ♥♦ ♣❛ss❛❞♦✳ ❆ s✐♠✐❧❛r✐❞❛❞❡ ❡♥tr❡ ❞♦✐s ✉s✉ár✐♦s é ❝❛❧❝✉❧❛❞❛ ❜❛s❡❛❞❛ ♥❛ s✐♠✐❧❛r✐❞❛❞❡ ❞♦ ❤✐stór✐❝♦ ❞❡ ❛✈❛❧✐❛çã♦✴❝♦♠♣r❛ ❞♦s ✉s✉ár✐♦s✳ ❆ ✐❞❡✐❛ ❝❤❛✈❡ é q✉❡ ❛ ♥♦t❛ ❞♦ ✉s✉ár✐♦ ❛t✐✈♦u
♣❛r❛ ✉♠ ♥♦✈♦ ✐t❡♠ié ♣r♦✈❛✈❡❧♠❡♥t❡ s✐♠✐❧❛r ❛ ♥♦t❛ ❞❡ ♦✉tr♦ ✉s✉ár✐♦v✱ s❡u❡v ❛✈❛❧✐❛r❛♠
✐t❡♥s ♥♦ ♣❛ss❛❞♦ ❞❡ ❢♦r♠❛ s❡♠❡❧❤❛♥t❡ ✭ ❬❉❡sr♦s✐❡rs ❡ ❑❛r②♣✐s ✷✵✶✶❪✮ ✳
❆ ❛❜♦r❞❛❣❡♠ tr❛❞✐❝✐♦♥❛❧ ❞❡ ❋✐❧tr❛❣❡♠ ❈♦❧❛❜♦r❛t✐✈❛ ❢♦✐ ✐♥tr♦❞✉③✐❞❛ ❡♠ ❬❘❡s♥✐❝❦ ❡t ❛❧✳ ✶✾✾✹❪✱ s❡♥❞♦ ❡st❡ ♦ tr❛❜❛❧❤♦ ❝♦♥s✐❞❡r❛❞♦ ❝♦♠♦ ♣r✐♥❝✐♣❛❧ ♣r❡❝✉rs♦r ❞♦s ❙✐st❡♠❛s ❞❡ ❘❡✲ ❝♦♠❡♥❞❛çã♦✳ ❖s ❞❛❞♦s sã♦ r❡♣r❡s❡♥t❛❞♦s ♣❡❧❛ ♠❛tr✐③ ✉s✉ár✐♦×✐t❡♠✱ ❛♣r❡s❡♥t❛❞❛ ♥❛
✷✻ ❈❛♣ít✉❧♦ ✷✳ ❈♦♥❝❡✐t♦s ♣r❡❧✐♠✐♥❛r❡s
❞❡❧❛ é ♣♦ssí✈❡❧ ❝❛❧❝✉❧❛r r❡❝♦♠❡♥❞❛çõ❡s ❛♦s ✉s✉ár✐♦s✳ ❖s ❡s♣❛ç♦s ❝♦♠ ✧✯✧✐♥❞✐❝❛♠ q✉❡ ♦ ✈❛❧♦r ❞❛ ❛✈❛❧✐❛çã♦ ♥ã♦ ❢♦✐ ✐♥❢♦r♠❛❞♦✳
i1 i2 i3 i4 i5 i6
P❛✉❧♦ ✺ ✷ ✹ ✺ ✯ ✯
❏♦ã♦ ✯ ✯ ✯ ✹ ✷ ✺
▼ár❝✐❛ ✯ ✸ ✺ ✸ ✷ ✹
❈❛r❧♦s ✸ ✷ ✯ ✷ ✸ ✯
❆♥❛ ✺ ✹ ✸ ✹ ✸ ✸
▼❛✉r♦ ✶ ✯ ✷ ✺ ✯ ✹
❏♦❛q✉✐♠ ✸ ✶ ✯ ✹ ✺ ✸ ❚❛❜❡❧❛ ✷✳✶✿ ▼❛tr✐③ ✉s✉ár✐♦×✐t❡♠
❈♦♠♦ ❡①❡♠♣❧♦ ✈❛♠♦s ❝❛❧❝✉❧❛r r❡❝♦♠❡♥❞❛çõ❡s ♣❛r❛ ♦ ✉s✉ár✐♦ ❏♦ã♦✳ ❖ ♣r✐♠❡✐r♦ ♣❛ss♦ é ❡♥❝♦♥tr❛r q✉❛✐s sã♦ ♦s ✉s✉ár✐♦s q✉❡ ♣♦ss✉❡♠ ❣♦st♦ s❡♠❡❧❤❛♥t❡ ❛♦ ❞❡❧❡✳ P❛r❛ t❛❧✱ ❝❛❧❝✉❧❛✲ s❡ ❛ s✐♠✐❧❛r✐❞❛❞❡ ❞❡ ❏♦ã♦ ❝♦♠ ♦s ♦✉tr♦s ✉s✉ár✐♦s ❛ ♣❛rt✐r ❞❛s ♥♦t❛s ❞❛❞❛s ❛♦s ✐t❡♥s ❡♠ ❝♦♠✉♠✳ ❆ ♠❡❞✐❞❛ ❞❡ s✐♠✐❧❛r✐❞❛❞❡ ♠❛✐s ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞❛ é ♦ P❡❛rs♦♥ ❈♦rr❡❧❛t✐♦♥ ❈♦❡✜❝✐❡♥t ✭P❈❈✮✱ ❞❛❞♦ ♣❡❧❛ ❢ór♠✉❧❛✿
sim(u, v) =
P
i∈Iuv(rui−ru)(rvi−rv) q
P
i∈Iuv(rui−ru)
2P
i∈Iuv(rvi−rv)
2
❖♥❞❡ Iuv r❡♣r❡s❡♥t❛ ♦ ❝♦♥❥✉♥t♦ ❞❡ ✐t❡♥s q✉❡ ♦s ✉s✉ár✐♦s u ❡ v ❛✈❛❧✐❛r❛♠ ❡♠ ❝♦♠✉♠✳
ru é ❛ ♠é❞✐❛ ❞❛s ♥♦t❛s ❞❛❞❛s ♣❡❧♦ ✉s✉ár✐♦ u ❛♦s ✐t❡♥s q✉❡ ❡❧❡ ❛✈❛❧✐♦✉ ❡♠ ❝♦♠✉♠ ❝♦♠ ♦
✉s✉ár✐♦ v✳ ❆ss✐♠✱ ❛ s✐♠✐❧❛r✐❞❛❞❡ ❡♥tr❡ ♦ ✉s✉ár✐♦ ❏♦ã♦ ❡ ♦s ❞❡♠❛✐s ✉s✉ár✐♦s✱ ❛ ♣❛rt✐r ❞♦s
❞❛❞♦s ❞❛ t❛❜❡❧❛ ✷✳✶✱ é✿
• sim(❏♦ã♦✱ P❛✉❧♦) = 0❀ • sim(❏♦ã♦✱ ▼ár❝✐❛) = 0.98❀
• sim(❏♦ã♦✱ ❈❛r❧♦s) = −1❀ • sim(❏♦ã♦✱ ❆♥❛) = 0.19❀
• sim(❏♦ã♦✱ ▼❛✉r♦) =−1❀
• sim(❏♦ã♦✱ ❏♦❛q✉✐♠) =−0.98✳
❖ ✈❛❧♦r ❞❡ s✐♠✐❧❛r✐❞❛❞❡ r❡t♦r♥❛❞♦ ♣❡❧♦ P❈❈ s❡ ❡♥❝♦♥tr❛ ♥♦ ✐♥t❡r✈❛❧♦ ❞❡[−1,1]✳ ❱❛❧♦r❡s
♣ró①✐♠♦s ❛ ✶ ✐♥❞✐❝❛♠ q✉❡ ♦s ❞♦✐s ✉s✉ár✐♦s t❡♥❞❡♠ ❛ ❝♦♥❝♦r❞❛r✱ ❡ ✈❛❧♦r❡s ♣ró①✐♠♦s ❛ ✲✶ ✐♥❞✐❝❛♠ q✉❡ ♦s ❞♦✐s ✉s✉ár✐♦s t❡♥❞❡♠ ❛ ❞✐s❝♦r❞❛r ✉♠ ❞♦ ♦✉tr♦✳ ❱❛❧♦r❡s ✐❣✉❛❧ ❛ ✵ ✐♥❞✐❝❛♠ q✉❡ ♦ ❤✐stór✐❝♦ ❞❡ ❛✈❛❧✐❛çõ❡s ❞♦s ❞♦✐s ✉s✉ár✐♦s ♥ã♦ sã♦ ❝♦rr❡❧❛❝✐♦♥❛❞♦s✳ ❈❛s♦ ❞♦✐s ✉s✉ár✐♦s ♥ã♦ t❡♥❤❛♠ ❛✈❛❧✐❛❞♦ ✐t❡♥s ❡♠ ❝♦♠✉♠ ♥ã♦ é ♣♦ssí✈❡❧ ❝❛❧❝✉❧❛r ❛ s✐♠✐❧❛r✐❞❛❞❡ ❡♥tr❡ ❡❧❡s✳
✷✳✶✳ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ✷✼
ˆ
rui=ru+
P
v∈U,v6=u(rvi−rv)∗sim(u, v)
P
v∈U,v6=u|sim(u, v)|
◆❛ ❢ór♠✉❧❛ U é ♦ ❝♦♥❥✉♥t♦ ❞❡ ✉s✉ár✐♦s ❡①✐st❡♥t❡s ♥♦ ❜❛♥❝♦ ❞❡ ❞❛❞♦s ❞♦ s✐st❡♠❛✳ ❆
♣r❡❞✐çã♦ ❞❛s ♥♦t❛s ♣❛r❛ ♦s ✐t❡♥s q✉❡ ❏♦ã♦ ❛✐♥❞❛ ♥ã♦ ❛✈❛❧✐♦✉✱ ❛ ♣❛rt✐r ❞♦s ❞❛❞♦s ❞❛ t❛❜❡❧❛ ✷✳✶✱ ♣❛r❛ ♦ ✉s✉ár✐♦ ❏♦ã♦ é✿
• i1❂ ✶✳✸✺❀
• i2❂ ✶✳✶✸❀
• i3❂ ✷✳✵✷✳
❖s ✐t❡♥s ❝♦♠ ♠❛✐♦r❡s ✈❛❧♦r❡s ♣r❡❞✐t♦s sã♦ ♦s r❡❝♦♠❡♥❞❛❞♦s ❛♦ ✉s✉ár✐♦ ❏♦ã♦✳ ❈♦♥str✉✲ ✐♥❞♦ ✉♠ r❛♥❦✐♥❣✱ ♦s ✐t❡♥s s❡r✐❛♠ r❡❝♦♠❡♥❞❛❞♦s ♥❛ s❡❣✉✐♥t❡ ♦r❞❡♠✿ i3✱ i1 ❡i2✳
❖❜s❡r✈❛✲s❡ q✉❡ ❛ ❛❜♦r❞❛❣❡♠ ❞❡ ❋✐❧tr❛❣❡♠ ❈♦❧❛❜♦r❛t✐✈❛ ♥ã♦ é ❝❛♣❛③ ❞❡ r❡❝♦♠❡♥❞❛r ✉♠ ✐t❡♠ q✉❡ ❛✐♥❞❛ ♥ã♦ r❡❝❡❜❡✉ ❛✈❛❧✐❛çã♦✳ ❉❛ ♠❡s♠❛ ❢♦r♠❛✱ s❡ ♦ ✉s✉ár✐♦ ❛t✐✈♦ ♥ã♦ ❛✈❛❧✐♦✉ ✐t❡♥s ❡♠ ❝♦♠✉♠ ❝♦♠ ♦✉tr♦s ✉s✉ár✐♦s ❛ ❛❜♦r❞❛❣❡♠ ♥ã♦ ❝♦♥s❡❣✉❡ r❡❝♦♠❡♥❞❛r ♦✉tr♦s ✐t❡♥s✳ ❊♥tr❡t❛♥t♦✱ ❛ ❛❜♦r❞❛❣❡♠ ❞❡ ❋✐❧tr❛❣❡♠ ❈♦❧❛❜♦r❛t✐✈❛ ❛♣r❡s❡♥t❛ ❜♦♥s r❡s✉❧t❛❞♦s ♥❛ ❧✐t❡r❛✲ t✉r❛ ❡ ♣❡r♠✐t❡ ❛ r❡❝♦♠❡♥❞❛çã♦ ❞❡ ✉♠❛ ❞✐✈❡rs✐❞❛❞❡ ❞❡ ✐t❡♥s ❥á ❛✈❛❧✐❛❞♦s ♣❡❧♦s ✉s✉ár✐♦s s✐♠✐❧❛r❡s ❛♦ ✉s✉ár✐♦ ❛t✐✈♦✳
❉✐✈❡rs♦s ♦✉tr♦s tr❛❜❛❧❤♦s ♣❛rt✐r❛♠ ❞❡ss❛ ✐❞❡✐❛ ✐♥✐❝✐❛❧ ❡ ♣r♦♣✉s❡r❛♠ ♦✉tr♦s r❡❝✉rs♦s ♣❛r❛ ❛♣r✐♠♦r❛r ❛s r❡❝♦♠❡♥❞❛çõ❡s✳ ❆ss✐♠✱ ❞❡✜♥✐r❛♠✲s❡ ❝❛t❡❣♦r✐❛s ✭✜❣✉r❛ ✷✳✶✮ ❞❡♥tr♦ ❞❛ ❛❜♦r❞❛❣❡♠ ❞❡ ❋✐❧tr❛❣❡♠ ❈♦❧❛❜♦r❛t✐✈❛ ♣❛r❛ ♠❡❧❤♦r ❝❧❛ss✐✜❝❛r ❡ ❝♦♠♣r❡❡♥❞❡r ❛s ♣r♦♣♦st❛s ❞❡s❡♥✈♦❧✈✐❞❛s✳
❆ ✐❞❡✐❛ ✐♥✐❝✐❛❧ ❞❡ ❬❘❡s♥✐❝❦ ❡t ❛❧✳ ✶✾✾✹❪ é ❝❛t❡❣♦r✐③❛❞❛ ❝♦♠♦ ✉s❡r✲❜❛s❡❞ ❡ ♠❡♠♦r②✲ ❜❛s❡❞✳ ❉❡♥♦♠✐♥❛✲s❡ ✉s❡r✲❜❛s❡❞ ♣♦r ✉s❛r ❛s ❛✈❛❧✐❛çõ❡s ❞❡ ♦✉tr♦s ✉s✉ár✐♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❛ r❡❝♦♠❡♥❞❛çã♦✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❡①✐st❡ ❛ ❛❜♦r❞❛❣❡♠ ✐t❡♠✲❜❛s❡❞✱ ❬❙❛r✇❛r ❡t ❛❧✳ ✷✵✵✶❪✱ q✉❡ ❝❛❧❝✉❧❛ ❛ ♣r❡❞✐çã♦ ❞❡ ✉♠ ✐t❡♠ ❡♥❝♦♥tr❛♥❞♦ ✐t❡♥s s✐♠✐❧❛r❡s ❛ ♣❛rt✐r ❞❛s ❛✈❛❧✐❛çõ❡s q✉❡ ❡❧❡s r❡❝❡❜❡r❛♠✳ ▼❡♠♦r②✲❜❛s❡❞ s❡ r❡❢❡r❡ ❛♦ ❝á❧❝✉❧♦ ❞❛s ♣r❡❞✐çõ❡s✱ ❜❛s❡❛♥❞♦✲s❡ ❡♠ ✉♠❛ ❝♦❧❡çã♦ ✐♥t❡✐r❛ ❞❡ ✐t❡♥s ♣r❡✈✐❛♠❡♥t❡ ❛✈❛❧✐❛❞♦s ♣❡❧♦s ✉s✉ár✐♦s✳ ❊♠ ❝♦♥tr❛♣❛rt✐❞❛✱ ❡①✐st❡ ❛ ❛❜♦r❞❛❣❡♠ ♠♦❞❡❧✲❜❛s❡❞✱ q✉❡ ❛♣❧✐❝❛ ❛❧❣♦r✐t♠♦s ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ❞❛❞♦s ♣❛r❛ ❝♦♥str✉✐r ✉♠ ♠♦❞❡❧♦ ❛ ♣❛rt✐r ❞♦s ❞❛❞♦s ❞✐s♣♦♥í✈❡✐s✱ ♦ q✉❛❧ é ❡♥tã♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ r❡❛❧✐③❛r ♣r❡❞✐çõ❡s ❞❡ ❛✈❛❧✐❛çã♦✳
❇❛s❡❛❞♦ ❡♠ ❈♦♥t❡ú❞♦
✷✽ ❈❛♣ít✉❧♦ ✷✳ ❈♦♥❝❡✐t♦s ♣r❡❧✐♠✐♥❛r❡s
❋✐❣✉r❛ ✷✳✶✿ ❈❛t❡❣♦r✐❛s ❞❛ ❋✐❧tr❛❣❡♠ ❈♦❧❛❜♦r❛t✐✈❛
r❡s✉❧t❛❞♦ é ✉♠ ❥✉❧❣❛♠❡♥t♦ ❞❡ r❡❧❡✈â♥❝✐❛ q✉❡ r❡♣r❡s❡♥t❛ ♦ ♥í✈❡❧ ❞❡ ✐♥t❡r❡ss❡ ❞♦ ✉s✉ár✐♦ ♥❛q✉❡❧❡ ✐t❡♠✳ ❙❡ ♦ ♣❡r✜❧ r❡✢❡t❡ ❜❡♠ ❛s ♣r❡❢❡rê♥❝✐❛s ❞♦ ✉s✉ár✐♦✱ ❡❧❡ ✈❛✐ s❡r ❞❡ ❣r❛♥❞❡ ❡✜❝á❝✐❛ ♣❛r❛ ♦ ♣r♦❝❡ss♦ ❞❡ r❡❝♦♠❡♥❞❛çã♦✳
❙❡ ✉♠ ✉s✉ár✐♦ ❛✈❛❧✐♦✉ ♣♦s✐t✐✈❛♠❡♥t❡ ✉♠ ✜❧♠❡ ❞♦ ❣ê♥❡r♦ ❝♦♠é❞✐❛✱ ♣♦r ❡①❡♠♣❧♦✱ ♦ s✐st❡♠❛ ❛♣r❡♥❞❡ ❛ r❡❝♦♠❡♥❞❛r ♦✉tr♦s ✜❧♠❡s ❞♦ ♠❡s♠♦ ❣ê♥❡r♦✳ ❊ss❛ ❛❜♦r❞❛❣❡♠ ❞❡ ❙✐s✲ t❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ♣❛rt❡ ❞❛ ♦❜s❡r✈❛çã♦ ❞❡ q✉❡✱ s❡ ♦ ✉s✉ár✐♦ t❡♠ ♣r❡❢❡rê♥❝✐❛ s♦❜r❡ ❞❡t❡r♠✐♥❛❞❛ ❝❛r❛❝t❡ríst✐❝❛ ❤♦❥❡✱ ❡❧❡ t❡♥❞❡ ❛ ♠❛♥t❡r ❡ss❛ ♣r❡❢❡rê♥❝✐❛ ❞✉r❛♥t❡ ❛❧❣✉♠ t❡♠♣♦ ✭ ❬❉❡sr♦s✐❡rs ❡ ❑❛r②♣✐s ✷✵✶✶❪✮✳
❆ ❛❜♦r❞❛❣❡♠ ❇❛s❡❛❞❛ ❡♠ ❈♦♥t❡ú❞♦✱ ❝♦♠♦ ♦❜s❡r✈❛ ❬❇✉r❦❡ ✷✵✵✼❪✱ tr❛t❛ ❛ t❛r❡❢❛ ❞❡ r❡❝♦♠❡♥❞❛çã♦ ❝♦♠♦ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❡s♣❡❝í✜❝♦ ♣❛r❛ ❝❛❞❛ ✉s✉ár✐♦✳ ❯♠ ❝❧❛s✲ s✐✜❝❛❞♦r é tr❡✐♥❛❞♦ ❛ ♣❛rt✐r ❞♦s ✐t❡♥s q✉❡ ♦ ✉s✉ár✐♦ ✐♥❢♦r♠♦✉ s❡r❡♠ ♣r❡❢❡r✐❞♦s ♦✉ ♥ã♦✱ ❡ ❛s ❝❧❛ss❡s sã♦ ❛s ♥♦t❛s ✐♥❢♦r♠❛❞❛s ♣❡❧♦ ✉s✉ár✐♦✳ ❯♠ ❞♦s ♠ét♦❞♦s ♠❛✐s ✉t✐❧✐③❛❞♦s ❡ ❝♦♠ ❜♦♥s r❡s✉❧t❛❞♦s é ♦ ❝❧❛ss✐✜❝❛❞♦r ❜❛②❡s✐❛♥♦ ♥❛✐✈❡ ❜❛②❡s✳ ❊st❡ ❝❧❛ss✐✜❝❛❞♦r é ✉♠❛ ❛❜♦r❞❛❣❡♠ ♣r♦❜❛❜✐❧íst✐❝❛ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❡ ❣❡r❛ ✉♠ ♠♦❞❡❧♦ ❜❛s❡❛❞♦ ♥♦s ❛tr✐❜✉t♦s ❞♦s ✐t❡♥s ❛✈❛❧✐❛❞♦s ♣r❡✈✐❛♠❡♥t❡✳
❖ ❝❧❛ss✐✜❝❛❞♦r ❡st✐♠❛ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❞❡ P(c|i) ❞♦ ✐t❡♠ i ♣❡rt❡♥❝❡r ❛ ❝❧❛ss❡ c✳ ❈♦♥✲
s✐❞❡r❛♥❞♦ q✉❡ ♦ ✐t❡♠i✱ ♥❛ ❛❜♦r❞❛❣❡♠ ❇❛s❡❛❞❛ ❡♠ ❈♦♥t❡ú❞♦✱ é ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❛tr✐❜✉t♦s
(a1, a2, ..., an)✱ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ P(c|i) é ❞❛❞❛ ♣❡❧❛ ❢ór♠✉❧❛✿
P(c|i) = P(c)
P(i)
n
Y
k=1
P(ak|c)
❆s ♣r♦❜❛❜✐❧✐❞❛❞❡s P(c) ❡ P(ak|c) sã♦ ❡st✐♠❛❞❛s ❛ ♣❛rt✐r ❞♦s ❞❛❞♦s ❞❡ tr❡✐♥❛♠❡♥t♦ ❡
