❯❋▼● ✲ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛
Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛
❘❡❞❡ ♣❡r❝❡♣tr♦♥ ❝♦♠ ❝❛♠❛❞❛s ♣❛r❛❧❡❧❛s
✭P▲P ✲ P❛r❛❧❧❡❧ ▲❛②❡r P❡r❝❡♣tr♦♥✮
❉♦✉❣❧❛s ❆❧❡①❛♥❞r❡ ●♦♠❡s ❱✐❡✐r❛
❚❡①t♦ s✉❜♠❡t✐❞♦ à ❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛ ❞❡s✐❣♥❛❞❛ ♣❡❧♦ ❝♦❧❡❣✐❛❞♦ ❞♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛✲ r✐❛ ❊❧étr✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s ❝♦♠♦ r❡q✉✐s✐t♦ ♥❡❝❡ssár✐♦ ♣❛r❛ ❝♦♥❝❧✉sã♦ ❞♦ ❞♦✉t♦r❛❞♦✳
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❏♦ã♦ ❆✳ ❞❡ ❱❛s❝♦♥❝❡❧♦s ❈♦✲❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❲❛❧♠✐r ▼✳ ❈❛♠✐♥❤❛s
❆❞✈✐s♦r ❛t ❖①❢♦r❞ ❯♥✐✈❡rs✐t②✿ Pr♦❢✳ ❱❛s✐❧❡ P❛❧❛❞❡
✏✳✳✳ ❝❡ ♥❡ s❡r❛ q✉✬❛✈❡❝ ✉♥❡ ❛r❞❡♥t❡ ♣❛t✐❡♥❝❡ q✉❡ ♥♦✉s ❝♦♥q✉❡rr♦♥s ❧❛ ✈✐❧❧❡ s♣❧❡♥❞✐❞❡ q✉✐ ❞♦♥♥❡r❛ ❧✉♠✐èr❡✱ ❥✉st✐❝❡ ❡t ❞✐❣♥✐té à t♦✉s ❧❡s ❤♦♠♠❡s✳ ❊t ❛✐♥s✐ ❧❛ ♣♦és✐❡ ♥✬❛✉r❛ ♣❛s ❝❤❛♥té ❡♥ ✈❛✐♥✳✳✳ ✑
✏✳✳✳ só ❝♦♠ ✉♠❛ ❛r❞❡♥t❡ ♣❛❝✐ê♥❝✐❛ q✉❡
❝♦♥q✉✐st❛r❡♠♦s ❛ ❝✐❞❛❞❡ ❡①♣❧ê♥❞✐❞❛ q✉❡ ❞❛rá ❧✉③✱ ❥✉st✐ç❛ ❡ ❞✐❣♥✐❞❛❞❡ ❛ t♦❞♦s ♦s ❤♦♠❡♥s✳ ◆❡st❡ ❞✐❛ ❛ ♣♦❡s✐❛ ♥ã♦ t❡rá ❝❛♥t❛❞♦ ❡♠ ✈ã♦✳✳✳✧✳
➚ ❋❛♠í❧✐❛
P♦❞❡r✐❛ ❢❛❝✐❧♠❡♥t❡ ❡s❝r❡✈❡r ♠✐❧ ♣❛❧❛✈r❛s ♣❛r❛ ❛❣r❛❞❡❝❡r à ♠✐♥❤❛ ❢❛♠í❧✐❛ ♣❡❧♦ ❛♣♦✐♦ ✐♥❝♦♠♣❛rá✈❡❧ q✉❡ t✐✈❡ ♣❛r❛ tr✐❧❤❛r ❡st❡s ❝❛♠✐♥❤♦s t♦rt✉♦s♦s ❞❛ ✈✐❞❛✳ ❚✐✈❡ ❞❡ t✉❞♦ q✉❡ ♣r❡❝✐s❡✐✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ✉♠❛ ✈✐❞❛ ❢❡❧✐③ ♥❡st❡s ❛♥♦s✳ ▼✐♥❤❛ ❝❛s❛ ❢♦✐ ♠❡✉ r❡❢ú❣✐♦ ♦♥❞❡ r❡❝❛rr❡❣✉❡✐ ❛s ♠✐♥❤❛s ❜❛t❡r✐❛s✳
▼✐♥❤❛ ♠ã❡ s❡♠♣r❡ ♠❡ tr♦✉①❡ ❞❡ ✈♦❧t❛ à r❡❛❧✐❞❛❞❡✱ ♠❡s♠♦ ❡♠ ♠♦♠❡♥✲ t♦s ♥♦s q✉❛✐s ❝❤❡❣✉❡✐ ❛ ♣❡♥s❛r q✉❡ ❛ r❡❛❧✐❞❛❞❡ ❡r❛ s♦♠❡♥t❡ ✉♠❛ ❞✐✈❡rsã♦ ♣❛ss❛❣❡✐r❛✳ ❚r❛❜❛❧❤❛r ❝♦♠ t❡♦r✐❛ ♣♦❞❡ s❡r ♠✉✐t♦ ❛❧✐❡♥❛♥t❡✳
◆♦ ♠❡✐♦ ❞❛s ❡q✉❛çõ❡s ❞♦ ♠ét♦❞♦ ▼●▼ ♣❛r❛ ❛ P▲P✱ q✉❡ é ♦ ♥ú❝❧❡♦ ❞❡st❛ t❡s❡✱ ❤á ✉♠ s✐♥❣❡❧♦ ❞❡s❡♥❤♦ ❞❡ ✉♠❛ ✏♠❡♥✐♥❛ s✉♣❡r✲♣♦❞❡r♦s❛✑✦ ❊♥tã♦ ❛❝❤♦ q✉❡ ❡st❛ t❡s❡ t❡♠ ❛ ❝♦✲❛✉t♦r✐❛ ❞❡ ♠✐♥❤❛ ♠❡♥✐♥❛✱ ●✐✉❧✐❛✱ ❝♦♠ ♦s s✉♣❡r ♣♦❞❡r❡s ❞❡♣♦s✐t❛❞♦s ♥♦ ♠❡✉ r❛s❝✉♥❤♦ ♥❛q✉❡❧❡ ❞✐❛✳
▼❡✉ ♣❛✐ s❡♠♣r❡ ❛❝r❡❞✐t♦✉✱ ❡ ♠❡ ❢❡③ ❛❝r❡❞✐t❛r q✉❡ ♦ ❝é✉ é ♦ ❧✐♠✐t❡✳ ➱ ♣♦r ✐st♦ q✉❡ s❡♠♣r❡ ❛♣♦st❡✐ ❛❧t♦✱ ♣♦✐s ❛✐♥❞❛ ❡st♦✉ ❧♦♥❣❡ ❞♦ ♠❡✉ ❧✐♠✐t❡✳ ❙♦✉ ❡♥❣❡♥❤❡✐r♦ ♣♦r ❝❛✉s❛ ❞❡❧❡✱ ♣r❡❝✐s❛ ❞✐③❡r ♠❛✐s❄
❊♠ ❞♦✐s s❤♦✇s ❞♦ ❉❊❯❑✱ ❛ ❜❛♥❞❛ ❞❡ r♦❝❦ ♥❛ q✉❛❧ ❡✉ t♦❝❛✈❛ ❛♥t❡s ❞❡ ✐r ♣❛r❛ ❖①❢♦r❞✱ ♠❡✉ ✐r♠ã♦ ❝❛♥t♦✉ ❝♦♠✐❣♦ ❛❧❣✉♠❛s ♠ús✐❝❛s✳ ❆ ♠ús✐❝❛ s❡♠♣r❡ ❢♦✐ ❛ ♠✐♥❤❛ ❝✐ê♥❝✐❛ ❢❛✈♦r✐t❛ q✉❡ ❝♦♠♣❛rt✐❧❤♦ ❝♦♠ ♦ ♠❡✉ ✐r♠ã♦✳
▼❡❧❤♦r t✐❛ ❡ ✐r♠ã ❞♦ ♠✉♥❞♦ q✉❡❜r♦✉ ✉♠ ♠♦♥t❡ ❞❡ ❣❛❧❤♦s ♣❛r❛ ♠✐♠✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♥♦ t❡♠♣♦ q✉❡ ❡st✐✈❡ ❡♠ ❖①❢♦r❞✳ ◗✉❛♥❞♦ ♦s ♠❡✉s s♦❜r✐♥❤♦s ❝❤❡❣❛r❡♠ ❡s♣❡r♦ r❡tr✐❜✉✐r✳
❆♦s ❆♠✐❣♦s
❆♦s ♠❡✉s ❛♠✐❣♦s ❞❛ ❊♥❣❡♥❤❛r✐❛ r❡♣r❡s❡♥t❛❞♦s ♣❡❧♦ ❚ú❧✐♦✱ ❙ér❣✐♦ ▼❛r✈❛❞❡③❛✱ ❘♦❞r✐❣♦ ❱❛❧❛❞ã♦✱ ❆❞r✐❛♥♦ ❡ ❘✐❝❛r❞♦✳ ●r✉♣♦ ❞❡ ♠❡♥t❡s ❜r✐❧❤❛♥✲ t❡s ❜r✐❣❛♥❞♦ ♣❛r❛ ❡♥❝♦♥tr❛r ✉♠ ❧✉❣❛r ❛♦ s♦❧✳ ❖ ♠❡❧❤♦r ♣❛r❛ ✈♦❝ês é ♠❡✉ ❞❡s❡❥♦✳
❆♦s ♠❡✉s ❛♠✐❣♦s ❣✉❡rr❡✐r♦s ▼❛r❝❡❧♦ ●❡r❛r❞✐✱ ◆❡✇t♦♥ ❱❡❧❧♦s♦✱ ●✉✐❞♦ ▼❡❧♦ ❡ ❳✉①❛ ♣♦r ❡st❡s ♠❛✐s ❞❡ ✶✵ ❛♥♦s ❞❡ ❝♦♥✈í✈✐♦ ❡♠ t❡♠♣♦s ❞❡ ♦♥❞❛s ❜♦❛s ❡ r✉✐♥s✳ ◆♦ss♦s s♦♥❤♦s sã♦ ♦s ♠❡s♠♦s ❤á ♠✉✐t♦ t❡♠♣♦✳✳✳
❚♦ ♠✐♥❡ ❖①♦♥ ❋r✐❡♥❞s ❈❧❛✐r❡✱ ❑r✐st❡❧❧✱ ❛♥❞ ❈✐♥t❤✐❛ ❢♦r t❤❡ ❝♦♠♣❛♥② ✐♥ t❤❡ ❝♦❧❞✱ ❝❧♦✉❞②✱ ❣r❛②✐s❤ ❛♥❞ r❛✐♥② ❖①❢♦r❞✳ ❨♦✉ ❛r❡ t❤❡ ♣r♦♦❢ t❤❛t ❣♦♦❞ ❢r✐❡♥❞s❤✐♣ ✐s ♥♦t ❛ ♠❛tt❡r ♦❢ t✐♠❡ ♦r ❣❡♦❣r❛♣❤②❀ ②♦✉ ✇❡r❡ t❤❡ s✉♥❧✐❣❤t ❛♠♦♥❣ t❤❡ ❝❧♦✉❞s✳
❆❣r❛❞❡❝✐♠❡♥t♦s ❛♦s ♠❡str❡s
Pr♦❢✳ ❏♦ã♦ ❢♦✐ ♠❡✉ ♦r✐❡♥t❛❞♦r ❞❡s❞❡ ❛ ✐♥✐❝✐❛çã♦ ❝✐❡♥tí✜❝❛ ♥♦s ✐❞♦s ❞❡ ✷✵✵✶✳ ▼♦t✐✈♦✉ ♠❡ ❛ s❡❣✉✐r ❛ ❝❛rr❡✐r❛ ❝✐❡♥tí✜❝❛ ❣✉✐❛♥❞♦ ♠❛s ♠❡ ❞❛♥❞♦ ❧✐❜❡r✲ ❞❛❞❡ ♦ s✉✜❝✐❡♥t❡ ♣❛r❛ ❡✈♦❧✉✐r✳ ❚❡✈❡ ❛ ❝♦r❛❣❡♠✱ q✉❡ ♣♦✉❝♦s t❡r✐❛♠✱ ❞❡ ♠❡ ✐♥❞✐❝❛r ❛♦ ❞♦✉t♦r❛❞♦ s❡♠ ♣❛ss❛r ♣❡❧♦ ♠❡str❛❞♦✳ ❙❡✐ q✉❡ ♠✉✐t♦s ♣r♦❢❡ss♦r❡s ♥ã♦ ♠❡ ❞❡✐①❛r✐❛♠ ❛❧ç❛r ✈ô♦s tã♦ ❛❧t♦s✱ ♠❛s ♦ Pr♦❢✳ ❏♦ã♦ s❡♠♣r❡ ❢♦✐ ✉♠ ❣r❛♥❞❡ ❡♥t✉s✐❛st❛✳ ▼❡✉s s✐♥❝❡r♦s ❛❣r❛❞❡❝✐♠❡♥t♦s ♣❡❧♦s ✺ ❛♥♦s ❞❡ ❝♦♥✈í✈✐♦✳Pr♦❢✳ ❲❛❧♠✐r ♠❡ ❝♦♥✈✐❞♦✉✱ q✉❛♥❞♦ ❡✉ ❛✐♥❞❛ ❡r❛ ❛❧✉♥♦ ❞❡ ❣r❛❞✉❛çã♦✱ ♣❛r❛ ❞❡s❡♥✈♦❧✈❡r ✉♠❛ r❡❞❡✱ q✉❡ ♥♦ ✜♥❛❧ s❡ tr❛♥s❢♦r♠♦✉ ♥❛ P▲P✱ t❡♠❛ ❝❡♥tr❛❧ ❞❡st❛ t❡s❡✳ ❋♦✐ ♦ ♣r✐♠❡✐r♦ ♣r♦❢❡ss♦r q✉❡ ♥♦t❡✐ q✉❡ s❡ ✐♠♣♦rt❛✈❛ ❡ ❝♦♥✜❛✈❛ ♥♦ ♣♦t❡♥❝✐❛❧ ❞♦s ❛❧✉♥♦s✳ ❊st❡ ❢❛t♦ ❢❡③ ❝♦♠ q✉❡ ♦ tr❛❜❛❧❤♦ ✜♥❛❧ ❞❛ ❞✐s❝✐♣❧✐♥❛ ✏■♥t❡❧✐❣ê♥❝✐❛ ❈♦♠♣✉t❛❝✐♦♥❛❧✑ q✉❡ ❝✉rs❡✐ ❝♦♠ ❡❧❡ ✹ ❛♥♦s ❛trás s❡ tr❛♥s❢♦r✲ ♠❛ss❡ ♥❛ t❡s❡ ❞❡ ❞♦✉t♦r❛❞♦ q✉❡ ❛♣r❡s❡♥t♦ ❛❣♦r❛✳ ❖❜r✐❣❛❞♦ ♣❡❧❛ ❝♦♥✜❛♥ç❛ ❞❡♣♦s✐t❛❞❛ ❞❡s❞❡ ♦ ❝♦♠❡ç♦✳
Pr♦❢✳ ❱❛s✐❧❡ ✇❛s ♠② t✉t♦r ❞✉r✐♥❣ ♠② ♦♥❡✲②❡❛r st❛② ❛t ❖①❢♦r❞ ❯♥✐✈❡rs✐t②✳ ❍❡ ❡①♣❧❛✐♥❡❞ ♠❡ ❛❜♦✉t t❤❡ ❝❤❡❛♣❡st ✇❛②s t♦ tr❛✈❡❧ ✐♥ ❊✉r♦♣❡✱ ✇❤❡r❡ t♦ ❜✉② ❢♦♦❞ ❛♥❞ s♦ ♦♥✳ ❖♥ t❤❡ t♦♣ ♦❢ t❤❡s❡ ✇❡ ❛❧s♦ r❡s❡❛r❝❤❡❞✦ ❖①❢♦r❞ ✇❛s ❛ r❡♠❛r❦❛❜❧❡ ♠♦♠❡♥t ✐♥ ♠② ❧✐❢❡✱ ♦♥❡ ♦❢ t❤❡s❡ t✉r♥✐♥❣ ♣♦✐♥ts t❤❛t s❡❧❞♦♠ ❤❛♣♣❡♥s✳ ❚❤❛♥❦s ❢♦r t❤❡ ✐♥❝❡♥t✐✈❡ ❛♥❞ ❛❞✈✐❝❡s✳
❆♦ Pr♦❢ ❚❛❦❛❤❛s❤✐ ♣❡❧❛ ❛❥✉❞❛ s✐st❡♠át✐❝❛ ❡♠ ❞✐✈❡rs♦s t❡♠❛s q✉❡ ❝♦♥tr✐❜✉✐r❛♠ ❡♠ ♠✉✐t♦ ♥❡st❛ t❡s❡✳
❆♦ Pr♦❢✳ ❘♦❞♥❡② q✉❡ s❡♠♣r❡ ❛❜❡rt♦ ❛ ❝♦♥✈❡rs❛ ❝♦♥tr✐❜✉✐✉ ❡♠ ♠✉✐t♦ ♥❛ ♠✐♥❤❛ ❢♦r♠❛çã♦ ❝✐❡♥tí✜❝❛ ❡ ♥❛ ❝♦♥str✉çã♦ ❞❡ ♠✉✐t❛s ❞❡ ♠✐♥❤❛s ✐❞é✐❛s✳ ❙❡r❡✐ ❡t❡r♥❛♠❡♥t❡ ❣r❛t♦✳
●❛✉❝❤❡ ❖❤✦✦✦ ❱❛st♦✲♠✉♥❞♦ ❞❡ ❣r❛♥❞✐♦s❛✲❞✐♠❡♥sã♦
t✉ és ♠✉♥❞♦✲❣✐❣❛♥t❡ ♠❛s ❝❛❜❡♥♦♠❡✉❝♦r❛çã♦
❖❤✦✦✦ ●❡♦❞és✐❝♦✲♠✉♥❞♦✲✐♥s✐❣♥✐✜❝❛♥t❡ ♠❡s♠♦ ♠✉♥❞♦✲❣r❛♥❞❡
❘❡s✉♠♦
❊st❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ ✉♠❛ ♥♦✈❛ ❛❜♦r❞❛❣❡♠ ♣❛r❛ ❧✐❞❛r ❝♦♠ ♦ ♣r♦❜❧❡♠❛ ❞❡ ♠✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡str✉t✉r❛❧ ✭str✉❝t✉r❛❧ r✐s❦ ♠✐♥✐♠✐③❛t✐♦♥ ✲ ❙❘▼✮ ❛♣❧✐❝❛❞♦ ❛♦ ♣r♦❜❧❡♠❛ ❣❡r❛❧ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛s✳ ❆ ❢♦r♠✉❧❛çã♦ é ❜❛s❡❛❞❛ ♥♦ ❝♦♥❝❡✐t♦ ❢✉♥❞❛♠❡♥t❛❧ ❞❡ q✉❡ ♦ ❛♣r❡♥❞✐③❛❞♦ s✉♣❡r✈✐s✐♦♥❛❞♦ é ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦ ❜✐✲♦❜❥❡t✐✈♦ ♦♥❞❡ ❞♦✐s ♦❜❥❡t✐✈♦s ❝♦♥✢✐t❛♥t❡s ❞❡✈❡♠ s❡r ♠✐♥✐♠✐③❛❞♦s✳ ❊st❡s ♦❜❥❡t✐✈♦s ❡stã♦ r❡❧❛❝✐♦♥❛❞♦s ❛♦ ❡rr♦ ❞❡ tr❡✐♥❛♠❡♥t♦✱ r✐s❝♦ ❡♠♣ír✐❝♦ ✭Remp✮✱ ❡ à ❝♦♠♣❧❡①✐❞❛❞❡ ✭❝❛♣❛❝✐❞❛❞❡✮ ❞❛ ♠áq✉✐♥❛ ❞❡ ❛♣r❡♥❞✐③❛❞♦
❆❜str❛❝t
❚❤✐s ✇♦r❦ ♣r❡s❡♥ts ❛ ♥♦✈❡❧ ❛♣♣r♦❛❝❤ t♦ ❞❡❛❧ ✇✐t❤ t❤❡ str✉❝t✉r❛❧ r✐s❦ ♠✐♥✐✲ ♠✐③❛t✐♦♥ ✭❙❘▼✮ ❛♣♣❧✐❡❞ t♦ ❛ ❣❡♥❡r❛❧ ♠❛❝❤✐♥❡ ❧❡❛r♥✐♥❣ ♣r♦❜❧❡♠✳ ❚❤❡ ❢♦r✲ ♠✉❧❛t✐♦♥ ✐s ❜❛s❡❞ ♦♥ t❤❡ ❢✉♥❞❛♠❡♥t❛❧ ❝♦♥❝❡♣t t❤❛t s✉♣❡r✈✐s❡❞ ❧❡❛r♥✐♥❣ ✐s ❛ ❜✐✲♦❜❥❡❝t✐✈❡ ♦♣t✐♠✐③❛t✐♦♥ ♣r♦❜❧❡♠ ✐♥ ✇❤✐❝❤ t✇♦ ❝♦♥✢✐❝t✐♥❣ ♦❜❥❡❝t✐✈❡s s❤♦✉❧❞ ❜❡ ♠✐♥✐♠✐③❡❞✳ ❚❤❡ ♦❜❥❡❝t✐✈❡s ❛r❡ r❡❧❛t❡❞ t♦ t❤❡ tr❛✐♥✐♥❣ ❡rr♦r✱ ❡♠♣✐r✐❝❛❧ r✐s❦ ✭Remp✮✱ ❛♥❞ t❤❡ ♠❛❝❤✐♥❡ ❝♦♠♣❧❡①✐t② ✭Ω✮✳ ■♥ t❤✐s ✇♦r❦ ♦♥❡ ❣❡♥❡r❛❧ Q✲♥♦r♠
▲✐st❛ ❞❡ ❆❜r❡✈✐❛çõ❡s
❆❇ ❆❞❛❇♦♦st
❆❇❘ ❘❡❣✉❧❛r✐③❡❞ ❆❞❛❇♦♦st
❈❱ ❈r♦ss ✈❛❧✐❞❛t✐♦♥ ✲ ❱❛❧✐❞❛çã♦ ❝r✉③❛❞❛
❊❘▼ ❊♠♣✐r✐❝❛❧ ❘✐s❦ ▼✐♥✐♠✐③❛t✐♦♥ ✲ ▼✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡♠♣ír✐❝♦ ❊❙ ❊❛r❧② st♦♣ ✲ ♣❛r❛❞❛ ♣r❡♠❛t✉r❛
❋❋❚ ❋❛st ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ ✲ ❚r❛♥s❢♦r♠❛❞❛ rá♣✐❞❛ ❞❡ ❋♦✉r✐❡r ✐✐❞ ■♥❞❡♣❡♥❞❡♥t❡ ❡ ✐❞❡♥t✐❝❛♠❡♥t❡ ❞✐str✐❜✉í❞❛
❑❋❉ ❑❡r♥❡❧ ❋✐s❤❡r ❉✐s❝r✐♠✐♥❛♥t ✲ ❉✐s❝r✐♠✐♥❛♥t❡ ❞❡ ❋✐s❤❡r ✉s❛♥❞♦ ❦❡r♥❡❧s ▲❆❙❙❖ ●❡♥❡r❛❧✐③❡❞ ▲❡❛st ❆❜s♦❧✉t❡ ❙❤r✐♥❦❛❣❡ ❛♥❞ ❙❡❧❡❝t✐♦♥ ❖♣❡r❛t♦r
▲▼ ▲❡✈❡♥❜❡r❣✲▼❛rq✉❛r❞t
▲❙❊ ▲❡❛st ❙q✉❛r❡s ❊st✐♠❛t❡ ✲ ❊st✐♠❛❞♦r ❞❡ ♠í♥✐♠♦s q✉❛❞r❛❞♦s ▲❖❖ ▲❡❛✈❡✲❖♥❡✲❖✉t ❑❋❉
▲❖❖▼ ▲❡❛✈❡✲❖♥❡✲❖✉t ❙❱▼
▼●▼ ▼✐♥✐♠✉♠ ●r❛❞✐❡♥t ▼❡t❤♦❞ ✲ ▼ét♦❞♦ ❞♦ ❣r❛❞✐❡♥t❡ ♠í♥✐♠♦ ▼▲P ▼✉❧t✐✲❧❛②❡r ♣❡r❝❡♣tr♦♥ ✲ ❘❡❞❡ ♣❡r❝❡♣tr♦♥ ❞❡ ♠ú❧t✐♣❧❛s ❝❛♠❛❞❛s ▼❖❇❏ ▼✉❧t✐♦❜❥❡t✐✈♦
▼❙❊ ▼❡❛♥ ❙q✉❛r❡❞ ❊rr♦r ✲ ❊rr♦ ◗✉❛❞rát✐❝♦ ▼é❞✐♦ ❖❇❉ ❖♣t✐♠❛❧ ❇r❛✐♥ ❉❛♠❛❣❡
P▲P P❛r❛❧❧❡❧ ▲❛②❡r P❡r❝❡♣tr♦♥ ✲ ❘❡❞❡ ♣❡r❝❡♣tr♦♥ ❝♦♠ ❝❛♠❛❞❛s P❛r❛❧❡❧❛s P❖ P❛r❡t♦✲ót✐♠❛
PP❙❱▼ P♦st❡r✐♦r Pr♦❜❛❜✐❧✐t② ❙❱▼
❘❇❋ ❘❛❞✐❛❧ ❇❛s✐s ❋✉♥❝t✐♦♥ ✲ ❋✉♥çõ❡s ❞❡ ❜❛s❡ r❛❞✐❛❧
❙❘▼ ❙tr✉❝t✉r❛❧ ❘✐s❦ ▼✐♥✐♠✐③❛t✐♦♥ ✲ ▼✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡str✉t✉r❛❧ ❙❱▼ ❙✉♣♣♦rt ❱❡❝t♦r ▼❛❝❤✐♥❡ ✲ ▼áq✉✐♥❛s ❞❡ ✈❡t♦r❡s s✉♣♦rt❡
❱❈ ❱❛♣♥✐❦ ❈❤❡r✈♦♥❡♥❦✐s ❳✈❛❧ k✲❢♦❧❞ ❑❋❉
▲✐st❛ ❞❡ ❙✐♠❜♦❧♦s
C ▼❛tr✐③ q✉❡ ♠✉❧t✐♣❧✐❝❛❞❛ ♣❡❧♦s ♣❛râ♠❡tr♦s ❧✐♥❡❛r❡s r❡s✉❧t❛ ♥❛ s❛í❞❛ ❞❛ ♠áq✉✐♥❛ D ▼❛tr✐③ q✉❡ ♠✉❧t✐♣❧✐❝❛❞❛ ♣❡❧♦s ♣❛râ♠❡tr♦s ❧✐♥❡❛r❡s
r❡s✉❧t❛ ♥❛ ❞❡r✐✈❛❞❛ ❞❛ s❛í❞❛ ❞❛ ♠áq✉✐♥❛ e(.) ❊rr♦ ♣❛r❛ ✉♠ ❞❛❞♦ ♣❛❞rã♦
err(.) ❊rr♦ ❞❡ ❣❡♥❡r❛❧✐③❛çã♦ ❊[.] ❊s♣❡r❛♥ç❛ ♠❛t❡♠át✐❝❛ f(.) ❋✉♥çã♦ ♦✉ ❤✐♣ót❡s❡
f1(.) ❋✉♥çã♦ q✉❡ r❡♣r❡s❡♥t❛ ❛ ♠✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡♠♣ír✐❝♦
f2(.) ❋✉♥çã♦ q✉❡ r❡♣r❡s❡♥t❛ ❛ ♠✐♥✐♠✐③❛çã♦ ❞❛ ❝❛♣❛❝✐❞❛❞❡ ❞❛ ❢✉♥çã♦
F(.) ❚r❛♥s❢♦r♠❛❞❛ ❞❡ ❋♦✉r✐❡r ❞❡f(.) F(x) ❋✉♥çã♦ ❉✐str✐❜✉✐çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡
F(y|x) ❋✉♥çã♦ ❞❡ ❉✐str✐❜✉✐çã♦ ❝♦♥❞✐❝✐♦♥❛❧ ❞❡y ❞❛❞♦ x F(y, x) ❋✉♥çã♦ ❞❡ ❉✐str✐❜✉✐çã♦ ❈♦♥❥✉♥t❛ ❞❡y ❡x
F(.) ❊s♣❛ç♦ ❞❛s ❢✉♥çõ❡s ♦✉ ❤✐♣ót❡s❡s f atF(γ) ❆ ❞✐♠❡♥sã♦ ❢❛t✲s❤❛tt❡r✐♥❣ G(.) ❋✉♥çã♦ ❞❡ ❝r❡s❝✐♠❡♥t♦
h ❉✐♠❡♥sã♦ ❱❛♣✐♥✐❦ ❡ ❈❤❡r♥♦♥❡❦✐s ✭❱❈ ❞✐♠♥❡s✐♦♥✮ H P❡s♦s ❞❛ ❝❛♠❛❞❛ ❡s❝♦♥❞✐❞❛ ❞❡ ✉♠❛ ▼▲P
H(.) ❊s♣❡r❛♥ç❛ ❞❛ ❡♥tr♦♣✐❛ ❛❧❡❛tór✐❛ H1(.) ❊♥tr♦♣✐❛ ❛❧❡❛tór✐❛
Hann(.) ❊♥tr♦♣✐❛ r❡❝♦③✐❞❛
i ❮♥❞✐❝❡
I(.) ❋✉♥çã♦ ✐♥❞✐❝❛❞♦r❛
j ❮♥❞✐❝❡ ❡ ♥ú♠❡r♦ ✐♠❛❣✐♥ár✐♦ ♥❛ ❞❡✜♥✐çã♦ ❞❛ tr❛♥s❢♦r♠❛❞❛ ❞❡ ❋♦✉r✐❡r J(.) ❏❛❝♦❜✐❛♥♦
k ◆ú♠❡r♦ ❞❡ ❡rr♦s ♥♦ ❝♦♥❥✉♥t♦ ❞❡ tr❡✐♥❛♠❡♥t♦ k(.) ◆ú❝❧❡♦ ✭❑❡r♥❡❧✮
l P❛râ♠❡tr♦s ❧✐♥❡❛r❡s
L(.) ▼❡❞✐❞❛ ❞❡ ♣❡r❞❛ ♦✉ ❞✐s❝r❡♣â♥❝✐❛
L(.) ▲❛❣r❛♥❣❡❛♥♦
m(.) ▼❡♥♦r ♠❛r❣❡♠ ❞♦ ❝♦♥❥✉♥t♦
M(.) ▼❛r❣❡♠ ❡♠ r❡❧❛çã♦ ❛♦ ❝♦♥❥✉♥t♦ ❞❡ tr❡✐♥❛♠❡♥t♦ n ❉✐♠❡♥sã♦ ❞♦ ❡s♣❛ç♦ ❞❡ ❡♥tr❛❞❛s✱ x∈Rn
N(.) ❉✐✈❡rs✐❞❛❞❡ ❞❡ ✉♠❛ ❝❧❛ss❡ ❞❡ ❢✉♥çõ❡s Ω(.) ▼❡❞✐❞❛ ❞❡ ❝♦♠♣❧❡①✐❞❛❞❡ ✭❝❛♣❛❝✐❞❛❞❡✮ R ❊s❢❡r❛ q✉❡ ❝♦♥t❡♠ ♦s ✈❡t♦r❡s x∈X
R(.) ❋✉♥❝✐♦♥❛❧ ❞❡ r✐s❝♦
Remp(.) ❋✉♥❝✐♦♥❛❧ ❞❡ r✐s❝♦ ❡♠♣ír✐❝♦
S ❈♦♥❥✉♥t♦ ❞❡ tr❡✐♥❛♠❡♥t♦
P P❛râ♠❡tr♦s ❧✐♥❡❛r❡s ✭▼❛tr✐③ ♣❛r❛ ❛ P▲P ❡ ✈❡t♦r ♣❛r❛ ♦s ♣♦❧✐♥ô♠✐♦s✮ P(.) Pr♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ ❡✈❡♥t♦
pji ❈♦♠♣♦♥❡♥t❡ ❞❛ ♠❛tr✐③ ❞❡ ♣❡s♦sP
Q ▼❛tr✐③ q✉❡ ❞❡✜♥❡ ❛ ♠❡❞✐❞❛ ❞❡ ❝♦♠♣❧❡①✐❞❛❞❡✱Q=ATA
t ❈♦♥t❛❞♦r r❡❢❡r❡♥t❡ ❛s ❛♠♦str❛s ❞♦ ❝♦♥❥✉♥t♦ ❞❡ tr❡✐♥❛♠❡♥t♦ T ◆ú♠❡r♦ ❞❡ ❛♠♦str❛s ♥♦ ❝♦♥❥✉♥t♦ ❞❡ tr❡✐♥❛♠❡♥t♦
U P❡s♦s ❞❛ ❝❛♠❛❞❛ ❞❡ s❛í❞❛ ❞❡ ✉♠❛ ▼▲P V P❛râ♠❡tr♦s ♥ã♦✲❧✐♥❡❛r❡s ✭▼❛tr✐③ ♣❛r❛ ❛ P▲P✮ vji ❈♦♠♣♦♥❡♥t❡ ❞❛ ♠❛tr✐③ ❞❡ ♣❡s♦sV
w P❛râ♠❡tr♦s ❞❛ ♠áq✉✐♥❛ ❞❡ ❛♣r❡♥❞✐③❛❞♦✱w∈Λ x ❱❛r✐á✈❡✐s ❞❡ ❡♥tr❛❞❛ ♦✉ ❝♦♥tr♦❧❡
X ❊s♣❛ç♦ ♦♥❞❡ ♦ ✈❡t♦r x ❡stá ❞❡✜♥✐❞♦✱x∈X yd ❘❡s♣♦st❛ ♦❜t✐❞❛ ❞♦ s✉♣❡r✈✐s♦r✱ s❛í❞❛ ❞❡s❡❥❛❞❛ z ❱❛r✐á✈❡❧ ❛❧❡❛tór✐❛✱z = (x, y)✱z ∈Z
α ▼✉❧t✐♣❧✐❝❛❞♦r ❞❡ ▲❛❣r❛♥❣❡✱ t❡r♠♦ ❞❡ ♣♦♥❞❡r❛çã♦
δ ❈♦♥st❛♥t❡ ♣♦s✐t✐✈❛ ✲❃Pr♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ ❡✈❡♥t♦ ♦❝♦rr❡r
∆ ▼❛r❣❡♠ ❞❡ s❡♣❛r❛çã♦ ♣❛r❛ ❢✉♥çõ❡s ❧✐♥❡❛r❡s ♥♦ ❡s♣❛ç♦ ❞❛s ✈❛r✐á✈❡✐s ǫ ❈♦♥st❛♥t❡ ♣♦s✐t✐✈❛
η P❛ss♦ ♥♦s ♠ét♦❞♦s ❜❛s❡❛❞♦s ♥♦ ❣r❛❞✐❡♥t❡ γ ▼❛r❣❡♠ ❞❡ s❡♣❛r❛çã♦ ♥♦ ❡s♣❛ç♦ ❞❛s ❢✉♥çõ❡s γ(.) ❋✉♥çã♦ ❞❡ ❛t✐✈❛çã♦
λ ❚❡r♠♦ ❞❡ r❡❣✉❧❛r✐③❛çã♦ Λ ❊s♣❛ç♦ ❞❡ ❤✐♣ót❡s❡s ω ❋r❡qüê♥❝✐❛
φ(.) ❋✉♥çã♦ ♥ã♦ ❧✐♥❡❛r ✉t✐❧✐③❛❞❛ ♣❛r❛ ❛ ❝♦♥str✉çã♦ ❞❡ ♠áq✉✐♥❛s ❞❡ ❛♣r❡♥❞✐③❛❣❡♠ ̺ ❈♦♥st❛♥t❡ ♥ã♦ ✐♥✜♥✐t❛
ϑ(.) ▼❡❞✐❞❛ ❞❡ ♣❡r❞❛ ♦✉ ❞✐s❝r❡♣â♥❝✐❛ ♥♦ ❡s♣❛ç♦Rn+1
τ ❖r❞❡♠ ❞♦s ❛♣r♦①✐♠❛❞♦r❡s ♣♦❧✐♥♦♠✐❛✐s θ(.) ❋✉♥çã♦ ❞❡❣r❛✉
ξ(.) ❱❛r✐á✈❡❧ ❞❡ ❢♦❧❣❛ ❞❡ ✉♠❛ ♠❛r❣❡♠ ✭s♦❢t ♠❛r❣✐♥✮ ζ ▲✐♠✐t❡ s✉♣❡r✐♦r ❞♦ r✐s❝♦ ❡s♣❡r❛❞♦
∇f ●r❛❞✐❡♥t❡ ❞❡ f ˜
O(.) ❖r❞❡♠ ❞❡ ❣r❛♥❞❡③❛ ❛ss✐♥tót✐❝❛ : ❚❛❧ q✉❡ ✭s✉❝❤ t❤❛t✮
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ❋✐❣✉r❛ ♠♦str❛♥❞♦ ♣♦ssí✈❡✐s s♦❧✉çõ❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ r❡✲ ❣r❡ssã♦ t❡♥❞♦ ♦s ♣♦♥t♦s ❝♦♠♦ ♦ ❝♦♥❥✉♥t♦ ❝♦♥❤❡❝✐❞♦✳ ◆♦t❛✲s❡ q✉❡ ♦ ♠♦❞❡❧♦ ❡♠ ❧✐♥❤❛ ❝♦♥tí♥✉❛ ❛♣r❡s❡♥t❛ ❛❧❣✉♥s ❡rr♦s ♥❛ ❛♣r♦①✐♠❛çã♦ ♠❛s ❡♠ ❝♦♥tr❛♣❛rt✐❞❛ é ✉♠ ♠♦❞❡❧♦ ♠❛✐s s✐♠✲ ♣❧❡s✳ ❖ ♠♦❞❡❧♦ ❡♠ ❧✐♥❤❛ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ✉♠ ♠♦❞❡❧♦ ❝♦♠ ♠❛✐s ❝♦♠♣❧❡①✐❞❛❞❡ ❡ q✉❡ ❛❥✉st❛✲s❡ ❛♦s ❞❛❞♦s ♣r❡❝✐s❛♠❡♥t❡✳ ✳ ✳ ✶✵
✷✳✷ ◆❡st❛ ✜❣✉r❛ ♦❜s❡r✈❛✲s❡ ❞✉❛s s✐t✉❛çõ❡s ❞✐st✐♥t❛s ♦♥❞❡ ♦s ❝ír✲ ❝✉❧♦s r❡♣r❡s❡♥t❛♠ ❛ ❤✐♣❡r✲❡s❢❡r❛ ❞❡ r❛✐♦ R q✉❡ ❝♦♥té♠ ❛s
❛♠♦str❛s x ∈ X✳ ◆❛ ♣r✐♠❡✐r❛ s✐t✉❛çã♦ é ❛♣r❡s❡♥t❛❞♦ ❤✐♣❡r✲
♣❧❛♥♦s ❝♦♠ ♠❛r❣❡♠ ∆1✱ ❡ ♣♦❞❡✲s❡ ♦❜s❡r✈❛r q✉❡ ❡st❡s ♣♦❞❡♠
❝❧❛ss✐✜❝❛r ❛té três ❛♠♦str❛s ❞✐st✐♥t❛s✳ ◆❛ s❡❣✉♥❞❛ é ♠♦str❛❞♦ ✉♠ ❤✐♣❡r♣❧❛♥♦ ❝♦♠ ♠❛r❣❡♠ ∆2✱ s❡♥❞♦ q✉❡ ❡st❡ só ♣♦❞❡ ❞✐s✲
t✐♥❣✉✐r ❞✉❛s ❛♠♦str❛s ❞✐st✐♥t❛s✳ ❉❡st❛ ❢♦r♠❛ é ❝❧❛r♦ q✉❡ ❛ ❞✐♠❡♥sã♦ ❱❈ é ❞❡♣❡♥❞❡♥t❡ ❞❛ ♠❛r❣❡♠ ❞❡ s❡♣❛r❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✷✷
✷✳✸ ❊①❡♠♣❧♦ ✐❧✉str❛♥❞♦ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❖t✐♠❛❧✐❞❛❞❡ ❞❡ P❛r❡t♦✳ ◆♦ ❡✐①♦x✱ ❡stá r❡♣r❡s❡♥t❛❞❛ ❛ ❝♦♠♣❧❡①✐❞❛❞❡Ω❡ ❡♠ y♦ r✐s❝♦ ❡♠✲
♣ír✐❝♦ Remp✳ P♦❞❡✲s❡ ♥♦t❛r q✉❡ Ω(w1)<Ω(w2)❡ Remp(w1) >
Remp(w2)✱ ❧♦❣♦ ❛ ♠áq✉✐♥❛ ❞❡ ❛♣r❡♥❞✐③❛❣❡♠ r❡♣r❡s❡♥t❛❞❛ ♣♦r
w1 ♥ã♦ ❞♦♠✐♥❛ w2✱ w1 ⊀ w2✳ ❚❛♠❜é♠ é ❝❧❛r♦ q✉❡ w2 ⊀ w1✱
w1 ⊀ w3✱ w3 ⊀ w1✱ w2 ⊀ w3 ❡ w3 ⊀ w2✱ ✐✳❡✳✱ ♥ã♦ ❤á r❡❧❛çã♦
❞❡ ❞♦♠✐♥â♥❝✐❛ ❡♥tr❡ w1, w2 e w3✳ ❆ ♠áq✉✐♥❛ w3 ❞♦♠✐♥❛
w5✱ w3 ≺ w5✱ ❡ w2 ≺ w4✱ ❧♦❣♦ ♥ã♦ é ✐♥t❡r❡ss❛♥t❡ ✉t✐❧✐③❛r ❛s
♠áq✉✐♥❛s w4 ❡ w5✱ ♣♦✐s ❡st❛s sã♦ ♣✐♦r❡s ♥♦s ❞♦✐s ❛tr✐❜✉t♦s✳ ❆
❢r♦♥t❡✐r❛ P❖ ♥❡st❡ ❡①❡♠♣❧♦ éP O ={w1, w2, w3}✱ ❡st❛s sã♦ ❛s
♠áq✉✐♥❛s ❞❡ ✐♥t❡r❡ss❡ ❞❡st❡ tr❛❜❛❧❤♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✸✳✶ ❚♦♣♦❧♦❣✐❛ ❞❛ ♠✉❧t✐✲❧❛②❡r ♣❡r❝❡♣tr♦♥ ✭▼▲P✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✸✳✷ ❚♦♣♦❧♦❣✐❛ ❞❡ ✉♠❛ ❘◆❆ ❝♦♠ ❢✉♥çõ❡s ❞❡ ❜❛s❡ r❛❞✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✸✳✸ ▼❛♣❡❛♠❡♥t♦ ♥ã♦ ❧✐♥❡❛r r❡❛❧✐③❛❞♦ ♣❡❧❛ ❙❱▼ ❞❡ t❛❧ ❢♦r♠❛ q✉❡ ❡♠ ✉♠ ❡s♣❛ç♦ ❝❛r❛❝t❡ríst✐❝♦✱ ❛ s❡♣❛r❛çã♦ ❞❛s ❝❧❛ss❡s ♣♦ss❛ s❡r r❡❛❧✐③❛❞❛ ❞❡ ❢♦r♠❛ ❧✐♥❡❛r✱ s❡♥❞♦ q✉❡ ♦ ❤✐♣❡r♣❧❛♥♦ ❞❡ s❡♣❛r❛çã♦ ót✐♠♦ é ❞❡✜♥✐❞♦ ❝♦♠♦ ♦ q✉❡ ♠❛①✐♠✐③❛ ❛ ♠❛r❣❡♠ ❡♥tr❡ ❛s ❝❧❛ss❡s✳ ✹✶
✸✳✹ P❛r❛ ❡st❡ ♣r♦❜❧❡♠❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❜✐♥ár✐♦ ♦ ❤✐♣❡r♣❧❛♥♦ ❞❡ s❡♣❛r❛çã♦ ót✐♠♦ é ♦rt♦❣♦♥❛❧ à ❧✐♥❤❛ ♠❛✐s ❝✉rt❛ q✉❡ ❝♦♥❡❝t❛ ❛s ❝❛s❝❛s ❝♦♥✈❡①❛s ❞❛s ❞✉❛s ❝❧❛ss❡s✱ s❡♥❞♦ q✉❡ ❡st❡ ✐♥t❡r❝❡♣t❛ ❡st❛ ❡♠ s✉❛ ♠❡t❛❞❡ ✭❞✐stâ♥❝✐❛ ✐❣✉❛❧ ❡♥tr❡ ❛s ❞✉❛s ❝❧❛ss❡s✮✳ P❛r❛ s✐t✉❛çõ❡s ♦♥❞❡ ❛s ❝❧❛ss❡s sã♦ s❡♣❛rá✈❡✐s ❡①✐st❡ ✉♠ ✈❡t♦r ❞❡ ♣❡s♦s ❡ ✉♠❛ ♣♦❧❛r✐③❛çã♦ t❛❧ q✉❡ ydt((wxt) +b) > 0(t = 1, .., T)✳ ❊s❝❛❧♦♥❛♥❞♦ ✇ ❡ ❜ ❞❡ t❛❧ ❢♦r♠❛ q✉❡ ♦s ♣♦♥t♦s ♠❛✐s
♣ró①✐♠♦s ❞♦ ❤✐♣❡r♣❧❛♥♦ s❛t✐s❢❛ç❛♠ |(wxt) +b| = 1✱ ♦❜té♠✲s❡
❛ ❢ór♠✉❧❛ ❝❛♥ô♥✐❝❛ ❞♦ ❤✐♣❡r♣❧❛♥♦✳ P❛r❛ ❡st❡ ❝❛s♦✱ ❛ ♠❛r❣❡♠ ♣❡r♣❡♥❞✐❝✉❧❛r ❛♦ ❤✐♣❡r♣❧❛♥♦ é ✐❣✉❛❧ ❛ 2/kwk✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✸✳✺ ❚♦♣♦❧♦❣✐❛ ❞❡ ✉♠❛ ♠áq✉✐♥❛ ❙❱▼✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✹✳✶ ❋✉♥çã♦ ❝♦♥✈❡①❛ ✉♥✐❞✐♠❡♥s✐♦♥❛❧ ❛♣r♦①✐♠❛❞❛ ♣♦r ❝✐♥❝♦ s❡❣♠❡♥✲ t♦s ❞❡ r❡t❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹
✺✳✶ Pr♦❜❧❡♠❛ ❞❡ ❛♣r♦①✐♠❛çã♦ ❞❡ ✉♠❛ r❡t❛ ❝♦♥t❛♠✐♥❛❞❛ ♣♦r ✉♠ r✉í❞♦ ●❛✉ss✐❛♥♦✳ P♦❞❡✲s❡ ♦❜s❡r✈❛r q✉❡ ❛ ❢✉♥çã♦ ❛♣r♦①✐♠❛❞❛ ❝♦♠ ❛ r❡❣✉❧❛r✐③❛çã♦ é ♠❛✐s ♣ró①✐♠❛ ❞❛ ♦r✐❣✐♥❛❧✱ ❡ ❛♣❛r❡♥t❡✲ ♠❡♥t❡ ♠❛✐s ✏s✉❛✈❡✑✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹
✺✳✷ ❊rr♦ ❞❡ tr❡✐♥❛♠❡♥t♦ ♣❛r❛ fP1✳ ❊st❡ é ❡♠ ❣❡r❛❧ ♠♦♥♦tô♥✐❝♦
❞❡❝r❡s❝❡♥t❡✱ ❝❛s♦ ♥ã♦ ♦❝♦rr❛♠ ♣r♦❜❧❡♠❛s ♥✉♠ér✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✻✺
✺✳✸ ❊rr♦ ❞❡ ✈❛❧✐❞❛çã♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ fP1✳ ➱ ✐♥t❡r❡ss❛♥t❡ ♥♦t❛r
q✉❡ ♦ ❡rr♦ ❞❡ ✈❛❧✐❞❛çã♦ t❡♠ ✉♠ ♠í♥✐♠♦ ❜❡♠ ❞❡✜♥✐❞♦✱ ❝♦♠♦ ♠♦str❛❞♦ ♥❛ ✜❣✉r❛✳ ❊st❛ s✐t✉❛çã♦ é ❣❡r❛❧ ♣♦✐s ❡st❛ é ✉♠❛ ❢✉♥çã♦ q✉❛❞rát✐❝❛ ♥♦s ♣❛râ♠❡tr♦s ✭s❛❧✈♦ ❝❛s♦s ♦♥❞❡ ♦❝♦rr❛♠ ♣r♦❜❧❡♠❛s ♥✉♠ér✐❝♦s✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✺✳✹ ❋r♦♥t❡✐r❛ P❛r❡t♦✲Ót✐♠❛ ✭P❖✮ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡✜♥✐❞♦ ♥❛ ❊q✉❛çã♦ ✺✳✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼
✺✳✺ ❊♥❡r❣✐❛ ❞❛ s❛í❞❛ ❞♦ ✜❧tr♦ ♣❛ss❛✲❛❧t❛s ❡q✉✐✈❛❧❡♥t❡ à ♠✐♥✐♠✐③❛✲ çã♦ ❞♦ ❣r❛❞✐❡♥t❡ s❡♥❞♦ ❡st❛ ✉♠❛ ❢✉♥çã♦ ♠♦♥♦tô♥✐❝❛ ❝r❡s❝❡♥t❡✱ ❝♦♠♦ ❡s♣❡r❛❞♦ t❡♦r✐❝❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽
✺✳✻ Pr♦❜❧❡♠❛ ❞❡ ❛♣r♦①✐♠❛çã♦ ❞❡ ✉♠ ♣♦❧✐♥ô♠✐♦ ❞❡ t❡r❝❡✐r♦ ❣r❛✉ ❝♦♥t❛♠✐♥❛❞♦ ♣♦r ✉♠ r✉í❞♦ ●❛✉ss✐❛♥♦✳ P♦❞❡✲s❡ ♦❜s❡r✈❛r q✉❡ ❛ ❢✉♥çã♦ ❛♣r♦①✐♠❛❞❛ ❝♦♠ ❛ r❡❣✉❧❛r✐③❛çã♦ é ♠❛✐s ♣ró①✐♠❛ ❞❛ ♦r✐❣✐♥❛❧✱ ❡ ❛♣❛r❡♥t❡♠❡♥t❡ ♠❛✐s ✏s✉❛✈❡✑✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾
✺✳✼ ❊rr♦ ❞❡ tr❡✐♥❛♠❡♥t♦ ♣❛r❛ fP3✳ ❊st❡ é ❡♠ ❣❡r❛❧ ♠♦♥♦tô♥✐❝♦
❞❡❝r❡s❝❡♥t❡✱ ❝❛s♦ ♥ã♦ ♦❝♦rr❛♠ ♣r♦❜❧❡♠❛s ♥✉♠ér✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✼✵
✺✳✽ ❊rr♦ ❞❡ ✈❛❧✐❞❛çã♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ fP3✳ ➱ ✐♥t❡r❡ss❛♥t❡ ♥♦t❛r
q✉❡ ♦ ❡rr♦ ❞❡ ✈❛❧✐❞❛çã♦ t❡♠ ✉♠ ♠í♥✐♠♦ ❜❡♠ ❞❡✜♥✐❞♦✱ ❝♦♠♦ ♠♦str❛❞♦ ♥❛ ✜❣✉r❛✳ ❊st❛ s✐t✉❛çã♦ é ❣❡r❛❧ ♣♦✐s ❡st❛ é ✉♠❛ ❢✉♥çã♦ q✉❛❞rát✐❝❛ ♥♦s ♣❛râ♠❡tr♦s ✭s❛❧✈♦ ♦s ❝❛s♦s ♦♥❞❡ ♦❝♦r✲ r❛♠ ♣r♦❜❧❡♠❛s ♥✉♠ér✐❝♦s✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶
✺✳✾ ❋r♦♥t❡✐r❛ P❛r❡t♦✲Ót✐♠❛ ✭P❖✮ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡✜♥✐❞♦ ♥❛ ❊q✉❛çã♦ ✺✳✶✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷
✺✳✶✵ ❊♥❡r❣✐❛ ❞❛ s❛í❞❛ ❞♦ ✜❧tr♦ ♣❛ss❛✲❛❧t❛s ❡q✉✐✈❛❧❡♥t❡ à ♠✐♥✐♠✐③❛✲ çã♦ ❞♦ ❣r❛❞✐❡♥t❡✳ P♦❞❡✲s❡ ♦❜s❡r✈❛r q✉❡ tr❛t❛✲s❡ ❞❡ ✉♠❛ ❢✉♥çã♦ ♠♦♥♦tô♥✐❝❛ ❝r❡s❝❡♥t❡✱ ❝♦♠♦ ❡s♣❡r❛❞♦ t❡♦r✐❝❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸
✻✳✶ ❆rq✉✐t❡t✉r❛ ❞❡ r❡❞❡ ♣❡r❝❡♣tr♦♥ ❝♦♠ ❝❛♠❛❞❛s ❡♠ ♣❛r❛❧❡❧♦✳ ✳ ✳ ✼✻
✻✳✷ P❛râ♠❡tr♦s ❧✐♥❡❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽
✻✳✸ P❛râ♠❡tr♦s ♥ã♦ ❧✐♥❡❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾
✻✳✹ Pr♦❞✉t♦ ❡♥tr❡ ♦s ♣❛râ♠❡tr♦s ❧✐♥❡❛r❡s ❡ ♥ã♦ ❧✐♥❡❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✼✾
✻✳✺ ❋✉♥çã♦ ❛♣r♦①✐♠❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵
✻✳✻ Pr♦❜❧❡♠❛ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❞❛ ❢✉♥çã♦ f1 ❝♦♥t❛♠✐♥❛❞❛ ♣♦r ✉♠
r✉í❞♦ ●❛✉ss✐❛♥♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾
✻✳✼ ❩♦♦♠ ❞❛ ❢✉♥çã♦ ✭❧❛❞♦ ❡sq✉❡r❞♦✮✱ ♠♦str❛♥❞♦ q✉❡ ❛ s♦❧✉çã♦ r❡❣✉❧❛r✐③❛❞❛ ✏♦s❝✐❧❛ ♠❡♥♦s✑ q✉❡ ❛ ♥ã♦ r❡❣✉❧❛r✐③❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵
✻✳✽ ❩♦♦♠ ❞❛ ❢✉♥çã♦ ✭❧❛❞♦ ❞✐r❡✐t♦✮✱ ♠♦str❛♥❞♦ q✉❡ ❛ s♦❧✉çã♦ r❡❣✉✲ ❧❛r✐③❛❞❛ ✏♦s❝✐❧❛ ♠❡♥♦s✑ q✉❡ ❛ ♥ã♦ r❡❣✉❧❛r✐③❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶
✻✳✾ Pr♦❜❧❡♠❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❞❡✜♥✐❞♦ ♥❛ ❊q✉❛çã♦ ✻✳✹✶✳ ❆ ❝✉r✈❛ ❝♦♥tí♥✉❛ r❡♣r❡s❡♥t❛ ❛ r❡s♣♦st❛ ❡♥❝♦♥tr❛❞❛ s❡♠ ❛ ✉t✐❧✐③❛çã♦ ❞❛ r❡❣✉❧❛r✐③❛çã♦✱ ❡ ❛ ❝✉r✈❛ tr❛❝❡❥❛❞❛ ❛ r❡s♣♦st❛ r❡❣✉❧❛r✐③❛❞❛✳✳ ✳ ✳ ✾✸
✼✳✶ ❖ ♣r♦❜❧❡♠❛ ❞♦ ❛❧t♦ ❢❛❧❛♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼
✽✳✶ ◆❡st❛ ❋✐❣✉r❛ sã♦ ♠♦str❛❞♦s ❞♦✐s ❝♦♥❥✉♥t♦s ❞❡ r❡❞❡s✱ P O1 ❡
P O2✱ ♦♥❞❡ ❛s r❡❞❡s ❡♠P O2❞♦♠✐♥❛♠ ❛s ❞❡P O1✳ ❉❡st❛ ❢♦r♠❛
é ✐♥t❡r❡ss❛♥t❡ ♦❜t❡r ♦ ❝♦♥❥✉♥t♦ P O2 ❞✉r❛♥t❡ ♦ tr❡✐♥❛♠❡♥t♦✱
s❡♥❞♦ ❡st❡ ♦ tr❛❜❛❧❤♦ ❢✉t✉r♦ ♠❛✐s ❞✐r❡t♦ ❞❡r✐✈❛❞♦ ❞❡st❛ t❡s❡✳ ✳ ✶✵✼
❆✳✶ ■♥t❡r♣r❡t❛çã♦ ❣rá✜❝❛ ❞♦ ♠ét♦❞♦ ♣♦♥❞❡r❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵
❆✳✷ ■♥t❡r♣r❡t❛çã♦ ❣rá✜❝❛ ♣❛r❛ ♦ ♠ét♦❞♦ ♣♦♥❞❡r❛❞♦ q✉❛♥❞♦ ❛ ❢r♦♥✲ t❡✐r❛ t❡♠ r❡❣✐õ❡s ♥ã♦ ❝♦♥✈❡①❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵
❆✳✸ ■♥t❡r♣r❡t❛çã♦ ❣rá✜❝❛ ❞♦ ♠ét♦❞♦ǫ✲r❡str✐t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶
❆✳✹ ■♥t❡r♣r❡t❛çã♦ ❣rá✜❝❛ ❞♦ ♠ét♦❞♦ ❞❛ r❡❧❛①❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✻✳✶ ❘❡s✉❧t❛❞♦s ♣❛r❛ ❛ ❢✉♥çã♦ ❢✶ ✉t✐❧✐③❛♥❞♦ ❛ ♠é❞✐❛ ❞❡ 100 s✐♠✉✲
❧❛çõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷
✻✳✷ ❘❡s✉❧t❛❞♦s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❝♦♥s✐❞❡r❛♥❞♦ ❛ ♠é❞✐❛ ❞❡ 100 s✐♠✉❧❛çõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷
✼✳✶ P❛râ♠❡tr♦s ❞♦ ❛❧t♦ ❢❛❧❛♥t❡✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼
✼✳✷ ❘❡s✉❧t❛❞♦s ♣❛r❛ ♦ ❛❧t♦ ❢❛❧❛♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽
✼✳✸ ■❞❛ r❡♣♦s✐t♦r② ■ ✭❊rr♦s ♠é❞✐♦s✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾
✼✳✹ ■❞❛ r❡♣♦s✐t♦r② ■■ ✭❊rr♦s ♠é❞✐♦s✮✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵
✼✳✺ ■❞❛ r❡♣♦s✐t♦r② ■■■ ✭❊rr♦s ♠é❞✐♦s✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶
✼✳✻ ❈❧❛ss✐✜❝❛çã♦ ♠é❞✐❛ ❝♦♥s✐❞❡r❛♥❞♦ ♦s ♣r♦❜❧❡♠❛s ❞♦ ■❉❆ r❡♣♦s✲ ✐t♦r②✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷
✼✳✼ ❈♦♠♣❛r❛çã♦ ❞❛ P▲P✲▼●✱ ❙❱▼✲❙ ❡ ❙❱▼✲❚ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❞✐❛❣♥óst✐❝♦ ❞❡ ❞♦❡♥ç❛ ❝❛r❞í❛❝❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸
✼✳✽ ❈♦♠♣❛r❛çã♦ ❞❛ P▲P✲▼● ❝♦♠ ❞✐✈❡rs♦s ❛❧❣♦r✐t♠♦s ♣❛r❛ ♦ ♣r♦✲ ❜❧❡♠❛ ❞❡ ❛♥á❧✐s❡ ❞❡ ❝ré❞✐t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹
❙✉♠ár✐♦
■ ❈♦♥s✐❞❡r❛çõ❡s ♣r❡❧✐♠✐♥❛r❡s
✶
✶ ■♥tr♦❞✉çã♦ ✷
✶✳✶ P✉❜❧✐❝❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺
✷ ❚❡♦r✐❛ ❞♦ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛s ✾
✷✳✶ ❖ ♣r♦❜❧❡♠❛ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶
✷✳✷ ❆ ♠✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶
✷✳✸ ▼✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡♠♣ír✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹
✷✳✹ ❚❡♦r✐❛ ❞❛ ❝♦♥s✐stê♥❝✐❛ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺
✷✳✹✳✶ ❆ ❞✐♠❡♥sã♦ ❱❈ ✭❱❛♣♥✐❦ ❛♥❞ ❈❤❡r✈♦♥❡♥❦✐s ❞✐♠❡♥s✐♦♥✮ ✶✾
✷✳✹✳✷ ❊①❡♠♣❧♦s ❞❛ ❞✐♠❡♥sã♦ ❱❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵
✷✳✺ ▲✐♠✐t❡s ♥❛ t❛①❛ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ✳ ✷✷
✷✳✺✳✶ ▲✐♠✐t❡s ❞❡ ❣❡♥❡r❛❧✐③❛çã♦ ❜❛s❡❛❞♦s ♥❛ ♠❛r❣❡♠ ✳ ✳ ✳ ✳ ✳ ✷✹
✷✳✺✳✷ ▲✐♠✐t❡s ❝♦♠ ♠❛r❣❡♥s s✉❛✈❡s ✭❙♦❢t ♠❛r❣✐♥✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✷✳✻ ▼✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡str✉t✉r❛❧ ✭❙❘▼ ✲ ❙tr✉❝t✉r❛❧ ❘✐s❦ ▼✐✲ ♥✐♠✐③❛t✐♦♥✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻
✷✳✼ Pr♦❜❧❡♠❛s ♠❛❧ ❝♦❧♦❝❛❞♦s ✭❚❡♦r✐❛ ❞❡ r❡❣✉❧❛r✐③❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✷✳✽ ❉✐s❝✉ssã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✸ ▼áq✉✐♥❛s ❞❡ ❛♣r❡♥❞✐③❛❣❡♠ q✉❡ ❛♣❧✐❝❛♠ ♦ ♣r✐♥❝í♣✐♦ ❞❛ ♠✐♥✲ ✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡str✉t✉r❛❧ ✭❙❘▼✮ ✸✸
✸✳✶ P❡r❝❡♣tr♦♥ ❞❡ ♠ú❧t✐♣❧❛s ❝❛♠❛❞❛s ✭▼▲P ✲ ▼✉❧t✐✲❧❛②❡r ♣❡r❝❡♣✲ tr♦♥✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✸✳✶✳✶ ❚♦♣♦❧♦❣✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✸✳✶✳✷ ❆❧❣♦r✐t♠♦s ❞❡ tr❡✐♥❛♠❡♥t♦ ♣❛r❛ ❛ ♠✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡♠♣ír✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺
✸✳✶✳✸ ❆❧❣♦r✐t♠♦s ❞❡ tr❡✐♥❛♠❡♥t♦ ♣❛r❛ ❛ ♠✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡str✉t✉r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻
✸✳✷ ❋✉♥çõ❡s ❞❡ ❜❛s❡ r❛❞✐❛❧ ✭❘❇❋ ✲ ❘❛❞✐❛❧ ❜❛s✐s ❢✉♥❝t✐♦♥✮ ✳ ✳ ✳ ✳ ✳ ✸✽
✸✳✸ ▼áq✉✐♥❛s ❞❡ ✈❡t♦r❡s s✉♣♦rt❡ ✭❙❱▼ ✲ ❙✉♣♣♦rt ✈❡❝t♦r ♠❛❝❤✐♥❡✮ ✹✵
✸✳✸✳✶ ❊s♣❛ç♦ ❝❛r❛❝t❡ríst✐❝♦ ❡ ♥ú❝❧❡♦s ✭❑❡r♥❡❧s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
✸✳✹ ❉✐s❝✉ssã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺
■■ ❈♦♥tr✐❜✉✐çõ❡s
✹✽
✹ ❆ ♠❡❞✐❞❛ ❞❡ ❝♦♠♣❧❡①✐❞❛❞❡ ❜❛s❡❛❞❛ ♥❛ ♥♦r♠❛✲Q✱ ♦ ♠ét♦❞♦
❞♦ ❣r❛❞✐❡♥t❡ ♠í♥✐♠♦ ❡ s✉❛s ✐♠♣❧✐❝❛çõ❡s ✹✾
✹✳✶ ❆ ♠❡❞✐❞❛ ❞❡ ❝♦♠♣❧❡①✐❞❛❞❡ ♥♦r♠❛✲Q ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
✹✳✷ ❖ ♠ét♦❞♦ ❞♦ ●r❛❞✐❡♥t❡ ▼í♥✐♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✹✳✸ ▼❛①✐♠✐③❛çã♦ ❞❛ ♠❛r❣❡♠ ❞❡ ❝♦♥❥✉♥t♦ ❞❡ ❡①❡♠♣❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✹✳✹ ❖ ❤✐♣❡r♣❧❛♥♦ ❞❡ s❡♣❛r❛çã♦ ót✐♠♦ r❡✈✐s✐t❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✹✳✺ ❆♥á❧✐s❡ ♣❛r❛ ❢✉♥çõ❡s ♠♦♥♦tô♥✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✹✳✻ ❖ ♣r♦❜❧❡♠❛ ❞❡ ♠✐♥✐♠✐③❛çã♦ ❞❛s ❝♦♠♣♦♥❡♥t❡s ❞❡ ❛❧t❛ ❢r❡qüê♥✲ ❝✐❛ r❡✈✐s✐t❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
✹✳✼ ▼✐♥✐♠✐③❛çã♦ ❞❛ ♥♦r♠❛ ❞♦s ♣❡s♦s r❡✲✈✐s✐t❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
✹✳✽ ❙❱▼s ♥ã♦ ❧✐♥❡❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✹✳✾ ❉✐s❝✉ssã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✺ ❆♣r♦①✐♠❛❞♦r❡s ♣♦❧✐♥♦♠✐❛✐s ❞❡ ❣r❛❞✐❡♥t❡ ♠í♥✐♠♦ ✻✵
✺✳✶ ❋♦r♠✉❧❛çã♦ ♣❛r❛ ❛♣r♦①✐♠❛❞♦r❡s ♣♦❧✐♥♦♠✐❛✐s ❞❡ ❣r❛❞✐❡♥t❡ ♠í♥✲ ✐♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵
✺✳✷ ❊①♣❡r✐♠❡♥t♦s ✉t✐❧✐③❛♥❞♦ ♦ ❛♣r♦①✐♠❛❞♦r ♣♦❧✐♥♦♠✐❛❧ ❞❡ ❣r❛❞✐✲ ❡♥t❡ ♠í♥✐♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸
✺✳✸ ❉✐s❝✉ssã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾
✻ ❘❡❞❡ ♣❡r❝❡♣tr♦♥ ❝♦♠ ❝❛♠❛❞❛s ♣❛r❛❧❡❧❛s ✭P▲P✲♣❛r❛❧❧❡❧ ❧❛②❡r
♣❡r❝❡♣tr♦♥✮ ✼✺
✻✳✶ ❚♦♣♦❧♦❣✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺
✻✳✷ ❚❡♦r❡♠❛ ❞❛ ❛♣r♦①✐♠❛çã♦ ✉♥✐✈❡rs❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼
✻✳✸ ❆❧❣♦r✐t♠♦s ♣❛r❛ ❛ ♠✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡♠♣ír✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽
✻✳✸✳✶ ●r❛❞✐❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵
✻✳✸✳✷ ❍í❜r✐❞♦ ✲ ●r❛❞✐❡♥t❡ ❡ ♠í♥✐♠♦s q✉❛❞r❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷
✻✳✸✳✸ ❍í❜r✐❞♦ ✲ ▲❡✈❡♥❜❡r❣✲▼❛q✉❛r❞t ❡ ♠í♥✐♠♦s q✉❛❞r❛❞♦s ✳ ✽✸
✻✳✹ ▼✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡str✉t✉r❛❧ ❞❛ r❡❞❡
P▲P ✉t✐❧✐③❛♥❞♦ ❛ ✐❞é✐❛ ❞♦ ❣r❛❞✐❡♥t❡ ♠í♥✐♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹
✻✳✺ ❊①❡♠♣❧♦s ♥✉♠ér✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽
✻✳✺✳✶ Pr♦❜❧❡♠❛ ❞❡ r❡❣r❡ssã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽
✻✳✺✳✷ Pr♦❜❧❡♠❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶
✻✳✻ ❉✐s❝✉ssã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸
✼ ❘❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ✾✻
✼✳✶ ❆❧t♦✲❢❛❧❛♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻
✼✳✷ Pr♦❜❧❡♠❛s ❞♦ ■❉❆ ❜❡♥❝❤♠❛r❦ r❡♣♦s✐t♦r② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽
✼✳✸ ❉✐❛❣♥óst✐❝♦ ❞❡ ❞♦❡♥ç❛ ❝❛r❞í❛❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶
✼✳✹ ❆♣❧✐❝❛çã♦ à ❛♥❛❧✐s❡ ❞❡ ❝ré❞✐t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶
✼✳✺ ❉✐s❝✉ssã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷
✽ ❈♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s ✶✵✺
❆ Pr♦❜❧❡♠❛s ♠✉❧t✐♦❜❥❡t✐✈♦ ✶✵✽
❆✳✶ ❆s ❝♦♥❞✐çõ❡s ❞❡ ♦♣t✐♠❛❧✐❞❛❞❡ ❞❡ ❑✉❤♥✲❚✉❝❦❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾
❆✳✷ ▼ét♦❞♦s ♣❛r❛ ❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ♠✉❧t✐♦❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✶✵✾
❆✳✷✳✶ ▼ét♦❞♦ ❞❛ s♦♠❛ ♣♦♥❞❡r❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾
❆✳✷✳✷ ▼ét♦❞♦ ǫ✲r❡str✐t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶
❆✳✷✳✸ Pr♦❣r❛♠❛çã♦ ♣♦r ♠❡t❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶
❆✳✷✳✹ ▼ét♦❞♦ ❞❛s r❡❧❛①❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷
P❛rt❡ ■
❈♦♥s✐❞❡r❛çõ❡s ♣r❡❧✐♠✐♥❛r❡s
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
❯♠ ❞♦s ❣r❛♥❞❡s ❞❡s❡❥♦s ❞♦ ❤♦♠❡♠✱ q✉❡ ❛♣❛r❡❝❡ ❥✉♥t♦ ❝♦♠ ❛ ❡✈♦❧✉çã♦ ❞❛s ♠áq✉✐♥❛s✱ é ❛ ❝♦♥❝❡♣çã♦ ❞❡ ✉♠❛ ♠áq✉✐♥❛ q✉❡ ♣♦ss❛ ♦♣❡r❛r ❡♠ ❛♠❜✐❡♥t❡s ❞❡s❝♦♥❤❡❝✐❞♦s ♣♦r ❡❧❛✱ ✉t✐❧✐③❛♥❞♦ ♦ s❡✉ ♣ró♣r✐♦ ❛♣r❡♥❞✐③❛❞♦✱ ✐♥❞❡♣❡♥❞❡♥t❡ ❞♦ ❝♦♥tr♦❧❡ ❤✉♠❛♥♦✳ ❯♠❛ ♠áq✉✐♥❛ q✉❡ ♣♦ss❛ s❡r ❝❤❛♠❛❞❛ ❞❡ ❛✉tô♥♦♠❛ ♦✉ ❝♦❣✲ ♥✐t✐✈❛✳ ❆ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❧✐❞❛r ❝♦♠ ❡✈❡♥t♦s ♣❛r❛ ♦s q✉❛✐s ♥ã♦ ❢♦✐ ♣r❡✈✐❛♠❡♥t❡ tr❡✐♥❛❞❛ ❞❡t❡r♠✐♥❛r✐❛ ♦ s✉❝❡ss♦✱ ♦✉ ✐♥s✉❝❡ss♦ ❞❡st❛✳
❉❡♥tr♦ ❞❡st❡ ❝♦♥t❡①t♦ ❜✉s❝❛✲s❡ ❡♥❝♦♥tr❛r ♠♦❞❡❧♦s q✉❡ s❡❥❛♠ ❝❛♣❛③❡s ❞❡ r❡s♦❧✈❡r t❛r❡❢❛s ❝♦♠♣❧❡①❛s✱ ❡ q✉❡ s❡❥❛♠ ❡✜❝✐❡♥t❡s ❝♦♠♣✉t❛❝✐♦♥❛❧♠❡♥t❡✳ ❊♥tr❡ ❛s ♣♦ssí✈❡✐s té❝♥✐❝❛s ❞❡st❛❝❛♠✲s❡ ❛s r❡❞❡s ♣❡r❝❡♣tr♦♥ ❞❡ ♠ú❧t✐♣❧❛s ❝❛♠❛❞❛s ✭▼▲Ps✮✱ ❛s ❘❡❞❡s ❞❡ ❋✉♥çõ❡s ❞❡ ❇❛s❡ ❘❛❞✐❛❧ ✭❘❇❋s✮ ❡ ❛s ▼áq✉✐♥❛s ❞❡ ❱❡t♦r❡s ❙✉♣♦rt❡ ✭❙❱▼s✮✳ P❛r❛ ✉♠❛ r❡❢❡rê♥❝✐❛ ✐♥tr♦❞✉tór✐❛ s♦❜r❡ ♦ ❛ss✉♥t♦ ❝♦♥s✉❧t❡ ❬❍❛②✾✾❪✳
❆♦ t❡♥t❛r ✉t✐❧✐③❛r té❝♥✐❝❛s ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛ ❡♠ ♣r♦❜❧❡♠❛s r❡❛✐s ❛❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s sã♦ ❞❡s❡❥á✈❡✐s✿
• ❜♦♥s r❡s✉❧t❛❞♦s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛❞♦❀
• t❡♠♣♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❞❛ ♠áq✉✐♥❛ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ✭q✉❛♥t♦ ♠❛✐s rá♣✐❞♦
♠❡❧❤♦r✮❀
• ❡ q✉❡ ❡st❛ s❡❥❛ ♣♦✉❝♦ ❞❡♣❡♥❞❡♥t❡ ❞♦ ♣r♦❥❡t✐st❛✱ ✐✳❡✳✱ s❡❥❛ ♣♦✉❝♦ ❞❡♣❡♥✲
❞❡♥t❡ ❞❛ ✐♥t❡r❢❡rê♥❝✐❛ ❤✉♠❛♥❛ ♥❛ ❞❡✜♥✐çã♦ ❞♦s ♣❛râ♠❡tr♦s ❞❡ tr❡✐♥❛✲ ♠❡♥t♦✳
❊st❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡s❡❥á✈❡✐s ♠♦t✐✈❛r❛♠ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❛ t❡s❡ ❞❡ ❞♦✉t♦r❛❞♦✳ P❛r❛ s❡ ❛❜♦r❞❛r ❡st❡s três ♣♦♥t♦s é ♥❡❝❡ssár✐♦ ❡st✉❞❛r t❛♥t♦
q✉❡stõ❡s t❡ór✐❝❛s ❝♦♠♦ ♣rát✐❝❛s✳ ❆s t❡ór✐❝❛s sã♦✿ ♦ q✉❡ é ✉♠ ❜♦♠ r❡s✉❧t❛❞♦ ♣❛r❛ ✉♠ ❞❛❞♦ ♣r♦❜❧❡♠❛❄ ◗✉❛✐s sã♦ ♦s ❢❛t♦r❡s q✉❡ ❧❡✈❛♠ ❛ ✉♠❛ ♠áq✉✐♥❛ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❛ ❛❧❝❛♥ç❛r t❛❧ r❡s✉❧t❛❞♦❄ ❉❡♣♦✐s ♥❛s❝❡ ❛ q✉❡stã♦ ♣rát✐❝❛ ❞❡ ❝♦♠♦ ✉t✐❧✐③❛r ❡st❛s ✐❞é✐❛s ❞❡ ❢♦r♠❛ ❡✜❝✐❡♥t❡ ❝♦♠♣✉t❛❝✐♦♥❛❧♠❡♥t❡✳ ❚♦❞♦s ❡st❡s ❛s♣❡❝t♦s sã♦ ❝♦♥s✐❞❡r❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦✳
❖ ♣r✐♥❝í♣✐♦ q✉❡ ♥♦rt❡♦✉ ❛ ár❡❛ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛s s✉♣❡r✈✐s✐♦✲ ♥❛❞♦ ❞✉r❛♥t❡ ♠✉✐t♦s ❛♥♦s ❢♦✐ ♦ ♣r✐♥❝í♣✐♦ ✐♥❞✉t✐✈♦ ❞❛ ♠✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡♠♣ír✐❝♦ ✭❊♠♣✐r✐❝❛❧ ❘✐s❦ ▼✐♥✐♠✐③❛t✐♦♥ ✲ ❊❘▼✮✳ ❊st❡ é ❜❛s❡❛❞♦ ♥♦ ❝♦♥❝❡✐t♦ s✐♠♣❧❡s ❞❡ q✉❡ ❛ ♠✐♥✐♠✐③❛çã♦ ❞♦ ❡rr♦ ❞❡ tr❡✐♥❛♠❡♥t♦✱ ♦ r✐s❝♦ ❡♠♣ír✐❝♦✱ é ✉♠❛ ❜♦❛ ❡str❛té❣✐❛ ♣❛r❛ s❡ ❣❡r❛r ♠áq✉✐♥❛s ❝♦♠ ❜♦♠ ❛♣r❡♥❞✐③❛❞♦✳ ❊♥tr❡✲ t❛♥t♦✱ ❢♦✐ t❡♦r✐❝❛♠❡♥t❡ ♣r♦✈❛❞♦ q✉❡ ❛ ♠✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡♠♣ír✐❝♦ ♥ã♦ ❡r❛ s✉✜❝✐❡♥t❡ ♣❛r❛ ❣❛r❛♥t✐r ❛ ❝♦♥✈❡r❣ê♥❝✐❛ ❞❛ ♠áq✉✐♥❛ ❞❡ ❛♣r❡♥❞✐③❛❣❡♠❬❱❛♣✾✽❪✳ P❛r❛ ❣❛r❛♥t✐r ❛ ❝♦♥s✐stê♥❝✐❛ ❞♦ ❛♣r❡♥❞✐③❛❞♦ s✉r❣❡ ❡♥tã♦ ♦ ♣r✐♥❝í♣✐♦ ✐♥❞✉t✐✈♦ ❞❛ ♠✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡str✉t✉r❛❧ ✭❙tr✉❝t✉r❛❧ ❘✐s❦ ▼✐♥✐♠✐③❛t✐♦♥ ✲ ❙❘▼✮✳ ❊st❡ ♣r✐♥❝í♣✐♦ ❞✐③ q✉❡ ❛❧é♠ ❞❡ s❡ ♠✐♥✐♠✐③❛r ♦ r✐s❝♦ ❡♠♣ír✐❝♦ é ♥❡❝❡ssár✐♦ t❛♠❜é♠ ❧✐♠✐t❛r ❛ ❝❛♣❛❝✐❞❛❞❡ ✭❝♦♠♣❧❡①✐❞❛❞❡✮ ❞❛ ♠áq✉✐♥❛ ❞❡ ❛♣r❡♥❞✐③❛❣❡♠✳ ❊st❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ ✉♠❛ ♥♦✈❛ ❛❜♦r❞❛❣❡♠ ♣❛r❛ ❧✐❞❛r ❝♦♠ ♦ ♣r♦❜❧❡♠❛ ❞❡ ♠✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡str✉t✉r❛❧ ✭str✉❝t✉r❛❧ r✐s❦ ♠✐♥✐♠✐③❛t✐♦♥ ✲ ❙❘▼✮ ❛♣❧✐❝❛❞♦ ❛♦ ♣r♦❜❧❡♠❛ ❣❡r❛❧ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛s✳ ❆ ❢♦r♠✉❧❛çã♦ é ❜❛s❡❛❞❛ ♥♦ ❝♦♥❝❡✐t♦ ❢✉♥❞❛♠❡♥t❛❧ ❞❡ q✉❡ ♦ ❛♣r❡♥❞✐③❛❞♦ s✉♣❡r✈✐s✐♦♥❛❞♦ é ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦ ❜✐✲♦❜❥❡t✐✈♦ ♦♥❞❡ ❞♦✐s ♦❜❥❡t✐✈♦s ❝♦♥✢✐t❛♥t❡s ❞❡✈❡♠ s❡r ♠✐♥✐♠✐③❛❞♦s✳ ❊st❡s ❡stã♦ r❡❧❛❝✐♦♥❛❞♦s ❛♦ ❡rr♦ ❞❡ tr❡✐♥❛♠❡♥t♦✱ r✐s❝♦ ❡♠♣ír✐❝♦ ✭Remp✮✱ ❡ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ✭❝❛♣❛❝✐❞❛❞❡✮ ❞❛ ♠áq✉✐♥❛ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ✭Ω✮✳
◆❡st❡ tr❛❜❛❧❤♦ ✉♠❛ ❢♦r♠✉❧❛çã♦ ❣❡r❛❧ ❜❛s❡❛❞❛ ♥❛ ♥♦r♠❛✲Q é ✉t✐❧✐③❛❞❛ ♣❛r❛ ❝❛❧❝✉❧❛r ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❛ ♠áq✉✐♥❛ ❞❡ ❛♣r❡♥❞✐③❛❣❡♠ ❡ ❡st❛ ♣♦❞❡ s❡r ✉t✐❧✐③❛❞❛ ♣❛r❛ ♠♦❞❡❧❛r ❡ ❝♦♠♣❛r❛r ❛ ♠❛✐♦r✐❛ ❞❛s ♠áq✉✐♥❛s ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❡♥❝♦♥tr❛❞❛s ♥❛ ❧✐t❡r❛t✉r❛✳ ❆ ♣r✐♥❝✐♣❛❧ ✈❛♥t❛❣❡♠ ❞❛ ♠❡❞✐❞❛ ❞❡ ❝♦♠♣❧❡①✐✲ ❞❛❞❡ ♣r♦♣♦st❛ é q✉❡ ❡st❛ é ✉♠❛ ♠❛♥❡✐r❛ s✐♠♣❧❡s ❞❡ s❡♣❛r❛r ❛s ✐♥✢✉ê♥❝✐❛s ❞♦s ♣❛râ♠❡tr♦s ❧✐♥❡❛r❡s ❡ ♥ã♦✲❧✐♥❡❛r❡s ♥❛ ♠❡❞✐❞❛ ❞❡ ❝♦♠♣❧❡①✐❞❛❞❡✱ ❧❡✈❛♥❞♦ ❛ ✉♠ ♠❡❧❤♦r ❡♥t❡♥❞✐♠❡♥t♦ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❛♣r❡♥❞✐③❛❣❡♠✳ ▼❛t❡♠❛t✐❝❛♠❡♥t❡ ✐st♦ s✐❣♥✐✜❝❛ q✉❡✱ ❞❛❞♦s ♦s ♣❛râ♠❡tr♦s ❧✐♥❡❛r❡s l ❡ ♦s ♥ã♦✲❧✐♥❡❛r❡s V✱ ❛ ❝♦♠✲ ♣❧❡①✐❞❛❞❡ ♣♦❞❡ s❡r ❡s❝r✐t❛ ❝♦♠♦ Ω = (A(V)l)TA(V)l = lTQ(V)l✳ ❖❜s❡r✈❡
q✉❡ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ é ❛ ♥♦r♠❛ ❞♦ ✈❡t♦r A(V)l✱ ❡✱ ❝♦♠♦ ♦ ♣r♦❞✉t♦ ❡♥tr❡ A(V) ❡l é ✉t✐❧✐③❛❞♦✱ ❡st❛ ♣♦❞❡ s❡r ♥❛t✉r❛❧♠❡♥t❡ ✐♠♣❧❡♠❡♥t❛❞❛ ❡♠ ♣❛r❛❧❡❧♦✳ P❛r❛ t❛❧ ❛ r❡❞❡ ♣❡r❝❡♣tr♦♥ ❝♦♠ ❝❛♠❛❞❛s ♣❛r❛❧❡❧❛s ✭P❛r❛❧❧❡❧ ▲❛②❡r P❡r❝❡♣tr♦♥ ✲P▲P✮ ❝♦♠ ✉♠❛ ❝❛♠❛❞❛ ❧✐♥❡❛r ❡♠ ♣❛r❛❧❡❧♦ ❝♦♠ ✉♠❛ ❝❛♠❛❞❛ ♥ã♦✲❧✐♥❡❛r é ✉♠❛ s♦❧✉çã♦ ♥❛t✉r❛❧✳ ❆ P▲P t❛♠❜é♠ é ✉♠❛ ❝♦♥tr✐❜✉✐çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳
▼✉✐t❛s ❞❡✜♥✐çõ❡s ❞❛ ♠❛tr✐③ Q✱ ❞❛❞♦ xTQx > 0✱
❧✐③❛❞❛s ♥❡st❛ ❝♦♥str✉çã♦✳ ◆❡st❛ t❡s❡ ❛ ♠✐♥✐♠✐③❛çã♦ ❞❛ ♥♦r♠❛ ❞♦ ❣r❛❞✐❡♥t❡ ❞❛ s❛í❞❛ ❞❛ r❡❞❡ é ✉t✐❧✐③❛❞❛✱ ❣❡r❛♥❞♦ ♦ ▼ét♦❞♦ ❞♦ ●r❛❞✐❡♥t❡ ▼í♥✐♠♦ ✭▼✐♥✐♠✉♠ ●r❛❞✐❡♥t ▼❡t❤♦❞✲▼●▼✮✳ ❆ ❝♦♠❜✐♥❛çã♦ ❞❛ P▲P ❝♦♠ ♦ ▼●▼ ✭P▲P✲▼●▼✮ é ❢❡✐t❛ ✉t✐❧✐③❛♥❞♦ ♦ ❡st✐♠❛❞♦r ❞❡ ♠í♥✐♠♦s q✉❛❞r❛❞♦s✱ s❡♥❞♦ ❡st❛ ❛ ❝♦♥tr✐❜✉✐çã♦ ♣rát✐❝❛ ❞❡st❡ tr❛❜❛❧❤♦✳
❖ t❡①t♦ ❡stá ❞✐✈✐❞✐❞♦ ❡♠ ❞✉❛s ♣❛rt❡s✱ s❡♥❞♦ ❛ ♣r✐♠❡✐r❛ ❝♦♥s✐❞❡r❛çõ❡s ❣❡r❛✐s s♦❜r❡ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛s ✭❝❛♣ít✉❧♦s 2 ❡ 3✮✱ ❡ ❛ s❡❣✉♥❞❛ ❛s ❝♦♥tr✐❜✉✐çõ❡s ❞❡st❡ tr❛❜❛❧❤♦✳ ◆♦ ❝❛♣ít✉❧♦2é ❞❡✜♥✐❞♦ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛ q✉❡ s❡rá tr❛t❛❞♦✱ ♦ ❛♣r❡♥❞✐③❛❞♦ s✉♣❡r✈✐s✐♦♥❛❞♦✳ ❆s ✐❞é✐❛s ❛♣r❡s❡♥t❛❞❛s ♥❡st❡ s❡❣✉✐rã♦ ❛ ❧✐♥❤❛ ❞♦ ❛♣r❡♥❞✐③❛❞♦ ❡st❛tíst✐❝♦✳ ◆♦ ❝❛♣ít✉❧♦ 3 s❡rã♦ ♠♦str❛❞❛s ❞❡ ❢♦r♠❛ s✉❝✐♥t❛ ❛❧❣✉♠❛s ♠áq✉✐♥❛s ❞❡ ❛♣r❡♥✲ ❞✐③❛❞♦ q✉❡ ❛♣❧✐❝❛♠ ♦ ♣r✐♥❝í♣✐♦ ✐♥❞✉t✐✈♦ ❞❛ ♠✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡str✉t✉r❛❧ ✭❙❘▼✮✳ ❙❡rã♦ tr❛t❛❞❛s ❛s ▼▲Ps ❡ s✉❛s ❞✐✈❡rs❛s té❝♥✐❝❛s✱ ♠✉✐t❛s ❤❡✉ríst✐❝❛s✱ ♣❛r❛ ❛ ♠✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡str✉t✉r❛❧✱ ❛ss✐♠ ❝♦♠♦ ❛s ❘❇❋s ❡ ❛s ❙❱▼s✳ ❙❡rá ❞❛❞❛ ê♥❢❛s❡ ♥❛s ♣r♦♣r✐❡❞❛❞❡s ❞❡ ❝❛❞❛ ♠ét♦❞♦ ❡♥✈♦❧✈✐❞♦✱ ❡ ♥ã♦ ❡♠ ❞❡t❛❧❤❡s ♣rát✐❝♦s✳ ❊st❛s ♣r♦♣r✐❡❞❛❞❡s s❡rã♦ ❞❡ s✉♠❛ r❡❧❡✈â♥❝✐❛ ♣❛r❛ ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞❛ té❝♥✐❝❛ ♣r♦♣♦st❛✳
◆♦ ❝❛♣ít✉❧♦4 é ❛♣r❡s❡♥t❛❞❛ ❛ ♥♦r♠❛✲Q ❝♦♠♦ ✉♠❛ ♠❡❞✐❞❛ ❞❡ ❝♦♠♣❧❡①✐✲ ❞❛❞❡ ❡ ❛s s✉❛s ✐♠♣❧✐❝❛çõ❡s✳ ❯♠❛ ♠❡❞✐❞❛ q✉❡ ❡♠♣r❡❣❛ ❛ ✐❞é✐❛ ❝✐t❛❞❛ ❛❝✐♠❛ é ❣❡r❛❞❛ ✉t✐❧✐③❛♥❞♦ ❛ ♠✐♥✐♠✐③❛çã♦ ❞♦ ❣r❛❞✐❡♥t❡ ❞❛ s❛í❞❛ ❞❛ r❡❞❡✳ ❆ ❞❡r✐✈❛çã♦ ❞❡st❛ s❡❣✉❡ ❛ ❧✐♥❤❛ ❞♦s r❡s✉❧t❛❞♦s ❛♣r❡s❡♥t❛❞♦s ♥♦ ❝❛♣ít✉❧♦ 2✳ ❖ ♠ét♦❞♦ ❞♦ ❣r❛❞✐❡♥t❡ ♠í♥✐♠♦ ♣r♦♣♦st♦ ♥❡st❡ ❝❛♣ít✉❧♦ ❡s❝r❡✈❡ ✉♠ ♣r♦❜❧❡♠❛ ♠✉❧t✐✲ ♦❜❥❡t✐✈♦✱ ♥❛ r❡❛❧✐❞❛❞❡ ❜✐✲♦❜❥❡t✐✈♦✱ ♦♥❞❡ s❡ ❞❡s❡❥❛ ♠✐♥✐♠✐③❛r ❞♦✐s ♦❜❥❡t✐✈♦s ❝♦♥✢✐t❛♥t❡s✱ ♦ ❡rr♦ ❡♠♣ír✐❝♦ ❡ ❛ ♥♦r♠❛ ❞♦ ❣r❛❞✐❡♥t❡ ❡♠ ✉♠ ❞♦♠í♥✐♦ ❞❡ ✐♥✲ t❡r❡ss❡✳ ❖ ♠ét♦❞♦ ♣r♦♣♦st♦ é ❝♦♠♣❛r❛❞♦ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ t❡ór✐❝♦ ❝♦♠ ♦s ♠ét♦❞♦s ❞❡s❝r✐t♦s ♥♦ ❝❛♣ít✉❧♦ 3✱ s❡♥❞♦ q✉❡ ❡①✐st❡♠ ❞✐✈❡rs❛s ❡q✉✐✈❛❧ê♥❝✐❛s ❡♥tr❡ t♦❞♦s ♦s ♠ét♦❞♦s ❝♦♠♦ ♠♦str❛❞♦ ♥♦ ❈❛♣ít✉❧♦ ✹✳
❯t✐❧✐③❛♥❞♦ ❛s ✐❞é✐❛s ❞❡s❝r✐t❛s ♥♦ ❝❛♣ít✉❧♦4✱ é ❞❡r✐✈❛❞♦ ♦ ❛♣r♦①✐♠❛❞♦r ♣♦❧✐✲ ♥♦♠✐❛❧ ❞❡ ❣r❛❞✐❡♥t❡ ♠í♥✐♠♦✳ ❆ ✐❞é✐❛ ❞❡ s❡ ❛♣❧✐❝❛r ❛ ❢♦r♠✉❧❛çã♦ ❛♣r❡s❡♥t❛❞❛ ♥♦ ❝❛♣ít✉❧♦ 4 ❡♠ ♣♦❧✐♥ô♠✐♦s✱ ❛♥t❡s ❞❡ ❛♥❛❧✐s❛r ❛ ❛♣❧✐❝❛❜✐❧✐❞❛❞❡ ❡♠ r❡❞❡s ♥❡✉r❛✐s✱ s❡ ❞❡✈❡ à s✐♠♣❧✐❝✐❞❛❞❡ ❞♦s ♠❡s♠♦s✱ s✐♠♣❧✐✜❝❛♥❞♦ ❛s ❛♥á❧✐s❡s✳ ❉❡ ❢❛t♦✱ ♣❛r❛ ❛♣r♦①✐♠❛❞♦r❡s ♣♦❧✐♥♦♠✐❛✐s✱ ❛ ❢♦r♠✉❧❛çã♦ t❡ór✐❝❛ ❞❡s❡♥✈♦❧✈✐❞❛ ♥♦ ❝❛♣ít✉❧♦ 4s❡ tr❛♥s❢♦r♠❛ ❡♠ ✉♠ ♣r♦❜❧❡♠❛ ♣rát✐❝♦ ♦♥❞❡ ❛s ❢✉♥çõ❡s ❡♥✈♦❧✈✐❞❛s sã♦ ❝♦♥✈❡①❛s✳ ❊♠ ❛❧❣✉♥s ❡①♣❡r✐♠❡♥t♦s r❡❛❧✐③❛❞♦s ❞✉r❛♥t❡ ❡st❡ tr❛❜❛❧❤♦ ✜❝♦✉ ❞❡♠♦♥str❛❞♦ q✉❡ s❡ tr❛t❛ ❞❡ ✉♠❛ ❢❡rr❛♠❡♥t❛ ❛♣❧✐❝á✈❡❧ ✐♥❝❧✉s✐✈❡ ❡♠ ♣r♦❜❧❡✲ ♠❛s ♦♥❞❡ ❛s ❛♠♦str❛s ❡stã♦ ❝♦♥t❛♠✐♥❛❞❛s ♣♦r r✉í❞♦s✳ ❊♥tr❡t❛♥t♦✱ t❛♠❜é♠ é ✐♠♣♦rt❛♥t❡ r❡ss❛❧t❛r q✉❡ ♦s ♣♦❧✐♥ô♠✐♦s s♦❢r❡♠ ❞♦ ❢❛♠♦s♦ ✏♠❛❧ ❞❛ ❞✐♠❡♥✲ s✐♦♥❛❧✐❞❛❞❡✑ s❡♥❞♦ ♣♦✉❝♦ ❛♣❧✐❝á✈❡✐s ❡♠ ♣r♦❜❧❡♠❛s ❞❡ ❛❧t❛ ❞✐♠❡♥sã♦ ✭♠✉✐t❛s
✈❛r✐á✈❡✐s ❞❡ ❡♥tr❛❞❛✮✳
❱✐s❛♥❞♦ r❡s♦❧✈❡r ♦s ♣r♦❜❧❡♠❛s ❛♣r❡s❡♥t❛❞♦s ♣❛r❛ ♦s ♣♦❧✐♥ô♠✐♦s✱ ♥♦ ❝❛♣í✲ t✉❧♦ 6 é ♣r♦♣♦st❛ ❛ r❡❞❡ ♣❡r❝❡♣tr♦♥ ❝♦♠ ❝❛♠❛❞❛s ♣❛r❛❧❡❧❛s ✭P▲P✲ P❛r❛❧❧❡❧ ▲❛②❡r P❡r❝❡♣tr♦♥✮✳ ❯♠ ❞♦s ❝❛s♦s ♣❛rt✐❝✉❧❛r❡s ❞❛ P▲P ✉t✐❧✐③❛ ❞✉❛s ❝❛♠❛❞❛s ❡♠ ♣❛r❛❧❡❧♦✱ s❡♥❞♦ q✉❡ ✉♠❛ ✉t✐❧✐③❛ ✉♠ ❛♣r♦①✐♠❛❞♦r ♣♦❧✐♥♦♠✐❛❧✱ ❞❡ ❢❛t♦ ✉♠ ❛♣r♦①✐♠❛❞♦r ❧✐♥❡❛r ♣❛r❛ ❡✈✐t❛r ♦ ♠❛❧ ❞❛ ❞✐♠❡♥s✐♦♥❛❧✐❞❛❞❡✳ P❛r❛ ❡st❡ ❝❛s♦ ♣❛rt✐❝✉❧❛r é ❞❡r✐✈❛❞❛ ❛ r❡❞❡ P▲P ❞❡ ❣r❛❞✐❡♥t❡ ♠í♥✐♠♦✱ ♦♥❞❡ ♦ ❛❥✉st❡ ❞♦ ❣r❛❞✐❡♥t❡ é r❡❛❧✐③❛❞♦ s♦♠❡♥t❡ ♥❛ ❝❛♠❛❞❛ ♣♦❧✐♥♦♠✐❛❧ ♣❛r❛ ❛♣r♦✈❡✐t❛r ❛ ❝♦♥✲ ✈❡①✐❞❛❞❡ ❞♦s ❢✉♥❝✐♦♥❛✐s ❡♥✈♦❧✈✐❞♦s✳ ❆ r❡❞❡ P▲P ❝♦♠ ❣r❛❞✐❡♥t❡ ♠í♥✐♠♦ é ❛ ♣r✐♥❝✐♣❛❧ ❝♦♥tr✐❜✉✐çã♦ ♣rát✐❝❛ ❞❡st❡ tr❛❜❛❧❤♦✳ ❆✐♥❞❛ ♥♦ ❝❛♣ít✉❧♦ 6 ❛❧❣✉♥s ❡①❡♠♣❧♦s ✉t✐❧✐③❛♥❞♦ ❞❛❞♦s s✐♥tét✐❝♦s sã♦ ♠♦str❛❞♦s ❡ ❛ té❝♥✐❝❛ ♣r♦♣♦st❛ s❡ ♠♦str♦✉ s✉♣❡r✐♦r às ❞❡♠❛✐s t❡st❛❞❛s✳
❋✐♥❛❧♠❡♥t❡ ♥♦ ❝❛♣ít✉❧♦7❛ té❝♥✐❝❛ ♣r♦♣♦st❛ é t❡st❛❞❛ ❡♠ ♣r♦❜❧❡♠❛s r❡❛✐s✱ ❡♥tr❡ ❡❧❡s ♣r♦❜❧❡♠❛s ❜❡♥❝❤♠❛r❦ ♥❛ ár❡❛ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛s ❡ ✉♠ ♣r♦❜❧❡♠❛ ❡❧❡tr♦♠❛❣♥ét✐❝♦✳ ❆❧❣✉♠❛s ❝♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s sã♦ ❛♣r❡s❡♥t❛❞❛s ♥♦ ❝❛♣ít✉❧♦ 8✱ ❡♥tr❡ ❡st❛s ✉♠❛ ✈✐sã♦ ❣❡r❛❧ ❞♦ tr❛❜❛❧❤♦ ❡ ❛❧❣✉♠❛s ♣❡rs♣❡❝t✐✈❛s ❢✉t✉r❛s✳
✶✳✶ P✉❜❧✐❝❛çõ❡s
◆❡st❡ ♠♦♠❡♥t♦ ❛❧❣✉♥s tr❛❜❛❧❤♦s ❞❡r✐✈❛❞♦s ❞❡st❡ t❡①t♦ ❥á ❢♦r❛♠ ♣✉❜❧✐❝❛❞♦s✱ s❡♥❞♦ q✉❛tr♦ ♣✉❜❧✐❝❛çõ❡s ❡♠ r❡✈✐st❛s ❡ s❡t❡ ❡♠ ❝♦♥❣r❡ss♦s✳ ◆♦ ♣r❡s❡♥t❡ ♠♦♠❡♥t♦ ✸ ❛rt✐❣♦s ❡stã♦ s✉❜♠❡t✐❞♦s r❡✈✐st❛s ❡ ✉♠ ♣❛r❛ ❝♦♥❣r❡ss♦✳ ❆ ❧✐st❛ ❞♦s tr❛❜❛❧❤♦s é ❛♣r❡s❡♥t❛❞❛ ❛ s❡❣✉✐r✿
✶✳ ❲✳ ▼✳ ❈❆▼■◆❍❆❙✱ ❉✳ ❆✳ ●✳ ❱■❊■❘❆ ❛♥❞ ❏✳ ❆✳ ❱❆❙❈❖◆❈❊▲❖❙ ✲ ✏P❛r❛❧❧❡❧ ▲❛②❡r P❡r❝❡♣tr♦♥✑ ✲ ◆❡✉r♦❝♦♠♣✉t✐♥❣ ✭❊❧s❡✈✐❡r✮✱ ♥♦✳ ✺✺✱ ♣♣✳ ✼✼✶✲✼✼✽✱ ❖❝t♦❜❡r ✷✵✵✸✳
✷✳ ❉✳ ❆✳ ●✳ ❱■❊■❘❆✱ ❘✳ ❍✳ ❈✳ ❚❆❑❆❍❆❙❍■✱ ❱✳ P❆▲❆❉❊✱ ❏✳ ❆✳ ❱❆❙✲ ❈❖◆❈❊▲❖❙ ❛♥❞ ❲✳ ▼✳ ❈❆▼■◆❍❆❙ ✲ ✏❚❤❡ ◗✲♥♦r♠ ❝♦♠♣❧❡①✐t② ♠❡❛✲ s✉r❡ ❛♥❞ t❤❡ ▼✐♥✐♠✉♠ ●r❛❞✐❡♥t ▼❡t❤♦❞✿ ❛ ♥♦✈❡❧ ❛♣♣r♦❛❝❤ t♦ t❤❡ ♠❛❝❤✐♥❡ ❧❡❛r♥✐♥❣ str✉❝t✉r❛❧ r✐s❦ ♠✐♥✐♠✐③❛t✐♦♥ ♣r♦❜❧❡♠✑ ✲ s✉❜♠✐tt❡❞ t♦ ■❊❊❊ ❚r❛♥s❛❝t✐♦♥s ♦♥ ◆❡✉r❛❧ ◆❡t✇♦r❦s ♦♥ ❙❡♣t❡♠❜❡r✲✷✵✵✺✳
✸✳ ❉✳ ❆✳ ●✳ ❱■❊■❘❆✱ ❏✳ ❆✳ ❱❆❙❈❖◆❈❊▲❖❙ ❛♥❞ ❲✳ ▼✳ ❈❆▼■◆❍❆❙ ✲ ✏❈♦♥tr♦❧❧✐♥❣ t❤❡ P❛r❛❧❧❡❧ ▲❛②❡r P❡r❝❡♣tr♦♥ ❝♦♠♣❧❡①✐t② ✉s✐♥❣ ❛ ♠✉❧t✐✲ ♦❜❥❡❝t✐✈❡ ❧❡❛r♥✐♥❣ ❛❧❣♦r✐t❤♠✑ ✲ ◆❡✉r❛❧ ❈♦♠♣✉t✐♥❣ ❛♥❞ ❆♣♣❧✐❝❛t✐♦♥s✱ ❛❝❝❡♣t❡❞ t♦ ♣✉❜❧✐❝❛t✐♦♥ ✭❛✈❛✐❧❛❜❧❡ ♦♥✲❧✐♥❡✮✳
✹✳ ❉✳ ●✳ ❱■❊■❘❆✱ ❉✳ ❆✳ ●✳ ❱■❊■❘❆✱ ❲✳ ▼✳ ❈❆▼■◆❍❆❙✱ ❏✳ ❆✳ ❱❆❙✲ ❈❖◆❈❊▲❖❙ ✲ ✏❆ ❍②❜r✐❞ ❆♣♣r♦❛❝❤ ❈♦♠❜✐♥✐♥❣ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠ ❛♥❞ ❙❡♥s✐t✐✈✐t② ■♥❢♦r♠❛t✐♦♥ ❊①tr❛❝t❡❞ ❢r♦♠ P❛r❛❧❧❡❧ ▲❛②❡r ◆❡t✇♦r❦✑ ✲ ■❊❊❊ ❚r❛♥s❛❝t✐♦♥s ♦♥ ▼❛❣♥❡t✐❝s✱ ✈✳ ✹✶✱ ♥✳ ✺✱ ♣✳ ✶✼✹✵✲✶✼✹✸✱ ✷✵✵✺✳
✺✳ ❉✳ ❆✳ ●✳ ❱■❊■❘❆✱ ❲✳ ▼✳ ❈❆▼■◆❍❆❙ ❛♥❞ ❏✳ ❆✳ ❱❆❙❈❖◆❈❊▲❖❙ ✲ ✏❊①tr❛❝t✐♥❣ ❙❡♥s✐t✐✈✐t② ■♥❢♦r♠❛t✐♦♥ ♦❢ ❊❧❡❝tr♦♠❛❣♥❡t✐❝ ❉❡✈✐❝❡ ▼♦❞❡❧s ❢r♦♠ ❛ ▼♦❞✐✜❡❞ ❆◆❋■❙ ❚♦♣♦❧♦❣②✑ ✲ ■❊❊❊ ❚r❛♥s❛❝t✐♦♥s ♦♥ ▼❛❣♥❡t✐❝s✱ ✈♦❧✳ ✹✵✱ ♥♦✳ ✷✱ ♣♣✳ ✶✶✽✽✲✶✶✾✶✱ ▼❛r❝❤ ✷✵✵✹✳
✻✳ ❉✳ ❆✳ ●✳ ❱■❊■❘❆✱ ❏✳ ❆✳ ❱❆❙❈❖◆❈❊▲❖❙ ❛♥❞ ❲✳ ▼✳ ❈❆▼■◆❍❆❙ ✲ ✏■♠♣r♦✈✐♥❣ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❙❡♥s✐t✐✈✐t② ❊①tr❛❝t✐♦♥ ♦❢ ❊❧❡❝tr♦♠❛❣♥❡t✐❝ ❉❡✈✐❝❡s ❯s✐♥❣ t❤❡ P❛r❛❧❧❡❧ ▲❛②❡r P❡r❝❡♣tr♦♥ ❚r❛✐♥❡❞ ✇✐t❤ t❤❡ ▼✐♥✐♠✉♠ ●r❛❞✐❡♥t ▼❡t❤♦❞✑ ✲ ✶✷t❤ ❈❊❋❈ ✲ ■❊❊❊ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❊❧❡❝tr♦♠❛❣♥❡t✐❝ ❋✐❡❧❞ ❈♦♠♣✉t❛t✐♦♥ ✲ ❆❜r✐❧✴✷✵✵✻✱ ▼✐❛♠✐✱ ❯❙❆✳
✼✳ ❉✳ ❆✳ ●✳ ❱■❊■❘❆✱ ❲✳ ▼✳ ❈❆▼■◆❍❆❙ ❛♥❞ ❏✳ ❆✳ ❱❆❙❈❖◆❈❊▲❖❙ ✲ ✏▼✉❧t✐♦❜❥❡❝t✐✈❡ ▼❡t❤♦❞♦❧♦❣② t♦ ❈♦♠♣❛r❡ ◆❡✉r❛❧ ◆❡t✇♦r❦s ❆♣♣❧✐❡❞ ✐♥ ❊❧❡❝tr♦♠❛❣♥❡t✐❝s✑ ✲ ✶✶t❤ ❈❊❋❈ ✲ ■❊❊❊ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❊❧❡❝tr♦♠❛❣♥❡t✐❝ ❋✐❡❧❞ ❈♦♠♣✉t❛t✐♦♥ ✭❉✐❣✐t❛❧ ♣r♦❝❡❡❞✐♥❣s✮ ✲ ❏✉♥❡✴✷✵✵✹ ❙❡♦✉❧✱ ❑♦r❡❛✳ ✽✳ ❉✳ ●✳ ❱■❊■❘❆✱ ❉✳ ❆✳ ●✳ ❱■❊■❘❆✱ ❲✳ ▼✳ ❈❆▼■◆❍❆❙ ❛♥❞ ❏✳ ❆✳ ❱❆❙✲
❈❖◆❈❊▲❖❙ ✲ ✏❆ ❍②❜r✐❞ ❆♣♣r♦❛❝❤ ❈♦♠❜✐♥✐♥❣ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠ ❛♥❞ ❙❡♥s✐t✐✈✐t② ■♥❢♦r♠❛t✐♦♥ ❊①tr❛❝t❡❞ ❢r♦♠ ❛ P❛r❛❧❧❡❧ ▲❛②❡r P❡r❝❡♣tr♦♥✑ ✲ ✶✶t❤ ❈❊❋❈ ✲ ■❊❊❊ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❊❧❡❝tr♦♠❛❣♥❡t✐❝ ❋✐❡❧❞ ❈♦♠♣✉t❛t✐♦♥ ✭❉✐❣✐t❛❧ ♣r♦❝❡❡❞✐♥❣s✮ ✲ ❏✉♥❡✴✷✵✵✹ ❙❡♦✉❧✱ ❑♦r❡❛✳
✾✳ ❉✳ ❆✳ ●✳ ❱■❊■❘❆✱ ❲✳ ▼✳ ❈❆▼■◆❍❆❙✱ ❏✳ ❆✳ ❘❆▼■❘❊❩ ❛♥❞ ❏✳ ❆✳ ❱❆❙❈❖◆❈❊▲❖❙ ✲ ✏❊①tr❛❝t✐♥❣ ❙❡♥s✐t✐✈✐t② ■♥❢♦r♠❛t✐♦♥ ♦❢ ❊❧❡❝tr♦♠❛❣✲ ♥❡t✐❝ ❉❡✈✐❝❡ ▼♦❞❡❧s ❢r♦♠ ❛ ▼♦❞✐✜❡❞ ❆◆❋■❙ ❚♦♣♦❧♦❣②✑ ✲ ✶✹t❤ ❈❖▼✲ P❯▼❆● ✲ ■❊❊❊ ❈♦♥❢❡r❡♥❝❡ ♦♥ t❤❡ ❈♦♠♣✉t❛t✐♦♥ ♦❢ ❊❧❡❝tr♦♠❛❣♥❡t✐❝ ❋✐❡❧❞s ✭❉✐❣✐t❛❧ ♣r♦❝❡❡❞✐♥❣s✮ ✲ P ✾✺✷✼✾ ✲ ❏✉❧②✴✷✵✵✸ ✲❙❛r❛t♦❣❛ ❙♣r✐♥❣s✱ ◆❡✇ ❨♦r❦✱ ❯❙❆✳
✶✵✳ ❚✳ ▼❊❉❊■❘❖❙✱ ❉✳ ❆✳ ●✳ ❱■❊■❘❆✱ ❲✳ ▼✳ ❈❆▼■◆❍❆❙✱ ❏✳ ❆✳ ❱❆❙✲ ❈❖◆❈❊▲❖❙✱ ❆✳ P✳ ❇❘❆●❆✱ ❘✳ ❘✳ ❙❆▲❉❆◆❍❆ ❛♥❞ ❘✳ ❚✳ ❆▲❇❯✲ ◗❯❊❘◗❯❊ ✲✏◆❡✉r❛❧ ♥❡t✇♦r❦s tr❛✐♥❡❞ ✇✐t❤ ♠✉❧t✐♦❜❥❡❝t✐✈❡ ❧❡❛r♥✐♥❣ ❛❧✲ ❣♦r✐t❤♠ ❛♣♣❧✐❡❞ t♦ ♦♣t✐♠✐③❛t✐♦♥ ♣r♦❜❧❡♠s✑ ✲ ✷✹t❤ ❈■▲❆▼❈❊ ✲■❜❡r✐❛♥ ▲❛t✐♥✲❆♠❡r✐❝❛♥ ❈♦♥❣r❡ss ♦♥ ❈♦♠♣✉t❛t✐♦♥❛❧ ▼❡t❤♦❞s ✐♥ ❊♥❣✐♥❡❡r✐♥❣ ✭❉✐❣✐t❛❧ ♣r♦❝❡❡❞✐♥❣s✮ ✲ ❈■▲ ✻✷✺✲✸✾ ✲ ❖❝t♦❜❡r✴✷✵✵✸ ✲ ❖✉r♦ Pr❡t♦✱ ❇r❛③✐❧✳
