❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡
❞♦ ◆♦rt❡
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦
❋ís✐❝❛ ❊st❛tíst✐❝❛ ❆♣❧✐❝❛❞❛ ❛
❙✐st❡♠❛s ❙♦❝✐❛✐s ❆tr❛✈és ❞♦ ❊st✉❞♦
❞❡ ❘❡❞❡s ❈♦♠♣❧❡①❛s
❆✉t♦r❛✿
●❡r❞✐✈❛♥❡ ❋❡rr❡✐r❛ ❉✉❛rt❡
❖r✐❡♥t❛❞♦r✿
Pr♦❢✳ ❉r✳ ▲✉❝✐❛♥♦ ❘♦❞r✐❣✉❡s ❞❛ ❙✐❧✈❛
❈♦♦r✐❡♥t❛❞♦r✿
Pr♦❢✳ ❉r✳ ▼❛❞r❛s ❱✐s✇❛♥❛t❤❛♥ ●❛♥❞❤✐ ▼♦❤❛♥
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❚❡ór✐❝❛ ❡ ❊①♣❡r✐♠❡♥t❛❧ ✭❉❋❚❊✮ ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❛ ❚❡rr❛ ✭❈❈❊❚✮
●❡r❞✐✈❛♥❡ ❋❡rr❡✐r❛ ❉✉❛rt❡
❋ís✐❝❛ ❊st❛tíst✐❝❛ ❆♣❧✐❝❛❞❛ ❛
❙✐st❡♠❛s ❙♦❝✐❛✐s ❆tr❛✈és ❞♦ ❊st✉❞♦
❞❡ ❘❡❞❡s ❈♦♠♣❧❡①❛s
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡
Pós✲●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛ ❞♦
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛
❚❡ór✐❝❛ ❡ ❊①♣❡r✐♠❡♥t❛❧
❞❛
❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦
●r❛♥❞❡ ❞♦ ◆♦rt❡
❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ❛ ♦❜t❡♥çã♦
❞♦ ❣r❛✉ ❞❡ ▼❡str❛ ❡♠ ❋ís✐❝❛✳
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ▲✉❝✐❛♥♦ ❘♦❞r✐❣✉❡s ❞❛ ❙✐❧✈❛
❈♦♦r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ▼❛❞r❛s ❱✐s✇❛♥❛t❤❛♥ ●❛♥❞❤✐
▼♦❤❛♥
✏●r❛ç❛s ❛ ♠✐♥❤❛ só❧✐❞❛ ❢♦r♠❛çã♦ ❛❝❛❞ê♠✐❝❛✱ ❤♦❥❡ ❡✉ ♣♦ss♦ ❡s❝r❡✈❡r ❝❡♥t❡♥❛s ❞❡ ♣❛❧❛✈r❛s s♦❜r❡ ✬❋ís✐❝❛ ❊st❛tíst✐❝❛ ❆♣❧✐❝❛❞❛ ❛ ❙✐st❡♠❛s ❙♦❝✐❛✐s ❆tr❛✈és ❞♦ ❊st✉❞♦ ❞❡ ❘❡❞❡s ❈♦♠♣❧❡①❛s✬✱ ♦ q✉❡ ♠❡ ❡♥✈❛✐❞❡❝❡ ❡①tr❡♠❛♠❡♥t❡ ❝♦❜r✐♥❞♦ ♠✐♥❤❛ ❛❧♠❛ ❝♦♠ ✉♠ ❧✉①♦ ❞❡ s❡♥s❛çõ❡s ♥✉♥❝❛ ❛♥t❡s ❡①♣❡r✐♠❡♥t❛❞❛s✳ ❉❡✈♦ t❛❧ ❢❛t♦ ❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡✳✧
❉❡❞✐❝♦ ❡st❡ tr❛❜❛❧❤♦✿
❆❣r❛❞❡❝✐♠❡♥t♦s
❆ ❉❡✉s ♣❡❧♦ t❛❧❡♥t♦ ❡ ❢♦rç❛ ♠❡s♠♦ ♥♦s ♠♦♠❡♥t♦s ❡♠ q✉❡ ❛❝r❡❞✐t❡✐ q✉❡ ♥ã♦ ❝♦♥t✐♥✉❛r✐❛❀
❆♦ ♠❡✉ ♣❛✐ ❏♦ã♦ ❋❡rr❡✐r❛✱ q✉❡ ♠❡ ❡♥s✐♥♦✉ ❛ ❛♠❛r ♠❛t❡♠át✐❝❛ q✉❛♥❞♦ ❡✉ ❛✐♥❞❛ ❡r❛ ✉♠❛ ❝r✐❛♥ç❛❀
➚ ♠✐♥❤❛ ♠ã❡ ▼❛r✐❛ ❏♦sé ❋❡rr❡✐r❛✱ q✉❡ ❡♠ ♠✉✐t♦s ♠♦♠❡♥t♦s ❞❡ s✉❛ ✈✐❞❛✱ ❝✉✐❞♦✉ ❞❡ ♠✐♠ ♠❛✐s q✉❡ ❞❡❧❛ ♠❡s♠❛❀
❆♦s ♠❡✉s ✐r♠ã♦s✱ ●❡r❞✐✈❛♥ ❋❡rr❡✐r❛ ❡ ❊❞✐✈❛♥ ❖❧✐✈❡✐r❛✱ ❡ ✐r♠ãs✱ ❏❛♥❡ ❑❡②❧❡s ❋❡rr❡✐r❛✱ ●❡✐s❡ ❚❛✐s❡ ❋❡rr❡✐r❛ ❡ ❏♦s✐❛♥❡ ❋❡rr❡✐r❛✱ q✉❡ ♥✉♥❝❛ ❡♥t❡♥❞❡r❛♠ ❛s r❛③õ❡s ♣❡❧❛s q✉❛✐s ❡s❝♦❧❤✐ ♠❡ ❞❡❞✐❝❛r à ❝✐ê♥❝✐❛✱ ♠❡s♠♦ ❛ss✐♠ s❡♠♣r❡ ❛♣♦✐❛r❛♠ ❡st❡ s♦♥❤♦✱ ❝♦♠ ♣❛❧❛✈r❛s ❞❡ ❛♠♦r ❡ ✐♥❝❡♥t✐✈♦❀
❆♦ ♠❡✉ ❖r✐❡♥t❛❞♦r Pr♦❢✳ ❉r✳ ▲✉❝✐❛♥♦ ❘♦❞r✐❣✉❡s ❞❛ ❙✐❧✈❛✱ ♣❡❧❛ ♦♣♦rt✉♥✐✲ ❞❛❞❡✱ ♦r✐❡♥t❛çã♦✱ ❝♦♥✈❡rs❛s ❞❡s❝♦♥tr❛í❞❛s✱ s❡r❡♥✐❞❛❞❡ ❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❡❧♦ ❡♥✲ t✉s✐❛s♠♦ ❝♦♠ q✉❡ ❝♦♥❞✉③✐✉ ❡ss❡ tr❛❜❛❧❤♦✳ ◆ã♦ ❤á ♣❛❧❛✈r❛ ♠❡❧❤♦r ♣❛r❛ tr❛❞✉③✐r ♦ ♣r♦❢❡ss♦r ▲✉❝✐❛♥♦ q✉❡ ✏❡♥t✉s✐❛s♠♦✑✱ ❡st❡ ❡❧❡ ♣❛rt✐❧❤♦✉ ❣❡♥❡r♦s❛♠❡♥t❡ ❝♦♠✐❣♦ ❡ ❡ss❡ ❢❛t♦ ♠❡ tr♦✉①❡ ❛té ❛q✉✐❀
❆♦ ♠❡✉ ❈♦♦r✐❡♥t❛❞♦r Pr♦❢✳ ❉r✳ ▼❛❞r❛s ❱✐s✇❛♥❛t❤❛♥ ●❛♥❞❤✐ ▼♦❤❛♥✱ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ ❡ ♣♦r ♣❛rt✐❧❤❛r ❝♦♠✐❣♦ ✉♠ ♣♦✉❝♦ ❞❛ s✉❛ s❛❜❡❞♦r✐❛ ❡ ❡①♣❡r✐ê♥❝✐❛✱ ♣❡❧♦s ♠♦♠❡♥t♦s ❞❡ ❛♠♣❛r♦ ❡ ❛❝♦❧❤✐♠❡♥t♦✱ ♣❡❧❛ ❝♦♥✜❛♥ç❛ ❡ ♣❡❧❛s ♣❛❧❛✈r❛s ❞❡ ❢♦rç❛ ❡ ✐♥❝❡♥t✐✈♦ q✉❡ ♣♦ss✐❜✐❧✐t❛r❛♠ ❡ss❛ ❝♦♥q✉✐st❛ ❞❡ ✉♠❛ ♠❛♥❡✐r❛ tã♦ ❛❢á✈❡❧❀
❆♦ ❆♠✐❣♦ ▼❡ ❚✐❛❣♦ ▼❡❞❡✐r♦s ❱✐❡✐r❛✱ ♣❡❧♦s ❝♦♠❡♥tár✐♦s✱ ❞✐s❝✉ssõ❡s✱ ❛♠♣❛r♦ ❡ ❝♦♥tr✐❜✉✐çõ❡s q✉❡ ♣r♦♣♦r❝✐♦♥❛r❛♠ ♠❡❧❤♦r❛r ❡st❡ tr❛❜❛❧❤♦❀
❆♦s ❝♦❧❡❣❛s ❞❡ t✉r♠❛✱ ❘✐❝❛r❞♦ ❇♦r❣❡s✱ ❆♥♥❛ ❈❡❝í❧✐❛✱ ❲❡❧❧✐♥❣t♦♥ ❡ ❊❧♦✐s❡ ❈r✐st✐♥❛✱ ❝♦♠ ♦s q✉❛✐s ❞✐✈✐❞✐ ♠♦♠❡♥t♦s ❞❡ ❞❡s❝♦♥tr❛çã♦✱ ❞❡ ❞❡❞✐❝❛çã♦ ❡ ❡♥tr❡❣❛ ❛♦s ❝♦♥t❡ú❞♦s q✉❡ ♣r❡❝✐sá✈❛♠♦s ❞♦♠✐♥❛r ❡ t❛♠❜é♠ ❛❧❣✉♠❛s ♣♦✉❝❛s t❛r❞❡s ❞❡ t♦t❛❧ ✐♠♣r♦❞✉t✐✈✐❞❛❞❡❀
❊♠ ❡s♣❝✐❛❧ ❛♦ ♠❡✉ ❣r❛♥❞❡ ❛♠✐❣♦ ❏✉s❝✐♠ár✐♦ ●r❡❣ór✐♦ ❈r✉③ ✲ ✏■♥ ♠❡♠♦r✐❛♠✳✧❀
❆♦s ❝♦❧❡❣❛s ❞♦ ❣r✉♣♦ ❞❡ ♣❡sq✉✐s❛❋ís✐❝❛ ❊st❛tíst✐❝❛ ❡ ❙✐st❡♠❛s ❈♦♠♣❧❡①♦s❀ ❆♦s ♣r♦❢❡ss♦r❡s ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❚❡ór✐❝❛ ❡ ❊①♣❡r✐♠❡♥t❛❧ q✉❡ ❝♦♥✲ tr✐❜✉ír❛♠ ♣❛r❛ ♠✐♥❤❛ ❢♦r♠❛çã♦ ♣r♦✜ss✐♦♥❛❧ ❡ ❛♦s ❢✉♥❝✐♦♥ár✐♦s ❞♦ ❞❡♣❛rt❛♠❡♥t♦✱ ❡s♣❡❝✐❛❧♠❡♥t❡ ❛ ❈❡❧✐♥❛✳
✏❆♠❡ ❛ t♦❞♦s✱ ❝♦♥✜❡ ❡♠ ♣♦✉❝♦s✱ ♥ã♦ ❢❛ç❛ ♠❛❧ ❛ ♥✐♥✲ ❣✉é♠✳✧
❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡ ✭❯❋❘◆✮
❘❡s✉♠♦
❯❋❘◆
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❚❡ór✐❝❛ ❡ ❊①♣❡r✐♠❡♥t❛❧
▼❡str❛ ❡♠ ❋ís✐❝❛
❋ís✐❝❛ ❊st❛tíst✐❝❛ ❆♣❧✐❝❛❞❛ ❛ ❙✐st❡♠❛s ❙♦❝✐❛✐s ❆tr❛✈és ❞♦ ❊st✉❞♦ ❞❡ ❘❡❞❡s ❈♦♠♣❧❡①❛s
♣♦r ●❡r❞✐✈❛♥❡ ❋❡rr❡✐r❛ ❉✉❛rt❡
◆❡st❡ tr❛❜❛❧❤♦ é ❛♣r❡s❡♥t❛❞♦ ✉♠ ❡st✉❞♦ ❞❛s r❡❞❡s s♦❝✐❛✐s ❜❛s❡❛❞♦ ♥❛ ❛♥á❧✐s❡ ❞♦s ♥♦♠❡s ❞❡ ❢❛♠í❧✐❛s✳ ❋❛③✲s❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❜ás✐❝❛ ❞♦ ❢♦r♠❛❧✐s♠♦ ♠❛t❡♠át✐❝♦ ❞♦s ❣r❛❢♦s ❡ ❡♠ s❡❣✉✐❞❛ ❛♣r❡s❡♥t❛✲s❡ ♦s ♣r✐♥❝✐♣❛✐s ♠♦❞❡❧♦s t❡ór✐❝♦s ♣❛r❛ ❛s ❘❡❞❡s ❈♦♠♣❧❡①❛s ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❢✉♥❞❛♠❡♥t❛r ❛ ❛♥á❧✐s❡ ❞❛s r❡❞❡s ❞♦s s♦❜r❡♥♦♠❡s✳ ❊st❛s✱ ♣♦r s✉❛ ✈❡③✱ sã♦ tr❛❜❛❧❤❛❞❛s ❞❡ ♠♦❞♦ ❛ s❡r❡♠ ❡①tr❛í❞❛s ❛s ♣r✐♥❝✐♣❛✐s ❣r❛♥✲ ❞❡③❛s✱ t❛✐s ❝♦♠♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ❛❣r❡❣❛çã♦✱ ♠❡♥♦r ❝❛♠✐♥❤♦ ♠é❞✐♦ ❡ ❞✐str✐❜✉✐çã♦ ❞❡ ❝♦♥❡❝t✐✈✐❞❛❞❡s✳ ❈♦♠ ❜❛s❡ ♥❡st❛s ❣r❛♥❞❡③❛s✱ ♣♦❞❡✲s❡ ❛✜r♠❛r q✉❡ ❛s r❡❞❡s ❞❡ s♦✲ ❜r❡♥♦♠❡s sã♦ ✉♠ ❡①❡♠♣❧♦ ❞❡ r❡❞❡ ❝♦♠♣❧❡①❛✱ ❡①✐❜✐♥❞♦ ❝❛r❛❝t❡ríst✐❝❛s ✐♠♣♦rt❛♥t❡s ❝♦♠♦ ❧✐❣❛çã♦ ♣r❡❢❡r❡♥❝✐❛❧ ❡ ♦ ❝❛rát❡r ❞❡ ♠✉♥❞♦ ♣❡q✉❡♥♦✳
❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡ ✭❯❋❘◆✮
❆❜str❛❝t
❯❋❘◆
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❚❡ór✐❝❛ ❡ ❊①♣❡r✐♠❡♥t❛❧
▼❡str❛ ❡♠ ❋ís✐❝❛
❋ís✐❝❛ ❊st❛tíst✐❝❛ ❆♣❧✐❝❛❞❛ ❛ ❙✐st❡♠❛s ❙♦❝✐❛✐s ❆tr❛✈és ❞♦ ❊st✉❞♦ ❞❡ ❘❡❞❡s ❈♦♠♣❧❡①❛s
❜② ●❡r❞✐✈❛♥❡ ❋❡rr❡✐r❛ ❉✉❛rt❡
■♥ t❤✐s ✇♦r❦ ❛ st✉❞② ♦❢ s♦❝✐❛❧ ♥❡t✇♦r❦s ❜❛s❡❞ ♦♥ ❛♥❛❧②s✐s ♦❢ ❢❛♠✐❧② ♥❛♠❡s ✐s ♣r❡s❡♥t❡❞✳ ❆ ❜❛s✐❝ ❛♣♣r♦❛❝❤ t♦ t❤❡ ♠❛t❤❡♠❛t✐❝❛❧ ❢♦r♠❛❧✐s♠ ♦❢ ❣r❛♣❤s ✐s ❞❡✈❡❧♦♣❡❞ ❛♥❞ t❤❡♥ ♠❛✐♥ t❤❡♦r❡t✐❝❛❧ ♠♦❞❡❧s ❢♦r ❝♦♠♣❧❡① ♥❡t✇♦r❦s ❛r❡ ♣r❡s❡♥t❡❞ ❛✐♠✐♥❣ t♦ s✉♣♣♦rt t❤❡ ❛♥❛❧②s✐s ♦❢ s✉r♥❛♠❡s ♥❡t✇♦r❦s ♠♦❞❡❧s✳ ❚❤❡s❡✱ ✐♥ t✉r♥✱ ❛r❡ ✇♦r❦❡❞ s♦ ❛s t♦ ❜❡ ❞r❛✇♥ ❧❡❛❞✐♥❣ q✉❛♥t✐t✐❡s✱ s✉❝❤ ❛s ❛❣❣r❡❣❛t✐♦♥ ❝♦❡✣❝✐❡♥t✱ ♠✐♥✐♠✉♠ ❛✈❡✲ r❛❣❡ ♣❛t❤ ❧❡♥❣t❤ ❛♥❞ ❝♦♥♥❡❝t✐✈✐t② ❞✐str✐❜✉t✐♦♥✳ ❇❛s❡❞ ♦♥ t❤❡s❡ q✉❛♥t✐t✐❡s✱ ✐t ❝❛♥ ❜❡ st❛t❡❞ t❤❛t s✉r♥❛♠❡s ♥❡t✇♦r❦s ❛r❡ ❛♥ ❡①❛♠♣❧❡ ♦❢ ❝♦♠♣❧❡① ♥❡t✇♦r❦✱ s❤♦✇✐♥❣ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡s s✉❝❤ ❛s ♣r❡❢❡r❡♥t✐❛❧ ❛tt❛❝❤♠❡♥t ❛♥❞ s♠❛❧❧✲✇♦r❧❞ ❝❤❛r❛❝t❡r✳
❙✉♠ár✐♦
❆❣r❛❞❡❝✐♠❡♥t♦s ✐✐✐
❘❡s✉♠♦ ✈
❆❜str❛❝t ✈✐✐
❙✉♠ár✐♦ ✈✐✐✐
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✐✈
❆❜r❡✈✐❛çõ❡s ①✈
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ❆♣r❡s❡♥t❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶
✶✳✷ ❖ s✉r❣✐♠❡♥t♦ ❞❛ ❆♥á❧✐s❡ ❞❡ ❘❡❞❡s ❙♦❝✐❛✐s ✭❆❘❙✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷
✶✳✸ ❖ ♣r♦❜❧❡♠❛ ♣❛r❛ ❡ss❛ ❉✐ss❡rt❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹
✶✳✸✳✶ ❖❜❥❡t✐✈♦ ●❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺
❙✉♠ár✐♦ ✐①
✶✳✹ P♦r q✉❡ ❡st✉❞❛r ❆❘❙❄ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻
✷ ❚❡♦r✐❛ ❞♦s ●r❛❢♦s ✲ ❯♠❛ ❛❜♦r❞❛❣❡♠ s✉❝✐♥t❛ ✽
✷✳✶ ❆♣r❡s❡♥t❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽
✷✳✷ ❯♠ ♣♦✉❝♦ ❞❛ ❍✐stór✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✷✳✶ ❆s ❊s❝♦❧❛s ❞❛ ❚● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸
✷✳✸ ❋♦r♠❛❧✐s♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹
✷✳✸✳✶ ❉❡✜♥✐çã♦ ❞❡ ●r❛❢♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹
✷✳✹ ❚✐♣♦s ❞❡ ●r❛❢♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽
✷✳✹✳✶ ●r❛❢♦s s✐♠♣❧❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽
✷✳✹✳✷ ●r❛❢♦ ❝♦♠♣❧❡t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾
✷✳✹✳✸ ●r❛❢♦s ❜✐♣❛rt✐❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾
✷✳✹✳✹ ●r❛❢♦s ♣❧❛♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵
✷✳✹✳✺ ●r❛❢♦ ❝♦♥❡①♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵
✷✳✹✳✻ ●r❛❢♦ ♦r✐❡♥t❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶
✷✳✹✳✼ ●r❛❢♦ ♥ã♦ ♦r✐❡♥t❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷
✷✳✹✳✽ ●r❛❢♦s ♣♦♥❞❡r❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷
✷✳✹✳✾ ●r❛❢♦s ❛❧❡❛tór✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✸ ❘❡❞❡s ❈♦♠♣❧❡①❛s ✲ ▼♦❞❡❧♦s ❡ ❛♥á❧✐s❡s ❞❡ ❘❡❞❡s ❙♦❝✐❛✐s ✷✺
✸✳✶ ❆♣r❡s❡♥t❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✸✳✷ ❆s♣❡❝t♦s ❤✐stór✐❝♦s ❞❛ ❆❘❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻
❙✉♠ár✐♦ ①
✸✳✸✳✶ ❉✐str✐❜✉✐çã♦ ❡♠ ▲❡✐ ❞❡ P♦tê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵
✸✳✸✳✷ ❘❡❞❡s ▲✐✈r❡s ❞❡ ❊s❝❛❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✸✳✸✳✷✳✶ ▼❡♥♦r ❈❛♠✐♥❤♦ ▼é❞✐♦ ❡ ♦ ❊❢❡✐t♦ ❞❡ ▼✉♥❞♦ P❡q✉❡♥♦ ✸✺
✸✳✹ Pr♦♣r✐❡❞❛❞❡s ❞❛s ❘❡❞❡s ❈♦♠♣❧❡①❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻
✸✳✹✳✶ ❋♦r♠❛çã♦ ❞❡ Pó❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻
✸✳✹✳✷ ❈♦❡✜❝✐❡♥t❡ ❞❡ ❆❣r❡❣❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼
✸✳✹✳✸ ❘♦❜✉st❡③✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✸✳✺ ▼♦❞❡❧♦s ❞❡ ❘❡❞❡s ❈♦♠♣❧❡①❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✸✳✺✳✶ ▼♦❞❡❧♦ ❞❡ Pr✐❝❡ ❡ ❧✐❣❛çã♦ ♣r❡❢❡r❡♥❝✐❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✸✳✺✳✷ ▼♦❞❡❧♦ ❞❡ ❇❛r❛❜❛s✐✲❆❧❜❡rt✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵
✸✳✺✳✸ ▼♦❞❡❧♦ ❞❡ ❇✐❛♥❝♦♥✐✲❇❛r❛❜ás✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✹ ❘❡❞❡ ❞♦s ❙♦❜r❡♥♦♠❡s ✹✺
✹✳✶ ❆♣r❡s❡♥t❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺
✹✳✶✳✶ Pr❡❧✐♠✐♥❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻
✹✳✶✳✷ ▼♦t✐✈❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼
✹✳✶✳✸ ▼❡t♦❞♦❧♦❣✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼
✹✳✶✳✸✳✶ ❚✐♣♦ ❞❡ P❡sq✉✐s❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼
✹✳✶✳✸✳✷ Pr♦❣r❛♠❛s ❯t✐❧✐③❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽
✹✳✶✳✸✳✸ Pr♦❣r❛♠❛ ♣❛r❛ ❛❞q✉✐r✐r ❛s ❧✐st❛❣❡♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽
✹✳✶✳✸✳✹ Pr♦❣r❛♠❛s ♣❛r❛ ♦ tr❛t❛♠❡♥t♦ ❞♦s ❞❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
❙✉♠ár✐♦ ①✐
✺ ❈♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s ✺✾
✺✳✶ ❈♦♥❝❧✉sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✺✳✷ P❡rs♣❡❝t✐✈❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶✳✶ ❘❡❞❡s ❙♦❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸
✶✳✷ ❘❡❞❡s ❙♦❝✐❛✐s ❱✐rt✉❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹
✶✳✸ ▼❛♥✐❢❡st❛çõ❡s ❙♦❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺
✶✳✹ P✉❜❧✐❝❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✷✳✶ ●r❛❢♦ ❈♦♥❡①♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❞❛s P♦♥t❡s ❞❡ ❑ö♥✐❣s❜❡r❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵
✷✳✸ ●r❛❢♦ r✲r❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼
✷✳✹ ▼❛tr✐③ ❞❡ ❛❞❥❛❝ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼
✷✳✺ ❈❛♠✐♥❤♦ ❣❡♦❞és✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽
✷✳✻ ●r❛❢♦ s✐♠♣❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾
✷✳✼ ●r❛❢♦ ❈♦♠♣❧❡t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾
✷✳✽ ●r❛❢♦ ❜✐♣❛rt✐❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵
✷✳✾ ●r❛❢♦ ♣❧❛♥❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶
✷✳✶✵ ●r❛❢♦ ❝♦♥❡①♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶
✷✳✶✶ ●r❛❢♦ ♦r✐❡♥t❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐✐✐
✷✳✶✸ ●r❛❢♦ ♣♦♥❞❡r❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✷✳✶✹ ●rá✜❝♦ ❞♦ ▼♦❞❡❧♦ ❞❡ ❊r❞ös✲❘é♥②✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
✷✳✶✺ ●r❛❢♦ ❆❧❡❛tór✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
✸✳✶ ●r❛❢♦ ▼✉❧❤❡r❡s ❞♦ ❙✉❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✸✳✷ ●r❛❢♦ ♠♦✈✐♠❡♥t♦ s♦❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✸✳✸ ❘❡❞❡ ♣❧❛♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✸✳✹ ▲❡✐ ❞❡ ♣♦tê♥❝✐❛ ① ❢✉♥çã♦ ❡①♣♦♥❡♥❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✸✳✺ ❍✐st♦❣r❛♠❛ ❞♦ ▼♦❞❡❧♦ ❞❡ ❇❛r❛❜❛s✐✲❆❧❜❡rt ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶
✸✳✻ ❘❡❞❡ ❇❛r❛❜ás✐✲❆❧❜❡rt ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✸✳✼ ❍✐st♦❣r❛♠❛ ❞♦ ▼♦❞❡❧♦ ❞❡ ❇✐❛♥❝♦♥✐✲❇❛r❛❜ás✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
✸✳✽ ❘❡❞❡ ❇✐❛♥❝♦♥✐✲❇❛r❛❜ás✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
✹✳✶ Pr♦❣r❛♠❛ ●❡♣❤✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽
✹✳✷ ❊sq✉❡♠❛ ❙♦❜r❡♥♦♠❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵
✹✳✸ ❘❡❞❡ P❛✉❧♦s❴P❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✹✳✹ ❘❡❞❡ ▲✉❝✐❛♥♦s❴❇❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹
✹✳✺ ●rá✜❝♦ ▼❛r✐❛s❴❇❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
✹✳✻ ❘❡❞❡ ❏♦sés❴P❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ ❚❛❜❡❧❛ ▲✐st❛ ❞❡ ❛❞❥❛❝ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽
✸✳✶ ❚❛❜❡❧❛ ❝♦♥❡❝t✐✈✐❞❛❞❡ ❞♦s ♥ós ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✹✳✶ ❚❛❜❡❧❛ ◆♦♠❡s ❞❡ ❢❛♠í❧✐❛s ♥♦ ❇r❛s✐❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✹✳✷ ❚❛❜❡❧❛ ◆♦♠❡s ❞❡ ❢❛♠í❧✐❛s ❡♠ P♦rt✉❣❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
✹✳✸ ❚❛❜❡❧❛ ❘❡❞❡s ❞♦s ❙♦❜r❡♥♦♠❡s ❳ ●r❛❢♦s ❆❧❡❛tór✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
❆❜r❡✈✐❛çõ❡s
❙✐❣❧❛ ❖ q✉❡ ❡❧❛ ❘❡♣r❡s❡♥t❛ ❆❘❙ ❆♥á❧✐s❡ ❞❡ ❘❡❞❡s ❙♦❝✐❛✐s
❈❆P❊❙ ❈♦♦r❞❡♥❛çã♦ ❞❡ ❆♣❡r❢❡✐ç♦❛♠❡♥t♦ ❞❡ P❡ss♦❛❧ ❞❡ ◆í✈❡❧ ❙✉♣❡r✐♦r ▲❛❜✐❝ ▲❛❜♦r❛tór✐♦ ❞❡ ❡st✉❞♦s s♦❜r❡ ■♠❛❣❡♠ ❡ ❈✐❜❡r❝✉❧t✉r❛
❈▼❆❋❯▲ ❈❡♥tr♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❆♣❧✐❝❛çõ❡s ❋✉♥❞❛♠❡♥t❛✐s ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ▲✐s❜♦❛
❘❙ ❘❡❞❡s ❞♦s ❙♦❜r❡♥♦♠❡s ❙❈ ❙✐st❡♠❛s ❈♦♠♣❧❡①♦s ❚● ❚❡♦r✐❛ ❞♦s ●r❛❢♦s
❚❘❈ ❚❡♦r✐❛ ❞❡ ❘❡❞❡s ❈♦♠♣❧❡①❛s
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
✏❆❧❣✉♠❛s ♣❡ss♦❛s ❛❝❤❛♠ q✉❡ ❢♦❝♦ s✐❣♥✐✜❝❛ ❞✐③❡r s✐♠ ♣❛r❛ ❛ ❝♦✐s❛ ❡♠ q✉❡ ✈♦❝ê ✈❛✐ s❡ ❢♦❝❛r✳ ▼❛s ♥ã♦ é ♥❛❞❛ ❞✐ss♦✳ ❙✐❣♥✐✜❝❛ ❞✐③❡r ♥ã♦ às ❝❡♥t❡♥❛s ❞❡ ♦✉tr❛s ❜♦❛s ✐❞❡✐❛s q✉❡ ❡①✐st❡♠✳ ❱♦❝ê ♣r❡❝✐s❛ s❡❧❡❝✐♦♥❛r ❝✉✐❞❛❞♦s❛♠❡♥t❡✳✧
❙t❡✈❡ ❏♦❜s
✶✳✶ ❆♣r❡s❡♥t❛çã♦
❊st❡ ❝❛♣ít✉❧♦ t❡♠ ❝♦♠♦ ✜♥❛❧✐❞❛❞❡ ❛ ❛♣r❡s❡♥t❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦ ❡ ❞♦s ♦❜❥❡✲ t✐✈♦s ❞❡❧✐♥❡❛❞♦s ♣❛r❛ ❛ ❝♦♥❝r❡t✐③❛çã♦ ❞♦ ♠❡s♠♦✱ ❛❧é♠ ❞❡ ❡①♣♦r ❛ ❡str✉t✉r❛ ♦r❣❛✲ ♥✐③❛❝✐♦♥❛❧ ❞❡st❡ ❞♦❝✉♠❡♥t♦✳
❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ✷
✶✳✷ ❖ s✉r❣✐♠❡♥t♦ ❞❛ ❆♥á❧✐s❡ ❞❡ ❘❡❞❡s ❙♦❝✐❛✐s ✭❆❘❙✮
❖ s♦❝✐ó❧♦❣♦ ❢r❛♥❝ês ➱♠✐❧❡ ❉✉r❦❤❡✐♠ ✭✶✽✺✽✲✶✾✶✼✮✱ t✐❞♦ ♣♦r ♠✉✐t♦s ❝♦♠♦ ✉♠ ❞♦s ♣❛✐s ❞❛ s♦❝✐♦❧♦❣✐❛ ♠♦❞❡r♥❛✱ ❞❡✜♥❡ ❡♠ s❡✉ ❧✐✈r♦✱ ✏❆s ❘❡❣r❛s ❞♦ ▼ét♦❞♦ ❙♦❝✐✲ ♦❧ó❣✐❝♦✑ ✭✶✽✾✺✮ ❬✶❪✱ q✉❡ ♦ ♦❜❥❡t♦ ❞❡ ❡st✉❞♦ ❞❛ ❙♦❝✐♦❧♦❣✐❛ ❞❡✈❡ s❡r ♦ ❢❛t♦ s♦❝✐❛❧✶✱
♣♦✐s ❡❧❡ ❞❡r✐✈❛ ❞❛ ✈✐❞❛ ❡♠ s♦❝✐❡❞❛❞❡✱ q✉❡ é ❝❛r❛❝t❡r✐③❛❞❛ ♣❡❧♦ ❝♦♥❥✉♥t♦ ❞❡ ❢❛t♦s s♦❝✐❛✐s ❡st❛❜❡❧❡❝✐❞♦s✳
❉❡s❞❡ q✉❡ ♦ ❤♦♠❡♠ s❡ ♦r❣❛♥✐③♦✉ ❡♠ s♦❝✐❡❞❛❞❡✱ r❡❣r❛s ❡ ❞❡✜♥✐çõ❡s ♣❛r❛ ♦ ❡s✲ t❛❜❡❧❡❝✐♠❡♥t♦ ❞❛ ♠❡s♠❛ sã♦ ❝r✐❛❞❛s✱ ♠♦❞✐✜❝❛❞❛s✱ ❛❞❛♣t❛❞❛s ❡ s❡❧❡❝✐♦♥❛❞❛s ❝♦♥s✲ t❛♥t❡♠❡♥t❡✳ ❙❡♣❛r❛r ❣r✉♣♦s ❡ ❞✐t❛r ❝♦♠♦ ❝❛❞❛ ✉♠ ❞❡❧❡s ❞❡✈❡ s❡ ♣♦rt❛r ♣❡r❛♥t❡ ♦s ❞❡♠❛✐s s❡♠♣r❡ ❢♦✐ ✉♠❛ ❞❛s ❣r❛♥❞❡s ♣r❡♦❝✉♣❛çõ❡s ❞♦s ♠❡♥t♦r❡s✷ ❞❡ss❡ s✐st❡♠❛✳
❆ss✐♠ ❢♦r❛♠ ❞❡✜♥✐❞♦s ♠♦❞❡❧♦s ❞❡ ❝♦♥❞✉t❛ ❛ s❡r❡♠ s❡❣✉✐❞♦s ♣♦r♠❡♥♦r✐③❛❞❛♠❡♥t❡ ♣♦r t♦❞♦s✱ ♣♦r ✈❡③❡s✱ ❡st❛s ❞❡✜♥✐çõ❡s ❞❡ ❝♦♠♦ ♦s ♠❡♠❜r♦s ❞❛ s♦❝✐❡❞❛❞❡ ❞❡✈❡r✐❛♠ s❡ ♣♦rt❛r ♣r✐✈✐❧❡❣✐❛✈❛ ✉♠❛ ❡❧✐t❡✱ ❝❛✉s❛♥❞♦ ♠✉✐t♦ ❞❡s❝♦♥❢♦rt♦ ♥♦s ❞❡♠❛✐s ✐♥t❡❣r❛♥✲ t❡s✳ ❚♦❞♦s ❡ss❡s ♣♦♥t♦s ❢♦r❛♠ ♠♦t✐✈♦s ♣❛r❛ ❡st✉❞♦s ♥♦ t♦❝❛♥t❡ à ❙♦❝✐♦❧♦❣✐❛✳ ❖ ❢♦r♠❛❧✐s♠♦ ♠❛t❡♠át✐❝♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ♦ ❡st✉❞♦ ❞❛ ❆❘❙✱ s✉r❣✐✉ ❞♦✐s sé❝✉❧♦s ❛♥t❡s q✉❛♥❞♦ ❊✉❧❡r r❡s♦❧✈❡✉ ✏❖ Pr♦❜❧❡♠❛ ❞❛s P♦♥t❡s ❞❡ ❑ö♥✐❣s❜❡r❣✧ ✸✳
❆❧❣✉♥s ❛✉t♦r❡s ❛♣♦♥t❛♠ ❝♦♠♦ ♠❛r❝♦ ✐♥✐❝✐❛❧ ❞♦s ❡st✉❞♦s s♦❜r❡ ❛ ❆❘❙ ♥❛ ❙♦❝✐♦❧♦❣✐❛✱ ♦ tr❛❜❛❧❤♦ ❞❡ ❏❛❝♦❜ ▲❡✈② ▼♦r❡♥♦ ✭✶✾✸✹✮✱ q✉❡ ✐♥tr♦❞✉③✐✉ s♦❝✐♦❣r❛♠❛s ♣❛r❛ r❡♣r❡s❡♥t❛r ❛s r❡❞❡s ❞❡ r❡❧❛çõ❡s ✐♥t❡r♣❡ss♦❛✐s ♥❛ ❍✉❞s♦♥ ❙❝❤♦♦❧ ❢♦r ●✐r❧s✳ ❊♥tr❡t❛♥t♦ ✉♠ ✐♠♣♦rt❛♥t❡ ❡st✉❞♦ s♦❜r❡ r❡❞❡s s♦❝✐❛✐s ❢♦✐ r❡❛❧✐③❛❞♦ ❛♣❡♥❛s ♥❛ ❞é✲ ❝❛❞❛ ❞❡ ✶✾✻✵ ♣♦r ❍❛rr✐s♦♥ ❈♦②❧❡r ❲❤✐t❡ ❡ s❡✉s ❛❧✉♥♦s✱ q✉❡ ❝♦♥s❡❣✉✐r❛♠ ✜♥❛❧♠❡♥t❡ ❝♦♥str✉✐r ✉♠❛ ❜❛s❡ ❝♦♥s✐st❡♥t❡ ♣❛r❛ ❛ ✐♥✈❡st✐❣❛çã♦ ❞❛s r❡❞❡s s♦❝✐❛✐s ♣♦r ♠❡✐♦ ❞❡ ❡st✉❞♦s s♦❜r❡ ❡str✉t✉r❛s s♦❝✐❛✐s ❝♦♠♣❧❡①❛s✳ ❲❤✐t❡ ♣♦ss✉✐❛ ❢♦r♠❛çã♦ ❡♠ ❋ís✐❝❛✱ ♦ q✉❡ ♣♦❞❡ t❡r ♣r♦♣♦r❝✐♦♥❛❞♦ ❢❡rr❛♠❡♥t❛s ❛❞❡q✉❛❞❛s ❛♦ ❡st✉❞♦ q✉❛♥t✐t❛t✐✈♦ ❞❡ ❡str✉t✉r❛s ❡ ♣r♦❝❡ss♦s q✉❡ ❡♥✈♦❧✈❡♠ ❛s r❡❞❡s s♦❝✐❛✐s ❬✷❪✳
✶❖ ❢❛t♦ s♦❝✐❛❧ é ♦ ♦❜❥❡t♦ ❝❡♥tr❛❧ ❞❛ t❡♦r✐❛ s♦❝✐♦❧ó❣✐❝❛ ❞❡ ➱♠✐❧❡ ❉✉r❦❤❡✐♠✱ ❝♦♥s✐st❡ ❡♠ ♠❛♥❡✐r❛s
❞❡ ❛❣✐r✱ ♣❡♥s❛r ❡ s❡♥t✐r ❡①t❡r✐♦r❡s ❛♦ ✐♥❞✐✈í❞✉♦✱ ✉♠❛ ♥♦r♠❛ ❝♦❧❡t✐✈❛ ❝♦♠ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❡ ♣♦❞❡r ❞❡ ❝♦❡rçã♦ s♦❜r❡ ♦ ✐♥❞✐✈í❞✉♦✳
✷❖ t❡r♠♦ ❛q✉✐ ❡stá s❡♥❞♦ ✉s❛❞♦ ❝♦♠♦ ✉♠❛ ❛❧✉sã♦ ❛ ✉♠ ❣r✉♣♦ ❞❛ s♦❝✐❡❞❛❞❡ ✭❣❡r❛❧♠❡♥t❡ ❝♦♠
❢✉♥çõ❡s ♣♦❧ít✐❝❛s ❡✴♦✉ ❡❝♦♥ô♠✐❝❛s✮ q✉❡ ♣♦ss✉❡♠ ♦ ♣♦❞❡r ❞❡ ❡st❛❜❡❧❡❝❡r ♦ ❝♦♥tr♦❧❡ ❞♦s ✏♠❡✐♦s s♦❝✐❛✐s ❞❡ ♣r♦❞✉çã♦✑✱ ♥❡❧❡ ✐♥❝❧✉í❞♦ ♦ ❞♦♠í♥✐♦ ✭❣❡r❛❧♠❡♥t❡✱ ♥ã♦ ❛♣❛r❡♥t❡✮ s♦❜r❡ ♦s ✈❡í❝✉❧♦s ❞❡ ❝♦♠✉♥✐❝❛çã♦✱ ♦s ❡st❛❜❡❧❡❝✐♠❡♥t♦s ❞❡ ❡♥s✐♥♦ ❡ ❛ ♣r♦❞✉çã♦ ❝✉❧t✉r❛❧✳
❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ✸
❋✐❣✉r❛ ✶✳✶✿ ❆ ✐♥t❡r❛çã♦ ❡♥tr❡ ♣❡ss♦❛s ❛tr❛✈és ❞❡ ✐♥t❡r❡ss❡s ❡♠ ❝♦♠✉♠ ❛ ✉♠ ♠❡s♠♦ ❣r✉♣♦ ✭❋♦♥t❡✿ ❈❛❞❡r♥♦ ❞❡ ❙♦❝✐♦❧♦❣✐❛✮ ❬✸❪✳
P♦❞❡✲s❡ ❞✐③❡r✱ ❣r♦ss♦ ♠♦❞♦✱ q✉❡ r❡❞❡ s♦❝✐❛❧ é ✉♠❛ ❡str✉t✉r❛ s♦❝✐❛❧ ❝♦♠♣♦st❛ ♣♦r ♣❡ss♦❛s ♦✉ ♦r❣❛♥✐③❛çõ❡s✱ ❝♦♥❡❝t❛❞❛s ♣♦r ✉♠ ♦✉ ✈ár✐♦s t✐♣♦s ❞❡ r❡❧❛çõ❡s✱ q✉❡ ❣❡r❛❧♠❡♥t❡ ♣❛rt✐❧❤❛♠ ✈❛❧♦r❡s ❡ ♦❜❥❡t✐✈♦s ❝♦♠✉♥s✳ ❯♠❛ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❢✉♥❞❛✲ ♠❡♥t❛✐s ♥❛ ❞❡✜♥✐çã♦ ❞❛s r❡❞❡s é ❛ s✉❛ ❛❜❡rt✉r❛ ✭❡♥tr❛❞❛ ❡ s❛í❞❛ ❞❡ ❝♦♠♣♦♥❡♥t❡s✮✱ ♣♦ss✐❜✐❧✐t❛♥❞♦ r❡❧❛❝✐♦♥❛♠❡♥t♦s ❤♦r✐③♦♥t❛✐s ❡ ♥ã♦ ❤✐❡rárq✉✐❝♦s ❡♥tr❡ ♦s ♣❛rt✐❝✐♣❛♥✲ t❡s✳ ❯♠ ❡st✉❞♦ ♠❛✐s ❞❡t❛❧❤❛❞♦ s♦❜r❡ ❛s r❡❞❡s s♦❝✐❛✐s é ❡♥❝♦♥tr❛❞♦ ❡♠ ❬✹❪✳
❆ t❡♥❞ê♥❝✐❛ ♥❛t✉r❛❧ ❞♦ s❡r ❤✉♠❛♥♦ é ❛❣r✉♣❛r✲s❡✱ ✈✐✈❡r ❡♠ ❝♦♠✉♥✐❞❛❞❡✱ ❝♦♥s✲ t✐t✉✐♥❞♦ ✉♠❛ ❝♦♥✈✐✈ê♥❝✐❛ q✉❡ ♣♦ss✐❜✐❧✐t❛ ♦ ❝♦♠♣❛rt✐❧❤❛♠❡♥t♦ ❞❡ ✐♥❢♦r♠❛çõ❡s ❡ ❡①♣❡r✐ê♥❝✐❛s q✉❡ ♣❛ss❛♠ ❛ s❡r ❡ss❡♥❝✐❛✐s ❛♦ ✐♥❞✐✈í❞✉♦✳ ❊ss❛ ❡str✉t✉r❛ s♦❝✐❛❧ q✉❡ é ❝r✐❛❞❛✱ ♥♦s ❞✐❢❡r❡♥t❡s ❝ír❝✉❧♦s ❢r❡q✉❡♥t❛❞♦s ♣❡❧♦s ✐♥❞✐✈í❞✉♦s✱ é q✉❡ ♦s ❢♦rt❛❧❡❝❡ ❡ ❛❜r❡ ♦♣♦rt✉♥✐❞❛❞❡s ♣❛r❛ r❡❛❧✐③❛çõ❡s✳ ❆ss✐♠✱ é ♥❡ss❡ ❝♦♥t❡①t♦ q✉❡ s❡ ❡♥❝♦♥tr❛♠ ❛s r❡❞❡s s♦❝✐❛✐s✱ q✉❡ r❡♣r❡s❡♥t❛♠ ❛ ❡str✉t✉r❛✱ ❡♠ q✉❡ ♦s s❡r❡s ❡stã♦ ✐♥s❡r✐❞♦s ❡ ❛rt✐❝✉❧❛♠ t♦❞❛ ❛ s✉❛ ❝♦♥✈✐✈ê♥❝✐❛ ❬✺❪✳
❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ✹
❋✐❣✉r❛ ✶✳✷✿ ❘❡❞❡s ❙♦❝✐❛✐s ❱✐rt✉❛✐s ❬✻❪✳
❚✇✐tt❡r✱ ❇❛❞♦♦✮✱ r❡❞❡s ♣r♦✜ss✐♦♥❛✐s ✭▲✐♥❦❡❞■♥✮✱ ❡♥tr❡ ♦✉tr❛s ✭❋✐❣✉r❛ ✶✳✷✮✳ P♦❞❡✲s❡ ❝✐t❛r ❛✐♥❞❛ ❛s r❡❞❡s ❝♦♠✉♥✐tár✐❛s ✭r❡❞❡s s♦❝✐❛✐s ❡♠ ❜❛✐rr♦s ♦✉ ❝✐❞❛❞❡s✮✱ ❛s r❡❞❡s ♣♦❧ít✐❝❛s✱ ❡t❝✳✱ ♦ q✉❡ ♣❡r♠✐t❡ ❛♥❛❧✐s❛r ❛ ❢♦r♠❛ ❝♦♠♦ ❛s ♦r❣❛♥✐③❛çõ❡s ❞❡s❡♥✈♦❧✈❡♠ ❛ s✉❛ ❛t✐✈✐❞❛❞❡✱ ❝♦♠♦ ♦s ✐♥❞✐✈í❞✉♦s ❛❧❝❛♥ç❛♠ ♦s s❡✉s ♦❜❥❡t✐✈♦s ♦✉ ♠❡❞✐r ♦ ❝❛♣✐t❛❧ s♦❝✐❛❧ ✕ ♦ ✈❛❧♦r q✉❡ ♦s ✐♥❞✐✈í❞✉♦s ♦❜tê♠ ❞❛ r❡❞❡ s♦❝✐❛❧✳ ❊st❛s r❡❞❡s tê♠ ❛❞q✉✐r✐❞♦ ✐♠♣♦rtâ♥❝✐❛ ❝r❡s❝❡♥t❡ ♥❛ s♦❝✐❡❞❛❞❡ ♠♦❞❡r♥❛✳ ❙ã♦ ❝❛r❛❝t❡r✐③❛❞❛s ♣r✐♠❛r✐❛♠❡♥t❡ ♣❡❧❛ ❛✉t♦❣❡r❛çã♦ ❞❡ s❡✉ ❞❡s❡♥❤♦✱ ♣❡❧❛ s✉❛ ❤♦r✐③♦♥t❛❧✐❞❛❞❡ ❡ s✉❛ ❞❡s❝❡♥tr❛❧✐③❛çã♦✳ ❯♠ ♣♦♥t♦ ❡♠ ❝♦♠✉♠ ❞❡♥tr❡ ♦s ❞✐✈❡rs♦s t✐♣♦s ❞❡ r❡❞❡ s♦❝✐❛❧ é ♦ ❝♦♠♣❛rt✐❧❤❛♠❡♥t♦ ❞❡ ✐♥❢♦r♠❛çõ❡s✱ ❝♦♥❤❡❝✐♠❡♥t♦s✱ ✐♥t❡r❡ss❡s ❡ ❡s❢♦rç♦s ❡♠ ❜✉s❝❛ ❞❡ ♦❜❥❡t✐✈♦s ❝♦♠✉♥s ✭❋✐❣✉r❛ ✶✳✸✮✳ ❆ ✐♥t❡♥s✐✜❝❛çã♦ ❞❛ ❢♦r♠❛çã♦ ❞❛s r❡❞❡s s♦❝✐❛✐s✱ ♥❡ss❡ s❡♥t✐❞♦✱ ❣❡r❛❧✲ ♠❡♥t❡ r❡✢❡t❡ ✉♠ ♣r♦❝❡ss♦ ❞❡ ❢♦rt❛❧❡❝✐♠❡♥t♦ ❞❛ ❙♦❝✐❡❞❛❞❡ ❈✐✈✐❧✱ ❡♠ ✉♠ ❝♦♥t❡①t♦ ❞❡ ♠❛✐♦r ♣❛rt✐❝✐♣❛çã♦ ❞❡♠♦❝rát✐❝❛ ❡ ♠♦❜✐❧✐③❛çã♦ s♦❝✐❛❧✳
✶✳✸ ❖ ♣r♦❜❧❡♠❛ ♣❛r❛ ❡ss❛ ❉✐ss❡rt❛çã♦
❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ✺
❋✐❣✉r❛ ✶✳✸✿ ▼♦✈✐♠❡♥t♦ ❡st✉❞❛♥t✐❧ ❡♠ ✷✵✶✸ q✉❡ ✜❝♦✉ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ Pr✐♠❛✲ ✈❡r❛ ❜r❛s✐❧❡✐r❛ ✭❋♦♥t❡✿ ❇❧♦❣ ❞♦ ❙❛❝❤❛✮❬✼❪✳
✏❯♠ ❞♦s ❣r❛♥❞❡s ♦❜❥❡t✐✈♦s ❞❛ ❋ís✐❝❛ ❊st❛tíst✐❝❛ é ♦ ❡st✉❞♦ ❞♦s ❙✐st❡♠❛s ❈♦♠♣❧❡✲ ①♦s ✭❙❈✮✳ ❚❡♠✲s❡ ✉♠ ❙❈ q✉❛♥❞♦ s✉❛s ♣r♦♣r✐❡❞❛❞❡s ♥ã♦ sã♦ ✉♠❛ ❝♦♥s❡q✉ê♥❝✐❛ ♥❛t✉r❛❧ ❞❡ s❡✉s ❡❧❡♠❡♥t♦s ❝♦♥st✐t✉✐♥t❡s ✈✐st♦s ✐s♦❧❛❞❛♠❡♥t❡✳ ❆s ♣r♦♣r✐❡❞❛❞❡s ❡♠❡r✲ ❣❡♥t❡s ❞❡ ✉♠ ❙❈ ❞❡❝♦rr❡♠ ❡♠ ❣r❛♥❞❡ ♣❛rt❡ ❞❛ r❡❧❛çã♦ ♥ã♦✲❧✐♥❡❛r ❡♥tr❡ ❛s ♣❛rt❡s✳ ❈♦st✉♠❛✲s❡ ❞✐③❡r q✉❡ ❡♠ ✉♠ ❙❈ ♦ t♦❞♦ é ♠❛✐s q✉❡ ❛ s♦♠❛ ❞❛s ♣❛rt❡s✳ ❖ ❡st✉❞♦ ❞♦s ❙❈ ✐♥❝❧✉❡♠ s✐st❡♠❛s s♦❝✐❛✐s ✭r❡❞❡s s♦❝✐❛✐s✮✱ ❜✐♦❧ó❣✐❝♦s ✭❝♦❧ô♥✐❛s ❞❡ ❛♥✐♠❛✐s✮✱ ❢ís✐❝♦s ✭❝❧✐♠❛✮ ❡♥tr❡ ♦✉tr♦s✳ ◆♦ q✉❡ s❡ r❡❢❡r❡ ❛s r❡❞❡s s♦❝✐❛✐s✱ ❝♦♠♦ s❡ ❝♦♠♣♦rt❛♠ ❛s r❡❞❡s r❡❛✐s❄✧
P❛r❛ ❛❜♦r❞❛r ❡st❡ ♣r♦❜❧❡♠❛✱ ❛ ❞✐ss❡rt❛çã♦ é ❞✐✈✐❞✐❞❛ s❡❣✉♥❞♦ ♦s ♦❜❥❡t✐✈♦s ❣❡r❛❧ ❡ ❡s♣❡❝í✜❝♦s ❛ s❡❣✉✐r✳
✶✳✸✳✶ ❖❜❥❡t✐✈♦ ●❡r❛❧
❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ✻
✶✳✸✳✷ ❖❜❥❡t✐✈♦s ❊s♣❡❝í✜❝♦s
❈♦♠ ❛ ✜♥❛❧✐❞❛❞❡ ❞❡ ❛❧❝❛♥ç❛r ♦ ♦❜❥❡t✐✈♦ ❣❡r❛❧ ❞❡st❛ ❞✐ss❡rt❛çã♦✱ ❢♦r❛♠ ❝♦♥s✐✲ ❞❡r❛❞♦s ♦s s❡❣✉✐♥t❡s ♦❜❥❡t✐✈♦s ❡s♣❡❝í✜❝♦s✿
• ❘❡♣r♦❞✉③✐r ❛tr❛✈és ❞❡ s✐♠✉❧❛çõ❡s ❝♦♠♣✉t❛❝✐♦♥❛✐s ♦s ♠♦❞❡❧♦s t❡ór✐❝♦s ♣❛r❛
♣♦st❡r✐♦r❡s ❛♥❛❧♦❣✐❛s❀
• ❈❛❧❝✉❧❛r ♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ ❛❣r❡❣❛çã♦ ❧♦❝❛❧ ❡ ♠é❞✐♦ ❞❛s r❡❞❡s s✐♠✉❧❛❞❛s❀
• ❈❛❧❝✉❧❛r ♦ ♠❡♥♦r ❝❛♠✐♥❤♦ ♠é❞✐♦ ♥❛s r❡❞❡s s✐♠✉❧❛❞❛s❀
• ❱❡r✐✜❝❛r ♦ ✈❛❧♦r ❞♦ ❡①♣♦❡♥t❡ ❞❛ ❧❡✐ ❞❡ ♣♦tê♥❝✐❛ q✉❡ ❣♦✈❡r♥❛ ❛ ❞✐str✐❜✉✐çã♦
❞❡ ❝♦♥❡❝t✐✈✐❞❛❞❡s ❞❡ ❝❛❞❛ r❡❞❡ s✐♠✉❧❛❞❛❀
• ❙✐♠✉❧❛r ❣r❛❢♦s ❛❧❡❛tór✐♦s ❝♦♠ ♦ ♠❡s♠♦ t❛♠❛♥❤♦ ❞❛s r❡❞❡s✳
✶✳✹ P♦r q✉❡ ❡st✉❞❛r ❆❘❙❄
❆ ♣❛rt✐r ❞❛ ❛♥á❧✐s❡ ❞❛s r❡❧❛çõ❡s ❡♥tr❡ ♦s ❛t♦r❡s✹ ❞❡ ✉♠❛ r❡❞❡ s♦❝✐❛❧✱ ♣♦❞❡♠♦s
♦❜t❡r ✐♥❢♦r♠❛çõ❡s s♦❜r❡ ❛ ❞✐♥â♠✐❝❛ ❞❡ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ♣❛r❝❡❧❛ ❞❛ s♦❝✐❡❞❛❞❡ ❛♥❛❧✐s❛❞❛ ❡✱ ❛ss✐♠✱ ❝♦♥str✉✐r ❡st✐♠❛t✐✈❛s ❡st❛tíst✐❝❛s ❛❝❡r❝❛ ❞❛ s♦❝✐❡❞❛❞❡ ❝♦♠♦ ✉♠ t♦❞♦✳ ❆❧é♠ ❞✐ss♦✱ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞♦s ❞❛❞♦s ❞❛ ❆❘❙ s❡r✈❡ ❞❡ ❜❛s❡ ♣❛r❛ ❛ ✐♥s♣❡çã♦ ❡ ❛♥á❧✐s❡ ❞❡ r❡s✉❧t❛❞♦s ❞❡ ✐♥✈❡st✐♠❡♥t♦s ❡♠ ❞✐✈❡rs♦s ❝❛♠♣♦s ❞❡ ✐♥t❡r❡ss❡✱ s❡❥❛♠ ❡st❡s ❡❝♦♥ô♠✐❝♦s✱ s♦❝✐❛✐s✱ ♠✉❞❛♥ç❛s ♥♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❝♦❧❡t✐✈♦✱ ❡t❝✳
❱❛❧❡ ❛ ♣❡♥❛ ❢r✐s❛r q✉❡ ♥♦s ú❧t✐♠♦s ❛♥♦s r❡✈✐st❛s ✐♠♣♦rt❛♥t❡s ♣❛r❛ ❛ ❝♦♠✉♥✐✲ ❞❛❞❡ ❝✐❡♥tí✜❝❛ t❛✐s ❝♦♠♦ P❤②s✐❝❛❧ ❘❡✈✐❡✇✱ ◆❛t✉r❡ ❡ ❙❝✐❡♥❝❡✱ ♣✉❜❧✐❝❛r❛♠ ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ ❛rt✐❣♦s s♦❜r❡ ❆❘❙ ❡✴♦✉ ❘❡❞❡s ❝♦♠♣❧❡①❛s✱ ♥❛ ✜❣✉r❛ ✶✳✹ é ♠♦str❛❞♦ ✉♠ ❣rá✜❝♦ ❝♦♠ ❛s ♣✉❜❧✐❝❛çõ❡s ♥❡ss❛ ár❡❛ ❞✉r❛♥t❡ ♦ ✜♥❛❧ ❞♦ sé❝✉❧♦ ❳❳ ❡ ❛ ♣r✐♠❡✐r❛ ❞é❝❛❞❛ ❞♦ sé❝✉❧♦ ❳❳■✳
✹❆q✉✐ ♦ t❡r♠♦ ❛t♦r❡s ❡stá s❡ r❡❢❡r✐♥❞♦ ❛ ❛çã♦ ❞♦s ❛❣❡♥t❡s q✉❡ ❢♦r♠❛♠ ❛ r❡❞❡✱ ♥♦ ❝❛♣ít✉❧♦ ✷
❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ✼
❈❛♣ít✉❧♦ ✷
❚❡♦r✐❛ ❞♦s ●r❛❢♦s ✲ ❯♠❛ ❛❜♦r❞❛❣❡♠
s✉❝✐♥t❛
✏❖s ❝♦♠♣✉t❛❞♦r❡s sã♦ ✐♥❝r✐✈❡❧♠❡♥t❡ rá♣✐❞♦s✱ ♣r❡❝✐s♦s ❡ ❜✉rr♦s❀ ♦s ❤♦♠❡♥s sã♦ ✐♥❝r✐✈❡❧♠❡♥t❡ ❧❡♥t♦s✱ ✐♠♣r❡❝✐s♦s ❡ ❜r✐❧❤❛♥t❡s❀ ❥✉♥t♦s✱ s❡✉s ♣♦❞❡r❡s ✉❧tr❛♣❛ss❛♠ ♦s ❧✐♠✐t❡s ❞❛ ✐♠❛❣✐♥❛çã♦✳✧
❆❧❜❡rt ❊✐♥st❡✐♥
✷✳✶ ❆♣r❡s❡♥t❛çã♦
◆❡st❡ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛♠✲s❡ ♦s ❛s♣❡❝t♦s ❤✐stór✐❝♦s ❞❛ ❝♦♥str✉çã♦ ❞❛ ❚❡♦r✐❛ ❞♦s ●r❛❢♦s✱ ♦s ❝♦♥❝❡✐t♦s ❜ás✐❝♦s ❞❡ ❣r❛❢♦✶ ❡♠ s✉❛ ❢♦r♠❛❧✐③❛çã♦ ♠❛t❡♠át✐❝❛✱ ❛ss✐♠
❝♦♠♦ ✉♠❛ ❛♣r❡s❡♥t❛çã♦ ❞♦s t✐♣♦s ❞❡ ❣r❛❢♦s✳ ❊st❡ tr❛❜❛❧❤♦ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❛❜♦r❞❛r ♦ t❡♠❛ ❞❛ ❢♦r♠❛ ♠❛✐s ❡①♣❧í❝✐t❛ ♣♦ssí✈❡❧✱ ♣❛r❛ t❛♥t♦ é ❢❡✐t❛ ✉♠❛ ❛♣r❡s❡♥✲ t❛çã♦ rá♣✐❞❛ ❡ s✐♠♣❧❡s q✉❡ ♣❡r♠✐t❛ ✉♠❛ ♠❡❧❤♦r ❝♦♠♣r❡❡♥sã♦ ❞♦s ❣r❛❢♦s ❡ ❛ s✉❛ ✉t✐❧✐❞❛❞❡ ♥♦ ❝♦t✐❞✐❛♥♦✳ ❖s ❝♦♥❝❡✐t♦s ❛❜♦r❞❛❞♦s ❛♦ ❧♦♥❣♦ ❞❡st❡ ❝❛♣ít✉❧♦ ♣♦❞❡♠
✶◆❛ ❝♦♥♦t❛çã♦ ❛t✉❛❧✱ ❛ ♣❛❧❛✈r❛ ✏❣r❛❢♦✑ ❢♦✐ ✉s❛❞❛ ♣r✐♠❡✐r❛♠❡♥t❡ ♣❡❧♦ ♠❛t❡♠át✐❝♦ ✐♥❣❧ês ❏❛♠❡s
❏♦s❡♣❤ ❙②❧✈❡st❡r ✭✶✽✶✹✲✶✽✾✼✮✳
❈❛♣ít✉❧♦ ✷✳ ❚❡♦r✐❛ ❞♦s ●r❛❢♦s ✲ ❯♠❛ ❛❜♦r❞❛❣❡♠ s✉❝✐♥t❛ ✾
s❡r ❡♥❝♦♥tr❛❞♦s ❡♠ ❬✾❪ ❡ ❬✶✵❪✳ ❆s ✜❣✉r❛s ✉s❛❞❛s ♥❡st❡ tr❛❜❛❧❤♦ sã♦ ❞❡✈✐❞❛♠❡♥t❡ ❝r❡❞✐t❛❞❛s✱ ❡①❝❡t✉❛♥❞♦✲s❡ ❛s q✉❡ ❢♦r❛♠ ❢❡✐t❛s ♣❡❧❛ ♣ró♣r✐❛ ❛✉t♦r❛✳
✷✳✷ ❯♠ ♣♦✉❝♦ ❞❛ ❍✐stór✐❛
❍✐st♦r✐❝❛♠❡♥t❡ ❛ ❚● ❢♦✐ ✐♥tr♦❞✉③✐❞❛ ♣❡❧♦ ♠❛t❡♠át✐❝♦ ▲❡♦♥❤❛r❞ P❛✉❧ ❊✉❧❡r ♥♦ sé❝✉❧♦ ❳❱■■■✳ ❉❡s❝♦♥s✐❞❡r❛♥❞♦ ♦ r✐❣♦r ♠❛t❡♠át✐❝♦✱ ✉♠ ❣r❛❢♦ ♣♦❞❡ s❡r ♣❡♥s❛❞♦ ❝♦♠♦ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣♦♥t♦s✱ ❝❤❛♠❛❞♦s ✈ért✐❝❡s ✭♥ós ♦✉ ♥♦❞♦s✮✱ ❝♦♥❡❝t❛❞♦s ♣♦r ❧✐♥❤❛s✱ ❝❤❛♠❛❞❛s ❞❡ ❛r❡st❛s✱ ❡ ❛ ❡st❛ ❡str✉t✉r❛ ❞❛r✲s❡ t❛♠❜é♠ ♦ ♥♦♠❡ ❞❡ r❡❞❡✳
❋✐❣✉r❛ ✷✳✶✿ ●r❛❢♦ ❝♦♠ ✹ ✈ért✐❝❡s ❡ ✻ ❛r❡st❛s✳
❊✉❧❡r ✜❝♦✉ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ♦ ♣❛✐ ❞❛ ❚● q✉❛♥❞♦ r❡s♦❧✈❡✉ ✭❡♠ ✶✼✸✻✮ ✉♠ ❢❛♠♦s♦ ♣r♦❜❧❡♠❛ ❞❡ s✉❛ é♣♦❝❛✱ ♦ Pr♦❜❧❡♠❛ ❞❛s P♦♥t❡s ❞❡ ❑ö♥✐❣s❜❡r❣✳ ❊①✐st✐❛♠ ❞✉❛s ✐❧❤❛s ❧✐❣❛❞❛s ✉♠❛ à ♦✉tr❛ ❡ ❛♦ r✐♦ Pr❡❣❡❧✷ ♣♦r s❡t❡ ♣♦♥t❡s ✭❋✐❣✉r❛ ✷✳✷❛✮✳ ❖
♣r♦❜❧❡♠❛ ❝♦♥s✐st✐❛ ❡♠ s❛✐r ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ♣♦♥t♦ q✉❛❧q✉❡r✱ ♣❛ss❛r ♣♦r t♦❞❛s ❛s ♣♦♥t❡s ✉♠❛ ú♥✐❝❛ ✈❡③ ❡ r❡t♦r♥❛r ❛♦ ♣♦♥t♦ ❞❡ ♣❛rt✐❞❛✳ ❊✉❧❡r ❞❡♠♦♥str♦✉ q✉❡ ♦ ♣r♦❜❧❡♠❛ ♥ã♦ t✐♥❤❛ s♦❧✉çã♦ ❡ ♣❛r❛ t❛♥t♦ ❛♣r❡s❡♥t♦✉ à ❆❝❛❞❡♠✐❛ ❞❡ ❈✐ê♥❝✐❛s ❘✉ss❛ ❞❡ ❙ã♦ P❡t❡rs❜✉r❣♦ ✉♠ ❞✐❛❣r❛♠❛ ❡♠ q✉❡ ❢❛③✐❛ ❛ s❡❣✉✐♥t❡ ❛♥❛❧♦❣✐❛✿ à t❡rr❛✱ r❡♣r❡s❡♥t❛❞❛ ♣❡❧❛s ❞✉❛s ♠❛r❣❡♥s✱ ❡ às ❞✉❛s ✐❧❤❛s✱ ❛ss♦❝✐♦✉ q✉❛tr♦ ♣♦♥t♦s❀ às s❡t❡ ♣♦♥t❡s✱ ❛ss♦❝✐♦✉ s❡t❡ ❧✐♥❤❛s ❬✶✶❪✱ ♣r♦❞✉③✐♥❞♦ ❛ss✐♠ ♦ q✉❡ ❤♦❥❡ ❝❤❛♠❛♠♦s ❞❡ ❣r❛❢♦ ✭❋✐❣✉r❛ ✷✳✷❜✮✳
✷❘✐♦ q✉❡ ❜❛♥❤❛✈❛ ❛ ♣❡q✉❡♥❛ ❝✐❞❛❞❡ ✉♥✐✈❡rs✐tár✐❛ ♣r✉ss✐❛♥❛ ❞❡ ❑ö♥✐❣s❜❡r❣✱ ❤♦❥❡ ❑❛❧✐♥✐♥❣r❛❞✱
❈❛♣ít✉❧♦ ✷✳ ❚❡♦r✐❛ ❞♦s ●r❛❢♦s ✲ ❯♠❛ ❛❜♦r❞❛❣❡♠ s✉❝✐♥t❛ ✶✵
❋✐❣✉r❛ ✷✳✷✿ ✭❛✮ Pr♦❜❧❡♠❛ ❞❛s s❡t❡ ♣♦♥t❡s ❞❡ ❑ö♥✐❣s❜❡r❣ ✭❋♦♥t❡✿ ❙✐t❡ ❞♦ ❈▼❆✲ ❋❯▲✮ ❡ ✭❜✮ ●r❛❢♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❛s ♣♦♥t❡s ❞❡ ❑ö♥✐❣s❜❡r❣✳
▼♦str❛r q✉❡ ♦ ♣r♦❜❧❡♠❛ ♥ã♦ t❡♠ s♦❧✉çã♦ é ❡q✉✐✈❛❧❡♥t❡ ❛ ♠♦str❛r q✉❡ ♦ ❣r❛❢♦ ❞❛ ❋✐❣✉r❛ ✷✳✷❜ ♥ã♦ ♣♦❞❡ s❡r ❛tr❛✈❡ss❛❞♦ ❬✾❪✳ ❊✉❧❡r ❣❡♥❡r❛❧✐③♦✉ ♦ ♣r♦❜❧❡♠❛ ❡ ❞❡s❡♥✈♦❧✈❡✉ ✉♠ ❝r✐tér✐♦ ♣❛r❛ q✉❡ ✉♠ ❣r❛❢♦ ♣✉❞❡ss❡ s❡r ❛tr❛✈❡ss❛❞♦✱ ❡st❡ ❞❡✈❡r✐❛ ❡st❛r ❝♦♥❡❝t❛❞♦ ❡ ❝❛❞❛ ✉♠ ❞❡ s❡✉s ♣♦♥t♦s s❡r ✐♥❝✐❞❡♥t❡ ❛ ✉♠ ♥ú♠❡r♦ ♣❛r ❞❡ ❧✐♥❤❛s✳ ◆♦ ❝❛s♦ ❞❛s ♣♦♥t❡s ❞❡ ❑ö♥✐❣s❜❡r❣ ❛ ♣r✐♠❡✐r❛ ❝♦♥❞✐çã♦ ❡r❛ s❛t✐s❢❡✐t❛✱ t♦❞❛✈✐❛ ❛ s❡❣✉♥❞❛ ♥ã♦✱ ✉♠❛ ✈❡③ q✉❡ ♦ ❣r❛❢♦ ♥ã♦ ♣♦ss✉í❛ ♥❡♥❤✉♠ ♣♦♥t♦ q✉❡ ❢♦ss❡ ✐♥❝✐❞❡♥t❡ ❛ ✉♠ ♣❛r ❞❡ ❧✐♥❤❛s✳ ❙❡♥❞♦ ❛ss✐♠ ❡r❛ ♥❡❝❡ssár✐♦ ❛ ✐♥❝❧✉sã♦ ❞❡ ♣❡❧♦ ♠❡♥♦s ♠❛✐s ✉♠❛ ♣♦♥t❡ ♣❛r❛ t♦r♥❛r ♦ ♣r♦❜❧❡♠❛ s♦❧✉❝✐♦♥á✈❡❧✳
❉❡ ❛❝♦r❞♦ ❝♦♠ ❍❛r❛r②✸✱ ✏❆ t❡♦r✐❛ ❞♦s ❣r❛❢♦s ❢♦✐ r❡❞❡s❝♦❜❡rt❛ ♠✉✐t❛s ✈❡③❡s✑✳
◆❡st❡ ❝❛s♦ ✈❛❧❡ ♦❜s❡r✈❛r q✉❡ ❞✉r❛♥t❡ ✉♠ ♣❡rí♦❞♦ ❞❡ ♠❛✐s ❞❡ ✶✺✵ ❛♥♦s✱ ❡♥tr❡ ❛ ❞❡♠♦♥str❛çã♦ ❞❡ ❊✉❧❡r ❡ ❛ ú❧t✐♠❛ ❞é❝❛❞❛ ❞♦ sé❝✉❧♦ ❳■❳✱ ❢♦✐ ✈❡r✐✜❝❛❞♦ ♦ s✉r❣✐♠❡♥t♦ ❞❡ ♣♦✉❝♦s tr❛❜❛❧❤♦s✳ ❊♥tr❡ ❡st❡s✱ ❡stá ♦ tr❛❜❛❧❤♦ ❞❡ ❑✐r❝❤❤♦✛✹ q✉❡✱ ❡♠ ✶✽✹✼✱
✉t✐❧✐③♦✉ ♠♦❞❡❧♦s ❞❡ ❣r❛❢♦s ♥♦ ❡st✉❞♦ ❞❡ ❝✐r❝✉✐t♦s ❡❧étr✐❝♦s ❝r✐❛♥❞♦ ❛ss✐♠ ♦ q✉❡
✸▼❛t❡♠át✐❝♦ ❡st❛❞✉♥✐❞❡♥s❡ ❋r❛♥❦ ❍❛r❛r② ✭✶✾✷✶✲✷✵✵✺✮ ❡s♣❡❝✐❛❧✐③❛❞♦ ❡♠ ❚●✳
✹●✉st❛✈ ❘♦❜❡rt ❑✐r❝❤❤♦✛ ✭✶✽✷✹ ✖ ✶✽✽✼✮ ✲ ❋ís✐❝♦ ❛❧❡♠ã♦✳ ❙✉❛s ❝♦♥tr✐❜✉✐çõ❡s ❝✐❡♥tí✜❝❛s ❢♦r❛♠
❈❛♣ít✉❧♦ ✷✳ ❚❡♦r✐❛ ❞♦s ●r❛❢♦s ✲ ❯♠❛ ❛❜♦r❞❛❣❡♠ s✉❝✐♥t❛ ✶✶
✜❝♦✉ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ❛ t❡♦r✐❛ ❞❛s ár✈♦r❡s✺✳ ❯♠❛ ❞é❝❛❞❛ ❞❡♣♦✐s✱ ❈❛②❧❡②✻❛ ❡①❡♠♣❧♦
❞❡ ❑✐r❝❤❤♦✛ tr✐❧❤❛r✐❛ ❛s ♠❡s♠❛s ✐❞❡✐❛s✱ ❡♠❜♦r❛ t❡♥❞♦ ♦✉tr❛ ✜♥❛❧✐❞❛❞❡ ❡ ♦✉tr❛s ❛♣❧✐❝❛çõ❡s ❡♠ ♠❡♥t❡✱ ❞❡♥tr❡ ❛s q✉❛✐s s❡ ❞❡st❛❝❛ ❛ ❡♥✉♠❡r❛çã♦ ❞♦s ✐sô♠❡r♦s ❞♦s ❤✐❞r♦❝❛r❜♦♥❡t♦s ❛❧✐❢át✐❝♦s s❛t✉r❛❞♦s✱ ❡♠ q✉í♠✐❝❛ ♦r❣â♥✐❝❛✳ ❊♠ ✶✽✻✾✱ ❏♦r❞❛♥✼ s❡
♦❝✉♣♦✉ t❛♠❜é♠ ❞❛s ár✈♦r❡s✱ ♣♦ré♠ ❝♦♠ ✉♠ ❡♥❢♦q✉❡ ❡str✐t❛♠❡♥t❡ ♠❛t❡♠át✐❝♦✳
▼✉✐t♦s ❡✈❡♥t♦s q✉❡ ❝♦♠ ♦ ♣❛ss❛r ❞♦s ❛♥♦s ♣r♦✈❛r❛♠ s❡r ✐♠♣♦rt❛♥t❡s✱ ♥♦ q✉❡ s❡ r❡❢❡r❡ ❛ ♠❛t❡♠át✐❝❛ ♣✉r❛✱ sã♦ r❡❧❛❝✐♦♥❛❞♦s ❝♦♠ ♣r♦❜❧❡♠❛s ❝♦♠ ♣♦✉❝❛ ❛♣❧✐❝❛çã♦ ♣rát✐❝❛✿ ❍❛♠✐❧t♦♥✽✱ ❡♠ ✶✽✺✾✱ ✐♥✈❡♥t♦✉ ✉♠ ❥♦❣♦ q✉❡ ❝♦♥s✐st✐❛ ♥❛ ❜✉s❝❛
❞❡ ✉♠ ♣❡r❝✉rs♦ ❢❡❝❤❛❞♦ ❡♥✈♦❧✈❡♥❞♦ t♦❞♦s ♦s ✈ért✐❝❡s ❞❡ ✉♠ ❞♦❞❡❝❛❡❞r♦ r❡❣✉❧❛r✱ ❞❡ t❛❧ ♠♦❞♦ q✉❡ ❝❛❞❛ ✉♠ ❞❡❧❡s ❢♦ss❡ ✈✐s✐t❛❞♦ ✉♠❛ ú♥✐❝❛ ✈❡③✳ ➱ ✐♥t❡r❡ss❛♥t❡✱ ❛❧✐ás✱ ♦❜s❡r✈❛r q✉❡ ♦s ♣r♦❜❧❡♠❛s ❞❡ ❍❛♠✐❧t♦♥ ❡ ❞❡ ❊✉❧❡r ❡♥❝♦♥tr❛r❛♠ ❛♣❧✐❝❛çã♦✱ r❡s♣❡❝t✐✈❛♠❡♥t❡ ✉♠ ❡ ❞♦✐s sé❝✉❧♦s ♠❛✐s t❛r❞❡✱ ♥♦ ❝❛♠♣♦ ❞❛ ♣❡sq✉✐s❛ ♦♣❡r❛❝✐♦♥❛❧✾✳
❑❡♠♣❡✶✵ ❡♠ ✶✽✼✾ ♣r♦❝✉r♦✉✱ s❡♠ s✉❝❡ss♦✱ ❞❡♠♦♥str❛r ❛ ✧❝♦♥❥❡❝t✉r❛ ❞❛s q✉❛tr♦
❝♦r❡s✧✶✶✱ ❛♣r❡s❡♥t❛❞❛ ♣♦r ●✉t❤r✐❡✶✷ ❛ ❉❡ ▼♦r❣❛♥✶✸✱ ❡♠ ✶✽✺✷✳
▼✉✐t♦s ❞♦s ♠❡❧❤♦r❡s ♠❛t❡♠át✐❝♦s ❞♦ sé❝✉❧♦ ❳❳ tr❛❜❛❧❤❛r❛♠ s❡r✐❛♠❡♥t❡ ♥♦ ♣r♦❜❧❡♠❛ ❞❛s q✉❛tr♦ ❝♦r❡s✳ ❊st❡ ❡st✉❞♦ t❡✈❡ ✉♠ ♣❛♣❡❧ ♠✉✐t♦ ✐♠♣♦rt❛♥t❡ ♥♦ ❞❡✲ s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ❚❡♦r✐❛ ❞♦s ●r❛❢♦s✳ P❡❧♦ ❝❛♠✐♥❤♦ ♠✉✐t❛s q✉❡stõ❡s ❢♦r❛♠ ♣♦st❛s ❡ ✈ár✐♦s ♣r♦❜❧❡♠❛s r❡❧❛❝✐♦♥❛❞♦s ❢♦r❛♠ r❡s♦❧✈✐❞♦s ❬✶✷❪✳
❍❡❛✇♦♦❞✶✹ ❡♠ ✶✽✾✵ ♠♦str♦✉ q✉❡ ❛ ♣r♦✈❛ ❞❡ ❑❡♠♣❡ ❡st❛✈❛ ❡rr❛❞❛✱ ♦❜t❡♥❞♦
✉♠❛ ♣r♦✈❛ ✈á❧✐❞❛✱ ♣♦ré♠ ♣❛r❛ ❝✐♥❝♦ ❝♦r❡s❀ ❛ ♣r♦✈❛ ♣❛r❛ ❛s q✉❛tr♦ ❝♦r❡s ❢♦✐ ♦❜t✐❞❛ ❛♣❡♥❛s ❡♠ ✶✾✼✻✳ ❆ ✐♠♣♦rtâ♥❝✐❛ ❞♦ ♣r♦❜❧❡♠❛ r❡s✐❞❡ ♥♦s ❞❡s❡♥✈♦❧✈✐♠❡♥t♦s t❡ór✐❝♦s
✺❯♠❛ ár✈♦r❡ é ✉♠ ❣r❛❢♦ ♥♦ q✉❛❧ ❡①✐st❡ ✉♠ ❝❛♠✐♥❤♦ ❡♥tr❡ q✉❛✐sq✉❡r ❞♦✐s ❞❡ s❡✉s ✈ért✐❝❡s ❡
q✉❡ ♥ã♦ ♣♦ss✉✐ ❝✐❝❧♦s✳
✻❆rt❤✉r ❈❛②❧❡② ✭ ✶✽✷✶ ✖ ✶✽✾✺✮ ✲ ▼❛t❡♠át✐❝♦ ❜r✐tâ♥✐❝♦✳ ❆s s✉❛s ❝♦♥tr✐❜✉✐çõ❡s ✐♥❝❧✉❡♠ ❛
♠✉❧t✐♣❧✐❝❛çã♦ ❞❡ ♠❛tr✐③❡s ❡ ♦ t❡♦r❡♠❛ ❞❡ ❈❛②❧❡②✳
✼❲✐❧❤❡❧♠ ❏♦r❞❛♥ ✭✶✽✹✷ ✖ ✶✽✾✾✮ ✲ ●❡♦❞❡s✐st❛ ❡ ♠❛t❡♠át✐❝♦ ❛❧❡♠ã♦✳
✽❲✐❧❧✐❛♠ ❘♦✇❛♥ ❍❛♠✐❧t♦♥ ✭✶✽✵✺ ✖ ✶✽✻✺✮ ✲ ▼❛t❡♠át✐❝♦✱ ❢ís✐❝♦ ❡ ❛strô♥♦♠♦ ✐r❧❛♥❞ês✳ ✾➱ ♦ ✉s♦ ❞❡ ♠♦❞❡❧♦s ♠❛t❡♠át✐❝♦s✱ ❡st❛tíst✐❝❛ ❡ ❛❧❣♦r✐t♠♦s ♣❛r❛ ❛❥✉❞❛r ♥❛ t♦♠❛❞❛ ❞❡ ❞❡❝✐sõ❡s✳
➱ ✉♠❛ ❢♦r♠❛ ❞❡ ♠❛t❡♠át✐❝❛ ❛♣❧✐❝❛❞❛✳
✶✵❙✐r ❆❧❢r❡❞ ❇r❛② ❑❡♠♣❡ ✭✶✽✹✾ ✕ ✶✾✷✷✮ ✲ ▼❛t❡♠át✐❝♦ ✐♥❣❧ês✳
✶✶❚r❛t❛✲s❡ ❞❡ ♣r♦✈❛r q✉❡ t♦❞♦ ♠❛♣❛ ❞❡s❡♥❤❛❞♦ ♥♦ ♣❧❛♥♦ ❡ ❞✐✈✐❞✐❞♦ ❡♠ ✉♠ ♥ú♠❡r♦ q✉❛❧q✉❡r
❞❡ r❡❣✐õ❡s ♣♦❞❡ s❡r ❝♦❧♦r✐❞♦ ❝♦♠ ✉♠ ♠á①✐♠♦ ❞❡ q✉❛tr♦ ❝♦r❡s s❡♠ q✉❡ ❞✉❛s r❡❣✐õ❡s ❢r♦♥t❡✐r✐ç❛s r❡❝❡❜❛♠ ❛ ♠❡s♠❛ ❝♦r✳
✶✷❋r❛♥❝✐s ●✉t❤r✐❡ ✭✶✽✸✶ ✲ ✶✽✾✾✮ ✲ ▼❛t❡♠át✐❝♦ ❡ ❜♦tâ♥✐❝♦ s✉❧✲❛❢r✐❝❛♥♦✳
✶✸❆✉❣✉st✉s ❉❡ ▼♦r❣❛♥ ✭✶✽✵✻ ✖ ✶✽✼✶✮ ✲ ▼❛t❡♠át✐❝♦ ❡ ❧ó❣✐❝♦ ❜r✐tâ♥✐❝♦✳ ❋♦r♠✉❧♦✉ ❛s ▲❡✐s ❞❡
❉❡ ▼♦r❣❛♥ ❡ ❢♦✐ ♦ ♣r✐♠❡✐r♦ ❛ ✐♥tr♦❞✉③✐r ♦ t❡r♠♦ ❡ t♦r♥❛r r✐❣♦r♦s❛ ❛ ✐❞❡✐❛ ❞❛ ✐♥❞✉çã♦ ♠❛t❡♠át✐❝❛✳
❈❛♣ít✉❧♦ ✷✳ ❚❡♦r✐❛ ❞♦s ●r❛❢♦s ✲ ❯♠❛ ❛❜♦r❞❛❣❡♠ s✉❝✐♥t❛ ✶✷
tr❛③✐❞♦s ♣❡❧❛s t❡♥t❛t✐✈❛s ❞❡ r❡s♦❧✈ê✲❧♦✱ ❛s q✉❛✐s ❡♥r✐q✉❡❝❡r❛♠ ❛ ❚● ❡♠ ❞✐✈❡rs♦s r❡❝✉rs♦s ❛♦ ❧♦♥❣♦ ❞❛ ♣r✐♠❡✐r❛ ♠❡t❛❞❡ ❞♦ sé❝✉❧♦ ❳❳✿ ❡①❡♠♣❧✐✜❝❛♥❞♦✱ ❇✐r❦❤♦✛✶✺
❡♠ ✶✾✶✷ ❞❡✜♥✐✉ ♦s ♣♦❧✐♥ô♠✐♦s ❝r♦♠át✐❝♦s❀ ❲❤✐t♥❡②✶✻ ❡♠ ✶✾✸✶ ❝r✐♦✉ ❛ ♥♦çã♦ ❞❡
❣r❛❢♦ ❞✉❛❧ ❡ ❇r♦♦❦s✶✼❬✶✸❪ ❡♠ ✶✾✹✶ ❡♥✉♥❝✐♦✉ ✉♠ t❡♦r❡♠❛ ❢♦r♥❡❝❡♥❞♦ ✉♠ ❧✐♠✐t❡ ♣❛r❛
♦ ♥ú♠❡r♦ ❝r♦♠át✐❝♦ ❞❡ ✉♠ ❣r❛❢♦✳
P♦❞❡✲s❡ ❝✐t❛r t❛♠❜é♠ ♦✉tr♦s ❡✈❡♥t♦s ❝♦♥s✐❞❡rá✈❡✐s✿ ▼❡♥❣❡r✶✽✭✶✾✷✻✮ ❞❡♠♦♥s✲
tr♦✉ ✉♠ ✐♠♣♦rt❛♥t❡ t❡♦r❡♠❛ s♦❜r❡ ❛ ❝♦♥❡❝t✐✈✐❞❛❞❡ ❡♠ ❣r❛❢♦s ✜♥✐t♦s ♥ã♦ ❞✐r❡❝✐✲ ♦♥❛❞♦s q✉❡ ✜❝♦✉ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ✭❚❡♦r❡♠❛ ❞❡ ▼❡♥❣❡r✮ ❡ ❑✉r❛t♦✇s❦✐✶✾ ❡♠ ✶✾✸✵
❡♥❝♦♥tr♦✉ ✉♠❛ ❝♦♥❞✐çã♦ ♣❛r❛ ❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞❡ ❣r❛❢♦s ♣❧❛♥❛r❡s✳ ❚✉rá♥✷✵ ❡♠
✶✾✹✶ ❢♦✐ ♦ ♣✐♦♥❡✐r♦ ♥❛ t❡♦r✐❛ ❡①tr❡♠❛❧ ❞♦s ❣r❛❢♦s q✉❡ r❡s✉❧t♦✉ ♥♦ ✭❚❡♦r❡♠❛ ❞❡ ❚✉rá♥✮ ❡ ❚✉tt❡✷✶ ❡♠ ✶✾✹✼ ❝❧❛ss✐✜❝♦✉ ♦s ❣r❛❢♦s s✐♠étr✐❝♦s ❝ú❜✐❝♦s ♣❡❧♦ ♠❡♥♦r ♥ú✲
♠❡r♦ ✐♥t❡✐r♦ st❛❧ q✉❡ ❝❛❞❛ ❞♦✐s ❝❛♠✐♥❤♦s ♦r✐❡♥t❛❞♦s ❞❡ ❝♦♠♣r✐♠❡♥t♦s ♣♦❞❡♠ s❡r
♠❛♣❡❛❞♦s ❡♥tr❡ s✐ ♣♦r ❡①❛t❛♠❡♥t❡ ✉♠❛ s✐♠❡tr✐❛ ❞♦ ❣r❛❢♦✳ ❊❧❡ ♠♦str♦✉ q✉❡s é ♥♦
♠á①✐♠♦ ✺✱ ❡ ❞❡✉ ❡①❡♠♣❧♦s ❞❡ ❣r❛❢♦s ❝♦♠ ❝❛❞❛ ✈❛❧♦r ♣♦ssí✈❡❧ ❞❡ s ❞❡ ✶ ❛ ✺❬✶✹❪✳ ➱
✐♠♣♦rt❛♥t❡ ❢r✐s❛r q✉❡ ♦ ♣r✐♠❡✐r♦ ❧✐✈r♦ s♦❜r❡ ❚● ❢♦✐ ✭❚❤❡♦r✐❡ ❞❡r ❡♥❞❧✐❝❤❡♥ ✉♥❞ ✉♥❡♥❞❧✐❝❤❡♥ ●r❛♣❤❡♥✮✱ ♣✉❜❧✐❝❛❞♦ ♣❡❧❛ ❆❦❛❞❡♠✐s❝❤❡♥ ❱❡r❧❛❣s❣❡s❡❧❧s❝❤❛❢t ❊❞✐t♦r❛ ❆❝❛❞ê♠✐❝❛ ❞❡ ▲❡✐♣③✐❣ ❡♠ ✶✾✸✻ ❡s❝r✐t♦ ♣♦r ❑ö♥✐❣✷✷✱ ✉♠❛ é♣♦❝❛ ♥❛ q✉❛❧✱ ❝♦♥❢♦r♠❡
❲✐❧❞❡r✷✸✱ ♦ ❛ss✉♥t♦ ❡r❛ ❝♦♥s✐❞❡r❛❞♦ ✧✉♠ ❝❛♠♣♦ ♠♦rt♦✧✳
❆ ♣❛rt✐r ❞❡ ✶✾✺✻✱ ❝♦♠ ❛ ♣✉❜❧✐❝❛çã♦ ❞♦s tr❛❜❛❧❤♦s ❞❡ ❋♦r❞✷✹ ❡ ❋✉❧❦❡rs♦♥✷✺✱
✶✺●❡♦r❣❡ ❉❛✈✐❞ ❇✐r❦❤♦✛ ✭✶✽✽✹ ✖ ✶✾✹✹✮ ✲ ▼❛t❡♠át✐❝♦ ❡st❛❞✉♥✐❞❡♥s❡✱ ♠❛✐s ❝♦♥❤❡❝✐❞♦ ♣❡❧❛
❡❧❛❜♦r❛çã♦ ❞♦ t❡♦r❡♠❛ ❡r❣ó❞✐❝♦✳
✶✻❍❛ss❧❡r ❲❤✐t♥❡② ✭✶✾✵✼ ✲ ✶✾✽✾✮ ✲ ▼❛t❡♠át✐❝♦ ❡st❛❞✉♥✐❞❡♥s❡✳ ❋♦✐ ✉♠ ❞♦s ❢✉♥❞❛❞♦r❡s ❞❛ t❡♦r✐❛
❞❛ s✐♥❣✉❧❛r✐❞❛❞❡✳
✶✼❘♦✇❧❛♥❞ ▲❡♦♥❛r❞ ❇r♦♦❦s ✭✶✾✶✻ ✲ ✶✾✾✸✮ ✲ ▼❛t❡♠át✐❝♦ ✐♥❣❧ês✳ ✶✽❑❛r❧ ▼❡♥❣❡r ✭✶✾✵✷ ✖ ✶✾✽✺✮ ✲ ▼❛t❡♠át✐❝♦ ❛✉strí❛❝♦✳
✶✾❑❛③✐♠✐❡r③ ❑✉r❛t♦✇s❦✐ ✭✶✽✾✻✲✶✾✽✵✮ ✲ ▼❛t❡♠át✐❝♦ ♣♦❧♦♥ês ❝✉❥❛ ♣❡sq✉✐s❛ s❡ ❝♦♥❝❡♥tr♦✉ ♥❛
ár❡❛ ❞❡ t♦♣♦❧♦❣✐❛✳
✷✵P❛✉❧ ✭Pá❧✮ ❚✉rá♥ ✭✶✾✶✵ ✖ ✶✾✼✻✮ ✲ ▼❛t❡♠át✐❝♦ ❤ú♥❣❛r♦✳ ❚r❛❜❛❧❤♦✉ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❝♦♠
t❡♦r✐❛ ❞♦s ♥ú♠❡r♦s✳ ❚❡✈❡ ✉♠❛ ❧♦♥❣❛ ❝♦❧❛❜♦r❛çã♦ ❝♦♠ P❛✉❧ ❊r❞ös✳
✷✶❲✐❧❧✐❛♠ ❚❤♦♠❛s ❚✉tt❡ ✱ t❛♠❜é♠ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ❇✐❧❧ ❚✉tt❡ ✭✶✾✶✼ ✲ ✷✵✵✷✮ ✲ ▼❛t❡♠át✐❝♦ ❡
✏❈♦❞❡❜r❡❛❦❡r✑ ❜r✐tâ♥✐❝♦✳ ❉✉r❛♥t❡ ❛ ■■ ●✉❡rr❛ ▼✉♥❞✐❛❧✱ ❡❧❡ ❢❡③ ✉♠ ❛✈❛♥ç♦ ❜r✐❧❤❛♥t❡ ❡ ❢✉♥❞❛♠❡♥✲ t❛❧ ❡♠ ❈r✐♣t♦❛♥á❧✐s❡ ❞❛ ❝✐❢r❛ ▲♦r❡♥③✱ ✉♠ ❞♦s ♣r✐♥❝✐♣❛✐s s✐st❡♠❛s ❞❡ ❝✐❢r❛s ❛❧❡♠ã♦✳ ❆ ✐♥t❡❧✐❣ê♥❝✐❛ ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞❡ s❡✉ tr❛❜❛❧❤♦ t❡✈❡ ✉♠ ✐♠♣❛❝t♦ s✐❣♥✐✜❝❛t✐✈♦ s♦❜r❡ ❛ ✈✐tór✐❛ ❞♦s ❆❧✐❛❞♦s ♥❛ ❊✉r♦♣❛✳
✷✷❉é♥❡s ❑ö♥✐❣ ✭✶✽✽✹ ✖ ✶✾✹✹✮ ✲ ▼❛t❡♠át✐❝♦ ❤ú♥❣❛r♦✳
✷✸❘❛②♠♦♥❞ ▲♦✉✐s ❲✐❧❞❡r ✭✶✽✾✻ ✲ ✶✾✽✷✮ ✲ ▼❛t❡♠át✐❝♦ ❡st❛❞✉♥✐❞❡♥s❡✱ q✉❡ s❡ ❡s♣❡❝✐❛❧✐③♦✉ ❡♠
t♦♣♦❧♦❣✐❛ ❡ ❣r❛❞✉❛❧♠❡♥t❡ ❛❞q✉✐r✐✉ ✐♥t❡r❡ss❡s ✜❧♦só✜❝♦s ❡ ❛♥tr♦♣♦❧ó❣✐❝♦s✳
❈❛♣ít✉❧♦ ✷✳ ❚❡♦r✐❛ ❞♦s ●r❛❢♦s ✲ ❯♠❛ ❛❜♦r❞❛❣❡♠ s✉❝✐♥t❛ ✶✸
❇❡r❣❡✷✻ ❡♠ ✶✾✺✼ ❡ ❖r❡✷✼ ❡♠ ✶✾✻✷✱ ♦ ✐♥t❡r❡ss❡ ♣❡❧❛ ❚● ❝♦♠❡ç♦✉ ❛ ❛✉♠❡♥t❛r✱
❝r❡s❝❡♥❞♦ r❛♣✐❞❛♠❡♥t❡ ♥♦ ♠✉♥❞♦ t♦❞♦✳ ❆ ✐♠❡♥s❛ ♠❛✐♦r✐❛ ❞♦s ❧✐✈r♦s s♦❜r❡ ❣r❛❢♦s ❢♦✐ ♣✉❜❧✐❝❛❞❛ ❞❡♣♦✐s ❞❡ ✶✾✼✵✱ ❡♠ ❣r❛♥❞❡ ♣❛rt❡ s♦❜ ❛ ✐♥✢✉ê♥❝✐❛ ❞❛s ♦❜r❛s ❞❡ ❇❡r❣❡ ❡ ❍❛r❛r②✳ ❖ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦s ❝♦♠♣✉t❛❞♦r❡s ❧❡✈♦✉ à ♣✉❜❧✐❝❛çã♦ ❞❡ ✈ár✐❛s ♦❜r❛s ❞❡❞✐❝❛❞❛s ❛♦s ❛❧❣♦r✐t♠♦s ❞❡ ❣r❛❢♦s✱ ❛❜r✐♥❞♦ ❛ss✐♠ ♣♦ss✐❜✐❧✐❞❛❞❡s ❝r❡s❝❡♥t❡s ❞❡ ✉t✐❧✐③❛çã♦ ❛♣❧✐❝❛❞❛ ❞❛ t❡♦r✐❛✳
✷✳✷✳✶ ❆s ❊s❝♦❧❛s ❞❛ ❚●
•❆ ♣r✐♠♦❣ê♥✐t❛ é ❛ ❊s❝♦❧❛ ❤ú♥❣❛r❛✱ t❡✈❡ ♦r✐❣❡♠ ♥♦s tr❛❜❛❧❤♦s ❞❡ ❑ö♥✐❣ ❡ ❢♦✐
❞❡s❡♥✈♦❧✈✐❞❛ ♣♦r ❊r❞ös✱ ❍❛❥♥ã❧✱ ❚✉rá♥ ❡♥tr❡ ♦✉tr♦s✳ ❖ ♣r✐♥❝✐♣❛❧ ✐♥t❡r❡ss❡ ❞❡ss❛ ❡s❝♦❧❛ ❞❡r✐✈♦✉ ❞❛ ❛♥á❧✐s❡ ❝♦♠❜✐♥❛tór✐❛ ❡ ❛❧❣✉♥s ❞❡ s❡✉s ❛✉t♦r❡s s❡ ❞❡❞✐❝❛r❛♠ à t❡♦r✐❛ ❡①tr❡♠❛❧✳ ❍❛❜✐t✉❛❧♠❡♥t❡✱ ❡ss❛ ❡s❝♦❧❛ tr❛❜❛❧❤❛ ❝♦♠ ❣r❛❢♦s ♥ã♦ ♦r✐❡♥t❛❞♦s✳
• ❆ ❊s❝♦❧❛ ❢r❛♥❝❡s❛✱ tr❛❜❛❧❤❛ ❝♦♠ ❣r❛❢♦s ♦r✐❡♥t❛❞♦s✳ ◆❛s ♣❛❧❛✈r❛s ❞❡ ❈❧❛✉❞❡
❇❡r❣❡✿ ✏t♦❞♦ ❣r❛❢♦ é ♦r✐❡♥t❛❞♦✱ ♣♦❞❡♥❞♦✲s❡ ❡✈❡♥t✉❛❧♠❡♥t❡ ❞❡s❝♦♥s✐❞❡r❛r ❛ ♦r✐❡♥✲ t❛çã♦✑❀ ❡ss❛ ❡s❝♦❧❛ ❞❡❞✐❝❛✲s❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ às ❛♣❧✐❝❛çõ❡s ♥♦ ❝❛♠♣♦ ❞❛ ♣❡sq✉✐s❛ ♦♣❡r❛❝✐♦♥❛❧✳ ❆❧❣✉♥s ♥♦♠❡s ❞❡ ❡①tr❡♠❛ r❡❧❡✈â♥❝✐❛ t❛♥t♦ ♥❛ ♣❡sq✉✐s❛ q✉❛♥t♦ ♥❛ ❞✐✲ ✈✉❧❣❛çã♦ ❞❛ t❡♦r✐❛ ❡ ❞❡ s✉❛s ❛♣❧✐❝❛çõ❡s sã♦ ●❤♦✉✐❧❛✲❍♦✉r✐✱ ❑❛✉❢♠❛♥♥✱ ❘♦✉❝❛✐r♦❧✱ ❋❛✉r❡ ❡ ▼✐♥♦✉①✳
• ❆ ❊s❝♦❧❛ ❛♠❡r✐❝❛♥❛ t❡♠ ❣r❛♥❞❡ ✐♥✢✉ê♥❝✐❛ ❞♦ tr❛❜❛❧❤♦ ❞❡ ❍❛r❛r②✳ ◆❡st❛
❡s❝♦❧❛ ❤á ♣r❡❢❡rê♥❝✐❛ ♣❡❧♦ ❡st✉❞♦ ❞❡ ❣r❛❢♦s ♥ã♦ ♦r✐❡♥t❛❞♦s ❝♦♠♦ ♥❛ ❡s❝♦❧❛ ❤ú♥❣❛r❛✱ ♠❛s t❛♠❜é♠ ❞❛r✲s❡ ❞❡✈✐❞❛ ❛t❡♥çã♦ ❛♦ ❣r❛❢♦s ♦r✐❡♥t❛❞♦s✳ P❡sq✉✐s❛❞♦r❡s ✐♠♣♦rt❛♥✲ t❡s ❞❡ss❛ ❡s❝♦❧❛ sã♦ ❈❤❛rtr❛♥❞✱ ❖r❡✱ ❍✉✱ ❋✉❧❦❡rs♦♥ ❡ ❲❤✐t♥❡②✳
• ❆ ■♥❣❧❛t❡rr❛✱ ♦ ❈❛♥❛❞á ❡ ❛ ❡①✲❯♥✐ã♦ ❙♦✈✐ét✐❝❛✷✽✱ ❞❡r❛♠ ❝♦♥tr✐❜✉✐çõ❡s s✐❣✲
♥✐✜❝❛t✐✈❛s ♣❛r❛ ♦ t❡♠❛ ❛ss✐♠ ❝♦♠♦ ♣♦ss✉❡♠ ❞✐✈❡rs♦s ♥♦♠❡s ❞❡ r❡❧❡✈♦✳
✷✻❈❧❛✉❞❡ ❇❡r❣❡ ✭✶✾✷✻ ✖ ✷✵✵✷✮ ✲ ▼❛t❡♠át✐❝♦ ❢r❛♥❝ês✳ ➱ ❝♦♥❤❡❝✐❞♦ ♣❡❧❛ ❝♦♥❥❡❝t✉r❛ ❞♦ ❣r❛❢♦
♣❡r❢❡✐t♦ ❡ ♣❡❧♦ ❧❡♠❛ ❞❡ ❇❡r❣❡✳
✷✼Ø②st❡✐♥ ❖r❡ ✭✶✽✾✾ ✖ ✶✾✻✽✮ ✲ ▼❛t❡♠át✐❝♦ ♥♦r✉❡❣✉ês✳
✷✽ ❖✜❝✐❛❧♠❡♥t❡ ❯♥✐ã♦ ❞❛s ❘❡♣ú❜❧✐❝❛s ❙♦❝✐❛❧✐st❛s ❙♦✈✐ét✐❝❛s ❯❘❙❙✱ ❡r❛ ✉♠ ❊st❛❞♦ s♦❝✐❛❧✐st❛
❈❛♣ít✉❧♦ ✷✳ ❚❡♦r✐❛ ❞♦s ●r❛❢♦s ✲ ❯♠❛ ❛❜♦r❞❛❣❡♠ s✉❝✐♥t❛ ✶✹
•❚❡♠♦s ❛✐♥❞❛ ♦s ♣❡sq✉✐s❛❞♦r❡s ❞❡ ❛♣❧✐❝❛çõ❡s ❡s♣❡❝í✜❝❛s✱ ❡♠ ♣❛rt✐❝✉❧❛r ♦s ❞❡✲
❞✐❝❛❞♦s às ❛♣❧✐❝❛çõ❡s ❡♠ ❡❧❡❝tr✐❝✐❞❛❞❡✿ ❈❤❡♥✱ ❙❡s❤✉✱ ❘❡❡❞✱ ❏♦❤♥s♦♥✳ ❊ss❡ tr❛❜❛❧❤♦ s❡ ❝❛r❛❝t❡r✐③❛ ♣❡❧♦ ✉s♦ ❞❡ ✉♠ s✉❜❝♦♥❥✉♥t♦ ❜❛st❛♥t❡ ❝❛r❛❝t❡ríst✐❝♦ ❞♦s r❡❝✉rs♦s ❞❛ t❡♦r✐❛✱ ❛s ♦r✐❣❡♥s✱ ❡✈✐❞❡♥t❡♠❡♥t❡✱ ❡stã♦ ♥♦ tr❛❜❛❧❤♦ ❞❡ ❑✐r❝❤❤♦✛✳ ❚ê♠✲s❡ t❛♠❜é♠ ❛ ❝❤❛♠❛❞❛ ✏t❡♦r✐❛ ❞♦ ❡q✉✐❧í❜r✐♦ ❡str✉t✉r❛❧✑ ♥❛s ❛♣❧✐❝❛çõ❡s ❛ ♣s✐❝♦ss♦❝✐♦❧♦❣✐❛✱ ❜❛s❡✲ ❛❞❛ ♥❛s ✐❞❡✐❛s ❞❡ ▼♦r❡♥♦❀ ❞✐✈❡rs♦s ❛s♣❡❝t♦s ❞❛ t❡♦r✐❛ ❞❛s ár✈♦r❡s ♥❛s ❛♣❧✐❝❛çõ❡s à ❝♦♠♣✉t❛çã♦❀ ❡ ❛ t❡♦r✐❛ ❞♦s ✢✉①♦s ❡♠ r❡❞❡s ♥❛s ❛♣❧✐❝❛çõ❡s ❞❡ ♣❡sq✉✐s❛ ♦♣❡r❛❝✐♦♥❛❧ ❡♠ tr❛♥s♣♦rt❡s ❡ ❝♦♠✉♥✐❝❛çõ❡s ❬✶✺❪✳
✷✳✸ ❋♦r♠❛❧✐s♠♦
✷✳✸✳✶ ❉❡✜♥✐çã♦ ❞❡ ●r❛❢♦s
▼✉✐t❛s s✐t✉❛çõ❡s ♣♦❞❡♠ s❡r ❝♦♥✈❡♥✐❡♥t❡♠❡♥t❡ ❞❡s❝r✐t❛s ❛tr❛✈és ❞❡ ❞✐❛❣r❛♠❛s q✉❡ ❝♦♥s✐st❡♠ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣♦♥t♦s✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❧✐♥❤❛s q✉❡ ❧✐❣❛♠ ❛❧❣✉♥s ♣❛r❡s ❞❡st❡s ♣♦♥t♦s✳ P♦r ❡①❡♠♣❧♦✿ ♦s ♣♦♥t♦s ♣♦❞❡♠ r❡♣r❡s❡♥t❛r ♣❡ss♦❛s✱ ❛s ❧✐♥❤❛s ❧✐❣❛♠ ♣❛r❡s ❞❡ ❛♠✐❣♦s❀ ♦s ♣♦♥t♦s ♣♦❞❡♠ r❡♣r❡s❡♥t❛r ❝❡♥tr♦s ❞❡ ❝♦♠✉♥✐❝❛çã♦✱ ❛s ❧✐♥❤❛s ❧✐❣❛çõ❡s ❡♥tr❡ ♦s ❝❡♥tr♦s✳ ❆ ❛❜str❛çã♦ ♠❛t❡♠át✐❝❛ ❞❡ s✐t✉❛çõ❡s ❞❡ss❡ t✐♣♦ ❞á ❧✉❣❛r ❛♦ ❝♦♥❝❡✐t♦ ❞❡ ❣r❛❢♦ ❬✶✻❪✳
❉♦r❛✈❛♥t❡ s❡rã♦ tr❛❜❛❧❤❛❞♦s ♦s ❛s♣❡❝t♦s ❜ás✐❝♦s ❞❛ ❚● ❞❡ ❢♦r♠❛ s✐♥tét✐❝❛ s♦❜ ❛ ❧✉③ ❞♦s ❢✉♥❞❛♠❡♥t♦s ♠❛t❡♠át✐❝♦s✳ P❛r❛ q✉❛❧q✉❡r ❝♦♥❥✉♥t♦V✱ s❡rá ❞❡♥♦t❛❞♦ ♣♦r V(2) ♦ ❝♦♥❥✉♥t♦ ❞❡ t♦❞♦s ♦s ♣❛r❡s ♥ã♦ ♦r❞❡♥❛❞♦s ❞❡ ❡❧❡♠❡♥t♦s ❞❡ V✳ ❙❡ V t❡♠ n
❡❧❡♠❡♥t♦s ❡♥tã♦ V(2) t❡♠
n
2
= n(n−1)
2 ✭✷✳✶✮
❡❧❡♠❡♥t♦s✳ ❖s ❡❧❡♠❡♥t♦s ❞❡V(2) s❡rã♦ ✐❞❡♥t✐✜❝❛❞♦s ❝♦♠ ♦s s✉❜❝♦♥❥✉♥t♦s ❞❡V q✉❡
tê♠ ❝❛r❞✐♥❛❧✐❞❛❞❡✷✾ ✷✳ ❆ss✐♠✱ ❝❛❞❛ ❡❧❡♠❡♥t♦ ❞❡ V(2) t❡rá ❛ ❢♦r♠❛ {v, w} s❡♥❞♦ v
❡ w ❞♦✐s ❡❧❡♠❡♥t♦s ❞✐st✐♥t♦s ❞❡ V✳
