❯s♦ ❞❡ ❆❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ♥♦
❛❥✉st❡ ❧✐♥❡❛r ❛tr❛✈és ❞❡ ❞❛❞♦s
❡①♣❡r✐♠❡♥t❛✐s
♣♦r
❊r✐♥❛❧❞♦ ▲❡✐t❡ ❙✐q✉❡✐r❛ ❏ú♥✐♦r
❯s♦ ❞❡ ❆❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ♥♦
❛❥✉st❡ ❧✐♥❡❛r ❛tr❛✈és ❞❡ ❞❛❞♦s
❡①♣❡r✐♠❡♥t❛✐s
†
♣♦r
❊r✐♥❛❧❞♦ ▲❡✐t❡ ❙✐q✉❡✐r❛ ❏ú♥✐♦r
s♦❜ ♦r✐❡♥t❛çã♦ ❞❡
Pr♦❢✳ ❉r✳ ◆❛♣♦❧❡♦♥ ❈❛r♦ ❚✉❡st❛
Pr♦❥❡t♦ ❞❡ ❚r❛❜❛❧❤♦ ❞❡ ❈♦♥❝❧✉sã♦ ❞❡ ❈✉rs♦ ❞♦ ❈✉rs♦ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ▼❛t❡♠át✐❝❛ ❡♠ r❡❞❡ ◆❛❝✐♦♥❛❧ ✲ P❘❖❋▼❆❚ ✲ ❉▼ ✲ ❈❈❊◆ ✲ ❯❋P❇✱ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ▼❛t❡♠át✐❝❛✳
▼❛✐♦✴✷✵✶✺ ❏♦ã♦ P❡ss♦❛ ✲ P❇
S618u Siqueira Júnior, Erinaldo Leite.
Uso de algoritmo genético no ajuste linear através de dados experimentais / Erinaldo Leite Siqueira Júnior.- João Pessoa, 2015.
52f. : il.
Orientador: Napoleón Caro Tuesta Dissertação (Mestrado) - UFPB/CCEN
1. Matemática. 2. Algoritmo genético. 3. Otimização. 4. Ajuste linear. 5. Mínimos quadrados. 6. Computação natural.
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s ♣✳ ✈✐✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ♣✳ ✐①
❘❡s✉♠♦ ♣✳ ✶✵
❆❜str❛❝t ♣✳ ✶✶
✶ ■♥tr♦❞✉çã♦ ❡ ▼♦t✐✈❛çã♦ ♣✳ ✶
✷ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ♣✳ ✺
✷✳✶ ❈♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺
✷✳✷ ❍✐stór✐❝♦ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻
✷✳✸ ❈♦♥t❡①t♦ ❜✐♦❧ó❣✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽
✷✳✹ ❈♦♠♣♦♥❡♥t❡s ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❡✈♦❧✉t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵
✷✳✹✳✶ ❘❡♣r❡s❡♥t❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵
✷✳✹✳✷ ❋✉♥çã♦ ❞❡ ❛✈❛❧✐❛çã♦ ✭❋✉♥çã♦ ❞❡ ✜t♥❡ss✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✷
✷✳✹✳✸ P♦♣✉❧❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✷
✷✳✹✳✹ ▼❡❝❛♥✐s♠♦ ❞❡ s❡❧❡çã♦ ❞♦s r❡♣r♦❞✉t♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✸
▼✉t❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✺
❘❡❝♦♠❜✐♥❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✺
✷✳✹✳✻ ▼❡❝❛♥✐s♠♦ ❞❡ s❡❧❡çã♦ ❞♦s s♦❜r❡✈✐✈❡♥t❡s ✭❙✉❜st✐t✉✐çã♦✮ ✳ ✳ ♣✳ ✶✻
✷✳✺ ❈♦❞✐✜❝❛çã♦ ❞❡ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✵
✷✳✺✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ❣❡♥ót✐♣♦ ✲ ❆● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✵
✷✳✺✳✷ ❖♣❡r❛❞♦r ❞❡ ▼✉t❛çã♦ ✲ ❆● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✶
✷✳✺✳✸ ❖♣❡r❛❞♦r ❞❡ r❡❝♦♠❜✐♥❛çã♦ ✲ ❆● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✶
✷✳✺✳✹ ▼♦❞❡❧♦ ❞❡ ♣♦♣✉❧❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✷
✷✳✺✳✺ ▼❡❝❛♥✐s♠♦ ❞❡ s❡❧❡çã♦ ❞♦s r❡♣r♦❞✉t♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✸
❙❡❧❡çã♦ ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ ✜t♥❡ss ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✸
❙❡❧❡çã♦ ♣♦r r❛♥❦✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✹
✷✳✺✳✺✳✶ ❙❡❧❡çã♦ ♣❡❧♦ ❛❧❣♦r✐t♠♦ r♦❧❡t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✺
❙❡❧❡çã♦ ♣♦r t♦r♥❡✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✺
✷✳✺✳✻ ▼❡❝❛♥✐s♠♦ ❞❡ s❡❧❡çã♦ ❞♦s s♦❜r❡✈✐✈❡♥t❡s ✭s✉❜st✐t✉✐çã♦✮ ✳ ✳ ♣✳ ✷✻
❙♦❜r❡✈✐✈ê♥❝✐❛ ❞♦s ❣❡♥ót✐♣♦s ♠❛✐s ♥♦✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✻
❙♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❡❛❞❛ ♥♦ ✈❛❧♦r ❞❛ ❢✉♥çã♦ ❞❡ ✜t♥❡ss ✳ ✳ ✳ ✳ ♣✳ ✷✼
✷✳✻ ❆❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ✉t✐❧✐③❛❞♦ ♥♦ tr❛❜❛❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✼
✸ ▼❡t♦❞♦❧♦❣✐❛ ♣✳ ✷✽
✸✳✶ ❇❛♥❝♦ ❞❡ ❞❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✽
✸✳✷ ❆♥á❧✐s❡ ❞❡ ❘❡❣r❡ssã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✵
✸✳✸ ❚❡st❛♥❞♦ ❛ ♥♦r♠❛❧✐❞❛❞❡ ❞♦s ❞❛❞♦s ❡ ❞♦s r❡sí❞✉♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✹
✸✳✸✳✷ ❆◆❖❱❆ ✲ ❆♥á❧✐s❡ ❞❡ ❱❛r✐â♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✽
✸✳✹ ▼♦❞❡❧❛♥❞♦ ♦ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✶
P♦♣✉❧❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✶
✹ ❘❡s✉❧t❛❞♦s ♣✳ ✹✻
❘❡❢❡rê♥❝✐❛s ♣✳ ✹✾
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶ ❉✐❛❣r❛♠❛ ❞❡ ❞✐s♣❡rsã♦ ♣❛r❛ ✐❞❛❞❡ ❞❡ ❤♦♠❡♥s ❡ ♠✉❧❤❡r❡s ❬✷✵❪✳ ✳ ✳ ♣✳ ✷
✷ ■❧✉str❛çã♦ ❞♦ ❝♦♠♣❛r❛t✐✈♦ ❡♥tr❡ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛ ❡ ❛ ❡✈♦❧✉çã♦
♥❛t✉r❛❧ ❡♠ s✉❛s ❛❜♦r❞❛❣❡♥s ♣❛r❛ s♦❧✉❝✐♦♥❛r s❡✉s ♣r♦❜❧❡♠❛s✳ ❬✶✹❪ ✳ ♣✳ ✻
✸ ■❧✉str❛çã♦ ❞❛ ❝❛r❛❝t❡ríst✐❝❛ ♠♦♥ót♦♥❛ ❡ ♥ã♦ ♥❡❣❛t✐✈❛ ❞❛ ❢✉♥çã♦ ❞❡
❛✈❛❧✐❛çã♦ ✭❊✐❜❡♥✱ ✷✵✵✽✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✼
✹ ■❧✉str❛çã♦ ❞❡ ✉♠ ❣❡♥ót✐♣♦ ❡♠ s✉❛ ❝♦❞✐✜❝❛çã♦ ❜✐♥ár✐❛✳ ◆♦t❡ q✉❡✱
♥❡st❡ ❡①❡♠♣❧♦✱ ❛ ❝❛❞❛ ✹ ❜✐ts ❢♦r♠❛♠♦s ✉♠ ❛❧❡❧♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✵
✺ ■❧✉str❛çã♦ ❞♦ ♣r♦❝❡ss♦ ❞❡ ♠✉t❛çã♦ ♥❛ ❝♦❞✐✜❝❛çã♦ ❜✐♥ár✐❛✱ ❛tr❛✈és ❞♦ ♣r♦❝❡ss♦ ❜✐t ✢✐♣✳ ❊♠ ✭❛✮ ♦ ❣❡♥ót✐♣♦ ✐♥✐❝✐❛❧ ❡ ❡♠ ✭❜✮ ♦ ♠❡s♠♦
❣❡♥ót✐♣♦ ❛♣ós ❛ ♠✉t❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✶
✻ ■❧✉str❛çã♦ ❞♦ ♦♣❡r❛❞♦r ❞❡ r❡❝♦♠❜✐♥❛çã♦ ❛t✉❛♥❞♦ s♦❜r❡ ❞♦✐s
❣❡♥ót✐♣♦s ♣❛✐s ❛tr❛✈és ❞❡ ✉♠❛ r❡❝♦♠❜✐♥❛çã♦ ❞❡ ✉♠ ú♥✐❝♦ ♣♦♥t♦✳ ✳ ♣✳ ✷✷
✼ ■❧✉str❛çã♦ ❞♦ ♦♣❡r❛❞♦r ❞❡ r❡❝♦♠❜✐♥❛çã♦ ❛t✉❛♥❞♦ s♦❜r❡ ❞♦✐s ❣❡♥ót✐♣♦s ♣❛✐s ❛tr❛✈és ❞❡ ✉♠❛ r❡❝♦♠❜✐♥❛çã♦ ❞❡ três ♣♦♥t♦s✳ ◆♦t❡
q✉❡ ❛s ♣❛rt❡s ✷ ❡ ✹ ❞❡ ❝❛❞❛ ❢❡♥ót✐♣♦ ❢♦r❛♠ ♣❡r♠✉t❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✸
✽ ❉✐s♣❡rsã♦ ❞❛s ♥♦t❛s s❡♠❡str❛✐s✱ Pr♦✈❛ ✶× Pr♦✈❛ ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✶
✾ ■❧✉str❛çã♦ ♣❛r❛ ❛ t❛❜❡❧❛ ❞♦ t❡st❡ ❙❤❛♣✐r♦✲❲✐❧❦✳ ❬✸✸❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✻
✶✵ ❉✐s♣❡rsã♦ ❞❛s ♥♦t❛s s❡♠❡str❛✐s✱ Pr♦✈❛ ✶×Pr♦✈❛ ✷ ❡ ♦ ❛❥✉st❡ ❧✐♥❡❛r
♣r♦♣♦st♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✵
✶✶ ❉✐s♣❡rsã♦ ❞♦s r❡sí❞✉♦s ❛♣r❡s❡♥t❛♥❞♦ ❛ t❡♥❞ê♥❝✐❛ ❞❡ ♥♦r♠❛❧✐❞❛❞❡✱
✶✷ ●rá✜❝♦ ❞❛ s✐♠✉❧❛çã✿ ●❡r❛çõ❡s× ❋✐t♥❡ss ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✼
✶✸ ❆❥✉st❡ ❧✐♥❡❛r ♣r♦♣♦st♦ ♣❡❧♦ ✐♥❞✐✈í❞✉♦ ✶✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✼
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✶ ❉❡s❡♠♣❡♥❤♦ s❡♠❡str❛❧ ❚✉r♠❛ ❞❡ ❊st❛tíst✐❝❛ ✲ ❚❛❜✉❧❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✽
✷ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ♣❛r❛ ♦ ❞❡s❡♠♣❡♥❤♦ ❞❛ t✉r♠❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✾
✸ ❊st✐♠❛❞♦r❡s ♣❛r❛ ♦ ✐♥t❡r❝❡♣t♦ α ❡ ❛ ✐♥❝❧✐♥❛çã♦ β✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✷
✹ ◗✉❛❞r♦ ♣❛r❛ ♦ t❡st❡ ❙❤❛♣✐r♦✲❲✐❧❦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✺
✺ ◗✉❛❞r♦ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❛ ❛♥á❧✐s❡ ❞❡ ✈❛r✐â♥❝✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✾
✻ ◗✉❛❞r♦ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❛ ❛♥á❧✐s❡ ❞❡ ✈❛r✐â♥❝✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✵
✶✵
❘❡s✉♠♦
◆❡st❡ tr❛❜❛❧❤♦ ❛❜♦r❞❛r❡♠♦s ♦ ♣r♦❜❧❡♠❛ ❞❡ ❛❥✉st❡ ❧✐♥❡❛r ♣❛r❛ ❞❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❛tr❛✈és ❞❡ ✉♠ ♠ét♦❞♦ ❞❡ ♦t✐♠✐③❛çã♦ ❜✐♦✲✐♥s♣✐r❛❞♦✱ ✐st♦ é✱ q✉❡ ♠✐♠❡t✐③❛ ❝♦♥❝❡✐t♦s ❜✐♦❧ó❣✐❝♦s ♥❛ t❡♥t❛t✐✈❛ ❞❡ ❜✉s❝❛r r❡s✉❧t❛❞♦s ót✐♠♦s ♦✉ s✉❜✲ót✐♠♦s✳ ❖ ♠ét♦❞♦ ✉t✐❧✐③❛❞♦ é ♦ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ✭❆●✮✱ ❆● ❢❛③ ✉s♦ ❞❛ t❡♦r✐❛ ❞❛ ❡✈♦❧✉çã♦ ❉❛r✇✐♥✐❛♥❛ ♣❛r❛ ❜✉s❝❛r ❛ ♠❡❧❤♦r r♦t❛ ♣❛r❛ ♦ ♣♦♥t♦ ❞❡ ♠á①✐♠♦ ❞❡s❡❥❛❞♦✳ ❚r❛❞✐❝✐♦♥❛❧♠❡♥t❡✱ ♦ ❛❥✉st❡ ❧✐♥❡❛r é ❢❡✐t♦ ❛tr❛✈és ❞♦ ♠ét♦❞♦ ❞❡ ♠í♥✐♠♦s q✉❛❞r❛❞♦s✳ ❚❛❧ ♠ét♦❞♦ é ❡✜❝✐❡♥t❡✱ ♣♦ré♠ é ❞❡ ❞✐❢í❝✐❧ ❥✉st✐✜❝❛t✐✈❛ ♣❛r❛ ❛s t✉r♠❛s ♣ré✲❝á❧❝✉❧♦✳ ❉✐❛♥t❡ ❞✐ss♦✱ ❛ ❛❧t❡r♥❛t✐✈❛ ❞♦ ❆● ✈❡♠ ❝♦♠♦ ✉♠ ♣r♦❝❡❞✐♠❡♥t♦ ❡①❛✉st✐✈♦ ❝♦♠♣✉t❛❝✐♦♥❛❧♠❡♥t❡✱ ❡♥tr❡t❛♥t♦ ❞❡ ❢á❝✐❧ ❥✉st✐✜❝❛t✐✈❛ ♣❛r❛ ❡ss❛s t✉r♠❛s✳ ❆ss✐♠✱ ❛ ♣r♦♣♦st❛ ❞♦ tr❛❜❛❧❤♦ é ❝♦♠♣❛r❛r ♦s r❡s✉❧t❛❞♦s ❞❡ ❛❥✉st❡ ❧✐♥❡❛r ♣❛r❛ ❛❧❣✉♥s ❝❡♥ár✐♦s ❞❡ ❝♦♥tr♦❧❡ ❛tr❛✈és ❞♦s ❞♦✐s ♠ét♦❞♦s ❡ ❝❡rt✐✜❝❛r ❛ q✉❛❧✐❞❛❞❡ ❞♦s ❛❥✉st❡s ♦❜t✐❞♦s ♣❡❧♦ ♠ét♦❞♦ ❛♣r♦①✐♠❛❞♦✳ ◆♦ ✜♥❛❧ ❞♦ tr❛❜❛❧❤♦ ❝♦♥st❛t♦✉✲s❡ q✉❡ ♦s r❡s✉❧t❛❞♦s ❡♥❝♦♥tr❛❞♦s s➹➾♦ só❧✐❞♦s ♦ ❜❛st❛♥t❡ ♣❛r❛ ❥✉st✐✜❝❛r ♦ ♠ét♦❞♦ ❛❧t❡r♥❛t✐✈♦ ❡ q✉❡ ❛ ♣r♦♣♦st❛ ❞❛ ✉t✐❧✐③❛çã♦ ❞❡ss❡ ♣r♦❝❡ss♦ ❞❡ ♦t✐♠✐③❛çã♦ t❡♠ ♣♦t❡♥❝✐❛❧ ♣❛r❛ ❞❡s♣❡rt❛r ✐♥t❡r❡ss❡ ❡♠ ♦✉tr❛s ár❡❛s ❞❛ ♠❛t❡♠át✐❝❛✳
✶✶
❆❜str❛❝t
■♥ t❤✐s ♣❛♣❡r ✇❡ ❞✐s❝✉ss t❤❡ ♣r♦❜❧❡♠ ♦❢ ❧✐♥❡❛r ✜tt✐♥❣ t♦ ❡①♣❡r✐♠❡♥t❛❧ ❞❛t❛ ✉s✐♥❣ ❛ ♠❡t❤♦❞ ❜✐♦✲✐♥s♣✐r❡❞ ♦❢ ♦♣t✐♠✐③❛t✐♦♥✱ ✐✳❡✳✱ ✐t ✐♠✐t❛t❡s t❤❡ ❜✐♦❧♦❣✐❝❛❧ ❝♦♥❝❡♣ts ❛tt❡♠♣t t♦ ✜♥❞ ♦♣t✐♠❛❧ ♦r s✉❜♦♣t✐♠❛❧ r❡s✉❧ts✳ ❚❤❡ ♠❡t❤♦❞ ✉s❡❞ ✐s t❤❡ ❣❡♥❡t✐❝ ❛❧❣♦r✐t❤♠ ✭●❆✮✱ ❆● ♠❛❦❡s ✉s❡ ♦❢ t❤❡ t❤❡♦r② ♦❢ ❉❛r✇✐♥✐❛♥ ❡✈♦❧✉t✐♦♥ t♦ ✜♥❞ t❤❡ ❜❡st r♦✉t❡ ❢♦r t❤❡ ❞❡s✐r❡❞ ♠❛①✐♠✉♠ ♣♦✐♥t✳ ❚r❛❞✐t✐♦♥❛❧❧②✱ t❤❡ ❧✐♥❡❛r ✜tt✐♥❣ ✐s ♠❛❞❡ t❤r♦✉❣❤ t❤❡ ♠❡t❤♦❞ ♦❢ ❧❡❛st sq✉❛r❡s✳ ❚❤❡ ♠❡t❤♦❞ ✐s ❡✣❝✐❡♥t✱ ❜✉t ✐s ❞✐✣❝✉❧t t♦ ❥✉st✐❢② t❤❡ ♣r❡✲❝❛❧❝✉❧✉s ❝❧❛ss❡s✳ ❚❤❡r❡❢♦r❡✱ t❤❡ ❛❧t❡r♥❛t✐✈❡ ❆● ❝♦♠❡s ❛s ❛ ❝♦♠♣✉t❛t✐♦♥❛❧❧② ❡①❤❛✉st✐✈❡ ♣r♦❝❡❞✉r❡✱ ❤♦✇❡✈❡r ❡❛s② ❥✉st✐✜❝❛t✐♦♥ ❢♦r t❤❡s❡ ❝❧❛ss❡s✳ ❚❤✉s✱ t❤❡ ♣✉r♣♦s❡ ♦❢ t❤✐s st✉❞② ✐s t♦ ❝♦♠♣❛r❡ t❤❡ r❡s✉❧ts ♦❢ ❧✐♥❡❛r ✜tt✐♥❣ ❢♦r s♦♠❡ ❝♦♥tr♦❧ s❝❡♥❛r✐♦s ✉s✐♥❣ t❤✐s ♠❡t❤♦❞s ❛♥❞ ❝❡rt✐❢② t❤❡ q✉❛❧✐t② ♦❢ t❤❡ ❛❞❥✉st♠❡♥ts ♦❜t❛✐♥❡❞ ❜② t❤❡ ❛♣♣r♦①✐♠❛t❡ ♠❡t❤♦❞✳ ❆t t❤❡ ❡♥❞ ♦❢ t❤❡ ✇♦r❦ ✐t ✇❛s ❢♦✉♥❞ t❤❛t t❤❡ r❡s✉❧ts ❛r❡ s♦❧✐❞ ❡♥♦✉❣❤ t♦ ❥✉st✐❢② t❤❡ ❛❧t❡r♥❛t✐✈❡ ♠❡t❤♦❞ ❛♥❞ t❤❡ ♣r♦♣♦s❡❞ ✉s❡ ♦❢ t❤✐s ♦♣t✐♠✐③❛t✐♦♥ ♣r♦❝❡ss ❤❛s t❤❡ ♣♦t❡♥t✐❛❧ t♦ s♣❛r❦ ✐♥t❡r❡st ✐♥ ♦t❤❡r ❛r❡❛s ♦❢ ♠❛t❤❡♠❛t✐❝s✳
✶
✶ ■♥tr♦❞✉çã♦ ❡ ▼♦t✐✈❛çã♦
❆ r❡❣r❡ssã♦ ❧✐♥❡❛r é ✉♠ ♠ét♦❞♦ ♣❛r❛ ❡st✐♠❛r ❛ ✈❛r✐á✈❡❧ Y ✭❡♠ ❣❡r❛❧ ❛ r❡s♣♦st❛
♣❛r❛ ♦ ❡①♣❡r✐♠❡♥t♦ ❢❡✐t♦✮ ❡♠ ❢✉♥çã♦ ❞❛s ♦❜s❡r✈❛çõ❡s s♦❜ ❛ ✈❛r✐á✈❡❧ X✳ ❊♠
❣❡r❛❧✱ ❝♦♥s✐st❡ ❞❡ ♦❜t❡r ✉♠❛ r❡❧❛çã♦ ❢✉♥❝✐♦♥❛❧ ❡♥tr❡ ❛s ✈❛r✐á✈❡✐s ❞❡♣❡♥❞❡♥t❡s ❡ ✐♥❞❡♣❡♥❞❡♥t❡s✱ ❡ ❛tr❛✈és ❞✐ss♦✱ ❛❥✉st❛r ♦s ✈❛❧♦r❡s ♣r♦✈á✈❡✐s ♣❛r❛ ❛ ✈❛r✐á✈❡❧Y ❞❡♥tr♦
❞♦ ✐♥t❡r✈❛❧♦ ♦❜s❡r✈❛❞♦ ❬✾❪✳
P❛r❛ ♦❜t❡r♠♦s ❛ r❡t❛ ❛❥✉st❛❞❛ ❛♦s ❞❛❞♦s é ♣♦ssí✈❡❧ ❛♣r❡s❡♥t❛r ♦ ❣rá✜❝♦ ❞❛ ❞✐s♣❡rsã♦ ❞♦s ♣♦♥t♦s ♦❜s❡r✈❛❞♦s (x, y) ❡♠ q✉❡ x é ❛ ♦❜s❡r✈❛çã♦ tr❛❜❛❧❤❛❞❛ ❡ y é ❛
✈❛r✐á✈❡❧ r❡s♣♦st❛ ♦❜t✐❞❛✱ ❝♦♥❢♦r♠❡ ✜❣✉r❛ ✶✳
➱ ❢á❝✐❧ ♣❡r❝❡❜❡r q✉❡ q✉❛❧q✉❡r r❡t❛ ❛❥✉st❛❞❛ ❛♦ ❞✐❛❣r❛♠❛ ♥ã♦ ♣♦❞❡rá ❝♦♥t❡r t♦❞♦s ♦s ♣♦♥t♦s ❞♦ ❞✐❛❣r❛♠❛✱ ✐ss♦ s❡ ❞❡✈❡ ❡♠ s✉❛ ❣r❛♥❞❡ ♠❛✐♦r✐❛ ❛ ❡rr♦s ❞❡ ♠❡❞✐çã♦ ❞♦ ❡①♣❡r✐♠❡♥t♦✱ ♦✉ ❝❛s✉❛❧✐❞❛❞❡s ✐♥❡r❡♥t❡s ❛♦ ❡①♣❡r✐♠❡♥t♦ ♦ q✉❡ ❛ss❡❣✉r❛ q✉❡ ♦ ❡✈❡♥t♦ ❡st✉❞❛❞♦ ♥ã♦ é ✉♠ ❢❡♥ô♠❡♥♦ ♠❛t❡♠át✐❝♦✳ ❆ ♣❛rt✐r ❞✐ss♦✱ é ♥❡❝❡ssár✐♦ q✉❡ s❡❥❛ ✉t✐❧✐③❛❞♦ ♠❡t♦❞♦❧♦❣✐❛s q✉❡ ♦t✐♠✐③❡♠ ❛ r❡t❛ ❛❥✉st❛❞❛ ❝♦♠ ❛ ✜♥❛❧✐❞❛❞❡ ❞❡ q✉❡ ❛s ❞✐stâ♥❝✐❛s ❞❡ q✉❛❧q✉❡r ♣♦♥t♦ ❛ r❡t❛ s❡❥❛ ♠í♥✐♠❛✳
✷
❋✐❣✉r❛ ✶✿ ❉✐❛❣r❛♠❛ ❞❡ ❞✐s♣❡rsã♦ ♣❛r❛ ✐❞❛❞❡ ❞❡ ❤♦♠❡♥s ❡ ♠✉❧❤❡r❡s ❬✷✵❪✳
❙❡❥❛ Y ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡✜♥✐❞♦ ♣♦r✿
Y =α+β·X+ǫ ✭✶✳✶✮
❡♠ q✉❡✿
α é ♦ ♣❛râ♠❡tr♦ ❞♦ ♠♦❞❡❧♦ ❝❤❛♠❛❞♦ ❢❛t♦r ❧✐♥❡❛r❀
β é ♦ ♣❛râ♠❡tr♦ ❞♦ ♠♦❞❡❧♦ ❝❤❛♠❛❞♦ ❢❛t♦r ❞❡ ✐♥❝❧✐♥❛çã♦ ❞❛ ✈❛r✐á✈❡❧X❀
ǫ é ♦ ❡rr♦✱ ♦✉ ✈❛r✐❛çã♦ ❞❡ Y q✉❡ ♥ã♦ ♣♦❞❡ s❡r ❡①♣❧✐❝❛❞❛ ♣❡❧♦ ♠♦❞❡❧♦✳
❆ss✐♠✱ ❛♦ ❡st✐♠❛r ♦ ♠♦❞❡❧♦ ✉s❛♥❞♦ ❛s ♦❜s❡r✈❛çõ❡s t❡r❡♠♦s ❛ r❡♣r❡s❡♥t❛çã♦✿
yi =α+β·xi+ǫi ✭✶✳✷✮
s❡♥❞♦ i ✉♠❛ ❞❛s n ♦❜s❡r✈❛çõ❡s ❞❛ ❜❛s❡ ❞❡ ❞❛❞♦s✱ i∈1,2, . . . , n✳ P❛r❛ ♦ ♠ét♦❞♦ ❞❡
✸
S(a, b) =
n
X
i=1
e21 =
n
X
i=1
(yi−bxi−a)2 ✭✶✳✸✮
P❛r❛ ♠✐♥✐♠✐③❛r✱ ❝❛❧❝✉❧❛✲s❡ ❛ ❞❡r✐✈❛❞❛ ♣❛r❝✐❛❧ ❝♦♠ r❡❧❛çã♦ ❛ a ❡ b ❡ ✐❣✉❛❧❛♥❞♦ ❛
③❡r♦✿
∂S(a, b)
∂a =−2
n
X
i=1
(yi−bxi−a) = 0 ✭✶✳✹✮
∂S(a, b)
∂b =−2
n
X
i=1
xi(yi−bxi−a) = 0 ✭✶✳✺✮
❉✐str✐❜✉✐♥❞♦ ❡ ❞✐✈✐❞✐♥❞♦ ❛ ❡①♣r❡ssã♦ ✭✶✳✹✮ ♣♦r ✷♥✿
∂S(a,b)
∂a
2n =−
Pn
i=1(yi−bxi−a)
n = 0 ✭✶✳✻✮
−y+bx+a= 0 ✭✶✳✼✮
a =y−bx¯ ✭✶✳✽✮
❈♦♠ y¯❡x¯ s❡♥❞♦ ❛s ♠é❞✐❛s ❛♠♦str❛✐s ❞❡ y ❡x r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❙✉❜st✐t✉✐♥❞♦ ♦
r❡s✉❧t❛❞♦ ♥❛ ❡①♣r❡ssã♦ ✶✳✺✿
−2
n
X
i=1
xi(yi−bxi−a) = 0 ✭✶✳✾✮
−2
n
X
i=1
xi(yi−bxi−y+bx) =−2
n
X
i=1
✹
n
X
i=1
[xi(yi−y) +bxi(x−xi)] = n
X
i=1
xi(yi−y) +b n
X
i=1
xi(x−xi) = 0 ✭✶✳✶✶✮
−b
n
X
i=1
xi(xi−x) = −
n
X
i=1
xi(yi−y) ✭✶✳✶✷✮
b =
Pn
i=1xi(yi−y)
Pn
i=1xi(xi−x)
✭✶✳✶✸✮
❡♠ q✉❡ ✭✶✳✽✮ ❡ ✭✶✳✶✸✮ sã♦ ❛s ❡st✐♠❛çõ❡s ♣❛r❛ α ❡β ♣❛r❛ ♦ ❛❥✉st❡ ❞❛ r❡t❛✳
❖ ❣r❛♥❞❡ ♣r♦❜❧❡♠❛ ❡♠ s❡ tr❛❜❛❧❤❛r ❝♦♠ ♦ ♠ét♦❞♦ ❞❡ ♠í♥✐♠♦s q✉❛❞r❛❞♦s ♥❛s ❡s❝♦❧❛s ❜ás✐❝❛s ♥♦ ♠♦♠❡♥t♦ ❡♠ q✉❡ é ❡♥s✐♥❛❞♦ tr❛t❛♠❡♥t♦ ❞❛ ✐♥❢♦r♠❛çã♦ ✴ ❡st❛tíst✐❝❛ ❜ás✐❝❛ ❡stá ♥♦ ❢❛t♦ ❞❡ ❛♣❡♥❛s ❛♣r❡s❡♥t❛r ♦s ❡st✐♠❛❞♦r❡s a ❡ b s❡♠
❛♣r❡s❡♥t❛r ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ r❛❝✐♦❝í♥✐♦ q✉❡ r❡♠❡t❡ ❛ ❝á❧❝✉❧♦ ❞✐❢❡r❡♥❝✐❛❧✱ ❡♠ ❡s♣❡❝✐❛❧ ❞❡ ✈ár✐❛s ✈❛r✐á✈❡✐s✱ t❡♠❛ ❡ss❡ q✉❡ ♥ã♦ é ❛❜♦r❞❛❞♦ ♥♦ ❝✉rrí❝✉❧♦ ♠é❞✐♦✳
❯♠❛ ❛❧t❡r♥❛t✐✈❛ ❛ ❡ss❛ ♠❡t♦❞♦❧♦❣✐❛ é r❡❝♦rr❡r ❛ ♣r♦❝❡ss♦s ❞❡ ♦t✐♠✐③❛çã♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♣❛r❛ ♦ ❛❥✉st❡ ❞♦s ♣❛râ♠❡tr♦s ❞❡✈✐❞♦ ❛ ❢❛❝✐❧✐❞❛❞❡ ❞❡ ❝♦♠♣r❡❡♥sã♦ ❞❛ ✐❞❡✐❛ ❞❛ r❡❝♦rrê♥❝✐❛ ♣♦r ♣❛rt❡ ❞♦ ❛❧✉♥❛❞♦✱ ♠❡s♠♦ q✉❡ ♥ã♦ s❡❥❛ ♣♦ssí✈❡❧ ❛t✐♥❣✐r ♦ ♥í✈❡❧ ❞❡ ❡①♣❧✐❝✐t❛r ❛ ♣r♦❣r❛♠❛çã♦ ❡♥✈♦❧✈✐❞❛✳ ❯♠ ♠ét♦❞♦ ♣❛rt✐❝✉❧❛r♠❡♥t❡ ✐♥t❡r❡ss❛♥t❡ é ♦ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ q✉❡ ❝♦♥s✐st❡ ♥✉♠ ♣r♦❝❡ss♦ ❞❡ ❜✉s❝❛ q✉❡ t❡♠ ❡♠❜❛s❛♠❡♥t♦ ❡♠ ❡✈♦❧✉çã♦ ❣❡♥ét✐❝❛ ✭t❡♠❛ tr❛❜❛❧❤❛❞♦ ❡♠ s❛❧❛ ❞❡ ❛✉❧❛ ♣♦r ♦✉tr❛s ❞✐s❝✐♣❧✐♥❛s✮ ❢❛❝✐❧✐t❛♥❞♦ ❛ ❝♦♠♣r❡❡♥sã♦ ❞♦ ♠ét♦❞♦ ❡ ❛ ❛❝❡✐t❛çã♦ ❡♠ s❛❧❛ ❬✺❪✳
✺
✷ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦
✷✳✶ ❈♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛
➱ ♣♦ssí✈❡❧ ❞❡✜♥✐r ❛ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛ ❝♦♠♦ ✉♠❛ ár❡❛ ❞❡ ♣❡sq✉✐s❛ ❞❛ ♠♦❞❡❧❛❣❡♠ ❝♦♠♣✉t❛❝✐♦♥❛❧ q✉❡ t❡♠ ❝♦♠♦ ♣r✐♥❝✐♣❛❧ ♣♦♥t♦ ❞❡ ✐♥s♣✐r❛çã♦ ♦ ♣r♦❝❡ss♦ ❞❡ ❡✈♦❧✉çã♦ ♥❛t✉r❛❧✳ ◆♦t❛❞❛♠❡♥t❡✱ é ♣♦ssí✈❡❧ ♣❡r❝❡❜❡r ❝♦♠♦ ❝♦❧ô♥✐❛s ❞❡ ❢♦r♠✐❣❛s✱ ❛ ♣ró♣r✐❛ ❡✈♦❧✉çã♦ ❣❡♥ét✐❝❛✱ ❡♥①❛♠❡ ❞❡ ❛❜❡❧❤❛s ❡♥tr❡ ♦✉tr♦s ❛♣r❡s❡♥t❛♠ ❢♦r♠❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ❡❧✐♠✐♥❛r ❛s t❡♥t❛t✐✈❛s ♠❡♥♦s ♣rát✐❝❛s ♦✉ ❞❛♥♦s❛s ❡ r❡♣❡t✐r✴♠❡❧❤♦r❛r ♥❛ ♣♦♣✉❧❛çã♦ ♦s ❝❛s♦s ❡♠ q✉❡ ❤♦✉✈❡ ♠❛✐s s✉❝❡ss♦ ♦✉ q✉❡ ❛♦ ♠❡♥♦s ♥ã♦ ❧❡✈❛r❛♠ ❛ ♣❡r❞❛s ✭❬✷✹❪❀ ❬✶❪✮✳
❚❛❧ ✜❧♦s♦✜❛ é ✉s❛❞❛ ❝♦♠♦ ♠❡t♦❞♦❧♦❣✐❛ ♣❛r❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s q✉❡ ♣♦❞❡♠ s❡r tr❛♥s❝r✐t♦s ❝♦♠♦ ✉♠ ❞✐❧❡♠❛ ❡✈♦❧✉❝✐♦♥ár✐♦✱ ❝♦♠ ❜❛s❡ ♥✐ss♦ ❡ s❡ ❛♣r♦♣r✐❛♥❞♦ ❞❛ ♦❜s❡r✈❛çã♦ ❞❡ ❝♦♠♦ ❛ ♥❛t✉r❡③❛ s♦❧✉❝✐♦♥❛ t❛✐s ❞✐❧❡♠❛s✱ ❛ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉❝✐♦♥ár✐❛ s✉r❣❡ ❝♦♠♦ ✉♠❛ ❢♦r♠❛ ❞❡ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❜❛s❡❛❞♦ ❡♠ t❡♥t❛t✐✈❛✲❡✲❡rr♦ ✭❞✐r❡❝✐♦♥❛❞♦✮ ✭❬✶✹❪✮✳
❈❛♣ít✉❧♦ ✷✳ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ✷✳✷✳ ❍✐stór✐❝♦ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛
✭❡ q✉ã♦ ❜♦❛ é ❛ s♦❧✉çã♦✱ ❡ t❛❧ ❝r✐tér✐♦ s❡rá ✉t✐❧✐③❛❞♦ ♣❛r❛ ❞❡✜♥✐r ❛s ❝❤❛♥❝❡s ❞❡ss❛ ♣♦ssí✈❡❧ s♦❧✉çã♦ ♣❡r♠❛♥❡❝❡r ♥❛ ❝♦❧❡çã♦ ❡ s❡r✈✐r ❞❡ ♣❛râ♠❡tr♦ ♣❛r❛ s♦❧✉çõ❡s ❢✉t✉r❛s✮✳
❋✐❣✉r❛ ✷✿ ■❧✉str❛çã♦ ❞♦ ❝♦♠♣❛r❛t✐✈♦ ❡♥tr❡ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛ ❡ ❛ ❡✈♦❧✉çã♦ ♥❛t✉r❛❧ ❡♠ s✉❛s ❛❜♦r❞❛❣❡♥s ♣❛r❛ s♦❧✉❝✐♦♥❛r s❡✉s ♣r♦❜❧❡♠❛s✳ ❬✶✹❪
✷✳✷ ❍✐stór✐❝♦ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛
❆ ✉t✐❧✐③❛çã♦ ❞♦s ♣r✐♥❝í♣✐♦s ❛♣r❡s❡♥t❛❞♦s ♣♦r ❈❤❛r❧❡s ❉❛r✇✐♥ ♥❛ t❡♥t❛t✐✈❛ ❞❡ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❞❡ ❢♦r♠❛ ❛✉tô♥♦♠❛ t❡✈❡ ✐♥í❝✐♦ ♥❛ ❞é❝❛❞❛ ❞❡ ✹✵✱ ❜❡♠ ❛♥t❡s ❞❛ ❞✐ss❡♠✐♥❛çã♦ ❞❡ ❝♦♠♣✉t❛❞♦r❡s❀ ❉❛✈✐❞ ❇✳ ❋♦❣❡❧ ❡♠ s❡✉ ❧✐✈r♦ ❊✈♦❧✉t✐♦♥❛r② ❈♦♠♣✉t❛t✐♦♥✿ ❚❤❡ ❋♦ss✐❧ ❘❡❝♦r❞ ✭❬✶✼❪✮ ❛♣r❡s❡♥t❛ ♦s ❛rt✐❣♦s q✉❡ ❢✉♥❞❛♠❡♥t❛♠ ❛ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛✳ ❊♠ ✶✾✹✽✱ ❚✉r✐♥❣ ♣r♦♣ôs ♦ ♣r♦❝❡ss♦ ❞❡ ❜✉s❝❛ ✐♥t✐t✉❧❛❞♦ ✏❇✉s❝❛ ❣❡♥ét✐❝❛✑ ✭❬✸✽❪✮ ❡ ❡♠ ✶✾✻✷✱ ❇r❡♠❡r♠❛♥♥ ✭❬✽❪✮ ❡①❡❝✉t♦✉ ❡①♣❡r✐♠❡♥t♦s ❡♠ ♦t✐♠✐③❛çã♦ ❛tr❛✈és ❞❡ ❡✈♦❧✉çã♦ ❡ r❡❝♦♠❜✐♥❛çã♦✳
❱❛r✐❛çõ❡s ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ♦❝♦rr❡r❛♠ ♥❛ ❞é❝❛❞❛ ❞❡ ✻✵ ❡♠ três ❧♦❝❛✐s ❞✐st✐♥t♦s✿ ✲ ◆♦s ❊st❛❞♦s ❯♥✐❞♦s✱ ♥♦s ❛♥♦s ❞❡ ✶✾✻✺ ❡ ✶✾✻✻✱ ♦s ♣r✐♠❡✐r♦s ❛rt✐❣♦s s♦❜r❡ ♣r♦❣r❛♠❛çã♦ ❡✈♦❧✉t✐✈❛ ❢♦r❛♠ ♣✉❜❧✐❝❛❞♦s ♣♦r ❋♦❣❡❧✱ ❖✇❡♥s ❡ ❲❛❧s❤✳ ❆ ♣r♦❣r❛♠❛çã♦ ❡✈♦❧✉❝✐♦♥ár✐❛ ❢♦✐ ✐♥✈❡♥t❛❞❛ ♣♦r ▲❛✇r❡♥❝❡ ❏✳ ❋♦❣❡❧ ✭✶✾✷✽✲✷✵✵✼✮ ❡♥q✉❛♥t♦ ❢❛③✐❛ ♣❛rt❡ ❞❛ ❋✉♥❞❛çã♦ ❞❛ ❝✐ê♥❝✐❛ ♥❛❝✐♦♥❛❧ ❡♠ ✶✾✻✵✱ ❡♠ s✉❛ ✈❛r✐❛çã♦✱ ❋♦❣❡❧ tr❛❜❛❧❤❛✈❛ ❡♠ ✉♠❛ sér✐❡ ❞❡ ❡①♣❡r✐♠❡♥t♦s ❡♠ q✉❡ ❛s ♠áq✉✐♥❛s ❞❡ ❡st❛❞♦s ✜♥✐t♦s r❡♣r❡s❡♥t❛♠ ♦r❣❛♥✐s♠♦s ✐♥❞✐✈✐❞✉❛✐s ❡♠ ✉♠❛ ♣♦♣✉❧❛çã♦ ❞❡ s♦❧✉❝✐♦♥❛❞♦r❡s ❞❡ ♣r♦❜❧❡♠❛s✳ ❊st❡s ♠♦❞❡❧♦s ❣rá✜❝♦s sã♦ ✉s❛❞♦s ♣❛r❛ ❞❡s❝r❡✈❡r ♦ ❝♦♠♣♦rt❛♠❡♥t♦✱ é ♣♦r ✐ss♦ q✉❡ ❝❤❛♠♦✉ s✉❛ ❛❜♦r❞❛❣❡♠ ❞❡ ♣r♦❣r❛♠❛çã♦ ❡✈♦❧✉t✐✈❛ ✭❬✶✽❪❀❬✶✾❪✮✳
❈❛♣ít✉❧♦ ✷✳ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ✷✳✷✳ ❍✐stór✐❝♦ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛
✲ ◆❛ ❆❧❡♠❛♥❤❛✱ ❘❡❝❤❡♥❜❡r❣ ❡ ❙❝❤✇❡❢❡❧ ♥❛ ❯♥✐✈❡rs✐❞❛❞❡ ❚é❝♥✐❝❛ ❞❡ ❇❡r❧✐♥ ❛♣r❡s❡♥t❛r❛♠ ❛ ❡str❛té❣✐❛ ❡✈♦❧✉t✐✈❛ ♣❛r❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❞❡ ♦t✐♠✐③❛çã♦ ❝♦♥tí♥✉❛ ❞❡ ♣❛râ♠❡tr♦s ❞❡ ❝♦♥tr♦❧❡ ❡ sã♦ ❞❡s❝r✐t❛s ❞❡ ❢♦r♠❛ ❝♦♠♣❧❡t❛ ♥♦ tr❛❜❛❧❤♦ ❊✈♦❧✉t✐♦♥str❛t❡❣✐❡✿ ❖♣t✐♠✐❡r✉♥❣ ❚❡❝❤♥✐s❤❡r ❙②st❡♠❡ ♥❛❝❤ Pr✐♥③✐♣✐❡♥ ❞❡s ❇✐♦❧♦❣✐s❝❤❡♥ ❊✈♦❧✉t✐♦♥ ❞❡ ✶✾✼✸❀ ❛ ❣r❛♥❞❡ ♠✉❞❛♥ç❛ ❛♣r❡s❡♥t❛❞❛ ♥❡ss❛ té❝♥✐❝❛ é ❞❛❞❛ ♣❡❧❛ ✉t✐❧✐③❛çã♦ ❞❡ ✉♠ ♦♣❡r❛❞♦r ♠✉t❛çã♦ ❜❛s❡❛❞♦ ❡♠ ✉♠❛ ❞✐str✐❜✉✐çã♦ ◆♦r♠❛❧ ✭❬✸✹❪✮✳
✲ ◆♦✈❛♠❡♥t❡ ♥♦s ❊st❛❞♦s ❯♥✐❞♦s✱ ❏♦❤♥ ❍❡♥r② ❍♦❧❧❛♥❞ ❞❡♥♦♠✐♥♦✉ s❡✉ ♠ét♦❞♦ ♣♦r ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦✱ ♠ét♦❞♦ ❡st❡ q✉❡ é ✉s❛❞♦ ♣❛r❛ ❛❝❤❛r s♦❧✉çõ❡s ❛♣r♦①✐♠❛❞❛s ❡♠ ♣r♦❜❧❡♠❛s ❞❡ ♦t✐♠✐③❛çã♦ ❡ ❜✉s❝❛✳ ❖s ❛❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s ❞✐❢❡r❡♠ ❞♦s ❛❧❣♦r✐t♠♦s tr❛❞✐❝✐♦♥❛✐s ❞❡ ♦t✐♠✐③❛çã♦ ❡♠ q✉❛tr♦ ❛s♣❡❝t♦s ✭❬✶✸❪❀❬✷✷❪❀❬✷✸❪✮✿
• ❇❛s❡✐❛♠✲s❡ ❡♠ ✉♠❛ ❝♦❞✐✜❝❛çã♦ ❞♦ ❝♦♥❥✉♥t♦ ❞❛s s♦❧✉çõ❡s ♣♦ssí✈❡✐s✱ ❡ ♥ã♦ ♥♦s
♣❛râ♠❡tr♦s ❞❛ ♦t✐♠✐③❛çã♦ ❡♠ sí❀
• ❖s r❡s✉❧t❛❞♦s sã♦ ❛♣r❡s❡♥t❛❞♦s ❝♦♠♦ ✉♠❛ ♣♦♣✉❧❛çã♦ ❞❡ s♦❧✉çõ❡s ❡ ♥ã♦ ❝♦♠♦
✉♠❛ s♦❧✉çã♦ ú♥✐❝❛❀
• ❯s❛♠ tr❛♥s✐çõ❡s ♣r♦❜❛❜✐❧íst✐❝❛s ❡ ♥ã♦ ❞❡t❡r♠✐♥íst✐❝❛s❀
• ◆ã♦ ♥❡❝❡ss✐t❛♠ ❞❡ ♥❡♥❤✉♠ ❝♦♥❤❡❝✐♠❡♥t♦ ✐♥❡r❡♥t❡ ❛♦ ♣r♦❜❧❡♠❛✱ ❛♣❡♥❛s ❞❡ ✉♠❛
❢♦r♠❛ ❞❡ ❛✈❛❧✐❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ✭♣❛rt✐❝✉❧❛r♠❡♥t❡✱ ♦ ❛s♣❡❝t♦ ♠❛✐s ✐♥t❡r❡ss❛♥t❡ ❞♦ ♠ét♦❞♦✮✳ P♦✐s✱ ✉♠❛ ✈❡③ q✉❡ é r❡t✐r❛❞❛ ❛ r❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ❞❡ s❡ ❝♦♥❤❡❝❡r ❛ s✐♥❣✉❧❛r✐❞❛❞❡ ❞❛ r❡s♦❧✉çã♦ ❞❡ ✉♠ ♣r♦❜❧❡♠❛✱ ♦ ❛❧❣♦r✐t♠♦ ❡stá ❛♣t♦ ❛ ✉t✐❧✐③❛r ♦ ♣r♦❝❡❞✐♠❡♥t♦ ❡♠ ♣r♦❜❧❡♠❛s ❞❡ ♥❛t✉r❡③❛ ❛❧❡❛tór✐❛ ♦✉ q✉❡ s❡ t❡♥❤❛ ♣♦✉❝♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❛❝❡r❝❛ ❞❡ s✉❛ ❞✐♥â♠✐❝❛✳ ✭❬✷✶❪✮
P♦r ❝❡r❝❛ ❞❡ ✶✺ ❛♥♦s ❡ss❛s ár❡❛s ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞❛s s❡♣❛r❛❞❛♠❡♥t❡✱ ♣♦ré♠✱ ♥❛ ❞é❝❛❞❛ ❞❡ ✾✵ ♣❛ss❛r❛♠ ❛ s❡r ✈✐st♦s ❝♦♠♦ r❡♣r❡s❡♥t❛çõ❡s ❞✐❢❡r❡♥t❡s ❞❡ ✉♠❛ ♠❡s♠❛ t❡❝♥♦❧♦❣✐❛ q✉❡ ✜❝♦✉ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛✳ ❯♠❛ q✉❛rt❛ ❝♦rr❡♥t❡ s❡❣✉✐♥❞♦ ❛s ✐❞é✐❛s ❣❡r❛✐s s✉r❣✐✉✱ ♣r♦❣r❛♠❛çã♦ ❣❡♥ét✐❝❛✱ ❞❡❢❡♥❞✐❞❛ ♣♦r ❑♦③❛ ✭❬✷✻❪❀ ❬✷✼❪✮✳ ◆❛ ♣r♦❣r❛♠❛çã♦ ❣❡♥ét✐❝❛✱ ❝♦♥s✐st❡ ♥✉♠❛ té❝♥✐❝❛ ❛✉t♦♠át✐❝❛ ❞❡
❈❛♣ít✉❧♦ ✷✳ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ✷✳✸✳ ❈♦♥t❡①t♦ ❜✐♦❧ó❣✐❝♦
♣r♦❣r❛♠❛çã♦ q✉❡ ♣r♦♣✐❝✐❛ ❛ ❡✈♦❧✉çã♦ ❞❡ ♣r♦❣r❛♠❛s ❞❡ ❝♦♠♣✉t❛❞♦r❡s ♣❛r❛ r❡s♦❧✈❡r❡♠ ✭♦✉ ❛♣r♦①✐♠❛r ❛ r❡s♦❧✉çã♦✮ ❞❡ ♣r♦❜❧❡♠❛✳
❆ t❡r♠✐♥♦❧♦❣✐❛ ❝♦♥t❡♠♣♦râ♥❡❛ ❞❡♥♦t❛ t♦❞♦s ♦s ❝❛♠♣♦s ❞❛ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛✱ ♦s ❛❧❣♦r✐t♠♦s ❝♦♥t✐❞♦s ♥❡ss❛ t❡r♠✐♥♦❧♦❣✐❛ sã♦ ❝❤❛♠❛❞♦s ❞❡ ❛❧❣♦r✐t♠♦s ❡✈♦❧✉t✐✈♦s✱ ❡ ❡st❛ ❝❧❛ss✐✜❝❛çã♦ ❝♦♥s✐❞❡r❛ ❛ ♣r♦❣r❛♠❛çã♦ ❡✈♦❧✉t✐✈❛✱ ❡str❛té❣✐❛ ❡✈♦❧✉t✐✈❛✱ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ❡ ♣r♦❣r❛♠❛çã♦ ❣❡♥❡t✐❝❛ ❝♦♠♦ s✉❜✲ár❡❛s ♣❡rt❡♥❝❡♥t❡s ❛ ✈❛r✐❛♥t❡s ❞❡st❡✳
❯♠❛ ✈❡rt❡♥t❡ ♠❛✐s r❡❝❡♥t❡ é ❛ ❝♦♠♣✉t❛çã♦ ❞❡ ❡♥①❛♠❡s✱ ♦ ❛❧❣♦r✐t♠♦ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ❖t✐♠✐③❛çã♦ ♣♦r ❊♥①❛♠❡ ❞❡ P❛rtí❝✉❧❛s ✭P❙❖ ✲ P❛rt✐❝❧❡ ❙✇❛r♠ ❖♣t✐♠✐③❛t✐♦♥✮✳ ❖ ❛❧❣♦r✐t♠♦ P❙❖ ❢♦✐ ♣r♦♣♦st♦ ✐♥✐❝✐❛❧♠❡♥t❡ ♣♦r ❏✳ ❑❡♥♥❡❞② ❡ ❘✳ ❊❜❡r❤❛rt ✭❑❡♥♥❡❞②✱ ✶✾✾✺✮ ❡ é ✉♠ té❝♥✐❝❛ ✐♥s♣✐r❛❞❛ ♥♦ ❝♦♠♣♦rt❛♠❡♥t♦ s♦❝✐❛❧ ❞❡ ❜❛♥❞♦s ❞❡ ♣áss❛r♦s✳ ❆ ❜✉s❝❛ ♣♦r ❛❧✐♠❡♥t♦ ❡ ❛ ✐♥t❡r❛çã♦ ❡♥tr❡ ♦s ♣áss❛r♦s ❛♦ ❧♦♥❣♦ ❞♦ ✈ô♦ sã♦ ♠♦❞❡❧❛❞❛s ❝♦♠♦ ✉♠ ♠❡❝❛♥✐s♠♦ ❞❡ ♦t✐♠✐③❛çã♦✳ ◆♦ ❝❛s♦✱ ❛ ár❡❛ s♦❜r❡✈♦❛❞❛ é ❡q✉✐✈❛❧❡♥t❡ ❛♦ ❡s♣❛ç♦ ❞❡ ❜✉s❝❛ ❡ ❡♥❝♦♥tr❛r ♦ ❧♦❝❛❧ ❝♦♠ ♠❛✐♦r q✉❛♥t✐❞❛❞❡ ❞❡ ❝♦♠✐❞❛ ❝♦rr❡s♣♦♥❞❡ ❛ ❡♥❝♦♥tr❛r ❛ s♦❧✉çã♦ ót✐♠❛✳
✷✳✸ ❈♦♥t❡①t♦ ❜✐♦❧ó❣✐❝♦
P♦❞❡✲s❡ ❞✐③❡r q✉❡ ❛ t❡♦r✐❛ ❞❛ ❡✈♦❧✉çã♦ t❡♠ ♣❛rt✐❝✐♣❛çã♦ ❢✉♥❞❛♠❡♥t❛❧ ♥❛ ❝♦♠♣r❡❡♥sã♦ ❞❡st❡ ❝❛♣ít✉❧♦ ✭❡ ❝♦♠ ✐ss♦✱ ❝♦♠♣r❡❡♥sã♦ ❞♦s ❛❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s✮✱ ❞❛í✱ é ♥❡❝❡ssár✐♦ ❝♦♥❤❡❝❡r ❛❧❣✉♠❛s ❞❡✜♥✐çõ❡s✿
•❯♠ ❣❡♥❡ é ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ❜❛s❡s ❞❡ ❉◆❆ q✉❡ ❝♦❞✐✜❝❛♠ ♣❛r❛ ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛✱
♣♦r ❡①❡♠♣❧♦✱ ❝♦r ❞❡ ❝❛❜❡❧♦ ♦✉ ❞❛ ♣❡❧❡❀
• ❯♠ ❛❧❡❧♦ é ♦ ✈❛❧♦r ❞❡ ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛✳ ❖ ❣❡♥❡ ❞❛ ❝♦r ❞♦ ❝❛❜❡❧♦ ♣♦❞❡ t❡r ✉♠
❛❧❡❧♦ ♣r❡t♦ ♦✉ ✉♠ ❛❧❡❧♦ ✈❡r♠❡❧❤♦ ❡♠ ❞✐❢❡r❡♥t❡s ♣❡ss♦❛s✳
❈♦♠ ✐ss♦✱ é ♣♦ssí✈❡❧ ❞❡✜♥✐r ❛ ❡✈♦❧✉çã♦✿
❊✈♦❧✉çã♦ é ❛ ✈❛r✐❛çã♦ ❞❛ ❢r❡q✉ê♥❝✐❛ ❛❧é❧✐❝❛ ♥❛ ♣♦♣✉❧❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦ ✭❬✸✼❪✮✳
❈❛♣ít✉❧♦ ✷✳ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ✷✳✸✳ ❈♦♥t❡①t♦ ❜✐♦❧ó❣✐❝♦
◆❡ss❛ ❞❡✜♥✐çã♦✱ ❝♦♥❝❡✐t✉❛✲s❡ s♦❜r❡ ❛ ♣♦♣✉❧❛çã♦✳ ❖✉ s❡❥❛✱ t♦❞❛ ✈❡③ q✉❡ ♥❛s❝❡ ✉♠❛ ❝r✐❛♥ç❛ ❞❡ ❝❛❜❡❧♦s ♣r❡t♦s✱ ❡♥tã♦ ❛ ❢r❡q✉ê♥❝✐❛ ❞❛ ♣♦♣✉❧❛çã♦ q✉❛♥t♦ ❛♦ ❣❡♥❡ ❝♦r ❞❡ ❝❛❜❡❧♦ t❡♠ ❛ ❢r❡q✉ê♥❝✐❛ ❞♦ ❛❧❡❧♦ ♣r❡t♦ ❛✉♠❡♥t❛❞❛ ✭❛♥❛❧♦❣❛♠❡♥t❡✱ ♣❛r❛ ♦ ❝❛s♦ ❞❡ ♠♦rt❡ ❞❡ ✉♠ ❤♦♠❡♠ ❞❡ ❝❛❜❡❧♦s ♣r❡t♦s✮✱ ❞❛í✱ é ♣♦ssí✈❡❧ ♥♦t❛r q✉❡ ❛ ❢r❡q✉ê♥❝✐❛ ❛❧é❧✐❝❛ ♠✉❞❛ ❛ t♦❞♦ t❡♠♣♦✱ ❥á q✉❡ ♥❛s❝❡♠ ❡ ♠♦rr❡♠ ♣❡ss♦❛s ❛ t♦❞♦ ✐♥st❛♥t❡✳ ❊♥✜♠✱ ♥♦t❛✲ s❡ q✉❡ ❛ ❡✈♦❧✉çã♦ ❛❝♦♥t❡❝❡ ❛ t♦❞♦ t❡♠♣♦ ✭♣♦❞❡♠♦s ❞❡✜♥✐r ♦ ♣❛râ♠❡tr♦ t ❞✐s❝r❡t♦
s♦❜ ❡ss❡ ❝❛s♦ ❥á q✉❡ ♦ ❡✈❡♥t♦ ♥❛s❝✐♠❡♥t♦✴♠♦rt❡ ♣♦❞❡ s❡r ❞✐s❝r❡t✐③❛❞♦ ❛té ✉♠ ♣❛ss♦ ❞❡ t❡♠♣♦ ❡♠ q✉❡ ♥❛s❝❡✴♠♦rr❡ ✉♠ ú♥✐❝♦ ✐♥❞✐✈í❞✉♦✮✳
❈♦♠♦ ❛ ❡✈♦❧✉çã♦ ♣r♦❞✉③ ♥♦✈♦s ✐♥❞✐✈í❞✉♦s❄ ❍á ❞✉❛s ❢♦r♠❛s ♦♣♦st❛s q✉❡ ❝♦♥❞✉③❡♠ ❛ ❡✈♦❧✉çã♦✿ ✈❛r✐❛çã♦ ❡ s❡❧❡çã♦✳ ❱❛r✐❛çã♦ é ♦ ♣r♦❝❡ss♦ q✉❡ ♣r♦❞✉③ ♥♦✈♦s ❛❧❡❧♦s ❡✱ ♠❛✐s ❧❡♥t❛♠❡♥t❡✱ ❣❡♥❡s✳ ❱❛r✐❛çã♦ t❛♠❜é♠ ♣♦❞❡ ♠✉❞❛r ♦s ❣❡♥❡s q✉❡ sã♦ ❡ ♥ã♦ sã♦ ❡①♣r❡ss♦s ❡♠ ✉♠ ❞❛❞♦ ✐♥❞✐✈í❞✉♦✱ ♦ ♠ét♦❞♦ ❞❡ ❢❛③❡r ✐ss♦ é ❛ r❡♣r♦❞✉çã♦ s❡①✉❛❧ ❝♦♠ ❛ s✉❛ ✐♥t❡r❛çã♦ ❞❡ ❣❡♥❡s ❞♦♠✐♥❛♥t❡s ❡ r❡❝❡ss✐✈♦s✳ ❙❡❧❡çã♦ é ♦ ♣r♦❝❡ss♦ ❡♠ q✉❡ ❛❧❣✉♥s ❛❧❡❧♦s s♦❜r❡✈✐✈❡♠ ❡ ♦✉tr♦s ♥ã♦✳ ❊♠ r❡s✉♠♦✱ ❛ ✈❛r✐❛çã♦ ❛✉♠❡♥t❛ ❛ ❞✐✈❡rs✐❞❛❞❡ ❡ ❛ s❡❧❡çã♦ ❛ ❞✐♠✐♥✉✐✳
❖ ♣r♦❝❡ss♦ ❞❡ ✈❛r✐❛çã♦ é ❝♦♠♣❧❡①♦ ❡ ♦❝♦rr❡ ❛ ♥í✈❡❧ ♠♦❧❡❝✉❧❛r✳ ❇✐ó❧♦❣♦s ❛♣r❡♥❞❡♠ ♥♦✈♦s s✐st❡♠❛s ♣❛r❛ ❣❡r❛r ✈❛r✐❛çã♦ ❛ ♥í✈❡❧ ♠♦❧❡❝✉❧❛r✳ ❙❡❧❡çã♦ ❜✐♦❧ó❣✐❝❛ é ♠❡❧❤♦r ❡♥t❡♥❞✐❞❛ ❞♦ q✉❡ ❛ ✈❛r✐❛çã♦ ❜✐♦❧ó❣✐❝❛✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❛ s❡❧❡çã♦ ♥❛t✉r❛❧ ✲ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦s ♠❛✐s ❛❞❛♣t❛❞♦s ❛♦ ♠❡✐♦ ❡♠ q✉❡ ✈✐✈❡♠ ✲ t❡♠ s✐❞♦ ♦ ♣r✐♥❝✐♣❛❧ t✐♣♦ ❞❡ s❡❧❡çã♦ ❜✐♦❧ó❣✐❝❛ ✭❬✶✷❪❀ ❬✸✷❪✮✳
◆❛ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛✱ ❛s ♦♣❡r❛çõ❡s s♦❜r❡ ❛ ❡str✉t✉r❛ ❞❡ ❞❛❞♦s ✭♣♦♣✉❧❛çã♦✮ q✉❡ ❣❡r❛♠ ❛ ✈❛r✐❛çã♦ r❡❝❡❜❡♠ ♦s ♥♦♠❡s ❞❡ ♠✉t❛çã♦ ❡ ❝r✉③❛♠❡♥t♦ ❡ ❛t✉❛♠ ♣♦r ♠✉❞❛♥ç❛s ❛❧❡❛tór✐❛s ♥❡ss❛ ❡str✉t✉r❛ ❡ ♠✐st✉r❛♥❞♦ ♣❛rt❡s ❞❡ ❡str✉t✉r❛s ❞✐❢❡r❡♥t❡s✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❏á ❛ s❡❧❡çã♦✱ ♣♦❞❡ s❡r ✐♥t❡r♣r❡t❛❞❛ ❝♦♠♦ q✉❛❧q✉❡r ❛❧❣♦r✐t♠♦ q✉❡ ❢❛✈♦r❡ç❛ ❡str✉t✉r❛s ❝♦♠ ♠❛✐♦r ❛❞❛♣t❛❜✐❧✐❞❛❞❡ ❛♦ ♥♦ss♦ ♣r♦❜❧❡♠❛✳ ❍á ♠✉✐t♦s ♠ét♦❞♦s ♣♦ssí✈❡✐s ❞❡ s❡❧❡çã♦✳
▼✉t❛çõ❡s ❜✐♦❧ó❣✐❝❛s ♥♦ ❉◆❆ ❞❡ ❛❧❣✉♠ ♦r❣❛♥✐s♠♦✱ s♦❜ ✉♠ ♣♦♥t♦ ❞❡ ✈✐st❛ ❛❧❡❛tór✐♦✱ sã♦ t✐♣✐❝❛♠❡♥t❡ ♥❡✉tr❛s✳ ▼✉✐t♦s tr❡❝❤♦s ❞♦ ❉◆❆ ♥ã♦ ❝♦❞✐✜❝❛♠ ✐♥❢♦r♠❛çã♦ út✐❧ ✭❝♦♥❤❡❝✐❞❛✮✳ ❆ ♣❛rt❡ ❞♦ ❉◆❆ q✉❡ ❝♦❞✐✜❝❛ ✐♥❢♦r♠❛çã♦ út✐❧ ✉t✐❧✐③❛
❈❛♣ít✉❧♦ ✷✳ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ✷✳✹✳ ❈♦♠♣♦♥❡♥t❡s ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❡✈♦❧✉t✐✈♦
✉♠❛ ❝♦❞✐✜❝❛çã♦ r♦❜✉st❛ ♦ q✉❡ ❛ss❡❣✉r❛ q✉❡ ♠♦❞✐✜❝❛çõ❡s ❞❡ ❜❛s❡ s✐♠♣❧❡s ♥ã♦ ❛❧t❡r❛♠ ❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡ ❞♦ ❣❡♥❡✳ ❆ r❡❞❡ ❞❡ ✐♥t❡r❛çã♦ ❡♥tr❡ ♦s ❣❡♥❡s é✱ ♣♦r sí só✱ r♦❜✉st❛ ❝♦♠ ♠✉❧t✐♣❧❛s ❝ó♣✐❛s ❞❡ ❛❧❣✉♥s ❣❡♥❡s ❡ ♠ú❧t✐♣❧♦s ❣❡♥❡s q✉❡ ❡①❡❝✉t❛♠ ✉♠❛ ♠❡s♠❛ t❛r❡❢❛ ❡s♣❡❝í✜❝❛ ✭❬✸✵❪✮✳
❙❡rá ✉s❛❞♦ ❡ss❡ r❡❢❡r❡❝✐❛❧ ♣❛r❛ ❛❜♦r❞❛r ♦s ❝♦♠♣♦♥❡♥t❡s ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❡✈♦❧✉t✐✈♦✳
✷✳✹ ❈♦♠♣♦♥❡♥t❡s ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❡✈♦❧✉t✐✈♦
❯♠ ❛❧❣♦r✐t♠♦ ❡✈♦❧✉t✐✈♦ ❛♣r❡s❡♥t❛ ❝♦♠♣♦♥❡♥t❡s ❜❡♠ ❝❛r❛❝t❡ríst✐❝♦s q✉❡ ❞❡✈❡♠ s❡r ❜❡♠ ❞❡✜♥✐❞♦s ♥❛ ❡❧❛❜♦r❛çã♦ ❞❛ ❝♦❞✐✜❝❛çã♦ ❞♦ ♣r♦❜❧❡♠❛ q✉❡ s❡rá ♦t✐♠✐③❛❞♦✱ sã♦ ❡st❡s✿
• ❘❡♣r❡s❡♥t❛çã♦ ✲ ❉❡✜♥✐çã♦ ❞♦s ✐♥❞✐✈í❞✉♦s❀
• ❋✉♥çã♦ ❞❡ ❛✈❛❧✐❛çã♦ ✭❋✉♥çã♦ ❞❡ ❛❥✉st❡ ♦✉ ❋✉♥çã♦ ❞❡ ✜t♥❡ss✮❀
• P♦♣✉❧❛çã♦❀
• ▼❡❝❛♥✐s♠♦ ❞❡ s❡❧❡çã♦ ❞♦s r❡♣r♦❞✉t♦r❡s❀
• ❖♣❡r❛❞♦r❡s ❞❡ ✈❛r✐❛çã♦✿ ♠✉t❛çã♦ ❡ r❡❝♦♠❜✐♥❛çã♦❀
• ▼❡❝❛♥✐s♠♦ ❞❡ s❡❧❡çã♦ ❞♦s s♦❜r❡✈✐✈❡♥t❡s ✭❙✉❜st✐t✉✐çã♦✮✳
♥❡ss❡ ♣❛ss♦✱ s❡rá ❞✐s❝✉t✐❞♦ ❝❛❞❛ ✉♠ ❞❡ss❡s ❝♦♠♣♦♥❡♥t❡s ♥❛ t❡♥t❛t✐✈❛ ❞❡ ✐❞❡♥t✐✜❝❛r ❝❛❞❛ ♣❛rt✐❝✉❧❛r✐❞❛❞❡ ❛ss♦❝✐❛❞❛ ❛ ❡❧❡s✳
✷✳✹✳✶ ❘❡♣r❡s❡♥t❛çã♦
❊ss❛ é ❛ ❡t❛♣❛ ❡♠ q✉❡ s❡ ❞❡✈❡ ❝♦♥✜❣✉r❛r ❛ ❝♦♥❡①ã♦ ❡♥tr❡ ♦ ❝❡♥ár✐♦ ❞♦ ♣r♦❜❧❡♠❛ ❡ ♦ ❡s♣❛ç♦ ❞❡ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛✳ ❖s ♦❜❥❡t♦s q✉❡ ❢♦r♠❛♠ ♣♦ssí✈❡✐s s♦❧✉çõ❡s ♥♦ ❝♦♥t❡①t♦ ♦r✐❣✐♥❛❧ ❞♦ ♣r♦❜❧❡♠❛ sã♦ r❡❢❡r❡♥❝✐❛❞♦s ❝♦♠♦ ❢❡♥ót✐♣♦s✱ ❡♥q✉❛♥t♦ q✉❡ ❛s
❈❛♣ít✉❧♦ ✷✳ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ✷✳✹✳ ❈♦♠♣♦♥❡♥t❡s ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❡✈♦❧✉t✐✈♦
❡str✉t✉r❛s ❞❡ ❞❛❞♦s✱ ♦✉ s❡❥❛✱ ✐♥❞✐✈í❞✉♦s ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❡✈♦❧✉t✐✈♦ sã♦ ❝❤❛♠❛❞♦s ❞❡ ❣❡♥ót✐♣♦s✳
■♥✐❝✐❛✲s❡ ❞❡✜♥✐♥❞♦ ♦ ♠❛♣❡❛♠❡♥t♦ q✉❡ r❡❧❛❝✐♦♥❛ ♦s ❢❡♥ót✐♣♦s ✭♣♦ssí✈❡✐s s♦❧✉çõ❡s✮ ❝♦♠ ♦s ❣❡♥ót✐♣♦s✱ ❞❡ ❢♦r♠❛ q✉❡ ❝❛❞❛ ❣❡♥ót✐♣♦ ❝♦rr❡s♣♦♥❞❡ ❛ ✉♠ ❢❡♥ót✐♣♦ ♥♦ ❝❡♥ár✐♦ ❞♦ ♣r♦❜❧❡♠❛✳ ❖ ❡s♣❛ç♦✲❣❡♥ót✐♣♦ ♣♦❞❡ s❡r ❝♦♠♣❧❡t❛♠❡♥t❡ ❞✐❢❡r❡♥t❡ ❞♦ ❡s♣❛ç♦✲❢❡♥ót✐♣♦✱ ♣♦r ❡①❡♠♣❧♦✱ ♦ ♣r♦❜❧❡♠❛ ❡♠ q✉❡stã♦ ♣♦❞❡ s❡r ❛❝❤❛r ♦ ♣♦♥t♦ ❞❡ ♠á①✐♠♦ ❛❜s♦❧✉t♦ ❞❡ ✉♠❛ ❢✉♥çã♦ r❡❛❧ ❞❡ ✈❛r✐á✈❡✐s r❡❛✐s❀ ❝♦♠♦ é ✉♠❛ ❢✉♥çã♦ r❡❛❧✱ s❡✉ ❝♦♥❥✉♥t♦ ❞❡ ❢❡♥ót✐♣♦ t❡♠ r❡♣r❡s❡♥t❛çã♦ ❞❡❝✐♠❛❧ ❡ ❛❧❣✉é♠ ♣♦❞❡ ❝♦❞✐✜❝❛r s❡✉s ❡❧❡♠❡♥t♦s ❣❡♥ót✐♣♦s ❡♠ r❡♣r❡s❡♥t❛çã♦ ❜✐♥ár✐❛ ✭❝♦♠♣❧❡t❛♠❡♥t❡ ❞✐st✐♥t♦ ❞♦ ❡s♣❛ç♦✲ ❢❡♥ót✐♣♦✮✱ ❛ss✐♠✱ t♦❞❛ ❛ ❜✉s❝❛ ♣♦r s♦❧✉çõ❡s ót✐♠❛s s❡ ❞á ♥♦ ❡s♣❛ç♦ ❣❡♥ót✐♣♦✱ ✐st♦ é✱ ♥♦ ❡s♣❛ç♦ ❞❡ r❡♣r❡s❡♥t❛çã♦ ❜✐♥ár✐❛✳
❙❡♠♣r❡ q✉❡ s❡ ❡♥❝♦♥tr❛ ✉♠❛ s♦❧✉çã♦ ót✐♠❛ ✭♦✉ s✉❜✲ót✐♠❛✮ ♥♦ ❡s♣❛ç♦✲❣❡♥ót✐♣♦✱ é ♣♦ssí✈❡❧ ♦❜t❡r ❛ s♦❧✉çã♦ ❛ss♦❝✐❛❞❛ ♥♦ ❡s♣❛ç♦✲❢❡♥ót✐♣♦ ❛tr❛✈és ❞❛ ❞❡❝♦❞✐✜❝❛çã♦ ❞❛ ❡str✉t✉r❛ ❞❡ ❞❛❞♦s ❛♦ ✜♥❛❧ ❞♦ ♣r♦❝❡ss♦ ❞❡ ♦t✐♠✐③❛çã♦✳
❆ t❡r♠✐♥♦❧♦❣✐❛ ❛❞♦t❛❞❛ ♣❛r❛ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛ ❞❡♥♦♠✐♥❛ ♣♦r✿ ♣♦ssí✈❡❧ s♦❧✉çã♦✱ ❢❡♥ót✐♣♦ ♦✉ ✐♥❞✐✈í❞✉♦ ♦s ♣♦♥t♦s ❞♦ ❡s♣❛ç♦ ❞❡ ♣♦ssí✈❡✐s s♦❧✉çõ❡s✱ ♦ ♣ró♣r✐♦ ❡s♣❛ç♦ ❞❡ ♣♦ssí✈❡✐s s♦❧✉çõ❡s é ❝❤❛♠❛❞♦ ❞❡ ❡s♣❛ç♦✲❢❡♥ót✐♣♦✳ ❏á ♦ ❣❡♥ót✐♣♦✱ ❝r♦♠♦ss♦♠♦s ❡ ♥♦✈❛♠❡♥t❡ ✐♥❞✐✈í❞✉♦ ♣♦❞❡♠ s❡r ✉s❛❞♦s ♣❛r❛ ♣♦♥t♦s ♦♥❞❡ ❛ ❜✉s❝❛ ❡✈♦❧✉❝✐♦♥ár✐❛ ♦❝♦rr❡ ✭❡s♣❛ç♦✲❣❡♥ót✐♣♦✮✳
❍á t❛♠❜é♠ ♠✉✐t♦s t❡r♠♦s r❡❧❛❝✐♦♥❛♥❞♦ ♦s ❡❧❡♠❡♥t♦s ❞❡ ✉♠ ✐♥❞✐✈í❞✉♦✱ ❝❛❞❛ ❝♦♠♣♦♥❡♥t❡ ❞♦ ✐♥❞✐✈í❞✉♦ é ❝❤❛♠❛❞♦ ❞❡ ✈❛r✐á✈❡❧✱ ❧♦❝✉s✱ ♣♦s✐çã♦ ♦✉ ❣❡♥❡✳ ❯♠ ♦❜❥❡t♦ ❡♠ t❛❧ ❧✉❣❛r ♣♦❞❡ s❡r ❝❤❛♠❛❞♦ ❞❡ ✈❛❧♦r ♦✉ ✉♠ ❛❧❡❧♦✳
❖ tr❛❜❛❧❤♦ ❞❡ ◆✐❝♦❧ ◆✳ ❙❝❤r❛✉❞♦❧♣❤ ✐♥t✐t✉❧❛❞♦ ❉②♥❛♠✐❝ ♣❛r❛♠❡t❡r ❡♥❝♦❞✐♥❣ ❢♦r ❣❡♥❡t✐❝ ❛❧❣♦r✐t❤♠s ❛♣r❡s❡♥t❛ ✉♠❛ ✐♥t❡r❡ss❛♥t❡ ❝♦❞✐✜❝❛çã♦ ❞✐♥â♠✐❝❛ ♣❛r❛ ❡✈✐t❛r ♦ ❞✐❧❡♠❛ ❞❡ s❛❝r✐✜❝❛r ❛ ♣r❡❝✐sã♦ ❞❛ r❡♣r❡s❡♥t❛çã♦ ♥✉♠ér✐❝❛ ♦✉ ❛ ❡✜❝✐ê♥❝✐❛ ♥❛ ❜✉s❝❛ ♣♦r ✉♠❛ s♦❧✉çã♦ ót✐♠❛ q✉❛♥❞♦ s❡ tr❛❜❛❧❤❛ ❝♦♠ ♦t✐♠✐③❛çã♦ ❞❡ ❢✉♥çõ❡s ❞❡ ✈❛❧♦r r❡❛❧ ✭❬✸✺❪✮✳
❈❛♣ít✉❧♦ ✷✳ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ✷✳✹✳ ❈♦♠♣♦♥❡♥t❡s ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❡✈♦❧✉t✐✈♦
✷✳✹✳✷ ❋✉♥çã♦ ❞❡ ❛✈❛❧✐❛çã♦ ✭❋✉♥çã♦ ❞❡ ✜t♥❡ss✮
❆ ❢✉♥çã♦ ❞❡ ❛✈❛❧✐❛çã♦ t❡♠ ♦ ♣❛♣❡❧ ❞❡ ❛♣r❡s❡♥t❛r ♦s r❡q✉✐s✐t♦s ♣❛r❛ ❛ ❛❞❛♣t❛çã♦✱ ❡❧❛ é ♦ ♣❛râ♠❡tr♦ ♣❛r❛ ❛ s❡❧❡çã♦ ❞♦s ❣❡♥ót✐♣♦s ♣❛✐s q✉❡ ❞❛rã♦ ♦r✐❣❡♠ ❛ ♥♦✈♦s r❡♣r❡s❡♥t❛♥t❡s ♠❛✐s ❛❞❛♣t❛❞♦s ♦✉ ♥ã♦✳ ❆tr❛✈és ❞❛ ❢✉♥çã♦ ❞❡ ❛✈❛❧✐❛çã♦ é ♣♦ssí✈❡❧ ♠❡❞✐r ♦ q✉❛♥t♦ ✉♠ ❣❡♥ót✐♣♦ ❡stá r❡s♦❧✈❡♥❞♦ ♦ ♣r♦❜❧❡♠❛ ❛ss♦❝✐❛❞♦✱ s✉❛ ♠❡❞✐❞❛ ❞❡ q✉❛❧✐❞❛❞❡ ❡stá ❛ss♦❝✐❛❞❛ ❛♦ ❡s♣❛ç♦ ❞♦s ❣❡♥ót✐♣♦s✳
❊♠ ❣❡r❛❧✱ ❛ ❢✉♥çã♦ ❞❡ ✜t♥❡ss é q✉❛❧q✉❡r ❢✉♥çã♦ q✉❡ ❝❛♣t❛ ❛ q✉❛❧✐❞❛❞❡ ♥♦s ❣❡♥ót✐♣♦s✱ q✉❛❧✐❞❛❞❡s ❡st❛s q✉❡ ♦ t♦r♥❛♠ ♠❛✐s ♣ró①✐♠♦s ❞❛ s♦❧✉çã♦ ót✐♠❛ ♦✉ s✉❜✲ ót✐♠❛ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✳ P♦ré♠✱ ❤á ❝❛s♦s ❡♠ q✉❡ ❛ ❢✉♥çã♦ ❞❡ ✜t♥❡ss ♣♦❞❡ ✈✐r ❛ s❡r ❛ ♣ró♣r✐❛ ❢✉♥çã♦ ❛ss♦❝✐❛❞❛ ❛♦ ❝♦♥t❡①t♦ ❞♦ ♣r♦❜❧❡♠❛ ♦✉ ✉♠❛ s✐♠♣❧❡s tr❛♥❢♦r♠❛çã♦ ❞❡st❛✳
◆♦ ❛rt✐❣♦ ❚❤❡ ❊✛❡❝ts ♦❢ ❋✐t♥❡ss ❋✉♥❝t✐♦♥s ♦♥ ●❡♥❡t✐❝ Pr♦❣r❛♠♠✐♥❣✲❇❛s❡❞ ❘❛♥❦✐♥❣ ❉✐s❝♦✈❡r② ❋♦r ❲❡❜ ❙❡❛r❝❤ ❡s❝r✐t♦ ♣♦r ❲❡✐❣✉♦ ❋❛♥✱ é ❛♣r❡s❡♥t❛❞♦ ♦ ❡st✉❞♦ ❛ r❡s♣❡✐t♦ ❞❛ ❢✉♥çã♦ ❞❡ ✜t♥❡ss ❝♦♠ r❡❧❛çã♦ à ❡✜❝✐ê♥❝✐❛ ❡ à ❡❢❡t✐✈✐❞❛❞❡ ❞❡ ❛❧❣♦r✐t♠♦s ❡✈♦❧✉t✐✈♦s✳ ❖ ❛✉t♦r ❝♦♥❝❧✉✐ q✉❡ ❛ ❛❞❡q✉❛çã♦ ❞❛ ❢✉♥çã♦ ❞❡ ✜t♥❡ss é ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ ❛ ♠❡❧❤♦r✐❛ ♥♦ ❞❡s❡♠♣❡♥❤♦ ✭❬✶✻❪✮✳
✷✳✹✳✸ P♦♣✉❧❛çã♦
❆ ♣♦♣✉❧❛çã♦ ❝♦♥té♠ ❛s ♣♦ssí✈❡✐s s♦❧✉çõ❡s ✭r❡♣r❡s❡♥t❛çã♦ ❞❡st❛s✮✱ ♥❡ss❡s t❡r♠♦s✱ ❛ ♣♦♣✉❧❛çã♦ é ✉♠❛ ❝♦❧❡çã♦ ❞❡ ❣❡♥ót✐♣♦s✳ ❊❧❛ é ✉♠ ♣❛ss♦ ❞❛ ❡✈♦❧✉çã♦✱ s❡✉s ✐♥❞✐✈í❞✉♦s sã♦ ❡stát✐❝♦s✱ ✐st♦ é✱ ♥ã♦ s♦❢r❡♠ ❛❞❛♣t❛çã♦ ♥❡♠ s❡ ♠♦❞✐✜❝❛♠ ❞❡♥tr♦ ❞❛ ♣♦♣✉❧❛çã♦ s♦❜ ✉♠❛ ❣❡r❛çã♦ ✜①❛❀ ❡♠ ❣❡r❛❧✱ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ✐♥❞✐✈í❞✉♦s ❝♦♥t✐❞♦s ♥❛ ♣♦♣✉❧❛çã♦ s❡ ♠❛♥té♠ ✜①❛ ❞✉r❛♥t❡ t♦❞♦ ♦ ♣r♦❝❡ss♦ ❞❡ ❜✉s❝❛ ❡✈♦❧✉t✐✈❛✳
❖s ♦♣❡r❛❞♦r❡s ❞❡ ✈❛r✐❛çã♦ ❛t✉❛♠ ❛ ♥í✈❡❧ ❞❡ ✐♥❞✐✈í❞✉♦s✱ ✐st♦ é✱ ✉♠❛ ✈❡③ q✉❡ ♦ ✐♥❞✐✈í❞✉♦ é s❡❧❡❝✐♦♥❛❞♦ t❛✐s ♦♣❡r❛❞♦r❡s ❛t✉❛♠✳ ❏á ♦s ♦♣❡r❛❞♦r❡s ❞❡ s❡❧❡çã♦ ❛❣❡♠ ❛ ♥í✈❡❧ ❞❡ ♣♦♣✉❧❛çã♦✱ ❞❛í✱ ❧❡✈❛♠ ❡♠ ❝♦♥t❛ ❛ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ t♦❞♦s ♦s ❣❡♥ót✐♣♦s ❡♥✈♦❧✈✐❞♦s ♥❛ ♣♦♣✉❧❛çã♦ ❡ ❞❡❝✐❞❡ s✉❛ ❛çã♦ ❡♠ ❢✉♥çã♦ ❞❡ss❛✳
❈❛♣ít✉❧♦ ✷✳ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ✷✳✹✳ ❈♦♠♣♦♥❡♥t❡s ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❡✈♦❧✉t✐✈♦
❆ ♠❡❞✐❞❛ ❞❡ ❞✐✈❡rs✐❞❛❞❡ ❡stá ❛ss♦❝✐❞❛❞❛ ❛♦ ♥ú♠❡r♦ ❞❡ ❞✐❢❡r❡♥t❡s s♦❧✉çõ❡s q✉❡ ❡stã♦ ❝♦♥t✐❞❛s ❡♠ ✉♠ ❞❛❞♦ ♠♦♠❡♥t♦ ❞❛ ♣♦♣✉❧❛çã♦✱ ❛ss✐♠✱ é ♣♦ssí✈❡❧ ♣❡r❝❡❜❡r q✉❡ ❝♦♠♦ ❛ ♣♦♣✉❧❛çã♦ é ♠✉tá✈❡❧ ❡ ♥❡ss❡ ❝♦♥t❡①t♦ ❛❧t❡r❛ s❡✉s ✐♥❞✐✈í❞✉♦s ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✱ ❛ ❞✐✈❡rs✐❞❛❞❡ t❡♥❞❡ ❛ s❡r ♠♦❞✐✜❝❛❞❛ ❞✉r❛♥t❡ t♦❞❛ ❛ ❜✉s❝❛✳ ➱ ✐♠♣♦rt❛♥t❡ ❝♦♠♣r❡❡♥❞❡r q✉❡ ❡♠❜♦r❛ s❡❥❛ ♣♦ssí✈❡❧ t❡r ✉♠ ú♥✐❝♦ ✈❛❧♦r ❞❡ ✜t♥❡ss✱ ❛♦ ✜♠ ❞❡ ✉♠ ♣r♦❝❡ss♦ ❞❡ ❜✉s❝❛✱ ♥ã♦ s✐❣♥✐✜❝❛ q✉❡ s❡ t❡♥❤❛ ✉♠ ú♥✐❝♦ ❣❡♥ót✐♣♦❀ t❛♠❜é♠✱ ✉♠ ú♥✐❝♦ ❢❡♥ót✐♣♦ ♥ã♦ s✐❣♥✐✜❝❛ q✉❡ s❡ t❡♥❤❛ ✉♠ ú♥✐❝♦ ❣❡♥ót✐♣♦✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ♦ ❝♦♥trár✐♦ ♥ã♦ é ✈❡r❞❛❞❡✐r♦✱ s❡ ❤♦✉✈❡r ✉♠ ú♥✐❝♦ ❣❡♥ót✐♣♦ t❡rá ✉♠ ú♥✐❝♦ ✈❛❧♦r ❞❡ ✜t♥❡ss ❡ t❛♠❜é♠ ✉♠ ú♥✐❝♦ ❢❡♥ót✐♣♦ ❛ss♦❝✐❛❞♦✳
❆❧❛♥❞❡r ❏✳ ❚✳ ❡♠ s❡✉ tr❛❜❛❧❤♦ ❖♥ ♦♣t✐♠❛❧ ♣♦♣✉❧❛t✐♦♥ s✐③❡ ♦❢ ❣❡♥❡t✐❝ ❛❧❣♦r✐t❤♠s ❛♣r❡s❡♥t❛ ✉♠ ❡st✉❞♦ s♦❜r❡ ♦ t❛♠❛♥❤♦ ót✐♠♦ ❞❛ ♣♦♣✉❧❛çã♦ ❝♦♠♦ ❢✉♥çã♦ ❞❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦ ♣r♦❜❧❡♠❛✱ ♦ ❛✉t♦r ❝♦♥❝❧✉✐ q✉❡ ❡♠ ♠áq✉✐♥❛s s❡q✉❡♥❝✐❛✐s ♣❛r❛ ♣r♦❜❧❡♠❛s ❞❡ ❝♦♠♣❧❡①✐❞❛❞❡ ♠♦❞❡r❛❞❛✱ ♦ t❛♠❛♥❤♦ ót✐♠♦ ❞❛ ♣♦♣✉❧❛çã♦ é ❢✉♥çã♦ ❞♦ t❛♠❛♥❤♦ ❞♦ ✈❡t♦r q✉❡ r❡♣r❡s❡♥t❛ ✉♠ ❣❡♥ót✐♣♦✳ ❏á ❡♠ ❛rq✉✐t❡t✉r❛ ♣❛r❛❧❡❧❛✱ ♦ t❛♠❛♥❤♦ ót✐♠♦ é ♠❛✐♦r q✉❡ ♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❝❛s♦ ❡♠ ❛rq✉✐t❡t✉r❛ s❡q✉❡♥❝✐❛❧ ❡ q✉❡ ♦ t❛♠❛♥❤♦ ❡①❛t♦ é s❡♥sí✈❡❧ ❛ ❞❡t❛❧❤❡s ♥❛ ✐♠♣❧❡♠❡♥t❛çã♦ ✭❬✷❪✮✳ ❏á ♦ tr❛❜❛❧❤♦ ❞❡ ❆r❛❜❛s ❏✳✱ ✐♥t✐t✉❧❛❞♦ ●❆❱❛P❙✲❛ ❣❡♥❡t✐❝ ❛❧❣♦r✐t❤♠ ✇✐t❤ ✈❛r②✐♥❣ ♣♦♣✉❧❛t✐♦♥ s✐③❡ ❛♣r❡s❡♥t❛ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞❡ ♣♦♣✉❧❛çã♦ ✈❛r✐á✈❡❧ q✉❡ ❛✉♠❡♥t❛ ♦✉ ❞✐♠✐♥✉✐ ❡♠ ❢✉♥çã♦ ❞❡ ❛❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❛ ♣❡sq✉✐s❛✱ ❡❧❡ ❥✉st✐✜❝❛ q✉❡ s❡ ♦ t❛♠❛♥❤♦ ❞❛ ♣♦♣✉❧❛çã♦ ❢♦r ♠✉✐t♦ ♣❡q✉❡♥♦ ❛ ❝♦♥✈❡r❣ê♥❝✐❛ ♣♦❞❡ s❡r ♠✉✐t♦ rá♣✐❞❛ ❡ ❧❡✈❛r✐❛ ❛ ✉♠ ♠á①✐♠♦✴♠í♥✐♠♦ ❧♦❝❛❧❀ ❡ q✉❡ s❡ ❛ ♣♦♣✉❧❛çã♦ ❢♦r ♠✉✐t♦ ❣r❛♥❞❡✱ ❤❛✈❡rá ❞❡s♣❡r❞í❝✐♦ ❞♦s r❡❝✉rs♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❡ ♦ t❡♠♣♦ ❞❡ ❡s♣❡r❛ ♣♦r ✉♠❛ ♠❡❧❤♦r✐❛ ♣♦❞❡ s❡r ❞❡♠❛s✐❛❞♦ ❧♦♥❣♦ ✭❬✸❪✮✳
✷✳✹✳✹ ▼❡❝❛♥✐s♠♦ ❞❡ s❡❧❡çã♦ ❞♦s r❡♣r♦❞✉t♦r❡s
❖s ♠❡❝❛♥✐s♠♦s ❛❞♦t❛❞♦s ♣❛r❛ s❡❧❡❝✐♦♥❛r ♦s r❡♣r♦❞✉t♦r❡s sã♦ q✉❛✐sq✉❡r ❛❧❣♦r✐t♠♦s q✉❡ ❜❡♥❡✜❝✐❛♠ ✉♠ ❣❡♥ót✐♣♦ ♣r♦♣♦r❝✐♦♥❛❧♠❡♥t❡ à s✉❛ q✉❛❧✐❞❛❞❡ ♥❛ ❢✉♥çã♦ ❞❡ ❛✈❛❧✐❛çã♦✳ ◆❡ss❡ s❡♥t✐❞♦✱ ♦s ♠❡❧❤♦r❡s ❣❡♥ót✐♣♦s t❡rã♦ ♠❛✐♦r ❝❤❛♥❝❡ ❞❡ s❡ t♦r♥❛r❡♠ ♦s ❣❡♥ót✐♣♦s✲♣❛✐s ✭✉♠ ❣❡♥ót✐♣♦ s❡rá ❞❡✜♥✐❞♦ ❝♦♠♦ ❣❡♥ót✐♣♦✲♣❛✐ s❡ ♦
❈❛♣ít✉❧♦ ✷✳ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ✷✳✹✳ ❈♦♠♣♦♥❡♥t❡s ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❡✈♦❧✉t✐✈♦
♠❡s♠♦ ❢♦r s❡❧❡❝✐♦♥❛❞♦ ❛tr❛✈és ❞❡ ❛❧❣✉♠ ♠❡❝❛♥✐s♠♦ ❞❡ s❡❧❡çã♦ ❞♦s r❡♣r♦❞✉t♦r❡s✮✳ ❆ ❝♦♠♣♦s✐çã♦ ❞♦ ♠❡❝❛♥✐s♠♦ ❞❡ s❡❧❡çã♦ ❞♦s r❡♣r♦❞✉t♦r❡s ❡ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ s❡❧❡çã♦ ❞♦s s♦❜r❡✈✐✈❡♥t❡s sã♦ r❡s♣♦♥sá✈❡✐s ♣❡❧❛ ♠❡❧❤♦r❛ ♥❛ q✉❛❧✐❞❛❞❡ ❞❛ ♣♦♣✉❧❛çã♦ ❛tr❛✈és ❞❛ ❡❧✐♠✐♥❛çã♦✴✐♥s❡rçã♦ ❞❡ ✐♥❞✐✈í❞✉♦s ♠❡♥♦s✴♠❛✐s q✉❛❧✐✜❝❛❞♦s✳
❱❛❧❡ s❛❧✐❡♥t❛r q✉❡ ♦ ❛❧❣♦r✐t♠♦ q✉❡ t❡rá ♦ ♣❛♣❡❧ ❞❡ s❡❧❡❝✐♦♥❛r ♦s ❣❡♥ót✐♣♦s t❡♠ ❝❛r❛❝t❡ríst✐❝❛s ❡st♦❝ást✐❝❛s✱ ✐st♦ é✱ ❛ s❡❧❡çã♦ ❞♦ ✐♥❞✐✈í❞✉♦ ♠❛✐s q✉❛❧✐✜❝❛❞♦ ♥ã♦ é ❞❡t❡r♠✐♥íst✐❝♦✱ ❡ s✐♠ ♣r♦❜❛❜✐❧✐st✐❝❛♠❡♥t❡✱ ❞❡ ❢♦r♠❛ q✉❡✱ ✐♥❞✐✈í❞✉♦s ♠❛✐s q✉❛❧✐✜❝❛❞♦s t❡rã♦ ♠❛✐♦r ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ s❡r❡♠ s❡❧❡❝✐♦♥❛❞♦s✳ Pr♦❜❛❜✐❧✐❞❛❞❡ ❡st❛ q✉❡ é ♣r♦♣♦r❝✐♦♥❛❧ à s✉❛ q✉❛❧✐❞❛❞❡ ✭q✉ã♦ ♠❡❧❤♦r ❢♦r ❛ q✉❛❧✐❞❛❞❡✱ ♠❛✐♦r s❡rá ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ s❡❧❡çã♦ ❛ss♦❝✐❛❞❛ ❛ t❛❧ ❣❡♥ót✐♣♦✮✱ ❡♠❜♦r❛ t♦❞♦s ♦s ✐♥❞✐✈í❞✉♦s t❡♥❤❛♠ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♣♦s✐t✐✈❛ ❞❛♥❞♦ ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ q✉❡ ♦ ❣❡♥ót✐♣♦ ♠❡♥♦s q✉❛❧✐✜❝❛❞♦ t❛♠❜é♠ ♣♦ss❛ s❡r s❡❧❡❝✐♦♥❛❞♦✳ ❊ss❛ ❝♦♥❞✐çã♦ ❣❛r❛♥t❡ q✉❡ ❛ s❡❧❡çã♦ ♥ã♦ s❡♥t❡♥❝✐❡ q✉❡ ❛ ❢✉♥çã♦ ❞❡ ❛✈❛❧✐❛çã♦ t❡♥❞❛ ♣❛r❛ ✉♠ ♠á①✐♠♦✴♠í♥✐♠♦ ❧♦❝❛❧✱ ❛ss❡❣✉r❛♥❞♦ ❛ ❞✐✈❡rs✐❞❛❞❡ ❞♦s ❛❧❡❧♦s q✉❡ s❡ ❡♥❝♦♥tr❛♠ ❡s♣❛❧❤❛❞♦s ♣♦r t♦❞❛ ❛ ♣♦♣✉❧❛çã♦ ✭❜❛st❛ ✐♠❛❣✐♥❛r ♦ ❝❛s♦ ❡♠ q✉❡ ❞❛❞♦ ✉♠ ♠♦♠❡♥t♦ ❞❛ ❡✈♦❧✉çã♦✱ ❤❛❥❛ s♦♠❡♥t❡ ✉♠❛ q✉❛❧✐❞❛❞❡ ❧✐♠✐t❛❞❛ ❞❡ ❛❧❡❧♦s ❝♦♠✉♥s ❛♦s ❣❡♥ót✐♣♦s ♠❛✐s q✉❛❧✐✜❝❛❞♦s✳ ❉❛í✱ s❡ ✈✐❡r ❛ s❡❧❡❝✐♦♥❛r ❞❡t❡r♠✐♥✐st✐❝❛♠❡♥t❡ ♦s ♠❛✐s q✉❛❧✐✜❝❛❞♦s✱ ❡stá ❛♣❡♥❛s ❝♦♠❜✐♥❛♥❞♦ ❛ ♠❡s♠❛ ❝♦❧❡çã♦ ❞❡ ❛❧❡❧♦s✱ ❡ ❛ss✐♠✱ ❛ ❝♦t❛ s✉♣❡r✐♦r ❞❛ ❢✉♥çã♦ ❞❡ ❛✈❛❧✐❛çã♦ s❡r✐❛ ❧✐♠✐t❛❞❛ ❛ ❝♦♠❜✐♥❛çã♦ ❞♦s ❛❧❡❧♦s ♠❛✐s s✐❣♥✐✜❝❛t✐✈♦s ❞❡ss❡ s✉❜❝♦♥❥✉♥t♦ ♣ró♣r✐♦ ❞♦s ❛❧❡❧♦s ❞❛ ♣♦♣✉❧❛çã♦✮✳
❖ ♣r♦❜❧❡♠❛ ❞♦ ❈❛✐①❡✐r♦ ✈✐❛❥❛♥t❡ ✲ ❚r❛✈❡❧❧✐♥❣ ❙❛❧❡s♠❛♥ Pr♦❜❧❡♠ ✭❬✹❪✮ ❝♦♥s✐st❡ ❞❡ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦ ❡♠ q✉❡ s❡ ❜✉s❝❛ ❛ ♠❡❧❤♦r r♦t❛ ♣❛ss❛♥❞♦ ✉♠❛ ú♥✐❝❛ ✈❡③ ♣♦r ❞✐✈❡rs♦s ♣♦♥t♦s ❡♠ ✉♠❛ t♦♣♦❧♦❣✐❛ q✉❛❧q✉❡r✱ é ❛♣r❡s❡♥t❛❞♦ ♣♦r ▲❛rr❛ñ❛❣❛ ❡♠ s❡✉ tr❛❜❛❧❤♦ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠s ❢♦r t❤❡ ❚r❛✈❡❧❧✐♥❣ ❙❛❧❡s♠❛♥ Pr♦❜❧❡♠✿ ❆ ❘❡✈✐❡✇ ♦❢ ❘❡♣r❡s❡♥t❛t✐♦♥s ❛♥❞ ❖♣❡r❛t♦rs ✭❬✷✽❪✮✳ ◆❡st❡ tr❛❜❛❧❤♦ ♦ ❛✉t♦r ❛♣r❡s❡♥t❛ ♦s ♦♣❡r❛❞♦r❡s ❞❡ s❡❧❡çã♦✱ ❞❡♥tr❡ ♦✉tr♦s ♦♣❡r❛❞♦r❡s✱ ❡♠ ❞✐✈❡rs❛s r❡♣r❡s❡♥t❛çõ❡s ✭❜✐♥ár✐❛✱ ❝❛♠✐♥❤♦✱ ❛❞❥❛❝ê♥❝✐❛✱ ♦r❞✐♥❛❧ ❡ ♠❛tr✐❝✐❛❧✮ ✈❡r✐✜❝❛♥❞♦ ♦s ❞❡s❡♠♣❡♥❤♦s ❡①♣❡r✐♠❡♥t❛✐s ❞❡ t❛✐s ♦♣❡r❛❞♦r❡s ❡♠ ❢✉♥çã♦ ❞❛s ❞✐✈❡rs❛s r❡♣r❡s❡♥t❛çõ❡s✳
❏á ♦ tr❛❜❛❧❤♦ ❞❡ ●♦❧❞❜❡r❣ ❡ ❉❡❜✱ ✐♥t✐t✉❧❛❞♦ ❆ ❝♦♠♣❛r❛t✐✈❡ ❛♥❛❧②s✐s ♦❢ s❡❧❡❝t✐♦♥
❈❛♣ít✉❧♦ ✷✳ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ✷✳✹✳ ❈♦♠♣♦♥❡♥t❡s ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❡✈♦❧✉t✐✈♦
s❝❤❡♠❡s ✉s❡❞ ✐♥ ❣❡♥❡t✐❝ ❛❧❣♦r✐t❤♠s ✭❬✷✶❪✮ ❛♣r❡s❡♥t❛ ✉♠❛ ❛♥á❧✐s❡ s♦❜r❡ ♦s ♦♣❡r❛❞♦r❡s ❞❡ s❡❧❡çã♦ ♠❛✐s ✉t✐❧✐③❛❞♦s ❡♠ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛✱ ❡♥tr❡ ❡❧❡s t❡♠♦s✿ r❡♣r♦❞✉çã♦ ♣r♦♣♦r❝✐♦♥❛❧✱ r❛♥❦✐♥❣✱ t♦r♥❡✐♦ ❡ ❣❡♥✐t♦r ✭❡st❛❞♦ ❡st❛❝✐♦♥ár✐♦✮✳ ❈♦♠♦ r❡s✉❧t❛❞♦✱ sã♦ ❢♦r♥❡❝✐❞❛s s♦❧✉çõ❡s ❛♣r♦①✐♠❛❞❛s ❡ ❡①❛t❛s ♣❛r❛ s✐♠✉❧❛çõ❡s✱ ❜❡♠ ❝♦♠♦ t❡♠♣♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ út✐❧ ❡ t❛①❛ ❞❡ ❝r❡s❝✐♠❡♥t♦❀ ❛ ♣r✐♥❝✐♣❛❧ ❝♦♥tr✐❜✉✐çã♦ é ❞❛❞❛ ♣♦r s✉❣❡stã♦ ❞❡ ❝❛♠✐♥❤♦s ♣❛r❛ ✐♥✈❡st✐❣❛çã♦ ❛♥❛❧ít✐❝❛ ♠❛✐s ❞❡t❛❧❤❛❞❛ ❞❛s té❝♥✐❝❛s ❞❡ s❡❧❡çã♦✳
✷✳✹✳✺ ❖♣❡r❛❞♦r❡s ❞❡ ✈❛r✐❛çã♦✿ ♠✉t❛çã♦ ❡ r❡❝♦♠❜✐♥❛çã♦
❖s ♦♣❡r❛❞♦r❡s ❞❡ ✈❛r✐❛çã♦ ❛t✉❛♠ ♥♦s ❣❡♥ót✐♣♦s ♠♦❞✐✜❝❛♥❞♦✲♦s ❛ ✜♠ ❞❡ ♦❜t❡r ♠❡❧❤♦r❛♠❡♥t♦s ♥❛ q✉❛❧✐❞❛❞❡ ❞♦ ✐♥❞✐✈í❞✉♦✱ ✐st♦ é✱ r❡❝❡❜❡♠ ❣❡♥ót✐♣♦s s❡❧❡❝✐♦♥❛❞♦s ♥❛ ♣♦♣✉❧❛çã♦ ❛tr❛✈és ❞❡ ♦♣❡r❛❞♦r❡s ❞❡ s❡❧❡çã♦ ❡ ♦s ♠♦❞✐✜❝❛ s❡❣✉✐♥❞♦ ❛❧❣✉♠ ❛❧❣♦r✐t♠♦✳ ❇❛s✐❝❛♠❡♥t❡ ❤á ❞♦✐s t✐♣♦s ❞❡ ♦♣❡r❛❞♦r❡s✿ ▼✉t❛çã♦ ❡ r❡❝♦♠❜✐♥❛çã♦ ♦✉ ❝r✉③❛♠❡♥t♦✳
▼✉t❛çã♦
❆ ♠✉t❛çã♦ t❡♠ ❛ t❛r❡❢❛ ❞❡ ♠♦❞✐✜❝❛r ♦ ❣❡♥ót✐♣♦ s❡❧❡❝✐♦♥❛❞♦ ❛t✉❛♥❞♦ ❞✐r❡t❛♠❡♥t❡ ♥❛ ♠♦❞✐✜❝❛çã♦ ❞❡ ✉♠ ♦✉ ♠❛✐s ❛❧❡❧♦s ❛tr❛✈és ❞❡ ❛❧❣✉♠❛ r♦t✐♥❛ ❡st♦❝ást✐❝❛ q✉❡ ❞❡✜♥❡ ♦ ❛❧❡❧♦ q✉❡ s♦❢r❡rá ❛ ♠✉t❛çã♦ ✭❊ss❛ ❝♦♥❞✐çã♦ ❣❛r❛♥t❡ q✉❡ ❛s ♠♦❞✐✜❝❛çõ❡s ♦❝♦rr❛♠ ❡♠ ❞✐❢❡r❡♥t❡s s❡❣♠❡♥t♦s ❡ ❛ss❡❣✉r❡ ❣❡♥ót✐♣♦s ❞✐st✐♥t♦s ❛ ❝❛❞❛ ❛♣❧✐❝❛çã♦ ❞❛ ♠✉t❛çã♦✱ ♠❡s♠♦ q✉❡ s❡❥❛ ✉t✐❧✐③❛❞♦ ♦ ♠❡s♠♦ ❣❡♥ót✐♣♦ ❝♦♠♦ ❡♥tr❛❞❛ ♣❛r❛ ♦ ♦♣❡r❛❞♦r✮✳
❙♦❜ ♦ ❡s♣❛ç♦ ❞♦s ❢❡♥ót✐♣♦s✱ ✐st♦ é✱ ♦ ❡s♣❛ç♦ ❞❡ s♦❧✉çõ❡s✱ ♦ ❛t♦ ❞❡ ❛♣❧✐❝❛r ♦ ♦♣❡r❛❞♦r ♠✉t❛çã♦ é ♥❛ ✈❡r❞❛❞❡ t♦♠❛r ✉♠❛ ♥♦✈❛ s♦❧✉çã♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❡♠ ❡st✉❞♦✳ ❆ss✐♠✱ é ♣♦ssí✈❡❧ ♣❡r❝❡❜❡r q✉❡ ♣❛r❛ ✉♠ t❡♠♣♦ t✱ s✉✜❝✐❡♥t❡♠❡♥t❡ ❣r❛♥❞❡✱ ❛ ♠✉t❛çã♦
♣♦ss✐❜✐❧✐t❛rá q✉❡ ❛tr❛✈és ❞❡ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛ s❡ ♦❜t❡♥❤❛ ♦ ót✐♠♦ ✭♠á①✐♠♦ ♦✉ ♠í♥✐♠♦✮ ❣❧♦❜❛❧ ✭❬✶✺❪✮✳
❘❡❝♦♠❜✐♥❛çã♦
❆ r❡❝♦♠❜✐♥❛çã♦ ✭♦✉ ❝r✉③❛♠❡♥t♦✮ é ❛ ❝r✐❛çã♦ ❞❡ ❣❡♥ót✐♣♦s✳ ❆ss✐♠✱ ✉♠❛ ✈❡③ q✉❡ ❛tr❛✈és ❞❡ ✉♠ ♦♣❡r❛❞♦r ❞❡ s❡❧❡çã♦ ❢♦r❛♠ ❡s❝♦❧❤✐❞♦s ♦s ❣❡♥ót✐♣♦s ♣❛✐s✱ ❛
❈❛♣ít✉❧♦ ✷✳ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ✷✳✹✳ ❈♦♠♣♦♥❡♥t❡s ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❡✈♦❧✉t✐✈♦
r❡❝♦♠❜✐♥❛çã♦ ❛t✉❛ s❡❧❡❝✐♦♥❛♥❞♦ ✉♠ ✭♦✉ ♠❛✐s ❞❡ ✉♠✮ ♣♦♥t♦ ❞❡ ❝♦rt❡ ❞❡ ❢♦r♠❛ ❛❧❡❛tór✐❛ ❡♠ q✉❡ s❡rá ♣❡r♠✉t❛❞♦ ♦s ❛❧❡❧♦s ❞❡ ✉♠ ❣❡♥ót✐♣♦ ♣❛✐ ♣❛r❛ ♦✉tr♦✳ ❊♠ ♦✉tr❛s ♣❛❧❛✈r❛s✱ ♦ ♣r♦❝❡ss♦ ❞❡ r❡❝♦♠❜✐♥❛çã♦ tr❛♥s♠✐t❡ ♣❛rt❡ ❞❛ ✐♥❢♦r♠❛çã♦ ✭❛❧❡❧♦s✮ ❞♦s ♣❛✐s ♣❛r❛ ♦s ✜❧❤♦s✳ ❚❛❧ ❛t✐t✉❞❡✱ ❣❡r❛ ❣❡♥ót✐♣♦s ✜❧❤♦s q✉❡ ❝♦♠♣õ❡♠ ♣❛rt❡ ❞♦s ❛❧❡❧♦s ❞❡ ❝❛❞❛ ✉♠ ❞❡ s❡✉s ❣❡♥ót✐♣♦s ♣❛✐s✳
➱ ♣♦ssí✈❡❧ ♣❡r❝❡❜❡r q✉❡ ❛ ❡s❝♦❧❤❛ ❛❧❡❛tór✐❛ ❞♦ ♣♦♥t♦ ❞❡ ❝♦rt❡ ✭❛ ♣❛rt✐r ❞❡ q✉❡ ♠♦♠❡♥t♦ ❛ ✐♥❢♦r♠❛çã♦ s❡rá ♠✐st✉r❛❞❛✮ ❣❛r❛♥t❡ q✉❡ ♠❡s♠♦ q✉❡✱ ♣♦r ✈❡♥t✉r❛✱ ❡s❝♦❧❤❛✲s❡ ❡♠ ✉♠ ♦✉tr♦ ♠♦♠❡♥t♦ ♦s ♠❡s♠♦s ❣❡♥ót✐♣♦s ♣❛✐s ♣❛r❛ ♦❜t❡r ✐♥❢♦r♠❛çã♦✱ t❡rá ♣♦✉❝❛ ❝❤❛♥❝❡ ❞❡ q✉❡ ♦s ❛t✉❛✐s ❣❡♥ót✐♣♦s ✜❧❤♦s s❡❥❛♠ s❡♠❡❧❤❛♥t❡s ✭♥♦ q✉❡s✐t♦ ✐♥❢♦r♠❛çã♦ ❣❡♥ét✐❝❛✮ ❞❡ ♦✉tr♦s ❣❡♥ót✐♣♦s ✜❧❤♦s ❣❡r❛❞♦s ❛♥t❡r✐♦r♠❡♥t❡ ♣♦r ❡ss❡s s❡❧❡❝✐♦♥❛❞♦s✳
❖ ❡s♣❛ç♦ ❞♦s ❢❡♥ót✐♣♦s ❡♥❝❛r❛ t❛❧ ♠♦❞✐✜❝❛çã♦ ❝♦♠♦ ✉♠❛ ♥♦✈❛ s♦❧✉çã♦ ♦❜t✐❞❛ ❛tr❛✈és ❞❡ ✉♠❛ ❢✉♥çã♦ ❞❡ ♦✉tr❛s ❞✉❛s s♦❧✉çõ❡s✱ q✉❡ ♥❛q✉❡❧❡ ♠♦♠❡♥t♦✱ s❡ ♠♦str❛✈❛♠ ❛s ♠❡❧❤♦r❡s s♦❧✉çõ❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✳
◆♦ tr❛❜❛❧❤♦ ❆❞❛♣t✐✈❡ ♣r♦❜❛❜✐❧✐t✐❡s ♦❢ ❝r♦ss♦✈❡r ❛♥❞ ♠✉t❛t✐♦♥ ✐♥ ❣❡♥❡t✐❝ ❛❧❣♦r✐t❤♠s ✭❬✸✻❪✮ ❢♦✐ ❛♣r❡s❡♥t❛❞❛ ✉♠❛ ❛❜♦r❞❛❣❡♠ s♦❜r❡ ♦♣❡r❛❞♦r❡s ❞❡ ♠✉t❛çã♦ ❡ r❡❝♦♠❜✐♥❛çã♦ s♦❜ ♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❛❞❛♣t❛t✐✈♦✱ ✐st♦ é✱ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ♠✉t❛çã♦ ❡ r❡❝♦♠❜✐♥❛çã♦ ✈❛r✐❛ ❞❡♣❡♥❞❡♥❞♦ ❞♦ ✈❛❧♦r ❞❛ ❢✉♥çã♦ ❞❡ ❛✈❛❧✐❛çã♦ ❞♦s ❣❡♥ót✐♣♦s ❡♥✈♦❧✈✐❞♦s✳ ❊ss❛ t❡♥t❛t✐✈❛ ✈✐s❛ ❛ ♣r♦t❡❣❡r ❛s s♦❧✉çõ❡s ❞❡ ❛❧t♦ ✈❛❧♦r ❞❡ ✜t♥❡ss✳ ❆✐♥❞❛ ♥❡ss❡ tr❛❜❛❧❤♦✱ t❛♠❜é♠ é ♣♦ssí✈❡❧ ❞❡✜♥✐r ♦ ✈❛❧♦r ót✐♠♦ ♣❛r❛ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ♠✉t❛çã♦ ❡ r❡❝♦♠❜✐♥❛çã♦ ♣❛r❛ ❝❛❞❛ ❝❛s♦✱ ♥ã♦ s❡♥❞♦ ♥❡❝❡ssár✐♦ ❛r❜✐tr❛r ✉♠❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♣❛r❛ ❡ss❡s ♦♣❡r❛❞♦r❡s ❞❡ ❢♦r♠❛ ❣❡r❛❧✳ ❖ ❛✉t♦r ❥✉st✐✜❝❛ q✉❡ ❡ss❛ ❛❜♦r❞❛❣❡♠ s❡ ♠♦str❛ s❛t✐s❢❛tór✐❛ ❡♠ ❞♦✐s s❡♥t✐❞♦s✿ ▼❛♥t❡r ❛ ❞✐✈❡rs✐❞❛❞❡ ❞❛ ♣♦♣✉❧❛çã♦ ❡ s✉st❡♥t❛r ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ❛❧❣♦r✐t♠♦✳
✷✳✹✳✻ ▼❡❝❛♥✐s♠♦ ❞❡ s❡❧❡çã♦ ❞♦s s♦❜r❡✈✐✈❡♥t❡s ✭❙✉❜st✐t✉✐çã♦✮
❯♠❛ ✈❡③ q✉❡ s❡ t❡♥❤❛ ✉♠❛ ❝♦❧❡çã♦ ❞❡ ❣❡♥ót✐♣♦s ✭♣♦♣✉❧❛çã♦✮✱ ❡ ❛♣ós ❛ ❛♣❧✐❝❛çã♦ ❞♦s ♦♣❡r❛❞♦r❡s ❞❡ s❡❧❡çã♦ ✲ ♠✉t❛çã♦ ✲ r❡❝♦♠❜✐♥❛çã♦✱ t❡rá t❛♠❜é♠ ♦s ❣❡♥ót✐♣♦s ✜❧❤♦s✳
