❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦
❊s❝♦❧❛ ❞❡ ❆rt❡s✱ ❈✐ê♥❝✐❛s ❡ ❍✉♠❛♥✐❞❛❞❡s
Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ▼♦❞❡❧❛❣❡♠ ❞❡ ❙✐st❡♠❛s
❈♦♠♣❧❡①♦s
▲❊❆◆❉❘❖ ❆❯●❯❙❚❖ ❋❊❘❘❊■❘❆
❆s r❡❞❡s ❝♦♠♣❧❡①❛s ❡ ♦ ❡st✉❞♦ ❞♦ r✐s❝♦ s✐stê♠✐❝♦ ♥♦
s✐st❡♠❛ ✜♥❛♥❝❡✐r♦
❆s r❡❞❡s ❝♦♠♣❧❡①❛s ❡ ♦ ❡st✉❞♦ ❞♦ r✐s❝♦ s✐stê♠✐❝♦ ♥♦
s✐st❡♠❛ ✜♥❛♥❝❡✐r♦
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ à ❊s❝♦❧❛ ❞❡ ❆rt❡s ❈✐ê♥❝✐❛s ❡ ❍✉♠❛♥✐❞❛❞❡s ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✱ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❚ít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛s ♣❡❧♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ▼♦❞❡❧❛❣❡♠ ❞❡ ❙✐st❡♠❛s ❈♦♠♣❧❡①♦s✳
❖r✐❡♥t❛❞♦r✿ ❋❡r♥❛♥❞♦ ❋❛❣✉♥❞❡s ❋❡rr❡✐r❛
❬❱❡rsã♦ ❈♦rr✐❣✐❞❛❪
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CATALOGAÇÃO-NA-PUBLICAÇÃO Biblioteca
Escola de Artes, Ciências e Humanidades da Universidade de São Paulo
Ferreira, Leandro Augusto
As redes complexas e o estudo do risco sistêmico no sistema financeiro / Leandro Augusto Ferreira ; orientador, Fernando Fagundes Ferreira. – São Paulo, 2013.
77 f.
Dissertação (Mestrado em Ciências) – Programa de Pós-Graduação em Modelagem em Sistemas Complexos, Escola de Artes, Ciências e Humanidades da Universidade de São Paulo, em 2013.
Versão corrigida
1. Análise de risco. 2. Sistema financeiro – Simulação computacional. 3. Crise financeira. 4. Sistemas dinâmicos. I. Ferreira, Fernando Fagundes, orient. II. Título.
❚ít✉❧♦✿ ❆s r❡❞❡s ❝♦♠♣❧❡①❛s ❡ ♦ ❡st✉❞♦ ❞♦ r✐s❝♦ s✐stê♠✐❝♦ ♥♦ s✐st❡♠❛ ✜♥❛♥❝❡✐r♦
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ▼♦❞❡❧❛❣❡♠ ❞❡ ❙✐st❡♠❛s ❈♦♠♣❧❡①♦s ❞❛ ❊s❝♦❧❛ ❞❡ ❆rt❡s ❈✐ê♥❝✐❛s ❡ ❍✉♠❛♥✐❞❛❞❡s ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✱ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛s✳
❆♣r♦✈❛❞♦ ❡♠✿ ✶✷✴✵✼✴✷✵✶✸
❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛
Pr♦❢✳ ❉r✳ ❋❡r♥❛♥❞♦ ❋❛❣✉♥❞❡s ❋❡rr❡✐r❛
■♥st✐t✉✐çã♦✿ ❊❆❈❍✲❯❙P ❆ss✐♥❛t✉r❛✿
Pr♦❢✳ ❉r✳ ▲✉✐③ ❏✉r❛♥❞✐r ❙✐♠õ❡s ❞❡ ❆r❛ú❥♦
■♥st✐t✉✐çã♦✿ ❋❊❆✲❯❙P ❆ss✐♥❛t✉r❛✿
Pr♦❢✳ ❉r✳ P❛✉❧♦ ❋❡r♥❛♥❞♦ ❈♦✐♠❜r❛ ❚✐❧❧❡s
❆❣r❛❞❡❝✐♠❡♥t♦s
❆❣r❛❞❡ç♦ ♣r✐♠❡✐r❛♠❡♥t❡ ❛ ❉❡✉s✱ ♣♦r ♠❡ ❝❛♣❛❝✐t❛r ❡ ❝♦♥s♦❧❛r ♥❛s ❤♦r❛s ❞❡ ❞✐✜❝✉❧❞❛❞❡ ❡ à ♠✐♥❤❛ ♠ã❡✱ ❊❧✐③❛❜❡t❤ ❆✉❣✉st❛ ❞❡ ▲✐♠❛✱ ♣♦r t❡r ♠❡ ❡❞✉❝❛❞♦ ❝♦♠ s❛❜❡❞♦r✐❛ ❡ ❞❡❞✐❝❛çã♦✳ ➚ ♠✐♥❤❛ ❢❛♠í❧✐❛✱ ❡♠ ❡s♣❡❝✐❛❧✱ ❛♦ ♠❡✉ ♣❛✐✱ ❆❧❜❡rt♦ ❋❡rr❡✐r❛ ❞❡ ▲✐♠❛✱ ♠✐♥❤❛ ❛✈ó✱ ❚❡♦tô♥✐❛ ❆✉❣✉st❛ ❞❡ ▲✐♠❛✱ ♠❡✉s ✐r♠ã♦s✱ ❆♥❞❡rs♦♥ ❆✉❣✉st♦ ❋❡rr❡✐r❛ ❡ ❋❡r♥❛♥❞❛ ❆✉✲ ❣✉st❛ ❋❡rr❡✐r❛ ❞❡ ●✐✉❧✐✱ ❛♦s ♠❡✉s ❝✉♥❤❛❞♦s ❆r♥❛❧❞♦ ❞❡ ●✐✉❧✐ ◆❡t♦ ❡ ❆♥❛ P❛✉❧❛ ❆♥❣❡❧♦③✐ ▲✐♠❛ ❡ ❛♦s ♠❡✉s s♦❜r✐♥❤♦s ❙❛r❛❤ ❆♥❣❡❧♦③✐ ❋❡rr❡✐r❛ ▲✐♠❛ ❡ ▼✐❣✉❡❧ ❋❡rr❡✐r❛ ❞❡ ●✐✉❧✐✱ ♣♦r ❛❝r❡❞✐t❛r❡♠ ♥❛ r❡❛❧✐③❛çã♦ ❞❡ss❡ ♣r♦❥❡t♦✳
❆♦s ❛♠✐❣♦s✱ ❆❧❡ss❛♥❞r❛ ▼❡❧♦✱ ❆❧✐♥❡ ❉✉tr❛✱ ❇r✉♥❛ P❛trí❝✐❛✱ ❇r✉♥♦ ❱✐tór✐♦✱ ❈❛r❧♦s ❍✐rt❤✱ ❊❞❡r ❋♦♥s❡❝❛✱ ●❛❜r✐❡❧ P❛✐s✱ ●✐❧❜❡rt♦ ❙❛ss✐✱ ❏♦sé ❊♠í❧✐♦✱ ▼✐❝❤❡❧ ❆❧❡①❛♥❞r❡✱ Pr✐s❝✐❧❛ ❙♦❛r❡s✱ ❘❛♦♥✐ ❱❡♥t✉r✐❡r✐✱ ❚✐❛❣♦ ❈♦❧❧✐r✐ ♣❡❧♦ ✐♥❝❡♥t✐✈♦ ❡ ❝♦♥tr✐❜✉✐çõ❡s✳
❆♦ Pr♦❢❡ss♦r ❋❡r♥❛♥❞♦ ❋❛❣✉♥❞❡s ❋❡rr❡✐r❛✱ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ ♣♦r ♠❡ ✐♥❝❡♥t✐✈❛r ❡ ❛♣♦✐❛r ❞✉r❛♥t❡ ❡ss❡ ♣r♦❥❡t♦✳
➚ ♣r♦❢❡ss♦r❛ ❋❧❛✈✐❛ ❙❛rt✐✱ ❝♦♠♦ ❝♦♦r❞❡♥❛❞♦r❛ ❞♦ ♣r♦❣r❛♠❛ ❞❡ ♠❡str❛❞♦✳
❆♦s ♣r♦❢❡ss♦r❡s✱ ❆❧❡①❛♥❞r❡ ❘❛♠♦s✱ ❈❛♠✐❧♦ ◆❡t♦✱ ❈❛r❧♦s ❞❡ ❇r✐t♦✱ ▲✉✐③ ❏✉r❛♥❞✐r✱ ▼❛s❛②✉❦✐ ❍❛s❡✱ ◆✐❦♦❧❛✐ ❑♦❧❡✈ ♣❡❧❛s ❛✉❧❛s ♠✐♥✐str❛❞❛s ❞✉r❛♥t❡ ♦ ▼❡str❛❞♦✳
➚ ❊s❝♦❧❛ ❞❡ ❆rt❡s✱ ❈✐ê♥❝✐❛s ❡ ❍✉♠❛♥✐❞❛❞❡s ♣❡❧❛ ❝r✐❛çã♦ ❞♦ ♣r♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❙✐st❡♠❛s ❈♦♠♣❧❡①♦s✳
P♦rq✉❡ ❡st❡ ❉❡✉s é ♦ ♥♦ss♦ ❉❡✉s
♣❛r❛ s❡♠♣r❡❀ ❊❧❡ s❡rá ♥♦ss♦ ❣✉✐❛ ❛té
à ♠♦rt❡✳
❘❡s✉♠♦
❋❊❘❘❊■❘❆✱ ▲✳ ❆✳ ❆s r❡❞❡s ❝♦♠♣❧❡①❛s ❡ ♦ ❡st✉❞♦ ❞♦ r✐s❝♦ s✐stê♠✐❝♦ ♥♦ s✐st❡♠❛ ✜♥❛♥❝❡✐r♦✳ ✷✵✶✸✳ ✼✼ ❢✳ ❉✐ss❡rt❛çã♦ ✭▼❡str❛❞♦✮ ✲ ❊s❝♦❧❛ ❞❡ ❆rt❡s✱ ❈✐ê♥❝✐❛s ❡ ❍✉♠❛♥✐❞❛❞❡s✱ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✱ ❙ã♦ P❛✉❧♦✱ ✷✵✶✸✳
❆s ❝r✐s❡s ✜♥❛♥❝❡✐r❛s sã♦ ♣r♦❝❡ss♦s ❞❡ ♣❡r❞❛s ❞❡❝♦rr❡♥t❡s ❞♦ ♠❡❝❛♥✐s♠♦ ❞♦ ♠❡r❝❛❞♦ ✜♥❛♥❝❡✐r♦✳ ❊❧❛s ❛❢❡t❛♠ ❛s ✐♥st✐t✉✐çõ❡s ❞♦ s✐st❡♠❛ ✜♥❛♥❝❡✐r♦ ❡ ♣♦r ♠❡✐♦ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❝♦♥tá❣✐♦ s❡ ❡s♣❛❧❤❛♠ ♣♦r ❡❧❡✱ ❛❧❣✉♠❛s ✈❡③❡s ❛♥❛❧♦❣❛♠❡♥t❡ ❛♦ ❡❢❡✐t♦ ❞♦♠✐♥ó✳ ❊st❡ ♣r♦✲ ❝❡ss♦ ♣♦❞❡ ❧❡✈❛r ♠✉✐t❛s ✐♥st✐t✉✐çõ❡s ✜♥❛♥❝❡✐r❛s s❛✉❞á✈❡✐s ❛ s❡ t♦r♥❛r❡♠ ✐♥s♦❧✈❡♥t❡s✳ ■ss♦ ❛❝♦♥t❡❝❡ ♣♦rq✉❡ ♦s ❛❣❡♥t❡s ❡❝♦♥ô♠✐❝♦s ❡stã♦ ✐♥t❡r❧✐❣❛❞♦s ♣♦r ♠❡✐♦ ❞❡ r❡❧❛çõ❡s ❝♦♥tr❛t✉✲ ❛✐s ❡ s❡ t♦r♥❛♠ ❞❡♣❡♥❞❡♥t❡s ✉♥s ❛♦s ♦✉tr♦s✳ ❖ r✐s❝♦ s✐stê♠✐❝♦ ♣♦❞❡ s❡r ❡♥t❡♥❞✐❞♦ ❝♦♠♦ ♦ r✐s❝♦ ❞❡ ✉♠❛ ❣r❛♥❞❡ ♣❡r❞❛ ❡♠ ✉♠ s✐st❡♠❛✳ ❖ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ✉t✐❧✐③❛r ❛s ♣r♦♣r✐❡❞❛❞❡s ❞❡ ✉♠ ♠♦❞❡❧♦ ❞❡ ❝♦♥tá❣✐♦✱ ♣r♦♣♦st♦ ♣❛r❛ ❡st✉❞❛r ♦s ❡❢❡✐t♦s ❞❛ ♣r♦♣❛❣❛çã♦ ❞❡ ❝r✐s❡s ✜♥❛♥❝❡✐r❛s✱ ❜❡♠ ❝♦♠♦ ❛ ♠❡♥s✉r❛çã♦ ❞♦ r✐s❝♦ s✐stê♠✐❝♦ ♥♦ s✐st❡♠❛ ✐♥t❡r❜❛♥❝ár✐♦✳ ❊st❡ ♣r♦❜❧❡♠❛ ❢♦✐ ✐♥✈❡st✐❣❛❞♦ ❝♦♥s✐❞❡r❛♥❞♦ três ❞✐❢❡r❡♥t❡s t♦♣♦❧♦❣✐❛s ❞❡ r❡❞❡✿ ❊r❞ös✲❘é♥②✐✱ ▲✐✈r❡ ❞❡ ❊s❝❛❧❛ ✭♦✉ ❙❝❛❧❡✲❋r❡❡✮ ❡ ■♥t❡r❜❛♥❝ár✐❛ ❊♠♣ír✐❝❛✳ ❆ ❡s❝♦❧❤❛ ❞❡st❛s t♦♣♦❧♦❣✐❛s ❢♦✐ ♣❡❧♦ ❢❛t♦ ❞❡ q✉❡ ❞✉❛s ❞❡❧❛s ✖ ▲✐✈r❡ ❞❡ ❊s❝❛❧❛ ❡ ■♥t❡r❜❛♥❝ár✐❛ ❊♠✲ ♣ír✐❝❛ ✖ ♣♦❞❡♠ ❡♠✉❧❛r ♦ s✐st❡♠❛ ❜❛♥❝ár✐♦ r❡❛❧ ❡ ❛ ❞❡ ❊r❞ös✲❘é♥②✐ t❡r s✐❞♦ ✉t✐❧✐③❛❞❛ ❡♠ ❞✐✈❡rs♦s ♠♦❞❡❧♦s ❞❛ ❧✐t❡r❛t✉r❛✳ ❈❛❞❛ ♥ó r❡♣r❡s❡♥t❛ ✉♠ ❜❛♥❝♦ q✉❡ ♣♦ss✉✐ ❜❛❧❛♥ç♦ ♣❛✲ tr✐♠♦♥✐❛❧ ❝♦♥st✐t✉í❞♦ ❞❡ ♣❛ss✐✈♦s ✭♣❛tr✐♠ô♥✐♦ ❧íq✉✐❞♦✱ ❡♠♣rést✐♠♦s ❡ ❞❡♣ós✐t♦s✮ ❡ ❛t✐✈♦s ✭❡♠♣rést✐♠♦s✱ tít✉❧♦s ❡ ✈❛❧♦r❡s ♠♦❜✐❧✐ár✐♦s✮✳ ❋♦✐ ❛♥❛❧✐s❛❞❛ ❛ ✐♥✢✉ê♥❝✐❛ ❞❛ ❛❧❛✈❛♥❝❛❣❡♠ ❞♦ s✐st❡♠❛✱ ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ✐♥✐❝✐❛❧ ❞❡ ❞❡❢❛✉❧t ❡ ❞♦ ♥ú♠❡r♦ ❞❡ ❝❧✉st❡rs ❞❛ r❡❞❡ ■♥t❡r❜❛♥❝ár✐❛ ❊♠♣ír✐❝❛✳ ❖ r✐s❝♦ s✐stê♠✐❝♦ ❢♦✐ ♠❡❞✐❞♦ ✉t✐❧✐③❛♥❞♦ ♦ ■♥❞✐❝❛❞♦r ❞❡ ❘✐s❝♦ ❙✐stê♠✐❝♦✱ ♦ í♥❞✐❝❡ ❞❡ ❘✐s❝♦ ❙✐stê♠✐❝♦ ❡ ♦ ❱❛❘ ❙✐stê♠✐❝♦✳ ▼♦str♦✉✲s❡ q✉❡ ❛s r❡❞❡s ▲✐✈r❡s ❞❡ ❊s❝❛❧❛ sã♦ ♠❛✐s r♦❜✉st❛s ❡♠ r❡❧❛çã♦ ❛♦s ❛t❛q✉❡s ❛❧❡❛tór✐♦s ❡✈✐t❛♥❞♦ ♦ ❛✉♠❡♥t♦ ❞❛ ✐♥❛❞✐♠♣❧ê♥❝✐❛✳ ❖ ❛✉✲ ♠❡♥t♦ ❛❜r✉♣t♦ ❞♦ ✐♠♣❛❝t♦ ❝❛✉s❛❞♦s ♣❡❧❛ ❝r✐s❡ ❛❝♦♥t❡❝❡ ❞❡✈✐❞♦ ❛♦ ❛✉♠❡♥t♦ ❞♦ ❣r❛✉ ❞❡ ❛❧❛✈❛♥❝❛❣❡♠ ❞♦ s✐st❡♠❛✳ ❖ ♥ú♠❡r♦ ❞❡ ❝❧✉st❡rs ❞❛ r❡❞❡ ■♥t❡r❜❛♥❝ár✐❛ ❊♠♣ír✐❝❛ ✐♠♣❛❝t❛ ❛ r♦✉❜✉t❡③ ❞♦ s✐st❡♠❛✳ ❖ ♠♦❞❡❧♦ r❡♣r♦❞✉③ ♦ r❡s✉❧t❛❞♦ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ▼✉✐t♦ ■♥t❡r❝♦♥❡❝t❛❞♦ ♣❛r❛ ❋❛❧❤❛r✱ q✉❡ é q✉❛♥❞♦ ❜❛♥❝♦s ♠❛✐s ✐♥t❡r❝♦♥❡❝t❛❞♦s ♦❢❡r❡❝❡♠ ♠❛✐♦r r✐s❝♦ ❛♦ s✐st❡♠❛✳
❆❜str❛❝t
❋❊❘❘❊■❘❆✱ ▲✳ ❆✳ ❈♦♠♣❧❡① ♥❡t✇♦r❦s ❛♥❞ t❤❡ st✉❞② ♦❢ s②st❡♠✐❝ r✐s❦ ♦♥ ✜♥❛♥❝✐❛❧ s②st❡♠✳ ✷✵✶✸✳ ✼✼ ❢✳ ❉✐ss❡rt❛çã♦ ✭▼❡str❛❞♦✮ ✲ ❊s❝♦❧❛ ❞❡ ❆rt❡s✱ ❈✐ê♥❝✐❛s ❡ ❍✉♠❛♥✐❞❛❞❡s✱ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✱ ❙ã♦ P❛✉❧♦✱ ✷✵✶✸✳
❚❤❡ ✜♥❛♥❝✐❛❧ ❝r✐s❡s ❛r❡ ♣r♦❝❡ss❡s ♦❢ ❧♦ss❡s ❛r✐s✐♥❣ ❢r♦♠ ✜♥❛♥❝✐❛❧ ♠❛r❦❡t ♠❡❝❤❛♥✐s♠✳ ❚❤❡② ❛✛❡❝t t❤❡ ✐♥st✐t✉t✐♦♥s ♦❢ t❤❡ ✜♥❛♥❝✐❛❧ s②st❡♠ ❜② t❤❡ ♣r♦❝❡ss ♦❢ ❝♦♥t❛❣✐♦♥✳ ❙♦♠❡✲ t✐♠❡s ✐t ✐s ❡q✉❛❧ t♦ t❤❡ ❞♦♠✐♥♦ ❡✛❡❝t✳ ❚❤✐s ♣r♦❝❡ss ❝❛♥ ♠❛❦❡ ♠❛♥② ❤❡❛❧t❤② ✜♥❛♥❝✐❛❧ ✐♥st✐t✉t✐♦♥s ❜❡❝♦♠❡ ✐♥s♦❧✈❡♥ts✳ ■t ❤❛♣♣❡♥s ❜❡❝❛✉s❡ ❡❝♦♥♦♠✐❝ ❛❣❡♥ts ❛r❡ ✐♥t❡r❝♦♥♥❡❝t❡❞ t❤r♦✉❣❤ ❝♦♥tr❛❝t✉❛❧ r❡❧❛t✐♦♥s ❛♥❞ ❜❡❝♦♠❡ ❞❡♣❡♥❞❡♥t ♦♥ ❡❛❝❤ ♦t❤❡r✳ ❙②st❡♠✐❝ r✐s❦ ❝❛♥ ❜❡ ✉♥❞❡rst♦♦❞ ❛s t❤❡ r✐s❦ ♦❢ ❛ ❤✉❣❡ ❧♦ss ✐♥ ❛ s②st❡♠✳ ❚❤❡ ♣r❡s❡♥t ✇♦r❦ ❛✐♠s t♦ st✉❞② t❤❡ ♣r♦♣❡rt✐❡s ♦❢ ❛ ❝♦♥t❛❣✐♦♥ ♠♦❞❡❧ ♣r♦♣♦s❡❞ t♦ st✉❞② t❤❡ ❡✛❡❝ts ♦❢ t❤❡ s♣r❡❛❞ ♦❢ ✜♥❛♥❝✐❛❧ ❝r✐s❡s✱ ❛s ✇❡❧❧ ❛s t❤❡ ♠❡❛s✉r❡♠❡♥t ♦❢ s②st❡♠✐❝ r✐s❦ ✐♥ t❤❡ ✐♥t❡r❜❛♥❦ s②st❡♠✳ ❚❤✐s ♣r♦❜❧❡♠ ✇❛s ✐♥✈❡st✐❣❛t❡❞ ❝♦♥s✐❞❡r✐♥❣ t❤r❡❡ ❞✐✛❡r❡♥t ♥❡t✇♦r❦ t♦♣♦❧♦❣✐❡s✿ ❊r❞ös✲❘é♥②✐✱ ❙❝❛❧❡✲❋r❡❡ ❛♥❞ ❊♠♣✐r✐❝❛❧ ■♥t❡r❜❛♥❦✳ ❚❤❡ ❝❤♦✐❝❡ ♦❢ t❤❡s❡ t♦♣♦❧♦❣✐❡s ✇❛s ♠❛❞❡ ❜② t❤❡ ❢❛❝t t❤❛t t✇♦ ♦❢ t❤❡♠ ✖ ❙❝❛❧❡✲❋r❡❡ ❛♥❞ ❊♠♣✐r✐❝❛❧ ■♥t❡r❜❛♥❦ ✖ ♠❛② ❡♠✉❧❛t❡ t❤❡ r❡❛❧ ❜❛♥❦✐♥❣ s②st❡♠ ❛♥❞ ❊r❞ös✲❘é♥②✐ ❤❛s ❜❡❡♥ ✉s❡❞ ✐♥ s❡✈❡r❛❧ ♠♦❞❡❧s ✐♥ t❤❡ ❧✐t❡r❛t✉r❡✳ ❊❛❝❤ ♥♦❞❡ ✐s ❛ ❜❛♥❦ ❛♥❞ ❝♦♥s✐sts ♦♥ ❛ ❜❛❧❛♥❝❡ s❤❡❡t s♣❧✐t ❛s ❧✐❛❜✐❧✐t✐❡s ✭❡q✉✐t②✱ ❜♦rr♦✇✐♥❣s ❛♥❞ ❞❡♣♦s✐ts✮ ❛♥❞ ❛ss❡ts ✭❧❡♥❞✐♥❣s✱ ❜♦♥❞s ❛♥❞ s❡❝✉r✐t✐❡s✮✳ ■t ✇❛s ❛♥❛❧②③❡❞ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤❡ ❝♦❡✣❝✐❡♥t ♦❢ ❧❡✈❡r❛❣❡✱ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤❡ ✐♥✐t✐❛❧ ♣r♦❜❛❜✐❧✐t② ♦❢ ❞❡❢❛✉❧t ❛♥❞ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤❡ ♥✉♠✲ ❜❡r ♦❢ ❝❧✉st❡rs ♦♥ t❤❡ ❊♠♣✐r✐❝❛❧ ■♥t❡r❜❛♥❦✳ ❚❤❡ s②st❡♠✐❝ r✐s❦ ✇❛s ♠❡❛s✉r❡❞ ✉s✐♥❣ t❤❡ ❙②st❡♠✐❝ ❘✐s❦ ■♥❞✐❝❛t♦r✱ ❙②st❡♠✐❝ ■♥❞❡① ❛♥❞ ❙②st❡♠✐❝ ❱❛❧✉❡ ❛t ❘✐s❦✳ ■t ✇❛s s❤♦✇♥ t❤❛t ❙❝❛❧❡✲❋r❡❡ ♥❡t✇♦r❦s ❛r❡ ♠♦r❡ r♦❜✉st ❛❣❛✐♥st r❛♥❞♦♠ ❛tt❛❝❦s✱ ❛✈♦✐❞✐♥❣ ✐♥❝r❡❛s❡s ✐♥ t❤❡ ♥✉♠❜❡r ♦❢ ❞❡❢❛✉❧ts✳ ❚❤❡ ❛❜r✉♣t ✐♥❝r❡❛s❡ ✐♥ t❤❡ ✐♠♣❛❝t ❝❛✉s❡❞ ❜② t❤❡ ❝r✐s✐s ❤❛♣♣❡♥s ❞✉❡ t♦ t❤❡ ✐♥❝r❡❛s❡ ✐♥ ❝♦❡✣❝✐❡♥t ♦❢ ❧❡✈❡r❛❣❡✳ ❚❤❡ ♥✉♠❜❡r ♦❢ ❝❧✉st❡rs ♦♥ ❊♠♣✐r✐❝❛❧ ■♥t❡r❜❛♥❦ ♥❡t✇♦r❦ ✐♠♣❛❝ts t❤❡ r♦❜✉st♥❡ss ♦❢ t❤❡ s②st❡♠✳ ❚❤❡ ♠♦❞❡❧ r❡♣r♦❞✉❝❡s t❤❡ r❡s✉❧t ❦♥♦✇♥ ❛s ❚♦♦ ■♥t❡r❝♦♥♥❡❝t❡❞ t♦ ❋❛✐❧✱ t❤❛t ✐s✱ ❜❛♥❦s ♠♦r❡ ✐♥t❡r❝♦♥♥❡❝t❡❞ ♦✛❡r ❤✐❣❤❡r r✐s❦ t♦ t❤❡ s②st❡♠✳
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s ✶✶
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ✶✹
✶ ■♥tr♦❞✉çã♦ ✶✺
✶✳✶ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✶✳✷ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚r❛❜❛❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼
✷ ❘❡✈✐sã♦ ❞❛ ▲✐t❡r❛t✉r❛ ✶✽
✸ ❘❡❞❡s ❈♦♠♣❧❡①❛s ✷✹
✸✳✶ ❋✉♥❞❛♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✷ ❉✐str✐❜✉✐çã♦ ❞❡ ❣r❛✉s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✷✳✶ ❉✐str✐❜✉✐çã♦ ❞❡ P♦✐ss♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✷✳✷ ▲❡✐ ❞❡ P♦tê♥❝✐❛ ✭P♦✇❡r ▲❛✇✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✸ ▼♦❞❡❧♦s ❞❡ ❘❡❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✸✳✶ ❊r❞ös✲❘é♥②✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✸✳✷ ▲✐✈r❡ ❞❡ ❡s❝❛❧❛ ✭❙❝❛❧❡✲❢r❡❡✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✸✳✸ ■♥t❡r❜❛♥❝ár✐❛ ❊♠♣ír✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✹ ❖ ❘✐s❝♦ ❋✐♥❛♥❝❡✐r♦ ✸✻
✹✳✶ ❈❧❛ss✐✜❝❛çã♦ ❞♦ ❘✐s❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✹✳✷ ❱❛❧✉❡ ❛t ❘✐s❦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✹✳✷✳✶ ▼♦❞❡❧♦ ♣♦r s✐♠✉❧❛çã♦ ❤✐stór✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✷✳✷ ▼♦❞❡❧♦ P❛r❛♠étr✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✹✳✷✳✸ ▼♦❞❡❧♦ ♣♦r s✐♠✉❧❛çã♦ ❞❡ ▼♦♥t❡ ❈❛r❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✺ ❘✐s❝♦ ❙✐stê♠✐❝♦ ✹✺
✺✳✸ ▼❡❞✐❞❛s ❞❡ ❘✐s❝♦ ❙✐stê♠✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✺✳✸✳✶ ■♥❞✐❝❛❞♦r ❞❡ ❘✐s❝♦ ❙✐stê♠✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✺✳✸✳✷ ❮♥❞✐❝❡ ❞❡ ❘✐s❝♦ ❙✐stê♠✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✺✳✸✳✸ ❱❛❘ ❙✐stê♠✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
✻ ❘❡s✉❧t❛❞♦s ✺✻
✻✳✶ ▼✉✐t♦ ■♥t❡r❝♦♥❡❝t❛❞♦ ♣❛r❛ ❢❛❧❤❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✻✳✷ ❊❢❡✐t♦s ❞❛ ❛❧❛✈❛♥❝❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✻✳✸ ❘♦❜✉st❡③ ❞❛s t♦♣♦❧♦❣✐❛s ❞❡ r❡❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✻✳✹ ❖ ❡❢❡✐t♦ ❞❛ ♣r❡s❡♥ç❛ ❞❡ ❝❧✉st❡rs ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✻✳✺ ❮♥❞✐❝❡ ❞❡ ❘✐s❝♦ ❙✐stê♠✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✻✳✻ ❱❛r ❙✐stê♠✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽
✼ ❈♦♥❝❧✉sõ❡s ✻✾
✼✳✶ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✼✳✷ ❙✉❣❡stõ❡s ♣❛r❛ P❡sq✉✐s❛s ❋✉t✉r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
❆ ❆❧❣♦r✐t♠♦s ❞❛ ❙✐♠✉❧❛çã♦ ✼✶
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ▼❡❝❛♥✐s♠♦ ❞❡ ❞✐❢✉sã♦ ❞❡ ❝r✐s❡s ✜♥❛♥❝❡✐r❛s✿ ❉ r❡♣r❡s❡♥t❛ ❛s ✜r♠❛s ❞❡ ❜❡♥s ❞❡ ❝♦♥s✉♠♦✱ ❯ ❛s ✜r♠❛s q✉❡ ❢♦r❝❡♥❡♠ ✐♥s✉♠♦s ❡ ❇ ♦s ❜❛♥❝♦s q✉❡ ✜♥❛♥❝✐❛♠ ♦ ♠❡r❝❛❞♦✳ ❆s ✐♥t❡r❛çõ❡s ❡♥tr❡ ♦s ❜❛♥❝♦s ❡ ✜r♠❛s ♠✉❞❛♠ ❛ ❝❛❞❛ r♦❞❛❞❛✱ ❞❡ ❛❝♦r❞♦ ❝♦♠❡r❝✐❛❧ ♦ ❝❡♥ár✐♦ ❡❝♦♥ô♠✐❝♦✳ ❆s ❧✐❣❛çõ❡s ♥❛ ❝♦r ✈❡r♠❡❧❤❛ ✐♥❞✐❝❛♠ ♦s ❡❢❡✐t♦s ❝❛✉s❛❞♦s ♣❡❧❛ ✐♥❛❞✐♠♣❧ê♥❝✐❛ ❞❛s ✜r♠❛s ❉4✱❉6 ❡ ❉7 q✉❡ ❛❢❡t❛♠
s❡✉s ♣❛r❝❡✐r♦s ❝♦♥tr❛t✉❛✐s ✭❜❛♥❝♦s ❡ ✜r♠❛s✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✷✳✷ ■❧✉str❛çã♦ ❞❛ ✈❛r✐❛çã♦ ❞♦ ♣❛râ♠❡tr♦ γ ❣❡r❛♥❞♦ ❞✐❢❡r❡♥t❡s t♦♣♦❧♦❣✐❛s ❞❡
r❡❞❡✳ ❋✐❣✉r❛ ✭❛✮ é ✉♠❛ r❡❞❡ ❛❧❡❛tór✐❛ ❣❡r❛❞❛ ♣❡❧♦ ♣❛râ♠❡♥tr♦ γ = 0✱ ✜❣✉r❛
✭❜✮ é ✉♠❛ r❡❞❡ ❧✐✈r❡ ❞❡ ❡s❝❛❧❛ ❣❡r❛❞❛ ♣❡❧♦ ♣❛râ♠❡♥tr♦ γ = 12 ❡ ✜❣✉r❛ ✭❝✮
é ✉♠❛ r❡❞❡ ♣s❡✉❞♦✲❡str❡❧❛ ❣❡r❛❞❛ ♣❡❧♦ ♣❛râ♠❡♥tr♦ γ = 40✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✸✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❛s s❡t❡ ♣♦♥t❡s ❞❡ ❑ö♥✐❣s❜❡r❣✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠❛ ❝❛❞❡✐❛ ❛❧✐♠❡♥t❛r ♣♦r ♠❡✐♦ ❞❡ ✉♠❛ r❡❞❡✳ ❈❛❞❛ ♥ó
r❡♣r❡s❡♥t❛ ✉♠ ❛♥✐♠❛❧ ♥❛ ❞❡♥tr♦ ❞❛ ❝❛❞❡✐❛ ❡ ❝❛❞❛ ❧✐❣❛çã♦ ❛ r❡❧❛çã♦ ❡♥tr❡ ♣r❡❞❛❞♦r ♣r❡s❛✳ ❖ ♥ó ❡♠ ❝♦r ♠❛✐s ❡s❝✉r❛ r❡♣r❡s❡♥t❛ ✉♠❛ ♣r❡s❛ ❞❡ ✉♠ ♣r❡❞❛❞♦s ❝✉❥♦ ♥ó ❡stá ❡♠ ❝♦r ♠❛✐s ❝❧❛r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✸ ❊①❡♠♣❧♦ ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ ❣r❛❢♦ ♥ã♦ ❞✐r❡❝✐♦♥❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✹ ❊①❡♠♣❧♦ ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ ❣r❛❢♦ ❞✐r❡❝✐♦♥❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✺ ❉✐str✐❜✉✐çã♦ ❡♠♣ír✐❝❛ ❞❡ r❡♥❞❛ ❞❡ ✉♠❛ ♣♦♣✉❧❛çã♦✱ ❝✉❥❛ ❞✐str✐❜✉✐çã♦ s❡❣✉❡
✉♠❛ ❧❡✐ ❞❡ ♣♦tê♥❝✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✻ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ r❡❞❡ ❛❧❡❛tór✐❛ ❞❡ ❊r❞ös✲❘é♥②✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✼ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ❘❡❞❡ ❊r❞ös✲❘é♥②✐ ❝♦♠ 50❜❛♥❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✸✳✽ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ r❡❞❡ ▲✐✈r❡ ❞❡ ❊s❝❛❧❛ ❞❡ ❆✳✲▲✳ ❇❛r❛❜ás✐✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✾ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ r❡❞❡ ▲✐✈r❡ ❞❡ ❡s❝❛❧❛ ❝♦♠ ✶✵✵ ❜❛♥❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✸✳✶✵ ❚♦♣♦❧♦❣✐❛ ❞❛ r❡❞❡ ✐♥t❡r❜❛♥❝ár✐❛ ❜r❛s✐❧❡✐r❛ ❡♠ ❏✉❧❤♦ 2008✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✸✳✶✶ ❘❡❞❡ ■♥t❡r❜❛♥❝ár✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✸✳✶✷ ❘❡❞❡ ■♥t❡r❜❛♥❝ár✐❛ ❊♠♣ír✐❝❛ s✐♠✉❧❛❞❛ ❝♦♠ 200 ♥ós ❡ ✸ ❝❧✉st❡rs✳ ❆s ❞✐❢❡r✲
❡♥t❡s ❝♦r❡s r❡♣r❡s❡♥t❛♠ ❛ ❢♦r♠❛çã♦ ❞♦s ❝❧✉st❡rs✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺
✹✳✸ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ❝♦♥str✉çã♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❞♦s ♣r❡ç♦s ♦❜t✐❞❛s ♣♦r ♠❡✐♦ ❞❡ tr❛❥❡tór✐❛s ❛❧❡❛tór✐❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
✺✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ❙✐st❡♠❛ ❋✐♥❛♥❝❡✐r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✺✳✷ ❘❡s✉♠♦ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❢♦r♠❛çã♦ ❞❡ ✉♠❛ ❝r✐s❡ ✜♥❛♥❝❡✐r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✺✳✸ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ❆❝♦r❞♦s ❞❡ ❇❛s✐❧é✐❛ ■■ ❡ ■■■✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✺✳✹ ❇❛❧❛♥ç♦ ♣❛tr✐♠♦♥✐❛❧ ❞❡ ✉♠ ❜❛♥❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✺✳✺ ■❧✉str❛çã♦ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❝♦♥tá❣✐♦ ✜♥❛♥❝❡✐r♦✳ ◆♦ ♣r✐♠❡✐r♦ ❡stá❣✐♦✱ ♦ ❜❛♥❝♦
✐♥❛❞✐♠♣❧❡♥t❡ ✖ ❡♠ ✈❡r♠❡❧❤♦ ✖ ❛❢❡t❛ s❡✉s três ❝r❡❞♦r❡s✳ ◆♦ s❡❣✉♥❞♦ ❡s✲ tá❣✐♦✱ ❛♣❡♥❛s ✉♠ ❞♦s ❝r❡❞♦r❡s ❛❢❡t❛❞♦s ♥♦ ♣r✐♠❡✐r♦ ❡stá❣✐♦ é ❝♦♥t❛❣✐❛❞♦✱ ❡ ♣♦rt❛♥t♦ ✜❝❛ ✐♥❛❞✐♠♣❧❡♥t❡✳ ◆♦ t❡r❝❡✐r♦ ❡stá❣✐♦✱ ✉♠ ❞♦s ❜❛♥❝♦s ❛t✐❣✐♥✲ ❞♦s ♥♦s ❡stá❣✐♦s ❛♥t❡r✐♦r❡s é ❛t✐♥❣✐❞♦ ♥♦✈❛♠❡♥t❡✱ ❞❡st❛ ✈❡③✱ s❡ t♦r♥❛♥❞♦ ✐♥❛❞✐♠♣❧❡♥t❡❀ ✉♠ ❞♦s ❜❛♥❝♦s s❡q✉❡r é ❛t✐♥❣✐❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✺✳✻ ❉✐str✐❜✉✐çõ❡s ❞❡ ❣r❛✉ ❞❡ s❛í❞❛✱ ❡♠ ✈❡r♠❡❧❤♦ ❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ❜❛♥❝♦s
✐♥❛❞✐♠♣❧❡♥t❡s✱ ❡♠ ❛③✉❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✺✳✼ ❉✐str✐❜✉✐çõ❡s ❞❡ ❣r❛✉ ❞❡ s❛í❞❛✱ ❡♠ ✈❡r♠❡❧❤♦ ❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ❜❛♥❝♦s
✐♥❛❞✐♠♣❧❡♥t❡s✱ ❡♠ ❛③✉❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✺✳✽ ❍♦♠❡♦r✜s♠♦ ❡♥tr❡ ♦s ✐♥t❡r✈❛❧♦s(a, b)❡ (0,1) ❞❛ r❡t❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✺✳✾ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ■♥❞✐❝❛❞♦r ❞❡ ❘✐s❝♦ ❙✐stê♠✐❝♦✳ ◆♦ ❝❛s♦ ✭❛✮ ♦s ❜❛♥❝♦s ♠❛✐s ❝♦♥❡❝t❛❞♦s ♣♦ss✉❡♠ ♠❛✐♦r r✐s❝♦ ❞❡ ✐♥❛❞✐♠♣❧ê♥❝✐❛✱ ♥♦ ❝❛s♦ ✭❜✮ ♦s ❜❛♥❝♦s ♠❡♥♦s ❝♦♥❡❝t❛❞♦s ♣♦ss✉❡♠ ♠❛✐♦r r✐s❝♦ ❞❡ ✐♥❛❞✐♠♣❧ê♥❝✐❛✳ ❖ t❛♠❛♥❤♦ ❞♦s ❝ír❝✉❧♦s ❡♠ ❛③✉❧ ✐♥❞✐❝❛ ❛ ♣r♦♣♦rçã♦ ❞❡ ❜❛♥❝♦s ❝♦♠ ♦ r❡s♣❡❝t✐✈♦ ❣r❛✉ ❞❡ s❛í❞❛✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹
✻✳✶ ❖s t❛♠❛♥❤♦s ❞♦s ❝ír❝✉❧♦s ♥❛ ❝♦r ❛③✉❧ ♠♦str❛♠ ❛ ♣r♦♣♦rçã♦ ❞♦s ❜❛♥❝♦s ❝♦♠ ❣r❛✉ ❞❡ s❛í❞❛ kout✳ ❆ r❡t❛ ✈❡r❞❡ ✐♥❞✐❝❛ ♦ ❣r❛✉ ♠é❞✐♦ ❞❡ ❝❛❞❛ t♦♣♦❧♦❣✐❛
❞❡ r❡❞❡ ✭❛✮ ❊r❞ös✲❘é♥②✐✱ ✭❜✮ ■♥t❡r❜❛♥❝ár✐❛ ❡ ✭❝✮ ▲✐✈r❡ ❞❡ ❡s❝❛❧❛ ❡ ❛ r❡t❛ ✈❡r♠❡❧❤❛ ✐♥❞✐❝❛ ❛ ✐❣✉❛❧❞❛❞❡ ❡♥tr❡ ❛s ❞✐str✐❜✉✐çõ❡s ❞❡ ❣r❛✉ ❡ ❞❡ ❞❡❢❛✉❧t✱ ♦✉ s❡❥❛✱ ❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ❝ír❝✉❧♦s à ❞✐r❡✐t❛ ❞❛ r❡t❛ ✈❡r❞❡✱ ❛❝✐♠❛ ❞❛ r❡t❛ ✈❡r✲ ♠❡❧❤❛ ✭1◦ q✉❛❞r❛♥t❡✮✱ à ❡sq✉❡r❞❛ ❞❛ r❡t❛ ✈❡r❞❡ ❡ ❛❜❛✐①♦ ❞❛ r❡t❛ ✈❡r♠❡❧❤❛
✭3◦ q✉❛❞r❛♥t❡✮✱ ✐♥❞✐❝❛♠ q✉❡ ❜❛♥❝♦s ❝♦♠ ❣r❛✉ ❞❡ s❛í❞❛ ♠❛✐♦r q✉❡ ❛ ♠é❞✐❛✱
♣♦ss✉❡♠ ♠❛✐♦r r✐s❝♦ ❞❡♥tr♦ ❞♦ s✐st❡♠❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✻✳✷ ❆♥á❧✐s❡ ❞♦ ❡❢❡✐t♦ ❞❛ ❛❧❛✈❛♥❝❛❣❡♠ ♣❛r❛ ❛ r❡❞❡ ❊r❞ös✲❘é♥②✐ ❝♦♠100❜❛♥❝♦s✳
◆❛ ❝♦r ♣r❡t❛ ♦ r❡s✉❧t❛❞♦ ♣❛r❛ pdi = 0.05 ❡ ♥❛ ❝♦r ❛③✉❧ ♦ r❡s✉❧t❛❞♦ ♣❛r❛
pdi = 0.1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✻✳✸ ❆♥á❧✐s❡ ❞♦ ❡❢❡✐t♦ ❞❛ ❛❧❛✈❛♥❝❛❣❡♠ ♣❛r❛ ❛ r❡❞❡ ❊r❞ös✲❘é♥②✐ ❝♦♠200❜❛♥❝♦s✳
◆❛ ❝♦r ♣r❡t❛ ♦ r❡s✉❧t❛❞♦ ♣❛r❛ pdi = 0.05 ❡ ♥❛ ❝♦r ❛③✉❧ ♦ r❡s✉❧t❛❞♦ ♣❛r❛
pdi = 0.1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✻✳✹ ❆♥á❧✐s❡ ❞♦ ❡❢❡✐t♦ ❞❛ ❛❧❛✈❛♥❝❛❣❡♠ ♣❛r❛ ❛ r❡❞❡ ❊r❞ös✲❘é♥②✐ ❝♦♠500❜❛♥❝♦s✳
◆❛ ❝♦r ♣r❡t❛ ♦ r❡s✉❧t❛❞♦ ♣❛r❛ pdi = 0.05 ❡ ♥❛ ❝♦r ❛③✉❧ ♦ r❡s✉❧t❛❞♦ ♣❛r❛
✶✵✵ ❜❛♥❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✻✳✻ ❆♥á❧✐s❡ ❞♦ ❡❢❡✐t♦ ❞❛ ❛❧❛✈❛♥❝❛❣❡♠ ♣❛r❛ ❛ r❡❞❡ ■♥t❡r❜❛♥❝ár✐❛ ❊♠♣ír✐❝❛ ❝♦♠
✷✵✵ ❜❛♥❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✻✳✼ ❆♥á❧✐s❡ ❞♦ ❡❢❡✐t♦ ❞❛ ❛❧❛✈❛♥❝❛❣❡♠ ♣❛r❛ ❛ r❡❞❡ ■♥t❡r❜❛♥❝ár✐❛ ❊♠♣ír✐❝❛ ❝♦♠
✺✵✵ ❜❛♥❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✻✳✽ ❆♥á❧✐s❡ ❞♦ ❡❢❡✐t♦ ❞❛ ❛❧❛✈❛♥❝❛❣❡♠ ♣❛r❛ ❛ r❡❞❡ ▲✐✈r❡ ❞❡ ❊s❝❛❧❛ ❝♦♠ ✶✵✵ ❜❛♥❝♦s✳ ✻✶ ✻✳✾ ❆♥á❧✐s❡ ❞♦ ❡❢❡✐t♦ ❞❛ ❛❧❛✈❛♥❝❛❣❡♠ ♣❛r❛ ❛ r❡❞❡ ▲✐✈r❡ ❞❡ ❊s❝❛❧❛ ❝♦♠ ✷✵✵ ❜❛♥❝♦s✳ ✻✷ ✻✳✶✵ ❆♥á❧✐s❡ ❞♦ ❡❢❡✐t♦ ❞❛ ❛❧❛✈❛♥❝❛❣❡♠ ♣❛r❛ ❛ r❡❞❡ ▲✐✈r❡ ❞❡ ❊s❝❛❧❛ ❝♦♠ ✺✵✵ ❜❛♥❝♦s✳ ✻✷ ✻✳✶✶ ❈♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ❞❡ ❞❡s❡♠♣❡♥❤♦ ❞❡ r♦❜✉st❡③ ❡♥tr❡ ❛s três t♦♣♦❧♦✲
❣✐❛s ❞❡ r❡❞❡s ❡st✉❞❛❞❛s✳ ◆❛s ✜❣✉r❛s ✭❛✮ ❡ ✭❜✮ t❡♠✲s❡✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❜❛♥❝♦s ❛❢❡t❛❞♦s ❡ ✐♥❛❞✐♠♣❧❡♥t❡s ♣❛r❛ pdi = 0.05 ❡ ♥❛s ✜❣✲
✉r❛s ✭❝✮ ❡ ✭❞✮ t❡♠✲s❡✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❜❛♥❝♦s ❛❢❡t❛❞♦s ❡ ✐♥❛❞✐♠♣❧❡♥t❡s ♣❛r❛ pdi = 0.1✱ ♣❛r❛ r❡❞❡s ❝♦♠ ✶✵✵ ❜❛♥❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸
✻✳✶✷ ❈♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ❞❡ ❞❡s❡♠♣❡♥❤♦ ❞❡ r♦❜✉st❡③ ❡♥tr❡ ❛s três t♦♣♦❧♦✲ ❣✐❛s ❞❡ r❡❞❡s ❡st✉❞❛❞❛s✳ ◆❛s ✜❣✉r❛s ✭❛✮ ❡ ✭❜✮ t❡♠✲s❡✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❜❛♥❝♦s ❛❢❡t❛❞♦s ❡ ✐♥❛❞✐♠♣❧❡♥t❡s ♣❛r❛ pdi = 0.05 ❡ ♥❛s ✜❣✲
✉r❛s ✭❝✮ ❡ ✭❞✮ t❡♠✲s❡✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❜❛♥❝♦s ❛❢❡t❛❞♦s ❡ ✐♥❛❞✐♠♣❧❡♥t❡s ♣❛r❛ pdi = 0.1✱ ♣❛r❛ r❡❞❡s ❝♦♠ ✺✵✵ ❜❛♥❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹
✻✳✶✸ ❆♥á❧✐s❡ ❞♦ ❈❧✉st❡r ❢❡✐t❛ ♣❛r❛ ❛ r❡❞❡ ■♥t❡r❜❛♥❝ár✐❛ ❊♠♣ír✐❝❛ ❝♦♠100❜❛♥❝♦s✱
❝♦♠ 3✱ 4❡ 5 ❝❧✉st❡rs ❡ ✈❛❧♦r ❞❡ pdi = 0.05✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺
✻✳✶✹ ❆♥á❧✐s❡ ❞♦ ❈❧✉st❡r ❢❡✐t❛ ♣❛r❛ ❛ r❡❞❡ ■♥t❡r❜❛♥❝ár✐❛ ❊♠♣ír✐❝❛ ❝♦♠100❜❛♥❝♦s✱
❝♦♠ 3✱ 4❡ 5 ❝❧✉st❡rs ❡ ✈❛❧♦r ❞❡ pdi = 0.1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺
✻✳✶✺ ❆♥á❧✐s❡ ❞♦ ❈❧✉st❡r ❢❡✐t❛ ♣❛r❛ ❛ r❡❞❡ ■♥t❡r❜❛♥❝ár✐❛ ❊♠♣ír✐❝❛ ❝♦♠ ✷✵✵ ❜❛♥❝♦s✱ ❝♦♠ 3✱ 4❡ 5 ❝❧✉st❡rs ❡ ✈❛❧♦r ❞❡ pdi = 0.05✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✻✳✶✻ ❆♥á❧✐s❡ ❞♦ ❈❧✉st❡r ❢❡✐t❛ ♣❛r❛ ❛ r❡❞❡ ■♥t❡r❜❛♥❝ár✐❛ ❊♠♣ír✐❝❛ ❝♦♠ ✷✵✵ ❜❛♥❝♦s✱ ❝♦♠ 3✱ 4❡ 5 ❝❧✉st❡rs ❡ ✈❛❧♦r ❞❡ pdi = 0.1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✻✳✶✼ ❈♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ❞♦ ❮♥❞✐❝❡ ❞❡ ❘✐s❝♦ ❙✐stê♠✐❝♦ ♣❛r❛ ❛s três t♦♣♦❧♦✲ ❣✐❛s ❞❡ r❡❞❡s ❡st✉❞❛❞❛s ❡ três ✈❛❧♦r❡s ♣❛r❛ ❛ ❛❧❛✈❛♥❝❛❣❡♠ ρ✳ ❆ ✜❣✉r❛ ✭❛✮
❝♦♥s✐❞❡r❛ ρ= 0.8✱ ❛ ✜❣✉r❛ ✭❜✮ ❝♦♥s✐❞❡r❛ρ= 4 ❡✱ ✜❣✉r❛ ✭❝✮ ❝♦♥s✐❞❡r❛ ρ= 8✳ ✻✼
✻✳✶✽ ❘❡s✉❧t❛❞♦ ♣❛r❛ V aR ❙✐stê♠✐❝♦ ❝♦♠ ♥í✈❡❧ ❞❡ ❝♦♥✜❛♥ç❛ ❞❡ 99% ❝❛❧❝✉❧❛❞♦
♣❛r❛ ❛s ❞✐❢❡r❡♥t❡s t♦♣♦❧♦❣✐❛s ❞❡ r❡❞❡ ❡ ✈❛❧♦r❡s ❞❡ ❛❧❛✈❛♥❝❛❣❡♠ ❡st✉❞❛❞♦s✳ ❋✐❣✉r❛ ✭❛✮ ♠♦str❛ ♦ V aR ❝❛❧❝✉❧❛❞♦ ♣❛r❛ pdi = 0.05 ❡ ✜❣✉r❛ ✭❜✮ ♠♦str❛ ♦
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
❆s ✐♥st✐t✉✐çõ❡s ✜♥❛♥❝❡✐r❛s ❢❛③❡♠ ♦♣❡r❛çõ❡s ❝♦♠ ❛❧t♦ ❣r❛✉ ❞❡ ❛❧❛✈❛♥❝❛❣❡♠✿ ❡❧❛s ✉s❛♠ ❝❛♣✐t❛❧ ❞❡ t❡r❝❡✐r♦s ♦✉ r❡❛❧✐③❛♠ ♦♣❡r❛çõ❡s ❢✉t✉r❛s ♣♦r ♠❡✐♦ ❞❛ ❛♣❧✐❝❛çã♦ ❞❡ ✉♠❛ ❢r❛çã♦ ❞♦ ✈❛❧♦r ❞♦ ❛t✐✈♦ ♣❛r❛ ❛✉♠❡♥t❛r s❡✉s ❧✉❝r♦s ✭❆❞r✐❛♥ ❡ ❙❤✐♥✱✷✵✶✵✮✳ ❙❛❜❡♥❞♦✲s❡ q✉❡ ♦ ♣❛ss✐✈♦ ❜❛♥❝ár✐♦ é ❢♦r♠❛❞♦ ❡♠ ❣r❛♥❞❡ ♣❛rt❡ ♣♦r r❡❝✉rs♦s ♦r✐✉♥❞♦s ❞♦ s❡t♦r ♣r♦❞✉t✐✈♦✱ ❞♦ ❝♦♠ér❝✐♦ ❡ ❞❛ ♣♦✉♣❛♥ç❛ ♣♦♣✉❧❛r✱ ✉♠❛ ❝r✐s❡ ✜♥❛♥❝❡✐r❛ ♣♦❞❡ ❝♦♠♣r♦♠❡t❡r t♦❞❛ ❡str✉t✉r❛ ❡❝♦♥ô♠✐❝❛ ❞❡ ✉♠❛ s♦❝✐❡❞❛❞❡✳ ❱❛❧❡ ❛✐♥❞❛ ♥♦t❛r q✉❡ ❛s ❝r✐s❡s tê♠ s✐❞♦ r❡❝♦rr❡♥t❡s ❝♦♠ ❞✐❢❡r❡♥t❡s ✐♥t❡♥s✐❞❛❞❡s✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ♦ ❝r❡s❝❡♥t❡ ❛✉♠❡♥t♦ ❞❛ ❝♦♥❡❝t✐✈✐❞❛❞❡ ❞♦ ♠❡r❝❛❞♦ ❣❧♦❜❛❧✱ ♣♦r ♠❡✐♦ ❞❡ tr❛♥s❛çõ❡s ❝♦♠❡r❝✐❛✐s ✭✢✉①♦ ❞❡ ♣r♦❞✉t♦s✮ ❡ ✜♥❛♥❝❡✐r❛s ✭✢✉①♦ ❞❡ ❝❛♣✐t❛❧✮✱ ❣❡r❛ ♠❛✐♦r ❣r❛✉ ❞❡ ❛♣r❡❡♥sã♦ ♦✉ ♠❡❞♦ ❞❡ q✉❡ ❡st❛s ❝r✐s❡s s❡ t♦r♥❡♠ ♠❛✐s ❢r❡q✉❡♥t❡s ❡ s❡ ♣r♦♣❛❣✉❡♠ ♠❛✐s ✈❡❧♦③♠❡♥t❡ ✭❍❛❧❞❛♥❡✱✷✵✶✵✮✳
❉♦ ♣♦♥t♦ ❞❡ ✈✐st❛ t❡ór✐❝♦✱ ♦✉ s❡❥❛✱ ♥♦s ♠♦❞❡❧♦s ❝❧áss✐❝♦s✱ ♦ s❡t♦r ✜♥❛♥❝❡✐r♦ r❡❛❧♠❡♥t❡ t❡♠ ✉♠ ♣❛♣❡❧ ♠✉✐t♦ r✉❞✐♠❡♥t❛r✿ ♦ ❜❛♥❝♦ ❝❡♥tr❛❧ ❞❡✜♥❡ ❛ t❛①❛ ❞❡ ❥✉r♦s✱ q✉❡ ♣♦r s✉❛ ✈❡③ ❛❢❡t❛ ❛s ❞❡❝✐sõ❡s ❞❡ ❝♦♥s✉♠♦ ❡ ❞❡ ♣♦✉♣❛♥ç❛ ❞❛s ❢❛♠í❧✐❛s✳ ❖s ❛t♦r❡s r❡❛✐s ❞♦ s❡t♦r ✜♥❛♥❝❡✐r♦ ❡ ♦s s❡✉s ❞✐✈❡rs♦s t✐♣♦s ❞❡ tr❛♥s❛çõ❡s ♥ã♦ ❞❡s❡♠♣❡♥❤❛♠ ✉♠ ♣❛♣❡❧ ✐♠♣♦rt❛♥t❡ ♥❡ss❡s ♠♦❞❡❧♦s ✭❲✐❡❧❛♥❞ ❡t ❛❧✳✱ ✷✵✶✷✮✳ ❋❡♥ô♠❡♥♦s ❝♦♠♦ ❛s ❜♦❧❤❛s ❡s♣❡❝✉❧❛t✐✈❛s✱ s✉♣❡r✲ ✐♥✈❡st✐♠❡♥t♦✱ ♦s ❡❢❡✐t♦s ❞❛s ♠✉❞❛♥ç❛s ❞♦s ❜❛❧❛♥ç♦s ❡ ❧✐q✉✐❞❡③✱ ❡ ♦s ❡❢❡✐t♦s ❞♦♠✐♥ó ❞❡ ❢❛❧ê♥❝✐❛s ❜❛♥❝ár✐❛s ❡stã♦ ❡①❝❧✉í❞♦s✱ ❛ ♣r✐♦r✐✳ ❆ ♦r✐❣❡♠ ❞❛ ✐♥st❛❜✐❧✐❞❛❞❡ ❞♦ s❡t♦r ✜♥❛♥❝❡✐r♦ ❡ s✉❛ ♣r♦♣❛❣❛çã♦ ♣❛r❛ ❛ ❡❝♦♥♦♠✐❛ r❡❛❧ ♥ã♦ ❡stá ❡♥❞❡r❡ç❛❞❛ ♥❛ ❡str✉t✉r❛ ❜ás✐❝❛ ❞❡ss❡s ♠♦❞❡❧♦s ✭❇r✉♥♥❡r♠❡✐❡r ❡ ❖❡❤♠❦❡✱ ✷✵✶✷❀ ▼✐s❤❦✐♥✱ ✷✵✵✾❀❲✐❡❧❛♥❞ ❡t ❛❧✳✱✷✵✶✷✮✳
❆ ♠❛♥❡✐r❛ ❝♦♠♦ ❛s ❝r✐s❡s ✜♥❛♥❝❡✐r❛s tê♠ ❛❢❡t❛❞♦ ❛ ❡❝♦♥♦♠✐❛ ❡①✐❣❡ q✉❡ ❛ ♣❡sq✉✐s❛ ♥❡ss❛ ár❡❛ ❡♥❝♦♥tr❡ ✉♠ ♥♦✈♦ ❝❛♠✐♥❤♦ ❡♠ ♠✉✐t♦s ❛s♣❡❝t♦s✳ ❉❡ ♠♦❞♦ ❣❡r❛❧✱ ❛s ❡str✉t✉r❛s ❞♦ ♠❡r❝❛❞♦ ✜♥❛♥❝❡✐r♦ ❧♦❝❛❧ ❡ ❣❧♦❜❛❧✱ ❜❡♠ ❝♦♠♦ s✉❛ ❝❛♣❛❝✐❞❛❞❡ ✐♥trí♥s❡❝❛ ❞❡ ❣❡r❛r ❞❡✲ s❡st❛❜✐❧✐③❛çã♦✱ ♣r❡❝✐s❛♠ s❡r ❡st✉❞❛❞❛s✱ ❛ss✐♠ ❝♦♠♦ ❛ ♣r♦♣❛❣❛çã♦ ❞❛ ❝r✐s❡ ❞❡♥tr♦ ❞♦ s❡t♦r ❜❛♥❝ár✐♦ ❡ ♣❛r❛ ♦ r❡st♦ ❞❛ ❡❝♦♥♦♠✐❛ ✭❲✐❡❧❛♥❞ ❡t ❛❧✳✱ ✷✵✶✷✮✳
❆ ♣r♦♣❛❣❛çã♦ ❞❡ ✉♠❛ ❝r✐s❡ ♣♦❞❡ t❡r ❡❢❡✐t♦s ♠✉✐t♦ ❞✐❢❡r❡♥t❡s ❝♦♠ ❛ ♣❡q✉❡♥❛ ♠✉❞❛♥ç❛ ❞❛s ❝♦♥❞✐çõ❡s ❞♦ ❝❡♥ár✐♦ ❡❝♦♥ô♠✐❝♦ ♦✉ ✐♥❡r❡♥t❡s ❛ ❝❛❞❛ ♠❡r❝❛❞♦✳ P❛r❛ ❡①❡♠♣❧✐✜❝❛r ❡ss❡ ❢❛t♦✱ ❜❛st❛ r❡❧❡♠❜r❛r ❛s ❝r✐s❡s ✐♠♦❜✐❧✐ár✐❛s ❞♦ ❏❛♣ã♦✱ ❡♠ ♠❡❛❞♦s ❞❡ ✶✾✾✵✱ ❡ ❞❛ ❛♠❡r✐❝❛♥❛✱ ❡♠ ✷✵✵✽✳
❈❆P❮❚❯▲❖ ✶✳ ■◆❚❘❖❉❯➬➹❖
❊♠❜♦r❛ ❛ ❝r✐s❡ ✐♠♦❜✐❧✐ár✐❛ ♥♦ ❏❛♣ã♦ t❡♥❤❛ t✐❞♦ ❡❢❡✐t♦s r❡❣✐♦♥❛✐s ✭❙❤✐r❛ts✉❦❛✱ ✷✵✵✺✮✱ ❛ ❝r✐s❡ ❞♦ ♠❡r❝❛❞♦ ✐♠♦❜✐❧✐ár✐♦ ❞♦s ❊st❛❞♦s ❯♥✐❞♦s s❡ ❡s♣❛❧❤♦✉ r❛♣✐❞❛♠❡♥t❡ ♣❛r❛ ♦✉tr❛s ✐♥st✐t✉✐çõ❡s ✜♥❛♥❝❡✐r❛s q✉❡ ❞❡t✐♥❤❛♠ tít✉❧♦s ❝✉❥♦s r❡♥❞✐♠❡♥t♦s ❞❡♣❡♥❞✐❛♠ ❞♦ r❡s✉❧t❛❞♦ ❞♦s ❡♠♣rést✐♠♦s ❤✐♣♦t❡❝ár✐♦s ❛♠❡r✐❝❛♥♦ ✭●❦♦✉❣❦♦✉s✐ ❡ ❘♦♦s❡♥❜♦♦♠✱ ✷✵✶✵✮✳ ❊st❛s ✐♥st✐✲ t✉✐çõ❡s t✐✈❡r❛♠ q✉❡ ❛❥✉st❛r s❡✉s ❜❛❧❛♥ç♦s ❝♦♠ ❛ ✈❡♥❞❛ ❞❡ ♦✉tr♦s tít✉❧♦s✱ ❧❡✈❛♥❞♦✲♦s à ❞❡s✈❛❧♦r✐③❛çã♦ ❞♦s ♠❡s♠♦s✱ ❝❛✉s❛♥❞♦ ♣r❡❥✉í③♦s ♣❛r❛ ♦s t✐t✉❧❛r❡s ❞❡ ♦✉tr❛s ✐♥st✐t✉✐çõ❡s✳ ❉❡♣♦✐s q✉❡ ♦ ▲❡❤♠❛♥ ❇r♦t❤❡rs ❢❛❧✐✉✱ ❛s ✐♥st✐t✉✐çõ❡s ✜♥❛♥❝❡✐r❛s ❛❝❛❜❛r❛♠ ♣♦r ❡①❛❝❡r❜❛r ❛ ♣r♦♣❛❣❛çã♦ ❞❛ ❝r✐s❡✿ ❡❧❛s ♣❛r❛r❛♠ ❞❡ ❞❛r ❡♠♣rést✐♠♦s ❛ ❝✉rt♦ ♣r❛③♦ ♥♦ s❡t♦r ✐♥t❡r✲ ❜❛♥❝ár✐♦✱ ♠❛s ✐st♦ só ❝❛✉s♦✉ ✉♠ ❛❣r❛✈❛♠❡♥t♦ ❞❡ ♣r♦❜❧❡♠❛s ❞❡ ❧✐q✉✐❞❡③ ✭❉❛t③✱ ✷✵✵✷✮✳ ❈♦♠♦ q✉❛s❡ t♦❞❛s ❛s ✐♥st✐t✉✐çõ❡s ✜♥❛♥❝❡✐r❛s ❞❡♣❡♥❞❡♠ ❞❡ ✉♠ ♠❡r❝❛❞♦ ✐♥t❡r❜❛♥❝ár✐♦ q✉❡ ❢✉♥❝✐♦♥❡ ❜❡♠✱ ❛ r❡tr❛çã♦ ❞♦ s❡t♦r ❜❛♥❝ár✐♦ ❛♠♣❧✐✜❝♦✉ ♦s ❡❢❡✐t♦s ❞❛ ❝r✐s❡ ❞❡ ❧✐q✉✐❞❡③ q✉❡ ❛♠❡❛ç♦✉ t♦❞♦ ♦ s✐st❡♠❛ ✜♥❛♥❝❡✐r♦✳ ●♦✈❡r♥♦s ❡ ❜❛♥❝♦s ❝❡♥tr❛✐s t✐✈❡r❛♠ q✉❡ ✐♥t❡r✈✐r ♣❛r❛ ❡✈✐t❛r q✉❡ t♦❞♦ ♦ s✐st❡♠❛ ❡♥tr❛ss❡ ❡♠ ❝♦❧❛♣s♦ ✭❙❛♥t♦s✱✷✵✶✵✮✳
❆ ❡①♣❧✐❝❛çã♦ ♣❛r❛ ❡ss❡ ❢❡♥ô♠❡♥♦ ♣♦❞❡ s❡r ❡♥❝♦♥tr❛❞❛ ♣♦r ♠❡✐♦ ❞♦ ❡st✉❞♦ ❞♦ r✐s❝♦ s✐stê♠✐❝♦✱ ♣♦✐s ❛s ❢❡rr❛♠❡♥t❛s ❛t✉❛✐s ♣♦✉❝♦ s✉rt✐r❛♠ ❡❢❡✐t♦ ♥❡st❡ s❡♥t✐❞♦✳ ❉❡♥tr♦ ❞❡st❡ ❝♦♥t❡①t♦✱ ❛ ❛❜♦r❞❛❣❡♠ ♠❡t♦❞♦❧ó❣✐❝❛ q✉❡ ❝♦♠❜✐♥❛ r✐s❝♦ s✐stê♠✐❝♦ ❝♦♠ r❡❞❡s ❝♦♠♣❧❡①❛s tê♠ ❞❛❞♦ ✉♠ ♥♦rt❡ ❛♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ às ♣♦❧ít✐❝❛s ♣r❡✈❡♥t✐✈❛s✱ ❡ ✐ss♦ tê♠ ❢❡✐t♦ ♦ ❈♦♠✐tê ❞❛ ❇❛s✐❧é✐❛ r❡❢♦r♠✉❧❛r ♦ ❆❝♦r❞♦ ❞❡ ❇❛s✐❧é✐❛ ■■✱ ❝r✐❛♥❞♦ ♦ ♥♦✈♦ ❆❝♦r❞♦ ❞❡ ❇❛s✐❧é✐❛ ■■■✱ q✉❡ ❧❡✈❛ ❡♠ ❝♦♥t❛ ♠❡❞✐❞❛s ❞❡ r✐s❝♦ ❞❡ ❧✐q✉✐❞❡③✱ ❛ ❝♦♥❡❝t✐✈✐❞❛❞❡ ❡♥tr❡ ♦s ❜❛♥❝♦s ❡ ❛ ❞❡♣❡♥❞ê♥❝✐❛ ❞❡ r✐s❝♦ ✈✐❛ ❞❡r✐✈❛t✐✈♦s ✭❇■❙✱ ✷✵✶✵✮✳
❆s r❡❞❡s ❝♦♠♣❧❡①❛s ❡♠✉❧❛♠ ❛s r❡❧❛çõ❡s ❝♦♥tr❛t✉❛✐s ❞❡ ❝ré❞✐t♦ ❡♥tr❡ ❛s ✐♥st✐t✉✐çõ❡s ✜♥❛♥❝❡✐r❛s ♣❡r♠✐t✐♥❞♦ ✉♠ ❡st✉❞♦ ❛♣r♦❢✉♥❞❛❞♦ s♦❜r❡ ♦ s✐st❡♠❛ ✜♥❛♥❝❡✐r♦❀ ♦ ❢♦r♠❛t♦ ❞❡ss❛s ❧✐❣❛çõ❡s é ❞❡♥♦♠✐♥❛❞♦ t♦♣♦❧♦❣✐❛ ❞❡ r❡❞❡✳ ❆✐♥❞❛ ♥ã♦ s❡ s❛❜❡ q✉❛❧ s❡r✐❛ ♦ ✐♠♣❛❝t♦ ❞❡ss❛s t♦♣♦❧♦❣✐❛s ♥♦ s✐st❡♠❛✱ ♦✉ q✉❛❧ ❞❡❧❛s s❡r✐❛ ♠❛✐s r♦❜✉st❛✱ ♦✉ s❡❥❛✱ ♦ ✉s♦ ❞❡ ❛❧❣✉♠❛ t♦♣♦❧♦❣✐❛ r❡❞✉③✐r✐❛ ♦✉ ❛✉♠❡♥t❛r✐❛ ♦ r✐s❝♦ s✐stê♠✐❝♦❄
P❛rt❡ ❞❡ss❛s r❡s♣♦st❛s ♣♦❞❡♠ s❡r ♦❜t✐❞❛s ♣♦r ♠❡✐♦ ❞♦ ❡st✉❞♦ ❞❡ss❛s t♦♣♦❧♦❣✐❛s ❡ ❞❡ ❝♦♠♦ ❛s ♠❡s♠❛s ❞❡s❝r❡✈❡♠ ❛ s❡♥s✐❜✐❧✐❞❛❞❡ ❞♦s s✐st❡♠❛s ❡♠ ✉♠❛ ❝r✐s❡✳ ◆❡st❡ tr❛❜❛❧❤♦✱ s❡rã♦ ❞✐s❝✉t✐❞♦s ♦s ❡❢❡✐t♦s ❞❛s t♦♣♦❧♦❣✐❛s ❞❡ r❡❞❡✱ ✉t✐❧✐③❛♥❞♦ ✉♠ ♠♦❞❡❧♦ ❞❡ ♣r♦♣❛❣❛çã♦ ❞❡ ❝r✐s❡s ✜♥❛♥❝❡✐r❛s✳
✶✳✶ ❖❜❥❡t✐✈♦s
❖ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t✐✈♦ ❞❡ss❡ ❡st✉❞♦ é ✐♥✈❡st✐❣❛r ♦ ♣❛♣❡❧ ❞❛ ❡str✉t✉r❛ ❞❛ r❡❞❡ q✉❡ ❞❡s❝r❡✈❡ ♦ s❡t♦r ✜♥❛♥❝❡✐r♦✳ ❆ ❝♦♠♣r❡❡♥sã♦ ❞❡ss❛s r❡❞❡s ♣❛r❡❝❡ s❡r ❞❡ ✐♠♣♦rtâ♥❝✐❛ ❝❡♥tr❛❧ ♥❛ ❛♥á❧✐s❡ ❞❡ ✐♥st❛❜✐❧✐❞❛❞❡s s✐stê♠✐❝❛s✳ ❊❧❛ ❢♦r♥❡❝❡ ❛ ❜❛s❡ ❝✐❡♥tí✜❝❛ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ ❝♦♠♦ ❛s ❝r✐s❡s s❡ ♣r♦♣❛❣❛♠ ✭❍❛❧❞❛♥❡ ❡ ▼❛②✱ ✷✵✶✶✮✳ ■ss♦ ♣❡r♠✐t❡ ❞✐s❝✉t✐r ❡str❛té❣✐❛s ❡ ♣♦❧ít✐❝❛s ❞❡ r❡❣✉❧❛♠❡♥t❛çã♦ ❞♦ s❡t♦r ❜❛♥❝ár✐♦ q✉❡ ❞❡✈❡♠ ❧❡✈❛r ❡♠ ❝♦♥t❛ ♥ã♦ ❛♣❡♥❛s ♦s r✐s❝♦s ❡s♣❡❝í✜❝♦s ❞♦ ❜❛♥❝♦✱ ♠❛s t❛♠❜é♠ ♦s ❢❛t♦r❡s ❞❡ r✐s❝♦s ❣❧♦❜❛✐s✱ q✉❡ ❞❡✈❡♠ s❡r ❡st✉❞❛❞♦s ❞❡ ❢♦r♠❛ ✐♥t❡❣r❛❞❛ ✭❈❤❛♥✲▲❛✉✱ ✷✵✶✵✮✳
◆❡st❡ tr❛❜❛❧❤♦ s❡rã♦ ❞✐s❝✉t✐❞♦s✱ ♣♦r ♠❡✐♦ ❞❡ ✉♠ ♠♦❞❡❧♦ ❞❡ ♣r♦♣❛❣❛çã♦ ❞❡ ❝r✐s❡s✱ ♦s ❡❢❡✐t♦s ❞❛s t♦♣♦❧♦❣✐❛s ❞❡ r❡❞❡✱ ❜❡♠ ❝♦♠♦ ❛ ❛❧❛✈❛♥❝❛❣❡♠ ❡ ♦ ♥í✈❡❧ ❞❡ ❡♥❞✐✈✐❞❛♠❡♥t♦ ✐♥✐❝✐❛❧ ❞♦ s✐st❡♠❛✳
✶✳✷ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚r❛❜❛❧❤♦
❖ tr❛❜❛❧❤♦ ❡stá ❞✐✈✐❞✐❞♦ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿ ❖ ❝❛♣ít✉❧♦✷❛♣r❡s❡♥t❛ ❛ r❡✈✐sã♦ ❞❛ ❧✐t❡✲ r❛t✉r❛ ❞❛ ár❡❛✱ ♦✉ s❡❥❛✱ ♠♦str❛ ♦s ♣r✐♥❝✐♣❛✐s tr❛❜❛❧❤♦s ♣✉❜❧✐❝❛❞♦s ♥❛ ár❡❛ ❞❡ r✐s❝♦ s✐stê♠✐❝♦ s♦❜ ❛ ❛❜♦r❞❛❣❡♠ ❞❡ r❡❞❡s ❝♦♠♣❧❡①❛s✳ ❉❡st❛ ♠❛♥❡✐r❛✱ ✐♥tr♦❞✉③✲s❡ ❛♦ ❧❡✐t♦r ♦s ❝♦♥❝❡✐t♦s q✉❡ s❡r✈✐rã♦ ❝♦♠♦ ❜❛s❡ ♣❛r❛ ♦ r❡st❛♥t❡ ❞♦ t❡①t♦❀ ♦ ❝❛♣ít✉❧♦ ✸ ❞✐s❝✉t❡ ♦s ❝♦♥❝❡✐t♦s ❞❡ r❡❞❡s ❝♦♠♣❧❡①❛s r❡❧❡✈❛♥t❡s ❛ ❡ss❡ tr❛❜❛❧❤♦✱ ❜❡♠ ❝♦♠♦ ✉♠❛ ❜r❡✈❡ ❞❡s❝r✐çã♦ ❞❛s t♦♣♦❧♦❣✐❛s ❞❡ r❡❞❡ ✉t✐❧✐③❛❞❛s ♥❛s s✐♠✉❧❛çõ❡s✱ ♦ ❧❡✐t♦r q✉❡ s❡ s❡♥t✐r ❢❛♠✐❧✐❛r✐③❛❞♦ ❝♦♠ ♦s ❡ss❡s ❝♦♥❝❡✐t♦s ♣♦❞❡rá ♣✉❧❛r ❡st❡ ❝❛♣ít✉❧♦✱ ❛ss✐♠ ❝♦♠♦ ♦ ❝❛♣ít✉❧♦ ✹✱ q✉❡ tr❛t❛ s♦❜r❡ ♦ ❝♦♥❝❡✐t♦ ❞❡ r✐s❝♦ ✜♥❛♥❝❡✐r♦✱ s✉❛ ❝❧❛ss✐✜❝❛çã♦ ❡ t❛♠❜é♠ ❞❡s❝r❡✈❡ ✉♠ ❞♦s ♣r✐♥❝✐♣❛✐s ♠♦❞❡❧♦s ❞❡ ♠❡♥s✉r❛çã♦ ❞❡ r✐s❝♦✱ ❞❡♥♦♠✐♥❛❞♦ ❱❛❧✉❡ ❛t ❘✐s❦✱ t❛♠❜é♠ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ❱❛❘❀ ♦ ❝❛♣ít✉❧♦ ✺ ✈❡rs❛ s♦❜r❡ ♦ r✐s❝♦ s✐stê♠✐❝♦ ❡ s♦❜r❡ ❛s ❝r✐s❡s ✜♥❛♥❝❡✐r❛s✱ ❛❧é♠ ❞❡ tr❛③❡r ❝♦♠❡♥tár✐♦s s♦❜r❡ ♦s ❛❝♦r❞♦s ❞❡ ❇❛s✐❧é✐❛ ■■ ❡ ■■■✱ ❡ ❛♣r❡s❡♥t❛r ♦s ♠♦❞❡❧♦s ✉t✐❧✐③❛❞♦s ♥❡ss❡ ❡st✉❞♦✿ ✉♠ ♠♦❞❡❧♦ ❞❡ ❝r✐❛çã♦ ❞❡ r❡❞❡ ✐♥t❡r❜❛♥❝ár✐❛ ❡ ♦✉tr♦ ❞❡ ❝♦♥tá❣✐♦ ✜♥❛♥❝❡✐r♦✱ ♦✉ s❡❥❛✱ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ♣r♦♣❛❣❛çã♦ ❞❛ ❝r✐s❡✳ ◆❡st❡ ♠❡s♠♦ ❝❛♣ít✉❧♦ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛s três ♠❡❞✐❞❛s ❞❡ r✐s❝♦ s✐stê♠✐❝♦ ✉t✐❧✐③❛❞❛s ♥❡ss❡ ❡st✉❞♦❀ ♦ ❝❛♣ít✉❧♦ ✻ ❞❡s❝r❡✈❡ ❡ ❛♥❛❧✐s❛ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♥❡ss❛ ♣❡sq✉✐s❛❀ ♦ ❝❛♣ít✉❧♦ ✼ tr❛③ ❛s ❝♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s s♦❜r❡ ♦ ♠♦❞❡❧♦ ❡ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣♦r ♠❡✐♦ ❞❛s s✐♠✉❧❛çõ❡s✱ ❜❡♠ ❝♦♠♦ s✉❣❡stõ❡s ♣❛r❛ ♣❡sq✉✐s❛s ❢✉t✉r❛s❀ ♣♦r ✜♠✱ ❛s r❡❢❡rê♥❝✐❛s ❜✐❜❧✐♦❣rá✜❝❛s ✉t✐❧✐③❛❞❛s ❡ ❝♦♠♦ ❛♣ê♥❞✐❝❡ ♦s ❛❧❣♦r✐t♠♦s ❞♦ ♠♦❞❡❧♦ ❞❡ ❝♦♥tá❣✐♦ ❡ ❞❛ r❡❞❡ ♣r♦♣♦st❛ ♣♦r ▲✐ ❡t ❛❧✳ ✭✷✵✶✵✮✱ ❡ss❡s ♠♦❞❡❧♦s✱ ❛ss✐♠ ❝♦♠♦ t♦❞♦s ♦s ♦✉tr♦s✱ ❢♦r❛♠ ✐♠♣❧❡♠❡♥t❛❞♦s ❡♠ P②t❤♦♥✳
❈❛♣ít✉❧♦ ✷
❘❡✈✐sã♦ ❞❛ ▲✐t❡r❛t✉r❛
❆s ❝r✐s❡s ✜♥❛♥❝❡✐r❛s tê♠ ❞❡s♣❡rt❛❞♦ ✐♥t❡r❡ss❡ ❡♠ ❞✐✈❡rs❛s ár❡❛s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✱ ❞✐✈❡rs♦s ♠♦❞❡❧♦s s✉r❣✐r❛♠ ♥❛ t❡♥t❛t✐✈❛ ❞❡ ❡①♣❧✐❝❛r ❝♦♠♦ ❡ ♣♦rq✉❡ ❡❧❛s ❛❝♦♥t❡❝❡♠✳
❆s ❞✐✈❡rs❛s ❧✐♥❤❛s ❞❡ ♣❡sq✉✐s❛ ❡♥❣❧♦❜❛♠ ♦s ♠♦❞❡❧♦s ❞❡ ❝♦rr✐❞❛s ❜❛♥❝ár✐❛s
✭❉✐❛♠♦♥❞ ❡ ❉②❜✈✐❣✱ ✶✾✽✸❀▼✐s❤❦✐♥✱✷✵✵✾✮✱ ♦✉ s❡❥❛✱ q✉❛♥❞♦ ♦s ❞❡♣♦s✐t❛♥t❡s✱ ❝♦♠ ♠❡❞♦ ❞❡ s❡r❡♠ ✐♠♣❡❞✐❞♦s ❞❡ r❡❝✉♣❡r❛r s❡✉s ✐♥✈❡st✐♠❡♥t♦s✱ r❡❛❧✐③❛♠ s❛q✉❡s ❡♠ ♠❛ss❛✱ ♣r♦✈♦❝❛♥❞♦ ❛ q✉❡❜r❛ ❞❛s ✐♥st✐t✉✐çõ❡s✱ ♦s ♠♦❞❡❧♦s ❞❡ ❆ss✐♠❡tr✐❛ ❞❡ ■♥❢♦r♠❛çã♦ ✭❈❤❡♥✱ ✶✾✾✾✮✱ q✉❡ é✱ q✉❛♥❞♦ ❛❧❣✉♥s ♣❛rt✐❝✐♣❛♥t❡s ❝♦♠ ✐♥❢♦r♠❛çõ❡s ♣r✐✈✐❧❡❣✐❛❞❛s s♦❜r❡ ❛ s❛ú❞❡ ✜♥❛♥❝❡✐r❛ ❞❛s ✐♥st✐t✉✐çõ❡s t♦♠❛♠ ❛t✐t✉❞❡s ❡q✉✐✈♦❝❛❞❛s✱ ❝❛✉s❛♥❞♦ ❛ ✐♥st❛❜✐❧✐❞❛❞❡ ✜♥❛♥❝❡✐r❛✱ ♦✉ ❛✐♥❞❛ ♦s ♠♦❞❡❧♦s ♣r❡❞✐t✐✈♦s✳ ❊st❡s✱ ❡♠ ❣❡r❛❧✱ ❛♥❛❧✐s❛♠ ❛s ♣♦ssí✈❡✐s q✉❡❜r❛s ♥❛ ❜♦❧s❛ ❞❡ ✈❛❧♦r❡s✱ ♣♦r ♠❡✐♦ ❞❛s ❢❡rr❛♠❡♥t❛s tr❛❞✐❝✐♦♥❛✐s ❞❛ ❡st❛tíst✐❝❛ ✭❘❡✐♥❤❛rt ❡ ❘♦❣♦✛✱ ✷✵✶✶✮ ♦✉✱ ♠❛✐s r❡❝❡♥t❡♠❡♥t❡✱ ❝♦♠ ❛ ❛♥á❧✐s❡ ❞❡ ♠✉❧t✐❢r❛❝t❛❜✐❧✐❞❛❞❡ ✭❋♦♥s❡❝❛✱ ✷✵✶✷✮✱ ❛♠❜♦s ♠✉♥✐❞♦s ❞❡ sér✐❡s t❡♠♣♦r❛✐s ✜♥❛♥❝❡✐r❛s✳
❊♠❜♦r❛ ❡ss❡s ♠♦❞❡❧♦s s❡❥❛♠ ✐♥t❡r❡ss❛♥t❡s✱ ❛✐♥❞❛ ❛ss✐♠ ♥ã♦ ❡①❝❧✉❡♠ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ♠♦❞❡❧♦s q✉❡ ❡①♣❧✐q✉❡♠ ❝♦♠♦ ❛s ♠❡s♠❛s sã♦ ♣r♦♣❛❣❛❞❛s✳ ❆ ♣r♦♣❛❣❛çã♦ é ♣❡ç❛ ❢✉♥❞❛♠❡♥✲ t❛❧ ♥♦ ❝♦♥t❡①t♦ ❞❡ ✉♠❛ ❝r✐s❡ ✜♥❛♥❝❡✐r❛✱ ❡❧❛ ❛❝♦♥t❡❝❡ ❞❡✈✐❞♦ à ✐♥t❡r❝♦♥❡❝t✐✈✐❞❛❞❡ ❡♥tr❡ ♦s ❜❛♥❝♦s ❡ ❛s ✜r♠❛s✳ ❆ ❝r✐s❡ ❞♦ ♠❡r❝❛❞♦ ❞❡ ❤✐♣♦t❡❝❛s ❡♠2008 ❡✈✐❞❡♥❝✐♦✉ ❡ss❡ ❢❛t♦✱ ✐♥❞✐✲ ❝❛♥❞♦ ❛ ❢r❛❣✐❧✐❞❛❞❡ ❞❡ ✉♠ s✐st❡♠❛ ❛♣❛r❡♥t❡♠❡♥t❡ s❛✉❞á✈❡❧ ✭●❦♦✉❣❦♦✉s✐ ❡ ❘♦♦s❡♥❜♦♦♠✱ ✷✵✶✵❀▼♦✉ss❛✱✷✵✶✶❀ ❙❛♥t♦s✱ ✷✵✶✵✮✱ ♣♦ré♠ ❡①tr❡♠❛♠❡♥t❡ s✉s❝❡tí✈❡❧ ❛♦ ❝♦♥tá❣✐♦ ✜♥❛♥❝❡✐r♦ ✭❆❧❧❡♥ ❡ ●❛❧❡✱ ✷✵✵✵❀ ❏❛r❛♠✐❧❧♦ ❡t ❛❧✳✱ ✷✵✶✵❀ ❯♣♣❡r ❡ ❲♦r♠s✱ ✷✵✵✹❀ ❲❡❧❧s✱ ✷✵✵✹✮✳
❆s ✐♥st✐t✉✐çõ❡s ❝♦♥❤❡❝✐❞❛s ❝♦♠♦ ▼✉✐t♦ ❝♦♥❡❝t❛❞❛s ♣❛r❛ ❢❛❧❤❛r✱ sã♦ ❤♦❥❡ ❛ ❣r❛♥❞❡ ♣r❡✲ ♦❝✉♣❛çã♦ ♥♦ q✉❡ s❡ ❞✐③ r❡s♣❡✐t♦ à r❡❣✉❧❛çã♦ ✜♥❛♥❝❡✐r❛✱ ❡ ❞❡✈❡♠ r❡❝❡❜❡r ❛t❡♥çã♦ ❡s♣❡❝✐❛❧ ✭❇■❙✱✷✵✶✵❀❈❤❛♥✲▲❛✉✱✷✵✶✵✮✳ ❉❡♥tr♦ ❞❡st❡ ❝♦♥t❡①t♦✱ ♦s ♠♦❞❡❧♦s q✉❡ ✉t✐❧✐③❛♠ ❛s r❡❞❡s ❝♦♠✲ ♣❧❡①❛s ❝♦♠♦ ❢❡rr❛♠❡♥t❛ ❞❡♠♦♥str❛♠ ❝❛❞❛ ✈❡③ ♠❛✐s ✐♠♣♦rtâ♥❝✐❛ ♥❡ss❡ t✐♣♦ ❞❡ ❛♥á❧✐s❡✱ ❡❧❡s tê♠ ❝r✐❛❞♦ ✉♠❛ ♥♦✈❛ ❧✐t❡r❛t✉r❛ q✉❡ ❞❛rá s✉♣♦rt❡ às ❞❡❝✐sõ❡s✱ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ s✐stê♠✐❝♦✳ ❯♠❛ ♠❡❞✐❞❛ ❞❡ r✐s❝♦ s✐stê♠✐❝♦ ♣♦❞❡ ❛✉①✐❧✐❛r ♦s ❜❛♥❝♦s ❝❡♥tr❛✐s ❡♠ s✉❛s ✐♥t❡r✈❡♥çõ❡s✱ ✉♠❛ ✈❡③ q✉❡ ❛s ♠❡❞✐❞❛s tr❛❞✐❝✐♦♥❛✐s ❞❡ r✐s❝♦✱ ♠❡s♠♦ q✉❡ ✐♥t❡❣r❛❞❛s✱ sã♦ ❢❡✐t❛s ✐♥❞✐✈✐❞✉✲ ❛❧♠❡♥t❡ ♣❛r❛ ❝❛❞❛ ✐♥st✐t✉✐çã♦ ❡ ♥ã♦ ♠♦str❛♠ ❛ s✐t✉❛çã♦ ♥❛ q✉❛❧ ♦ s✐st❡♠❛ s❡ ❡♥❝♦♥tr❛✳
P♦❞❡✲s❡ ❞✐③❡r q✉❡ ♦ ♣r✐♠❡✐r♦ ♠♦❞❡❧♦ q✉❡ tr❛t❛ ❞❡ r✐s❝♦ s✐stê♠✐❝♦ ✉t✐❧✐③❛♥❞♦ r❡❞❡s ❢♦✐ ♦
♠♦❞❡❧♦ ♣r♦♣♦st♦ ♣♦r❆❧❧❡♥ ❡ ●❛❧❡✭✷✵✵✵✮✳ ◆ã♦ s❡ tr❛t❛ ❞❡ ✉♠ ♠♦❞❡❧♦ ❞❡ r❡❞❡s ❝♦♠♣❧❡①❛s✱ ♥♦ ❡♥t❛♥t♦✱ ❢♦r❛♠ ✉t✐❧✐③❛❞❛s r❡❞❡s ❝♦♠♣❧❡t❛s ❡ ✐♥❝♦♠♣❧❡t❛s✳ ❘❡♣r❡s❡♥t❛♥❞♦ ❝❛❞❛ ✐♥st✐t✉✲ ✐çã♦ ♣♦r ✉♠ ♥ó✱ ❢♦✐ ♣♦ssí✈❡❧ ❝♦♥❝❧✉✐r q✉❡ ♥♦ ❝❛s♦ ❞❛ r❡❞❡ ❝♦♠♣❧❡t❛ ♦s ❡❢❡✐t♦s ❞❛ ❝r✐s❡ sã♦ ❛♠❡♥✐③❛❞♦s✱ ♣♦✐s ❛♣ós r❡❝❡❜❡r ✉♠ ❝❤♦q✉❡ ✜♥❛♥❝❡✐r♦✱ ♦s r✐s❝♦s sã♦ ❝♦♠♣❛rt✐❧❤❛❞♦s ❡♥tr❡ t♦❞♦s ♦s ♣❛rt✐❝✐♣❛♥t❡s ❞♦ s✐st❡♠❛✳ ❖ ✐♥✈❡rs♦ ♦❝♦rr❡ ❝♦♠ ❛ ✉t✐❧✐③❛çã♦ ❞❡ r❡❞❡s ✐♥❝♦♠♣❧❡✲ t❛s✱ ♦✉ s❡❥❛✱ ♦s ❡❢❡✐t♦s ❞❛ ❝r✐s❡ sã♦ ♠❛✐♦r❡s✱ ♣♦✐s ♦s r✐s❝♦s sã♦ ❝♦♠♣❛rt✐❧❤❛❞♦s ❝♦♠ ♠❡♥♦s ♣❛rt✐❝✐♣❛♥t❡s ❞♦ s✐st❡♠❛✳
❊♠❜♦r❛ ❛✐♥❞❛ ♠✉✐t♦ s✐♠♣❧✐st❛✱ ❡ss❡ ♠♦❞❡❧♦ ✐♥s♣✐r♦✉ ❞✐✈❡rs♦s tr❛❜❛❧❤♦s q✉❡ ❝♦♥s✐❞❡r❛♠ ❛ ✐♥t❡r❝♦♥❡❝t✐✈✐❞❛❞❡ ✉♠ ❢❛t♦r ❞❡t❡r♠✐♥❛♥t❡ ♣❛r❛ q✉❡ ✉♠❛ ❝r✐s❡ s❡❥❛ ♣r♦♣❛❣❛❞❛✳ ❈♦♠♦ ♣♦r ❡①❡♠♣❧♦✱ ♦s tr❛❜❛❧❤♦s ❞❡❚❡t❡r②❛t♥✐❦♦✈❛✭✷✵✶✵✮✳ ❊st❡✱ ♣♦r ✐♥t❡r♠é❞✐♦ ❞♦ ✉s♦ ❞❡ ✉♠❛ r❡❞❡ ❧✐✈r❡ ❞❡ ❡s❝❛❧❛✱ ❡ ❆❝❡♠♦❣❧✉ ❡t ❛❧✳ ✭✷✵✶✸✮✱ ♣♦r ♠❡✐♦ ❞❡ ✉♠ ♠♦❞❡❧♦ t❡ór✐❝♦ ❝♦♠ r❡❞❡s ❡♠ ❢♦r♠❛t♦ ❞❡ ❛♥é✐s✱ ♦❜t✐✈❡r❛♠ r❡s✉❧t❛❞♦s s❡♠❡❧❤❛♥t❡s ❛♦s ❞❡ ❆❧❧❡♥ ❡ ●❛❧❡ ✭✷✵✵✵✮✳
❆♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✱ ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ tr❛❜❛❧❤♦s ✉t✐❧✐③❛r❛♠ ❛ ❡str✉t✉r❛ ❞❡ ❜❛❧❛♥ç♦ ♣❛tr✐♠♦♥✐❛❧ ❞❡✜♥✐❞❛ ❛ ♣❛rt✐r ❞❡ ✉♠❛ ❡str✉t✉r❛ ❞❡ r❡❞❡ ♣r❡✈✐❛♠❡♥t❡ ❡s❝♦❧❤✐❞❛✳ ❊♠ ❣❡r❛❧✱ ♦ ❜❛❧❛♥ç♦ é ❞❡✜♥✐❞♦ ♣❛r❛ ❝❛❞❛ ❜❛♥❝♦i ❞♦ s✐st❡♠❛ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿
pli |{z} ♣❛tr✐♠ô♥✐♦ ❧íq✉✐❞♦
=
❛t✐✈♦
z }| {
ei |{z} ♦✉tr♦s
+ li
|{z} ❡♠♣rést✐♠♦s
−
♣❛ss✐✈♦
z }| {
di |{z} ❞❡♣ós✐t♦s
− bi |{z} ❡♠♣rést✐♠♦s
. ✭✷✳✶✮
P♦r ❞✐✈❡rs❛s r❛③õ❡s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✱ ✐♥✈❡st✐♠❡♥t♦s ♠❛❧ s✉❝❡❞✐❞♦s✱ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❛s ✐♥st✐t✉✐çõ❡s✱ ❢❛❧t❛ ❞❡ ❧✐q✉✐❞❡③ ❞♦s ❛t✐✈♦s✱ r✐s❝♦s ♠❛❧ ❣❡r✐❞♦s✱ ❡rr♦s ❡♠ ♣r❡❝✐✜❝❛çõ❡s ❞❡ ❛t✐✈♦s ❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛ ✐♥❛❞✐♠♣❧ê♥❝✐❛✱ ❛❢❡t❛♠ ❛s ✐♥st✐t✉✐çõ❡s✱ ♦✉ s❡❥❛✱ ♦s ❝❤♦q✉❡s si r❡♣r❡s❡♥t❛♠ ♣r❡❥✉í③♦s ✜♥❛♥❝❡✐r♦s ❞❛❞♦s às ✐♥st✐t✉✐çõ❡s✳ ▲♦❣♦✱ ♦s ❝❤♦q✉❡s ❞❡s❡st❛❜✐❧✐③❛♠ ♦ s✐st❡♠❛✱ ♣♦✐s ❛❢❡t❛♠ ♦s ♣❛tr✐♠ô♥✐♦s ❧íq✉✐❞♦s ❞❛s ✐♥st✐t✉✐çõ❡s✳
❉✐③❡r q✉❡ ✉♠❛ ✐♥st✐t✉✐çã♦ ❡stá ✐♥❛❞✐♠♣❧❡♥t❡ ✭❞❡❢❛✉❧t✮ s✐❣♥✐✜❝❛ q✉❡ ❛ ♠❡s♠❛ ♥ã♦ ♣♦❞❡rá ❤♦♥r❛r ❝♦♠ s❡✉s ❝♦♠♣r♦♠✐ss♦s✱ ✐ss♦ é ❝❛r❛❝t❡r✐③❛❞♦ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿
pli |{z} ♣❛tr✐♠ô♥✐♦ ❧íq✉✐❞♦
< si |{z} ❝❤♦q✉❡
. ✭✷✳✷✮
➱ ♥❛ s✐t✉❛çã♦ ❞❡ ✐♥❛❞✐♠♣❧ê♥❝✐❛ q✉❡ ❛ ✐♥st✐t✉✐çã♦ ♣r♦♣❛❣❛ ♦ ❝❤♦q✉❡✱ ❢❛③❡♥❞♦ ❝♦♠ q✉❡ s❡✉s ❝r❡❞♦r❡s s♦❢r❛♠ ✉♠ ♥♦✈♦ ❝❤♦q✉❡✱ t♦r♥❛♥❞♦✲♦s ♦✉ ♥ã♦ ✐♥❛❞✐♠♣❧❡♥t❡s✳
➱ ♥❡ss❡ s❡♥t✐❞♦ q✉❡◆✐❡r ❡t ❛❧✳✭✷✵✵✼✮ ♣r♦♣✉s❡r❛♠ ✉♠ ♠♦❞❡❧♦ ✉t✐❧✐③❛♥❞♦ ❛ t♦♣♦❧♦❣✐❛ ❞❡ r❡❞❡ ❛❧❡❛tór✐❛ ❞❡ ❊r❞ös✲❘é♥②✐ ❝♦♠25❜❛♥❝♦s ❡ ✉♠❛ ❡str✉t✉r❛ ❞❡ ❜❛❧❛♥ç♦ ♣❛tr✐♠♦♥✐❛❧ q✉❡ ❡st❛❜❡❧❡❝❡ss❡ ❛s r❡❧❛çõ❡s ❞❡ ❡♠♣rést✐♠♦s ✐♥t❡r❜❛♥❝ár✐♦s✱ ❜❡♠ ❝♦♠♦ ♦ ♥í✈❡❧ ❞❡ ❡①♣♦s✐çã♦ ❞❡ ❝❛❞❛ ✐♥st✐t✉✐çã♦ ♥♦ s✐st❡♠❛✳ ❊st❡ é ❢❡✐t♦ ❝♦♥t❛❜✐❧✐③❛♥❞♦ ♦ ♥ú♠❡r♦ ❞❡ ♥ós ❞❡ ❡♥tr❛❞❛ ❡ s❛í❞❛ ❞❛ r❡❞❡✳ ❈♦♠ ❛ ✈❛r✐❛çã♦ ❞❡ ❞✐✈❡rs♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦✱ ♦s ❛✉t♦r❡s ❝♦♥❝❧✉ír❛♠ q✉❡ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞♦ ♣❛tr✐♠ô♥✐♦ ❧íq✉✐❞♦✱ ❛ ✐♥s♦❧✈ê♥❝✐❛ ❞✐♠✐♥✉✐✱ s✉❣❡r✐♥❞♦ ✉♠❛ ♠✉❞❛♥ç❛ ♥♦ ♥í✈❡❧ ❞❡ ❛❧❛✈❛♥❝❛❣❡♠ ♣r❛t✐❝❛❞❛ ♣❡❧♦s ❜❛♥❝♦s✳ ❆ ♣♦✉❝❛ ♣r♦①✐♠✐❞❛❞❡ ❞❡ ✉♠❛ r❡❞❡ ✐♥t❡r❜❛♥❝ár✐❛ r❡❛❧ ❝♦♠ ❛s r❡❞❡s ❞❡ ❊r❞ös✲❘é♥②✐ é ✉♠❛ ❞❛s ❝rít✐❝❛s ❛ ❡ss❡ ♠♦❞❡❧♦✱ ♦ q✉❡ ♦ t♦r♥❛ ♣♦✉❝♦ r❡❛❧íst✐❝♦✳
❈❆P❮❚❯▲❖ ✷✳ ❘❊❱■❙➹❖ ❉❆ ▲■❚❊❘❆❚❯❘❆
❖✉tr♦ ♠♦❞❡❧♦ q✉❡ ✉t✐❧✐③❛ ❡str✉t✉r❛ ❞❡ ❜❛❧❛♥ç♦ ♣❛tr✐♠♦♥✐❛❧ é ♦ ♠♦❞❡❧♦ ❞❡❍❛❧❞❛♥❡ ❡ ▼❛② ✭✷✵✶✶✮✳ ❖s ❛✉t♦r❡s ❛✜r♠❛♠ q✉❡ ❤á ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ q✉❡ ❡①✐st❛♠ ♠♦❞❡❧♦s q✉❡ ❧❡✈❡♠ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ♦s ❜❛❧❛♥ç♦s ♣❛tr✐♠♦♥✐❛✐s✱ ♣♦✐s ♦s ♠❡s♠♦s s❡ ❛❞❡q✉❛♠ ❛♦s ❝r✐tér✐♦s ❞❡ r❡❣✉✲ ❧❛çã♦ ❞❛ ❇❛s✐❧é✐❛✳ ❈♦♠♣❛r❛✲s❡ t❛♠❜é♠ ♦s s✐st❡♠❛s ✜♥❛♥❝❡✐r♦s ❝♦♠ ♦s s✐st❡♠❛s ❡❝♦❧ó❣✐❝♦s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✱ ❛s r❡❞❡s ❞❡ ❝❛❞❡✐❛ ❛❧✐♠❡♥t❛r✳ ❯♠ ❛♣❛♥❤❛❞♦ ❞❡ r❡s✉❧t❛❞♦s sã♦ ❞✐s❝✉t✐✲ ❞♦s✱ ❞❡♥tr❡ ❡❧❡s✱ ♦ ❡st✉❞♦ s♦❜r❡ r❡s✐❧✐ê♥❝✐❛ ❡ r♦❜✉st❡③ ❞❡ t♦♣♦❧ó❣✐❛s ❞❡ r❡❞❡s✳ ❙❡❣✉♥❞♦ ♦s ♠❡s♠♦s✱ ❛ ❝♦♥❡①ã♦ ❞❡ ♥ós ❝♦♠ ♣r♦♣r✐❡❞❛❞❡s ❞✐❢❡r❡♥t❡s✱ ♣♦ss✐❜✐❧✐t❛ q✉❡ ♦ s✐st❡♠❛ s❡❥❛ ♠❛✐s r♦❜✉st♦ ❡ r❡s✐❧✐❡♥t❡✳ ❖✉tr♦ ❢❛t♦ ✐♠♣♦rt❛♥t❡ é q✉❡ ❛ ♣r✐♥❝✐♣❛❧ ❝❛✉s❛ ♣❛r❛ q✉❡ ❛❝♦♥t❡❝❡ss❡ ✉♠ ❝❤♦q✉❡ ✜♥❛♥❝❡✐r♦ é ❛tr✐❜✉í❞❛ ❛♦ ♠❡r❝❛❞♦ ❞❡ ❞❡r✐✈❛t✐✈♦s✱ ♣♦✐s sã♦ ♦s ♣r✐♥❝✐♣❛✐s ♠♦t✐✈♦s ♣❛r❛ ❛ ❛❧❛✈❛♥❝❛❣❡♠ ❜❛♥❝ár✐❛✳
●❛✐ ❡ ❑❛♣❛❞✐❛ ✭✷✵✶✵✮ ❡st✉❞❛r❛♠ ❛ r❡❧❛çã♦ ❡♥tr❡ ❝♦♥❡❝t✐✈✐❞❛❞❡ ♠é❞✐❛ ❡ ❝♦♥tá❣✐♦✳ ❙❡✲ ❣✉♥❞♦ ♦s ❛✉t♦r❡s✱ q✉❛♥t♦ ♠❛✐♦r ❛ ❝♦♥❡❝t✐✈✐❞❛❞❡ ♠é❞✐❛✱ ♠❡♥♦r s❡rá ♦ ❝♦♥tá❣✐♦✳ ❆♣❡s❛r ❞❡ s❡ ❜❛s❡❛r ❡♠ ✉♠❛ ❡str✉t✉r❛ ❞❡ ❜❛❧❛♥ç♦ ♣❛tr✐♠♦♥✐❛❧✱ ♦ ♠♦❞❡❧♦ ❡s♣❡❝✐✜❝❛ ❞✐✈❡rs♦s t✐♣♦s ❞❡ ❛t✐✈♦s ❞❡ ✉♠❛ ✐♥st✐t✉✐çã♦ ✜♥❛♥❝❡✐r❛✱ t♦r♥❛♥❞♦ ♦ ♠♦❞❡❧♦ ♣♦✉❝♦ ♣rát✐❝♦ ❡ ♠✉✐t♦ ❝♦♠♣❧✐❝❛❞♦✳ ❈❛♥❡❞♦ ❡ ❏❛r❛♠✐❧❧♦ ✭✷✵✵✾✮ ❡st✐♠❛r❛♠ ♦ ▲♦ss ❣✐✈❡♥ ❞❡❢❛✉❧t✱ ❛ ♣❡r❞❛ ❞❛❞❛ à ✐♥❛❞✐♠✲ ♣❧ê♥❝✐❛✱ ✉t✐❧✐③❛♥❞♦ ✉♠ ♠♦❞❡❧♦ ❞❡ ❝♦♥tá❣✐♦ ❜❛s❡❛❞♦ ❡♠ ✉♠❛ ❜❛s❡ ❞❡ ❞❛❞♦s ▼❡①✐❝❛♥❛ ❝♦♠ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ 30 ❜❛♥❝♦s✳ ❈♦♠♦ ❡ss❛ r❡❞❡ é ❝♦♥s✐❞❡r❛❞❛ ♣❡q✉❡♥❛✱ ♥ã♦ ❢♦✐ ♥❡❝❡ssár✐♦ ✉t✐❧✐③❛r ♥❡♥❤✉♠❛ ❡st✐♠❛çã♦ ♣♦r ♠á①✐♠❛ ❡♥tr♦♣✐❛✱ té❝♥✐❝❛ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❝♦♠♣❧❡t❛r ❜❛s❡s ❞❡ ❞❛❞♦s ✭❈❛❥✉❡✐r♦ ❡ ❚❛❜❛❦✱ ✷✵✵✽✮✳ ❙❡❣✉♥❞♦ ♦s ❛✉t♦r❡s✱ ❡ss❡ ♠ét♦❞♦ é t♦t❛❧♠❡♥t❡ ✐rr❡✲ ❛❧íst✐❝♦✳
❆ té❝♥✐❝❛ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❛ ❡st✐♠❛çã♦ ❞❛s ♣❡r❞❛s ❞♦ s✐st❡♠❛✱ ❛ss✉♠❡ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ♥❛ ♠❡❞✐❞❛ ❞❡ss❛ ♣r♦❜❛❜✐❧✐❞❛❞❡✱ ♦✉ s❡❥❛✱ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛s ♣❡r❞❛s ❞♦ s✐st❡♠❛ é ♦ ♣r♦❞✉t♦ ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛s ♣❡r❞❛s ❞❡ ❝❛❞❛ ✐♥st✐t✉✐çã♦✳ ❖ ♠♦❞❡❧♦ t❛♠❜é♠ ❛ss✉♠❡ ❡①✐stê♥❝✐❛ ❞❡ ✉♠ ❧✐♠✐❛r ❞❡ ♣❡r❞❛✳ ❖ ♠❡s♠♦ ❢♦✐ r❡♣r❡s❡♥t❛❞♦ ♣❡❧♦ ❝❛♣✐t❛❧ ❞♦ t✐♣♦ ✶✱ ♦✉ s❡❥❛✱ ♣❛tr✐♠ô♥✐♦ ❧íq✉✐❞♦ ♠❛✐s ❧✉❝r♦s ✭♣r❡❥✉í③♦s✮✳ ❉❡♥tr♦ ❞❛ ❜❛s❡ ❞❡ ❞❛❞♦s t❛❧ ❧✐♠✐❛r ✐♥❞✐❝❛ q✉❛♥❞♦ ✉♠ ❜❛♥❝♦ ❡stá ♦✉ ♥ã♦ ✐♥❛❞✐♠♣❧❡♥t❡✳ ❆s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ ✐♥❛❞✐♠♣❧ê♥❝✐❛ sã♦ ❛tr✐❜✉í❞❛s ❛❧❡❛t♦r✐❛✲ ♠❡♥t❡✳ ❆s ❜❛s❡ ❞❡ ❞❛❞♦s ✐♥❞✐❝❛♠ ❛s ❡①♣♦s✐çõ❡s ✐♥t❡r❜❛♥❝ár✐❛s✱ q✉❡ ♣♦r s✉❛ ✈❡③✱ ❝♦♥s✐❞❡r❛♠ ❝♦♠♦ ♣❡r❞❛ ❛ ♣♦r❝❡♥t❛❣❡♠ ❞❡ ❛t✐✈♦s ♥ã♦ r❡❝✉♣❡r❛❞♦s q✉❛♥❞♦ ♦ ❜❛♥❝♦ ❡stá ❡♠ ❞❡❢❛✉❧t ♦✉ ♦ t♦t❛❧ ❞❡ ❡①♣♦s✐çõ❡s ❜❛♥❝ár✐❛s ♥ã♦ ♣❛❣❛s✳
❖ ♠♦❞❡❧♦ ❞❡ ❏❛r❛♠✐❧❧♦ ❡t ❛❧✳ ✭✷✵✶✵✮ ❞❡✉ ❝♦♥t✐♥✉✐❞❛❞❡ ❛♦ tr❛❜❛❧❤♦ ❞❡ ❈❛♥❡❞♦ ❡ ❏❛r❛♠✐❧❧♦ ✭✷✵✵✾✮✱ r❡t✐r❛♥❞♦ ❛ ❤✐♣ót❡s❡ ❞❡ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❞❛s ♣r♦❜❛❜✐❧✐✲ ❞❛❞❡s ❞❛s ♣❡r❞❛s ♠❡❞✐❛♥t❡ ♦ ✉s♦ ❞❛ t❡♦r✐❛ ❞❡ ❝ó♣✉❧❛s✱ té❝♥✐❝❛ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❡st✉❞❛r ❛ ❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ✈❛r✐á✈❡✐s ❛❧❡❛tór✐❛s ✭◆❡❧s❡♥✱ ✷✵✵✻✮✳
❉✐✈❡rs♦s tr❛❜❛❧❤♦s q✉❡ t❛♠❜é♠ ✉t✐❧✐③❛♠ r❡❞❡s ❡♠♣ír✐❝❛s ✭❇♦ss ❡t ❛❧✳✱ ✷✵✵✹❀ ❈❛♥❡❞♦ ❡ ❏❛r❛♠✐❧❧♦✱✷✵✵✾❀■♦r✐ ❡t ❛❧✳✱✷✵✵✽❀▼♦✉ss❛✱✷✵✶✶❀❙❛♥t♦s✱✷✵✶✵❀❙♦✉♠❛ ❡t ❛❧✳✱✷✵✵✸❀ ❲❡❧❧s✱ ✷✵✵✹✮✱ s✉❣❡r❡♠ q✉❡ ❛s r❡❞❡s ✐♥t❡r❜❛♥❝ár✐❛s s❡❥❛♠ r❡❞❡s ❝♦♠ ❞✐str✐❜✉✐çõ❡s ❞❡ ❣r❛✉s ❞❡ ❡♥tr❛❞❛ ❡ s❛í❞❛ ❝✉❥❛s ❝❛❧❞❛s s✐❣❛♠ ✉♠❛ ❧❡✐ ❞❡ ♣♦tê♥❝✐❛ ✭♣♦✇❡r ❧❛✇✮ ❝♦♠ ❡①♣♦❡♥t❡ ❡♥tr❡ 2❡ 3✳
❙❡❣✉✐♥❞♦ ❡ss❛ ♠❡s♠❛ ❞✐r❡çã♦✱ ▼♦✉ss❛ ✭✷✵✶✶✮ ❝♦♥str✉✐✉ ✉♠ ♠♦❞❡❧♦ ❡st♦❝ást✐❝♦ q✉❡ r❡♣r♦❞✉③ ❡ss❡s ❢❛t♦s ❡st✐❧✐③❛❞♦s✱ ❛❞♠✐t✐♥❞♦ ✉♠❛ r❡❞❡ ❧✐✈r❡ ❞❡ ❡s❝❛❧❛ ❞✐r❡❝✐♦♥❛❞❛✱ ❜❛s❡❞❛ ❡♠
