Um Sistema Evolutivo para a Construção da Taxonomia dos Seres Vivos (SETAX)

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❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦

❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦❯♠ ❙✐st❡♠❛ ❊✈♦❧✉t✐✈♦ ♣❛r❛ ❛ ❈♦♥str✉çã♦ ❞❛ ❚❛①♦♥♦♠✐❛ ❞♦s ❙❡r❡s ❱✐✈♦s ✭❙❊❚❆❳✮ ▲❯■❙ ❍❊◆❘■◗❯❊ ▲❊▼❊ P❆❈❍❊❈❖ r✐❝❦♣❛❝❤❡❝♦❅❣♠❛✐❧✳❝♦♠▼❛❝❡✐ó✱ ✶✽ ❞❡ ▼❛rç♦ ❞❡ ✷✵✶✶ ▲❯■❙ ❍❊◆❘■◗❯❊ ▲❊▼❊ P❆❈❍❊❈❖❯♠ ❙✐st❡♠❛ ❊✈♦❧✉t✐✈♦ ♣❛r❛ ❛ ❈♦♥str✉çã♦ ❞❛ ❚❛①♦♥♦♠✐❛ ❞♦s ❙❡r❡s ❱✐✈♦s ✭❙❊❚❆❳✮ ❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ♣❡❧♦ ❈✉rs♦ ❞❡ ▼❡str❛❞♦❡♠ ▼♦❞❡❧❛❣❡♠ ❈♦♠♣✉t❛❝✐♦♥❛❧ ❞❡ ❈♦♥❤❡❝✐♠❡♥t♦ ❞♦ ■♥st✐t✉t♦ ❞❡ ❈♦♠♣✉t❛çã♦ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡❆❧❛❣♦❛s✳ ❖r✐❡♥t❛❞♦r❡s✿ ❖r✐❡♥t❛❞♦r❛✿ Pr♦❢❛✳ ❉r❛✳ ❘♦❜❡rt❛ ❱✐❧❤❡♥❛ ❱✐❡✐r❛ ▲♦♣❡s ❈♦✲❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❊✈❛♥❞r♦ ❞❡ ❇❛rr♦s ❈♦st❛ ▼❛❝❡✐ó✱ ✶✽ ❞❡ ▼❛rç♦ ❞❡ ✷✵✶✶ Catalogação na fonte Universidade Federal de AlagoasBiblioteca Central Divisão de Tratamento TécnicoLuis Henrique Leme Pacheco. – 2011. Um sistema evolutivo para a construção da taxonomia dos seres vivos (SETAX) / P116u Pacheco, Luis Henrique Leme. Bibliotecária Responsável: Helena Cristina Pimentel do Vale 60 f. : il. Co-Orientador: Evandro de Barros Costa. Orientadora: Roberta Vilhena Vieira Lopes. Bibliografia: f. 56-60. Universidade Federal de Alagoas. Instituto de Computação. Maceió, 2011. Dissertação (mestrado em Modelagem Computacional de Conhecimento) – 1. Algoritmos evolucionários. 2. Otimização combinatória CDU: 004.421 4. Problema do caixeiro viajante. I. Título. – Multiobjetivo. ❆❣r❛❞❡❝✐♠❡♥t♦s ❊✉ t❡♥❤♦ ♠✉✐t♦ q✉❡ ❛❣r❛❞❡❝❡r✱ ❛ ❝♦♠❡ç❛r ♣❡❧♦ ❢❛t♦ ❞❡ ❡st❛r ✈✐✈♦✱ ❡ ❞❡ ♣♦❞❡r ❝♦♠♣❛r✲ t✐❧❤❛r ❡st❡ tr❛❜❛❧❤♦ ❝♦♠ ♦✉tr♦s s❡r❡s✱ ✐❣✉❛✐s ❛ ♠✐♠✱ q✉❡ ❣♦st❛♠ ❞❡ s❡ ❛♣♦❞❡r❛r❡♠ ❞♦s❝♦♥❤❡❝✐♠❡♥t♦s ❤❡r❞❛❞♦s ❞❡ ♥♦ss♦s ❛♥t❡♣❛ss❛❞♦s✳ ❊❧❡s sã♦ ♠❡✉s ❤❡ró✐s ❡ ♠❡r❡❝❡♠ ♠❡✉s ❛❣r❛❞❡❝✐♠❡♥t♦s✱ t♦❞♦s ❡❧❡s✱ ❛♦s s❡r❡s ❤✉♠❛♥♦s q✉❡ ✈✐✈❡r❛♠ ❛♥t❡s ❞❡ ♠✐♠✱ ♦ ♠❡✉ ♠✉✐t♦ ♦❜r✐❣❛❞♦✦❆♦s q✉❡ ♣❛rt✐❝✐♣❛r❛♠ ❞❡ ♠✐♥❤❛ ✈✐❞❛✱ ❞❡ ❢♦r♠❛ ❞✐r❡t❛✱ q✉❡r♦ ❛❣r❛❞❡❝❡r ♠✉✐t♦ ❛ ♠✐♥❤❛ ♠ã❡✱ q✉❡ ♥❛s ❤♦r❛s ❞✐❢í❝❡✐s✱ ♠❛♥t❡✈❡ ✜r♠❡♠❡♥t❡ ❛ ✈♦♥t❛❞❡ ❞❡ ❡s❝♦❧❛r✐③❛r ♦s ✜❧❤♦s✱ ❛♦ ♠❡✉♣❛✐ ❝❛❜❡ ♦ ❛❣r❛❞❡❝✐♠❡♥t♦ ❞❡ ♥❡st❡ ♣♦♥t♦ ♦❜❡❞❡❝❡r ❛ ♠✐♥❤❛ ♠ã❡ ❡ ❛❥✉❞❛r ♥❛ ❢♦r♠❛çã♦ ❞♦♠❡✉ ❝❛r❛t❡r✳ ❆ ♠✐♥❤❛ ✐r♠ã ❊st❡❧✐t❛ ❡ ♠✐♥❤❛ ♥❛♠♦r❛❞❛ ❊❧✐sâ♥❣❡❧❛✱ ❛❧❡♠ ❞❡ ♣❛r❡♥t❡s ♣ró①✐♠♦s✱ t♦❞♦s❡st✐✈❡r❛♠ ♣r❡s❡♥t❡s ♥❛ ❧♦♥❣❛ ❝❛♠✐♥❤❛❞❛ ❞❡st❡ ▼❡str❛❞♦✳ ▼❡✉ ♦❜r✐❣❛❞♦ ❡ ♠❡✉ ❝❛r✐♥❤♦ ❛ t♦❞♦s✳ ❆♦s ♣r♦❢❡ss♦r❡s q✉❡ ♣❛ss❛r❛♠ ♣♦r ♠✐♥❤❛ ✈✐❞❛✱ q✉❡ ❢♦r❛♠ ♠✉✐t♦s✱ q✉❡r♦ ❛❣r❛❞❡❝❡r ❛ ❡s♣❡❝✐❛❧♠❡♥t❡ ❛ ♣r✐♠❡✐r❛✱ Pr♦❢ ✳ ❉r✳ ❘♦❜❡rt❛✱ ❡①❝❡❧❡♥t❡ ♣r♦❢❡ss♦r❛ ❡ ♦r✐❡♥t❛❞♦r❛✳ ❙❡♠❛ s❡♥❤♦r❛ s❡r✐❛ ✐♠♣♦ssí✈❡❧ ❡ ❛♦ Pr♦❢✳ ❆❣❛♠❡♠♥♦♥ ✱ ♠✉✐t♦ ♦❜r✐❣❛❞♦✦✳ ❖s Pr♦❢❡ss♦r❡s ❉r✳■●✱ ❘❛❢❛❡❧ ❉r✳ P❛r❛❣✉❛ç✉✱ t❛♠❜é♠ ❛♦ ♣r♦❢❡ss♦r ❉r✳ ❊✈❛♥❞r♦✳ ❊①❝❡❧❡♥t❡ ♣r♦❢❡ss♦r❡s✳ ◆❛ ❯❋❆▲ q✉❡r♦ ❛❣r❛❞❡❝❡r ❛♦ s❡❝r❡t❛r✐♦ ❱✐t♦r✱ q✉❡ ❛❧❡♠ ❞❡ s❡r ✉♠ ❢✉♥❝✐♦♥ár✐♦ ♠✉✐t♦❝♦♠♣❡t❡♥t❡ é ✉♠ ❛♠✐❣♦ ❡ ❡st❛ s❡♠♣r❡ ♣r♦♥t♦ ♣❛r❛ ❛t❡♥❞❡r q✉❛❧q✉❡r s♦❧✐❝✐t❛çã♦✳ ◆❛ s❛❧❛✱ ♥♦ ❝♦♥✈í✈✐♦ ❞❡ ❝❛❞❛ ❞✐❛✱ ❚❛rs✐s ❡ ❈❛r♦❧✱ ♠❡✉s ❡t❡r♥♦s ❛♠✐❣♦s✱ q✉❡ ❡st❡✈❡♣r❡s❡♥t❡ ❞✉r❛♥t❡ t♦❞♦ ♦ ❝✉rs♦ ♣♦ss✉✐ ♠✐♥❤❛ ❛❞♠✐r❛çã♦ ❡ ♠❡✉ ❝❛r✐♥❤♦✳ ◗✉❡r♦ ♠✉✐t♦ ❛❣r❛❞❡❝❡r t❛♠❜é♠ ❛ t♦❞♦s ♦s ❝♦❧❡❣❛s ❞❡ t✉r♠❛ ❡ ❛♠✐❣♦s✱ ❡s♣❡❝✐❛❧♠❡♥t❡❛ ❊❧✈②s✱ ❍✐❣♦r✱ ❏❡❛♥✱ ▼❛r❝♦s✱ ●✉st❛✈♦✱ ❆♥❣❡❧❛✱ ❏❛r❜❛s✱ P❈ ❡ ❋❛❜rí❝✐♦✳ ❋♦✐ ❜♦♠ ❝♦♥✈✐✈❡r❝♦♠ ✈♦❝ês✱ ▼✉✐t♦ ♦❜r✐❣❛❞♦✦ ❊ ✜♥❛❧♠❡♥t❡ à ❋❆P❊❆▲✱ ♣❡❧♦ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦ ❡♠ ♣❛rt❡ ❞❡st❡ tr❛❜❛❧❤♦✳ ❘❡s✉♠♦ ❊st❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ ✉♠ s✐st❡♠❛ q✉❡ ✉t✐❧✐③❛ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❡✈♦❧✉t✐✈❛ ♣❛r❛ ❝♦♥str✉çã♦❞❡ ár✈♦r❡s ❋✐❧♦❣❡♥ét✐❝❛s ❞❡♥♦♠✐♥❛❞♦ ❙❊❚❆❳✳ ◆❡st❡ s✐st❡♠❛ ♦ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ❜❛s❡❛❞♦❡♠ t✐♣♦s ❛❜str❛t♦s ❞❡ ❞❛❞♦s ✭●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠ ❇❛s❡❞ ♦♥ ❆❜str❛❝t ❉❛t❛ ❚②♣❡s ✲●❆❆❉❚✮❢♦✐ ✐♥st❛♥❝✐❛❞♦ ♣❛r❛ ❡♥❝♦♥tr❛r ❛ ♠❡♥♦r ❞✐stâ♥❝✐❛ ❡♥tr❡ ♦s ❣r✉♣♦s t❛①♦♥ô♠✐❝♦s ✐♥✈❡st✐❣❛✲❞♦s✱ ❣❡r❛♥❞♦ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ár✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s ❝♦♠ ♦ ♠❡s♠♦ ✈❛❧♦r ♣❛r❛ ♦ s♦♠❛tór✐♦❞❛s ❞✐stâ♥❝✐❛ t❛①♦♥ô♠✐❝❛ ❡♥tr❡ ❛s s✉❜✲ár✈♦r❡s ❜✐♥ár✐❛s q✉❡ ❛ ❝♦♠♣õ❡✳ ❚❛♠❜é♠ é ❛q✉✐❛♣r❡s❡♥t❛❞♦✱ ✉♠ ❡st✉❞♦ ❞❡ ár✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s✱ ♦s ♣r✐♥❝✐♣❛✐s ❛❧❣♦r✐t♠♦s ♣❛r❛ ❝♦♥str✉çã♦❞❡ ár✈♦r❡s ✐♥s♣✐r❛❞♦s ❡♠ ♠ét♦❞♦s ❞❡ ✐♥t❡❧✐❣ê♥❝✐❛ ❛rt✐✜❝✐❛❧❀ ✉♠ r❡s✉♠♦ ❜✐♦❧ó❣✐❝♦ ♣❛r❛ ♦❡♥t❡♥❞✐♠❡♥t♦ ❞❛ ❝♦♥str✉çã♦ ❞❡ ✉♠❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛✱ ❛ ✐♥st❛♥❝✐❛çã♦ ❞♦ ●❆❆❉❚ ♣❛r❛❝♦♥str✉çã♦ ❞❡ ár✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s ❞❡ s❡r❡s ✈✐✈♦s ❜❡♠ ❝♦♠♦ ❛❧❣✉♥s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❝♦♠♦ s✐st❡♠❛ ♣r♦♣♦st♦ ❡ ❝♦♠♣❛r❛çõ❡s ❝♦♠ ♦s ❞❡♠❛✐s ♠ét♦❞♦s✳ P❛❧❛✈r❛s✲❝❤❛✈❡✿ ■♥t❡❧✐❣ê♥❝✐❛ ❛rt✐✜❝✐❛❧✱ ❋✐❧♦❣❡♥✐❛✱ ➪r✈♦r❡s ❋✐❧♦❣❡♥ét✐❝❛s✱ ❇✐♦❧♦❣✐❛❈♦♠♣✉t❛❝✐♦♥❛❧✱ ❖t✐♠✐③❛çã♦ ❈♦♠❜✐♥❛tór✐❛✱ ❆❧❣♦r✐t♠♦s ❊✈♦❧✉❝✐♦♥ár✐♦s ❡ ❆❧❣♦r✐t♠♦s ●❡✲♥ét✐❝♦s✳ ❆❜str❛❝t ❚❤✐s ✇♦r❦ ♣r❡s❡♥ts ❛ s②st❡♠ t❤❛t ✉s❡ ❡✈♦❧✉t✐♦♥❛r② ❛♣♣r♦❛❝❤ t♦ P❤②❧♦❣❡♥❡t✐❝ tr❡❡ ❝♦♥✲ str✉❝t✐♦♥ ❝❛❧❧❡❞ ❙❊❚❆❳✳ ■♥ t❤✐s s②st❡♠✱ t❤❡ ❣❡♥❡t✐❝ ❛❧❣♦r✐t❤♠ ❜❛s❡❞ ♦♥ ❛❜str❛❝t t②♣❡s♦❢ ❞❛t❛ ✭●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠ ❇❛s❡❞ ♦♥ ❆❜str❛❝t ❉❛t❛ ❚②♣❡s ✲●❆❆❉❚✮✇❛s ✐♥st❛♥t✐❛t❡❞ t♦❢♦✉♥❞ t❤❡ ♠✐♥✐♠✉♠ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ t❛①♦♥♦♠✐❝ ❣r♦✉♣s ✐♥✈❡st✐❣❛t❡❞✱ ❣❡♥❡r❛t✐♥❣ ❛ s❡t ♦❢P❤②❧♦❣❡♥❡t✐❝ tr❡❡s ✇✐t❤ t❤❡ s❛♠❡ ✈❛❧✉❡ ❢♦r t❤❡ s✉♠ ♦❢ t❛①♦♥♦♠✐❝ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ ❜✐♥❛r② s✉❜tr❡❡s ✇❤✐❝❤ ❝♦♠♣♦s❡s ✐t✳ ❆❧s♦ r❡♣♦rt ❤❡r❡✱ ❛ st✉❞② ♦❢ P❤②❧♦❣❡♥❡t✐❝ tr❡❡s✱ t❤❡ ♠❛✐♥❛❧❣♦r✐t❤♠ ❢♦r ❝♦♥str✉❝t✐♦♥ tr❡❡s ✐♥s♣✐r❡❞ ❜② ♠❡t❤♦❞s ❛rt✐✜❝✐❛❧ ✐♥t❡❧❧✐❣❡♥❝❡❀ ❛ ❜✐♦❧♦❣✐❝❛❧ s✉✲♠♠❛r② ❢♦r t❤❡ ❦♥♦✇❧❡❞❣❡ ♦❢ P❤②❧♦❣❡♥❡t✐❝ tr❡❡s ❝♦♥tr✉❝t✐♦♥✱ t❤❡ ✐♥st❛♥❝✐❛t✐♦♥ ♦❢ ●❆❆❉❚ t♦ P❤②❧♦❣❡♥❡t✐❝ tr❡ss ♦❢ ❧✐✈✐♥❣ ❜❡✐♥❣s ❛s ✇❡❧❧ ❛s s♦♠❡ r❡s✉❧ts ❛❝q✉✐r❡❞ ❜② t❤❡ ♣r♦♣♦s❡❞s②st❡♠ ❛♥❞ ❝♦♠♣❛r✐s♦♥ ✇✐t❤ ♦t❤❡r ♠❡t❤♦❞s✳ ❑❡②✇♦r❞s✿ ❆rt✐✜❝✐❛❧ ✐♥t❡❧❧✐❣❡♥❝❡✱ P❤②❧♦❣❡♥②✱ P❤②❧♦❣❡♥❡t✐❝ tr❡❡s✱ ❈♦♠♣✉t❛t✐♦♥❛❧ ❇✐✲♦❧♦❣②✱ ❈♦♠❜✐♥❛t♦r✐❛❧ ❖♣t✐♠✐③❛t✐♦♥✱ ❊✈♦❧✉t✐♦♥❛r② ❆❧❣♦r✐t❤♠s ❛♥❞ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠s✳ ▲✐st❛ ❞❡ ❋✐❣✉r❛s ✶✳✶ ❘❡s✉♠♦ ❛❞❛♣t❛❞♦ ❞❡ ❬✻❪ s♦❜r❡ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉❝✐♦♥ár✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✳✷ Pr♦❞✉çã♦ ❞❡ ♠✉❞❛s ❡♠ ❧❛❜♦r❛tór✐♦✱ ❢♦♥t❡ s✐t❡ ❞❛ ❊♠❜r❛♣❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶✳✸ ❋❧✉①♦❣r❛♠❛ ❞❡ ♣r♦❣r❛♠❛ ❞❡ ♠❡❧❤♦r❛♠❡♥t♦ ❣❡♥ét✐❝♦ ❞❛ ❝❛♥❛✲❞❡✲❛çú❝❛r✳ ✳ ✳ ✻✷✳✶ ❊①❡♠♣❧♦ ❞❡ ➪r✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷✳✷ ■♥s❡t♦s ❞❛ ❢❛♠í❧✐❛ ❤♦❧♦♠❡t❛❜ó❧✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷✳✸ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❡ ❝❡rt♦s ✈ír✉s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷✳✹ ❙ér✐❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✷✳✺ ❙ér✐❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✷✳✻ ➪r✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ♣❛r❛ ❛s ❡s♣é❝✐❡s ❞❛ ✜❣✉r❛ ✹✳✻ ♦❜t✐❞❛ ♣❡❧❛ ❛♥á❧✐s❡ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s t❡r♠✐♥❛✐s✿ ✶ ✭❛✮✱ ✷✭❜✮✱ ✸✭❝✮✱ ✹✭❞✮✱ ✺✭❡✮ ❡ ✻✭❢✮✳ ❆ ❝♦♠❜✐♥❛çã♦❞❡ss❛s ár✈♦r❡s é ♠♦str❛❞❛ ❡♠ ✭❣✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✼ ➪r✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s ❝♦♥str✉í❞❛s ♣❡❧❛ ♣r✐♠❡✐r❛ ✭❛✮✱ s❡❣✉♥❞❛ ✭❜✮ ❡ t❡r❝❡✐r❛✭❝✮ ❡①❡❝✉çã♦ ❞♦ ✺♦ ♣❛ss♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ❲❛❣♥❡r ♣❛r❛ ❛s ❡s♣é❝✐❡s ❞❛ ✜❣✉r❛✹✳✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✷✳✽ ➪r✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s ❝♦♥str✉í❞❛s ♣❡❧♦ ♣r✐♠❡✐r❛ ✭❛✮✱ s❡❣✉♥❞❛ ✭❜✮ ❡ t❡r❝❡✐r❛✭❝✮ ❡①❡❝✉çã♦ ❞♦ ✺♦ ♣❛ss♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❛s ♠é❞✐❛s ♣❛r❛ ❛s ❡s♣é❝✐❡s ❞❛ ❚❛❜❡❧❛✷✳✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✶ Ps❡✉❞♦❝ó❞✐❣♦ ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺✸✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ❚❡r♠♦ ❇✐♦❧ó❣✐❝♦ ✲❃ ❚❡r♠♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❬✶✹❪ ✳ ✳ ✳ ✳ ✷✻✸✳✸ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ ●❡♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻✸✳✹ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ ❈r♦♠♦ss♦♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼✹✳✶ ❆rq✉✐t❡t✉r❛ ✉t✐❧✐③❛❞❛ ♥❛ s♦❧✉çã♦ ✐♠♣❧❡♠❡♥t❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵✹✳✷ ❚❡❧❛ ♣r✐♥❝✐♣❛❧ ❞♦ s✐st❡♠❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶✹✳✸ ❚❡❧❛ ♣r✐♥❝✐♣❛❧ ❝♦♠ ♦ ♠❡♥✉ ❞♦ s✐st❡♠❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷✹✳✹ ❚❡❧❛ ❞❡ ❛❧❡rt❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷✹✳✺ ❆♠♦str❛ ❞❡ ✉♠❛ ❜❛s❡ ✭❈❛♥❛ ❞❡ ❛çú❝❛r✮ ❞♦ ❡st✉❞♦ ❞❡ ❝❛s♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷✹✳✻ ❊①❡♠♣❧♦ ❞❡ ár✈♦r❡ ❣❡r❛❞❛ ♣❡❧♦ s✐st❡♠❛ ❛tr❛✈és ❞❛ ❜❛s❡ ❞❡ ❞❛❞♦s ✭❈❛♥❛ ❞❡ ❛çú❝❛r✮ ❞♦ ❡st✉❞♦ ❞❡ ❝❛s♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸✹✳✼ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ❣❡♥❡ ♥♦ ❙❊❚❆❳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹✹✳✽ ❋❡❝✉♥❞❛çã♦ ❡♥tr❡ ❞♦✐s ❣❡♥❡s ♥♦ ❙❊❚❆❳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹✹✳✾ ■♠❛❣❡♠ ❞❛ ❙❡rr❛ ❞♦ ❖✉r♦ ❧♦❝❛❧✐③❛❞❛ ❡♠ ▼✉r✐❝✐✲❆❧ ❋♦♥t❡✿ ❈❡❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻✹✳✶✵ ➪r✈♦r❡ ❣❡r❛❞❛ ♣❡❧❛ r❡❣r❛ ❞❡ ■♥❝❧✉sã♦ ❡ ❊①❝❧✉sã♦ ♥❛ ♠❛tr✐③ s❡♠ ♣❛r❝✐♠ô♥✐❛ ✹✾✹✳✶✶ ➪r✈♦r❡ ❣❡r❛❞❛ ♣❡❧♦ ❆❧❣♦r✐t♠♦ ❞❡ ❲❛❣♥❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾✹✳✶✷ ➪r✈♦r❡ ❣❡r❛❞❛ ♣❡❧♦ ❆❧❣♦r✐t♠♦ ❞❡ ▼é❞✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵✹✳✶✸ ➪r✈♦r❡s ❣❡r❛❞❛s ♣❡❧♦ ❙❊❚❆❳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙✈ ✹✳✶✹ ➪r✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s ❝♦♥str✉í❞❛s ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❞❡ ✐♥❝❧✉sã♦ ❡ ❡①❝❧✉sã♦ ❛♣❛rt✐r ❞❛ ❚❛❜❡❧❛ ✹✳✻ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✹✳✶✺ ➪r✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s ❝♦♥str✉í❞❛s ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❞❛s ♠é❞✐❛s ❛ ♣❛rt✐r ❞❛❚❛❜❡❧❛ ✹✳✼✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ▲✐st❛ ❞❡ ❚❛❜❡❧❛s ✷✳✶ ❈♦❞✐✜❝❛çã♦ ❡♠ ✉♠❛ ♠❛tr✐③ ♣♦❧❛r✐③❛❞❛ ❞❡ sér✐❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐✲③❛❞❛s ❧✐♥❡❛r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✷ ❈♦❞✐✜❝❛çã♦ ❡♠ ✉♠❛ ♠❛tr✐③ ♣♦❧❛r✐③❛❞❛ ❞❡ sér✐❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐✲③❛❞❛s ✈✐❛ ❞❡❝♦♠♣♦s✐çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✸ ▼❛tr✐③ ♣♦❧❛r✐③❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✷✳✹ ▼❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✷✳✺ ▼❛tr✐③ s✐♠✐❧❛r✐❞❛❞❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✷✳✻ ▼❛tr✐③ ❞✐st❛♥❝✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✷✳✼ ▼❛tr✐③ ❞✐stâ♥❝✐❛ ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞♦s ❞❛❞♦s ❞❛ ❚❛❜❡❧❛ ✷✳✻ ❝♦♥s✐❞❡r❛♥❞♦ q✉❡ ❛s ❡s♣é❝✐❡s ❆ ❡ ❇ t❡♠ ❛ s✉♣❡r✲❡s♣é❝✐❡ ❙✶ ❝♦♠♦ ❛♥❝❡str❛❧ ❞✐r❡t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸✷✳✽ ▼❛tr✐③ ❞✐stâ♥❝✐❛ ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞♦s ❞❛❞♦s ❞❛ t❛❜❡❧❛ ✷✳✼ ❝♦♥s✐❞❡r❛♥❞♦ q✉❡12 ❛s ❡s♣é❝✐❡s S ❡ ❈ t❡♠ ❛ s✉♣❡r✲❡s♣é❝✐❡ S ❝♦♠♦ ❛♥❝❡str❛❧ ❞✐r❡t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸✹✳✶ ▼❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ s❡♠ ♣❛r❝✐♠ô♥✐❛ ✉s❛❞❛ ♣❛r❛ t❡st❛r ♦s ❛❧❣♦r✐t♠♦s✳ ✳ ✳ ✳ ✹✽✹✳✷ ▼❛tr✐③ ❞✐stâ♥❝✐❛ s❡♠ ♣❛r❝✐♠ô♥✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽✹✳✸ ▼❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❝♦♠ ♣❛r❝✐♠ô♥✐❛ ✉s❛❞❛ ♣❛r❛ t❡st❛r ♦s ❛❧❣♦r✐t♠♦s✳ ✳ ✳ ✳ ✹✽✹✳✹ ▼❛tr✐③ ❉✐stâ♥❝✐❛ ❝♦♠ ♣❛r❝✐♠ô♥✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽✹✳✺ ❙❝♦r❡ ❞❡ ❝❛❞❛ ❛❧❣♦r✐t♠♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶✹✳✻ ▼❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❝♦♠ ❝♦♥✢✐t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶✹✳✼ ▼❛tr✐③ ❞✐stâ♥❝✐❛ ❝♦♠ ❝♦♥✢✐t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ❙✉♠ár✐♦ ✶ ■♥tr♦❞✉çã♦✶ ✶✳✶ ❈♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛ ♦✉ ❡✈♦❧✉❝✐♦♥ár✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✳✶✳✶ ▼♦t✐✈❛çã♦ ❞❛ ❉✐ss❡rt❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶✳✶✳✷ ❖❜❥❡t✐✈♦s ❞❛ ❉✐ss❡rt❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶✳✶✳✸ ❖r❣❛♥✐③❛çã♦ ❞❛ ❉✐ss❡rt❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷ ➪r✈♦r❡ ❋✐❧♦❣❡♥ét✐❝❛✶✵ ✷✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷✳✷ ❉❡s❝r✐çã♦ ❋♦r♠❛❧ ❞❛ ➪r✈♦r❡ ❋✐❧♦❣❡♥ét✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷✳✸ ▼❛tr✐③ P♦❧❛r✐③❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✷✳✹ ▼❛tr✐③ ❈❛r❛❝t❡ríst✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✷✳✺ ▼❛tr✐③ ❙✐♠✐❧❛r✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✷✳✻ ▼❛tr✐③ ❉✐stâ♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✷✳✼ ❆❧❣✉♥s ❆❧❣♦r✐t♠♦s ❞❡ ❈♦♥str✉çã♦ ❞❡ ➪r✈♦r❡s ❋✐❧♦❣❡♥ét✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✼✳✶ ❆ ❘❡❣r❛ ❞❡ ■♥❝❧✉sã♦ ❡ ❊①❝❧✉sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✷✳✼✳✷ ❖ ❆❧❣♦r✐t♠♦ ❞❡ ❲❛❣♥❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✷✳✼✳✸ ❖ ❆❧❣♦r✐t♠♦ ❞❛s ▼é❞✐❛s ✭❯P●▼❆✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸ ❖ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ❇❛s❡❛❞♦ ❡♠ ❚✐♣♦s ❆❜str❛t♦s ❞❡ ❉❛❞♦s ♣❛r❛ ❈♦♥s✲ tr✉çã♦ ❞❡ ➪r✈♦r❡ ❋✐❧♦❣❡♥ét✐❝❛✷✹ ✸✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹✸✳✷ ❚✐♣♦s ❇ás✐❝♦s ❞♦ ●❆❆❉❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼✸✳✸ ❖♣❡r❛❞♦r❡s ●❡♥ét✐❝♦s ❞♦ ●❆❆❉❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾✸✳✹ ❆♠❜✐❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷✸✳✺ ❆❧❣♦r✐t♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸✸✳✻ ❊s♣❡❝✐✜❝❛çã♦ ❞♦ ●❆❆❉❚ ♣❛r❛ ♦ Pr♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✸✳✻✳✶ ❚✐♣♦s ❇ás✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺✸✳✻✳✷ ❖♣❡r❛❞♦r❡s ●❡♥ét✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✹ ❖ s✐st❡♠❛ ♣r♦♣♦st♦ ♣❛r❛ ❝♦♥str✉çã♦ ❞❡ ➪r✈♦r❡ ❋✐❧♦❣❡♥ét✐❝❛✭❙❊❚❆❳✮ ✸✾✹✳✶ ❆rq✉✐t❡t✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾✹✳✷ ❋✉♥❝✐♦♥❛❧✐❞❛❞❡s ❞♦ ❙❊❚❆❳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵✹✳✸ ❯♠ ❡st✉❞♦ ❞❡ ❝❛s♦ r❡❛❧✿ ❇❛s❡❛❞♦ ♥♦ ♠❡❧❤♦r❛♠❡♥t♦ ❣❡♥ét✐❝♦ ❞❛ ❝❛♥❛ ❞❡ ❛çú❝❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺✹✳✸✳✶ ❉❡s❝r✐çã♦ ❞❛ ❇❛s❡ ❞♦ ❡st✉❞♦ ❞❡ ❝❛s♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✹✳✹ ❈♦♠♣❛r❛çõ❡s ❡♥tr❡ ♦s ❛❧❣♦r✐t♠♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼✹✳✺ Pr♦❜❧❡♠❛s ❊♥❝♦♥tr❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ❙❯▼➪❘■❖✈✐✐✐ ✺ ❈♦♥❝❧✉sõ❡s✺✹ ❈❛♣ít✉❧♦ ✶ ■♥tr♦❞✉çã♦✶✳✶ ❈♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛ ♦✉ ❡✈♦❧✉❝✐♦♥ár✐❛ ❈♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛ ♦✉ ❡✈♦❧✉❝✐♦♥ár✐❛ é ✉♠❛ ár❡❛ ❞❛ ❝✐ê♥❝✐❛ ❞❛ ❝♦♠♣✉t❛çã♦ q✉❡ ♣r♦♣õ❡✉♠ ♥♦✈♦ ♣❛r❛❞✐❣♠❛ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ❞❛❞♦s✳ ❊st❡ ♣❛r❛❞✐❣♠❛✱ ❞✐❢❡r❡♥t❡♠❡♥t❡ ❞♦❝♦♥✈❡♥❝✐♦♥❛❧✱ ♥ã♦ ❡①✐❣❡ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♣ré✈✐♦ ❞♦s ❡❧❡♠❡♥t♦s ❞♦ ❞♦♠í♥✐♦ ❞♦ ♣r♦❜❧❡♠❛♣❛r❛ ❡♥❝♦♥tr❛r ✉♠ r❡s✉❧t❛❞♦❬✷✵❪✳ ❆ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉❝✐♦♥ár✐❛ é ❜❛s❡❛❞❛ ❡♠ ♠❡❝❛♥✐s♠♦s ❡✈♦❧✉t✐✈♦s ❡♥❝♦♥tr❛❞♦s ♥❛ ♥❛✲ t✉r❡③❛✱ t❛✐s ❝♦♠♦ ❛ ❛✉t♦✲♦r❣❛♥✐③❛çã♦ ❡ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❛❞❛♣t❛t✐✈♦ ❬✶✾❪✱ ❬✷✷❪✳ ❊ss❡s♠❡❝❛♥✐s♠♦s ❢♦r❛♠ ❞❡s❝♦❜❡rt♦s ❡ ❞❡s❝r✐t♦s ♣♦r ❉❆❘❲■◆ ✭✶✽✺✾✮ ❡♠ s✉❛ t❡♦r✐❛ ❞❛ ❡✈♦❧✉✲çã♦ ❞❛s ❡s♣é❝✐❡s✳ ◆❡❧❛✱ ❡❧❡ ❛✜r♠❛ q✉❡ ❛ ✈✐❞❛ ♥❛ t❡rr❛ é ♦ r❡s✉❧t❛❞♦ ❞❡ ✉♠ ♣r♦❝❡ss♦ ❞❡ s❡❧❡çã♦✱ ♣❡❧♦ ♠❡✐♦ ❛♠❜✐❡♥t❡✱ ❞❛s ❡s♣é❝✐❡s ♦✉ ✐♥❞✐✈í❞✉♦s ♠❛✐s ❛♣t♦s ❡ ❛❞❛♣t❛❞♦s✱ ❡ ♣♦r❡st❡ ♠♦t✐✈♦ ❡❧❡s tê♠ ♠❛✐s ❝❤❛♥❝❡s ❞❡ r❡♣r♦❞✉③✐r✲s❡✳ ❉❡st❛ ❢♦r♠❛✱ ❛ ❞✐✈❡rs✐❞❛❞❡ ❞❛ ✈✐❞❛✱❛ss♦❝✐❛❞❛ ❛♦ ❢❛t♦ ❞❡ q✉❡ t♦❞♦s ♦s s❡r❡s ✈✐✈♦s ❝♦♠♣❛rt✐❧❤❛♠ ✉♠❛ ❜❛❣❛❣❡♠ ❣❡♥ét✐❝❛ ❝♦✲♠✉♠✱ ♣❡❧♦ ♠❡♥♦s ❡♠ t❡r♠♦s ❞❡ s❡✉s ❝♦♠♣♦♥❡♥t❡s ❜ás✐❝♦s✱ é ✉♠ ❡①❡♠♣❧♦ ❡❧♦q✉❡♥t❡ ❞❛s♣♦ss✐❜✐❧✐❞❛❞❡s ❞♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❡✈♦❧✉çã♦ ♥❛t✉r❛❧✳ ❖✉tr❛s ❛❜♦r❞❛❣❡♥s ❝♦♠♣✉t❛❝✐♦♥❛✐s ✐♥s♣✐r❛❞❛s ♥❛ t❡♦r✐❛ ❞❛ ❡✈♦❧✉çã♦ ❞❛s ❡s♣é❝✐❡s s✉r✲❣✐r❛♠ ❝♦♠♦✿ ♣r♦❣r❛♠❛çã♦ ❣❡♥ét✐❝❛ ❬✷✾❪ ❡ ❡str❛té❣✐❛ ❡✈♦❧✉❝✐♦♥ár✐❛ ❬✹✶❪✳ ◆❛ ♣r♦❣r❛♠❛çã♦❣❡♥ét✐❝❛✭P●✮✱ ♦s ✐♥❞✐✈í❞✉♦s ❞❛ ♣♦♣✉❧❛çã♦ ♥ã♦ sã♦ ❝❛❞❡✐❛s ❞❡ ✏❜✐ts✑✱ ♠❛s s✐♠ ♣r♦❣r❛♠❛s❞❡ ❝♦♠♣✉t❛❞♦r ❛r♠❛③❡♥❛❞♦s ♥❛ ❢♦r♠❛ ❞❡ ár✈♦r❡s s✐♥tát✐❝❛s ♦✉ r❡❣r❛s ❞❡ s❡♠â♥t✐❝❛✳ ❉❡st❛❢♦r♠❛✱ ♦s ♣r♦❣r❛♠❛s é q✉❡ sã♦ ♦s ❝❛♥❞✐❞❛t♦s à s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ♣r♦♣♦st♦✱ ❡♥q✉❛♥t♦ ♥❛❊str❛té❣✐❛ ❊✈♦❧✉❝✐♦♥ár✐❛✭❊❊✮ r❡❣r❛s s❡♠â♥t✐❝❛✱ é q✉❡ sã♦ ❝❛♥❞✐❞❛t❛s ❛ ✉♠❛ ❝❧❛ss✐✜❝❛çã♦✳ ❆s té❝♥✐❝❛s ❞❡ ❆❧❣♦r✐t♠♦s ●❡♥ét✐❝♦s✭❆●✮✱ ❊str❛té❣✐❛s ❊✈♦❧✉❝✐♦♥ár✐❛✭❊❊✮ ❡ Pr♦❣r❛✲♠❛çã♦ ❡✈♦❧✉❝✐♦♥ár✐❛ ✭P❊✮ ♣♦ss✉❡♠ ❛❧❣♦ ❢✉♥❞❛♠❡♥t❛❧ ❡♠ ❝♦♠✉♠✱ ❝❛❞❛ ✉♠❛ ❞❡❧❛s tr❛t❛ r❡♣r♦❞✉çã♦✱ ✈❛r✐❛çã♦ ❛❧❡❛tór✐❛✱ ❝♦♠♣❡t✐çã♦ ❡ s❡❧❡çã♦ ❞❡ ✐♥❞✐✈í❞✉♦s ❞❡ ✉♠❛ ♣♦♣✉❧❛çã♦✳❊st❡s q✉❛tr♦ ❡❧❡♠❡♥t♦s ❢♦r♠❛♠ ❛ ❡ssê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❊✈♦❧✉t✐✈❛ ❬✹❪✱ ❬✼❪✳ ❉✐❛♥t❡ ❞❡ ✉♠❛ ♣❡rs♣❡❝t✐✈❛ ❤✐stór✐❝❛✱ ❛s ♣r✐♠❡✐r❛s ✐♥✐❝✐❛t✐✈❛s ♥❛ ár❡❛ ❞❡ ❝♦♠♣✉t❛çã♦❡✈♦❧✉❝✐♦♥ár✐❛ ❢♦r❛♠ ❞❡ ❜✐ó❧♦❣♦s ❡ ❣❡♥❡t✐❝✐st❛s ✐♥t❡r❡ss❛❞♦s ❡♠ s✐♠✉❧❛r ♦s ♣r♦❝❡ss♦s ✈✐✲ ✶✳✶✳ ❈❖▼P❯❚❆➬➹❖ ❊❱❖▲❯❚■❱❆ ❖❯ ❊❱❖▲❯❈■❖◆➪❘■❆ ✷ t❛✐s ♥♦ ❝♦♠♣✉t❛❞♦r✱ ♦ q✉❡ r❡❝❡❜❡✉ ♥❛ é♣♦❝❛ ♦ ♥♦♠❡ ❞❡ ✧Pr♦❝❡ss♦s ●❡♥ét✐❝♦s✧✭P●✮✬❬✷✹❪✳❆❧❣✉♥s ❞❡ss❡s ❝✐❡♥t✐st❛s✱ sã♦✿ ❬✽❪✱ ❬✾❪✱ ❬✷✸❪✱ ▼❛rt✐♥ ❡ ❬✶✸❪✳ ❖ ❜✐ó❧♦❣♦ ❬✸✾❪✱ s✐♠✉❧♦✉ ✉♠❛♣♦♣✉❧❛çã♦ ❞❡ s❡r❡s ✉♥✐❝❡❧✉❧❛r❡s✱ ❡str✉t✉r❛ ❣❡♥ét✐❝❛ ❝❧áss✐❝❛ ✭✉♠ ❣❡♥❡✱ ✉♠❛ ❡♥③✐♠❛✮✱ ❝♦♠❡str✉t✉r❛ ❞✐♣❧ó✐❞❡✱ ❝♦♠ ❝r♦♠♦ss♦♠♦s ❞❡ ✷✵ ❣❡♥❡s ❡ ✶✻ ❛❧❡❧♦s ♣❡r♠✐t✐❞♦s ❡♠ ❝❛❞❛ ✉♠✳ ◆❛ ❞é❝❛❞❛ ❞❡ ✻✵✱ ❬✷✼❪ ❡ ♦✉tr♦s ♣❡sq✉✐s❛❞♦r❡s ❝♦♠❡ç❛r❛♠ ❛ ❡st✉❞❛r ♦s s✐st❡♠❛s ❛❞❛♣✲ t❛t✐✈♦s ❝♦♠♣❧❡①♦s✱ q✉❡ ❢♦r❛♠ ♠♦❞❡❧❛❞♦s ❝♦♠♦ s✐st❡♠❛s ❞❡ ❛♣r❡♥❞✐③❛❣❡♠ ❞❡ ♠áq✉✐♥❛✳❊ss❡s ♠♦❞❡❧♦s✱ ❝♦♥❤❡❝✐❞♦s ❝♦♠♦ ❛❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s ✱ ✐♠♣❧❡♠❡♥t❛✈❛♠ ♣♦♣✉❧❛çõ❡s ❞❡✐♥❞✐✈í❞✉♦s ❝♦♥t❡♥❞♦ ✉♠ ❣❡♥ót✐♣♦✱ ❢♦r♠❛❞♦ ♣♦r ❝r♦♠♦ss♦♠♦s ✭q✉❡ ♥❡st❡ ♠♦❞❡❧♦ ❡r❛♠ r❡♣r❡s❡♥t❛❞♦s ♣♦r ❝❛❞❡✐❛s ❞❡ ✏❜✐ts✑✮ ❛♦s q✉❛✐s s❡ ❛♣❧✐❝❛✈❛♠ ♦♣❡r❛❞♦r❡s ❞❡ s❡❧❡çã♦✱ r❡❝♦♠✲❜✐♥❛çã♦✱ ♠✉t❛çã♦ ❡ ❛ ✐♥✈❡rsã♦✱ ❡st❡ ú❧t✐♠♦ ♦♣❡r❛❞♦r ♥ã♦ ❝❤❡❣♦✉ ❛ s❡r ❧❛r❣❛♠❡♥t❡ ✉t✐❧✐③❛❞♦ s❡❣✉♥❞♦ ❬✹✹❪✳ ❯♠❛ ❞❛s ♣r✐♠❡✐r❛s ❛♣❧✐❝❛çõ❡s ♣r♦♣♦st❛s ♣❛r❛ ♦s ❛❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s✭❝✉❥♦ ✉s♦ ❞♦ t❡r♠♦❝❛❜❡ ❛ ❇❛❣❧❡② ♥❛ s✉❛ ❞✐ss❡rt❛çã♦ ❞❡ ✶✾✻✼✮✱ s❡❣✉✐♥❞♦ ♦ ❡♥❢♦q✉❡ ❞❡ ❍♦❧❧❛♥❞❬✷✼❪✱ ❢♦r❛♠ ♦s s✐st❡♠❛s ❝❧❛ss✐✜❝❛❞♦r❡s✱ q✉❡ sã♦ s✐st❡♠❛s ❞❡ ♣r♦❞✉çã♦ ❡ ✉s❛♠ ♦s ❛❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s❝♦♠♦ ❢✉♥çõ❡s ❡♠ ✉♠❛ ♣❛rt❡ ❞♦ ❛❧❣♦r✐t♠♦ ❣❧♦❜❛❧✳ ❉❡st❛ ❢♦r♠❛✱ s❡❣✉❡ ❛ ❚❛❜❡❧❛ ✶✳✶ ❞❡ ❬✻❪ ❝♦♠ ✉♠ r❡s✉♠♦ ❞❛s ♣r♦♣r✐❡❞❛❞❡s q✉❡ ❝❛r❛❝t❡✲ r✐③❛♠ ❝❛❞❛ ✉♠❛ ❞❛s ❛❜♦r❞❛❣❡♠ r❡❢❡r❡♥❝✐❛❞❛s ❛q✉✐ ❞❡ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉❝✐♦♥ár✐❛✳❋✐❣✉r❛ ✶✳✶✿ ❘❡s✉♠♦ ❛❞❛♣t❛❞♦ ❞❡ ❬✻❪ s♦❜r❡ ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉❝✐♦♥ár✐❛✳ ❖s ❆● ♣♦ss✉❡♠ ✉♠❛ ❧❛r❣❛ ❛♣❧✐❝❛çã♦ ❡♠ ♠✉✐t❛s ár❡❛s ❝✐❡♥tí✜❝❛s✱ ❞❡♥tr❡ ❛s q✉❛✐s ♣♦❞❡♠ s❡r ❞❡st❛❝❛❞❛s✿❙í♥t❡s❡ ❞❡ ❝✐r❝✉✐t♦s ❛♥❛❧ó❣✐❝♦s✿ ♣❛r❛ ✉♠❛ ❝❡rt❛ ❡♥tr❛❞❛ ❡ ✉♠❛ s❛í❞❛ ❞❡s❡❥❛❞❛✱ ✶✳✶✳ ❈❖▼P❯❚❆➬➹❖ ❊❱❖▲❯❚■❱❆ ❖❯ ❊❱❖▲❯❈■❖◆➪❘■❆ ✸ s♦❢t✇❛r❡ ♣❛r❛ q✉❡ ✉♠ ❞❡s❡♠♣❡♥❤♦ ❛❝❡✐tá✈❡❧ s❡❥❛ ❛❧❝❛♥ç❛❞♦❀●❡r❡♥❝✐❛♠❡♥t♦ ❞❡ r❡❞❡s✿ s✉♣❡r✈✐sã♦ ❞♦ trá❢❡❣♦ ♥♦s ❧✐♥❦s ❡ ❞❛s ✜❧❛s ♥♦s ✧❜✉❢✲ ❆❧❣♦r✐t♠♦s ●❡♥ét✐❝♦s t❛♠❜é♠ ♣♦❞❡♠ s❡r ❛♣❧✐❝❛❞♦s ❡♠ ❞✐✈❡rs❛s ár❡❛s ❞❡ ❞❡s❡♥✈♦❧✈✐✲♠❡♥t♦✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ❞❡st❛❝❛♠♦s ❛s s❡❣✉✐♥t❡s ár❡❛s✿ ❙❡t♦r ❞❡ P❡tró❧❡♦ ❡ ●ás✱ ▼✉s✐❝❛❧✱❚❡❧❡❝♦♠✉♥✐❝❛çõ❡s✱ ❙❛ú❞❡ ❡ ♥❛ ár❡❛ ❞❡ ❇✐♦❧♦❣✐❛ ❡ ❆❣r♦♥♦♠✐❛✳ P❡tró❧❡♦ ❡ ●ás✲■♥✈❡rsã♦ ❙ís♠✐❝❛✿ ❈♦♥❢♦r♠❡ ▲■◆❉❊◆ ✭✷✵✵✽✮✱ ♦ ♣r♦❜❧❡♠❛ ❞❛ ✐♥✲✈❡rsã♦ sís♠✐❝❛✱ q✉❡ é ✉♠ ✐♠♣♦rt❛♥t❡ ❝❛♠♣♦ ❞❛ ❣❡♦❧♦❣✐❛✱ ❝♦♥s✐st❡ ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞❛❡str✉t✉r❛ ❞♦s ❞❛❞♦s ❞❡ s✉❜s♦❧♦ ❛ ♣❛rt✐r ❞❛ ♣r♦s♣❡❝çã♦ ❣❡♦❧ó❣✐❝❛✱ t❡♥❞♦ ❝♦♠♦ ♦❜❥❡t✐✈♦ ♣r✐✲♠ár✐♦ ♦❜t❡r ✉♠❛ s❡çã♦ ❣❡♦❧ó❣✐❝❛ ♦✉ ✉♠ ♠♦❞❡❧♦ ✸❉✳ ❊st❡ ♣r♦❜❧❡♠❛ é s✉s❝❡tí✈❡❧ à ❛♣❧✐❝❛çã♦❞❡ ❛❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s✱ ♣♦✐s s✉❛ ❢✉♥çã♦ ♦❜❥❡t✐✈♦ é ♠✉✐t♦ ✐rr❡❣✉❧❛r✱ s❡♥❞♦ ❛❧t❛♠❡♥t❡ ♥ã♦❧✐♥❡❛r✱ ♣♦ss✉✐♥❞♦ ♠✉✐t♦s ♠í♥✐♠♦s ❡ ♠á①✐♠♦s ❧♦❝❛✐s ❡ ♣♦❞❡♥❞♦ ❛♣r❡s❡♥t❛r ❞❡s❝♦♥t✐♥✉✐❞❛✲❞❡s✳ P♦❞❡♠♦s ❝♦♥❝❧✉✐r✱ q✉❡ ♦ ✉s♦ ❞❡ ❆●s t♦r♥❛✲s❡ ❜❛st❛♥t❡ út✐❧ ♥♦ ❝❛♠♣♦ ❞❡ P❡tró❧❡♦ ❡ ●ás✱♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❛r❛ ♦ ❝❛s♦ ❛❝✐♠❛✱ ♣♦✐s ♦ ♠❡s♠♦ ❛♣r❡s❡♥t❛ ❞❛❞♦s t♦t❛❧♠❡♥t❡ ✐♥❝♦♥s✐st❡♥t❡s❡ ✐♥❝❡rt♦s✳ ❆ ♣❛rt✐r ❞❡ s✉❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❡ ❝♦♠ ❡st✉❞♦s ❞❡t❛❧❤❛❞♦s✱ ♣♦❞❡♠♦s ♦❜t❡r✐♥❢♦r♠❛çõ❡s ✈❛❧✐♦s❛s ♣❛r❛ ❛ s♦❧✉çã♦ ❞❡ss❡s ♣r♦❜❧❡♠❛s✳ ▼ús✐❝❛✿ ❢♦✐ ❛♣r❡s❡♥t❛❞♦ ❡♠ ✶✾✾✾ ♥♦ ❡✈❡♥t♦ ❈❊❈✾✾ ✭■❊❊❊ ✲ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡♦♥ ❊✈♦❧✉t✐♦♥❛r② ❈♦♠♣✉t❛t✐♦♥✮ ✉♠ ❛♠❜✐❡♥t❡ ✐♥t❡r❛t✐✈♦✱ ✉t✐❧✐③❛♥❞♦ ❆❧❣♦r✐t♠♦s ●❡♥ét✐❝♦s✱♣❛r❛ ❛ ❛✈❛❧✐❛çã♦ ❞❡ s❡q✉ê♥❝✐❛s ❞❡ ❛❝♦r❞❡s t♦❝❛❞❛s ❡♠ ❛rq✉✐✈♦s ▼■❉■✳ ◆♦ ❝❛s♦✱ ♦s ✐♥❞✐✈í✲❞✉♦s ❞❛ ♣♦♣✉❧❛çã♦ ❢♦r❛♠ ❞❡✜♥✐❞♦s ❡♠ ❣r✉♣♦s ❞❡ q✉❛tr♦ ✈♦③❡s ✭s♦♣r❛♥♦✱ ❝♦♥tr❛❧t♦✱ t❡♥♦r ❡❜❛✐①♦✮ ♦✉ ❝♦r♦s✳ ❈❛❞❛ ✉♠ é ❛✈❛❧✐❛❞♦ s❡❣✉♥❞♦ três ❝r✐tér✐♦s✿ ♠❡❧♦❞✐❛✱ ❤❛r♠♦♥✐❛ ❡ ♦✐t❛✈❛s✳❆ ❝♦♠♣♦s✐çã♦ ❞❡st❡s três ❝r✐tér✐♦s ❞❡✜♥✐❛ ❛ ❛♣t✐❞ã♦ ✭✜t♥❡ss✮ ❞❡✜♥✐❞❛ ♣❡❧❛ ❢✉♥çã♦ ❞❡ s❡❧❡✲çã♦✱ q✉❡ r❡t♦r♥❛ ♦ ♠❡❧❤♦r ✐♥❞✐✈í❞✉♦ ♦✉ ♠❡❧❤♦r ❝♦r♦✳ ❯♠ ❝✐❝❧♦ ❣❡♥ét✐❝♦ é ♦♣❡r❛❝✐♦♥❛❧✐③❛❞♦✱❝r✐❛♥❞♦ ♥♦✈♦s ✐♥❞✐✈í❞✉♦s ❞♦s ❛♥t❡r✐♦r❡s ❡ ♣r♦❝✉r❛♥❞♦ s❡♠♣r❡ ♣❡❧♦ ♠❡❧❤♦r✳ ◗✉❛♥❞♦ ✉♠♥♦✈♦ ❣r✉♣♦ é s❡❧❡❝✐♦♥❛❞♦✱ ❡❧❡ é t♦❝❛❞♦ ❡♠ ▼■❉■✳ ❆ ❞✉r❛çã♦ ❞♦ ❝✐❝❧♦ ❣❡♥ét✐❝♦ ❞❡t❡r♠✐♥❛♦ r✐t♠♦ ❞❛ ❡✈♦❧✉çã♦✳ ❖ s✐st❡♠❛ ❝r✐❛❞♦ ❢♦✐ ❞❡♥♦♠✐♥❛❞♦ ❱♦① P♦♣✉❧✐ ✭❋✉❦✉s❤✐♠❛✱ ✶✾✾✾✮✳ ✶✳✶✳ ❈❖▼P❯❚❆➬➹❖ ❊❱❖▲❯❚■❱❆ ❖❯ ❊❱❖▲❯❈■❖◆➪❘■❆ ✹❚❡❧❡❝♦♠✉♥✐❝❛çõ❡s✿ ❞❡ ❛❝♦r❞♦ ❝♦♠ ✭❇❧❛♥❝❤❛r❞✱✶✾✾✹✮✱ ♥♦ ❡✈❡♥t♦ ❲❈❈■✬✾✹ ✭❲♦r❧❞ ❈♦♥❣r❡ss ♦♥ ❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡✮✱ ♠♦str♦✉ ✉♠❛ sér✐❡ ❞❡ s♦❧✉çõ❡s ♣r♦♠✐ss♦r❛s ❛ s✐t✉❛çõ❡s r❡❛✐s ✉t✐❧✐③❛♥❞♦ ❆❧❣♦r✐t♠♦s ●❡♥ét✐❝♦s✳ ❇❧❛♥❝❤❛r❞ ♠♦str♦✉✲s❡ ♦ ❝❛s♦ ❞❛ ❯❙ ❲❡st✱✉♠❛ ❝♦♠♣❛♥❤✐❛ r❡❣✐♦♥❛❧ ❞❡ t❡❧❡❝♦♠✉♥✐❝❛çõ❡s ❞♦ ❡st❛❞♦ ❞♦ ❈♦❧♦r❛❞♦✱ q✉❡ ✈❡♠ ✉s❛♥❞♦ ✉♠ s✐st❡♠❛ ❜❛s❡❛❞♦ ❡♠ ❆●s q✉❡ ♣♦ss✐❜✐❧✐t❛ ♣r♦❥❡t❛r✱ ❡♠ ❞✉❛s ❤♦r❛s✱ r❡❞❡s ót✐❝❛s ❡s♣❡❝✐❛❧✐③❛✲❞❛s✱ tr❛❜❛❧❤♦ q✉❡ ❧❡✈❛r✐❛ s❡✐s ♠❡s❡s ✉t✐❧✐③❛♥❞♦ ❡s♣❡❝✐❛❧✐st❛s ❤✉♠❛♥♦s✳ ❖ s✐st❡♠❛ ♣r♦❞✉③ r❡s✉❧t❛❞♦s ❛✐♥❞❛ ❞❡③ ♣♦r ❝❡♥t♦ ♠❡❧❤♦r❡s q✉❡ ♦s r❡❛❧✐③❛❞♦s ♣❡❧♦ ❤♦♠❡♠✳ ❆ ❝♦♠♣❛♥❤✐❛✱❛✜r♠♦✉ q✉❡ ♦ s✐st❡♠❛ ❢♦✐ ❝❛♣❛③ ❞❡ tr❛③❡r ✉♠❛ ❡❝♦♥♦♠✐❛ ❞❡ ✶✵✵ ♠✐❧❤õ❡s ❞❡ ❞ó❧❛r❡s ❛té ♦✜♥❛❧ ❞♦ sé❝✉❧♦ ✷✵✳ ❙❛ú❞❡✿ té❝♥✐❝❛s ❞❡ r❡❛❧✐❞❛❞❡ ✈✐rt✉❛❧ sã♦ ✉s❛❞❛s ♥❛ ❝♦♥str✉çã♦ ❞❡ s♦❢t✇❛r❡ ♣❛r❛ ❛✉✲①✐❧✐❛r ♦ tr❡✐♥❛♠❡♥t♦✱ ♣❧❛♥❡❥❛♠❡♥t♦ ❡ r❡❛❧✐③❛çã♦ ❞❡ ❝✐r✉r❣✐❛s✳ ❊♠ ❬✸✷❪ ❡ ❬✹✵❪ sã♦ ❞❡s❝r✐t♦s❛❧❣✉♥s s♦❢t✇❛r❡ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❝✐rúr❣✐❝♦✳ ❆ ❡♥tr❛❞❛ ❞❡st❡s s♦❢t✇❛r❡ sã♦ ✐♥❢♦r♠❛çõ❡s❡①tr❛í❞❛s ❞❡ ❡①❛♠❡s✱ t❛✐s ❝♦♠♦ t♦♠♦❣r❛✜❛ ❝♦♠♣✉t❛❞♦r✐③❛❞❛ ❡ r❡ss♦♥â♥❝✐❛ ♠❛❣♥ét✐❝❛ ❞❛♣❛rt❡ ❞♦ ♦r❣❛♥✐s♠♦ ❛ s❡r ♦♣❡r❛❞❛✳ ❈♦♠ ❜❛s❡ ♥❛ ❡♥tr❛❞❛ ❢♦r♥❡❝✐❞❛✱ ♦ s♦❢t✇❛r❡ ❝♦♥stró✐✉♠ ♦r❣❛♥✐s♠♦ ✈✐rt✉❛❧ ♣❛r❛ q✉❡ ♦ ♠é❞✐❝♦ ♣♦ss❛✱ ❞❡♥tr♦ ❞♦ ❛♠❜✐❡♥t❡ ✈✐rt✉❛❧✱ t❡st❛r ✈á✲ r✐♦s ♣r♦❝❡❞✐♠❡♥t♦s ❝✐rúr❣✐❝♦s ❡ ❛ss✐♠ ♣❧❛♥❡❥❛r ❛ s✉❛ ❡str❛té❣✐❛ ❞❡ tr❛❜❛❧❤♦✳ ❏á ❡♠ ❬✸✹❪✱sã♦ ❡♥❝♦♥tr❛❞❛s ❞❡s❝r✐çõ❡s ❞❡ ✉♠ s♦❢t✇❛r❡ ❞❡ t❡❧❡❝✐r✉r❣✐❛ q✉❡ ♣❡r♠✐t❡ q✉❡ ✉♠ ♠é❞✐❝♦♥❛ ❆❧❡♠❛♥❤❛ ♦♣❡r❡ ✉♠ ♣❛❝✐❡♥t❡ ♥♦ ❇r❛s✐❧✳ ❆s ❡♥tr❛❞❛s ❞❡st❡ s♦❢t✇❛r❡ sã♦ ✐♥❢♦r♠❛çõ❡s❝❛♣t❛❞❛s ♣♦r s❡♥s♦r❡s ✐♥st❛❧❛❞♦s s♦❜r❡ ♦ ♦r❣❛♥✐s♠♦ ❞♦ ♣❛❝✐❡♥t❡✱ ❝✉❥❛s ✐♥❢♦r♠❛çõ❡s sã♦❡♥✈✐❛❞❛s ♣❛r❛ ♦ s❡r✈✐❞♦r r❡♠♦t♦✱ ❝♦♥✈❡rt✐❞❛s ❡♠ ✉♠ ♦r❣❛♥✐s♠♦ ✈✐rt✉❛❧✱ s♦❜r❡ ♦ q✉❛❧ ♦♠é❞✐❝♦ r❡❛❧✐③❛ ❛ ♦♣❡r❛çã♦✱ ❡ s✉❛s ❛çõ❡s sã♦ ❡♥✈✐❛❞❛s ❞❡ ✈♦❧t❛ ❛ s❛❧❛ ❝✐rúr❣✐❝❛✱ ♦♥❞❡ ❜r❛ç♦s♠❡❝â♥✐❝♦s r❡❛❧✐③❛♠ ❛ ♦♣❡r❛çã♦ ❝♦♠ ❛ ❛❥✉❞❛ ❞❡ ✉♠❛ ❡q✉✐♣❡ ♠é❞✐❝❛✳ ❇✐♦❧♦❣✐❛✿ ✉♠ ❞♦s ♣r✐♥❝✐♣❛✐s ♣r♦❜❧❡♠❛s ❞❡♥tr♦ ❞❛ ❜✐♦❧♦❣✐❛ ♠♦❧❡❝✉❧❛r é ❛ ✐♥❢❡rê♥❝✐❛ ❞❛s❝❛r❛❝t❡ríst✐❝❛s ❞❡ ✉♠ s❡r ✈✐✈♦✳ ❊ss❡ ♣r♦❜❧❡♠❛ ❝♦♥s✐st❡ ❡♠ ❞❡t❡r♠✐♥❛r ❛ ❝❛❞❡✐❛ ❞❡ ❉◆❆ r❡s♣♦♥sá✈❡❧ ♣❡❧♦ ❢❡♥ót✐♣♦ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❡s♣é❝✐❡s ❞❛ ♠❡s♠❛ ❢❛♠í❧✐❛✳ ❖s ❛❧❣♦r✐t♠♦sq✉❡ r❡❛❧✐③❛♠ ❡st❛ t❛r❡❢❛ sã♦ ✐❞❡♥t✐✜❝❛❞♦s ❝♦♠♦ ❛❧❣♦r✐t♠♦s ❞❡ ❛❧✐♥❤❛♠❡♥t♦✳ ❯♠ ❛❧❣♦r✐t♠♦❞❡ ❛❧✐♥❤❛♠❡♥t♦ r❡❝❡❜❡ ❝♦♠♦ ❡♥tr❛❞❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❉◆❆ ❞❡ ❡s♣é❝✐❡s ❡ t❡♥t❛ ❛rr✉♠❛r❡st❡s ❉◆❆✬s ❡♠ ❧✐♥❤❛s ❞❡ t❛❧ ♠♦❞♦ q✉❡ ♦ ❝❛r❛❝t❡r q✉❡ ♦❝✉♣❛ ❛ ♠❡s♠❛ ♣♦s✐çã♦ ❡♠ t♦❞❛s❛s ❧✐♥❤❛s s❡❥❛ ♦ ♠❡s♠♦✳ ❖s ❛❧❣♦r✐t♠♦s ❞❡ ❛❧✐♥❤❛♠❡♥t♦ ♠❛✐s ❝♦♥❤❡❝✐❞♦s sã♦ ♦ ❇▲❆❙❚ ❬✶❪❡ ♦ ❋❆❙❚ ❬✶✶❪✳ ❆❣r♦♥♦♠✐❛✿ ♦ ♠❡❧❤♦r❛♠❡♥t♦ ❣❡♥ét✐❝♦ ❞❛ ❝❛♥❛✲❞❡✲❛çú❝❛r ❜✉s❝❛ ❞❡s❡♥✈♦❧✈❡r ✈❛r✐❡❞❛✲ ✶ ❞❡s ❛❞❛♣t❛❞❛s ❛s ❞✐✈❡rs❛s ❝♦♥❞✐çõ❡s ❡❞❛❢♦❝❧✐♠❛t✐❝❛s ❞❡ ❝❛❞❛ r❡❣✐ã♦ ❞♦ ❇r❛s✐❧✳ ❇❛s✐✲❝❛♠❡♥t❡ ❛s ♥♦✈❛s ✈❛r✐❡❞❛❞❡s ❞❡✈❡♠ t❡r ❣❛♥❤♦s ♥❛ ár❡❛ ❛❣r♦✐♥❞✉str✐❛❧✱ t❛✐s ❝♦♠♦✿ ♠❛✐♦r♣r♦❞✉t✐✈✐❞❛❞❡ ❡ ❝♦♠ ♠❛✐♦r t♦❧❡râ♥❝✐❛ ❛♦ ❡str❡ss❡ ❤í❞r✐❝♦✱ ♠❛✐♦r r❡s✐stê♥❝✐❛ às ♣r❛❣❛s ❡ ❞♦✲❡♥ç❛s ❡ ♠❡❧❤♦r ❛❞❛♣t❛çã♦ à ❝♦❧❤❡✐t❛ ♠❡❝❛♥✐③❛❞❛✳ ❖s ór❣ã♦s ❞❡ ♣❡sq✉✐s❛ q✉❡ ❞❡s❡♥✈♦❧✈❡♠♣r♦❣r❛♠❛s ❞❡ ♠❡❧❤♦r❛♠❡♥t♦ ❣❡♥ét✐❝♦ ❞❛ ❝❛♥❛ ✉t✐❧✐③❛♠✱ ❣❡r❛❧♠❡♥t❡✱ ❝♦♥❤❡❝✐♠❡♥t♦s ❞❛s ✶ r❡❧❛çã♦ ♣❧❛♥t❛✲s♦❧♦✲❝❧✐♠❛ ♣❛r❛ ♣❧❛♥t✐♦✳ ❖s ❢❛t♦r❡s ❡❞❛❢♦❝❧✐♠át✐❝♦s sã♦ r❡❢❡r✐❞♦s ❝♦♠♦ ♦s ♠❛✐s ✐♠✲ ♣♦rt❛♥t❡s ♥ã♦ só ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛s ❝✉❧t✉r❛s✱ ❝♦♠♦ t❛♠❜é♠ ♣❛r❛ ❛ ❞❡✜♥✐çã♦ ❞❡ s✐st❡♠❛s ❞❡♣r♦❞✉çã♦✳ ✶✳✶✳ ❈❖▼P❯❚❆➬➹❖ ❊❱❖▲❯❚■❱❆ ❖❯ ❊❱❖▲❯❈■❖◆➪❘■❆ ✺ár❡❛s ❞❡ ❜✐♦t❡❝♥♦❧♦❣✐❛ ✈✐❞❡ ❋✐❣✉r❛ ✶✳✷ ✱ ❝✐ê♥❝✐❛s ❞♦ s♦❧♦✱ ♥✉tr✐çã♦ ❞❡ ♣❧❛♥t❛s✱ ❝❧✐♠❛t♦❧♦❣✐❛✱✜s✐♦❧♦❣✐❛✱ ✜t♦♣❛t♦❧♦❣✐❛✱ ❡♥t♦♠♦❧♦❣✐❛✱ ❡❝♦♥♦♠✐❛ ❡ ♦✉tr❛s✳ ✷ ❋✐❣✉r❛ ✶✳✷✿ Pr♦❞✉çã♦ ❞❡ ♠✉❞❛s ❡♠ ❧❛❜♦r❛tór✐♦✱ ❢♦♥t❡ s✐t❡ ❞❛ ❊♠❜r❛♣❛ ✳❆ ♠❛✐♦r✐❛ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❛ ❝❛♥❛✲❞❡✲❛çú❝❛r é ❤❡r❞❛❞❛ ❞❡ ❢♦r♠❛ ❛❞✐t✐✈❛✳ P♦r ❡①❡♠♣❧♦✱ ♦ ❝r✉③❛♠❡♥t♦ ❞❡ ❞✉❛s ✈❛r✐❡❞❛❞❡s ❛❧t❛s ❞❡✈❡ r❡s✉❧t❛r ♥✉♠❛ ✈❛r✐❡❞❛❞❡ ❛✐♥❞❛ ♠❛✐s❛❧t❛✳ P♦ré♠✱ ❡①✐st❡ ✉♠❛ ✐♠♣♦rt❛♥t❡ ❡①❝❡çã♦ q✉❡ é ❛ ❝❛r❛❝t❡ríst✐❝❛ ♣❛r❛ ❛ ♣r♦❞✉t✐✈✐❞❛❞❡✱❡♠ q✉❡ ❛s ✈❛r✐❛çõ❡s ❣❡♥ét✐❝❛s ❛❞✐t✐✈❛s ❡ ♥ã♦✲❛❞✐t✐✈❛ ♣❛r❡❝❡♠ ❡st❛r ❡♠ ✐❣✉❛❧ ❣r❛✉ ❞❡✐♠♣♦rtâ♥❝✐❛✳ ■ss♦ ✈❡♠ s❡♥❞♦ ♦ ♣r✐♥❝✐♣❛❧ ❞❡s❛✜♦ ♥❛s ♣❡sq✉✐s❛s ❞❡ ♠❡❧❤♦r❛♠❡♥t♦ ❣❡♥ét✐❝♦❞❛ ❝❛♥❛✲❞❡✲❛çú❝❛r✳ ❖✉tr❛ q✉❡stã♦ ❜❛st❛♥t❡ r❡❧❡✈❛♥t❡ ❡♠ r❡❧❛çã♦ ❛♦ ♠❡❧❤♦r❛♠❡♥t♦ ❣❡♥ét✐❝♦ ❞❛ ❝❛♥❛ é ❛❛✈❛❧✐❛çã♦ ❞❡ ♥♦✈❛s ✈❛r✐❡❞❛❞❡s q✉❛♥t♦ à ❛❞❛♣t❛çã♦ ❛ ❞✐❢❡r❡♥t❡s ❛♠❜✐❡♥t❡s✳ ■ss♦ é ✐♠♣♦r✲ t❛♥t❡ ♣❛r❛ ❛ r❡❝♦♠❡♥❞❛çã♦ ❞❛s ♠❡❧❤♦r❡s ✈❛r✐❡❞❛❞❡s ♣❛r❛ ❛s r❡❣✐õ❡s ♠❛✐s ❛♣t❛s✳ ❆ ❘❡❞❡ ■♥t❡r✉♥✐✈❡rs✐tár✐❛ ♣❛r❛ ♦ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ❙❡t♦r ❙✉❝r♦❛❧❝♦♦❧❡✐r♦ ✭❘✐❞❡s❛✮♣♦ss✉✐ ❛ ❡st❛çã♦ ❞❡ ♣❡sq✉✐s❛ ❙❡rr❛ ❞♦ ❖✉r♦ ♥♦ ♠✉♥✐❝í♣✐♦ ❞❡ ▼✉r✐❝✐✱ ❆▲✳ ❆ ✉♥✐❞❛❞❡ ❡stá ♦ ♥❛ ❧❛t✐t✉❞❡ ✾ ✶✸ ❙✱ ❛ ✺✵✵ ♠❡tr♦s ❞❡ ❛❧t✐t✉❞❡✱ ♦♥❞❡ ❛ ♣❧✉✈✐♦s✐❞❛❞❡ ♠é❞✐❛ é ❞❡ ♣❡❧♦ ♠❡♥♦s ♦ ❞♦✐s ♠✐❧ ♠✐❧í♠❡tr♦s ❛♥✉❛✐s ❡ ❛s t❡♠♣❡r❛t✉r❛s ♠é❞✐❛s✱ ❞❡ ✶✾✱✺ ❛ ✷✻✱✺ ❈ ✭❈❡❧s✐✉s✮✳❊ss❛s ❝♦♥❞✐çõ❡s t♦r♥❛♠ ♦ ❧♦❝❛❧ ♠✉✐t♦ ♣r♦♣í❝✐♦ ♣❛r❛ ♦ ✢♦r❡s❝✐♠❡♥t♦ ❞❛ ♠❛✐♦r✐❛ ❞❛s ✈❛r✐❡❞❛❞❡s ❞❡ ❝❛♥❛✲❞❡✲❛çú❝❛r ❡✱ t❛♠❜é♠✱ ♣❛r❛ ❛ ❜♦❛ ❢❡rt✐❧✐❞❛❞❡ ❞♦ ♣ó❧❡♥✳ ❆s ♠✉❞❛s ❞❡❝❛♥❛ sã♦ ♣❧❛♥t❛❞❛s ❡♠ ❝❛♠♣♦s ❡①♣❡r✐♠❡♥t❛✐s ❞❛s ✉♥✐❞❛❞❡s ❞❡ ♣❡sq✉✐s❛✳ P♦r ❡ss❡s ♠♦t✐✈♦s ❡st❡ ❞♦♠í♥✐♦ s❡rá ♦ ❡st✉❞♦ ❞❡ ❝❛s♦ ✉t✐❧✐③❛❞♦ ♥❡st❛ ❞✐ss❡rt❛çã♦✳ ✶✳✶✳✶ ▼♦t✐✈❛çã♦ ❞❛ ❉✐ss❡rt❛çã♦ ◆❡st❛ ❞✐ss❡rt❛çã♦ ❡①✐st❡♠ ❞✉❛s ♠♦t✐✈❛çõ❡s✿ ✉♠❛ ❜✐♦❧ó❣✐❝❛ ❡ ♦✉tr❛ ❝♦♠♣✉t❛❝✐♦♥❛❧✳ ❆ ♠♦t✐✲✈❛çã♦ ❜✐♦❧ó❣✐❝❛ ❝♦♥s✐st❡ ❡♠ ❞❡t❡r♠✐♥❛r ❛s r❡❧❛çõ❡s ❡✈♦❧✉t✐✈❛s ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❡s♣é❝✐❡s✳❖ ♥ú♠❡r♦ ❞❡ r❡❧❛çõ❡s ❡✈♦❧✉t✐✈❛s ❝r❡s❝❡ ❡①♣♦♥❡♥❝✐❛❧♠❡♥t❡ à ♠❡❞✐❞❛ q✉❡ ♥♦✈❛s ❡s♣é❝✐❡s sã♦ ❝♦♥s✐❞❡r❛❞❛s✳ ◆❛ t❡♥t❛t✐✈❛ ❞❡ ❣❡r❛r ❛ ❤✐stór✐❛ ❡✈♦❧✉t✐✈❛ ❞❛s ❡s♣é❝✐❡s ♠❛♥✉❛❧♠❡♥t❡✱ ✶✳✶✳ ❈❖▼P❯❚❆➬➹❖ ❊❱❖▲❯❚■❱❆ ❖❯ ❊❱❖▲❯❈■❖◆➪❘■❆ ✻❋✐❣✉r❛ ✶✳✸✿ ❋❧✉①♦❣r❛♠❛ ❞❡ ♣r♦❣r❛♠❛ ❞❡ ♠❡❧❤♦r❛♠❡♥t♦ ❣❡♥ét✐❝♦ ❞❛ ❝❛♥❛✲❞❡✲❛çú❝❛r✳ ❛❧❣✉♥s ♣❡sq✉✐s❛❞♦r❡s ♣❛ss❛r❛♠ ❛ r❡♣r❡s❡♥tá✲❧❛ ♣♦r ❡str✉t✉r❛s ❣rá✜❝❛s ❞❡♥♦♠✐♥❛❞❛ ár✈♦r❡✜❧♦❣❡♥ét✐❝❛✳ ■ss♦ ✐♥✈✐❛❜✐❧✐③❛ ❛ ❝♦♥str✉çã♦ ❞❛ ❤✐stór✐❛ ❡✈♦❧✉t✐✈❛ ❞❛s ❡s♣é❝✐❡s ♠❛♥✉❛❧♠❡♥t❡✳❉❡st❛ ❢♦r♠❛ s✉r❣❡♠ ♦s ♣r✐♠❡✐r♦s ♣r♦❣r❛♠❛s ♣❛r❛ ❝♦♥str✉çã♦ ❞❡ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛✳ ❆♣❡s❛r ❞❡ ❛s ár✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s s❡r❡♠ ❞❡ ❢á❝✐❧ ♠❛♥✐♣✉❧❛çã♦✱ ❛ ❝♦♥str✉çã♦ ❞❡ ár✈♦r❡s✜❧♦❣❡♥ét✐❝❛s ♣♦r ♣r♦❝❡ss♦s ♠❛♥✉❛✐s ❢♦✐ s❡ t♦r♥❛♥❞♦ ❝❛❞❛ ✈❡③ ♠❛✐s ❝♦♠♣❧❡①❛✳ ❆❧é♠ ❞✐ss♦✱❡ss❡s ♣r♦❝❡ss♦s r❡q✉❡r❡♠ ♠✉✐t♦ t❡♠♣♦ ❞♦ ✜❧♦❣❡♥❡t✐❝✐st❛ ❡ ♣r♦♣✐❝✐❛♠ ❛ ✐♥tr♦❞✉çã♦ ❞❡ ❡rr♦s❤✉♠❛♥♦s ♥❛ ❛♥á❧✐s❡ ❬✷❪✳ ❆ ❝♦♥str✉çã♦ ❞❡ ár✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s é ✉♠ ♣r♦❜❧❡♠❛ ◆✲P ❝♦♠♣❧❡t♦✱ ♣♦✐s ♦ ♥ú♠❡r♦ ❞❡♣♦ssí✈❡✐s ár✈♦r❡s ♣❛r❛ ◆ ❡s♣é❝✐❡s é ◆✦✳ ❉❡st❛ ❢♦r♠❛ ♦s ❛❧❣♦r✐t♠♦s q✉❡ ❣❛r❛♥t❡♠ ❛ ♦❜t❡♥çã♦❞❛ s♦❧✉çã♦ ót✐♠❛ sã♦ ✐♥❢❛❝tí✈❡✐s ♣❛r❛ ♣r♦❜❧❡♠❛s ◆P✲❝♦♠♣❧❡t♦s ❝♦♠♦ ♦ ❞❡ ❝♦♥str✉çã♦ ❞❡ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛s✳ ❊♥tã♦ ❝♦♠♦ r❡s♦❧✈ê✲❧♦s❄ ❆❜r✐♥❞♦ ♠ã♦ ❞❛ ❣❛r❛♥t✐❛ ❞❡ ♦❜t❡♥çã♦ ❞❛ s♦❧✉çã♦ ót✐♠❛ ❡♠ ♣r♦❧ ❞❛ ❢❛❝t✐❜✐❧✐❞❛❞❡✳ P♦r ❡st❛ r❛③ã♦✱ ♦s ♠ét♦❞♦s ❞❡ ✐♥❢❡rê♥❝✐❛ ✜❧♦❣❡♥ét✐❝❛s ♥♦r♠❛❧♠❡♥t❡ s❡ ❜❛s❡✐❛♠ ❡♠❛❧❣♦r✐t♠♦s ❞❡ ❛❣r✉♣❛♠❡♥t♦ ♦✉ ❡str❛té❣✐❛s ❤❡✉ríst✐❝❛s ❞❡ ❜✉s❝❛ q✉❡ ♣❡r♠✐t❡♠ ♠✐♥✐♠✐③❛r ❛ q✉❛♥t✐❞❛❞❡ ❞❡ t❡♠♣♦ ❣❛st♦ ❛♥❛❧✐s❛♥❞♦ ❛s ár✈♦r❡s ❝❛♥❞✐❞❛t❛s ❬✸✶❪✳ ❆ ✐❞é✐❛ ♣♦r trás ❞❡st❡s❛❧❣♦r✐t♠♦s é q✉❡ ✉♠❛ s♦❧✉çã♦ ❜♦❛✱ ♥ã♦ ♥❡❝❡ss❛r✐❛♠❡♥t❡ ❛ ót✐♠❛✱ é ♠❡❧❤♦r q✉❡ ♥❡♥❤✉♠❛ s♦❧✉çã♦ ♦✉ q✉❡ ✉♠❛ s♦❧✉çã♦ t♦♠❛❞❛ ❛❧❡❛t♦r✐❛♠❡♥t❡ ❞♦ ❡s♣❛ç♦ ❞❡ ❜✉s❝❛✳ ❈♦♠ ✐ss♦✱ ♣r♦♣♦r ✶✳✶✳ ❈❖▼P❯❚❆➬➹❖ ❊❱❖▲❯❚■❱❆ ❖❯ ❊❱❖▲❯❈■❖◆➪❘■❆ ✼❛❧❣♦r✐t♠♦s q✉❡ ❡①♣❧♦r❡♠ ♦ ❡s♣❛ç♦ ❞❡ ❜✉s❝❛ ❞❡ ❢♦r♠❛ ❡✜❝❛③✱ ✈✐s❛♥❞♦ ❧♦❝❛❧✐③❛r s♦❧✉çõ❡s ❞❡❜♦❛ q✉❛❧✐❞❛❞❡✱ ❡ q✉❡ ❡✈❡♥t✉❛❧♠❡♥t❡ ♣♦❞❡♠ ❝♦rr❡s♣♦♥❞❡r à s♦❧✉çã♦ ót✐♠❛✳ ❉❡st❛ ❢♦r♠❛✱ ♦s ❛❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s✱ ❡stã♦ ❡st❛❜❡❧❡❝✐❞♦s s♦❜r❡ ♦s s❡❣✉✐♥t❡s ♣r✐♥❝í♣✐♦s✿♣❛r❛ ❛ ♠❛✐♦r✐❛ ❞♦s ♣r♦❜❧❡♠❛s ❡①✐st❡ ✉♠❛ ❢✉♥çã♦ ❞❡ ❝♦❞✐✜❝❛çã♦ q✉❡ ♠❛♣❡✐❛ ♦s ♣♦s✲ ❘❡❝❡♥t❡♠❡♥t❡✱ ❡str❛té❣✐❛s ❡♥✈♦❧✈❡♥❞♦ ❛❧❣♦r✐t♠♦s ❡✈♦❧✉t✐✈♦s tê♠ s✐❞♦ ✐♥✈❡st✐❣❛❞❛s♥❡st❛ ár❡❛✱ ♠♦str❛♥❞♦ r❡s✉❧t❛❞♦s r❡❧❡✈❛♥t❡s ✭❬✶✷❪❀ ❬✸✼❪❀ ❬✹✼❪✮✳ ◆❡ss❡ s❡♥t✐❞♦✱ ♣r♦♣õ❡♠✲s❡ ✉s❛r ♦ ♠♦❞❡❧♦ ❞❡ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ❇❛s❡❛❞♦ ❡♠ ❚✐♣♦s❆❜str❛t♦s ❞❡ ❉❛❞♦s ✭●❆❆❉❚✮✳ ❚r❛t❛✲s❡ ❞❡ ✉♠ ♣❛r❛❞✐❣♠❛ ♥♦✈♦✱ ✉t✐❧✐③❛❞♦ ♥❡st❡ tr❛❜❛❧❤♦✱♦r✐❣✐♥❛❧♠❡♥t❡ ♣r♦♣♦st♦ ♣♦r ❬✹✺❪ ❡ ❬✹✻❪ ❡ tr❛❜❛❧❤❛ s♦❜r❡ ✉♠ ❛♠❜✐❡♥t❡ ❞❡✜♥✐❞♦ ❝♦♠♦ ✉♠❛❡str✉t✉r❛ ♥❛ q✉❛❧ ✉♠ ❞♦s ❝♦♠♣♦♥❡♥t❡s é ❛ ♣♦♣✉❧❛çã♦✳ ❙❡❣✉♥❞♦ ❡st❡ ♠♦❞❡❧♦✱ ❛s ♠✉❞❛♥ç❛s❛♠❜✐❡♥t❛✐s sã♦ ✈✐st❛s ❝♦♠♦ ♦ ♠❛r❝♦ ❞♦ ✐♥í❝✐♦ ❞❡ ✉♠ ♥♦✈♦ ♣❡rí♦❞♦ ❞❡ ❡✈♦❧✉çã♦ ❞✉r❛♥t❡♦ q✉❛❧ ♦s ❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦ ❛t✉❛❧ ✐rã♦ s♦❢r❡r ❛ ❛çã♦ ❞♦s ♦♣❡r❛❞♦r❡s ❣❡♥ét✐❝♦s❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ❝♦♥str✉✐r ✉♠❛ ♥♦✈❛ ♣♦♣✉❧❛çã♦ ❢♦r♠❛❞❛ s♦♠❡♥t❡ ♣♦r ❝r♦♠♦ss♦♠♦s q✉❡ s❛t✐s❢❛③❡♠ ❛♦s r❡q✉✐s✐t♦s ❞♦ ❛♠❜✐❡♥t❡ ❛t✉❛❧✳ ❆♣ós ♦ ♣❡rí♦❞♦ ❞❡ ❡✈♦❧✉çã♦ ✈❡♠ ♦ ♣❡rí♦❞♦ ❞❡❡st❛❣♥❛çã♦✱ ❞✉r❛♥t❡ ♦ q✉❛❧ ❛ ♣♦♣✉❧❛çã♦ ♥ã♦ ❡✈♦❧✉✐✳ ❖ ♣❡rí♦❞♦ ❞❡ ❡st❛❣♥❛çã♦ é ✜♥❛❧✐③❛❞♦ q✉❛♥❞♦ ✉♠❛ ♥♦✈❛ ❛❧t❡r❛çã♦ ❛♠❜✐❡♥t❛❧ ♦❝♦rr❡✱ ❞❛♥❞♦ ✐♥í❝✐♦ ❛ ✉♠ ♥♦✈♦ ❝✐❝❧♦ ❞❡ ✉♠ ♣❡rí♦❞♦❞❡ ❡✈♦❧✉çã♦ s❡❣✉✐❞♦ ♣♦r ✉♠ ♣❡rí♦❞♦ ❞❡ ❡st❛❣♥❛çã♦✳ ❖ r❡s✉❧t❛❞♦ ❞♦ ♣r♦❜❧❡♠❛ ♣❛r❛ ♦ ❛♠❜✐❡♥t❡ ❛t✉❛❧ é ♦ ❝r♦♠♦ss♦♠♦ ♠❛✐s ❛❞❛♣t❛❞♦ ♥❛♣♦♣✉❧❛çã♦ ❞❡ ❡st❛❣♥❛çã♦ ❛t✐♥❣✐❞❛✳ ❆ ❝❛❞❛ ♣❡rí♦❞♦ ❞❡ ❡✈♦❧✉çã♦ ❡①✐st❡ ✉♠❛ ♣♦♣✉❧❛çã♦ ❞❡❝r♦♠♦ss♦♠♦s ❡①t✐♥t♦s ❛ss♦❝✐❛❞❛✳ ❖s ❝r♦♠♦ss♦♠♦s ❞❡st❛ ♣♦♣✉❧❛çã♦ sã♦ ♣r♦✈❡♥✐❡♥t❡s ❞❡✉♠❛ ❞❛s ♣♦♣✉❧❛çõ❡s ❥á tr❛❜❛❧❤❛❞❛s ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦✱ ♦s q✉❛✐s ❢♦r❛♠ ❛✈❛❧✐❛❞♦s ❡❞❡s❝❛rt❛❞♦s ❞❡✈✐❞♦ ❛♦ s❡✉ ❜❛✐①♦ ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ às ❝♦♥✜❣✉r❛çõ❡s ❛t✉❛✐s ❞♦ ❛♠❜✐❡♥t❡✳ ❆ tr❛♥s♠✐ssã♦ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❛❞❛♣t❛❞❛s ❛♦ ❛♠❜✐❡♥t❡ ❞♦s ❝r♦♠♦ss♦♠♦s ♣❛✐s q✉❡❞❡✈❡♠ s❡r ♣❛ss❛❞❛s ♣❛r❛ ♦s ❝r♦♠♦ss♦♠♦s ✜❧❤♦s✳ ❘❡❛❧✐③❛❞♦ ♣❡❧♦ ♦♣❡r❛❞♦r ❞❡ ❝r✉③❛♠❡♥t♦ ❛♣r❡s❡♥t❛❞♦ ♥♦ ●❆❆❉❚ ❝♦♥stró✐ ♥♦✈♦s ❝r♦✲♠♦ss♦♠♦s s♦♠❡♥t❡ ❝♦♠ ❛s ❝❛r❛❝t❡ríst✐❝❛s r❡s♣♦♥sá✈❡✐s ♣❡❧❛ ❛❞❛♣t❛çã♦ ❞♦s ❝r♦♠♦ss♦♠♦s♣❛✐s ❛♦ ❛♠❜✐❡♥t❡✱ ❛s q✉❛✐s s❡rã♦ ❞❡♥♦♠✐♥❛❞❛s ❞❡ ❣❡♥❡s ❞♦♠✐♥❛♥t❡s✳ ❯♠❛ ❢✉♥çã♦ ❞❡♥♦♠✐✲♥❛❞❛ ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ ❞♦ ❣❡♥❡ é ❞❡✜♥✐❞❛ ♣❛r❛ ✐♥❢♦r♠❛r ♦ q✉❛♥t♦ ✉♠❛ ❞❛❞❛ ❝❛r❛❝t❡ríst✐❝❛♣♦❞❡ ❝♦♥tr✐❜✉✐r ❝♦♠ ❛ ❛❞❛♣t❛çã♦ ❞♦ ❝r♦♠♦ss♦♠♦ ❛♦ ❛♠❜✐❡♥t❡✳ ✶✳✶✳ ❈❖▼P❯❚❆➬➹❖ ❊❱❖▲❯❚■❱❆ ❖❯ ❊❱❖▲❯❈■❖◆➪❘■❆ ✽❆ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞♦s ❝r♦♠♦ss♦♠♦s ♥ã♦ ❛❞❛♣t❛❞♦s ❛♦ ❛♠❜✐❡♥t❡ ❡✈♦❧✉ír❡♠ ❡ ❛té ❝♦♥❞✉③✐✲ r❡♠ à ❣❡r❛çã♦ ❞❡ ❝r♦♠♦ss♦♠♦s ♠❛✐s ❛❞❛♣t❛❞♦s é tr❛❜❛❧❤❛❞❛ ♣❡❧♦ ♦♣❡r❛❞♦r ❞❡ ♠✉t❛çã♦ ❞♦ ●❆❆❉❚✱ q✉❡ é ❛♣❧✐❝❛❞♦ s♦♠❡♥t❡ s♦❜r❡ ♦s ❝r♦♠♦ss♦♠♦s ♥ã♦ ❛❞❛♣t❛❞♦s✱ ❝♦♠♦ ✉♠❛ ❢♦r♠❛❞❡ ❣❛r❛♥t✐r ❛ ♣r❡s❡♥ç❛ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❛❞❛♣t❛❞❛s ❛♦ ❛♠❜✐❡♥t❡ ❞❡st❡s ❝r♦♠♦ss♦♠♦s ♥❛s♣ró①✐♠❛s ❣❡r❛çõ❡s✳ ❚❛♠❜é♠ ❢❛③ ♣❛rt❡ ❞♦ ❛♠❜✐❡♥t❡ ❞♦ ●❆❆❉❚ ♦ r❡❣✐str♦ ❞❛ ❤✐stór✐❛ ❣❡♥❡❛❧ó❣✐❝❛ ✭tá✲①♦♥✮ ❞♦s ❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦ ❛t✉❛❧✱ ♣❛r❛ q✉❡ ✉♠❛ ❡①♣❧✐❝❛çã♦ s♦❜r❡ ♦ r❡s✉❧t❛❞♦❡♥❝♦♥tr❛❞♦ ♣❛r❛ ✉♠ ❞❛❞♦ ♣r♦❜❧❡♠❛ ♣♦ss❛ s❡r ❣❡r❛❞❛ s❡♠♣r❡ q✉❡ ♥❡❝❡ssár✐♦✳ ✶✳✶✳✷ ❖❜❥❡t✐✈♦s ❞❛ ❉✐ss❡rt❛çã♦ ❖ ♦❜❥❡t✐✈♦ ❞❡st❛ ❞✐ss❡rt❛çã♦✱ é ♣r♦♣♦r ✉♠ s✐st❡♠❛ ❡✈♦❧✉t✐✈♦ ♣❛r❛ ❛ ❝♦♥str✉çã♦ ❞❡ ár✈♦r❡✜❧♦❣❡♥ét✐❝❛ q✉❡ ✉s❛ ♦ ●❆❆❉❚ ♣❛r❛ ❝♦♥str✉✐r ❛ ✐♥❢❡rê♥❝✐❛ ✜❧♦❣❡♥ét✐❝❛✳ ❚❛❧ s✐st❡♠❛ ❞❡✈❡✿ ♠❛♥✐♣✉❧❛r ❞❛❞♦s ❜✐♦❧ó❣✐❝♦s ❝♦♠ ❞✐❢❡r❡♥t❡s r❡♣r❡s❡♥t❛çõ❡s❀ P❛r❛ ❝✉♠♣r✐r ♦s ♦❜❥❡t✐✈♦s ❞❡✜♥✐❞♦s ♥❛s s❡çõ❡s ❛♥t❡r✐♦r❡s ❞❡st❡ ❝❛♣ít✉❧♦✱ ♦r❣❛♥✐③♦✉✲s❡ ❡st❡ tr❛❜❛❧❤♦ ❡♠ ❝✐♥❝♦ ❝❛♣ít✉❧♦s✱ ✐♥❝❧✉✐♥❞♦ ❡st❛ ✐♥tr♦❞✉çã♦✳◆♦ ❝❛♣ít✉❧♦ ✷✱ s❡rá ❞❡♠♦str❛❞♦ ✉♠ ❤✐stór✐❝♦ s♦❜r❡ ➪r✈♦r❡ ❋✐❧♦❣❡♥ét✐❝❛ ❡ ❞❡✜♥✐r❡♠♦s ❛ ❉❡s❝r✐çã♦ ❋♦r♠❛❧ ❞❛ ➪r✈♦r❡ ❋✐❧♦❣❡♥ét✐❝❛ ❡ ❛♥❛❧✐s❛r❡♠♦s ❛s ♠❛tr✐③❡s ❞✐stâ♥❝✐❛ ✉t✐❧✐③❛❞❛s♣❡❧♦s ✜❧♦❣❡♥❡t✐❝✐st❛s ♣❛r❛ ❛r♠❛③❡♥❛r ♦s ❞❛❞♦s ❞✐s♣♦♥í✈❡✐s s♦❜r❡ ❛ ❡✈♦❧✉çã♦ ❞❛s ❡s♣é❝✐❡s✐♥✈❡st✐❣❛❞❛s✳ ❊♠ s❡❣✉✐❞❛✱ s❡rã♦ ❛♣r❡s❡♥t❛❞♦s ❛❧❣✉♥s ♣r♦❜❧❡♠❛s ❣❡r❛❞♦s ♣❡❧❛ ♦❝♦rrê♥❝✐❛ ❞❡❞❛❞♦s ✐♥❝♦♠♣❧❡t♦s ❡ ❛♠❜í❣✉♦s✱ ❡ ♦s ❝r✐tér✐♦s ✉t✐❧✐③❛❞♦s ♣❛r❛ s♦❧✉❝✐♦♥❛r ❡ss❡s ♣r♦❜❧❡♠❛s ❡❞❡♠♦str❛r❡♠♦s ❛❧❣✉♥s ❛❧❣♦r✐t♠♦s ❞❡ ❝♦♥str✉çã♦ ❞❡ ár✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s q✉❡ sã♦✿ ❆ ❘❡❣r❛❞❡ ■♥❝❧✉sã♦ ❡ ❊①❝❧✉sã♦✱ ❖ ❆❧❣♦r✐t♠♦ ❞❡ ❲❛❣♥❡r ❡ ❖ ❆❧❣♦r✐t♠♦ ❞❛s ▼é❞✐❛s ✭❯P●▼❆✮✳ ◆♦ ❈❛♣ít✉❧♦ ✸✱ s❡rá ❛♣r❡s❡♥t❛❞❛ ❛ ❡s♣❡❝✐✜❝❛çã♦ ❞♦ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ❇❛s❡❛❞♦ ❡♠❚✐♣♦s ❆❜str❛t♦s ❞❡ ❉❛❞♦s✭●❆❆❉❚✮ ❛♦ ♠❡s♠♦ t❡♠♣♦ ❡♠ q✉❡ s❡✉s t✐♣♦s ❜ás✐❝♦s ❡ ♦♣❡r❛✲ ✶✳✶✳ ❈❖▼P❯❚❆➬➹❖ ❊❱❖▲❯❚■❱❆ ❖❯ ❊❱❖▲❯❈■❖◆➪❘■❆ ✾❞♦r❡s ✈ã♦ s❡♥❞♦ ✐♥st❛♥❝✐❛❞♦s ♣❛r❛ ❝♦♥str✉✐r ár✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s✳ ❆♣ós ❛ ❞❡s❝r✐çã♦ ❞❡ss❛✐♠♣❧❡♠❡♥t❛çã♦✱ s❡rá ❞❡♠♦str❛❞❛ ✉♠❛ ❛♣❧✐❝❛çõ❡s ♣rát✐❝❛ ❞♦ s✐st❡♠❛ ♣r♦♣♦st♦✳ ◆♦ ❝❛♣ít✉❧♦ ✹✱ s❡rá ♠♦str❛❞♦s ♦ s✐st❡♠❛ ♣r♦♣♦st♦ ♣❛r❛ ❝♦♥str✉çã♦ ❞❡ ❆r✈♦r❡ ❋✐❧♦✲❣❡♥ét✐❝❛✭❙❊❚❆❳✮ ❡ ♦s r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❞♦ s✐st❡♠❛ ❞❡s❡♥✈♦❧✈✐❞♦ ♣❛r❛ ❝♦♥str✉✐rár✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s ♣❡❧❛ ❛♥á❧✐s❡ ❞❡ ♣❡q✉❡♥♦s ❡ ❣r❛♥❞❡s ✈♦❧✉♠❡s ❞❡ ❞❛❞♦s ❝♦♠ ❡ s❡♠❛♠❜✐❣✉✐❞❛❞❡s ❡ ❝♦♠♣❛r❛❞♦s ❝♦♠ ♦✉tr♦s ❛❧❣♦r✐t♠♦s ♣❛r❛ ❝♦♥str✉çã♦ ❞❡ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛❜❛s❡❛❞♦ ❡♠ ♠ét♦❞♦s ❞❡ ✐♥t❡❧✐❣❡♥❝✐❛ ❛rt✐✜❝✐❛❧✳ ◆♦ ❝❛♣ít✉❧♦ ✺✱ s❡rá ♠♦str❛❞❛ ❛ ❝♦♥❝❧✉sã♦ ❞❡ss❛ ❞✐ss❡rt❛çã♦ ❡ ❛s ♣❡rs♣❡❝t✐✈❛s ❞❡ tr❛✲❜❛❧❤♦s ❢✉t✉r♦s ❛ s❡r❡♠ ❞❡s❡♥✈♦❧✈✐❞♦s✳ ❈❛♣ít✉❧♦ ✷ ➪r✈♦r❡ ❋✐❧♦❣❡♥ét✐❝❛✷✳✶ ■♥tr♦❞✉çã♦ P❛r❛ q✉❡ ♦ ❡st✉❞♦ ❞♦s s❡r❡s ✈✐✈♦s ❢♦ss❡ ♠❛✐s ♣r❡❝✐s♦✱ ❝✐❡♥t✐st❛s ❛❞♦t❛r❛♠ ✉♠❛ s✐st❡♠át✐❝❛❞❡ ❝❧❛ss✐✜❝❛çã♦ q✉❡ s❡ ❜❛s❡✐❛ ♥❛ s❡♠❡❧❤❛♥ç❛ ❡♥tr❡ ❛s ❡s♣é❝✐❡s✱ ♦♥❞❡ ❝❛❞❛ r❡✐♥♦ s❡ ❞✐✈✐❞❡ ❡♠✜❧♦s✱ ❝❛❞❛ ✜❧♦ s❡ ❞✐✈✐❞❡ ❡♠ ❝❧❛ss❡s✱ ❝❛❞❛ ❝❧❛ss❡ ❡♠ ♦r❞❡♥s ❡ ❛ss✐♠ ♣♦r ❞✐❛♥t❡✱ ❛té ❛t✐♥❣✐r ✶ ♦ ♥í✈❡❧ ✧❡s♣é❝✐❡✧ ✳ ❊s♣é❝✐❡s ❝♦♠ ❝❛r❛❝t❡ríst✐❝❛s ❝♦♠✉♥s ❢♦r♠❛♠ ✉♠ ❣ê♥❡r♦✳ ●ê♥❡r♦s ❝♦♠❝❛r❛❝t❡ríst✐❝❛s ❡♠ ❝♦♠✉♠ ❢♦r♠❛♠ ✉♠❛ ❢❛♠í❧✐❛✳ ❆s ❢❛♠í❧✐❛s s❡ ❛❣r✉♣❛♠ ❡♠ ♦r❞❡♥s ❡ ❡st❛s❡♠ ❝❧❛ss❡s✳ ❆s ❝❧❛ss❡s s❡ ❛❣r✉♣❛♠ ❡♠ ✜❧♦s✳ ❆ r❡✉♥✐ã♦ ❞❡ ✜❧♦s ❢♦r♠❛ ♦ r❡✐♥♦✳ ❊♠ ❛❧❣✉♥s❝❛s♦s ❡①✐st❡♠ s✉❜❞✐✈✐sõ❡s ❝♦♠♦✿ s✉❜✜❧♦✱ s✉❜❝❧❛ss❡✱ s✉❜❣ê♥❡r♦✱ ❡t❝✳ ❖s ♣r✐♥❝✐♣❛✐s r❡✐♥♦s sã♦✿ ❘❡✐♥♦ ❆♥✐♠❛❧✐❛✱ ❘❡✐♥♦ P❧❛♥t❛❡✱ ❘❡✐♥♦ ❋✉♥❣✐✱ ❘❡✐♥♦ Pr♦t✐st❛ ❡ ❘❡✐♥♦ ▼♦♥❡r❛✳ ❍á♥♦✈♦s r❡✐♥♦s s❡♥❞♦ ❝r✐❛❞♦s✳ ❊♣✐❞❡♥❞r✉♠ ❢♦✐ ✉♠ ❞♦s ♣r✐♠❡✐r♦s ❣ê♥❡r♦s ❞❡ ♦rq✉í❞❡❛s tr♦♣✐❝❛✐s ❛ s❡r❡♠ ♣✉❜❧✐❝❛❞♦s✳❊❧❡ ❢♦✐ ❝r✐❛❞♦ ♣❡❧♦ ♣r✐♠❡✐r♦ s✐st❡♠❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❞♦s s❡r❡s ✈✐✈♦s✱ ▲✐♥❡✉ ✭✶✼✺✾✮✱ ❝♦♠❛ ❞❡s❝r✐çã♦ ❞❛ ❡s♣é❝✐❡ ❊♣✐❞❡♥❞r✉♠ ♥♦❞♦s✉♠ ▲✳ ❝♦❧❡t❛❞❛ ❡♠ P♦rt♦ ❘✐❝♦✱ ❤♦❥❡ ❝♦♥❤❡❝✐❞❛❝♦♠♦ ❇r❛ss❛✈♦❧❛ ♥♦❞♦s❛✳ ❖ ❊♣✐❞❡♥❞r✉♠ ♥♦❝t✉r♥✉♠ ❏❛❝q✉✐♥ ❢♦✐ s❡❧❡❝✐♦♥❛❞♦ ♣♦st❡r✐♦r✲♠❡♥t❡ ❝♦♠♦ s✉❛ ♥♦✈❛ ❡s♣é❝✐❡ ♣❛r❛ ❡✈✐t❛r ❛ ❛❧t❡r❛çã♦ ❞♦ ♥♦♠❡ ❞❡ ♠❛✐s ❞❡ ♠✐❧ ❡s♣é❝✐❡s q✉❛♥❞♦ ❛ ❛♥t✐❣❛ ♣❧❛♥t❛ t✐♣♦ ❞❡ ❊♣✐❞❡♥❞r✉♠ ❢♦✐ r❡♠♦✈✐❞❛ ♣❛r❛ ♦ ❣ê♥❡r♦ ❇r❛ss❛✈♦❧❛✳ ❖♥♦♠❡ ❞♦ ❣ê♥❡r♦ é ✉♠❛ r❡❢❡rê♥❝✐❛ ❛♦ ❢❛t♦ ❞❛s ♣r✐♠❡✐r❛s ♦rq✉í❞❡❛s ❛tr✐❜✉í❞❛s ❛ ❡st❡ ❣ê♥❡r♦ ✷ s❡r❡♠ ❡♣í✜t❛s ✳❙✉❛ ❝✐r❝✉♥s❝r✐çã♦ ❡①❛t❛✱ ♦✉ s❡❥❛✱ q✉❡ ❡s♣é❝✐❡s ♣❡rt❡♥❝❡♠ ❛ ❡st❡ ❣ê♥❡r♦ ❡ q✉❛✐s ❞❡✈❡♠ s❡r ❛tr✐❜✉í❞❛s ❛ ♦✉tr♦s é ❞✐s❝✉tí✈❡❧✳ ❊♣✐❞❡♥❞r✉♠ ❥á ✐♥❝❧✉✐✉ ♠✉✐t❛s ❡s♣é❝✐❡s ❤♦❥❡ ♣❡rt❡♥❝❡♥t❡s❛ ♦✉tr♦s ❣ê♥❡r♦s✱ ❝♦♠♦ ❊♥❝②❝❧✐❛ ❡ Pr♦st❤❡❝❤❡❛✳ ◗✉❛♥❞♦ ▲✐♥❡✉ ♣r♦♣ôs ❛ ❝r✐❛çã♦ ❞♦ ❣ê♥❡r♦❊♣✐❞❡♥❞r✉♠✱ ❤❛✈✐❛ s♦♠❡♥t❡ ♦✐t♦ ❣ê♥❡r♦s ❞❡ ♦rq✉í❞❡❛s✳ ❆ss✐♠✱ ♣r❛t✐❝❛♠❡♥t❡ t♦❞❛s ❛s♣r✐♠❡✐r❛s ♦rq✉í❞❡❛s ❡♣í✜t❛s ❞❡s❝♦❜❡rt❛s ❡r❛♠ ❝❧❛ss✐✜❝❛❞❛s ❝♦♠♦ ❊♣✐❞❡♥❞r✉♠✳ ❆♦ ❧♦♥❣♦ ✶ ❉❡♥♦♠✐♥❛✲s❡ ❡s♣é❝✐❡ ♦ ❝♦♥❥✉♥t♦ ❞❡ ✐♥❞✐✈í❞✉♦s q✉❡✱ ♣♦r t❡r❡♠ ❛ ♠❡s♠❛ ❝♦♥st✐t✉✐çã♦ ❣❡♥ét✐❝❛ ♣♦ss❛♠ ❣❡r❛r ❞❡s❝❡♥❞ê♥❝✐❛ s❡♠❡❧❤❛♥t❡✳✷ sã♦ ❛q✉❡❧❡s q✉❡ ✈✐✈❡♠ s♦❜r❡ ✈❡❣❡t❛✐s✳ P♦❞❡♠ s❡r ❛♥✐♠❛✐s q✉❡ ✈✐✈❡♠ ❛ss♦❝✐❛❞♦s à ✉♠ ✈❡❣❡t❛❧ ♦✉♣❧❛♥t❛s q✉❡ ✈✐✈❡♠ s♦❜r❡ ♦✉tr❛ ♣❧❛♥t❛✱ ♥❡st❡ ❝❛s♦✱ sã♦ ❝❤❛♠❛❞❛s ❞❡ ❡♣í✜t❛s✳ ✷✳✷✳ ❉❊❙❈❘■➬➹❖ ❋❖❘▼❆▲ ❉❆ ➪❘❱❖❘❊ ❋■▲❖●❊◆➱❚■❈❆ ✶✶❞♦s ❛♥♦s✱ ❝♦♥❢♦r♠❡ ♦✉tr❛s ❡s♣é❝✐❡s ❢♦r❛♠ s❡♥❞♦ ❞❡s❝♦❜❡rt❛s ❡ ❛❣r✉♣❛❞❛s✱ ♠✉✐t♦s ♦✉tr♦s❣r❛♥❞❡s ❣ê♥❡r♦s ❢♦r❛♠ ❝r✐❛❞♦s ❛ ♣❛rt✐r ❞❡❧❡✳ ❙✉❛ ❞❡❧✐♠✐t❛çã♦ ❢♦✐ s❡ ❡str❡✐t❛♥❞♦ ♠❛s✱♥♦ ❡♥t❛♥t♦✱ ♦ ❣ê♥❡r♦ s❡♠♣r❡ t❡♠ s❡r✈✐❞♦ ♣❛r❛ ❛❣r✉♣❛r ❡s♣é❝✐❡s ❞❡ ▲❛❡❧✐✐♥❛❡ q✉❡ ♥ã♦❡♥❝❛✐①❛♠ ❜❡♠ ❡♠ ♦✉tr♦s ❣ê♥❡r♦s✳ ■ss♦ ❛❝♦♥t❡❝❡ t❛♠❜é♠ ❝♦♠ ❞✐✈❡rs♦s ♦✉tr♦s ❣ê♥❡r♦s ❞❛❢❛♠í❧✐❛ ❖r❝❤✐❞❛❝❡❛❡✱ ♦s ♣r✐♥❝✐♣❛✐s ❞❡♥tr❡ ❡❧❡s sã♦ P❧❡✉r♦t❤❛❧❧✐s✱ ✬❇✉❧❜♦♣❤②❧❧✉♠✱ ❖♥❝✐❞✐✉♠✱▼❛①✐❧❧❛r✐❛ ❡ ❉❡♥❞r♦❜✐✉♠✳ ❚♦❞♦s ❡st❡s ❣ê♥❡r♦s sã♦ ❣r❛♥❞❡s ❡ ♣♦r ❞❡♠❛✐s ❤❡t❡r♦❣ê♥❡♦s✳ ❆ ❧♦♥❣♦ ❞❛s ❞é❝❛❞❛s✱ ❛ ❝❧❛ss✐✜❝❛çã♦ ❞❡ ❊♣✐❞❡♥❞r✉♠ ♣❛ss♦✉ ♣♦r ❞✐✈❡rs❛s ♠✉❞❛♥ç❛s❝♦♥❢♦r♠❡ ♦s ❝♦♥❝❡✐t♦s ❛❞♦t❛❞♦s ♣❡❧♦s t❛①♦♥♦♠✐st❛s✳ ❍♦✉✈❡ é♣♦❝❛ ❡♠ q✉❡ s❡ ♣r❡❢❡r✐❛❞✐✈✐❞✐r ♠❛✐s ❡ ❡♥tã♦ ♦ ❣ê♥❡r♦ ❞✐♠✐♥✉í❛ ❞❡ t❛♠❛♥❤♦✱ ❞❡♣♦✐s s✉r❣✐❛♠ ♥♦✈♦s t❛①♦♥♦♠✐st❛s❝♦♠ ♦✉tr♦s ❝♦♥❝❡✐t♦s ❡ ❥✉♥t❛✈❛♠ t✉❞♦ ♥♦✈❛♠❡♥t❡✳ ◆♦ ❡♥t❛♥t♦✱ ❛ ♠✉❞❛♥ç❛ ❞♦ ❝♦♥❝❡✐t♦❞❡ ❝❧❛ss✐✜❝❛çã♦ ❞❛s ❡s♣é❝✐❡s ❤♦❥❡ ♣❛ss❛ ♣♦r ❣r❛♥❞❡s ♠✉❞❛♥ç❛s ❝♦♠ ❛ ✐♥❝♦r♣♦r❛çã♦ ❞♦s❝♦♥❝❡✐t♦s ♦r✐✉♥❞♦s ❞❛ ✜❧♦❣❡♥✐❛✱ ♦✉ s❡❥❛✱ ❛❝r❡s❝❡♥t❛♥❞♦ ✐♥❢♦r♠❛çõ❡s s♦❜r❡ ❛ ❡✈♦❧✉çã♦ ❞❛s❡s♣é❝✐❡s ❛ ♣❛rt✐r ❞❡ ♣❡sq✉✐s❛s ❣❡♥ét✐❝❛s✳ ❆t✉❛❧♠❡♥t❡✱ ♠✉✐t♦s t❛①♦♥♦♠✐st❛s ❝♦♥s✐❞❡r❛♠ q✉❡❛ ♠❛✐♦r ❞✐✈✐sã♦ ♥♦ ♥í✈❡❧ ❞❡ ❣ê♥❡r♦ é ♠❛✐s ❞✐❞át✐❝❛ q✉❡ ❞✐✈✐sõ❡s ❡♠ ♥í✈❡✐s ❞❡ s✉❜❣ê♥❡r♦ ♦✉ s❡çõ❡s✳ ❈♦♠ ✐ss♦✱ ❛ ♣r✐♠❡✐r❛ r❡♣r❡s❡♥t❛çã♦ ❞✐❛❣r❛♠át✐❝❛ ❞❛ ❤✐stór✐❛ ♦✉ ❣❡♥❡❛❧♦❣✐❛ ❞❡ s❡r❡s✈✐✈♦s ❢♦✐ ♣♦ss✐✈❡❧♠❡♥t❡ ❛ ❞❡ ▲❛♠❛r❦✱ ❡♠ ✶✽✵✾✳ ❯♠ ❞✐❛❣r❛♠❛ ❞❡ss❡ ❣ê♥❡r♦ é ♦ ú♥✐❝♦ ❞❡s❡✲♥❤♦ q✉❡ s❡ ❡♥❝♦♥tr❛ ♥❛ ❖r✐❣❡♠ ❞❛s ❊s♣é❝✐❡s ✭✶✽✺✾✮ ❞❡ ❉❛r✇✐♥✳ ❊♠ ✶✽✻✻✱ ❊✳ ❍❛❡❝❦❡❧ ❢❡③♦ q✉❡ ❉❛r✇✐♥ ♥ã♦ r❡❛❧✐③❛r❛✿ ✉♠❛ t❡♥t❛t✐✈❛ ❞❡ ✜❧♦❣❡♥✐❛ ❣❡r❛❧✱ ❛❜r❛♥❣❡♥❞♦ t♦❞♦s ♦s ❣r✉♣♦s❞❡ s❡r❡s ✈✐✈♦s✱ ♠✐❝r♦♦r❣❛♥✐s♠♦s✱ ♣❧❛♥t❛s ❡ ❛♥✐♠❛✐s❀ r❡♣r❡s❡♥t♦✉✲❛ ♣♦r ♦✉tr♦ ❞✐❛❣r❛♠❛❞❡♥♦♠✐♥❛❞♦ ❞❡ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛✳ P❛r❛ ❬✸✽❪✱ ✜❧♦❣❡♥✐❛ ♣♦❞❡ s❡r ♠❡❧❤♦r ❡①♣❧✐❝❛❞❛ ❝♦♠♦ s❡♥❞♦ ✉♠❛ ❡str✉t✉r❛ ❡♠ ❢♦r♠❛❞❡ ár✈♦r❡ q✉❡ ❞❡✜♥❡ ❝❡rt♦s r❡❧❛❝✐♦♥❛♠❡♥t♦s ❛♥❝❡str❛✐s ❡♥tr❡ ❝♦♥❥✉♥t♦s r❡❧❛❝✐♦♥❛❞♦s ❞❡♦❜❥❡t♦s ✭♣r♦t❡í♥❛s✱ ❡s♣é❝✐❡s✱ ❡t❝✳✮✳ ❖ ♥ó ♥❛ ❜❛s❡ ❞❛ ár✈♦r❡✱ ❞❡♥♦♠✐♥❛❞♦ r❛✐③✱ r❡♣r❡s❡♥t❛♦ ❛♥❝❡str❛❧ ❡♠ ❝♦♠✉♠ ❛ t♦❞♦s ♦s ♦❜❥❡t♦s r❡❧❛❝✐♦♥❛❞♦s✳ ✷✳✷ ❉❡s❝r✐çã♦ ❋♦r♠❛❧ ❞❛ ➪r✈♦r❡ ❋✐❧♦❣❡♥ét✐❝❛ ❯♠❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ é ✉♠❛ ❡str✉t✉r❛ ❋ ❂ ✭❳✱ Υ, Φ, Γ ✮✱ ♦♥❞❡✿❳ é ✉♠ ❝♦♥❥✉♥t♦ ✜♥✐t♦ ❞❡ ❡s♣é❝✐❡s ❞✐❢❡r❡♥t❡ ❞♦ ❝♦♥❥✉♥t♦ ✈❛③✐♦✱ é ✉♠ ❝♦♥❥✉♥t♦ ✜♥✐t♦ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❛♣r❡s❡♥t❛❞❛s ♣❡❧♦s ❡❧❡♠❡♥t♦s ❞❡ ❳✱ é ✉♠❛ r❡❧❛çã♦ ❞❡ ♦r❞❡♠ ♣❛r❝✐❛❧ s♦❜r❡ ♦s ❡❧❡♠❡♥t♦s ❞♦ ❝♦♥❥✉♥t♦ ❳✱ t❛❧ q✉❡✿■ ✲ ∀ ① ∈ ❳✱ ① Φ ①❀ ✭r❡✢❡①✐✈❛✮1 2 ∈122112 Φ x Φ x■■ ✲ ∀ x ✱ x ❳✱ s❡ x ❡ x ❡♥tã♦ x ❂ x ❀ ✭❛♥t✐✲s✐♠étr✐❝❛✮1 2 ∈ 1 Φ x2 2 Φ x1 ■■■ ✲ ∀ x ✱ x ❳✱ s❡ x ✱ ❡♥tã♦ x ❀ ✭s✐♠❡tr✐❝❛✮12 3 ∈ 1 Φ x2 2 Φ x3 1 Φ x3■❱ ✲ ∀ x ✱ x ✱ x ❳✱ s❡ x ❡ x ✱ ❡♥tã♦ x ✳ ✭tr❛♥s✐t✐✈❛✮ ✷✳✷✳ ❉❊❙❈❘■➬➹❖ ❋❖❘▼❆▲ ❉❆ ➪❘❱❖❘❊ ❋■▲❖●❊◆➱❚■❈❆ ✶✷ k = (x k,1 , x k,2 )❆ q✉❛❧ é r❡♣r❡s❡♥t❛❞❛ ♣❡❧♦ ❣rá✜❝♦ G = (X,Φ ✮comcadaarco❛ ❞❡ G r♦t✉❧❛❞♦ ♣❡❧❛ s❡qüê♥❝✐❛ ❞♦s ❡❧❡♠❡♥t♦ ❞♦ ❝♦♥❥✉♥t♦ k = xk, 2xk, 1 ✿ ❳ → P✭ Υ ✮✱ ❛ q✉❛❧ é r❡♣r❡s❡♥t❛❞❛ ♣❡❧♦ ❣rá✜❝♦ ● ❂ ✭❳✱ Φ ✮ ❢♦r♠❛❞♦ ♣❡❧♦ k = (x k,1 k,2 k,1 x k,2 ∈ X(∩ k,2 ) = X k,2 ) C❛r❝♦ a ✱ x ✮ t❛❧ q✉❡ ∀x ❈ ❣❡r♦✉ (x ❣❡r♦✉ P12(x k,1 ) = {x|x ∈ X(x k,1 |x ∈ Xex ❣❡r♦✉ x) t❛❧ q✉❡ x ❣❡r♦✉ x ❞❡ ● r♦t✉❧❛❞♦ ♣❡❧❛ k k,2 k,1 s❡q✉ê♥❝✐❛ ❞♦s ❡❧❡♠❡♥t♦ ❞♦ ❝♦♥❥✉♥t♦ Σ ❂ Γ ✭ x ✮ ✲ Γ ✭ x ✮✳❊①❡♠♣❧♦✱ s❡❥❛ ❋ ❂ ✭❳✱ ❨✱ ❣❡r♦✉✱ Γ ✮✱ ♦♥❞❡✿1234567 ❳ ❂ {esp ✱ esp ✱ esp ✱ esp ✱ esp ✱ esp ✱ esp ⑥❀1231 ′ ′ ′ ′′232Υ ❂ {c ✱ c ✱ c ✱ c ✱ c ✱ c ✱ c ⑥❀ esp11❣❡r♦✉ esp ❀ esp12 ❣❡r♦✉ esp ❀ esp13❣❡r♦✉ esp ❀ esp33 ❣❡r♦✉ esp ❀ esp343 ❣❡r♦✉ esp ❀5 esp5 ❣❡r♦✉ esp ❀5 esp5 ❣❡r♦✉ esp ❀6 esp5 ❣❡r♦✉ esp ❀7 esp❣❡r♦✉ esp ❀1123 Γ✭esp ✮ ❂ c ✱ c ✱ c ❀21 ′23 Γ✭esp ✮ ❂ c ✱ c ✱ c ❀312 ′3 Γ✭esp ✮ ❂ c ✱ c ✱ c ❀41 ′ ′′23 Γ✭esp ✮ ❂ c ✱ c ✱ c ❀ ′ ′ Γ5123✭esp ✮ ❂ c ✱ c ✱ c ❀ ′ ′ ′ Γ6123✭esp ✮ ❂ c ✱ c ✱ c ❀ ′ ′ Γ7123✭esp ✮ ❂ c ✱ c ✱ c ❀ ♣♦❞❡♥❞♦ s❡r r❡♣r❡s❡♥t❛❞❛ ❣r❛✜❝❛♠❡♥t❡ ♣❡❧❛ ❋✐❣✉r❛✷✳✶ ✳❆ ❛♥á❧✐s❡ ❞❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ❞❛ ❋✐❣✉r❛ ✷✳✶ ♣♦❞❡ s❡r ❛ss✐♠ ❞❡s❝r✐t❛✿ ✐♥✐❝✐❛❧♠❡♥t❡ ❛11232 ❡s♣é❝✐❡ esp ❛♣r❡s❡♥t❛✈❛ ❛s ❝❛r❛❝t❡ríst✐❝❛s c ✱ c ❡ c ❛ q✉❛❧ ❞❡✉ ♦r✐❣❡♠ ❛s ❡s♣é❝✐❡s esp ❡31 ′ ′231233 espq✉❡ ❛♣r❡s❡♥t❛♠ ❛s ❝❛r❛❝t❡ríst✐❝❛s c ✱ c ✱ c ❡ c ✱ c ✱ c ✳ ❆ ❡s♣é❝✐❡ esp ❞❡✉ ♦r✐❣❡♠451 ′2 , c❛s ❡s♣é❝✐❡s esp ❡ esp q✉❡ ❝♦♥t❡♠ ❛s ❝❛r❛❝t❡ríst✐❝❛s c312 ′ ′3567 ec , c , c ✱ ❝ ✳ ❆ ❡s♣é❝✐❡ esp ❞❡✉ ♦r✐❣❡♠ ❛s ❡s♣é❝✐❡s esp ❡ esp ❝♦♥t❡♥❞♦ ❛s ❝❛r❛❝t❡✲1 ′ ′ ′ ′ ′23123 ríst✐❝❛s c ✱ c ✱ c ❡ c ✱ c ✱ c ✳❚♦❞❛s ❛s ❝❛r❛❝t❡ríst✐❝❛s ♣r✐♥❝✐♣❛✐s ❛♥❛❧✐s❛❞❛s ♣❡❧♦s ♣r♦❝❡ss♦s ✜❧♦❣❡♥ét✐❝♦s ❝♦rr❡s♣♦♥✲ ❞❡♠ às ♠♦❞✐✜❝❛çõ❡s ♦❝♦rr✐❞❛s ❡♠ q✉❛❧q✉❡r ❡①♣r❡ssã♦ ❢❡♥♦tí♣✐❝❛ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❡s♣é❝✐❡❝♦♠ ❜❛s❡ ❣❡♥ét✐❝❛✳ ❈♦♠♦ ❡①❡♠♣❧♦✱ ❛ ❡①♣r❡ssã♦ ❢❡♥♦tí♣✐❝❛ ✧❛s❛✧✐♥s❡r✐❞❛ ♥♦ ❝♦♥❥✉♥t♦ ❞❡✐♥s❡t♦s ❤♦❧♦♠❡t❛❜ó❧✐❝♦s ❞❛ ❋✐❣✉r❛ ✷✳✷ ❛♣r❡s❡♥t❛ ❛s ❝❛r❛❝t❡ríst✐❝❛s✿ ❛s❛s ♣♦st❡r✐♦r❡s s❡♠❡✲ ✸ ❧❤❛♥t❡s às ❛s❛s ❛♥t❡r✐♦r❡s ✭❆✱❇✮ ❡ ❤❛❧t❡r ✭❈✱❉✮✳ ✸ ❍❛❧t❡r✲ ❈❛r❛❝t❡ríst✐❝❛ q✉❡ ❝♦rr❡s♣♦♥❞❡ à ♣r❡s❡♥ç❛ só ❞❛s ❛s❛s ♣♦st❡r✐♦r❡s✳ ✷✳✷✳ ❉❊❙❈❘■➬➹❖ ❋❖❘▼❆▲ ❉❆ ➪❘❱❖❘❊ ❋■▲❖●❊◆➱❚■❈❆ ✶✸❋✐❣✉r❛ ✷✳✶✿ ❊①❡♠♣❧♦ ❞❡ ➪r✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ❋✐❣✉r❛ ✷✳✷✿ ■♥s❡t♦s ❞❛ ❢❛♠í❧✐❛ ❤♦❧♦♠❡t❛❜ó❧✐❝♦s✳❏á ♥♦s ❝❛s♦s ❞♦s ✈ír✉s✱ ❛s ❡①♣r❡ssõ❡s ❢❡♥♦tí♣✐❝❛s ✧♣r❡s❡♥ç❛ ❞❡ ❡♥✈♦❧tór✐♦✧✱ ✧❛✉sê♥❝✐❛ ❞❡ ❡♥✈♦❧tór✐♦✧✱ ✜t❛ ✧❞✉♣❧❛✧✱ ✜t❛ ✧s✐♠♣❧❡s✧✱ ❡ ♥❛t✉r❡③❛ ❞♦ á❝✐❞♦ ♥✉❝❧é✐❝♦ ✈✐r❛❧ é ✧❘◆❆✧✴♦✉✧❉◆❆✧sã♦ ❛♥❛❧✐s❛❞❛s ♥❛ ❝♦♥str✉çã♦ ❞❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ❞❡ss❛ ❡s♣é❝✐❡✳ ❆ ❋✐❣✉r❛ ✷✳✸❛♣r❡s❡♥t❛ ❝❡rt♦s ✈ír✉s q✉❡ ❛♣r❡s❡♥t❛♠ ❡st❛s ❝❛r❛❝t❡ríst✐❝❛s✳ ❋✐❣✉r❛ ✷✳✸✿ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❡ ❝❡rt♦s ✈ír✉s✳ ✷✳✸✳ ▼❆❚❘■❩ P❖▲❆❘■❩❆❉❆✶✹ ❖s ♣r♦❝❡ss♦s ❞❛ ♥❛t✉r❡③❛ r❡s♣♦♥sá✈❡✐s ♣❡❧❛ ❛❧t❡r❛çã♦ ❞❛s ❡①♣r❡ssõ❡s ❢❡♥♦tí♣✐❝❛s ❞❛s❡s♣é❝✐❡s ❞✉r❛♥t❡ ❛ s✉❛ ❡✈♦❧✉çã♦ r❡❝❡❜❡♠ ♦ ♥♦♠❡ ❞❡ ♣r♦❝❡ss♦s ✜❧♦❣❡♥ét✐❝♦s ❢✉♥❞❛♠❡♥t❛✐s❬✶✵❪ ❡ ❝♦♠♣r❡❡♥❞❡♠ ♦s ♣r♦❝❡ss♦s ❞❡✿ ◆❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ❛s r❡❧❛çõ❡s ❞❡ ♣❛r❡♥t❡s❝♦ ❡♥tr❡ ❛s ❡s♣é❝✐❡s sã♦✿ ❡ esp j ♦♥❞❡ esp i ❣❡r♦✉ esp j ✱♦✉ ✈✐❝❡✲✈❡rs❛ ✭♣♦r ❡①❡♠♣❧♦✱ ♥❛ ❋✐❣✉r❛ ✷✳✶ ✱ esp1 é ❛♥❝❡str❛❧ ❞✐r❡t♦ ❞❡ esp2 ❡ esp3 ✮❀ ❡ esp j ♦♥❞❡ ❛ ❡s♣é❝✐❡ esp i❣❡r♦✉ ❛ ❡s♣é❝✐❡s esp i+1 ✱ ❛ ❡s♣é❝✐❡ esp i+1 ❣❡r♦✉ ❛ ❡s♣é❝✐❡s esp i+2 ✱ ❡ ❛ss✐♠ ♣♦r ❞✐❛♥t❡❛té ❛ ❡s♣❡❝✐❡ esp j−1 ❣❡r❛r ❛ ❡s♣❡❝✐❡ esp j ♦✉ ✈✐❝❡✲✈❡rs❛ ✭❝♦♠♦ ♥❛ ❋✐❣✉r❛ ✷✳✶✱ esp1 é ❛♥❝❡str❛❧ ✐♥❞✐r❡t♦ ❞❡ esp4 ✮❀ ❡ esp j q✉❡ ♥ã♦ ❛♣r❡s❡♥t❛♠✉♠❛ r❡❧❛çã♦ ❛♥❝❡str❛❧ ❞✐r❡t♦ ♦✉ ✐♥❞✐r❡t❛ ❡♥tr❡ s✐✱ ♠❛s ♣♦ss✉❡♠ ✉♠❛ ❡s♣é❝✐❡ esp k q✉❡ é ❛♥❝❡str❛❧ ❞✐r❡t♦ ♦✉ ✐♥❞✐r❡t♦ ❛ ❛♠❜♦s ✭♣♦r ❡①❡♠♣❧♦✱ ♥❛ ❋✐❣✉r❛ ✷✳✶ ✱ esp2 ❡ esp3 t❡♠ ❝♦♠♦ ❛♥❝❡str❛❧ ❝♦♠✉♠ esp1 ✮✳ ✷✳✸ ▼❛tr✐③ P♦❧❛r✐③❛❞❛ ◆♦r♠❛❧♠❡♥t❡✱ ❛s ✐♥❢♦r♠❛çõ❡s s♦❜r❡ ❛ ❡✈♦❧✉çã♦ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❛♣r❡s❡♥t❛❞❛s ♣❡❧❛s ❡s✲♣é❝✐❡s ✐♥✈❡st✐❣❛❞❛s sã♦ ❛r♠❛③❡♥❛❞❛s ❡♠ ✉♠❛ ♠❛tr✐③ ♣♦❧❛r✐③❛❞❛ q✉❡ r❡❧❛❝✐♦♥❛ ❛ ❡s♣é❝✐❡ à sér✐❡ ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛ ✭❙❚P✮ ❞❡ ❝❛❞❛ ✉♠❛ ❞❛s ❡①♣r❡ssõ❡s ❢❡♥♦tí♣✐❝❛s ❛♣r❡s❡♥✲t❛❞❛s ♣❡❧❛s ❡s♣é❝✐❡s ✐♥✈❡st✐❣❛❞❛s ❬✷❪ ❬✶✵❪ ❬✸✵❪ ❬✸❪✳ ❊ss❛ sér✐❡ ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛ ✐♥❢♦r♠❛ ❛ ♦r❞❡♠ ❝r♦♥♦❧ó❣✐❝❛ ♥❛ q✉❛❧ ❛s ❝❛r❛❝✲ t❡ríst✐❝❛s ❞❡ss❛ ❡①♣r❡ssã♦ ❢❡♥♦tí♣✐❝❛ ♦❝♦rr❡r❛♠ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✳ ❈♦♠♦ ❡①❡♠♣❧♦✱ s❡❥❛♠Θ ✱ǫ ❡ ς ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ✉♠❛ ♠❡s♠❛ ❡①♣r❡ssã♦ ❢❡♥♦tí♣✐❝❛✳ ❉❡♣❡♥❞❡♥❞♦ ❞❛ ♦r❞❡♠ ♥❛ q✉❛❧ ❡ss❛s ❝❛r❛❝t❡ríst✐❝❛s s✉r❣✐r❛♠ ❛♦ ❧♦♥❣♦ ❞❛ ❡✈♦❧✉çã♦ ❞❛s ❡s♣é❝✐❡s ♥❛ ❚❡rr❛✱ ♣♦❞❡✲s❡t❡r ❛s s❡❣✉✐♥t❡s sér✐❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛✱ ✈✐❞❡ ❋✐❣✉r❛ ✷✳✹✳ ❆s sér✐❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛ ❧✐♥❡❛r❡s ❞♦ t✐♣♦✱ ❛ ❝❛r❛❝t❡ríst✐❝❛ Θ ❣❡r♦✉ ❛❝❛r❛❝t❡ríst✐❝❛ ǫ ❡ ❛ ❝❛r❛❝t❡ríst✐❝❛ ǫ ❣❡r♦✉ ❛ ❝❛r❛❝t❡ríst✐❝❛ ς✱ ♠♦str❛ ✉♠❛ r❡❧❛çã♦ ❛♥❝❡str❛❧ ✷✳✸✳ ▼❆❚❘■❩ P❖▲❆❘■❩❆❉❆✶✺ ❋✐❣✉r❛ ✷✳✹✿ ❙ér✐❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛s✳❞✐r❡t♦ ❡♥tr❡ ❛s ❡s♣é❝✐❡s q✉❡ ❛♣r❡s❡♥t❛♠ ❛ ❝❛r❛❝t❡ríst✐❝❛ Θ ❡ ǫ✱ ✉♠❛ r❡❧❛çã♦ ❛♥❝❡str❛❧ ❞✐r❡t♦❡♥tr❡ ❛s ❡s♣é❝✐❡s q✉❡ ❛♣r❡s❡♥t❛♠ ❛ ❝❛r❛❝t❡ríst✐❝❛ ǫ ❡ ς✱ ❡ ✉♠❛ r❡❧❛çã♦ ❛♥❝❡str❛❧ ✐♥❞✐r❡t♦❡♥tr❡ ❛s ❡s♣é❝✐❡s q✉❡ ❛♣r❡s❡♥t❛♠ ❛ ❝❛r❛❝t❡ríst✐❝❛ Θ ❡ ς✳ ❊♥q✉❛♥t♦ q✉❡ ❛s sér✐❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛s ♣❛r❛❧❡❧❛s ❞♦ t✐♣♦✱ ❛ ❝❛r❛❝t❡ríst✐❝❛Θ ❣❡r♦✉ ❛ ❝❛r❛❝t❡ríst✐❝❛ ǫ ❡ ❛ ❝❛r❛❝t❡ríst✐❝❛ ς✱ ❡①♣r❡ss❛♠ ✉♠❛ r❡❧❛çã♦ ❛♥❝❡str❛❧ ❞✐r❡t♦ ❡♥tr❡❛s ❡s♣é❝✐❡s q✉❡ ❛♣r❡s❡♥t❛♠ ❛ ❝❛r❛❝t❡ríst✐❝❛ Θ ❡ ǫ✱ ✉♠❛ r❡❧❛çã♦ ❛♥❝❡str❛❧ ❞✐r❡t♦ ❡♥tr❡ ❛s❡s♣é❝✐❡s q✉❡ ❛♣r❡s❡♥t❛♠ ❛ ❝❛r❛❝t❡ríst✐❝❛ Θ ❡ ς✱ ❡ ✉♠❛ r❡❧❛çã♦ ❛♥❝❡str❛❧ ❝♦♠✉♠ ❡♥tr❡ ❛s❡s♣é❝✐❡s q✉❡ ❛♣r❡s❡♥t❛♠ ❛ ❝❛r❛❝t❡ríst✐❝❛ ǫ ❡ ς✳ P♦ré♠✱ ♣❛r❛ q✉❡ ✉♠❛ sér✐❡ ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛ ♣♦ss❛ s❡r ❛r♠❛③❡♥❛❞❛ ❡♠✉♠❛ ♠❛tr✐③✱ s❡ ❢❛③ ♥❡❝❡ssár✐♦ ♣r✐♠❡✐r♦ ❝♦❞✐✜❝á✲❧❛ ❞❡ ♠♦❞♦ q✉❡✱ ❞❡ ♣♦ss❡ ❞❡ss❡ ❝ó❞✐❣♦✱ q✉❛❧q✉❡r ♣❡ss♦❛ ♣♦ss❛ r❡❝♦♥st✐t✉✐r ❛ sér✐❡ ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛ ❞❡ ✉♠❛ ❡①♣r❡ssã♦❢❡♥♦tí♣✐❝❛ ❛ ♣❛rt✐r ❞❛s ✐♥❢♦r♠❛çõ❡s ❝♦♥t✐❞❛s ♥❡ss❛ ♠❛tr✐③✳ ❙❡ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ✉♠❛ ❡①♣r❡ssã♦ ❢❡♥♦tí♣✐❝❛✱ ❡♠ ✉♠❛ sér✐❡ ❞❡ tr❛♥s❢♦r♠❛çã♦♣♦❧❛r✐③❛❞❛✱ sã♦ tr❛♥s♠✐t✐❞❛s ❞❡ ♠❛♥❡✐r❛ ❧✐♥❡❛r ❝♦♠♦ ♥❛s sér✐❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ■✱ ■■✱ ■❱✱❱✱ ❱■■ ❡ ❱■■■ ♠♦str❛❞❛s ❛♥t❡r✐♦r♠❡♥t❡✱ ❛ s✉❛ ❝♦❞✐✜❝❛çã♦ s❡rá ♣r♦❝❡ss❛❞❛ ♣❡❧❛ ❡♥✉♠❡r❛çã♦❞❛s ❝❛r❛❝t❡ríst✐❝❛s ♦❝♦rr✐❞❛s ♥❡ss❛ ❡①♣r❡ssã♦ ❢❡♥♦tí♣✐❝❛ ❡♠ ♦r❞❡♠ ❝r♦♥♦❧ó❣✐❝❛ ❝♦♠♦ ♥❛❚❛❜❡❧❛ ✷✳✶✳ P♦ré♠✱ s❡ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ✉♠❛ ❡①♣r❡ssã♦ ❢❡♥♦tí♣✐❝❛ sã♦ tr❛♥s♠✐t✐❞❛s ❞❡ ♠❛♥❡✐r❛♣♦❧❛r✐③❛❞❛ ♣❛r❛❧❡❧❛✱ ❝♦♠♦ ♥❛s sér✐❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ■■■✱ ❱■ ❡ ■❳ ♠♦str❛❞❛s ❛♥t❡r✐✲♦r♠❡♥t❡✱ ❡♥tã♦ ❞❡✈❡✲s❡ ♣r✐♠❡✐r♦ ❞❡❝♦♠♣♦r ❝❛❞❛ sér✐❡ ❞❡ss❡ t✐♣♦✱ ❡♠ t❛♥t❛s sér✐❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛ ❧✐♥❡❛r❡s q✉❛♥t♦ ❢♦r ♦ ♥ú♠❡r♦ ❞❡ ❝❛r❛❝t❡ríst✐❝❛s ♦❝♦rr✐❞❛s s✐♠✉❧✲ ✷✳✹✳ ▼❆❚❘■❩ ❈❆❘❆❈❚❊❘❮❙❚■❈❆✶✻ ❚❛❜❡❧❛ ✷✳✶✿ ❈♦❞✐✜❝❛çã♦ ❡♠ ✉♠❛ ♠❛tr✐③ ♣♦❧❛r✐③❛❞❛ ❞❡ sér✐❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛s❧✐♥❡❛r✳ → ǫ → ς → ς → ǫ → θ → ς → ς → θ → θ → ǫ ς → ǫ → θ P❊s♣é❝✐❡✭θ) ✵ ✵ ✶ ✷ ✶ ✷ ❊s♣é❝✐❡✭ǫ) ✶ ✷ ✵ ✵ ✷ ✶ ❊s♣é❝✐❡✭ς) ✷ ✶ ✷ ✶ ✵ ✵ t❛♥❡❛♠❡♥t❡ ♥❛ sér✐❡ ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛ ♣❛r❛❧❡❧❛ ❡♠ ❞❡❝♦♠♣♦s✐çã♦✳ ❙❡❣✉♥❞♦✱❝♦❞✐✜❝❛♠✲s❡ s❡♣❛r❛❞❛♠❡♥t❡ ❝❛❞❛ ✉♠❛ ❞❡ss❛s sér✐❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛ ❧✐♥❡❛r❡s✈✐❞❡ ❚❛❜❡❧❛ ✷✳✷✳❚❛❜❡❧❛ ✷✳✷✿ ❈♦❞✐✜❝❛çã♦ ❡♠ ✉♠❛ ♠❛tr✐③ ♣♦❧❛r✐③❛❞❛ ❞❡ sér✐❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛s✈✐❛ ❞❡❝♦♠♣♦s✐çã♦✳ ❉❡❝♦♠♣♦s✐çã♦ θ → ǫ θ → ς ǫ → θ ǫ → ς ς → θ ς → ǫ ❊s♣é❝✐❡✭θ) ✵ ✵ ✶ ✵ ✶ ✵❊s♣é❝✐❡✭ǫ) ✶ ✵ ✵ ✵ ✵ ✶ ❊s♣é❝✐❡✭ς) ✵ ✶ ✵ ✶ ✵ ✵ ❆ ✉t✐❧✐③❛çã♦ ❞❛ ♠❛tr✐③ ♣♦❧❛r✐③❛❞❛ r❡str✐♥❣❡ ♦ t✐♣♦ ❞❡ ❞❛❞♦s ❛♥❛❧✐s❛❞♦s ❛♦s ❞❛❞♦s ❞❡♥❛t✉r❡③❛ ♠♦r❢♦❧ó❣✐❝❛✱ ❞❡✐①❛♥❞♦ ❞❡ ❧❛❞♦ ❞❛❞♦s ❞❡ ♦✉tr❛s ♥❛t✉r❡③❛s✱ t❛✐s ❝♦♠♦ ❣❡♥ét✐❝❛✱❝✐t♦❧ó❣✐❝❛✱ ❡t❝✳✱ q✉❡ sã♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ ♠❡❧❤♦r❛r ❛ ❝♦♠♣r❡❡♥sã♦ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❡✈♦❧✉çã♦❞❛s ❡s♣é❝✐❡s ❬✷✽❪✳ ✷✳✹ ▼❛tr✐③ ❈❛r❛❝t❡ríst✐❝❛ ❆❧❣✉♠❛s ✈❡③❡s ❛s ✐♥❢♦r♠❛çõ❡s s♦❜r❡ ❛ ❡✈♦❧✉çã♦ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❛♣r❡s❡♥t❛❞❛s ♣♦r ✉♠❝♦♥❥✉♥t♦ ❞❡ ❡s♣é❝✐❡s sã♦ r❡♣r❡s❡♥t❛❞❛s ❡♠ ✉♠❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛✳ ❯♠❛ ♠❛tr✐③ ❝❛✲ r❛❝t❡ríst✐❝❛ é ✉♠❛ ✈❡rsã♦ s✐♠♣❧✐✜❝❛❞❛ ❞❛ ♠❛tr✐③ ♣♦❧❛r✐③❛❞❛ q✉❡ r❡❧❛❝✐♦♥❛ ❝❛❞❛ ❡s♣é❝✐❡ às❝❛r❛❝t❡ríst✐❝❛s t❡r♠✐♥❛✐s ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❡s♣é❝✐❡s ✐♥✈❡st✐❣❛❞❛s✳ ❉✐③✲s❡ q✉❡✱ ① é ✉♠❛ ❝❛✲ r❛❝t❡ríst✐❝❛ t❡r♠✐♥❛❧ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❡s♣é❝✐❡s ✐♥✈❡st✐❣❛❞❛s✱ s❡ ♥❡♥❤✉♠❛ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s❛♣r❡s❡♥t❛❞❛s ♣❡❧❛s ❡s♣é❝✐❡s ❞♦ ❝♦♥❥✉♥t♦ ❢♦r❡♠ ❣❡r❛❞❛s ❛ ♣❛rt✐r ❞❡ ①✳ P♦r ❡①❡♠♣❧♦✱ s❡❥❛♠Θ, ω, ǫ, ρ, τ1 ✱ κ, π, α, β, σ ❡ δ ❝❛r❛❝t❡ríst✐❝❛s ❞❛s ❡①♣r❡ssõ❡s ❢❡♥♦tí♣✐❝❛s ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❡s✲234 , esp , esp , esp♣é❝✐❡s esp q✉❡ ♣♦ss✉❡♠ ❛s sér✐❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛ ♠♦str❛❞❛♥❛ ❋✐❣✉r❛ ✷✳✺✳12 ❆ ❡s♣é❝✐❡ esp ❛♣r❡s❡♥t❛ ❛s ❝❛r❛❝t❡ríst✐❝❛s Θ, δ, ρ, α ❡ κ ✱ ❛ ❡s♣é❝✐❡ esp ❛♣r❡s❡♥t❛ ❛s3❝❛r❛❝t❡ríst✐❝❛s ω, δ, ρ, α ❡ κ ❀ ❛ ❡s♣é❝✐❡ esp ❛♣r❡s❡♥t❛ ❛s ❝❛r❛❝t❡ríst✐❝❛s ω, ǫ, τ, α ❡ π❀ ❡ ❛4 ❡s♣é❝✐❡ esp ❛♣r❡s❡♥t❛ ❛s ❝❛r❛❝t❡ríst✐❝❛s ω, ǫ, τ, β ❡ σ ✳ ❆ ❚❛❜❡❧❛ ✷✳✸ ❛♣r❡s❡♥t❛ ❛ ♠❛tr✐③♣♦❧❛r✐③❛❞❛ ♣❛r❛ ❡ss❛s ❡s♣é❝✐❡s✳ ✷✳✹✳ ▼❆❚❘■❩ ❈❆❘❆❈❚❊❘❮❙❚■❈❆✶✼ ❋✐❣✉r❛ ✷✳✺✿ ❙ér✐❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛s✳❚❛❜❡❧❛ ✷✳✸✿ ▼❛tr✐③ ♣♦❧❛r✐③❛❞❛✳ ❉❡❝♦♠♣♦s✐çã♦ θ → ω δ → ǫ ρ → τ α → β κ → π κ → σ1 ❡s♣ ✵ ✵ ✵ ✵ ✵ ✵2 ❡s♣ ✶ ✵ ✵ ✵ ✵ ✵3 ❡s♣ ✶ ✶ ✶ ✵ ✶ ✵4 ❡s♣ ✶ ✶ ✶ ✶ ✵ ✶ ❆ ♣❛rt✐r ❞❛ ❚❛❜❡❧❛ ✷✳✸✱ ❝♦♥stró✐✲s❡ ❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❞❛s ❡s♣é❝✐❡s ✐♥✈❡st✐❣❛❞❛s♥❛ ❚❛❜❡❧❛ ✷✳✹✳ Pr✐♠❡✐r♦ ❝♦❧♦❝❛✲s❡ ♥❛ s❡❣✉♥❞❛ ❧✐♥❤❛ ❡ ♥❛ ♣r✐♠❡✐r❛ ❝♦❧✉♥❛ ❛ ❧❡tr❛ r♦♠❛♥❛1 ♠❛✐ús❝✉❧❛ A ♣❛r❛ r❡♣r❡s❡♥t❛r ❛ ❡s♣é❝✐❡ esp ✱ ♥❛ t❡r❝❡✐r❛ ❧✐♥❤❛ ❡ ♥❛ ♣r✐♠❡✐r❛ ❝♦❧✉♥❛ ❛2❧❡tr❛ r♦♠❛♥❛ ♠❛✐ús❝✉❧❛ B ♣❛r❛ r❡♣r❡s❡♥t❛r ❛ ❡s♣é❝✐❡ esp ✱ ❡ ❛ss✐♠ s✉❝❡ss✐✈❛♠❡♥t❡ ❛té q✉❡✱ t♦❞❛s ❛s ❡s♣é❝✐❡s ❞❛ ❚❛❜❡❧❛ ✷✳✸ ❡st❡❥❛♠ r❡♣r❡s❡♥t❛❞♦s ♣♦r ✉♠❛ ❧❡tr❛ r♦♠❛♥❛ ♠❛✐ús✲❝✉❧❛✳ ❊♠ s❡❣✉✐❞❛✱ ❝♦❧♦❝❛✲s❡ ♥❛ ♣r✐♠❡✐r❛ ❧✐♥❤❛ ❡ ♥❛ s❡❣✉♥❞❛ ❝♦❧✉♥❛ ♦ ♥ú♠❡r♦ ✶✭✉♠✮ ♣❛r❛ r❡♣r❡s❡♥t❛r ❛ ❝❛r❛❝t❡ríst✐❝❛ t❡r♠✐♥❛❧ ω✱ ♥❛ ♣r✐♠❡✐r❛ ❧✐♥❤❛ ❡ ♥❛ t❡r❝❡✐r❛ ❝♦❧✉♥❛ ♦ ♥✉♠❡r♦✷✭❞♦✐s✮ ♣❛r❛ r❡♣r❡s❡♥t❛r ❛ ❝❛r❛❝t❡ríst✐❝❛ t❡r♠✐♥❛❧ ǫ✱ ❡ ❛ss✐♠ s✉❝❡ss✐✈❛♠❡♥t❡ ❛té q✉❡✱ t♦❞❛s❛s ❝❛r❛❝t❡ríst✐❝❛s t❡r♠✐♥❛✐s ❞❛s sér✐❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦❧❛r✐③❛❞❛s ❞❛ ❚❛❜❡❧❛ ✷✳✸ ❡st❡❥❛♠ r❡♣r❡s❡♥t❛❞♦s ♣♦r ✉♠ ♥ú♠❡r♦✳ ❖s ❡❧❡♠❡♥t♦s ❞❡ss❛ ♠❛tr✐③✱ ❞❛s i ❧✐♥❤❛s ❡ j ❝♦❧✉♥❛s✱ ❝♦♠ ✷✭❞♦✐s✮ ≤ i ≤ ♥ú♠❡r♦ ❞❡ ❧✐♥❤❛s❞❛ ♠❛tr✐③ ♣♦❧❛r✐③❛❞❛ ❛♥❛❧✐s❛❞❛ ❡ ✷✭❞♦✐s✮ ≤ ❥ ≤ ♥ú♠❡r♦ ❞❡ ❝♦❧✉♥❛s ❞❛ ♠❛tr✐③ ♣♦❧❛r✐③❛❞❛ i,j i+1,j❛♥❛❧✐s❛❞❛✱ sã♦ r❡♣r❡s❡♥t❛❞♦s ♣♦r c ❡ t❡♠ ♦ ♠❡s♠♦ ✈❛❧♦r ❞♦ ❡❧❡♠❡♥t♦ p ❞❛ ♠❛tr✐③♣♦❧❛r✐③❛❞❛ ❛♥❛❧✐s❛❞❛ ❬✸✺❪✳ ✷✳✺✳ ▼❆❚❘■❩ ❙■▼■▲❆❘■❉❆❉❊✶✽ ❚❛❜❡❧❛ ✷✳✹✿ ▼❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛✳ ✶ ✷ ✸ ✹ ✺ ✻ ❆ ✵ ✵ ✵ ✵ ✵ ✵❇ ✶ ✵ ✵ ✵ ✵ ✵ ❈ ✶ ✶ ✶ ✵ ✶ ✵❉ ✶ ✶ ✶ ✶ ✵ ✶ ✷✳✺ ▼❛tr✐③ ❙✐♠✐❧❛r✐❞❛❞❡ ❆ ♠❛tr✐③ s✐♠✐❧❛r✐❞❛❞❡ é ✉♠❛ ♠❛tr✐③ q✉❛❞r❛❞❛ ❞❡ ❞✐♠❡♥sã♦ ♥ q✉❡ r❡❧❛❝✐♦♥❛ ❞✉❛s ❡s♣é❝✐❡s❛ ✉♠❛ ♠❡❞✐❞❛ ❞❡ s✐♠✐❧❛r✐❞❛❞❡✱ ♦♥❞❡ n é ✐❣✉❛❧ ❛♦ ♥ú♠❡r♦ ❞❡ ❡s♣é❝✐❡s ✐♥✈❡st✐❣❛❞❛s ♠❛✐s✶✭✉♠✮✳ ❖s ❡❧❡♠❡♥t♦s ❞❡ss❛ ♠❛tr✐③ sã♦ ♦❜t✐❞♦s ❛ ♣❛rt✐r ❞❛ ❛♥á❧✐s❡ ❞♦s ❡❧❡♠❡♥t♦s c u,v ❞❛ ♠❛tr✐③❝❛r❛❝t❡ríst✐❝❛ ❡ sã♦ r❡♣r❡s❡♥t❛❞♦s ♣♦r s i,j ✳ ❖s ❡❧❡♠❡♥t♦s ❞❛ ♣r✐♠❡✐r❛ ❧✐♥❤❛ ❡ ❝♦❧✉♥❛ ❝♦♥tê♠✉♠❛ ❧❡tr❛ r♦♠❛♥❛ ♠❛✐ús❝✉❧❛ q✉❡ ❝♦rr❡s♣♦♥❞❡ ❛♦ ♥♦♠❡ ❞❛s ❡s♣é❝✐❡s ✐♥✈❡st✐❣❛❞❛s✳ ❖ ✈❛❧♦r ❞♦ ❡❧❡♠❡♥t♦ s i,j é ✐❣✉❛❧ ❛♦ ♥ú♠❡r♦ ❞❡ ❞❛❞♦s c i,k ❂ c j,k ✱ ❝♦♠ ✷ ≤ ✐✱❥ ≤ ♥ú♠❡r♦❞❡ ❧✐♥❤❛s ❞❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❛♥❛❧✐s❛❞❛s ❡ ✶ ≤ ❦ ≤ ♥ú♠❡r♦ ❞❡ ❝♦❧✉♥❛s ❞❛ ♠❛tr✐③❝❛r❛❝t❡ríst✐❝❛ ❛♥❛❧✐s❛❞❛s✳ P♦r ❡①❡♠♣❧♦✱ ♦ ✈❛❧♦r ❞♦s ❡❧❡♠❡♥t♦s ❞❛ s❡❣✉♥❞❛ ❧✐♥❤❛ ❞❛ ♠❛tr✐③ s✐♠✐❧❛r✐❞❛❞❡ ❞❛ ❚❛❜❡❧❛✷✳✺ ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞❛ t❛❜❡❧❛ ✷✳✹✱ é ♦ s❡❣✉✐♥t❡✿ s2 ,2 = (c2 ,1 = c2 ,1 ) + (c2 ,2 = c2 ,2 ) + (c2 ,3 = c2 ,3 ) + (c2 ,4 = c2 ,4 ) + (c2 ,5 = c2 ,5 ) + (c2 ,6 = c2 ,6 ) ❂ |(0 = 0)| + |(0 = 0)| + |(0 = 0)| + |(0 = 0)| + |(0 = 0)| + |(0 = 0)|❂ ✻ s2 ,3 = (c2 ,1 = c3 ,1 ) + (c2 ,2 = c3 ,2 ) + (c2 ,3 = c3 ,3 ) + (c2 ,4 = c3 ,4 ) + (c2 ,5 = c3 ,5 ) + (c2 ,6 = c3 ,6 ) ❂ ✭✵❂✶✮ ✰ |(0 = 0)| + |(0 = 0)| + |(0 = 0)| + |(0 = 0)| + |(0 = 0)|❂ ✺ s2 ,4 = (c 2 ,1 = c 4 ,1 ) + (c 2 ,2 = c 4 ,2 ) + (c 2 ,3 = c 4 ,3 ) + (c 2 ,4 = c 4 ,4 ) + (c 2 ,5 = c 4 ,5 ) + (c 2 ,6 = c 4 ,6 ) ❂ ✭✵❂✶✮ ✰ ✭✵❂✶✮ ✰ ✭✵❂✶✮ ✰ |(0 = 0)| + (0 = 1) + |(0 = 0)|❂ ✷ s2 ,5 = (c 2 ,1 = c 5 ,1 ) + (c 2 ,2 = c 5 ,2 ) + (c 2 ,3 = c 5 ,3 ) + (c 2 ,4 = c 5 ,4 ) + (c 2 ,5 = c 5 ,5 ) + (c 2 ,6 = c 5 ,6 ) ❂ ✭✵❂✶✮ ✰ ✭✵❂✶✮ ✰ ✭✵❂✶✮ ✰ ✭✵❂✶✮ ✰ |(0 = 0)| + (0 = 1)❂ ✶ ✷✳✻ ▼❛tr✐③ ❉✐stâ♥❝✐❛ ❆ ♠❛tr✐③ ❞✐stâ♥❝✐❛ é ✉♠❛ ♠❛tr✐③ q✉❛❞r❛❞❛ ❞❡ ❞✐♠❡♥sã♦ ♥ q✉❡ r❡❧❛❝✐♦♥❛ ❞✉❛s ❡s♣é❝✐❡s ❛✉♠❛ ♠❡❞✐❞❛ ❞❡ ❞✐stâ♥❝✐❛✱ ♦♥❞❡ ♥ é ✐❣✉❛❧ ❛♦ ♥ú♠❡r♦ ❞❡ ❡s♣é❝✐❡s ✐♥✈❡st✐❣❛❞❛s ♠❛✐s ✶✭✉♠❛✮✳ ✷✳✻✳ ▼❆❚❘■❩ ❉■❙❚➶◆❈■❆✶✾ ❚❛❜❡❧❛ ✷✳✺✿ ▼❛tr✐③ s✐♠✐❧❛r✐❞❛❞❡✳ ❆ ❇ ❈ ❉ ❆ ✻ ✺ ✷ ✶❇ ✺ ✻ ✸ ✷ ❈ ✷ ✸ ✻ ✸❉ ✶ ✷ ✸ ✻ u,v ❖s ❡❧❡♠❡♥t♦s ❞❡ss❛ ♠❛tr✐③ sã♦ ♦❜t✐❞♦s ❛ ♣❛rt✐r ❞❛ ❛♥á❧✐s❡ ❞♦s ❡❧❡♠❡♥t♦s c ❞❛ ♠❛tr✐③ i,j❝❛r❛❝t❡ríst✐❝❛ ❡ sã♦ r❡♣r❡s❡♥t❛❞♦s ♣♦r d ✳ ❖s ❡❧❡♠❡♥t♦s ❞❛ ♣r✐♠❡✐r❛ ❧✐♥❤❛ ❡ ❝♦❧✉♥❛ ❝♦♥té♠ ✉♠❛ ❧❡tr❛ r♦♠❛♥❛ ♠❛✐ús❝✉❧❛ q✉❡ i,j❝♦rr❡s♣♦♥❞❡ ❛♦ ♥♦♠❡ ❞❛s ❡s♣é❝✐❡s ✐♥✈❡st✐❣❛❞❛s✳ ❖ ✈❛❧♦r ❞♦ ❡❧❡♠❡♥t♦ d é ✐❣✉❛❧ ❛♦ ♥ú♠❡r♦ i,k j,k 6= c❞❡ ❞❛❞♦s c ✱ ❝♦♠ ✷ ≤ ✐✱❥ ≤ ♥ú♠❡r♦ ❞❡ ❧✐♥❤❛s ❞❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❛♥❛❧✐s❛❞❛ ❡✶ ≤ ❦ ≤ ♥ú♠❡r♦ ❞❡ ❝♦❧✉♥❛s ❞❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❛♥❛❧✐s❛❞❛✳ P♦r ❡①❡♠♣❧♦✱ ♦ ✈❛❧♦r ❞♦s❡❧❡♠❡♥t♦s ❞❛ s❡❣✉♥❞❛ ❧✐♥❤❛ ❞❛ ♠❛tr✐③ ❞✐stâ♥❝✐❛ ❞❛ t❛❜❡❧❛ ✷✳✻ ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞❛ t❛❜❡❧❛✷✳✹✱ é ♦ s❡❣✉✐♥t❡✿ d2 ,2 = (c 2 ,1 6= c 2 ,1 )+(c 2 ,2 6= c 2 ,2 )+(c 2 ,3 6= c 2 ,3 )+(c 2 ,4 6= c 2 ,4 )+(c 2 ,5 6= c 2 ,5 )+(c 2 ,6 6= c 2 ,6 ) ❂ ✭✵ ✵✮ ✰ ✭✵ ✵✮ ✰ ✭✵ ✵✮ ✰ ✭✵ ✵✮ ✰ ✭✵ ✵✮ ✰ ✭✵ ✵✮❂ ✵2232323232323 d ,3 = (c ,1 6= c ,1 )+(c ,2 6= c ,2 )+(c ,3 6= c ,3 )+(c ,4 6= c ,4 )+(c ,5 6= c ,5 )+(c ,6 6= c ,6 ) ❂ ✭✵ ✶✮ ✰ ✭✵ ✵✮ ✰ ✭✵ ✵✮ ✰ ✭✵ ✵✮ ✰ ✭✵ ✵✮✰✭✵ ✵✮❂ ✶2242424242424 d ,4 = (c ,1 6= c ,1 )+(c ,2 6= c ,2 )+(c ,3 6= c ,3 )+(c ,4 6= c ,4 )+(c ,5 6= c ,5 )+(c ,6 6= c ,6 ) ❂ ✭✵ ✶✮ ✰ ✭✵ ✶✮ ✰ ✭✵ ✶✮ ✰ ✭✵ ✵✮ ✰ ✭✵ ✶✮✰✭✵ ✵✮❂ ✹2 2 6= c5 2 6= c5 2 6= c5 2 6= c5 2 6= c5 2 6= c5 d ,5 = (c ,1 ,1 )+(c ,2 ,2 )+(c ,3 ,3 )+(c ,4 ,4 )+(c ,5 ,5 )+(c ,6 ,6 ) ❂ ✭✵ ✶✮ ✰ ✭✵ ✶✮ ✰ ✭✵ ✶✮ ✰ ✭✵ ✶✮ ✰ ✭✵ ✵✮✰✭✵ ✶✮❂ ✺ ❚❛❜❡❧❛ ✷✳✻✿ ▼❛tr✐③ ❞✐st❛♥❝✐❛✳ ❆ ❇ ❈ ❉ ❆ ✵ ✶ ✹ ✺❇ ✶ ✵ ✸ ✺ ❈ ✹ ✸ ✵ ✸❉ ✺ ✹ ✸ ✵ ✷✳✼✳ ❆▲●❯◆❙ ❆▲●❖❘■❚▼❖❙ ❉❊ ❈❖◆❙❚❘❯➬➹❖ ❉❊ ➪❘❱❖❘❊❙ ❋■▲❖●❊◆➱❚■❈❆❙ ✷✵ ✷✳✼ ❆❧❣✉♥s ❆❧❣♦r✐t♠♦s ❞❡ ❈♦♥str✉çã♦ ❞❡ ➪r✈♦r❡s ❋✐❧♦✲ ❣❡♥ét✐❝❛s ◆❡st❛ s❡❝çã♦ ✐r❡♠♦s ❛♣r❡s❡♥t❛r três ❛❧❣♦r✐t♠♦s ✉s❛❞♦s ♣❛r❛ ❝r✐❛çã♦ ❞❡ ár✈♦r❡s ✜❧♦❣❡♥ét✐✲❝❛s✳ ✷✳✼✳✶ ❆ ❘❡❣r❛ ❞❡ ■♥❝❧✉sã♦ ❡ ❊①❝❧✉sã♦ ❆ r❡❣r❛ ❞❡ ✐♥❝❧✉sã♦ ❡ ❡①❝❧✉sã♦ é ✉♠ ❛❧❣♦r✐t♠♦ ❞❡ ❝♦♥str✉çã♦ ❞❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ❞❡✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❡s♣é❝✐❡s✱ q✉❡ r❡❝❡❜❡ ❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ss❛s ❡s♣é❝✐❡s ❡ ❞❡✈♦❧✈❡♦ ❝♦♥❥✉♥t♦ ❞❡ t♦❞❛s ❛s ♣♦ssí✈❡✐s ár✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s ❞❡ss❛s ❡s♣é❝✐❡s✳ ❆ s❡❣✉✐r s❡rã♦❛♣r❡s❡♥t❛❞♦s ♦s ♣❛ss♦s ❞❡ss❡ ❛❧❣♦r✐t♠♦ ❬✹✽❪✳ o 1♣❛ss♦ ✲ P❛r❛ ❝❛❞❛ ❝❛r❛❝t❡ríst✐❝❛ t❡r♠✐♥❛❧ ◆ ❝♦♥s✐❞❡r❛❞❛ ♥♦ ❡st✉❞♦✱ s❡rá ❝♦♥str✉í❞❛ ✉♠❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ❆❋✐ ✭❋✐❣✳✷✳✻❛✱ ❜✱ ❝✱ ❞✱ ❡ ❡ ❢✮✱ ❝♦♠ ✶ ≤ i ≤ ♥ú♠❡r♦ ❞❡ ❝❛r❛❝t❡ríst✐❝❛s t❡r♠✐♥❛✐s ❝♦♥s✐❞❡r❛❞❛s❀o 2i♣❛ss♦ ✲ ❈♦♠❜✐♥❡ t♦❞❛s ❛s r❡❧❛çõ❡s ❞❡ ♣❛r❡♥t❡s❝♦s ♣r❡s❡♥t❡s ♥❛s AF ❝♦♥str✉í❞❛s ♥♦ i ♣❛ss♦ ❛♥t❡r✐♦r✱ ❞❡ ♠♦❞♦ q✉❡✱ ❛s r❡❧❛çõ❡s ❞❡ ♣❛r❡♥t❡s❝♦ ♣r❡s❡♥t❡s ♥❛ AF s❡❥❛♠ ♣r❡s❡r✈❛❞❛s j♣❡❧❛ ❛❞✐çã♦ ❞❛s r❡❧❛çõ❡s ❞❡ ♣❛r❡♥t❡s❝♦ ♣r❡s❡♥t❡s ♥❛ AF ❝♦♠ ✐ ❁ ❥ ✭❋✐❣✳✷✳✻❣✮✳❋✐❣✉r❛ ✷✳✻✿ ➪r✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ♣❛r❛ ❛s ❡s♣é❝✐❡s ❞❛ ✜❣✉r❛ ✹✳✻ ♦❜t✐❞❛ ♣❡❧❛ ❛♥á❧✐s❡ ❞❛s❝❛r❛❝t❡ríst✐❝❛s t❡r♠✐♥❛✐s✿ ✶ ✭❛✮✱ ✷✭❜✮✱ ✸✭❝✮✱ ✹✭❞✮✱ ✺✭❡✮ ❡ ✻✭❢✮✳ ❆ ❝♦♠❜✐♥❛çã♦ ❞❡ss❛s ár✈♦r❡sé ♠♦str❛❞❛ ❡♠ ✭❣✮✳ ✷✳✼✳✷ ❖ ❆❧❣♦r✐t♠♦ ❞❡ ❲❛❣♥❡r ❖ ❛❧❣♦r✐t♠♦ ❞❡ ❲❛❣♥❡r✱ é ✉♠ ❛❧❣♦r✐t♠♦ ❝❛♣❛③ ❞❡ ❝♦♥str✉✐r ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ❞❡ ✉♠❝♦♥❥✉♥t♦ ❞❡ ❡s♣é❝✐❡s✱ r❡❝❡❜❡♥❞♦ ❝♦♠♦ ❡♥tr❛❞❛ ❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❞❛ ❡s♣é❝✐❡s ❡ r❡✲ t♦r♥❛ ✉♠❛ ❞❛s ár✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s ♣♦ssí✈❡✐s ♣❛r❛ ❡st❛ ❡s♣é❝✐❡s✳ ◆❡ss❡ s❡♥t✐❞♦✱ ✐r❡♠♦s❞❡♠♦♥str❛r ♦s ♣❛ss♦s ❞❡ss❡ ❛❧❣♦r✐t♠♦ s❡❣✉♥❞♦ ❬✷❪ ❡ ❬✹✽❪✳ o 1♣❛ss♦ ✲ ❊s♣❡❝✐✜❝❛r ❛ ❡s♣é❝✐❡ r❛✐③❀ ✷✳✼✳ ❆▲●❯◆❙ ❆▲●❖❘■❚▼❖❙ ❉❊ ❈❖◆❙❚❘❯➬➹❖ ❉❊ ➪❘❱❖❘❊❙ ❋■▲❖●❊◆➱❚■❈❆❙ ✷✶ o 2♣❛ss♦ ✲ ❈♦♥str✉✐r ❛ ♠❛tr✐③ ❞✐stâ♥❝✐❛ ♣❛r❛ ❛s ❡s♣é❝✐❡s ❞❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❢♦r✲ ♥❡❝✐❞❛❀ o 3♣❛ss♦ ✲ ❙❡❧❡❝✐♦♥❛r ❛ ❡s♣é❝✐❡ q✉❡ t✐✈❡r ❛ ♠❡♥♦r ❞✐stâ♥❝✐❛ ♣❛r❛ ❛ ❡s♣é❝✐❡ r❛✐③✳ ❊st❛ s❡rá ❛ ❡s♣é❝✐❡ s❡❧❡❝✐♦♥❛❞❛❀o 4♣❛ss♦ ✲ ❈r✐❛r ✉♠ r❛♠♦ ❧✐❣❛♥❞♦ ❛ ❡s♣é❝✐❡ s❡❧❡❝✐♦♥❛❞❛ ❛ ❡s♣é❝✐❡ r❛✐③ ❝♦♠ ❝♦♠♣r✐♠❡♥t♦ ✐❣✉❛❧ à ❞✐stâ♥❝✐❛ ❡♥tr❡ ❡ss❛s ❞✉❛s ❡s♣é❝✐❡s❀ o 5♣❛ss♦ ✲ ❙❡❧❡❝✐♦♥❛r ❛ ♣ró①✐♠❛ ❡s♣é❝✐❡ q✉❡ ❛♣r❡s❡♥t❡ ❛ ♠❡♥♦r ❞✐stâ♥❝✐❛ ♣❛r❛ ❛ ❡s♣é❝✐❡ r❛✐③✱ ❡st❛ s❡rá ❛ ❛t✉❛❧ ❡s♣é❝✐❡ s❡❧❡❝✐♦♥❛❞❛❀o 6♣❛ss♦ ✲ ❈❛❧❝✉❧❛r ❛ ❞✐stâ♥❝✐❛✱ ✉s❛♥❞♦ ❛ ❡q✉❛çã♦ ❛❜❛✐①♦✱ ❡♥tr❡ ❛ ❡s♣é❝✐❡ s❡❧❡❝✐♦♥❛❞❛ ❡ t♦❞❛s ❛s ♦✉tr❛s ❡s♣é❝✐❡s ❥á s❡❧❡❝✐♦♥❛❞❛s❀ nx , Esp y ) caract x − caract y P P ❉✐st (Esp ❂ x=1 y ✭✷✳✶✮ i i,1 i,n i i,j ♦♥❞❡ caract é ♦ ✈❡t♦r ❝❛r❛❝t❡ríst✐❝❛ ✭c ✒✳✳✳✱ c ✮ ❞❛ ❡s♣é❝✐❡ Esp ✱ c é ♦ ❡❧❡♠❡♥t♦ ❞❛✐ ❧✐♥❤❛ ❡ ❥ ❝♦❧✉♥❛ ❞❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❈ ❞❡ ❞✐♠❡♥sã♦ ♥✳ o 7♣❛ss♦ ✲ ❙❡❧❡❝✐♦♥❛r ❛ ❡s♣é❝✐❡ q✉❡ ❛♣r❡s❡♥t❛ ❛ ♠❡♥♦r ❞✐stâ♥❝✐❛ ♥♦ ♣❛ss♦ ❛♥t❡r✐♦r ❛ ❛t✉❛❧ ❡s♣é❝✐❡ s❡❧❡❝✐♦♥❛❞❛✳ ❊st❛ s❡rá ❛ ❡s♣é❝✐❡ ✐r♠ã s❡❧❡❝✐♦♥❛❞❛❀ o 8♣❛ss♦ ✲ ❈r✐❛r ✉♠ r❛♠♦ ❧✐❣❛♥❞♦ ❛ ❛t✉❛❧ ❡s♣é❝✐❡ s❡❧❡❝✐♦♥❛❞❛ ❙ ❛♦ ♠❡✐♦ ❞♦ r❛♠♦ q✉❡ ❝❤❡❣❛ ♥❛ ❡s♣é❝✐❡ ✐r♠ã s❡❧❡❝✐♦♥❛❞❛ ■ ❞❡ ❝♦♠♣r✐♠❡♥t♦ ❈♦♠♣ ❝❛❧❝✉❧❛❞♦ ♣♦r ❡q✉❛çã♦ ✷✳✼✳✷✭❋✐❣✳ ✷✳✼✳✷❛✱❜✱❝✮❀❈♦♠♣✭❙✱■✮=(Dist (S, I) + Dist (S, Ancestral (I))) − Dist (I, Ancestral (I)) ✭✷✳✷✮2 o 9 A A,1 A,n ♣❛ss♦ ✲ ❉❡t❡r♠✐♥❡ ♦ ✈❡t♦r ❝❛r❛❝t❡ríst✐❝❛ ❞♦ ❛♥❝❡str❛❧ ❝♦♠✉♠ ❆ Caract ❂✭c ✱✳✳✳✱c ✮ ❡♥tr❡ ❛ ❛t✉❛❧ ❡s♣é❝✐❡ s❡❧❡❝✐♦♥❛❞❛ ❙ ❡ ❛ ❡s♣é❝✐❡ ✐r♠ã s❡❧❡❝✐♦♥❛❞❛ ■✱ ♦♥❞❡ c A,i O,i , c I,i x,y ❂ ♠❡♥♦r✭c ✮ ❡ c é ♦ ❡❧❡♠❡♥t♦ ❞❛ ① ❧✐♥❤❛ ❡ ② ❝♦❧✉♥❛ ❞❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛❈❀ o 10♣❛ss♦✲ ❊♥q✉❛♥t♦ ❡①✐st✐r ✉♠❛ ❡s♣é❝✐❡ q✉❡ ❛✐♥❞❛ ♥ã♦ ❢♦✐ s❡❧❡❝✐♦♥❛❞❛ ✈♦❧t❡ ❛♦ ♣❛ss♦ ✺✳ ✷✳✼✳ ❆▲●❯◆❙ ❆▲●❖❘■❚▼❖❙ ❉❊ ❈❖◆❙❚❘❯➬➹❖ ❉❊ ➪❘❱❖❘❊❙ ❋■▲❖●❊◆➱❚■❈❆❙ ✷✷❋✐❣✉r❛ ✷✳✼✿ ➪r✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s ❝♦♥str✉í❞❛s ♣❡❧❛ ♣r✐♠❡✐r❛ ✭❛✮✱ s❡❣✉♥❞❛ ✭❜✮ ❡ t❡r❝❡✐r❛ ✭❝✮❡①❡❝✉çã♦ ❞♦ ✺♦ ♣❛ss♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ❲❛❣♥❡r ♣❛r❛ ❛s ❡s♣é❝✐❡s ❞❛ ✜❣✉r❛ ✹✳✻✳ ✷✳✼✳✸ ❖ ❆❧❣♦r✐t♠♦ ❞❛s ▼é❞✐❛s ✭❯P●▼❆✮ ❖ ❛❧❣♦r✐t♠♦ ❞❛s ♠é❞✐❛s é ✉♠ ❛❧❣♦r✐t♠♦ ❞❡ ❝♦♥str✉çã♦ ❞❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ❞❡ ✉♠ ❝♦♥✲❥✉♥t♦ ❞❡ ❡s♣é❝✐❡s q✉❡ r❡❝❡❜❡ ❛ ♠❛tr✐③ ❞✐stâ♥❝✐❛ ❞❡ss❛s ❡s♣é❝✐❡s ❡ ❞❡✈♦❧✈❡ ✉♠❛ ❞❛s ár✈♦r❡s✜❧♦❣❡♥ét✐❝❛s ♣♦ssí✈❡✐s ♣❛r❛ ❡ss❛s ❡s♣é❝✐❡s✳ ◆♦t❡ q✉❡ ♦s r❛♠♦s ❞❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ❝♦♥s✲ tr✉í❞❛ ♣♦r ❡ss❡ ❛❧❣♦r✐t♠♦✱ ♥ã♦ ❝♦♥té♠ rót✉❧♦s✳ ❆ s❡❣✉✐r s❡rã♦ ❛♣r❡s❡♥t❛❞♦ ♦s ♣❛ss♦s ❞❡st❡❛❧❣♦r✐t♠♦ ❬✸✻❪✳ o 1♣❛ss♦ ✲ ❚♦♠❡ ♦ ♣❛r ❞❡ ❡s♣é❝✐❡s ❝♦♠ ♠❡♥♦r ❞✐stâ♥❝✐❛ ❡♥tr❡ s✐ ❡ ❛❣r✉♣❡✲♦s ♥✉♠❛ s✉♣❡r✲❡s♣é❝✐❡✳ ❊st❡ ♣❛r ❞❡ ❡s♣é❝✐❡s t❡rá ✉♠ ❛♥❝❡str❛❧ ❝♦♠✉♠ ❞✐r❡t♦ ✭❋✐❣✳ ✷✳✽❛ ❇ ❡ ❆✱ ✷✳✽❜ ❈ ❡ ❙✶ ❡ ✷✳✽❝ ❉ ❡ ❙✷✮❀❋✐❣✉r❛ ✷✳✽✿ ➪r✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s ❝♦♥str✉í❞❛s ♣❡❧♦ ♣r✐♠❡✐r❛ ✭❛✮✱ s❡❣✉♥❞❛ ✭❜✮ ❡ t❡r❝❡✐r❛ ✭❝✮❡①❡❝✉çã♦ ❞♦ ✺♦ ♣❛ss♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❛s ♠é❞✐❛s ♣❛r❛ ❛s ❡s♣é❝✐❡s ❞❛ ❚❛❜❡❧❛ ✷✳✼ o 2♣❛ss♦ ✲ ❘❡❝❛❧❝✉❧❡ ❛ ❞✐stâ♥❝✐❛ ❞❡ ❝❛❞❛ ✉♠❛ ❞❛s ❞❡♠❛✐s ❡s♣é❝✐❡s ❙✐ ♣❛r❛ ❛ s✉♣❡r✲ ❡s♣é❝✐❡ r❡❝é♠ ❝r✐❛❞❛ ❝♦♠♦ s❡♥❞♦ ❛ ♠é❞✐❛ ❞❛s ❞✐stâ♥❝✐❛s ❞❡ ❙✐ ♣❛r❛ ❝❛❞❛ ✉♠❛ ❞❛s ❡s♣é❝✐❡s q✉❡ ❝♦♥st✐t✉❡♠ ❛ s✉♣❡r✲❡s♣é❝✐❡ ✭❚❛❜❡❧❛s ✷✳✼ ❡ ✷✳✽✮❀o 3♣❛ss♦ ✲ ❘❡♣✐t❛ ♦s ♣❛ss♦s ✶ ❡ ✷ ❡♥q✉❛♥t♦ ❤♦✉✈❡r ❞✉❛s ♦✉ ♠❛✐s ✭s✉♣❡r✲✮❡s♣é❝✐❡s ♥ã♦ ✷✳✼✳ ❆▲●❯◆❙ ❆▲●❖❘■❚▼❖❙ ❉❊ ❈❖◆❙❚❘❯➬➹❖ ❉❊ ➪❘❱❖❘❊❙ ❋■▲❖●❊◆➱❚■❈❆❙ ✷✸✈✐s✐t❛❞❛s✳❚❛❜❡❧❛ ✷✳✼✿ ▼❛tr✐③ ❞✐stâ♥❝✐❛ ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞♦s ❞❛❞♦s ❞❛ ❚❛❜❡❧❛ ✷✳✻ ❝♦♥s✐❞❡r❛♥❞♦ q✉❡ ❛s❡s♣é❝✐❡s ❆ ❡ ❇ t❡♠ ❛ s✉♣❡r✲❡s♣é❝✐❡ ❙✶ ❝♦♠♦ ❛♥❝❡str❛❧ ❞✐r❡t♦✳ S1 ❈ ❉S1 ✵ ✷✱✺ ✺✱✺ ❈ ✷✱✺ ✵ ✸ ❉ ✺✱✺ ✸ ✵ ❚❛❜❡❧❛ ✷✳✽✿ ▼❛tr✐③ ❞✐stâ♥❝✐❛ ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞♦s ❞❛❞♦s ❞❛ t❛❜❡❧❛ ✷✳✼ ❝♦♥s✐❞❡r❛♥❞♦ q✉❡ ❛s12❡s♣é❝✐❡s S ❡ ❈ t❡♠ ❛ s✉♣❡r✲❡s♣é❝✐❡ S ❝♦♠♦ ❛♥❝❡str❛❧ ❞✐r❡t♦ S2 ❉S2 ✵ ✹✱✷✺ ❉ ✹✱✷✺ ✵ ◆♦ ♣ró①✐♠♦ ❝❛♣ít✉❧♦ s❡rá ❛♣r❡s❡♥t❛❞♦ ♦ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ❜❛s❡❛❞♦ ❡♠ t✐♣♦s ❛❜str❛t♦s❞❡ ❞❛❞♦s ♣❛r❛ ❝♦♥str✉çã♦ ❞❡ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛✳ ❈❛♣ít✉❧♦ ✸ ❖ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ❇❛s❡❛❞♦ ❡♠❚✐♣♦s ❆❜str❛t♦s ❞❡ ❉❛❞♦s ♣❛r❛ ❈♦♥str✉çã♦ ❞❡ ➪r✈♦r❡ ❋✐❧♦❣❡♥ét✐❝❛✸✳✶ ■♥tr♦❞✉çã♦ ❆❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s sã♦ ✉♠❛ ❢❛♠í❧✐❛ ❞❡ ♠♦❞❡❧♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ✐♥s♣✐r❛❞❛s ♥❛ t❡♦r✐❛❞❡ ❡✈♦❧✉çã♦ ❞❛s ❡s♣é❝✐❡s ❞❡ ❈❤❛r❧❡s ❬✶✻❪✳ ❊st❡s ❛❧❣♦r✐t♠♦s ♠♦❞❡❧❛♠ ✉♠❛ s♦❧✉çã♦ ♣❛r❛✉♠ ♣r♦❜❧❡♠❛ ❡s♣❡❝í✜❝♦ ❡♠ ✉♠❛ ❡str✉t✉r❛ ❞❡ ❞❛❞♦s ❞❡♥♦♠✐♥❛❞❛ ❞❡ ❝r♦♠♦ss♦♠♦ ❡ ❛♣❧✐✲❝❛♠ ♦♣❡r❛❞♦r❡s q✉❡ r❡❝♦♠❜✐♥❛♠ ❡ s❡❧❡❝✐♦♥❛♠ ❡ss❛s ❡str✉t✉r❛s ♣r❡s❡r✈❛♥❞♦ ✐♥❢♦r♠❛çõ❡s❝rít✐❝❛s✳ ❖ ♣r✐♠❡✐r♦ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ❢♦✐ ♣r♦♣♦st♦ ♥❛ ❞é❝❛❞❛ ❞❡ s❡t❡♥t❛ ♣♦r ✉♠ ❡st✉❞❛♥t❡❞❡ ❞♦✉t♦r❛❞♦ ❡♠ ❝✐ê♥❝✐❛ ❞❛ ❝♦♠♣✉t❛çã♦ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ▼✐❝❤✐❣❛♥ ❝❤❛♠❛❞♦ ❏♦❤♥ ❍✳❍♦❧❧❛♥❞✳ ❊❧❡ t❡♥t❛✈❛ ❞❡s❡♥✈♦❧✈❡r ✉♠ ♠ét♦❞♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ✈♦❧t❛❞♦ ♣❛r❛ ❛ ❛❜♦r❞❛❣❡♠ ❞❡ ✶ ❢❡♥ô♠❡♥♦s ❣❡r❛❞♦s ♣♦r s✐st❡♠❛s ❛❞❛♣t❛t✐✈♦s ❝♦♠♣❧❡①♦s ❡ ❞✉r❛♥t❡ s❡✉ tr❛❜❛❧❤♦ ♣❡r❝❡❜❡✉❛ ❡✈✐❞❡♥t❡ s❡♠❡❧❤❛♥ç❛ ❡♥tr❡ t❛✐s ❢❡♥ô♠❡♥♦s ❡ ♦ ♣r♦❝❡ss♦ ❞❡ ❡✈♦❧✉çã♦ ❞❛s ❡s♣é❝✐❡s❀ ❛ss✐♠❝♦♠♦ ❛ ✐♥t❡r❛çã♦ ❡♥tr❡ ♦s ❛❣❡♥t❡s ❛❞❛♣t❛t✐✈♦s ❞❡t❡r♠✐♥❛✈❛ ♦ r❡s✉❧t❛❞♦ ❞♦s ❢❡♥ô♠❡♥♦s ♣♦r❡❧❡ ✐♥✈❡st✐❣❛❞♦s✱ ❛ ✐♥t❡r❛çã♦ ❡♥tr❡ ♦s ❢❛t♦r❡s ❛♠❜✐❡♥t❛✐s ❞❡t❡r♠✐♥❛✈❛ ❛ ♣ró①✐♠❛ ♣♦♣✉❧❛çã♦❞❡ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ r❡❣✐ã♦✳ ❋♦✐ ❜❛s❡❛❞♦ ♥❡st❛ ♣❡r❝❡♣çã♦ q✉❡ ❍♦❧❧❛♥❞ ♣r♦♣ôs ✉♠ ♠♦❞❡❧♦❝♦♠♣✉t❛❝✐♦♥❛❧ ♣❛r❛ s✐♠✉❧❛r ♦ ♣r♦❝❡ss♦ ❞❡ ❡✈♦❧✉çã♦ ❞❛s ❡s♣é❝✐❡s✱ ♦s ❛❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s✳ ❆❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s tr❛❜❛❧❤❛♠ s♦❜r❡ ✉♠❛ ♣♦♣✉❧❛çã♦ ❞❡ ♣♦ssí✈❡✐s s♦❧✉çõ❡s ✭❝r♦♠♦ss♦✲♠♦s✮ ♣❛r❛ ✉♠ ♣r♦❜❧❡♠❛✱ ♦s q✉❛✐s sã♦ ♠❡❧❤♦r❛❞♦s ❛tr❛✈és ❞❡ ✈ár✐❛s ✐t❡r❛çõ❡s ❝♦♠ ♦ ✐♥t✉✐t♦❞❡ ❣❡r❛r ✉♠ ❝r♦♠♦ss♦♠♦ s❛t✐s❢❛tór✐♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✳ ❖ ♠❡❝❛♥✐s♠♦ ❞❡ tr❛♥s❢♦r♠❛çã♦❞❡ ✉♠❛ ♣♦♣✉❧❛çã♦ ❡♠ ♦✉tr❛ ♦❜❡❞❡❝❡ ❛♦ ♣r✐♥❝í♣✐♦ ❞❡ s❡❧❡çã♦ ♥❛t✉r❛❧✱ ❞❡s❝r✐t♦ ♣♦r ❉❛r✇✐♥❬✶✻❪✱ s❡❣✉♥❞♦ ♦ q✉❛❧✱ ♥❛ ♥❛t✉r❡③❛✱ ♦s ✐♥❞✐✈í❞✉♦s ♠❛✐s ❛❞❛♣t❛❞♦s tê♠ ♠❛✐♦r ❝❤❛♥❝❡ ❞❡ s♦❜r❡✈✐✈❡r✳✶ ❋❡♥ô♠❡♥♦s ❝✉❥♦s r❡s✉❧t❛❞♦s ❞❡♣❡♥❞❡♠ ❞❛s ✐♥t❡r❛çõ❡s ♥ã♦ ❧✐♥❡❛r❡s ❡♥tr❡ ✈ár✐♦s ❛❣❡♥t❡s ❛❞❛♣t❛t✐✈♦s✳ ✸✳✶✳ ■◆❚❘❖❉❯➬➹❖✷✺ ❖ ❛❧❣♦r✐t♠♦ ❞❡s❝r✐t♦ ♥❛ ❋✐❣✉r❛ ✸✳✶ ❛♣r❡s❡♥t❛ ✉♠ ♣s❡✉❞♦❝ó❞✐❣♦ ♣❛r❛ ❛❧❣♦r✐t♠♦s ❣❡✲♥ét✐❝♦s✳ ❙❡❣✉♥❞♦ ❡st❡ ♣s❡✉❞♦❝ó❞✐❣♦✱ ✉♠ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ t❡♠ ✐♥í❝✐♦ ❝♦♠ ❛ ❣❡r❛çã♦ ❞❛♣♦♣✉❧❛çã♦ ✐♥✐❝✐❛❧ p ❝♦♠♣♦st❛ ♣♦r n ❝r♦♠♦ss♦♠♦s✱ q✉❡ ♣♦❞❡♠ s❡r ❢♦r♥❡❝✐❞♦s ♣❡❧♦ ✉s✉á✲ r✐♦✱ ❣❡r❛❞♦s ❛❧❡❛t♦r✐❛♠❡♥t❡ ♦✉ ❝♦♥str✉í❞♦s ♣♦r ✉♠ ❛❧❣♦r✐t♠♦ ❜❛s❡❛❞♦ ♥♦ ❝♦♥❤❡❝✐♠❡♥t♦❡①✐st❡♥t❡ s♦❜r❡ ♦ ♣r♦❜❧❡♠❛ ❛ s❡r s♦❧✉❝✐♦♥❛❞♦✳ ❊♠ s❡❣✉✐❞❛✱ é ❝❛❧❝✉❧❛❞❛ ❛ ❛❞❛♣t❛çã♦ ❞♦s❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦✱ ♣❛r❛ ✈❡r✐✜❝❛r ❛ q✉❛❧✐❞❛❞❡ ❞❡st❡s ❝r♦♠♦ss♦♠♦s ♣❛r❛ ♦ ♣r♦✲❜❧❡♠❛ ✐♥✈❡st✐❣❛❞♦✳ ❊♥q✉❛♥t♦ ♦ ❝r✐tér✐♦ ❞❡ ♣❛r❛❞❛ ❞❡✜♥✐❞♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ♥ã♦ ❢♦r s❛t✐s❢❡✐t♦✱ ❡♥tã♦ ✉♠♥♦✈♦ ❝✐❝❧♦ ✐♥❝r❡♠❡♥t❛ ♦ ❝♦♥t❛❞♦r ❞❡ ✐t❡r❛çõ❡s t✱ s❡❧❡❝✐♦♥❛ ❝r♦♠♦ss♦♠♦s ♣❛r❛ ❣❡r❛r ❞❡s❝❡♥✲❞❡♥t❡s✱ ❣❡r❛ ❞❡s❝❡♥❞❡♥t❡s✱ ♥❛s❝✐♠❡♥t♦ ❞❡ ❛❧❣✉♥s ❞♦s ❝r♦♠♦ss♦♠♦s ❣❡r❛❞♦s ❡ ♠♦rt❡ ❞♦s❝r♦♠♦ss♦♠♦s ❡①✐st❡♥t❡s ♥❛ ♣♦♣✉❧❛çã♦ ❞❡♣❡♥❞❡♥❞♦ ❞♦ ✈❛❧♦r ❞❛ ❛❞❛♣t❛çã♦ ❞❡ss❡s ❝r♦♠♦s✲ s♦♠♦s ❝♦♥❢♦r♠❡ ❡①♣❧✐❝✐t❛❞♦ ♥♦ ♣s❡✉❞♦❝ó❞✐❣♦ ❞❛ ❋✐❣✉r❛ ✸✳✶✳ ❋✐❣✉r❛ ✸✳✶✿ Ps❡✉❞♦❝ó❞✐❣♦ ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦❆ ♣♦♣✉❧❛çã♦ ❞♦s ❝r♦♠♦ss♦♠♦s ❝❛♣❛③❡s ❞❡ ❣❡r❛r ❞❡s❝❡♥❞❡♥t❡ ˇp é ❝♦♥str✉í❞❛ ♣❡❧❛ s❡❧❡çã♦ ❞❡ h ❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦ p ❜❛s❡❛❞❛ ♥❛ ❛❞❛♣t❛çã♦ ❞♦s ❝r♦♠♦ss♦♠♦s ♦✉ ❡♠ ✉♠❛♠❡❞✐❞❛ r❡❧❛t✐✈❛ ❛♦ ♠ér✐t♦ ❞♦s ❝r♦♠♦ss♦♠♦s ❞❡♥tr♦ ❞❛ ♣♦♣✉❧❛çã♦✳ ❖s ❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦ ˇp sã♦ s✉❜♠❡t✐❞♦s à ❛çã♦ ❞♦s ♦♣❡r❛❞♦r❡s ❣❡♥ét✐❝♦s ❞❡❝r✉③❛♠❡♥t♦ ❡ ♠✉t❛çã♦ ♣❛r❛ ❣❡r❛r ❞❡s❝❡♥❞❡♥t❡s✳ ❊ss❡s ♦♣❡r❛❞♦r❡s ❣❡♥ét✐❝♦s✱ tê♠ ♣♦r♦❜❥❡t✐✈♦✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✿ ❝♦♥str✉✐r ❞♦✐s ♥♦✈♦s ❝r♦♠♦ss♦♠♦s ❛ ♣❛rt✐r ❞❛ ❝♦♠❜✐♥❛çã♦ ❞❛❝❛❞❡✐❛ ❞❡ ❞♦✐s ❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦ ˇp ❡ ❝♦♥str✉✐r ✉♠ ♥♦✈♦ ❝r♦♠♦ss♦♠♦ ❛ ♣❛rt✐r❞❛ ❛❧t❡r❛çã♦ ❞❛ ❝❛❞❡✐❛ ❞❡ ✉♠ ❝r♦♠♦ss♦♠♦ ❞❛ ♣♦♣✉❧❛çã♦ ˇp✳ ❆ ❢r❡q✉ê♥❝✐❛ ❝♦♠ q✉❡ ♦s❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦ ˇp ❣❡r❛♠ ❞❡s❝❡♥❞❡♥t❡s é ❡st❛❜❡❧❡❝✐❞❛ ♣♦r ✉♠❛ ♠❡❞✐❞❛ ❞❡ ♣r♦✲❜❛❜✐❧✐❞❛❞❡ ❛ss♦❝✐❛❞❛ ❛ ❝❛❞❛ ♦♣❡r❛çã♦✱ ♣❛r❛ ❢❛❝✐❧✐t❛r ♦ ❡♥t❡♥❞✐♠❡♥t♦ s❡❣✉❡ ❛ ❋✐❣✉r❛ ✸✳✷ q✉❡ r❡♣r❡s❡♥t❛ ✉♠❛ ❝♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s t❡r♠♦s ❜✐♦❧ó❣✐❝♦s ❝♦♠ ♦s t❡r♠♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s✳ ❆ ♥♦✈❛ ♣♦♣✉❧❛çã♦ p é ❢♦r♠❛❞❛ ♣♦r l ❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦ ˙p ❡ ♣♦r n − l ❝r♦✲♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦ p✳ ❖ ❝r✐tér✐♦ ❛❞♦t❛❞♦ ♣❛r❛ ♦ ♥❛s❝✐♠❡♥t♦ ❞♦s l ❝r♦♠♦ss♦♠♦s ❞❛♣♦♣✉❧❛çã♦ ˙p é ♦ ♠❡s♠♦ ✉s❛❞♦ ♣❛r❛ ❛ ❡s❝♦❧❤❛ ❞♦s ❝r♦♠♦ss♦♠♦s ♣r♦❣❡♥✐t♦r❡s ❞❛ ♣♦♣✉❧❛çã♦ ✸✳✶✳ ■◆❚❘❖❉❯➬➹❖✷✻ ❋✐❣✉r❛ ✸✳✷✿ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ❚❡r♠♦ ❇✐♦❧ó❣✐❝♦ ✲❃ ❚❡r♠♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❬✶✹❪ p✱ ♦ q✉❛❧ é ❛♣❧✐❝❛❞♦ ♥♦ s❡♥t✐❞♦ ✐♥✈❡rs♦ ♣❛r❛ ❞❡t❡r♠✐♥❛r ♦s l ❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦ pq✉❡ ❞❡✈❡♠ ♠♦rr❡r✳ P♦r ✜♠✱ é ❝❛❧❝✉❧❛❞♦ ♦ ✈❛❧♦r ❞❛ ❛❞❛♣t❛çã♦ ❞♦s ❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦ p r❡❝é♠ ❝♦♥str✉í❞❛✳ ❆ ♣♦♣✉❧❛çã♦ é r❡♣r❡s❡♥t❛❞❛ ♣♦r ✉♠ ✈❡t♦r✱ ❞❡ t❛♠❛♥❤♦✜①♦✱ ❞❡ ❝r♦♠♦ss♦♠♦s✱ q✉❡ ♣♦r s✉❛ ✈❡③✱ sã♦ r❡♣r❡s❡♥t❛❞♦s ♣♦r ✈❡t♦r❡s ❜✐♥ár✐♦s ❞❡ t❛♠❛✲♥❤♦ ✜①♦✱ ♦✉ s❡❥❛✱ ✈❡t♦r❡s ❞❡ t❛♠❛♥❤♦ ✜①♦ ❞❡ ❡❧❡♠❡♥t♦s ♣❡rt❡♥❝❡♥t❡s ❛♦ ❝♦♥❥✉♥t♦ {0, 1}✳❍♦❧❧❛♥❞✱ ❝❤❛♠♦✉ ❞❡ ❧♦❝✉ ❛s ♣♦s✐çõ❡s ❞♦ ❝r♦♠♦ss♦♠♦✱ ❛❧❡❧♦ ♦ ✈❛❧♦r q✉❡ ♦❝✉♣❛ ✉♠ ❧♦❝✉ ♥♦❝r♦♠♦ss♦♠♦ ❡ ❣❡♥❡ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❛❧❡❧♦s q✉❡ ♣♦❞❡♠ ♦❝✉♣❛r ✉♠ ❧♦❝✉ ♥♦ ❝r♦♠♦ss♦♠♦✳ ❖ ❛❧❣♦r✐t♠♦ ♣r♦♣♦st♦ ♣♦r ❍♦❧❧❛♥❞ ♣♦ss✉✐ ❛❧❣✉♠❛s ❧✐♠✐t❛çõ❡s ❝♦♠♦ ❛ r❡♣r❡s❡♥t❛çã♦❜✐♥ár✐❛✱ ❝♦♥✈❡r❣ê♥❝✐❛ ♣r❡♠❛t✉r❛✱t❛♠❛♥❤♦ ✜①♦ ❞♦s ❝r♦♠♦ss♦♠♦s ❡ ❞❛s ♣♦♣✉❧❛çõ❡s✳ ❆ q✉❡stã♦ ❞❛ r❡♣r❡s❡♥t❛çã♦ ❜✐♥ár✐❛ ❞♦ ❝r♦♠♦ss♦♠♦ ❛♣r❡s❡♥t❛❞❛ ♣♦r ❍♦❧❧❛♥❞ ♣❛r❡❝❡❧❡✈❛r ❝rít✐❝❛s s♦❜r❡ ❛ ♣ré✲❞❡✜♥✐çã♦ ❞❛ ❡str✉t✉r❛ ❞❡ ❞❛❞♦s ❛ s❡r ❛❞♦t❛❞❛✱ ♥♦ ❝❛s♦ ✈❡t♦r ❞❡ t❛♠❛♥❤♦ ✜①♦✱ q✉❡ ❡stá ♥♦ s❡♥t✐❞♦ ✐♥✈❡rs♦ ❞♦ ♣❡r❝✉rs♦ ♥❛t✉r❛❧ ❛❞♦t❛❞♦ ♣❡❧♦s ❡♥❣❡♥❤❡✐r♦s❞❛ ❝♦♠♣✉t❛çã♦ ♥❛ ❜✉s❝❛ ❞❡ ✉♠❛ s♦❧✉çã♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♣❛r❛ ✉♠ ♣r♦❜❧❡♠❛✱ ♦♥❞❡ ♣r✐♠❡✐r♦ s❡ ❡st✉❞❛ ♦ ♣r♦❜❧❡♠❛ ♣❛r❛ só ❞❡♣♦✐s ❞❡✜♥✐r ❛ ❡str✉t✉r❛ ❞❡ ❞❛❞♦s ✉t✐❧✐③❛❞❛ ♣❛r❛ ♠♦❞❡❧❛r♦s ♦❜❥❡t♦s ❞♦ ❞♦♠í♥✐♦ ❞♦ ♣r♦❜❧❡♠❛ ❬✹✺✱ ✹✻❪✳ ❖✉tr♦ ♣r♦❜❧❡♠❛ r❡❧❛❝✐♦♥❛❞♦ ❝♦♠ ❛ r❡♣r❡s❡♥t❛çã♦ ♣r♦♣♦st❛ ♣♦r ❍♦❧❧❛♥❞ é ❛ ✐♥✢✉ê♥✲❝✐❛ q✉❡ ♦ t❛♠❛♥❤♦ ❞❛ ♣♦♣✉❧❛çã♦ t❡♠ s♦❜r❡ ❛ q✉❛❧✐❞❛❞❡ ❞♦s ❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦ r❡t♦r♥❛❞❛ ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ❬✶✾❪✳ ❖ ♣r✐♠❡✐r♦ r❡❣✐str♦ ❞❡st❡ ♣r♦❜❧❡♠❛ ❢♦✐ r❡♣♦r✲t❛❞♦ ♣♦r ●r❡❢❡♥st❡tt❡ ✭✶✾✽✻✮ ❛♦ ✉s❛r ✉♠ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ♣❛r❛ ❞❡✜♥✐r ♦ ✈❛❧♦r ✐❞❡❛❧ ❞♦s♣❛râ♠❡tr♦s ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ❍♦❧❧❛♥❞ ♥❛ ❛❜♦r❞❛❣❡♠ ❞❡ ✉♠ ♣r♦❜❧❡♠❛✳ ❆♣❡s❛r ❞❡ t♦❞♦ ♦ ❡s❢♦rç♦ ❡♠ ❝♦♥t♦r♥❛r ♦s ♣r♦❜❧❡♠❛s ❛♣♦♥t❛❞♦s ♥♦ tr❛❜❛❧❤♦ ❞❡ ❍♦❧✲❧❛♥❞✱ ♠✉✐t♦s ❞❡st❡s ♣r♦❜❧❡♠❛s ♣❡r♠❛♥❡❝❡♠ ❛té ♦ ❞✐❛ ❞❡ ❤♦❥❡ s❡♠ ✉♠❛ r❡s♣♦st❛✱ ❝♦♠♦ ♦♣r♦❜❧❡♠❛ ❞♦ t❡♠♣♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛✱ ❞❛ ❝♦♥✈❡r❣ê♥❝✐❛ ♣r❡♠❛t✉r❛ ❡ ❞❛ ❡♣✐st❛s✐s✳ ❖ ♣r♦✲❜❧❡♠❛ ❞♦ t❡♠♣♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❡stá r❡❧❛❝✐♦♥❛❞♦ ❛♦ t❡♠♣♦ ❣❛st♦s ♣♦r ❡st❡ ❛❧❣♦r✐t♠♦ ♣❛r❛♣r♦❞✉③✐r r❡s✉❧t❛❞♦s ❞❡ ♠❡❧❤♦r q✉❛❧✐❞❛❞❡ ❞♦ q✉❡ ♦✉tr♦s ♠ét♦❞♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s✳ ❆s s♦❧✉çõ❡s ❛♣r❡s❡♥t❛❞❛s ♣❛r❛ ❡st❡ ♣r♦❜❧❡♠❛ ♦❜❥❡t✐✈❛♠ ❡①♣❧♦r❛r✱ ❛♦ ♠á①✐♠♦✱ ❛s ♣♦ss✐✲❜✐❧✐❞❛❞❡s ❞❡ ♣❛r❛❧❡❧✐③❛r ❡ ❞✐str✐❜✉✐r ❛ ❡①❡❝✉çã♦ ❞♦ ❛❧❣♦r✐t♠♦✱ ❝♦♠♦ ♥♦s ❛❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s ✸✳✷✳ ❚■P❖❙ ❇➪❙■❈❖❙ ❉❖ ●❆❆❉❚✷✼ ♣❛r❛❧❡❧♦s ❬✷✻❪✱ ♥♦s ❛❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s ❞❡ t❡♠♣♦ ❝♦♥tí♥✉♦ ❬✶✺❪ ❡ ♥♦s ❤❛r❞✇❛r❡ ❡✈♦❧✉t✐✈♦s❬✹✸❪✳ ◗✉❛♥❞♦ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❡stá ❛ss♦❝✐❛❞❛ ❛♣❡♥❛s ❛♦ ❝á❧❝✉❧♦ ❞❛ ❛❞❛♣t❛çã♦ ❞♦ ❝r♦✲♠♦ss♦♠♦✱ ✉♠❛ ✈❡rsã♦ s✐♠♣❧✐✜❝❛❞❛ ❞❛ ♠❡s♠❛ ♣♦❞❡ s❡r ❛ s♦❧✉çã♦✱ ❝♦♠♦ ♥♦s ❛❧❣♦r✐t♠♦s❣❡♥ét✐❝♦s ❜❛s❡❛❞♦s ❡♠ té❝♥✐❝❛s ❞❡ r❡❧❛①❛♠❡♥t♦ ❬✹✷❪✳ ❆ ❝♦♥✈❡r❣ê♥❝✐❛ ♣r❡♠❛t✉r❛ ❛❝♦♥t❡❝❡ q✉❛♥❞♦ ❛s ✐♥❢♦r♠❛çõ❡s ❝♦♥t✐❞❛s ♥♦s ❝r♦♠♦ss♦♠♦s♠❛✐s ❛❞❛♣t❛❞♦s ❞❛ ♣♦♣✉❧❛çã♦ ♥ã♦ sã♦ ót✐♠❛s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✱ ♦s q✉❛✐s ♣❛ss❛♠ ❛ ♣r❡❞♦✲♠✐♥❛r ♥❛s ♣ró①✐♠❛s ♣♦♣✉❧❛çõ❡s ❣❡r❛❞❛s ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦✱ ❞✐r❡❝✐♦♥❛♥❞♦ ❛ss✐♠ ❡st❡❛❧❣♦r✐t♠♦ ♣❛r❛ ✉♠❛ ♣♦♣✉❧❛çã♦ ❞❡ ❝r♦♠♦ss♦♠♦s ót✐♠♦s ❧♦❝❛✐s✳ ❆ ❡♣✐st❛s✐s ♦❝♦rr❡ q✉❛♥❞♦ ❛ ❛❞❛♣t❛çã♦ ❞❡ ✉♠ ❝r♦♠♦ss♦♠♦ ❞❡♣❡♥❞❡ ❢♦rt❡♠❡♥t❡ ❞❛ ✐♥✲ t❡r❛çã♦ ❡♥tr❡ ❛s ✐♥❢♦r♠❛çõ❡s ♣r❡s❡♥t❡s ❡♠ s✉❛ r❡♣r❡s❡♥t❛çã♦ ❬✶✾❪✳ ❆ ❞✐✜❝✉❧❞❛❞❡ ❡♠ tr❛t❛r♣r♦❜❧❡♠❛s ❝♦♠ ❡♣✐st❛s✐s ♣♦❞❡ s❡r ❞❡ ♥❛t✉r❡③❛ r❡♣r❡s❡♥t❛❝✐♦♥❛❧ ❡ t❡ór✐❝❛✳ ❉❡♣❡♥❞❡♥❞♦ ❞♦♣r♦❜❧❡♠❛✱ ♦ ❝✉st♦ ♣❛r❛ ❞❡s❡♥✈♦❧✈❡r ✉♠ ♥♦✈♦ ♣r♦❥❡t♦ ❞❡ r❡♣r❡s❡♥t❛çã♦ ♣❛r❛ ♦ ❝r♦♠♦ss♦♠♦❧✐✈r❡ ❞❡ ❡♣✐st❛s✐s ♣♦❞❡ s❡r ♠✉✐t♦ ❣r❛♥❞❡ ❬✷✺❪✳ ❆ss✐♠✱ ✉♠❛ ❛❧t❡r♥❛t✐✈❛ ♣❛r❛ tr❛t❛r ❡st❡♣r♦❜❧❡♠❛ é ❛❞♦t❛r ✉♠❛ ♥♦✈❛ ❢♦r♠❛ ❞❡ r❡♣r❡s❡♥t❛çã♦ ♣❛r❛ ♦ ❝r♦♠♦ss♦♠♦ ❡ ❞❡s❡♥✈♦❧✈❡r♦♣❡r❛❞♦r❡s ❣❡♥ét✐❝♦s ❞❡ ❝r✉③❛♠❡♥t♦ ❡✴♦✉ ♠✉t❛çã♦ ❛❞❡q✉❛❞♦s ❬✶✼❪✳ ❇✉s❝❛♥❞♦ s♦❧✉❝✐♦♥❛r ♦s ♣r♦❜❧❡♠❛s ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ❍♦❧❧❛♥❞ ❢♦✐ ❝r✐❛❞♦ ♦ ●❆❆❉❚ ✭❛❧✲❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ❜❛s❡❛❞♦ ❡♠ t✐♣♦s ❛❜str❛t♦s ❞❡ ❞❛❞♦s✮ ❬✹✺✱ ✹✻❪✱ ❞❡♥♦♠✐♥❛❞♦ ●❆❆❉❚✱❞♦ ✐♥❣❧ês ❣❡♥❡t✐❝ ❛❧❣♦r✐t❤♠ ❜❛s❡❞ ♦♥ ❛❜str❛❝t ❞❛t❛ t②♣❡s✳ ❖s ❛s♣❡❝t♦s q✉❡ ♦ ❛❧❣♦r✐t♠♦ ❝♦♥✲ tr✐❜✉✐ sã♦ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛ ❧✐❜❡r❛çã♦ ❞❡ss❡s ❛❧❣♦r✐t♠♦s ❞❛ r❡str✐çã♦ s♦❜r❡ ❛ r❡♣r❡s❡♥t❛çã♦✜①❛ ❞♦ ❛❧❢❛❜❡t♦ ✵✱✶ ❡ ❞♦ t❛♠❛♥❤♦ ✜①♦ ❞❛ ♣♦♣✉❧❛çã♦✱ ❜❡♠ ❝♦♠♦ ❛ r❡❞✉çã♦ ❞❛s ♦♣❡r❛çõ❡s❣❡♥ét✐❝❛s ❛ s♦♠❡♥t❡ ❞✉❛s✿ ❝r✉③❛♠❡♥t♦ ❡ ♠✉t❛çã♦✳ ❆ ❛❞♦çã♦ ❞❛ ❛❜♦r❞❛❣❡♠ ❞❡ ❚❆❉✱ ♣❛r❛ ❝♦♥str✉çã♦ ❞❡ ❛❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s ♣❡r♠✐t❡✱❡♥tr❡ ♦✉tr❛s ❝♦✐s❛s✱ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠❛ s✐st❡♠át✐❝❛ ❞❡ ❡s♣❡❝✐✜❝❛çã♦ ❞♦ ♠❡s♠♦ ❛♣❛rt✐r ❞♦ ❡st✉❞♦ ❞♦s ❝♦♠♣♦♥❡♥t❡s ❜ás✐❝♦s ❞♦ ♣r♦❜❧❡♠❛✱ ♣❛r❛ ♦ q✉❛❧ ♦ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦❛ s❡r ❞❡s❡♥✈♦❧✈✐❞♦ ♣r♦✈ê ❛ s♦❧✉çã♦✳ ❖✉tr♦ ✐♠♣♦rt❛♥t❡ ❣❛♥❤♦ ♣♦t❡♥❝✐❛❧ ❝♦♠ ❛ ✈✐sã♦ ❛❝✐♠❛ r❡❢❡r✐❞❛ é ❛ ♣♦rt❛❜✐❧✐❞❛❞❡ ❞❛s s♦❧✉çõ❡s ✈✐❛ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦✱ ✉♠❛ ✈❡③ q✉❡ ♦ ♠❡s♠♦❡sq✉❡♠❛ ❞❡ s♦❧✉çã♦ ♣♦❞❡ r❡s♦❧✈❡r ✉♠❛ ❢❛♠í❧✐❛ ❞❡ ♣r♦❜❧❡♠❛s✱ ❞❡♣❡♥❞❡♥❞♦ ❞❛ ♥❛t✉r❡③❛ ❡❞♦ ❛♠❜✐❡♥t❡ ❞♦s ♠❡s♠♦s✳ ◆❡st❡ ❝❛♣ít✉❧♦ s❡rá ❛♣r❡s❡♥t❛❞♦ ♦ ●❆❆❉❚✱ ♦s t✐♣♦s ❛❜str❛t♦s ♠❛♥✐♣✉❧❛❞♦s ♣♦r ❡st❡❛❧❣♦r✐t♠♦✱ ♦s ♦♣❡r❛❞♦r❡s ❣❡♥ét✐❝♦s ✉t✐❧✐③❛❞♦s ♣❛r❛ ♣r♦♠♦✈❡r ❛ ❛❞❛♣t❛çã♦ ❞❛ ♣♦♣✉❧❛çã♦✱♦ ❛♠❜✐❡♥t❡ ❛♦ q✉❛❧ ♦s ❝r♦♠♦ss♦♠♦s ❞♦ ●❆❆❉❚ ❞❡✈❡♠ s❡ ❛❞❛♣t❛r✱ ❛❧é♠ ❞❛ ❞❡✜♥✐çã♦ ❞♦❛❧❣♦r✐t♠♦ ♣r♦♣r✐❛♠❡♥t❡ ❞✐t♦ ❡ ❛ ❡s♣❡❝✐✜❝❛çã♦ ❞♦ ●❆❆❉❚ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✳ ✸✳✷ ❚✐♣♦s ❇ás✐❝♦s ❞♦ ●❆❆❉❚ ◆♦ ●❆❆❉❚ ❬✹✺✱ ✹✻❪✱ ♦s ❝r♦♠♦ss♦♠♦s sã♦ r❡♣r❡s❡♥t❛❞♦s ♣♦r s❡✉ ♠❛t❡r✐❛❧ ❣❡♥ét✐❝♦✱ ♦ q✉❛❧ tê♠ ♥❛s ❜❛s❡s s✉❛s ✉♥✐❞❛❞❡s ❡❧❡♠❡♥t❛r❡s ❞❡ ❢♦r♠❛çã♦✳ ✸✳✷✳ ❚■P❖❙ ❇➪❙■❈❖❙ ❉❖ ●❆❆❉❚✷✽ ❉❡✜♥✐çã♦ ✸✳✷✳✶ ✭❇❛s❡✮ ❯♠❛ ❜❛s❡ B é ♦ ❝♦♥❥✉♥t♦ ❞❡ t♦❞❛s ❛s ✉♥✐❞❛❞❡s ❣❡♥ét✐❝❛s ❡❧❡✲♠❡♥t❛r❡s q✉❡ ♣♦❞❡♠ s❡r ✉s❛❞❛s ♥❛ ❢♦r♠❛çã♦ ❞♦ ♠❛t❡r✐❛❧ ❣❡♥ét✐❝♦ ❞♦s ❝r♦♠♦ss♦♠♦s ❞❡✉♠❛ ♣♦♣✉❧❛çã♦✳ ❖s ❡❧❡♠❡♥t♦s ❞❡ ✉♠❛ ❜❛s❡ s❡ ❛❣r✉♣❛♠ ❡♠ s❡q✉ê♥❝✐❛s ♣❛r❛ ❢♦r♠❛r ❛s ❝❛r❛❝t❡ríst✐❝❛s✭❣❡♥❡s✮ ❞♦s ❝r♦♠♦ss♦♠♦s✱ ❡♥tr❡t❛♥t♦✱ ♥❡♠ t♦❞❛ s❡q✉ê♥❝✐❛ ❞❡ ❜❛s❡s r❡♣r❡s❡♥t❛ ✉♠❛ ❝❛✲ r❛❝t❡ríst✐❝❛ ♣❛r❛ ♦ ❝r♦♠♦ss♦♠♦✱ ♣♦rt❛♥t♦✱ ❞❡✈❡ ❡①✐st✐r ✉♠❛ ❧❡✐ ❞❡ ❢♦r♠❛çã♦ ♣❛r❛ ✐♥❞✐❝❛r❝♦♠♦ ❛s ❜❛s❡s ❞❡✈❡♠ s❡r ❛❣r✉♣❛❞❛s ♣❛r❛ ❢♦r♠❛r ✉♠❛ ❞❛❞❛ ❝❛r❛❝t❡ríst✐❝❛✳ ❖ ●❆❆❉❚ r❡♣r❡s❡♥t❛ ❛ ❧❡✐ ❞❡ ❢♦r♠❛çã♦ ❞❡ ❝❛r❛❝t❡ríst✐❝❛s ♣❡❧♦ ❝♦♥❥✉♥t♦ ❞❡ ❆①✐♦♠❛s ❞❡ ❋♦r♠❛çã♦❞❡ ●❡♥❡s ✭AF G✮✱ ♦ q✉❛❧ ❞❡✈❡rá s❡r ❞❡✜♥✐❞♦ ♣❛r❛ ❝❛❞❛ ❝❛s♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ s❡♠â♥t✐❝❛❛tr✐❜✉í❞❛ ❛♦ ❣❡♥❡✳❉❡✜♥✐çã♦ ✸✳✷✳✷ ✭●❡♥❡✮ ❯♠ ❣❡♥❡ g é ✉♠❛ s❡q✉ê♥❝✐❛ ❢♦r♠❛❞❛ ♣❡❧♦s ❡❧❡♠❡♥t♦s ❞❛ ❜❛s❡ q✉❡ ♣❡rt❡♥❝❡ ❛♦ ❝♦♥❥✉♥t♦ AF G✳ ❖s ❣❡♥❡s sã♦ ❛❣r✉♣❛❞♦s ❡♠ ❝♦♥❥✉♥t♦s ♣❛r❛ ❢♦r♠❛r ♦s ❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦✳ ❖1 2 }, g , . . . , g n ❝♦♥❥✉♥t♦ ❞❡ ❣❡♥❡s {g q✉❡ ❝♦♠♣õ❡ ✉♠ ❞❛❞♦ ❝r♦♠♦ss♦♠♦ s❡r✈❡ ♣❛r❛ ✐❞❡♥t✐✜❝❛r❡st❡ ❝r♦♠♦ss♦♠♦ ❞❡♥tr♦ ❞❛ ♣♦♣✉❧❛çã♦✳ ❆ ✐❞❡♥t✐❞❛❞❡ ❞♦s ❝r♦♠♦ss♦♠♦s s❡rá ✉s❛❞❛ ♣❛r❛ ✐♠✲♣❡❞✐r q✉❡ ✈ár✐❛s ❝ó♣✐❛s ❞❡ ✉♠ ❝r♦♠♦ss♦♠♦ ♣♦ss❛♠ ❝♦❡①✐st✐r ♦✉ r❡♥❛s❝❡r ♥❛ ♣♦♣✉❧❛çã♦ ❡♠ q✉❛❧q✉❡r t❡♠♣♦ ❞✉r❛♥t❡ ♦ ♣r♦❝❡ss♦ ❞❡ ❡✈♦❧✉çã♦ ❞❛ ♠❡s♠❛ ♥❛ ❜✉s❝❛ ♣♦r ✉♠ ❝r♦♠♦ss♦♠♦♠❛✐s ❛❞❛♣t❛❞♦✳ ❆s ❝❛r❛❝t❡ríst✐❝❛s ❛♣r❡s❡♥t❛❞❛s ♣❡❧♦s ❝r♦♠♦ss♦♠♦s ❞❡ ✉♠❛ ♣♦♣✉❧❛çã♦ s❡r✈❡♠ t❛♠❜é♠♣❛r❛ ❝❧❛ss✐✜❝á✲❧♦s ❡♠ ❣r✉♣♦s t❛①♦♥ô♠✐❝♦s ✭❡s♣é❝✐❡s ❡ ❢❛♠í❧✐❛s✮ ❡♠ ❢✉♥çã♦ ❞♦ ❣r❛✉ ❞❡ s✐♠✐✲❧❛r✐❞❛❞❡ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❝♦♠♣❛rt✐❧❤❛❞❛s ♣❡❧♦s ♠❡s♠♦s✳ ❖ ✐♥í❝✐♦ ❡ ♦ ✜♠ ❞❛ ❢♦r♠❛çã♦ ❞❡✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ ❡♠ ❞❡t❡r♠✐♥❛❞❛ ❡s♣é❝✐❡✱ ♥♦ ●❆❆❉❚✱ é r❡♣r❡s❡♥t❛❞♦ ♣❡❧♦ ❝♦♥❥✉♥t♦ ❞❡❆①✐♦♠❛s ❞❡ ❋♦r♠❛çã♦ ❞❡ ❈r♦♠♦ss♦♠♦s ✭AF C✮ q✉❡ ❞❡✈❡ t❛♠❜é♠ ❣❛r❛♥t✐r q✉❡ ♦ ❝r✉③❛✲♠❡♥t♦ ❞❡ ❞♦✐s ❝r♦♠♦ss♦♠♦s ❞❡ ✉♠❛ ♠❡s♠❛ ❡s♣é❝✐❡ r❡s✉❧t❡ ❡♠ ✉♠ ❝r♦♠♦ss♦♠♦ ❞❛ ♠❡s♠❛❡s♣é❝✐❡✳ ❆ss✐♠ ❝♦♠♦ ♦ AF G✱ ♦ AF C t❛♠❜é♠ ❞❡✈❡rá s❡r ❞❡✜♥✐❞♦ ♣❛r❛ ❝❛❞❛ s✐t✉❛çã♦ ❞❡❛❝♦r❞♦ ❝♦♠ ❛ s❡♠â♥t✐❝❛ ❛❞♦t❛❞❛ ♣❛r❛ ♦ ❝r♦♠♦ss♦♠♦✳❉❡✜♥✐çã♦ ✸✳✷✳✸ ✭❈r♦♠♦ss♦♠♦✮ ❯♠ ❝r♦♠♦ss♦♠♦ c é ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❣❡♥❡s q✉❡ ♦❜❡❞❡❝❡às ❝♦♥❞✐çõ❡s ❡st❛❜❡❧❡❝✐❞❛s ♣❡❧♦ ❆❋❈✳ ❈r♦♠♦ss♦♠♦s sã♦ ❛❣r✉♣❛❞♦s ❡♠ ❝♦♥❥✉♥t♦s ♣❛r❛ ❢♦r♠❛r ✉♠❛ ♣♦♣✉❧❛çã♦✳ ❊st❛ r❡♣r❡✲ s❡♥t❛çã♦ ♣❛r❛ ❛ ♣♦♣✉❧❛çã♦ ✐rá ❣❛r❛♥t✐r ❛ ✐♠♣❛r❝✐❛❧✐❞❛❞❡ ♥❛ ❛✈❛❧✐❛çã♦ ❞♦s ❝r♦♠♦ss♦♠♦s q✉❡❝♦♠♣õ❡♠ ❛ ♣♦♣✉❧❛çã♦✱ ❥á q✉❡ ❝❛❞❛ ❝r♦♠♦ss♦♠♦ só ♣♦❞❡rá ♦❝♦rr❡r ✉♠❛ ✈❡③ ♥❛ ♣♦♣✉❧❛çã♦✳❉❡✜♥✐çã♦ ✸✳✷✳✹ ✭P♦♣✉❧❛çã♦✮ ❯♠❛ ♣♦♣✉❧❛çã♦ P é ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❝r♦♠♦ss♦♠♦s ❝♦♥s✲ tr✉í❞♦s ❝♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ♥❛ ❉❡✜♥✐çã♦ ✸✳✷✳✸ ❖ t✐♣♦ ♣♦♣✉❧❛çã♦ é ♦ ❝♦♥❥✉♥t♦ ❢♦r♠❛❞♦ ♣♦r t♦❞♦s ♦s ❝♦♥❥✉♥t♦s ❢♦r♠❛❞♦s ♣♦r ♦❜❥❡t♦s❞♦ t✐♣♦ ❝r♦♠♦ss♦♠♦ q✉❡ sã♦ ♣♦ssí✈❡✐s r❡s✉❧t❛❞♦s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❡♠ ❢♦❝♦✱ s❡❣✉♥❞♦ ❛ ✐♥✲ t❡r♣r❡t❛çã♦ ❛❞♦t❛❞❛ ♣❛r❛ ♦s t✐♣♦s C✱ G ❡ B✳ ❆ ❣❡r❛çã♦ ❞❛ ♣♦♣✉❧❛çã♦ ✈❛③✐❛ ♣❡❧♦ ❛❧❣♦r✐t♠♦✐♥❞✐❝❛ q✉❡ ❛ ✐♥t❡r♣r❡t❛çã♦ ❛❞♦t❛❞❛ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❡stá ❡rr❛❞❛✳ ✸✳✸✳ ❖P❊❘❆❉❖❘❊❙ ●❊◆➱❚■❈❖❙ ❉❖ ●❆❆❉❚ ✷✾ ✸✳✸ ❖♣❡r❛❞♦r❡s ●❡♥ét✐❝♦s ❞♦ ●❆❆❉❚ ❖ ●❆❆❉❚ tr❛❜❛❧❤❛ ❝♦♠ ❞♦✐s t✐♣♦s ❞❡ ♦♣❡r❛❞♦r❡s ❣❡♥ét✐❝♦s✿ ♦ ❞❡ ❝r✉③❛♠❡♥t♦ ❡ ♦ ❞❡♠✉t❛çã♦✳ ❖ ♦♣❡r❛❞♦r ❣❡♥ét✐❝♦ ❞❡ ❝r✉③❛♠❡♥t♦ ❝❛r❛❝t❡r✐③❛✲s❡ ♣♦r ❝♦♠❜✐♥❛r ♦s ❣❡♥❡s ❞❡❞♦✐s ❝r♦♠♦ss♦♠♦s ✭❝r♦♠♦ss♦♠♦s ✲ ♣❛✐✮ ♣❛r❛ ❢♦r♠❛r ♦✉tr♦s ❝r♦♠♦ss♦♠♦s ✭❝r♦♠♦ss♦♠♦s ✲✜❧❤♦✮✱ ❡♥q✉❛♥t♦ q✉❡ ♦ ♦♣❡r❛❞♦r ❣❡♥ét✐❝♦ ❞❡ ♠✉t❛çã♦ ❝❛r❛❝t❡r✐③❛✲s❡ ♣♦r ❛❧t❡r❛r ❛ ✐❞❡♥t✐❞❛❞❡❞❡ ✉♠ ❝r♦♠♦ss♦♠♦ ♣❛r❛ ❢♦r♠❛r ✉♠ ♦✉tr♦ ❝r♦♠♦ss♦♠♦ ✭❝r♦♠♦ss♦♠♦✲♠✉t❛♥t❡✮✳ ❖ ❣❡♥❡ ❞♦s ❝r♦♠♦ss♦♠♦s ✲ ♣❛✐ ♣❛r❛ ✉♠❛ ❞❛❞❛ ❝❛r❛❝t❡ríst✐❝❛ q✉❡ ❢❛rá ♣❛rt❡ ❞♦s ❝r♦♠♦s✲ s♦♠♦s ✲ ✜❧❤♦ é ❛q✉❡❧❡ q✉❡ ♠❡❧❤♦r s❛t✐s❢❛③ ❛s r❡str✐çõ❡s ❞♦ ♣r♦❜❧❡♠❛ s♦❜r❡ ❛ ❝❛r❛❝t❡ríst✐❝❛❡①♣r❡ss❛ ♣♦r ❡st❡ ❣❡♥❡✱ ❡ r❡❝❡❜❡ ♦ ♥♦♠❡ ❞❡ ❣❡♥❡✲❞♦♠✐♥❛♥t❡✳12 ❉❛❞♦s ❞♦✐s ❣❡♥❡s g ❡ g ✱ q✉❡ ❡①♣r❡ss❡♠ ✉♠❛ ♠❡s♠❛ ❝❛r❛❝t❡ríst✐❝❛ ❝♦♠ ❞✐❢❡r❡♥t❡s ✷1 ❢❡♥ót✐♣♦s ✱ ❞✐③✲s❡ q✉❡ ✉♠ ❣❡♥❡ g ♠❡❧❤♦r s❛t✐s❢❛③ ❛s r❡str✐çõ❡s ❞♦ ♣r♦❜❧❡♠❛ ❞♦ q✉❡ ♦ ❣❡♥❡21 g✱ s❡ ♦ ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ ❞♦ ❣❡♥❡ g ❢♦r s✉♣❡r✐♦r ♦✉ ✐❣✉❛❧ ❛♦ ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ ❞♦2 ❣❡♥❡ g ✳ ◆♦ ●❆❆❉❚✱ ♦ ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ ❞❡ ✉♠ ❣❡♥❡ é ❞❛❞♦ ♣♦r ✉♠❛ ❢✉♥çã♦ ❣r❛✉ ❡ λé ❝♦♥s✐❞❡r❛❞❛ ❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠ ❣❡♥❡ g ✱ ❞❡♥♦♠✐♥❛❞♦ ❞❡ ❣❡♥❡✲✐♥ó❝✉♦✱ q✉❡ é ✉s❛❞♦ ♣❛r❛ r❡♣r❡s❡♥t❛r ✉♠ ❣❡♥❡ q✉❡ ♥ã♦ ❡①♣r❡ss❛ q✉❛❧q✉❡r ❝❛r❛❝t❡ríst✐❝❛✱ ❞❡ ❢♦r♠❛ q✉❡ ❛ s✉❛ ♣r❡s❡♥ç❛♦✉ ❛✉sê♥❝✐❛ ♥ã♦ ❛❧t❡r❛ ❛ ✐❞❡♥t✐❞❛❞❡ ❞♦ ❝r♦♠♦ss♦♠♦✱ ♦ q✉❛❧ s❛t✐s❢❛③ ❛s r❡str✐çõ❡s ✐♠♣♦st❛s♣❡❧♦ ❝♦♥❥✉♥t♦ ❞❡ ❛①✐♦♠❛s ❞❡ ❢♦r♠❛çã♦ ❞❡ ❣❡♥❡s✳ ❙❡✉ ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ é ♠❡♥♦r q✉❡ ♦❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ ❞❡ q✉❛❧q✉❡r ♦✉tr♦ ❡❧❡♠❡♥t♦ ❞♦ t✐♣♦ ❣❡♥❡✳❉❡✜♥✐çã♦ ✸✳✸✳✶ ✭●r❛✉✮ ❖ ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ ❞❡ ✉♠ ❣❡♥❡ é ✉♠❛ ❢✉♥çã♦ ❣r❛✉ ❞♦ s❡❣✉✐♥t❡ t✐♣♦✿grau : G → K t❛❧ q✉❡✱ ❛ ❝❛❞❛ ❣❡♥❡ g✱ g ∈ G✱ é ❛ss♦❝✐❛❞♦ ✉♠ ú♥✐❝♦ ♥ú♠❡r♦ k✱ k ∈ K ✸ ✭K é ✉♠ ❝♦r♣♦ ♦r❞❡♥❛❞♦ ✮✱ ❝❤❛♠❛❞♦ ❞❡ grau(g) ❡ q✉❡ r❡✢❡t❡✱ s❡❣✉♥❞♦ ❛ ✐♥t❡r♣r❡t❛çã♦❛❞♦t❛❞❛ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✱ ✉♠❛ ❡str❛t✐✜❝❛çã♦ ❝♦♠♣❛r❛t✐✈❛ ❡♥tr❡ ❛ ❛❞❛♣t❛çã♦ ❞♦s ❣❡♥❡s✳ ✹ ❖ ❣❡♥❡ ✐♥ó❝✉♦ é ✉♠❛ ❝♦♥st❛♥t❡ ❞♦ s✐st❡♠❛✱ ❝✉❥♦ ✈❛❧♦r ❞❡✈❡rá s❡r ❞❡✜♥✐❞♦ ♥♦ ♠♦♠❡♥t♦❞❛ ✐♥st❛♥❝✐❛çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❛ ✉♠ ❞❛❞♦ ♣r♦❜❧❡♠❛✱ ♣❡rt❡♥❝❡ ❛♦ t✐♣♦ ❣❡♥❡✱ t❡♠ ❣r❛✉ ❞❡❛❞❛♣t❛çã♦ ✐❣✉❛❧ ❛♦ ❡❧❡♠❡♥t♦ ♥❡✉tr♦ ❞♦ ❝♦r♣♦ K ♣❛r❛ ❛ ♦♣❡r❛çã♦ ❞❡ ❛❞✐çã♦✱ ❡ ♣❛r❛ t♦❞♦ λ grau(g) λ )❣❡♥❡ g ❝♦♠ g 6= g é ♠❛✐♦r ❞♦ q✉❡ grau(g ✳ P♦r ✉♠❛ q✉❡stã♦ ❞❡ ♥♦♠❡♥❝❧❛t✉r❛✱ é ❞❡✜♥✐❞❛ ✉♠❛ r❡❧❛çã♦ ❞❡ ❡q✉✐✈❛❧ê♥❝✐❛ ❝r♦♠♦ssô✲ C C C : C ↔ C 1 ≡ c2♠✐❝❛✱ ❞❡♥♦t❛❞❛ ♣♦r ≡ ✱ ❞❡✜♥✐❞❛ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿ ≡ ✱ t❛❧ q✉❡ c ✱ s❡ 1 − {g λ } 2 − {g λ }❡ s♦♠❡♥t❡ s❡✱ c ❂c ✳ ❖ ❣❡♥❡ ❞♦♠✐♥❛♥t❡ é ✐❞❡♥t✐✜❝❛❞♦ ♣❡❧❛ ❢✉♥çã♦ domi q✉❡ r❡❝❡❜❡ ✉♠ ♣❛r ❞❡ ❣❡♥❡s✱ ✉♠ ❞❡❝❛❞❛ ✉♠ ❞♦s ❝r♦♠♦ss♦♠♦s ✲ ♣❛✐✱ ❡ r❡t♦r♥❛ ♦ ❣❡♥❡ ❞❡ ♠❛✐♦r ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ s❡ ♦s ❣❡♥❡s❢♦r♥❡❝✐❞♦s ❡①♣r❡ss❛r❡♠ ✉♠❛ ♠❡s♠❛ ❝❛r❛❝t❡ríst✐❝❛✳ ❈❛s♦ ♦s ❣❡♥❡s ❢♦r♥❡❝✐❞♦s ♥ã♦ ❡①♣r❡ss❡♠ ✷✸ ❈❛r❛❝t❡ríst✐❝❛s ♦❜s❡r✈á✈❡✐s ❞❡ ✉♠ ♦r❣❛♥✐s♠♦ q✉❡ r❡s✉❧t❛♠ ❞❛ ✐♥t❡r❛çã♦ ❡♥tr❡ ♦ ❣❡♥ót✐♣♦ ❡ ♦ ❛♠❜✐❡♥t❡✳ ❊str✉t✉r❛ ❛❧❣é❜r✐❝❛✱ ❝♦♠ ❞✉❛s ♦♣❡r❛çõ❡s✱ s❡♠ ❞✐✈✐s♦r❡s ♣ró♣r✐♦s ❞❡ ③❡r♦ ❡ ♠✉♥✐❞♦ ❞❡ ✉♠❛ ♦r❞❡♠✳ ❊①✿ hR, ≤, +, ×, 0, 1i✳ ✹ ❖ ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ é ♠❡♥♦r q✉❡ ♦ ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ ❞❡ q✉❛❧q✉❡r ♦✉tr♦ ❡❧❡♠❡♥t♦ ❞♦ t✐♣♦ ❣❡♥❡✳ ❚❛❧❣❡♥❡ s❡rá ❞❡♥♦♠✐♥❛❞♦ ❞❡ ❣❡♥❡✲✐♥ó❝✉♦✳ ✸✳✸✳ ❖P❊❘❆❉❖❘❊❙ ●❊◆➱❚■❈❖❙ ❉❖ ●❆❆❉❚ ✸✵ λ✉♠❛ ♠❡s♠❛ ❝❛r❛❝t❡ríst✐❝❛✱ ❡♥tã♦ ❛ ❢✉♥çã♦ domi r❡t♦r♥❛rá g ✳ ❉❛❞♦s ❞♦✐s ❣❡♥❡s✱ ❞✐③✲s❡ q✉❡❡❧❡s ❡①♣r❡ss❛♠ ✉♠❛ ♠❡s♠❛ ❝❛r❛❝t❡ríst✐❝❛ s❡ ❡①✐st❡ ✉♠ ❛tr✐❜✉t♦ r❡❧❡✈❛♥t❡ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛❡♠ ❢♦❝♦ q✉❡ s❡❥❛ s❛t✐s❢❡✐t♦ ♣❡❧♦s ❣❡♥❡s ❢♦r♥❡❝✐❞♦s✳ ◆♦ ●❆❆❉❚✱ ♦ ❛tr✐❜✉t♦ r❡❧❡✈❛♥t❡ ♣❛r❛ ♦♣r♦❜❧❡♠❛ é ❡s♣❡❝✐✜❝❛❞♦ ♣❡❧♦ ❝♦♥❥✉♥t♦ atributoRelevante✱ q✉❡ é ✉♠❛ ❝♦♥st❛♥t❡ ❞♦ s✐st❡♠❛❝✉❥♦ ❝♦♥t❡ú❞♦ ❞❡♣❡♥❞❡rá ❞❛ ✐♥t❡r♣r❡t❛çã♦ ❛❞♦t❛❞❛ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✳ ❆ ❝♦♠♣❛r❛çã♦ ❡♥tr❡❡ss❡s ❞♦✐s ❣❡♥❡s ♣❛r❛ ❝♦♥st❛t❛r s❡ ❡①♣r❡ss❛♠ ✉♠❛ ♠❡s♠❛ ❝❛r❛❝t❡ríst✐❝❛✱ ♦✉ s❡❥❛✱ s❡ ❡①✐st❡✉♠ atributoRelevante ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❡♠ q✉❡stã♦ q✉❡ s❡❥❛ s❛t✐s❢❡✐t♦ ♣❡❧♦s ❞♦✐s ❣❡♥❡s✱ é❢❡✐t❛ ❛tr❛✈és ❞❛ r❡❧❛çã♦ mesma✱ q✉❡ ♦❜❡❞❡❝❡ ❛♦s s❡❣✉✐♥t❡s ♣r❡❝❡✐t♦s✿▲❡♠❛ ✸✳✸✳✶ ∀g : G • (g, g) ∈ mesma✳121221 , g : G|(g , g ) ∈ mesma • (g , g ) ∈ mesma▲❡♠❛ ✸✳✸✳✷ ∀g1231223 ✳13 , g , g : G|(g , g ) ∈ mesma ∧ (g , g ) ∈ mesma • (g , g ) ∈ mesma▲❡♠❛ ✸✳✸✳✸ ∀g ✳❖ ❣❡♥❡ ❞♦♠✐♥❛♥t❡✱ ♣♦rt❛♥t♦✱ é ❞❡✜♥✐❞♦ ❝♦♠♦✿ ❉❡✜♥✐çã♦ ✸✳✸✳✷ ✭❉♦♠✐♥❛♥t❡✮ ❖ ❣❡♥❡ ❞♦♠✐♥❛♥t❡ é ✉♠❛ ❢✉♥çã♦ domi ❞♦ s❡❣✉✐♥t❡ t✐♣♦✿ domi : G × G → G12 g λ , g ) / ∈ mesma,  s❡ (g domi(g1 , g 2 ) =11212 g , g ) ∈ mesma ∧ grau(g ) ≥ grau(g ),s❡ (g 21212 g , g ) ∈ mesma ∧ grau(g ) < grau(g ).s❡ (g ❆ ♣r♦❞✉çã♦ ❞❡ ♥♦✈♦s ❝r♦♠♦ss♦♠♦s ❞✉r❛♥t❡ ♦ ♣r♦❝❡ss♦ ❡✈♦❧✉t✐✈♦ ❞❡ ✉♠❛ ♣♦♣✉❧❛çã♦ s❡r✈❡ ♣❛r❛ ❞✐r❡❝✐♦♥❛r ❛ ❜✉s❝❛ ♣♦r ❝r♦♠♦ss♦♠♦s ♠❛✐s ❛❞❛♣t❛❞♦s ❛tr❛✈és ❞❛ tr❛♥s♠✐ssã♦❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ♠❛✐♦r ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ ♣r❡s❡♥t❡s ♥♦s ❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦❛t✉❛❧✳ ❆ ❛❞❛♣t❛çã♦ ❞❡ ✉♠ ❝r♦♠♦ss♦♠♦ é ❞❛❞❛ ♣❡❧❛ ❢✉♥çã♦ ❛❞❛♣t✳❉❡✜♥✐çã♦ ✸✳✸✳✸ ✭❆❞❛♣t❛çã♦✮ ❆ ❛❞❛♣t❛çã♦ ❞❡ ✉♠ ❝r♦♠♦ss♦♠♦ é ✉♠❛ ❢✉♥çã♦ adapt ❞♦ s❡❣✉✐♥t❡ t✐♣♦✿adapt : C → K P adapt(c) = Θ c,g × grau(g)c,g g∈c♦♥❞❡ Θ é ♦ ♣❡s♦ ❝♦♠ ♦ q✉❛❧ ♦ ❣❡♥❡ g ❝♦♥tr✐❜✉✐ ♣❛r❛ ❛ ❛❞❛♣t❛çã♦ ❞♦ ❝r♦♠♦ss♦♠♦ c✳ ❖ ✈❛❧♦r ❞♦ ♣❛râ♠❡tr♦ ♣❡s♦ ✉s❛❞♦ ♥♦ ❝á❧❝✉❧♦ ❞❛ ❛❞❛♣t❛çã♦ ❞❡ ✉♠ ❝r♦♠♦ss♦♠♦ é ❞❡✜♥✐❞♦❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ♣r♦❜❧❡♠❛ ❡♠ q✉❡ ♦ ●❆❆❉❚ s❡rá ❛♣❧✐❝❛❞♦✱ ❥á q✉❡ ❡st❡ ❝á❧❝✉❧♦ ♣♦❞❡ ❧❡✈❛r❡♠ ❝♦♥s✐❞❡r❛çã♦ ❛ ♣r❡s❡♥ç❛ ♦✉ ❛✉sê♥❝✐❛ ❞❡ ✉♠ ❞❛❞♦ ❣❡♥❡ ♥♦ ❝r♦♠♦ss♦♠♦✳ ❆ ♦♣❡r❛çã♦ ❞❡ ❝r✉③❛♠❡♥t♦ r❡❝❡❜❡ ❞♦✐s ❝r♦♠♦ss♦♠♦s ✲ ♣❛✐✱ ❛♣t♦s ❛ ❝r✉③❛r✱ ❡ r❡t♦r♥❛✉♠❛ ♣♦♣✉❧❛çã♦ ❝✉❥♦s ❝r♦♠♦ss♦♠♦s sã♦ ❢♦r♠❛❞♦s s♦♠❡♥t❡ ♣❡❧♦s ❣❡♥❡s ❞♦♠✐♥❛♥t❡s ❞♦s ❝r♦✲♠♦ss♦♠♦s ❢♦r♥❡❝✐❞♦s✳ ▲♦❣♦✱ ♣❛r❛ s❡ ❞❡✜♥✐r ❡st❛ ❢✉♥çã♦ ♣r❡❝✐s❛✲s❡ ❛♥t❡s ❞❡✜♥✐r ✉♠❛ ❢✉♥çã♦♣❛r❛ s❡❧❡❝✐♦♥❛r ♦s ❝r♦♠♦ss♦♠♦s ❛♣t♦s ❛ ❝r✉③❛r❡♠ ✭s❡❧❡çã♦✮ ❡ ✉♠❛ ❢✉♥çã♦ ♣❛r❛ r❡t♦r♥❛r ♦ ✸✳✸✳ ❖P❊❘❆❉❖❘❊❙ ●❊◆➱❚■❈❖❙ ❉❖ ●❆❆❉❚ ✸✶❝♦♥❥✉♥t♦ ❞❡ ❣❡♥❡s ❞♦♠✐♥❛♥t❡s ♣❛r❛ t♦❞❛s ❛s ❝❛r❛❝t❡ríst✐❝❛s ❡①✐st❡♥t❡s ♥♦s ❝r♦♠♦ss♦♠♦s ✲♣❛✐ ✭❢❡❝✉♥❞❛çã♦✮✳11 ❆ ❢✉♥çã♦ ❞❡ s❡❧❡çã♦ r❡❝❡❜❡ ✉♠❛ ♣♦♣✉❧❛çã♦ P ❡ r❡t♦r♥❛ ❛ s✉❜♣♦♣✉❧❛çã♦ ❞❡ P ❢♦r♠❛❞❛♣❡❧♦s ❝r♦♠♦ss♦♠♦s q✉❡ s❛t✐s❢❛③❡♠ ✉♠ r❡q✉✐s✐t♦ ❞♦ ♣r♦❜❧❡♠❛ r✱ ❞❡s❝r✐t♦ ♣♦r ✉♠❛ ❢ór♠✉❧❛❡♠ ❧ó❣✐❝❛ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✱ ♦ q✉❛❧ ✐♥❞✐❝❛ q✉❛♥❞♦ ✉♠ ❞❛❞♦ ❝r♦♠♦ss♦♠♦ é ❝♦♥s✐❞❡r❛❞♦❛♣t♦ ❛ ❝r✉③❛r✳❉❡✜♥✐çã♦ ✸✳✸✳✹ ✭❙❡❧❡çã♦✮ ❆ s❡❧❡çã♦ ❞♦s ❝r♦♠♦ss♦♠♦s q✉❡ s❛t✐s❢❛③❡♠ ✉♠ ♣r❡❞✐❝❛❞♦ ré ✉♠❛ ❢✉♥çã♦ sel ❞♦ s❡❣✉✐♥t❡ t✐♣♦✿ sel : P(P ) × P(P ) → P(P )sel(P 1 , r) = P 1 ∩ r ✳❆ ❢✉♥çã♦ ❢❡❝✉♥❞❛çã♦ r❡❝❡❜❡ ❞♦✐s ❝r♦♠♦ss♦♠♦s ❡ r❡t♦r♥❛ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❣❡♥❡s ❞♦♠✐✲ ♥❛♥t❡s ❡♥tr❡ t♦❞♦s ♦s ❣❡♥❡s ❞♦s ❝r♦♠♦ss♦♠♦s ❢♦r♥❡❝✐❞♦s✳❉❡✜♥✐çã♦ ✸✳✸✳✺ ✭❋❡❝✉♥❞❛çã♦✮ ❆ ❢❡❝✉♥❞❛çã♦ é ✉♠❛ ❢✉♥çã♦ fec ❞♦ s❡❣✉✐♥t❡ t✐♣♦✿ f ec : C × C → P(G)12112212 f ec(c , c ) = {g|∀g ∈ c ∀g ∈ c (g = domi(g , g ))}C ▲❡♠❛ ✸✳✸✳✹ ∀c : C • (fec(c, c), c) ∈≡ ✳❖s ❝r♦♠♦ss♦♠♦s ✲ ♣❛✐ ❛♣t♦s ❛ ❝r✉③❛r❡♠ sã♦ r❡♣r❡s❡♥t❛❞♦s ♣❡❧♦ ❝♦♥❥✉♥t♦ MACHO ❡ F EM EA1 , M ) 1 , F )1 ✱ ❢♦r♠❛❞♦s ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ MACHO = sel(P ❡ F EMEA = sel(P ✱♦♥❞❡ P é ✉♠❛ s✉❜♣♦♣✉❧❛çã♦ ❞❛ ♣♦♣✉❧❛çã♦ ❛t✉❛❧ ❢♦r♠❛❞❛ ♣♦r ❝r♦♠♦ss♦♠♦s ❛❞❛♣t❛❞♦s ❛♦❛♠❜✐❡♥t❡ ❡✱ M ❡ F sã♦ ❞♦✐s ♣r❡❞✐❝❛❞♦s s♦❜r❡ ♦ t✐♣♦ ♣♦♣✉❧❛çã♦ ♣❡rt❡♥❝❡♥t❡s ❛♦ ❝♦♥❥✉♥t♦❞❡ r❡q✉✐s✐t♦s ❞♦ ❛♠❜✐❡♥t❡ Rq✱ ❡s❝r✐t♦s ❡♠ ✉♠❛ ❧✐♥❣✉❛❣❡♠ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✳ ❉❡♣❡♥❞❡♥❞♦ ❞❛ ❡s♣❡❝✐✜❝❛çã♦ ❞♦s r❡q✉✐s✐t♦s ❞♦ ❛♠❜✐❡♥t❡ M ❡ F ✱ ❛ r❡♣r♦❞✉çã♦ ❣❡r❛❞❛♣♦❞❡ s❡r s❡①✉❛❞❛✱ ❛ss❡①✉❛❞❛ ♦✉ ♠✐st❛✳ ❆ r❡♣r♦❞✉çã♦ s❡①✉❛❞❛ ♦❝♦rr❡ q✉❛♥❞♦ M ∩ F = ∅✱❛ ❛ss❡①✉❛❞❛ q✉❛♥❞♦ M = F ✱ ❡ ❛ ♠✐st❛ q✉❛♥❞♦ M ∩ F 6= ∅ ❡ M 6= F ✳❉❡✜♥✐çã♦ ✸✳✸✳✻ ✭❈r✉③❛♠❡♥t♦✮ ❖ ❝r✉③❛♠❡♥t♦ é ✉♠❛ ❢✉♥çã♦ ❝r✉③ ❞♦ s❡❣✉✐♥t❡ t✐♣♦✿ cruz : M ACHO × F EM EA → P1212 cruz(c , c ) = {c|c ⊆ f ec(c , c )} ❖ ♦♣❡r❛❞♦r ❣❡♥ét✐❝♦ ❞❡ ♠✉t❛çã♦✱ ❞❡✜♥✐❞♦ ♣❛r❛ ♦ ●❆❆❉❚✱ é ❝♦♠♣♦st♦ ♣❡❧❛s ❢✉♥çõ❡s ❞❡✐♥s❡rçã♦✱ s✉♣r❡ssã♦ ❡ tr♦❝❛✱ t❛❧ q✉❡ ♦s ❝r♦♠♦ss♦♠♦s r❡s✉❧t❛♥t❡s ❞❛ ❛çã♦ ❞❡st❡s ♦♣❡r❛❞♦r❡s❛♣r❡s❡♥t❛rã♦ ♣❛rt❡ ❞♦s ❣❡♥❡s ❝♦♥t✐❞♦s ♥♦ ❝r♦♠♦ss♦♠♦ q✉❡ ❧❤❡ ❞❡✉ ♦r✐❣❡♠✳ ❆ ♦♣❡r❛çã♦ ❞❡✐♥s❡rçã♦ ins ❛❞✐❝✐♦♥❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❣❡♥❡s ❛♦ ❝r♦♠♦ss♦♠♦ ❞❡ ♦r✐❣❡♠✳❉❡✜♥✐çã♦ ✸✳✸✳✼ ✭■♥s❡rçã♦✮ ❆ ✐♥s❡rçã♦ é ✉♠❛ ❢✉♥çã♦ ins ❞♦ s❡❣✉✐♥t❡ t✐♣♦✿ ins : C × P(G) → C (11 c ∪ G ∈ AF C,s❡ c ∪ G ins(c, G1 ) = c ❝❛s♦ ❝♦♥trár✐♦✳ ✸✳✹✳ ❆▼❇■❊◆❚❊✸✷ ❆ ♦♣❡r❛çã♦ ❞❡ s✉♣r❡ssã♦ del r❡♠♦✈❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❣❡♥❡s ❞♦ ❝r♦♠♦ss♦♠♦ ❞❡ ♦r✐❣❡♠✳❉❡✜♥✐çã♦ ✸✳✸✳✽ ✭❙✉♣r❡ssã♦✮ ❆ s✉♣r❡ssã♦ é ✉♠❛ ❢✉♥çã♦ del ❞♦ s❡❣✉✐♥t❡ t✐♣♦✿ del : C × P(G) → C (11 c − G ∈ AF C,s❡ c − G del(c, G1 ) = c ❝❛s♦ ❝♦♥trár✐♦✳❆ ♦♣❡r❛çã♦ ❞❡ tr♦❝❛ troc r❡♠♦✈❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❣❡♥❡s ❞♦ ❝r♦♠♦ss♦♠♦ ❞❡ ♦r✐❣❡♠ ❡ ❧❤❡ ❛❞✐❝✐♦♥❛ ♦✉tr♦ ❝♦♥❥✉♥t♦ ❞❡ ❣❡♥❡s✳❉❡✜♥✐çã♦ ✸✳✸✳✾ ✭❚r♦❝❛✮ ❆ tr♦❝❛ é ✉♠❛ ❢✉♥çã♦ troc ❞♦ s❡❣✉✐♥t❡ t✐♣♦✿ troc : C × P(G) × P(G) → C 12112 (c ∪ G ) − G ) ∈ AF C ∧ (c ∪ G ) − G ∈ AF C, s❡ (c ∪ G1112 c ∪ G ) ∈ AF C ∧ (c ∪ G ) − G ∈ AF C, /s❡ (c ∪ G troc(c, G1 , G 2 ) =2 1 ∈ AF C ∧ c − G 2 ∈ AF C,  c − G ) / s❡ (c ∪ G 1 ∈ AF C ∧ c − G 2 ∈ AF C.c ) / / s❡ (c ∪ G ❆çõ❡s ❞❛ ❢✉♥çã♦ ❞❡ ✐♥s❡rçã♦ ❡ s✉♣r❡ssã♦ ♣♦❞❡♠ s❡r ✈✐st❛s ❝♦♠♦ ❝❛s♦s ♣❛rt✐❝✉❧❛r❡s ❞❛❛çã♦ ❞❛ ❢✉♥çã♦ ❞❡ tr♦❝❛✳ ❈♦♥❢♦r♠❡ ❡st❛❜❡❧❡❝❡ ♦ s❡❣✉✐♥t❡ ❝♦r♦❧ár✐♦✿121212 , G : P(G) • troc(c, G , G ) = del(ins(c, G ), G )❈♦r♦❧ár✐♦ ✸✳✸✳✶ ∀c : C; G❉❡✜♥✐çã♦ ✸✳✸✳✶✵ ✭▼✉t❛çã♦✮ ❆ ♠✉t❛çã♦ é ✉♠ ♣r❡❞✐❝❛❞♦ mut ⊆ P(P )✱ t❛❧ q✉❡✿121211211122 mut(c ) = {c |∃G , G : P(G) ((#G ≤ #c ÷2)∧(#G ≤ #c ÷2)∧(troc(c , G , G ) = c ) ∧(adapt(c21), adapt(c ))}21 ), adapt(c ))❆ r❡str✐çã♦ (adapt(c ❣❛r❛♥t❡ q✉❡ t♦❞♦ ❝r♦♠♦ss♦♠♦✲♠✉t❛♥t❡ é ♠❛✐s ❛❞❛♣✲ t❛❞♦ ❞♦ q✉❡ ♦ ❝r♦♠♦ss♦♠♦ q✉❡ ❧❤❡ ❞❡✉ ♦r✐❣❡♠✳ ❆ ❛❧t❡r❛çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ❣❡♥❡s ❞♦ ❝r♦♠♦ss♦♠♦ ♥♦ ❝r♦♠♦ss♦♠♦✲♠✉t❛♥t❡ é ❧✐♠✐t❛❞❛ ❡♠ ❝✐♥q✉❡♥t❛ ♣♦r ❝❡♥t♦ ❞♦ t❛♠❛♥❤♦ ❞♦❝r♦♠♦ss♦♠♦ ❢♦r♥❡❝✐❞♦ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ q✉❡ s❡ ❛s ♠✉t❛çõ❡s ♦❝♦rr✐❞❛s ❡♠ ✉♠ ❝r♦♠♦ss♦♠♦❞❡ ✉♠❛ ❞❛❞❛ ❡s♣é❝✐❡ ❢♦r❡♠ ♠✉✐t♦ ❣r❛♥❞❡s✱ ❡♥tã♦ ❡st❡ ❝r♦♠♦ss♦♠♦ s❡r✐❛ r❡♣❡❧✐❞♦ ♣❡❧♦s❝r♦♠♦ss♦♠♦s ❞❛ s✉❛ ❡s♣é❝✐❡✱ ♣♦r ♥ã♦ s❡r ❝♦♥s✐❞❡r❛❞♦ ♠❛✐s ✉♠ ✐❣✉❛❧ ❛ ❡st❡s✳ ✸✳✹ ❆♠❜✐❡♥t❡ ❖ ●❆❆❉❚ ♦♣❡r❛ s♦❜r❡ ♣♦♣✉❧❛çõ❡s ❞❡ ❝r♦♠♦ss♦♠♦s q✉❡ ❡✈♦❧✉❡♠ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛s ❝❛r❛❝✲ t❡ríst✐❝❛s ❞❡ ✉♠ ❛♠❜✐❡♥t❡ ❆✳i ❯♠ ❛♠❜✐❡♥t❡ ❆ é ✉♠❛ ✽✲t✉♣❧❛ hP, P(P ), Rq, AF G, AF C, T x, Σ, P ✱ ♦♥❞❡✿ é ♦ ❝♦♥❥✉♥t♦ ♣♦tê♥❝✐❛ ❞❡ P ✱ ✸✳✺✳ ❆▲●❖❘■❚▼❖✸✸ ❧✐♥❣✉❛❣❡♠ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✮ ❞♦ ♣r♦❜❧❡♠❛ q✉❡ ✐♥✢✉❡♥❝✐❛♠ ❛ ❣❡♥❡❛❧♦❣✐❛ ❞❛ ♣♦♣✉✲❧❛çã♦ P ✱ P✱ é ♦ ❝♦♥❥✉♥t♦ ❞❡ ♣❛r❡s ❞❡ ❝r♦♠♦ss♦♠♦s (x, y)✱ ♦♥❞❡ x é ✉♠ ❝r♦♠♦ss♦♠♦ ❝♦♥s✲ tr✉í❞♦ ❛ ♣❛rt✐r ❞♦ ❝r♦♠♦ss♦♠♦ y✱ ♣❡❧❛ ❛çã♦ ❞❛ ♦♣❡r❛çã♦ ❞❡ ❝r✉③❛♠❡♥t♦ ♦✉ ♠✉t❛çã♦✱r❡❣✐str❛♥❞♦ ❞❡st❛ ❢♦r♠❛ ❛ ❣❡♥❡❛❧♦❣✐❛ ❞♦s ❝r♦♠♦ss♦♠♦s ♣❡rt❡♥❝❡♥t❡s às ♣♦♣✉❧❛çõ❡s❣❡r❛❞❛s ♣❡❧♦ ●❆❆❉❚ ❞✉r❛♥t❡ ❛ s✉❛ ❡①❡❝✉çã♦✱ é ♦ ❝♦♥❥✉♥t♦ ❞❡ ♦♣❡r❛❞♦r❡s ❣❡♥❡❛❧ó❣✐❝♦s q✉❡ ❛t✉❛♠ s♦❜r❡ ❛ ♣♦♣✉❧❛çã♦ P ✱ ♠í♥✐♠♦ ✉♠ ❝r♦♠♦ss♦♠♦✳❖ ♣r♦❝❡ss♦ ❞❡ ❡✈♦❧✉çã♦ ❞❛r✇✐♥✐st❛✱ s❡❣✉♥❞♦ ♦ q✉❛❧ t♦❞❛s ❛s ❡s♣é❝✐❡s ❞❡s❡♥✈♦❧✈❡r❛♠✲ s❡ ❛ ♣❛rt✐r ❞❡ ♦✉tr❛s ❡s♣é❝✐❡s✱ ♣❡❧❛ tr❛♥s♠✐ssã♦ ❤❡r❡❞✐tár✐❛ ❞❡ ♣❡q✉❡♥❛s ✈❛r✐❛çõ❡s✱ ❡♠s✉❝❡ss✐✈❛s ❣❡r❛çõ❡s✱ r❡s✉❧t❛♥❞♦ ♥❛ s♦❜r❡✈✐✈ê♥❝✐❛ ❞❛s ❡s♣é❝✐❡s q✉❡ ♠❡❧❤♦r ❛❞❛♣t❛r❛♠✲s❡ ❛♦❛♠❜✐❡♥t❡ ❬✶✻❪✱ é ✐♥❞✉③✐❞♦ ♣❡❧❛s ❛❧t❡r❛çõ❡s ❛♠❜✐❡♥t❛✐s ♣r♦❞✉③✐❞❛s ♣❡❧❛ ♥❛t✉r❡③❛✳ ❊st❡ ♣❛♣❡❧❞❡s❡♠♣❡♥❤❛❞♦ ♣❡❧❛ ♥❛t✉r❡③❛✱ ♥❛ ✈✐sã♦ ❞❡ ❡✈♦❧✉çã♦ ❞❛r✇✐♥✐st❛✱ ❛q✉✐ s❡rá r❡♣r❡s❡♥t❛❞♦ ♣❡❧♦●❆❆❉❚✱ q✉❡ é q✉❡♠ s✉❜♠❡t❡ ♦s ❝r♦♠♦ss♦♠♦s ❞❡ ✉♠❛ ♣♦♣✉❧❛çã♦ à ❛çã♦ ❞♦s r❡q✉✐s✐t♦s❞♦ ♣r♦❜❧❡♠❛ Rq✱ r❡s✉❧t❛♥❞♦ ❛ss✐♠ ♥❛ ❣❡r❛çã♦ ❞❡ ♥♦✈♦s ❝r♦♠♦ss♦♠♦s ❛ ♣❛rt✐r ❞❛q✉❡❧❡s ❥á❡①✐st❡♥t❡s ❬✹✺✱ ✹✻❪✳ ✸✳✺ ❆❧❣♦r✐t♠♦ ❖ ●❆❆❉❚ é ✉♠❛ ❢✉♥çã♦ q✉❡ r❡❝❡❜❡ ❛ ♣♦♣✉❧❛çã♦ P ❡✱ ❞❡♣♦✐s ❞❡ s✉❜♠❡tê✲❧❛ à s✐♠✉❧❛çã♦ t t❞❡ ✉♠ ♣r♦❝❡ss♦ ❡✈♦❧✉t✐✈♦✱ ❞❡✈♦❧✈❡ ✉♠❛ ♣♦♣✉❧❛çã♦ P ✳ ❖s ❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦ P1 t−1 sã♦ ♦s ❝r♦♠♦ss♦♠♦s ❞❛s ♣♦♣✉❧❛çõ❡s P ✱P ✱✳ ✳ ✳ ✱P q✉❡ ❛✐♥❞❛ s❛t✐s❢❛③❡♠ ♦s r❡q✉✐s✐t♦s ❞♦ ♣r♦❜❧❡♠❛ Rq✱ ♦✉ ❡♥tã♦ sã♦ ♥♦✈♦s ❝r♦♠♦ss♦♠♦s r❡s✉❧t❛♥t❡s ❞❛ ❛çã♦ ❣❡♥❡❛❧ó❣✐❝❛ ❞❛s ♦♣❡r❛✲ t−1çõ❡s ❞❡ ❝r✉③❛♠❡♥t♦ ❡ ♠✉t❛çã♦ s♦❜r❡ ♦s ❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦ P q✉❡ ❛♣r❡s❡♥t❛♠❛❞❛♣t❛çã♦ ♠❛✐♦r ❞♦ q✉❡ ❛ ❛❞❛♣t❛çã♦ ❞♦s ❝r♦♠♦ss♦♠♦s q✉❡ ❧❤❡s ❞❡r❛♠ ♦r✐❣❡♠✳ ❉✐③✲s❡ t❡♥tã♦ q✉❡ ❛ ♣♦♣✉❧❛çã♦ P ❡✈♦❧✉✐✉ ❞❛ ♣♦♣✉❧❛çã♦ P ✳1 t−1 ❖s ❝r♦♠♦ss♦♠♦s ❞❛s ♣♦♣✉❧❛çõ❡s P ✱P ✱✳ ✳ ✳ ✱P q✉❡ ♥ã♦ ♠❛✐s s❛t✐s❢❛ç❛♠ ♦s r❡q✉✐s✐t♦s t❞♦ ♣r♦❜❧❡♠❛ Rq ♥ã♦ ♣❛rt✐❝✐♣❛rã♦ ❞❛ ❝♦♥str✉çã♦ ❞❛ ♣♦♣✉❧❛çã♦ P ✱ ♣♦❞❡♥❞♦ s❡r ❛ss✐♠❡♥t❡♥❞✐❞♦s ❝♦♠♦ ❢❛③❡♥❞♦ ♣❛rt❡ ❞❛ ♣♦♣✉❧❛çã♦ ❞❡ ❝r♦♠♦ss♦♠♦s ✏♠♦rt♦s✑✱ q✉❡ ♥ã♦ ✜❣✉r❛rã♦ t❡♥tr❡ ♦s ❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦ P ❡ ❞❛s ♣♦♣✉❧❛çõ❡s s❡❣✉✐♥t❡s ♠❛♥✐♣✉❧❛❞❛s ♣❡❧❛ ❢✉♥çã♦ ✸✳✻✳ ❊❙P❊❈■❋■❈❆➬➹❖ ❉❖ ●❆❆❉❚ P❆❘❆ ❖ P❘❖❇▲❊▼❆ ✸✹GAADT ✳ ◆ã♦ ♦❜st❛♥t❡✱ t❛✐s ❝r♦♠♦ss♦♠♦s s❡rã♦ r❡❝✉♣❡r❛❞♦s ♣❡❧❛ ❛♥á❧✐s❡ ❞❛ t❛①♦♥♦♠✐❛T x ❞♦s ❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦ ❛t✉❛❧ ♣❛r❛ ❡✈✐t❛r q✉❡ ❡❧❡s ❛♣❛r❡ç❛♠ ♥♦✈❛♠❡♥t❡ ♥❛s♣ró①✐♠❛s ✐t❡r❛çõ❡s ❞❛ ❢✉♥çã♦ GAADT ✳ ❊st❛ r❡str✐çã♦ ❛t❡♥❞❡ ❛♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞♦ ♣r♦❝❡ss♦❞❡ ❡✈♦❧✉çã♦ ❞❛r✇✐♥✐st❛✱ q✉❡ ♥ã♦ ❝♦♥t❡♠♣❧❛ ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ✉♠❛ ❡s♣é❝✐❡ ❡①t✐♥t❛ ✈♦❧t❛r❛ ❛♣❛r❡❝❡r ♥✉♠ ♦✉tr♦ ♠♦♠❡♥t♦ ❢✉t✉r♦✳ ◆❛ ❞❡✜♥✐çã♦ ❞❛ ❢✉♥çã♦ GAADT ✱ ✉♠ ❝r✐tér✐♦ ❞❡ ♣r❡s❡r✈❛çã♦ s♦❜r❡ ❛ ♣♦♣✉❧❛çã♦ ❛t✉❛❧P t é ❡st❛❜❡❧❡❝✐❞♦ ♣❛r❛ ♦r✐❡♥t❛r ♦ ❝♦rt❡ ❞♦s ❝r♦♠♦ss♦♠♦s q✉❡ ♥ã♦ ❞❡✈❡♠ ✜❣✉r❛r ♥❛s ♣♦♣✉✲ t+1 t+2corte❧❛çõ❡s P ✱P ✱✳ ✳ ✳ ✳ ❊st❡ ♣♦♥t♦ ❞❡ ❝♦rt❡ é r❡♣r❡s❡♥t❛❞♦ ♣♦r ✉♠ ♣r❡❞✐❝❛❞♦ ✉♥ár✐♦ p♣❡rt❡♥❝❡♥t❡ ❛♦ ❝♦♥❥✉♥t♦ ❞❡ r❡q✉✐s✐t♦s ❞♦ ♣r♦❜❧❡♠❛ Rq✱ q✉❡ ❛t✉❛ s♦❜r❡ ♦s ❝r♦♠♦ss♦♠♦s ❞❡P t ✳❖s ❝r✐tér✐♦s ❞❡ ♣❛r❛❞❛ ❛❞♦t❛❞♦s ♣❡❧❛ ❢✉♥çã♦ GAADT sã♦✿ ♦ ♥ú♠❡r♦ ♠á①✐♠♦ ❞❡ ✐t❡r❛çõ❡s ❞❡s❡❥❛❞❛s❀ ❡ ♦ ✈❛❧♦r ❞❛ ❛❞❛♣t❛çã♦ ❞♦s ❝r♦♠♦ss♦♠♦s ❝♦♥s✐❞❡r❛❞♦ s❛t✐s❢❛tór✐♦♣❛r❛ ❛ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❡♠ ❛♥á❧✐s❡✳ ❊st❡s ❝r✐tér✐♦s t❛♠❜é♠ ❢❛③❡♠ ♣❛rt❡ ❞♦ ❝♦♥❥✉♥t♦❞❡ r❡q✉✐s✐t♦sRq ❞♦ ♣r♦❜❧❡♠❛✳❉❡✜♥✐çã♦ ✸✳✺✳✶ ✭●❆❆❉❚✮ ❖ ●❆❆❉❚ é ✉♠❛ ❢✉♥çã♦ GAADT ❞♦ s❡❣✉✐♥t❡ t✐♣♦✿GAADT : A → A P otm otm = {c|∀c : P t (adapt(c) ≥ k)} 6= ∅,  s❡ P GAADT (P ) = t P t+1 s❡ t + 2 = T, GAADT (P t+1 ) t+1 = cruz(a, b) ∪ mut(c) ∪ p corte (P t ) t ❝❛s♦ ❝♦♥trár✐♦✳♦♥❞❡ P ❝♦♠ ❡ a, b, c ∈ P ✱ P é ❛ ♣♦♣✉❧❛çã♦ ✐♥✐❝✐❛❧❝♦♥s✐❞❡r❛❞❛✱ k ∈ K é ✉♠ ✈❛❧♦r ✐♠♣♦st♦ ♣❡❧♦ ❛♠❜✐❡♥t❡ A✱ ❝♦♠♦ ❝r✐tér✐♦ ❞❡ ❛❝❡✐t❛çã♦ ❞❡ t❝r♦♠♦ss♦♠♦s ❡♠ P q✉❡ s❛t✐s❢❛③❡♠ ♦ ♣r♦❜❧❡♠❛ ❡ T ∈ N é ✉♠ ♥ú♠❡r♦ ❞❛❞♦ ❝♦♠♦ ❝r✐tér✐♦❞❡ s❛t✐s❢❛çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ✐t❡r❛çõ❡s✳ ❆ s❡❣✉♥❞❛ ❝♦♥❞✐çã♦ ❞❡ ♣❛r❛❞❛ ♦❝♦rr❡rá ❣❛r❛♥t✐❞❛♠❡♥t❡ s❡ ❡✈❡♥t✉❛❧♠❡♥t❡ ❛ ♣r✐♠❡✐r❛ t♥ã♦ ♦❝♦rr❡r✳ P❛r❛ q✉❛❧q✉❡r ❡♥tr❛❞❛ P ✱ ♦ ♣r♦❝❡ss♦ GAADT ❞á ✉♠❛ s❛í❞❛ ❜❡♠ ❞❡t❡r♠✐✲♥❛❞❛✱ ♦ q✉❡ ✐♠♣❧✐❝❛ ❞✐③❡r q✉❡ ♦ GAADT é ✉♠ ❛❧❣♦r✐t♠♦ ❡ ❞❡st❛ ❢♦r♠❛ ✉♠ ♣r♦❝❡❞✐♠❡♥t♦❝♦rr❡t♦✳ ✸✳✻ ❊s♣❡❝✐✜❝❛çã♦ ❞♦ ●❆❆❉❚ ♣❛r❛ ♦ Pr♦❜❧❡♠❛ ❖ ●❆❆❉❚ ❢♦✐ ♣r♦♣♦st♦ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ s❡r ❛♣❧✐❝❛❞♦ ❛ ❞✐❢❡r❡♥t❡s ♣r♦❜❧❡♠❛s✱ ❛ q✉❛❧✐❞❛❞❡❞♦s r❡s✉❧t❛❞♦ ❡♥❝♦♥tr❛❞♦ ❞❡♣❡♥❞❡ ❞❛ ✐♥st❛♥❝✐❛çã♦ ❞♦s t✐♣♦s ❛❜str❛t♦s ♠❛♥✐♣✉❧❛❞♦ ♣♦r❡st❡ ❛❧❣♦r✐t♠♦✱ ❞❛ ❛❞❡q✉❛çã♦ ❞♦s ♦♣❡r❛❞♦r❡s ❣❡♥ét✐❝♦s t✐❝♦s ❡ ❞❛s r❡str✐çõ❡s ✐♠♣♦st❛s♣❡❧♦ ❛♠❜✐❡♥t❡✳ P♦rt❛♥t♦✱ ♦ ●❆❆❉❚✱ q✉❛♥❞♦ ✐♥st❛♥❝✐❛❞♦ ♣❛r❛ ✉♠ ♣r♦❜❧❡♠❛ ♣❛rt✐❝✉❧❛r✱❞❡✈❡ ♣r❡s❡r✈❛r t♦❞❛s ❛s s✉❛s ♣r♦♣r✐❡❞❛❞❡s ❢✉♥❞❛♠❡♥t❛✐s✳ ❊♠ ❱✐❡✐r❛ ❬✹✺✱ ✹✻❪ ❛♣r❡s❡♥t❛❞❛✉♠❛ ♠❡t♦❞♦❧♦❣✐❛ q✉❡ ❛✉①✐❧✐❡ ❛ ♠♦❞❡❧❛r ♦s r❡q✉✐s✐t♦s ❞♦ ♣r♦❜❧❡♠❛✱ ❜❛s❡❛❞❛ ❡♠ ✼ ♣❛ss♦s✿ ✶✳ ❊①❛♠✐♥❛r ♦ ♣r♦❜❧❡♠❛✱ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❞❡t❡r♠✐♥❛r q✉❛❧ ❛ ♥❛t✉r❡③❛ ❞❛ s♦❧✉çã♦ ✸✳✻✳ ❊❙P❊❈■❋■❈❆➬➹❖ ❉❖ ●❆❆❉❚ P❆❘❆ ❖ P❘❖❇▲❊▼❆ ✸✺ r❡q✉❡r✐❞❛ ♥♦ s❡♥t✐❞♦ ❞❡ ♦r✐❡♥t❛r ❛ ❡s❝♦❧❤❛ ♠❡t❛❢ór✐❝❛ ❞♦s t✐♣♦s ❜ás✐❝♦s✿ ❜❛s❡✱ ❣❡♥❡❡ ❝r♦♠♦ss♦♠♦❀ λ ✷✳ ■❞❡♥t✐✜❝❛r ♦ ❣❡♥❡ ✐♥ó❝✉♦ g ❡ ❛ ♣♦♣✉❧❛çã♦ ✐♥✐❝✐❛❧ P ❀✸✳ ❉❡✜♥✐r ❛s ❢✉♥çõ❡s ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ ❞♦ ❣❡♥❡ ❣r❛✉ ❡ ♣❡s♦ ❞♦ ❣❡♥❡ ♥♦ ❝r♦♠♦ss♦♠♦ Θ, earelao❛tr✐❜✉t♦❘❡❧❡✈❛♥t❡; DefiniroselementosdeRq(F, Mer)usadospelafuno❝r✉③deacordocomopr ✹✳ ❉❡✜♥✐r ♦s ❡❧❡♠❡♥t♦s ❞❡ ❘q ✭♣❝♦rt❡✱ t ❡ ❦✮ ✉t✐❧✐③❛❞♦s ♣❡❧❛ ❢✉♥çã♦ ●❆❆❉❚❀ ✹✳✺✳ ❈♦♥str✉✐r ♦ ❛❧❣♦r✐t♠♦❀✻✳ ❱❡r✐✜❝❛r ♦s ❡✈❡♥t✉❛✐s ❛❥✉st❡s r❡❧❛t✐✈♦s ♣❛r❛ ✈❡r✐✜❝❛çã♦ ❞♦s t✐♣♦s ♠❛♥✐♣✉❧❛❞♦s ♣❡❧❛s ❢✉♥✲ çõ❡s✱ r❡❧❛çõ❡s ❡ ♦♣❡r❛çõ❡s ♠❛♥✐♣✉❧❛❞❛s ♣❡❧❛ ❢✉♥çã♦ ❞♦ ●❆❆❉❚✱ ❡ ❛ ♠♦❞❡❧❛❣❡♠ ❞♦ ♣r♦✲❜❧❡♠❛ ❛tr❛✈és ❞❛ ❞❡✜♥✐çã♦ ❞♦s ❝♦♠♣♦♥❡♥t❡s ❞♦ ❛♠❜✐❡♥t❡✳ ❖ r❡st❛♥t❡ ❞❡st❛ s❡çã♦ s❡ ❞❡st✐♥❛ ❛ ❞❡s❝r❡✈❡r ❝♦♠♦ ♦ ●❆❆❉❚ ♣♦❞❡ s❡r ❛♣❧✐❝❛❞♦ ❡ r❡✜♥❛❞♦ ❛♦ ♣r♦❜❧❡♠❛ ❞♦ ♠❡❧❤♦r❛♠❡♥t♦ ❣❡♥ét✐❝♦ ❞❛ ❝❛♥❛ ❞❡ ❛çú❝❛r❞❛✳❙❡❣✉❡ ❛❜❛✐①♦ ♦s ❡❧❡♠❡♥t♦s ❜ás✐❝♦s ❞♦ ●❆❆❉❚ ❛♣❧✐❝❛❞♦ ❛♦ ♣r♦❜❧❡♠❛ ❞❡ ✐♥t❡r❡ss❡✿ ✸✳✻✳✶ ❚✐♣♦s ❇ás✐❝♦s ◆❡st❡ tr❛❜❛❧❤♦✱ ♦s ❝r♦♠♦ss♦♠♦s s❡rã♦ r❡♣r❡s❡♥t❛❞♦s ♣♦r s❡✉ ♠❛t❡r✐❛❧ ❣❡♥ét✐❝♦✱ ♦ q✉❛❧ tê♠♥❛s ❜❛s❡s s✉❛s ✉♥✐❞❛❞❡s ❡❧❡♠❡♥t❛r❡s ❞❡ ❢♦r♠❛çã♦✳ ❆ ú♥✐❝❛ ❡①✐❣ê♥❝✐❛ ♣❛r❛ ♦ t✐♣♦ ❛❜str❛t♦ λ❜❛s❡ ❞♦ ●❆❆❉❚ é q✉❡ ❡❧❡ t❡♥❤❛ ♣❡❧♦ ♠❡♥♦s ✉♠❛ ❜❛s❡ b ✱ ❞❡♥♦♠✐♥❛❞♦ ❞❡ ❜❛s❡✲✐♥ó❝✉♦✱ q✉❡ λ λ s❡rá ✉s❛❞♦ ♥❛ ❝♦♥str✉çã♦ ❞♦ ❣❡♥❡✲✐♥ó❝✉♦ g ❡ ❞♦ ❝r♦♠♦ss♦♠♦✲✐♥ó❝✉♦ c ✳ ❆s ❝♦♥st❛♥t❡s❞♦ ●❆❆❉❚ ❜❛s❡✲✐♥ó❝✉❛✱ ❣❡♥❡✲✐♥ó❝✉♦ ❡ ❝r♦♠♦ss♦♠♦✲✐♥ó❝✉♦ ❞❡✈❡rã♦ t❡r s❡✉ ✈❛❧♦r ❞❡✜♥✐❞♦♥♦ ♠♦♠❡♥t♦ ❞❛ ✐♥st❛♥❝✐❛çã♦ ❞♦ ●❆❆❉❚ ❛ ✉♠ ❞❛❞♦ ♣r♦❜❧❡♠❛✳ ❖s ✐♥❞✐✈í❞✉♦s s❡rã♦ r❡♣r❡s❡♥t❛❞♦s ♣♦r s❡✉ ♠❛t❡r✐❛❧ ❣❡♥ét✐❝♦ ✭❝r♦♠♦ss♦♠♦s✮✱ ♦ q✉❛❧ t❡♠ ♥❛s ❜❛s❡s ♥✉❝❧é✐❝❛s s✉❛s ✉♥✐❞❛❞❡s ❡❧❡♠❡♥t❛r❡s ❞❡ ❢♦r♠❛çã♦✳ ❖ t✐♣♦ ❛❜str❛t♦ ❜❛s❡s♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❝♦♥str✉çã♦ ❞❡ ár✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s é ♦ ❝♦♥❥✉♥t♦ ❢♦r♠❛❞♦ ♣❡❧♦ ♥♦♠❡ ❞❛s❡s♣é❝✐❡s ✐♥✈❡st✐❣❛❞❛s ❛❝r❡s❝✐❞♦ ❞❡ ✉♠❛ ❡s♣é❝✐❡ ❞❡♥♦♠✐♥❛❞❛ ❞❡ ✐♥ó❝✉❛✱ q✉❡ s❡rá ✉s❛❞❛ ♣❛r❛❢♦r♠❛r ♦ ❣❡♥❡ ✐♥ó❝✉♦✳ λ λ }❉❡✜♥✐çã♦ ✸✳✻✳✶ ✭❇❛s❡✮ ❖ ❝♦♥❥✉♥t♦ ❜❛s❡ B = X ∪{e ✱ ♦♥❞❡ e é ❞❡♥♦♠✐♥❛❞♦ ❞❡ ❣❡♥❡✲✐♥ó❝✉♦ ❡ X é ♦ ❝♦♥❥✉♥t♦ ❞❡ ❡s♣é❝✐❡s ❛♥❛❧✐s❛❞♦✳❖♥❞❡ ❝❛❞❛ ✐♥stâ♥❝✐❛ r❡♣r❡s❡♥t❛ ✉♠❛ ❡s♣❡❝✐❡ ❡ s✉❛s ❝❛r❛❝t❡ríst✐❝❛✱ ❛ ♣❛rt✐r ❞❡st❛ ❜❛s❡ é❣❡r❛❞❛ ✉♠❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛✳ ❆❧é♠ ❞✐ss♦✱ ♦ s✐st❡♠❛ ❣❡r❛ ✉♠ ✈❡t♦r ❞❡ ❜❛s❡s ❝♦♠♦ ❣r❛✉ ❞❡ s✐♠✐❧❛r✐❞❛❞❡ ❡♥tr❡ ❛s ✐♥stâ♥❝✐❛s ❞❛ ❜❛s❡✳ y , e x , e z > /e y , e x , e z ∈ B}❉❡✜♥✐çã♦ ✸✳✻✳✷ ✭●❡♥❡✮ ❖ ❝♦♥❥✉♥t♦ ❣❡♥❡ ● ❂ {< e q✉❡ s❛t✐s✲❢❛③ ♦ s❡❣✉✐♥t❡ ❝♦♥❥✉♥t♦ ❞❡ ❛①✐♦♠❛s ❞❡ ❢♦r♠❛çõ❡s ❞❡ ❣❡♥❡s✿ ∈ C(x = raiz(g i ))} ∩ {x ∈ X/∀g i ∈ C(x = f olha L (g i ))} ∪{x ∈ X/∀g i ∈ C(x = f olha R (g i ))}) = 1). ❋✐❣✉r❛ ✸✳✸✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ ●❡♥❡❉❡✜♥✐çã♦ ✸✳✻✳✸ ✭❈r♦♠♦ss♦♠♦✮ ❖ ❝♦♥❥✉♥t♦ ❝r♦♠♦ss♦♠♦ C = {c = {g 1 , g 2 , ..., g j } /{g1 , g2 , ..., g j } ⊆ G q✉❡ s❛t✐s❢❛③ ♦s s❡❣✉✐♥t❡s ❛①✐♦♠❛s ❞❡ ❢♦r♠❛çã♦ ❞❡ ❝r♦♠♦ss♦♠♦✿ , e1 , e3 )✳ , e3 , e5 )❡ (e2 , e5 , e7 )✱ (e4 ❖ ❣❡♥❡ ✐♥ó❝✉♦ ♥❡st❡ ❝❛s♦ é ♦ ❣❡♥❡ ❁e λ ✱e λ ✱e λ ❃✳ P♦r ❡①❡♠♣❧♦✱ ♦s ❣❡♥❡s ❞❛ ár✈♦r❡✜❧♦❣❡♥ét✐❝❛ ❞❛ ✜❣✉r❛ ✹✳✼ sã♦ (e6 ❢♦❧❤❛ R ❁❡ y , e x , e z >= e z ⇔ e z 6= e λ ♣❛r❛ t♦❞♦ ❣❡♥❡ s❡ ❛ ❜❛s❡ ❞❛ r❛✐③ ❡ ❢♦❧❤❛s❢♦r❡♠ ❞✐❢❡r❡♥t❡s ❞❛ ❜❛s❡ e λ ✱ ❡♥tã♦ ❡❧❛s ❞❡✈❡♠ s❡r t♦❞❛s ❞✐❢❡r❡♥t❡s✳ ❆ ✐♥t❡r♣r❡t❛çã♦ ❞❛❞❛ ♣❛r❛ ♦ t✐♣♦ ❛❜str❛t♦ ❣❡♥❡ g =< e y , e x , e z > é q✉❡ ❡❧❡ r❡♣r❡s❡♥t❛♣♦r ✉♠❛ ❞❡ ár✈♦r❡s s✐♠♣❧❡s ✭❋✐❣✉r❛ ✹✳✼✮✱ ❝♦♠ r❛✐③ ❡♠ e x ✱ ❢♦❧❤❛ à ❡sq✉❡r❞❛ e y ❡ ❢♦❧❤❛ à❞✐r❡✐t❛ e z ✱ ♦s q✉❛✐s s❛t✐s❢❛③❡♠ ♦ s❡❣✉✐♥t❡ ❝♦♥❥✉♥t♦ ❞❡ ❛①✐♦♠❛s ❞❡ ❢♦r♠❛çã♦ ❞❡ ❣❡♥❡s✿ ❞✐❢❡r❡♥t❡ ❞❛ ❜❛s❡ e λ ✱ ❡♥tã♦ ❛ ❜❛s❡ ♥❛s ❢♦❧❤❛s ❞❡✈❡ s❡r ❞✐❢❡r❡♥t❡ ❞❛ ❜❛s❡ ❞❛ r❛✐③ e x ❀ ⇔ e y 6= e λ♣❛r❛ t♦❞♦ ❣❡♥❡ s❡ ❛ ❜❛s❡ ❞❛ r❛✐③ ❢♦r ∀ y ∀ z❢♦❧❤❛ L ❁❡ y , e x , e z >= e y ♣❛r❛ t♦❞♦ ❣❡♥❡ s❡ ❛ ❜❛s❡ ❞❛ r❛✐③ ❢♦r ❛ ❜❛s❡ e λ✱ ❡♥tã♦ ❛ ❜❛s❡ ♥❛s ❢♦❧❤❛s t❛♠❜é♠ s❡rá ❛ ❜❛s❡ e λ ❀ ∀ y ∀ z r❛✐③ < ey , e x , e z >= e x⇔ e x 6= e λ ✸✳✻✳ ❊❙P❊❈■❋■❈❆➬➹❖ ❉❖ ●❆❆❉❚ P❆❘❆ ❖ P❘❖❇▲❊▼❆ ✸✻ ❖ ❝r♦♠♦ss♦♠♦ ❛q✉✐ é ✈✐st♦ ❝♦♠♦ ♦ ❝♦♥❥✉♥t♦ ❞❛s ár✈♦r❡s ❡❧❡♠❡♥t❛r❡s✱ ♦ q✉❛❧ ❛t❡♥❞❡❛s ❡①✐❣ê♥❝✐❛s ✐♠♣♦st❛ ♣❡❧♦s ❛①✐♦♠❛s ❞❡ ❢♦r♠❛çã♦ ❞❡ ❝r♦♠♦ss♦♠♦s ❧✐st❛❞♦s ❛❜❛✐①♦✿ ✸✳✻✳ ❊❙P❊❈■❋■❈❆➬➹❖ ❉❖ ●❆❆❉❚ P❆❘❆ ❖ P❘❖❇▲❊▼❆ ✸✼♣❛r❛ t♦❞♦ ❝r♦♠♦ss♦♠♦ ♦ ♥ú♠❡r♦ ♠á①✐♠♦ ❞❡ ♦❝♦rrê♥❝✐❛s ❞♦s ❡❧❡♠❡♥t♦s ❞♦ t✐♣♦ ❜❛s❡ ❋✐❣✉r❛ ✸✳✹✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ ❈r♦♠♦ss♦♠♦❯♠ ❝♦♥❥✉♥t♦ ❞❡ ❣❡♥❡s ❝♦♥t❡♥❞♦ t♦❞♦s ♦s ♣♦ssí✈❡✐s ❣❡♥❡s q✉❡ ♣♦❞❡rã♦ ❝♦♠♣♦r ♦s ❝r♦✲ ♠♦ss♦♠♦s ✭♦ ❝r♦♠♦ss♦♠♦ é ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❣❡♥❡s✱ q✉❡ ♥ã♦ s❡ r❡♣❡t❡♠✮ ❞❡ ❞❡t❡r♠✐♥❛❞❛♣♦♣✉❧❛çã♦✳ ✸✳✻✳✷ ❖♣❡r❛❞♦r❡s ●❡♥ét✐❝♦s ❆ss✐♠ ❝♦♠♦ ❛ ✐♥st❛♥❝✐❛çã♦ ❞♦s t✐♣♦s ❛❜str❛t♦s ❞❛❞♦s✿ ❜❛s❡✱ ❣❡♥❡✱ ❝r♦♠♦ss♦♠♦ ❡ ♣♦♣✉✲❧❛çã♦✱ ♣r❡s❡r✈❛r❛♠ ❛s ❡①✐❣ê♥❝✐❛s ❝♦♥t✐❞❛s ♥❛ ❞❡✜♥✐çã♦ ❞♦ ●❆❆❉❚✳ ❆ ✐♥st❛♥❝✐❛çã♦ ❞❛❢✉♥çõ❡s ❡ r❡❧❛çõ❡s ♥❡❝❡ssár✐❛s ♣❛r❛ ♦ ❝❛❧❝✉❧♦ ❞❛ ❢✉♥çã♦ ●❆❆❉❚ ❞❡✈❡♠ ❛t❡♥❞❡ ❛ t♦❞♦s ❛s♣ré✲❝♦♥❞✐çõ❡s ❞❡ s✉❛ ❞❡✜♥✐çã♦ ♦r✐❣✐♥❛❧✳ ◆❡st❛ s❡çã♦ s❡rã♦ ❛♣r❡s❡♥t❛❞♦ ❛ ❞❡✜♥✐çã♦ s♦♠❡♥t❡❞❛s ❢✉♥çõ❡s ❡ r❡❧❛çõ❡s ❝✉❥❛ ✐♥st❛♥❝✐❛çã♦ ♣❛r❛ ♦ ♣r❡s❡♥t❡ ♣r♦❜❧❡♠❛ ♠❛✐s ❝♦♥❝r❡t❛ ❞♦ q✉❡❛ ❞❡✜♥✐çã♦ ♦r✐❣✐♥❛❧✱ ✜❝❛♥❞♦ s✉❜t❡♥❞✐❞♦ q✉❡ ❛s ❢✉♥çõ❡s ❡ r❡❧❛çõ❡s q✉❡ ❢♦r❡♠ r❡✲❞❡✜♥✐❞❛s♥❡st❛ s❡çã♦ ❡ ♣r❡s❡r✈❛❞❛ s✉❛ ❞❡✜♥✐çã♦ ♦r✐❣✐♥❛❧✳❉❡✜♥✐çã♦ ✸✳✻✳✹ ✭●r❛✉✮ ❖ ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ ❞❡ ✉♠ ❣❡♥❡ é ✉♠❛ ❢✉♥çã♦ ❣r❛✉ ❞♦ s❡❣✉✐♥t❡ t✐♣♦✿ P y , e x , e z e ,i + m e i e i i |m − 2m |❣r❛✉✿ P → K t❛❧ q✉❡ ❣r❛✉✭he ✮ ❂ y z x ♦♥❞❡ K é ✉♠ ❝♦r♣♦ ✺ ♦r❞❡♥❛❞♦ ✳ ✺ ❯♠ ❝♦r♣♦ ♦r❞❡♥❛❞♦ é ✉♠❛ ❡str✉t✉r❛ ❛❧❣é❜r✐❝❛✱ ❝♦♠ ❞✉❛s ♦♣❡r❛çõ❡s✱ s❡♠ ❞✐✈✐s♦r❡s ♣ró♣r✐♦ ❞❡ ③❡r♦ ❡ ♠✉♥✐❞♦ ❞❡ ✉♠❛ ♦r❞❡♠✳ Ex :< R, ≤, +,①, 0, 1❃ ✸✳✻✳ ❊❙P❊❈■❋■❈❆➬➹❖ ❉❖ ●❆❆❉❚ P❆❘❆ ❖ P❘❖❇▲❊▼❆ ✸✽213, e , e P♦r ❡①❡♠♣❧♦✱ ♦ ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ ❞♦ ❣❡♥❡ ✭e ✮ é✿213 h) = |(m − 2m grau (i e , e , e e2 ,1 + m e 3 ,1 e 1 ,1 )| + ... + |(m e 2 ,7 + m e 3 ,7−2 m e 1 ,7 )| = |(1 + 0 − 2①1)| + |(1 + 1 − 2①0)| + |(1 + 1 − 2①1)| + |(0 + 1 − 2①0)| + |(0 + 0 − 2①1)| + |(0 + 0 − 2①0)| + |(0 + 0 − 2①0)| = 6 ❉❡✜♥✐çã♦ ✸✳✻✳✺ ✭❉♦♠✐♥❛♥t❡✮ ❖ ❣❡♥❡✲❞♦♠✐♥❛♥t❡✱ ♦✉ s✐♠♣❧❡s♠❡♥t❡ domi✱ é ✉♠❛ ❢✉♥✲çã♦ ❞♦ s❡❣✉✐♥t❡ t✐♣♦✿ domi : G × G → G  g λs❡ ¬(raiz (g) = raiz (bg))  gdomi(g, bg) = s❡ (raiz (g) = raiz (bg) ∧ (grau((g) ≤ grau(bg)) P♦r ❝♦♥✈❡♥çã♦✱ ♦  gb s❡ (raiz(g) = raiz(bg) ∧ (grau(bg) ≤ grau(g)). ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ ❞♦ ❣❡♥❡✲✐♥ó❝✉♦ ✐❣✉❛❧ ❛♦ ❡❧❡♠❡♥t♦ ♥❡✉tr♦ ❞♦ ❝♦r♣♦ ❑ ♣❛r❛ ❛ ♦♣❡r❛çã♦❞❡ ❛❞✐çã♦✱ ❧♦❣♦ ♦ ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ ❞♦ ❣❡♥❡✲✐♥ó❝✉♦ ♠❡♥♦r ❞♦ q✉❡ ♦ ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦❞♦s ♦✉tr♦s ❣❡♥❡s ♣❡rt❡♥❝❡♥t❡s ❛♦ t✐♣♦ ❛❜str❛t♦ ●✳ ❖ ❣❡♥❡ ❞♦♠✐♥❛♥t❡ ♣❛r❛ ✉♠❛ ❞❛❞❛ ❝❛r❛❝t❡ríst✐❝❛ ❞♦ ❣❡♥❡ q✉❡ ❝♦rr❡s♣♦♥❞❡ ❛ ❡①♣r❡ssã♦❢❡♥♦tí♣✐❝❛ ❞❡st❛ ❝❛r❛❝t❡ríst✐❝❛ ♠❛✐s ❛❞❛♣t❛❞❛ ❛ ❝♦♥✜❣✉r❛çã♦ ❛t✉❛❧ ❞♦ ❛♠❜✐❡♥t❡✳ ❆ ❢✉♥çã♦❞♦♠✐ ❢♦✐ ❞❡✜♥✐❞❛ ♣❛r❛ ✐♥❢♦r♠❛r ♦ ❣❡♥❡ ❞♦♠✐♥❛♥t❡ ❞❡ ✉♠ ♣❛r ❞❡ ❣❡♥❡✱ s❡ ♦s ❣❡♥❡s ❢♦r♥❡❝✐❞♦s λ♥ã♦ ❡①♣r❡ss❡♠ ✉♠❛ ♠❡s♠❛ ❝❛r❛❝t❡ríst✐❝❛ ❛ ❢✉♥çã♦ ❞♦♠✐ r❡t♦r♥❛♥❞♦ ♦ g ✱ ❝❛s♦ ❝♦♥trár✐♦❛ ❢✉♥çã♦ ❞♦♠✐ r❡t♦r♥❛ ♦ ❣❡♥❡ ❢♦r♥❡❝✐❞♦ ♠❛✐s ❛❞❛♣t❛❞♦ ♦ ❛♠❜✐❡♥t❡ ❛t✉❛❧✳ ❆ ♣r♦❞✉çã♦ ❞❡ ♥♦✈♦s ❝r♦♠♦ss♦♠♦s ❞✉r❛♥t❡ ♦ ♣r♦❝❡ss♦ ❡✈♦❧✉t✐✈♦ ❞❡ ✉♠❛ ♣♦♣✉❧❛çã♦ s❡r✈❡ ♣❛r❛ ❞✐r❡❝✐♦♥❛r ❛ ❜✉s❝❛ ♣♦r ❝r♦♠♦ss♦♠♦s ♠❛✐s ❛❞❛♣t❛❞♦s ❛tr❛✈és ❞❛ tr❛♥s♠✐ssã♦❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ♠❛✐♦r ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ ♣r❡s❡♥t❡s ♥♦s ❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦❛t✉❛❧✳ ❆ ❛❞❛♣t❛çã♦ ❞❡ ✉♠ ❝r♦♠♦ss♦♠♦ é ❞❛❞❛ ♣❡❧❛ ❢✉♥çã♦ ❛❞❛♣t✳❉❡✜♥✐çã♦ ✸✳✻✳✻ ✭❆❞❛♣t❛çã♦✮ ❖ ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ ❞❡ ✉♠ ❝r♦♠♦ss♦♠♦ é ✉♠❛ ❢✉♥çã♦ adpt ❞♦ s❡❣✉✐♥t❡ t✐♣♦✿ adapt : P → KP adapt(c) = grau(g)g∈c ❈❛♣ít✉❧♦ ✹ ❖ s✐st❡♠❛ ♣r♦♣♦st♦ ♣❛r❛ ❝♦♥str✉çã♦ ❞❡➪r✈♦r❡ ❋✐❧♦❣❡♥ét✐❝❛✭❙❊❚❆❳✮✹✳✶ ❆rq✉✐t❡t✉r❛ ◆♦r♠❛❧♠❡♥t❡ ❛ ❝♦♥str✉çã♦ ❞❡ ✉♠❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ é r❡❛❧✐③❛❞❛ ♣♦r ✉♠ t❛①♦♥♦♠✐st❛ ❡✉♠ ❣❡♥❡t✐❝✐st❛ q✉❡ ❛ ❝♦♥str♦❡♠ ♠❛♥✉❛❧♠❡♥t❡✳ ❖ ❙❊❚❆❳ ❛✉①✐❧✐❛ ♥❡st❛ t❛r❡❢❛ ❡✈✐t❛♥❞♦♣♦ssí✈❡✐s ❡rr♦s ♥❛ ❤♦r❛ ❞❛ ❝♦♥str✉çã♦ ❡ ♥♦ tr❛t❛♠❡♥t♦ ❞❡ ❞❛❞♦s ❛♠❜í❣✉♦s ❡ ✐♥❝♦♠♣❧❡t♦s✳❊❧❡ t❛♠❜é♠ ♣❡r♠✐t❡ ♠❛♥✐♣✉❧❛r ❞❛❞♦s ❝♦♠ ❞✐❢❡r❡♥t❡s r❡♣r❡s❡♥t❛çõ❡s✱ ❣❡r❡♥❝✐❛r ❡①♣❧♦sõ❡s ✶ ❝♦♠❜✐♥❛tór✐❛s ❞❡ t♦❞❛s ❛s ♣♦ssí✈❡✐s s♦❧✉çõ❡s ❣❡r❛❞❛s ♣❡❧❛ ♣r❡s❡♥ç❛ ♣❛r❝✐♠ô♥✐❝❛ ✳❉❡st❛ ❢♦r♠❛✱ ❡st❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ ✉♠ s✐st❡♠❛ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♣❛r❛ ❝r✐❛çã♦ ❞❡ ár✈♦✲ r❡s ✜❧♦❣❡♥ét✐❝❛s ❛ ♣❛rt✐r ❞❛ ❡♥tr❛❞❛ ❞❡ ✉♠❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❞❛s ❡s♣é❝✐❡s✱ ❡ss❡ s✐st❡♠❛ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ✉t✐❧✐③❛♥❞♦ ❛ ❧✐♥❣✉❛❣❡♠ ❞❡ ♣r♦❣r❛♠❛ ❏❆❱❆ ❝♦♠ ❛ ♣❧❛t❛❢♦r♠❛ ❞❡ ❞❡s❡♥✲✈♦❧✈✐♠❡♥t♦ ◆❡t❇❡❛♥s ■❉❊ ✻✳✼✳✶✳ ❖ r❡❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ss❛ ❜❛s❡ ❞❡ ❞❛❞♦s sér❛ ❢❡✐t❛ ❛tr❛✈és❞❛ ✐♥t❡r❢❛❝❡ ❞♦ s✐st❡♠❛ ❡ ❛ ❝r✐❛çã♦ ❞❛s ♣♦ssí✈❡✐s ár✈♦r❡s ❝❛♥❞✐❞❛t❛s sér❛ ❢❡✐t❛ ❛tr❛✈és ❞♦●❆❆❉❚ ✭❱✐❡✐r❛✱ ✷✵✵✸✮✱ ❝♦♥❢♦r♠❡ ✐❧✉str❛ ❛ ❋✐❣✉r❛ ✹✳✶✳ ❯s✉ár✐♦✿ ❖ ✉s✉ár✐♦ ❡s❝♦❧❤❡ q✉❛❧ ❛ ❜❛s❡ ❞❡ ❞❛❞♦s ❝♦♠ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❛s ❡s♣❡❝✐❡s ❧❤♦r ár✈♦r❡ ❣❡r❛❞❛ q✉❡ ❛t❡♥❞❛ ❛ ❞❡t❡r♠✐♥❛❞❛ r❡q✉✐s✐çã♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❝r✐tér✐♦s ❈♦♥❝❡✐t♦ ✉t✐❧✐③❛❞♦ ♥❛ s✐st❡♠át✐❝❛ ♠♦❞❡r♥❛ q✉❡ ❡st❛❜❡❧❡❝❡ q✉❡ ❛♦ ❝♦♥str✉✐r ❡ s❡❧❡❝✐♦♥❛r ár✈♦r❡s ✜❧♦✲ ❣❡♥ét✐❝❛s✱ ♦✉ s❡❥❛✱ ♦s ❝❧❛❞♦s✱ ♦ ♠❡❧❤♦r ❝r✐tér✐♦ é ❜❛s❡❛❞♦ ❡♠ s❡✉s ♣r✐♥❝í♣✐♦s✿ ♥♦r♠❛❧♠❡♥t❡ é ❝♦rr❡t♦ ♦r❡❧❛❝✐♦♥❛♠❡♥t♦ ♠❛✐s s✐♠♣❧❡s ❡♥❝♦♥tr❛❞♦ ❡♥tr❡ ❞♦✐s ✐♥❞✐✈í❞✉♦s✱ ❛q✉❡❧❡ q✉❡ ❛♣r❡s❡♥t❡ ♦ ♠❡♥♦r ♥ú♠❡r♦s ❞❡ ♣❛ss♦s ✐♥t❡r♠❡❞✐ár✐♦s ♦✉ ♠✉❞❛♥ç❛s ❡✈♦❧✉❝✐♦♥ár✐❛s✳ ✹✳✷✳ ❋❯◆❈■❖◆❆▲■❉❆❉❊❙ ❉❖ ❙❊❚❆❳✹✵ ❋✐❣✉r❛ ✹✳✶✿ ❆rq✉✐t❡t✉r❛ ✉t✐❧✐③❛❞❛ ♥❛ s♦❧✉çã♦ ✐♠♣❧❡♠❡♥t❛❞❛✳♣ré✲❡st❛❜❡❧❡❝✐❞♦s✳ ❙❡✉s t✐♣♦s ❡ ♦♣❡r❛❞♦r❡s ❡s♣❡❝í✜❝♦s ❛t✉❛♠ ♥♦s s❡r✈✐ç♦s ❞❛ ❝❛♠❛❞❛❛♥t❡r✐♦r ❞❡ ❢♦r♠❛ ❛ ♦rq✉❡str❛r ♦s ♠❡s♠♦s ♣❛r❛ ❝r✐❛çã♦ ❞❛s ár✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s✳ P❛r❛✐ss♦ ❡❧❡ ♥❡❝❡ss✐t❛ ❞❡ s❡✉s ❡❧❡♠❡♥t♦s ❜ás✐❝♦s ❛❞❛♣t❛❞♦ ❛♦ ♦ ♣r♦❜❧❡♠❛✳ ❆❧é♠ ❞✐ss♦✱ é ♥❡❝❡ssár✐♦ r❡ss❛❧t❛r q✉❡ ❡st❡ s✐st❡♠❛ ❢♦✐ ♣r♦❥❡t❛❞♦ ♣❛r❛ ❛✉①✐❧✐❛r ❡ ♦r✐❡♥t❛r♦ ✉s✉ár✐♦ ❞✉r❛♥t❡ ♦ ♣r♦❝❡ss♦ ❞❡ ❡①❡❝✉çã♦ ❡ s❡♠♣r❡ q✉❡ ✉♠ ❞❛❞♦ ❢♦r ♥❡❝❡ssár✐♦ ♦✉ ✉♠♣❛râ♠❡tr♦ ❢♦r ✐♥❞✐s♣❡♥sá✈❡❧ ❡ ♥ã♦ ❡st✐✈❡r ♥♦s ✈❛❧♦r❡s ✐♥✐❝✐❛✐s✱ ♦ ✉s✉ár✐♦ s❡rá s♦❧✐❝✐t❛❞♦ ❛❢♦r♥❡❝❡r ❡st❡ ❞❛❞♦ ♦✉ ✐♥❢♦r♠❛çã♦ ❢❛❧t❛♥t❡✳ P♦r ❡①❡♠♣❧♦✱ ♦ ♥♦♠❡ ❞♦ ❛rq✉✐✈♦ q✉❡ ❝♦♥té♠♦ ❝♦♥❥✉♥t♦ ❞❡ ❡s♣é❝✐❡s ❛ s❡r❡♠ ❛♥❛❧✐s❛❞❛s ♥ã♦ ♣♦❞❡ ❢❛③❡r ♣❛rt❡ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ✈❛❧♦r❡s✐♥✐❝✐❛✐s✱ r❛③ã♦ ♣❡❧❛ q✉❛❧ ❡❧❡ é s♦❧✐❝✐t❛❞♦ s❡♠♣r❡ q✉❡ ♦ ✉s✉ár✐♦ ♦r❞❡♥❛r ♦ ✐♥í❝✐♦ ❞❡ ❡①❡❝✉çã♦✳❯♠❛ t❡❧❛ ❡s♣❡❝í✜❝❛ ❞❡ ❜✉s❝❛ ❞❡ ❛rq✉✐✈♦s ♥♦ ♣❛❞rã♦ ❲✐♥❞♦✇s s❡rá ❡①✐❜✐❞❛ ♣❛r❛ q✉❡♦ ✉s✉ár✐♦ ❛♣♦♥t❡ ♣❛r❛ ♦ ❛rq✉✐✈♦ ❞❡s❡❥❛❞♦✳ ❉❡st❛ ❢♦r♠❛✱ ♦s r❡❝✉rs♦s ❡ ❛s ❢❛❝✐❧✐❞❛❞❡s❞✐s♣♦♥í✈❡✐s ♥❡st❛ ❢❡rr❛♠❡♥t❛ ❛❥✉❞❛r❛♠ ♠✉✐t♦ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦ ❡ ♣♦❞❡rã♦ s❡r út❡✐s t❛♠❜é♠ ♣❛r❛ ♥♦✈❛s ♣❡sq✉✐s❛s s♦❜r❡ ❋✐❧♦❣❡♥✐❛ ❡ s♦❜r❡ ❈♦♠♣✉t❛çã♦ ❊✈♦❧✉t✐✈❛✳ ❆s s❡❣✉✐♥t❡s ❝❛r❛❝t❡ríst✐❝❛s ♥ã♦ ❢♦r❛♠ ✐♠♣❧❡♠❡♥t❛❞❛s ♥❡st❛ ✈❡rsã♦ ❞♦ ❙❊❚❆❳✿❡s❝♦❧❤❡r ❛❧❣✉♠ ♦✉tr♦ ♠ét♦❞♦ ❞❡ ❜✉s❝❛❀ ❖ ❙❊❚❆❳ ❛✉①✐❧✐❛ ♥❛ t❛r❡❢❛ ❞❡ ❝♦♥str✉çã♦ ❞❡ ár✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s ❡✈✐t❛♥❞♦ ♣♦ssí✈❡✐s ❡rr♦s♥❛ ❤♦r❛ ❞❛ ❝♦♥str✉çã♦✱ ♣♦✐s ❢♦r♥❡❝❡ ❡①♣❧✐❝❛çõ❡s ♣❛r❛ ❞❡❝✐sõ❡s t♦♠❛❞❛s ♣❡❧♦ s✐st❡♠❛✱ ♥♦ ✹✳✷✳ ❋❯◆❈■❖◆❆▲■❉❆❉❊❙ ❉❖ ❙❊❚❆❳✹✶ tr❛t❛♠❡♥t♦ ❞❡ ❞❛❞♦s ❛♠❜í❣✉♦s ❡ ✐♥❝♦♠♣❧❡t♦s✳ ❊❧❡ t❛♠❜é♠ ♣❡r♠✐t❡ ♠❛♥✐♣✉❧❛r ❞❛❞♦s ❝♦♠ ❞✐❢❡r❡♥t❡s r❡♣r❡s❡♥t❛çõ❡s✱ ❣❡r❡♥❝✐❛r ❡①♣❧♦sõ❡s ❝♦♠❜✐♥❛tór✐❛s ❞❡ t♦❞❛s ❛s ♣♦ssí✈❡✐s s♦❧✉çõ❡s❣❡r❛❞❛s ♣❡❧❛ ♣r❡s❡♥ç❛ ♣❛r❝✐♠ô♥✐❝❛✳ ❖ s✐st❡♠❛ ♣♦ss✉✐ ✐♥t❡r❢❛❝❡ ❣rá✜❝❛ q✉❡ ❢♦✐ ♣r♦❥❡t❛❞❛ ♣❛r❛ ❢❛❝✐❧✐t❛r s✉❛ ❡①❡❝✉çã♦ ♣❡❧♦s✉s✉ár✐♦s✱ ♠❡s♠♦ q✉❡ ❡st❡s ♥ã♦ ❞♦♠✐♥❡♠ ❝♦♠♣❧❡t❛♠❡♥t❡ ❛s té❝♥✐❝❛s ❞❡ ❝♦♠♣✉t❛çã♦ ❡ ♣❡r✲♠✐t❡ ❛❥✉st❡ ❞♦s ♣r✐♥❝✐♣❛✐s ♣❛râ♠❡tr♦s r❡❧❛t✐✈♦s ❛♦ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ✉t✐❧✐③❛❞♦✱ t❛✐s ❝♦♠♦ t❛♠❛♥❤♦ ❞❛ ♣♦♣✉❧❛çã♦ ✐♥✐❝✐❛❧✱ ♣♦r❝❡♥t❛❣❡♠ ❞❡ ♠✉t❛çõ❡s✱ ♣♦r❝❡♥t❛❣❡♠ ❞❡ ❝r✉③❛♠❡♥t♦ ❡t❛①❛ ❞❡ s❡❧❡çã♦✳ ■♥✐❝✐❛❧♠❡♥t❡ ♦ ✉s✉ár✐♦ ❡①❡❝✉t❛rá ❛ ✐♥str✉çã♦ ❞❡ ✐♥✐❝✐❛❧✐③❛çã♦ ❞♦ ❙❊❚❆❳✳ ❆♣ós ❛ ❡①❡❝✉✲çã♦ ❞❡ss❛ ✐♥str✉çã♦✱ ♦ ♠ó❞✉❧♦ s✐♠❜ó❧✐❝♦ ❞♦ ❙❊❚❆❳ ❛♣r❡s❡♥t❛rá ❛ t❡❧❛ ♣r✐♥❝✐♣❛❧ ♠♦str❛❞❛♥❛ ❋✐❣✳✹✳✷✳ ❆❝❡ss❛♥❞♦ ❛s ♦♣çõ❡s ❞❡st❛ t❡❧❛✱ ♦ ✉s✉ár✐♦ ♣♦❞❡rá ❢♦r♥❡❝❡r ♦s ❞❛❞♦s s♦❜r❡ ❛s❡s♣é❝✐❡s ✐♥✈❡st✐❣❛❞❛s ✭✧❙❡❧❡❝✐♦♥❛ ❇❛s❡✧✮ ❋✐❣✉r❛ ✹✳✸✱ ❣❡r❛r ✉♠❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ♣❛r❛❡ss❛s ❡s♣é❝✐❡s ✭✧●❡r❛r ➪r✈♦r❡✧✮✱ ♠♦str❛r q✉❡♠ ❝r✐♦✉ ♦ s✐st❡♠❛ ✭✧❙♦❜r❡✧✮ ❡ ♣❡❞✐r ❛❥✉❞❛♣❛r❛ ❡♥t❡♥❞❡r ♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞♦ s✐st❡♠❛ ✭✧❆❥✉❞❛✧✮✳ ■♥✐❝✐❛❧♠❡♥t❡✱ ✉s❛♥❞♦ ❛ ♦♣çã♦ ✧❙❡✲❧❡❝✐♦♥❛ ❇❛s❡✧✱ ♦ ✉s✉ár✐♦ ❢♦r♥❡❝❡rá ❛ ❜❛s❡ q✉❡ ❡❧❡ ♣r❡t❡♥❞❡ ❣❡r❛r ❛ ár✈♦r❡✱ ❛❝❡ss❛♥❞♦ ❛♦♣çã♦ ✧●❡r❛r ➪r✈♦r❡✧❞♦ ♠❡♥✉ ♣✉❧❧✲❞♦✇♥ ❞❛ ♦♣çã♦✭❋✐❣✉r❛✳ ✹✳✸✮ ❡ ❡①✐❜❡ ❛ ♠❡❧❤♦r s♦❧✉çã♦✳ ❋✐❣✉r❛ ✹✳✷✿ ❚❡❧❛ ♣r✐♥❝✐♣❛❧ ❞♦ s✐st❡♠❛✳P❛r❛ ❛❜r✐r ♦ ❛rq✉✐✈♦ q✉❡ ❝♦♥t❡♠ ❛ ❜❛s❡ ❢♦r♥❡❝✐❞❛ ♣❡❧♦ ✉s✉ár✐♦ ♦ ❙❊❚❆❳ s♦❧✐❝✐t❛ ♦ ❛rq✉✐✈♦ q✉❡ ❝♦♥t❡rá ❡ss❛ ❜❛s❡ ❝♦♠♦ ♥❛ ❋✐❣✉r❛ ✹✳✸ ✳❙❡ ♦ ❛rq✉✐✈♦ ♥ã♦ ❢♦r s❡❧❡❝✐♦♥❛❞♦ ♦✉ ♥ã♦ ❢♦r ❝♦♠♣❛tí✈❡❧✱ ❙❊❚❆❳ ♠♦str❛rá ✉♠❛ ❥❛♥❡❧❛ ❞❡ ❛❧❡rt❛ ✐♥❢♦r♠❛♥❞♦ ♣❛r❛ ♦ ✉s✉ár✐♦ q✉❡ ♦ ❛rq✉✐✈♦ ♥ã♦ ❡①✐st❡ ❡ q✉❡ ♦ s✐st❡♠❛ ♥ã♦ ♣♦❞❡❛❜r✐✲❧♦ ✈✐❞❡ ❋✐❣✳✹✳✹✳ ❉❡ ♣♦ss❡ ❞❛ ❜❛s❡ ❝♦♠♦ ♥❛ ❋✐❣✉r❛ ✹✳✺✱ ♦ ✉s✉ár✐♦ ♣♦❞❡ s♦❧✐❝✐t❛r ❛♦ s✐st❡♠❛ q✉❡ ❣❡r❡❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ✈✐❞❡ ❋✐❣✳✹✳✸ ✧●❡r❛ ➪r✈♦r❡✧✱ ♥❡st❡ ♠♦♠❡♥t♦✱ ♦s ❞❛❞♦s ❢♦r♥❡❝✐❞♦ sã♦♣r❡♣❛r❛❞♦s ♣❛r❛ s❡r❡♠ ❡♥✈✐❛❞♦s ❛♦ ❛❧❣♦r✐t♠♦ ❞❡s❝r✐t♦ ♥♦ ❝❛♣ít✉❧♦ ✸ ❡ ♦ s✐st❡♠❛ ❣❡r❛ ❛ár✈♦r❡ ❝♦♠♦ ♥❛ ❋✐❣✉r❛ ✹✳✻✳ ❈♦♥❢♦r♠❡ ❛ ❞❡♠♦str❛çã♦ ♦ ●❆❆❉❚ é r❡s♣♦♥sá✈❡❧ ♣❡❧❛ ♣r❡❞✐çã♦ ❞❛s ♣♦ssí✈❡✐s ár✈♦✲ r❡s ✜❧♦❣❡♥ét✐❝❛s✱ ♣❛r❛ t❛❧✱ r❡❝❡❜❡ ❝♦♠♦ ❡♥tr❛❞❛ ✉♠❛ ❜❛s❡ ❞❡ ❞❛❞♦s r❡♣r❡s❡♥t❛❞❛ ♣❡❧❛s❝❛r❛❝t❡ríst✐❝❛ ❞❛ ❡s♣é❝✐❡ ❡ ❢♦r♥❡❝❡ ❝♦♠♦ s❛í❞❛ ❛s ár✈♦r❡s✳ ✹✳✷✳ ❋❯◆❈■❖◆❆▲■❉❆❉❊❙ ❉❖ ❙❊❚❆❳✹✷ ❋✐❣✉r❛ ✹✳✸✿ ❚❡❧❛ ♣r✐♥❝✐♣❛❧ ❝♦♠ ♦ ♠❡♥✉ ❞♦ s✐st❡♠❛✳❋✐❣✉r❛ ✹✳✹✿ ❚❡❧❛ ❞❡ ❛❧❡rt❛✳ ❋✐❣✉r❛ ✹✳✺✿ ❆♠♦str❛ ❞❡ ✉♠❛ ❜❛s❡ ✭❈❛♥❛ ❞❡ ❛çú❝❛r✮ ❞♦ ❡st✉❞♦ ❞❡ ❝❛s♦✳❆ s❡q✉ê♥❝✐❛ ❞❡ ❞❛❞♦s ❜✐♦❧ó❣✐❝♦s sã♦ r❡♣r❡s❡♥t❛❞❛s ♥♦ ❝♦♠♣✉t❛❞♦r ♣♦r ✐♥stâ♥❝✐❛s ❞❛ ❜❛s❡ ❞❡ ❞❛❞♦s✳ ❆♦ ✉t✐❧✐③❛r ♦ s✐st❡♠❛ ♣r♦♣♦st♦ ♥❡st❡ tr❛❜❛❧❤♦✱ ♦ ✉s✉ár✐♦ ❞❡✈❡ ✐♥❢♦r♠❛r❝♦♠♦ ❡♥tr❛❞❛ ♦ ❛rq✉✐✈♦ ❞❛ ❜❛s❡ ❢♦r♠❛t❛❞♦ ✭❜❛♥❝♦✳❝s✈✮✱ ♦✉ s❡❥❛✱ ❛s ✐♥stâ♥❝✐❛s ❞❛ ❜❛s❡✱ r❡♣r❡s❡♥t❛♥❞♦ ❛ ❝❛r❛❝t❡ríst✐❝❛ ❞❛ ❡s♣é❝✐❡✱ ♣❛r❛ ❛ q✉❛❧ ❞❡s❡❥❛ ♦❜t❡r s✉❛s ♣♦ssí✈❡✐s ár✈♦r❡s✳ ❖ ●❆❆❉❚ r❡❝❡❜❡ ❝♦♠♦ ❡♥tr❛❞❛ ❛ ❜❛s❡✱ ♦✉ ✐♥stâ♥❝✐❛s ❞❛ ❜❛s❡ ❞❡ ❞❛❞♦s✱ ♦♥❞❡ ❝❛❞❛ ✹✳✷✳ ❋❯◆❈■❖◆❆▲■❉❆❉❊❙ ❉❖ ❙❊❚❆❳✹✸ ❋✐❣✉r❛ ✹✳✻✿ ❊①❡♠♣❧♦ ❞❡ ár✈♦r❡ ❣❡r❛❞❛ ♣❡❧♦ s✐st❡♠❛ ❛tr❛✈és ❞❛ ❜❛s❡ ❞❡ ❞❛❞♦s ✭❈❛♥❛ ❞❡❛çú❝❛r✮ ❞♦ ❡st✉❞♦ ❞❡ ❝❛s♦✳✐♥stâ♥❝✐❛ r❡♣r❡s❡♥t❛ ✉♠❛ ❡s♣❡❝✐❡ ❡ s✉❛s ❝❛r❛❝t❡ríst✐❝❛✱ ❛ ♣❛rt✐r ❞❡st❛ ❜❛s❡ ❞❡ ❞❛❞♦s ❞❡❡♥tr❛❞❛ ♦ ❙❊❚❆❳ ❣❡r❛ ✉♠❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❝♦♠♦ ♥❛ ❋✐❣✉r❛ ✹✳✺✳ ❆❧é♠ ❞✐ss♦✱ ♦ s✐st❡♠❛ ❣❡r❛ ✉♠ ✈❡t♦r ❞❡ ❜❛s❡s ❝♦♠ ♦ ❣r❛✉ ❞❡ s✐♠✐❧❛r✐❞❛❞❡ ❡♥tr❡ ❛s ✐♥stâ♥❝✐❛s ❞❛ ❜❛s❡✳❋❡✐t♦ ✐ss♦✱ ♦ s✐st❡♠❛ ❣❡r❛ ❛ ♣♦♣✉❧❛çã♦ ✐♥✐❝✐❛❧ q✉❡ ♣❛rt✐r ❞♦ ✈❡t♦r ❞❡ ❜❛s❡ ✉♠ ♥ú♠❡r♦s❞❡ ❣❡♥❡s sã♦ ❣❡r❛❞♦s ❛❧❡❛t♦r✐❛♠❡♥t❡ r❡s♣❡✐t❛♥❞♦ ♦ ❛①✐♦♠❛ ❞❡ ❢♦r♠❛çã♦ ❞♦s ❣❡♥❡s ❝♦♠♦❞❡♠♦♥str❛❞♦ ♥♦ ❝❛♣ít✉❧♦ ✸✳ ❈❛❞❛ ❣❡♥❡ ♣♦❞❡ ❛ss✉♠✐r ✉♠❛ ♣♦ssí✈❡✐s ❡str✉t✉r❛s ❞❡✜♥✐❞❛s ♥❡st❡ tr❛❜❛❧❤♦✱ ❝♦♥❢♦r♠❡✐❧✉str❛ ❛ ❋✐❣✉r❛ ✹✳✼✳ ❏✉♥t♦ à ❣❡r❛çã♦ ❞❛ ♣♦♣✉❧❛çã♦ ✐♥✐❝✐❛❧✱ é ❣❡r❛❞♦ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❣❡♥❡s❝♦♥t❡♥❞♦ t♦❞♦s ♦s ♣♦ssí✈❡✐s ❣❡♥❡s q✉❡ ♣♦❞❡rã♦ ❝♦♠♣♦r ♦s ❝r♦♠♦ss♦♠♦s ✭♦ ❝r♦♠♦ss♦♠♦ é✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❣❡♥❡s✱ q✉❡ ♥ã♦ s❡ r❡♣❡t❡♠✮ ❞❡ ❞❡t❡r♠✐♥❛❞❛ ♣♦♣✉❧❛çã♦✳ ❚♦❞♦s ♦s ❣❡♥❡s❞♦s ❝r♦♠♦ss♦♠♦s ❞❡ q✉❛❧q✉❡r ♣♦♣✉❧❛çã♦ ❢❛③❡♠ ♣❛rt❡ ❞♦ r❡❢❡r✐❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❣❡♥❡s✳ ◆❛♣♦♣✉❧❛çã♦ ✐♥✐❝✐❛❧✱ ❝❛❞❛ ❝r♦♠♦ss♦♠♦ é ❝♦♥st✐t✉í❞♦ ❞❡ ❣❡♥❡s ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❣❡♥❡s✳ ◆❡st❛ ♣♦♣✉❧❛çã♦ ✐♥✐❝✐❛❧✱ ❛ ❧✐st❛ ❞❡ ❣❡♥❡s ❣❡r❛❞♦s ❛❧❡❛t♦r✐❛♠❡♥t❡ ♣❛ss❛ ♣❡❧♦ ♦♣❡r❛❞♦r❞❡ ❢❡❝✉♥❞❛çã♦ q✉❡ ❣❡r❛ ❛ ♣♦♣✉❧❛çã♦ ✐♥✐❝✐❛❧✳ ◆❡ss❛ ❧✐st❛ ❞❡ ❢❡❝✉♥❞❛çã♦ ✉♠ ❣❡♥❡ é ❡s❝♦✲❧❤✐❞♦ ❛❧❡❛t♦r✐❛♠❡♥t❡ ❡ ❛s ❢♦❧❤❛s ❞❡ss❡ ❣❡♥❡ sã♦ ❝♦♠❜✐♥❛❞❛s ❝♦♠ ❛ r❛✐③ ❞❡ ✉♠ ♦✉tr♦ ❣❡♥❡ q✉❡ ❝♦♠❜✐♥❡✱ ❢♦r♠❛♥❞♦ ✉♠❛ ár✈♦r❡ ❝♦♥❢♦r♠❡ ✐❧✉str❛ ❛ ❋✐❣✉r❛ ✹✳✽✳ ❖ ❝r♦♠♦ss♦♠♦ é ✉♠❝♦♥❥✉♥t♦ ❞❡ ❣❡♥❡s✱ q✉❡ r❡s♣❡✐t❛ ❢♦r♠❛çã♦ ❞❡ ❝r♦♠♦ss♦♠♦s q✉❡ ♦ ♠❡s♠♦ ❝r♦♠♦ss♦♠♦ ♥ã♦❛♣❛r❡ç❛ ♠❛✐s ❞❡ ✉♠❛ ✈❡③ ❡♠ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ♣♦♣✉❧❛çã♦✳ ✹✳✷✳ ❋❯◆❈■❖◆❆▲■❉❆❉❊❙ ❉❖ ❙❊❚❆❳✹✹ ❋✐❣✉r❛ ✹✳✼✿ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ❣❡♥❡ ♥♦ ❙❊❚❆❳✳❋✐❣✉r❛ ✹✳✽✿ ❋❡❝✉♥❞❛çã♦ ❡♥tr❡ ❞♦✐s ❣❡♥❡s ♥♦ ❙❊❚❆❳ ❆♣ós ❛ ❝r✐❛çã♦ ❞❛ ♣♦♣✉❧❛çã♦ ✐♥✐❝✐❛❧✱ ♦s ♦♣❡r❛❞♦r❡s sã♦ ❛♣❧✐❝❛❞♦s à ♣♦♣✉❧❛çã♦✱ ♦ ♣r✐✲♠❡✐r♦ ♦♣❡r❛❞♦r ❛♣❧✐❝❛❞♦ é ♦ ❞❡ s❡❧❡çã♦✳ ◆♦ ❡♥t❛♥t♦✱ ❛♥t❡s ❞♦ ♣r♦❝❡ss♦ ❞❡ s❡❧❡çã♦✱ é❛♣❧✐❝❛❞❛ ❛ s❡❧❡çã♦ ❡❧✐t✐st❛✱ ♦♥❞❡ é s❡❧❡❝✐♦♥❛❞♦ ♦s ♠❡❧❤♦r❡s ✐♥❞✐✈í❞✉♦s ❞❛ ♣♦♣✉❧❛çã♦ ❡ ♦s❛❞✐❝✐♦♥❛♠ ♥❛ ♣ró①✐♠❛ ❣❡r❛çã♦ s❡♠ t❡r q✉❡ ♣❛ss❛r ♣❡❧♦s ♦✉tr♦s ♦♣❡r❛❞♦r❡s✳ ◆♦ ♦♣❡r❛❞♦r ❣❡♥ét✐❝♦ ❞❡ s❡❧❡çã♦ ♦ ♣♦♥t♦ ❞❡ ❝♦rt❡ ❡st❛❜❡❧❡❝✐❞♦ é ❛ ❛❞❛♣t❛çã♦ ♠é❞✐❛ ❞♦s❝r♦♠♦ss♦♠♦s ❞❛ ♣♦♣✉❧❛çã♦✳ ❊st❛ ❛❞❛♣t❛çã♦ ♠é❞✐❛ é ♦❜t✐❞❛ ❛tr❛✈és ❞❛ ♠é❞✐❛ ❛r✐t♠ét✐❝❛❞❛ ♣♦♣✉❧❛çã♦✱ ♦ s♦♠❛tór✐♦ ❞❛s ❛❞❛♣t❛çõ❡s ❞❡ ❝❛❞❛ ❝r♦♠♦ss♦♠♦ ❞❛ ♣♦♣✉❧❛çã♦ é ❞✐✈✐❞✐❞♦♣❡❧♦ ♥ú♠❡r♦ ❞❡ ✐♥❞✐✈í❞✉♦s ❞❛ ♣♦♣✉❧❛çã♦✳ ❆ ❛❞❛♣t❛çã♦ ❞❡ ❝❛❞❛ ❝r♦♠♦ss♦♠♦ é ♦❜t✐❞❛♣❡❧♦ s♦♠❛tór✐♦ ❞♦ ❣r❛✉ ❞❡ ❛❞❛♣t❛çã♦ ❞❡ ❝❛❞❛ ❣❡♥❡ q✉❡ ❝♦♠♣õ❡ ♦ ❝r♦♠♦ss♦♠♦✱ ♦♥❞❡ ❛❛❞❛♣t❛çã♦ ❞❡ ❝❛❞❛ ❣❡♥❡ é ❛ s♦♠❛ ❞❛ ❝❛r❛❝t❡ríst✐❝❛s ❝♦♠✉♥s ❡♥tr❡ ❛ r❛✐③ ❡ ❛s ❢♦❧❤❛s✳❆ss✐♠✱ ♦s ✐♥❞✐✈í❞✉♦s q✉❡ ❡st✐✈❡r❡♠ ❛❝✐♠❛ ❞❡ss❡ ♣♦♥t♦ ❞❡ ❝♦rt❡ sã♦ s❡❧❡❝✐♦♥❛❞♦s✳ ❆♣ós ❛ s❡❧❡çã♦✱ ♦ ♦♣❡r❛❞♦r ❞❡ ❝r✉③❛♠❡♥t♦ é ❛♣❧✐❝❛❞♦✳ ◆♦ ♦♣❡r❛❞♦r ❣❡♥ét✐❝♦ ❞❡ ❝r✉③❛♠❡♥t♦✱ ♦s ✐♥❞✐✈í❞✉♦s ❡s❝♦❧❤✐❞♦s ♥❛ s❡❧❡çã♦ sã♦ s❡❧❡❝✐♦✲ ✹✳✸✳ ❯▼ ❊❙❚❯❉❖ ❉❊ ❈❆❙❖ ❘❊❆▲✿ ❇❆❙❊❆❉❖ ◆❖ ▼❊▲❍❖❘❆▼❊◆❚❖●❊◆➱❚■❈❖ ❉❆ ❈❆◆❆ ❉❊ ❆➬Ú❈❆❘ ✹✺♥❛❞♦s ❛❧❡❛t♦r✐❛♠❡♥t❡✱ ♦s ❝♦♠♣❛r❛✱ ♦s ❣❡♥❡s ❞♦♠✐♥❛♥t❡s ❞❡ ❝❛❞❛ ❝r♦♠♦ss♦♠♦ é ❡s❝♦❧❤✐❞♦❡ ❡ss❛ ❧✐st❛ ❞❡ ❣❡♥❡s ❞♦♠✐♥❛♥t❡s ♣❛ss❛ ♣❡❧♦ ♣r♦❝❡ss♦ ❞❡ ❢❡❝✉♥❞❛çã♦✳ ❆ss✐♠✱ t♦❞♦s ♦s✐♥❞✐✈í❞✉♦s ♣❛ss❛♠ ♣❡❧♦ ♣r♦❝❡ss♦ ❞❡ ❝r✉③❛♠❡♥t♦✳ ❆♣ós ♦ ❝r✉③❛♠❡♥t♦✱ ♦ ♦♣❡r❛❞♦ ❣❡♥ét✐❝♦ ❞❡ ♠✉t❛çã♦ é ❛♣❧✐❝❛❞♦✳ ❖ ♦♣❡r❛❞♦r ❣❡♥ét✐❝♦❞❡ ♠✉t❛çã♦ ❛♦ q✉❛❧ ❛ ♣♦♣✉❧❛çã♦ é s✉❜♠❡t✐❞❛ ✉t✐❧✐③❛ ❛♣❡♥❛s ❛ ❢✉♥çã♦ ❞❡ r❡♠♦çã♦✱ q✉❡ r❡♠♦✈❡ ❛ ❢♦❧❤❛ ❞❡ ✉♠ ❣❡♥❡ ❞♦s ❝r♦♠♦ss♦♠♦s ❛❧❡❛t♦r✐❛♠❡♥t❡✳ ❆♣ós ❛ ♠✉t❛çã♦ s❡r ❛♣❧✐❝❛❞❛ ♦ ❝✐❝❧♦ s❡ r❡♣❡t❡✳ ❆ ❝♦♥❞✐çã♦ ❞❡ ♣❛r❛❞❛ ❞♦ ●❆❆❉❚ é ♦✈❛❧♦r ❞❛ ❛❞❛♣t❛çã♦ ♠é❞✐❛ ❞❛ ♣♦♣✉❧❛çã♦ r❡s✉❧t❛♥t❡ ❞♦ ♦♣❡r❛❞♦r ❣❡♥ét✐❝♦ ❞❡ ♠✉t❛çã♦ s❡r✐❣✉❛❧ ❛♦ ✈❛❧♦r ❞❛ ❛❞❛♣t❛çã♦ ♠é❞✐❛ ❞❛ ♣♦♣✉❧❛çã♦ ❞❡ ♦r✐❣❡♠✱ ♦ q✉❡ ✐♠♣❧✐❝❛ q✉❡ ❛ ♦♣❡r❛çã♦❣❡♥ét✐❝❛ ❞❡ ♠✉t❛çã♦ ♥ã♦ ❛❞✐❝✐♦♥♦✉ ❣❡♥❡s ❛ ♥❡♥❤✉♠ ❝r♦♠♦ss♦♠♦ ❞❛ ♣♦♣✉❧❛çã♦ ❞❡ ♦r✐❣❡♠ ❡❝♦♥té♠✱ ♣♦rt❛♥t♦✱ ♦s ❝r♦♠♦ss♦♠♦s q✉❡ r❡♣r❡s❡♥t❛♠ ❛s ♣♦ssí✈❡✐s ár✈♦r❡s ❡♠ q✉❡stã♦✳ ❈❛s♦✐ss♦ ♥ã♦ ❛❝♦♥t❡ç❛✱ ♦ ♣♦♥t♦ ❞❡ ♣❛r❛❞❛ ♣♦❞❡rá s❡r ♦ ♥ú♠❡r♦ ❞❡ ❣❡r❛çõ❡s ♣ré✲❞❡t❡r♠✐♥❛❞♦♣❡❧♦ ✉s✉ár✐♦✳ ✹✳✸ ❯♠ ❡st✉❞♦ ❞❡ ❝❛s♦ r❡❛❧✿ ❇❛s❡❛❞♦ ♥♦ ♠❡❧❤♦r❛♠❡♥t♦ ❣❡♥ét✐❝♦ ❞❛ ❝❛♥❛ ❞❡ ❛çú❝❛r ❖ ♣♦♥t♦ ❞❡ ♣❛rt✐❞❛ ❞♦ ♣r♦❣r❛♠❛ ❞❡ ♠❡❧❤♦r❛♠❡♥t♦ ❣❡♥ét✐❝♦ ❞❛ ❈❛♥❛✲❞❡✲❆çú❝❛r ❞❛ ❘■✲❉❊❙❆ é ♦ ❜❛♥❝♦ ❞❡ ❣❡r♠♦♣❧❛s♠❛ ❧♦❝❛❧✐③❛❞♦ ♥❛ ❡st❛çã♦ ❞❡ ✢♦r❛çã♦ ❡ ❝r✉③❛♠❡♥t♦ ❞❛ ❙❡rr❛❞♦ ❖✉r♦ ✭❯❋❆▲✮✱ ♥♦ ♠✉♥✐❝í♣✐♦ ❞❡ ▼✉r✐❝✐✱ ❊st❛❞♦ ❞❡ ❆❧❛❣♦❛s✳ ◆❡ss❡ ❜❛♥❝♦ ❡stã♦ r❡✉♥✐❞♦s♠❛✐s ❞❡ ✷✵✵✵ ❣❡♥ót✐♣♦s✱ ❡♥tr❡ ❝✉❧t✐✈❛r❡s ✉t✐❧✐③❛❞♦s ♥♦ ♣❛ís✱ ❝❧♦♥❡s✱ ♦✉tr❛s ❡s♣é❝✐❡s r❡❧❛❝✐♦✲♥❛❞❛s ❛♦ ❣ê♥❡r♦ ❙❛❝❝❤❛r✉♠ ❡ ❝✉❧t✐✈❛r❡s ✐♠♣♦rt❛❞❛s ❞❛s ❞✐❢❡r❡♥t❡s r❡❣✐õ❡s ❝❛♥❛✈✐❡✐r❛s ❞♦♠✉♥❞♦✱ q✉❡ ❡st❛r ❧♦❝❛❧✐③❛❞♦ ♥❛ ✉♥✐❞❛❞❡ ❛❝❛❞ê♠✐❝❛ ❝❡♥tr♦ ❞❡ ❝✐ê♥❝✐❛s ❛❣rár✐❛s ❯✳❆✳❈❊❈❆ ✷ ✴❯❋❆▲ ✭❋✐❣✉r❛ ✹✳✾✮ ✳❆♣ós ❛ ♦❜t❡♥çã♦ ❞❛s s❡♠❡♥t❡s ❡♠ ❝r✉③❛♠❡♥t♦s ♣ré✲❡st❛❜❡❧❡❝✐❞♦s ♣❡❧❛s ❡q✉✐♣❡s ❞❛s ✉♥✐✈❡rs✐❞❛❞❡s q✉❡ ❝♦♠♣õ❡♠ ❛ ❘■❉❊❙❆✱ ❛s ♠❡s♠❛s sã♦ ❡♥✈✐❛❞❛s ❛♦s r❡s♣❡❝t✐✈♦s ❊st❛❞♦s✱♦♥❞❡ sã♦ ♣r♦❞✉③✐❞❛s ❛s ♣❧â♥t✉❧❛s q✉❡✱ ✉♠❛ ✈❡③ tr❛♥s♣❧❛♥t❛❞❛s ♣❛r❛ ♦ ❝❛♠♣♦✱ ❞❡✜♥❡♠ ❛♣r✐♠❡✐r❛ ❢❛s❡ ❞❡ s❡❧❡çã♦ (T 1)✳ ❆ ❘■❉❊❙❆ t❡♠ ♣r♦❞✉③✐❞♦ ❛♥✉❛❧♠❡♥t❡ ♠❛✐s ❞❡ ✶✳✺✵✵✳✵✵✵♣❧â♥t✉❧❛s ♣❛r❛ ❛ ❢❛s❡ ❚✶✳ ❊♠ ❛❧❣✉♠❛s ✉♥✐✈❡rs✐❞❛❞❡s ❛ s❡❧❡çã♦ é ❢❡✐t❛ ❡♠ ❞✉❛s é♣♦❝❛s✱ ❛❜r✐❧❡ ❥✉❧❤♦✱ ❞❡ ❢♦r♠❛ ❛ s❡ ❜✉s❝❛r✱ ♥❛q✉❡❧❛ ♣r✐♠❡✐r❛ é♣♦❝❛✱ ❝❧♦♥❡s q✉❡ ❛♣r❡s❡♥t❡♠ ❛ ❝❛r❛❝t❡✲ ríst✐❝❛ ✐♠♣♦rt❛♥t❡ ❞❡ ♣r❡❝♦❝✐❞❛❞❡✳ ❊st❡ r❛♠♦ ❞❡ s❡❧❡çã♦ ❧❡✈❛ ❛ s✐❣❧❛ ❍P ✭❍✐♣❡r ♣r❡❝♦❝❡✮✳▼❛✐s ❞❡ ✺ ♠✐❧ ♥♦✈♦s ❝❧♦♥❡s tê♠ s✐❞♦ ❣❡r❛❞♦s ❛♥✉❛❧♠❡♥t❡ ♣❡❧❛s ✉♥✐✈❡rs✐❞❛❞❡s✱ ✐♥❝❧✉✐♥❞♦ t❛♠❜é♠ ♦s ❍P✳ ❊st❡s ❝❧♦♥❡s sã♦ ❛✈❛❧✐❛❞♦s ♣♦st❡r✐♦r♠❡♥t❡ ♥❛s ❡st❛çõ❡s ❡①♣❡r✐♠❡♥t❛✐s ♥❛❢❛s❡ ❞❡♥♦♠✐♥❛❞❛ ❚✷✳ ❖s ❝❧♦♥❡s sã♦ ❛✈❛❧✐❛❞♦s ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ❡♠ ♣❛r❝❡❧❛s ❞❡ ✉♠ s✉❧❝♦ ✸ ❞❡ ✺ ❛ ✽ ♠❡tr♦s ❞❡ ❝♦♠♣r✐♠❡♥t♦ ❢♦♥t❡ ✳ ✷ ◆❛ s❡❣✉♥❞❛ ❢❛s❡ ❞❡ s❡❧❡çã♦ (T 2) s❡❧❡❝✐♦♥❛✲s❡ ❡♠ ♣❧❛♥t❛ ❡ s♦❝❛ ♦s ❝❧♦♥❡s s✉♣❡r✐♦r❡s✸ ❤tt♣✿✴✴✇✇✇✳❝❡❝❛✳✉❢❛❧✳❜r✴ ❤tt♣✿✴✴✇✇✇✳r✐❞❡s❛✳❝♦♠✳❜r✴♠❣❡♥❡t✐❝♦✳❤t♠ ✹✳✸✳ ❯▼ ❊❙❚❯❉❖ ❉❊ ❈❆❙❖ ❘❊❆▲✿ ❇❆❙❊❆❉❖ ◆❖ ▼❊▲❍❖❘❆▼❊◆❚❖●❊◆➱❚■❈❖ ❉❆ ❈❆◆❆ ❉❊ ❆➬Ú❈❆❘ ✹✻ q✉❡ ♣♦r s✉❛ ✈❡③ sã♦ ❛✈❛❧✐❛❞♦s ♥❛ ❢❛s❡ T 3✳ ❆ ❘■❉❊❙❆ t❡♠ s❡❧❡❝✐♦♥❛❞♦ ♣❛r❛ ❛ ❢❛s❡ T 3♠❛✐s ❞❡ ✸✵✵✵ ♥♦✈♦s ❝❧♦♥❡s ♣♦r ❛♥♦✳ ❆ ♣❛rt✐r ❞❡st❛ ❢❛s❡ ♦s ❝❧♦♥❡s s❡❧❡❝✐♦♥❛❞♦s ❡♠ ❝❛❞❛✉♥✐✈❡rs✐❞❛❞❡ sã♦ ✐♥t❡r❝❛♠❜✐❛❞♦s ❡♥tr❡ ❡❧❛s✳ ◆❡st❛ ❡t❛♣❛ ♦s ♥♦✈♦s ❝❧♦♥❡s sã♦ ♠✉❧t✐♣❧✐❝❛❞♦s❡ ✐♥tr♦❞✉③✐❞♦s ♥❛s ✉s✐♥❛s ❡ ❞❡st✐❧❛r✐❛s ❝♦♥✈❡♥✐❛❞❛s ❝♦♠ ❛s r❡s♣❡❝t✐✈❛s ✉♥✐✈❡rs✐❞❛❞❡s q✉❡❛t✉❛♠ ♥❛s ❞✐❢❡r❡♥t❡s r❡❣✐õ❡s ❝❛♥❛✈✐❡✐r❛s ❞♦ ❇r❛s✐❧✳ ◆❛s t❡rr❛s ❞❛s ✉s✐♥❛s ❡ ❞❡st✐❧❛r✐❛s t❡♠ s✐❞♦ ❛✈❛❧✐❛❞♦s ♣♦r ♠❡✐♦ ❞❡ ❡①♣❡r✐♠❡♥t♦s ♣♦r três ❛♥♦s ❝♦♥s❡❝✉t✐✈♦s ♦s ❝❧♦♥❡s ♣r♦♠✐ss♦r❡s✳❊st❛ ❢❛s❡ é ❞❡♥♦♠✐♥❛❞❛ ❋❛s❡ ❊①♣❡r✐♠❡♥t❛❧ F E✳ ❖ ♣r♦❣r❛♠❛ ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♥♦✈♦s ❝✉❧t✐✈❛r❡s ❞❡ ❝❛♥❛✲❞❡✲❛çú❝❛r é ♣♦r ♥❛t✉r❡③❛❡ss❡♥❝✐❛❧♠❡♥t❡ ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦✳ ▲♦❣♦✱ ❛ ♣❡rs✐stê♥❝✐❛ é ✉♠❛ ✈✐rt✉❞❡ ❞❛s ♣❡ss♦❛s ❡♥✈♦❧✲✈✐❞❛s ♥❡st❡ ♣r♦❝❡ss♦✳ ◆♦r♠❛❧♠❡♥t❡ ♦ ❧❛♥ç❛♠❡♥t♦ ❞❡ ♥♦✈♦s ❝✉❧t✐✈❛r❡s t❡♠ ♦❝♦rr✐❞♦ ❛♣ós❝❡r❝❛ ❞❡ ✶✸ ❛♥♦s ❞❡ ✐♥ú♠❡r❛s ❛✈❛❧✐❛çõ❡s ❞♦s ❝❧♦♥❡s ♣♦r ♠❡✐♦ ❞❡ ❡①♣❡r✐♠❡♥t♦s ♦❜s❡r✈❛♥❞♦✲ s❡ ❛ r❡❛çã♦ ❞♦s ❝❧♦♥❡s às ❞♦❡♥ç❛s ❡ ♣r❛❣❛s ❡ ❛ ♣r♦❞✉t✐✈✐❞❛❞❡ ❞♦s ♠❡s♠♦s ❡♠ ❞✐❢❡r❡♥t❡s❛♠❜✐❡♥t❡s ❞❡ ♣r♦❞✉çã♦✳ ❇✉s❝❛♥❞♦ ❞✐♠✐♥✉✐r ❡ss❡ t❡♠♣♦✱ ✐♥✐❝✐❛♠♦s ✉♠ ❡st✉❞♦ s♦❜r❡ ❛ ❜❛s❡ ❞❡ ❞❛❞♦s ❡①✐st❡♥t❡♥❛ ❘■❉❊❙❆✱ ❡st❡ ❡st✉❞♦ ❞❡ ❝❛s♦ r❡❢❡r❡✲s❡ ❛ ✉♠ ❜❛♥❝♦ ❞❡ ❝❛r❛❝t❡r✐③❛çã♦ ♣❡rt❡♥❝❡ ❛♦Pr♦❣r❛♠❛ ❞❡ ▼❡❧❤♦r❛♠❡♥t♦ ❣❡♥ét✐❝♦ ❞❛ ❝❛♥❛✲❞❡✲❛çú❝❛r ✲ P▼●❈❆✳ ❋✐❣✉r❛ ✹✳✾✿ ■♠❛❣❡♠ ❞❛ ❙❡rr❛ ❞♦ ❖✉r♦ ❧♦❝❛❧✐③❛❞❛ ❡♠ ▼✉r✐❝✐✲❆❧ ❋♦♥t❡✿ ❈❡❝❛ ✹✳✸✳✶ ❉❡s❝r✐çã♦ ❞❛ ❇❛s❡ ❞♦ ❡st✉❞♦ ❞❡ ❝❛s♦✳ ❊♠ ❜✉s❝❛ ❞❡ ✉♠ ♠❡❧❤♦r ❡♥t❡♥❞✐♠❡♥t♦ ❞❛ ❜❛s❡ ❞❡ ❞❛❞♦s ✐r❡♠♦s ❞❡s❝r❡✈❡r ❛s ❝❛r❛❝t❡ríst✐❝❛s❡①✐st❡♥t❡ ♥❛ ❜❛s❡✳ ✹✳✹✳ ❈❖▼P❆❘❆➬Õ❊❙ ❊◆❚❘❊ ❖❙ ❆▲●❖❘■❚▼❖❙ ✹✼❙❡❣✉❡ ❛❜❛✐①♦ ✉♠❛ ❧❡✈❡ ❡①♣❧✐❝❛çã♦ s♦❜r❡ ❝❛❞❛ ❛tr✐❜✉t♦ ❞❛ ❡s♣é❝✐❡s ❞❡ ❝❛♥❛✲❞❡✲❛çú❝❛r ❡①✐st❡♥t❡ ♥❛ ❜❛s❡✿❇❘■❳ ✲ é ✉♠❛ ❡s❝❛❧❛ ♥✉♠ér✐❝❛ q✉❡ ♠❡❞❡ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ só❧✐❞♦s s♦❧ú✈❡✐s ❡♠ ✉♠❛ ❇❘❖ ✲ ❇r♦t❛çã♦ ❞❡ s♦❝❛r✐❛✲ ◗✉❛♥t✐✜❝❛çã♦ ❞♦ ❛♣❛r❡❝✐♠❡♥t♦ ❞❡ ❜r♦t♦s ♥❛ s♦❝❛ ✭✷ ✹✳✹ ❈♦♠♣❛r❛çõ❡s ❡♥tr❡ ♦s ❛❧❣♦r✐t♠♦s ◆❡st❛ s❡çã♦ ✐r❡♠♦s ❝♦♠♣❛r❛r ❞✉❛s ♠❛tr✐③❡s ❝❛r❛❝t❡ríst✐❝❛s✱ ✉♠❛ s❡♠ ♣❛r❝✐♠ô♥✐❛ ❡ ♦✉tr❛❝♦♠ ♣❛r❝✐♠ô♥✐❛✳ P❛r❛ ✐ss♦ s❡rá ❣❡r❛❞❛ ✉♠❛ ár✈♦r❡ ♣❛r❛ ❝❛❞❛ t✐♣♦ ❞❡ ❛❧❣♦r✐t♠♦ ❞❡s❝r✐t♦♥❡st❡ tr❛❜❛❧❤♦ ✉s❛♥❞♦ ❡ss❛s ♠❛tr✐③❡s ❡ t❛♠❜é♠ s❡rã♦ ❣❡r❛❞❛s ár✈♦r❡s ♣❛r❛ r❡♣r❡s❡♥t❛r ♦ r❡s✉❧t❛❞♦ ❞❡ ❝❛❞❛ ✉♠ ❞❡ss❡s ❛❧❣♦r✐t♠♦s ♠❡♥❝✐♦♥❛❞♦s✳ ❚♦❞♦s ♦s ❛❧❣♦r✐t♠♦s ✐rã♦ ✉s❛r ❛s ✹✳✹✳ ❈❖▼P❆❘❆➬Õ❊❙ ❊◆❚❘❊ ❖❙ ❆▲●❖❘■❚▼❖❙ ✹✽♠❡s♠❛s ❜❛s❡s ❞❡ t❡st❡ q✉❡ é ✉♠❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ s❡♠ ♣❛r❝✐♠ô♥✐❛ ✈✐❞❡ ❚❛❜❡❧❛ ✹✳✶ ❡♦✉tr❛ ❜❛s❡ ❝♦♠ ♣❛r❝✐♠ô♥✐❛ ✈✐❞❡ ❚❛❜❡❧❛✹✳✺✳ ❚❛❜❡❧❛ ✹✳✶✿ ▼❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ s❡♠ ♣❛r❝✐♠ô♥✐❛ ✉s❛❞❛ ♣❛r❛ t❡st❛r ♦s ❛❧❣♦r✐t♠♦s✳ ❈✶ ❈✷ ❈✸ ❈✹ ❈✺ ❈✻ ❆ ✵ ✵ ✵ ✵ ✵ ✵❇ ✶ ✵ ✵ ✵ ✵ ✵ ❈ ✶ ✶ ✶ ✵ ✶ ✵ ❉ ✶ ✶ ✶ ✶ ✵ ✶ ❚❛❜❡❧❛ ✹✳✷✿ ▼❛tr✐③ ❞✐stâ♥❝✐❛ s❡♠ ♣❛r❝✐♠ô♥✐❛✳ ❆ ❇ ❈ ❉ ❆ ✵ ✵ ✵❇ ✵ ✶ ✶ ❈ ✵ ✶ ✸❉ ✵ ✶ ✸ ❚❛❜❡❧❛ ✹✳✸✿ ▼❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❝♦♠ ♣❛r❝✐♠ô♥✐❛ ✉s❛❞❛ ♣❛r❛ t❡st❛r ♦s ❛❧❣♦r✐t♠♦s✳ ❈✶ ❈✷ ❈✸ ❈✹ ❈✺ ❈✻ ❈✼ ❈✽ ❆ ✶ ✶ ✵ ✵ ✵ ✵ ✶ ✶❇ ✶ ✶ ✶ ✶ ✵ ✵ ✵ ✵ ❈ ✶ ✶ ✵ ✵ ✶ ✶ ✵ ✵ ❉ ✵ ✵ ✶ ✶ ✶ ✶ ✶ ✶ ❚❛❜❡❧❛ ✹✳✹✿ ▼❛tr✐③ ❉✐stâ♥❝✐❛ ❝♦♠ ♣❛r❝✐♠ô♥✐❛✳ ❆ ❇ ❈ ❉ ❆ ✷ ✷ ✷❇ ✷ ✷ ✷ ❈ ✷ ✷ ✷❉ ✷ ✷ ✷ ❙❡❣✉❡♠ ♦s r❡s✉❧t❛❞♦s ❡ ❛s ár✈♦r❡s ❣❡r❛❞❛ ❝♦♠ ♦s ❛❧❣♦r✐t♠♦s ♠❡♥❝✐♦♥❛❞♦s ❛♥t❡r✐♦r✲♠❡♥t❡✳ ✹✳✹✳ ❈❖▼P❆❘❆➬Õ❊❙ ❊◆❚❘❊ ❖❙ ❆▲●❖❘■❚▼❖❙ ✹✾❋✐❣✉r❛ ✹✳✶✵✿ ➪r✈♦r❡ ❣❡r❛❞❛ ♣❡❧❛ r❡❣r❛ ❞❡ ■♥❝❧✉sã♦ ❡ ❊①❝❧✉sã♦ ♥❛ ♠❛tr✐③ s❡♠ ♣❛r❝✐♠ô♥✐❛ ❖ ♣r✐♠❡✐r♦ ❛❧❣♦r✐t♠♦ ♠❡♥❝✐♦♥❛❞♦ ♥❡st❡ tr❛❜❛❧❤♦ ❢♦✐ ♦ ❞❡ r❡❣r❛ ❞❡ ■♥❝❧✉sã♦ ❡ ❊①❝❧✉✲ sã♦✳ ❊st❡ ♣♦r s✉❛ ✈❡③ ❣❡r♦✉ ❛ ár✈♦r❡ ❝♦♠ ❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ s❡♠ ♣❛r❝✐♠ô♥✐❛ ✈✐❞❡❚❛❜❡❧❛ ✹✳✶✱ ❣❡r♦✉ ❛ ár✈♦r❡ ♠♦str❛❞❛ ♥❛ ❋✐❣✉r❛ ✹✳✶✵✳ ◆♦t❛♠♦s q✉❡ ♦ ❛❧❣♦r✐t♠♦ ♦❜t❡✈❡ ✉♠ ❡s❝♦r❡ ♠á①✐♠♦ ❞❡ ✸✭três✮✱ ❛ ♣r✐♠❡✐r❛ r❛✐③ ❣❡r❛❞❛❢♦✐ ❛ A✱ ♥♦t❛♠♦s q✉❡ ♥❛ ♠❛tr✐③ ❛ ❡s♣é❝✐❡ A t❡♠ ♦s ✈❛❧♦r❡s ❞❡ s✉❛s ❝❛r❛❝t❡ríst✐❝❛s ✵✭③❡r♦✮✳■st♦ s✐❣♥✐✜❝❛ q✉❡ ❡st❛ ❡s♣é❝✐❡ ♥ã♦ t❡♠ ♥❡♥❤✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ s✐♠✐❧❛r ❛ ♦✉tr❛✱ ♣♦rt❛♥t♦✱❞❡✈❡r✐❛ s❡r ❣❡r❛❞❛ ♣♦r ú❧t✐♠♦✳ ❏á ♥❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❝♦♠ ♣❛r❝✐♠ô♥✐❛ ✈✐❞❡ ❚❛❜❡❧❛ ✹✳✺ ❡ss❡ ❛❧❣♦r✐t♠♦ ♥ã♦ ❝♦♥s❡❣✉❡❣❡r❛r ❛ ár✈♦r❡✱ ♣♦✐s t♦❞❛s ❛s ❡s♣é❝✐❡s tê♠ ❛ ♠❡s♠❛ ❝❛r❞✐♥❛❧✐❞❛❞❡✳ ❖ s❡❣✉♥❞♦ ❛❧❣♦r✐t♠♦ ✭❆❧❣♦r✐t♠♦ ❞❡ ❲❛❣♥❡r✮ ✉s❛♥❞♦ ❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ s❡♠ ♣❛r✲❝✐♠ô♥✐❛ ❣❡r♦✉ ❛ s❡❣✉✐♥t❡ ár✈♦r❡✱ ❝♦♥❢♦r♠❡ ♠♦str❛❞♦ ♥❛ ❋✐❣✉r❛ ✹✳✶✶✳ ❋✐❣✉r❛ ✹✳✶✶✿ ➪r✈♦r❡ ❣❡r❛❞❛ ♣❡❧♦ ❆❧❣♦r✐t♠♦ ❞❡ ❲❛❣♥❡r❆ ár✈♦r❡ ❣❡r❛❞❛ ✈❛✐ ❞❡♣❡♥❞❡r ❞❛ ♦r❞❡♠ ♥❛ q✉❛❧ ❛s ❡s♣é❝✐❡s ❡stã♦ ❞✐s♣♦st❛s ♥❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛✳ P❛r❛ s❡ ♦❜t❡r ✉♠❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ót✐♠❛ ♥❡ss❡ ❝❛s♦✱ é ♥❡❝❡ssár✐♦ ❛❧t❡r❛r❛s ♣♦s✐çõ❡s ❞❛s ❡s♣é❝✐❡s ♥❛ ♠❛tr✐③ ❛♥❛❧✐s❛❞❛✳ ✹✳✹✳ ❈❖▼P❆❘❆➬Õ❊❙ ❊◆❚❘❊ ❖❙ ❆▲●❖❘■❚▼❖❙ ✺✵◆♦ ❝❛s♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ❲❛❣♥❡r ❛♣❧✐❝❛❞♦ à ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❝♦♠ ♣❛r❝✐♠ô♥✐❛✱ ♥ã♦ ❝♦♥s❡❣✉✐♠♦s ❝r✐❛r ❛ ár✈♦r❡✱ ♠❡s♠♦ ❛❧t❡r❛♥❞♦ ❛ ♦r❞❡♠ ❞❛s ❡s♣é❝✐❡s✱ ♣♦✐s ❛s ❡s♣é❝✐❡s tê♠❛s ♠❡s♠❛s ❝❛r❞✐♥❛❧✐❞❛❞❡s✳ ❏á ♦ ❝❛s♦ ❞♦ ❆❧❣♦r✐t♠♦ ❞❛s ▼é❞✐❛s ❝♦♥s❡❣✉✐♠♦s ❣❡r❛r ❛ s❡❣✉✐♥t❡ ár✈♦r❡ ✈✐❞❡ ❋✐❣✉r❛✹✳✶✷ ♣❛r❛ ❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ s❡♠ ♣❛r❝✐♠ô♥✐❛✳ ❋✐❣✉r❛ ✹✳✶✷✿ ➪r✈♦r❡ ❣❡r❛❞❛ ♣❡❧♦ ❆❧❣♦r✐t♠♦ ❞❡ ▼é❞✐❛s◆❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ s❡♠ ♣❛r❝✐♠ô♥✐❛✱ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ▼é❞✐❛s ❝♦♥stró✐ ❛ ár✈♦r❡ ót✐♠❛ ❝♦♠♦ ♠♦♥str❛❞♦ ♥❛ ❋✐❣✉r❛ ✹✳✶✷✱ ♣♦✐s ♦ ♠❡s♠❛ ♥ã♦ t❡♠ ♣❛r❝✐♠ô♥✐❛✳ ❈❛s♦ t❡✲♥❤❛✱ ❡ss❡ ❛❧❣♦r✐t♠♦ ✐rá ❞❡♣❡♥❞❡r ❞❛ ♦r❞❡♠ ♥❛ q✉❛❧ ❛s ❡s♣é❝✐❡s ❡stã♦ ❞✐s♣♦st❛s ♥❛ ♠❛tr✐③❞✐stâ♥❝✐❛✳ ❖ ❛❧❣♦r✐t♠♦ ♥❡st❡ ❝❛s♦ ❢✉♥❝✐♦♥❛ ✐❣✉❛❧ ❛♦ ♦ ❞❡ ❲❛❣♥❡r✳ P♦r ú❧t✐♠♦✱ ❢♦r❛♠ ❛♥❛❧✐s❛❞❛s ❛s ár✈♦r❡s ❣❡r❛❞❛s ♣❡❧♦ ❙❊❚❆❳ ♣❛r❛ ❛s ♠❡s♠❛s ♠❛tr✐③❡s✱❝♦♥❢♦r♠❡ ❛ ❋✐❣✉r❛ ✹✳✶✸✳ ❋✐❣✉r❛ ✹✳✶✸✿ ➪r✈♦r❡s ❣❡r❛❞❛s ♣❡❧♦ ❙❊❚❆❳✳❈♦♥❢♦r♠❡ ❛s ár✈♦r❡s ❣❡r❛❞❛s ♣❡❧♦ ❙❊❚❆❳✱ ♣♦❞❡♠♦s ❝♦♥❝❧✉✐r q✉❡ ♦ ♠❡s♠♦ ♥ã♦ ❛♣r❡✲ ✹✳✺✳ P❘❖❇▲❊▼❆❙ ❊◆❈❖◆❚❘❆❉❖❙✺✶ s❡♥t❛ ♦s ♣r♦❜❧❡♠❛s ❞♦s ♦✉tr♦s ❛❧❣♦r✐t♠♦s✱ ♣♦✐s ♦ ♠❡s♠♦ ❣❡r❛ ár✈♦r❡s ót✐♠❛s ♣❛r❛ ❛s ❞✉❛s ♠❛tr✐③❡s✱ ♣❡r❝❡❜❡✲s❡ t❛♠❜é♠ q✉❡ ❡❧❡ ❣❡r❛ t♦❞❛s ❛s ár✈♦r❡s ót✐♠❛s✱ ❞❡✐①❛♥❞♦ ♣❛r❛ ♦✉s✉ár✐♦ ♦ ❝r✐tér✐♦ ❞❛ ❡s❝♦❧❤❛✳ ❚❛❜❡❧❛ ✹✳✺✿ ❙❝♦r❡ ❞❡ ❝❛❞❛ ❛❧❣♦r✐t♠♦✳ ❆❧❣♦r✐t♠♦s ❚❛❜✳ ❈♦♠ P❛r❝✐♠ô♥✐❛ ❚❛❜✳ s❡♠ P❛r❝✐♠ô♥✐❛ ■♥❝❧✉sã♦ ❡ ❊①❝❧✉sã♦ ✶ ✸❲❛❣♥❡r ✶ ✹ ▼é❞✐❛s ✭❯P●▼❆✮ ✶ ✹❙❊❚❆❳ ✹ ✹ ❆ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ❝♦♥str✉í❞❛ ♣❡❧♦ ❙❊❚❆❳ ❡stá r❡s♣❛❧❞❛❞❛ s♦❜ ❛s ♣r❡♠✐ss❛s ❇✐♦✲❧ó❣✐❝❛s✱ ❥á q✉❡ ❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ❝♦♥str✉í❞❛ é r❡s✉❧t❛♥t❡ ❞❛ ❛♥á❧✐s❡ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s❛♣r❡s❡♥t❛❞❛s ♥❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛s ❞♦s s❡r❡s ✐♥✈❡st✐❣❛❞♦ ❡ ♥♦s ❢❛t♦s ❢♦r♥❡❝✐❞♦s ♣❡❧♦✉s✉ár✐♦ ❬✷❪ ✱ ❬✸✼❪✱ ❬✹✼❪✱ ❬✸✸❪✳ ❉❡✈❡✲s❡ r❡ss❛❧t❛r q✉❡ ❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ❝♦♥str✉í❞❛ ♣❡❧♦❙❊❚❆❳ ♥ã♦ s❡rá ❞❡♣❡♥❞❡♥t❡ ❞❛ ♦r❞❡♠ ♥❛ q✉❛❧ ♦s ♦r❣❛♥✐s♠♦s ❡stã♦ ❞✐s♣♦st♦s ♥❛ ♠❛tr✐③❝❛r❛❝t❡ríst✐❝❛✳ ✹✳✺ Pr♦❜❧❡♠❛s ❊♥❝♦♥tr❛❞♦s ❖ ❛❧❣♦r✐t♠♦ ❞❛ r❡❣r❛ ❞❡ ✐♥❝❧✉sã♦ ❡ ❡①❝❧✉sã♦ ❡ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❲❛❣♥❡r s❡r✈❡♠ ♠✉✐t♦❜❡♠ ♣❛r❛ ❝♦♥str✉✐r ❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ót✐♠❛ q✉❛♥❞♦ ♦s ❞❛❞♦s s♦❜r❡ ❛ ❡✈♦❧✉çã♦ ❞❛s ✹ ❝❛r❛❝t❡ríst✐❝❛s ❛♣r❡s❡♥t❛❞❛s ♣❡❧❛s ❡s♣é❝✐❡s ♥ã♦ ❛♣r❡s❡♥t❛♠ ❝♦♥✢✐t♦s ✳ P♦✐s✱ s❡ ❡ss❡s ❞❛❞♦s❢♦r❡♠ ❝♦♥✢✐t❛♥t❡s✱ ❡♥tã♦ ❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ ❞✐♠❡♥sã♦ n①m t❡rá ❞✉❛s ❝♦❧✉♥❛s ✐ ❡❥✱ t❛❧ q✉❡✿ ∀ x n,x 6= i ∩ S j 6= ⊘, Si ⊂ Sj① ∈ 1, ..., m,∃S ❂ ♥⑤ c ✵ ❝♦♠ S ❡ ✈✐❝❡✲✈❡rs❛✳ P♦r ❡①❡♠♣❧♦✱ ❝♦♥s✐❞❡r❡ ❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❞❛ ❚❛❜❡❧❛ ✹✳✻✳❚❛❜❡❧❛ ✹✳✻✿ ▼❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❝♦♠ ❝♦♥✢✐t♦ ✶ ✷ ✸ ✹ ✺ ✻ ❆ ✵ ✵ ✵ ✵ ✵ ✵❇ ✶ ✶ ✵ ✵ ✶ ✶ ❈ ✶ ✶ ✶ ✶ ✶ ✶❉ ✶ ✶ ✶ ✶ ✵ ✵1234✹ ■♥✐❝✐❛❧♠❡♥t❡ ❝♦♥stró✐✲s❡ ♦s ❝♦♥❥✉♥t♦ S ❂ {B, C, D} ,❙ ❂ {B, C, D} ,❙ ❂ {C, D} ,❙ ❈♦♥✢✐t♦ ✲ ❖ ❝♦♥✢✐t♦ ♦❝♦rr❡ q✉❛♥❞♦ ❛s r❡❧❛çõ❡s ❞❡ ♣❛r❡♥t❡s❝♦ ❡①♣r❡ss❛s ♣♦r ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ ❝♦♥✲ tr❛❞✐③❡♠ ❛s r❡❧❛çõ❡s ❞❡ ♣❛r❡♥t❡s❝♦ ❡①♣r❡ss❛s ♣♦r ✉♠❛ ♦✉tr❛ ❝❛r❛❝t❡ríst✐❝❛✳ ✹✳✺✳ P❘❖❇▲❊▼❆❙ ❊◆❈❖◆❚❘❆❉❖❙56123456 ✺✷= S , S = S , eS = S ❂ {C, D} ,❙ ❂ {B, C} ,❙ ❂ {B, C} , noteque❙ ✱ ❡♥tã♦ t❡♠✲s❡ ❛ s❡❣✉✐♥t❡ ❛♥á❧✐s❡ ❞♦s ❞❛❞♦s✿ ❡ S ✱ ❧♦❣♦ ❛s ❝❛r❛❝t❡ríst✐❝❛s ✶ ❡ ✷ ♥ã♦ ❛♣r❡s❡♥t❛♠ ❝♦♥✢✐t♦s❝♦♠ ❛s ❝❛r❛❝t❡ríst✐❝❛s ✸✱ ✹✱ ✺ ❡ ✻❀ ❝❛r❛❝t❡ríst✐❝❛s ✺ ❡ ✻✳◆❡ss❡ ❝❛s♦✱ ♦ ❛❧❣♦r✐t♠♦ ❞❛ r❡❣r❛ ❞❡ ✐♥❝❧✉sã♦ ❡ ❡①❝❧✉sã♦ ✐rá ❝♦♥str✉✐r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ár✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s ♣❛r❛ ❛s ❡s♣é❝✐❡s ❛♥❛❧✐s❛❞❛s ❝♦♠ ❝❛r❞✐♥❛❧✐❞❛❞❡ ♠❛✐♦r q✉❡ ✶✭✉♠✮ ✈✐❞❡❋✐❣✉r❛ ✹✳✶✹✳ ❆ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ót✐♠❛✱ ♣❛r❛ ❛s ❡s♣é❝✐❡s ❞❡ ✉♠❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛❝♦♠ ❝♦♥✢✐t♦ ❝♦♥str✉í❞❛ ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❞❛ r❡❣r❛ ❞❡ ✐♥❝❧✉sã♦ ❡ ❡①❝❧✉sã♦✱ s❡rá ❛ ár✈♦r❡✜❧♦❣❡♥ét✐❝❛ ♦❜t✐❞❛ ♣❡❧❛ ❛♣❧✐❝❛çã♦ ❞❡ ✉♠ ❝r✐tér✐♦ ❞❡ ♦t✐♠✐③❛çã♦ ❛♦ ❝♦♥❥✉♥t♦ ❞❡ ár✈♦r❡s✜❧♦❣❡♥ét✐❝❛s ❝♦♥str✉í❞♦✳ ❊♥q✉❛♥t♦ q✉❡ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❲❛❣♥❡r ✐rá ❝♦♥str✉✐r ✉♠❛ ár✈♦r❡✜❧♦❣❡♥ét✐❝❛ q✉❡ s❡rá ❞❡♣❡♥❞❡♥t❡ ❞❛ ♦r❞❡♠ ♥❛ q✉❛❧ ❛s ❡s♣é❝✐❡s ❡stã♦ ❞✐s♣♦st❛s ♥❛ ♠❛tr✐③❝❛r❛❝t❡ríst✐❝❛ ❝♦♠ ❝♦♥✢✐t♦ ❛♥❛❧✐s❛❞❛ ✭❋✐❣✉r❛ ✹✳✶✹❛✮✳ P❛r❛ s❡ ♦❜t❡r ❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ót✐♠❛ ❝♦♠ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❲❛❣♥❡r✱ ❞❡✈❡✲s❡ ♣r✐♠❡✐r♦ ❛❧t❡r♥❛r ❛s ♣♦s✐çõ❡s ❞❛s ❡s♣é❝✐❡s ♥❛♠❛tr✐③ ❛♥❛❧✐s❛❞❛✱ ♣❛r❛ s❡ ♦❜t❡r ♦ ❝♦♥❥✉♥t♦ ❞❡ t♦❞❛s ❛s ♣♦ssí✈❡✐s ár✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s ♣❛r❛❡ss❛s ❡s♣é❝✐❡s✳ ❊ ❞❡♣♦✐s✱ ❛♣❧✐❝❛✲s❡ s♦❜r❡ ❡ss❡ ❝♦♥❥✉♥t♦ ✉♠ ❝r✐tér✐♦ ❞❡ ♦t✐♠✐③❛çã♦✳❋✐❣✉r❛ ✹✳✶✹✿ ➪r✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s ❝♦♥str✉í❞❛s ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❞❡ ✐♥❝❧✉sã♦ ❡ ❡①❝❧✉sã♦ ❛♣❛rt✐r ❞❛ ❚❛❜❡❧❛ ✹✳✻ ❖ ❛❧❣♦r✐t♠♦ ❞❛s ♠é❞✐❛s ❝♦♥stró✐ ❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ót✐♠❛✱ q✉❛♥❞♦ ♦s ❞❛❞♦s s♦❜r❡ ❛❡✈♦❧✉çã♦ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❛♣r❡s❡♥t❛❞❛s ♣❡❧❛s ❡s♣é❝✐❡s ♥ã♦ ❛♣r❡s❡♥t❛ ❝♦♥✢✐t♦✳ P♦✐s✱ s❡ ♦s❞❛❞♦s s♦❜r❡ ❛ ❡✈♦❧✉çã♦ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❛♣r❡s❡♥t❛❞❛s ♣❡❧❛s ❡s♣é❝✐❡s ❢♦r❡♠ ❝♦♥✢✐t❛♥t❡s✱❡♥tã♦ ❛ ♠❛tr✐③ ❞✐stâ♥❝✐❛ ❞❡ ❞✐♠❡♥sã♦ ♥①♥✱ ❝♦♠ θ ✐❣✉❛❧ ❛♦ ♠❡♥♦r ✈❛❧♦r ❛r♠❛③❡♥❛❞♦✱ t❡rá ✹✳✺✳ P❘❖❇▲❊▼❆❙ ❊◆❈❖◆❚❘❆❉❖❙ i,j = d u,v✺✸ ❞♦✐s ♦✉ ♠❛✐s ❡❧❡♠❡♥t♦s d ❂ θ ✱ t❛❧ q✉❡✿ ✐✱ ❥ 6= ✉✱ ✈ ❡ ✐✱ ❥ 6= ✈✱ ✉✳ P♦r ❡①❡♠♣❧♦✱❝♦♥s✐❞❡r❡ ❛ ♠❛tr✐③ ❞✐stâ♥❝✐❛ ❞❛ ❚❛❜❡❧❛ ✹✳✼ ❝♦♥str✉í❞❛ ❛ ♣❛rt✐r ❞❛ ❚❛❜❡❧❛ ✹✳✻✳ ❚❛❜❡❧❛ ✹✳✼✿ ▼❛tr✐③ ❞✐stâ♥❝✐❛ ❝♦♠ ❝♦♥✢✐t♦ ❆ ❇ ❈ ❉ ❆ ✵ ✹ ✻ ✹❇ ✹ ✵ ✷ ✹ ❈ ✻ ✷ ✵ ✷❉ ✹ ✹ ✷ ✵ ❖ ♠❡♥♦r ✈❛❧♦r ♥ã♦✲♥✉❧♦ ❛r♠❛③❡♥❛❞♦ ♥❡st❛ t❛❜❡❧❛ é ✷✭❞♦✐s✮ ♣♦✐s ♦ ✈❛❧♦r ③❡r♦ s✐❣♥✐✜❝❛ q✉❡ ❛ ❡s♣é❝✐❡ é ❛ ♠❡s♠❛ ✳ ❖ ✈❛❧♦r ✷✭❞♦✐s✮ ❝♦rr❡s♣♦♥❞❡ ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❛s ❡s♣é❝✐❡s B ❡C ✱ ❡ ❡♥tr❡ ❛s ❡s♣é❝✐❡s C ❡ D✱ ♦ q✉❡ é ✉♠ ❝♦♥✢✐t♦✳ ◗✉❛♥❞♦ ❛ ♠❛tr✐③ ❞✐stâ♥❝✐❛ ❛♥❛❧✐s❛❞❛♣❡❧♦ ❛❧❣♦r✐t♠♦ ❞❛s ♠é❞✐❛s ❛♣r❡s❡♥t❛ ❝♦♥✢✐t♦✱ ❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ❝♦♥str✉í❞❛ ✐rá ❞❡♣❡♥❞❡r❞❛ ♦r❞❡♠ ♥❛ q✉❛❧ ❛s ❡s♣é❝✐❡s ❡stã♦ ❞✐s♣♦st❛s ♥❛ ♠❛tr✐③ ❞✐stâ♥❝✐❛ ✭❋✐❣✳ ✹✳✶✺✮✳ ❆ ár✈♦r❡✜❧♦❣❡♥ét✐❝❛ ót✐♠❛✱ ❝♦♥str✉í❞❛ ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❞❛s ♠é❞✐❛s ❛ ♣❛rt✐r ❞❡ ✉♠❛ ♠❛tr✐③ ❞✐stâ♥❝✐❛❝♦♠ ❝♦♥✢✐t♦✱ s❡rá ♦❜t✐❞❛ ❞❛ ♠❡s♠❛ ❢♦r♠❛ q✉❡ ❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ót✐♠❛ ❝♦♥str✉í❞❛ ♣❡❧♦❛❧❣♦r✐t♠♦ ❞❡ ❲❛❣♥❡r ❛ ♣❛rt✐r ❞❡ ✉♠❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❝♦♠ ❝♦♥✢✐t♦✳❋✐❣✉r❛ ✹✳✶✺✿ ➪r✈♦r❡s ✜❧♦❣❡♥ét✐❝❛s ❝♦♥str✉í❞❛s ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❞❛s ♠é❞✐❛s ❛ ♣❛rt✐r ❞❛❚❛❜❡❧❛ ✹✳✼✳ ◆♦ ♣ró①✐♠♦ ❝❛♣ít✉❧♦ s❡rá ❛♣r❡s❡♥t❛❞❛ ❛ ❝♦♥❝❧✉sã♦ ❡ tr❛❜❛❧❤♦s ❢✉t✉r♦s✳ ❈❛♣ít✉❧♦ ✺ ❈♦♥❝❧✉sõ❡s ❋✐❧♦❣❡♥✐❛ ♥ã♦ é ✉♠ ❛ss✉♥t♦ r❡❝❡♥t❡✱ ❞❡s❞❡ ♦s t❡♠♣♦s ❞❡ ❉❛r✇✐♥ ❬✶✻❪ s❡ ♣r♦❝✉r❛ ♠♦♥t❛r❛ ár✈♦r❡ ❞❛s ❡s♣é❝✐❡s✳ ❈♦♠♦ ♦ ❡s♣❛ç♦ ❞❡ s♦❧✉çõ❡s ❞❡st❡ ♣r♦❜❧❡♠❛ é ❣✐❣❛♥t❡s❝♦ ✭❛♣r❡s❡♥t❛❝✉st♦ ❢❛t♦r✐❛❧✮✱ ♦ ❡♠♣r❡❣♦ ❞❡ ❛❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s s❡ ❛♣r❡s❡♥t❛ ❝♦♠♦ s❡♥❞♦ ✉♠❛ ❜♦❛❛❧t❡r♥❛t✐✈❛ ♣❛r❛ s✉❛ ❡①♣❧♦r❛çã♦✳ ❖ ✉s♦ ❞❡ ❈♦♠♣✉t❛çã♦ ❊✈♦❧✉t✐✈❛ s❡ ♠♦str♦✉ ♠✉✐t♦ ❡✜❝✐❡♥t❡ ❡ ❡✜❝❛③ ❡♠ s✉❛ ❡①♣❧♦r❛çã♦❛♦ ❧♦♥❣♦ ❞❡st❛ ♣❡sq✉✐s❛✳ ❊♠ t♦❞❛s ❛s s✐♠✉❧❛çõ❡s✱ s❡♠♣r❡ ❢♦✐ ♦❜t✐❞♦ ✉♠ ❜♦♠ r❡s✉❧t❛❞♦❞❡♥tr♦ ❞❡ ✉♠ ♣❡rí♦❞♦ ❞❡ t❡♠♣♦ r❛③♦á✈❡❧✭❞❡ ✸✵ ♠✐♥✉t♦s ❛ ✉♠❛ ❤♦r❛✮✳ ❊ s❡✉s r❡s✉❧t❛❞♦s❣❡r❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦ ❢♦r❛♠ ❛✈❛❧✐❛❞♦s ♣♦r ✉♠ ♣❡sq✉✐s❛❞♦r ❞❛ ár❡❛ ❞❡ ❆❣r♦♥♦♠✐❛✭❇r✉♥♦ ✶ ◆❛s❝✐♠❡♥t♦ ✮✳❯♠❛ ❣r❛♥❞❡ ✈❛♥t❛❣❡♠ ❞❡ s❡ ✉s❛r ❝♦♠♣✉t❛çã♦ ❡✈♦❧✉t✐✈❛ é ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ s❡ tr❛✲ ❜❛❧❤❛r ❝♦♠ ♠✉✐t♦s ♣♦♥t♦s ❞❡ ♣❛rt✐❞❛ s✐♠✉❧t❛♥❡❛♠❡♥t❡✱ ❛❧é♠ ❞❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❞❡ ♠❡✲❝❛♥✐s♠♦s ❞❡ r❡❝♦♠❜✐♥❛çã♦ ❞❛s s♦❧✉çõ❡s ❡①✐st❡♥t❡s✳ ❈♦♠ ✐ss♦✱ ❛✉♠❡♥t❛♠✲s❡ ❛s ❝❤❛♥❝❡s❞❡ ❡s❝❛♣❛r ❞❡ ♠á①✐♠♦s ❧♦❝❛✐s r✉✐♥s ❡ ❛t✐♥❣✐r ♦ ♠á①✐♠♦ ❣❧♦❜❛❧ ♦✉ ♣❡❧♦ ♠❡♥♦s ✉♠ ❜♦♠♠á①✐♠♦ ❧♦❝❛❧ ❬✷✶❪ ❡ ❬✶✽❪✳ ❖✉tr♦ ♣♦♥t♦ q✉❡ ♠❡r❡❝❡ s❡r ❞❡st❛❝❛❞♦ é ♦ ✉s♦ ❞❡ té❝♥✐❝❛s ❞❡ ❈♦♠♣✉t❛çã♦ ❊✈♦❧✉t✐✈❛✱ q✉❡ s❡ ♠♦str♦✉ ✉♠❛ ♣♦❞❡r♦s❛ ❢❡rr❛♠❡♥t❛ ♣❛r❛ ❛❥✉❞❛r ♥♦ ♣r♦❜❧❡♠❛ ❞❡ ❡♥❝♦♥tr❛r ✉♠❛ ❜♦❛ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛✱ ❛ ♣❛rt✐r ❞❡ ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ❜❛s❡s ❛♥❛❧✐s❛❞❛s✱ ❞❡✈✐❞♦ ❛♦ s❡✉ ❡❧❡✈❛❞♦♣♦❞❡r ❞❡ ❡①♣❧♦r❛çã♦ ❞❡ ✉♠ ✈❛st♦s ❡s♣❛ç♦s ❞❡ s♦❧✉çã♦ ❝♦♥❢♦r♠❡ ❈❛♥❝✐♥♦❬✶✷❪✳ ❖ s✐st❡♠❛ ✭❙❊❚❆❳✮ q✉❡ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ❡ ✉t✐❧✐③❛❞♦ ❛♦ ❧♦♥❣♦ ❞❡st❡ ♠❡str❛❞♦✳ ❆✐♥t❡r❢❛❝❡ ❣rá✜❝❛ ❞❡st❡ s✐st❡♠❛ ❢♦✐ ❝r✐❛❞❛ ♣❛r❛ ❢❛❝✐❧✐t❛r ♦ s❡✉ ✉s♦ ♣♦r ♣❛rt❡ ❞♦ ✉s✉ár✐♦✱♠❡s♠♦ q✉❡ ❡st❡ ♥ã♦ ❞♦♠✐♥❡ ❛ ❝♦♠♣✉t❛çã♦✱ ♥❡❧❡ é ♣♦ssí✈❡❧ ❛❧t❡r❛r ♦s ♣❛râ♠❡tr♦s ✐♥✐❝✐❛✐s s♦❜r❡ ♦ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ✉t✐❧✐③❛❞♦ ✐♥t❡r♥❛♠❡♥t❡✱ t❛✐s ❝♦♠♦ t❛♠❛♥❤♦ ❞❛ ♣♦♣✉❧❛çã♦ ✐♥✐❝✐❛❧✭♣❛❞rã♦ ✷✵✵✮✱ ♣♦r❝❡♥t❛❣❡♠ ❞❡ ♠✉t❛çõ❡s✭♣❛❞rã♦ ✸✵✪✮✱ q✉❛♥t✐❞❛❞❡ ❞❡ ✐t❡r❛çõ❡s ✭♣❛❞rã♦✶✵✮ q✉❡ ❧✐♠✐t❛ ♦ t❡♠♣♦ ♠á①✐♠♦ ❞❡ ❜✉s❝❛✳ ◆ã♦ é ♥❡❝❡ssár✐❛ ❛ ❞✐❣✐t❛çã♦ ❞❡ t♦❞♦s ❡st❡s♣❛râ♠❡tr♦s✱ ♣♦✐s ♦ ❙❊❚❆❳ ♣♦ss✉✐ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ✈❛❧♦r❡s ✐♥✐❝✐❛✐s q✉❡ s❡ ♠♦str❛r❛♠❜❛st❛♥t❡ ❡✜❝✐❡♥t❡s ♥❛ ♠❛✐♦r✐❛ ❞♦s t❡st❡s r❡❛❧✐③❛❞♦s✳ ✶ ❤tt♣✿✴✴✇✇✇✳❝❡❝❛✳✉❢❛❧✳❜r✴✳ ✺✺❆❧é♠ ❞✐ss♦✱ é ♥❡❝❡ssár✐♦ r❡ss❛❧t❛r q✉❡ ❡st❡ s✐st❡♠❛ ❢♦✐ ♣r♦❥❡t❛❞♦ ♣❛r❛ ❛✉①✐❧✐❛r ❡ ♦r✐❡♥t❛r ♦ ✉s✉ár✐♦ ❞✉r❛♥t❡ ♦ ♣r♦❝❡ss♦ ❞❡ ❡①❡❝✉çã♦ ❡ s❡♠♣r❡ q✉❡ ✉♠ ❞❛❞♦ ❢♦r ♥❡❝❡ssár✐♦ ♦✉ ✉♠♣❛râ♠❡tr♦ ❢♦r ✐♥❞✐s♣❡♥sá✈❡❧ ❡ ♥ã♦ ❡st✐✈❡r ♥♦s ✈❛❧♦r❡s ✐♥✐❝✐❛✐s✱ ♦ ✉s✉ár✐♦ s❡rá s♦❧✐❝✐t❛❞♦ ❛❢♦r♥❡❝❡r ❡st❡ ❞❛❞♦ ♦✉ ✐♥❢♦r♠❛çã♦ ❢❛❧t❛♥t❡✳ P♦r ❡①❡♠♣❧♦✱ ♦ ♥♦♠❡ ❞♦ ❛rq✉✐✈♦ q✉❡ ❝♦♥té♠♦ ❝♦♥❥✉♥t♦ ❞❡ ❡s♣é❝✐❡s ❛ s❡r❡♠ ❛♥❛❧✐s❛❞❛s ♥ã♦ ♣♦❞❡ ❢❛③❡r ♣❛rt❡ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ✈❛❧♦r❡s✐♥✐❝✐❛✐s✱ r❛③ã♦ ♣❡❧❛ q✉❛❧ ❡❧❡ é s♦❧✐❝✐t❛❞♦ s❡♠♣r❡ q✉❡ ♦ ✉s✉ár✐♦ ♦r❞❡♥❛r ♦ ✐♥í❝✐♦ ❞❡ ❡①❡❝✉çã♦✳❯♠❛ t❡❧❛ ❡s♣❡❝í✜❝❛ ❞❡ ❜✉s❝❛ ❞❡ ❛rq✉✐✈♦s ♥♦ ♣❛❞rã♦ ❲✐♥❞♦✇s s❡rá ❡①✐❜✐❞❛ ♣❛r❛ q✉❡♦ ✉s✉ár✐♦ ❛♣♦♥t❡ ♣❛r❛ ♦ ❛rq✉✐✈♦ ❞❡s❡❥❛❞♦✳ ❉❡st❛ ❢♦r♠❛✱ ♦s r❡❝✉rs♦s ❡ ❛s ❢❛❝✐❧✐❞❛❞❡s❞✐s♣♦♥í✈❡✐s ♥❡st❛ ❢❡rr❛♠❡♥t❛ ❛❥✉❞❛r❛♠ ♠✉✐t♦ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦ ❡ ♣♦❞❡rã♦ s❡r út❡✐s t❛♠❜é♠ ♣❛r❛ ♥♦✈❛s ♣❡sq✉✐s❛s s♦❜r❡ ❋✐❧♦❣❡♥✐❛ ❡ s♦❜r❡ ❈♦♠♣✉t❛çã♦ ❊✈♦❧✉t✐✈❛✳ ❆s s❡❣✉✐♥t❡s ❝❛r❛❝t❡ríst✐❝❛s ♥ã♦ ❢♦r❛♠ ✐♠♣❧❡♠❡♥t❛❞❛s ♥❡st❛ ✈❡rsã♦ ❞♦ ❙❊❚❆❳✿❡s❝♦❧❤❡r ❛❧❣✉♠ ♦✉tr♦ ♠ét♦❞♦ ❞❡ ❜✉s❝❛❀ ◆❡ss❡ s❡♥t✐❞♦✱ ❛s té❝♥✐❝❛s ❞❡ ❈♦♠♣✉t❛çã♦ ❊✈♦❧✉t✐✈❛ ♣❡r♠✐t❡♠ ❡①♣❧♦r❛r ❞❡ ♠❛♥❡✐r❛♠✉✐t♦ ❡✜❝✐❡♥t❡ ♦ ❡s♣❛ç♦ ❞❡ s♦❧✉çã♦ ❡✱ ❣❡r❛❧♠❡♥t❡✱ ✉♠❛ ❜♦❛ r❡s♣♦st❛ ♣♦❞❡ s❡r ❡♥❝♦♥tr❛❞❛❡♠ t❡♠♣♦ r❛③♦á✈❡❧ ✭❬✺❪✮✳ P♦r ♦✉tr♦ ❧❛❞♦✱ é ♣r❡❝✐s♦ r❡ss❛❧t❛r q✉❡ ♥ã♦ ❡①✐st❡♠ ❣❛r❛♥t✐❛s ❞❡ s❡r ❡♥❝♦♥tr❛❞❛ ❛ ♠❡❧❤♦r s♦❧✉çã♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✿ ♦ q✉❡ s❡ ❣❛r❛♥t❡ é ✉♠❛ ❜♦❛ s♦❧✉çã♦✱❝❛s♦ s❡ ♣r♦❝❡❞❛ ❛ ✉♠❛ ❡s❝♦❧❤❛ ❛❞❡q✉❛❞❛ ❞❡ ♣❛râ♠❡tr♦s ❡st❛❜❡❧❡❝✐❞♦s ♣❛r❛ ❛ ❜✉s❝❛✳ ❆s té❝♥✐❝❛s r❡❧❛t✐✈❛s à ❈♦♠♣✉t❛çã♦ ❊✈♦❧✉t✐✈❛ ❢♦r❛♠ ❞✐s❝✉t✐❞❛s ♥♦ ❈❛♣ít✉❧♦ ✶✳ ❉✉r❛♥t❡ t♦❞♦ ♦ ♣r♦❝❡ss♦ ❞❡ ❝♦♥str✉çã♦ ❞♦ ❙❊❚❆❳✱ ❞❡s❞❡ ♣r♦♣♦s✐çõ❡s ❞❡ ✐❞é✐❛s ❛té❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❛♣❧✐❝❛çõ❡s✱ ❢♦r❛♠ s✉❜♠❡t✐❞❛s ❛ ❝♦♥❣r❡ss♦s ❡ ♣❡r✐ó❞✐❝♦s ♥❛❝✐♦♥❛✐s ❡✐♥t❡r♥❛❝✐♦♥❛✐s ♦❜❥❡t✐✈❛♥❞♦ ✉♠❛ ♠❡❧❤♦r ❛✈❛❧✐❛çã♦✴✈❛❧✐❞❛çã♦ ❞❛ ♣r♦♣♦st❛✳ ❉❡♥tr❡ ❡❧❡s ♣♦✲❞❡♠♦s ❞❡st❛❝❛r ✶✸t❤ ■❊❊❊ ❏♦✐♥t ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♠♣✉t❡r ❙❝✐❡♥❝❡ ❛♥❞ ■♥❢♦r♠❛t✐♦♥ ❚❡❝❤✲♥♦❧♦❣② ❈♦♥❢❡r❡♥❝❡✭❏■❈❙■❚ ✷✵✶✶✮✱ ♦♥❞❡ t✐✈❡♠♦s ♦ ❛rt✐❣♦ ❛❝❡✐t♦✱ ♦ ❏♦✉r♥❛❧ ♦❢ ❊♥❣✐♥❡❡r✐♥❣❛♥❞ ❈♦♠♣✉t❡r ■♥♥♦✈❛t✐♦♥s t❛♠❜é♠ t✐✈❡♠♦s ♦ ❛rt✐❣♦ ❛❝❡✐t♦ ♥♦ ❙✐♠♣ós✐♦ ❞❡ ❈♦♠♣✉t❛çã♦❆♣❧✐❝❛❞❛ ❙❈❆✱ ♦♥❞❡ ♦ tr❛❜❛❧❤♦ t❛♠❜é♠ ❢♦✐ ♣✉❜❧✐❝❛❞♦✳ ❈♦♠ ✐ss♦✱ ❡s♣❡r❛✲s❡ t❡r ❝♦♥tr✐❜✉í❞♦ ♥❛s ár❡❛s ❞❡ ✐✮ ■♥t❡❧✐❣ê♥❝✐❛ ❆rt✐✜❝✐❛❧✱✐✐✮❆❣r♦♥♦♠✐❛❡ ✐✐✐✮ ❇✐♦✐♥❢♦r♠át✐❝❛✳ ✺✻◆❡st❛ ❞✐ss❡rt❛çã♦ ♣r♦❝✉r♦✉✲s❡ ❧✐❞❛r ❝♦♠ ❛ ❡①♣❧♦sã♦ ❝♦♠❜✐♥❛tór✐❛ ❡ ❝♦♠ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ❣❡r❛r ✉♠❛ ❥✉st✐✜❝❛t✐✈❛ ♣❛r❛ ❛ s♦❧✉çã♦ ❞❡ ✉♠ ♣r♦❜❧❡♠❛ ❞♦ t✐♣♦ ◆P✲❝♦♠♣❧❡t♦ r❡s♦❧✈✐❞♦❝♦♠ ✉♠ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦✳ ❖ ❞♦♠í♥✐♦ ❞❡ ❛♣❧✐❝❛çã♦ r❡str✐♥❣✐✉✲s❡ à ❆❣r♦♥♦♠✐❛✳ ❆ ✐❞é✐❛✐♥✐❝✐❛❧ ❡r❛ ❝♦♥str✉✐r ✉♠ s✐st❡♠❛ q✉❡ ❣❡r❛ss❡ ❛ ár✈♦r❡ ✜❧♦❣❡♥ét✐❝❛ ♣❛r❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ s❡r❡s ✈✐✈♦s ❛ ♣❛rt✐r ❞❡ ❞❛❞♦s ❞❡ s✉❛ ♠❛tr✐③ ❝❛r❛❝t❡ríst✐❝❛ ❢♦r♥❡❝✐❞❛ ♣❡❧♦ ✉s✉ár✐♦✳ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s◗✉❛♥t♦ ❛♦s tr❛❜❛❧❤♦s ❢✉t✉r♦s✱ ♣♦❞❡♠♦s ❞❡st❛❝❛r✿ ❯t✐❧✐③❛çã♦ ❡ ❛♥á❧✐s❡ ❞❡ ❞❡s❡♠♣❡♥❤♦ ❡♥tr❡ ❛s ❞✐✈❡rs❛s ❡str❛té❣✐❛s✱ ❛ ✜♠ ❞❡ ♦❜t❡r ✺✼ ❘❡❢❡rê♥❝✐❛s ❬✶❪ ❆❧ts❝❤✉❧✱ ❙✳ ❋✳✱ ▼❛❞❞❡♥✱ ❚✳ ▲✳✱ ❙❝❤ä✛❡r✱ ❆✳ ❆✳✱ ❩❤❛♥❣✱ ❏✳✱ ❩❤❛♥❣✱ ❩✳✱ ▼✐❧❧❡r✱ ❲✳✫ ▲✐♣♠❛♥✱ ❉✳ ❏✳ ✭✶✾✾✼✮✱ ❵●❛♣♣❡❞ ❜❧❛st ❛♥❞ ♣s✐❜❧❛st✿ ❛ ♥❡✇ ❣❡♥❡r❛t✐♦♥ ♦❢ ♣r♦t❡✐♥❞❛t❛❜❛s❡ s❡❛r❝❤ ♣r♦❣r❛♠s✬✱ ◆❯❈▲❊■❈ ❆❈■❉❙ ❘❊❙❊❆❘❈❍ ✷✺✭✶✼✮✱ ✸✸✽✾✕✸✹✵✷✳ ❬✷❪ ❆♠♦r✐♠✱ ❉✳ ✭✶✾✾✹✮✱ ❵❊❧❡♠❡♥t♦s ❜ás✐❝♦s ❞❡ s✐st❡♠át✐❝❛ ✜❧♦❣ê♥✐❝❛✬✱ ❙♦❝✐❡❞❛❞❡ ❇r❛s✐✲❧❡✐r❛ ❞❡ ❊♥t♦♠♦❧♦❣✐❛✱ ❙ã♦ P❛✉❧♦✲❙P✱ ✸✶✹♣✳ ❬✸❪ ❆♥❞r❡❛tt❛✱ ❆✳ ❆✳ ✫ ❘✐❜❡✐r♦✱ ❈✳ ❈✳ ✭✷✵✵✷✮✱ ❵❍❡✉r✐st✐❝s ❢♦r t❤❡ ♣❤②❧♦❣❡♥② ♣r♦❜❧❡♠✬✱❏♦✉r♥❛❧ ♦❢ ❍❡✉r✐st✐❝s ✽✱ ✹✷✾✕✹✹✼✳ ❯❘▲ ❤tt♣✿✴✴♣♦rt❛❧✳❛❝♠✳♦r❣✴❝✐t❛t✐♦♥✳❝❢♠❄✐❞❂✺✾✹✾✺✻✳✺✾✺✵✾✻✳ ❬✹❪ ❆t♠❛r✱ ❲✳ ✭✶✾✾✹✮✱ ❵◆♦t❡s ♦♥ t❤❡ s✐♠✉❧❛t✐♦♥ ♦❢ ❡✈♦❧✉t✐♦♥✬✱ ■❊❊❊ ❚r❛♥s❛❝t✐♦♥s ♦♥◆❡✉r❛❧ ◆❡t✇♦r❦s✱ ❱♦❧✳ ✺✿✶✱ ♣♣✳ ✶✸✵✕✶✹✼✳ ❬✺❪ ❇ä❝❦✱ ❚✳ ✭✶✾✾✻✮✱ ❊✈♦❧✉t✐♦♥❛r② ❛❧❣♦r✐t❤♠s ✐♥ t❤❡♦r② ❛♥❞ ♣r❛❝t✐❝❡✿ ❡✈♦❧✉t✐♦♥ str❛t❡❣✐❡s✱❡✈♦❧✉t✐♦♥❛r② ♣r♦❣r❛♠♠✐♥❣✱ ❣❡♥❡t✐❝ ❛❧❣♦r✐t❤♠s✱ ❖①❢♦r❞ ❯♥✐✈❡rs✐t② Pr❡ss✱ ❖①❢♦r❞✱ ❯❑✳ ❬✻❪ ❇ä❝❦✱ ❚✳ ✫ ❙❝❤✇❡❢❡❧✱ ❍✳✲P✳ ✭✶✾✾✸✮✱ ❵❆♥ ♦✈❡r✈✐❡✇ ♦❢ ❡✈♦❧✉t✐♦♥❛r② ❛❧❣♦r✐t❤♠s ❢♦r ♣❛✲ r❛♠❡t❡r ♦♣t✐♠✐③❛t✐♦♥✬✱ ❊✈♦❧✳ ❈♦♠♣✉t✳ ✶✱ ✶✕✷✸✳ ❯❘▲ ❤tt♣✿✴✴❞①✳❞♦✐✳♦r❣✴✶✵✳✶✶✻✷✴❡✈❝♦✳✶✾✾✸✳✶✳✶✳✶✳ ❬✼❪ ❇❛❝❦✱ ❚✳✱ ❋♦❣❡❧✱ ❉✳ ❇✳ ✫ ▼✐❝❤❛❧❡✇✐❝③✱ ❩✳✱ ❡❞s ✭✶✾✾✾✮✱ ❇❛s✐❝ ❆❧❣♦r✐t❤♠s ❛♥❞ ❖♣❡r❛t♦rs✱■❖P P✉❜❧✐s❤✐♥❣ ▲t❞✳✱ ❇r✐st♦❧✱ ❯❑✱ ❯❑✳ ❬✽❪ ❇❛rr✐❝❡❧❧✐✱ ◆✳ ❆✳ ✭✶✾✺✼✮✱ ❵❙②♠❜✐♦❣❡♥❡t✐❝ ❡✈♦❧✉t✐♦♥ ♣r♦❝❡ss❡s r❡❛❧✐③❡❞ ❜② ❛rt✐✜❝✐❛❧♠❡t❤♦❞s✬✱ ▼❡t❤♦❞♦s ✾✿✸✺✲✸✻✳ ❬✾❪ ❇❛rr✐❝❡❧❧✐✱ ◆✳ ❆✳ ✭✶✾✻✷✮✱ ❵◆✉♠❡r✐❝❛❧ t❡st✐♥❣ ♦❢ ❡✈♦❧✉t✐♦♥ t❤❡♦r✐❡s✬✱ P❛rt ■✳ ❚❤❡r♦❡t✐❝❛❧■♥tr♦❞✉❝t✐♦♥ ❛♥❞ ❇❛s✐❝ ❚❡sts✳ ❆❝t❛ ❇✐♦t❤❡♦r❡t③❝❛✳ ❬✶✵❪ ❇❡r♥❛r❞✐✱ ◆✳ ✭✶✾✾✾✮✱ ❵❘❡s✉♠♦ ❞❛s ❛✉❧❛s s♦❜r❡✿ ❙✐st❡♠át✐❝❛ ✜❧♦❣❡♥ét✐❝❛✱ ✐ ❝✉rs♦ ❡s♣❡✲❝✐❛❧ ❞❡ s✐st❡♠át✐❝❛ ③♦♦❧ó❣✐❝❛ ❞♦ ❞❡♣❛rt❛♠❡♥t♦ ❞❡ ❝✐ê♥❝✐❛s ❜✐♦❧ó❣✐❝❛s✬✱ ❙ã♦ ❈❛r❧♦s ✲❙P✳ ❬✶✶❪ ❇♦✉❦❡r❝❤❡✱ ❆✳✱ ❞❡ ▼❡❧♦✱ ❆✳ ❈✳ ▼✳ ❆✳✱ ❆②❛❧❛✲❘✐♥❝ó♥✱ ▼✳ ✫ ❲❛❧t❡r✱ ▼✳ ❊✳ ▼✳ ❚✳✭✷✵✵✼✮✱ ❵P❛r❛❧❧❡❧ str❛t❡❣✐❡s ❢♦r t❤❡ ❧♦❝❛❧ ❜✐♦❧♦❣✐❝❛❧ s❡q✉❡♥❝❡ ❛❧✐❣♥♠❡♥t ✐♥ ❛ ❝❧✉st❡r ♦❢✇♦r❦st❛t✐♦♥s✬✱ ❏✳ P❛r❛❧❧❡❧ ❉✐str✐❜✳ ❈♦♠♣✉t✳ ✻✼✱ ✶✼✵✕✶✽✺✳ ❯❘▲ ❤tt♣✿✴✴❞①✳❞♦✐✳♦r❣✴✶✵✳✶✵✶✻✴❥✳❥♣❞❝✳✷✵✵✻✳✶✶✳✵✵✶✳ ❬✶✷❪ ❈❛♥❝✐♥♦✱ ❲✳ ✫ ❉❡❧❜❡♠✱ ❆✳ ❈✳ ❇✳ ✭✷✵✵✼✮✱ ❆ ♠✉❧t✐✲♦❜❥❡❝t✐✈❡ ❡✈♦❧✉t✐♦♥❛r② ❛♣♣r♦❛❝❤ ❢♦r♣❤②❧♦❣❡♥❡t✐❝ ✐♥❢❡r❡♥❝❡✱ ✐♥ ❵Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✹t❤ ✐♥t❡r♥❛t✐♦♥❛❧ ❝♦♥❢❡r❡♥❝❡ ♦♥ ❊✈♦❧✉✲ t✐♦♥❛r② ♠✉❧t✐✲❝r✐t❡r✐♦♥ ♦♣t✐♠✐③❛t✐♦♥✬✱ ❊▼❖✬✵✼✱ ❙♣r✐♥❣❡r✲❱❡r❧❛❣✱ ❇❡r❧✐♥✱ ❍❡✐❞❡❧❜❡r❣✱♣♣✳ ✹✷✽✕✹✹✷✳ ❯❘▲ ❤tt♣✿✴✴♣♦rt❛❧✳❛❝♠✳♦r❣✴❝✐t❛t✐♦♥✳❝❢♠❄✐❞❂✶✼✻✷✺✹✺✳✶✼✻✷✺✽✹✳ ✺✽❬✶✸❪ ❈♦❝❦❡r❤❛♠✱ ❈✳ ✭✶✾✻✸✮✱ ❵❊st✐♠❛t✐♦♥ ♦❢ ❣❡♥❡t✐❝ ✈❛r✐❛♥❝❡s✱ ✐♥✿ ❲✳❞✳ ❤❛♥s♦♥✱ ❤✳❢✳ r♦❜✐♥✲ s♦♥ ✭❡❞s✳✮✬✱ ❙t❛t✐st✐❝❛❧ ●❡♥❡t✐❝s ❛♥❞ P❧❛♥t ❇r❡❡❞✐♥❣✱ ◆❛t✐♦♥❛❧ ❆❝❛❞❡♠② ♦❢ ❙❝✐❡♥❝❡s✱ ❲❛s❤✐♥❣t♦♥✱ ❉❈✳❬✶✹❪ ❈♦❡❧❤♦✱ ●✳ P✳✱ ❞❛ ❙✐❧✈❛✱ ❆✳ ❊✳ ❆✳ ✫ ❱♦♥ ❩✉❜❡♥✱ ❋✳ ❏✳ ✭✷✵✵✼✮✱ ❊✈♦❧✈✐♥❣ ♣❤②❧♦❣❡♥❡t✐❝ tr❡❡s✿ ❛ ♠✉❧t✐♦❜❥❡❝t✐✈❡ ❛♣♣r♦❛❝❤✱ ✐♥ ❵Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✷♥❞ ❇r❛③✐❧✐❛♥ ❝♦♥❢❡r❡♥❝❡ ♦♥ ❆❞✈❛♥❝❡s ✐♥ ❜✐♦✐♥❢♦r♠❛t✐❝s ❛♥❞ ❝♦♠♣✉t❛t✐♦♥❛❧ ❜✐♦❧♦❣②✬✱ ❇❙❇✬✵✼✱ ❙♣r✐♥❣❡r✲❱❡r❧❛❣✱❇❡r❧✐♥✱ ❍❡✐❞❡❧❜❡r❣✱ ♣♣✳ ✶✶✸✕✶✷✺✳ ❯❘▲ ❤tt♣✿✴✴♣♦rt❛❧✳❛❝♠✳♦r❣✴❝✐t❛t✐♦♥✳❝❢♠❄✐❞❂✶✼✼✻✹✼✹✳✶✼✼✻✹✽✻✳ ❬✶✺❪ ❈♦❤♦♦♥✱ ❏✳ P✳✱ ❍❡❣❞❡✱ ❙✳ ❯✳✱ ▼❛rt✐♥✱ ❲✳ ◆✳ ✫ ❘✐❝❤❛r❞s✱ ❉✳ ✭✶✾✽✼✮✱ P✉♥❝t✉❛t❡❞❡q✉✐❧✐❜r✐❛✿ ❛ ♣❛r❛❧❧❡❧ ❣❡♥❡t✐❝ ❛❧❣♦r✐t❤♠✱ ✐♥ ❵Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ❙❡❝♦♥❞ ■♥t❡r♥❛t✐♦♥❛❧❈♦♥❢❡r❡♥❝❡ ♦♥ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠s ♦♥ ●❡♥❡t✐❝ ❛❧❣♦r✐t❤♠s ❛♥❞ t❤❡✐r ❛♣♣❧✐❝❛t✐♦♥✬✱ ▲✳❊r❧❜❛✉♠ ❆ss♦❝✐❛t❡s ■♥❝✳✱ ❍✐❧❧s❞❛❧❡✱ ◆❏✱ ❯❙❆✱ ♣♣✳ ✶✹✽✕✶✺✹✳ ❯❘▲ ❤tt♣✿✴✴♣♦rt❛❧✳❛❝♠✳♦r❣✴❝✐t❛t✐♦♥✳❝❢♠❄✐❞❂✹✷✺✶✷✳✹✷✺✸✷✳ ❛ ❬✶✻❪ ❉❛r✇✐♥✱ ❈✳ ✭✶✽✺✾✮✱ ❆ ❖r✐❣❡♠ ❞❛s ❊s♣é❝✐❡s ❡ ❛ ❙❡❧❡çã♦ ◆❛t✉r❛❧✱ ✺ ❡❞✳✱ ❊❞✐t♦r❛ ❍❡♠✉s✳❬✶✼❪ ❉❛✈✐s✱ ▲✳ ✭✶✾✽✺✮✱ ❏♦❜ s❤♦♣ s❝❤❡❞✉❧✐♥❣ ✇✐t❤ ❣❡♥❡t✐❝ ❛❧❣♦r✐t❤♠s✱ ✐♥ ❵Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶st ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠s✬✱ ▲✳ ❊r❧❜❛✉♠ ❆ss♦❝✐❛t❡s ■♥❝✳✱❍✐❧❧s❞❛❧❡✱ ◆❏✱ ❯❙❆✱ ♣♣✳ ✶✸✻✕✶✹✵✳ ❯❘▲ ❤tt♣✿✴✴♣♦rt❛❧✳❛❝♠✳♦r❣✴❝✐t❛t✐♦♥✳❝❢♠❄✐❞❂✻✹✺✺✶✶✳✻✺✼✵✽✹✳ ❬✶✽❪ ❞❡ ❈❛str♦✱ ▲✳ ◆✳ ✭✷✵✵✻✮✱ ❋✉♥❞❛♠❡♥t❛❧s ♦❢ ◆❛t✉r❛❧ ❈♦♠♣✉t✐♥❣✿ ❇❛s✐❝ ❈♦♥❝❡♣ts✱ ❆❧❣♦✲ r✐t❤♠s✱ ❛♥❞ ❆♣♣❧✐❝❛t✐♦♥s ✭❈❤❛♣♠❛♥ ✫ ❍❛❧❧✴❈r❝ ❈♦♠♣✉t❡r ❛♥❞ ■♥❢♦r♠❛t✐♦♥ ❙❝✐❡♥✲❝❡s✮✱ ❈❤❛♣♠❛♥ ✫ ❍❛❧❧✴❈❘❈✳ ❯❘▲ ❤tt♣✿✴✴✇✇✇✳✇♦r❧❞❝❛t✳♦r❣✴✐s❜♥✴✶✺✽✹✽✽✻✹✸✾✳ ❬✶✾❪ ❉❡ ❏♦♥❣✱ ❑✳ ❆✳ ✭✷✵✵✷✮✱ ❊✈♦❧✉t✐♦♥❛r② ❈♦♠♣✉t❛t✐♦♥✿ ❆ ❯♥✐✜❡❞ ❆♣♣r♦❛❝❤✱ ✶st ❡❞✳✱ ❚❤❡▼■❚ Pr❡ss✳ ❯❘▲ ❤tt♣✿✴✴✇✇✇✳✇♦r❧❞❝❛t✳♦r❣✴✐s❜♥✴✵✷✻✷✵✹✶✾✹✹✳ ❬✷✵❪ ❉❡❜✱ ❑✳ ✫ ❑❛❧②❛♥♠♦②✱ ❉✳ ✭✷✵✵✶✮✱ ▼✉❧t✐✲❖❜❥❡❝t✐✈❡ ❖♣t✐♠✐③❛t✐♦♥ ❯s✐♥❣ ❊✈♦❧✉t✐♦♥❛r②❆❧❣♦r✐t❤♠s✱ ❏♦❤♥ ❲✐❧❡② ✫ ❙♦♥s✱ ■♥❝✳✱ ◆❡✇ ❨♦r❦✱ ◆❨✱ ❯❙❆✳ ❬✷✶❪ ❋♦❣❡❧✱ ❉✳ ✭✶✾✾✹✮✱ ❵❆♥ ✐♥tr♦❞✉❝t✐♦♥ t♦ s✐♠✉❧❛t❡❞ ❡✈♦❧✉t✐♦♥❛r② ❝♦♠♣✉t❛t✐♦♥✬✱ ■❊❊❊❚r❛♥s❛❝t✐♦♥s ♦♥ ◆❡✉r❛❧ ◆❡t✇♦r❦s✱ ✈♦❧✳ ✺✱ ♥♦✳ ✶✱ ♣♣✳ ✸✲ ✶✹✳ ❬✷✷❪ ❋♦❣❡❧✱ ❉✳ ✭✶✾✾✾✮✱ ❵❊✈♦❧✉t✐♦♥❛r② ❝♦♠♣✉t❛t✐♦♥ t♦✇❛r❞ ❛ ♥❡✇ ♣❤✐❧♦s♦♣❤② ♦❢ ♠❛❝❤✐♥❡✐♥t❡❧❧✐❣❡♥❝❡✬✱ ✷♥❞ ❡❞✐t✐♦♥✱ ■❊❊❊ Pr❡ss✳ ❬✷✸❪ ❋r❛s❡r✱ ❲✳ ✫ ❍❛rt✱ ❏✳ ❋✳ ✭✶✾✻✹✮✱ ❵❘❡♠❛r❦ ♦♥ ❛❧❣♦r✐t❤♠ ✶✻✷✿ ◆❡❛r✲♠✐♥✐♠❛① ♣♦❧②♥♦✲♠✐❛❧ ❛♣♣r♦①✐♠❛t✐♦♥s ❛♥❞ ♣❛rt✐t✐♦♥✐♥❣ ♦❢ ✐♥t❡r✈❛❧s✬✱ ❈♦♠♠✉♥✳ ❆❈▼ ✼✱ ✹✽✻✕✹✽✾✳ ❯❘▲❤tt♣✿✴✴❞♦✐✳❛❝♠✳♦r❣✴✶✵✳✶✶✹✺✴✸✺✺✺✽✻✳✸✻✹✽✷✵✳ ✺✾❬✷✹❪ ●♦❧❞❜❡r❣✱ ❉✳ ❊✳ ✭✶✾✽✾✮✱ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠s ✐♥ ❙❡❛r❝❤✱ ❖♣t✐♠✐③❛t✐♦♥ ❛♥❞ ▼❛❝❤✐♥❡ ▲❡❛r♥✐♥❣✱ ❆❞❞✐s♦♥✲❲❡s❧❡② ▲♦♥❣♠❛♥ P✉❜❧✐s❤✐♥❣ ❈♦✳✱ ■♥❝✳✱ ❇♦st♦♥✱ ▼❆✱ ❯❙❆✳❬✷✺❪ ●r❡❡♥❡✱ ❲✳ ❆✳ ✭✷✵✵✺✮✱ ❙❝❤❡♠❛ ❞✐sr✉♣t✐♦♥ ✐♥ tr❡❡✲str✉❝t✉r❡❞ ❝❤r♦♠♦s♦♠❡s✱ ✐♥ ❵Pr♦✲ ❝❡❡❞✐♥❣s ♦❢ t❤❡ ✷✵✵✺ ❝♦♥❢❡r❡♥❝❡ ♦♥ ●❡♥❡t✐❝ ❛♥❞ ❡✈♦❧✉t✐♦♥❛r② ❝♦♠♣✉t❛t✐♦♥✬✱ ●❊❈❈❖✬✵✺✱ ❆❈▼✱ ◆❡✇ ❨♦r❦✱ ◆❨✱ ❯❙❆✱ ♣♣✳ ✶✹✵✶✕✶✹✵✽✳ ❯❘▲ ❤tt♣✿✴✴❞♦✐✳❛❝♠✳♦r❣✴✶✵✳✶✶✹✺✴✶✵✻✽✵✵✾✳✶✵✻✽✷✸✸✳ ❬✷✻❪ ❍❛✉s❡r✱ ❘✳ ✫ ▼ä♥♥❡r✱ ❘✳ ✭✶✾✾✹✮✱ ❵■♠♣❧❡♠❡♥t❛t✐♦♥ ♦❢ st❛♥❞❛r❞ ❣❡♥❡t✐❝ ❛❧❣♦r✐t❤♠ ♦♥♠✐♥❞ ♠❛❝❤✐♥❡s✬✱ P❛r❛❧❧❡❧ Pr♦❜❧❡♠ ❙♦❧✈✐♥❣ ❢r♦♠ ◆❛t✉r❡ ■■■✳ ❬✷✼❪ ❍♦❧❧❛♥❞✱ ❏✳ ❍✳ ✭✶✾✼✺✮✱ ❵❆❞❛♣t❛t✐♦♥ ✐♥ ♥❛t✉r❛❧ ❛♥❞ ❛rt✐✜❝✐❛❧ s②st❡♠s✿ ❛♥ ✐♥tr♦❞✉❝t♦r②❛♥❛❧②s✐s ✇✐t❤ ❛♣♣❧✐❝❛t✐♦♥s t♦ ❜✐♦❧♦❣②✱ ❝♦♥tr♦❧✱ ❛♥❞ ❛rt✐✜❝✐❛❧ ✐♥t❡❧❧✐❣❡♥❝❡✬✱ ▼■❚ Pr❡ss✳ ❬✷✽❪ ❑✳✱ ❇✳ ✭✶✾✾✺✮✱ ❵Pr♦❣r❡ss ❛♥❞ ♣✐t❢❛❧❧s ✐♥ s②st❡♠❛t✐❝s✿ ❝❧❛❞✐st✐❝s✱ ❞♥❛ ❛♥❞ ♠♦r♣❤♦❧♦❣②✬✱❆❝t❛ ❇♦t✳ ◆❡❡r❧✳ ❬✷✾❪ ❑♦③❛✱ ❏✳ ❘✳ ✭✶✾✾✷✮✱ ●❡♥❡t✐❝ Pr♦❣r❛♠♠✐♥❣✿ ❖♥ t❤❡ Pr♦❣r❛♠♠✐♥❣ ♦❢ ❈♦♠♣✉t❡rs ❜②▼❡❛♥s ♦❢ ◆❛t✉r❛❧ ❙❡❧❡❝t✐♦♥ ✭❈♦♠♣❧❡① ❆❞❛♣t✐✈❡ ❙②st❡♠s✮✱ ✶ ❡❞✳✱ ❚❤❡ ▼■❚ Pr❡ss✳❯❘▲ ❤tt♣✿✴✴✇✇✇✳✇♦r❧❞❝❛t✳♦r❣✴✐s❜♥✴✵✷✻✷✶✶✶✼✵✺✳ ❬✸✵❪ ▲❛✇r❡♥❝❡✱ ●✳ ❍✳ ▼✳ ✭✶✾✺✶✮✱ ❵❚❛①♦♥♦♠② ♦❢ ✈❛s❝✉❧❛r ♣❧❛♥ts✬✱ ▼❛❝♠✐❧❧❛♥✳❬✸✶❪ ▲❡✇✐s✱ ❉✳ ❉✳ ✭✶✾✾✽✮✱ ◆❛✐✈❡ ✭❜❛②❡s✮ ❛t ❢♦rt②✿ ❚❤❡ ✐♥❞❡♣❡♥❞❡♥❝❡ ❛ss✉♠♣t✐♦♥ ✐♥ ✐♥❢♦r✲ ♠❛t✐♦♥ r❡tr✐❡✈❛❧✱ ❙♣r✐♥❣❡r ❱❡r❧❛❣✱ ♣♣✳ ✹✕✶✺✳❬✸✷❪ ▼❛rs❤✱ ❆✳✱ ❙✐♠✐st✐r❛✱ ❋✳ ✫ ❘♦❜❜✱ ❘✳ ✭✶✾✾✽✮✱ ❵❱r ✐♥ ♠❡❞✐❝✐♥❡✿ ❱✐rt✉❛❧ ❝♦❧♦♥♦s❝♦♣②✬✱ ❋✉t✉r❡ ●❡♥❡r✳ ❈♦♠♣✉t✳ ❙②st✳ ✶✹✱ ✷✺✸✕✷✻✹✳ ❯❘▲ ❤tt♣✿✴✴❞①✳❞♦✐✳♦r❣✴✶✵✳✶✵✶✻✴❙✵✶✻✼✲✼✸✾❳✭✾✽✮✽✵✵✷✺✲✸✳ ❬✸✸❪ ▼❛r✉②❛♠❛✱ ❖✳✱ ▼❛ts✉❞❛✱ ❆✳ ✫ ❑✉❤❛r❛✱ ❙✳ ✭✷✵✵✺✮✱ ❵❘❡❝♦♥str✉❝t✐♥❣ ♣❤②❧♦❣❡♥❡t✐❝ tr❡❡s♦❢ ♣r♦❦❛r②♦t❡ ❣❡♥♦♠❡s ❜② r❛♥❞♦♠❧② s❛♠♣❧✐♥❣ ♦❧✐❣♦♣❡♣t✐❞❡s✬✱ ■♥t✳ ❏✳ ❇✐♦✐♥❢♦r♠❛t✐❝s❘❡s✳ ❆♣♣❧✳ ✶✱ ✹✷✾✕✹✹✻✳ ❯❘▲ ❤tt♣✿✴✴♣♦rt❛❧✳❛❝♠✳♦r❣✴❝✐t❛t✐♦♥✳❝❢♠❄✐❞❂✶✸✺✻✹✾✺✳✶✸✺✻✺✵✶✳ ❬✸✹❪ ▼❛②❡r✱ ❍✳✱ ◆❛❣②✱ ■✳✱ ❑♥♦❧❧✱ ❆✳✱ ❇r❛✉♥✱ ❊✳ ❯✳✱ ❇❛✉❡r♥s❝❤♠✐tt✱ ❘✳ ✫ ▲❛♥❣❡✱ ❘✳ ✭✷✵✵✼✮✱❵❍❛♣t✐❝ ❢❡❡❞❜❛❝❦ ✐♥ ❛ t❡❧❡♣r❡s❡♥❝❡ s②st❡♠ ❢♦r ❡♥❞♦s❝♦♣✐❝ ❤❡❛rt s✉r❣❡r②✬✱ Pr❡s❡♥❝❡✿❚❡❧❡♦♣❡r✳ ❱✐rt✉❛❧ ❊♥✈✐r♦♥✳ ✶✻✱ ✹✺✾✕✹✼✵✳ ❯❘▲ ❤tt♣✿✴✴♣♦rt❛❧✳❛❝♠✳♦r❣✴❝✐t❛t✐♦♥✳❝❢♠❄✐❞❂✶✷✾✼✵✶✼✳✶✷✾✼✵✶✾✳ ❬✸✺❪ ▼❝❦❛②✱ ❘✳ ■✳✱ ❍♦❛✐✱ ◆✳ ❳✳✱ ❲❤✐❣❤❛♠✱ P✳ ❆✳✱ ❙❤❛♥✱ ❨✳ ✫ ❖✬◆❡✐❧❧✱ ▼✳ ✭✷✵✶✵✮✱ ❵●r❛♠♠❛r✲❜❛s❡❞ ❣❡♥❡t✐❝ ♣r♦❣r❛♠♠✐♥❣✿ ❛ s✉r✈❡②✬✱ ●❡♥❡t✐❝ Pr♦❣r❛♠♠✐♥❣ ❛♥❞ ❊✈♦❧✈❛❜❧❡ ▼❛❝❤✐✲♥❡s ✶✶✱ ✸✻✺✕✸✾✻✳ ❯❘▲ ❤tt♣✿✴✴❞①✳❞♦✐✳♦r❣✴✶✵✳✶✵✵✼✴s✶✵✼✶✵✲✵✶✵✲✾✶✵✾✲②✳ ✻✵❬✸✻❪ ▼❡✐❞❛♥✐s ❏✳✱ ❙✳ ❏✳ ✭✶✾✾✹✮✱ ❵❯♠❛ ✐♥tr♦❞✉çã♦ à ❜✐♦❧♦❣✐❛ ❝♦♠♣✉t❛❝✐♦♥❛❧✬✱ ❘❡❝✐❢❡ ✲ P❊✳❬✸✼❪ P♦❧❛❞✐❛♥✱ ▲✳ ✫ ❏❡r♠✐✐♥✱ ▲✳ ❙✳ ✭✷✵✵✻✮✱ ❵▼✉❧t✐✲♦❜❥❡❝t✐✈❡ ❡✈♦❧✉t✐♦♥❛r② ❛❧❣♦r✐t❤♠s ❛♥❞ ♣❤②❧♦❣❡♥❡t✐❝ ✐♥❢❡r❡♥❝❡ ✇✐t❤ ♠✉❧t✐♣❧❡ ❞❛t❛ s❡ts✬✱ ❙♦❢t ❈♦♠♣✉t✳ ✶✵✱ ✸✺✾✕✸✻✽✳ ❯❘▲❤tt♣✿✴✴♣♦rt❛❧✳❛❝♠✳♦r❣✴❝✐t❛t✐♦♥✳❝❢♠❄✐❞❂✶✶✵✷✽✽✻✳✶✶✵✷✽✾✺✳ ❬✸✽❪ ❘❡✐❥♠❡rs✱ ❚✳ ✭✶✾✾✾✮✱ ❵❯s✐♥❣ ❣❡♥❡t✐❝ ❛❧❣♦r✐t❤♠s ❢♦r t❤❡ ❝♦♥str✉❝t✐♦♥ ♦❢ ♣❤②❧♦❣❡♥❡t✐❝ tr❡❡s✿ ❛♣♣❧✐❝❛t✐♦♥ t♦ ❣✲♣r♦t❡✐♥ ❝♦✉♣❧❡❞ r❡❝❡♣t♦r s❡q✉❡♥❝❡s✳✬✱ ❇✐♦❙②st❡♠s ✲ ◆❡t❤❡r✲❧❛♥❞s✱ ✹✾✿✸✶✹✸✳ ❬✸✾❪ ❘♦s❡♥❜❡r❣✱ ❆✳ ▲✳ ✭✶✾✻✼✮✱ ❵❘❡❛❧✲t✐♠❡ ❞❡✜♥❛❜❧❡ ❧❛♥❣✉❛❣❡s✬✱ ❏✳ ❆❈▼ ✶✹✱ ✻✹✺✕✻✻✷✳ ❯❘▲❤tt♣✿✴✴❞♦✐✳❛❝♠✳♦r❣✴✶✵✳✶✶✹✺✴✸✷✶✹✷✵✳✸✷✶✹✷✸✳ ❬✹✵❪ ❘♦ss✱ ❏✳ ❈✳✱ ❊sté♣❛r✱ ❘✳ ❙✳✱ ❉í❛③✱ ❆✳✱ ❲❡st✐♥✱ ❈✳✲❋✳✱ ❑✐❦✐♥✐s✱ ❘✳✱ ❙✐❧✈❡r♠❛♥✱ ❊✳ ❑✳ ✫❲❛s❤❦♦✱ ●✳ ❘✳ ✭✷✵✵✾✮✱ ▲✉♥❣ ❡①tr❛❝t✐♦♥✱ ❧♦❜❡ s❡❣♠❡♥t❛t✐♦♥ ❛♥❞ ❤✐❡r❛r❝❤✐❝❛❧ r❡❣✐♦♥❛ss❡ss♠❡♥t ❢♦r q✉❛♥t✐t❛t✐✈❡ ❛♥❛❧②s✐s ♦♥ ❤✐❣❤ r❡s♦❧✉t✐♦♥ ❝♦♠♣✉t❡❞ t♦♠♦❣r❛♣❤② ✐♠❛❣❡s✱✐♥ ❵Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✷t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ▼❡❞✐❝❛❧ ■♠❛❣❡ ❈♦♠♣✉t✐♥❣❛♥❞ ❈♦♠♣✉t❡r✲❆ss✐st❡❞ ■♥t❡r✈❡♥t✐♦♥✿ P❛rt ■■✬✱ ▼■❈❈❆■ ✬✵✾✱ ❙♣r✐♥❣❡r✲❱❡r❧❛❣✱ ❇❡r❧✐♥✱❍❡✐❞❡❧❜❡r❣✱ ♣♣✳ ✻✾✵✕✻✾✽✳ ❯❘▲ ❤tt♣✿✴✴❞①✳❞♦✐✳♦r❣✴✶✵✳✶✵✵✼✴✾✼✽✲✸✲✻✹✷✲✵✹✷✼✶✲✸❴✽✹✳ ❬✹✶❪ ❘✉❞♦❧♣❤✱ ●✳ ✭✶✾✾✸✮✱ ❵▼❛ss✐✈❡❧② ♣❛r❛❧❧❡❧ s✐♠✉❧❛t❡❞ ❛♥♥❡❛❧✐♥❣ ❛♥❞ ✐ts r❡❧❛t✐♦♥ t♦ ❡✈♦❧✉✲ t✐♦♥❛r② ❛❧❣♦r✐t❤♠s✬✱ ❊✈♦❧✳ ❈♦♠♣✉t✳ ✶✱ ✸✻✶✕✸✽✸✳ ❯❘▲ ❤tt♣✿✴✴❞①✳❞♦✐✳♦r❣✴✶✵✳✶✶✻✷✴❡✈❝♦✳✶✾✾✸✳✶✳✹✳✸✻✶✳ ❬✹✷❪ ❙❛str②✱ ❑✳ ✭✷✵✵✶✮✱ ❵❊✈❛❧✉❛t✐♦♥✲r❡❧❛①❛t✐♦♥ s❝❤❡♠❡s ❢♦r ❣❡♥❡t✐❝ ❛♥❞ ❡✈♦❧✉t✐♦♥❛r② ❛❧❣♦✲ r✐t❤♠s✳ ♠❛st❡r✬s t❤❡s✐s✱ ✉♥✐✈❡rs✐t② ♦❢ ✐❧❧✐♥♦✐s ❛t ✉r❜❛♥❛✲❝❤❛♠♣❛✐❣♥✱ ❣❡♥❡r❛❧ ❡♥❣✐♥❡❡✲r✐♥❣ ❞❡♣❛rt♠❡♥t✬✱ ●❡♥❡r❛❧ ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❯r❜❛♥❛✱ ■▲✳ ❬✹✸❪ ❙❝♦tt✱ ❙✳ ❉✳✱ ❙❛♠❛❧✱ ❆✳ ✫ ❙❡t❤✱ ❙✳ ✭✶✾✾✺✮✱ ❍❣❛✿ ❛ ❤❛r❞✇❛r❡✲❜❛s❡❞ ❣❡♥❡t✐❝ ❛❧❣♦✲ r✐t❤♠✱ ✐♥ ❵Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✾✾✺ ❆❈▼ t❤✐r❞ ✐♥t❡r♥❛t✐♦♥❛❧ s②♠♣♦s✐✉♠ ♦♥ ❋✐❡❧❞✲♣r♦❣r❛♠♠❛❜❧❡ ❣❛t❡ ❛rr❛②s✬✱ ❋P●❆ ✬✾✺✱ ❆❈▼✱ ◆❡✇ ❨♦r❦✱ ◆❨✱ ❯❙❆✱ ♣♣✳ ✺✸✕✺✾✳ ❯❘▲❤tt♣✿✴✴❞♦✐✳❛❝♠✳♦r❣✴✶✵✳✶✶✹✺✴✷✵✶✸✶✵✳✷✵✶✸✶✾✳ ❬✹✹❪ ❙❡❛r❧s✱ ❉✳ ❇✳ ✭✶✾✾✾✮✱ ❵❋♦r♠❛❧ ❧❛♥❣✉❛❣❡ t❤❡♦r② ❛♥❞ ❜✐♦❧♦❣✐❝❛❧ ♠❛❝r♦♠♦❧❡❝✉❧❡s✬✳❬✹✺❪ ❱✐❡✐r❛✱ ❘✳ ❱✳ ✭✷✵✵✸✮✱ ❯♠ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ❇❛s❡❛❞♦ ❡♠ ❚✐♣♦s ❆❜str❛t♦s ❞❡ ❉❛❞♦s ❡ s✉❛ ❊s♣❡❝✐✜❝❛çã♦ ❡♠ ❩✱ ✭t❡s❡ ❞❡ ❞♦✉t♦r❛❞♦✮✱ ❈❡♥tr♦ ❞❡ ■♥❢♦r♠át✐❝❛✭❈■♥✮ ❯♥✐✈❡r✲ s✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ P❡r♥❛♠❜✉❝♦✱ ❘❡❝✐❢❡ ✲ P❊✳❬✹✻❪ ❱✐❡✐r❛✱ ❘✳ ❱✳ ✫ ▲♦♣❡s✱ ▼✳ ❆✳ ✭✶✾✾✾✮✱ ❵❯♠❛ ❛❜♦r❞❛❣❡♠ t❡ór✐❝❛ ✐♥✐❝✐❛❧ ♣❛r❛ ♦s ❛❧❣♦✲ r✐t♠♦s ❣❡♥ét✐❝♦s ❛tr❛✈és ❞❡ t✐♣♦s ❛❜str❛t♦s ❞❡ ❞❛❞♦s✬✱ ❘❡❧❛tór✐♦ ❚é❝♥✐❝♦ ❞♦ ❉❡♣❛rt❛✲ ♠❡♥t♦ ❞❡ ■♥❢♦r♠át✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ P❡r♥❛♠❜✉❝♦✳ ✻✶❬✹✼❪ ❲✐❡♥s✱ ❏✳ ❏✳ ✭✷✵✵✻✮✱ ❵▼✐ss✐♥❣ ❞❛t❛ ❛♥❞ t❤❡ ❞❡s✐❣♥ ♦❢ ♣❤②❧♦❣❡♥❡t✐❝ ❛♥❛❧②s❡s✬✱ ❏✳ ♦❢ ❇✐✲

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