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Análise do efeito da precisão finita no algoritmo adaptativo sigmoidal

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(1)❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ▼❛r❛♥❤ã♦ ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❚❡❝♥♦❧♦❣✐❛ ❈✉rs♦ ❞❡ Pós✲❣r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛. ❏♦sé ❞❡ ❘✐❜❛♠❛r ❙✐❧✈❛ ❋♦♥s❡❝❛. ❆♥á❧✐s❡ ❞♦ ❊❢❡✐t♦ ❞❛ Pr❡❝✐sã♦ ❋✐♥✐t❛ ♥♦ ❆❧❣♦r✐t♠♦ ❆❞❛♣t❛t✐✈♦ ❙✐❣♠♦✐❞❛❧. ❙ã♦ ▲✉ís ✷✵✶✼.

(2) ❏♦sé ❞❡ ❘✐❜❛♠❛r ❙✐❧✈❛ ❋♦♥s❡❝❛. ❆♥á❧✐s❡ ❞♦ ❊❢❡✐t♦ ❞❛ Pr❡❝✐sã♦ ❋✐♥✐t❛ ♥♦ ❆❧❣♦r✐t♠♦ ❆❞❛♣t❛t✐✈♦ ❙✐❣♠♦✐❞❛❧ ❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛❝ã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛ ❞❛ ❯❋▼❆✱ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ♣❛r❝✐❛❧ ❞♦ ❣r❛✉ ❞❡ ▼❊❙❚❘❊ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛✳. ❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❆❧❧❛♥ ❑❛r❞❡❝ ❉✉❛✐❧✐❜❡ ❇❛rr♦s ❋✐❧❤♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛ ✲ ❯❋▼❆. ❈♦✲♦r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❆♥❞ré ❇♦r❣❡s ❈❛✈❛❧❝❛♥t❡ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛ ✲ ❯❋▼❆. ❙ã♦ ▲✉ís ✷✵✶✼.

(3) Ficha gerada por meio do SIGAA/Biblioteca com dados fornecidos pelo(a) autor(a). Núcleo Integrado de Bibliotecas/UFMA. Fonseca, José de Ribamar Silva. Análise do Efeito da Precisão Finita no Algoritmo Adaptativo Sigmoidal / José de Ribamar Silva Fonseca. 2017. 64 p. Coorientador(a): André Borges Cavalcante. Orientador(a): Allan Kardec Duailibe Barros Filho. Dissertação (Mestrado) - Programa de Pós-graduação em Engenharia de Eletricidade/ccet, Universidade Federal do Maranhão, PIB3, 2017. 1. Aritmética de Ponto Fixo. 2. Filtros Adaptativos. 3. Quantização. 4. Sigmoidal. I. Barros Filho, Allan Kardec Duailibe. II. Cavalcante, André Borges. III. Título..

(4) José de Ribamar Silva Fonseca. Análise do Efeito da Precisão Finita no Algoritmo Adaptativo Sigmoidal. Dissertação apresentada ao Programa de PósGraduação em Engenharia Elétrica da UFMA, como requisito para a obtenção parcial do grau de MESTRE em Engenharia Elétrica.. Aprovado em 16 de Fevereiro de 2017.. BANCA EXAMINADORA. __________________________________________ Prof. Dr. Allan Kardec Duailibe Barros Filho Departamento de Engenharia Elétrica –UFMA. __________________________________________ Prof. Dr. André Borges Cavalcante Departamento de Engenharia Elétrica –UFMA. __________________________________________ Prof. Dr. Francisco das Chagas de Souza Departamento de Engenharia Elétrica –UFMA. __________________________________________ Prof. Dr. Fausto Lucena de Oliveira. __________________________________________ Prof. Dr. Marcos Antonio Ferreira de Araújo Departamento de Matemática -UFMA.

(5) ➚ ♠✐♥❤❛ ❡s♣♦s❛ ❘❛q✉❡❧✱ à ♠✐♥❤❛ ✜❧❤❛ ❈❡❝í❧✐❛ ❡ ❛♦ ♠❡✉ ✜❧❤♦ ❈❛✐♦✳.

(6) ❘❡s✉♠♦ ❆ ✜❧tr❛❣❡♠ ❛❞❛♣t❛t✐✈❛ ❝♦♥st✐t✉✐ ❛t✉❛❧♠❡♥t❡ ✉♠❛ ❢❡rr❛♠❡♥t❛ ✐♠♣♦rt❛♥t❡ ♥♦ ♣r♦❝❡ss❛♠❡♥t♦ ❡st❛tíst✐❝♦ ❞❡ s✐♥❛✐s✱ ❡s♣❡❝✐❛❧♠❡♥t❡ q✉❛♥❞♦ é ♥❡❝❡ssár✐♦ ♣r♦❝❡ss❛r s✐♥❛✐s ♣r♦✈❡♥✐❡♥t❡s ❞❡ ❛♠❜✐❡♥t❡s ❝♦♠ ❡st❛tíst✐❝❛s ❞❡s❝♦♥❤❡❝✐❞❛s q✉❡ ✈❛r✐❛♠ ❝♦♠ ♦ t❡♠♣♦✳ ❖ ❡s✲ t✉❞♦ ❞❡ ✜❧tr❛❣❡♠ ❛❞❛♣t❛t✐✈❛ ❢♦✐ ✐♠♣✉❧s✐♦♥❛❞♦ ❝♦♠ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ❛❧❣♦r✐t♠♦ ▲❡❛st ▼❡❛♥ ❙q✉❛r❡ ✭▲▼❙✮ ❡♠ ✶✾✻✵✳ ❉❡s❞❡ ❡♥tã♦ ♦✉tr♦s ❛❧❣♦r✐t♠♦s ❛❞❛♣t❛t✐✈♦s tê♠ s✉r❣✐❞♦ ❝♦♠ ✉♠ ❞❡s❡♠♣❡♥❤♦ s✉♣❡r✐♦r ❛♦ ❛❧❣♦r✐t♠♦ ▲▼❙ ❡♠ r❡❧❛çã♦ ❛♦ ❞❡s❛❥✉st❡ ❡ à t❛①❛ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛✳ ❊♥tr❡ ❡❧❡s✱ ♦ ❛❧❣♦r✐t♠♦ ❙✐❣♠♦✐❞❛❧ ✭❙❆✮ q✉❡ s❡ ❛♣r❡s❡♥t♦✉ s✉♣❡r✐♦r ❛♦ ▲▼❙✱ ❡♠ r❡❧❛çã♦ ❛ t❛①❛ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❡ ♦ ❞❡s❛❥✉st❡ ❡♠ s✉❛s ✐♠♣❧❡♠❡♥t❛çõ❡s ♥❛ ❢♦r♠❛ ❛♥❛✲ ❧ó❣✐❝❛✳ ◆♦s ❞✐s♣♦s✐t✐✈♦s ❞❡ ❤❛r❞✇❛r❡✱ t❛✐s ❝♦♠♦ ❉❙Ps✱ ▼✐❝r♦❝♦♥tr♦❧❛❞♦r❡s ❡ ❋P●❆s✱ ♦s ❛❧❣♦r✐t♠♦s ❛❞❛♣t❛t✐✈♦s sã♦ ✐♠♣❧❡♠❡♥t❛❞♦s ♥❛ ❢♦r♠❛ ❞✐❣✐t❛❧✱ ♦♥❞❡ ❛ ♣r❡❝✐sã♦ é ✜♥✐t❛✱ ❡♠ ❣❡r❛❧✱ ❝♦♠ ❛r✐t♠ét✐❝❛ ❞❡ ♣♦♥t♦ ✜①♦✳ ◗✉❛♥❞♦ ♦s ✜❧tr♦s ❛❞❛♣t❛t✐✈♦s sã♦ ✐♠♣❧❡♠❡♥t❛❞♦s ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛ ❛❧❣✉♥s ❡❢❡✐t♦s ♣♦❞❡♠ ❛❢❡t❛r ♦ s❡✉ ❞❡s❡♠♣❡♥❤♦✳ ❊♠ ú❧t✐♠❛ ❛♥á❧✐s❡✱ ❧❡✈❛r à ❞✐✈❡r❣ê♥❝✐❛ ❞❡✈✐❞♦ ❛♦s ❡rr♦s ❞❡ q✉❛♥t✐③❛çã♦ ❡s♣❡❝✐✜❝❛❞♦s ♥♦ ♣r♦❝❡ss♦ ❞❡ ❛♣r♦①✐✲ ♠❛çã♦ ❞♦s ✈❛❧♦r❡s ❞❛s ✈❛r✐á✈❡✐s ❡♥✈♦❧✈✐❞❛s ♥♦ ♣r♦❝❡ss❛♠❡♥t♦ ❛❞❛♣t❛t✐✈♦ ❞❡ s❡✉s ✈❛❧♦r❡s ♦r✐❣✐♥❛✐s✳ ❆ss✐♠✱ ❡st❡ tr❛❜❛❧❤♦ ♣r♦♣õ❡ ❛♥❛❧✐s❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ ❛❧❣♦r✐t♠♦ ❛❞❛♣t❛t✐✈♦ ❙✐❣♠♦✐❞❛❧ ✭❙❆✮ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛✱ q✉❛♥❞♦ ✐♠♣❧❡♠❡♥t❛❞♦ ✉t✐❧✐③❛♥❞♦ ❛r✐t♠ét✐❝❛ ❞❡ ♣♦♥t♦ ✜①♦✳ ❊♠ ♣❛rt✐❝✉❧❛r✱ ❛ ❛♥á❧✐s❡ ❞❡ s✉❛ ❝✉r✈❛ ❞❡ ❞❡s❡♠♣❡♥❤♦ ❡ ♦ ❞❡s❛❥✉st❡✱ ❝♦♠♣❛r❛♥❞♦✲♦s ❡♠ ❞✐❢❡r❡♥t❡s ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♣❛❧❛✈r❛s ✭♥ú♠❡r♦ ❞❡ ❜✐ts✮✳ ❖s r❡s✉❧t❛❞♦s ❛♣r❡s❡♥t❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦ ♣r♦♣õ❡ ✉♠❛ ❛♣r♦①✐♠❛çã♦ ❡♠ sér✐❡ ❞❡ ❚❛②❧♦r ❞♦ ❣r❛❞✐❡♥t❡ ❞❛ ❢✉♥çã♦ ❞❡ ❝✉st♦ ▲♥✭❝♦s❤ αe✮ ❞♦ ❛❧❣♦r✐t♠♦ ❙❆ ♣❛r❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛✳ ❆♥❛❧✐s❛♠♦s ❛ s✉❛ ❝✉r✈❛ ❞❡ ❞❡s❡♠♣❡♥❤♦ ♣❛r❛ ❞✐❢❡r❡♥t❡s ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♣❛❧❛✈r❛s✳ ▼♦str❛✲s❡ q✉❡ ♦ ❛❧❣♦r✐t♠♦ ❛♣r❡s❡♥t❛ ❡st❛❜✐❧✐❞❛❞❡ ❡♠ s❡✉ ❞❡s❡♠♣❡♥❤♦ ❡♠ r❡❧❛çã♦ à ❝♦♥✈❡r❣ê♥❝✐❛✱ ♣❛r❛ ❞✐❢❡r❡♥t❡s ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♣❛❧❛✈r❛s✱ ❡ q✉❡ ♦ ❛✉♠❡♥t♦ ♥♦ ♥í✈❡❧ ❞♦ ❞❡s❛❥✉st❡ ❡♠ ❡st❛❞♦ ❡s✲ t❛❝✐♦♥ár✐♦ é s❡♥sí✈❡❧ ♦✉ ✐♥✢✉❡♥❝✐❛❞♦ ♣❡❧❛ q✉❛♥t✐③❛çã♦ ❞♦s ✈❛❧♦r❡s ❞❛s ✈❛r✐á✈❡✐s ❡♥✈♦❧✈✐❞❛s ♥♦s ❝á❧❝✉❧♦s ❞❡ss❡ ❛❧❣♦r✐t♠♦✳ P❛❧❛✈r❛s✲❝❤❛✈❡s✿ ❋✐❧tr♦s ❆❞❛♣t❛t✐✈♦s✱ ◗✉❛♥t✐③❛çã♦✱ ❆r✐t♠ét✐❝❛ ❞❡ P♦♥t♦✲❋✐①♦✱ ❙✐❣♠♦✐❞❛❧✳.

(7) ❆❜str❛❝t ❚❤❡ ❛❞❛♣t✐✈❡ ✜❧t❡r✐♥❣ ✐s ❝✉rr❡♥t❧② ❛♥ ✐♠♣♦rt❛♥t t♦♦❧ ✐♥ t❤❡ st❛t✐st✐❝❛❧ ♣r♦❝❡s✲ s✐♥❣ ♦❢ s✐❣♥❛❧s✱ ❡s♣❡❝✐❛❧❧② ✇❤❡♥ ✐t ✐s ♥❡❝❡ss❛r② t♦ ♣r♦❝❡ss s✐❣♥❛❧s ❢r♦♠ ❡♥✈✐r♦♥♠❡♥ts ✇✐t❤ ✉♥❦♥♦✇♥ st❛t✐st✐❝s ✈❛r②✐♥❣ ✇✐t❤ t✐♠❡✳ ❚❤❡ ❛❞❛♣t✐✈❡ ✜❧t❡r✐♥❣ st✉❞② ✇❛s ❞r✐✈❡♥ ❜② t❤❡ ❞❡✲ ✈❡❧♦♣♠❡♥t ♦❢ t❤❡ ▲❡❛st ▼❡❛♥ ❙q✉❛r❡ ❛❧❣♦r✐t❤♠ ✭▲▼❙✮ ✐♥ ✶✾✻✵✳ ❙✐♥❝❡ t❤❡♥ ♦t❤❡r ❛❞❛♣t✐✈❡ ❛❧❣♦r✐t❤♠s ❤❛✈❡ ❝♦♠❡ ✉♣ ✇✐t❤ ❛ ❜❡tt❡r ♣❡r❢♦r♠❛♥❝❡ t❤❛♥ ▲▼❙ ❛❧❣♦r✐t❤♠ ✇✐t❤ r❡s♣❡❝t t♦ ♠✐s❛❞❥✉st♠❡♥t ❛♥❞ ❝♦♥✈❡r❣❡♥❝❡ r❛t❡✳ ❆♠♦♥❣ t❤❡♠✱ t❤❡ ❙✐❣♠♦✐❞❛❧ ❛❧❣♦r✐t❤♠ ✭❙❆✮ ✇❤✐❝❤ s❤♦✇❡❞ s✉♣❡r✐♦r t♦ t❤❡ ▲▼❙✱ ❢♦r t❤❡ ❝♦♥✈❡r❣❡♥❝❡ r❛t❡ ❛♥❞ t❤❡ ♠✐s♠❛t❝❤ ✐♥ t❤❡✐r ✐♠♣❧❡✲ ♠❡♥t❛t✐♦♥s ✐♥✜♥✐t❡ ♣r❡❝✐s✐♦♥✳ ■♥ ❤❛r❞✇❛r❡ ❞❡✈✐❝❡s s✉❝❤ ❛s ❉❙Ps✱ ♠✐❝r♦❝♦♥tr♦❧❧❡rs ❛♥❞ ❋P●❆s✱ ❛❞❛♣t✐✈❡ ❛❧❣♦r✐t❤♠s ❛r❡ ✐♠♣❧❡♠❡♥t❡❞ ✐♥ ✜♥✐t❡ ♣r❡❝✐s✐♦♥✱ ✐♥ ❣❡♥❡r❛❧✱ ✜①❡❞ ♣♦✐♥t ❛r✐t❤♠❡t✐❝✳ ❲❤❡♥ t❤❡ ❛❞❛♣t✐✈❡ ✜❧t❡rs ❛r❡ ✐♠♣❧❡♠❡♥t❡❞ ✐♥ ✜♥✐t❡ ♣r❡❝✐s✐♦♥ s♦♠❡ ❡✛❡❝ts ❝❛♥ ❛✛❡❝t t❤❡✐r ♣❡r❢♦r♠❛♥❝❡✳ ❯❧t✐♠❛t❡❧② ❧❡❛❞ t♦ ❞✐✈❡r❣❡♥❝❡ ❞✉❡ t♦ q✉❛♥t✐③❛t✐♦♥ ❡rr♦rs s♣❡❝✐✜❡❞ ✐♥ t❤❡ ❛♣♣r♦①✐♠❛t✐♦♥ ♣r♦❝❡ss ♦❢ t❤❡ ✈❛r✐❛❜❧❡s ✐♥✈♦❧✈❡❞ ✐♥ t❤❡ ❛❞❛♣t✐✈❡ ♣r♦❝❡ss✐♥❣ ♦❢ t❤❡✐r ♦r✐❣✐♥❛❧ ✈❛❧✉❡s✳ ❚❤✉s✱ t❤✐s ❛rt✐❝❧❡ ❛✐♠s t♦ ❛♥❛❧②③❡ t❤❡ ♣❡r❢♦r♠❛♥❝❡ ♦❢ t❤❡ ❛❞❛♣t✐✈❡ ❛❧❣♦r✐t❤♠ ❙✐❣♠♦✐❞❛❧ ✭❙❆✮ ✐♥ ✜♥✐t❡ ♣r❡❝✐s✐♦♥ ✇❤❡♥ ✐♠♣❧❡♠❡♥t❡❞ ✉s✐♥❣ ✜①❡❞✲♣♦✐♥t ❛r✐t❤♠❡✲ t✐❝✳ ■♥ ♣❛rt✐❝✉❧❛r✱ t❤❡ ❛♥❛❧②s✐s ♦❢ ✐ts ♣❡r❢♦r♠❛♥❝❡ ❝✉r✈❡ ❛♥❞ ♠✐s♠❛t❝❤✱ ❝♦♠♣❛r✐♥❣ t❤❡♠ ✐♥ ❞✐✛❡r❡♥t ✇♦r❞ ❧❡♥❣t❤s ✭♥✉♠❜❡r ♦❢ ❜✐ts✮✳ ❚❤❡ r❡s✉❧ts ♣r❡s❡♥t❡❞ ✐♥ t❤✐s ❛rt✐❝❧❡ ♣r♦♣♦s❡s ❛ s❡r✐❡s ♦❢ ❚❛②❧♦r ▲♥ ❣r❛❞✐❡♥t ♦❢ ❝♦st ❢✉♥❝t✐♦♥ ✭❝♦s❤ αe✮ ❛❧❣♦r✐t❤♠ ❙❆ ❢♦r ✐♠♣❧❡♠❡♥t❛t✐♦♥ ✐♥ ✜♥✐t❡ ♣r❡❝✐s✐♦♥✳ ❲❡ ❛♥❛❧②③❡ ✐ts ♣❡r❢♦r♠❛♥❝❡ ❝✉r✈❡ ❢♦r ❞✐✛❡r❡♥t ❧❡♥❣t❤s ♦❢ ✇♦r❞s✳ ■t s❤♦✇s t❤❛t t❤❡ ❛❧❣♦r✐t❤♠ ✐s st❛❜❧❡ ✐♥ ✐ts ♣❡r❢♦r♠❛♥❝❡ ❝♦♠♣❛r❡❞ t♦ ❝♦♥✈❡r❣❡♥❝❡ t♦ ❞✐✛❡r❡♥t ❧❡♥❣t❤s ♦❢ ✇♦r❞s✱ ❛♥❞ t❤❛t t❤❡ ✐♥❝r❡❛s❡ ✐♥ ♠✐s♠❛t❝❤ ❧❡✈❡❧ ❛t st❡❛❞② st❛t❡ ✐s s❡♥s✐t✐✈❡ ♦r ❛✛❡❝t❡❞ ❜② t❤❡ q✉❛♥t✐③❛t✐♦♥ ♦❢ t❤❡ ✈❛r✐❛❜❧❡s ✐♥✈♦❧✈❡❞ ✐♥ t❤❡ ❝❛❧❝✉❧❛t✐♦♥s ♦❢ t❤✐s ❛❧❣♦r✐t❤♠✳ ❑❡②✇♦r❞s✿ ❆❞❛♣t✐✈❡ ❋✐❧t❡rs✱ ◗✉❛♥t✐③❛t✐♦♥✱ ❋✐①❡❞✲P♦✐♥t ❆r✐t❤♠❡t✐❝✱ ❙✐❣♠♦✐❞❛❧.

(8) ❆❣r❛❞❡❝✐♠❡♥t♦s ❆♦ ♣r♦❢❡ss♦r ❆❧❧❛♥ ❑❛r❞❡❝ ❉✉❛✐❧✐❜❡ ❇❛rr♦s ❋✐❧❤♦✱ ♣❡❧❛ ❝♦♥✜❛♥ç❛✱ ♦r✐❡♥t❛çã♦ ❡ ❞❡❞✐❝❛çã♦ ❝♦♠ q✉❡ ❡♥❝❛♠✐♥❤♦✉ ❡st❡ tr❛❜❛❧❤♦✳ ❆♦ ♣r♦❢❡ss♦r ❆♥❞ré ❇♦r❣❡s ❈❛✈❛❧❝❛♥t❡ ❡ ❛♦ ♣r♦❢❡ss♦r ❊✇❛❧❞♦ ❊❞❡r ❈❛r✈❛❧❤♦ ❙❛♥t❛♥❛ ✱ ♣❡❧❛ ❡♠♣❡♥❤♦ ❡ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ♥❛ ♦r✐❡♥t❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ❆❣r❛❞❡ç♦ ❛♦s ♣r♦❢❡ss♦r❡s ❡ ❛♠✐❣♦s ❞♦ ▲❛❜♦r❛tór✐♦ ❞❛ ■♥❢♦r♠❛çã♦ ❇✐♦❧ó❣✐❝❛✲ P■❇✳ ➚ t♦❞❛ ♠✐♥❤❛ ❢❛♠í❧✐❛ ❡ ❛♠✐❣♦s✳ ➚ ❈◆P◗✱ ♣❡❧♦ r❡❧❡✈❛♥t❡ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦✳.

(9) ✏❱❡♥❝❡r ❛ s✐ ♣ró♣r✐♦ é ❛ ♠❛✐♦r ❞❛s ✈✐tó✲ r✐❛s✑✳ P❧❛tã♦.

(10) ❙✉♠ár✐♦ ▲✐st❛ ❞❡ ❋✐❣✉r❛s. ✽. ▲✐st❛ ❞❡ ❚❛❜❡❧❛s. ✶✶. ▲✐st❛ ❞❡ ❆❜r❡✈✐❛çõ❡s. ✶✷. ❆rt✐❣♦s ♣✉❜❧✐❝❛❞♦s✱ ❛❝❡✐t♦s ❡ ❛♣r❡s❡♥t❛❞♦s. ✶✸. ✶. ✶✹. ✷. ✸. ■♥tr♦❞✉çã♦ ✶✳✶. Pr♦❜❧❡♠❛. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✶✺. ✶✳✷. ❖❜❥❡t✐✈♦s. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✶✺. ✶✳✸. ▼♦t✐✈❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✶✺. ✶✳✹. ❊st❛❞♦ ❞❛ ❆rt❡. ✶✻. ✶✳✺. ❖r❣❛♥✐③❛çã♦ ❞♦ ❚❡①t♦. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ❋✐❧tr❛❣❡♠ ❆❞❛♣t❛t✐✈❛. ✶✻. ✶✽. ✷✳✶. ❈❛r❛❝t❡ríst✐❝❛s ❞♦s ❋✐❧tr♦s ❆❞❛♣t❛t✐✈♦s. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✶✾. ✷✳✷. ❆♣❧✐❝❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✷✷. ❊❢❡✐t♦s ❞❛ Pr❡❝✐sã♦ ❋✐♥✐t❛. ✷✹. ✸✳✶. ❊rr♦s ❞❡ ◗✉❛♥t✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✷✻. ✸✳✷. ❋✐❧tr❛❣❡♠ ❆❞❛♣t❛t✐✈❛ ❡♠ Pr❡❝✐sã♦ ❋✐♥✐t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✷✼. ✸✳✷✳✶. ✷✾. ❖ ▲▼❙ ❡♠ Pr❡❝✐sã♦ ❋✐♥✐t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✳✸. ■♠♣❧❡♠❡♥t❛çã♦ ❡♠ ❉✐s♣♦s✐t✐✈♦ ❞❡ ❍❛r❞✇❛r❡ ❉✐❣✐t❛❧. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✶. ✸✳✹. ❙✐♠✉❧❛çã♦ ❞❡ ▼♦♥t❡ ❈❛r❧♦. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✷.

(11) ✼. ✹ ❆♥á❧✐s❡ ❡♠ Pr❡❝✐sã♦ ❋✐♥✐t❛ ❞♦ ❆❧❣♦r✐t♠♦ ❆❞❛♣t❛t✐✈♦ ❇❛s❡❛❞♦ ♥♦ ❊rr♦ ◆ã♦ ▲✐♥❡❛r. ✸✸. ✹✳✶. ❆♥á❧✐s❡ ❞❡ ❆❞❛♣t❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✻. ✹✳✷. ❈♦♠♣♦rt❛♠❡♥t♦ ❞❡ ❈♦♥✈❡r❣ê♥❝✐❛. ✹✵. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺ ❖ ❆❧❣♦r✐t♠♦ ❙✐❣♠♦✐❞❛❧ ❡♠ Pr❡❝✐sã♦ ❋✐♥✐t❛. ✹✸. ✺✳✶. ▼ét♦❞♦. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✹. ✺✳✷. ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✻. ✻ ❉✐s❝✉ssã♦. ✺✸. ✼ ❈♦♥❝❧✉sõ❡s ❋✐♥❛✐s ❡ P❡rs♣❡❝t✐✈❛s. ✺✼. ❘❡❢❡rê♥❝✐❛s. ✺✽. ❆♣ê♥❞✐❝❡s. ✻✶.

(12) ▲✐st❛ ❞❡ ❋✐❣✉r❛s ✷✳✶ ❈♦♥✜❣✉r❛çã♦ ❣❡r❛❧ ❞❡ ✉♠ ✜❧tr♦ ❛❞❛♣t❛t✐✈♦✳ ❊♠ q✉❡ k r❡♣r❡s❡♥t❛ ♦ ♥ú♠❡r♦ ❞❡ ✐t❡r❛çã♦✱ xk ❞❡s✐❣♥❛ ♦ s✐♥❛❧ ❞❡ ❡♥tr❛❞❛✱ yk é ♦ s✐♥❛❧ ❞❡ s❛í❞❛ ❞♦ ✜❧tr♦ ❛❞❛♣t❛t✐✈♦✱ ❡ dk ❞❡✜♥❡ ♦ s✐♥❛❧ ❞❡s❡❥❛❞♦✳ ❖ s✐♥❛❧ ❞❡ ❡rr♦ ek é ❝❛❧❝✉❧❛❞❛ ❝♦♠♦ dk − yk ✳ ❖ s✐♥❛❧ ❞❡ ❡rr♦ é ❡♥tã♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❢♦r♠❛r ✉♠❛ ❢✉♥çã♦ ❞❡ ❞❡s❡♠♣❡♥❤♦ ✭♦✉ ♦❜❥❡t✐✈♦✮ q✉❡ é ❡①✐❣✐❞❛ ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❞❡ ❛❞❛♣t❛çã♦ ♣❛r❛ ❞❡t❡r♠✐♥❛r ❛ ❛t✉❛❧✐③❛çã♦ ❛♣r♦♣r✐❛❞❛ ❞♦s ❝♦❡✜❝✐❡♥t❡s ❞♦ ✜❧tr♦ wk ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✷ ▼♦❞❡❧♦ ❞❡ ✉♠ ✜❧tr♦ ❛❞❛♣t❛t✐✈♦ ❞✐s❝r❡t♦ ❛♣❧✐❝❛❞♦ ❛♦ ♣r♦❜❧❡♠❛ ❞❡ ✐❞❡♥t✐✜✲ ❝❛çã♦ ❞❡ s✐st❡♠❛ ❞❡s❝♦♥❤❡❝✐❞♦✱ ♦♥❞❡ z I r❡♣r❡s❡♥t❛ ❛s ✉♥✐❞❛❞❡s ❞♦ s✐♥❛❧ ❞❡ ❡♥tr❛❞❛ xk ❛tr❛s❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✸ P♦rçã♦ ❞❛ s✉♣❡r❢í❝✐❡ q✉❛❞rát✐❝❛ tr✐❞✐♠❡♥s✐♦♥❛❧ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛❧❣✉♥s ❝♦♥✲ t♦r♥♦s✳ ❖ ❡rr♦ q✉❛❞rát✐❝♦ ♠é❞✐♦ ❡stá ♣❧♦t❛❞♦ ♥❛ ✈❡rt✐❝❛❧✱ w0 ❡ w1 ✈❛r✐❛♠ ❞❡ ✲✶ ❛ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✹ ▼♦❞❡❧♦ ❞❡ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ s✐st❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✷✳✺ ▼♦❞❡❧♦ ❞❡ ▼♦❞❡❧❛❣❡♠ ■♥✈❡rs❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✻ ▼♦❞❡❧♦ ❞❡ Pr❡❞✐çã♦ ▲✐♥❡❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✼ ▼♦❞❡❧♦ ❞❡ ❈❛♥❝❡❧❛♠❡♥t♦ ❞❡ ❘✉í❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✸✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❡♠ ♣r❡❝✐sã♦ ✐♥✜♥✐t❛✳ ❖ ❙✐♥❛❧ ❛ss✉♠❡ ✈❛❧♦r❡s ✐♥✜♥✐t♦s ♥♦ ✐♥t❡r✈❛❧♦ ❝♦♥s✐❞❡r❛❞♦✳ ■♥t❡r✈❛❧♦ ❞❡ ❛♠♣❧✐t✉❞❡ ❬✵✱▲❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛✳ ❖ ❙✐♥❛❧ ❛ss✉♠❡ ✈❛❧♦r❡s ✜♥✐t♦s ♥♦ ✐♥t❡r✲ ✈❛❧♦✳ ❖ ❡rr♦ é ❞✐❢❡r❡♥t❡ ❞❡ ③❡r♦✳ ■♥t❡r✈❛❧♦ ❞❡ ❛♠♣❧✐t✉❞❡ ❬✵✱▲❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✸ ❊sq✉❡♠❛ ❣❡r❛❧ ❞❛ ❛r✐t♠ét✐❝❛ ❞❡ ♣♦♥t♦ ✜①♦✳ ❈♦♥s✐❞❡r❛♥❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♣❛❧❛✈✈r❛ b ✰ 1bit ❞❡ s✐♥❛❧✳ ❉❡✜♥❡ ♥ú♠❡r♦ ❞❡ bn ♣❛rt❡ ✐♥t❡r✐❛ ❡ b−n ♣❛rt❡ ❢r❛❝✐♦♥ár✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✹ ❘❡♣r❡s❡♥t❛çã♦ ◆í✈❡✐s ❞❡ ◗✉❛♥t✐③❛çã♦✳ ❛✮ ◗✉❛♥t✐❞❛❞❡s ❞❡ ♥í✈❡✐s ◆❂✹✳ ❜✮◗✉❛♥t✐❞❛❞❡s ❞❡ ♥í✈❡✐s ◆❂✽✳. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻.

(13) ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙. ✾. ✸✳✺ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❡ ♥í✈❡✐s ❞❡ q✉❛♥t✐③❛çã♦ ♣❛r❛ ♦ ❝❛s♦ ❞❡ b = 2 ❜✐ts ❡ △ = L/4✳ ❈♦♥s✐❞❡r❛♠♦s ✉♠ ✈❛❧♦r L ❧✐♠✐❛r✳ ❯s❛♥❞♦ b ❜✐ts✱ ♦ ✐♥t❡r✈❛❧♦ ❞❡ [0, L] ♣♦❞❡ s❡r ❞✐✈✐❞✐❞♦ ❡♠ 2b ♥í✈❡✐s ❞❡ ❧❛r❣✉r❛ △ = L/2b ❝❛❞❛✳ ❙❡✱ ❛❧é♠ ❞✐ss♦✱ ✉s❛♠♦s ✶ ✭✉♠✮ ❜✐t ❞❡ s✐♥❛❧✱ ♦s r❡s✉❧t❛♥t❡s ✭b + 1) ❜✐ts ❞✐✈✐❞❡ ♦ ✐♥t❡r✈❛❧♦ [−L, L] ❡♠ 22b ♥í✈❡✐s✳ ❆q✉✐ ❛ss✉♠✐♠♦s ♦♣❡r❛çã♦ ❞❡ ❛rr❡❞♦♥❞❛♠❡♥t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✻ ❱❛r✐â♥❝✐❛ ❞❡✈✐❞♦ à q✉❛♥t✐③❛çã♦ ❝♦♠ ❛r✐t♠ét✐❝❛ ❞❡ ♣♦♥t♦ ✜①♦✳ P❛r❛ C = 1 ♥ú♠❡r♦ ❞❡ bits ✈❛r✐❛♥❞♦ ❡♥tr❡ 7bits à 32bits ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✹✳✶ ❋✐❧tr❛❣❡♠ ❛❞❛♣t❛t✐✈❛ ❡♠ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ s✐st❡♠❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✹✳✷ ■❞❡♥t✐✜❝❛çã♦ ❞❡ s✐st❡♠❛ ✐♠♣❧❡♠❡♥t❛❞♦ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛✳ ❖♥❞❡ xk ❞❡s✐❣♥❛ ♦ s✐♥❛❧ ❞❡ ❡♥tr❛❞❛✳ ❖s ❜❧♦❝♦s Qd ❡ Qc sã♦ q✉❛♥t✐③❛❞♦r❡s ❞❡ b ❜✐ts✳ ❆ss✐♠✱ ♦ q✉❛♥t✐③❛❞♦r✱ Qd ✱ ✉s❛ bd ❜✐ts ♣❛r❛ ♦s ❞❛❞♦s ❞❡ ❡♥tr❛❞❛ ❡ Qc q✉❛♥t✐③❛ ♦s ❝♦❡✜❝✐❡♥t❡s ❡♠ bc ❜✐ts✳ ❖ s✐♥❛❧ ❞❡ s❛í❞❛ yQk ✐♥❞✐❝❛ ❛ ❢♦r♠❛ q✉❛♥t✐③❛❞❛✳ ❖ s✐♥❛❧ ❞❡s❡❥❛❞♦ ❞❡✜♥✐❞♦ ♣♦r dk ❞♦ s✐st❡♠❛ ❞❡s❝♦♥❤❡❝✐❞♦ ❡ dQk s✉❛ ❢♦r♠❛ q✉❛♥t✐③❛❞❛✳ ❖ r✉í❞♦ ❞❡ ♠❡❞✐çã♦ nk ❡ ♦ s✐♥❛❧ ❞❡ ❡rr♦ q✉❛♥t✐③❛❞♦ eQk ✳ ❖s ❝♦❡✜❝✐❡♥t❡s wk ❞♦ s✐st❡♠❛ ❞❡s❝♦♥❤❡❝✐❞♦ ❡ wQk ❞♦ ✜❧tr♦ ❛❞❛♣t❛t✐✈♦✳ ✳ ✳ ✳ ✳ ✸✼ ✺✳✶ P♦rçã♦ ❞❛ s✉♣❡r❢í❝✐❡ tr✐❞✐♠❡♥s✐♦♥❛❧ ❣❡r❛❞❛ ♣❡❧❛ ❢✉♥çã♦ Ln cosh (αe)✱ ❥✉♥✲ t❛♠❡♥t❡ ❝♦♠ ❛❧❣✉♥s ❝♦♥t♦r♥♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✺✳✷ ❉✐❛❣r❛♠❛ ❞♦ ✢✉①♦ ❞♦ ♣r♦❥❡t♦ ❙❆ ❡♠ ♣r❡❝✐ã♦ ✜♥✐t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✺✳✸ ❈♦♠♣❛r❛çã♦ ❞❛ ❢✉♥çã♦ tanh(e) ❡ s✉❛ ❢✉♥çã♦ ❡♠ sér✐❡ ❞❡ ❚❛②❧♦r✭✺♦ ❣r❛✉✮ ❡♠ ♣♦♥t♦ ✢✉t✉❛♥t❡ ❝♦♠ ✻✹ ❜✐ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✺✳✹ ❙❆ ① ▲▼❙ ❡♠ ♣♦♥t♦ ✜①♦ ✸✷ ❜✐ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✺✳✺ ❙❆ ❡♠ ❞✐❢❡r❡♥t❡ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♣❛❧❛✈r❛ ❜✐♥ár✐❛ ❡♠ ❛r✐t♠ét✐❝❛ ❞❡ ♣♦♥t♦ ✜①♦✿ ✽ ❜✐ts✱ ✶✻ ❜✐ts ❡ ✸✷ ❜✐ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✺✳✻ ❈✉r✈❛ ❞❡ ❛♣r❡♥❞✐③❛❣❡♠ ❙❆ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛ ♣❛r❛ C = 0, 0590 ❡ nk = 10−3 ❡♠ ❞✐❢❡r❡♥t❡s ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♣❛❧❛✈r❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✺✳✼ ❈✉r✈❛ ❞❡ ❛♣r❡♥❞✐③❛❣❡♠ ❙❆ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛ ♣❛r❛ C = 0, 0590 ❡♠ ❞✐❢❡✲ r❡♥t❡s ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♣❛❧❛✈r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵.

(14) ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙. ✶✵. ✺✳✽ ❈✉r✈❛ ❞❡ ❛♣r❡♥❞✐③❛❣❡♠ ❙❆ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛ ♣❛r❛ bd = 15bits✱ nk = 10−3 ❡ C = 0, 0590 ❡♠ ❞✐❢❡r❡♥t❡s ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♣❛❧❛✈r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶.

(15) ▲✐st❛ ❞❡ ❚❛❜❡❧❛s ✺✳✶ ❉❡s❛❥✉st❡ ❡ ▼❙❊ ❞♦ ❙❆ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✺✳✷ ❉❡s❛❥✉st❡ ❡ ▼❙❊ ❞♦ ❙❆ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛ ♣❛r❛ C = 0, 0590 ❡ nk = 10−3 ✳ ✹✾ ✺✳✸ ❉❡s❛❥✉st❡ ❡ ▼❙❊ ❞♦ ❙❆ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛ ♣❛r❛ bd = 15bits✱ nk = 10−2 ❡ C = 0, 0590 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵. ✺✳✹ ❉❡s❛❥✉st❡ ❡ ▼❙❊ ❞♦ ❙❆ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛ ♣❛r❛ bd = 15bits✱ nk = 10−3 ❡ C = 0, 0590 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷.

(16) ✶✷. ▲✐st❛ ❞❡ ❆❜r❡✈✐❛çõ❡s ❬❆❉❈❪. ❈♦♥✈❡rs♦r ❆♥❛❧ó❣✐❝♦ ❉✐❣✐t❛❧. ❬❉❙P❪. ❉✐❣✐t❛❧ ❙✐❣♥❛❧ Pr♦❝❡ss✐♥❣. ❬❋■❘❪. ❋✐♥✐t❡ ■♠♣✉❧s❡ ❘❡s♣♦♥s❡. ❬❋P●❆❪ ❋✐❡❧❞ Pr♦❣r❛♠♠❛❜❧❡ ●❛t❡ ❆rr❛② ❬■❘❘❪. ■♥✜♥✐t❡ ■♠♣✉❧s❡ ❘❡s♣♦♥s❡. ❬▲▼❙❪. ▲❡❛st ▼❡❛♥ ❙q✉❛r❡. ❬▼❙❊❪. ❊rr♦ ◗✉❛❞rát✐❝♦ ▼é❞✐♦. ❬❘▲❙❪. ❘❡❝✉rs✐✈❡ ▲❡❛st ❙q✉❛r❡. ❬❙❆❪. ❙✐❣♠♦✐❞❛❧. ❬❚▲❈❪. ❚❡♦r❡♠❛ ❞♦ ▲✐♠✐t❡ ❈❡♥tr❛❧.

(17) ✶✸. ❆rt✐❣♦s ♣✉❜❧✐❝❛❞♦s✱ ❛❝❡✐t♦s ❡ ❛♣r❡s❡♥t❛❞♦s. ✶✳ ❏♦sé ❞❡ ❘✳❙✳ ❋♦♥s❡❝❛✱ ❊✇❛❧❞♦ ❊✳ ❈✳ ❙❛♥t❛♥❛✱ ❆♥❞ré ❈✳ ❇✳ ❈❛✈❛❧❝❛♥t❡✱ ❘❛✐✲ ♠✉♥❞♦ ❈✳ ❙✳ ❋r❡✐r❡ ❛♥❞ ❆❧❧❛♥ ❑✳ ❇❛rr♦s✳ ✧❋■◆■❚❊ P❘❊❈■❙■❖◆ ❊❋❋❊❈❚ ❖❋ ❆❉❆P✲ ❚■❱❊ ❆▲●❖❘■❚❍▼ ❙■●▼❖■❉❆▲✧❨♦✉r ♣❛♣❡r ✶✺✼✵✸✷✺✺✵✾✳ ❬❆▼❈✷✵✶✻❪✲❑♦t❛ ❑✐♥❛❜❛❧✉✱ ❙❛❜❛❤ ✲▼❛❧❛②s✐❛✳ ❤tt♣✿✴✴✉❦s✐♠✳✐♥❢♦✴❛♠❝✷✵✶✻✴❛♠❝✷✵✶✻✳ ❆♥♦✿ ✷✵✶✻ ✷✳ ❏♦sé ❞❡ ❘✳❙✳ ❋♦♥s❡❝❛✱ ❊✇❛❧❞♦ ❊✳ ❈✳ ❙❛♥t❛♥❛✱ ❆♥❞ré ❈✳ ❇✳ ❈❛✈❛❧❝❛♥t❡✱ ❘❛✐♠✉♥❞♦ ❈✳ ❙✳ ❋r❡✐r❡ ❛♥❞ ❆❧❧❛♥ ❑✳ ❇❛rr♦s✳ ✧❆◆➪▲■❙❊ ❉❖ ❊❋❊■❚❖ ❉❆ P❘❊❈■✲ ❙➹❖ ❋■◆■❚❆ ◆❖ ❆▲●❖❘■❚▼❖ ❆❉❆P❚❆❚■❱❖ ❙■●▼❖■❉❆▲✧❳✲❊❆▼❈✲ P❡tr♦♣ó❧✐s✲ ❘❏✱❇❘❆❙■▲✳ ❤tt♣✿✴✴✇✇✇✳❡❛♠❝✳❧♥❝❝✳❜r✴ ❆♥♦✿ ✷✵✶✼.

(18) ✶✹. ✶ ■♥tr♦❞✉çã♦ ❖ ❡st✉❞♦ ❞❡ s✐♥❛✐s t❡✈❡ ✉♠ ❣r❛♥❞❡ ❛✈❛♥ç♦ ❡♠ s✉❛s ❛♣❧✐❝❛çõ❡s ❝♦♠ ♦ s✉r❣✐✲ ♠❡♥t♦ ❡ ❛♣❡r❢❡✐ç♦❛♠❡♥t♦s ❞♦s ❉❙Ps ✭❞♦ ✐♥❣❧ês ❉✐❣✐t❛❧. ❙✐❣♥❛❧ Pr♦❝❡ss✐♥❣ ✮ q✉❡ sã♦ ♠✐❝r♦✲. ♣r♦❝❡ss❛❞♦r❡s ❡s♣❡❝✐❛❧✐③❛❞♦s ❡♠ ♣r♦❝❡ss❛♠❡♥t♦ ❞✐❣✐t❛❧ ❞❡ s✐♥❛❧✳ ❖ q✉❡ ❛♥t❡s ❡r❛ ❢❡✐t♦ ❞❡ ❢♦r♠❛ ❛♥❛❧ó❣✐❝❛✱ ❝♦♠ ♣♦✉❝♦ ❝♦♥tr♦❧❡ s♦❜r❡ ♦s ❢❡♥ô♠❡♥♦s ❢ís✐❝♦s ❡♥✈♦❧✈✐❞♦s✱ ♣♦❞❡ s❡r ❢❡✐t♦ ❞❡ ❢♦r♠❛ ❞✐❣✐t❛❧✱ ❝♦♥tr♦❧❛❞❛✱ ♠✉✐t♦ ♠❛✐s ♣r❡❝✐s❛ ❡ rá♣✐❞❛✳ ❖ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❛s r❡❣r❛s q✉❡ ❣♦✈❡r♥❛♠ ♦s s✐♥❛✐s ❞✐s❝r❡t♦s✱ ❜❡♠ ❝♦♠♦ ♦s ❞✐s♣♦s✐t✐✈♦s q✉❡ ♦s ♣r♦❝❡ss❛♠✱ ❛❧t❡r♥❛✲ t✐✈❛♠❡♥t❡ ❛♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ s✐♥❛✐s ❛♥❛❧ó❣✐❝♦s✱ ❛♣r❡s❡♥t❛♥❞♦ ❞✐✈❡rs❛s ✈❛♥t❛❣❡♥s✳ ◆♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ s✐♥❛❧ ❛♥❛❧ó❣✐❝♦ ❛s q✉❛♥t✐❞❛❞❡s ❢ís✐❝❛s ✈❛r✐❛♠ ❛♦ ❧♦♥❣♦ ❞❡ ✉♠❛ ❢❛✐①❛ ❞❡ ✈❛❧♦r❡s ❝♦♥tí♥✉♦s✳ P❛r❛ q✉❡ ♦ s✐♥❛❧ s❡❥❛ ♣r♦❝❡ss❛❞♦ ❞✐❣✐t❛❧♠❡♥t❡✱ ♥❡❝❡ss✐t❛ s❡r✱ ♣r✐♠❡✐r❛✲ ♠❡♥t❡✱ ❞✐s❝r❡t✐③❛❞♦✳ ❆❧❣✉♠❛s ✈❛♥t❛❣❡♥s s❡ ❞❡st❛❝❛♠ ♥♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞✐❣✐t❛❧ ❞❡ s✐♥❛✐s✱ ❝♦♠♦ ❛ ♣r♦❣r❛♠❛❜✐❧✐❞❛❞❡✱ ❡st❛❜✐❧✐❞❛❞❡✱ r❡❞✉çã♦ ❞❡ ❝✉st♦s ❡ ❢❛❝✐❧✐❞❛❞❡ ❞❡ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❡ ❛❧❣♦r✐t♠♦s ❛❞❛♣t❛t✐✈♦s✳ ▼✉✐t♦s ❞♦s ♣r♦❜❧❡♠❛s r❡❧❛❝✐♦♥❛❞♦s ❛♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ s✐✲ ♥❛✐s t❡♠ s♦❧✉çã♦ ❛tr❛✈és ❞❛ ✜❧tr❛❣❡♠ ❛❞❛♣t❛t✐✈❛ ❬❖♣♣❡♥❤❡✐♠✱ ✭✶✾✾✻✮❪✳ ❖ t❡r♠♦ ✧✜❧tr♦✧é ❣❡r❛❧♠❡♥t❡ ❛♣❧✐❝❛❞♦ ❛ q✉❛❧q✉❡r ❞✐s♣♦s✐t✐✈♦ ♦✉ s✐st❡♠❛ q✉❡ ♣r♦❝❡ss❛ ♦s s✐♥❛✐s r❡❝❡❜✐❞♦s ♦✉ ♦✉tr♦s ❞❛❞♦s✱ ❞❡ ❢♦r♠❛ ❛ ❡❧✐♠✐♥❛r ♦ r✉í❞♦✱ ♦✉ s✉❛✈✐③❛r ♦s s✐♥❛✐s✱ ♦✉ ✐❞❡♥t✐✜❝❛r ❝❛❞❛ ✉♠ ❞♦s s✐♥❛✐s ❝♦♠♦ ♣❡rt❡♥❝❡♥t❡s ❛ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❝❧❛ss❡✱ ♦✉ ♠❡s♠♦ ♣r❡✈❡r ♦ ♣ró①✐♠♦ s✐♥❛❧ ❞❡ ♠♦♠❡♥t♦ ❛ ♠♦♠❡♥t♦ ❬❲✐❞r♦✇✱ ✭✶✾✽✺✮❪✳ ◆♦s ú❧t✐♠♦s ❛♥♦s ❛ ❞❡♠❛♥❞❛ ♣♦r ❡q✉✐♣❛♠❡♥t♦s ♣♦rtát❡✐s✱ ❞❡ ❢á❝✐❧ ♠❛♥✉s❡✐♦ ❡ q✉❡ t❡♥❤❛♠ ✉♠❛ ✐♥t❡r❢❛❝❡ s✐♠♣❧❡s ❝♦♠ ♦ ✉s✉ár✐♦ t❡♠ ❝r❡s❝✐❞♦ ♠✉✐t♦✳ ❆❧❣✉♥s ❞✐s♣♦✲ s✐t✐✈♦s ❞❡ ❤❛r❞✇❛r❡ ❞✐❣✐t❛✐s ♣r♦❝✉r❛♠ ✉♥✐r t♦❞♦s ❡ss❡s ♣r❡❝❡✐t♦s✱ ❞✐✈❡rs♦s ❞✐s♣♦s✐t✐✈♦s ❞❡ ❤❛r❞✇❛r❡ ✭❡❧❡trô♥✐❝♦s✮ q✉❡ ✉t✐❧✐③❛♠ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ s✐♥❛❧ ❞✐❣✐t❛❧✱ t❛✐s ❝♦♠♦ ❉❙Ps✱ ♠✐❝r♦❝♦♥tr♦❧❛❞♦r❡s ❡ ❋P●❆s ✭ ❞♦ ✐♥❣❧ês ❋✐❡❧❞. Pr♦❣r❛♠♠❛❜❧❡ ●❛t❡ ❆rr❛②s ✮✳ ❊st❡s ❞✐s♣♦✲. s✐t✐✈♦s ❞❡ ❤❛r❞✇❛r❡ ❞✐❣✐t❛✐s sã♦ ♠✉✐t♦ ✈❡rsát❡✐s✱ ♣♦❞❡♥❞♦ s❡ ❡♥q✉❛❞r❛r ❡♠ q✉❛✐sq✉❡r t✐♣♦s ❞❡ ♣r♦❥❡t♦s ❬❚♦❝❝✐✱ ✭✷✵✶✸✮❪✳ ❯♠❛ ❞❛s ❣r❛♥❞❡s ❞❡s✈❛♥t❛❣❡♥s ❞❛ té❝♥✐❝❛ ❞✐❣✐t❛❧ é q✉❡ ❛ ♠❛✐✲ ♦r✐❛ ❞❛s ❣r❛♥❞❡③❛s ❢ís✐❝❛s ♥♦ ♠✉♥❞♦ r❡❛❧ ❝♦♥s✐st❡ ❞❡ ✉♠❛ ✐♥✜♥✐❞❛❞❡ ❞❡ s✐♥❛✐s ❛♥❛❧ó❣✐❝♦s ❬❍❛②❦✐♥✱ ✭✷✵✶✹✮❪✳ ❆♦ s❡ tr❛❜❛❧❤❛r ❝♦♠ s✐♥❛✐s ♦✉ s✐st❡♠❛s ❞✐❣✐t❛✐s ♣♦❞❡♠♦s r❡♣r❡s❡♥tá✲❧♦s ❡♠ ♣r❡❝✐sã♦ ✐♥✜♥✐t❛ ✭s✐♥❛❧ ❛♥❛❧ó❣✐❝♦✮ ❡ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛ ✭s✐♥❛❧ ❞✐❣✐t❛❧✮✳ ◆♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ s✐♥❛✐s ❞✐❣✐t❛✐s r❡❛❧✐③❛✲s❡ ✉♠❛ ❛♣r♦①✐♠❛çã♦ ❞❡ ✉♠❛ ❣r❛♥❞❡③❛ ❛♥❛❧ó❣✐❝❛ ♣♦r ✉♠ ✈❛❧♦r ❞✐❣✐t❛❧.

(19) ✶✳✶ Pr♦❜❧❡♠❛. ✶✺. ✭❞✐s❝r❡t♦✮✱ t❡♥❞♦ ❝♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛ ✉♠ ❡rr♦ ❞❡ ❛♣r♦①✐♠❛çã♦ ♦✉ ❡rr♦ ❞❡ q✉❛♥t✐③❛çã♦ ❬❉✐♥✐③✱ ✭✷✵✶✸✮❪✳. ✶✳✶. Pr♦❜❧❡♠❛. ❊rr♦s ❞❡ q✉❛♥t✐③❛çã♦ ♣♦❞❡♠ ❞❡❣r❛❞❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❞❡ ✉♠ ✜❧tr♦ ❛❞❛♣t❛t✐✈♦ ❞❡ ✈ár✐❛s ♠❛♥❡✐r❛s✳ P♦r ❡①❡♠♣❧♦✱ ❡❧❡s ♣♦❞❡♠ ❛❢❡t❛r ❛ ❡st❛❜✐❧✐❞❛❞❡ ❞♦ ✜❧tr♦ ❡✱ ❡♠ ú❧t✐♠❛ ❛♥á❧✐s❡ ❝♦♥❞✉③✐r à s✉❛ ❞✐✈❡r❣ê♥❝✐❛✳ ❚❛♠❜é♠ ♣♦❞❡♠ ❞❡❣r❛❞❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❡♠ ❡st❛❞♦ ❡st❛❝✐♦♥ár✐♦ ❞♦ ✜❧tr♦ ❢❛③❡♥❞♦✲♦ ❛t✐♥❣✐r ✉♠ ❡rr♦ q✉❛❞rát✐❝♦ ♠é❞✐♦ ♠❛✐♦r ❞♦ q✉❡ ♦ ❡s♣❡r❛❞♦ ❛ ♣❛rt✐r ❞❡ ✉♠❛ ❛♥á❧✐s❡ ❞❡ ♣r❡❝✐sã♦ ✐♥✜♥✐t❛ ❬●✉♣t❛ ❡t ❛❧✳✱ ✭✷✵✵✵✮❪✳. ✶✳✷. ❖❜ ❥❡t✐✈♦s. • ❉❡t❡r♠✐♥❛r s❡ ♦ ❛❧❣♦r✐t♠♦ ❙✐❣♠♦✐❞❛❧ ✭❙❆✮ é ❡stá✈❡❧ ♥✉♠❡r✐❝❛♠❡♥t❡ ♦✉ ♥ã♦ q✉❛♥❞♦. s❡ ✉t✐❧✐③❛ ♣r❡❝✐sã♦ ✜♥✐t❛✳ • ▼♦❞❡❧❛r ❛♥❛❧✐t✐❝❛♠❡♥t❡ ♦ ❛❧❣♦r✐t♠♦ ❙✐❣♠♦✐❞❛❧ ✭❙❆✮ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛✳. ✶✳✸. ▼♦t✐✈❛çõ❡s. ❊♠ t❡r♠♦s ♣rát✐❝♦s✱ ♦s ❛❧❣♦r✐t♠♦s ❛❞❛♣t❛t✐✈♦s sã♦ ✐♠♣❧❡♠❡♥t❛❞♦s ♥♦s ❞✐s♣♦s✐✲ t✐✈♦s ❞❡ ❤❛r❞✇❛r❡ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛✱ ❡ ♠✉✐t❛s ✈❡③❡s ❝♦♠ ❛r✐t♠ét✐❝❛ ❞❡ ♣♦♥t♦ ✜①♦ ❬●✉♣t❛ ❛♥❞ ❍❡r♦✱ ✭✷✵✵✵✮❪✳ ❆ ♣❡♥❛❧✐❞❛❞❡ ♥♦ ❞❡s❡♠♣❡♥❤♦ ❞❡ ❛❧❣✉♥s ❛❧❣♦r✐t♠♦s ❛❞❛♣t❛t✐✈♦s ✐♥❝♦rr✐✲ ❞♦s ❝♦♠ ♦ r❡s✉❧t❛❞♦ ❞❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛ t❡♠ s✐❞♦ ❛♥❛❧✐s❛❞❛s ❡♠ ❡st✉❞♦s r❡❧❛❝✐♦♥❛❞♦s ❛ ✜❧tr❛❣❡♠ ❛❞❛♣t❛t✐✈❛✳ ❖ s❡✉ ❝♦♠♣♦rt❛♠❡♥t♦ ♣♦❞❡ ♦❜t❡r r❡s✉❧t❛❞♦s ♦✉ ❡❢❡✐✲ t♦s ✐♥❞❡s❡❥á✈❡✐s ❞❡✈✐❞♦ ❛♦s ❡rr♦s ❞❡ q✉❛♥t✐③❛çã♦ ✐♥tr♦❞✉③✐❞♦s ♥♦s ❝á❧❝✉❧♦s ❡♥✈♦❧✈✐❞♦s ♥♦ ♣r♦❝❡ss❛♠❡♥t♦ ❛❞❛♣t❛t✐✈♦ ❞❡ss❡s ✜❧tr♦s ❬❍❛②❦✐♥✱ ✭✷✵✶✹✮❪✳.

(20) ✶✳✹ ❊st❛❞♦ ❞❛ ❆rt❡ ✶✳✹. ✶✻. ❊st❛❞♦ ❞❛ ❆rt❡. ❆ ❞❡❣r❛❞❛çã♦ ❞♦ ❞❡s❡♠♣❡♥❤♦ t❡♥❞❡ ❛ s❡r ♠❛✐s ❣r❛✈❡ ♣❛r❛ ♦ ❛❧❣♦r✐t♠♦ ❘▲❙ ✭❘❡❝✉rs✐✈❡ ▲❡❛st ❙q✉❛r❡ ✮ ❝♦♥✈❡♥❝✐♦♥❛❧ ♣♦❞❡♥❞♦ s❡r ♠❛✐s s❡♥sí✈❡❧ ❛ ❡rr♦s ❞❡ ♣r❡❝✐sã♦ ✜♥✐t❛ ❡ ❞✐✈❡r❣✐r ❝♦♠♦ r❡s✉❧t❛❞♦ ❬❙❛②❡❞✱ ✭✷✵✶✸✮❪ ❡♠ ♦♣♦s✐çã♦ ❛♦ ❛❧❣♦r✐t♠♦ ▲▼❙ ✭▲❡❛st ▼❡❛♥. ❙q✉❛r❡ ✮ ❬●✉♣t❛ ❡t ❛❧✳✱ ✭✷✵✵✵✮❪✳ ■st♦ ♣♦rq✉❡ ♣❛r❛ ✜❧tr♦s ❞♦ t✐♣♦ ▲▼❙✱ ❡rr♦s ❞❡ ♣r❡❝✐sã♦ ✜♥✐t❛ ❡♠ ❛❧❣♦r✐t♠♦s ❜❛s❡❛❞♦s ♥♦ ❣r❛❞✐❡♥t❡ ❞❛ ❢✉♥çã♦ ❞❡ ❝✉st♦✱ sã♦ ♠❛✐s s✐❣♥✐✜❝❛t✐✈♦s ❞♦ q✉❡ ♦s ❡rr♦s ❞❡ ♣r❡❝✐sã♦ ✜♥✐t❛ ❞✉r❛♥t❡ ❛ ❢❛s❡ tr❛♥s✐tór✐❛ ❡♠ ❛❧❣♦r✐t♠♦s ♥ã♦ ❜❡s❡❛❞♦ ♥❡st❛ té❝♥✐❝❛✳ ◆♦ ❡♥t❛♥t♦✱ ❡♠ ❡st❛❞♦ ❡st❛❝✐♦♥ár✐♦✱ ✉♠ s✐❣♥✐✜❝❛t✐✈♦ ❡①❝❡ss♦ ❞❡ ❡rr♦ q✉❛❞rát✐❝♦ ♣♦❞❡ s❡r ❢♦r♠❛❞♦ ❬❱❡r❤❛❡❣❡♥✱ ✭✶✾✽✾✮❪✳ ❚r❛❜❛❧❤♦s r❡❝❡♥t❡s ❛♥❛❧✐s❛♠ ✜❧tr♦s ❛❞❛♣t❛t✐✈♦s ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛ ✉t✐❧✐③❛♥❞♦ ❛r✐t♠ét✐❝❛ ❞❡ ♣♦♥t♦ ✜①♦✳ ❊♠ ▼❛❧✉❡♥❞❛ ✭✷✵✵✺✮✱ ♣♦r ❡①❡♠♣❧♦✱ ❛♣r❡s❡♥t❛ ♥♦✈❛ ♠♦❞❡❧❛❣❡♠ ♣❛r❛ ♦ ❛❧❣♦r✐t♠♦ ▲▼❙✳ ▼❡❤❡r ✭✷✵✶✹✮✱ tr❛③ ✉♠❛ ❛rq✉✐t❡t✉r❛ ❡✜❝✐❡♥t❡ ♣❛r❛ ♦ ❛❧❣♦r✐t♠♦ ▲▼❙ ❡ ❞❡r✐✈❛ ❡①♣r❡ssõ❡s ❞❡ ❡rr♦s ❞❡ ❡st❛❞♦s✳ ❆❧❣♦r✐t♠♦s ❞❡ ✜❧tr❛❣❡♠ ❛❞❛♣t❛t✐✈❛ ❝♦♠ ❜❛s❡ ❡♠ ❡rr♦ ♥ã♦ q✉❛❞rát✐❝♦ ♠é❞✐♦ t❡♠ s✐❞♦ s✉❣❡r✐❞♦s ♣♦r ✈ár✐♦s ❛✉t♦r❡s✱ q✉❡r ❝♦♠♦ ✉♠❛ ❢♦r♠❛ ❞❡ ♠❡❧❤♦r❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❞❡ ❛❞❛♣t❛çã♦ ❞❡st❡s ❛❧❣♦r✐t♠♦s ♣❛r❛ ❛♠❜✐❡♥t❡s ❡st❛tíst✐❝♦s ♣❛rt✐❝✉❧❛r❡s✱ ♦✉ ❝♦♠♦ ❢♦r♠❛ ❞❡ s✐♠♣❧✐✜❝❛r ♦ ❝á❧❝✉❧♦ ❞♦ ❛❧❣♦r✐t♠♦ ❡♠ ❤❛r❞✇❛r❡ ❬❉♦✉❣❧❛s ❛♥❞ ▼❡♥❣✱ ✭✶✾✾✹✮❪✳. ✶✳✺. ❖r❣❛♥✐③❛çã♦ ❞♦ ❚❡①t♦. ❊st❡ tr❛❜❛❧❤♦ ❡stá ❞✐✈✐❞✐❞♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ ◆♦ ❝❛♣ít✉❧♦ ✷ ❛♣r❡s❡♥t❛♠♦s ✐♥✐✲ ❝✐❛❧♠❡♥t❡ ♦s ❝♦♥❝❡✐t♦s r❡❧❛❝✐♦♥❛❞♦ ❛♦s ✜❧tr♦s ❛❞❛♣t❛t✐✈♦s ❜❡♠ ❝♦♠♦ ❛s s✉❛s ❝❛r❛❝t❡ríst✐❝❛s ❡ ❛♣❧✐❝❛çõ❡s✳ ◆♦ ❝❛♣ít✉❧♦ ✸ ❛♣r❡s❡♥t❛♠♦s ♦s ❡❢❡✐t♦s ❞❛ ♣r❡❝✐sã♦ ✜♥✐t❛✱ ❞❡✜♥✐♥❞♦ ♦ ❡rr♦ ❞❡ q✉❛♥t✐③❛çã♦✱ ✐♠♣❧❡♠❡♥t❛çã♦ ❡♠ ❞✐s♣♦st✐✈♦s ❞❡ ❤❛r❞✇❛r❡ ❡ ♣♦r ú❧t✐♠♦ ♠♦str❛♠♦s ♦ ❝♦✲ ♥❤❡❝✐❞♦ ❛❧❣♦r✐t♠♦ ❛❞❛♣t❛t✐✈♦ ▲▼❙ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛✳ ◆♦ ❝❛♣ít✉❧♦ ✹ r❡❛❧✐③❛♠♦s ✉♠❛ ❛♥á❧✐s❡ ❞❡ ✉♠❛ ❢❛♠í❧✐❛ ❞❡ ❛❧❣♦r✐t♠♦s ❜❛s❡❛❞♦s ❡♠ ♥ã♦ ❧✐♥❡❛r❡❞❛❞❡ ❞♦ ❡rr♦ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛✱ ♦♥❞❡ ♠♦str❛♠♦s ✉♠❛ ❛♥á❧✐s❡ ❞❡ ❛❞❛♣t❛çã♦ ❡ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛✳ ◆♦ ❝❛♣ít✉❧♦ ✺ ✐♠♣❧❡♠❡♥t❛♠♦s ♦ ❛❧❣♦r✐♠t♦ ❙✐❣♠♦✐❞❛❧ ✭❙❆✮ ❡♠ ♣r❡❝✐sã♦ ✜♥✐t❛✱.

(21) ✶✳✺ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚❡①t♦. ✶✼. ♦♥❞❡ ♠♦str❛♠♦s ♦ ♠ét♦❞♦ ✉t✐❧✐③❛❞♦ ❡ ♦s r❡s✉❧t❛❞♦s ❡♥❝♦♥tr❛❞♦s✳ ◆♦ ❝❛♣ít✉❧♦ ✻ r❡❛❧✐③❛♠♦s ❛s ❞✐s❝✉ssõ❡s ❞♦s r❡s✉❧t❛❞♦s ❡♥❝♦♥tr❛❞♦s ❡ ♥♦ ❝❛♣ít✉❧♦ ✼ r❡❛❧✐③❛♠♦s ❛s ❝♦♥❝❧✉sõ❡s ✜♥❛✐s ❥✉♥t❛♠❡♥t❡ ❝♦♠ ♣❡rs♣❡❝t✐✈❛s ❢✉t✉r❛s s♦❜r❡ ♦ ❡♥❝❛♠✐♥❤❛✲ ♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳.

(22) ✶✽. ✷ ❋✐❧tr❛❣❡♠ ❆❞❛♣t❛t✐✈❛ ❆ ✜❧tr❛❣❡♠ ❛❞❛♣t❛t✐✈❛ t❡♠ s✐❞♦ ❢♦rt❡♠❡♥t❡ ✉t✐❧✐③❛❞❛ ❝♦♠♦ té❝♥✐❝❛ ♣❛r❛ ♦ ♣r♦✲ ❝❡ss❛♠❡♥t♦ ❞❡ s✐♥❛✐s ❞✐❣✐t❛✐s✱ ❡ ❝♦♠ ♦s ❛✈❛♥ç♦s ❞❡st❛ t❡♦r✐❛ ❡ ❞❛ t❡❝♥♦❧♦❣✐❛ ❞♦s ❝✐r❝✉✐✲ t♦s ✐♥t❡❣r❛❞♦s t♦r♥❛✲s❡ ❝❛❞❛ ✈❡③ ♠❛✐s s♦✜st✐❝❛❞❛✱ ❬▼❡❤❡r✱ ✭✷✵✶✹✮❪✳ ❋✐❧tr♦s ❛❞❛♣t❛t✐✈♦s sã♦ ❞✐s♣♦s✐t✐✈♦s ❛✉t♦✲❛❥✉stá✈❡✐s✱ ❜❛s❡❛❞♦s ❡♠ ❛❧❣♦r✐t♠♦s r❡❝✉rs✐✈♦s✱ q✉❡ ♠♦❞✐✜❝❛♠ s❡✉s ♣❛râ♠❡tr♦s ❞❡ ❛❝♦r❞♦ ❝♦♠ ❝r✐tér✐♦s ♣ré✲❡st❛❜❡❧❡❝✐❞♦s✳ ❊♠ ❛♠❜✐❡♥t❡ ❡st❛❝✐♦♥ár✐♦✱ ❛❝♦♠✲ ♣❛♥❤❛♠ ❛ s♦❧✉çã♦ ót✐♠❛ ❞♦ ♣r♦❜❧❡♠❛✳ ❊♠ ❛♠❜✐❡♥t❡ ♥ã♦ ❡st❛❝✐♦♥ár✐♦✱ ❛❝♦♠♣❛♥❤❛♠ ❛s ♠♦❞✐✜❝❛çõ❡s ❞♦ s✐♥❛❧ ❡♥✈♦❧✈✐❞♦ ❬❲✐❞r♦✇✱ ✭✶✾✽✺✮❪✳ ❖s ✜❧tr♦s ❛❞❛♣t❛t✐✈♦s sã♦ ❝❧❛ss✐✜❝❛❞♦s ❡♠ ❞♦✐s ❣r✉♣♦s ♣r✐♥❝✐♣❛✐s✿ ❧✐♥❡❛r❡s ❡ ♥ã♦ ❧✐♥❡❛r❡s✳ ❋✐❧tr♦s ❛❞❛♣t❛t✐✈♦s ❧✐♥❡❛r❡s ❝♦♠♣✉t❛♠ ✉♠ ✈❛❧♦r ❡st✐♠❛❞♦ ❞❛ r❡s♣♦st❛ ❞❡s❡❥❛❞❛ ✉t✐❧✐③❛♥❞♦ ✉♠❛ ❝♦♠❜✐♥❛çã♦ ❧✐♥❡❛r ❞♦s s✐♥❛✐s ❞❡ ❡♥tr❛❞❛✱ ❞❡ ♦✉tr❛ ❢♦r♠❛✱ ❞✐③✲s❡ q✉❡ ♦s ✜❧tr♦s ❛❞❛♣t❛t✐✈♦s sã♦ ♥ã♦ ❧✐♥❡❛r❡s ❬❇♦r♦✉❥❡♥②✱ ✭✷✵✶✸✮❪✳ ❯♠ tr❛❜❛❧❤♦ ♣✐♦♥❡✐r♦ ♥♦ ❝❛♠♣♦ ❞❡ ♣r♦❥❡t♦s ❞❡ ✜❧tr♦s ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ♣♦r ◆♦r❜❡rt ❲✐❡♥❡r ❡♠ ✶✾✹✾✳ ❙❡✉s ❡s❢♦rç♦s t♦r♥❛r❛♠ ♣♦ssí✈❡❧ ♦ ♣r♦❥❡t♦ ❞❡ ✜❧tr♦s ❧✐♥❡❛r❡s ♣❛r❛ ❡❧✐♠✐♥❛çã♦ ❞❡ r✉í❞♦ ❡ ♣❛r❛ ♣r❡❞✐çã♦ ❡ s✉❛✈✐③❛♠❡♥t♦ ❞❡ s✐♥❛✐s ❡st❛t✐st✐❝❛♠❡♥t❡ ❡st❛✲ ❝✐♦♥ár✐♦s✳ ❖✉tr♦ tr❛❜❛❧❤♦ ♠❛✐s r❡❝❡♥t❡ ❞❡ ❑❛❧♠❛♥ ❡ ❇✉❝② ✭✶✾✻✶✮ ❝♦♥❞✉③✐✉ à ❝♦♥❝❡♣çã♦ ❞❡ ✜❧tr♦s ❧✐♥❡❛r❡s ❞❡ t❡♠♣♦ ✈❛r✐á✈❡❧ ♣❛r❛ s✐♥❛✐s ♥ã♦ ❡st❛❝✐♦♥ár✐♦s✳ P❛r❛ t❛✐s s✐♥❛✐s✱ ✜❧tr♦s ❞❡ ❑❛❧♠❛♥✲❇✉❝② ♣♦❞❡♠ ❡♥tr❡❣❛r ✉♠ ❞❡s❡♠♣❡♥❤♦ ❝♦♥s✐❞❡r❛✈❡❧♠❡♥t❡ ♠❡❧❤♦r ❞♦ q✉❡ ♦s ✜❧tr♦s ❞❡ ❲✐❡♥❡r ❬❉♦✉❣❧❛s ❛♥❞ ▼❡♥❣✱ ✭✶✾✾✷✮❪✳ ❆s ❛♣❧✐❝❛çõ❡s tí♣✐❝❛s ❞♦s ✜❧tr♦s ❛❞❛♣t❛t✐✈♦s sã♦✿ ♣r❡❞✐çã♦✱ ♠♦❞❡❧❛♠❡♥t♦✱ ❝❛♥✲ ❝❡❧❛♠❡♥t♦ ❞❡ r✉í❞♦✱ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ s✐st❡♠❛✱ ❞❡♥tr❡ ♦✉tr❛s ❬❉✐♥✐③✱ ✭✷✵✶✸✮❪✳ ❉✉❛s ♠❡❞✐❞❛s s❡ ❞❡st❛❝❛♠ ♥❛ ❛♥á❧✐s❡ ❞♦ ❞❡s❡♠♣❡♥❤♦ ❞♦s ❛❧❣♦r✐t♠♦s ❛❞❛♣t❛t✐✈♦s✿ ♦ ❞❡s❛❥✉st❡ ❡ ❛ t❛①❛ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❬❈❛r❛✐s❝♦s ❡ ▲✐✉✱ ✭✶✾✽✹✮❪✳ ❉❡♥tr❡ ♦s ❛❧❣♦r✐t♠♦s ❛❞❛♣t❛t✐✈♦s ♦ ▲▼❙ é r❡❢❡rê♥❝✐❛ ❡ é ❞❡ ❧♦♥❣❡ ♦ ♠❛✐s ❝♦♥❤❡❝✐❞♦ ❬✭❍❛②❦✐♥✱ ✭✷✵✶✹✮❪✳ ◆♦✈♦s ❛❧❣♦r✐t♠♦s ❛❞❛♣t❛t✐✈♦s tê♠ s✉r❣✐❞♦ ❝♦♠ ✉♠ ❞❡s❡♠♣❡♥❤♦ s✉♣❡r✐♦r ❛♦ ▲▼❙ ❡♠ r❡❧❛çã♦ ❛♦ ❞❡s❛❥✉st❡ ❡ à t❛①❛ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛✱ ❡♥tr❡ ❡ss❡s✱ t❡♠✲s❡ ♦ ❛❧❣♦r✐t♠♦ ❘▲❙ ❬❍❛②❦✐♥✱ ✭✷✵✶✹✮❪✳ ❖✉tr♦ ❛❧❣♦r✐t♠♦✱ q✉❡ t❡♠ ❝♦♠♦ ❜❛s❡ ❡st❡ tr❛❜❛❧❤♦ é ♦ ❙✐❣♠♦✐❞❛❧ ✭❙❆✮✱ ♦♥❞❡ ❙❛♥t❛♥❛ ✭✷✵✵✻✮ ❞❡♠♦♥str♦✉ ❛ s✉❛ s✉♣❡r✐♦r✐❞❛❞❡ ❡♠ r❡❧❛çã♦ ❛♦ ▲▼❙ ❝♦♠♣❛r❛♥❞♦ ♦ ❞❡s❛❥✉st❡ ❡ ❛ t❛①❛ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛✳.

(23) ✷✳✶ ❈❛r❛❝t❡ríst✐❝❛s ❞♦s ❋✐❧tr♦s ❆❞❛♣t❛t✐✈♦s ✷✳✶. ✶✾. ❈❛r❛❝t❡ríst✐❝❛s ❞♦s ❋✐❧tr♦s ❆❞❛♣t❛t✐✈♦s. ❆ ❝♦♥✜❣✉r❛çã♦ ❣❡r❛❧ ❞❡ ✉♠ ❛♠❜✐❡♥t❡ ❞❡ ✜❧tr❛❣❡♠ ❛❞❛♣t❛t✐✈❛ é ✐❧✉str❛❞❛ ♥❛ ❋✐❣✳ ✷✳✶✳. ❋✐❣✉r❛ ✷✳✶✿ ❈♦♥✜❣✉r❛çã♦ ❣❡r❛❧ ❞❡ ✉♠ ✜❧tr♦ ❛❞❛♣t❛t✐✈♦✳ ❊♠ q✉❡ k r❡♣r❡s❡♥t❛ ♦ ♥ú♠❡r♦ ❞❡ ✐t❡r❛çã♦✱ xk ❞❡s✐❣♥❛ ♦ s✐♥❛❧ ❞❡ ❡♥tr❛❞❛✱ yk é ♦ s✐♥❛❧ ❞❡ s❛í❞❛ ❞♦ ✜❧tr♦ ❛❞❛♣t❛t✐✈♦✱ ❡ dk ❞❡✜♥❡ ♦ s✐♥❛❧ ❞❡s❡❥❛❞♦✳ ❖ s✐♥❛❧ ❞❡ ❡rr♦ ek é ❝❛❧❝✉❧❛❞❛ ❝♦♠♦ dk − yk ✳ ❖ s✐♥❛❧ ❞❡ ❡rr♦ é ❡♥tã♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❢♦r♠❛r ✉♠❛ ❢✉♥çã♦ ❞❡ ❞❡s❡♠♣❡♥❤♦ ✭♦✉ ♦❜❥❡t✐✈♦✮ q✉❡ é ❡①✐❣✐❞❛ ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❞❡ ❛❞❛♣t❛çã♦ ♣❛r❛ ❞❡t❡r♠✐♥❛r ❛ ❛t✉❛❧✐③❛çã♦ ❛♣r♦♣r✐❛❞❛ ❞♦s ❝♦❡✜❝✐❡♥t❡s ❞♦ ✜❧tr♦ wk ✳. ❆ ❡s♣❡❝✐✜❝❛çã♦ ❝♦♠♣❧❡t❛ ❞❡ ✉♠ s✐st❡♠❛ ❛❞❛♣t❛t✐✈♦✱ ♠♦str❛❞♦ ♥❛ ❋✐❣✳ ✷✳✶✱ ❝♦♥s✐st❡ ❡♠ três ✐t❡♥s✿ ❊str✉t✉r❛ ❞♦ ✜❧tr♦ ❛❞❛♣t❛t✐✈♦✱ ❛♣❧✐❝❛çã♦ ❡ ❛❧❣♦r✐t♠♦ ❛❞❛♣t❛t✐✈♦✳ ❆ ❡str✉t✉r❛ ❞❡ ✉♠ ✜❧tr♦ ❛❞❛♣t❛t✐✈♦ ♣♦❞❡ s❡r ❞❛❞❛ ❞❡ ❞✉❛s ❢♦r♠❛s✿ ❋✐♥✐t❡. ■♠♣✉❧s❡ ❘❡s♣♦♥s❡ ✭❋■❘✮ ♦✉ ■♥✜♥✐t❡ ■♠♣✉❧s❡ ❘❡s♣♦♥s❡ ✭■❘❘✮✳ ❊♠ ♥♦ss♦ tr❛❜❛❧❤♦ ❝♦♥s✐✲ ❞❡r❛♠♦s ❛♣❡♥❛s ❛ r❡❛❧✐③❛çã♦ ❡♠ ❡str✉t✉r❛ ❋■❘✳ ❋✐❧tr♦s ❛❞❛♣t❛t✐✈♦s ♣♦❞❡♠ s❡r ❝♦♥tí♥✉♦ ♦✉ ❞✐s❝r❡t♦s✳ ❯♠❛ ❢♦r♠❛ ♣❛rt✐❝✉❧❛r ❞❡ ✜❧tr♦ ❛❞❛♣t❛t✐✈♦ ❛ s❡r ❝♦♥s✐❞❡r❛❞❛ é ✉♠ t✐♣♦ ❞✐s❝r❡t♦ ✭❞❛❞♦s ❛♠♦str❛❞♦s✮✳ ❖ ✜❧tr♦ ❞✐s❝r❡t♦ ❝♦♥s✐st❡ ❞❡ ✉♠❛ ❧✐♥❤❛ ❞❡ ❛tr❛s♦✱ ♣❡s♦s ✈❛r✐á✈❡✐s ✭❣❛♥❤♦s ✈❛r✐á✈❡✐s✮ ❝✉❥❛ ❡♥tr❛❞❛ ❞❡ s✐♥❛✐s sã♦ ♦s s✐♥❛✐s ♥❛ ❧✐♥❤❛ ❞❡ ❡♥tr❛❞❛ ❛tr❛s❛❞♦s✱ ✉♠❛ s♦♠❛ ♣❛r❛ ❛❞✐❝✐♦♥❛r ♦s s✐♥❛✐s ♣♦♥❞❡r❛❞♦s✱ ❡ ♦ ♠❡❝❛♥✐s♠♦ ♣❛r❛ ❛❥✉st❛r ❛✉t♦♠❛t✐❝❛♠❡♥t❡ ♦s ♣❡s♦s✳ ❆ r❡s♣♦st❛ ❞❡ ✐♠♣✉❧s♦ ❞❡ ✉♠ s✐st❡♠❛ t❛❧ ❞✐s❝r❡t♦ é ❝♦♠♣❧❡t❛♠❡♥t❡ ❝♦♥tr♦❧❛❞❛ ♣❡❧❛s ❝♦♥✜❣✉r❛çõ❡s ❞❡ ♣❡s♦✳ ❖ ♣r♦❝❡ss♦ ❞❡ ❛❞❛♣t❛çã♦ ♣r♦❝✉r❛ ❛✉t♦♠❛t✐❝❛♠❡♥t❡ ✉♠❛ r❡s♣♦st❛ ❛♦ ✐♠♣✉❧s♦ ❞♦ ✜❧tr♦ ✐❞❡❛❧✱ ❛❥✉st❛♥❞♦ ♦s ♣❡s♦s✳ ❆ ❋✐❣✳ ✷✳✷✱ ✐❧✉str❛ ❡sq✉❡♠❛t✐❝❛♠❡♥t❡✱ ❛ ♠❛✐♦r✐❛ ❞♦s ❝♦♠♣♦♥❡♥t❡s ❞❡.

(24) ✷✳✶ ❈❛r❛❝t❡ríst✐❝❛s ❞♦s ❋✐❧tr♦s ❆❞❛♣t❛t✐✈♦s. ✷✵. ✉♠ ✜❧tr♦ ❛❞❛♣t❛t✐✈♦✱ q✉❡ é ✉t✐❧✐③❛❞♦ ♥❡st❡ ❝❛s♦ ♣❛r❛ ❛ ♠♦❞❡❧❛çã♦ ❞❡ ✉♠ s✐st❡♠❛ ❞✐♥â♠✐❝♦ ❞❡s❝♦♥❤❡❝✐❞♦✳. ❋✐❣✉r❛ ✷✳✷✿ ▼♦❞❡❧♦ ❞❡ ✉♠ ✜❧tr♦ ❛❞❛♣t❛t✐✈♦ ❞✐s❝r❡t♦ ❛♣❧✐❝❛❞♦ ❛♦ ♣r♦❜❧❡♠❛ ❞❡ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ s✐st❡♠❛ ❞❡s❝♦♥❤❡❝✐❞♦✱ ♦♥❞❡ z I r❡♣r❡s❡♥t❛ ❛s ✉♥✐❞❛❞❡s ❞♦ s✐♥❛❧ ❞❡ ❡♥tr❛❞❛ xk ❛tr❛s❛❞❛s✳ ❖ s✐♥❛❧ ❞❡ s❛í❞❛ yk é ✉♠❛ ❝♦♠❜✐♥❛çã♦ ❧✐♥❡❛r ❞♦s ❝♦❡✜❝✐❡♥t❡s ❞♦ ✜❧tr♦ wkt xk ✱ q✉❡ ♣r♦❞✉③ ✉♠ ▼❙❊ ✭❊rr♦. ◗✉❛❞rát✐❝♦ ▼é❞✐♦ ✮ r❡♣r❡s❡♥t❛❞♦ ♣♦r E[(ek )2 )] ❝♦♠♦ ❢✉♥çã♦. ❞❡ ✉♠❛ s♦❧✉çã♦ ót✐♠❛ ♦r✐❣✐♥❛❧ ❬❉✐♥✐③✱ ✭✷✵✶✸✮❪✳ ▼✉✐t♦s ❛❧❣♦r✐t♠♦s ❛❞❛♣t❛t✐✈♦s ✉t✐❧✐③❛♠✲s❡ ❞♦ ▼❙❊ ❝♦♠♦ ❢✉♥çã♦ ❞❡ ❝✉st♦ ❛♣❧✐✲ ❝❛❞❛ s♦❜r❡ ♦ ❡rr♦✱ ♥♦ q✉❛❧ ❞❡s❡❥❛✲s❡ ♠✐♥✐♠✐③❛r✳ ❖ ▼❙❊ é ✉♠❛ ❢✉♥çã♦ ❝♦♥✈❡①❛ ❞♦s ❝♦♠♣♦✲ ♥❡♥t❡s ❞♦ ✈❡t♦r ♣❡s♦ ❡ ❣❡r❛ ✉♠❛ s✉♣❡r❢í❝✐❡ ❤✐♣❡r♣❛r❛❜♦❧ó✐❞❡ q✉❡ ❣❛r❛♥t❡ ❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠ ♠í♥✐♠♦ ❣❧♦❜❛❧✱ ✈❡r ❋✐❣✳ ✷✳✸✳ ❖ ♣r♦❜❧❡♠❛ é ❝♦♠♦ ❞❡t❡r♠✐♥❛r ♣r♦❝❡❞✐♠❡♥t♦s ❞❡ ❢♦r♠❛ t❛❧ ❛ ❡♥❝♦♥tr❛r ❡ss❡ ♠í♥✐♠♦✱ ♦ ♠❛✐s rá♣✐❞♦ ♣♦ssí✈❡❧ ❡ ❝♦♠ ♦ ♠❡♥♦r ❡rr♦ ✜♥❛❧ ❬❲✐❞r♦✇✱ ✭✶✾✽✺✮❪✳ ❉♦✐s t✐♣♦s ❞❡ ♣r♦❝❡ss♦s ♦❝♦rr❡♠ ♥❛ ✜❧tr❛❣❡♠ ❛❞❛♣t❛t✐✈❛✿ tr❡✐♥❛♠❡♥t♦ ❡ ♦♣❡r❛✲ çã♦✳ ❖ ♣r♦❝❡ss♦ ❞❡ tr❡✐♥❛♠❡♥t♦ ✈❡r✐✜❝❛ ❛ ❛❞❛♣t❛çã♦ ❞❛s ♣♦♥❞❡r❛çõ❡s ♥❛ ❧✐♥❤❛ ❞❡ ❛tr❛s♦ ❛♣r♦✈❡✐t❛❞♦✳ ❖ ♣r♦❝❡ss♦ ❞❡ ♦♣❡r❛çã♦ ❝♦♥s✐st❡ ❡♠ ❢♦r♠❛r ♦s s✐♥❛✐s ❞❡ s❛í❞❛ ♣♦♥❞❡r❛♥❞♦ ♦s s✐♥❛✐s ❞❛ ❧✐♥❤❛ ❞❡ ❛tr❛s♦✱ ✉t✐❧✐③❛♥❞♦ ♦s ♣❡s♦s r❡s✉❧t❛♥t❡s ❞♦ ♣r♦❝❡ss♦ ❞❡ ❛❞❛♣t❛çã♦ ❬❙❛②❡❞✱ ✭✷✵✶✸✮❪✳ ❊①✐st❡ ✉♠❛ ❣r❛♥❞❡ ✈❛r✐❡❞❛❞❡ ❞❡ ❛❧❣♦r✐t♠♦s ❛❞❛♣t❛t✐✈♦s✱ ❛ ❡s❝♦❧❤❛ ❞❡ ✉♠ ♦✉ ♦✉tr♦ ❛❧❣♦r✐t♠♦ é ❞❡t❡r♠✐♥❛❞❛ ♣❡❧♦s s❡❣✉✐♥t❡s ❢❛t♦r❡s ❬❙❛②❡❞✱ ✭✷✵✶✸✮❪✿ • ❚❛①❛ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛✿ ❞❡✜♥✐❞❛ ❝♦♠♦ ♦ ♥ú♠❡r♦ ❞❡ ✐t❡r❛çõ❡s ♥❡❝❡ssár✐❛s ♣❛r❛ q✉❡.

Referências

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