❘❆❋❆❊▲ ❆◆❚❖◆■❖ ●❖◆➬❆▲❱❊❙ ▲■▼❆

❯❚■▲■❩❆➬➹❖ ❉❊ ❙■❙❚❊▼❆❙ ■◆❚❊▲■●❊◆❚❊❙P❆❘❆ ❈▲❆❙❙■❋■❈❆➬➹❖ ❉❊ ❚❘➪❋❊●❖

▼❆▲■❈■❖❙❖

❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ à ❯♥✐✈❡rs✐❞❛❞❡ ❋❡✲❞❡r❛❧ ❞❡ ❱✐ç♦s❛✱ ❝♦♠♦ ♣❛rt❡ ❞❛s ❡①✐❣ê♥❝✐❛s❞♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛❞❛ ❈♦♠♣✉t❛çã♦✱ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡▼❛❣✐st❡r ❙❝✐❡♥t✐❛❡✳

❱■➬❖❙❆▼■◆❆❙ ●❊❘❆■❙ − ❇❘❆❙■▲

2014

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❉❡❞✐❝♦ ❡st❡ tr❛❜❛❧❤♦ ❛ ♠✐♥❤❛ ❡s♣♦s❛ ▲í✈❡❛ ❡ ♠❡✉s ♣❛✐s✱ ❈❛r❧♦s ❡ ❈❡❧✐♥❛ ♣♦r t♦❞❛

❝♦♥✜❛♥ç❛ ❡ ✐♥❝❡♥t✐✈♦s✳

✐✐

✏▼❡s♠♦ q✉❡ ❥á t❡♥❤❛ ❢❡✐t♦ ✉♠❛ ❧♦♥❣❛ ❝❛♠✐♥❤❛❞❛✱

s❡♠♣r❡ ❤❛✈❡rá ♠❛✐s ✉♠ ❝❛♠✐♥❤♦ ❛ ♣❡r❝♦rr❡r✳✑

✭❙❛♥t♦ ❆❣♦st✐♥❤♦✮

✐✐✐

❆❣r❛❞❡❝✐♠❡♥t♦s

❆♦ ♣r♦❢❡ss♦r ❡ ♦r✐❡♥t❛❞♦r✱ ❈❛r❧♦s ❞❡ ❈❛str♦ ●♦✉❧❛rt✱ ♣❡❧❛s ♦r✐❡♥t❛çõ❡s ✈❛❧✐♦s❛s ❡✱ s♦✲

❜r❡t✉❞♦ ♣❡❧♦s ❡♥s✐♥❛♠❡♥t♦s tr❛♥s♠✐t✐❞♦s ❡ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ ❡ ❝♦♥✜❛♥ç❛ ❞❡♣♦s✐t❛❞❛✳

❆♦ ❡①✲❛❧✉♥♦ ❡ ♣r♦❢❡ss♦r ❏❛❝s♦♥ ❘♦❞r✐❣✉❡s✱ q✉❡ ♠✉✐t♦ ♠❡ ✐♥❝❡♥t✐✈♦✉ ❡ tr❛♥s♠✐t✐✉

s✉❛ ❡①♣❡r✐ê♥❝✐❛ ❛❞q✉✐r✐❞❛ ❛ r❡s♣❡✐t♦ ❞♦ t❡♠❛ ❞❡st❡ tr❛❜❛❧❤♦✳

❆♦s ♣r♦❢❡ss♦r❡s ♣♦r t♦❞♦ ❛♣♦✐♦ ❡ ❡♥s✐♥❛♠❡♥t♦s r❡♣❛ss❛❞♦s ❞✉r❛♥t❡ t♦❞❛ ❣r❛❞✉❛çã♦

❡ ♠❡str❛❞♦✳

❆♦s ♠❡✉s ❝♦❧❡❣❛s ♣♦r t♦❞♦s ♦s ❝♦♥❤❡❝✐♠❡♥t♦s ❝♦♠♣❛rt✐❧❤❛❞♦s✱ ❞✐s❝✉t✐❞♦s ❡ ❞✐✜✲

❝✉❧❞❛❞❡s s✉♣❡r❛❞❛s✳

❆♦s ♠❡✉s ♣❛✐s✱ ❈❛r❧♦s ❡ ❈❡❧✐♥❛✱ ♣♦r t♦❞♦ ❛♣♦✐♦ ❡ ❡♥s✐♥❛♠❡♥t♦s ❞✉r❛♥t❡ t♦❞❛

♠✐♥❤❛ ✈✐❞❛✳

❆s ♠✐♥❤❛s ✐r♠ãs✱ ■❧❧✐❛♥ ❡ ▲❛✉r❛✱ ♠❡✉s ❛♠✐❣♦s ❡ ❞❡♠❛✐s ❢❛♠✐❧✐❛r❡s ♣♦r t♦❞♦s ♦s

❛♣♦✐♦s ❡ ✐♥❝❡♥t✐✈♦s✳

❆ ♠✐♥❤❛ ❡s♣♦s❛✱ ▲í✈❡❛✱ q✉❡ ♠❡s♠♦ ♥❛s ❤♦r❛s ♠❛✐s ❞✐❢í❝❡✐s✱ s❡♠♣r❡ ♠❡ ❛♣♦✐♦✉ ❡

♠❡ ❛❥✉❞♦✉ ❛ ❡♥❝♦♥tr❛r ♦ t❡♠♣♦ q✉❡ s❡♠♣r❡ ♥❡❝❡ss✐t❛✈❛✳

❆ ❉❡✉s ♣♦r ✐❧✉♠✐♥❛r ♠✐♥❤❛ ✈✐❞❛ ❡ ♣❡r♠✐t✐r q✉❡ ❡✉ ❝❤❡❣❛ss❡ ❛té ❡ss❛ ❡t❛♣❛ ❝♦♠

✜r♠❡③❛✱ ❝r❡s❝✐♠❡♥t♦ ♣❡ss♦❛❧ ❡ ♣r♦✜ss✐♦♥❛❧✳

✐✈

❙✉♠ár✐♦

▲✐st❛ ❞❡ ❋✐❣✉r❛s ✈✐✐

▲✐st❛ ❞❡ ❚❛❜❡❧❛s ✐①

❘❡s✉♠♦ ①

❆❜str❛❝t ①✐

✶ ■♥tr♦❞✉çã♦ ✶

✶✳✶ ❖ ♣r♦❜❧❡♠❛ ❡ s✉❛ ✐♠♣♦rtâ♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷

✶✳✷ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹

✶✳✸ ❖r❣❛♥✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺

✷ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✻

✷✳✶ ❘❡❞❡s ❞❡ ❈♦♠♣✉t❛❞♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

✷✳✶✳✶ Pr♦t♦❝♦❧♦s ■P✱ ❯❉P ❡ ❚❈P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼

✷✳✷ ❙❡❣✉r❛♥ç❛ ❡♠ ❘❡❞❡s ❞❡ ❈♦♠♣✉t❛❞♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵

✷✳✷✳✶ ❈❧❛ss✐✜❝❛çã♦ ❞❡ ❆t❛q✉❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶

✷✳✸ ❙✐st❡♠❛s ❞❡ ❉❡t❡❝çã♦ ❞❡ ■♥tr✉sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸

✷✳✹ ❉❡t❡❝çã♦ ❞❡ ❆♥♦♠❛❧✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼

✷✳✺ ❚é❝♥✐❝❛s ❞❡ ❈❧❛ss✐✜❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽

✷✳✺✳✶ ➪r✈♦r❡ ❞❡ ❉❡❝✐sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

✷✳✺✳✷ ❘❡❞❡s ◆❡✉r❛✐s ❆rt✐✜❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹

✷✳✺✳✸ ❆❧❣♦r✐t♠♦s ●❡♥ét✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵

✷✳✺✳✹ ▼áq✉✐♥❛ ❞❡ ❱❡t♦r❡s ❞❡ ❙✉♣♦rt❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺

✷✳✺✳✺ ❙✐st❡♠❛s ■♥t❡❧✐❣❡♥t❡s ❍í❜r✐❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼

✷✳✻ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾

✸ ▼ét♦❞♦s ✹✶

✈

✸✳✶ ❇❛s❡s ❞❡ ❉❛❞♦s ❝♦♠ ❚rá❢❡❣♦ ❞❡ ❘❡❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶

✸✳✷ Pr❡♣❛r❛çã♦ ❞❛ ❇❛s❡ ❞❡ ❉❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✸✳✸ ❚❡st❡s ❞❡ ❈❧❛ss✐✜❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼

✹ ❘❡s✉❧t❛❞♦s ✺✵

✹✳✶ ❘❡s✉❧t❛❞♦s ❞❛s ❚é❝♥✐❝❛s ❞❡ ❈❧❛ss✐✜❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶

✹✳✷ ❘❡s✉❧t❛❞♦s ❞♦ ❙✐st❡♠❛ ■♥t❡❧✐❣❡♥t❡ ❍í❜r✐❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

✺ ❈♦♥❝❧✉sõ❡s ✺✽

❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✻✵

❆♥❡①♦ ❆ ❈ó❞✐❣♦ ♣❛r❛ ♣❛❞r♦♥✐③❛çã♦ ❞♦s ❛rq✉✐✈♦s ✳❝s✈ ✻✸

❆♥❡①♦ ❇ ❈ó❞✐❣♦ ♣❛r❛ ❣❡r❛r ❛rq✉✐✈♦ ✳❛r✛ ✻✽

❆♥❡①♦ ❈ ❈ó❞✐❣♦ ❞♦ s✐st❡♠❛ ✐♥t❡❧✐❣❡♥t❡ ❤í❜r✐❞♦ ✼✹

❆♥❡①♦ ❉ ❈ó❞✐❣♦ ❞♦ ❛✈❛❧✐❛❞♦r ❞❛ ❘◆❆ ✼✼

✈✐

▲✐st❛ ❞❡ ❋✐❣✉r❛s

✶✳✶ ❚♦t❛❧ ❞❡ ✐♥❝✐❞❡♥t❡s r❡♣♦rt❛❞♦s ❛♦ ❈❊❘❚✳❜r ♣♦r ❛♥♦ ❬❈❊❘❚✳❜r✱ ✷✵✶✹❪ ✳ ✳ ✳ ✷

✶✳✷ ■♥❝✐❞❡♥t❡s r❡♣♦rt❛❞♦s ❛♦ ❈❊❘❚✳❜r ✭❥✉♥❤♦ ❛ s❡t❡♠❜r♦ ❞❡ ✷✵✶✸✮ ❬❈❊❘❚✳❜r✱

✷✵✶✹❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸

✶✳✸ ■♥❝✐❞❡♥t❡s r❡♣♦rt❛❞♦s ❛♦ ❈❊❘❚✳❜r ✭❛❜r✐❧ ❛ ❥✉♥❤♦ ❞❡ ✷✵✶✸✮ ❬❈❊❘❚✳❜r✱ ✷✵✶✹❪ ✸

✷✳✶ ❖ ❝❛❜❡ç❛❧❤♦ ■P✈✹ ❬❚❛♥❡♥❜❛✉♠✱ ✷✵✶✶❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼

✷✳✷ ❖ ❝❛❜❡ç❛❧❤♦ ❯❉P ❬❚❛♥❡♥❜❛✉♠✱ ✷✵✶✶❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

✷✳✸ ❖ ❝❛❜❡ç❛❧❤♦ ❚❈P ❬❚❛♥❡♥❜❛✉♠✱ ✷✵✶✶❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾

✷✳✹ ❯♠ ❝❡♥ár✐♦ ❞❡ r❡❞❡ ❝♦♠ s❡♥s♦r❡s ♣❛r❛ ❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sã♦ ❬❑✉r♦s❡ ✫ ❘♦ss✱

✷✵✶✵❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺

✷✳✺ ❈❧❛ss✐✜❝❛çã♦ ❝♦♠♦ ❛ t❛r❡❢❛ ❞❡ ♠❛♣❡❛r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❛tr✐❜✉t♦s x ♥♦ s❡✉

rót✉❧♦ ❞❡ ❝❧❛ss❡ y ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾

✷✳✻ ❯♠❛ ár✈♦r❡ ❞❡ ❞❡❝✐sã♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❞❡ ♠❛♠í❢❡r♦s ❬❚❛♥

❡t ❛❧✳✱ ✷✵✵✾❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

✷✳✼ ❈❧❛ss✐✜❝❛çã♦ ❞❡ ✉♠ ✈❡rt❡❜r❛❞♦ s❡♠ rót✉❧♦ ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶

✷✳✽ ❈♦♠♣♦♥❡♥t❡s ❞♦ ♥❡✉rô♥✐♦ ❜✐♦❧ó❣✐❝♦ ❬❇r❛❣❛ ❡t ❛❧✳✱ ✷✵✵✼❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹

✷✳✾ ◆❡✉rô♥✐♦ ❞❡ ▼❝❈✉❧❧♦❝❤ ❡ P✐tts✱ ♥♦ q✉❛❧∑

r❡♣r❡s❡♥t❛ ❛ s♦♠❛ ♣♦♥❞❡r❛❞❛

❞❛s ❡♥tr❛❞❛s ❡ f(·) ❛ ❢✉♥çã♦ ❞❡ ❛t✐✈❛çã♦ ❬❇r❛❣❛ ❡t ❛❧✳✱ ✷✵✵✼❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺

✷✳✶✵ ❋✉♥çã♦ ❞❡ ❛t✐✈❛çã♦ ❞❡❣r❛✉ ✭❛✮ ❡ s✐❣♠♦✐❞❛❧ ✭❜✮ ❬❇r❛❣❛ ❡t ❛❧✳✱ ✷✵✵✼❪ ✳ ✳ ✳ ✳ ✳ ✷✻

✷✳✶✶ ❋✉♥çã♦ ❞❡ ❛t✐✈❛çã♦ ❧✐♥❡❛r ✭❛✮ ❡ ❣❛✉ss✐❛♥❛ ✭❜✮ ❬❇r❛❣❛ ❡t ❛❧✳✱ ✷✵✵✼❪ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻

✷✳✶✷ ❘❡❞❡ ❢❡❡❞❢♦r✇❛r❞ ❞❡ ✉♠❛ ❝❛♠❛❞❛ ✭❛✮ ❡ ❞❡ ❞✉❛s ❝❛♠❛❞❛s ✭❜✮ ❬❇r❛❣❛ ❡t ❛❧✳✱

✷✵✵✼❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼

✷✳✶✸ ❘❡❞❡ ❝♦♠ r❡❝♦rrê♥❝✐❛ ❡♥tr❡ s❛í❞❛s ❡ ❝❛♠❛❞❛ ✐♥t❡r♠❡❞✐ár✐❛ ✭❛✮ ❡ r❡❞❡ ❝♦♠

r❡❝♦rrê♥❝✐❛ ❛✉t♦✲❛ss♦❝✐❛t✐✈❛ ✭❜✮ ❬❇r❛❣❛ ❡t ❛❧✳✱ ✷✵✵✼❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼

✷✳✶✹ ❊t❛♣❛s ❞♦ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ❬❆rt❡r♦✱ ✷✵✵✾❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶

✷✳✶✺ ❆❧❣♦r✐t♠♦ ❞❡ ❛❧t♦ ♥í✈❡❧ ❞❡ ✉♠ ❆● ❬❘❡③❡♥❞❡✱ ✷✵✵✺❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷

✷✳✶✻ ❘♦❧❡t❛ ❝♦♠ t❛♠❛♥❤♦s ❞❡ s❡t♦r❡s ♣r♦♣♦r❝✐♦♥❛✐s à ❝❤❛♥❝❡ ❞♦ ❝r♦♠♦ss♦♠♦ s❡r

s❡❧❡❝✐♦♥❛❞♦ ❬❆rt❡r♦✱ ✷✵✵✾❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷

✈✐✐

✷✳✶✼ ❈r✉③❛♠❡♥t♦s ❝♦♠ ✉♠ ❝♦rt❡ ✭❛✮ ❡ ❝♦♠ ❞♦✐s ❝♦rt❡s ✭❜✮ ❬❆rt❡r♦✱ ✷✵✵✾❪ ✳ ✳ ✳ ✳ ✸✸

✷✳✶✽ ▼❛r❣❡♠ ❞❡ ✉♠ ❧✐♠✐t❡ ❞❡ ❞❡❝✐sã♦ ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺

✷✳✶✾ ▲✐♠✐t❡ ❞❡ ❞❡❝✐sã♦ ❞❡ ❙❱▼ ♣❛r❛ ❝❛s♦ ♥ã♦ s❡♣❛rá✈❡❧ ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪ ✳ ✳ ✳ ✳ ✸✻

✷✳✷✵ P❛r❛❞✐❣♠❛s ❡ ♠ét♦❞♦s s❡ s♦❜r❡♣õ❡♠ ❝♦♠♦ té❝♥✐❝❛s ❞❡ r❡s♦❧✉çã♦ ❞❡ ♣r♦✲

❜❧❡♠❛ ❬❘❡③❡♥❞❡✱ ✷✵✵✺❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽

✷✳✷✶ ❈❧❛ss✐✜❝❛çã♦ ❞❡ s✐st❡♠❛s ❤í❜r✐❞♦s ✐♥t❡❧✐❣❡♥t❡s ❬❘❡③❡♥❞❡✱ ✷✵✵✺❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽

✸✳✶ ❆rq✉✐t❡t✉r❛ ❞❡ r❡❞❡ ✉t✐❧✐③❛❞❛ ♥❛ ■❙❈❳ ✷✵✶✷ ❬❙❤✐r❛✈✐ ❡t ❛❧✳✱ ✷✵✶✷❪ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷

✸✳✷ Pr♦❝❡ss♦ ❞❡ ❉❡s❝♦❜❡rt❛ ❞❡ ❈♦♥❤❡❝✐♠❡♥t♦ ❡♠ ❇❛♥❝♦ ❞❡ ❉❛❞♦s ✭❑❉❉✮ ❬❍❛♥

❡t ❛❧✳✱ ✷✵✶✶❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹

✹✳✶ ❘♦♦t ❘❡❧❛t✐✈❡ ❙q✉❛r❡❞ ❊rr♦r ✭❘❘❙❊✮ ✲ ❱❛❧✐❞❛çã♦ ❈r✉③❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸

✹✳✷ ❚❡♠♣♦ ❣❛st♦ ❝♦♠ ❝r✐❛çã♦ ❞♦ ♠♦❞❡❧♦ ✭s✮ ✲ ❱❛❧✐❞❛çã♦ ❈r✉③❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸

✹✳✸ ❉✐❢❡r❡♥ç❛ ❘❘❙❊ ✭❍♦❧❞♦✉t ✲ ❱❛❧✐❞❛çã♦ ❈r✉③❛❞❛✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹

✹✳✹ ❚❡♠♣♦ ❣❛st♦ ❝♦♠ ❝r✐❛çã♦ ❞♦ ♠♦❞❡❧♦ ✭s✮ ✲ ❍♦❧❞♦✉t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

✈✐✐✐

▲✐st❛ ❞❡ ❚❛❜❡❧❛s

✸✳✶ ▲✐st❛ ❞❡ ❛tr✐❜✉t♦s ❞❛ ❜❛s❡ ■❙❈❳ ✷✵✶✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✸✳✷ ❉❡s❝r✐çã♦ ❞♦ trá❢❡❣♦ ❞❡ r❡❞❡ ♣♦r ❞✐❛ ❞❛ ❜❛s❡ ■❙❈❳ ✷✵✶✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺

✸✳✸ ❋♦r♠❛t♦ ❞♦s ❛rq✉✐✈♦s ✳❛r✛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺

✸✳✹ ❆tr✐❜✉t♦s ❞♦s ❛rq✉✐✈♦s ❣❡r❛❞♦s ❡♠ ❢♦r♠❛t♦ ✳❛r✛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻

✸✳✺ ▼❡❧❤♦r❡s ♣❛râ♠❡tr♦s ❞♦ ❆● ♣❛r❛ ❛s ❘◆❆s ▼▲P ❝♦♠ ✶✸ ❡♥tr❛❞❛s ✳ ✳ ✳ ✳ ✳ ✹✽

✸✳✻ ▼❡❧❤♦r❡s ♣❛râ♠❡tr♦s ❞♦ ❆● ♣❛r❛ ❛s ❘◆❆s ▼▲P ❝♦♠ ✼ ❡♥tr❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✹✾

✹✳✶ ▼♦❞❡❧♦ ❞❡ ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶

✹✳✷ ❘❡s✉❧t❛❞♦s ❣❡r❛✐s ❞❛s té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✭♦✤✐♥❡✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷

✹✳✸ ❘❡s✉❧t❛❞♦s ❞❛s té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✭♦✤✐♥❡✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸

✹✳✹ ❘❡s✉❧t❛❞♦s ❣❡r❛✐s ❞❛s té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✭t❡♠♣♦ r❡❛❧✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺

✹✳✺ ❘❡s✉❧t❛❞♦s ❞❛s té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✭t❡♠♣♦ r❡❛❧✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺

✹✳✻ ❘❡s✉❧t❛❞♦s ❣❡r❛✐s ❞♦ s✐st❡♠❛ ✐♥t❡❧✐❣❡♥t❡ ❤í❜r✐❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

✹✳✼ ❘❡s✉❧t❛❞♦s ❞♦ s✐st❡♠❛ ✐♥t❡❧✐❣❡♥t❡ ❤í❜r✐❞♦ ✭♦✤✐♥❡✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

✹✳✽ ❘❡s✉❧t❛❞♦s ❞♦ s✐st❡♠❛ ✐♥t❡❧✐❣❡♥t❡ ❤í❜r✐❞♦ ✭t❡♠♣♦ r❡❛❧✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼

✐①

❘❡s✉♠♦

▲■▼❆✱ ❘❛❢❛❡❧ ❆♥t♦♥✐♦ ●♦♥ç❛❧✈❡s✱ ▼✳❙❝✳✱ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❱✐ç♦s❛✱ ❋❡✈❡r❡✐r♦

❞❡ ✷✵✶✹✳ ❯t✐❧✐③❛çã♦ ❞❡ ❙✐st❡♠❛s ■♥t❡❧✐❣❡♥t❡s ♣❛r❛ ❈❧❛ss✐✜❝❛çã♦ ❞❡ ❚rá❢❡❣♦

▼❛❧✐❝✐♦s♦✳ ❖r✐❡♥t❛❞♦r✿ ❈❛r❧♦s ❞❡ ❈❛str♦ ●♦✉❧❛rt✳ ❈♦♦r✐❡♥t❛❞♦r❡s✿ ❆❧❝✐♦♥❡ ❞❡ P❛✐✈❛

❖❧✐✈❡✐r❛ ❡ ❘✐❝❛r❞♦ ❞♦s ❙❛♥t♦s ❋❡rr❡✐r❛✳

◆♦s ú❧t✐♠♦s ❛♥♦s✱ ✈ár✐❛s ♣❡sq✉✐s❛s ❡♠ ❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sã♦ tê♠ s✐❞♦ r❡❛❧✐③❛❞❛s✱

❜✉s❝❛♥❞♦ ♠❡❧❤♦r✐❛s ♥♦s í♥❞✐❝❡s ❞❡ ❞❡t❡❝çõ❡s ❡ ❞✐♠✐♥✉✐çã♦ ❞♦s ❛❧❛r♠❡s ❢❛❧s♦s✳ ◆♦

❡♥t❛♥t♦✱ ✈ár✐❛s ❞❡❧❛s sã♦ ❝r✐t✐❝❛❞❛s ♣❡❧❛ ✉t✐❧✐③❛çã♦ ❞❡ ❜❛s❡s ❞❡ ❞❛❞♦s q✉❡ ♥ã♦ r❡♣r❡✲

s❡♥t❛♠ ❛ r❡❛❧✐❞❛❞❡ ❛t✉❛❧ ❞♦ trá❢❡❣♦ ❞❛s r❡❞❡s ❞❡ ❝♦♠♣✉t❛❞♦r❡s✱ ❞❡✈✐❞♦ ❛♦s s❡✉s ♥♦✈♦s

♣❛r❛❞✐❣♠❛s ❡ ♦♥❞❡ ❛s ❛♠❡❛ç❛s ❡ ❛ s♦✜st✐❝❛çã♦ ❞♦s ❛t❛q✉❡s tê♠ ❛✉♠❡♥t❛❞♦✳ ❆ss✐♠✱

❡st❡ tr❛❜❛❧❤♦ tr❛③ ✉♠ ❡st✉❞♦ s♦❜r❡ ✉♠❛ ❜❛s❡ ❞❡ ❞❛❞♦s ♠❛✐s r❡❝❡♥t❡✱ ❛ ■❙❈❳ ✷✵✶✷✱

❝♦♠ ❝❛r❛❝t❡ríst✐❝❛s ❝❤❛✈❡s ♣❛r❛ ♥♦✈❛s ❜❛s❡s ❞❡ ❞❛❞♦s ❡ ♣❡sq✉✐s❛s✳ ❖ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦

✉t✐❧✐③❛ ❡t❛♣❛s ❞♦ ♣r♦❝❡ss♦ ❞❡ ❉❡s❝♦❜❡rt❛ ❞❡ ❈♦♥❤❡❝✐♠❡♥t♦ ❡♠ ❇❛♥❝♦ ❞❡ ❉❛❞♦s ✭❑❉❉✮

❡ té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❝♦♠♦ ár✈♦r❡s ❞❡ ❞❡❝✐sã♦ ❡ r❡❞❡s ♥❡✉r❛✐s ❛rt✐✜❝✐❛✐s ❛tr❛✈és

❞♦ s♦❢t✇❛r❡ ❲❡❦❛ ❡ ❞❡ ✉♠ s✐st❡♠❛ ✐♥t❡❧✐❣❡♥t❡ ❤í❜r✐❞♦✱ ❛❧é♠ ❞❡ r❡❛❧✐③❛r ❛♥á❧✐s❡s ❡

❝♦♠♣❛r❛çõ❡s ❞♦s r❡s✉❧t❛❞♦s ❡♥❝♦♥tr❛❞♦s✳

①

❆❜str❛❝t

▲■▼❆✱ ❘❛❢❛❡❧ ❆♥t♦♥✐♦ ●♦♥ç❛❧✈❡s✱ ▼✳❙❝✳✱ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❱✐ç♦s❛✱ ❋❡❜r✉❛r②

♦❢ ✷✵✶✹✳ ❯t✐❧✐③❛t✐♦♥ ❢♦r ■♥t❡❧❧✐❣❡♥t ❙②st❡♠s t♦ ❈❧❛ss✐✜❝❛t✐♦♥ ♦❢ ▼❛❧✐❝✐♦✉s

❚r❛✣❝✳ ❆❞✈✐s❡r✿ ❈❛r❧♦s ❞❡ ❈❛str♦ ●♦✉❧❛rt✳ ❈♦✲❛❞✈✐s❡rs✿ ❆❧❝✐♦♥❡ ❞❡ P❛✐✈❛ ❖❧✐✈❡✐r❛

❛♥❞ ❘✐❝❛r❞♦ ❞♦s ❙❛♥t♦s ❋❡rr❡✐r❛✳

■♥ t❤❡ ❧❛st ②❡❛rs s❡✈❡r❛❧ r❡s❡❛r❝❤❡s ♦♥ ❞❡t❡❝t✐♦♥ ♦❢ ✐♥tr✉s✐♦♥ ❤❛✈❡ ❜❡❡♥ ❞♦♥❡✱

s❡❡❦✐♥❣ ❢♦r ✐♠♣r♦✈❡♠❡♥ts ✐♥ ❞❡t❡❝t✐♦♥ ❛♥❞ ❞❡❝r❡❛s✐♥❣ r❛t❡s ♦❢ ❢❛❧s❡ ❛❧❛r♠s✳ ❍♦✇❡✈❡r✱

s❡✈❡r❛❧ ♦❢ t❤❡♠ ❛r❡ ❝r✐t✐❝✐③❡❞ ❜② ✉s✐♥❣ ❞❛t❛❜❛s❡s ✇❤✐❝❤ ❞♦ ♥♦t r❡♣r❡s❡♥t t❤❡ ❝✉rr❡♥t

r❡❛❧✐t② ❢r♦♠ ❝♦♠♣✉t❡rs ♥❡t✇♦r❦s tr❛✣❝ ❝♦♠✐♥❣ ♦✛ t❤❡✐r ♥❡✇ ♣❛r❛❞✐❣♠s ❛♥❞ ✇❤❡r❡

t❤❡ t❤r❡❛ts ❛♥❞ t❤❡ s♦♣❤✐st✐❝❛t✐♦♥ ♦❢ t❤❡ ❛tt❛❝❦s ❤❛✈❡ ✐♥❝r❡❛s❡❞✳ ❚❤✐s ✇❛②✱ t❤❛t

✇♦r❦ ❝♦♠❡s ✉♣ ❛ st✉❞② ❜❛s❡❞ ♦♥ ❛ ♠♦r❡ r❡❝❡♥t ❞❛t❛❜❛s❡✱ ■❙❈❳ ✷✵✶✷✱ ✇✐t❤ ❢❡❛t✉r❡s

❦❡② t♦ ♥❡✇ ❞❛t❛❜❛s❡s ❛♥❞ r❡s❡❛r❝❤❡s✳ ❚❤❡ ♣r❡s❡♥t ✇♦r❦ ✉s❡s ❑♥♦✇❧❡❞❣❡ ❉✐s❝♦✈❡r②

✐♥ ❉❛t❛❜❛s❡ ✭❑❉❉✮ ❛♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ t❡❝❤♥✐q✉❡s ❧✐❦❡ ❞❡❝✐s✐♦♥ tr❡❡s ❛♥❞ ❛rt✐✜❝✐❛❧

♥❡✉r❛❧ ♥❡t✇♦r❦s t❤r♦✉❣❤ s♦❢t✇❛r❡ ❲❡❦❛ ❛♥❞ s♦❢t ❝♦♠♣✉t✐♥❣✱ ❜❡s✐❞❡s ❞♦ ❛♥❛❧②s✐s ❛♥❞

❝♦♠♣❛r✐s♦♥s ❢r♦♠ t❤❡ r❡s✉❧ts ❢♦✉♥❞✳

①✐

❈❛♣ít✉❧♦ ✶

■♥tr♦❞✉çã♦

◆❛s ú❧t✐♠❛s ❞é❝❛❞❛s✱ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❛ s❡❣✉r❛♥ç❛ ❞❛ ✐♥❢♦r♠❛çã♦ ♥❛s ♦r❣❛♥✐③❛çõ❡s s♦❢r❡✉

♠✉❞❛♥ç❛s ✐♠♣♦rt❛♥t❡s✳ ❆♥t❡s✱ ❛ s❡❣✉r❛♥ç❛ ❡r❛ r❡❛❧✐③❛❞❛ ❜❛s✐❝❛♠❡♥t❡ ❛tr❛✈és ❞❡ ♠❡✐♦s

❢ís✐❝♦s ❡ ❛❞♠✐♥✐str❛t✐✈♦s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ✉t✐❧✐③❛çã♦ ❞❡ tr❛♥❝❛s ❝♦♠ s❡❣r❡❞♦s ♥♦s

❛r♠ár✐♦s ♣❛r❛ ♣r♦t❡❣❡r ❞♦❝✉♠❡♥t♦s ✐♠♣♦rt❛♥t❡s✳ ❈♦♠ ♦ s✉r❣✐♠❡♥t♦ ❞♦ ❝♦♠♣✉t❛❞♦r✱

♥♦✈❛s ❢❡rr❛♠❡♥t❛s ❛✉t♦♠❛t✐③❛❞❛s s❡ t♦r♥❛r❛♠ ♥❡❝❡ssár✐❛s ♣❛r❛ ♣r♦t❡❣❡r ❛rq✉✐✈♦s ❡

♦✉tr❛s ✐♥❢♦r♠❛çõ❡s ❛r♠❛③❡♥❛❞❛s ♥♦ ❝♦♠♣✉t❛❞♦r ❬❙t❛❧❧✐♥❣s✱ ✷✵✶✵❪✳

❯♠❛ ✐♠♣♦rt❛♥t❡ ♠✉❞❛♥ç❛ ♦❝♦rr❡✉ ❛♦ s✉r❣✐r ♦s s✐st❡♠❛s ❞✐str✐❜✉í❞♦s✱ ♦ ✉s♦ ❞❛s

r❡❞❡s ❡ ❞♦s r❡❝✉rs♦s ❞❡ ❝♦♠✉♥✐❝❛çã♦✳ ◆❡st❡ ❝❡♥ár✐♦✱ ♦ ❝♦♠♣❛rt✐❧❤❛♠❡♥t♦ ❞❡ r❡❝✉rs♦s

t♦r♥♦✉✲s❡ ❝❛❞❛ ✈❡③ ♠❛✐s ✉s✉❛❧ ❡ ♥♦✈❛s ❢❡rr❛♠❡♥t❛s s✉r❣✐r❛♠ ♣❛r❛ ♠❛♥t❡r ❛ ✏s❡❣✉r❛♥ç❛

❞❡ r❡❞❡✑✱ ♣r♦t❡❣❡♥❞♦ ♦s ❞❛❞♦s ❞✉r❛♥t❡ s✉❛ tr❛♥s♠✐ssã♦✳

❆t✉❛❧♠❡♥t❡✱ ❡♠ q✉❛❧q✉❡r ❞✐s❝✉ssã♦ sér✐❛ q✉❡ ❡♥✈♦❧✈❛ r❡❞❡s ❞❡ ❝♦♠♣✉t❛❞♦r❡s✱ é

♦❜r✐❣❛tór✐♦ t❡r ❛ ■♥t❡r♥❡t ❡♠ ♠❡♥t❡✳ ❖ ♠❛✐♦r ❝r❡s❝✐♠❡♥t♦ ♥❡ss❛ ár❡❛ ♦❝♦rr❡✉ ♥♦ â♠❜✐t♦

❞♦s s❡r✈✐ç♦s ❡ ❞❛s ❛♣❧✐❝❛çõ❡s✱ ❝♦♠♦ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ❲❡❜✱ ♣❡❧❛ ✉t✐❧✐③❛çã♦ ❞♦s s❡r✲

✈✐ç♦s ❞❡ ❝♦rr❡✐♦ ❡❧❡trô♥✐❝♦ ♣♦r ♠✐❧❤❛r❡s ❞❡ ✉s✉ár✐♦s s✐♠✉❧tâ♥❡♦s✱ ♣❡❧❛ r❡❝❡♣çã♦ ❞❡ á✉❞✐♦

❡ ✈í❞❡♦✱ ♣❡❧❛ t❡❧❡❢♦♥✐❛ ❛tr❛✈és ❞❛ ■♥t❡r♥❡t✱ ♣❡❧♦s s❡r✈✐ç♦s ❞❡ ♠❡♥s❛❣❡♥s ✐♥st❛♥tâ♥❡❛s✱

♣❡❧❛s ❛♣❧✐❝❛çõ❡s P✷P ✭P❡❡r✲t♦✲P❡❡r✮ ❡ ♣❡❧♦ ❝♦♠ér❝✐♦ ❡❧❡trô♥✐❝♦ ❬❑✉r♦s❡ ✫ ❘♦ss✱ ✷✵✶✵❪✳

❊♠❜♦r❛ ❛♥t✐❣❛♠❡♥t❡ ♦ ✉s♦ ❞❛s r❡❞❡s ❡ ❞❡ ❝♦♠♣✉t❛❞♦r❡s ❢♦ss❡ ♣r✐✈✐❧é❣✐♦ ❞❡ ♣♦✉❝❛s

♦r❣❛♥✐③❛çõ❡s ❡ ✉s✉ár✐♦s✱ ❝♦♠ ♦ ❛❞✈❡♥t♦ ❞❛ ■♥t❡r♥❡t ❡ s❡✉ ❛✉♠❡♥t♦ ❞❡ ✉t✐❧✐③❛çã♦✱ ❛

♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡❣✉r❛♥ç❛ ✜❝♦✉ ♠❛✐s ❡✈✐❞❡♥t❡✳ ◆❡st❡ ❝❡♥ár✐♦✱ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❞❛❞♦s

❡ ✐♥❢♦r♠❛çõ❡s tr❛♥s♠✐t✐❞❛s ❡ ❛r♠❛③❡♥❛❞❛s ♥♦s s✐st❡♠❛s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❛✉♠❡♥t♦✉ ❡ ❛

■♥t❡r♥❡t s❡ t♦r♥♦✉ ✉♠❛ ❢❡rr❛♠❡♥t❛ ♣❛❞rã♦ ❞❡ ❝♦♠✉♥✐❝❛çã♦ ♥♦ ♠✉♥❞♦✱ ❞❡s❡♠♣❡♥❤❛♥❞♦

✉♠ ♣❛♣❡❧ ❡ss❡♥❝✐❛❧ ♥❛ ❣❡stã♦ ❞❛s ❡♠♣r❡s❛s ♠❛✐s ❜❡♠ s✉❝❡❞✐❞❛s ❬▼③✐❧❛ ✫ ❉✉❜❡✱ ✷✵✶✸❪✳

❈♦♥t✉❞♦✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛s ✈❛♥t❛♥❣❡♥s q✉❡ ❛ ■♥t❡r♥❡t tr❛③✱ ❤á t❛♠❜é♠ ✉♠❛

❞❡s✈❛♥t❛❣❡♠ s✉❜st❛♥❝✐❛❧ q✉❡ é ❛ ❡①♣♦s✐çã♦ ❞❡ ✐♥❢♦r♠❛çõ❡s ✈❛❧✐♦s❛s ❡ ❝♦♥✜❞❡♥❝✐❛✐s ❛♦s

r✐s❝♦s ❞❡ ✐♥✈❛sõ❡s ❡ ❛♠❡❛ç❛s ❝✐❜❡r♥ét✐❝❛s ❬▼③✐❧❛ ✫ ❉✉❜❡✱ ✷✵✶✸❪✳

✶

✶✳ ■♥tr♦❞✉çã♦ ✷

✶✳✶ ❖ ♣r♦❜❧❡♠❛ ❡ s✉❛ ✐♠♣♦rtâ♥❝✐❛

❱ár✐♦s ♠❡❝❛♥✐s♠♦s ❞❡ s❡❣✉r❛♥ç❛ tê♠ s✐❞♦ ✉t✐❧✐③❛❞♦s ♣❡❧❛s ❡♠♣r❡s❛s ♣❛r❛ ❛ ♣r♦t❡çã♦

❞❡ s❡✉s ❞❛❞♦s ❝♦♥tr❛ ❛❝❡ss♦s ✐♥❞❡✈✐❞♦s✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣r♦✈❡♥✐❡♥t❡s ❞❡ ✉♠ ❛♠❜✐❡♥t❡

❡①t❡r♥♦ ❝♦♠♦ ❛ ■♥t❡r♥❡t✳ ❊ss❡s ♠❡❝❛♥✐s♠♦s ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦ tê♠ s❡ ❛❞❛♣t❛❞♦ ❡

✐♥❝♦r♣♦r❛❞♦ ❞✐✈❡rs❛s ❢✉♥çõ❡s ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ❛❜r❛♥❣❡r ❛ r❡❛❧ ♥❡❝❡ss✐❞❛❞❡ ❞❛s ❡♠♣r❡s❛s

❡ ✉s✉ár✐♦s✳

❈♦♥t✉❞♦✱ ❛ s❡❣✉r❛♥ç❛✱ q✉❡ ♠❛✐s r❡❝❡♥t❡♠❡♥t❡ s❡ t♦r♥♦✉ ✉♠ ❞❡st❛q✉❡ ♥♦s ♠❡✐♦s

❞❡ ❝♦♠✉♥✐❝❛çã♦✱ ♣♦r ♠✉✐t♦ t❡♠♣♦ ❢♦r❛ ✉♠ q✉❡s✐t♦ ❞❡✐①❛❞♦ ❡♠ s❡❣✉♥❞♦ ♣❧❛♥♦✱ ♣♦✐s

❡♥✈♦❧✈✐❛ ✐♥✈❡st✐♠❡♥t♦s ❛❞✐❝✐♦♥❛✐s q✉❡ ♣♦❞❡r✐❛♠ ✐♥✈✐❛❜✐❧✐③❛r ❞✐✈❡rs♦s ♣r♦❥❡t♦s✳

❱ár✐❛s ❛♠❡❛ç❛s s❡♠♣r❡ ❡①✐st✐r❛♠✱ ♠❛s ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦ ♥ã♦ ❡r❛♠ ♣r❡♦❝✉♣❛✲

çõ❡s ♣❛r❛ ❛ ♠❛✐♦r✐❛ ❞❛ ♣♦♣✉❧❛çã♦✱ ♣♦✐s ♥ã♦ ❤❛✈✐❛ ❝❡♥ár✐♦ ♣r♦♣í❝✐♦ ❛♦s ❞❛♥♦s✳ ❍♦❥❡✱

❡♥tr❡t❛♥t♦✱ ❡st❛ s✐t✉❛çã♦ ♠✉❞♦✉✳ ❆ ■♥t❡r♥❡t é ✉♠❛ r❡❞❡ ❞❡ ♥í✈❡❧ ♠✉♥❞✐❛❧ ❡♠ q✉❡ ❛s

♣❡ss♦❛s ❢❛③❡♠ ✐♥ú♠❡r❛s ♦♣❡r❛çõ❡s ✜♥❛♥❝❡✐r❛s✱ ❝♦♠♦ ❝♦♠♣r❛s✱ ♣❛❣❛♠❡♥t♦s✱ ❡t❝✳

❆ss✐♠✱ ❛s r❡❞❡s ❞❡ ❝♦♠♣✉t❛❞♦r❡s ❛t✉❛✐s sã♦ ❝❛❞❛ ✈❡③ ♠❛✐s ❛❧✈♦s ❞❡ ❛♠❡❛ç❛s✳ ❖

♣ró♣r✐♦ ❈❊❘❚✳❜r ✭❈❡♥tr♦ ❞❡ ❊st✉❞♦s✱ ❘❡s♣♦st❛ ❡ ❚r❛t❛♠❡♥t♦ ❞❡ ■♥❝✐❞❡♥t❡s ❞❡ ❙❡❣✉✲

r❛♥ç❛ ♥♦ ❇r❛s✐❧✮ ❛♦ ❧♦♥❣♦ ❞♦s ú❧t✐♠♦s ❛♥♦s t❡♠ ❞✐✈✉❧❣❛❞♦ ♦ t♦t❛❧ ❞❡ ✐♥❝✐❞❡♥t❡s q✉❡

✉s✉ár✐♦s ❡ ♦r❣❛♥✐③❛çõ❡s t❡♠ r❡♣♦rt❛❞♦✱ ♠♦str❛❞♦ ♥❛ ❋✐❣✉r❛ ✶✳✶✳

❋✐❣✉r❛ ✶✳✶✳ ❚♦t❛❧ ❞❡ ✐♥❝✐❞❡♥t❡s r❡♣♦rt❛❞♦s ❛♦ ❈❊❘❚✳❜r ♣♦r ❛♥♦ ❬❈❊❘❚✳❜r✱ ✷✵✶✹❪

❖s ♠❡❝❛♥✐♠♦s ❞❡ s❡❣✉r❛♥ç❛ ♥ã♦ tê♠ ❛t❡♥❞✐❞♦ às ♥❡❝❡ss✐❞❛❞❡s ❝❛❞❛ ✈❡③ ♠❛✐s ❝❧❛r❛s

✶✳ ■♥tr♦❞✉çã♦ ✸

❞♦s ✉s✉ár✐♦s ❡ ♦r❣❛♥✐③❛çõ❡s✳ ▼✉✐t♦s ❛t❛q✉❡s sã♦ ✈❛r✐❛çõ❡s ❞❡ té❝♥✐❝❛s ❥á ❝♦♥❤❡❝✐❞❛s ❡✱

♣♦rt❛♥t♦✱ ♠✉✐t♦s ❞❡✈❡♠ s❡r ❝❛♣❛③❡s ❞❡ s❡r❡♠ ✐❞❡♥t✐✜❝❛❞♦s✳

❈♦♠♦ ❡①❡♠♣❧♦✱ ♥❛s ❋✐❣✉r❛s ✶✳✷ ❡ ✶✳✸ sã♦ ♠♦str❛❞♦s r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ♦s t✐♣♦s

❞❡ ❛t❛q✉❡s r❡♣♦rt❛❞♦s ❛♦ ❈❊❘❚✳❜r ❞❡ ❥✉♥❤♦ ❛ s❡t❡♠❜r♦ ❞❡ ✷✵✶✸✱ ❡ ❞❡ ❛❜r✐❧ ❛ ❥✉♥❤♦

❞❡ ✷✵✶✸✳ ◆❡ss❡ ❝❛s♦ é ❝❧❛r♦ ♦s ✈ár✐♦s t✐♣♦s ❞❡ ❛t❛q✉❡s ❥á ❝♦♥❤❡❝✐❞♦s✱ q✉❡ r❡♣r❡s❡♥t❛♠

❛❝✐♠❛ ❞❡ ✽✵✪ ❞♦s ✐♥❝✐❞❡♥t❡s✳

❋✐❣✉r❛ ✶✳✷✳ ■♥❝✐❞❡♥t❡s r❡♣♦rt❛❞♦s ❛♦ ❈❊❘❚✳❜r ✭❥✉♥❤♦ ❛ s❡t❡♠❜r♦ ❞❡ ✷✵✶✸✮❬❈❊❘❚✳❜r✱ ✷✵✶✹❪

❋✐❣✉r❛ ✶✳✸✳ ■♥❝✐❞❡♥t❡s r❡♣♦rt❛❞♦s ❛♦ ❈❊❘❚✳❜r ✭❛❜r✐❧ ❛ ❥✉♥❤♦ ❞❡ ✷✵✶✸✮ ❬❈❊❘❚✳❜r✱✷✵✶✹❪

❖s ❙✐st❡♠❛s ❞❡ ❉❡t❡❝çã♦ ❞❡ ■♥tr✉sã♦ ✭❙❉■s✮ sã♦ ♦s ♠❡❝❛♥✐s♠♦s q✉❡ ♣❡r♠✐t❡♠

t❛✐s ❞❡t❡❝çõ❡s✱ ♥♦ ❡♥t❛♥t♦✱ ❝♦♠♣❧✐❝❛❞♦r❡s tê♠ ✐♠♣❡❞✐❞♦ ♦ r❡❛❧ s✉❝❡ss♦ ❞❡ t❛✐s s✐st❡♠❛s✳

❊♥tr❡ ❡ss❡s ❝♦♠♣❧✐❝❛❞♦r❡s✱ ♣♦❞❡♠♦s ❝✐t❛r ❛s r❡❞❡s ❞❡ ❛❧t❛ ✈❡❧♦❝✐❞❛❞❡✱ ❛s q✉❛✐s ❣❡r❛♠

✶✳ ■♥tr♦❞✉çã♦ ✹

✉♠ ❣r❛♥❞❡ ✈♦❧✉♠❡ ❞❡ ❞❛❞♦s✱ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ♣r♦t❡çã♦ ❡♠ t❡♠♣♦ r❡❛❧✱ r❡❞❡s ♠ó✈❡✐s✱

❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ ❛❧❛r♠❡s ❢❛❧s♦s ❣❡r❛❞♦s ♣♦r ❡st❡s s✐st❡♠❛s ❡ ❛ ❢❛❧t❛ ❞❡ ❜❛s❡s ❞❡ ❞❛❞♦s

q✉❡ r❡♣r❡s❡♥t❡♠ ❛ r❡❛❧✐❞❛❞❡ ❛t✉❛❧ ❞❛s r❡❞❡s✳

❊ss❡s ❝♦♠♣❧✐❝❛❞♦r❡s tê♠ ❢♦♠❡♥t❛❞♦ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ❞✐✈❡rs❛s té❝♥✐❝❛s ♣❡❧♦s ♣❡s✲

q✉✐s❛❞♦r❡s✱ ❝♦♠♦ ▼✐♥❡r❛çã♦ ❞❡ ❉❛❞♦s ❡ ■♥t❡❧✐❣ê♥❝✐❛ ❆rt✐✜❝✐❛❧ ✭■❆✮✱ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡

♠❡❧❤♦r❛r ❛s t❛①❛s ❞❡ ❞❡t❡❝çã♦✱ ❞✐♠✐♥✉✐r ♦s ❛❧❛r♠❡s ❢❛❧s♦s ❡ ❛✉♠❡♥t❛r ♦ ❞❡s❡♠♣❡♥❤♦

❞❡st❡s s✐st❡♠❛s✳ ❈❛r❛❝t❡ríst✐❝❛s ❝♦♠♦ ❞❡t❡❝çã♦ ❡♠ t❡♠♣♦ r❡❛❧ ❡ ❛çõ❡s ♣❛r❛ ♣r❡✈❡♥✐r ❛

✐♥tr✉sã♦ é ❛❧❣♦ ❝❛❞❛ ✈❡③ ♠❛✐s ❜✉s❝❛❞♦ ♣❡❧❛s ♣❡sq✉✐s❛s✳ ❖ ✐❞❡❛❧ s❡r✐❛ ✉♠ ❙❉■ ❝♦♠ ❞❡✲

t❡❝çã♦ ❡♠ t❡♠♣♦ r❡❛❧✱ q✉❡ ♣✉❞❡ss❡ ♣r❡✈❡♥✐r ✉♠ ❛t❛q✉❡ ❞❡ ❢♦r♠❛ ❛✉t♦♠át✐❝❛✱ r❡❣✐str❛r

✉♠ ❡✈❡♥t♦ ❛❧❡rt❛♥❞♦ ♦ ❛❞♠✐♥✐str❛❞♦r ❡ s❡♠ ❣❡r❛r ❛❧❛r♠❡s ❢❛❧s♦s✳

◆❡ss❛ ❜✉s❝❛ ♣❡❧❛ s♦❧✉çã♦ ✐❞❡❛❧✱ ❛ ✐♠♣♦rtâ♥❝✐❛ s❡ ❥✉st✐✜❝❛ ❛✐♥❞❛ ♣❡❧❛ ❝❛♣❛❝✐❞❛❞❡

❞❡ss❡s s✐st❡♠❛s ❞❡t❡❝t❛r❡♠ t❛♥t♦ ❛t❛q✉❡s ❡①t❡r♥♦s✱ ❝♦♠♦ ❛q✉❡❧❡s ❣❡r❛❞♦s ✐♥t❡r♥❛♠❡♥t❡

❡♠ ✉♠❛ ♦r❣❛♥✐③❛çã♦✱ ❛❧é♠ ❞❡ ✐❞❡♥t✐✜❝❛r ❛t❛q✉❡s ♥ã♦ ❝♦♥❤❡❝✐❞♦s✳ ❆ss✐♠✱ s✉r❣❡ ✉♠ ♥♦✈♦

❝♦♠♣❧✐❝❛❞♦r✱ ♣♦✐s ♦ s✐st❡♠❛ ♥❡❝❡ss✐t❛ ❝r✐❛r ✉♠ ♣❡r✜❧ ❞♦ ❛♠❜✐❡♥t❡ q✉❡ s❡r✐❛ ♥♦r♠❛❧✱ ♣❛r❛

q✉❡✱ ❛ ♣❛rt✐r ❞❡st❡ ♣❡r✜❧ ❝♦♥s✐❣❛ ✐❞❡♥t✐✜❝❛r ♦ q✉❡ s❡r✐❛ ✉♠ ❛t❛q✉❡✳ ❖✉tr♦ ♣r♦❜❧❡♠❛

é q✉❡✱ ❡①✐st❡♠ ♣♦✉❝❛s ❜❛s❡s ❞❡ ❞❛❞♦s r❡❝❡♥t❡s✳ ❆ ♠❛✐♦r✐❛ ❞♦s tr❛❜❛❧❤♦s ✉t✐❧✐③❛ ❜❛s❡s

❞❡ ❞❛❞♦s ❛♥t✐❣❛s✱ q✉❡ tê♠ r❡❝❡❜✐❞♦ ❝rít✐❝❛s ❞❡ ✈ár✐♦s ♣❡sq✉✐s❛❞♦r❡s✱ ❝♦♠♦ ❡♠ ▼❝❍✉❣❤

❬✷✵✵✵❪ ❡ ❙❤✐r❛✈✐ ❡t ❛❧✳ ❬✷✵✶✷❪✳ ❉❡ ♠❛♥❡✐r❛ ❣❡r❛❧✱ ♠✉✐t❛s ❜❛s❡s ❞❡ ❞❛❞♦s ♥ã♦ sã♦ ❞✐s✲

♣♦♥✐❜✐❧✐③❛❞❛s ♣♦r q✉❡stõ❡s ❞❡ s❡❣✉r❛♥ç❛ ❞❛ ♦r❣❛♥✐③❛çã♦ ❡ ♦✉tr❛s ♥ã♦ ♣♦ss✉❡♠ t♦❞♦ ♦

trá❢❡❣♦ ❝❛♣t✉r❛❞♦ ❡ ✐❞❡♥t✐✜❝❛❞♦✳

✶✳✷ ❖❜❥❡t✐✈♦s

❖ ♦❜❥❡t✐✈♦ ❣❡r❛❧ ❞❡st❡ tr❛❜❛❧❤♦ é ❛✈❛❧✐❛r ✈ár✐♦s ♠ét♦❞♦s ❞❡ ❝❧❛ss✐✜❝❛çã♦✱ ❛ ♣❛rt✐r ❞❡

✉♠❛ ❜❛s❡ ❞❡ ❞❛❞♦s ♠❛✐s r❡❝❡♥t❡✱ ❛♦ ✐❞❡♥t✐✜❝❛r ♦ trá❢❡❣♦ ♠❛❧✐❝✐♦s♦ ❞❡ ✉♠❛ r❡❞❡ ❞❡

❝♦♠♣✉t❛❞♦r❡s✳

❊s♣❡❝✐✜❝❛♠❡♥t❡✱ ♣r❡t❡♥❞❡✲s❡✿

• ❛✈❛❧✐❛r ♦s ♥í✈❡✐s ❞❛s t❛①❛s ❞❡ ❞❡t❡❝çõ❡s ❡ ❡s❢♦rç♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❞❡ ❞✐✈❡rs❛s té❝♥✐✲

❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦✱ ❞❡ ❢♦r♠❛ q✉❡ s❡ ❝♦♠♣❛r❡ ❛s té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✉t✐❧✐③❛❞❛s

❡♥tr❡ s✐ ❡ ❝♦♠ tr❛❜❛❧❤♦s r❡❧❛❝✐♦♥❛❞♦s❀

• ✐❞❡♥t✐✜❝❛r ❛s ♠❡❧❤♦r❡s té❝♥✐❝❛s ❞❡ ❞❡t❡❝çã♦ ❡✱ ❡♠ q✉❛✐s s✐t✉❛çõ❡s ❝❛❞❛ ✉♠❛ s❡

❛❞❛♣t❛ ♠❡❧❤♦r❀

• ❛✈❛❧✐❛r ❛s t❛①❛s ❞❡ ❞❡t❡❝çõ❡s ❞❡ ✐♥tr✉sã♦ ✉t✐❧✐③❛♥❞♦ ✉♠ ❙✐st❡♠❛ ■♥t❡❧✐❣❡♥t❡ ❍í✲

❜r✐❞♦ ✭❙■❍✮✱ ❞❡ ❢♦r♠❛ q✉❡ s❡❥❛ ♣♦ssí✈❡❧ ♠❡❧❤♦r❛r ♦ ♥í✈❡❧ ❞❡ ❞❡t❡❝çã♦ ❛♦ ❝♦♠❜✐♥❛r

♠❛✐s ❞❡ ✉♠❛ té❝♥✐❝❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦❀

✶✳ ■♥tr♦❞✉çã♦ ✺

• ❞❡t❡❝t❛r ❛ ✐♥tr✉sã♦ ❞❡ ✉♠ trá❢❡❣♦ ❞❡ r❡❞❡ ❛♥t❡s q✉❡ ❝❤❡❣✉❡ ❛♦ ❞❡st✐♥♦✱ ❡❧✐♠✐♥❛♥❞♦

❝❛r❛❝t❡ríst✐❝❛s ❞❡s♥❡❝❡ssár✐❛s ♥♦ ♣r♦❝❡ss♦ ❞❡ ❝❧❛ss✐✜❝❛çã♦✱ s❡♥❞♦ ✉♠ ❡♥❢♦q✉❡ ✐♠✲

♣♦rt❛♥t❡ ♣❛r❛ ❛ ❞❡t❡❝çã♦ ❡♠ t❡♠♣♦ r❡❛❧✳

✶✳✸ ❖r❣❛♥✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦

❖ r❡st❛♥t❡ ❞♦ tr❛❜❛❧❤♦ é ♦r❣❛♥✐③❛❞♦ ❝♦♠ ❛ ❡str✉t✉r❛ ❛ s❡❣✉✐r✳ ◆♦ ❈❛♣ít✉❧♦ ✷ é ❛♣r❡✲

s❡♥t❛❞♦ ♦ r❡❢❡r❡♥❝✐❛❧ t❡ór✐❝♦✱ ♦ q✉❛❧ ❞❡t❛❧❤❛ ♦s ❝♦♥❝❡✐t♦s ♠❛✐s ♣❡rt✐♥❡♥t❡s r❡❧❛❝✐♦♥❛❞♦s

❛ ❡st❡ tr❛❜❛❧❤♦ s♦❜r❡ r❡❞❡s ❞❡ ❝♦♠♣✉t❛❞♦r❡s✱ s❡❣✉r❛♥ç❛ ❡♠ r❡❞❡s ❞❡ ❝♦♠♣✉t❛❞♦r❡s✱

s✐st❡♠❛s ❞❡ ❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sã♦✱ ❞❡t❡❝çã♦ ❞❡ ❛♥♦♠❛❧✐❛s✱ té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❡

tr❛❜❛❧❤♦s r❡❧❛❝✐♦♥❛❞♦s✳

◆♦ ❈❛♣ít✉❧♦ ✸ é ❛♣r❡s❡♥t❛❞❛ ❛ ♠❡t♦❞♦❧♦❣✐❛ ❞♦ tr❛❜❛❧❤♦✱ ❞❡s❝r❡✈❡♥❞♦ ❛❧❣✉♠❛s

❜❛s❡s ❞❡ ❞❛❞♦s ❝♦♠ trá❢❡❣♦ ❞❡ r❡❞❡✱ ✐♥❝❧✉✐♥❞♦ ❛ ❜❛s❡ ❞❡ ❞❛❞♦s ♣r✐♥❝✐♣❛❧ ❝♦♥s✐❞❡r❛❞❛

♥❡st❡ ❡st✉❞♦✳ ❙ã♦ ❞❡s❝r✐t♦s t❛♠❜é♠✱ ♦s ♣❛ss♦s ♣❛r❛ ❛ ♣r❡♣❛r❛çã♦ ❞♦s ❞❛❞♦s ❛tr❛✈és ❞♦

♣r♦❝❡ss♦ ❞❡ ❉❡s❝♦❜❡rt❛ ❞❡ ❈♦♥❤❡❝✐♠❡♥t♦ ❡♠ ❇❛♥❝♦ ❞❡ ❉❛❞♦s ✭❑❉❉✮ ❡ ❝♦♠♦ ❢♦r❛♠

r❡❛❧✐③❛❞♦s ♦s t❡st❡s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❡ ❛s té❝♥✐❝❛s ✉s❛❞❛s✳

❊♠ s❡❣✉✐❞❛✱ ♥♦ ❈❛♣ít✉❧♦ ✹ sã♦ ♠♦str❛❞♦s ❡ ❞✐s❝✉t✐❞♦s ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s✳ ❊

♣♦r ✜♠✱ ♦ ❈❛♣ít✉❧♦ ✺ ❛♣r❡s❡♥t❛ ❛s ❝♦♥❝❧✉sõ❡s ❡ tr❛❜❛❧❤♦s ❢✉t✉r♦s✳

❈❛♣ít✉❧♦ ✷

❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦

◆❡st❡ ❝❛♣ít✉❧♦✱ sã♦ ❛♣r❡s❡♥t❛❞♦s ♣r✐♠❡✐r❛♠❡♥t❡ ♦s ❝♦♥❝❡✐t♦s ♠❛✐s ♣❡rt✐♥❡♥t❡s q✉❡ ♣❡r✲

♠✐t✐r❛♠ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦ ❝♦♠♦✱ r❡❞❡s ❞❡ ❝♦♠♣✉t❛❞♦r❡s✱ s❡❣✉r❛♥ç❛

❡♠ r❡❞❡s ❞❡ ❝♦♠♣✉t❛❞♦r❡s✱ s✐st❡♠❛s ❞❡ ❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sã♦✱ ❞❡t❡❝çã♦ ❞❡ ❛♥♦♠❛❧✐❛s

❡ té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦✳ ❆ s❡❣✉✐r sã♦ ❛♣r❡s❡♥t❛❞♦s ❛❧❣✉♥s tr❛❜❛❧❤♦s ❝♦rr❡❧❛t♦s✱ q✉❡

❢♦r❛♠ ✐♠♣♦rt❛♥t❡s ♣❛r❛ ❛♣r♦❢✉♥❞❛r s♦❜r❡ ♦ t❡♠❛ ❞❡s❡♥✈♦❧✈✐❞♦✳

✷✳✶ ❘❡❞❡s ❞❡ ❈♦♠♣✉t❛❞♦r❡s

◆♦ ✐♥í❝✐♦ ❞❡ s✉❛ ❡①✐stê♥❝✐❛✱ ❛s r❡❞❡s ❞❡ ❝♦♠♣✉t❛❞♦r❡s ❢♦r❛♠ ✉s❛❞❛s ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣♦r

♣❡sq✉✐s❛❞♦r❡s ✉♥✐✈❡rs✐tár✐♦s ♣❛r❛ ❡♥✈✐❛r ♠❡♥s❛❣❡♥s ❞❡ ❝♦rr❡✐♦ ❡❧❡trô♥✐❝♦ ❡✱ t❛♠❜é♠✱ ♣♦r

❢✉♥❝✐♦♥ár✐♦s ❞❡ ❡♠♣r❡s❛s ♣❛r❛ ❝♦♠♣❛rt✐❧❤❛r r❡❝✉rs♦s ❝♦♠♦ ✐♠♣r❡ss♦r❛s✳ ❆s r❡❞❡s ❞❡

❝♦♠♣✉t❛❞♦r❡s ❛❝❛❜❛r❛♠ ❝♦♠ ♦ ❛♥t✐❣♦ ♠♦❞❡❧♦ ❞❡ q✉❡ ❛♣❡♥❛s ✉♠ ❝♦♠♣✉t❛❞♦r ❛t❡♥❞✐❛ às

♥❡❝❡ss✐❞❛❞❡s ❞♦ ✉s✉ár✐♦ ♦✉ ❞❛ ♦r❣❛♥✐③❛çã♦✳ ❈♦♥t✉❞♦✱ ❡①✐st❡♠ ♠✉✐t❛s r❡❞❡s ♥♦ ♠✉♥❞♦

q✉❡ ❛♣r❡s❡♥t❛♠ ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ ❤❛r❞✇❛r❡ ❡ s♦❢t✇❛r❡✱ ♠❛s q✉❡ ♣r❡❝✐s❛♠ s❡ ❝♦♠✉♥✐❝❛r

❡♥tr❡ s✐✳ P❛r❛ q✉❡ ❡ss❡ ❞❡s❡❥♦ s❡ t♦r♥❡ r❡❛❧✐❞❛❞❡ é ♣r❡❝✐s♦ q✉❡ ❡st❛❜❡❧❡ç❛♠ ❝♦♥❡①õ❡s

❡♥tr❡ r❡❞❡s✱ ✐♥❝❧✉s✐✈❡ ✐♥❝♦♠♣❛tí✈❡✐s✳ ❊st❡ ❝♦♥❥✉♥t♦ ❞❡ r❡❞❡s ✐♥t❡r❝♦♥❡❝t❛❞❛s ❢♦r♠❛♠

✉♠❛ r❡❞❡ ♠❛✐s ❛♠♣❧❛✱ ✐♥t❡r❧✐❣❛❞❛ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ■♥t❡r♥❡t q✉❡ t❡♠ ❛❧❝❛♥❝❡ ❡♠

♥í✈❡❧ ♠✉♥❞✐❛❧ ❬❚❛♥❡♥❜❛✉♠✱ ✷✵✶✶❪✳

❉✉❛s ✐♠♣♦rt❛♥t❡s ❛rq✉✐t❡t✉r❛s sã♦ ♦ ♠♦❞❡❧♦ ❞❡ r❡❢❡rê♥❝✐❛ ❖❙■ ❝♦♠♣♦st♦ ♣♦r ✼

❝❛♠❛❞❛s✱ ❞❡s❡♥✈♦❧✈✐❞♦ ♣❡❧❛ ■❙❖ ✭■♥t❡r♥❛t✐♦♥❛❧ ❙t❛♥❞❛r❞s ❖r❣❛♥✐③❛t✐♦♥✮ ❝♦♠ ♦ ♦❜❥❡t✐✈♦

❞❡ ♣❛❞r♦♥✐③❛çã♦ ✐♥t❡r♥❛❝✐♦♥❛❧ ❞♦s ♣r♦t♦❝♦❧♦s ✉s❛❞♦s ♥❛s ✈ár✐❛s ❝❛♠❛❞❛s ❡ ♦ ♠♦❞❡❧♦

❚❈P✴■P q✉❡ s✉r❣✐✉ ❞❡s❞❡ ❛ ❆❘P❆◆❊❚ q✉❡ ❡r❛ ✉♠❛ r❡❞❡ ❞❡ ♣❡sq✉✐s❛❞♦r❡s ♣❛tr♦❝✐♥❛❞❛

♣❡❧♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❉❡❢❡s❛ ❞♦s ❊st❛❞♦s ❯♥✐❞♦s ✭❉♦❉✮ ❡✱ q✉❡ ♣♦st❡r✐♦r♠❡♥t❡ ❢♦✐

♠❡❧❤♦r❛❞♦ ❡ ❞❡✜♥✐❞♦ ❝♦♠♦ ✉♠ ♣❛❞rã♦

✻

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✼

❉❡♥tr❡ ❛s ❝❛♠❛❞❛s ❡ ❢✉♥çõ❡s ❞♦s ❞♦✐s ♠♦❞❡❧♦s✱ ❛ ❝❛♠❛❞❛ ■♥t❡r♥❡t ✭❝❛♠❛❞❛ ❞❡

❘❡❞❡✮ ❡ ❛ ❝❛♠❛❞❛ ❞❡ ❚r❛♥s♣♦rt❡ ♣♦ss✉❡♠ ❢✉♥çõ❡s s✐♠✐❧❛r❡s ♥♦s ❞♦✐s ♠♦❞❡❧♦s✳ ❆ ❝❛✲

♠❛❞❛ ❞❡ ❘❡❞❡ t❡♠ ♣♦r ❢✉♥çã♦ ❡♥tr❡❣❛r ♣❛❝♦t❡s ✭❞❛t❛❣r❛♠❛s✮ ♦♥❞❡ ❡❧❡s sã♦ ♥❡❝❡ssár✐♦s✱

♣♦❞❡♥❞♦ ❝❤❡❣❛r ❛té ♠❡s♠♦ ❡♠ ✉♠❛ ♦r❞❡♠ ❞✐❢❡r❡♥t❡✱ ✐♠♣♦rt❛♥❞♦✲s❡ ❝♦♠ ♦ r♦t❡❛♠❡♥t♦✱

♠❡s♠♦ ❡♠ ❝❛s♦ ❞❡ ❢❛❧❤❛s ❡♠ ❛❧❣✉♥s ♥ós ✭❡①✳✿ r♦t❡❛❞♦r❡s✮✳ ❆ ❝❛♠❛❞❛ ❞❡ ❚r❛♥s♣♦rt❡

♣❡r♠✐t❡ ❛ ❝♦♥✈❡rs❛çã♦ ❞♦s ♣❛r❡s ❞♦s ❤♦sts ❞❡ ♦r✐❣❡♠ ❡ ❞❡st✐♥♦✳

◆❛ ■♥t❡r♥❡t✱ ♦s ♣r♦t♦❝♦❧♦s ♠❛✐s ❝♦♠✉♥s sã♦ ♦ ■P ✭■♥t❡r♥❡t Pr♦t♦❝♦❧✮ ♣❛r❛ ❛ ❝❛✲

♠❛❞❛ ❞❡ ❘❡❞❡❀ ❡ ♦ ❚❈P ✭❚r❛♥s♠✐ss✐♦♥ ❈♦♥tr♦❧ Pr♦t♦❝♦❧✮ ❡ ♦ ❯❉P ✭❯s❡r ❉❛t❛❣r❛♠

Pr♦t♦❝♦❧✮ ♣❛r❛ ❛ ❝❛♠❛❞❛ ❞❡ ❚r❛♥s♣♦rt❡✳ ❖ ♠♦❞❡❧♦ ❚❈P✴■P ♥ã♦ t❡♠ ❛s ❝❛♠❛❞❛s ❞❡

s❡ssã♦ ♦✉ ❞❡ ❛♣r❡s❡♥t❛çã♦✱ ❛♦ ✐♥✈és ❞✐ss♦✱ ❛s ❛♣❧✐❝❛çõ❡s s✐♠♣❧❡s♠❡♥t❡ ✐♥❝❧✉❡♠ q✉❛✐sq✉❡r

❢✉♥çõ❡s ❞❡ s❡ssã♦ ❡ ❛♣r❡s❡♥t❛çã♦ q✉❡ ❢♦r❡♠ ♥❡❝❡ssár✐❛s ✭❬❚❛♥❡♥❜❛✉♠✱ ✷✵✶✶❪✮✳

✷✳✶✳✶ Pr♦t♦❝♦❧♦s ■P✱ ❯❉P ❡ ❚❈P

❖ ♣r♦t♦❝♦❧♦ ■P é ♦ ❡❧❡♠❡♥t♦ q✉❡ ♠❛♥té♠ ❛ ■♥t❡r♥❡t ✉♥✐❞❛✱ ♣❡r♠✐t✐♥❞♦ ♦ r♦t❡❛♠❡♥t♦ ❞❡

♣❛❝♦t❡s ❞❛ ♦r✐❣❡♠ ♣❛r❛ ♦ ❞❡st✐♥♦ s❡♠ ❣❛r❛♥t✐❛s✱ ✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞❡ ❡ss❛s ♠áq✉✐♥❛s

❡st❛r❡♠ ♥❛ ♠❡s♠❛ r❡❞❡ ♦✉ ❞❡ ❤❛✈❡r ♦✉tr❛s r❡❞❡s ❡♥tr❡ ❡❧❛s✳ ❖s r♦t❡❛❞♦r❡s ■P ❡♥❝❛✲

♠✐♥❤❛♠ ❝❛❞❛ ♣❛❝♦t❡ ♣❡❧❛ ■♥t❡r♥❡t✱ ♣♦r ✉♠ ❝❛♠✐♥❤♦ ❞❡ ✉♠ r♦t❡❛❞♦r ♣❛r❛ ♦ s❡❣✉✐♥t❡✱

❛té q✉❡ ♦ ❞❡st✐♥♦ s❡❥❛ ❛❧❝❛♥ç❛❞♦✳ ◆♦ ❞❡st✐♥♦✱ ❛ ❝❛♠❛❞❛ ❞❡ ❘❡❞❡ ❡♥tr❡❣❛ ♦s ❞❛❞♦s

à ❝❛♠❛❞❛ ❞❡ ❚r❛♥s♣♦rt❡✱ q✉❡ ♦s ♦❢❡r❡❝❡ ❛♦ ♣r♦❝❡ss♦ r❡❝❡♣t♦r✳ ❖ ♣r♦t♦❝♦❧♦ ■P ♠❛✐s

❝♦♠✉♠ ❛t✉❛❧♠❡♥t❡✱ é ♦ ■P ✈❡rsã♦ ✹ ✭■P✈✹✮✱ ❡♠ q✉❡ ✉♠ ❞❛t❛❣r❛♠❛ ■P✈✹ ❝♦♥s✐st❡ ❡♠

♣❛rt❡ ❞❡ ❝❛❜❡ç❛❧❤♦ ❡ ✉♠❛ ♣❛rt❡ ❞❡ ❞❛❞♦s✱ ❝♦♥❢♦r♠❡ ❛ ❋✐❣✉r❛ ✷✳✶✳ ❖ ❝❛❜❡ç❛❧❤♦ t❡♠

✉♠❛ ♣❛rt❡ ✜①❛ ❞❡ ✷✵ ❜②t❡s ❡ ✉♠❛ ♣❛rt❡ ♦♣❝✐♦♥❛❧ ❞❡ t❛♠❛♥❤♦ ✈❛r✐á✈❡❧ ❞❡ ❛té ✹✵ ❜②t❡s✳

❖ t❛♠❛♥❤♦ t♦t❛❧ ❞♦ ❞❛t❛❣r❛♠❛ é ❞❡ ✻✺✳✺✸✺ ❜②t❡s✱ ❝♦♥s✐❞❡r❛♥❞♦ ♦ ❝❛❜❡ç❛❧❤♦ ❡ ♦ ❝❛♠♣♦

❞❡ ❞❛❞♦s✳

❋✐❣✉r❛ ✷✳✶✳ ❖ ❝❛❜❡ç❛❧❤♦ ■P✈✹ ❬❚❛♥❡♥❜❛✉♠✱ ✷✵✶✶❪

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✽

❆ ■♥t❡r♥❡t ♣♦ss✉✐ ❞♦✐s ♣r♦t♦❝♦❧♦s ♣r✐♥❝✐♣❛✐s ♥❛ ❝❛♠❛❞❛ ❞❡ ❚r❛♥s♣♦rt❡✱ ♦ ❯❉P

❡ ♦ ❚❈P✳ ❖ ♣r♦t♦❝♦❧♦ ❯❉P é ♦ ♠❛✐s s✐♠♣❧❡s✱ ♥ã♦ ♦r✐❡♥t❛❞♦ à ❝♦♥❡①õ❡s✱ ❝❛♣❛③ ❞❡

❡♥✈✐❛r ❞❛t❛❣r❛♠❛s ■P ❡♥❝❛♣s✉❧❛❞♦s s❡♠ q✉❡ s❡❥❛ ♥❡❝❡ssár✐♦ ❡st❛❜❡❧❡❝❡r ✉♠❛ ❝♦♥❡①ã♦✳

❖ ❝❛❜❡ç❛❧❤♦ ❞❡ ✉♠ ♣❛❝♦t❡ ❯❉P é ❝♦♠♣♦st♦ ♣♦r ✽ ❜②t❡s✱ s❡❣✉✐❞♦ ♣❡❧❛ ❝❛r❣❛ út✐❧✱

♠♦str❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✷✳ ❊♠ s❡✉s ❝❛♠♣♦s t❡♠♦s ❛ ✏P♦rt❛ ❞❡ ♦r✐❣❡♠✑ ❡ ✏P♦rt❛ ❞❡

❞❡st✐♥♦✑ q✉❡ s❡r✈❡♠ ♣❛r❛ ✐❞❡♥t✐✜❝❛r ♦s ♣♦♥t♦s ❡①tr❡♠♦s ♥❛s ♠áq✉✐♥❛s ❞❡ ♦r✐❣❡♠ ❡

❞❡st✐♥♦✳ ❖ ✏❈♦♠♣r✐♠❡♥t♦ ❞♦ ❯❉P✑ ✐♥❝❧✉✐ ♦ ❝❛❜❡ç❛❧❤♦ ❞❡ ✽ ❜②t❡s ❡ ♦s ❞❛❞♦s✳ ❖

❝♦♠♣r✐♠❡♥t♦ ♠í♥✐♠♦ é ❞❡ ✽ ❜②t❡s ❡ ♦ ♠á①✐♠♦ é ❞❡ ✻✺✳✺✶✺ ❜②t❡s✱ ❞❡✈✐❞♦ ❛♦ ❧✐♠✐t❡

❞❡ t❛♠❛♥❤♦ ♥♦s ♣❛❝♦t❡s ■P✳ ❯♠ ❝❛♠♣♦ ♦♣❝✐♦♥❛❧ ❞❡ ✏❈❤❡❝❦s✉♠ ❞♦ ❯❉P✑ é ❢♦r♥❡❝✐❞♦

♣❛r❛ ❣❡r❛r ❝♦♥✜❛❜✐❧✐❞❛❞❡ ❡①tr❛✳ ❊❧❡ ❢❛③ ♦ ❝❤❡❝❦s✉♠ ❞♦ ❝❛❜❡ç❛❧❤♦✱ ❞♦s ❞❛❞♦s ❡ ❞❡ ✉♠

♣s❡✉❞♦❝❛❜❡ç❛❧❤♦ ❝♦♥❝❡✐t✉❛❧ ❞♦ ■P✳

❋✐❣✉r❛ ✷✳✷✳ ❖ ❝❛❜❡ç❛❧❤♦ ❯❉P ❬❚❛♥❡♥❜❛✉♠✱ ✷✵✶✶❪

❖ ♣r♦t♦❝♦❧♦ ❚❈P é ✉♠ ♣r♦t♦❝♦❧♦ ♦r✐❡♥t❛❞♦ à ❝♦♥❡①õ❡s✱ ❝♦♥✜á✈❡❧✱ q✉❡ ♣❡r♠✐t❡ ❛

❡♥tr❡❣❛ s❡♠ ❡rr♦s ❞❡ ✉♠ ✢✉①♦ ❞❡ ❜②t❡s✱ ♥♦ q✉❛❧ é ❢r❛❣♠❡♥t❛❞♦ ♥❛ ❡♥tr❛❞❛ ❡♠ ♠❡♥s❛❣❡♥s

❞✐s❝r❡t❛s ❡ ♣❛ss❛ ❝❛❞❛ ✉♠❛ ❞❡❧❛s ♣❛r❛ ❛ ❝❛♠❛❞❛ ❞❡ ❘❡❞❡ ❡✱ ♥♦ ❞❡st✐♥♦✱ ♦ ♣r♦❝❡ss♦ ❚❈P

r❡❝❡♣t♦r ✈♦❧t❛ ❛ ♠♦♥t❛r ❛s ♠❡♥s❛❣❡♥s r❡❝❡❜✐❞❛s ♥♦ ✢✉①♦ ❞❡ s❛í❞❛✳ ❖ ❚❈P t❛♠❜é♠

❝✉✐❞❛ ❞♦ ❝♦♥tr♦❧❡ ❞❡ ✢✉①♦✱ ✐♠♣❡❞✐♥❞♦ q✉❡ ✉♠ tr❛♥s♠✐ss♦r s♦❜r❡❝❛rr❡❣✉❡ ✉♠ r❡❝❡♣t♦r

❧❡♥t♦ ❝♦♠ ✉♠ ✈♦❧✉♠❡ ❞❡ s❡❣♠❡♥t♦s ♠❛✐♦r ❞♦ q✉❡ ❡❧❡ ♣♦❞❡ ♠❛♥✐♣✉❧❛r ❬❚❛♥❡♥❜❛✉♠✱

✷✵✶✶❪✳

❆s ❡♥t✐❞❛❞❡s tr❛♥s♠✐ss♦r❛s ❡ r❡❝❡♣t♦r❛s ❞♦ ❚❈P tr♦❝❛♠ ❞❛❞♦s ♥❛ ❢♦r♠❛ ❞❡ s❡❣✲

♠❡♥t♦s✳ ❯♠ s❡❣♠❡♥t♦ ❚❈P ❝♦♥s✐st❡ ❡♠ ✉♠ ❝❛❜❡ç❛❧❤♦ ✜①♦ ❞❡ ✷✵ ❜②t❡s ❡ ✉♠❛ ♣❛rt❡

♦♣❝✐♦♥❛❧✱ s❡❣✉✐❞♦ ♣♦r ✉♠❛ ♣❛rt❡ ❞❡ ❞❛❞♦s✳ ❖ s♦❢t✇❛r❡ ❚❈P ❞❡❝✐❞❡ q✉❛❧ ❞❡✈❡ s❡r ♦

s❡✉ t❛♠❛♥❤♦✱ ♥♦ ❡♥t❛♥t♦✱ ❞♦✐s ❢❛t♦r❡s r❡str✐♥❣❡♠ ♦ t❛♠❛♥❤♦ ❞❡❧❡s✳ Pr✐♠❡✐r♦✱ ❝❛❞❛

s❡❣♠❡♥t♦ ❚❈P ❞❡✈❡ ❝❛❜❡r ♥❛ ❝❛r❣❛ út✐❧ ❞♦ ■P✱ q✉❡ é ❞❡ ✻✺✳✺✶✺ ❜②t❡s ❡✱ s❡❣✉♥❞♦✱ ❝❛❞❛

❡♥❧❛❝❡ ❣❡r❛❧♠❡♥t❡ t❡♠ ✉♠❛ ✉♥✐❞❛❞❡ ♠á①✐♠❛ ❞❡ tr❛♥s❢❡rê♥❝✐❛ ✭▼❚❯ ✲▼❛①✐♠✉♠ ❚r❛♥s✲

❢❡r ❯♥✐t✮ ❡✱ ♦ s❡❣♠❡♥t♦ ❞❡✈❡ ❝❛❜❡r ♥❛ ▼❚❯ ❞♦ tr❛♥s♠✐ss♦r ❡ ❞♦ r❡❝❡♣t♦r✱ ❞❡ ♠♦❞♦

q✉❡ ♣♦ss❛ s❡r ❡♥✈✐❛❞♦ ❡ r❡❝❡❜✐❞♦ ❡♠ ✉♠ ú♥✐❝♦ ♣❛❝♦t❡ ♥ã♦ ❢r❛❣♠❡♥t❛❞♦✳ ◆❛ ♣rát✐❝❛✱

❛ ▼❚❯ ❣❡r❛❧♠❡♥t❡ t❡♠ ✶✳✺✵✵ ❜②t❡s✱ t❛♠❛♥❤♦ ❞❛ ❝❛r❣❛ út✐❧ ❞♦s q✉❛❞r♦s ❊t❤❡r♥❡t ❡✱

♣♦rt❛♥t♦✱ ❞❡✜♥❡ ♦ ❧✐♠✐t❡ s✉♣❡r✐♦r ❞❡ t❛♠❛♥❤♦ ❞♦s s❡❣♠❡♥t♦s ❬❚❛♥❡♥❜❛✉♠✱ ✷✵✶✶❪✳

P❛r❛ ✉♠ ♠❡❧❤♦r ❡♥t❡♥❞✐♠❡♥t♦✱ ❛ ❋✐❣✉r❛ ✷✳✸ ♠♦str❛ ♦s ❝❛♠♣♦s ❞♦ s❡❣♠❡♥t♦

❚❈P ❡✱ ❛❧❣✉♥s ❞❡❧❡s s❡rã♦ ❛♥❛❧✐s❛❞♦s✱ ♣♦✐s sã♦ ✐♠♣♦rt❛♥t❡s ♣❛r❛ ❡♥t❡♥❞❡r ♦ tr❛❜❛❧❤♦

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✾

❞❡s❡♥✈♦❧✈✐❞♦✳

❋✐❣✉r❛ ✷✳✸✳ ❖ ❝❛❜❡ç❛❧❤♦ ❚❈P ❬❚❛♥❡♥❜❛✉♠✱ ✷✵✶✶❪

❖s ❝❛♠♣♦s ✏P♦rt❛ ❞❡ ♦r✐❣❡♠✑ ❡ ✏P♦rt❛ ❞❡ ❞❡st✐♥♦✑ ✐❞❡♥t✐✜❝❛♠ ♦s ♣♦♥t♦s t❡r♠✐✲

♥❛✐s ❞❛ ❝♦♥❡①ã♦✱ ❞❛ ♠❡s♠❛ ❢♦r♠❛ q✉❡ ❞♦ ❯❉P✳ ❆ ♣♦rt❛ ❚❈P ♠❛✐s ♦ ❡♥❞❡r❡ç♦ ■P ❞❡

s❡✉ ❤♦st ❢♦r♠❛ ✉♠❛ ❡①tr❡♠✐❞❛❞❡ ❡①❝❧✉s✐✈❛ ❞❡ ✹✽ ❜✐ts✳ ❆s ❡①tr❡♠✐❞❛❞❡s ❞❡ ♦r✐❣❡♠ ❡

❞❡st✐♥♦ ❥✉♥t❛s ✐❞❡♥t✐✜❝❛♠ ❛ ❝♦♥❡①ã♦✳ ❖s ❝❛♠♣♦s ✏◆ú♠❡r♦ ❞❡ s❡q✉ê♥❝✐❛✑ ❡ ✏◆ú♠❡r♦ ❞❡

❝♦♥✜r♠❛çã♦✑ ❞❡s❡♠♣❡♥❤❛♠ s✉❛s ❢✉♥çõ❡s ❤❛❜✐t✉❛✐s✱ s❡♥❞♦ ♦ s❡❣✉♥❞♦ ❛ ❡s♣❡❝✐✜❝❛çã♦ ❞♦

♣ró①✐♠♦ ❜②t❡ ❡s♣❡r❛❞♦✳ ❖ ❝❛♠♣♦ ✏❈♦♠♣r✐♠❡♥t♦ ❞♦ ❝❛❜❡ç❛❧❤♦ ❚❈P✑ ✐♥❢♦r♠❛ q✉❛♥t❛s

♣❛❧❛✈r❛s ❞❡ ✸✷ ❜✐ts ❡①✐st❡♠ ♥♦ ❝❛❜❡ç❛❧❤♦ ❚❈P✳ ❊ss❛ ✐♥❢♦r♠❛çã♦ é ♥❡❝❡ssár✐❛✱ ♣❡❧♦ ❢❛t♦

❞♦ ❝❛❜❡ç❛❧❤♦ t❡r t❛♠❛♥❤♦ ✈❛r✐á✈❡❧✱ ❞❡✈✐❞♦ ❛♦ ❝❛♠♣♦ ✏❖♣çõ❡s✑✳ ❊♠ s❡❣✉✐❞❛✱ ❡①✐st❡ ✉♠

❝❛♠♣♦ ❞❡ ✹ ❜✐ts q✉❡ ♥ã♦ é ✉t✐❧✐③❛❞♦ ❡ ✽ ✢❛❣s ❞❡ ✶ ❜✐t ❬❚❛♥❡♥❜❛✉♠✱ ✷✵✶✶❪✳

❆s ✢❛❣s ❈❲❘ ✭❈♦♥❣❡st✐♦♥ ❲✐♥❞♦✇ ❘❡❞✉❝❡❞✮ ❡ ❊❈❊ ✭❊❈◆✲❊❝❤♦✮ sã♦ ✉s❛❞❛s

♣❛r❛ s✐♥❛❧✐③❛r ❝♦♥❣❡st✐♦♥❛♠❡♥t♦ ❛♦ ✉t✐❧✐③❛r ❊❈◆ ✭❊①♣❧✐❝✐t ❈♦♥❣❡st✐♦♥ ◆♦t✐✜❝❛t✐♦♥✮✳ ❆

❊❈❊ é ❞❡✜♥✐❞❛ ♣❛r❛ s✐♥❛❧✐③❛r ✉♠❛ ♠❡♥s❛❣❡♠ ❊❈◆✲❊❝❤♦ ❛ ✉♠ tr❛♥s♠✐ss♦r ❚❈P ♣❛r❛

s♦❧✐❝✐t❛r ❛ r❡❞✉çã♦ ❞❡ ✈❡❧♦❝✐❞❛❞❡ q✉❛♥❞♦ ♦ r❡❝❡♣t♦r ❚❈P r❡❝❡❜❡r ✉♠❛ ✐♥❞✐❝❛çã♦ ❞❡

❝♦♥❣❡st✐♦♥❛♠❡♥t♦ ❞❛ r❡❞❡✳ ❆ ✢❛❣ ❈❲❘ é ✉s❛❞❛ ♣❛r❛ s✐♥❛❧✐③❛r ✏❏❛♥❡❧❛ ❞❡ ❝♦♥❣❡st✐♦♥❛✲

♠❡♥t♦ r❡❞✉③✐❞❛✑ ❞♦ tr❛♥s♠✐ss♦r ❚❈P ♣❛r❛ ♦ r❡❝❡♣t♦r ❚❈P✱ ❞❡ ♠♦❞♦ q✉❡ ❡❧❡ s❛✐❜❛ q✉❡

♦ tr❛♥s♠✐ss♦r ❞✐♠✐♥✉✐✉ ❛ ✈❡❧♦❝✐❞❛❞❡ ❡ ♣♦❞❡ ♣❛r❛r ❞❡ ❡♥✈✐❛r ✉♠❛ ♠❡♥s❛❣❡♠ ❊❈◆✲❊❝❤♦

❬❚❛♥❡♥❜❛✉♠✱ ✷✵✶✶❪✳

❆ ✢❛❣ ❯❘● é ♣r❡❡♥❝❤✐❞❛ ❝♦♠ ♦ ✈❛❧♦r ✶ s❡ ♦ ❝❛♠♣♦ ✏P♦♥t❡✐r♦ ♣❛r❛ ✉r❣❡♥t❡✑ ❡st✐✈❡r

s❡♥❞♦ ✉s❛❞♦✳ ❖ ✏P♦♥t❡✐r♦ ♣❛r❛ ✉r❣❡♥t❡✑ é ✉s❛❞♦ ♣❛r❛ ✐♥❞✐❝❛r ✉♠ ❞❡s❧♦❝❛♠❡♥t♦ ❞❡ ❜②t❡s

❛ ♣❛rt✐r ❞♦ ♥ú♠❡r♦ ❞❡ s❡q✉ê♥❝✐❛ ❛t✉❛❧ ❡♠ q✉❡ ♦s ❞❛❞♦s ✉r❣❡♥t❡s ❞❡✈❡♠ s❡r ❡♥❝♦♥tr❛❞♦s✳

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✶✵

➚ ✢❛❣ ❆❈❑ é ❛tr✐❜✉í❞♦ ♦ ❜✐t ✶ ♣❛r❛ ✐♥❞✐❝❛r q✉❡ ♦ ✏◆ú♠❡r♦ ❞❡ ❝♦♥✜r♠❛çã♦✑ é ✈á❧✐❞♦✳

■ss♦ ❛❝♦♥t❡❝❡ ♣❛r❛ ❛ ♠❛✐♦r✐❛ ❞♦s s❡❣♠❡♥t♦s✳ ❙❡ ❆❈❑ ❢♦r ✐❣✉❛❧ ❛ ③❡r♦✱ s✐❣♥✐✜❝❛ q✉❡ ♦

s❡❣♠❡♥t♦ ♥ã♦ ❝♦♥té♠ ✉♠❛ ❝♦♥✜r♠❛çã♦ ❡ ❛ss✐♠ ♦ ❝❛♠♣♦ ✏◆ú♠❡r♦ ❞❡ ❝♦♥✜r♠❛çã♦✑ é

✐❣♥♦r❛❞♦ ❬❚❛♥❡♥❜❛✉♠✱ ✷✵✶✶❪✳

❆ ✢❛❣ P❙❍ ✐♥❞✐❝❛ ❞❛❞♦s ❝♦♠ P❯❙❍✱ ♥♦ q✉❛❧ ♦ r❡❝❡♣t♦r é s♦❧✐❝✐t❛❞♦ ❛ ❡♥tr❡❣❛r

♦s ❞❛❞♦s à ❛♣❧✐❝❛çã♦ ♠❡❞✐❛♥t❡ s✉❛ ❝❤❡❣❛❞❛✱ ❡♠ ✈❡③ ❞❡ ❛r♠❛③❡♥á✲❧♦s ❛té q✉❡ ✉♠ ❜✉✛❡r

❝♦♠♣❧❡t♦ t❡♥❤❛ s✐❞♦ r❡❝❡❜✐❞♦✳ ❆ ✢❛❣ ❘❙❚ é ✉t✐❧✐③❛❞❛ ♣❛r❛ r❡✐♥✐❝✐❛r ✉♠❛ ❝♦♥❡①ã♦ q✉❡

t❡♥❤❛ ✜❝❛❞♦ ❝♦♥❢✉s❛ ❞❡✈✐❞♦ ❛ ✉♠❛ ❢❛❧❤❛ ♥♦ ❤♦st ♦✉ ♣♦r q✉❛❧q✉❡r ♦✉tr❛ r❛③ã♦✳ ❆ ❘❙❚

t❛♠❜é♠ é ✉t✐❧✐③❛❞❛ ♣❛r❛ r❡❥❡✐t❛r ✉♠ s❡❣♠❡♥t♦ ✐♥✈á❧✐❞♦ ♦✉ ♣❛r❛ r❡❝✉s❛r ✉♠❛ t❡♥t❛t✐✈❛

❞❡ ❝♦♥❡①ã♦✳ ❊♠ ❣❡r❛❧✱ s❡ r❡❝❡❜❡r ✉♠ s❡❣♠❡♥t♦ ❝♦♠ ♦ ❜✐t ❘❙❚ ❛t✐✈❛❞♦✱ ♣♦❞❡ ✐♥❞✐❝❛r

❛❧❣✉♠ ♣r♦❜❧❡♠❛ ❬❚❛♥❡♥❜❛✉♠✱ ✷✵✶✶❪✳

❆s ❞❡♠❛✐s ✢❛❣s✱ ❙❨◆ ❡ ❋■◆✱ sã♦ ✉s❛❞❛s r❡s♣❡❝t✐✈❛♠❡♥t❡ ♣❛r❛ ♦ ❡st❛❜❡❧❡❝✐♠❡♥t♦

❡ ❡♥❝❡rr❛♠❡♥t♦ ❞❡ ❝♦♥❡①õ❡s✳ ❆ s♦❧✐❝✐t❛çã♦ ❞❡ ❝♦♥❡①ã♦ t❡♠ ❙❨◆❂✶ ❡ ❆❈❑❂✵ ✭❈❖◆✲

◆❊❈❚■❖◆ ❘❊◗❯❊❙❚ ✮ ❡ ❛ r❡s♣♦st❛ ❝♦♥té♠ ✉♠❛ ❝♦♥✜r♠❛çã♦ ❡✱ ♣♦rt❛♥t♦✱ ❙❨◆❂✶ ❡

❆❈❑❂✶ ✭❈❖◆◆❊❈❚■❖◆ ❆❈❈❊P❚❊❉✮✳ ❆ ✢❛❣ ❋■◆ ✐♥❞✐❝❛ q✉❡ ♦ tr❛♥s♠✐ss♦r ♥ã♦ t❡♠

♠❛✐s ❞❛❞♦s ♣❛r❛ tr❛♥s♠✐t✐r ❬❚❛♥❡♥❜❛✉♠✱ ✷✵✶✶❪✳

❖s ❞❡♠❛✐s ❝❛♠♣♦s✱ ✏❚❛♠❛♥❤♦ ❞❡ ❥❛♥❡❧❛✑ ✐♥❞✐❝❛ q✉❛♥t♦s ❜②t❡s ♣♦❞❡♠ s❡r ❡♥✈✐❛❞♦s

❛ ♣❛rt✐r ❞♦ ❜②t❡ ❝♦♥✜r♠❛❞♦✱ ♦ ✏❈❤❡❝❦s✉♠✑ q✉❡ é ❢♦r♥❡❝✐❞♦ ♣❛r❛ ❛✉♠❡♥t❛r ❛ ❝♦♥✜❛❜✐❧✐✲

❞❛❞❡✱ ❝♦♥❢❡r✐♥❞♦ ♦ ❝❤❡❝❦s✉♠ ❞♦ ❝❛❜❡ç❛❧❤♦✱ ❞♦s ❞❛❞♦s ❡ ❞♦ ♣s❡✉❞♦❝❛❜❡ç❛❧❤♦✱ ❡ ♦ ❝❛♠♣♦

✏❖♣çõ❡s✑ q✉❡ ❢♦✐ ♣r♦❥❡t❛❞♦ ♣❛r❛ ❢♦r♥❡❝❡r r❡❝✉rs♦s ❡①tr❛s✱ q✉❡ ♥ã♦ ❢♦r❛♠ ♣r❡✈✐st♦s ♥♦

❝❛❜❡ç❛❧❤♦ ❝♦♠✉♠✱ ♣♦❞❡♥❞♦ t❡r ❛té ✹✵ ❜②t❡s ❬❚❛♥❡♥❜❛✉♠✱ ✷✵✶✶❪✳

❊st❛ s❡çã♦ t❡✈❡ ♣♦r ♦❜❥❡t✐✈♦ ❛♣r❡s❡♥t❛r ❛❧❣✉♥s ❝♦♥❝❡✐t♦s q✉❡✱ ❛♣❡s❛r ❞❡ s❡r❡♠

❜ás✐❝♦s ❞❛ ár❡❛ ❞❡ ❘❡❞❡s ❞❡ ❈♦♠♣✉t❛❞♦r❡s✱ ❢♦r❛♠ ❡ss❡♥❝✐❛✐s ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦

❞❡st❡ tr❛❜❛❧❤♦✳ ■ss♦ ♣❡r♠✐t✐✉ ✉♠ ♠❛✐♦r ❡s❝❧❛r❡❝✐♠❡♥t♦ ❞❛s ✐♥❢♦r♠❛çõ❡s ♣r❡s❡♥t❡s ♥❛

❜❛s❡ ❞❡ ❞❛❞♦s ✉s❛❞❛ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❝❛♠♣♦s ❞♦s ♣r♦t♦❝♦❧♦s✱ ✢❛❣s ❡ st❛t✉s ❞❛s

❝♦♥❡①õ❡s✳

✷✳✷ ❙❡❣✉r❛♥ç❛ ❡♠ ❘❡❞❡s ❞❡ ❈♦♠♣✉t❛❞♦r❡s

❆ s❡❣✉r❛♥ç❛ ❡♠ r❡❞❡s ❞❡ ❝♦♠♣✉t❛❞♦r❡s ♣♦❞❡ s❡r ❞❡✜♥✐❞❛ ❝♦♠♦ ✉♠❛ s✐t✉❛çã♦ s❡♠ r✐s❝♦

♦✉ s❡♠ s❡♥s♦ ❞❡ ❛♠❡❛ç❛ ❡ é ❝❛r❛❝t❡r✐③❛❞❛ ❛tr❛✈és ❞❡ ❛❧❣✉♠❛s ♣r♦♣r✐❡❞❛❞❡s ❜ás✐❝❛s✱

❝♦♠♦ ❝♦♥✜❞❡♥❝✐❛❧✐❞❛❞❡✱ ✐♥t❡❣r✐❞❛❞❡✱ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡✱ ❛✉t❡♥t✐❝❛çã♦ ❡ ♦ ♥ã♦ r❡♣ú❞✐♦✳

❊♥q✉❛♥t♦ ❛ ❝♦♥✜❞❡♥❝✐❛❧✐❞❛❞❡ é ❛ ♣r♦♣r✐❡❞❛❞❡ ❞❡ ♣r♦t❡çã♦ ❞♦ ❝♦♥t❡ú❞♦ ❞❛ ✐♥❢♦r✲

♠❛çã♦ ♣❛r❛ ❛♣❡♥❛s ♦s ✉s✉ár✐♦s ❛✉t♦r✐③❛❞♦s✱ ❛ ✐♥t❡❣r✐❞❛❞❡ é ❛ ♣r♦♣r✐❡❞❛❞❡ ❞❡ ♣r♦t❡❣❡r ❛

✐♥❢♦r♠❛çã♦ ❝♦♥tr❛ ❛❧t❡r❛çõ❡s ♣♦r ✉s✉ár✐♦s ♥ã♦ ❛✉t♦r✐③❛❞♦s✳ ❚♦❞❛✈✐❛✱ ❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡

é ❛ ♣r♦♣r✐❡❞❛❞❡ q✉❡ ❣❛r❛♥t❡ q✉❡ ❛ ✐♥❢♦r♠❛çã♦ s❡♠♣r❡ ❡st❡❥❛ ❞✐s♣♦♥í✈❡❧ ♣❛r❛ ✉s♦ ❧❡❣í✲

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✶✶

t✐♠♦ ❡ ❛ ❛✉t❡♥t✐❝❛çã♦ t❡♠ ♣♦r ♦❜❥❡t✐✈♦ ❛ss❡❣✉r❛r q✉❡ ❛ ✐♥❢♦r♠❛çã♦ ♣r♦✈é♠ ❞❛s ❢♦♥t❡s

❡♥✉♥❝✐❛❞❛s✳ P♦r ✜♠✱ ♦ ♥ã♦ r❡♣ú❞✐♦ ✈✐s❛ ❣❛r❛♥t✐r q✉❡ ♦ ❛✉t♦r ❞❛ ✐♥❢♦r♠❛çã♦ ♥ã♦ ♥❡❣✉❡

t❡r r❡❛❧✐③❛❞♦ ❞❡t❡r♠✐♥❛❞❛ ❛çã♦ ❬❉♦✉❧✐❣❡r✐s ✫ ❙❡r♣❛♥♦s✱ ✷✵✵✼❪✳

❆t✉❛❧♠❡♥t❡ ♠✐❧❤❛r❡s ❞❡ ♣❡ss♦❛s ✉s❛♠ ❛s r❡❞❡s ♣❛r❛ ❡①❡❝✉t❛r ♦♣❡r❛çõ❡s ❜❛♥❝ár✐❛s✱

r❡❛❧✐③❛r ❝♦♠♣r❛s ❡ ♦✉tr❛s ❛t✐✈✐❞❛❞❡s✱ s✉r❣✐♥❞♦ ♣♦♥t♦s ❢❛❧❤♦s ❡ ❛ s❡❣✉r❛♥ç❛ t♦r♥♦✉✲s❡

✉♠ ♣r♦❜❧❡♠❛ ❞❡ ❣r❛♥❞❡s ♣r♦♣♦rçõ❡s✳

❆ ♠❛✐♦r ♣❛rt❡ ❞♦s ♣r♦❜❧❡♠❛s ❞❡ s❡❣✉r❛♥ç❛ é ❝❛✉s❛❞❛ ♣r♦♣♦s✐t❛❧♠❡♥t❡ ♣♦r ♣❡s✲

s♦❛s ♠❛❧✲✐♥t❡♥❝✐♦♥❛❞❛s✱ q✉❡ t❡♥t❛♠ ♦❜t❡r ❛❧❣✉♠ ❜❡♥❡❢í❝✐♦✳ ❆❧❣✉♥s ❞♦s ✐♥✈❛s♦r❡s ♠❛✐s

❝♦♠✉♥s sã♦ ♣❡ss♦❛s r❡ss❡♥t✐❞❛s ❝♦♠ ❛ ♦r❣❛♥✐③❛çã♦ ❛ q✉❡ ♣❡rt❡♥❝❡♠✳ ❖s s✐st❡♠❛s ❞❡

s❡❣✉r❛♥ç❛ ❞❡✈❡♠ s❡r ♣r♦❥❡t❛❞♦s t❡♥❞♦ ❡♠ ✈✐st❛ ❡ss❡ ❢❛t♦ ❡ ♥ã♦ ❛♣❡♥❛s ♣r♦❜❧❡♠❛s ❝♦♠♦

❡rr♦s ❞❡ ♣r♦❣r❛♠❛çã♦ ❬❚❛♥❡♥❜❛✉♠✱ ✷✵✶✶❪✳

❈♦♥t✉❞♦✱ ❛ ❛♠♣❧❛ ✈❛r✐❡❞❛❞❡ ❞❡ s✐st❡♠❛s ❡ t❡❝♥♦❧♦❣✐❛s q✉❡ ♣r❡❝✐s❛♠ ❡st❛r ♣r♦t❡✲

❣✐❞♦s t❡♥❞❡ ❛ s❡r ✉♠ ❞✐✜❝✉❧t❛❞♦r ♣❛r❛ ♦s ❛♥❛❧✐st❛s ❞❡ s❡❣✉r❛♥ç❛✳ ❆s ❡♠♣r❡s❛s ❣❛st❛♠

♠✐❧❤õ❡s ❞❡ ❞♦❧ár❡s ❡♠ ❡q✉✐♣❛♠❡♥t♦ ❡ ♣❡ss♦❛❧ ♣❛r❛ ♣r♦t❡❣❡r ✏❝♦✐s❛s✑ q✉❡ ♥ã♦ ♣r❡❝✐s❛♠

❞❡ ♣r♦t❡çã♦✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❝♦♥❝♦r❞❛♠ q✉❡ s❡✉s ✉s✉ár✐♦s✱ ❛❝✐❞❡♥t❛❧♠❡♥t❡ ♦✉ ♣♦r ✐♥✲

t❡♥çã♦✱ sã♦ s❡✉ ♠❛✐♦r ♣r♦❜❧❡♠❛ ❞❡ s❡❣✉r❛♥ç❛✱ ♣♦✐s ✉t✐❧✐③❛♠ ❞❡ ❢♦r♠❛ ✐♥❛♣r♦♣r✐❛❞❛ ♦s

r❡❝✉rs♦s ❞❛ ❡♠♣r❡s❛✱ ❝♦♠♦ ♠á ✉t✐❧✐③❛çã♦ ❞❡ s❡♥❤❛s ❞❡ ❛❝❡ss♦ ❡ r❡❛❧✐③❛çã♦ ❞❡ ❞♦✇♥❧♦❛❞s

❞❡ ✈ír✉s ❡ s♦❢t✇❛r❡s ✐♥❞❡✈✐❞♦s ❬❙t❛❧❧✐♥❣s✱ ✷✵✶✵❪✳

❆✐♥❞❛ ❛ss✐♠✱ ♦s ❞✐s♣♦s✐t✐✈♦s ❞❡ ✉s✉ár✐♦ ✜♥❛❧✱ ❣❡r❛❧♠❡♥t❡ sã♦ ♦s ♠❛✐s ❝♦♠✉♥s

❞❡ s❡r❡♠ ❛t❛❝❛❞♦s✱ ❡ ❛ ♠❛✐♦r✐❛ ❞❛s ❛♠❡❛ç❛s ♣♦❞❡r✐❛♠ s❡r r❡s♦❧✈✐❞❛s ♦✉ ❜❧♦q✉❡❛❞❛s

❝♦♠ s✐♠♣❧❡s ❛t✉❛❧✐③❛çõ❡s ❞❡ s✐st❡♠❛s✱ ❛♥t✐✈ír✉s ❡ ✜r❡✇❛❧❧s ♣❡ss♦❛✐s✳ ❉❡ss❡ ♠♦❞♦✱ ❝♦♠

❛ s❡❣✉r❛♥ç❛ ❞❡ r❡❞❡s ❞❡ ❝♦♠♣✉t❛❞♦r❡s✱ t❡♥t❛♠♦s ❡✈✐t❛r ♦ trá❢❡❣♦ s❡♠ ❛✉t♦r✐③❛çã♦ ❡

❡♥t❡♥❞❡r ❛ ♥❛t✉r❡③❛ ❞❛ ❛♠❡❛ç❛✱ ❛ ✜♠ ❞❡ ❛ss❡❣✉r❛r ❛s s✉❛s ♣r♦♣r✐❡❞❛❞❡s ❜ás✐❝❛s✳

✷✳✷✳✶ ❈❧❛ss✐✜❝❛çã♦ ❞❡ ❆t❛q✉❡s

❯♠ ♠♦❞♦ ❞❡ ❝❧❛ss✐✜❝❛r ♦s ❛t❛q✉❡s ❞❡ s❡❣✉r❛♥ç❛ é ❞❡✜♥✐❞♦ ♥❛ ❘❋❈ ✷✽✷✽✱ ♥❛ q✉❛❧

❝♦♥s✐❞❡r❛ ♦s ❛t❛q✉❡s ❝♦♠♦ ♣❛ss✐✈♦s ❡ ❛t✐✈♦s✳ ➚ ♠❡❞✐❞❛ q✉❡ ✉♠ ❛t❛q✉❡ ♣❛ss✐✈♦ t❡♥t❛

❛♣r❡♥❞❡r ♦✉ ✉t✐❧✐③❛r ✐♥❢♦r♠❛çõ❡s ❞♦ s✐st❡♠❛ s❡♠ ❛❢❡t❛r ♦s r❡❝✉rs♦s ❞♦ ♠❡s♠♦✱ ✉♠

❛t❛q✉❡ ❛t✐✈♦ t❡♥t❛ ❛❧t❡r❛r ♦s r❡❝✉rs♦s ❞♦ s✐st❡♠❛ ♦✉ ❛❢❡t❛r s✉❛ ♦♣❡r❛çã♦ ❬❙t❛❧❧✐♥❣s✱

✷✵✶✵❪✳

❉♦✐s t✐♣♦s ❞❡ ❛t❛q✉❡s ♣❛ss✐✈♦s ♠✉✐t♦ ❝♦♠✉♥s sã♦ ♦ ✈❛③❛♠❡♥t♦ ❞❡ ❝♦♥t❡ú❞♦ ❞❡

♠❡♥s❛❣❡♥s ❡ ❛ ❛♥á❧✐s❡ ❞❡ trá❢❡❣♦✱ q✉❡ ♣♦❞❡♠ s❡r ❡①❡♠♣❧✐✜❝❛❞♦s ❢❛❝✐❧♠❡♥t❡ q✉❛♥❞♦ ✉♠

❡✲♠❛✐❧ ♦✉ ✉♠ ❛rq✉✐✈♦ ❞❛ ♦r❣❛♥✐③❛çã♦ é tr❛♥s❢❡r✐❞♦ ♣❛r❛ ✉♠ t❡r❝❡✐r♦ ♥ã♦ ❛✉t♦r✐③❛❞♦✱ ❡

q✉❛♥❞♦ ♦ trá❢❡❣♦ ❞❛ r❡❞❡ é ❝❛♣t✉r❛❞♦ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ❡①tr❛✐r ✐♥❢♦r♠❛çõ❡s r❡❧❡✈❛♥t❡s

❞♦ trá❢❡❣♦✳

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✶✷

◆❡ss❡ t✐♣♦ ❞❡ ❛t❛q✉❡✱ ❛ ❞❡t❡❝çã♦ é ♠✉✐t♦ ❞✐❢í❝✐❧ ♣♦✐s ♥ã♦ ❡♥✈♦❧✈❡ q✉❛❧q✉❡r ❛❧✲

t❡r❛çã♦ ♥♦s ❞❛❞♦s✳ ❖ trá❢❡❣♦ ❞❡ ♠❡♥s❛❣❡♠ é ❡♥✈✐❛❞♦ ❡ r❡❝❡❜✐❞♦ ❞❡ ✉♠❛ ♠❛♥❡✐r❛

❛♣❛r❡♥t❡♠❡♥t❡ ♥♦r♠❛❧ ❡✱ ♦ r❡❝❡♣t♦r ❡ ♦ ❡♠✐ss♦r ♥ã♦ ♣❡r❝❡❜❡♠ q✉❡ t❡r❝❡✐r♦s ✐♥t❡r❝❡♣t❛✲

r❛♠ ❛ ♠❡♥s❛❣❡♠ ♦✉ q✉❡ ♦❜s❡r✈❛r❛♠ ♦ ♣❛❞rã♦ ❞♦ trá❢❡❣♦ tr❛♥s♠✐t✐❞♦ ❬❙t❛❧❧✐♥❣s✱ ✷✵✶✵❪✳

❯♠ ❡①❡♠♣❧♦ ♠✉✐t♦ ❝♦♠✉♠✱ ❡①❡♠♣❧✐✜❝❛❞♦ ♥♦s ✐♥❝✐❞❡♥t❡s ❞♦ ❈❊❘❚✳❜r ❬✷✵✶✹❪✱ sã♦ ♦s

❛t❛q✉❡s ❞❡ ✏s❝❛♥✑✱ q✉❡ r❡❛❧✐③❛ ✈❛rr❡❞✉r❛s ❡♠ r❡❞❡s ❞❡ ❝♦♠♣✉t❛❞♦r❡s✱ ❝♦♠ ♦ ✐♥t✉✐t♦

❞❡ ✐❞❡♥t✐✜❝❛r q✉❛✐s ❝♦♠♣✉t❛❞♦r❡s ❡stã♦ ❛t✐✈♦s ❡ q✉❛✐s s❡r✈✐ç♦s ❡stã♦ s❡♥❞♦ ❞✐s♣♦♥✐✲

❜✐❧✐③❛❞♦s ♣♦r ❡❧❡s✳ ➱ ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞♦ ♣♦r ❛t❛❝❛♥t❡s ♣❛r❛ ✐❞❡♥t✐✜❝❛r ♣♦t❡♥❝✐❛✐s

❛❧✈♦s✱ ♣♦✐s ♣❡r♠✐t❡ ❛ss♦❝✐❛r ♣♦ssí✈❡✐s ✈✉❧♥❡r❛❜✐❧✐❞❛❞❡s ❛♦s s❡r✈✐ç♦s ❤❛❜✐❧✐t❛❞♦s ❡♠ ✉♠

❝♦♠♣✉t❛❞♦r✳

❯♠❛ té❝♥✐❝❛ ♣❛r❛ ♠❛s❝❛r❛r ♦ ❝♦♥t❡ú❞♦✱ ♣r♦t❡❣❡♥❞♦✲♦✱ é ❛ ❝r✐♣t♦❣r❛✜❛ ✭q✉❡ ✈❡♠

❞❛s ♣❛❧❛✈r❛s ❣r❡❣❛s q✉❡ s✐❣♥✐✜❝❛♠ ✏❡s❝r✐t❛ s❡❝r❡t❛✑✮✱ ❡♠❜♦r❛ ❛✐♥❞❛ ♣❡r♠✐t❛ ❛ ❛♥á❧✐s❡ ❞❡

❛❧❣✉♠ ♣❛❞rã♦ ❞♦ trá❢❡❣♦✱ ❝♦♠♦ ♦r✐❣❡♠ ❡ ❞❡st✐♥♦ ❞❛ ♠❡♥s❛❣❡♠✱ t❛♠❛♥❤♦ ❞❛ ♠❡♥s❛❣❡♠✱

❞✉r❛çã♦✱ ❢r❡q✉ê♥❝✐❛✱ ❡t❝✳

❖s ❛t❛q✉❡s ❛t✐✈♦s✱ ♥♦ ❡♥t❛♥t♦✱ sã♦ ❝❛r❛❝t❡r✐③❛❞♦s ♣♦r ❛❧❣✉♠❛ ♠♦❞✐✜❝❛çã♦ ❞♦ ✢✉①♦

❞❡ ❞❛❞♦s tr❛♥s♠✐t✐❞♦✱ ♦✉ ❛té ♣❡❧❛ ❝r✐❛çã♦ ❞❡ ✉♠ ✢✉①♦ ❢❛❧s♦ ❡ ♣♦❞❡♠ s❡r s✉❜❞✐✈✐❞✐❞♦s

❡♠ q✉❛tr♦ ❝❛t❡❣♦r✐❛s✿ ❞❡ ❢❛❧s✐❞❛❞❡✱ ❞❡ r❡♣❡t✐çã♦✱ ❞❡ ♠♦❞✐✜❝❛çã♦ ❞❡ ♠❡♥s❛❣❡♥s ❡ ❞❡

♥❡❣❛çã♦ ❞❡ s❡r✈✐ç♦✳

❯♠ ❛t❛q✉❡ ❞❡ ❢❛❧s✐❞❛❞❡✱ ♣♦r ❡①❡♠♣❧♦✱ s❡q✉ê♥❝✐❛s ❞❡ ❛✉t❡♥t✐❝❛çã♦ sã♦ ❝❛♣t✉r❛❞❛s

❡ r❡♣❡t✐❞❛s ❛♣ós ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ❛✉t❡♥t✐❝❛çã♦ ✈á❧✐❞❛✱ ♦❝♦rr❡ q✉❛♥❞♦ ✉♠❛ ❡♥t✐❞❛❞❡

✜♥❣❡ s❡r ✉♠❛ ❡♥t✐❞❛❞❡ ❞✐❢❡r❡♥t❡ ❡✱ ♥♦r♠❛❧♠❡♥t❡ ✐♥❝❧✉✐ ✉♠❛ ❞❛s ♦✉tr❛s ❢♦r♠❛s ❞❡ ❛t❛q✉❡

❛t✐✈♦✱ ❝♦♠♦ ♦ ❛t❛q✉❡ ❞❡ r❡♣❡t✐çã♦✳ ◆❡ss❡ ❝❛s♦✱ ❛ ❝❛♣t✉r❛ ♣❛ss✐✈❛ ❞❡ ✉♠❛ ✉♥✐❞❛❞❡ ❞❡

❞❛❞♦s ❡ s✉❛ r❡tr❛♥s♠✐ssã♦ ♣♦❞❡♠ ♣r♦❞✉③✐r ✉♠ ❡❢❡✐t♦ ♥ã♦ ❛✉t♦r✐③❛❞♦ ❬❙t❛❧❧✐♥❣s✱ ✷✵✶✵❪✳

❖✉tr♦ ❛t❛q✉❡✱ ❛ ♠♦❞✐✜❝❛çã♦ ❞❡ ♠❡♥s❛❣❡♥s✱ s✐❣♥✐✜❝❛ q✉❡ ❛❧❣✉♠❛ ♣❛rt❡ ❞❡ ✉♠❛

♠❡♥s❛❣❡♠ ❧❡❣ít✐♠❛ é ❛❧t❡r❛❞❛✱ ♦✉ q✉❡ ❡ss❛s ♠❡♥s❛❣❡♥s sã♦ ❛tr❛s❛❞❛s ♦✉ r❡♦r❞❡♥❛❞❛s✱ ❛

✜♠ ❞❡ ♣r♦❞✉③✐r ✉♠ ❡❢❡✐t♦ ♥ã♦ ❛✉t♦r✐③❛❞♦✳ ❯♠ ❡①❡♠♣❧♦ s❡r✐❛ ❛ ❛❧t❡r❛çã♦ ❞❡ ✉♠ ❡✲♠❛✐❧

❡♠ q✉❡ ❝♦♥❝❡❞❡ ✉♠❛ ♣❡r♠✐ssã♦ ❞❡ ❛❝❡ss♦ ♣❛r❛ ❞❡t❡r♠✐♥❛❞♦ ❝♦❧❛❜♦r❛❞♦r✳ ◆❡st❡ ❝❛s♦✱

❛ ❛❧t❡r❛çã♦ ♣♦❞❡ s✐♠♣❧❡s♠❡♥t❡ ♥❡❣❛r ❡ss❛ ❛✉t♦r✐③❛çã♦ ♦✉ s✉❜st✐t✉✐r ♦ ♥♦♠❡ ❛✉t♦r✐③❛❞♦

♣♦r ✉♠ t❡r❝❡✐r♦ ❬❙t❛❧❧✐♥❣s✱ ✷✵✶✵❪✳

❆t❛q✉❡s q✉❡ ✈✐s❛♠ ❡s♣❡❝✐✜❝❛♠❡♥t❡ ♦ ❝♦♠♣r♦♠❡t✐♠❡♥t♦ ❞❡ s❡r✈✐❞♦r❡s ❲❡❜ ♦✉

❞❡s✜❣✉r❛çõ❡s ❞❡ ♣á❣✐♥❛s ♥❛ ■♥t❡r♥❡t t❛♠❜é♠ sã♦ ❛t❛q✉❡s ❛t✐✈♦s ❝♦♠✉♥s✱ ✐❞❡♥t✐✜❝❛✲

❞♦s ♣❡❧♦ ❈❊❘❚✳❜r ❬✷✵✶✹❪ ❝♦♠♦ ❛t❛q✉❡s ✏✇❡❜✑✳ ❖✉tr❛s ❝❛t❡❣♦r✐❛s ✐❞❡♥t✐✜❝❛❞❛s ♣❡❧♦

❈❊❘❚✳❜r ❬✷✵✶✹❪ sã♦ ❛s ✏✐♥✈❛sõ❡s✑✱ ❛s q✉❛✐s r❡s✉❧t❛♠ ♥♦ ❛❝❡ss♦ ♥ã♦ ❛✉t♦r✐③❛❞♦ ❛ ✉♠

❝♦♠♣✉t❛❞♦r ♦✉ r❡❞❡✱ ♣♦❞❡♥❞♦ s❡r ❝❧❛ss✐✜❝❛❞♦ ❝♦♠♦ ❛t✐✈♦ ♦✉ ♣❛ss✐✈♦ ❞❡♣❡♥❞❡♥❞♦ ❞❛

❛çã♦ ❞♦ ✐♥✈❛s♦r✱ ♦s ✏✇♦r♠s✑✱ q✉❡ sã♦ ❛t✐✈✐❞❛❞❡s ♠❛❧✐❝✐♦s❛s r❡❧❛❝✐♦♥❛❞❛s ❝♦♠ ♦ ♣r♦❝❡ss♦

❛✉t♦♠❛t✐③❛❞♦ ❞❡ ♣r♦♣❛❣❛çã♦ ❞❡ ❝ó❞✐❣♦s ♠❛❧✐❝✐♦s♦s ♥❛ r❡❞❡ ❡ ❛s ✏❢r❛✉❞❡s✑✱ q✉❡ ❡♥❣❧♦✲

❜❛♠ ❛s ♥♦t✐✜❝❛çõ❡s ❞❡ t❡♥t❛t✐✈❛s ❞❡ ❢r❛✉❞❡s✱ ♦✉ s❡❥❛✱ ❞❡ ✐♥❝✐❞❡♥t❡s ❡♠ q✉❡ ♦❝♦rr❡ ✉♠❛

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✶✸

t❡♥t❛t✐✈❛ ❞❡ ♦❜t❡r ✈❛♥t❛❣❡♠✳

❖s ❛t❛q✉❡s ❞❡ ♥❡❣❛çã♦ ❞❡ s❡r✈✐ç♦ ✭❉♦❙ ✲ ❉❡♥✐❛❧ ♦❢ ❙❡r✈✐❝❡✮ ✐♠♣❡❞❡♠ ♦✉ ✐♥✐❜❡♠

♦ ✉s♦ ♦✉ ♦ ❣❡r❡♥❝✐❛♠❡♥t♦ ♥♦r♠❛❧ ❞♦s r❡❝✉rs♦s ❞❡ ❝♦♠✉♥✐❝❛çã♦✱ ♣♦❞❡♥❞♦ t❡r ✉♠ ❛❧✈♦

❡s♣❡❝í✜❝♦ ♦✉ ✉♠ ❞✐stúr❜✐♦ ❞❡ t♦❞❛ ✉♠❛ r❡❞❡ ♦✉ s❡r✈✐❞♦r✱ s♦❜r❡❝❛rr❡❣❛♥❞♦ ♦s s❡✉s

r❡❝✉rs♦s✱ ❞❡ ♠♦❞♦ q✉❡ ❝♦♠♣r♦♠❡t❛ ♦ ❞❡s❡♠♣❡♥❤♦ ♦✉ ❝❛✉s❡ tr❛✈❛♠❡♥t♦ ❞❡ ❞❡t❡r♠✐♥❛❞♦

s❡r✈✐ç♦✳

❖s ❞♦✐s t✐♣♦s ❞❡ ❛t❛q✉❡s ❛♣r❡s❡♥t❛♠ ❝❛r❛❝t❡ríst✐❝❛s ♦♣♦st❛s✳ ❊♠❜♦r❛ ♦s ❛t❛q✉❡s

♣❛ss✐✈♦s sã♦ ❞✐❢í❝❡✐s ❞❡ ❞❡t❡❝t❛r✱ ♠❡❞✐❞❛s ❡stã♦ ❞✐s♣♦♥í✈❡✐s ♣❛r❛ ✐♠♣❡❞✐r s❡✉ s✉❝❡ss♦✳

P♦r ♦✉tr♦ ❧❛❞♦✱ ♦s ❛t❛q✉❡s ❛t✐✈♦s sã♦ ❞✐❢í❝❡✐s ❞❡ ♣r❡✈❡♥✐r ❬❙t❛❧❧✐♥❣s✱ ✷✵✶✵❪✳ ❆ss✐♠✱

✉♠ ♦❜❥❡t✐✈♦ ❝♦♠✉♠ é ✐♠♣❡❞✐r ♦ s✉❝❡ss♦ ❞♦s ❛t❛q✉❡s ❛♥t❡s q✉❡ ❛❝♦♥t❡ç❛♠✱ ❜❡♠ ❝♦♠♦

❞❡t❡❝t❛r ❡ r❡❝✉♣❡r❛r q✉❛❧q✉❡r ♣r❡❥✉í③♦ ❝❛✉s❛❞♦✱ ❝❛s♦ ♦❝♦rr❛♠✳

◆❡st❡ tr❛❜❛❧❤♦✱ ♦ trá❢❡❣♦ ❞❡ ✉♠ ❛♠❜✐❡♥t❡ ❞❡ r❡❞❡ ❝♦♥tr♦❧❛❞♦ ❢♦✐ ❝♦♥s✐❞❡r❛❞♦✱ ❞❡

♠♦❞♦ ❛ ❞❡t❡❝t❛r ♦s ❛t❛q✉❡s ♣❛ss✐✈♦s ♦✉ ❛t✐✈♦s✳ ❆♣❡s❛r ❞❛ ❞❡t❡❝çã♦ ♥ã♦ ❡s♣❡❝✐✜❝❛r

❝❛❞❛ t✐♣♦ ❞❡ ❛t❛q✉❡✱ ♣r♦❝✉r♦✉✲s❡ ❝❧❛ss✐✜❝❛r ❝❛❞❛ trá❢❡❣♦ tr❛♥s♠✐t✐❞♦ ♥❛ r❡❞❡ ❡♠ ✉♠❛

❛t✐✈✐❞❛❞❡ ✏♥♦r♠❛❧✑ ♦✉ ❡♠ ✉♠ ✏❛t❛q✉❡✑✳

✷✳✸ ❙✐st❡♠❛s ❞❡ ❉❡t❡❝çã♦ ❞❡ ■♥tr✉sã♦

❆ s❡❣✉r❛♥ç❛ ❡♠ r❡❞❡s ❞❡ ❝♦♠♣✉t❛❞♦r❡s ✈✐s❛ ❛ss❡❣✉r❛r ❛s ♣r♦♣r✐❡❞❛❞❡s ❜ás✐❝❛s ❞❡s❝r✐t❛s

❛♥t❡r✐♦r♠❡♥t❡✱ ❝♦♥t✉❞♦✱ ❡①✐st❡♠ ♠✉✐t♦s t✐♣♦s ❞❡ ❛t❛q✉❡s q✉❡ ✈✐s❛♠ ❜✉r❧❛r ❡ss❛s ♣r♦✲

♣r✐❡❞❛❞❡s✱ ❝♦♠♦ ❛❜✉s♦ ❞❡ ❧♦❣♦♥✱ ✐♥t❡r❝❡♣t❛çã♦ ♥ã♦ ❛✉t♦r✐③❛❞❛ ❞❡ ✐♥❢♦r♠❛çõ❡s ✭❡❛✈❡s✲

❞r♦♣♣✐♥❣✮✱ ♠❛s❝❛r❛♠❡♥t♦ ❞❡ ❡♥❞❡r❡ç♦s ❞❡ r❡❞❡ ✭s♣♦♦✜♥❣✮✱ r♦✉❜♦ ❞❡ s❡ssã♦ ✭❤✐❥❛❝❦✐♥❣✮✱

✐♥tr✉sõ❡s q✉❡ ✈✐s❛♠ ❛❝❡ss♦ ♥ã♦ ❛✉t♦r✐③❛❞♦✱ ❛t❛q✉❡s ❞❡ ♥❡❣❛çã♦ ❞❡ s❡r✈✐ç♦ ✭❉❡♥✐❛❧ ♦❢

❙❡r✈✐❝❡s ✲ ❉♦❙✮ ❡ ❞❡♠❛✐s ❛t❛q✉❡s ♥♦ ♥í✈❡❧ ❞❡ ❛♣❧✐❝❛çã♦ ❝♦♠♦ ✈ír✉s✱ tr♦❥❛♥s✱ ❡♥tr❡ ♦✉tr♦s

❬❉♦✉❧✐❣❡r✐s ✫ ❙❡r♣❛♥♦s✱ ✷✵✵✼❪✳

❊♥tr❡ ❡ss❡s t✐♣♦s ❞❡ ❛t❛q✉❡s✱ ❛s ✐♥tr✉sõ❡s sã♦ ❛❧❣✉♠❛s ❞❛s ❢♦r♠❛s ❞❡ ❛♠❡❛ç❛s ♠❛✐s

❞✐✈✉❧❣❛❞❛s ❡✱ q✉❡ tê♠ t✐❞♦ ✉♠❛ ❣r❛♥❞❡ ❛t❡♥çã♦ ❞❛ ✐♥❞ústr✐❛ ❡ ❞❡ ♣❡sq✉✐s❛s ♥♦s ú❧t✐♠♦s

❛♥♦s ❬❙t❛❧❧✐♥❣s✱ ✷✵✶✵❪✳ P♦rt❛♥t♦✱ ♦s s✐st❡♠❛s ❞❡ ❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sã♦ tê♠ s✉r❣✐❞♦ ❝♦♠

♦ ✐♥t✉✐t♦ ❞❡ ❝♦♠❜❛t❡r t❛✐s ❛♠❡❛ç❛s✳

P❛r❛ ♠❡❧❤♦r ❡♥t❡♥❞❡r♠♦s s♦❜r❡ ♦s ❙✐st❡♠❛s ❞❡ ❉❡t❡❝çã♦ ❞❡ ■♥tr✉sã♦ ✭❙❉■s✮✱

❞❡✈❡♠♦s ❛✐♥❞❛ ❝♦♥❤❡❝❡r ❛s ❢♦r♠❛s ❞❡ ❛♠❡❛ç❛s q✉❡ ❛t✐♥❣❡♠ ♦s s✐st❡♠❛s ❝♦♠♣✉t❛❝✐♦♥❛✐s✳

❊♠ r❡❧❛çã♦ à ♦r✐❣❡♠ ❞❡ ❛♠❡❛ç❛s✱ ♦s ✐♥tr✉s♦s ♣♦t❡♥❝✐❛✐s ♣♦❞❡♠ s❡r ❝❧❛ss✐✜❝❛❞♦s ❡♠ ❞✉❛s

❝❛t❡❣♦r✐❛s ❬❩❤❛♥❣ ❡t ❛❧✳✱ ✷✵✵✶❪✿

• ■♥tr✉s♦s ❊①t❡r♥♦s✿ ❖ ❛t❛q✉❡ é ❧❛♥ç❛❞♦ ♣♦r ✉♠ ✉s✉ár✐♦ ❞❡ ❝♦♠♣✉t❛❞♦r ♥ã♦ ❛✉✲

t♦r✐③❛❞♦✱ ✉t✐❧✐③❛♥❞♦ té❝♥✐❝❛s ❝♦♠♦ r♦✉❜♦ ♦✉ ✈✐♦❧❛çõ❡s ❞❡ s❡♥❤❛✱ ✈✉❧♥❡r❛❜✐❧✐❞❛❞❡s

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✶✹

❞♦ s✐st❡♠❛✱ ♠ás ❝♦♥✜❣✉r❛çõ❡s ♦✉ té❝♥✐❝❛s ❞❡ ❡♥❣❡♥❤❛r✐❛ s♦❝✐❛❧✱ ❝♦♠ ♦ ♦❜❥❡t✐✈♦

❞❡ ♦❜t❡r ♦ ❛❝❡ss♦ ❛♦s ❝♦♠♣✉t❛❞♦r❡s✳

• ■♥tr✉s♦s ■♥t❡r♥♦s✿ ❖ ✐♥tr✉s♦ ♣♦ss✉✐ ✉♠ ❛❝❡ss♦ ❧❡❣ít✐♠♦ ❛♦ s✐st❡♠❛✱ ♠❛s ✉t✐❧✐③❛ ❛❧✲

❣✉♠❛s ❞❛s té❝♥✐❝❛s ♠❡♥❝✐♦♥❛❞❛s ❛♥t❡r✐♦r♠❡♥t❡ ♣❛r❛ ♦❜t❡r ♣r✐✈✐❧é❣✐♦s ❛❞✐❝✐♦♥❛✐s✱

❛ ✜♠ ❞❡ ✉s❛r ❞❡ ❢♦r♠❛ ✐♥❛♣r♦♣r✐❛❞❛ ♦✉ ❝❛✉s❛r ❞❛♥♦s ❛♦s ❞❛❞♦s✳ ❊ss❡ t✐♣♦ ❞❡

❛t❛q✉❡ é ♦ ♠❛✐s ❝♦♠✉♠ ❞❡♥tr♦ ❞❛s ♦r❣❛♥✐③❛çõ❡s✳

❉❡ss❛ ❢♦r♠❛✱ é ♥❡❝❡ssár✐♦ ❞❡t❡❝t❛r ❛♠❜♦s ♦s t✐♣♦s ❞❡ ✐♥tr✉sã♦✱ s❡♥❞♦ ♦s ❙❉■s

❝♦♥s✐❞❡r❛❞♦s ✉♠❛ s❡❣✉♥❞❛ ❧✐♥❤❛ ❞❡ ❞❡❢❡s❛ q✉❡ ❜✉s❝❛ ♣❡❧♦ ♠❡♥♦s ♠✐♥✐♠✐③❛r ♦s ❞❛♥♦s

♦❝❛s✐♦♥❛❞♦s ♣❡❧❛s ✐♥tr✉sõ❡s✳ ❊ss❡ t✐♣♦ ❞❡ s✐st❡♠❛ ♣♦ss✉✐ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❞❡t❡❝t❛r ❡

♣r❡✈❡♥✐r ❞✐✈❡rs❛s ❢♦r♠❛s ❞❡ ❛♠❡❛ç❛s✱ s❡♥❞♦ ♥❡ss❡ ❝❛s♦ ✉♠❛ ❞❡ s✉❛s ♣r✐♥❝✐♣❛✐s ✈❛♥t❛✲

❣❡♥s✳ ◆♦ ❡♥t❛♥t♦✱ ❛s té❝♥✐❝❛s ❡ ♦s ♣❛❞rõ❡s ❞❡ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦s ✐♥tr✉s♦s ❡stã♦ ❡♠

❝♦♥st❛♥t❡ ❛❧t❡r❛çã♦ ❡ ♦s ❛t❛q✉❡s ❡stã♦ ❝❛❞❛ ✈❡③ ♠❛✐s s♦✜st✐❝❛❞♦s ❬❙t❛❧❧✐♥❣s✱ ✷✵✶✵❪✳

◆❡ss❡ t✐♣♦ ❞❡ s✐st❡♠❛✱ ❛s ✐♥❢♦r♠❛çõ❡s ❝♦❧❡t❛❞❛s ❞❡ ✈ár✐♦s ❧♦❝❛✐s sã♦ ❛♥❛❧✐s❛❞❛s✱

❝♦♠♦ ✉♠ ❝♦♠♣✉t❛❞♦r ✭❙❉■ ❜❛s❡❛❞♦ ❡♠ ❤♦st✮ ♦✉ r❡❞❡ ✭❙❉■ ❜❛s❡❛❞♦ ❡♠ r❡❞❡✮ ♣❛r❛

✐❞❡♥t✐✜❝❛r ❛s ♣♦ssí✈❡✐s ❜r❡❝❤❛s ❞❡ s❡❣✉r❛♥ç❛✳ ❊♠ ✉♠❛ r❡❞❡✱ ♣♦r ❡①❡♠♣❧♦✱ ♦ ❙❉■ ♣♦❞❡

❡st❛r ❧♦❝❛❧✐③❛❞♦ ❡♠ ✉♠ s✇✐t❝❤ ♦✉ r♦t❡❛❞♦r ❡ ♠♦♥✐t♦r❛ ♦ trá❢❡❣♦ ❡♠ ♠♦❞♦ ♣r♦♠ís❝✉♦✱

❝♦♠♦ ✉♠ s♥♥✐❢❡r✳ ❖s ♣❛❝♦t❡s ❞❛ r❡❞❡ sã♦ ❡♥tã♦ ❝♦❧❡t❛❞♦s ❡ ❛♥❛❧✐s❛❞♦s ♣❛r❛ ✈✐♦❧❛çõ❡s ❞❡

r❡❣r❛s ❛ ♣❛rt✐r ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❞❡ r❡❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ ♣❛❞rõ❡s✳ ◗✉❛♥❞♦ ❡ss❛s ✈✐♦❧❛çõ❡s

sã♦ ❞❡t❡❝t❛❞❛s✱ ♦ ❙❉■ r❡❛❧✐③❛ ❞❡t❡r♠✐♥❛❞❛ ❛çã♦✱ ❝♦♠♦ ✉♠❛ ❡♠✐ssã♦ ❞❡ ❛❧❡rt❛ ❬P❛t❝❤❛

✫ P❛r❦✱ ✷✵✵✼❪✳ ❈❛s♦ ❡st❡ s✐st❡♠❛ ✜❧tr❡ ♦ trá❢❡❣♦ s✉s♣❡✐t♦✱ é ❝♦♥s✐❞❡r❛❞♦ t❛♠❜é♠ ✉♠

s✐st❡♠❛ ❞❡ ♣r❡✈❡♥çã♦ ❞❡ ✐♥tr✉sõ❡s ❬❉♦✉❧✐❣❡r✐s ✫ ❙❡r♣❛♥♦s✱ ✷✵✵✼❪✳

❉❡ ♠♦❞♦ ❣❡r❛❧ ♦ t❡r♠♦ ■❉❙✴■P❙ ✭■♥tr✉s✐♦♥ ❉❡t❡❝t✐♦♥ ❙②st❡♠✴■♥tr✉s✐♦♥ Pr❡✈❡♥✲

t✐♦♥ ❙②st❡♠✮ é ❜❛st❛♥t❡ ✉t✐❧✐③❛❞♦ ❝♦♠❡r❝✐❛❧♠❡♥t❡ ♣❛r❛ ✐♥❞✐❝❛r q✉❡ ♦ s✐st❡♠❛✱ ❛❧é♠ ❞❡

r❡❛❧✐③❛r ❛ ❞❡t❡❝çã♦✱ r❡❛❧✐③❛ ♦s ✜❧tr♦s ♥❡❝❡ssár✐♦s✳

❈♦♠♦ ❡①❡♠♣❧♦✱ ❛ ❋✐❣✉r❛ ✷✳✹ ♠♦str❛ ✉♠ ❝❡♥ár✐♦ ❞❡ r❡❞❡ ❝♦♠ ✈ár✐♦s s❡♥s♦r❡s ❞❡

❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sã♦✱ ♦✉ s❡❥❛✱ ✈ár✐♦s ♣♦♥t♦s ❞❡ ❝♦❧❡t❛ ❞❡ ✐♥❢♦r♠❛çõ❡s✱ ❞✐s♣♦st♦s ❡♠

❝❛❞❛ s❡❣♠❡♥t♦ ❞❡ r❡❞❡✱ ♠♦♥✐t♦r❛♥❞♦ ♦ trá❢❡❣♦ ♣❛ss❛♥t❡✳

❯♠ ❙❉■ ❛✐♥❞❛ ♣♦❞❡ s❡r ❝❛r❛❝t❡r✐③❛❞♦ ♣❡❧❛ ❢♦r♠❛ ❝♦♠♦ ❛♥❛❧✐s❛ ❛s ✐♥❢♦r♠❛çõ❡s✱

s❡❥❛ ❞❡ ❢♦r♠❛ ❝❡♥tr❛❧✐③❛❞❛ ♦✉ ❞❡s❝❡♥tr❛❧✐③❛❞❛✳ ❊♠ ✉♠ ❙❉■ ❝❡♥tr❛❧✐③❛❞♦✱ ♦ ♠♦♥✐t♦r❛✲

♠❡♥t♦✱ ❞❡t❡❝çã♦ ❡ ❛s ✐♥❢♦r♠❛çõ❡s r❡♣♦rt❛❞❛s sã♦ ❝♦♥tr♦❧❛❞❛s ❞✐r❡t❛♠❡♥t❡ ❞❡ ✉♠ ❧♦❝❛❧

❝❡♥tr❛❧✱ ❡♥q✉❛♥t♦ q✉❡ ❡♠ ✉♠ ❙❉■ ❞❡s❝❡♥tr❛❧✐③❛❞♦✱ ♦ ♠♦♥✐t♦r❛♠❡♥t♦ ❡ ❛ ❞❡t❡❝çã♦ sã♦

❝♦♥tr♦❧❛❞♦s ❛ ♣❛rt✐r ❞❡ ✉♠ ♥ó✱ ♦ q✉❛❧ r❡♣♦rt❛ ❤✐❡r❛rq✉✐❝❛♠❡♥t❡ ♣❛r❛ ✉♠ ♦✉ ♠❛✐s ❧♦❝❛✐s

❝❡♥tr❛✐s ❬❆❧✲❏❛♥❛❜✐ ✫ ❙❛❡❡❞✱ ✷✵✶✶❪✳

❈♦♥❢♦r♠❡ ♦ t✐♣♦ ❞❡ ❞❡t❡❝çã♦ r❡❛❧✐③❛❞❛✱ ♦s ❙❉■s ♣♦❞❡♠ s❡r ❝❧❛ss✐✜❝❛❞♦s ❡♠ três

t✐♣♦s ❝♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ❡♠ ❩❤❛♥❣ ❡t ❛❧✳ ❬✷✵✵✶❪ ❡ ▼❛r❤✉s✐♥ ❡t ❛❧✳ ❬✷✵✵✽❪✳

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✶✺

❋✐❣✉r❛ ✷✳✹✳ ❯♠ ❝❡♥ár✐♦ ❞❡ r❡❞❡ ❝♦♠ s❡♥s♦r❡s ♣❛r❛ ❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sã♦ ❬❑✉r♦s❡✫ ❘♦ss✱ ✷✵✶✵❪

• ❉❡t❡❝çã♦ ❜❛s❡❛❞❛ ❡♠ ❛❜✉s♦ ♦✉ r❡❣r❛s ✭r✉❧❡✲❜❛s❡❞ ✴ ♠✐s✉s❡ ❞❡t❡❝t✐♦♥✮✿ ♣r♦❝✉r❛

♣♦r té❝♥✐❝❛s ❝♦♥❤❡❝✐❞❛s ✭❛ss✐♥❛t✉r❛s✮ ♦✉ ✈✉❧♥❡r❛❜✐❧✐❞❛❞❡s ❞♦ s✐st❡♠❛✳

• ❉❡t❡❝çã♦ ❜❛s❡❛❞❛ ❡♠ ❛♥♦♠❛❧✐❛s ✭❛♥♦♠❛❧②✲❜❛s❡❞ ❞❡t❡❝t✐♦♥✮✿ ❝r✐❛ ✉♠ ♣❡r✜❧ ❞❡

trá❢❡❣♦ ❡♥q✉❛♥t♦ ♦❜s❡r✈❛ ♦ trá❢❡❣♦ ❡♠ ♦♣❡r❛çã♦ ♥♦r♠❛❧ ❡ ❞❡t❡❝t❛ ✐♥tr✉sõ❡s✱ ♣r♦✲

❝✉r❛♥❞♦ ♣♦r ❝❛❞❡✐❛s ❞❡ ♣❛❝♦t❡ q✉❡ sã♦ ❡st❛t✐st✐❝❛♠❡♥t❡ ✐♥❝♦♠✉♥s✳

• ❉❡t❡❝çã♦ ❤í❜r✐❞❛ ✭❤②❜r✐❞ ❞❡t❡❝t✐♦♥✮✿ ❝♦♠❜✐♥❛ ♦ ✉s♦ ❞♦s ♠♦❞❡❧♦s ❜❛s❡❛❞♦s ❡♠

❛❜✉s♦ ❡ ❛♥♦♠❛❧✐❛s✱ ♣♦❞❡♥❞♦ ❛❧❝❛♥ç❛r ♦ ♠❡❧❤♦r ❞❛s ❞✉❛s ❛❜♦r❞❛❣❡♥s✳

❈♦♠❡r❝✐❛❧♠❡♥t❡ ♦s ❙❉■s sã♦ ♣r❡❞♦♠✐♥❛♥t❡♠❡♥t❡ ❜❛s❡❛❞♦s ❡♠ ❞❡t❡❝çã♦ ♣♦r ❛ss✐✲

♥❛t✉r❛s✳ ❊♠ ❝♦♥tr❛st❡ ❝♦♠ ♦s s✐st❡♠❛s ♣r❡❞♦♠✐♥❛♥t❡s✱ ♦s ❙❉■s ❜❛s❡❛❞♦s ❡♠ ❛♥♦♠❛❧✐❛s

sã♦ ❜❛st❛♥t❡ ❛tr❛t✐✈♦s ❝♦♥❝❡✐t✉❛❧♠❡♥t❡ ♣❡❧♦ ❢❛t♦ ❞❡ t❛♠❜é♠ ♣♦❞❡r❡♠ ❞❡t❡❝t❛r ❛t❛q✉❡s

❞❡s❝♦♥❤❡❝✐❞♦s ❡ ❞♦ ✏❞✐❛ ③❡r♦✑ ✭❢❛❧❤❛s ❝♦♥❤❡❝✐❞❛s✱ ♠❛s ♥ã♦ ❝♦rr✐❣✐❞❛s✮✳ ❊♥tr❡t❛♥t♦✱ ❡ss❡

t✐♣♦ ❞❡ s✐st❡♠❛ ♣♦ss✉✐ ♣r♦❜❧❡♠❛s q✉❡ ♦ ✐♠♣❡❞❡ ❞❡ s❡r ❧❛r❣❛♠❡♥t❡ ❛❞♦t❛❞♦✱ t❛✐s ❝♦♠♦

❛❧t♦ ♣❡r❝❡♥t✉❛❧ ❞❡ ❛❧❛r♠❡s ❢❛❧s♦s✱ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ ♣❛r❛ ♠❛✐♦r❡s ✈❡❧♦❝✐❞❛❞❡s✱ ♣r♦t❡çã♦ ❡♠

t❡♠♣♦ r❡❛❧✱ ❡t❝ ❬P❛t❝❤❛ ✫ P❛r❦✱ ✷✵✵✼❪✳

P❛r❛ ❡①❡♠♣❧✐✜❝❛r✱ ❛❧❣✉♥s s✐st❡♠❛s ❝♦♠❡r❝✐❛✐s ❝♦♠♦ ♦ ❋♦rt✐●❛t❡ ❋✐r❡✇❛❧❧ ❞❛ ❋♦rt✐✲

♥❡t ❡ ♦ ❆❦❡r ❋✐r❡✇❛❧❧ ❞❛ ❆❦❡r ❙❡❝✉r✐t② ❙♦❧✉t✐♦♥s ♣♦ss✉❡♠ ❞✐✈❡rs♦s s❡r✈✐ç♦s ✐♥t❡❣r❛❞♦s✱

❛❧é♠ ❞❡ ✉♠❛ ✐♥t❡r❢❛❝❡ ❞❡ ❣❡r❡♥❝✐❛♠❡♥t♦ ✉♥✐✜❝❛❞❛ ❞❡ ❛♠❡❛ç❛s✱ s❡♥❞♦ ❝♦♥❤❡❝✐❞♦s ❝♦♠♦

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✶✻

❯❚▼ ✭❯♥✐✜❡❞ ❚❤r❡❛t ▼❛♥❛❣❡♠❡♥t✮✳ ❖ ♠ó❞✉❧♦ ❞❡ ■❉❙✴■P❙ ❞❡ss❡s s✐st❡♠❛s ✉t✐❧✐③❛ ❛

❛❜♦r❞❛❣❡♠ ❞❡ ❞❡t❡❝çã♦ ❤í❜r✐❞❛ ❡ sã♦ ❝❡♥tr❛❧✐③❛❞♦s✱ ♣♦✐s t♦❞♦ ♦ ♣r♦❝❡ss❛♠❡♥t♦✱ ♠♦♥✐✲

t♦r❛♠❡♥t♦ ❡ ❛s ✐♥❢♦r♠❛çõ❡s r❡♣♦rt❛❞❛s sã♦ r❡❛❧✐③❛❞❛s ❧♦❝❛❧♠❡♥t❡✳

❊♥tr❡ ❛❧❣✉♥s ❞♦s ♦✉tr♦s s❡r✈✐ç♦s ♦❢❡r❡❝✐❞♦s ♣♦r ❡st❡s s✐st❡♠❛s ❡stã♦✿ ✜❧tr♦s ❞❡

♣❛❝♦t❡s ❝♦♠ ❝♦♥tr♦❧❡ ❞❡ ❡st❛❞♦✱ ♦s q✉❛✐s ❛♥❛❧✐s❛♠ ♦ ❝♦♥t❡ú❞♦ ❞♦s ❝❛❜❡ç❛❧❤♦s ■P ❡

❚❈P✴❯❉P✱ ❡ ♦s ❣❛t❡✇❛②s ❞❡ ❛♣❧✐❝❛çã♦✱ ❝♦♥❤❡❝✐❞♦s t❛♠❜é♠ ❝♦♠♦ ♣r♦①✐❡s✱ ♦s q✉❛✐s

t♦♠❛♠ ❞❡❝✐sõ❡s ❝♦♠ ❜❛s❡ ❡♠ ❞❛❞♦s ❞❡ ❞❡t❡r♠✐♥❛❞❛ ❛♣❧✐❝❛çã♦✳ ◆❡st❡ ❝❛s♦✱ ✈ár✐♦s

❣❛t❡✇❛②s ❞❡ ❛♣❧✐❝❛çã♦ ♣♦❞❡♠ s❡r ❡①❡❝✉t❛❞♦s ♥❡st❡s s✐st❡♠❛s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✱ ✉♠

♣r♦①② ❍❚❚P✱ ❋❚P✱ ❚❡❧♥❡t✱ ❙▼❚P✱ ❡t❝ ❬❑✉r♦s❡ ✫ ❘♦ss✱ ✷✵✶✵❪✳

❖✉tr♦s s✐st❡♠❛s ❝♦♠❡r❝✐❛✐s t❛♠❜é♠ sã♦ ✈❡r✐✜❝❛❞♦s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✱ ❙②♠❛♥t❡❝

❊♥❞ P♦✐♥t Pr♦t❡❝t✐♦♥ ❡ ❑❛s♣❡rs❦② ❊♥❞ P♦✐♥t ❢♦r ❇✉s✐♥❡ss✱ ♦s q✉❛✐s t❛♠❜é♠ ♣♦ss✉❡♠

❞✐✈❡rs♦s s❡r✈✐ç♦s ✐♥t❡❣r❛❞♦s✱ ❝♦♠♦ ❛♥tí✈✐r✉s✱ ❛♥t✐s♣②✇❛r❡ ❡ ✜r❡✇❛❧❧ ♣❡ss♦❛❧✱ ❛❧é♠ ❞♦

♠ó❞✉❧♦ ❞❡ ■❉❙✴■P❙ q✉❡ ♣♦❞❡ r❡♣♦rt❛r ❛s ✐♥❢♦r♠❛çõ❡s ❤✐❡r❛rq✉✐❝❛♠❡♥t❡ ♣❛r❛ s❡r✈✐❞♦r❡s

r❡♠♦t♦s✱ ❢✉♥❝✐♦♥❛♥❞♦ ♣♦rt❛♥t♦ ❞❡ ❢♦r♠❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛✳

❈♦♥❢♦r♠❡ ❙❤✐r❛✈✐ ❡t ❛❧✳ ❬✷✵✶✷❪✱ ❛ ❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sã♦ t❡♠ ❛tr❛í❞♦ ❛ ❛t❡♥çã♦ ❞❡

♠✉✐t♦s ♣❡sq✉✐s❛❞♦r❡s ❡♠ ✐❞❡♥t✐✜❝❛r ♦ ♣r♦❜❧❡♠❛ ❝❛❞❛ ✈❡③ ♠❛✐♦r ❞❡ ❛t✐✈✐❞❛❞❡s ✐♥tr✉s✐✈❛s✱

❡s♣❡❝✐❛❧♠❡♥t❡✱ ❛ ❞❡t❡❝çã♦ ❞❡ ❛♥♦♠❛❧✐❛s✱ ❞❡✈✐❞♦ ❛ s✉❛ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ ❞❡t❡❝t❛r ♥♦✈♦s

❛t❛q✉❡s✳ ❖s s✐st❡♠❛s tr❛❞✐❝✐♦♥❛✐s ♥ã♦ tê♠ s❡ ❛❞❛♣t❛❞♦ ❛❞❡q✉❛❞❛♠❡♥t❡ ❛♦s ♥♦✈♦s

♣❛r❛❞✐❣♠❛s ❞❡ r❡❞❡s✱ ❝♦♠♦ r❡❞❡s s❡♠ ✜♦✱ r❡❞❡s ♠ó✈❡✐s ❡ r❡❞❡s ❞❡ ❛❧t❛ ✈❡❧♦❝✐❞❛❞❡✳

❖✉tr♦s ❢❛t♦r❡s ❝♦♠♦ ❝♦♥st❛♥t❡s ♠✉❞❛♥ç❛s ❞❡ trá❢❡❣♦ ❡ ❛✉♠❡♥t♦ ❞♦ trá❢❡❣♦ ❞❡ r❡❞❡s

t❛♠❜é♠ tê♠ ❞✐✜❝✉❧t❛❞♦ ❛ ❝♦♥str✉çã♦ ❞❡ ♣❡r✜s ❝♦♠ trá❢❡❣♦ ♥♦r♠❛❧✱ ✐♠♣❧✐❝❛♥❞♦ ❛ss✐♠

❡♠ ♠✉❞❛♥ç❛s ❢✉♥❞❛♠❡♥t❛✐s ♥❛s ❛❜♦r❞❛❣❡♥s ❞❡ ❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sã♦ ❬P❛t❝❤❛ ✫ P❛r❦✱

✷✵✵✼❪✳

▼✉✐t❛s té❝♥✐❝❛s tê♠ s✐❞♦ ✉t✐❧✐③❛❞❛s ♣❛r❛ ❛ ❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sã♦ ♥♦s ❙❉■s ❜❛s❡❛❞♦s

❡♠ ❛♥♦♠❛❧✐❛s ♦✉ ❤í❜r✐❞♦s✳ ❊♥tr❡ ❡ss❛s té❝♥✐❝❛s✱ ♣♦❞❡♠♦s ❝✐t❛r ❛s ➪r✈♦r❡s ❞❡ ❉❡❝✐sã♦

✭❉❚✮✱ ❘❡❞❡s ◆❡✉r❛✐s ❆rt✐✜❝✐❛✐s ✭❘◆❆s✮✱ ❆❧❣♦r✐t♠♦s ●❡♥ét✐❝♦s ✭❆●s✮✱ ▲ó❣✐❝❛ ◆❡❜✉✲

❧♦s❛✱ ▼áq✉✐♥❛ ❞❡ ❱❡t♦r❡s ❞❡ ❙✉♣♦rt❡ ✭❙❱▼✮✱ ❙✐st❡♠❛ ■♠✉♥❡ ❆rt✐✜❝✐❛❧ ❡ ♦s ❙✐st❡♠❛s

■♥t❡❧✐❣❡♥t❡s ❍í❜r✐❞♦s ✭❙■❍✮✱ s❡♥❞♦ ❡st❡ ú❧t✐♠♦ ❝♦♥❤❡❝✐❞♦ t❛♠❜é♠ ❝♦♠♦ ❙♦❢t ❈♦♠♣✉t✐♥❣✱

♥♦ q✉❛❧ ❝♦♠❜✐♥❛ ❞✉❛s ♦✉ ♠❛✐s té❝♥✐❝❛s ❞✐st✐♥t❛s ♣❛r❛ r❡s♦❧✈❡r ✉♠ ♣r♦❜❧❡♠❛ ❬❘❡③❡♥❞❡✱

✷✵✵✺❪✳

❖ tr❛❜❛❧❤♦ ❞❡s❡♥✈♦❧✈✐❞♦ r❡❛❧✐③♦✉ ❛ ❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sã♦ ❜❛s❡❛❞❛ ❡♠ ❛♥♦♠❛❧✐❛s✱

❞❡✈✐❞♦ ❛s s✉❛s ❝❛r❛❝t❡ríst✐❝❛s ❡ ♥❡❝❡ss✐❞❛❞❡s✳ ◆ã♦ ♦❜st❛♥t❡✱ s✉❛s ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s ♣♦✲

❞❡♠ s❡r ❡st❡♥❞✐❞❛s ♣❛r❛ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞❡ ❞❡t❡❝çã♦ ❤í❜r✐❞❛✳

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✶✼

✷✳✹ ❉❡t❡❝çã♦ ❞❡ ❆♥♦♠❛❧✐❛s

❆ ❞❡t❡❝çã♦ ❞❡ ❛♥♦♠❛❧✐❛s t❛♠❜é♠ é ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❞❡t❡❝çã♦ ❞❡ ❞❡s✈✐♦s✱ t❡♥❞♦ ❝♦♠♦

♦❜❥❡t✐✈♦ ❡♥❝♦♥tr❛r ♦❜❥❡t♦s q✉❡ s❡❥❛♠ ❞✐❢❡r❡♥t❡s ❞❛ ♠❛✐♦r✐❛✳ ❊ss❡s ♦❜❥❡t♦s tê♠ ❝❛r❛❝t❡✲

ríst✐❝❛s q✉❡ s❡ ❞❡s✈✐❛♠ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ❞♦s ✈❛❧♦r❡s ❞❡ ❛tr✐❜✉t♦s ❡s♣❡r❛❞♦s ♦✉ tí♣✐❝♦s

❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

❯♠❛ ❞✐✈❡rs✐❞❛❞❡ ❞❡ ❛❜♦r❞❛❣❡♥s ❞❡ ❞❡t❡❝çã♦ ❞❡ ❛♥♦♠❛❧✐❛s ❡①✐st❡ ❡♠ ❞✐✈❡rs❛s

ár❡❛s✱ ❛s q✉❛✐s ✐♥❝❧✉❡♠ ❡st❛tíst✐❝❛✱ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛s ❡ ♠✐♥❡r❛çã♦ ❞❡ ❞❛❞♦s✳

❚♦❞❛s ❡❧❛s t❡♥t❛♠ ✐❞❡♥t✐✜❝❛r ♦s ♦❜❥❡t♦s ❛♥ô♠❛❧♦s ❝♦♠♦ s❡♥❞♦ ❞✐❢❡r❡♥t❡s ♦✉ ❞❡ ❛❧❣✉♠❛

❢♦r♠❛ ✐♥❝♦♥s✐st❡♥t❡s ❡♠ r❡❧❛çã♦ ❛♦s ♦✉tr♦s ♦❜❥❡t♦s✳ ❆♣❡s❛r ❞❡ss❡s ♦❜❥❡t♦s s❡r❡♠ r❡✲

❧❛t✐✈❛♠❡♥t❡ r❛r♦s✱ ✐st♦ ♥ã♦ s✐❣♥✐✜❝❛ q✉❡ ❡❧❡s ♥ã♦ ♦❝♦rr❛♠ ❝♦♠ ❢r❡q✉ê♥❝✐❛ ❡♠ t❡r♠♦s

❛❜s♦❧✉t♦s ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳ ❈♦♠♦ ❡①❡♠♣❧♦✱ ✉♠ ❡✈❡♥t♦ q✉❡ ♦❝♦rr❡ ✏✉♠ ❡♠ ✉♠ ♠✐❧❤ã♦✑

♣♦❞❡ ♦❝♦rr❡r ♠✐❧❤õ❡s ❞❡ ✈❡③❡s q✉❛♥❞♦ ❜✐❧❤õ❡s ❞❡ ❡✈❡♥t♦s sã♦ ❝♦♥s✐❞❡r❛❞♦s✳

❆s ❝❛✉s❛s ♠❛✐s ❝♦♠✉♥s ❞❡ ❛♥♦♠❛❧✐❛s sã♦✿ ❞❛❞♦s ❞❡ ❝❧❛ss❡s ❞✐❢❡r❡♥t❡s✱ ✈❛r✐❛çã♦

♥❛t✉r❛❧ ❡ ❡rr♦s ❞❡ ❝♦❧❡t❛✳ ◆❛ ♣r✐♠❡✐r❛ ❝❛✉s❛✱ ✉♠ ♦❜❥❡t♦ ❛♥ô♠❛❧♦ ♣♦❞❡ s❡r ❞✐❢❡r❡♥t❡

❞❡ ♦✉tr♦s ♣♦rq✉❡ é ❞❡ ✉♠ t✐♣♦ ♦✉ ❝❧❛ss❡ ❞✐❢❡r❡♥t❡✳ ❱ár✐♦s ❡①❡♠♣❧♦s s❡ ❡♥q✉❛❞r❛♠

♥❡st❡ ❝❛s♦✱ ❝♦♠♦ ❛❧❣✉é♠ ❝♦♠❡t❡♥❞♦ ❢r❛✉❞❡ ❞❡ ❝❛rtã♦ ❞❡ ❝ré❞✐t♦✱ ✐♥tr✉s♦s ❡♠ r❡❞❡s

❞❡ ❝♦♠♣✉t❛❞♦r❡s ❡ ❞❡♠❛✐s s✐st❡♠❛s ❝♦♠♣✉t❛❝✐♦♥❛✐s✱ s✉rt♦s ❞❡ ❞♦❡♥ç❛s✱ ❡t❝✳ ❊ss❛s

❛♥♦♠❛❧✐❛s sã♦ ♠✉✐t❛s ✈❡③❡s ❞❡ ❝♦♥s✐❞❡rá✈❡❧ ✐♥t❡r❡ss❡ ❡ sã♦ ♦ ❢♦❝♦ ❞❡ ❞❡t❡❝çã♦ ♥❛ ár❡❛

❞❡ ♠✐♥❡r❛çã♦ ❞❡ ❞❛❞♦s✱ s❡♥❞♦ q✉❡ ♠✉✐t❛s sã♦ ❞❡t❡❝t❛❞❛s ❡ r❡♠♦✈✐❞❛s ❢r❡q✉❡♥t❡♠❡♥t❡

❝♦♠♦ ✉♠❛ ♣❛rt❡ ❞♦ ♣ré✲♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ❞❛❞♦s ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

◆❛ ❞❡t❡❝çã♦ ❞❡ ❛♥♦♠❛❧✐❛s✱ ❛❧❣✉♠❛s ❛❜♦r❞❛❣❡♥s sã♦ ✈❡r✐✜❝❛❞❛s✱ ❝♦♠♦ té❝♥✐❝❛s

❜❛s❡❛❞❛s ❡♠ ♠♦❞❡❧♦s✱ ❜❛s❡❛❞❛s ❡♠ ♣r♦①✐♠✐❞❛❞❡ ♦✉ ❞✐stâ♥❝✐❛ ♦✉ ❜❛s❡❛❞❛s ❡♠ ❞❡♥s✐✲

❞❛❞❡✳ ❉❡✈✐❞♦ à ✉t✐❧✐③❛çã♦ ♥❡st❡ tr❛❜❛❧❤♦✱ ❛s té❝♥✐❝❛s q✉❡ ♣r✐♠❡✐r❛♠❡♥t❡ ❝♦♥str♦❡♠

✉♠ ♠♦❞❡❧♦ ❞♦s ❞❛❞♦s ♠❡r❡❝❡♠ ✉♠ ❞❡st❛q✉❡✳ ◆❡st❡ t✐♣♦✱ ♣♦r ❡①❡♠♣❧♦✱ ✉♠ ♠♦❞❡❧♦ ❞❛

❞✐str✐❜✉✐çã♦ ❞♦s ❞❛❞♦s ♣♦❞❡ s❡r ❝r✐❛❞♦ ♣❛r❛ ❛✈❛❧✐❛r ♦s ♣❛râ♠❡tr♦s ❞❡ ✉♠❛ ❞✐str✐❜✉✐çã♦

❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡✳ ❯♠ ♦❜❥❡t♦ q✉❡ ♥ã♦ s❡ ❡♥q✉❛❞r❛ ♠✉✐t♦ ❜❡♠ ❞❡♥tr♦ ❞♦ ♠♦❞❡❧♦✱ é

♣♦rt❛♥t♦ ❝♦♥s✐❞❡r❛❞♦ ❝♦♠♦ ❛♥♦♠❛❧✐❛ s❡ ♥ã♦ ❢♦r ♠✉✐t♦ ♣r♦✈á✈❡❧ ♥❛ ❞✐str✐❜✉✐çã♦✳ ❙❡

❡st❡ ♠♦❞❡❧♦ ❢♦r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❛❣r✉♣❛♠❡♥t♦s✱ ❛ ❛♥♦♠❛❧✐❛ ❡♥tã♦ é ✉♠ ♦❜❥❡t♦ q✉❡ ♥ã♦

♣❡rt❡♥❝❡ ❝♦♥✈✐♥❝❡♥t❡♠❡♥t❡ ❛ ❛❧❣✉♠ ❣r✉♣♦✳ ❊ q✉❛♥❞♦ ✉♠ ♠♦❞❡❧♦ ❞❡ r❡❣r❡ssã♦ é ✉s❛❞♦✱

✉♠❛ ❛♥♦♠❛❧✐❛ é ✉♠ ♦❜❥❡t♦ q✉❡ ❡st❡❥❛ ❞✐st❛♥t❡ ❞♦ s❡✉ ✈❛❧♦r ♣r❡✈✐st♦ ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

❖ ❢❛t♦ ❞❛s ❛♥♦♠❛❧✐❛s ❡ ♦❜❥❡t♦s ♥♦r♠❛✐s ♣♦❞❡r❡♠ s❡r ✈✐st♦s ❝♦♠♦ ❞✉❛s ❝❧❛ss❡s

❞✐st✐♥t❛s✱ té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ♣♦❞❡♠ s❡r ❝♦♥s✐❞❡r❛❞❛s ♣❛r❛ ❝♦♥str✉✐r ♠♦❞❡❧♦s ❞❡s✲

t❛s ❞✉❛s ❝❧❛ss❡s✱ ❞❡s❞❡ q✉❡ ❛❧❣✉♥s rót✉❧♦s ❞❡ ❝❧❛ss❡s ❡st❡❥❛♠ ❞✐s♣♦♥í✈❡✐s ♣❛r❛ ❛❧❣✉♥s

❞♦s ♦❜❥❡t♦s✱ ♣❡r♠✐t✐♥❞♦ q✉❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ tr❡✐♥❛♠❡♥t♦ ♣♦ss❛ s❡r ❝r✐❛❞♦✳ ❊♠ ♦✉✲

tr♦s ❝❛s♦s✱ s❡ ❛ ❞✐str✐❜✉✐çã♦ ❡st❛tíst✐❝❛ ❞♦s ❞❛❞♦s ❢♦r ❞❡s❝♦♥❤❡❝✐❞❛ ♦✉ ♥❡♥❤✉♠ ❞❛❞♦ ❞❡

tr❡✐♥❛♠❡♥t♦ ❡st❡❥❛ ❞✐s♣♦♥í✈❡❧✱ té❝♥✐❝❛s q✉❡ ♥ã♦ sã♦ ❜❛s❡❛❞❛s ❡♠ ♠♦❞❡❧♦s ♣♦❞❡♠ s❡r

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✶✽

✉s❛❞❛s ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

❖✉tr♦ ❞❡st❛q✉❡ ♥❛ ❞❡t❡❝çã♦ ❞❡ ❛♥♦♠❛❧✐❛s é ❝♦♠♦ ❞✐❢❡r❡♥❝✐❛r ♦ ❣r❛✉ ♥♦ q✉❛❧ ♦s

rót✉❧♦s ❞❡ ❝❧❛ss❡s ✭❛♥ô♠❛❧❛ ♦✉ ♥♦r♠❛❧✮ ❡stã♦ ❞✐s♣♦♥í✈❡✐s ♣❛r❛ ♣❡❧♦ ♠❡♥♦s ❛❧❣✉♥s ❞♦s

❞❛❞♦s✳ ❇❛s✐❝❛♠❡♥t❡✱ ❤á três tr❛t❛♠❡♥t♦s ♣♦ssí✈❡✐s ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

• ❉❡t❡❝çã♦ s✉♣❡r✈✐s✐♦♥❛❞❛ ❞❡ ❛♥♦♠❛❧✐❛s✿ ❡♠ q✉❡ ❛s té❝♥✐❝❛s ❞❡ ❞❡t❡❝çã♦ r❡q✉❡r❡♠

❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ tr❡✐♥❛♠❡♥t♦ ❝♦♠ ♦❜❥❡t♦s ❛♥ô♠❛❧♦s ❡ ♥♦r♠❛✐s✱

♣♦❞❡♥❞♦ ❤❛✈❡r ♠❛✐s ❞❡ ✉♠❛ ❝❧❛ss❡ ♥♦r♠❛❧ ❡ ❛♥ô♠❛❧❛✳

• ❉❡t❡❝çã♦ ♥ã♦ s✉♣❡r✈✐s✐♦♥❛❞❛ ❞❡ ❛♥♦♠❛❧✐❛s✿ ❡♠ q✉❡ ♦s rót✉❧♦s ❞❡ ❝❧❛ss❡s ♥ã♦

❡stã♦ ❞✐s♣♦♥í✈❡✐s✳ ◆❡st❡ ❝❛s♦✱ ♦ ♦❜❥❡t✐✈♦ é ❛tr✐❜✉✐r ✉♠ ✈❛❧♦r ✭♦✉ ✉♠ rót✉❧♦✮ ❛

❝❛❞❛ ✐♥stâ♥❝✐❛ q✉❡ r❡✢✐t❛ ♦ ❣r❛✉✱ ♥♦ q✉❛❧ ❛ ♠❡s♠❛ é ❛♥ô♠❛❧❛✳ ❉❡✈❡✲s❡ ♦❜s❡r✈❛r

q✉❡ ❝❛s♦ ❛s ❛♥♦♠❛❧✐❛s s❡❥❛♠ s❡♠❡❧❤❛♥t❡s ❡♥tr❡ s✐ ♣♦❞❡ ❢❛③❡r ❝♦♠ q✉❡ t♦❞❛s s❡❥❛♠

r♦t✉❧❛❞❛s ❝♦♠♦ ♥♦r♠❛✐s✳ ❉❡ss❛ ❢♦r♠❛✱ ♣❛r❛ q✉❡ ❛ ❞❡t❡❝çã♦ ♥ã♦ s✉♣❡r✈✐s✐♦♥❛❞❛

s❡❥❛ ❡❢❡t✉❛❞❛ ❝♦♠ s✉❝❡ss♦✱ ❛s ❛♥♦♠❛❧✐❛s ❞❡✈❡♠ s❡r ❞✐st✐♥t❛s ❡♥tr❡ s✐✳

• ❉❡t❡❝çã♦ s❡♠✐✲s✉♣❡r✈✐s✐♦♥❛❞❛ ❞❡ ❛♥♦♠❛❧✐❛s✿ ❡♠ q✉❡ ♦❝♦rr❡ q✉❛♥❞♦ ❝♦♥tê♠ ♦s ❞❛✲

❞♦s ♥♦r♠❛✐s r♦t✉❧❛❞♦s✱ ♠❛s ♥ã♦ ♣♦ss✉✐ ✐♥❢♦r♠❛çõ❡s s♦❜r❡ ♦s ♦❜❥❡t♦s ❛♥ô♠❛❧♦s✳ ❖

♦❜❥❡t✐✈♦ é ❡♥❝♦♥tr❛r ✉♠ rót✉❧♦ ♦✉ ✈❛❧♦r ❞❡ ❛♥♦♠❛❧✐❛ ♣❛r❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♦❜❥❡t♦s✱

✉s❛♥❞♦ ❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ♦❜❥❡t♦s ♥♦r♠❛✐s r♦t✉❧❛❞♦s✳ ❈♦♥t✉❞♦✱ ♥❛ ♣rát✐❝❛✱ ♣♦❞❡

s❡r ❞✐❢í❝✐❧ ❡♥❝♦♥tr❛r ✉♠ ❝♦♥❥✉♥t♦ ♣❡q✉❡♥♦ ❞❡ ♦❜❥❡t♦s ♥♦r♠❛✐s r❡♣r❡s❡♥t❛t✐✈♦s✳

◆❡st❡ tr❛❜❛❧❤♦✱ ♣❡❧♦ ❢❛t♦ ❞❛ ❜❛s❡ ❞❡ ❞❛❞♦s ✉s❛❞❛ ♣♦ss✉✐r s❡✉s r❡❣✐str♦s r♦t✉❧❛❞♦s✱

♣❡r♠✐t✐✉ ❛ ✉t✐❧✐③❛çã♦ ❞❡ té❝♥✐❝❛s ❜❛s❡❛❞❛s ❡♠ ♠♦❞❡❧♦s ❝♦♥s✐❞❡r❛♥❞♦ ✉♠❛ ❞❡t❡❝çã♦

s✉♣❡r✈✐s✐♦♥❛❞❛ ❞❡ ❛♥♦♠❛❧✐❛s✳

✷✳✺ ❚é❝♥✐❝❛s ❞❡ ❈❧❛ss✐✜❝❛çã♦

❆s té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ♣♦ss✉❡♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ♦r❣❛♥✐③❛r ♦❜❥❡t♦s ❡♠ ✉♠❛ ❝❛t❡❣♦r✐❛✱

❡♥tr❡ ❞✐✈❡rs❛s✱ ♣ré✲❞❡✜♥✐❞❛s✱ s❡♥❞♦ ✉♠ ♣r♦❜❧❡♠❛ ✉♥✐✈❡rs❛❧ q✉❡ ❡♥❣❧♦❜❛ ♠✉✐t❛s ❛♣❧✐❝❛✲

çõ❡s ❞✐❢❡r❡♥t❡s✳ ❈♦♠♦ ❡①❡♠♣❧♦s✱ ♣♦❞❡♠♦s ❝✐t❛r ❛ ❞❡t❡❝çã♦ ❞❡ ♠❡♥s❛❣❡♥s ❞❡ s♣❛♠ ❡♠

❡✲♠❛✐❧s ❜❛s❡❛❞❛ ♥♦ ❝❛❜❡ç❛❧❤♦ ❡ ❝♦♥t❡ú❞♦ ❞❛ ♠❡♥s❛❣❡♠✱ ❛ ❝❛t❡❣♦r✐③❛çã♦ ❞❡ ❝é❧✉❧❛s ❝♦♠♦

♠❛❧✐❣♥❛s ♦✉ ❜❡♥✐❣♥❛s ❜❛s❡❛❞❛ ♥♦s r❡s✉❧t❛❞♦s ❞❡ ✈❛rr❡❞✉r❛s ▼❘■ ✭▼❛❣♥❡t✐❝ ❘❡s♦♥❛♥❝❡

■♠❛❣✐♥❣✮ ❡ ♥❛ ❞❡t❡❝çã♦ ❞❡ trá❢❡❣♦ ♠❛❧✐❝✐♦s♦ ❡♠ r❡❞❡s ❞❡ ❝♦♠♣✉t❛❞♦r❡s ❜❛s❡❛❞❛ ♥♦s

❝❛❜❡ç❛❧❤♦s ❞♦s P❉❯s ✭Pr♦t♦❝♦❧ ❉❛t❛ ❯♥✐ts✮✱ ❡♥tr❡ ♦✉tr♦s ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

❊♠ ✉♠❛ t❛r❡❢❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦✱ t❡♠♦s ♦s ❞❛❞♦s ❞❡ ❡♥tr❛❞❛✱ q✉❡ sã♦ ✉♠ ❝♦♥❥✉♥t♦

❞❡ r❡❣✐str♦s✱ ❝♦♥❤❡❝✐❞♦s t❛♠❜é♠ ❝♦♠♦ ✐♥stâ♥❝✐❛s ♦✉ ❡①❡♠♣❧♦s✳ ❈❛❞❛ r❡❣✐str♦ é ❝❛r❛❝t❡✲

r✐③❛❞♦ ♣♦r ✉♠❛ ❞✉♣❧❛ (x, y)✱ ♦♥❞❡ x é ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❛tr✐❜✉t♦s ❡ y ♦ ❛tr✐❜✉t♦ ❡s♣❡❝✐❛❧✱

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✶✾

❞❡s✐❣♥❛❞♦ ❝♦♠♦ rót✉❧♦ ❞❛ ❝❧❛ss❡ ♦✉ ❛tr✐❜✉t♦ ❛❧✈♦✳ ❖ ❝♦♥❥✉♥t♦ ❞❡ ❛tr✐❜✉t♦s ❡♠ s✉❛

♠❛✐♦r✐❛ sã♦ ❞✐s❝r❡t♦s✱ ♣♦❞❡♥❞♦ s❡r t❛♠❜é♠ ❝♦♥tí♥✉♦s✳ ◆♦ ❡♥t❛♥t♦✱ ♦ rót✉❧♦ ❞❛ ❝❧❛ss❡✱

❞❡✈❡ s❡r ✉♠ ❛tr✐❜✉t♦ ❞✐s❝r❡t♦✳ ❊st❛ é ❛ ❝❛r❛❝t❡ríst✐❝❛ q✉❡ ❞✐st✐♥❣✉❡ ❛ ❝❧❛ss✐✜❝❛çã♦ ❞❛

r❡❣r❡ssã♦✱ s❡♥❞♦ ❡st❛ ✉♠❛ té❝♥✐❝❛ ❞❡ ♠♦❞❡❧❛❣❡♠ ♣r❡❞✐t✐✈❛ ♦♥❞❡ ❛ ✈❛r✐á✈❡❧ ❛❧✈♦ ❛ s❡r

❛✈❛❧✐❛❞❛ é ❝♦♥tí♥✉❛✳

❆ss✐♠✱ ❛ r❡❣r❡ssã♦ ♣♦ss✉✐ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❛♣r❡♥❞❡r ✉♠❛ ❢✉♥çã♦ ❛❧✈♦ f q✉❡ ♠❛✲

♣❡✐❡ ❝❛❞❛ ❝♦♥❥✉♥t♦ ❞❡ ❛tr✐❜✉t♦s x ❡♠ ✉♠❛ s❛í❞❛ ❞❡ ✈❛❧♦r❡s ❝♦♥tí♥✉♦s y✱ ❡♥q✉❛♥t♦ ❛

❝❧❛ss✐✜❝❛çã♦ é ❛ t❛r❡❢❛ ❞❡ ❛♣r❡♥❞❡r ✉♠❛ ❢✉♥çã♦ ❛❧✈♦ f q✉❡ ♠❛♣❡✐❡ ❝❛❞❛ ❝♦♥❥✉♥t♦ ❞❡

❛tr✐❜✉t♦s x ♣❛r❛ ✉♠ ❞♦s rót✉❧♦s ❞❡ ❝❧❛ss❡s y ♣ré✲❞❡t❡r♠✐♥❛❞♦s✳ ❆ ❢✉♥çã♦ ❛❧✈♦ é ❝♦♥❤❡✲

❝✐❞❛ t❛♠❜é♠ ❝♦♠♦ ♠♦❞❡❧♦ ❞❡ ❝❧❛ss✐✜❝❛çã♦✳ ❊st❡ ♠♦❞❡❧♦ ♣♦❞❡ s❡r tr❛t❛❞♦ ❝♦♠♦ ✉♠❛

❝❛✐①❛ ♣r❡t❛ q✉❡ ❛tr✐❜✉✐ ❛✉t♦♠❛t✐❝❛♠❡♥t❡ ✉♠ rót✉❧♦ ❞❡ ❝❧❛ss❡ ❛♦ r❡❝❡❜❡r ✉♠ ❝♦♥❥✉♥t♦

❞❡ ❛tr✐❜✉t♦s ❞❡ ✉♠ r❡❣✐str♦ ❞❡s❝♦♥❤❡❝✐❞♦✱ ❝♦♥❢♦r♠❡ ✈❡r✐✜❝❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✺ ❬❚❛♥ ❡t ❛❧✳✱

✷✵✵✾❪✳

❋✐❣✉r❛ ✷✳✺✳ ❈❧❛ss✐✜❝❛çã♦ ❝♦♠♦ ❛ t❛r❡❢❛ ❞❡ ♠❛♣❡❛r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❛tr✐❜✉t♦s x♥♦ s❡✉ rót✉❧♦ ❞❡ ❝❧❛ss❡ y ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪

❆ ❝❧❛ss✐✜❝❛çã♦ ❞❡ ❞❛❞♦s é ✉♠ ♣r♦❝❡ss♦ ❞❡ ❞✉❛s ❡t❛♣❛s✱ q✉❡ ❝♦♥s✐st❡ ♥❛ ❡t❛♣❛s ❞❡

❛♣r❡♥❞✐③❛❞♦ ♦✉ ❡t❛♣❛ ❞❡ tr❡✐♥❛♠❡♥t♦✱ ♦♥❞❡ ♦ ♠♦❞❡❧♦ ❞❡ ❝❧❛ss✐✜❝❛çã♦ é ❝♦♥str✉í❞♦ ❡

❛ ❡t❛♣❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦✱ ♦♥❞❡ ♦ ♠♦❞❡❧♦ é ✉s❛❞♦ ♣❛r❛ ♣r❡❞✐③❡r ♦ rót✉❧♦ ❞❛ ❝❧❛ss❡ ❬❍❛♥

❡t ❛❧✳✱ ✷✵✶✶❪✳

◆❛ ♣r✐♠❡✐r❛ ❡t❛♣❛✱ ❞❡ ❛♣r❡♥❞✐③❛❞♦✱ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❝♦♥stró✐ ♦ ❝❧❛ss✐✲

✜❝❛❞♦r ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❛♥á❧✐s❡ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ tr❡✐♥❛♠❡♥t♦ ❢♦r♠❛❞♦ ♣❡❧❛s t✉♣❧❛s✱

❝♦♥❤❡❝✐❞❛s t❛♠❜é♠ ❝♦♠♦ s❡♥❞♦ ♦s r❡❣✐str♦s ❞❛ ❜❛s❡ ❞❡ ❞❛❞♦s ❡ ❞❡ s❡✉s rót✉❧♦s ❞❡ ❝❧❛ss❡s

❛ss♦❝✐❛❞♦s✳ ❆ t✉♣❧❛ x é r❡♣r❡s❡♥t❛❞❛ ♣♦r ✉♠ ✈❡t♦r ♥✲❞✐♠❡♥s✐♦♥❛❧✱ x = (x1, x2, ..., xn)✳

P❡❧♦ ❢❛t♦ ❞❡ ❝❛❞❛ t✉♣❧❛ t❡r s✉❛ ❝❧❛ss❡ ❝♦♥❤❡❝✐❞❛✱ ❡st❡ ♣❛ss♦ t❛♠❜é♠ é ❝♦♥❤❡❝✐❞♦

❝♦♠♦ ❛♣r❡♥❞✐③❛❞♦ s✉♣❡r✈✐s✐♦♥❛❞♦ ♦✉ ❛✐♥❞❛ ♣♦❞❡ s❡r ✈✐st♦ ❝♦♠♦ ❛♣r❡♥❞✐③❛❣❡♠ ❞❡ ✉♠

♠❛♣❡❛♠❡♥t♦ ♦✉ ❢✉♥çã♦ y = f(x)✱ q✉❡ ♣♦❞❡ ♣r❡✈❡r ❛ ❝❧❛ss❡ ❛ss♦❝✐❛❞❛ ❛♦ rót✉❧♦ y ❞❡

✉♠❛ ❞❡t❡r♠✐♥❛❞❛ t✉♣❧❛ x ❬❍❛♥ ❡t ❛❧✳✱ ✷✵✶✶❪✳

❉❡ ♠❛♥❡✐r❛ ❣❡r❛❧✱ ❡st❡ ♠❛♣❡❛♠❡♥t♦ é r❡♣r❡s❡♥t❛❞♦ ❡♠ ❢♦r♠❛ ❞❡ r❡❣r❛s ❞❡ ❝❧❛ss✐✲

✜❝❛çã♦✱ ár✈♦r❡s ❞❡ ❞❡❝✐sã♦ ♦✉ ❢ór♠✉❧❛s ♠❛t❡♠át✐❝❛s✱ s❡♥❞♦ ♣♦ssí✈❡❧ ❛✐♥❞❛ ❛ ✉t✐❧✐③❛çã♦

❞❡ ♦✉tr❛s té❝♥✐❝❛s ❞❡ ✐♥t❡❧✐❣ê♥❝✐❛ ❝♦♠♣✉t❛❝✐♦♥❛❧✳

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✷✵

◆❛ s❡❣✉♥❞❛ ❡t❛♣❛✱ ♦ ♠♦❞❡❧♦ é ✉s❛❞♦ ♣❛r❛ ❝❧❛ss✐✜❝❛çã♦✳ Pr✐♠❡✐r❛♠❡♥t❡✱ ❛ ♣r❡❝✐sã♦

❞❛ ♣r❡✈✐sã♦ ❞♦ ❝❧❛ss✐✜❝❛❞♦r é ❡st✐♠❛❞❛ ❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ t❡st❡s ❝♦♠♣♦st♦ ❞❡ s✉❛s t✉♣❧❛s

❡ s❡✉s rót✉❧♦s ❞❡ ❝❧❛ss❡ é ✉t✐❧✐③❛❞♦✳ ❊st❡ ❝♦♥❥✉♥t♦ ♥ã♦ ❢♦✐ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❛ ❝♦♥str✉çã♦

❞♦ ❝❧❛ss✐✜❝❛❞♦r✳ ❆ ♣r❡❝✐sã♦ ❞❡ ✉♠ ❝❧❛ss✐✜❝❛❞♦r é ♦ ♣❡r❝❡♥t✉❛❧ ❞❛s t✉♣❧❛s ❞♦ ❝♦♥❥✉♥t♦

❞❡ t❡st❡s q✉❡ ❢♦r❛♠ ❝♦rr❡t❛♠❡♥t❡ ❝❧❛ss✐✜❝❛❞❛s✳ ❖ rót✉❧♦ ❞❡ ❝❧❛ss❡ ❞❡ ❝❛❞❛ t✉♣❧❛ ❞❡

t❡st❡ é ❝♦♠♣❛r❛❞❛ ❝♦♠ ❛ ♣r❡✈✐sã♦ ❞❛ ❝❧❛ss❡ ❛♣r❡❡♥❞✐❞❛ ♣❛r❛ ❛ t✉♣❧❛✳

❖ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ✉t✐❧✐③♦✉ ❞✐✈❡rs❛s té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦✱ ❛s q✉❛✐s ♣❡r♠✐t✐r❛♠

✐❞❡♥t✐✜❝❛r ♣❛r❛ ❝❛❞❛ ✢✉①♦ ❞♦ trá❢❡❣♦ ❞❡ r❡❞❡✱ ❞❛ ❜❛s❡ ❞❡ ❞❛❞♦s ❡s❝♦❧❤✐❞❛✱ s❡ ❢❡③ ♣❛rt❡

❞❛ ❝❧❛ss❡ ❞❡ ✏❛t❛q✉❡✑ ♦✉ ❞❡ trá❢❡❣♦ ✏♥♦r♠❛❧✑ ❞❡ r❡❞❡✳

✷✳✺✳✶ ➪r✈♦r❡ ❞❡ ❉❡❝✐sã♦

❯♠❛ ár✈♦r❡ ❞❡ ❞❡❝✐sã♦ é ✉♠❛ té❝♥✐❝❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ s✐♠♣❧❡s✱ ♣♦ré♠ ♠✉✐t♦ ✉s❛❞❛✳

❉✐❛♥t❡ ❞❡ ✉♠❛ sér✐❡ ❞❡ q✉❡stõ❡s✱ s✉❛s r❡s♣♦st❛s ♣♦❞❡♠ s❡r ♦r❣❛♥✐③❛❞❛s ❡♠ ❢♦r♠❛

❞❡ ár✈♦r❡ ❞❡ ❞❡❝✐sã♦✱ ❝♦♠ s✉❛ ❡str✉t✉r❛ ❤✐❡rárq✉✐❝❛ ❝♦♥s✐st✐♥❞♦ ❞❡ ♥♦❞♦s ❡ ❛r❡st❛s

❞✐r❡❝✐♦♥❛❞❛s✳ ❆ ár✈♦r❡ t❡♠ ❛❧❣✉♥s t✐♣♦s ❞❡ ♥♦❞♦s✿ ✉♠ ♥♦❞♦ r❛✐③ q✉❡ ♥ã♦ ♣♦ss✉✐

❛r❡st❛s ❝❤❡❣❛♥❞♦✱ ❡ ③❡r♦ ♦✉ ♠❛✐s ❛r❡st❛s s❛✐♥❞♦❀ ♥♦❞♦s ✐♥t❡r♥♦s✱ ❝❛❞❛ q✉❛❧ ♣♦ss✉✐♥❞♦

❡①❛t❛♠❡♥t❡ ✉♠❛ ❛r❡st❛ ❝❤❡❣❛♥❞♦ ❡ ❞✉❛s ♦✉ ♠❛✐s s❛✐♥❞♦❀ ❡ ♥♦❞♦s ❢♦❧❤❛ ♦✉ t❡r♠✐♥❛✐s✱

❡♠ q✉❡ ❝❛❞❛ ✉♠ ♣♦ss✉✐ ❡①❛t❛♠❡♥t❡ ✉♠❛ ❛r❡st❛ ❝❤❡❣❛♥❞♦ ❡ ♥❡♥❤✉♠❛ s❛✐♥❞♦✱ ❝♦♥❢♦r♠❡

♠♦str❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✻ ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

❋✐❣✉r❛ ✷✳✻✳ ❯♠❛ ár✈♦r❡ ❞❡ ❞❡❝✐sã♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❞❡ ♠❛♠í❢❡r♦s❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪

◆❛ ár✈♦r❡ ❞❡ ❞❡❝✐sã♦✱ ❝❛❞❛ ♥♦❞♦ ❢♦❧❤❛ r❡❝❡❜❡ ✉♠ rót✉❧♦ ❞❡ ❝❧❛ss❡✳ ❖s ♥♦❞♦s

♥ã♦ t❡r♠✐♥❛✐s✱ q✉❡ ✐♥❝❧✉❡♠ ♦ ♥♦❞♦ r❛✐③ ❡ ♦✉tr♦s ♥♦❞♦s ✐♥t❡r♥♦s✱ ❝♦♥tê♠ ❝♦♥❞✐çõ❡s ❞❡

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✷✶

t❡st❡s ❞❡ ❛tr✐❜✉t♦s ♣❛r❛ s❡♣❛r❛r r❡❣✐str♦s q✉❡ ♣♦ss✉❛♠ ❝❛r❛❝t❡ríst✐❝❛s ❞✐❢❡r❡♥t❡s✳ P♦r

❡①❡♠♣❧♦✱ ♦ ♥♦❞♦ r❛✐③ ♠♦str❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✼ ✉s❛ ♦ ❛tr✐❜✉t♦ ❚❡♠♣❡r❛t✉r❛ ❈♦r♣♦r❛❧

♣❛r❛ s❡♣❛r❛r ✈❡rt❡❜r❛❞♦s ❞❡ s❛♥❣✉❡ q✉❡♥t❡ ❞♦s ❞❡ s❛♥❣✉❡ ❢r✐♦✳

❆♦ r❡❛❧✐③❛r ✉♠❛ ❝❧❛ss✐✜❝❛çã♦ ❞❡ ✉♠ r❡❣✐str♦ ❞❡ t❡st❡s✱ ♦ r❡s✉❧t❛❞♦ é ❞✐r❡t♦✱ ♣♦✐s

♥❡st❡ ❝❛s♦ ❛ ár✈♦r❡ ❞❡ ❞❡❝✐sã♦ ❥á ❢♦✐ ❝♦♥str✉í❞❛✳ ❈♦♠❡ç❛♥❞♦ ❞♦ ♥♦❞♦ r❛✐③✱ ❛♣❧✐❝❛♠♦s ❛

❝♦♥❞✐çã♦ ❞❡ t❡st❡ ❛♦ r❡❣✐str♦ ❡ s❡❣✉✐♠♦s ❛ r❛♠✐✜❝❛çã♦ ❛♣r♦♣r✐❛❞❛ ❜❛s❡❛❞♦s ♥♦ r❡s✉❧t❛❞♦

❞♦ t❡st❡✳ ❆ss✐♠✱ ♦ ♣ró①✐♠♦ ♣❛ss♦ s❡rá ❛ ❛♥á❧✐s❡ ❞❡ ✉♠❛ ♥♦✈❛ ❝♦♥❞✐çã♦ ❡♠ ♦✉tr♦ ♥♦❞♦

✐♥t❡r♥♦✱ ♦✉ ❧❡✈❛rá ❛ ✉♠ ♥♦❞♦ ❢♦❧❤❛✳ ◗✉❛♥❞♦ ❝❤❡❣❛r ❛ ✉♠ ♥♦❞♦ ❢♦❧❤❛✱ ♦ rót✉❧♦ ❞❛ ❝❧❛ss❡

é ❛tr✐❜✉í❞♦ ❛♦ r❡❣✐str♦✳

❋✐❣✉r❛ ✷✳✼✳ ❈❧❛ss✐✜❝❛çã♦ ❞❡ ✉♠ ✈❡rt❡❜r❛❞♦ s❡♠ rót✉❧♦ ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪

❆ ♣❛rt✐r ❞❡ ✉♠ ♠❡s♠♦ ❝♦♥❥✉♥t♦ ❞❡ ❛tr✐❜✉t♦s✱ é ♣♦ssí✈❡❧ ❝♦♥str✉✐r ♠✉✐t❛s ár✈♦r❡s

❞❡ ❞❡❝✐sã♦✳ ❊♠❜♦r❛ ❛❧❣✉♠❛s ár✈♦r❡s s❡❥❛♠ ♠❛✐s ♣r❡❝✐s❛s q✉❡ ♦✉tr❛s✱ ❡♥❝♦♥tr❛r ár✈♦r❡s

ót✐♠❛s é ❝♦♠♣✉t❛❝✐♦♥❛❧♠❡♥t❡ ✐♥✈✐á✈❡❧ ♣♦r ❝❛✉s❛ ❞♦ t❛♠❛♥❤♦ ❡①♣♦♥❡♥❝✐❛❧ ❞♦ ❡s♣❛ç♦ ❞❡

♣❡sq✉✐s❛✳ ◆♦ ❡♥t❛♥t♦✱ ✈ár✐♦s ❛❧❣♦r✐t♠♦s ❡✜❝✐❡♥t❡s tê♠ s✐❞♦ ❞❡s❡♥✈♦❧✈✐❞♦s ♣❛r❛ ✐♥❞✉③✐r

❛ ✉♠❛ ár✈♦r❡ ❞❡ ❞❡❝✐sã♦ r❛③♦❛❧✈❡♠❡♥t❡ ♣r❡❝✐s❛✱ ♥ã♦ ót✐♠❛✱ ♠❛s ❡♠ ✉♠❛ r❛③♦á✈❡❧

q✉❛♥t✐❞❛❞❡ ❞❡ t❡♠♣♦✳ ❉❡ ♠♦❞♦ ❣❡r❛❧✱ ✉t✐❧✐③❛♠ ✉♠ ❡str❛té❣✐❛ q✉❡ ❝r❡s❝❡ ✉♠❛ ár✈♦r❡

❞❡ ❞❡❝✐sã♦ t♦♠❛♥❞♦ ✉♠❛ sér✐❡ ❞❡ ❞❡❝✐sõ❡s ❧♦❝❛❧♠❡♥t❡ ót✐♠❛s s♦❜r❡ q✉❛❧ ❛tr✐❜✉t♦ ✉s❛r

♣❛r❛ ♣❛rt✐❝✐♦♥❛r ♦s ❞❛❞♦s ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

❉❡ss❛ ♠❛♥❡✐r❛✱ ❝❛❞❛ ♣❛ss♦ r❡❝✉rs✐✈♦ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❞❛ ár✈♦r❡ ❞❡✈❡

s❡❧❡❝✐♦♥❛r ✉♠❛ ❝♦♥❞✐çã♦ ❞❡ t❡st❡ ❞❡ ❛tr✐❜✉t♦ ♣❛r❛ ❞✐✈✐❞✐r ♦s r❡❣✐str♦s ❡♠ s✉❜❝♦♥❥✉♥t♦s

♠❡♥♦r❡s ❡✱ ❡st❡ ♣r♦❝❡ss♦ s❡rá ❧✐♠✐t❛❞♦ ❛tr❛✈és ❞❡ ✉♠❛ ❝♦♥❞✐çã♦ ❞❡ ♣❛r❛❞❛✳

P❛r❛ s❡❧❡❝✐♦♥❛r ❛ ♠❡❧❤♦r ❢♦r♠❛ ❞❡ ❞✐✈✐sã♦ ❞❛ ár✈♦r❡✱ ❡①✐st❡♠ ✈ár✐❛s ♠étr✐❝❛s✱

❞❡✜♥✐❞❛s ❡♠ t❡r♠♦s ❞❛ ❞✐str✐❜✉✐çã♦ ❞❛ ❝❧❛ss❡ ❞♦s r❡❣✐str♦s ❛♥t❡s ❡ ❞❡♣♦✐s ❞❛ ❞✐✈✐✲

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✷✷

sã♦✳ ❆❧❣✉♠❛s ❞❛s ♣♦ss✐❜✐❧✐❞❛❞❡s ♣❛r❛ ❡s❝♦❧❤❡r ♦ ❛tr✐❜✉t♦ q✉❡ ♣❛rt✐❝✐♦♥❛ ♦ ❝♦♥❥✉♥t♦ ❞❡

❡①❡♠♣❧♦s ❡♠ ❝❛❞❛ ✐t❡r❛çã♦ sã♦ ❬❘❡③❡♥❞❡✱ ✷✵✵✺❪✿

• ❛❧❡❛tór✐❛✿ s❡❧❡❝✐♦♥❛ q✉❛❧q✉❡r ❛tr✐❜✉t♦ ❛❧❡❛t♦r✐❛♠❡♥t❡❀

• ♠❡♥♦s ✈❛❧♦r❡s✿ s❡❧❡❝✐♦♥❛ ♦ ❛tr✐❜✉t♦ ❝♦♠ ❛ ♠❡♥♦r q✉❛♥t✐❞❛❞❡ ❞❡ ✈❛❧♦r❡s ♣♦ssí✈❡✐s❀

• ♠❛✐s ✈❛❧♦r❡s✿ s❡❧❡❝✐♦♥❛ ♦ ❛tr✐❜✉t♦ ❝♦♠ ❛ ♠❛✐♦r q✉❛♥t✐❞❛❞❡ ❞❡ ✈❛❧♦r❡s ♣♦ssí✈❡✐s❀

• ❣❛♥❤♦ ♠á①✐♠♦✿ s❡❧❡❝✐♦♥❛ ♦ ❛tr✐❜✉t♦ q✉❡ ♣♦ss✉✐ ♦ ♠❛✐♦r ❣❛♥❤♦ ❞❡ ✐♥❢♦r♠❛çã♦

❡s♣❡r❛❞♦✱ ♦✉ s❡❥❛✱ ♦ ❛tr✐❜✉t♦ q✉❡ r❡s✉❧t❛rá ♥♦ ♠❡♥♦r t❛♠❛♥❤♦ ❡s♣❡r❛❞♦ ❞❛s s✉❜✲

ár✈♦r❡s❀

• ❡ ♦ í♥❞✐❝❡ ●✐♥✐✿ ♠♦str❛❞♦ ♥❛ ❡q✉❛çã♦ ✷✳✷✳

❊ss❛s ♠étr✐❝❛s sã♦ ❣❡r❛❧♠❡♥t❡ ❜❛s❡❛❞❛s ♥♦ ❣r❛✉ ❞❡ ✐♠♣✉r❡③❛ ❞♦s ♥♦❞♦s ✜❧❤♦s✱

s❡♥❞♦ q✉❡✱ q✉❛♥t♦ ♠❡♥♦r ♦ ❣r❛✉ ❞❡ ✐♠♣✉r❡③❛✱ ♠❛✐s ❞✐st♦r❝✐❞❛ é ❛ ❞✐str✐❜✉✐çã♦ ❞❛s

❝❧❛ss❡s✳ P♦r ❡①❡♠♣❧♦✱ ✉♠ ♥♦❞♦ ❝♦♠ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❝❧❛ss❡ ✭✵✱✶✮ ♣♦ss✉✐ ✐♠♣✉r❡③❛ ③❡r♦✱

❡♥q✉❛♥t♦ q✉❡ ✉♠ ♥♦❞♦ ❝♦♠ ❞✐str✐❜✉✐çã♦ ❞❡ ❝❧❛ss❡s ✉♥✐❢♦r♠❡ ✭✵✳✺✱ ✵✳✺✮ ♣♦ss✉✐ ❛ ♠❛✐♦r

✐♠♣✉r❡③❛✱ ❣❡r❛♥❞♦ ♣♦rt❛♥t♦ ✉♠❛ ❞✐✈✐sã♦ ♠❛✐s ❜❛❧❛♥❝❡❛❞❛ ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

❆s ❡q✉❛çõ❡s ✷✳✶ ❡ ✷✳✷ sã♦ ❡①❡♠♣❧♦s ❞❡ ♠étr✐❝❛s ❞❡ ✐♠♣✉r❡③❛✱ ♦♥❞❡ c− 1 ✐♥❞✐❝❛

❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❝❧❛ss❡s ❡ p(i|t) ❛ ❢r❛çã♦ ❞❡ r❡❣✐str♦s q✉❡ ♣❡rt❡♥❝❡♠ à ❝❧❛ss❡ i ❡♠ ✉♠

❞❡t❡r♠✐♥❛❞♦ ♥♦❞♦ t✳

Entropia(t) = −c−1∑

i=0

p(i|t)log2p(i|t) ✭✷✳✶✮

Gini(t) = 1−c−1∑

i=0

[p(i|t)]2 ✭✷✳✷✮

❈♦♠♦ ❡①❡♠♣❧♦ ❞❡ ❝á❧❝✉❧♦✱ ❝♦♥s✐❞❡r❡ ♦ ♥♦❞♦ N1 ❝♦♠ ❞✉❛s ❝❧❛ss❡s✱ ♦ q✉❛❧ ♣♦ss✉✐

1 r❡❣✐str♦ ♥❛ ❝❧❛ss❡ ❆ ❡ 5 r❡❣✐str♦s ♥❛ ❝❧❛ss❡ ❇✳ ❖s ❝á❧❝✉❧♦s ❞❡ ❊♥tr♦♣✐❛ ❡ ●✐♥✐ sã♦

r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❛s ❡q✉❛çõ❡s ✷✳✸ ❡ ✷✳✹✳

Entropia(N1) = −(1/6)log2(1/6)− (5/6)log2(5/6) = 0.650 ✭✷✳✸✮

Gini(N1) = 1− (1/6)2 − (5/6)2 = 0.278 ✭✷✳✹✮

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✷✸

P❛r❛ ❞❡t❡r♠✐♥❛r ♦ q✉ã♦ ❜❡♠ ✉♠❛ ❝♦♥❞✐çã♦ ❞❡ t❡st❡ é ❡①❡❝✉t❛❞❛✱ ♣r❡❝✐s❛♠♦s

❝♦♠♣❛r❛r ♦ ❣r❛✉ ❞❡ ✐♠♣✉r❡③❛ ❞♦ ♥♦❞♦ ♣❛✐ ✭❛♥t❡s ❞❛ ❞✐✈✐sã♦✮ ❝♦♠ ♦ ❣r❛✉ ❞❡ ✐♠♣✉r❡③❛

❞♦s ♥♦❞♦s ✜❧❤♦s ✭❛♣ós ❛ ❞✐✈✐sã♦✮✳ ◗✉❛♥t♦ ♠❛✐♦r ❛ ❞✐❢❡r❡♥ç❛✱ ♠❡❧❤♦r ❛ ❝♦♥❞✐çã♦ ❞❡

t❡st❡✳ ❖ ❣❛♥❤♦✱ ∆✱ é ✉♠ ❝r✐tér✐♦ q✉❡ ♣♦❞❡ s❡r ✉s❛❞♦ ♣❛r❛ ❞❡t❡r♠✐♥❛r ❛ q✉❛❧✐❞❛❞❡ ❞❡

✉♠❛ ❞✐✈✐sã♦✱ ❝♦♥❢♦r♠❡ ❛ ❡q✉❛çã♦ ✷✳✺ ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

∆ = I(pai)−k∑

j=1

N(vj)

NI(vj) ✭✷✳✺✮

❖♥❞❡ I(t) é ❛ ♠❡❞✐❞❛ ❞❡ ✐♠♣✉r❡③❛ ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ♥♦❞♦ t✱ N é ♦ ♥ú♠❡r♦ t♦t❛❧

❞❡ r❡❣✐str♦s ♥♦ ♥♦❞♦ ♣❛✐✱ k é ♦ ♥ú♠❡r♦ ❞❡ ✈❛❧♦r❡s ❞♦s ❛tr✐❜✉t♦s ❡ N(vj) é ♦ ♥ú♠❡r♦

❞❡ r❡❣✐str♦s ❛ss♦❝✐❛❞♦s ❛♦ ♥♦❞♦ ✜❧❤♦ vj✳ ❉❡ ♠♦❞♦ ❣❡r❛❧✱ ♠✉✐t♦s ❛❧❣♦r✐t♠♦s ❞❡ ár✈♦r❡

❞❡ ❞❡❝✐sã♦ ❡s❝♦❧❤❡♠ ✉♠❛ ❝♦♥❞✐çã♦ ❞❡ t❡st❡s q✉❡ ♠❛①✐♠✐❛ ♦ ❣❛♥❤♦ ∆✱ ❡ ♣❡❧♦ ❢❛t♦ ❞❡

I(pai) s❡r ♦ ♠❡s♠♦ ♣❛r❛ t♦❞❛s ❛s ❝♦♥❞✐çõ❡s ❞❡ t❡st❡✱ ♠❛①✐♠✐③❛r ♦ ❣❛♥❤♦ é ❡q✉✐✈❛❧❡♥t❡

❛ ♠✐♥✐♠✐③❛r ❛s ♠❡❞✐❞❛s ❞❡ ♠é❞✐❛ ♣♦♥❞❡r❛❞❛ ❞❡ ✐♠♣✉r❡③❛ ❞♦s ♥♦❞♦s ✜❧❤♦s✳

◗✉❛♥❞♦ ❛ ❡♥tr♦♣✐❛ é ✉s❛❞❛ ❝♦♠♦ ♠étr✐❝❛ ❞❡ ✐♠♣✉r❡③❛ ♥❛ ❡q✉❛çã♦ ✷✳✺✱ ❛ ❞✐❢❡r❡♥ç❛

♥❛ ❡♥tr♦♣✐❛ é ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ●❛♥❤♦ ❞❡ ■♥❢♦r♠❛çã♦✱ ∆info✱ ❛ q✉❛❧ ♠❡❞❡ ❛ ❡✜❝á❝✐❛ ❞❡

✉♠ ❛tr✐❜✉t♦ ❡♠ ❝❧❛ss✐✜❝❛r ♦s ❞❛❞♦s ❞❡ tr❡✐♥♦✳ ❆ ❡s❝♦❧❤❛ ❞♦ ❛tr✐❜✉t♦ ♠❛✐s ❡✜❝❛③✱ ♦

q✉❛❧ ♠❛✐s r❡❞✉③ ❛ ❡♥tr♦♣✐❛✱ ❢❛③ ❝♦♠ q✉❡ ❛ t❡♥❞ê♥❝✐❛ s❡❥❛ ❛ ❞❡ ❣❡r❛r ár✈♦r❡s ♠❡♥♦s

♣r♦❢✉♥❞❛s✱ ♣♦ss✉✐♥❞♦ ♠❡♥♦s ♥♦❞♦s ❡ r❛♠✐✜❝❛çõ❡s✳

❯♠ ❛❧❣♦r✐t♠♦ ♣❛r❛ ✐♥❞✉çã♦ ❞❡ ár✈♦r❡s ❞❡ ❞❡❝✐sã♦ é ✉♠ ❡①❡♠♣❧♦ ❞❡ ❛❧❣♦r✐t♠♦

❞❡ ❡str✉t✉r❛ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ❚❉■❉❚ ✭❚♦♣✲❉♦✇♥ ■♥❞✉❝t✐♦♥ ♦❢ ❉❡❝✐s✐♦♥ ❚r❡❡s✮✳ ❊st❡

❛❧❣♦r✐t♠♦ ✉t✐❧✐③❛ ❛ ❡str❛té❣✐❛ ✏❞✐✈✐❞✐r ♣❛r❛ ❝♦♥q✉✐st❛r✑✱ ❡♠ q✉❡ ✉♠ ♣r♦❜❧❡♠❛ ❝♦♠♣❧❡①♦

é ❞✐✈✐❞♦ ❡♠ s✉❜♣r♦❜❧❡♠❛s ♠❛✐s s✐♠♣❧❡s✳

◆♦ ❛❧❣♦r✐t♠♦ q✉❡ ❝♦♥stró✐ ✉♠❛ ár✈♦r❡ ❞❡ ❞❡❝✐sã♦✱ ♦ ♣❛ss♦ ♣r✐♥❝✐♣❛❧ é ❛ ❡s❝♦❧❤❛

❞❡ ✉♠ ❛tr✐❜✉t♦ ♣❛r❛ r♦t✉❧❛r ♦ ♥ó ❛t✉❛❧ ❞❛ ár✈♦r❡✳ ❉❡✈❡✲s❡ ❡s❝♦❧❤❡r ♦ ❛tr✐❜✉t♦ q✉❡

t❡♥❤❛ ♦ ♠❛✐♦r ♣♦❞❡r ❞❡ ❞✐s❝r✐♠✐♥❛çã♦ ❡♥tr❡ ❛s ❝❧❛ss❡s ♣❛r❛ ♦s ❡①❡♠♣❧♦s ♥♦ ♥ó ❛t✉❛❧✳

◆♦ ♣r♦❝❡ss♦ ❞❡ ✐♥❞✉çã♦ ❞❛ ár✈♦r❡✱ ♦ ❛❧❣♦r✐t♠♦ ❡s❝♦❧❤❡ ✉♠ ❛tr✐❜✉t♦✱ ❡st❡♥❞❡ ❛ ár✈♦r❡

❛❞✐❝✐♦♥❛♥❞♦ ✉♠ r❛♠♦ ♣❛r❛ ❝❛❞❛ ✈❛❧♦r ❞♦ ❛tr✐❜✉t♦✱ ♣❛ss❛ ♦s ❡①❡♠♣❧♦s ♣❛r❛ ❛s ❢♦❧❤❛s ❡

❛ss♦❝✐❛ ♣❛r❛ ❝❛❞❛ ♥ó ❢♦❧❤❛ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❝❧❛ss❡ q✉❛♥❞♦ s❡✉s ❡①❡♠♣❧♦s sã♦ t♦❞♦s ❞❛

♠❡s♠❛ ❝❧❛ss❡✱ s❡♥ã♦ r❡♣❡t❡ ♦ ♣r♦❝❡ss♦✳

◆♦ ❡♥t❛♥t♦✱ ❛ ár✈♦r❡ ❝♦♥str✉í❞❛ ♣♦❞❡♠ ❡st❛r ❛❥✉st❛❞❛ ❞❡♠❛✐s ❛♦s ❞❛❞♦s ❞❡ tr❡✐✲

♥❛♠❡♥t♦ ♥❡❝❡ss✐t❛♥❞♦✱ ♣♦rt❛♥t♦✱ ❞❡ ✉♠ ❞♦ ♣r♦❝❡❞✐♠❡♥t♦ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ✏♣♦❞❛ ❞❡

ár✈♦r❡✑✱ ♦ q✉❛❧ ♣♦❞❡ s❡r ❡①❡❝✉t❛❞♦ ♣❛r❛ r❡❞✉③✐r ♦ s❡✉ t❛♠❛♥❤♦✱ ♠❡❧❤♦r❛♥❞♦ ❛ss✐♠ ❛

s✉❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❣❡♥❡r❛❧✐③❛çã♦ ❡ ♥ã♦ ♦❝♦rr❡♥❞♦ ♦ ❢❡♥ô♠❡♥♦ ♦✈❡r✜tt✐♥❣✱ ♥♦ q✉❛❧ ♦ ❡rr♦

❞❡ tr❡✐♥❛♠❡♥t♦ ❞✐♠✐♥✉✐✱ ♠❛s ♦ ❡rr♦ ❞❡ t❡st❡ ❛✉♠❡♥t❛ ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✷✹

◆❛ ❧✐t❡r❛t✉r❛ ❡①✐st❡♠ ✈ár✐♦s ❛❧❣♦r✐t♠♦s ♣❛r❛ ✐♥❞✉çã♦ ❞❡ ár✈♦r❡s ❞❡ ❞❡❝✐sã♦ ❝♦♠♦✱

◆❇❚r❡❡✱ ❘❊P ❚r❡❡✱ ❘❛♥❞♦♠ ❚r❡❡✱ ❏✹✽✱ ❡♥tr❡ ♦✉tr♦s✱ q✉❡ ❢♦r❛♠ ✉t✐❧✐③❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦

❛tr❛✈és ❞♦ s♦❢t✇❛r❡ ❲❡❦❛✱ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ r❡❛❧✐③❛r ❛ ❝❧❛ss✐✜❝❛çã♦ ❞♦ trá❢❡❣♦ ♠❛❧✐❝✐♦s♦

❞❡ r❡❞❡✳ ❖s ❞✐✈❡rs♦s ❛❧❣♦r✐t♠♦s ❡s❝♦❧❤✐❞♦s ❢♦r❛♠ ❜❛s❡❛❞♦s ❡♠ r❡s✉❧t❛❞♦s ❞❡ tr❛❜❛❧❤♦s

r❡❧❛❝✐♦♥❛❞♦s✱ ♦s q✉❛✐s ♣❡r♠✐t✐r❛♠ r❡❛❧✐③❛r ❛♥á❧✐s❡s ❡ ❝♦♠♣❛r❛çõ❡s ♥♦ ❈❛♣ít✉❧♦ ✹✳

✷✳✺✳✷ ❘❡❞❡s ◆❡✉r❛✐s ❆rt✐✜❝✐❛✐s

❆ ár❡❛ ❞❛s r❡❞❡s ♥❡✉r❛✐s ❛rt✐✜❝✐❛✐s✱ t❛♠❜é♠ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❝♦♥❡①✐♦♥✐s♠♦ ♦✉ s✐st❡✲

♠❛s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ♣❛r❛❧❡❧♦ ❡ ❞✐str✐❜✉í❞♦✱ é ❝❛r❛❝t❡r✐③❛❞❛ ♣♦r s✐st❡♠❛s q✉❡✱ ❡♠

❛❧❣✉♠ ♥í✈❡❧✱ r❡❧❡♠❜r❛♠ ❛ ❡str✉t✉r❛ ❞♦ ❝ér❡❜r♦ ❤✉♠❛♥♦ ❡✱ ❝♦♥st✐t✉✐ ✉♠❛ ❛❧t❡r♥❛t✐✈❛

à ❝♦♠♣✉t❛çã♦ ❛❧❣♦rít♠✐❝❛ ❝♦♥✈❡♥❝✐♦♥❛❧ ♣♦r ♥ã♦ s❡r ❜❛s❡❛❞❛ ❡♠ r❡❣r❛s ❬❇r❛❣❛ ❡t ❛❧✳✱

✷✵✵✼❪✳

❖ ❝ér❡❜r♦ ❤✉♠❛♥♦ ❝♦♥s✐st❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❞❡ ❝é❧✉❧❛s ♥❡r✈♦s❛s ❝❤❛♠❛❞❛s ♥❡✉rô✲

♥✐♦s✱ ❝♦♥❢♦r♠❡ ♠♦str❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✽✱ q✉❡ sã♦ ❧✐❣❛❞♦s ❝♦♠ ♦✉tr♦s ❛tr❛✈és ❞❡ ✜♦s ❞❡

✜❜r❛ ❝❤❛♠❛❞♦s ❛①ô♥✐♦s✳ ❊st❡s sã♦ ✉s❛❞♦s ♣❛r❛ tr❛♥s♠✐t✐r ✐♠♣✉❧s♦s ♥❡r✈♦s♦s ❞❡ ✉♠

♥❡✉rô♥✐♦ ♣❛r❛ ♦✉tr♦✱ s❡♠♣r❡ q✉❡ ♦s ♥❡✉rô♥✐♦s ❢♦r❡♠ ❡st✐♠✉❧❛❞♦s✳ ❯♠ ♥❡✉rô♥✐♦ é ❝♦✲

♥❡❝t❛❞♦ ❛♦s ❛①ô♥✐♦s ❞❡ ♦✉tr♦s ♥❡✉rô♥✐♦s ❛tr❛✈és ❞❡ ❞❡♥tr✐t♦s✱ q✉❡ sã♦ ❡①t❡♥sõ❡s ❞♦

❝♦r♣♦ ❞❛ ❝é❧✉❧❛ ❞♦ ♥❡✉rô♥✐♦ ❡✱ ♦ ♣♦♥t♦ ❞❡ ❝♦♥t❛t♦ ❡♥tr❡ ✉♠ ❞❡♥❞r✐t♦ ❡ ✉♠ ❛①ô♥✐♦ é

❝❤❛♠❛❞♦ ❞❡ s✐♥❛♣s❡✳ ❖ ❝ér❡❜r♦ ❤✉♠❛♥♦ ❛♣r❡♥❞❡ q✉❛♥❞♦ s❡ ❛❧t❡r❛ ❛ ❢♦rç❛ ❞❛ ❝♦♥❡①ã♦

❞❛ s✐♥❛♣s❡ ❡♥tr❡ ♥❡✉rô♥✐♦s ❡♠ r❡♣❡t✐❞♦s ❡stí♠✉❧♦s ♣❡❧♦ ♠❡s♠♦ ✐♠♣✉❧s♦ ❬❚❛♥ ❡t ❛❧✳✱

✷✵✵✾❪✳

❋✐❣✉r❛ ✷✳✽✳ ❈♦♠♣♦♥❡♥t❡s ❞♦ ♥❡✉rô♥✐♦ ❜✐♦❧ó❣✐❝♦ ❬❇r❛❣❛ ❡t ❛❧✳✱ ✷✵✵✼❪

❆s ❘❡❞❡s ◆❡✉r❛✐s ❆rt✐✜❝✐❛✐s ✭❘◆❆s✮ sã♦ s✐st❡♠❛s ❝♦♠♣♦st♦s ♣♦r ✉♥✐❞❛❞❡s ❞❡

♣r♦❝❡ss❛♠❡♥t♦ s✐♠♣❧❡s ✭♥❡✉rô♥✐♦s ❛rt✐✜❝✐❛✐s✮✱ q✉❡ ❝❛❧❝✉❧❛♠ ❞❡t❡r♠✐♥❛❞❛s ❢✉♥çõ❡s ♠❛✲

t❡♠át✐❝❛s ✭♥♦r♠❛❧♠❡♥t❡ ♥ã♦✲❧✐♥❡❛r❡s✮✱ s❡♥❞♦ ❞✐s♣♦st❛s ❡♠ ✉♠❛ ♦✉ ♠❛✐s ❝❛♠❛❞❛s ❡

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✷✺

✐♥t❡r❧✐❣❛❞❛s ♣♦r ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ ❝♦♥❡①õ❡s✳ ◆❛ ♠❛✐♦r✐❛ ❞♦s ♠♦❞❡❧♦s ❡ss❛s ❝♦✲

♥❡①õ❡s ❡stã♦ ❛ss♦❝✐❛❞❛s ❛ ♣❡s♦s✱ ♦s q✉❛✐s ❛r♠❛③❡♥❛♠ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❛❞q✉✐r✐❞♦ ♣❡❧♦

♠♦❞❡❧♦ ❡ s❡r✈❡♠ ♣❛r❛ ♣♦♥❞❡r❛r ❛ ❡♥tr❛❞❛ r❡❝❡❜✐❞❛ ♣♦r ❝❛❞❛ ♥❡✉rô♥✐♦ ❞❛ r❡❞❡ ❬❇r❛❣❛

❡t ❛❧✳✱ ✷✵✵✼❪✳

P❡❧♦ ❢❛t♦ ❞❡ ♣♦ss✉✐r❡♠ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❛♣r❡♥❞❡r ♣♦r ♠❡✐♦ ❞❡ ❡①❡♠♣❧♦s ❡ ❣❡♥❡✲

r❛❧✐③❛r ❛ ✐♥❢♦r♠❛çã♦ ❛♣r❡♥❞✐❞❛ t♦r♥❛✲s❡ ♦ ❛tr❛t✐✈♦ ♣r✐♥❝✐♣❛❧ ❞❛ s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s

♣♦r ♠❡✐♦ ❞❛s ❘◆❆s✳ ❆ ❣❡♥❡r❛❧✐③❛çã♦ ❡stá ❛ss♦❝✐❛❞❛ à ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❛ r❡❞❡ ❛♣r❡♥❞❡r

♣♦r ♠❡✐♦ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ r❡❞✉③✐❞♦ ❞❡ ❡①❡♠♣❧♦s ❡ ❡♥tã♦ ❛♣r❡s❡♥t❛r r❡s♣♦st❛s ❝♦❡r❡♥t❡s

♣❛r❛ ❞❛❞♦s ♥ã♦ ❝♦♥❤❡❝✐❞♦s✳ ❊❧❛s✱ ♣♦rt❛♥t♦✱ sã♦ ❝❛♣❛③❡s ❞❡ ❛t✉❛r ❝♦♠♦ ♠❛♣❡❛❞♦r❡s

✉♥✐✈❡rs❛✐s ❞❡ ❢✉♥çõ❡s ♠✉❧t✐✈❛r✐á✈❡✐s✱ ❛❧é♠ ❞❡ t❡r❡♠ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❛✉t♦✲♦r❣❛♥✐③❛çã♦

❡ ♣r♦❝❡ss❛♠❡♥t♦ t❡♠♣♦r❛❧✱ ♣❡r♠✐t✐♥❞♦ ❛ss✐♠ ❛ s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❝♦♠♣❧❡①♦s ❬❇r❛❣❛

❡t ❛❧✳✱ ✷✵✵✼❪✳

❖ ♣r✐♠❡✐r♦ ♠♦❞❡❧♦ ❛rt✐✜❝✐❛❧ ❞❡ ✉♠ ♥❡✉rô♥✐♦ ❜✐♦❧ó❣✐❝♦ ❢♦✐ ❢r✉t♦ ❞♦ tr❛❜❛❧❤♦ ❞❡

❲❛rr❡♥ ▼❝❈✉❧❧♦❝❤ ❡ ❲❛❧t❡r P✐tts ❡♠ ✶✾✹✸✳ ❙✉❛ ❞❡s❝r✐çã♦ ♠❛t❡♠át✐❝❛ r❡s✉❧t♦✉ ❡♠ ✉♠

♠♦❞❡❧♦ ❝♦♠ n t❡r♠✐♥❛✐s ❞❡ ❡♥tr❛❞❛ ✭❞❡♥tr✐t♦s✮ q✉❡ r❡❝❡❜❡♠ ♦s ✈❛❧♦r❡s x1, x2, ..., xn ✭q✉❡

r❡♣r❡s❡♥t❛♠ ❛s ❛t✐✈❛çõ❡s ❞♦s ♥❡✉rô♥✐♦s✮ ❡ ❛♣❡♥❛s ✉♠ t❡r♠✐♥❛❧ ❞❡ s❛í❞❛ y ✭r❡♣r❡s❡♥t❛♥❞♦

♦ ❛①ô♥✐♦✮✳ P❛r❛ r❡♣r❡s❡♥t❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛s s✐♥❛♣s❡s✱ ♦s t❡r♠✐♥❛✐s ❞❡ ❡♥tr❛❞❛

❞♦ ♥❡✉rô♥✐♦ t❡♠ ♣❡s♦s ❛❝♦♣❧❛❞♦s w1, w2, ..., wn ❝♦♥❢♦r♠❡ ♠♦str❛ ❛ ❋✐❣✉r❛ ✷✳✾ ❬❇r❛❣❛

❡t ❛❧✳✱ ✷✵✵✼❪✳

❋✐❣✉r❛ ✷✳✾✳ ◆❡✉rô♥✐♦ ❞❡ ▼❝❈✉❧❧♦❝❤ ❡ P✐tts✱ ♥♦ q✉❛❧∑

r❡♣r❡s❡♥t❛ ❛ s♦♠❛♣♦♥❞❡r❛❞❛ ❞❛s ❡♥tr❛❞❛s ❡ f(·) ❛ ❢✉♥çã♦ ❞❡ ❛t✐✈❛çã♦ ❬❇r❛❣❛ ❡t ❛❧✳✱ ✷✵✵✼❪

❖ ♣r✐♠❡✐r♦ ♠ó❞✉❧♦ ❞♦ ♥❡✉rô♥✐♦ ❛rt✐✜❝✐❛❧✱ ❞❡♥♦♠✐♥❛❞♦ r❡❣r❛ ❞❡ ♣r♦♣❛❣❛çã♦✱ ❡①❡✲

❝✉t❛ ✉♠❛ s♦♠❛ ♣♦♥❞❡r❛❞❛ ❞❛s ❡♥tr❛❞❛s xi ♠✉❧t✐♣❧✐❝❛❞❛s ♣❡❧♦s s❡✉s ♣❡s♦s s✐♥á♣t✐❝♦s wi✱

❛ss♦❝✐❛❞♦s ❛ ❝❛❞❛ ❡♥tr❛❞❛✳ ❖ s❡❣✉♥❞♦ ♠ó❞✉❧♦✱ ❞❡♥♦♠✐♥❛❞♦ ❢✉♥çã♦ ❞❡ ❛t✐✈❛çã♦✱ ❛♣❧✐❝❛

✉♠❛ ❢✉♥çã♦ ❛♦ r❡s✉❧t❛❞♦ ❞❛ r❡❣r❛ ❞❡ ♣r♦♣❛❣❛çã♦✳ ❊ss❛ ❢✉♥çã♦ é r❡s♣♦♥sá✈❡❧ ♣♦r ❣❡r❛r

❛ s❛í❞❛ y ❞♦ ♥❡✉rô♥✐♦ ❛ ♣❛rt✐r ❞♦s ✈❛❧♦r❡s ❞♦s ✈❡t♦r❡s ❞❡ ♣❡s♦ ❡ ❞❡ ❡♥tr❛❞❛✳

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✷✻

❆♣❡s❛r ❞❛s ❞✐✈❡rs❛s ❢✉♥çõ❡s ❞❡ ❛t✐✈❛çõ❡s ♣♦ssí✈❡✐s✱ ❝♦♠♦ ❛s ♠♦str❛❞❛s ♥❛s ✜❣✉r❛s

✷✳✶✵ ❡ ✷✳✶✶✱ ♦s ♥❡✉rô♥✐♦s ✐♥❞✐✈✐❞✉❛✐s ♣♦ss✉❡♠ ❝❛♣❛❝✐❞❛❞❡ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❧✐♠✐t❛❞❛✳

❊♥tr❡t❛♥t♦✱ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♥❡✉rô♥✐♦s ❛rt✐✜❝✐❛✐s ❝♦♥❡❝t❛❞♦s ♥❛ ❢♦r♠❛ ❞❡ ✉♠❛ r❡❞❡ é

❝❛♣❛③ ❞❡ r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s ❝♦♠♣❧❡①♦s✳ ❆ss✐♠✱ ❞✐✈❡rs❛s ❢♦r♠❛s ❞❡ ♦r❣❛♥✐③❛çã♦ ❞♦s

♥❡✉rô♥✐♦s sã♦ ♣♦ssí✈❡✐s✱ ❞❡♥♦♠✐♥❛❞❛s ❛rq✉✐t❡t✉r❛s✳

❋✐❣✉r❛ ✷✳✶✵✳ ❋✉♥çã♦ ❞❡ ❛t✐✈❛çã♦ ❞❡❣r❛✉ ✭❛✮ ❡ s✐❣♠♦✐❞❛❧ ✭❜✮ ❬❇r❛❣❛ ❡t ❛❧✳✱ ✷✵✵✼❪

❋✐❣✉r❛ ✷✳✶✶✳ ❋✉♥çã♦ ❞❡ ❛t✐✈❛çã♦ ❧✐♥❡❛r ✭❛✮ ❡ ❣❛✉ss✐❛♥❛ ✭❜✮ ❬❇r❛❣❛ ❡t ❛❧✳✱ ✷✵✵✼❪

P♦r ❡①❡♠♣❧♦✱ ✉♠❛ ❛rq✉✐t❡t✉r❛ s✐♠♣❧❡s ♠♦str❛❞❛ ♥❛ ❋✐❣✉r❛ ✷✳✶✷✭❛✮✱ ❝♦rr❡s♣♦♥❞❡

❛ ✉♠❛ r❡❞❡ ♥❡✉r❛❧ ú♥✐❝❛ ❛❧✐♠❡♥t❛❞❛ ♣❛r❛ ❛ ❢r❡♥t❡ ✭❢❡❡❞❢♦r✇❛r❞✮✱ ❛ q✉❛❧ é ❝❛♣❛③ ❞❡

r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s ♠✉❧t✐✈❛r✐á✈❡✐s ❞❡ ♠ú❧t✐♣❧❛s ❢✉♥çõ❡s ❛❝♦♣❧❛❞❛s✱ ♠❛s ❛✐♥❞❛ ❝♦♠ ❛❧❣✉✲

♠❛s r❡str✐çõ❡s ❞❡ ❝♦♠♣❧❡①✐❞❛❞❡✱ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ ♣♦ss✉✐r ❛♣❡♥❛s ✉♠❛ ❝❛♠❛❞❛✳ ❖✉tr❛

❡str✉t✉r❛✱ ♠♦str❛❞❛ ♥❛ ❋✐❣✉r❛ ✷✳✶✷✭❜✮✱ ♣♦ss✉✐ ✉♠❛ ❝❛♠❛❞❛ ❛❞✐❝✐♦♥❛❧✱ ❝♦♥❢❡r✐♥❞♦ à

❘◆❆ ✉♠❛ ♠❛✐♦r ❝❛♣❛❝✐❞❛❞❡ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❡ ✉♥✐✈❡rs❛❧✐❞❛❞❡ ♥❛ ❛♣r♦①✐♠❛çã♦ ❞❡ ❢✉♥✲

çõ❡s ❝♦♥tí♥✉❛s✳ ❊ss❛s ❡str✉t✉r❛s ♣♦r ♥ã♦ ♣♦ss✉✐r❡♠ r❡❝♦rrê♥❝✐❛ ✭r❡❛❧✐♠❡♥t❛çã♦✮✱ sã♦

❝♦♥s✐❞❡r❛❞❛s ❡stát✐❝❛s✱ ❛♦ ❝♦♥trár✐♦ ❞❛s ❡str✉t✉r❛s ♠♦str❛❞❛s ♥❛ ❋✐❣✉r❛ ✷✳✶✸✱ ❛s q✉❛✐s

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✷✼

sã♦ ❣❡r❛❧♠❡♥t❡ ✉t✐❧✐③❛❞❛s ❡♠ ♣r♦❜❧❡♠❛s q✉❡ ❡♥✈♦❧✈❛♠ ♣r♦❝❡ss❛♠❡♥t♦ t❡♠♣♦r❛❧✱ ❝♦♠♦

♣r❡✈✐sã♦ ❞❡ ❡✈❡♥t♦s ❢✉t✉r♦s✳

❋✐❣✉r❛ ✷✳✶✷✳ ❘❡❞❡ ❢❡❡❞❢♦r✇❛r❞ ❞❡ ✉♠❛ ❝❛♠❛❞❛ ✭❛✮ ❡ ❞❡ ❞✉❛s ❝❛♠❛❞❛s ✭❜✮ ❬❇r❛❣❛❡t ❛❧✳✱ ✷✵✵✼❪

❋✐❣✉r❛ ✷✳✶✸✳ ❘❡❞❡ ❝♦♠ r❡❝♦rrê♥❝✐❛ ❡♥tr❡ s❛í❞❛s ❡ ❝❛♠❛❞❛ ✐♥t❡r♠❡❞✐ár✐❛ ✭❛✮ ❡r❡❞❡ ❝♦♠ r❡❝♦rrê♥❝✐❛ ❛✉t♦✲❛ss♦❝✐❛t✐✈❛ ✭❜✮ ❬❇r❛❣❛ ❡t ❛❧✳✱ ✷✵✵✼❪

❊♥tr❡ ♦s t✐♣♦s ❞❡ ❘◆❆s ♠❛✐s ✉t✐❧✐③❛❞❛s ♣♦❞❡♠♦s ❝✐t❛r ❛s r❡❞❡s ❞❡ ♠ú❧t✐♣❧❛s ❝❛♠❛✲

❞❛s ▼▲P ✭▼✉❧t✐❧❛②❡r P❡r❝❡♣tr♦♥s✮✱ ❛s q✉❛✐s sã♦ ❢♦r♠❛❞❛s ♣♦r ✉♠❛ ❝❛♠❛❞❛ ❞❡ ❡♥tr❛❞❛✱

✉♠❛ ♦✉ ♠❛✐s ❝❛♠❛❞❛s ✐♥t❡r♠❡❞✐ár✐❛s ✭♦❝✉❧t❛s✮ ❡ ✉♠❛ ❝❛♠❛❞❛ ❞❡ s❛í❞❛✳ ❖✉tr♦ t✐♣♦✱

❝♦♥st✐t✉í❞❛ ❣❡r❛❧♠❡♥t❡ ❞❡ três ❝❛♠❛❞❛s sã♦ ❛s r❡❞❡s ❘❇❋ ✭❘❛❞✐❛❧ ❇❛s❡ ❋✉♥❝t✐♦♥s✮✳

◆❡ss❛ ❛rq✉✐t❡t✉r❛ ♦s ♥❡✉rô♥✐♦s ❞❛ ❝❛♠❛❞❛ ✐♥t❡r♠é❞✐❛r✐❛ ✉t✐❧✐③❛♠ ❢✉♥çõ❡s ❞❡ ❜❛s❡s r❛✲

❞✐❛✐s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ❢✉♥çã♦ ❣❛✉ss✐❛♥❛ ♠♦str❛❞❛ ♥❛ ❋✐❣✉r❛ ✷✳✶✶✭❜✮✱ ❡♠ q✉❡ ❛

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✷✽

❛t✐✈❛çã♦ ❞❡ ✉♠ ♥❡✉rô♥✐♦ ♣♦❞❡ s❡r ❢✉♥çã♦ ❞❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ s❡✉s ✈❡t♦r❡s ❞❡ ❡♥tr❛❞❛ ❡ ❞❡

♣❡s♦✱ ❛♦ ❝♦♥trár✐♦ ❞❛s r❡❞❡s ▼▲P q✉❡ ✉t✐❧✐③❛♠ ❣❡r❛❧♠❡♥t❡ ❢✉♥çõ❡s ❞❡ ❜❛s❡ s✐❣♠♦❞❛✐s

❬❇r❛❣❛ ❡t ❛❧✳✱ ✷✵✵✼❪✳

❚❛♥t♦ ❛s r❡❞❡s ❘❇❋ ❝♦♠♦ ❛s r❡❞❡s ▼▲P sã♦ ❛♣r♦①✐♠❛❞♦r❛s ✉♥✐✈❡rs❛✐s ❞❡ ❢✉♥çõ❡s✱

s❡♥❞♦ ♣♦rt❛♥t♦ ❡q✉✐✈❛❧❡♥t❡s✳ ❊♥tr❡t❛♥t♦✱ ❡①✐st❡♠ ❞✐❢❡r❡♥ç❛s ❝♦♠♦ ❛ ♣❛rt✐çã♦ ❞♦ ❡s♣❛ç♦

❞❡ ♣❛❞rõ❡s ❞❡ ❡♥tr❛❞❛ r❡❛❧✐③❛❞❛ ♣❡❧❛ ❝❛♠❛❞❛ ✐♥t❡r♠❡❞✐ár✐❛ ❞♦ ♠♦❞❡❧♦✳ ❊♥q✉❛♥t♦ ✉♠❛

r❡❞❡ ❘❇❋ ❝♦♥stró✐ ❛♣r♦①✐♠❛❞♦r❡s ❧♦❝❛✐s ❛tr❛✈és ❞❡ ❤✐♣❡r❧✐♣só✐❞❡✱ ✐st♦ é✱ ❛♣❡♥❛s ❛s

r❡❣✐õ❡s ❞♦ ❡s♣❛ç♦ ❞❡ ❡♥tr❛❞❛ q✉❡ ❛♣r❡s❡♥t❛♠ ❞❛❞♦s ❞❡ tr❡✐♥❛♠❡♥t♦ t❡rã♦ r❡s♣♦st❛ ❞❛

r❡❞❡✳ ❆s r❡❞❡s ▼▲P✱ ♣♦r ♦✉tr♦ ❧❛❞♦✱ ♣❛rt✐❝✐♦♥❛♠ ♦ ❡s♣❛ç♦ ❞❡ ❡♥tr❛❞❛s ❛tr❛✈és ❞❡

❤✐♣❡r♣❧❛♥♦s ❬❇r❛❣❛ ❡t ❛❧✳✱ ✷✵✵✼❪✳

❆ss✐♠✱ ❛s r❡❞❡s ▼▲P ♣♦ss✉❡♠ ♠❛✐♦r ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❣❡♥❡r❛❧✐③❛çã♦ ❡ ♥❡❝❡ss✐t❛♠✱

❡♠ ❣❡r❛❧✱ ❞❡ ♠❡♥♦s ❞❛❞♦s ♣❛r❛ tr❡✐♥❛♠❡♥t♦ q✉❡ ❛s r❡❞❡s ❘❇❋✳ ❊st❛s ♥♦ ❡♥t❛♥t♦✱ ♥❡❝❡s✲

s✐t❛♠ ❞❡ ♠❛✐s ❞❛❞♦s ♣❛r❛ ❣❡♥❡r❛❧✐③❛r ❛ ✐♥❢♦r♠❛çã♦ ❡ sã♦ ✉t✐❧✐③❛❞❛s ❣❡r❛❧♠❡♥t❡ ❡♠ ♣r♦✲

❜❧❡♠❛s ❜❡♠ ❞❡✜♥✐❞♦s✱ q✉❡ ♣♦ss✉❡♠ ❞❛❞♦s ❞✐♥â♠✐❝♦s ❡ q✉❡ ♥❡❝❡ss✐t❛♠ ❞❡ ❛♣r❡♥❞✐③❛❞♦

❝♦♥t✐♥✉❛❞♦ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ♣r❡✈✐sõ❡s ❞❡ sér✐❡s t❡♠♣♦r❛r✐s ❡ ♦♣❡r❛çõ❡s ✜♥❛♥❝❡✐r❛s

❬❇r❛❣❛ ❡t ❛❧✳✱ ✷✵✵✼❪✳

P❛r❛ ❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s✱ ❛ ❡s❝♦❧❤❛ ❞❡ ✉♠❛ ❛rq✉✐t❡t✉r❛ ❝♦rr❡t❛ é ❢✉♥❞❛♠❡♥✲

t❛❧✱ ❛ q✉❛❧ ❞❡♣❡♥❞❡ ❞❡ ✈ár✐♦s ❢❛t♦r❡s ❝♦♠♦ ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦ ♣r♦❜❧❡♠❛✱ ❞✐♠❡♥s✐♦♥❛❧✐❞❛❞❡

❞♦ ❡s♣❛ç♦ ❞❡ ❡♥tr❛❞❛✱ ❝❛r❛❝t❡ríst✐❝❛s ❞✐♥â♠✐❝❛s ♦✉ ❡stát✐❝❛s✱ ❝♦♥❤❡❝✐♠❡♥t♦ ❛ ♣r✐♦r✐ ❞♦

♣r♦❜❧❡♠❛ ❡ r❡♣r❡s❡♥t❛t✐✈✐❞❛❞❡ ❞♦s ❞❛❞♦s✳ ❚♦❞❛✈✐❛✱ ♦ ❛♣r❡♥❞✐③❛❞♦ ❞❛s ❘◆❆s✱ ❝♦♥❢♦r♠❡

❛ ❛❜♦r❞❛❣❡♠ ❝♦♥❡①✐♦♥✐st❛✱ ♥ã♦ é ❛❞q✉✐r✐❞♦ ❛tr❛✈és ❞❡ r❡❣r❛s ❡①♣❧í❝✐t❛s✱ ♠❛s ❛tr❛✈és ❞♦

❛❥✉st❡ ❞❡ ✐♥t❡♥s✐❞❛❞❡s ❞❛s ❝♦♥❡①õ❡s ❡♥tr❡ ♦s ♥❡✉rô♥✐♦s ❬❇r❛❣❛ ❡t ❛❧✳✱ ✷✵✵✼❪✳

❆ ❡t❛♣❛ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ✉♠❛ ❘◆❆ ❝♦♥s✐st❡ ❡♠ ✉♠ ♣r♦❝❡ss♦ ✐t❡r❛t✐✈♦✱ ♦ q✉❛❧

❛❥✉st❛ ♦s ♣❡s♦s ❞❛s ❝♦♥❡①õ❡s✱ q✉❡ ❣✉❛r❞❛♠ ❛♦ ✜♥❛❧ ❞♦ ♣r♦❝❡ss♦✱ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ q✉❡ ❛

r❡❞❡ ❛❞q✉✐r✐✉ ❞♦ ❛♠❜✐❡♥t❡ ❡①t❡r♥♦✳ ❊st❡ ❝♦♥❤❡❝✐♠❡♥t♦ ❡stá r❡❧❛❝✐♦♥❛❞♦ ❝♦♠ ❛ ♠❡❧❤♦r✐❛

❞❡ ❞❡s❡♠♣❡♥❤♦ ❞❛ r❡❞❡ s❡❣✉♥❞♦ ❛❧❣✉♠ ❝r✐tér✐♦ ♣r❡❡st❛❜❡❧❡❝✐❞♦✳ P♦r ❡①❡♠♣❧♦✱ ♦ ❡rr♦

q✉❛❞rát✐❝♦ ♠é❞✐♦ ❞❛ r❡s♣♦st❛ ❞❛ r❡❞❡ é ✉t✐❧✐③❛❞♦ ❝♦♠♦ ❝r✐tér✐♦ ❞❡ ❞❡s❡♠♣❡♥❤♦ ♣❡❧♦s

❛❧❣♦r✐t♠♦s ❞❡ ❝♦rr❡çã♦ ❞❡ ❡rr♦s✱ q✉❡ sã♦ ✉t✐❧✐③❛❞♦s ♥♦ tr❡✐♥❛♠❡♥t♦ ❞❛s ❘◆❆s✳ ❉❡ss❛

❢♦r♠❛✱ ❡s♣❡r❛✲s❡ q✉❡ ♦ ❡rr♦ ❞✐♠✐♥✉❛ à ♠❡❞✐❞❛ q✉❡ ♦ ❛♣r❡♥❞✐③❛❞♦ ♣r♦ss✐❣❛✳ ●❡♥❡r✐❝❛✲

♠❡♥t❡✱ ♦ ✈❛❧♦r ❞♦ ✈❡t♦r ❞❡ ♣❡s♦s w(t + 1) ♥♦ ✐♥st❛♥t❡ t + 1 ♣♦❞❡ s❡r ❡s❝r✐t♦ ❝♦♥❢♦r♠❡

❛ ❊q✉❛çã♦ ✷✳✻✱ ♦♥❞❡ w(t) ❡ w(t+ 1) r❡♣r❡s❡♥t❛♠ ♦s ✈❛❧♦r❡s ❞♦s ♣❡s♦s ♥♦s ✐♥st❛♥t❡s t ❡

t + 1✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❡ ∆w(t) é ♦ ❛❥✉st❡ ❛♣❧✐❝❛❞♦ ❛♦s ♣❡s♦s✳ ➱ ❥✉st❛♠❡♥t❡ ❛ ❢♦r♠❛

❝♦♠♦ ❝❛❧❝✉❧❛ ❡st❡ ❛❥✉st❡ ∆w(t) q✉❡ ❞✐❢❡r❡♥❝✐❛ ♦s ❞✐✈❡rs♦s ❛❧❣♦r✐t♠♦s ♣❛r❛ tr❡✐♥❛♠❡♥t♦

❞❛s ❘◆❆s✳ ❊ss❡s ❛❧❣♦r✐t♠♦s ♣♦❞❡♠ s❡r ❛❣r✉♣❛❞♦s ❡♠ ❞♦✐s ♣❛r❛❞✐❣♠❛s ♣r✐♥❝✐♣❛✐s✿

❛♣r❡♥❞✐③❛❞♦ s✉♣❡r✈✐s✐♦♥❛❞♦ ❡ ❛♣r❡♥❞✐③❛❞♦ ♥ã♦✲s✉♣❡r✈✐s✐♦♥❛❞♦ ❬❇r❛❣❛ ❡t ❛❧✳✱ ✷✵✵✼❪✳

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✷✾

w(t+ 1) = w(t) + ∆w(t) ✭✷✳✻✮

P❛r❛ ♦ tr❛❜❛❧❤♦ ❞❡s❡♥✈♦❧✈✐❞♦✱ ♦ q✉❛❧ ❝♦♥s✐st❡ ❡♠ r❡❛❧✐③❛r t❛r❡❢❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦✱

♦ ❛♣r❡♥❞✐③❛❞♦ s✉♣❡r✈✐s✐♦♥❛❞♦ é ♦ ❛♣❧✐❝❛❞♦✳ ❊st❡ ♣❛r❛❞✐❣♠❛ ✐♠♣❧✐❝❛✱ ♥❡❝❡ss❛r✐❛♠❡♥t❡✱

❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠ s✉♣❡r✈✐s♦r✱ ♦ q✉❛❧ é r❡s♣♦♥sá✈❡❧ ♣♦r ❡st✐♠✉❧❛r ❛s ❡♥tr❛❞❛s ❞❛ r❡❞❡

♣♦r ♠❡✐♦ ❞❡ ♣❛❞rõ❡s ❞❡ ❡♥tr❛❞❛ ❡ ♦❜s❡r✈❛r ❛ s❛í❞❛ ❝❛❧❝✉❧❛❞❛✱ ❝♦♠♣❛r❛♥❞♦✲❛ ❝♦♠ ❛

s❛í❞❛ ❞❡s❡❥❛❞❛✳

❆ss✐♠✱ ♦s ♣❡s♦s sã♦ ❛❥✉st❛❞♦s ❛♣r♦①✐♠❛♥❞♦ ❛ s❛í❞❛ ❞❛ r❡❞❡ ❞❛ s❛í❞❛ ❞❡s❡❥❛❞❛✳

❊ss❡ ♣r♦❝❡ss♦ é r❡❛❧✐③❛❞♦ ♣❛r❛ ❝❛❞❛ ♣❛❞rã♦ ❞❡ ❡♥tr❛❞❛✱ ❡♠ q✉❡ ❛ r❡❞❡ t❡♠ s✉❛ s❛í❞❛ ❝♦r✲

r❡♥t❡ ❝♦♠♣❛r❛❞❛ ❝♦♠ ❛ s❛í❞❛ ❞❡s❡❥❛❞❛ ♣❡❧♦ s✉♣❡r✈✐s♦r✱ q✉❡ ❢♦r♥❡❝❡ ✐♥❢♦r♠❛çõ❡s s♦❜r❡

❛ ❞✐r❡çã♦ ❞❡ ❛❥✉st❡ ❞♦s ♣❡s♦s✳ ❖ ❛♣r❡♥❞✐③❛❞♦ s✉♣❡r✈✐s✐♦♥❛❞♦ ♣♦❞❡ s❡r ✐♠♣❧❡♠❡♥t❛❞♦

t❛♥t♦ ♦✤✐♥❡ ❝♦♠♦ ♦♥❧✐♥❡ s❡♥❞♦ q✉❡✱ ♥♦ ♣r✐♠❡✐r♦✱ ♦s ❞❛❞♦s ❞♦ ❝♦♥❥✉♥t♦ ❞❡ tr❡✐♥❛♠❡♥t♦

♥ã♦ ♠✉❞❛♠ ❡✱ ❛♦ ❡♥❝♦♥tr❛r ✉♠❛ s♦❧✉çã♦ ♣❛r❛ ❛ r❡❞❡✱ ❡st❛ ❞❡✈❡ ♣❡r♠❛♥❡❝❡r ✜①❛✳ ❙❡

♥♦✈♦s ❞❛❞♦s ❢♦r❡♠ ❛❞✐❝✐♦♥❛❞♦s✱ ✉♠ ♥♦✈♦ tr❡✐♥❛♠❡♥t♦✱ ✐♥❝❧✉s✐✈❡ ❝♦♠ ♦s ❞❛❞♦s ❛♥t❡r✐♦✲

r❡s✱ ❞❡✈❡ s❡r r❡❛❧✐③❛❞♦ ♥♦✈❛♠❡♥t❡✳ ◆♦ s❡❣✉♥❞♦✱ ♣♦r s✉❛ ✈❡③✱ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ♠✉❞❛

❝♦♥t✐♥✉❛♠❡♥t❡ ❡ ❛ r❡❞❡ ♣r❡❝✐s❛ ❡st❛r ❡♠ ✉♠ ❝♦♥tí♥✉♦ ♣r♦❝❡ss♦ ❞❡ ❛❞❛♣t❛çã♦ ❬❇r❛❣❛

❡t ❛❧✳✱ ✷✵✵✼❪✳

❉❡ ♠❛♥❡✐r❛ ❣❡r❛❧✱ ♦ ❛♣r❡♥❞✐③❛❞♦ s✉♣❡r✈✐s✐♦♥❛❞♦ é ❛♣❧✐❝❛❞♦ ❡♠ ♣r♦❜❧❡♠❛s ❡♠ q✉❡

s❡ ❞❡s❡❥❛ ♦❜t❡r ✉♠ ♠❛♣❡❛♠❡♥t♦ ❡♥tr❡ ♣❛❞rõ❡s ❞❡ ❡♥tr❛❞❛ ❡ s❛í❞❛ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱

♣r♦❜❧❡♠❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦✱ ❡♠ q✉❡ ♣❛❞rõ❡s sã♦ ❛♣r❡s❡♥t❛❞♦s às ❡♥tr❛❞❛s ❡ ❛s ❝❧❛ss❡s

❝♦rr❡s♣♦♥❞❡♥t❡s sã♦ ❛♣r❡s❡♥t❛❞❛s às s❛í❞❛s ❞❛ r❡❞❡ ❞✉r❛♥t❡ ♦ ♣r♦❝❡ss♦ ❞❡ ❛♣r❡♥❞✐③❛❞♦✳

◆❡st❡ ❡①❡♠♣❧♦✱ ❛ r❡❞❡ ❞❡✈❡rá ❛❞❛♣t❛r ♦s s❡✉s ♣❡s♦s ❞❡ ❢♦r♠❛ ❛ ♠❛♣❡❛r ❛s r❡❧❛çõ❡s

❡♥tr❡ ♣❛❞rõ❡s ❞❡ ❡♥tr❛❞❛ ❡ ❝❧❛ss❡s ❝♦rr❡s♣♦♥❞❡♥t❡s ❞❡ s❛í❞❛✱ t❡♥❞♦ ♣♦r ❜❛s❡ ♦s ❞❛❞♦s ❞♦

❝♦♥❥✉♥t♦ ❞❡ tr❡✐♥❛♠❡♥t♦✳ ❖✉tr♦s ❡①❡♠♣❧♦s q✉❡ ✉t✐❧✐③❛♠ ♦ ❛♣r❡♥❞✐③❛❞♦ s✉♣❡r✈✐s✐♦♥❛❞♦

sã♦ ♦s ♣r♦❜❧❡♠❛s ❞❡ ❛♣r♦①✐♠❛çã♦ ❡ ♣r❡✈✐sã♦ ❬❇r❛❣❛ ❡t ❛❧✳✱ ✷✵✵✼❪✳

❖s ♠❛✐s ❝♦♥❤❡❝✐❞♦s ❛❧❣♦r✐t♠♦s ♣❛r❛ ❛♣r❡♥❞✐③❛❞♦ s✉♣❡r✈✐s✐♦♥❛❞♦ sã♦ ❛ r❡❣r❛ ❞❡❧t❛✱

❝♦♥❤❡❝✐❞♦ t❛♠❜é♠ ❝♦♠♦ ▲▼❙ ✭▲❡❛st ▼❡❛♥ ❙q✉❛r❡✮✱ ❡ s✉❛ ❣❡♥❡r❛❧✐③❛çã♦ ♣❛r❛ ❛s r❡✲

❞❡s ❞❡ ♠ú❧t✐♣❧❛s ❝❛♠❛❞❛s✱ ♦ ❛❧❣♦r✐t♠♦ ❜❛❝❦✲♣r♦♣❛❣❛t✐♦♥✱ q✉❡ ❜❛s❡✐❛✲s❡ ♥❛ ❤❡✉ríst✐❝❛

♣♦r ❝♦rr❡çã♦ ❞❡ ❡rr♦✱ ♦ q✉❛❧ é r❡tr♦♣r♦♣❛❣❛❞♦ ❞❛ ❝❛♠❛❞❛ ❞❡ s❛í❞❛ ♣❛r❛ ❛s ❝❛♠❛❞❛s

✐♥t❡r♠❡❞✐ár✐❛s ❞❛ ❘◆❆ ❬❇r❛❣❛ ❡t ❛❧✳✱ ✷✵✵✼❪✳

◆❡st❡ tr❛❜❛❧❤♦✱ ♦ ❛♣r❡♥❞✐③❛❞♦ s✉♣❡r✈✐s✐♦♥❛❞♦ ❢♦✐ ❝♦♥s✐❞❡r❛❞♦✱ ♣♦✐s ❝♦♥s✐st✐✉ ❡♠

r❡❛❧✐③❛r ❛ ❝❧❛ss✐✜❝❛çã♦ ❞♦ trá❢❡❣♦ ❞❡ r❡❞❡✳ ❆ss✐♠✱ ❛ ♣❛rt✐r ❞❡ ✉♠❛ ❛♠♦str❛ ❞♦s ❞❛❞♦s

✉t✐❧✐③❛♥❞♦ ♦ s♦❢t✇❛r❡ ❲❡❦❛✱ ❛s ❘◆❆s ❘❇❋ ❡ ▼▲P ❢♦r❛♠ ✉s❛❞❛s ♣❛r❛ ❝❧❛ss✐✜❝❛r ♦s

r❡❣✐str♦s✳ ❆❧é♠ ❞✐ss♦✱ ❛s ❘◆❆s ▼▲P t❛♠❜é♠ ❢♦r❛♠ ❡♠♣r❡❣❛❞❛s ❡♠ ❝♦♥❥✉♥t♦ ❝♦♠ ❛

té❝♥✐❝❛ ❞❡ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦✱ ❛ q✉❛❧ ♣❡r♠✐t✐✉ ♠❡❧❤♦r❛r ♦s r❡s✉❧t❛❞♦s✳

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✸✵

✷✳✺✳✸ ❆❧❣♦r✐t♠♦s ●❡♥ét✐❝♦s

❖✉tr❛ té❝♥✐❝❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❜❛st❛♥t❡ ✉t✐❧✐③❛❞❛ sã♦ ♦s ❆❧❣♦r✐t♠♦s ●❡♥ét✐❝♦s✱ q✉❡

❢❛③❡♠ ♣❛rt❡ ❞❛ ❈♦♠♣✉t❛çã♦ ❊✈♦❧✉t✐✈❛ ✭❈❊✮✱ ❛ q✉❛❧ ❜❛s❡✐❛✲s❡ ❡♠ ♠❡❝❛♥✐s♠♦s ❡✈♦❧✉t✐✈♦s

❡♥❝♦♥tr❛❞♦s ♥❛ ♥❛t✉r❡③❛✳ ❖s ❆●s sã♦ ✐♥s♣✐r❛❞♦s ♥♦s ♠♦❞❡❧♦s ❜✐♦❧ó❣✐❝♦s✱ ♦s q✉❛✐s

❢✉♥❞❛♠❡♥t❛♠✲s❡ ♥❛ ●❡♥ét✐❝❛ ❞❡ ▼❡♥❞❡❧ ❡ ♥❛ ❚❡♦r✐❛ ❞❛ ❊✈♦❧✉çã♦ ❞❡ ❉❛r✇✐♥ ❬❆rt❡r♦✱

✷✵✵✾❪

❖s ❆●s sã♦ ♠ét♦❞♦s ❡st♦❝ást✐❝♦s ❞❡ ❜✉s❝❛ q✉❡ ♣r♦❝✉r❛♠ s♦❧✉çõ❡s ♣ró①✐♠❛s ❞❛s

♠❡❧❤♦r❡s✳ ❊♠ s❡✉ ♣r♦❝❡ss♦✱ ✐♥✐❝✐❛❧♠❡♥t❡ é ❢♦r♠❛❞❛ ✉♠❛ ♣♦♣✉❧❛çã♦ ❝♦♠ ✉♠ ❝♦♥❥✉♥t♦

❛❧❡❛tór✐♦ ❞❡ ✐♥❞✐✈í❞✉♦s ❣❡r❛♥❞♦ ♣♦ssí✈❡✐s s♦❧✉çõ❡s ❞❡ ✉♠ ♣r♦❜❧❡♠❛✳ ▲♦❣♦ ❛♣ós✱ é

✐♥✐❝✐❛❞♦ ♦ ♣r♦❝❡ss♦ ❡✈♦❧✉t✐✈♦✱ ♦♥❞❡ ❝❛❞❛ ✐♥❞✐✈í❞✉♦ é ❛✈❛❧✐❛❞♦ s♦❜r❡ s✉❛ ❛❞❛♣t❛çã♦

❛♦ ❛♠❜✐❡♥t❡✳ ❆ss✐♠✱ ✉♠❛ ♣♦r❝❡♥t❛❣❡♠ ❞♦s ♠❡♠❜r♦s ♠❛✐s ❛❞❛♣t❛❞♦s é ♠❛♥t✐❞❛ ❡ ❛

r❡st❛♥t❡ é ❞❡s❝❛rt❛❞❛✳ ❉❡♥tr❡ ♦s ✐♥❞✐✈í❞✉♦s ♠❛♥t✐❞♦s✱ ❛✐♥❞❛ ♣♦❞❡ ♦❝♦rr❡r ❛ ♠✉t❛çã♦

❡ ♦ ❝r✉③❛♠❡♥t♦✱ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ r❡❝♦♠❜✐♥❛çã♦ ❣❡♥ét✐❝❛✱ ❣❡r❛♥❞♦ ♠❛✐s ♠❡♠❜r♦s ❬❇r✐tt

❡t ❛❧✳✱ ✷✵✵✼❪✳

❚♦❞♦ ❡ss❡ ♣r♦❝❡ss♦✱ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ r❡♣r♦❞✉çã♦✱ é r❡♣❡t✐❞♦ ❛té ❡♥❝♦♥tr❛r ✉♠❛

s♦❧✉çã♦ s❛t✐s❢❛tór✐❛✳ ❉❡ ♠❛♥❡✐r❛ ❣❡r❛❧✱ ❜✉s❝❛✲s❡ r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s ♣❛r❛ ♦s q✉❛✐s ❛✐♥❞❛

♥ã♦ ❡①✐st❡ ✉♠ ❛❧❣♦r✐t♠♦ ❝♦♥❤❡❝✐❞♦✳ ❈♦♥t✉❞♦✱ ❡st❛ té❝♥✐❝❛ t❛♠❜é♠ é ❜❛st❛♥t❡ ✉t✐❧✐✲

③❛❞❛ ♣❛r❛ ❛♣r✐♠♦r❛r ♦✉tr❛s té❝♥✐❝❛s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦ ❛s ❘❡❞❡s ◆❡✉r❛✐s ❆rt✐✜❝✐❛✐s✱

❝♦♥tr✐❜✉✐♥❞♦ ♣❛r❛ ❡♥❝♦♥tr❛r ♦s s❡✉s ♣❛râ♠❡tr♦s ✐♥✐❝✐❛✐s✳

❈♦♠♦ ♦s ❆❧❣♦rt✐♠♦s ●❡♥ét✐❝♦s ✉t✐❧✐③❛♠ ❝♦♥❝❡✐t♦s ✐♥s♣✐r❛❞♦s ♥❛ ●❡♥ét✐❝❛✱ ✈ár✐♦s

❞❡ s❡✉s t❡r♠♦s sã♦ ✉t✐❧✐③❛❞♦s✱ t❛✐s ❝♦♠♦ ❬❆rt❡r♦✱ ✷✵✵✾❪✿

• ●❡♥❡s✿ ❝♦rr❡s♣♦♥❞❡♠ ❛ ✉♠❛ r❡♣r❡s❡♥t❛çã♦ ❞❡ ❛❧❣✉♠ ♣❛râ♠❡tr♦ ❞❡ ✐♥t❡r❡ss❡✱ ❞❡

❛❝♦r❞♦ ❝♦♠ ❛❧❣✉♠ ❛❧❢❛❜❡t♦✱ ♣♦❞❡♥❞♦ ✉s❛r ✈❛❧♦r❡s ✐♥t❡✐r♦s✱ r❡❛✐s ❡ ❝❛❞❡✐❛s ❞❡

❝❛r❛❝t❡r❡s✱ ❝♦♥t✉❞♦✱ ♦ ♠❛✐s ❝♦♠✉♠ é ✉t✐❧✐③❛r ❛♣❡♥❛s ♦s ✈❛❧♦r❡s ✵ ❡ ✶ ❞❡ ✉♠

❛❧❢❛❜❡t♦ ❜✐♥ár✐♦✳

• ❈r♦♠♦ss♦♠♦s✿ ❝♦rr❡s♣♦♥❞❡♠ ❛ ✉♠❛ ❝❛❞❡✐❛ ❞❡ ❣❡♥❡s q✉❡ r❡♣r❡s❡♥t❛♠ ❝❛❞❛ ✐♥✲

❞✐✈í❞✉♦ ❞❛ ♣♦♣✉❧❛çã♦✳ ❈♦♠♦ ❡①❡♠♣❧♦s ❞❡ r❡♣r❡s❡♥t❛çã♦✱ t❡♠♦s r❡s♣❡❝t✐✈❛✲

♠❡♥t❡✿ cromossomo1 = {4.8; 3.2; 5.3} ✉t✐❧✐③❛♥❞♦ ♥ú♠❡r♦s r❡❛✐s✱ cromossomo2 =

{3; 2; 6; 7} ✉t✐❧✐③❛♥❞♦ ✐♥t❡✐r♦s ❡ cromossomo3 = {0001101010101} ✉t✐❧✐③❛♥❞♦ ♥ú✲

♠❡r♦s ❜✐♥ár✐♦s✳

• ■♥❞✐✈í❞✉♦s✿ ✉♠ ✐♥❞✐✈í❞✉♦ ❝♦rr❡s♣♦♥❞❡ ❛ ✉♠ ❝r♦♠♦ss♦♠♦✱ s❡♥❞♦ ✉s❛❞♦s ♣❛r❛

r❡♣r❡s❡♥t❛r ❛s s♦❧✉çõ❡s ❛ s❡r❡♠ ❡♥❝♦♥tr❛❞❛s ❡♠ ✉♠ ♣r♦❜❧❡♠❛✳

• P♦♣✉❧❛çã♦✿ ❢♦r♠❛❞❛ ♣♦r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ✐♥❞✐✈í❞✉♦s q✉❡ ✐rã♦ ❝♦♠♣❡t✐r ♣❡❧❛ s♦✲

❜r❡✈✐✈ê♥❝✐❛ ❡ ♣❡❧❛ r❡♣r♦❞✉çã♦✱ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ♣❡r♣❡t✉❛r s✉❛s ❝❛r❛❝t❡ríst✐❝❛s✳

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✸✶

• ●❡r❛çã♦✿ ✉♠❛ ❣❡r❛çã♦ ❝♦rr❡s♣♦♥❞❡ ❛ ✉♠❛ ♣♦♣✉❧❛çã♦ ❡♠ ❞❡t❡r♠✐♥❛❞♦ ♣❡rí♦❞♦✱

s❡♥❞♦ ♣♦rt❛♥t♦✱ ♦s ✈❛❧♦r❡s ❞♦s ✐♥❞✐✈í❞✉♦s ♦❜t✐❞♦s ❡♠ ✉♠❛ ❞❛❞❛ ✐t❡r❛çã♦✳

• ❋✉♥çã♦ ❞❡ ❛♣t✐❞ã♦✿ ❛ ❢✉♥çã♦ ❞❡ ❛♣t✐❞ã♦ é ✉s❛❞❛ ♣❛r❛ ♠❡❞✐r ❛ ❤❛❜✐❧✐❞❛❞❡ ❞♦

✐♥❞✐✈í❞✉♦ ♣❛r❛ s♦❜r❡✈✐✈❡r ❡ s❡ r❡♣r♦❞✉③✐r✳ ◆♦s ❆●s sã♦ r❡♣r❡s❡♥t❛❞❛s ♣♦r ❢✉♥çõ❡s

♠❛t❡♠át✐❝❛s✱ q✉❡ ❝♦♥❢♦r♠❡ ♦ ♣r♦❜❧❡♠❛ ❛ s❡r r❡s♦❧✈✐❞♦✱ ❞❡✈❡♠ s❡r ♠❛①✐♠✐③❛❞❛s

♦✉ ♠✐♥✐♠✐③❛❞❛s✳

❖s ❛❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s ♣♦ss✉❡♠ ❛❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s q✉❡ ♦s ❞✐❢❡r❡♠ ❞❡ ♦✉tr❛s

té❝♥✐❝❛s ❝♦♥✈❡♥❝✐♦♥❛✐s✱ tr❛❜❛❧❤❛♥❞♦ ❝♦♠ ✉♠❛ ❝♦❞✐✜❝❛çã♦ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ♣❛râ♠❡tr♦s

❡ ❝♦♠ ✉♠❛ ♣♦♣✉❧❛çã♦✱ ❡ ♥ã♦ ❛♣❡♥❛s ❝♦♠ ✉♠ ✈❛❧♦r ❡ ❝♦♠ ♦s ♣ró♣r✐♦s ♣❛râ♠❡tr♦s✳ ❖

♣r♦❝❡ss❛♠❡♥t♦ r❡❛❧✐③❛❞♦ ♣♦r ✉♠ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ é r❡❛❧✐③❛❞♦ ❡♠ ❛❧❣✉♠❛s ❡t❛♣❛s✱

❝♦♥❢♦r♠❡ ♣♦❞❡♠♦s ✈❡r✐✜❝❛r ♥❛ ❋✐❣✉r❛ ✷✳✶✹✳ ❖ ❛❧❣♦r✐t♠♦ ♠♦str❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✶✺

❛♣r❡s❡♥t❛ ♦ ❞✐❛❣r❛♠❛ ❣❡r❛❧ ❞❛s ❡t❛♣❛s ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦✳

❋✐❣✉r❛ ✷✳✶✹✳ ❊t❛♣❛s ❞♦ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ❬❆rt❡r♦✱ ✷✵✵✾❪

❆ ❡t❛♣❛ ❞❡ s❡❧❡çã♦ é ✉s❛❞❛ ♣❛r❛ ❡s❝♦❧❤❡r ♦s ✐♥❞✐✈í❞✉♦s ♣❛r❛ ❛ r❡♣r♦❞✉çã♦✱ ♣♦❞❡♥❞♦

s❡r r❡❛❧✐③❛❞❛ ❞❡ ❞✐❢❡r❡♥t❡s ♠❛♥❡✐r❛s✱ ♣♦ré♠✱ ❛s ♣r♦♣♦st❛s ♠❛✐s ❝♦♠✉♥s sã♦ ❛ s❡❧❡çã♦

❛❧❡❛tór✐❛✱ ❛ s❡❧❡çã♦ ♣♦r t♦r♥❡✐♦ ❡ ❛ s❡❧❡çã♦ ✉s❛♥❞♦ ❛ r♦❧❡t❛✳ ◆❛ s❡❧❡çã♦ ❛❧❡❛tór✐❛✱ ❞♦✐s

✐♥❞✐✈í❞✉♦s ❞❛ ♣♦♣✉❧❛çã♦ sã♦ ❡s❝♦❧❤✐❞♦s ❛♦ ❛❝❛s♦✳ ◆❛ s❡❧❡çã♦ ♣♦r t♦r♥❡✐♦✱ ♦ ♠❡❧❤♦r ❞❡❧❡s✱

❝♦♥❢♦r♠❡ ❛ ❢✉♥çã♦ ❞❡ ❛♣t✐❞ã♦✱ s❡rá s❡❧❡❝✐♦♥❛❞♦ ♣❛r❛ ❛ r❡♣r♦❞✉çã♦✳ ❊st❡ ♣r♦❝❡ss♦ s❡rá

r❡♣❡t✐❞♦ ♣❛r❛ ❡♥❝♦♥tr❛r t❛♠❜é♠ ♦ s❡❣✉♥❞♦ ✐♥❞✐✈í❞✉♦ ❛ ♣❛rt✐❝✐♣❛r ❞♦ ❝r✉③❛♠❡♥t♦✳ ◆❛

♠♦❞❛❧✐❞❛❞❡ ❞❡ s❡❧❡çã♦ ♣♦r r♦❧❡t❛✱ ❛s ❤❛❜✐❧✐❞❛❞❡s ❞❡ t♦❞♦s ♦s ✐♥❞✐✈í❞✉♦s ❞❛ ♣♦♣✉❧❛çã♦

sã♦ ❝❛❧❝✉❧❛❞❛s ❡ ♦s ✈❛❧♦r❡s ♦❜t✐❞♦s ❝♦rr❡s♣♦♥❞❡rã♦✱ ♣r♦♣♦r❝✐♦♥❛❧♠❡♥t❡✱ ❛♦s s❡t♦r❡s ❞❡

✉♠❛ r♦❧❡t❛✱ ❝♦♥❢♦r♠❡ ♦ ❡①❡♠♣❧♦ ❞❛ ❋✐❣✉r❛ ✷✳✶✻✳ ❉❡ss❛ ♠❛♥❡✐r❛✱ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞♦s

s❡t♦r❡s ♠❛✐♦r❡s s❡r❡♠ s❡❧❡❝✐♦♥❛❞♦s s❡rá ♠❛✐♦r ❛♦ ❣✐r❛r ❛ r♦❧❡t❛✱ ❝♦♥t✉❞♦ ♦s s❡t♦r❡s

♠❡♥♦r❡s ❛✐♥❞❛ ♣♦❞❡♠ s❡r s❡❧❡❝✐♦♥❛❞♦s✱ ❛♣❡s❛r ❞❛ ♠❡♥♦r ♣r♦❜❛❜✐❧✐❞❛❞❡ ❬❆rt❡r♦✱ ✷✵✵✾❪✳

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✸✷

❋✐❣✉r❛ ✷✳✶✺✳ ❆❧❣♦r✐t♠♦ ❞❡ ❛❧t♦ ♥í✈❡❧ ❞❡ ✉♠ ❆● ❬❘❡③❡♥❞❡✱ ✷✵✵✺❪

❋✐❣✉r❛ ✷✳✶✻✳ ❘♦❧❡t❛ ❝♦♠ t❛♠❛♥❤♦s ❞❡ s❡t♦r❡s ♣r♦♣♦r❝✐♦♥❛✐s à ❝❤❛♥❝❡ ❞♦ ❝r♦✲♠♦ss♦♠♦ s❡r s❡❧❡❝✐♦♥❛❞♦ ❬❆rt❡r♦✱ ✷✵✵✾❪

▲♦❣♦✱ ❛ ❡t❛♣❛ ❞❡ ❝r✉③❛♠❡♥t♦ ✭❝r♦ss♦✈❡r✮ ❝♦♥s✐st❡ ♥♦ ❝r✉③❛♠❡♥t♦ ❡♥tr❡ ♦ ♠❛t❡r✐❛❧

❣❡♥ét✐❝♦ ❞❡ ❞♦✐s ✐♥❞✐✈í❞✉♦s✳ ◆♦ ❝❛s♦ ❞❡ ✉t✐❧✐③❛r ✈❛❧♦r❡s ❜✐♥ár✐♦s✱ sã♦ ✉s❛❞♦s ♣♦♥t♦s ❞❡

❝♦rt❡ ❛❧❡❛t♦r✐❛♠❡♥t❡ ♣♦s✐❝✐♦♥❛❞♦s ❡♥tr❡ ♦s ❜✐ts✳ ❈♦♠♦ ❡①❡♠♣❧♦ t❡♠♦s ❛ ❋✐❣✉r❛ ✷✳✶✼✱

♦♥❞❡ ❛s ❧✐♥❤❛s ✈❡rt✐❝❛✐s ✐♥❞✐❝❛♠ ♦s ♣♦♥t♦s ❞❡ ❝♦rt❡ ❬❆rt❡r♦✱ ✷✵✵✾❪✳

❖s ❜✐ts ❞♦ C1 ❛♥t❡s ❞♦ ♣r✐♠❡✐r♦ ❝♦rt❡ sã♦ ❝♦♣✐❛❞♦s ♣❛r❛ ♦ filho1✱ ❡ ❛♣ós ♦ ❝♦rt❡✱

♦s ❜✐ts sã♦ ❝♦♣✐❛❞♦s ♣❛r❛ ♦ filho2✳ ❙✐♠✐❧❛r♠❡♥t❡✱ ♦s ❜✐ts ❞♦ C2 ❛♥t❡s ❞♦ ♣r✐♠❡✐r♦ ❝♦rt❡

sã♦ ❝♦♣✐❛❞♦s ♣❛r❛ ♦ filho2✱ ❡ ❛♣ós ♦ ❝♦rt❡✱ ♦s ❜✐ts sã♦ ❝♦♣✐❛❞♦s ♣❛r❛ ♦ filho1✳ ❈♦♠

❞♦✐s ❝♦rt❡s✱ ♦s ❜✐ts ❛♥t❡s ❞♦ ♣r✐♠❡✐r♦ ❝♦rt❡ ❡ ❛♣ós ♦ s❡❣✉♥❞♦ ❝♦rt❡ sã♦ ❡♥✈✐❛❞♦s ♣❛r❛

♦ filho1✱ ❡♥q✉❛♥t♦ q✉❡ ♦s ❜✐ts ❡♥tr❡ ♦ ♣r✐♠❡✐r♦ ❡ s❡❣✉♥❞♦ ❝♦rt❡s sã♦ ❡♥✈✐❛❞♦s ♣❛r❛ ♦

filho2 ❬❆rt❡r♦✱ ✷✵✵✾❪✳

➱ ♣♦ssí✈❡❧ t❛♠❜é♠ ♦❝♦rr❡r ♠ú❧t✐♣❧♦s ❝♦rt❡s q✉❛♥❞♦ ♦s ❜✐ts ❛♥t❡s ❞♦ ♣r✐♠❡✐r♦ ♥ã♦

sã♦ tr♦❝❛❞♦s✳ ◆❡st❡ ❝❛s♦✱ ❛ ♣❛rt✐r ❞♦ ♣r✐♠❡✐r♦ ❝♦rt❡✱ ♦s ❜✐ts sã♦ tr♦❝❛❞♦s ❛té q✉❡ s❡❥❛

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✸✸

❋✐❣✉r❛ ✷✳✶✼✳ ❈r✉③❛♠❡♥t♦s ❝♦♠ ✉♠ ❝♦rt❡ ✭❛✮ ❡ ❝♦♠ ❞♦✐s ❝♦rt❡s ✭❜✮ ❬❆rt❡r♦✱ ✷✵✵✾❪

❡♥❝♦♥tr❛❞♦ ♦ ♣ró①✐♠♦ ❝♦rt❡✳ ❆ s❡❣✉✐r✱ ♦s ❜✐ts ♥ã♦ s❡rã♦ tr♦❝❛❞♦s ❛té ♦ ♣ró①✐♠♦ ❝♦rt❡✱

s❡♥❞♦ ❡st❡ ♣r♦❝❡ss♦ r❡♣❡t✐❞♦ ♣❛r❛ ♦s ❞❡♠❛✐s ❝♦rt❡s ❬❆rt❡r♦✱ ✷✵✵✾❪✳

❆♣❡s❛r ❞♦s ❆●s t❡r❡♠ s✐❞♦ ♣r♦♣♦st♦s ♦r✐❣✐♥❛❧♠❡♥t❡ ♣❛r❛ ♦♣❡r❛r ❝♦♠ ✈❛❧♦r❡s

❜✐♥ár✐♦s✱ ❛s ♣❡r❞❛s ❞❡ ♣r❡❝✐sã♦ ❞❡❝♦rr❡♥t❡s ❞❛ r❡♣r❡s❡♥t❛çã♦ ❞♦s ♥ú♠❡r♦s r❡❛✐s ❡♠

❜✐♥ár✐♦✱ ❧❡✈❛r❛♠ ❛♦ s✉r❣✐♠❡♥t♦ ❞❡ ♣r♦♣♦st❛s ♣❛r❛ s❡ ♦♣❡r❛r ❞✐r❡t❛♠❡♥t❡ ❝♦♠ ✈❛❧♦r❡s

r❡❛✐s✳ ◆❡st❡ ❝❡♥ár✐♦✱ ♦ ❝r✉③❛♠❡♥t♦ ♣♦❞❡ s❡r ❡❢❡t✉❛❞♦ ✉s❛♥❞♦ ✉♠❛ ♠é❞✐❛ ❛r✐t♠ét✐❝❛

♦✉ ❣❡♦♠étr✐❝❛ ❡♥tr❡ ♦s ♣❛✐s {x1, x2, ..., xn} ❡ {y1, y2, ..., yn}✳ ❉♦✐s ♠ét♦❞♦s ❝♦♥❤❡❝✐❞♦s

q✉❡ ❢✉♥❝✐♦♥❛♠ ❞❡st❛ ♠❛♥❡✐r❛ sã♦✿ ❈r✉③❛♠❡♥t♦ ❆r✐t♠ét✐❝♦ Ú♥✐❝♦ ✭❙✐♥❣❧❡ ❆r✐t❤♠❡t✐❝

❈r♦ss♦✈❡r✮ ❡ ❈r✉③❛♠❡♥t♦ ❆r✐t♠ét✐❝♦ ❙✐♠♣❧❡s ✭❙✐♠♣❧❡ ❆r✐t❤♠❡t✐❝ ❈r♦ss♦✈❡r✮ ❬❆rt❡r♦✱

✷✵✵✾❪✳

◆♦ ♣r✐♠❡✐r♦✱ t♦♠❛✲s❡ ✉♠ ✈❛❧♦r k✱ ❛❧❡❛tór✐♦ ❡ ✐♥t❡✐r♦✱ r❡s♣♦♥sá✈❡❧ ♣♦r ❞❡t❡r♠✐♥❛r

❛ ♣♦s✐çã♦ ❞♦s ❣❡♥❡s ❛ s❡r❡♠ ❝r✉③❛❞♦s ❡ t❛♠❜é♠ ✉♠ ✈❛❧♦r r❡❛❧ ❛❧❡❛tór✐♦✱ α ∈ [0, 1]✱

❣❡r❛♥❞♦ ♦s ✜❧❤♦s✿ {x1, x2, ..., αyk+(1−α)xk, ..., xn} ❡ {11, y2, ..., αxk+(1−α)yk, ..., yn}

❬❆rt❡r♦✱ ✷✵✵✾❪✳ P♦r ❡①❡♠♣❧♦✱ ❝♦♥s✐❞❡r❛♥❞♦ α = 0.4✱ k = 3✱ Pai1 = {0.5, 1.0, 1.5, , 2.0}

❡ Pai2 = {0.2, 0.7, 0.2, 0.7}✱ r❡s✉❧t❛rá ♥♦s ✜❧❤♦s✿ filho1 = {0.5, 1.0, (0.4)(0.2) +

(0.6)(1.5), 2.0} = {0.5, 1.0, 0.98, 2.0}} ❡ filho2 = {0.2, 0.7, (0.4)(1.5)+(0.6)(0.2), 0.7} =

{0.2, 0.7, 0.72, 0.7}}✳

P❛r❛ ♦ ❈r✉③❛♠❡♥t♦ ❆r✐t♠ét✐❝♦ ❙✐♠♣❧❡s✱ ❞❡ ❢♦r♠❛ s✐♠✐❧❛r✱ t❛♠❜é♠ t♦♠❛✲s❡

✉♠ ✈❛❧♦r ❛❧❡❛tór✐♦ k✱ q✉❡ ✈❛✐ ❞❡t❡r♠✐♥❛r ❛ ♣♦s✐çã♦ ❞♦s ❣❡♥❡s ❛ s❡r❡♠ ❝r✉③❛❞♦s

❡ α ∈ [0, 1]✱ ❝♦♠ ♦s ✜❧❤♦s ♦❜t✐❞♦s✿ {x1, x2, ..., αyk + (1 − α)xk, ..., (1 − α)xn, } ❡

{11, y2, ..., αxk + (1 − α)yk, ..., (1 − α)yn} ❬❆rt❡r♦✱ ✷✵✵✾❪✳ P♦r ❡①❡♠♣❧♦✱ ❝♦♥s✐❞❡r❛♥❞♦

α = 0.4✱ k = 3✱ Pai1 = {0.5, 1.0, 1.5, 2.0} ❡ Pai2 = {0.2, 0.7, 0.2, 0.7}✱ r❡s✉❧✲

t❛rá ♥♦s ✜❧❤♦s✿ filho1 = {0.5, 1.0, (0.4)(0.2) + (0.6)(1.5), (0.4)(0.7) + (0.6)(2.0)} =

{0.5, 1.0, 0.98, 1.48}} ❡ filho2 = {0.2, 0.7, (0.4)(1.5) + (0.6)(0.2), (0.4)(2.0) +

(0.6)(0.7)} = {0.2, 0.7, 0.72, 1.22}}✳

❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❡♠ ❛❧❣✉♠❛s s✐t✉❛çõ❡s✱ ♦ ❝r♦♠♦ss♦♠♦ ♣♦❞❡ s❡r ♠♦❞✐✜❝❛❞♦ ❡♠

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✸✹

❛❧❣✉♠❛s ❞❡ s✉❛s ♣❛rt❡s✱ ❛ss✉♠✐♥❞♦ ♥♦✈❛s ❝❛r❛❝t❡ríst✐❝❛s✱ q✉❡ ♥ã♦ ❢♦r❛♠ ❤❡r❞❛❞❛s ❞❡

s❡✉s ♣❛✐s✳ ❊st❡ ❝❡♥ár✐♦✱ ♦ q✉❛❧ ❝♦♥s✐st❡ ❛ ❡t❛♣❛ ❞❡ ♠✉t❛çã♦✱ ♣♦ss✉✐ ✉♠❛ ♣r♦❜❛❜✐❧✐❞❛❞❡

❜❛✐①❛ ❞❡ ♦❝♦rr❡r✱ s❡♥❞♦ q✉❡ ❛♦ ✉t✐❧✐③❛r ♥ú♠❡r♦s ❜✐♥ár✐♦s✱ ❝♦♥s✐st❡ ♥❛ ✐♥✈❡rsã♦ ❞❡ ❛❧❣✉♥s

❜✐ts✱ ❡♥q✉❛♥t♦ q✉❡ ♥♦ ❝❛s♦ ❞❡ ♥ú♠❡r♦s r❡❛✐s✱ s♦♠❛♠✲s❡ ♣❡q✉❡♥♦s ✈❛❧♦r❡s ❛❧❡❛tór✐♦s

✭♣♦s✐t✐✈♦s ♦✉ ♥❡❣❛t✐✈♦s✮✳ ❙❡ ❛ r❡♣r❡s❡♥t❛çã♦ ❢♦r ❢❡✐t❛ ✉s❛♥❞♦ ❝❛❞❡✐❛s ❞❡ ❝❛r❛❝t❡r❡s✱

❛❧❣✉♥s ❝❛r❛❝t❡r❡s ♣♦❞❡♠ s❡r ❛❧t❡r❛❞♦s ❛❧❡❛t♦r✐❛♠❡♥t❡ ❬❆rt❡r♦✱ ✷✵✵✾❪✳

❖✉tr♦ ❛s♣❡❝t♦ ✐♠♣♦rt❛♥t❡ ❞❡ ✉♠ ❆● é ❛ ❞❡✜♥✐çã♦ ❞❡ s❡✉s ♣❛râ♠❡tr♦s q✉❡ ✐♥✢✉✲

❡♥❝✐❛♠ ❢♦rt❡♠❡♥t❡ s❡✉ ❞❡s❡♠♣❡♥❤♦✳ ❊♥tr❡ ❡ss❡s ♣❛râ♠❡tr♦s✱ ♦ t❛♠❛♥❤♦ ❞❛ ♣♦♣✉❧❛çã♦

❛❢❡t❛ ♦ ❞❡s❡♠♣❡♥❤♦ ❣❧♦❜❛❧ ❡ ❛ ❡✜❝✐ê♥❝✐❛ ❞♦s ❆●s✳ ❖ ❞❡s❡♠♣❡♥❤♦ ♥❡st❡ ❝❛s♦ ♣♦❞❡

❝❛✐r s❡ ❛ ♣♦♣✉❧❛çã♦ ❢♦r ♣❡q✉❡♥❛✱ ♣♦✐s ❡❧❛ ❢♦r♥❡❝❡ ✉♠❛ ♣❡q✉❡♥❛ ❝♦❜❡rt✉r❛ ❞♦ ❡s♣❛ç♦

❞❡ ❜✉s❝❛ ❞♦ ♣r♦❜❧❡♠❛✱ ❡♥q✉❛♥t♦ q✉❡ ✉♠❛ ♣♦♣✉❧❛çã♦ ❣r❛♥❞❡ ❢♦r♥❡❝❡ ✉♠❛ ❝♦❜❡rt✉r❛

r❡♣r❡s❡♥t❛t✐✈❛ ❞♦ ❞♦♠í♥✐♦ ❞♦ ♣r♦❜❧❡♠❛✱ ❛❧é♠ ❞❡ ♣r❡✈❡♥✐r ❝♦♥✈❡r❣ê♥❝✐❛s ♣r❡♠❛t✉r❛s

♣❛r❛ s♦❧✉çõ❡s ❧♦❝❛✐s ❡♠ ✈❡③ ❞❡ ❣❧♦❜❛✐s✳ ◆♦ ❡♥t❛♥t♦✱ ❣r❛♥❞❡s ♣♦♣✉❧❛çõ❡s ♥❡❝❡ss✐t❛♠ ❞❡

♠❛✐s r❡❝✉rs♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ♦✉ q✉❡ ♦ ❛❧❣♦r✐t♠♦ tr❛❜❛❧❤❡ ♣♦r ✉♠ ♣❡rí♦❞♦ ❞❡ t❡♠♣♦

♠✉✐t♦ ♠❛✐♦r ❬❘❡③❡♥❞❡✱ ✷✵✵✺❪✳

❆ t❛①❛ ❞❡ ❝r✉③❛♠❡♥t♦ q✉❛♥t♦ ♠❛✐♦r✱ ♠❛✐s r❛♣✐❞❛♠❡♥t❡ ♥♦✈❛s ❡str✉t✉r❛s sã♦

✐♥tr♦❞✉③✐❞❛s ♥❛ ♣♦♣✉❧❛çã♦✳ ❈♦♥t✉❞♦✱ s❡ ❢♦r ♠✉✐t♦ ❛❧t❛✱ ❡str✉t✉r❛s ❝♦♠ ❜♦❛s ❛♣t✐❞õ❡s

♣♦❞❡rã♦ s❡r r❡t✐r❛❞❛s ♠❛✐s r❛♣✐❞❛♠❡♥t❡ q✉❡ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❛ s❡❧❡çã♦ ❡♠ ❝r✐❛r ♠❡❧❤♦r❡s

❡str✉t✉r❛s✳ ❙❡ ❛ t❛①❛ ❢♦r ♠✉✐t♦ ❜❛✐①❛✱ ❛ ❜✉s❝❛ ♣♦❞❡ ❡st❛❣♥❛r ❬❘❡③❡♥❞❡✱ ✷✵✵✺❪✳

❆ t❛①❛ ❞❡ ♠✉t❛çã♦ ❜❛✐①❛ ♣r❡✈✐♥❡ q✉❡ ❛ ❜✉s❝❛ ✜q✉❡ ❡st❛❣♥❛❞❛ ❡♠ s✉❜✲r❡❣✐õ❡s

❞♦ ❡s♣❛ç♦ ❞❡ ❜✉s❝❛✳ P♦ss✐❜✐❧✐t❛ ❛✐♥❞❛ q✉❡ q✉❛❧q✉❡r ♣♦♥t♦ ❞♦ ❡s♣❛ç♦ ❞❡ ❜✉s❝❛ s❡❥❛

❛♥t✐❣✐❞♦✱ ❡♥tr❡t❛♥t♦✱ ✉♠❛ t❛①❛ ♠✉✐t♦ ❛❧t❛ ❢❛③ ❝♦♠ q✉❡ ❛ ❜✉s❝❛ s❡❥❛ ❡ss❡♥❝✐❛❧♠❡♥t❡

❛❧❡❛tór✐❛ ❬❘❡③❡♥❞❡✱ ✷✵✵✺❪✳

❖✉tr♦ ♣❛râ♠❡tr♦ ✐♠♣♦rt❛♥t❡ é ♦ ✐♥t❡r✈❛❧♦ ❞❡ ❣❡r❛çã♦✱ ♦ q✉❛❧ ❝♦♥tr♦❧❛ ❛ ♣♦r❝❡♥✲

t❛❣❡♠ ❞❛ ♣♦♣✉❧❛çã♦ q✉❡ s❡rá s✉❜st✐t✉í❞❛ ♣❛r❛ ❛ ♣ró①✐♠❛ ❣❡r❛çã♦✳ ❈♦♠ ✉♠ ✐♥t❡r✈❛❧♦

❣r❛♥❞❡✱ ❛ ♠❛✐♦r ♣❛rt❡ ❞❛ ♣♦♣✉❧❛çã♦ s❡rá s✉❜st✐t✉í❞❛ ♣♦❞❡♥❞♦ ♦❝❛s✐♦♥❛r ♣❡r❞❛s ❞❡ ❡s✲

tr✉t✉r❛s ❞❡ ❛❧t❛ ❛♣t✐❞ã♦✳ ❯♠ ✐♥t❡r✈❛❧♦ ♣❡q✉❡♥♦✱ ♥♦ ❡♥t❛♥t♦✱ ♣♦❞❡ ❢❛③❡r ❝♦♠ q✉❡ ♦

❛❧❣♦r✐t♠♦ s❡ t♦r♥❡ ♠✉✐t♦ ❧❡♥t♦ ❬❘❡③❡♥❞❡✱ ✷✵✵✺❪✳

P♦r ✜♠✱ ♦ ♣❛râ♠❡tr♦ ❝r✐tér✐♦ ❞❡ ♣❛r❛❞❛ é ✐♠♣♦rt❛♥t❡ ♣❛r❛ t❡r♠✐♥❛r ❛ ❡①❡❝✉çã♦ ❞❡

✉♠ ❆●✳ ❊①✐st❡♠ ❞✐✈❡rs♦s ❝r✐tér✐♦s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❞❛❞♦ ✉♠ ♥ú♠❡r♦ ❞❡ ❣❡r❛çõ❡s✱

q✉❛♥❞♦ ❛ ❛♣t✐❞ã♦ ♠é❞✐❛ ♦✉ ❞♦ ♠❡❧❤♦r ✐♥❞✐✈í❞✉♦ ♥ã♦ ♠❡❧❤♦r❛r ♠❛✐s ♦✉ q✉❛♥❞♦ ❛s

❛♣t✐❞õ❡s ❞♦s ✐♥❞✐✈í❞✉♦s ❞❡ ✉♠❛ ♣♦♣✉❧❛çã♦ s❡ t♦r♥❛r❡♠ ♠✉✐t♦ ♣❛r❡❝✐❞❛s✳ ❆♦ ❝♦♥❤❡❝❡r

❛ r❡s♣♦st❛ ♠á①✐♠❛ ❞❛ ❢✉♥çã♦ ♦❜❥❡t✐✈♦✱ é ♣♦ssí✈❡❧ ✉t✐❧✐③❛r ❡st❡ ✈❛❧♦r ❝♦♠♦ ❝r✐tér✐♦ ❞❡

♣❛r❛❞❛✳

◆❡st❡ tr❛❜❛❧❤♦✱ ❛ té❝♥✐❝❛ ❞❡ ❆❧❣♦r✐t♠♦s ●❡♥ét✐❝♦s ❢♦✐ ✉s❛❞❛ ♣❛r❛ ❡♥❝♦♥tr❛r ♦s

♣❛râ♠❡tr♦s ✐♥✐❝✐❛✐s ❞❛s ❘◆❆s ▼▲P✳ ❉❡ss❡ ♠♦❞♦✱ ♠❡s♠♦ q✉❡ ♥ã♦ t❡♥❤❛ ❡♥❝♦♥tr❛❞♦

✉♠❛ s♦❧✉çã♦ ót✐♠❛✱ ♦s ✈❛❧♦r❡s ❡♥❝♦♥tr❛❞♦s ♣❡r♠✐t✐r❛♠ ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s✱ ❝♦♥❢♦r♠❡

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✸✺

❛♣r❡s❡♥t❛❞♦s ♥♦ ❈❛♣ít✉❧♦ ✹✱ ❞♦ q✉❡ s✐♠♣❧❡s♠❡♥t❡ ✉t✐❧✐③❛r ❛s ❘◆❆s ❞❡ ❢♦r♠❛ ✐s♦❧❛❞❛✳

✷✳✺✳✹ ▼áq✉✐♥❛ ❞❡ ❱❡t♦r❡s ❞❡ ❙✉♣♦rt❡

❖✉tr❛ té❝♥✐❝❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ q✉❡ t❡♠ r❡❝❡❜✐❞♦ ❛t❡♥çã♦ é ❛ ▼áq✉✐♥❛ ❞❡ ❱❡t♦r❡s ❞❡

❙✉♣♦rt❡ ✭❙✉♣♣♦rt ❱❡❝t♦r ▼❛❝❤✐♥❡ ✲ ❙❱▼ ✮✱ q✉❡ ♣♦ss✉✐ s❡✉s ❢✉♥❞❛♠❡♥t♦s ♥❛ t❡♦r✐❛ ❞❡

❛♣r❡♥❞✐③❛❣❡♠ ❡st❛tíst✐❝❛ ❡ t❡♠ ♠♦str❛❞♦ r❡s✉❧t❛❞♦s ❡♠♣ír✐❝♦s ♣r♦♠✐ss♦r❡s ❡♠ ✈ár✐❛s

❛♣❧✐❝❛çõ❡s ♣rát✐❝❛s✱ ❝♦♠♦ r❡❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ ❞í❣✐t♦s ❡s❝r✐t♦s à ♠ã♦ ❡ ❝❛t❡❣♦r✐③❛çã♦ ❞❡

t❡①t♦s ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

❊st❛ té❝♥✐❝❛ ❢✉♥❝✐♦♥❛ ❜❡♠ ❝♦♠ ❞❛❞♦s ❞❡ ❛❧t❛ ❞✐♠❡♥s✐♦♥❛❧✐❞❛❞❡✱ ❛❧é♠ ❞❡ r❡♣r❡s❡♥✲

t❛r ♦ ❧✐♠✐t❡ ❞❡ ❞❡❝✐sã♦ ✉s❛♥❞♦ ✉♠ s✉❜❝♦♥❥✉♥t♦ ❞♦s ❡①❡♠♣❧♦s ❞❡ tr❡✐♥❛♠❡♥t♦✱ ❝♦♥❤❡❝✐❞♦s

❝♦♠♦ ♦s ✏✈❡t♦r❡s ❞❡ s✉♣♦rt❡✑✳ ❆ ❙❱▼ ♣♦❞❡ s❡r tr❡✐♥❛❞❛ ♣❛r❛ r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s t❛♥t♦

❧✐♥❡❛r♠❡♥t❡ s❡♣❛rá✈❡✐s ❝♦♠♦ ♦s ♥ã♦ ❧✐♥❡❛r♠❡♥t❡ s❡♣❛rá✈❡✐s ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

P❛r❛ ✉♠ ♠❡❧❤♦r ❡♥t❡♥❞✐♠❡♥t♦✱ s❡rá ❛♣r❡s❡♥t❛❞♦ ♦ ❝♦♥❝❡✐t♦ ❞❡ ✏❤✐♣❡r♣❧❛♥♦ ❞❡

♠❛r❣❡♠ ♠á①✐♠❛✑✳ ❈♦♥❢♦r♠❡ ❛ ❋✐❣✉r❛ ✷✳✶✽✱ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❝♦♥t❡♥❞♦ ❡①❡♠♣❧♦s

q✉❡ ♣❡rt❡♥❝❡♠ ❛ ❞✉❛s ❝❧❛ss❡s✱ sã♦ ♠♦str❛❞♦s✳ ◆❡st❡ ❡①❡♠♣❧♦✱ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s é

❧✐♥❡❛r♠❡♥t❡ s❡♣❛rá✈❡❧✱ ♣♦✐s é ♣♦ssí✈❡❧ ❡♥❝♦♥tr❛r ✉♠ ❤✐♣❡r♣❧❛♥♦ ❡♠ q✉❡ t♦❞♦s ♦s q✉❛✲

❞r❛❞♦s ✜q✉❡♠ ❞❡ ✉♠ ❧❛❞♦ ❞♦ ❤✐♣❡r♣❧❛♥♦ ❡ ♦s ❝ír❝✉❧♦s ❞♦ ♦✉tr♦ ❧❛❞♦✳ ❈♦♥t✉❞♦✱ ♠✉✐t♦s

❤✐♣❡r♣❧❛♥♦s sã♦ ♣♦ssí✈❡✐s ❡ ♦ ❝❧❛ss✐✜❝❛❞♦r ❞❡✈❡ ❡s❝♦❧❤❡r ❛♣❡♥❛s ✉♠ ♣❛r❛ r❡♣r❡s❡♥t❛r

s❡✉ ❧✐♠✐t❡ ❞❡ ❞❡❝✐sã♦ ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

❋✐❣✉r❛ ✷✳✶✽✳ ▼❛r❣❡♠ ❞❡ ✉♠ ❧✐♠✐t❡ ❞❡ ❞❡❝✐sã♦ ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪

❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❧✐♠✐t❡s ❞❡ ❞❡❝✐sã♦ ❝♦♠ ♠❛r❣❡♥s ❣r❛♥❞❡s t❡♥❞❡♠ ❛ t❡r ❡rr♦s

❞❡ ❣❡♥❡r❛❧✐③❛çã♦ ♠❡❧❤♦r❡s ❞♦ q✉❡ ❛q✉❡❧❡s ❝♦♠ ♠❛r❣❡♥s ♣❡q✉❡♥❛s✳ ❉❡ss❡ ♠♦❞♦✱ ❝❛s♦ ❛

♠❛r❣❡♠ s❡❥❛ ♣❡q✉❡♥❛✱ q✉❛❧q✉❡r ♣❡rt✉r❜❛çã♦ ♠í♥✐♠❛ ♥♦ ❧✐♠✐t❡ ❞❡ ❞❡❝✐sã♦ ♣♦❞❡ t❡r ✉♠

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✸✻

✐♠♣❛❝t♦ ❜❛st❛♥t❡ s✐❣♥✐✜❝❛t✐✈♦ s♦❜r❡ s✉❛ ❝❧❛ss✐✜❝❛çã♦✳ ❆ss✐♠✱ ❝❧❛ss✐✜❝❛❞♦r❡s q✉❡ ♣r♦✲

❞✉③❡♠ ❧✐♠✐t❡s ❞❡ ❞❡❝✐sã♦ ❝♦♠ ♠❛r❣❡♥s ♣❡q✉❡♥❛s sã♦ ♠❛✐s s✉s❝❡♣tí✈❡✐s ❛ ♦✈❡r✜tt✐♥❣ ❞❡

♠♦❞❡❧♦ ❡ t❡♥❞❡♠ ❛ ❣❡♥❡r❛❧✐③❛r ❞❡ ❢♦r♠❛ ❢r❛❝❛ s♦❜r❡ ❡①❡♠♣❧♦s ♥ã♦ ✈✐st♦s ❛♥t❡r✐♦r♠❡♥t❡

❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

❈♦♥❢♦r♠❡ ♠♦str❛❞♦ ❡♠ ❚❛♥ ❡t ❛❧✳ ❬✷✵✵✾❪✱ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ✉♠ ♠♦❞❡❧♦ ❧✐♥❡❛r ❡stá

✐♥✈❡rs❛♠❡♥t❡ r❡❧❛❝✐♦♥❛❞❛ ❛ s✉❛ ♠❛r❣❡♠✳ ▼♦❞❡❧♦s ❝♦♠ ♠❛r❣❡♥s ♣❡q✉❡♥❛s ♣♦ss✉❡♠

❝❛♣❛❝✐❞❛❞❡s ♠❛✐♦r❡s✱ s❡♥❞♦ ♠❛✐s ✢❡①í✈❡✐s ❡ ♣♦❞❡♥❞♦ ❝♦♥t❡r ♠❛✐s ❝♦♥❥✉♥t♦s ❞❡ tr❡✐♥❛✲

♠❡♥t♦✱ ❛♦ ❝♦♥trár✐♦ ❞♦s ♠♦❞❡❧♦s ❝♦♠ ♠❛r❣❡♥s ❣r❛♥❞❡s✳ ❊♥tr❡t❛♥t♦✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦

♣r✐♥❝í♣✐♦ ❞❡ ❛♣r❡♥❞✐③❛❣❡♠ ❡st❛tíst✐❝♦ ❙❘▼ ✭♠✐♥✐♠✐③❛çã♦ ❞♦ r✐s❝♦ ❡str✉t✉r❛❧✮✱ à ♠❡❞✐❞❛

q✉❡ ❛ ❝❛♣❛❝✐❞❛❞❡ ❛✉♠❡♥t❛✱ ♦ ❧✐♠✐t❡ ❞♦ ❡rr♦ ❞❡ ❣❡♥❡r❛❧✐③❛çã♦ t❛♠❜é♠ ❛✉♠❡♥t❛rá✳ ❉❡ss❛

❢♦r♠❛✱ ♣r♦❥❡t❛r ❝❧❛ss✐✜❝❛❞♦r❡s ❧✐♥❡❛r❡s q✉❡ ♠❛①✐♠✐③❡♠ ❛s ♠❛r❣❡♥s ❞♦s s❡✉s ❧✐♠✐t❡s ❞❡

❞❡❝✐sã♦ é ❞❡s❡❥á✈❡❧ ♣❛r❛ ❛ss❡❣✉r❛r q✉❡ s❡✉s ❡rr♦s ❞❡ ❣❡♥❡r❛❧✐③❛çã♦ ❞♦ ♣✐♦r ❝❛s♦ s❡❥❛♠

♠✐♥✐♠✐③❛❞♦s✳ ❈♦♠♦ ❡①❡♠♣❧♦✱ t❡♠♦s ♦ ❝❧❛ss✐✜❝❛❞♦r ❙❱▼ ❧✐♥❡❛r q✉❡ ❢✉♥❝✐♦♥❛ ❞❡ss❛

♠❛♥❡✐r❛ ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

❚♦❞❛✈✐❛✱ ♦ ❙❱▼ ❧✐♥❡❛r ♣♦❞❡ s❡r ❡①t❡♥❞✐❞♦ ♣❛r❛ ❛ ❝❧❛ss✐✜❝❛çã♦ ❞❡ ❞❛❞♦s ♥ã♦

❧✐♥❡❛r♠❡♥t❡ s❡♣❛rá✈❡✐s✱ ✉t✐❧✐③❛♥❞♦ ♣❛r❛ ✐ss♦ ✉♠ ♠ét♦❞♦ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ❛ ❛❜♦r❞❛❣❡♠

❞❛ ✏♠❛r❣❡♠ ✢❡①í✈❡❧✑✳ ❊ss❡ ♠ét♦❞♦ é ❝❛♣❛③ ❞❡ ❞❡s❝♦❜r✐r ✉♠ ❧✐♠✐t❡ ❞❡ ❞❡❝✐sã♦ q✉❡ s❡❥❛

t♦❧❡rá✈❡❧ ❛ ♣❡q✉❡♥♦s ❡rr♦s ❞❡ tr❡✐♥❛♠❡♥t♦✳ P❛r❛ ❢❛③❡r ✐ss♦✱ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❞❡s❝♦❜❡rt❛

❡♠ ❙❱▼ ❞❡✈❡ ❝♦♥s✐❞❡r❛r ♦ ❜❛❧❛♥❝❡❛♠❡♥t♦ ❡♥tr❡ ❛ ❧❛r❣✉r❛ ❞❛ ♠❛r❣❡♠ ❡ ♦ ♥ú♠❡r♦ ❞❡

❡rr♦s ❞❡ tr❡✐♥❛♠❡♥t♦ ❝♦♠❡t✐❞♦s ♣❡❧♦ ❧✐♠✐t❡ ❞❡ ❞❡❝✐sã♦ ❧✐♥❡❛r ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

❋✐❣✉r❛ ✷✳✶✾✳ ▲✐♠✐t❡ ❞❡ ❞❡❝✐sã♦ ❞❡ ❙❱▼ ♣❛r❛ ❝❛s♦ ♥ã♦ s❡♣❛rá✈❡❧ ❬❚❛♥ ❡t ❛❧✳✱✷✵✵✾❪

❈♦♠♦ ❡①❡♠♣❧♦✱ ❛ ❋✐❣✉r❛ ✷✳✶✾ ♠♦str❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s q✉❡ é s❡♠❡❧❤❛♥t❡ à

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✸✼

❋✐❣✉r❛ ✷✳✶✽✱ ❡①❝❡t♦ q✉❡ ♣♦ss✉✐ ❞♦✐s ♥♦✈♦s ❡①❡♠♣❧♦s✱ P ❡ ◗✳ ◆❡st❡ ❝❛s♦✱ ❡♠❜♦r❛ ♦ ❧✐♠✐t❡

❞❡ ❞❡❝✐sã♦ B1 ❝❧❛ss✐✜q✉❡ ❡rr♦♥❡❛♠❡♥t❡ ♦s ♥♦✈♦s ❡①❡♠♣❧♦s ❡ B2 ❝❧❛ss✐✜❝❛ ❝♦rr❡t❛♠❡♥t❡✱

✐st♦ ♥ã♦ s✐❣♥✐✜❝❛ q✉❡ B2 s❡❥❛ ✉♠ ❧✐♠✐t❡ ❞❡ ❞❡❝✐sã♦ ♠❡❧❤♦r ❞♦ q✉❡ B1 ♣♦rq✉❡ ♦s ♥♦✈♦s

❡①❡♠♣❧♦s ♣♦❞❡♠ ❝♦rr❡s♣♦♥❞❡r ❛ r✉í❞♦s ♥♦s ❞❛❞♦s ❞❡ tr❡✐♥❛♠❡♥t♦✳ ❆ss✐♠✱ B1 ❛✐♥❞❛

❞❡✈❡ s❡r ♣r❡❢❡r✐❞♦ ❝♦♠ r❡❧❛çã♦ ❛ B2 ♣♦r q✉❡ ♣♦ss✉✐ ✉♠❛ ♠❛r❣❡♠ ♠❛✐♦r✱ s❡♥❞♦ ♣♦rt❛♥t♦✱

♠❡♥♦s s✉s❝❡♣tí✈❡❧ ❛ ♦✈❡r✜tt✐♥❣ ❬❚❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪✳

◆❡st❡ tr❛❜❛❧❤♦✱ ❛ té❝♥✐❝❛ ❙❱▼ ❢♦✐ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❛ ❝❧❛ss✐✜❝❛çã♦ ❞♦ trá❢❡❣♦ ❞❡

r❡❞❡ ❛tr❛✈és ❞♦ s♦❢t✇❛r❡ ❲❡❦❛✳ ❊♠❜♦r❛ ♥ã♦ t❡♥❤❛ ❛❧❝❛♥ç❛❞♦ ♦s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s

❡♠ r❡❧❛çã♦ ❛s ❞❡♠❛✐s té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦✱ s❡r✈✐✉ ♣❛r❛ ❛♥á❧✐s❡ ❡ ❝♦♠♣❛r❛çã♦ ❝♦♠

♦✉tr♦s tr❛❜❛❧❤♦s✳

✷✳✺✳✺ ❙✐st❡♠❛s ■♥t❡❧✐❣❡♥t❡s ❍í❜r✐❞♦s

❖s ❙✐st❡♠❛s ■♥t❡❧✐❣❡♥t❡s ❍í❜r✐❞♦s ✭❙■❍s✮ sã♦ r❡s✉❧t❛❞♦s ❞❛ ❝♦♠❜✐♥❛çã♦ ❞❡ ❞✉❛s ♦✉

♠❛✐s té❝♥✐❝❛s ❞✐st✐♥t❛s✱ s❡♥❞♦ ♣❡❧♦ ♠❡♥♦s ✉♠❛ ❞❡❧❛s ❞❡ ■♥t❡❧✐❣ê♥❝✐❛ ❆rt✐✜❝✐❛❧ ✭■❆✮✳ ❆

✈❛♥t❛❣❡♠ ❞❡ss❡s s✐st❡♠❛s ❡stá ♥♦ ❢❛t♦ ❞❡ q✉❡ ❡♠ ❛❧❣✉♥s ❝❛s♦s✱ ❛♣❡♥❛s ✉♠❛ té❝♥✐❝❛

❛♣r❡s❡♥t❛ ❞❡✜❝✐ê♥❝✐❛s ♥❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❡✱ ❡♥tã♦✱ ❛ ❝♦♠❜✐♥❛çã♦ ❞❡ ♠❛✐s ❞❡

✉♠❛ té❝♥✐❝❛ ♣♦❞❡ ❝♦♠❜✐♥❛r ❛s ✈❛♥t❛❣❡♥s✱ s✉♣❡r❛♥❞♦ ❛s ❞❡s✈❛♥t❛❣❡♥s q✉❡ ❝❛❞❛ té❝♥✐❝❛

❛♣r❡s❡♥t❛ ✐♥❞✐✈✐❞✉❛❧♠❡♥t❡ ❬❘❡③❡♥❞❡✱ ✷✵✵✺❪✳

➱ ❝♦♠✉♠ ❛ ✉t✐❧✐③❛çã♦ ❞❡ té❝♥✐❝❛s ❝♦♠♦ ❘❡❞❡s ◆❡✉r❛✐s ❛rt✐✜❝✐❛✐s ❡♠ ❝♦♥❥✉♥t♦ ❝♦♠

té❝♥✐❝❛s ❞❡ ❈♦♠♣✉t❛çã♦ ❊✈♦❧✉t✐✈❛ ✭❈❊✮ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❆❧❣♦r✐t♠♦s ●❡♥ét✐❝♦s ❡

té❝♥✐❝❛s q✉❡ ✉t✐❧✐③❛♠ ❝♦♥❤❡❝✐♠❡♥t♦ ❝♦♠♦ ▲ó❣✐❝❛ ◆❡❜✉❧♦s❛✳ ❉❡ss❛ ❢♦r♠❛✱ ❛ ❝♦♠❜✐♥❛çã♦

❞❡ ✈ár✐❛s té❝♥✐❝❛s ♣♦❞❡ ❧❡✈❛r ❛ ✉♠❛ s♦❧✉çã♦ ♠❛✐s r♦❜✉st❛ ❡ ❡✜❝✐❡♥t❡ ❬❘❡③❡♥❞❡✱ ✷✵✵✺❪✳

❆s ❘◆❆s ♦❢❡r❡❝❡♠ ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❛ ♣❛rt✐r ❞❡ ❞❛❞♦s✱ ♠♦❞❡❧❛❣❡♠

❡♠♣ír✐❝❛ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❤✉♠❛♥♦✱ té❝♥✐❝❛s ❞❡ ❛♣r♦①✐♠❛çã♦ ✉♥✐✈❡rs❛❧✱ ♠ét♦❞♦s ❞❡

❡①tr❛çã♦ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ❛ ♣❛rt✐r ❞♦s ❞❛❞♦s✱ ♠❡♠ór✐❛ ❛ss♦❝✐❛t✐✈❛✱ ❡♥tr❡ ♦✉tr❛s✳ ❈♦♥✲

t✉❞♦✱ ❛s ❘◆❆s ❡①✐❣❡♠ ✉♠ t❡♠♣♦ ❞❡ tr❡✐♥❛♠❡♥t♦ ❡❧❡✈❛❞♦✱ ❛❧é♠ ❞❡ ♥ã♦ ♣♦ss✉✐r❡♠ ✉♠

♠❡❝❛♥✐s♠♦ ❡①♣❧✐❝❛t✐✈♦✱ ♥❡♠ ✉♠ ♠❡❝❛♥✐s♠♦ ❛✉t♦♠át✐❝♦ ❡ ❡✜❝✐❡♥t❡ ♣❛r❛ ❛✉①✐❧✐❛r ♦ ❞❡✲

s❡♥✈♦❧✈❡❞♦r ♥♦ ♣r♦❥❡t♦ ❞❛ r❡❞❡✳ ❊♥q✉❛♥t♦ ✐ss♦✱ ❛ ❈❊ ❛♣r❡s❡♥t❛ ♦✉tr❛s ✈❛♥t❛❣❡♥s ❝♦♠♦✱

♥ã♦ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ✉♠ ❝♦♥❤❡❝✐♠❡♥t♦ ♠❛t❡♠át✐❝♦ ❛♣r♦❢✉♥❞❛❞♦ ❞♦ ♣r♦❜❧❡♠❛ ❝♦♥s✐❞❡✲

r❛❞♦✱ t♦❧❡râ♥❝✐❛ ❛ r✉í❞♦s ❡ ❞❛❞♦s ✐♥❝♦♠♣❧❡t♦s✱ ❛❧é♠ ❞❛ ♦t✐♠✐③❛çã♦ ❞❡ ♣❛râ♠❡tr♦s ❞❡

❢✉♥çõ❡s ♦❜❥❡t✐✈♦s ❝♦♠♣❧❡①❛s ❬❘❡③❡♥❞❡✱ ✷✵✵✺❪✳

❆ss✐♠ s❡♥❞♦✱ ♦s ♣❛r❛❞✐❣♠❛s ❞❛ ❋✐❣✉r❛ ✷✳✷✵ ♣♦❞❡♠ s❡r ✈✐st♦s ❝♦♠♦ ❝♦♠♣❧❡♠❡♥t❛✲

r❡s✱ ♣♦❞❡♥❞♦ t❛♠❜é♠ ♣r♦♣✐❝✐❛r s♦❧✉çõ❡s s✐♠✐❧❛r❡s ❡ ❡q✉✐✈❛❧❡♥t❡s✳ ❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱

✉♠ ♠ét♦❞♦ ♣♦❞❡ s❡r ❛♣❧✐❝❛❞♦ ♣❛r❛ ♠❡❧❤♦r❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ ♦✉tr♦✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦

❬❘❡③❡♥❞❡✱ ✷✵✵✺❪✿

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✸✽

❋✐❣✉r❛ ✷✳✷✵✳ P❛r❛❞✐❣♠❛s ❡ ♠ét♦❞♦s s❡ s♦❜r❡♣õ❡♠ ❝♦♠♦ té❝♥✐❝❛s ❞❡ r❡s♦❧✉çã♦❞❡ ♣r♦❜❧❡♠❛ ❬❘❡③❡♥❞❡✱ ✷✵✵✺❪

• ❈❊ ♣♦❞❡ s❡r ✉s❛❞❛ ♣❛r❛ ✐♥✐❝✐❛❧✐③❛r ❛ ❡str✉t✉r❛ ❞❡ ✉♠❛ ❘◆❆ ❛ ✜♠ ❞❡ ❛❝❡❧❡r❛r ♦

tr❡✐♥❛♠❡♥t♦ ❡ ♠❡❧❤♦r❛r ❛ ❣❡♥❡r❛❧✐③❛çã♦❀

• ❘◆❆s ❡ ❈❊ ♣♦❞❡♠ s❡r ❡♠♣r❡❣❛❞❛s ♣❛r❛ ❛♣r❡♥❞❡r r❡❣r❛s ✭❞❡ ❧ó❣✐❝❛ ♥❡❜✉❧♦s❛ ♦✉

♥ã♦✮❀

• ❘◆❆s ♣♦❞❡♠ s❡r ✉s❛❞❛s ♣❛r❛ r❡✜♥❛r r❡❣r❛s ✭❞❡ ❧ó❣✐❝❛ ♥❡❜✉❧♦s❛ ♦✉ ♥ã♦✮❀

• ❈❊ ♣♦❞❡ s❡r ✉s❛❞❛ ♣❛r❛ ❛❥✉st❛r ❛ t♦♣♦❧♦❣✐❛ ❡ ♦s ♣❡s♦s ❞❡ ✉♠❛ ❘◆❆❀

• ❘◆❆ ❡ ❈❊ ♣♦❞❡♠ s❡r ✉s❛❞❛s ❝♦♠♦ ♣❛rt❡ ❞❡ ✉♠❛ ♠áq✉✐♥❛ ❞❡ r❛❝✐♦❝í♥✐♦ s✐♠❜ó❧✐❝♦✳

❉✐❛♥t❡ ❞✐ss♦✱ ♦s ❙■❍s tê♠ s✐❞♦ ❝❧❛ss✐✜❝❛❞♦s ❡♠ ✉♠ ❡sq✉❡♠❛ ❝♦♠♣♦st♦ ♣♦r ✸ ❝❧❛s✲

s❡s✱ ❝♦♥❢♦r♠❡ ❛ ❋✐❣✉r❛ ✷✳✷✶✳ ❊ss❛ ❝❧❛ss✐✜❝❛çã♦ ❝♦♥s✐❞❡r❛ ❢❛t♦r❡s ❝♦♠♦✿ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡✱

❛rq✉✐t❡t✉r❛ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❡ r❡q✉✐s✐t♦s ❞❡ ❝♦♠✉♥✐❝❛çã♦✳ ❖ ♣r✐♠❡✐r♦ t✐♣♦ é ✏s✉❜s✲

t✐t✉✐çã♦ ❞❡ ❢✉♥çã♦✑ ✭❢✉♥❝✐♦♥ r❡♣❧❛❝✐♥❣✮✱ ❛ q✉❛❧ ✉t✐❧✐③❛ ✉♠❛ té❝♥✐❝❛ ♣❛r❛ ✐♠♣❧❡♠❡♥t❛r

❛ ❢✉♥çã♦ ❞❡ ♦✉tr❛ té❝♥✐❝❛✳ ◆❡ss❡ ❝❛s♦✱ ♥ã♦ ❤á ♥❡♥❤✉♠❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡ ❡①tr❛ ❛♦ s✐s✲

t❡♠❛✱ ♣♦✐s ❛♣❡♥❛s t❡♥t❛ s✉♣❡r❛r ❛❧❣✉♠❛ ❧✐♠✐t❛çã♦ ❞❛ té❝♥✐❝❛ ♣r✐♥❝✐♣❛❧ ♦✉ ♦t✐♠✐③❛r s✉❛

❡①❡❝✉çã♦✳

❋✐❣✉r❛ ✷✳✷✶✳ ❈❧❛ss✐✜❝❛çã♦ ❞❡ s✐st❡♠❛s ❤í❜r✐❞♦s ✐♥t❡❧✐❣❡♥t❡s ❬❘❡③❡♥❞❡✱ ✷✵✵✺❪

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✸✾

❆ s❡❣✉♥❞❛ ❝❧❛ss✐✜❝❛çã♦ sã♦ ❞♦s ✏❤í❜r✐❞♦s ✐♥t❡r❝♦♠✉♥✐❝❛t✐✈♦s✑ ✭✐♥t❡r❝♦♠♠✉♥✐❝❛✲

t✐♥❣ ❤②❜r✐❞s✮✱ q✉❡ ♣r♦❝✉r❛♠ r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s ❝♦♠♣❧❡①♦s q✉❡ ♣♦ss❛♠ s❡r ❞✐✈✐❞✐❞♦s

❡♠ ✈ár✐❛s s✉❜t❛r❡❢❛s ✐♥❞❡♣❡♥❞❡♥t❡s✳ ❖ s✐st❡♠❛ ❤í❜r✐❞♦ é ❢♦r♠❛❞♦ ♣♦r ✈ár✐♦s ♠ó❞✉✲

❧♦s ✐♥❞❡♣❡♥❞❡♥t❡s✱ ♥♦s q✉❛✐s ❝❛❞❛ ✉♠ ✉s❛ ✉♠❛ té❝♥✐❝❛ ✐♥t❡❧✐❣❡♥t❡ ♣❛r❛ r❡s♦❧✈❡r ✉♠❛

❞❛s s✉❜t❛r❡❢❛s ❞♦ ♣r♦❜❧❡♠❛ ♣r✐♥❝✐♣❛❧✳ P♦r ✜♠✱ ♦ ✏❤í❜r✐❞♦s ♣♦❧✐♠ór✜❝♦s✑ é q✉❛♥❞♦

✉♠❛ ú♥✐❝❛ té❝♥✐❝❛ é ❛❞❛♣t❛❞❛ ♣❛r❛ r❡❛❧✐③❛r ✉♠❛ t❛r❡❢❛ ✐♥❡r❡♥t❡ ❛ ✉♠❛ ♦✉tr❛ té❝♥✐❝❛

❬❘❡③❡♥❞❡✱ ✷✵✵✺❪✳

◆❡st❡ tr❛❜❛❧❤♦✱ ✉♠ ❙■❍ ✐♥t❡r❝♦♠✉♥✐❝❛t✐✈♦ ❢♦✐ ✉t✐❧✐③❛❞♦ ❞❡ ♠♦❞♦ q✉❡ ♦ ❆● ✐♥✐❝✐❛✲

❧✐③❛ss❡ ❛ ❡str✉t✉r❛ ❞❛s ❘◆❆s ▼▲P✱ ❞❡✜♥✐♥❞♦ ♠❡❧❤♦r❡s ♣❛râ♠❡tr♦s✱ ♦s q✉❛✐s ♣❡r♠✐t✐r❛♠

✉♠❛ ♠❡❧❤♦r ❣❡♥❡r❛❧✐③❛çã♦ ❞♦s r❡s✉❧t❛❞♦s✳

✷✳✻ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s

◆♦s ú❧t✐♠♦s ❛♥♦s ♠✉✐t❛s ♣❡sq✉✐s❛s tê♠ s✐❞♦ ❞❡s❡♥✈♦❧✈✐❞❛s s♦❜r❡ ♦s ❙❉■s ❡ ❛♣❡s❛r ❞♦s

❛✈❛♥ç♦s✱ ❛✐♥❞❛ ❡①✐st❡ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ♠❡❧❤♦r✐❛s ❞❡✈✐❞♦ às ♠✉❞❛♥ç❛s ❞❡ ❝♦♠♣♦rt❛♠❡♥t♦

❞♦s ✉s✉ár✐♦s ❡ ♦r❣❛♥✐③❛çõ❡s ❡ ❞❛ ❡✈♦❧✉çã♦ ❞❛s r❡❞❡s ❡ s✐st❡♠❛s ❝♦♠♣✉t❛❝✐♦♥❛✐s✳ ❉❡ss❛

❢♦r♠❛ sã♦ ❛♣r❡s❡♥t❛❞♦s ❛❧❣✉♥s tr❛❜❛❧❤♦s r❡❧❛❝✐♦♥❛❞♦s✳

❊♠ ❚❛✈❛❧❧❛❡❡ ❡t ❛❧✳ ❬✷✵✵✾❪ é ♣r♦♣♦st❛ ❛ ❜❛s❡ ❞❡ ❞❛❞♦s ◆❙▲✲❑❉❉ q✉❡ tr❛③ ❛✈❛♥✲

ç♦s ❡♠ r❡❧❛çã♦ à ❜❛s❡ ❑❉❉❈❯P✬✾✾✳ ❆❧é♠ ❞❡ r❡❛❧✐③❛r ✉♠❛ ❛♥á❧✐s❡ ❞❡t❛❧❤❛❞❛ ❞❛ ❜❛s❡

❑❉❉❈❯P✬✾✾✱ ♣r♦❝✉r♦✉ ❡❧✐♠✐♥❛r ❛❧❣✉♥s ❞❡ s❡✉s ♣r♦❜❧❡♠❛s✱ q✉❡ tê♠ s✐❞♦ ❛❧✈♦s ❞❡ ❝rí✲

t✐❝❛s ❛ ♠❛✐s ❞❡ ✉♠❛ ❞é❝❛❞❛ ❬▼❝❍✉❣❤✱ ✷✵✵✵❪✱ ✉t✐❧✐③❛♥❞♦ ❛s té❝♥✐❝❛s ❞♦ s♦❢t✇❛r❡ ❲❡❦❛

❝♦♠♦ ➪r✈♦r❡s ❞❡ ❉❡❝✐sã♦ ❡ ❘❡❞❡s ◆❡✉r❛✐s ❆rt✐✜❝✐❛✐s ✭❘◆❆s✮ ♣❛r❛ ❣❡r❛r ♦s r❡s✉❧t❛❞♦s✳

❖ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛❞♦ ❡♠ ▲✐ ❬✷✵✶✵❪ ✉t✐❧✐③❛ ✶✵✪ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s

❑❉❉❈❯P✬✾✾ ❛tr❛✈és ❞❡ ❘◆❆s ❝♦♠ ✉♠❛ ❡str✉t✉r❛ ✢❡①í✈❡❧ ❡ ♠♦❞✉❧❛r✱ ✉t✐❧✐③❛♥❞♦ ❆●

♣❛r❛ ❛❥✉st❛r ♦s s❡✉s ♣❛râ♠❡tr♦s ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ♠❡❧❤♦r❡s t❛①❛s ❞❡ ❞❡t❡❝çã♦ ❡

♠❡♥♦r❡s t❛①❛s ❞❡ ❢❛❧s♦ ♣♦s✐t✐✈♦s ❢♦r❛♠ ❛t✐♥❣✐❞❛s✳

❊♠ P❛❝❤❣❤❛r❡ ✫ ❑✉❧❦❛r♥✐ ❬✷✵✶✶❪ é r❡❛❧✐③❛❞♦ ✉♠ ❡st✉❞♦ ❝♦♠♣❛r❛t✐✈♦ ❞❡ ✈ár✐♦s

t✐♣♦s ❞❡ ❛❧❣♦r✐t♠♦s ❞❡ ➪r✈♦r❡ ❞❡ ❉❡❝✐sã♦✱ ❝♦♥s✐❞❡r❛♥❞♦ ♠étr✐❝❛s ❝♦♠♦ t❡♠♣♦ ❞❡ tr❡✐✲

♥❛♠❡♥t♦✱ ♣r❡❝✐sã♦ ❡ t❛♠❛♥❤♦ ❞❛ ár✈♦r❡✳ ◆❡st❡ ❡st✉❞♦ ❢♦✐ ✉t✐❧✐③❛❞♦ ✉♠❛ ♣❡q✉❡♥❛ ♣❛rt❡

❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❞❛ ❑❉❉❈❯P✬✾✾✱ s❡♥❞♦ q✉❡ ❛ ➪r✈♦r❡ ❞❡ ❉❡❝✐sã♦ ❞♦ t✐♣♦ ❏✹✽❣r❛❢t

♦❜t❡✈❡ ♦s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s✳

◆♦ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛❞♦ ❡♠ ❉❡✈❛r❛❥✉ ✫ ❘❛♠❛❦r✐s❤♥❛♥ ❬✷✵✶✶❪✱ ♦ ❞❡s❡♠♣❡♥❤♦ ❞❡

❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sã♦ ✉t✐❧✐③❛♥❞♦ ❛ ❑❉❉❈❯P✬✾✾ é ❝♦♠♣❛r❛❞♦ ❛tr❛✈és ❞❡ ✈ár✐♦s ❝❧❛ss✐✲

✜❝❛❞♦r❡s ❞❡ ❘◆❆s✱ ❛❧é♠ ❞❡ ❝♦♠♣❛r❛r ♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❝♦♠♣❧❡t♦ ❝♦♠ ✉♠❛ ✈❡rsã♦

r❡❞✉③✐❞❛ ❞❛ ❑❉❉❈❯P✬✾✾✱ ♠♦str❛♥❞♦ q✉❡ ❛ ✉t✐❧✐③❛çã♦ ❞♦ ❝♦♥❥✉♥t♦ r❡❞✉③✐❞♦ s❡ ❥✉st✐✜❝❛

❞❡✈✐❞♦ ❛♦ ♠❡❧❤♦r ❞❡s❡♠♣❡♥❤♦ ❡♠ r❡❧❛çã♦ à ✉t✐❧✐③❛çã♦ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❝♦♠♣❧❡t♦✳

✷✳ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✹✵

❖ tr❛❜❛❧❤♦ ❞❡ ❙✐❧✈❛ ❬✷✵✶✶❪ ❞❡s❡♥✈♦❧✈❡ ♠ét♦❞♦s ❞❡ ❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sã♦ ❝♦♠ té❝♥✐✲

❝❛s ❞❡ ■❆ ❝♦♠♦ ❆●✱ ❘◆❆s ❡ ▲ó❣✐❝❛ ◆❡❜✉❧♦s❛✱ ❝r✐❛♥❞♦ ❛ss✐♠ ✉♠ ❙■❍ q✉❡ r❡❛❧✐③♦✉ ✉♠❛

❛♥á❧✐s❡ ❞❡t❛❧❤❛❞❛ ❡ ♠❡❧❤♦r✐❛s ❞❛s t❛①❛s ❞❡ ❞❡t❡❝çã♦ ❝♦♠ ❛ ❜❛s❡ ❞❡ ❞❛❞♦s ◆❙▲✲❑❉❉✱

❛❧é♠ ❞❡ ❢❛③❡r ❝♦♠♣❛r❛çõ❡s ❝♦♠ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❡♠ ❚❛✈❛❧❧❛❡❡ ❡t ❛❧✳ ❬✷✵✵✾❪✳

❊♠ ❙❤✐r❛✈✐ ❡t ❛❧✳ ❬✷✵✶✷❪✱ ❢♦✐ ♣r♦♣♦st❛ ✉♠❛ ♥♦✈❛ ❜❛s❡ ❞❡ ❞❛❞♦s✱ ❛ ■❙❈❳ ✷✵✶✷✱ q✉❡

❢♦✐ ❣❡r❛❞❛ ❛ ♣❛rt✐r ❞❡ trá❢❡❣♦ r❡❛❧ ❡♠ ✉♠ ❛♠❜✐❡♥t❡ ♠♦♥✐t♦r❛❞♦✱ ❢♦r♥❡❝❡♥❞♦ ✉♠ ❣✉✐❛

❝♦♠ ❝❛r❛❝t❡ríst✐❝❛s ✐♠♣♦rt❛♥t❡s ♣❛r❛ ❝r✐❛çã♦ ❞❡ ♥♦✈❛s ❜❛s❡s ❞❡ ❞❛❞♦s✱ ❛❧é♠ ❞❡ r❡❛❧✐③❛r

❝♦♠♣❛r❛çõ❡s ❝♦♠ ♦✉tr❛s ❝♦♠♦ ❛ ❑❉❉❈❯P✬✾✾✱ ❉❊❋❈❖▼ ❡ ❈❆■❉❆✳

❆ ♣❛rt✐r ❞❛ ❜❛s❡ ■❙❈❳ ✷✵✶✷✱ ❛❧❣✉♥s tr❛❜❛❧❤♦s r❡❝❡♥t❡s tê♠ s✉r❣✐❞♦✱ ❝♦♠♦ ❡♠

▼③✐❧❛ ✫ ❉✉❜❡ ❬✷✵✶✸❪ ♦♥❞❡ ❛♣❧✐❝❛ ♦ ❝❧❛ss✐✜❝❛❞♦r ❦✲◆◆ ✭❦✲◆❡❛r❡st ◆❡✐❣❤❜♦r✮ ❡ ❡❧✐♠✐♥❛

❛❧❣✉♥s ❛tr✐❜✉t♦s ❝♦♠ ❝❛r❛❝t❡ríst✐❝❛s ❧✐❣❛❞❛s ❛♦ ❞❡st✐♥♦✱ ♣❡r♠✐t✐♥❞♦ q✉❡ ♦ ♠♦❞❡❧♦ s❡❥❛

✉t✐❧✐③❛❞♦ ♣❛r❛ ❞❡t❡❝çã♦ ❡♠ t❡♠♣♦ r❡❛❧✳

P♦r ✜♠✱ ❡♠ ❙❛❧❧❛② ❡t ❛❧✳ ❬✷✵✶✸❪ ✉t✐❧✐③♦✉ ❛ ■❙❈❳ ✷✵✶✷ ❡ ♣r♦♣ôs ✉♠ ❝❧❛ss✐✜❝❛❞♦r ♣❛r❛

r❡❞❡s ❞❡ ❛❧t❛ ✈❡❧♦❝✐❞❛❞❡ ❜❛s❡❛❞♦ ❡♠ tr❡✐♥❛♠❡♥t♦ ♦♥❧✐♥❡ ❝♦♠ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❛♣r❡♥❞✐③❛❞♦

❞❡ ♠áq✉✐♥❛ ✭❙❱▼✮✱ ✉t✐❧✐③❛♥❞♦ ✈ár✐❛s ❡str❛té❣✐❛s ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❡ ♠♦❞♦s ❞❡ ❡①❡❝✉çã♦✳

❈♦♠♦ ❝♦♥❝❧✉sã♦✱ ♦ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ ✉♠ ❜♦♠ r❡s✉❧t❛❞♦ ❡♥tr❡ ❛ ♣r❡❝✐sã♦ ❡ ♦ t❡♠♣♦

❞❡ ♣r♦❝❡ss❛♠❡♥t♦✳

❈❛♣ít✉❧♦ ✸

▼ét♦❞♦s

◆❡st❡ ❝❛♣ít✉❧♦✱ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛s ❡t❛♣❛s r❡❛❧✐③❛❞❛s ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ tr❛❜❛✲

❧❤♦✳ ❉❡s❞❡ ♦ ✐♥í❝✐♦✱ ♣r♦❝✉r♦✉✲s❡ ❛♣r♦❢✉♥❞❛r s♦❜r❡ ♦ t❡♠❛ ♣r♦♣♦st♦ ❛tr❛✈és ❞❡ ✐♥❢♦r♠❛✲

çõ❡s ❝♦♠♣r♦✈❛❞❛s ❡ ♣✉❜❧✐❝❛❞❛s ♥❛ ❧✐t❡r❛t✉r❛✱ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ✐♥❞❡♥t✐✜❝❛r ❛s ♣r✐♥❝✐♣❛✐s

♥❡❝❡ss✐❞❛❞❡s ❡ s❡r ✉♠ ❣✉✐❛ ♣❛r❛ ♦ ♣r♦❣r❡ss♦ ❞♦ tr❛❜❛❧❤♦✳ ❋♦✐ ✐❞❡♥t✐✜❝❛❞❛ ❛ ♥❡❝❡ss✐❞❛❞❡

❞❡ ❜✉s❝❛r ✉♠❛ ❜❛s❡ ❞❡ ❞❛❞♦s ❝♦♠ trá❢❡❣♦ ❞❡ r❡❞❡ ♠❛✐s ❛t✉❛❧ ❡ ❝♦♠ ❝❛r❛❝t❡ríst✐❝❛s

✐♠♣♦rt❛♥t❡s ♣❛r❛ ❛ ❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sõ❡s✳

❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❢♦✐ ♣r❡❝✐s♦ ♣r❡♣❛r❛r ❛ ❜❛s❡ ❞❡ ❞❛❞♦s ❡s❝♦❧❤✐❞❛✳ P❛r❛ t❛❧✱

✉t✐❧✐③♦✉✲s❡ ♦ ♣r♦❝❡ss♦ ❞❡ ❉❡s❝♦❜❡rt❛ ❞♦ ❈♦♥❤❡❝✐♠❡♥t♦ ❡♠ ❇❛s❡ ❞❡ ❉❛❞♦s ✭❑❉❉✮✱ ♦

q✉❛❧ ❡❧✐♠✐♥♦✉ ✐♥❝♦♥s✐stê♥❝✐❛s✱ ❞❡✜♥✐✉ ♦ ❢♦r♠❛t♦ ❞♦s ❞❛❞♦s✱ s❡❧❡❝✐♦♥♦✉ ✉♠❛ ❛♠♦str❛✱

♣❛r❛ q✉❡ ❡♥tã♦ ❢♦ss❡ ♣♦ssí✈❡❧ ❛♣❧✐❝❛r ❛ ❡t❛♣❛ ❞❡ ♠✐♥❡r❛çã♦ ❞♦s ❞❛❞♦s✳

❆ss✐♠✱ ❡s❝♦❧❤❡✉✲s❡ ❛s ♣r✐♥❝✐♣❛✐s té❝♥✐❝❛s ❡ ❞❡✜♥✐✉✲s❡ ❝♦♠♦ ❛♣❧✐❝á✲❧❛s ♥❛ ❝❧❛ss✐✜❝❛✲

çã♦ ❞♦ trá❢❡❣♦ ❞❡ r❡❞❡✳ ◆❡ss❛ ❡t❛♣❛✱ ✉t✐❧✐③♦✉✲s❡ ❝♦♠♦ ❜❛s❡ ❞✐✈❡rs❛s té❝♥✐❝❛s ❡♠♣r❡❣❛❞❛s

❡♠ tr❛❜❛❧❤♦s ❝♦rr❡❧❛t♦s✱ ❛s q✉❛✐s ♦❜t✐✈❡r❛♠ r❡s✉❧t❛❞♦s ♣r♦♠✐ss♦r❡s✳

❈♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ♠❡❧❤♦r❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❡ r❡s✉❧t❛❞♦s ❞❛s ❝❧❛ss✐✜❝❛çõ❡s✱ ❜✉s❝♦✉✲s❡

t❛♠❜é♠ r❡❛❧✐③❛r t❡st❡s ❝♦♠ ♠❡♥♦s ❛tr✐❜✉t♦s ❞❡ ❡♥tr❛❞❛✱ ❝♦♥s✐❞❡r❛❞♦s ❞❡s♥❡❝❡ssár✐♦s

♣❛r❛ ✉♠❛ ❞❡t❡❝çã♦ ❡♠ t❡♠♣♦ r❡❛❧✱ ❛❧é♠ ❞❡ ✉t✐❧✐③❛r ✉♠ ❙✐st❡♠❛ ■♥t❡❧✐❣❡♥t❡ ❍í❜r✐❞♦

✭❙■❍✮✱ ♦ q✉❛❧ ❝♦♠❜✐♥♦✉ ♠❛✐s ❞❡ ✉♠❛ té❝♥✐❝❛ ♣❛r❛ ❛ ❝❧❛ss✐✜❝❛çã♦ ❞♦ trá❢❡❣♦✳

✸✳✶ ❇❛s❡s ❞❡ ❉❛❞♦s ❝♦♠ ❚rá❢❡❣♦ ❞❡ ❘❡❞❡

◆❡st❛ s❡çã♦ sã♦ ❛♣r❡s❡♥t❛❞❛s ❞✉❛s ❞❛s ❜❛s❡s ❞❡ ❞❛❞♦s q✉❡ tê♠ s✐❞♦ ♠❛✐s ✉t✐❧✐③❛❞❛s ♥♦s

tr❛❜❛❧❤♦s r❡❧❛❝✐♦♥❛❞♦s ❡ ✉♠❛ ❜❛s❡ ♠❛✐s r❡❝❡♥t❡ q✉❡ é ❛ ❝❤❛✈❡ ❞❡st❡ tr❛❜❛❧❤♦ ❞❡s❡♥✈♦❧✲

✈✐❞♦✳

❉❡s❞❡ ✶✾✾✾✱ ❛ ❜❛s❡ ❞❡ ❞❛❞♦s ❑❉❉❈❯P✬✾✾ t❡♠ s✐❞♦ ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞❛ ❡♠

♣❡sq✉✐s❛s s♦❜r❡ ♠ét♦❞♦s ❞❡ ❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sã♦✳ ❊st❡ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❢♦✐ ❝♦♥str✉í❞♦

✹✶

✸✳ ▼ét♦❞♦s ✹✷

❛ ♣❛rt✐r ❞❡ ❞❛❞♦s ❝❛♣t✉r❛❞♦s ♣❡❧♦ ♣r♦❣r❛♠❛ ❞❡ ❛✈❛❧✐❛çã♦ ❞❡ ❙❉■s ❞❛ ❉❆❘P❆✬✾✽ ❡

♣r❡♣❛r❛❞❛ ♣❡❧♦ ▼■❚ ▲✐♥❝♦❧♥ ▲❛❜s✳ ❊st❡ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ♣♦ss✉✐ q✉❛r❡♥t❛ ❡ ❞♦✐s

❛tr✐❜✉t♦s q✉❡ ❝❛r❛❝t❡r✐③❛♠ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ trá❢❡❣♦ ❞❡ r❡❞❡ s❡♣❛r❛❞♦s ❡♠ ✹ ❝❧❛ss❡s

❞❡ ❛t❛q✉❡s ❡ ❝❡r❝❛ ❞❡ ✹✳✾✵✵✳✵✵✵ ❞❡ r❡❣✐str♦s ❬❑❉❉✲❈✉♣✱ ✶✾✾✾❪✳

◆♦ ❡♥t❛♥t♦✱ ✉♠❛ ❞❛s ♣r✐♥❝✐♣❛✐s ❞❡✜❝✐ê♥❝✐❛s ❞❡ss❛ ❜❛s❡ é ♦ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡

r❡❣✐str♦s r❡❞✉♥❞❛♥t❡s✳ ❆ss✐♠✱ ❡♠ ❚❛✈❛❧❧❛❡❡ ❡t ❛❧✳ ❬✷✵✵✾❪ ❢♦✐ ♣r♦♣♦st❛ ❛ ❜❛s❡ ❞❡ ❞❛❞♦s

◆❙▲✲❑❉❉✱ ❛ q✉❛❧ é ✉♠❛ ✈❡rsã♦ ♠❡❧❤♦r❛❞❛ ❞❛ ❑❉❉❈❯P✬✾✾ ❬◆❙▲✲❑❉❉✱ ✷✵✵✾❪✱ ♠❛s q✉❡

❛✐♥❞❛ ♣♦ss✉✐ ♣r♦❜❧❡♠❛s ❞❛ ❑❉❉❈❯P✬✾✾ ❝♦♠♦ ❞❛❞♦s ❛♥t✐❣♦s ❡ q✉❡ ♥ã♦ r❡♣r❡s❡♥t❛♠ ❛

r❡❛❧✐❞❛❞❡ ❛t✉❛❧ ❞❛s r❡❞❡s ❞❡ ❝♦♠♣✉t❛❞♦r❡s✳

❆ ❜❛s❡ ❞❡ ❞❛❞♦s ■❙❈❳ ✷✵✶✷ ❢♦✐ ❛♣r❡s❡♥t❛❞❛ ❡♠ ❙❤✐r❛✈✐ ❡t ❛❧✳ ❬✷✵✶✷❪✱ ❛ q✉❛❧ ❝♦♥s✐st❡

❞❡ ♣♦rçõ❡s ❞❡ trá❢❡❣♦ ❞❡ r❡❞❡ q✉❡ ✐♥❝❧✉❡♠ ✈ár✐❛s ✐♥❢♦r♠❛çõ❡s ❛❧é♠ ❞❡ s❡✉s ♣❛②❧♦❛❞s

❝♦♠♣❧❡t♦s✳ ❆ ■❙❈❳ ✷✵✶✷ ❢♦✐ ❣❡r❛❞❛ ❛ ♣❛rt✐r ❞❡ ✉♠ trá❢❡❣♦ r❡❛❧ ❡♠ ✉♠ ❛♠❜✐❡♥t❡

❝♦♥tr♦❧❛❞♦✱ ♣❡❧♦ ■♥❢♦r♠❛t✐♦♥ ❙❡❝✉r✐t② ❈❡♥tr❡ ♦❢ ❊①❝❡❧❧❡♥❝❡ ✭■❙❈❳✮ ♥❛ ❯♥✐✈❡rs✐t② ♦❢

◆❡✇ ❇r✉♥s✇✐❝❦ ❞♦ ❈❛♥❛❞á✱ ❝♦♥❢♦r♠❡ ❛ ❋✐❣✉r❛ ✸✳✶✱ ♣♦ss✉✐♥❞♦ ✷✳✵✼✶✳✻✺✼ r❡❣✐str♦s q✉❡

❢♦r❛♠ r♦t✉❧❛❞♦s✱ ✐♥❞✐❝❛♥❞♦ ♣❛r❛ ❝❛❞❛ ❝♦♥❡①ã♦ ♦ t✐♣♦ ❞❡ trá❢❡❣♦✳

❋✐❣✉r❛ ✸✳✶✳ ❆rq✉✐t❡t✉r❛ ❞❡ r❡❞❡ ✉t✐❧✐③❛❞❛ ♥❛ ■❙❈❳ ✷✵✶✷ ❬❙❤✐r❛✈✐ ❡t ❛❧✳✱ ✷✵✶✷❪

❆ss✐♠✱ ❡st❛ ❜❛s❡ ❢♦✐ ❡❧❛❜♦r❛❞❛ ❝♦♠ ♦s ♣r✐♥❝✐♣❛✐s ♦❜❥❡t✐✈♦s ❡ ❝❛r❛❝t❡ríst✐❝❛s ♣❛r❛

q✉❡ s❡❥❛ ❛❝❡✐tá✈❡❧✱ ❡❧✐♠✐♥❛♥❞♦ ❞❡✜❝✐ê♥❝✐❛s ❡♥❝♦♥tr❛❞❛s ❡♠ ♦✉tr❛s ❜❛s❡s✳ P♦rt❛♥t♦✱ ♦s

♦❜❥❡t✐✈♦s ❛ s❡❣✉✐r s❡r✈❡♠ ❝♦♠♦ ✉♠ ❣✉✐❛ ♣❛r❛ ❛ ❣❡r❛çã♦ ❞❡ ❢✉t✉r❛s ❜❛s❡s ♣❛r❛ ❛♥á❧✐s❡

❞❡ trá❢❡❣♦ ❞❡ r❡❞❡ ❬❙❤✐r❛✈✐ ❡t ❛❧✳✱ ✷✵✶✷❪✿

✸✳ ▼ét♦❞♦s ✹✸

• r❡❞❡ r❡❛❧✐st❛ ❡ trá❢❡❣♦ r❡❛❧✿ t♦❞♦s ♦s ❞❛❞♦s ❢♦r❛♠ ❝❛♣t✉r❛❞♦s ❞❡ ✉♠❛ r❡❞❡ r❡❛❧✱ ❡

♥ã♦ ❛♣❡♥❛s ❛tr❛✈és ❞❡ s✐♠✉❧❛❞♦r❡s❀

• ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s r♦t✉❧❛❞♦s✿ t♦❞♦ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s é r♦t✉❧❛❞♦✱ ✐❞❡♥t✐✜❝❛♥❞♦

♣❛r❛ ❝❛❞❛ ❝♦♥❡①ã♦ s❡ é ✉♠ trá❢❡❣♦ ♥♦r♠❛❧ ❞❡ r❡❞❡ ♦✉ s❡ é ✉♠ ❛t❛q✉❡❀

• ❝❛♣t✉r❛ t♦t❛❧ ❞❡ ✐♥t❡r❛çõ❡s ❞❡ r❡❞❡✿ t♦❞❛s ❛s ✐♥t❡r❛çõ❡s ❞❡ r❡❞❡ sã♦ ❝❛♣t✉r❛❞❛s✱

❝♦♠♦ ❞✉r❛çã♦ ❞❡ ❝❛❞❛ ❝♦♥❡①ã♦✱ ❡♥❞❡r❡ç♦s✴♣♦rt❛s ❞❡ ♦r✐❣❡♠ ❡ ❞❡st✐♥♦✱ ❡t❝❀

• ❝❛♣t✉r❛ ❝♦♠♣❧❡t❛ ❞❡ ❞❛❞♦s✿ ♦ trá❢❡❣♦ ❞❡ r❡❞❡ ❢♦✐ ❝❛♣t✉r❛❞♦ ✉t✐❧✐③❛♥❞♦ ✉♠ s♥♥✐❢❡r

❡ s❛❧✈❛♥❞♦ ♦s ❛rq✉✐✈♦s ❡♠ ❢♦r♠❛t♦ ✳♣❝❛♣ ♣❛r❛ ❛♥á❧✐s❡s ♣♦st❡r✐♦r❡s❀

• ❞✐✈❡rs♦s ❝❡♥ár✐♦s ❞❡ ✐♥tr✉sõ❡s✿ sã♦ r❡❛❧✐③❛❞♦s ✈ár✐♦s t❡st❡s ❞❡ ✐♥tr✉sõ❡s ❝♦♠ ❞✐❢❡✲

r❡♥t❡s té❝♥✐❝❛s✱ ❝♦♠♦ ❛t❛q✉❡ ❞❡ ♥❡❣❛çã♦ ❞❡ s❡r✈✐ç♦ ✭❉♦❙ ✮✱ ❢♦rç❛ ❜r✉t❛✱ ❡t❝✳

❊st❛ ❜❛s❡ ❞❡ ❞❛❞♦s é ❝♦♠♣♦st❛ ♣♦r ✶✼ ❛tr✐❜✉t♦s ♠♦str❛❞♦s ♥❛ ❚❛❜❡❧❛ ✸✳✶ ❡ ♦

❛tr✐❜✉t♦ ✏t❛❣✑ ✐♥❞✐❝❛ s❡ ♦ trá❢❡❣♦ é ♥♦r♠❛❧ ♦✉ ✉♠ ❛t❛q✉❡✳

❚❛❜❡❧❛ ✸✳✶✳ ▲✐st❛ ❞❡ ❛tr✐❜✉t♦s ❞❛ ❜❛s❡ ■❙❈❳ ✷✵✶✷

❛♣♣◆❛♠❡ ♣r♦t♦❝♦❧◆❛♠❡t♦t❛❧❙♦✉r❝❡❇②t❡s t♦t❛❧❉❡st✐♥❛t✐♦♥❇②t❡st♦t❛❧❙♦✉r❝❡P❛❝❦❡ts t♦t❛❧❉❡st✐♥❛t✐♦♥P❛❝❦❡ts

s♦✉r❝❡P❛②❧♦❛❞❆s❇❛s❡✻✹ ❞❡st✐♥❛t✐♦♥P❛②❧♦❛❞❆s❇❛s❡✻✹s♦✉r❝❡❚❈P❋❧❛❣s❉❡s❝r✐♣t✐♦♥ ❞❡st✐♥❛t✐♦♥❚❈P❋❧❛❣s❉❡s❝r✐♣t✐♦♥

s♦✉r❝❡ ❞❡st✐♥❛t✐♦♥s♦✉r❝❡P♦rt ❞❡st✐♥❛t✐♦♥P♦rt

st❛rt❉❛t❡❚✐♠❡ st♦♣❉❛t❡❚✐♠❡❞✐r❡❝t✐♦♥ t❛❣

✸✳✷ Pr❡♣❛r❛çã♦ ❞❛ ❇❛s❡ ❞❡ ❉❛❞♦s

◆❡st❛ s❡çã♦✱ sã♦ ❛♣r❡s❡♥t❛❞♦s ♦s ♣❛ss♦s ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ tr❛❜❛❧❤♦ ❝♦♠♦ ♦ ♣r♦✲

❝❡ss♦ ❞❡ ❉❡s❝♦❜❡rt❛ ❞❡ ❈♦♥❤❡❝✐♠❡♥t♦ ❡♠ ❇❛♥❝♦ ❞❡ ❉❛❞♦s ✭❑❉❉ ✲❑♥♦✇❧❡❞❣❡ ❉✐s❝♦✈❡r②

✐♥ ❉❛t❛❜❛s❡✮✱ ❢❡rr❛♠❡♥t❛s ✉t✐❧✐③❛❞❛s ❡ ❛ ♣r❡♣❛r❛çã♦ ❞❛ ❜❛s❡ ■❙❈❳ ✷✵✶✷ ❛♣r❡s❡♥t❛❞❛

♣♦r ❙❤✐r❛✈✐ ❡t ❛❧✳ ❬✷✵✶✷❪✳ ❋♦r❛♠ ❛♣❧✐❝❛❞❛s ❡t❛♣❛s ❞♦ ♣r♦❝❡ss♦ ❞❡ ❑❉❉✱ ♠♦str❛❞❛s ♥❛

❋✐❣✉r❛ ✸✳✷✱ ❝♦♠♦ ❧✐♠♣❡③❛✱ ✐♥t❡❣r❛çã♦✱ tr❛♥s❢♦r♠❛çã♦✱ s❡❧❡çã♦ ❡ ♠✐♥❡r❛çã♦ ❞♦s ❞❛❞♦s

❬❍❛♥ ❡t ❛❧✳✱ ✷✵✶✶❪✳

◆❛ ❡t❛♣❛ ❞❡ ❧✐♠♣❡③❛ ❞❡ ❞❛❞♦s✱ ❛tr❛✈és ❞❛ ❧✐♥❣✉❛❣❡♠ P②t❤♦♥✱ ❢♦r❛♠ r❡♠♦✈✐❞♦s

♦s ❞❛❞♦s ✐♥❝♦♥s✐st❡♥t❡s✱ ❝♦♠♦ s❡♣❛r❛çõ❡s ♣♦r ✈ír❣✉❧❛s q✉❡ ❡st❛✈❛♠ ❡①❝❡❞❡♥t❡s ♥♦s

r❡❣✐str♦s✱ q✉❡ ❝r✐❛✈❛♠ ❝❛♠♣♦s ❛❞✐❝✐♦♥❛✐s ♥❛ ❜❛s❡ ♦r✐❣✐♥❛❧✱ ❛❧é♠ ❞❡ r❡♦r❣❛♥✐③❛r ❝♦❧✉♥❛s

✸✳ ▼ét♦❞♦s ✹✹

❋✐❣✉r❛ ✸✳✷✳ Pr♦❝❡ss♦ ❞❡ ❉❡s❝♦❜❡rt❛ ❞❡ ❈♦♥❤❡❝✐♠❡♥t♦ ❡♠ ❇❛♥❝♦ ❞❡ ❉❛❞♦s✭❑❉❉✮ ❬❍❛♥ ❡t ❛❧✳✱ ✷✵✶✶❪

q✉❡ ❡st❛✈❛♠ ❢♦r❛ ❞❡ ♦r❞❡♠ ♥♦s ❛rq✉✐✈♦s✳ ❖ ❝ó❞✐❣♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❡st❛ ❡t❛♣❛ é ♠♦str❛❞♦

♥♦ ❆♥❡①♦ ❆✳

❊♠ s❡❣✉✐❞❛✱ ♥❛ ✐♥t❡❣r❛çã♦ ❞♦s ❞❛❞♦s✱ ❢♦r❛♠ ❛❣r✉♣❛❞♦s ♦s ❞❛❞♦s ❞♦s ❞✐✈❡rs♦s ❞✐❛s

❞❡ ❝♦❧❡t❛ ❞❡ ✐♥❢♦r♠❛çõ❡s ❡♠ ✉♠ ú♥✐❝♦ ❛rq✉✐✈♦✳ ❖ ♦❜❥❡t✐✈♦ ❞❡ss❛ ✐♥t❡❣r❛çã♦ ❞❡✈❡✲s❡

❛♦ ❢❛t♦ ❞❡ q✉❡✱ ♣❛r❛ ❝❛❞❛ ❞✐❛ ❞❡ ❝♦❧❡t❛ ❞❡ ✐♥❢♦r♠❛çõ❡s✱ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ té❝♥✐❝❛ ❞❡

❛t❛q✉❡ ❢♦✐ ✉t✐❧✐③❛❞❛ ❝♦♥❢♦r♠❡ ♣♦❞❡♠♦s ✈❡r✐✜❝❛r ❡♠ ❙❤✐r❛✈✐ ❡t ❛❧✳ ❬✷✵✶✷❪ ❡ ❞❡s❝r✐t❛ ♥❛

❚❛❜❡❧❛ ✸✳✷✳ ❆ss✐♠✱ ❛♦ ❛❣r✉♣❛r♠♦s ♦s ❞❛❞♦s ❞❡ t♦❞♦s ♦s ❞✐❛s✱ ❛✉♠❡♥t❛♠♦s ♦ ❣r❛✉ ❞❡

❞✐✜❝✉❧❞❛❞❡ q✉❡ ♥♦ss♦ tr❛❜❛❧❤♦ t❡rá ♣❛r❛ ❞❡t❡❝t❛r s❡ é ✉♠ ✏❛t❛q✉❡✑ ♦✉ ✉♠❛ ❛t✐✈✐❞❛❞❡

✏♥♦r♠❛❧✑✳

◆❛ ❡t❛♣❛ ❞❡ tr❛♥s❢♦r♠❛çã♦ ❞♦s ❞❛❞♦s✱ ♦s ❛rq✉✐✈♦s r♦t✉❧❛❞♦s ❞❛ ❜❛s❡ ■❙❈❳ ✷✵✶✷

❢♦r❛♠ ❢♦r♠❛t❛❞♦s ❝♦♠ ❛ ❡①t❡♥sã♦ ✳❛r✛✱ ❢♦r♠❛t♦ ♣❛❞rã♦ ❞♦ s♦❢t✇❛r❡ ❲❡❦❛✱ ❢❡rr❛♠❡♥t❛

❡st❛ ❜❛st❛♥t❡ ✉t✐❧✐③❛❞❛ ♣❛r❛ ♠✐♥❡r❛çã♦ ❞❡ ❞❛❞♦s✱ ❝♦♠♦ ❝❧❛ss✐✜❝❛çã♦ ❞❡ ♣❛❞rõ❡s✱ té❝♥✐❝❛s

❞❡ ❝❧✉st❡r✐③❛çã♦ ❡ ❛ss♦❝✐❛çã♦ ❬❲❡❦❛✱ ✷✵✶✸❪✳ ❖ ❝ó❞✐❣♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❢♦r♠❛t❛r ♦s ❛rq✉✐✈♦s

é ♠♦str❛❞♦ ♥♦ ❆♥❡①♦ ❇✳

✸✳ ▼ét♦❞♦s ✹✺

❚❛❜❡❧❛ ✸✳✷✳ ❉❡s❝r✐çã♦ ❞♦ trá❢❡❣♦ ❞❡ r❡❞❡ ♣♦r ❞✐❛ ❞❛ ❜❛s❡ ■❙❈❳ ✷✵✶✷

❉✐❛ ❉❡s❝r✐çã♦❙❡①t❛ ❆t✐✈✐❞❛❞❡ ♥♦r♠❛❧✳ ❙❡♠ trá❢❡❣♦ ♠❛❧✐❝✐♦s♦✳❙á❜❛❞♦ ❆t✐✈✐❞❛❞❡ ♥♦r♠❛❧✳ ❙❡♠ trá❢❡❣♦ ♠❛❧✐❝✐♦s♦✳❉♦♠✐♥❣♦ ■♥✜❧tr❛çã♦ ♥❛ r❡❞❡ ❝♦♠ ♦r✐❣❡♠ ✐♥t❡r♥❛ ♠❛✐s ❛t✐✈✐❞❛❞❡ ♥♦r♠❛❧✳❙❡❣✉♥❞❛ ❆t❛q✉❡ ❞❡ ♥❡❣❛çã♦ ❞❡ s❡r✈✐ç♦ ✭❉♦❙✮ ❍❚❚P ♠❛✐s ❛t✐✈✐❞❛❞❡ ♥♦r♠❛❧✳❚❡rç❛ ❆t❛q✉❡ ❞❡ ♥❡❣❛çã♦ ❞❡ s❡r✈✐ç♦ ❞✐str✐❜✉✐❞♦ ✭❉❉♦❙✮ ✉s❛♥❞♦ ■❘❈ ❇♦t♥❡t✳◗✉❛rt❛ ❆t✐✈✐❞❛❞❡ ♥♦r♠❛❧✳ ❙❡♠ trá❢❡❣♦ ♠❛❧✐❝✐♦s♦✳◗✉✐♥t❛ ❆t❛q✉❡ ❞❡ ❢♦rç❛ ❜r✉t❛ ❙❙❍ ♠❛✐s trá❢❡❣♦ ♥♦r♠❛❧✳

❋♦r❛♠ ❣❡r❛❞♦s ♦s ❛rq✉✐✈♦s ♣❛r❛ ❛♥á❧✐s❡ ❞❡ ❝❛❞❛ ❞✐❛✱ ❡①❝❡t✉❛♥❞♦ ❞❛ s❡①t❛✲❢❡✐r❛✱

❞✐❛ ❡♠ q✉❡ ♥ã♦ ❤♦✉✈❡ ❛t❛q✉❡ r❡❣✐str❛❞♦ ❡ t♦❞♦ ♦ trá❢❡❣♦ ❢♦✐ ♥♦r♠❛❧✳ ❖ ❢♦r♠❛t♦ ✜♥❛❧

❞♦s ❛rq✉✐✈♦s é ♠♦str❛❞♦ ♥❛ ❚❛❜❡❧❛ ✸✳✸✳

❚❛❜❡❧❛ ✸✳✸✳ ❋♦r♠❛t♦ ❞♦s ❛rq✉✐✈♦s ✳❛r✛

❅r❡❧❛t✐♦♥ ✬✐s❝①✷✵✶✷✬❅❛ttr✐❜✉t❡ ✬❞✉r❛t✐♦♥✬ r❡❛❧❅❛ttr✐❜✉t❡ ✬♣r♦t♦❝♦❧◆❛♠❡✬ ④✬t❝♣✬✱✬✉❞♣✬✱✬✐❝♠♣✬⑥❅❛ttr✐❜✉t❡ ✬s♦✉r❝❡❚❈P❋❧❛❣s❉❡s❝r✐♣t✐♦♥✬ ④✬◆✴❆✬✱✬❙P❆✬✱ ✬❙❘P❆✬✱✬❋❙P❆✬✱ ✬❋❘P❆✬✱ ✬❋❙❘P❆✬✱ ✬❋❆✬✱✬❋❘❆✬✱ ✬❋P❆✬✱✬❋❙❆✬✱ ✬❙❘❆✬✱ ✬❘P❆✬✱ ✬❘✬✱ ✬❙✬✱ ✬❆✬✱✬❘❆✬✱✬P❆✬✱ ✬❙❆✬✱ ✬❙❘✬✱ ✬❋❙❘❆✬✱ ✬❋P❯✬✱ ✬❋❙P❯✬✱ ✬❋❙❘P❯✬⑥❅❛ttr✐❜✉t❡ ✬❞❡st✐♥❛t✐♦♥❚❈P❋❧❛❣s❉❡s❝r✐♣t✐♦♥✬ ④✬◆✴❆✬✱✬❙P❆✬✱ ✬❙❘P❆✬✱✬❋❙P❆✬✱ ✬❋❘P❆✬✱ ✬❋❙❘P❆✬✱ ✬❋❆✬✱✬❋❘❆✬✱✬❋P❆✬✱ ✬❋❙❆✬✱ ✬❙❘❆✬✱ ✬❘P❆✬✱ ✬❘✬✱ ✬❙✬✱ ✬❆✬✱✬❘❆✬✱ ✬P❆✬✱✬❙❆✬✱ ✬❋❙❘❆✬⑥❅❛ttr✐❜✉t❡ ✬t♦t❛❧❙♦✉r❝❡❇②t❡s✬ r❡❛❧❅❛ttr✐❜✉t❡ ✬t♦t❛❧❉❡st✐♥❛t✐♦♥❇②t❡s✬ r❡❛❧❅❛ttr✐❜✉t❡ ✬s♦✉r❝❡✬ ④✬✵✬✱✬✶✬✱ ✬✷✬✱ ✬✸✬✱ ✬✹✬✱ ✬✺✬✱ ✬✻✬⑥❅❛ttr✐❜✉t❡ ✬❞❡st✐♥❛t✐♦♥✬ ④✬✵✬✱✬✶✬✱ ✬✷✬✱ ✬✸✬✱ ✬✹✬✱ ✬✺✬✱ ✬✻✬⑥❅❛ttr✐❜✉t❡ ✬s♦✉r❝❡P♦rt✬ ♥✉♠❡r✐❝❅❛ttr✐❜✉t❡ ✬❞❡st✐♥❛t✐♦♥P♦rt✬ ♥✉♠❡r✐❝❅❛ttr✐❜✉t❡ ✬t♦t❛❧❙♦✉r❝❡P❛❝❦❡ts✬ r❡❛❧❅❛ttr✐❜✉t❡ ✬t♦t❛❧❉❡st✐♥❛t✐♦♥P❛❝❦❡ts✬ r❡❛❧❅❛ttr✐❜✉t❡ ✬❞✐r❡❝t✐♦♥✬ ④✬▲✷❘✬✱✬▲✷▲✬✱✬❘✷❘✬✱✬❘✷▲✬⑥❅❛ttr✐❜✉t❡ ✬t❛❣✬ ④✬◆♦r♠❛❧✬✱✬❆tt❛❝❦✬⑥❅❞❛t❛✶✽✶✶✱t❝♣✱❙P❆✱❙P❆✱✶✹✽✺✵✷✱✸✶✶✶✶✶✺✱✷✱✵✱✷✸✷✽✱✺✶✹✶✸✱✷✷✶✾✱✷✼✺✺✱▲✷❘✱◆♦r♠❛❧✹✺✱✉❞♣✱◆✴❆✱◆✴❆✱✻✹✼✾✱✶✵✽✷✻✵✱✷✱✵✱✺✽✵✹✵✱✸✼✻✹✷✱✽✵✱✸✹✵✱▲✷❘✱◆♦r♠❛❧✸✼✹✻✱t❝♣✱❙P❆✱❙P❆✱✶✶✶✾✽✾✻✱✶✸✶✽✶✷✷✽✱✷✱✵✱✷✶✶✺✱✺✶✹✶✸✱✶✼✵✻✻✱✷✹✻✺✵✱▲✷❘✱◆♦r♠❛❧❄✱t❝♣✱❙✱❄✱✾✾✵✱✵✱✷✱✵✱✷✶✸✵✱✺✺✺✺✱✶✺✱✵✱▲✷❘✱❆tt❛❝❦✼✱t❝♣✱❙P❆✱❋❙P❆✱✻✺✾✱✷✼✻✺✱✹✱✵✱✷✸✼✼✱✽✵✱✼✱✼✱▲✷❘✱◆♦r♠❛❧✵✱✐❝♠♣✱◆✴❆✱◆✴❆✱✼✹✱✵✱✵✱✷✱✵✱✵✱✶✱✵✱❘✷▲✱◆♦r♠❛❧

❆♣ós ❛ tr❛♥s❢♦r♠❛çã♦ ❞♦s ❞❛❞♦s r❡❧❛❝✐♦♥❛❞♦s ❛ ❝❛❞❛ ❞✐❛ ❞❡ ❝♦❧❡t❛✱ ♦s ❞❛❞♦s

❢♦r❛♠ ❛❣r✉♣❛❞♦s ❡♠ ✉♠ ú♥✐❝♦ ❛rq✉✐✈♦✱ ❝♦♠ ✷✳✵✼✶✳✻✺✼ r❡❣✐str♦s ❡✱ ♦s ♣❛②❧♦❛❞s ❢♦r❛♠

❞❡s❝♦♥s✐❞❡r❛❞♦s✱ ❝♦♥❝❡♥tr❛♥❞♦✲s❡ ❡♥tã♦ ♥♦s ❞❡♠❛✐s ❛tr✐❜✉t♦s✱ ❝♦♥❢♦r♠❡ ❛ ❚❛❜❡❧❛ ✸✳✹✳

P♦rt❛♥t♦✱ ♥♦ ❛rq✉✐✈♦ ❛❣r✉♣❛❞♦ ❝♦♠ t♦❞♦s ♦s r❡❣✐str♦s ❡♠ ❢♦r♠❛t♦ ✳❛r✛ ❢♦r❛♠ r❡❛✲

❧✐③❛❞♦s ♦✉tr♦s ♣❛ss♦s ❛tr❛✈és ❞♦ s♦❢t✇❛r❡ ❲❡❦❛✱ ❝♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ❛❜❛✐①♦✳ ❊♠ s❡❣✉✐❞❛

❢♦✐ r❡❛❧✐③❛❞❛ ❛ ❡t❛♣❛ ✜♥❛❧ ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ❞❛❞♦s ❛tr❛✈és ❞❛s té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦✳

• ◆♦r♠❛❧✐③❛çã♦ ❞♦s ❞❛❞♦s✿ ♦s ❞❛❞♦s ❢♦r❛♠ ♥♦r♠❛❧✐③❛❞♦s ❡♥tr❡ ♦s ✈❛❧♦r❡s ❬✵✿✶❪ ❛tr❛✲

✈és ❞♦ ✜❧tr♦ ✉♥s✉♣❡r✈✐s❡❞✲❛ttr✐❜✉t❡✲♥♦r♠❛❧✐③❡✱ ❛ ✜♠ ❞❡ ❝♦♥s✐❞❡r❛r ♦s ❛tr✐❜✉t♦s

✸✳ ▼ét♦❞♦s ✹✻

❚❛❜❡❧❛ ✸✳✹✳ ❆tr✐❜✉t♦s ❞♦s ❛rq✉✐✈♦s ❣❡r❛❞♦s ❡♠ ❢♦r♠❛t♦ ✳❛r✛

◆♦ ❆tr✐❜✉t♦ ❉❡s❝r✐çã♦✶ ❞✉r❛t✐♦♥ ❘❡❢❡r❡✲s❡ à s✉❜tr❛çã♦ ❞♦s ❝❛♠♣♦s st♦♣❉❛t❡❚✐♠❡ ❡ st❛rt❉❛✲

t❡❚✐♠❡ ❡♠ s❡❣✉♥❞♦s✷ ♣r♦t♦❝♦❧◆❛♠❡ ■❞❡♥t✐✜❝❛ s❡ ♦ ♣r♦t♦❝♦❧♦ é ✬t❝♣✬✱ ✬✉❞♣✬ ♦✉ ✬✐❝♠♣✬✸ s♦✉r❝❡❚❈P❋❧❛❣s❉❡s❝r✐♣t✐♦♥ ■❞❡♥t✐✜❝❛ ❛s ✢❛❣s ❡♥❝♦♥tr❛❞❛s ♥❛ ❝♦♠✉♥✐❝❛çã♦ ❞♦ ✢✉①♦ ❞❡

❞❛❞♦s ❞❡ ♦r✐❣❡♠✹ ❞❡st✐♥❛t✐♦♥❚❈P❋❧❛❣s❉❡s❝r✐♣t✐♦♥ ■❞❡♥t✐✜❝❛ ❛s ✢❛❣s ❡♥❝♦♥tr❛❞❛s ♥❛ ❝♦♠✉♥✐❝❛çã♦ ❞♦ ✢✉①♦ ❞❡

❞❛❞♦s ❞❡ ❞❡st✐♥♦✺ t♦t❛❧❙♦✉r❝❡❇②t❡s ◆ú♠❡r♦ ❞❡ ❜②t❡s ❡♥✈✐❛❞♦s ❞❛ ❢♦♥t❡ ♣❛r❛ ♦ ❞❡st✐♥♦✻ t♦t❛❧❉❡st✐♥❛t✐♦♥❇②t❡s ◆ú♠❡r♦ ❞❡ ❜②t❡s ❡♥✈✐❛❞♦s ❞♦ ❞❡st✐♥♦ ♣❛r❛ ❛ ❢♦♥t❡✼ s♦✉r❝❡ ✵ ♣❛r❛ ❡♥❞❡r❡ç♦s ❞❡ ♦r✐❣❡♠ ❞❛ ■♥t❡r♥❡t✱ ❡ ✶ ❛ ✻ r❡❢❡r❡♥t❡s às

s✉❜✲r❡❞❡s ✐♥t❡r♥❛s ✶✾✷✳✶✻✽✳①✳✵✴✷✹ ♦♥❞❡ ① ✈❛r✐❛ ❡♥tr❡ ✶ ❡ ✻✽ ❞❡st✐♥❛t✐♦♥ ✵ ♣❛r❛ ❡♥❞❡r❡ç♦s ❝♦♠ ❞❡st✐♥♦ à ■♥t❡r♥❡t✱ ❡ ✶ ❛ ✻ r❡❢❡r❡♥t❡s

às s✉❜✲r❡❞❡s ✐♥t❡r♥❛s ✶✾✷✳✶✻✽✳①✳✵✴✷✹ ♦♥❞❡ ① ✈❛r✐❛ ❡♥tr❡ ✶ ❡✻

✾ s♦✉r❝❡P♦rt ♣♦rt❛ ❞❡ ♦r✐❣❡♠ ❞♦ ♣r♦t♦❝♦❧♦ ❞❡ tr❛♥s♣♦rt❡✶✵ ❞❡st✐♥❛t✐♦♥P♦rt ♣♦rt❛ ❞❡ ❞❡st✐♥♦ ❞♦ ♣r♦t♦❝♦❧♦ ❞❡ tr❛♥s♣♦rt❡✶✶ t♦t❛❧❙♦✉r❝❡P❛❝❦❡ts ◆ú♠❡r♦ ❞❡ ♣❛❝♦t❡s ❡♥✈✐❛❞♦s ❞❛ ❢♦♥t❡ ♣❛r❛ ♦ ❞❡st✐♥♦✶✷ t♦t❛❧❉❡st✐♥❛t✐♦♥P❛❝❦❡ts ◆ú♠❡r♦ ❞❡ ♣❛❝♦t❡s ❡♥✈✐❛❞♦s ❞♦ ❞❡st✐♥♦ ♣❛r❛ ❛ ❢♦♥t❡✶✸ ❞✐r❡❝t✐♦♥ ❉✐r❡çã♦ ❞♦ ✢✉①♦ ❞❡ ♣❛❝♦t❡s✶✹ t❛❣ ❘ót✉❧♦ ✐♥❢♦r♠❛♥❞♦ s❡ ♦ trá❢❡❣♦ é ✬◆♦r♠❛❧✬ ♦✉ ✬❆tt❛❝❦✬

❝♦♠ ❛ ♠❡s♠❛ ✐♠♣♦rtâ♥❝✐❛✳

• ❊♠❜❛r❛❧❤❛♠❡♥t♦ ❞♦s ❞❛❞♦s✿ ❢♦✐ ✉t✐❧✐③❛❞♦ ♦ ✜❧tr♦ ✉♥s✉♣❡r✈✐s❡❞✲✐♥st❛♥❝❡✲

r❛♥❞♦♠✐③❡ ♣❛r❛ ❡♠❜❛r❛❧❤❛r ♦s ❞❛❞♦s✱ ✉♠❛ ✈❡③ q✉❡ ❛♦ ❛❣r✉♣❛r t♦❞♦s ♦s ❞❛❞♦s

✭r❡❣✐str♦s✮✱ ❞❡t❡r♠✐♥❛❞❛s té❝♥✐❝❛s ❞❡ ✐♥tr✉sã♦ ✉t✐❧✐③❛❞❛s ✜❝❛r❛♠ ❧♦❝❛❧✐③❛❞❛s ❡♠

r❡❣✐str♦s ♣ró①✐♠♦s ❞❡✈✐❞♦ ❛♦ ❞✐❛ ❞❡ ❝♦❧❡t❛✳

• ❆♠♦str❛❣❡♠ ❛❧❡❛tór✐❛ s✐♠♣❧❡s✿ ❞❡✈✐❞♦ ❛♦ ❣r❛♥❞❡ ✈♦❧✉♠❡ ❞❡ ❞❛❞♦s ❞❛ ❜❛s❡ ■❙❈❳

✷✵✶✷✱ ❢♦✐ r❡t✐r❛❞❛ ✉♠❛ ❛♠♦str❛ ❛❧❡❛tór✐❛ s✐♠♣❧❡s ❞❡ ✷✶✷✽✻✻ ✭❝❡r❝❛ ❞❡ ✶✵✱✷✽✪✮

r❡❣✐str♦s ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❛tr❛✈és ❞♦ ✜❧tr♦ ✉♥s✉♣❡r✈✐s❡❞✲✐♥st❛♥❝❡✲r❡s❛♠♣❧❡✳

❖ ♦❜❥❡t✐✈♦ ❞❡ss❛ tr❛♥s❢♦r♠❛çã♦ é r❡❞✉③✐r ♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s s❡♠ s❛❝r✐✜❝❛r s✉❛

✐♥t❡❣r✐❞❛❞❡ ❡ ♣❡r♠✐t✐r ❛ ✉t✐❧✐③❛çã♦ ❞❛s té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦✳ P❛r❛ ❞❡✜♥✐r ♦

✈❛❧♦r ❞❛ ❛♠♦str❛ n✱ ✉t✐❧✐③♦✉✲s❡ ❛ ❊q✉❛çã♦ ✸✳✶✱ ❝♦♥s✐❞❡r❛♥❞♦ ✉♠ ♥í✈❡❧ ❞❡ ❝♦♥✜❛♥ç❛

c ❞❡ ✾✾✪ ✭q✉❡ ❞❡✜♥❡ ♦ ✈❛❧♦r ❞❡ Zc = 2, 575✮✱ ✉♠ ❡rr♦ ❞❡ ❡st✐♠❛t✐✈❛ E = 0, 001✱

❡ ✈❛❧♦r❡s ❞❡ p = 0, 033206 ❡ (1 − p) = 0, 966794✱ ❛ ♣r♦♣♦rçã♦ ❞❡ r❡❣✐str♦s ❞❡

❛t❛q✉❡s ❡ ♥♦r♠❛✐s✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❝♦♠♣❧❡t♦ ❬▲❛rs♦♥ ✫

❋❛r❜❡r✱ ✷✵✵✹❪✳

n = p(1− p)(

Zc

E

)2

✭✸✳✶✮

✸✳ ▼ét♦❞♦s ✹✼

◆❛ ♣ró①✐♠❛ s❡çã♦ s❡rá ❛♣r❡s❡♥t❛❞♦ ❝♦♠♦ ❢♦r❛♠ r❡❛❧✐③❛❞♦s ♦s t❡st❡s ❞❡ ❝❧❛ss✐✜❝❛✲

çã♦ ❡ ❛s té❝♥✐❝❛s ❡♠♣r❡❣❛❞❛s✳

✸✳✸ ❚❡st❡s ❞❡ ❈❧❛ss✐✜❝❛çã♦

P❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞♦s t❡st❡s ❞❡ ❝❧❛ss✐✜❝❛çã♦✱ ❞✉❛s ❛❜♦r❞❛❣❡♥s ❢♦r❛♠ ❡s❝♦❧❤✐❞❛s✳ ❆

♣r✐♠❡✐r❛✱ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❛❜♦r❞❛❣❡♠ ❍♦❧❞♦✉t✱ ♥❛ q✉❛❧ ♦s ❞❛❞♦s sã♦ ♣❛rt✐❝✐♦♥❛❞♦s

❡♠ ❞♦✐s ❝♦♥❥✉♥t♦s ❞✐st✐♥t♦s✱ ✉♠ ♣❛r❛ ❛ ❡t❛♣❛ ❞❡ tr❡✐♥❛♠❡♥t♦ ❡ ❝r✐❛çã♦ ❞♦ ♠♦❞❡❧♦

❡ ♦ ♦✉tr♦ ♣❛r❛ ❛ ❡t❛♣❛ ❞❡ t❡st❡s✳ ❊st❛ té❝♥✐❝❛ é r❡❝♦♠❡♥❞❛❞❛ q✉❛♥❞♦ s❡ t❡♠ ✉♠❛

❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ❞❛❞♦s ❬❍❛♥ ❡t ❛❧✳✱ ✷✵✶✶❪✳ ❆ss✐♠✱ ♥❛ ❛❜♦r❞❛❣❡♠ ❍♦❧❞♦✉t ❢♦r❛♠

❝♦♥s✐❞❡r❛❞♦s ✷✵✪ ❞♦s ❞❛❞♦s ❞❛ ❛♠♦str❛ ♣❛r❛ ♦ ❝♦♥❥✉♥t♦ ❞❡ tr❡✐♥❛♠❡♥t♦✱ s✐♠✐❧❛r♠❡♥t❡

❝♦♠♦ ❡♠ ❙✐❧✈❛ ❬✷✵✶✶❪ ❡ ❚❛✈❛❧❧❛❡❡ ❡t ❛❧✳ ❬✷✵✵✾❪ ❡✱ ♦s ✽✵✪ r❡st❛♥t❡s ♣❛r❛ ♦ ❝♦♥❥✉♥t♦ ❞❡

t❡st❡s✳

❆ s❡❣✉♥❞❛ ❛❜♦r❞❛❣❡♠ é ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❱❛❧✐❞❛çã♦ ❈r✉③❛❞❛ ✭❈r♦ss✲❱❛❧✐❞❛t✐♦♥✮✱

s❡♥❞♦ ✉♠ ♠ét♦❞♦ ♠❛✐s ❡✜❝✐❡♥t❡ q✉❡ ♦ ❍♦❧❞♦✉t✱ ❡♠ ❡s♣❡❝✐❛❧ q✉❛♥❞♦ s❡ t❡♠ ✉♠❛ q✉❛♥✲

t✐❞❛❞❡ ♠❡♥♦r ❞❡ ❞❛❞♦s✳ ◆❡st❡ ♠ét♦❞♦✱ ♣❛r❛ ♦ tr❛❜❛❧❤♦ ❞❡s❡♥✈♦❧✈✐❞♦✱ ♦s ❞❛❞♦s ❞❛

❛♠♦str❛ ❢♦r❛♠ ♣❛rt✐❝✐♦♥❛❞♦s ❡♠ ✶✵ ♣❛rt❡s ❡✱ ❛ ❝❛❞❛ ❡①❡❝✉çã♦✱ ✉♠❛ ❞❛s ♣❛rt✐çõ❡s ❢♦✐

❡s❝♦❧❤✐❞❛ ♣❛r❛ t❡st❡✱ ❡♥q✉❛♥t♦ q✉❡ ❛s ♦✉tr❛s ❢♦r❛♠ ✉s❛❞❛s ♣❛r❛ tr❡✐♥❛♠❡♥t♦✳

❆♦ ✉t✐❧✐③❛r ♦ s♦❢t✇❛r❡ ❲❡❦❛✱ ❛s ❞✉❛s ❛❜♦r❞❛❣❡♥s ❢♦r❛♠ ❝♦♥s✐❞❡r❛❞❛s✱ ❡s❝♦❧❤❡♥❞♦

❞✐✈❡rs❛s té❝♥✐❝❛s✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❞❡ ár✈♦r❡s ❞❡ ❞❡❝✐sã♦✱ r❡❞❡s ♥❡✉r❛✐s ❛rt✐✜❝✐❛✐s ❡ ❛♣r❡♥✲

❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛✳ ❖s ❝r✐tér✐♦s ♣❛r❛ ❛ ❡s❝♦❧❤❛ ❞❡st❛s té❝♥✐❝❛s ❢♦r❛♠ ❜❛s❡❛❞♦s ❡♠ ❛❧✲

❣✉♥s tr❛❜❛❧❤♦s r❡❧❛❝✐♦♥❛❞♦s ❝♦♠♦ ❚❛✈❛❧❧❛❡❡ ❡t ❛❧✳ ❬✷✵✵✾❪✱ P❛❝❤❣❤❛r❡ ✫ ❑✉❧❦❛r♥✐ ❬✷✵✶✶❪✱

❙✐❧✈❛ ❬✷✵✶✶❪ ❡ ❇✉❦❤t♦②❛r♦✈ ✫ ❙❡♠❡♥❦✐♥ ❬✷✵✶✷❪✳

❆♣ós ❛ r❡❛❧✐③❛çã♦ ❞♦s t❡st❡s ❝♦♠ ♦ s♦❢t✇❛r❡ ❲❡❦❛✱ ❢♦✐ ✉t✐❧✐③❛❞❛ ❛ ❧✐♥❣✉❛❣❡♠

P②t❤♦♥ ♣❛r❛ ✉♥✐r ❛s té❝♥✐❝❛s ❞❡ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ✭❆●✮ ❡ ❘❡❞❡s ◆❡✉r❛✐s ❆rt✐✜❝✐❛✐s

✭❘◆❆s✮✱ ❣❡r❛♥❞♦ ✉♠ ❙✐st❡♠❛ ■♥t❡❧✐❣❡♥t❡ ❍í❜r✐❞♦ ✭❙■❍✮✳ ❖s ❝ó❞✐❣♦s ✉t✐❧✐③❛❞♦s ♣❡❧♦ ❙■❍

sã♦ ♠♦str❛❞♦s ♥♦s ❛♥❡①♦s ❈ ❡ ❉✳

P❛r❛ ❡st❡ ♥♦✈♦ t❡st❡✱ ❛ ♠❡s♠❛ ❛♠♦str❛ ❞♦s ❞❛❞♦s ❢♦✐ ❝♦♥s✐❞❡r❛❞❛ ❡ ❡♥tã♦ r❡❛❧✐③❛✲

❞❛s ❛s ❡t❛♣❛s ❞❡ tr❡✐♥❛♠❡♥t♦ ❡ t❡st❡s ❛tr❛✈és ❞❛ ❛❜♦r❞❛❣❡♠ ❍♦❧❞♦✉t✳ Pr✐♠❡✐r❛♠❡♥t❡

❢♦r❛♠ ❝♦♥s✐❞❡r❛❞♦s ♥♦s t❡st❡s ✶✸ ❡♥tr❛❞❛s ✭❛tr✐❜✉t♦s✮ ♣❛r❛ ❛s ❘◆❆s ▼▲P ❡ ✉♠❛ s❛í❞❛

✭❛tr✐❜✉t♦ ❛❧✈♦✮✱ ❝♦♥❢♦r♠❡ ❚❛❜❡❧❛ ✸✳✹ ❥á ❛♣r❡s❡♥t❛❞❛✳

❖ ♦❜❥❡t✐✈♦ ❢♦✐ ✉t✐❧✐③❛r ♦ ❆● ♣❛r❛ ❜✉s❝❛r ✉♠❛ ❡str✉t✉r❛ ♣❛r❛ ❛ ❘◆❆ q✉❡ ❢♦r♥❡ç❛

✉♠❛ t❛①❛ ❞❡ ❛❝❡rt♦ ♠❛✐♦r✱ ❝♦♠♦ ❡♠ ❙✐❧✈❛ ❬✷✵✶✶❪ ❡ ▲✐ ❬✷✵✶✵❪✳ ❖ t❡st❡ ❝♦♥s✐st✐✉ ♥❛

❝♦♠❜✐♥❛çã♦ ❞❛ té❝♥✐❝❛ ❞❡ ❆● ❝♦♠ ❛s ❘◆❆s ▼▲P✱ r❡❛❧✐③❛♥❞♦ ♣❡r♠✉t❛çõ❡s ❡♠ ✈ár✐♦s

♣❛râ♠❡tr♦s ❞❛s ❘◆❆s✱ ❜✉s❝❛♥❞♦ ♠❡❧❤♦r❡s ✈❛❧♦r❡s ♣❛r❛ ❛ t❛①❛ ❞❡ ❛♣r❡♥❞✐③❛❞♦✱ ♠♦✲

✸✳ ▼ét♦❞♦s ✹✽

♠❡♥t✉♠✱ ❞❡❝❛②✱ q✉❛♥t✐❞❛❞❡ ❞❡ ♥❡✉rô♥✐♦s ♦❝✉❧t♦s✱ ❞✐❢❡r❡♥t❡s ❢✉♥çõ❡s ❞❡ tr❡✐♥❛♠❡♥t♦ ❡

q✉❛♥t✐❞❛❞❡ ❞❡ é♣♦❝❛s ❞❡ tr❡✐♥❛♠❡♥t♦✳ ❊♠ t♦❞♦s ♦s t❡st❡s ❝♦♠ ♦ ❆● ❢♦r❛♠ ❝♦♥s✐❞❡r❛✲

❞❛s ✶✵✵ ❣❡r❛çõ❡s✳ ❖s ♠❡❧❤♦r❡s ♣❛râ♠❡tr♦s ❡♥❝♦♥tr❛❞♦s ♣❛r❛ ❛s ✹ ❘◆❆s ❝♦♠ ♠❡❧❤♦r❡s

r❡s✉❧t❛❞♦s✱ sã♦ ♦s ♠♦str❛❞♦s ♥❛ ❚❛❜❡❧❛ ✸✳✺✳

❚❛❜❡❧❛ ✸✳✺✳ ▼❡❧❤♦r❡s ♣❛râ♠❡tr♦s ❞♦ ❆● ♣❛r❛ ❛s ❘◆❆s ▼▲P ❝♦♠ ✶✸ ❡♥tr❛❞❛s

❚é❝♥✐❝❛s ❞❡ ❋✉♥çã♦ ❞❛ ❋✉♥çã♦ ❞❛❈❧❛ss✐✜❝❛çã♦ ❈❛♠❛❞❛ ❖❝✉❧t❛ ❈❛♠❛❞❛ ❞❡ ❙❛í❞❛ ❈✶ ❈✷ ❈✸ ❈✹ ❈✺ ❈✻

❘◆❆ ✶ ❣❛✉ss✐❛♥❛ s✐♠étr✐❝❛ s✐❣♠♦✐❞❡ ♣❛ss♦ ❛ ♣❛ss♦ ✶✷ r♣r♦♣ ✵✱✸ ✵✱✻ ✵✱✸ ✸✵✵❘◆❆ ✷ s✐❣♠♦✐❞❡ s✐♠étr✐❝❛ s✐❣♠♦✐❞❡ ♣❛ss♦ ❛ ♣❛ss♦ ✽ r♣r♦♣ ✵✱✷ ✵✱✻ ✵✱✼ ✸✵✵❘◆❆ ✸ ❡❧❧✐♦t s✐♠étr✐❝❛ ❣❛✉ss✐❛♥❛ ✷✼ r♣r♦♣ ✵✱✻ ✵✱✸ ✵✱✶ ✸✵✵❘◆❆ ✹ ❡❧❧✐♦t ❧✐♥❡❛r ♣♦r ♣❛rt❡s ✶✷ r♣r♦♣ ✵✱✸ ✵✱✹ ✵✱✶ ✸✵✵

❈✶✿ ◗t❞✳ ❞❡ ◆❡✉rô♥✐♦s ❖❝✉❧t♦s ❈✸✿ ❚❛①❛ ❞❡ ❆♣r❡♥❞✐③❛❞♦ ❈✺✿ ❉❡❝❛②❈✷✿ ❆❧❣♦r✐t♠♦ ❞❡ ❚r❡✐♥❛♠❡♥t♦ ❈✹✿ ▼♦♠❡♥t✉♠ ❈✻✿ ◗t❞✳ ❞❡ ➱♣♦❝❛s ❞❡ ❚r❡✐♥❛♠❡♥t♦

❖ ❆● ❡①❡❝✉t♦✉ ✈ár✐♦s t❡st❡s ♥❛s ❘◆❆s ▼▲P ♣♦r ❝❡r❝❛ ❞❡ ✺✻ ♠✐♥✉t♦s✱ ✉t✐❧✐③❛♥❞♦

✶✵✵ ❣❡r❛çõ❡s✳ P❛r❛ r❡❛❧✐③❛r t❛✐s t❡st❡s✱ ❢♦✐ ✉s❛❞❛ ❛ ❧✐♥❣✉❛❣❡♠ P②t❤♦♥ ❝♦♠ ❛ ❜✐❜❧✐♦t❡❝❛

❋❆◆◆ ✭❋❛st ❆rt✐✜❝✐❛❧ ◆❡✉r❛❧ ◆❡t✇♦r❦ ▲✐❜r❛r②✮ ❬❋❆◆◆✱ ✷✵✶✶❪✳ ❊st❛ ❜✐❜❧✐♦t❡❝❛ ❧✐✈r❡

✐♠♣❧❡♠❡♥t❛ ❘❡❞❡s ◆❡✉r❛✐s ❆rt✐✜❝✐❛✐s ❡♠ ❈ ❡ ❢♦r♥❡❝❡ ✉♠ ❢r❛♠❡✇♦r❦ ♣❛r❛ ❝r✐❛çã♦✱

tr❡✐♥❛♠❡♥t♦ ❡ ❛♣❧✐❝❛çã♦✳

❆ ❜✐❜❧✐♦t❡❝❛ ❋❆◆◆ ♣♦ss✉✐ s✉♣♦rt❡ às s❡❣✉✐♥t❡s ❢✉♥çõ❡s ❞❡ ❛t✐✈❛çã♦ ❡ q✉❡ ❢♦r❛♠

✉t✐❧✐③❛❞❛s ❝♦♠♦ ❣❡♥❡s ❞♦ ❆●✱ ❡ ❡♥tã♦ ❞❡✜♥✐❞❛s ♣❛r❛ ❛s ❝❛♠❛❞❛s ❞❛s ❘◆❆s✿

• ❢✉♥çõ❡s ❞❡ ❛t✐✈❛çã♦ ❧✐♥❡❛r✱ ❧✐♥❡❛r ♣♦r ♣❛rt❡s ❡ ❧✐♥❡❛r ♣♦r ♣❛rt❡s s✐♠étr✐❝❛s❀

• ❢✉♥çõ❡s ❞❡ ❛t✐✈❛çã♦ ❧✐♠✐❛r ❡ ❧✐♠✐❛r s✐♠étr✐❝❛❀

• ❢✉♥çõ❡s ❞❡ ❛t✐✈❛çã♦ s✐❣♠♦✐❞❡✱ s✐❣♠♦✐❞❡ ♣❛ss♦ ❛ ♣❛ss♦✱ s✐❣♠♦✐❞❡ ❝♦♠ ❣r❛❞✐❡♥t❡ ❡

s✐❣♠♦✐❞❡ s✐♠étr✐❝❛ ❝♦♠ ❣r❛❞✐❡♥t❡❀

• ❢✉♥çõ❡s ❞❡ ❛t✐✈❛çã♦ ❣❛✉ss✐❛♥❛ ❡ ❣❛✉ss✐❛♥❛ s✐♠étr✐❝❛❀

• ❢✉♥çõ❡s ❞❡ ❛t✐✈❛çã♦ ❡❧❧✐♦t ❡ ❡❧❧✐♦t s✐♠étr✐❝❛❀

• ❢✉♥çõ❡s ❞❡ ❛t✐✈❛çã♦ s❡♥♦ ❡ s❡♥♦ s✐♠étr✐❝❛❀

• ❢✉♥çõ❡s ❞❡ ❛t✐✈❛çã♦ ❝♦ss❡♥♦ ❡ ❝♦ss❡♥♦ s✐♠étr✐❝♦✳

❆❧é♠ ❞❛ ❞❡✜♥✐çã♦ ❞❛s ❢✉♥çõ❡s ❞❡ ❛t✐✈❛çã♦ ❡ ✈❛❧♦r❡s ❞♦s ❞❡♠❛✐s ♣❛râ♠❡tr♦s✱ ❢♦✐

❞❡✜♥✐❞♦ ♦ ❛❧❣♦r✐t♠♦ ❞❡ tr❡✐♥❛♠❡♥t♦✱ q✉❡ é r❡s♣♦♥sá✈❡❧ ♣❡❧❛ ❛t✉❛❧✐③❛çã♦ ❞♦s ♣❡s♦s

❞❛s ❘◆❆s à ♣r♦❝✉r❛ ❞❡ ✉♠❛ r❡s♣♦st❛ ♠❡❧❤♦r✳ ❊♥tr❡ ♦s ❛❧❣♦r✐t♠♦s s✉♣♦rt❛❞♦s ♣❡❧❛

❜✐❜❧✐♦t❡❝❛ ❋❆◆◆ ❡ q✉❡ ❢♦r❛♠ ✉t✐❧✐③❛❞♦s ♣❡❧♦ ❆● ❡stã♦✿

• ❇❛❝❦✲♣r♦♣❛❣❛t✐♦♥❀

✸✳ ▼ét♦❞♦s ✹✾

• ❘❡tr♦♣r♦♣❛❣❛çã♦ ❘❡s✐❧✐❡♥t❡ ✭❘♣r♦♣✮❀

• ◗✉✐❝❦ Pr♦♣❛❣❛t✐♦♥ ✭◗✉✐❝❦Pr♦♣✮✳

❖s ❞❡♠❛✐s ♣❛râ♠❡tr♦s✱ ❝♦♠♦ t❛①❛ ❞❡ ❞❡❝❛②✱ ♠♦♠❡♥t✉♠ ❡ t❛①❛ ❞❡ ❛♣r❡♥❞✐③❛❞♦✱

❢♦r❛♠ ❡s❝♦❧❤✐❞♦s ❞❡♥tr❡ ♦s ✈❛❧♦r❡s✿ ✵✱✶❀ ✵✱✷❀ ✵✱✸❀ ✵✱✹❀ ✵✱✺❀ ✵✱✻❀ ✵✱✼❀ ✵✱✽ ❡ ✵✱✾✳ P❛r❛ ♦

❆●✱ ❢♦r❛♠ ❝♦♥s✐❞❡r❛❞♦s ✉♠❛ ♣♦♣✉❧❛çã♦ ❞❡ ✷✵ ✐♥❞✐✈í❞✉♦s✱ s❛t✐s❢❛çã♦ ❞❡ ✶✪ ❞❡ ❡rr♦ ❡ ♦

♠á①✐♠♦ ❞❡ ✶✵✵ ❣❡r❛çõ❡s✱ s✐♠✐❧❛r♠❡♥t❡ ❝♦♠♦ ❡♠ ❙✐❧✈❛ ❬✷✵✶✶❪✳

❆❧é♠ ❞♦s t❡st❡s q✉❡ ❝♦♥s✐❞❡r❛r❛♠ ♦s ✶✸ ❛tr✐❜✉t♦s✱ ❢♦r❛♠ r❡❛❧✐③❛❞♦s ♥♦✈♦s t❡s✲

t❡s ❝♦♠ ✼ ❛tr✐❜✉t♦s✱ ✉t✐❧✐③❛♥❞♦ t❛♥t♦ ♦ ❲❡❦❛✱ ❝♦♠♦ ♦ ❙■❍✳ ◆❡st❡ ❝❛s♦✱ ♦ ♦❜❥❡t✐✈♦ é

❞❡t❡❝t❛r ❛ ❛♠❡❛ç❛ ❛♥t❡s q✉❡ ❝❤❡❣✉❡ ❛♦ ❞❡st✐♥♦✱ s❡♥❞♦ ✉♠ ❡♥❢♦q✉❡ ✐♠♣♦rt❛♥t❡ ♣❛r❛ ❛ ❞❡✲

t❡❝çã♦ ❡♠ t❡♠♣♦ r❡❛❧✳ ❆s ❝❛r❛❝t❡ríst✐❝❛s ❞❡s♥❡❝❡ssár✐❛s r❡❢❡r❡♥t❡s ❛♦ ❞❡st✐♥♦ ✭❞✉r❛t✐♦♥✱

❞❡st✐♥❛t✐♦♥❚❈P❋❧❛❣s❉❡s❝r✐♣t✐♦♥✱ t♦t❛❧❉❡st✐♥❛t✐♦♥❇②t❡s✱ ❞❡st✐♥❛t✐♦♥✱ ❞❡st✐♥❛t✐♦♥P♦rt✱

t♦t❛❧❉❡st✐♥❛t✐♦♥P❛❝❦❡ts✮ ❢♦r❛♠✱ ♣♦rt❛♥t♦✱ ❡❧✐♠✐♥❛❞❛s✱ s✐♠✐❧❛r♠❡♥t❡ ❝♦♠♦ ❡♠ ▼③✐❧❛ ✫

❉✉❜❡ ❬✷✵✶✸❪✳ ❉❡ss❛ ♠❛♥❡✐r❛✱ ♦s t❡st❡s ❝♦♠ ✼ ❛tr✐❜✉t♦s sã♦ r❡❢❡r❡♥t❡s ❛ ✉♠❛ s✐♠✉❧❛çã♦

♣❛r❛ ❞❡t❡❝çã♦ ❡♠ t❡♠♣♦ r❡❛❧✳ ◆♦ ❙■❍ ♦s ♠❡❧❤♦r❡s ♣❛râ♠❡tr♦s ❡♥❝♦♥tr❛❞♦s✱ ♣❛r❛ ❛s

✹ ❘◆❆s ❝♦♠ ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s✱ sã♦ ♦s ♠♦str❛❞♦s ♥❛ ❚❛❜❡❧❛ ✸✳✻✳ ❖s t❡st❡s ❢♦r❛♠

❡①❡❝✉t❛❞♦s ❡ s❡✉s r❡s✉❧t❛❞♦s sã♦ ❛♣r❡s❡♥t❛❞♦s ♥♦ ♣ró①✐♠♦ ❝❛♣ít✉❧♦✳

❚❛❜❡❧❛ ✸✳✻✳ ▼❡❧❤♦r❡s ♣❛râ♠❡tr♦s ❞♦ ❆● ♣❛r❛ ❛s ❘◆❆s ▼▲P ❝♦♠ ✼ ❡♥tr❛❞❛s

❚é❝♥✐❝❛s ❞❡ ❋✉♥çã♦ ❞❛ ❋✉♥çã♦ ❞❛❈❧❛ss✐✜❝❛çã♦ ❈❛♠❛❞❛ ❖❝✉❧t❛ ❈❛♠❛❞❛ ❞❡ ❙❛í❞❛ ❈✶ ❈✷ ❈✸ ❈✹ ❈✺ ❈✻

❘◆❆ ✶ ❣❛✉ss✐❛♥❛ s✐♠étr✐❝❛ s✐❣♠♦✐❞❡ ♣❛ss♦ ❛ ♣❛ss♦ ✶✺ r♣r♦♣ ✵✱✶ ✵✱✷ ✵✱✸ ✸✵✵❘◆❆ ✷ ❣❛✉ss✐❛♥❛ s✐♠étr✐❝❛ s✐❣♠♦✐❞❡ ♣❛ss♦ ❛ ♣❛ss♦ ✶✺ r♣r♦♣ ✵✱✻ ✵✱✼ ✵✱✸ ✸✵✵❘◆❆ ✸ ❣❛✉ss✐❛♥❛ s✐♠étr✐❝❛ s✐❣♠♦✐❞❡ ♣❛ss♦ ❛ ♣❛ss♦ ✶✺ r♣r♦♣ ✵✱✹ ✵✱✷ ✵✱✸ ✸✵✵❘◆❆ ✹ ❣❛✉ss✐❛♥❛ s✐♠étr✐❝❛ s✐❣♠♦✐❞❡ ♣❛ss♦ ❛ ♣❛ss♦ ✶✺ r♣r♦♣ ✵✱✹ ✵✱✷ ✵✱✸ ✸✵✵

❈✶✿ ◗t❞✳ ❞❡ ◆❡✉rô♥✐♦s ❖❝✉❧t♦s ❈✸✿ ❚❛①❛ ❞❡ ❆♣r❡♥❞✐③❛❞♦ ❈✺✿ ❉❡❝❛②❈✷✿ ❆❧❣♦r✐t♠♦ ❞❡ ❚r❡✐♥❛♠❡♥t♦ ❈✹✿ ▼♦♠❡♥t✉♠ ❈✻✿ ◗t❞✳ ❞❡ ➱♣♦❝❛s ❞❡ ❚r❡✐♥❛♠❡♥t♦

❈❛♣ít✉❧♦ ✹

❘❡s✉❧t❛❞♦s

◆❡st❡ ❝❛♣ít✉❧♦ sã♦ ❛♣r❡s❡♥t❛❞♦s ♦s r❡s✉❧t❛❞♦s ❞♦s t❡st❡s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❞❛s ❞✐✈❡rs❛s

té❝♥✐❝❛s ✉s❛❞❛s✱ ✉t✐❧✐③❛♥❞♦ t❛♥t♦ ♦ s♦❢t✇❛r❡ ❲❡❦❛ ❝♦♠♦ ♦ ❙✐st❡♠❛ ■♥t❡❧✐❣❡♥t❡ ❍í❜r✐❞♦

✭❙■❍✮✳ ❉❡ ♠♦❞♦ ❣❡r❛❧✱ ♦s r❡s✉❧t❛❞♦s ❢♦r❛♠ ♣r♦♠✐ss♦r❡s✱ ❞❡✈✐❞♦ ❛s ❛❧t❛s t❛①❛s ❞❡ ❞❡t❡❝✲

çã♦✳ ❊♠❜♦r❛✱ ❛❧❣✉♠❛s té❝♥✐❝❛s t❡♥❤❛♠ ❞❡♠♦♥str❛❞♦ ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s q✉❡ ♦✉tr❛s✱

♦s r❡s✉❧t❛❞♦s ❡♥❝♦♥tr❛❞♦s ❝♦♠ ❡ss❛ ♥♦✈❛ ❜❛s❡ ❞❡ ❞❛❞♦s ♥♦s ♠♦str❛r❛♠ q✉❡ ❡ss❛s té❝✲

♥✐❝❛s sã♦ ❢✉♥❞❛♠❡♥t❛✐s✱ ♣♦❞❡♥❞♦ ❡✈♦❧✉✐r ❡♠ tr❛❜❛❧❤♦s ♣♦st❡r✐♦r❡s✳

❖s r❡s✉❧t❛❞♦s ❛♣r❡s❡♥t❛❞♦s ♥❡st❡ ❝❛♣ít✉❧♦ sã♦ r❡❢❡r❡♥t❡s à ✉t✐❧✐③❛çã♦ ❞❛ ❛♠♦str❛

❞❡ ❞❛❞♦s ❝♦♠ ✷✶✷✽✻✻ r❡❣✐str♦s ✭❝❡r❝❛ ❞❡ ❝❡r❝❛ ❞❡ ✶✵✱✷✽✪✮✱ ❡♥tr❡t❛♥t♦✱ ❢♦r❛♠ r❡❛❧✐③❛✲

❞♦s t❡st❡s ❝♦♥s✐❞❡r❛♥❞♦ ✉♠❛ ❛♠♦str❛ ❞❡ ❞❛❞♦s ♠❛✐♦r✱ ❞❡ ✸✵✪ ❡ ❝♦♠ ♦ ❝♦♥❥✉♥t♦ ❞❡

❞❛❞♦s ❝♦♠♣❧❡t♦✳ ◆❡st❡ ❝❛s♦ ✈❡r✐✜❝♦✉✲s❡ q✉❡ ♦s r❡s✉❧t❛❞♦s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ♥ã♦ ❛♣r❡s❡♥✲

t❛r❛♠ ❞✐❢❡r❡♥ç❛s s✐❣♥✐✜❝❛t✐✈❛s q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦s ❛♦ r❡s✉❧t❛❞♦s ✉t✐❧✐③❛♥❞♦ ❛ ❛♠♦str❛

❞❡ ✷✶✷✽✻✻ r❡❣✐str♦s✱ ❛❧é♠ ❞❡ ❛✉♠❡♥t❛r❡♠ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ♦ t❡♠♣♦ ❣❛st♦ ❝♦♠ ♦ tr❡✐✲

♥❛♠❡♥t♦✳ ❆❧é♠ ❞✐ss♦✱ ❛s té❝♥✐❝❛s ❞❡ ❘◆❆s ❛♣r❡s❡♥t❛r❛♠ ♣r♦❜❧❡♠❛s ❞❡ ❣❡♥❡r❛❧✐③❛çã♦

❞♦s r❡s✉❧t❛❞♦s q✉❛♥❞♦ ✉t✐❧✐③♦✉✲s❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ♠❛✐♦r✳ ❆ss✐♠✱ ❛ ✉t✐❧✐③❛çã♦

❞❡ ✉♠❛ ❛♠♦str❛ ♠❛✐♦r ❡ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❝♦♠♣❧❡t♦ ❢♦r❛♠ ❞❡s❝♦♥s✐❞❡r❛❞❛s ♥❡st❡

❝❛♣ít✉❧♦✳

◆♦ s♦❢t✇❛r❡ ❲❡❦❛✱ ♦s t❡st❡s ❝♦♥s✐❞❡r❛r❛♠ t❛♥t♦ ❛ ❛❜♦r❞❛❣❡♠ ❍♦❧❞♦✉t✱ ❝♦♠♦ ❞❡

❱❛❧✐❞❛çã♦ ❈r✉③❛❞❛✱ s❡♥❞♦ q✉❡ ♥❡st❛ ú❧t✐♠❛✱ ❢♦✐ ✉s❛❞❛ ❛♣❡♥❛s ♥❛ ❞❡t❡❝çã♦ ❡♠ ♠♦❞♦

♦✤✐♥❡✱ ❛ q✉❛❧ ✉t✐❧✐③♦✉✲s❡ ✶✸ ❛tr✐❜✉t♦s ❞❡ ❡♥tr❛❞❛✱ ❞❡✈✐❞♦ à ♥❡❝❡ss✐❞❛❞❡ ❞❡ ✉♠ ❝✉st♦

❝♦♠♣✉t❛❝✐♦♥❛❧ ♠❛✐♦r✳ ❊♥q✉❛♥t♦ ✐ss♦✱ ❛ ❛❜♦r❞❛❣❡♠ ❍♦❧❞♦✉t✱ ✉s❛❞❛ ♥♦ ❲❡❦❛ ❡ ♥♦ ❙■❍✱

❢♦✐ ❝♦♥s✐❞❡r❛❞❛ t❛♥t♦ ♥❛ ❞❡t❡❝çã♦ ❡♠ ♠♦❞♦ ♦✤✐♥❡✱ ❝♦♠♦ ♥❛ s✐♠✉❧❛çã♦ ❡♠ t❡♠♣♦ r❡❛❧

✭♦♥❧✐♥❡✮✱ ❛ q✉❛❧ ✉t✐❧✐③♦✉ ✼ ❛tr✐❜✉t♦s ❞❡ ❡♥tr❛❞❛✳

P❛r❛ ❡st❛s ❞✉❛s ❛❜♦r❞❛❣❡♥s✱ ❢♦r❛♠ r❡❛❧✐③❛❞❛s ❛s ❝❧❛ss✐✜❝❛çõ❡s ✉t✐❧✐③❛♥❞♦ ✈ár✐❛s

té❝♥✐❝❛s✱ ❝♦♠♦ ❡♠ ❚❛✈❛❧❧❛❡❡ ❡t ❛❧✳ ❬✷✵✵✾❪ ❡ P❛❝❤❣❤❛r❡ ✫ ❑✉❧❦❛r♥✐ ❬✷✵✶✶❪✳ ❊♥tr❡ ❡❧❛s✱

❡stã♦ ❛s ➪r✈♦r❡s ❞❡ ❉❡❝✐sã♦ ✭❏✹✽✱ ❏✹✽❣r❛❢t✱ ◆❇❚r❡❡✱ ❘❛♥❞♦♠ ❋♦r❡st✱ ❘❛♥❞♦♠ ❚r❡❡ ❡

✺✵

✹✳ ❘❡s✉❧t❛❞♦s ✺✶

❚❛❜❡❧❛ ✹✳✶✳ ▼♦❞❡❧♦ ❞❡ ❘❡s✉❧t❛❞♦s

❚rá❢❡❣♦ ❉❡t❡❝t❛❞♦ ◆ã♦ ❉❡t❡❝t❛❞♦

◆♦r♠❛❧❱❡r❞❛❞❡✐r♦s P♦s✐t✐✈♦s ❋❛❧s♦ P♦s✐t✐✈♦s

NormaisDetectados× 100

TotaldeNormais

NormaisNaoDetectados× 100

TotaldeNormais

❆t❛q✉❡❱❡r❞❛❞❡✐r♦s P♦s✐t✐✈♦s ❋❛❧s♦ ◆❡❣❛t✐✈♦s

AtaquesDetectados× 100

TotaldeAtaques

AtaquesNaoDetectados× 100

TotaldeAtaques

❘❊P ❚r❡❡✮✱ ❛s ❘❡❞❡s ◆❡✉r❛✐s ❆rt✐✜❝✐❛✐s ✭▼▲P ❡ ❘❇❋✮✱ ◆❛✐✈❡ ❇❛②❡s ❡ ▼áq✉✐♥❛ ❞❡

❱❡t♦r❡s ❞❡ ❙✉♣♦rt❡ ✭❙❱▼✮ ❬❈❤❛♥❣ ✫ ▲✐♥✱ ✷✵✶✶❪✳

◆♦s t❡st❡s✱ ✉t✐❧✐③❛r❛♠✲s❡ ❡♠ t♦❞❛s ❛s té❝♥✐❝❛s ♦s ♣❛râ♠❡tr♦s ♣❛❞rõ❡s ❞♦ ❲❡❦❛✱

s✐♠✐❧❛r♠❡♥t❡ ❝♦♠♦ ❡♠ ❚❛✈❛❧❧❛❡❡ ❡t ❛❧✳ ❬✷✵✵✾❪ ❡ P❛❝❤❣❤❛r❡ ✫ ❑✉❧❦❛r♥✐ ❬✷✵✶✶❪✳ ❋♦r❛♠

❡①❡❝✉t❛❞♦s ❡♠ ✉♠❛ ♠áq✉✐♥❛ ✈✐rt✉❛❧ ❝♦♠ ♦ s✐st❡♠❛ ♦♣❡r❛❝✐♦♥❛❧ ❯❜✉♥t✉ ✶✷✳✵✹ ✭✻✹ ❜✐ts✮

❝♦♠ ✶✻ ●❇ ❞❡ ♠❡♠ór✐❛ ❘❆▼ ❡ ✷ ♣r♦❝❡ss❛❞♦r❡s ❧ó❣✐❝♦s✳ ❋♦r❛♠ ❞❡❞✐❝❛❞♦s ✶✷ ●❇ ❞❡

♠❡♠ór✐❛ ❘❆▼ ♣❛r❛ ❛ ✐♥✐❝✐❛❧✐③❛çã♦ ❞♦ s♦❢t✇❛r❡❲❡❦❛ ✈❡rsã♦ ✸✳✻✳✻✳ ❖ s✐st❡♠❛ ❤②♣❡r✈✐s♦r

✉t✐❧✐③❛❞♦ ❢♦✐ ♦ ▼✐❝r♦s♦❢t ❍②♣❡r✲❱ ❙❡r✈❡r ✷✵✵✽ ❘✷ ❡♠ ✉♠ s❡r✈✐❞♦r ❢ís✐❝♦ ❉❡❧❧ P♦✇❡r

❊❞❣❡ ❘✽✶✵ ❝♦♠ ♣r♦❝❡ss❛❞♦r❡s ■♥t❡❧ ❳❡♦♥ ❊✼✺✹✵ ❞❡ ✷✳✵✵ ●❤③✳

❖s r❡s✉❧t❛❞♦s ❛❧❝❛♥ç❛❞♦s r❡❢❡r❡♥t❡s às t❛①❛s ❞❡ ❱❡r❞❛❞❡✐r♦s P♦s✐t✐✈♦s ✭❱P✮✱ ❋❛❧s♦

P♦s✐t✐✈♦s ✭❋P✮ ❡ ❋❛❧s♦ ◆❡❣❛t✐✈♦s ✭❋◆✮ s❡❣✉✐rã♦ ♦ ♠♦❞❡❧♦ ❞❛ ❚❛❜❡❧❛ ✹✳✶ ❡ sã♦ ❛♣r❡s❡♥✲

t❛❞♦s ♥❛s s❡çõ❡s ✹✳✶ ❡ ✹✳✷✳

✹✳✶ ❘❡s✉❧t❛❞♦s ❞❛s ❚é❝♥✐❝❛s ❞❡ ❈❧❛ss✐✜❝❛çã♦

◆❡st❛ s❡çã♦✱ ♦s r❡s✉❧t❛❞♦s ❞❛s té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✉t✐❧✐③❛❞❛s ❛tr❛✈és ❞♦ ❲❡❦❛ sã♦

❛♣r❡s❡♥t❛❞♦s✳ Pr✐♠❡✐r❛♠❡♥t❡✱ ❛ ❛❜♦r❞❛❣❡♠ ❞❡ ❱❛❧✐❞❛çã♦ ❈r✉③❛❞❛ ❢♦✐ ❝♦♥s✐❞❡r❛❞❛✱ ❞❡✲

✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ ❣❡r❛r r❡s✉❧t❛❞♦s ♠❛✐s ❝♦♥✜á✈❡✐s✱ ❡♠❜♦r❛ t❡♥❤❛ ✉♠ ❝✉st♦ ❝♦♠♣✉t❛❝✐♦♥❛❧

♠❛✐♦r✳ ➚ ✈✐st❛ ❞✐ss♦✱ ❡ss❛ ❛❜♦r❞❛❣❡♠ ❢♦✐ ✉s❛❞❛ ❛♣❡♥❛s ♣❛r❛ ❛ ❞❡t❡❝çã♦ ❡♠ ♠♦❞♦ ♦✤✐♥❡✳

P♦r ♦✉tr♦ ❧❛❞♦✱ ❛ ❛❜♦r❞❛❣❡♠ ❍♦❧❞♦✉t t❛♠❜é♠ ❢♦✐ ❝♦♥s✐❞❡r❛❞❛ ❡ ❡♥tã♦ ❝♦♠♣❛r❛❞❛

❡♠ r❡❧❛çã♦ à ❱❛❧✐❞❛çã♦ ❈r✉③❛❞❛✳ ▲♦❣♦ ❛♣ós✱ ♥♦✈♦s r❡s✉❧t❛❞♦s ❢♦r❛♠ ❝♦❧❡t❛❞♦s✱ ✉t✐❧✐✲

③❛♥❞♦ ❛♣❡♥❛s ❛ ❛❜♦r❞❛❣❡♠ ❍♦❧❞♦✉t ♥✉♠❛ ❞❡t❡❝çã♦ ❡♠ t❡♠♣♦ r❡❛❧✱ ♣♦✐s ♥❡st❡ ❡♥❢♦q✉❡✱

♦ ♦❜❥❡t✐✈♦ ❢♦✐ ♦❜t❡r ✉♠ ♠❡❧❤♦r ❞❡s❡♠♣❡♥❤♦ ♥❛ ❞❡t❡❝çã♦✱ ❝♦♠ ♠❡♥♦r ❝✉st♦ ❝♦♠♣✉t❛❝✐✲

♦♥❛❧✳

❉❡ss❡ ♠♦❞♦✱ ♦s r❡s✉❧t❛❞♦s ❣❡r❛✐s ❞❛ ❛❜♦r❞❛❣❡♠ ❞❡ ❱❛❧✐❞❛çã♦ ❈r✉③❛❞❛✱ ♣❛r❛ ✉♠❛

❞❡t❡❝çã♦ ❡♠ ♠♦❞♦ ♦✤✐♥❡✱ ✐♥❢♦r♠❛r❛♠ ❛s t❛①❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❝♦rr❡t❛ ✭❛❝❝✉r❛❝②✮ ❡

✐♥❝♦rr❡t❛ ✭❡rr♦r r❛t❡✮✱ q✉❡ sã♦ ❛♣r❡s❡♥t❛❞❛s ♥❛ ❚❛❜❡❧❛ ✹✳✷✳

✹✳ ❘❡s✉❧t❛❞♦s ✺✷

❚❛❜❡❧❛ ✹✳✷✳ ❘❡s✉❧t❛❞♦s ❣❡r❛✐s ❞❛s té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✭♦✤✐♥❡✮

❚é❝♥✐❝❛s ❞❡ ❚❛①❛ ❞❡ ❈❧❛ss✐✜❝❛çã♦ ❘♦♦t ❘❡❧❛t✐✈❡ ❙q✉❛r❡❞❈❧❛ss✐✜❝❛çã♦ ❈♦rr❡t❛ ■♥❝♦rr❡t❛ ❊rr♦r ✭❘❘❙❊✮

❏✹✽ ✾✾✱✽✵✶✽✪ ✵✱✶✾✽✷✪ ✷✸✱✻✻✽✵✪❏✹✽❣r❛❢t ✾✾✱✼✼✺✾✪ ✵✱✷✷✹✶✪ ✷✺✱✸✽✷✻✪◆❇❚r❡❡ ✾✾✱✾✸✻✶✪ ✵✱✵✻✸✾✪ ✶✸✱✼✾✹✼✪

❘❛♥❞♦♠ ❋♦r❡st ✾✾✱✾✹✻✵✪ ✵✱✵✺✹✵✪ ✶✷✱✷✵✷✽✪❘❛♥❞♦♠ ❚r❡❡ ✾✾✱✾✷✺✸✪ ✵✱✵✼✹✼✪ ✶✺✱✷✵✻✹✪❘❊P ❚r❡❡ ✾✾✱✾✸✵✾✪ ✵✱✵✻✾✶✪ ✶✹✱✹✻✻✾✪

◆❛✐✈❡ ❇❛②❡s ✾✺✱✶✻✽✸✪ ✹✱✽✸✶✼✪ ✶✷✵✱✵✶✶✶✪❙❱▼ ✾✽✱✸✶✾✻✪ ✶✱✻✽✵✹✪ ✼✷✱✾✻✶✾✪

❘◆❆ ❘❇❋ ✾✼✱✸✶✺✷✪ ✷✱✻✽✹✽✪ ✼✸✱✵✽✹✺✪❘◆❆ ▼▲P ✾✽✱✻✼✹✸✪ ✶✱✸✷✺✼✪ ✹✽✱✽✸✶✹✪

❚♦t❛❧ ❞❡ ❘❡❣✐str♦s✿ ✷✶✷✽✻✻❚♦t❛❧ ❞❡ ❘❡❣✐str♦s ❈❧❛ss✐✜❝❛❞♦s✿ ✷✶✷✽✻✻

❆ ❘❛♥❞♦♠ ❋♦r❡st ♣♦ss✉✐✉ ♦s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s✱ ❝♦♠ ✉♠❛ t❛①❛ ❞❡ ❡rr♦ ❘❘❙❊

♠❡♥♦r q✉❡ ✶✷✱✺✪✱ ♠♦str❛❞❛ ♥❛ ❋✐❣✉r❛ ✹✳✶✳ ❊ss❛ té❝♥✐❝❛ ❛♣r❡s❡♥t♦✉ ❛s ♠❡❧❤♦r❡s t❛①❛s

❞❡ ❱❡r❞❛❞❡✐r♦s P♦s✐t✐✈♦s ♣❛r❛ ♦ trá❢❡❣♦ ✏♥♦r♠❛❧✑ ❡ ❋❛❧s♦s P♦s✐t✐✈♦s✳ ◆♦ ❡♥t❛♥t♦✱ ❛

◆❇❚r❡❡ ❢♦✐ ❛ q✉❡ ♠❛✐s ❞❡t❡❝t♦✉ ♦ trá❢❡❣♦ ❞♦ t✐♣♦ ✏❛t❛q✉❡✑✱ ❝♦♠ ♠❡♥♦s ❋❛❧s♦s ◆❡❣❛t✐✈♦s✱

❝♦♥❢♦r♠❡ ❛ ❚❛❜❡❧❛ ✹✳✸✳

❆ ♠étr✐❝❛ ❞❡ ❡rr♦ ❘❛✐③ ◗✉❛❞r❛❞❛ ❞♦ ❊rr♦ ❘❡❧❛t✐✈♦ ✭❘❘❙❊ ✲ ❘♦♦t ❘❡❧❛t✐✈❡ ❙q✉❛r❡❞

❊rr♦r✮ ❢♦✐ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❝♦♠♣❛r❛r ♦s ❞❡s✈✐♦s ❞♦s ✈❛❧♦r❡s ♣r❡❞✐t♦s ❝♦♠ ♦s ❞❡s✈✐♦s ❞♦s

✈❛❧♦r❡s ❛❧✈♦s ✭❞❡s❡❥❛❞♦s✮✳ ◗✉❛♥t♦ ♠❛✐s ♣ró①✐♠♦ ❞❡ ③❡r♦✱ ♠❡❧❤♦r ♦ r❡s✉❧t❛❞♦✳ ❖ s❡✉

❝á❧❝✉❧♦ é ❛❢❡r✐❞♦ ❝♦♥❢♦r♠❡ ❛ ❊q✉❛çã♦ ✹✳✶✱ ♦♥❞❡ Pi ❡ Ti sã♦ ♦s ✈❛❧♦r❡s ♣r❡❞✐t♦s ❡ ❛t✉❛✐s

❞♦ ❡①❡♠♣❧♦ ❞❡ t❡st❡ i✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❡♥q✉❛♥t♦ T = 1n

n∑

1é ❛ ♠é❞✐❛ ❞♦s ✈❛❧♦r❡s ❛t✉❛✐s

❞♦s ❡①❡♠♣❧♦s ❞❡ t❡st❡✳

Ei =

√

√

√

√

√

√

n∑

i=1

(Pi−Ti)2

n∑

i=1

(Ti−T )2✭✹✳✶✮

❱❡r✐✜❝♦✉✲s❡ t❛♠❜é♠ q✉❡✱ ❛♦ ❝♦♥s✐❞❡r❛r ♦ t❡♠♣♦ ♣❛r❛ ❝r✐❛çã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ❝❧❛s✲

s✐✜❝❛çã♦✱ ❛ ❘❛♥❞♦♠ ❚r❡❡ t♦r♥❛✲s❡ ✉♠❛ ♦♣çã♦ ❛♣r♦♣r✐❛❞❛✱ s❡❣✉✐❞❛ ❞❛ ❘❊P ❚r❡❡✱ ♣♦✐s

s✉❛ t❛①❛ ❞❡ ❡rr♦ ❘❘❙❊ ❢♦✐ ❛❜❛✐①♦ ❞❡ ✶✻✪ ❡ ♦ t❡♠♣♦ ❣❛st♦ ❢♦✐ ❝❡r❝❛ ❞❡ ✽ ✈❡③❡s ♠❡♥♦r

q✉❡ ❞❛ ❘❛♥❞♦♠ ❋♦r❡st✳ ❆s ❞❡♠❛✐s té❝♥✐❝❛s ❛♣r❡s❡♥t❛r❛♠ t❡♠♣♦s ♠❛✐♦r❡s ♣❛r❛ ❝r✐❛çã♦

❞♦ ♠♦❞❡❧♦✱ ❝♦♥❢♦r♠❡ ❛♣r❡s❡♥t❛❞♦ ♥❛ ❋✐❣✉r❛ ✹✳✹✱ ❡①❝❡t✉❛♥❞♦ ❛ ◆❛✐✈❡ ❇❛②❡s q✉❡✱ ❛♣❡s❛r

❞❡ ♣♦ss✉✐r ✉♠ t❡♠♣♦ ♠❡♥♦r✱ ❛♣r❡s❡♥t♦✉ ❛s ♠❛✐♦r❡s t❛①❛s ❞❡ ❡rr♦✳ ❆ ◆❇❚r❡❡✱ ❛♣❡s❛r

❞❡ t❡r ❞❡t❡❝t❛❞♦ ❛ ♠❛✐♦r ♣❛rt❡ ❞♦s ✏❛t❛q✉❡s✑✱ ❢♦✐ ✉♠❛ ❞❛s q✉❡ ♠❛✐s ❣❛st❛r❛♠ t❡♠♣♦

♣❛r❛ ❝r✐❛çã♦ ❞♦ ♠♦❞❡❧♦✱ s❡♥❞♦ ✐♥❢❡r✐♦r ❛♣❡♥❛s às té❝♥✐❝❛s ❙❱▼ ❡ ❘◆❆ ▼▲P✳

❏á ❡♠ r❡❧❛çã♦ às ❘◆❆s✱ ♣❛r❛ t♦❞❛s ❛s ❛♥á❧✐s❡s✱ ❛ t❛①❛ ❞❡ ❡rr♦ ❘❘❙❊ ❢♦✐ ♠❛✐♦r q✉❡

✹✳ ❘❡s✉❧t❛❞♦s ✺✸

❋✐❣✉r❛ ✹✳✶✳ ❘♦♦t ❘❡❧❛t✐✈❡ ❙q✉❛r❡❞ ❊rr♦r ✭❘❘❙❊✮ ✲ ❱❛❧✐❞❛çã♦ ❈r✉③❛❞❛

❚❛❜❡❧❛ ✹✳✸✳ ❘❡s✉❧t❛❞♦s ❞❛s té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✭♦✤✐♥❡✮

❚é❝♥✐❝❛s ❞❡ ◆♦r♠❛❧ ❆t❛q✉❡ ❋❛❧s♦ ❋❛❧s♦❈❧❛ss✐✜❝❛çã♦ ❱❡r❞✳ P♦s✐t✐✈♦s ❱❡r❞✳ P♦s✐t✐✈♦s P♦s✐t✐✈♦s ◆❡❣❛t✐✈♦s

❏✹✽ ✷✵✺✺✼✾ ✭✾✾✱✽✸✪✮ ✻✽✻✺ ✭✾✽✱✽✸✪✮ ✸✹✶ ✭✵✱✶✼✪✮ ✽✶ ✭✶✱✶✼✪✮❏✹✽❣r❛❢t ✷✵✺✺✽✸ ✭✾✾✱✽✹✪✮ ✻✽✵✻ ✭✾✼✱✾✽✪✮ ✸✸✼ ✭✵✱✶✻✪✮ ✶✹✵ ✭✷✱✵✷✪✮◆❇❚r❡❡ ✷✵✺✽✺✷ ✭✾✾✱✾✼✪✮ ✻✽✼✽ ✭✾✾✱✵✷✪✮ ✻✽ ✭✵✱✵✸✪✮ ✻✽ ✭✵✱✾✽✪✮

❘❛♥❞♦♠ ❋♦r❡st ✷✵✺✽✼✺ ✭✾✾✱✾✽✪✮ ✻✽✼✻ ✭✾✽✱✾✾✪✮ ✹✺ ✭✵✱✵✷✪✮ ✼✵ ✭✶✱✵✶✪✮❘❛♥❞♦♠ ❚r❡❡ ✷✵✺✽✸✽ ✭✾✾✱✾✻✪✮ ✻✽✻✾ ✭✾✽✱✽✾✪✮ ✽✷ ✭✵✱✵✹✪✮ ✼✼ ✭✶✱✶✶✪✮❘❊P ❚r❡❡ ✷✵✺✽✺✸ ✭✾✾✱✾✼✪✮ ✻✽✻✻ ✭✾✽✱✽✺✪✮ ✻✼ ✭✵✱✵✸✪✮ ✽✵ ✭✶✱✶✺✪✮

◆❛✐✈❡ ❇❛②❡s ✶✾✺✼✻✼ ✭✾✺✱✵✼✪✮ ✻✽✶✹ ✭✾✽✱✶✵✪✮ ✶✵✶✺✸ ✭✹✱✾✸✪✮ ✶✸✷ ✭✶✱✾✵✪✮❙❱▼ ✷✵✹✺✷✼ ✭✾✾✱✸✷✪✮ ✹✼✻✷ ✭✻✽✱✺✻✪✮ ✶✸✾✸ ✭✵✱✻✽✪✮ ✷✶✽✹ ✭✸✶✱✹✹✪✮

❘◆❆ ❘❇❋ ✷✵✹✺✶✸ ✭✾✾✱✸✷✪✮ ✷✻✸✽ ✭✸✼✱✾✽✪✮ ✶✹✵✼ ✭✵✱✻✽✪✮ ✹✸✵✽ ✭✻✷✱✵✷✪✮❘◆❆ ▼▲P ✷✵✹✽✹✺ ✭✾✾✱✹✽✪✮ ✺✶✾✾ ✭✼✹✱✽✺✪✮ ✶✵✼✺ ✭✵✱✺✷✪✮ ✶✼✹✼ ✭✷✺✱✶✺✪✮

❋✐❣✉r❛ ✹✳✷✳ ❚❡♠♣♦ ❣❛st♦ ❝♦♠ ❝r✐❛çã♦ ❞♦ ♠♦❞❡❧♦ ✭s✮ ✲ ❱❛❧✐❞❛çã♦ ❈r✉③❛❞❛

❞❛s ár✈♦r❡s ❞❡ ❞❡❝✐sã♦✳ ❱❡r✐✜❝♦✉✲s❡ ❛✐♥❞❛ q✉❡ ❛ ✉t✐❧✐③❛çã♦ ❞❡ t♦❞♦s ♦s r❡❣✐str♦s ❝♦♠ ❛s

té❝♥✐❝❛s ❞❡ ❘◆❆ ❛♣r❡s❡♥t❛ ♣r♦❜❧❡♠❛s ❞❡ ❞❡s❡♠♣❡♥❤♦ ❡ ❣❡♥❡r❛❧✐③❛çã♦ ❞♦s r❡s✉❧t❛❞♦s✱

s❡♥❞♦ ♦ ♠♦t✐✈♦ ♣❡❧♦ q✉❛❧ ❞❡❝✐❞✐✉✲s❡ ✉s❛r ✉♠❛ ❛♠♦str❛ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s✳ ❆ ❘◆❆

▼▲P t♦r♥❛✲s❡ ♠❛✐s ❛♣r♦♣r✐❛❞❛ q✉❛♥❞♦ sã♦ ❡♠♣r❡❣❛❞♦s ♠❡♥♦s r❡❣✐str♦s✱ q✉❡ ❝♦♥❢♦r♠❡

❞❡s❝r✐t♦ ❡♠ ❇r❛❣❛ ❡t ❛❧✳ ❬✷✵✵✼❪ ❣❡r❛❧♠❡♥t❡ ❝♦♥s❡❣✉❡ ❣❡♥❡r❛❧✐③❛r ❛ ✐♥❢♦r♠❛çã♦✱ ♠❡s♠♦ ❛

♣❛rt✐r ❞❡ ♣♦✉❝♦s ❞❛❞♦s ❞❡ tr❡✐♥❛♠❡♥t♦✳ ❖ t❡♠♣♦ ❣❛st♦ ❝♦♠ ❛ ❝r✐❛çã♦ ❞♦ ♠♦❞❡❧♦ ♣❡❧❛

❘◆❆ ▼▲P ❢♦✐ ♠✉✐t♦ ❛❧t♦ ✭✾✾✶✻✱✾✸ s✮✱ ♠♦t✐✈♦ ♣❡❧♦ q✉❛❧ ♥ã♦ ❢♦✐ ❛♣r❡s❡♥t❛❞♦ s❡✉ ✈❛❧♦r

✹✳ ❘❡s✉❧t❛❞♦s ✺✹

♥❛ ❋✐❣✉r❛ ✹✳✹✳ ❆ ❘◆❆ ❘❇❋ ♥ã♦ ❝♦♥s❡❣✉✐✉ ❣❡♥❡r❛❧✐③❛r ❛❞❡q✉❛❞❛♠❡♥t❡ ❛ ✐♥❢♦r♠❛çã♦

❛♣r❡♥❞✐❞❛✱ ♣♦ss✉✐♥❞♦ ♠❛✐♦r❡s t❛①❛s ❞❡ ❡rr♦ q✉❡ ❛ ❘◆❆ ▼▲P✳

P♦r ✜♠✱ ❛♦ ❛♥❛❧✐s❛r♠♦s ❛s ❞✉❛s ❛❜♦r❞❛❣❡♥s ✉t✐❧✐③❛❞❛s✱ ❍♦❧❞♦✉t ❡ ❱❛❧✐❞❛çã♦ ❈r✉✲

③❛❞❛✱ ✈❡r✐✜❝♦✉✲s❡ q✉❡ ❛s té❝♥✐❝❛s ❏✹✽❣r❛❢t✱ ❘◆❆ ▼▲P✱ ◆❛✐✈❡ ❇❛②❡s✱ ❙❱▼ ❡ ❘◆❆ ❘❇❋✱

♣♦r ❡①❡♠♣❧♦✱ ♣♦ss✉ír❛♠ ❛ ♠❡♥♦r ❞✐❢❡r❡♥ç❛ ❞❛s t❛①❛s ❘❘❙❊✱ ❝♦♥❢♦r♠❡ ♠♦str❛❞♦ ♥❛ ❋✐✲

❣✉r❛ ✹✳✸✱ ❡ ❛ss✐♠✱ ❛ ✉t✐❧✐③❛çã♦ ❞❛ ❍♦❧❞♦✉t ♣♦❞❡ s❡r ❛ ♠❛✐s ❛♣r♦♣r✐❛❞❛✱ ♣♦✐s s❡✉ ♣r♦❝❡ss♦

❞❡ ❝❧❛ss✐✜❝❛çã♦ é ♠❛✐s rá♣✐❞♦ ❡♠ ❝♦♠♣❛r❛çã♦ ❛♦ ♣r♦❝❡ss♦ ❞❛ ❱❛❧✐❞❛çã♦ ❈r✉③❛❞❛✳

❋✐❣✉r❛ ✹✳✸✳ ❉✐❢❡r❡♥ç❛ ❘❘❙❊ ✭❍♦❧❞♦✉t ✲ ❱❛❧✐❞❛çã♦ ❈r✉③❛❞❛✮

◆♦ ❡♥t❛♥t♦✱ ❛ ❘❊P ❚r❡❡ ❛♣r❡s❡♥t♦✉ ❛ ♠❛✐♦r ❞✐❢❡r❡♥ç❛ ❞❛ t❛①❛ ❘❘❙❊✱ s❡♥❞♦

❛❝✐♠❛ ❞❡ ✾✪✳ ◆❡st❡ ❝❛s♦✱ ❛ ✉t✐❧✐③❛çã♦ ❞❛ ❱❛❧✐❞❛çã♦ ❈r✉③❛❞❛ ♣♦❞❡ s❡r ♠❛✐s ❛❞❡q✉❛❞❛

♣♦r ❛♣r❡s❡♥t❛r ♦s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s✱ ❡♠ ❝♦♠♣❛r❛çã♦ à ❛❜♦r❞❛❣❡♠ ❍♦❧❞♦✉t✱ ♠❡s♠♦

♣♦ss✉✐♥❞♦ ✉♠ ♠❛✐♦r ❝✉st♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♣❛r❛ s✉❛ ❡①❡❝✉çã♦✳

❆♦ ❝♦♠♣❛r❛r ♦s r❡s✉❧t❛❞♦s ❞♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ❝♦♠ P❛❝❤❣❤❛r❡ ✫ ❑✉❧❦❛r♥✐ ❬✷✵✶✶❪✱

✈❡r✐✜❝♦✉✲s❡ q✉❡ ❛ ❘❊P ❚r❡❡ ❛♣r❡s❡♥t♦✉ t❛♠❜é♠ ✉♠ ❞♦s ♠❡❧❤♦r❡s t❡♠♣♦s ❞❡ ❝r✐❛çã♦

❞♦ ♠♦❞❡❧♦ ✭✼✱✻✶ s✮ ❡♠ r❡❧❛çã♦ ❛s ❞❡♠❛✐s té❝♥✐❝❛s ❞❡ ár✈♦r❡s ❞❡ ❞❡❝✐sã♦✱ ✜❝❛♥❞♦ ❛❜❛✐①♦

❛♣❡♥❛s ❞❛ ❘❛♥❞♦♠ ❚r❡❡ q✉❡ ❣❛st♦✉ ✸✱✾✻ s✳ ❊♥tr❡t❛♥t♦✱ ♦s r❡s✉❧t❛❞♦s ❞❡ ❝❧❛ss✐✜❝❛çõ❡s

❝♦rr❡t❛s ❢♦r❛♠ ❧✐❣❡✐r❛♠❡♥t❡ ♣✐♦r❡s q✉❡ ❞❡ ❛❧❣✉♠❛s ár✈♦r❡s ❞❡ ❞❡❝✐sã♦✳ ◆❡st❡ tr❛❜❛❧❤♦✱

❡st❛ té❝♥✐❝❛ ❛❧é♠ ❞❡ t❡r ❛♣r❡s❡♥t❛❞♦ ♦ ✷♦ ♠❡❧❤♦r ❞❡s❡♠♣❡♥❤♦ ❡♠ r❡❧❛çã♦ ❛♦ t❡♠♣♦ ❞❡

❝r✐❛çã♦ ❞♦ ♠♦❞❡❧♦ ❞❛s ár✈♦r❡s ❞❡ ❞❡❝✐sã♦✱ ♣♦ss✉✐✉ ✉♠❛ t❛①❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ♠❡❧❤♦r

q✉❡ ❛s ár✈♦r❡s ❞❡ ❞❡❝✐sã♦ ❏✹✽ ❡ ❏✹✽❣r❛❢t ❡ ❘❛♥❞♦♠ ❚r❡❡✳

❆♦ ❝♦♥s✐❞❡r❛r ♦ tr❛❜❛❧❤♦ ❞❡ ❚❛✈❛❧❧❛❡❡ ❡t ❛❧✳ ❬✷✵✵✾❪✱ ❛s ár✈♦r❡s ❞❡ ❞❡❝✐sã♦ ❏✹✽ ❡

◆❇❚r❡❡ ❢♦r❛♠ ❛s q✉❡ ❛♣r❡s❡♥t❛r❛♠ ♦s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❞❡ ❝❧❛ss✐✜❝❛çõ❡s ❝♦rr❡t❛s✱

❡♥q✉❛♥t♦ ❛ ❘◆❆ ▼▲P ❛♣r❡s❡♥t♦✉ r❡s✉❧t❛❞♦s ♣✐♦r❡s ❞♦ q✉❡ t♦❞❛s ❛s ár✈♦r❡s ❞❡ ❞❡❝✐sã♦✳

❊ss❡ r❡s✉❧t❛❞♦✱ r❡❢❡r❡♥t❡ às ❘◆❆s ▼▲P ❡ ❛ ◆❇❚r❡❡ t❛♠❜é♠ s❡ ❛ss❡♠❡❧❤❛ ❛♦ ❡♥❝♦♥tr❛❞♦

♥♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦✳

❖✉tr♦s r❡s✉❧t❛❞♦s ✐♠♣♦rt❛♥t❡s sã♦ r❡❢❡r❡♥t❡s ❛♦s t❡st❡s ❝♦♠ ❛♣❡♥❛s ✼ ❛tr✐❜✉t♦s

✭♠♦❞♦ ❞❡ ❞❡t❡❝çã♦ ❡♠ t❡♠♣♦ r❡❛❧✮✳ ◆❡st❡ ❝❛s♦✱ ✈❡r✐✜❝♦✉✲s❡ q✉❡ ❛♦ ❡❧✐♠✐♥❛r ❛s ❝❛r❛❝✲

t❡ríst✐❝❛s r❡❧❛❝✐♦♥❛❞❛s ❛♦ ❞❡st✐♥♦✱ ♦ t❡♠♣♦ ❣❛st♦ ♣❛r❛ ❝r✐❛çã♦ ❞♦ ♠♦❞❡❧♦ ❢♦✐ ♠❛✐♦r ❡♠

✹✳ ❘❡s✉❧t❛❞♦s ✺✺

t♦❞❛s ❛s té❝♥✐❝❛s✳ ❚♦❞❛✈✐❛✱ ❛♣❡♥❛s ✉♠❛ ♣❡q✉❡♥❛ ❞✐❢❡r❡♥ç❛ ♥❛ t❛①❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦

❝♦rr❡t❛ ❢♦✐ ❝♦♥st❛t❛❞❛✱ s✐♠✐❧❛r♠❡♥t❡ ❝♦♠♦ ❡♠ ▼③✐❧❛ ✫ ❉✉❜❡ ❬✷✵✶✸❪✱ ❥✉st✐✜❝❛♥❞♦✱ ♣♦r✲

t❛♥t♦✱ ❛ ✉t✐❧✐③❛çã♦ ❞❡ t❛❧ ❡♥❢♦q✉❡ ♣❛r❛ ✉♠❛ ❞❡t❡❝çã♦ ❡♠ t❡♠♣♦ r❡❛❧✱ ❝♦♠♦ ♣♦❞❡ s❡r

♦❜s❡r✈❛❞♦ ♥❛s t❛❜❡❧❛s ✹✳✹ ❡ ✹✳✺✳

◆❡st❡ ❝❛s♦✱ ❛♣❡s❛r ❞♦ t❡♠♣♦ ❞❡ ❝r✐❛çã♦ ❞♦ ♠♦❞❡❧♦ t❡r s✐❞♦ ♠❛✐♦r ❡♠ t♦❞❛s ❛s

té❝♥✐❝❛s✱ ❛✐♥❞❛ ❛ss✐♠✱ ❡st❡ ❡♥❢♦q✉❡ ♣♦❞❡ t❡r ✉♠ ♠❡❧❤♦r ❞❡s❡♠♣❡♥❤♦ ♣♦r ♥❡❝❡ss✐t❛r

❝♦❧❡t❛r ♠❡♥♦s ✐♥❢♦r♠❛çõ❡s ❞♦s P❉❯s tr❛♥s♠✐t✐❞♦s✳

❚❛❜❡❧❛ ✹✳✹✳ ❘❡s✉❧t❛❞♦s ❣❡r❛✐s ❞❛s té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✭t❡♠♣♦ r❡❛❧✮

❚é❝♥✐❝❛s ❞❡ ❚❛①❛ ❞❡ ❈❧❛ss✐✜❝❛çã♦ ❘♦♦t ❘❡❧❛t✐✈❡ ❙q✉❛r❡❞❈❧❛ss✐✜❝❛çã♦ ❈♦rr❡t❛ ■♥❝♦rr❡t❛ ❊rr♦r ✭❘❘❙❊✮

❏✹✽ ✾✾✱✼✷✹✺✪ ✵✱✷✼✷✺✪ ✷✼✱✹✸✼✾✪❏✹✽❣r❛❢t ✾✾✱✻✼✶✼✪ ✵✱✸✷✽✸✪ ✸✵✱✼✷✹✵✪◆❇❚r❡❡ ✾✾✱✽✼✸✷✪ ✵✱✶✷✻✽✪ ✶✼✱✹✺✶✽✪

❘❛♥❞♦♠ ❋♦r❡st ✾✾✱✽✻✼✸✪ ✵✱✶✸✷✼✪ ✶✽✱✾✷✵✺✪❘❛♥❞♦♠ ❚r❡❡ ✾✾✱✽✶✽✺✪ ✵✱✶✽✶✺✪ ✷✸✱✼✶✼✽✪❘❊P ❚r❡❡ ✾✾✱✽✹✺✻✪ ✵✱✶✺✹✹✪ ✷✶✱✷✻✶✵✪

◆❛✐✈❡ ❇❛②❡s ✾✻✱✻✾✽✻✪ ✸✱✸✵✶✹✪ ✽✸✱✸✷✾✻✪❙❱▼ ✾✼✱✼✻✻✽✪ ✷✱✷✸✸✷✪ ✽✹✱✵✹✹✶✪

❘◆❆ ❘❇❋ ✾✽✱✸✷✸✺✪ ✶✱✻✼✻✺✪ ✻✻✱✹✺✷✷✪❘◆❆ ▼▲P ✾✽✱✸✾✷✽✪ ✶✱✻✵✼✷✪ ✺✼✱✷✼✽✵✪

❚♦t❛❧ ❞❡ ❘❡❣✐str♦s✿ ✷✶✷✽✻✻❚♦t❛❧ ❞❡ ❘❡❣✐str♦s ❈❧❛ss✐✜❝❛❞♦s✿ ✶✼✵✷✾✸

❚❛❜❡❧❛ ✹✳✺✳ ❘❡s✉❧t❛❞♦s ❞❛s té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✭t❡♠♣♦ r❡❛❧✮

❚é❝♥✐❝❛s ❞❡ ◆♦r♠❛❧ ❆t❛q✉❡ ❋❛❧s♦ ❋❛❧s♦❈❧❛ss✐✜❝❛çã♦ ❱❡r❞✳ P♦s✐t✐✈♦s ❱❡r❞✳ P♦s✐t✐✈♦s P♦s✐t✐✈♦s ◆❡❣❛t✐✈♦s

❏✹✽ ✶✻✹✸✻✻ ✭✾✽✱✼✽✪✮ ✺✹✻✸ ✭✾✽✱✶✺✪✮ ✸✻✶ ✭✵✱✷✷✪✮ ✶✵✸ ✭✶✱✽✺✪✮❏✹✽❣r❛❢t ✶✻✹✸✾✻ ✭✾✾✱✽✵✪✮ ✺✸✸✽ ✭✾✺✱✾✵✪✮ ✸✸✶ ✭✵✱✷✵✪✮ ✷✷✽ ✭✹✱✶✵✪✮◆❇❚r❡❡ ✶✻✹✻✵✾ ✭✾✾✱✾✸✪✮ ✺✹✻✽ ✭✾✽✱✷✹✪✮ ✶✶✽ ✭✵✱✵✼✪✮ ✾✽ ✭✶✱✼✻✪✮

❘❛♥❞♦♠ ❋♦r❡st ✶✻✹✻✷✼ ✭✾✾✱✾✹✪✮ ✺✹✹✵ ✭✾✼✱✼✹✪✮ ✶✵✵ ✭✵✱✵✻✪✮ ✶✷✻ ✭✷✱✷✻✪✮❘❛♥❞♦♠ ❚r❡❡ ✶✻✹✻✵✵ ✭✾✾✱✾✷✪✮ ✺✸✽✹ ✭✾✻✱✼✸✪✮ ✶✷✼ ✭✵✱✵✽✪✮ ✶✽✷ ✭✸✱✷✼✪✮❘❊P ❚r❡❡ ✶✻✹✺✾✾ ✭✾✾✱✾✷✪✮ ✺✹✸✶ ✭✾✼✱✺✼✪✮ ✶✷✽ ✭✵✱✵✽✪✮ ✶✸✺ ✭✷✱✹✸✪✮

◆❛✐✈❡ ❇❛②❡s ✶✺✾✷✵✸ ✭✾✻✱✻✺✪✮ ✺✹✻✽ ✭✾✽✱✷✹✪✮ ✺✺✷✹ ✭✸✱✸✺✪✮ ✾✽ ✭✶✱✼✻✪✮❙❱▼ ✶✻✹✵✽✷ ✭✾✾✱✻✶✪✮ ✷✹✵✽ ✭✹✸✱✷✻✪✮ ✻✹✺ ✭✵✱✸✾✪✮ ✸✶✺✽ ✭✺✻✱✼✹✪✮

❘◆❆ ❘❇❋ ✶✻✸✹✹✶ ✭✾✾✱✷✷✪✮ ✸✾✾✼ ✭✼✶✱✽✶✪✮ ✶✷✽✻ ✭✵✱✼✽✪✮ ✶✺✻✾ ✭✷✽✱✶✾✪✮❘◆❆ ▼▲P ✶✻✸✾✹✻ ✭✾✾✱✺✸✪✮ ✸✻✶✵ ✭✻✹✱✽✻✪✮ ✼✽✶ ✭✵✱✹✼✪✮ ✶✾✺✻ ✭✸✺✱✶✹✪✮

❆ ár✈♦r❡ ❞❡ ❞❡❝✐sã♦ ◆❇❚r❡❡ t❡✈❡ ❛ ♠❡❧❤♦r ♣r❡❝✐sã♦ ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡ ♦ ♠❡♥♦r

❡rr♦✱ ❝♦♥t✉❞♦ ♦ s❡✉ t❡♠♣♦ ❣❛st♦ ♣❛r❛ ❝r✐❛çã♦ ❞♦ ♠♦❞❡❧♦ ❢♦✐ ✸✸✱✾✻ s✱ s❡♥❞♦ ❝❡r❝❛ ❞❡

✶✵ ✈❡③❡s ♠❛✐♦r q✉❡ ❞❡ ♦✉tr❛s té❝♥✐❝❛s✱ ❝♦♠♦ ❘❛♥❞♦♠ ❚r❡❡ ❡ ❘❊P ❚r❡❡✱ ❡ q✉❛s❡ ✷

✈❡③❡s ♠❛✐♦r q✉❡ ❞❛ ❘❛♥❞♦♠ ❋♦r❡st✱ ❝♦♥❢♦r♠❡ ♠♦str❛❞♦ ♥❛ ❋✐❣✉r❛ ✹✳✸ ❖✉tr♦ ♣♦♥t♦ q✉❡

♠❡r❡❝❡ ❞❡st❛q✉❡ é q✉❡✱ ❛ ❘❛♥❞♦♠ ❋♦r❡st ❝♦♥s❡❣✉✐✉ ❞❡t❡❝t❛r ♠❡❧❤♦r ♦ trá❢❡❣♦ ♥♦r♠❛❧✱

❡♥q✉❛♥t♦ ❛ ◆❇❚r❡❡ ❞❡t❡❝t♦✉ ♠❡❧❤♦r ♦ trá❢❡❣♦ r❡❢❡r❡♥t❡ ❛♦s ❛t❛q✉❡s✳

✹✳ ❘❡s✉❧t❛❞♦s ✺✻

❋✐❣✉r❛ ✹✳✹✳ ❚❡♠♣♦ ❣❛st♦ ❝♦♠ ❝r✐❛çã♦ ❞♦ ♠♦❞❡❧♦ ✭s✮ ✲ ❍♦❧❞♦✉t

✹✳✷ ❘❡s✉❧t❛❞♦s ❞♦ ❙✐st❡♠❛ ■♥t❡❧✐❣❡♥t❡ ❍í❜r✐❞♦

◆❡st❛ s❡çã♦✱ ♦s r❡s✉❧t❛❞♦s ❞♦ ❙✐st❡♠❛ ■♥t❡❧✐❣❡♥t❡ ❍í❜r✐❞♦ ✭❙■❍✮ sã♦ ❛♣r❡s❡♥t❛❞♦s✳ ◆❡st❡

❝❛s♦✱ ✈❡r✐✜❝♦✉✲s❡ q✉❡✱ ❛♦ ❝♦♠❜✐♥❛r ❛ té❝♥✐❝❛ ❞❡ ❆● ❝♦♠ ❛s ❘◆❆s ▼▲P✱ ♠❡❧❤♦r❡s

r❡s✉❧t❛❞♦s ❢♦r❛♠ ❛❧❝❛♥ç❛❞♦s✳

❆ ❡s❝♦❧❤❛ ❞♦s ♣❛râ♠❡tr♦s ✐♥✐❝✐❛✐s ❞❛ r❡❞❡ ♥❡✉r❛❧ ♣❡❧♦ ❆● ♣❡r♠✐t✐✉ ❛♣❡r❢❡✐ç♦❛r ❛

❡str✉t✉r❛ ✐♥✐❝✐❛❧ ❞❛ ❘◆❆ ▼▲P✱ ♠✐♥✐♠✐③❛♥❞♦ ❡st❡ ♣r♦❜❧❡♠❛ ✐♥✐❝✐❛❧ ❡ ♠❡❧❤♦r❛♥❞♦ s❡✉s

r❡s✉❧t❛❞♦s ✜♥❛✐s✳ ◆❡st❡s r❡s✉❧t❛❞♦s✱ ❛ ❛❜♦r❞❛❣❡♠ ❍♦❧❞♦✉t ❢♦✐ ❝♦♥s✐❞❡r❛❞❛✱ s❡♣❛r❛♥❞♦

❡♠ ❞♦✐s ❣r✉♣♦s ✭tr❡✐♥❛♠❡♥t♦ ❡ t❡st❡s✮✱ ❞❡ ❢♦r♠❛ s✐♠✐❧❛r✱ q✉❛♥❞♦ ✉t✐❧✐③❛❞♦s ♥♦ ❲❡❦❛✳

❆ss✐♠✱ ♦s r❡s✉❧t❛❞♦s ♣❛r❛ ❛s ✹ ♠❡❧❤♦r❡s ❘◆❆s ❡♥❝♦♥tr❛❞❛s ♣❡❧♦ ❙■❍✱ ✉t✐❧✐③❛♥❞♦

❛ ❛❜♦r❞❛❣❡♠ ❍♦❧❞♦✉t✱ sã♦ ❛♣r❡s❡♥t❛❞♦s ♥❛s t❛❜❡❧❛s ✹✳✻✱ ✹✳✼ ❡ ✹✳✽✳

❚❛❜❡❧❛ ✹✳✻✳ ❘❡s✉❧t❛❞♦s ❣❡r❛✐s ❞♦ s✐st❡♠❛ ✐♥t❡❧✐❣❡♥t❡ ❤í❜r✐❞♦

❚é❝♥✐❝❛s ❞❡ ❚❛①❛ ❞❡ ❈❧❛ss✐✜❝❛çã♦ ✭♦✤✐♥❡✮ ❚❛①❛ ❞❡ ❈❧❛ss✐✜❝❛çã♦ ✭t❡♠♣♦ r❡❛❧✮❈❧❛ss✐✜❝❛çã♦ ❈♦rr❡t❛ ■♥❝♦rr❡t❛ ❈♦rr❡t❛ ■♥❝♦rr❡t❛

❘◆❆ ✶ ✾✾✱✼✼✼✹✪ ✵✱✷✷✷✻✪ ✾✾✱✺✺✼✽✪ ✵✱✹✹✷✷✪❘◆❆ ✷ ✾✾✱✼✻✸✾✪ ✵✱✷✸✻✶✪ ✾✾✱✺✺✼✽✪ ✵✱✹✹✷✷✪❘◆❆ ✸ ✾✾✱✼✻✷✽✪ ✵✱✷✸✼✷✪ ✾✾✱✺✺✹✾✪ ✵✱✹✹✺✶✪❘◆❆ ✹ ✾✾✱✼✺✸✸✪ ✵✱✷✹✻✼✪ ✾✾✱✺✺✹✸✪ ✵✱✹✹✺✼✪

❚♦t❛❧ ❞❡ ❘❡❣✐str♦s✿ ✷✶✷✽✻✻❚♦t❛❧ ❞❡ ❘❡❣✐str♦s ❈❧❛ss✐✜❝❛❞♦s✿ ✶✼✵✷✾✸

❚❛❜❡❧❛ ✹✳✼✳ ❘❡s✉❧t❛❞♦s ❞♦ s✐st❡♠❛ ✐♥t❡❧✐❣❡♥t❡ ❤í❜r✐❞♦ ✭♦✤✐♥❡✮

❚é❝♥✐❝❛s ❞❡ ◆♦r♠❛❧ ❆t❛q✉❡ ❋❛❧s♦ ❋❛❧s♦❈❧❛ss✐✜❝❛çã♦ ❱❡r❞✳ P♦s✐t✐✈♦s ❱❡r❞✳ P♦s✐t✐✈♦s P♦s✐t✐✈♦s ◆❡❣❛t✐✈♦s

❘◆❆ ✶ ✶✻✹✺✵✻ ✭✾✾✱✽✺✪✮ ✺✹✵✽ ✭✾✼✱✻✼✪✮ ✷✺✵ ✭✵✱✶✺✪✮ ✶✷✾ ✭✷✱✸✸✪✮❘◆❆ ✷ ✶✻✹✹✾✺ ✭✾✾✱✽✹✪✮ ✺✸✾✻ ✭✾✼✱✹✺✪✮ ✷✻✶ ✭✵✱✶✻✪✮ ✶✹✶ ✭✷✱✺✺✪✮❘◆❆ ✸ ✶✻✹✹✼✶ ✭✾✾✱✽✸✪✮ ✺✹✶✽ ✭✾✼✱✽✺✪✮ ✷✽✺ ✭✵✱✶✼✪✮ ✶✶✾ ✭✷✱✶✺✪✮❘◆❆ ✹ ✶✻✹✹✻✷ ✭✾✻✱✽✷✪✮ ✺✹✶✶ ✭✾✼✱✼✷✪✮ ✷✾✹ ✭✵✱✶✽✪✮ ✶✷✻ ✭✷✱✷✽✪✮

❈♦♥❢♦r♠❡ ♠♦str❛❞♦ ♥❛ ❚❛❜❡❧❛ ✹✳✻✱ ♣♦❞❡✲s❡ ✈❡r✐✜❝❛r q✉❡ ❡♠ ❛♠❜♦s ♦s ♠♦❞♦s ❞❡

❞❡t❡❝çã♦✱ ♦✤✐♥❡ ✭✶✸ ❡♥tr❛❞❛s✮ ❡ t❡♠♣♦ r❡❛❧ ✭✼ ❡♥tr❛❞❛s✮✱ ♦ ❆● ♣❡r♠✐t✐✉ ✉♠ ❛❝❡rt♦

✹✳ ❘❡s✉❧t❛❞♦s ✺✼

♠❛✐♦r ❞❛s t❛①❛s ❞❡ ❞❡t❡❝çã♦✱ ♣❡r♠✐t✐♥❞♦ q✉❡ ❛s ❘◆❆s ✉t✐❧✐③❛ss❡♠ ♥♦✈♦s ♣❛râ♠❡tr♦s

❝❛♣❛③❡s ❞❡ ❛♣r♦①✐♠❛r s✉❛s ❝❧❛ss✐✜❝❛çõ❡s ❞❡ ✉♠ ♠❡❧❤♦r ❣❧♦❜❛❧✳ ❙❡✉s ✈❛❧♦r❡s✱ ❝♦♥s✐❞❡✲

r❛♥❞♦ ♦ ♠♦❞♦ ♦✤✐♥❡✱ ❛♣r♦①✐♠❛r❛♠✲s❡ ❞♦s ❡♥❝♦♥tr❛❞♦s ♣❡❧❛ ❏✹✽✱ s✉♣❡r❛♥❞♦ ♦s ✈❛❧♦r❡s

❡♥❝♦♥tr❛❞♦s ❛tr❛✈és ❞❛s ❘◆❆s ❘❇❋ ❡ ▼▲P ♣❡❧❛s ❛❜♦r❞❛❣❡♥s ❍♦❧❞♦✉t ❡ ❞❡ ❱❛❧✐❞❛çã♦

❈r✉③❛❞❛✱ q✉❛♥❞♦ ✉t✐❧✐③❛❞❛s ❞❡ ❢♦r♠❛ ✐s♦❧❛❞❛✳

❆♦ ❝♦♠♣❛r❛r♠♦s ❝♦♠ ♦ tr❛❜❛❧❤♦ ❞❡ ❙✐❧✈❛ ❬✷✵✶✶❪✱ é ❝♦♥st❛t❛❞♦ t❛♠❜é♠ ✉♠❛ ♠❡✲

❧❤♦r❛ ♥❛s t❛①❛s ❞❡ ❛❝❡rt♦ ❡ ✉♠❛ ❞✐♠✐♥✉✐çã♦ ❞♦s ❛❧❛r♠❡s ❢❛❧s♦s✳ ❱❡r✐✜❝❛♠♦s q✉❡✱ ❛♣❡s❛r

❞❡ ✉t✐❧✐③❛r ✉♠❛ ❜❛s❡ ❞❡ ❞❛❞♦s ❞✐❢❡r❡♥t❡✱ ❛s té❝♥✐❝❛s ❝♦♠❜✐♥❛❞❛s ❝♦♥tr✐❜✉❡♠ ♣❛r❛ ✉♠❛

♠❡❧❤♦r ♣r❡❝✐sã♦✳

❚❛❜❡❧❛ ✹✳✽✳ ❘❡s✉❧t❛❞♦s ❞♦ s✐st❡♠❛ ✐♥t❡❧✐❣❡♥t❡ ❤í❜r✐❞♦ ✭t❡♠♣♦ r❡❛❧✮

❚é❝♥✐❝❛s ❞❡ ◆♦r♠❛❧ ❆t❛q✉❡ ❋❛❧s♦ ❋❛❧s♦❈❧❛ss✐✜❝❛çã♦ ❱❡r❞✳ P♦s✐t✐✈♦s ❱❡r❞✳ P♦s✐t✐✈♦s P♦s✐t✐✈♦s ◆❡❣❛t✐✈♦s

❘◆❆ ✶ ✶✻✹✷✼✻ ✭✾✾✱✼✶✪✮ ✺✷✻✹ ✭✾✺✱✵✼✪✮ ✹✽✵ ✭✵✱✷✾✪✮ ✷✼✸ ✭✹✱✾✸✪✮❘◆❆ ✷ ✶✻✹✷✽✹ ✭✾✾✱✼✶✪✮ ✺✷✺✻ ✭✾✹✱✾✸✪✮ ✹✼✷ ✭✵✱✷✾✪✮ ✷✽✶ ✭✺✱✵✼✪✮❘◆❆ ✸ ✶✻✹✷✻✹ ✭✾✾✱✼✵✪✮ ✺✷✼✶ ✭✾✺✱✷✵✪✮ ✹✾✷ ✭✵✱✸✵✪✮ ✷✻✻ ✭✹✱✽✵✪✮❘◆❆ ✹ ✶✻✹✷✻✽ ✭✾✾✱✼✵✪✮ ✺✷✻✻ ✭✾✺✱✶✶✪✮ ✹✽✽ ✭✵✱✸✵✪✮ ✷✼✶ ✭✹✱✽✾✪✮

P❛r❛ ♦ ♠♦❞♦ ❞❡ ❞❡t❡❝çã♦ ❡♠ t❡♠♣♦ r❡❛❧✱ ♦ ❙■❍ ♦❜t❡✈❡ ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡♠

r❡❧❛çã♦ às té❝♥✐❝❛s ◆❛✐✈❡ ❇❛②❡s✱ ❙❱▼✱ ❘◆❆ ❘❇❋ ❡ ❘◆❆ ▼▲P✱ ❡♥tr❡t❛♥t♦✱ ❛s ár✈♦r❡s

❞❡ ❞❡❝✐sã♦ ❛✐♥❞❛ ❛♣r❡s❡♥t❛r❛♠ ♦s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s✱ ❝♦♥❢♦r♠❡ ♠♦str❛❞♦ ♥❛s t❛❜❡❧❛s

✹✳✹ ❡ ✹✳✺✳

■ss♦ ♠♦str❛ q✉❡ ❛ ❣❡♥❡r❛❧✐③❛çã♦ ❞❛s ❘◆❆s ❣❛r❛♥t❡ ❛❧t❛s t❛①❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ♥❛

❜❛s❡ ❞❡ ❞❛❞♦s✱ ♣♦ré♠ ♦ r❡❝♦♥❤❡❝✐♠❡♥t♦ ❜❛s❡❛❞♦ ♥❛ ❛♥á❧✐s❡ ❞❡ s❡♠❡❧❤❛♥ç❛s ❞❡ ❞❛❞♦s✱

❢♦r♥❡❝✐❞♦ ♣❡❧❛s ár✈♦r❡s ❞❡ ❞❡❝✐sã♦✱ ❛✐♥❞❛ ❝♦♥s❡❣✉✐✉ ❛♣r❡s❡♥t❛r t❛①❛s ♠❛✐♦r❡s ❞❡ ❛❝❡rt♦✱

❞❡♠♦♥str❛♥❞♦ q✉❡ ❛ ❛♥á❧✐s❡ ❣❡♥❡r❛❧✐③❛❞❛ ❞♦s ❞❛❞♦s ♣♦ss✉✐ ❧✐♠✐t❛çõ❡s ❡ q✉❡ ❛❧❣♦r✐t♠♦s

q✉❡ tr❛❜❛❧❤❛♠ ♥♦ ❛❣r✉♣❛♠❡♥t♦ ❞❡ s✐♠✐❧❛r✐❞❛❞❡s ♣♦ss✉❡♠ ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ♣❛r❛ ❡ss❡

t✐♣♦ ❞❡ ❞❛❞♦s✳

❈❛♣ít✉❧♦ ✺

❈♦♥❝❧✉sõ❡s

❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❡r♠✐t❡♠ ❝♦♥❝❧✉✐r q✉❡ ❛s ♠❡❧❤♦r❡s té❝♥✐❝❛s ♣♦❞❡♠ s❡r ❝♦♠❜✐✲

♥❛❞❛s ❡♠ ✉♠ s✐st❡♠❛ ❞❡ ❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sã♦ r❡❛❧ ❡✱ ❛ss✐♠✱ ❞❡♣❡♥❞❡♥❞♦ ❞♦ ❛♠❜✐❡♥t❡✱

♣♦❞❡✲s❡ ♦♣t❛r ♣♦r ✉♠❛ ♦✉ ♣♦r ♦✉tr❛✱ ♦✉ ♣♦r ✉♠ ❝♦♥❥✉♥t♦ ❞❡❧❛s✳ ❈♦♠♦ ❡①❡♠♣❧♦s✱ ✈ár✐♦s

♣r♦❞✉t♦s ❛t✉❛❧♠❡♥t❡ ❞♦ ♠❡r❝❛❞♦ ✉t✐❧✐③❛♠ ❛ ❛❜♦r❞❛❣❡♠ ❞❡ ❞❡t❡❝çã♦ ❤í❜r✐❞❛✱ ❛♣❡s❛r ❞❡

♥ã♦ ✐♥❢♦r♠❛r❡♠ ❝❡rt❛♠❡♥t❡ q✉❛✐s té❝♥✐❝❛s ✉t✐❧✐③❛♠✱ ❛❧❣✉♥s ❝♦♠♦ ♦ ❆❦❡r ❋✐r❡✇❛❧❧✱ ♣❡r✲

♠✐t❡ ❡st❡♥❞❡r ♦ ♣r♦❞✉t♦ ❝♦♠ ✉♠ ♠ó❞✉❧♦ ❞❡ ■❉❙ ❡①t❡r♥♦✱ q✉❡ ♣♦❞❡ s❡r ❞❡s❡♥✈♦❧✈✐❞♦

♦✉ ✉t✐❧✐③❛❞♦ ❝♦♠ ♦✉tr♦ ♣r♦❞✉t♦✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦ ♦ s♦❢t✇❛r❡ ♦♣❡♥s♦✉r❝❡ ❙♥♦rt✳

❆♦ ❝❧❛ss✐✜❝❛r ♦s r❡❣✐str♦s ❞❛ ❜❛s❡ ■❙❈❳ ✷✵✶✷ é ♣♦ss✐✈❡❧ ❝♦♥❝❧✉✐r t❛♠❜é♠ q✉❡ ❛s

té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✉t✐❧✐③❛❞❛s sã♦ ♣r♦♠✐ss♦r❛s ♠❡s♠♦ ♥❛s ❜❛s❡s ♠❛✐s r❡❝❡♥t❡s✱ ❡♠

q✉❡ ♦ ♣❡r✜❧ ❞❡ trá❢❡❣♦ t❡♥❞❡ ❛ s❡r ❞✐❢❡r❡♥t❡✳ ❊ ❝♦♠ ❛ t❡♥❞ê♥❝✐❛ ❞❡ ✈❛r✐❛❜✐❧✐❞❛❞❡ ♥♦

♣❡r✜❧ ❞❡ trá❢❡❣♦ ❡♠ r❡❞❡s r❡❛✐s✱ é ✐♠♣♦rt❛♥t❡ ✐♥✈❡st✐❣❛r té❝♥✐❝❛s q✉❡ t❡♥❤❛♠ ❝❛♣❛❝✐❞❛❞❡

❞❡ ❛❞❛♣t❛çã♦ às ❜❛s❡s ❞❡ ❞❛❞♦s ❞❡ ♣❡r✜s ❞❡ trá❢❡❣♦ ❞✐❢❡r❡♥t❡s✳

◆❛ ✉t✐❧✐③❛çã♦ ❞❛s ❛❜♦r❞❛❣❡♥s ❍♦❧❞♦✉t ❡ ❱❛❧✐❞❛çã♦ ❈r✉③❛❞❛✱ ❛s té❝♥✐❝❛s ❘❛♥❞♦♠

❋♦r❡st ❡ ◆❇❚r❡❡✱ ♣♦r ❡①❡♠♣❧♦✱ ❛♣r❡s❡♥t❛r❛♠ ♦s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s q✉❛♥t♦ à ♣r❡❝✐sã♦✱

♠❛s ❡♠ r❡❧❛çã♦ ❛♦ t❡♠♣♦ ❣❛st♦ ♣❛r❛ ❝r✐❛çã♦ ❞♦ ♠♦❞❡❧♦✱ ❢♦r❛♠ ♣✐♦r❡s ❞♦ q✉❡ ❛s ❞❡♠❛✐s✳

◆❡st❡ ❝❛s♦✱ ♦ ❛♠❜✐❡♥t❡ q✉❡ ♥❡❝❡ss✐t❛ ❞❡ ✉♠ ♠❡❧❤♦r t❡♠♣♦ ❞❡ r❡s♣♦st❛✱ ❝♦♠♦ ✉♠❛

❞❡t❡❝çã♦ ❡♠ t❡♠♣♦ r❡❛❧ ❡ q✉❡ ♣♦ss✉❛ ✉♠ ❣r❛♥❞❡ ✈♦❧✉♠❡ ❞❡ ❞❛❞♦s✱ ❛ ❛♣❧✐❝❛çã♦ ❞❛

té❝♥✐❝❛ q✉❡ ❣❛st❡ ♠❡♥♦s t❡♠♣♦ t♦r♥❛✲s❡ ♠❛✐s ❛♣r♦♣r✐❛❞❛✳

❊♥tr❡t❛♥❞♦✱ ❡♠ ✉♠ ❛♠❜✐❡♥t❡✱ ♦♥❞❡ ❛ ❞❡t❡❝çã♦ s❡❥❛ ❡♠ ♠♦❞♦ ♦✤✐♥❡ ♦✉ q✉❡

t❡♥❤❛ ✉♠ ✈♦❧✉♠❡ ♠❡♥♦r ❞❡ ❞❛❞♦s✱ ♦✉ q✉❡ ♦ s✐st❡♠❛ ❝♦♠♣✉t❛❝✐♦♥❛❧ s❡❥❛ ♠❛✐s r♦❜✉st♦✱

❛ ◆❇❚r❡❡ ❡ ❘❛♥❞♦♠ ❋♦r❡st sã♦ ❛s ♠❛✐s ❛❞❡q✉❛❞❛s✳

❆♦ ❝♦♥s✐❞❡r❛r♠♦s ✉♠❛ ❞❡t❡❝çã♦ ❡♠ t❡♠♣♦ r❡❛❧✱ ♥♦ss♦ tr❛❜❛❧❤♦ ❡❧✐♠✐♥♦✉ ❛❧❣✉♥s

❛tr✐❜✉t♦s r❡❢❡r❡♥t❡s ❛♦ ❞❡st✐♥♦✳ ◆❡st❡ ❝❡♥ár✐♦✱ ❛ té❝♥✐❝❛ ♠❛✐s ❛♣r♦♣r✐❛❞❛ ❢♦✐ ❛ ◆❇❚r❡❡✱

❡♠❜♦r❛✱ ❛ té❝♥✐❝❛ ❘❛♥❞♦♠ ❋♦r❡st t❡♥❤❛ ❞❡t❡❝t❛❞♦ ♠❡❧❤♦r ♦ trá❢❡❣♦ ♥♦r♠❛❧✳

❆ ❝♦♠❜✐♥❛çã♦ ❞♦ ❆● ❡ ❞❛s ❘◆❆s ♣❡r♠✐t✐✉ ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s✱ ❢♦r♠❛♥❞♦ ✉♠

✺✽

✺✳ ❈♦♥❝❧✉sõ❡s ✺✾

❙✐st❡♠❛ ■♥t❡❧✐❣❡♥t❡ ❍í❜r✐❞♦ ✭❙■❍✮✳ ◆❡st❡ ❝❛s♦✱ ♦ ❆● ❡♥❝♦♥tr♦✉ ♠❡❧❤♦r❡s ♣❛râ♠❡tr♦s

♣❛r❛ ❛s ❘◆❆s✱ ♠✐♥✐♠✐③❛♥❞♦ s❡✉s ♣r♦❜❧❡♠❛s ❡♠ r❡❧❛çã♦ à ❡s❝♦❧❤❛ ✐♥✐❝✐❛❧ ❞♦s ♣❛râ♠❡tr♦s✳

❉❡ss❛ ❢♦r♠❛✱ ❛ ❛♣❧✐❝❛çã♦ ❞❡ ❞❡t❡r♠✐♥❛❞❛s té❝♥✐❝❛s s❡❧❡❝✐♦♥❛❞❛s ♣❡r♠✐t❡ ❝♦♠❜✐♥❛r ❛s

s✉❛s ✈❛♥t❛❣❡♥s ❡ ♠✐♥✐♠✐③❛r s✉❛s ❞❡s✈❛♥t❛❣❡♥s✱ s❡♥❞♦ ✉♠❛ t❡♥❞ê♥❝✐❛ ♣❛r❛ r❡❛❧✐③❛r ♥♦✈❛s

❝♦♠❜✐♥❛çõ❡s✱ ❛✉♠❡♥t❛♥❞♦ ❝❛❞❛ ✈❡③ ♠❛✐s ❛ ♣r❡❝✐sã♦ ❞♦s r❡s✉❧t❛❞♦s✳

◆♦s ❞✐✈❡rs♦s tr❛❜❛❧❤♦s r❡❧❛❝✐♦♥❛❞♦s✱ ♠❡s♠♦ ✉t✐❧✐③❛♥❞♦ ❜❛s❡s ❞❡ ❞❛❞♦s ❞✐❢❡r❡♥t❡s✱

❛s té❝♥✐❝❛s ✉t✐❧✐③❛❞❛s sã♦ ✐♠♣♦rt❛♥t❡s ♣❛r❛ ♣r♦✈❡r ❛ s❡❣✉r❛♥ç❛ ❞❛s r❡❞❡s ❡ ❝♦♠♣✉t❛❞♦r❡s

❡✱ ♦ ❢❛t♦ ❞❡st❡ tr❛❜❛❧❤♦ t❡r ✉t✐❧✐③❛❞♦ ✉♠❛ ❜❛s❡ ❞❡ ❞❛❞♦s ❞❡ ♣❡r✜s ❞❡ trá❢❡❣♦ ♠❛✐s r❡❝❡♥t❡

❡ ❛s té❝♥✐❝❛s t❡r❡♠ ❛♣r❡s❡♥t❛❞♦ r❡s✉❧t❛❞♦s ♣r♦♠✐ss♦r❡s✱ ♠♦t✐✈❛ ❛ ✉t✐❧✐③❛r ❡ ❡st❡♥❞❡r

❡st❛s té❝♥✐❝❛s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❝r✐❛♥❞♦ ♦✉tr♦s s✐st❡♠❛s ✐♥t❡❧✐❣❡♥t❡s ❤í❜r✐❞♦s✱ q✉❡

♣❡r♠✐t✐rã♦ ❡✈♦❧✉✐r ❝❛❞❛ ✈❡③ ♠❛✐s ♦s s✐st❡♠❛s ❞❡ ❞❡❝t❡❝çã♦ ❡ ♣r❡✈❡♥çã♦ ❞❡ ✐♥tr✉sõ❡s✳

❈♦♠♦ tr❛❜❛❧❤♦s ❢✉t✉r♦s s✉❣❡r❡✲s❡ ❛ ❝r✐❛çã♦ ❞❡ ✉♠ ❝❧❛ss✐✜❝❛❞♦r q✉❡ ✐❞❡♥t✐✜q✉❡

❝❛❞❛ t✐♣♦ ❞❡ ❛t❛q✉❡✱ ❛♣❧✐❝❛♥❞♦ ♦ ❛❧❣♦r✐t♠♦ q✉❡ ♠❡❧❤♦r ❛♣r❡s❡♥t♦✉ r❡s♣♦st❛s✱ ❛❧é♠ ❞❡

r❡❛❧✐③❛r ❛ ❝❧❛ss✐✜❝❛çã♦ ❞❛s ✐♥tr✉sõ❡s ✉t✐❧✐③❛♥❞♦ ♠❛✐s té❝♥✐❝❛s ❞❡ ■❆ ❞❡ ❢♦r♠❛ ❝♦♠❜✐♥❛❞❛

❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ♠❡❧❤♦r❛r ❛s t❛①❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❡ t❡♠♣♦ ❣❛st♦✳ P♦❞❡✲s❡ t❛♠❜é♠

r❡❛❧✐③❛r ❛ ❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sõ❡s ❛ ♣❛rt✐r ❞❡ ✉♠❛ ✐♥s♣❡çã♦ ♣r♦❢✉♥❞❛ ❞♦s ❞❛❞♦s ❛tr❛✈és

❞♦s ♣❛②❧♦❛❞s ❞❛ ❜❛s❡ ■❙❈❳ ✷✵✶✷✱ ❡ ♥ã♦ ❛♣❡♥❛s ❛ ♣❛rt✐r ❞❡ ✐♥❢♦r♠❛çõ❡s ❞♦s ♥í✈❡✐s ❞❡

r❡❞❡ ❡ ❞❡ tr❛♥s♣♦rt❡✳ ❆❧é♠ ❞✐ss♦✱ ❛s ♣ró♣r✐❛s ❜✐❜❧✐♦t❡❝❛s ❡♠ ❏❛✈❛ ❞♦ s♦❢t✇❛r❡ ❲❡❦❛✱ ♦✉

❛s ❜✐❜❧✐♦t❡❝❛s ❡♠ P②t❤♦♥✱ ♣♦❞❡♠ s❡r ✉t✐❧✐③❛❞❛s ♣❛r❛ ❞❡s❡♥✈♦❧✈❡r ♦✉ ❡st❡♥❞❡r ❡♠ ✉♠

s✐st❡♠❛ ❞❡ ■❉❙✴■P❙ r❡❛❧✳

❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s

❆❧✲❏❛♥❛❜✐✱ ❙✳ ✫ ❙❛❡❡❞✱ ❍✳ ✭✷✵✶✶✮✳ ❆ ♥❡✉r❛❧ ♥❡t✇♦r❦ ❜❛s❡❞ ❛♥♦♠❛❧② ✐♥tr✉s✐♦♥ ❞❡t❡❝t✐♦♥

s②st❡♠✳ ❊♠ ❉❡✈❡❧♦♣♠❡♥ts ✐♥ ❊✲s②st❡♠s ❊♥❣✐♥❡❡r✐♥❣ ✭❉❡❙❊✮✱ ♣♣✳ ✷✷✶✕✷✷✻✳

❆rt❡r♦✱ ❆✳ ❖✳ ✭✷✵✵✾✮✳ ■♥t❡❧✐❣ê♥❝✐❛ ❆rt✐✜❝✐❛❧✿ ❚❡ór✐❝❛ ❡ Prát✐❝❛✳ ▲✐✈r❛r✐❛ ❞❛ ❋ís✐❝❛✱ ✶

❡❞✐çã♦✳ ■❙❇◆ ✾✼✽✽✺✼✽✻✶✵✷✾✻✳

❇r❛❣❛✱ ❆✳ ❞✳ P✳❀ ❈❛r✈❛❧❤♦✱ ❆✳ P✳ ❞✳ ▲✳ ❋✳ ❞✳ ✫ ▲✉❞❡r♠✐r✱ ❚✳ ❇✳ ✭✷✵✵✼✮✳ ❘❡❞❡s ♥❡✉r❛✐s

❛rt✐✜❝✐❛✐s✿ t❡♦r✐❛ ❡ ❛♣❧✐❝❛çõ❡s✳ ▲❚❈ ❊❞✐t♦r❛✱ ✷ ❡❞✐çã♦✳ ■❙❇◆ ✾✼✽✽✺✷✶✻✶✺✻✹✹✳

❇r✐tt✱ ❲✳❀ ●♦♣❛❧❛s✇❛♠②✱ ❙✳❀ ❍❛♠✐❧t♦♥✱ ❏✳ ❆✳❀ ❉♦③✐❡r✱ ●✳ ❱✳ ✫ ❈❤❛♥❣✱ ❑✳ ❍✳ ✭✷✵✵✼✮✳

❈♦♠♣✉t❡r ❞❡❢❡♥s❡ ✉s✐♥❣ ❛rt✐✜❝✐❛❧ ✐♥t❡❧❧✐❣❡♥❝❡✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✷✵✵✼ s♣r✐♥❣

s✐♠✉❧❛t✐♦♥ ♠✉❧t✐❝♦♥❢❡r❡♥❝❡✱ ✈♦❧✉♠❡ ✸ ♦❢ ❙♣r✐♥❣❙✐♠ ✬✵✼✱ ♣♣✳ ✸✼✽✕✸✽✻✱ ❙❛♥ ❉✐❡❣♦✱

❈❆✱ ❯❙❆✳ ❙♦❝✐❡t② ❢♦r ❈♦♠♣✉t❡r ❙✐♠✉❧❛t✐♦♥ ■♥t❡r♥❛t✐♦♥❛❧✳

❇✉❦❤t♦②❛r♦✈✱ ❱✳ ✫ ❙❡♠❡♥❦✐♥✱ ❊✳ ✭✷✵✶✷✮✳ ◆❡✉r❛❧ ♥❡t✇♦r❦s ❡♥s❡♠❜❧❡ ❛♣♣r♦❛❝❤ ❢♦r ❞❡✲

t❡❝t✐♥❣ ❛tt❛❝❦s ✐♥ ❝♦♠♣✉t❡r ♥❡t✇♦r❦s✳ ❊♠ ❊✈♦❧✉t✐♦♥❛r② ❈♦♠♣✉t❛t✐♦♥ ✭❈❊❈✮✱ ✷✵✶✷

■❊❊❊ ❈♦♥❣r❡ss✱ ♣♣✳ ✶✕✻✳

❈❊❘❚✳❜r ✭✷✵✶✹✮✳ ❊st❛tíst✐❝❛s ❞♦s ✐♥❝✐❞❡♥t❡s r❡♣♦rt❛❞♦s✳ ❉✐s♣♦♥í✈❡❧ ❡♠✿

❤tt♣✿✴✴✇✇✇✳❝❡rt✳❜r✴st❛ts✴✐♥❝✐❞❡♥t❡s✴✳

❈❤❛♥❣✱ ❈✳✲❈✳ ✫ ▲✐♥✱ ❈✳✲❏✳ ✭✷✵✶✶✮✳ ▲■❇❙❱▼✿ ❆ ❧✐❜r❛r② ❢♦r s✉♣♣♦rt ✈❡❝t♦r ♠❛❝❤✐♥❡s✳

❆❈▼ ❚r❛♥s❛❝t✐♦♥s ♦♥ ■♥t❡❧❧✐❣❡♥t ❙②st❡♠s ❛♥❞ ❚❡❝❤♥♦❧♦❣②✱ ✷✿✷✼✿✶✲✲✷✼✿✷✼✳ ❉✐s♣♦♥í✈❡❧

❡♠✿ ❤tt♣✿✴✴✇✇✇✳❝s✐❡✳♥t✉✳❡❞✉✳t✇✴ ❝❥❧✐♥✴❧✐❜s✈♠✳

❉❡✈❛r❛❥✉✱ ❙✳ ✫ ❘❛♠❛❦r✐s❤♥❛♥✱ ❙✳ ✭✷✵✶✶✮✳ P❡r❢♦r♠❛♥❝❡ ❛♥❛❧②s✐s ♦❢ ✐♥tr✉s✐♦♥ ❞❡t❡❝t✐♦♥

s②st❡♠ ✉s✐♥❣ ✈❛r✐♦✉s ♥❡✉r❛❧ ♥❡t✇♦r❦ ❝❧❛ss✐✜❡rs✳ ❊♠ ❘❡❝❡♥t ❚r❡♥❞s ✐♥ ■♥❢♦r♠❛t✐♦♥

❚❡❝❤♥♦❧♦❣② ✭■❈❘❚■❚✮✱ ✷✵✶✶ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡✱ ♣♣✳ ✶✵✸✸✕✶✵✸✽✳

❉♦✉❧✐❣❡r✐s✱ ❈✳ ✫ ❙❡r♣❛♥♦s✱ ❉✳ ✭✷✵✵✼✮✳ ◆❡t✇♦r❦ s❡❝✉r✐t②✿ ❝✉rr❡♥t st❛t✉s ❛♥❞ ❢✉t✉r❡

❞✐r❡❝t✐♦♥s✳ ❲✐❧❡② ❊❞✐t♦r❛✳ ■❙❇◆ ✾✼✽✵✹✼✶✼✵✸✺✺✻✳

✻✵

❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá❢✐❝❛s ✻✶

❋❆◆◆ ✭✷✵✶✶✮✳ ❋❛♥♥✿ ❋❛st ❛rt✐✜❝✐❛❧ ♥❡✉r❛❧ ♥❡t✇♦r❦ ❧✐❜r❛r②✳ ❆❝❡ss♦ ❡♠✿ ❏✉❧❤♦ ❞❡ ✷✵✶✸✳

❉✐s♣♦♥í✈❡❧ ❡♠✿ ❤tt♣✿✴✴❧❡❡♥✐ss❡♥✳❞❦✴❢❛♥♥✴✇♣✴✳

❍❛♥✱ ❏✳❀ ❑❛♠❜❡r✱ ▼✳ ✫ P❡✐✱ ❏✳ ✭✷✵✶✶✮✳ ❉❛t❛ ▼✐♥✐♥❣✿ ❈♦♥❝❡♣ts ❛♥❞ ❚❡❝❤♥✐q✉❡s✿ ❈♦♥✲

❝❡♣ts ❛♥❞ ❚❡❝❤♥✐q✉❡s✳ ❚❤❡ ▼♦r❣❛♥ ❑❛✉❢♠❛♥♥ ❙❡r✐❡s ✐♥ ❉❛t❛ ▼❛♥❛❣❡♠❡♥t ❙②st❡♠s✳

❊❧s❡✈✐❡r ❙❝✐❡♥❝❡ ❊❞✐t♦r❛✳ ■❙❇◆ ✾✼✽✵✶✷✸✽✶✹✽✵✼✳

❑❉❉✲❈✉♣ ✭✶✾✾✾✮✳ ❑❞❞✲❝✉♣ ✶✾✾✾ ❞❛t❛ s❡t✳ ❆❝❡ss♦ ❡♠✿ ❏✉❧❤♦ ❞❡ ✷✵✶✸✳ ❉✐s♣♦♥í✈❡❧ ❡♠✿

❤tt♣✿✴✴❦❞❞✳✐❝s✳✉❝✐✳❡❞✉✴❞❛t❛❜❛s❡s✴❦❞❞❝✉♣✾✾✴❦❞❞❝✉♣✾✾✳❤t♠❧✳

❑✉r♦s❡✱ ❏✳ ✫ ❘♦ss✱ ❑✳ ✭✷✵✶✵✮✳ ❘❡❞❡s ❞❡ ❝♦♠♣✉t❛❞♦r❡s ❡ ❛ ✐♥t❡r♥❡t✿ ✉♠❛ ❛❜♦r❞❛❣❡♠

t♦♣✲❞♦✇♥✳ P❡❛rs♦♥ ❊❞✐t♦r❛✳ ■❙❇◆ ✾✼✽✽✺✽✽✻✸✾✾✼✸✳

▲❛rs♦♥✱ ❘✳ ✫ ❋❛r❜❡r✱ ❇✳ ✭✷✵✵✹✮✳ ❊st❛tíst✐❝❛ ❛♣❧✐❝❛❞❛✳ Pr❡♥t✐❝❡ ❍❛❧❧ ❊❞✐t♦r❛✱ ✷ ❡❞✐çã♦✳

■❙❇◆ ✾✼✽✽✺✽✼✾✶✽✺✾✽✳

▲✐✱ ❋✳ ✭✷✵✶✵✮✳ ❍②❜r✐❞ ♥❡✉r❛❧ ♥❡t✇♦r❦ ✐♥tr✉s✐♦♥ ❞❡t❡❝t✐♦♥ s②st❡♠ ✉s✐♥❣ ❣❡♥❡t✐❝ ❛❧❣♦✲

r✐t❤♠✳ ❊♠ ▼✉❧t✐♠❡❞✐❛ ❚❡❝❤♥♦❧♦❣② ✭■❈▼❚✮✱ ✷✵✶✵ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡✱ ♣♣✳ ✶✕✹✳

▼❛r❤✉s✐♥✱ ▼✳❀ ❈♦r♥❢♦rt❤✱ ❉✳ ✫ ▲❛r❦✐♥✱ ❍✳ ✭✷✵✵✽✮✳ ❆♥ ♦✈❡r✈✐❡✇ ♦❢ r❡❝❡♥t ❛❞✈❛♥❝❡s ✐♥

✐♥tr✉s✐♦♥ ❞❡t❡❝t✐♦♥✳ ❊♠ ❈♦♠♣✉t❡r ❛♥❞ ■♥❢♦r♠❛t✐♦♥ ❚❡❝❤♥♦❧♦❣②✱ ✷✵✵✽✳ ❈■❚ ✷✵✵✽✳

✽t❤ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡✱ ♣♣✳ ✹✸✷✕✹✸✼✳

▼❝❍✉❣❤✱ ❏✳ ✭✷✵✵✵✮✳ ❚❡st✐♥❣ ✐♥tr✉s✐♦♥ ❞❡t❡❝t✐♦♥ s②st❡♠s✿ ❛ ❝r✐t✐q✉❡ ♦❢ t❤❡ ✶✾✾✽ ❛♥❞ ✶✾✾✾

❞❛r♣❛ ✐♥tr✉s✐♦♥ ❞❡t❡❝t✐♦♥ s②st❡♠ ❡✈❛❧✉❛t✐♦♥s ❛s ♣❡r❢♦r♠❡❞ ❜② ❧✐♥❝♦❧♥ ❧❛❜♦r❛t♦r②✳

❆❈▼ ❚r❛♥s✳ ■♥❢✳ ❙②st✳ ❙❡❝✉r✳✱ ✸✭✹✮✿✷✻✷✲✲✷✾✹✳ ■❙❙◆ ✶✵✾✹✲✾✷✷✹✳

▼③✐❧❛✱ P✳ ✫ ❉✉❜❡✱ ❊✳ ✭✷✵✶✸✮✳ ❚❤❡ ❡✛❡❝t ♦❢ ❞❡st✐♥❛t✐♦♥ ❧✐♥❦❡❞ ❢❡❛t✉r❡ s❡❧❡❝t✐♦♥ ✐♥ r❡❛❧✲

t✐♠❡ ♥❡t✇♦r❦ ✐♥tr✉s✐♦♥ ❞❡t❡❝t✐♦♥✳ ❊♠ ■❈■▼P ✷✵✶✸ ✿ ✽t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡

♦♥ ■♥t❡r♥❡t ▼♦♥✐t♦r✐♥❣ ❛♥❞ Pr♦t❡❝t✐♦♥✳

◆❙▲✲❑❉❉ ✭✷✵✵✾✮✳ ❚❤❡ ♥s❧✲❦❞❞ ❞❛t❛ s❡t✳ ❆❝❡ss♦ ❡♠✿ ❏✉❧❤♦ ❞❡ ✷✵✶✸✳ ❉✐s♣♦♥í✈❡❧ ❡♠✿

❤tt♣✿✴✴♥s❧✳❝s✳✉♥❜✳❝❛✴◆❙▲✲❑❉❉✴✳

P❛❝❤❣❤❛r❡✱ ❱✳ ❑✳ ✫ ❑✉❧❦❛r♥✐✱ P✳ ✭✷✵✶✶✮✳ P❛tt❡r♥ ❜❛s❡❞ ♥❡t✇♦r❦ s❡❝✉r✐t② ✉s✐♥❣ ❞❡❝✐s✐♦♥

tr❡❡s ❛♥❞ s✉♣♣♦rt ✈❡❝t♦r ♠❛❝❤✐♥❡✳ ❊♠ ❊❧❡❝tr♦♥✐❝s ❈♦♠♣✉t❡r ❚❡❝❤♥♦❧♦❣② ✭■❈❊❈❚✮✱

✷✵✶✶ ✸r❞ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡✱ ✈♦❧✉♠❡ ✺✱ ♣♣✳ ✷✺✹✕✷✺✼✳

P❛t❝❤❛✱ ❆✳ ✫ P❛r❦✱ ❏✳ ✭✷✵✵✼✮✳ ❆♥ ♦✈❡r✈✐❡✇ ♦❢ ❛♥♦♠❛❧② ❞❡t❡❝t✐♦♥ t❡❝❤♥✐q✉❡s✿ ❊①✐st✐♥❣

s♦❧✉t✐♦♥s ❛♥❞ ❧❛t❡st t❡❝❤♥♦❧♦❣✐❝❛❧ tr❡♥❞s✳ ❈♦♠♣✉t❡r ◆❡t✇♦r❦s✱ ✷✵✵✼✱ ✺✶✭✶✷✮✿✸✹✹✽✕

✸✹✼✵✳

❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá❢✐❝❛s ✻✷

❘❡③❡♥❞❡✱ ❙✳ ✭✷✵✵✺✮✳ ❙✐st❡♠❛s ■♥t❡❧✐❣❡♥t❡s✿ ❋✉♥❞❛♠❡♥t♦s ❡ ❆♣❧✐❝❛çõ❡s✳ ▼❛♥♦❧❡ ❊❞✐t♦r❛✳

■❙❇◆ ✾✼✽✽✺✷✵✹✶✻✽✸✾✳

❙❛❧❧❛②✱ ❍✳❀ ❆♠♠❛r✱ ❆✳❀ ❇❡♥ ❙❛❛❞✱ ▼✳ ✫ ❇♦✉r♦✉✐s✱ ❙✳ ✭✷✵✶✸✮✳ ❆ r❡❛❧ t✐♠❡ ❛❞❛♣t✐✈❡

✐♥tr✉s✐♦♥ ❞❡t❡❝t✐♦♥ ❛❧❡rt ❝❧❛ss✐✜❡r ❢♦r ❤✐❣❤ s♣❡❡❞ ♥❡t✇♦r❦s✳ ❊♠ ◆❡t✇♦r❦ ❈♦♠♣✉t✐♥❣

❛♥❞ ❆♣♣❧✐❝❛t✐♦♥s ✭◆❈❆✮✱ ✷✵✶✸ ✶✷t❤ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❙②♠♣♦s✐✉♠ ♦♥✱ ♣♣✳ ✼✸✕✽✵✳

❙❤✐r❛✈✐✱ ❆✳❀ ❙❤✐r❛✈✐✱ ❍✳❀ ❚❛✈❛❧❧❛❡❡✱ ▼✳ ✫ ●❤♦r❜❛♥✐✱ ❆✳ ❆✳ ✭✷✵✶✷✮✳ ❚♦✇❛r❞ ❞❡✈❡❧♦✲

♣✐♥❣ ❛ s②st❡♠❛t✐❝ ❛♣♣r♦❛❝❤ t♦ ❣❡♥❡r❛t❡ ❜❡♥❝❤♠❛r❦ ❞❛t❛s❡ts ❢♦r ✐♥tr✉s✐♦♥ ❞❡t❡❝t✐♦♥✳

❈♦♠♣✉t❡rs ❛♥❞ ❙❡❝✉r✐t②✱ ✸✶✭✸✮✿✸✺✼✕✸✼✹✳ ■❙❙◆ ✵✶✻✼✲✹✵✹✽✳

❙✐❧✈❛✱ ❏✳ ❘✳ ❈✳ ❞✳ ✭✷✵✶✶✮✳ ❙✐st❡♠❛s ❞❡ ❞❡t❡❝çã♦ ❞❡ ✐♥tr✉sã♦ ❝♦♠ té❝♥✐❝❛s ❞❡ ✐♥t❡❧✐❣ë♥❝✐❛

❛rt✐✜❝✐❛❧✳ ✷✵✶✶✳ ✶✺✼ ❢✳ ❉✐ss❡rt❛çã♦ ❞❡ ♠❡str❛❞♦✱ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠

❈✐ë♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✱ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❱✐ç♦s❛✱ ❱✐ç♦s❛ ✲ ▼●✳

❙t❛❧❧✐♥❣s✱ ❲✳ ✭✷✵✶✵✮✳ ◆❡t✇♦r❦ ❙❡❝✉r✐t② ❊ss❡♥t✐❛❧s✿ ❆♣♣❧✐❝❛t✐♦♥s ❛♥❞ ❙t❛♥❞❛r❞s✳ Pr❡♥✲

t✐❝❡ ❍❛❧❧ ❊❞✐t♦r❛✳ ■❙❇◆ ✾✼✽✵✶✸✻✶✵✽✵✺✹✳

❚❛♥✱ P✳❀ ❙t❡✐♥❜❛❝❤✱ ▼✳ ✫ ❑✉♠❛r✱ ❱✳ ✭✷✵✵✾✮✳ ■♥tr♦❞✉çã♦ ❛♦ ❞❛t❛♠✐♥✐♥❣✿ ♠✐♥❡r❛çã♦ ❞❡

❞❛❞♦s✳ ❈✐ë♥❝✐❛ ▼♦❞❡r♥❛ ❊❞✐t♦r❛✳ ■❙❇◆ ✾✼✽✽✺✼✸✾✸✼✻✶✾✳

❚❛♥❡♥❜❛✉♠✱ ❆✳ ❙✳ ✭✷✵✶✶✮✳ ❘❡❞❡s ❞❡ ❝♦♠♣✉t❛❞♦r❡s✳ P❡❛rs♦♥ ❊❞✐t♦r❛✳ ■❙❇◆

✾✼✽✽✺✼✻✵✺✾✷✹✵✳

❚❛✈❛❧❧❛❡❡✱ ▼✳❀ ❇❛❣❤❡r✐✱ ❊✳❀ ▲✉✱ ❲✳ ✫ ●❤♦r❜❛♥✐✱ ❆✳ ✭✷✵✵✾✮✳ ❆ ❞❡t❛✐❧❡❞ ❛♥❛❧②s✐s ♦❢

t❤❡ ❦❞❞ ❝✉♣ ✾✾ ❞❛t❛ s❡t✳ ❊♠ ❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ❢♦r ❙❡❝✉r✐t② ❛♥❞ ❉❡❢❡♥s❡

❆♣♣❧✐❝❛t✐♦♥s✱ ✷✵✵✾✳ ❈■❙❉❆ ✷✵✵✾✳ ■❊❊❊ ❙②♠♣♦s✐✉♠✱ ♣♣✳ ✶✕✻✳

❲❡❦❛ ✭✷✵✶✸✮✳ ❲❡❦❛ ✸✿ ❉❛t❛ ♠✐♥✐♥❣ s♦❢t✇❛r❡ ✐♥ ❥❛✈❛✳ ❆❝❡ss♦ ❡♠✿ ❏✉❧❤♦ ❞❡ ✷✵✶✸✳

❉✐s♣♦♥í✈❡❧ ❡♠✿ ❤tt♣✿✴✴✇✇✇✳❝s✳✇❛✐❦❛t♦✳❛❝✳♥③✴♠❧✴✇❡❦❛✴✳

❩❤❛♥❣✱ ❘✳❀ ◗✐❛♥✱ ❉✳❀ ❇❛✱ ❈✳❀ ❲✉✱ ❲✳ ✫ ●✉♦✱ ❳✳ ✭✷✵✵✶✮✳ ▼✉❧t✐✲❛❣❡♥t ❜❛s❡❞ ✐♥tr✉✲

s✐♦♥ ❞❡t❡❝t✐♦♥ ❛r❝❤✐t❡❝t✉r❡✳ ❊♠ ❈♦♠♣✉t❡r ◆❡t✇♦r❦s ❛♥❞ ▼♦❜✐❧❡ ❈♦♠♣✉t✐♥❣✱ ✷✵✵✶✳

Pr♦❝❡❡❞✐♥❣s✳ ✷✵✵✶ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡✱ ♣♣✳ ✹✾✹✕✺✵✶✳

❆♥❡①♦ ❆

❈ó❞✐❣♦ ♣❛r❛ ♣❛❞r♦♥✐③❛çã♦ ❞♦s

❛rq✉✐✈♦s ✳❝s✈

❊st❡ ❝ó❞✐❣♦ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ♥❛ ❧✐♥❣✉❛❣❡♠ P②t❤♦♥ ♣❡❧♦ ❛✉t♦r ❞❡st❡ tr❛❜❛❧❤♦✱ s❡♥❞♦

r❡s♣♦♥sá✈❡❧ ♣❡❧❛ ♣❛❞r♦♥✐③❛çã♦ ❞♦s ❛rq✉✐✈♦s ✳❝s✈ ❞❛ ❜❛s❡ ■❙❈❳ ✷✵✶✷✱ ♦s q✉❛✐s ♣♦ss✉❡♠

✐♥❢♦r♠❛çõ❡s ❞♦ trá❢❡❣♦ ❞❡ r❡❞❡ ❝❛♣t✉r❛❞♦ ❡ r♦t✉❧❛❞♦✳

❊st❡s ❛rq✉✐✈♦s ♣♦ss✉✐❛♠ ❝♦❧✉♥❛s ❛❞✐❝✐♦♥❛✐s ♦✉ ❢♦r❛ ❞❡ ♦r❞❡♠✱ ❛❧é♠ ❞❡ ✐♥❝♦♥s✐s✲

tê♥❝✐❛s ❣❡r❛❞❛s ♣♦r ✈ír❣✉❧❛s ❞❛ ❝♦❧✉♥❛ ❯❚❋✱ ❛ q✉❛❧ ❝♦♥t✐♥❤❛ ✐♥❢♦r♠❛çõ❡s ❞♦s ♣❛②❧♦❛❞s

❞♦s ♣❛❝♦t❡s✱ q✉❡ ❣❡r❛✈❛♠ ❝♦❧✉♥❛s ❛❞✐❝✐♦♥❛✐s ♥♦s r❡❣✐str♦s✱ ❛s q✉❛✐s ❢♦r❛♠ r❡♠♦✈✐❞❛s

♦✉ r❡♦r❣❛♥✐③❛❞❛s ♣❛r❛ q✉❡ t♦❞♦s ♦s ❛rq✉✐✈♦s t✐✈❡ss❡♠ ♦ ♠❡s♠♦ ❢♦r♠❛t♦✳

♣❛❞r♦♥✐③❛❝❛♦❆rq✉✐✈♦s❈❙❱✳♣②

✶ ★ −∗− ❝♦❞✐♥❣ ✿ ✉t❢−✽ −∗−

✬ ✬ ✬

✸ ❈r❡❛t❡❞ ♦♥ ❆❜r✴✷✵✶✸

✺ ❅❛✉t❤♦r ✿ ❘❛❢❛❡ ❧ ❆♥t♦♥✐♦ ●♦♥ç❛❧✈❡s ▲✐♠❛ ✭ r ❛ ❢ ❛ ❡ ❧ ✳ ❛ ✳ ❧✐♠❛❅✉❢✈ ✳ ❜r ✴

r❛ ❢❛❡ ❧❣ ❧ ✐♠❛❅❣♠❛✐ ❧ ✳ ❝♦♠✮

✬ ✬ ✬

✼

✐♠♣♦rt ❝s✈ ✱ s②s ✱ ♦s

✾

★❞ ✐ r ❡ t ♦ r ✐ ♦ ❞❛ ❜❛s❡ ❞❡ ❞❛❞♦s ❡ q✉❛ ✐ s ❛rq✉ ✐✈♦s

✶✶ ❞✐r❴❛rq✉✐✈♦s ❂ ✬ ✴❤♦♠❡✴ r ❛ ❢ ❛ ❡ ❧ ✴ Pr♦ ❥❡ t♦ ✴ ✐ s ❝①✷✵✶✷ ✴ ❧❛❜❡ ❧ ❡❞❴❢ ❧♦✇s ✴ ✬

✶✸ ★❧ ✐ s t ❛ ❞❡ ❛rq✉ ✐✈♦s ❛ s❡r❡♠ ✈ ❡ r ✐ ❢ ✐ ❝ ❛ ❞ ♦ s

❛rq✉ ✐✈♦s❴t❡s t❡ ❂ ❬ ❞ ✐ r❴❛rq✉✐✈♦s ✰ ✬❚❡st❜❡❞▼♦♥❏✉♥✶✹ ✳ ❝s✈ ✬ ✱ ★ r ❡ t ✐ r ♦ ✉ ❛

❝♦❧✉♥❛ s♦✉r❝❡P❛②❧♦❛❞❆s❯❚❋

✶✺ ❞✐r❴❛rq✉✐✈♦s ✰ ✬ ❚❡st❜❡❞❙❛t❏✉♥✶✷ ✳ ❝s✈ ✬ ✱ ★ ♥❛♦ ♣ r ❡ ❝ ✐ s ❛

✻✸

❆✳ ❈ó❞✐❣♦ ♣❛r❛ ♣❛❞r♦♥✐③❛çã♦ ❞♦s ❛rq✉✐✈♦s ✳❝s✈ ✻✹

❞❡ ❛ ❧ t ❡ r ❛ ❝ ❛♦

❞✐r❴❛rq✉✐✈♦s ✰ ✬ ❚❡st❜❡❞❙✉♥❏✉♥✶✸ ✳ ❝s✈ ✬ ✱ ★ ♥❛♦ ♣ r ❡ ❝ ✐ s ❛

❞❡ ❛ ❧ t ❡ r ❛ ❝ ❛♦

✶✼ ❞✐r❴❛rq✉✐✈♦s ✰ ✬❚❡st❜❡❞❚❤✉❏✉♥✶✼−❛ ✳ ❝s✈ ✬ ✱ ★ r ❡ t ✐ r ♦ ✉ ❛

❝♦❧✉♥❛ ❞❡st✐♥❛t✐♦♥P❛②❧♦❛❞❯❚❋

❞✐r❴❛rq✉✐✈♦s ✰ ✬❚❡st❜❡❞❚❤✉❏✉♥✶✼−❜ ✳ ❝s✈ ✬ ✱ ★ r ❡ t ✐ r ♦ ✉ ❛

❝♦❧✉♥❛ ❞❡st✐♥❛t✐♦♥P❛②❧♦❛❞❯❚❋

✶✾ ❞✐r❴❛rq✉✐✈♦s ✰ ✬❚❡st❜❡❞❚❤✉❏✉♥✶✼−❝ ✳ ❝s✈ ✬ ✱ ★ r ❡ t ✐ r ♦ ✉ ❛

❝♦❧✉♥❛ ❞❡st✐♥❛t✐♦♥P❛②❧♦❛❞❯❚❋

❞✐r❴❛rq✉✐✈♦s ✰ ✬ ❚❡st❜❡❞❚✉❡❏✉♥✶✺−❛ ✳ ❝s✈ ✬ ✱ ★ r ❡ t ✐ r ♦ ✉ ❛s

❝♦ ❧✉♥❛s ❞❡st✐♥❛t✐♦♥P❛②❧♦❛❞❯❚❋ ❡ s ❡♥ s♦ r ■♥ t ❡ r ❢ ❛ ❝ ❡ ■❉

✷✶ ❞✐r❴❛rq✉✐✈♦s ✰ ✬ ❚❡st❜❡❞❚✉❡❏✉♥✶✺−❜ ✳ ❝s✈ ✬ ✱ ★ r ❡ t ✐ r ♦ ✉ ❛

❝♦❧✉♥❛ ❞❡st✐♥❛t✐♦♥P❛②❧♦❛❞❯❚❋

❞✐r❴❛rq✉✐✈♦s ✰ ✬ ❚❡st❜❡❞❚✉❡❏✉♥✶✺−❝ ✳ ❝s✈ ✬ ✱ ★ r ❡ t ✐ r ♦ ✉ ❛

❝♦❧✉♥❛ ❞❡st✐♥❛t✐♦♥P❛②❧♦❛❞❯❚❋

✷✸ ❞✐r❴❛rq✉✐✈♦s ✰ ✬❚❡st❜❡❞❲❡❞❏✉♥✶✻−❛ ✳ ❝s✈ ✬ ✱ ★ r ❡ t ✐ r ♦ ✉ ❛s

❝♦ ❧✉♥❛s ❞❡st✐♥❛t✐♦♥P❛②❧♦❛❞❯❚❋ ❡ st❛rt❚✐♠❡

❞✐r❴❛rq✉✐✈♦s ✰ ✬❚❡st❜❡❞❲❡❞❏✉♥✶✻−❜ ✳ ❝s✈ ✬ ✱ ★ r ❡ t ✐ r ♦ ✉ ❛

❝♦❧✉♥❛ ❞❡st✐♥❛t✐♦♥P❛②❧♦❛❞❯❚❋

✷✺ ❞✐r❴❛rq✉✐✈♦s ✰ ✬❚❡st❜❡❞❲❡❞❏✉♥✶✻−❝ ✳ ❝s✈ ✬ ✱ ❪ ★ r ❡ t ✐ r ♦ ✉ ❛

❝♦❧✉♥❛ ❞❡st✐♥❛t✐♦♥P❛②❧♦❛❞❯❚❋

✷✼ ★❧♦♦♣ ♣❛r❛ ❛✈❛ ❧ ✐ ❛ ❝❛♦ ❞♦s ❛rq✉ ✐✈♦s

❢ ♦ r ✐♥❞❡① ✐♥ r❛♥❣❡ ✭ ❧ ❡♥ ✭ ❛rq✉ ✐✈♦s❴t❡s t❡ ✮ ✮ ✿

✷✾

♣r ✐♥ t ✬ ❆rq✉✐✈♦ ❞❡ t ❡ s t ❡ ✿ ✬ ✱ ❛ rq✉ ✐✈♦s❴t❡s t❡ ❬ ✐♥❞❡① ❪

✸✶

★❛rq✉✐✈♦ ✳ ❝s✈ ❛ s ❡ r ❝ r ✐ ❛❞♦

✸✸ ❛rq❴s❡♠❯❚❋ ❂ ♦♣❡♥ ✭ ❛rq✉ ✐✈♦s❴t❡s t❡ ❬ ✐♥❞❡① ❪✰ ✬❴s❡♠❯❚❋ ✬ ✱ ✧✇❜✧ ✮

❢❴s❡♠❯❚❋ ❂ ❝s✈ ✳ ✇r ✐ t ❡ r ✭❛rq❴s❡♠❯❚❋ ✱ ❞ ❡ ❧ ✐♠ ✐ t ❡ r❂✬ ❭ t ✬ ✮

✸✺

★❛❜r❡ ♦ ❛rq✉✐✈♦ ✳ ❝s✈ ❡♠ ♠♦❞♦ ❧ ❡ ✐ t ✉ r ❛

✸✼ ❢ ❂ ♦♣❡♥ ✭ ❛rq✉ ✐✈♦s❴t❡s t❡ ❬ ✐♥❞❡① ❪ ✱ ✬ r❜ ✬ ✮

✸✾ r❡❛❞❡r ❂ ❝s✈ ✳ r ❡❛❞❡r ✭ ❢ ✱ ❞ ❡ ❧ ✐♠ ✐ t ❡ r❂✬ ✱ ✬ ✮

t r② ✿

✹✶ ★❝♦♥t❛❞♦r

❝♦✉♥t ❂ ✵

✹✸

❢ ♦ r r♦✇ ✐♥ r❡❛❞❡r ✿

✹✺ ★♣r ✐♥ t r♦✇ ❬ ✵ ❪ ❬ ✿ ✿ − ✶ ❪ ★✐♥✈ ❡ r t ❡ ❛ ♣❛ ❧❛✈r❛ ❞❛ ♣r ✐♠❡ ✐ r❛ ❝♦❧✉♥❛

★♣r ✐♥ t r♦✇ ❬ ✿ ✿ − ✶ ❪ ★✐♥✈ ❡ r t ❡ ❛ ❧ ✐ ♥❤❛

✹✼ ★♣r ✐♥ t ❝♦✉♥t ✱ ✬❭ t ✬ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✵ ❪ ✱ ✬❭ t ✬ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ❪ ✱ ✬❭ t ✬ ✱

r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✷ ❪ ✱ ✬❭ t ✬ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✸ ❪ ✱ ✬❭ t ✬ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✹ ❪ ✱ ✬❭ t

❆✳ ❈ó❞✐❣♦ ♣❛r❛ ♣❛❞r♦♥✐③❛çã♦ ❞♦s ❛rq✉✐✈♦s ✳❝s✈ ✻✺

✬ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✺ ❪ ✱ ✬❭ t ✬ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✻ ❪ ✱ ✬❭ t ✬ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✼ ❪ ✱

✬❭ t ✬ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✽ ❪ ✱ ✬❭ t ✬ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✾ ❪ ✱ ✬❭ t ✬ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✵ ❪

✹✾ ★❡s❝ r ❡✈❡ ♥♦ ❛rq✉✐✈♦ ♣❡❣❛♥❞♦ ❛s ❝♦ ❧✉♥❛s ❞❡ ✵ à ✻ ♣❡ ❧❛ ❡sq✉❡r❞❛

✱ ❡ ❛s ❝♦ ❧✉♥❛s ✶✽ à ✽ ♣❡ ❧❛ ❞ ✐ r ❡ ✐ t ❛

★❡❧ ✐♠✐♥❛♥❞♦ ❛ss✐♠ ❛ ❝♦❧✉♥❛ ❝♦♠ ❯❚❋ ♥❛ q✉❛❧ ❡s t❛✈❛ ❣❡r❛♥❞♦

✐ ♥ ❝ ♦ ♥ s ✐ s t ê ♥ ❝ ✐ ❛ s ♣♦r t❛♠❜é♠ ❤❛✈❡r ✈ ✐ r ❣ ✉ ❧ ❛ s

✺✶ ✐ ❢ ✐♥❞❡① ❂❂ ✵ ✿

❢❴s❡♠❯❚❋ ✳ ✇r✐t❡r♦✇ ✭ ❬ r♦✇ ❬ ✵ ❪ ✱ r♦✇ ❬ ✶ ❪ ✱ r♦✇ ❬ ✷ ❪ ✱ r♦✇ ❬ ✸ ❪ ✱ r♦✇

❬ ✹ ❪ ✱ r♦✇ ❬ ✺ ❪ ✱ r♦✇ ❬ ✻ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✵ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✾ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✽ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✼ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✻ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✺ ❪ ✱

r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✹ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✸ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✷ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✶ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✵ ❪ ❪ ✮

✺✸ ❡ ❧ ✐ ❢ ✐♥❞❡① ❂❂ ✶ ✿

❢❴s❡♠❯❚❋ ✳ ✇r✐t❡r♦✇ ✭ ❬ r♦✇ ❬ ✵ ❪ ✱ r♦✇ ❬ ✶ ❪ ✱ r♦✇ ❬ ✷ ❪ ✱ r♦✇ ❬ ✸ ❪ ✱ r♦✇

❬ ✹ ❪ ✱ r♦✇ ❬ ✺ ❪ ✱ r♦✇ ❬ ✻ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✷ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✶ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✵ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✾ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✽ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✼ ❪ ✱

r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✻ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✺ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✹ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✸ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✷ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✵ ❪ ❪ ✮

✺✺ ❡ ❧ ✐ ❢ ✐♥❞❡① ❂❂ ✷ ✿

❢❴s❡♠❯❚❋ ✳ ✇r✐t❡r♦✇ ✭ ❬ r♦✇ ❬ ✵ ❪ ✱ r♦✇ ❬ ✶ ❪ ✱ r♦✇ ❬ ✷ ❪ ✱ r♦✇ ❬ ✸ ❪ ✱ r♦✇

❬ ✹ ❪ ✱ r♦✇ ❬ ✺ ❪ ✱ r♦✇ ❬ ✻ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✷ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✶ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✵ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✾ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✽ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✼ ❪ ✱

r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✻ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✺ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✹ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✸ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✷ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✵ ❪ ❪ ✮

✺✼ ❡ ❧ ✐ ❢ ✐♥❞❡① ❂❂ ✸ ✿

❢❴s❡♠❯❚❋ ✳ ✇r✐t❡r♦✇ ✭ ❬ r♦✇ ❬ ✵ ❪ ✱ r♦✇ ❬ ✶ ❪ ✱ r♦✇ ❬ ✷ ❪ ✱ r♦✇ ❬ ✸ ❪ ✱ r♦✇

❬ ✹ ❪ ✱ r♦✇ ❬ ✺ ❪ ✱ r♦✇ ❬ ✻ ❪ ✱ r♦✇ ❬ ✼ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✵ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✾ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✽ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✼ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✻ ❪ ✱

r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✺ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✹ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✸ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✷ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✵ ❪ ❪ ✮

✺✾ ❡ ❧ ✐ ❢ ✐♥❞❡① ❂❂ ✹ ✿

❢❴s❡♠❯❚❋ ✳ ✇r✐t❡r♦✇ ✭ ❬ r♦✇ ❬ ✵ ❪ ✱ r♦✇ ❬ ✶ ❪ ✱ r♦✇ ❬ ✷ ❪ ✱ r♦✇ ❬ ✸ ❪ ✱ r♦✇

❬ ✹ ❪ ✱ r♦✇ ❬ ✺ ❪ ✱ r♦✇ ❬ ✻ ❪ ✱ r♦✇ ❬ ✼ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✵ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✾ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✽ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✼ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✻ ❪ ✱

r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✺ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✹ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✸ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✷ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✵ ❪ ❪ ✮

✻✶ ❡ ❧ ✐ ❢ ✐♥❞❡① ❂❂ ✺ ✿

❢❴s❡♠❯❚❋ ✳ ✇r✐t❡r♦✇ ✭ ❬ r♦✇ ❬ ✵ ❪ ✱ r♦✇ ❬ ✶ ❪ ✱ r♦✇ ❬ ✷ ❪ ✱ r♦✇ ❬ ✸ ❪ ✱ r♦✇

❬ ✹ ❪ ✱ r♦✇ ❬ ✺ ❪ ✱ r♦✇ ❬ ✻ ❪ ✱ r♦✇ ❬ ✼ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✵ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✾ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✽ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✼ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✻ ❪ ✱

r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✺ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✹ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✸ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✷ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✵ ❪ ❪ ✮

❆✳ ❈ó❞✐❣♦ ♣❛r❛ ♣❛❞r♦♥✐③❛çã♦ ❞♦s ❛rq✉✐✈♦s ✳❝s✈ ✻✻

✻✸ ❡ ❧ ✐ ❢ ✐♥❞❡① ❂❂ ✻ ✿

❢❴s❡♠❯❚❋ ✳ ✇r✐t❡r♦✇ ✭ ❬ r♦✇ ❬ ✵ ❪ ✱ r♦✇ ❬ ✶ ❪ ✱ r♦✇ ❬ ✷ ❪ ✱ r♦✇ ❬ ✸ ❪ ✱ r♦✇

❬ ✹ ❪ ✱ r♦✇ ❬ ✺ ❪ ✱ r♦✇ ❬ ✻ ❪ ✱ r♦✇ ❬ ✼ ❪ ✱ r♦✇ ❬ ✽ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✵ ❪ ✱

r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✾ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✽ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✼ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✻ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✺ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✹ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✸ ❪ ✱

r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✷ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✵ ❪ ❪ ✮

✻✺ ❡ ❧ ✐ ❢ ✐♥❞❡① ❂❂ ✼ ✿

❢❴s❡♠❯❚❋ ✳ ✇r✐t❡r♦✇ ✭ ❬ r♦✇ ❬ ✵ ❪ ✱ r♦✇ ❬ ✶ ❪ ✱ r♦✇ ❬ ✷ ❪ ✱ r♦✇ ❬ ✸ ❪ ✱ r♦✇

❬ ✹ ❪ ✱ r♦✇ ❬ ✺ ❪ ✱ r♦✇ ❬ ✻ ❪ ✱ r♦✇ ❬ ✼ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✵ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✾ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✽ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✼ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✻ ❪ ✱

r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✺ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✹ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✸ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✷ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✵ ❪ ❪ ✮

✻✼ ❡ ❧ ✐ ❢ ✐♥❞❡① ❂❂ ✽ ✿

❢❴s❡♠❯❚❋ ✳ ✇r✐t❡r♦✇ ✭ ❬ r♦✇ ❬ ✵ ❪ ✱ r♦✇ ❬ ✶ ❪ ✱ r♦✇ ❬ ✷ ❪ ✱ r♦✇ ❬ ✸ ❪ ✱ r♦✇

❬ ✹ ❪ ✱ r♦✇ ❬ ✺ ❪ ✱ r♦✇ ❬ ✻ ❪ ✱ r♦✇ ❬ ✼ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✵ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✾ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✽ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✼ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✻ ❪ ✱

r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✺ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✹ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✸ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✷ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✵ ❪ ❪ ✮

✻✾ ❡ ❧ ✐ ❢ ✐♥❞❡① ❂❂ ✾ ✿

❢❴s❡♠❯❚❋ ✳ ✇r✐t❡r♦✇ ✭ ❬ r♦✇ ❬ ✵ ❪ ✱ r♦✇ ❬ ✶ ❪ ✱ r♦✇ ❬ ✷ ❪ ✱ r♦✇ ❬ ✸ ❪ ✱ r♦✇

❬ ✹ ❪ ✱ r♦✇ ❬ ✺ ❪ ✱ r♦✇ ❬ ✻ ❪ ✱ r♦✇ ❬ ✼ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✶ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✵ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✾ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✽ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✼ ❪ ✱

r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✻ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✺ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✹ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✸ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✷ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✵ ❪ ❪ ✮

✼✶ ❡ ❧ ✐ ❢ ✐♥❞❡① ❂❂ ✶✵ ✿

❢❴s❡♠❯❚❋ ✳ ✇r✐t❡r♦✇ ✭ ❬ r♦✇ ❬ ✵ ❪ ✱ r♦✇ ❬ ✶ ❪ ✱ r♦✇ ❬ ✷ ❪ ✱ r♦✇ ❬ ✸ ❪ ✱ r♦✇

❬ ✹ ❪ ✱ r♦✇ ❬ ✺ ❪ ✱ r♦✇ ❬ ✻ ❪ ✱ r♦✇ ❬ ✼ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✵ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✾ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✽ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✼ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✻ ❪ ✱

r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✺ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✹ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✸ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✷ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✵ ❪ ❪ ✮

✼✸ ❡ ❧ ✐ ❢ ✐♥❞❡① ❂❂ ✶✶ ✿

❢❴s❡♠❯❚❋ ✳ ✇r✐t❡r♦✇ ✭ ❬ r♦✇ ❬ ✵ ❪ ✱ r♦✇ ❬ ✶ ❪ ✱ r♦✇ ❬ ✷ ❪ ✱ r♦✇ ❬ ✸ ❪ ✱ r♦✇

❬ ✹ ❪ ✱ r♦✇ ❬ ✺ ❪ ✱ r♦✇ ❬ ✻ ❪ ✱ r♦✇ ❬ ✼ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ✵ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✾ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✽ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✼ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✻ ❪ ✱

r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✺ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✹ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✸ ❪ ✱ r♦✇

❬ ✿ ✿ − ✶ ❪ ❬ ✷ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ❪ ✱ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✵ ❪ ❪ ✮

✼✺

★✐♥❝r❡♠❡♥t❛ ♦ ❝♦♥t❛❞♦r ✱ ❛♣❡♥❛s ♣❛r❛ ♠♦str❛r ❛ ❧ ✐ ♥❤❛ ❛t✉❛ ❧

✼✼ ❝♦✉♥t ✰❂ ✶

✼✾ ❡①❝❡♣t ❝s✈ ✳ ❊rr♦r ✱ ❡ ✿

s②s ✳ ❡ ① ✐ t ✭ ✬ ❢ ✐ ❧ ❡ ✪s ✱ ❧ ✐ ♥ ❡ ✪❞ ✿ ✪s ✿ ✬ ✪ ✭ ❛rq✉ ✐✈♦s❴t❡s t❡ ❬ ✐♥❞❡① ❪ ✱ r ❡❛❞❡r

✳ ❧✐♥❡❴♥✉♠ ✱ ❡ ✮ ✮

✽✶

❆✳ ❈ó❞✐❣♦ ♣❛r❛ ♣❛❞r♦♥✐③❛çã♦ ❞♦s ❛rq✉✐✈♦s ✳❝s✈ ✻✼

★❢❡❝❤❛ ♦ ❛rq✉✐✈♦

✽✸ ❢ ✳ ❝ ❧ ♦ s ❡ ✭ ✮

★❢ ✐ ♥ ❛ ❧ ✐ ③ ❛ ♦ ♣r♦❣r❛♠❛

✽✺ s②s ✳ ❡ ① ✐ t

❆♥❡①♦ ❇

❈ó❞✐❣♦ ♣❛r❛ ❣❡r❛r ❛rq✉✐✈♦ ✳❛r✛

❊st❡ ❝ó❞✐❣♦ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ♥❛ ❧✐♥❣✉❛❣❡♠ P②t❤♦♥ ♣❡❧♦ ❛✉t♦r ❞❡st❡ tr❛❜❛❧❤♦✱ s❡♥❞♦

r❡s♣♦♥sá✈❡❧ ♣♦r tr❛♥s❢♦r♠❛r ♦s ❛rq✉✐✈♦s ✳❝s✈ ♥♦ ❢♦r♠❛t♦ ✳❛r✛ ✭✉t✐❧✐③❛❞♦ ♣❡❧♦ s♦❢t✇❛r❡

❲❡❦❛✮✱ ❛❞✐❝✐♦♥❛♥❞♦ ♦ ❝❛❜❡ç❛❧❤♦ ❝♦♠ ✐♥❢♦r♠❛çõ❡s ❞♦s ❛tr✐❜✉t♦s✱ ❛❧é♠ ❞❡ ❡❧✐♠✐♥❛r ❛❧✲

❣✉♠❛s ✐♥❝♦♥s✐stê♥❝✐❛s ❞❡ r❡❣✐str♦s✳

❣❡r❛❆rq✉✐✈♦❆r✛✳♣②

✶ ★ −∗− ❝♦❞✐♥❣ ✿ ✉t❢−✽ −∗−

✬ ✬ ✬

✸ ❈r❡❛t❡❞ ♦♥ ❆❜r✴✷✵✶✸

✺ ❅❛✉t❤♦r ✿ ❘❛❢❛❡ ❧ ❆♥t♦♥✐♦ ●♦♥ç❛❧✈❡s ▲✐♠❛ ✭ r ❛ ❢ ❛ ❡ ❧ ✳ ❛ ✳ ❧✐♠❛❅✉❢✈ ✳ ❜r ✴

r❛ ❢❛❡ ❧❣ ❧ ✐♠❛❅❣♠❛✐ ❧ ✳ ❝♦♠✮

✬ ✬ ✬

✼

✐♠♣♦rt ❝s✈ ✱ s②s ✱ ♦s

✾ ✐♠♣♦rt r❡

✶✶ ❞❡ ❢ ❝❛❜❡❝❛❧❤♦❲❡❦❛ ✭ ✮ ✿

✶✸ ❝❛❜❡❝❛ ❧❤♦ ❂ ✧✧✧ ❅r❡ ❧❛ t ✐ ♦♥ ❭ ✬ ✐ s ❝①✷✵✶✷ ❭ ✬

❅❛ttr ✐❜✉t❡ ❭ ✬ ❞✉r❛t ✐♦♥ ❭ ✬ r ❡ ❛ ❧

✶✺ ❅❛ttr ✐❜✉t❡ ❭ ✬ ♣r♦t♦❝♦❧◆❛♠❡ ❭ ✬ ④❭ ✬ t❝♣ ❭ ✬ ✱ ❭ ✬ ✉❞♣ ❭ ✬ ✱ ❭ ✬ ✐❝♠♣ ❭ ✬⑥

❅❛ttr ✐❜✉t❡ ❭ ✬ s♦✉r❝❡❚❈P❋❧❛❣s❉❡s❝r ✐♣t ✐♦♥ ❭ ✬ ④❭ ✬◆✴❆❭ ✬ ✱ ❭ ✬❙P❆❭ ✬ ✱ ❭ ✬❙❘P❆❭ ✬ ✱ ❭ ✬

❋❙P❆❭ ✬ ✱ ❭ ✬❋❘P❆❭ ✬ ✱ ❭ ✬❋❙❘P❆❭ ✬ ✱ ❭ ✬❋❆❭ ✬ ✱ ❭ ✬❋❘❆❭ ✬ ✱ ❭ ✬❋P❆❭ ✬ ✱ ❭ ✬❋❙❆❭ ✬ ✱ ❭ ✬❙❘❆

❭ ✬ ✱ ❭ ✬❘P❆❭ ✬ ✱ ❭ ✬❘❭ ✬ ✱ ❭ ✬❙ ❭ ✬ ✱ ❭ ✬❆❭ ✬ ✱ ❭ ✬❘❆❭ ✬ ✱ ❭ ✬P❆❭ ✬ ✱ ❭ ✬❙❆❭ ✬ ✱ ❭ ✬❙❘❭ ✬ ✱ ❭ ✬❋❙❘❆

❭ ✬ ✱ ❭ ✬❋P❯❭ ✬ ✱ ❭ ✬❋❙P❯❭ ✬ ✱ ❭ ✬❋❙❘P❯❭ ✬⑥

✶✼ ❅❛ttr ✐❜✉t❡ ❭ ✬ ❞❡st ✐♥❛t ✐♦♥❚❈P❋❧❛❣s❉❡s❝r ✐♣t ✐♦♥ ❭ ✬ ④❭ ✬◆✴❆❭ ✬ ✱ ❭ ✬❙P❆❭ ✬ ✱ ❭ ✬❙❘P❆

❭ ✬ ✱ ❭ ✬❋❙P❆❭ ✬ ✱ ❭ ✬❋❘P❆❭ ✬ ✱ ❭ ✬❋❙❘P❆❭ ✬ ✱ ❭ ✬❋❆❭ ✬ ✱ ❭ ✬❋❘❆❭ ✬ ✱ ❭ ✬❋P❆❭ ✬ ✱ ❭ ✬❋❙❆❭ ✬ ✱

❭ ✬❙❘❆❭ ✬ ✱ ❭ ✬❘P❆❭ ✬ ✱ ❭ ✬❘❭ ✬ ✱ ❭ ✬❙ ❭ ✬ ✱ ❭ ✬❆❭ ✬ ✱ ❭ ✬❘❆❭ ✬ ✱ ❭ ✬P❆❭ ✬ ✱ ❭ ✬❙❆❭ ✬ ✱ ❭ ✬❋❙❘❆

✻✽

❇✳ ❈ó❞✐❣♦ ♣❛r❛ ❣❡r❛r ❛rq✉✐✈♦ ✳❛r❢❢ ✻✾

❭ ✬⑥

❅❛ttr ✐❜✉t❡ ❭ ✬ t♦ t❛ ❧❙♦✉r❝❡❇②t❡ s ❭ ✬ r ❡ ❛ ❧

✶✾ ❅❛ttr ✐❜✉t❡ ❭ ✬ t ♦ t ❛ ❧❉❡ s t ✐ ♥❛ t ✐ ♦♥❇②t❡ s ❭ ✬ r ❡ ❛ ❧

❅❛ttr ✐❜✉t❡ ❭ ✬ s♦✉r❝❡ ❭ ✬ ④❭ ✬ ✵❭ ✬ ✱ ❭ ✬ ✶❭ ✬ ✱ ❭ ✬✷❭ ✬ ✱ ❭ ✬✸❭ ✬ ✱ ❭ ✬✹❭ ✬ ✱ ❭ ✬✺❭ ✬ ✱ ❭ ✬✻❭ ✬⑥

✷✶ ❅❛ttr ✐❜✉t❡ ❭ ✬ ❞ ❡ s t ✐ ♥ ❛ t ✐ ♦♥ ❭ ✬ ④❭ ✬ ✵❭ ✬ ✱ ❭ ✬ ✶❭ ✬ ✱ ❭ ✬ ✷❭ ✬ ✱ ❭ ✬ ✸❭ ✬ ✱ ❭ ✬ ✹❭ ✬ ✱ ❭ ✬ ✺❭ ✬ ✱

❭ ✬✻❭ ✬⑥

❅❛ttr ✐❜✉t❡ ❭ ✬ s♦✉r❝❡P♦rt ❭ ✬ ♥✉♠❡r✐❝

✷✸ ❅❛ttr ✐❜✉t❡ ❭ ✬ ❞ ❡ s t ✐ ♥❛ t ✐ ♦♥P♦r t ❭ ✬ ♥✉♠❡r✐❝

❅❛ttr ✐❜✉t❡ ❭ ✬ t♦ t❛ ❧❙♦✉r❝❡P❛❝❦❡ t s ❭ ✬ r ❡ ❛ ❧

✷✺ ❅❛ttr ✐❜✉t❡ ❭ ✬ t ♦ t ❛ ❧❉❡ s t ✐ ♥❛ t ✐ ♦♥P❛❝❦❡ t s ❭ ✬ r ❡ ❛ ❧

❅❛ttr ✐❜✉t❡ ❭ ✬ ❞ ✐ r ❡ ❝ t ✐ ♦ ♥ ❭ ✬ ④❭ ✬▲✷❘❭ ✬ ✱ ❭ ✬▲✷▲❭ ✬ ✱ ❭ ✬❘✷❘❭ ✬ ✱ ❭ ✬❘✷▲❭ ✬⑥

✷✼ ❅❛ttr ✐❜✉t❡ ❭ ✬ t❛❣ ❭ ✬ ④❭ ✬◆♦r♠❛❧ ❭ ✬ ✱ ❭ ✬ ❆tt❛❝❦ ❭ ✬⑥

❅❞❛t❛

✷✾ ✧✧✧

r❡t✉r♥ ❝❛❜❡❝❛ ❧❤♦

✸✶

❞❡ ❢ ❝❛❧❝✉❧❛❉✉r❛❝❛♦❙❡❣✉♥❞♦s ✭ ❞❛t❡❚✐♠❡ ✮ ✿

✸✸ ❞❛t❛ ❂ ✵

❤♦r❛ r ✐ ♦ ❂ ✵

✸✺ ❞✉r❛❝❛♦ ❂ ✵

❤♦r❛ ❂ ✵

✸✼ ♠✐♥✉t♦s ❂ ✵

s❡❣✉♥❞♦s ❂ ✵

✸✾ t r② ✿

❞❛t❛ ✱ ❤♦ r❛ r ✐ ♦ ❂ ❞❛t❡❚✐♠❡ ✳ s ♣ ❧ ✐ t ✭ ✬ ✬ ✮

✹✶ ❤♦r❛ ✱ ♠✐♥✉t♦s ✱ s❡❣✉♥❞♦s ❂ ❤♦r❛ r ✐ ♦ ✳ s ♣ ❧ ✐ t ✭ ✬ ✿ ✬ ✮

❞✉r❛❝❛♦ ❂ ✐♥ t ✭ s❡❣✉♥❞♦s ✮ ✰ ✐♥ t ✭ ♠✐♥✉t♦s ✮ ∗✻✵ ✰ ✐♥ t ✭ ❤♦r❛ ✮ ∗✸✻✵ ❀

✹✸ ❡①❝❡♣t ❚②♣❡❊rr♦r ✱ ❡ r r ♦ ✿

♣ r ✐ ♥ t ✧✉♠ ❡r r♦ ♦❝♦rr❡✉ ✿ ✪s ✧ ✪ ❡r r♦

✹✺ ♣r ✐♥ t ❞❛t❡❚✐♠❡

❞✉r❛❝❛♦ ❂ ✵ ❀

✹✼

✐ ❢ ❞✉r❛❝❛♦ ❁ ✵ ✿

✹✾ r❡ t✉r♥ ✵

❡ ❧ s ❡ ✿

✺✶ r❡ t✉r♥ ❞✉r❛❝❛♦

✺✸ ❞❡ ❢ ❡♥❞❡r❡❝♦❘❡❞❡ ✭ ❡♥❞❡r❡❝♦ ✮ ✿

✺✺ r ❡ s ✉ ❧ t ❂ ✬ ❄ ✬

✐ ❢ ❡♥❞❡r❡❝♦ ❬ ✵ ✿ ✽ ❪ ✦❂ ✬ ✶✾✷ ✳ ✶✻✽ ✳ ✬ ✿

✺✼ r ❡ s ✉ ❧ t ❂ ✬ ✵ ✬ ★❡♥❞❡r❡❝♦ ✐ ♥ t ❡ r ♥ ❡ t

❡ ❧ ✐ ❢ ❡♥❞❡r❡❝♦ ❬ ✵ ✿ ✶ ✵ ❪ ❂❂ ✬ ✶ ✾ ✷ ✳ ✶ ✻ ✽ ✳ ✶ ✳ ✬ ✿

✺✾ r ❡ s ✉ ❧ t ❂ ✬ ✶ ✬

❇✳ ❈ó❞✐❣♦ ♣❛r❛ ❣❡r❛r ❛rq✉✐✈♦ ✳❛r❢❢ ✼✵

❡ ❧ ✐ ❢ ❡♥❞❡r❡❝♦ ❬ ✵ ✿ ✶ ✵ ❪ ❂❂ ✬ ✶ ✾ ✷ ✳ ✶ ✻ ✽ ✳ ✷ ✳ ✬ ✿

✻✶ r ❡ s ✉ ❧ t ❂ ✬ ✷ ✬

❡ ❧ ✐ ❢ ❡♥❞❡r❡❝♦ ❬ ✵ ✿ ✶ ✵ ❪ ❂❂ ✬ ✶ ✾ ✷ ✳ ✶ ✻ ✽ ✳ ✸ ✳ ✬ ✿

✻✸ r ❡ s ✉ ❧ t ❂ ✬ ✸ ✬

❡ ❧ ✐ ❢ ❡♥❞❡r❡❝♦ ❬ ✵ ✿ ✶ ✵ ❪ ❂❂ ✬ ✶ ✾ ✷ ✳ ✶ ✻ ✽ ✳ ✹ ✳ ✬ ✿

✻✺ r ❡ s ✉ ❧ t ❂ ✬ ✹ ✬

❡ ❧ ✐ ❢ ❡♥❞❡r❡❝♦ ❬ ✵ ✿ ✶ ✵ ❪ ❂❂ ✬ ✶ ✾ ✷ ✳ ✶ ✻ ✽ ✳ ✺ ✳ ✬ ✿

✻✼ r ❡ s ✉ ❧ t ❂ ✬ ✺ ✬

❡ ❧ ✐ ❢ ❡♥❞❡r❡❝♦ ❬ ✵ ✿ ✶ ✵ ❪ ❂❂ ✬ ✶ ✾ ✷ ✳ ✶ ✻ ✽ ✳ ✻ ✳ ✬ ✿

✻✾ r ❡ s ✉ ❧ t ❂ ✬ ✻ ✬

r ❡ t✉r♥ r ❡ s ✉ ❧ t

✼✶

★❞ ✐ r ❡ t ♦ r ✐ ♦ ❞❛s ❡♥tr❛❞❛s ■❙❈❳✷✵✶✷

✼✸ ❞✐r❴❛rq✉✐✈♦s ❂ ✬ ✴❤♦♠❡✴ r ❛ ❢ ❛ ❡ ❧ ✴ ✐ s ❝①✷✵✶✷ ✴ ❧❛❜❡ ❧ ❡❞❴❢ ❧♦✇s ✴ ✬

✼✺ ★❧ ✐ s t ❛ ❞❡ ❛rq✉ ✐✈♦s ❛ s❡r❡♠ ✈ ❡ r ✐ ❢ ✐ ❝ ❛ ❞ ♦ s

❛rq✉ ✐✈♦s❴t❡s t❡ ❂ ❬ ❞ ✐ r❴❛rq✉✐✈♦s ✰ ✬❚❡st❜❡❞❲❡❞❏✉♥✶✻−❛ ✳ ❝s✈ ✬ ✱

✼✼ ❞✐r❴❛rq✉✐✈♦s ✰ ✬❚❡st❜❡❞❲❡❞❏✉♥✶✻−❜ ✳ ❝s✈ ✬ ✱

❞ ✐ r❴❛rq✉✐✈♦s ✰ ✬❚❡st❜❡❞❲❡❞❏✉♥✶✻−❝ ✳ ❝s✈ ✬ ❪

✼✾

★❧♦♦♣ ♣❛r❛ ❛✈❛ ❧ ✐ ❛ ❝❛♦ ❞♦s ❛rq✉ ✐✈♦s

✽✶ ❢ ♦ r ✐♥❞❡① ✐♥ r❛♥❣❡ ✭ ❧ ❡♥ ✭ ❛rq✉ ✐✈♦s❴t❡s t❡ ✮ ✮ ✿

✽✸ ★❛rr❛② ♣❛r❛ ❡♥tr❛❞❛s

❡♥tr❛❞❛s ❂ ❬ ❬ ✵ ❢ ♦ r ① ✐♥ ①r❛♥❣❡ ✭✶✹✮ ❪ ❢ ♦ r ① ✐♥ ①r❛♥❣❡ ✭ ❧ ❡♥ ✭

❛rq✉ ✐✈♦s❴t❡s t❡ ✮ ✮ ❪

✽✺

★♣r ✐♥ t ❡♥tr❛❞❛s

✽✼ ♣r ✐♥ t ✬ ❆rq✉✐✈♦ ❞❡ t ❡ s t ❡ ✿ ✬ ✱ ❛ rq✉ ✐✈♦s❴t❡s t❡ ❬ ✐♥❞❡① ❪

✽✾ ★❛❜r❡ ♦ ❛rq✉✐✈♦ ✳ ❝s✈ ❡♠ ♠♦❞♦ ❧ ❡ ✐ t ✉ r ❛

❢ ❂ ♦♣❡♥ ✭ ❛rq✉ ✐✈♦s❴t❡s t❡ ❬ ✐♥❞❡① ❪ ✱ ✬ r❜ ✬ ✮

✾✶

★❛rq✉✐✈♦ ✳ ❝s✈ ❛ s ❡ r ❝ r ✐ ❛❞♦ ❞❡ ❡♥tr❛❞❛s

✾✸ ❢❊♥tr❛❞❛s ❂ ♦♣❡♥ ✭ ❛rq✉ ✐✈♦s❴t❡s t❡ ❬ ✐♥❞❡① ❪✰ ✬ ✳ ❛ r ❢ ❢ ✬ ✱ ✧✇❜✧ ✮

★❛❞ ✐ ❝ ✐ ♦♥❛ ❝❛❜❡❝❛ ❧❤♦ ❲❡❦❛

✾✺ ❢❊♥tr❛❞❛s ✳ ✇r ✐ t ❡ ✭ ❝❛❜❡❝❛❧❤♦❲❡❦❛ ✭ ✮ ✮

★❡s ❝ r ❡✈ ❡ ❝♦♠♦ ✳ ❝s✈

✾✼ ❢❊♥tr❛❞❛s ❂ ❝s✈ ✳ ✇r ✐ t ❡ r ✭ ❢❊♥tr❛❞❛s ✱ ❞ ❡ ❧ ✐♠ ✐ t ❡ r❂✬ ✱ ✬ ✮

✾✾ r❡❛❞❡r ❂ ❝s✈ ✳ r ❡❛❞❡r ✭ ❢ ✱ ❞ ❡ ❧ ✐♠ ✐ t ❡ r❂✬ ❭ t ✬ ✮

t r② ✿

✶✵✶

★♣❡r❝♦ r r ❡ ♦ ❛rq✉✐✈♦

❇✳ ❈ó❞✐❣♦ ♣❛r❛ ❣❡r❛r ❛rq✉✐✈♦ ✳❛r❢❢ ✼✶

✶✵✸ ❢ ♦ r r♦✇ ✐♥ r❡❛❞❡r ✿

✶✵✺ ★❝♦♥t❛❞♦r

❝♦✉♥t ❂ ✵

✶✵✼

✐ ❢ r♦✇ ❬ ✵ ❪ ✦❂ ✬❛♣♣◆❛♠❡ ✬ ✿

✶✵✾

★❞✉r❛t ✐♦♥ ❂ ❙t♦♣❚✐♠❡ − ❙t❛rt❚✐♠❡

✶✶✶ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✵ ❪ ❂ ❝❛❧❝✉❧❛❉✉r❛❝❛♦❙❡❣✉♥❞♦s ✭ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✶ ❪ ✮

− ❝❛❧❝✉❧❛❉✉r❛❝❛♦❙❡❣✉♥❞♦s ✭ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✷ ❪ ✮

✐ ❢ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✵ ❪ ❁ ✵ ✿

✶✶✸ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✵ ❪ ❂ ✬ ❄ ✬ ★❝❛s♦ ♦ ✈❛ ❧♦ r ❞✉r❛t ✐♦♥ s ❡ ❥ ❛

♥❡❣❛t ✐✈♦ ✱ s ❡ rá ❝♦♥s ✐❞❡r❛❞♦ ✧♥✉❧♦ ✧ ♣❡ ❧♦ ❲❡❦❛

✶✶✺ ★♣r♦t♦❝♦❧◆❛♠❡

✐ ❢ r♦✇ ❬ ✿ ✿ −✶ ❪ ❬✻ ❪❂❂ ✬ t❝♣❴✐♣ ✬ ✿

✶✶✼ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✶ ❪ ❂ ✬ t❝♣ ✬

❡ ❧ ✐ ❢ r♦✇ ❬ ✿ ✿ −✶ ❪ ❬✻ ❪❂❂ ✬✉❞♣❴✐♣ ✬ ✿

✶✶✾ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✶ ❪ ❂ ✬✉❞♣ ✬

❡ ❧ ✐ ❢ r♦✇ ❬ ✿ ✿ −✶ ❪ ❬✻ ❪❂❂ ✬ ✐❝♠♣❴✐♣ ✬ ✿

✶✷✶ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✶ ❪ ❂ ✬ ✐❝♠♣ ✬

✶✷✸ ★s♦✉r❝❡❚❈P❋❧❛❣s❉❡s❝r ✐♣t ✐♦♥

✐ ❢ r♦✇ ❬ ✾ ❪ ❂❂ ✬ ✬ ✿

✶✷✺ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✷ ❪ ❂ ✬ ❄ ✬

❡ ❧ s ❡ ✿

✶✷✼ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✷ ❪ ❂ r❡ ✳ s✉❜ ✭ ✬ ✱ ✬ ✱ ✬ ✬ ✱ r♦✇ ❬ ✾ ❪ ✮ ★r❡♠♦✈❡ ❛

✈ í r ❣✉ ❧ ❛ ❡♥t r ❡ ❛s ❢ ❧ ❛ ❣ s

✶✷✾ ✐ ❢ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✷ ❪ ❂❂ ✬ ❙❘ ■ ❧ ❧ ❡ ❣ ❛ ❧ ✼ ■ ❧ ❧ ❡ ❣ ❛ ❧ ✽ ✬ ✿ ★t r❛ t❛

r ❡ ❣ ✐ s t r ♦ ❡rr❛❞♦

❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✷ ❪ ❂ ✬❙❘ ✬

✶✸✶

★❞❡st ✐♥❛t ✐♦♥❚❈P❋❧❛❣s❉❡s❝r ✐♣t ✐♦♥

✶✸✸ ✐ ❢ r♦✇ ❬ ✶ ✵ ❪ ❂❂ ✬ ✬ ✿

❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂ ✬ ❄ ✬

✶✸✺ ❡ ❧ s ❡ ✿

❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂ r❡ ✳ s✉❜ ✭ ✬ ✱ ✬ ✱ ✬ ✬ ✱ r♦✇ ❬ ✶ ✵ ❪ ✮

✶✸✼

✐ ❢ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂❂ ✬ ❋❙P❆■❧ ❧❡❣❛❧✽ ✬ ✿ ★t r❛ t❛

r ❡ ❣ ✐ s t r ♦ ❡rr❛❞♦

✶✸✾ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂ ✬❋❙P❆ ✬

❡ ❧ ✐ ❢ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂❂ ✬ ❙❘❆■❧ ❧ ❡❣❛ ❧✽ ✬ ✿

✶✹✶ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂ ✬❙❘❆ ✬

❇✳ ❈ó❞✐❣♦ ♣❛r❛ ❣❡r❛r ❛rq✉✐✈♦ ✳❛r❢❢ ✼✷

❡ ❧ ✐ ❢ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂❂ ✬ ❘ ■ ❧ ❧ ❡ ❣ ❛ ❧ ✽ ✬ ✿

✶✹✸ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂ ✬❘ ✬

❡ ❧ ✐ ❢ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂❂ ✬ ❙P❆■ ❧ ❧ ❡❣❛ ❧✽ ✬ ✿

✶✹✺ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂ ✬❙P❆ ✬

❡ ❧ ✐ ❢ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂❂ ✬ ❋❙❘P❆■❧❧❡❣❛❧✽ ✬ ✿

✶✹✼ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂ ✬❋❙❘P❆ ✬

❡ ❧ ✐ ❢ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂❂ ✬ ❘❆ ■ ❧ ❧ ❡ ❣ ❛ ❧ ✼ ■ ❧ ❧ ❡ ❣ ❛ ❧ ✽ ✬ ✿

✶✹✾ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂ ✬❘❆✬

❡ ❧ ✐ ❢ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂❂ ✬ ❘❆■ ❧ ❧ ❡❣❛ ❧✼ ✬ ✿

✶✺✶ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂ ✬❘❆✬

❡ ❧ ✐ ❢ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂❂ ✬ ❘❆■ ❧ ❧ ❡❣❛ ❧✽ ✬ ✿

✶✺✸ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂ ✬❘❆✬

❡ ❧ ✐ ❢ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂❂ ✬ ❋P❆■❧ ❧❡❣❛ ❧✽ ✬ ✿

✶✺✺ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ❂ ✬❋P❆ ✬

✶✺✼ ★t♦t❛ ❧❙♦✉r❝❡❇②t❡ s

❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✹ ❪ ❂ r♦✇ ❬ ✶ ❪

✶✺✾ ★t♦t❛ ❧❉❡ s t ✐ ♦♥❛ t ✐ ♦♥❇②t❡ s

❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✺ ❪ ❂ r♦✇ ❬ ✷ ❪

✶✻✶ ★s♦✉r❝❡

❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✻ ❪ ❂ ❡♥❞❡r❡❝♦❘❡❞❡ ✭ r♦✇ ❬ ✶ ✶ ❪ ✮ ★✵ s❡ ❢ ♦ r

❡♥❞❡r❡❝♦ ❞❛ ✐ ♥ t ❡ r ♥ ❡ t ❡ ✷−✻ s❡ ❢ ♦ r ❞❛s s✉❜−r ❡❞❡s

✐ ♥ t ❡ r♥❛ s

✶✻✸ ★❞❡ s t ✐ ♥ ❛ t ✐ ♦♥

❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✼ ❪ ❂ ❡♥❞❡r❡❝♦❘❡❞❡ ✭ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✹ ❪ ✮ ★✵ s❡ ❢ ♦ r

❡♥❞❡r❡❝♦ ❞❛ ✐ ♥ t ❡ r ♥ ❡ t ❡ ✷−✻ s❡ ❢ ♦ r ❞❛s s✉❜−r ❡❞❡s

✐ ♥ t ❡ r♥❛ s

✶✻✺ ★s♦✉r❝❡P♦rt

❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✽ ❪ ❂ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✺ ❪

✶✻✼ ★❞❡s t ✐ ♥❛ t ✐ ♦♥P♦r t

❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✾ ❪ ❂ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✸ ❪

✶✻✾ ★t♦t❛ ❧❙♦✉r❝❡P❛❝❦❡ t s

❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✶ ✵ ❪ ❂ r♦✇ ❬ ✹ ❪

✶✼✶ ★t♦t❛ ❧❉❡ s t ✐ ♥❛ t ✐ ♦♥P❛❝❦❡ t s

❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✶ ✶ ❪ ❂ r♦✇ ❬ ✸ ❪

✶✼✸

★❞ ✐ r ❡ ❝ t ✐ ♦ ♥

✶✼✺ ✐ ❢ r♦✇ ❬ ✽ ❪ ✦❂ ✬ ✱▲✷❘✧ ✬ ✿

① ❂ r♦✇ ❬ ✽ ❪

✶✼✼ ① ❂ ① ❬ −✼ ✿ ❪ ★♣❡❣❛ ♦s ✼ ✉ ❧ t ✐♠♦s ❝ ❛ r ❛ ❝ t ❡ r ❡ s

r ❡ t ✐ r ❛♥❞♦ ♦ ♣❛②❧♦❛❞ q✉❡ ✈❡ ✐♦ ♥♦ ❝❛♠♣♦

♠❛t❝❤ ❂ r❡ ✳ s ❡❛r❝❤ ✭ ✬ ❭✇❭✇❭✇ ✬ ✱ ① ✮

✶✼✾ ✐ ❢ ♠❛t❝❤ ✿

❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✶ ✷ ❪ ❂ ♠❛t❝❤ ✳ ❣r♦✉♣ ✭ ✮

❇✳ ❈ó❞✐❣♦ ♣❛r❛ ❣❡r❛r ❛rq✉✐✈♦ ✳❛r❢❢ ✼✸

✶✽✶ ❡ ❧ s ❡ ✿

❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✶ ✷ ❪ ❂ ①

✶✽✸ ❡ ❧ s ❡ ✿

❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✶ ✷ ❪ ❂ ✬▲✷❘ ✬

✶✽✺

★t❛❣

✶✽✼ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✶ ✸ ❪ ❂ r♦✇ ❬ ✿ ✿ − ✶ ❪ ❬ ✵ ❪ ★✬◆♦r♠❛❧ ✬ ♦✉ ✬ ❆tt❛❝❦ ✬

✶✽✾ ❢❊♥tr❛❞❛s ✳ ✇r✐t❡r♦✇ ✭ ❬ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✵ ❪ ✱ ❡♥tr❛❞❛s ❬ ❝♦✉♥t

❪ ❬ ✶ ❪ ✱ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✷ ❪ ✱ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✸ ❪ ✱ ❡♥tr❛❞❛s

❬ ❝♦✉♥t ❪ ❬ ✹ ❪ ✱ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✺ ❪ ✱ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✻ ❪ ✱

❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✼ ❪ ✱ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✽ ❪ ✱ ❡♥tr❛❞❛s ❬ ❝♦✉♥t

❪ ❬ ✾ ❪ ✱ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✶ ✵ ❪ ✱ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✶ ✶ ❪ ✱

❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✶ ✷ ❪ ✱ ❡♥tr❛❞❛s ❬ ❝♦✉♥t ❪ ❬ ✶ ✸ ❪ ❪ ✮

✶✾✶ ❡①❝❡♣t ❝s✈ ✳ ❊rr♦r ✱ ❡ ✿

s②s ✳ ❡ ① ✐ t ✭ ✬ ❢ ✐ ❧ ❡ ✪s ✱ ❧ ✐ ♥ ❡ ✪❞ ✿ ✪s ✿ ✬ ✪ ✭ ❛rq✉ ✐✈♦s❴t❡s t❡ ❬ ✐♥❞❡① ❪ ✱ r ❡❛❞❡r

✳ ❧✐♥❡❴♥✉♠ ✱ ❡ ✮ ✮

✶✾✸

★❢❡❝❤❛ ♦ ❛rq✉✐✈♦ ❞❡ ❧ ❡ ✐ t ✉ r ❛

✶✾✺ ❢ ✳ ❝ ❧ ♦ s ❡ ✭ ✮

★❢ ✐ ♥ ❛ ❧ ✐ ③ ❛ ♦ ♣r♦❣r❛♠❛

✶✾✼ s②s ✳ ❡ ① ✐ t

❆♥❡①♦ ❈

❈ó❞✐❣♦ ❞♦ s✐st❡♠❛ ✐♥t❡❧✐❣❡♥t❡

❤í❜r✐❞♦

❊st❡ ❝ó❞✐❣♦ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ♥❛ ❧✐♥❣✉❛❣❡♠ P②t❤♦♥ ❡ ❝r✐❛❞♦ ♣❡❧♦ ▼s❝✳ ❏❛❝s♦♥ ❘♦❞r✐❣✉❡s

❈♦rr❡✐❛ ❞❛ ❙✐❧✈❛ ❡ ❡♥tã♦ ❛❞❛♣t❛❞♦ ♣❛r❛ ❡st❡ tr❛❜❛❧❤♦✳ ❊❧❡ é r❡s♣♦♥sá✈❡❧ ♣♦r ❡①❡❝✉t❛r

♦ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ❞❡✜♥✐♥❞♦ ♦s ♣❛râ♠❡tr♦s ✐♥✐❝✐❛✐s ♣❛r❛ ❛ ❡str✉t✉r❛ ❞❛ ❘◆❆ ▼▲P✳

❘◆❆●❡♥❡t✐❝♦✳♣②

✶ ★ −∗− ❝♦❞✐♥❣ ✿ ✉t❢−✽ −∗−

✬ ✬ ✬

✸ ❈r❡❛t❡❞ ♦♥ ❏❛♥✴✷✵✶✶

✺ ❅❛✉t❤♦r ✿ ❏❛❝s♦♥ ❘❈ ❙ ✐ ❧ ✈ ❛ ❁❥❛❝ s♦♥ r ❝ s ✐ ❧ ✈❛❅❣♠❛ ✐ ❧ ✳ ❝♦♠ ✴ ❥❛❝ s♦♥ ✳ s ✐ ❧ ✈ ❛❅✉ ❢ ❡ s ✳ ❜r❃

✬ ✬ ✬

✼

❢r♦♠ ❛❧❣♦r ✐ t♠♦●❡♥❡t ✐ ❝♦ ✳ ❆❧❣♦r ✐t♠♦●❡♥❡t✐❝♦ ✐♠♣♦rt ❆❧❣●❡♥❡t✐❝♦

✾ ❢r♦♠ ♣②❢❛♥♥ ✐♠♣♦rt ❧ ✐ ❜ ❢ ❛♥♥

❢r♦♠ ♠❛t❤ ✐♠♣♦rt sq r t

✶✶

❧ ♦ ❣❋ ✐ ❧ ❡ ❂ ✧❊①❡❝✉❝❛♦❴❆❧❣❴●❡♥ ✳ ❧ ♦❣ ✧

✶✸

q♥t◆❡✉r♦♥✐♦s❊♥tr❛❞❛ ❂ ✼ ★ ❛❞❛♣t❛❞♦ ♣❛r❛ ❡ s t ❡ t r❛❜❛ ❧❤♦ ✉ t ✐ ❧ ✐ ③ ❛ ♥❞♦ ✶✸ ❡ ✼

❡♥tr❛❞❛s ★

✶✺ q♥t◆❡✉r♦♥✐♦s❙❛✐❞❛ ❂ ✷

✶✼ ★ ●❡♥❡s ❞❡ ✉♠ ❝r♦♠♦ss♦♠♦

★ ① ∗✵ ✳✶ ❢ ♦ r ① ✐♥ ✭ r❛♥❣❡ ✭✶ ✱ ✾ ✮ ✮ ❂ ✵ ✳ ✶ ✱ ✳ ✳ ✳ ✱ ✵ ✳ ✾

✶✾ ❧ ❡❛ r♥ ✐♥❣❘❛t❡ ❂ ❬ ① ∗✵ ✳✶ ❢ ♦ r ① ✐♥ ✭ r❛♥❣❡ ✭✶ ✱ ✾ ✮ ✮ ❪

♠♦♠❡♥t✉♠ ❂ ❬ ① ∗✵ ✳✶ ❢ ♦ r ① ✐♥ ✭ r❛♥❣❡ ✭✶ ✱ ✾ ✮ ✮ ❪

✷✶ ❧ r❞❡❝❛② ❂ ❬ ① ∗✵ ✳✶ ❢ ♦ r ① ✐♥ ✭ r❛♥❣❡ ✭✶ ✱ ✾ ✮ ✮ ❪

✼✹

❈✳ ❈ó❞✐❣♦ ❞♦ s✐st❡♠❛ ✐♥t❡❧✐❣❡♥t❡ ❤í❜r✐❞♦ ✼✺

t r ❛ ✐ ♥ ❡ r s ❂ ❬ ❧ ✐ ❜ ❢ ❛♥♥ ✳❚❘❆■◆❴■◆❈❘❊▼❊◆❚❆▲✱ ❧ ✐ ❜ ❢ ❛♥♥ ✳❚❘❆■◆❴◗❯■❈❑P❘❖P✱

✷✸ ❧ ✐ ❜ ❢ ❛♥♥ ✳❚❘❆■◆❴❘P❘❖P✱ ❧ ✐ ❜ ❢ ❛♥♥ ✳❚❘❆■◆❴❇❆❚❈❍ ❪

❝❛♠❛❞❛s ❂ ❬ ❧ ✐ ❜ ❢ ❛♥♥ ✳❙■●▼❖■❉✱ ❧ ✐ ❜ ❢ ❛♥♥ ✳❙■●▼❖■❉❴❙❨▼▼❊❚❘■❈✱

✷✺ ❧ ✐ ❜ ❢ ❛♥♥ ✳❙■●▼❖■❉❴❙❚❊P❲■❙❊✱ ❧ ✐ ❜ ❢ ❛♥♥ ✳

❙■●▼❖■❉❴❙❨▼▼❊❚❘■❈❴❙❚❊P❲■❙❊✱

❧ ✐ ❜ ❢ ❛♥♥ ✳▲■◆❊❆❘✱ ❧ ✐ ❜ ❢ ❛♥♥ ✳▲■◆❊❆❘❴P■❊❈❊✱

✷✼ ❧ ✐ ❜ ❢ ❛♥♥ ✳▲■◆❊❆❘❴P■❊❈❊❴❙❨▼▼❊❚❘■❈✱ ❧ ✐ ❜ ❢ ❛♥♥ ✳❚❍❘❊❙❍❖▲❉

✱

❧ ✐ ❜ ❢ ❛♥♥ ✳❚❍❘❊❙❍❖▲❉❴❙❨▼▼❊❚❘■❈✱ ❧ ✐ ❜ ❢ ❛♥♥ ✳●❆❯❙❙■❆◆✱

✷✾ ❧ ✐ ❜ ❢ ❛♥♥ ✳●❆❯❙❙■❆◆❴❙❚❊P❲■❙❊✱ ❧ ✐ ❜ ❢ ❛♥♥ ✳

●❆❯❙❙■❆◆❴❙❨▼▼❊❚❘■❈✱

❧ ✐ ❜ ❢ ❛♥♥ ✳❊▲▲■❖❚✱ ❧ ✐ ❜ ❢ ❛♥♥ ✳❊▲▲■❖❚❴❙❨▼▼❊❚❘■❈✱

✸✶ ❧ ✐ ❜ ❢ ❛♥♥ ✳❈❖❙❴❙❨▼▼❊❚❘■❈✱ ❧ ✐ ❜ ❢ ❛♥♥ ✳❙■◆❴❙❨▼▼❊❚❘■❈ ❪

✸✸ ♥❡✉r♦♥ ✐♦s❖❝✉ ❧ t♦s ❂ ❬ ✺ ✱ ✽ ✱ ✶✵ ✱ ✶✷ ✱ ✶✺ ✱

✐ ♥ t ✭ s q r t ✭ q♥t◆❡✉r♦♥✐♦s❊♥tr❛❞❛✰q♥t◆❡✉r♦♥✐♦s❙❛✐❞❛ ✮ ∗✷✮ ✱

✸✺ ✐ ♥ t ✭ ✭ q♥t◆❡✉r♦♥✐♦s❊♥tr❛❞❛✰q♥t◆❡✉r♦♥✐♦s❙❛✐❞❛ ✮ ✴✷✮ ✱

✭✷∗ q♥t◆❡✉r♦♥✐♦s❊♥tr❛❞❛✰✶✮ ❪

✸✼ ❡♣♦❝❛s❚r❡✐♥❛♠❡♥t♦ ❂ ❬ ✶✵✵ ✱ ✷✵✵ ✱ ✸✵✵ ❪

✸✾ ★ ❆rq✉✐✈♦ q✉❡ ❝♦♥t❡rá t♦❞❛ ❛ s❛ í❞❛ ❞❛ ❛✈❛ ❧ ✐ ❛ çã♦ ❛ ❧❣♦r ✐ t♠♦ ❣❡♥é t ✐ ❝ ♦

✹✶ ♦♣❡♥ ✭ ❧ ♦ ❣❋ ✐ ❧ ❡ ✱ ✧✇✧ ✮ ✳ ❝ ❧ ♦ s ❡ ✭ ✮

✹✸ ❞❡ ❢ ❛✈❛❧✐❛❝❛♦❘◆❆ ✭ ❝r♦♠♦ ✮ ✿

✬ ✬ ✬ ❋✉♥çã♦ r ❡ s♣♦♥sá✈❡ ❧ ♣❡ ❧❛ ❛✈❛ ❧ ✐ ❛ çã♦ ❞❛ ❘◆❆

✹✺ ✬ ✬ ✬

t r② ✿

✹✼ ❧ ♦❣ ❂ ♦♣❡♥ ✭ ❧ ♦ ❣❋ ✐ ❧ ❡ ✱ ✧❛✧ ✮

❝ ❂ ❝r♦♠♦ ✳ ❣❡t❈r♦♠♦ss♦♠♦ ✭ ✮

✹✾ ❧ ♦❣ ✳ ✇r ✐ t ❡ ✭ ✧❚r❡✐♥❛♥❞♦ ✪s✧✪❝ ✮

❢r♦♠ ♦s ✐♠♣♦rt ♣♦♣❡♥

✺✶ r ❡ s✉ ❧ t ❛❞♦ ❂ ♣♦♣❡♥ ✭

✧♣②t❤♦♥ ❆✈❛❧✐❛❞♦r❴❋❛♥♥ ✳ ♣② ✪s ✪s ✪s ✪s ✪s ✪s ✪s ✪s✧ ✪ ❭

✺✸ ✭ ❝ ❬ ✵ ❪ ✱ ❝ ❬ ✶ ❪ ✱ ❝ ❬ ✷ ❪ ✱ ❝ ❬ ✸ ❪ ✱ ❝ ❬ ✹ ❪ ✱ ❝ ❬ ✺ ❪ ✱ ❝ ❬ ✻ ❪ ✱ ❝ ❬ ✼ ❪ ✮ ✮ ✳

r ❡ ❛ ❞ ❧ ✐ ♥ ❡ s ✭ ✮

✺✺ ❢ ♦ r ✐ ✐♥ r ❡ s✉ ❧ t ❛❞♦ ✿

❧ ♦❣ ✳ ✇r ✐ t ❡ ✭ ✐ ✮

✺✼

❧ ♦❣ ✳ ✇r ✐ t ❡ ✭ ✧❴✧∗✺✵✰ ✬ ❭♥ ✬ ✮

✺✾ ❧ ♦❣ ✳ ❝ ❧ ♦ s ❡ ✭ ✮

r❡ t✉r♥ ❢ ❧ ♦ ❛ t ✭ r ❡ s✉ ❧ t ❛❞♦ ❬ −✶ ❪ ✳ s ♣ ❧ ✐ t ✭ ✮ ❬−✶❪✮

✻✶ ❡①❝❡♣t ✿

❈✳ ❈ó❞✐❣♦ ❞♦ s✐st❡♠❛ ✐♥t❡❧✐❣❡♥t❡ ❤í❜r✐❞♦ ✼✻

❧ ♦❣ ✳ ✇r ✐ t ❡ ✭ ✧❘❡s✉❧t❛❞♦ ✿ ✾✾✾ ✳✵ ✧ ❭

✻✸ ✧ ✭❊❘❘❖✿ ❈♦♠❜✐♥❛çã♦ ❞❡ r❡❞❡ ❡rr❛❞❛ ✮ ❭♥✧ ✮

❧ ♦❣ ✳ ✇r ✐ t ❡ ✭ ✧❴✧∗✺✵✰ ✬ ❭♥ ✬ ✮

✻✺ ❧ ♦❣ ✳ ❝ ❧ ♦ s ❡ ✭ ✮

❞❡ ❧ r ❡ s✉ ❧ t ❛❞♦

✻✼ r❡ t✉r♥ ✾✾✾ ✳✵

✻✾

★ ▼❛tr✐③ ❝♦♠ ♦s t ✐ ♣ ♦ s ❞❡ ❣❡♥❡s

✼✶ t ✐♣♦●❡♥❡s ❂ ❬ ❝❛♠❛❞❛s ✱ ❝❛♠❛❞❛s ✱ ♥❡✉r♦♥✐♦s❖❝✉❧t♦s ✱ t r ❛ ✐ ♥ ❡ r s ✱

❧ ❡❛r♥ ✐♥❣❘❛t❡ ✱ ♠♦♠❡♥t✉♠✱ ❧ r❞❡❝❛② ✱ ❡♣♦❝❛s❚r❡✐♥❛♠❡♥t♦ ❪

✼✸ ✬ ✬ ✬ ❈♦♥t❡ú❞♦ ❞♦ ✈❡t♦r t ✐♣♦●❡♥❡s ✿

❬ ✵ ❪ ❋✉♥çã♦ ❞❛ ❝❛♠❛❞❛ ♦❝✉ ❧ t ❛

✼✺ ❬ ✶ ❪ ❋✉♥çã♦ ❞❛ ❝❛♠❛❞❛ ❞❡ s❛ í❞❛

❬ ✷ ❪ ◗✉❛♥t✐❞❛❞❡ ❞❡ ◆❡✉rô♥✐♦s ❖❝✉❧t♦s

✼✼ ❬ ✸ ❪ ❆❧❣♦r✐t♠♦ ❞❡ ❆♣r❡♥❞✐③❛❞♦

❬ ✹ ❪ ▲❡❛r♥✐♥❣ ❘❛t❡

✼✾ ❬ ✺ ❪ ▼♦♠❡♥t✉♠

❬ ✻ ❪ ▲r ❉❡❝❛②

✽✶ ❬ ✼ ❪ ◗✉❛♥t✐❞❛❞❡ ❞❡ é♣♦❝❛s ❛ t r ❡ ✐ ♥ ❛ r

✬ ✬ ✬

✽✸

★ ■♥s t â♥❝ ✐ ❛ ❞♦ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ✿

✽✺ ❆● ❂ ❆❧❣●❡♥❡t✐❝♦ ✭ t✐♣♦●❡♥❡s ✱ ✷✵ ✱ ❛✈❛❧✐❛❝❛♦❘◆❆ ✱ ❝ r ✐ t ❡ r ✐ ♦ ❙ ❛ t ✐ s ❢ ❛ ❝ ❛ ♦ ❂✵✳✵✵✶ ✱

❝♦♥s ✐❞▼❛✐♦r❆✈❛❧ ✐❛❝❛♦❂❋❛❧s❡ ✱ ♠❛①●❡r❛❝♦❡s❂✶✵✵ ✱

✽✼ ✈❡r❜♦s♦❂❚r✉❡ ✮

★ ❖❜t❡♥❞♦ ♦s r ❡ s✉ ❧ t ❛❞♦ s ✿

✽✾ r ❡ s✉ ❧ t ❛❞♦ ❂ ❆●✳ ❡ ✈ ♦ ❧ ✉ ✐ r ✭ ✮

✾✶ ★ ❙❛❧✈❛♥❞♦ ♦s r ❡ s✉ ❧ t ❛❞♦ s ✿

❛rq❘❡s✉❧t❛❞♦ ❂ ♦♣❡♥ ✭ ✧❘❡s✉❧t❛❞♦❴❆❧❣−●❡♥❡t✐❝♦ ✳ t①t ✧ ✱ ✧✇✧ ✮

✾✸ ❢ ♦ r ✐ ✐♥ r ❡ s✉ ❧ t ❛❞♦ ✿

❢ ♦ r ❝ ✐♥ ✐ ✳ ❣❡t❈r♦♠♦ss♦♠♦ ✭ ✮ ✿

✾✺ ❛rq❘❡s✉❧t❛❞♦ ✳ ✇r ✐ t ❡ ✭ s t r ✭ ❝ ✮✰✬ ✬ ✮

❛rq❘❡s✉❧t❛❞♦ ✳ ✇r ✐ t ❡ ✭ ✬ ❭♥ ✬✰s t r ✭ ✐ ✳ ❣❡ t❆✈❛ ❧ ✐❛❝❛♦ ✭ ✮ ✮✰✬ ❭♥ ✬ ✮

✾✼ ❛rq❘❡s✉❧t❛❞♦ ✳ ✇r ✐ t ❡ ✭ ✬ ❭♥ ✬ ✮

❛rq❘❡s✉❧t❛❞♦ ✳ ❝ ❧ ♦ s ❡ ✭ ✮

❆♥❡①♦ ❉

❈ó❞✐❣♦ ❞♦ ❛✈❛❧✐❛❞♦r ❞❛ ❘◆❆

❊st❡ ❝ó❞✐❣♦ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ♥❛ ❧✐♥❣✉❛❣❡♠ P②t❤♦♥ ❡ ❝r✐❛❞♦ ♣❡❧♦ ▼s❝✳ ❏❛❝s♦♥ ❘♦❞r✐❣✉❡s

❈♦rr❡✐❛ ❞❛ ❙✐❧✈❛ ❡ ❡♥tã♦ ❛❞❛♣t❛❞♦ ♣❛r❛ ❡st❡ tr❛❜❛❧❤♦✳ ❊❧❡ é r❡s♣♦♥sá✈❡❧ ♣♦r r❡❝❡❜❡r ♦s

♣❛râ♠❡tr♦s ❞♦ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ❡ ❝r✐❛r ❛ ❘◆❆ ▼▲P r❡❢❡r❡♥t❡✱ r❡❛❧✐③❛♥❞♦ ❛s ❡t❛♣❛s

❞❡ tr❡✐♥❛♠❡♥t♦ ❡ t❡st❡s ❞❛ ❘◆❆✳

◆♦ ✜♥❛❧ ❞♦ ❝ó❞✐❣♦ sã♦ r❡t♦r♥❛❞❛s ❛s t❛①❛s ❞❡ ❞❡t❡❝çõ❡s ❝♦♠♦ ❋❛❧s♦s P♦s✐t✐✈♦s

✭❋P✮✱ ❋❛❧s♦s ◆❡❣❛t✐✈♦s ✭❋◆✮✱ ❱❡r❞❛❞❡✐r♦s P♦s✐t✐✈♦s ✭❱P✮ ❡ ❱❡r❞❛❞❡✐r♦s ◆❡❣❛t✐✈♦s ✭❱◆✮✱

❛❧é♠ ❞❛ ❡①♣r❡ssã♦ ✧❘❡s✉❧t❛❞♦✿✧✱ s❡❣✉✐❞❛ ❞❛ t❛①❛ ❝❧❛ss✐✜❝❛çã♦ ✐♥❝♦rr❡t❛ ✭❡rr♦r r❛t❡✮✳

❆✈❛❧✐❛❞♦r❴❋❛♥♥✳♣②

★ −∗− ❝♦❞✐♥❣ ✿ ✉t❢−✽ −∗−

✷ ✬ ✬ ✬

❈r❡❛t❡❞ ♦♥ ❏❛♥✴✷✵✶✶

✹

❅❛✉t❤♦r ✿ ❏❛❝s♦♥ ❘❈ ❙ ✐ ❧ ✈ ❛ ❁❥❛❝ s♦♥ r ❝ s ✐ ❧ ✈❛❅❣♠❛ ✐ ❧ ✳ ❝♦♠ ✴ ❥❛❝ s♦♥ ✳ s ✐ ❧ ✈ ❛❅✉ ❢ ❡ s ✳ ❜r❃

✻ ✬ ✬ ✬

✽ ❢r♦♠ s②s ✐♠♣♦rt ❛r❣✈ ✱ ❡ ① ✐ t

✶✵ ✐ ❢ ❧ ❡♥ ✭ ❛r❣✈ ✮ ❁ ✽ ✿

♣ r ✐ ♥ t ✬ ❯ t ✐ ❧ ✐ ③ ❡ ✿ ✪s ❢✉♥çã♦−❈❛♠✳ ❖❝✉❧t❛ ❢✉♥çã♦−❈❛♠✳ ❙❛í❞❛ ◗♥t−◆❡✉r ✳ ❖❝✉❧t♦s

❭❭ ✬ ✪ ❛r❣✈ ❬ ✵ ❪

✶✷ ♣r ✐♥ t ✬ ❆❧❣ ✳ ❆♣r❡♥❞✐③❛❞♦ ▲❡❛r♥✐♥❣❘❛t❡ ▼♦♠❡♥t✉♠ ❉❡❝❛② ✬ ❭

✬ ❡♣♦❝❛s❚r❡✐♥❛♠❡♥t♦ ✬

✶✹ ❡ ① ✐ t ✭✶ ✮

✶✻ ❢r♦♠ ♣②❢❛♥♥ ✐♠♣♦rt ❧ ✐ ❜ ❢ ❛♥♥

✶✽ ❝r♦♠♦ ❂ ❛r❣✈

✼✼

❉✳ ❈ó❞✐❣♦ ❞♦ ❛✈❛❧✐❛❞♦r ❞❛ ❘◆❆ ✼✽

q♥t◆❡✉r♦♥✐♦s❊♥tr❛❞❛ ❂ ✼ ★ ❛❞❛♣t❛❞♦ ♣❛r❛ ❡ s t ❡ t r❛❜❛ ❧❤♦ ✉ t ✐ ❧ ✐ ③ ❛ ♥❞♦ ✶✸ ❡ ✼

❡♥tr❛❞❛s ★

✷✵ q♥t◆❡✉r♦♥✐♦s❙❛✐❞❛ ❂ ✷

✷✷ ★ ❣❡♥❡s ❞♦ ❝r♦♠♦ss♦♠♦

♥♦♠❡❆rq❚r❡✐♥♦ ❂ ✧✷✵❴♣❡r❝❡♥t ✳ t r ❛ ✐ ♥ ✧

✷✹ ♥♦♠❡❆rq❚❡st❡ ❂ ✧✽✵❴♣❡r❝❡♥t ✳ t r ❛ ✐ ♥ ✧

❢❝❖❝✉ ❧ t❛ ❂ ✐♥ t ✭ ❝r♦♠♦ ❬ ✶ ❪ ✮

✷✻ ❢ ❝❙❛ ✐❞❛ ❂ ✐♥ t ✭ ❝r♦♠♦ ❬ ✷ ❪ ✮

♥❡✉r❖❝✉❧t♦s ❂ ✐♥ t ✭ ❝r♦♠♦ ❬ ✸ ❪ ✮

✷✽ ❛❧❣❆♣r❡♥❞ ❂ ✐♥ t ✭ ❝r♦♠♦ ❬ ✹ ❪ ✮

❧❡❛r♥❘ ❂ ❢ ❧ ♦ ❛ t ✭ ❝r♦♠♦ ❬ ✺ ❪ ✮

✸✵ ♠♦♠❡♥t ❂ ❢ ❧ ♦ ❛ t ✭ ❝r♦♠♦ ❬ ✻ ❪ ✮

❞❡❝❛② ❂ ❢ ❧ ♦ ❛ t ✭ ❝r♦♠♦ ❬ ✼ ❪ ✮

✸✷ ❡♣♦❝❛s❚r❡ ✐♥♦ ❂ ✐♥ t ✭ ❝r♦♠♦ ❬ ✽ ❪ ✮

✸✹ ★ ❛❜r✐♥❞♦ ❛rq ✳ t r ❡ ✐ ♥ ♦ ❡ t ❡ s t ❡ s

❞❛❞♦s❚r❡✐♥♦ ❂ ❧ ✐ ❜ ❢ ❛♥♥ ✳ tr❛ ✐♥ ✐♥❣❴❞❛t❛ ✭ ✮

✸✻ ❞❛❞♦s❚❡st❡ ❂ ❧ ✐ ❜ ❢ ❛♥♥ ✳ tr❛ ✐♥ ✐♥❣❴❞❛t❛ ✭ ✮

❞❛❞♦s❚r❡✐♥♦ ✳ r❡❛❞❴tr❛✐♥❴❢r♦♠❴❢✐ ❧❡ ✭ ♥♦♠❡❆rq❚r❡✐♥♦ ✮

✸✽ ❞❛❞♦s❚❡st❡ ✳ r❡❛❞❴tr❛✐♥❴❢r♦♠❴❢✐ ❧❡ ✭ ♥♦♠❡❆rq❚❡st❡ ✮

✹✵ ★ ❝r ✐❛♥❞♦ r❡❞❡

❘◆❆ ❂ ❧ ✐ ❜ ❢ ❛♥♥ ✳ ♥❡✉r❛❧❴♥❡t ✭ ✮

✹✷ ❘◆❆✳ ❝r❡❛t❡❴s♣❛rs❡❴❛rr❛② ✭✶ ✱

✭ q♥t◆❡✉r♦♥✐♦s❊♥tr❛❞❛ ✱ ♥❡✉r❖❝✉❧t♦s ✱

q♥t◆❡✉r♦♥✐♦s❙❛✐❞❛ ✮ ✮

✹✹ ❘◆❆✳ s❡t❴❧❡❛r♥ ✐♥❣❴r❛t❡ ✭ ❧❡❛r♥❘ ✮

❘◆❆✳ s❡t❴❧❡❛r♥✐♥❣❴♠♦♠❡♥t✉♠ ✭ ♠♦♠❡♥t ✮

✹✻

★ tr❡✐♥❛♠❡♥t♦

✹✽ ❘◆❆✳ s❡t❴❛❝t ✐✈❛t ✐♦♥❴❢✉♥❝t ✐♦♥❴❤✐❞❞❡♥ ✭ ❢❝❖❝✉ ❧ t❛ ✮

❘◆❆✳ s❡t❴❛❝t ✐✈❛t ✐♦♥❴❢✉♥❝t ✐♦♥❴♦✉t♣✉t ✭ ❢ ❝❙❛ ✐❞❛ ✮

✺✵ ❘◆❆✳ s❡t❴tr❛ ✐♥ ✐♥❣❴❛❧❣♦r ✐ t❤♠ ✭ ❛❧❣❆♣r❡♥❞ ✮

✐ ❢ ❘◆❆✳ ❣❡t❴tr❛ ✐♥ ✐♥❣❴❛❧❣♦r ✐ t❤♠ ✭ ✮ ❂❂ ❧ ✐ ❜ ❢ ❛♥♥ ✳❚❘❆■◆❴◗❯■❈❑P❘❖P✿

✺✷ ❘◆❆✳ s❡t❴q✉✐❝❦♣r♦♣❴❞❡❝❛② ✭ ❞❡❝❛② ✮

✺✹ ♠❛①■t❡r❛t ✐♦♥s ❂❡♣♦❝❛s❚r❡ ✐♥♦

✐ t ❡ r❛t ✐♦♥s❇❡t✇❡❡♥❘❡♣♦rt s ❂ ✺✵

✺✻ ❞❡ s ✐ r ❡❞❊r r♦ r ❂ ✵✳✵✵✵✵✶

tr② ✿

✺✽ ❘◆❆✳ tr❛✐♥❴♦♥❴❞❛t❛ ✭ ❞❛❞♦s❚r❡✐♥♦ ✱ ♠❛①■t❡r❛t ✐♦♥s ✱

✐ t ❡ r❛t ✐♦♥s❇❡t✇❡❡♥❘❡♣♦rts ✱ ❞ ❡ s ✐ r ❡❞❊r r♦ r ✮

✻✵ ❡①❝❡♣t ✿

❉✳ ❈ó❞✐❣♦ ❞♦ ❛✈❛❧✐❛❞♦r ❞❛ ❘◆❆ ✼✾

✐♠♣♦rt s②s

✻✷ ♣r ✐♥ t ✧❘❡s✉❧t❛❞♦ ✿ ✾✾✾ ✳✵ ✧

s②s ✳ ❡ ① ✐ t ✭✶ ✮

✻✹

★ ❆✈❛❧ ✐❛çã♦ ♣❡ ❧❛ t❛①❛ ❞❡ ❛❝❡ r t♦

✻✻ ❡♥tr❛❞❛ ❂ ❞❛❞♦s❚❡st❡ ✳ ❣❡t❴✐♥♣✉t ✭ ✮

s❛ ✐❞❛ ❂ ❞❛❞♦s❚❡st❡ ✳ ❣❡t❴♦✉t♣✉t ✭ ✮

✻✽ ◆♦r♠❛❧ ❂ ✵

◆♦r♠❛❧❴❆t❛q✉❡ ❂ ✵

✼✵ ◆♦r♠❛❧❴◆♦r♠❛❧ ❂ ✵

❆t❛q✉❡ ❂ ✵

✼✷ ❆t❛q✉❡❴◆♦r♠❛❧ ❂ ✵

❆t❛q✉❡❴❆t❛q✉❡ ❂ ✵

✼✹ ❢ ♦ r ✐ ✐♥ r❛♥❣❡ ✭ ❧ ❡♥ ✭ ❡♥tr❛❞❛ ✮ ✮ ✿

t r② ✿

✼✻ r ❡ s♣♦ s t❛ ❂ ❘◆❆✳ r✉♥ ✭ ❡♥tr❛❞❛ ❬ ✐ ❪ ✮

✐ ❢ s ❛ ✐❞❛ ❬ ✐ ❪ ❬ ✵ ❪ ❂❂ ✶ ✳ ✵ ✿

✼✽ ❆t❛q✉❡✰❂✶

✐ ❢ r ❡ s♣♦ s t❛ ❬ ✵ ❪ ❃ r❡ s♣♦ s t❛ ❬ ✶ ❪ ✿

✽✵ ❆t❛q✉❡❴❆t❛q✉❡✰❂✶

❡ ❧ s ❡ ✿

✽✷ ❆t❛q✉❡❴◆♦r♠❛❧✰❂✶

❡ ❧ s ❡ ✿

✽✹ ◆♦r♠❛❧✰❂✶

✐ ❢ r ❡ s♣♦ s t❛ ❬ ✵ ❪ ❃ r❡ s♣♦ s t❛ ❬ ✶ ❪ ✿

✽✻ ◆♦r♠❛❧❴❆t❛q✉❡✰❂✶

❡ ❧ s ❡ ✿

✽✽ ◆♦r♠❛❧❴◆♦r♠❛❧✰❂✶

❡①❝❡♣t ✿

✾✵ ✐♠♣♦rt s②s

♣ r ✐ ♥ t ✧❘❡s✉❧t❛❞♦ ✿ ✾✾✾ ✳✵ ✧

✾✷ s②s ✳ ❡ ① ✐ t ✭✶ ✮

✾✹ ❞❛❞♦s❚❡st❡ ✳ ❞❡s t r♦②❴tr❛ ✐♥ ✭ ✮

✾✻ t r② ✿

♣ r ✐ ♥ t ✧❋P✿ ✪❞ ❋◆✿ ✪❞ ❱P✿ ✪❞ ❱◆✿ ✪❞ ✭ ❚♦t❛❧ ✿ ✪❞✮ ✧ ✪ ❭

✾✽ ✭◆♦r♠❛❧❴❆t❛q✉❡ ✱ ❆t❛q✉❡❴◆♦r♠❛❧ ✱ ❆t❛q✉❡❴❆t❛q✉❡ ✱ ◆♦r♠❛❧❴◆♦r♠❛❧ ✱

◆♦r♠❛❧✰❆t❛q✉❡ ✮

✶✵✵ ★ ♦ r❡ s✉ ❧ t ❛❞♦ é ❛ t❛①❛ ❞❡ ❡ r r♦

r ❡ s✉ ❧ t ❛❞♦ ❂ ✭ ❢ ❧ ♦ ❛ t ✭◆♦r♠❛❧❴❆t❛q✉❡ ✮✰❢ ❧ ♦ ❛ t ✭❆t❛q✉❡❴◆♦r♠❛❧ ✮ ✮ ✴✭ ❢ ❧ ♦ ❛ t ✭◆♦r♠❛❧

✮✰❢ ❧ ♦ ❛ t ✭❆t❛q✉❡ ✮ ✮

✶✵✷ ★ ❞❡✈♦❧✈❡ ❛ t❛①❛ ❞❡ ❡ r r♦

❉✳ ❈ó❞✐❣♦ ❞♦ ❛✈❛❧✐❛❞♦r ❞❛ ❘◆❆ ✽✵

♣r ✐♥ t ✧❘❡s✉❧t❛❞♦ ✿ ✧ ✱ r ❡ s✉ ❧ t ❛❞♦

✶✵✹ ❡①❝❡♣t ✿

♣ r ✐ ♥ t ✧❘❡s✉❧t❛❞♦ ✿ ✾✾✾ ✳✵ ✧

✶✵✻

❘◆❆✳ ❞❡s t r♦② ✭ ✮