❉❊❚❊❈➬➹❖ ❉❊ ❆◆❖▼❆▲■❆❙ ❊▼
❚❊▲❊❈❖▼❯◆■❈❆➬Õ❊❙ ❆❚❘❆❱➱❙ ❉❊ ❯▼ ❙■❙❚❊▼❆
❇❆❙❊❆❉❖ ❊▼ ❈❖◆❍❊❈■▼❊◆❚❖ ◗❯❊ ❯❚■▲■❩❆
❈❖◆❙❯▲❚❆ P❖❘ ❙■▼■▲❆❘■❉❆❉❊✱ ❉❲❚ ❊ ❘❉❘ ❈❖▼❖
❋❊❘❘❆▼❊◆❚❆❙ ❉❊ ❆P❖■❖
♣♦r
❯♠❜❡rt♦ ▼❛✐❛ ❇❛r❝❡❧♦s
❉■❙❙❊❘❚❆➬➹❖ ❆P❘❊❙❊◆❚❆❉❆ ➚ ❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆
❯❇❊❘▲➶◆❉■❆✱ ▼■◆❆❙ ●❊❘❆■❙ ❈❖▼❖ P❆❘❚❊ ❉❖❙ ❘❊◗❯■❙■❚❖❙ ❊❳■●■❉❖❙
P❆❘❆ ❖❇❚❊◆➬➹❖ ❉❖ ❚❮❚❯▲❖ ❉❊ ▼❊❙❚❘❊ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❙❊❚❊▼❇❘❖ ✷✵✵✺
❝
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈❖▼P❯❚❆➬➹❖
❖s ❛❜❛✐①♦ ❛ss✐♥❛❞♦s✱ ♣♦r ♠❡✐♦ ❞❡st❡✱ ❝❡rt✐✜❝❛♠ q✉❡ ❧❡r❛♠ ❡ r❡❝♦♠❡♥❞❛♠ ♣❛r❛ ❛ ❋❛❝✉❧❞❛❞❡ ❞❡ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈♦♠♣✉t❛çã♦ ❛ ❛❝❡✐t❛çã♦ ❞❛ ❞✐ss❡rt❛çã♦ ✐♥t✐t✉❧❛❞❛ ✏❉❡t❡❝çã♦ ❞❡ ❆♥♦♠❛❧✐❛s ❡♠ ❚❡❧❡❝♦♠✉♥✐❝❛çõ❡s ❛tr❛✈és ❞❡ ✉♠ ❙✐st❡♠❛ ❇❛s❡❛❞♦ ❡♠ ❈♦♥❤❡❝✐♠❡♥t♦ q✉❡ ✉t✐❧✐③❛ ❈♦♥s✉❧t❛ ♣♦r ❙✐♠✐❧❛r✐❞❛❞❡✱ ❉❲❚ ❡ ❘❉❘ ❝♦♠♦ ❢❡rr❛♠❡♥t❛s ❞❡ ❛♣♦✐♦✑ ♣♦r ❯♠❜❡rt♦ ▼❛✐❛ ❇❛r❝❡❧♦s ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ❡①✐❣✐❞♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳
❉❛t❛✿ ❙❡t❡♠❜r♦ ✷✵✵✺
❖r✐❡♥t❛❞♦r❛✿
Pr♦❢✳❛✳ ❉r❛✳ ❘✐t❛ ▼❛r✐❛ ❞❛ ❙✐❧✈❛ ❏✉❧✐❛ ✭❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛✮
❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛✿
Pr♦❢✳ ❉r✳ P❡❞r♦ P❛✉❧♦ ❇❛❧❜✐ ❞❡ ❖❧✐✈❡✐r❛
✭❯♥✐✈❡rs✐❞❛❞❡ Pr❡s❜✐t❡r✐❛♥❛ ▼❛❝❦❡♥③✐❡✮
Pr♦❢✳ ❉r✳ ❆♥tô♥✐♦ ❊❞✉❛r❞♦ ❈♦st❛ P❡r❡✐r❛
✭❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛✮
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆
❉❛t❛✿ ❙❡t❡♠❜r♦ ✷✵✵✺
❆✉t♦r✿ ❯♠❜❡rt♦ ▼❛✐❛ ❇❛r❝❡❧♦s
❚ít✉❧♦✿ ❉❡t❡❝çã♦ ❞❡ ❆♥♦♠❛❧✐❛s ❡♠ ❚❡❧❡❝♦♠✉♥✐❝❛çõ❡s ❛tr❛✈és ❞❡ ✉♠ ❙✐st❡♠❛ ❇❛s❡❛❞♦ ❡♠
❈♦♥❤❡❝✐♠❡♥t♦ q✉❡ ✉t✐❧✐③❛ ❈♦♥s✉❧t❛ ♣♦r
❙✐♠✐❧❛r✐❞❛❞❡✱ ❉❲❚ ❡ ❘❉❘ ❝♦♠♦ ❢❡rr❛♠❡♥t❛s ❞❡ ❛♣♦✐♦
❋❛❝✉❧❞❛❞❡✿ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈♦♠♣✉t❛çã♦ ●r❛✉✿ ▼❡str❡
❋✐❝❛ ❣❛r❛♥t✐❞♦ à ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛ ♦ ❞✐r❡✐t♦ ❞❡ ❝✐r❝✉❧❛çã♦ ❡ ✐♠♣r❡ssã♦ ❞❡ ❝ó♣✐❛s ❞❡st❡ ♠❛t❡r✐❛❧ ♣❛r❛ ✜♥s ♥ã♦ ❝♦♠❡r❝✐❛❧✱ ❜❡♠ ❝♦♠♦ ♦ ❞✐r❡✐t♦ ❞❡ ❞✐str✐❜✉✐çã♦ ♣♦r s♦❧✐❝✐t❛çã♦ ❞❡ q✉❛❧q✉❡r ♣❡ss♦❛ ♦✉ ✐♥st✐t✉✐çã♦✳
❆ss✐♥❛t✉r❛ ❞♦ ❆✉t♦r
❖ ❆❯❚❖❘ ❘❊❙❊❘❱❆ P❆❘❆ ❙■ ◗❯❆▲◗❯❊❘ ❖❯❚❘❖ ❉■❘❊■❚❖ ❉❊ P❯❇▲■❈❆➬➹❖ ❉❊❙❚❊ ▼❆❚❊❘■❆▲✳
➚ ❑❧❡✐♠❛♥s✱ ♠✐♥❤❛ q✉❡r✐❞❛ ❡s♣♦s❛✱ q✉❡ ❝❡rt❛♠❡♥t❡ s♦✉❜❡ ❡s♣❡r❛r ❡ ❝♦♠♣r❡❡♥❞❡r✱ ♠❛s ❛❝✐♠❛ ❞❡ t✉❞♦✱ s♦✉❜❡ ❞❛r ❝❛r✐♥❤♦✱ ❛♣♦✐♦ ❡ ✐♥❝❡♥t✐✈♦✳ ❱♦❝ê ❝❛♠✐♥❤♦✉ ❝♦♠✐❣♦ ❛ ❝❛❞❛ ♠♦♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✱ s❡♠♣r❡ ♠❡ ❛❥✉❞❛♥❞♦ ❛ ✈❡♥❝❡r ❡st❡ ❞❡s❛✜♦✳ ▼✉✐t♦ ♦❜r✐❣❛❞♦ ♣♦r ❢❛③❡r ♣❛rt❡ ❞❛ ♠✐♥❤❛ ✈✐❞❛✦
❆❣r❛❞❡❝✐♠❡♥t♦s
❊st❛ ❞✐ss❡rt❛çã♦ ♥✉♥❝❛ t❡r✐❛ s✐❞♦ ❝♦♥❝r❡t✐③❛❞❛ s❡♠ ❛ ❝♦♥tr✐❜✉✐çã♦ ❞❡ ✈ár✐❛s ♣❡ss♦❛s ♣❛r❛ ❛s q✉❛✐s ❡✉ t❡♥❤♦ ♦ ♣r❛③❡r ❞❡ ❡①♣r❡ss❛r ♠✐♥❤❛ ❛♣r❡❝✐❛çã♦ ❡ ❣r❛t✐❞ã♦✳
Pr✐♠❡✐r❛♠❡♥t❡✱ ❡✉ ❣♦st❛r✐❛ ❞❡ ❛❣r❛❞❡❝❡r à ♠✐♥❤❛ ❖r✐❡♥t❛❞♦r❛✱ ❛ Pr♦❢❡ss♦r❛ ❘✐t❛✱ ♣❡❧❛ ♣❡rs✐stê♥❝✐❛ ❡ ♣❡❧♦ ❛♣♦✐♦ ♥♦s ♠♦♠❡♥t♦s ❞✐❢í❝❡✐s✳ ❊❧❛ ❢♦✐ r❡s♣♦♥sá✈❡❧ ♣❡❧❛ ✐♥s♣✐✲ r❛çã♦ ❞❡ ♠✉✐t❛s ❞❛s ✐❞é✐❛s ❛♣r❡s❡♥t❛❞❛s ❛q✉✐✳
❚❛♠❜é♠ ❣♦st❛r✐❛ ❞❡ ❛❣r❛❞❡❝❡r ❛♦ ♠❡✉ ❣r❛♥❞❡ ❛♠✐❣♦ ❏♦♥② ♣❡❧♦ ✐♥❝❡♥t✐✈♦✱ ❛♠✐③❛❞❡ ❡ ❝♦♠♣❛♥❤❡✐r✐s♠♦✳
❆♦s ❛♠✐❣♦s ❆❞r✐❛♥♦✱ ❘❡❣✐♥❛❧❞♦✱ ❊❞✉❛r❞♦✱ ❆♣♦❧ô♥✐♦✱ ●❡r♠❛♥♦✱ ❊r❛s♠♦✱ ▼❛✐②♠✐✱ ❱❛❣♥❡r✱ ▼✐❝❤❡❧❛✱ ▼❡❧✐ss❛ ❡ ▲✐♥✐♥❤❛ ❛❣r❛❞❡ç♦ ♣❡❧♦ ❛♣♦✐♦ ❞❡♠♦♥str❛❞♦ ❛♦ ❧♦♥❣♦ ❞❡st❡s ❛♥♦s✳
❆♦ ♠❡✉ ♣r♦❢❡ss♦r ❡ ❛♠✐❣♦ ❏♦❤♥ ❏♦❡ ❖✬❈♦♥♥❡❧❧ ❛❣r❛❞❡ç♦ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ ❡ ♣❡❧♦ ✐♥t❡r❡ss❡ ❡♠ ❛❥✉❞❛r✳
❆❣r❛❞❡ç♦ ❛ ♠✐♥❤❛ ❝✉♥❤❛❞❛ ❙✉s❛♥♥❡✱ ❛♦ ♠❡✉ ❝✉♥❤❛❞♦ ❩❛✐❞❡♥③✐♥❤♦ ❡ ❛♦ ♣❡q✉❡♥✐♥♦ ❱✐♥í❝✐✉s ♣❡❧♦s ♠♦♠❡♥t♦s ❢❡❧✐③❡s q✉❡ ✈♦❝ês ♠❡ ♣r♦♣♦r❝✐♦♥❛♠ q✉❛♥❞♦ ❡st❛♠♦s ❥✉♥t♦s✳ ◆ã♦ ♣♦❞❡r✐❛ ❞❡✐①❛r ❞❡ ❛❣r❛❞❡❝❡r ❡♠ ❡s♣❡❝✐❛❧ à ❉❛r❧❡♥❡ ♣❡❧♦ ❛♣♦✐♦✱ ✐♥❝❡♥t✐✈♦ ❡ ❝♦♠♣r❡❡♥sã♦✳
❆❣r❛❞❡ç♦ t❛♠❜é♠ ❡♠ ❡s♣❡❝✐❛❧ à ❋❆P❊▼■● ❡ à ❈❚❇❈ ❚❡❧❡❝♦♠ ♣❡❧♦ ❛♣♦✐♦ ✜♥❛♥✲ ❝❡✐r♦ ♣❛r❛ ❛♣r❡s❡♥t❛çã♦ ❞❡ ❛rt✐❣♦✳
●♦st❛r✐❛ ❞❡ ❛❣r❛❞❡❝❡r ❛♦s ♠❡✉s ♣❛✐s q✉❡ ♥✉♥❝❛ ♠❡❞✐r❛♠ ❡s❢♦rç♦s ❡♠ ♠❡ ❞❛r ❛ ♠❡❧❤♦r ❡❞✉❝❛çã♦ ♣♦ssí✈❡❧ ❡ ❛♦ ♠❡✉ ✐r♠ã♦ ❈és❛r ♣❡❧❛ ❛❧❡❣r✐❛ ❡ ♣❡❧❛ ❛♠✐③❛❞❡✳
❋✐♥❛❧♠❡♥t❡✱ ❛❣r❛❞❡ç♦ ❡s♣❡❝✐❛❧♠❡♥t❡ à ♠✐♥❤❛ ❡s♣♦s❛ ❑❧❡✐♠❛♥s ♣❡❧♦ ❛♠♦r✱ ✐♥❝❡♥t✐✈♦ ❡ ❝♦♠♣❛♥❤❡✐r✐s♠♦✳
❘❡s✉♠♦
❆ ❋r❛✉❞❡ ❡♠ t❡❧❡❢♦♥✐❛ é ✉♠ ❢❡♥ô♠❡♥♦ ♠✉♥❞✐❛❧✳ ❊st✐♠❛t✐✈❛s ❝♦rr❡♥t❡s ❝♦♥t❛❜✐✲ ❧✐③❛♠ ♣❡r❞❛s ❞❡ ✶✺ ❆ ✺✺ ❜✐❧❤õ❡s ❞❡ ❞ó❧❛r❡s ♣♦r ❛♥♦ ♥❛ ✐♥❞ústr✐❛ ❞❡ t❡❧❡❢♦♥✐❛✱ q✉❡ ♠♦✈✐♠❡♥t❛ ♥❡❣ó❝✐♦s ♥❛ ♦r❞❡♠ ❞❡ ✶✱✺ tr✐❧❤ã♦ ❞❡ ❞ó❧❛r❡s ❬✹✷❪✳ ❆ ❞❡t❡❝çã♦ ❞❡ ❢r❛✉❞❡ é ✉♠ ♣♦♥t♦ ❝rít✐❝♦ ♥❡st❛s ❡♠♣r❡s❛s✳ ❖s r✐s❝♦s ❞❡ ❢r❛✉❞❡ ❢♦rç❛♠ ❛s ❡♠♣r❡s❛s ❛ ❡♠♣r❡❡♥✲ ❞❡r ❡❧❡✈❛❞♦s ❡s❢♦rç♦s ♥❛ ❛♥á❧✐s❡ ❞♦ trá❢❡❣♦ ❞❡ ❧✐❣❛çõ❡s ❞❡ ❝❧✐❡♥t❡s✳ ◆❡st❛ ❞✐ss❡rt❛çã♦✱ ♣r♦♣õ❡✲s❡ ✉t✐❧✐③❛r ✉♠ s✐st❡♠❛ ❝♦♠♣♦st♦ ♣♦r ♠ó❞✉❧♦s ♣❛r❛ ❡❢❡t✉❛r ❝♦♥s✉❧t❛s ♣♦r s✐♠✐✲ ❧❛r✐❞❛❞❡ ❡♠ sér✐❡s t❡♠♣♦r❛✐s ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❞❡t❡❝t❛r✱ ♣r❡♠❛t✉r❛♠❡♥t❡✱ ❛♥♦♠❛❧✐❛s ♥♦ trá❢❡❣♦ ❞❡ ❧✐❣❛çõ❡s ❞❡ ❝❧✐❡♥t❡s✳ P❛r❛ ❛✉♠❡♥t❛r ❛ ❡✜❝✐ê♥❝✐❛ ❞❛s ❝♦♥s✉❧t❛s✱ ✉♠❛ ✈❡③ q✉❡ ♦ ✈♦❧✉♠❡ ❞❡ ❞❛❞♦s ❛ s❡r ❛♥❛❧✐s❛❞♦ é ♠✉✐t♦ ❣r❛♥❞❡✱ ♦ s✐st❡♠❛ ✉t✐❧✐③❛ ❛s ❍❛❛r ❲❛✲ ✈❡❧❡ts ❝♦♠♦ té❝♥✐❝❛ ❞❡ r❡❞✉çã♦ ❞❡ ❞❛❞♦s✳ ❆ ✜♠ ❞❡ ✐♥❞✐❝❛r ❛s ❛çõ❡s q✉❡ ❞❡✈❡rã♦ s❡r ❞❡s❡♥❝❛❞❡❛❞❛s ❡♠ ❢✉♥çã♦ ❞♦s r❡s✉❧t❛❞♦s ❞❛s ❝♦♥s✉❧t❛s ♣♦r s✐♠✐❧❛r✐❞❛❞❡✱ é ✉t✐❧✐③❛❞♦ ✉♠ ❙✐st❡♠❛ ❇❛s❡❛❞♦ ❡♠ ❈♦♥❤❡❝✐♠❡♥t♦ q✉❡ ❝♦rr❡s♣♦♥❞❡ ❛ ✉♠❛ ❝♦♠❜✐♥❛çã♦ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ♣r♦❞✉çã♦ ❡ ❞❡ ✉♠ s✐st❡♠❛ ❜❛s❡❛❞♦ ❡♠ ❝❛s♦s✳ ❚❛❧ s✐st❡♠❛ ❝♦rr❡s♣♦♥❞❡ à ❡str✉t✉r❛ ❘✐♣♣❧❡ ❉♦✇♥ ❘✉❧❡s ✭❘❉❘✮✳ ❖ s✐st❡♠❛ ♣r♦♣♦st♦ r❡♣r❡s❡♥t❛ ✉♠❛ ❛❧t❡r♥❛t✐✈❛ t❡❝♥✐❝❛♠❡♥t❡ ❡✜❝✐❡♥t❡ ❡ ✐♥♦✈❛❞♦r❛ ♥❛ ❞❡t❡❝çã♦ ❞❡ ❛♥♦♠❛❧✐❛s ❡♠ s✐st❡♠❛s ❞❡ t❡❧❡❢♦♥✐❛✳ P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❲❛✈❡❧❡t✱ ❈♦♥s✉❧t❛ ♣♦r ❙✐♠✐❧❛r✐❞❛❞❡✱ ❚❡❧❡❝♦♠✉♥✐❝❛çõ❡s✱ ❘❉❘✱ ❙✐st❡♠❛ ❜❛s❡❛❞♦ ❡♠ ❝♦♥❤❡❝✐♠❡♥t♦
❆❜str❛❝t
❚❡❧❡♣❤♦♥② ❢r❛✉❞ ✐s ❛ ✇♦r❧❞ ♣❤❡♥♦♠❡♥♦♥✳ ❈✉rr❡♥t ❡st✐♠❛t❡s s❤♦✇ ❧♦ss❡s ♦❢ ❢r♦♠ ✶✺ t♦ ✺✺ ❜✐❧❧✐♦♥ ❞♦❧❧❛rs ❛ ②❡❛r ✐♥ t❤❡ t❡❧❡♣❤♦♥② ✐♥❞✉str②✱ ✇❤✐❝❤ r✉♥s ❜✉s✐♥❡ss❡s ❛r♦✉♥❞ ✶✳✺ tr✐❧❧✐♦♥ ❞♦❧❧❛rs ❬✹✷❪✳ ❋r❛✉❞ ❞❡t❡❝t✐♦♥ ✐s ❛ ❝r✐t✐❝❛❧ ♣♦✐♥t ❢♦r t❤❡s❡ ❝♦♠♣❛♥✐❡s✳ ❋r❛✉❞ r✐s❦s ❢♦r❝❡ ❝♦♠♣❛♥✐❡s t♦ ♠❛❦❡ ❛ ❣r❡❛t ❡✛♦rt t♦ ❛♥❛❧②③❡ ❝❧✐❡♥ts✬ ❝❛❧❧s tr❛✣❝✳ ❚❤✐s ♣❛♣❡r ♣r♦♣♦s❡s ❛ ❑♥♦✇❧❡❞❣❡ ❙②st❡♠ ✭❑❙✮ t❤❛t ♣❡r❢♦r♠s s✐♠✐❧❛r✐t② s❡❛r❝❤ ✐♥ t✐♠❡ s❡r✐❡s ✇✐t❤ t❤❡ ♣✉r♣♦s❡ ♦❢ ❞❡t❡❝t✐♥❣ ❛♥♦♠❛❧✐❡s✱ ✐♥ ❛❞✈❛♥❝❡✱ ✐♥ t❤❡ ❝❧✐❡♥ts✬ ❝❛❧❧ tr❛✣❝✳ ❙✐♥❝❡ t❤❡r❡ ✐s ❛ ❣r❡❛t ❛♠♦✉♥t ♦❢ ❞❛t❛ ✭❝❛❧❧✮ t♦ ❜❡ ❛♥❛❧②③❡❞✱ t❤❡ s②st❡♠ ✉s❡s ❍❛❛r ❲❛✈❡❧❡ts ❛s ❛ ❞✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥ t❡❝❤♥✐q✉❡ t♦ ✐♠♣r♦✈❡ t❤❡ ❡✣❝✐❡♥❝② ♦❢ t❤❡ s❡❛r❝❤❡s✳ ❋♦r t❤❡ ♣✉r♣♦s❡ ♦❢ ✐♥❞✐❝❛t✐♥❣ t❤❡ ❛❝t✐♦♥s t❤❛t s❤♦✉❧❞ ❜❡ t❛❦❡♥ ❛s ❛ r❡s✉❧t ♦❢ s✐♠✐❧❛r✐t② s❡❛r❝❤❡s✱ ❛ ❦♥♦✇❧❡❞❣❡ s②st❡♠ ❜❛s❡❞ ♦♥ ♣r♦❞✉❝t✐♦♥ s②st❡♠s ❛♥❞ ♦♥ ❝❛s❡ ❜❛s❡❞ r❡❛s♦♥✐♥❣ s②st❡♠ ✐s ✉t✐❧✐③❡❞✳ ❚❤✐s ❤②❜r✐❞ s②st❡♠ ✐s ❝❛❧❧❡❞ ❘✐♣♣❧❡ ❉♦✇♥ ❘✉❧❡s ✭❘❉❘✮✳
❚❤❡ s②st❡♠ ♣r♦♣♦s❡❞ r❡♣r❡s❡♥ts ❛ t❡❝❤♥✐❝❛❧❧② ❡✣❝✐❡♥t ❛♥❞ ✐♥♥♦✈❛t✐♥❣ ❛❧t❡r♥❛t✐✈❡ ❢♦r ❞❡t❡❝t✐♥❣ ❛♥♦♠❛❧✐❡s ✐♥ t❡❧❡♣❤♦♥② s②st❡♠s✳
❑❡②✇♦r❞s✿ ❲❛✈❡❧❡t✱ ❙✐♠✐❧❛r✐t② ❙❡❛r❝❤✱ ❚❡❧❡❝♦♠♠✉♥✐❝❛t✐♦♥✱ ❘❉❘✱ ❑♥♦✇❧❡❞❣❡ ❙②st❡♠ ❇❛s❡❞
❙✉♠ár✐♦
❆❣r❛❞❡❝✐♠❡♥t♦s ✈
❘❡s✉♠♦ ✈✐
❆❜str❛❝t ✈✐✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ❈♦♥s✐❞❡r❛çõ❡s ■♥✐❝✐❛✐s ❡ ▼♦t✐✈❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ✶✳✷ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✸ ❊str✉t✉r❛ ❞❛ ❉✐ss❡rt❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸
✷ ❙✉♣♦rt❡ ❚❡ór✐❝♦ ✹
✷✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✷✳✷ ❆s ❙ér✐❡s ❚❡♠♣♦r❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✷✳✷✳✶ ❖❜❥❡t✐✈♦s ❞❛ ❆♥á❧✐s❡ ❞❡ ❙ér✐❡s ❚❡♠♣♦r❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✷✳✷ ❯♠ ▼♦❞❡❧♦ ♣❛r❛ ❘❡♣r❡s❡♥t❛r ❙ér✐❡ ❚❡♠♣♦r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✷✳✸ ❈♦♥s✉❧t❛s ❡♠ ❙ér✐❡s ❚❡♠♣♦r❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✸ ❚é❝♥✐❝❛s ❞❡ ❘❡❞✉çã♦ ❞❡ ❉❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✸✳✶ ❉✐s❝r❡t❡ ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✸✳✷ ❲❛✈❡❧❡ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✸✳✸ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ✲ ❙✐♥❣✉❧❛r ❱❛❧✉❡ ❉❡❝♦♠♣♦s✐t✐♦♥
✭❙❱❉✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✸✳✹ P✐❡❝❡✇✐s❡ ❆❣❣r❡❣❛t❡ ❆♣r♦①✐♠❛t✐♦♥ ✭P❆❆✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
✷✳✹ Pr♦❝❡ss♦ ❞❡ ❘❡❞✉çã♦ ❞❛ ❉✐♠❡♥sã♦ ❞♦s ❉❛❞♦s ❡ ❞❡ ■♥❞❡①❛çã♦ ❞❛s ❙ér✐❡s ❚❡♠♣♦r❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✺ ❙✐st❡♠❛s ❇❛s❡❛❞♦s ❡♠ ❈♦♥❤❡❝✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✺✳✶ ▼ó❞✉❧♦ ❞♦ ❈♦♥❤❡❝✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✺✳✷ ❆ ♠áq✉✐♥❛ ❞❡ ■♥❢❡rê♥❝✐❛ ✭❘❡❝✉♣❡r❛çã♦ ❞❛ ■♥❢♦r♠❛çã♦✮ ✳ ✳ ✳ ✳ ✸✵ ✷✳✺✳✸ ❚✐♣♦s ❞❡ ❙✐st❡♠❛s ❞❡ ❈♦♥❤❡❝✐♠❡♥t♦s ❝♦♠ r❡❧❛çã♦ à ❘❡♣r❡s❡♥✲
t❛çã♦ ❞♦ ❈♦♥❤❡❝✐♠❡♥t♦ ❡ à ❘❡❝✉♣❡r❛çã♦ ❞❛ ■♥❢♦r♠❛çã♦ ✳ ✳ ✳ ✳ ✸✶ ✷✳✺✳✹ ❙✐st❡♠❛s ❞❡ Pr♦❞✉çã♦ ❛ ❊♥❝❛❞❡❛♠❡♥t♦ Pr♦❣r❡ss✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✻ ❘✐♣♣❧❡ ❉♦✇♥ ❘✉❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✳✻✳✶ ❋✉♥❝✐♦♥❛♠❡♥t♦ ❞♦ ❘❉❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✸ ❊st❛❞♦ ❞❛ ❆rt❡ ✹✷
✸✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✷ ❲❛✈❡❧❡ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✷✳✶ ❲❛✈❡❧❡ts ❡♠ ▼✐♥❡r❛çã♦ ❞❡ ❉❛❞♦s ✭❉❛t❛♠✐♥✐♥❣✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✷✳✷ ❲❛✈❡❧❡ts ❝♦♠♦ ❋❡rr❛♠❡♥t❛ ❞❡ ❈♦♠♣❛❝t❛çã♦ ❞❡ ❉❛❞♦s ❡♠ ❙é✲
r✐❡s ❚❡♠♣♦r❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✸✳✸ ❙✐st❡♠❛s ❞❡ ❈♦♥❤❡❝✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽
✹ ❙✐st❡♠❛ ▼♦❞✉❧❛r ♣❛r❛ ❚❡❧❡❝♦♠✉♥✐❝❛çõ❡s✲❙▼❚ ✺✷ ✹✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✹✳✷ ❉❡t❡❝çã♦ ❞❡ ❆♥♦♠❛❧✐❛s ❡♠ ❚❡❧❡❝♦♠✉♥✐❝❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✷✳✶ ❆♥♦♠❛❧✐❛s r❡❢❡r❡♥t❡s à ❋r❛✉❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✷✳✷ ❆♥♦♠❛❧✐❛s r❡❢❡r❡♥t❡ ❛♦ ♣❡r✜❧ ❞❡ ✬❯s♦✬ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✸ ❆rq✉✐t❡t✉r❛ ❞♦ ❙✐st❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✸✳✶ ▼ó❞✉❧♦ ❊①tr❛t♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✸✳✷ ●❡r❛❞♦r ❞❡ ❈♦♥s✉❧t❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✹✳✸✳✸ ❖ ▼ó❞✉❧♦ ❞❡ ❈♦♥❤❡❝✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ✹✳✸✳✹ ❋❧✉①♦ ❞❡ ❚r❛❜❛❧❤♦ ❞♦ ❙▼❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽
✺ ❈♦♥❝❧✉sõ❡s ❡ ❘❡s✉❧t❛❞♦s ❖❜t✐❞♦s ✶✵✷
❇✐❜❧✐♦❣r❛✜❛ ✶✵✻
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ ❇r❡✈❡ ❤✐stór✐❝♦ s♦❜r❡ ✇❛✈❡❧❡ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✷ ❊①❡♠♣❧♦ ❞❛ ❞❡❝♦♠♣♦s✐çã♦ ❞❛s ❍❛❛r ❲❛✈❡❧❡ts✱ ❝♦♠ ❢❛t♦r ❞❡ ♥♦r♠❛❧✐✲
③❛çã♦ 1
√
2✳ ❊st❡ ❢❛t♦r é ✉s❛❞♦ ♣❛r❛ ❧❡✈❛r ❡♠ ❝♦♥s✐❞❡r❛çã♦ ❛ ✐♠♣♦rtâ♥❝✐❛
❞♦s ❝♦❡✜❝✐❡♥t❡s ❡♠ r❡❧❛çã♦ à r❡❝♦♥str✉çã♦ ❞❛ sér✐❡ t❡♠♣♦r❛❧ ❬✷✸❪✳ ✳ ✳ ✳ ✷✷ ✷✳✸ ❊①❡♠♣❧♦ ❞❛ ❞❡❝♦♠♣♦s✐çã♦ ❞❛s ❍❛❛r ❲❛✈❡❧❡ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷
✹✳✶ ❊①❡♠♣❧♦ ❞❡ ❛rq✉✐✈♦ ❈❉❘ ♣r♦❝❡ss❛❞♦ ♣❡❧♦ ▼❡❞✐❛❞♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✷ ▲✐❣❛çõ❡s ❞♦ t❡❧❡❢♦♥❡ T1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹
✹✳✸ ▼♦❞❡❧♦ ✈✐st♦ ❝♦♠♦ ❚❛❜❡❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✹ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ❙ér✐❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ●rá✜❝♦ ❞❛ ❙ér✐❡ ✭❛♣❡♥❛s ♦ ♠ês ❞❡ ❥❛♥❡✐r♦✮✿ ❱❡♥❞❛s ❞❡ ❈❛rr♦s ♥♦ ▼❡r✲ ❝❛❞♦ ❊s♣❛♥❤♦❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✷✳✷ ▼é❞✐❛ ❞❡ ❚❡♠♣❡r❛t✉r❛ ❛♥✉❛❧ ❞❛ ❝✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✳ ❋♦♥t❡✿ ✇❡✲
❛t❤❡r✳❝♦♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✸ ◆ú♠❡r♦ ❞❡ ❧✐❣❛çõ❡s ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ t❡❧❡❢♦♥❡✳ ❋♦♥t❡✿ ❈t❜❝ ❚❡❧❡❝♦♠ ✼ ✷✳✹ ❊①❡♠♣❧♦ ❞❡ ❚r❛♥s❢♦r♠❛çõ❡s ❙❤✐❢t✐♥❣ ❡ ❙❝❛❧✐♥❣ ❡♠ ✉♠❛ ❙ér✐❡ ❚❡♠♣♦r❛❧ ✶✷ ✷✳✺ ❊①❡♠♣❧♦ ❞❛ ◆♦r♠❛❧✐③❛çã♦ ❡♠ ✉♠❛ ❙ér✐❡ ❚❡♠♣♦r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✻ ❊①❡♠♣❧♦ ❞❡ ❝♦♥s✉❧t❛ ♣♦r s✐♠✐❧❛r✐❞❛❞❡ ✭❘❛♥❣❡ ◗✉❡r②✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✼ ❊①❡♠♣❧♦ ❞❡ ❝♦♥s✉❧t❛ ♣♦r s✐♠✐❧❛r✐❞❛❞❡ ✭❑✲❱✐③✐♥❤♦s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✽ ❊①❡♠♣❧♦ ❞❡ ▼❇❘✬s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✾ ❆ ❡str✉t✉r❛ ❘✲❚r❡❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✶✵ ❆♣r♦①✐♠❛çõ❡s ❞❡ ✉♠❛ sér✐❡ t❡♠♣♦r❛❧ ✭r❡♣r❡s❡♥t❛❞❛ ♥❛ ❧✐♥❤❛ tr❛❝❡❥❛❞❛✮✳
❉❡ ❝✐♠❛ ♣❛r❛ ❜❛✐①♦✱ ✭❛✮✲Pr✐♠❡✐r♦s ✷✵ ❝♦❡✜❝✐❡♥t❡s ✭❍❛❛r ❲❛✈❡❧❡t✮❀ ✭❜✮ ✲ ❖s ✺ ❝♦❡✜❝✐❡♥t❡s ♠❛✐s s✐❣♥✐✜❝❛t✐✈♦s❀ ✭❝✮ ✲ ❖s ✶✵ ❝♦❡✜❝✐❡♥t❡s ♠❛✐s s✐❣♥✐✜❝❛t✐✈♦s❀ ✭❝✮ ✲ ❖s ✷✵ ❝♦❡✜❝✐❡♥t❡s ♠❛✐s s✐❣♥✐✜❝❛t✐✈♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✷✳✶✶ ■❞é✐❛ ❣❡r❛❧ ❞♦ ❛❧❣♦r✐t♠♦ ❘❊❚❊ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✳✶✷ ❊str✉t✉r❛ ❞❡ ✉♠ ❘✐♣♣❧❡ ❉♦✇♥ ❘✉❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✷✳✶✸ ❊①❡♠♣❧♦s ❞❡ ❘✐♣♣❧❡ ❉♦✇♥ ❘✉❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✷✳✶✹ ❋✉♥❝✐♦♥❛♠❡♥t♦ ❞♦ ❘❉❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✹✳✶ P❡r✜❧ ❞❡ ✉s♦ ❞❡ ▲✐❣❛çõ❡s ❚❡❧❡❢ô♥✐❝❛s ❞❡ ✉♠ ❚❡❧❡❢♦♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✷ P❡r✜❧ ❞❡ ✉s♦ ❞❡ ▲✐❣❛çõ❡s ❚❡❧❡❢ô♥✐❝❛s ❞❡ ✉♠ ❚❡❧❡❢♦♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✸ ❆rq✉✐t❡t✉r❛ ❞❡ ✉♠ ❙✐st❡♠❛ ❆♥t✐✲❋r❛✉❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✹ ❱✐sã♦ ●❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵
✹✳✺ ❙ér✐❡ ❚❡♠♣♦r❛❧ r❡♣r❡s❡♥t❛♥❞♦ ❧✐❣❛çõ❡s t❡❧❡❢ô♥✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✹✳✻ ❋❧✉①♦ ❞♦ ♣r♦❝❡ss♦ ❞❡ ●❡r❛çã♦ ❞❛s ❙ér✐❡s ❚❡♠♣♦r❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✼ ❙ér✐❡ ❚❡♠♣♦r❛❧ ♦❜t✐❞❛ ❞♦s ❛rq✉✐✈♦s ❡①tr❛í❞♦s ❞❛s ❝❡♥tr❛✐s t❡❧❡❢ô♥✐❝❛s ✻✾ ✹✳✽ ❋♦r♠❛ ❞❡ ♣❡sq✉✐s❛r ✉♠❛ sér✐❡ ❞❡s❧♦❝❛♥❞♦ ❛ ❥❛♥❡❧❛ ❞❡ t❛♠❛♥❤♦ ✼ ✳ ✳ ✳ ✼✶ ✹✳✾ ❙✉❜s❡qüê♥❝✐❛s ❣❡r❛❞❛s ♣❛r❛ ❝♦♥s✉❧t❛ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ sér✐❡ t❡♠♣♦r❛❧ ✼✷ ✹✳✶✵ ❋❧✉①♦ ❞❡ ❝r✐❛çã♦ ❞♦ ❮♥❞✐❝❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✹✳✶✶ q✉❛♥t✐❞❛❞❡ ❞❡ sér✐❡s ❳ t❡♠♣♦ ❞❛ ❝♦♥s✉❧t❛ ❡♠ s❡❣✉♥❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✹✳✶✷ q✉❛♥t✐❞❛❞❡ ❞❡ sér✐❡s ❳ t❡♠♣♦ ❞❛ ❝♦♥s✉❧t❛ ❡♠ s❡❣✉♥❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✹✳✶✸ ❙ér✐❡ ❚❡♠♣♦r❛❧ ♦❜t✐❞❛ ❞♦s ❛rq✉✐✈♦s ❡①tr❛í❞♦s ❞❛s ❝❡♥tr❛✐s t❡❧❡❢ô♥✐❝❛s ✼✻ ✹✳✶✹ Pr♦❝❡ss♦ ❞❡ ❝r✐❛çã♦ ❞♦ ❮♥❞✐❝❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✹✳✶✺ ❙✉❜s❡qüê♥❝✐❛s ♥♦r♠❛❧✐③❛❞❛s ✭P❘✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✹✳✶✻ P❋✱ ❚❡♠♣♦ ❳ P♦♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✹✳✶✼ ❞✐stâ♥❝✐❛s ❡✉❝❧✐❞✐❛♥❛s r❡❛✐s ❡♥tr❡ P❋ ❡ P❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✹✳✶✽ ◗t❞❡ ❞❡ ❙ér✐❡s ❳ ❚❡♠♣♦ ●❛st♦ ♥❛ ❣❡r❛çã♦ ❞♦s í♥❞✐❝❡s ✭s❡❣✉♥❞♦s✮ ✳ ✳ ✽✵ ✹✳✶✾ ❚❡♠♣♦ ❣❛st♦ ♥❛ ❣❡r❛çã♦ ❞♦ í♥❞✐❝❡ ♣♦r ❞✐♠❡♥sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✹✳✷✵ P❡r❝❡♥t✉❛❧ ❞❡ t❡♠♣♦ ❣❛st♦ ♥❛ ❣❡r❛çã♦ ❞♦ í♥❞✐❝❡ ♣♦r ❞✐♠❡♥sã♦ ✳ ✳ ✳ ✳ ✽✷ ✹✳✷✶ ❏❛♥❡❧❛ ❞❡ ✼ ❞✐❛s ❞❛ ❙ér✐❡S1 ✈✐st❛ ❛ ♣❛rt✐r ❞♦ ♣♦♥t♦ ✬✵✽✴✵✶✴✷✵✵✺ ✵✵✿✵✵✬
❡ ✜♥❛❧✐③❛♥❞♦ ♥♦ ♣♦♥t♦ ✬✶✹✴✵✶✴✷✵✵✺ ✷✸✿✵✵✬✳ ❆ sér✐❡ ❥á ❡stá ✐♥❞❡①❛❞❛✳ ✳ ✽✻ ✹✳✷✷ P❉ Sq ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼
✹✳✷✸ Sq ♥♦r♠❛❧✐③❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼
✹✳✷✹ ❆ ❝♦♥s✉❧t❛ ♥❛ ❜❛s❡ ❞❡ ❞❛❞♦s✱ r❡t♦r♥♦✉ ✸ s✉❜s❡qüê♥❝✐❛s ♠❛✐s ♣ró①✐✲ ♠❛s✳ ❆ ♣r✐♠❡✐r❛ s✉❜s❡qüê♥❝✐❛✱ q✉❡ ❡stá ❡♠ ❞❡st❛q✉❡✱ t❡♠ ❞✐stâ♥❝✐❛ ❡✉❝❧✐❞✐❛♥❛ ✐❣✉❛❧ ❛ ✵ ❡♠ r❡❧❛çã♦ ❛♦ P❉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✹✳✷✺ ❙❡❧❡t✐✈✐❞❛❞❡ ♣♦r ❉✐♠❡♥sã♦ ❡ ❞✐❢❡r❡♥t❡s ❋❡❛t✉r❡ ❊①tr❛❝t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✹✳✷✻ ❚❛♠❛♥❤♦ ❞♦ ❛rq✉✐✈♦ ♣♦r ❉✐♠❡♥sã♦ ❡ ❞✐❢❡r❡♥t❡s ❋❡❛t✉r❡ ❊①tr❛❝t✐♦♥ ✳ ✳ ✽✾ ✹✳✷✼ ❚❡♠♣♦ ❣❛st♦ ♣♦r ❉✐♠❡♥sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵ ✹✳✷✽ ❊①❡♠♣❧♦ ❞❡ ❘❡❣r❛s ♥❛ ❊str✉t✉r❛ ❘❉❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻ ✹✳✷✾ ❋❧✉①♦ ❞❡ ❚r❛❜❛❧❤♦ ❞♦ ❙✐st❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾ ✹✳✸✵ ❊str✉t✉r❛ ❘❉❘✱ R1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
✶✳✶ ❈♦♥s✐❞❡r❛çõ❡s ■♥✐❝✐❛✐s ❡ ▼♦t✐✈❛çõ❡s
❆ ❢r❛✉❞❡ ❞❡ t❡❧❡❢♦♥✐❛ é ✉♠ ❢❡♥ô♠❡♥♦ ♠✉♥❞✐❛❧✳ ❊st✐♠❛t✐✈❛s ❝♦rr❡♥t❡s ❝♦♥t❛❜✐✲ ❧✐③❛♠ ♣❡r❞❛s ❞❡ ✶✺ ❆ ✺✺ ❜✐❧❤õ❡s ❞❡ ❞ó❧❛r❡s ♣♦r ❛♥♦ ♥❛ ✐♥❞ústr✐❛ ❞❡ t❡❧❡❢♦♥✐❛✱ q✉❡ ♠♦✈✐♠❡♥t❛ ♥❡❣ó❝✐♦s ♥❛ ♦r❞❡♠ ❞❡ ✶✱✺ tr✐❧❤ã♦ ❞❡ ❞ó❧❛r❡s ❬✹✷❪✳ ❖ ✈♦❧✉♠❡ ❞❡ ❧✐❣❛çõ❡s é ❣✐❣❛♥t❡s❝♦✱ ♦ q✉❡ ❞✐✜❝✉❧t❛ ❛ ❛♥á❧✐s❡ ❞♦s ❞❛❞♦s✶✳ ❆ ❞❡t❡❝çã♦ ❞❡ ❢r❛✉❞❡ é ✉♠ ♣♦♥t♦ ❝rí✲
t✐❝♦ ♥❡st❛s ❡♠♣r❡s❛s✳ ❆t✉❛❧♠❡♥t❡✱ ❡①✐st❡♠ ✈ár✐♦s s✐st❡♠❛s ❝♦♠❡r❝✐❛✐s ♣❛r❛ ❞❡t❡❝çã♦ ❞❡ ❢r❛✉❞❡s ❝❛❞❛ ✈❡③ ♠❛✐s s♦✜st✐❝❛❞♦s✱ ♠✉✐t♦s ❞❡❧❡s ❢❛③❡♥❞♦ ✉s♦ ❞❡ té❝♥✐❝❛s ❞❡ ■♥t❡❧✐✲ ❣ê♥❝✐❛ ❆rt✐✜❝✐❛❧ ❬✹✷❪✳ ❖s r✐s❝♦s ❞❡ ❢r❛✉❞❡ ❢♦rç❛♠ ❛s ❡♠♣r❡s❛s ❛ ❡♠♣r❡❡♥❞❡r ❡❧❡✈❛❞♦s ❡s❢♦rç♦s ♥❛ ❛♥á❧✐s❡ ❞♦ trá❢❡❣♦ ❞❡ ❧✐❣❛çõ❡s ❞❡ ❝❧✐❡♥t❡s✳
◆❡st❛ ❞✐ss❡rt❛çã♦✱ ♣r♦♣õ❡✲s❡ ✉♠ s✐st❡♠❛ ♠♦❞✉❧❛r ♣❛r❛ t❡❧❡❝♦♠✉♥✐❝❛çõ❡s ✭❙▼❚✮ q✉❡ ❡❢❡t✉❛ ❝♦♥s✉❧t❛s ♣♦r s✐♠✐❧❛r✐❞❛❞❡ ❡♠ sér✐❡s t❡♠♣♦r❛✐s ♣❛r❛ ❛✉①✐❧✐❛r ♥❛ ❞❡t❡❝çã♦ ❞❡ ❛♥♦♠❛❧✐❛s ❞❡ ❝♦♥s✉♠♦ ❜❛s❡❛❞❛s ♥♦ ♣❡r✜❧ ❞❡ ✉s♦ ❞❡ t❡❧❡❢♦♥❡ ❡ q✉❡ ♣r♦♣õ❡ ❛çõ❡s ❛ s❡r❡♠ ❡❢❡t✉❛❞❛s ❝❛s♦ t❛✐s ❛♥♦♠❛❧✐❛s s❡ ❝♦♥✜r♠❡♠✳ P❛r❛ t❛♥t♦✱ ♦ ❙▼❚ r❡♣r❡s❡♥t❛ ♦s ❞❛❞♦s r❡❢❡r❡♥t❡s às ❝❤❛♠❛❞❛s t❡❧❡❢ô♥✐❝❛s ❛tr❛✈és ❞❡ sér✐❡s t❡♠♣♦r❛✐s q✉❡ sã♦ ❝r✐❛❞❛s ♣♦r ✉♠ ♠ó❞✉❧♦ ●❡r❛❞♦r ❞❡ ❙ér✐❡s✳
❆ ❛♥á❧✐s❡ ✈✐s❛♥❞♦ ❛ ❞❡t❡❝çã♦ ❞❡ ❛♥♦♠❛❧✐❛s é ❡❢❡t✉❛❞❛ ❛tr❛✈és ❞❡ ♣❡sq✉✐s❛ ❞❡ s✐♠✐❧❛r✐❞❛❞❡ ❡♥tr❡ ❛s sér✐❡s t❡♠♣♦r❛✐s q✉❡ r❡♣r❡s❡♥t❛♠ ❛ ✉t✐❧✐③❛çã♦ r❡❛❧ ❞❛s ❧✐♥❤❛s t❡❧❡❢ô♥✐❝❛s ❡ ❛s sér✐❡s q✉❡ r❡♣r❡s❡♥t❛♠ ✉♠ ♣❛❞rã♦ ❞❡ ✉s♦ ✐❞❡❛❧ ❡st❛❜❡❧❡❝✐❞♦ ♣❡❧♦s
✶❊st❛♠♦s ❝♦♥s✐❞❡r❛♥❞♦ ❛♣❡♥❛s ✐♥❢♦r♠❛çõ❡s ❝♦♥t✐❞❛s ♥♦s ❈❉❘✬s ✭❈❛❧❧ ❉❡t❛✐❧ ❘❡❝♦r❞s✮✳
✷
♣r♦♣r✐❡tár✐♦s ❞❛ ❧✐♥❤❛ ♦✉ ✉♠ ♣❡r✜❧ ❞❡ ❢r❛✉❞❡✳
❯♠ ♦✉tr♦ ♠ó❞✉❧♦ ❞♦ ❙▼❚ é ♦ ♠ó❞✉❧♦ ●❡r❛❞♦r ❞❡ ❈♦♥s✉❧t❛s✳ ❚❛❧ ♠ó❞✉❧♦ t❡♠ ❝♦♠♦ ❢✉♥çã♦ ❡①❡❝✉t❛r ❛s ❝♦♥s✉❧t❛s ♣r♦♣♦st❛s ♣❡❧♦s ✉s✉ár✐♦s ❞♦ ❙▼❚ ✐♥❞❛❣❛♥❞♦ s♦❜r❡ ❛ ♥♦r♠❛❧✐❞❛❞❡ ♦✉ ♥ã♦ ❞❛ ✉t✐❧✐③❛çã♦ ❞❛s ❧✐♥❤❛s t❡❧❡❢ô♥✐❝❛s✳
❯♠❛ ✈❡③ t❡r♠✐♥❛❞♦ ♦ ♣r♦❝❡ss♦ ❞❡ ❝♦♥s✉❧t❛s✱ ♦ ❙▼❚ ❛❝✐♦♥❛ ✉♠ ú❧t✐♠♦ ♠ó❞✉❧♦✿ ♦ ❙✐st❡♠❛ ❞❡ ❈♦♥❤❡❝✐♠❡♥t♦ ✭♦✉ ❙✐st❡♠❛ ❇❛s❡❛❞♦ ❡♠ ❈♦♥❤❡❝✐♠❡♥t♦✮✱ r❡s♣♦♥sá✈❡❧ ♣♦r ✐♥❞✐❝❛r ❛s ❛çõ❡s q✉❡ ❞❡✈❡rã♦ s❡r ❞❡s❡♥❝❛❞❡❛❞❛s ❡♠ ❢✉♥çã♦ ❞♦s r❡s✉❧t❛❞♦s ❞❛s ❛♥á❧✐s❡s ❞❡ s✐♠✐❧❛r✐❞❛❞❡✳ ❚❛❧ ♠ó❞✉❧♦ ❝♦rr❡s♣♦♥❞❡ ❛ ✉♠❛ ❝♦♠❜✐♥❛çã♦ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ♣r♦✲ ❞✉çã♦ ❡ ❞❡ ✉♠ s✐st❡♠❛ ❜❛s❡❛❞♦ ❡♠ ❝❛s♦s ✭❈❛s❡ ❇❛s❡❞ ❘❡❛s♦♥✐♥❣✮✱ s❡♥❞♦ ❝♦♥str✉í❞♦ ♥♦s ♠♦❧❞❡s ❞❛ ❡str✉t✉r❛ ❘❉❘ ✭❘✐♣♣❧❡ ❉♦✇♥ ❘✉❧❡s✮✳ ❊st❡ ♠ó❞✉❧♦ é ❝♦♠♣♦st♦ ♣♦r r❡❣r❛s r❡❧❛❝✐♦♥❛❞❛s ❛♦ ✉♥✐✈❡rs♦ ❞❛ t❡❧❡❢♦♥✐❛✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✿ ❙❡ ♦ ♣❡r✜❧ ❞❡ ❧✐❣❛çõ❡s ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ t❡❧❡❢♦♥❡ ✭sér✐❡ t❡♠♣♦r❛❧✮ ❡st✐✈❡r ❙❊▼❊▲❍❆◆❚❊ ❛ ✉♠ ♣❛❞rã♦ ❞❡ ❢r❛✉❞❡s ✭sér✐❡ t❡♠♣♦r❛❧✮ ❝♦♥❤❡❝✐❞♦✱ ❡♥tã♦ ❡st❡ t❡❧❡❢♦♥❡ ♣♦❞❡ s❡r ❡♥✈✐❛❞♦ ❛ ✉♠❛ ár❡❛ r❡s♣♦♥sá✈❡❧ ♣♦r ❢r❛✉❞❡s ♣❛r❛ s❡r ❛♥❛❧✐s❛❞♦✳
❯♠ ❞♦s ♣r♦❜❧❡♠❛s q✉❡ ❝♦♠♣r♦♠❡t❡♠ ❛ ❡✜❝✐ê♥❝✐❛ ❞❡ss❛s ❛♥á❧✐s❡s é ♦ ❣r❛♥❞❡ ✈♦✲ ❧✉♠❡ ❞❡ ❞❛❞♦s ❛ s❡r ❛♥❛❧✐s❛❞♦✳ P❛r❛ r❡s♦❧✈❡r ❡st❡ ♣r♦❜❧❡♠❛✱ ♦ ❙▼❚ ❧❛♥ç❛ ♠ã♦ ❞❡ ❞✉❛s ❢❡rr❛♠❡♥t❛s✿ ❛s ❍❛❛r ❲❛✈❡❧❡ts✱ ❝♦♠♦ té❝♥✐❝❛ ♣❛r❛ r❡❞✉③✐r ♦s ❞❛❞♦s s❡♠ ❝♦♠♣r♦♠❡t❡r ♦s r❡s✉❧t❛❞♦s ❞❛ ❛♥á❧✐s❡✱ ❡ ❛ ✐♥❞❡①❛çã♦✱ ❝♦♠♦ té❝♥✐❝❛ ❞❡ ♦t✐♠✐③❛çã♦ ❞❡ ❝♦♥s✉❧t❛✳ ❯♠ s❡❣✉♥❞♦ ♣r♦❜❧❡♠❛ ❝♦♥s✐st❡ ♥♦ ❢❛t♦ ❞❡ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ s❡r ♠✉✐t♦ ❞✐♥â♠✐❝♦✱ ❡①✐❣✐♥❞♦ ❢r❡qü❡♥t❡s ❛t✉❛❧✐③❛çõ❡s ♥❛ ❇❛s❡ ❞❡ ❈♦♥❤❡❝✐♠❡♥t♦✳ ➱ ♣❛r❛ ❧✐❞❛r ❝♦♠ ❡st❡ ♣r♦❜❧❡♠❛ q✉❡ ♦ ❙▼❚ ✉t✐❧✐③❛ ♦ ❘❉❘ ❝♦♠♦ ❢❡rr❛♠❡♥t❛ ❞❡ ❝♦♥str✉çã♦ ✐♥❝r❡♠❡♥t❛❧ ❞❛ ❜❛s❡ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦✳
✶✳✷ ❖❜❥❡t✐✈♦s
✸
✶✳✸ ❊str✉t✉r❛ ❞❛ ❉✐ss❡rt❛çã♦
❈❛♣ít✉❧♦ ✷
❙✉♣♦rt❡ ❚❡ór✐❝♦
✷✳✶ ■♥tr♦❞✉çã♦
❖ ♣r♦♣ós✐t♦ ❞❡st❡ ❝❛♣ít✉❧♦ é ❞❛r s✉♣♦rt❡ t❡ór✐❝♦ ♣❛r❛ ✉♠❛ ♠❡❧❤♦r ❝♦♠♣r❡❡♥sã♦ ❞♦ s✐st❡♠❛ ♣r♦♣♦st♦ ♥❡st❡ tr❛❜❛❧❤♦✳ ❈♦♥❢♦r♠❡ ✐♥tr♦❞✉③✐❞♦ ❛♥t❡r✐♦r♠❡♥t❡✱ t❛❧ s✐st❡♠❛ r❡♣r❡s❡♥t❛ ❞❛❞♦s ❞♦s ❝❧✐❡♥t❡s ❞❡ ✉♠❛ ❡♠♣r❡s❛ ❞❡ t❡❧❡❝♦♠✉♥✐❝❛çõ❡s ❛tr❛✈és ❞❡ sér✐❡s t❡♠♣♦r❛✐s✳ ❆ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ❞❛❞♦s ❛ s❡r❡♠ ❛r♠❛③❡♥❛❞♦s ❡ ❛♥❛❧✐s❛❞♦s ❡①✐❣❡✱ ❛ tít✉❧♦ ❞❡ ❡✜❝✐ê♥❝✐❛✱ ❛ ❛♣❧✐❝❛çã♦ ❞❡ ✉♠❛ té❝♥✐❝❛ ❞❡ r❡❞✉çã♦ ❞❡ ❞❛❞♦s q✉❡✱ ♥♦ ❝❛s♦ ❞❛ ♣r❡s❡♥t❡ ♣r♦♣♦st❛✱ ❝♦♥s✐st❡ ♥❛s ❍❛❛r ❲❛✈❡❧❡ts✳ ❆ ✜♠ ❞❡ ❡①♣❧♦r❛r ❛s ✐♥❢♦r♠❛çõ❡s ❝♦♥t✐❞❛s ♥❡ss❡s ❞❛❞♦s✱ ✉t✐❧✐③❛✲s❡ ❛ ❡str✉t✉r❛ ❞❡ ✉♠ ❙✐st❡♠❛ ❇❛s❡❛❞♦ ❡♠ ❈♦♥❤❡❝✐♠❡♥t♦ ✭❙❈✮ ❝✉❥❛ ❇❛s❡ ❞❡ ❈♦♥❤❡❝✐♠❡♥t♦ ✭❇❈✮ é ❝♦♥str✉í❞❛ ✐♥❝r❡♠❡♥t❛❧♠❡♥t❡✱ ❛tr❛✈és ❞❛ ❢❡rr❛♠❡♥t❛ ❘❉❘✳ ❚❛❧ ❡①♣❧♦r❛çã♦ é ❝♦♥s❡❣✉✐❞❛ ♣♦r ♠❡✐♦ ❞❡ té❝♥✐❝❛s ❞❡ ❝♦♥s✉❧t❛s ❛♣❧✐❝❛❞❛s às sér✐❡s t❡♠♣♦r❛✐s✳ ◆❛s s❡çõ❡s q✉❡ s❡ s❡❣✉❡♠ ❛♣r❡s❡♥t❛✲s❡ ✉♠ r❡s✉♠♦ ❞❛s ❢❡rr❛♠❡♥t❛s q✉❡ s❡r✈❡♠ ❞❡ s✉♣♦rt❡ ❛♦ s✐st❡♠❛✳
✷✳✷ ❆s ❙ér✐❡s ❚❡♠♣♦r❛✐s
❯♠❛ sér✐❡ t❡♠♣♦r❛❧ é ✉♠❛ ❝♦❧❡çã♦ ❞❡ ♦❜s❡r✈❛çõ❡s ❢❡✐t❛s s❡qü❡♥❝✐❛❧♠❡♥t❡ ♥♦ t❡♠♣♦ ❬✶✵❪✳ ❊st❛s ♦❜s❡r✈❛çõ❡s✱ ♥♦r♠❛❧♠❡♥t❡✱ sã♦ ♥ú♠❡r♦s r❡❛✐s r❡♣r❡s❡♥t❛❞♦s ❡♠ ✐♥✲ t❡r✈❛❧♦s r❡❣✉❧❛r❡s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❛♥✉❛❧♠❡♥t❡✱ ♠❡♥s❛❧♠❡♥t❡✱ ❞✐❛r✐❛♠❡♥t❡✳ ❋r❡qü❡♥✲ t❡♠❡♥t❡✱ ♦s ❞❛❞♦s ✐rr❡❣✉❧❛r❡s sã♦ ✐♥t❡r♣♦❧❛❞♦s ♣❛r❛ ❢♦r♠❛r ✈❛❧♦r❡s r❡❣✉❧❛r❡s ❛♥t❡s ❞❡
✺
s❡r❡♠ ❛♥❛❧✐s❛❞♦s ❬✹✽❪✳ ❈♦♠♦ ❡①❡♠♣❧♦ ❞❡ sér✐❡s t❡♠♣♦r❛✐s✱ ♣♦❞❡♠♦s ❝✐t❛r ❬✸✶❪✿
✶✳ ❡st✐♠❛t✐✈❛s tr✐♠❡str❛✐s ❞❡ P◆❇ ❀
✷✳ ✈❛❧♦r❡s ❞✐ár✐♦s ❞❡ t❡♠♣❡r❛t✉r❛ ❞❡ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❝✐❞❛❞❡❀
✸✳ ✈❛❧♦r❡s ♠❡♥s❛✐s ❞❡ ✈❡♥❞❛s ❞❡ ❛✉t♦♠ó✈❡✐s ♥♦ ❇r❛s✐❧❀
✹✳ ✉♠ r❡❣✐str♦ ❞❡ ♠❛rés ♥♦ ♣♦rt♦ ❞❡ ❙❛♥t♦s✳
❆s ❙ér✐❡s ❚❡♠♣♦r❛✐s sã♦ ❝❤❛♠❛❞❛s ❝♦♥tí♥✉❛s s❡ ❛s ♦❜s❡r✈❛çõ❡s sã♦ r❡❛❧✐③❛❞❛s ❝♦♥t✐✲ ♥✉❛♠❡♥t❡ ♥♦ t❡♠♣♦ ❡✱ ❞✐s❝r❡t❛s✱ s❡ ❡❧❛s sã♦ ❢❡✐t❛s ❛♣❡♥❛s ❡♠ ❞❡t❡r♠✐♥❛❞♦s ♣♦♥t♦s✳ ◆♦s ❡①❡♠♣❧♦s ✶✲✸ ❛s sér✐❡s t❡♠♣♦r❛✐s sã♦ ❞✐s❝r❡t❛s✱ ❡♥q✉❛♥t♦ q✉❡✱ ♥♦ ❡①❡♠♣❧♦ ✹✱ sã♦ ❝♦♥tí♥✉❛s✳ ▼✉✐t❛s ✈❡③❡s✱ ✉♠❛ sér✐❡ t❡♠♣♦r❛❧ ❞✐s❝r❡t❛ é ♦❜t✐❞❛ ❛tr❛✈és ❞❡ ❛♠♦str❛❣❡♠ ❞❡ ✉♠❛ sér✐❡ t❡♠♣♦r❛❧ ❝♦♥tí♥✉❛ ❡♠ ✐♥t❡r✈❛❧♦s ❞❡ t❡♠♣♦s ✐❣✉❛✐s✱∆t✳ ❊♠ ♦✉tr♦s ❝❛s♦s✱
t❡♠✲s❡ ♦ ✈❛❧♦r ❞❛ sér✐❡ ❛❝✉♠✉❧❛❞♦ ❡♠ ✉♠ ❞❛❞♦ ✐♥st❛♥t❡✱ ❝♦♠♦ ✐❧✉str❛ ♦ ❡①❡♠♣❧♦ ✸✳ ❊♠ ❣❡r❛❧✱ ✉♠❛ sér✐❡ t❡♠♣♦r❛❧ é ❝❤❛♠❛❞❛ ❞❡ r❡❣✉❧❛r s❡ ♦s ♣♦♥t♦s ♦❜s❡r✈❛❞♦s sã♦ ❢❡✐t♦s ♥♦ ♠❡s♠♦ ❡s♣❛ç♦✱ ❝❛s♦ ❝♦♥trár✐♦ ❡❧❛s sã♦ ❝❤❛♠❛❞❛s ❞❡ ✐rr❡❣✉❧❛r❡s✳ ❋♦r♠❛❧✲ ♠❡♥t❡✱ ✉♠❛ sér✐❡ t❡♠♣♦r❛❧ q✉❡ ❞❡s❝r❡✈❡ ♦ ❡st❛❞♦ ❞❡ ✉♠ ♦❜❥❡t♦ ❞❡ ❞❛❞♦s ❡♠ ♥ ♣♦♥t♦s ♣♦❞❡ s❡r ❞❡✜♥✐❞❛ ❝♦♠♦ ✉♠❛ s❡qüê♥❝✐❛ ♦r❞❡♥❛❞❛✿
S ={Si}n−1
i=0, Si = (ti, vi) ✭✷✳✷✳✶✮
♦♥❞❡ vi é ♦ ✈❛❧♦r ❞♦ ♦❜❥❡t♦ ❞❡ ❞❛❞♦s ♥♦ ♣♦♥t♦ ti✳ ◆♦r♠❛❧♠❡♥t❡ ♦ ✈❛❧♦r ❞❡ ✉♠
♦❜❥❡t♦ ❞❡ ❞❛❞♦s é ✉♠ ✈❛❧♦r ♥✉♠ér✐❝♦ ✭❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ♣r❡ç♦s✱ t❡♠♣❡r❛t✉r❛s ❡t❝✳✮✱ ♣♦ré♠✱ ♣♦❞❡ ❤❛✈❡r ✐♥ú♠❡r❛s s✐t✉❛çõ❡s ♦♥❞❡ ♦ ✈❛❧♦r ❞♦ ❞❛❞♦ ♥ã♦ s❡❥❛ ✉♠ s✐♠♣❧❡s ✐♥t❡✐r♦✱ ♠❛s ✉♠❛ s❡qüê♥❝✐❛ ❞❡ ✐♠❛❣❡♥s q✉❡ ✈❛r✐❛♠ ❝♦♠ ♦ t❡♠♣♦✱ ✉♠❛ sér✐❡ ❞❡ ♣✉❧s♦s t❡❧❡❢ô♥✐❝♦s✱ ❡t❝✳ ❯♠ ♠♦❞❡❧♦ ❝❧áss✐❝♦ ♣❛r❛ sér✐❡s t❡♠♣♦r❛✐s s✉♣õ❡ q✉❡ ❛ sér✐❡ t❡♠♣♦r❛❧
Zt, t = 1, ...N ♣♦ss❛ s❡r ❡s❝r✐t❛ ❝♦♠♦ ❛ s♦♠❛ ❞❡ três ❝♦♠♣♦♥❡♥t❡s✿ ✉♠❛ t❡♥❞ê♥❝✐❛✱
✉♠❛ ❝♦♠♣♦♥❡♥t❡ s❛③♦♥❛❧ ❡ ✉♠ t❡r♠♦ ❛❧❡❛tór✐♦✿
✻
❆ t❡♥❞ê♥❝✐❛ é ❝❛✉s❛❞❛ ♣♦r ❢❛t♦r❡s q✉❡ sã♦ ♠❡❞✐❞♦s ❞✉r❛♥t❡ ♣❡rí♦❞♦s ❧♦♥❣♦s ❞❡ t❡♠♣♦✳ ❏á ❛ ❝♦♠♣♦♥❡♥t❡ s❛③♦♥❛❧ ❛♣❛r❡❝❡ q✉❛♥❞♦ ❛s ♦❜s❡r✈❛çõ❡s sã♦ r❡❣✐str❛❞❛s ❡♠ ♣❡rí♦❞♦s ❝✉rt♦s ❡ ❛♣r❡s❡♥t❛ ✉♠❛ ♣❡r✐♦❞✐❝✐❞❛❞❡ ♠❛r❝❛♥t❡✳
P❛r❛ ❢❛❝✐❧✐t❛r ♥♦ss♦ ❡♥t❡♥❞✐♠❡♥t♦✱ s❡❣✉❡ ❛❜❛✐①♦ ❡①❡♠♣❧♦s ❞❡ sér✐❡s t❡♠♣♦r❛✐s r❡❛✐s ❬✸✶❪✿
✶✳ Pr♦❞✉çã♦ ❞❡ ❧❡✐t❡ ♥♦ ❊st❛❞♦ ❞❡ ❙ã♦ P❛✉❧♦✱ ❝♦♠♣♦st❛ ❞❡ ✼✼ ❞❛❞♦s ♠❡❞✐❞♦s ♠❡♥s❛❧♠❡♥t❡ ❡ ❝♦♠ ♣❡r✐♦❞✐❝✐❞❛❞❡ ❞❡ ✶✷ ♠❡s❡s❀
✷✳ ❮♥❞✐❝❡ ❞❡ Pr♦❞✉t♦ ■♥❞✉str✐❛❧ ❞♦ ❇r❛s✐❧✱ ❝♦♠♣♦st❛ ❞❡ ✶✸✾ ♦❜s❡r✈❛çõ❡s ♠❡♥s❛✐s ❡ ❝♦♠ ♣❡r✐♦❞✐❝✐❞❛❞❡ ❞❡ ✶✷ ♠❡s❡s❀
✸✳ ❮♥❞✐❝❡ ❞❡ ❈✉st♦ ❞❡ ❱✐❞❛ ❞❡ ❙ã♦ P❛✉❧♦✱ ❝♦♠ ✶✷✻ ♦❜s❡r✈❛çõ❡s ♠❡♥s❛✐s ❡ ♥ã♦✲ s❛③♦♥❛❧❀
❖ ❣rá✜❝♦ ❛ s❡❣✉✐r ♠♦str❛ ✉♠❛ sér✐❡ t❡♠♣♦r❛❧ ❝✐t❛❞❛ ❡♠ ❬✹❪✿ ❖ ♣ró①✐♠♦ ❡①❡♠♣❧♦✱
❋✐❣✉r❛ ✷✳✶✿ ●rá✜❝♦ ❞❛ ❙ér✐❡ ✭❛♣❡♥❛s ♦ ♠ês ❞❡ ❥❛♥❡✐r♦✮✿ ❱❡♥❞❛s ❞❡ ❈❛rr♦s ♥♦ ▼❡r❝❛❞♦ ❊s♣❛♥❤♦❧
✼
❋✐❣✉r❛ ✷✳✷✿ ▼é❞✐❛ ❞❡ ❚❡♠♣❡r❛t✉r❛ ❛♥✉❛❧ ❞❛ ❝✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✳ ❋♦♥t❡✿ ✇❡❛t❤❡r✳❝♦♠
✽
✷✳✷✳✶ ❖❜❥❡t✐✈♦s ❞❛ ❆♥á❧✐s❡ ❞❡ ❙ér✐❡s ❚❡♠♣♦r❛✐s
❆ t❡♥❞ê♥❝✐❛ ❛t✉❛❧ ❡♠ ❛♥❛❧✐s❛r ❙ér✐❡s ❚❡♠♣♦r❛✐s ✈✐s❛✱ ❜❛s✐❝❛♠❡♥t❡ ❬✸✶❪✿
✶✳ ■♥✈❡st✐❣❛r ♦ ♠❡❝❛♥✐s♠♦ ❣❡r❛❞♦r ❞❛ sér✐❡ t❡♠♣♦r❛❧❀
✷✳ ❋❛③❡r ♣r❡✈✐sõ❡s ❞❡ ✈❛❧♦r❡s ❢✉t✉r♦s ❞❛ sér✐❡❀
✸✳ ❉❡s❝r❡✈❡r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛ sér✐❡❀
✹✳ Pr♦❝✉r❛r ♣❡r✐♦❞✐❝✐❞❛❞❡s r❡❧❡✈❛♥t❡s ♥♦s ❞❛❞♦s❀
✺✳ ■❞❡♥t✐✜❝❛r ♣❛❞rõ❡s✳
✷✳✷✳✷ ❯♠ ▼♦❞❡❧♦ ♣❛r❛ ❘❡♣r❡s❡♥t❛r ❙ér✐❡ ❚❡♠♣♦r❛❧
❇❛s❡❛❞♦ ♥❛ ❞❡✜♥✐çã♦ ✭✷✳✷✳✶✮✱ ✉♠❛ sér✐❡ t❡♠♣♦r❛❧ ♣♦❞❡ s❡r r❡♣r❡s❡♥t❛❞❛ ❝♦♠♦ ✉♠❛ s❡qüê♥❝✐❛ ♦r❞❡♥❛❞❛ ❞❡ ♣♦♥t♦s ❡ s❡✉s ✈❛❧♦r❡s✳ ◆❛ r❡♣r❡s❡♥t❛çã♦ ♣r♦♣♦st❛ ❡♠ ❬✶✵❪ ❢♦✐ ❛❞✐❝✐♦♥❛❞♦ ✉♠ ✐❞❡♥t✐✜❝❛❞♦r ♣❛r❛ ❞✐❢❡r❡♥❝✐❛r ✉♠❛ sér✐❛ ❞❛ ♦✉tr❛✳ ❙❡ ♦ ✐❞ é ú♥✐❝♦✱ ✉♠❛ sér✐❡ ♣♦❞❡ s❡r r❡♣r❡s❡♥t❛❞❛ ❝♦♠♦ ✿
< id,(t0, v0), ....,(tn−1, vn−1)> ✭✷✳✷✳✸✮
P♦ré♠✱ ♥ã♦ ❤á ♥❡♥❤✉♠❛ r❛③ã♦ ♣❛r❛ r❡str✐♥❣✐r ❛ sér✐❡ t❡♠♣♦r❛❧ ❞❡ ♠♦❞♦ q✉❡ ❡❧❛ ❛r♠❛③❡♥❡ ♦ ✈❛❧♦r ❞❡ ❛♣❡♥❛s ✉♠ ♦❜❥❡t♦ ❞❡ ❞❛❞♦✳ ❋❛③❡♥❞♦ ✉♠❛ ❡①t❡♥sã♦ ❞❛ ❞❡✜♥✐çã♦ ✭✷✳✷✳✶✮✱ ♣♦❞❡♠♦s ❝♦♥s✐❞❡r❛r q✉❡ ✉♠❛ sér✐❡ t❡♠♣♦r❛❧ ♣♦❞❡ ❝♦♥s✐st✐r ❡♠ ♠❛✐s ❞❡ ✉♠ ♦❜❥❡t♦ ❞❡ ❞❛❞♦s✳ ❙❡v1, ..., vksã♦ ♦❜❥❡t♦s ❞❡ ❞❛❞♦s q✉❡ ❝♦♥st✐t✉❡♠ ✉♠❛ sér✐❡ t❡♠♣♦r❛❧✱
❡ vij ♦ ✈❛❧♦r ❞♦ ♦❜❥❡t♦ ❞❡ ❞❛❞♦s vi ♥♦ ♣♦♥t♦ t
j✱ ✉♠❛ r❡♣r❡s❡♥t❛çã♦ ❣❡r❛❧ é✿
< id,(t0, v10, ...v1k), ....,(tn−1, v
1
n−1, ...v
k
n−1)> ✭✷✳✷✳✹✮
❊♠❜♦r❛ s❡❥❛ ❝♦♠♣❧❡t❛✱ ❡st❛ r❡♣r❡s❡♥t❛çã♦ ❞❡✈❡ s❡❣✉✐r ❛s ♣r♦♣r✐❡❞❛❞❡s ❣❡r❛✐s ❞❡ sér✐❡s t❡♠♣♦r❛✐s✳ ❊st❛s ♣r♦♣r✐❡❞❛❞❡s sã♦ ❬✶✵❪✿
✾
✷✳ ❖ ❞♦♠í♥✐♦ ❞♦ t❡♠♣♦ ❡ ❣r❛♥✉❧❛r✐❞❛❞❡✱ ♦✉ s❡❥❛✱ ♦ t✐♣♦ ❞❡ ♣♦♥t♦s ❡ ❛ ❞✐stâ♥✲ ❝✐❛ ♠í♥✐♠❛ ❡♥tr❡ ❡❧❡s✳ ◆ós ♣♦❞❡♠♦s t❡r ✉♠❛ r❡♣r❡s❡♥t❛çã♦ ♦r❞✐♥❛❧ ♦♥❞❡ ♣♦♥t♦s s✉❝❡ss✐✈♦s sã♦ r❡♣r❡s❡♥t❛❞♦s ♣♦r ✐♥t❡✐r♦s s✉❝❡ss✐✈♦s ✭✶✱✷✱✸✱❡t❝✳✮✱ ♦✉ ✉♠❛ r❡♣r❡✲ s❡♥t❛çã♦ t✐♣♦ ❝❛❧❡♥❞ár✐♦✱ ♦♥❞❡ ❛ ❤✐❡r❛rq✉✐❛ ❞❡ t❡♠♣♦ ✭ ❛♥♦✱ ♠ês✱ ❞✐❛✱ ❡t❝✳✮ é ✉s❛❞❛✳
✸✳ ■♥t❡r✈❛❧♦ ✈á❧✐❞♦ é ♦ ✐♥t❡r✈❛❧♦ ✈á❧✐❞♦ ❞♦s ♣♦♥t♦s ❞❛ sér✐❡ t❡♠♣♦r❛❧✳
✹✳ ❘❡❣✉❧❛r✐❞❛❞❡✱♦✉ s❡❥❛✱ ❞❡✜♥❡ s❡ ❛ sér✐❡ t❡♠♣♦r❛❧ t❡♠ ✉♠ ✈❛❧♦r ♣❛r❛ ❝❛❞❛ ♣♦♥t♦ ♥♦ ✐♥t❡r✈❛❧♦ ✐♥t❡r✈❛❧♦ ✈á❧✐❞♦
✷✳✷✳✸ ❈♦♥s✉❧t❛s ❡♠ ❙ér✐❡s ❚❡♠♣♦r❛✐s
✶✵
t♦♠♦❣r❛✜❛ s❡❥❛ ❜❛st❛♥t❡ s✐♠✐❧❛r à ❞♦ ♣❛❝✐❡♥t❡ ❡♠ ❡st✉❞♦✧❬✶✼❪✳
❆ ❛✈❛❧✐❛çã♦ ❞❛ s✐♠✐❧❛r✐❞❛❞❡ ❡♥tr❡ ❞❛❞♦s ❝♦♠♣❧❡①♦s✱ ♦✉ s❡❥❛✱ ♦❜❥❡t♦s✱ é r❡❛❧✐③❛❞❛ ❛tr❛✲ ✈és ❞❡ ❢✉♥çõ❡s q✉❡ ♠❡❞❡♠ ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❡❧❡s✳ ❊♥tã♦✱ ❞❛❞❛s ❞✉❛s sér✐❡s t❡♠♣♦r❛✐s
~x={x0, x1, ..., xn−1}❡~y={y0, y1, ..., yn−1}✱ ♦♥❞❡x1..xn❡y1..ynsã♦ ♦s ✈❛❧♦r❡s ❞❛ sér✐❡
t❡♠♣♦r❛❧ ♥♦s ✐♥st❛♥t❡s t1..tn ❝♦rr❡s♣♦♥❞❡♥t❡s✳ ❯♠❛ ❛♣r♦①✐♠❛çã♦ ♣❛❞rã♦ é ❝♦♠♣✉t❛r
❛ ❞✐stâ♥❝✐❛ ❊✉❝❧✐❞✐❛♥❛ D~(~x, ~y) ❡♥tr❡ ❛s sér✐❡s~x ❡ ~y ❬✾❪
D(~x, ~y) =
n−1 X
i=0
|xi−yi|2
!12
✭✷✳✷✳✺✮
❯s❛♥❞♦ ❡st❡ ♠♦❞❡❧♦ ❞❡ s✐♠✐❧❛r✐❞❛❞❡✱ ♣♦❞❡♠♦s r❡❝✉♣❡r❛r sér✐❡s t❡♠♣♦r❛✐s ❝♦♥s✐❞❡✲ r❛♥❞♦ ❛ ❞✐stâ♥❝✐❛ D(~x, ~y)✳ ❆ ❞✐stâ♥❝✐❛ ❡✉❝❧✐❞✐❛♥❛ ♥ã♦ é ❛❞❡q✉❛❞❛ q✉❛♥❞♦ s❡ q✉❡r
✉♠❛ ♠❡❞✐❞❛ ✢❡①í✈❡❧ ❡♥tr❡ sér✐❡s t❡♠♣♦r❛✐s✳ ❆s r❛③õ❡s sã♦ ❛s s❡❣✉✐♥t❡s ❬✹✽❪✿
• ❉✉❛s sér✐❡s ♣♦❞❡♠ s❡r ♠✉✐t♦ s✐♠✐❧❛r❡s ♠❡s♠♦ q✉❡ t❡♥❤❛♠ ❡s❝❛❧❛s ❞✐❢❡r❡♥t❡s ❞❡
❛♠♣❧✐t✉❞❡✳ ❙❡ ❝❛❧❝✉❧❛❞❛ ❛ ❞✐stâ♥❝✐❛ ❡✉❝❧✐❞✐❛♥❛✱ ❞❛rá ✉♠❛ ❞✐s❝r❡♣â♥❝✐❛ ♠✉✐t♦ ❣r❛♥❞❡ ❡♥tr❡ ❡st❛s sér✐❡s✳
• ❆ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❞✉❛s sér✐❡s ❞❡ t❛♠❛♥❤♦s ❞✐❢❡r❡♥t❡s é ✐♥❞❡✜♥✐❞❛✱ ♠❡s♠♦ s❡♥❞♦
s❡♠❡❧❤❛♥t❡s✳
• ❉✉❛s sér✐❡s ♣♦❞❡♠ s❡r ♠✉✐t♦ s✐♠✐❧❛r❡s ♠❡s♠♦ ♥ã♦ ❡st❛♥❞♦ ♣❡r❢❡✐t❛♠❡♥t❡ s✐♥❝r♦✲
♥✐③❛❞❛s✳ ❙❡ ❝❛❧❝✉❧❛❞❛ ❛ ❞✐stâ♥❝✐❛ ❡✉❝❧✐❞✐❛♥❛✱ ✈❡r❡♠♦s ✉♠❛ ❣r❛♥❞❡ ❞✐✈❡r❣ê♥❝✐❛✳
❉❡✈✐❞♦ ❛ ❡st❛ r✐❣✐❞❡③ ❞❛ ❞✐stâ♥❝✐❛ ❡✉❝❧✐❞✐❛♥❛✱ ❛❧❣✉♠❛s tr❛♥s❢♦r♠❛çõ❡s ♥❛s sér✐❡s ♣♦✲ ❞❡♠ s❡r ♥❡❝❡ssár✐❛s ❬✹✽✱ ✶✵❪✱ t❛✐s ❝♦♠♦ ❛s tr❛♥s❢♦r♠❛çõ❡s s❤✐❢t✐♥❣ ❡ s❝❛❧✐♥❣✳
❚r❛♥s❢♦r♠❛çõ❡s ❙❤✐❢t✐♥❣
✶✶
♥♦ ❡✐①♦ ❨ ❡ é ❛❧❝❛♥ç❛❞❛ ♣❡❧❛ ❛❞✐çã♦ ✉♠ ✈❛❧♦r ❛ ❝❛❞❛ ♣♦♥t♦ yi ❞❛ sér✐❡ x ✭ ♦ q✉❡
❝♦rr❡s♣♦♥❞❡ ❛ ❞❡s❧♦❝❛r ❛ sér✐❡ ♥♦ ❡✐①♦ ❨ ❞❡ ✉♠ ✈❛❧♦rα✮✱ ♦✉ s❡❥❛✿
x=x1+α, x2+α, ...xn+α ✭✷✳✷✳✻✮
❚r❛♥s❢♦r♠❛çã♦ s❝❛❧✐♥❣
➱ ❛❧❝❛♥ç❛❞❛ ♠✉❧t✐♣❧✐❝❛♥❞♦ ❝❛❞❛ ♣♦♥t♦ yi ❞❛ sér✐❡ ♣♦r x ✉♠ ❞❡t❡r♠✐♥❛❞♦ ✈❛❧♦r✱
♦✉ s❡❥❛✱
x=x1∗α, x2∗α, ...xn∗α ✭✷✳✷✳✼✮
◆♦r♠❛❧✐③❛çã♦
➱ ✉♠❛ tr❛♥s❢♦r♠❛çã♦ q✉❡ ❢❛③ ❛ sér✐❡ ✜❝❛r ✐♥✈❛r✐❛♥t❡ ❡♠ r❡❧❛çã♦ à s❤✐❢t✐♥❣ ❡ s❝❛❧✐♥❣✳ ❆ ❢♦r♠❛ ♥♦r♠❛❧ ❞❡ ✉♠❛ sér✐❡ x ♣♦❞❡ s❡r ❞❛❞❛✿
xi =
xi−avg(x)
std(x) ✭✷✳✷✳✽✮
♦♥❞❡✱ avg ❡std✐♥❞✐❝❛♠ ❛ ♠é❞✐❛ ❡ ♦ ❞❡s✈✐♦ ♣❛❞rã♦ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❡xi r❡♣r❡s❡♥t❛ ♦
✐✲és✐♠♦ ❡❧❡♠❡♥t♦ ❞❛ sér✐❡ x✳
❊st❡ t✐♣♦ ❞❡ ♥♦r♠❛❧✐③❛çã♦ é ❝❤❛♠❛❞♦ ❞❡ ♥♦r♠❛❧✐③❛çã♦ ♣❛❞rã♦ ❡ é ❜❛s❡❛❞♦ ❡♠ ♣r♦♣r✐❡❞❛❞❡s ❡st❛tíst✐❝❛s ❞❛ sér✐❡✳ ❊❧❛ ❝♦♥✈❡rt❡ ❛ sér✐❡ ❡♠ ♦✉tr❛ sér✐❡✱ ♦♥❞❡ ❛ ♠é❞✐❛ é ✐❣✉❛❧ ❛ ✵ ❡ ♦ ❞❡s✈✐♦ ♣❛❞rã♦ é ✐❣✉❛❧ ❛ ✶✶✳
❖✉tr♦ t✐♣♦ ❞❡ ♥♦r♠❛❧✐③❛çã♦ é ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ♥♦r♠❛❧✐③❛çã♦ ♣♦r ❢❛✐①❛ ✜①❛✳ ❊❧❛ t❛♠✲ ❜é♠ ❞❡✐①❛ ❛ sér✐❡ ✐♥✈❛r✐❛♥t❡ ❡♠ r❡❧❛çã♦ ❛ s❤✐❢t✐♥❣ ❡ s❝❛❧✐♥❣✱ ♣♦ré♠✱ ❢♦rç❛ ❛ sér✐❡ t❡r ✉♠ ✈❛❧♦r ♠á①✐♠♦ ❡ ✉♠ ✈❛❧♦r ♠í♥✐♠♦✳ ❆ ❢ór♠✉❧❛ ♠❛t❡♠át✐❝❛ é✿
xi =
xi−mx
Mx−mx
✭✷✳✷✳✾✮
♦♥❞❡✱ Mx ❡mx sã♦ ♦ ♠á①✐♠♦ ❡ ♠í♥✐♠♦ ✈❛❧♦r❡s ❞❛ sér✐❡✳
❆ ✜❣✉r❛ ✷✳✹✱ ✐❧✉str❛ ❝❛❞❛ ✉♠❛ ❞❡st❛s tr❛♥s❢♦r♠❛çõ❡s✱ ♦♥❞❡ α ❂ ✸ ✭s❤✐❢t✐♥❣✮ ❡ ✷✺
✭s❝❛❧✐♥❣✮✳ ❊ ❛ ✜❣✉r❛ ✷✳✺ ♠♦str❛ ❛ ♠❡s♠❛ sér✐❡ ♥♦r♠❛❧✐③❛❞❛✱ ♦✉ s❡❥❛✱ ❢♦✐ ❛♣❧✐❝❛❞❛ ❛
✶✷
✷✳✷✳✾ ❡♠ ❝❛❞❛ ♣♦♥t♦ ❞❛ sér✐❡✱ ❞❡✐①❛♥❞♦ ❛ ♥♦✈❛ sér✐❡ ❝♦♠ ✈❛❧♦r❡s ❡♥tr❡ ✵ ❡ ✶✳ ❊st❛ sér✐❡✱ ❛♣ós ❛ ♥♦r♠❛❧✐③❛çã♦✱ ❡stá ✐♥✈❛r✐❛♥t❡ ❛ s❤✐❢t✐♥❣ ❡ s❝❛❧✐♥❣✱ ❛ss✐♠ s❡♥❞♦✱ ♦ ❝á❧❝✉❧♦ ❞❛ ❞✐stâ♥❝✐❛ ❡✉❝❧✐❞✐❛♥❛ t♦r♥❛✲s❡ ♠❛✐s ✢❡①í✈❡❧✷✳
❋✐❣✉r❛ ✷✳✹✿ ❊①❡♠♣❧♦ ❞❡ ❚r❛♥s❢♦r♠❛çõ❡s ❙❤✐❢t✐♥❣ ❡ ❙❝❛❧✐♥❣ ❡♠ ✉♠❛ ❙ér✐❡ ❚❡♠♣♦r❛❧
❚✐♣♦s ♠❛✐s ❝♦♠✉♥s ❞❡ ❝♦♥s✉❧t❛ ♣♦r s✐♠✐❧❛r✐❞❛❞❡
❖ ❝á❧❝✉❧♦ ❞❛ ♠❡❞✐❞❛ ❞❡ s✐♠✐❧❛r✐❞❛❞❡ ❡♥tr❡ ❞✉❛s sér✐❡s t❡♠♣♦r❛✐s ✈✐s❛ ❞❡t❡❝t❛r ♦ q✉ã♦ ✉♠❛ sér✐❡ é ♣ró①✐♠❛ ✭s✐♠✐❧❛r✮ à ♦✉tr❛✳ P❛r❛ t❛♥t♦✱ ❡❧❡ ♣♦❞❡ s❡r ❡❢❡t✉❛❞♦ s❡❣✉♥❞♦ ❛ ❡str❛té❣✐❛ ✇❤♦❧❡ ♠❛t❝❤✐♥❣ ♦✉ s✉❜s❡q✉❡♥❝❡ ♠❛t❝❤✐♥❣ ❬✶✻❪✳ ❆s ❲❤♦❧❡ ▼❛t❝❤✐♥❣ sã♦ ❛q✉❡❧❛s ❡♠ q✉❡✱ ❞❛❞♦ ✉♠❛ ❝♦❧❡çã♦ ❞❡ N s❡qüê♥❝✐❛s ❞❡ ♥ú♠❡r♦s r❡❛✐s S1, S2, ..., SN
❡ ✉♠❛ ❝♦♥s✉❧t❛ Q✱ ❞❡s❡❥❛✲s❡ ❡♥❝♦♥tr❛r ❛q✉❡❧❛s s❡qüê♥❝✐❛s q✉❡ ❡stã♦ ❛ ✉♠❛ ❞✐stâ♥❝✐❛
≤ε ❞❡ Q✳ ❆s s❡qüê♥❝✐❛s ❡ ❛ ❝♦♥s✉❧t❛ ❞❡✈❡♠ t❡r ♦ ♠❡s♠♦ t❛♠❛♥❤♦✱ ✐st♦ é✱ ♦ ♠❡s♠♦
♥ú♠❡r♦ ❞❡ ♣♦♥t♦s✳ ❆s ❙✉❜s❡q✉❡♥❝❡ ▼❛t❝❤✐♥❣ sã♦ ❛q✉❡❧❛s ❡♠ q✉❡✱ ❞❛❞❛ ✉♠❛ ❝♦❧❡çã♦ ❞❡N s❡qüê♥❝✐❛s ❞❡ ♥ú♠❡r♦s r❡❛✐sS1, S2, ..., SN ❞❡ t❛♠❛♥❤♦s ❛r❜✐trár✐♦s✱ ✉♠❛ ❝♦♥s✉❧t❛
Q ❡ ✉♠❛ t♦❧❡râ♥❝✐❛ ε ✱ ❞❡s❡❥❛✲s❡ ✐❞❡♥t✐✜❝❛r ❛s s❡qüê♥❝✐❛s Si(1 ≤ i ≤ N) q✉❡ ❡stã♦
❛ ✉♠❛ ❞✐stâ♥❝✐❛ ≤ ε ❞❛ ❝♦♥s✉❧t❛ Q✳ ❈❛s♦ ✉♠❛ s❡qüê♥❝✐❛ Si ❡ ❛ ❝♦♥s✉❧t❛ Q t❡♥❤❛♠
t❛♠❛♥❤♦s ❞✐❢❡r❡♥t❡s✱ ♣❛r❛ ❡❢❡✐t♦ ❞❡ ❛♥á❧✐s❡ ❞❡ s✐♠✐❧❛r✐❞❛❞❡ ❞✐✈✐❞❡✲s❡Si ❡♠ ♣❛rt❡s q✉❡
✶✸
❋✐❣✉r❛ ✷✳✺✿ ❊①❡♠♣❧♦ ❞❛ ◆♦r♠❛❧✐③❛çã♦ ❡♠ ✉♠❛ ❙ér✐❡ ❚❡♠♣♦r❛❧
t❡♥❤❛♠ ♦ ♠❡s♠♦ t❛♠❛♥❤♦ ❞❡ Q✳ ❚❛♥t♦ ♥❛ ✇❤♦❧❡ ♠❛t❝❤✐♥❣✱ q✉❛♥t♦ ♥❛ s✉❜s❡q✉❡♥❝❡
♠❛t❝❤✐♥❣ ♣♦❞❡♠✲s❡ ✉t✐❧✐③❛r ♦s t✐♣♦s ❞❡ ❝♦♥s✉❧t❛s ❛♣r❡s❡♥t❛❞❛s ❛ s❡❣✉✐r✳
❈♦♥s✉❧t❛ ♣♦r ❋❛✐①❛ ✭❘❛♥❣❡ ◗✉❡r②✮
❈♦♥s✉❧t❛ q✉❡ ✈✐s❛ r❡❝✉♣❡r❛r ♦❜❥❡t♦s q✉❡ s❡ ❡♥❝♦♥tr❛♠ ❛ ✉♠❛ ❞✐stâ♥❝✐❛ ♠á①✐♠❛r
✭r❛✐♦ ❞❡ ❜✉s❝❛✮✱ ❛ ♣❛rt✐r ❞♦ ♦❜❥❡t♦ ❞❡ r❡❢❡rê♥❝✐❛O✭♦❜❥❡t♦ ❞❡ ❜✉s❝❛✮✱ ❝♦♠♦ ✐❧✉str❛❞♦ ♥❛
✜❣✉r❛ ❬✷✳✻❪✳ ❋♦r♠❛❧♠❡♥t❡✱ ❞❛❞♦ ♦ ❝♦♥❥✉♥t♦ ❞❡ ♦❜❥❡t♦s ❙ ❡ ✉♠ ❡❧❡♠❡♥t♦ q✉❛❧q✉❡r ❞❡st❡
❋✐❣✉r❛ ✷✳✻✿ ❊①❡♠♣❧♦ ❞❡ ❝♦♥s✉❧t❛ ♣♦r s✐♠✐❧❛r✐❞❛❞❡ ✭❘❛♥❣❡ ◗✉❡r②✮
❝♦♥❥✉♥t♦✱ si ∈S✱ ✉♠❛ ❝♦♥s✉❧t❛ ♣♦r ❢❛✐①❛RQ(o, r)✱ ♣r❡t❡♥❞❡ ❡♥❝♦♥tr❛r ♦ s✉❜❝♦♥❥✉♥t♦
A ⊆ S ❡♠ q✉❡ A = {si ∈ S|d(o, si) ≤ r}✳ ❈♦♠♦ ❡①❡♠♣❧♦✱ ♣♦❞❡♠♦s ❝♦♥s✐❞❡r❛r
✶✹
❣r❛✉ ❞❡ s✐♠✐❧❛r✐❞❛❞❡ ❡♥tr❡ s✉❛ t♦♠♦❣r❛✜❛ ❡ ❛ ❞♦ ♣❛❝✐❡♥t❡ ❡♠ ❡st✉❞♦ s❡❥❛ ✐♥❢❡r✐♦r ❛
r✧✱ ♦♥❞❡ r é ♦❜t✐❞❛ ❛tr❛✈és ❞♦ ❝á❧❝✉❧♦ ❞❛ ❞✐stâ♥❝✐❛ ❡✉❝❧✐❞✐❛♥❛✳ ❖ ✈❛❧♦r ❛❝❡✐tá✈❡❧ ♣❛r❛ r ❞❡✈❡rá s❡r ❞❡✜♥✐❞♦ ♣♦r ✉♠ ❡s♣❡❝✐❛❧✐st❛ ❞❛ ár❡❛✳
❈♦♥s✉❧t❛ ❞♦s ❦✲❱✐③✐♥❤♦s ♠❛✐s ♣ró①✐♠♦s ✭❦✲◆❡❛r❡st ◆❡✐❣❤❜♦r ◗✉❡r②✮
❈♦♥s✉❧t❛ q✉❡ ✈✐s❛ r❡❝✉♣❡r❛r ♦s ❦ ♦❜❥❡t♦s ♠❛✐s ♣ró①✐♠♦s ❛♦ ♦❜❥❡t♦ ❞❡ r❡❢❡rê♥❝✐❛
O✱ ❝♦♠♦ ✐❧✉str❛❞♦ ♥❛ ✜❣✉r❛ ❬✷✳✼❪✳ ❋♦r♠❛❧♠❡♥t❡✱ ❞❛❞♦ ♦ ❝♦♥❥✉♥t♦ ❞❡ ♦❜❥❡t♦s ❙ ❡ ✉♠
❋✐❣✉r❛ ✷✳✼✿ ❊①❡♠♣❧♦ ❞❡ ❝♦♥s✉❧t❛ ♣♦r s✐♠✐❧❛r✐❞❛❞❡ ✭❑✲❱✐③✐♥❤♦s✮
❡❧❡♠❡♥t♦ q✉❛❧q✉❡r ❞❡st❡ ❝♦♥❥✉♥t♦✱ s∈S✱ ✉♠❛ ❝♦♥s✉❧t❛ ❞♦s ❦✲✈✐③✐♥❤♦s ♠❛✐s ♣ró①✐♠♦s
❦N N Q(o, k) ♣r❡t❡♥❞❡ ❡♥❝♦♥tr❛r ♦ s✉❜❝♦♥❥✉♥t♦ A ⊆ S ❡♠ q✉❡ A = {s ∈ S|k = |A|
❡ ∀ai ∈ A,∀x ∈ [S −A], d(o, ai) ≤ d(o, x)}✳ ❈♦♠♦ ❡①❡♠♣❧♦ ♣♦❞❡♠♦s ❝♦♥s✐❞❡r❛r ❛
❝♦♥s✉❧t❛ ✧♦❜t❡r ♦ ❝❛❞❛str♦ ❞♦s ♣❛❝✐❡♥t❡s ❝♦♠ t✉♠♦r ♥♦ ❝ér❡❜r♦ ❝✉❥❛s t♦♠♦❣r❛✜❛s s❡❥❛♠ ❛s ❦ ♠❛✐s ♣ró①✐♠❛s à ❞♦ ♣❛❝✐❡♥t❡ ❡♠ ❡st✉❞♦✧✳
Pr♦❜❧❡♠❛s ❡♥❝♦♥tr❛❞♦s ❡♠ ❝♦♥s✉❧t❛s s♦❜r❡ ❙ér✐❡s ❚❡♠♣♦r❛✐s
✶✺
■♥❞❡①❛çã♦
❯♠ í♥❞✐❝❡ é ✉♠❛ ❡str✉t✉r❛ ♦r❣❛♥✐③❛❞❛ ❞❡ ❞❛❞♦s q✉❡ ♣❡r♠✐t❡ ❛ ❜✉s❝❛ ❞❡ ✐♥❢♦r✲ ♠❛çõ❡s r❛♣✐❞❛♠❡♥t❡✳ ❙❡♠ ❛ ✉t✐❧✐③❛çã♦ ❞♦s í♥❞✐❝❡s✱ ❛s ❝♦♥s✉❧t❛s ❡♠ sér✐❡s t❡♠♣♦r❛✐s s❡r✐❛♠ ❡①tr❡♠❛♠❡♥t❡ ✐♥❡✜❝✐❡♥t❡s ❡♠ t❡r♠♦s ❞❡ ❝✉st♦ ❞❡ ❈P❯ ❡ ■❖ ❬✹✽❪✳ ❈♦♠♦ ❛ ♠❛✐♦r✐❛ ❞❛s sér✐❡s t❡♠♣♦r❛✐s t❡♠ ✉♠❛ ❣r❛♥❞❡ ❞✐♠❡♥s✐♦♥❛❧✐❞❛❞❡✱ ♦✉ s❡❥❛✱ ✉♠❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ♣♦♥t♦s✱ s❡r✐❛ ✐♥❡✜❝✐❡♥t❡ ✐♥❞❡①á✲❧❛s ❞✐r❡t❛♠❡♥t❡ ❬✸✻❪✳ ❖s ♠ét♦❞♦s ♠❛✐s ♣r♦♠✐ss♦r❡s sã♦ ❛q✉❡❧❡s q✉❡ ✉t✐❧✐③❛♠ ❛ té❝♥✐❝❛ ❞❡ r❡❞✉③✐r ❛ ❞✐♠❡♥sã♦ ❞♦ ❞❛❞♦ ✭❞❡t❛✲ ❧❤❛❞♦ ♥❛ ♣ró①✐♠❛ s❡çã♦✮✱ ❡ ❡♥tã♦ ✉s❛ ♠ét♦❞♦s ♣❛r❛ ✐♥❞❡①❛r ♦s ❞❛❞♦s ❛ ♣❛rt✐r ❞♦ ♥♦✈♦ ❡s♣❛ç♦ ❞✐♠❡♥s✐♦♥❛❧ ❬✷✹❪✳
❙ér✐❡s t❡♠♣♦r❛✐s ♣♦❞❡♠ s❡r ✐♥❞❡①❛❞❛s ✉s❛♥❞♦ ♠ét♦❞♦s ❥á ❝♦♥❤❡❝✐❞♦s ❝♦♠♦ ❘✲ tr❡❡ ❡ s✉❛s ✈❛r✐❛♥t❡s ❬✶✵❪✳ ❊st❡s ♠ét♦❞♦s ✈✐s❛♠ ❛✉♠❡♥t❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❞❛s ❝♦♥s✉❧t❛s✱ ✉♠❛ ✈❡③ q✉❡ sã♦ ♠✉✐t♦ ♠❛✐s rá♣✐❞♦s ❞♦ q✉❡ ❛q✉❡❧❡s q✉❡ ✉t✐❧✐③❛♠ ❛ ❜✉s❝❛ ❧✐♥❡❛r✱ ✐st♦ é✱ s❡qüê♥❝✐❛❧ ♥♦s ❞❛❞♦s✳
❖ ❘✲❚r❡❡ ❡st❡♥❞❡ ♦ ♣♦♣✉❧❛r ❇✲❚r❡❡ ✭✉t✐❧✐③❛ ❛♣❡♥❛s ✶ ❞✐♠❡♥sã♦✮ ♣❛r❛ ✉♠ ♥ú✲ ♠❡r♦ ♠❛✐♦r ❞❡ ❞✐♠❡♥sã♦ ❬✹✽❪✳ ❙❡ ❢♦r ❜❡♠ ✐♠♣❧❡♠❡♥t❛❞♦✱ ❡❧❡ é ✉♠❛ ❢♦r♠❛ ❡✜❝✐❡♥t❡ ❞❡ ✐♥❞❡①❛çã♦ ♥✲❞✐♠❡♥s✐♦♥❛❧ ✐♥❝❧✉✐♥❞♦ ♣♦♥t♦s ❡ r❡❣✐õ❡s✸✳ ❙✐♠✐❧❛r♠❡♥t❡ ❛♦ ❇✲❚r❡❡✱ ♦
❘✲❚r❡❡ é ✉♠❛ ár✈♦r❡ ❜❛❧❛♥❝❡❛❞❛ ❝♦♠ ♦s í♥❞✐❝❡s ❞♦s ❞❛❞♦s ❛r♠❛③❡♥❛❞♦s ♥❛s ❢♦❧❤❛s✳ ◆❛ ❇✲❚r❡❡✱ ❝❛❞❛ ♥ó q✉❡ ♥ã♦ é ❢♦❧❤❛ ❞❛ ár✈♦r❡ ❝♦rr❡s♣♦♥❞❡ ❛ ✉♠ ✐♥t❡r✈❛❧♦✳ ❊st❡♥✲ ❞❡♥❞♦ ❡st❛ ✐❞é✐❛ ♣❛r❛ ♠✉❧t✐✲❞✐♠❡♥sõ❡s✱ ❝❛❞❛ ♥ó ♥ã♦ ❢♦❧❤❛ ♥♦ ❘✲❚r❡❡ ❝♦rr❡s♣♦♥❞❡rá ❛ ✐♥t❡r✈❛❧♦s ♠✉❧t✐✲❞✐♠❡♥s✐♦♥❛✐s✱ ❝❤❛♠❛❞♦s ❞❡ ♠❡♥♦r❡s r❡tâ♥❣✉❧♦s ✭♠✐♥✐♠✉♠ ❜♦✉♥❞✐♥❣ ❜♦①❡s✲▼❇❘✮✳ ❖ ▼❇❘ é ♦ ♦❜❥❡t♦ ❜❛s❡ ❞♦ ❘✲❚r❡❡✳ ◆♦ ❇✲❚r❡❡✱ ♦ ✐♥t❡r✈❛❧♦ ❛ss♦❝✐❛❞♦ ❝♦♠ ♦s ♥ós ✐♥❝❧✉❡♠ t♦❞♦s ♦s ✐♥t❡r✈❛❧♦s ❛ss♦❝✐❛❞♦s ❝♦♠ ♦s ♥ós ✜❧❤♦s❀ ♥♦ ❘✲❚r❡❡✱ ♦ ▼❇❘ ❛ss♦❝✐❛❞♦ ❛♦ ♥ó t❛♠❜é♠ ✐♥❝❧✉✐ t♦❞♦s ♦s ▼❇❘✬s ❞❡ s❡✉s ♥ós ✜❧❤♦s✳ ◆♦ ❇✲tr❡❡✱ ♦ ✐♥t❡r✈❛❧♦ ❛ss♦❝✐❛❞♦ ❛ ✉♠ ♥ó✱ ♥ã♦ s♦❜r❡♣õ❡ ♦s ✐♥t❡r✈❛❧♦s ❛ss♦❝✐❛❞♦s ❝♦♠ ♥ós ✐r♠ã♦s✳ ❉❡st❛ ❢♦r♠❛✱ ♦ ♥ú♠❡r♦ ❞❡ ♥ós ❛ s❡r❡♠ ❛❝❡ss❛❞♦s ♥❛ ♣❡sq✉✐s❛ ✉t✐❧✐③❛♥❞♦ ♦ ❇✲❚r❡❡ ❞❡♣❡♥❞❡rá ❞❛ ♣r♦❢✉♥❞✐❞❛❞❡ ❞❛ ár✈♦r❡✳ ◆♦ ❘✲❚r❡❡✱ ❡♥tr❡t❛♥t♦✱ ♦s ▼❇❘✬s ❛ss♦❝✐❛❞♦s ❛♦s ♥ós ♣♦❞❡♠ s❡r s♦❜r❡♣♦st♦s ❝♦♠ ▼❇❘✬s ❞❡ ♥ós ✐r♠ã♦s✳ ❉❡st❛ ❢♦r♠❛✱ ❛ ♣❡sq✉✐s❛
✶✻
♥♦ í♥❞✐❝❡ ♣♦❞❡rá t❡r q✉❡ ♣❡r❝♦rr❡r ✈ár✐♦s ❝❛♠✐♥❤♦s ❞✐❢❡r❡♥t❡s✳
◆❛ ✜❣✉r❛ ✷✳✽✱ ♣♦❞❡✲s❡ ✈❡r ✉♠ ❡①❡♠♣❧♦ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ r❡tâ♥❣✉❧♦s ❡ s❡✉s ▼❇❘✬s✳ P♦r s✐♠♣❧✐❝✐❞❛❞❡ é ❛♣r❡s❡♥t❛❞❛ ✉♠❛ ✜❣✉r❛ q✉❡ ❝♦♥s✐❞❡r❛ ❛♣❡♥❛s ❞✉❛s ❞✐✲ ♠❡♥sõ❡s✳ ❆ ❡str✉t✉r❛ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ ✉♠ ❘✲❚r❡❡ ♣♦❞❡ s❡r ✈✐st❛ ♥❛ ✜❣✉r❛ ✷✳✾✳
❋✐❣✉r❛ ✷✳✽✿ ❊①❡♠♣❧♦ ❞❡ ▼❇❘✬s
❋✐❣✉r❛ ✷✳✾✿ ❆ ❡str✉t✉r❛ ❘✲❚r❡❡
✶✼
❊♠ ❣❡r❛❧✱ q✉❛❧q✉❡r ♠ét♦❞♦ ❞❡ ✐♥❞❡①❛çã♦ ❞❡✈❡ s✉♣♦rt❛r ❞♦✐s ♣r♦❜❧❡♠❛s✿ ❋❛❧s♦✲ ◆❡❣❛t✐✈♦ ❡ ♦ ❋❛❧s♦✲P♦s✐t✐✈♦✳ ◆❛ ❛♥á❧✐s❡ ❞❡ sér✐❡s t❡♠♣♦r❛✐s✱ ❖ ❋❛❧s♦✲P♦s✐t✐✈♦ ♦❝♦rr❡ q✉❛♥❞♦✱ ♥❛ r❡❛❧✐③❛çã♦ ❞❡ ✉♠❛ ❝♦♥s✉❧t❛✱ ❛s sér✐❡s q✉❡ ♣❛r❡❝❡♠ s❡r ♣ró①✐♠❛s ♥♦ í♥❞✐❝❡✱ ♥❛ ✈❡r❞❛❞❡ ♥ã♦ ♦ sã♦✱ ❡♥q✉❛♥t♦ q✉❡ ♦ ❋❛❧s♦✲◆❡❣❛t✐✈♦ ♦❝♦rr❡ q✉❛♥❞♦ ❛s sér✐❡s ♥ã♦ sã♦ ❝♦♥s✐❞❡r❛❞❛s ♥❛ ♣❡sq✉✐s❛ ♣♦r ❛♣❛r❡♥t❡♠❡♥t❡ ❡st❛r❡♠ ❞✐st❛♥t❡s ♥♦ í♥❞✐❝❡✱ s❡♥❞♦ q✉❡✱ ♥❛ r❡❛❧✐❞❛❞❡✱ sã♦ ♣ró①✐♠❛s✳ ❆ ❡①✐stê♥❝✐❛ ❞♦ ❋❛❧s♦✲◆❡❣❛t✐✈♦ ✐♠♣❧✐❝❛ ❡♠ ♣❡r❞❛ ❞❡ ✐♥❢♦r♠❛çõ❡s✱ ❢❛t♦ q✉❡ ♥ã♦ ♦❝♦rr❡ ❝♦♠ ♦ ❋❛❧s♦✲P♦s✐t✐✈♦✳ ❊♥tr❡t❛♥t♦✱ ♦ ❋❛❧s♦✲P♦s✐t✐✈♦ ❣❡r❛ ✉♠❛ ♣❡r❞❛ ❞❡ ❞❡s❡♠♣❡♥❤♦✱ ♣♦✐s ❞❡✈❡ ❤❛✈❡r ✉♠ ♣ós✲♣r♦❝❡ss❛♠❡♥t♦ ♣❛r❛ r❡t✐r❛r ❛s sér✐❡s s❡❧❡❝✐♦♥❛❞❛s ♣♦r ♠❡✐♦ ❞♦ ❋❛❧s♦✲P♦s✐t✐✈♦✳
❖ ♣r♦❝❡ss♦ ❞❡ ❝r✐❛çã♦ ❞❡ ✉♠ í♥❞✐❝❡ ❞❡✈❡ t❡r ❛s s❡❣✉✐♥t❡s ♣r♦♣r✐❡❞❛❞❡s ❬✶✻❪✿
✶✳ ❉❡✈❡ s❡r rá♣✐❞♦✱ ♦✉ s❡❥❛✱ ♠❛✐s rá♣✐❞♦ ❞♦ q✉❡ ✉♠❛ ❜✉s❝❛ s❡qü❡♥❝✐❛❧❀
✷✳ ❉❡✈❡ s❡r ❝♦rr❡t♦✱ ♦✉ s❡❥❛✱ ♥ã♦ ♣♦❞❡ ♣❡r♠✐t✐r ❋❛❧s♦✲◆❡❣❛t✐✈♦✳ ❖ ❋❛❧s♦✲P♦s✐t✐✈♦ é ♠❡♥♦s ♣r♦❜❧❡♠át✐❝♦ ♣♦rq✉❡ ♣♦❞❡ s❡r tr❛t❛❞♦ ♥♦ ♣ós ♣r♦❝❡ss❛♠❡♥t♦❀
✸✳ ❉❡✈❡ r❡q✉❡r❡r ✉♠ ♣❡q✉❡♥♦ ❡s♣❛ç♦ ❞❡ ♦✈❡r❤❡❛❞❀
✹✳ ❉❡✈❡ s❡r ❞✐♥â♠✐❝♦✱ ♣❡r♠✐t✐♥❞♦ q✉❡ ❛ ✐♥s❡rçã♦ ❡ ❛ ❡①❝❧✉sã♦ ❞❡ s❡qüê♥❝✐❛s s❡❥❛♠ ❢❡✐t❛s ❢❛❝✐❧♠❡♥t❡✱ s❡♠ q✉❡ s❡ ♥❡❝❡ss✐t❡ r❡❝♦♥str✉✐r t♦❞♦ í♥❞✐❝❡✳
✺✳ ❉❡✈❡ tr❛t❛r s❡qüê♥❝✐❛s ❞❡ ✈ár✐♦s t❛♠❛♥❤♦s✳
❊♠ ❬✷✹❪ ❢♦r❛♠ ♣r♦♣♦st❛s ❞✉❛s ♥♦✈❛s ♣r♦♣r✐❡❞❛❞❡s✿
✶✳ ❖ í♥❞✐❝❡ ❞❡✈❡ s❡r ❝♦♥str✉í❞♦ ❡♠ ✉♠ t❡♠♣♦ ❛❝❡✐tá✈❡❧❀
✷✳ ❖ í♥❞✐❝❡ ❞❡✈❡rá s❡r ❝❛♣❛③ ❞❡ tr❛t❛r ❞✐❢❡r❡♥t❡s ♠❡❞✐❞❛s ❞❡ s✐♠✐❧❛r✐❞❛❞❡❀
❯♠❛ sér✐❡ t❡♠♣♦r❛❧ X ♣♦❞❡ s❡r ❝♦♥s✐❞❡r❛❞❛ ❝♦♠♦ ✉♠ ♣♦♥t♦ ❡♠ ✉♠ ❡s♣❛ç♦ ♥✲
