Localização cooperativa e descentralizada em enxames robóticos

(1)

▲❖❈❆▲■❩❆➬➹❖ ❈❖❖P❊❘❆❚■❱❆ ❊

❉❊❙❈❊◆❚❘❆▲■❩❆❉❆ ❊▼

(2)

(3)

❆◆❉❊❘❙❖◆ ●❘❆◆❉■ P■❘❊❙

▲❖❈❆▲■❩❆➬➹❖ ❈❖❖P❊❘❆❚■❱❆ ❊

❉❊❙❈❊◆❚❘❆▲■❩❆❉❆ ❊▼

❊◆❳❆▼❊❙ ❘❖❇Ó❚■❈❖❙

❚❡s❡ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲ ✲●r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❞♦ ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❞❛ ❯♥✐✈❡rs✐✲ ❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s ❝♦♠♦ r❡q✉✐✲ s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ❉♦✉✲ t♦r ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳

❖r✐❡♥t❛❞♦r✿ ▲✉✐③ ❈❤❛✐♠♦✇✐❝③

(4)

� ��

��

(5)

(6)

(7)

❉❡❞✐❝♦ ❡st❛ ❝♦♥q✉✐st❛ à ♠✐♥❤❛ ❡s♣♦s❛ ❊❞✉❛r❞❛ ❡ às ♠✐♥❤❛s ✜❧❤❛s ▼❛♥♦❡❧❛ ❡ ❙♦♣❤✐❛✳

(8)

(9)

❆❣r❛❞❡❝✐♠❡♥t♦s

❆❣r❛❞❡ç♦ ♣r✐♠❡✐r❛♠❡♥t❡ ❛ ❉❡✉s ♣♦r t❡r ♠❡ ♣♦ss✐❜✐❧✐t❛❞♦ ❛❧❝❛♥ç❛r ❡st❛ ❝♦♥q✉✐st❛ ❝♦♠ ♣❡rs✐stê♥❝✐❛ ❡ s❛❜❡❞♦r✐❛✳

➚ ♠✐♥❤❛ ❡s♣♦s❛ ❊❞✉❛r❞❛ ❡ às ♠✐♥❤❛s ✜❧❤❛s ▼❛♥♦❡❧❛ ❡ ❙♦♣❤✐❛ q✉❡ ❝♦♠♣❛rt✐❧❤❛r❛♠ ❝♦♠✐❣♦ t♦❞♦s ♦s ♠♦♠❡♥t♦s✱ ✐♥❝❡♥t✐✈❛♥❞♦✲♠❡ ❡ s❡r✈✐♥❞♦ ❞❡ ✐♥s♣✐r❛çã♦ ♣❛r❛ q✉❡ ❡✉ ✜③❡ss❡ ♦ ♠❡✉ ♠❡❧❤♦r ❛ ❝❛❞❛ ♠♦♠❡♥t♦✳

❆♦s ♠❡✉s ♣❛✐s ♣❡❧♦s ❡♥s✐♥❛♠❡♥t♦s q✉❡ ♠❡ ❢♦r❛♠ ♣❛ss❛❞♦s ❞✉r❛♥t❡ t♦❞♦s ♦s ♠♦✲ ♠❡♥t♦s ❞❛ ♠✐♥❤❛ ✈✐❞❛✳ P❡❧♦s ✈❛❧♦r❡s q✉❡ ❤♦❥❡ ❝❛rr❡❣♦✱ s❡♥❞♦ ❡ss❡s ❛ ♠✐♠ tr❛♥s♠✐t✐❞♦s ♣♦r ♠❡✐♦ ❞❡ ❛t✐t✉❞❡s ❡ ❡①❡♠♣❧♦s✳

❆♦ ♣r♦❢❡ss♦r ❡ ❛♠✐❣♦ ❉✐♥✐③ ❋é❧✐① ❞♦s ❙❛♥t♦s✱ q✉❡ ❞✉r❛♥t❡ ❛ ♠✐♥❤❛ ❣r❛❞✉❛çã♦ ♠❡ ♠♦t✐✈♦✉ ❡ ✐♥❝❡♥t✐✈♦✉ ❛ ❛❧ç❛r ✈♦♦s ♠❛✐s ❛❧t♦s✳

❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ ♣r♦❢❡ss♦r ▲✉✐③ ❈❤❛✐♠♦✇✐❝③✱ ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ❞❡s❡♥✈♦❧✲ ✈❡r ❡st❡ tr❛❜❛❧❤♦ s♦❜ s✉❛ ♦r✐❡♥t❛çã♦✱ ♣❡❧❛ ❝♦♥✜❛♥ç❛ ❞❡♣♦s✐t❛❞❛✱ ♣❡❧♦s ❡♥s✐♥❛♠❡♥t♦s ❡✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡✱ ♣❡❧❛ ❛♠✐③❛❞❡ ❝♦♥str✉í❞❛✳ ❖s ❝r❡s❝✐♠❡♥t♦s ♣❡ss♦❛❧ ❡ ♣r♦✜ss✐♦♥❛❧ ♣♦ss✐✲ ❜✐❧✐t❛❞♦s ♣❡❧♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ ❞♦✉t♦r❛❞♦ ❢♦r❛♠ ❡①tr❡♠❛♠❡♥t❡ s✐❣♥✐✜❝❛t✐✈♦s ♣❛r❛ ❛ ♠✐♥❤❛ ✈✐❞❛✱ ♦ q✉❡ s❡r❡✐ s❡♠♣r❡ ❣r❛t♦✳

❆♦s ♠❡♠❜r♦s ❞❛ ❜❛♥❝❛✱ ♣r♦❢❡ss♦r❡s ❉❡♥✐s ❋❡r♥❛♥❞♦ ❲♦❧❢ ✭■❈▼❈ ✲ ❯❙P✮✱ ❆r✲ ♠❛♥❞♦ ❆❧✈❡s ◆❡t♦ ✭❯❋❙❏✮✱ ▲✉❝✐❛♥♦ ❈✉♥❤❛ ❞❡ ❆r❛ú❥♦ P✐♠❡♥t❛ ✭❉❊❊ ✲ ❯❋▼●✮✱ ▼❛r✐♦ ❋❡r♥❛♥❞♦ ▼♦♥t❡♥❡❣r♦ ❈❛♠♣♦s ✭❉❈❈ ✲ ❯❋▼●✮✱ ❛❧é♠ ❞♦ ♣r♦❢❡ss♦r ❘❡♥❛t♦ ▼❛rt✐♥s ❆ss✉♥çã♦ ✭❉❈❈ ✲ ❯❋▼●✮ ♣❡❧❛ ♣❛rt✐❝✐♣❛çã♦ ♥❛ ❜❛♥❝❛ ❞❡ q✉❛❧✐✜❝❛çã♦✳ ❖s ❞✐r❡❝✐♦♥❛✲ ♠❡♥t♦s✱ ❛s s✉❣❡stõ❡s ❡ ❛s ❝rít✐❝❛s ❢♦r❛♠ ❡ss❡♥❝✐❛✐s ♣❛r❛ ❛ ♠❡❧❤♦r✐❛ ❡ ❝♦♥s♦❧✐❞❛çã♦ ❞♦ tr❛❜❛❧❤♦✳

❆♦s ❛♠✐❣♦s ❞❡ ❞♦✉t♦r❛♠❡♥t♦✱ ❆♥tô♥✐♦ ❲✐❧s♦♥✱ ❘❛❢❛❡❧ ❈♦❧❛r❡s✱ ❘❛❢❛❡❧ ❙❛♥t✐♥ ❡ ❘❡♥ê ❱❡❧♦s♦ ♣❡❧♦s ✐♥ú♠❡r♦s ♠♦♠❡♥t♦s ❞❡ ❞❡s❝♦♥tr❛çã♦✱ ❡st✉❞♦s ❡ ❞✐s❝✉ssõ❡s✳ ❆ ❛♠✐③❛❞❡ ❞❡ ✈♦❝ês ❢❡③ ❣r❛♥❞❡ ❞✐❢❡r❡♥ç❛ ♣❛r❛ ❛ s✉♣❡r❛çã♦ ❞❛s ❞✐✜❝✉❧❞❛❞❡s ❡ ♣❛r❛ t♦r♥❛r ❡ss❡ ♣❡rí♦❞♦ ♠❛✐s ❛❣r❛❞á✈❡❧✳

❆♦s ❝♦❧❡❣❛s ❡ ❛♠✐❣♦s ❞♦ ▲❛❜♦r❛tór✐♦ ❞❡ ❱✐sã♦ ❡ ❘♦❜ót✐❝❛ ✭❱❡❘▲❛❜✮✱ ♣❡❧❛s ✐♥ú✲ ♠❡r❛s tr♦❝❛s ❞❡ ✐♥❢♦r♠❛çã♦ q✉❡ ♣❡r♠✐t✐r❛♠ ♦ ♠❡✉ ❛♠❛❞✉r❡❝✐♠❡♥t♦ ❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ♥❛s ár❡❛s ❞❡ ❝♦♠♣✉t❛çã♦ ❡ r♦❜ót✐❝❛✳ ❖s ♠♦♠❡♥t♦s ♣❛ss❛❞♦s ❞❡♥tr♦ ❞❡ss❡ ❧❛❜♦r❛tór✐♦

(10)

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

❆♦ ❛♠✐❣♦ ❡ ♣r♦❢❡ss♦r ❉♦✉❣❧❛s ▼❛❝❤❛r❡t✱ ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ tr❛❜❛❧❤❛r♠♦s ❥✉♥✲ t♦s ♥❛ ❡t❛♣❛ ✜♥❛❧ ❞♦ ❞♦✉t♦r❛❞♦ ❡ ♣❡❧❛s ✐♥ú♠❡r❛s tr♦❝❛s ❞❡ ✐♥❢♦r♠❛çã♦✳ ❚❛♠❜é♠ ❛♦ ♣r♦❢❡ss♦r ▲✉❝✐❛♥♦ P✐♠❡♥t❛ ❡ ❛♦ ❱✐♥í❝✐✉s ❙❛♥t♦s✱ ❝♦♠ q✉❡♠ t✐✈❡ ❛ ❣r❛t❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ✐♥t❡r❛❣✐r ❡ ❛♣r❡♥❞❡r ❞✉r❛♥t❡ ♦ ❞♦✉t♦r❛❞♦✳

❆♦s ✐♥t❡❣r❛♥t❡s ❞❛ s❡❝r❡t❛r✐❛ ❞♦ Pr♦❣r❛♠❛ ❞❡ Pós✲❣r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠✲ ♣✉t❛çã♦ ✭PP●❈❈ ✲ ❯❋▼●✮✱ ♣❡❧❛ ♣r❡st❡③❛ ❡ q✉❛❧✐❞❛❞❡ ♥♦s ❛t❡♥❞✐♠❡♥t♦s ❝♦♠♦✱ t❛♠✲ ❜é♠✱ ♣❡❧❛ ❞❡❞✐❝❛çã♦ ❞✐s♣❡♥s❛❞❛ ❛♦s ❛❧✉♥♦s ❡♠ t♦❞♦s ♦s ♠♦♠❡♥t♦s ❞♦ ♦ ❝✉rs♦✳

❆ t♦❞♦s ❛q✉❡❧❡s q✉❡ ❞✐r❡t❛ ♦✉ ✐♥❞✐r❡t❛♠❡♥t❡ ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ q✉❡ ❡st❡ tr❛❜❛❧❤♦ ❢♦ss❡ ❝♦♥❝❧✉í❞♦ ❝♦♠ ê①✐t♦✳

(11)

❘❡s✉♠♦

❯♠❛ ❡str❛té❣✐❛ ❛♠♣❧❛♠❡♥t❡ ❡♠♣r❡❣❛❞❛ ♣❛r❛ ♣r♦✈❡r ❧♦❝❛❧✐③❛çã♦ ❡♠ s✐st❡♠❛s ♠✉❧t✐rr♦✲ ❜ót✐❝♦s ❝♦♥s✐st❡ ♥♦s r♦❜ôs ✉t✐❧✐③❛r❡♠ ✉♥s ❛♦s ♦✉tr♦s ❝♦♠♦ ♠❛r❝♦s ❞✐♥â♠✐❝♦s✱ ❡♠ ✉♠ ♣r♦❝❡ss♦ ❞❡♥♦♠✐♥❛❞♦ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛✳ ❊t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♦❝♦r✲ r❡♠ q✉❛♥❞♦ ❞♦✐s ♦✉ ♠❛✐s r♦❜ôs s❡ ❡♥❝♦♥tr❛♠ ❡ tr♦❝❛♠ ✐♥❢♦r♠❛çõ❡s✱ ♣♦ss✐❜✐❧✐t❛♥❞♦✲♦s ♠❡❧❤♦r❛r s✉❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❖ ❡♠♣r❡❣♦ ❞❡ss❛ ❡str❛té❣✐❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❡♠ s✐st❡♠❛s ❝♦♠♣♦st♦s ♣♦r ✉♠ ♥ú♠❡r♦ s✐❣♥✐✜❝❛t✐✈♦ ❞❡ r♦❜ôs ❛✐♥❞❛ é ♣♦✉❝♦ ✐♥✈❡st✐❣❛❞♦✱ ♣♦ss✐✈❡❧♠❡♥t❡ ❞❡✈✐❞♦ à ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦ ❡ ❡s♣❛ç♦ ♣❛r❛ s❡ ❣❡r❛r ❡st✐♠❛t✐✈❛s ❝♦♥s✐st❡♥t❡s ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ♣r♦♣♦♠♦s ✉♠❛ ❛❜♦r❞❛❣❡♠ ♣❛r❛ ❧♦❝❛❧✐③❛r ❝♦♦♣❡r❛t✐✈❛♠❡♥t❡ ❡ ❞❡ ♠❛♥❡✐r❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ❡♥①❛♠❡s r♦✲ ❜ót✐❝♦s✳ ❚❛❧ ❛❜♦r❞❛❣❡♠ ❝♦♥s✐❞❡r❛ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛ ❞♦ ❡♥①❛♠❡✱ ✉♠❛ ✈❡③ q✉❡ ❛ ♠❡s♠❛ ❛♠♣❧✐❛ ❛ ♦❝♦rrê♥❝✐❛ ❞♦s ❡♥❝♦♥tr♦s✱ ✐♠♣❛❝t❛♥❞♦ ❞✐r❡t❛♠❡♥t❡ ♥❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❣r✉♣♦✳ P❛r❛ ✐ss♦✱ ✉♠❛ ♠♦❞✐✜❝❛çã♦ ❢♦✐ ♣r♦♣♦st❛ ❡♠ ✉♠ ❛❧❣♦r✐t♠♦ ❞❡ ❛❣r❡❣❛çã♦✴s❡❣r❡❣❛çã♦ ❞❡ ❢♦r♠❛ ❛ ♠❛♥t❡r ♦ ❣r✉♣♦ ❝♦❡s♦✳ ❆ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❢♦✐ ❝♦♥s✐❞❡r❛❞❛ ❛♦ ✉t✐❧✐③❛r♠♦s ♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✲ ✈❛r✐â♥❝✐❛s✱ ♦ q✉❛❧✱ ♣r♦✈❛❞❛♠❡♥t❡✱ ❣❡r❛ ❡st✐♠❛t✐✈❛s ❝♦♥s✐st❡♥t❡s ❡♠ s✐t✉❛çõ❡s ♥❛s q✉❛✐s ❛ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ♦s ❞❛❞♦s é ❞❡s❝♦♥❤❡❝✐❞❛✳ ❆ss✐♠✱ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❡s❝❛❧á✈❡❧✱ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ❡ ❝♦♥s✐st❡♥t❡ é ❛♣r❡s❡♥t❛❞❛ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛r ❝♦♦♣❡r❛t✐✈❛✲ ♠❡♥t❡ ✉♠ ❡♥①❛♠❡ ❞❡ r♦❜ôs✳ ❙✐♠✉❧❛çõ❡s ❢♦r❛♠ ✉t✐❧✐③❛❞❛s ♣❛r❛ ❛✈❛❧✐❛r ❛ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ ❡ ❛ ❝♦♥s✐stê♥❝✐❛ ❞❛ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛✱ ❛❧é♠ ❞❡ ❛❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s q✉❡ ♣♦❞❡♠ ✐♥✲ ✢✉❡♥❝✐❛r ♥❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦✳ ❆❧é♠ ❞✐ss♦✱ ❡①♣❡r✐♠❡♥t♦s ❝♦♠ r♦❜ôs r❡❛✐s ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞♦s ❝♦♠♦ ♣r♦✈❛ ❞❡ ❝♦♥❝❡✐t♦ ♣❛r❛ ♠♦str❛r ❛ ✈✐❛❜✐❧✐❞❛❞❡ ❞❛ ✉t✐❧✐③❛çã♦ ❞❡ t❛❧ ♣r♦♣♦st❛ ❡♠ ❛♠❜✐❡♥t❡s r❡❛✐s✳ ❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♥❛s s✐♠✉❧❛çõ❡s ❡ ♥♦s ❡①♣❡r✐♠❡♥t♦s r❡❛✐s ♠♦str❛♠ ❛ ❡✜❝á❝✐❛ ❞❛ ❛❜♦r❞❛❣❡♠ ❞❡ ❧♦❝❛❧✐③❛çã♦ ♣r♦♣♦st❛✳

P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❊♥①❛♠❡ ❞❡ ❘♦❜ôs✱ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛✱ ▼♦✈✐♠❡♥t❛çã♦ ❈♦❧❡✲ t✐✈❛✱ ❘♦❜ót✐❝❛ Pr♦❜❛❜✐❧íst✐❝❛✱ ❙✐st❡♠❛s ▼✉❧t✐rr♦❜ót✐❝♦s✳

(12)

(13)

❆❜str❛❝t

❆ ❝♦♠♠♦♥ str❛t❡❣② t♦ ♣r♦✈✐❞❡ ❧♦❝❛❧✐③❛t✐♦♥ ✐♥ ♠✉❧t✐✲r♦❜♦t s②st❡♠s ✐s t♦ ✉s❡ ♣❛rt ♦❢ t❤❡ ❣r♦✉♣ ❛s ❞②♥❛♠✐❝ ❧❛♥❞♠❛r❦s✱ ✐♥ ♦r❞❡r t♦ ✐♠♣r♦✈❡ t❤❡ q✉❛❧✐t② ♦❢ t❤❡ ♣♦s❡ ❡st✐♠❛t✐♦♥ ✐♥ ❛ ♣r♦❝❡ss ❦♥♦✇♥ ❛s ❈♦♦♣❡r❛t✐✈❡ ▲♦❝❛❧✐③❛t✐♦♥✳ ❚❤✐s ♦❝❝✉r ✇❤❡♥ t✇♦ ♦r ♠♦r❡ r♦❜♦ts ♠❡❡t ❛♥❞ ❡①❝❤❛♥❣❡ ✐♥❢♦r♠❛t✐♦♥ ✇✐t❤ t❤❡ ❛✐♠ t♦ ✐♠♣r♦✈❡ t❤❡✐r ❧♦❝❛❧✐③❛t✐♦♥ ❡st✐♠❛t❡✳ ■♥ ❙✇❛r♠ ❘♦❜♦t✐❝s✱ t❤❡ ✉s❛❣❡ ♦❢ t❤✐s ❦✐♥❞ ♦❢ t❡❝❤♥✐q✉❡ ✐s ❧✐tt❧❡ ❡①♣❧♦r❡❞✱ ♣♦ss✐❜❧② ❜❡❝❛✉s❡ t❤❡ t✐♠❡ ❛♥❞ s♣❛❝❡ ❝♦♠♣❧❡①✐t② t♦ ❣❡♥❡r❛t❡ ❝♦♥s✐st❡♥t ❧♦❝❛❧✐③❛t✐♦♥ ❡st✐♠❛t❡s✳ ■♥ t❤✐s ✇♦r❦✱ ✇❡ ♣r♦♣♦s❡ ❛♥ ❛♣♣r♦❛❝❤ t♦ ❝♦♦♣❡r❛t✐✈❡❧② ❧♦❝❛❧✐③❡ s✇❛r♠s ✐♥ ❛ ❞❡❝❡♥tr❛❧✐③❡❞ ✇❛②✳ ❲❡ ❝♦♥s✐❞❡r t❤❡ ❝♦❧❧❡❝t✐✈❡ ♠♦✈❡♠❡♥t ♦❢ t❤❡ ❣r♦✉♣✱ ♦♥❝❡ t❤✐s ❝❛♥ ✐♠♣r♦✈❡ t❤❡ ♣♦ss✐❜✐✲ ❧✐t② ♦❢ ❡♥❝♦✉♥t❡rs✱ ✇❤✐❝❤ ❛✛❡❝ts t❤❡ q✉❛❧✐t② ♦❢ t❤❡ ❣r♦✉♣ ❧♦❝❛❧✐③❛t✐♦♥✳ ❚❤❡ ❝♦❧❧❡❝t✐✈❡ ♠♦✈❡♠❡♥t str❛t❡❣② ✐s ❛❧s♦ ♣r♦♣♦s❡❞ ✐♥ t❤✐s ✇♦r❦✱ ❞❡s♣✐t❡ t❤❡ ♣r❡s❡♥t❡❞ ❧♦❝❛❧✐③❛t✐♦♥ ♠❡t❤♦❞ ❝❛♥ ❜❡ ❛♣♣❧✐❡❞ ❜② ♠❛❦✐♥❣ ✉s❡ ♦❢ ♦t❤❡r ♠♦t✐♦♥ str❛t❡❣✐❡s✳ ❲❡ ❞❡❛❧ ✇✐t❤ t❤❡ ❝♦♠♣❧❡①✐t② r❡❧❛t❡❞ t♦ t❤❡ ❝♦♦♣❡r❛t✐✈❡ ❧♦❝❛❧✐③❛t✐♦♥ ♦❢ ❛ ❧❛r❣❡ ♥✉♠❜❡r ♦❢ r♦❜♦ts ❜② ✉s✐♥❣ t❤❡ ❈♦✈❛r✐❛♥❝❡ ■♥t❡rs❡❝t✐♦♥ ❆❧❣♦r✐t❤♠✱ ✇❤✐❝❤ ✇❛s ♣r♦✈❡❞ ✐♥ t❤❡ ❧✐t❡r❛t✉r❡ t♦ ❣❡♥❡r❛t❡ ❝♦♥s✐st❡♥t ❡st✐♠❛t❡s ✐♥ s✐t✉❛t✐♦♥s ✇❤❡r❡ t❤❡ ✐♥t❡r❞❡♣❡♥❞❡♥❝❡ ✐♥❢♦r♠❛t✐♦♥ ✐s ✉♥❦♥♦✇♥✳ ❚❤✉s✱ t❤✐s ✇♦r❦ ♣r♦♣♦s❡s ❛ s❝❛❧❛❜❧❡✱ ❞❡❝❡♥tr❛❧✐③❡❞ ❛♥❞ ❝♦♥s✐st❡♥t ❛♣♣r♦❛❝❤ t♦ ♣❡r❢♦r♠ ❝♦♦♣❡r❛t✐✈❡ ❧♦❝❛❧✐③❛t✐♦♥ ✐♥ s✇❛r♠s✳ ❙✐♠✉❧❛t✐♦♥s ✇❡r❡ ❡♠♣❧♦②❡❞ t♦ ❛♥❛❧②③❡ t❤❡ s❝❛❧❛❜✐✲ ❧✐t② ❛♥❞ ♦t❤❡r ❛s♣❡❝ts t❤❛t ❝❛♥ ✐♥✢✉❡♥❝❡ ✐♥ t❤❡ ❧♦❝❛❧✐③❛t✐♦♥ q✉❛❧✐t②✳ ❘❡❛❧ ❡①♣❡r✐♠❡♥ts ✇❡r❡ ❛❧s♦ ❞❡✈❡❧♦♣❡❞ ❛s ❛ ♣r♦♦❢ ♦❢ ❝♦♥❝❡♣t ✇✐t❤ t❤❡ ❛✐♠ t♦ s❤♦✇ t❤❡ ❢❡❛s✐❜✐❧✐t② ♦❢ ✉s✐♥❣ t❤✐s ❛♣♣r♦❛❝❤ ✐♥ r❡❛❧ r♦❜♦ts✳ ❘❡s✉❧ts s❤♦✇ t❤❡ ❡✛❡❝t✐✈❡♥❡ss ♦❢ t❤❡ ♣r♦♣♦s❡❞ ❛♣♣r♦❛❝❤✳

❑❡②✇♦r❞s✿ ❈♦❧❧❡❝t✐✈❡ ▼♦✈❡♠❡♥t✱ ❈♦♦♣❡r❛t✐✈❡ ▲♦❝❛❧✐③❛t✐♦♥✱ ▼✉❧t✐✲r♦❜♦t ❙②st❡♠s✱ Pr♦❜❛❜✐❧✐st✐❝ ❘♦❜♦t✐❝s✱ ❙✇❛r♠ ❘♦❜♦t✐❝s✳

(14)

(15)

▲✐st❛ ❞❡ ❋✐❣✉r❛s

✷✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ❡st❛❞♦ ❞❡ ✉♠ r♦❜ô ❡♠ ✉♠ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ✐♥❡r❝✐❛❧ ✽ ✷✳✷ ❋♦r♠❛çã♦ ❞✐♥â♠✐❝❛ ❞❡ ✈✐③✐♥❤❛♥ç❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✸ ■♥t❡r❛çã♦ ❡♥tr❡ r♦❜ôs ❡♠ ✉♠❛ ♠❡s♠❛ ✈✐③✐♥❤❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✹ ❊①❡♠♣❧♦s ❞❡ ❡♥①❛♠❡s ♥❛t✉r❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✺ ❉✐s♣❡rsã♦ ❡s♣❛❝✐❛❧ ❡♠ ❛♠❜✐❡♥t❡ ✐♥t❡r♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✻ ❆♣❧✐❝❛çã♦ ❞❡ té❝♥✐❝❛ ❞❡ ❣r❛❞✐❡♥t❡ ♣❛r❛ ❞✐❢✉sã♦ ❞❡ ♠❡♥s❛❣❡♥s ✭❢❡r♦♠ô♥✐♦s✮ ✷✸ ✷✳✼ ❚r❛♥s♣♦rt❡ ❝♦♦♣❡r❛t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✷✳✽ ❊①❡♠♣❧♦s ❞❡ ❢♦r♠❛s ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❡♠ ✉♠ ♠❛♣❛ ♠étr✐❝♦ ✷✻ ✷✳✾ ❊①❡♠♣❧♦s ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ ♠❛♣❛ t♦♣♦❧ó❣✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✶✵ ❉❡s❧♦❝❛♠❡♥t♦ ❞♦ r♦❜ô ❡♠ r❡❧❛çã♦ ❛ ✉♠ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ✐♥❡r❝✐❛❧ ✳ ✳ ✷✽ ✷✳✶✶ ❙❡♥s♦r ♣r♦♣r✐♦❝❡♣t✐✈♦✿ ❡♥❝♦❞❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✶✷ ❊①❡♠♣❧♦s ❞❡ ♠❛r❝♦s ♣❛ss✐✈♦s ❡ ❛t✐✈♦s ♣r❡s❡♥t❡s ❡♠ ✉♠ ❛♠❜✐❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✶✸ ❊t❛♣❛s ❞❡ ✉♠ ♠ét♦❞♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❣❧♦❜❛❧ ❜❛s❡❛❞♦ ❡♠ té❝♥✐❝❛s ❞❡ ❛♠♦s✲

tr❛❣❡♠ ♣r♦❜❛❜✐❧ís✐t✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✶✹ ❙✐st❡♠❛ ❞❡ P♦s✐❝✐♦♥❛♠❡♥t♦ ●❧♦❜❛❧ ◆❆❱❙❚❆❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✶✺ ❙✐st❡♠❛ ❞❡ P♦s✐❝✐♦♥❛♠❡♥t♦ ●❧♦❜❛❧ ❉✐❢❡r❡♥❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✳✶✻ ❊①❡♠♣❧♦ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❣❧♦❜❛❧ ♣❛r❛ ❛♠❜✐❡♥t❡ ✐♥t❡r♥♦ ✳ ✳ ✳ ✳ ✸✹

✸✳✶ ❊t❛♣❛s ❞❛ ❡str❛té❣✐❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✷ ■♠♣❧❡♠❡♥t❛çã♦ ❡♠ r♦❜ôs r❡❛✐s ❞♦ ♠ét♦❞♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ✳ ✳ ✳ ✳ ✹✺

✹✳✶ ❉✐stâ♥❝✐❛ ❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛s ❡♥tr❡ r♦❜ôs ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✹✳✷ ❉✐ss❡♠✐♥❛çã♦ ❞❡ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ♣♦r ✉♠ r♦❜ô ♠❛r❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✸ ❈á❧❝✉❧♦ ❞❛ ♣♦s❡ ❞❡ ✉♠ r♦❜ô ❝♦♠ ❜❛s❡ ❡♠ ✉♠ r♦❜ô ♠❛r❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✹ ❊①❡♠♣❧♦ ❞❡ ❛♣❧✐❝❛çã♦ ❞❛ r❡❣r❛ ❞❡ s❡♣❛r❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✹✳✺ ❊①❡♠♣❧♦ ❞❡ ❛♣❧✐❝❛çã♦ ❞❛ r❡❣r❛ ❞❡ ❝♦❡sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✹✳✻ ❊①❡♠♣❧♦ ❞❡ ❛♣❧✐❝❛çã♦ ❞❛ r❡❣r❛ q✉❡ ❞✐t❛ ❛ ❞✐r❡çã♦ ❛ s❡r s❡❣✉✐❞❛ ♣❡❧♦ ❣r✉♣♦✳ ✻✽

(16)

✹✳✼ ▼♦♠❡♥t♦s ❞✐st✐♥t♦s ❞✉r❛♥t❡ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦ r♦❜ô ❧í❞❡r ✭♣♦♥t♦ ❛③✉❧✮ ❡♠ ❞✐r❡çã♦ ❛♦ ❝❡♥tr♦ ❞♦ ❣r✉♣♦ ✭❛❧✈♦ ❛③✉❧✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷

✺✳✶ ❊①❡♠♣❧♦ ❞❡ ❝❛♠✐♥❤♦ ❡①❡❝✉t❛❞♦ ♣❡❧♦s r♦❜ôs ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✺✳✷ ❊rr♦ ♠é❞✐♦ ❛♦ s❡ ✈❛r✐❛r ♦ ♥ú♠❡r♦ ❞❡ ♠❛r❝♦s ✉t✐❧✐③❛❞♦ ❡♠ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐✲

③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✺✳✸ ❊rr♦ ♠é❞✐♦ ❡♠ ❝❛❞❛ ✐t❡r❛çã♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ✉♠ ♥ú♠❡r♦ ❞✐❢❡r❡♥t❡ ❞❡ ♠❛r❝♦s

✉t✐❧✐③❛❞♦s ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✺✳✹ ❊st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ ✉♠ r♦❜ô ❞♦ ❡♥①❛♠❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✺✳✺ ❊rr♦ ♠é❞✐♦ ❞❛s ❡st✐♠❛t✐✈❛s ❞❡ ♣♦s✐çã♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ❝r✐tér✐♦ ❞❡ s❡❧❡çã♦

❞❡ ♠❛r❝♦s ✉t✐❧✐③❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✺✳✻ ❊①❡♠♣❧♦ ❞❡ ✉♠ ❝❛♠✐♥❤♦ ❡①❡❝✉t❛❞♦ ♣❡❧♦ ❡♥①❛♠❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✺✳✼ ❆❣r✉♣❛♠❡♥t♦s ✉t✐❧✐③❛❞♦s s♦♠❡♥t❡ ♣❛r❛ ❛✉①✐❧✐❛r ♥❛ ❛♥á❧✐s❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵ ✺✳✽ ❊rr♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛ss♦❝✐❛❞♦ ❛♦s três t✐♣♦s ❞❡ ❡①♣❡r✐♠❡♥t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ✺✳✾ ❊rr♦ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❝♦♠ ✉♠ r♦❜ô ❡q✉✐♣❛❞♦ ❝♦♠ s✐st❡♠❛ ❞❡

♣♦s✐❝✐♦♥❛♠❡♥t♦ ❣❧♦❜❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ✺✳✶✵ ■♥t❡♥s✐❞❛❞❡ ❞♦ ❡rr♦ ❛❝✉♠✉❧❛❞♦ ♣❡❧♦s r♦❜ôs ❛♣ós ❛ ❡①❡❝✉çã♦ ❞❡ ✉♠ ❝❛♠✐♥❤♦ ✾✸ ✺✳✶✶ ❆✉♠❡♥t♦ ♥♦ ♥ú♠❡r♦ ❞❡ ❛❣r✉♣❛♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✺✳✶✷ Pr♦♣♦rçã♦ ❞♦ ❡rr♦ ♠é❞✐♦ ❞❡ ❝❛❞❛ ❣r✉♣♦g ❡♠ r❡❧❛çã♦ ❛♦ ❣r✉♣♦ ♠❛✐s ♣ró①✐♠♦

❛♦ ❧í❞❡r ✭●g✴●1✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✺✳✶✸ ▼♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛ ❞♦ ❡♥①❛♠❡ ♥♦ ❛♠❜✐❡♥t❡ s✐♠✉❧❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✺✳✶✹ P❛râ♠❡tr♦ ❞♦ ♠♦❞❡❧♦ ♥ã♦✲❤♦❧♦♥ô♠✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✺✳✶✺ ❊①❡♠♣❧♦ ❞❡ ❝❛♠✐♥❤♦ ❡①❡❝✉t❛❞♦ ♣♦r ✉♠ ❞♦s r♦❜ôs ❞✉r❛♥t❡ ❛ ♠♦✈✐♠❡♥t❛çã♦

❞♦ ❡♥①❛♠❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵ ✺✳✶✻ ❊✈♦❧✉çã♦ ❞♦ ❡rr♦ ❡ ❞❛ ✐♥❝❡rt❡③❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❣r✉♣♦ ♥♦s ❡①♣❡r✐♠❡♥t♦s

❡♠ q✉❡ ♦ ❧í❞❡r t❡✈❡ ❛❝❡ss♦ ❛ ♦❜s❡r✈❛çõ❡s ❛❜s♦❧✉t❛s r❡❣✉❧❛r♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶ ✺✳✶✼ ❆❝❡ss♦ ❡s♣♦rá❞✐❝♦ ♣❡❧♦ ❧í❞❡r à ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛ ❞✉r❛♥t❡

❛ ♠♦✈✐♠❡♥t❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷ ✺✳✶✽ ❊✈♦❧✉çã♦ ❞♦ ❡rr♦ ❡ ❞❛ ✐♥❝❡rt❡③❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❣r✉♣♦ ♥♦s ❡①♣❡r✐♠❡♥t♦s

❡♠ q✉❡ ♦ ❧í❞❡r t❡✈❡ ❛❝❡ss♦ ❛ ♦❜s❡r✈❛çõ❡s ❛❜s♦❧✉t❛s ❡s♣♦r❛❞✐❝❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✶✵✸ ✺✳✶✾ ❋❛❧❤❛ ✐♥t❡r♠✐t❡♥t❡ ♥♦ s❡♥s♦r ✉t✐❧✐③❛❞♦ ♣❡❧♦ ❧í❞❡r ♣❛r❛ ♦❜t❡r ❡st✐♠❛t✐✈❛s ❞❡

❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛ ❞✉r❛♥t❡ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦ ❡♥①❛♠❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹ ✺✳✷✵ ❊✈♦❧✉çã♦ ❞♦ ❡rr♦ ❡ ❞❛ ✐♥❝❡rt❡③❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞✉r❛♥t❡ ♦s ❡①♣❡r✐♠❡♥t♦s

❡♠ q✉❡ ♦❝♦rr❡ ❢❛❧❤❛ ♥♦ s❡♥s♦r ❡①t❡r♦❝❡♣t✐✈♦ ✉t✐❧✐③❛❞♦ ♣❡❧♦ ❧í❞❡r ♣❛r❛ ♦❜t❡r ❡st✐♠❛t✐✈❛s ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❛❜s♦❧✉t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺ ✺✳✷✶ ❘❡s✉❧t❛❞♦ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♥❛ ♦❝♦rrê♥❝✐❛ ❞❡ ❢❛❧❤❛s ♥♦ ♠❡❝❛♥✐s♠♦

❞❡ ❝♦♠✉♥✐❝❛çã♦ ❞♦s r♦❜ôs✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻

(17)

✺✳✷✷ ❊rr♦ ♠é❞✐♦ ❡ ✐♥❝❡rt❡③❛ r❡❢❡r❡♥t❡ à ♣♦s✐çã♦ ❡ ♦r✐❡♥t❛çã♦ ✭❢❛❧❤❛ ♥❛ ❝♦♠✉♥✐❝❛çã♦✮✶✵✻ ✺✳✷✸ ❘❡s✉❧t❛❞♦ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♥❛ ❛✉sê♥❝✐❛ ❞❡ s❡♥s♦r❡s ❞❡ ❧♦❝❛❧✐③❛çã♦

❛❜s♦❧✉t❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼ ✺✳✷✹ ❊✈♦❧✉çã♦ ❞♦ ❡rr♦ ♠é❞✐♦ ❡ ❞❛ ✐♥❝❡rt❡③❛ ♥❛ ❛✉sê♥❝✐❛ ❞❡ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛✲

❧✐③❛çã♦ ❛❜s♦❧✉t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽ ✺✳✷✺ ❆♠❜✐❡♥t❡ ✉t✐❧✐③❛❞♦ ♥❛s s✐♠✉❧❛çõ❡s ❘❖❙✴❙t❛❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✺✳✷✻ P♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦s r♦❜ôs ♥❛ ❢❛s❡ ✐♥✐❝✐❛❧ ❞♦ ❛❧❣♦r✐t♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✺✳✷✼ P♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦s r♦❜ôs ✉t✐❧✐③❛♥❞♦ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶ ✺✳✷✽ ▼♦✈✐♠❡♥t❛çã♦ ❞♦s r♦❜ôs ♥♦ ❛♠❜✐❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷ ✺✳✷✾ ❈❛♠✐♥❤♦ ♣❡r❝♦rr✐❞♦✱ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡ ♦❞♦♠❡tr✐❛

❞♦s ❞✐✈❡rs♦s r♦❜ôs ❞♦ ❣r✉♣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸ ✺✳✸✵ ❊rr♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❡ ✐♥❝❡rt❡③❛ r❡❢❡r❡♥t❡ à ♣♦s✐çã♦ ❞❡ ❝❛❞❛ r♦❜ô ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺ ✺✳✸✶ ❊rr♦ r❡❢❡r❡♥t❡ à ♦r✐❡♥t❛çã♦ ❡ ✐♥❝❡rt❡③❛ r❡❧❛t✐✈♦s ❛ ❝❛❞❛ r♦❜ô ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✻ ✺✳✸✷ ❘♦❜ôs ❡✲♣✉❝❦ ✉t✐❧✐③❛❞♦s ♥♦s ❡①♣❡r✐♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼ ✺✳✸✸ ❊①❡♠♣❧♦ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞✐s♣♦♥✐❜✐❧✐③❛❞❛ ♣❡❧♦ ❙✐st❡♠❛s ❞❡ P♦s✐❝✐♦♥❛♠❡♥t♦

●❧♦❜❛❧ ♣❛r❛ ❛♠❜✐❡♥t❡s ✐♥t❡r♥♦s ✭✐●P❙✮ ❡ ❛ ♦❞♦♠❡tr✐❛ r❡❢❡r❡♥t❡s ❛♦ ❝❛♠✐♥❤♦ ❡①❡❝✉t❛❞♦ ♣♦r ✉♠ r♦❜ô ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼ ✺✳✸✹ P♦s✐❝✐♦♥❛♠❡♥t♦ ✐♥✐❝✐❛❧ ❞♦s r♦❜ôs✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ✺✳✸✺ P♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦s r♦❜ôs ❝♦♠ ❜❛s❡ ❡♠ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵ ✺✳✸✻ ▼♦✈✐♠❡♥t❛çã♦ ❞♦s r♦❜ôs ❝♦♠ ❜❛s❡ ❡♠ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶ ✺✳✸✼ ❈❛♠✐♥❤♦ ♣❡r❝♦rr✐❞♦✱ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡ ♦❞♦♠❡tr✐❛

❞♦s r♦❜ôs ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ✺✳✸✽ ❊rr♦ ❡ ✐♥❝❡rt❡③❛ r❡❢❡r❡♥t❡s à ♣♦s✐çã♦ ❞❡ ❝❛❞❛ r♦❜ô✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✸ ✺✳✸✾ ❊rr♦ ❡ ✐♥❝❡rt❡③❛ r❡❢❡r❡♥t❡s à ♦r✐❡♥t❛çã♦ ❞❡ ❝❛❞❛ r♦❜ô✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹

❆✳✶ ❋✉♥çã♦ ❞❡ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ✉♥✐✈❛r✐❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✾

❈✳✶ ❊①❡♠♣❧♦ ❞❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❜✐✈❛r✐❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✶ ❈✳✷ ❈♦♠❜✐♥❛çã♦ ❞❡ ❡st✐♠❛t✐✈❛s ❝♦♠ ✐♥❢♦r♠❛çã♦ ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❝♦♥❤❡❝✐❞❛

❡ ❞❡s❝♦♥❤❡❝✐❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✷

(18)

(19)

▲✐st❛ ❞❡ ❚❛❜❡❧❛s

✸✳✶ ❘❡s✉♠♦ ❞❡ ❛❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦s ♠ét♦❞♦s ❞❡s❝r✐t♦s ♥♦s ♣r✐♥❝✐♣❛✐s tr❛❜❛❧❤♦s r❡✈✐s❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺

✺✳✶ ❈♦♦♣❡r❛çã♦ ✐♥t❡r❣r✉♣♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸

(20)

(21)

▲✐st❛ ❞❡ ❆❜r❡✈✐❛çõ❡s

❈❈❉ ❈❤❛r❣❡ ❈♦✉♣❧❡❞ ❉❡✈✐❝❡

❈■ ❈♦✈❛r✐❛♥❝❡ ■♥t❡rs❡❝t✐♦♥ ❆❧❣♦r✐t❤♠ ✲ ❆❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s ❈❙❆ ❈r✐tér✐♦ ❞❡ ❙❡❧❡çã♦ ❆❧❡❛tór✐❛

❈❙▼■ ❈r✐tér✐♦ ❞❡ ❙❡❧❡çã♦ ❞❛ ▼❡♥♦r ■♥❝❡rt❡③❛ ❈❙P ❈r✐tér✐♦ ❞❡ ❙❡❧❡çã♦ ♣♦r Pr♦①✐♠✐❞❛❞❡

❉❆❘❙ ■♥t❡r♥❛t✐♦♥❛❧ ❙②♠♣♦s✐✉♠ ♦♥ ❉✐str✐❜✉t❡❞ ❆✉t♦♥♦♠♦✉s ❘♦❜♦t✐❝ ❙②st❡♠s

❉●P❙ ❉✐✛❡r❡♥t✐❛❧ ●❧♦❜❛❧ P♦s✐t✐♦♥✐♥❣ ❙②st❡♠s ✲ ❙✐st❡♠❛s ❞❡ P♦s✐❝✐♦♥❛♠❡♥t♦ ●❧♦❜❛❧ ❉✐❢❡r❡♥❝✐❛❧

❑❋ ❑❛❧♠❛♥ ❋✐❧t❡r ✲ ❋✐❧tr♦ ❞❡ ❑❛❧♠❛♥

❊❑❋ ❊①t❡♥❞❡❞ ❑❛❧♠❛♥ ❋✐❧t❡r ✲ ❋✐❧tr♦ ❞❡ ❑❛❧♠❛♥ ❊st❡♥❞✐❞♦

●P❙ ●❧♦❜❛❧ P♦s✐t✐♦♥✐♥❣ ❙②st❡♠s ✲ ❙✐st❡♠❛s ❞❡ P♦s✐❝✐♦♥❛♠❡♥t♦ ●❧♦❜❛❧ ■❈❆❘ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆❞✈❛♥❝❡❞ ❘♦❜♦t✐❝s

✐●P❙ ✐♥❞♦♦r ●❧♦❜❛❧ P♦s✐t✐♦♥✐♥❣ ❙②st❡♠s ✲ ❙✐st❡♠❛s ❞❡ P♦s✐❝✐♦♥❛♠❡♥t♦ ●❧♦❜❛❧ ♣❛r❛ ❛♠❜✐❡♥t❡s ✐♥t❡r♥♦s

■▲▼ ■♥tr✐♥s✐❝ ▲♦❝❛❧✐③❛t✐♦♥ ❛♥❞ ▼❛♣♣✐♥❣

■▼❯ ■♥❡rt✐❛❧ ▼❡❛s✉r❡♠❡♥t ❯♥✐t

▼❆P ▼❛①✐♠✉♠ ❛ P♦st❡r✐♦r✐ ❡st✐♠❛t♦r ✲ ❊st✐♠❛❞♦r ❞❡ ▼á①✐♠❛ ❱❡r♦ss✐♠✐❧❤❛♥ç❛ ▼❈▲ ▼♦♥t❡ ❈❛r❧♦ ▲♦❝❛❧✐③❛t✐♦♥ ✲ ▲♦❝❛❧✐③❛çã♦ ❞❡ ▼♦♥t❡ ❈❛r❧♦

▼❖❊k _{❊rr♦ ♠é❞✐♦ r❡❧❛t✐✈♦ à ♦r✐❡♥t❛çã♦ ♥❛} _k_{✲és✐♠❛ ✐t❡r❛çã♦}

▼P❊k _{❊rr♦ ♠é❞✐♦ ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ♥❛} _k_{✲és✐♠❛ ✐t❡r❛çã♦}

❖❊k

s ❊rr♦ ❞❡ ♦r✐❡♥t❛çã♦ ♥❛ k✲és✐♠❛ ✐t❡r❛çã♦ ❞❛ s✐♠✉❧❛çã♦ s

P❊k

s ❊rr♦ ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ♥❛ k✲és✐♠❛ ✐t❡r❛çã♦ ❞❛ s✐♠✉❧❛çã♦ s

P❋ P❛rt✐❝❧❡ ❋✐❧t❡r ✲ ❋✐❧tr♦ ❞❡ P❛rtí❝✉❧❛s

❘▼❙❊ ❊rr♦ ♠é❞✐♦

❘❖❙ ❘♦❜♦t ❖♣❡r❛t✐♥❣ ❙②st❡♠

❙❈■ ❙♣❧✐t ❈♦✈❛r✐❛♥❝❡ ■♥t❡rs❡❝t✐♦♥ ❆❧❣♦r✐t❤♠

❙▲❆▼ ❙✐♠✉❧t❛♥❡♦✉s ▲♦❝❛❧✐③❛t✐♦♥ ❛♥❞ ▼❛♣♣✐♥❣ ✲ ▲♦❝❛❧✐③❛çã♦ ❡ ▼❛♣❡❛♠❡♥t♦ ❙✐♠✉❧tâ♥❡♦s ❱❡❘▲❛❜ ▲❛❜♦r❛tór✐♦ ❞❡ ❱✐sã♦ ❈♦♠♣✉t❛❝✐♦♥❛❧ ❡ ❘♦❜ót✐❝❛

(22)

(23)

▲✐st❛ ❞❡ ❙í♠❜♦❧♦s

R ❊♥①❛♠❡ ❞❡ r♦❜ôs

||R_|| ◆ú♠❡r♦ ❞❡ r♦❜ôs ♥♦ ❡♥①❛♠❡

Ri ✐✲és✐♠♦ r♦❜ô ❞♦ ❡♥①❛♠❡

✭❳W,❨W) ❙✐st❡♠❛ ❞❡ ❈♦♦r❞❡♥❛❞❛s ■♥❡r❝✐❛❧

✭❳Ri,❨Ri✮ ❙✐st❡♠❛ ❞❡ ❈♦♦r❞❡♥❛❞❛s ▲♦❝❛❧ r❡❧❛t✐✈♦ ❛♦ ✐✲és✐♠♦ r♦❜ô

Ni ✈✐③✐♥❤❛♥ç❛ ❞♦i✲és✐♠♦ r♦❜ô

ε ♠❡❞✐❞❛ ❞♦ r❛✐♦ ❞❛s ✈✐③✐♥❤❛♥ç❛s

pi ♣♦s✐çã♦ (xi, yi) ❞♦ ✐✲és✐♠♦ r♦❜ô ❡♠ r❡❧❛çã♦ ❛ ✭❳W,❨W)

θi ♦r✐❡♥t❛çã♦ ❞♦ i✲és✐♠♦ r♦❜ô ❡♠ r❡❧❛çã♦ ❛ ✭❳W,❨W)

q_i ♣♦s❡(xi, yi, θi) ❞♦i✲és✐♠♦ r♦❜ô ❡♠ r❡❧❛çã♦ ❛ ✭❳W,❨W)

x_i ✈❡t♦r ❞❡ ❡st❛❞♦s ❞♦ r♦❜ô i

b

xi ✈❡t♦r ❞❡ ❡st❛❞♦s ❡st✐♠❛❞♦ ❞♦ r♦❜ô i

Pi ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛s ❛ss♦❝✐❛❞❛ à bxi

ρij ❞✐stâ♥❝✐❛ r❡❧❛t✐✈❛ ♣❛r❛ ♦ r♦❜ô j ♠❡❞✐❞❛ ♣❡❧♦ r♦❜ô i

φij ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛ ♣❛r❛ ♦ r♦❜ôj ♠❡❞✐❞❛ ♣❡❧♦ r♦❜ô i

zij ✈❡t♦r ❞❡ ♦❜s❡r✈❛çã♦ ❡①t❡r♦❝❡♣t✐✈❛ t♦♠❛❞❛ ♣❡❧♦ r♦❜ô i❞❡ j

Zi ❝♦♥❥✉♥t♦ ❞❛s ♦❜s❡r✈❛çõ❡s ❡①t❡r♦❝❡♣t✐✈❛s ❞♦ r♦❜ô i

vxi ✈❡❧♦❝✐❞❛❞❡ ❧✐♥❡❛r ❞♦i✲és✐♠♦ r♦❜ô ♥❛ ❞✐r❡çã♦ x ❞❡ ✭❳W,❨W)

vyi ✈❡❧♦❝✐❞❛❞❡ ❧✐♥❡❛r ❞♦i✲és✐♠♦ r♦❜ô ♥❛ ❞✐r❡çã♦ y ❞❡ ✭❳W,❨W)

vi ✈❡❧♦❝✐❞❛❞❡ ❧✐♥❡❛r ❞♦i✲és✐♠♦ r♦❜ô ♥♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ✭❳Ri,❨Ri✮

wi ✈❡❧♦❝✐❞❛❞❡ ❛♥❣✉❧❛r ❞♦ i✲és✐♠♦ r♦❜ô ♥♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ✭❳Ri,❨Ri✮

ǫ̟ r✉í❞♦ r❡❧❛t✐✈♦ à ✈❛r✐á✈❡❧ ̟

b

̟ ❡st✐♠❛t✐✈❛ r❡❧❛t✐✈❛ à ✈❛r✐á✈❡❧̟

∆̟ ✈❛r✐❛çã♦ r❡❢❡r❡♥t❡ à ✈❛r✐á✈❡❧ ̟

∇̟ ❣r❛❞✐❡♥t❡ r❡❧❛t✐✈♦ à ✈❛r✐á✈❡❧ ̟

ui ✈❡t♦r r❡❧❛t✐✈♦ à ❛çã♦ ❞❡ ❝♦♥tr♦❧❡ ❞♦ r♦❜ô i

vi ✈❡t♦r ✈❡❧♦❝✐❞❛❞❡ r❡❧❛t✐✈♦ ❛♦ r♦❜ôi

E[·] ✈❛❧♦r ❡s♣❡r❛❞♦

(24)

N(a,Q) ❞✐str✐❜✉✐çâ♦ ●❛✉ss✐❛♥❛ ♠✉❧t✐✈❛r✐á✈❡❧ ❝♦♠ ✈❡t♦r ❞❡ ♠é❞✐❛s a❡ ♠❛tr✐③ ❞❡

❝♦✈❛r✐â♥❝✐❛ Q

❞✐❛❣(_·) ♠❛tr✐③ ❞✐❛❣♦♥❛❧

∆x ❡rr♦ ❛ss♦❝✐❛❞♦ à ❡st✐♠❛t✐✈❛ _bx

g(xi,ui) ❢✉♥çã♦ q✉❡ ♣r♦❥❡t❛ ♦ ❡st❛❞♦ ❞♦ r♦❜ô i ✉♠❛ ✐t❡r❛çã♦ à ❢r❡♥t❡✱ ❝♦♠ ❜❛s❡ ♥♦ ❡st❛❞♦

❛t✉❛❧ xi ❡ ♥❛ ❛çã♦ ❞❡ ❝♦♥tr♦❧❡ ui

h(x_i,x_j) ❢✉♥çã♦ ❞❡ ♠❡❞✐❞❛s r❡❧❛t✐✈❛s t♦♠❛❞❛s ♣❡❧♦ r♦❜ô i ❞❡j

Jf ❏❛❝♦❜✐❛♥♦ ❞❛ ❢✉♥çã♦ f

ω ♣❛râ♠❡tr♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s

rs r❛✐♦ ❞❛ r❡❣✐ã♦ ❝✐r❝✉❧❛r ✉t✐❧✐③❛❞♦ ♥❛ r❡❣r❛ ❞❡ s❡♣❛r❛çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ✢♦❝❦✐♥❣

rc r❛✐♦ ❞❛ r❡❣✐ã♦ ❝✐r❝✉❧❛r ✉t✐❧✐③❛❞♦ ♥❛ r❡❣r❛ ❞❡ ❝♦❡sã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ✢♦❝❦✐♥❣

dij ✈❡t♦r ❞❡s❧♦❝❛♠❡♥t♦ ❡♥tr❡ ♦s r♦❜ôsi ❡ j

v_isep ✈❡t♦r ❞❛ ❝♦♠♣♦♥❡♥t❡ ❞❡ s❡♣❛r❛çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ✢♦❝❦✐♥❣ r❡❧❛t✐✈♦ ❛♦ r♦❜ôi

vcoh_i ✈❡t♦r ❞❛ ❝♦♠♣♦♥❡♥t❡ ❞❡ ❝♦❡sã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ✢♦❝❦✐♥❣ r❡❧❛t✐✈♦ ❛♦ r♦❜ô i

vdir_i ✈❡t♦r ❞✐r❡çã♦ r❡❧❛t✐✈♦ ❛ ✉♠ ✇❛②♣♦✐♥t

τk ♣❛rt✐çã♦ ❞♦ ❡♥①❛♠❡ ❝♦♠ t♦❞♦s ♦s r♦❜ôs ❞♦ t✐♣♦ k

kp_ij_k ♥♦r♠❛ ❊✉❝❧✐❞❡❛♥❛ ❞♦ ✈❡t♦r p_i₋p_j

Uij(kpijk) ❢✉♥çã♦ ♣♦t❡♥❝✐❛❧ ❛rt✐✜❝✐❛❧ q✉❡ ❡st❛❜❡❧❡❝❡ ❛s r❡❣r❛s ❞❡ ✐♥t❡r❛çã♦ ❡♥tr❡ ✉♠ ♣❛r ❞❡

r♦❜ôsi ❡ j

α ❣❛♥❤♦ ❞❡ ❝♦♥tr♦❧❡ ❡s❝❛❧❛r

dij ♣❛râ♠❡tr♦ ♣♦s✐t✐✈♦ q✉❡ ❝♦♥tr♦❧❛ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ ❣r✉♣♦

δil ❢✉♥çã♦ ❞❡❧t❛ ❞❡ ❑r♦♥❡❝❦❡r✱ s❡♥❞♦l ♦ í♥❞✐❝❡ ❞♦ r♦❜ô ❧í❞❡r ❡ i ♦ í♥❞✐❝❡ ❞❡ ✉♠

♦✉tr♦ r♦❜ô

γ ❣❛♥❤♦ ♣r♦♣♦r❝✐♦♥❛❧ ❞♦ t❡r♠♦ ❞❡ ❛♠♦rt❡❝✐♠❡♥t♦ ❞❛ ❛çã♦ ❞❡ ❝♦♥tr♦❧❡ Uit(kpitk) ❝❛♠♣♦ ♣♦t❡♥❝✐❛❧ ❛tr❛t✐✈♦ ❡♠ r❡❧❛çã♦ ❛ ✉♠ ✇❛②♣♦✐♥t t

β ❣❛♥❤♦ ♣r♦♣♦r❝✐♦♥❛❧ ❞♦ ❝❛♠♣♦ ♣♦t❡♥❝✐❛❧ ❛tr❛t✐✈♦ Uit

I₂ ♠❛tr✐③ ✐❞❡♥t✐❞❛❞❡ ❞❡ ♦r❞❡♠ 2

∆t ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦

σρ r✉í❞♦ ❞❡ ♦❜s❡r✈❛çã♦ r❡❢❡r❡♥t❡ à ♠❡❞✐❞❛ ❞❡ ❞✐stâ♥❝✐❛ r❡❧❛t✐✈❛ρ

σφ r✉í❞♦ ❞❡ ♦❜s❡r✈❛çã♦ r❡❢❡r❡♥t❡ à ♠❡❞✐❞❛ ❞❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛φ

b ❞✐stâ♥❝✐❛ ❡♥tr❡ ❛s ❞✉❛s r♦❞❛s ❞❡ ✉♠ r♦❜ô ❝♦♠ ❞✐r❡çã♦ ❞✐❢❡r❡♥❝✐❛❧

d ♣❛râ♠❡tr♦ ❛ s❡r ❛❥✉st❛❞♦ ❡♠ r❡❧❛çã♦ ❛ ✉♠ ♣♦♥t♦ p ❞❡ r❡❢❡rê♥❝✐❛ s♦❜r❡ ✉♠ r♦❜ô

❝♦♠ ❞✐r❡çã♦ ❞✐❢❡r❡♥❝✐❛❧

Es ❊rr♦ ♠é❞✐♦ ♥❛ s✐♠✉❧❛çã♦ s

Ek

s ❊rr♦ ♠é❞✐♦ ♥❛ ✐t❡r❛çã♦ k ❞❛ s✐♠✉❧❛çã♦ s

●j ❈♦♥❥✉♥t♦ ❞❡ r♦❜ôs q✉❡ ❝♦♠♣õ❡♠ ♦ ❣r✉♣♦j

(25)

||●j|| ◆ú♠❡r♦ ❞❡ r♦❜ôs ♥♦ ❣r✉♣♦ j

E●j

s ❊rr♦ ♠é❞✐♦ ❞♦s r♦❜ôs ❞♦ ❣r✉♣♦ j ♥❛ s✐♠✉❧❛çã♦ s

Ki ◆ú♠❡r♦ ❞❡ ✐t❡r❛çõ❡s ❡①❡❝✉t❛❞❛s ♣❡❧♦ r♦❜ôi ❡♠ ✉♠❛ ❞❛❞❛ s✐♠✉❧❛çã♦

❘▼❙❊ ❊rr♦ ♠é❞✐♦ ❞❛s s✐♠✉❧❛çõ❡s ❞❡ ✉♠ ❡①♣❡r✐♠❡♥t♦

(26)

(27)

❙✉♠ár✐♦

❆❣r❛❞❡❝✐♠❡♥t♦s ✐①

❘❡s✉♠♦ ①✐

❆❜str❛❝t ①✐✐✐

▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✈

▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✐①

▲✐st❛ ❞❡ ❆❜r❡✈✐❛çõ❡s ①①✐

▲✐st❛ ❞❡ ❙í♠❜♦❧♦s ①①✐✐✐

✶ ■♥tr♦❞✉çã♦ ✶

✶✳✶ ❉❡✜♥✐çã♦ ❞♦ Pr♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✶✳✷ ❖❜❥❡t✐✈♦s ❡ ❈♦♥tr✐❜✉✐çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✶✳✸ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚❡①t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

✷ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ✼

✷✳✶ ❈♦♥s✐❞❡r❛çõ❡s ■♥✐❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✷ ❙✐st❡♠❛s ▼✉❧t✐rr♦❜ót✐❝♦s ❈♦♦♣❡r❛t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✷✳✶ ▼♦✈✐♠❡♥t❛çã♦ ❈♦❧❡t✐✈❛ ❞❡ ❘♦❜ôs ▼ó✈❡✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✸ ❊♥①❛♠❡ ❞❡ ❘♦❜ôs ▼ó✈❡✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✸✳✶ Pr✐♥❝✐♣❛✐s ❈❛r❛❝t❡ríst✐❝❛s ❞❡ ❊♥①❛♠❡s ❘♦❜ót✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✸✳✷ ❆❧❣✉♥s ❞♦♠í♥✐♦s ❞❡ ❛♣❧✐❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✹ ▲♦❝❛❧✐③❛çã♦ ❞❡ ❘♦❜ôs ▼ó✈❡✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✷✳✹✳✶ ❆❧❣✉♠❛s ❞✐♠❡♥sõ❡s ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✳✹✳✷ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛✿ ♣r✐♥❝✐♣❛✐s ❝♦♥❝❡✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✷✳✺ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵

(28)

✸ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s ✹✸ ✸✳✶ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✷ ▼♦✈✐♠❡♥t❛çã♦ ❈♦❧❡t✐✈❛ ❡ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✸✳✸ ❊s❝❛❧❛❜✐❧✐❞❛❞❡ ❡♠ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✸✳✹ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹

✹ ▼❡t♦❞♦❧♦❣✐❛ ✺✼

✹✳✶ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛ ❡♠ ❊♥①❛♠❡s ❘♦❜ót✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✹✳✷ ❊str❛té❣✐❛s ❞❡ ▼♦✈✐♠❡♥t❛çã♦ ❞♦ ❊♥①❛♠❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✷✳✶ ▼♦✈✐♠❡♥t❛çã♦ ❆❧t❡r♥❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✷✳✷ ▼♦✈✐♠❡♥t❛çã♦ ❈♦♥tí♥✉❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✸ ❙❡❧❡çã♦ ❡ ❈❛r❛❝t❡r✐③❛çã♦ ❞❡ ▼❛r❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✹✳✹ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺

✺ ❊①♣❡r✐♠❡♥t♦s ✼✼

✺✳✶ ❆♥á❧✐s❡ ❞❛ ❱❛r✐❛çã♦ ❞♦ ◆ú♠❡r♦ ❞❡ ▼❛r❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✺✳✶✳✶ ▼♦✈✐♠❡♥t❛çã♦ ❆❧t❡r♥❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✺✳✶✳✷ ▼♦✈✐♠❡♥t❛çã♦ ❈♦♥tí♥✉❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✺✳✷ ❈♦♥s✐stê♥❝✐❛ ❞❛s ❊st✐♠❛t✐✈❛s ❞❡ ▲♦❝❛❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻ ✺✳✷✳✶ ❊st✐♠❛t✐✈❛s ❆❜s♦❧✉t❛s ❡♠ ■♥t❡r✈❛❧♦s ❘❡❣✉❧❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾ ✺✳✷✳✷ ❊st✐♠❛t✐✈❛s ❆❜s♦❧✉t❛s ❊s♣♦rá❞✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷ ✺✳✷✳✸ ❋❛❧❤❛s ♥♦s ▼❡❝❛♥✐s♠♦s ❙❡♥s♦r✐❛✐s ♦✉ ❞❡ ❈♦♠✉♥✐❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸ ✺✳✸ Pr♦✈❛s ❞❡ ❈♦♥❝❡✐t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽ ✺✳✸✳✶ ❙✐♠✉❧❛çõ❡s ❝♦♠ ❘❖❙✴❙t❛❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾ ✺✳✸✳✷ ❊①♣❡r✐♠❡♥t♦s ❝♦♠ ❘♦❜ôs ❘❡❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹ ✺✳✹ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷

✻ ❈♦♥❝❧✉sã♦ ✶✷✼

✻✳✶ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✾

❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✶✸✶

❆♣ê♥❞✐❝❡ ❆ ❆r❝❛❜♦✉ç♦ Pr♦❜❛❜✐❧íst✐❝♦ ♣❛r❛ ▲♦❝❛❧✐③❛çã♦ ✶✹✸

❆✳✶ ❋✉♥çõ❡s ❞❡ ❉❡♥s✐❞❛❞❡ ❞❡ Pr♦❜❛❜✐❧✐❞❛❞❡ ●❛✉ss✐❛♥❛s ❯♥✐✈❛r✐❛❞❛s ✳ ✳ ✳ ✳ ✶✹✽

❆♣ê♥❞✐❝❡ ❇ ❇r❡✈❡ ■♥tr♦❞✉çã♦ ❛♦ ❋✐❧tr♦ ❞❡ ❑❛❧♠❛♥ ✶✺✸

❆♣ê♥❞✐❝❡ ❈ ■♥tr♦❞✉çã♦ ❛♦ ❆❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s ✶✺✾

(29)

❈❛♣ít✉❧♦ ✶

■♥tr♦❞✉çã♦

❊♠ ❘♦❜ót✐❝❛ ▼ó✈❡❧✱ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♥s✐st❡ ❡♠ ❞❡t❡r♠✐♥❛r ❛ ♣♦s❡ ✭♣♦s✐çã♦ ❡ ♦r✐❡♥t❛çã♦✮ ❞❡ ✉♠ r♦❜ô ❡♠ r❡❧❛çã♦ ❛ ✉♠ ♠❛♣❛ ❞♦ ❛♠❜✐❡♥t❡ ♣r❡✈✐❛♠❡♥t❡ ❡st❛❜❡❧❡❝✐❞♦✳ ◆❡ss❡ ❝♦♥t❡①t♦✱ ✉♠ r♦❜ô ✉t✐❧✐③❛ s❡♥s♦r❡s ❡①t❡r♦❝❡♣t✐✈♦s✶ _{❝♦♠ ✈✐st❛s ❛ ✐❞❡♥t✐✜❝❛r s✉❛}

♣♦s❡ ❝♦♠ ❜❛s❡ ♥♦ ❡st❛❜❡❧❡❝✐♠❡♥t♦ ❞❡ ❛ss♦❝✐❛çõ❡s ❡♥tr❡ ❛s ✐♥❢♦r♠❛çõ❡s ❡①tr❛í❞❛s ❞♦ ❛♠❜✐❡♥t❡ ❡ ❛q✉❡❧❛s ❞✐s♣♦♥í✈❡✐s ♥♦ ♠❛♣❛✱ t❛✐s ❝♦♠♦ ✉♠ ♠❛r❝♦✳ ❉❡ss❡ ♠♦❞♦✱ ❛ ♣♦s❡ ❞♦ r♦❜ô ♥ã♦ é ♠❡❞✐❞❛ ❞✐r❡t❛♠❡♥t❡✱ ♠❛s s✐♠ ✐♥❢❡r✐❞❛ ❛ ♣❛rt✐r ❞❛s ✐♥❢♦r♠❛çõ❡s s❡♥s♦r✐❛✐s ❛❞q✉✐r✐❞❛s✳ ▲♦❝❛❧✐③❛r ✉♠ r♦❜ô ♥♦ ❛♠❜✐❡♥t❡ s❡ ❛♣r❡s❡♥t❛ ❝♦♠♦ ✉♠ ♣r♦❜❧❡♠❛ ❞✐❢í❝✐❧ ❞❡✲ ✈✐❞♦ às ✐♥❝❡rt❡③❛s ❡ r✉í❞♦s ❛ss♦❝✐❛❞♦s ❛♦s ♣r♦❝❡ss♦s ❞❡ ♠❡❞✐çã♦ s❡♥s♦r✐❛❧✱ ❞✐s❝r❡t✐③❛çã♦ ❡ r❡♣r❡s❡♥t❛çã♦ ❞♦ ❛♠❜✐❡♥t❡✳ ❊ss❡ ♣r♦❜❧❡♠❛ t♦r♥❛✲s❡ ♠❛✐s ❝♦♠♣❧❡①♦ ❛♦ s❡ ❝♦♥s✐❞❡r❛r r♦❜ôs ❞❡s♣r♦✈✐❞♦s ❞❡ s❡♥s♦r❡s ♠❛✐s s♦✜st✐❝❛❞♦s ♦✉ ❛♠❜✐❡♥t❡s ♥ã♦ ❡str✉t✉r❛❞♦s✳

❖ r❛str❡❛♠❡♥t♦ ❞❡ ♣♦s✐çã♦ ✭♣♦s✐t✐♦♥ tr❛❝❦✐♥❣✮ ❝♦♠♣r❡❡♥❞❡ ✉♠❛ ✈❛r✐❛♥t❡ ❞♦ ♣r♦✲ ❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❡ ❝♦♥s✐st❡ ♥❛ t❛r❡❢❛ ❞❡ ❛❝♦♠♣❛♥❤❛r ♦✉ s❡❣✉✐r ✉♠❛ ✐♥❢♦r♠❛çã♦ ♣ré✈✐❛ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ ✉♠ r♦❜ô✳ P❛r❛ ✐ss♦✱ s❡♥s♦r❡s ♣r♦♣r✐♦❝❡♣t✐✈♦s✷ _{sã♦ ✉t✐❧✐③❛❞♦s}

♣❛r❛ ♠❡❞✐r ♦ ❞❡s❧♦❝❛♠❡♥t♦ ❡❢❡t✉❛❞♦ ♣❡❧♦ r♦❜ô ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ❡st✐♠❛r ♥♦✈❛s ♣♦s❡s✳ ❆s ✐♥❢♦r♠❛çõ❡s ♦❜t✐❞❛s ✈✐❛ s❡♥s♦r❡s ♣r♦♣r✐♦❝❡♣t✐✈♦s t❛♠❜é♠ ✐♥❝♦r♣♦r❛♠ ✐♥❝❡rt❡③❛ ❡ r✉í❞♦ ❛♦ ♣r♦❝❡ss♦ ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱ t❡♠✲s❡ ✉♠❛ ❞❡t❡r✐♦r❛çã♦ ♣❡r♠❛♥❡♥t❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ r♦❜ô ❡♠ ❞❡❝♦rrê♥❝✐❛ ❞❡ s✉❛ ♠♦✈✐♠❡♥t❛çã♦✳

▲♦❝❛❧✐③❛çã♦ é ✉♠❛ q✉❡stã♦ ❝❡♥tr❛❧ ♥❛ ❘♦❜ót✐❝❛✱ ✉♠❛ ✈❡③ q✉❡ ♠✉✐t❛s t❛r❡❢❛s ❡①✐✲ ❣❡♠ q✉❡ ✉♠ r♦❜ô ♣♦ss✉❛ ✐♥❢♦r♠❛çõ❡s ♣r❡❝✐s❛s ❞❡ s✉❛ ❧♦❝❛❧✐③❛çã♦ ♣❛r❛ q✉❡ ♣♦ss❛♠ s❡r ❡①❡❝✉t❛❞❛s✳ ❉❡✈✐❞♦ à ❞✐✜❝✉❧❞❛❞❡ ❞❡ s❡ ❡❢❡t✉❛r ❛ ❧♦❝❛❧✐③❛çã♦ ❡♥q✉❛♥t♦ s❡ ❡①❡❝✉t❛ ♦✉✲

✶_{❙❡♥s♦r❡s ❡①t❡r♦❝❡♣t✐✈♦s ❢♦r♥❡❝❡♠ ✐♥❢♦r♠❛çõ❡s ❛ r❡s♣❡✐t♦ ❞♦ ❛♠❜✐❡♥t❡ ❡♠ q✉❡ ♦ r♦❜ô ❡♥❝♦♥tr❛✲s❡}

✐♥s❡r✐❞♦✱ t❛✐s ❝♦♠♦ ❡st✐♠❛t✐✈❛s ❞❡ ♠❡❞✐❞❛s ❞❡ ❞✐stâ♥❝✐❛ ❞❡ ♦❜❥❡t♦s ❞✐s♣♦st♦s ♥♦ ❛♠❜✐❡♥t❡ ♦✉ ❛ ❢♦r♠❛ ❞♦s ♠❡s♠♦s✳ ❚❛✐s ♠❡❞✐❞❛s sã♦ r❡❧❛t✐✈❛s ❛♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ❧♦❝❛❧ ❞♦ r♦❜ô✳ ❊①❡♠♣❧♦s✿ s♦♥❛r✱ ❧❛s❡r✱ ✐♥❢r❛✲✈❡r♠❡❧❤♦ ❡ ❝â♠❡r❛s ❈❈❉ ✭❈❤❛r❣❡ ❈♦✉♣❧❡❞ ❉❡✈✐❝❡✮✳

✷_{❙❡♥s♦r❡s ♣r♦♣r✐♦❝❡♣t✐✈♦s ♠♦♥✐t♦r❛♠ ❡ ❝♦♥tr♦❧❛♠ ♦ ❡st❛❞♦ ✐♥t❡r♥♦ ❞♦ r♦❜ô✱ t❛✐s ❝♦♠♦ ♦ ♠♦✈✐♠❡♥t♦✱}

❛ ❛❝❡❧❡r❛çã♦ ❡ ❛ ❞✐r❡çã♦✳ ❊①❡♠♣❧♦s✿ ♦❞ô♠❡tr♦✱ s❡♥s♦r ✐♥❡r❝✐❛❧ ❡ ❜úss♦❧❛✳

(30)

✷ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦

tr❛s t❛r❡❢❛s✱ ❞✐✈❡rs♦s ♠ét♦❞♦s ♣r♦♣♦st♦s ♥❛ ❧✐t❡r❛t✉r❛ ✉t✐❧✐③❛♠ ♦✉ s✉♣õ❡♠ ✐♥❢♦r♠❛çõ❡s ❣❧♦❜❛✐s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ▼ét♦❞♦s q✉❡ ❢❛③❡♠ ✉s♦ ❞❡ss❛s s✉♣♦s✐çõ❡s ♣♦r ✈❡③❡s tê♠ ❛♣❧✐✲ ❝❛❜✐❧✐❞❛❞❡ r❡str✐t❛ ❡♠ r♦❜ôs r❡❛✐s✱ ♣♦✐s ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❣❧♦❜❛❧ ♥❡♠ s❡♠♣r❡ ❡stã♦ ❞✐s♣♦♥í✈❡✐s✳ ❆♣❡s❛r ❞❡ ♣♦ss✉ír❡♠ ❛❧❣✉♠❛s ❧✐♠✐t❛çõ❡s✱ s✐st❡♠❛s ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❣❧♦❜❛❧ tê♠ s✐❞♦ ❛♠♣❧❛♠❡♥t❡ ❡♠♣r❡❣❛❞♦s ❝♦♠♦ ❢♦♥t❡ ❞❡ ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❡♠ s✐st❡♠❛s r♦❜ót✐❝♦s✳

◆♦ â♠❜✐t♦ ❞❡ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s✱ té❝♥✐❝❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♣♦❞❡♠ s❡r ❡♠♣r❡❣❛❞❛s ♣❛r❛ ♣❡r♠✐t✐r ♦ ❛❥✉st❡ ❞❛s ❝r❡♥ç❛s ❞♦s r♦❜ôs✱ ❡♠ ❞❡❝♦rrê♥❝✐❛ ❞❛ tr♦❝❛ ❞❡ ✐♥❢♦r♠❛çõ❡s ❡♥tr❡ ♦s ♠❡s♠♦s✳ ❊ss❛ tr♦❝❛ ❞❡ ✐♥❢♦r♠❛çõ❡s ♦❝♦rr❡ q✉❛♥❞♦ ♦s r♦❜ôs s❡ ❡♥❝♦♥tr❛♠ ❡✱ ❞❡✈✐❞♦ ❛ ✐ss♦✱ ♦s ❡♥❝♦♥tr♦s✸ _{❝♦♥st✐t✉❡♠ ✉♠❛ ❡①❝❡❧❡♥t❡ ❢♦r♠❛ ❞❡ ❛♣r✐♠♦r❛r}

❛ ♣r❡❝✐sã♦ ❞❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❆ss✐♠✱ ♦s r♦❜ôs ❛t✉❛♠ ❝♦♠♦ ♠❛r❝♦s ❞✐♥â✲ ♠✐❝♦s ♣r♦✈❡♥❞♦ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❆ ❛t✉❛çã♦ ❞❡ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s ❡♠ ❛♠❜✐❡♥t❡s ❝♦♠ ❣r❛♥❞❡s ❞✐♠❡♥sõ❡s ✐❧✉str❛ ✉♠❛ s✐t✉❛çã♦ ♦♥❞❡ ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ❡♥❝♦♥tr♦s é r❡str✐t❛✳ ❊♠ ❝❡♥ár✐♦s ❝♦♠♦ ❡ss❡✱ ❛ ❧♦❝❛❧✐③❛çã♦ ❞♦s r♦❜ôs é ❜❛s❡❛❞❛ ❡♠ ❣r❛♥❞❡ ♣❛rt❡ ♥❛s ✐♥❢♦r♠❛çõ❡s ❛❞✈✐♥❞❛s ❞♦s s❡♥s♦r❡s ♣r♦♣r✐♦❝❡♣t✐✈♦s✳ ❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱ t❡♠✲s❡ ✉♠ ❛❝ú♠✉❧♦ ♣❡r♠❛♥❡♥t❡ ❞❡ ✐♥❝❡rt❡③❛✱ t❡♥❞♦ ❡♠ ✈✐st❛ q✉❡ t❛❧ ❛❝ú♠✉❧♦ ❡stá ❞✐r❡t❛♠❡♥t❡ r❡❧❛❝✐♦♥❛❞♦ à ❞✐stâ♥❝✐❛ ♣❡r❝♦rr✐❞❛ ♣❡❧♦ r♦❜ô✳ ❈♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛ ✐♠❡❞✐❛t❛ ❞✐ss♦✱ t❡♠✲ s❡ ♦ ❝♦♠♣r♦♠❡t✐♠❡♥t♦ ❞❛ q✉❛❧✐❞❛❞❡ ❞❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞♦ r♦❜ô✱ ♦ q✉❡ ♣♦❞❡ r❡str✐♥❣✐r s✉❛ ❛t✉❛çã♦ ❝♦♠♦ ♠❛r❝♦ ❞✐♥â♠✐❝♦✳

❯♠❛ ❢♦r♠❛ ❞❡ ❛♠♣❧✐❛r ♦ ♥ú♠❡r♦ ❞❡ ❡♥❝♦♥tr♦s ❝♦♥s✐st❡ ❡♠ ❛✉♠❡♥t❛r ❛ ❞❡♥s✐❞❛❞❡ ❞❡ r♦❜ôs ♥♦ ❛♠❜✐❡♥t❡✳ ■ss♦ ♣♦❞❡ s❡r ❛❧❝❛♥ç❛❞♦ ❛♦ s❡ ❧✐♠✐t❛r ♦ t❛♠❛♥❤♦ ❞♦s ❛♠❜✐❡♥t❡s ♦♥❞❡ ✉♠ s✐st❡♠❛ ♠✉❧t✐rr♦❜ót✐❝♦ s❡r✐❛ ✉t✐❧✐③❛❞♦✳ ◆♦ ❡♥t❛♥t♦✱ t❛❧ ❡str❛té❣✐❛ ♣♦❞❡ r❡❞✉③✐r s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ♦s ❞♦♠í♥✐♦s ❞❡ ❛♣❧✐❝❛çã♦ ♥♦s q✉❛✐s ❡ss❡ s✐st❡♠❛ ♣♦❞❡r✐❛ s❡r ❡♠♣r❡✲ ❣❛❞♦✳ ❖✉tr❛ ♠❛♥❡✐r❛ ❞❡ ❛✉♠❡♥t❛r ❛ ❞❡♥s✐❞❛❞❡ ❝♦♥s✐st❡ ❡♠ ❛♠♣❧✐❛r ❝♦♥s✐❞❡r❛✈❡❧♠❡♥t❡ ♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs ♣❛rt✐❝✐♣❛♥t❡s ❡♠ ✉♠ s✐st❡♠❛ ♠✉❧t✐rrót✐❝♦✳ ❉✐❢❡r❡♥t❡♠❡♥t❡ ❞❛ ❡s✲ tr❛té❣✐❛ ❛♥t❡r✐♦r✱ ❡ss❛ ❛❜♦r❞❛❣❡♠ t❡♠ ❝♦♠♦ ✈❛♥t❛❣❡♠ ❛ ❛♠♣❧✐❛çã♦ ❞♦ ♥ú♠❡r♦ ❡ t✐♣♦ ❞❡ t❛r❡❢❛s q✉❡ ♣♦❞❡r✐❛♠ s❡r ❡①❡❝✉t❛❞❛s ♣❡❧♦ s✐st❡♠❛✳ ❆❧é♠ ❞✐ss♦✱ ❛ r❡❞✉♥❞â♥❝✐❛ ❡①✐s✲ t❡♥t❡ ❡♠ s✐st❡♠❛s ❝♦♠♣♦st♦s ♣♦r ❣r❛♥❞❡s ❣r✉♣♦s ❞❡ r♦❜ôs tr❛③ ❝♦♥s✐❣♦ ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ s❡ ✉t✐❧✐③❛r ♣❛rt❡ ❞♦ ❣r✉♣♦ ❝♦♠♦ ♣r♦✈❡❞♦r❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ✭♠❛r❝♦s ❡ ❜❡❛❝♦♥s✮✱ s❡♠ ♥❡❝❡ss❛r✐❛♠❡♥t❡ ❝♦♠♣r♦♠❡t❡r ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ s✐st❡♠❛✳

❆♣❡s❛r ❞❛ ❛♠♣❧❛ ✉t✐❧✐③❛çã♦ ❞❡ té❝♥✐❝❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡♠ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s✱ ♦ ❡♠♣r❡❣♦ ❞❡ t❛✐s té❝♥✐❝❛s ❡♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s ❛✐♥❞❛ é ♣♦✉❝♦ ❡①✲ ♣❧♦r❛❞♦✳ ◆♦ ❝♦♥t❡①t♦ ❞❡ ❡♥①❛♠❡s✱ ❛❧❣✉♠❛s q✉❡stõ❡s s❡ ❛♣r❡s❡♥t❛♠ q✉❛♥❞♦ ❛s té❝♥✐❝❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ sã♦ ❡♠♣r❡❣❛❞❛s✱ ❞❡♥tr❡ ❡❧❛s✿ ❛✉♠❡♥t♦ ❞❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡

✸_{❊♥❝♦♥tr♦s ♦❝♦rr❡♠ q✉❛♥❞♦ ♦s r♦❜ôs ❝♦♠♣❛rt✐❧❤❛♠ ✉♠❛ ♠❡s♠❛ r❡❣✐ã♦ ❞♦ ❛♠❜✐❡♥t❡ ❡ ❡stã♦ s✐t✉❛✲}

(31)

✸

t❡♠♣♦ ❡ ❡s♣❛ç♦ ♣❛r❛ ❣❡r❛r ❡ ❛r♠❛③❡♥❛r ❛s ❡st✐♠❛t✐✈❛s ❝♦♥❥✉♥t❛s ❞❡ ❧♦❝❛❧✐③❛çã♦❀ ❛♠✲ ♣❧✐❛çã♦ ❞❛ q✉❛♥t✐❞❛❞❡ ❞❡ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ s❡♥❞♦ ❣❡r❛❞❛s ❡ q✉❡ tr❛❢❡❣❛♠ ♣♦r ❞✐✈❡rs♦s ♣♦♥t♦s ❞♦ ❣r✉♣♦✱ ♦ q✉❡ ✐♠♣❧✐❝❛ ♥❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ❧✐❞❛r ❝♦♠ q✉❡stõ❡s r❡❧❛❝✐♦♥❛✲ ❞❛s à s✐♥❝r♦♥✐③❛çã♦ ❞❡ t❛✐s ✐♥❢♦r♠❛çõ❡s❀ ❡ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ✉♠ tr❛t❛♠❡♥t♦ ❛❞❡q✉❛❞♦ ❛♦ ❢❡♥ô♠❡♥♦ ❞❡♥♦♠✐♥❛❞♦ r❛❝✐♦❝í♥✐♦ ❝✐r❝✉❧❛r q✉❡ ♣♦❞❡ ♦❝♦rr❡r ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ q✉❛♥❞♦ ❞❡t❡r♠✐♥❛❞❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ é ✉t✐❧✐③❛❞❛ ♠❛✐s ❞❡ ✉♠❛ ✈❡③ ♣❡❧♦s r♦❜ôs✳ ❖ ❞❡✈✐❞♦ tr❛t❛♠❡♥t♦ ❛ ❡ss❛s q✉❡stõ❡s s❡ ❛♣r❡s❡♥t❛ ❝♦♠♦ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ♣❡sq✉✐s❛ r❡❧❡✈❛♥t❡✱ t❡♥❞♦ ❡♠ ✈✐st❛ ❛ ❛♠♣❧✐❛çã♦ ❞❛ q✉❛♥t✐❞❛❞❡ ❞❡ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞✐s♣♦♥í✈❡✐s ❡♠ ✉♠ ❡♥①❛♠❡ r♦❜ót✐❝♦✱ ❛❧é♠ ❞❛ ❞✐ss❡♠✐♥❛çã♦ ❞❛s ♠❡s♠❛s ♥♦ ✐♥t❡r✐♦r ❞♦ ❣r✉♣♦✳

❊♠ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s ❞❡s❝❡♥tr❛❧✐③❛❞♦s✱ ❛ ❛✉sê♥❝✐❛ ❞❡ ✉♠❛ ❡♥t✐❞❛❞❡ ❝❡♥tr❛❧ ❡①✐❣❡ q✉❡ ❛s ✐♥❢♦r♠❛çõ❡s ❛ss♦❝✐❛❞❛s às ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛✱ s❡❥❛♠ ❝♦♠♣❛rt✐❧❤❛❞❛s ❝♦♠ t♦❞♦s ♦s ♠❡♠❜r♦s ❞♦ ❣r✉♣♦✳ ❆❧é♠ ❞✐ss♦✱ ♦ r❡❣✐str♦ ❞❡ t❛✐s ✐♥❢♦r♠❛çõ❡s ❞❡✈❡ s❡r ♠❛♥t✐❞♦ ❛t✉❛❧✐③❛❞♦ ❡♠ ❝❛❞❛ ✐♥t❡❣r❛♥t❡ ❞♦ ❣r✉♣♦ ❞❡ ♠♦❞♦ q✉❡ ❝❛❞❛ r♦❜ô ♣♦ss❛ ❣❡r❛r ✉♠❛ ❡st✐♠❛t✐✈❛ ❝♦♥✲ ❥✉♥t❛ ✭❡st❛t✐st✐❝❛♠❡♥t❡ ót✐♠❛✮ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ ♠❛♥❡✐r❛ ✐♥❞❡♣❡♥❞❡♥t❡✳ ❊♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s✱ ❡ss❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ tr♦❝❛ ❞❡ ✐♥❢♦r♠❛çõ❡s ❡♥tr❡ t♦❞♦s ♦s ♠❡♠❜r♦s ❞♦ ❣r✉♣♦ ✐♠♣õ❡ ✈ár✐❛s ❧✐♠✐t❛çõ❡s✱ t❡♥❞♦ ❡♠ ✈✐st❛ ❛s ❝❛r❛❝t❡ríst✐❝❛s s✐♠♣❧✐st❛s ❞♦s ❛❣❡♥t❡s ❡ s✉❛s ❝❛♣❛❝✐❞❛❞❡s ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❡ ♣r♦❝❡ss❛♠❡♥t♦ ❧✐♠✐t❛❞❛s✳

❯♠ ❞♦s ♣r✐♥❝✐♣❛✐s ❛❧❣♦r✐t♠♦s ❞❡ ✜❧tr❛❣❡♠ ♣r♦❜❛❜✐❧íst✐❝❛ ✉t✐❧✐③❛❞♦s ♥❛s té❝♥✐❝❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ é ♦ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥✱ ❞♦ ✐♥❣❧ês ❑❛❧♠❛♥ ❋✐❧t❡r ✭❑❋✮✳ ❚❛❧ ❛❧❣♦r✐t♠♦ s♦♠❡♥t❡ ♣♦❞❡ ❝♦♠❜✐♥❛r✱ ❞❡ ♠❛♥❡✐r❛ ❝♦♥s✐st❡♥t❡✱ ✐♥❢♦r♠❛çõ❡s ❛ss♦❝✐❛❞❛s ❛ ✉♠❛ ♠❡s♠❛ ❡st✐♠❛t✐✈❛✱ ❛❞✈✐♥❞❛s ❞❡ ✈ár✐❛s ❢♦♥t❡s✱ ❝❛s♦ t❛✐s ✐♥❢♦r♠❛çõ❡s s❡❥❛♠ ✐♥❞❡✲ ♣❡♥❞❡♥t❡s ♦✉ s❡ ♦ ♥í✈❡❧ ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❛s ♠❡s♠❛s s❡❥❛ ❝♦♥❤❡❝✐❞♦✳ ❈♦♥❢♦r♠❡ s❡rá ❛♣r❡s❡♥t❛❞♦ ♥♦ ❈❛♣ít✉❧♦ ✸✱ ❡ss❡ ♣r♦❜❧❡♠❛ t❡♠ s✐❞♦ ❝♦♥t♦r♥❛❞♦ ❞❡ ✈ár✐❛s ❢♦r♠❛s ❡♠ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s✳ ❯♠❛ ❞❡❧❛s ❝♦♥s✐st❡ ❡♠ ✉t✐❧✐③❛r ✉♠❛ ✉♥✐❞❛❞❡ ❝❡♥tr❛❧✐③❛❞♦r❛ ♣❛r❛ ❣❡r❛r ✉♠❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ t♦❞♦s ♦s ✐♥t❡❣r❛♥t❡s ❞♦ s✐st❡♠❛✳ ❉❡✈✐❞♦ ❛♦ ❢❛t♦ ❞♦s ❞❛❞♦s ❡st❛r❡♠ t♦❞♦s ❞✐s♣♦♥í✈❡✐s ♣❛r❛ t❛❧ ❡♥t✐❞❛❞❡✱ ❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ sã♦ ♠❛♥t✐❞❛s ❡ ✉t✐❧✐③❛❞❛s ❝❛❞❛ ✈❡③ q✉❡ ❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ é ❣❡r❛❞❛✳ ❆♣❡s❛r ❞❡ss❛ s♦❧✉çã♦ ❝❡♥tr❛❧✐③❛❞❛ ❣❡r❛r ❜♦♥s r❡s✉❧t❛❞♦s✱ ❛ s✉❛ ❛♣❧✐❝❛❜✐❧✐❞❛❞❡ ❡♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s ❝♦♠♣r♦♠❡t❡ ❛ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ ❞♦ s✐st❡♠❛✳