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Localização cooperativa e descentralizada em enxames robóticos

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▲❖❈❆▲■❩❆➬➹❖ ❈❖❖P❊❘❆❚■❱❆ ❊ ❉❊❙❈❊◆❚❘❆▲■❩❆❉❆ ❊▼

▲❖❈❆▲■❩❆➬➹❖ ❈❖❖P❊❘❆❚■❱❆ ❊ ❉❊❙❈❊◆❚❘❆▲■❩❆❉❆ ❊▼❊◆❳❆▼❊❙ ❘❖❇Ó❚■❈❖❙ ❆◆❉❊❘❙❖◆ ●❘❆◆❉■ 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 ❇❡❧♦ ❍♦r✐③♦♥t❡ ✕ ▼●❉❡③❡♠❜r♦ ❞❡ ✷✵✶✺ � ����� �������� ������ ����������� �� �������� ����������� ������ �������� ����������� ����������� ����������� � ��������������� �� ������� ��������� � �������� ������ ������ � ������������� � ��� ���� ������� ��� �� � ��� � �������� ����������� � ������������ ������� �� ����� ������ � ������������ �� ������� �� ��������������������� ���� ������������ ���������� � ������ �� ����� � ���������� �� ��������� �� ����������� ��� ���������� ���������� ����� ❉❡❞✐❝♦ ❡st❛ ❝♦♥q✉✐st❛ à ♠✐♥❤❛ ❡s♣♦s❛ ❊❞✉❛r❞❛ ❡ às ♠✐♥❤❛s ✜❧❤❛s ▼❛♥♦❡❧❛ ❡❙♦♣❤✐❛✳ ❆❣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✐♦ ❝♦♥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♦✳ ❘❡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✳ ❆❜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✳ ▲✐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✉♣♦✳ ✻✽ ✹✳✼ ▼♦♠❡♥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✐♠♦ g 1 ❛♦ ❧í❞❡r ✭● ✴● ✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹✺✳✶✸ ▼♦✈✐♠❡♥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✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ✺✳✷✷ ❊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❝♦♥❤❡❝✐❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✷ ▲✐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 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸ ▲✐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♦ k▼P❊ ❊rr♦ ♠é❞✐♦ ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ♥❛ k✲és✐♠❛ ✐t❡r❛çã♦ k ❖❊ ❊rr♦ ❞❡ ♦r✐❡♥t❛çã♦ ♥❛ k✲és✐♠❛ ✐t❡r❛çã♦ ❞❛ s✐♠✉❧❛çã♦ s k sP❊ ❊rr♦ ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ♥❛ k✲és✐♠❛ ✐t❡r❛çã♦ ❞❛ s✐♠✉❧❛çã♦ s 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✐❝❛ ▲✐st❛ ❞❡ ❙í♠❜♦❧♦s R❊♥①❛♠❡ ❞❡ r♦❜ôs ||R|| ◆ú♠❡r♦ ❞❡ r♦❜ôs ♥♦ ❡♥①❛♠❡ i ✐✲és✐♠♦ r♦❜ô ❞♦ ❡♥①❛♠❡R , )✭❳ W ❨ W ❙✐st❡♠❛ ❞❡ ❈♦♦r❞❡♥❛❞❛s ■♥❡r❝✐❛❧ R , R ✭❳ i ❨ i ✮ ❙✐st❡♠❛ ❞❡ ❈♦♦r❞❡♥❛❞❛s ▲♦❝❛❧ r❡❧❛t✐✈♦ ❛♦ ✐✲és✐♠♦ r♦❜ô iN ✈✐③✐♥❤❛♥ç❛ ❞♦ i✲és✐♠♦ r♦❜ô ε♠❡❞✐❞❛ ❞♦ r❛✐♦ ❞❛s ✈✐③✐♥❤❛♥ç❛s p , y ) , )i i i W W ♣♦s✐çã♦ (x ❞♦ ✐✲és✐♠♦ r♦❜ô ❡♠ r❡❧❛çã♦ ❛ ✭❳ ❨θ iW W , ) ♦r✐❡♥t❛çã♦ ❞♦ i✲és✐♠♦ r♦❜ô ❡♠ r❡❧❛çã♦ ❛ ✭❳ ❨ q , y , θ ) , )i i i i W W♣♦s❡ (x ❞♦ i✲és✐♠♦ r♦❜ô ❡♠ r❡❧❛çã♦ ❛ ✭❳ ❨ xi ✈❡t♦r ❞❡ ❡st❛❞♦s ❞♦ r♦❜ô i xi b ✈❡t♦r ❞❡ ❡st❛❞♦s ❡st✐♠❛❞♦ ❞♦ r♦❜ô iP ii ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛s ❛ss♦❝✐❛❞❛ à bxρ ij ❞✐stâ♥❝✐❛ r❡❧❛t✐✈❛ ♣❛r❛ ♦ r♦❜ô j ♠❡❞✐❞❛ ♣❡❧♦ r♦❜ô iφ ij ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛ ♣❛r❛ ♦ r♦❜ô j ♠❡❞✐❞❛ ♣❡❧♦ r♦❜ô i zij i ❝♦♥❥✉♥t♦ ❞❛s ♦❜s❡r✈❛çõ❡s ❡①t❡r♦❝❡♣t✐✈❛s ❞♦ r♦❜ô i ✈❡t♦r ❞❡ ♦❜s❡r✈❛çã♦ ❡①t❡r♦❝❡♣t✐✈❛ t♦♠❛❞❛ ♣❡❧♦ r♦❜ô i ❞❡ jZ vx i ✈❡❧♦❝✐❞❛❞❡ ❧✐♥❡❛r ❞♦ i✲és✐♠♦ r♦❜ô ♥❛ ❞✐r❡çã♦ x ❞❡ ✭❳ W ❨ W , ) v yi ✈❡❧♦❝✐❞❛❞❡ ❧✐♥❡❛r ❞♦ i✲és✐♠♦ r♦❜ô ♥❛ ❞✐r❡çã♦ y ❞❡ ✭❳ ❨ W , W ) v iR i , R i ✈❡❧♦❝✐❞❛❞❡ ❧✐♥❡❛r ❞♦ i✲és✐♠♦ r♦❜ô ♥♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ✭❳ ❨ ✮ w iR i , R i✈❡❧♦❝✐❞❛❞❡ ❛♥❣✉❧❛r ❞♦ i✲és✐♠♦ r♦❜ô ♥♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ✭❳ ❨ ✮ ǫ ̟ 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♦❜ô i E[· ] ✈❛❧♦r ❡s♣❡r❛❞♦ ❞✐❛❣(· ) ♠❛tr✐③ ❞✐❛❣♦♥❛❧∆x ❡rr♦ ❛ss♦❝✐❛❞♦ à ❡st✐♠❛t✐✈❛ bx g(x i , u i )❢✉♥çã♦ q✉❡ ♣r♦❥❡t❛ ♦ ❡st❛❞♦ ❞♦ r♦❜ô i ✉♠❛ ✐t❡r❛çã♦ à ❢r❡♥t❡✱ ❝♦♠ ❜❛s❡ ♥♦ ❡st❛❞♦ i i❛t✉❛❧ x ❡ ♥❛ ❛çã♦ ❞❡ ❝♦♥tr♦❧❡ u h(x , x )i j ❢✉♥çã♦ ❞❡ ♠❡❞✐❞❛s r❡❧❛t✐✈❛s t♦♠❛❞❛s ♣❡❧♦ r♦❜ô i ❞❡ jJ f ❏❛❝♦❜✐❛♥♦ ❞❛ ❢✉♥çã♦ fω ♣❛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♠♦ ❞❡ ✢♦❝❦✐♥❣r c r❛✐♦ ❞❛ r❡❣✐ã♦ ❝✐r❝✉❧❛r ✉t✐❧✐③❛❞♦ ♥❛ r❡❣r❛ ❞❡ ❝♦❡sã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ✢♦❝❦✐♥❣d ij sep ✈❡t♦r ❞❡s❧♦❝❛♠❡♥t♦ ❡♥tr❡ ♦s r♦❜ôs i ❡ j vcoh i ✈❡t♦r ❞❛ ❝♦♠♣♦♥❡♥t❡ ❞❡ s❡♣❛r❛çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ✢♦❝❦✐♥❣ r❡❧❛t✐✈♦ ❛♦ r♦❜ô i vi dir ✈❡t♦r ❞❛ ❝♦♠♣♦♥❡♥t❡ ❞❡ ❝♦❡sã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ✢♦❝❦✐♥❣ r❡❧❛t✐✈♦ ❛♦ r♦❜ô i vi ✈❡t♦r ❞✐r❡çã♦ r❡❧❛t✐✈♦ ❛ ✉♠ ✇❛②♣♦✐♥t τ k ij i j ♣❛rt✐çã♦ ❞♦ ❡♥①❛♠❡ ❝♦♠ t♦❞♦s ♦s r♦❜ôs ❞♦ t✐♣♦ k kp k ♥♦r♠❛ ❊✉❝❧✐❞❡❛♥❛ ❞♦ ✈❡t♦r p − pU ij ( ij kp k) ❢✉♥çã♦ ♣♦t❡♥❝✐❛❧ ❛rt✐✜❝✐❛❧ q✉❡ ❡st❛❜❡❧❡❝❡ ❛s r❡❣r❛s ❞❡ ✐♥t❡r❛çã♦ ❡♥tr❡ ✉♠ ♣❛r ❞❡r♦❜ôs i ❡ j α❣❛♥❤♦ ❞❡ ❝♦♥tr♦❧❡ ❡s❝❛❧❛r dij ♣❛râ♠❡tr♦ ♣♦s✐t✐✈♦ q✉❡ ❝♦♥tr♦❧❛ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ ❣r✉♣♦δ il ❢✉♥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♦❧❡ U ( it it kp k) ❝❛♠♣♦ ♣♦t❡♥❝✐❛❧ ❛tr❛t✐✈♦ ❡♠ r❡❧❛çã♦ ❛ ✉♠ ✇❛②♣♦✐♥t tβit ❣❛♥❤♦ ♣r♦♣♦r❝✐♦♥❛❧ ❞♦ ❝❛♠♣♦ ♣♦t❡♥❝✐❛❧ ❛tr❛t✐✈♦ U I2♠❛tr✐③ ✐❞❡♥t✐❞❛❞❡ ❞❡ ♦r❞❡♠ 2 ∆t✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ σ ρ r✉í❞♦ ❞❡ ♦❜s❡r✈❛çã♦ r❡❢❡r❡♥t❡ à ♠❡❞✐❞❛ ❞❡ ❞✐stâ♥❝✐❛ r❡❧❛t✐✈❛ ρσ φ r✉í❞♦ ❞❡ ♦❜s❡r✈❛çã♦ r❡❢❡r❡♥t❡ à ♠❡❞✐❞❛ ❞❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛ φb ❞✐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❡♥❝✐❛❧ E s k ❊rr♦ ♠é❞✐♦ ♥❛ s✐♠✉❧❛çã♦ sE s ❊rr♦ ♠é❞✐♦ ♥❛ ✐t❡r❛çã♦ k ❞❛ s✐♠✉❧❛çã♦ s j● ❈♦♥❥✉♥t♦ ❞❡ r♦❜ôs q✉❡ ❝♦♠♣õ❡♠ ♦ ❣r✉♣♦ j ||● j || ◆ú♠❡r♦ ❞❡ r♦❜ôs ♥♦ ❣r✉♣♦ j j ● E s❊rr♦ ♠é❞✐♦ ❞♦s r♦❜ôs ❞♦ ❣r✉♣♦ j ♥❛ s✐♠✉❧❛çã♦ s K i◆ú♠❡r♦ ❞❡ ✐t❡r❛çõ❡s ❡①❡❝✉t❛❞❛s ♣❡❧♦ r♦❜ô i ❡♠ ✉♠❛ ❞❛❞❛ s✐♠✉❧❛çã♦ ❘▼❙❊ ❊rr♦ ♠é❞✐♦ ❞❛s s✐♠✉❧❛çõ❡s ❞❡ ✉♠ ❡①♣❡r✐♠❡♥t♦ ❙✉♠ár✐♦ ❆❣r❛❞❡❝✐♠❡♥t♦s✐① ❘❡s✉♠♦①✐ ❆❜str❛❝t①✐✐✐ ▲✐st❛ ❞❡ ❋✐❣✉r❛s①✈ ▲✐st❛ ❞❡ ❚❛❜❡❧❛s①✐① ▲✐st❛ ❞❡ ❆❜r❡✈✐❛çõ❡s①①✐ ▲✐st❛ ❞❡ ❙í♠❜♦❧♦s①①✐✐✐ ✶ ■♥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 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸ ❚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 ✶✺✾ ❈❛♣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♦❧❛✳ ✷❈❛♣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♦sé 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✉❛✲ ❞♦s ❞❡♥tr♦ ❞❛s r❡s♣❡❝t✐✈❛s ár❡❛s s❡♥s♦r✐❛✐s ❞❡ s❡✉s ✈✐③✐♥❤♦s✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ♦ ❝♦♥❝❡✐t♦ ❞❡ ✈✐③✐♥❤❛♥ç❛✭❞❡s❝r✐t♦ ♥❛ ❙❡çã♦ ✷✳✶✮ s❡rá ✉t✐❧✐③❛❞♦ ♣❛r❛ ❞❡✜♥✐r ❡ss❛s r❡❣✐õ❡s✳ ✸ 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❡♠❛✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ♦ ❛✉♠❡♥t♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❢♦✐ ❛❧❝❛♥ç❛❞♦ ❝♦♠ ♦ ❡♠♣r❡❣♦ ❞❡ ❡♥①❛♠❡s r♦❜ót✐❝♦s ✭❘♦❜♦t✐❝ ❙✇❛r♠s✮ ❛❧✐❛❞♦ à ✉t✐❧✐③❛çã♦ ❞❡ ❡str❛té❣✐❛s ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡✲t✐✈❛ q✉❡ ♣♦ss✐❜✐❧✐t❛♠ ❛♦s r♦❜ôs ❛t✉❛r❡♠ ❝♦♥❥✉♥t❛♠❡♥t❡✳ ❈♦♠ ❛ ❛t✉❛çã♦ ❝♦♥❥✉♥t❛ ❞♦❡♥①❛♠❡ t❡♠✲s❡ ✉♠❛ ❛♠♣❧✐❛çã♦ ❞❛s ♣♦ss✐❜✐❧✐❞❛❞❡s ❞❡ ❡♥❝♦♥tr♦s✱ ♣❡r♠✐t✐♥❞♦ q✉❡ ❡t❛♣❛s❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♣♦ss❛♠ ♦❝♦rr❡r ❝♦♠ ♠❛✐♦r ❢r❡q✉ê♥❝✐❛✳ ❉✉❛s ❡str❛té❣✐❛s ❞❡♠♦✈✐♠❡♥t❛çã♦ ❢♦r❛♠ ✐♠♣❧❡♠❡♥t❛❞❛s ❝♦♠ ♦ ♣r♦♣ós✐t♦ ❞❡ ♣r✐✈✐❧❡❣✐❛r ♦s ❡♥❝♦♥tr♦s✳ ❆ ✹❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ♣r✐♠❡✐r❛ ❡str❛té❣✐❛ ❝♦♥s✐st❡ ❡♠ ✉♠❛ ♣❡q✉❡♥❛ ❡①t❡♥sã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❝❧áss✐❝♦ ❞❡ ✢♦❝❦✐♥❣❞❡s❡♥✈♦❧✈✐❞♦ ♣♦r ❘❡②♥♦❧❞s ❬✶✾✽✼❪✱ q✉❡ ♣r♦✈ê ❛ ♠♦✈✐♠❡♥t❛çã♦ ❛❧t❡r♥❛❞❛ ❞♦ ❣r✉♣♦✳ ❆ s❡❣✉♥❞❛ ❡str❛té❣✐❛ ❢♦✐ ✐♠♣❧❡♠❡♥t❛❞❛ ♥❛ ❢♦r♠❛ ❞❡ ✉♠❛ ❡①t❡♥sã♦✴❝♦♠❜✐♥❛çã♦ ❞♦s ❛❧✲❣♦r✐t♠♦s ❞❡ s❡❣r❡❣❛çã♦ ❬❑✉♠❛r ❡t ❛❧✳✱ ✷✵✶✵❀ ❙❛♥t♦s ❡t ❛❧✳✱ ✷✵✶✹❪ ❡ ❛❣r❡❣❛çã♦ ❬❑✉♠❛r✫ ●❛r❣✱ ✷✵✶✶❪✱ ♣r♦✈❡♥❞♦ ✉♠❛ ♠♦✈✐♠❡♥t❛çã♦ ❝♦♥tí♥✉❛ ❞♦ ❣r✉♣♦✱ ❛❧é♠ ❞❡ ✈✐❛❜✐❧✐③❛r ♦♣♦s✐❝✐♦♥❛♠❡♥t♦ ❛✉tô♥♦♠♦ ❞❡ ✉♠ r♦❜ô ❧í❞❡r ♥♦ ✐♥t❡r✐♦r ❞♦ ❡♥①❛♠❡✳ ▼♦❞❡❧♦s ❞❡ r♦❜ôs❤♦❧♦♥ô♠✐❝♦s ❡ ♥ã♦ ❤♦❧♦♥ô♠✐❝♦s ❢♦r❛♠ ✉t✐❧✐③❛❞♦s ❡♠ ❡t❛♣❛s ❞✐st✐♥t❛s ❞♦ tr❛❜❛❧❤♦✳ ❆ ê♥❢❛s❡ ❞❡st❡ tr❛❜❛❧❤♦ é ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠❛ ❡str❛té❣✐❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛♣❛r❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s✳ ❉❡✈✐❞♦ às ♣❛rt✐❝✉❧❛r✐❞❛❞❡s ❞❡ss❡ t✐♣♦ ❞❡ s✐st❡♠❛✱ ❛❧❣✉♥s ❛s♣❡❝t♦s ❢♦r❛♠ ❡st✉❞❛❞♦s ❝♦♠ ♦ ♣r♦♣ós✐t♦ ❞❡ ❛✈❛❧✐❛r ♦ ✐♠♣❛❝t♦❞♦s ♠❡s♠♦s ♥❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❡♥①❛♠❡✳ ◆♦s ❡stá❣✐♦s ✐♥✐❝✐❛✐s ❞♦ tr❛❜❛❧❤♦✱♦ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥ ❢♦✐ ✐♠♣❧❡♠❡♥t❛❞♦ ♣❛r❛ s❡ ❡❢❡t✉❛r ❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ◆♦ ❡♥✲ t❛♥t♦✱ ❛♣ós ❛ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ ❛❧❣✉♠❛s ❞❡ss❛s ♣❛rt✐❝✉❧❛r✐❞❛❞❡s✱ ❛ ❡t❛♣❛ ❞❡ ❝♦rr❡çã♦ ❞♦✜❧tr♦ ❞❡ ❑❛❧♠❛♥ ❢♦✐ s✉❜st✐t✉í❞❛ ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s✱ ❞❡✈✐❞♦❛♦ ❢❛t♦ ❞❡ t❛❧ té❝♥✐❝❛ ❣❡r❛r ❡st✐♠❛t✐✈❛s ❝♦♥s✐st❡♥t❡s q✉❛♥❞♦ ♥ã♦ s❡ t❡♠ ✐♥❢♦r♠❛çõ❡s ❛ r❡s♣❡✐t♦ ❞❛s ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛s ❞❛s ❡st✐♠❛t✐✈❛s✳ ❉❡ss❡ ♠♦❞♦✱ ♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡s❝❡♥✲tr❛❧✐③❛❞♦ ❞❛s ❡st✐♠❛t✐✈❛s é ❡❢❡t✉❛❞♦ s❡♠ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ♠❛♥✉t❡♥çã♦ ❞♦ r❡❣✐str♦ ❞❛s✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛s ❡♠ ❝❛❞❛ ❡♥t✐❞❛❞❡ r♦❜ót✐❝❛✱ ✈✐❛❜✐❧✐③❛♥❞♦ ❛ss✐♠ ✉♠❛ s♦❧✉çã♦ ❡s❝❛❧á✈❡❧♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s✳ ❊①♣❡r✐♠❡♥t♦s s✐✲♠✉❧❛❞♦s ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞♦s t❡♥❞♦ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❛ ❝♦♠♣❛r❛çã♦ ❡♥tr❡ t❛✐s ❛❜♦r❞❛❣❡♥s❡ ❛ ❛♥á❧✐s❡ ❞♦ ✐♠♣❛❝t♦ ❞❛s ♠❡s♠❛s ♥❛ ❧♦❝❛❧✐③❛çã♦ r❡s✉❧t❛♥t❡✳ ❆❧é♠ ❞✐ss♦✱ ❡①♣❡r✐♠❡♥✲ t♦s ❝♦♠ r♦❜ôs r❡❛✐s ♠♦str❛♠ ❛ ✈✐❛❜✐❧✐❞❛❞❡ ♣❛r❛ ❛♣❧✐❝❛çã♦ ❞❛ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛ ❡♠❛♠❜✐❡♥t❡s r❡❛✐s✳ ✶✳✶ ❉❡✜♥✐çã♦ ❞♦ Pr♦❜❧❡♠❛ 1 , 2 , . . . , N ❙❡❥❛ ✉♠ ❡♥①❛♠❡ R = {R R R } ❝♦♠♣♦st♦ ❞❡ N r♦❜ôs✱ ❝♦♠ ❝❛r❛❝t❡ríst✐❝❛s❤♦♠♦❣ê♥❡❛s ♦✉ ❤❡t❡r♦❣ê♥❡❛s✱ ♦♥❞❡ ♦ ♥ú♠❡r♦ N ♥ã♦ ♣r❡❝✐s❛ s❡r ❝♦♥❤❡❝✐❞♦ ♣❡❧♦s r♦❜ôs✳ i i i i i i = (x , y )❆s ❝♦♦r❞❡♥❛❞❛s ❝❛rt❡s✐❛♥❛s x ❡ y ❞❛ ♣♦s✐çã♦ p ✱ ❛❧é♠ ❞❛ ♦r✐❡♥t❛çã♦ θ ✱ i i i i i = (x , y , θ )❝♦♠♣õ❡♠ ❛ ♣♦s❡ q ❞♦ ✐✲és✐♠♦ r♦❜ô ✭R ✮ ❡♠ ✉♠ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s✐♥❡r❝✐❛❧✳ ❈❛❞❛ r♦❜ô é ❡q✉✐♣❛❞♦ ❝♦♠ s❡♥s♦r❡s ♣r♦♣r✐♦❝❡♣t✐✈♦s q✉❡ ♦ ♣❡r♠✐t❡♠ ❡st✐♠❛r s✉❛ ♥♦✈❛ ♣♦s❡✱ t❡♥❞♦ ❝♦♠♦ ❜❛s❡ ✉♠❛ ♣♦s❡ ❛♥t❡r✐♦r♠❡♥t❡ ❞❡✜♥✐❞❛✳ ❆❧é♠ ❞✐ss♦✱ ❝❛❞❛r♦❜ô é ❡q✉✐♣❛❞♦ ❝♦♠ s❡♥s♦r❡s ❡①t❡r♦❝❡♣t✐✈♦s q✉❡ ♦ ♣♦ss✐❜✐❧✐t❛♠ ✐❞❡♥t✐✜❝❛r ♦✉tr♦s r♦❜ôs q✉❡ s❡ ❡♥❝♦♥tr❡♠ ♥❛ ✈✐③✐♥❤❛♥ç❛✱ ❛❧é♠ ❞❡ ❡st✐♠❛r ❞✐stâ♥❝✐❛ ρ ❡ ♦r✐❡♥t❛çã♦ φ r❡❧❛t✐✈❛s❛ ❡ss❡s r♦❜ôs✳ ❊ss❛s ❡st✐♠❛t✐✈❛s ✐♥❝♦r♣♦r❛♠ ✐♥❝❡rt❡③❛s ✐♥❡r❡♥t❡s ❛♦s t✐♣♦s ❞❡ s❡♥s♦r❡s✉t✐❧✐③❛❞♦s✳ ❆ ✈✐③✐♥❤❛♥ç❛ N i ❞♦ i✲és✐♠♦ r♦❜ô✱ ❡♠ ✉♠ ❞❛❞♦ ♠♦♠❡♥t♦✱ é ❢♦r♠❛❞❛ ♣❡❧♦ ✶✳✷✳ ❖❜❥❡t✐✈♦s ❡ ❈♦♥tr✐❜✉✐çõ❡s i ✺❝♦♥❥✉♥t♦ ❞❡ r♦❜ôs q✉❡ s❡ ❡♥❝♦♥tr❛♠ ❞❡♥tr♦ ❞❛ ár❡❛ s❡♥s♦r✐❛❧ ❞❡ R ✳ ❆❧é♠ ❞❡ ✐♥t❡r❛❣✐r❡♠✈✐❛ s❡♥s♦r❡s ❡①t❡r♦❝❡♣t✐✈♦s✱ r♦❜ôs ❝♦♠♣❛rt✐❧❤❛♥❞♦ ✈✐③✐♥❤❛♥ç❛s ❡stã♦ ❛♣t♦s ❛ ❡st❛❜❡❧❡❝❡r❝♦♠✉♥✐❝❛çã♦ ❡♥tr❡ s✐✳ ❉❛❞❛s ❡ss❛s ❡s♣❡❝✐✜❝❛çõ❡s✱ ♦ ♣r♦❜❧❡♠❛ tr❛t❛❞♦ ♥❡st❛ t❡s❡ ♣♦❞❡ s❡r ❞❡✜♥✐❞♦ ❝♦♠♦ s❡❣✉❡✿❉❡✜♥✐çã♦ ✶✳ ❉❛❞♦ ✉♠ ❡♥①❛♠❡ ❞❡ r♦❜ôs R s❡ ♠♦✈✐♠❡♥t❛♥❞♦ ❝♦❧❡t✐✈❛♠❡♥t❡ ❡ ❝♦♠❝❛♣❛❝✐❞❛❞❡s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❡ ❝♦♠✉♥✐❝❛çã♦ ❧✐♠✐t❛❞♦s✱ ❡st❛❜❡❧❡❝❡r ✉♠❛ ❡str❛té❣✐❛ ❞❡s✲❝❡♥tr❛❧✐③❛❞❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ q✉❡ ♣❡r♠✐t❛ ❧♦❝❛❧✐③❛r ♦s r♦❜ôs ❞❡ ♠❛♥❡✐r❛ ❝♦♥✲ s✐st❡♥t❡✳ ✶✳✷ ❖❜❥❡t✐✈♦s ❡ ❈♦♥tr✐❜✉✐çõ❡s ❖ ♦❜❥❡t✐✈♦ ❣❡r❛❧ ❞❡st❛ t❡s❡ ❝♦♥s✐st❡ ❡♠ ♣r♦♣♦r ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞❡s❝❡♥tr❛❧✐③❛❞❛❡ ❡s❝❛❧á✈❡❧ ♣❛r❛ ❧♦❝❛❧✐③❛r ❝♦♦♣❡r❛t✐✈❛♠❡♥t❡ ❡♥①❛♠❡s ❞❡ r♦❜ôs ♠ó✈❡✐s ❞❡ ♠❛♥❡✐r❛❝♦♥s✐st❡♥t❡✱ t❛♥t♦ ♣❛r❛ ❣r✉♣♦s ❤♦♠♦❣ê♥❡♦s q✉❛♥t♦ ❤❡t❡r♦❣ê♥❡♦s✳ ❚❡♥❞♦ ❡♠ ✈✐st❛ ♦ ✐♥t❡r❡ss❡ ❡♠ ❛✈❛❧✐❛r ❛ ❛♣❧✐❝❛❜✐❧✐❞❛❞❡ ❡ ❛ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ ❞♦ ♠é✲ t♦❞♦✱ ♦s ♦❜❥❡t✐✈♦s ❡s♣❡❝í✜❝♦s ❝♦♠♣r❡❡♥❞❡♠✿❼ ✐❞❡♥t✐✜❝❛r ❡ ❛❞❛♣t❛r ♠ét♦❞♦s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♣❛r❛ ❛♣❧✐❝❛çã♦ ❡♠ ❡♥✲ ①❛♠❡s ❞❡ r♦❜ôs❀❼ ✉t✐❧✐③❛r ❡str❛té❣✐❛s ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛ ♣❛r❛ ❛♠♣❧✐❛r ❛s ♦❝♦rrê♥❝✐❛s ❞❡ ❡♥✲ ❝♦♥tr♦s ❡ ♣♦ss✐❜✐❧✐t❛r ❛✉♠❡♥t❛r ❛ ❢r❡q✉ê♥❝✐❛ ❞❡ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛❀❼ ❛✈❛❧✐❛r ♦ ✐♠♣❛❝t♦ ❞❛ ✉t✐❧✐③❛çã♦ ❞❡ ❞✐❢❡r❡♥t❡s ❝r✐tér✐♦s ♣❛r❛ ❛ s❡❧❡çã♦ ❞❡ r♦❜ôs ♠❛r❝♦ ♥❛s ❡t❛♣❛s ❞❡ ❢✉sã♦ s❡♥s♦r✐❛❧❀❼ ❛✈❛❧✐❛r ❛ ✉t✐❧✐③❛çã♦ ❞❡ ❣r✉♣♦s ❤♦♠♦❣ê♥❡♦s ❡ ❤❡t❡r♦❣ê♥❡♦s ❡ ♦ r❡✢❡①♦ ♥❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❣r✉♣♦✳❉❡st❛ ❢♦r♠❛✱ ❛s ♣r✐♥❝✐♣❛✐s ❝♦♥tr✐❜✉✐çõ❡s ❞❡st❡ tr❛❜❛❧❤♦ sã♦✿ ❼ ❛ ♣r♦♣♦s✐çã♦ ❞❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ♣❛r❛ ❧♦❝❛❧✐③❛r ❝♦♦♣❡r❛t✐✈❛♠❡♥t❡❡♥①❛♠❡s ❞❡ r♦❜ôs ♠ó✈❡✐s✱ t❡♥❞♦ ❡♠ ✈✐st❛ ♦ ♣❡q✉❡♥♦ ♥ú♠❡r♦ ❞❡ tr❛❜❛❧❤♦s ❡♠❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❝♦♠ ❡♥①❛♠❡s❀ ❼ ❛ ❛♥á❧✐s❡ ❞❛ ✈❛r✐❛çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs ♠❛r❝♦ ✉t✐❧✐③❛❞♦s ♥❛s ❡♣❛t❛s ❞❡ ❧♦❝❛❧✐✲③❛çã♦ ❝♦♦♣❡r❛t✐✈❛❀ ❼ ❛ ❛✈❛❧✐❛çã♦ ❞❛ ❝♦♥s✐stê♥❝✐❛ ❞❛s ❡st✐♠❛t✐✈❛s r❡s✉❧t❛♥t❡s ❞❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦❝♦♦♣❡r❛t✐✈❛ ❡♠ ❡♥①❛♠❡s ❤❡t❡r♦❣ê♥❡♦s❀ ✻❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ❼ ❛ ♣r♦♣♦s✐çã♦ ❞❡ ✉♠❛ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛ ❜❛s❡❛❞❛ ♥♦s ❝♦♠♣♦r✲ t❛♠❡♥t♦s ❞❡ ❛❣r❡❣❛çã♦✱ s❡❣r❡❣❛çã♦ ❡ ❧í❞❡r✲s❡❣✉✐❞♦r✳❉✉r❛♥t❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❛ ♣❡sq✉✐s❛✱ ♣❛rt❡s ❞♦ tr❛❜❛❧❤♦ ❢♦r❛♠ ♣✉❜❧✐❝❛❞❛s ❝♦♠ ♦ ♣r♦♣ós✐t♦ ❞❡ ❞✐✈✉❧❣❛r ♦s r❡s✉❧t❛❞♦s ❛❧❝❛♥ç❛❞♦s✱ ❛ s❛❜❡r✿❼ ❆♥❞❡rs♦♥ ●✳ P✐r❡s❀ ▲✉✐③ ❈❤❛✐♠♦✇✐❝③✳ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛✱ ❉❡s❝❡♥tr❛❧✐③❛❞❛ ❡ ❇❛s❡❛❞❛ ❡♠ ▼❛r❝♦s ❉✐♥â♠✐❝♦s ❡♠ ❊♥①❛♠❡s ❞❡ ❘♦❜ôs ▼ó✈❡✐s✳ ■ ❲♦r❦s❤♦♣ ❞❡❚❡s❡s ❡ ❉✐ss❡rt❛çõ❡s ❡♠ ❘♦❜ót✐❝❛ ✲ ■ ❙✐♠♣ós✐♦ ❇r❛s✐❧❡✐r♦ ❞❡ ❘♦❜ót✐❝❛✱ ✷✵✶✷✳ ❼ ❆♥❞❡rs♦♥ ●✳ P✐r❡s❀ ❉♦✉❣❧❛s ●✳ ▼❛❝❤❛r❡t❀ ▲✉✐③ ❈❤❛✐♠♦✇✐❝③✳ ❚♦✇❛r❞s ❈♦♦♣❡r❛✲ t✐✈❡ ▲♦❝❛❧✐③❛t✐♦♥ ✐♥ ❘♦❜♦t✐❝ ❙✇❛r♠s✳ Pr♦❝❡❡❞✐♥❣s ♦❢ ■♥t❡r♥❛t✐♦♥❛❧ ❙②♠♣♦s✐✉♠ ♦♥❉✐str✐❜✉t❡❞ ❆✉t♦♥♦♠♦✉s ❘♦❜♦t✐❝ ❙②st❡♠s ✭❉❆❘❙✮✱ ✷✵✶✹✳ ❼ ❆♥❞❡rs♦♥ ●r❛♥❞✐ P✐r❡s❀ ❉♦✉❣❧❛s ●✳ ▼❛❝❤❛r❡t❀ ▲✉✐③ ❈❤❛✐♠♦✇✐❝③✳ ❊①♣❧♦r✐♥❣ ❍❡✲ t❡r♦❣❡♥❡✐t② ❢♦r ❈♦♦♣❡r❛t✐✈❡ ▲♦❝❛❧✐③❛t✐♦♥ ✐♥ ❙✇❛r♠ ❘♦❜♦t✐❝s✳ Pr♦❝❡❡❞✐♥❣s ♦❢ ■♥✲t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆❞✈❛♥❝❡❞ ❘♦❜♦t✐❝s ✭■❈❆❘✮✱ ✷✵✶✺✳ ❖s ❛rt✐❣♦s ❝✐t❛❞♦s ❛♥t❡r✐♦r♠❡♥t❡ ❝♦♠♣r❡❡♥❞❡♠ ❛ ♣❛rt❡ ❞❛ t❡s❡ q✉❡ ❡♠♣r❡❣❛ ♠♦✲❞❡❧♦s ❞❡ r♦❜ôs ❤♦❧♦♥ô♥✐❝♦s ❡ ❛♥á❧✐s❡ ❞❛ ✈❛r✐❛çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs ♠❛r❝♦s✳ ❆ ♦✉tr❛♣❛rt❡✱ q✉❡ ❢❛③ ✉s♦ ❞❡ ♠♦❞❡❧♦s ♥ã♦ ❤♦❧♦♥ô♠✐❝♦s ❡ q✉❡ ❛✈❛❧✐❛ ❛ ❝♦♥s✐stê♥❝✐❛ ❞❛s ❡st✐♠❛✲ t✐✈❛s✱ ❝✉❥♦s r❡s✉❧t❛❞♦s sã♦ ❛♣r❡s❡♥t❛❞♦s ♥❛ ❙❡çã♦ ✺✳✷✱ ❡stá s❡♥❞♦ ♦r❣❛♥✐③❛❞❛ ♥❛ ❢♦r♠❛❞❡ ✉♠ ❛rt✐❣♦ ❝✐❡♥tí✜❝♦ ♣❛r❛ s✉❜♠✐ssã♦ ❡♠ ✉♠ ♣❡r✐ó❞✐❝♦ ✐♥t❡r♥❛❝✐♦♥❛❧✳ ✶✳✸ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚❡①t♦ ❊st❛ t❡s❡ ❡stá ♦r❣❛♥✐③❛❞❛ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿ ♦ ❈❛♣ít✉❧♦ ✷ ❛♣r❡s❡♥t❛ ✉♠❛ ❢✉♥❞❛♠❡♥✲ t❛çã♦ t❡ór✐❝❛ q✉❡ s❡r✈❡ ❞❡ ❜❛s❡ ♣❛r❛ ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ tr❛❜❛❧❤♦✳◆♦ ❈❛♣ít✉❧♦ ✸ sã♦ ❛♣r❡s❡♥t❛❞♦s tr❛❜❛❧❤♦s r❡❧❡✈❛♥t❡s ❡♠ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ ❝♦♠ ❛❞✐s❝✉ssã♦ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ♠❛✐s r❡❧❛❝✐♦♥❛❞❛s ❛♦s ♦❜❥❡t✐✈♦s ❡s♣❡❝í✜❝♦s ❞❡st❡ tr❛❜❛❧❤♦✳❖ ❈❛♣ít✉❧♦ ✹ ❞❡s❝r❡✈❡ ❛ ♠❡t♦❞♦❧♦❣✐❛ ✉t✐❧✐③❛❞❛✱ ❡♥q✉❛♥t♦ q✉❡ ♦ ❈❛♣ít✉❧♦ ✺ ❛♣r❡s❡♥t❛ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s t❛♥t♦ ❡♠ s✐♠✉❧❛çã♦ q✉❛♥t♦ ❡♠ ❡①♣❡r✐♠❡♥t♦s ❝♦♠ r♦❜ôs r❡❛✐s✳ P♦r✜♠✱ ♦ ❈❛♣ít✉❧♦ ✻ ❛♣r❡s❡♥t❛ ❛s ❝♦♥tr✐❜✉✐çõ❡s✱ ♦s tr❛❜❛❧❤♦s ❢✉t✉r♦s ❡ ❛s ❝♦♥❝❧✉sõ❡s✳ ❈❛♣ít✉❧♦ ✷ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ❊st❡ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛ ❛❧❣✉♥s ❢✉♥❞❛♠❡♥t♦s q✉❡ ❛✉①✐❧✐❛♠ ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ■♥✐❝✐❛❧♠❡♥t❡ s❡rã♦ ❝❛r❛❝t❡r✐③❛❞♦s ♦s ❝♦♥❝❡✐t♦s ❞❡ ♣♦s❡✱ ✈✐③✐♥❤❛♥ç❛ ❡ ❡♥❝♦♥✲tr♦s✳ P♦st❡r✐♦r♠❡♥t❡✱ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s ❝♦♦♣❡r❛t✐✈♦s s❡rã♦ ✐♥tr♦❞✉③✐❞♦s✱ s✉❛s♣r✐♥❝✐♣❛✐s ❝❛r❛❝t❡ríst✐❝❛s ❛♣r❡s❡♥t❛❞❛s ❡ ❡♥①❛♠❡s r♦❜ót✐❝♦s✱ q✉❡ ❝♦♥s✐st❡♠ ❡♠ s✐st❡✲♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s ❝♦♠♣♦st♦s ♣♦r ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ r♦❜ôs✱ s❡rã♦ ❞❡st❛❝❛❞♦s✳ ❆s♣r✐♥❝✐♣❛✐s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ss❡ t✐♣♦ ❞❡ s✐st❡♠❛ s❡rã♦ ❞✐s❝✉t✐❞❛s✱ ❛❧é♠ ❞❛ ❛♣r❡s❡♥t❛✲çã♦ ❞❡ ❛❧❣✉♥s ❞♦♠í♥✐♦s ❞❡ ❛♣❧✐❝❛çã♦ ♥♦s q✉❛✐s t❛✐s s✐st❡♠❛s tê♠ s✐❞♦ ✉t✐❧✐③❛❞♦s✳ ❊♠ s❡❣✉✐❞❛✱ ✉♠❛ ✐♥tr♦❞✉çã♦ ❞❛s ♣r✐♥❝✐♣❛✐s té❝♥✐❝❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❡♠♣r❡❣❛❞❛s ❡♠ s✐st❡✲♠❛s r♦❜ót✐❝♦s s❡rã♦ ❛♣r❡s❡♥t❛❞❛s✳ ◆❡ss❛s té❝♥✐❝❛s✱ ♦ ♣r♦❝❡ss♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ ✉♠ r♦❜ô é ❡❢❡t✉❛❞♦ ♣♦r ♠❡✐♦ ❞❡ ♠❡❞✐çõ❡s ✐♥t❡r♥❛s ❡ ❡①t❡r♥❛s ✭❛♠❜✐❡♥t❡✮✳ ❉❡✈✐❞♦ às ✐♥ú✲♠❡r❛s ✐♥❝❡rt❡③❛s ♣r❡s❡♥t❡s ❡♠ ♣r♦❝❡ss♦s ❞❡ ♠❡❞✐çã♦✱ ♦ ❛r❝❛❜♦✉ç♦ ♣r♦❜❛❜✐❧íst✐❝♦ q✉❡❢✉♥❞❛♠❡♥t❛ ❛s té❝♥✐❝❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ s❡rá ❛♣r❡s❡♥t❛❞♦✳ P♦r ✜♠✱ ✉♠❛ ✐♥tr♦❞✉çã♦ ❛♦s❝♦♥❝❡✐t♦s ❣❡r❛✐s ❞❛ té❝♥✐❝❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ s❡rá ❛♣r❡s❡♥t❛❞❛ ❝♦♠ ✉♠❛ ❜r❡✈❡❞✐s❝✉ssã♦ ❞❡ s❡✉s ♣r✐♥❝✐♣❛✐s ❝♦♥❝❡✐t♦s✳ ✷✳✶ ❈♦♥s✐❞❡r❛çõ❡s ■♥✐❝✐❛✐s ◆❡st❡ tr❛❜❛❧❤♦✱ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦s r♦❜ôs é r❡str✐t❛ ❛ ❛♠❜✐❡♥t❡s ♣❧❛♥❛r❡s✳ ❘♦❜ôs❤♦❧♦♥ô♠✐❝♦s ❡ ♥ã♦ ❤♦❧♦♥ô♠✐❝♦s ❢♦r❛♠ ❡♠♣r❡❣❛❞♦s ❡ ❛♠❜♦s ✉t✐❧✐③❛♠ s❡♥s♦r❡s ♣r♦♣r✐♦✲❝❡♣t✐✈♦s ♣❛r❛ ♠❡❞✐r s✉❛s ✈❡❧♦❝✐❞❛❞❡s✳ ◆♦ ♠♦❞❡❧♦ ❤♦❧♦♥ô♠✐❝♦✱ ❛s ✈❡❧♦❝✐❞❛❞❡s ❧✐♥❡❛r❡s vx y ❡ v sã♦ ✉t✐❧✐③❛❞❛s ❝♦♠♦ ❡♥tr❛❞❛ ❞❡ ❝♦♥tr♦❧❡✱ ❡♥q✉❛♥t♦ q✉❡ ♦ ♠♦❞❡❧♦ ♥ã♦ ❤♦❧♦♥ô♠✐❝♦✉t✐❧✐③❛ ❛s ✈❡❧♦❝✐❞❛❞❡s ❧✐♥❡❛r ✭v✮ ❡ ❛♥❣✉❧❛r ✭w✮✳ ◆♦ ❡s♣❛ç♦ ❜✐✲❞✐♠❡♥s✐♦♥❛❧✱ ♦ ❡st❛❞♦ x❞❡ ✉♠ r♦❜ô ♣♦❞❡ s❡r r❡♣r❡s❡♥t❛❞♦ ♣♦r s✉❛ ♣♦s✐çã♦ (x, y) ❡♠ r❡❧❛çã♦ ❛ ✉♠ s✐st❡♠❛ ❞❡ W W , )❝♦♦r❞❡♥❛❞❛s ✐♥❡r❝✐❛❧ ✭❳ ❨ ✱ ❛❧✐❛❞❛ à s✉❛ ♦r✐❡♥t❛çã♦ θ✱ ♦✉ s❡❥❛✱ x = (x, y, θ)✳ ❚❛❧♦r✐❡♥t❛çã♦ r❡♣r❡s❡♥t❛ ♦ ❞❡s❧♦❝❛♠❡♥t♦ ❛♥❣✉❧❛r t♦♠❛❞♦ ❛ ♣❛rt✐r ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ❝♦✲ ✽❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ R R , ) ♦r❞❡♥❛❞❛s ❧♦❝❛❧ ✭❳ ❨ ❡♠ r❡❧❛çã♦ ❛♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ✐♥❡r❝✐❛❧ ✭❋✐❣✉r❛ ✷✳✶✮✳❖ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ❧♦❝❛❧ é ❞❡✜♥✐❞♦ ❞❡ ♠♦❞♦ q✉❡ ❛ ❞✐r❡çã♦ ❢r♦♥t❛❧ ✭❤❡❛❞✐♥❣ ❞✐✲ R r❡❝t✐♦♥✮ ❞♦ r♦❜ô ❝♦✐♥❝✐❞❛ ❝♦♠ ♦ s❡♥t✐❞♦ ♣♦s✐t✐✈♦ ❞❡ ❳ ✳ ◆♦ ♠♦❞❡❧♦ ❤♦❧♦♥ô♠✐❝♦✱ ♦❡st❛❞♦ ❞❡ ✉♠ r♦❜ô ❝♦♥t❡♠♣❧❛ s♦♠❡♥t❡ s✉❛ ♣♦s✐çã♦✱ ♣♦✐s é ❛ss✉♠✐❞♦ q✉❡ ❛ ♦r✐❡♥t❛çã♦❞♦ s✐st❡♠❛s ❞❡ ❝♦♦r❞❡♥❛❞❛s ❧♦❝❛❧ ❞♦ r♦❜ô ❝♦✐♥❝✐❞❡ ❝♦♠ ❛ ♦r✐❡♥t❛çã♦ ❞♦ s✐st❡♠❛s ❞❡ ❝♦✲♦r❞❡♥❛❞❛s ✐♥❡r❝✐❛❧✳ ❖ t❡r♠♦ ♣♦s❡ ♣♦❞❡rá t❛♠❜é♠ s❡r ❡♠♣r❡❣❛❞♦ ♣❛r❛ ❢❛③❡r r❡❢❡rê♥❝✐❛às ❝♦♦r❞❡♥❛❞❛s (x, y, θ) ❞❡ ✉♠ r♦❜ô ❝♦♠ r❡❧❛çã♦ ❛♦ s✐st❡♠❛ ✐♥❡r❝✐❛❧✳ Y W Y R ii X R i θy i R i xi X Wi i i i i = (x , y , θ ) ❋✐❣✉r❛ ✷✳✶✿ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ❡st❛❞♦ x ❞♦ r♦❜ô i ✭R ✮ ❡♠ ✉♠ s✐st❡♠❛ ❞❡ W , W ) R i , R i❝♦♦r❞❡♥❛❞❛s ✐♥❡r❝✐❛❧ ✭❳ ❨ ✳ ❖ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ✭❳ ❨ ✮ é ❧♦❝❛❧ ❛♦ r♦❜ô❡ t❡♠ ❝♦♠♦ ♦r✐❣❡♠ ✉♠ ♣♦♥t♦ ❞❡ r❡❢❡rê♥❝✐❛ s♦❜r❡ ♦ ♠❡s♠♦✳ ◆❛ ♠♦✈✐♠❡♥t❛çã♦ ❞❡ ✉♠ ❣r✉♣♦ ❞❡ r♦❜ôs✱ ♦s ♠❡s♠♦s ♣♦❞❡♠ ❝♦♠♣❛rt✐❧❤❛r ✉♠❛❞❡t❡r♠✐♥❛❞❛ r❡❣✐ã♦ ❞♦ ❛♠❜✐❡♥t❡✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ♦ ❝♦♥❝❡✐t♦ ❞❡ ✈✐③✐♥❤❛♥ç❛ s❡rá ✉t✐✲❧✐③❛❞♦ ♣❛r❛ ❝❛r❛❝t❡r✐③❛r s✉❜✲❣r✉♣♦s ❞❡ r♦❜ôs ❛t✉❛♥❞♦ ❡♠ ✉♠❛ ♠❡s♠❛ r❡❣✐ã♦ ❡ q✉❡✱❞❡✈✐❞♦ ❛ ✐ss♦✱ ♣♦❞❡♠ ✐♥t❡r❛❣✐r ❡ tr♦❝❛r ✐♥❢♦r♠❛çõ❡s✳ ❆s ✈✐③✐♥❤❛♥ç❛s sã♦ ❢♦r♠❛❞❛s ❞✐✲♥❛♠✐❝❛♠❡♥t❡✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❞✐s♣♦s✐çã♦ ❞♦s r♦❜ôs ♥♦ ❛♠❜✐❡♥t❡✳ ❯♠❛ ✈✐③✐♥❤❛♥ç❛ é❞❡✜♥✐❞❛ ♣❡❧❛ ár❡❛ ✐♥t❡r✐♦r ❛ ✉♠ ❝ír❝✉❧♦ ❞❡ r❛✐♦ ε✱ ❝✉❥♦ ❝❡♥tr♦ ❡♥❝♦♥tr❛✲s❡ ❧♦❝❛❧✐③❛❞♦❡♠ ✉♠ ♣♦♥t♦ ❞❡ r❡❢❡rê♥❝✐❛ ♥♦ ❝♦r♣♦ ❞♦ r♦❜ô ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ s❡✉ ❝❡♥tr♦ ❞❡ ♠❛ss❛✳❘♦❜ôs s✐t✉❛❞♦s ❛ ❛té ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❞✐stâ♥❝✐❛ ❞❡ ✉♠ ❞❛❞♦ r♦❜ô ✭R k ✮ sã♦ ❝♦♥s✐❞❡r❛✲ k❞♦s ✈✐③✐♥❤♦s ❞❡ss❡ ❡ ❝♦♥st✐t✉❡♠ ❛ s✉❛ ✈✐③✐♥❤❛♥ç❛ N ✳ ❆ ❋✐❣✉r❛ ✷✳✷ ✐❧✉str❛ ❛ ❢♦r♠❛çã♦❞❡ ❛❧❣✉♠❛s ✈✐③✐♥❤❛♥ç❛s✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ✉♠ ❡♥❝♦♥tr♦ é ❝❛r❛❝t❡r✐③❛❞♦ q✉❛♥❞♦ ❞♦✐s ♦✉ ♠❛✐s r♦❜ôs ❡stã♦❧♦❝❛❧✐③❛❞♦s ❡♠ ✉♠❛ ♠❡s♠❛ r❡❣✐ã♦ ❞♦ ❛♠❜✐❡♥t❡✱ ♦✉ s❡❥❛✱ ❝♦♠♣❛rt✐❧❤❛♠ ✉♠❛ ✈✐③✐♥❤❛♥ç❛✳❉❡ss❡ ♠♦❞♦✱ r♦❜ôs ❝♦♠♣❛rt✐❧❤❛♥❞♦ ✈✐③✐♥❤❛♥ç❛s ♣♦❞❡♠ ✐♥t❡r❛❣✐r ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱♠❡❞✐r ❞✐stâ♥❝✐❛s ρ ❡ ♦r✐❡♥t❛çõ❡s φ r❡❧❛t✐✈❛s ❛ ♦✉tr♦s r♦❜ôs✱ ❛❧é♠ ❞❡ tr♦❝❛r❡♠ ✐♥❢♦r♠❛çã♦ i ij✈✐❛ ❝♦♠✉♥✐❝❛çã♦ ✭❋✐❣✉r❛ ✷✳✸✮✳ ❆ss✐♠✱ ✉♠ r♦❜ô R é ❝❛♣❛③ ❞❡ ❡st✐♠❛r ❛ ❞✐stâ♥❝✐❛ ρ ❡ ij j i ij i❛ ♦r✐❡♥t❛çã♦ φ r❡❧❛t✐✈❛s ❛ ✉♠ r♦❜ô R ∈ N ✱ r❡♣r❡s❡♥t❛♥❞♦ ✉♠❛ ♦❜s❡r✈❛çã♦ z ∈ Z ✱ s❡♥❞♦ Z i ♦ ❝♦♥❥✉♥t♦ ❞❛s ♦❜s❡r✈❛çõ❡s ❡①t❡r♦❝❡♣t✐✈❛s ❞♦ r♦❜ô R i ✳ ❆s ♦❜s❡r✈❛çõ❡s ♦❜t✐❞❛s ✷✳✶✳ ❈♦♥s✐❞❡r❛çõ❡s ■♥✐❝✐❛✐s✾ ε R k R ε N k R j ε i N iN j ❋✐❣✉r❛ ✷✳✷✿ ❋♦r♠❛çã♦ ❞✐♥â♠✐❝❛ ❞❡ ✈✐③✐♥❤❛♥ç❛s✳ ❆ ✈✐③✐♥❤❛♥ç❛ ❞❡ ✉♠ r♦❜ô é ❡st❛❜❡❧❡❝✐❞❛❞✐♥❛♠✐❝❛♠❡♥t❡ ❡ ❝♦♠♣r❡❡♥❞❡ ❛ ár❡❛ ✐♥t❡r♥❛ ❛ ✉♠ ❝ír❝✉❧♦ ❞❡ r❛✐♦ ε✱ ❝❡♥tr❛❞♦ ♥♦ r♦❜ô✳❉❡ss❡ ♠♦❞♦✱ r♦❜ôs s✐t✉❛❞♦s ❛ ✉♠❛ ❞✐stâ♥❝✐❛ ✐♥❢❡r✐♦r ❛ ε sã♦ ❝♦♥s✐❞❡r❛❞♦s ✈✐③✐♥❤♦s✳ j i k◆❡st❡ ❡①❡♠♣❧♦✱ R ♣❛rt✐❝✐♣❛ t❛♥t♦ ❞❛ ✈✐③✐♥❤❛♥ç❛ N q✉❛♥t♦ ❞❛ ✈✐③✐♥❤❛♥ç❛ N ✳♣♦r ✉♠ r♦❜ô ♣♦❞❡♠ s❡r ❞✐ss❡♠✐♥❛❞❛s ❞❡ ♠♦❞♦ ❛ ♣r♦✈❡r ✐♥❢♦r♠❛çõ❡s ♣❛r❛ ♦s ❞❡♠❛✐s j r♦❜ôs ❞❡ s✉❛ ✈✐③✐♥❤❛♥ç❛✳ ❈♦♥❢♦r♠❡ ♣♦❞❡ s❡r ♦❜s❡r✈❛❞♦✱ ♥❛ ❋✐❣✉r❛ ✷✳✷ ♦ r♦❜ô R♣❛rt✐❝✐♣❛ t❛♥t♦ ❞❛ ✈✐③✐♥❤❛♥ç❛ N i q✉❛♥t♦ ❞❛ ✈✐③✐♥❤❛♥ç❛ N k ✱ ❞❡ ♠♦❞♦ q✉❡ ❛s ✐♥❢♦r♠❛çõ❡s❞✐ss❡♠✐♥❛❞❛s ♣♦r R i ❡ R k ❡st❛rã♦ ❛❝❡ssí✈❡✐s ❛ R j ✳ N1ε R 1 13 13 φ ρ R 3R 2 ❋✐❣✉r❛ ✷✳✸✿ ■♥t❡r❛çã♦ ❡♥tr❡ r♦❜ôs ❡♠ ✉♠❛ ♠❡s♠❛ ✈✐③✐♥❤❛♥ç❛✳ ◆❛ ✈✐③✐♥❤❛♥ç❛ ♦s r♦❜ôs♣♦❞❡♠ ✐♥t❡r❛❣✐r ✭✈✐❛ s❡♥s♦r❡s✮ ❡ tr♦❝❛r ✐♥❢♦r♠❛çõ❡s ✭✈✐❛ ❝♦♠✉♥✐❝❛çã♦✮✳ ✶✵❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ✷✳✷ ❙✐st❡♠❛s ▼✉❧t✐rr♦❜ót✐❝♦s ❈♦♦♣❡r❛t✐✈♦s ❉✐✈❡rs♦s tr❛❜❛❧❤♦s✱ ❞❡♥tr❡ ❡❧❡s ❬Pr❡♠✈✉t✐ ✫ ❨✉t❛✱ ✶✾✾✵❪✱ ❬❉✉❞❡❦ ❡t ❛❧✳✱ ✶✾✾✻❪✱ ❬❈❛♦❡t ❛❧✳✱ ✶✾✾✼❪✱ ❬❋❛r✐♥❡❧❧✐ ❡t ❛❧✳✱ ✷✵✵✹❪ ❡ ❬P❛r❦❡r✱ ✷✵✵✽❪✱ tê♠ ♣r♦♣♦st♦ t❛①♦♥♦♠✐❛s ♣❛r❛❝❛r❛❝t❡r✐③❛r s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s q✉❡ ❡♠♣r❡❣❛♠ ❛❧❣✉♠ t✐♣♦ ❞❡ ❝♦♠♣♦rt❛♠❡♥t♦❝♦♦♣❡r❛t✐✈♦ ♥❛ ❡①❡❝✉çã♦ ❞❛s t❛r❡❢❛s✳ ❚❛✐s t❛①♦♥♦♠✐❛s tê♠ s✐❞♦ ❛♣r❡s❡♥t❛❞❛s ♥❛ ❢♦r♠❛❞❡ ❡✐①♦s q✉❡ ✐♥❝♦r♣♦r❛♠ ♣r♦❜❧❡♠❛s ❞❡ ♣❡sq✉✐s❛ ❡♠ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦✳ ❆ ❞✐s❝✉ssã♦❛♣r❡s❡♥t❛❞❛ ❛ s❡❣✉✐r ❝♦♥t❡♠♣❧❛ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s ✭t❛♠❜é♠❞❡♥♦♠✐♥❛❞♦s ♠✉❧t✐rr♦❜ôs✮ ♠❛✐s r❡❧❡✈❛♥t❡s ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ■♥ú♠❡r❛s ♣❡sq✉✐s❛s tê♠ ❡①♣❧♦r❛❞♦ ❛s ♣♦t❡♥❝✐❛❧✐❞❛❞❡s ❞❡ s❡ ✉t✐❧✐③❛r ❣r✉♣♦s ❞❡ r♦❜ôs ♣❛r❛ s♦❧✉❝✐♦♥❛r ♦s ♠❛✐s ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ t❛r❡❢❛s✳ ❆ ✉t✐❧✐③❛çã♦ ❞❡ s✐st❡♠❛s♠✉❧t✐rr♦❜ót✐❝♦s t❡♠ s✐❞♦ ♠♦t✐✈❛❞❛ ♣❡❧❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ♠❡❧❤♦r✐❛ ♥♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ s✐st❡♠❛ ❡ ❛ ❞✐✈✐sã♦ ❞❡ t❛r❡❢❛s✱ ♦ q✉❡ t❡♥❞❡ ❛ ♠❛①✐♠✐③❛r ❛ ✉t✐❧✐③❛çã♦ ❞♦s r❡❝✉rs♦s❞✐s♣♦♥í✈❡✐s✳ ❊str❛té❣✐❛s ❝♦♦♣❡r❛t✐✈❛s ♣♦ss✐❜✐❧✐t❛♠ q✉❡ ✉♠ ❣r✉♣♦ ❞❡ r♦❜ôs ❡①❡❝✉t❡ t❛r❡❢❛s ❝✉❥❛ ❝♦♠♣❧❡①✐❞❛❞❡ s❡❥❛ s✉♣❡r✐♦r às ❝❛♣❛❝✐❞❛❞❡s ✐♥❞✐✈✐❞✉❛✐s ❞❡ss❡s r♦❜ôs✳ ❖❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠ ú♥✐❝♦ r♦❜ô ❡s♣❡❝✐❛❧✐③❛❞♦ ♣❛r❛ ❧✐❞❛r ❝♦♠ ♦s ❞✐✈❡rs♦s ❛s♣❡❝t♦s ❞❡❞❡t❡r♠✐♥❛❞❛ t❛r❡❢❛ ♣♦❞❡✱ ♣♦r ✈❡③❡s✱ ✐♥❝r❡♠❡♥t❛r s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ♦ ❝✉st♦ ❡ ♦ t❡♠♣♦❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ s✐st❡♠❛✳ ❆❧é♠ ❞✐ss♦✱ t❛❧ ❡s♣❡❝✐❛❧✐③❛çã♦ ♣♦❞❡ ❞✐✜❝✉❧t❛r ♦ ❡♠♣r❡❣♦❞♦ r❡s♣❡❝t✐✈♦ r♦❜ô ❡♠ ♦✉tr♦s t✐♣♦s t❛r❡❢❛s✱ ❡①✐❣✐♥❞♦ ❛ ❛❞❛♣t❛çã♦ ♦✉ r❡❝♦♥str✉çã♦ ❞♦♠❡s♠♦✳ ❊♠ ❝♦♥tr❛♣❛rt✐❞❛✱ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❣r✉♣♦s ❞❡ r♦❜ôs ♠❛✐s s✐♠♣❧❡s ❡❞❡ ♠❡♥♦r ❝✉st♦ ✈✐❛❜✐❧✐③❛♠ ❛♠♣❧✐❛r ❛ r♦❜✉st❡③✱ ❛ ✢❡①✐❜✐❧✐❞❛❞❡ ❡ ❛ ❝♦♥✜❛❜✐❧✐❞❛❞❡ ❞♦ s✐st❡♠❛✱ ❞❡ ♠♦❞♦ ❛ ♣❡r♠✐t✐r s♦❧✉❝✐♦♥❛r ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ t❛r❡❢❛s ❝♦♠ ♥í✈❡✐s ✈❛r✐❛❞♦s❞❡ ❝♦♠♣❧❡①✐❞❛❞❡✳ ❙✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s tê♠ ♦❜t✐❞♦ r❡s✉❧t❛❞♦s ♠❛✐s r❡❧❡✈❛♥t❡s q✉❛♥❞♦ s❡✉s ❝♦♠✲♣♦♥❡♥t❡s ❝♦♦♣❡r❛♠ ♥❛ ❡①❡❝✉çã♦ ❞❛ t❛r❡❢❛✳ ❋❛r✐♥❡❧❧✐ ❡t ❛❧✳ ❬✷✵✵✹❪ ❝❛r❛❝t❡r✐③❛♠ ♦ ❝♦♠♣♦r✲ t❛♠❡♥t♦ ❝♦♦♣❡r❛t✐✈♦ ❝♦♠♦ ❛q✉❡❧❡ ❡♠ q✉❡ ♦s r♦❜ôs ❛t✉❛♠ ❝♦♥❥✉♥t❛♠❡♥t❡ ♣❛r❛ ❡①❡❝✉t❛r❛❧❣✉♠❛ t❛r❡❢❛ ❣❧♦❜❛❧✳ P❛r❦❡r ❬✷✵✵✽❪ ❛♠♣❧✐❛ ❡ss❛ ❞❡✜♥✐çã♦ ♥♦ s❡♥t✐❞♦ ❞❡ ❝❛r❛❝t❡r✐③❛r ❛❝♦♦♣❡r❛çã♦ ❝♦♠♦ ❛ ❛t✉❛çã♦ ❝♦♥❥✉♥t❛ ❡♠ q✉❡ ♦s ❡♥✈♦❧✈✐❞♦s ♣♦ss✉❡♠ ❝✐ê♥❝✐❛ ❞❛ ❡①✐stê♥✲❝✐❛ ❞♦s ❞❡♠❛✐s✱ ❞❡ ♠♦❞♦ q✉❡ ❛s ❛çõ❡s ❞❡ ❝❛❞❛ ✐♥t❡❣r❛♥t❡ ❝♦♥tr✐❜✉✐ ♣♦s✐t✐✈❛♠❡♥t❡ ♣❛r❛ ♦ r❡♥❞✐♠❡♥t♦ ❞♦ ❣r✉♣♦✳ ❆❧é♠ ❞✐ss♦✱ ♦ ♦❜❥❡t✐✈♦ ❣❧♦❜❛❧ é ❝♦♠♣❛rt✐❧❤❛❞♦ ❡♥tr❡ ♦s ✐♥t❡❣r❛♥✲t❡s ❞♦ s✐st❡♠❛✳ ❈❛♦ ❡t ❛❧✳ ❬✶✾✾✼❪ ❝♦♥❝❡✐t✉❛♠ ❛ ❝♦♦♣❡r❛çã♦ ❞❡ ♠♦❞♦ s❡♠❡❧❤❛♥t❡ à P❛r❦❡r✱♠❛s r❡❢♦rç❛♠ ♦ ❢❛t♦ ❞❡ q✉❡ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s ❛♣r❡s❡♥t❛♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❝♦♦✲♣❡r❛t✐✈♦ q✉❛♥❞♦ ♦❝♦rr❡ ✉♠❛ ❛♠♣❧✐❛çã♦ ♥❛ ✉t✐❧✐❞❛❞❡ t♦t❛❧ ❞♦ s✐st❡♠❛✱ ❝❛r❛❝t❡r✐③❛♥❞♦ ♦ q✉❡ s❡r✐❛ ❛❧❣✉♠ t✐♣♦ ❞❡ s✐♥❡r❣✐❛✳ ❈♦♥❝❡✐t♦ s✐♠✐❧❛r é ❛♣r❡s❡♥t❛❞♦ ❡♠ ❬Pr❡♠✈✉t✐ ✫ ❨✉t❛✱✶✾✾✵❪ s♦❜ ❛ ❞❡♥♦♠✐♥❛çã♦ ❞❡ ❝♦♦♣❡r❛çã♦ ❛t✐✈❛✱ ❡♥q✉❛♥t♦ q✉❡ ❛ ❞❡✜♥✐çã♦ ❞❡ ❝♦♦♣❡r❛çã♦♥ã♦ ❛t✐✈❛ s❡ ❛ss❡♠❡❧❤❛ àq✉❡❧❛ ❞❡ ❝♦♠♣♦rt❛♠❡♥t♦ ❝♦♦♣❡r❛t✐✈♦ ❛♣r❡s❡♥t❛❞❛ ♣♦r ❋❛r✐♥❡❧❧✐❡t ❛❧✳ ❬✷✵✵✹❪✱ ♥❛ q✉❛❧ ❛ ❝♦♦♣❡r❛çã♦ é ❝❛r❛❝t❡r✐③❛❞❛ ♣❡❧❛ s✐♠♣❧❡s ❛t✉❛çã♦ ❝♦♥❥✉♥t❛✳ ✷✳✷✳ ❙✐st❡♠❛s ▼✉❧t✐rr♦❜ót✐❝♦s ❈♦♦♣❡r❛t✐✈♦s ✶✶❆ ✉t✐❧✐③❛çã♦ ❞❡ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s t❡♠ s✐❞♦ ♠♦t✐✈❛❞❛ ♣❡❧❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ r❡❞✉çã♦ ❞❡ ❝✉st♦s ❡ ❝♦♠♣❧❡①✐❞❛❞❡ ❛ss♦❝✐❛❞❛ à ❝♦♥❝❡♣çã♦ ❞❛s ❡♥t✐❞❛❞❡s q✉❡ ❝♦♠✲♣õ❡♠ t❛✐s s✐st❡♠❛s✱ ❛❧é♠ ❞❛ ✢❡①✐❜✐❧✐❞❛❞❡ ❞♦ ♠❡s♠♦ ♣❛r❛ ❡①❡❝✉t❛r t❛r❡❢❛s ❞✐st✐♥t❛s✳◆♦ ❡♥t❛♥t♦✱ ♥♦✈❛s q✉❡stõ❡s s✉r❣❡♠ ♥❡ss❡ ❝♦♥t❡①t♦✱ ✉♠❛ ✈❡③ q✉❡ s❡ ❢❛③ ♥❡❝❡ssár✐♦ ❡s✲ t❛❜❡❧❡❝❡r ❡str❛té❣✐❛s ♣❛r❛ ♦ ❝♦♥tr♦❧❡ ❡ ❛ ♣r♦♣❛❣❛çã♦ ❞❡ ✐♥❢♦r♠❛çõ❡s ❡♥tr❡ ❛s ❡♥t✐❞❛❞❡s❞♦ ❣r✉♣♦✱ ✈✐st♦ q✉❡ ❡ss❛s ✐♥❢♦r♠❛çõ❡s ♣♦❞❡♠ ❡st❛r ❞✐str✐❜✉í❞❛s ♥♦ s✐st❡♠❛✳ ❚❛r❡❢❛s q✉❡ sã♦ ✐♥❡r❡♥t❡♠❡♥t❡ ❞✐str✐❜✉í❞❛s ♥♦ t❡♠♣♦✱ ♥♦ ❡s♣❛ç♦ ♦✉ ❡♠ s✉❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡ sã♦♣♦t❡♥❝✐❛❧♠❡♥t❡ ♠❡❧❤♦r s♦❧✉❝✐♦♥❛❞❛s ♣♦r s✐st❡♠❛s ♠✉❧t✐rr♦❜ôs✳ ❙✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s ♣♦❞❡♠ s❡r ❝❛r❛❝t❡r✐③❛❞♦s ❝♦♠♦ ❤♦♠♦❣ê♥❡♦s ♦✉ ❤❡t❡r♦✲❣ê♥❡♦s✳ ❙✐st❡♠❛s ❤♦♠♦❣ê♥❡♦s sã♦ ❝♦♠♣♦st♦s ♣♦r r♦❜ôs ❝♦♠ ♠❡s♠❛s ❝❛r❛❝t❡ríst✐❝❛s❢ís✐❝❛s ❡ q✉❡ ❛♣r❡s❡♥t❛♠ ❝♦♠♣♦rt❛♠❡♥t♦s ❝♦♠♣❛tí✈❡✐s ♥♦ ♥í✈❡❧ ❞❛s ✐♥t❡r❛çõ❡s✳ ❉❡ss❡♠♦❞♦✱ r♦❜ôs q✉❡ ❝♦♠♣❛rt✐❧❤❛♠ ❛ ♠❡s♠❛ ❝♦♥st✐t✉✐çã♦ ❢ís✐❝❛✱ ♣♦ré♠ ❛♣r❡s❡♥t❛♠ ❝♦♠✲♣♦rt❛♠❡♥t♦s ❡ ❝❛♣❛❝✐❞❛❞❡s ❞✐st✐♥t♦s✱ ♣♦❞❡♠ s❡r ❝♦♥s✐❞❡r❛❞♦s ❤❡t❡r♦❣ê♥❡♦s✳ ❆ s✐♠♣❧❡s❡①✐stê♥❝✐❛ ❞❡ s✐st❡♠❛s ❞❡ ❝♦♥tr♦❧❡ ❞✐st✐♥t♦s✱ ♠❡s♠♦ ❡♠ r♦❜ôs ❝♦♠ ❤❛r❞✇❛r❡s ❝♦♠♣❛tí✲✈❡✐s✱ é s✉✜❝✐❡♥t❡ ♣❛r❛ ❝❛r❛❝t❡r✐③❛r ❛ ❤❡t❡r♦❣❡♥❡✐❞❛❞❡ ❞♦ ❣r✉♣♦✳ ●r✉♣♦s ❤❡t❡r♦❣ê♥❡♦s tê♠ ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ❡①♣❧♦r❛r ❛s ❝♦♠♣❡tê♥❝✐❛s ❡s♣❡❝✐❛❧✐③❛❞❛s ❞❡ s❡✉s ♠❡♠❜r♦s ♥❛❡①❡❝✉çã♦ ❞❡ t❛r❡❢❛s✳ ❉❡ss❡ ♠♦❞♦✱ ❛ ❛t✉❛çã♦ ❝♦♦♣❡r❛t✐✈❛ t✐r❛ ♣r♦✈❡✐t♦ ❞❡ss❛ ❞✐✈❡rs✐✲❞❛❞❡ ❡ ❡①♣❛♥❞❡ ❛s ❝❛♣❛❝✐❞❛❞❡s ✐♥❞✐✈✐❞✉❛✐s ❞♦s r♦❜ôs ❝♦♠ ❛ ❝♦♥s❡q✉❡♥t❡ ❣❡r❛çã♦ ❞❡❝♦♠♣♦rt❛♠❡♥t♦s ❝♦❧❡t✐✈♦s ♠❛✐s ❡❧❛❜♦r❛❞♦s✳ ◆♦ ❡♥t❛♥t♦✱ ♦ ❝♦♥tr♦❧❡ ❡ ❛ ❛❧♦❝❛çã♦ ❞❡ t❛r❡❢❛s ♣♦❞❡♠ s❡ t♦r♥❛r ✉♠ t❛♥t♦ ❝♦♠♣❧❡①♦s✱ ♣♦✐s ♥❡♠ t♦❞♦s ♦s r♦❜ôs ❡st❛rã♦ ❛♣t♦s ❛❡①❡❝✉t❛r ♦s ❞✐✈❡rs♦s t✐♣♦s ❞❡ ❝♦♠♣♦rt❛♠❡♥t♦s✳ ❖ ❝♦♥tr♦❧❡ ❞❡ ✉♠ ❣r✉♣♦ ❞❡ r♦❜ôs é ❡st❛❜❡❧❡❝✐❞♦ ❡♠ ❢✉♥çã♦ ❞♦ t✐♣♦ ❞❡ ✐♥❢♦r♠❛çã♦❞✐s♣♦♥í✈❡❧✱ q✉❡ ♣♦❞❡ s❡r ❧♦❝❛❧ ♦✉ ❣❧♦❜❛❧✳ ❉♦✐s t✐♣♦s ❞❡ ✐♥❢♦r♠❛çã♦ r❡❧❡✈❛♥t❡s ♣❛r❛ ❛❞❡✜♥✐çã♦ ❞♦ ❝♦♥tr♦❧❡ sã♦ ❞✐s❝✉t✐❞♦s ❡♠ ❬P❛r❦❡r✱ ✶✾✾✸❪ ❡ ❝♦♠♣r❡❡♥❞❡♠ ♦ ♦❜❥❡t✐✈♦ ❞♦ s✐st❡♠❛ ❡ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❛ r❡s♣❡✐t♦ ❞♦ ❡st❛❞♦ ❞♦ ❛♠❜✐❡♥t❡✳ ❖❜❥❡t✐✈♦s ❣❧♦❜❛✐s ✐♥❞✐❝❛♠ ❛t❛r❡❢❛ ❛ s❡r ❡①❡❝✉t❛❞❛ ♣❡❧♦ ❣r✉♣♦✱ ❡♥q✉❛♥t♦ q✉❡ ♦❜❥❡t✐✈♦s ❧♦❝❛✐s ❡stã♦ ❛ss♦❝✐❛❞♦s ❛ s✉❜✲ t❛r❡❢❛s ✐♥❞✐✈✐❞✉❛✐s ♦✉ r❡str✐t❛s ❛ ♣❛rt❡ ❞♦ ❣r✉♣♦✳ ❖s ♦❜❥❡t✐✈♦s ❣❧♦❜❛✐s sã♦ ♥♦r♠❛❧♠❡♥t❡✐♠♣♦st♦s ❛♦ ❣r✉♣♦ ♣♦r ✉♠❛ ❡♥t✐❞❛❞❡ ❝❡♥tr❛❧✐③❛❞♦r❛✱ t❛✐s ❝♦♠♦ ✉♠ ❛❣❡♥t❡ ❡①t❡r♥♦ ♦✉✉♠ ❧í❞❡r✳ ❖ ❝♦♥❤❡❝✐♠❡♥t♦ ❞♦ ❡st❛❞♦ ❞♦ ❛♠❜✐❡♥t❡ ♣♦❞❡ s❡r ❛❞q✉✐r✐❞♦ t❛♥t♦ ♣♦r ♠❡✐♦❞❛s ❝❛♣❛❝✐❞❛❞❡s s❡♥s♦r✐❛✐s ❞♦s r♦❜ôs q✉❛♥t♦ ♣♦r ✐♥t❡r♠é❞✐♦ ❞❡ ✉♠❛ ❡♥t✐❞❛❞❡ ❡①t❡r♥❛✳■♥❢♦r♠❛çõ❡s ❧♦❝❛✐s sã♦ ♥♦r♠❛❧♠❡♥t❡ ♦❜t✐❞❛s ❞✉r❛♥t❡ ❛ ❡①❡❝✉çã♦ ❞♦ s✐st❡♠❛ ✈✐❛ s❡♥s♦r❡s✱♦s q✉❛✐s r❡✢❡t❡♠ ♦ ❡st❛❞♦ ❞♦ ❛♠❜✐❡♥t❡ ♥❛s ♣r♦①✐♠✐❞❛❞❡s ❞♦ r♦❜ô✳ P♦r ♦✉tr♦ ❧❛❞♦✱✐♥❢♦r♠❛çõ❡s ❣❧♦❜❛✐s ♣♦❞❡♠ ❡st❛r ❞✐s♣♦♥í✈❡✐s ❞✉r❛♥t❡ ❛ ❝♦♥❝❡♣çã♦ ❞♦ s✐st❡♠❛✱ s♦♠❡♥t❡♥♦ ❞❡❝♦rr❡r ❞❛ ❡①❡❝✉çã♦ ❞♦ ♠❡s♠♦ ♦✉ ❡♠ ❛♠❜♦s ♦s ❝❛s♦s✳ ❉♦✐s t✐♣♦s ❞❡ ❛rq✉✐t❡t✉r❛s ❞❡ ❝♦♥tr♦❧❡ tê♠ s✐❞♦ ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞♦s ❡♠ s✐st❡✲♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s✿ ❝♦♥tr♦❧❡ ❝❡♥tr❛❧✐③❛❞♦ ❡ ❝♦♥tr♦❧❡ ❞❡s❝❡♥tr❛❧✐③❛❞♦✳ ❆rq✉✐t❡t✉r❛s ❞❡❝♦♥tr♦❧❡ ❝❡♥tr❛❧✐③❛❞♦ sã♦ ❝❛r❛❝t❡r✐③❛❞❛s ♣❡❧❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠ ú♥✐❝♦ ❛❣❡♥t❡ ❞❡ ❝♦♥tr♦❧❡ ✶✷❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ✭❧í❞❡r✮ r❡s♣♦♥sá✈❡❧ ♣♦r ❣r❛♥❞❡ ♣❛rt❡ ❞♦ ♣r♦❝❡ss♦ ❞❡ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦✳ ❉❡✈✐❞♦ ❛♦ ❝❛✲ rát❡r ❝❡♥tr❛❧✐③❛❞♦r ❞♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝♦♥tr♦❧❡✱ ❛❧❣✉♥s ❝♦♥✢✐t♦s ♣♦❞❡♠ s❡r ✐❞❡♥t✐✜❝❛❞♦s❡ ♣r❡✈✐❛♠❡♥t❡ r❡s♦❧✈✐❞♦s✳ ❆ ❡①✐stê♥❝✐❛ ❞❡ ✉♠❛ ✉♥✐❞❛❞❡ ❝❡♥tr❛❧✐③❛❞♦r❛ tr❛③ ❛ ✈❛♥t❛❣❡♠❞❡ ❝♦♥s♦❧✐❞❛r ❛s ✐♥❢♦r♠❛çõ❡s ❞♦ ❣r✉♣♦ ❡♠ ✉♠ ú♥✐❝♦ ❧♦❝❛❧✱ ♦ q✉❡ ❢❛❝✐❧✐t❛ ♦ ♣r♦❝❡ss♦❞❡ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦✳ ◆♦ ❡♥t❛♥t♦✱ t❛❧ ❛rq✉✐t❡t✉r❛ ❛♣r❡s❡♥t❛ ❜❛✐①❛ r♦❜✉st❡③ ❡ t♦❧❡✲ râ♥❝✐❛ ❛ ❢❛❧❤❛s✱ ✉♠❛ ✈❡③ q✉❡ ❛ ✐♥♦♣❡râ♥❝✐❛ ❞❡ss❛ ✉♥✐❞❛❞❡ ❝❡♥tr❛❧✐③❛❞♦r❛ ❝♦♠♣r♦♠❡t❡❝♦♠♣❧❡t❛♠❡♥t❡ ❛ ❡①❡❝✉çã♦ ❞❛ t❛r❡❢❛✳ ❋❛r✐♥❡❧❧✐ ❡t ❛❧✳ ❬✷✵✵✹❪ ❝❛r❛❝t❡r✐③❛♠ ❛ ❝♦♦r❞❡♥❛çã♦ ❝♦♠♦ ✉♠ t✐♣♦ ❞❡ ❝♦♦♣❡r❛çã♦ ❡♠ q✉❡ ❛s ❛çõ❡s ❡①❡❝✉t❛❞❛s ♣♦r ❝❛❞❛ ❛❣❡♥t❡ ❡♠ ✉♠ ❣r✉♣♦ ❧❡✈❛♠ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ❛s ❛çõ❡s❡①❡❝✉t❛❞❛s ♣❡❧♦s ❞❡♠❛✐s ❛❣❡♥t❡s ❞❡ss❡ ❣r✉♣♦✱ ❞❡ ♠♦❞♦ ❛ ❡st❛❜❡❧❡❝❡r ✉♠❛ ♦♣❡r❛çã♦❝♦❡r❡♥t❡ ❡ ❝♦♠ ❛❧t♦ ❞❡s❡♠♣❡♥❤♦✳ ◆❡ss❡ ❝♦♥t❡①t♦✱ ❋❛r✐♥❡❧❧✐ ❡t ❛❧✳ ❛♣r❡s❡♥t❛♠ ✉♠❛ s✉❜❝❧❛ss✐✜❝❛çã♦ ♣❛r❛ ❛s ❛rq✉✐t❡t✉r❛s ❞❡ ❝♦♥tr♦❧❡ ❝❡♥tr❛❧✐③❛❞♦ ♥♦ s❡♥t✐❞♦ ❞❡ ❝❛r❛❝t❡r✐③á✲❧❛s ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❢♦r♠❛ ❞❡ ❛t✉❛çã♦ ❞❛ ✉♥✐❞❛❞❡ ❝❡♥tr❛❧✐③❛❞♦r❛ ✭❧í❞❡r✮✳ ❈♦♥tr♦❧❡❝❡♥tr❛❧✐③❛❞♦ ❢♦rt❡ ✭str♦♥❣✮ é ❛ ❞❡♥♦♠✐♥❛çã♦ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❝❛r❛❝t❡r✐③❛r s✐st❡♠❛s ♥♦s q✉❛✐s ❛ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦ é ❢❡✐t❛ ♣♦r ✉♠ ♠❡s♠♦ ❧í❞❡r ❞✉r❛♥t❡ t♦❞❛ ❛ ❡①❡❝✉çã♦ ❞❛t❛r❡❢❛✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ♦ t❡r♠♦ ❝♦♥tr♦❧❡ ❝❡♥tr❛❧✐③❛❞♦ ❢r❛❝♦ ✭✇❡❛❦✮ ❝❛r❛❝t❡r✐③❛ s✐st❡♠❛s❡♠ q✉❡ ♠❛✐s ❞❡ ✉♠ ❛❣❡♥t❡ ❛ss✉♠❡ ♦ ♣❛♣❡❧ ❞❡ ❧í❞❡r ❞✉r❛♥t❡ ❛ ♠✐ssã♦✳ ❆rq✉✐t❡t✉r❛s ❞❡s❝❡♥tr❛❧✐③❛❞❛s t❡♥❞❡♠ ❛ s❡r ♠❛✐s r♦❜✉st❛s ❡ ♠❡♥♦s s✉s❝❡tí✈❡✐s ❛❢❛❧❤❛s✱ ❞❡✈✐❞♦ à ♣♦✉❝❛ ❞❡♣❡♥❞ê♥❝✐❛ ❞❡ ✉♠❛ ú♥✐❝❛ ✉♥✐❞❛❞❡ ❝❡♥tr❛❧✐③❛❞♦r❛ ♥♦ s✐st❡♠❛✳❈❛♦ ❡t ❛❧✳ ❬✶✾✾✼❪ ❝❧❛ss✐✜❝❛♠ ❛s ❛rq✉✐t❡t✉r❛s ❞❡s❝❡♥tr❛❧✐③❛❞❛s ❝♦♠♦ ❞✐str✐❜✉í❞❛s ❡ ❤✐❡✲ rárq✉✐❝❛s✳ ◆❛ ❛❜♦r❞❛❣❡♠ ❞✐str✐❜✉í❞❛✱ t♦❞♦s ♦s ❛❣❡♥t❡s sã♦ ✐❣✉❛✐s ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦❛♦ ❝♦♥tr♦❧❡✱ ❡♥q✉❛♥t♦ q✉❡ ♥❛ ❛❜♦r❞❛❣❡♠ ❤✐❡rárq✉✐❝❛✱ ♦ ❣r✉♣♦ é ❞✐✈✐❞✐❞♦ ❡ ♦ ❝♦♥tr♦❧❡é ❢❡✐t♦ ❧♦❝❛❧♠❡♥t❡ ♥♦ â♠❜✐t♦ ❞♦s s✉❜✲❣r✉♣♦s✳ ◆❛s ❛❜♦r❞❛❣❡♥s ❞❡s❝❡♥tr❛❧✐③❛❞❛s✱ ♦s❛❣❡♥t❡s sã♦ ❝♦♠♣❧❡t❛♠❡♥t❡ ❛✉tô♥♦♠♦s ♥♦ ♣r♦❝❡ss♦ ❞❡ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦ ❡ ✉t✐❧✐③❛♠✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s ♣❛r❛ ❛♠♣❧✐❛r s❡✉s ❝♦♥❤❡❝✐♠❡♥t♦s ❛ r❡s♣❡✐t♦ ❞♦ ❡st❛❞♦ ❞♦ s✐st❡♠❛✱ s❡❥❛ ✈✐❛ s❡♥s♦r❡s ♦✉ ✉t✐❧✐③❛♥❞♦ ❛❧❣✉♠❛ ❢♦r♠❛ ❞❡ ❝♦♠✉♥✐❝❛çã♦✳ ▼❡❝❛♥✐s♠♦s ❞❡ ❝♦♠✉♥✐❝❛çã♦ ✈✐❛❜✐❧✐③❛♠ ❛ ✐♥t❡r❛çã♦ ❡♥tr❡ ♦s ❛❣❡♥t❡s ❡♠ ✉♠ ❣r✉♣♦✳❊♠ s✐st❡♠❛s ❝♦♦♣❡r❛t✐✈♦s✱ ❛ tr♦❝❛ ❞❡ ✐♥❢♦r♠❛çõ❡s ♣♦ss✐❜✐❧✐t❛ ❡st❡♥❞❡r s✐❣♥✐✜❝❛t✐✈❛✲♠❡♥t❡ ❛s ❝❛♣❛❝✐❞❛❞❡s ✐♥❞✐✈✐❞✉❛✐s ❞♦s ❛❣❡♥t❡s✳ ❉❡♥tr❡ ❛s ❢♦r♠❛s ❞❡ ❝♦♠✉♥✐❝❛çã♦ ♠❛✐s✉t✐❧✐③❛❞❛s ♥❡ss❡s s✐st❡♠❛s✱ t❡♠✲s❡ ❛ ❝♦♠✉♥✐❝❛çã♦ ❞✐r❡t❛ ❡ ❛ ❝♦♠✉♥✐❝❛çã♦ ✐♥❞✐r❡t❛ ❬❈❛♦❡t ❛❧✳✱ ✶✾✾✼❀ ❋❛r✐♥❡❧❧✐ ❡t ❛❧✳✱ ✷✵✵✹❀ ▼♦❤❛♥ ✫ P♦♥♥❛♠❜❛❧❛♠✱ ✷✵✵✾❪✳ ◆❛ ❝♦♠✉♥✐❝❛çã♦❞✐r❡t❛✱ t❛♠❜é♠ r❡❢❡r❡♥❝✐❛❞❛ ❝♦♠♦ ❡①♣❧í❝✐t❛✱ ♠❡♥s❛❣❡♥s sã♦ ✉t✐❧✐③❛❞❛s ❝♦♠♦ ♠❡✐♦ ♣❛r❛ s❡ tr♦❝❛r ✐♥❢♦r♠❛çã♦✳ ❆s ♠❡♥s❛❣❡♥s ♣♦❞❡♠ s❡r ❞✐r✐❣✐❞❛s ♦✉ ♥ã♦ ❛ ❞❡st✐♥❛tár✐♦s ❡s♣❡❝í✲✜❝♦s✳ ▼❡♥s❛❣❡♥s ❞✐r✐❣✐❞❛s ♣♦ss✉❡♠ ♦ ❡♥❞❡r❡ç♦ ❞♦ ❞❡st✐♥❛tár✐♦ ❡①♣❧✐❝✐t❛♠❡♥t❡ ❞❡✜♥✐❞♦❡♠ s❡✉ ❝❛❜❡ç❛❧❤♦✱ ♦ q✉❡ ♣♦ss✐❜✐❧✐t❛ ❛ ❝r✐❛çã♦ ❞❡ s✉❜❣r✉♣♦s✳ ❆♣❡s❛r ❞✐ss♦✱ ❡ss❡ t✐♣♦ ❞❡❝♦♠✉♥✐❝❛çã♦ ♣♦❞❡ ❝♦♠♣r♦♠❡t❡r ❛ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ ❞♦ s✐st❡♠❛✱ ✉♠❛ ✈❡③ q✉❡ ❛ ✐♥❝❧✉sã♦♦✉ ❡①❝❧✉sã♦ ❞❡ ❡❧❡♠❡♥t♦s ♥♦ ❣r✉♣♦ ❡①✐❣❡ ❛❞❛♣t❛çã♦ ♥❛ ♣♦❧ít✐❝❛ ❞❡ tr♦❝❛ ❞❡ ♠❡♥s❛❣❡♥s✳ ✷✳✷✳ ❙✐st❡♠❛s ▼✉❧t✐rr♦❜ót✐❝♦s ❈♦♦♣❡r❛t✐✈♦s ✶✸▼❡♥s❛❣❡♥s ♥ã♦ ❞✐r✐❣✐❞❛s✱ t❛✐s ❝♦♠♦ ❜r♦❛❞❝❛st✱ sã♦ ✉♠❛ ❢♦r♠❛ ❞❡ s✉♣❡r❛r ❡ss❛s ❧✐♠✐t❛✲çõ❡s✱ ♣❡r♠✐t✐♥❞♦ ♠❛✐♦r ✢❡①✐❜✐❧✐❞❛❞❡ ❡ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ ❛♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝♦♠✉♥✐❝❛çã♦✳ ❆ ❝♦♠✉♥✐❝❛çã♦ ✐♥❞✐r❡t❛ é ❝❛r❛❝t❡r✐③❛❞❛ ♣❡❧❛ ❛✉sê♥❝✐❛ ❞❡ tr♦❝❛ ❞❡ ♠❡♥s❛❣❡♥s✳◆❡ss❛ ❛❜♦r❞❛❣❡♠ ♦ ♣ró♣r✐♦ ❛♠❜✐❡♥t❡ ❢ís✐❝♦ s❡ ❛♣r❡s❡♥t❛ ❝♦♠♦ ♠❡✐♦ ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❡❛s ✐♥❢♦r♠❛çõ❡s sã♦ ♦❜t✐❞❛s ✈✐❛ s❡♥s♦r❡s✳ ❉❡♥tr❡ ❛s ❢♦r♠❛s ❞❡ ❝♦♠✉♥✐❝❛çã♦ ✐♥❞✐r❡t❛✱ t❡♠✲s❡✿ ❛ ♣❡r❝❡♣çã♦ ❞❡ ❛çõ❡s ❡ ❝♦♠♣♦rt❛♠❡♥t♦s ❞❡ ♦✉tr♦s ❛❣❡♥t❡s❀ ❡ ❛ ❡st✐❣♠❡r❣✐❛✳❊ss❡s t✐♣♦s ❞❡ ❝♦♠✉♥✐❝❛çã♦ sã♦ r❡❧❛❝✐♦♥❛❞♦s ❛ ✐♥t❡r❛çõ❡s ❧♦❝❛✐s ♥♦s q✉❛✐s ♦s ❛❣❡♥✲ t❡s s❡ ❝♦♠✉♥✐❝❛♠ ♣♦r ✐♥t❡r♠é❞✐♦ ❞❛s s❡♥s❛çõ❡s ♣r♦✈✐❞❛s ♣♦r ❛❧❣✉♠ ✐t❡♠ ♠❛♥✐♣✉❧❛❞♦❝♦♥❥✉♥t❛♠❡♥t❡✱ ♣❡❧❛ ♦❜s❡r✈❛çã♦ ❞❡ ❝♦♠♣♦rt❛♠❡♥t♦s ❡①♣❧í❝✐t♦s ♦✉ ♣❡❧❛ ♣❡r❝❡♣çã♦ ❡♠♦❞✐✜❝❛çã♦ ❞♦ ❛♠❜✐❡♥t❡ ♥❛s ♣r♦①✐♠✐❞❛❞❡s ❞♦ r♦❜ô✳ ✷✳✷✳✶ ▼♦✈✐♠❡♥t❛çã♦ ❈♦❧❡t✐✈❛ ❞❡ ❘♦❜ôs ▼ó✈❡✐s ❖ ♠♦✈✐♠❡♥t♦ ❝♦❧❡t✐✈♦ ♣♦❞❡ s❡r ❝♦♠♣r❡❡♥❞✐❞♦ ❝♦♠♦ ♦ ❢❡♥ô♠❡♥♦ q✉❡ ♠❛♥té♠ ✉♠ ❣r✉♣♦❞❡ ❛❣❡♥t❡s ❛t✉❛♥❞♦ ❞❡ ❢♦r♠❛ ❝♦❡s❛ ❡♠ ❞✐r❡çã♦ ❛ ✉♠ ❛❧✈♦ ❝♦♠✉♠ ❬◆❛✈❛rr♦ ✫ ▼❛tí❛✱✷✵✶✸❪✳ ❖ ♠♦✈✐♠❡♥t♦ ❝♦❧❡t✐✈♦ é ❛♠♣❧❛♠❡♥t❡ ❡♥❝♦♥tr❛❞♦ ♥❛ ♥❛t✉r❡③❛ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱♥♦s ❝♦♠♣♦rt❛♠❡♥t♦s ❞❡ ❡♥①❛♠❡s✱ ❝❛r❞✉♠❡s ❡ ❜❛♥❞♦s✳ ◆❡ss❡s s✐st❡♠❛s ♥❛t✉r❛✐s✱ ♦s❛❣❡♥t❡s ✉t✐❧✐③❛♠ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s ♣❛r❛ ❡♥tr❛r❡♠ ❡♠ ❝♦♥s❡♥s♦ ❝♦♠ r❡❧❛çã♦ às t❛r❡❢❛s s❡♥❞♦ ❞❡s❡♥✈♦❧✈✐❞❛s✳ ❯♠ ❞♦s ♣r✐♠❡✐r♦s tr❛❜❛❧❤♦s ❡♥✈♦❧✈❡♥❞♦ ❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❡ ♠♦✈✐♠❡♥t♦ ❝♦❧❡t✐✈♦❝♦♠ ❛❣❡♥t❡s ❛rt✐✜❝✐❛✐s ❢♦✐ ❬❘❡②♥♦❧❞s✱ ✶✾✽✼❪✳ ◆❡ss❡ tr❛❜❛❧❤♦✱ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛❞❡ ✉♠ ❣r✉♣♦ ❞❡ ❛❣❡♥t❡s é ♣r♦♣♦r❝✐♦♥❛❞❛ ♣♦r três r❡❣r❛s s✐♠♣❧❡s✿ ✭✐✮ s❡♣❛r❛çã♦❀ ✭✐✐✮❛❧✐♥❤❛♠❡♥t♦❀ ❡ ✭✐✐✐✮ ❝♦❡sã♦✳ ❚❛✐s r❡❣r❛s sã♦ ❛♣❧✐❝❛❞❛s ❧♦❝❛❧♠❡♥t❡ ♣♦r ❝❛❞❛ ❛❣❡♥t❡ ❝♦♠❜❛s❡ ❡♠ s❡✉s r❡s♣❡❝t✐✈♦s ✈✐③✐♥❤♦s✱ ❞❡ ♠♦❞♦ q✉❡ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛ ❡ ❝♦❡s❛ ❞♦❣r✉♣♦ s✉r❣❡ ❝♦♠♦ ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❡♠❡r❣❡♥t❡✳ ❆❧é♠ ❞✐ss♦✱ ✐♥ú♠❡r❛s ❝❛r❛❝t❡ríst✐❝❛s♣r❡s❡♥t❡s ❡♠ s✐st❡♠❛s ❝♦♠♣♦st♦s ♣♦r ❣r❛♥❞❡s ❣r✉♣♦s ❞❡ ❛❣❡♥t❡s ♥❛t✉r❛✐s sã♦ t❛♠❜é♠✐❞❡♥t✐✜❝❛❞❛s ♥❡ss❡ tr❛❜❛❧❤♦✱ t❛✐s ❝♦♠♦ ❡s❝❛❧❛❜✐❧✐❞❛❞❡✱ ✢❡①✐❜✐❧✐❞❛❞❡ ❡ r♦❜✉st❡③✳ ◆♦ â♠❜✐t♦ ❞❛ r♦❜ót✐❝❛✱ ❡str❛té❣✐❛s ❞❡ ❝♦♥tr♦❧❡ ❞♦ ♠♦✈✐♠❡♥t♦ ❞❡ r♦❜ôs sã♦ ❡♠✲♣r❡❣❛❞❛s ♣❛r❛ ♣♦ss✐❜✐❧✐t❛r ❛ ❛t✉❛çã♦ ❞♦ ❣r✉♣♦ ❝♦♠♦ ✉♠❛ ✉♥✐❞❛❞❡✳ ◆♦ ❝✉rs♦ ❞❛ ♠♦✈✐✲♠❡♥t❛çã♦✱ ♦s r♦❜ôs ♣♦❞❡♠ s❡r ❝♦♥tr♦❧❛❞♦s ❞❡ ❢♦r♠❛ ❛ ♠❛♥t❡r❡♠ ♦✉ ♥ã♦ ✉♠❛ ❢♦r♠❛çã♦✜①❛ ✭❡✳❣✳ ❬❉❡s❛✐ ❡t ❛❧✳✱ ✶✾✾✽❀ ❖❧❢❛t✐✲❙❛❜❡r ✫ ▼✉rr❛②✱ ✷✵✵✷❪✮✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ❡♠❬❇❛❧❝❤ ✫ ❆r❦✐♥✱ ✶✾✾✽❪✱ ♦ ❝♦♥tr♦❧❡ ❞❡ ❢♦r♠❛çã♦ ♣♦❞❡ s❡r ❢❡✐t♦ ❞❡ três ❢♦r♠❛s✿ r❡❧❛t✐✈♦à ♣♦s✐çã♦ ❞♦ ❝❡♥tr♦ ❞❡ ♠❛ss❛ ❞♦ ❣r✉♣♦❀ r❡❧❛t✐✈♦ à ♣♦s✐çã♦ ❞❡ ✉♠ ❧í❞❡r❀ ❡ ❝♦♠ r❡❧❛çã♦à ♣♦s✐çã♦ ❞❡ r♦❜ôs ✈✐③✐♥❤♦s✳ ❆s ❞✉❛s ♣r✐♠❡✐r❛s ❢♦r♠❛s ♣r❡ss✉♣õ❡♠ q✉❡ ♦s r♦❜ôs ♣♦s✲ s✉❛♠ ✉♠ ❝♦♥❤❡❝✐♠❡♥t♦ ♠❛✐♦r ❞♦ ❣r✉♣♦✱ ♦ q✉❡ ♣♦❞❡ ❝♦♠♣r♦♠❡t❡r ❛ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ ❡❛ r♦❜✉st❡③ ❞♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝♦♥tr♦❧❡ ❞❡ ❢♦r♠❛çã♦✳ ❆ ú❧t✐♠❛✱ ♣♦r s✉❛ ✈❡③✱ é ❜❛s❡❛❞❛ s♦♠❡♥t❡ ❡♠ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s✱ ✈✐❛❜✐❧✐③❛♥❞♦ ❛ss✐♠ ♦ ❡♠♣r❡❣♦ ❞❡ ❡str❛té❣✐❛s ❞❡ ❝♦♥tr♦❧❡ ✶✹❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ❞❡s❝❡♥tr❛❧✐③❛❞♦ ❡ ♦ ❝♦♥s❡q✉❡♥t❡ ❛✉♠❡♥t♦ ❞❛ r♦❜✉st❡③ ❞♦ ♠❡❝❛♥✐s♠♦✳❊str❛té❣✐❛s ❞❡ ❝♦♥tr♦❧❡ ❝♦❧❡t✐✈♦ q✉❡ ♥ã♦ ❡①✐❣❡♠ ❛ ♠❛♥✉t❡♥çã♦ ❞❡ ❢♦r♠❛çã♦ ✜①❛ ❞♦ ❣r✉♣♦ ❞❡ r♦❜ôs✱ t❛✐s ❝♦♠♦ ❡str❛té❣✐❛s ❞❡ ✢♦❝❦✐♥❣ ✭❡✳❣✳ ❬❘❡②♥♦❧❞s✱ ✶✾✽✼❀ ❚❛♥♥❡r ❡t ❛❧✳✱✷✵✵✺❪✮ ♦✉ ❧❛tt✐❝❡s ✭❡✳❣ ❬❙♣❡❛rs ❡t ❛❧✳✱ ✷✵✵✹❀ ❖❧❢❛t✐✲❙❛❜❡r✱ ✷✵✵✻❪✮✱ tê♠ ❝♦♠♦ ♣r✐♥❝✐♣❛❧♦❜❥❡t✐✈♦ ♠❛♥t❡r ♦ ❣r✉♣♦ ❝♦❡s♦ ❞✉r❛♥t❡ ❛ ♠♦✈✐♠❡♥t❛çã♦✳ ◆❡ss❛s ❡str❛té❣✐❛s✱ ♦s r♦❜ôs♥ã♦ ♣♦ss✉❡♠ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ✜①♦ ♥♦ ❣r✉♣♦✱ ♣♦ré♠ ♣r♦❝✉r❛♠ ♠❛♥t❡r ✉♠❛ ♣♦s✐çã♦ r❡❧❛t✐✈❛ ❛ s❡✉s ✈✐③✐♥❤♦s✳ ■♥ú♠❡r❛s ❛❜♦r❞❛❣❡♥s ❝♦♥s✐❞❡r❛♠ ❛ tr❛♥s♣♦s✐çã♦ ❞❡ ♦❜stá❝✉❧♦s❝♦♠ ❛ r❡s♣❡❝t✐✈❛ ❞✐✈✐sã♦ ❞♦ ❣r✉♣♦ ❡ ♦ ❝♦♥s❡q✉❡♥t❡ r❡❛❣r✉♣❛♠❡♥t♦ ❛♣ós ♦ ♦❜stá❝✉❧♦ t❡r s✐❞♦ s✉♣❡r❛❞♦✳ ■♥ú♠❡r❛s t❛r❡❢❛s ❞❡ ❛❧t♦ ♥í✈❡❧✱ t❛✐s ❝♦♠♦ ♠❛♣❡❛♠❡♥t♦✱ s❡♥s♦r✐❛♠❡♥t♦ ❝♦❧❡t✐✈♦ ❡❜✉s❝❛✴s❛❧✈❛♠❡♥t♦✱ ♣♦❞❡♠ s❡r ❡①❡❝✉t❛❞❛s t❡♥❞♦ ♦ ♠♦✈✐♠❡♥t♦ ❝♦❧❡t✐✈♦ ❝♦♠♦ ❛t✐✈✐❞❛❞❡ s✉♣♦rt❡ ✭❡✳❣✳ ❬❘❡❦❧❡✐t✐s ❡t ❛❧✳✱ ✶✾✾✼❀ ●r❛❜♦✇s❦✐ ❡t ❛❧✳✱ ✷✵✵✵❪✮✳ ❊♠ ❛❧❣✉♠❛s ❛t✐✈✐❞❛✲❞❡s✱ ❛ ♣❡r❢♦r♠❛♥❝❡ ❞❡ ❡①❡❝✉çã♦ ❞❛s t❛r❡❢❛s é ❜❡♥❡✜❝✐❛❞❛ ♣❡❧❛ ❛t✉❛çã♦ ❝♦❧❡t✐✈❛ ❞♦s r♦❜ôs✱ ❡♥q✉❛♥t♦ q✉❡ ❡♠ ♦✉tr❛s✱ ♦ ❣r✉♣♦ é ♣r❡✈✐❛♠❡♥t❡ ❣✉✐❛❞♦ ❞❡ ♠❛♥❡✐r❛ ❝♦❧❡t✐✈❛ ♣❛r❛❞❡t❡r♠✐♥❛❞❛s r❡❣✐õ❡s ❞♦ ❛♠❜✐❡♥t❡ ♦♥❞❡ ❛s t❛r❡❢❛s s❡rã♦ ❡①❡❝✉t❛❞❛s✳ ❙✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s ❝♦♠♣♦st♦s ♣♦r ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ r♦❜ôs✱ ❝♦♠ ❝❛✲♣❛❝✐❞❛❞❡s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❡ ❝♦♠✉♥✐❝❛çã♦ ❧✐♠✐t❛❞♦s✱ tê♠ s❡ ❜❡♥❡✜❝✐❛❞♦ ❞❡ té❝♥✐❝❛s❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛ ❡ ❝♦♠♣♦rt❛♠❡♥t♦ ❝♦♦♣❡r❛t✐✈♦ ♣❛r❛ s✉♣❡r❛r ❛s ❧✐♠✐t❛çõ❡s✐♥❞✐✈✐❞✉❛✐s ❞♦s ❛❣❡♥t❡s✱ ❞❡ ♠♦❞♦ ❛ ❝♦♥s❡❣✉✐r❡♠ ❡①❡❝✉t❛r t❛r❡❢❛s ❝♦♠♣❧❡①❛s✳ ❊ss❡s s✐st❡♠❛s ♣♦ss✉❡♠ ❝❛r❛❝t❡ríst✐❝❛s ♣ró♣r✐❛s ❡ tê♠ s✐❞♦ ❞❡st❛❝❛❞♦s ❞♦s ❞❡♠❛✐s s✐st❡♠❛s♠✉❧t✐rr♦❜ót✐❝♦s ❡♠ ✉♠❛ ár❡❛ ❡s♣❡❝í✜❝❛ ❞❡♥♦♠✐♥❛❞❛ ❊♥①❛♠❡s ❘♦❜ót✐❝♦s✳ ✷✳✸ ❊♥①❛♠❡ ❞❡ ❘♦❜ôs ▼ó✈❡✐s ❖ t❡r♠♦ ❊♥①❛♠❡s ❘♦❜ót✐❝♦s ✭❞♦ ✐♥❣❧ês✱ ❘♦❜♦t✐❝ ❙✇❛r♠s✮✱ t❡♠ s✐❞♦ ❡♠♣r❡❣❛❞♦ ♣❛r❛ r❡❢❡r❡♥❝✐❛r s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s q✉❡ ✉t✐❧✐③❛♠ ❞❡③❡♥❛s✱ ❝❡♥t❡♥❛s ❡ ❛té ♠✐❧❤❛r❡s ❞❡r♦❜ôs✳ ❖s tr❛❜❛❧❤♦s ❞❡ ❇❛②✐♥❞✐r ✫ ❙❛❤✐♥ ❬✷✵✵✼❪ ❡ ❙❛❤✐♥ ❡t ❛❧✳ ❬✷✵✵✽❪ ❛♣r❡s❡♥t❛♠ ✉♠❛✈✐sã♦ ❣❡r❛❧ ❞❛ ár❡❛ ❞❡ ❡♥①❛♠❡s ❞❡ r♦❜ôs ✭❞♦ ✐♥❣❧ês✱ ❙✇❛r♠ ❘♦❜♦t✐❝s✮✱ ❛❧é♠ ❞❡ ♣r♦❜❧❡♠❛s q✉❡ tê♠ s✐❞♦ s♦❧✉❝✐♦♥❛❞♦s ✉t✐❧✐③❛♥❞♦ ❣r❛♥❞❡s ❣r✉♣♦s ❞❡ r♦❜ôs✳ ◆❡ss❡ ❝♦♥t❡①t♦✱ ✉♠❡♥①❛♠❡ é ❢♦r♠❛❞♦ q✉❛s❡ s❡♠♣r❡ ♣♦r r♦❜ôs ❤♦♠♦❣ê♥❡♦s✱ s❡♥❞♦ ❡ss❡s ❡♥t✐❞❛❞❡s s✐♠♣❧❡s✱❛✉tô♥♦♠❛s✱ ❝♦♠ ♣♦❞❡r ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❡ ❝♦♠✉♥✐❝❛çã♦ ❧✐♠✐t❛❞♦s✳ ❉❡✈✐❞♦ à ❧✐♠✐t❛çã♦❞❛s ❝❛♣❛❝✐❞❛❞❡s ✐♥❞✐✈✐❞✉❛✐s ❞♦s r♦❜ôs✱ ❢❛③✲s❡ ♥❡❝❡ssár✐♦ ❝♦♦r❞❡♥❛r ♦ ❡♥①❛♠❡ ❞❡ ♠♦❞♦❛ s❡ ♦❜t❡r ê①✐t♦ ♥❛ ❡①❡❝✉çã♦ ❞❡ t❛r❡❢❛s ♠❛✐s ❝♦♠♣❧❡①❛s✳ ❖ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t♦ ❞❡ ✐♥s♣✐r❛çã♦ ♣❛r❛ ♦ ✉s♦ ❞❡ ❡♥①❛♠❡s é ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❝♦✲❧❡t✐✈♦ ❞❡ ❣r❛♥❞❡s s✐st❡♠❛s s♦❝✐❛✐s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❝♦❧ô♥✐❛s ❞❡ ✐♥s❡t♦s✱ ❜❛♥❞♦s ❞❡♣áss❛r♦s ❡ ❝❛r❞✉♠❡s ❞❡ ♣❡✐①❡s ✭❋✐❣✉r❛ ✷✳✹✮✳ ❚❛✐s s✐st❡♠❛s sã♦ ❞❡s❝❡♥tr❛❧✐③❛❞♦s ❡ ♣♦s✲ ✷✳✸✳ ❊♥①❛♠❡ ❞❡ ❘♦❜ôs ▼ó✈❡✐s✶✺ s✉❡♠ ❝❛r❛❝t❡ríst✐❝❛s ❞❡s❡❥á✈❡✐s ❡♠ s✐st❡♠❛s ♠✉❧t✐❛❣❡♥t❡s✱ s❡♥❞♦ r♦❜✉st❡③✱ ✢❡①✐❜✐❧✐❞❛❞❡ ❡ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ ❛s ♠❛✐s r❡❧❡✈❛♥t❡s✳ ❇❛②✐♥❞✐r ✫ ❙❛❤✐♥ ❬✷✵✵✼❪ ❞❡✜♥❡♠ ❡ss❛s três ❝❛r❛❝✲ t❡ríst✐❝❛s ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿ r♦❜✉st❡③ é ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ✉♠ s✐st❡♠❛ ❢✉♥❝✐♦♥❛r ♥❛♣r❡s❡♥ç❛ ❞❡ ♣❡q✉❡♥❛s ❢❛❧❤❛s ♦✉ ❝♦♥❞✐çõ❡s ❛♥♦r♠❛✐s❀ ✢❡①✐❜✐❧✐❞❛❞❡ é ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡❛❞❛♣t❛çã♦ ❛ ♥♦✈❛s s✐t✉❛çõ❡s❀ ❡ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ é ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ✉♠ s✐st❡♠❛ s✉♣♦rt❛r❛✉♠❡♥t♦ ♦✉ ❞✐♠✐♥✉✐çã♦ ♥♦ ♥ú♠❡r♦ ❞❡ ✐♥t❡❣r❛♥t❡s✱ s❡♠ q✉❡ ❤❛❥❛ ✉♠ ✐♠♣❛❝t♦ ❝♦♥s✐❞❡rá✲✈❡❧ ♥♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ s✐st❡♠❛✳ ❈♦♥❢♦r♠❡ ❝✐t❛❞♦ ♣❡❧♦s ❛✉t♦r❡s✱ ❛♣❡s❛r ❞❛ s✐♠✐❧❛r✐❞❛❞❡❡♥t❡ r♦❜✉st❡③ ❡ ✢❡①✐❜✐❧✐❞❛❞❡✱ ❛ ♣r✐♥❝✐♣❛❧ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ❡ss❡s ❝♦♥❝❡✐t♦s ❡♥❝♦♥tr❛✲s❡ ♥♦♥í✈❡❧ ❞♦ ♣r♦❜❧❡♠❛✳ ❆ss✐♠✱ q✉❛♥❞♦ ♦ ♣r♦❜❧❡♠❛ ❛ s❡r s♦❧✉❝✐♦♥❛❞♦ ♣♦r ✉♠ s✐st❡♠❛ ♠✉❞❛✱❡ss❡ ú❧t✐♠♦ t❡♠ q✉❡ s❡r ✢❡①í✈❡❧ ♦ s✉✜❝✐❡♥t❡ ♣❛r❛ s❡ ❛❞❛♣t❛r à ♠✉❞❛♥ç❛✱ ♦ q✉❡ ♥ã♦ ❡stá❞✐r❡t❛♠❡♥t❡ r❡❧❛❝✐♦♥❛❞♦ à s✉❛ r♦❜✉st❡③✳ ✭❛✮ ✭❜✮ ✭❝✮ ❋✐❣✉r❛ ✷✳✹✿ ❊①❡♠♣❧♦s ❞❡ ❡♥①❛♠❡s ♥❛t✉r❛✐s✿ ✭❛✮ ❝♦❧ô♥✐❛ ❞❡ ❢♦r♠✐❣❛s❀ ✭❜✮ ❜❛♥❞♦ ❞❡♣áss❛r♦s❀ ❡ ✭❝✮ ❝❛r❞✉♠❡ ❞❡ ♣❡✐①❡s✳ ❙✐st❡♠❛s r♦❜✉st♦s ❞❡✈❡♠ s❡r ❝❛♣❛③❡s ❞❡ ♦♣❡r❛r ♠❡s♠♦ q✉❛♥❞♦ s✉r❣❡♠ ❞✐stúr❜✐♦s♥♦ ❛♠❜✐❡♥t❡ ♦✉ ♠❛❧ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❡♠ ♣❛rt❡ ❞❡ s❡✉s ❝♦♠♣♦♥❡♥t❡s✳ ❊ss❛ ♣r♦♣r✐❡❞❛❞❡♣♦❞❡ s❡r ❛❧❝❛♥ç❛❞❛ q✉❛♥❞♦ s❡ t❡♠ ✉♠ ❣r❛♥❞❡ ❣r✉♣♦ ❞❡ ✐♥❞✐✈í❞✉♦s s✐♠♣❧❡s✱ s❡♠ ❝♦♥tr♦❧❡❝❡♥tr❛❧ ❡ ❝♦♠ s❡♥s♦r✐❛♠❡♥t♦ ❞✐str✐❜✉í❞♦✳ ❯♠ ♥ú♠❡r♦ s✐❣♥✐✜❝❛t✐✈♦ ❞❡ ❡❧❡♠❡♥t♦s s✐♠♣❧❡s❛✉♠❡♥t❛ ❛ r❡❞✉♥❞â♥❝✐❛ ♥♦ s✐st❡♠❛✱ ❞❡ ♠♦❞♦ q✉❡ ❢❛❧❤❛s ✐♥❞✐✈✐❞✉❛✐s ♣♦❞❡rã♦ s❡r s✉♣r✐❞❛s♣♦r ♦✉tr♦s ✐♥❞✐✈í❞✉♦s✳ ❆ ❡①✐stê♥❝✐❛ ❞❡ ✉♠ ❝♦♥tr♦❧❡ ❞❡s❝❡♥tr❛❧✐③❛❞♦ ❝♦♥tr✐❜✉✐ ♣❛r❛ ♦ s✐st❡♠❛ s❡ t♦r♥❛r ♠❡♥♦s s✉s❝❡tí✈❡❧ ❛ ❢❛❧❤❛s ❞❡ ♦♣❡r❛çõ❡s q✉❛♥❞♦ ♣❛rt❡ ❞♦ ♠❡s♠♦ ❡♥tr❛❡♠ ❝♦❧❛♣s♦✳ ❆❧é♠ ❞✐ss♦✱ ✉♠ s❡♥s♦r✐❛♠❡♥t♦ ❞✐str✐❜✉í❞♦ ❞✐♠✐♥✉✐ ❛ s❡♥s✐❜✐❧✐❞❛❞❡ ❞♦ s✐st❡♠❛ ♥♦ q✉❡ t❛♥❣❡ ❛ ♣❡rt✉r❜❛çõ❡s ❧♦❝❛✐s ♥♦ ❛♠❜✐❡♥t❡✳ ❙✐st❡♠❛s ❞❡ ❡♥①❛♠❡s ❞❡ r♦❜ôs ❞❡✈❡♠ s❡r ✢❡①í✈❡✐s ♦ s✉✜❝✐❡♥t❡✱ ❞❡ ♠♦❞♦ q✉❡ s❡✉s✐♥❞✐✈í❞✉♦s s❡❥❛♠ ❛♣t♦s ❛ ❧✐❞❛r ❝♦♠ t❛r❡❢❛s ❞❡ ♥❛t✉r❡③❛s ❞✐st✐♥t❛s✳ ❊♠ s♦❝✐❡❞❛❞❡s❞❡ ✐♥s❡t♦s✱ ♣♦r ❡①❡♠♣❧♦✱ ♦s ✐♥❞✐✈í❞✉♦s ❛t✉❛♠ ❝♦❧❡t✐✈❛♠❡♥t❡ ❝♦♠ ✈✐st❛s ❛ s♦❧✉❝✐♦♥❛r ✶✻❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ♦s ♠❛✐s ❞✐✈❡rs♦s ♣r♦❜❧❡♠❛s✱ t❛✐s ❝♦♠♦ ❡♥❝♦♥tr❛r ❢♦♥t❡s ❞❡ ❝♦♠✐❞❛ ♥♦ ❛♠❜✐❡♥t❡ ♦✉❝❛rr❡❣❛r ✉♠❛ ♣r❡s❛ ❝✉❥♦ t❛♠❛♥❤♦ ❡①✐❥❛ ❛ ♣❛rt✐❝✐♣❛çã♦ ❞❡ ✈ár✐♦s ♠❡♠❜r♦s ❞❛ s♦❝✐❡❞❛❞❡✳❈♦♥s✐❞❡r❛♥❞♦ ❛ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ ❡s❝❛❧❛❜✐❧✐❞❛❞❡✱ ✉♠ ❡♥①❛♠❡ ❞❡ r♦❜ôs ❞❡✈❡ ❡st❛r ❛♣t♦❛ ♦♣❡r❛r ❛❞❡q✉❛❞❛♠❡♥t❡ q✉❛♥❞♦ s✉❥❡✐t♦ ❛ ❣r❛♥❞❡s ✈❛r✐❛çõ❡s ♥♦ ♥ú♠❡r♦ ❞❡ ✐♥t❡❣r❛♥t❡s✱ s❡♠ ✉♠ ❝♦♥s❡q✉❡♥t❡ ✐♠♣❛❝t♦ ❝♦♥s✐❞❡rá✈❡❧ ♥♦ ❞❡s❡♠♣❡♥❤♦ ❛♣r❡s❡♥t❛❞♦ ♣❡❧♦ s✐st❡♠❛✳❆ss✐♠ s❡♥❞♦✱ ♦s ❛❧❣♦r✐t♠♦s ❡ ❡str❛té❣✐❛s ❞❡ ❝♦♦r❞❡♥❛çã♦ ❞❡✈❡♠ ❣❛r❛♥t✐r ❛ ♦♣❡r❛çã♦ ❞♦ s✐st❡♠❛ s♦❜ ❛ ✐♥✢✉ê♥❝✐❛ ❞❛ ✈❛r✐❛çã♦ ♥♦ t❛♠❛♥❤♦ ❞♦ ❡♥①❛♠❡✳ ❙✐st❡♠❛s r♦❜ót✐❝♦s ❝♦♠♣♦st♦s ♣♦r ❣r❛♥❞❡s ❣r✉♣♦s ❞❡ r♦❜ôs s✐♠♣❧❡s ♣♦ss✉❡♠ ❛❝❛r❛❝t❡ríst✐❝❛ ❞❡ ♣♦ss✐❜✐❧✐t❛r ❛ ❡♠❡r❣ê♥❝✐❛ ❞❡ ❝♦♠♣♦rt❛♠❡♥t♦s ❣❧♦❜❛✐s ❛ ♣❛rt✐r ❞❛ ✐♥✲ t❡r❛çã♦ ❧♦❝❛❧ ❡♥tr❡ s❡✉s ✐♥t❡❣r❛♥t❡s✳ ❆ s✐♠♣❧✐❝✐❞❛❞❡ ❞❡ss❡s ❛❣❡♥t❡s ♥ã♦ s❡ ❧✐♠✐t❛ ❡①✲❝❧✉s✐✈❛♠❡♥t❡ às ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ❤❛r❞✇❛r❡ ♦✉ ❛♦s ❛❧❣♦r✐t♠♦s ❞❡ ❝♦♥tr♦❧❡ ✉t✐❧✐③❛❞♦s✳❚❛❧ s✐♠♣❧✐❝✐❞❛❞❡ ❡stá ♠❛✐s r❡❧❛❝✐♦♥❛❞❛ às ❧✐♠✐t❛çõ❡s ❞❛s ❝❛♣❛❝✐❞❛❞❡s ✐♥❞✐✈✐❞✉❛✐s ❞♦s❛❣❡♥t❡s✱ ♥♦ q✉❡ s❡ r❡❢❡r❡ à t❛r❡❢❛ ❛ s❡r ❡①❡❝✉t❛❞❛✳ ❉❡✈✐❞♦ à s✐♠♣❧✐❝✐❞❛❞❡ ❞♦s r♦❜ôs✱ s✉❛ ❝♦♥str✉çã♦ ❡ ✉t✐❧✐③❛çã♦ s❡ t♦r♥❛ ♠❛✐s ❢á❝✐❧✱ ✢❡①í✈❡❧ ❡ t♦❧❡r❛♥t❡ ❛ ❢❛❧❤❛s✱ ❛❧é♠ ❞❡ s❡r♠❡♥♦s ♦♥❡r♦s❛✳ ❙✐st❡♠❛s ❝♦♠ ❣r❛♥❞❡s ❣r✉♣♦s ❞❡ r♦❜ôs ♣♦ss✉❡♠ ♠❛✐♦r r❡❞✉♥❞â♥❝✐❛❡ t❡♥❞❡♠ ❛ s❡r ♠❛✐s ❡✜❝✐❡♥t❡s ❞❡✈✐❞♦ à ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ❞✐✈✐sã♦ ❞❛s t❛r❡❢❛s ❡♥tr❡ ♦s✐♥t❡❣r❛♥t❡s ❞♦ ❣r✉♣♦✳ ❉✐✈❡rs♦s ❛✉t♦r❡s✱ ❞❡♥tr❡ ❡❧❡s ❉✉❞❡❦ ❡t ❛❧✳ ❬✶✾✾✸❪✱ ❙❛❤✐♥ ❬✷✵✵✺❪✱ ❇❛②✐♥❞✐r ✫ ❙❛❤✐♥❬✷✵✵✼❪ ❡ ❙❤❛r❦❡② ❬✷✵✵✼❪✱ tê♠ ♣r♦♣♦st♦ t❛①♦♥♦♠✐❛s ❝♦♠ ✈✐st❛s ❛ ❡st❛❜❡❧❡❝❡r ✉♠ ❛❞❡✲ q✉❛❞❛ ❝❛r❛❝t❡r✐③❛çã♦ ♣❛r❛ ❛ ár❡❛ ❞❡ ❡♥①❛♠❡s ❞❡ r♦❜ôs✳ ❆♣❡s❛r ❞✐ss♦✱ ❛✐♥❞❛ ♥ã♦ s❡ t❡♠✉♠ ❝♦♥s❡♥s♦ ❝♦♠ r❡❧❛çã♦ ❛ ✉♠❛ ❞❡✜♥✐çã♦ q✉❡ s❡❥❛ ✉♥✐✈❡rs❛❧♠❡♥t❡ ❛❝❡✐t❛ ♣❡❧❛ ❝♦♠✉✲♥✐❞❛❞❡ ❝✐❡♥tí✜❝❛✳ ❆ ♣r♦♣♦st❛ ❛♣r❡s❡♥t❛❞❛ ♣♦r ❉✉❞❡❦ ❡t ❛❧✳ ❬✶✾✾✸❪ s✉❣❡r❡ ❛ ❞✐✈✐sã♦ ❞❛ár❡❛ ❡♠ ❡✐①♦s✱ ❞❡ ❢♦r♠❛ ❛ ❝❛♣t✉r❛r ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ s✐st❡♠❛ ❝♦♠♦ ✉♠ t♦❞♦✱ ❡♠❝♦♥tr❛♣❛rt✐❞❛ à ❝❛r❛❝t❡r✐③❛çã♦ ❞♦s r♦❜ôs ✐♥❞✐✈✐❞✉❛❧♠❡♥t❡✳ ❚❡♠✲s❡✱ ❡♥tã♦✱ ❛ ✐❞❡♥t✐✜✲❝❛çã♦ ❞❡ ❝❛r❛❝t❡ríst✐❝❛s ❛ss♦❝✐❛❞❛s ❛♦ t❛♠❛♥❤♦ ❞♦ ❡♥①❛♠❡✱ à ❢♦r♠❛ ❞❡ ❝♦♠✉♥✐❝❛çã♦❡♥tr❡ ♦s ❛❣❡♥t❡s✱ à ❝❛♣❛❝✐❞❛❞❡ ❞❡ r❡❝♦♥✜❣✉r❛çã♦ ♦✉ ❝♦♠♣♦s✐çã♦ ❞♦ ❡♥①❛♠❡ ❡ ❛♦ ♠♦✲❞❡❧♦ ❞❡ ❝♦♠♣✉t❛çã♦ ✉t✐❧✐③❛❞♦✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❙❛❤✐♥ ❬✷✵✵✺❪ s✉❣❡r❡ ♦ s❡❣✉✐♥t❡ ❝♦♥❥✉♥t♦❞❡ ❝r✐tér✐♦s ❛ s❡r❡♠ ✉t✐❧✐③❛❞♦s ❞❡ ❢♦r♠❛ ❛ ❞✐st✐♥❣✉✐r ❛ ár❡❛✿ ❛✉t♦♥♦♠✐❛✱ t❛♠❛♥❤♦ ❞♦❡♥①❛♠❡✱ ❝♦♠♣♦s✐çã♦ ❞♦ ❡♥①❛♠❡✱ ❝❛♣❛❝✐❞❛❞❡ ❞♦s r♦❜ôs ❡ ❝♦♠✉♥✐❝❛çã♦✳ ❆❧t❡r♥❛t✐✈❛✲♠❡♥t❡✱ ❙❤❛r❦❡② ❬✷✵✵✼❪ ♣r♦♣õ❡ ✉♠❛ ❞✐✈✐sã♦ ❞❛ ár❡❛ ❡♠ ❞✉❛s✿ ❙❝❛❧❛❜❧❡ ❙✇❛r♠ ❘♦❜♦t✐❝s❡ ▼✐♥✐♠❛❧✐s♠ ❙✇❛r♠ ❘♦❜♦t✐❝s✳ ❆ ♣r✐♠❡✐r❛ ❡♥❢❛t✐③❛ ❛ ❞❡s❝❡♥tr❛❧✐③❛çã♦✱ ♦ ❝♦♥tr♦❧❡ ❧♦❝❛❧❡ ❛ ❢♦r♠❛ ❞❡ ❝♦♠✉♥✐❝❛çã♦✱ ❡♥q✉❛♥t♦ q✉❡ ❛ s❡❣✉♥❞❛ ❡♥❢❛t✐③❛ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ❡♥t✐❞❛❞❡s s✐♠♣❧❡s ❡ ♠❛✐s ✢❡①í✈❡✐s✳ ❆ ❞✐s❝✉ssã♦ ❛♣r❡s❡♥t❛❞❛ ❛ s❡❣✉✐r ♣r♦❝✉r❛ ❝♦♥s♦❧✐❞❛r ❛s ❝❛r❛❝t❡ríst✐❝❛s ♠❛✐s r❡❧❡✲✈❛♥t❡s ❡♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s ♣r❡s❡♥t❡s ♥♦s tr❛❜❛❧❤♦s ❞❡s❝r✐t♦s ❛♥t❡r✐♦r♠❡♥t❡✳ ✷✳✸✳ ❊♥①❛♠❡ ❞❡ ❘♦❜ôs ▼ó✈❡✐s✶✼ ✷✳✸✳✶ Pr✐♥❝✐♣❛✐s ❈❛r❛❝t❡ríst✐❝❛s ❞❡ ❊♥①❛♠❡s ❘♦❜ót✐❝♦s ❯♠❛ ❝❛r❛❝t❡ríst✐❝❛ ♣r❡s❡♥t❡ ♥♦s ❞✐✈❡rs♦s tr❛❜❛❧❤♦s q✉❡ s❡ ♣r♦♣õ❡♠ ❛ ❡st❛❜❡❧❡❝❡r ♦s❧✐♠✐t❡s ❞❛ ár❡❛ ❞❡ ❡♥①❛♠❡s r♦❜ót✐❝♦s é ♦ t❛♠❛♥❤♦ ❞♦ ❣r✉♣♦✳ ❉✉❞❡❦ ❡t ❛❧✳ ❬✶✾✾✸❪ r❡s✲ s❛❧t❛♠ ❛ ♥ã♦ ✐♠♣♦s✐çã♦ ❞❡ ✉♠ ❧✐♠✐t❡ ❝♦♠ r❡❧❛çã♦ à q✉❛♥t✐❞❛❞❡ ❞❡ r♦❜ôs q✉❡ ❝♦♠♣õ❡✉♠ ❡♥①❛♠❡✳ ❆❧é♠ ❞✐ss♦✱ r❡ss❛❧t❛♠ ❛✐♥❞❛ q✉❡✱ ✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞❛ q✉❛♥t✐❞❛❞❡ ❞❡✐♥t❡❣r❛♥t❡s✱ ♦s r♦❜ôs ❞❡✈❡r✐❛♠ ♦♣❡r❛r ❞❡ ❢♦r♠❛ ❝♦♠♣❧❡t❛♠❡♥t❡ ✐♥❞❡♣❡♥❞❡♥t❡ ✉♥s ❞♦s♦✉tr♦s✳ ❙❛❤✐♥ ❬✷✵✵✺❪ ❞✐s❝✉rs❛ ❛ r❡s♣❡✐t♦ ❞❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ✉♠ ♥ú♠❡r♦ s✐❣♥✐✜❝❛t✐✈♦ ❞❡✐♥t❡❣r❛♥t❡s ♥♦ s✐st❡♠❛ ♣❛r❛ q✉❡ ♦ ♠❡s♠♦ ♣♦ss❛ s❡r ❝❛r❛❝t❡r✐③❛❞♦ ❝♦♠♦ ❡♥①❛♠❡✳ ◆♦❡♥t❛♥t♦✱ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ s❡ t❡r ✉♠ ❝✉st♦ ❝♦♥s✐❞❡rá✈❡❧ ♣❛r❛ s❡ tr❛❜❛❧❤❛r ❝♦♠ ❣r❛♥✲❞❡s ❣r✉♣♦s ❞❡ r♦❜ôs r❡❛✐s✱ ♦s ❛✉t♦r❡s ❝♦♥s✐❞❡r❛♠ q✉❡ ♠❡s♠♦ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s❝♦♠♣♦st♦s ♣♦r ✶✵ ❛ ✷✵ ✐♥t❡❣r❛♥t❡s ♣♦❞❡♠ s❡r ❝♦♥s✐❞❡r❛❞♦s ❡♥①❛♠❡s✳ ❊♥tr❡t❛♥t♦✱ ♠❛✐s✐♠♣♦rt❛♥t❡ ❞♦ q✉❡ ❛ ❞❡✜♥✐çã♦ ❞❡ ✉♠ ✈❛❧♦r ❡①❛t♦ ❛ ♣❛rt✐r ❞♦ q✉❛❧ ✉♠ ❣r✉♣♦ ❞❡ r♦❜ôs♣❛ss❛ ❛ s❡r ❝♦♥s✐❞❡r❛❞♦ ✉♠ ❡♥①❛♠❡ é ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡ ❛♣r❡s❡♥t❛r ❡✈✐❞ê♥❝✐❛s ❡①♣❡✲ r✐♠❡♥t❛✐s r❡❧❛t✐✈❛s à ❡s❝❛❧❛❜✐❧✐❞❛❞❡ ❞♦ s✐st❡♠❛✱ ♦ q✉❡ ♣♦❞❡ s❡r ❢❡✐t♦ ❝♦♠ ♦ ❛✉①í❧✐♦ ❞❡s✐♠✉❧❛çõ❡s✳ ❆ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ é ♦ t❡♠❛ ❝❡♥tr❛❧ ❞❛ s✉❜ár❡❛ ❙❝❛❧❛❜❧❡ ❙✇❛r♠ ❘♦❜♦t✐❝s ♣r♦♣♦st❛♣♦r ❙❤❛r❦❡② ❬✷✵✵✼❪✳ ◆❡ss❛ s✉❜ár❡❛✱ ♦ ❝♦♥tr♦❧❡ ❡ ❛ ❢♦r♠❛ ❞❡ ❝♦♠✉♥✐❝❛çã♦ sã♦ ❞❡s❝❡♥✲ tr❛❧✐③❛❞♦s ❡ ❧♦❝❛✐s✳ ❊ss❡s r❡q✉✐s✐t♦s ✈✐❛❜✐❧✐③❛♠ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❡s❝❛❧á✈❡❧✱ ✉♠❛ ✈❡③ q✉❡✉♠ ♠❡s♠♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝♦♦r❞❡♥❛çã♦ ♣♦❞❡ s❡r ❛♣❧✐❝❛❞♦ ❛ s✐st❡♠❛s ❝♦♠ ✉♠ ♥ú♠❡r♦✈❛r✐❛❞♦ ❞❡ r♦❜ôs✳ ❆ r❡❞✉♥❞â♥❝✐❛ t❛♠❜é♠ é ❡✈✐❞❡♥❝✐❛❞❛ ♥❡ss❛ s✉❜ár❡❛✱ ❞❡ ♠♦❞♦ q✉❡✉♠❛ ❢❛❧❤❛ ❡♠ ♣❛rt❡ ❞♦s ✐♥t❡❣r❛♥t❡s ❞❡ ✉♠ ❣r✉♣♦ ♥ã♦ ❝♦♠♣r♦♠❡t❛ ❛ ❡①❡❝✉çã♦ ❞❛ t❛r❡❢❛✳❈♦♥❢♦r♠❡ ❙❤❛r❦❡② ❬✷✵✵✼❪✱ r♦❜ôs ♣♦❞❡♠ s❡r ✐♥s❡r✐❞♦s ♦✉ r❡♠♦✈✐❞♦s ❞♦ s✐st❡♠❛✱ ♣♦✐s ♦s♠❡❝❛♥✐s♠♦s ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❡♠♣r❡❣❛❞♦s ♥ã♦ r❡q✉❡r❡♠ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ ✐♥❞✐✈í❞✉♦s ❡♠♣❛rt✐❝✉❧❛r✱ ❝❛r❛❝t❡r✐③❛♥❞♦ ❛ss✐♠ ❛ ❝♦♠✉♥✐❝❛çã♦ ✐♥❞✐r❡t❛✳ ❆ ❢♦r♠❛ ❞❡ ❝♦♠✉♥✐❝❛çã♦ é ♦✉tr❛ ❝❛r❛❝t❡ríst✐❝❛ q✉❡ t❡♠ s✐❞♦ ❝♦♥st❛♥t❡♠❡♥t❡ ✉t✐✲❧✐③❛❞❛ ♣❛r❛ ❝❛r❛❝t❡r✐③❛r ❛ ár❡❛✳ ❉✉❞❡❦ ❡t ❛❧✳ ❬✶✾✾✸❪ ❛♣r❡s❡♥t❛♠ ❞✉❛s ❢♦r♠❛s ❞❡ s❡❡st❛❜❡❧❡❝❡r ❛ ❝♦♠✉♥✐❝❛çã♦ ❡♥tr❡ ♦s ✐♥t❡❣r❛♥t❡s ❞❡ ✉♠ ❡♥①❛♠❡✿ ❞✐r❡t❛ ♦✉ ✐♥❞✐r❡t❛✳ ❈♦♥✲❢♦r♠❡ ❞❡s❝r✐t♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ♥❛ ❝♦♠✉♥✐❝❛çã♦ ❞✐r❡t❛ ♦ ✢✉①♦ ❞❡ ✐♥❢♦r♠❛çõ❡s é ❞✐r✐❣✐❞♦❛ ✉♠ ❞❡st✐♥❛tár✐♦ ❡s♣❡❝í✜❝♦✱ ❡♥q✉❛♥t♦ q✉❡ ♥❛ ❝♦♠✉♥✐❝❛çã♦ ✐♥❞✐r❡t❛ t❛✐s ✐♥❢♦r♠❛çõ❡s sã♦ ❞✐s♣♦♥✐❜✐❧✐③❛❞❛s ♥♦ ❛♠❜✐❡♥t❡✳ ❆♣❡s❛r ❞♦s ❛✉t♦r❡s t❡r❡♠ ❝❛t❡❣♦r✐③❛❞♦ ❛ ❢♦r♠❛ ❞❡❝♦♠✉♥✐❝❛çã♦✱ ♥❡♥❤✉♠❛ r❡str✐çã♦ ❢♦✐ ✐♠♣♦st❛ ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ ❛♦ ❛❧❝❛♥❝❡ ❞❛ ♠❡s♠❛✳❉❡ss❡ ♠♦❞♦✱ ♦s r♦❜ôs ♣♦❞❡♠ ❡❢❡t✉❛r ❝♦♠✉♥✐❝❛çã♦ ❧♦❝❛❧ ✭r❡str✐t❛ ❛ s✉❛ ✈✐③✐♥❤❛♥ç❛✮ ♦✉❣❧♦❜❛❧ ✭❝♦♠ t♦❞♦s ♦s ❞❡♠❛✐s ✐♥t❡❣r❛♥t❡s ❞♦ ❣r✉♣♦✮✳ ❉✐❢❡r❡♥t❡♠❡♥t❡ ❞❡ ❉✉❞❡❦ ❡t ❛❧✳✱ ❙❛❤✐♥ ❬✷✵✵✺❪ r❡str✐♥❣❡ ❛ ❢♦r♠❛ ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❞❡♠♦❞♦ q✉❡ ♦s r♦❜ôs ❞❡✈❡r✐❛♠ t❡r ❝❛♣❛❝✐❞❛❞❡s ❧✐♠✐t❛❞❛s ❞❡ s❡♥s♦r✐❛♠❡♥t♦ ❡ ❝♦♠✉♥✐❝❛çã♦❧♦❝❛❧✳ ❉❡ss❡ ♠♦❞♦✱ ❣❛r❛♥t✐r✲s❡✲✐❛ ✉♠❛ ❢♦r♠❛ ❞❡ ❝♦♦r❞❡♥❛çã♦ ❞✐str✐❜✉í❞❛ ❡♥tr❡ ♦s r♦❜ôs✱ ✶✽❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ❡♥q✉❛♥t♦ q✉❡ ♦ ✉s♦ ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❣❧♦❜❛❧ ✐♠♣❧✐❝❛r✐❛ ❡♠ ♠❡❝❛♥✐s♠♦s ❞❡ ❝♦♦r❞❡♥❛çã♦♥ã♦ ❡s❝❛❧á✈❡✐s✳ ◆♦ â♠❜✐t♦ ❞❛ ❛❜♦r❞❛❣❡♠ ♠✐♥✐♠❛❧✐st❛ ♣r♦♣♦st❛ ♣♦r ❙❤❛r❦❡② ❬✷✵✵✼❪✱ ♦♠❡❝❛♥✐s♠♦ ❞❡ ❝♦♠✉♥✐❝❛çã♦ ♠❛✐s ✉t✐❧✐③❛❞♦ t❡♠ s✐❞♦ ❛ ❡st✐❣♠❡r❣✐❛✱ ♥♦ q✉❛❧ ♦ ❛♠❜✐❡♥t❡é ✉t✐❧✐③❛❞♦ ❝♦♠♦ ♦ ú♥✐❝♦ ♠❡✐♦ ❞❡ ❝♦♠✉♥✐❝❛çã♦✱ ❡♠ ❝♦♥s♦♥â♥❝✐❛ ❝♦♠ ♦ ♦❜❥❡t♦ ❞❡ ✐♥s✲ ✶ ♣✐r❛çã♦ ✉t✐❧✐③❛❞♦✳ ❊♥tr❡t❛♥t♦✱ ❡st✉❞♦s ❝♦♠♦ ♦s ❞❡ ❍ö❧❧❞♦❜❧❡r ❛♥❞ ❲✐❧s♦♥ ✱ ✭❝✐t❛❞♦ ♣♦r❬❙❤❛r❦❡②✱ ✷✵✵✼❪✮✱ tê♠ ♠♦str❛❞♦ q✉❡ ✐♥s❡t♦s✱ t❛✐s ❝♦♠♦ ❛s ❢♦r♠✐❣❛s✱ t❛♠❜é♠ tr♦❝❛♠✐♥❢♦r♠❛çã♦ ❞✐r❡t❛♠❡♥t❡ ♣♦r ♠❡✐♦ ❞❡ ❝♦♥t❛t♦ ❢ís✐❝♦✳ ❆ ❝♦♠♣♦s✐çã♦ ❞♦ ❡♥①❛♠❡ ❝♦♥s✐st❡ ❡♠ ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ r❡❧❡✈❛♥t❡✱ ♣♦✐s ♦ ♦❜❥❡t♦❞❡ ✐♥s♣✐r❛çã♦ ♥❛t✉r❛❧ é ❝♦♠✉♠❡♥t❡ r❡❢❡r❡♥❝✐❛❞♦ ♣♦r ♣♦ss✉✐r ❡♥t✐❞❛❞❡s s✐♠♣❧❡s ❡ ❤♦♠♦✲❣ê♥❡❛s✳ ◆♦ ❡♥t❛♥t♦✱ ♥♦ â♠❜✐t♦ ❞❡ s✐st❡♠❛s r♦❜ót✐❝♦s✱ ✉♠ ❡♥①❛♠❡ ♣♦❞❡ s❡r ❤♦♠♦❣ê♥❡♦♦✉ ❤❡t❡r♦❣ê♥❡♦✳ ❖ ❝♦♥❝❡✐t♦ ❞❡ ❝♦♠♣♦s✐çã♦ ❛♣r❡s❡♥t❛❞♦ ♥❡ss❡s tr❛❜❛❧❤♦s s❡ ❡st❡♥❞❡ ✉♠♣♦✉❝♦ ❛❧é♠ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❡str✉t✉r❛✐s ❞♦s r♦❜ôs✱ ❞❡ ♠♦❞♦ q✉❡ r♦❜ôs ❤♦♠♦❣ê♥❡♦s✜s✐❝❛♠❡♥t❡ ♣♦❞❡♠ s❡r ❞✐❢❡r❡♥❝✐❛❞♦s ♣♦r ❝♦♠♣♦rt❛♠❡♥t♦s ♦✉ ❛❧❣♦r✐t♠♦s ❞❡ ❝♦♥tr♦❧❡✳ ❈♦♠ r❡❧❛çã♦ à s✐♠♣❧✐❝✐❞❛❞❡ ❞♦s ✐♥t❡❣r❛♥t❡s ❞❡ ✉♠ ❡♥①❛♠❡✱ ❙❛❤✐♥ ❬✷✵✵✺❪ ❞❡❢❡♥❞❡ q✉❡ ❡♥①❛♠❡s ❞❡ r♦❜ôs ❞❡✈❛♠ ♣♦ss✉✐r ✐♥t❡❣r❛♥t❡s ❝✉❥❛s ❝❛♣❛❝✐❞❛❞❡s s❡❥❛♠ ❧✐♠✐t❛❞❛s ♥♦q✉❡ ❞✐③ r❡s♣❡✐t♦ à t❛r❡❢❛ ❛ s❡r ❡①❡❝✉t❛❞❛✳ ❉❡ss❡ ♠♦❞♦✱ ♦s r♦❜ôs ❞❡✈❡r✐❛♠ s❡r ✐♥❝❛♣❛③❡s♦✉ ✐♥❡✜❝✐❡♥t❡s ♣❛r❛ s♦❧✉❝✐♦♥❛r❡♠ ❛ t❛r❡❢❛ ✐♥❞✐✈✐❞✉❛❧♠❡♥t❡✳ ◆❡ss❡ s❡♥t✐❞♦✱ ❛ ❝♦♦♣❡r❛çã♦❡♥tr❡ ♦s ✐♥t❡❣r❛♥t❡s ❞♦ s✐st❡♠❛ s❡ t♦r♥❛ ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ ❡ss❡♥❝✐❛❧ ♣❛r❛ ❛ ❡①❡❝✉çã♦ ❞❛ t❛r❡❢❛✳ ❆❧é♠ ❞✐ss♦✱ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ❣r❛♥❞❡s ❣r✉♣♦s ❞❡ r♦❜ôs s✐♠♣❧❡s ❞❡✈❡r✐❛ ❛✉♠❡♥t❛r❛ r♦❜✉st❡③ ❡ ❛ ♣❡r❢♦r♠❛♥❝❡ ❞♦ s✐st❡♠❛✳ ❚❛❧ ❝❛r❛❝t❡ríst✐❝❛ ♥ã♦ ✐♠♣õ❡ q✉❛❧q✉❡r r❡str✐çã♦ s♦❜r❡ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦ ❤❛r❞✇❛r❡ ♦✉ s♦❢t✇❛r❡ ❞♦s r♦❜ôs✱ ✈✐st♦ q✉❡ ❛ ✐♥❝❛♣❛❝✐❞❛❞❡ ♦✉✐♥❡✜❝✐ê♥❝✐❛ ❞♦s r♦❜ôs ❡stá r❡❧❛❝✐♦♥❛❞❛ à t❛r❡❢❛ ❛ s❡r ❡①❡❝✉t❛❞❛✳ ❆ ❛❜♦r❞❛❣❡♠ ♠✐♥✐♠❛❧✐st❛ ❛♣r❡s❡♥t❛❞❛ ❡♠ ❬❙❤❛r❦❡②✱ ✷✵✵✼❪ ❡st❛❜❡❧❡❝❡ ✉♠ ❝♦♠♣r♦✲♠❡t✐♠❡♥t♦ ❝♦♠ ♦ ✉s♦ ❞❡ ❡♥t✐❞❛❞❡s r♦❜ót✐❝❛s s✐♠♣❧❡s✱ ♥♦ ❡♥t❛♥t♦ s❡ ♣r♦♣õ❡ ❛ s❡r ❡s❝❛❧á✲✈❡❧ ❡♠ ❞❡❝♦rrê♥❝✐❛ ❞❡ ❧✐♠✐t❛r ❧♦❝❛❧♠❡♥t❡ ♦ ❝♦♥tr♦❧❡ ❡ ❛ ❝♦♠✉♥✐❝❛çã♦✳ ◆❡ss❛ ❛❜♦r❞❛❣❡♠✱♦s r♦❜ôs sã♦ ♠❛✐s ❜❛r❛t♦s✱ r♦❜✉st♦s ❡ ❛♣t♦s ❛ r❡s♣♦♥❞❡r r❛♣✐❞❛♠❡♥t❡ ❛ ♠✉❞❛♥ç❛s ♥♦❛♠❜✐❡♥t❡✳ ❚r❛❜❛❧❤♦s r❡❧❛❝✐♦♥❛❞♦s à ❛❜♦r❞❛❣❡♠ ♠✐♥✐♠❛❧✐st❛ tê♠ ✉t✐❧✐③❛❞♦ ♦s ✐♥s❡t♦s❝♦♠♦ ♦❜❥❡t♦ ❞❡ ✐♥s♣✐r❛çã♦✳ ◆❡ss❡ s❡♥t✐❞♦✱ ✐♠♣õ❡✲s❡ ✉♠ ❧✐♠✐t❡ ❝♦♠ r❡❧❛çã♦ às ❤❛❜✐❧✐❞❛✲❞❡s ❞♦s ❛❣❡♥t❡s✱ ♦ q✉❡ ❣❛r❛♥t❡ ❛ ♠❛♥✉t❡♥çã♦ ❞❛ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ ❞♦ s✐st❡♠❛✳ ❆❧é♠ ❞✐ss♦✱❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦s r♦❜ôs ♥ã♦ ❝♦♥st✐t✉✐ ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ r❡❧❡✈❛♥t❡✱ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ s✉❛s ✐♥t❡r❛çõ❡s s❡r❡♠ ❧♦❝❛✐s ❡ ❞❡s❝❡♥tr❛❧✐③❛❞❛s✳ ❈♦♠ ❜❛s❡ ♥❡ss❡s tr❛❜❛❧❤♦s✱ ♣❡r❝❡❜❡✲s❡ ✉♠❛ ✐♥t❡rs❡çã♦ ❞❡ ❝❛r❛❝t❡ríst✐❝❛s q✉❡ tê♠ s✐❞♦ ✉t✐❧✐③❛❞❛s ♣❛r❛ ❝❛r❛❝t❡r✐③❛r ❛ ár❡❛ ❞❡ ❡♥①❛♠❡s r♦❜ót✐❝♦s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✿ ❛✉✲t♦♥♦♠✐❛✱ t❛♠❛♥❤♦ ❞♦ ❡♥①❛♠❡✱ r♦❜✉st❡③✱ ✢❡①✐❜✐❧✐❞❛❞❡✱ ❡s❝❛❧❛❜✐❧✐❞❛❞❡✱ ❝♦♠♣♦s✐çã♦ ❞♦❣r✉♣♦✱ ❝♦♠✉♥✐❝❛çã♦ ❡ s❡♥s♦r✐❛♠❡♥t♦ ❧♦❝❛❧✳ ❆♣❡s❛r ❞❡ t❛✐s ❝❛r❛❝t❡ríst✐❝❛s ♥ã♦ t❡r❡♠ ✶ ❍ö❧❧❞♦❜❧❡r✱ ❇✳ ❛♥❞ ❲✐❧s♦♥✱ ❊✳ ❖✳ ✭✶✾✾✵✮✳ ❚❤❡ ❆♥ts✱ ❈❛♠❜r✐❞❣❡✱ ▼❆✿ ❍❛r✈❛r❞ ❯♥✐✈❡rs✐t② Pr❡ss✳ ✷✳✸✳ ❊♥①❛♠❡ ❞❡ ❘♦❜ôs ▼ó✈❡✐s✶✾ s✐❞♦ ❡st❛❜❡❧❡❝✐❞❛s ❝♦♠ ♦ ♣r♦♣ós✐t♦ ❞❡ ❞❡✜♥✐r ❝♦♠♣❧❡t❛♠❡♥t❡ ❛s ❢r♦♥t❡✐r❛s ❞❡ss❛ ♥♦✈❛ ár❡❛✱ ❛s ♠❡s♠❛s ♣♦❞❡♠ s❡r✈✐r ❞❡ ❜❛s❡ ♣❛r❛ ♥♦rt❡❛r ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♥♦✈♦s tr❛❜❛✲❧❤♦s✳ ❆ss✐♠✱ ♥♦r♠❛❧♠❡♥t❡ é ❡s♣❡r❛❞♦ q✉❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦s ❜❛s❡❛❞♦s ❡♠ ❡♥①❛♠❡s ❞❡ r♦❜ôs ♣♦ss✉❛♠ t❛✐s ❝❛r❛❝t❡ríst✐❝❛s✱ ♠❡s♠♦ q✉❡ ❛❧❣✉♠❛s ❞❡❧❛s ♥ã♦ ❡st❡❥❛♠ tã♦ ❡✈✐❞❡♥t❡s✳ ❆ s❡❣✉✐r s❡rá ❛♣r❡s❡♥t❛❞❛ ✉♠❛ ✈✐sã♦ ❣❡r❛❧ ❞❡ ❛❧❣✉♥s ❞♦s ❞♦♠í♥✐♦s ❞❡ ❛♣❧✐❝❛çã♦❡♠ q✉❡ s❡ t❡♠ ✉t✐❧✐③❛❞♦ ❡♥①❛♠❡s r♦❜ót✐❝♦s ❝♦♠♦ ♠ét♦❞♦ ❞❡ s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s✳ ✷✳✸✳✷ ❆❧❣✉♥s ❞♦♠í♥✐♦s ❞❡ ❛♣❧✐❝❛çã♦ ❆s ❛♣❧✐❝❛çõ❡s ❞❡ ❡♥①❛♠❡s r♦❜ót✐❝♦s ❛✐♥❞❛ s❡ r❡str✐♥❣❡♠✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡✱ ❛♦s ❛♠❜✐❡♥t❡s❞❡ ♣❡sq✉✐s❛✳ ❊♠ ❞❡❝♦rrê♥❝✐❛ ❞✐ss♦✱ ✈ár✐♦s ❞♦♠í♥✐♦s ❞❡ ❛♣❧✐❝❛çã♦ tê♠ s✐❞♦ ✉t✐❧✐③❛❞♦s❝♦♠♦ ♣❧❛t❛❢♦r♠❛s ❞❡ t❡st❡ ♣❛r❛ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❞❡ ❛❧❣♦r✐t♠♦s ❞❡ ❝♦♦r❞❡♥❛çã♦ ❞❡ ❡♥✲①❛♠❡s ❞❡ r♦❜ôs✳ ❚❛✐s ❛❧❣♦r✐t♠♦s ♣♦ss✉❡♠ ❝❛r❛❝t❡ríst✐❝❛s ❡♠ ❝♦♠✉♠✱ ❛♣❡s❛r ❞❡ ❛♣r❡✲ s❡♥t❛r❡♠ ❝♦♠♣♦rt❛♠❡♥t♦s ❡♠❡r❣❡♥t❡s ❞✐st✐♥t♦s✳ ❉❡♥tr❡ ❡ss❛s ❝❛r❛❝t❡ríst✐❝❛s✱ t❡♠✲s❡✿❛✉t♦♥♦♠✐❛✱ ❝♦♥tr♦❧❡ ❞❡s❝❡♥tr❛❧✐③❛❞♦✱ s❡♥s♦r✐❛♠❡♥t♦ ❡ ❝♦♠✉♥✐❝❛çã♦ ❧♦❝❛✐s✱ s✐♠♣❧✐❝✐❞❛❞❡❞♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝♦♥tr♦❧❡ ❡ ❡s❝❛❧❛❜✐❧✐❞❛❞❡✳ ❆ s❡❣✉✐r s❡rã♦ ❛♣r❡s❡♥t❛❞♦s ❛❧❣✉♥s ❞❡ss❡s❛❧❣♦r✐t♠♦s ❡ ✉♠❛ ❜r❡✈❡ ❞❡s❝r✐çã♦ ❞♦s ♠❡s♠♦s✳❆❣r❡❣❛çã♦❆ ❛❣r❡❣❛çã♦ ❝♦♥s✐st❡ ❡♠ ✉♠ ♠❡❝❛♥✐s♠♦ ♣❛r❛ ❛❣r✉♣❛r ❡❧❡♠❡♥t♦s ❞❡ ✉♠ s✐st❡♠❛ ❡♠ ✉♠❛ r❡❣✐ã♦ ❞♦ ❡s♣❛ç♦✳ ◆❛ ❘♦❜ót✐❝❛ ▼ó✈❡❧✱ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❛❣r❡❣❛çã♦ ❝♦♥s✐st❡ ❡♠ r❡♦r❣❛♥✐③❛r❛ ❞✐s♣♦s✐çã♦ ❡s♣❛❝✐❛❧ ❞❡ r♦❜ôs ❡s♣❛❧❤❛❞♦s ❛❧❡❛t♦r✐❛♠❡♥t❡ ♥♦ ❛♠❜✐❡♥t❡✳ ❯t✐❧✐③❛♥❞♦ ✉♠❛❛❜♦r❞❛❣❡♠ ❝❡♥tr❛❧✐③❛❞❛✱ ❛ s♦❧✉çã♦ ❞❡ss❡ ♣r♦❜❧❡♠❛ t♦r♥❛✲s❡ ✉♠ t❛♥t♦ q✉❛♥t♦ tr✐✈✐❛❧✳❚♦❞❛✈✐❛✱ ❡♠ s✐st❡♠❛s ❞❡ ❝♦♥tr♦❧❡ ❞❡s❝❡♥tr❛❧✐③❛❞♦✱ ❝♦♠ ❡♥t✐❞❛❞❡s ❛✉tô♥♦♠❛s ❡ ❝♦♠❝❛♣❛❝✐❞❛❞❡s s❡♥s♦r✐❛✐s ❧✐♠✐t❛❞❛s✱ t❛❧ ♣r♦❜❧❡♠❛ ❛♣r❡s❡♥t❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❝♦♥s✐❞❡rá✈❡❧✳P❛r❛ ✐❧✉str❛r ✐ss♦✱ ♦ ✉s♦ ❞❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ♥♦s q✉❛✐s ♦s r♦❜ôs s❡ ❞❡s❧♦❝❛♠ ❡♠ ❞✐r❡çã♦❛♦ ✈✐③✐♥❤♦ ♠❛✐s ♣ró①✐♠♦ ♣♦❞❡ ❣❡r❛r ✈ár✐♦s ❣r✉♣♦s ❛♦ ✐♥✈és ❞❡ ✉♠ ú♥✐❝♦✳ ❊♠ ❡str❛té❣✐❛s ❞❡s❝❡♥tr❛❧✐③❛❞❛s✱ ♥♦r♠❛❧♠❡♥t❡ ❢❛③✲s❡ ✉s♦ ❞❡ ❛❜♦r❞❛❣❡♥s q✉❡ ❝♦♥s✐✲❞❡r❛♠ ❢❡❡❞❜❛❝❦s ✭♣♦s✐t✐✈♦ ❡ ♥❡❣❛t✐✈♦✮ ❡♠ r❡❧❛çã♦ ❛♦s ✐♥t❡❣r❛♥t❡s ❞♦ ❣r✉♣♦ ❡ ♦ ❛♠❜✐❡♥t❡✳❖ ♣r✐♠❡✐r♦ s❡ ❛♣r❡s❡♥t❛ ❝♦♠♦ ✉♠❛ ❢♦rç❛ ❛tr❛t✐✈❛ ❡♠ ❞✐r❡çã♦ ❛ ❛❧❣✉♠❛ ❢♦♥t❡✱ ❡♥q✉❛♥t♦ q✉❡ ♦ s❡❣✉♥❞♦ ♣r♦✈ê ❛❧❣✉♠❛ ❢♦r♠❛ ❞❡ r❡♣✉❧sã♦ ❡♥tr❡ ♦s ❝♦♠♣♦♥❡♥t❡s ❞♦ s✐st❡♠❛✱ ❞❡❢♦r♠❛ ❛ ❝♦♥tr♦❧❛r ❛ ❢♦r♠❛çã♦ ❞❛ ❛❣r❡❣❛çã♦✳ ❆❧❣✉♥s ❡①❡♠♣❧♦s ❞❡ tr❛❜❛❧❤♦s ♥❡ss❛ ár❡❛ sã♦ ❬❚r✐❛♥♥✐ ❡t ❛❧✳✱ ✷✵✵✸❪✱ ❬❙♦②s❛❧ ❡t ❛❧✳✱ ✷✵✵✼❪ ❡ ❬❑✉♠❛r ✫ ●❛r❣✱ ✷✵✶✶❪✳ ✷✵❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ❈♦♥tr♦❧❡ ❞❡ ❢♦r♠❛çã♦❆❧❣✉♥s ❝♦♠♣♦rt❛♠❡♥t♦s ♦❜s❡r✈❛❞♦s ❡♠ ❜❛♥❞♦s ❞❡ ♣áss❛r♦s✱ ❝❛r❞✉♠❡s ❞❡ ♣❡✐①❡s✱ ❡♥tr❡♦✉tr❛s ❡s♣é❝✐❡s ❞❡ ❛♥✐♠❛✐s✱ ❛❧é♠ ❞❡ s♦❝✐❡❞❛❞❡s ❞❡ ✐♥s❡t♦s✱ sã♦ ❝♦♥s✐❞❡r❛❞♦s ❝♦♥tr♦❧❡ ❞❡❢♦r♠❛çã♦✳ ❚❛✐s ❝♦♠♣♦rt❛♠❡♥t♦s ❡♠❡r❣❡♠ ❞❛ ❝♦♦♣❡r❛çã♦ ❧♦❝❛❧ ❡♥tr❡ ♦s ♠❡♠❜r♦s ❞♦❣r✉♣♦✱ ❝✉❥❛s ❞✐stâ♥❝✐❛s ❡ ♦r✐❡♥t❛çã♦ sã♦ ♠❛♥t✐❞❛s ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ❝♦♥st❛♥t❡s✳ ❊♠❡♥①❛♠❡s r♦❜ót✐❝♦s✱ ♦ ❝♦♥tr♦❧❡ ❞❡ ❢♦r♠❛çã♦ ❝♦♥s✐st❡ ♥❛ ❝♦♦r❞❡♥❛çã♦ ❞❡ ✉♠ ❣r✉♣♦ ❞❡❛❣❡♥t❡s ♥♦ s❡♥t✐❞♦ ❞❡ s❡ ❡st❛❜❡❧❡❝❡r ❡ ♠❛♥t❡r ❞❡t❡r♠✐♥❛❞❛ ❢♦r♠❛çã♦ ❣❡♦♠étr✐❝❛✳ ❇❛❤❝❡❝✐ ❡t ❛❧✳ ❬✷✵✵✸❪ ❝❧❛ss✐✜❝❛♠ ♦s ❡st✉❞♦s ♥❡ss❛ ár❡❛ ❡♠ ❞♦✐s ❣r✉♣♦s✿ ❝❡♥tr❛❧✐③❛❞♦❡ ❞❡s❝❡♥tr❛❧✐③❛❞♦✳ ◆♦ ❝♦♥tr♦❧❡ ❞❡ ❢♦r♠❛çã♦ ❝❡♥tr❛❧✐③❛❞♦ ❛ ❝♦♦r❞❡♥❛çã♦ ❞♦ ❣r✉♣♦ é❢❡✐t❛ ♣♦r ✉♠❛ ❡♥t✐❞❛❞❡ ❝❡♥tr❛❧✐③❛❞♦r❛ q✉❡ ♥♦r♠❛❧♠❡♥t❡ ♣♦ss✉✐ ✐♥❢♦r♠❛çã♦ ❣❧♦❜❛❧ ❞♦❛♠❜✐❡♥t❡ ✭t❛✐s ❝♦♠♦ ✉♠ ♠❛♣❛✮ ❡ q✉❡ t❡♠ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❝♦♥tr♦❧❛r ❞✐r❡t❛♠❡♥t❡ ♦s❞❡♠❛✐s ✐♥t❡❣r❛♥t❡s✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ♦ ❝♦♥tr♦❧❡ ❞❡s❝❡♥tr❛❧✐③❛❞♦ ❢❛③ ✉s♦ ❞❡ ♠ét♦❞♦s ❞❡❝♦♥tr♦❧❡ ❞❡ ❢♦r♠❛çã♦ ❞✐str✐❜✉í❞♦s ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ❛❧❝❛♥ç❛r ❛ ❝♦♦r❞❡♥❛çã♦ ❞♦ ❣r✉♣♦✳ ❆❧❣♦r✐t♠♦s ❞❡ ❝♦♥tr♦❧❡ ❞❡ ❢♦r♠❛çã♦ q✉❡ r❡q✉❡r❡♠ ✐♥❢♦r♠❛çã♦ ❣❧♦❜❛❧ t❡♥❞❡♠ ❛ s❡r ❧✐♠✐t❛❞♦s ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ à ❡s❝❛❧❛❜✐❧✐❞❛❞❡✳ ❆❧é♠ ❞✐ss♦✱ ❝♦st✉♠❛♠ ♥❡❝❡ss✐t❛r ❞❡✉♠ t❡♠♣♦ ♠❛✐♦r ❞❡ ✐♥✐❝✐❛❧✐③❛çã♦ ❡ sã♦ ♠❛✐s s✉s❝❡tí✈❡✐s à ❢❛❧❤❛s✳ ◆♦ ❡♥t❛♥t♦✱ ♣❡r♠✐✲ t❡♠ ✉♠ ❝♦♥tr♦❧❡ ❞❡ ❢♦r♠❛çã♦ ♠❛✐s ♣r❡❝✐s♦✱ ❛❧é♠ ❞❡ ✈✐❛❜✐❧✐③❛r❡♠ ♠❛✐♦r ✈❛r✐❛❜✐❧✐❞❛❞❡❞❡ ❢♦r♠❛çõ❡s✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❛❧❣♦r✐t♠♦s q✉❡ ✉t✐❧✐③❛♠ ✐♥❢♦r♠❛çã♦ ❧♦❝❛❧ ♦❜t✐❞❛s ♣♦r✐♥t❡r♠é❞✐♦ ❞❡ ❧❡✐t✉r❛s s❡♥s♦r✐❛✐s t❡♥❞❡♠ ❛ s❡r ♠❛✐s ❡s❝❛❧á✈❡✐s✱ r♦❜✉st♦s ❡ ❢á❝❡✐s ❞❡ ❝♦♥s✲ tr✉✐r✳ ❈♦♥t✉❞♦✱ t❛✐s ❛❧❣♦r✐t♠♦s sã♦ ♠❛✐s ❧✐♠✐t❛❞♦s ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ à ♣r❡❝✐sã♦ ❡ à✈❛r✐❛❜✐❧✐❞❛❞❡ ❞❛s ❢♦r♠❛çõ❡s✳ ❖ ❝♦♥tr♦❧❡ ❞❡ ❛♥é✐s ❞❡ s❛té❧✐t❡s ❡♠ ór❜✐t❛ ❬▼❛rt✐♥ ❡t ❛❧✳✱✷✵✵✶❪✱ ♦ ❝♦♥tr♦❧❡ ❞❡ ❣r✉♣♦s ❞❡ ✈❡í❝✉❧♦s ❛ér❡♦s ♥ã♦ tr✐♣✉❧❛❞♦s ❬❑♦♦ ✫ ❙❤❛❤r✉③✱ ✷✵✵✶❪ ❡ ❛♠♦✈✐♠❡♥t❛çã♦ ❡♠ ❢♦r♠❛çã♦ ❬❈❛r♣✐♥ ✫ P❛r❦❡r✱ ✷✵✵✷❪ tê♠ s✐❞♦ ❛❧❣✉♠❛s ❞❛s ❛♣❧✐❝❛çõ❡s q✉❡ ❢❛③❡♠ ✉s♦ ❞❡ té❝♥✐❝❛s ❞❡ ❝♦♥tr♦❧❡ ❞❡ ❢♦r♠❛çã♦✳ ❆❜♦r❞❛❣❡♥s ❤✐❡rárq✉✐❝❛s t❛♠❜é♠ tê♠ s✐❞♦ ❡♠♣r❡❣❛❞❛s ❡♠ t❛r❡❢❛s ❞❡ ❝♦♥tr♦❧❡ ❞❡❢♦r♠❛çã♦✳ ❊♠ ❬❈❤❛✐♠♦✇✐❝③ ✫ ❑✉♠❛r✱ ✷✵✵✹❪ é ♣r♦♣♦st❛ ✉♠❛ ❛rq✉✐t❡t✉r❛ ❤✐❡rárq✉✐❝❛♥❛ q✉❛❧ ✈❡í❝✉❧♦s ❛ér❡♦s ♥ã♦ tr✐♣✉❧❛❞♦s sã♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ ❝♦♥tr♦❧❛r ✉♠ ❡♥①❛♠❡ ❞❡✈❡í❝✉❧♦s t❡rr❡str❡s✳ ❊ss❡s ú❧t✐♠♦s sã♦ ♦r❣❛♥✐③❛❞♦s ❡♠ ❣r✉♣♦s✱ ♦s q✉❛✐s sã♦ ♠♦♥✐t♦r❛❞♦s❡ ❝♦♥❞✉③✐❞♦s ♣❡❧♦s ✈❡í❝✉❧♦s ❛ér❡♦s✱ ♣♦r ♠❡✐♦ ❞❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞❡❧✐❜❡r❛t✐✈❛✳ ❆ss✐♠✱ ♦s✈❡í❝✉❧♦s ❛ér❡♦s ❝♦♥tr♦❧❛♠ ❛ ❢♦r♠❛✱ ❛ ♣♦s❡ ❡ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦s ❣r✉♣♦s✱ ♣❡r♠✐t✐♥❞♦ q✉❡♦s ♠❡s♠♦s ♣♦ss❛♠ s❡r ❞✐✈✐❞✐❞♦s ♦✉ ✉♥✐❞♦s ♣❛r❛ ❛ ❡①❡❝✉çã♦ ❞❡ ❞❡t❡r♠✐♥❛❞❛s t❛r❡❢❛s✱ t❛✐s❝♦♠♦ ❛ ❝♦❜❡rt✉r❛ ❞❡ ✉♠❛ r❡❣✐ã♦ ♦✉ ❛ tr❛♥s♣♦s✐çã♦ ❞❡ ♦❜stá❝✉❧♦s✳ ❯♠❛ ❝❛r❛❝t❡ríst✐❝❛✐♠♣♦rt❛♥t❡ ❞❡ss❛ ❛rq✉✐t❡t✉r❛ é r❡❢❡♥t❡ à ❡s❝❛❧❛❜✐❧✐❞❛❞❡✱ ✉♠❛ ✈❡③ q✉❡ ♦s r❡q✉✐s✐t♦s ❞❡❝♦♠✉♥✐❝❛çã♦ sã♦ r❡str✐t♦s✳ ❙❛♥t♦s ✫ ❈❤❛✐♠♦✇✐❝③ ❬✷✵✶✶❪ ♣r♦♣õ❡♠ ♦ ✉s♦ ❞❡ ❤✐❡r❛rq✉✐❛s ♣❛r❛ ❧✐❞❛r ❝♦♠ ♣r♦❜❧❡✲♠❛s ❞❡ ❝♦♥❣❡st✐♦♥❛♠❡♥t♦ ❡♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s✳ ◆❡ss❡ tr❛❜❛❧❤♦✱ ❛ ❛❜str❛çã♦ ❣❡♦♠é✲ ✷✳✸✳ ❊♥①❛♠❡ ❞❡ ❘♦❜ôs ▼ó✈❡✐s✷✶ tr✐❝❛ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❝❛❞❛ ❤✐❡r❛rq✉✐❛ é ✉♠❛ ❡❧✐♣s❡✳ ●r✉♣♦s ❞❡ r♦❜ôs s✉❜♠❡t✐❞♦s ❛ ✉♠❛ ❛❜str❛çã♦ sã♦ ❝♦♥tr♦❧❛❞♦s ✐♠♣❧✐❝✐t❛♠❡♥t❡ ♣♦r ✐♥t❡r♠é❞✐♦ ❞♦ ❝♦♥tr♦❧❡ ❞❡ss❛ ❛❜str❛çã♦✱♦ q✉❡ é ❢❡✐t♦ ♥❡ss❡ tr❛❜❛❧❤♦ ♣♦r ♠❡✐♦ ❞❛ ♠✉❞❛♥ç❛ ❞♦s ♣❛râ♠❡tr♦s ❞❛ ❡❧✐♣s❡✳ ❈❛♠♣♦s♣♦t❡♥❝✐❛✐s sã♦ ❡♠♣r❡❣❛❞♦s ♥❛s ❧❡✐s ❞❡ ❝♦♥tr♦❧❡ ❡ ✉♠ ❛❧❣♦r✐t♠♦ ❞❡ ❞❡s✈✐♦ ❞❡ ♦❜stá❝✉✲❧♦s ❢♦✐ ♣r♦♣♦st♦✱ t❡♥❞♦ ❝♦♠♦ ❜❛s❡ ❛ ✐♥t❡rs❡çã♦ ❞❡ss❛s ❤✐❡r❛rq✉✐❛s✳ ❉❡ss❛ ❢♦r♠❛✱ r♦❜ôs s✉❜♠❡t✐❞♦s ❛ ❤✐❡r❛rq✉✐❛s ❞✐st✐♥t❛s✱ ♣♦ré♠ ♦❜❥❡t✐✈❛♥❞♦ ✈✐s✐t❛r ✉♠❛ ♠❡s♠❛ r❡❣✐ã♦ ♥♦❛♠❜✐❡♥t❡✱ ❡✈✐t❛♠ ♦ ❝♦♥❣❡st✐♦♥❛♠❡♥t♦ ❛ss♦❝✐❛❞♦ ❛ ❡ss❛ t❛r❡❢❛ ♣♦r ♠❡✐♦ ❞♦ ❝♦♥tr♦❧❡ ❞❛s❛❜str❛çõ❡s✳❉✐s♣❡rsã♦❯♠ ❞♦s ♣r✐♠❡✐r♦s ❛❧❣♦r✐t♠♦s ✉t✐❧✐③❛❞♦s ❡♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s ❢♦✐ ❛ ❞✐s♣❡rsã♦ ✉♥✐❢♦r♠❡❡♠ ❛♠❜✐❡♥t❡s ✐♥t❡r♥♦s✳ ◆♦ ♣r♦❜❧❡♠❛ ❞❡ ❞✐s♣❡rsã♦✱ ♦ ❞❡s❛✜♦ é ♦❜t❡r ✉♠❛ ❞✐s♣♦s✐çã♦✉♥✐❢♦r♠❡ ❞♦s r♦❜ôs ♥❛ ár❡❛ ❞❡ ❛t✉❛çã♦✱ ❞❡ ♠♦❞♦ ❛ ♠❛①✐♠✐③❛r ❛ ár❡❛ ❞❡ ❝♦❜❡rt✉r❛✱❡♥q✉❛♥t♦ ♠❛♥té♠ ♦s r♦❜ôs ❡♠ ✉♠❛ r❡❞❡ ❝♦♥❡❝t❛❞❛ ♣♦r ✐♥t❡r♠é❞✐♦ ❞❡ ❛❧❣✉♠ ♠❡❝❛♥✐s♠♦❞❡ ❝♦♠✉♥✐❝❛çã♦✳ ❯♠❛ ❢♦r♠❛ ❝♦♠✉♠❡♥t❡ ❡♠♣r❡❣❛❞❛ ♣❛r❛ ❡❢❡t✉❛r ❛ ❞✐s♣❡rsã♦ ❝♦♥s✐st❡❡♠ ✐❞❡♥t✐✜❝❛r ♦s k ✈✐③✐♥❤♦s ♠❛✐s ♣ró①✐♠♦s ❞❡ ❝❛❞❛ r♦❜ô✱ ❝❛❧❝✉❧❛r ❛ r❡s✉❧t❛♥t❡ ❞❛s❢♦rç❛s ❡①❡r❝✐❞❛s ♥❡ss❡ s✉❜❣r✉♣♦ ❡ ✉t✐❧✐③á✲❧❛ ♣❛r❛ ❞❡✜♥✐r ♦ ♠♦✈✐♠❡♥t♦ ❞♦ r♦❜ô✳ ❆♠♦✈✐♠❡♥t❛çã♦ ❝♦♥❥✉♥t❛ ❞♦s r♦❜ôs r❡s✉❧t❛ ❡♠ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❡s♣❛❝✐❛❧ ✉♥✐❢♦r♠❡ ♥♦❛♠❜✐❡♥t❡✳ ❊st✉❞♦s ❡♠♣ír✐❝♦s tê♠ s✐❞♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ s❡ ❞❡✜♥✐r ♦ ✈❛❧♦r ❞❡ k✳ ❆❋✐❣✉r❛ ✷✳✺ ✐❧✉str❛ ❛ ❛♣❧✐❝❛çã♦ ❞❡ss❡ ❛❧❣♦r✐t♠♦✱ ❝♦♥❢♦r♠❡ ❛♣r❡s❡♥t❛❞♦ ❡♠ ❬▼❝❧✉r❦✐♥✫ ❙♠✐t❤✱ ✷✵✵✹❪✳ ▼✉✐t❛s ❛♣❧✐❝❛çõ❡s ♥♦ â♠❜✐t♦ ❞❡ ❡♥①❛♠❡s ❞❡ r♦❜ôs ♥❡❝❡ss✐t❛♠ ❞❡❛❧❣♦r✐t♠♦s q✉❡ ♣♦ss✐❜✐❧✐t❡♠ ❛♦s ✐♥t❡❣r❛♥t❡s ❞♦ ❡♥①❛♠❡ ❡❢❡t✉❛r ❛ ❝♦❜❡rt✉r❛ ❞❡ t♦❞❛ ❛ár❡❛ ❞❡ ❡①♣❧♦r❛çã♦✳ ❊①♣❧♦r❛çã♦ ❞❡ ❛♠❜✐❡♥t❡s ❡ ❜✉s❝❛ ♣♦r s♦❜r❡✈✐✈❡♥t❡s ❝♦♥st✐t✉❡♠❛♣❧✐❝❛çõ❡s ❡♠ ♣♦t❡♥❝✐❛❧ ♣❛r❛ ♦ ❡♠♣r❡❣♦ ❞❡ té❝♥✐❝❛s ❞❡ ❞✐s♣❡rsã♦✳ ❋✐❣✉r❛ ✷✳✺✿ ❉✐s♣❡rsã♦ ❡s♣❛❝✐❛❧ ❡♠ ❛♠❜✐❡♥t❡ ✐♥t❡r♥♦ ❬▼❝❧✉r❦✐♥ ✫ ❙♠✐t❤✱ ✷✵✵✹❪✳❊♠ ❬❆❧✐t❛♣♣❡❤ ✫ P✐♠❡♥t❛✱ ✷✵✶✹❪✱ ♦s ❛✉t♦r❡s ✐♥❝♦r♣♦r❛♠ s❡❣✉r❛♥ç❛ ❛♦ ♣r♦❜❧❡♠❛ ❞❡ ❞✐s♣❡rsã♦✳ P❛r❛ ✐ss♦✱ ❛ ❞✐s♣❡rsã♦ s❡❣✉r❛ ❞❡ ✉♠ ❣r✉♣♦ ❞❡ r♦❜ôs ♥♦ ❛♠❜✐❡♥t❡ é ✷✷❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ tr❛t❛❞❛ ❝♦♠ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦✳ ❉✐❛❣r❛♠❛s ❞❡ ❱♦r♦♥♦✐ sã♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ ♠❛①✐♠✐③❛r ❛ ❞✐stâ♥❝✐❛ ❡♠ r❡❧❛çã♦ ❛ ♦❜stá❝✉❧♦s ❡stát✐❝♦s ❞✐s♣♦st♦s ♥♦ ❛♠❜✐❡♥t❡✳ ❯♠❛♥♦✈❛ ♠étr✐❝❛ ❞❡ ❞✐stâ♥❝✐❛ é ♣r♦♣♦st❛✱ s❡♥❞♦ ❛ ♠❡s♠❛ ♠❛✐s r❡❛❧íst✐❝❛ ♣❛r❛ ❡st❡ t✐♣♦ ❞❡♣r♦❜❧❡♠❛ q✉❛♥❞♦ ❝♦♠♣❛r❛❞❛ à ❞✐stâ♥❝✐❛ ❊✉❝❧✐❞✐❛♥❛✳ ❆ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛ ❝♦♥s✐❞❡r❛✉♠ ❛❧❣♦r✐t♠♦ ❞✐str✐❜✉í❞♦ q✉❡ ❝❛❧❝✉❧❛ ❞❡ ♠❛♥❡✐r❛ ❡✜❝✐❡♥t❡ ✉♠❛ s♦❧✉çã♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✳❋♦rr❛❣❡❛♠❡♥t♦❊♠ s✐st❡♠❛s s♦❝✐❛✐s ❜✐♦❧ó❣✐❝♦s✱ ♦ ❢♦rr❛❣❡❛♠❡♥t♦ ✭❢♦r❛❣✐♥❣✮ ❝♦♥s✐st❡ ♥♦ ❛t♦ ❞❡ ❡①♣❧♦r❛r ♦❛♠❜✐❡♥t❡ ❡♠ ❜✉s❝❛ ❞❡ ❛❧✐♠❡♥t♦s✳ ■♥s♣✐r❛❞♦s ♥❡ss❡ ❝♦♠♣♦rt❛♠❡♥t♦✱ ❞✐✈❡rs♦s tr❛❜❛❧❤♦s tê♠ s❡ ✉t✐❧✐③❛❞♦ ❞❡ ❛❧❣♦r✐t♠♦s ❞❡ ❝♦♦r❞❡♥❛çã♦ ♣❛r❛ ❡❢❡t✉❛r ❝♦❧❡t❛ ❞❡ ♦❜❥❡t♦s ❞✐s♣♦st♦s♥♦ ❛♠❜✐❡♥t❡ ❬❇❛❧❝❤✱ ✶✾✾✾❪✳ ❱ár✐❛s té❝♥✐❝❛s tê♠ s✐❞♦ ✉t✐❧✐③❛❞❛s✱ ❞❡s❞❡ ❛q✉❡❧❛s ❛❞✈✐♥❞❛s❞❛ ár❡❛ ❞❡ ❙✇❛r♠ ■♥t❡❧❧✐❣❡♥❝❡ ❬❇♦♥❛❜❡❛✉ ❡t ❛❧✳✱ ✶✾✾✾❀ ▲✐✉ ✫ P❛ss✐♥♦✱ ✷✵✵✵❪ q✉❛♥t♦ ❞❡ár❡❛s ❝❧áss✐❝❛s ❞❛ ❘♦❜ót✐❝❛✳ ◆♦s ❛❧❣♦r✐t♠♦s ❞❡ ❢♦rr❛❣❡❛♠❡♥t♦✱ ❛ ❝♦♠✉♥✐❝❛çã♦ ❡♥tr❡ ♦s ✐♥t❡❣r❛♥t❡s ❞❡ ✉♠ ❡♥✲①❛♠❡ ❞❡ r♦❜ôs tê♠ s✐❞♦ ✐♠♣❧❡♠❡♥t❛❞❛ ❜❛s✐❝❛♠❡♥t❡ ❞❡ ❞✉❛s ❢♦r♠❛s✿ ❝♦♠✉♥✐❝❛çã♦ ✐♥❞✐✲ r❡t❛ ❡ ❝♦♠✉♥✐❝❛çã♦ ❞✐r❡t❛✳ ◆❛ ❝♦♠✉♥✐❝❛çã♦ ✐♥❞✐r❡t❛✱ ❝♦♠✉♠❡♥t❡ ❞❡♥♦♠✐♥❛❞❛ ❡st✐❣♠❡r✲❣✐❛✱ ♦s ✐♥t❡❣r❛♥t❡s ❞♦ ❡♥①❛♠❡ ✉t✐❧✐③❛♠ ♦ ❛♠❜✐❡♥t❡ ❝♦♠♦ ú♥✐❝♦ ♠❡✐♦ ❞❡ ❝♦♠✉♥✐❝❛çã♦✳❆❧❣✉♥s ✐♥s❡t♦s s♦❝✐❛✐s✱ ❡♥tr❡ ❡❧❡s ❛s ❢♦r♠✐❣❛s✱ ❞❡♣♦s✐t❛♠ ✉♠❛ s✉❜stâ♥❝✐❛ ❞❡♥♦♠✐♥❛❞❛❢❡r♦♠ô♥✐♦ ♥♦ ❛♠❜✐❡♥t❡ ❡✱ ♣♦r ♠❡✐♦ ❞❡ss❛✱ ❡st❛❜❡❧❡❝❡♠ ✉♠ ♣r♦❝❡ss♦ ❞❡ ❝♦♠✉♥✐❝❛çã♦❝♦♠ ♦✉tr♦s ❡❧❡♠❡♥t♦s ❞❛ s♦❝✐❡❞❛❞❡✳ ◆❛ ❧✐t❡r❛t✉r❛ ❡①✐st❡♠ ✈ár✐♦s tr❛❜❛❧❤♦s q✉❡ ✉t✐❧✐✲③❛♠ ❡♥❢♦q✉❡s ❞✐❢❡r❡♥t❡s ♣❛r❛ ✐♠♣❧❡♠❡♥t❛r ❢❡r♦♠ô♥✐♦s ✈✐rt✉❛✐s✱ t❛✐s ❝♦♠♦ ❬P❛②t♦♥ ❡t ❛❧✳✱✷✵✵✸❪ ❡ ❬P❛♥❛✐t ✫ ▲✉❦❡✱ ✷✵✵✹❪✳ ◆♦ ❡♥t❛♥t♦✱ ❛❧❣✉♥s ♣♦✉❝♦s tr❛❜❛❧❤♦s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦❬❘✉ss❡❧❧✱ ✷✵✵✵❪✱ ❛♣r❡s❡♥t❛♠ ❡①♣❡r✐♠❡♥t♦s ❝♦♠ ❢❡r♦♠ô♥✐♦s r❡❛✐s✳ ❆ té❝♥✐❝❛ ❞❡ ❙✇❛r♠ ■♥t❡❧❧✐❣❡♥❝❡ ❞❡♥♦♠✐♥❛❞❛ ❆♥t ❈♦❧♦♥② ❖♣t✐♠✐③❛t✐♦♥ ✭❆❈❖✮✭✈❡r ❬❉♦r✐❣♦ ✫ ❙tüt③❧❡✱ ✷✵✵✷❪✮ ✉t✐❧✐③❛ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❢❡r♦♠ô♥✐♦ ♣❛r❛ ✐♠♣❧❡♠❡♥t❛r ❛❧❣♦✲ r✐t♠♦s q✉❡ s♦❧✉❝✐♦♥❛♠ ♣r♦❜❧❡♠❛s ❞❡ ♦t✐♠✐③❛çã♦ ❝♦♠❜✐♥❛tór✐❛✳ ❈♦♠ ♦s ❜♦♥s r❡s✉❧t❛✲❞♦s ❛❞✈✐♥❞♦s ❞❛ ❛♣❧✐❝❛çã♦ ❞❡ss❛ té❝♥✐❝❛✱ ♣❡sq✉✐s❛❞♦r❡s ❡♠ ❘♦❜ót✐❝❛ ✈ê♠ ✉t✐❧✐③❛♥❞♦ ❛♠❡s♠❛ ❡♠ s✉❛s ♣❡sq✉✐s❛s✳ ❊♠ ❬❏✉❛♥✲♣✐♥❣ ❡t ❛❧✳✱ ✷✵✶✵❪✱ ♣♦r ❡①❡♠♣❧♦✱ ♦ ❝♦♥❝❡✐t♦ ❞❡❢❡r♦♠ô♥✐♦ ❢♦✐ ✉t✐❧✐③❛❞♦ ♣❛r❛ ✐♠♣❧❡♠❡♥t❛r ❛ ❝♦♠✉♥✐❝❛çã♦ ✐♥❞✐r❡t❛ ❡♥tr❡ ♦s ✐♥t❡❣r❛♥t❡s❞♦ s✐st❡♠❛✳ P❛②t♦♥ ❡t ❛❧✳ ❬✷✵✵✸❪ ♣r♦♣õ❡♠ ✉♠ ♠❡❝❛♥✐s♠♦ ❞❡ tr♦❝❛ ❞❡ ♠❡♥s❛❣❡♥s ♣❛r❛ ✐♠♣❧❡✲♠❡♥t❛r ♦ ❝♦♥❝❡✐t♦ ❞❡ ❢❡r♦♠ô♥✐♦✳ ❉❡ss❡ ♠♦❞♦✱ ❛♦ ✐♥✈és ❞❡ ✉t✐❧✐③❛r ♦ ♠❡✐♦✱ ♦s r♦❜ôs❡st❛❜❡❧❡❝❡♠ ❝♦♠✉♥✐❝❛çã♦ ❝♦♠ ✐♥t❡❣r❛♥t❡s ❞♦ ❣r✉♣♦ q✉❡ s❡ ❡♥❝♦♥tr❛♠ ❞✐s♣♦st♦s ❡♠ s✉❛s ✈✐③✐♥❤❛♥ç❛s✳ P♦r ♠❡✐♦ ❞❡ ✉♠ ♣r♦❝❡ss♦ ❞❡ tr♦❝❛ ❞❡ ♠❡♥s❛❣❡♥s ❡♠ ❝❛s❝❛t❛✱ t♦❞♦s♦s ✐♥t❡❣r❛♥t❡s ❞♦ ❡♥①❛♠❡ r❡❝❡❜❡♠ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ✐♥❢♦r♠❛çã♦✳ ❉❡ ♠♦❞♦ ❛ ♠❛♥t❡r❝♦❡rê♥❝✐❛ ❝♦♠ ♦ ♦❜❥❡t♦ ❞❡ ✐♥s♣✐r❛çã♦✱ ♦s ❛✉t♦r❡s ♣r❡s❡r✈❛r❛♠ ❛❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s ✷✳✸✳ ❊♥①❛♠❡ ❞❡ ❘♦❜ôs ▼ó✈❡✐s✷✸ ❡ss❡♥❝✐❛✐s✿ ✭✐✮ ❛s ♠❡♥s❛❣❡♥s ✭❢❡r♦♠ô♥✐♦s✮ sã♦ ❧♦❝❛❧♠❡♥t❡ tr❛♥s♠✐t✐❞❛s s❡♠ ❞❡st✐♥❛tár✐♦❞❡✜♥✐❞♦❀ ✭✐✐✮ ✉t✐❧✐③❛✲s❡ ✉♠❛ té❝♥✐❝❛ ❞❡ ❣r❛❞✐❡♥t❡ ♣❛r❛ ❞✐❢✉sã♦ ❞❛s ♠❡♥s❛❣❡♥s❀ ❡ ✭✐✐✐✮❛ ✐♥t❡♥s✐❞❛❞❡ ❞♦s ❢❡r♦♠ô♥✐♦s ❞❡❝❛❡♠ ❝♦♠ ♦ t❡♠♣♦✳ ❆ ❋✐❣✉r❛ ✷✳✻ ✐❧✉str❛ ❛ r❡❢❡r✐❞❛ té❝♥✐❝❛ ❞❡ ❞✐❢✉sã♦ ❞❡ ♠❡♥s❛❣❡♥s✳❋✐❣✉r❛ ✷✳✻✿ ❆♣❧✐❝❛çã♦ ❞❡ té❝♥✐❝❛ ❞❡ ❣r❛❞✐❡♥t❡ ♣❛r❛ ❞✐❢✉sã♦ ❞❡ ♠❡♥s❛❣❡♥s ✭❢❡r♦♠ô♥✐♦s✮ ❬P❛②t♦♥ ❡t ❛❧✳✱ ✷✵✵✸❪✳❙❡❣r❡❣❛çã♦❆ s❡❣r❡❣❛çã♦ ❡♠ s✐st❡♠❛s ❜✐♦❧ó❣✐❝♦s ❝♦♥s✐st❡ ❡♠ ✉♠ ♠❡❝❛♥✐s♠♦ ❞❡ ❝r✐❛çã♦ ❞❡ ❣r✉♣♦s❢✉♥❝✐♦♥❛✐s✳ ❊ss❡ ♠❡❝❛♥✐s♠♦ ❡❢❡t✉❛ ❛ s❡♣❛r❛çã♦ ❞❡ ❡❧❡♠❡♥t♦s q✉❡ ❝♦♠♣❛rt✐❧❤❛♠ ❞❡t❡r✲♠✐♥❛❞❛s ❝❛r❛❝t❡ríst✐❝❛s✳ ❚❛❧ ♠❡❝❛♥✐s♠♦ é ❛♠♣❧❛♠❡♥t❡ ❡♥❝♦♥tr❛❞♦ ♥❛ ♥❛t✉r❡③❛ ❝♦♠♦✱♣♦r ❡①❡♠♣❧♦✱ ♥❛ s❡❣r❡❣❛çã♦ ❝❡❧✉❧❛r ♣❛r❛ ❢♦r♠❛çã♦ ❞❡ t❡❝✐❞♦s ❡ ♥❛ s❡❣r❡❣❛çã♦ s♦❝✐❛❧ q✉❡ ❞á ♦r✐❣❡♠ ❛ ❣r✉♣♦s s♦❝✐❛✐s ♦✉ s♦❝✐❡❞❛❞❡s✳ ◆❡ss❡s s✐st❡♠❛s✱ ❛ s❡❣r❡❣❛çã♦ t❡♠ ✉♠♣❛♣❡❧ ❢✉♥❞❛♠❡♥t❛❧✱ ✉♠❛ ✈❡③ q✉❡ ❝♦♠♣õ❡ ❛ ❜❛s❡ ❞❛ ❡♠❡r❣ê♥❝✐❛ ❞❡ ✈ár✐❛s ❢♦r♠❛s ❞❡❝♦♦♣❡r❛çã♦✳ ❉✐❢❡r❡♥t❡s ❢♦r♠❛s ❞❡ s❡❣r❡❣❛çã♦ tê♠ s✐❞♦ ✐♠♣❧❡♠❡♥t❛❞❛s ❡♠ ❡♥①❛♠❡s r♦✲❜ót✐❝♦s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❛s ❡♥❝♦♥tr❛❞❛s ♥♦s tr❛❜❛❧❤♦s ❞❡ ●r♦ÿ ❡t ❛❧✳ ❬✷✵✵✾❪✱ ❑✉♠❛r❡t ❛❧✳ ❬✷✵✶✵❪✱ ❙❛♥t♦s ❡t ❛❧✳ ❬✷✵✶✹❪ ❡ ❋✐❧❤♦ ✫ P✐♠❡♥t❛ ❬✷✵✶✺❪✳ ◆❡ss❡s tr❛❜❛❧❤♦s✱ ❢✉♥çõ❡s♣♦t❡♥❝✐❛✐s tê♠ s✐❞♦ ❛♣❧✐❝❛❞❛s ♣❛r❛ ♣r♦♣✐❝✐❛r ❛ ❢♦r♠❛çã♦ ❞❡ ❣r✉♣♦s ❤♦♠♦❣ê♥❡♦s✳ ❊♠ ❬❑✉♠❛r ❡t ❛❧✳✱ ✷✵✶✵❪✱ ❛ s❡❣r❡❣❛çã♦ é ❡♠♣r❡❣❛❞❛ ♣❛r❛ ❞✐✈✐❞✐r ✉♠ ❡♥①❛♠❡❡♠ ❞♦✐s ❣r✉♣♦s✱ ❝✉❥♦s ✐♥t❡❣r❛♥t❡s ❝♦♠♣❛rt✐❧❤❛♠ ❝❛r❛❝t❡ríst✐❝❛s ❡♠ ❝♦♠✉♠✳ ❙❛♥t♦s❡t ❛❧✳ ❬✷✵✶✹❪ ❣❡♥❡r❛❧✐③❛♠ ❛ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛ ❡♠ ❬❑✉♠❛r ❡t ❛❧✳✱ ✷✵✶✵❪ ❛♦ ♣❡r♠✐t✐r ❛❞✐✈✐sã♦ ❞♦ ❡♥①❛♠❡ ❡♠ ✉♠ ♥ú♠❡r♦ ♠❛✐♦r ❞❡ ❣r✉♣♦s✳ ❆♣❡s❛r ❞♦s ❝♦♥tr♦❧❛❞♦r❡s ✉t✐❧✐③❛❞♦s♥❡ss❡s tr❛❜❛❧❤♦s s❡r❡♠ ❞✐str✐❜✉í❞♦s✱ ♦s r♦❜ôs ♥❡❝❡ss✐t❛♠ ❞❡ ✐♥❢♦r♠❛çõ❡s ❞❡ t♦❞♦s ♦s✐♥t❡❣r❛♥t❡s ❞♦ ❣r✉♣♦ ❡ ♦s s✉❜❣r✉♣♦s ❣❡r❛❞♦s tê♠ ❞❡ s❡r ❜❛❧❛♥❝❡❛❞♦s✳ ❋✐❧❤♦ ✫ P✐♠❡♥t❛❬✷✵✶✺❪ ❛❜♦r❞❛♠ ♦ ♣r♦❜❧❡♠❛ ❞❛ s❡❣r❡❣❛çã♦ ❝♦♠ ♦ ✉s♦ ❞❡ ❛❜str❛çõ❡s ❡ ♣r♦✈ê♠ ✉♠❛♣r♦✈❛ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ♣❛r❛ ❛ s❡❣r❡❣❛çã♦ ❞❡ ♠ú❧t✐♣❧♦s ❣r✉♣♦s✳ ❆❧é♠ ❞✐ss♦✱ ❛ ❛❜♦r❞❛❣❡♠ ✷✹❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ♣r♦♣♦st❛ ♥ã♦ ❡①✐❣❡ ♦ r❡❝❡❜✐♠❡♥t♦ ❞❡ ✐♥❢♦r♠❛çõ❡s ❞❡ t♦❞♦s ♦s ✐♥t❡❣r❛♥t❡s ❞♦ ❡♥①❛♠❡❞✉r❛♥t❡ t♦❞♦ ♦ t❡♠♣♦✳❚r❛♥s♣♦rt❡ ❝♦♦♣❡r❛t✐✈♦❆ ❝❛♣t✉r❛ ❞❡ ♣r❡s❛s ❡♠ ❝♦❧ô♥✐❛s ❞❡ ❢♦r♠✐❣❛s ✭❋✐❣✉r❛ ✷✳✼❛✮ é ✉♠ ❞♦s ❡①❡♠♣❧♦s ❝♦✲♠✉♠❡♥t❡ ❡♥❝♦♥tr❛❞♦ ♥❛ ♥❛t✉r❡③❛ ♥♦ q✉❡ s❡ r❡❢❡r❡ ❛♦ tr❛♥s♣♦rt❡ ❝♦♦♣❡r❛t✐✈♦ ❞❡ ✐t❡♥s✳◆♦r♠❛❧♠❡♥t❡✱ ✉♠❛ ❢♦r♠✐❣❛ ❡♥❝♦♥tr❛ ✉♠❛ ♣r❡s❛ ❡ t❡♥t❛ ❧❡✈á✲❧❛ ♣❛r❛ ♦ ♥✐♥❤♦✳ ◆ã♦❝♦♥s❡❣✉✐♥❞♦ ♦❜t❡r ê①✐t♦ ♥❡ss❛ t❛r❡❢❛✱ ❛ ♠❡s♠❛ r❡❝r✉t❛ ♦✉tr❛s ❢♦r♠✐❣❛s ♣❛r❛ ❛❥✉❞á✲❧❛✳❊ss❡ ♣r♦❝❡ss♦ ❝♦♥t✐♥✉❛ ❛té q✉❡ ❛ ♣r❡s❛ s❡❥❛ ❧❡✈❛❞❛ ❛♦ ♥✐♥❤♦ ♦✉ ❛té q✉❡ ❛s ❢♦r♠✐❣❛s❞❡s✐st❛♠ ❞❛ t❛r❡❢❛✳❋✐❣✉r❛ ✷✳✼✿ ❚r❛♥s♣♦rt❡ ❝♦♦♣❡r❛t✐✈♦✿ ✭❛✮ s✐st❡♠❛s ♥❛t✉r❛✐s ❡ ✭❜✮ s✐st❡♠❛s r♦❜ót✐❝♦s❬❈♦st❛ ❡t ❛❧✳✱ ✷✵✶✷❪✳ ❊st✉❞♦s ❡♠ ❘♦❜ót✐❝❛ tê♠ ✉t✐❧✐③❛❞♦ ❡ss❡ t✐♣♦ ❞❡ ❝♦♠♣♦rt❛♠❡♥t♦ ❝♦♠♦ ✐♥s♣✐r❛çã♦♣❛r❛ ❞❡s❡♥✈♦❧✈❡r ❛❧❣♦r✐t♠♦s ❞❡ ❝♦♥tr♦❧❡ q✉❡ ♣❡r♠✐t❛♠ s♦❧✉❝✐♦♥❛r t❛r❡❢❛s ❞❡ tr❛♥s♣♦rt❡❝♦♦r❞❡♥❛❞♦ ❞❡ ✐t❡♥s✳ ❊♠ ❬❑✉❜❡ ✫ ❇♦♥❛❜❡❛✉✱ ✷✵✵✵❪ é ❛♣r❡s❡♥t❛❞❛ ✉♠❛ ✈✐sã♦ ❣❡r❛❧ ❞❛ár❡❛✱ ❡♥q✉❛♥t♦ q✉❡ ❡♠ ❬❈♦st❛ ❡t ❛❧✳✱ ✷✵✶✷❪ é ❛♣r❡s❡♥t❛❞❛ ✉♠❛ ♠❡t♦❞♦❧♦❣✐❛ ♣❛r❛ ✐❞❡♥t✐✲✜❝❛çã♦ ❡ ♣♦st❡r✐♦r tr❛♥s♣♦rt❡ ❞❡ ✐t❡♥s ✭❋✐❣✉r❛ ✷✳✼❜✮✳ ◆♦r♠❛❧♠❡♥t❡ sã♦ ♥❡❝❡ssár✐♦s ♣❡❧♦♠❡♥♦s ❞♦✐s r♦❜ôs ♣❛r❛ s❡ ❝♦♠♣❧❡t❛r t❛r❡❢❛s ❞❡ss❡ t✐♣♦✱ ♣♦ré♠ ♦ ❛✉♠❡♥t♦ ♥♦ ♥ú♠❡r♦ ❞❡✐♥t❡❣r❛♥t❡s ✈✐❛❜✐❧✐③❛ ✉♠❛ ♠❡❧❤♦r❛ ♥❛ ❡✜❝✐ê♥❝✐❛✱ r♦❜✉st❡③ ❡ ♥♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ s✐st❡♠❛✳ ✷✳✹ ▲♦❝❛❧✐③❛çã♦ ❞❡ ❘♦❜ôs ▼ó✈❡✐s ❖ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ♣♦❞❡ s❡r r❡s✉♠✐❞♦ ❡♠ s❡ r❡s♣♦♥❞❡r à s❡❣✉✐♥t❡ ♣❡r❣✉♥t❛✿✏❖♥❞❡ ❡st♦✉❄✑✳ ◆♦ â♠❜✐t♦ ❞❛ ❘♦❜ót✐❝❛✱ ❡ss❛ ♣❡r❣✉♥t❛ ❞❡✈❡ s❡r r❡s♣♦♥❞✐❞❛ s♦❜ ♦ ♣♦♥t♦❞❡ ✈✐st❛ ❞♦ r♦❜ô✳ P❛r❛ ✐ss♦✱ ✉♠ r♦❜ô ❞❡✈❡rá ✉t✐❧✐③❛r ❛s ✐♥❢♦r♠❛çõ❡s q✉❡ s❡ ❡♥❝♦♥tr❛♠❞✐s♣♦♥í✈❡✐s ♣❛r❛ ✐❞❡♥t✐✜❝❛r s✉❛ ❧♦❝❛❧✐③❛çã♦ r❡❧❛t✐✈❛ ❛♦ ❛♠❜✐❡♥t❡✳ ◆❡ss❛ ♣❡rs♣❡❝t✐✈❛✱ ✷✳✹✳ ▲♦❝❛❧✐③❛çã♦ ❞❡ ❘♦❜ôs ▼ó✈❡✐s✷✺ q✉❛♥❞♦ ❛ r❡s♣♦st❛ à ♣❡r❣✉♥t❛ ❢♦r s❛t✐s❢❛tór✐❛✱ ♦✉ s❡❥❛✱ ❛ ♠❡s♠❛ ❝❛r❛❝t❡r✐③❛r ❜❡♠ ❛ ❧♦❝❛❧✐③❛çã♦ r❡❛❧ ❞♦ r♦❜ô ♥♦ ❛♠❜✐❡♥t❡✱ ♦ ♠❡s♠♦ ❡st❛rá ❛♣t♦ ❛ ❛t✉❛r ❞❡ ❢♦r♠❛ ❛✉tô♥♦♠❛✳❆ s♦❧✉çã♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ t❡♠ s✐❞♦ ❝♦♥s✐❞❡r❛❞♦ ❝♦♠♦ ♣❡ç❛ ❢✉♥❞❛♠❡♥t❛❧♣❛r❛ ♣r♦✈❡r ✉♠ r♦❜ô ♠ó✈❡❧ ❝♦♠ ❝❛♣❛❝✐❞❛❞❡s ✈❡r❞❛❞❡✐r❛♠❡♥t❡ ❛✉tô♥♦♠❛s ❬❇♦r❡♥st❡✐♥❡t ❛❧✳✱ ✶✾✾✼❀ ❚❤r✉♥ ❡t ❛❧✳✱ ✷✵✵✶❀ ▲❛❱❛❧❧❡✱ ✷✵✵✻❪✳ ❉❡t❡r♠✐♥❛r ❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ ✉♠ r♦❜ô ❡♠ r❡❧❛çã♦ ❛ ✉♠ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s✐♥❡r❝✐❛❧ ✭❣❧♦❜❛❧✮ é ❡ss❡♥❝✐❛❧ ♣❛r❛ ❞✐✈❡rs❛s t❛r❡❢❛s✱ t❛✐s ❝♦♠♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❡ ❝❛♠✐♥❤♦s❬▲❛❱❛❧❧❡✱ ✷✵✵✻❪✱ ❡①♣❧♦r❛çã♦ ❞❡ ❛♠❜✐❡♥t❡s ❬❇✉r❣❛r❞ ❡t ❛❧✳✱ ✷✵✵✵❪ ❡ ♠❛♣❡❛♠❡♥t♦ ❬❚❤r✉♥✱✷✵✵✷❪✳ ❈♦♥❢♦r♠❡ ❞✐s❝✉t✐❞♦ ♥❛ ❙❡çã♦ ✷✳✶✱ ❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ ✉♠ r♦❜ô ♥♦ ❡s♣❛ç♦ ❜✐❞✐♠❡♥✲ s✐♦♥❛❧ ♣♦❞❡ s❡r r❡♣r❡s❡♥t❛❞❛ ♣♦r s✉❛ ♣♦s❡ q = (x, y, θ)✱ s❡♥❞♦ p = (x, y) s✉❛ ♣♦s✐çã♦W , Y W ) ❡♠ r❡❧❛çã♦ ❛ ✉♠ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ✐♥❡r❝✐❛❧ (X ❡ θ s✉❛ ♦r✐❡♥t❛çã♦ ♥❡ss❡ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s✳◆❛ ❘♦❜ót✐❝❛ ▼ó✈❡❧✱ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♥s✐st❡ ❡♠ ❞❡t❡r♠✐♥❛r ❛ ♣♦s❡ ❞♦ r♦❜ô✱ ✉♠❛ ✈❡③ q✉❡ ♦ ♠❡s♠♦ ♥❡❝❡ss✐t❛ ❞❡ ♣❡❧♦ ♠❡♥♦s ❛❧❣✉♠❛ ✐❞❡✐❛ ❞❡ ♦♥❞❡ ❡st❡❥❛♣❛r❛ ♣♦❞❡r ♦♣❡r❛r ❡ ❛❣✐r ❞❡ ♠❛♥❡✐r❛ s❛t✐s❢❛tór✐❛ ♥♦ ❛♠❜✐❡♥t❡ ❬❇♦r❡♥st❡✐♥ ❡t ❛❧✳✱ ✶✾✾✼❪✳❆ ❞✐✜❝✉❧❞❛❞❡ ❡♠ s♦❧✉❝✐♦♥❛r ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❡stá ❞✐r❡t❛♠❡♥t❡ ❛ss♦❝✐❛❞❛às ✐♥❢♦r♠❛çõ❡s ❞✐s♣♦♥í✈❡✐s ♣❛r❛ ♦ r♦❜ô✳ ◆♦r♠❛❧♠❡♥t❡✱ ✉♠ r♦❜ô t❡♠ ❛❝❡ss♦ ❛ ❞♦✐s t✐♣♦s ❞❡ ✐♥❢♦r♠❛çã♦✿ ♥❛ ❡t❛♣❛ ❞❡ ✐♥✐❝✐❛❧✐③❛çã♦✱ ✉♠ r♦❜ô ♣♦❞❡ t❡r ❛❝❡ss♦ ❛ ❛❧❣✉♠❛✐♥❢♦r♠❛çã♦ ✐♥✐❝✐❛❧ ✭❛✲♣r✐♦r✐ ✐♥❢♦r♠❛t✐♦♥✮ ❞✐s♣♦♥✐❜✐❧✐③❛❞❛ ♣♦r ✉♠ ❛❣❡♥t❡ ❡①t❡r♥♦ ♦✉♦❜t✐❞❛ ❞✐r❡t❛♠❡♥t❡ ♣❡❧♦ ♣ró♣r✐♦ r♦❜ô❀ ♣♦r ♦✉tr♦ ❧❛❞♦✱ ✉♠ r♦❜ô ♣♦❞❡ ♦❜t❡r ✐♥❢♦r♠❛çõ❡s❞♦ ❛♠❜✐❡♥t❡ ♣♦r ✐♥t❡r♠é❞✐♦ ❞❛s ❛çõ❡s ❡ ♦❜s❡r✈❛çõ❡s ❡❢❡t✉❛❞❛s ❞✉r❛♥t❡ ❛ ♥❛✈❡❣❛çã♦✭❛✲♣♦st❡r✐♦r✐ ✐♥❢♦r♠❛t✐♦♥✮✳ ◆♦r♠❛❧♠❡♥t❡✱ ✉♠❛ ✐♥❢♦r♠❛çã♦ ✐♥✐❝✐❛❧ ❞❡s❝r❡✈❡ ❞❡ ❛❧❣✉♠❛ ❢♦r♠❛ ♦ ❛♠❜✐❡♥t❡ ♦♥❞❡♦ r♦❜ô s❡ ❡♥❝♦♥tr❛✳ ❊ss❛ ✐♥❢♦r♠❛çã♦ ❞❡s❝r❡✈❡ ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ❛♠❜✐❡♥t❡ ✐♥✈❛r✐❛♥t❡s♥♦ t❡♠♣♦ ❞❡ ♠♦❞♦ q✉❡ ♦ r♦❜ô ♣♦ss❛ ✉t✐❧✐③á✲❧❛s ♣❛r❛ s❡ ❧♦❝❛❧✐③❛r✳ ❯♠❛ ❢♦r♠❛ ❜❛st❛♥t❡✉s✉❛❧ ❞❡ ✐♥❢♦r♠❛çã♦ ✐♥✐❝✐❛❧ sã♦ ♦s ♠❛♣❛s✳ ❯♠ ♠❛♣❛ ❝♦♥s✐st❡ ❡♠ ✉♠❛ r❡♣r❡s❡♥t❛çã♦ ❞♦❛♠❜✐❡♥t❡ ❡✱ ❝♦♥s✐❞❡r❛♥❞♦✲s❡ ❛ r❡♣r❡s❡♥t❛çã♦ ❡s♣❛❝✐❛❧✱ ♦ ♠❡s♠♦ ♣♦❞❡ s❡r ❝❧❛ss✐✜❝❛❞♦✱❜❛s✐❝❛♠❡♥t❡✱ ❝♦♠♦ ♠étr✐❝♦ ♦✉ t♦♣♦❧ó❣✐❝♦✳ ▼❛♣❛s ♠étr✐❝♦s ✭❋✐❣✉r❛ ✷✳✽✮ sã♦ ❡st❛❜❡❧❡❝✐❞♦s ❝♦♠ ❜❛s❡ ❡♠ ✉♠ s✐st❡♠❛ ❞❡ ❝♦✲♦r❞❡♥❛❞❛s ♥♦s q✉❛✐s ❛ ❧♦❝❛❧✐③❛çã♦ ❞♦s ♦❜❥❡t♦s é ♥✉♠❡r✐❝❛♠❡♥t❡ ❞❡t❡r♠✐♥❛❞❛✳ ❘❡✲♣r❡s❡♥t❛çõ❡s ♣♦r ❣r❛❞❡s ❞❡ ♦❝✉♣❛çã♦ ♦✉ ♣r✐♠✐t✐✈❛s ❣❡♦♠étr✐❝❛s tê♠ s✐❞♦ ❛♠♣❧❛♠❡♥t❡✉t✐❧✐③❛❞❛s ♥❡ss❛ ❝❧❛ss❡ ❞❡ ♠❛♣❛s✳ ❆ ❞✐✈✐sã♦ ❞♦ ❛♠❜✐❡♥t❡ ❡♠ ❝é❧✉❧❛s ❡ ❛ r❡s♣❡❝t✐✈❛❛ss♦❝✐❛çã♦ ❞❡ ✐♥❢♦r♠❛çõ❡s r❡❢❡r❡♥t❡s à ♦❝✉♣❛çã♦ ❞❡ss❛s ❝é❧✉❧❛s ❝♦♠♣õ❡♠ ❛s ♣r✐♥❝✐♣❛✐s❝❛r❛❝t❡ríst✐❝❛s ❞❛ r❡♣r❡s❡♥t❛çã♦ ♣♦r ❣r❛❞❡s ❞❡ ♦❝✉♣❛çã♦ ❬❊❧❢❡s✱ ✶✾✾✵❪✳ ◆❛ r❡♣r❡s❡♥t❛çã♦♠étr✐❝❛✱ ♣r✐♠✐t✐✈❛s ❣❡♦♠étr✐❝❛s✱ t❛✐s ❝♦♠♦ ♣♦♥t♦s✱ ❧✐♥❤❛s✱ ❡♥tr❡ ♦✉tr❛s✱ sã♦ ✉t✐❧✐③❛❞❛s♣❛r❛ r❡♣r❡s❡♥t❛r ♦❜❥❡t♦s ❞✐s♣♦st♦s ♥♦ ❛♠❜✐❡♥t❡✳ ❉❡♣❡♥❞❡♥❞♦ ❞❛ r❡s♦❧✉çã♦ ✉t✐❧✐③❛❞❛ ♥❛ r❡♣r❡s❡♥t❛çã♦ ♠étr✐❝❛ ❞♦ ❛♠❜✐❡♥t❡✱ ❛ ❝♦♠♣✉t❛çã♦ ❡①❡❝✉t❛❞❛ s♦❜r❡ ❡ss❡ t✐♣♦ ❞❡ ♠❛♣❛ ✷✻❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ♣♦❞❡ s❡ t♦r♥❛r ❡①t❡♥s❛✳ ❉❡ss❡ ♠♦❞♦✱ ❢❛③✲s❡ ♥❡❝❡ssár✐♦ ❡st❛❜❡❧❡❝❡r ✉♠ tr❛❞❡✲♦✛ ❛❞❡✲ q✉❛❞♦ ❡♥tr❡ ❛ r❡s♦❧✉çã♦ ❞❛ r❡♣r❡s❡♥t❛çã♦ ❡ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ s❡ ❧♦❝❛❧✐③❛r ❝♦♠ ❜❛s❡ ♥❡ss❛r❡♣r❡s❡♥t❛çã♦✱ t❡♥❞♦ ❡♠ ✈✐st❛ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ r♦❜ô ❡ ❞❛ t❛r❡❢❛ s❡♥❞♦ ❡①❡❝✉t❛❞❛✳ ✭❛✮ ✭❜✮ ✭❝✮ ❋✐❣✉r❛ ✷✳✽✿ ❊①❡♠♣❧♦s ❞❡ ❢♦r♠❛s ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❡♠ ✉♠ ♠❛♣❛ ♠é✲ tr✐❝♦✳ ▼❛♣❛s ♠étr✐❝♦s✱ t❛✐s ❝♦♠♦ ❛♣r❡s❡♥t❛❞♦s ❡♠ ✭❛✮ ❡ ✭❜✮✱ sã♦ ❡st❛❜❡❧❡❝✐❞♦s ✉t✐❧✐③❛♥❞♦s✐st❡♠❛s ❞❡ ❝♦♦r❞❡♥❛❞❛s✱ ♥❛s q✉❛✐s ❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ ♦❜❥❡t♦s é ❞❡t❡r♠✐♥❛❞❛ ♣♦r ♠❡✐♦ ❞❡♣❛r❡s ♦r❞❡♥❛❞♦s ✭❡s♣❛ç♦ ❜✐❞✐♠❡♥s✐♦♥❛❧✮✳ ❊♠ ✭❝✮ é ❛♣r❡s❡♥t❛❞❛ ✉♠❛ ❞✐s❝r❡t✐③❛çã♦ ❞♦♠❛♣❛ ✭❜✮ ❡♠ ❝é❧✉❧❛s✱ t❛✐s ❝♦♠♦ ♦❝♦rr❡ ♥❛ r❡♣r❡s❡♥t❛çã♦ ♣♦r ❣r❛❞❡s ❞❡ ♦❝✉♣❛çã♦✳ ▼❛♣❛s t♦♣♦❧ó❣✐❝♦s ✭❋✐❣✉r❛ ✷✳✾✮ r❡♣r❡s❡♥t❛♠ ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❝♦♥❡❝t✐✈✐❞❛❞❡ ❡♥tr❡ r❡❣✐õ❡s ❞♦ ❛♠❜✐❡♥t❡✳ ❊ss❡s ♠❛♣❛s ❞❡s❝r❡✈❡♠ ❝❛r❛❝t❡ríst✐❝❛s ❡s♣❡❝í✜❝❛s ❞♦ ❛♠❜✐❡♥t❡ ❡s✉❛s r❡s♣❡❝t✐✈❛s ♣♦s✐çõ❡s✳ ❆❧é♠ ❞✐ss♦✱ ♦s ♠❛♣❛s t♦♣♦❧ó❣✐❝♦s ❞❡✜♥❡♠ ❛s ❢♦r♠❛s ❞❡ s❡ tr❛♥s✐t❛r ❞❡ ✉♠ ❧♦❝❛❧ ♣❛r❛ ♦✉tr♦ ♥♦ ♠❛♣❛✳ ❉❡ss❡ ♠♦❞♦✱ t❛✐s ♠❛♣❛s ♥♦r♠❛❧♠❡♥t❡ ♥ã♦✉t✐❧✐③❛♠ ✐♥❢♦r♠❛çõ❡s ♠étr✐❝❛s r❡❧❛❝✐♦♥❛❞❛s ❛ ✉♠ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s✳ ●r❛❢♦s tê♠ s✐❞♦ ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞♦s ♥❡ss❡ ❝♦♥t❡①t♦✱ t❡♥❞♦ ❡♠ ✈✐st❛ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ r❡♣r❡s❡♥t❛✲çã♦ ❞❡ss❛ ❡str✉t✉r❛ ❞❡ ❞❛❞♦s ❡ ❛ ❣❛♠❛ ❞❡ ❛❧❣♦r✐t♠♦s ❞❡s❡♥✈♦❧✈✐❞♦s ♣❛r❛ ♠❛♥✐♣✉❧❛çã♦❞❛ ♠❡s♠❛✳ ▼❛♣❛s t♦♣♦❧ó❣✐❝♦s ♣♦ss✉❡♠ ❛ ✈❛♥t❛❣❡♠ ❞❡ ♥❡❝❡ss✐t❛r❡♠ ❞❡ ✉♠ ♠❡♥♦r ❡s✲♣❛ç♦ ❞❡ ❛r♠❛③❡♥❛♠❡♥t♦✱ t❡♥❞♦ ❡♠ ✈✐st❛ q✉❡ ♦s ♠❡s♠♦s r❡♣r❡s❡♥t❛♠ ♦ ❛♠❜✐❡♥t❡ ❞❡♠❛♥❡✐r❛ ♠❛✐s ❝♦♠♣❛❝t❛✳ ❆♣❡s❛r ❞❡ss❛ ✈❛♥t❛❣❡♠✱ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞♦ r♦❜ô♣♦❞❡♠ s❡ t♦r♥❛r ♠❡♥♦s ♣r❡❝✐s❛s ♥❡ss❛ ❛❜♦r❞❛❣❡♠✱ ✉♠❛ ✈❡③ q✉❡ ✉♠ ♥ó ❞♦ ❣r❛❢♦ ♣♦❞❡ r❡♣r❡s❡♥t❛r ✉♠❛ r❡❣✐ã♦ ❛♠♣❧❛ ❞♦ ❛♠❜✐❡♥t❡✳ ❖ ♦✉tr♦ t✐♣♦ ❞❡ ✐♥❢♦r♠❛çã♦ q✉❡ ✉♠ r♦❜ô ♠ó✈❡❧ t❡♠ ❛❝❡ss♦ é ❛❞✈✐♥❞♦ ❞❡ s✉❛❝❛♣❛❝✐❞❛❞❡ ❞❡ ♥❛✈❡❣❛çã♦✳ ❯♠ r♦❜ô t✐♣✐❝❛♠❡♥t❡ ❡①❡❝✉t❛ ❞♦✐s t✐♣♦s ❞❡ ❛çõ❡s✿ ❡❧❡ ❛t✉❛♥♦ ❛♠❜✐❡♥t❡ ♣♦r ♠❡✐♦ ❞❡ s❡✉s ❛t✉❛❞♦r❡s ❡ ♣❡r❝❡❜❡ ♦ ❛♠❜✐❡♥t❡ ♣♦r ✐♥t❡r♠é❞✐♦ ❞❡ s❡✉s s❡♥s♦r❡s✳ ❊ss❛s ❛çõ❡s ❡st❛❜❡❧❡❝❡♠ t✐♣♦s ❡s♣❡❝í✜❝♦s ❞❡ ✐♥❢♦r♠❛çõ❡s q✉❡ ♣♦❞❡♠ s❡r ✉t✐❧✐✲③❛❞❛s ♣❡❧♦ r♦❜ô ♣❛r❛ ❡st✐♠❛r s✉❛ ❧♦❝❛❧✐③❛çã♦ ♥♦ ❛♠❜✐❡♥t❡✿ ✐♥❢♦r♠❛çõ❡s ♣r♦♣r✐♦❝❡♣t✐✈❛s❡ ❡①t❡r♦❝❡♣t✐✈❛s✳ ❖s ❛t✉❛❞♦r❡s ❞❡ ✉♠ r♦❜ô ♠ó✈❡❧✱ t❛✐s ❝♦♠♦ r♦❞❛s ❡ ♣❡r♥❛s✱ ❝♦♠♣õ❡♠ s❡✉ s✐st❡♠❛❞❡ ❝♦♥❞✉çã♦ ✭❞r✐✈✐♥❣ s②st❡♠✮✳ ❚❛❧ s✐st❡♠❛ é r❡s♣♦♥sá✈❡❧ ❞✐r❡t❛♠❡♥t❡ ♣❡❧❛ ♠✉❞❛♥ç❛ ❞❛♣♦s❡ ❞♦ r♦❜ô✳ ❖ ❝♦♥❤❡❝✐♠❡♥t♦ ❞♦ ♠♦❞❡❧♦ q✉❡ r❡❣❡ ♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞❡ss❡ s✐st❡♠❛ ♣❡r✲ ✷✳✹✳ ▲♦❝❛❧✐③❛çã♦ ❞❡ ❘♦❜ôs ▼ó✈❡✐s1✷✼13 11 8 5 3 12 6 9 2 1 4 7 1 4 7 3 8 3 8 5 5 10 10 13 13 12 1214 10 74 2 2 6 6 9 9 11 11 ✭❛✮ ✭❜✮ ✭❝✮ ❋✐❣✉r❛ ✷✳✾✿ ❊①❡♠♣❧♦s ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ ♠❛♣❛ t♦♣♦❧ó❣✐❝♦✳ ❆ r❡♣r❡s❡♥t❛çã♦ t♦♣♦✲❧ó❣✐❝❛ ❞❡ ✉♠ ♠❛♣❛✱ t❛✐s ❝♦♠♦ ❛q✉❡❧❛s ❛♣r❡s❡♥t❛❞❛s ❡♠ ✭❛✮ ❡ ✭❝✮✱ ❞❡s❝r❡✈❡ ✐♥❢♦r♠❛çõ❡s❞❡ ❝♦♥❡❝t✐✈✐❞❛❞❡ ❡♥tr❡ r❡❣✐õ❡s ❞✐st✐♥t❛s ❞♦ ❛♠❜✐❡♥t❡✳ ❊♠ ✭❜✮✱ ♦ ❛♠❜✐❡♥t❡ é ❞✐✈✐❞✐❞♦❡♠ r❡❣✐õ❡s r♦t✉❧❛❞❛s ❛ s❡r❡♠ ✉t✐❧✐③❛❞❛s ♣❛r❛ ❛ ❞❡✜♥✐çã♦ ❞♦ ♠❛♣❛ t♦♣♦❧ó❣✐❝♦ ❡♠ ✭❝✮✳♠✐t❡ ♣r❡✈❡r ♦s ❡❢❡✐t♦s ❞❛s ❛çõ❡s ❡①❡❝✉t❛❞❛s ♣❡❧♦ r♦❜ô✱ ❞❡ ♠♦❞♦ ❛ ♦❜t❡r ✉♠❛ ✐♥❞✐❝❛çã♦❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ♠❡s♠♦ ❛♣ós ❛ ❡①❡❝✉çã♦ ❞❡ss❛s ❛çõ❡s✳ ❖ ♠♦♥✐t♦r❛♠❡♥t♦ ❞❡ss❡ t✐♣♦❞❡ s✐st❡♠❛ ♣♦r ♠❡✐♦ ❞❡ s❡♥s♦r❡s ♣❡r♠✐t❡ ❡st✐♠❛r ♦ ❞❡s❧♦❝❛♠❡♥t♦ ❡❢❡t✉❛❞♦ ♣❡❧♦ r♦❜ô✳❖ r❡s✉❧t❛❞♦ ❞❡ss❡ ♠♦♥✐t♦r❛♠❡♥t♦ é ❝♦♠✉♠❡♥t❡ r❡❢❡r❡♥❝✐❛❞♦ ❝♦♠♦ ♠❡❞✐❞❛s ❞❡ ♣♦s✐✲çã♦ r❡❧❛t✐✈❛s ♦✉ ♠❡❞✐❞❛s ♣r♦♣r✐♦❝❡♣t✐✈❛s✳ ❉❡✈✐❞♦ ❛ ✐ss♦✱ s❡♥s♦r❡s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❡ss❡✜♠ sã♦ ❣❡r❛❧♠❡♥t❡ ❞❡♥♦♠✐♥❛❞♦s s❡♥s♦r❡s ♣r♦♣r✐♦❝❡♣t✐✈♦s✳ ❊ss❡s s❡♥s♦r❡s ♠♦♥✐t♦r❛♠❡ ❝♦♥tr♦❧❛♠ ♦ ❡st❛❞♦ ✐♥t❡r♥♦ ❞♦ r♦❜ô✱ t❛✐s ❝♦♠♦ ♦ ♠♦✈✐♠❡♥t♦✱ ❛ ❛❝❡❧❡r❛çã♦ ❡ ❛ ❞✐r❡✲çã♦✳ ❉❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ss❡s s❡♥s♦r❡s ♥ã♦ ✉t✐❧✐③❛r❡♠ ✐♥❢♦r♠❛çõ❡s ❡①t❡r♥❛s✱ ❛s ♠❡❞✐❞❛s♣r♦♣r✐♦❝❡♣t✐✈❛s sã♦ ❡st❛❜❡❧❡❝✐❞❛s ❡♠ r❡❧❛çã♦ à ❝♦♥✜❣✉r❛çã♦ ❞♦ ❡st❛❞♦ ✐♥t❡r♥♦ ❞❡✜♥✐❞♦❡♠ ✉♠ ✐♥st❛♥t❡ ❛♥t❡r✐♦r✳ ❊①❡♠♣❧♦s ❞❡ss❡ t✐♣♦ ❞❡ s❡♥s♦r sã♦ ♦ ♦❞ô♠❡tr♦ ❡ ♦s s❡♥s♦r❡s✐♥❡r❝✐❛✐s✳ ❯♠❛ ✈❡③ ❝♦♥❤❡❝✐❞❛ ❛ ♣♦s❡ ❞♦ r♦❜ô✱ ♠❡❞✐❞❛s ❞❡ ♣♦s✐çã♦ ♣♦❞❡♠ s❡r ✉t✐❧✐③❛❞❛s ♣❛r❛❡st❛❜❡❧❡❝❡r ♥♦✈❛s ♣♦s❡s r❡❧❛t✐✈❛s àq✉❡❧❛ ❡st❛❜❡❧❡❝✐❞❛ ❛♥t❡r✐♦r♠❡♥t❡✳ ❚❛✐s ♠❡❞✐❞❛s sã♦♦❜t✐❞❛s ♣♦r ✐♥t❡r♠é❞✐♦ ❞♦ ❛❝♦♠♣❛♥❤❛♠❡♥t♦ ❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ✭∆x, ∆y, ∆θ✮ ❡❢❡t✉❛❞♦♣❡❧♦ r♦❜ô ✭❋✐❣✉r❛ ✷✳✶✵✮✳ ❊ss❡ ♣r♦❝❡❞✐♠❡♥t♦ é ❝♦♠✉♠❡♥t❡ ❞❡♥♦♠✐♥❛❞♦ r❛str❡❛♠❡♥t♦ ❞❡♣♦s✐çã♦ ✭♣♦s✐t✐♦♥ tr❛❝❦✐♥❣✮✳ ❚é❝♥✐❝❛s ❞❡ ❞❡❛❞ r❡❝❦♦♥✐♥❣✱ t❛✐s ❝♦♠♦ ♦❞♦♠❡tr✐❛✱ tê♠ s✐❞♦❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞❛s ♣❛r❛ ❡ss❡ ✜♠✳ ❖ ♣r✐♥❝í♣✐♦ ❞❡ss❛s té❝♥✐❝❛s ❝♦♥s✐st❡ ♥♦ ❡♠♣r❡❣♦❞❡ s❡♥s♦r❡s ♣r♦♣r✐♦❝❡♣t✐✈♦s ♣❛r❛ ❡st✐♠❛r ✉♠❛ ♥♦✈❛ ♣♦s❡ ✉t✐❧✐③❛♥❞♦ ❛ ♦❜s❡r✈❛çã♦ ❞♦❞❡s❧♦❝❛♠❡♥t♦ ❡❢❡t✉❛❞♦ ♣❡❧♦ r♦❜ô✳ ❚❛❧ ♠❡❞✐çã♦ é ❡❢❡t✉❛❞❛ ♣♦r ✐♥t❡r♠é❞✐♦ ❞❛ ✐♥t❡❣r❛çã♦❞❛ ✐♥❢♦r♠❛çã♦ ❧♦❝❛❧ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ✐♥❝r❡♠❡♥t❛❞❛ ❝♦♠ ♦ tr❛♥s❝♦rr❡r ❞♦ t❡♠♣♦✳ ❯♠❛ ❢♦r♠❛ s✐♠♣❧❡s ❡ ❜❛st❛♥t❡ ✉t✐❧✐③❛❞❛ ♣❛r❛ ✐♠♣❧❡♠❡♥t❛r ❛ ♦❞♦♠❡tr✐❛ ❡♠ r♦❜ôs♠ó✈❡✐s ❝♦♠ r♦❞❛s ❝♦♥s✐st❡ ❡♠ ❛❝♦♣❧❛r ❡♥❝♦❞❡rs ♥♦ ❡✐①♦ ❞❡ r♦t❛çã♦ ❞❛s r♦❞❛s ❞♦ r♦❜ô✭❋✐❣✉r❛ ✷✳✶✶❛✮✳ ❈♦♠ ✐ss♦✱ ♣♦❞❡✲s❡ ♠❡❞✐r ❛s ✈❡❧♦❝✐❞❛❞❡s ❞♦ r♦❜ô ❝♦♠ ❜❛s❡ ❡♠ ✉♠ r❡❢❡r❡♥❝✐❛❧ ✐♥✐❝✐❛❧ ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❡st✐♠❛r ❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ r♦❜ô ♥♦ ❞❡❝♦rr❡r ❞♦t❡♠♣♦✳ ❆ ✐♥❝❡rt❡③❛ ✐♥❡r❡♥t❡ à ✉t✐❧✐③❛çã♦ ❞❡ss❡ t✐♣♦ ❞❡ s❡♥s♦r ❞❡❣r❛❞❛ ❛s ❡st✐♠❛t✐✈❛s ❞❡ ✷✽❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ Y W Y Ri Y R i R i XΔθ Δy RX Ri iRi Δx XW ❋✐❣✉r❛ ✷✳✶✵✿ ❉❡s❧♦❝❛♠❡♥t♦ (∆x, ∆y, ∆θ) ❞♦ r♦❜ô R i ❡♠ r❡❧❛çã♦ ❛ ✉♠ s✐st❡♠❛ ❞❡ I i I i R i R i i , Y ) , Y )❝♦♦r❞❡♥❛❞❛s ✐♥❡r❝✐❛❧ (X ✳ ❖ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s (X é ❧♦❝❛❧ ❛ R ✳❧♦❝❛❧✐③❛çã♦✳ ❉❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ss❛ ✐♥❝❡rt❡③❛ ❡st❛r ❝♦♥✜♥❛❞❛ ❛ ✉♠❛ r❡❣✐ã♦ ♣ró①✐♠❛ àq✉❡❧❛♦♥❞❡ s❡ ❡♥❝♦♥tr❛ ❛ ✈❡r❞❛❞❡✐r❛ ♣♦s❡ ❞♦ r♦❜ô✱ t❛❧ ✐♥❝❡rt❡③❛ t❡♠ s✐❞♦ ❝♦♠✉♠❡♥t❡ ♠♦❞❡❧❛❞❛♣♦r ✐♥t❡r♠é❞✐♦ ❞❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s ✉♥✐♠♦❞❛❧✳ ❊♠ ❞❡❝♦rrê♥❝✐❛ ❞♦s s❡♥s♦r❡s ✉t✐❧✐③❛❞♦s ❡ ❞♦ ❝♦♥✜♥❛♠❡♥t♦ ❞❛ ✐♥❝❡rt❡③❛ ❡♠ t♦r♥♦ ❞❛ ✈❡r❞❛❞❡✐r❛ ❧♦❝❛❧✐③❛çã♦✱t❛❧ t✐♣♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ é ❢r❡q✉❡♥t❡♠❡♥t❡ ❞❡♥♦♠✐♥❛❞♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ r❡❧❛t✐✈❛ ✭❧♦❝❛❧✮✳ ✭❛✮ P♦❧✉❧✉ ✇❤❡❡❧ ✭❜✮ ▼✐♥✐ ❆❚❘ ❋✐❣✉r❛ ✷✳✶✶✿ ❙❡♥s♦r ♣r♦♣r✐♦❝❡♣t✐✈♦✿ ✭❛✮ ❡♥❝♦❞❡r ❬❘♦❜♦t✐❝s ✫ ❊❧❡tr♦♥✐❝s P♦❧♦❧✉❧✉✱ ✷✵✶✷❪❀✭❜✮ ❡♥❝♦❞❡rs ✐♥st❛❧❛❞♦s ♥♦ ❡✐①♦ ❞❡ r♦t❛çã♦ ❞❛s r♦❞❛s ❞❡ ✉♠ ✈❡í❝✉❧♦ r♦❜ót✐❝♦ ❬❙✉♣❡r❉r♦✐❞❘♦❜♦ts ■♥❝✳✱ ✷✵✶✷❪✳ ❆ ❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ ✉♠ r♦❜ô✱ t❡♥❞♦ ❝♦♠♦ ❜❛s❡ ❛ ✐♥str✉♠❡♥t❛çã♦ ❞❛s r♦❞❛s✱ é s✉❥❡✐t❛ ❛ ❡rr♦s ❞❡✈✐❞♦ ❛ ✈ár✐♦s ❢❛t♦r❡s✳ ❚❛✐s ❡rr♦s sã♦ ❝♦♠✉♠❡♥t❡ ❝❧❛ss✐✜❝❛❞♦s❝♦♠♦ s✐st❡♠át✐❝♦s ♦✉ ♥ã♦ s✐st❡♠át✐❝♦s ✭❛❧❡❛tór✐♦s✮✳ ❊rr♦s s✐st❡♠át✐❝♦s sã♦ ♣r❡✈✐sí✈❡✐s❡ ✐♥t❡❣r❛❞♦s ❝♦♥st❛♥t❡♠❡♥t❡✱ ❡♥q✉❛♥t♦ q✉❡ ❡rr♦s ♥ã♦ s✐st❡♠át✐❝♦s sã♦ ✐♠♣r❡✈✐sí✈❡✐s✱♣♦❞❡♥❞♦ ♦❝♦rr❡r ❛ q✉❛❧q✉❡r ♠♦♠❡♥t♦✳ ❉❡ss❡ ♠♦❞♦✱ ❡rr♦s s✐st❡♠át✐❝♦s ❞✐st♦r❝❡♠ ❛✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ ♠♦❞♦ ❣r❛❞❛t✐✈♦✱ ❡♥q✉❛♥t♦ q✉❡ ❡rr♦s ♥ã♦ s✐st❡♠át✐❝♦s ✷✳✹✳ ▲♦❝❛❧✐③❛çã♦ ❞❡ ❘♦❜ôs ▼ó✈❡✐s✷✾ ♣♦❞❡♠ ❞✐st♦r❝❡r ❞❡ ♠❛♥❡✐r❛ s✐❣♥✐✜❝❛t✐✈❛ ❡ r❡♣❡♥t✐♥❛♠❡♥t❡ ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦✳❉✐❢❡r❡♥ç❛ ♥♦ ❞✐â♠❡tr♦ ❞❛s r♦❞❛s✱ t❛❧ ❝♦♠♦ ♦ ❞❡s❛❧✐♥❤❛♠❡♥t♦✱ ❛❧é♠ ❞❡ r❡s♦❧✉çã♦ ❡ t❛①❛❞❡ ❛♠♦str❛❣❡♠ ❧✐♠✐t❛❞❛s ❞♦s ❡♥❝♦❞❡rs sã♦ ❡①❡♠♣❧♦s ❞❡ ❝❛✉s❛s ❞❡ ❡rr♦s s✐st❡♠át✐❝♦s✳P♦r ♦✉tr♦ ❧❛❞♦✱ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞❡ ✉♠ r♦❜ô ❡♠ s♦❧♦ ✐rr❡❣✉❧❛r é ✉♠❛ ❞❛s s✐t✉❛çõ❡s❡♠ q✉❡ ❡rr♦s ♥ã♦ s✐st❡♠át✐❝♦s ♣♦❞❡♠ ♦❝♦rr❡r✱ ♣♦✐s t❛❧ ✐rr❡❣✉❧❛r✐❞❛❞❡ ♣♦❞❡ ♦❝❛s✐♦♥❛r ♦❞❡s❧✐③❛♠❡♥t♦ ❞❛s r♦❞❛s ✭✇❤❡❡❧✲s❧✐♣♣❛❣❡✮ ❞❡✈✐❞♦ à ❛❝❡❧❡r❛çã♦ ❡①❛❣❡r❛❞❛ ♦✉ ❛✉sê♥❝✐❛ ❞❡❛tr✐t♦ ❝♦♠ ♦ s♦❧♦✳ ❆❧é♠ ❞✐ss♦✱ ♦ ♠♦✈✐♠❡♥t♦ ❞❡ ❣✐r♦ ❞♦ r♦❜ô ❡♠ ✈❡❧♦❝✐❞❛❞❡s ♠❛✐s ❛❧t❛s♣♦❞❡ ❣❡r❛r ♣❡r❞❛ ❞❡ tr❛çã♦ ❡ ❞❡rr❛♣❛❣❡♠ ✭s❦✐❞❞✐♥❣✮✱ ♦ q✉❡ ❝♦♥s✐st❡ ❡♠ ♦✉tr❛ ❢♦♥t❡ ❡♠♣♦t❡♥❝✐❛❧ ♣❛r❛ ❛ ❣❡r❛çã♦ ❞❡ ❡rr♦s ♥ã♦ s✐st❡♠át✐❝♦s✳ ❆ ✐♥❝❡rt❡③❛ ❞❡❝♦rr❡♥t❡ ❞❛ ✉t✐❧✐③❛çã♦ ❞❡ss❡ t✐♣♦ ❞❡ s❡♥s♦r ♥❛s té❝♥✐❝❛s ❞❡ ❞❡❛❞ r❡❝❦♦♥✐♥❣ ❛❝❛rr❡t❛ ✉♠ ❛❝ú♠✉❧♦ ❞❡ ❡rr♦s ♣r♦♣♦r❝✐♦♥❛❧ à ❞✐stâ♥❝✐❛ ♣❡r❝♦rr✐❞❛ ♣❡❧♦ r♦❜ô✳❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱ t❡♠✲s❡ ✉♠ ✐♥❝r❡♠❡♥t♦ s✐❣♥✐✜❝❛t✐✈♦ ♥❛ ✐♥❝❡rt❡③❛ ❛ss♦❝✐❛❞❛ à ✐♥❢♦r✲♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ q✉❛♥❞♦ ♦ r♦❜ô ♣❡r❝♦rr❡ ❣r❛♥❞❡s ❞✐stâ♥❝✐❛s✳ ❊rr♦s s✐st❡♠át✐❝♦s♣♦❞❡♠ s❡r r❡❞✉③✐❞♦s ♣♦r ✐♥t❡r♠é❞✐♦ ❞❛ ❝❛❧✐❜r❛çã♦ ❞♦ s✐st❡♠❛✳ ❆❧❣✉♥s tr❛❜❛❧❤♦s✱ ❞❡♥tr❡❡❧❡s ❬❇♦r❡♥st❡✐♥ ✫ ❋❡♥❣✱ ✶✾✾✻❪✱ tê♠ ♠♦str❛❞♦ q✉❡ ❛ ❛❞❡q✉❛❞❛ ❝❛❧✐❜r❛çã♦ ❞❡ ✉♠ s✐st❡♠❛❞❡ ❞❡❛❞ r❡❝❦♦♥✐♥❣ ♣♦❞❡ ❞✐♠✐♥✉✐r s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ❛ ✐♥✢✉ê♥❝✐❛ ❞❡ss❡ t✐♣♦ ❞❡ ❡rr♦ ♥♦ r❡s✉❧t❛❞♦ ✜♥❛❧ ❞❛ ❧♦❝❛❧✐③❛çã♦✳ ◆♦ ❡♥t❛♥t♦✱ t❛❧ ❝❛❧✐❜r❛çã♦ ♥ã♦ ❡❧✐♠✐♥❛ t♦t❛❧♠❡♥t❡ ♦s ❡r✲r♦s s✐st❡♠át✐❝♦s ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞♦s ♠❡s♠♦s s❡r❡♠ ♦r✐❣✐♥❛❞♦s ❞❡ ❞✐✈❡rs❛s ❢♦♥t❡s✱ s❡♥❞♦✐♠♣r❛t✐❝á✈❡❧ ❡✱ ♣♦r ✈❡③❡s✱ ✐♠♣♦ssí✈❡❧ ❛ ❞❡t❡❝çã♦ ❞❡ t♦❞❛s ❡ss❛s ❢♦♥t❡s✳ ❙❡♥s♦r❡s ❡①t❡r♦❝❡♣t✐✈♦s ♣♦❞❡♠ s❡r ✉t✐❧✐③❛❞♦s ♣❛r❛ ❡①tr❛✐r ✐♥❢♦r♠❛çõ❡s ❞♦ ❛♠✲❜✐❡♥t❡ ❞❡ ♠♦❞♦ ❛ ♣r♦✈❡r❡♠ ✉♠❛ ✈✐sã♦ ♠♦♠❡♥tâ♥❡❛ ❞♦ ❡♥t♦r♥♦ ❞❡ ✉♠ r♦❜ô✳ ❚❛✐s✐♥❢♦r♠❛çõ❡s sã♦ ❝♦♠✉♠❡♥t❡ ❞❡♥♦t❛❞❛s ♥❛ ❧✐t❡r❛t✉r❛ ❝♦♠♦ ♦❜s❡r✈❛çõ❡s✳ ❖❜s❡r✈❛çõ❡s r❡❧❛❝✐♦♥❛❞❛s à ♣♦s❡ ❛t✉❛❧ ❞♦ r♦❜ô ♣♦r ♠❡✐♦ ❞❡ s❡♥s♦r❡s ❡①t❡r♦❝❡♣t✐✈♦s sã♦ ✐♥❞❡♣❡♥❞❡♥t❡s❞❡ ❡st✐♠❛t✐✈❛s ❛♥t❡r✐♦r❡s r❡❧❛❝✐♦♥❛❞❛s à s✉❛ ❧♦❝❛❧✐③❛çã♦✳ ❉❡ss❡ ♠♦❞♦✱ t❛✐s ♦❜s❡r✈❛çõ❡s❡st❛❜❡❧❡❝❡♠ ♠❡❞✐❞❛s ❞❡ ♣♦s✐çã♦ ❛❜s♦❧✉t❛✱ ❝♦♠✉♠❡♥t❡ r❡❢❡r❡♥❝✐❛❞❛s ❝♦♠♦ ♠❡❞✐❞❛s ❡①✲ t❡r♦❝❡♣t✐✈❛s✳ ❈♦♠ ❡ss❡ t❡r♠♦ ❜✉s❝❛✲s❡ ❡♥❢❛t✐③❛r q✉❡ ❛s ✐♥❢♦r♠❛çõ❡s ❣❡r❛❞❛s ♣♦r ❡ss❡ss❡♥s♦r❡s ♥ã♦ ❡stã♦ r❡❧❛❝✐♦♥❛❞❛s ❛♦ ❡st❛❞♦ ✐♥t❡r♥♦ ❞♦ r♦❜ô✱ ♠❛s s✐♠ ❛ ✐♥❢♦r♠❛çõ❡s ❡①✲ t❡r♥❛s ❛♦ ♠❡s♠♦✱ ♦✉ s❡❥❛✱ ❛q✉❡❧❛s ❞✐s♣♦♥í✈❡✐s ♥♦ ❛♠❜✐❡♥t❡✳ ❊①❡♠♣❧♦s ❞❡ss❡ t✐♣♦ ❞❡✐♥❢♦r♠❛çã♦ sã♦ ❡st✐♠❛t✐✈❛s ❞❡ ❞✐stâ♥❝✐❛ r❡❧❛t✐✈❛s ❛ ♦❜❥❡t♦s ❞✐s♣♦st♦s ♥♦ ❛♠❜✐❡♥t❡ ♦✉❡st✐♠❛t✐✈❛s ❛ss♦❝✐❛❞❛s à ❢♦r♠❛ ❞❡ss❡s ♦❜❥❡t♦s✳ ❚❛✐s ♠❡❞✐❞❛s sã♦ r❡❢❡r❡♥t❡s ❛♦ s✐st❡♠❛❞❡ ❝♦♦r❞❡♥❛❞❛s ❧♦❝❛❧ ❞♦ r♦❜ô✱ s❡♥❞♦ ♦s s♦♥❛r❡s✱ ♦s ❧❛s❡rs✱ ♦s s❡♥s♦r❡s ❞❡ ✐♥❢r❛✲✈❡r♠❡❧❤♦❡ ❛s ❝â♠❡r❛s ❛❧❣✉♥s ❡①❡♠♣❧♦s ❞❡ s❡♥s♦r❡s ❡♠♣r❡❣❛❞♦s ♣❛r❛ ❡ss❡ ✜♠✳ ❈♦♠ ♦ ❛✉①í❧✐♦ ❞❡ s❡♥s♦r❡s ❡①t❡r♦❝❡♣t✐✈♦s✱ ✉♠ r♦❜ô ♦❜té♠ ✐♥❢♦r♠❛çõ❡s ❞♦ ❛♠✲❜✐❡♥t❡ ❡ ❜✉s❝❛ ❡st❛❜❡❧❡❝❡r ✉♠❛ ❛ss♦❝✐❛çã♦ ❝♦♠ ❛s ✐♥❢♦r♠❛çõ❡s ❝♦♥t✐❞❛s ❡♠ ✉♠ ♠❛♣❛♣r❡✈✐❛♠❡♥t❡ ❝♦♥❤❡❝✐❞♦✱ ❞❡ ♠♦❞♦ ❛ ❞❡t❡r♠✐♥❛r s✉❛ ♣♦ssí✈❡❧ ❧♦❝❛❧✐③❛çã♦✳ ❉✐str✐❜✉✐çõ❡s❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♠✉❧t✐♠♦❞❛✐s ❡ té❝♥✐❝❛s ❞❡ ❛♠♦str❛❣❡♠ ♣r♦❜❛❜✐❧íst✐❝❛ tê♠ s✐❞♦ ❛♠♣❧❛✲♠❡♥t❡ ✉t✐❧✐③❛❞❛s ♣❛r❛ ♠♦❞❡❧❛r ❛ ✐♥❝❡rt❡③❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞♦ r♦❜ô ❬❚❤r✉♥ ❡t ❛❧✳✱ ✷✵✵✺❪✳ ✸✵❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ▼ét♦❞♦s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❜❛s❡❛❞♦s ♥❡ss❛s ❡str❛té❣✐❛s sã♦ ❝♦♠✉♠❡♥t❡ ❞❡♥♦♠✐♥❛❞♦s ❞❡♠ét♦❞♦s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛ ✭❣❧♦❜❛❧✮✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ❛s ♠❡❞✐❞❛s ❞❡ ♣♦s✐çã♦ ❛❜s♦❧✉t❛ ❡♠ ❣❡r❛❧ ♦❢❡✲ r❡❝❡♠ ✐♥❢♦r♠❛çõ❡s ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ r♦❜ô ❞❡ ❢♦r♠❛ ✐♥❞❡♣❡♥❞❡♥t❡ ❞❛s ❡st✐♠❛t✐✈❛s ❞❡❧♦❝❛❧✐③❛çã♦ ❛♥t❡r✐♦r❡s✳ ■ss♦ ♦❝♦rr❡ ♣♦rq✉❡ ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❣❡r❛❞❛ ♥ã♦ é❜❛s❡❛❞❛ ♥❛ ✐♥t❡❣r❛çã♦ ❞❡ ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ♠❡❞✐❞❛s✱ ♠❛s s✐♠ ♥❛ ♦❜s❡r✈❛çã♦ ❡❢❡t✉❛❞❛✳❉✐❢❡r❡♥t❡♠❡♥t❡ ❞❛s té❝♥✐❝❛s ❞❡ ❞❡❛❞ r❡❝❦♦♥✐♥❣✱ ❛s té❝♥✐❝❛s q✉❡ ✉t✐❧✐③❛♠ ♠❡❞✐❞❛s ❞❡♣♦s✐çã♦ ❛❜s♦❧✉t❛ ♣♦ss✉❡♠ ❛ ✈❛♥t❛❣❡♠ ❞❡ ❝♦♥tr♦❧❛r ♠❡❧❤♦r ♦ ❡rr♦ ❛ss♦❝✐❛❞♦ à ♠❡❞✐çã♦✱✉♠❛ ✈❡③ q✉❡ ♦ ♠❡s♠♦ ❡stá r❡❧❛❝✐♦♥❛❞♦ ✉♥✐❝❛♠❡♥t❡ à ♦❜s❡r✈❛çã♦ ❡♠ q✉❡stã♦✳ ▼❡❞✐❞❛s ❞❡ ♣♦s✐çã♦ ❛❜s♦❧✉t❛ ♣♦❞❡♠ s❡r ✉t✐❧✐③❛❞❛s ♣❛r❛ ❛♠❡♥✐③❛r ♦s ❡rr♦s ❣❡r❛✲❞♦s ♣❡❧♦ ❡♠♣r❡❣♦ ❞❛s té❝♥✐❝❛s ❞❡ ❞❡❛❞ r❡❝❦♦♥✐♥❣✳ ❯♠❛ ❢♦r♠❛ ❞❡ s❡ ❢❛③❡r ✐ss♦ é ♣♦r♠❡✐♦ ❞♦ ❡♠♣r❡❣♦ ❞❡ té❝♥✐❝❛s ❜❛s❡❛❞❛s ♥❛ ❞❡t❡❝çã♦ ❞❡ ♠❛r❝♦s ✭❧❛♥❞♠❛r❦✲❜❛s❡❞ t❡❝❤♥✐✲ q✉❡s✮ ❬❖✇❡♥ ✫ ◆❡❤♠③♦✇✱ ✶✾✾✽❀ ▲❛③❛♥❛s ✫ ▲❛t♦♠❜❡✱ ✶✾✾✺❪✳ ❖s ♠❛r❝♦s ❝♦♥s✐st❡♠ ❡♠❝❛r❛❝t❡ríst✐❝❛s ❞♦ ❛♠❜✐❡♥t❡ q✉❡ ✉♠ r♦❜ô ♣♦❞❡ ❞✐st✐♥❣✉✐r ❡✱ ♣♦rt❛♥t♦✱ ❛s ♦❜s❡r✈❛çõ❡s❡①t❡r♦❝❡♣t✐✈❛s ♣♦❞❡♠ s❡r ❛♥❛❧✐s❛❞❛s ♣♦r ✉♠ r♦❜ô ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ s❡ ❞❡t❡❝t❛r ♠❛r✲❝♦s✳ ◗✉❛♥❞♦ ♦❝♦rr❡ ❛ ❞❡t❡❝çã♦ ❞❡ ✉♠ ♠❛r❝♦✱ ♦ ♠❡s♠♦ é ❛ss♦❝✐❛❞♦ ❛ ✉♠❛ ✐♥❢♦r♠❛çã♦❞♦ ❛♠❜✐❡♥t❡ ✭♠❛♣❛✮ ❝♦♠ ✈✐st❛s ❛ ❞❡t❡r♠✐♥❛r ❛ ❧♦❝❛❧✐③❛çã♦ ❛t✉❛❧ ❞♦ r♦❜ô✳ ❖s ♠❛r❝♦s♣♦❞❡♠ s❡r ❛rt✐✜❝✐❛✐s ♦✉ ♥❛t✉r❛✐s✱ t❛✐s ❝♦♠♦ ❛t✐✈♦s ♦✉ ♣❛ss✐✈♦s✳ ▼❛r❝♦s ❛rt✐✜❝✐❛✐s sã♦ ♣r♦❥❡t❛❞♦s ♣❛r❛ s❡r❡♠ ❢❛❝✐❧♠❡♥t❡ ❞❡t❡❝t❛❞♦s ♣♦r r♦❜ôs✳❉❡ss❡ ♠♦❞♦✱ ✉♠ ♠❛r❝♦ ❛rt✐✜❝✐❛❧ é ♣♦s✐❝✐♦♥❛❞♦ ❡♠ ✉♠ ♣♦♥t♦ ❡s♣❡❝í✜❝♦ ♥♦ ❛♠❜✐❡♥t❡❝♦♠ ♦ ♣r♦♣ós✐t♦ ❞❡ ❢❛❝✐❧✐t❛r s❡✉ ❛❝❡ss♦ ❡ ✐❞❡♥t✐✜❝❛çã♦✳ ❆ ❋✐❣✉r❛ ✷✳✶✷❛ ❛♣r❡s❡♥t❛ ✉♠❡①❡♠♣❧♦ ❡♠ q✉❡ ♠❛r❝♦s ❛rt✐✜❝✐❛✐s sã♦ ♣♦s✐❝✐♦♥❛❞♦s ♥♦ ❛♠❜✐❡♥t❡ ♣❛r❛ ❛✉①✐❧✐❛r ♦ ♣r♦❝❡ss♦❞❡ ❧♦❝❛❧✐③❛çã♦ ❞♦ r♦❜ô✳ P♦r s❡r❡♠ ♣r♦❥❡t❛❞♦s ♣❛r❛ ❛✉①✐❧✐❛r ♦s r♦❜ôs✱ ♦s ♠❛r❝♦s ❛rt✐✜❝✐❛✐s sã♦ ❝♦♥❢❡❝❝✐♦♥❛❞♦s ❞❡ ♠♦❞♦ q✉❡ s✉❛ ♣♦s✐çã♦ s❡❥❛ ❞❡t❡r♠✐♥❛❞❛ ❞❡ ❢♦r♠❛ ♥ã♦ ❛♠❜í❣✉❛✳P♦r ♦✉tr♦ ❧❛❞♦✱ ♠❛r❝♦s ♥❛t✉r❛✐s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ♣♦rt❛s ❡ ❡♥❝♦♥tr♦s ❞❡ ♣❛r❡❞❡s♥ã♦ sã♦ ❡❧❡♠❡♥t♦s ♣r♦❥❡t❛❞♦s ❝♦♠ ♦ ♣r♦♣ós✐t♦ ❞❡ ❛✉①✐❧✐❛r ❛ t❛r❡❢❛ ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❚❛✐s♠❛r❝♦s ❢❛③❡♠ ♣❛rt❡ ❞♦ ❛♠❜✐❡♥t❡ ❡✱ ♣♦rt❛♥t♦✱ ❢❛③✲s❡ ♥❡❝❡ssár✐♦ ❛ ✉t✐❧✐③❛çã♦ ❞❡ té❝♥✐❝❛s♠❛✐s ❡❧❛❜♦r❛❞❛s ♣❛r❛ ❞❡t❡❝çã♦ ❡ ✐❞❡♥t✐✜❝❛çã♦ ❞♦s ♠❡s♠♦s✳ ▼❛r❝♦s ❛t✐✈♦s ✭❜❡❛❝♦♥s✮✱ t❛✐s ❝♦♠♦ s❛té❧✐t❡s ❡ s✐st❡♠❛s ❞❡ rá❞✐♦ ❢r❡q✉ê♥❝✐❛✱ ❡♠✐✲ t❡♠ r❡❣✉❧❛r♠❡♥t❡ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ◆❡ss❡s s✐st❡♠❛s✱ ❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦✲❝❛❧✐③❛çã♦ ♣♦❞❡♠ ❡st❛r ❞✐s♣♦♥í✈❡✐s ❛ ❣r❛♥❞❡s ❞✐stâ♥❝✐❛s ♦✉ ❡♠ r❡❣✐õ❡s ❡s♣❡❝í✜❝❛s ❞♦❛♠❜✐❡♥t❡ ✭❋✐❣✉r❛ ✷✳✶✷❜✮✳ ❊♠ ❝♦♥tr❛♣❛rt✐❞❛✱ ♦s ♠❛r❝♦s ♣❛ss✐✈♦s ✭❋✐❣✉r❛ ✷✳✶✷❛✮ ♥ã♦❡♠✐t❡♠ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❉❡ss❡ ♠♦❞♦✱ ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞✐s♣♦✲♥✐❜✐❧✐③❛❞❛ ♣♦r ❡ss❡ t✐♣♦ ❞❡ ♠❛r❝♦ ❞❡✈❡ s❡r ❞❡t❡❝t❛❞❛ ❞✐r❡t❛♠❡♥t❡ ♣♦r ❛❧❣✉♠ t✐♣♦ ❞❡ s❡♥s♦r ❡①t❡r♦❝❡♣t✐✈♦ ❞♦ r♦❜ô✱ ❞❡♥tr♦ ❞❡ ✉♠❛ ❢❛✐①❛ ❞❡ ❛❧❝❛♥❝❡ r❡str✐t♦✳ ❖s ♠❛r❝♦s✱ ✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞❡ s❡✉ t✐♣♦✱ ♣♦ss✉❡♠ ❧♦❝❛❧✐③❛çã♦ ❝♦♥❤❡❝✐❞❛✱ ♦ q✉❡✈✐❛❜✐❧✐③❛ ❛❥✉st❛r ❛ ❝r❡♥ç❛ q✉❡ ♦ r♦❜ô ♣♦ss✉✐ ❝♦♠ r❡❧❛çã♦ à s✉❛ ♣♦s❡ ❛t✉❛❧✳ ❚é❝♥✐❝❛s ❞❡ ✷✳✹✳ ▲♦❝❛❧✐③❛çã♦ ❞❡ ❘♦❜ôs ▼ó✈❡✐s Marco✸✶Natural Marco Artificial Natural Marco Artificial Marco ✭❛✮ ✭❜✮ ❋✐❣✉r❛ ✷✳✶✷✿ ❊①❡♠♣❧♦s ❞❡ ♠❛r❝♦s ♣❛ss✐✈♦s ❡ ❛t✐✈♦s ♣r❡s❡♥t❡s ❡♠ ✉♠ ❛♠❜✐❡♥t❡✳ ❊♠✭❛✮✱ ♠❛r❝♦s ♣❛ss✐✈♦s ✭❛rt✐✜❝✐❛✐s ♦✉ ♥❛t✉r❛✐s✮ sã♦ ✉t✐❧✐③❛❞♦s ♣❡❧♦ r♦❜ô ♣❛r❛ ♠❡❧❤♦r❛r s✉❛❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦✱ ❡♥q✉❛♥t♦ q✉❡ ❡♠ ✭❜✮ ♦ r♦❜ô r❡❝❡❜❡ ✐♥❢♦r♠❛çõ❡s ❛❞✈✐♥❞❛s ❞❡✉♠ ♠❛r❝♦ ❛t✐✈♦ ✭❜❡❛❝♦♥✮✳▲♦❝❛❧✐③❛çã♦ ❞❡ ▼♦♥t❡ ❈❛r❧♦ ✭▼❈▲✱ ❞♦ ✐♥❣❧ês ▼♦♥t❡ ❈❛r❧♦ ▲♦❝❛❧✐③❛t✐♦♥✮ ❡ ♦✉tr♦s ✜❧tr♦s♣r♦❜❛❜✐❧íst✐❝♦s ❬❚❤r✉♥ ❡t ❛❧✳✱ ✷✵✵✺❪ tê♠ s✐❞♦ ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞❛s ❝♦♠ ❡ss❡ ♣r♦♣ós✐t♦✳◆❡ss❛s té❝♥✐❝❛s✱ ♠ét♦❞♦s ❞❡ ❛♠♦str❛❣❡♠ ♣r♦❜❛❜✐❧íst✐❝❛ sã♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ r❡♣r❡s❡♥t❛r❞❡♥s✐❞❛❞❡s ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡✳ ❆ss✐♠✱ ❞✐str✐❜✉✐çõ❡s ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ sã♦ ❛♣r♦①✐♠❛❞❛s♣♦r ❝♦♥❥✉♥t♦s ❞❡ ❛♠♦str❛s✳ ◆♦ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❣❧♦❜❛❧✱ ❛ ❝r❡♥ç❛ ✐♥✐❝✐❛❧ ❞❡ ✉♠ r♦❜ô é ♥♦r♠❛❧♠❡♥t❡ r❡♣r❡s❡♥t❛❞❛ ♣♦r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣♦s❡s ❣❡r❛❞♦ ♣♦r ✉♠❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s✉♥✐❢♦r♠❡ s♦❜r❡ ♦ ❡s♣❛ç♦ ❞❡ ❛t✉❛çã♦ ❞♦ r♦❜ô ✭❋✐❣✉r❛ ✷✳✶✸❛✮✳ P♦r ✐♥t❡r♠é❞✐♦ ❞❡ s❡♥s♦r❡s❡①t❡r♦❝❡♣t✐✈♦s✱ ♦ r♦❜ô ✈❡r✐✜❝❛ s❡✉ ❛♠❜✐❡♥t❡ ❝♦♠ ✈✐st❛s ❛ ✐❞❡♥t✐✜❝❛r ♣♦t❡♥❝✐❛✐s r❡❣✐õ❡s♦♥❞❡ ♣♦ss✐✈❡❧♠❡♥t❡ ♣♦ss❛ ❡st❛r✳ ❉❡ss❡ ♠♦❞♦✱ ❛s ❛♠♦str❛s ❞✐s♣♦st❛s ♥❡ss❛s r❡❣✐õ❡s sã♦❝♦♥s✐❞❡r❛❞❛s✱ ❡♥q✉❛♥t♦ q✉❡ ❛s ❞❡♠❛✐s ❛♠♦str❛s sã♦ ❞❡s❝❛rt❛❞❛s ♦✉ ❛♠♦str❛❞❛s ♥♦✈❛✲♠❡♥t❡ ♥❡ss❛s ♣♦t❡♥❝✐❛✐s r❡❣✐õ❡s ✭❋✐❣✉r❛ ✷✳✶✸❜✮✳ ❊ss❡ ♣r♦❝❡ss♦ é ✐t❡r❛❞♦ ❝♦♥t✐♥✉❛♠❡♥t❡❛té q✉❡ ❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♥❞❡♥s❡♠ ❡♠ ✉♠❛ ❞❛❞❛ r❡❣✐ã♦ ❞♦ ❡s♣❛ç♦ ❞❡❛t✉❛çã♦ ❞♦ r♦❜ô✱ ✐♥❞✐❝❛♥❞♦ s✉❛ ♠❛✐s ♣r♦✈á✈❡❧ ❧♦❝❛❧✐③❛çã♦✳ ❊ss❡s ♠ét♦❞♦s ❜❛s❡❛❞♦s ♥❛ ♦❜s❡r✈❛çã♦ ❞❡ ♠❛r❝♦s ♦✉ ❞❡ ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ❛♠✲❜✐❡♥t❡ tê♠ ♦ ♣♦t❡♥❝✐❛❧ ❞❡ r❡❞✉③✐r ♦ ❡rr♦ ❛❝✉♠✉❧❛❞♦ ♣❡❧❛ ♦❞♦♠❡tr✐❛✳ ◆♦ ❡♥t❛♥t♦✱ t❛✐s♠ét♦❞♦s ♣r❡ss✉♣õ❡♠ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♣ré✈✐♦ ❞❡ ✉♠ ♠❛♣❛ ❞♦ ❛♠❜✐❡♥t❡✱ ❞❛ r❡s♣❡❝t✐✈❛❧♦❝❛❧✐③❛çã♦ ❞♦s ♠❛r❝♦s ♥❡ss❡ ♠❛♣❛ ♦✉ ❞❡ ❝❛r❛❝t❡ríst✐❝❛s ✐❞❡♥t✐✜❝á✈❡✐s ♥♦ ❛♠❜✐❡♥t❡ q✉❡♣♦ss❛♠ s❡r ✉t✐❧✐③❛❞❛s ♣❛r❛ ❞✐st✐♥❣✉✐r r❡❣✐õ❡s ❡s♣❡❝í✜❝❛s✳ ❊ss❡ ❝♦♥❤❡❝✐♠❡♥t♦ ♥❡♠ s❡♠✲♣r❡ ❡stá ❞✐s♣♦♥í✈❡❧✱ ♦ q✉❡ r❡str✐♥❣❡ ❛ ✉t✐❧✐③❛çã♦ ❞❡ss❡s ♠ét♦❞♦s ♥❛ ❡①♣❧♦r❛çã♦ ❞❡ ár❡❛s❞❡s❝♦♥❤❡❝✐❞❛s ❡ ❛♠❜✐❡♥t❡s ♥ã♦ ♣r❡✈✐❛♠❡♥t❡ ❡str✉t✉r❛❞♦s✳ ❙✐st❡♠❛s ❞❡ P♦s✐❝✐♦♥❛♠❡♥t♦ ●❧♦❜❛❧✱ ❞♦ ✐♥❣❧ês ●❧♦❜❛❧ P♦s✐t✐♦♥✐♥❣ ❙②st❡♠s ✭●P❙✮✱ ✸✷❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ✭❛✮ ❡t❛♣❛ ✐♥✐❝✐❛❧ ✭❜✮ ❡t❛♣❛ ✐♥t❡r♠❡❞✐ár✐❛ ❋✐❣✉r❛ ✷✳✶✸✿ ❊t❛♣❛s ❞❡ ✉♠ ♠ét♦❞♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❣❧♦❜❛❧ ❜❛s❡❛❞♦ ❡♠ té❝♥✐❝❛s ❞❡ ❛♠♦s✲ tr❛❣❡♠ ♣r♦❜❛❜✐❧íst✐❝❛✳ ◆❛ ❡t❛♣❛ ✐♥✐❝✐❛❧ ✭❛✮ ❛s ❛♠♦str❛s sã♦ ❞✐str✐❜✉í❞❛s ♥♦ ❛♠❜✐❡♥t❡s❡❣✉♥❞♦ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s ✉♥✐❢♦r♠❡✳ ❉✉r❛♥t❡ ♦ ♣r♦❝❡ss♦ ✐t❡r❛t✐✈♦❞❡ ❧♦❝❛❧✐③❛çã♦✱ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❛♠♦str❛s é r❡❛♠♦str❛❞♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛s ✐♥❢♦r♠❛çõ❡s s❡♥s♦r✐❛✐s r❡❝❡❜✐❞❛s✳ ❊♠ ✭❜✮ é ❛♣r❡s❡♥t❛❞❛ ✉♠❛ ❡t❛♣❛ ✐♥t❡r♠❡❞✐ár✐❛ ❞❡ss❡ ♣r♦❝❡ss♦✐t❡r❛t✐✈♦✳ tê♠ s✐❞♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ ♣r♦✈❡r ✐♥❢♦r♠❛çõ❡s ❛❜s♦❧✉t❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❡♠ ❛♠❜✐❡♥t❡s ❡①✲t❡r♥♦s ❬P❛r❦✐♥s♦♥ ✫ ❙♣✐❧❦❡r ❏r✳✱ ✶✾✾✻❪✳ ❆♣❡s❛r ❞❡ s✉❛ ❛♠♣❧❛ ✉t✐❧✐③❛çã♦✱ t❛✐s s✐st❡♠❛s♣♦ss✉❡♠ ❛❧❣✉♠❛s ❧✐♠✐t❛çõ❡s✱ t❛✐s ❝♦♠♦ ♣r❡❝✐sã♦ ❡ ❝♦❜❡rt✉r❛✳ ❆❧é♠ ❞✐ss♦✱ ❡ss❡s s✐st❡♠❛s♣♦ss✉❡♠ ❧✐♠✐t❛çõ❡s ♣❛r❛ ✉s♦ ❡♠ ❛♠❜✐❡♥t❡s ✐♥t❡r♥♦s ♦✉ ♣ró①✐♠♦s ❛ ❣r❛♥❞❡s ❡❞✐✜❝❛çõ❡s✳❖ s✐st❡♠❛ ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❣❧♦❜❛❧ ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞♦ ♥♦s ❞✐❛s ❛t✉❛✐s ❢♦✐ ❞❡s❡♥✲✈♦❧✈✐❞♦ ♣❡❧♦ ❞❡♣❛rt❛♠❡♥t♦ ❞❡ ❞❡❢❡s❛ ❞♦s ❊st❛❞♦s ❯♥✐❞♦s✳ ❊ss❡ s✐st❡♠❛✱ ❞❡♥♦♠✐♥❛❞♦◆❆❱❙❚❆❘ ●P❙ ✭◆❛✈✐❣❛t✐♦♥ ❙✐❣♥❛❧ ❚✐♠✐♥❣ ❛♥❞ ❘❛♥❣✐♥❣ ●❧♦❜❛❧ P♦s✐t✐♦♥✐♥❣ ❙②st❡♠✮✱❝♦♥s✐st❡ ❡♠ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ✷✹ s❛té❧✐t❡s ♦r❜✐t❛♥❞♦ ❛ ❚❡rr❛ ❡♠ ❝✐❝❧♦s ❞❡ ✶✷ ❤♦r❛s ❡❛ ✉♠❛ ❛❧t✉r❛ ❞❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✶✶✾✵✵ ♠✐❧❤❛s ♥á✉t✐❝❛s✳ ❙❡✐s ♣❧❛♥♦s ✐♥❝❧✐♥❛❞♦s ❛✺✺➦ ❡♠ r❡❧❛çã♦ ❛♦ ♣❧❛♥♦ ❞♦ ❡q✉❛❞♦r ❞❛ ❚❡rr❛ sã♦ ❞❡✜♥✐❞♦s✱ s❡♥❞♦ q✉❡ ❡♠ ❝❛❞❛ ✉♠❡stã♦ ❞✐s♣♦st♦s ✹ s❛té❧✐t❡s ✭❋✐❣✉r❛ ✷✳✶✹❛✮✳ ❈♦♥t✐♥✉❛♠❡♥t❡✱ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦❡ s✐♥❝r♦♥✐③❛çã♦ sã♦ tr❛♥s♠✐t✐❞❛s ♣❡❧♦s s❛té❧✐t❡s ❞❡ ♠♦❞♦ q✉❡ ❛s ♠❡s♠❛s ♣♦ss❛♠ s❡r✉t✐❧✐③❛❞❛s ♣❛r❛ ❡st✐♠❛r ❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ r❡❝❡♣t♦r❡s ❞❡ ●P❙ ❧♦❝❛❧✐③❛❞♦s ♥❛ s✉♣❡r❢í❝✐❡ t❡rr❡str❡✳ ❆s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ sã♦ ❣❡r❛❞❛s ✉t✐❧✐③❛♥❞♦ té❝♥✐❝❛s ❞❡ tr✐❧❛t❡r❛çã♦ ✭❋✐✲❣✉r❛ ✷✳✶✹❜✮✱ ❝✉❥♦ ❝á❧❝✉❧♦ é ❜❛s❡❛❞♦ ♥❛ ♠❡❞✐çã♦ ❞♦s t❡♠♣♦s ❞❡ tr❛♥s♠✐ssã♦ ❞♦s s✐♥❛✐s ❞❡ rá❞✐♦ ❡♠✐t✐❞♦s ♣❡❧♦s s❛té❧✐t❡s ❡ ♥❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ♠♦♠❡♥tâ♥❡❛ ❞♦s tr❛♥s✲♠✐ss♦r❡s✳ ❉❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ss❛s ❡st✐♠❛t✐✈❛s s❡r❡♠ ❝♦♥s✐❞❡r❛❞❛s ✐♥❞❡♣❡♥❞❡♥t❡s ❡♥tr❡ s✐✱ s✐st❡♠❛s ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❣❧♦❜❛❧ ♣♦ss✉❡♠ ❛ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ ♥ã♦ ❛❝✉♠✉❧❛r❡♠ ❡rr♦❝♦♠ ♦ t❡♠♣♦ ❬P❛r❦✐♥s♦♥ ✫ ❙♣✐❧❦❡r ❏r✳✱ ✶✾✾✻❪✳ ❚♦❞❛✈✐❛✱ ♦ ♣r♦❝❡ss♦ ❞❡ ♠❡❞✐çã♦ ✉t✐❧✐③❛❞♦é s✉❥❡✐t♦ à ✐♥❝❡rt❡③❛ ❡ r✉í❞♦✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❞❡✈✐❞♦ ❛♦s s❡❣✉✐♥t❡s ❢❛t♦r❡s✿ t❡♠♣♦ ❞❡ ✷✳✹✳ ▲♦❝❛❧✐③❛çã♦ ❞❡ ❘♦❜ôs ▼ó✈❡✐s✸✸ distância distânciadistância distância ✭❛✮ ◆❆❱❙❚❆❘ ●P❙ ✭❜✮ ❚r✐❧❛t❡r❛çã♦ ❋✐❣✉r❛ ✷✳✶✹✿ ✭❛✮ ❙✐st❡♠❛ ❞❡ P♦s✐❝✐♦♥❛♠❡♥t♦ ●❧♦❜❛❧ ◆❆❱❙❚❆❘ ❞❡s❡♥✈♦❧✈✐❞♦ ♣❡❧♦ ❞❡✲♣❛rt❛♠❡♥t♦ ❞❡ ❞❡❢❡s❛ ❞♦s ❊st❛❞♦s ❯♥✐❞♦s✳ ❊♠ ✭❜✮✱ t❡♠✲s❡ ✉♠❛ ✐❧✉str❛çã♦ s✐♠♣❧✐✜❝❛❞❛❞♦ ♣r♦❝❡ss♦ ❞❡ tr✐❧❛t❡r❛çã♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❧♦❝❛❧✐③❛r r❡❝❡♣t♦r❡s ❞❡ ●P❙ s✐t✉❛❞♦s ♥❛ s✉✲♣❡r❢í❝✐❡ t❡rr❡str❡✳ s✐♥❝r♦♥✐③❛çã♦ ❡♥tr❡ tr❛♥s♠✐ss♦r❡s ❡ r❡❝❡♣t♦r❡s❀ ❧♦❝❛❧✐③❛çã♦ ❡♠ t❡♠♣♦ r❡❛❧ ❞❛ ♣♦s✐çã♦❞♦s tr❛♥s♠✐ss♦r❡s❀ ♣r❡❝✐sã♦ ❞❛s ♠❡❞✐çõ❡s ❞♦ t❡♠♣♦ ❞❡ ♣r♦♣❛❣❛çã♦ ❞♦ s✐♥❛❧ ❞❡ rá❞✐♦❀✐♥t❡r❢❡rê♥❝✐❛s❀ ❡ ❞✐stâ♥❝✐❛s ❡♥✈♦❧✈✐❞❛s ♥♦ ♣r♦❝❡ss♦✳ ❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❛ ♣r❡❝✐sã♦ ❞❛s✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ♦❜t✐❞❛s ♣♦r ✐♥t❡r♠é❞✐♦ ❞❡ ✉♠ ●P❙ ♣♦❞❡ ✈❛r✐❛r s❡♥s✐✈❡❧✲♠❡♥t❡ ❡ ❧✐♠✐t❛r ♦ s❡✉ ✉s♦ ❡♠ ❛❧❣✉♠❛s s✐t✉❛çõ❡s✳ ❙✐st❡♠❛s ❞❡ P♦s✐❝✐♦♥❛♠❡♥t♦ ●❧♦❜❛❧ ❉✐❢❡r❡♥❝✐❛❧✱ ❞♦ ✐♥❣❧ês ❉✐❢❢❡r❡♥t✐❛❧ ●❧♦❜❛❧ P♦s✐✲ t✐♦♥✐♥❣ ❙②st❡♠s ✭❉●P❙✮✱ ❛♣r❡s❡♥t❛♠✲s❡ ❝♦♠♦ ♣♦t❡♥❝✐❛❧ s♦❧✉çã♦ ♣❛r❛ ❛ ♠❡❧❤♦r✐❛ ❞❡ss❛♣r❡❝✐sã♦✳ ❆ ❋✐❣✉r❛ ✷✳✶✺ ✐❧✉str❛ ❞❡ ♠❛♥❡✐r❛ s✐♠♣❧✐✜❝❛❞❛ ✉♠ ❉●P❙✱ ❡♠ q✉❡ ✉♠❛ ❡st❛çã♦❞❡ r❡❢❡rê♥❝✐❛ ❝♦♠ ❧♦❝❛❧✐③❛çã♦ ❝♦♥❤❡❝✐❞❛ é ✐♥st❛❧❛❞❛ ♥❛s ♣r♦①✐♠✐❞❛❞❡s ❞❡ ♦♥❞❡ s❡ ❞❡s❡❥❛❧♦❝❛❧✐③❛r ♦✉tr♦s r❡❝❡♣t♦r❡s✳ ❈♦♠ ❜❛s❡ ♥❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♥❤❡❝✐❞❛ ❞❡ss❛❡st❛çã♦ ❡ ❛ ❧♦❝❛❧✐③❛çã♦ ❡st✐♠❛❞❛ ♣❡❧♦ ●P❙✱ ♣♦❞❡✲s❡ ✐❞❡♥t✐✜❝❛r ✉♠ ♣❛❞rã♦ ❞❡ ❡rr♦ ❛ s❡r✉t✐❧✐③❛❞♦ ♥♦ ❛❥✉st❡ ❞❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞♦s ❞❡♠❛✐s r❡❝❡♣t♦r❡s✱ ♠❡❧❤♦r❛♥❞♦❝♦♥s✐❞❡r❛✈❡❧♠❡♥t❡ ❛ ♣r❡❝✐sã♦ ❞♦ s✐st❡♠❛✳ ❆♣❡s❛r ❞❡ss❡s s✐st❡♠❛s ♣r♦♣♦r❝✐♦♥❛r❡♠ ❛♠❡❧❤♦r✐❛ ❞❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❡st✐♠❛❞❛✱ ♦ ❝✉st♦ ❞♦s ❡q✉✐♣❛♠❡♥t♦s ❛✐♥❞❛ é ❛❧t♦✱ s❡♥❞♦ ❡ss❡ ✉♠ ♣♦ssí✈❡❧ ❢❛t♦r q✉❡ ❝♦♥tr✐❜✉✐ ♣❛r❛ ♦ ❡♠♣r❡❣♦ ❧✐♠✐t❛❞♦ ❞❡ss❡ t✐♣♦ ❞❡❡q✉✐♣❛♠❡♥t♦✳ ❙✐st❡♠❛s ❞❡ P♦s✐❝✐♦♥❛♠❡♥t♦ ●❧♦❜❛❧ ♣♦ss✉❡♠ ❧✐♠✐t❛çõ❡s ❝♦♠ r❡s♣❡✐t♦ à s✉❛ ✉t✐✲❧✐③❛çã♦ ❡♠ ❛♠❜✐❡♥t❡ ✐♥t❡r♥♦s ❡ ♥❛s ♣r♦①✐♠✐❞❛❞❡s ❞❡ ❣r❛♥❞❡s ❡❞✐✜❝❛çõ❡s✳ ❈♦♠ ✈✐st❛s❛ s✉♣❡r❛r ❡ss❛s ❧✐♠✐t❛çõ❡s✱ s✐st❡♠❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❣❧♦❜❛❧ ♣❛r❛ ❛♠❜✐❡♥t❡s ✐♥t❡r♥♦s✱ ❞♦✲ r❛✈❛♥t❡ ❞❡♥♦♠✐♥❛❞♦s ✐●P❙ ✭❞♦ ✐♥❣❧ês✱ ✐♥❞♦♦r ●❧♦❜❛❧ P♦s✐t✐♦♥✐♥❣ ❙②st❡♠s✮✱ tê♠ s✐❞♦❞❡s❡♥✈♦❧✈✐❞♦s✳ ❊①❡♠♣❧♦s ❞❡ss❡ t✐♣♦ ❞❡ s✐st❡♠❛ sã♦ ❞❡s❝r✐t♦s ❡♠ ❬●❛r❝✐❛ ❡t ❛❧✳✱ ✷✵✵✼❪❡ ❬▼✐❝❤❛❡❧ ❡t ❛❧✳✱ ✷✵✵✽❪✳ ❈♦♥❢♦r♠❡ ✐❧✉str❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✶✻✱ ❡ss❡s s✐st❡♠❛s ✉t✐❧✐③❛♠ ✸✹❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ Erro (Relógio)Dados de Correção Receptor do Estação de Usuário ReferênciaDistância mánima ❋✐❣✉r❛ ✷✳✶✺✿ ❙✐st❡♠❛ ❞❡ P♦s✐❝✐♦♥❛♠❡♥t♦ ●❧♦❜❛❧ ❉✐❢❡r❡♥❝✐❛❧ ❝♦♠ ✉♠❛ ❡st❛çã♦ ❞❡ r❡❢❡✲ rê♥❝✐❛ ✐♥st❛❧❛❞❛ ♥❛s ♣r♦①✐♠✐❞❛❞❡s ❞❡ ♦♥❞❡ s❡ ❞❡s❡❥❛ ❧♦❝❛❧✐③❛r r❡❝❡♣t♦r❡s ❞❡ ●P❙✳❝â♠❡r❛s ❞✐s♣♦st❛s s♦❜r❡ ❞❡t❡r♠✐♥❛❞❛ ár❡❛ ❞❡ tr❛❜❛❧❤♦✳ P♦r ✐♥t❡r♠é❞✐♦ ❞❡ té❝♥✐❝❛s❞❡ ❱✐sã♦ ❈♦♠♣✉t❛❝✐♦♥❛❧✱ t❛✐s s✐st❡♠❛s ❡st✐♠❛♠ ❛ ♣♦s❡ ❞❡ ♠❛r❝♦s ✈✐s✉❛✐s ❛❝♦♣❧❛❞♦s ❛♦❜❥❡t♦s q✉❡ s❡ ❡♥❝♦♥tr❛♠ ❞❡♥tr♦ ❞❛ ❢❛✐①❛ ❞❡ ❛❧❝❛♥❝❡ ❞♦ s✐st❡♠❛✳ ❆ ❜✐❜❧✐♦t❡❝❛ ♣❛r❛ r❛str❡❛♠❡♥t♦ ❞❡ ♠❛r❝♦s ✈✐s✉❛✐s ❞❡♥♦♠✐♥❛❞❛ ❆❘❚♦♦❧❦✐tP❧✉s ❬❲❛❣♥❡r ✫ ❙❝❤♠❛❧st✐❡❣✱✷✵✵✼❪ ❝♦♠♣r❡❡♥❞❡ ✉♠❛ ❢❡rr❛♠❡♥t❛ ❜❛st❛♥t❡ ❡♠♣r❡❣❛❞❛ ♣❛r❛ ✐♠♣❧❡♠❡♥t❛r ❧♦❝❛❧✐③❛çã♦❜❛s❡❛❞❛ ❡♠ ♠❛r❝♦s✳ ❙✐st❡♠❛s ✐●P❙ ❛♣r❡s❡♥t❛♠ ♣r❡❝✐sã♦ s✉♣❡r✐♦r ❛♦s ●P❙ ❞❡✈✐❞♦ ❛♦❢❛t♦ ❞❡ s❡r❡♠ ✉t✐❧✐③❛❞♦s ❡♠ ❛♠❜✐❡♥t❡s ❛❧t❛♠❡♥t❡ ❝♦♥tr♦❧❛❞♦s✳ ◆♦ ❡♥t❛♥t♦✱ ♦s ♠❡s♠♦s sã♦ ♥♦r♠❛❧♠❡♥t❡ ❝♦♥❢❡❝❝✐♦♥❛❞♦s s♦❜ ♠❡❞✐❞❛ ♣❛r❛ ✉t✐❧✐③❛çã♦ ❡♠ ❧♦❝❛✐s ❡s♣❡❝í✜❝♦s✱ ♦q✉❡ ❝♦♠♣r♦♠❡t❡ ❝♦♥s✐❞❡r❛✈❡❧♠❡♥t❡ s✉❛ ♣♦rt❛❜✐❧✐❞❛❞❡✱ ❛❧é♠ ❞❡ ♥❡❝❡ss✐t❛r❡♠ ❞❡ ❡str✉✲ t✉r❛çã♦ ♣ré✈✐❛ ❞♦ ❛♠❜✐❡♥t❡ ♦♥❞❡ s❡ ❞❡s❡❥❛ ❡❢❡t✉❛r ❛ ❧♦❝❛❧✐③❛çã♦✳ ✭❛✮✭❜✮ ❋✐❣✉r❛ ✷✳✶✻✿ ❊①❡♠♣❧♦ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❣❧♦❜❛❧ ♣❛r❛ ❛♠❜✐❡♥t❡ ✐♥t❡r♥♦✭✐●P❙✮✿ ✭❛✮ s✐st❡♠❛ ❞❡ ❝â♠❡r❛s ♣♦s✐❝✐♦♥❛❞❛s s♦❜r❡ ❛ ár❡❛ ❞❡ ❛t✉❛çã♦ ❞♦s r♦❜ôs ✭❛❞❛♣✲ t❛❞♦ ❞❡ ❬●❛r❝✐❛ ❡t ❛❧✳✱ ✷✵✵✼❪✮❀ ✭❜✮ ❡①❡♠♣❧♦s ❞❡ ♠❛r❝♦s ✈✐s✉❛✐s ✉t✐❧✐③❛❞♦s ♣❡❧❛ ❜✐❜❧✐♦t❡❝❛❆❘❚♦♦❧❦✐tP❧✉s✳ ✷✳✹✳ ▲♦❝❛❧✐③❛çã♦ ❞❡ ❘♦❜ôs ▼ó✈❡✐s✸✺ ✷✳✹✳✶ ❆❧❣✉♠❛s ❞✐♠❡♥sõ❡s ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ❡①✐st❡♠ ❞✐❢❡r❡♥t❡s ❢♦r♠❛s ❞❡ s❡ ❡❢❡t✉❛r ❛ ❧♦❝❛❧✐③❛çã♦❞❡ ✉♠ r♦❜ô✳ ❉❡♣❡♥❞❡♥❞♦ ❞♦ t✐♣♦ ❞❡ ✐♥❢♦r♠❛çã♦ ❞✐s♣♦♥í✈❡❧✱ ❡ss❛ t❛r❡❢❛ ♣♦❞❡ s❡ t♦r♥❛r♠❛✐s ♦✉ ♠❡♥♦s ❞✐❢í❝✐❧✳ ❉✐✈❡rs♦s tr❛❜❛❧❤♦s✱ ❞❡♥tr❡ ❡❧❡s ❬❚❤r✉♥ ❡t ❛❧✳✱ ✷✵✵✺❪✱ tê♠ ♣r♦♣♦st♦ t❛①♦♥♦♠✐❛s ♣❛r❛ ♦s ♣r♦❜❧❡♠❛s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❚❛✐s t❛①♦♥♦♠✐❛s sã♦ ❡st❛❜❡❧❡❝✐❞❛s ❝♦♠❜❛s❡ ♥♦ t✐♣♦ ❞❡ ✐♥❢♦r♠❛çã♦ ❞✐s♣♦♥✐❜✐❧✐③❛❞❛ ❛♦ r♦❜ô✱ t❛♥t♦ ✐♥✐❝✐❛❧♠❡♥t❡ q✉❛♥t♦ ❞✉r❛♥t❡ ❛❡①❡❝✉çã♦ ❞❛ t❛r❡❢❛✱ ❛❧é♠ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ❛♠❜✐❡♥t❡✱ ❞♦ t✐♣♦ ❞❡ ❝♦♥tr♦❧❡ ❡♠♣r❡❣❛❞♦❡ ❞♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs ✉t✐❧✐③❛❞♦✳ ❉❡✈✐❞♦ à ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦✱ ♦♠❡s♠♦ t❡♠ s✐❞♦ ❝❧❛ss✐✜❝❛❞♦ ✉t✐❧✐③❛♥❞♦ ❞✐✈❡rs❛s ❞✐♠❡♥sõ❡s✱ ❝❛❞❛ ✉♠❛ r❡s♣♦♥sá✈❡❧ ♣♦r❝❛r❛❝t❡r✐③❛r ❡ss❡ ♣r♦❜❧❡♠❛ s♦❜ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛✳ ◆♦ â♠❜✐t♦ ❞❡ ❝❛❞❛❞✐♠❡♥sã♦ t❡♠✲s❡ ❞✐❢❡r❡♥t❡s ❣r❛✉s ❞❡ ❞✐✜❝✉❧❞❛❞❡✳ ❆ s❡❣✉✐r sã♦ ❛♣r❡s❡♥t❛❞❛s ❛❧❣✉♠❛s❞✐♠❡♥sõ❡s ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦✳❉✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❞❡ ✐♥❢♦r♠❛çõ❡s❆ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❞❡ ✐♥❢♦r♠❛çõ❡s ❡st❛❜❡❧❡❝❡ ✉♠❛ ❞❛s ❞✐♠❡♥sõ❡s ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛✲❧✐③❛çã♦✳ ◆❡ss❛ ❞✐♠❡♥sã♦✱ ✉♠ r♦❜ô ♣♦❞❡ t❡r à s✉❛ ❞✐s♣♦s✐çã♦ ✉♠❛ ✐♥❢♦r♠❛çã♦ ❞❡ s✉❛♣♦s❡ ✐♥✐❝✐❛❧✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ❝♦♠ ❜❛s❡ ♥❡ss❛ ✐♥❢♦r♠❛çã♦ ✐♥✐❝✐❛❧ é♣♦ssí✈❡❧ ❡❢❡t✉❛r ✉♠ r❛str❡❛♠❡♥t♦ ❞❛ ♣♦s❡ ❞♦ r♦❜ô ✉t✐❧✐③❛♥❞♦ s❡♥s♦r❡s ♣r♦♣r✐♦❝❡♣t✐✈♦s✱❝♦♠ ♦ ♣r♦♣ós✐t♦ ❞❡ ❝♦♥✜♥❛r ❛ ✐♥❝❡rt❡③❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ♥❛s ♣r♦①✐♠✐❞❛❞❡s ❞❛ ✈❡r❞❛❞❡✐r❛❧♦❝❛❧✐③❛çã♦ ❞♦ r♦❜ô ✭♠ét♦❞♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ r❡❧❛t✐✈❛✮✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❛ ❛✉sê♥❝✐❛ ❞❡ss❛✐♥❢♦r♠❛çã♦ ✐♥✐❝✐❛❧ ✐♠♣❧✐❝❛ ♥❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡ ❡st❛❜❡❧❡❝❡r✱ ❣❧♦❜❛❧♠❡♥t❡✱ ✉♠❛ ❡st✐♠❛✲ t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ♣❛r❛ ♦ r♦❜ô ✭♠ét♦❞♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛✮✳ ❉❡✈✐❞♦ à ❡s❝❛ss❡③❞❡ ✐♥❢♦r♠❛çõ❡s✱ s❡♥s♦r❡s ❡①t❡r♦❝❡♣t✐✈♦s ❡ té❝♥✐❝❛s ♣r♦❜❛❜✐❧íst✐❝❛s sã♦ ❡♠♣r❡❣❛❞♦s ♣❛r❛✐❞❡♥t✐✜❝❛r r❡❣✐õ❡s ♥♦ ❛♠❜✐❡♥t❡ ♦♥❞❡ s❡❥❛ ♠❛✐s ♣r♦✈á✈❡❧ ❞♦ r♦❜ô ❡st❛r✳ ❆ ❧♦❝❛❧✐③❛çã♦❞❡ ✉♠ r♦❜ô s❡♠ ✉♠❛ ❡st✐♠❛t✐✈❛ ✐♥✐❝✐❛❧ s❡ ❛♣r❡s❡♥t❛ ❝♦♠♦ ✉♠ ♣r♦❜❧❡♠❛ ❝✉❥❛ s♦❧✉çã♦ é❝♦♥s✐❞❡r❛❞❛ ♠❛✐s ❞✐❢í❝✐❧ ❞♦ q✉❡ ♦s ♣r♦❜❧❡♠❛s ❡♠ q✉❡ t❛❧ ❡st✐♠❛t✐✈❛ é ❞✐s♣♦♥✐❜✐❧✐③❛❞❛✳❯♠ ♣r♦❜❧❡♠❛ ❝✉❥❛ s♦❧✉çã♦ é ❛✐♥❞❛ ♠❛✐s ❞✐❢í❝✐❧✱ ❝♦♠✉♠❡♥t❡ ❞❡♥♦♠✐♥❛❞♦ ♣r♦❜❧❡♠❛ ❞♦ r♦❜ô s❡q✉❡str❛❞♦✱ ❝♦♥s✐st❡ ❡♠ ❝❛♣t✉r❛r ♦ r♦❜ô ❞✉r❛♥t❡ s✉❛ ♦♣❡r❛çã♦ ❡ ♣♦s✐❝✐♦♥á✲❧♦ ❡♠✉♠ ♦✉tr♦ ❧♦❝❛❧ ❞♦ ❛♠❜✐❡♥t❡✳ ❈♦♠ ✐ss♦✱ ♦ r♦❜ô ♣♦❞❡r✐❛ ✏❛❝r❡❞✐t❛r✑ ❡st❛r ❡♠ ✉♠ ❧♦❝❛❧❞✐❢❡r❡♥t❡ ❞❛q✉❡❧❡ q✉❡ r❡❛❧♠❡♥t❡ ❡stá✳ ❚é❝♥✐❝❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❡ ♠❛♣❡❛♠❡♥t♦ s✐♠✉❧tâ♥❡♦s✱ ❞♦ ✐♥❣❧ês ❙✐♠✉❧t❛♥❡♦✉s ▲♦✲❝❛❧✐③❛t✐♦♥ ❛♥❞ ▼❛♣♣✐♥❣ ✭❙▲❆▼✮✱ ♣♦❞❡♠ s❡r ❡♠♣r❡❣❛❞❛s ❡♠ s✐t✉❛çõ❡s ♥❛s q✉❛✐s ♥ã♦ s❡ t❡♠ ❝♦♥❤❡❝✐♠❡♥t♦ ♣ré✈✐♦ ❞♦ ❛♠❜✐❡♥t❡✱ ♥❡♠ ✐♥❢♦r♠❛çõ❡s ❛ r❡s♣❡✐t♦ ❞❛ ♣♦s❡ ✐♥✐❝✐❛❧❞♦ r♦❜ô✳ ◆❡ss❛s té❝♥✐❝❛s✱ ♦ r♦❜ô ❝♦♥stró✐ ♦✉ ❛t✉❛❧✐③❛ ✉♠❛ r❡♣r❡s❡♥t❛çã♦ ✭♠❛♣❛✮ ❞♦❛♠❜✐❡♥t❡✱ ❡♥q✉❛♥t♦ s❡ ❧♦❝❛❧✐③❛ ✉t✐❧✐③❛♥❞♦ t❛❧ r❡♣r❡s❡♥t❛çã♦✳ ❆ ❞❡✜♥✐çã♦ ❞❡ ♠❛r❝♦s♥♦ ❛♠❜✐❡♥t❡ ❛✉①✐❧✐❛♠ ♥❛ ❝♦♥str✉çã♦ ❞❛ r❡♣r❡s❡♥t❛çã♦✱ ❛♣❡s❛r ❞❛ ♣♦s✐çã♦ ❞♦s ♠❡s♠♦s ✸✻❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ♥ã♦ s❡r ❝♦♥❤❡❝✐❞❛ ❛ ♣r✐♦r✐✳ ❖ ♦❜❥❡t✐✈♦ ❞❡ss❛s té❝♥✐❝❛s ❝♦♥s✐st❡ ❡♠ ❝♦♠♣✉t❛r ✉♠❛❞✐str✐❜✉✐çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s ❝♦♥❥✉♥t❛ ❞❛ ♣♦s✐çã♦ ❞♦s ♠❛r❝♦s ❡ ❞♦ ❡st❛❞♦ ❞♦ s✐st❡♠❛✱❞❛❞❛s ❛s ♦❜s❡r✈❛çõ❡s ❡ ❡♥tr❛❞❛s ❞❡ ❝♦♥tr♦❧❡ ❡❢❡t✉❛❞❛s✳ ❖ tr❛❜❛❧❤♦ ❞❡ ❉✉rr❛♥t✲❲❤②t❡ ✫❇❛✐❧❡② ❬✷✵✵✻❪ ❛♣r❡s❡♥t❛ ✉♠❛ ✈✐sã♦ ❣❡r❛❧ ❞❛ té❝♥✐❝❛ ❡ ♦s ♣r✐♥❝✐♣❛✐s ❛❧❣♦r✐t♠♦s ✉t✐❧✐③❛❞♦s✳❆♠❜✐❡♥t❡ ❞❡ ❛t✉❛çã♦❖ ❛♠❜✐❡♥t❡ ❡♠ q✉❡ ♦ r♦❜ô ❛t✉❛ ❝♦♠♣r❡❡♥❞❡ ♦✉tr❛ ❞✐♠❡♥sã♦ q✉❡ t❡♠ s✐❞♦ ❝♦♥s✐❞❡r❛❞❛♥❛s t❛①♦♥♦♠✐❛s ♣r♦♣♦st❛s✳ ◆❡ss❛s t❛①♦♥♦♠✐❛s✱ ✉♠ ❛♠❜✐❡♥t❡ é ♥♦r♠❛❧♠❡♥t❡ ❝❧❛ss✐✜✲❝❛❞♦ ❝♦♠♦ ❡stát✐❝♦ ♦✉ ❞✐♥â♠✐❝♦✳ ❆♠❜✐❡♥t❡s ❡stát✐❝♦s sã♦ ❝❛r❛❝t❡r✐③❛❞♦s ♣❡❧♦ ❢❛t♦ ❞❡ q✉❡ ❛ ú♥✐❝❛ ✐♥❢♦r♠❛çã♦ q✉❡ s♦❢r❡ ✈❛r✐❛çã♦ ♥♦ s✐st❡♠❛ é ❛ ♣♦s❡ ❞♦ r♦❜ô✳ ❚♦❞♦s ♦s ❞❡♠❛✐s♦❜❥❡t♦s ♥♦ ❛♠❜✐❡♥t❡ ♣❡r♠❛♥❡❝❡♠ ✜s✐❝❛♠❡♥t❡ ✐♥❡rt❡s✳ ❉❡ss❡ ♠♦❞♦✱ ♦ ❡st❛❞♦ ❞♦ s✐st❡♠❛♣♦❞❡ s❡r r❡♣r❡s❡♥t❛❞♦ ♣❡❧♦ ❡st❛❞♦ ❞♦ r♦❜ô✱ ✉♠❛ ✈❡③ q✉❡ ♦ ❛♠❜✐❡♥t❡ é ✐♠✉tá✈❡❧✳ P♦r♦✉tr♦ ❧❛❞♦✱ ❛♠❜✐❡♥t❡s ❞✐♥â♠✐❝♦s ♣♦ss✉❡♠ ❡♥t✐❞❛❞❡s✱ q✉❡ ♥ã♦ ♦ ♣ró♣r✐♦ r♦❜ô✱ q✉❡ ♠✉✲❞❛♠ s✉❛ ❧♦❝❛❧✐③❛çã♦ ♦✉ ❝♦♥✜❣✉r❛çã♦✳ ❆ss✐♠✱ t❛✐s ✐♥❢♦r♠❛çõ❡s ♣♦❞❡♠ s❡r ✐♥❝♦r♣♦r❛❞❛s❛♦ ❡st❛❞♦ ❞♦ s✐st❡♠❛ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛s ✐♥❢♦r♠❛çõ❡s ♣❡rt✐♥❡♥t❡s ❛♦ ❡st❛❞♦ ❞♦ r♦❜ô✳▲♦❝❛❧✐③❛r ✉♠ r♦❜ô ❛t✉❛♥❞♦ ❡♠ ✉♠ ❛♠❜✐❡♥t❡ ❞✐♥â♠✐❝♦ é ♠❛✐s ❞✐❢í❝✐❧ ❞❡✈✐❞♦ ❛ ❞✐✈❡rs❛s q✉❡stõ❡s q✉❡ s✉r❣❡♠ ❡♠ ❞❡❝♦rrê♥❝✐❛ ❞❛s ❝♦♥st❛♥t❡s ♠✉❞❛♥ç❛s ♥♦ ❡st❛❞♦ ❞♦ s✐st❡♠❛✳❆❧❣♦r✐t♠♦ ❞❡ ❧♦❝❛❧✐③❛çã♦❖✉tr❛ ❞✐♠❡♥sã♦ ❞✐③ r❡s♣❡✐t♦ ❛♦ ❛❧❣♦r✐t♠♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ✉t✐❧✐③❛❞♦✱ q✉❡ ♣♦❞❡ ♦✉ ♥ã♦❝♦♥s✐❞❡r❛r ❛ ❛t✉❛çã♦ ❞♦ r♦❜ô ❞✉r❛♥t❡ ♦ ♣r♦❝❡ss♦ ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ▼❡❝❛♥✐s♠♦s q✉❡ ✉t✐✲❧✐③❛♠ ❛ ❛t✉❛çã♦ ❞♦ r♦❜ô sã♦ ❞❡♥♦♠✐♥❛❞♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛t✐✈❛✳ ❊ss❡s♠❡❝❛♥✐s♠♦s ✈✐s❛♠ ✐♥str✉✐r ♦ r♦❜ô ❛ s❡ ♠♦✈✐♠❡♥t❛r ♣❛r❛ r❡❣✐õ❡s ❞♦ ❛♠❜✐❡♥t❡ ❝♦♥s✐❞❡✲ r❛❞❛s ♠❛✐s ♣r♦♠✐ss♦r❛s ♣❛r❛ ♦ ❛❥✉st❡ ❞❛ s✉❛ ❝r❡♥ç❛ ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❊ss❛s r❡❣✐õ❡s sã♦❡s❝♦❧❤✐❞❛s ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ❛❧❣♦r✐t♠♦ ✉t✐❧✐③❛❞♦ ❡ ❧❡✈❛♠ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ♦ ❝♦♥❥✉♥t♦❞❡ ✐♥❢♦r♠❛çõ❡s ❞✐s♣♦♥í✈❡✐s✳ ❆❜♦r❞❛❣❡♥s ♣❛ss✐✈❛s ♥ã♦ ✉t✐❧✐③❛♠ t❛✐s ✐♥❢♦r♠❛çõ❡s ♣❛r❛❢❛❝✐❧✐t❛r ♦ ♣r♦❝❡ss♦ ❞❡ ❧♦❝❛❧✐③❛çã♦✱ s❡♥❞♦ ❝♦♥s✐❞❡r❛❞❛s ♠❛✐s ❢á❝❡✐s ❞❡ s❡r❡♠ ✉t✐❧✐③❛❞❛s✳❚✐♣♦ ❞❡ s✐st❡♠❛ r♦❜ót✐❝♦P♦r ✜♠✱ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ♣♦❞❡ s❡r ❝♦♥s✐❞❡r❛❞♦ ♥♦ â♠❜✐t♦ ❞❡ s✐st❡♠❛s ❝♦♥s✲ t✐t✉í❞♦s ♣♦r ✉♠ ú♥✐❝♦ r♦❜ô ♦✉ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s✳ ❊♠ s✐st❡♠❛s ❝♦♠ ✉♠ ú♥✐❝♦r♦❜ô✱ t♦❞♦ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ é ❛❞q✉✐r✐❞♦ ♣♦r ✉♠❛ ú♥✐❝❛ ♣❧❛t❛❢♦r♠❛✳ ❉❡ss❡ ♠♦❞♦✱ ❛s❡t❛♣❛s ❞❡ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦ sã♦ ❢❛❝✐❧✐t❛❞❛s t❡♥❞♦ ❡♠ ✈✐st❛ q✉❡ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞✐s✲♣♦♥í✈❡❧ ❡stá s❡♠♣r❡ ❛❝❡ssí✈❡❧ ❛♦ r♦❜ô✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❡♠ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s✱♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❛❞q✉✐r✐❞♦ ♣❡❧♦s ❞✐✈❡rs♦s r♦❜ôs ❞❡✈❡ s❡r ✉t✐❧✐③❛❞♦ ♣❛r❛ ❛ t♦♠❛❞❛ ❞❡❞❡❝✐sã♦✳ P❛r❛ ✐ss♦✱ ❛❧❣✉♥s s✐st❡♠❛s ✉t✐❧✐③❛♠ ✉♠❛ ✉♥✐❞❛❞❡ ❝❡♥tr❛❧✐③❛❞♦r❛ q✉❡ r❡❝❡❜❡ ✷✳✹✳ ▲♦❝❛❧✐③❛çã♦ ❞❡ ❘♦❜ôs ▼ó✈❡✐s✸✼ t♦❞❛s ❛s ✐♥❢♦r♠❛çõ❡s ❡ ❛s ♣r♦❝❡ss❛ ❞❡ ♠❛♥❡✐r❛ ❝❡♥tr❛❧✐③❛❞❛✳ ❚❛❧ ♣r♦❝❡ss❛♠❡♥t♦ ❣❡r❛ ♥♦✈❛s ✐♥❢♦r♠❛çõ❡s ❛ s❡r❡♠ ❡♥✈✐❛❞❛s ♣❛r❛ ❝❛❞❛ ✐♥t❡❣r❛♥t❡ ❞♦ s✐st❡♠❛✳❆ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦ ❡♠ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s ♣♦❞❡ t❛♠❜é♠ s❡r ❢❡✐t❛ ❞❡ ♠❛✲ ♥❡✐r❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛✳ ❉❡ss❛ ❢♦r♠❛✱ ♦ ❡❧❡♠❡♥t♦ ❝❡♥tr❛❧✐③❛❞♦r ❞❡✐①❛ ❞❡ ❡①✐st✐r ❡ ❛❧❣♦r✐t✲♠♦s ❞❡ ❝♦♦r❞❡♥❛çã♦ sã♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ ✐♠♣❧❡♠❡♥t❛r ❛ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦ ❡♠ ❣r✉♣♦✳❙✐st❡♠❛s ♠✉❧t✐rr♦❜ôs ✈✐❛❜✐❧✐③❛♠ ❛ ❞✐✈✐sã♦ ❞❡ ❞❡t❡r♠✐♥❛❞❛ t❛r❡❢❛✱ ❞❡ ♠♦❞♦ q✉❡ ❛s s✉❜✲ t❛r❡❢❛s ♣♦ss❛♠ s❡r ❡①❡❝✉t❛❞❛s ♣♦r ❡♥t✐❞❛❞❡s ❞✐st✐♥t❛s ❞♦ ❣r✉♣♦✳ ❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱❡ss❛ ❞✐✈✐sã♦ ❛❝❛rr❡t❛ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❛ ❝♦♦r❞❡♥❛çã♦ ❞♦ ❣r✉♣♦✱ ❛❧é♠ ❞❡ s❡ ❡st❛❜❡❧❡✲❝❡r ♠❡✐♦s ♣❛r❛ ❡❢❡t✉❛r tr♦❝❛ ❞❡ ✐♥❢♦r♠❛çõ❡s✱ ♦ q✉❡ ✐♥s❡r❡ ❝♦♠♣❧❡①✐❞❛❞❡ ❛❞✐❝✐♦♥❛❧ ❛♦♠❡❝❛♥✐s♠♦✳ ❆ ❧♦❝❛❧✐③❛çã♦ ❞♦s ✐♥t❡❣r❛♥t❡s ❞❡ ✉♠ s✐st❡♠❛ ♠✉❧t✐rr♦❜ót✐❝♦ ♣♦❞❡ s❡r ❡❢❡t✉❛❞❛✉t✐❧✐③❛♥❞♦ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❝♦♦♣❡r❛t✐✈❛s ❡ ❝♦❧❛❜♦r❛t✐✈❛s ❞♦ ❣r✉♣♦✳ ◆❡ss❡ ❝♦♥t❡①t♦✱♦s r♦❜ôs ❝♦♦♣❡r❛♠ ♣♦r ♠❡✐♦ ❞♦ ❝♦♠♣❛rt✐❧❤❛♠❡♥t♦ ❞❡ ✐♥❢♦r♠❛çõ❡s ❝♦♠ ✈✐st❛s ❛ ❣❡r❛r✉♠❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❣r✉♣♦✱ ♥♦r♠❛❧♠❡♥t❡ ❡❢❡t✉❛❞❛ ♣♦r ♠❡✐♦❞❡ té❝♥✐❝❛s ♣r♦❜❛❜✐❧íst✐❝❛s ✭❆♣ê♥❞✐❝❡ ❆✮ ❡ ♠ét♦❞♦s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ✭❙❡çã♦✷✳✹✳✷✮✳ ❖ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥ ❬❑❛❧♠❛♥✱ ✶✾✻✵❪ ❡ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥✲❝✐❛s ❬❏✉❧✐❡r ✫ ❯❤❧♠❛♥♥✱ ✶✾✾✼✱ ✷✵✵✶❪ sã♦ ❡♠♣r❡❣❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦ ♣❛r❛ ❛ ❡st✐♠❛çã♦❡ ❛t✉❛❧✐③❛çã♦ ❞❛s ♣♦s❡s ❡♠ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ ❞❡ ♠♦❞♦ q✉❡ ✉♠❛ ❜r❡✈❡✐♥tr♦❞✉çã♦ ❛♦s ♠❡s♠♦s é ❛♣r❡s❡♥t❛❞❛ ♥♦s ❆♣ê♥❞✐❝❡s ❇ ❡ ❈✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✷✳✹✳✷ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛✿ ♣r✐♥❝✐♣❛✐s ❝♦♥❝❡✐t♦s ■♥ú♠❡r❛s t❛r❡❢❛s ❡♠ ❘♦❜ót✐❝❛ ▼ó✈❡❧ ❡①✐❣❡♠ q✉❡ ✉♠ ❣r✉♣♦ ❞❡ r♦❜ôs ❛t✉❡ ❡♠ ❝♦♥❥✉♥t♦✳◆❡ss❡ ❝♦♥t❡①t♦✱ ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ♣♦❞❡♠ s❡r ❛❧❝❛♥ç❛❞♦s q✉❛♥❞♦ ♦s r♦❜ôs ❝♦♦♣❡r❛♠♦✉ sã♦ ❝♦♦r❞❡♥❛❞♦s ❞❡ ♠❛♥❡✐r❛ ❛❞❡q✉❛❞❛✳ ●❡r❛❧♠❡♥t❡✱ ♣❛r❛ q✉❡ ❡ss❛ ❝♦♦r❞❡♥❛çã♦♣♦ss❛ ♦❝♦rr❡r ❞❡ ♠❛♥❡✐r❛ ❡✜❝✐❡♥t❡✱ ✐♥❢♦r♠❛çõ❡s ♣r❡❝✐s❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ♣r❡❝✐s❛♠ ❡st❛r❞✐s♣♦♥í✈❡✐s✳ ◆♦ â♠❜✐t♦ ❞❡ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s✱ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❣❛♥❤❛✉♠❛ ♥♦✈❛ ❞✐♠❡♥sã♦✱ ♣❛ss❛♥❞♦ ❛ ❝♦♥s✐❞❡r❛r ❛s ❝❛r❛❝t❡ríst✐❝❛s ❝♦❧❡t✐✈❛ ❡ ❝♦❧❛❜♦r❛t✐✈❛❞♦ ❣r✉♣♦✳ ❆s ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ ❝❛❞❛ ♠❡♠❜r♦ t♦r♥❛♠✲s❡ r❡❧❡✈❛♥t❡s ♣❛r❛♦ ❛❥✉st❡ ❞❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❣r✉♣♦✳ ❚❡♠✲s❡✱ ❡♥tã♦✱ ✉♠❛ ❡st✐♠❛t✐✈❛ ❞❡❧♦❝❛❧✐③❛çã♦ ❝♦♥❥✉♥t❛ q✉❡ ✈✐s❛ ♠✐♥✐♠✐③❛r ♦s ❡rr♦s ❧♦❝❛✐s ❛ss♦❝✐❛❞♦s ❛ ❝❛❞❛ ❝♦♠♣♦♥❡♥t❡❞♦ s✐st❡♠❛✱ ♣r♦❝❡ss♦ ❡ss❡ ❝♦♠✉♠❡♥t❡ ❞❡♥♦♠✐♥❛❞♦ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛✳ ❆ ✐❞❡✐❛ ❣❡r❛❧ ❞❛s té❝♥✐❝❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❝♦♥s✐st❡ ♥❛ ❣❡r❛çã♦ ❞❡ ✉♠❛❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ ✉♠ ❣r✉♣♦ ❞❡ r♦❜ôs✳ ❚❛❧ ❡st✐♠❛t✐✈❛ é ❜❛s❡❛❞❛ ♥♦❝♦♠♣❛rt✐❧❤❛♠❡♥t♦ ❞❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ t♦❞♦s ♦s r♦❜ôs ❞♦ ❣r✉♣♦✳ ❉❡ss❡♠♦❞♦✱ ❡ss❛s té❝♥✐❝❛s ♣r♦❝✉r❛♠ s♦❧✉❝✐♦♥❛r ♦ ❞✐❢í❝✐❧ ♣r♦❜❧❡♠❛ ❞❡ ❢✉sã♦ ❞❡ ✐♥❢♦r♠❛çõ❡s❛❞✈✐♥❞❛s ❞❡ ❞✐✈❡rs❛s ❢♦♥t❡s ✐♥❞❡♣❡♥❞❡♥t❡s ❡ ✐♥t❡r❞❡♣❡♥❞❡♥t❡s✱ ❝♦♠ ✈✐st❛s ❛ ❣❡r❛r ❛ ✸✽❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛✳ ■♥ú♠❡r♦s tr❛❜❛❧❤♦s tê♠ ✉t✐❧✐③❛❞♦ té❝♥✐❝❛s ♣r♦❜❛❜✐❧íst✐❝❛s ♣❛r❛❣❡r❛r t❛✐s ❡st✐♠❛t✐✈❛s✱ t❛✐s ❝♦♠♦ ♦ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥ ❬❘♦✉♠❡❧✐♦t✐s ✫ ❇❡❦❡②✱ ✷✵✵✷❪✱♦ ✜❧tr♦ ❞❡ ♣❛rtí❝✉❧❛s ❬❋♦① ❡t ❛❧✳✱ ✷✵✵✵❪ ❡ ❛ ❊st✐♠❛çã♦ ♣♦r ▼á①✐♠❛ ❱❡r♦ss✐♠✐❧❤❛♥ç❛❬❍♦✇❛r❞ ❡t ❛❧✳✱ ✷✵✵✷❪✳ ❆ ❣❡r❛çã♦ ❞❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ é ❡❢❡t✉❛❞❛ ♣♦r ♠❡✐♦ ❞❛ ❢✉sã♦ ❞❡ ✐♥❢♦r♠❛çõ❡s♣r♦♣r✐♦❝❡♣t✐✈❛s ❡ ❡①t❡r♦❝❡♣t✐✈❛s ❛❞q✉✐r✐❞❛s ♣❡❧♦s r♦❜ôs✳ ❆ ✉t✐❧✐③❛çã♦ ❞♦s ♣ró♣r✐♦s r♦❜ôs❝♦♠♦ ♠❛r❝♦s✱ ❛♦ ✐♥✈és ❞♦ ✉s♦ ❞❡ ♠❛r❝♦s ❛rt✐✜❝✐❛✐s ♦✉ ♥❛t✉r❛✐s ❞✐s♣♦st♦s ♥♦ ❛♠❜✐❡♥t❡✱❛♣r❡s❡♥t❛✲s❡ ❝♦♠♦ ❛ ♣r✐♥❝✐♣❛❧ ❢♦♥t❡ ❞❡ ✐♥❢♦r♠❛çã♦ s❡♥s♦r✐❛❧ ❡①t❡r♦❝❡♣t✐✈❛✳ ❚♦❞❛ ✈❡③ q✉❡ ❛ ❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ ✉♠ r♦❜ô é ❛t✉❛❧✐③❛❞❛ ❝♦♠ ❜❛s❡ ❡♠ ✐♥❢♦r♠❛çõ❡s❛❞✈✐♥❞❛s ❞❡ ♦✉tr♦s r♦❜ôs t❡♠✲s❡ ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ✉♠❛ ❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛✲ t✐✈❛✳ ❉✉r❛♥t❡ ♦s ✐♥t❡r✈❛❧♦s ❡♥tr❡ ❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ ♦s r♦❜ôs ❛t✉❛♠✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❡ ✉t✐❧✐③❛♠ s✐st❡♠❛s ❞❡ ❞❡❛❞ r❡❝❦♦♥✐♥❣✱ t❛✐s ❝♦♠♦ ♦❞♦♠❡tr✐❛✱ ♣❛r❛♣r♦♣❛❣❛r s✉❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❉❡✈✐❞♦ ❛♦ ❛❝ú♠✉❧♦ ♣❡r♠❛♥❡♥t❡ ❞❡ ✐♥❝❡rt❡③❛❞❡❝♦rr❡♥t❡ ❞❛ ✉t✐❧✐③❛çã♦ ❞❡ss❡s s✐st❡♠❛s✱ ♦s ❡♥❝♦♥tr♦s ❝♦♥s✐st❡♠ ❡♠ ✉♠ ❡s❢♦rç♦ ❝♦♦✲♣❡r❛t✐✈♦ ♣❛r❛ s❡ ❡❢❡t✉❛r ❛ ❛t✉❛❧✐③❛çã♦ ❞❛s ❝r❡♥ç❛s ✐♥❞✐✈✐❞✉❛✐s ✭❧♦❝❛✐s✮ ❞♦s r♦❜ôs ❡ ❛❝♦♥s❡q✉❡♥t❡ ❣❡r❛çã♦ ❞❡ ✉♠❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ♣❛r❛ ♦ ❣r✉♣♦✳ ❆ ❛t✉❛❧✐③❛çã♦ ❞❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ ✉♠ r♦❜ô✱ ❝♦♠ ❜❛s❡ ❡♠ ♦✉tr♦s r♦❜ôs ♥♦ ❣r✉♣♦✱ ❛♣r❡s❡♥t❛✲s❡ ❝♦♠♦ ✉♠ ❞❡s❛✜♦ s✐❣♥✐✜❝❛t✐✈♦✱ ❞❡✈✐❞♦ às ✐♥ú♠❡r❛s ❢♦♥t❡s❞❡ ✐♥❝❡rt❡③❛ ❡①✐st❡♥t❡s ♥❡ss❡ ♣r♦❝❡ss♦ ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ❛♥t❡r✐♦r♠❡♥t❡✱ s❡♥s♦r❡s ♣r♦♣r✐♦❝❡♣t✐✈♦s ❡ ❡①t❡r♦❝❡♣t✐✈♦s ✐♥❝♦r♣♦r❛♠ ✐♥❝❡rt❡③❛ ♥♦s ♣r♦❝❡ss♦s ❡♠ q✉❡sã♦ ✉t✐❧✐③❛❞♦s ❡ ❛♣r❡s❡♥t❛♠ ♠❡❞✐❞❛s r✉✐❞♦s❛s✳ ❉❡✈✐❞♦ ❛♦ ❢❛t♦ ❞♦s r♦❜ôs ❛t✉❛r❡♠ ❝♦♠♦♠❛r❝♦s ♥❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ ♦s ♠❡s♠♦s ♣♦ss✉❡♠ ✐♥❝❡rt❡③❛ ❛ss♦❝✐❛❞❛ às s✉❛s ✐♥✲❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦✱ ✉♠❛ ✈❡③ q✉❡ sã♦ ❡♥t✐❞❛❞❡s ❞✐♥â♠✐❝❛s q✉❡ t❛♠❜é♠ s❡ ❜❛s❡✐❛♠❡♠ ✐♥❢♦r♠❛çõ❡s s❡♥s♦r✐❛✐s ♣❛r❛ ❣❡r❛r s✉❛s ♣ró♣r✐❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❚❡♠✲s❡✱❡♥tã♦✱ ❡ss❛ ❢♦♥t❡ ❛❞✐❝✐♦♥❛❧ ❞❡ ✐♥❝❡rt❡③❛ q✉❡ ❞❡✈❡ s❡r ❛❞❡q✉❛❞❛♠❡♥t❡ ✜❧tr❛❞❛✳ ❉✐✈❡rs♦s ❛s♣❡❝t♦s ❞❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ tê♠ s✐❞♦ ❡①♣❧♦r❛❞♦s ❡♠ s✐st❡♠❛s♠✉❧t✐rr♦❜ót✐❝♦s✱ ❞❡s❞❡ ♦s t✐♣♦s ❞❡ té❝♥✐❝❛s ♣r♦❜❛❜✐❧íst✐❝❛s ✉t✐❧✐③❛❞❛s ❛té ❛ ❛♥á❧✐s❡ ❞❛❝♦♠♣❧❡①✐❞❛❞❡ ❞♦s ❛❧❣♦r✐t♠♦s ❡♠♣r❡❣❛❞♦s✳ ❊st✉❞♦s s✉❣❡r❡♠ q✉❡ ❛ q✉❛❧✐❞❛❞❡ ❞❛ ❡st✐♠❛✲ t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ♣♦❞❡ s❡r ✐♥✢✉❡♥❝✐❛❞❛ ♣♦r ✈ár✐♦s ❢❛t♦r❡s✱ ❞❡♥tr❡ ❡❧❡s ❛s ❡str❛té❣✐❛s ❞❡♠♦✈✐♠❡♥t❛çã♦ ❞❡ ❣r✉♣♦ ❡ ♦ t✐♣♦ ❞❡ ♠❡❞✐❞❛ s❡♥s♦r✐❛❧ ✉t✐❧✐③❛❞❛✳ ❈♦♥❢♦r♠❡ s❡rá ❞✐s❝✉t✐❞♦♥♦ ❈❛♣ít✉❧♦ ✸✱ ✐♥ú♠❡r♦s tr❛❜❛❧❤♦s tê♠ ❡♠♣r❡❣❛❞♦ té❝♥✐❝❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛♣❛r❛ ♠❛♥t❡r ❜♦❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❡♠ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s✳ ◆♦ ❡♥t❛♥t♦✱♦ ❡♠♣r❡❣♦ ❞❡ t❛✐s té❝♥✐❝❛s ❡♠ s✐st❡♠❛s ❝♦♠♣♦st♦s ♣♦r ❣r❛♥❞❡s ❣r✉♣♦s ❞❡ r♦❜ôs ❛✐♥❞❛ é♣♦✉❝♦ ❡①♣❧♦r❛❞♦✳ ◆❡ss❡ ❝♦♥t❡①t♦ s✉r❣❡♠ ♥♦✈♦s ❞❡s❛✜♦s✱ ✉♠❛ ✈❡③ q✉❡ ❛ ❝♦♠♣❧❡①✐❞❛❞❡♣❛r❛ s❡ ❣❡r❛r ❞❡ ♠❛♥❡✐r❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ✉♠❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛✱ ❛❧é♠ ❞❛ ♠❛♥✉t❡♥✲çã♦ ❞♦ r❡❣✐str♦ ❞❡ss❛s ❡st✐♠❛t✐✈❛s✱ ♣♦❞❡ ✐♥✈✐❛❜✐❧✐③❛r ♦ ✉s♦ ❞❡ té❝♥✐❝❛s ❞❡ ❧♦❝❛❧✐③❛çã♦❝♦♦♣❡r❛t✐✈❛ ❡♠ s✐st❡♠❛s r❡❛✐s ❝♦♠♣♦st♦s ♣♦r ✉♠ ♥ú♠❡r♦ s✐❣♥✐✜❝❛t✐✈♦ ❞❡ r♦❜ôs✳ ✷✳✹✳ ▲♦❝❛❧✐③❛çã♦ ❞❡ ❘♦❜ôs ▼ó✈❡✐s✸✾ ❆ ♠❛✐♦r✐❛ ❞❛s té❝♥✐❝❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡♠♣r❡❣❛❞❛s ❡♠ s✐st❡♠❛s ♠✉❧✲ t✐rr♦❜ôs ♣r❡ss✉♣õ❡ q✉❡ s❡✉s ✐♥t❡❣r❛♥t❡s ♣♦❞❡♠ s❡ ❝♦♠✉♥✐❝❛r ❡ tr♦❝❛r ✐♥❢♦r♠❛çõ❡s s❡♥✲s♦r✐❛✐s ❛ t♦❞♦ ♠♦♠❡♥t♦ ❝♦♠ t♦❞♦s ♦s ✐♥t❡❣r❛♥t❡s ❞♦ ❣r✉♣♦✳ ❊♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s t❛❧ s✉♣♦s✐çã♦ é ❝♦♥s✐❞❡r❛❞❛ ✉♠ ♣♦✉❝♦ ❢♦rt❡✱ t❡♥❞♦ ❡♠ ✈✐st❛ ❛s r❡str✐çõ❡s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦✱s❡♥s♦r✐❛♠❡♥t♦ ❡ ❝♦♠✉♥✐❝❛çã♦ ❧♦❝❛✐s✱ ❞❡❝♦rr❡♥t❡s ❞♦ t✐♣♦ ❞❡ r♦❜ôs ✉t✐❧✐③❛❞♦s✳ ◆♦r♠❛❧✲♠❡♥t❡✱ ♥❡ss❡ t✐♣♦ ❞❡ s✐st❡♠❛ ♦s r♦❜ôs ❡♠♣r❡❣❛❞♦s sã♦ ♠❛✐s s✐♠♣❧❡s ❡ ❛ ❡①❡❝✉çã♦ ❞❡ t❛r❡❢❛s ❝♦♠♣❧❡①❛s é ✈✐❛❜✐❧✐③❛❞❛ ♣♦r ♠❡✐♦ ❞❛ ❛❞❡q✉❛❞❛ ❝♦♦r❞❡♥❛çã♦ ❞♦s ❛❣❡♥t❡s✳ ❖ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❛♣❧✐❝❛❞♦ ❛ ❡♥①❛♠❡s r♦❜ót✐❝♦s ♣♦❞❡ s❡r✈✐st♦ ❝♦♠♦ ✉♠ s✐st❡♠❛ ❞❡ ❢✉sã♦ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ❞❡ ❞❛❞♦s✳ ❊ss❡ t✐♣♦ ❞❡ s✐st❡♠❛ ❝♦♥s✐st❡❡♠ ✉♠❛ ❝♦❧❡çã♦ ❞❡ ♥ós ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❧✐❣❛❞♦s ✈✐❛ ❝❛♥❛✐s ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❬❏✉❧✐❡r ✫❯❤❧♠❛♥♥✱ ✷✵✵✶❪✳ ◆❡ss❡ s✐st❡♠❛✱ ♥❡♥❤✉♠ ♥ó t❡♠ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❛ t♦♣♦❧♦❣✐❛ ✐♥t❡✐r❛ ❞❛ r❡❞❡ ❡ ❝❛❞❛ ✉♠ ❡①❡❝✉t❛ s✉❛ t❛r❡❢❛ ✉t✐❧✐③❛♥❞♦ s♦♠❡♥t❡ ❛s ✐♥❢♦r♠❛çõ❡s ❞✐s♣♦♥✐❜✐❧✐③❛❞❛s♣❡❧♦s ♥ós ❛♦s q✉❛✐s s❡ ❡♥❝♦♥tr❛ ❛ss♦❝✐❛❞♦ ✭♥ós ✈✐③✐♥❤♦s✮✳ ❉❡ss❡ ♠♦❞♦✱ ♥❡♥❤✉♠❛ ✉♥✐❞❛❞❡❝❡♥tr❛❧✐③❛❞♦r❛ ❡①❡❝✉t❛ ❛ ❢✉sã♦ ❞♦s ❞❛❞♦s✳ ❊♠ ✉♠ ❡♥①❛♠❡ r♦❜ót✐❝♦ ❝❛❞❛ r♦❜ô ✭♥ó✮ ♣♦ss✉✐ s❡♥s♦r❡s ❝♦♠♦ ❢♦♥t❡ ❞❡ ✐♥❢♦r♠❛✲çã♦✳ ❉❡ss❡ ♠♦❞♦✱ ✐♥❢♦r♠❛çõ❡s ❛❞✈✐♥❞❛s ❞❡ ❢♦♥t❡s ❞✐str✐❜✉í❞❛s sã♦ ♣r♦♣❛❣❛❞❛s ♣❡❧♦❡♥①❛♠❡ ✭s✐st❡♠❛✮ ❞❡ ♠♦❞♦ q✉❡ ❝❛❞❛ r♦❜ô ♣♦ss❛ t❡r ❛❝❡ss♦ ❛ ❞❛❞♦s r❡❧❡✈❛♥t❡s ❛ s❡✲ r❡♠ ✉s❛❞♦s ♥♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ s✉❛ t❛r❡❢❛✳ ◆❡ss❡ s❡♥t✐❞♦✱ ♦ ❝♦♠♣❛rt✐❧❤❛♠❡♥t♦ ❞❡✐♥❢♦r♠❛çõ❡s s❡♥s♦r✐❛✐s t♦r♥❛✲s❡ ❜❛st❛♥t❡ r❡❧❡✈❛♥t❡ ❡♠ ❣r❛♥❞❡s ❣r✉♣♦s ❞❡ r♦❜ôs ♦✉ ❡♠❣r✉♣♦s ❤❡t❡r♦❣ê♥❡♦s✱ ✉♠❛ ✈❡③ q✉❡ ❝❛♣❛❝✐❞❛❞❡s ✐♥❞✐✈✐❞✉❛✐s sã♦ ♣r♦♣❛❣❛❞❛s ♣❡❧♦ s✐st❡♠❛❡ ❝♦♠♣❛rt✐❧❤❛❞❛s ♣♦r s❡✉s ♠❡♠❜r♦s✳ ❯♠ ♣r♦❜❧❡♠❛ ✐♥❡r❡♥t❡ à ❢✉sã♦ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ❞❡❞❛❞♦s ❞✐③ r❡s♣❡✐t♦ ❛♦ ❛❞❡q✉❛❞♦ tr❛t❛♠❡♥t♦ ❞❡ ✐♥❢♦r♠❛çõ❡s r❡❞✉♥❞❛♥t❡s✳ ▼❛✐s ❡s♣❡❝✐✲✜❝❛♠❡♥t❡✱ ♦s ♣r✐♥❝✐♣❛✐s ❛❧❣♦r✐t♠♦s ❞❡ ✜❧tr❛❣❡♠ ✉t✐❧✐③❛❞♦s ❡♠ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s s♦♠❡♥t❡ ♣♦❞❡♠ ❝♦♠❜✐♥❛r ✐♥❢♦r♠❛çõ❡s ❛ r❡s♣❡✐t♦ ❞❡ ✉♠ ❞❛❞♦ ❛♦ ❛ss✉♠✐r❡♠ q✉❡ t❛✐s✐♥❢♦r♠❛çõ❡s s❡❥❛♠ ✐♥❞❡♣❡♥❞❡♥t❡s✳ ◆♦ ❡♥t❛♥t♦✱ ❛ s✉♣♦s✐çã♦ ❞❡ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ♣♦❞❡❣❡r❛r ❡st✐♠❛t✐✈❛s ✐♥❝♦♥s✐st❡♥t❡s ❡♠ ✐♥ú♠❡r❛s s✐t✉❛çõ❡s ♥❛s q✉❛✐s ♦s ❞❛❞♦s ♥ã♦ sã♦ ✈❡r✲❞❛❞❡✐r❛♠❡♥t❡ ✐♥❞❡♣❡♥❞❡♥t❡s✳ ◆❡ss❛s s✐t✉❛çõ❡s✱ ♦ ♥í✈❡❧ ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❛s✐♥❢♦r♠❛çõ❡s ❞❡✈❡ s❡r ❝♦♥❤❡❝✐❞♦ ♣❛r❛ q✉❡ ❡st✐♠❛t✐✈❛s ❝♦♥s✐st❡♥t❡s s❡❥❛♠ ❣❡r❛❞❛s✳ ❈♦♥❢♦r♠❡ s❡rá ❛♣r❡s❡♥t❛❞♦ ♥♦ ❈❛♣ít✉❧♦ ✸✱ ❡♠ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s ❡ss❡ ♣r♦✲❜❧❡♠❛ t❡♠ s✐❞♦ ❝♦♥t♦r♥❛❞♦ ❞❡ ✈ár✐❛s ❢♦r♠❛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 ❝❛❞❛ ✈❡③q✉❡ ❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ é ❣❡r❛❞❛✳ ❊♠ s✐st❡♠❛s ❞❡s❝❡♥tr❛❧✐③❛❞♦s✱ ❛ ❛✉sê♥❝✐❛ ❞❡ ✉♠❛❡♥t✐❞❛❞❡ ❝❡♥tr❛❧ ❡①✐❣❡ q✉❡ ❛s ✐♥❢♦r♠❛çõ❡s ❛ss♦❝✐❛❞❛s ❛ ✉♠❛ ❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦✲♣❡r❛t✐✈❛✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛✱ s❡❥❛♠ ❡♥✈✐❛❞❛s ♣❛r❛ ♦s❞❡♠❛✐s ♠❡♠❜r♦s ❞♦ ❣r✉♣♦✳ ❊ss❛ s♦❧✉çã♦ ✐♠♣❧✐❝❛ ❡♠ ✉♠❛ r❡❞❡ t♦t❛❧♠❡♥t❡ ❝♦♥❡❝t❛❞❛✱ ✹✵❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ♦ q✉❡ ♣♦❞❡ ❝♦♠♣r♦♠❡t❡r ❛ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ ❡ r♦❜✉st❡③ ❞♦ s✐st❡♠❛✳ ❆❧é♠ ❞✐ss♦✱ ♦ r❡❣✐str♦❞❡ t❛✐s ✐♥❢♦r♠❛çõ❡s ❞❡✈❡ s❡r ♠❛♥t✐❞♦ ✐♥❞✐✈✐❞✉❛❧♠❡♥t❡ ♣♦r ❝❛❞❛ ✐♥t❡❣r❛♥t❡ ❞♦ ❣r✉♣♦✱❞❡ ♠♦❞♦ q✉❡ ❝❛❞❛ r♦❜ô ♣♦ss❛ ❣❡r❛r ✉♠❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ ✭ót✐♠❛✮ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡♠❛♥❡✐r❛ ✐♥❞❡♣❡♥❞❡♥t❡✳ ❖ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥ é ✉♠ ❡st✐♠❛❞♦r ót✐♠♦ q✉❛♥❞♦ ❛s ❡st✐♠❛t✐✈❛s ✉t✐❧✐③❛❞❛s ♥❛s❡t❛♣❛s ❞❡ ❢✉sã♦ s❡♥s♦r✐❛❧ sã♦ ✐♥❞❡♣❡♥❞❡♥t❡s ♦✉ s❡ t❡♠ ✐♥❢♦r♠❛çõ❡s ❛ r❡s♣❡✐t♦ ❞❛ ✐♥t❡r✲❞❡♣❡♥❞ê♥❝✐❛ ❞❡ t❛✐s ❡st✐♠❛t✐✈❛s✳ ◆♦ ❡♥t❛♥t♦✱ ❡♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s✱ ♦ r❡❣✐str♦ ❞❡ss❛s✐♥❢♦r♠❛çõ❡s ❡ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ♣❛r❛ ♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❛s ♠❡s♠❛s ✐♠♣õ❡ ✉♠❛ ❧✐♠✐t❛çã♦ s✐❣♥✐✜❝❛t✐✈❛ ♣❛r❛ ❛ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ ❡ ❛ ❛♣❧✐❝❛çã♦ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡♠ s✐st❡♠❛sr❡❛✐s✳ ❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❛ ❛✉sê♥❝✐❛ ❞❡ss❡ r❡❣✐str♦ ♣♦❞❡ ❣❡r❛r ❡st✐♠❛t✐✈❛s ♦t✐♠✐st❛s ❡❝♦♠♣r♦♠❡t❡r ❛ q✉❛❧✐❞❛❞❡ ❞♦s r❡s✉❧t❛❞♦s✳ ❖ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s é ❛♣❧✐❝❛❞♦ ♥❡st❡ tr❛❜❛❧❤♦ ♣♦r s❡ tr❛t❛r❞❡ ✉♠❛ té❝♥✐❝❛ q✉❡ ♣r♦✈❛❞❛♠❡♥t❡ ❣❡r❛ ❡st✐♠❛t✐✈❛s ❝♦♥s✐st❡♥t❡s q✉❛♥❞♦ ♥ã♦ s❡ t❡♠✐♥❢♦r♠❛çõ❡s ❛ r❡s♣❡✐t♦ ❞❛s ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛s ✭✈❡r ❆♣ê♥❞✐❝❡ ❈✮✳ ❉❡ss❡ ♠♦❞♦✱ ♣❛r❛ ♦♣r♦❝❡ss❛♠❡♥t♦ ❞❡s❝❡♥tr❛❧✐③❛❞♦ ❞❛s ❡st✐♠❛t✐✈❛s✱ ♥ã♦ s❡ ❢❛③ ♥❡❝❡ssár✐♦ ❛ ♠❛♥✉t❡♥çã♦❞♦ r❡❣✐str♦ ❞❛s ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛s ❡♠ ❝❛❞❛ ❡♥t✐❞❛❞❡ r♦❜ót✐❝❛✱ ✈✐❛❜✐❧✐③❛♥❞♦ ❛ss✐♠ ✉♠❛ s♦❧✉çã♦ ❡s❝❛❧á✈❡❧ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s✳◆♦ ♣ró①✐♠♦ ❝❛♣ít✉❧♦ s❡rá ❛♣r❡s❡♥t❛❞❛ ✉♠❛ r❡✈✐sã♦ ❞❡ tr❛❜❛❧❤♦s s❡❧❡❝✐♦♥❛❞♦s ♥❛ ár❡❛ ❞❡❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ✉♠❛ ❞❡s❝r✐çã♦ ♠❛✐s ❞❡t❛❧❤❛❞❛ ❞❛s q✉❡stõ❡s❞✐s❝✉t✐❞❛s ♥❡ss❛ s❡çã♦✳ ✷✳✺ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ❖ ♣r♦❜❧❡♠❛ ❞❡ ❝♦♦r❞❡♥❛r ❛❞❡q✉❛❞❛♠❡♥t❡ ✉♠ ❣r❛♥❞❡ ❣r✉♣♦ ❞❡ r♦❜ôs ♣r❡ss✉♣õ❡ ❛ ✉t✐❧✐✲③❛çã♦ ❞❡ ❛❧❣✉♠❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❉✐✈❡rs♦s tr❛❜❛❧❤♦s ❡♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s✉t✐❧✐③❛♠ ♦✉ s✉♣õ❡♠ ❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❞❡ ❛❧❣✉♠ s✐st❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❣❧♦❜❛❧ ♣❛r❛ ♦s r♦❜ôs✱ t❛✐s ❝♦♠♦ s✐st❡♠❛s ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❣❧♦❜❛❧✳ ❉❡✈✐❞♦ às r❡str✐çõ❡s ❞❡ ✉s♦ ❞❡ss❡ss✐st❡♠❛s✱ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ té❝♥✐❝❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♣❛r❛ ❡♥①❛♠❡s r♦❜ó✲ t✐❝♦s t♦r♥❛✲s❡ ✉♠❛ t❛r❡❢❛ ✐♠♣♦rt❛♥t❡ q✉❛♥❞♦✱ ♣♦r ❡①❡♠♣❧♦✱ ♦ ❣r✉♣♦ ♥ã♦ ❞✐s♣õ❡ ❞❡ ✉♠s✐st❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❣❧♦❜❛❧ ♦✉ ❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❞❡ t❛❧ s✐st❡♠❛ é ✐♥t❡r♠✐t❡♥t❡✳ ❆❧é♠❞✐ss♦✱ té❝♥✐❝❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♣♦❞❡♠ s❡r ❡♠♣r❡❣❛❞❛s ♣❛r❛ s❡ t✐r❛r ♣r♦✈❡✐t♦❞❡ ❣r✉♣♦s ❞❡ r♦❜ôs ❝♦♠ ❝❛♣❛❝✐❞❛❞❡s ❞✐st✐♥t❛s ✭❤❡t❡r♦❣ê♥❡♦s✮ ♦✉ q✉❛♥❞♦ s♦♠❡♥t❡ ❛❧❣✉♥s✐♥t❡❣r❛♥t❡s ❞♦ ❡♥①❛♠❡ tê♠ ❛❝❡ss♦ ❛ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ♠❛✐s ♣r❡❝✐s❛s✳ ❊♥①❛♠❡s r♦❜ót✐❝♦s ♣♦ss✉❡♠ ❛ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ s❡r❡♠ ❛❧t❛♠❡♥t❡ r❡❞✉♥❞❛♥t❡s✳ ❚❛❧❝❛r❛❝t❡ríst✐❝❛ é ✈✐st❛ ❝♦♠♦ ✉♠❛ ❞❛s ✈❛♥t❛❣❡♥s ❞❡ s❡ ✉t✐❧✐③❛r ❣r❛♥❞❡s ❣r✉♣♦s ❞❡ r♦❜ôs✱♣♦✐s ♠❛①✐♠✐③❛ ❛s ❝❤❛♥❝❡s ❞❡ s❡ ❝♦♠♣❧❡t❛r ❞❡t❡r♠✐♥❛❞❛ t❛r❡❢❛✱ ❛❧é♠ ❞❡ ❛✉♠❡♥t❛r ❛ ✷✳✺✳ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s✹✶ r♦❜✉st❡③ ❞♦ s✐st❡♠❛✳ ❊♠ ❞❡❝♦rrê♥❝✐❛ ❞❡ss❛ ❣r❛♥❞❡ r❡❞✉♥❞â♥❝✐❛✱ ♣❛rt❡ ❞♦ ❡♥①❛♠❡ ♣♦❞❡s❡r ✉t✐❧✐③❛❞❛ ❡♠ t❛r❡❢❛s ❞❡ ❛♣♦✐♦ s❡♠✱ ♥❡❝❡ss❛r✐❛♠❡♥t❡✱ ❝♦♠♣r♦♠❡t❡r ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦❣r✉♣♦✳ ❈♦♠ ✐ss♦✱ ♦ ♣ró♣r✐♦ ❣r✉♣♦ ❝r✐❛ ❢❛❝✐❧✐❞❛❞❡s ♣❛r❛ ❛ ❡①❡❝✉çã♦ ❞❛ t❛r❡❢❛ ✜♠ ♣❛r❛ ♦ q✉❛❧ ❢♦✐ ♣r♦❥❡t❛❞♦✳ ❆ ✉t✐❧✐③❛çã♦ ❞❡ ♣❛rt❡ ❞♦s ❝♦♠♣♦♥❡♥t❡s ❞❡ ✉♠ ❡♥①❛♠❡ ❝♦♠♦ ♠❛r❝♦s❞✐♥â♠✐❝♦s ♣♦❞❡ ✈✐❛❜✐❧✐③❛r ♦ ❡st❛❜❡❧❡❝✐♠❡♥t♦ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ q✉❡ t❡♥❤❛♣♦✉❝❛ ♦✉ ♥❡♥❤✉♠❛ ❞❡♣❡♥❞ê♥❝✐❛ ❞❡ s✐st❡♠❛s ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❣❧♦❜❛❧✳ ❆❧é♠ ❞✐ss♦✱ s✐st❡♠❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❜❛s❡❛❞♦s ❡♠ ♠❛r❝♦s ❞✐♥â♠✐❝♦s sã♦ ♣♦t❡♥❝✐❛❧♠❡♥t❡ ❛❞❡q✉❛❞♦s♣❛r❛ ✉t✐❧✐③❛çã♦ ❡♠ ❛♠❜✐❡♥t❡s ❞❡s❝♦♥❤❡❝✐❞♦s ❡ ♥ã♦ ♣r❡✈✐❛♠❡♥t❡ ❡str✉t✉r❛❞♦s✳ ❆ r❡✈✐sã♦ ❞❡ ❧✐t❡r❛t✉r❛ ❛♣r❡s❡♥t❛❞❛ ❛ s❡❣✉✐r t❡♠ ê♥❢❛s❡ ♥❛s té❝♥✐❝❛s ❞❡ ❧♦❝❛❧✐✲③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❛♣❧✐❝❛❞❛s ❛ s✐st❡♠❛s ♠✉❧t✐rr♦❜ôs✳ ❆♣❡s❛r ❞♦s tr❛❜❛❧❤♦s ❞✐s❝✉t✐❞♦s♥ã♦ ❡♥❢❛t✐③❛r❡♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s✱ té❝♥✐❝❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♣♦❞❡♠ s❡r ❡s✲ t❡♥❞✐❞❛s ♣❛r❛ ❧✐❞❛r ❝♦♠ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ❡♥①❛♠❡s✳ ❆❧é♠ ❞✐ss♦✱ ❛❧❣✉♥s ♣r♦❜❧❡♠❛s✐❞❡♥t✐✜❝❛❞♦s ♥♦s tr❛❜❛❧❤♦s r❡✈✐s❛❞♦s ♣♦❞❡♠ s❡r s♦❧✉❝✐♦♥❛❞♦s q✉❛♥❞♦ s❡ t❡♠ ❣r❛♥❞❡s❣r✉♣♦s ❞❡ r♦❜ôs ❛t✉❛♥❞♦ ❝♦♥❥✉♥t❛♠❡♥t❡✳ ❈❛♣ít✉❧♦ ✸ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s ❊st❡ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛ ✉♠❛ ❞✐s❝✉ssã♦ ❞♦s ♣r✐♥❝✐♣❛✐s tr❛❜❛❧❤♦s ❞❡s❡♥✈♦❧✈✐❞♦s ❡♠ ❧♦❝❛✲❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛✱ ❞❡ ❢♦r♠❛ ❛ r❡❧❛❝✐♦♥á✲❧♦s ❛♦s ♣r♦♣ós✐t♦s❞❡st❛ t❡s❡✳ ■♥✐❝✐❛❧♠❡♥t❡✱ ♦s ♣r✐♠❡✐r♦s tr❛❜❛❧❤♦s ❞❡s❡♥✈♦❧✈✐❞♦s ❡♠ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛✲ t✐✈❛ sã♦ ❛♣r❡s❡♥t❛❞♦s✳ P♦st❡r✐♦r♠❡♥t❡✱ ❛❧❣✉♥s ❛s♣❡❝t♦s ❞❡ss❡ t✐♣♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ q✉❡tê♠ s✐❞♦ ❡st✉❞❛❞♦s ❡♠ s✐st❡♠❛s ♠✉❧t✐rr♦❜ôs s❡rã♦ ❞✐s❝✉t✐❞♦s✱ ❛ s❛❜❡r✿ ❡str❛té❣✐❛s ❞❡♠♦✈✐♠❡♥t❛çã♦❀ t✐♣♦s ❞❡ s❡♥s♦r❡s ❡ ♠❡❞✐❞❛s ❡①t❡r♦❝❡♣t✐✈❛s ✉t✐❧✐③❛❞♦s❀ ♠ét♦❞♦s ♣r♦❜❛✲❜✐❧íst✐❝♦s ❡♠♣r❡❣❛❞♦s❀ ❢r❡q✉ê♥❝✐❛ ❞❡ ❛t✉❛❧✐③❛çã♦ ❞❛s ❝r❡♥ç❛s❀ ❝♦♠♣♦s✐çã♦ ❞♦s ❣r✉♣♦s❀ ❡ q✉❛♥t✐❞❛❞❡ ❞❡ r♦❜ôs ❡♠♣r❡❣❛❞♦s ♥♦s tr❛❜❛❧❤♦s✳ ✸✳✶ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛ ❖s ♣r✐♠❡✐r♦s tr❛❜❛❧❤♦s ❛ r❡❧❛t❛r❡♠ ♦ ✉s♦ ❞❡ r♦❜ôs ♠ó✈❡✐s ❝♦♠♦ ♠❛r❝♦s ❞✐♥â♠✐❝♦s ❚r❛❜❛❧❤♦s ♣❛r❛ ❡①❡❝✉t❛r ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❢♦r❛♠ ❬❑✉r❛③✉♠❡ ❡t ❛❧✳✱ ✶✾✾✹❪ ❡ ❬❘❡❦❧❡✐t✐s ❡t ❛❧✳✱ s❡♠✐♥❛✐s ✶✾✾✽❪✳ ◆❡ss❡s tr❛❜❛❧❤♦s✱ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦s r♦❜ôs é ❝♦♦r❞❡♥❛❞❛ ❞❡ ❢♦r♠❛ q✉❡ ❛ t♦❞♦♠♦♠❡♥t♦ ✉♠❛ ♣❛rt❡ ❞♦ ❣r✉♣♦ s❡ ♠❛♥té♠ ❡st❛❝✐♦♥ár✐❛ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ s❡r✈✐r ❞❡ ♠❛r❝♦♣❛r❛ ♦s ❞❡♠❛✐s r♦❜ôs✳ ❊ss❡s r♦❜ôs ♠❛r❝♦ ♦❜s❡r✈❛♠ ✭❡ sã♦ ♦❜s❡r✈❛❞♦s ♣♦r✮ ♦✉tr♦s r♦❜ôs❞♦ ❣r✉♣♦✱ ❞❡ ❢♦r♠❛ ❛ ✉t✐❧✐③❛r❡♠ t❛✐s ♦❜s❡r✈❛çõ❡s ♣❛r❛ ❛t✉❛❧✐③❛çã♦ ❞❡ s✉❛s ❝r❡♥ç❛s ❝♦♠♦ r❡s✉❧t❛❞♦ ❞❡ ✉♠ ♣r♦❝❡ss♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❊♠ ❬❑✉r❛③✉♠❡ ❡t ❛❧✳✱ ✶✾✾✹✱ ✶✾✾✻❪✱ ✉♠ ❣r✉♣♦ ❞❡ r♦❜ôs é ❞✐✈✐❞♦ ❡♠ ❞♦✐s✱ ❞❡ ♠♦❞♦ q✉❡ ✉♠ ❞♦s ❣r✉♣♦s✱ ❝✉❥❛ ♣♦s❡ ✐♥✐❝✐❛❧ é ❝♦♥❤❡❝✐❞❛✱ ♠❛♥té♠✲s❡ ❡st❛❝✐♦♥ár✐♦ s❡r✈✐♥❞♦❝♦♠♦ ♠❛r❝♦✱ ❡♥q✉❛♥t♦ ♦ ♦✉tr♦ ❣r✉♣♦ s❡ ♠♦✈✐♠❡♥t❛✳ ❉✉r❛♥t❡ ❛ ♠♦✈✐♠❡♥t❛çã♦✱ ♦s r♦❜ôs✉t✐❧✐③❛♠ ♠ét♦❞♦s ❞❡ ❞❡❛❞ r❡❝❦♦♥✐♥❣ ♣❛r❛ ♣r♦♣❛❣❛r❡♠ s✉❛s r❡s♣❡❝t✐✈❛s ✐♥❢♦r♠❛çõ❡s ❞❡❧♦❝❛❧✐③❛çã♦✳ ❆♣ós ✉♠❛ ❝♦♥❞✐çã♦ ♣r❡❡st❛❜❡❧❡❝✐❞❛ s❡r ❛❧❝❛♥ç❛❞❛✱ ♦ ❣r✉♣♦ ❡♠ ♠♦✈✐♠❡♥t♦♣❛r❛ ❡ ✉t✐❧✐③❛ ♦ ♦✉tr♦ ♣❛r❛ s❡ ❧♦❝❛❧✐③❛r✳ ❊ss❡ ♣r♦❝❡❞✐♠❡♥t♦ é ❡❢❡t✉❛❞♦ ♣♦r ♠❡✐♦ ❞❡♠❡❞✐❞❛s ❡①t❡r♦❝❡♣t✐✈❛s t♦♠❛❞❛s ❛ ♣❛rt✐r ❞♦s r♦❜ôs q✉❡✱ ♥❛q✉❡❧❡ ♠♦♠❡♥t♦✱ ❛t✉❛♠ ❝♦♠♦ ✹✹ ❈❛♣ít✉❧♦ ✸✳ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s♠❛r❝♦s✳ ❚❛✐s ♠❡❞✐❞❛s sã♦ ✉t✐❧✐③❛❞❛s ♣❛r❛ ❛t✉❛❧✐③❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦❞♦s r♦❜ôs q✉❡ ❡st❛✈❛♠ ❡♠ ♠♦✈✐♠❡♥t♦✳ ❊ss❡s r♦❜ôs s❡ t♦r♥❛♠✱ ❡♥tã♦✱ ♣♦t❡♥❝✐❛✐s ❢♦♥t❡s❞❡ ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ✭♠❛r❝♦s✮✱ ♣❡r♠❛♥❡❝❡♥❞♦ ✐♥❡rt❡s✳ ◆❡ss❡ ♠♦♠❡♥t♦✱ ♦❝♦rr❡❛ tr♦❝❛ ❞❡ ♣❛♣❡❧ ❡♥tr❡ ♦s ❣r✉♣♦s✱ ❞❡ ♠♦❞♦ q✉❡ ❛q✉❡❧❡s r♦❜ôs q✉❡ ✐♥✐❝✐❛❧♠❡♥t❡ ❡st❛✈❛♠♣❛r❛❞♦s ♣♦ss❛♠ ❡♥tr❛r ❡♠ ♠♦✈✐♠❡♥t♦ ❡✱ ♣♦st❡r✐♦r♠❡♥t❡✱ ✉t✐❧✐③❡♠ ❡st❡s ♥♦✈♦s ♠❛r❝♦s♣❛r❛ ❛❥✉st❛r s✉❛s ❝r❡♥ç❛s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❖s ❣r✉♣♦s ❝♦♥t✐♥✉❛♠❡♥t❡ ❡❢❡t✉❛♠ ❡ss❛ tr♦❝❛❞❡ ♣❛♣❡❧ ✭♠❛r❝♦✴♠♦✈✐♠❡♥t❛çã♦✮ ❞❡ ♠♦❞♦ ❛ ♣❡r♠✐t✐r❡♠ q✉❡ ♦s r♦❜ôs ♣r♦♣❛❣✉❡♠ s✉❛s❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❡♥q✉❛♥t♦ s❡ ♠♦✈✐♠❡♥t❛♠ ♣❡❧♦ ❛♠❜✐❡♥t❡ ✭❋✐❣✉r❛ ✸✳✶✮✳ ✭❛✮ ✭❜✮ ✭❝✮ ✭❞✮ ❋✐❣✉r❛ ✸✳✶✿ ❊t❛♣❛s ❞❛ ❡str❛té❣✐❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♣r♦♣♦st❛ ♣♦r ❑✉r❛③✉♠❡❡t ❛❧✳ ❬✶✾✾✻❪✱ ♥❛ q✉❛❧ ♦ r♦❜ô ✵ ❝♦♦r❞❡♥❛ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦ ❣r✉♣♦✳ ❊♠ ✭❛✮ ♦s r♦❜ôs ✶❡ ✷ sã♦ ✐♥str✉í❞♦s ❛ s❡ ♠♦✈✐♠❡♥t❛r❡♠✳ ❊♠ ✭❜✮ ❡ ✭❝✮✱ ❛♣ós ❡❢❡t✉❛r❡♠ ❛ ♠♦✈✐♠❡♥t❛çã♦✱♦s r♦❜ôs ✶ ❡ ✷ ♣❡r♠❛♥❡❝❡♠ ♣❛r❛❞♦s ❡♥q✉❛♥t♦ ♦ r♦❜ô ✵ ❡st✐♠❛ ❞✐stâ♥❝✐❛s ❡ ♦r✐❡♥t❛çõ❡s r❡❧❛t✐✈❛s ❛ ❡ss❡s ❡ ❡❢❡t✉❛ ❛ ❧♦❝❛❧✐③❛çã♦ ❞♦s ♠❡s♠♦s✳ ❊♠ ✭❞✮✱ ♦s r♦❜ôs ✶ ❡ ✷ ♣❡r♠❛♥❡❝❡♠♣❛r❛❞♦s✱ ❡♥q✉❛♥t♦ ♦ r♦❜ô ✵ s❡ ♠♦✈✐♠❡♥t❛✳ P♦st❡r✐♦r♠❡♥t❡✱ ♦ r♦❜ô ✵ ♣❛r❛ ❡ ✉t✐❧✐③❛ ♦s r♦❜ôs ✶ ❡ ✷ ♣❛r❛ s❡ ❧♦❝❛❧✐③❛r✳ ❆❞❛♣t❛❞♦ ❞❡ ❬❑✉r❛③✉♠❡ ❡t ❛❧✳✱ ✶✾✾✻❪✳ ❆❧❣✉♠❛s ❡①t❡♥sõ❡s ❞❡ss❡ ♠ét♦❞♦ ❡ ❛ r❡s♣❡❝t✐✈❛ ❛♣❧✐❝❛çã♦ ❡♠ ❛♠❜✐❡♥t❡s r❡❛✐s sã♦❛♣r❡s❡♥t❛❞❛s ❡♠ ❬❑✉r❛③✉♠❡ ✫ ❍✐r♦s❡✱ ✶✾✾✽❪✱ ❬❑✉r❛③✉♠❡ ✫ ❍✐r♦s❡✱ ✷✵✵✵❜❪ ❡ ❬❑✉r❛③✉♠❡❡t ❛❧✳✱ ✷✵✵✼❪✳ ❊ss❡s tr❛❜❛❧❤♦s ✉t✐❧✐③❛♠ três r♦❜ôs ♣❛r❛ ❡①❡❝✉t❛r ❛ t❛r❡❢❛ ❞❡ ❧♦❝❛❧✐③❛çã♦❝♦♦♣❡r❛t✐✈❛✳ ❯♠ ❞♦s r♦❜ôs✱ ❞❡♥♦♠✐♥❛❞♦ ♠❡str❡ ✭♣❛✐✮✱ ❡①❡❝✉t❛ ♦ ❝♦♥tr♦❧❡ ❝❡♥tr❛❧✐③❛❞♦❞❡ t♦❞❛ ❛ t❛r❡❢❛ ❝♦♦♣❡r❛t✐✈❛✳ ❖ ❝♦♥tr♦❧❡ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❞♦ ❣r✉♣♦ é ❞❡t❡r♠✐♥❛❞♦♣❡❧♦ ♠❡str❡ q✉❡ ♦r❛ ✉t✐❧✐③❛ s✉❛ ♣ró♣r✐❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ♣❛r❛ ❧♦❝❛❧✐③❛r ♦s r♦❜ôs❡s❝r❛✈♦s ✭✜❧❤♦s✮ ❡ ♦r❛ ✉t✐❧✐③❛ ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ss❡s r♦❜ôs ♣❛r❛ s❡ ❧♦❝❛❧✐③❛r✳❖ r♦❜ô ♠❡str❡ é ❡q✉✐♣❛❞♦ ❝♦♠ s❡♥s♦r❡s ❡①t❡r♦❝❡♣t✐✈♦s ❝❛♣❛③❡s ❞❡ ♠❡❞✐r ✐♥❢♦r♠❛çõ❡s❞❡ ❧♦❝❛❧✐③❛çã♦ ✭❞✐stâ♥❝✐❛s ❡ ♦r✐❡♥t❛çõ❡s r❡❧❛t✐✈❛s✮ ✉t✐❧✐③❛♥❞♦ ♠❛r❝❛❞♦r❡s ✐♥st❛❧❛❞♦s ♥♦s r♦❜ôs ❡s❝r❛✈♦s✳ ❯♠❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❡ss❛ té❝♥✐❝❛ ❡♠ r♦❜ôs r❡❛✐s é ❛♣r❡s❡♥t❛❞❛ ♥❛❋✐❣✉r❛ ✸✳✷✱ s❡♥❞♦ q✉❡ ✐♥str✉♠❡♥t♦s s❡♠❡❧❤❛♥t❡s àq✉❡❧❡s ✉t✐❧✐③❛❞♦s ❡♠ ❧❡✈❛♥t❛♠❡♥t♦s t♦♣♦❣rá✜❝♦s ❢♦r❛♠ ❡♠♣r❡❣❛❞♦s ❝♦♠♦ s❡♥s♦r❡s ❡①t❡r♦❝❡♣t✐✈♦s✳ ❖s r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❛♣r❡s❡♥t❛❞♦s ♥♦s tr❛❜❛❧❤♦s ❞❡s❝r✐t♦s ❛♥t❡r✐♦r♠❡♥t❡♠♦str❛♠ q✉❡ ♦ ❛❝ú♠✉❧♦ ❞❡ ❡rr♦ ❞♦ r❡s♣❡❝t✐✈♦ ♠ét♦❞♦ é ❝♦♥s✐❞❡r❛✈❡❧♠❡♥t❡ ♠❡♥♦r ❞♦ q✉❡❛q✉❡❧❡ ❣❡r❛❞♦ ♣❡❧❛s té❝♥✐❝❛s ❞❡ ❞❡❛❞ r❡❝❦♦♥✐♥❣✳ ❈♦♥t✉❞♦✱ ❛❧❣✉♠❛s ❧✐♠✐t❛çõ❡s ♣♦❞❡♠ ✸✳✶✳ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛✹✺ Mestre Escravo 1 Escravo 2 ❋✐❣✉r❛ ✸✳✷✿ ■♠♣❧❡♠❡♥t❛çã♦ ❡♠ r♦❜ôs r❡❛✐s ❞♦ ♠ét♦❞♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♣r♦✲♣♦st♦ ♣♦r ❑✉r❛③✉♠❡ ❡t ❛❧✳ ❬✶✾✾✹❪✳ ❆❞❛♣t❛❞♦ ❞❡ ❬❑✉r❛③✉♠❡ ✫ ❍✐r♦s❡✱ ✷✵✵✵❛❪✳ s❡r ♦❜s❡r✈❛❞❛s✱ t❛✐s ❝♦♠♦✿ ❜❛✐①❛ r♦❜✉st❡③ ❛ ❢❛❧❤❛s ❞❡✈✐❞♦ ❛♦ ❝♦♥tr♦❧❡ ❝❡♥tr❛❧✐③❛❞♦❀❞❡s❡♠♣❡♥❤♦ ❧✐♠✐t❛❞♦ ❡♠ ❞❡❝♦rrê♥❝✐❛ ❞❛ ♣❛r❛❧✐s❛çã♦ ❞♦s r♦❜ôs ❞✉r❛♥t❡ ❛ ❧♦❝❛❧✐③❛çã♦❀ ❡✐♠♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ✉♠❛ r❡❛❧ tr♦❝❛ ❞❡ ♣❛♣❡❧ ❡♥tr❡ ♦s ❣r✉♣♦s ✭♠❡str❡ ❡ ❡s❝r❛✈♦s✮ ❞❡✈✐❞♦ à❤❡t❡r♦❣❡♥❡✐❞❛❞❡ ❞❡ ❤❛r❞✇❛r❡✴s♦❢t✇❛r❡ ❞♦s r♦❜ôs ❡ ❛♦ ❝♦♥tr♦❧❡ ❢♦rt❡♠❡♥t❡ ❝❡♥tr❛❧✐③❛❞♦✳ ▼ét♦❞♦s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ tê♠ s✐❞♦ ✉t✐❧✐③❛❞♦s ❝♦♠♦ s✉♣♦rt❡ ♣❛r❛ ❛ ❡①❡✲ ▲♦❝❛❧✐③❛çã♦ ❝✉çã♦ ❞❡ t❛r❡❢❛s ❞❡ ❛❧t♦ ♥í✈❡❧✱ t❛✐s ❝♦♠♦ ♠❛♣❡❛♠❡♥t♦ ❡ ❡①♣❧♦r❛çã♦ ❞❡ ❛♠❜✐❡♥t❡s✳ ❘❡✲ ❈♦♦♣❡r❛t✐✈❛ ❦❧❡✐t✐s ❡t ❛❧✳ ❬✶✾✾✽✱ ✷✵✵✵❪ ✉t✐❧✐③❛♠ ✉♠❛ ❛❜♦r❞❛❣❡♠ s❡♠❡❧❤❛♥t❡ àq✉❡❧❛ ❡♠♣r❡❣❛❞❛ ♥♦s ❝♦♠♦ ❜❛s❡ ♣❛r❛ t❛r❡❢❛s tr❛❜❛❧❤♦s ❞❡ ❑✉r❛③✉♠❡ ❡t ❛❧✳ ♣❛r❛ ❡❢❡t✉❛r ❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❆ té❝♥✐❝❛ é ✉t✐❧✐✲ ❞❡ ❛❧t♦ ♥í✈❡❧ ③❛❞❛ ❡♠ ♠❛♣❡❛♠❡♥t♦ ❞❡ ❛♠❜✐❡♥t❡s✱ ❞❡ ♠♦❞♦ q✉❡ ❛ ❝❛❞❛ ✐♥st❛♥t❡ ♣❡❧♦ ♠❡♥♦s ✉♠ r♦❜ô❛t✉❛ ❝♦♠♦ ♠❛r❝♦✳ P❛r❛ ❡❢❡t✉❛r ♦ ♠❛♣❡❛♠❡♥t♦✱ ♦s r♦❜ôs sã♦ ❝♦♦r❞❡♥❛❞♦s ❞❡ ♠♦❞♦ ❛♠❛♥t❡r❡♠✱ ❛ t♦❞♦ ✐♥st❛♥t❡✱ ✉♠❛ ❧✐♥❤❛ ❞❡ ✈✐sã♦ ❡♥tr❡ s✐✳ ❈♦♠ ❜❛s❡ ♥❡ss❛ ✐♥❢♦r♠❛çã♦✱♦s r♦❜ôs ✐❞❡♥t✐✜❝❛♠ ár❡❛s ❧✐✈r❡s ♥♦ ❛♠❜✐❡♥t❡✳ ❈❛s♦ ❡ss❛ ❧✐♥❤❛ ❞❡ ✈✐sã♦ s❡❥❛ ♣❡r❞✐❞❛✱ ♦s r♦❜ôs ♣❛r❛♠ ❛ t❛r❡❢❛ ❞❡ ♠❛♣❡❛♠❡♥t♦ ❡ ❡❢❡t✉❛♠ ✉♠❛ ♠♦✈✐♠❡♥t❛çã♦ ♥♦ s❡♥t✐❞♦ ✐♥✈❡rs♦àq✉❡❧❡ q✉❡ ❡st❛✈❛♠ ❡①❡❝✉t❛♥❞♦ ❛té r❡❡st❛❜❡❧❡❝❡r❡♠ ❝♦♥t❛t♦ ✏✈✐s✉❛❧✑✱ ♠♦♠❡♥t♦ ❡♠ q✉❡❛ t❛r❡❢❛ ❞❡ ♠❛♣❡❛♠❡♥t♦ é r❡t♦♠❛❞❛✳ ❉❡❧❧❛❡rt ❡t ❛❧✳ ❬✷✵✵✸❪ ❡❢❡t✉❛♠ ♠❛♣❡❛♠❡♥t♦ ❜✐✲❞✐♠❡♥s✐♦♥❛❧ ✉t✐❧✐③❛♥❞♦ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡ ❞❡♥♦♠✐♥❛♠ ❡ss❛ té❝♥✐❝❛ ❞❡ ■♥tr✐♥s✐❝▲♦❝❛❧✐③❛t✐♦♥ ❛♥❞ ▼❛♣♣✐♥❣ ✭■▲▼✮✱ ❝♦♠♦ ✉♠❛ ❛❧✉sã♦ ❛♦ t❡r♠♦ ❙✐♠✉❧t❛♥❡♦✉s ▲♦❝❛❧✐③❛✲ t✐♦♥ ❛♥❞ ▼❛♣♣✐♥❣ ✭❙▲❆▼✮✳ ❆ ♣r✐♥❝✐♣❛❧ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ❛s ❞✉❛s té❝♥✐❝❛s é ❛ ✉t✐❧✐③❛çã♦❞❡ ♠❛r❝♦s ♠ó✈❡✐s ✭r♦❜ôs✮ ♥♦ ♠❛♣❡❛♠❡♥t♦✳ ❖✉tr❛ ❛❜♦r❞❛❣❡♠ ♣❛r❛ ❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ é ❛♣r❡s❡♥t❛❞❛ ❡♠ ❬❋♦① ❡t ❛❧✳✱ ❆❜♦r❞❛❣❡♠ ✷✵✵✵❪✳ ❊ss❛ ❛❜♦r❞❛❣❡♠ ❝♦♥s✐st❡ ❡♠ ✉♠❛ ❡①t❡♥sã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ▲♦❝❛❧✐③❛çã♦ ❞❡ ▼❈▲ ▼♦♥t❡ ❈❛r❧♦✱ ❞♦ ✐♥❣❧ês ▼♦♥t❡ ❈❛r❧♦ ▲♦❝❛❧✐③❛t✐♦♥ ✭▼❈▲✮✱ ♣❛r❛ ♦ ❝❛s♦ ❞❡ ♠ú❧t✐♣❧♦s r♦❜ôs ❝♦♠ ❛❝❡ss♦ ❛ ✉♠ ♠❛♣❛ ❞♦ ❛♠❜✐❡♥t❡ ✭✈❡r ❬❚❤r✉♥ ❡t ❛❧✳✱ ✷✵✵✵❪✮✳ ◆❛ ♦❝♦rrê♥❝✐❛ ❞❡✉♠ ❡♥❝♦♥tr♦ é ❢❡✐t❛ ❛ ❝♦♠❜✐♥❛çã♦ ❞❛s ❢✉♥çõ❡s ❞❡ ❞✐str✐❜✉✐çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s q✉❡ ✹✻ ❈❛♣ít✉❧♦ ✸✳ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s r❡♣r❡s❡♥t❛♠ ❛s ❝r❡♥ç❛s ❞♦s r♦❜ôs✳ ❊ss❡ ♣r♦❝❡❞✐♠❡♥t♦ ❛✉①✐❧✐❛ ♥♦ ♣r♦❝❡ss♦ ❞❡ ❧♦❝❛❧✐③❛çã♦❣❧♦❜❛❧✳ ❆♣❡s❛r ❞❡ss❡ ♠ét♦❞♦ ❛♣r❡s❡♥t❛r ❜♦♥s r❡s✉❧t❛❞♦s✱ ♦ ♠❡s♠♦ s♦♠❡♥t❡ s❡ ❛♣❧✐❝❛ ❛ s✐t✉❛çõ❡s ❡♠ q✉❡ s❡ t❡♠ ✉♠ ❝♦♥❤❡❝✐♠❡♥t♦ ♣ré✈✐♦ ❞♦ ❛♠❜✐❡♥t❡ ✭♠❛♣❛✮✳ ❘♦✉♠❡❧✐♦t✐s ✫ ❇❡❦❡② ❬✷✵✵✵❛❪ ❛♣r❡s❡♥t❛♠ ✉♠❛ ❛❜♦r❞❛❣❡♠ ♠❛✐s ❣❡r❛❧ ♣❛r❛ ❡❢❡t✉❛r ❙♦❧✉çã♦ ❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♥❛ q✉❛❧ ✉♠❛ s♦❧✉çã♦ ❡st❛t✐st✐❝❛♠❡♥t❡ ót✐♠❛ é ❛❧❝❛♥ç❛❞❛✳ ❚❛❧ ót✐♠❛ ❛❜♦r❞❛❣❡♠ ❝♦♥s✐st❡ ❡♠ ❡st✐♠❛r ❝♦♥❥✉♥t❛♠❡♥t❡ ❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ ✉♠ ❣r✉♣♦ ❞❡ r♦❜ôs ♣♦r♠❡✐♦ ❞❛ ❛♣❧✐❝❛çã♦ ❞❡ té❝♥✐❝❛s ❞❡ ✜❧tr❛❣❡♠ ♣r♦❜❛❜✐❧íst✐❝❛✱ ♠❛✐s ❡s♣❡❝✐✜❝❛♠❡♥t❡✱ ✉♠✜❧tr♦ ❞❡ ❑❛❧♠❛♥ ❊st❡♥❞✐❞♦✱ ❞♦ ✐♥❣❧ês ❊①t❡♥❞❡❞ ❑❛❧♠❛♥ ❋✐❧t❡r ✭❊❑❋✮ ✭✈❡r ❆♣ê♥❞✐❝❡❇✮✳ ◆❡ss❛ ❛❜♦r❞❛❣❡♠✱ ♦s r♦❜ôs ♣❛rt❡♠ ❞❡ ✉♠❛ ♣♦s❡ ❝♦♥❤❡❝✐❞❛ ✭✐♥❢♦r♠❛çã♦ ✐♥✐❝✐❛❧✮❡ ✉t✐❧✐③❛♠ s❡♥s♦r❡s ♣r♦♣r✐♦❝❡♣t✐✈♦s ✭♦❞♦♠❡tr✐❛✮ ♣❛r❛ ❡st✐♠❛r ♥♦✈❛s ♣♦s❡s✳ ❖ r❡❣✐str♦❞❛s ❡st✐♠❛t✐✈❛s ❞❡ ♣♦s❡ ❞❡ t♦❞♦s ♦s r♦❜ôs ✭❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛✮ é ♠❛♥t✐❞♦ ❡♠ ✉♠❛✉♥✐❞❛❞❡ ❝❡♥tr❛❧✐③❛❞♦r❛✳ ◆❛ ♦❝♦rrê♥❝✐❛ ❞❡ ✉♠ ❡♥❝♦♥tr♦✱ ♦s r♦❜ôs ✉t✐❧✐③❛♠ s❡♥s♦r❡s❡①t❡r♦❝❡♣t✐✈♦s ♣❛r❛✱ ♠✉t✉❛♠❡♥t❡✱ ❡st✐♠❛r ❞✐stâ♥❝✐❛s ❡ ♦r✐❡♥t❛çõ❡s r❡❧❛t✐✈❛s✳ ❊ss❛s♠❡❞✐❞❛s sã♦ ❡♥✈✐❛❞❛s ♣❛r❛ ❛ ✉♥✐❞❛❞❡ ❝❡♥tr❛❧✐③❛❞♦r❛✱ ❞❡ ♠♦❞♦ q✉❡ ❛ ♠❡s♠❛ ♣♦ss❛✉t✐❧✐③á✲❧❛s ♣❛r❛ ❝♦rr✐❣✐r ❛s ❛t✉❛✐s ❡st✐♠❛t✐✈❛s ❞❡ t♦❞♦s ♦s r♦❜ôs✳ P❛r❛ q✉❡ ✉♠❛ s♦❧✉çã♦ ót✐♠❛ ♣♦ss❛ s❡r ❣❡r❛❞❛✱ ❛ ✉♥✐❞❛❞❡ ❝❡♥tr❛❧✐③❛❞♦r❛ ♥❡❝❡ss✐t❛♠❛♥t❡r ♦ r❡❣✐str♦ ❞❛s ❛t✉❛❧✐③❛çõ❡s ❡①❡❝✉t❛❞❛s ❞✉r❛♥t❡ t♦❞❛ ❛ ❤✐stór✐❛ ❞❡ ❡✈♦❧✉çã♦ ❞♦❣r✉♣♦✳ ❈♦♥❢♦r♠❡ s❡rá ❜r❡✈❡♠❡♥t❡ ❞✐s❝✉t✐❞♦ ♥♦ ❆♣ê♥❞✐❝❡ ❇✱ ❛♦ ✉t✐❧✐③❛r ✉♠ ✜❧tr♦ ❞❡❑❛❧♠❛♥✱ t❛❧ r❡❣✐str♦ ♣♦❞❡ s❡r ❢❡✐t♦ ♣♦r ♠❡✐♦ ❞❛ ♠❛♥✉t❡♥çã♦ ❞♦s ❞♦✐s ♣r✐♠❡✐r♦s ♠♦✲♠❡♥t♦s ❞❛s ❞✐str✐❜✉✐çõ❡s ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❛ss♦❝✐❛❞❛s ❛♦ ❡st❛❞♦ ❞❡ ❝❛❞❛ r♦❜ô✱ ❛❧é♠ ❞♦❤✐stór✐❝♦ ❞❛s tr♦❝❛s ❞❡ ✐♥❢♦r♠❛çã♦ ♦❝♦rr✐❞❛s ❡♠ ❝❛❞❛ ❡♥❝♦♥tr♦✳ ❊ss❡ ❤✐stór✐❝♦ r❡❣✐str❛ ❛✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ✭❝♦rr❡❧❛çã♦✮ r❡❢❡r❡♥t❡ às ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❣❡r❛❞❛s ♣♦r ♣❛r❡s❞❡ r♦❜ôs✳ ◗✉❛♥❞♦ ✉♠ r♦❜ô ✉t✐❧✐③❛ ❛ ❡st✐♠❛t✐✈❛ ❞❡ ♣♦s❡ ❞❡ ✉♠ ♦✉tr♦ r♦❜ô ♣❛r❛ ❛t✉❛❧✐③❛r s✉❛ ♣ró♣r✐❛ ❡st✐♠❛t✐✈❛✱ t❛✐s ❡st✐♠❛t✐✈❛s s❡ t♦r♥❛♠ ❝♦rr❡❧❛❝✐♦♥❛❞❛s ✭✐♥t❡r❞❡♣❡♥❞❡♥t❡s✮✳❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ❡♠ ❬❘♦✉♠❡❧✐♦t✐s ✫ ❇❡❦❡②✱ ✷✵✵✵❛❪✱ ♦ tr❛t❛♠❡♥t♦ ✐♥❛❞❡q✉❛❞♦ ♦✉ ♦♥ã♦ tr❛t❛♠❡♥t♦ ❞❡ss❛s ❝♦rr❡❧❛çõ❡s ♣♦❞❡ ❧❡✈❛r à ❣❡r❛çã♦ ❞❡ ❡st✐♠❛t✐✈❛s ✐♥❝♦♥s✐st❡♥t❡s✭♦t✐♠✐st❛s✮ ❡♠ ❡t❛♣❛s ❢✉t✉r❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ q✉❡ ❡♥✈♦❧✈❛♠ ❛q✉❡❧❡s r♦❜ôs✳ ❆ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ r❡s✉❧t❛♥t❡ ❞❛ ❣❡r❛çã♦ ❝♦♥❥✉♥t❛ ❞❛s ❡st✐♠❛t✐✈❛s ♦❝♦rr❡❡♠ ❞❡tr✐♠❡♥t♦ ❞♦s ❝✉st♦s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❡ ❛r♠❛③❡♥❛♠❡♥t♦✿ ❝♦♠♣❧❡①✐❞❛❞❡ ❝♦♠♣✉✲4 ) t❛❝✐♦♥❛❧ t♦t❛❧ ❞❡ O(n ♣❛r❛ ❛ ✉♥✐❞❛❞❡ ❝❡♥tr❛❧✐③❛❞♦r❛ ♣r♦❝❡ss❛r ✉♠❛ ♠❡❞✐❞❛ ❡①t❡r♦❝❡♣✲t✐✈❛ ❞✉r❛♥t❡ ❝❛❞❛ ❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ s❡♥❞♦ n ♦ ♥ú♠❡r♦ t♦t❛❧ ❞❡ r♦❜ôs♥♦ ❣r✉♣♦✳ ❆❧é♠ ❞✐ss♦✱ ✉♠❛ ❞❡♠❛♥❞❛ s✐❣♥✐✜❝❛t✐✈❛ ❞❡ ❝♦♠✉♥✐❝❛çã♦ é ❣❡r❛❞❛✱ t❡♥❞♦❡♠ ✈✐st❛ q✉❡ ♦s r♦❜ôs ♣r❡❝✐s❛♠ ❝♦♥st❛♥t❡♠❡♥t❡ ❡♥✈✐❛r ✐♥❢♦r♠❛çõ❡s ♣❛r❛ ❛ ✉♥✐❞❛❞❡❝❡♥tr❛❧✐③❛❞♦r❛✳ ❯♠❛ ✈❡rsã♦ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ❞❡ss❡ ♠ét♦❞♦ t❛♠❜é♠ é ❛♣r❡s❡♥t❛❞❛ ❡♠ ❬❘♦✉♠❡❧✐♦✲ ❙♦❧✉çã♦ t✐s ✫ ❇❡❦❡②✱ ✷✵✵✵❛❪ ❡ ❢❛③ ✉s♦ ❞❡ ✜❧tr♦s ❞❡ ❑❛❧♠❛♥ ❞✐str✐❜✉í❞♦s✱ ❡♠ ❡①❡❝✉çã♦ ❡♠ ❝❛❞❛ ót✐♠❛ ✭❞❡s✲ ❝❡♥tr❛❧✐③❛❞❛✮ r♦❜ô✳ P❛r❛ ✐ss♦✱ ❝❛❞❛ r♦❜ô ♥❡❝❡ss✐t❛ ❛r♠❛③❡♥❛r✱ ❛❧é♠ ❞❡ s✉❛s ❡st✐♠❛t✐✈❛s✱ ❛s ❡st✐♠❛✲ ✸✳✶✳ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛✹✼ t✐✈❛s ❞♦s ❞❡♠❛✐s r♦❜ôs ❞♦ ❣r✉♣♦ ❡ ❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛✳ P❛r❛ ❛ ✈❡rsã♦ ❞❡s❝❡♥tr❛❧✐③❛❞❛ s❡r ❝♦♠♣❛tí✈❡❧ ❝♦♠ ❛ ❝❡♥tr❛❧✐③❛❞❛✱ ❛s ✐♥❢♦r♠❛çõ❡s ❣❡r❛❞❛s ❡♠ ✉♠❛❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ✭❡♥❝♦♥tr♦✮ ❞❡✈❡♠ s❡r ❝♦♠♣❛rt✐❧❤❛❞❛s ❝♦♠ ♦s ❞❡♠❛✐s♠❡♠❜r♦s ❞♦ ❣r✉♣♦ ✭✈✐❛ ♠❡❝❛♥✐s♠♦s ❞❡ ❝♦♠✉♥✐❝❛çã♦✮✳ ❆❧é♠ ❞✐ss♦✱ ❛ ❝❛❞❛ ❡♥❝♦♥tr♦❢❛③✲s❡ ♥❡❝❡ssár✐♦ ❛t✉❛❧✐③❛r ❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❛r♠❛③❡♥❛❞❛s ❡♠ ❝❛❞❛ r♦❜ô✱ ✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞♦ ❢❛t♦ ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ r♦❜ô t❡r ♦✉ ♥ã♦ ♣❛rt✐❝✐♣❛❞♦ ❞♦❡♥❝♦♥tr♦✳ ❉❡ss❡ ♠♦❞♦✱ q✉❛♥❞♦ ✉♠ r♦❜ô ♣❛rt✐❝✐♣❛r ❞❡ ✉♠ ❡♥❝♦♥tr♦ ❡ ❢♦r ❛❥✉st❛r s✉❛❝r❡♥ç❛ ❡♠ ✉♠❛ ❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ ♦ ♠❡s♠♦ t❡rá à ❞✐s♣♦s✐çã♦ t♦❞❛s ❛s✐♥❢♦r♠❛çõ❡s ♥❡❝❡ssár✐❛s ♣❛r❛ ❣❡r❛r ✉♠❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ ❞♦ ❣r✉♣♦✳ ◆❡ss❛ ✈❡rsã♦ ❞❡s❝❡♥tr❛❧✐③❛❞❛✱ ♦ tr❛t❛♠❡♥t♦ ❞❛ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❡①✐❣❡ ♦ ❝♦♥❤❡❝✐✲♠❡♥t♦ ♣ré✈✐♦ ❞♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs ♥♦ ❣r✉♣♦ ♣❛r❛ s❡ ❡❢❡t✉❛r ♦ r❡❣✐str♦ ❞❛s ✐♥❢♦r♠❛çõ❡s✳❆❧é♠ ❞✐ss♦✱ ❡ss❛ ✈❡rsã♦ ❛♣r❡s❡♥t❛ ❛❧t♦ ❝✉st♦ ❞❡ ❛r♠❛③❡♥❛♠❡♥t♦✱ ✉♠❛ ✈❡③ q✉❡ ❝❛❞❛ r♦❜ô♥❡❝❡ss✐t❛ ♠❛♥t❡r ✐♥❢♦r♠❛çã♦ ❛ r❡s♣❡✐t♦ ❞❡ t♦❞♦s ♦s ♠❡♠❜r♦s ❞♦ ❣r✉♣♦✳ ❈♦♥s❡q✉❡♥t❡✲♠❡♥t❡✱ t❡♠✲s❡ ✉♠ ✢✉①♦ ❝♦♥s✐❞❡rá✈❡❧ ❞❡ tr♦❝❛ ❞❡ ♠❡♥s❛❣❡♥s q✉❡ ❝r❡s❝❡ ❝♦♠ ♦ t❛♠❛♥❤♦❞♦ ❣r✉♣♦✱ ❝♦♠ ❝✉st♦ ✐♥❞✐✈✐❞✉❛❧ ❞❡ ❝♦♠✉♥✐❝❛çã♦ O(n) ♣❛r❛ tr❛♥s♠✐t✐r ✉♠❛ ❡st✐♠❛t✐✈❛❛t✉❛❧✐③❛❞❛ ❡ ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❛ss♦❝✐❛❞❛✳ ❉❡✈✐❞♦ ❛ ❡ss❛s q✉❡stõ❡s✱ ❛❡s❝❛❧❛❜✐❧✐❞❛❞❡ ❞♦ ♠ét♦❞♦ ✜❝❛ ❝♦♠♣r♦♠❡t✐❞❛✳ ◆❡r✉r❦❛r ❡t ❛❧✳ ❬✷✵✵✾❪ ❛♣r❡s❡♥t❛♠ ✉♠ ❛❧❣♦r✐t♠♦ ót✐♠♦ ❡ ❝♦♠♣❧❡t❛♠❡♥t❡ ❞✐str✐✲❜✉í❞♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ✉t✐❧✐③❛♥❞♦ ✉♠ ❡st✐♠❛❞♦r ❞❡ ▼á①✐♠❛❱❡r♦ss✐♠✐❧❤❛♥ç❛✱ ❞♦ ✐♥❣❧ês ▼❛①✐♠✉♠ ❛ P♦st❡r✐♦r✐ ❡st✐♠❛t♦r ✭▼❆P✮✳ ❆ ❛❜♦r❞❛❣❡♠2 )♣♦ss✉✐ ❝✉st♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ O(n ❡ é r♦❜✉st❛ ❛ ❢❛❧❤❛s ♣♦♥t✉❛✐s✱ t❛✐s ❝♦♠♦ ♦ ♠❛❧ ❢✉♥✲❝✐♦♥❛♠❡♥t♦ ❞❡ ✉♠ r♦❜ô✳ P❛r❛ ❛❧❝❛♥ç❛r ✉♠❛ ❛❜♦r❞❛❣❡♠ ❝♦♠♣❧❡t❛♠❡♥t❡ ❞✐str✐❜✉í❞❛✱♦ ♠ét♦❞♦ ♣r♦♣♦st♦ r❡q✉❡r ❝♦♠✉♥✐❝❛çã♦ sí♥❝r♦♥❛ ❡♥tr❡ ♦s r♦❜ôs✱ ❛❧é♠ ❞♦ ❢❛t♦ ❞❡ q✉❡❝❛❞❛ r♦❜ô ♣r❡❝✐s❛ s❡ ❝♦♠✉♥✐❝❛r ❝♦♠ ♦s ❞❡♠❛✐s ❡♠ t♦❞❛ ✐t❡r❛çã♦✳ ❊ss❡s r❡q✉✐s✐t♦s sã♦ r❛③♦á✈❡✐s q✉❛♥❞♦ s❡ t❡♠ ✉♠ ♥ú♠❡r♦ ♣❡q✉❡♥♦ ❞❡ r♦❜ôs ❛t✉❛♥❞♦ ❡♠ ✉♠❛ ♠❡s♠❛ r❡❣✐ã♦❞♦ ❛♠❜✐❡♥t❡✳ ◆♦ ❡♥t❛♥t♦✱ t❛✐s r❡q✉✐s✐t♦s r❡str✐♥❣❡♠ ❛ ✉t✐❧✐③❛çã♦ ❞♦ ♠ét♦❞♦ ❡♠ ❛❧❣✉♠❛s s✐t✉❛çõ❡s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❡♠ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s ❝♦♠♣♦st♦s ♣♦r ✉♠ ♥ú♠❡r♦♠❛✐♦r ❞❡ r♦❜ôs ♦✉ q✉❛♥❞♦ ♦s r♦❜ôs ❛t✉❛♠ ❡♠ ❛♠❜✐❡♥t❡s ❡①t❡♥s♦s✳ ❊♠ ❬❇❛✐❧❡② ❡t ❛❧✳✱ ✷✵✶✶❪✱ ❛ s♦❧✉çã♦ ♣r♦♣♦st❛ ♣❡❧♦s ❛✉t♦r❡s ♣❛r❛ ❝♦♥s✐❞❡r❛r ❛ ✐♥✲ t❡r❞❡♣❡♥❞ê♥❝✐❛ ❝♦♥s✐st❡ ❡♠ ♠❛♥t❡r ❛ ❤✐stór✐❛ ❝♦♠♣❧❡t❛ ❞❡ ❛t✉❛❧✐③❛çõ❡s ❡❢❡t✉❛❞❛s ♥❛❢♦r♠❛ ❞❡ ❝❛❞❡✐❛s ❞❡ ▼❛r❦♦✈ ✭✈❡r ❬❑❡♠❡♥② ✫ ❙♥❡❧❧✱ ✶✾✽✸❪✮✳ ❖ ♠ét♦❞♦ ✉t✐❧✐③❛❞♦ ♣♦ss✉✐2 )❝✉st♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ O(n ❡ ❡✈✐t❛ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ❝♦♠✉♥✐❝❛çã♦ sí♥❝r♦♥❛✱ ❝♦♥t✉❞♦♥❡❝❡ss✐t❛ ❞❡ r❡❧ó❣✐♦s s✐♥❝r♦♥✐③❛❞♦s ❡♠ t♦❞♦s ♦s r♦❜ôs✳ ❆ ❡str❛té❣✐❛ ✉t✐❧✐③❛❞❛ ♣♦r ❇❛❤r❡t ❛❧✳ ❬✷✵✵✾❪ ♣❛r❛ r❡❣✐str❛r ❛s ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛s ❝♦♥s✐st❡ ❡♠ ♠❛♥t❡r ❡♠ ❝❛❞❛ r♦❜ô ✉♠✜❧tr♦ ❞❡ ❑❛❧♠❛♥ ♣❛r❛ ❝❛❞❛ r❡❧❛❝✐♦♥❛♠❡♥t♦ ❡st❛❜❡❧❡❝✐❞♦ ♣❡❧♦ r♦❜ô✳ ❉❡ss❡ ♠♦❞♦✱ ❡ss❡s❜❛♥❝♦s ❞❡ ✜❧tr♦s ❞❡ ❑❛❧♠❛♥ r❡❣✐str❛♠ ♦s r❡❧❛❝✐♦♥❛♠❡♥t♦s ♦❝♦rr✐❞♦s ❞✉r❛♥t❡ ❡t❛♣❛s ❞❡❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❆♣❡s❛r ❞❡ss❛s ❡str❛té❣✐❛s ♣r♦♣✐❝✐❛r❡♠ ❛ ❣❡r❛çã♦ ❞❡ ✉♠❛ ❡s✲ ✹✽ ❈❛♣ít✉❧♦ ✸✳ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s t✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ ✭ót✐♠❛✮ ❞♦ s✐st❡♠❛✱ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❡ ♦s r❡q✉✐s✐t♦s ❞❡ ❝♦♠✉♥✐❝❛çã♦❝♦♠♣r♦♠❡t❡♠ ❛ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ ❞♦s ♠ét♦❞♦s ♣r♦♣♦st♦s✳ ❆❧❣✉♠❛s té❝♥✐❝❛s ❞❡s❝❡♥tr❛❧✐③❛❞❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♥ã♦ ❣❡r❛♠ ✉♠❛❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛✳ ❉❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ ♥ã♦ ✉t✐❧✐③❛r❡♠ ❛ ✐♥❢♦r♠❛çã♦ ❞❡ t♦❞♦s ♦s r♦❜ôs ❙♦❧✉çõ❡s ❞♦ ❣r✉♣♦✱ t❛✐s té❝♥✐❝❛s ❣❡r❛♠ ✉♠❛ s♦❧✉çã♦ ❛♣r♦①✐♠❛❞❛✳ ❆❧❣✉♥s ❞♦s tr❛❜❛❧❤♦s q✉❡ ❛♣r♦①✐♠❛❞❛s ✉t✐❧✐③❛♠ ✐♥❢♦r♠❛çõ❡s ♣❛r❝✐❛✐s ♥♦s ♣r♦❝❡ss♦s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ sã♦ ❬▼♦✉r✐❦✐s✫ ❘♦✉♠❡❧✐♦t✐s✱ ✷✵✵✻❪✱ ❬❑❛r❛♠ ❡t ❛❧✳✱ ✷✵✵✻❪ ❡ ❬Pr♦r♦❦ ❡t ❛❧✳✱ ✷✵✶✷❪✳ ❊♠ ❬▼♦✉r✐❦✐s ✫❘♦✉♠❡❧✐♦t✐s✱ ✷✵✵✻❪✱ ❝❛❞❛ r♦❜ô ✉t✐❧✐③❛ s♦♠❡♥t❡ ✉♠ s✉❜❝♦♥❥✉♥t♦ ❞❡ ✈✐③✐♥❤♦s ♣❛r❛ ❛❥✉st❛r s✉❛ ❝r❡♥ç❛✱ t❡♥❞♦ ❡♠ ✈✐st❛ ❛s ❧✐♠✐t❛çõ❡s ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❡ ♣r♦❝❡ss❛♠❡♥t♦✳ ❑❛r❛♠❡t ❛❧✳ ❬✷✵✵✻❪ ✉t✐❧✐③❛♠ ❛ ❡str❛té❣✐❛ ❞❡ ♠❛♥t❡r ❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ ❛r♠❛③❡♥❛❞❛ ❡♠❝❛❞❛ r♦❜ô✱ ♥♦ ❡♥t❛♥t♦ ✉♠ r♦❜ô ✉t✐❧✐③❛ s♦♠❡♥t❡ ❛s ✐♥❢♦r♠❛çõ❡s ❛ss♦❝✐❛❞❛s às ♠❡❞✐❞❛s❡①t❡r♦❝❡♣t✐✈❛s ♦❜t✐❞❛s✳ Pr♦r♦❦ ❡t ❛❧✳ ❬✷✵✶✷❪ ❛♣r❡s❡♥t❛♠ ✉♠ ♠ét♦❞♦ ❞❡s❝❡♥tr❛❧✐③❛❞♦ q✉❡✉t✐❧✐③❛ ♦ ❛❣r✉♣❛♠❡♥t♦ ❞❡ ✜❧tr♦s ❞❡ ♣❛rtí❝✉❧❛s ♣❛r❛ r❡❞✉③✐r ♦ ❝✉st♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❞♦❝ô♠♣✉t♦ ❞❛s ❡st✐♠❛t✐✈❛s✳ ❚❛✐s té❝♥✐❝❛s tê♠ s✐❞♦ ❡♠♣r❡❣❛❞❛s ❝♦♠♦ ❛❧t❡r♥❛t✐✈❛ àq✉❡❧❛s q✉❡ ❣❡r❛♠ ❡st✐♠❛t✐✈❛s ót✐♠❛s✱ ❞❡ ❢♦r♠❛ ❛ ❧✐❞❛r ❝♦♠ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦ ❡ ❡s♣❛ç♦♦✉ r❡❞✉③✐r ♦s r❡q✉✐s✐t♦s ❞❡ ❝♦♠✉♥✐❝❛çã♦✳ ◆❛s té❝♥✐❝❛s ❛♣r♦①✐♠❛❞❛s✱ s♦♠❡♥t❡ ♣❛rt❡ ❞❛✐♥❢♦r♠❛çã♦ ❞✐s♣♦♥í✈❡❧ é ✉t✐❧✐③❛❞❛✳ ❯♠❛ q✉❡stã♦ r❡❧❡✈❛♥t❡ ♥❛s té❝♥✐❝❛s ❛♣r♦①✐♠❛❞❛s é ♦ ❞❡✈✐❞♦ tr❛t❛♠❡♥t♦ ❛ ✉♠❢❡♥ô♠❡♥♦ ❞❡♥♦♠✐♥❛❞♦ ❞♦✉❜❧❡✲❝♦✉♥t✐♥❣✱ q✉❡ ❝♦♥s✐st❡ ❡♠ ✉t✐❧✐③❛r ♠❛✐s ❞❡ ✉♠❛ ✈❡③ ✉♠❛ ❘❛❝✐♦❝í♥✐♦ ♠❡s♠❛ ✐♥❢♦r♠❛çã♦ ♣❛r❛ ❛t✉❛❧✐③❛r ✉♠❛ ❡st✐♠❛t✐✈❛ ❞❡ ♣♦s❡ ✭r❛❝✐♦❝í♥✐♦ ❝✐r❝✉❧❛r✮✳ ❊ss❡ ❝✐r❝✉❧❛r ❢❡♥ô♠❡♥♦ ♦❝♦rr❡ q✉❛♥❞♦ ✉♠ ♣❛r ❞❡ r♦❜ôs ❛t✉❛❧✐③❛♠ s✉❛s ❝r❡♥ç❛s ❡♠ ❡t❛♣❛s ❞❡ ❧♦✲❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ ♣♦ré♠ s❡♠ ❧❡✈❛r ❡♠ ❝♦♥s✐❞❡r❛çã♦ s✉❛s ❤✐stór✐❛s ♣r❡❣r❡ss❛s ❞❡❛t✉❛❧✐③❛çã♦ ✭✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛✮✳ ❆ ❝♦♥s✐❞❡r❛çã♦ ❞❛ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ♥❛s té❝♥✐❝❛s ♥ã♦❛♣r♦①✐♠❛❞❛s ✐♠♣❧✐❝❛ ❡♠ ♠❛✐♦r ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦ ❡ ❡s♣❛ç♦ ♣❛r❛ ❛ ❣❡r❛çã♦ ❞❛s❡st✐♠❛t✐✈❛s ❝♦♥❥✉♥t❛s✳ ❉❡✈✐❞♦ ❛ ✐ss♦✱ ❛❧❣✉♥s tr❛❜❛❧❤♦s ✐❣♥♦r❛♠ ❛ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❛♦❝♦♥s✐❞❡r❛r❡♠ q✉❡ ❛ ❡st✐♠❛t✐✈❛ ❞❡ ♣♦s❡ ❞❡ ✉♠ r♦❜ô ❡ ❛q✉❡❧❛s r❡❝❡❜✐❞❛s ❞❡ s❡✉s ✈✐③✐✲♥❤♦s s❡❥❛♠ t♦t❛❧♠❡♥t❡ ✐♥❞❡♣❡♥❞❡♥t❡s✳ ◆♦ ❡♥t❛♥t♦✱ ♥❛ ♠❛✐♦r✐❛ ❞♦s ❝❛s♦s✱ ❛ s✉♣♦s✐çã♦❞❡ ✐♥❞❡♣❡♥❞ê♥❝✐❛ é ✐♥❛❞❡q✉❛❞❛✱ ✉♠❛ ✈❡③ q✉❡ ♦s r♦❜ôs ✉t✐❧✐③❛♠ ✉♥s ❛♦s ♦✉tr♦s ♣❛r❛❛❥✉st❛r❡♠ s✉❛s ❝r❡♥ç❛s✳ ❚❛❧ ❝♦♠♦ ❞✐s❝✉t✐❞♦ ❡♠ ❬❘♦✉♠❡❧✐♦t✐s ✫ ❇❡❦❡②✱ ✷✵✵✵❛❪✱ ❛ ✐♥❝❡rt❡③❛ P ❛ss♦❝✐❛❞❛ à❡st✐♠❛t✐✈❛ bx ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ ✉♠ r♦❜ô ♣♦❞❡ s❡r r❡❞✉③✐❞❛ ✐♥❛❞❡q✉❛❞❛♠❡♥t❡ ❡♠ ✉♠❛❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ q✉❡ ✉t✐❧✐③❡ ✉♠ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥ ❞❡ ♠❛♥❡✐r❛ ✐♥❛♣r♦✲♣r✐❛❞❛✱ ❣❡r❛♥❞♦✱ ❛ss✐♠✱ ✉♠❛ ❡st✐♠❛t✐✈❛ ♦t✐♠✐st❛✳ ❊ss❛ s✐t✉❛çã♦ ♣♦❞❡ s❡r ✐❧✉str❛❞❛ ❊st✐♠❛t✐✈❛ 1 2 ✉t✐❧✐③❛♥❞♦ ❞✉❛s ❝ó♣✐❛s ✕ X ❡ X ✕ ❞❡ ✉♠❛ ♠❡s♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ✉♥✐❞✐♠❡♥s✐♦♥❛❧ X ♦t✐♠✐st❛ ❡ ❡♠♣r❡❣❛♥❞♦ ✐♥❛❞❡q✉❛❞❛♠❡♥t❡ ❛ s✉♣♦s✐çã♦ ❞❡ ✐♥❞❡♣❡♥❞ê♥❝✐❛✳ ◆❡ss❡ ❝❛s♦✱ ❛s ✐♥❝❡rt❡✲ 1 2③❛s ✭✈❛r✐â♥❝✐❛s✮ P ❡ P ❝♦♠♣r❡❡♥❞❡♠ ❛ ♠❡s♠❛ ✐♥❢♦r♠❛çã♦✱ ♣♦rt❛♥t♦ ❝♦rr❡❧❛❝✐♦♥❛❞❛s✳❆♦ ❡♠♣r❡❣❛r ❛ s✉♣♦s✐çã♦ ❞❡ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❡ ✉t✐❧✐③❛r ❛ ❡t❛♣❛ ❞❡ ❝♦rr❡çã♦ ❞❛ ✈❡rsã♦ ❞♦ ✸✳✶✳ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛✹✾ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥ q✉❡ ♣r❡ss✉♣õ❡ ❛ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❞❛s ❡st✐♠❛t✐✈❛s✱ t❡♠✲s❡ q✉❡✿P P 1 2 P =P 1 2 =P + P 1 1P 1 =✭✸✳✶✮ 2 1 2❘❡s✉❧t❛❞♦ s❡♠❡❧❤❛♥t❡ ♣♦❞❡ s❡r ♦❜t✐❞♦ ❛♦ s✉❜st✐t✉✐r♠♦s P ♣♦r P ✱ ♦✉ s❡❥❛✱ P P 1 2 P= = ✳ ❊ss❡ r❡s✉❧t❛❞♦ ♠♦str❛ q✉❡ ❛ s✉♣♦s✐çã♦ ✐♥❛❞❡q✉❛❞❛ ❞❡ ✐♥❞❡♣❡♥❞ê♥❝✐❛ 2 2❛❝❛rr❡t❛ ♥❛ r❡❞✉çã♦ ❞❛s ✐♥❝❡rt❡③❛s ❛ss♦❝✐❛❞❛s às ❡st✐♠❛t✐✈❛s✱ ❣❡r❛♥❞♦ ✉♠❛ ❡st✐♠❛t✐✈❛✐♥❝♦♥s✐st❡♥t❡ ✭♦t✐♠✐st❛✮✳ ❆ ❛❞❡q✉❛❞❛ ❝♦♠❜✐♥❛çã♦ ❞❡ t❛✐s ✐♥❢♦r♠❛çõ❡s✱ ❛♦ s❡ ❝♦♥s✐❞❡r❛r 1 2❛ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❞❛s ♠❡s♠❛s✱ ❣❡r❛ ✉♠❛ ❡st✐♠❛t✐✈❛ r❡s✉❧t❛♥t❡ ❞❛ ❢♦r♠❛ P❂P ❂P ✳ ❍♦✇❛r❞ ❡t ❛❧✳ ❬✷✵✵✸❪ ♣r♦♣õ❡♠ ✉♠❛ ❢♦r♠❛ ❞❡ ❡✈✐t❛r ♦ r❛❝✐♦❝í♥✐♦ ❝✐r❝✉❧❛r ♠❛♥t❡♥❞♦✉♠❛ ár✈♦r❡ ❞❡ ❞❡♣❡♥❞ê♥❝✐❛s ✭❞❡♣❡♥❞❡♥❝② tr❡❡✮✳ ◆❡ss❛ ár✈♦r❡✱ ❝❛❞❛ ♥ó r❡♣r❡s❡♥t❛ ✉♠❛❞✐str✐❜✉✐çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❛ss♦❝✐❛❞❛ à ❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ ✉♠ r♦❜ô✳ ❆s❞✐str✐❜✉✐çõ❡s ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♥❛ ár✈♦r❡ ♣♦ss✉❡♠ ❡①❛t❛♠❡♥t❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❛♥❝❡s✲ tr❛❧ ❡ ③❡r♦ ♦✉ ♠❛✐s ❞✐str✐❜✉✐çõ❡s ❞❡s❝❡♥❞❡♥t❡s✳ ❉❡ss❡ ♠♦❞♦✱ ❛ ❡str❛té❣✐❛ ✉t✐❧✐③❛❞❛ ❡♠✉♠❛ ❡t❛♣❛ ❞❡ ❛t✉❛❧✐③❛çã♦ ❝♦♥s✐st❡ ❡♠ ❞❡✜♥✐r ✉♠❛ ❞✐r❡çã♦ ♣❛r❛ ❛ ❛t✉❛❧✐③❛çã♦ ❞❛s ❞✐s✲ tr✐❜✉✐çõ❡s✳ ❆ss✐♠✱ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❡①✐st❡♥t❡ ♥❛ ár✈♦r❡ é ✉t✐❧✐③❛❞❛ ♣❛r❛ ❛t✉❛❧✐③❛r ❛s❞✐str✐❜✉✐çõ❡s ❞❡ s❡✉s ♥ós ❞❡s❝❡♥❞❡♥t❡s✱ ♣♦ré♠ ♥ã♦ ♣♦❞❡ s❡r ✉t✐❧✐③❛❞❛ ♣❛r❛ ❛t✉❛❧✐③❛r❛s ❞✐str✐❜✉✐çõ❡s ❞❡ s❡✉s ❛♥❝❡str❛✐s✳ ❆❧é♠ ❞✐ss♦✱ ✉♠❛ ❞✐str✐❜✉✐çã♦ q✉❡ ❛✐♥❞❛ ♥ã♦ ♣❡r✲ t❡♥ç❛ à ❛r✈♦r❡ ❡ é ✉t✐❧✐③❛❞❛ ♣❛r❛ ❛t✉❛❧✐③❛r ❛❧❣✉♠❛ ♦✉tr❛ ❞✐str✐❜✉✐çã♦ s❡ t♦r♥❛ ✉♠ ♥ó❛♥❝❡str❛❧ ❞❡ss❛ ú❧t✐♠❛ ♥❛ ár✈♦r❡✳ ◆❡ss❛ ❡str✉t✉r❛ ❡♠ ár✈♦r❡ ♦s ❝✐❝❧♦s sã♦ ❡✈✐t❛❞♦s✱❝♦♥s❡q✉❡♥t❡♠❡♥t❡ ❡❧✐♠✐♥❛♥❞♦ ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ❞♦✉❜❧❡✲❝♦✉♥t✐♥❣s✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ❡♠ s✐st❡♠❛s ❞❡s❝❡♥tr❛❧✐③❛❞♦s✱ ❛ s✉♣♦s✐çã♦ ❞❡✐♥❞❡♣❡♥❞ê♥❝✐❛ ❝♦♠ r❡❧❛çã♦ às ❡st✐♠❛t✐✈❛s ❣❡r❛❞❛s ❡♠ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛é ✐♥❛❞❡q✉❛❞❛✳ ◆❛s ❛❜♦r❞❛❣❡♥s ❛♣r❡s❡♥t❛❞❛s✱ ♦ tr❛t❛♠❡♥t♦ ❞❛ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❝♦♠✲♣r❡❡♥❞❡ ♦ r❡❣✐str♦ ❡ ♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❛s ✐♥❢♦r♠❛çõ❡s ❞❡ t♦❞♦s ♦s ✐♥t❡❣r❛♥t❡s ❞♦ ❣r✉♣♦✱♦ q✉❡ ❝♦♠♣r♦♠❡t❡ ❛ ❛♣❧✐❝❛çã♦ ❞❡ss❛s ❛❜♦r❞❛❣❡♥s ❡♠ s✐st❡♠❛s ❝♦♠♣♦st♦s ♣♦r ✉♠ ❣r❛♥❞❡♥ú♠❡r♦ ❞❡ ❛❣❡♥t❡s✳ ❖ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s✱ ❞♦ ✐♥❣❧ês ❈♦✈❛r✐❛♥❝❡ ❆❧❣♦r✐t♠♦s ■♥t❡rs❡❝t✐♦♥ ❆❧❣♦r✐t❤♠ ✭❈■✮ ❡ s✉❛ ✈❡rsã♦ ❣❡♥❡r❛❧✐③❛❞❛ ❙♣❧✐t ❈♦✈❛r✐❛♥❝❡ ■♥t❡rs❡❝t✐♦♥ ■♥t❡rs❡çã♦ ❈♦✈❛r✐â♥❝✐❛s ❆❧❣♦r✐t❤♠ ✭❙❈■✮✱ ♣r♦♣♦st♦s ❡♠ ❬❏✉❧✐❡r ✫ ❯❤❧♠❛♥♥✱ ✶✾✾✼✱ ✷✵✵✶❪✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ sã♦❞❡s❝r✐t♦s ❡♠ ♠❛✐♦r❡s ❞❡t❛❧❤❡s ♥♦ ❆♣ê♥❞✐❝❡ ❈✳ ❚❛✐s ❛❧❣♦r✐t♠♦s ❝♦♥s✐st❡♠ ❡♠ ✉♠❛ té❝✲♥✐❝❛ q✉❡ ❣❡r❛ ❡st✐♠❛t✐✈❛s ❝♦♥s✐st❡♥t❡s ❬▲✐ ❡t ❛❧✳✱ ✷✵✶✸❪ ❡♠ ✉♠ ♣r♦❝❡ss♦ ❞❡ ❢✉sã♦ ❞❡❞❛❞♦s ❞❡s❝❡♥tr❛❧✐③❛❞❛✱ ♥❛q✉❡❧❛s s✐t✉❛çõ❡s ♥❛s q✉❛✐s ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛❡♥tr❡ ❛s ❡st✐♠❛t✐✈❛s é ❞❡s❝♦♥❤❡❝✐❞❛✳ ❆ ❡str❛té❣✐❛ ✉t✐❧✐③❛❞❛ ♥❡ss❡s ❛❧❣♦r✐t♠♦s ♣❛r❛ ❛ ✺✵ ❈❛♣ít✉❧♦ ✸✳ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s❛t✉❛❧✐③❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ❡✈✐t❛ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡ r❡❣✐str❛r ♦ ❤✐stór✐❝♦ ❞❡ ❛t✉❛❧✐③❛✲çõ❡s ♦❝♦rr✐❞❛s ❞✉r❛♥t❡ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱ t❡♠✲s❡✉♠❛ ❜❛✐①❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦ ❡ ❡s♣❛ç♦ ♣❛r❛ ❧✐❞❛r ❛❞❡q✉❛❞❛♠❡♥t❡ ❝♦♠ ❛ ✐♥t❡r✲❞❡♣❡♥❞ê♥❝✐❛ ❡ ♦ ❢❡♥ô♠❡♥♦ ❞❡ ❞♦✉❜❧❡✲❝♦✉♥t✐♥❣ ✭r❛❝✐♦❝í♥✐♦ ❝✐r❝✉❧❛r✮✱ ❞❡ ♠♦❞♦ q✉❡ t❛❧❛❜♦r❞❛❣❡♠ s❡ ❛♣r❡s❡♥t❛ ❝♦♠♦ ✉♠❛ s♦❧✉çã♦ ❡s❝❛❧á✈❡❧ ♣❛r❛ ❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡♠ s✐st❡♠❛s ❝♦♠♣♦st♦s ♣♦r ❣r❛♥❞❡s ❣r✉♣♦s ❞❡ r♦❜ôs✳ ❆♣❡s❛r ❞❡ss❛ ❝♦♥st❛t❛çã♦✱ ♦s tr❛❜❛✲❧❤♦s q✉❡ tê♠ ✉t✐❧✐③❛❞♦ ❡ss❡s ❛❧❣♦r✐t♠♦s ♦ ❢❛③❡♠ ❡♠ s✐st❡♠❛s ❝♦♠ ✉♠ ♥ú♠❡r♦ ❧✐♠✐t❛❞♦❞❡ ❛❣❡♥t❡s✳ ❯♠❛ ❞❛s ♣r✐♠❡✐r❛s ❛♣❧✐❝❛çõ❡s ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s ♣❛r❛❡st✐♠❛çã♦ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ❞❡ ❡st❛❞♦s é ❛♣r❡s❡♥t❛❞❛ ❡♠ ❬❆r❛♠❜❡❧ ❡t ❛❧✳✱ ✷✵✵✶❪✳ ◆❡ss❡ tr❛❜❛❧❤♦✱ ✉♠ ❣r✉♣♦ ❞❡ r♦❜ôs ✉t✐❧✐③❛♥❞♦ ✉♠❛ t♦♣♦❧♦❣✐❛ ✜①❛ ❡♠ ❛♥❡❧ ❡♠♣r❡❣❛♠ ❝♦♠✉♥✐✲❝❛çã♦ ❧♦❝❛❧ ♣❛r❛ ✈✐❛❜✐❧✐③❛r ❛ ❡①❡❝✉çã♦ ❞❡ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❈❛❞❛ r♦❜ô♣r♦♣❛❣❛ ♦ ♠♦❞❡❧♦ ❞❡ tr❛♥s✐çã♦ ❞♦ ❣r✉♣♦ ✐♥t❡✐r♦✱ ❞❡ ♠♦❞♦ ❛ r❡❣✐str❛r ❛s ❡st✐♠❛t✐✈❛s ❞❡ t♦❞♦s ♦s r♦❜ôs✳ ❯♠❛ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛s nN × nN é ❛r♠❛③❡♥❛❞❛ ❡♠ ❝❛❞❛ r♦❜ô✱s❡♥❞♦ n ♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs ❡ N ❛ ❞✐♠❡♥sã♦ ❞♦ ✈❡t♦r ❞❡ ❡st❛❞♦s ❞♦s r♦❜ôs✳ ❉❡ss❡ ♠♦❞♦✱❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ♣♦❞❡ s❡r ❣❡r❛❞❛ ❡♠ ❝❛❞❛ ❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦✲♦♣❡r❛t✐✈❛✳ ◆❡ss❡ tr❛❜❛❧❤♦✱ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ sã♦ ❡❢❡t✉❛❞❛s ✉t✐❧✐③❛♥❞♦♦ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥ ✭✐❣♥♦r❛♥❞♦ ♦s t❡r♠♦s ❞❡ ❝♦rr❡❧❛çã♦ ❝r✉③❛❞❛ ✕ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛✮ ❡ ♦❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s✳ ❯♠❛ ❝♦♠♣❛r❛çã♦ é ❛♣r❡s❡♥t❛❞❛ ❝♦♥s✐❞❡r❛♥❞♦❛s ❡st✐♠❛t✐✈❛s ❣❡r❛❞❛s ♣❡❧❛s ❞✉❛s ❛❜♦r❞❛❣❡♥s ❡ ♦s r❡s✉❧t❛❞♦s ♠♦str❛♠ ❛ ❞✐✈❡r❣ê♥❝✐❛ ❞♦✜❧tr♦ ❞❡ ❑❛❧♠❛♥✱ ❡♥q✉❛♥t♦ q✉❡ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s s❡ ❝♦♠♣♦rt❛❛❞❡q✉❛❞❛♠❡♥t❡ ❝♦♠ ❛ ❣❡r❛çã♦ ❞❡ ❡st✐♠❛t✐✈❛s ❝♦♥s✐st❡♥t❡s✳ ▼❛✐s r❡❝❡♥t❡♠❡♥t❡✱ ❛❧❣✉♥s tr❛❜❛❧❤♦s tê♠ ✉t✐❧✐③❛❞♦ ♦s ❛❧❣♦r✐t♠♦s ❞❡ ■♥t❡rs❡çã♦❞❡ ❈♦✈❛r✐â♥❝✐❛s ❡♠ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❊♠ ❬▲✐ ✫ ◆❛s❤❛s❤✐❜✐✱ ✷✵✶✷❪✱❝❛❞❛ r♦❜ô ❛r♠❛③❡♥❛ ❡ ❛t✉❛❧✐③❛ n ♠❛tr✐③❡s N × N ✭❞❡♥♦♠✐♥❛❞♦ ❡st❛❞♦ ❞❡s❛❝♦♣❧❛❞♦❞♦ ❣r✉♣♦✮ ❛♦ ✐♥✈és ❞❡ ✉♠❛ ♠❛tr✐③ ❞❡♥s❛ nN × nN✳ ❉❡ss❛ ❢♦r♠❛✱ ❝❛❞❛ r♦❜ô ❛♦ ♦❜t❡r✉♠❛ ♠❡❞✐❞❛ ❡①t❡r♦❝❡♣t✐✈❛✱ ❛t✉❛❧✐③❛ ❛ ❡st✐♠❛t✐✈❛ ❧♦❝❛❧ r❡❢❡r❡♥t❡ ❛♦ r♦❜ô ♦❜s❡r✈❛❞♦✉s❛♥❞♦ ❙❈■ ❝♦♠ ✉♠ ❝✉st♦ O(1) ❡ ❝♦♠✉♥✐❝❛ ♦ r❡s✉❧t❛❞♦ ❛♦s ❞❡♠❛✐s r♦❜ôs ❝♦♠ ❝✉st♦O(n) ✳ ❆♦ r❡❝❡❜❡r ✉♠❛ ✐♥❢♦r♠❛çã♦✱ ✉♠ r♦❜ô ❡❢❡t✉❛ ❛ ❡t❛♣❛ ✐♥❞✐✈✐❞✉❛❧ ❞❡ ❧♦❝❛❧✐③❛çã♦❝♦♦♣❡r❛t✐✈❛ ✉t✐❧✐③❛♥❞♦ t❛♠❜é♠ ❙❈■✳ ❊ss❛ ❛❜♦r❞❛❣❡♠✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ♦✉tr❛s ❞✉❛s❛❜♦r❞❛❣❡♥s ✉t✐❧✐③❛♥❞♦ ♦ ❊❑❋ ✭✉♠❛ ❛❜♦r❞❛❣❡♠ ✐♥❣ê♥✉❛ ❡♠ q✉❡ ❛ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❞❛s❡st✐♠❛t✐✈❛s ♥ã♦ é ❝♦♥s✐❞❡r❛❞❛ ❡ ✉♠❛ ♦✉tr❛ ❡str❛té❣✐❛ q✉❡ ❝♦♥s✐❞❡r❛ ❛ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛✮❢♦r❛♠ ❝♦♠♣❛r❛❞❛s ❝♦♠ ❛ ♦❞♦♠❡tr✐❛✳ ❖s r❡s✉❧t❛❞♦s ❛♣r❡s❡♥t❛❞♦s ♠♦str❛♠ ❛ ❡✜❝á❝✐❛❞♦ ♠ét♦❞♦ q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦ à ♦❞♦♠❡tr✐❛✱ t❛♥t♦ ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ à q✉❛❧✐❞❛❞❡ ❞❛✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ q✉❛♥t♦ ♥♦ q✉❡ t❛♥❣❡ à ❝♦♥s✐stê♥❝✐❛ ❞❛s ❡st✐♠❛t✐✈❛s ❣❡r❛❞❛s✳❆♣❡s❛r ❞❛ ❞✐♠✐♥✉✐çã♦ ❞❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ ❡s♣❛ç♦ ❛ss♦❝✐❛❞❛ à ✐♥❢♦r♠❛çã♦ ❛r♠❛③❡♥❛❞❛❡♠ ❝❛❞❛ r♦❜ô✱ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ✐♥❢♦r♠❛çã♦ ❛r♠❛③❡♥❛❞❛ é ❛✐♥❞❛ ✉♠ ❢❛t♦r ❝♦♥s✐❞❡rá✈❡❧ ✸✳✶✳ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛✺✶ ♥❛ ❛♣❧✐❝❛çã♦ ❞❡ss❛ ❛❜♦r❞❛❣❡♠ ❡♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s✳❈❛rr✐❧❧♦✲❆r❝❡ ❡t ❛❧✳ ❬✷✵✶✸❪ ❛♣r❡s❡♥t❛♠ ✉♠ ❛❧❣♦r✐t♠♦ ❛♣r♦①✐♠❛❞♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❜❛s❡❛❞♦ ♥♦s ❛❧❣♦r✐t♠♦s ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s✳ ◆❡ss❛❛❜♦r❞❛❣❡♠✱ ❝❛❞❛ r♦❜ô ♠❛♥té♠ s♦♠❡♥t❡ s✉❛ ♣ró♣r✐❛ ❡st✐♠❛t✐✈❛ ❡ ❛ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐✲â♥❝✐❛ ❛ss♦❝✐❛❞❛✳ ❆s ❡t❛♣❛s ❞❡ ❢✉sã♦ s❡♥s♦r✐❛❧ sã♦ ❡❢❡t✉❛❞❛s ✉t✐❧✐③❛♥❞♦ ■♥t❡rs❡çã♦ ❞❡❈♦✈❛r✐â♥❝✐❛s✱ ❝♦♠ ❝♦♠♣❧❡①✐❞❛❞❡ O(n)✱ t❛♥t♦ ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ ❛♦ ♣r♦❝❡ss❛♠❡♥t♦ ✭❢✉✲ sã♦ s❡♥s♦r✐❛❧✮ q✉❛♥t♦ ♥♦ q✉❡ t❛♥❣❡ à ❝♦♠✉♥✐❝❛çã♦✳ ◆♦s ❡①♣❡r✐♠❡♥t♦s ❞❡s❡♥✈♦❧✈✐❞♦s✱❝❛❞❛ r♦❜ô ♣r♦♣❛❣❛ s✉❛ ♣ró♣r✐❛ ❡st✐♠❛t✐✈❛ ❛ ❝❛❞❛ ✐t❡r❛çã♦ ❡ ❛t✉❛❧✐③❛ t❛❧ ❡st✐♠❛t✐✈❛ ❝♦♠♠❡❞✐❞❛s ❡①t❡r♦❝❡♣t✐✈❛s ❛ ❝❛❞❛ ✺ ✐t❡r❛çõ❡s✳ ❖s r❡s✉❧t❛❞♦s ❛♣r❡s❡♥t❛❞♦s ❝♦rr❡s♣♦♥❞❡♠ à❝♦♠♣❛r❛çã♦ ❞♦ ♠ét♦❞♦ ♣r♦♣♦st♦ ❝♦♠ ♦ ❊❑❋ ❝♦♥s✐❞❡r❛♥❞♦ ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ✐♥t❡r❞❡♣❡♥✲❞ê♥❝✐❛s✳ ❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱ t❡♠✲s❡ ✉♠❛ ♠❛tr✐③ ❞❡♥s❛ nN × nN ❛r♠❛③❡♥❛❞❛ ❡♠ ❝❛❞❛ r♦❜ô ♣❛r❛ ♦ ❝ô♠♣✉t♦ ❞❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ ❝♦♠ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❡ ❝♦✲4 )♠✉♥✐❝❛çã♦ ❞❡ O(n ❡ O(n)✱ r❡s♣❡t✐✈❛♠❡♥t❡✳ ❆ ❧♦❝❛❧✐③❛çã♦ ❣❡r❛❞❛ ♣❡❧♦ ❊❑❋ é ✉t✐❧✐③❛❞❛❝♦♠♦ ✉♠ ❜❡♥❝❤♠❛r❦ ♣❛r❛ ❡❢❡✐t♦s ❞❡ ❝♦♠♣❛r❛çã♦✳ ❆ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❣❡r❛❞❛♣❡❧♦ ❈■ é ❝♦♥s✐❞❡r❛❞❛ ❜♦❛ ❡♠ ❝♦♠♣❛r❛çã♦ ❛♦ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥✱ ♣♦ré♠ ♠❡♥♦s ❡①❛t❛✳❚♦❞❛✈✐❛✱ s❡✉ ❡♠♣r❡❣♦ é ❥✉st✐✜❝❛❞♦ ❞❡✈✐❞♦ à ❞✐♠✐♥✉✐çã♦ s✐❣♥✐✜❝❛t✐✈❛ ❞❛ ❝♦♠♣❧❡①✐❞❛❞❡♣❛r❛ ♣r♦❝❡ss❛♠❡♥t♦ ❞❛s ✐♥❢♦r♠❛çõ❡s✳ ❲❛♥❛s✐♥❣❤❡ ❡t ❛❧✳ ❬✷✵✶✹❪ ✉t✐❧✐③❛♠ ❙❈■ ♣❛r❛ ❡❢❡t✉❛r ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡✲ r❛t✐✈❛ ❡♠ ✉♠ s✐st❡♠❛ ♠✉❧t✐rr♦❜ôs ❤❡t❡r♦❣ê♥❡♦ ❝♦♠ três ✐♥t❡❣r❛♥t❡s✳ ❯♠ ❞♦s r♦❜ôsr❡❝❡❜❡ ✐♥❢♦r♠❛çõ❡s ❞❡ s✉❛ ♣♦s✐çã♦ ❡♠ ✐♥t❡r✈❛❧♦s r❡❣✉❧❛r❡s✱ ❡♥q✉❛♥t♦ q✉❡ ♦s ❞❡♠❛✐s sã♦ ❞❡s♣r♦✈✐❞♦s ❞❡ t❛❧ r❡❝✉rs♦✳ ❖s r♦❜ôs ✉t✐❧✐③❛♠ s❡✉s ✈✐③✐♥❤♦s ♣❛r❛ ❛t✉❛❧✐③❛r❡♠ s✉❛s♣♦s❡s✱ ♣♦ré♠ ❛ r❡❞❡ ❛❞✲❤♦❝ ❢♦r♠❛❞❛ ♣❡❧♦s r♦❜ôs ♥ã♦ é ✉♠ ❣r❛❢♦ ❝♦♠♣❧❡t♦✳ ❆s ❛t✉❛✲❧✐③❛çõ❡s ♦❝♦rr❡♠ ❞❡ ♠♦❞♦ q✉❡ ❛ t♦♣♦❧♦❣✐❛ ❞❛ r❡❞❡ s❡ ♠❛♥té♠ ❡stát✐❝❛✱ ♦ q✉❡ ❢❛③ ❝♦♠ q✉❡ ❞♦✐s ❞❡ss❡s r♦❜ôs ♥ã♦ t❡♥❤❛♠ ❛❝❡ss♦ ❞✐r❡t♦ às ✐♥❢♦r♠❛çõ❡s ✉♠ ❞♦ ♦✉tr♦ ❞✉r❛♥t❡♦s ❡①♣❡r✐♠❡♥t♦s✳ ❖s r❡s✉❧t❛❞♦s ♠♦str❛♠ q✉❡ ♠❡s♠♦ ♥❡ss❛s ❝♦♥❞✐çõ❡s ♦s três r♦❜ôs❛♣r❡s❡♥t❛♠ ❜♦❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❆♣❡s❛r ❞❡ss❡s tr❛❜❛❧❤♦s r❡❝❡♥t❡s ❛❜♦r❞❛r❡♠ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❢✉sã♦ ❞❡ ❞❛❞♦s ✉t✐✲❧✐③❛♥❞♦ té❝♥✐❝❛s q✉❡ ❡♠♣r❡❣❛♠ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s✱ ♦ ♥ú♠❡r♦❞❡ r♦❜ôs ❝♦♥s✐❞❡r❛❞♦ é ♣❡q✉❡♥♦✳ ◆♦s r❡s✉❧t❛❞♦s ❛♣r❡s❡♥t❛❞♦s ♥❡ss❡s tr❛❜❛❧❤♦s✱ ♦s ❛❧✲❣♦r✐t♠♦s ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s s❡ ♠♦str❛♠ ♣♦t❡♥❝✐❛❧♠❡♥t❡ ❛❞❡q✉❛❞♦s ♣❛r❛ s❡❡❢❡t✉❛r ❛ ❢✉sã♦ s❡♥s♦r✐❛❧ ❞❡ ❞❛❞♦s ❞❡ ♠❛♥❡✐r❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛✱ ❝♦♥❢♦r♠❡ s❡r✐❛ ❡s♣❡r❛❞♦❡♠ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s✳ ❆❧é♠ ❞✐ss♦✱ ❛❣❡r❛çã♦ ❞❡ ❡st✐♠❛t✐✈❛s ❝♦♥s✐st❡♥t❡s ♥❛ ❛✉sê♥❝✐❛ ❞❡ ✐♥❢♦r♠❛çõ❡s ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛❡♥tr❡ ❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♠♣r❡❡♥❞❡ ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ ♠✉✐t♦ ✐♠♣♦rt❛♥t❡✱✉♠❛ ✈❡③ q✉❡ ❛ ♠❛♥✉t❡♥çã♦ ❞❡ t❛✐s ✐♥❢♦r♠❛çõ❡s ❛✉♠❡♥t❛r✐❛ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦❡ ❡s♣❛ç♦ ♣❛r❛ s❡ ❡❢❡t✉❛r ❛ ❢✉sã♦ s❡♥s♦r✐❛❧✳ ✺✷ ❈❛♣ít✉❧♦ ✸✳ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s ✸✳✷ ▼♦✈✐♠❡♥t❛çã♦ ❈♦❧❡t✐✈❛ ❡ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛ ❊♠ ✈ár✐♦s tr❛❜❛❧❤♦s ♥♦ â♠❜✐t♦ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ t❛✐s ❝♦♠♦ ❬❘♦✉♠❡❧✐♦t✐s ✫❇❡❦❡②✱ ✷✵✵✵❛❪ ❡ ❬◆❡r✉r❦❛r ❡t ❛❧✳✱ ✷✵✵✾❪✱ ♦s r♦❜ôs s❡ ♠♦✈✐♠❡♥t❛♠ ❞❡ ❢♦r♠❛ ✐♥❞❡♣❡♥✲❞❡♥t❡ ❡✱ ♣♦r ✈❡③❡s✱ ❞❡ ♠❛♥❡✐r❛ ❛❧❡❛tór✐❛✳ ◆❡ss❡s tr❛❜❛❧❤♦s ♥ã♦ ❡①✐st❡ ❛ ♣r❡♦❝✉♣❛çã♦ ❞❡♠❛♥t❡r ♦s r♦❜ôs ❛t✉❛♥❞♦ ❡♠ ✉♠❛ ♠❡s♠❛ r❡❣✐ã♦ ❞♦ ❛♠❜✐❡♥t❡✱ ♦ q✉❡ ♣♦❞❡ ❝♦♠♣r♦♠❡t❡r❛ ♦❝♦rrê♥❝✐❛ ❞❡ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❊str❛té❣✐❛s ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❝♦♦r✲❞❡♥❛❞❛ tê♠ s✐❞♦ ✉t✐❧✐③❛❞❛s ❝♦♠ ✈✐st❛s ❛ ♠❡❧❤♦r❛r ❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦s r♦❜ôs❡♠ ✉♠ ❣r✉♣♦✳ ❖s r❡s✉❧t❛❞♦s ❛♣r❡s❡♥t❛❞♦s ❡♠ ❬❘❡❦❧❡✐t✐s ❡t ❛❧✳✱ ✷✵✵✷❪ ❝♦♥t❡♠♣❧❛♠ ✉♠❛ r❡❞✉çã♦ ♥♦ ❡rr♦ ♠é❞✐♦ ❛ss♦❝✐❛❞♦ à ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡❝♦rr❡♥t❡ ❞❛ ✉t✐❧✐③❛çã♦❞❛ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦✳ ❉✐✈❡rs♦s tr❛❜❛❧❤♦s✱ ❞❡♥tr❡ ❡❧❡s ❬❑✉r❛③✉♠❡ ✫ ❍✐r♦s❡✱✶✾✾✽❪✱ ❬❩❤❛♥❣ ❡t ❛❧✳✱ ✷✵✵✹❜❪ ❡ ❬❩❤♦✉ ❡t ❛❧✳✱ ✷✵✶✶❪✱ tê♠ ❡①♣❧♦r❛❞♦ ♠ét♦❞♦s ❞❡ ♦t✐♠✐③❛çã♦♣❛r❛ ✐❞❡♥t✐✜❝❛r ❛ ♠❡❧❤♦r ♣♦s✐çã♦ ❞♦s r♦❜ôs ♥♦ ❣r✉♣♦✳ ❚r❛✇♥② ✫ ❇❛r❢♦♦t ❬✷✵✵✹❪ ❛♣r❡✲ s❡♥t❛♠ ✉♠❛ ❛❜♦r❞❛❣❡♠ ♣❛r❛ ♦t✐♠✐③❛r tr❛❥❡tór✐❛s ✐♥t❡✐r❛s ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❞♦ ❣r✉♣♦✳❖ ♠ét♦❞♦ ❡st✐♠❛ ❛ ♠❡❧❤♦r ❢♦r♠❛çã♦ ♣❛r❛ ♦ ❣r✉♣♦ ❞❡ ❢♦r♠❛ ❛ ♣r✐✈✐❧❡❣✐❛r ❛ ❡①❡❝✉çã♦❞❡ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❆ ❛♥á❧✐s❡ ✐♥✐❝✐❛❧ ❞❡s❡♥✈♦❧✈✐❞❛ ♣♦r ❡❧❡s ✐♥❞✐❝❛ ❛❢♦r♠❛çã♦ tr✐❛♥❣✉❧❛r ❝♦♠♦ ❛ ♠❛✐s ❛❞❡q✉❛❞❛✱ ♥♦ ❡♥t❛♥t♦ ♦ ♦t✐♠✐③❛❞♦r ❛♣r❡s❡♥t♦✉ ✉♠❛ tr❛❥❡tór✐❛ r❡s✉❧t❛♥t❡ q✉❡ ♥ã♦ ♠❛♥t❡✈❡ ❛ ❢♦r♠❛çã♦ tr✐❛♥❣✉❧❛r ❞♦s r♦❜ôs✳ ❚✉❧❧② ❡t ❛❧✳ ❬✷✵✶✵❪ ❛♣r❡s❡♥t❛♠ ✉♠❛ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❞❡♥♦♠✐♥❛❞❛ ❧❡❛♣✲❢r♦❣ ♥❛ q✉❛❧ três r♦❜ôs ✉t✐❧✐③❛♠ ✉♠❛ ❢♦r♠❛çã♦ tr✐❛♥❣✉❧❛r ✈❛r✐á✈❡❧✳ ◆❡ss❡ tr❛❜❛❧❤♦✱ ✉♠❛❢♦r♠❛çã♦ é ✐♥✐❝✐❛❧♠❡♥t❡ ❡st❛❜❡❧❡❝✐❞❛ ❡st❛♥❞♦ ♦s r♦❜ôs ♣♦s✐❝✐♦♥❛❞♦s ♥♦s ✈ért✐❝❡s ❞❡ ✉♠ tr✐â♥❣✉❧♦ ❡q✉✐❧át❡r♦✳ ❉♦✐s r♦❜ôs ❡♥tã♦ ♣❡r♠❛♥❡❝❡♠ ♣❛r❛❞♦s✱ ❡♥q✉❛♥t♦ ✉♠ t❡r❝❡✐r♦ s❡♠♦✈✐♠❡♥t❛ ❛té q✉❡ ✉♠ ♥♦✈♦ tr✐â♥❣✉❧♦ ❡q✉✐❧át❡r♦ s❡❥❛ ❡st❛❜❡❧❡❝✐❞♦✳ ❆ ❝♦♦r❞❡♥❛çã♦❞❡ss❛ ♠♦✈✐♠❡♥t❛çã♦ é ❡❢❡t✉❛❞❛ ❝♦♥t✐♥✉❛♠❡♥t❡ ❛té ❝♦♠♣❧❡t❛r ❞❡t❡r♠✐♥❛❞❛ t❛r❡❢❛✳ ❖s r❡s✉❧t❛❞♦s ♠♦str❛♠ q✉❡ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❧❡❛♣✲❢r♦❣ ❛♣r❡s❡♥t❛ r❡s✉❧t❛❞♦s s✉♣❡r✐♦r❡s à♠♦✈✐♠❡♥t❛çã♦ ❝♦♠ ❢♦r♠❛çã♦ tr✐❛♥❣✉❧❛r ✜①❛✳ ❖ tr❛❜❛❧❤♦ ❞❡ ❍✐❞❛❦❛ ❡t ❛❧✳ ❬✷✵✵✺❪ ❞✐❢❡r❡ ❞♦s ❞❡s❝r✐t♦s ❛♥t❡r✐♦r♠❡♥t❡ ♣♦r ❝♦♥✲ s✐❞❡r❛r ✉♠ ❣r✉♣♦ ❞❡ r♦❜ôs q✉❡ s❡ ♠♦✈✐♠❡♥t❛ ❡♥q✉❛♥t♦ ♠❛♥té♠ ❛ ❢♦r♠❛çã♦✳ ◆❡ss❡tr❛❜❛❧❤♦ é ♣r♦♣♦st♦ ✉♠ ♠ét♦❞♦ ♣❛r❛ ♦t✐♠✐③❛r ❛ ❣❡♦♠❡tr✐❛ ❞❛ ❢♦r♠❛çã♦ ❞♦ ❣r✉♣♦ ❝♦♠♦ ♣r♦♣ós✐t♦ ❞❡ ♦❜t❡r ✉♠❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♠ ♠á①✐♠❛ ❡①❛t✐❞ã♦✳ ❘♦❜ôs ❤❡t❡r♦❣ê♥❡♦s sã♦✉t✐❧✐③❛❞♦s✱ s❡♥❞♦ q✉❡ ✉♠ ❞❡❧❡s ♣♦ss✉✐ s❡♥s♦r❡s q✉❡ ♣r♦✈❡❡♠ ❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛✳ ❖s r❡s✉❧t❛❞♦s ♠♦str❛♠ q✉❡ ♥✉♠❛ ❢♦r♠❛çã♦ ♦♥❞❡ ♦s r♦❜ôs sã♦✱ três ❛ três✱ ♣♦s✐❝✐♦♥❛❞♦s♥♦s ✈ért✐❝❡s ❞❡ ✉♠ tr✐â♥❣✉❧♦ ❡q✉✐❧át❡r♦✱ t❡♥❞♦ ♦ r♦❜ô ❝♦♠ ❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛ s✐❞♦♣♦s✐❝✐♦♥❛❞♦ ♥♦ ❝❡♥tr♦ ❞♦ ❣r✉♣♦✱ ❝♦♥s✐st❡ ♥❛ ❢♦r♠❛çã♦ ót✐♠❛ ♣❛r❛ s❡ ❡❢❡t✉❛r ❧♦❝❛❧✐③❛çã♦❝♦♦♣❡r❛t✐✈❛✳ ✸✳✸✳ ❊s❝❛❧❛❜✐❧✐❞❛❞❡ ❡♠ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛ ✺✸❆❧t❡r♥❛t✐✈❛♠❡♥t❡✱ ❛❧❣✉♥s tr❛❜❛❧❤♦s ❡♠ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ t❛✐s ❝♦♠♦ ❬❨❛♦ ❡t ❛❧✳✱ ✷✵✵✾❪ ❡ ❬❩❤♦✉ ❡t ❛❧✳✱ ✷✵✶✶❪✱ tê♠ ❡①♣❧♦r❛❞♦ ❡str❛té❣✐❛s ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❡♠ q✉❡♦ ❣r✉♣♦ ♣♦ss✉✐ ✉♠ ❧í❞❡r ✭❡str❛té❣✐❛s ❧❡❛❞❡r✲❢♦❧❧♦✇❡r✮✳ ❊♠ ❬❩❤♦✉ ❡t ❛❧✳✱ ✷✵✶✶❪✱ ♦ ❧í❞❡r❛t✉❛ ❞❡ ♠❛♥❡✐r❛ ✐♥❞❡♣❡♥❞❡♥t❡ ❡ ♦ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦ ❝♦♥s✐st❡ ❡♠ ✐❞❡♥t✐✜❝❛r ✉♠❛❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ♣❛r❛ ♦s s❡❣✉✐❞♦r❡s q✉❡ ♠✐♥✐♠✐③❡ ❛ ✐♥❝❡rt❡③❛ ❞❡ ❧♦❝❛❧✐③❛✲çã♦✳ ❖s ❡①♣❡r✐♠❡♥t♦s ❢♦r❛♠ ❡❢❡t✉❛❞♦s ❝♦♠ três r♦❜ôs✱ s❡♥❞♦ ✉♠ ❧í❞❡r ❡ ❞♦✐s s❡❣✉✐❞♦r❡s✉t✐❧✐③❛♥❞♦ ♠❡❞✐❞❛s ❞❡ ♦❜s❡r✈❛çã♦ ❞✐st✐♥t❛s ✭❞✐stâ♥❝✐❛ ♦✉ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛s✮✳ ❖ tr❛✲❜❛❧❤♦ ❛♣r❡s❡♥t♦✉ ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❞♦ q✉❡ ♦s ♠ét♦❞♦s ❝♦♥❢r♦♥t❛❞♦s✱ ❞❡♥tr❡ ❡❧❡s ❛♦❞♦♠❡tr✐❛ ❡ ♦ ♠ét♦❞♦ ♣r♦♣♦st♦ ❡♠ ❬▼❛r✐♦tt✐♥✐ ❡t ❛❧✳✱ ✷✵✵✾❪✳ ❊str❛té❣✐❛s ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ♣♦❞❡♠ ✐♥✢✉❡♥❝✐❛r ❛ ❢r❡q✉ê♥❝✐❛ ❝♦♠ q✉❡ ❡st✐♠❛t✐✈❛s❞❡ ❧♦❝❛❧✐③❛çã♦ sã♦ ❡❢❡t✉❛❞❛s✳ ◆♦s tr❛❜❛❧❤♦s ❞❡ ❑✉r❛③✉♠❡ ❡t ❛❧✳ ❬✶✾✾✻❪ ❡ ❘❡❦❧❡✐t✐s ❡t ❛❧✳❬✷✵✵✵❪✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦ ❣r✉♣♦ ❞❡ r♦❜ôs s❡ ❞á ❞❡ ❢♦r♠❛ ❝♦♦r❞❡♥❛❞❛ ❡❡t❛♣❛s ❞❡ ❛t✉❛❧✐③❛çã♦ ❞❛ ❝r❡♥ç❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ♦❝♦rr❡♠ ❡♠ ✐♥t❡r✈❛❧♦s r❡❣✉❧❛r❡s✱ t❡♥❞♦❡♠ ✈✐st❛ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡ ♠❛♥t❡r ❝♦♥t❛t♦ ✈✐s✉❛❧ ❡♥tr❡ ♦s r♦❜ôs✳ ❊♠ ❬❘♦✉♠❡❧✐♦t✐s✫ ❇❡❦❡②✱ ✷✵✵✵❛❪✱ ♣♦r ♦✉tr♦ ❧❛❞♦✱ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦ ❣r✉♣♦ é ❡❢❡t✉❛❞❛ ❞❡ ♠❛♥❡✐r❛♥ã♦ ❝♦♦r❞❡♥❛❞❛ ❡ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♦❝♦rr❡♠ s❡♠♣r❡ q✉❡ ❞♦✐s r♦❜ôs s❡❡♥❝♦♥tr❛♠✳ ❯♠❛ ✈❡③ q✉❡ ♦s ❡♥❝♦♥tr♦s ♦❝♦rr❡♠ ♣♦r ❛❝❛s♦✱ ❛ ❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦❞❡ ✉♠ r♦❜ô ♣♦❞❡ ❛❝✉♠✉❧❛r ✉♠ ♥í✈❡❧ ❡❧❡✈❛❞♦ ❞❡ ✐♥❝❡rt❡③❛ ❡ ❝♦♠♣r♦♠❡t❡r ❛ ✉t✐❧✐③❛çã♦❞♦ ♠❡s♠♦ ❝♦♠♦ ♠❛r❝♦✳ ❆♣❡s❛r ❞❡ss❡s tr❛❜❛❧❤♦s ♥ã♦ ✉t✐❧✐③❛r❡♠ ♦ ♥í✈❡❧ ❞❡ ✐♥❝❡rt❡③❛❝♦♠♦ ❝r✐tér✐♦ ♣❛r❛ s❡ ❞❡✜♥✐r ❛ ❢r❡q✉ê♥❝✐❛ ❝♦♠ q✉❡ ❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ sã♦❛t✉❛❧✐③❛❞❛s✱ t❛❧ ❝r✐tér✐♦ s❡ ♠♦str❛ ❛❞❡q✉❛❞♦ ♣❛r❛ ♦ ❡st❛❜❡❧❡❝✐♠❡♥t♦ ❞❡ ✉♠❛ r❡❣✉❧❛r✐❞❛❞❡♥❛s ❛t✉❛❧✐③❛çõ❡s✳ P❛r❛ ✐ss♦✱ ❢❛③✲s❡ ♥❡❝❡ssár✐♦ q✉❡ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❡st❡❥❛♠❞✐s♣♦♥í✈❡✐s ❝♦♠ ♠❛✐s ❢r❡q✉ê♥❝✐❛✳ ✸✳✸ ❊s❝❛❧❛❜✐❧✐❞❛❞❡ ❡♠ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛ ❆ ✐♥✢✉ê♥❝✐❛ ❞♦ t❛♠❛♥❤♦ ❞♦ ❣r✉♣♦ ♥❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❢♦✐ ❛♥❛❧✐s❛❞❛❡♠ ❛❧❣✉♥s tr❛❜❛❧❤♦s✳ ❘❡❦❧❡✐t✐s ❡t ❛❧✳ ❬✷✵✵✷❪ ❛✈❛❧✐❛♠ ❡ss❡ ❛s♣❡❝t♦✱ ♣♦r ♠❡✐♦ ❞❡ s✐♠✉❧❛✲çõ❡s✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ♦ t✐♣♦ ❞❡ ♠❡❞✐❞❛ s❡♥s♦r✐❛❧ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❡st✐♠❛r ❛s ❞✐stâ♥❝✐❛s ❡♦r✐❡♥t❛çõ❡s r❡❧❛t✐✈❛s ❡♥tr❡ ♦s r♦❜ôs✳ ❆♣❡s❛r ❞♦s r❡s✉❧t❛❞♦s ♠♦str❛r❡♠ q✉❡ ♦ ❛❝rés❝✐♠♦❞❡ r♦❜ôs ♥♦ ❣r✉♣♦ r❡❞✉③ ❛ ✐♥❝❡rt❡③❛ ❞❡ ❧♦❝❛❧✐③❛çã♦✱ ❛❧❣✉♥s ❞❡t❛❧❤❡s r❡❧❡✈❛♥t❡s ♣❛r❛❡ss❛ ❝♦♥❝❧✉sã♦ ♥ã♦ ❢♦r❛♠ ❡①♣❧✐❝✐t❛❞♦s✳ ❖ ❛❧❝❛♥❝❡ s❡♥s♦r✐❛❧ ❡ ♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs ♠❛r❝♦✉t✐❧✐③❛❞♦s ♣❛r❛ s❡ ❡❢❡t✉❛r ❛ ❧♦❝❛❧✐③❛çã♦ sã♦ ❞♦✐s ❞❡ss❡s ❛s♣❡❝t♦s✳ ❘♦✉♠❡❧✐♦t✐s ✫ ❘❡❦❧❡✐t✐s ❬✷✵✵✹❪ t❛♠❜é♠ ❛♣r❡s❡♥t❛♠ ✉♠❛ ❛♥á❧✐s❡ ♣❛r❛ ❛ q✉❛❧✐❞❛❞❡❞❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♠ r❡s♣❡✐t♦ ❛♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs ♥♦ ❣r✉♣♦✳ ◆❡ss❡ tr❛❜❛❧❤♦✱ ♦s r♦❜ôs s❡♠♦✈✐♠❡♥t❛♠ ❝♦♥t✐♥✉❛♠❡♥t❡ ❞❡ ♠❛♥❡✐r❛ ♥ã♦ ❝♦♦r❞❡♥❛❞❛✳ ➱ ❝♦♥s✐❞❡r❛❞♦ q✉❡ ❝❛❞❛ r♦❜ô ✺✹ ❈❛♣ít✉❧♦ ✸✳ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s♠❡❞❡ ❝♦♥t✐♥✉❛♠❡♥t❡ ❛ ♣♦s✐çã♦ ❞❡ t♦❞♦s ♦s ❞❡♠❛✐s r♦❜ôs ♥♦ ❣r✉♣♦✱ ❛❧é♠ ❞❡ ♣♦ss✉✐r♦r✐❡♥t❛çã♦ ❛❜s♦❧✉t❛ ❝♦♠ ❡①❛t✐❞ã♦ ❧✐♠✐t❛❞❛✳ ❈♦♥s✐❞❡r❛♥❞♦ ❡ss❛s s✉♣♦s✐çõ❡s✱ ♦s ❛✉t♦✲ r❡s ❛♣r❡s❡♥t❛♠ ✉♠ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❛♥❛❧ít✐❝♦ ❝✉❥♦ r❡s✉❧t❛❞♦ ❡st❛❜❡❧❡❝❡ q✉❡ ❛ t❛①❛ ❞❡❝r❡s❝✐♠❡♥t♦ ❞❛ ✐♥❝❡rt❡③❛ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❣r✉♣♦ é ✐♥✈❡rs❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ ♥ú✲♠❡r♦ ❞❡ r♦❜ôs✳ ❆♣❡s❛r ❞❡ss❡ r❡s✉❧t❛❞♦✱ ♦s ❡①♣❡r✐♠❡♥t♦s r❡❛✐s ❡ s✐♠✉❧❛❞♦s ❡♥✈♦❧✈❡r❛♠♥♦ ♠á①✐♠♦ ❝✐♥❝♦ r♦❜ôs✳ ❆ s✉♣♦s✐çã♦ ❞❡ q✉❡ ❝❛❞❛ r♦❜ô ♠❡❞❡ ❝♦♥t✐♥✉❛♠❡♥t❡ ✐♥❢♦r♠❛✲çõ❡s r❡❧❛t✐✈❛s ❛ t♦❞♦s ♦s ♠❡♠❜r♦s ❞♦ ❣r✉♣♦ ❧✐♠✐t❛ ❛ ❣❡♥❡r❛❧✐③❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ♣❛r❛❣r❛♥❞❡s ❣r✉♣♦s ❞❡ r♦❜ôs✳ ❙❝❤♥❡✐❞❡r ✫ ❲✐❧❞❡r♠✉t❤ ❬✷✵✶✷❪ ❛♣r❡s❡♥t❛♠ ✉♠ ❡st✉❞♦ ❛ r❡s♣❡✐t♦ ❞❛ ✐♥✢✉ê♥❝✐❛❞♦ t❛♠❛♥❤♦ ❞♦ ❣r✉♣♦ ❞❡ r♦❜ôs ♥❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❖ ❝❡♥ár✐♦✉t✐❧✐③❛❞♦ é ✉♠ ❛♠❜✐❡♥t❡ ❡stát✐❝♦ ❡ ♦s r♦❜ôs ♥ã♦ ♣♦ss✉❡♠ ❝♦♥❤❡❝✐♠❡♥t♦ ♣ré✈✐♦ ❛ r❡s♣❡✐t♦❞♦ ♠❡s♠♦✳ ❖s r♦❜ôs sã♦ ✉t✐❧✐③❛❞♦s ❝♦♠♦ ♠❛r❝♦s ❡ ♣r♦✈❡❡♠ ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦♣❛r❛ ♦s ❞❡♠❛✐s✳ ❯♠ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥ ❊st❡♥❞✐❞♦ ♣r♦❝❡ss❛ s❡q✉❡♥❝✐❛❧♠❡♥t❡ t♦❞♦s ♦s❞❛❞♦s ❡♥✈✐❛❞♦s ♣❡❧♦s r♦❜ôs ❡ ♠❛♥té♠ ✉♠❛ ú♥✐❝❛ ❡st✐♠❛t✐✈❛ ❞♦ ❡st❛❞♦ ❞♦ s✐st❡♠❛✳ ❖s❡①♣❡r✐♠❡♥t♦s sã♦ ❡①❡❝✉t❛❞♦s ❝♦♠ ✉♠ ♥ú♠❡r♦ ✈❛r✐á✈❡❧ ❞❡ r♦❜ôs✱ ❝♦♠ ❣r✉♣♦s ❝♦♠♣♦st♦s❞❡ ❞♦✐s ❛ ❝✐♥❝♦ ✐♥t❡❣r❛♥t❡s✳ ❆ ❢♦r♠❛çã♦ ✭t♦♣♦❧♦❣✐❛✮ ❞♦ ❣r✉♣♦ é ❡st❛t✐❝❛♠❡♥t❡ ❞❡✜♥✐❞❛❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ t❛♠❛♥❤♦ ❞♦ ♠❡s♠♦✳ ❆ ❤✐♣ót❡s❡ ✐♥✐❝✐❛❧ ❞♦s ❛✉t♦r❡s ❞❡ q✉❡ ❛ ♣r❡❝✐sã♦❞❛ ❧♦❝❛❧✐③❛çã♦ ♠❡❧❤♦r❛r✐❛ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞♦ t❛♠❛♥❤♦ ❞♦ ❣r✉♣♦ ♥ã♦ ❢♦✐ ❝♦♥✜r♠❛❞❛ ♥❛s s✐♠✉❧❛çõ❡s✱ t❡♥❞♦ ❡♠ ✈✐st❛ q✉❡ ❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❢♦✐ ❛❢❡t❛❞❛ ❞✐r❡t❛♠❡♥t❡ ♣❡❧♦t✐♣♦ ❞❡ ❝❡♥ár✐♦ ✉t✐❧✐③❛❞♦✳ ✸✳✹ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ❆ ❚❛❜❡❧❛ ✸✳✶ r❡s✉♠❡ ❛❧❣✉♠❛s ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦s ♠ét♦❞♦s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛✲ t✐✈❛ ❞❡s❝r✐t♦s ♥♦s ♣r✐♥❝✐♣❛✐s tr❛❜❛❧❤♦s r❡✈✐s❛❞♦s✳ ❖ ♠ét♦❞♦ ♣r♦❜❛❜✐❧íst✐❝♦ ❡♠♣r❡❣❛❞♦❡♠ ❝❛❞❛ tr❛❜❛❧❤♦ é ✐♥❞✐❝❛❞♦✿ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥ ✭❑❋✮✱ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥ ❊st❡♥❞✐❞♦✭❊❑❋✮✱ ▼❛①✐♠✉♠ à P♦st❡r✐♦r✐ ✭▼❆P✮✱ ❋✐❧tr♦ ❞❡ P❛rtí❝✉❧❛s ❞♦ ✐♥❣❧ês P❛rt✐❝❧❡ ❋✐❧t❡r✭P❋✮ ❡ ♦s ❛❧❣♦r✐t♠♦s ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s ✭❈■✮✳ ❉♦✐s t✐♣♦s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦❞❛ ❧♦❝❛❧✐③❛çã♦ ❢♦r❛♠ ❡♠♣r❡❣❛❞♦s✿ ❝❡♥tr❛❧✐③❛❞♦ ✭❈✮ ❡ ❞✐str✐❜✉í❞♦✴❞❡s❝❡♥tr❛❧✐③❛❞♦ ✭❉✮✳❆ ❢r❡q✉ê♥❝✐❛ ❝♦♠ q✉❡ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ sã♦ ❡❢❡t✉❛❞❛s ❢♦✐ ✐♥❞✐❝❛❞❛✱ ❞❡♠♦❞♦ q✉❡ ❘❡❣✉❧❛r ✐♥❞✐❝❛ q✉❡ ❛ ♠❡s♠❛ ♦❝♦rr❡ r❡❣✉❧❛r♠❡♥t❡ ❛♣ós ❛❧❣✉♠ t✐♣♦ ❞❡ ♠♦✈✐✲♠❡♥t❛çã♦ t❡r s✐❞♦ ❡①❡❝✉t❛❞♦ ♦✉ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❞✐stâ♥❝✐❛ t❡r s✐❞♦ ♣❡r❝♦rr✐❞❛ ♣❡❧♦s r♦❜ôs✳ ❆ ❝♦♠♣♦s✐çã♦ ❞♦ ❣r✉♣♦ é ❛♣r❡s❡♥t❛❞❛✱ s❡♥❞♦ q✉❡ ❛❧❣✉♥s tr❛❜❛❧❤♦s sã♦ ✢❡①í✲✈❡✐s ♦ s✉✜❝✐❡♥t❡ ♣❛r❛ t❡r❡♠ s❡✉s ♠♦❞❡❧♦s ❛❞❛♣t❛❞♦s ♣❛r❛ ♦s ❞♦✐s t✐♣♦s ❞❡ ❝♦♠♣♦s✐çã♦✿❍♦♠♦❣ê♥❡❛ ❡ ❍❡t❡r♦❣ê♥❡❛✳ ❆ ❞❡s❝r✐çã♦ ❞♦ t✐♣♦ ❞❡ ❡st✉❞♦ ✭t❡ór✐❝♦ ✭❚✮✱ s✐♠✉❧❛❞♦ ✭❙✮❡ ❡①♣❡r✐♠❡♥t❛❧ ✭❊✮✮ ❡♠♣r❡❣❛❞♦✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ♦ q✉❛♥t✐t❛t✐✈♦ ❞❡ r♦❜ôs ✉t✐❧✐③❛❞♦ sã♦ ✸✳✹✳ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s✺✺ ✐♥❞✐❝❛❞♦s✳ ❊st✉❞♦s q✉❡ ✈❛r✐❛r❛♠ ♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs ♣♦ss✉❡♠ t❛❧ ✐♥❢♦r♠❛çã♦ r❡♣r❡s❡♥✲ t❛❞❛ ♣♦r ✉♠❛ ❢❛✐①❛ ❞❡ ✈❛❧♦r❡s ✭min − max✮✱ ✐♥❞✐❝❛♥❞♦ q✉❡ ❢♦r❛♠ ✉t✐❧✐③❛❞♦s ❞❡s❞❡ min❛té max r♦❜ôs✳❚❛❜❡❧❛ ✸✳✶✿ ❘❡s✉♠♦ ❞❡ ❛❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦s ♠ét♦❞♦s ❞❡s❝r✐t♦s ♥♦s tr❛❜❛❧❤♦s r❡✲✈✐s❛❞♦s✳ ❖ ♣r♦❝❡ss♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ é ❝❛r❛❝t❡r✐③❛❞♦ ♣❡❧♦ ♠ét♦❞♦ ♣r♦❜❛❜✐❧íst✐❝♦ ✉t✐❧✐③❛❞♦✭▼ét♦❞♦✮✱ ♣❡❧❛ ❢♦r♠❛ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ✉t✐❧✐③❛❞❛ ✭❈❡♥tr❛❧✐③❛❞♦ ✭❈✮ ♦✉ ❉✐str✐❜✉í❞♦✭❉✮✮ ❡ ♣❡❧❛ ❢r❡q✉ê♥❝✐❛ ❝♦♠ q✉❡ ♦ ❛❥✉st❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ é ❡❢❡t✉❛❞❛✳ ❆ ❝♦♠♣♦s✐çã♦ ❞♦❣r✉♣♦ é ❛♣r❡s❡♥t❛❞❛✱ ❛❧é♠ ❞♦ t✐♣♦ ❞❡ ❡st✉❞♦ ❡♠♣r❡❣❛❞♦✿ t❡ór✐❝♦ ✭❚✮✱ s✐♠✉❧❛çã♦ ✭❙✮♦✉ ❡①♣❡r✐♠❡♥t♦s ❝♦♠ r♦❜ôs r❡❛✐s ✭❊✮✳ ❆ q✉❛♥t✐❞❛❞❡ ❞❡ r♦❜ôs ✭s✐♠✉❧❛❞♦s ♦✉ r❡❛✐s✮ ✉t✐✲❧✐③❛❞❛ ♥♦ ❡st✉❞♦ é ✐♥❞✐❝❛❞❛✳ ❆ ♥♦♠❡♥❝❧❛t✉r❛ min − max ♥❛ ❝♦❧✉♥❛ ❘♦❜ôs ✐♥❞✐❝❛ q✉❡♦s ❡①♣❡r✐♠❡♥t♦s ❢♦r❛♠ ❡❢❡t✉❛❞♦s ✈❛r✐❛♥❞♦ ♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs ❞❡s❞❡ min ❛té max✳ ❚r❛❜❛❧❤♦ ▲♦❝❛❧✐③❛çã♦❈♦♠♣♦s✐çã♦ ❊st✉❞♦ ▼ét♦❞♦ ▼♦❞❡❧♦ ❋r❡q✉ê♥❝✐❛ ❚✐♣♦ ❘♦❜ôs ❬❑✉r❛③✉♠❡ ❡t ❛❧✳✱ ✶✾✾✹❪ ✲ ❈ ❘❡❣✉❧❛r ❍❡t❡r♦❣ê♥❡❛ ❚ ✲❬❑✉r❛③✉♠❡ ❡t ❛❧✳✱ ✶✾✾✻❪ ✲ ❈ ❘❡❣✉❧❛r ❍❡t❡r♦❣ê♥❡❛ ❊ ✸ ❬❋♦① ❡t ❛❧✳✱ ✷✵✵✵❪ P❋ ❈ ❊♥❝♦♥tr♦ ❍❡t❡r♦❣ê♥❡❛ ❚ ✴ ❙ ✽❬❘❡❦❧❡✐t✐s ❡t ❛❧✳✱ ✷✵✵✵❪ ✲ ❈ ❘❡❣✉❧❛r ❍❡t❡r♦❣ê♥❡❛ ❚ ✴ ❙ ✷ ❬❘♦✉♠❡❧✐♦t✐s ✫ ❇❡❦❡②✱ ✷✵✵✵❜❪ ❑❋ ❈ ✴ ❉ ❊♥❝♦♥tr♦ ❍♦♠♦❣ê♥❡❛ ❚ ✴ ❙ ✸❬❆r❛♠❜❡❧ ❡t ❛❧✳✱ ✷✵✵✶❪ ❈■ ❉ ❘❡❣✉❧❛r ❍♦♠♦❣ê♥❡❛ ❙ ✺ ❬❘❡❦❧❡✐t✐s ❡t ❛❧✳✱ ✷✵✵✷❪ ❑❋ ❈ ❘❡❣✉❧❛r ❍♦♠♦❣ê♥❡❛ ❚ ✴ ❙ ✸ − ✹✵❬❚r❛✇♥② ✫ ❇❛r❢♦♦t✱ ✷✵✵✹❪ ❊❑❋ ❈ ❘❡❣✉❧❛r ❍♦♠♦❣ê♥❡❛ ❚ ✴ ❙ ✸ ❬❩❤❛♥❣ ❡t ❛❧✳✱ ✷✵✵✹❛❪ ✲ ❈ ❊♥❝♦♥tr♦ ❍♦♠♦❣ê♥❡❛ ❚ ✴ ❊ ✸ − ✺❬❍✐❞❛❦❛ ❡t ❛❧✳✱ ✷✵✵✺❪ ❊❑❋ ❈ ❘❡❣✉❧❛r ❍♦♠♦❣ê♥❡❛ ❚ ✸ − ✻ ❬▼❛rt✐♥❡❧❧✐ ❡t ❛❧✳✱ ✷✵✵✺❪ ❊❑❋ ❈ ❊♥❝♦♥tr♦ ❍♦♠♦❣ê♥❡❛ ❙ ✷ − ✼❬▼❛r✐♦tt✐♥✐ ❡t ❛❧✳✱ ✷✵✵✾❪ ❊❑❋ ❈ ❘❡❣✉❧❛r ❍♦♠♦❣ê♥❡❛ ❙ ✸ ❬◆❡r✉r❦❛r ❡t ❛❧✳✱ ✷✵✵✾❪ ▼❆P ❉ ❘❡❣✉❧❛r ❍♦♠♦❣ê♥❡❛ ❚ ✴ ❙ ✶✽❬❚✉❧❧② ❡t ❛❧✳✱ ✷✵✶✵❪ ❊❑❋ ❈ ❘❡❣✉❧❛r ❍♦♠♦❣ê♥❡❛ ❙ ✴ ❊ ✸ ❬❇❛✐❧❡② ❡t ❛❧✳✱ ✷✵✶✶❪ ❊❑❋ ❉ ❊♥❝♦♥tr♦ ❍❡t❡r♦❣ê♥❡❛ ❊ ✸❬❩❤♦✉ ❡t ❛❧✳✱ ✷✵✶✶❪ ❊❑❋ ❈ ❘❡❣✉❧❛r ❍♦♠♦❣ê♥❡❛ ❚ ✴ ❊ ✸ ❬❙❝❤♥❡✐❞❡r ✫ ❲✐❧❞❡r♠✉t❤✱ ✷✵✶✷❪ ❊❑❋ ❈ ❊♥❝♦♥tr♦ ❍❡t❡r♦❣ê♥❡❛ ❚ ✴ ❙ ✷ − ✺❬▲✐ ✫ ◆❛s❤❛s❤✐❜✐✱ ✷✵✶✷❪ ❈■ ❉ ❘❡❣✉❧❛r ❍♦♠♦❣ê♥❡❛ ❙ ✽ ❬▲✐ ❡t ❛❧✳✱ ✷✵✶✸❪ ❈■ ❉ ❘❡❣✉❧❛r ❍♦♠♦❣ê♥❡❛ ❙ ✽❬❈❛rr✐❧❧♦✲❆r❝❡ ❡t ❛❧✳✱ ✷✵✶✸❪ ❈■ ❉ ❘❡❣✉❧❛r ❍♦♠♦❣ê♥❡❛ ❙ ✴ ❊ ✸ ✴ ✹ ❬❲❛♥❛s✐♥❣❤❡ ❡t ❛❧✳✱ ✷✵✶✹❪ ❈■ ❉ ❘❡❣✉❧❛r ❍♦♠♦❣ê♥❡❛ ❙ ✸❊❙❚❆ P❘❖P❖❙❚❆ ❊❑❋ ✴ ❈■ ❉ ❘❡❣✉❧❛r ❍❡t❡r♦❣ê♥❡❛ ❙ ✴ ❊ ❛té ✶✵✵ ❆ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ t❡♠ ❛♣r❡s❡♥t❛❞♦ r❡s✉❧t❛❞♦s s❛t✐s❢❛tór✐♦s ❡♠ s✐st❡♠❛s♠✉❧t✐rr♦❜ôs✳ ◆❡ss❡ ❝♦♥t❡①t♦✱ ♦s ❡♥❝♦♥tr♦s ❡♥tr❡ ♦s r♦❜ôs ❞❡s❡♠♣❡♥❤❛♠ ✉♠ ♣❛♣❡❧ ❡s✲ s❡♥❝✐❛❧ ♥❛s ❡t❛♣❛s ❞❡ ❛t✉❛❧✐③❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❆ ❢r❡q✉ê♥❝✐❛ ❞❡ss❡s❡♥❝♦♥tr♦s✱ ♦ ♠♦♠❡♥t♦ ❞♦ ❛❥✉st❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❡ ❛ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ✉t✐❧✐✲③❛❞❛ ♣♦❞❡♠ ✐♥✢✉❡♥❝✐❛r ❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❣r✉♣♦✳ ❈♦♥❢♦r♠❡ ❞✐s❝✉t✐❞♦ ♥❡st❡❝❛♣ít✉❧♦✱ ❞✐✈❡rs♦s ❛s♣❡❝t♦s ❞❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ tê♠ s✐❞♦ ❡①♣❧♦r❛❞♦s ♥❛ ❧✐t❡r❛✲ t✉r❛✳ ◆♦ ❡♥t❛♥t♦✱ ❛ ♠❛✐♦r✐❛ ❞♦s tr❛❜❛❧❤♦s tê♠ ✉t✐❧✐③❛❞♦ ✉♠ ♥ú♠❡r♦ r❡str✐t♦ ❞❡ r♦❜ôs ❡❛ ❡①t❡♥sã♦ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❛r❛ ❣r❛♥❞❡s ❣r✉♣♦s ❛✐♥❞❛ é ♣♦✉❝♦ ❡①♣❧♦r❛❞❛✳ ❆❧é♠❞✐ss♦✱ ❛❧❣✉♠❛s s✉♣♦s✐çõ❡s ✉t✐❧✐③❛❞❛s ♥❡ss❡s tr❛❜❛❧❤♦s✱ t❛✐s ❝♦♠♦ ♦ ❛❝❡ss♦ à t♦❞❛ ✐♥❢♦r✲♠❛çã♦ ❞✐s♣♦♥í✈❡❧ ♥♦ ❣r✉♣♦ ❡ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❡ ✐♥t❡r❛çã♦ ❡♥tr❡ t♦❞♦s ♦s r♦❜ôs✱ ♣♦❞❡♠ ♥ã♦ s❡r r❛③♦á✈❡✐s q✉❛♥❞♦ s❡ t❡♠ ✉♠ s✐st❡♠❛ ❝♦♠♣♦st♦ ♣♦r ✉♠ ♥ú♠❡r♦ ✺✻ ❈❛♣ít✉❧♦ ✸✳ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s♠❛✐♦r ❞❡ r♦❜ôs✳ ❉❡✈✐❞♦ às ❝❛♣❛❝✐❞❛❞❡s ❧✐♠✐t❛❞❛s ❞❡ s❡♥s♦r✐❛♠❡♥t♦ ❡ ♣r♦❝❡ss❛♠❡♥t♦❞♦s r♦❜ôs q✉❡ ♥♦r♠❛❧♠❡♥t❡ ❝♦♠♣õ❡♠ ✉♠ ❡♥①❛♠❡✱ ❢❛③✲s❡ ♥❡❝❡ssár✐♦ ❡str❛té❣✐❛s ❞❡ ❧♦✲❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ q✉❡ ❝♦♥s✐❞❡r❡♠ ✉♠ ♥ú♠❡r♦ r❡str✐t♦ ❞❡ r♦❜ôs ♠❛r❝♦s✱ t❡♥❞♦ ❡♠✈✐st❛ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦ ❡ ❡s♣❛ç♦ ♣❛r❛ ♣r♦❝❡ss❛♠❡♥t♦ ❞❛s ✐♥❢♦r♠❛çõ❡s✳ ❈♦♥✲❢♦r♠❡ s❡rá ❛♣r❡s❡♥t❛❞♦ ♥♦ ❝❛♣ít✉❧♦ ❞❡ ❡①♣❡r✐♠❡♥t♦s✱ ❛ ❛t✉❛❧✐③❛çã♦ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ❞❛s❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ✉t✐❧✐③❛♥❞♦ ✉♠ ♥ú♠❡r♦ r❡str✐t♦ ❞❡ ♠❛r❝♦s ❡ ❛ ✉t✐❧✐③❛çã♦ ❞❡✉♠❛ ❡str❛té❣✐❛ ❞❡ ❢✉sã♦ s❡♥s♦r✐❛❧ q✉❡ ♣❡r♠✐t❛ ❧✐❞❛r ❝♦♠ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦ ❡ ❡s✲♣❛ç♦ ❡①✐st❡♥t❡ ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ ♣❡r♠✐t✐r❛♠ ❛♣❧✐❝❛r ❛ ♠❡t♦❞♦❧♦❣✐❛♣r♦♣♦st❛ ♥❡st❡ tr❛❜❛❧❤♦ ❛ ❣r✉♣♦s ❝♦♠♣♦st♦s ♣♦r ✉♠ ♥ú♠❡r♦ s✐❣♥✐✜❝❛t✐✈♦ ❞❡ r♦❜ôs✳ ❆ ♠❡t♦❞♦❧♦❣✐❛ ❛♣r❡s❡♥t❛❞❛ ❛ s❡❣✉✐r ❞❡s❝r❡✈❡ ❛ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛ ♣❛r❛ ❧♦❝❛❧✐③❛r❝♦♦♣❡r❛t✐✈❛♠❡♥t❡ ✉♠ ❡♥①❛♠❡ ❞❡ r♦❜ôs✳ ◆❡st❛ ❛❜♦r❞❛❣❡♠✱ ❛ ❧♦❝❛❧✐③❛çã♦ é ❡❢❡t✉❛❞❛ ❞❡♠❛♥❡✐r❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛✱ s❡♥❞♦ q✉❡ ❡str❛té❣✐❛s ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛ sã♦ ❡♠♣r❡✲❣❛❞❛s ♣❛r❛ ♣r♦♣✐❝✐❛r ❛ ❡①❡❝✉çã♦✱ ❝♦♠ ♠❛✐♦r ❢r❡q✉ê♥❝✐❛✱ ❞❡ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦✲♣❡r❛t✐✈❛✳ ◆❡ss❛ ❛❜♦r❞❛❣❡♠✱ ❝❛❞❛ r♦❜ô ✉t✐❧✐③❛ ❝♦♠♦ ♠❛r❝♦ s♦♠❡♥t❡ ♦s r♦❜ôs ❞✐s♣♦st♦s♥❛s ♣r♦①✐♠✐❞❛❞❡s✱ ♣❡r♠✐t✐♥❞♦ ❛ss✐♠ ❞✐♠✐♥✉✐r ♦ ❝✉st♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❞❛s ✐♥❢♦r♠❛✲çõ❡s ❡ ❧✐♠✐t❛♥❞♦ ♦ ❛❧❝❛♥❝❡ s❡♥s♦r✐❛❧✳ ❆ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❡s❛ ❞♦ ❣r✉♣♦ ❡ ❛ ✉t✐❧✐③❛çã♦❞♦s ❛❧❣♦r✐t♠♦s ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s ♣❡r♠✐t❡♠ ❛♦s r♦❜ôs ✉t✐❧✐③❛r❡♠ s♦♠❡♥t❡✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ ❞❡ ♠♦❞♦ q✉❡ ❛ ❛❜♦r❞❛❣❡♠♣r♦♣♦st❛ s❡❥❛ ❡s❝❛❧á✈❡❧ ❡✱ ♣♦rt❛♥t♦✱ ❛❞❡q✉❛❞❛ ♣❛r❛ ❡♥①❛♠❡s r♦❜ót✐❝♦s✳ ❈❛♣ít✉❧♦ ✹ ▼❡t♦❞♦❧♦❣✐❛ ❉✐✈❡rs♦s ❛s♣❡❝t♦s ❞❡✈❡♠ s❡r ❛♥❛❧✐s❛❞♦s q✉❛♥❞♦ s❡ ❞❡s❡❥❛ ❧♦❝❛❧✐③❛r ❝♦♦♣❡r❛t✐✈❛♠❡♥t❡✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ r♦❜ôs ❞❡✈✐❞♦ às ♣♦ss✐❜✐❧✐❞❛❞❡s ❛❞✈✐♥❞❛s ❞❡ s❡ t❡r ✐♥❢♦r♠❛çõ❡s❞❡ ❧♦❝❛❧✐③❛çã♦ ♠❛✐s ❛❜✉♥❞❛♥t❡s ❡ ❞✐str✐❜✉í❞❛s ♥♦ ❡♥①❛♠❡✳ ❆❧é♠ ❞✐ss♦✱ ❛s ✐♥❢♦r♠❛çõ❡s❞❡ ❧♦❝❛❧✐③❛çã♦ ❞✐s♣♦♥í✈❡✐s ♣♦❞❡♠ ❡st❛r ❛ss♦❝✐❛❞❛s à ❡st✐♠❛t✐✈❛s ❡st❛t✐st✐❝❛♠❡♥t❡ ✐♥❞❡✲♣❡♥❞❡♥t❡s ♦✉ ✐♥t❡r❞❡♣❡♥❞❡♥t❡s✱ ❞❡♣❡♥❞❡♥❞♦ ❞❡ s✉❛ ♦r✐❣❡♠✳ ❆ ♠❡t♦❞♦❧♦❣✐❛ ❛❞♦t❛❞❛♥❡st❡ tr❛❜❛❧❤♦ ❡①♣❧♦r❛ ❡ss❡s ❛s♣❡❝t♦s ❝♦♠ ✈✐st❛s ❛ ♣r♦✈❡r ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞❡s❝❡♥tr❛✲❧✐③❛❞❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♣❛r❛ ❡♥①❛♠❡s r♦❜ót✐❝♦s q✉❡ ♣♦ss❛ s❡r ✉t✐❧✐③❛❞❛ ❡♠❞✐✈❡rs❛s s✐t✉❛çõ❡s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✿ ❛♠❜✐❡♥t❡s ❡①t❡♥s♦s❀ ❛♠❜✐❡♥t❡s ❞❡s❝♦♥❤❡❝✐❞♦s♦✉ ♥ã♦ ♣r❡✈✐❛♠❡♥t❡ ❡str✉t✉r❛❞♦s❀ ❡ s✐t✉❛çõ❡s ❝♦♠ ❧✐♠✐t❛çõ❡s ❛♦ ✉s♦ ❞❡ s✐st❡♠❛s ❞❡♣♦s✐❝✐♦♥❛♠❡♥t♦ ❣❧♦❜❛❧✳ ✹✳✶ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛ ❡♠ ❊♥①❛♠❡s ❘♦❜ót✐❝♦s ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ♥❛ ❙❡çã♦ ✷✳✶✱ ♥❡st❡ tr❛❜❛❧❤♦ ♦s r♦❜ôs s❡ ♠♦✈✐♠❡♥t❛♠ ❡♠ ✉♠ ❛♠✲❜✐❡♥t❡ ♣❧❛♥❛r✳ ❖s r♦❜ôs ✉t✐❧✐③❛♠ s❡♥s♦r❡s ♣r♦♣r✐♦❝❡♣t✐✈♦s ♣❛r❛ ♠❡❞✐r s✉❛s ✈❡❧♦❝✐❞❛❞❡s i❧✐♥❡❛r❡s ❡ ❛♥❣✉❧❛r❡s✳ ❖ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ❞❡t❡r♠✐♥❛❞♦ r♦❜ô R ♣♦❞❡ s❡r ❞❡s❝r✐t♦ ♣❡❧❛s❡q✉❛çõ❡s ▼♦❞❡❧♦ ❞❡ ❛t✉❛çã♦ ˙x i = v i i ),❝♦s(θ ˙y i = v i i ), s❡♥(θ˙θ i = w i , ✭✹✳✶✮ ✺✽❈❛♣ít✉❧♦ ✹✳ ▼❡t♦❞♦❧♦❣✐❛ i i i , y , θ )i i s❡♥❞♦ (x s✉❛ ♣♦s❡ ❡♠ ✉♠ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ✐♥❡r❝✐❛❧✱ v ❡ w s✉❛s ✈❡❧♦❝✐✲ ❞❛❞❡s ❧✐♥❡❛r ❡ ❛♥❣✉❧❛r✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❆ ✈❡rsã♦ ❞✐s❝r❡t❛ ❞❡ ✭✹✳✶✮ é ❞❡s❝r✐t❛ ❛ s❡❣✉✐r✿ k+1|k k k k x = x + v )∆t,i i i ❝♦s(θ i k+1|k k k k y = y + v )∆t,i i i i k+1|k k k s❡♥(θθ = θ + w ∆t, i i i ✭✹✳✷✮ ♥❛ q✉❛❧ k r❡♣r❡s❡♥t❛ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ✐♥st❛♥t❡ ❡ ∆t ♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦✳P❛r❛ ♠❛♥t❡r ❝♦❡rê♥❝✐❛ ❝♦♠ ❛ ♥♦♠❡♥❝❧❛t✉r❛ ✉t✐❧✐③❛❞❛ ♥❛s ♣r✐♥❝✐♣❛✐s r❡❢❡rê♥❝✐❛s ❞❡ ✜❧tr❛❣❡♠ ♣r♦❜❛❜✐❧íst✐❝❛✱ ❛ r❡♣r❡s❡♥t❛çã♦ ❡♠ ❡s♣❛ç♦s ❞❡ ❡st❛❞♦s s❡rá ✉t✐❧✐③❛❞❛ ✭✈❡r❆♣ê♥❞✐❝❡s ❇ ❡ ❈✮✳ ❉❡ss❡ ♠♦❞♦✱ ❛ ✈❡rsã♦ ❡♠ ❡s♣❛ç♦ ❞❡ ❡st❛❞♦s ❞❡ ✭✹✳✷✮ é ❞❡s❝r✐t❛ ❝♦♠♦       k+1|k k k" # x x )∆ti i i ❝♦s(θ k k+1|k k k v i       y y )∆ts❡♥(θ ✭✹✳✸✮  i  =  i  +  i  k k+1|k k w iθ θ ∆t i i ♦✉ s❡❥❛✱ k+1|k k k k k k k ⊤ x = g(x , u ), i i i ✭✹✳✹✮= [x y θ ] ❡♠ q✉❡ x i i i i ❝♦♠♣r❡❡♥❞❡ ♦ ✈❡t♦r ❞❡ ❡st❛❞♦s ❞♦ r♦❜ô i ♥♦ ✐♥st❛♥t❡ k✱ k k k ⊤ u = v wi i i ❛ ❛çã♦ ❞❡ ❝♦♥tr♦❧❡ ❡ g ❛ ❢✉♥çã♦ q✉❡ ♣r♦❥❡t❛ ♦ ❡st❛❞♦ ✉♠❛ ✐t❡r❛çã♦ à❢r❡♥t❡✱ ❝♦♠ ❜❛s❡ ♥♦ ❡st❛❞♦ ❛t✉❛❧ ❡ ♥❛ ❛çã♦ ❞❡ ❝♦♥tr♦❧❡✳ o o o o ⊤ = [x y θ ]❆ ❊q✉❛çã♦ ✭✹✳✹✮✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛ ❝♦♥❞✐çã♦ ✐♥✐❝✐❛❧ x i i i i ✱ ❝♦♠♣õ❡♠ ❊st✐♠❛t✐✈❛ ♦ s✐st❡♠❛ ❞✐♥â♠✐❝♦ ❞✐s❝r❡t♦ q✉❡ ❞❡s❝r❡✈❡ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ r♦❜ô i✳ ❊ss❡ s✐st❡♠❛ ✭♣r❡❞✐çã♦✮i ❞✐♥â♠✐❝♦ ♣♦❞❡ s❡r ✉t✐❧✐③❛❞♦ ♣❛r❛ ♣r♦♣❛❣❛r ✉♠❛ ❡st✐♠❛t✐✈❛ bx ❞❛ ♣♦s❡ ❞♦ r♦❜ô k+1|k k k x x u= g( , ), ✭✹✳✺✮ k k k ⊤ k k k k k k b i b i b i w ] = v + ǫ w = w + ǫs❡♥❞♦ bu i = [bv i b i ✱ bv i i v ❡ b i i w ❛s ✈❡❧♦❝✐❞❛❞❡s ❧✐♥❡❛r ❡ ❛♥❣✉❧❛r k k♠❡❞✐❞❛s ✭♦❞♦♠❡tr✐❛✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❝♦♠ r✉í❞♦s ǫ v ❡ ǫ w ❛ss♦❝✐❛❞♦s✳ ❚❛✐s r✉í❞♦s sã♦❝♦♥s✐❞❡r❛❞♦s ✐♥❞❡♣❡♥❞❡♥t❡s ❡ ♥ã♦ ❝♦rr❡❧❛❝✐♦♥❛❞♦s✱ s❡♥❞♦ ♠♦❞❡❧❛❞♦s ♣♦r ✉♠ ♣r♦❝❡ss♦ 2 2 2 2 = E[ǫ ] = E[ǫ ]❡st♦❝ást✐❝♦ ●❛✉ss✐❛♥♦ ❜r❛♥❝♦ ❝♦♠ ♠é❞✐❛s ③❡r♦ ❡ ✈❛r✐â♥❝✐❛s σ v v ❡ σ w w 2 2 [σ σ ] = u + ǫ i i❝♦♥❤❡❝✐❞❛s✱ s❡♥❞♦ Q = ❞✐❛❣ v w ❛ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛✳ ❖✉ s❡❥❛✱ bu ❡ǫ ∼ N(0, Q)✳ l|m❆ ♥♦t❛çã♦ by r❡♣r❡s❡♥t❛ ❛ ❡st✐♠❛t✐✈❛ ❞❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ y ♥♦ ✐♥st❛♥t❡ ❞❡ t❡♠♣♦ l✱ ❞❛❞❛s ❛s ♦❜s❡r✈❛çõ❡s ❡❢❡t✉❛❞❛s ❛té ♦ ✐♥st❛♥t❡ ❞❡ t❡♠♣♦ m✳ ❖✉ s❡❥❛✱ t❛❧ ❡st✐♠❛t✐✈❛ ♥ã♦ ✐♥❝♦r♣♦r❛ q✉❛❧q✉❡r ♦❜s❡r✈❛çã♦ ❛ss♦❝✐❛❞❛ ❛♦ ✐♥st❛♥t❡ ❞❡ t❡♠♣♦ l✳ ✹✳✶✳ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛ ❡♠ ❊♥①❛♠❡s ❘♦❜ót✐❝♦s ✺✾ i❆ ✐♥❝❡rt❡③❛ ✐♥✐❝✐❛❧ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛ss♦❝✐❛❞❛ à ❡st✐♠❛❞❛ bx é ♠♦❞❡❧❛❞❛ ♣♦r ♠❡✐♦ ❞❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ♠✉❧t✐✈❛r✐❛❞❛ ❝♦♠ ♠é❞✐❛s ③❡r♦ ❡ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛ o 2 2 2 o o o oP = diag [σ σ σ ] , P ) i x y θ ✱ ♦✉ s❡❥❛✱ N(bx i ✳ ❆ ♣r♦♣❛❣❛çã♦ ❞❛ ✐♥❝❡rt❡③❛ ❞❡ ❧♦❝❛❧✐③❛✲ i i i içã♦ ♣♦❞❡ s❡r ❢❡✐t❛ ✉t✐❧✐③❛♥❞♦✲s❡ ❛ ❡t❛♣❛ ❞❡ ♣r❡❞✐çã♦ ✭❆♣ê♥❞✐❝❡ ❇✮ ❞♦ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥✿ k+1|k k k k ⊤ k k k ⊤ P P Q= Φ (Φ ) + G (G ) , i i i i i i i ✭✹✳✻✮ s❡♥❞♦   k k 1 0 )∆tk k −v i s✐♥(θ i k ∂g(x , u ) i i k k  Φ = = 0 1 v )∆t i k   i ❝♦s(θ i∂x i x i x i u i u i 0 0 1 =b =b ❡  k )∆t k k ❝♦s(θ i k i i ∂g(x , u ) k  G = = i s✐♥(θ k  i  , )∆t∂u i x x u u i i i i ∆t =b =b ♦s ❏❛❝♦❜✐❛♥♦s ❞❡ ✭✹✳✸✮ ❡♠ r❡❧❛çã♦ ❛♦ ✈❡t♦r ❞❡ ❡st❛❞♦s ❡ à ❛çã♦ ❞❡ ❝♦♥tr♦❧❡✱ r❡s♣❡❝t✐✈❛✲♠❡♥t❡✳ ❯♠❛ ❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ r❡❢❡r❡♥t❡ ❛ ✉♠ r♦❜ô R i ❝♦♥s✐st❡ ♥❛ ❛t✉❛✲ ❊t❛♣❛ ❞❡ ❧✐③❛çã♦ ❞❡ s✉❛ ❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ✭bx i ✱ P i ✮ ✉t✐❧✐③❛♥❞♦ ✐♥❢♦r♠❛çõ❡s r❡❧❛t✐✈❛s ❛♦s ▲♦❝❛❧✐③❛çã♦ r♦❜ôs ♠❛r❝♦ ❞✐s♣♦st♦s ♥❛ ✈✐③✐♥❤❛♥ç❛ N i ✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ♣❛r❛ ❣❡r❛r ❈♦♦♣❡r❛t✐✈❛✉♠❛ ♥♦✈❛ ❡st✐♠❛t✐✈❛ ✉♠ ❛❧❣♦r✐t♠♦ ót✐♠♦ ✉t✐❧✐③❛ ❛s ✐♥❢♦r♠❛çõ❡s ❞❡ t♦❞♦s ♦s ✐♥t❡❣r❛♥t❡s❞❡ ✉♠ s✐st❡♠❛ ♠✉❧t✐rr♦❜ôs✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❛❧❣♦r✐t♠♦s ❛♣r♦①✐♠❛❞♦s ✉t✐❧✐③❛♠ ✐♥❢♦r✲♠❛çõ❡s ♣r♦✈❡♥✐❡♥t❡s ❞❡ ♣❛rt❡ ❞♦ s✐st❡♠❛✳ ❚❡♥❞♦ ❡♠ ✈✐st❛ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ❡♥①❛♠❡s✱❛ ❝♦♠♣❧❡①✐❞❛❞❡ ♣❛r❛ ♣r♦❝❡ss❛♠❡♥t♦ ❡ ❛r♠❛③❡♥❛♠❡♥t♦ ❞❡ t♦❞❛ ✐♥❢♦r♠❛çã♦ ✐♥✈✐❛❜✐❧✐③❛❛ ❛♣❧✐❝❛çã♦ ❡♠ s✐st❡♠❛s r❡❛✐s✳ ❉❡ss❡ ♠♦❞♦✱ ♥❡st❡ tr❛❜❛❧❤♦ s♦♠❡♥t❡ ❛s ✐♥❢♦r♠❛çõ❡s❞✐s♣♦♥í✈❡✐s ♥❛ ✈✐③✐♥❤❛♥ç❛ ❞❡ ✉♠ r♦❜ô ♣♦❞❡rã♦ s❡r ✉t✐❧✐③❛❞❛s ❡♠ ✉♠❛ ❡t❛♣❛ ❞❡ ❧♦❝❛❧✐✲③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ ❞❡ ♠♦❞♦ q✉❡ s❡ ❢❛③ ♥❡❝❡ssár✐♦ ❛ ❞❡✜♥✐çã♦ ❞❡ ❝r✐tér✐♦s ♣❛r❛ ❛ s❡❧❡çã♦❞♦s ♠❛r❝♦s ✉t✐❧✐③❛❞♦s ❡♠ ❞❛❞♦ ♠♦♠❡♥t♦✳ ❆ ❙❡çã♦ ✹✳✸ ❛♣r❡s❡♥t❛ ✉♠❛ ❞✐s❝✉ssã♦ ❞♦s❝r✐tér✐♦s ✉t✐❧✐③❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦✳ ❘♦❜ôs ❡①❡❝✉t❛♥❞♦ ✉♠❛ ❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ s❡❧❡❝✐♦♥❛♠ ♠❛r❝♦s ❞❡♥tr❡ s❡✉s ✈✐③✐♥❤♦s ❡✱ ♣♦r ♠❡✐♦ ❞❡ s❡♥s♦r❡s ❡①t❡r♦❝❡♣t✐✈♦s✱ ❡st✐♠❛♠ ❞✐stâ♥❝✐❛ ❡ ♦r✐❡♥t❛çã♦i r❡❧❛t✐✈❛s àq✉❡❧❡s r♦❜ôs s❡❧❡❝✐♦♥❛❞♦s✳ ❆ ❋✐❣✉r❛ ✹✳✶❛ ✐❧✉str❛ ❛ s✐t✉❛çã♦ ❡♠ q✉❡ ♦ r♦❜ô Rij ij j♠❡❞❡ ❞✐stâ♥❝✐❛ ρ ❡ ♦r✐❡♥t❛çã♦ φ r❡❧❛t✐✈❛s ❛ ✉♠ r♦❜ô R ♣r❡s❡♥t❡ ❡♠ s✉❛ ✈✐③✐♥❤❛♥ç❛✳ 1 2❈♦♠♦ ❡①❡♠♣❧♦✱ ❛ ❋✐❣✉r❛ ✹✳✶❜ ✐❧✉str❛ ♠❡❞✐❞❛s ❡❢❡t✉❛❞❛s ♣♦r R r❡❧❛t✐✈❛s ❛♦s r♦❜ôs R❡ R 3 ✳ ❆s ✐♥❢♦r♠❛çõ❡s ❡stã♦ r❡♣r❡s❡♥t❛❞❛s ♥♦s s✐st❡♠❛s ❞❡ ❝♦♦r❞❡♥❛❞❛s ❧♦❝❛✐s ❛ R i ❡ ✻✵1❈❛♣ít✉❧♦ ✹✳ ▼❡t♦❞♦❧♦❣✐❛ R ✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳R 2 R jY ρ Y ρ 12 ij 1 RRi φ 12 φ ij X R X 1 θ i Ri θ 1R i R 1 φ 13X W X W ρ 13 R 3✭❛✮ ✭❜✮ ❋✐❣✉r❛ ✹✳✶✿ ❉✐stâ♥❝✐❛ ❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛s ❡♥tr❡ r♦❜ôs✳ ❊♠ ✭❛✮✱ ❛ ❞✐stâ♥❝✐❛ ρ ij ❡ ij j i♦r✐❡♥t❛çã♦ φ r❡❧❛t✐✈❛s ❛ R sã♦ ♦❜t✐❞❛s ♣♦r R ✳ ❊♠ ✭❜✮✱ ♠❡❞✐❞❛s r❡❧❛t✐✈❛s ❞❡ ♠❛✐s ❞❡1 ✉♠ r♦❜ô sã♦ t♦♠❛❞❛s ♣♦r R ✳ j i❉✐stâ♥❝✐❛ ❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛s ❛ R ✱ ♦❜t✐❞❛s ♣♦r R ♥♦ ✐♥st❛♥t❡ ❞❡ t❡♠♣♦ k✱ sã♦ k k (i, j = 1, . . . , η, i ) i❞❡♥♦t❛❞❛s✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ♣♦r ρ ij ❡ φ ij 6= j, j ∈ N ✱ ❝♦♥❢♦r♠❡ s❡❣✉❡✿   q" # k k k 2 k k 2 k k ρ (x ) + (y ) ij j − x i j − y i h(x , x )= =   .i j k k k k k k ✭✹✳✼✮ φ ij , x )❛t❛♥✷(y j − y i j − x i − θ i k k k ⊤ b ρ φ ]❊st✐♠❛t✐✈❛s r❡❧❛t✐✈❛s ❝♦♠♣r❡❡♥❞❡♠ ♦ ♠♦❞❡❧♦ ❞❡ ♦❜s❡r✈❛çã♦ z ij = [b ij ij ♥♦ ▼♦❞❡❧♦ ❞❡ i j ✐♥st❛♥t❡ k✱ ♦❝❛s✐ã♦ ❡♠ q✉❡ R ♦❜té♠ ✉♠❛ ♠❡❞✐❞❛ r❡❧❛t✐✈❛ ❛ R ✿ ♦❜s❡r✈❛çã♦ k k k k z = h(x , x ) + n . ij i j ij ✭✹✳✽✮❖ ❡rr♦ ❛❞✐t✐✈♦ ✭ǫ ρ ❡ ǫ φ ✮ ❞❡ss❛s ♠❡❞✐❞❛s é ♠♦❞❡❧❛❞♦ ♣♦r ♠❡✐♦ ❞❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ 2 2 2 2 = E[ǫ ] = E[ǫ ]❜✐✈❛r✐❛❞❛ ❝♦♠ ♠é❞✐❛s ③❡r♦ ❡ ✈❛r✐â♥❝✐❛s σ ❡ σ ✱ ❛ss♦❝✐❛❞❛s à ❞✐stâ♥❝✐❛ ρ ρ φ φ ij❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛s✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❉❡ss❡ ♠♦❞♦✱ n ❝♦♥s✐st❡ ❡♠ ✉♠ r✉í❞♦ ❛❞✐t✐✈♦ ij = diag [σ σ ] 2 2●❛✉ss✐❛♥♦ ❜r❛♥❝♦✱ ❝♦♠ ♠é❞✐❛s ③❡r♦ ❡ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛ R ρ ✱ ♦✉ φ ij ij ij ) s❡❥❛✱ n ∼ N(0, R ✳ ❆ ♠❛tr✐③ R é ❝♦♥s✐❞❡r❛❞❛ ❞✐❛❣♦♥❛❧ ❞❡✈✐❞♦ à s✉♣♦s✐çã♦ ❞❡ij ij ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❛s ♠❡❞✐❞❛s r❡❧❛t✐✈❛s ρ ❡ φ ✳ i❯♠ ❞❛❞♦ r♦❜ô R ✱ ❛t✉❛♥❞♦ ❝♦♠♦ ♠❛r❝♦✱ ❞✐ss❡♠✐♥❛ ♠❡♥s❛❣❡♥s ♥ã♦ ❞✐r❡❝✐♦♥❛❞❛s i i ✭❜r♦❛❞❝❛st✮ ❝♦♥t❡♥❞♦ s❡✉ ✐❞❡♥t✐✜❝❛❞♦r ú♥✐❝♦✱ s✉❛ ❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ✭bx ✱ P ✮ ❡ i1 i1 im im , R , . . . , z , R )✉♠❛ ❧✐st❛ ❝♦♠ ❛s ❡st✐♠❛t✐✈❛s r❡❧❛t✐✈❛s ♣❛r❛ s❡✉s m ✈✐③✐♥❤♦s (z ✱❝♦♥❢♦r♠❡ ✐❧✉str❛❞♦ ♥❛ ❋✐❣✉r❛ ✹✳✷✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❙❡çã♦ ✷✳✶✱ ✉♠❛ ✈✐③✐♥❤❛♥ç❛ é❞✐♥â♠✐❝❛✱ ❞❡ ♠♦❞♦ q✉❡ ♦ ♥ú♠❡r♦ m ❞❡ ✈✐③✐♥❤♦s ♣♦❞❡ ✈❛r✐❛r ❞✉r❛♥t❡ ❛ ❛t✉❛çã♦ ❞♦s r♦❜ôs✳ ✹✳✶✳ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛ ❡♠ ❊♥①❛♠❡s ❘♦❜ót✐❝♦s ✻✶τ (1, x 1 , P 1 , z 12 , R 12 , z 13 , R 13 ) ^ R 2 (1, x 1 , P 1 , z 12 , R 12 , z 13 , R 13 ) ^ R1 R 3 N 1❋✐❣✉r❛ ✹✳✷✿ ❉✐ss❡♠✐♥❛çã♦ ✭❜r♦❛❞❝❛st✮ ❞❡ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ♣❡❧♦ r♦❜ô ♠❛r❝♦11 R ♣❛r❛ r♦❜ôs s✐t✉❛❞♦s ❡♠ s✉❛ r❡s♣❡❝t✐✈❛ ✈✐③✐♥❤❛♥ç❛ N ✳ ❈♦♠ ❜❛s❡ ♥❛s ✐♥❢♦r♠❛çõ❡s ❞✐ss❡♠✐♥❛❞❛s ♣♦r ✉♠ r♦❜ô ❛t✉❛♥❞♦ ❝♦♠♦ ♠❛r❝♦ ✭i✱ ♣♦r❡①❡♠♣❧♦✮✱ ✉♠ ❞❛❞♦ r♦❜ô j ♣♦❞❡ ❡st❛❜❡❧❡❝❡r ✉♠❛ ♥♦✈❛ ❡st✐♠❛t✐✈❛ ❞❡ s✉❛ ♣♦s❡✳ P❛r❛ ✐ss♦✱❛s ♠❡❞✐❞❛s r❡❧❛t✐✈❛s t♦♠❛❞❛s ♣♦r R i ❞❡ R j ♣r❡❝✐s❛♠ ❡st❛r ❞✐s♣♦♥í✈❡✐s ♥❛ ♠❡♥s❛❣❡♠ r❡❝❡❜✐❞❛✱ ❛❧é♠ ❞❡ s❡r ♣♦ssí✈❡❧ ❛ R j ♠❡❞✐r ❞✐stâ♥❝✐❛ ρ ji ❡ ♦r✐❡♥t❛çã♦ φ ji r❡❧❛t✐✈❛s ❛ R i ✳⊤ = [x y θ ]◆❛ ❋✐❣✉r❛ ✹✳✸✱ ❡ ♥♦ r❡st❛♥t❡ ❞❡st❡ tr❛❜❛❧❤♦✱ ❛ ♥♦t❛çã♦ x ji ji ji ji s❡rá ✉t✐❧✐③❛❞❛ j♣❛r❛ ✐♥❞✐❝❛r q✉❡ ❛ ♣♦s❡ ❞❡ R ❢♦✐ ❡st❛❜❡❧❡❝✐❞❛ ❝♦♠ ❜❛s❡ ❡♠ ✐♥❢♦r♠❛çõ❡s r❡❧❛t✐✈❛s ❛♦ i r♦❜ô ♠❛r❝♦ R ✳ X Rj θji = ?Y Y X WRj ji Rjφ (x ,y ) = ?ji ji ρ Y ijRi YRi φ ij X Xφ Riij Riθ i θji θYi Rjφ ji X W X W✭❛✮ ✭❜✮ ❋✐❣✉r❛ ✹✳✸✿ ❈á❧❝✉❧♦ ❞❛ ♣♦s❡ ❞❡ ✉♠ r♦❜ô ❝♦♠ ❜❛s❡ ❡♠ ✉♠ r♦❜ô ♠❛r❝♦✳ ❊♠ ✭❛✮✱ ❛s ij ij ji i i♠❡❞✐❞❛s r❡❧❛t✐✈❛s ρ ✱ φ ❡ φ ✱ ❛❧é♠ ❞❛ ♣♦s❡ x ❞❡ R ✱ ♣♦❞❡♠ s❡r ✉t✐❧✐③❛❞❛s ♣❛r❛ s❡ ji j ji❝❛❧❝✉❧❛r ❛ ♣♦s❡ x ❞❡ R ✳ ❖ ❝ô♠♣✉t♦ ❞❡ θ ♣♦❞❡ s❡r ♠❡❧❤♦r ❝♦♠♣r❡❡♥❞✐❞♦ ❡♠ ✭❜✮✳ ✻✷ ji ❈❛♣ít✉❧♦ ✹✳ ▼❡t♦❞♦❧♦❣✐❛❖ ❝á❧❝✉❧♦ ❞❡ x ♣♦❞❡ s❡r ❞❡s❝r✐t♦ ♣♦r       x x ρ + θ )ji i ij ij i❝♦s(φ       y y ρ + θ )ji i ij s✐♥(φ ij i ✭✹✳✾✮  =   +   , θ θ π + φ ji i ij − φ ji♦✉ s❡❥❛✱ k k k k k x = f (x , h(x , x ), φ ), ji i i j ji ✭✹✳✶✵✮♦♥❞❡ f é ✉♠❛ ❢✉♥çã♦ ❞♦ ❡st❛❞♦ ❛t✉❛❧ ❡ ❞❛s ♠❡❞✐❞❛s r❡❧❛t✐✈❛s✳ P♦rt❛♥t♦✱ ♥❡st❡ tr❛❜❛❧❤♦✱ ❛ ❡str❛té❣✐❛ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❛❥✉st❛r ❛ ❡st✐♠❛t✐✈❛ ❞❡ ♣♦s❡❞❡ ✉♠ r♦❜ô✱ t❡♥❞♦ ❝♦♠♦ ❜❛s❡ ✐♥❢♦r♠❛çõ❡s r❡❧❛t✐✈❛s ❛ ✉♠ r♦❜ô ♠❛r❝♦✱ ❝♦♥s✐st❡ ♥❛ tr♦❝❛ ❞❡ ✐♥❢♦r♠❛çõ❡s s❡♥s♦r✐❛✐s ❡ ❞❛s ❡st✐♠❛t✐✈❛s ❞❡ ♣♦s❡ ❞♦s r♦❜ôs✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦❛♥t❡r✐♦r♠❡♥t❡✱ ✉♠ r♦❜ô ♠❛r❝♦ tr❛♥s♠✐t❡ ✭❜r♦❛❞❝❛st✮ s✉❛ ❡st✐♠❛t✐✈❛ ❛t✉❛❧✱ ❥✉♥t❛♠❡♥t❡ j❝♦♠ ❛s ♠❡❞✐❞❛s ❡①t❡r♦❝❡♣t✐✈❛s ❛❞q✉✐r✐❞❛s✳ ❈♦♠ ❜❛s❡ ♥❡ss❛s ✐♥❢♦r♠❛çõ❡s✱ R ♣♦❞❡rá ji ji❣❡r❛r✱ ❞❡ ❢♦r♠❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛✱ ✉♠❛ ❡st✐♠❛t✐✈❛ ❞❡ s✉❛ ♣♦s❡ ✭bx ❡ P ✮ ✉t✐❧✐③❛♥❞♦ ❛ ❊st✐♠❛t✐✈❛ i ii ❡st✐♠❛t✐✈❛ ✭bx ❡ P ✮ ❞♦ r♦❜ô ♠❛r❝♦✱ ❛s ♠❡❞✐❞❛s ❡①t❡r♦❝❡♣t✐✈❛s t♦♠❛❞❛s ♣♦r R ❡♠ ✭♦❜s❡r✈❛çã♦ r❡❧❛t✐✈❛✮ j ijji r❡❧❛çã♦ ❛ R ✭z ✮ ❡ ❛ ♠❡❞✐❞❛ ♦❜t✐❞❛ ♣❡❧♦ ♣ró♣r✐♦ r♦❜ô ✭bφ ✮✿ k+1 k+1 k+1 k+1 x x= f ( , z , b φ ). ✭✹✳✶✶✮ b ji b i ij ji❖ ❡rr♦ ∆x ji ❛ss♦❝✐❛❞♦ à ❡st✐♠❛t✐✈❛ bx ji ✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❡①♣❛♥sã♦ ❡♠ sér✐❡ ❞❡ a ❚❛②❧♦r ❞❡ 1 ♦r❞❡♠✱ ♣♦❞❡ s❡r ❞❡✜♥✐❞♦ ❝♦♠♦✿∆x ji = J f ∆f (x i , h(x i , x j ), φ ji ), ✭✹✳✶✷✮ s❡♥❞♦∂f (x , h(x , x ), φ ) i i j ji J = f∂x ji x x x i i , x j j , φ ji = b φ ji =b =b  1 0 + φ ) + φ ) + φ )ij i ij i ij ij i ij −ρ s✐♥(θ ❝♦s(θ −ρ s✐♥(θ J = 0 1 ρ + φ ) + φ ) ρ + φ ) f ij i ij i ij ij i ij ❝♦s(θ s✐♥(θ ❝♦s(θ  0 0 1 1−1 ❡ #. −ρ k+1 ij s✐♥(θ k+1 i R ij 2×1 1×2σ2 φ ji =" ❡ ∗R ij  x i =b x i φ ji = b φ ji 1−1 ) ρ k+1 ij ❝♦s(θ k+1 i + φ k+1 ij ) ) s✐♥(θk+1 i )−ρ k+1 ij s✐♥(θ k+1 i ❝♦s(θ k+1 i = ∂f (x k+1 i , z k+1 ij , φ k+1 ji )∂(z k+1 ij , φ k+1 ji ) x i =b x i φ ji = b φ ji ,S k+1 ij = ) 0 1 ρk+1 ij ❝♦s(θ k+1 i + φ k+1 ij ) 0 0 1 x i =b x i φ ji = b φ ji  1 0 ∂x k+1 i x i =b x i φ ji = b φ ji= F k+1 ij =∂f (x k+1 i , z k+1 ij , φ k+1 ji ) P k+1 ji = F k+1 ij P k+1 i (F k+1 ij ) ⊤ + S k+1 ij ∗ R k+1 ij (S k+1 ij ) ⊤ ,✭✹✳✶✹✮ s❡♥❞♦ ✈❛s✱ ❛ ✐♥❝❡rt❡③❛ ✭✹✳✶✸✮ ❛ss♦❝✐❛❞❛ à ❡st✐♠❛t✐✈❛ bx k+1 ji ♣♦❞❡ s❡r ❝♦♠♣✉t❛❞❛ ❞❡ ♠❛♥❡✐r❛❞❡s❝❡♥tr❛❧✐③❛❞❛ ❝♦♥❢♦r♠❡ s❡❣✉❡✿ ✭✹✳✶✸✮❉❡ ♣♦ss❡ ❞❛s ✐♥❢♦r♠❛çõ❡s r❡❝❡❜✐❞❛s ❞♦ r♦❜ô ♠❛r❝♦ ❡ ❞❛s ♠❡❞✐❞❛s ❡①t❡r♦❝❡♣t✐✲ E[∆x ji (∆x ji ) ⊤ ] = E[J f ∆f (J f ∆f ) ⊤ ]P ji = E[J f ∆f (J f ∆f ) ⊤ ]. ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ❡♠ ❬❙♠✐t❤ ✫ ❈❤❡❡s❡♠❛♥✱ ✶✾✽✻❪✱ ♦ ❏❛❝♦❜✐❛♥♦ J f s❡ ❛♣r❡s❡♥t❛❝♦♠♦ ✉♠❛ ❜♦❛ ❛♣r♦①✐♠❛çã♦ ❧✐♥❡❛r q✉❛♥❞♦ ❛s ✈❛r✐á✈❡✐s ♣♦❞❡♠ s❡r r❡♣r❡s❡♥t❛❞❛s ♣♦r❞✐str✐❜✉✐çõ❡s ♥♦r♠❛✐s ♥ã♦ t❡♥❞❡♥❝✐♦s❛s ❝♦♠ ❞❡s✈✐♦s ♣❛❞rã♦ ♣❡q✉❡♥♦s✳ ❆ss✐♠✱ ❛♦ ♠✉❧✲ t✐♣❧✐❝❛r ❛♠❜♦s ♦s ❧❛❞♦s ❞❛ ❊q✉❛çã♦ ✭✹✳✶✷✮ ♣♦r s✉❛s r❡s♣❡❝t✐✈❛s tr❛♥s♣♦st❛s ❡ t♦♠❛r ♦✈❛❧♦r ❡s♣❡r❛❞♦ ❞♦ r❡s✉❧t❛❞♦✱ t❡♠✲s❡ ❛ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛s ❝♦♠♦✿ .  ∆φ ij∆φ ji ∆θ i∆ρ ij ∆x i∆y i  ✹✳✶✳ ▲♦❝❛❧✐③❛çã♦ ❈♦♦♣❡r❛t✐✈❛ ❡♠ ❊♥①❛♠❡s ❘♦❜ót✐❝♦s ✻✸∆f (x i , h(x i , x j ), φ ji ) = ✻✹ j ❈❛♣ít✉❧♦ ✹✳ ▼❡t♦❞♦❧♦❣✐❛◆❛s s✐t✉❛çõ❡s ❡♠ q✉❡ ♦ r♦❜ô R ❡stá ❞❡ ♣♦ss❡ ❞❡ ❞✉❛s ❡st✐♠❛t✐✈❛s ❞❡ s✉❛ ♣♦s❡✱ ❈♦rr❡çã♦ k+1|k k+1|k k+1 k+1 ❛ s❛❜❡r ✭bx j ❡ P j ✮ ❡ ✭bx ji ❡ P ji ✮✱ ❢❛③✲s❡ ♥❡❝❡ssár✐♦ ❞❡✜♥✐r ❛ ❡str❛té❣✐❛ ❛ s❡r ✭❡st✐♠❛t✐✈❛ r❡❧❛t✐✈❛✮ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❛ ❝♦♠❜✐♥❛çã♦ ❞❡ss❛s ❡st✐♠❛t✐✈❛s ❡♠ ✉♠ ♣r♦❝❡ss♦ ❞❡ ❢✉sã♦ s❡♥s♦r✐❛❧ ❞❡s✲❝❡♥tr❛❧✐③❛❞♦✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ♥♦ ❆♣ê♥❞✐❝❡ ❇✱ ♦ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥ ♣♦❞❡ s❡r ✉t✐❧✐③❛❞♦♣❛r❛ ❝♦♠❜✐♥❛r ❛❞❡q✉❛❞❛♠❡♥t❡ ❡st✐♠❛t✐✈❛s ✐♥❞❡♣❡♥❞❡♥t❡s ♦✉ ❛q✉❡❧❛s ❝✉❥♦ ♥í✈❡❧ ❞❡ ✐♥✲ t❡r❞❡♣❡♥❞ê♥❝✐❛ s❡❥❛ ❝♦♥❤❡❝✐❞♦✳ ❈♦♥t✉❞♦✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ❡①♣♦st♦ ♥❛ ❙❡çã♦ ✷✳✹✳✷✱ ❛❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦ ❡ ❡s♣❛ç♦ ♣❛r❛ ♣r♦❝❡ss❛r ❡ ❛r♠❛③❡♥❛r ♦ ❤✐stór✐❝♦ ❞❡ ✐♥t❡r❞❡✲♣❡♥❞ê♥❝✐❛ ✭❝♦rr❡❧❛çã♦✮ ❡♥tr❡ ❛s ❡st✐♠❛t✐✈❛s ❞♦s ❞✐✈❡rs♦s r♦❜ôs ❡♠ ✉♠ ❡♥①❛♠❡ r♦❜ót✐❝♦✐♥✈✐❛❜✐❧✐③❛ ❛ ✉t✐❧✐③❛çã♦ ❞❡ss❛ ❛❜♦r❞❛❣❡♠ ❡♠ s✐st❡♠❛s r❡❛✐s✳ ■❣♥♦r❛r ❛ ✐♥❢♦r♠❛çã♦ ❞❡✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ♥❛ ❢✉sã♦ ❞❛s ❡st✐♠❛t✐✈❛s ❞✐♠✐♥✉✐ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❛ t❛r❡❢❛✳ ◆♦ ❡♥✲ t❛♥t♦✱ ❡♠ s✐t✉❛çõ❡s ♥❛s q✉❛✐s ❛ s✉♣♦s✐çã♦ ❞❡ ✐♥❞❡♣❡♥❞ê♥❝✐❛ é ✐♥❛❞❡q✉❛❞❛✱ ❛ ❢✉sã♦ ♣♦❞❡r❡s✉❧t❛r ❡♠ ❡st✐♠❛t✐✈❛s ✐♥❝♦♥s✐st❡♥t❡s✳ ◆❡st❡ tr❛❜❛❧❤♦✱ t❛❧ ♣r♦❝❡❞✐♠❡♥t♦ s❡rá ❞❡♥♦t❛❞♦❝♦♠♦ ❛❜♦r❞❛❣❡♠ ✐♥❣ê♥✉❛ ❞♦ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥✳ ❖ t❡r♠♦ ✐♥❣ê♥✉❛ é ✉t✐❧✐③❛❞♦ ♣❛r❛ r❡❛❧✲ ❆❜♦r❞❛❣❡♠ ç❛r ♦ ❢❛t♦ ❞❡ t❛❧ ❛❜♦r❞❛❣❡♠ ❡st❛r s❡♥❞♦ ✉t✐❧✐③❛❞❛ ❡♠ ✉♠❛ s✐t✉❛çã♦ ✐♥❛❞❡q✉❛❞❛✱ ♣♦ré♠ ✐♥❣ê♥✉❛ ❛ ♠❡s♠❛ s❡ ❛♣r❡s❡♥t❛ ❝♦♠♦ ✉♠❛ ♣♦ssí✈❡❧ s♦❧✉çã♦ ❢r❡♥t❡ à ❝♦♠♣❧❡①✐❞❛❞❡ ♥❡❝❡ssár✐❛ ♣❛r❛❧✐❞❛r ❝♦♠ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❢♦r♠❛ ❛❞❡q✉❛❞❛✳ ❖ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s✱ ❞❡s❝r✐t♦ ♥♦ ❆♣ê♥❞✐❝❡ ❈✱ ❛♣r❡s❡♥t❛✉♠❛ ❛❜♦r❞❛❣❡♠ ❛♣r♦①✐♠❛❞❛ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❢✉sã♦ s❡♥s♦r✐❛❧✱ ❝♦♥t✉❞♦ ♥ã♦ ❢❛③ ❞✐s✲ t✐♥çã♦ ❡♥tr❡ ❡st✐♠❛t✐✈❛s ❝♦rr❡❧❛❝✐♦♥❛❞❛s ❡ ✐♥❞❡♣❡♥❞❡♥t❡s✱ ♣♦✐s ❝♦♥s✐❞❡r❛ t♦❞❛ ❡t❛♣❛ ❞❡❢✉sã♦ s❡♥s♦r✐❛❧ ❝♦♠♦ s❡ ❛s ❡st✐♠❛t✐✈❛s ❢♦ss❡♠ ✐♥t❡r❞❡♣❡♥❞❡♥t❡s✱ ❝♦♠ ❝♦rr❡❧❛çã♦ ❞❡s✲❝♦♥❤❡❝✐❞❛✳ ❆ s✉♣♦s✐çã♦ ❞❡ t♦t❛❧ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ♣♦❞❡ ❣❡r❛r ❡st✐♠❛t✐✈❛s ♣❡ss✐♠✐st❛s q✉❛♥❞♦ ✐♥❢♦r♠❛çõ❡s ✐♥❞❡♣❡♥❞❡♥t❡s ❡st✐✈❡r❡♠ ❞✐s♣♦♥í✈❡✐s✱ ♣♦ré♠ ♥ã♦ ❢♦r❡♠ tr❛t❛❞❛s❝♦♠♦ t❛❧✳ ❊♠ r❡s✉♠♦✱ ❛ s✉♣♦s✐çã♦ ❞❡ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ✉t✐❧✐③❛❞❛ ♥♦ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥ ♣♦❞❡❣❡r❛r ❡st✐♠❛t✐✈❛s ♦t✐♠✐st❛s ♥❛q✉❡❧❛s ♦❝❛s✐õ❡s ❡♠ q✉❡ t❛❧ s✉♣♦s✐çã♦ s❡❥❛ ✐♥❛❞❡q✉❛❞❛✳P♦r ♦✉tr♦ ❧❛❞♦✱ ❛ s✉♣♦s✐çã♦ ❞❡ t♦t❛❧ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ♣r❡s❡♥t❡ ♥♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡r✲ s❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s ♣♦❞❡ ❣❡r❛r ❡st✐♠❛t✐✈❛s ♣❡ss✐♠✐st❛s✱ ♥❛ ♣r❡s❡♥ç❛ ❞❡ ✐♥❢♦r♠❛çõ❡s✐♥❞❡♣❡♥❞❡♥t❡s✳ ❚❡♠✲s❡✱ ❡♥tã♦✱ ❞♦✐s ❡①tr❡♠♦s r❡♣r❡s❡♥t❛❞♦s ♣♦r ❡ss❛s ❛❜♦r❞❛❣❡♥s✱ ♦✉ s❡❥❛✱ t♦t❛❧ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ✭✜❧tr♦ ❞❡ ❑❛❧♠❛♥✮ ♦✉ t♦t❛❧ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ✭■♥t❡rs❡çã♦ ❞❡❈♦✈❛r✐â♥❝✐❛s✮✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ❡♥①❛♠❡s r♦❜ót✐❝♦s ❤♦♠♦❣ê♥❡♦s ❡ ❤❡t❡r♦❣ê♥❡♦s sã♦ ❡♠♣r❡❣❛❞♦s✱ s❡♥❞♦ q✉❡ ♥❡ss❡ ú❧t✐♠♦ ❛ ❤❡t❡r♦❣❡♥❡✐❞❛❞❡ é ❡st❛❜❡❧❡❝✐❞❛ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ ❛❧❣✉♥s r♦❜ôss❡r❡♠ ❡q✉✐♣❛❞♦s ❝♦♠ s❡♥s♦r❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ✏❛❜s♦❧✉t❛✑✳ ❚❛✐s s❡♥s♦r❡s ♣♦ss✐❜✐❧✐t❛♠❛❝❡ss♦ ❛ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ r❡❢❡r❡♥t❡s ❛♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ❞❡ r❡❢❡rê♥❝✐❛✳❊ss❛s ✐♥❢♦r♠❛çõ❡s ♣♦ss✉❡♠ ♠❡♥♦r ✐♥❝❡rt❡③❛✱ ❛❧é♠ ❞❡ s❡r❡♠ ❡st❛t✐st✐❝❛♠❡♥t❡ ✐♥❞❡♣❡♥✲ ❈♦rr❡çã♦ ❞❡♥t❡s ❞❛s ❛t✉❛✐s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞♦s r♦❜ôs ✭♣r❡❞✐çã♦✮✳ ❉❡✈✐❞♦ ❛ ✐ss♦✱ ✉♠ ✭❡st✐♠❛t✐✈❛ ❛❜s♦❧✉t❛✮ r♦❜ô q✉❡ ♣♦ss✉❛ t❛✐s s❡♥s♦r❡s ❞❡✈❡ ❢❛③❡r ✉s♦ ❞♦ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥ ♣❛r❛ ❡❢❡t✉❛r ❛ ❢✉sã♦ ✹✳✷✳ ❊str❛té❣✐❛s ❞❡ ▼♦✈✐♠❡♥t❛çã♦ ❞♦ ❊♥①❛♠❡ ✻✺ s❡♥s♦r✐❛❧ ❞❡ss❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ P♦r ♦✉tr♦ ❧❛❞♦✱ r♦❜ôs s❡♠ ❛❝❡ss♦ ❛ ❡ss❛s✐♥❢♦r♠❛çõ❡s s❡♥s♦r✐❛✐s ♣♦❞❡♠ ✉t✐❧✐③❛r ♦✉tr♦s r♦❜ôs ♥♦ ❣r✉♣♦ ♣❛r❛ ❛❥✉st❛r s✉❛s ❡st✐✲♠❛t✐✈❛s ❡♠ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ◆♦ ❡♥t❛♥t♦✱ ❞❡✈✐❞♦ à ❛✉sê♥❝✐❛ ❞❡ ✉♠ r❡❣✐str♦ ❞❛ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❛s ❡st✐♠❛t✐✈❛s ❞♦s r♦❜ôs✱ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦❞❡ ❈♦✈❛r✐â♥❝✐❛s ❞❡✈❡ s❡r ✉t✐❧✐③❛❞♦ ♣❛r❛ s❡ ❡❢❡t✉❛r ♦ ❛❥✉st❡ ❞❛s ❝r❡♥ç❛s✱ ❞❡ ♠♦❞♦ ❛❡✈✐t❛r ❛ ❣❡r❛çã♦ ❞❡ ❡st✐♠❛t✐✈❛s ♦t✐♠✐st❛s✳ P❛r❛ ❛ ✉t✐❧✐③❛çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s✱ ❝❛❞❛ r♦❜ô ♣r❡❝✐s❛♠❛♥t❡r ♦ r❡❣✐str♦ ❞❡ ✉♠❛ ú♥✐❝❛ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛ r❡❢❡r❡♥t❡ à s✉❛ ❡st✐♠❛t✐✈❛ ❞❡❧♦❝❛❧✐③❛çã♦✳ P❛r❛ ♣r♦♣❛❣❛r t❛❧ ❡st✐♠❛t✐✈❛✱ ❡t❛♣❛s ❞❡ ♣r❡❞✐çã♦ ❞♦ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥ sã♦❡①❡❝✉t❛❞❛s✱ ❝♦♥❢♦r♠❡ ❊q✉❛çõ❡s ✭✹✳✺✮ ❡ ✭✹✳✻✮✳ ❖ ❛❥✉st❡ ❞❡ss❛ ❡st✐♠❛t✐✈❛ r❡❢❡r❡♥t❡ ❛✉♠ r♦❜ô j✱ ❝♦♠ ❜❛s❡ ❡♠ ✐♥❢♦r♠❛çõ❡s ❞✐ss❡♠✐♥❛❞❛s ♣♦r ✉♠ r♦❜ô ♠❛r❝♦ i✱ ♣♦❞❡ s❡r❢❡✐t♦ ✉t✐❧✐③❛♥❞♦ ♦ ❛❧❣♦r✐t♠♦ ❈■✳ P❛r❛ ✐ss♦✱ ♦s r♦❜ôs ♣r❡❝✐s❛♠ ❝♦♠♣❛rt✐❧❤❛r ✈✐③✐♥❤❛♥ç❛s✱♣❡r♠✐t✐♥❞♦✲♦s tr♦❝❛r ✐♥❢♦r♠❛çõ❡s s❡♥s♦r✐❛✐s ❡ ✈✐❛ ❝♦♠✉♥✐❝❛çã♦✳ ❆ss✐♠✱ q✉❛♥❞♦ ✉♠❛ k+1 k+1❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ✭bx ji ❡ P ji ✮ r❡❢❡r❡♥t❡ ❛♦ r♦❜ô j é ❣❡r❛❞❛ ♣❡❧♦ r♦❜ô ♠❛r❝♦ k+1|k k+1|k i ✱ ♦ r♦❜ô j ♣♦❞❡ ❛t✉❛❧✐③❛r s✉❛ ❛t✉❛❧ ❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ✭bx j ❡ P j ✮ ❡♠ ✉♠❛❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ✉t✐❧✐③❛♥❞♦ ♦ ❛❧❣♦r✐t♠♦ ❈■✱ ❝♦♠♦ s❡❣✉❡✿ k+1 k+1 k+1|k −1 −1 −1 P P P= ω + (1 , j j ji − ω) ✭✹✳✶✺✮ ❡ k+1 k+1 k+1 k+1 k+1|k k+1|k −1 −1 x = P ω P x + (1 P x ,b j j j b j − ω) ji b ji ✭✹✳✶✻✮ k+1|k s❡♥❞♦ ♦ ♣❛râ♠❡tr♦ ω ∈ [0, 1] r❡s♣♦♥sá✈❡❧ ♣♦r ❡❢❡t✉❛r ❛ ❝♦♠❜✐♥❛çã♦ ❝♦♥✈❡①❛ ❞❡ P jk+1 ❡ P ji ✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ♥♦ ❆♣ê♥❞✐❝❡ ❈✱ ♦ ♣❛râ♠❡tr♦ ω ♣♦❞❡ s❡r ❛❞❡q✉❛❞❛♠❡♥t❡♦t✐♠✐③❛❞♦ ❡♠ r❡❧❛çã♦ ❛ ❞✐❢❡r❡♥t❡s ❝r✐tér✐♦s✱ t❛✐s ❝♦♠♦ ♦ ❞❡t❡r♠✐♥❛♥t❡ ♦✉ ♦ tr❛ç♦ ❞❛♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛✳ ✹✳✷ ❊str❛té❣✐❛s ❞❡ ▼♦✈✐♠❡♥t❛çã♦ ❞♦ ❊♥①❛♠❡ ❊str❛té❣✐❛s ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛ ❢♦r❛♠ ❡♠♣r❡❣❛❞❛s ♥❡st❡ tr❛❜❛❧❤♦ ♣❛r❛ ♠❛♥t❡r♦ ❣r✉♣♦ ❝♦❡s♦ ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❛✉♠❡♥t❛r ❛ ❞❡♥s✐❞❛❞❡ ❞❡ r♦❜ôs ❡♠ ❞❡t❡r♠✐♥❛❞❛ r❡❣✐ã♦ ❞♦ ❛♠❜✐❡♥t❡✳ ❈♦♥❢♦r♠❡ ❡①♣♦st♦ ♥❛ ❙❡çã♦ ✷✳✹✱ ❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ r♦❜ôs t❡♥❞♦ ❝♦♠♦❜❛s❡ s♦♠❡♥t❡ s❡♥s♦r❡s ♣r♦♣r✐♦❝❡♣t✐✈♦s ❛❝❛rr❡t❛ ♥❛ ❞❡❣r❛❞❛çã♦ ❞❛ ✐♥❢♦r♠❛çã♦ ✐♥✐❝✐❛❧ ❞❡❧♦❝❛❧✐③❛çã♦✳ ❆ ♠❛♥✉t❡♥çã♦ ❞❛ ❝♦❡sã♦ ❞❡ ✉♠ ❣r✉♣♦ ❞❡ r♦❜ôs ♣❡r♠✐t❡ q✉❡ ❡t❛♣❛s ❞❡❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♣♦ss❛♠ s❡r ❡❢❡t✉❛❞❛s ❝♦♠ ♠❛✐♦r ❢r❡q✉ê♥❝✐❛✱ ♦ q✉❡ ♣♦ss✐❜✐❧✐t❛ ✻✻❈❛♣ít✉❧♦ ✹✳ ▼❡t♦❞♦❧♦❣✐❛ ❛♠❡♥✐③❛r ♦s ❡❢❡✐t♦s ❝❛✉s❛❞♦s ♣❡❧❛ ✉t✐❧✐③❛çã♦ ❞❡ s❡♥s♦r❡s ♣r♦♣r✐♦❝❡♣t✐✈♦s ♣♦r ❧♦♥❣♦s♣❡rí♦❞♦s✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ❞✉❛s ❡str❛té❣✐❛s ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❢♦r❛♠ ✐♠♣❧❡♠❡♥t❛❞❛s✱ ♣❡r✲♠✐t✐♥❞♦ q✉❡ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♣✉❞❡ss❡♠ ♦❝♦rr❡r ❝♦♠ ❞❡t❡r♠✐♥❛❞❛❢r❡q✉ê♥❝✐❛✳ ◆❛ ♣r✐♠❡✐r❛ ❡str❛té❣✐❛ ❛♣r❡s❡♥t❛❞❛✱ ❛ ❝♦♦r❞❡♥❛çã♦ ❞♦ ❣r✉♣♦ é ❡❢❡t✉❛❞❛❞❡ ♠♦❞♦ ❛ ♦❝♦rr❡r ✉♠❛ ❛❧t❡r♥â♥❝✐❛ ❡♥tr❡ ♦s r♦❜ôs q✉❡ s❡ ♠♦✈✐♠❡♥t❛♠ ❡ ❛q✉❡❧❡s q✉❡♣❡r♠❛♥❡❝❡♠ ♣❛r❛❞♦s ❛t✉❛♥❞♦ ❝♦♠♦ ♠❛r❝♦s ❞✐♥â♠✐❝♦s✳ ◆❛ ♦✉tr❛ ❡str❛té❣✐❛✱ ♦s r♦❜ôs s❡♠♦✈✐♠❡♥t❛♠ ❝♦♥t✐♥✉❛♠❡♥t❡ ❞❡ ❢♦r♠❛ ❛ ♠❡❧❤♦r❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ ❣r✉♣♦ ♥❛ ❡①❡❝✉çã♦❞❡ ❞❡t❡r♠✐♥❛❞❛s t❛r❡❢❛s✳ ❉❡✈✐❞♦ à ❝♦♥st❛♥t❡ ❞❡❣r❛❞❛çã♦ ❞❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐✲③❛çã♦✱ r♦❜ôs ❝♦♠ ♠❡❧❤♦r❡s ❝❛♣❛❝✐❞❛❞❡s s❡♥s♦r✐❛✐s ♣♦❞❡♠ s❡r ✐♥s❡r✐❞♦s ♥♦ ❣r✉♣♦ ♣❛r❛♠❡❧❤♦r❛r ❛ q✉❛❧✐❞❛❞❡ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ t♦❞♦s ♦s r♦❜ôs✳ ❆♠❜❛s ❛s ❡str❛té❣✐❛s ✉t✐❧✐③❛♠♠♦❞❡❧♦s ❞❡ r♦❜ôs ❝♦♠♣❧❡t❛♠❡♥t❡ ❛t✉❛❞♦s ✭♠♦❞❡❧♦ ❤♦❧♦♥ô♠✐❝♦✮✱ ♥♦ ❡♥t❛♥t♦ ❛ tr❛♥s❢♦r✲♠❛çã♦ ❞❛s ❧❡✐s ❞❡ ❝♦♥tr♦❧❡ ♣❛r❛ ♦✉tr♦s ♠♦❞❡❧♦s ♣♦❞❡ s❡r ❛❞❡q✉❛❞❛♠❡♥t❡ ❡❢❡t✉❛❞❛✱ t❛❧❝♦♠♦ ❞❡s❝r✐t♦ ❡♠ ❬❉❡ ▲✉❝❛ ✫ ❖r✐♦❧♦✱ ✶✾✾✹❪✱ ❬❉❡s❛✐ ❡t ❛❧✳✱ ✶✾✾✽❪ ❡ ❬❇❡❧t❛ ❡t ❛❧✳✱ ✷✵✵✸❪✳ ✹✳✷✳✶ ▼♦✈✐♠❡♥t❛çã♦ ❆❧t❡r♥❛❞❛ ◆❡ss❛ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦✱ ♦ ❡♥①❛♠❡ é ❞✐✈✐❞✐❞♦ ❡♠ ❞♦✐s s✉❜❣r✉♣♦s✿ ✉♠ ❞❡❧❡s♣❡r♠❛♥❡❝❡ ♣❛r❛❞♦ ❛t✉❛♥❞♦ ❝♦♠♦ ♠❛r❝♦✱ ❡♥q✉❛♥t♦ ♦ ♦✉tr♦ s❡ ♠♦✈✐♠❡♥t❛✳ ❆♣ós ✉♠❛❝♦♥❞✐çã♦ ♣r❡❡st❛❜❡❧❡❝✐❞❛✱ t❛✐s ❝♦♠♦ ♥ú♠❡r♦ ❞❡ ✐t❡r❛çõ❡s ♦✉ ❞✐stâ♥❝✐❛ ♣❡r❝♦rr✐❞❛✱ ♦s s✉❜❣r✉♣♦s tr♦❝❛♠ ❞❡ ♣❛♣é✐s✳ ❙❡❥❛♠ R m ❡ R s ❛s ❞❡♥♦♠✐♥❛çõ❡s ✉t✐❧✐③❛❞❛s ♣❛r❛ ♦ ❣r✉♣♦❡♠ ♠♦✈✐♠❡♥t♦ ✭♠♦t✐♦♥ ❣r♦✉♣✮ ❡ ♦ ❣r✉♣♦ ❡st❛❝✐♦♥ár✐♦ ✭st❛t✐♦♥❛r② ❣r♦✉♣✮✱ r❡s♣❡❝t✐✈❛✲♠❡♥t❡✳ ❖ ♠♦✈✐♠❡♥t♦ ❞♦s r♦❜ôs ♥❡ss❡s ❣r✉♣♦s é ❝♦♦r❞❡♥❛❞♦ ♣♦r ❧❡✐s ❞❡s❝❡♥tr❛❧✐③❛❞❛s q✉❡ ♦s ♣❡r♠✐t❡♠ ❛t✉❛r ❞❡ ❢♦r♠❛ ❝♦❡s❛ ❡ ❡✈✐t❛r ❝♦❧✐sõ❡s ❝♦♠ ♦s ❞❡♠❛✐s r♦❜ôs✳ ❆ ❡s✲tr❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ é ❜❛s❡❛❞❛ ♥♦ ❛❧❣♦r✐t♠♦ ❞❡ ✢♦❝❦✐♥❣ ♣r♦♣♦st♦ ♣♦r ❘❡②♥♦❧❞s❬✶✾✽✼❪✳ ❆s ❞✉❛s ♣r✐♥❝✐♣❛✐s ♠✉❞❛♥ç❛s ❡❢❡t✉❛❞❛s ♥♦ ❛❧❣♦r✐t♠♦ ♦r✐❣✐♥❛❧♠❡♥t❡ ♣r♦♣♦st♦♣♦r ❘❡②♥♦❧❞s ❢♦r❛♠ ❛ ✐♥❡①✐stê♥❝✐❛ ❞❡ ✉♠❛ r❡❣r❛ ♣❛r❛ ❡❢❡t✉❛r ♦ ❝♦♥s❡♥s♦ ❞❡ ✈❡❧♦❝✐❞❛❞❡s❡ ♦ ❢❛t♦ ❞❛ r❡❣r❛ ❞❡ ❝♦❡sã♦ t❡r s✐❞♦ ❧✐❣❡✐r❛♠❡♥t❡ ❛❧t❡r❛❞❛ ♣❛r❛ ❝♦♥s✐❞❡r❛r ❛ ❡①✐stê♥✲❝✐❛ ❞❡ ✉♠ s✉❜❣r✉♣♦ ❡stát✐❝♦✳ ❉❡ss❡ ♠♦❞♦✱ ❝♦♥❢♦r♠❡ s❡rá ❞❡s❝r✐t♦ ❛ s❡❣✉✐r✱ ❞✉r❛♥t❡ ❛♠♦✈✐♠❡♥t❛çã♦ ❞❡ ✉♠ s✉❜❣r✉♣♦✱ s♦♠❡♥t❡ ♦s r♦❜ôs q✉❡ ♣❡rt❡♥❝❡♠ àq✉❡❧❡ s✉❜❣r✉♣♦ sã♦❝♦♥s✐❞❡r❛❞♦s ♥♦ ❝á❧❝✉❧♦ ❞❛ ❝♦♠♣♦♥❡♥t❡ ❞❡ ❝♦❡sã♦✳ ❆ ♣r✐♠❡✐r❛ r❡❣r❛ ✐♠♣❧❡♠❡♥t❛❞❛ ❣❡r❛ ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ s❡♣❛r❛çã♦ ❡ t❡♠ ❝♦♠♦♦❜❥❡t✐✈♦ ♠❛♥t❡r ✉♠❛ ❞✐stâ♥❝✐❛ ❞❡ s❡❣✉r❛♥ç❛ ❡♥tr❡ ♦s r♦❜ôs ♥♦ ❣r✉♣♦✳ ❚❛❧ ❝♦♠♣♦rt❛✲♠❡♥t♦ é ❣❡r❛❞♦ ♣❡❧❛ s❡❣✉✐♥t❡ ❡q✉❛çã♦ X sep s r v = d , ,i − 1 kd k ≤ r ✭✹✳✶✼✮ ij ij ij s j∈R,j6=i kd k ✹✳✷✳ ❊str❛té❣✐❛s ❞❡ ▼♦✈✐♠❡♥t❛çã♦ ❞♦ ❊♥①❛♠❡ ✻✼ sep ij i♥❛ q✉❛❧ ♦ ✈❡t♦r s❡♣❛r❛çã♦ v i é ❜❛s❡❛❞♦ ♥♦ ✈❡t♦r ❞❡s❧♦❝❛♠❡♥t♦ d ❡♥tr❡ ✉♠ r♦❜ô R ❡ s i♦✉tr♦s r♦❜ôs s✐t✉❛❞♦s ❛ ✉♠❛ ❞✐stâ♥❝✐❛ ♠á①✐♠❛ ✭r ✮ ❞❡ R ✱ ✐♥❞❡♣❡♥❞❡♥t❡ ❞❡ ♣❡rt❡♥❝❡r❡♠ m s❛ R ♦✉ R ✱ ❝♦♥❢♦r♠❡ ✐❧✉str❛ ❛ ❋✐❣✉r❛ ✹✳✹✳R i d ij r s R j ❋✐❣✉r❛ ✹✳✹✿ ❊①❡♠♣❧♦ ❞❡ ❛♣❧✐❝❛çã♦ ❞❛ r❡❣r❛ ❞❡ s❡♣❛r❛çã♦ ♣❡❧♦ r♦❜ô i✱ ✐❧✉str❛♥❞♦ ✉♠❛ s r❡❣✐ã♦ s❡♥s♦r✐❛❧ ❝✐r❝✉❧❛r ❞❡ r❛✐♦ r ✉t✐❧✐③❛❞❛ ♥❡ss❛ r❡❣r❛✳ ❖s r♦❜ôs ♥❛ ❝♦r ❝✐♥③❛ ❝♦♠♣õ❡♠♦ s✉❜❣r✉♣♦ ❡♠ ♠♦✈✐♠❡♥t♦ ✭s✉❜❣r✉♣♦ R m ✮✱ ❡♥q✉❛♥t♦ q✉❡ ♦s r♦❜ôs ♥❛ ❝♦r ✈❡r❞❡ ✐❧✉str❛♠ s♦s r♦❜ôs ❡stát✐❝♦s ✭s✉❜❣r✉♣♦ R ✮✳ ❙♦♠❡♥t❡ ♦s r♦❜ôs ❡♠ ♠♦✈✐♠❡♥t♦ ❛♣❧✐❝❛♠ ❡st❛ r❡❣r❛✱ s♥♦ ❡♥t❛♥t♦ t♦❞♦s ♦s r♦❜ôs ❧♦❝❛❧✐③❛❞♦s ❛ ✉♠❛ ❞✐stâ♥❝✐❛ ♠á①✐♠❛ r ❞❡ ✉♠ r♦❜ô sã♦❝♦♥s✐❞❡r❛❞♦s✱ ✐♥❞❡♣❡♥❞❡♥t❡ ❞♦ s✉❜❣r✉♣♦ ❛♦ q✉❛❧ ♣❡rt❡♥❝❡♠✳ ❖ ♣r♦♣ós✐t♦ ❞❛ s❡❣✉♥❞❛ r❡❣r❛ é ♠❛♥t❡r ♦s r♦❜ôs ❥✉♥t♦s✱ ❛t✉❛♥❞♦ ❝♦♠♦ ✉♠❛✉♥✐❞❛❞❡✳ ❊ss❛ r❡❣r❛ ❞❡ ❝♦❡sã♦ ❝❛❧❝✉❧❛ ❛ ♣♦s✐çã♦ ♠é❞✐❛ ❞♦s k r♦❜ôs ❡♠ ♠♦✈✐♠❡♥t♦ mc ✭♣❡rt❡♥❝❡♥t❡s ❛ R ✮ q✉❡ s❡ ❡♥❝♦♥tr❛♠ ❛ ✉♠❛ ❞✐stâ♥❝✐❛ ♠á①✐♠❛ ✭r ✮ ❞❡ ✉♠ r♦❜ô ✭♣♦r i❡①❡♠♣❧♦ R ✮✳ ❆ss✐♠✱ q✉❛♥❞♦ ❝♦♠♣❛r❛❞❛ ❛♦ ❛❧❣♦r✐t♠♦ ♦r✐❣✐♥❛❧ ❞❡ ❘❡②♥♦❧❞s ❬✶✾✽✼❪✱❡ss❛ r❡❣r❛ ❢♦✐ ❧✐❣❡✐r❛♠❡♥t❡ ♠♦❞✐✜❝❛❞❛ ❞❡ ♠♦❞♦ q✉❡ ♦s r♦❜ôs ❡st❛❝✐♦♥ár✐♦s ♥ã♦ ❢♦ss❡♠✐♥❝❧✉í❞♦s ♥♦ ❝ô♠♣✉t♦ ❞❛ ♣♦s✐çã♦ ♠é❞✐❛✱ ❡✈✐t❛♥❞♦ q✉❡ ♦s ♠❡s♠♦s ❝♦♠♣r♦♠❡t❡ss❡♠ ❛ m coh♠♦✈✐♠❡♥t❛çã♦ ❞♦ s✉❜❣r✉♣♦ R ✭❋✐❣✉r❛ ✹✳✺✮✳ ❖ ✈❡t♦r v ❣❡r❛❞♦ t❡♠ ❝♦♠♦ ♦r✐❣❡♠ i✉♠ ♣♦♥t♦ ❞❡ r❡❢❡rê♥❝✐❛ s♦❜r❡ ♦ r♦❜ô i ✭❡✳❣✳✱ ♦ ❝❡♥tr♦ ❞❡ ♠❛ss❛✮ ❡ ❛♣♦♥t❛ ♥❛ ❞✐r❡çã♦ ❞❛♣♦s✐çã♦ ♠é❞✐❛ ❝❛❧❝✉❧❛❞❛✱ ❝♦♠♦ s❡❣✉❡✿ X coh1 v di kd k ≤ r = , . ji ji c ✭✹✳✶✽✮ kj∈R m ,j6=i ❆ t❡r❝❡✐r❛ r❡❣r❛ é ✉t✐❧✐③❛❞❛ ♣❛r❛ ❣✉✐❛r ♦ ❣r✉♣♦ ♥♦ ❛♠❜✐❡♥t❡✳ P❛r❛ ✐ss♦✱ ✇❛②♣♦✐♥ts sã♦ ❡st❛❜❡❧❡❝✐❞♦s ❡♠ ❞❡t❡r♠✐♥❛❞❛s ♣♦s✐çõ❡s ❞♦ ❛♠❜✐❡♥t❡ ❞❡ ♠♦❞♦ q✉❡ ❝❛❞❛ r♦❜ô ♣♦ss❛✉t✐❧✐③á✲❧♦s ♣❛r❛ ❡st❛❜❡❧❡❝❡r ❛ ❞✐r❡çã♦ ❞❡ ♠♦✈✐♠❡♥t♦✳ ❚❛✐s ✇❛②♣♦✐♥ts sã♦ ♣r❡✈✐❛♠❡♥t❡❞❡✜♥✐❞♦s ❞❡ ♠♦❞♦ q✉❡ ❝❛❞❛ r♦❜ô ♣♦ss✉❛ ✉♠❛ ❧✐st❛ ♦r❞❡♥❛❞❛ ❝♦♠ ❛ ♣♦s✐çã♦ ❞♦s ✇❛②✲♣♦✐♥ts✳ ❖ ♣r✐♠❡✐r♦ ❛❧✈♦ ❞❛ ❧✐st❛ é ❞❡✜♥✐❞♦ ❝♦♠♦ ❛❧✈♦ ✐♥✐❝✐❛❧ ♣❛r❛ t♦❞♦s ♦s r♦❜ôs✳◗✉❛♥❞♦ t❛❧ ❛❧✈♦ é ❛❧❝❛♥ç❛❞♦ ♣♦r ❛❧❣✉♠ ✐♥t❡❣r❛♥t❡ ❞♦ ❣r✉♣♦✱ ✉♠❛ ♠❡♥s❛❣❡♠ ❞❡ ❜r♦✲❛❞❝❛st é ❡♥✈✐❛❞❛ ♣❡❧♦ ♠❡s♠♦ ♣❛r❛ q✉❡ t♦❞♦s ♦s r♦❜ôs ❞♦ ❣r✉♣♦ ♣♦ss❛♠ s❡❧❡❝✐♦♥❛r ♦ ✻✽❈❛♣ít✉❧♦ ✹✳ ▼❡t♦❞♦❧♦❣✐❛R i d ij r c R j ❋✐❣✉r❛ ✹✳✺✿ ❊①❡♠♣❧♦ ❞❡ ❛♣❧✐❝❛çã♦ ❞❛ r❡❣r❛ ❞❡ ❝♦❡sã♦ ♣❡❧♦ r♦❜ô i✱ ✐❧✉str❛♥❞♦ ❛ r❡❣✐ã♦ s❡♥s♦r✐❛❧ ❝✐r❝✉❧❛r ❞❡ r❛✐♦ r c ✉t✐❧✐③❛❞❛ ♥❡ss❛ r❡❣r❛✳ ❙♦♠❡♥t❡ ♦s r♦❜ôs ❡♠ ♠♦✈✐♠❡♥t♦coh❧♦❝❛❧✐③❛❞♦s ❞❡♥tr♦ ❞❛ r❡❣✐ã♦ ❝✐r❝✉❧❛r ❞♦ r♦❜ô i sã♦ ✉t✐❧✐③❛❞♦s ♥♦ ❝ô♠♣✉t♦ ❞❡ v i ✳♣ró①✐♠♦ ❛❧✈♦ ❞❛ ❧✐st❛✳ ❉❡ss❡ ♠♦❞♦✱ ❛ ❝❛❞❛ ♠♦♠❡♥t♦✱ ✉♠ ♠❡s♠♦ ❛❧✈♦ é ✉t✐❧✐③❛❞♦ ♣♦r t♦❞♦s ♦s r♦❜ôs ❞❡ ✉♠ s✉❜❣r✉♣♦✳ ❖s ✇❛②♣♦✐♥ts sã♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ ❝❛❧❝✉❧❛r ✉♠ ✈❡t♦rdir ❞✐r❡çã♦ ✭v ✮ q✉❡ é ❜❛s❡❛❞♦ ♥♦ ✈❡t♦r ❞❡s❧♦❝❛♠❡♥t♦ ❡♥tr❡ ✉♠ r♦❜ô i ❡ ♦ ♣ró①✐♠♦ ❛❧✈♦ i t it✱ s❡♥❞♦ r❡♣r❡s❡♥t❛❞♦ ♣♦r d ✭❋✐❣✉r❛ ✹✳✻✮✳ ❆ s❡❣✉✐♥t❡ ❡q✉❛çã♦ é ✉t✐❧✐③❛❞❛ ♣❛r❛ ❣❡r❛r ♦ ✈❡t♦r ❞✐r❡çã♦ dir d it v = .i it ✭✹✳✶✾✮ kd kR i d it virtual Alvo❋✐❣✉r❛ ✹✳✻✿ ❊①❡♠♣❧♦ ❞❡ ❛♣❧✐❝❛çã♦ ❞❛ r❡❣r❛ q✉❡ ❞❡✜♥❡ ❛ ❞✐r❡çã♦ ❛ s❡r s❡❣✉✐❞❛ ♣❡❧♦❣r✉♣♦✱ t❡♥❞♦ ❝♦♠♦ ❜❛s❡ ✉♠ ✇❛②♣♦✐♥t✳ i i ❚❡♥❞♦ ❝♦♠♦ ❜❛s❡ ❛s três r❡❣r❛s ❞❡✜♥✐❞❛s✱ ❛ ❛çã♦ ❞❡ ❝♦♥tr♦❧❡ u ✉t✐❧✐③❛❞❛ ♣♦r Ré ❡♥tã♦ ❞❡✜♥✐❞❛ ❝♦♠♦✿ coh sep dir u = k v + k v + k v ,i c s d i i i ✭✹✳✷✵✮ c s❡♥❞♦ ❝♦♠♣♦st❛ ♣❡❧❛ ❝♦♠❜✐♥❛çã♦ ❧✐♥❡❛r ❞♦s três ✈❡t♦r❡s ❞❡✜♥✐❞♦s✳ ❖s ❝♦❡✜❝✐❡♥t❡s k ✱k s ❡ k d sã♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛❥✉st❛r ❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛❞❛ t❡r♠♦ ❞❛ ❡q✉❛çã♦✳ ❊ss❛ ❛çã♦ ✹✳✷✳ ❊str❛té❣✐❛s ❞❡ ▼♦✈✐♠❡♥t❛çã♦ ❞♦ ❊♥①❛♠❡ ✻✾ x i y i❞❡ ❝♦♥tr♦❧❡ é ❡♥tã♦ ❞❡❝♦♠♣♦st❛ ❡♠ ✈❡❧♦❝✐❞❛❞❡s ❧✐♥❡❛r❡s v ❡ v q✉❡ sã♦ ✉t✐❧✐③❛❞❛s ♣❛r❛❝♦♥tr♦❧❛r ♦ r♦❜ô i ♥❛s ❞✐r❡çõ❡s x ❡ y✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ◆❡st❛ ❡str❛té❣✐❛ é ❝♦♥s✐❞❡r❛❞♦ q✉❡ t♦❞♦s ♦s r♦❜ôs ♣♦ss✉❡♠ r❡❧ó❣✐♦s s✐♥❝r♦♥✐③❛❞♦s✳❆ ❞❡❝✐sã♦ ♣❛r❛ s❡ ❡❢❡t✉❛r ❛s ♠✉❞❛♥ç❛s ❞❡ ❝♦♠♣♦rt❛♠❡♥t♦s ❞♦s r♦❜ôs ❡st❛❝✐♦♥ár✐♦s ♣❛r❛ s m ⇄ R r♦❜ôs ❡♠ ♠♦✈✐♠❡♥t♦✱ ❡ ✈✐❝❡✲✈❡rs❛ ✭R ✮✱ é ❢❡✐t❛ ♣❡r✐♦❞✐❝❛♠❡♥t❡ ❞❡ ♠❛♥❡✐r❛❞❡s❝❡♥tr❛❧✐③❛❞❛✳ ■♥✐❝✐❛❧♠❡♥t❡✱ ♦ ❡♥①❛♠❡ é ❞✐✈✐❞✐❞♦ ❡♠ ❞♦✐s s✉❜❣r✉♣♦s ❡ ♦s r❡❧ó❣✐♦s sã♦✐♥✐❝✐❛❧✐③❛❞♦s✳ ❆ss✐♠ q✉❡ ✉♠ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ ♣r❡❡st❛❜❡❧❡❝✐❞♦ é ❛❧❝❛♥ç❛❞♦✱ ♦s r♦❜ôs tr♦❝❛♠ ❞❡ ♣❛♣é✐s ❡ ♦s r❡❧ó❣✐♦s sã♦ r❡✐♥✐❝✐❛❞♦s✳ ❊ss❡ ♣r♦❝❡❞✐♠❡♥t♦ é r❡♣❡t✐❞♦ ❛té q✉❡ ❛t❛r❡❢❛ s❡❥❛ ❝♦♥❝❧✉í❞❛✳ ✹✳✷✳✷ ▼♦✈✐♠❡♥t❛çã♦ ❈♦♥tí♥✉❛ ❊ss❛ ❡str❛té❣✐❛ ❡♠♣r❡❣❛ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❝❛♠♣♦s ♣♦t❡♥❝✐❛✐s ❛rt✐✜❝✐❛✐s ♣❛r❛ ♣♦s✐❝✐♦♥❛r❞❡t❡r♠✐♥❛❞♦s r♦❜ôs ❡♠ ❧♦❝❛✐s ❞❡s❡❥❛❞♦s ♥♦ ❡♥①❛♠❡✱ ❛❧é♠ ❞❡ ❡st❛❜❡❧❡❝❡r ✉♠❛ ❞❡t❡r✲♠✐♥❛❞❛ ❢♦r♠❛çã♦✳ ■♥✐❝✐❛❧♠❡♥t❡✱ ✉♠ r♦❜ô ❧í❞❡r ❡q✉✐♣❛❞♦ ❝♦♠ s❡♥s♦r❡s ❡①t❡r♦❝❡♣t✐✈♦s q✉❡ ♦ ♣♦ss✐❜✐❧✐t❛ ♦❜t❡r ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ♠❛✐s ♣r❡❝✐s❛s é ❛✉t♦♥♦♠❛♠❡♥t❡ ♣♦✲s✐❝✐♦♥❛❞♦ ♣ró①✐♠♦ ❛♦ ❝❡♥tr♦ ❞♦ ❡♥①❛♠❡✱ ❣❡r❛♥❞♦ ✉♠❛ ❢♦r♠❛çã♦ ✐♥✐❝✐❛❧ ♣❛r❛ ♦ ❣r✉♣♦✭❝♦♥❢♦r♠❡ s❡rá ❞✐s❝✉t✐❞♦ ♥❛ ❙❡çã♦ ✹✳✷✳✷✳✶✮✳ ❈♦♥❝❧✉í❞❛ ❡ss❛ ❡t❛♣❛ ✐♥✐❝✐❛❧✱ ❝❛❞❛ r♦❜ô t❡♠❛❝❡ss♦ ❛ ✉♠❛ ❜♦❛ ❡st✐♠❛t✐✈❛ ✐♥✐❝✐❛❧ ❞❡ s✉❛ ♣♦s✐çã♦ ❡♠ ✉♠ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ❞❡ r❡✲❢❡rê♥❝✐❛✳ ❊ss❛ ❢♦r♠❛çã♦ ✐♥✐❝✐❛❧ é ✉t✐❧✐③❛❞❛ ❝♦♠♦ ♣♦♥t♦ ❞❡ ♣❛rt✐❞❛ ♣❛r❛ ❛ ♠♦✈✐♠❡♥t❛çã♦❞♦ ❣r✉♣♦✱ ❛❧é♠ ❞❡ s❡r ✉t✐❧✐③❛❞❛ ❝♦♠♦ ❜❛s❡ ♣❛r❛ ♦ ♠ét♦❞♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳❈♦♥s✐❞❡r❛✲s❡ q✉❡ ♦ r♦❜ô ❧í❞❡r ♣♦ss✉✐ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❛ ♣♦s✐çã♦ ❞❡ ❛❧❣✉♥s ✇❛②♣♦✐♥ts♣❛r❛ ❣✉✐❛r ❛ ♥❛✈❡❣❛çã♦ ❞♦ ❣r✉♣♦ ♥♦ ❛♠❜✐❡♥t❡✳ ❖ ❡♥①❛♠❡ s❡ ♠♦✈✐♠❡♥t❛ ❝♦♠♦ ✉♠❛✉♥✐❞❛❞❡ ❝♦❡s❛ ❞❡✈✐❞♦ à ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❞❡s❝r✐t❛ ♥❛ ❙❡çã♦ ✹✳✷✳✷✳✷✳ ❉✉r❛♥t❡❛ ♠♦✈✐♠❡♥t❛çã♦✱ ❝❛❞❛ r♦❜ô ✉t✐❧✐③❛ s❡♥s♦r❡s ♣r♦♣r✐♦❝❡♣t✐✈♦s ♣❛r❛ ❡st✐♠❛r s✉❛s r❡s♣❡❝t✐✲✈❛s ♣♦s❡s✱ ❛❧é♠ ❞❡ s❡♥s♦r❡s ❡①t❡r♦❝❡♣t✐✈♦s ♣❛r❛ ❡st✐♠❛r ❞✐stâ♥❝✐❛ ❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛s❛ r♦❜ôs ♣♦s✐❝✐♦♥❛❞♦s ❞❡♥tr♦ ❞❡ s✉❛s ✈✐③✐♥❤❛♥ç❛s✳✹✳✷✳✷✳✶ ❋♦r♠❛çã♦ ✐♥✐❝✐❛❧ ❞♦ ❡♥①❛♠❡◆❡ss❛ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦✱ ✉♠ ❣r✉♣♦ ❞❡ r♦❜ôs ❤❡t❡r♦❣ê♥❡♦s é ❝♦♥s✐❞❡r❛❞♦✳❯♠ r♦❜ô ❧í❞❡r é ❡q✉✐♣❛❞♦ ❝♦♠ s❡♥s♦r❡s q✉❡ ❞✐s♣♦♥✐❜✐❧✐③❛♠ ❡st✐♠❛t✐✈❛s ❝♦♠ ✉♠ ❞❡✲ t❡r♠✐♥❛❞♦ ♥í✈❡❧ ❞❡ ♣r❡❝✐sã♦ ❞❡ s✉❛ ❧♦❝❛❧✐③❛çã♦✱ t❛✐s ❝♦♠♦ ●P❙ ♦✉ ■▼❯ ✭❞♦ ✐♥❣❧ês✱■♥❡rt✐❛❧ ▼❡❛s✉r❡♠❡♥t ❯♥✐t✮✳ ◆❡ss❛ ❡t❛♣❛ ❞❡ ❢♦r♠❛çã♦ ✐♥✐❝✐❛❧✱ ♦s r♦❜ôs tê♠ ❛❝❡ss♦ ❛✉♠❛ ✐♥❢♦r♠❛çã♦ ❣❧♦❜❛❧ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ t♦❞♦s ♦s ✐♥t❡❣r❛♥t❡s ❞♦ ❣r✉♣♦ q✉❡ ♣♦❞❡ s❡r♣r♦✈✐❞❛ ♣♦r ❞✐✈❡rs♦s ❞✐s♣♦s✐t✐✈♦s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ✐●P❙✳ ❯t✐❧✐③❛♥❞♦ t❛❧ ✐♥❢♦r♠❛çã♦✱♦s r♦❜ôs ❢♦r♠❛♠ ✉♠ ❣r✉♣♦ ❝♦❡s♦ ❡ ♦ r♦❜ô ❧í❞❡r é ❛✉t♦♥♦♠❛♠❡♥t❡ ♣♦s✐❝✐♦♥❛❞♦ ♣ró①✐♠♦ ✼✵❈❛♣ít✉❧♦ ✹✳ ▼❡t♦❞♦❧♦❣✐❛ ❛♦ ❝❡♥tr♦ ❞♦ ❣r✉♣♦✳ ❆♣ós ❡st❛ ❡t❛♣❛✱ ❛ tr♦❝❛ ❞❡ ✐♥❢♦r♠❛çõ❡s ❡♥tr❡ ♦s r♦❜ôs ♦❝♦rr❡❧♦❝❛❧♠❡♥t❡ ♥♦ â♠❜✐t♦ ❞❛s ✈✐③✐♥❤❛♥ç❛s✳ ❊ss❛ ❡str❛té❣✐❛ ✉t✐❧✐③❛ ♠♦❞❡❧♦s ❞❡ r♦❜ôs ❤♦❧♦♥ô♠✐❝♦s ❝♦♠ ❞✐♥â♠✐❝❛ ❞❛❞❛ ♣♦r˙p i = v i i = u i , i i i 2 2 2 ❡ ˙v ✭✹✳✷✶✮ ♥♦s q✉❛✐s p ∈ R ✱ v ∈ R ❡ u ∈ R ❝♦♠♣r❡❡♥❞❡♠ ❛ ♣♦s✐çã♦✱ ✈❡❧♦❝✐❞❛❞❡ ❡ ❡♥tr❛❞❛ i1 2 k , τ❞❡ ❝♦♥tr♦❧❡ ❞♦ r♦❜ô i ✭R ✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❆ ♣❛rt✐çã♦ τ = {τ }✱ τ ⊂ R = 1 2 η , , . . . ,{R R R }✱ ❝♦♥té♠ t♦❞♦s ♦s r♦❜ôs ❞❡ ✉♠ t✐♣♦ k ❡ ♠♦❞❡❧❛ ❛ ❤❡t❡r♦❣❡♥❡✐❞❛❞❡ j l =❞♦ s✐st❡♠❛✳ ❆ss✉♠❡✲s❡ q✉❡ ∀j, l : j 6= l → τ ∩ τ ∅✱ ✐✳❡✳✱ ❝❛❞❛ r♦❜ô é ✉♥✐❝❛♠❡♥t❡❛tr✐❜✉í❞♦ ❛ ✉♠❛ ú♥✐❝❛ ♣❛rt✐çã♦✳ ◆❡ss❛ ❡str❛té❣✐❛✱ ♣❛rt✐çõ❡s ♥ã♦ ❜❛❧❛♥❝❡❛❞❛s ❢♦r❛♠12 ❝♦♥s✐❞❡r❛❞❛s✱ s❡♥❞♦ q✉❡ τ ♣♦ss✉✐ ✉♠ ú♥✐❝♦ ♠❡♠❜r♦ ✭r♦❜ô ❧í❞❡r✮✱ ❡♥q✉❛♥t♦ q✉❡ τ❝♦♥t❡♠♣❧❛ ♦s ❞❡♠❛✐s r♦❜ôs✳ ❆ ❧❡✐ ❞❡ ❝♦♥tr♦❧❡ ❞❡s❝r✐t❛ ♥❛ ❊q✉❛çã♦ ✭✹✳✷✷✮ ❢♦✐ ♣r♦♣♦st❛ ❡♠ ❬❙❛♥t♦s ❡t ❛❧✳✱ ✷✵✶✹❪❡ é ✉t✐❧✐③❛❞❛ ♥❡st❡ tr❛❜❛❧❤♦✿ X X u = U ( (v ).i p i ij ij i j− ∇ kp k) − − v ✭✹✳✷✷✮ j6=i j6=i ij ij ( ◆❡ss❛ ❡q✉❛çã♦✱ U kp k) ❝♦♥s✐st❡ ❡♠ ✉♠❛ ❢✉♥çã♦ ♣♦t❡♥❝✐❛❧ ❛rt✐✜❝✐❛❧ q✉❡ ❡st❛❜❡❧❡❝❡ ij❛s r❡❣r❛s ❞❡ ✐♥t❡r❛çã♦ ❡♥tr❡ ❛❣❡♥t❡s i ❡ j✱ s❡♥❞♦ kp k ❛ ♥♦r♠❛ ❊✉❝❧✐❞❡❛♥❛ ❞♦ ✈❡t♦r p pi j i − p ❡ ∇ ♦ ❣r❛❞✐❡♥t❡ ❝♦♠ r❡s♣❡✐t♦ às ❝♦♦r❞❡♥❛❞❛s ❞♦ ❛❣❡♥t❡ i✳ ❖ ♣r✐♠❡✐r♦ t❡r♠♦ r❡♣r❡s❡♥t❛ ❛s ✐♥t❡r❛çõ❡s ❞♦ r♦❜ô i ❝♦♠ t♦❞♦s ♦s ❞❡♠❛✐s✱ ❡♥q✉❛♥t♦ q✉❡ ♦ s❡❣✉♥❞♦ t❡r♠♦é ✉t✐❧✐③❛❞♦ ♣❛r❛ s❡ ❛❧❝❛♥ç❛r ✉♠ ❝♦♥s❡♥s♦ ❞❡ ✈❡❧♦❝✐❞❛❞❡s✳ ij ❖ ❝❛♠♣♦ ♣♦t❡♥❝✐❛❧ ❛rt✐✜❝✐❛❧ U ❝♦♥s✐st❡ ❡♠ ✉♠❛ ❢✉♥çã♦ ❞❛s ❞✐stâ♥❝✐❛s r❡❧❛t✐✈❛s❡♥tr❡ ✉♠ ♣❛r ❞❡ ❛❣❡♥t❡s i ❡ j✱ ♦✉ s❡❥❛ 1 d2 ij U ( ( ) + ln , ij ij ij ij ij kp k) = α kp k − d kp k + ✭✹✳✷✸✮2 ij ij kp k + ♥♦s q✉❛✐s α ∈ R é ✉♠ ❣❛♥❤♦ ❞❡ ❝♦♥tr♦❧❡ ❡s❝❛❧❛r ❡ d é ✉♠ ♣❛râ♠❡tr♦ ♣♦s✐t✐✈♦ q✉❡❝♦♥tr♦❧❛ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ ❣r✉♣♦✳ ❊ss❡ ❝♦♠♣♦rt❛♠❡♥t♦ ♣♦❞❡ s❡r ♠♦❞✐✜❝❛❞♦ q✉❛♥❞♦ ij s❡ ❡s❝♦❧❤❡ ❛❞❡q✉❛❞❛♠❡♥t❡ ♦ ✈❛❧♦r d ✳ ❊ss❡ ♣❛râ♠❡tr♦ é ✉♠❛ ❢♦r♠❛ ❞❡ ✐♠♣❧❡♠❡♥t❛r ♦❝♦♥❝❡✐t♦ ❞❡♥♦♠✐♥❛❞♦ ♣♦t❡♥❝✐❛❧ ❞✐❢❡r❡♥❝✐❛❧ ✭❞✐✛❡r❡♥t✐❛❧ ♣♦t❡♥t✐❛❧✮ ❬❑✉♠❛r ❡t ❛❧✳✱ ✷✵✶✵❪✱ q✉❡ ❡st❛❜❡❧❡❝❡ q✉❡ ♣❛r❡s ❞❡ ❛❣❡♥t❡s ❡①♣❡r✐❡♥❝✐❛♠ ♠❛❣♥✐t✉❞❡s ❞✐❢❡r❡♥t❡s ❞❡ ♣♦t❡♥❝✐❛❧q✉❛♥❞♦ ♣♦ss✉❡♠ t✐♣♦s ❞✐❢❡r❡♥t❡s✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ❡♠ ❬❙❛♥t♦s ❡t ❛❧✳✱ ✷✵✶✹❪✱ ♦ ♣❛râ♠❡tr♦ d ij ❞❡ ✭✹✳✷✸✮ é ❜❛s❡❛❞♦ ✹✳✷✳ ❊str❛té❣✐❛s ❞❡ ▼♦✈✐♠❡♥t❛çã♦ ❞♦ ❊♥①❛♠❡ ✼✶ iτ ♥❛s ♣❛rt✐çõ❡s ❧♦❝❛✐s ✱ t❛❧ q✉❡✿ d ,AA k k i ✐❢ i ∈ τ ❛♥❞ j ∈ τ d ( τ ) = .ij ✭✹✳✷✹✮ d ,AB k k ✐❢ i ∈ τ ❛♥❞ j 6∈ τ❆ ❊q✉❛çã♦ ✭✹✳✷✹✮ ❞❡✜♥❡ q✉❡ ❛s ✐♥t❡r❛çõ❡s ❡♥tr❡ t✐♣♦s s✐♠✐❧❛r❡s ❡ ❞✐❢❡r❡♥t❡s ❞❡ r♦❜ôs AA AB sã♦ r❡❣✐❞❛s ♣♦r d ❡ d ✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ P♦r ❝♦♥str✉çã♦✱ t❛✐s ❝♦♥st❛♥t❡s ❡stã♦r❡❧❛❝✐♦♥❛❞❛s às ❞✐stâ♥❝✐❛s ✐♥t❡r❛❣❡♥t❡s ♥♦ ❡st❛❞♦ ❡stá✈❡❧✳ ❊♠ ❙❛♥t♦s ❡t ❛❧✳ ❬✷✵✶✹❪✱ ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ s❡❣r❡❣❛t✐✈♦ é ❛❧❝❛♥ç❛❞♦ q✉❛♥❞♦ ♦s♣❛râ♠❡tr♦s ❛ss✉♠❡♠ ✈❛❧♦r❡s ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ s❡❣✉✐♥t❡ r❡❣r❛✿ 0 < d < d .AA AB ✭✹✳✷✺✮P♦r ♦✉tr♦ ❧❛❞♦✱ ❑✉♠❛r ✫ ●❛r❣ ❬✷✵✶✶❪ ❛♣r❡s❡♥t❛♠ ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❛❣r❡❣❛t✐✈♦ ❛♦ ij❞❡✜♥✐r ♦s ♣❛râ♠❡tr♦s d ❝♦♠♦✿ 0 < d AB < d AA = d BB . ✭✹✳✷✻✮❆s r❡❣r❛s ❞❡ s❡❣r❡❣❛çã♦ ❡ ❛❣r❡❣❛çã♦✱ ❡①♣r❡ss❛❞❛s ♣❡❧❛s ❊q✉❛çõ❡s ✭✹✳✷✺✮ ❡ ✭✹✳✷✻✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ♣♦❞❡♠ s❡r ❝♦♠❜✐♥❛❞❛s ❞❡ ♠♦❞♦ ❛ ♣♦s✐❝✐♦♥❛r ✉♠ ❣r✉♣♦ ♥♦ ✐♥t❡r✐♦r ❞❡ ♦✉tr♦✳ ❆ss✐♠✱ ♥❡st❡ tr❛❜❛❧❤♦✱ ♦s ❝♦♠♣♦rt❛♠❡♥t♦s s❡❣r❡❣❛t✐✈♦ ❡ ❛❣r❡❣❛t✐✈♦ ❢♦r❛♠❝♦♠❜✐♥❛❞♦s t❡♥❞♦ ♦s ♣❛râ♠❡tr♦s d ij ❛❥✉st❛❞♦s ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿ 0 < d AA < d AB < d BB . ✭✹✳✷✼✮❊ss❛ ❝♦♠♣♦s✐çã♦ ❞❡ ❝♦♠♣♦rt❛♠❡♥t♦s ❢♦✐ ✉t✐❧✐③❛❞❛ ♣❛r❛ ♣♦s✐❝✐♦♥❛r ♦ r♦❜ô ❧í❞❡r ♣ró①✐♠♦❛♦ ❝❡♥tr♦ ❞♦ ❡♥①❛♠❡✱ ♦✉ s❡❥❛✱ ♥♦ ✐♥t❡r✐♦r ❞♦ ♦✉tr♦ ❣r✉♣♦✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ❛♥t❡r✐♦r✲♠❡♥t❡✱ s♦♠❡♥t❡ ❞♦✐s ❣r✉♣♦s ❢♦r❛♠ ✉t✐❧✐③❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦✱ s❡♥❞♦ q✉❡ ✉♠ ❞❡❧❡s ♣♦ss✉✐ AA s♦♠❡♥t❡ ✉♠ r♦❜ô ✭❧í❞❡r✮✳ ❉❡✈✐❞♦ ❛ ✐ss♦✱ ♦ ♣❛râ♠❡tr♦ ✭d ✮ r❡❧❛❝✐♦♥❛❞♦ ❛ ❡ss❡ ❣r✉♣♦BB t♦r♥❛✲s❡ ✐rr❡❧❡✈❛♥t❡✱ ❞❡ ♠♦❞♦ q✉❡ s♦♠❡♥t❡ ♦ ♣❛râ♠❡tr♦ ❛ss♦❝✐❛❞♦ ❛♦ ♦✉tr♦ ❣r✉♣♦ ✭d ✮ ♥❛ ❊q✉❛çã♦ ✭✹✳✷✼✮ é ✉t✐❧✐③❛❞♦✿ 0 < d < d .AB BB ✭✹✳✷✽✮❆ ❋✐❣✉r❛ ✹✳✼ ♠♦str❛ ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ❝♦♥✜❣✉r❛çõ❡s ❞♦ ❡♥①❛♠❡ q✉❡ ✐❧✉str❛♠ ♦ ♠♦✈✐♠❡♥t♦ ❞♦ r♦❜ô ❧í❞❡r ✭♣♦♥t♦ ❛③✉❧✮ ❡♠ ❞✐r❡çã♦ ❛♦ ❝❡♥tr♦ ❞♦ ♦✉tr♦ ❣r✉♣♦ ✭♣♦♥t♦s✈❡r♠❡❧❤♦s✮✱ ❡♠ ❞❡❝♦rrê♥❝✐❛ ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ❝♦♥tr♦❧❛❞♦r ❞❡s❝r✐t♦ ♥❛s ❊q✉❛çõ❡s ✭✹✳✷✷✮✱✭✹✳✷✸✮ ❡ ❝♦♠ ♣❛râ♠❡tr♦s ❞❡✜♥✐❞♦s ❝♦♥❢♦r♠❡ ✭✹✳✷✽✮✳ ❈♦♠♦ ♣♦❞❡ s❡r ✈✐st♦✱ ♦s r♦❜ôs s❡ ✼✷❈❛♣ít✉❧♦ ✹✳ ▼❡t♦❞♦❧♦❣✐❛ ♦r❣❛♥✐③❛♠ ❡♠ ✉♠❛ ❢♦r♠❛çã♦ ❝✐r❝✉❧❛r ❡♠ t♦r♥♦ ❞♦ ❝❡♥tr♦ ❞❡ ♠❛ss❛ ❞♦ ❣r✉♣♦✳ ◆❡ss❛♦r❣❛♥✐③❛çã♦✱ r♦❜ôs ❧♦❝❛❧✐③❛❞♦s ♥❛ ♣❛rt❡ ❡①t❡r✐♦r ❞♦ ❣r✉♣♦ ♣♦ss✉❡♠ ❞✐stâ♥❝✐❛s ♠❛✐♦r❡s❡♠ r❡❧❛çã♦ ❛ s❡✉s ✈✐③✐♥❤♦s✱ ❡♥q✉❛♥t♦ q✉❡ r♦❜ôs ♣ró①✐♠♦s ❛♦ ❝❡♥tr♦ ❞♦ ❣r✉♣♦ ♣♦ss✉❡♠❞✐stâ♥❝✐❛s ♠❡♥♦r❡s ♣❛r❛ s❡✉s ✈✐③✐♥❤♦s✳ ❊ss❡ ❞❡s❡q✉✐❧í❜r✐♦ ♥❛ ❢♦r♠❛çã♦ ❞♦ ❣r✉♣♦ ♣♦❞❡✐♥✢✉❡♥❝✐❛r ❞✐r❡t❛♠❡♥t❡ ♥❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ ✉♠ r♦❜ô✱ ❞❡♣❡♥❞❡♥❞♦ ❞❛ ♣♦s✐çã♦ r❡❧❛t✐✈❛ ❞♦ ♠❡s♠♦ ♥♦ ❣r✉♣♦✳ ❆ss✐♠✱ ♠❡❞✐❞❛s r❡❧❛t✐✈❛s t♦♠❛❞❛s ♣♦r r♦❜ôs ❧♦❝❛❧✐③❛❞♦s♥❛ ♣❛rt❡ ❡①t❡r♥❛ ❞♦ ❣r✉♣♦ t❡♥❞❡♠ ❛ ✐♥❝♦r♣♦r❛r ♠❛✐s ✐♥❝❡rt❡③❛ ❞♦ q✉❡ ❛q✉❡❧❛s t♦♠❛❞❛s♣♦r r♦❜ôs s✐t✉❛❞♦s ♥♦ ✐♥t❡r✐♦r ❞♦ ❣r✉♣♦✳ ❆♣ós ❡ss❛ ✐❞❡♥t✐✜❝❛çã♦✱ ❛ ❧❡✐ ❞❡ ❝♦♥tr♦❧❡ ✭✹✳✷✷✮❢♦✐ ❧✐❣❡✐r❛♠❡♥t❡ ♠♦❞✐✜❝❛❞❛ ❞❡ ❢♦r♠❛ q✉❡ ✉♠ r♦❜ô ❢♦ss❡ ✐♥✢✉❡♥❝✐❛❞♦ s♦♠❡♥t❡ ♣♦r s❡✉s✈✐③✐♥❤♦s✿ X X u = U ( (v ),i p i ij ij i j i − ∇ kp k) − − v ✭✹✳✷✾✮ j∈N i j∈N i j6=i j6=i i s❡♥❞♦ N ♦ ❣r✉♣♦ ❞❡ r♦❜ôs ❧♦❝❛❧✐③❛❞♦s ♥❛ ✈✐③✐♥❤❛♥ç❛ ❞❡ R ✳❋✐❣✉r❛ ✹✳✼✿ ▼♦♠❡♥t♦s ❞✐st✐♥t♦s ❞❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦ r♦❜ô ❧í❞❡r ✭♣♦♥t♦ ❛③✉❧✮ ❡♠ ❞✐r❡çã♦❛♦ ❝❡♥tr♦ ❞♦ ❣r✉♣♦ ✭❛❧✈♦ ❛③✉❧✮✳ ◆❛ s❡q✉ê♥❝✐❛ ❛♣r❡s❡♥t❛❞❛✱ ❛ ♣r✐♠❡✐r❛ ❡ q✉✐♥t❛ ✐♠❛❣❡♠ r❡♣r❡s❡♥t❛♠ ❛ ❝♦♥✜❣✉r❛çã♦ ✐♥✐❝✐❛❧ ❡ ✜♥❛❧ ❞♦ ❣r✉♣♦✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❆♦ ✉t✐❧✐③❛r ❛ ❊q✉❛çã♦ ✭✹✳✷✾✮✱ ❢♦r♠❛çõ❡s r❡❣✉❧❛r❡s ✭❧❛tt✐❝❡s✮ ♦❝♦rr❡♠ ❧♦❝❛❧♠❡♥t❡ ❡ t♦❞♦s ♦s r♦❜ôs ❛♣r❡s❡♥t❛♠ ❞✐stâ♥❝✐❛s s✐♠✐❧❛r❡s ❡♥tr❡ s✐✳ ❆♣❡s❛r ❞♦ ♣♦t❡♥❝✐❛❧ ❛rt✐✜❝✐❛❧ij✭✹✳✷✸✮ s❡ ♠❛♥t❡r ♦ ♠❡s♠♦✱ ♦s ♣❛râ♠❡tr♦s d sã♦ ♠♦❞✐✜❝❛❞♦s ♣❛r❛ ❣❡r❛r ♦ ❝♦♠♣♦rt❛✲♠❡♥t♦ ❛❣r❡❣❛t✐✈♦✱ ❞❡ ♠♦❞♦ q✉❡ 0 < d AB = d AA . ✭✹✳✸✵✮◆❛ ♣r✐♠❡✐r❛ ❢❛s❡ ❞❛ ❢♦r♠❛çã♦ ❞♦ ❣r✉♣♦✱ ♦s r♦❜ôs ✉t✐❧✐③❛♠ ❛ ❧❡✐ ❞❡ ❝♦♥tr♦❧❡ ❣❧♦✲ ❜❛❧ ❞❡s❝r✐t❛ ♥❛ ❊q✉❛çã♦ ✭✹✳✷✷✮✳ ◆❛q✉❡❧❛ ❢❛s❡✱ ✉♠ r♦❜ô ♥❡❝❡ss✐t❛ ❝❛❧❝✉❧❛r ❞✐stâ♥❝✐❛s r❡❧❛t✐✈❛s ♣❛r❛ t♦❞♦s ♦s r♦❜ôs ♥♦ ❣r✉♣♦✳ ❆ss✐♠✱ ♦ r♦❜ô ❧í❞❡r ♣♦❞❡ s❡r ❛✉t♦♠❛t✐❝❛♠❡♥t❡♣♦s✐❝✐♦♥❛❞♦ ♣ró①✐♠♦ ❛♦ ❝❡♥tr♦ ❞♦ ❣r✉♣♦ ❛♦ ❝♦♥✜❣✉r❛r ♦s ♣❛râ♠❡tr♦s ❞❡ ❛❝♦r❞♦ ❝♦♠✭✹✳✷✽✮✳ ◆♦ ❡♥t❛♥t♦✱ ❢❛③✲s❡ ♥❡❝❡ssár✐♦ ❞❡✜♥✐r ✉♠❛ ❝♦♥❞✐çã♦ ♣❛r❛ q✉❡ ❝❛❞❛ r♦❜ô s✉❜st✐t✉❛❛ ❧❡✐ ❞❡ ❝♦♥tr♦❧❡ ❡♠ ✉s♦ ✭✹✳✷✷✮ ♣♦r ✭✹✳✷✾✮✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ♦ r♦❜ô ❧í❞❡r é r❡s♣♦♥sá✈❡❧♣♦r ❝♦♦r❞❡♥❛r ❡ss❛ t❛r❡❢❛ ❡ ❡❧❡ ❛ ❢❛③ ✈✐❛ ❝♦♠✉♥✐❝❛çã♦✳ ❆ss✐♠✱ ❛♣ós ♦ ❧í❞❡r ❛❧❝❛♥ç❛r✉♠❛ ♣♦s✐çã♦ ♣ró①✐♠❛ ❞♦ ❝❡♥tr♦ ❛♦ ❣r✉♣♦ ❡❧❡ ❡♥✈✐❛ ✉♠❛ ♠❡♥s❛❣❡♠ ❞❡ ❜r♦❛❞❝❛st ♣❛r❛ ✹✳✷✳ ❊str❛té❣✐❛s ❞❡ ▼♦✈✐♠❡♥t❛çã♦ ❞♦ ❊♥①❛♠❡ ✼✸ t♦❞♦s ♦s r♦❜ôs✱ ❞❡ ♠♦❞♦ q✉❡ ♦s ♠❡s♠♦s ♣♦ss❛♠ s✉❜st✐t✉✐r ❛ ❛t✉❛❧ ❧❡✐ ❞❡ ❝♦♥tr♦❧❡ ♣♦r❛q✉❡❧❛ ❞❡s❝r✐t❛ ❡♠ ✭✹✳✷✾✮ ❡ ❝♦♥✜❣✉r❛r s❡✉s ♣❛râ♠❡tr♦s ❞❡ ❛❝♦r❞♦ ❝♦♠ ✭✹✳✸✵✮✳✹✳✷✳✷✳✷ ▼♦✈✐♠❡♥t❛çã♦ ❞♦ ❡♥①❛♠❡❆♣ós ♦ ❡♥①❛♠❡ ❛❧❝❛♥ç❛r ❛ ❢♦r♠❛çã♦ ✐♥✐❝✐❛❧ ✉t✐❧✐③❛♥❞♦ ♦s ♣❛ss♦s ❞❡s❝r✐t♦s ♥❛ s❡çã♦ ❛♥t❡✲ r✐♦r✱ ❛❧❣✉♥s ✇❛②♣♦✐♥ts✱ ❞❡✜♥✐❞♦s ❡♠ ♣♦s✐çõ❡s ❝♦♥❤❡❝✐❞❛s ♣❡❧♦ r♦❜ô ❧í❞❡r✱ sã♦ ✉t✐❧✐③❛❞♦s♣❛r❛ ❣✉✐❛r ♦ ❣r✉♣♦✳ ❉❡ss❡ ♠♦❞♦✱ ♦ ❧í❞❡r é ❣✉✐❛❞♦ ♣❡❧♦ ❛♠❜✐❡♥t❡ ✉t✐❧✐③❛♥❞♦ ✉♠ ♣♦t❡♥❝✐❛❧❛tr❛t✐✈♦ ♣❛r❛ ♦s ✇❛②♣♦✐♥ts ❡ ♦s ❞❡♠❛✐s r♦❜ôs ♦ s❡❣✉❡♠✳ ❆ ❧❡✐ ❞❡ ❝♦♥tr♦❧❡ ✭✹✳✷✾✮ ✉t✐❧✐✲③❛❞❛ ♥♦ ❡stá❣✐♦ ❛♥t❡r✐♦r é ❧✐❣❡✐r❛♠❡♥t❡ ♠♦❞✐✜❝❛❞❛ ♣❛r❛ ✐♥❝♦r♣♦r❛r ♦ ♣♦t❡♥❝✐❛❧ ❛tr❛t✐✈♦♣❛r❛ ✉♠ ✇❛②♣♦✐♥t ❡ ✉♠ t❡r♠♦ ❞❡ ❛♠♦rt❡❝✐♠❡♥t♦✱ ❝♦♥❢♦r♠❡ s❡❣✉❡✿ X X ui − ∇ i ij kp ij k) − i − v j − δ il ∇ i it kp it k) − γv i ✭✹✳✸✶✮ = p U ( (v ) p U ( , j∈N i j∈N i j6=i j6=i it i (p )t s❡♥❞♦ U ❛ ❢✉♥çã♦ ♣♦t❡♥❝✐❛❧ ❛rt✐✜❝✐❛❧ q✉❡ ❣✉✐❛ ♦ ❧í❞❡r ❡♠ ❞✐r❡çã♦ ❛♦ ❛❧✈♦✱ p ❛it i t p i❧♦❝❛❧✐③❛çã♦ ❞♦ ❛❧✈♦✱ kp k ❛ ♥♦r♠❛ ❞♦ ✈❡t♦r p − p ✭❞✐stâ♥❝✐❛ ❊✉❝❧✐❞✐❛♥❛✮ ❡ ∇ ♦ il❣r❛❞✐❡♥t❡ ❝♦♠ r❡s♣❡✐t♦ às ❝♦♦r❞❡♥❛❞❛s ❞♦ r♦❜ô i✳ ❖ ♣❛râ♠❡tr♦ δ ❝♦♥s✐st❡ ♥❛ ❢✉♥çã♦❞❡❧t❛ ❞❡ ❑r♦♥❡❝❦❡r ❞❡s❝r✐t❛ ♣♦r  1,✐❢ i = l δ = il 0,✐❢ i 6= l, ❡♠ q✉❡ l r❡♣r❡s❡♥t❛ ♦ í♥❞✐❝❡ ❞♦ r♦❜ô ❧í❞❡r✳ ❖ ú❧t✐♠♦ t❡r♠♦ ❝♦♠♣r❡❡♥❞❡ ✉♠ ❝♦♠♣♦✲♥❡♥t❡ ❞❡ ❛rr❛st♦ q✉❡ ❛✉①✐❧✐❛ ♥❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦s r♦❜ôs✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ q✉❛♥❞♦ s❡❢❛③ ♥❡❝❡ssár✐♦ ❡❢❡t✉❛r ♠✉❞❛♥ç❛s ❞❡ ❞✐r❡çã♦ ♠❛✐s ❛❝❡♥t✉❛❞❛s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ♥❛s♠✉❞❛♥ç❛s ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❛❧✈♦✳ ❚❛❧ t❡r♠♦ é ❛❥✉st❛❞♦ ✉t✐❧✐③❛♥❞♦ ✉♠❛ ❝♦♥st❛♥t❡ ❞❡♣r♦♣♦r❝✐♦♥❛❧✐❞❛❞❡ γ✳ ❖ ❝❛♠♣♦ ♣♦t❡♥❝✐❛❧ ❛tr❛t✐✈♦ U it é ✉♠❛ ❢✉♥çã♦ ❞❛ ❞✐stâ♥❝✐❛ r❡❧❛t✐✈❛ ❡♥tr❡ ♦ ❧í❞❡r ❡✉♠ ✇❛②♣♦✐♥t 1 2U ( β , it kp it k) = kp it k ✭✹✳✸✷✮ 2♥♦ q✉❛❧ β é ♦ ❣❛♥❤♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❝♦♥tr♦❧❛r ❛ ✐♥t❡♥s✐❞❛❞❡ ❞♦ ♣♦t❡♥❝✐❛❧✳ ❯♠ ❛❥✉st❡❛❞❡q✉❛❞♦ ❞♦s ❣❛♥❤♦s α✱ β ❡ γ ♣❡r♠✐t❡ ❛♦ ❣r✉♣♦ ♠❛♥t❡r ❞❡t❡r♠✐♥❛❞❛ ❢♦r♠❛çã♦ ❞✉r❛♥t❡ s✉❛ ♠♦✈✐♠❡♥t❛çã♦✳ ❆♣❡s❛r ❞♦ ❧í❞❡r s❛❜❡r ❛ ♣♦s✐çã♦ ❞♦s ✇❛②♣♦✐♥ts✱ ♦ ♠♦✈✐♠❡♥t♦ ❞♦❣r✉♣♦ é ❜❛s❡❛❞♦ ❡♠ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s✳ P♦❞❡✲s❡ ♦❜s❡r✈❛r q✉❡ ❛s ❊q✉❛çõ❡s ✭✹✳✷✾✮ ❡ ✭✹✳✸✶✮ sã♦ ✐❞ê♥t✐❝❛s ♣❛r❛ ♦s r♦❜ôs✱ ❝♦♠❡①❝❡çã♦ ❞♦ ❧í❞❡r✳ ❉❡ss❛ ❢♦r♠❛✱ s♦♠❡♥t❡ ♦ ❧í❞❡r ♥❡❝❡ss✐t❛ ♠♦❞✐✜❝❛r s✉❛ ❧❡✐ ❞❡ ❝♦♥tr♦❧❡ ✼✹❈❛♣ít✉❧♦ ✹✳ ▼❡t♦❞♦❧♦❣✐❛ ♣❛r❛ ❝♦❧♦❝❛r ♦ ❣r✉♣♦ ❡♠ ♠♦✈✐♠❡♥t♦✱ ♦ q✉❡ ♣♦❞❡ s❡r ❢❡✐t♦ ❞❡ ♠❛♥❡✐r❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛✳◗✉❛♥❞♦ ❛ ❧❡✐ ❞❡ ❝♦♥tr♦❧❡ ✭✹✳✷✷✮ é ✉t✐❧✐③❛❞❛ ❡♠ s✐st❡♠❛s ❝♦♠♣♦st♦s ♣♦r ♠✉✐t♦s r♦❜ôs✱✉♠❛ ❢♦r♠❛çã♦ ♥ã♦ ✉♥✐❢♦r♠❡ é ❣❡r❛❞❛✿ r♦❜ôs ❧♦❝❛❧✐③❛❞♦s ♣ró①✐♠♦ ❛♦ ❝❡♥tr♦ ❞♦ ❣r✉♣♦❡stã♦ ♠❛✐s ♣ró①✐♠♦s ❡♥tr❡ s✐ ❞♦ q✉❡ ♦s q✉❡ s❡ ❡♥❝♦♥tr❛♠ ♠❛✐s ❞✐st❛♥t❡s ❞♦ ❝❡♥tr♦✳ ❆♦❛♣❧✐❝❛r ❡ss❛ ❧❡✐ ❞❡ ❝♦♥tr♦❧❡✱ ❛♣❛r❡♥t❡♠❡♥t❡ ♦ ❝❡♥tr♦ ❞♦ ❣r✉♣♦ t♦r♥❛✲s❡ ❛ ♣♦s✐çã♦ ♠❛✐s♣r♦✈á✈❡❧ ❞❡ ✉♠ r♦❜ô ❡st❛r ❡q✉✐❞✐st❛♥t❡ ❞❡ s❡✉s ✈✐③✐♥❤♦s ✐♠❡❞✐❛t♦s✱ ♣♦✐s ❛❝r❡❞✐t❛♠♦s q✉❡ t❛❧ ♣♦s✐çã♦ s❡❥❛ ✉♠ ♠í♥✐♠♦ ❣❧♦❜❛❧ ❞❛ ❡q✉❛çã♦ ❞❡ ❝♦♥tr♦❧❡ ✭✹✳✷✷✮✳ ❊ss❛ s✉♣♦s✐çã♦❢♦✐✱ ❡♥tã♦✱ ❡♠♣r❡❣❛❞❛ ♣❛r❛ ❞❡✜♥✐r ♦ ♠♦♠❡♥t♦ ❛ ♣❛rt✐r ❞♦ q✉❛❧ ♦ r♦❜ô ❧í❞❡r ❝♦❧♦❝❛ ♦❣r✉♣♦ ❡♠ ♠♦✈✐♠❡♥t♦✳ ❊ss❡ ♠♦♠❡♥t♦ é ❡st❛❜❡❧❡❝✐❞♦ q✉❛♥❞♦ ❛s ❞✐stâ♥❝✐❛s ❞♦ ❧í❞❡r ♣❛r❛ AB s❡✉s ✈✐③✐♥❤♦s ✐♠❡❞✐❛t♦s t❡♥❤❛♠ ❝♦♥✈❡r❣✐❞♦ ♣❛r❛ ✈❛❧♦r❡s ♣ró①✐♠♦s ❞❡ d ✱ ❞❡ ♠♦❞♦ q✉❡il ♦ ♣❛râ♠❡tr♦ δ ♥❛ ❊q✉❛çã♦ ✭✹✳✸✶✮ ♣♦ss❛ s❡r ❝♦♥✜❣✉r❛❞♦ ♣❛r❛ ♦ ✈❛❧♦r 1✳ ✹✳✸ ❙❡❧❡çã♦ ❡ ❈❛r❛❝t❡r✐③❛çã♦ ❞❡ ▼❛r❝♦s ❊♠ s✐st❡♠❛s ♠✉❧t✐rr♦❜ót✐❝♦s ❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♦❝♦rr❡♠ q✉❛♥❞♦ ♦s r♦❜ôs s❡ ❡♥❝♦♥tr❛♠ ♥♦ ❛♠❜✐❡♥t❡✳ ❊♠ ✈ár✐♦s tr❛❜❛❧❤♦s✱ ❛ ♦❝♦rrê♥❝✐❛ ❞❡ss❡s ❡♥❝♦♥tr♦ss❡ ❞á ♣♦r ❛❝❛s♦ ❡ ❛ ❢r❡q✉ê♥❝✐❛ ❞♦s ♠❡s♠♦s ♥ã♦ é ♣❧❛♥❡❥❛❞❛✳ ◆❡ss❡s s✐st❡♠❛s✱ ❛ ❡s❝❛ss❡③❞❡ ❡♥❝♦♥tr♦s ♣♦❞❡ ❝♦♠♣r♦♠❡t❡r s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦✱ ❞❡✈✐❞♦❛♦ ❝♦♥st❛♥t❡ ❛❝ú♠✉❧♦ ❞❡ ✐♥❝❡rt❡③❛ ❞❡❝♦rr❡♥t❡ ❞❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦s r♦❜ôs✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ♥❛ ❙❡çã♦ ✹✳✷✱ ❡str❛té❣✐❛s ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛ sã♦ ❡♠♣r❡✲❣❛❞❛s ♥❡st❡ tr❛❜❛❧❤♦ ❞❡ ♠♦❞♦ ❛ ♠❛♥t❡r ♦ ❡♥①❛♠❡ ❞❡ r♦❜ôs ❛t✉❛♥❞♦ ❞❡ ♠❛♥❡✐r❛ ❝♦❡s❛✳❚❛❧ ❝♦❡sã♦ ♣❡r♠✐t❡ s❡ ❢❛③❡r ✉♠ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❛ ❢r❡q✉ê♥❝✐❛ ❝♦♠ q✉❡ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐✲③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♣♦ss❛♠ ♦❝♦rr❡r✱ ✉♠❛ ✈❡③ q✉❡ ❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❞❡ r♦❜ôs ✈✐③✐♥❤♦s é♠❛♥t✐❞❛ ❞✉r❛♥t❡ t♦❞❛ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦ ❣r✉♣♦✳ ❆❧é♠ ❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ ❛t✉❛❧✐③❛çã♦✱ ❛ s❡❧❡çã♦ ❡ ❝❛r❛❝t❡r✐③❛çã♦ ❞❡ r♦❜ôs ❛t✉❛♥t❡s ❝♦♠♦ ♠❛r❝♦s ♣♦❞❡ ✐♥✢✉❡♥❝✐❛r ♥♦ ❞❡s❡♠♣❡✲♥❤♦ ❞♦ ❣r✉♣♦ ❡ ♥❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ r❡s✉❧t❛♥t❡✱ t❡♥❞♦ ❡♠ ✈✐st❛ ❛ ❝♦♠♣❧❡①✐❞❛❞❡❝♦♠♣✉t❛❝✐♦♥❛❧ ❡♥✈♦❧✈✐❞❛ ♣❛r❛ ♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❛s ✐♥❢♦r♠❛çõ❡s ❡♠ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛✲çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❉❡ss❡ ♠♦❞♦✱ t♦r♥❛✲s❡ r❡❧❡✈❛♥t❡ ♦ ❡st❛❜❡❧❡❝✐♠❡♥t♦ ❞❡ ✉♠❛ ❡str❛té❣✐❛♣❛r❛ s❡❧❡çã♦ ❞❛s ❢♦♥t❡s ❞❡ ✐♥❢♦r♠❛çã♦ ✭r♦❜ôs ♠❛r❝♦✮ q✉❡ s❡rã♦ ✉t✐❧✐③❛❞❛s ♥❛s ❡t❛♣❛s❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ ♣♦✐s t❛✐s ❡str❛té❣✐❛s ♣❡r♠✐t❡♠ ❡st❛❜❡❧❡❝❡r ✉♠❛ ❜♦❛ r❡❧❛çã♦❡♥tr❡ ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❡ ❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ r❡s✉❧t❛♥t❡✳ ❊♥①❛♠❡s ❞❡ r♦❜ôs ✐♥❡✈✐t❛✈❡❧♠❡♥t❡ ❝r✐❛♠ ♠❛✐♦r ❞❡♥s✐❞❛❞❡ ❡s♣❛❝✐❛❧ ♥♦ ❛♠❜✐❡♥t❡✳❚❛❧ ❞❡♥s✐❞❛❞❡ ❛♠♣❧✐❛ ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ❡♥❝♦♥tr♦s ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❛✉♠❡♥t❛ ❛ ♣♦ss✐✲❜✐❧✐❞❛❞❡ ❞❡ tr♦❝❛ ❞❡ ✐♥❢♦r♠❛çõ❡s ❡♥tr❡ s❡✉s ✐♥t❡❣r❛♥t❡s✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ♥♦ ❈❛♣ít✉❧♦✸✱ ❞✐✈❡rs♦s tr❛❜❛❧❤♦s ❡♠ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ✉t✐❧✐③❛♠ ❝r✐tér✐♦s ♣❛r❛ ❞❡✜♥✐r ♦s ♠♦✲♠❡♥t♦s ❡♠ q✉❡ ♦ ❛❥✉st❡ ❞❛s ❝r❡♥ç❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡✈❡ ♦❝♦rr❡r✳ ◆♦ ❡♥t❛♥t♦✱ t❛✐s ✹✳✹✳ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s✼✺ ❝r✐tér✐♦s sã♦ ❞❡♣❡♥❞❡♥t❡s ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ♠ét♦❞♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❡♠♣r❡❣❛❞♦ ❡✱♣♦r ✈❡③❡s✱ ✉♠ ú♥✐❝♦ ❝r✐tér✐♦ ❡stá ❞✐s♣♦♥í✈❡❧✳ ❆ ❞✐stâ♥❝✐❛ ♣❡r❝♦rr✐❞❛ ❡ ❛ ✐♥❝❡rt❡③❛ ❛❝✉✲♠✉❧❛❞❛ sã♦ ❞♦✐s ❝r✐tér✐♦s ✉t✐❧✐③❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦ q✉❡ ❛♣r❡s❡♥t❛♠ ✐♥❞í❝✐♦s ❞❡ q✉❡ ❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ r❡s✉❧t❛♥t❡ ♣♦❞❡ s❡r ❛❢❡t❛❞❛ ♣❡❧❛ ❢♦r♠❛ ❡ ❢r❡q✉ê♥❝✐❛ ❝♦♠ q✉❡❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ sã♦ ❡❢❡t✉❛❞❛s✳ ◆❛ ♠♦✈✐♠❡♥t❛çã♦ s✐♠✉❧tâ♥❡❛✱ ❛ ✐♥❝❡rt❡③❛ ❛ss♦❝✐❛❞❛ à ❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦❞❡ ✉♠ ❞❛❞♦ r♦❜ô ♠✉❞❛ ❝♦♥st❛♥t❡♠❡♥t❡✱ ❞❡✈✐❞♦ à ❝♦♥t✐♥✉✐❞❛❞❡ ❞❡ s❡✉ ♠♦✈✐♠❡♥t♦✳ ❊ss❛✐♥❝❡rt❡③❛ ♣♦❞❡ s❡r ✉t✐❧✐③❛❞❛ ❝♦♠♦ ❝r✐tér✐♦ ♣❛r❛ ❝❛r❛❝t❡r✐③❛r ♣♦t❡♥❝✐❛✐s r♦❜ôs ♥♦ ❣r✉♣♦❝♦♠♦ ♠❛r❝♦s✳ ❆ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ ❧✐♠✐❛r❡s ❞❡ ✐♥❝❡rt❡③❛ ❛ ♣❛rt✐r ❞♦ q✉❛❧ ✉♠ r♦❜ô ❞❡✐✲①❛rá ❞❡ s❡r ❝❛r❛❝t❡r✐③❛❞♦ ❝♦♠♦ ♠❛r❝♦ ❝♦♥s✐st❡ ❡♠ ✉♠ ❛s♣❡❝t♦ ❞❡ ❞✐❢í❝✐❧ ❞❡t❡r♠✐♥❛çã♦✱♣♦ré♠ ♦ ♠❡s♠♦ ♣♦❞❡ ✐♥✢✉❡♥❝✐❛r ❞✐r❡t❛♠❡♥t❡ ❛ ♣r❡❝✐sã♦ ❞❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦❞♦ ❣r✉♣♦✳ ◆❡st❡ tr❛❜❛❧❤♦ ❜✉s❝♦✉✲s❡ ✐❞❡♥t✐✜❝❛r ❡♠♣✐r✐❝❛♠❡♥t❡ ✉♠ ❡q✉✐❧í❜r✐♦ ❡♥tr❡ ❛❢r❡q✉ê♥❝✐❛ ❞❡ ❛t✉❛❧✐③❛çã♦ ✭❜❛s❡❛❞❛ ❡♠ ♥í✈❡✐s ❞❡ ✐♥❝❡rt❡③❛✮ ❡ ❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦❞♦ ❣r✉♣♦✱ t❡♥❞♦ ❡♠ ✈✐st❛ ♦ ❝✉st♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❡♥✈♦❧✈✐❞♦ ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦❝♦♦♣❡r❛t✐✈❛✳ ❆ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ♣♦❞❡ s❡r t❛♠❜é♠ ✐♥✢✉❡♥❝✐❛❞❛ ♣❡❧♦ ❝r✐tér✐♦ ✉t✐❧✐③❛❞♦♣❛r❛ s❡❧❡❝✐♦♥❛r ✉♠ r♦❜ô ❝♦♠♦ ♠❛r❝♦✳ ❉♦✐s ❝r✐tér✐♦s ♣❛r❛ s❡❧❡çã♦ ❞❡ ♠❛r❝♦s ❢♦r❛♠❡①♣❧♦r❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦✱ s❡♥❞♦ q✉❡ ✉♠ ❞❡❧❡s é ❜❛s❡❛❞♦ ♥❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ♦s r♦❜ôs❡♥✈♦❧✈✐❞♦s ❡♠ ✉♠❛ ❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡ ♦ ♦✉tr♦ ♥♦ ♥í✈❡❧ ❞❡ ✐♥❝❡rt❡③❛❛ss♦❝✐❛❞♦ ❛ ✉♠ ♣♦t❡♥❝✐❛❧ ♠❛r❝♦✳ ❉❡ss❡ ♠♦❞♦✱ ❞❛❞♦ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ r♦❜ôs ✈✐③✐♥❤♦s✱ ♦s♠❡s♠♦s sã♦ ♦r❞❡♥❛❞♦s ❞❡ ❛❝♦r❞♦ ❝♦♠ ✉♠ ❞♦s ❝r✐tér✐♦s ❞❡✜♥✐❞♦s ✭❞✐stâ♥❝✐❛ ♦✉ ♥í✈❡❧ ❞❡✐♥❝❡rt❡③❛✮ ❡ s❡❧❡❝✐♦♥❛❞♦s s❡❣✉✐♥❞♦ ❛ ♦r❞❡♠ ❡st❛❜❡❧❡❝✐❞❛✳ ✹✳✹ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ❆ ♠❡t♦❞♦❧♦❣✐❛ ❛♣r❡s❡♥t❛❞❛ ♣r♦♣õ❡ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ❡str❛té❣✐❛s ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡✲ t✐✈❛ ❝♦♠♦ ❢♦r♠❛ ❞❡ ♣❡r♠✐t✐r ❛ ❡①❡❝✉çã♦ ❞❡ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❝♦♠ ♠❛✐♦r❢r❡q✉ê♥❝✐❛✳ ❆❧é♠ ❞✐ss♦✱ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛ ♣❡r♠✐t❡ s✉♣❡r❛r ❛❧❣✉♠❛s ❞✐✜❝✉❧❞❛✲❞❡s ✐♠♣♦st❛s às té❝♥✐❝❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ q✉❛♥❞♦ ✉♠ ❣r✉♣♦ ❞❡ r♦❜ôs ❛t✉❛❡♠ ❛♠❜✐❡♥t❡s ❝♦♠ ❣r❛♥❞❡s ❞✐♠❡♥sõ❡s✳ ❆ ♠❡t♦❞♦❧♦❣✐❛ ❛♣r❡s❡♥t❛❞❛ ♣♦❞❡ s❡r ❛♣❧✐❝❛❞❛❞❡ ♠❛♥❡✐r❛ ❝♦♥s✐st❡♥t❡ t❛♥t♦ ❛ ❡♥①❛♠❡s r♦❜ót✐❝♦s ❤♦♠♦❣ê♥❡♦s q✉❛♥t♦ ❤❡t❡r♦❣ê♥❡♦s✳❉❡✈✐❞♦ às ❝❛♣❛❝✐❞❛❞❡s ❧✐♠✐t❛❞❛s ❞♦s r♦❜ôs ♥♦r♠❛❧♠❡♥t❡ ❡♠♣r❡❣❛❞♦s ❡♠ ❡♥①❛♠❡s✱ ❛✉t✐❧✐③❛çã♦ ❞♦s ❛❧❣♦r✐t♠♦s ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s ♣❡r♠✐t❡ ❡❢❡t✉❛r ❞❡ ♠❛♥❡✐r❛❞❡s❝❡♥tr❛❧✐③❛❞❛ ❛ ❢✉sã♦ s❡♥s♦r✐❛❧ ❝♦♠ ❜❛s❡ ❡♠ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s ❡ ❞❡ ♠❛♥❡✐r❛ ❝♦♥s✐s✲ t❡♥t❡✳ ❉❡ss❛ ❢♦r♠❛✱ t❡♠✲s❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❡s❝❛❧á✈❡❧ ♣❛r❛ ❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛❡♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s✳ ❈❛♣ít✉❧♦ ✺ ❊①♣❡r✐♠❡♥t♦s ❊st❡ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛ ♦s ❡①♣❡r✐♠❡♥t♦s ❞❡s❡♥✈♦❧✈✐❞♦s ❞✉r❛♥t❡ ❛ ❡①❡❝✉çã♦ ❞❡st❡ tr❛✲❜❛❧❤♦✳ ■♥✐❝✐❛❧♠❡♥t❡✱ ✉♠❛ ❛♥á❧✐s❡ ❞❛ ✈❛r✐❛çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs ♠❛r❝♦s ✉t✐❧✐③❛❞♦s♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡♠ ✉♠ ❡♥①❛♠❡ r♦❜ót✐❝♦ ❛♣r❡s❡♥t❛❞❛✳ ❊♠ s❡✲❣✉✐❞❛✱ ❛❧❣✉♠❛s s✐♠✉❧❛çõ❡s sã♦ ❡❢❡t✉❛❞❛s ♣❛r❛ ❛✉①✐❧✐❛r ♥❛ ❛♥á❧✐s❡ ❞❛ ❝♦♥s✐stê♥❝✐❛ ❞❛s❡st✐♠❛t✐✈❛s ❣❡r❛❞❛s ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ P♦r ✜♠✱ ✉♠❛ ♣r♦✈❛ ❞❡ ❝♦♥✲❝❡✐t♦ é ❛♣r❡s❡♥t❛❞❛ ♣❛r❛ ♠♦str❛r ❛ ✈✐❛❜✐❧✐❞❛❞❡ ❞❡ ❛♣❧✐❝❛r ❛ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛ ❡♠ s✐st❡♠❛s r❡❛✐s✳ ▼♦❞❡❧♦s ❞❡ r♦❜ôs ❤♦❧♦♥ô♠✐❝♦s ❡ ♥ã♦ ❤♦❧♦♥ô♠✐❝♦s ❢♦r❛♠ ❡♠♣r❡❣❛❞♦s♥❛s s✐♠✉❧❛çõ❡s✱ ❡♥q✉❛♥t♦ q✉❡ r♦❜ôs ❝♦♠ ❞✐r❡çã♦ ❞✐❢❡r❡♥❝✐❛❧ ✭♠♦❞❡❧♦ ♥ã♦ ❤♦❧♦♥ô♠✐❝♦✮❢♦r❛♠ ✉s❛❞♦s ♥♦s ❛♠❜✐❡♥t❡s r❡❛✐s✳ ❆s ❡str❛té❣✐❛s ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❛♣r❡s❡♥t❛❞❛s ♥❛❙❡çã♦ ✹✳✷ ❢♦r❛♠ ✉t✐❧✐③❛❞❛s ❡♠ ♠♦♠❡♥t♦s ❞✐st✐♥t♦s ❞✉r❛♥t❡ ❛ ❡①❡❝✉çã♦ ❞❡st❡ tr❛❜❛❧❤♦✱♥♦ ❡♥t❛♥t♦ s♦♠❡♥t❡ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❝♦♥tí♥✉❛ ❢♦✐ ❛✈❛❧✐❛❞❛ ♥♦s ❡①♣❡r✐♠❡♥t♦s ❝♦♠ r♦❜ôs r❡❛✐s✳ ✺✳✶ ❆♥á❧✐s❡ ❞❛ ❱❛r✐❛çã♦ ❞♦ ◆ú♠❡r♦ ❞❡ ▼❛r❝♦s ❊st❡s ❡①♣❡r✐♠❡♥t♦s ❛♣r❡s❡♥t❛♠ ✉♠❛ ❛♥á❧✐s❡ r❡❢❡r❡♥t❡ ❛♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs ♠❛r❝♦ ❡♠✲♣r❡❣❛❞♦s ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡♠ ✉♠ ❡♥①❛♠❡ r♦❜ót✐❝♦✳ ❆ss✐♠✱ ❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦s r♦❜ôs ❢♦✐ ❛♥❛❧✐s❛❞❛ ❛♦ s❡ ❝♦♥s✐❞❡r❛r ❛ ✈❛r✐❛çã♦ ❞❡ ❛❧❣✉♥s❛s♣❡❝t♦s✱ ❛ s❛❜❡r✿ ♦ ♥ú♠❡r♦ ❞❡ ♠❛r❝♦s ✉t✐❧✐③❛❞♦s ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛✲ t✐✈❛❀ ❝r✐tér✐♦s ♣❛r❛ s❡❧❡çã♦ ❞♦s ♠❛r❝♦s❀ ❡ ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ ✐♥❝❡rt❡③❛ ♥❛s ♠❡❞✐❞❛s❡①t❡r♦❝❡♣t✐✈❛s✳ ❊st❡ ❝♦♥❥✉♥t♦ ❞❡ ❡①♣❡r✐♠❡♥t♦s s✐♠✉❧❛❞♦s ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ✉t✐❧✐③❛♥❞♦♠♦❞❡❧♦s ❞❡ r♦❜ôs ❤♦❧♦♥ô♠✐❝♦s✳ ❉❡ss❡ ♠♦❞♦✱ ♦ ❡st❛❞♦ ❞❡ ❝❛❞❛ r♦❜ô ❝♦♥s✐st❡ ❛♣❡♥❛s❡♠ s✉❛ r❡s♣❡❝t✐✈❛ ♣♦s✐çã♦ ❡ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦s ♠❡s♠♦s ♦❝♦rr❡ ❡♠ q✉❛❧q✉❡r ❞✐r❡çã♦♥♦ ♣❧❛♥♦ ❜✐❞✐♠❡♥s✐♦♥❛❧✳ ❖s ❡①♣❡r✐♠❡♥t♦s ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞♦s ✉t✐❧✐③❛♥❞♦ ♦ ❛♠❜✐❡♥t❡ r▼❆❚▲❆❇ ✳ ✼✽❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s ✺✳✶✳✶ ▼♦✈✐♠❡♥t❛çã♦ ❆❧t❡r♥❛❞❛ ❖s ❡①♣❡r✐♠❡♥t♦s s✐♠✉❧❛❞♦s ❢♦r❛♠ ❡①❡❝✉t❛❞♦s ❝♦♠ ✉♠ ❡♥①❛♠❡ ❝♦♠♣♦st♦ ♣♦r ✸✵ r♦❜ôs i i❤♦❧♦♥ô♠✐❝♦s✳ ❆ss✐♠ s❡♥❞♦✱ ♦ ❡st❛❞♦ x ❞♦ ✐✲és✐♠♦ r♦❜ô R é r❡♣r❡s❡♥t❛❞♦ ♣♦r s✉❛ i = [x i y i ] ⊤♣♦s✐çã♦ p ♥♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ❞❡ r❡❢❡rê♥❝✐❛ ✭✈❡r ❋✐❣✉r❛ ✷✳✶✮✳ ❖ ✈❡t♦r ⊤ u = [v v ]i x i y ix i y i r❡♣r❡s❡♥t❛ ❛ ❡♥tr❛❞❛ ❞❡ ❝♦♥tr♦❧❡✱ s❡♥❞♦ v ❡ v ❛s ✈❡❧♦❝✐❞❛❞❡s ❧✐♥❡❛r❡s ❞♦ r♦❜ô ♥❛s ❞✐r❡çõ❡s x ❡ y✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❆ss✐♠✱ ♥❡st❡s ❡①♣❡r✐♠❡♥t♦s✱ ❝❛❞❛ r♦❜ô é❞♦ t✐♣♦ ✐♥t❡❣r❛❞♦r s✐♠♣❧❡s✱ ❛t✉❛❞♦ ❞✐r❡t❛♠❡♥t❡ ❡♠ ✈❡❧♦❝✐❞❛❞❡✳ ❖ ♠♦❞❡❧♦ ❞✐s❝r❡t♦ ❞❡ tr❛♥s✐çã♦ é ❡①♣r❡ss❛❞♦ ♣♦r✿ k+1|k k k xi = g(x , u ), i i" # k k x + v ∆ti x i ✭✺✳✶✮= . k k i y + v ∆t i y i ❆ ❡st✐♠❛t✐✈❛ bx é ♣r♦♣❛❣❛❞❛ ✉t✐❧✐③❛♥❞♦ ✭✺✳✶✮ ❡♠ ❡t❛♣❛s ❞❡ ♣r❡❞✐çã♦ ❞♦ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥✿ k+1|k k k x = g( x , u ).k k k k k ⊤ k b i b i b i ✭✺✳✷✮= u +ǫ = [ˆ v v ˆ ] ❆ ❡♥tr❛❞❛ bu i i i x i y i ❝♦♥s✐st❡ ♥❛s ✈❡❧♦❝✐❞❛❞❡s ❝♦♠❛♥❞❛❞❛s u i ✱ ♥♦ ✐♥st❛♥t❡ ⊤ i v v = [ǫ ǫ ]❞❡ t❡♠♣♦ k✱ ❛✉♠❡♥t❛❞❛s ❝♦♠ r✉í❞♦ ǫ ❛❞✐t✐✈♦✱ ●❛✉ss✐❛♥♦✱ ❝♦♠ ♠é❞✐❛s ③❡r♦ xi yi ⊤ i i (ǫ )❡ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛ Q = diag(E{ǫ })✳ ◆♦ ❞❡❝♦rr❡r ❞❛ ♠♦✈✐♠❡♥t❛çã♦✱ ❝❛❞❛ r♦❜ô ❡✈♦❧✉✐ ✐♥❞✐✈✐❞✉❛❧♠❡♥t❡ ❡ss❡ ♠♦❞❡❧♦ ❡♠ ✐♥t❡r✈❛❧♦s ❞❡ t❡♠♣♦ ❞❡ ❝♦♠♣r✐♠❡♥t♦ ∆t✳k ❆ ♣r♦♣❛❣❛çã♦ ❞❛ ✐♥❝❡rt❡③❛ é ❝❛❧❝✉❧❛❞❛ ❝♦♥❢♦r♠❡ ✭✹✳✻✮✱ s❡♥❞♦ Φ i ✉♠❛ ♠❛tr✐③ ✐❞❡♥t✐❞❛❞❡ k❞❡ ♦r❞❡♠ 2 ✭I 2 ✮ ❡ G ❛ ♠❡s♠❛ ♠❛tr✐③ ♠✉❧t✐♣❧✐❝❛❞❛ ♣❡❧♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ ∆t✳ i ❖ ♠♦❞❡❧♦ ❞❡ ♦❜s❡r✈❛çã♦ é s❡♠❡❧❤❛♥t❡ à ❊q✉❛çã♦ ✭✹✳✼✮✳ ❉❡✈✐❞♦ à ✉t✐❧✐③❛çã♦ ❞❡✉♠ ♠♦❞❡❧♦ ❤♦❧♦♥ô♠✐❝♦ ❡ ❛ s✉♣♦s✐çã♦ ❞❡ ❝♦✐♥❝✐❞ê♥❝✐❛ ❞❡ ♦r✐❡♥t❛çã♦ ❞♦s s✐st❡♠❛s ❞❡ ji❝♦♦r❞❡♥❛❞❛s ❞❡ r❡❢❡rê♥❝✐❛ ❡ ❞♦ r♦❜ô✱ ❛ ♣❛rt❡ ❞❛ ❡st✐♠❛t✐✈❛ bx ❛ss♦❝✐❛❞❛ à ♦r✐❡♥t❛çã♦ j♥ã♦ é ❝♦♥s✐❞❡r❛❞❛✳ ❉❡ss❡ ♠♦❞♦✱ ❛ ♣♦s✐çã♦ ❞❡ R ❝♦♠♣✉t❛❞❛ ❛ ♣❛rt✐r ❞❛s ♠❡❞✐❞❛s ❞❡ i❞✐stâ♥❝✐❛ ❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛s t♦♠❛❞❛s ♣♦r ✉♠ r♦❜ô ♠❛r❝♦ R ❡ ❞❛ ♣♦s✐çã♦ ❞❡st❡✱❝♦♥s✐st❡ ❡♠✿ " # " # " # x ji x i ρ ij ij )❝♦s(φ = ,✭✺✳✸✮ ♦✉ s❡❥❛✱ xji = f (x i , h(x i , x j )). ✭✺✳✹✮❯t✐❧✐③❛♥❞♦ ❛ ❢♦r♠✉❧❛çã♦ ❛♣r❡s❡♥t❛❞❛ ♥❛ ♠❡t♦❞♦❧♦❣✐❛✱ ♦ ❝á❧❝✉❧♦ ❞❛ ❡st✐♠❛t✐✈❛ bx ji ✺✳✶✳ ❆♥á❧✐s❡ ❞❛ ❱❛r✐❛çã♦ ❞♦ ◆ú♠❡r♦ ❞❡ ▼❛r❝♦s ✼✾é ❢❡✐t♦ ❝♦♥❢♦r♠❡ ✭✹✳✶✶✮✱ ❡♥q✉❛♥t♦ q✉❡ ❛ ✐♥❝❡rt❡③❛ é ❝♦♠♣✉t❛❞❛ ✉t✐❧✐③❛♥❞♦ ✭✹✳✶✹✮✱ s❡♥❞♦ k+1 k+1 k+1 " # ∂f (x , h(x , x )) k+1 i i j 1 0F = = , ij k+1 k+1 k+1 k+1 ∂x x x i =b x j x j i i 0 1 =b k+1 ∂f (x , h(x , x )) i i j S = ij k+1∂(z ) ij =b x j x j x i x i =b " # k+1 k+1 k+1) ) ❝♦s(φ ij −ρ ij s✐♥(φ ij= k+1 k+1 k+1 ) ρ ) x x i i ij = σ ]) 2 2 s✐♥(φ ij ij ❝♦s(φ ij =b x x j j =b j❡ R ❞✐❛❣([σ ✳ ❚❡♠✲s❡✱ ❡♥tã♦✱ ❞✉❛s ❡st✐♠❛t✐✈❛s ❛ss♦❝✐❛❞❛s ❛♦ ❡st❛❞♦ ❞❡ R ✱ k+1|k k+1 ρ φ x ❡ bx ✱ ❝♦♠❜✐♥❛❞❛s ✉t✐❧✐③❛♥❞♦ ❛ ❡t❛♣❛ ❞❡ ❝♦rr❡çã♦ ❞♦ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥ ❊st❡♥❞✐❞♦ b j ji✭♠❛✐♦r❡s ❞❡t❛❧❤❡s✱ ✈❡r ❊q✉❛çõ❡s ✭❇✳✶✷✮ ❡ ✭❇✳✶✸✮ ♥♦ ❆♣ê♥❞✐❝❡ ❇✮✳ 1 η , . . . , ◆❡st❡s ❡①♣❡r✐♠❡♥t♦s✱ ✉♠ ❣r✉♣♦ ❞❡ r♦❜ôs R = {R R } ♥❛✈❡❣❛ ❡♠ ✉♠ ❛♠✲❜✐❡♥t❡ ❧✐✈r❡ ❞❡ ♦❜stá❝✉❧♦s ❝♦♠ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✶✵✵ ♠❡tr♦s q✉❛❞r❛❞♦s ✭10 m × 10 m✮✳❖ ♠♦✈✐♠❡♥t♦ ❞♦s r♦❜ôs é ❞❡✜♥✐❞♦ ❝♦♠ ❜❛s❡ ❡♠ q✉❛tr♦ ✇❛②♣♦✐♥ts✱ ✉t✐❧✐③❛❞♦s ♥❛ t❛r❡❢❛ dir❞❡ ♥❛✈❡❣❛çã♦✳ ❚❛✐s ✇❛②♣♦✐♥ts ❞❡✜♥❡♠ ❛ ❞✐r❡çã♦ ✭v ✮ ❛ s❡r s❡❣✉✐❞❛ ♣♦r ❝❛❞❛ r♦❜ô✱ i i x i y i❛ q✉❛❧ é ✉t✐❧✐③❛❞❛ ♥♦ ❝ô♠♣✉t♦ ❞❛ ❛çã♦ ❞❡ ❝♦♥tr♦❧❡ u ✳ ❆s ✈❡❧♦❝✐❞❛❞❡s v ❡ v ❝❛❧✲ i❝✉❧❛❞❛s ❛ ♣❛rt✐r ❞❡ u ❢♦r❛♠ ❧✐♠✐t❛❞❛s ❛ 10 cm/s✱ ❛❧é♠ ❞❡ s❡r❡♠ s✉❥❡✐t❛s ❛ ✉♠ r✉í❞♦❛❞✐t✐✈♦✱ ❜r❛♥❝♦ ❡ ●❛✉ss✐❛♥♦✳ ❚❛❧ r✉í❞♦ ♣♦ss✉✐ ♠é❞✐❛ ③❡r♦ ❡ ✐♥❝❡rt❡③❛ ♣r♦♣♦r❝✐♦♥❛❧ ❛10% ❞♦ ✈❛❧♦r ❞❛ ✈❡❧♦❝✐❞❛❞❡✳ ❈❛❞❛ s✐♠✉❧❛çã♦ ✉t✐❧✐③♦✉ ❝❡r❝❛ ❞❡ 6500 ✐t❡r❛çõ❡s✱ s❡♥❞♦∆t = 100 ms ❛ ❞✉r❛çã♦ ❞❡ ❝❛❞❛ ✐t❡r❛çã♦✳ ❆ ❞✐stâ♥❝✐❛ t♦t❛❧ ♣❡r❝♦rr✐❞❛ ♣❡❧♦s r♦❜ôs ❢♦✐❞❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ 30 m✳ ❙❡❣✉✐♥❞♦ ❛ ♠❡t♦❞♦❧♦❣✐❛✱ ♦s r♦❜ôs ❢♦r❛♠ ✐♥✐❝✐❛❧♠❡♥t❡ ❞✐s♣♦st♦s ❥✉♥t♦s ❡ ❞✐✈✐❞✐❞♦s❡♠ ❞♦✐s s✉❜❣r✉♣♦s✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ♥❛ ❙❡çã♦ ✹✳✷✳✶✱ é ❛ss✉♠✐❞♦ q✉❡ ♦s r♦❜ôs ♣♦ss✉❡♠ r❡❧ó❣✐♦s s✐♥❝r♦♥✐③❛❞♦s✱ s❡♥❞♦ q✉❡ ❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♦❝♦rr❡♠ ♥♦ ♠♦✲♠❡♥t♦ q✉❡ ❛♥t❡❝❡❞❡ ❛ tr♦❝❛ ❞❡ ♣❛♣é✐s ❡♥tr❡ ♦s s✉❜❣r✉♣♦s✳ ❖ ♠♦✈✐♠❡♥t♦ ❞♦ ❡♥①❛♠❡ ❢♦✐❝♦♦r❞❡♥❛❞♦ ❞❡ ♠♦❞♦ q✉❡ ♦s s✉❜❣r✉♣♦s s❡ ♠♦✈❡ss❡♠ ❡♠ t✉r♥♦s ❝♦♠ ✐♥t❡r✈❛❧♦s ❞❡ t❡♠♣♦♣r❡❡st❛❜❡❧❡❝✐❞♦s✳ ❯♠ s✉❜❣r✉♣♦ é s❡❧❡❝✐♦♥❛❞♦ ♣❛r❛ ✐♥✐❝✐❛r ❛ ♠♦✈✐♠❡♥t❛çã♦✱ ❡♥q✉❛♥t♦ ♦♦✉tr♦ s❡ ♠❛♥té♠ ❡stát✐❝♦✳ ❆♣ós ❛ ♠♦✈✐♠❡♥t❛çã♦✱ ♦ s✉❜❣r✉♣♦ ♣❛r❛ ❡ ❝❛❞❛ ✉♠ ❞❡ s❡✉s♠❡♠❜r♦s ❡st✐♠❛ ❞✐stâ♥❝✐❛ ❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛s ♣❛r❛ ♦s r♦❜ôs ❡stát✐❝♦s ❞♦ ♦✉tr♦ s✉❜✲❣r✉♣♦ q✉❡ s❡ ❡♥❝♦♥tr❛♠ ❞❡♥tr♦ ❞❡ s✉❛s r❡s♣❡❝t✐✈❛s ✈✐③✐♥❤❛♥ç❛s✳ ❚❛✐s ✐♥❢♦r♠❛çõ❡s sã♦❡♥tã♦ ✉t✐❧✐③❛❞❛s ♣❛r❛ ❛t✉❛❧✐③❛r ❛s ❝r❡♥ç❛s ❞♦s r♦❜ôs q✉❡ ❡st❛✈❛♠ ❡♠ ♠♦✈✐♠❡♥t♦✱ ❡♠✉♠❛ ❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ◆❡st❡s ❡①♣❡r✐♠❡♥t♦s✱ ♦ r❛✐♦ ❞❛s ✈✐③✐♥❤❛♥ç❛s ❢♦✐❛♠♣❧✐❛❞♦ ♦ s✉✜❝✐❡♥t❡ ♣❛r❛ ♣❡r♠✐t✐r ❡❢❡t✉❛r ❛ ❛♥á❧✐s❡ ❞♦ ✐♠♣❛❝t♦ ❞❡ s❡ ✉t✐❧✐③❛r ✉♠ ♥ú✲ ✽✵❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s ♠❡r♦ ✈❛r✐á✈❡❧ ❞❡ ♠❛r❝♦s ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❆ ❋✐❣✉r❛ ✺✳✶ ❛♣r❡s❡♥t❛✉♠ ❡①❡♠♣❧♦ ❞♦ ❝❛♠✐♥❤♦ ❡①❡❝✉t❛❞♦ ♣❡❧♦ ❡♥①❛♠❡✱ ♥❛ q✉❛❧ ♦s ♣♦♥t♦s ♥❛s ❝♦r❡s ✈❡r♠❡❧❤❛❡ ❛③✉❧ ✐❧✉str❛♠ ❛ ♣♦s✐çã♦ ❞♦s ✐♥t❡❣r❛♥t❡s ❞❡ ❝❛❞❛ s✉❜❣r✉♣♦ ❞✉r❛♥t❡ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦❡♥①❛♠❡✳ ❖s ❝ír❝✉❧♦s r❡♣r❡s❡♥t❛♠ ❛ ♣♦s✐çã♦ ❞♦s r♦❜ôs ❡♠ q✉❛tr♦ ♠♦♠❡♥t♦s ❞✐st✐♥t♦s♥♦s q✉❛✐s ✉♠❛ ❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❢♦✐ ❡❢❡t✉❛❞❛✳42 3 y (m)1 −2 −1 −4 −3 −4 −3 −2 −1 1 2 3 4 x (m) ❋✐❣✉r❛ ✺✳✶✿ ❊①❡♠♣❧♦ ❞❡ ❝❛♠✐♥❤♦ ❡①❡❝✉t❛❞♦ ♣❡❧♦s r♦❜ôs✳ ❖s s✉❜❣r✉♣♦s sã♦ r❡♣r❡✲ s❡♥t❛❞♦s ♣❡❧❛s ❝♦r❡s ✈❡r♠❡❧❤❛ ❡ ❛③✉❧✱ s❡♥❞♦ ♦s ♣♦♥t♦s ❛ ♣♦s✐çã♦ ❞♦s r♦❜ôs ❞✉r❛♥t❡ ❛♥❛✈❡❣❛çã♦✳ ❖s ❝ír❝✉❧♦s r❡♣r❡s❡♥t❛♠ ♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦ ❡♥①❛♠❡ ❡♠ q✉❛tr♦ ♠♦♠❡♥t♦s❞✐st✐♥t♦s ❡♠ q✉❡ ♦❝♦rr❡✉ ✉♠❛ ❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❖ ♣r✐♠❡✐r♦ ❡①♣❡r✐♠❡♥t♦ ❢♦✐ ❡①❡❝✉t❛❞♦ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ❛✈❛❧✐❛r ♦ ✐♠♣❛❝t♦ ❞❛✉t✐❧✐③❛çã♦ ❞❡ ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ r✉í❞♦ ♥❛s ❡st✐♠❛t✐✈❛s ❡①t❡r♦❝❡♣t✐✈❛s✳ ❖ r✉í❞♦ n ❞♦♠♦❞❡❧♦ ❞❡ ♦❜s❡r✈❛çã♦ ✭✹✳✽✮✱ ❢♦✐ ❞❡✜♥✐❞♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ ❛s ♠❡❞✐❞❛s ❞❡ ❞✐stâ♥❝✐❛ ρ = ρ r❡❧❛t✐✈❛ ✐♥❝♦r♣♦r❛♠ ✉♠ r✉í❞♦ ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ ✈❛❧♦r r❡❛❧ ❞❛s ❞✐stâ♥❝✐❛s✱ s❡♥❞♦ σ ×{0,05, 0,10, 0,20, 0,30, 0,40}✱ ❡♥q✉❛♥t♦ q✉❡ ♦ r✉í❞♦ ❛ss♦❝✐❛❞♦ às ♠❡❞✐❞❛s ❞❡ ♦r✐❡♥t❛çã♦ ◦ ◦ ◦ φ = , 2 , 3 r❡❧❛t✐✈❛ ❢♦✐ ❞❡✜♥✐❞♦ ❝♦♠ ❜❛s❡ ❡♠ ✈❛❧♦r❡s ✜①♦s✱ ❞❡ ❢♦r♠❛ q✉❡ σ {1 }✳ ❖✐♠♣❛❝t♦ ❞❛ ✉t✐❧✐③❛çã♦ ❞❡ss❡s ♣❛râ♠❡tr♦s ❢♦✐ ❛♥❛❧✐s❛❞♦ ❡♠ r❡❧❛çã♦ à ✈❛r✐❛çã♦ ❞♦ ♥ú♠❡r♦❞❡ r♦❜ôs ♠❛r❝♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❝♦rr✐❣✐r ❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ♥❛s ❡t❛♣❛s ❞❡❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❋♦r❛♠ ✉t✐❧✐③❛❞♦s ❝♦♠♦ r♦❜ôs ♠❛r❝♦ ❞❡s❞❡ ✉♠ ú♥✐❝♦ r♦❜ô ❛té s♦ ♥ú♠❡r♦ t♦t❛❧ ❞❡ r♦❜ôs ❡♠ R ✱ ♦✉ s❡❥❛✱ ✶✺ r♦❜ôs✳ P❛r❛ ❝❛❞❛ ❝♦♠❜✐♥❛çã♦ ❡s♣❡❝í✜❝❛ ρ φ , σ❞♦s ✈❛❧♦r❡s ❞❡ r✉í❞♦ ✭σ ✮ ❡ ♦ ♥ú♠❡r♦ ❞❡ ♠❛r❝♦s✱ ✉♠ t♦t❛❧ ❞❡ 30 s✐♠✉❧❛çõ❡s ❢♦r❛♠❡①❡❝✉t❛❞❛s✳ ❖ ❡rr♦ ♠é❞✐♦ ❞❛ ❡st✐♠❛t✐✈❛ ❞❡ ♣♦s✐çã♦ ❞❡ ❝❛❞❛ r♦❜ô ❢♦✐ ❝♦♠♣✉t❛❞♦ ❛♣ós ✺✳✶✳ ❆♥á❧✐s❡ ❞❛ ❱❛r✐❛çã♦ ❞♦ ◆ú♠❡r♦ ❞❡ ▼❛r❝♦s ✽✶♦ ❝❛♠✐♥❤♦ ❝♦♠♣❧❡t♦ t❡r s✐❞♦ ♣❡r❝♦rr✐❞♦ ✭❋✐❣✉r❛ ✺✳✷✮✳ ❚❛❧ ❡rr♦ ❢♦✐ ❡st❛❜❡❧❡❝✐❞♦ t❡♥❞♦❝♦♠♦ r❡❢❡rê♥❝✐❛ ❛ ❞✐stâ♥❝✐❛ ❡✉❝❧✐❞✐❛♥❛ ❡♥tr❡ ♦ ❝❛♠✐♥❤♦ ❡①❡❝✉t❛❞♦ ♣♦r ❝❛❞❛ r♦❜ô ❡❛q✉❡❧❡ ❡st✐♠❛❞♦✳0.91σ σ φ σ φ φ =1 =3 =2( m)0.60.7 0.8 S E R M0.30.40.5σ ρ = 0,40ρ0.20.1σ ρ σ σ ρ = 0,20ρ σ ρ ρ = 0,10ρ = 0,30ρ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Número de marcos utilizados = 0,05ρ ❋✐❣✉r❛ ✺✳✷✿ ❊rr♦ ♠é❞✐♦ ❛♦ s❡ ✈❛r✐❛r ♦ ♥ú♠❡r♦ ❞❡ ♠❛r❝♦s ✉t✐❧✐③❛❞♦ ❡♠ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐✲③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ P❛r❛ ❝❛❞❛ s✐♠✉❧❛çã♦ s✱ ♦ ❡rr♦ ♠é❞✐♦ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❡♥①❛♠❡ ❢♦✐ ❝❛❧❝✉❧❛❞♦ ❝♦♠❜❛s❡ ♥♦ ✈❛❧♦r ❞♦s ❡rr♦s ❞❡ ♣♦s✐çã♦ ❞❡ t♦❞♦s ♦s r♦❜ôs✱ q✉❛♥❞♦ ✉♠ ♥ú♠❡r♦ ❡s♣❡❝í✜❝♦ ❞❡✈✐③✐♥❤♦s ❢♦✐ ✉t✐❧✐③❛❞♦ ❝♦♠♦ ♠❛r❝♦✿ X X s = , 1 1 k❊ ❡ ✭✺✳✺✮ i K i k ||R|| i k k= s❡♥❞♦ ♦ ❡rr♦ ❞❡ ♣♦s✐çã♦ ❡ ❛ss♦❝✐❛❞♦ ❛ ✉♠ r♦❜ô i ♥❛ ✐t❡r❛çã♦ k ❞❡✜♥✐❞♦ ♣♦r ❡k k k ii g g p pi || − p ||✱ ♦♥❞❡ é ❛ ❡st✐♠❛t✐✈❛ ❞❡ ♣♦s✐çã♦ r❡❧❛t✐✈❛ ❛♦ ❣r♦✉♥❞ tr✉t❤✱ K ♦ ♥ú♠❡r♦ i i i❞❡ ✐t❡r❛çõ❡s ❡①❡❝✉t❛❞❛s ♣❡❧♦ r♦❜ô i ❡ ||R|| ♦ ♥ú♠❡r♦ t♦t❛❧ ❞❡ r♦❜ôs✳ ❖ ❡rr♦ ♠é❞✐♦✭❘▼❙❊✮ ❛ss♦❝✐❛❞♦ ❛ ✉♠ ❡①♣❡r✐♠❡♥t♦ ❢♦✐ ❝❛❧❝✉❧❛❞♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ X1 s , ❘▼❙❊ = ❊ ✭✺✳✻✮S s s❡♥❞♦ S ♦ ♥ú♠❡r♦ ❞❡ s✐♠✉❧❛çõ❡s ❡❢❡t✉❛❞❛s ♥♦ ❡①♣❡r✐♠❡♥t♦✳ ❖s r❡s✉❧t❛❞♦s ✐♥❞✐❝❛♠ q✉❡ ♦ r✉í❞♦ ❛ss♦❝✐❛❞♦ à ♠❡❞✐❞❛ ❞❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛ φ t❡♠ ✉♠❛ ✐♥✢✉❡♥❝✐❛ ♠❡♥♦r ♥♦ ✈❛❧♦r ❞♦ ❡rr♦ ♠é❞✐♦✳ ◆♦ ❡♥t❛♥t♦✱ ❛♦ s❡ ❛✉♠❡♥t❛r ♦r✉í❞♦ r❡❧❛t✐✈♦ à ♠❡❞✐❞❛ ❞❡ ❞✐stâ♥❝✐❛ ρ✱ ✉♠ r♦❜ô ♥❡❝❡ss✐t❛ ✉t✐❧✐③❛r ✉♠ ♥ú♠❡r♦ ♠❛✐♦r ✽✷❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s ❞❡ ♠❛r❝♦s ♣❛r❛ ❛❧❝❛♥ç❛r ❡st✐♠❛t✐✈❛s ❝♦♠ ❞❡t❡r♠✐♥❛❞♦ ♥í✈❡❧ ❞❡ q✉❛❧✐❞❛❞❡✳ P♦❞❡✲s❡♦❜s❡r✈❛r t❛♠❜é♠✱ ♥❛q✉❡❧❛s s✐t✉❛çõ❡s ♦♥❞❡ ♦ r✉í❞♦ é ♣❡q✉❡♥♦✱ q✉❡ ♦ ❛✉♠❡♥t♦ ♥♦ ♥ú♠❡r♦❞❡ ♠❛r❝♦s✱ ❛❝✐♠❛ ❞❡ ❞❡t❡r♠✐♥❛❞♦s ✈❛❧♦r❡s✱ ♥ã♦ ❝♦♥tr✐❜✉✐ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ♣❛r❛ ❛ ρ = 0,05ρ r❡❞✉çã♦ ❞♦ ❡rr♦ ❞❡ ❧♦❝❛❧✐③❛çã♦✳ P♦r ❡①❡♠♣❧♦✱ ♣❛r❛ σ ✱ ♦ ❡rr♦ ❞✐♠✐♥✉✐ ♠✉✐t♦❧❡♥t❛♠❡♥t❡ ♣❛r❛ ✉♠ ♥ú♠❡r♦ ❞❡ ♠❛r❝♦s s✉♣❡r✐♦r ❛ s❡✐s✳ ❊♠ ♦✉tr❛s ♣❛❧❛✈r❛s✱ ❞❡♣❡♥❞❡♥❞♦❞♦ r✉í❞♦ ❞❡ ♦❜s❡r✈❛çã♦✱ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ✉♠ ♥ú♠❡r♦ ♣❡q✉❡♥♦ ❞❡ ♠❛r❝♦s é s✉✜❝✐❡♥t❡ ♣❛r❛♠❡❧❤♦r❛r ❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❖✉tr❛ ❛♥á❧✐s❡ ❡❢❡t✉❛❞❛ ❞✐③ r❡s♣❡✐t♦ à ✈❛r✐❛çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ♠❛r❝♦s ✉t✐❧✐③❛❞♦ ❡ ♦❝♦♥s❡q✉❡♥t❡ ✐♠♣❛❝t♦ ♥♦ ❡rr♦ ♠é❞✐♦ ❞❡ ❧♦❝❛❧✐③❛çã♦✱ ❛♦ ❧♦♥❣♦ ❞❛ ❡①❡❝✉çã♦ ❞♦ ❝❛♠✐♥❤♦✳❆ ❋✐❣✉r❛ ✺✳✸ ♠♦str❛ ♦s r❡s✉❧t❛❞♦s ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ 30 s✐♠✉❧❛çõ❡s ❡♠ q✉❡ ♦ r✉í❞♦ ◦ ρ φ = 0,10ρ = 3❞❡ ♦❜s❡r✈❛çã♦ ❢♦✐ ✜①❛❞♦ ❡♠ σ ❡ σ ✳ ❈♦♥❢♦r♠❡ ♣♦❞❡ s❡r ♦❜s❡r✈❛❞♦✱ ♦❡rr♦ ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❝r❡s❝❡ ♠❛✐s r❛♣✐❞❛♠❡♥t❡ q✉❛♥❞♦ ♥ã♦ s❡ ✉t✐❧✐③❛ ❝♦♦♣❡r❛çã♦ ♥♦s♣r♦❝❡ss♦s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❈♦♠ ❛ ❝♦♦♣❡r❛çã♦✱ ♦ ❡rr♦ ♠é❞✐♦ é s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ r❡❞✉③✐❞♦ q✉❛♥❞♦ ♣❡❧♦ ♠❡♥♦s ✉♠ r♦❜ô ♠❛r❝♦ é ✉t✐❧✐③❛❞♦✱ ♣♦ré♠ t❛❧ r❡❞✉çã♦ é ♠❡♥♦r ♣❛r❛ ♠❛✐s❞❡ q✉❛tr♦ ♠❛r❝♦s✳ ❊ss❛ ❝♦♥st❛t❛çã♦ r❡❢♦rç❛ ♦ r❡s✉❧t❛❞♦ ❛♣r❡s❡♥t❛❞♦ ❛♥t❡r✐♦r♠❡♥t❡ q✉❡✐♥❞✐❝❛ q✉❡ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ✉♠ ♥ú♠❡r♦ ♣❡q✉❡♥♦ ❞❡ r♦❜ôs ♠❛r❝♦ ♣♦❞❡ s❡r s✉✜❝✐❡♥t❡ ♣❛r❛♠❡❧❤♦r❛r ❛ ❧♦❝❛❧✐③❛çã♦ ❡♠ ❡♥①❛♠❡s ❞❡ r♦❜ôs✳2 nenhum1.5 15 marcos 8 marcos 4 marcos 1 marco E ( m ) P M1 0.5 1000 2000 3000 4000 5000 6000Iterações ❋✐❣✉r❛ ✺✳✸✿ ❊rr♦ ♠é❞✐♦ ❡♠ ❝❛❞❛ ✐t❡r❛çã♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ✉♠ ♥ú♠❡r♦ ❞✐❢❡r❡♥t❡ ❞❡ ♠❛r❝♦s✉t✐❧✐③❛❞♦s ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ k ◆❡st❡ ❡①♣❡r✐♠❡♥t♦✱ ♣❛r❛ ❝❛❞❛ s✐♠✉❧❛çã♦ s✱ ♦ ❡rr♦ ♠é❞✐♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ E s ❢♦✐❝❛❧❝✉❧❛❞♦ ❡♠ ❝❛❞❛ ✐t❡r❛çã♦ k✱ ❝♦♠ ❜❛s❡ ♥♦ ✈❛❧♦r ❞♦s ❡rr♦s ❞❡ ♣♦s✐çã♦ ❞♦s r♦❜ôs✱ ❝♦♥✲ ✺✳✶✳ ❆♥á❧✐s❡ ❞❛ ❱❛r✐❛çã♦ ❞♦ ◆ú♠❡r♦ ❞❡ ▼❛r❝♦s ✽✸ s✐❞❡r❛♥❞♦ ❞❡t❡r♠✐♥❛❞♦ ♥ú♠❡r♦ ❞❡ ✈✐③✐♥❤♦s ❝♦♠♦ ♠❛r❝♦✿X k k 1 = ,P❊ s ❡ i ✭✺✳✼✮ k ||R|| i s❡♥❞♦ ❡ ♦ ❡rr♦ ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ♥❛ ✐t❡r❛çã♦ k ❞❡s❝r✐t♦ ❛♥t❡r✐♦r♠❡♥t❡ ❡ ❞❡✜♥✐❞♦ ♣♦rk k k k i p p = g g❡ || − p ||✱ ♦♥❞❡ é ❛ ❡st✐♠❛t✐✈❛ ❞❡ ♣♦s✐çã♦ ❞♦ r♦❜ô r❡❧❛t✐✈❛ ❛♦ ❣r♦✉♥❞ tr✉t❤ i i i i❡ ||R|| ♦ ♥ú♠❡r♦ t♦t❛❧ ❞❡ r♦❜ôs✳ ❖ ❡rr♦ ♠é❞✐♦ ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ✭▼P❊✮ ❡♠ ❝❛❞❛✐t❡r❛çã♦ ❛ss♦❝✐❛❞♦ ❛ ✉♠ ❡①♣❡r✐♠❡♥t♦ ❢♦✐ ❝❛❧❝✉❧❛❞♦ ❝♦♥❢♦r♠❡ s❡❣✉❡ X k k 1= , ▼P❊ P❊ s ✭✺✳✽✮S s s❡♥❞♦ S ♦ ♥ú♠❡r♦ ❞❡ s✐♠✉❧❛çõ❡s ❡❢❡t✉❛❞❛s✳ ◆❛ ❋✐❣✉r❛ ✺✳✸✱ ♦ ✈❛❧♦r ❞❡ ▼P❊✱ ❛♦ s❡ ❝♦♥s✐❞❡r❛r ♦ ✉s♦ ❞❡ ✶✺ ♠❛r❝♦s✱ ❛♣r❡s❡♥t❛✉♠❛ t❡♥❞ê♥❝✐❛ ❛ ❝♦♥✈❡r❣✐r ♣❛r❛ ✉♠❛ t❛①❛ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❝♦♥st❛♥t❡ ❛♣ós ✉♠ ❝❡rt♦♥ú♠❡r♦ ❞❡ ✐t❡r❛çõ❡s✳ ■ss♦ s❡ ❛♣r❡s❡♥t❛ ❝♦♠♦ ✉♠ r❡s✉❧t❛❞♦ ✐♠♣♦rt❛♥t❡✱ ✉♠❛ ✈❡③ q✉❡♦ ♠❡s♠♦ ♣r♦✈ê ❛ ♥♦çã♦ ❞❡ q✉❡ s❡r✐❛ ♣♦ssí✈❡❧ ♦❜t❡r ✉♠ ❧✐♠✐t❡ ♠á①✐♠♦ ♣❛r❛ ♦ ❡rr♦ ❞❡❧♦❝❛❧✐③❛çã♦ ❞♦ ❡♥①❛♠❡✳ ❆ ♠❡❧❤♦r✐❛ ♥❛ ❧♦❝❛❧✐③❛çã♦ ♣♦❞❡ s❡r ♦❜s❡r✈❛❞❛ ♥❛ ❋✐❣✉r❛ ✺✳✹✳ ❖ ❝❛♠✐♥❤♦ ❡①❡❝✉t❛❞♦♣♦r ✉♠ ❞♦s r♦❜ôs é ❛♣r❡s❡♥t❛❞♦✱ ♥♦ q✉❛❧ ❞✐❢❡r❡♥t❡s q✉❛♥t✐❞❛❞❡s ❞❡ ♠❛r❝♦s ❢♦r❛♠✉t✐❧✐③❛❞♦s ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ◆❡ss❛ ✜❣✉r❛✱ ❛ ❧✐♥❤❛ ♥❛ ❝♦r ♣r❡t❛ r❡♣r❡s❡♥t❛ ♦ ❝❛♠✐♥❤♦ ✈❡r❞❛❞❡✐r♦ ❡①❡❝✉t❛❞♦ ✭❣r♦✉♥❞ tr✉t❤✮✱ ❛ ❧✐♥❤❛ ✈❡r♠❡❧❤❛ r❡♣r❡s❡♥t❛❛ ❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞♦ r♦❜ô s❡♠ ❡❢❡t✉❛r ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ✭♦❞♦♠❡tr✐❛✮ ❡❛ ❧✐♥❤❛ ❛③✉❧ ✐♥❞✐❝❛ ❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ r♦❜ô q✉❛♥❞♦ ❡ss❡ ✉t✐❧✐③♦✉ ✉♠ ♥ú♠❡r♦ ❡s♣❡❝í✜❝♦ ❞❡ r♦❜ôs ♠❛r❝♦ ♣❛r❛ ♠❡❧❤♦r❛r s✉❛ ❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❚❛♥t♦ ❛ ❋✐❣✉r❛ ✺✳✸ q✉❛♥t♦❛ ❋✐❣✉r❛ ✺✳✹ sã♦ r❡❧❛❝✐♦♥❛❞❛s ❛♦ ♠❡s♠♦ ❣r✉♣♦ ❞❡ ❡①♣❡r✐♠❡♥t♦s✳ ◆♦s ❡①♣❡r✐♠❡♥t♦s ❛♣r❡s❡♥t❛❞♦s✱ ♦s ♠❛r❝♦s ❛ s❡r❡♠ ✉t✐❧✐③❛❞♦s ♥❛s ❡t❛♣❛s ❞❡ ❧♦✲❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❢♦r❛♠ ❡s❝♦❧❤✐❞♦s ❛❧❡❛t♦r✐❛♠❡♥t❡✱ s❡♠ ❛ ✉t✐❧✐③❛çã♦ ❞❡ q✉❛❧q✉❡r❝r✐tér✐♦ ❞❡ s❡❧❡çã♦✱ ❞♦r❛✈❛♥t❡ ❞❡♥♦♠✐♥❛❞♦ ❈r✐tér✐♦ ❞❡ ❙❡❧❡çã♦ ❆❧❡❛tór✐❛ ✭❈❙❆✮✳ ❆s ❡s✲ t✐♠❛t✐✈❛s ❛ss♦❝✐❛❞❛s às ♦❜s❡r✈❛çõ❡s ❢♦r❛♠ ✉t✐❧✐③❛❞❛s ♥❛s ❡t❛♣❛s ❞❡ ❝♦rr❡çã♦ ❞♦ ✜❧tr♦ ❞❡❑❛❧♠❛♥ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ♦r❞❡♠ ❞❡ ❝❤❡❣❛❞❛ ❞❛s ♠❡♥s❛❣❡♥s✳ ❈♦♠ ♦ ♣r♦♣ós✐t♦ ❞❡ ❛✈❛❧✐❛r♦ ✐♠♣❛❝t♦ ❞❡❝♦rr❡♥t❡ ❞❛ ✉t✐❧✐③❛çã♦ ❞❡ ❞✐❢❡r❡♥t❡s ❡str❛té❣✐❛s ♣❛r❛ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ss❛s♦❜s❡r✈❛çõ❡s✱ ❞♦✐s ❝r✐tér✐♦s ❢♦r❛♠ ❞❡✜♥✐❞♦s✳ ❖ ♣r✐♠❡✐r♦✱ ❞❡♥♦♠✐♥❛❞♦ ❈r✐tér✐♦ ❞❡ ❙❡❧❡✲çã♦ ♣♦r Pr♦①✐♠✐❞❛❞❡ ✭❈❙P✮✱ ❝♦♥s✐❞❡r❛ ✉♠❛ ♦r❞❡♥❛çã♦ ❞❛s ♦❜s❡r✈❛çõ❡s ❞❡ ♠♦❞♦ q✉❡❛q✉❡❧❛s ❛ss♦❝✐❛❞❛s ❛ ♠❛r❝♦s ❧♦❝❛❧✐③❛❞♦s ♠❛✐s ♣ró①✐♠♦s ❛ ✉♠ r♦❜ô t❡♥t❛♥❞♦ s❡ ❧♦❝❛❧✐③❛r sã♦ ♣r♦❝❡ss❛❞❛s ♣r✐♠❡✐r♦✳ ❖ s❡❣✉♥❞♦ ❝r✐tér✐♦ ❝♦♥s✐❞❡r❛ ❛ ✐♥❝❡rt❡③❛ ❞❛s ✐♥❢♦r♠❛çõ❡s❞❡ ❧♦❝❛❧✐③❛çã♦ ❞♦s ♠❛r❝♦s✱ ❞❡ ♠♦❞♦ q✉❡ ♠❛r❝♦s ❝♦♠ ♠❡♥♦r❡s ♥í✈❡✐s ❞❡ ✐♥❝❡rt❡③❛ sã♦ ✽✹❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s −5 −4 −3 −2 −1 1 2 3 4 5 −5 −4 −3 −2 −11234 x (m) y (m) Posição final Posição inicial✭❛✮ ✶ ♠❛r❝♦ −5 −4 −3 −2 −1 1 2 3 4 5 −5 −4 −3 −2 −1 1 2 3 4 x (m) y (m) ✭❜✮ ✹ ♠❛r❝♦s −5 −4 −3 −2 −1 1 2 3 4 5 −5 −4 −3 −2 −11234 x (m) y (m)✭❝✮ ✽ ♠❛r❝♦s −5 −4 −3 −2 −1 1 2 3 4 5 −5 −4 −3 −2 −1 1 2 3 4 x (m) y (m) ✭❞✮ ✶✺ ♠❛r❝♦s ❋✐❣✉r❛ ✺✳✹✿ ❊st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ ✉♠ r♦❜ô ❞♦ ❡♥①❛♠❡✳ ❆ ❧✐♥❤❛ ♣r❡t❛ ✐♥❞✐❝❛ ♦❝❛♠✐♥❤♦ r❡❛❧ ❡①❡❝✉t❛❞♦ ♣❡❧♦ r♦❜ô ✭❣r♦✉♥❞ tr✉t❤✮ ❡♥q✉❛♥t♦ q✉❡ ❛ ❧✐♥❤❛ ❛③✉❧ ✐♥❞✐❝❛ ❛ ❡s✲ t✐♠❛t✐✈❛ r❡s✉❧t❛♥t❡ ❞❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❆ ❧✐♥❤❛ ✈❡r♠❡❧❤❛ r❡♣r❡s❡♥t❛❛ ❧♦❝❛❧✐③❛çã♦ ❡st✐♠❛❞❛ s❡♠ ✉t✐❧✐③❛r ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ✭♦❞♦♠❡tr✐❛✮✳ ❆✈❛r✐❛çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ♠❛r❝♦s ✉t✐❧✐③❛❞♦ ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ é ✐♥❞✐✲❝❛❞❛ ♥❛s ✜❣✉r❛s✳ ✺✳✶✳ ❆♥á❧✐s❡ ❞❛ ❱❛r✐❛çã♦ ❞♦ ◆ú♠❡r♦ ❞❡ ▼❛r❝♦s ✽✺♣r♦❝❡ss❛❞♦s ♣r✐♠❡✐r❛♠❡♥t❡ ✭❈r✐tér✐♦ ❞❡ ❙❡❧❡çã♦ ❞❛ ▼❡♥♦r ■♥❝❡rt❡③❛ ✲ ❈❙▼■✮✱ ✐♥❞❡♣❡♥✲❞❡♥t❡ ❞❛ ♣r♦①✐♠✐❞❛❞❡ ❞❡ss❡s ♠❛r❝♦s ❡♠ r❡❧❛çã♦ ❛♦ r♦❜ô q✉❡ ❡stá t❡♥t❛♥❞♦ s❡ ❧♦❝❛❧✐③❛r✳❖s r✉í❞♦s ❞❡ ♦❜s❡r✈❛çã♦ ❢♦r❛♠ ❞❡✜♥✐❞♦s ✉t✐❧✐③❛♥❞♦ ♦s ♠❡s♠♦s ✈❛❧♦r❡s ❞♦ ❡①♣❡r✐♠❡♥t♦ ◦ ρ φ = 0,10 ρ = 3❛♥t❡r✐♦r✿ σ ❡ σ ✳ ❖s ❝r✐tér✐♦s ❈❙P ❡ ❈❙▼■ ❢♦r❛♠ ❝♦♠♣❛r❛❞♦s ❝♦♠♦ ❝r✐tér✐♦ ❞❡ s❡❧❡çã♦ ❛❧❡❛tór✐❛ ❡♠♣r❡❣❛❞♦ ♥♦s ❡①♣❡r✐♠❡♥t♦s ❛♥t❡r✐♦r❡s✳ ◆❡st❡ ❡①♣❡r✐✲♠❡♥t♦✱ ♦ ❡rr♦ ♠é❞✐♦ ❢♦✐ ❝❛❧❝✉❧❛❞♦ ✉t✐❧✐③❛♥❞♦ ❛ ❊q✉❛çã♦ ✭✺✳✻✮✳ ❆ ❋✐❣✉r❛ ✺✳✺ ♠♦str❛ q✉❡❛♠❜♦s ♦s ❝r✐tér✐♦s ✭❈❙P ❡ ❈❙▼■✮ ♠❡❧❤♦r❛♠ ❛ ❧♦❝❛❧✐③❛çã♦ q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦s ❝♦♠ ♦❈❙❆✳ ❈♦♥s✐❞❡r❛♥❞♦ s♦♠❡♥t❡ ♦s ❞♦✐s ❝r✐tér✐♦s ❞❡✜♥✐❞♦s✱ ❛ s❡❧❡çã♦ ❞❡ r♦❜ôs ♠❛r❝♦ ❝♦♠♠❡♥♦r❡s ♥í✈❡✐s ❞❡ ✐♥❝❡rt❡③❛ ♠♦str❛✲s❡ ❧✐❣❡✐r❛♠❡♥t❡ ♠❡❧❤♦r ❞♦ q✉❡ ❛ s❡❧❡çã♦ ❜❛s❡❛❞❛ ♥❛♣r♦①✐♠✐❞❛❞❡✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ q✉❛♥❞♦ ♦ ♥ú♠❡r♦ ❞❡ ♠❛r❝♦s ✉t✐❧✐③❛❞♦ é ♣❡q✉❡♥♦✳1.21.3CSP CSA1.10.91 0.60.7 0.30.40.50.10.2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Número de marcos ❋✐❣✉r❛ ✺✳✺✿ ❊rr♦ ♠é❞✐♦ ❞❛s ❡st✐♠❛t✐✈❛s ❞❡ ♣♦s✐çã♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ❝r✐tér✐♦ ❞❡ s❡❧❡çã♦❞❡ ♠❛r❝♦s ✉t✐❧✐③❛❞♦✳❆❧❣✉♠❛s ❈♦♥s✐❞❡r❛çõ❡s❖s ❡①♣❡r✐♠❡♥t♦s ❞❡s❡♥✈♦❧✈✐❞♦s ♥❡st❛ s❡çã♦ ✉t✐❧✐③❛r❛♠ ❛❧❣✉♠❛s s✉♣♦s✐çõ❡s q✉❡ ♣♦❞❡✲ r✐❛♠ s❡r ❝♦♥s✐❞❡r❛❞❛s ❢♦rt❡s ❡♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s✱ ❞❡✈✐❞♦ às ❧✐♠✐t❛çõ❡s ❞❡ ♣r♦❝❡ss❛✲♠❡♥t♦ ❡ s❡♥s♦r✐❛♠❡♥t♦ ❧♦❝❛❧✱ ❝♦♠✉♠❡♥t❡ ♣r❡s❡♥t❡s ♥❡ss❡ t✐♣♦ ❞❡ s✐st❡♠❛✳ ❆s ♣r✐♥❝✐♣❛✐s❧✐♠✐t❛çõ❡s ❞✐③❡♠ r❡s♣❡✐t♦ à ♦❜t❡♥çã♦ ❞❡ ❡st✐♠❛t✐✈❛s ❞❡ ❞✐stâ♥❝✐❛ ❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛s s❡♠ ❝♦♥s✐❞❡r❛r ♦❝❧✉sõ❡s ♦✉ ✉♠ ❧✐♠✐t❡ ♣❛r❛ ♦ ❛❧❝❛♥❝❡ s❡♥s♦r✐❛❧✳ ◆♦ ❡♥t❛♥t♦✱ t❛✐s s✉✲♣♦s✐çõ❡s ❢♦r❛♠ ❡♠♣r❡❣❛❞❛s ♣❛r❛ ♣♦ss✐❜✐❧✐t❛r ✉♠❛ ❛♥á❧✐s❡ ❞♦ ✐♠♣❛❝t♦ ♥❛ q✉❛❧✐❞❛❞❡ ❞❛❧♦❝❛❧✐③❛çã♦ ❛♦ s❡ ✉t✐❧✐③❛r ✉♠ ♥ú♠❡r♦ ✈❛r✐á✈❡❧ ❞❡ r♦❜ôs ♠❛r❝♦ ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ✽✻❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s ❝♦♦♣❡r❛t✐✈❛✱ ❛❧é♠ ❞❡ ❛✈❛❧✐❛r ♦ ❡♠♣r❡❣♦ ❞❡ ❞✐❢❡r❡♥t❡s ❝r✐tér✐♦s ♣❛r❛ ❛ s❡❧❡çã♦ ❞❡ss❡s♠❛r❝♦s✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ♥♦ ❈❛♣ít✉❧♦ ✷✱ é ❞❡s❡❥á✈❡❧ q✉❡ té❝♥✐❝❛s ❛♣❧✐❝❛❞❛s ❛ ❡♥①❛♠❡s r♦❜ót✐❝♦s s❡❥❛♠ ❞❡s❝❡♥tr❛❧✐③❛❞❛s✱ ♣❡r♠✐t✐♥❞♦ q✉❡ ❝❛❞❛ r♦❜ô ♥♦ ❣r✉♣♦ ✉t✐❧✐③❡ s♦♠❡♥t❡✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s✱ s❡❥❛♠ ❡❧❛s ❞❛❞♦s s❡♥s♦r✐❛✐s ♦✉ ♣r♦✈❡♥✐❡♥t❡s ❞❡ ❝♦♠✉♥✐❝❛çã♦✳ ❖s r❡✲ s✉❧t❛❞♦s ♦❜t✐❞♦s ♥❡st❛ s❡çã♦ ♠♦str❛♠ q✉❡ ❝♦♠ ✉♠ ♥ú♠❡r♦ ♣❡q✉❡♥♦ ❞❡ ♠❛r❝♦s ♣♦❞❡✲s❡♦❜t❡r ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♠ ❜♦❛ q✉❛❧✐❞❛❞❡✱ ❣❡r❛❞❛s ♥♦ ♣r♦❝❡ss♦ ❞❡ ❧♦❝❛❧✐③❛çã♦❝♦♦♣❡r❛t✐✈❛✳ ❊ss❡ r❡s✉❧t❛❞♦ é r❡❧❡✈❛♥t❡✱ ♣♦✐s ♣❡r♠✐t❡ q✉❡ ♦s r♦❜ôs ❡♠ ✉♠ ❡♥①❛♠❡♦❜t❡♥❤❛♠ ❜♦❛ ❧♦❝❛❧✐③❛çã♦ ❛♦ ✉t✐❧✐③❛r❡♠ s♦♠❡♥t❡ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s✱ ♦✉ s❡❥❛✱ s❡✉s ✈✐✲③✐♥❤♦s✳ ❉❡ss❡ ♠♦❞♦✱ ♦ t❛♠❛♥❤♦ ❞♦ ❡♥①❛♠❡ ❞❡✐①❛ ❞❡ s❡r ❞❡❝✐s✐✈♦ ♣❛r❛ ❛ q✉❛❧✐❞❛❞❡ ❞❛❧♦❝❛❧✐③❛çã♦✱ ❛tr✐❜✉✐♥❞♦ ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ à ❛❜♦r❞❛❣❡♠ ❡♠♣r❡❣❛❞❛✳ ❊ss❡s r❡s✉❧t❛❞♦s sã♦ t❛♠❜é♠ ✐♥✢✉❡♥❝✐❛❞♦s ♣❡❧❛ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❡♠✲♣r❡❣❛❞❛✱ ✉♠❛ ✈❡③ q✉❡ ❛ ♠❡s♠❛ ♠❛♥té♠ ♣❛rt❡ ❞♦ ❣r✉♣♦ ✐♥❡rt❡ ❡ ❛t✉❛♥❞♦ ❝♦♠♦ ♠❛r❝♦✳❉❡✈✐❞♦ ❛ ✐ss♦✱ ♦ ❡rr♦ ❛ss♦❝✐❛❞❛ às ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ♣♦ss✉✐ t❛①❛ ❞❡ ❝r❡s❝✐♠❡♥t♦♠❡♥♦r q✉❛♥❞♦ ❝♦♠♣❛r❛❞❛ ❛ ✉♠❛ ❡str❛té❣✐❛ q✉❡ ♠♦✈✐♠❡♥t❛ t♦❞♦s ♦s r♦❜ôs s✐♠✉❧t❛♥❡❛✲♠❡♥t❡✳ ❆♣❡s❛r ❞❛ ❞❡t❡r✐♦r❛çã♦ ♠❛✐s rá♣✐❞❛ ❞❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ♥❛ ♠♦✈✐♠❡♥✲ t❛çã♦ s✐♠✉❧tâ♥❡❛✱ ❛ ♠❡s♠❛ ♣♦ss✉✐ ♣❡r❢♦r♠❛♥❝❡ ♠❡❧❤♦r ❞♦ q✉❡ ❛ ❡str❛té❣✐❛ q✉❡ ❛❧t❡r♥❛♦s ♠♦✈✐♠❡♥t♦s ❞♦s r♦❜ôs✳ ❈♦♥s✐❞❡r❛♥❞♦ ❡ss❛s q✉❡stõ❡s✱ ❛ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❝♦♥tí♥✉❛ ♣r♦♣♦st❛♥❡st❡ tr❛❜❛❧❤♦ ❢❛③ ✉s♦ ❞❡ ✉♠ ❡♥①❛♠❡ ❤❡t❡r♦❣ê♥❡♦✱ ♥♦ q✉❛❧ ✉♠ r♦❜ô ❡q✉✐♣❛❞♦ ❝♦♠ s❡♥s♦r❡s q✉❡ ♦ ♣r♦✈ê♠ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♠ ❜♦❛ ♣r❡❝✐sã♦ é ✉t✐❧✐③❛❞♦ ♣❛r❛❞✐♠✐♥✉✐r ❛ ❞❡❣r❛❞❛çã♦ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❣r✉♣♦✳ ❉❡✈✐❞♦ à q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ss❡ r♦❜ô✱ ♦ ♠❡s♠♦ é ✉t✐❧✐③❛❞♦ ❝♦♠♦ ❧í❞❡r ♣❛r❛ ❣✉✐❛r ♦ ❡♥①❛♠❡ ♣❡❧♦ ❛♠❜✐❡♥t❡ ✉t✐❧✐③❛♥❞♦ ✉♠❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ❧í❞❡r✲s❡❣✉✐❞♦r✳ ❆ ♣ró①✐♠❛ s❡çã♦ ❛♣r❡s❡♥t❛ ♦s r❡s✉❧t❛❞♦s ❞❡❝♦rr❡♥t❡s❞❛ ✉t✐❧✐③❛çã♦ ❞❡ss❛ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦✳ ✺✳✶✳✷ ▼♦✈✐♠❡♥t❛çã♦ ❈♦♥tí♥✉❛ ❉✐❢❡r❡♥t❡♠❡♥t❡ ❞❛ s❡çã♦ ❛♥t❡r✐♦r✱ ♦s ❡①♣❡r✐♠❡♥t♦s ❛♣r❡s❡♥t❛❞♦s ♥❡st❛ s❡çã♦ ❢♦r❛♠❞❡s❡♥✈♦❧✈✐❞♦s ❝♦♠ ♦ ♣r♦♣ós✐t♦ ❞❡ ❛♥❛❧✐s❛r ❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ ✉♠ ❡♥①❛♠❡✱ ♥♦ q✉❛❧ ✉♠ ❞♦s r♦❜ôs é ❡q✉✐♣❛❞♦ ❝♦♠ s❡♥s♦r❡s q✉❡ ♦ ♣❡r♠✐t❡♠ ♠❛♥t❡r ✉♠❛ ❜♦❛ ❡st✐♠❛t✐✈❛❞❡ s✉❛ ❧♦❝❛❧✐③❛çã♦✳ ❯♠ ♦✉tr♦ ♦❜❥❡t✐✈♦ ❞❡ss❡s ❡①♣❡r✐♠❡♥t♦s é ❛✈❛❧✐❛r ❛ q✉❛❧✐❞❛❞❡ ❞❛❧♦❝❛❧✐③❛çã♦ ❞♦s r♦❜ôs✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛ ✐♥✢✉ê♥❝✐❛ ❞♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦ ❧í❞❡r ❡♠ r❡❧❛çã♦❛♦ ❣r✉♣♦✳ P♦r ✐♥t❡r♠é❞✐♦ ❞❡ss❡ r♦❜ô✱ ♦ ❣r✉♣♦ s❡ ♠♦✈❡ ❝♦♥t✐♥✉❛♠❡♥t❡ ❡ é ❣✉✐❛❞♦ ♣❡❧♦❛♠❜✐❡♥t❡ ❞❡ ♠♦❞♦ ❛ ✈✐s✐t❛r r❡❣✐õ❡s ♣r❡✈✐❛♠❡♥t❡ ❡st❛❜❡❧❡❝✐❞❛s✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ♥❛❙❡çã♦ ✹✳✷✳✷ ❞❛ ♠❡t♦❞♦❧♦❣✐❛✱ ❛ ♠♦✈✐♠❡♥t❛çã♦ é ❡❢❡t✉❛❞❛ ✉t✐❧✐③❛♥❞♦ ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦❞❡ ❧í❞❡r✲s❡❣✉✐❞♦r✱ ❛❧é♠ ❞❡ ❝♦♠♣♦rt❛♠❡♥t♦s ❞❡ ❛❣r❡❣❛çã♦ ❡ s❡❣r❡❣❛çã♦✱ r❡s♣♦♥sá✈❡✐s ♣♦r ✺✳✶✳ ❆♥á❧✐s❡ ❞❛ ❱❛r✐❛çã♦ ❞♦ ◆ú♠❡r♦ ❞❡ ▼❛r❝♦s ✽✼♠❛♥t❡r ❛ ❝♦❡sã♦ ❞♦ ❣r✉♣♦✳ ❆ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❞❡s❝r✐t❛ ♥❛ ❙❡çã♦ ✹✳✷✳✷ ❢♦✐ ❡♠♣r❡❣❛❞❛ ♣❛r❛ ♠❛♥t❡r❛ ❝♦❡sã♦ ❞♦ ❣r✉♣♦✳ ❯♠ ❡♥①❛♠❡ ❝♦♠♣♦st♦ ❞❡ ✶✵✵ r♦❜ôs ❤♦❧♦♥ô♠✐❝♦s ❝♦♠ ❛♣r♦①✐♠❛❞❛✲♠❡♥t❡ ✼✵ mm ❞❡ ❞✐â♠❡tr♦ ❢♦✐ ✉t✐❧✐③❛❞♦✱ s❡♥❞♦ q✉❡ ♦ ♠❡s♠♦ ♥❛✈❡❣❛ ❡♠ ✉♠ ❛♠❜✐❡♥t❡ 2❡stát✐❝♦✱ ❧✐✈r❡ ❞❡ ♦❜stá❝✉❧♦s✱ ❝♦♠ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ 200 m ✭15 m × 15 m✮✳ ❖ ❡♥①❛♠❡ é❣✉✐❛❞♦ ♣♦r ✉♠❛ sér✐❡ ❞❡ ✇❛②♣♦✐♥ts✱ ❛ s❡r❡♠ ❛❧❝❛♥ç❛❞♦s ♣❡❧♦ ❣r✉♣♦✳ ❆ ❧♦❝❛❧✐③❛çã♦ ❞❡ss❡s✇❛②♣♦✐♥ts é ✉t✐❧✐③❛❞❛ ♥❛ ❊q✉❛çã♦ ✭✹✳✸✶✮ ♣❛r❛ ❝❛❧❝✉❧❛r ♦ ♣❡♥ú❧t✐♠♦ t❡r♠♦ ❞❛ ❡q✉❛çã♦✱❛ q✉❛❧ ❡st❛❜❡❧❡❝❡ ❛ ❛çã♦ ❞❡ ❝♦♥tr♦❧❡ q✉❡ ❣✉✐❛ ♦ ❧í❞❡r ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡ ♦s ❞❡♠❛✐s r♦❜ôs✱ ♣❛r❛ ❞❡t❡r♠✐♥❛❞❛s r❡❣✐õ❡s ❞♦ ❛♠❜✐❡♥t❡✳ ❆ ❛❝❡❧❡r❛çã♦ ❣❡r❛❞❛ ♣❡❧❛ ❧❡✐ ❞❡ ❝♦♥tr♦❧❡é s✉❥❡✐t❛ ❛ ✉♠ r✉í❞♦ ●❛✉ss✐❛♥♦✱ ❛❞✐t✐✈♦✱ ❝♦♠ ♠é❞✐❛ ③❡r♦ ❡ ❞❡s✈✐♦ ♣❛❞rã♦ ♣r♦♣♦r❝✐♦♥❛❧❛ 10% ❞♦ ✈❛❧♦r ✈❡r❞❛❞❡✐r♦✳ ❈❛❞❛ s✐♠✉❧❛çã♦ ✉t✐❧✐③❛ ❝❡r❝❛ ❞❡ 56300 ✐t❡r❛çõ❡s✱ s❡♥❞♦∆t = 10 ms ❛ ❞✉r❛çã♦ ❞❡ ❝❛❞❛ ✐t❡r❛çã♦✳ ❖ ❝♦♠♣r✐♠❡♥t♦ t♦t❛❧ ❞♦ ❝❛♠✐♥❤♦ ♣❡r❝♦rr✐❞♦é ❞❡✱ ❛♣r♦①✐♠❛❞❛♠❡♥t❡✱ 35,5 m✳ ◆❡st❡s ❡①♣❡r✐♠❡♥t♦s✱ ❝❛❞❛ r♦❜ô é ❞♦ t✐♣♦ ✐♥t❡❣r❛❞♦r ❞✉♣❧♦✳ ❆ ❛çã♦ ❞❡ ❝♦♥tr♦❧❡é ❜❛s❡❛❞❛ ♥❛ ❢♦r♠✉❧❛çã♦ ❞❡s❝r✐t❛ ♥❛ ❙❡çã♦ ✹✳✷✳✷✳ ❉❡ss❛ ❢♦r♠❛✱ ♦s ✈❡t♦r❡s ❞❡ ❡st❛❞♦ ❡ i = [a x i a y i ] ⊤✈❡❧♦❝✐❞❛❞❡s sã♦ ❞❡✜♥✐❞♦s ❝♦♠ ❜❛s❡ ♥♦ ✈❡t♦r u ✱ q✉❡ ❝♦♥s✐st❡ ♥❛ ❛çã♦ ❞❡ i❝♦♥tr♦❧❡ ❞♦ ✐✲és✐♠♦ r♦❜ô ♥♦ ❣r✉♣♦✳ ❖ ❡st❛❞♦ ❞❡ R ♥♦ ✐♥st❛♥t❡ ❞❡ t❡♠♣♦ k é ❞❡✜♥✐❞♦ k k k ⊤ = [x y ]❝♦♠♦ x i i i ❡ ♦ s❡❣✉✐♥t❡ ♠♦❞❡❧♦ ❞✐s❝r❡t♦ é ✉t✐❧✐③❛❞♦ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ♠❡s♠♦❡♠ ❝❛❞❛ ✐t❡r❛çã♦✿ k+1 k k v = f (v , u )i i i k k = v + u ∆t, i = 1, . . . , η i i k+1 k k+1 ✭✺✳✾✮ x = f (x , v )i i i k k+1= x + v ∆t. i i ✭✺✳✶✵✮ ❆ ♣r♦♣❛❣❛çã♦ ❞♦ ❡st❛❞♦ ❞♦ ✐✲és✐♠♦ r♦❜ô é ❡❢❡t✉❛❞❛ ✉t✐❧✐③❛♥❞♦ ♦ ♠♦❞❡❧♦ ❞✐s❝r❡t♦✭✺✳✶✵✮✱ ❝♦♠♦ s❡❣✉❡✿ k+1|k k|k k+1 x x v = f ( , ), i = 1, . . . , η. k k k k k ⊤ b b b i i i✭✺✳✶✶✮ = u + ǫ = [a a ]❆ ❡♥tr❛❞❛ bu i i i x i y i é ❝♦♠♣♦st❛✱ ❜❛s✐❝❛♠❡♥t❡✱ ❞❛s ❛❝❡❧❡r❛çõ❡s ❝♦♠❛♥✲ k⊤ i a a = [ǫ ǫ ] ❞❛❞❛s u i ✱ ❛♠♣❧✐❛❞❛s ❝♦♠ ✉♠ r✉í❞♦ ❛❞✐t✐✈♦ ●❛✉ss✐❛♥♦ ǫ ✱ ❝♦♠ ♠é❞✐❛s ③❡r♦ ⊤ xi yi i i i = diag(E (ǫ )❡ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛ ❞✐❛❣♦♥❛❧ Q {ǫ })✳ ❊ss❡ ♠♦❞❡❧♦ é ❝♦♠♣✉t❛❞♦✐♥❞✐✈✐❞✉❛❧♠❡♥t❡ ♣♦r ❝❛❞❛ r♦❜ô ❡♠ ✐♥t❡r✈❛❧♦s ❞❡ t❡♠♣♦ ❞❡ ❝♦♠♣r✐♠❡♥t♦ ∆t✳ ❉❡ ♠♦❞♦ s✐♠✐❧❛r ❛♦ q✉❡ ❢♦✐ ❢❡✐t♦ ♥❛ ♠♦✈✐♠❡♥t❛çã♦ ❛❧t❡r♥❛❞❛✱ ❛ ✐♥❝❡rt❡③❛ é ❝❛❧❝✉❧❛❞❛ ✉t✐❧✐③❛♥❞♦kk 2 2 = ∆t I ✭✹✳✶✹✮✱ s❡♥❞♦ Φ i ✉♠❛ ♠❛tr✐③ ✐❞❡♥t✐❞❛❞❡ ❞❡ ♦r❞❡♠ 2 ✭I ✮ ❡ G i ✳ ❖ ♠♦❞❡❧♦ ❞❡♦❜s❡r✈❛çã♦ é ❞❡s❝r✐t♦ ♣❡❧❛ ❊q✉❛çã♦ ✭✺✳✸✮✱ ❛♣r❡s❡♥t❛❞❛ ♥❛ s❡çã♦ ❛♥t❡r✐♦r✳ ✽✽❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s ❙❡❣✉✐♥❞♦ ❛ ♠❡t♦❞♦❧♦❣✐❛✱ ♦s r♦❜ôs sã♦ ✐♥✐❝✐❛❧♠❡♥t❡ ❞✐s♣♦st♦s ❛❧❡❛t♦r✐❛♠❡♥t❡ ❡♠❞❡t❡r♠✐♥❛❞❛ r❡❣✐ã♦ ❞♦ ❛♠❜✐❡♥t❡✳ ❯t✐❧✐③❛♥❞♦ ❛ ❧❡✐ ❞❡ ❝♦♥tr♦❧❡ ✭✹✳✷✷✮✱ ♦ ❧í❞❡r é ❣✉✐❛❞♦❡♠ ❞✐r❡çã♦ ❛♦ ❝❡♥tr♦ ❞♦ ❡♥①❛♠❡ ✭✈❡r ❋✐❣✉r❛ ✹✳✼✮✳ ❉✉r❛♥t❡ ❡ss❛ ❢♦r♠❛çã♦ ✐♥✐❝✐❛❧✱ ♦ ABAA = 1,0 m ♣❛râ♠❡tr♦ d ❢♦✐ ❞❡✜♥✐❞♦ ❝♦♠♦ 0,5 m✱ ❡♥q✉❛♥t♦ q✉❡ d ✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦♥❛ ❙❡çã♦ ✹✳✶✱ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ✉t✐❧✐③❛ ♠❡❞✐❞❛s r❡❧❛t✐✈❛s ❡♥tr❡ ♣❛r❡s ❞❡ r♦❜ôs❝♦♠♣❛rt✐❧❤❛♥❞♦ ✉♠❛ ♠❡s♠❛ ✈✐③✐♥❤❛♥ç❛✳ ❉❡✈✐❞♦ à ♥ã♦ ✉♥✐❢♦r♠✐❞❛❞❡ ❞❛s ❞✐stâ♥❝✐❛s✐♥t❡r❛❣❡♥t❡s r❡s✉❧t❛♥t❡s ❞❛ ❢♦r♠❛çã♦ ✐♥✐❝✐❛❧✱ ❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❛q✉❡❧❡s r♦❜ôs ♠❛✐s ❞✐st❛♥t❡s ❞♦ ❝❡♥tr♦ ❞♦ ❣r✉♣♦ ❞❡❣r❛❞❛♠ ♠❛✐s r❛♣✐❞❛♠❡♥t❡✳ P❛r❛ s♦❧✉❝✐♦♥❛r❡ss❡ ♣r♦❜❧❡♠❛✱ ❛ ❧❡✐ ❞❡ ❝♦♥tr♦❧❡ ❧♦❝❛❧ ✭✹✳✷✾✮ ❢♦✐ ❛♣❧✐❝❛❞❛ ❞❡ ❢♦r♠❛ ❛ ❣❡r❛r ✉♠❛ ❢♦r♠❛çã♦♠❛✐s ✉♥✐❢♦r♠❡✱ ❡♥q✉❛♥t♦ q✉❡ ✭✹✳✸✶✮ ♣♦ss✐❜✐❧✐t♦✉ ❛♦ ❣r✉♣♦ s❡ ♠♦✈✐♠❡♥t❛r ✉t✐❧✐③❛♥❞♦ s♦♠❡♥t❡ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s✳ ◆❡ss❛s ❧❡✐s ❞❡ ❝♦♥tr♦❧❡✱ ♦s ♣❛râ♠❡tr♦s ✉t✐❧✐③❛❞♦s ♥❛ ❢✉♥çã♦AA AB = d = 0,2 m ♣♦t❡♥❝✐❛❧ ✭✹✳✷✸✮ ❢♦r❛♠ ❞❡✜♥✐❞♦s ❝♦♠♦ d ✳ ❖ ❛❧❝❛♥❝❡ ❞♦ s❡♥s♦r ✈✐rt✉❛❧ AB )✭r❛✐♦ ε ❞❛s ✈✐③✐♥❤❛♥ç❛s✮ ❢♦✐ ❞❡✜♥✐❞♦ ❝♦♠♦ 0,266 m (1, 33 × d ✱ ❧✐♠✐t❛♥❞♦ ❝❛❞❛ r♦❜ô✐♥t❡r❛❣✐r s♦♠❡♥t❡ ❝♦♠ s❡✉s ✈✐③✐♥❤♦s ✐♠❡❞✐❛t♦s✳ ❆ ❋✐❣✉r❛ ✺✳✻ ❛♣r❡s❡♥t❛ ✉♠ ❡①❡♠♣❧♦ ❞❡ ❝❛♠✐♥❤♦ ❡❢❡t✉❛❞♦ ♣❡❧♦ ❡♥①❛♠❡ ♥♦ ❛♠❜✐✲❡♥t❡✳ ❆ ❡str❛té❣✐❛ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦ ❣r✉♣♦ ❝♦♥s✐❞❡r❛ ✐♥❢♦r♠❛çõ❡s ❞❡❧♦❝❛❧✐③❛çã♦ ♣❡r❢❡✐t❛✳ ◆♦ ❡♥t❛♥t♦✱ ❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❣❡r❛❞❛s ♣❡❧❛s ❛❜♦r❞❛✲❣❡♥s ❛✈❛❧✐❛❞❛s ✭❊❑❋ ❡ ❈■✮ sã♦ s✉❥❡✐t❛s ❛ r✉í❞♦s✱ ❝♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ♥♦s ❡①♣❡r✐♠❡♥t♦s✳❖s ❝ír❝✉❧♦s ♠❛✐♦r❡s ♥❛ ❝♦r ❝✐♥③❛ r❡♣r❡s❡♥t❛♠ ❛s r❡❣✐õ❡s q✉❡ ♦ ❡♥①❛♠❡ ♣r❡❝✐s❛ ✈✐s✐t❛r✱❝✉❥♦s ❝❡♥tr♦s ❞❡✜♥❡♠ ♦s ✇❛②♣♦✐♥ts✳ ❖s ♣♦♥t♦s ♥❛ ✜❣✉r❛ ✐♥❞✐❝❛♠ ❛ ♣♦s✐çã♦ ❞♦s r♦❜ôs❞✉r❛♥t❡ ❛ ♥❛✈❡❣❛çã♦✳ ❆ ❝♦r ❛③✉❧ ❝❛r❛❝t❡r✐③❛ ♦ r♦❜ô ❧í❞❡r✱ ❡♥q✉❛♥t♦ q✉❡ ❛ ❝♦r ✈❡r♠❡✲❧❤❛ r❡♣r❡s❡♥t❛ ♦s ❞❡♠❛✐s r♦❜ôs✳ ❖s ❝ír❝✉❧♦s sã♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ ✐♥❞✐❝❛r ❛ ❢♦r♠❛çã♦ ❞♦❣r✉♣♦ ❞✉r❛♥t❡ ❛ ♠♦✈✐♠❡♥t❛çã♦ ♣❡❧♦ ❛♠❜✐❡♥t❡✳ P♦❞❡✲s❡ ♦❜s❡r✈❛r q✉❡ t❛❧ ❢♦r♠❛çã♦ ❢♦✐♠❛♥t✐❞❛ ❞✉r❛♥t❡ ❛ ♥❛✈❡❣❛çã♦ ❞♦ ❡♥①❛♠❡✳ ◆❡st❡s ❡①♣❡r✐♠❡♥t♦s✱ ❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ é ❡①❡❝✉t❛❞❛ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ s❡✲❣✉✐♥t❡ ❞❡s❝r✐çã♦✳ ❖s r♦❜ôs ❝♦♠ ✉♠ ♥í✈❡❧ ❞❡ ✐♥❝❡rt❡③❛ ♠❡♥♦r ❞♦ q✉❡ ❞❡t❡r♠✐♥❛❞♦✈❛❧♦r ♣ré✲❡s♣❡❝✐✜❝❛❞♦ ❛t✉❛♠ ❝♦♠♦ ♠❛r❝♦s ❡ tr❛♥s♠✐t❡♠ ✭❜r♦❛❞❝❛st✮ ♠❡♥s❛❣❡♥s ❝♦♠✲♣♦st❛s ♣♦r s❡✉ ✐❞❡♥t✐✜❝❛❞♦r✱ ❡st❛❞♦ ❡ ❛ ✐♥❝❡rt❡③❛ ❛ss♦❝✐❛❞❛✳ ❆♣ós ❛❧❝❛♥ç❛r ♦ ❧✐♠✐❛r❞❡ ✐♥❝❡rt❡③❛ ♣r❡❞❡✜♥✐❞♦✱ ✉♠ r♦❜ô ❞❡✐①❛ ❞❡ s❡r ❝♦♥s✐❞❡r❛❞♦ ♠❛r❝♦ ❡ ♣❛r❛ ❞❡ tr❛♥s♠✐t✐r♠❡♥s❛❣❡♥s✳ P❛r❛ r❡str✐♥❣✐r ♦ ❛❧❝❛♥❝❡ s❡♥s♦r✐❛❧ ❞♦s r♦❜ôs✱ s♦♠❡♥t❡ ♦s r♦❜ôs ❞✐s♣♦st♦s ❛✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❞✐stâ♥❝✐❛ ❞❡ ✉♠ r♦❜ô q✉❡ ❡stá tr❛♥s♠✐t✐♥❞♦ sã♦ ❝♦♥s✐❞❡r❛❞♦s ❛♣t♦s❛ r❡❝❡❜❡r t❛✐s ♠❡♥s❛❣❡♥s✳ ❉✉r❛♥t❡ ♦ ♠♦✈✐♠❡♥t♦✱ ❛♣ós ✉♠ r♦❜ô t❡r ❛❝✉♠✉❧❛❞♦ ✉♠❞❡t❡r♠✐♥❛❞♦ ♥í✈❡❧ ❞❡ ✐♥❝❡rt❡③❛✱ ❡❧❡ ❛t✉❛❧✐③❛ s✉❛ ❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♠ ❛s ✐♥❢♦r✲♠❛çõ❡s r❡❝❡❜✐❞❛s ❞❡ r♦❜ôs ♠❛r❝♦s✱ ❝❛s♦ ❝♦♥s✐❣❛ ❡st✐♠❛r ❞✐stâ♥❝✐❛ ❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛s❛ ❡ss❡s✳ ❆♣❡s❛r ❞❡ s❡r ♣♦ssí✈❡❧ ❛t✉❛❧✐③❛r ❛ ❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ ✉♠ r♦❜ô ❝♦♠✐♥❢♦r♠❛çõ❡s ♣r♦✈❡♥✐❡♥t❡s ❞❡ ♠❛✐s ❞❡ ✉♠ r♦❜ô ♠❛r❝♦✱ ♥❡st❡s ❡①♣❡r✐♠❡♥t♦s s♦♠❡♥t❡ ❛✐♥❢♦r♠❛çã♦ r❡❝❡❜✐❞❛ ❞♦ ♠❛r❝♦ ❝♦♠ ♠❡♥♦r ✐♥❝❡rt❡③❛ é ✉t✐❧✐③❛❞❛✳ ✺✳✶✳ ❆♥á❧✐s❡ ❞❛ ❱❛r✐❛çã♦ ❞♦ ◆ú♠❡r♦ ❞❡ ▼❛r❝♦s ✽✾❋✐❣✉r❛ ✺✳✻✿ ❊①❡♠♣❧♦ ❞❡ ✉♠ ❝❛♠✐♥❤♦ ❡①❡❝✉t❛❞♦ ♣❡❧♦ ❡♥①❛♠❡✳ ❆ ❝♦r ❛③✉❧ r❡♣r❡s❡♥t❛ ❛s♣♦s✐çõ❡s ❞♦ r♦❜ô ❧í❞❡r ❡♥q✉❛♥t♦ q✉❡ ❛ ❝♦r ✈❡r♠❡❧❤❛ ✐♥❞✐❝❛ ❛ ♣♦s✐çã♦ ❞♦s ❞❡♠❛✐s r♦❜ôs✳ ❖s r❡s✉❧t❛❞♦s ❞❡ três t✐♣♦s ❞❡ ❡①♣❡r✐♠❡♥t♦s sã♦ ♠♦str❛❞♦s ❡♠ s❡❣✉✐❞❛✳ ◆♦ ♣r✐✲♠❡✐r♦✱ ❛ ❧♦❝❛❧✐③❛çã♦ ❢♦✐ ❢❡✐t❛ s❡♠ ❝♦♥s✐❞❡r❛r ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❝♦♦♣❡r❛t✐✈♦ ❞❡ ♠♦❞♦ q✉❡ ❝❛❞❛ r♦❜ô ✉t✐❧✐③❛ s♦♠❡♥t❡ s❡✉s s❡♥s♦r❡s ♣r♦♣r✐♦❝❡♣t✐✈♦s ✭♦❞♦♠❡tr✐❛✮✳ ❖ s❡❣✉♥❞♦❡①♣❡r✐♠❡♥t♦ ❢❡③ ✉s♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ ♥♦ ❡♥t❛♥t♦ ♥❡♥❤✉♠ r♦❜ô ❢♦✐ ❡q✉✐♣❛❞♦❝♦♠ ❛❧❣✉♠ s✐st❡♠❛ ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❣❧♦❜❛❧✳ ❚♦❞♦s ♦s r♦❜ôs t❡♥t❛♠ ❛t✉❛❧✐③❛r s✉❛s ❡s✲ t✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♠ ❜❛s❡ ❡♠ s❡✉s ✈✐③✐♥❤♦s ✐♠❡❞✐❛t♦s✳ ◆♦ ú❧t✐♠♦ ❡①♣❡r✐♠❡♥t♦✱✉♠ r♦❜ô ✭❧í❞❡r✮ ❡q✉✐♣❛❞♦ ❝♦♠ s❡♥s♦r ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❣❧♦❜❛❧ ♣r♦♣❛❣❛ s✉❛s ❡st✐♠❛t✐✲✈❛s ♣❛r❛ ♦s ✈✐③✐♥❤♦s ✐♠❡❞✐❛t♦s✳ ◆❡st❡ ❡①♣❡r✐♠❡♥t♦✱ ♦ ❧í❞❡r ❛t✉❛❧✐③❛ s✉❛ ❡st✐♠❛t✐✈❛ ❞❡❧♦❝❛❧✐③❛çã♦ ✉t✐❧✐③❛♥❞♦ s♦♠❡♥t❡ ❛s ✐♥❢♦r♠❛çõ❡s ❞♦ s❡♥s♦r ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❣❧♦❜❛❧✱ ♦✉ s❡❥❛✱ ♥ã♦ ✉t✐❧✐③❛ s❡✉s ✈✐③✐♥❤♦s ♣❛r❛ ❛❥✉st❛r s✉❛ ❝r❡♥ç❛✳ ◆♦s ❞♦✐s ú❧t✐♠♦s ❡①♣❡r✐♠❡♥t♦s✱❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❢♦r❛♠ ❡❢❡t✉❛❞❛s ❞❡ ♠♦❞♦ q✉❡ ❝❛❞❛ r♦❜ô ✭❝♦♠ ❡①✲❝❡çã♦ ❞♦ ❧í❞❡r✮ ✉t✐❧✐③❛ss❡ s♦♠❡♥t❡ ♦ ♠❛r❝♦ ❝♦♠ ❛ ♠❡❧❤♦r ❡st✐♠❛t✐✈❛ ✭♠❡♥♦r ✐♥❝❡rt❡③❛✮✳◆❡♥❤✉♠❛ s✐♥❝r♦♥✐③❛çã♦ ❢♦✐ ❡❢❡t✉❛❞❛✱ ❞❡ ♠♦❞♦ q✉❡ ✉♠ ❞❛❞♦ r♦❜ô t❡♥t❛ ❛t✉❛❧✐③❛r s✉❛❡st✐♠❛t✐✈❛ ❞❡ ❢♦r♠❛ ✐♥❞❡♣❡♥❞❡♥t❡ ❞♦s ❞❡♠❛✐s✳ ❆❧é♠ ❞✐ss♦✱ ♦s r✉í❞♦s ❛ss♦❝✐❛❞♦s às♠❡❞✐❞❛s ❞❡ ❞✐stâ♥❝✐❛ ❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛s ❢♦r❛♠ ❞❡✜♥✐❞♦s ❝♦♠ ❞❡s✈✐♦ ♣❛❞rã♦ ❞❡ 5%❞♦ ✈❛❧♦r r❡❛❧ ❞❡ t❛✐s ♠❡❞✐❞❛s✳ ❊ss❡s ❡①♣❡r✐♠❡♥t♦s s❡rã♦ r❡❢❡r❡♥❝✐❛❞♦s ❛ s❡❣✉✐r ❝♦♠♦ s❡♠ ❝♦♦♣❡r❛çã♦✱ ▲❈ s❡♠ ●P❙ ❡ ▲❈ ❝♦♠ ●P❙ ✭❧í❞❡r✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ◆❡st❛ ❛♥á❧✐s❡✱ ❝❛❞❛ ❡①♣❡r✐♠❡♥t♦ ❢♦✐ ❡①❡❝✉t❛❞♦ 30 ✈❡③❡s ❡ ♦ ❡rr♦ ♠é❞✐♦ ✭❘▼❙❊✮❢♦✐ ❝❛❧❝✉❧❛❞♦✳ ❖ ♦❜❥❡t✐✈♦ ❝♦♥s✐st❡ ❡♠ ❝♦♠♣❛r❛r ♦ ❡rr♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s❞❡ ♣♦s✐çã♦ ❞♦s r♦❜ôs ❛♦ ❝♦♥s✐❞❡r❛r ♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❞❡ ❝❛❞❛ r♦❜ô ❡♠ r❡❧❛çã♦ ❛♦ ❧í✲ ✾✵❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s ❞❡r✳ P❛r❛ ❛✉①✐❧✐❛r ♥❛ ❛♥á❧✐s❡ ❞❡ss❡ ❡rr♦✱ ♦ ♠ét♦❞♦ ❞❡ ❛❣r✉♣❛♠❡♥t♦ ❦✲♠❡❛♥s ✭❦✲♠❡❛♥s❝❧✉st❡r✐♥❣✮ ❢♦✐ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❞✐✈✐❞✐r ✭✈✐rt✉❛❧♠❡♥t❡✮ ♦ ❡♥①❛♠❡ ❡♠ s❡✐s ❣r✉♣♦s✳ ❖ ❝r✐✲ tér✐♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❛tr✐❜✉✐r ✉♠ r♦❜ô ❛ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❣r✉♣♦ g ✭●g✮ ❢♦✐ ❛ ❞✐stâ♥❝✐❛❊✉❝❧✐❞✐❛♥❛ ✈❡r❞❛❞❡✐r❛ ❡♥tr❡ t❛❧ r♦❜ô ❡ ♦ ❧í❞❡r✳ ◗✉❛♥t♦ ♠❡♥♦r ♦ ✈❛❧♦r ❞❡ g✱ ♠❡♥♦r é ❛❞✐stâ♥❝✐❛ ♠é❞✐❛ ❞❛q✉❡❧❡ ❣r✉♣♦ ❡♠ r❡❧❛çã♦ ❛♦ ❧í❞❡r✳ ❆ ❋✐❣✉r❛ ✺✳✼ ♠♦str❛ ♦ r❡s✉❧t❛❞♦❞❛ ❞✐✈✐sã♦ ❡①❡❝✉t❛❞❛ ❝♦♠ ♦ ♣❛râ♠tr♦ k = 6✳ ❖s ❝ír❝✉❧♦s r❡♣r❡s❡♥t❛♠ ❛ ♣♦s✐çã♦ ❞♦s r♦❜ôs ❡ ❛s ❝♦r❡s ❞✐st✐♥❣✉❡♠ ♦s ❣r✉♣♦s✳ ❖ r♦❜ô ❧í❞❡r é r❡♣r❡s❡♥t❛❞♦ ♣❡❧❛ ❝♦r ❜r❛♥❝❛ ❡❢♦✐ ❝♦♥s✐❞❡r❛❞♦ ❝♦♠♦ ♣♦♥t♦ ❞❡ r❡❢❡rê♥❝✐❛ ❛ ♣❛rt✐r ❞♦ q✉❛❧ ♦ ♣r♦❝❡ss♦ ❞❡ ❛❣r✉♣❛♠❡♥t♦❢♦✐ ❡①❡❝✉t❛❞♦✳G3 G2 G1 G4 G5 ❋✐❣✉r❛ ✺✳✼✿ ❆❣r✉♣❛♠❡♥t♦s ✉t✐❧✐③❛❞♦s s♦♠❡♥t❡ ♣❛r❛ ❛✉①✐❧✐❛r ♥❛ ❛♥á❧✐s❡✳ ❖ ❧í❞❡r é ❧♦✲❝❛❧✐③❛❞♦ ♥♦ ❝❡♥tr♦ ❞♦ ❡♥①❛♠❡ ✭❝ír❝✉❧♦ ❜r❛♥❝♦✮✱ ❡♥q✉❛♥t♦ q✉❡ ♦s ❞❡♠❛✐s r♦❜ôs sã♦❛tr✐❜✉í❞♦s ❛♦s ❣r✉♣♦s ✭●1 t♦ ●6✮ ❝♦♠ ❜❛s❡ ♥❛ ❞✐stâ♥❝✐❛ ❊✉❝❧✐❞✐❛♥❛ ♣❛r❛ ♦ r♦❜ô ❧í❞❡r✳ ❖ ❝á❧❝✉❧♦ ❞♦ ❡rr♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ✭❘▼❙❊✮ ❢♦✐ ❡❢❡t✉❛❞♦ t❡♥❞♦ ❝♦♠♦ ❜❛s❡ ♦s ❛❣r✉✲♣❛♠❡♥t♦s ❣❡r❛❞♦s✱ ❝♦♥❢♦r♠❡ s❡❣✉❡✿ X X j k 1 1 ● E = , s ❡ i ✭✺✳✶✷✮ j i K||● || i∈ j kk ● k = s❡♥❞♦ ♦ ❡rr♦ ❞❡ ♣♦s✐çã♦ ❡ i ❛ss♦❝✐❛❞♦ ❛ ✉♠ r♦❜ô i ♥❛ ✐t❡r❛çã♦ k ❞❡✜♥✐❞♦ ♣♦r ❡ ik k k g g x xi|| b i − bx i ||✱ ♦♥❞❡ b i é ❛ ❡st✐♠❛t✐✈❛ ❞❡ ♣♦s✐çã♦ r❡❧❛t✐✈❛ ❛♦ ❣r♦✉♥❞ tr✉t❤✱ K ♦ ♥ú♠❡r♦ j❞❡ ✐t❡r❛çõ❡s ❡①❡❝✉t❛❞❛s ♣❡❧♦ r♦❜ô i ❡ ||● || ♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs ♥♦ ❣r✉♣♦ j✳ ❖ ❡rr♦♠é❞✐♦ ❛ss♦❝✐❛❞♦ ❛♦ ❣r✉♣♦ j ❡♠ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❡①♣❡r✐♠❡♥t♦ ❢♦✐ ❝❛❧❝✉❧❛❞♦ ❞❛ s❡❣✉✐♥t❡❢♦r♠❛✿ X 1 ● j = E ,▼P❊ j s ✭✺✳✶✸✮ S s s❡♥❞♦ S ♦ ♥ú♠❡r♦ ❞❡ s✐♠✉❧❛çõ❡s✳ ✺✳✶✳ ❆♥á❧✐s❡ ❞❛ ❱❛r✐❛çã♦ ❞♦ ◆ú♠❡r♦ ❞❡ ▼❛r❝♦s ✾✶❆ ❋✐❣✉r❛ ✺✳✽ ❛♣r❡s❡♥t❛ ♦s ❡rr♦s ♣❛r❛ ♦s três t✐♣♦s ❞❡ ❡①♣❡r✐♠❡♥t♦s✳ ➱ ♣♦ssí✈❡❧ ♦❜s❡r✈❛r ♦ ❛✉♠❡♥t♦ ♥❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ q✉❛♥❞♦ ✉♠ ♠ét♦❞♦ ❞❡ ❧♦❝❛❧✐③❛çã♦❝♦♦♣❡r❛t✐✈❛ é ❡♠♣r❡❣❛❞♦✳ ❆❧é♠ ❞✐ss♦✱ ♦ ✉s♦ ❞❡ ✉♠ ú♥✐❝♦ r♦❜ô ❡q✉✐♣❛❞♦ ❝♦♠ s✐st❡♠❛ ❞❡♣♦s✐❝✐♦♥❛♠❡♥t♦ ❣❧♦❜❛❧ ❛✉♠❡♥t❛ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ t♦❞♦s♦s r♦❜ôs✳ ❚❛❧ ❝♦♠♦ ♦❝♦rr❡✉ ♥❛ ♠♦✈✐♠❡♥t❛çã♦ ❛❧t❡r♥❛❞❛ ✭❋✐❣✉r❛ ✺✳✸✮✱ ♥❛ ♠♦✈✐♠❡♥t❛çã♦❝♦♥tí♥✉❛ ♦ ❡rr♦ ❝r❡s❝❡ ♠❛✐s r❛♣✐❞❛♠❡♥t❡ q✉❛♥❞♦ ♥ã♦ s❡ ✉t✐❧✐③❛ ❝♦♦♣❡r❛çã♦ ♥♦s ♣r♦❝❡ss♦s❞❡ ❧♦❝❛❧✐③❛çã♦✳2.5 LC sem GPS LC com GPS (líder) sem cooperação) m1.5 2 M P E (1 0.5 G1 G2 G3 G4 G5 G6 Grupos ❋✐❣✉r❛ ✺✳✽✿ ❊rr♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛ss♦❝✐❛❞♦ ❛♦s três t✐♣♦s ❞❡ ❡①♣❡r✐♠❡♥t♦✳❆ ❋✐❣✉r❛ ✺✳✾ ❛♣r❡s❡♥t❛ ❛ ❛♥á❧✐s❡ ❞♦ ❡rr♦ r❡❧❛❝✐♦♥❛❞♦ ❛♦s ❡①♣❡r✐♠❡♥t♦s ❡♠ q✉❡ ♦ r♦❜ô ❧í❞❡r ❢♦✐ ❡q✉✐♣❛❞♦ ❝♦♠ s❡♥s♦r❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛ ❡ ♦s ❞❡♠❛✐s r♦❜ôs s❡❧♦❝❛❧✐③❛r❛♠ ✉t✐❧✐③❛♥❞♦ ♦ ♠ét♦❞♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❊ss❛ ✜❣✉r❛ ❝♦♠♣r❡❡♥❞❡✉♠❛ ✈❡rsã♦ ❛♠♣❧✐❛❞❛ ❞❛ ✐♥❢♦r♠❛çã♦ r❡❢❡r❡♥t❡ ❛♦s ❞❛❞♦s ✏▲❈ ❝♦♠ ●P❙ ✭❧í❞❡r✮✑ ✭❝♦r✈❡r♠❡❧❤❛✮ ♣r❡s❡♥t❡ ♥❛ ❋✐❣✉r❛ ✺✳✽✳ ❖ ❣r✉♣♦ ●1 ❢♦✐ ✉t✐❧✐③❛❞♦ ❝♦♠♦ r❡❢❡rê♥❝✐❛ ❞❡✈✐❞♦ à s✉❛ ♣r♦①✐♠✐❞❛❞❡ ❝♦♠ ♦ r♦❜ô ❧í❞❡r✳ ❉❡ss❡ ♠♦❞♦✱ ❝❛❞❛ ❜❛rr❛ ♥❛ ✜❣✉r❛ ♠♦str❛ ❛ ♣r♦♣♦rçã♦❞♦ ❡rr♦ ❞❡ ❞❡t❡r♠✐♥❛❞♦ ❣r✉♣♦ ❡♠ r❡❧❛çã♦ ❛ ●1✱ ♦✉ s❡❥❛✱ ●g✴●1✱ s❡♥❞♦ g = {2, 3, 4, 5, 6}✳➱ ♣♦ssí✈❡❧ ♥♦t❛r ❛ t❡♥❞ê♥❝✐❛ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❞♦ ❡rr♦ q✉❛♥❞♦ ✉♠ ❣r✉♣♦ ❡♥❝♦♥tr❛✲s❡ ♠❛✐s❛❢❛st❛❞♦ ❞❡ ●1 ✭❋✐❣✉r❛ ✺✳✾✮✳ ❖ ❡rr♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ ●6 é q✉❛s❡ 50% ♠❛✐♦r ❞♦ q✉❡ ♦❡rr♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❣r✉♣♦ ●1✳ ◆❛ ❋✐❣✉r❛ ✺✳✽✱ ♦s ❣r✉♣♦s ❛♣r❡s❡♥t❛♠ ❡rr♦s s✐♠✐❧❛r❡s q✉❛♥❞♦ ♦ ♠ét♦❞♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♥ã♦ ❢♦✐ ✉t✐❧✐③❛❞♦✳ ❖✉tr♦ ❞❛❞♦ ✐♥t❡r❡ss❛♥t❡ ❞✐③ r❡s♣❡✐t♦ ❛ q✉❡ ❣r✉♣♦ ♣❡rt❡♥❝❡ ✉♠ r♦❜ô ♠❛r❝♦ ✉t✐✲❧✐③❛❞♦ ♣♦r ❞❡t❡r♠✐♥❛❞♦ r♦❜ô ♣❛r❛ ❝♦rr✐❣✐r s✉❛ ❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❊ss❡ ❞❛❞♦♣♦ss✐❜✐❧✐t❛ ✈❡r✐✜❝❛r ❞❡ q✉❡ ❢♦r♠❛ ♦❝♦rr❡✉ ❛ ❝♦♦♣❡r❛çã♦ ✐♥t❡r❣r✉♣♦s✱ ♣♦ss✐❜✐❧✐t❛♥❞♦ ✐❞❡♥✲ t✐✜❝❛r ♦ s❡♥t✐❞♦ ❞♦ ✢✉①♦ ❞❡ ❛t✉❛❧✐③❛çõ❡s✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ❝❛❞❛ r♦❜ôs♦♠❡♥t❡ t❡♠ ❛❝❡ss♦ ❛ s❡✉s ✈✐③✐♥❤♦s ✐♠❡❞✐❛t♦s✱ ♦s q✉❛✐s ♣♦❞❡rã♦ s❡r ✉t✐❧✐③❛❞♦s ❝♦♠♦ ✾✷1.451.5 ❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s: G1) l (g rupo base1.251.351.3 1.4 ciona Err o pr opor1.051.151.1 1.2 1 G2 G3 G4 G5 G6 Grupos ❋✐❣✉r❛ ✺✳✾✿ ❊rr♦ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❝♦♠ ✉♠ r♦❜ô ❡q✉✐♣❛❞♦ ❝♦♠ s✐st❡♠❛ ❞❡♣♦s✐❝✐♦♥❛♠❡♥t♦ ❣❧♦❜❛❧✳ ❖s ❣r✉♣♦s Gg sã♦ ❞❡✜♥✐❞♦s ❝♦♠ ❜❛s❡ ❡♠ s✉❛s r❡s♣❡❝t✐✈❛s❞✐stâ♥❝✐❛s ♣❛r❛ ♦ r♦❜ô ❧í❞❡r ✭q✉❛♥t♦ ♠❡♥♦r ♦ ✈❛❧♦r ❞❡ g✱ ♠❡♥♦r é ❛ ❞✐stâ♥❝✐❛ ❞❡ ✉♠❣r✉♣♦ ♣❛r❛ ♦ ❧í❞❡r✮✳♠❛r❝♦✳ ◆❛ ❋✐❣✉r❛ ✺✳✼✱ ♣♦❞❡✲s❡ ♦❜s❡r✈❛r q✉❡ ❞❡✈✐❞♦ à ❢♦r♠❛ ❝♦♠ q✉❡ ♦s ❛❣r✉♣❛♠❡♥t♦s❢♦r❛♠ ❞❡✜♥✐❞♦s✱ ♦s r♦❜ôs ♣♦ss✉❡♠ ✈✐③✐♥❤♦s ♣❡rt❡♥❝❡♥t❡s ❛ ♠❛✐s ❞❡ ✉♠ ❣r✉♣♦✳ ❘♦❜ôs❞♦ ❣r✉♣♦ ●3✱ ♣♦r ❡①❡♠♣❧♦✱ ♣♦ss✉❡♠ ✈✐③✐♥❤♦s q✉❡ ♣❡rt❡♥❝❡♠ ❛♦ ♣ró♣r✐♦ ❣r✉♣♦✱ ❛❧é♠❞❡ r♦❜ôs ♣❡rt❡♥❝❡♥t❡s ❛♦s ❣r✉♣♦s ●2 ❡ ●4✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❛❧❣✉♥s r♦❜ôs ❞♦ ❣r✉♣♦ ●4♣♦ss✉❡♠ ✈✐③✐♥❤♦s ❞♦ ♣ró♣r✐♦ ❣r✉♣♦ ❡ ❞♦s ❣r✉♣♦s ●3✱ ●5 ❡ ●6✳ ❆ ❚❛❜❡❧❛ ✺✳✶ ❛♣r❡s❡♥t❛ ✉♠ r❡s✉♠♦ ❞❛ ❝♦♦♣❡r❛çã♦ ✐♥t❡r❣r✉♣♦s ♦❝♦rr✐❞❛ ♥❛s ❡t❛♣❛s❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ◆❡ss❛ t❛❜❡❧❛ sã♦ ♠♦str❛❞❛s ❛s ♣r♦♣♦rçõ❡s ✭✈❛❧♦r ♠é❞✐♦ ❞❛s 30❡①❡❝✉çõ❡s✮ ❝♦♠ r❡❧❛çã♦ à ✉t✐❧✐③❛çã♦ ❞♦s r♦❜ôs ♠❛r❝♦✳ ❈♦♠♦ ❡①❡♠♣❧♦✱ ♣♦❞❡✲s❡ ♦❜s❡r✈❛r q✉❡ ♦s r♦❜ôs ❡♠ ●2 ✉t✐❧✐③❛r❛♠ ❝♦♠♦ ♠❛r❝♦s r♦❜ôs ♣❡rt❡♥❝❡♥t❡s ❛✿ ●1 ❡♠53% ❀ ●2 ❡♠ 26%❀ ❡ ●3 ❡♠ 21% ❞❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ➱ ✐♠♣♦rt❛♥t❡♦❜s❡r✈❛r q✉❡ r♦❜ôs ❧♦❝❛❧✐③❛❞♦s ❡♠ ●1 ❝♦rr✐❣❡♠ s✉❛s ❡st✐♠❛t✐✈❛s ❞❡ ♣♦s✐çã♦ ✉t✐❧✐③❛♥❞♦♦ ❧í❞❡r✱ r❡♣r❡s❡♥t❛❞♦ ♣❡❧♦ ✈❛❧♦r 0 ❡♠ t♦❞♦s ♦s ❣r✉♣♦s ♥❛ ♣r✐♠❡✐r❛ ❧✐♥❤❛ ❞❛ t❛❜❡❧❛✳❈♦♥❢♦r♠❡ ❝✐t❛❞♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ♦ r❛✐♦ ε ❢♦✐ ❞❡✜♥✐❞♦ ❞❡ ❢♦r♠❛ q✉❡ ❝❛❞❛ r♦❜ô ✐♥t❡r❛❣✐✉❞✐r❡t❛♠❡♥t❡ s♦♠❡♥t❡ ❝♦♠ s❡✉s ✈✐③✐♥❤♦s ✐♠❡❞✐❛t♦s✳ ❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ✉♠ ❣r✉♣♦ s❡ r❡❧❛❝✐♦♥❛ s♦♠❡♥t❡ ❝♦♠ ❣r✉♣♦s ♣ró①✐♠♦s✳ ❆❧é♠ ❞♦ ♠❛✐s✱ ♣♦❞❡✲s❡ ♦❜s❡r✈❛r q✉❡ ❝❛❞❛❣r✉♣♦ ✉t✐❧✐③❛✱ ♥❛ ♠❛✐♦r✐❛ ❞❛s ✈❡③❡s✱ ❣r✉♣♦s ✈✐③✐♥❤♦s ♠❛✐s ♣ró①✐♠♦s ❞♦ ❧í❞❡r✳ ❆ ✐♠♣♦rtâ♥❝✐❛ ❞♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦ ❧í❞❡r ♥♦ ❣r✉♣♦ é ♠♦str❛❞❛ ♥❛ ❋✐❣✉r❛ ✺✳✶✵✳❈♦♠♦ ❞✐t♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ❛q✉❡❧❡s r♦❜ôs ♠❛✐s ❞✐st❛♥t❡s ❞♦ ❧í❞❡r ❛❝✉♠✉❧❛♠ ♠❛✐♦r ❡rr♦❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❉❡ss❛ ❢♦r♠❛✱ q✉❛♥❞♦ ✉♠ ú♥✐❝♦ r♦❜ô ❡q✉✐♣❛❞♦ ❝♦♠ s✐st❡♠❛ ❞❡ ♣♦s✐✲❝✐♦♥❛♠❡♥t♦ ❣❧♦❜❛❧ é ✉t✐❧✐③❛❞♦ ♥♦ ❡♥①❛♠❡✱ ♦ ♠❡❧❤♦r ♣♦s✐❝✐♦♥❛♠❡♥t♦ ♣❛r❛ ♦ ♠❡s♠♦ é♣ró①✐♠♦ ❛♦ ❝❡♥tr♦ ❞♦ ❣r✉♣♦✳ ◆❡ss❛ ✜❣✉r❛✱ ♦ ❝ír❝✉❧♦ ❝❧❛r♦ ✐♥❞✐❝❛ ❛ ♣♦s✐çã♦ ❞♦ ❧í❞❡r✱❡♥q✉❛♥t♦ q✉❡ ♦s ❞❡♠❛✐s r❡♣r❡s❡♥t❛♠ ❛ ♣♦s✐çã♦ ❞♦s ♦✉tr♦s r♦❜ôs✳ ❈ír❝✉❧♦s ♠❛✐s ❡s❝✉r♦s ✺✳✶✳ ❆♥á❧✐s❡ ❞❛ ❱❛r✐❛çã♦ ❞♦ ◆ú♠❡r♦ ❞❡ ▼❛r❝♦s ✾✸❚❛❜❡❧❛ ✺✳✶✿ ❈♦♦♣❡r❛çã♦ ✐♥t❡r❣r✉♣♦s ●r✉♣♦s●✶ ●✷ ●✸ ●✹ ●✺ ●✻ ●✶ ✵ ✵ ✵ ✵ ✵ ✵●✷ ✵✳✺✸ ✵✳✷✻ ✵✳✷✶ ✵ ✵ ✵ ♦s ●✸ ✵ ✵✳✹✸ ✵✳✸✷ ✵✳✷✺ ✵ ✵●✹ ✵ ✵ ✵✳✹✷ ✵✳✷✽ ✵✳✷✽ ✵✳✵✷ ●r✉♣ ●✺ ✵ ✵ ✵✳✵✷ ✵✳✹✸ ✵✳✷✺ ✵✳✸✵●✻ ✵ ✵ ✵ ✵✳✵✽ ✵✳✻✸ ✵✳✷✾ ✐♥❞✐❝❛♠ ❡rr♦s ❞❡ ❧♦❝❛❧✐③❛çã♦ ♠❛✐♦r❡s✳ ✭❛✮ ✭❜✮ ❋✐❣✉r❛ ✺✳✶✵✿ ■♥t❡♥s✐❞❛❞❡ ❞♦ ❡rr♦ ❛❝✉♠✉❧❛❞♦ ♣❡❧♦s r♦❜ôs ❛♣ós ❛ ❡①❡❝✉çã♦ ❞❡ ✉♠ ❝❛♠✐✲♥❤♦✳ ❖s ❝ír❝✉❧♦s r❡♣r❡s❡♥t❛♠ ❛ ♣♦s✐çã♦ ❞♦s r♦❜ôs ♥♦ ❡♥①❛♠❡✳ ❖ ❝ír❝✉❧♦ ❝❧❛r♦ ✐♥❞✐❝❛❛ ♣♦s✐çã♦ ❞♦ ❧í❞❡r✿ ✭❛✮ ❧í❞❡r ♣♦s✐❝✐♦♥❛❞♦ ♣ró①✐♠♦ ❛♦ ❝❡♥tr♦ ❞♦ ❡♥①❛♠❡❀ ✭❜✮ ❧í❞❡r ♣♦s✐✲❝✐♦♥❛❞♦ ♥❛ ❢r♦♥t❡✐r❛ ❞♦ ❣r✉♣♦✳ ❆s ❝♦r❡s ✐♥❞✐❝❛♠ ❛ ✐♥t❡♥s✐❞❛❞❡ ❞♦ ❡rr♦ ❞❡ ❧♦❝❛❧✐③❛çã♦✿❝♦r❡s ♠❛✐s ❡s❝✉r❛s r❡♣r❡s❡♥t❛♠ ♥í✈❡✐s ♠❛✐♦r❡s ❞❡ ❡rr♦✳ ➱ ♣♦ssí✈❡❧ ♦❜s❡r✈❛r ♥❛ ❋✐❣✉r❛ ✺✳✶✵❜✱ ♥❛ q✉❛❧ ♦ ❧í❞❡r é ♣♦s✐❝✐♦♥❛❞♦ ♥❛ ❢r♦♥t❡✐r❛ ❞♦❡♥①❛♠❡✱ q✉❡ ♦s r♦❜ôs s✐t✉❛❞♦s ♥♦ ❧❛❞♦ ♦♣♦st♦ ❞♦ ❡♥①❛♠❡ ♣♦ss✉❡♠ ♥í✈❡✐s ♠❛✐s ❡❧❡✈❛❞♦s❞❡ ❡rr♦ ❞♦ q✉❡ ❛q✉❡❧❡s ❧♦❝❛❧✐③❛❞♦s ♣ró①✐♠♦s ❛♦ ❧í❞❡r✳ ◆♦s ❡①♣❡r✐♠❡♥t♦s ❡♠ q✉❡ ♦ ❧í❞❡r❢♦✐ ♣♦s✐❝✐♦♥❛❞♦ ♥❛ ❢r♦♥t❡✐r❛ ❞♦ ❣r✉♣♦✱ ♦ ♥ú♠❡r♦ ❞❡ ❛❣r✉♣❛♠❡♥t♦s ❢♦✐ ❛♠♣❧✐❛❞♦ ♣❛r❛ 15❣r✉♣♦s ♣❛r❛ ❛✉①✐❧✐❛r ❛ ❛♥á❧✐s❡ ❞❛ ❞❡❣r❛❞❛çã♦ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦s r♦❜ôs ❡♠ r❡❧❛çã♦ ❛♦♣♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦s ♠❡s♠♦s ♥♦ ❣r✉♣♦ ✭✈❡r ❋✐❣✉r❛ ✺✳✶✶✮✳ ❆ ❛tr✐❜✉✐çã♦ ❞❡ ✉♠ r♦❜ô ❛ ✉♠❞❡t❡r♠✐♥❛❞♦ ❣r✉♣♦ ❢♦✐ ❢❡✐t❛ ♥♦s ♠❡s♠♦s ♠♦❧❞❡s ❞❛ ❛tr✐❜✉✐çã♦ ❞❡s❝r✐t❛ ❛♥t❡r✐♦r♠❡♥t❡✳ ❖ ❡rr♦ ♠é❞✐♦ ❞❛s ❡st✐♠❛t✐✈❛s ❞❡ ♣♦s✐çã♦ ❞♦s r♦❜ôs q✉❡ ❝♦♠♣õ❡♠ ✉♠ ❛❣r✉♣❛✲♠❡♥t♦ é ❛♣r❡s❡♥t❛❞♦ ❡♠ ❋✐❣✉r❛ ✺✳✶✷✳ ❈♦♠♦ ♣♦❞❡ s❡r ✈✐st♦✱ ❛ t❡♥❞ê♥❝✐❛ ❞❡ ❝r❡s❝✐♠❡♥t♦❞✐s❝✉t✐❞❛ ❛♥t❡r✐♦r♠❡♥t❡ ❢♦✐ ♠❛♥t✐❞❛✳ ❆ ❋✐❣✉r❛ ✺✳✶✷ s✉❣❡r❡ q✉❡ ❡♠ ❡♥①❛♠❡s ❝♦♠♣♦st♦s♣♦r ✉♠ ♥ú♠❡r♦ ♠❛✐♦r ❞❡ r♦❜ôs✱ ✉♠ ú♥✐❝♦ r♦❜ô ❝♦♠ ❝❛♣❛❝✐❞❛❞❡s s❡♥s♦r✐❛✐s ❛♠♣❧✐❛❞❛s✭✉s♦ ❞❡ ●P❙✱ ♣♦r ❡①❡♠♣❧♦✮ ♣♦❞❡ ♥ã♦ s❡r s✉✜❝✐❡♥t❡ ♣❛r❛ ♠❛♥t❡r ❜♦♥s ♥í✈❡✐s ❞❡ ❧♦❝❛❧✐✲ ✾✹❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s G2 G1G9 G8 G7 G6 G5 G4 G3 G14 G13 G11 G10 G15 G12 ❋✐❣✉r❛ ✺✳✶✶✿ ❆✉♠❡♥t♦ ♥♦ ♥ú♠❡r♦ ❞❡ ❛❣r✉♣❛♠❡♥t♦s ❞❡ ❢♦r♠❛ ❛ ♣❡r♠✐t✐r ✉♠❛ ♠❡❧❤♦r❛♥á❧✐s❡ ❞♦ ✐♠♣❛❝t♦ ♥❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ t❡♥❞♦ ❝♦♠♦ r❡❢❡rê♥❝✐❛ ❛ ❞✐s♣♦s✐çã♦ ❞♦s❣r✉♣♦s ❡♠ r❡❧❛çã♦ ❛♦ r♦❜ô ❧í❞❡r ✭❝ír❝✉❧♦ ❜r❛♥❝♦✮✳③❛çã♦ ♣❛r❛ t♦❞♦s ♦s ♠❡♠❜r♦s ❞♦ ❣r✉♣♦✳ ❆❧é♠ ❞✐ss♦✱ ♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❞❡ss❡s r♦❜ôs é✉♠ ❢❛t♦r r❡❧❡✈❛♥t❡ ❛ s❡r ❝♦♥s✐❞❡r❛❞♦✳1.71.8: G1)1.61.5 G9 G11 G13 G14 G15 ciona l (g rupo base1.31.4 G7 G5 G6 G8 G10 G12 Err opor o pr1.11.2 G3 G41 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 G2 Distância para o líder (m) ❋✐❣✉r❛ ✺✳✶✷✿ Pr♦♣♦rçã♦ ❞♦ ❡rr♦ ♠é❞✐♦ ❞❡ ❝❛❞❛ ❣r✉♣♦ g ❡♠ r❡❧❛çã♦ ❛♦ ❣r✉♣♦ ♠❛✐s♣ró①✐♠♦ ❛♦ ❧í❞❡r ✭● g ✴● 1 ✮✳ ❈♦♥s✐❞❡r❛çõ❡s ❋✐❧tr♦s ❞❡ ❑❛❧♠❛♥ ❢♦r❛♠ ✉t✐❧✐③❛❞♦s ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❞♦s ❡①♣❡r✐✲♠❡♥t♦s ❞❡s❡♥✈♦❧✈✐❞♦s ♥❡st❛ s❡çã♦✱ t❛♥t♦ ♥❛ ♠♦✈✐♠❡♥t❛çã♦ ❛❧t❡r♥❛❞❛ q✉❛♥t♦ ♥❛ ❝♦♥tí✲ ✺✳✶✳ ❆♥á❧✐s❡ ❞❛ ❱❛r✐❛çã♦ ❞♦ ◆ú♠❡r♦ ❞❡ ▼❛r❝♦s ✾✺♥✉❛✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ♥❛ ❙❡çã♦ ✸✳✶✱ ❛ s✉♣♦s✐çã♦ ❞❡ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❛s ❡st✐♠❛t✐✈❛s❞♦s ✈ár✐♦s r♦❜ôs ♥♦ ❣r✉♣♦ é ✐♥❛❞❡q✉❛❞❛✱ ♦ q✉❡ ♣♦❞❡ ❣❡r❛r ❡st✐♠❛t✐✈❛s ✐♥❝♦♥s✐st❡♥t❡s q✉❛♥❞♦ s❡ ✉t✐❧✐③❛ ♦ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥✱ ♣♦ré♠ ♥ã♦ s❡ t❡♠ ♦ r❡❣✐str♦ ❞❛s ✐♥t❡r❞❡♣❡♥❞ê♥✲❝✐❛s✳ ❆♣❡s❛r ❞✐ss♦✱ ✈ár✐♦s tr❛❜❛❧❤♦s ♥❛ ❧✐t❡r❛t✉r❛ ✉t✐❧✐③❛♠ ❡ss❛ s✉♣♦s✐çã♦✱ t❡♥❞♦ ❡♠✈✐st❛ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ♣❛r❛ ❧✐❞❛r ❝♦♠ ❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛✳ P❛r❛ ❡✈✐t❛r ❛ ❣❡r❛çã♦ ❞❡ ❡st✐♠❛t✐✈❛s ✐♥❝♦♥s✐st❡♥t❡s✱ ✉♠❛ ❛❜♦r❞❛❣❡♠ ♣♦ssí✈❡❧ é❛r♠❛③❡♥❛r ❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ♣❛r❛ ✉s♦ ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦✲♦♣❡r❛t✐✈❛✳ P❛r❛ ✐ss♦✱ ❢❛③✲s❡ ♥❡❝❡ssár✐♦ ✉t✐❧✐③❛r ✉♠ ❡❧❡♠❡♥t♦ ❝❡♥tr❛❧✐③❛❞♦r✱ r❡s♣♦♥sá✈❡❧♣❡❧❛ ❣❡r❛çã♦ ❞❡ ✉♠❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ ❡ ❝♦♥s✐st❡♥t❡ ♣❛r❛ ♦s r♦❜ôs✳ ❉❡ss❡ ♠♦❞♦✱✐♥❢♦r♠❛çõ❡s s❡♥s♦r✐❛✐s ❡ ❡st✐♠❛t✐✈❛s ♣r❡❝✐s❛♠ s❡r tr❛♥s♠✐t✐❞❛s ❡♥tr❡ ♦s r♦❜ôs ❡ ❡ss❛❡♥t✐❞❛❞❡ ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❊♠ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞❡s❝❡♥tr❛❧✐③❛❞❛✱❝❛❞❛ r♦❜ô ♣r❡❝✐s❛ ♠❛♥t❡r ❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ ❛t✉❛❧✐③❛❞❛✳ P❛r❛ t❛♥t♦✱ q✉❛♥❞♦ ❛❧❣✉♠ r♦❜ô ♣❛rt✐❝✐♣❛ ❞❡ ✉♠❛ ❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ ♦ ♠❡s♠♦ ♣r❡❝✐s❛ tr❛♥s♠✐t✐r ❛s✐♥❢♦r♠❛çõ❡s s❡♥s♦r✐❛✐s ❡ ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ♣❛r❛ ♦s ❞❡♠❛✐s r♦❜ôs✱ ❞❡ ♠♦❞♦ q✉❡ ❡❧❡s t❛♠❜é♠ ♣♦ss❛♠ ❣❡r❛r ❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ ❡ ❛t✉❛❧✐③❛r s✉❛s ✐♥❢♦r♠❛çõ❡s✳ ❊ss❛s ❛❜♦r✲❞❛❣❡♥s ♥♦r♠❛❧♠❡♥t❡ ❡①✐❣❡♠ s✐♥❝r♦♥✐s♠♦✱ ♦ q✉❡ ❛❝❛rr❡t❛ ❡♠ ♠❛✐♦r ❝♦♠♣❧❡①✐❞❛❞❡ ♣❛r❛❡❢❡t✉❛r ❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❆❧é♠ ❞✐ss♦✱ ❛♠❜❛s ❛❜♦r❞❛❣❡♥s ❝♦♠♣r♦♠❡✲ t❡♠ ❛ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ ❞♦ s✐st❡♠❛✱ q✉❛♥❞♦ ❡ss❡ é ❝♦♠♣♦st♦ ♣♦r ✉♠ ♥ú♠❡r♦ s✐❣♥✐✜❝❛t✐✈♦❞❡ r♦❜ôs✳ ❆✐♥❞❛✱ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦ ❡ ❡s♣❛ç♦ ♣❛r❛ ♦ tr❛t❛♠❡♥t♦ ❞❛s ✐♥❢♦r♠❛✲çõ❡s ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❡ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♣ré✈✐♦ ❞♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs ❡♠ ✉♠ ❡♥①❛♠❡♣♦❞❡♠ ❝♦♠♣r♦♠❡t❡r ❛ ❛♣❧✐❝❛çã♦ ❞❡ss❛s ❛❜♦r❞❛❣❡♥s ❡♠ s✐st❡♠❛s r❡❛✐s✳ P❛r❛ ❧✐❞❛r ❝♦♠ ❡st❛ q✉❡stã♦✱ ♦s ❡①♣❡r✐♠❡♥t♦s ❛♣r❡s❡♥t❛❞♦s ♥❛ ♣ró①✐♠❛ s❡çã♦❢❛③❡♠ ✉s♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦✲♣❡r❛t✐✈❛✳ ❖ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t✐✈♦ ❞❡ss❡s ❡①♣❡r✐♠❡♥t♦s é ✈❡r✐✜❝❛r ❛ ❝♦♥s✐stê♥❝✐❛ ❞❛s ❡s✲ t✐♠❛t✐✈❛s ❣❡r❛❞❛s ♣♦r ❡ss❡ ❛❧❣♦r✐t♠♦ ♥❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ ❡♥①❛♠❡s✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ♦❆♣ê♥❞✐❝❡ ❈✱ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s ❣❡r❛ ❡st✐♠❛t✐✈❛s ❝♦♥s✐st❡♥t❡s✱♠❡s♠♦ q✉❛♥❞♦ ♥ã♦ s❡ t❡♠ ♦ r❡❣✐str♦ ❞❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛✳ P♦r ❝❛✉s❛❞✐ss♦✱ t❛❧ ❛❧❣♦r✐t♠♦ s❡ ❛♣r❡s❡♥t❛ ❝♦♠♦ ✉♠❛ s♦❧✉çã♦ ❡♠ ♣♦t❡♥❝✐❛❧ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡✐♥❝♦♥s✐stê♥❝✐❛ q✉❡ ♣♦❞❡ s❡r ❣❡r❛❞♦ ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s✱ ♣♦✐s ♥ã♦ ❡①✐❣❡ ❛ ✉t✐❧✐③❛çã♦ ❞❡ t♦❞❛ ❛ ✐♥❢♦r♠❛çã♦ ❞✐s♣♦♥í✈❡❧ ♥♦ ❣r✉♣♦✳ ❉❡ss❡♠♦❞♦✱ ❛♦ ✉t✐❧✐③❛r ♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s✱ ✉♠ r♦❜ô ❝♦♥s❡❣✉❡ ❣❡r❛r ❞❡♠❛♥❡✐r❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ❡st✐♠❛t✐✈❛s ❝♦♥s✐st❡♥t❡s ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✉t✐❧✐③❛♥❞♦ s♦♠❡♥t❡ ♦s r♦❜ôs ♠❛r❝♦ ❞✐s♣♦♥í✈❡✐s ❡♠ s✉❛ ✈✐③✐♥❤❛♥ç❛✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ❛s té❝♥✐❝❛s ❛♣❧✐❝❛❞❛s ❛ ❡♥①❛♠❡s r♦❜ót✐❝♦s ❞❡✲✈❡♠ ♣♦ss✐❜✐❧✐t❛r q✉❡ ❝❛❞❛ r♦❜ô ✉t✐❧✐③❡ s♦♠❡♥t❡ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s✱ ♦✉ s❡❥❛✱ ❛q✉❡❧❛s❞✐s♣♦♥í✈❡✐s ♥❛ s✉❛ ✈✐③✐♥❤❛♥ç❛✳ ◆❡ss❛ ❛❜♦r❞❛❣❡♠✱ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞♦s r♦❜ôs ♥ã♦ ♣r❡✲❝✐s❛r❡♠ ❛r♠❛③❡♥❛r ❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛✱ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❛ss♦❝✐❛❞❛ às ✾✻❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♥ã♦ ❝r❡s❝❡ ❡♠ ❢✉♥çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs ♥♦ ❡♥①❛♠❡✿❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ ❡s♣❛ç♦ ♣❛r❛ ❛r♠❛③❡♥❛r ❛s ❡st✐♠❛t✐✈❛s é ❝♦♥st❛♥t❡✱ ❡♥q✉❛♥t♦ q✉❡ ❛❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦ ♣❛r❛ ♣r♦❝❡ss❛r ✉♠❛ ❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ é ♣r♦♣♦r✲❝✐♦♥❛❧ ❛♦ ♥ú♠❡r♦ ❞❡ ♠❛r❝♦s ✉t✐❧✐③❛❞♦✳ ❊ss❡ ♥ú♠❡r♦ é ♠❡♥♦r ♦✉ ✐❣✉❛❧ ❛♦ ♥ú♠❡r♦ ❞❡✈✐③✐♥❤♦s✱ ✉♠ ♥ú♠❡r♦ ♣❡q✉❡♥♦ q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦ ❛♦ t❛♠❛♥❤♦ ❞♦ ❡♥①❛♠❡✳ ✺✳✷ ❈♦♥s✐stê♥❝✐❛ ❞❛s ❊st✐♠❛t✐✈❛s ❞❡ ▲♦❝❛❧✐③❛çã♦ ◆❡st❛ s❡çã♦ sã♦ ❛♣r❡s❡♥t❛❞♦s ❡①♣❡r✐♠❡♥t♦s s✐♠✉❧❛❞♦s ✉t✐❧✐③❛♥❞♦ ♦ ❛♠❜✐❡♥t❡ r▼❆❚▲❆❇ ✳ ❯♠ ❡♥①❛♠❡ ❤❡t❡r♦❣ê♥❡♦ é ❡♠♣r❡❣❛❞♦ ♥❡ss❡s ❡①♣❡r✐♠❡♥t♦s✱ ♣♦ré♠✱ ❞✐✲❢❡r❡♥t❡♠❡♥t❡ ❞❛ s❡çã♦ ❛♥t❡r✐♦r✱ ♠♦❞❡❧♦s ❞❡ r♦❜ôs ♥ã♦ ❤♦❧♦♥ô♠✐❝♦s ❢♦r❛♠ ✉t✐❧✐③❛❞♦s✳❉❡ss❡ ♠♦❞♦✱ ❛ ❧♦❝❛❧✐③❛çã♦ é ❡❢❡t✉❛❞❛ ❝♦♥s✐❞❡r❛♥❞♦ ❛ ♣♦s❡ ❝♦♠♣❧❡t❛ ❞♦s r♦❜ôs✱ ♦✉ s❡❥❛✱❛ ♣♦s✐çã♦ ❡ ❛ ♦r✐❡♥t❛çã♦✳ ❖ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t✐✈♦ ❞❡ss❡s ❡①♣❡r✐♠❡♥t♦s é ❛♥❛❧✐s❛r ❛ ❝♦♥s✐s✲ tê♥❝✐❛ ❞❛s ❡st✐♠❛t✐✈❛s ❣❡r❛❞❛s ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ q✉❛♥❞♦ s❡ ✉t✐❧✐③❛♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s✳ ❚❛❧ ❝♦♥s✐stê♥❝✐❛ ❢♦✐ ❛♥❛❧✐s❛❞❛ ❡♠ ❞✐❢❡r❡♥t❡s s✐t✉❛çõ❡s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ♦❝♦rrê♥❝✐❛ ❞❡ ❢❛❧❤❛s ♥♦ s❡♥s♦r ❞♦ ❧í❞❡r ♦✉ ♥♦ ♠❡❝❛♥✐s♠♦❞❡ ❝♦♠✉♥✐❝❛çã♦✳ ❊st❡s ❡①♣❡r✐♠❡♥t♦s ❢♦r❛♠ ❝♦♥❞✉③✐❞♦s ❝♦♠ ✉♠ ❡♥①❛♠❡ ❝♦♠♣♦st♦ ♣♦r ✸✺ r♦❜ôs♥ã♦ ❤♦❧♦♥ô♠✐❝♦s ❝♦♠ 7 cm ❞❡ ❞✐â♠❡tr♦ ❝❛❞❛✳ ❯♠ r♦❜ô ❧í❞❡r é ❡q✉✐♣❛❞♦ ❝♦♠ s❡♥s♦r❡s❡①t❡r♦❝❡♣t✐✈♦s q✉❡ ♦ ❞✐s♣♦♥✐❜✐❧✐③❛♠ ❡st✐♠❛t✐✈❛s ❝♦♠ ❜♦❛ ♣r❡❝✐sã♦ ❞❡ s✉❛ ♣♦s❡✱ ♥♦ s✐s✲ t❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ❞❡ r❡❢❡rê♥❝✐❛✳ ❉❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ t❛❧ ❝❛♣❛❝✐❞❛❞❡ ♥ã♦ ❡st❛r ♣r❡s❡♥t❡❡♠ t♦❞♦s ♦s r♦❜ôs ❡ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ ❧í❞❡r s❡r ❧✐❣❡✐r❛♠❡♥t❡ ❞✐❢❡r❡♥t❡ ❞♦s ❞❡♠❛✐s✱ t❡♠✲s❡ ❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞❡ ✉♠ ❡♥①❛♠❡ ❤❡t❡r♦❣ê♥❡♦✳ ❖ ❡♥①❛♠❡ s❡ ♠♦✈✐♠❡♥t❛ ❝♦❧❡t✐✲✈❛♠❡♥t❡ ❡♠ ✉♠ ❛♠❜✐❡♥t❡ ❜✐❞✐♠❡♥s✐♦♥❛❧✱ ❧✐✈r❡ ❞❡ ♦❜stá❝✉❧♦s✱ ❝♦♠ ❛♣r♦①✐♠❛❞❛♠❡♥t❡2 25,00 m✭❋✐❣✉r❛ ✺✳✶✸✮✳ ◆❡ss❛ ❡str❛té❣✐❛✱ ♦ r♦❜ô ❧í❞❡r ✉t✐❧✐③❛ ❛❧❣✉♥s ✇❛②♣♦✐♥ts ♣❛r❛ ❝♦♥❞✉③✐r ♦ ❣r✉♣♦ ♣❡❧♦ ❛♠❜✐❡♥t❡✳❖ ♠♦✈✐♠❡♥t♦ ❝♦❧❡t✐✈♦ é ❜❛s❡❛❞♦ ♥❛ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ♣r♦♣♦st❛ ♥❛ ❙❡çã♦ ✹✳✷✳✷✳ ❆ ❛çã♦ ❞❡ ❝♦♥tr♦❧❡ ❞❡✜♥✐❞❛ ❡♠ ✭✹✳✸✶✮ é ❛❞❡q✉❛❞❛ ♣❛r❛ ❛t✉❛çã♦ ❡♠ ♠♦❞❡❧♦s ❞❡ x y r♦❜ôs ❤♦❧♦♥ô♠✐❝♦s ♣♦r ❣❡r❛r ❛❝❡❧❡r❛çõ❡s a ❡ a ♥❛s ❞✐r❡çõ❡s x ❡ y✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳❉❡ss❡ ♠♦❞♦✱ ❛♣ós ✐♥t❡❣r❛r t❛✐s ❛❝❡❧❡r❛çõ❡s ❡ ❣❡r❛r ❛s ✈❡❧♦❝✐❞❛❞❡s ❝♦rr❡s♣♦♥❞❡♥t❡s v x❡ v y ✱ ❛ ♣r♦♣♦st❛ ❛♣r❡s❡♥t❛❞❛ ❡♠ ❬❉❡s❛✐ ❡t ❛❧✳✱ ✶✾✾✽❪ é ✉t✐❧✐③❛❞❛ ♣❛r❛ ❝♦♥✈❡rtê✲❧❛s ❡♠✈❡❧♦❝✐❞❛❞❡s ❧✐♥❡❛r v ❡ ❛♥❣✉❧❛r w✱ ❝♦♥❢♦r♠❡ s❡❣✉❡✿  " # " # ❝♦s(θ) s❡♥(θ) v vx  = ,✭✺✳✶✹✮ −s❡♥(θ) ❝♦s(θ) w vy d d ✺✳✷✳ ❈♦♥s✐stê♥❝✐❛ ❞❛s ❊st✐♠❛t✐✈❛s ❞❡ ▲♦❝❛❧✐③❛çã♦ ✾✼ ✭❛✮✭❜✮ ❋✐❣✉r❛ ✺✳✶✸✿ ▼♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛ ❞♦ ❡♥①❛♠❡ ♥♦ ❛♠❜✐❡♥t❡ s✐♠✉❧❛❞♦✳ ❖s ❝ír❝✉❧♦s❝✐♥③❛ r❡♣r❡s❡♥t❛♠ r❡❣✐õ❡s ❞♦ ❛♠❜✐❡♥t❡ ✭❛❧✈♦s✮ q✉❡ ♦ ❡♥①❛♠❡ ❞❡✈❡ ✈✐s✐t❛r✳ ❖ ❝ír❝✉❧♦ ♥❛❝♦r ♣r❡t❛ ❡♠ t♦r♥♦ ❞♦ r♦❜ô ❧í❞❡r ✭❝♦r ✈❡r♠❡❧❤❛✮ ✐♥❞✐❝❛ ♦ r❛✐♦ ε ❞❡ s✉❛ ✈✐③✐♥❤❛♥ç❛✳ ❊♠✭❛✮ ❡ ✭❜✮ sã♦ ❛♣r❡s❡♥t❛❞♦s ❞♦✐s ♠♦♠❡♥t♦s ❞✐st✐♥t♦s ❞✉r❛♥t❡ ❛ ♥❛✈❡❣❛çã♦ ❞♦ ❡♥①❛♠❡✳ s❡♥❞♦ d ✉♠ ♣❛râ♠❡tr♦ ❛ s❡r ❛❥✉st❛❞♦ ❡♠ r❡❧❛çã♦ ❛ ✉♠ ♣♦♥t♦ p ❞❡ r❡❢❡rê♥❝✐❛ s♦❜r❡ ♦r♦❜ô ✭❋✐❣✉r❛ ✺✳✶✹✮✳ Y W Y Rp d θ X R X W ❋✐❣✉r❛ ✺✳✶✹✿ P❛râ♠❡tr♦ ❞♦ ♠♦❞❡❧♦ ♥ã♦✲❤♦❧♦♥ô♠✐❝♦✳❊ss❛s ✈❡❧♦❝✐❞❛❞❡s sã♦ s✉❥❡✐t❛s ❛ r✉í❞♦ ❛❞✐t✐✈♦ ●❛✉ss✐❛♥♦ ❜r❛♥❝♦✱ ❝♦♠ ♠é❞✐❛s ③❡r♦ v w = 0,05 v = 0,05 w ❡ ❞❡s✈✐♦ ♣❛❞rã♦ ♣r♦♣♦r❝✐♦♥❛❧ ❛♦s ✈❛❧♦r❡s ❝♦♠❛♥❞❛❞♦s✱ s❡♥❞♦ ǫ ❡ ǫ ✳❆s ♠❡❞✐❞❛s ❞❡ ❞✐stâ♥❝✐❛ ❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛s t❛♠❜é♠ sã♦ s✉❥❡✐t❛s ❛ ✉♠ r✉í❞♦ ❛❞✐✲ t✐✈♦ ●❛✉ss✐❛♥♦ ❜r❛♥❝♦✱ ❝♦♠ ♠é❞✐❛s ③❡r♦ ❡ ❞❡s✈✐♦ ♣❛❞rã♦ ♣r♦♣♦r❝✐♦♥❛❧ ❛ ❡ss❛s ♠❡❞✐❞❛s✱ρ = 0,03 ρ ❞❡ ❢♦r♠❛ q✉❡ ǫ ❝♦♠♣r❡❡♥❞❡ ♦ ❡rr♦ ❛ss♦❝✐❛❞♦ às ♠❡❞✐❞❛s ❞❡ ❞✐stâ♥❝✐❛s ❡ǫ = 0,01 φ φ ♦ ❡rr♦ r❡❢❡r❡♥t❡ às ♠❡❞✐❞❛ ❞❡ ♦r✐❡♥t❛çã♦✳ ◆❡st❡s ❡①♣❡r✐♠❡♥t♦s✱ ❝❛❞❛ s✐♠✉✲❧❛çã♦ ❞❡♠❛♥❞♦✉✱ ❛♣r♦①✐♠❛❞❛♠❡♥t❡✱ 2800 ✐t❡r❛çõ❡s✱ ❝♦♠ ❞✉r❛çã♦ ∆t = 100 ms ❝❛❞❛✳❖ ❝♦♠♣r✐♠❡♥t♦ ❞♦ ❝❛♠✐♥❤♦ ♣❡r❝♦rr✐❞♦ ♣♦r ❝❛❞❛ r♦❜ô ❢♦✐ ❡♠ t♦r♥♦ ❞❡ 11,0 m✳ ✾✽❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s ❙❡❣✉✐♥❞♦ ❛ ♠❡t♦❞♦❧♦❣✐❛✱ ♦s r♦❜ôs ❢♦r❛♠ ✐♥✐❝✐❛❧♠❡♥t❡ ❞✐s♣♦st♦s ❡♠ ✉♠❛ ♠❡s♠❛ r❡❣✐ã♦ ❞♦ ❛♠❜✐❡♥t❡ ❞❡ ❢♦r♠❛ ❛❧❡❛tór✐❛✳ ◆❛ ♣r✐♠❡✐r❛ ❡t❛♣❛ ❞❛ ♠♦✈✐♠❡♥t❛çã♦✱ ♦ r♦❜ô❧í❞❡r é ❛✉t♦♠❛t✐❝❛♠❡♥t❡ ❣✉✐❛❞♦ ❡♠ ❞✐r❡çã♦ ❛♦ ❝❡♥tr♦ ❞♦ ❣r✉♣♦✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ♥❛❙❡çã♦ ✹✳✷✳✷✳✶✱ ♥❡ss❛ ❢❛s❡ ✐♥✐❝✐❛❧ ❞❛ ♠♦✈✐♠❡♥t❛çã♦ é ❛ss✉♠✐❞♦ q✉❡ t♦❞♦s ♦s r♦❜ôs tê♠❛❝❡ss♦ à ✐♥❢♦r♠❛çã♦ ❣❧♦❜❛❧ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❡ q✉❡ ❝❛❞❛ r♦❜ô ❝♦♥s❡❣✉❡ ♠❡❞✐r ❞✐stâ♥❝✐❛ r❡❧❛t✐✈❛ ♣❛r❛ ♦s ❞❡♠❛✐s✳ ❖ ♣❛râ♠❡tr♦ d AB ❢♦✐ ❞❡✜♥✐❞♦ ❝♦♠♦ 0,5 m✱ ❡♥q✉❛♥t♦ q✉❡d = 1 m AA ✳ ❆♣ós ♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦ ❧í❞❡r✱ ❛ ❧❡✐ ❞❡ ❝♦♥tr♦❧❡ ❧♦❝❛❧ ✭✹✳✷✾✮ ❢♦✐ ❛♣❧✐❝❛❞❛❞❡ ❢♦r♠❛ ❛ ❣❡r❛r ✉♠❛ ❢♦r♠❛çã♦ ✉♥✐❢♦r♠❡ ✭❞✐stâ♥❝✐❛s ✐♥t❡r✲r♦❜ôs✮✱ ♣❡r♠✐t✐♥❞♦✱ ❛ss✐♠✱ q✉❡ ❝❛❞❛ r♦❜ô ♥♦ ❡♥①❛♠❡ ❛t✉❡ ✉t✐❧✐③❛♥❞♦ s♦♠❡♥t❡ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s✳ ❉✉r❛♥t❡ ❡ss❛AA AB ❢❛s❡✱ ❛♠❜♦s ♦s ♣❛râ♠❡tr♦s d ❡ d ❢♦r❛♠ ❝♦♥✜❣✉r❛❞♦s ❝♦♠♦ 0,2 m✳ ❖ r❛✐♦ ε ❞❛s AB )✈✐③✐♥❤❛♥ç❛s ❞♦s r♦❜ôs ❢♦✐ ❞❡✜♥✐❞♦ ❝♦♠♦ 0,266 m (1,33 × d ✱ ♦ q✉❡ r❡str✐♥❣✐✉ ❝❛❞❛ r♦❜ô ❛ ❛❝❡ss❛r s♦♠❡♥t❡ s❡✉s ✈✐③✐♥❤♦s ✐♠❡❞✐❛t♦s✳ ❆ ♠❡t♦❞♦❧♦❣✐❛ ✐♠♣❧❡♠❡♥t❛❞❛ ♣❡r♠✐t❡ q✉❡ ❝❛❞❛ r♦❜ô ❛t✉❛❧✐③❡ s✉❛ ❝r❡♥ç❛ ❞❡ ❧♦❝❛✲❧✐③❛çã♦ ❞❡ ♠❛♥❡✐r❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛✱ ❛ssí♥❝r♦♥❛ ❡ ✉t✐❧✐③❛♥❞♦ s♦♠❡♥t❡ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s✳❉❡ss❛ ❢♦r♠❛✱ t❡♠✲s❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❝✉❥❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❝♦♠♣✉t❛❝✐♦♥❛❧ é s✐❣♥✐✜❝❛t✐✈❛✲♠❡♥t❡ ✐♥❢❡r✐♦r ❞♦ q✉❡ ❛q✉❡❧❛ r❡❢❡r❡♥t❡ à ❛❜♦r❞❛❣❡♥s ❝❡♥tr❛❧✐③❛❞❛s✳ ❆❧é♠ ❞✐ss♦✱ ❞❡✈✐❞♦❛♦ ❢❛t♦ ❞♦s r♦❜ôs ✉t✐❧✐③❛r❡♠ s♦♠❡♥t❡ s❡✉s ✈✐③✐♥❤♦s ✐♠❡❞✐❛t♦s✱ ❛ ❛♠♣❧✐❛çã♦ ♦✉ r❡❞✉✲çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs ♥♦ ❣r✉♣♦ ♥ã♦ ✐♠♣❛❝t❛ ♥❛ ❝♦♠♣❧❡①✐❞❛❞❡ ♣❛r❛ s❡ ❡❢❡t✉❛r ❛s❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❖s ❡①♣❡r✐♠❡♥t♦s ❞❡s❝r✐t♦s ❛ s❡❣✉✐r sã♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ ❝♦♠♣❛r❛r ❛ ❧♦❝❛❧✐③❛çã♦❞♦ ❡♥①❛♠❡ ❤❡t❡r♦❣ê♥❡♦ ❛♦ ❝♦♥s✐❞❡r❛r q✉❡ ❝❛❞❛ ❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ é❡①❡❝✉t❛❞❛ ✉t✐❧✐③❛♥❞♦ ❛s s❡❣✉✐♥t❡s ❛❜♦r❞❛❣❡♥s✿ ✭✐✮ ❛ ❛❜♦r❞❛❣❡♠ ✐♥❣ê♥✉❛ ❞♦ ❊❑❋ ❡✭✐✐✮ ♦ ❛❧❣♦r✐t♠♦ ❈■✳ ❉❡ss❡ ♠♦❞♦✱ ❝❛❞❛ r♦❜ô ♠❛♥tê♠ três ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦✱ s❡♥❞♦ ❞✉❛s ❞❡❧❛s r❡❢❡r❡♥t❡s ❛ ❝❛❞❛ ✉♠❛ ❞❡ss❛s ❛❜♦r❞❛❣❡♥s ❡ ✉♠❛ ú❧t✐♠❛ r❡❧❛❝✐♦♥❛❞❛ à♦❞♦♠❡tr✐❛✱ q✉❡ ♥ã♦ ❢♦✐ ❛❧t❡r❛❞❛ ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❯♠ ❡①♣❡r✐♠❡♥t♦✜♥❛❧ ❢♦✐ ❢❡✐t♦ ♣❛r❛ ❛✈❛❧✐❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❝♦♦♣❡r❛t✐✈♦ ❡♠ ✉♠ ❡♥①❛♠❡ ♥♦ q✉❛❧ ♥❡♥❤✉♠ r♦❜ô ♣♦ss✉✐ s❡♥s♦r❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛✳ ◆❡ss❡s ❡①♣❡r✐♠❡♥t♦s✱ ❝❛❞❛ r♦❜ô ❛t✉❛❧✐③❛ s✉❛ ❡st✐♠❛t✐✈❛ ✉t✐❧✐③❛♥❞♦ ❛ ✐♥❢♦r♠❛çã♦❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ r♦❜ôs ♣r❡s❡♥t❡s ❡♠ s✉❛ ✈✐③✐♥❤❛♥ç❛✳ ❖s r♦❜ôs ❛t✉❛❧✐③❛♠ s✉❛s ❝r❡♥ç❛s❞❡ ♠❛♥❡✐r❛ ❛ssí♥❝r♦♥❛✱ ❛♣ós ❞❡t❡r♠✐♥❛❞❛ ❞✐stâ♥❝✐❛ t❡r s✐❞♦ ♣❡r❝♦rr✐❞❛✳ ❈♦♥❢♦r♠❡❡①♣♦st♦ ♥❛ ❙❡çã♦ ✹✳✶✱ t❛♥t♦ ♥❛ ❛❜♦r❞❛❣❡♠ ✐♥❣ê♥✉❛ ❞♦ ❊❑❋ q✉❛♥t♦ ♥♦ ❛❧❣♦r✐t♠♦ ❈■✱✉♠❛ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛ é ♠❛♥t✐❞❛ ❡♠ ❝❛❞❛ r♦❜ô ♣❛r❛ r❡♣r❡s❡♥t❛r ❛ ✐♥❝❡rt❡③❛ ❞❛❧♦❝❛❧✐③❛çã♦✳ ◆❡ss❡s ❡①♣❡r✐♠❡♥t♦s✱ ♦ tr❛ç♦ ❞❛s ♠❛tr✐③❡s ❞❡ ❝♦✈❛r✐â♥❝✐❛ ❢♦✐ ♦ ❝r✐tér✐♦✉t✐❧✐③❛❞♦ ♣❛r❛ ♦t✐♠✐③❛r ♦ ✈❛❧♦r ❞❡ ω✳ ✺✳✷✳ ❈♦♥s✐stê♥❝✐❛ ❞❛s ❊st✐♠❛t✐✈❛s ❞❡ ▲♦❝❛❧✐③❛çã♦ ✾✾ ✺✳✷✳✶ ❊st✐♠❛t✐✈❛s ❆❜s♦❧✉t❛s ❡♠ ■♥t❡r✈❛❧♦s ❘❡❣✉❧❛r❡s ◆❡st❡ ❡①♣❡r✐♠❡♥t♦✱ ❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛ ❢♦r❛♠ ❛❝❡ss❛❞❛s ♣❡❧♦ r♦❜ô❧í❞❡r ❡♠ ✐♥t❡r✈❛❧♦s ❞❡ t❡♠♣♦ r❡❣✉❧❛r❡s✳ ❆ ❝❛❞❛ 10 ✐t❡r❛çõ❡s✱ ♦✉ s❡❥❛✱ ❛ ❝❛❞❛ 1 s✱ ✉♠❛❡st✐♠❛t✐✈❛ ❛❜s♦❧✉t❛ ❢♦✐ ♦❜t✐❞❛ ♣❡❧♦ ❧í❞❡r ❡ ❝♦♠❜✐♥❛❞❛ ❝♦♠ s✉❛ ❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦❛t✉❛❧✱ ❣❡r❛❞❛ ❡♠ ❡t❛♣❛s ❞❡ ♣r❡❞✐çã♦ ❞♦ ❊❑❋✳ ❊ss❛ ❝♦♠❜✐♥❛çã♦ ❢♦✐ ❡❢❡t✉❛❞❛ ✉t✐❧✐③❛♥❞♦✉♠❛ ❡t❛♣❛ ❞❡ ❝♦rr❡çã♦ ❞♦ ❊❑❋✳ ❉❡✈✐❞♦ ❛ ❡ss❛s ❝♦rr❡çõ❡s✱ ♦ r♦❜ô ❧í❞❡r ♠❛♥t❡✈❡ ✉♠❛❜♦❛ ❡st✐♠❛t✐✈❛ ❞❡ s✉❛ ❧♦❝❛❧✐③❛çã♦✱ s❡♥❞♦ ❝♦♥s✐❞❡r❛❞♦ ✉♠ ♠❛r❝♦ ❡♠ ♣♦t❡♥❝✐❛❧✳ ❖ ❧í❞❡r♣❡r♠❛♥❡♥t❡♠❡♥t❡ ❞✐ss❡♠✐♥❛ s✉❛ ❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛s ✐♥❢♦r✲♠❛çõ❡s ❡①t❡r♦❝❡♣t✐✈❛s ♦❜t✐❞❛s ❞❡ s❡✉s ✈✐③✐♥❤♦s✳ ❆♣ós ♣❡r❝♦rr❡r ❞❡t❡r♠✐♥❛❞❛ ❞✐stâ♥❝✐❛ ✭10 cm✱ ♥❡st❡ ❝❛s♦✮✱ ✉♠ r♦❜ô q✉❡ r❡❝❡❜❡✉♠❛ ♠❡♥s❛❣❡♠ ❝♦♥t❡♠♣❧❛♥❞♦ ✐♥❢♦r♠❛çõ❡s ❛ s❡✉ r❡s♣❡✐t♦✱ ✉t✐❧✐③❛ ❛s ♠❡s♠❛s ❝❛s♦ ❝♦♥✲ s✐❣❛ ♦❜t❡r ✉♠❛ ♦❜s❡r✈❛çã♦ ✭♠❡❞✐❞❛ r❡❧❛t✐✈❛✮ r❡❢❡r❡♥t❡ ❛♦ r❡♠❡t❡♥t❡✳ ❉❡ss❡ ♠♦❞♦✱ ❛✐♥❢♦r♠❛çã♦ ♣r❡s❡♥t❡ ♥❛ ♠❡♥s❛❣❡♠ ❡ ❛ ♠❡❞✐❞❛ ♦❜t✐❞❛ ♣♦❞❡rã♦ s❡r ✉t✐❧✐③❛❞❛s ♣❛r❛ ❣❡r❛r✉♠❛ ♥♦✈❛ ❡st✐♠❛t✐✈❛ ❞❡ s✉❛ ❧♦❝❛❧✐③❛çã♦✱ ❝♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ♥❛s ❊q✉❛çõ❡s ✭✹✳✶✶✮ ❡ ✭✹✳✶✹✮✳❉❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ ❡①✐st✐r ♠❛✐s ❞❡ ✉♠ ✈✐③✐♥❤♦ ♣❛r❛ ❝❛❞❛ r♦❜ô✱ ♠❛✐s ❞❡ ✉♠❛ ❡st✐♠❛t✐✈❛♣♦❞❡rá s❡r ❣❡r❛❞❛✳ ❚❛✐s ❡st✐♠❛t✐✈❛s s❡rã♦ ✉t✐❧✐③❛❞❛s ♣❛r❛ ❛t✉❛❧✐③❛r ❛ ❝r❡♥ç❛ ❞❡ ✉♠ r♦❜ô✱❞❡ ♠❛♥❡✐r❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ❡ ❛ssí♥❝r♦♥❛✳ ❆♣ós ❛ ❛t✉❛❧✐③❛çã♦ ❞❛ ❡st✐♠❛t✐✈❛✱ ✉♠ r♦❜ô s❡ t♦r♥❛ ✉♠ ♠❛r❝♦ ❡♠ ♣♦t❡♥❝✐❛❧ ❡ ❞✐ss❡♠✐♥❛ ♣❛r❛ ♦ ❣r✉♣♦ s✉❛ ❡st✐♠❛t✐✈❛ ❞❡ ❧♦❝❛❧✐③❛çã♦❡ ❛s ♠❡❞✐❞❛s r❡❧❛t✐✈❛s ❛ s❡✉s ✈✐③✐♥❤♦s✳ ❈♦♥❢♦r♠❡ ♣♦❞❡ s❡r ♦❜s❡r✈❛❞♦✱ ❛ ♣r♦♣❛❣❛çã♦ ❞❛❧♦❝❛❧✐③❛çã♦ é ❢❡✐t❛ ❞♦ ❧í❞❡r ♣❛r❛ ❛s ❢r♦♥t❡✐r❛s ❞♦ ❡♥①❛♠❡✱ ♣❡r♠✐t✐♥❞♦ q✉❡ t♦❞♦s ♦s r♦❜ôs❞♦ ❣r✉♣♦ ♣♦ss❛♠ ❛t✉❛❧✐③❛r s✉❛s r❡s♣❡❝t✐✈❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❆ ❡str❛té❣✐❛❡♠♣r❡❣❛❞❛ ♣❡r♠✐t❡ ♠♦❞✐✜❝❛r ❛ ❢r❡q✉ê♥❝✐❛ ❞❡ ❛t✉❛❧✐③❛çã♦ ❞❛s ❝r❡♥ç❛s✱ ✉♠❛ ✈❡③ q✉❡ ♦❣r✉♣♦ ❛t✉❛ ❝♦❡s♦✳ ❆ ❋✐❣✉r❛ ✺✳✶✺ ❛♣r❡s❡♥t❛ ♦ ❝❛♠✐♥❤♦ ❡①❡❝✉t❛❞♦ ♣♦r ✉♠ ❞♦s r♦❜ôs ❞♦ ❡♥①❛♠❡✳ ❖s❝ír❝✉❧♦s ♠❛✐♦r❡s ♥❛ ❝♦r ❝✐♥③❛ r❡♣r❡s❡♥t❛♠ r❡❣✐õ❡s ♥♦ ❛♠❜✐❡♥t❡ q✉❡ ♦ ❣r✉♣♦ ♣r❡❝✐s❛✈✐s✐t❛r✱ s❡♥❞♦ q✉❡ ♦ ❝❡♥tr♦ ❞❡ t❛✐s ❝ír❝✉❧♦s ✭× ♥❛ ❝♦r ✈❡r♠❡❧❤❛✮ ❞❡✜♥❡ ♦s ❛❧✈♦s✳ ❖❝❛♠✐♥❤♦ r❡❛❧ ❡①❡❝✉t❛❞♦ ♣❡❧♦ r♦❜ô é r❡♣r❡s❡♥t❛❞♦ ♣❡❧❛ ❧✐♥❤❛ tr❛❝❡❥❛❞❛ ♥❛ ❝♦r ♣r❡t❛✱❡♥q✉❛♥t♦ q✉❡ ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ♦❞♦♠❡tr✐❛ é ✐♥❞✐❝❛❞❛ ♣❡❧❛ ❧✐♥❤❛s tr❛ç♦✲♣♦♥t♦ ♥❛ ❝♦r✈❡r♠❡❧❤❛✳ ❆ ❧✐♥❤❛ ❝♦♥tí♥✉❛ r❡♣r❡s❡♥t❛ ❛s ♣♦s✐çõ❡s ❡st✐♠❛❞❛s✱ ❣❡r❛❞❛s ♣❡❧♦s ♠ét♦❞♦s❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ ❛ s❛❜❡r✿ ❛❜♦r❞❛❣❡♠ ✐♥❣ê♥✉❛ ❞♦ ❊❑❋ ✭❝♦r ❛③✉❧✮ ❡ ♦ ❛❧❣♦r✐t♠♦❈■ ✭❝♦r ♠❛❣❡♥t❛✮✳ ❊♠ ❛❧❣✉♠❛s ✜❣✉r❛s✱ t❛✐s ❝♦♠♦ ❛ ❋✐❣✉r❛ ✺✳✶✺✱ ❡ss❛s ❧✐♥❤❛s ♣♦❞❡♠❛♣❛r❡❝❡r s♦❜r❡♣♦st❛s✳ ❆ ♣♦s✐çã♦ ❞♦s r♦❜ôs ❢♦✐ ❞❡st❛❝❛❞❛ ❡♠ ❛❧❣✉♥s ♠♦♠❡♥t♦s ❞✉r❛♥t❡❛ ♥❛✈❡❣❛çã♦✱ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✿ ❛ ♣♦s✐çã♦ ✐♥✐❝✐❛❧ ✭sí♠❜♦❧♦ •✮✱ ❛ ♣♦s✐çã♦ ✜♥❛❧ ✭sí♠❜♦❧♦∗✮✱ ❛❧é♠ ❞❡ ❛❧❣✉♠❛s ♣♦s✐çõ❡s ✐♥t❡r♠❡❞✐ár✐❛s ✭sí♠❜♦❧♦ ×✮✳ ❆ ❋✐❣✉r❛ ✺✳✶✻ ❛♣r❡s❡♥t❛ ❛ ❡✈♦❧✉çã♦ ❞♦ ❡rr♦ ♠é❞✐♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❡♥①❛♠❡ ❡❛ r❡s♣❡❝t✐✈❛ ✐♥❝❡rt❡③❛ ❛ss♦❝✐❛❞❛✳ ❖ ❝á❧❝✉❧♦ ❞♦ ❡rr♦ ♠é❞✐♦ r❡❧❛t✐✈♦ ❛♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ✶✵✵2 ❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s 1.51 Ground Truth y (m) 0.5 Posicao Intermediaria Posicao Inicial Algoritmo CI EKF Ingenuo Odometria −0.5−1 Posicao Final −1.5−2 −2 −1.5 −1 −0.5 0.5 1 1.5 2 x (m) ❋✐❣✉r❛ ✺✳✶✺✿ ❊①❡♠♣❧♦ ❞❡ ❝❛♠✐♥❤♦ ❡①❡❝✉t❛❞♦ ♣♦r ✉♠ ❞♦s r♦❜ôs ❞✉r❛♥t❡ ❛ ♠♦✈✐♠❡♥t❛çã♦❞♦ ❡♥①❛♠❡✳ ◆♦ ❞❡❝♦rr❡r ❞❛ ♥❛✈❡❣❛çã♦✱ ♦s r♦❜ôs ❡①❡❝✉t❛r❛♠ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦❝♦♦♣❡r❛t✐✈❛ r❡❣✉❧❛r♠❡♥t❡✳✭▼P❊✮ ❞♦s r♦❜ôs é ❡❢❡t✉❛❞♦ ❝♦♥❢♦r♠❡ ❊q✉❛çã♦ ✭✺✳✽✮ ❡ ❛♣r❡s❡♥t❛❞♦ ♥❛ ❋✐❣✉r❛ ✺✳✶✻❛✱❡♥q✉❛♥t♦ q✉❡ ✺✳✶✻❝ ❛♣r❡s❡♥t❛ ❛ ✐♥❝❡rt❡③❛ ✭1 ❞❡s✈✐♦ ♣❛❞rã♦✮✳ ❖ ❡rr♦ ♠é❞✐♦ ❞❡ ♦r✐❡♥t❛çã♦♥❛ k✲és✐♠❛ ✐t❡r❛çã♦ r❡❧❛t✐✈♦ ❛ ✉♠❛ s✐♠✉❧❛çã♦ é ❝❛❧❝✉❧❛❞♦ ❝♦♥❢♦r♠❡ s❡❣✉❡ s X k1 k = ,❖❊ s ♦ i ✭✺✳✶✺✮ k k k2 ||R|| i ˆ= g θi ♦♥❞❡ ♦ − ˆθ é ♦ ❡rr♦ ♠é❞✐♦ q✉❛❞r❛❞♦ ❞❛ ♦r✐❡♥t❛çã♦ ❞❡ R ♥❛ k✲és✐♠❛ ✐t❡r❛çã♦✱ k i i g θ ˆé ❛ ♦r✐❡♥t❛çã♦ ❞♦s r♦❜ôs r❡❧❛t✐✈❛ ❛♦ ❣r♦✉♥❞ tr✉t❤ ❡ ||R|| é ♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs✳ ❖ ❡rr♦ ♠é❞✐♦ r❡❧❛t✐✈♦ à ♦r✐❡♥t❛çã♦ ✭▼❖❊✮ ❡♠ ❡①♣❡r✐♠❡♥t♦ ❢♦✐ ❝❛❧❝✉❧❛❞♦ ❝♦♥❢♦r♠❡ ❛❜❛✐①♦X k k 1= , ▼❖❊ ❖❊ s ✭✺✳✶✻✮S s s❡♥❞♦ S ♦ ♥ú♠❡r♦ ❞❡ s✐♠✉❧❛çõ❡s ❡①❡❝✉t❛❞❛s✳ ❆ ❡✈♦❧✉çã♦ ❞❡ss❡ ❡rr♦ é ❛♣r❡s❡♥t❛❞❛ ♥❛ ❋✐❣✉r❛ ✺✳✶✻❜ ❡ ❛ ✐♥❝❡rt❡③❛ ❛ss♦❝✐❛❞❛ é ❛♣r❡s❡♥t❛❞❛ ♥❛ ❋✐❣✉r❛ ✺✳✶✻❞✳ ❚❛✐s ✐♥❢♦r♠❛çõ❡s❢♦r❛♠ ❣❡r❛❞❛s ❛ ♣❛rt✐r ❞♦ ❡rr♦ ♠é❞✐♦ ❞❡ ✶✵ ❡①❡❝✉çõ❡s✳ ◆♦s ❡①♣❡r✐♠❡♥t♦s ❞❡st❛ s❡çã♦✱♣♦❞❡✲s❡ ♦❜s❡r✈❛r ✉♠❛ ♣♦ssí✈❡❧ ✐♥❝♦♥s✐stê♥❝✐❛ ❞❛ ❛❜♦r❞❛❣❡♠ ✐♥❣ê♥✉❛ ❞♦ ❊❑❋✿ ♦ ❡rr♦❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ é ❝r❡s❝❡♥t❡ ❡♠ ❞❡t❡r♠✐♥❛❞♦s ♠♦♠❡♥t♦s✱ ❡♥q✉❛♥t♦ q✉❡ ❛ ✐♥❝❡rt❡③❛ ✺✳✷✳ ❈♦♥s✐stê♥❝✐❛ ❞❛s ❊st✐♠❛t✐✈❛s ❞❡ ▲♦❝❛❧✐③❛çã♦ ✶✵✶❛ss♦❝✐❛❞❛ ❛ t❛❧ ✐♥❢♦r♠❛çã♦ é ♥ã♦ ❝r❡s❝❡♥t❡✳ P♦❞❡✲s❡ ♦❜s❡r✈❛r✱ t❛♠❜é♠✱ q✉❡ ❛♣❡s❛r ❞♦s❡rr♦s ❞❡ ♣♦s✐çã♦ ❡ ♦r✐❡♥t❛çã♦ r❡❢❡r❡♥t❡s ❛♦ ❊❑❋ s❡r❡♠ s✉♣❡r✐♦r àq✉❡❧❡s r❡❧❛t✐✈♦s ❛♦❛❧❣♦r✐t♠♦ ❈■✱ ❛s ✐♥❝❡rt❡③❛s ❛ss♦❝✐❛❞❛s ❛♦ ❊❑❋ ♥ã♦ r❡♣r❡s❡♥t❛♠ t❛❧ ✐♥❢♦r♠❛çã♦✳1 CI EKF Odometria 0.4 0.5 EKF OdometriaMP ( E m)0.5 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Iterações ) E ra MO d CI ( 0.3 0.2 0.1 Iterações0.020.03 ✭❛✮ CI EKF 0.08 EKF 0.06 0.04 ✭❜✮ CI Incerteza (m)0.01 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Iterações Incerteza (rad) 0.02 Iterações✭❝✮ ✭❞✮ ❋✐❣✉r❛ ✺✳✶✻✿ ❊✈♦❧✉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❡✳ ❊♠ ✭❛✮ ❡ ✭❝✮ sã♦❛♣r❡s❡♥t❛❞❛s ❛ ❡✈♦❧✉çã♦ ❞♦ ❡rr♦ ♠é❞✐♦ r❡❢❡r❡♥t❡ à ♣♦s✐çã♦ ❡ ❛ r❡s♣❡❝t✐✈❛ ✐♥❝❡rt❡③❛ ✭1❞❡s✈✐♦ ♣❛❞rã♦✮✳ ■♥❢♦r♠❛çõ❡s s✐♠✐❧❛r❡s r❡❢❡r❡♥t❡s à ♦r✐❡♥t❛çã♦ sã♦ ❛♣r❡s❡♥t❛❞❛s ❡♠ ✭❜✮❡ ✭❞✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❊ss❛ ♣♦ssí✈❡❧ ✐♥❝♦♥s✐stê♥❝✐❛ ❣❡r❛❞❛ ♥❛s ❡t❛♣❛s ❞❡ ❝♦rr❡çã♦ ❞❛ ❛❜♦r❞❛❣❡♠ ✐♥❣ê♥✉❛❞♦ ❊❑❋✱ ❛ q✉❛❧ ♥ã♦ ❧❡✈❛ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛✱ ♣♦❞❡ ❝♦♠✲♣r♦♠❡t❡r s❡✉ ❡♠♣r❡❣♦ ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ♣♦❞❡♦❝♦rr❡r ❞❡ ❡st✐♠❛t✐✈❛s ✭♦❜s❡r✈❛çõ❡s✮ ❝♦♠ ❜❛✐①♦ ♥í✈❡❧ ❞❡ ✐♥❝❡rt❡③❛ s❡r❡♠ ♣r❛t✐❝❛♠❡♥t❡✐❣♥♦r❛❞❛s✱ ❝♦♥❢♦r♠❡ ♦❝♦rr❡✉ ❡♠ ✈ár✐♦s ♠♦♠❡♥t♦s ♥❡st❡s ❡①♣❡r✐♠❡♥t♦s✳ P♦r ♦✉tr♦ ❧❛❞♦✱❛ ❝♦♥s✐stê♥❝✐❛ ❞❛s ❡st✐♠❛t✐✈❛s ❣❡r❛❞❛s ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❈■ ♣❡r♠✐t❡ ✐♥❝♦r♣♦r❛r ♥♦✈❛s ♦❜✲ s❡r✈❛çõ❡s ❞❡ ♠❛♥❡✐r❛ ❛❞❡q✉❛❞❛✳ ◆❛ ❋✐❣✉r❛ ✺✳✶✺✱ t❛❧ ❢❛t♦ é ✐❧✉str❛❞♦ ♣❡❧❛ q✉❛❧✐❞❛❞❡ ❞❛s❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❣❡r❛❞❛ ♣♦r ❡ss❡ ❛❧❣♦r✐t♠♦✳ ❆ r♦❜✉st❡③ ❞❛s ❛❜♦r❞❛❣❡♥s ✉t✐❧✐③❛❞❛s ♣❛r❛ ❧♦❝❛❧✐③❛r ❝♦♦♣❡r❛t✐✈❛♠❡♥t❡ ❡ ❞❡ ♠❛✲♥❡✐r❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ✉♠ ❡♥①❛♠❡ r♦❜ót✐❝♦ é ❡ss❡♥❝✐❛❧ ♣❛r❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❡♠ r♦❜ôs r❡❛✐s✳ ❉❡ss❡ ♠♦❞♦✱ ♦s ❡①♣❡r✐♠❡♥t♦s ❞❡s❝r✐t♦s ❛ s❡❣✉✐r ♦❜❥❡t✐✈❛r❛♠ ❛✈❛❧✐❛r ❛ r♦❜✉s✲t❡③ ❞♦s ♠ét♦❞♦s ♥❛s s❡❣✉✐♥t❡s s✐t✉❛çõ❡s✿ ✭✐✮ ❡s♣♦r❛❞✐❝❛♠❡♥t❡✱ ♦ ❧í❞❡r t❡✈❡ ❛❝❡ss♦ ❛❡st✐♠❛t✐✈❛s ❛❜s♦❧✉t❛s❀ ✭✐✐✮ ♦❝♦rr❡r❛♠ ❢❛❧❤❛s ✐♥t❡r♠✐t❡♥t❡s ♥♦s s❡♥s♦r❡s ❡①t❡r♦❝❡♣t✐✈♦s❞♦s r♦❜ôs❀ ❡ ✭✐✐✐✮ ♦❝♦rr❡r❛♠ ❢❛❧❤❛s ♥❛ ❝♦♠✉♥✐❝❛çã♦ ❞♦s r♦❜ôs✳ P♦r ✜♠✱ ❛ ❛✉sê♥❝✐❛❝♦♠♣❧❡t❛ ❞❡ ❡st✐♠❛t✐✈❛s ❛❜s♦❧✉t❛s ❢♦✐ ❝♦♥s✐❞❡r❛❞❛ ♣❛r❛ s❡ ✈❡r✐✜❝❛r ♦ ✐♠♣❛❝t♦ q✉❡ ♦❝♦♠♣♦rt❛♠❡♥t♦ ❝♦♦♣❡r❛t✐✈♦ ❛❝❛rr❡t❛r✐❛ ♥❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❣r✉♣♦✳ ✶✵✷❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s ✺✳✷✳✷ ❊st✐♠❛t✐✈❛s ❆❜s♦❧✉t❛s ❊s♣♦rá❞✐❝❛s P❛r❛ ❛✈❛❧✐❛r ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❛s ❡str❛té❣✐❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡♠ ✐♥❝♦r♣♦r❛r♥♦✈❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ✭♦❜s❡r✈❛çõ❡s✮✱ ❛ ❢r❡q✉ê♥❝✐❛ ❝♦♠ q✉❡ ♦ ❧í❞❡r ❛❝❡ss❛r✐❛✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛ ❢♦✐ ❞r❛st✐❝❛♠❡♥t❡ r❡❞✉③✐❞❛✳ ❙✐♠✐❧❛r ❛♦ ❡①♣❡r✐♠❡♥t♦❛♥t❡r✐♦r✱ ♥❡st❡ ❡①♣❡r✐♠❡♥t♦ ♦s r♦❜ôs ❡①❡❝✉t❛r❛♠ r❡❣✉❧❛r♠❡♥t❡ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦❝♦♦♣❡r❛t✐✈❛✳ ◆♦ ❡♥t❛♥t♦✱ ♦ ❧í❞❡r s♦♠❡♥t❡ t❡✈❡ ❛❝❡ss♦ às ♦❜s❡r✈❛çõ❡s ❞❡ ♣♦s❡ ❛❜s♦❧✉t❛❡♠ ❛♣❡♥❛s três ♠♦♠❡♥t♦s ❞✐st✐♥t♦s✿ ✐t❡r❛çõ❡s 850✱ 1500 ❡ 2350✳ ◆♦ ❝❛♠✐♥❤♦ ❡❢❡t✉❛❞♦♣♦r ✉♠ ❞♦s r♦❜ôs ❞♦ ❡♥①❛♠❡✱ ❛♣r❡s❡♥t❛❞♦ ♥❛ ❋✐❣✉r❛ ✺✳✶✼✱ ♣♦❞❡✲s❡ ♣❡r❝❡❜❡r ♦s três✐♥st❛♥t❡s ❡♠ q✉❡ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛ ❢♦r❛♠ ♦❜t✐❞❛s ♣❡❧♦ ❧í❞❡r✱ ❝♦♠ ❛❝♦♥s❡q✉❡♥t❡ ❝♦rr❡çã♦ ❞♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦ r❡s♣❡❝t✐✈♦ r♦❜ô ✭✐♥❞✐❝❛❞♦ ♣❡❧❛s s❡t❛s✮✳2 1.51 Ground Truth y (m) −0.5 0.5 Posição Intermediária Posição Inicial Algoritmo CI EKF (Abord. Ingênua) Odometria −1.5 −1 Posição Final −2−2 −1.5 −1 −0.5 0.5 1 1.5 2 x (m) ❋✐❣✉r❛ ✺✳✶✼✿ ❆❝❡ss♦ ❡s♣♦rá❞✐❝♦ ♣❡❧♦ ❧í❞❡r à ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛ ❞✉✲ r❛♥t❡ ❛ ♠♦✈✐♠❡♥t❛çã♦✳ ❘❡❣✉❧❛r♠❡♥t❡✱ ♦s r♦❜ôs ❡①❡❝✉t❛r❛♠ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦✲♦♣❡r❛t✐✈❛✳ P♦r ✐♥t❡r♠é❞✐♦ ❞❡ s❡♥s♦r❡s ❡①t❡r♦❝❡♣t✐✈♦s✱ ♦ ❧í❞❡r ♦❜t❡✈❡ ❡st✐♠❛t✐✈❛s ❞❡❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛ ❡♠ três ♠♦♠❡♥t♦s ❡s♣❡❝í✜❝♦s✿ ✐t❡r❛çõ❡s 850✱ 1500 ❡ 2350✳ ❆ ❋✐❣✉r❛ ✺✳✶✽ ❛♣r❡s❡♥t❛ ❛ ❡✈♦❧✉çã♦ ❞♦ ❡rr♦ ♠é❞✐♦ ❡ ❞❛ ✐♥❝❡rt❡③❛ ❞♦ ❣r✉♣♦✳ ◆❡ss❛✜❣✉r❛✱ ❛s ❧✐♥❤❛s ✈❡rt✐❝❛✐s tr❛ç♦✲♣♦♥t♦ ✐♥❞✐❝❛♠ ❛s ✐t❡r❛çõ❡s ❡♠ q✉❡ ♦❜s❡r✈❛çõ❡s ❞❡ ❧♦✲❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛ ❢♦r❛♠ ❡❢❡t✉❛❞❛s ♣❡❧♦ ❧í❞❡r✳ ◆❡ss❛s ✐t❡r❛çõ❡s✱ é ♣♦ssí✈❡❧ ♦❜s❡r✈❛r❛ r❡❞✉çã♦ ❞♦ ❡rr♦ ❞❡ ♣♦s✐çã♦ ✭❋✐❣✉r❛ ✺✳✶✽❛✮ ❡ ♦ ❛❥✉st❡ ❞❛ ✐♥❝❡rt❡③❛ ❛ss♦❝✐❛❞❛ ✭❋✐✲❣✉r❛ ✺✳✶✽❝✮✱ r❡❧❛t✐✈♦s à ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❣❡r❛❞❛ ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❈■✳ ❉❡ ❢♦r♠❛ s❡♠❡❧❤❛♥t❡✱ ❛s ❋✐❣✉r❛s ✺✳✶✽❜ ❡ ✺✳✶✽❞ ❛♣r❡s❡♥t❛♠ ♦ ❡rr♦ ♠é❞✐♦ ❞❡ ♦r✐❡♥t❛çã♦ ❡ ❛ r❡s✲♣❡❝t✐✈❛ ✐♥❝❡rt❡③❛✳ ◆❡st❡ ❡①♣❡r✐♠❡♥t♦✱ ♦ ❡rr♦ ❛ss♦❝✐❛❞♦ às ❡st✐♠❛t✐✈❛s q✉❡ ❡♠♣r❡❣❛♠ ❛ ✺✳✷✳ ❈♦♥s✐stê♥❝✐❛ ❞❛s ❊st✐♠❛t✐✈❛s ❞❡ ▲♦❝❛❧✐③❛çã♦ ✶✵✸❛❜♦r❞❛❣❡♠ ✐♥❣ê♥✉❛ ❞♦ ❊❑❋ ♣r❛t✐❝❛♠❡♥t❡ ♥ã♦ ❢♦✐ ❛❧t❡r❛❞♦ ♥❛ ♣r❡s❡♥ç❛ ❞❡ ❡st✐♠❛t✐✈❛s❡s♣♦rá❞✐❝❛s✱ ❜❛s❡❛❞❛s ♥❛ ♦❜s❡r✈❛çã♦ ❞❡ ✉♠❛ ❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛ ❡❢❡t✉❛❞❛ ♣❡❧♦ ❧í❞❡r✳P♦r ♦✉tr♦ ❧❛❞♦✱ ❛ ❝♦♥s✐stê♥❝✐❛ ❞❛s ❡st✐♠❛t✐✈❛s ❣❡r❛❞❛s ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❈■ ♣❡r♠✐t✐✉ q✉❡♦s ❡rr♦s ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❡ ❞❡ ♦r✐❡♥t❛çã♦ ❢♦ss❡♠ r❡❞✉③✐❞♦s s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡✱ q✉❛♥❞♦❞❛ ♣r❡s❡♥ç❛ ❞❡ ♦❜s❡r✈❛çõ❡s ❛❜s♦❧✉t❛s ♥♦ ❡♥①❛♠❡✳1 CI EKF Odometria ) d 0.4 0.5 0.3 Odometria CI EKF MP m) E (0.5 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Iterações MO E ( ra 0.2 0.1 Iterações1.51 Odometria CI EKF ✭❛✮ 0.15 0.1 CI EKF Odometria ✭❜✮ Incerteza (m)0.5 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Iterações Incerteza (rad) 0.05 Iterações ✭❝✮✭❞✮ ❋✐❣✉r❛ ✺✳✶✽✿ ❊✈♦❧✉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❡✳ ❆s ❧✐♥❤❛s ✈❡rt✐✲❝❛✐s tr❛ç♦✲♣♦♥t♦ ✐❧✉str❛♠ ♦s ♠♦♠❡♥t♦s ❡♠ q✉❡ ♦ r♦❜ô ❧í❞❡r t❡✈❡ ❛❝❡ss♦ ❛ ♦❜s❡r✈❛çõ❡s❛❜s♦❧✉t❛s ❞❡ s✉❛ ♣♦s❡✳ ❊♠ ✭❛✮ ❡ ✭❝✮ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛ ❡✈♦❧✉çã♦ ❞♦ ❡rr♦ ♠é❞✐♦ ❡ ❛ r❡s♣❡❝t✐✈❛ ✐♥❝❡rt❡③❛ ✭1 ❞❡s✈✐♦ ♣❛❞rã♦✮✳ ■♥❢♦r♠❛çõ❡s s✐♠✐❧❛r❡s r❡❢❡r❡♥t❡s à ♦r✐❡♥t❛çã♦sã♦ ❛♣r❡s❡♥t❛❞❛s ❡♠ ✭❜✮ ❡ ✭❞✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✺✳✷✳✸ ❋❛❧❤❛s ♥♦s ▼❡❝❛♥✐s♠♦s ❙❡♥s♦r✐❛✐s ♦✉ ❞❡ ❈♦♠✉♥✐❝❛çã♦ ❖ ❡①♣❡r✐♠❡♥t♦ ❛♥t❡r✐♦r ♠♦str♦✉ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐✲â♥❝✐❛s ❡♠ ✐♥❝♦r♣♦r❛r ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❡s♣♦rá❞✐❝❛s✱ ♣♦ré♠ ❝♦♠ ❜♦❛ ♣r❡❝✐sã♦✳❊ss❡ ❢❛t♦ é ✉♠ ✐♥❞✐❝❛t✐✈♦ ❞❡ q✉❡ t❛✐s ❛❧❣♦r✐t♠♦s t❡♥❤❛♠ ♣♦t❡♥❝✐❛❧ ♣❛r❛ ❧✐❞❛r ❝♦♠♣♦ssí✈❡✐s ❢❛❧❤❛s ❞❡ ❝♦♠✉♥✐❝❛çã♦ ♦✉ s❡♥s♦r✐❛❧ ❞♦s r♦❜ôs✳ ❉❡ss❡ ♠♦❞♦✱ ♦s s❡❣✉✐♥t❡s❡①♣❡r✐♠❡♥t♦s ❛✈❛❧✐❛r❛♠ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞♦s ♠ét♦❞♦s ❡♠ ❧✐❞❛r ❝♦♠ ❡ss❡s t✐♣♦s ❞❡ ❢❛❧❤❛✳✺✳✷✳✸✳✶ ❙❡♥s♦r ❞❡ P♦s✐❝✐♦♥❛♠❡♥t♦ ❆❜s♦❧✉t♦ ❝♦♠ ❋❛❧❤❛ ■♥t❡r♠✐t❡♥t❡◆❡st❡ ❡①♣❡r✐♠❡♥t♦✱ ❛ r♦❜✉st❡③ ❞♦s ♠ét♦❞♦s é ❛✈❛❧✐❛❞❛ ❡♠ s✐t✉❛çõ❡s ♥❛s q✉❛✐s ♦ s❡♥s♦r❡①t❡r♦❝❡♣t✐✈♦ ❞♦ r♦❜ô ❧í❞❡r ❢❛❧❤❛✱ ❝♦♠♣r♦♠❡t❡♥❞♦ ♦ r❡❝❡❜✐♠❡♥t♦ ❞❡ ✐♥❢♦r♠❛çõ❡s ❞❡❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛✳ ❆s ❢❛❧❤❛s ♦❝♦rr❡r❛♠ ❞✉r❛♥t❡ t♦❞♦ ♦ ✐♥t❡r✈❛❧♦ r❡❢❡r❡♥t❡ às ✐t❡r❛✲çõ❡s 1200 ❡ 2000✳ ❉✉r❛♥t❡ ❡ss❡ ✐♥t❡r✈❛❧♦✱ ♦ ❧í❞❡r ♣❛rt✐❝✐♣❛ ❞❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ✶✵✹❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s ❝♦♦♣❡r❛t✐✈❛✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ♦s ❞❡♠❛✐s r♦❜ôs✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ❛♣ós♣❡r❝♦rr❡r ✉♠❛ ❞✐stâ♥❝✐❛ ❛♣r♦①✐♠❛❞❛ ❞❡ 10 cm✱ ✉♠ r♦❜ô t❡♥t❛ ❡❢❡t✉❛r ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐✲③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ♠❡❧❤♦r❛r s✉❛ ❡st✐♠❛t✐✈❛✳ ❆ ❋✐❣✉r❛ ✺✳✶✾ ♠♦str❛ ♦❝❛♠✐♥❤♦ ❡❢❡t✉❛❞♦ ♣♦r ✉♠ r♦❜ô ❞♦ ❡♥①❛♠❡ ✭❧✐♥❤❛ ♣r❡t❛ tr❛❝❡❥❛❞❛✮ ❡ ❛s ❡st✐♠❛t✐✈❛s ❞❡♣♦s✐çã♦ ❣❡r❛❞❛s ♣❡❧♦s ❞♦✐s ♠ét♦❞♦s✱ ❛❧é♠ ❞❛ ✐♥❢♦r♠❛çã♦ ❞❡ ♦❞♦♠❡tr✐❛✳ ❆s ❡st✐♠❛t✐✈❛s❞❡ ❧♦❝❛❧✐③❛çã♦ r❡❢❡r❡♥t❡s ❛♦ ❛❧❣♦r✐t♠♦ ❈■ ♠♦str❛♠ q✉❡ t❛❧ ❛❧❣♦r✐t♠♦ ❝♦♥s❡❣✉❡ ❛❝♦♠✲♣❛♥❤❛r ❛ ♣♦s✐çã♦ r❡❛❧ ❞♦ r♦❜ô✱ ❛té q✉❡ ❛ ❢❛❧❤❛ ❞♦ s❡♥s♦r ❡①t❡r♦❝❡♣t✐✈♦ ❞❡ ❧♦❝❛❧✐③❛çã♦❛❜s♦❧✉t❛ ❝♦♠❡ç❛ ❛ ♦❝♦rr❡r✳ ❊ss❛ ❢❛❧❤❛ ✐♥✐❝✐❛ q✉❛♥❞♦ ♦ ❣r✉♣♦ ❡stá ♣ró①✐♠♦ ❛♦ s❡❣✉♥❞♦❛❧✈♦✱ ❝❡♥tr❛❞♦ ♥❛ ♣♦s✐çã♦ ✭✲✶✱✼✺✱ ✶✱✼✺✮✱ ❡ s♦♠❡♥t❡ é r❡❡st❛❜❡❧❡❝✐❞❛ q✉❛♥❞♦ ♦ ❡♥①❛♠❡ s❡❡♥❝♦♥tr❛ ♣ró①✐♠♦ ❛♦ t❡r❝❡✐r♦ ❛❧✈♦✳ ❉✉r❛♥t❡ ❡ss❡ ✐♥t❡r✈❛❧♦✱ ❛♣❡s❛r ❞♦s r♦❜ôs ❡❢❡t✉❛r❡♠❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✱ ♦ ❡rr♦ ♠é❞✐♦ é ❝r❡s❝❡♥t❡✱ t❡♥❞♦ ❡♠ ✈✐st❛ ❛ ❛✉sê♥❝✐❛❞❡ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ♣r❡❝✐s❛s ❡ ♦ ❛❝ú♠✉❧♦ ❞❡ ❡rr♦ ❞♦s s❡♥s♦r❡s ♣r♦♣r✐♦❝❡♣t✐✈♦s✳2 1.51 y (m) −0.5 0.5 Posição Intermediária Posição Inicial EKF (Abord. Ingênua) Odometria Ground Truth Algoritmo CI −1.5 −1 Posição Final −2.5 −2 −2 −1.5 −1 −0.5 0.5 1 1.5 2 x (m) ❋✐❣✉r❛ ✺✳✶✾✿ ❋❛❧❤❛ ✐♥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❛♠❡✳ ❆ ❢❛❧❤❛ ✐♥✐❝✐❛ q✉❛♥❞♦ ♦❣r✉♣♦ ❡stá ♣ró①✐♠♦ ❛♦ s❡❣✉♥❞♦ ❛❧✈♦ ✭✲✶✱✼✺✱ ✶✱✼✺✮ ❡ s♦♠❡♥t❡ é r❡❡st❛❜❡❧❡❝✐❞❛ ♣ró①✐♠♦❛♦ t❡r❝❡✐r♦ ❛❧✈♦ ✭✲✶✱✼✺✱ ✲✶✱✼✺✮✳ ❚❛✐s ❧♦❝❛✐s sã♦ ✐♥❞✐❝❛❞♦s ♣❡❧❛s s❡t❛s✳ ❆ ❡✈♦❧✉çã♦ ❞♦ ❡rr♦ ♠é❞✐♦ ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s r♦❜ôs ❡ r❡s♣❡❝t✐✈❛s ✐♥❝❡rt❡③❛s sã♦❛♣r❡s❡♥t❛❞♦s ♥❛ ❋✐❣✉r❛s ✺✳✷✵✳ ➱ ♣♦ssí✈❡❧ ♦❜s❡r✈❛r q✉❡ ♦ ❛❧❣♦r✐t♠♦ ❈■ s❡ r❡❝✉♣❡r❛ ♠❛✐s rá♣✐❞♦ ❞❡ ✉♠❛ ❢❛❧❤❛ ❞♦ q✉❡ ❛ ❛❜♦r❞❛❣❡♠ ✐♥❣ê♥✉❛ ❞♦ ❊❑❋✳ ◆♦✈❛♠❡♥t❡✱ ✐ss♦ s❡ ❞❡✈❡❛♦ ❢❛t♦ ❞❡ss❡s ❛❧❣♦r✐t♠♦s ♠❛♥t❡r❡♠ ♥í✈❡✐s ❞❡ ✐♥❝❡rt❡③❛ ❝♦♠♣❛tí✈❡✐s ❝♦♠ ❛ q✉❛❧✐❞❛❞❡❞❡ s✉❛s ❡st✐♠❛t✐✈❛s✳ P♦❞❡✲s❡ ♦❜s❡r✈❛r✱ t❛♠❜é♠✱ q✉❡ ♦ ❡rr♦ ❛❝✉♠✉❧❛❞♦ ❛ss♦❝✐❛❞♦ às ✺✳✷✳ ❈♦♥s✐stê♥❝✐❛ ❞❛s ❊st✐♠❛t✐✈❛s ❞❡ ▲♦❝❛❧✐③❛çã♦ ✶✵✺❡st✐♠❛t✐✈❛s ❣❡r❛❞❛s ♣❡❧♦ ❊❑❋ ❛✐♥❞❛ s❡ ♠❛♥té♠ ❡♠ ✉♠ ✈❛❧♦r ❛❧t♦✱ q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦❛♦ ❡rr♦ ❛ss♦❝✐❛❞♦ às ❡st✐♠❛t✐✈❛s ❣❡r❛❞❛ ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❈■✳ ■ss♦ ♠♦str❛ q✉❡ ❛ ❛❜♦r❞❛❣❡♠✐♥❣ê♥✉❛ ❞♦ ❊❑❋ s♦♠❡♥t❡ ❝♦♥s❡❣✉❡ s❡ r❡❝✉♣❡r❛r ♣❛r❝✐❛❧♠❡♥t❡ ♥❡ss❡ t✐♣♦ ❞❡ ❢❛❧❤❛✳1 EKF Odometria Odometria de falha região 0.4 EKF( m) MP E0.5 CI d 0.3 CI 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Iterações MO E ( de falha ra ) 0.1 0.2 Iterações região0.150.1 ✭❛✮ de falha região CI EKF 0.06 0.08 EKF 0.04 ✭❜✮ de falha região CI Incerteza (m) 0.05 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Iterações Iterações Incerteza (rad) 0.02✭❝✮ ✭❞✮ ❋✐❣✉r❛ ✺✳✷✵✿ ❊✈♦❧✉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♦✳ ❆ ❢❛❧❤❛ ✐♥✐❝✐❛ ♥❛ ✐t❡r❛çã♦ 1200 ❡ s♦♠❡♥t❡ é r❡❡st❛❜❡❧❡❝✐❞❛♥❛ ✐t❡r❛çã♦ 2000✱ ✐♥❞✐❝❛❞❛s ♣❡❧❛s ❧✐♥❤❛s tr❛❝❡❥❛❞❛s✳✺✳✷✳✸✳✷ ❋❛❧❤❛s ♥♦ ▼❡❝❛♥✐s♠♦ ❞❡ ❈♦♠✉♥✐❝❛çã♦❆ r♦❜✉st❡③ ❞♦s ♠ét♦❞♦s ❡♠ s✐t✉❛çõ❡s ❞❡ ❢❛❧❤❛ ♥♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❢♦✐❛♥❛❧✐s❛❞❛ ♥❡st❡ ❡①♣❡r✐♠❡♥t♦✳ ◆❛ ♣r❡s❡♥ç❛ ❞❡ ❢❛❧❤❛s✱ ✉♠ r♦❜ô ♥ã♦ ♣ô❞❡ r❡❝❡❜❡r ✐♥❢♦r✲♠❛çõ❡s ❞❡ s❡✉s ✈✐③✐♥❤♦s ❡ ✜❝♦✉ ✐♠♣❡❞✐❞♦ ❞❡ ❡❢❡t✉❛r ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳❖s r♦❜ôs ❢♦r❛♠ s✉❥❡✐t♦s ❛ ❢❛❧❤❛s ❡♠ s❡✉s ♠❡❝❛♥✐s♠♦s ❞❡ ❝♦♠✉♥✐❝❛çã♦✱ ♠♦❞❡❧❛❞♦s ♣♦r✉♠❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❇❡r♥♦✉❧❧✐ ❝♦♠ ♣❛râ♠❡r♦ p = 0,5 ✳ ❆ss✐♠✱ ✉♠❛ ❢❛❧❤❛ ♣♦❞❡ ♦❝♦rr❡r✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❝♦♠ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ s✉❝❡ss♦ ❞❡ 50%✳ ❆ ❋✐❣✉r❛ ✺✳✷✶ ♠♦str❛ ❛s ❡st✐♠❛t✐✈❛s ❞❡ ♣♦s✐çã♦ ❞❡ ✉♠ r♦❜ô ❞♦ ❣r✉♣♦✳ P♦❞❡✲s❡♦❜s❡r✈❛r q✉❡✱ ❛♣❡s❛r ❞❛s ❢❛❧❤❛s ♥♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝♦♠✉♥✐❝❛çã♦✱ ❛s ❛❜♦r❞❛❣❡♥s s❡ ❝♦♠✲♣♦rt❛r❛♠ ❞❡ ♠❛♥❡✐r❛ r♦❜✉st❛✳ ■ss♦ ♦❝♦rr❡✉ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ ❤❛✈❡r ♠❛✐s ✐♥❢♦r♠❛çõ❡s❞❡ ❧♦❝❛❧✐③❛çã♦ ❞✐s♣♦♥í✈❡✐s ❡ ❝♦♠ ♠❛✐♦r ❢r❡q✉ê♥❝✐❛✱ ❝♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛ ❞❛ ❛t✉❛çã♦ ❝♦♥✲❥✉♥t❛ ❞♦ ❣r✉♣♦✳ ❆ss✐♠✱ ❛♣❡s❛r ❞❛s ❢❛❧❤❛s t❡r❡♠ ♦❝♦rr✐❞♦ ❝♦♠ ✉♠❛ ❝❡rt❛ ❢r❡q✉ê♥❝✐❛✱ ❛s♠❡s♠❛s ♥ã♦ ❝♦♠♣r♦♠❡t❡r❛♠ ❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❡♥①❛♠❡✳ ■ss♦ ♣♦❞❡ s❡r ❝♦♠♣r♦✈❛❞♦ ♥❛❋✐❣✉r❛ ✺✳✷✷✱ ♥❛ q✉❛❧ ♦s ❡rr♦s ♠é❞✐♦s ❡ ❛s r❡s♣❡❝t✐✈❛s ✐♥❝❡rt❡③❛s s❡ ❛ss❡♠❡❧❤❛♠ àq✉❡❧❡s❞❛ ❋✐❣✉r❛ ✺✳✶✻✳ ✶✵✻❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s −2 −1.5 −1 −0.5 0.5 1 1.5 2 −2.5 −2 −1.5 −1 −0.50.511.52 x (m) y (m) Ground Truth Odometria Algoritmo CI Posição Inicial Posição Intermediária Posição Final EKF (Abord. Ingênua) ❋✐❣✉r❛ ✺✳✷✶✿ ❘❡s✉❧t❛❞♦ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♥❛ ♦❝♦rrê♥❝✐❛ ❞❡ ❢❛❧❤❛s ♥♦ ♠❡❝❛✲♥✐s♠♦ ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❞♦s r♦❜ôs✳ 500 1000 1500 2000 25000.020.040.060.080.1 Iterações M P E ( m ) EKF CI✭❛✮ 500 1000 1500 2000 2500 0.05 0.1 0.15 Iterações M O E ( ra d ) EKF CI ✭❜✮500 1000 1500 2000 25000.010.020.03 Iterações Incerteza (m) EKF CI ✭❝✮ 500 1000 1500 2000 2500 0.02 0.04 0.06 0.08 Iterações Incerteza (rad) EKF CI✭❞✮ ❋✐❣✉r❛ ✺✳✷✷✿ ❊rr♦ ♠é❞✐♦ ✭❛✮ ❡ ❞❡s✈✐♦ ♣❛❞rã♦ ✭❝✮ r❡❢❡r❡♥t❡ à ♣♦s✐çã♦ ❞♦s r♦❜ôs✳ ■♥❢♦r♠❛✲çõ❡s s❡♠❡❧❤❛♥t❡s r❡❧❛t✐✈❛s à ♦r✐❡♥t❛çã♦ sã♦ ❛♣r❡s❡♥t❛❞❛s ❡♠ ✭❜✮ ❡ ✭❞✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✺✳✷✳ ❈♦♥s✐stê♥❝✐❛ ❞❛s ❊st✐♠❛t✐✈❛s ❞❡ ▲♦❝❛❧✐③❛çã♦ ✶✵✼✺✳✷✳✸✳✸ ❆✉sê♥❝✐❛ ❞❡ ■♥❢♦r♠❛çõ❡s ❞❡ ▲♦❝❛❧✐③❛çã♦ ❆❜s♦❧✉t❛◆❡st❡ ❡①♣❡r✐♠❡♥t♦ ♥❡♥❤✉♠ r♦❜ô t❡✈❡ ❛❝❡ss♦ ❛ ♠❡❞✐❞❛s ❞❡ ♣♦s✐çã♦ ❡ ♦r✐❡♥t❛çã♦ ❛❜s♦❧✉✲ t❛s✳ ◆♦ ❡♥t❛♥t♦✱ ❞❡ ❢♦r♠❛ s❡♠❡❧❤❛♥t❡ ❛♦s ❡①♣❡r✐♠❡♥t♦s ❛♥t❡r✐♦r❡s✱ ♦s r♦❜ôs ❡①❡❝✉t❛r❛♠❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ✉t✐❧✐③❛♥❞♦ ✐♥❢♦r♠❛çõ❡s ❡ ♠❡❞✐❞❛s r❡❧❛t✐✈❛s ❛ s❡✉s ✈✐✲③✐♥❤♦s ✐♠❡❞✐❛t♦s✳ ❖s r♦❜ôs ❝♦♥t✐♥✉❛♠❡♥t❡ ❞✐ss❡♠✐♥❛r❛♠ ✭❜r♦❛❞❝❛st✮ s✉❛s ❡st✐♠❛t✐✈❛s❛t✉❛✐s ❡ ❛s ♦❜s❡r✈❛çõ❡s r❡❧❛t✐✈❛s ❛ s❡✉s ✈✐③✐♥❤♦s✳ ❖s r♦❜ôs t❡♥t❛♠ ❡①❡❝✉t❛r ❡t❛♣❛s ❞❡❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❛♣ós t❡r❡♠ ♣❡r❝♦rr✐❞♦ ❛ ❞✐stâ♥❝✐❛ ♣r❡❡st❛❜❡❧❡❝✐❞❛✳ ❆ss✐♠✱ ✉♠ r♦❜ô ✉t✐❧✐③❛ t❛✐s ✐♥❢♦r♠❛çõ❡s✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛s ♠❡❞✐❞❛s ❡①t❡r♦❝❡♣t✐✈❛s r❡❢❡r❡♥t❡s ❛s❡✉s ✈✐③✐♥❤♦s✱ ♣❛r❛ ❣❡r❛r ♥♦✈❛s ❡st✐♠❛t✐✈❛s✳ ❆ ❋✐❣✉r❛ ✺✳✷✸ ♠♦str❛ ❛s ❡st✐♠❛t✐✈❛s ❞❡❧♦❝❛❧✐③❛çã♦ ❞❡ ✉♠ r♦❜ô ♥♦ ❣r✉♣♦✳ ❆♣❡s❛r ❞❡ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡st❛r❡♠ s❡♥❞♦ ❡①❡❝✉t❛❞❛s✱ ♦ ❡rr♦ ❞❛s ❡st✐♠❛t✐✈❛s ❝r❡s❝❡ ♣❡r♠❛♥❡♥t❡♠❡♥t❡✳20.5 1.51 y (m) −0.5 Posição Intermediária Posição Inicial Ground Truth Algoritmo CI EKF (Abord. Ingênua) Odometria −1.5 −1 Posição Final −2.5 −2 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5 x (m) ❋✐❣✉r❛ ✺✳✷✸✿ ❘❡s✉❧t❛❞♦ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♥❛ ❛✉sê♥❝✐❛ ❞❡ s❡♥s♦r❡s ❞❡ ❧♦❝❛❧✐③❛✲çã♦ ❛❜s♦❧✉t❛✳ ❆ ❋✐❣✉r❛ ✺✳✷✹ ❛♣r❡s❡♥t❛ ♦ ❡rr♦ ♠é❞✐♦ ❡ ❛ ✐♥❝❡rt❡③❛ r❡❧❛t✐✈♦s à ♣♦s✐çã♦ ❡ ♦r✐❡♥t❛çã♦❞♦ ❡♥①❛♠❡ ♥♦ q✉❡ s❡ r❡❢❡r❡ ❛♦s ❞♦✐s ♠ét♦❞♦s✱ ❛❧é♠ ❞❛ ✐♥❢♦r♠❛çã♦ ❞❡ ♦❞♦♠❡tr✐❛✳ ❈♦♠♦♣♦❞❡ s❡r ♦❜s❡r✈❛❞♦✱ ♦s ❞♦✐s ♠ét♦❞♦s ❛♣r❡s❡♥t❛r❛♠ ✉♠❛ ♣❡q✉❡♥❛ ♠❡❧❤♦r❛ ❝♦♠ r❡❧❛çã♦ à♦❞♦♠❡tr✐❛✳ ❆♣❡s❛r ❞♦s r♦❜ôs ❝♦♠♣❛rt✐❧❤❛r❡♠ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦✱ ❛ ❡str❛té❣✐❛❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❡♠♣r❡❣❛❞❛ ❢❛③ ❝♦♠ q✉❡ ♦s r♦❜ôs s❡❥❛♠ s✉❥❡✐t♦s ❛ ♥í✈❡✐s s❡♠❡❧❤❛♥t❡s❞❡ ❡rr♦ ❡ ✐♥❝❡rt❡③❛✳ ❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❛s ♦❜s❡r✈❛çõ❡s r❡❧❛t✐✈❛s ❝♦♥tr✐❜✉❡♠ ♣♦✉❝♦♣❛r❛ ❛ ♠❡❧❤♦r✐❛ ❞❛ ❡st✐♠❛t✐✈❛ ❛t✉❛❧ ❞❡ ✉♠ r♦❜ô✱ ✉♠❛ ✈❡③ q✉❡ ❛ ❡st✐♠❛t✐✈❛ ❞❡ ✉♠ r♦❜ô ✶✵✽❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s ✉t✐❧✐③❛❞♦ ❝♦♠♦ ♠❛r❝♦ t❛♠❜é♠ ❡stá s✉❥❡✐t❛ à ❞❡❣r❛❞❛çã♦ ❝❛✉s❛❞❛ ♣❡❧❛ ♠♦✈✐♠❡♥t❛çã♦♣❡r♠❛♥❡♥t❡✱ ❛❧é♠ ❞❛ ❛✉sê♥❝✐❛ ❞❡ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛✳1 OdometriaMP E (m)0.5 CI EKF 500 1000 1500 2000 2500Iterações0.30.4 CI EKF Odometria ✭❛✮ MO E (rad)0.10.2 500 1000 1500 2000 2500 Iterações✭❜✮ ❋✐❣✉r❛ ✺✳✷✹✿ ❊✈♦❧✉çã♦ ❞♦ ❡rr♦ ♠é❞✐♦ ❡ ❞❛ ✐♥❝❡rt❡③❛ ♥❛ ❛✉sê♥❝✐❛ ❞❡ ✐♥❢♦r♠❛çõ❡s ❞❡❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛✳ ❆ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ é ❡❢❡t✉❛❞❛ r❡❣✉❧❛r♠❡♥t❡ ♣❡❧♦s r♦❜ôs✳ ✺✳✸ Pr♦✈❛s ❞❡ ❈♦♥❝❡✐t♦ ◆❡st❛ s❡çã♦ sã♦ ❛♣r❡s❡♥t❛❞❛s ♣r♦✈❛s ❞❡ ❝♦♥❝❡✐t♦ ❡❢❡t✉❛❞❛s ❝♦♠ s✐♠✉❧❛❞♦r❡s r♦❜ót✐❝♦s♠❛✐s r❡❛❧íst✐❝♦s ❝♦♠♦✱ t❛♠❜é♠✱ ❡♠ ❡①♣❡r✐♠❡♥t♦s ❝♦♠ r♦❜ôs r❡❛✐s✳ ❖ s✐♠✉❧❛❞♦r ❙t❛❣❡ ✶ ❞❛ ♣❧❛t❛❢♦r♠❛ P❧❛②❡r✴❙t❛❣❡ ❬●❡r❦❡② ❡t ❛❧✳✱ ✷✵✵✸❪ ❢♦✐ ✉t✐❧✐③❛❞♦ ♥❛s s✐♠✉❧❛çõ❡s✳ ❊ss❡ s✐✲ ✷ ♠✉❧❛❞♦r ❢♦✐ ❡♠♣r❡❣❛❞♦ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ♦ ❢r❛♠❡✇♦r❦ ❘♦❜♦t ❖♣❡r❛t✐♥❣ ❙②st❡♠ ✭❘❖❙✮❬◗✉✐❣❧❡② ❡t ❛❧✳✱ ✷✵✵✾❪✱ ❞❡ ♠♦❞♦ ❛ s❡r✈✐r ❝♦♠♦ ❛♠❜✐❡♥t❡ ❡①♣❡r✐♠❡♥t❛❧ ♣❛r❛ ❛ ✐♠♣❧❡♠❡♥✲ t❛çã♦ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ❡♠ r♦❜ôs r❡❛✐s✳ ◆❡st❡s ❡①♣❡r✐♠❡♥t♦s✱ ♠♦❞❡❧♦s ♥ã♦ ❤♦❧♦♥ô♠✐❝♦s❢♦r❛♠ ❡♠♣r❡❣❛❞♦s✱ ❞❡ ♠♦❞♦ q✉❡ ❛ ❧♦❝❛❧✐③❛çã♦ é ❡❢❡t✉❛❞❛ ❝♦♥s✐❞❡r❛♥❞♦ ❛ ♣♦s❡ ❝♦♠♣❧❡t❛❞♦s r♦❜ôs✱ ♦✉ s❡❥❛✱ ❛ ♣♦s✐çã♦ ❡ ❛ ♦r✐❡♥t❛çã♦ ❞♦s ♠❡s♠♦s✳ ✶✷ P❧❛②❡r Pr♦❥❡❝t✳ ❉✐s♣♦♥í✈❡❧ ❡♠✿ ❤tt♣✿✴✴♣❧❛②❡rst❛❣❡✳s♦✉r❝❡❢♦r❣❡✳♥❡t✳ ❆❝❡ss♦✿ ✶✽✴✶✶✴✷✵✶✺✳ ❘♦❜♦t ❖♣❡r❛t✐♥❣ ❙②st❡♠✳ ❉✐s♣♦♥í✈❡❧ ❡♠✿ ❤tt♣✿✴✴✇✇✇✳r♦s✳♦r❣✳ ❆❝❡ss♦✿ ✶✽✴✶✶✴✷✵✶✺✳ ✺✳✸✳ Pr♦✈❛s ❞❡ ❈♦♥❝❡✐t♦✶✵✾ ✺✳✸✳✶ ❙✐♠✉❧❛çõ❡s ❝♦♠ ❘❖❙✴❙t❛❣❡ ❖s ❡①♣❡r✐♠❡♥t♦s ❞❡s❡♥✈♦❧✈✐❞♦s ♥❡st❛ s❡çã♦ tê♠ ♣♦r ♦❜❥❡t✐✈♦ ✈❛❧✐❞❛r ♣❛rt❡ ❞♦s r❡s✉❧✲ t❛❞♦s ♦❜t✐❞♦s ♥❛ s❡çã♦ ❛♥t❡r✐♦r✱ ♥❛ ❢♦r♠❛ ❞❡ ✉♠❛ ♣r♦✈❛ ❞❡ ❝♦♥❝❡✐t♦✳ ❆ ♣❧❛t❛❢♦r♠❛❘❖❙✴❙t❛❣❡ é ✉t✐❧✐③❛❞❛ ❝♦♠♦ ❢❡rr❛♠❡♥t❛ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❡ t❡st❡ ❞♦s ❛❧❣♦r✐t✲♠♦s✱ ❛♥t❡s ❞❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞♦s ♠❡s♠♦s ♥♦s r♦❜ôs r❡❛✐s✳ ❖ ❝♦♥tr♦❧❡ ❞♦s r♦❜ôs é❢❡✐t♦ ❞❡ ♠❛♥❡✐r❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ❝♦♠ ♦ ❢r❛♠❡✇♦r❦ ❘❖❙✳ ❈♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ❢❛❝✐❧✐t❛r ❛ tr❛♥s♣♦s✐çã♦ ❞❡ss❡s ❛❧❣♦r✐t♠♦s ♣❛r❛ ♦s r♦❜ôs✱ ✉♠ ❛♠❜✐❡♥t❡ ❢♦✐ ❞❡✜♥✐❞♦ ♥♦ s✐♠✉❧❛❞♦r❙t❛❣❡ ❝♦♠ ❝❛r❛❝t❡ríst✐❝❛s s❡♠❡❧❤❛♥t❡s àq✉❡❧❛s ❞♦s ❡①♣❡r✐♠❡♥t♦s r❡❛✐s✳ ❆ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❞❡s❝r✐t❛ ♥❛ ❙❡çã♦ ✹✳✷✳✷ ❢♦✐ ✉t✐❧✐③❛❞❛ ♥❡st❡ ❝♦♥❥✉♥t♦❞❡ ❡①♣❡r✐♠❡♥t♦s✱ ❝♦♠ ❛ r❡s♣❡❝t✐✈❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❛s três ❢❛s❡s q✉❡ ❝♦♠♣õ❡♠ ❛ ♠❡s♠❛✿♣♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦ r♦❜ô ❧í❞❡r✱ ❢♦r♠❛çã♦ ✐♥✐❝✐❛❧ ❝♦♠ ❞✐stâ♥❝✐❛s ✐♥t❡r✲r♦❜ôs r❡❣✉❧❛r❡s ❡♠♦✈✐♠❡♥t❛çã♦ ❝♦❡s❛✳ ❖✐t♦ r♦❜ôs ❢♦r❛♠ ✉t✐❧✐③❛❞♦s ♥♦s ❡①♣❡r✐♠❡♥t♦s ❞❡s❡♥✈♦❧✈✐❞♦s ♥❛♣❧❛t❛❢♦r♠❛ ❙t❛❣❡✱ ♣♦r s❡r ❡ss❡ ♦ ♥ú♠❡r♦ ❞❡ r♦❜ôs ❞✐s♣♦♥í✈❡✐s ♣❛r❛ ❡①♣❡r✐♠❡♥t❛çã♦ ♥♦ ✸ ▲❛❜♦r❛tór✐♦ ❞❡ ❱✐sã♦ ❈♦♠♣✉t❛❝✐♦♥❛❧ ❡ ❘♦❜ót✐❝❛ ✭❱❡❘▲❛❜✮✳ ❖s r♦❜ôs s✐♠✉❧❛❞♦s ❢♦r❛♠♠♦❞❡❧❛❞♦s ❝♦♠ ❝❛r❛❝t❡ríst✐❝❛s s❡♠❡❧❤❛♥t❡s àq✉❡❧❛s ❞♦s r♦❜ôs r❡❛✐s✱ s❡♥❞♦ ♦s ♠❡s♠♦s♥ã♦ ❤♦❧♦♥ô♠✐❝♦s✱ ❝♦♠ ❞✐r❡çã♦ ❞✐❢❡r❡♥❝✐❛❧ ❡ 7 cm ❞❡ ❞✐â♠❡tr♦✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ♥❛♠❡t♦❞♦❧♦❣✐❛✱ ✉♠ ❞♦s r♦❜ôs ❢♦✐ ❞❡✜♥✐❞♦ ❝♦♠♦ ❧í❞❡r✱ ❞❡ ♠♦❞♦ ❛ s❡r ♦ r❡s♣♦♥sá✈❡❧ ♣❡❧❛♥❛✈❡❣❛çã♦ ❞♦ ❣r✉♣♦ ❝♦♠ ❜❛s❡ ❡♠ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ✇❛②♣♦✐♥ts✱ ♣r❡✈✐❛♠❡♥t❡ ❡st❛❜❡❧❡❝✐❞♦✳ ❖s r♦❜ôs ❢♦r❛♠ ✐♥✐❝✐❛❧♠❡♥t❡ ❞✐s♣♦st♦s ❡♠ ❞❡t❡r♠✐♥❛❞❛ r❡❣✐ã♦ ❞♦ ❛♠❜✐❡♥t❡✱ ♦ q✉❛❧ ❝♦♥s✐st❡ ❡♠ ✉♠❛ ❛r❡♥❛ ❜✐❞✐♠❡♥s✐♦♥❛❧✱ ❧✐✈r❡ ❞❡ ♦❜stá❝✉❧♦s ❡ ❝♦♠ ❛♣r♦①✐♠❛❞❛♠❡♥t❡22,75 m ✭❋✐❣✉r❛ ✺✳✷✺✮✳ ❖s ❝ír❝✉❧♦s ♣♦♥t✐❧❤❛❞♦s ❡ ♥✉♠❡r❛❞♦s ✐♥❞✐❝❛♠ ♦s ✇❛②♣♦✐♥ts ♣❡❧♦ r♦❜ô ❧í❞❡r ♣❛r❛ ❣✉✐❛r ♦ ❣r✉♣♦✳ ■♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❣❧♦❜❛✐s ❢♦r❛♠ ❞✐s♣♦♥✐❜✐❧✐③❛✲❞❛s ♣❛r❛ t♦❞♦s ♦s r♦❜ôs ❞✉r❛♥t❡ ❛ ♣r✐♠❡✐r❛ ❡t❛♣❛ ❞❛ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦✱ ❞❡♠♦❞♦ q✉❡ ❞✐stâ♥❝✐❛s ✐♥t❡r✲r♦❜ôs ♣✉❞❡ss❡♠ s❡r ❝♦♠♣✉t❛❞❛s✳ ◆❡ss❛ ♣r✐♠❡✐r❛ ❡t❛♣❛✱ ♦s♣❛râ♠❡tr♦s ♣r❡s❡♥t❡s ❡♠ ✭✹✳✷✸✮ ❡ ✭✹✳✷✽✮ ❢♦r❛♠ ❛❥✉st❛❞♦s ❡♠♣✐r✐❝❛♠❡♥t❡ ❞❛ s❡❣✉✐♥t❡ AB AA AB = 0,125 cm = 1,33❢♦r♠❛✿ α = 0,25 ✱ d ❡ d × d ✳ ❖ ♣❛râ♠❡tr♦ d ♣r❡s❡♥t❡ ❡♠ −3✭✺✳✶✹✮ ❢♦✐ ❛❥✉st❛❞♦ ♣❛r❛ 2,63 × 10 ✱ ❡♥q✉❛♥t♦ q✉❡ ❛s ✈❡❧♦❝✐❞❛❞❡s ❧✐♥❡❛r❡s ❡ ❛♥❣✉❧❛r❡s p = 0,40❢♦r❛♠ ❛❥✉st❛❞❛s ❝♦♠ ✉♠ ❣❛♥❤♦ ♣r♦♣♦r❝✐♦♥❛❧ k ✳ ❖ r❛✐♦ ε ❞❛ ár❡❛ s❡♥s♦r✐❛❧ ✭✈✐③✐✲♥❤❛♥ç❛✮ ❢♦✐ ❞❡✜♥✐❞♦ ❞❡ ❢♦r♠❛ q✉❡ t♦❞♦s ♦s r♦❜ôs ♣❛rt✐❝✐♣❛ss❡♠ ❞❡ t♦❞❛s ❛s ✈✐③✐♥❤❛♥ç❛s❡st❛❜❡❧❡❝✐❞❛s✱ ❞❡ ♠♦❞♦ q✉❡ ♦s ♠❡s♠♦s ♣✉❞❡ss❡♠ ♠❡❞✐r ❞✐stâ♥❝✐❛s r❡❧❛t✐✈❛s ❡♥tr❡ s✐✳ ❆ s❡q✉ê♥❝✐❛ ❞❡ ✐♠❛❣❡♥s ❛♣r❡s❡♥t❛❞❛s ♥❛ ❋✐❣✉r❛ ✺✳✷✻ ❛♣r❡s❡♥t❛ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦ r♦❜ô❧í❞❡r ❡♠ ❞✐r❡çã♦ ❛♦ ✐♥t❡r✐♦r ❞♦ ❣r✉♣♦✳ P♦st❡r✐♦r♠❡♥t❡✱ ♥❛ s❡❣✉♥❞❛ ❡t❛♣❛✱ t❡♠✲s❡ s♦♠❡♥t❡ tr♦❝❛ ❞❡ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s✱ AA = d AB = 0,125✉♠❛ ✈❡③ q✉❡ d ❡ ♦ r❛✐♦ ❞❛s ✈✐③✐♥❤❛♥ç❛s ❢♦✐ ❞❡✜♥✐❞♦ ❝♦♠♦ ε =1,33 AB ✸ × d ✳ ❖s ✈❛❧♦r❡s ❞♦s ❞❡♠❛✐s ♣❛râ♠❡tr♦s ❢♦r❛♠ ♠❛♥t✐❞♦s ❝♦♥❢♦r♠❡ ❛ ❡t❛♣❛ ❍♦♠❡ ♣❛❣❡✿ ❤tt♣✿✴✴✇✇✇✳✈❡r❧❛❜✳❞❝❝✳✉❢♠❣✳❜r ✶✶✵❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s ❋✐❣✉r❛ ✺✳✷✺✿ ❆♠❜✐❡♥t❡ ✉t✐❧✐③❛❞♦ ♥❛s s✐♠✉❧❛çõ❡s ❘❖❙✴❙t❛❣❡✳ ❖s ❝ír❝✉❧♦s ♥✉♠❡r❛❞♦s❡ ❝♦♠ ❧✐♥❤❛s ♣♦♥t✐❧❤❛❞❛s ♥❛ ❝♦r ✈❡r❞❡ r❡♣r❡s❡♥t❛♠ ♦s ✇❛②♣♦✐♥ts ❛ s❡r❡♠ ❛❧❝❛♥ç❛❞♦s♣❡❧♦ ❣r✉♣♦✳ ❖ r♦❜ô ❧í❞❡r ❡stá ❞❡st❛❝❛❞♦ ❝♦♠ ❜♦r❞❛ ♥❛ ❝♦r ✈❡r♠❡❧❤❛✱ ❡♥q✉❛♥t♦ q✉❡ ♦s❞❡♠❛✐s ♣♦ss✉❡♠ ❜♦r❞❛s ♣r❡t❛s✳ ✭❛✮ ✭❜✮ ✭❝✮✭❞✮ ✭❡✮ ✭❢✮ ❋✐❣✉r❛ ✺✳✷✻✿ P♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦s r♦❜ôs ♥❛ ❢❛s❡ ✐♥✐❝✐❛❧ ❞♦ ❛❧❣♦r✐t♠♦✳ ❊♠ ✭❛✮ ♦s r♦❜ôs sã♦ ✐♥✐❝✐❛❧♠❡♥t❡ ❞✐s♣♦st♦s ♥♦ ❛♠❜✐❡♥t❡✱ ❡♥q✉❛♥t♦ q✉❡ ❡♠ ✭❢✮ ♦ ❧í❞❡r ✭❜♦r❞❛ ♥❛ ❝♦r✈❡r♠❡❧❤❛✮ ❡♥❝♦♥tr❛✲s❡ ♣♦s✐❝✐♦♥❛❞♦ ♥♦ ✐♥t❡r✐♦r ❞♦ ❣r✉♣♦✳ ❆s ❞❡♠❛✐s ✐♠❛❣❡♥s ❛♣r❡s❡♥t❛♠♠♦♠❡♥t♦s ✐♥t❡r♠❡❞✐ár✐♦s ❞✉r❛♥t❡ ♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦ ❣r✉♣♦✳ ✺✳✸✳ Pr♦✈❛s ❞❡ ❈♦♥❝❡✐t♦✶✶✶ ❛♥t❡r✐♦r✳ ❆s ✐♠❛❣❡♥s ❛♣r❡s❡♥t❛❞❛s ♥❛ ❋✐❣✉r❛ ✺✳✷✼ ♠♦str❛♠ ❛ ♠✉❞❛♥ç❛ ♥❛ ❢♦r♠❛çã♦❞♦ ❣r✉♣♦✱ ❞❡ ♠♦❞♦ q✉❡ s❡ ♣♦❞❡ ♣❡r❝❡❜❡r ♥❛ ❋✐❣✉r❛ ✺✳✷✼❜ ♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦s r♦❜ôs❞❡ ❢♦r♠❛ ❡q✉✐❞✐st❛♥t❡ ❞❡ s❡✉s ✈✐③✐♥❤♦s✳ ✭❛✮ ✭❜✮ ❋✐❣✉r❛ ✺✳✷✼✿ P♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦s r♦❜ôs ✉t✐❧✐③❛♥❞♦ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s✳ ❊♠ ✭❛✮✱ ❛s ❞✐stâ♥✲❝✐❛s ✐♥t❡r✲r♦❜ôs sã♦ ❞✐❢❡r❡♥t❡s ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞♦s ♣❡r❝❡❜❡r❡♠ t♦❞♦s ♦s ❞❡♠❛✐s✳ ❉❡✈✐❞♦à ❧✐♠✐t❛çã♦ ❞♦ ❛❧❝❛♥❝❡ s❡♥s♦r✐❛❧ ❞♦s r♦❜ôs ❡♠ ✭❜✮✱ ♦s ♠❡s♠♦s s♦♠❡♥t❡ sã♦ ✐♥✢✉❡♥❝✐❛❞♦s♣♦r s❡✉s ✈✐③✐♥❤♦s ✐♠❡❞✐❛t♦s ❡✱ ♣♦rt❛♥t♦✱ ♣♦s✐❝✐♦♥❛♠✲s❡ ❡q✉✐❞✐st❛♥t❡s ✉♥s ❞♦s ♦✉tr♦s✳ ◆❛ ú❧t✐♠❛ ❡t❛♣❛ ❞♦ ❛❧❣♦r✐t♠♦✱ ♦ r♦❜ô ❧í❞❡r ❣✉✐❛ ♦ ❣r✉♣♦ ❡♠ ❞✐r❡çã♦ ❛♦s ✇❛②✲♣♦✐♥ts ❡st❛❜❡❧❡❝✐❞♦s✳ ❖ ♣❛râ♠❡tr♦ β ♣r❡s❡♥t❡ ❡♠ ✭✹✳✸✷✮ ❢♦✐ ❛❥✉st❛❞♦ ♣❛r❛ 0,35 ❡ ♦s❞❡♠❛✐s ♣❛râ♠❡tr♦s ♠❛♥t✐✈❡r❛♠ ♦s ✈❛❧♦r❡s ❡st❛❜❡❧❡❝✐❞♦s ♥❛ ❡t❛♣❛ ❛♥t❡r✐♦r✳ ❖ ❣❛♥❤♦♣r♦♣♦r❝✐♦♥❛❧ ❞❡ ❛❥✉st❡ ❞❛s ✈❡❧♦❝✐❞❛❞❡s ❧✐♥❡❛r ❡ ❛♥❣✉❧❛r ❢♦✐ ❞❡✜♥✐❞♦ ❝♦♠♦ 0,8 ✳ ◆❡st❡s❡①♣❡r✐♠❡♥t♦s✱ ♦ ♣❛râ♠❡tr♦ γ ♣ô❞❡ s❡r ❞❡s❝❛rt❛❞♦✱ ♦✉ s❡❥❛✱ ♦ ♠❡s♠♦ ❢♦✐ ❞❡✜♥✐❞♦ ❝♦♠♦γ = 0 ✳ ❆ ❋✐❣✉r❛ ✺✳✷✽ ❛♣r❡s❡♥t❛ ❛❧❣✉♠❛s ❝♦♥✜❣✉r❛çõ❡s ❞♦ ❣r✉♣♦ ❞❡ r♦❜ôs ❞✉r❛♥t❡ ❛♠♦✈✐♠❡♥t❛çã♦ ♣❡❧♦ ❛♠❜✐❡♥t❡✳ P♦❞❡✲s❡ ♣❡r❝❡❜❡r q✉❡ ❛ ❢♦r♠❛çã♦ ❡st❛❜❡❧❡❝✐❞❛ ♥❛ ❡t❛♣❛❛♥t❡r✐♦r ❢♦✐ ♠❛♥t✐❞❛ ❞✉r❛♥t❡ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦ ❣r✉♣♦✳ ◆❡st❡s ❡①♣❡r✐♠❡♥t♦s✱ s♦♠❡♥t❡ ❛ ❛❜♦r❞❛❣❡♠ r❡❢❡r❡♥t❡ ❛♦ ❛❧❣♦r✐t♠♦ ❈■ ❢♦✐ ✐♠♣❧❡✲♠❡♥t❛❞❛✳ ❆ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❢♦✐ ❡♠♣r❡❣❛❞❛ ❛♣ós ♦ ❣r✉♣♦ ❡♥tr❛r ❡♠ ♠♦✈✐♠❡♥t♦✱♦✉ s❡❥❛✱ ♥❛ t❡r❝❡✐r❛ ❡t❛♣❛ ❞♦ ❛❧❣♦r✐t♠♦✳ ❖ ❡rr♦ r❡❢❡r❡♥t❡ à ♦❞♦♠❡tr✐❛ ❢♦✐ ❝♦♥✜❣✉r❛❞♦ ♥♦ ◦ s✐♠✉❧❛❞♦r ❞❡ ♠❛♥❡✐r❛ ♣r♦♣♦r❝✐♦♥❛❧✱ s❡♥❞♦ ❞❡ 10% ♣❛r❛ ❛ ✈❡❧♦❝✐❞❛❞❡ ❧✐♥❡❛r ❡ 5 ✭8.73%✮♣❛r❛ ❛ ✈❡❧♦❝✐❞❛❞❡ ❛♥❣✉❧❛r✳ ■♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛ ❢♦r❛♠ ❞✐s♣♦♥✐❜✐❧✐③❛❞❛s♣❛r❛ ♦ r♦❜ô ❧í❞❡r ❛ ❝❛❞❛ 1 s✱ ❛s q✉❛✐s ❢♦r❛♠ ✉t✐❧✐③❛❞❛s ♣♦r ✉♠ ❊❑❋ ♣❛r❛ ❛t✉❛❧✐③❛r ❛❝r❡♥ç❛ ❞♦ r♦❜ô✱ ❝♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ♥❛ ♠❡t♦❞♦❧♦❣✐❛✳ ❖s ❞❡s✈✐♦s ♣❛❞rã♦ ❞♦ ❡rr♦ ❞❡ ❧♦❝❛❧✐✲③❛çã♦ ❛❜s♦❧✉t❛ r❡❢❡r❡♥t❡s às ❞✐r❡çõ❡s x ❡ y ❢♦r❛♠ ❞❡✜♥✐❞♦s ❝♦♠♦ 1 mm✱ ❡♥q✉❛♥t♦ q✉❡ ♦❞❡s✈✐♦ ♣❛❞rã♦ ❞♦ ❡rr♦ r❡❧❛t✐✈♦ à ♦r✐❡♥t❛çã♦ ❢♦✐ ❞❡✜♥✐❞♦ ❝♦♠♦ 0,002 rad. ❆♣ós ❛ ❛t✉❛❧✐✲③❛çã♦ ❞❡ s✉❛ ❝r❡♥ç❛✱ ♦ r♦❜ô ❧í❞❡r ♠❡❞❡ ❞✐stâ♥❝✐❛ ❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛s ♣❛r❛ ❝❛❞❛ ✉♠ ❞❡ ✶✶✷❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s ✭❛✮ ✭❜✮ ✭❝✮✭❞✮ ✭❡✮ ✭❢✮ ✭❣✮ ✭❤✮ ✭✐✮ ❋✐❣✉r❛ ✺✳✷✽✿ ▼♦✈✐♠❡♥t❛çã♦ ❞♦s r♦❜ôs ♥♦ ❛♠❜✐❡♥t❡✱ ❣✉✐❛❞♦s ♣❡❧♦ r♦❜ô ❧í❞❡r ✭❜♦r❞❛ ♥❛❝♦r ✈❡r♠❡❧❤❛✮✳ ❉✉r❛♥t❡ ❛ ♠♦✈✐♠❡♥t❛çã♦✱ ♦s r♦❜ôs s❡ ♠❛♥té♠ ❡q✉✐❞✐st❛♥t❡s ❞❡ s❡✉s✈✐③✐♥❤♦s ❡ ✉t✐❧✐③❛♠ s♦♠❡♥t❡ ❡ss❡s ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ s❡✉s ✈✐③✐♥❤♦s ❡ tr❛♥s♠✐t❡ ✭❜r♦❛❞❝❛st✮ t❛✐s ✐♥❢♦r♠❛çõ❡s✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ s✉❛ ❡st✐♠❛t✐✈❛✱❞❡ ♠♦❞♦ ❛ ♣❡r♠✐t✐r q✉❡ s❡✉s ✈✐③✐♥❤♦s ♣♦ss❛♠ ❛t✉❛❧✐③❛r s✉❛s r❡s♣❡❝t✐✈❛s ❝r❡♥ç❛s✳ ❖❡rr♦ r❡❢❡r❡♥t❡ às ♠❡❞✐❞❛s r❡❧❛t✐✈❛s ❢♦✐ ❞❡✜♥✐❞♦ ❞❡ ♠♦❞♦ ♣r♦♣♦r❝✐♦♥❛❧ às ♠❡❞✐❞❛s r❡❛✐s✱ s❡♥❞♦ ❝♦♥✜❣✉r❛❞♦ ❝♦♠♦ 0,5 % ❞❛s ♠❡❞✐❞❛s ❞❡ ❞✐stâ♥❝✐❛ r❡❧❛t✐✈❛ ❡ 0,87 % ❞❛s ♠❡❞✐❞❛s❞❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛✳ ❉❡ ♠❛♥❡✐r❛ s❡♠❡❧❤❛♥t❡ ❛♦ q✉❡ ❢♦✐ ❞❡s❝r✐t♦ ♣❛r❛ ♦ r♦❜ô ❧í❞❡r✱ ♦s ❞❡♠❛✐s r♦❜ôs✱❛♦ r❡❝❡❜❡r❡♠ ✉♠❛ ✐♥❢♦r♠❛çã♦ ❡ ❛❥✉st❛r❡♠ s✉❛s ❝r❡♥ç❛s✱ ♠❡❞❡♠ ❞✐stâ♥❝✐❛ ❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛s ♣❛r❛ s❡✉s ✈✐③✐♥❤♦s ❡ ❡♥✈✐❛♠ ✭❜r♦❛❞❝❛st✮ t❛✐s ✐♥❢♦r♠❛çõ❡s ♣❛r❛ q✉❡ ♦s ♠❡s♠♦s♣♦ss❛♠ t❛♠❜é♠ ❛t✉❛❧✐③❛r s✉❛s ❝r❡♥ç❛s✳ ❉❡ss❛ ❢♦r♠❛✱ ❡st❛❜❡❧❡❝❡✲s❡ ✉♠❛ ❞✐ss❡♠✐♥❛✲çã♦ ❞❡ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛ ♣❛rt✐r ❞♦ r♦❜ô ❧í❞❡r ❛té ♦s r♦❜ôs ♣♦s✐❝✐♦♥❛❞♦s ♥❛ ✺✳✸✳ Pr♦✈❛s ❞❡ ❈♦♥❝❡✐t♦✶✶✸ ❢r♦♥t❡✐r❛ ❞♦ ❣r✉♣♦✳❆ ❋✐❣✉r❛ ✺✳✷✾ ❛♣r❡s❡♥t❛ ♦ ❝❛♠✐♥❤♦ ♣❡r❝♦rr✐❞♦ ♣❡❧♦ r♦❜ô ❧í❞❡r ❡ ♣❡❧♦s ❞❡♠❛✐s r♦❜ôs ✭❣r♦✉♥❞ tr✉t❤✱ ✐●P❙✮✳ ❆❧é♠ ❞✐ss♦✱ ✐♥❢♦r♠❛çõ❡s ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ r❡❢❡r❡♥t❡s às ❡st✐♠❛t✐✈❛s ❞❡ ♣♦s✐çã♦ ❣❡r❛❞❛s ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❈■ ♥❛s ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ sã♦ ❛♣r❡s❡♥t❛❞❛s✱ ❝♦♠♦ t❛♠❜é♠ ❛ ✐♥❢♦r♠❛çã♦ ❞❛ ♦❞♦♠❡tr✐❛✳ ◆❛ ✜❣✉r❛ r❡❢❡r❡♥t❡ ❛♦r♦❜ô ❧í❞❡r✱ ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛♣r❡s❡♥t❛❞❛ ✭❧✐♥❤❛ ♥❛ ❝♦r ♠❛❣❡♥t❛✮ ❝♦♠♣r❡❡♥❞❡♦ r❡s✉❧t❛❞♦ ❞❛ ❢✉sã♦ s❡♥s♦r✐❛❧ ❡❢❡t✉❛❞❛ ♣❡❧♦ ❊❑❋ ❛♦ ❝♦♠❜✐♥❛r ❛ ❡st✐♠❛t✐✈❛ ❣❡r❛❞❛ ♣❡❧❛♦❞♦♠❡tr✐❛ ❡ ❛ ❞✐s♣♦♥✐❜✐❧✐③❛❞❛ ♣❡❧♦ s❡♥s♦r ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❛❜s♦❧✉t♦✱ ❊❑❋ ✭❆❜s✮✳ − . 8 − . 6 − . 4 − .2 . .2 .4 .6 .. 8 −. 8 −. 6 −. 4 −. 2 .2 .4 .6 .(m 8 y ) L´ıder Ground truth Odometria EKF (Abs) − . 8 − . 6 − . 4 − .2 . .2 .4 .6 .. 8 −. 8 −. 6 −. 4 −. 2 .2 .4 .6 .8 Rob ˆo 1 Ground truth Odometria Algoritmo CI − . 8 − . 6 − . 4 − . 2 . . 2 . 4 . 6 . 8 − . 8 − . 6 − . 4 − . 2 . . 2 . 4 . 6 . 8 Rob ˆo 2 Ground truth Odometria Algoritmo CI − . 8 − . 6 − . 4 − . 2 . . 2 . 4 . 6 . 8 − . 8 − . 6 − . 4 − . 2 . . 2 . 4 . 6 . 8 Rob ˆo 3 Ground truth Odometria Algoritmo CI− . 8 − . 6 − . 4 − .2 . .2 .4 .6 .− . 8 x (m)8 − .6 − .4 − .. 2 .2 .4 .6 .(m 8 y ) Rob ˆo 4 Ground truth Odometria Algoritmo CI − . 8 − . 6 − . 4 − .2 . .2 .4 .6 .− . 8 x (m)8 − .6 − .4 − .. 2 .2 .4 .6 .8 Rob ˆo 5 Ground truth Odometria Algoritmo CI − . 8 − . 6 − . 4 − . 2 . . 2 . 4 . 6 . 8 x (m) − . 8 − . 6 − . 4 − . 2 . . 2 . 4 . 6 . 8 Rob ˆo 6 Ground truth Odometria Algoritmo CI − . 8 − . 6 − . 4 − . 2 . . 2 . 4 . 6 . 8 x (m) − . 8 − . 6 − . 4 − . 2 . . 2 . 4 . 6 . 8 Rob ˆo 7 Ground truth Odometria Algoritmo CI ❋✐❣✉r❛ ✺✳✷✾✿ ❈❛♠✐♥❤♦ ♣❡r❝♦rr✐❞♦ ✭●r♦✉♥❞ tr✉t❤✮✱ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛✲ t✐✈❛ ❣❡r❛❞❛s ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❈■ ❡ ♦❞♦♠❡tr✐❛ ❞♦s r♦❜ôs ❞♦ ❣r✉♣♦✳◆❡st❡s ❡①♣❡r✐♠❡♥t♦s✱ ♦ ❛❥✉st❡ ❞❛s ❝r❡♥ç❛s ❞♦s r♦❜ôs ♣♦❞❡ s❡r ❡❢❡t✉❛❞♦ ❝♦♠ ❜❛s❡ ❡♠ ♠❛✐s ❞❡ ✉♠❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ r❡❝❡❜✐❞❛✳ ❆ss✐♠✱ ❛♦ r❡❝❡❜❡r ✉♠❛ ♠❡♥s❛❣❡♠❞❡ ✉♠ ❞❡ s❡✉s ✈✐③✐♥❤♦s ❝♦♠ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦✱ ✉♠ r♦❜ô t❡♥t❛ ❡st✐♠❛r ❞✐stâ♥❝✐❛❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛s ♣❛r❛ ❡ss❡✱ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ♦❜t❡r ✐♥❢♦r♠❛çõ❡s s✉✜❝✐❡♥t❡s ♣❛r❛ ♦❛❥✉st❡ ❞❡ s✉❛ ❝r❡♥ç❛✳ ❈❛s♦ ❝♦♥s✐❣❛ ❡st✐♠❛r t❛✐s ♠❡❞✐❞❛s✱ ♦ r♦❜ô ✉t✐❧✐③❛ ❛s ✐♥❢♦r♠❛çõ❡s❞✐s♣♦♥í✈❡✐s ♣❛r❛ ❡❢❡t✉❛r ✉♠❛ ❡t❛♣❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ P❛r❛ ❡✈✐t❛r q✉❡ ✉♠ ♥ú♠❡r♦ ❡①❝❡ss✐✈♦ ❞❡ ♠❡♥s❛❣❡♥s ❢♦ss❡♠ r❡❡♥✈✐❛❞❛s ♣❡❧♦s r♦❜ôs❛♦ ❛t✉❛❧✐③❛r❡♠ s✉❛s ❝r❡♥ç❛s✱ ✉♠❛ ❡str❛té❣✐❛ ❢♦✐ ✐♠♣❧❡♠❡♥t❛❞❛ ❝♦♠ ❜❛s❡ ♥♦ ♥ú♠❡r♦ ❞❡❤♦♣s ❛♦ q✉❛❧ ✉♠❛ ♠❡♥s❛❣❡♠ é r❡tr❛♥s♠✐t✐❞❛✳ ❙❡♥❞♦ ♦ r♦❜ô ❧í❞❡r r❡s♣♦♥sá✈❡❧ ♣♦r ✐♥❞✐❝❛r♦ ♠♦♠❡♥t♦ ❞❡ s❡ ❢❛③❡r ❛t✉❛❧✐③❛çõ❡s ❞❛s ❝r❡♥ç❛s✱ ♦ ♠❡s♠♦ ❢♦✐ ❞❡✜♥✐❞♦ ❝♦♠♦ ♦r✐❣❡♠ ❞♦ s✐st❡♠❛ ❞❡ tr❛♥s♠✐ssã♦✳ ❉❡ss❡ ♠♦❞♦✱ ❛s ♠❡♥s❛❣❡♥s ❡♥✈✐❛❞❛s ♣❡❧♦ ❧í❞❡r ♣♦ss✉❡♠ ✉♠✐❞❡♥t✐✜❝❛❞♦r ❞❡ ❤♦♣ ✐❣✉❛❧ ❛ 1✳ ❈♦♥s✐❞❡r❛♥❞♦ ♦ t❛♠❛♥❤♦ ❞♦ ❣r✉♣♦✱ ❝❛❞❛ r♦❜ô✱ ❛♦ r❡❝❡❜❡r ✶✶✹❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s ✉♠❛ ♠❡♥s❛❣❡♠✱ ✈❡r✐✜❝❛ s❡ ♦ ✐❞❡♥t✐✜❝❛❞♦r ❞♦ ❤♦♣ é ✐♥❢❡r✐♦r ❛ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ✈❛❧♦r✱♥❡st❡ ❝❛s♦ 3✳ ❈❛s♦ s❡❥❛✱ ❛ ♠❡♥s❛❣❡♠ é ✉t✐❧✐③❛❞❛ ♣❛r❛ ❛t✉❛❧✐③❛çã♦ ❞❡ s✉❛ ❝r❡♥ç❛❀ ❝❛s♦❝♦♥trár✐♦ ❛ ♠❡♥s❛❣❡♠ é ❞❡s❝❛rt❛❞❛✳ ❆ss✐♠✱ ❛♣ós ❛t✉❛❧✐③❛çã♦ ❞❡ s✉❛ ❝r❡♥ç❛✱ ✉♠ r♦❜ô tr❛♥s♠✐t❡ ♠❡♥s❛❣❡♥s ❝♦♠ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ✉t✐❧✐③❛♥❞♦ ✉♠ ✐❞❡♥t✐✜❝❛❞♦r ❞❡❤♦♣ q✉❡ é ❝❛❧❝✉❧❛❞♦ ❛♦ ✐♥❝r❡♠❡♥t❛r ✉♠❛ ✉♥✐❞❛❞❡ ❛♦ ✈❛❧♦r ❞♦ ✐❞❡♥t✐✜❝❛❞♦r ❛ss♦❝✐❛❞♦ à♠❡♥s❛❣❡♠ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❛t✉❛❧✐③❛çã♦ ❞❛ ❝r❡♥ç❛✳ ❖ ❡rr♦ ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❞❡ ❝❛❞❛ r♦❜ô é ❛♣r❡s❡♥t❛❞♦ ♥❛ ❋✐❣✉r❛ ✺✳✸✵❛✳ P♦❞❡✲s❡♦❜s❡r✈❛r q✉❡ ❡♥q✉❛♥t♦ ♦ ❡rr♦ r❡❢❡r❡♥t❡ à ♦❞♦♠❡tr✐❛ ❝r❡s❝❡ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡✱ ♦ ♠ét♦❞♦❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❝♦♥s❡❣✉❡ ♠❛♥t❡r ✉♠ ❜❛✐①♦ ♥í✈❡❧ ❞❡ ❡rr♦ ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦✳❆ ✐♥❝❡rt❡③❛ ✭1 ❞❡s✈✐♦ ♣❛❞rã♦✮ ❞❡ss❡ ❡rr♦ é ❛♣r❡s❡♥t❛❞❛ ♥❛ ❋✐❣✉r❛ ✺✳✸✵❜✳ ❉❡ ♠❛♥❡✐r❛ s❡♠❡❧❤❛♥t❡✱ ♦ ❡rr♦ ❞❡ ♦r✐❡♥t❛çã♦ ✭♠❡❞✐❞♦ ❡♠ r❛❞✐❛♥♦s✮ r❡❢❡r❡♥t❡ ❛❝❛❞❛ r♦❜ô é ❛♣r❡s❡♥t❛❞♦ ♥❛ ❋✐❣✉r❛ ✺✳✸✶❛ ❡ ❛ ✐♥❝❡rt❡③❛ ❛ss♦❝✐❛❞❛✱ 1 ❞❡s✈✐♦ ♣❛❞rã♦✱ é❛♣r❡s❡♥t❛❞❛ ♥❛ ❋✐❣✉r❛ ✺✳✸✶❜✳ ❖s ♠♦♠❡♥t♦s ❡♠ q✉❡ ❛ t❛①❛ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❞♦ ❡rr♦ é♠❛✐s ❛❝❡♥t✉❛❞❛ ❞✐③ r❡s♣❡✐t♦ às ❝✉r✈❛s ❡①❡❝✉t❛❞❛s ♣❡❧♦ ❣r✉♣♦ ❞✉r❛♥t❡ ❛ ♠♦✈✐♠❡♥t❛çã♦✳ ✺✳✸✳✷ ❊①♣❡r✐♠❡♥t♦s ❝♦♠ ❘♦❜ôs ❘❡❛✐s ◆❡st❡s ❡①♣❡r✐♠❡♥t♦s✱ r♦❜ôs ❡✲♣✉❝❦ ✭❋✐❣✉r❛ ✺✳✸✷✮ ❢♦r❛♠ ❡♠♣r❡❣❛❞♦s ❡♠ ✉♠ ❛♠❜✐❡♥t❡♣r❡♣❛r❛❞♦ ♣❛r❛ ❡①♣❡r✐♠❡♥t❛çã♦ ❝♦♠ ❡♥①❛♠❡s ❞❡ r♦❜ôs ♥♦ ❱❊❘▲❛❜ ❬●❛r❝✐❛ ✫ ❈❤❛✐✲♠♦✇✐❝③✱ ✷✵✵✾❪✳ ❯♠❛ ❛r❡♥❛ ❞❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ 1,85 m × 1,50 m ❢♦✐ ✉t✐❧✐③❛❞❛✳ ❯♠❛❝â♠❡r❛ ❞✐s♣♦st❛ s♦❜r❡ ❛ ♠❡s♠❛ ❡ ❛ ✉t✐❧✐③❛çã♦ ❞❛ ❜✐❜❧✐♦t❡❝❛ ❆❘❚♦♦❧❦✐tP❧✉s ❡st❛❜❡❧❡✲❝❡r❛♠ ✉♠ s✐st❡♠❛ ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ✭✐●P❙✮✳ ❚❛❧ s✐st❡♠❛ ❞✐s♣♦♥✐❜✐❧✐③❛ ✐♥❢♦r♠❛çõ❡s❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❣❧♦❜❛❧ ❞♦s ♠❛r❝♦s ✜❞✉❝✐❛✐s✱ ❝♦❧♦❝❛❞♦s s♦❜r❡ ♦s r♦❜ôs✳ ❉❡ss❛ ❢♦r♠❛✱ t❛✐s ♠❛r❝♦s ♣♦ss✐❜✐❧✐t❛♠ q✉❡ ♦ s✐st❡♠❛ ✐❞❡♥t✐✜q✉❡ ❡ ❞✐s♣♦♥✐❜✐❧✐③❡ ❛ ♣♦s❡ ❝♦♠♣❧❡t❛ ❞❡❝❛❞❛ r♦❜ô ♥♦ ❛♠❜✐❡♥t❡✳ ❖ ❢r❛♠❡✇♦r❦ ❘❖❙ ❢♦✐ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❝♦♥tr♦❧❛r ♦s r♦❜ôs ❞❡ ♠❛♥❡✐r❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛✈✐❛ ❝♦♠✉♥✐❝❛çã♦ ❜❧✉❡t♦♦t❤✳ ❖ ❣r♦✉♥❞ tr✉t❤ r❡❢❡r❡♥t❡ ❛♦ ❝❛♠✐♥❤♦ ♣❡r❝♦rr✐❞♦ ♣♦r ❝❛❞❛ r♦❜ô é ♣r♦✈✐❞♦ ♣❡❧♦ ✐●P❙✳ ❆ ❋✐❣✉r❛ ✺✳✸✸ ❛♣r❡s❡♥t❛ ✉♠ ❡①❡♠♣❧♦ ❞❛ ❧♦❝❛❧✐③❛çã♦ ♣r♦✈✐❞❛♣❡❧♦ s✐st❡♠❛ ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦✳ ❉❡✈✐❞♦ à ❧✐♠✐t❛çã♦ ❞♦s s❡♥s♦r❡s ❡①✐st❡♥t❡s ♥♦s r♦❜ôs✉t✐❧✐③❛❞♦s✱ t❛❧ s✐st❡♠❛ ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❢♦✐ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❡st❛❜❡❧❡❝❡r ❛s ✈✐③✐♥❤❛♥ç❛s❞❡s❝r✐t❛s ♥❛ ❙❡çã♦ ✷✳ ❆ss✐♠ s❡♥❞♦✱ ✉♠❛ ár❡❛ s❡♥s♦r✐❛❧ ❝✐r❝✉❧❛r ❢♦✐ ❞❡✜♥✐❞❛✱ ❝✉❥♦ ❝❡♥tr♦é ❡st❛❜❡❧❡❝✐❞♦ ♥❛ ♣♦s✐çã♦ ❝❡♥tr❛❧ ❞♦ ♠❛r❝♦ ✜❞✉❝✐❛❧ ✐♥st❛❧❛❞♦ s♦❜r❡ ✉♠ r♦❜ô✳ ❖ r❛✐♦ ε❞❡ss❛ ár❡❛ é ❛❥✉st❛❞♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❡t❛♣❛ ❞❛ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛ s❡♥❞♦ ❡①❡❝✉t❛❞❛ ♣❡❧♦ ❣r✉♣♦✳ ❆❧é♠ ❞✐ss♦✱ ❛s ✐♥❢♦r♠❛çõ❡s ♣r♦✈✐❞❛s ♣❡❧♦ ✐●P❙ ❢♦r❛♠✉t✐❧✐③❛❞❛s ♣❛r❛ ❡st✐♠❛r ♠❡❞✐❞❛s ❞❡ ❞✐stâ♥❝✐❛ ❡ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛s✱ ❛s q✉❛✐s ❢♦r❛♠❜❛s❡❛❞❛s ♥❛s ♠❡❞✐❞❛s r❡❛✐s ♦❜t✐❞❛s✱ ✐♥❝♦r♣♦r❛❞❛s ❞❡ ✉♠ r✉í❞♦ ❛❞✐t✐✈♦ ●❛✉ss✐❛♥♦✱ ❡♠❝♦♥s♦♥â♥❝✐❛ ❝♦♠ ♦ q✉❡ ❡st❛❜❡❧❡❝✐❞♦ ♥♦ ❈❛♣ít✉❧♦ ✹✳ ✺✳✸✳ Pr♦✈❛s ❞❡ ❈♦♥❝❡✐t♦✶✶✺ . 50 100 150 200 250 300 350 40000 .05 .10 .15 .20 .25 .30 .35 .(m 40 E rr o ) L´ıder Odometria EKF (Abs) 50 100 150 200 250 300 350 400 .00 .05 .10 .15 .20 .25 .30 .35 .40 Rob ˆo 1 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 . 00 . 05 . 10 . 15 . 20 . 25 . 30 . 35 . 40 Rob ˆo 2 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 . 00 . 05 . 10 . 15 . 20 . 25 . 30 . 35 . 40 Rob ˆo 3 Odometria Algoritmo CI 50 100 150 200 250 300 350 400. iterac¸ ˜oes00 .05 .10 .15 .20 .25 .30 .35 .(m 40 E rr o ) Rob ˆo 4 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 iterac¸ ˜oes .00 .05 .10 .15 .20 .25 .30 .35 .40 Rob ˆo 5 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 iterac¸ ˜oes . 00 . 05 . 10 . 15 . 20 . 25 . 30 . 35 . 40 Rob ˆo 6 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 iterac¸ ˜oes . 00 . 05 . 10 . 15 . 20 . 25 . 30 . 35 . 40 Rob ˆo 7 Odometria Algoritmo CI✭❛✮ 0.000 50 100 150 200 250 300 350 400 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 Incerteza (m) Líder Odometria EKF (Abs) 50 100 150 200 250 300 350 400 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 Robô 1 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 Robô 2 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 Robô 3 Odometria Algoritmo CI 50 100 150 200 250 300 350 4000.000 iterações 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 Incerteza (m) Robô 4 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 iterações 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 Robô 5 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 iterações 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 Robô 6 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 iterações 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 Robô 7 Odometria Algoritmo CI✭❜✮ ❋✐❣✉r❛ ✺✳✸✵✿ ✭❛✮ ❊rr♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❡ ✭❜✮ ✐♥❝❡rt❡③❛✱ 1 ❞❡s✈✐♦ ♣❛❞rã♦✱ r❡❢❡r❡♥t❡s à♣♦s✐çã♦ ❞❡ ❝❛❞❛ r♦❜ô✳ ✶✶✻❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s . 50 100 150 200 250 300 350 400 .1 .2 .3 .4 .(r 5 E rr o a d ) L´ıder Odometria EKF (Abs) 50 100 150 200 250 300 350 400 . .1 .2 .3 .4 .5 .6 Rob ˆo 1 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 . . 1 . 2 . 3 . 4 . 5 Rob ˆo 2 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 . . 1 . 2 . 3 . 4 . 5 Rob ˆo 3 Odometria Algoritmo CI 50 100 150 200 250 300 350 400. iterac¸ ˜oes .1 .2 .3 .4 .5 .(r 6 E rr o a d ) Rob ˆo 4 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 iterac¸ ˜oes . .1 .2 .3 .4 .5 Rob ˆo 5 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 iterac¸ ˜oes . . 1 . 2 . 3 . 4 . 5 . 6 Rob ˆo 6 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 iterac¸ ˜oes . . 1 . 2 . 3 . 4 . 5 Rob ˆo 7 Odometria Algoritmo CI✭❛✮ . 50 100 150 200 250 300 350 40000 .01 .02 .03 .04 .05 .(r 06 In ce rt e za a d ) L´ıder Odometria EKF (Abs) 50 100 150 200 250 300 350 400 .00 .01 .02 .03 .04 .05 .06 Rob ˆo 1 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 . 00 . 01 . 02 . 03 . 04 . 05 . 06 Rob ˆo 2 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 . 00 . 01 . 02 . 03 . 04 . 05 . 06 Rob ˆo 3 Odometria Algoritmo CI 50 100 150 200 250 300 350 400. iterac¸ ˜oes00 .01 .02 .03 .04 .05 .(r 06 In ce rt e za a d ) Rob ˆo 4 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 iterac¸ ˜oes .00 .01 .02 .03 .04 .05 .06 Rob ˆo 5 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 iterac¸ ˜oes . 00 . 01 . 02 . 03 . 04 . 05 . 06 Rob ˆo 6 Odometria Algoritmo CI 50 100 150 200 250 300 350 400 iterac¸ ˜oes . 00 . 01 . 02 . 03 . 04 . 05 . 06 Rob ˆo 7 Odometria Algoritmo CI✭❜✮ ❋✐❣✉r❛ ✺✳✸✶✿ ❊♠ ✭❛✮✱ t❡♠✲s❡ ♦ ❡rr♦ r❡❢❡r❡♥t❡ à ♦r✐❡♥t❛çã♦✱ ❡♥q✉❛♥t♦ q✉❡ ❡♠ ✭❜✮ é♠♦str❛❞❛ ❛ r❡s♣❡❝t✐✈❛ ✐♥❝❡rt❡③❛ ✱ 1 ❞❡s✈✐♦ ♣❛❞rã♦✳ ✺✳✸✳ Pr♦✈❛s ❞❡ ❈♦♥❝❡✐t♦✶✶✼ ❋✐❣✉r❛ ✺✳✸✷✿ ❘♦❜ôs ❡✲♣✉❝❦ ❬▼♦♥❞❛❞❛ ❡t ❛❧✳✱ ✷✵✵✾❪ ✉t✐❧✐③❛❞♦s ♥♦s ❡①♣❡r✐♠❡♥t♦s ❡ ♦s♠❛r❝♦s ✜❞✉❝✐❛✐s ✉t✐❧✐③❛❞♦s ♣❡❧♦ ✐●P❙✳ Ground truth 0.4 Odometria 0.2 0.0y (m) −0.2 −0.4−0.6 −0.4 −0.2 0.0 0.2 0.4 0.6x (m) ❋✐❣✉r❛ ✺✳✸✸✿ ❊①❡♠♣❧♦ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞✐s♣♦♥✐❜✐❧✐③❛❞❛ ♣❡❧♦ ✐●P❙ ✭●r♦✉♥❞ tr✉t❤✮ ❡ ❞❛♦❞♦♠❡tr✐❛ r❡❢❡r❡♥t❡s ❛♦ ❝❛♠✐♥❤♦ ❡①❡❝✉t❛❞♦ ♣♦r ✉♠ r♦❜ô✳ ❆ ✐♥❢♦r♠❛çã♦ ❞❡ ♦❞♦♠❡tr✐❛ ❣❡r❛❞❛ ♣❡❧♦ r♦❜ô ❡✲♣✉❝❦ ❢♦✐ ✐♠♣❧❡♠❡♥t❛❞❛ ❝♦♠ ❜❛s❡♥♦ ♠♦❞❡❧♦ ❞❡ ✉♠ r♦❜ô ❞✐❢❡r❡♥❝✐❛❧ ❞❡s❝r✐t♦ ❡♠ ❬❙✐❡❣✇❛rt ✫ ◆♦✉r❜❛❦❤s❤✱ ✷✵✵✹✱ ♣✳✶✽✻❪✱❝♦♥❢♦r♠❡ s❡❣✉❡✿ x =f (x, y, θ, ∆s r , ∆s l ) k ✭✺✳✶✼✮      k+1|k k k ∆θ x x ∆s + ) ❝♦s(θ 2 k k+1|k   k   k ∆θ  y y ∆s ) ✭✺✳✶✽✮ s✐♥(θ θ θ ∆θ v = ∆s✭✺✳✶✾✮ ✶✶✽❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s ∆s + ∆s r l= , 2 w = ∆θ✭✺✳✷✵✮ ∆s r l− ∆s = , bs❡♥❞♦✿ r l ❼ ∆s ❡ ∆s ❛s ❞✐stâ♥❝✐❛s ♣❡r❝♦rr✐❞❛s ♣❡❧❛s r♦❞❛s ❞✐r❡✐t❛ ❡ ❡sq✉❡r❞❛✱ r❡s♣❡❝t✐✈❛✲♠❡♥t❡✱ ♥♦ ú❧t✐♠♦ ✐♥t❡r✈❛❧♦ ❛♠♦str❛❧❀ ❼ ∆θ ❛ ✈❛r✐❛çã♦ ♥❛ ♦r✐❡♥t❛çã♦ ♦❝♦rr✐❞❛ ♥♦ ú❧t✐♠♦ ✐♥t❡r✈❛❧♦ ❛♠♦str❛❧❀❼ b ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❛s ❞✉❛s r♦❞❛s ❞♦ r♦❜ô ❝♦♠ ❞✐r❡çã♦ ❞✐❢❡r❡♥❝✐❛❧✳ ❆ ✐♥❝❡rt❡③❛ ❛ss♦❝✐❛❞❛ ❛ ❡st❡ ♠♦❞❡❧♦ é ❝❛❧❝✉❧❛❞❛ ❝♦♥s✐❞❡r❛♥❞♦ q✉❡ ♥♦ ✐♥í❝✐♦ ❞❛♠♦✈✐♠❡♥t❛çã♦ ❛ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛ P é ❝♦♥❤❡❝✐❞❛✳ ❆❧é♠ ❞✐ss♦✱ ♦ ❡rr♦ ❛ss♦❝✐❛❞♦ r l∆ rl ❛ ∆s ❡ ∆s sã♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ ❝♦♠♣✉t❛r ❛ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛ P r❡❢❡r❡♥t❡ à✐♥❝❡rt❡③❛ ❞♦ ✐♥❝r❡♠❡♥t♦ ❞❡ ♠♦✈✐♠❡♥t❛çã♦✿ " # k r r|∆s | P = cov(∆s , ∆s ) = . ∆ rl r l✭✺✳✷✶✮ kl l r l |∆s | ❆s ❝♦♥st❛♥t❡s ❞❡ ♣r♦♣♦r❝✐♦♥❛❧✐❞❛❞❡ k ❡ k r❡♣r❡s❡♥t❛♠ ♣❛râ♠❡tr♦s ♥ã♦ ❞❡t❡r♠✐♥íst✐❝♦s❛ss♦❝✐❛❞♦s à ❞✐r❡çã♦ ❡ à ✐♥t❡r❛çã♦ ❞❛s r♦❞❛s ❝♦♠ ♦ ♣✐s♦✳ ◆❡ss❡ ♠♦❞❡❧♦ ❞❡ ❡rr♦✱ ❛❧❣✉♠❛s s✉♣♦s✐çõ❡s sã♦ ❡♠♣r❡❣❛❞❛s✱ ❡♥tr❡ ❡❧❛s✿ ✭✐✮ ♦s ❡rr♦s ❞❛s r♦❞❛s sã♦ ✐♥❞❡♣❡♥❞❡♥t❡s❀ ❡ ✭✐✐✮ ❛✈❛r✐â♥❝✐❛ ❞♦s ❡rr♦s sã♦ ♣r♦♣♦r❝✐♦♥❛✐s ❛♦ ✈❛❧♦r ❛❜s♦❧✉t♦ ❞❛s ❞✐stâ♥❝✐❛s ♣❡r❝♦rr✐❞❛s ∆s r❡ ∆s l ✳ ❆ss✉♠✐♥❞♦ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❛s ✐t❡r❛çõ❡s ❡ ✉t✐❧✐③❛♥❞♦ ❛ ❡①♣❛♥sã♦ ❡♠ sér✐❡ ❞❡❚❛②❧♦r ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✱ ♣♦❞❡✲s❡ ❡st❛❜❡❧❡❝❡r ♦ ♠♦❞❡❧♦ ❞❡ ♣r♦♣❛❣❛çã♦ ❞❛ ✐♥❝❡rt❡③❛✿ k+1|k k k ⊤ ⊤ P= + x f P ( x f ) ∆ f P ( ∆ f ) , ∇ ∇ ∇ rl ∆ ∇ rl ✭✺✳✷✷✮ rl s❡♥❞♦  ∆θ 1 0 ) −∆s s✐♥(θ + 2 x f =  ∆θ  0 1 ∆s )∇ ❝♦s(θ +   2 0 0 1 ✺✳✸✳ Pr♦✈❛s ❞❡ ❈♦♥❝❡✐t♦✶✶✾ ❡ 1 ∆θ ∆s ∆θ 1 ∆θ ∆s ∆θ  ) ) ) + ) 2 2 2b 2 2 2 2b 2 ❝♦s(θ + − s✐♥(θ + ❝♦s(θ + s✐♥(θ + 1 ∆θ ∆s ∆θ 1 ∆θ ∆s ∆θ  ∆ rl ) + ) ) ) f = ∇ s✐♥(θ + ❝♦s(θ + s✐♥(θ + − s✐♥(θ + 2 2 2b 2 2 2 2b 2 1 1  b b − ♦s ❏❛❝♦❜✐❛♥♦s ❞❛ ❢✉♥çã♦ f ❡♠ r❡❧❛çã♦ ❛♦ ❡st❛❞♦ x ❡ ❛♦ ✐♥❝r❡♠❡♥t♦ ❞❛ ♠♦✈✐♠❡♥t❛çã♦∆ rl ✳ ❆ ✐♥❢♦r♠❛çã♦ ❞❡ ♦❞♦♠❡tr✐❛ r❡❢❡r❡♥t❡ à ♠♦✈✐♠❡♥t❛çã♦ ❞❡ ✉♠ r♦❜ô ✉t✐❧✐③❛♥❞♦ ❡st❡ = k = 0,025♠♦❞❡❧♦ é ❛♣r❡s❡♥t❛❞❛ ♥❛ ❋✐❣✉r❛ ✺✳✸✸✱ s❡♥❞♦ k r l ✳ ❊♠ ❝♦♥s♦♥â♥❝✐❛ ❝♦♠ ❛ ♠❡t♦❞♦❧♦❣✐❛✱ ♦s r♦❜ôs ❢♦r❛♠ ❞✐s♣♦st♦s ❡♠ ✉♠❛ ♠❡s♠❛ r❡❣✐ã♦ ❞♦ ❛♠❜✐❡♥t❡✳ ◆❛ ❡t❛♣❛ ✐♥✐❝✐❛❧✱ ❛s ✐♥❢♦r♠❛çõ❡s ❝❛♣t✉r❛❞❛s ♣❡❧♦ ✐●P❙ ❢♦r❛♠❞✐s♣♦♥✐❜✐❧✐③❛❞❛s ♣❛r❛ t♦❞♦s ♦s r♦❜ôs✱ ♣❡r♠✐t✐♥❞♦ ❛ ❝❛❞❛ ✉♠ ❝❛❧❝✉❧❛r ❛s ❞✐stâ♥❝✐❛s r❡❧❛t✐✈❛s ♣❛r❛ ♦s ❞❡♠❛✐s✱ ❡♠ ❞❡❝♦rrê♥❝✐❛ ❞♦ ❛❥✉st❡ ❞♦ r❛✐♦ ε✳ ◆❡ss❛ ❡t❛♣❛✱ ♦s ♣❛râ♠❡tr♦sAB AA = 0,2 m = ❢♦r❛♠ ❞❡✜♥✐❞♦s ❡♠♣✐r✐❝❛♠❡♥t❡ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ α = 2,35 ✱ d ✱ d1,45 AB ✳ ❖ ♣❛râ♠❡tr♦ r❡❢❡r❡♥t❡ à tr❛♥s♣♦s✐çã♦ ❞♦ ♠♦❞❡❧♦ ❤♦❧♦♥ô♠✐❝♦ ♣❛r❛ ♥ã♦✲ × d❤♦❧♦♥ô♠✐❝♦ ❢♦✐ ❞❡✜♥✐❞♦ ❝♦♠♦ d = 3,00 ✳ ❆ ❋✐❣✉r❛ ✺✳✸✹ ❛♣r❡s❡♥t❛ ❛❧❣✉♠❛s ✐♠❛❣❡♥s❝❛♣t✉r❛❞❛s ♣❡❧❛ ❝â♠❡r❛ ❞✉r❛♥t❡ ♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ✐♥✐❝✐❛❧ ❞♦ ❧í❞❡r ♥♦ ✐♥t❡r✐♦r ❞♦ ❣r✉♣♦✳❖ ♠❛r❝❛❞♦r ✐♥st❛❧❛❞♦ s♦❜r❡ ♦ ❧í❞❡r ♣♦ss✉✐ ❛ ❝♦r ✈❡r♠❡❧❤❛ ♣❛r❛ ❞❡st❛❝á✲❧♦ ❞♦s ❞❡♠❛✐s✳ ✭❛✮ ✭❜✮ ✭❝✮✭❞✮ ✭❡✮ ✭❢✮ ❋✐❣✉r❛ ✺✳✸✹✿ P♦s✐❝✐♦♥❛♠❡♥t♦ ✐♥✐❝✐❛❧ ❞♦s r♦❜ôs✳ ❊♠ ✭❛✮ ♦s r♦❜ôs sã♦ ❞✐s♣♦st♦s ♥♦ ❛♠❜✐✲❡♥t❡ ❡♥q✉❛♥t♦ q✉❡ ❡♠ ✭❢✮ ♦ ❧í❞❡r ✭♠❛r❝❛❞♦r ♥❛ ❝♦r ✈❡r♠❡❧❤❛✮ ❡♥❝♦♥tr❛✲s❡ ♣♦s✐❝✐♦♥❛❞♦♥♦ ✐♥t❡r✐♦r ❞♦ ❣r✉♣♦✳ ◆❛ ❡t❛♣❛ ♣♦st❡r✐♦r✱ ♦s ♣❛râ♠❡tr♦s d AA ❡ d AB ❢♦r❛♠ ❞❡✜♥✐❞♦s ❝♦♠ ♦ ♠❡s♠♦ ✈❛❧♦r✱ ✶✷✵❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s AA AB = d = 0,185 ♦✉ s❡❥❛✱ d ✳ ❖ r❛✐♦ ❞❛s ✈✐③✐♥❤❛♥ç❛s✱ ♣♦r s✉❛ ✈❡③✱ ❢♦✐ ❞❡✜♥✐❞♦ ❝♦♠♦ε = 1,6 AB × d ✱ r❡str✐♥❣✐♥❞♦ ❛ ❝❛❞❛ r♦❜ô s♦♠❡♥t❡ ♦ ❛❝❡ss♦ ❛ s❡✉s ✈✐③✐♥❤♦s ✐♠❡❞✐❛t♦s✳❖s ❞❡♠❛✐s ♣❛râ♠❡tr♦s ❢♦r❛♠ ♠❛♥t✐❞♦s ✐♥❛❧t❡r❛❞♦s✳ ❆ ❋✐❣✉r❛ ✺✳✸✺ ❛♣r❡s❡♥t❛ ❛❧❣✉♠❛s❝♦♥✜❣✉r❛çõ❡s ❞♦ ❣r✉♣♦ ❞✉r❛♥t❡ ❡ss❛ ❡t❛♣❛✳ ✭❛✮ ✭❜✮ ✭❝✮ ❋✐❣✉r❛ ✺✳✸✺✿ P♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦s r♦❜ôs ❝♦♠ ❜❛s❡ ❡♠ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s✳❆♣ós ❝♦♥❝❧✉í❞♦ ♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦s r♦❜ôs✱ ✐♥✐❝✐♦✉✲s❡ ❛ ❡t❛♣❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛✳ ❆ ❋✐❣✉r❛ ✺✳✸✻ ❛♣r❡s❡♥t❛ ❛❧❣✉♥s ♠♦♠❡♥t♦s ❞✉r❛♥t❡ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦s r♦❜ôs✳❆ ❧♦❝❛❧✐③❛çã♦ ❞♦s ✇❛②♣♦✐♥ts ✈✐rt✉❛✐s ✉t✐❧✐③❛❞♦s ♣❡❧♦ ❧í❞❡r ♣❛r❛ ❣✉✐❛r ♦ ❣r✉♣♦ é r❡♣r❡✲ s❡♥t❛❞❛ ♣♦r ❝ír❝✉❧♦s ❝♦♠ ❧✐♥❤❛s tr❛❝❡❥❛❞❛s ❞❡s❡♥❤❛❞♦s ♥♦ ❛♠❜✐❡♥t❡✳ ❉✐❢❡r❡♥t❡♠❡♥t❡❞❛ ♠♦✈✐♠❡♥t❛çã♦ ❡❢❡t✉❛❞❛ ♥♦s ❡①♣❡r✐♠❡♥t♦s s✐♠✉❧❛❞♦s✱ ♥❡st❡s ❡①♣❡r✐♠❡♥t♦s ❛ ❞✐r❡çã♦✉t✐❧✐③❛❞❛ ♣❡❧♦ ❧í❞❡r ♣❛r❛ ❣✉✐❛r ♦ ❣r✉♣♦ ♥♦ ❛♠❜✐❡♥t❡ é ❞✐ss❡♠✐♥❛❞❛ ♣❛r❛ t♦❞♦s ♦s r♦❜ôs✱❞❡ ♠♦❞♦ ❛ ❢❛❝✐❧✐t❛r ♦ ❝♦♥tr♦❧❡ ❞♦s ♠❡s♠♦s✳ ❆ss✐♠✱ ❛ ❡q✉❛çã♦ ❞❡ ❝♦♥tr♦❧❡ ✭✹✳✸✶✮ ❢♦✐❧✐❣❡✐r❛♠❡♥t❡ ❛❧t❡r❛❞❛ ♣❛r❛ q✉❡ t♦❞♦s ♦s r♦❜ôs ♣✉❞❡ss❡♠ ✉t✐❧✐③❛r ❛ ✐♥❢♦r♠❛çã♦ r❡❢❡r❡♥t❡à ❞✐r❡çã♦ ❞❡ ♠♦✈✐♠❡♥t♦✿ X X ui = p i U ij ( ij (v i j ) p U lt ( lt i , p U ( l lt lt − ∇ kp k) − − v − ∇ l kp k) + γv ✭✺✳✷✸✮ j∈N i j∈N i j6=i j6=i s❡♥❞♦ ∇ kp k) ✉♠ ♣♦t❡♥❝✐❛❧ ❛rt✐✜❝✐❛❧ ❛tr❛t✐✈♦ ♣❛r❛ ♦ ❛❧✈♦ t✱ ❝❛❧❝✉❧❛❞♦ ❡ ❞✐ss❡♠✐✲♥❛❞♦ ♣❡❧♦ ❧í❞❡r l✿ 1 2U ( β . lt lt lt kp k) = kp k ✭✺✳✷✹✮ 2❙❡♠❡❧❤❛♥t❡♠❡♥t❡ ❛♦s ❡①♣❡r✐♠❡♥t♦s s✐♠✉❧❛❞♦s ❝♦♠ ❛ ♣❧❛t❛❢♦r♠❛ ❘❖❙✴❙t❛❣❡✱ ♥♦s ❡①✲♣❡r✐♠❡♥t♦s r❡❛✐s ❛ ❢♦rç❛ ❞❡ ❛rr❛st♦ ❢♦✐ ✐❣♥♦r❛❞❛✱ ♦✉ s❡❥❛✱ γ = 0✳ ❖s ❞❡♠❛✐s ♣❛râ♠❡tr♦s❢♦r❛♠ ❞❡✜♥✐❞♦s ❡♠♣✐r✐❝❛♠❡♥t❡ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ β = 13,0 ✱ α = 2,05 ❡ d = 1,5 ✳❖ ❛❧❝❛♥❝❡ ❞♦ s❡♥s♦r ✈✐rt✉❛❧✱ ♦✉ s❡❥❛✱ ♦ r❛✐♦ ❞❛s ✈✐③✐♥❤❛♥ç❛s ❢♦✐ ❝♦♥✜❣✉r❛❞♦ ❝♦♠♦ε = 1,33 AB × d ✳❖ ❞❡s✈✐♦ ♣❛❞rã♦ ❞♦ ❡rr♦ r❡❢❡r❡♥t❡ à ♣♦s✐çã♦ ✐♥✐❝✐❛❧ ❞❡ ❝❛❞❛ r♦❜ô ❢♦✐ ❞❡✜♥✐❞♦ ❝♦♠♦ −3 5 mm ♣❛r❛ ❛s ❞✐r❡çõ❡s x✱ y ❡ 1,75 ×10 r❛❞ ♣❛r❛ ❛ ♦r✐❡♥t❛çã♦✳ ❉✉r❛♥t❡ ❛ ♠♦✈✐♠❡♥t❛çã♦✱ ✺✳✸✳ Pr♦✈❛s ❞❡ ❈♦♥❝❡✐t♦✶✷✶ ✭❛✮ ✭❜✮ ✭❝✮ ✭❞✮✭❡✮ ✭❢✮ ✭❣✮ ✭❤✮ ❋✐❣✉r❛ ✺✳✸✻✿ ▼♦✈✐♠❡♥t❛çã♦ ❞♦s r♦❜ôs ❝♦♠ ❜❛s❡ ❡♠ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s✳ ❖ ❧í❞❡r ❣✉✐❛ ♦❣r✉♣♦ ✉t✐❧✐③❛♥❞♦ ✇❛②♣♦✐♥ts ✈✐rt✉❛✐s✱ ♦s q✉❛✐s sã♦ ❞❡st❛❝❛❞♦s ♣♦r ❝ír❝✉❧♦s ♣♦♥t✐❧❤❛❞♦s❞❡s❡♥❤❛❞♦s ♥❛ ❛r❡♥❛✳♦ r♦❜ô ❧í❞❡r r❡❝❡❜❡✉ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛ ❡♠ ✐♥t❡r✈❛❧♦s r❡❣✉❧❛r❡s ❞❡ 2 s✱ −3 s❡♥❞♦ 1 cm ♦ ❞❡s✈✐♦ ♣❛❞rã♦ ❞♦ ❡rr♦ r❡❧❛t✐✈♦ às ❞✐r❡çõ❡s x✱ y ❡ 8,73 ×10 r❛❞ ♦ ❞❡s✈✐♦❛ss♦❝✐❛❞♦ à ♦r✐❡♥t❛çã♦✳ ❈♦♥❢♦r♠❡ ❞❡s❝r✐t♦ ♥❛ ♠❡t♦❞♦❧♦❣✐❛✱ ✉♠ ❊❑❋ ❢♦✐ ✉t✐❧✐③❛❞♦ ♣❛r❛❝♦♠❜✐♥❛r t❛✐s ✐♥❢♦r♠❛çõ❡s ❝♦♠ ❛ ❡st✐♠❛t✐✈❛ ❞♦ ❧í❞❡r✱ ❣❡r❛❞❛ ♥❛s ❡t❛♣❛s ❞❡ ♣r❡❞✐çã♦ ❞♦✜❧tr♦✱ ❝✉❥♦ r❡s✉❧t❛❞♦ ♣♦❞❡ s❡r ♦❜s❡r✈❛❞♦ ♥❛ ❋✐❣✉r❛ ✺✳✸✼✳ ◆❡st❡ ❡①♣❡r✐♠❡♥t♦✱ ♦ r♦❜ô ❧í❞❡r ❞❡✜♥❡ ♦s ♠♦♠❡♥t♦s ♣❛r❛ s❡ ❡❢❡t✉❛r ❛s ❡t❛♣❛s❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❆ ❡str❛té❣✐❛ ❞❡s❝r✐t❛ ♥❛ ❙❡çã♦ ✺✳✸✳✶ ♣❛r❛ ❞✐ss❡♠✐♥❛çã♦❞❡ ♠❡♥s❛❣❡♥s é t❛♠❜é♠ ✉t✐❧✐③❛❞❛ ♥❡st❡s ❡①♣❡r✐♠❡♥t♦s✳ ❆❧é♠ ❞✐ss♦✱ ✉♠ r♦❜ô ♣♦❞❡✉t✐❧✐③❛r ♠❛✐s ❞❡ ✉♠❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ♣❛r❛ ❛t✉❛❧✐③❛r ❛ s✉❛ ❝r❡♥ç❛✳ ❆ ♦r❞❡♠❡♠ q✉❡ t❛✐s ✐♥❢♦r♠❛çõ❡s ❢♦r❛♠ ✐♥❝♦r♣♦r❛❞❛s é ❛ ♠❡s♠❛ ❞❛ s❡q✉ê♥❝✐❛ ❞❡ ♠❡♥s❛❣❡♥s r❡❝❡❜✐❞❛s✳ ❖ ❡rr♦ ❛ss♦❝✐❛❞♦ à ❧♦❝❛❧✐③❛çã♦ ❞♦s r♦❜ôs é ❛♣r❡s❡♥t❛❞♦ ♥❛ ❋✐❣✉r❛ ✺✳✸✽❛✱❡♥q✉❛♥t♦ q✉❡ ❛s r❡s♣❡❝t✐✈❛s ✐♥❝❡rt❡③❛s sã♦ ✐❧✉str❛❞❛s ♥❛ ❋✐❣✉r❛ ✺✳✸✽❜✳ ❈♦♥❢♦r♠❡ ♣♦❞❡ s❡r ♦❜s❡r✈❛❞♦✱ ♦ ❡rr♦ ❡ ❛ ✐♥❝❡rt❡③❛ ❛ss♦❝✐❛❞♦s à ♦❞♦♠❡tr✐❛ ❝r❡s❝❡ s❡♠ ❝♦♥tr♦❧❡✱ ❡♥q✉❛♥t♦q✉❡ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♠❛♥té♠ t❛✐s ✐♥❢♦r♠❛çõ❡s s♦❜ ✉♠ ❝❡rt♦♥í✈❡❧ ❞❡ ❝♦♥tr♦❧❡✳ ❊♠ ❛❧❣✉♠❛s ✐t❡r❛çõ❡s✱ ❛ t❛①❛ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❞♦ ❡rr♦ é ♠❛✐♦r ❞❡✈✐❞♦à ♠✉❞❛♥ç❛ ❞❡ ❞✐r❡çã♦ ❞♦s r♦❜ôs✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♥❛q✉❡❧❡s r♦❜ôs ♠❛✐s ❞✐st❛♥t❡s ❞♦ ❧í❞❡r✭❘♦❜ôs ✸ ❡ ✹✮✳ ❆ ❋✐❣✉r❛ ✺✳✸✾ ❛♣r❡s❡♥t❛ ♦ ❡rr♦ ❡ ❛ ✐♥❝❡rt❡③❛ ✭1 ❞❡s✈✐♦ ♣❛❞rã♦✮ r❡❢❡r❡♥t❡s à ♦r✐✲❡♥t❛çã♦ ❞♦s r♦❜ôs✳ P♦❞❡✲s❡ ♣❡r❝❡❜❡r ♦ ❝r❡s❝✐♠❡♥t♦ s✐❣♥✐✜❝❛t✐✈♦ ❞♦ ❡rr♦ ❡ ❞❛ ✐♥❝❡rt❡③❛❛ss♦❝✐❛❞♦s à ♦❞♦♠❡tr✐❛✱ ❡♥q✉❛♥t♦ q✉❡ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❛♣r❡✲ s❡♥t❛ ✈❛❧♦r❡s ♠❡♥♦r❡s✳ ❆s ✐t❡r❛çõ❡s ❡♠ q✉❡ ♦ ♥í✈❡❧ ❞❡ ❡rr♦ ❛❧❝❛♥ç❛ ✈❛❧♦r❡s s✐❣♥✐✜❝❛t✐✈♦s ✶✷✷ 0.6 0.6 0.6 0.8 Líder Robô 1 Robô 2 Robô 3 Odometria Odometria Odometria Odometria Ground truth Ground truth Ground truth Ground truth ❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦sy (m) −0.2 −0.2 −0.2 0.0 0.0 0.0 0.0 0.2 0.2 0.2 0.2 0.4 0.4 0.4 0.4 0.6 EKF (Abs) Algoritmo CI Algoritmo CI Algoritmo CI −0.6 −0.6 −0.6 −0.4 −0.4 −0.4 −0.4 −0.2 0.8 0.4 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 −0.2 0.0 0.2 0.4 0.6 0.8 −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 Robô 4 Robô 5 Robô 6 Robô 7 Odometria Odometria Odometria Odometria Ground truth Ground truth Ground truth Ground truth 0.8 0.8 y (m) 0.2 −0.2 0.4 0.0 0.6 0.2 Algoritmo CI Algoritmo CI Algoritmo CI Algoritmo CI 0.2 0.2 0.4 0.4 0.6 0.6 0.0 0.0 −0.2 −0.6 0.0 −0.4 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 −0.4 −0.2 0.0 0.2 0.4 0.6 −0.2 0.0 0.2 0.4 0.6 0.8 x (m) x (m) x (m) x (m) −0.4 −0.4 −0.2 −0.2❋✐❣✉r❛ ✺✳✸✼✿ ❈❛♠✐♥❤♦ ♣❡r❝♦rr✐❞♦ ✭❣r♦✉♥❞ tr✉t❤✮✱ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛✲ t✐✈❛ ❣❡r❛❞❛s ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❈■ ✭❧♦❝✳ ❝♦♦♣✳✮ ❡ ♦❞♦♠❡tr✐❛ ✭♦❞♦♠✮ ❞♦s r♦❜ôs✳ P❛r❛ ♦ ❧í❞❡ré ❛♣r❡s❡♥t❛❞❛ ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ✭❛❜s✮ r❡s✉❧t❛♥t❡ ❞❛ ✉t✐❧✐③❛çã♦ ❞♦ ✐●P❙✳❞✐③❡♠ r❡s♣❡✐t♦ ❛♦s ♠♦♠❡♥t♦s ❡♠ q✉❡ ♦s r♦❜ôs ❡❢❡t✉❛r❛♠ ♠✉❞❛♥ç❛s s✐❣♥✐✜❝❛t✐✈❛s ❡♠ s✉❛s r❡s♣❡❝t✐✈❛s ♦r✐❡♥t❛çõ❡s✳ ❆♣❡s❛r ❞✐ss♦✱ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛❝♦♥s❡❣✉✐✉ r❡st❛✉r❛r ♦s ✈❛❧♦r❡s ❞❡ ♦r✐❡♥t❛çã♦ ❞♦s ❞✐✈❡rs♦s r♦❜ôs✱ ❛♣ós ♦ r❡❝❡❜✐♠❡♥t♦ ❞❡✉♠❛ ✐♥❢♦r♠❛çã♦ ❛❜s♦❧✉t❛ ♣❡❧♦ r♦❜ô ❧í❞❡r✳ ❆ ❢r❡q✉ê♥❝✐❛ ❞❡ r❡❝❡❜✐♠❡♥t♦ ❞❡ss❡ t✐♣♦ ❞❡✐♥❢♦r♠❛çã♦ ♣❡❧♦ ❧í❞❡r ♣♦❞❡ ✐♥✢✉❡♥❝✐❛r ❛ r❛♣✐❞❡③ ❝♦♠ q✉❡ ♦ ♥í✈❡❧ ❞♦s ❡rr♦s é r❡st❛✉r❛❞♦✳ ✺✳✹ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ❖s ❡①♣❡r✐♠❡♥t♦s ❞❡s❡♥✈♦❧✈✐❞♦s ♠♦str❛r❛♠ ❛ s✉♣❡r✐♦r✐❞❛❞❡ ❞♦ ❡♠♣r❡❣♦ ❞❛ ❡str❛té❣✐❛❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♣r♦♣♦st❛ q✉❛♥❞♦ ❝♦♠♣❛r❛❞❛ à ✐♥❢♦r♠❛çã♦ ❣❡r❛❞❛ ♣❡❧❛ ♦❞♦✲♠❡tr✐❛✳ ❖ ✉s♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s ♣❡r♠✐t✐✉ ❡❢❡t✉❛r ❛ ❢✉sã♦ s❡♥s♦r✐❛❧ ❞❡ ♠❛♥❡✐r❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ❡ ❛ssí♥❝r♦♥❛✱ ❛❧é♠ ❞❡ s❡ ❡✈✐t❛r ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡t❡♠♣♦ ❡ ❡s♣❛ç♦ ♥❡❝❡ssár✐♦s ♣❛r❛ ❧✐❞❛r ❝♦♠ ❛ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡♠ ♦✉tr❛s ❛❜♦r✲❞❛❣❡♥s✳ ❚❛❧ ❝♦♠♣❧❡①✐❞❛❞❡✱ ❛♣❡s❛r ❞❡ ♥ã♦ s❡r ✉♠ ♣r♦❜❧❡♠❛ ❡♠ s✐st❡♠❛s ❝♦♠♣♦st♦s ♣♦r✉♠ ♣❡q✉❡♥♦ ♥ú♠❡r♦ ❞❡ ✐♥t❡❣r❛♥t❡s✱ t♦r♥❛✲s❡ ✉♠ ❢❛t♦r ✐♠♣♦rt❛♥t❡ q✉❛♥❞♦ s❡ ✉t✐❧✐③❛❡♥①❛♠❡s ❞❡ r♦❜ôs✳ ❖✉tr♦ ❢❛t♦r r❡❧❡✈❛♥t❡ ♥❛ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛ ❡ ❡✈✐❞❡♥❝✐❛❞♦ ♥♦s ❡①♣❡r✐♠❡♥t♦s✱❞✐③ r❡s♣❡✐t♦ ❛♦ ❢❛t♦ ❞♦ ❛❧❣♦r✐t♠♦ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s s❡ ♠♦str❛r ❝♦♥s✐st❡♥t❡❡ ♥ã♦ ❡①✐❣✐r ✉♠ tr❛t❛♠❡♥t♦ r❡❧❛❝✐♦♥❛❞♦ ❛♦ r❛❝✐♦❝í♥✐♦ ❝✐r❝✉❧❛r ❡ ❛♦s ❡❢❡✐t♦s ❝❛✉s❛❞♦s♣❡❧♦ ♠❡s♠♦✳ ❖s ❡①♣❡r✐♠❡♥t♦s ❞❡s❡♥✈♦❧✈✐❞♦s ♥❛ ❙❡çã♦ ✺✳✷ ♠♦str❛♠ ❛ ❝♦♥s✐stê♥❝✐❛ ❞♦ ✺✳✹✳ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s✶✷✸ 100 200 300 400 500 6000.000.050.100.150.200.25 Erro (m) Líder Odometria EKF (Abs) 100 200 300 400 500 6000.000.050.100.150.200.250.300.35 Robô 1 Odometria Algoritmo CI 100 200 300 400 500 600 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Robô 2 Odometria Algoritmo CI 100 200 300 400 500 600 0.00 0.05 0.10 0.15 0.20 0.25 Robô 3 Odometria Algoritmo CI 100 200 300 400 500 600iterações0.000.050.100.150.20 Erro (m) Robô 4 Odometria Algoritmo CI 100 200 300 400 500 600 iterações0.000.050.100.150.200.250.300.35 Robô 5 Odometria Algoritmo CI 100 200 300 400 500 600 iterações 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Robô 6 Odometria Algoritmo CI 100 200 300 400 500 600 iterações 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Robô 7 Odometria Algoritmo CI✭❛✮ 100 200 300 400 500 6000.000.050.100.150.200.250.300.350.400.45 Incert eza (m) Líder Odometria EKF (Abs) 100 200 300 400 500 6000.000.050.100.150.200.250.300.350.40 Robô 1 Odometria Algoritmo CI 100 200 300 400 500 600 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 Robô 2 Odometria Algoritmo CI 100 200 300 400 500 600 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 Robô 3 Odometria Algoritmo CI 100 200 300 400 500 600iterações0.000.050.100.150.200.250.300.350.40 Incerteza (m) Robô 4 Odometria Algoritmo CI 100 200 300 400 500 600 iterações0.000.050.100.150.200.250.300.350.40 Robô 5 Odometria Algoritmo CI 100 200 300 400 500 600 iterações 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Robô 6 Odometria Algoritmo CI 100 200 300 400 500 600 iterações 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Robô 7 Odometria Algoritmo CI✭❜✮ ❋✐❣✉r❛ ✺✳✸✽✿ ❊rr♦ ✭❛✮ ❡ ✐♥❝❡rt❡③❛ ✭❜✮ r❡❢❡r❡♥t❡s à ♣♦s✐çã♦ ❞❡ ❝❛❞❛ r♦❜ô✳ ✶✷✹❈❛♣ít✉❧♦ ✺✳ ❊①♣❡r✐♠❡♥t♦s 100 200 300 400 500 6000.00.10.20.30.40.50.6 Erro (rad ) Líder Odometria EKF (Abs) 100 200 300 400 500 6000.00.10.20.30.40.50.60.7 Robô 1 Odometria Algoritmo CI. 100 200 300 400 500 600 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 Robô 2 Odometria Algoritmo CI. 100 200 300 400 500 600 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Robô 3 Odometria Algoritmo CI. 100 200 300 400 500 600 iterações0.00.10.20.30.40.50.60.70.8 Erro (rad ) Robô 4 Odometria Algoritmo CI. 100 200 300 400 500 600 iterações0.00.10.20.30.40.50.60.70.80.9 Robô 5 Odometria Algoritmo CI. 100 200 300 400 500 600 iterações 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Robô 6 Odometria Algoritmo CI. 100 200 300 400 500 600 iterações 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Robô 7 Odometria Algoritmo CI. ✭❛✮100 200 300 400 500 6000.00.10.20.30.40.50.60.7 Incert eza (rad) Líder Odometria EKF (Abs) 100 200 300 400 500 6000.00.10.20.30.40.50.60.7 Robô 1 Odometria Algoritmo CI 100 200 300 400 500 600 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Robô 2 Odometria Algoritmo CI 100 200 300 400 500 600 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Robô 3 Odometria Algoritmo CI 100 200 300 400 500 600iterações0.00.10.20.30.40.50.60.7 Ince rteza (rad) Robô 4 Odometria Algoritmo CI 100 200 300 400 500 600 iterações0.00.10.20.30.40.50.60.7 Robô 5 Odometria Algoritmo CI 100 200 300 400 500 600 iterações 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Robô 6 Odometria Algoritmo CI 100 200 300 400 500 600 iterações 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Robô 7 Odometria Algoritmo CI ✭❜✮ ❋✐❣✉r❛ ✺✳✸✾✿ ❊rr♦ ✭❛✮ ❡ ✐♥❝❡rt❡③❛ ✭❜✮ r❡❢❡r❡♥t❡s à ♦r✐❡♥t❛çã♦ ❞❡ ❝❛❞❛ r♦❜ô✳ ✺✳✹✳ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s✶✷✺ ❛❧❣♦r✐t♠♦ ❡♠ ❞✐✈❡rs❛s s✐t✉❛çõ❡s✱ ♦ q✉❡ ♣❡r♠✐t✐✉ ❛ ✉t✐❧✐③❛çã♦✱ ❞❡ ♠❛♥❡✐r❛ ❛❞❡q✉❛❞❛✱ ❞❛s✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞✐s♣♦♥✐❜✐❧✐③❛❞❛s ❛♦s r♦❜ôs✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ♦ ❛❥✉st❡ ❞♦ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥ ❢♦✐ ❢❡✐t♦ ❞❡ ♠❛♥❡✐r❛ ❡♠♣ír✐❝❛ ❡ s❡✉❢✉♥❝✐♦♥❛♠❡♥t♦ s❡ ♠♦str♦✉ ✉♠ t❛♥t♦ q✉❛♥t♦ ❧✐♠✐t❛❞♦✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡ ❛♣r❡s❡♥t❛♥❞♦✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❜❛st❛♥t❡ ✐♠♣r❡❝✐s♦ ❡♠ ❛❧❣✉♠❛s s✐t✉❛çõ❡s✳ ❆♣❡s❛r ❞❡ ❡①✐st✐r ♠❛r✲❣❡♠ ♣❛r❛ ✉♠ ♠❡❧❤♦r ❛❥✉st❡ ❞♦ ✜❧tr♦ ♥♦s ❡①♣❡r✐♠❡♥t♦s ❡♠♣r❡❣❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦ ❡✱♣♦ss✐✈❡❧♠❡♥t❡✱ t❡r♠♦s ✉♠ r❡s✉❧t❛❞♦ ♠❛✐s ❛♣r♦①✐♠❛❞♦ ❝♦♠ r❡❧❛çã♦ ❛♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥✲ t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s✱ ♦ ❛❧❣♦r✐t♠♦ ❈■ ❛♣r❡s❡♥t❛ ❝❛r❛❝t❡ríst✐❝❛s ♠❛✐s ❛❞❡q✉❛❞❛s ♣❛r❛♦ ❡♠♣r❡❣♦ ❡♠ s✐st❡♠❛s ❞❡s❝❡♥tr❛❧✐③❛❞♦s ❝♦♠♦ ❡♥①❛♠❡s r♦❜ót✐❝♦s✱ ❝♦♥❢♦r♠❡ ❞✐s❝✉ssã♦❢❡✐t❛ ❛♦ ❧♦♥❣♦ ❞♦ t❡①t♦✳ ❆s ♣r♦✈❛s ❞❡ ❝♦♥❝❡✐t♦ ❞❡s❡♥✈♦❧✈✐❞❛s ❝♦♠ r♦❜ôs r❡❛✐s✱ ❛♣❡s❛r ❞❡ t❡r❡♠ ❡♠♣r❡❣❛❞♦♣♦✉❝♦s r♦❜ôs ❡ ❢❛③❡r❡♠ ✉s♦ ❞❡ s❡♥s♦r❡s ✈✐rt✉❛✐s✱ ♠♦str❛r❛♠ ❛ ❛♣❧✐❝❛❜✐❧✐❞❛❞❡ ❞❛ ♠❡t♦✲❞♦❧♦❣✐❛ ❡♠ ✉♠ s✐st❡♠❛ r❡❛❧✱ t❛♥t♦ ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ à ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ q✉❛♥t♦ à ❛❜♦r❞❛❣❡♠ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛✳ ❈❛♣ít✉❧♦ ✻ ❈♦♥❝❧✉sã♦ ❖ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛r ❝♦♦♣❡r❛t✐✈❛♠❡♥t❡ ✉♠ ❡♥①❛♠❡ ❞❡ r♦❜ôs é tr❛t❛❞♦ ♥❡st❛ t❡s❡✳◆❡ss❡ t✐♣♦ ❞❡ ❧♦❝❛❧✐③❛çã♦✱ ❛ ❢r❡q✉ê♥❝✐❛ ❝♦♠ q✉❡ ♦❝♦rr❡♠ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦✲♣❡r❛t✐✈❛ ✐♠♣❛❝t❛ ❞✐r❡t❛♠❡♥t❡ ♥❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❣r✉♣♦✳ ❉❡✈✐❞♦ ❛ ✐ss♦✱❡str❛té❣✐❛s ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛ ❢♦r❛♠ ❡♠♣r❡❣❛❞❛s ♣❛r❛ ♣♦ss✐❜✐❧✐t❛r ♦ ❝♦♥tr♦❧❡ ❞❛❢r❡q✉ê♥❝✐❛ ❞❡ ❛t✉❛❧✐③❛çã♦ ❞❛s ❝r❡♥ç❛s ❡ ❛ ❝♦♥s❡q✉❡♥t❡ ♠❛♥✉t❡♥çã♦ ❞❡ ❜❛✐①♦s ♥í✈❡✐s ❞❡✐♥❝❡rt❡③❛ ❛ss♦❝✐❛❞♦s às ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦✳ ❆ ♣r✐♠❡✐r❛ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❡♠♣r❡❣❛❞❛ ❝♦♥s✐st❡ ❡♠ ✉♠❛ ❧✐❣❡✐r❛ ♠♦✲❞✐✜❝❛çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ✢♦❝❦✐♥❣✱ ♦ q✉❡ ♣♦ss✐❜✐❧✐t♦✉ q✉❡ ♦s r♦❜ôs s❡ ♠♦✈✐♠❡♥t❛ss❡♠❞❡ ♠♦❞♦ ❛❧t❡r♥❛❞♦✱ ♣♦ré♠ ❞❡ ♠❛♥❡✐r❛ ❝♦❡s❛✳ ❆ ❛❧t❡r♥â♥❝✐❛ ❞❛ ♠♦✈✐♠❡♥t❛çã♦ ♣♦ss✐❜✐✲❧✐t❛ ✉♠❛ ♣❛rt❡ ❞♦ ❣r✉♣♦ s❡ ♠❛♥t❡r ✐♥❡rt❡✱ ❡♥q✉❛♥t♦ ❛ ♦✉tr❛ ♣❛rt❡ s❡ ♠♦✈✐♠❡♥t❛✳ ❚❛❧❡str❛té❣✐❛ ♣❡r♠✐t❡ ♠❛♥t❡r ❜♦♥s ♥í✈❡✐s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡✈✐❞♦ à ♠❛♥✉t❡♥çã♦ ❞❡ ♣❛rt❡ ❞♦❣r✉♣♦ ❛t✉❛♥❞♦ ❝♦♠♦ ♠❛r❝♦✱ ❞✉r❛♥t❡ t♦❞❛ ❛ ♠♦✈✐♠❡♥t❛çã♦✳ ❆♣❡s❛r ❞♦s ❜♦♥s r❡s✉❧t❛❞♦s❛♣r❡s❡♥t❛❞♦s✱ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❛❧t❡r♥❛❞❛ ❝♦♠♣r♦♠❡t❡ ❛ ♣❡r❢♦r♠❛♥❝❡ ❞♦ ❣r✉♣♦✳ P❛r❛ ♠❡❧❤♦r❛r ❛ ♣❡r❢♦r♠❛♥❝❡✱ ✉♠❛ s❡❣✉♥❞❛ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❢♦✐ ♣r♦✲♣♦st❛✱ ❛ q✉❛❧ ❢♦✐ ❡st❛❜❡❧❡❝✐❞❛ ♣❡❧❛ ❝♦♠❜✐♥❛çã♦ ❞♦s ❝♦♠♣♦rt❛♠❡♥t♦s ❞❡ ❛❣r❡❣❛çã♦ ❡ s❡❣r❡❣❛çã♦✱ ♣r❡✈✐❛♠❡♥t❡ ♣r♦♣♦st♦s ♥❛ ❧✐t❡r❛t✉r❛✱ ❛❧é♠ ❞❡ ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ❧í❞❡r✲s❡❣✉✐❞♦r✳ ❊♠ ❞❡❝♦rrê♥❝✐❛ ❞♦ ❛✉♠❡♥t♦ ♣❡r♠❛♥❡♥t❡ ❞❛ ✐♥❝❡rt❡③❛ ❛ss♦❝✐❛❞❛ à ✐♥❢♦r♠❛çã♦❞❡ ❧♦❝❛❧✐③❛çã♦ ❞♦s r♦❜ôs✱ ❡♠ ❝♦♥s❡q✉ê♥❝✐❛ ❞❛ ♠♦✈✐♠❡♥t❛çã♦ ❝♦♥tí♥✉❛ ❞♦ ❣r✉♣♦✱ ✉♠ r♦❜ô ✭❧í❞❡r✮ ❢♦✐ ♣r♦✈✐❞♦ ❝♦♠ s❡♥s♦r❡s ❝❛♣❛③❡s ❞❡ ♦❜t❡r ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛❜s♦✲❧✉t❛✱ ❝♦♠ ❜❛✐①❛ ✐♥❝❡rt❡③❛✱ ❡♠ ✐♥t❡r✈❛❧♦s ❞❡ t❡♠♣♦ r❡❣✉❧❛r❡s✳ ❉❡ss❡ ♠♦❞♦✱ t❛❧ ❧í❞❡r ❛t✉❛❝♦♠♦ r❡❢❡r❡♥❝✐❛❧ ♥♦ ❣r✉♣♦✱ ♣r♦✈❡♥❞♦ ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♠ ❜♦❛ q✉❛❧✐❞❛❞❡✱ ♦✉ s❡❥❛✱ ❜❛✐①❛ ✐♥❝❡rt❡③❛ ❡ ❛❧t❛ ❡①❛t✐❞ã♦✳ ❚❛✐s ✐♥❢♦r♠❛çõ❡s sã♦ ❡♠♣r❡❣❛❞❛s ♣❡❧♦s r♦❜ôs ♥❛✈✐③✐♥❤❛♥ç❛ ❞♦ ❧í❞❡r ♣❛r❛ ❛❥✉st❛r s✉❛s ❝r❡♥ç❛s ❡ ❛t✉❛r❡♠ ❝♦♠♦ ♠❛r❝♦s ♣❛r❛ ♦✉tr♦s r♦❜ôs♥♦ ❣r✉♣♦✳ ❆s ❝❛♣❛❝✐❞❛❞❡s ❞❡ s❡♥s♦r✐❛♠❡♥t♦ ❡ ❝♦♠✉♥✐❝❛çã♦ ❧✐♠✐t❛❞❛s✱ ♥♦r♠❛❧♠❡♥t❡ ♣r❡s❡♥✲ ✶✷✽❈❛♣ít✉❧♦ ✻✳ ❈♦♥❝❧✉sã♦ t❡s ❡♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s✱ ❞❡♠❛♥❞❛♠ ♦ ❡♠♣r❡❣♦ ❞❡ ❡str❛té❣✐❛s ❞❡s❝❡♥tr❛❧✐③❛❞❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❡♠ s✐st❡♠❛s r❡❛✐s✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛♣❡r♠✐t✐✉ ❛♦s r♦❜ôs ❡①❡❝✉t❛r❡♠ ❡t❛♣❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ✉t✐❧✐③❛♥❞♦ s♦♠❡♥t❡✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s✱ ♦ q✉❡ é ❝♦♥s✐❞❡r❛❞❛ ✉♠❛ s♦❧✉çã♦ ❛♣r♦①✐♠❛❞❛ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✱ ❞❡✲✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ ♥ã♦ ❣❡r❛r ✉♠❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ ❞❡ t♦❞♦s ♦s r♦❜ôs ♥♦ ❣r✉♣♦✳ P❛r❛❣❡r❛r ✉♠❛ ❡st✐♠❛t✐✈❛ ❝♦♥❥✉♥t❛ ✭ót✐♠❛✮✱ ❢❛③✲s❡ ♥❡❝❡ssár✐♦ ❛ ✉t✐❧✐③❛çã♦ ❞❛ ✐♥❢♦r♠❛çã♦ ❞❡✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❞❡ t♦❞♦s ♦s r♦❜ôs✱ ✉♠❛ ✈❡③ q✉❡ ❛s ❡st✐♠❛t✐✈❛s ♥ã♦ sã♦ ✐♥❞❡♣❡♥❞❡♥t❡s✳❊♠ ❡♥①❛♠❡s r♦❜ót✐❝♦s✱ ❛ ✉t✐❧✐③❛çã♦ ❞❡ t❛❧ ✐♥❢♦r♠❛çã♦ ♣♦ss✉✐ ✉♠❛ ❝♦♠♣❧❡①✐❞❛❞❡ q✉❡ r❡str✐♥❣❡ s❡✉ ❡♠♣r❡❣♦ ❡♠ s✐st❡♠❛s r❡❛✐s✳ ❆ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛ ♥❡st❛ t❡s❡ ❣❡r❛ ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♥s✐st❡♥t❡s✉t✐❧✐③❛♥❞♦ s♦♠❡♥t❡ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s✱ ♠❡s♠♦ s❡♠ ❛ ✉t✐❧✐③❛çã♦ ❞❛ ✐♥❢♦r♠❛çã♦ ❞❡ ✐♥t❡r✲❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❛s ❡st✐♠❛t✐✈❛s✳ ❚❛❧ ❝♦♥s✐stê♥❝✐❛ é ❛❧❝❛♥ç❛❞❛ ♣♦r ♠❡✐♦ ❞♦ ❛❧❣♦r✐t♠♦❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s✱ ♦ q✉❛❧ é ♣r♦✈❛❞❛♠❡♥t❡ ❝♦♥s✐st❡♥t❡✱ ♠❡s♠♦ ♥❛ ❛✉sê♥❝✐❛❞❡ t❛❧ ✐♥❢♦r♠❛çã♦✳ ❉❡ss❡ ♠♦❞♦✱ ❛ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛ ♥❡st❛ t❡s❡ ♣❛r❛ ❧♦❝❛❧✐③❛r ❝♦♦♣❡✲ r❛t✐✈❛♠❡♥t❡ ❡♥①❛♠❡s r♦❜ót✐❝♦s ❝♦♥t❡♠♣❧❛ ❛❧❣✉♠❛s q✉❡stõ❡s r❡❧❛t✐✈❛s à ❡s❝❛❧❛❜✐❧✐❞❛❞❡✱❛❧é♠ ❞❡ s❡r ❞❡s❝❡♥tr❛❧✐③❛❞❛ ❡ ❛ssí♥❝r♦♥❛✳ ❆s ♣r✐♥❝✐♣❛✐s ❝♦♥tr✐❜✉✐çõ❡s ❞❡st❡ tr❛❜❛❧❤♦ sã♦✿❼ ❯♠❛ ❛❜♦r❞❛❣❡♠ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ♣❛r❛ ❡♥①❛♠❡s r♦❜ó✲ t✐❝♦s q✉❡ ❣❡r❛ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♥s✐st❡♥t❡s✱ s❡♠ q✉❡ ♣❛r❛ ✐ss♦ s❡❥❛ ♥❡❝❡ssár✐♦ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ✐♥❢♦r♠❛çõ❡s ♣r♦✈❡♥✐❡♥t❡s ❞❡ t♦❞♦s ♦s r♦❜ôs ♥♦ ❣r✉♣♦✳❊ss❛ ❝❛r❛❝t❡ríst✐❝❛ ♣❡r♠✐t❡ ❞✐♠✐♥✉✐r ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦ ❡ ❡s♣❛ç♦✱ ♥❡❝❡ssá✲ r✐♦s ♣❛r❛ ❛ ❣❡r❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞♦s r♦❜ôs✱ ✈✐❛❜✐❧✐③❛♥❞♦ ❛ s✉❛✉t✐❧✐③❛çã♦ ❡♠ s✐st❡♠❛s r❡❛✐s✳ ❼ ❯♠❛ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛ ❞❡ ❡♥①❛♠❡s✱ ❜❛s❡❛❞❛ ♥♦ ❝♦♥❝❡✐t♦ ❞❡♣♦t❡♥❝✐❛❧ ❞✐❢❡r❡♥❝✐❛❧✳ ❖ ❝♦♠♣♦rt❛♠❡♥t♦ ❝♦❧❡t✐✈♦ é ❣❡r❛❞♦ ❛ ♣❛rt✐r ❞❛ ❝♦♠❜✐♥❛çã♦❞♦s ❝♦♠♣♦rt❛♠❡♥t♦s s❡❣r❡❣❛t✐✈♦ ❡ ❛❣r❡❣❛t✐✈♦✱ ❛❧é♠ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ❧í❞❡r✲ s❡❣✉✐❞♦r❀ ❈♦♥❢♦r♠❡ ❛♣r❡s❡♥t❛❞♦ ♥❛ r❡✈✐sã♦ ❞❡ ❧✐t❡r❛t✉r❛✱ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛r ❝♦♦♣❡r❛✲ t✐✈❛♠❡♥t❡ ❡♥①❛♠❡s r♦❜ót✐❝♦s ❛✐♥❞❛ é ♣♦✉❝♦ ❡①♣❧♦r❛❞♦ ♥❛ ❧✐t❡r❛t✉r❛✳ ❉❡ss❛ ❢♦r♠❛✱ ❡st❡tr❛❜❛❧❤♦ t❛♠❜é♠ ❝♦♥tr✐❜✉✐ ♥❡st❡ ❛s♣❡❝t♦ ♣♦r ❛♣r❡s❡♥t❛r ✉♠❛ ❛❜♦r❞❛❣❡♠ ♣❛r❛ ❡❢❡t✉❛r t❛❧ ❧♦❝❛❧✐③❛çã♦ ❞❡ ♠❛♥❡✐r❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ❡ ❛ssí♥❝r♦♥❛✳ ❆ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❝♦♥tí♥✉❛ ❡ ❛ ❛❜♦r❞❛❣❡♠ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛t✐✈❛❢♦r❛♠ ❛✈❛❧✐❛❞❛s t❛♥t♦ ❡♠ s✐♠✉❧❛çõ❡s q✉❛♥t♦ ❡♠ ❡①♣❡r✐♠❡♥t♦s ❝♦♠ r♦❜ôs r❡❛✐s✳ ◆❛s s✐♠✉❧❛çõ❡s✱ ✉♠ ♥ú♠❡r♦ s✐❣♥✐✜❝❛t✐✈♦ ❞❡ r♦❜ôs ❢♦✐ ❡♠♣r❡❣❛❞♦ ❡ ❛❧❣✉♥s ❛s♣❡❝t♦s ❞❛ ❧♦❝❛❧✐✲③❛çã♦ ❝♦♦♣❡r❛t✐✈❛ ❛♣❧✐❝❛❞❛ ❛ ❡♥①❛♠❡s r♦❜ót✐❝♦s ❢♦r❛♠ ❡①♣❧♦r❛❞♦s✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ♥♦s❡①♣❡r✐♠❡♥t♦s r❡❛✐s✱ ✉♠ ♥ú♠❡r♦ ♠❡♥♦r ❞❡ r♦❜ôs ❢♦✐ ❡♠♣r❡❣❛❞♦ ♥❛ ❢♦r♠❛ ❞❡ ✉♠❛ ♣r♦✈❛ ✻✳✶✳ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s✶✷✾ ❞❡ ❝♦♥❝❡✐t♦✳ ❖s r❡s✉❧t❛❞♦s ❞❡ ❛♠❜♦s ❢♦r❛♠ s❛t✐s❢❛tór✐♦s✱ ❛♣r❡s❡♥t❛♥❞♦ ✉♠❛ ♠❡❧❤♦r❛ s✐❣♥✐✜❝❛t✐✈❛ ♥❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❣r✉♣♦ q✉❛♥❞♦ ♦ ♠❡s♠♦ ❢❡③ ✉s♦ ❞❡ ❝♦♦♣❡r❛çã♦✳ ❆❧é♠❞✐ss♦✱ ♦s r❡s✉❧t❛❞♦s ♠♦str❛r❛♠ ❛ ❝♦♥s✐stê♥❝✐❛ ❞❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❣❡r❛❞❛s♣❡❧❛ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛✳ ✻✳✶ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ❊①t❡♥sõ❡s ❞❡st❡ tr❛❜❛❧❤♦ ♣♦❞❡♠ s❡r ❢❡✐t❛s t❛♥t♦ ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ à ❡str❛té❣✐❛ ❞❡♠♦✈✐♠❡♥t❛çã♦ ♣r♦♣♦st❛ q✉❛♥t♦ ♥♦ q✉❡ t❛♥❣❡ à ❛❜♦r❞❛❣❡♠ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❝♦♦♣❡r❛✲ t✐✈❛✳ ◆❛ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦✱ ✉♠❛ ♣♦ssí✈❡❧ ❡①t❡♥sã♦ s❡r✐❛ ❛ ❝♦♥s✐❞❡r❛çã♦ ❞❡♦❜stá❝✉❧♦s ❡ ❛♠❜✐❡♥t❡s ❞✐♥â♠✐❝♦s✳ ❯♠❛ ✐♥✈❡st✐❣❛çã♦ ✐♥✐❝✐❛❧ ♣♦❞❡r✐❛ ❝♦♥s✐❞❡r❛r ❛ ✉t✐❧✐✲③❛çã♦ ❞❡ ✉♠❛ ❡str❛té❣✐❛ s❡♠❡❧❤❛♥t❡ àq✉❡❧❛ ✐♠♣❧❡♠❡♥t❛❞❛ ❡♠ ❬P✐♠❡♥t❛✱ ✷✵✵✾❪✱ ♥❛ q✉❛❧♣❛rtí❝✉❧❛s ✈✐rt✉❛✐s sã♦ ❞✐s♣♦st❛s ♥❛s ❢r♦♥t❡✐r❛s ❞❡ ✉♠ ♦❜❥❡t♦✱ ❞❡ ♠♦❞♦ ❛ s❡r❡♠ ✉t✐❧✐③❛✲❞❛s ♣❛r❛ r❡♣r❡s❡♥t❛r ✉♠ ♦❜stá❝✉❧♦✳ ❚❛✐s ♣❛rtí❝✉❧❛s ♣♦❞❡r✐❛♠ s❡r ♠♦❞❡❧❛❞❛s ❞❡ ❢♦r♠❛ s❡♠❡❧❤❛♥t❡ ❛ ✉♠ r♦❜ô✱ ♣♦ré♠ ❛s ♠❡s♠❛s ♣❡rt❡♥❝❡r✐❛♠ ❛ ❣r✉♣♦s ❞✐❢❡r❡♥t❡s ❞❛q✉❡❧❡s✉t✐❧✐③❛❞♦s ♣❡❧♦ r♦❜ôs✳ ❉❡ss❡ ♠♦❞♦✱ t❛✐s ♣❛rtí❝✉❧❛s ❛t✉❛r✐❛♠ ❝♦♠♦ ♣♦t❡♥❝✐❛✐s ❛rt✐✜❝✐❛✐s r❡♣✉❧s✐✈♦s✱ ♣♦ss✐✈❡❧♠❡♥t❡ ♣❡r♠✐t✐♥❞♦ ❛♦s r♦❜ôs ❞❡s✈✐❛r❡♠ ❞♦s ♦❜stá❝✉❧♦s✳ ❉❡ ♠♦❞♦s❡♠❡❧❤❛♥t❡✱ ♠❛✐s ❞❡ ✉♠ ❡♥①❛♠❡ ♣♦❞❡r✐❛ s❡r ♠♦❞❡❧❛❞♦✱ s❡♥❞♦ q✉❡ r♦❜ôs ♣❡rt❡♥❝❡♥t❡s❛ ❡♥①❛♠❡s ❞✐st✐♥t♦s t❡r✐❛♠ t✐♣♦s ❞✐❢❡r❡♥t❡s✱ ♦ q✉❡ ♦s ♣❡r♠✐t✐r✐❛♠ ❡✈✐t❛r ❝♦❧✐sõ❡s✳ ❈♦♥❢♦r♠❡ ❝♦♥st❛t❛❞♦ ♥❡st❡ tr❛❜❛❧❤♦✱ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ✉♠ ú♥✐❝♦ r♦❜ô ❝♦♠ s❡♥s♦✲ r❡s ❝❛♣❛③❡s ❞❡ ♦❜t❡r ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦ ❛❜s♦❧✉t❛ ♣♦❞❡ ♥ã♦ s❡r s✉✜❝✐❡♥t❡ ♣❛r❛❡♥①❛♠❡s ♠✉✐t♦ ❣r❛♥❞❡s✳ ❆❧é♠ ❞✐ss♦✱ ♦ ❡♠♣r❡❣♦ ❞❡ ✉♠ ú♥✐❝♦ r♦❜ô ❝♦♠ t❛✐s ❝❛r❛❝t❡✲ ríst✐❝❛s ❝♦♠♣r♦♠❡t❡ ❛ r♦❜✉st❡③ ❞♦ s✐st❡♠❛✱ ✉♠❛ ✈❡③ q✉❡ ❛ ❢❛❧❤❛ ❞❡ss❡ r♦❜ô ♣♦❞❡r✐❛❞❡❣r❛❞❛r ❛ q✉❛❧✐❞❛❞❡ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ❣r✉♣♦✳ ❯♠❛ ♣♦ssí✈❡❧ ✐♥✈❡st✐❣❛çã♦ ❝♦♥s✐❞❡r❛✲ r✐❛ ♦ ❛✉♠❡♥t♦ ❞❡ r♦❜ôs ❝♦♠ t❛✐s ❝❛♣❛❝✐❞❛❞❡s✱ ❛❧é♠ ❞❡ ❡str❛té❣✐❛s ❞❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦♣❛r❛ ❞✐s♣♦r ❡ss❡s r♦❜ôs ❡♠ ❞❡t❡r♠✐♥❛❞♦s ❧♦❝❛✐s ♥♦ ❣r✉♣♦✳ ■ss♦ ♣♦❞❡r✐❛ ❝♦♥tr✐❜✉✐r ♣❛r❛♠❡❧❤♦r❛r ❛ r♦❜✉st❡③ ❞❛ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛✱ ✉♠❛ ✈❡③ q✉❡ ✐♥❢♦r♠❛çõ❡s ❞❡ ❧♦❝❛❧✐③❛çã♦♠❛✐s ❝♦♥✜á✈❡✐s ♣♦❞❡r✐❛♠ ❡st❛r ❛❞❡q✉❛❞❛♠❡♥t❡ ❞✐str✐❜✉í❞❛s ♥♦ ❡♥①❛♠❡ ❡ ❛ ❢❛❧❤❛ ❞❡❛❧❣✉♠ ❞❡ss❡s ✐♥t❡❣r❛♥t❡s ♣♦❞❡r✐❛ s❡r s✉♣r✐❞❛ ♣♦r ♦✉tr♦s ❛❣❡♥t❡s ♥♦ ❣r✉♣♦✳ ❊♠ ❡♥①❛✲♠❡s ❤❡t❡r♦❣ê♥❡♦s ❝♦♠♣♦st♦s ♣♦r ♠❛✐s r♦❜ôs ❝♦♠ ❝❛r❛❝t❡ríst✐❝❛s ❡s♣❡❝✐❛✐s✱ ❛ ✉t✐❧✐③❛çã♦❞❛ ✈❡rsã♦ ❣❡♥❡r❛❧✐③❛❞❛ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ■♥t❡rs❡çã♦ ❞❡ ❈♦✈❛r✐â♥❝✐❛s✱ ❙❈■✱ ❞❡s❝r✐t♦ ♥♦❆♣ê♥❞✐❝❡ ❈✱ ♣♦❞❡r✐❛ s❡r ❛✈❛❧✐❛❞❛✱ ❞❡ ❢♦r♠❛ ❛ ❧✐❞❛r ❝♦♠ ❛s ✐♥❢♦r♠❛çõ❡s ✐♥❞❡♣❡♥❞❡♥t❡s❡ ❝♦rr❡❧❛❝✐♦♥❛❞❛s✳ ❚❛❧ ❛❧❣♦r✐t♠♦ ❝♦♥t❡♠♣❧❛ s✐t✉❛çõ❡s ❞❡ t♦t❛❧ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ♦✉ t♦t❛❧✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❞❡ ♠❛♥❡✐r❛ ❛❞❡q✉❛❞❛✳ ❚❛r❡❢❛s ❞❡ ❝❛❣✐♥❣✱ ♥❛ q✉❛❧ ✉♠ ❝✐♥t✉rã♦ ❞❡ r♦❜ôs ❡♥✈♦❧✈❡ ✉♠ ❣r✉♣♦ ❡ ♦ ❝♦♥❞✉③ ♣❛r❛❞❡t❡r♠✐♥❛❞❛s r❡❣✐õ❡s ❞♦ ❛♠❜✐❡♥t❡✱ ♣♦❞❡r✐❛ s❡r ✉♠❛ ♣♦ssí✈❡❧ ❛♣❧✐❝❛çã♦ ♣❛r❛ ❡♥①❛♠❡s ✶✸✵❈❛♣ít✉❧♦ ✻✳ ❈♦♥❝❧✉sã♦ ❤❡t❡r♦❣ê♥❡♦s ❝♦♠ ♠❛✐s r♦❜ôs ❞♦t❛❞♦s ❞❡ s❡♥s♦r❡s ❝♦♠ ❝❛♣❛❝✐❞❛❞❡s ❡s♣❡❝✐❛✐s✳ ❆ss✐♠✱❡ss❡s r♦❜ôs s❡r✐❛♠ ❞✐s♣♦st♦s ❛✉t♦♥♦♠❛♠❡♥t❡ ♥❛ ❢r♦♥t❡✐r❛ ❞♦ ❣r✉♣♦✱ ♣♦ss✐❜✐❧✐t❛♥❞♦ ❛♠♦✈✐♠❡♥t❛çã♦ ❡♠ s❡❣✉r❛♥ç❛ ❞❡ ♦✉tr♦s r♦❜ôs ❞❡s♣r♦✈✐❞♦s ❞❡ t❛✐s ❝❛♣❛❝✐❞❛❞❡s✳ ❖s r♦❜ôs❞✐s♣♦st♦s ♥❛ ❢r♦♥t❡✐r❛ ✉t✐❧✐③❛r✐❛♠ s❡✉s s❡♥s♦r❡s ♣❛r❛ ♣r♦✈❡r ✉♠❛ ♠♦✈✐♠❡♥t❛çã♦ s❡❣✉r❛❞♦ ❣r✉♣♦ ♣❛r❛ ❞❡t❡r♠✐♥❛❞❛s r❡❣✐õ❡s ❞♦ ❛♠❜✐❡♥t❡✳ P♦r ✜♠✱ ♦✉tr♦ ❛s♣❡❝t♦ ❞❡ ✐♥✈❡st✐❣❛çã♦ ❢✉t✉r❛ s❡r✐❛ ❛ ❛♥á❧✐s❡ ♠❛t❡♠át✐❝❛ ❞♦s❝♦♥tr♦❧❛❞♦r❡s ✉t✐❧✐③❛❞♦s ♥❛s ❞✐✈❡rs❛s ❢❛s❡s ❞❛ ❡str❛té❣✐❛ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❝♦❧❡t✐✈❛✱ ❞❡♠♦❞♦ ❛ ♣r♦✈❡r ❣❛r❛♥t✐❛s ❞❡ ❡st❛❜✐❧✐❞❛❞❡ ❡ ❝♦♥✈❡r❣ê♥❝✐❛✳ ❚❛✐s ❣❛r❛♥t✐❛s ♣♦❞❡r✐❛♠ ❡st❛r r❡❧❛❝✐♦♥❛❞❛s t❛♥t♦ ❝♦♠ ♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❛✉tô♥♦♠♦ ❞♦ r♦❜ô ❧í❞❡r ♥♦ ❣r✉♣♦✱ q✉❛♥t♦♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ à ♠❛♥✉t❡♥çã♦ ❞❛ ❢♦r♠❛çã♦ ❛❧❝❛♥ç❛❞❛ ❞✉r❛♥t❡ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦❣r✉♣♦✳ ❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ❆❧✐t❛♣♣❡❤✱ ❘✳ ❏✳ ✫ P✐♠❡♥t❛✱ ▲✳ ❈✳ ❆✳ ✭✷✵✶✹✮✳ ❉✐str✐❜✉t❡❞ ❙❛❢❡ ❉❡♣❧♦②♠❡♥t ♦❢ ◆❡t✇♦r✲❦❡❞ ❘♦❜♦ts✳ ❊♠ ❚❤❡ ✶✷t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❙②♠♣♦s✐✉♠ ♦♥ ❉✐str✐❜✉t❡❞ ❆✉t♦♥♦♠♦✉s❘♦❜♦t✐❝ ❙②st❡♠s ✭❉❆❘❙ ✷✵✶✹✮✳ ❆r❛♠❜❡❧✱ P✳ ✳❀ ❘❛❣♦✱ ❈✳ ✫ ▼❡❤r❛✱ ❘✳ ❑✳ ✭✷✵✵✶✮✳ ❈♦✈❛r✐❛♥❝❡ ■♥t❡rs❡❝t✐♦♥ ❆❧❣♦r✐t❤♠ ❢♦r❉✐str✐❜✉t❡❞ ❙♣❛❝❡❝r❛❢t ❙t❛t❡ ❊st✐♠❛t✐♦♥✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ❆♠❡r✐❝❛♥ ❈♦♥tr♦❧❈♦♥❢❡r❡♥❝❡✱ ♣♣✳ ✹✸✾✽✕✹✹✵✸✱ ❆r❧✐♥❣t♦♥✱ ❱❆✳ ❆r✉❧❛♠♣❛❧❛♠✱ ▼✳ ❙✳❀ ▼❛s❦❡❧❧✱ ❙✳❀ ●♦r❞♦♥✱ ◆✳❀ ✫ ❈❧❛♣♣✱ ❚✳ ✭✷✵✵✷✮✳ ❆ ❚✉t♦r✐❛❧♦♥ P❛rt✐❝❧❡ ❋✐❧t❡rs ❢♦r ❖♥❧✐♥❡ ◆♦♥❧✐♥❡❛r✴◆♦♥✲●❛✉ss✐❛♥ ❇❛②❡s✐❛♥ ❚r❛❝❦✐♥❣✳ ■❊❊❊❚r❛♥s❛❝t✐♦♥s ♦♥ ❙✐❣♥❛❧ Pr♦❝❡ss✐♥❣✱ ✺✵✭✷✮✿✶✼✹✕✶✽✽✳ ❇❛❤❝❡❝✐✱ ❊✳❀ ❙♦②s❛❧✱ ❖✳ ✫ ❙❛❤✐♥✱ ❊✳ ✭✷✵✵✸✮✳ ❆ r❡✈✐❡✇✿ P❛tt❡r♥ ❢♦r♠❛t✐♦♥ ❛♥❞ ❛❞❛♣t❛t✐♦♥✐♥ ♠✉❧t✐✲r♦❜♦t s②st❡♠s✳ ❚❡❝❤♥✐❝❛❧ r❡♣♦rt✱ ❘♦❜♦t✐❝s ■♥st✐t✉t❡✳ ❇❛❤r✱ ❆✳❀ ❲❛❧t❡r✱ ▼✳ ❘✳ ✫ ▲❡♦♥❛r❞✱ ❏✳ ❏✳ ✭✷✵✵✾✮✳ ❈♦♥s✐st❡♥t ❈♦♦♣❡r❛t✐✈❡ ▲♦❝❛❧✐③❛t✐♦♥✳❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱♣♣✳ ✸✹✶✺✕✸✹✷✷✱ ❑♦❜❡✱ ❏❛♣❛♥✳ ❇❛✐❧❡②✱ ❚✳❀ ❇r②s♦♥✱ ▼✳❀ ▼✉✱ ❍✳❀ ❱✐❛❧✱ ❏✳❀ ▼❝❈❛❧♠❛♥✱ ▲✳ ✫ ❉✉rr❛♥t✲❲❤②t❡✱ ❍✳ ✭✷✵✶✶✮✳❉❡❝❡♥tr❛❧✐s❡❞ ❈♦♦♣❡r❛t✐✈❡ ▲♦❝❛❧✐s❛t✐♦♥ ❢♦r ❍❡t❡r♦❣❡♥❡♦✉s ❚❡❛♠s ♦❢ ▼♦❜✐❧❡ ❘♦❜♦ts✳❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱♣♣✳ ✷✽✺✾✕✷✽✻✺✱ ❙❤❛♥❣❤❛✐✱ ❈❤✐♥❛✳ ❇❛❧❝❤✱ ❚✳ ✭✶✾✾✾✮✳ ❚❤❡ ✐♠♣❛❝t ♦❢ ❞✐✈❡rs✐t② ♦♥ ♣❡r❢♦r♠❛♥❝❡ ✐♥ ♠✉❧t✐✲r♦❜♦t ❢♦r❛❣✐♥❣✳ ❊♠Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ t❤✐r❞ ❛♥♥✉❛❧ ❝♦♥❢❡r❡♥❝❡ ♦♥ ❆✉t♦♥♦♠♦✉s ❆❣❡♥ts✱ ❆●❊◆❚❙ ✬✾✾✱♣♣✳ ✾✷✕✾✾✱ ◆❡✇ ❨♦r❦✱ ◆❨✱ ❯❙❆✳ ❆❈▼✳ ❇❛❧❝❤✱ ❚✳ ✫ ❆r❦✐♥✱ ❘✳ ❈✳ ✭✶✾✾✽✮✳ ❇❡❤❛✈✐♦r✲❇❛s❡❞ ❋♦r♠❛t✐♦♥ ❈♦♥tr♦❧ ❢♦r ▼✉❧t✐r♦❜♦t❚❡❛♠s✳ ■❊❊❊ ❚r❛♥s❛❝t✐♦♥s ♦♥ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ✶✹✭✻✮✿✾✷✻✕✾✸✾✳ ✶✸✷❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá❢✐❝❛s ❇❛r✲❙❤❛❧♦♠✱ ❨✳❀ ▲✐✱ ❳✳✲❘✳ ✫ ❑✐r✉❜❛r❛❥❛♥✱ ❚✳ ✭✷✵✵✶✮✳ ❊st✐♠❛t✐♦♥ ✇✐t❤ ❆♣♣❧✐❝❛t✐♦♥s t♦❚r❛❝❦✐♥❣ ❛♥❞ ◆❛✈✐❣❛t✐♦♥✿ ❚❤❡♦r② ❆❧❣♦r✐t❤♠s ❛♥❞ ❙♦❢t✇❛r❡✳ ❏♦❤♥ ❲✐❧❡② ✫ ❙♦♥s✱ ■♥❝✳ ❇❛②✐♥❞✐r✱ ▲✳ ✫ ❙❛❤✐♥✱ ❊✳ ✭✷✵✵✼✮✳ ❆ r❡✈✐❡✇ ♦❢ st✉❞✐❡s ✐♥ s✇❛r♠ r♦❜♦t✐❝s✳ ❚✉r❦✐s❤ ❏♦✉r♥❛❧♦❢ ❊❧❡❝tr✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ❈♦♠♣✉t❡r ❙❝✐❡♥❝❡s✱ ✶✺✭✷✮✿✶✶✺✕✶✹✼✳ ❇❡❧t❛✱ ❈✳❀ P❡r❡✐r❛✱ ●✳ ❆✳ ❙✳ ✫ ❑✉♠❛r✱ ❱✳ ✭✷✵✵✸✮✳ ❈♦♥tr♦❧ ♦❢ ❛ t❡❛♠ ♦❢ ❝❛r✲❧✐❦❡ r♦❜♦ts✉s✐♥❣ ❛❜str❛❝t✐♦♥s✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❉❡❝✐s✐♦♥❛♥❞ ❈♦♥tr♦❧✱ ✈♦❧✉♠❡ ✷✱ ♣♣✳ ✶✺✷✵✕✶✺✷✺✳ ❇❡rts❡❦❛s✱ ❉✳ P✳ ✫ ❚s✐ts✐❦❧✐s✱ ❏✳ ◆✳ ✭✷✵✵✽✮✳ ■♥tr♦❞✉❝t✐♦♥ t♦ Pr♦❜❛❜✐❧✐t②✳ ❆t❤❡♥❛ ❙❝✐❡♥t✐✜❝✱✷♥❞ ❡❞✐çã♦✳ ❇♦♥❛❜❡❛✉✱ ❊✳❀ ❉♦r✐❣♦✱ ▼✳ ✫ ❚❤❡r❛❧❛③✱ ●✳ ✭✶✾✾✾✮✳ ❙✇❛r♠ ■♥t❡❧❧✐❣❡♥❝❡✿ ❋r♦♠ ◆❛t✉r❛❧ t♦ ❆rt✐✜❝✐❛❧ ❙②st❡♠s✳ ❖①❢♦r❞ ❯♥✐✈❡rs✐t② Pr❡ss✳❇♦r❡♥st❡✐♥✱ ❏✳❀ ❊✈❡r❡tt✱ ❍✳ ❘✳❀ ❋❡♥❣✱ ▲✳ ✫ ❲❡❤❡✱ ❉✳ ✭✶✾✾✼✮✳ ▼♦❜✐❧❡ ❘♦❜♦t P♦s✐t✐♦♥✐♥❣ ✕ ❙❡♥s♦rs ❛♥❞ ❚❡❝❤♥✐q✉❡s✳ ❏♦✉r♥❛❧ ♦❢ ❘♦❜♦t✐❝ ❙②st❡♠s✱ ✶✹✭✹✮✿✷✸✶✕✷✹✾✳❇♦r❡♥st❡✐♥✱ ❏✳ ✫ ❋❡♥❣✱ ▲✳ ✭✶✾✾✻✮✳ ▼❡❛s✉r❡♠❡♥t ❛♥❞ ❝♦rr❡❝t✐♦♥ ♦❢ s②st❡♠❛t✐❝ ♦❞♦♠❡tr② ❡rr♦rs ✐♥ ♠♦❜✐❧❡ r♦❜♦ts✳ ■❊❊❊ ❏♦✉r♥❛❧ ♦❢ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ✶✷✭✺✮✿✽✻✾✕✽✽✵✳❇✉r❣❛r❞✱ ❲✳❀ ▼♦♦rs✱ ▼✳❀ ❋♦①✱ ❉✳❀ ❙✐♠♠♦♥s✱ ❘✳ ✫ ❚❤r✉♥✱ ❙✳ ✭✷✵✵✵✮✳ ❈♦❧❧❛❜♦r❛t✐✈❡ ▼✉❧t✐✲❘♦❜♦t ❊①♣❧♦r❛t✐♦♥✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ✈♦❧✉♠❡ ✶✱ ♣♣✳ ✹✼✻✕✹✽✶✱ ❙❛♥ ❋r❛♥❝✐s❝♦✱ ❈❆✱ ❯❙❆✳ ❈❛♦✱ ❨✳ ❯✳❀ ❋✉❦✉♥❛❣❛✱ ❆✳ ❙✳ ✫ ❑❛❤♥❣✱ ❆✳ ❇✳ ✭✶✾✾✼✮✳ ❈♦♦♣❡r❛t✐✈❡ ▼♦❜✐❧❡ ❘♦❜♦t✐❝s✿❆♥t❡❝❡❞❡♥ts ❛♥❞ ❉✐r❡❝t✐♦♥s✳ ❆✉t♦♥♦♠♦✉s ❘♦❜♦ts✱ ✹✭✶✮✿✼✕✷✼✳ ❈❛r♣✐♥✱ ❙✳ ✫ P❛r❦❡r✱ ▲✳ ❊✳ ✭✷✵✵✷✮✳ ❈♦♦♣❡r❛t✐✈❡ ❧❡❛❞❡r ❢♦❧❧♦✇✐♥❣ ✐♥ ❛ ❞✐str✐❜✉t❡❞ ♠✉❧t✐✲ r♦❜♦t s②st❡♠✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❘♦❜♦t✐❝s❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ✈♦❧✉♠❡ ✸✱ ♣♣✳ ✷✾✾✹ ✕✸✵✵✶✳ ❈❛rr✐❧❧♦✲❆r❝❡✱ ▲✳ ❈✳❀ ◆❡r✉r❦❛r✱ ❊✳ ❉✳❀ ●♦r❞✐❧❧♦✱ ❏✳ ▲✳ ✫ ❘♦✉♠❡❧✐♦t✐s✱ ❙✳ ■✳ ✭✷✵✶✸✮✳❉❡❝❡♥tr❛❧✐③❡❞ ♠✉❧t✐✲r♦❜♦t ❝♦♦♣❡r❛t✐✈❡ ❧♦❝❛❧✐③❛t✐♦♥ ✉s✐♥❣ ❝♦✈❛r✐❛♥❝❡ ✐♥t❡rs❡❝t✐♦♥✳ ❊♠Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊✴❘❙❏ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ■♥t❡❧❧✐❣❡♥t ❘♦❜♦ts ❛♥❞❙②st❡♠s✱ ♣♣✳ ✶✹✶✷✕✶✹✶✼✱ ❚♦❦②♦✱ ❏❛♣❛♥✳ ❈❤❛✐♠♦✇✐❝③✱ ▲✳ ✫ ❑✉♠❛r✱ ❱✳ ✭✷✵✵✹✮✳ ❆❡r✐❛❧ ❙❤❡♣❤❡r❞s✿ ❈♦♦r❞✐♥❛t✐♦♥ ❛♠♦♥❣ ❯❆❱s❛♥❞ ❙✇❛r♠s ♦❢ ❘♦❜♦ts✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✼t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❙②♠♣♦s✐✉♠ ♦♥❉✐str✐❜✉t❡❞ ❆✉t♦♥♦♠♦✉s ❘♦❜♦t✐❝ ❙②st❡♠s✱ ♣♣✳ ✷✸✶✕✷✹✵✳ ❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá❢✐❝❛s✶✸✸ ❈♦st❛✱ ❊✳❀ ❙❤✐r♦♠❛✱ P✳ ✫ ❈❛♠♣♦s✱ ▼✳ ❋✳ ▼✳ ✭✷✵✶✷✮✳ ❈♦♦♣❡r❛t✐✈❡ r♦❜♦t✐❝ ❡①♣❧♦r❛t✐♦♥❛♥❞ tr❛♥s♣♦rt ♦❢ ✉♥❦♥♦✇♥ ♦❜❥❡❝ts✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✷✵✶✷ ▲❆❘❙✴❙❇❘ ▲❛t✐♥❆♠❡r✐❝❛♥ ❘♦❜♦t✐❝s ❙②♠♣♦s✐✉♠ ✴ ❇r❛③✐❧✐❛♥ ❘♦❜♦t✐❝s ❙②♠♣♦s✐✉♠✱ ✷✵✶✷✳✱ ❋♦rt❛❧❡③❛✳ ❉❡ ▲✉❝❛✱ ❆✳ ✫ ❖r✐♦❧♦✱ ●✳ ✭✶✾✾✹✮✳ ▲♦❝❛❧ ■♥❝r❡♠❡♥t❛❧ P❧❛♥♥✐♥❣ ❢♦r ◆♦♥❤♦❧♦♥♦♠✐❝ ▼♦❜✐❧❡❘♦❜♦ts✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❘♦❜♦t✐❝s ❛♥❞❆✉t♦♠❛t✐♦♥✳ ❉❡❧❧❛❡rt✱ ❋✳❀ ❆❧❡❣r❡✱ ❋✳ ✫ ▼❛rt✐♥s♦♥✱ ❊✳ ❇✳ ✭✷✵✵✸✮✳ ■♥tr✐♥s✐❝ ❧♦❝❛❧✐③❛t✐♦♥ ❛♥❞ ♠❛♣♣✐♥❣✇✐t❤ ✷ ❛♣♣❧✐❝❛t✐♦♥s✿ ❉✐✛✉s✐♦♥ ♠❛♣♣✐♥❣ ❛♥❞ ♠❛r❝♦ ♣♦❧♦ ❧♦❝❛❧✐③❛t✐♦♥✳ ❊♠ Pr♦❝❡❡❞✐♥❣s♦❢ t❤❡ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ✈♦❧✉♠❡ ✷✱ ♣♣✳✷✸✹✹✕✷✸✹✾✱ ❚❛✐♣❡✐✱ ❚❛✐✇❛♥✳ ❉❡s❛✐✱ ❏✳ P✳❀ ❖str♦✇s❦✐✱ ❏✳ ✫ ❑✉♠❛r✱ ❱✳ ✭✶✾✾✽✮✳ ❈♦♥tr♦❧❧✐♥❣ ❢♦r♠❛t✐♦♥s ♦❢ ♠✉❧t✐♣❧❡♠♦❜✐❧❡ r♦❜♦ts✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❘♦❜♦t✐❝s❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ✈♦❧✉♠❡ ✹✱ ♣♣✳ ✷✽✻✹✕✷✽✻✾✳ ❉♦r✐❣♦✱ ▼✳ ✫ ❙tüt③❧❡✱ ❚✳ ✭✷✵✵✷✮✳ ❚❤❡ ❛♥t ❝♦❧♦♥② ♦♣t✐♠✐③❛t✐♦♥ ♠❡t❛❤❡✉r✐st✐❝✿ ❆❧❣♦✲ r✐t❤♠s✱ ❛♣♣❧✐❝❛t✐♦♥s ❛♥❞ ❛❞✈❛♥❝❡s✳ ❊♠ ●❧♦✈❡r✱ ❋✳ ✫ ❑♦❝❤❡♥❜❡r❣❡r✱ ●✳✱ ❡❞✐t♦r❡s✱❍❛♥❞❜♦♦❦ ♦❢ ▼❡t❛❤❡✉r✐st✐❝s✱ ✈♦❧✉♠❡ ✺✼ ♦❢ ■♥t❡r♥❛t✐♦♥❛❧ ❙❡r✐❡s ✐♥ ❖♣❡r❛t✐♦♥s ❘❡s❡✲❛r❝❤ ✫ ▼❛♥❛❣❡♠❡♥t ❙❝✐❡♥❝❡✱ ❝❤❛♣t❡r ✾✱ ♣♣✳ ✷✺✶✕✷✽✺✳ ❑❧✉✇❡r ❆❝❛❞❡♠✐❝ P✉❜❧✐s❤❡rs✱❇♦st♦♥✱ ▼❆✳ ❉♦✉❝❡t✱ ❆✳❀ ❞❡ ❋r❡✐t❛s✱ ◆✳ ✫ ●♦r❞♦♥✱ ◆✳ ✭✷✵✵✶✮✳ ❙❡q✉❡♥t✐❛❧ ▼♦♥t❡ ❈❛r❧♦ ▼❡t❤♦❞s ✐♥Pr❛❝t✐❝❡✱ ❝❤❛♣t❡r ❆♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ❙❡q✉❡♥t✐❛❧ ▼♦♥t❡ ❈❛r❧♦ ▼❡t❤♦❞s✱ ♣♣✳ ✶✕✶✸✳❙♣r✐♥❣❡r✳ ❉✉❞❡❦✱ ●✳❀ ❏❡♥❦✐♥✱ ▼✳❀ ▼✐❧✐♦s✱ ❊✳ ✫ ❲✐❧❦❡s✱ ❉✳ ✭✶✾✾✸✮✳ ❆ ❚❛①♦♥♦♠② ❢♦r ❙✇❛r♠❘♦❜♦ts✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊✴❘❙❏ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ■♥t❡❧❧✐❣❡♥t❘♦❜♦ts ❛♥❞ ❙②st❡♠s✱ ❚♦❦②♦✱ ❏❛♣❛♥✳ ❉✉❞❡❦✱ ●✳❀ ❏❡♥❦✐♥✱ ▼✳ ❘✳ ▼✳❀ ▼✐❧✐♦s✱ ❊✳ ✫ ❲✐❧❦❡s✱ ❉✳ ✭✶✾✾✻✮✳ ❆ t❛①♦♥♦♠② ❢♦r ♠✉❧t✐✲❛❣❡♥t r♦❜♦t✐❝s✳ ❆✉t♦♥♦♠♦✉s ❘♦❜♦ts✱ ✸✭✹✮✿✸✼✺✕✸✾✼✳ ❉✉rr❛♥t✲❲❤②t❡✱ ❍✳ ✫ ❇❛✐❧❡②✱ ❚✳ ✭✷✵✵✻✮✳ ❙✐♠✉❧t❛♥❡♦✉s ❧♦❝❛❧✐③❛t✐♦♥ ❛♥❞ ♠❛♣♣✐♥❣ ✭s❧❛♠✮✿P❛rt ✐ t❤❡ ❡ss❡♥t✐❛❧ ❛❧❣♦r✐t❤♠s✳ ■❊❊❊ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥ ▼❛❣❛③✐♥❡✱ ✶✸✭✷✮✿✾✾✕✶✶✵✳ ❊❧❢❡s✱ ❆✳ ✭✶✾✾✵✮✳ ❖❝❝✉♣❛♥❝② ●r✐❞s✿ ❆ ❙t♦❝❤❛st✐❝ ❙♣❛t✐❛❧ ❘❡♣r❡s❡♥t❛t✐♦♥ ❢♦r ❆❝t✐✈❡ ❘♦✲❜♦t P❡r❝❡♣t✐♦♥✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ❙✐①t❤ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❯♥❝❡rt❛✐♥t② ✐♥ ❆rt✐✜❝✐❛❧■♥t❡❧❧✐❣❡♥❝❡ ✭❯❆■✶✾✾✵✮✱ ♣♣✳ ✶✸✻✕✶✹✻✳ ✶✸✹❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá❢✐❝❛s ❋❛r✐♥❡❧❧✐✱ ❆✳❀ ■♦❝❝❤✐✱ ▲✳ ✫ ◆❛r❞✐✱ ❉✳ ✭✷✵✵✹✮✳ ▼✉❧t✐r♦❜♦t ❙②st❡♠s✿ ❆ ❈❧❛ss✐✜❝❛t✐♦♥❋♦❝✉s❡❞ ♦♥ ❈♦♦r❞✐♥❛t✐♦♥✳ ■❊❊❊ ❚r❛♥s❛❝t✐♦♥s ♦♥ ❙②st❡♠s✱ ▼❛♥✱ ❛♥❞ ❈②❜❡r♥❡t✐❝s✖P❛rt ❇✿ ❈②❜❡r♥❡t✐❝s✱ ✸✹✭✺✮✿✷✵✶✺✕✷✵✷✽✳ ❋✐❧❤♦✱ ❊✳ ❇✳ ❋✳ ✫ P✐♠❡♥t❛✱ ▲✳ ❈✳ ❆✳ ✭✷✵✶✺✮✳ ❙❡❣r❡❣❛t✐♥❣ ▼✉❧t✐♣❧❡ ●r♦✉♣s ♦❢ ❍❡t❡r♦❣❡✲♥❡♦✉s ❯♥✐ts ✐♥ ❘♦❜♦t ❙✇❛r♠s ✉s✐♥❣ ❆❜str❛❝t✐♦♥s✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊✴❘❙❏■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ■♥t❡❧❧✐❣❡♥t ❘♦❜♦ts ❛♥❞ ❙②st❡♠s✳ ❋♦①✱ ❉✳❀ ❇✉r❣❛r❞✱ ❲✳❀ ❑r✉♣♣❛✱ ❍✳ ✫ ❚❤r✉♥✱ ❙✳ ✭✷✵✵✵✮✳ ❆ Pr♦❜❛❜✐❧✐st✐❝ ❆♣♣r♦❛❝❤ t♦❈♦❧❧❛❜♦r❛t✐✈❡ ▼✉❧t✐✲❘♦❜♦t ▲♦❝❛❧✐③❛t✐♦♥✳ ❆✉t♦♥♦♠♦✉s ❘♦❜♦ts✱ ✽✿✸✷✺✕✸✹✹✳ ❋♦①✱ ❉✳❀ ❍✐❣❤t♦✇❡r✱ ❏✳❀ ▲✐❛♦✱ ▲✳❀ ❙❝❤✉❧③✱ ❉✳ ✫ ❇♦rr✐❡❧❧♦✱ ●✳ ✭✷✵✵✸✮✳ ❇❛②❡s✐❛♥ ❋✐❧t❡r✐♥❣❢♦r ▲♦❝❛t✐♦♥ ❊st✐♠❛t✐♦♥✳ P❡r✈❛s✐✈❡ ❈♦♠♣✉t✐♥❣✱ ■❊❊❊✱ ✷✭✸✮✿✷✹✕✸✸✳ ●❛r❝✐❛✱ ❘✳ ❋✳ ✫ ❈❤❛✐♠♦✇✐❝③✱ ▲✳ ✭✷✵✵✾✮✳ ❯♠❛ ■♥❢r❛✲❡str✉t✉r❛ ♣❛r❛ ❊①♣❡r✐♠❡♥t❛çã♦❝♦♠ ❊♥①❛♠❡s ❞❡ ❘♦❜ôs✳ ❊♠ ❆♥❛✐s ❞♦ ❙✐♠♣ós✐♦ ❇r❛s✐❧❡✐r♦ ❞❡ ❆✉t♦♠❛çã♦ ■♥t❡❧✐❣❡♥t❡✭❙❇❆■✮✱ ❇r❛sí❧✐❛✱ ❉❋ ✲ ❇r❛s✐❧✳ ●❛r❝✐❛✱ ❘✳ ❋✳❀ ❙❤✐r♦♠❛✱ P✳ ▼✳❀ ❈❤❛✐♠♦✇✐❝③✱ ▲✳ ✫ ❈❛♠♣♦s✱ ▼✳ ❋✳ ▼✳ ✭✷✵✵✼✮✳ ❯♠❛r❝❛❜♦✉ç♦ ♣❛r❛ ❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ ❡♥①❛♠❡s ❞❡ r♦❜ôs✳ ❊♠ ❆♥❛✐s ❞♦ ❙✐♠♣ós✐♦ ❇r❛s✐❧❡✐r♦❞❡ ❆✉t♦♠❛çã♦ ■♥t❡❧✐❣❡♥t❡ ✭❙❇❆■✮✱ ❋❧♦r✐❛♥ó♣♦❧✐s✱ ❙❈ ✲ ❇r❛③✐❧✳ ●❡r❦❡②✱ ❇✳ P✳❀ ❱❛✉❣❤❛♥✱ ❘✳ ❚✳ ✫ ❍♦✇❛r❞✱ ❆✳ ✭✷✵✵✸✮✳ ❚❤❡ ♣❧❛②❡r✴st❛❣❡ ♣r♦❥❡❝t✿ ❚♦♦❧s ❢♦r♠✉❧t✐✲r♦❜♦t ❛♥❞ ❞✐str✐❜✉t❡❞ s❡♥s♦r s②st❡♠s✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✶✶t❤ ■♥t❡r♥❛t✐♦♥❛❧❈♦♥❢❡r❡♥❝❡ ♦♥ ❆❞✈❛♥❝❡❞ ❘♦❜♦t✐❝s ✭■❈❆❘ ✷✵✵✸✮✱ ♣♣✳ ✸✶✼✕✸✷✸✱ ❈♦✐♠❜r❛✱ P♦rt✉❣❛❧✳ ●♦r❞♦♥✱ ◆✳❀ ❙❛❧♠♦♥❞✱ ❉✳ ✫ ❙♠✐t❤✱ ❆✳ ❋✳ ▼✳ ✭✶✾✾✸✮✳ ◆♦✈❡❧ ❛♣♣r♦❛❝❤ t♦ ♥♦♥❧✐♥❡❛r✴♥♦♥✲●❛✉ss✐❛♥ ❇❛②❡s✐❛♥ st❛t❡ ❡st✐♠❛t✐♦♥✳ ■❊❊❊ Pr♦❝❡❡❞✐♥❣s ♦❢ ❘❛❞❛r ❛♥❞ ❙✐❣♥❛❧ Pr♦❝❡s✲ s✐♥❣✱ ✶✹✵✭✷✮✿✶✵✼✕✶✶✸✳ ●r❛❜♦✇s❦✐✱ ❘✳❀ ◆❛✈❛rr♦✲❙❡r♠❡♥t✱ ▲✳ ❊✳❀ P❛r❡❞✐s✱ ❈✳ ❏✳ ✫ ❑❤♦s❧❛✱ P✳ ❑✳ ✭✷✵✵✵✮✳ ❍❡✲ t❡r♦❣❡♥❡♦✉s ❚❡❛♠s ♦❢ ▼♦❞✉❧❛r ❘♦❜♦ts ❢♦r ▼❛♣♣✐♥❣ ❛♥❞ ❊①♣❧♦r❛t✐♦♥✳ ❆✉t♦♥♦♠♦✉s❘♦❜♦ts✱ ✽✿✷✾✸✕✸✵✽✳ ●r♦ÿ✱ ❘✳❀ ▼❛❣♥❡♥❛t✱ ❙✳ ✫ ▼♦♥❞❛❞❛✱ ❋✳ ✭✷✵✵✾✮✳ ❙❡❣r❡❣❛t✐♦♥ ✐♥ ❙✇❛r♠s ♦❢ ▼♦❜✐❧❡ ❘♦❜♦ts❇❛s❡❞ ♦♥ t❤❡ ❇r❛③✐❧ ◆✉t ❊✛❡❝t✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊✴❘❙❏ ■♥t❡r♥❛t✐♦♥❛❧❈♦♥❢❡r❡♥❝❡ ♦♥ ■♥t❡❧❧✐❣❡♥t ❘♦❜♦ts ❛♥❞ ❙②st❡♠s✱ ♣♣✳ ✹✸✹✾✕✹✸✺✻✱ ❙t✳ ▲♦✉✐s✱ ❯❙❆✳ ❍✐❞❛❦❛✱ ❨✳❀ ▼♦✉r✐❦✐s✱ ❆✳ ✫ ❘♦✉♠❡❧✐♦t✐s✱ ❙✳ ✭✷✵✵✺✮✳ ❖♣t✐♠❛❧ ❢♦r♠❛t✐♦♥s ❢♦r ❝♦♦♣❡r❛t✐✈❡❧♦❝❛❧✐③❛t✐♦♥ ♦❢ ♠♦❜✐❧❡ r♦❜♦ts✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡♦♥ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ♣♣✳ ✹✶✷✻✕✹✶✸✶✱ ❇❛r❝❡❧♦♥❛✱ ❙♣❛✐♥✳ ❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá❢✐❝❛s✶✸✺ ❍♦✇❛r❞✱ ❆✳❀ ▼❛t❛r✐❝✱ ▼✳ ✫ ❙✉❦❤❛t♠❡✱ ●✳ ✭✷✵✵✸✮✳ P✉tt✐♥❣ t❤❡ ✬✐✬ ✐♥ ✬t❡❛♠✬✿ ❛♥ ❡❣♦✲❝❡♥tr✐❝ ❛♣♣r♦❛❝❤ t♦ ❝♦♦♣❡r❛t✐✈❡ ❧♦❝❛❧✐③❛t✐♦♥✳ ❊♠ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ✷✵✵✸✳Pr♦❝❡❡❞✐♥❣s✳ ■❈❘❆ ✬✵✸✳ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥✱ ✈♦❧✉♠❡ ✶✱ ♣♣✳ ✽✻✽✕✽✼✹✱❚❛✐♣❡✐✱ ❚❛✐✇❛♥✳ ❍♦✇❛r❞✱ ❆✳❀ ▼❛t❛r✐➣✱ ▼✳ ❏✳ ✫ ❙✉❦❤❛t♠❡✱ ●✳ ❙✳ ✭✷✵✵✷✮✳ ▲♦❝❛❧✐③❛t✐♦♥ ❢♦r ▼♦❜✐❧❡ ❘♦❜♦t❚❡❛♠s ❯s✐♥❣ ▼❛①✐♠✉♠ ▲✐❦❡❧✐❤♦♦❞ ❊st✐♠❛t✐♦♥✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊✴❘❙❏■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ■♥t❡❧❧✐❣❡♥t ❘♦❜♦ts ❛♥❞ ❙②st❡♠s✱ ✈♦❧✉♠❡ ✶✱ ♣♣✳ ✹✸✹✕✹✸✾✱▲❛✉s❛♥♥❡✱ ❙✇✐t③❡r❧❛♥❞✳ ■s❛r❞✱ ▼✳ ✫ ❇❧❛❦❡✱ ❆✳ ✭✶✾✾✽✮✳ ❈♦♥❞❡♥s❛t✐♦♥ ✕ ❝♦♥❞✐t✐♦♥❛❧ ❞❡♥s✐t② ♣r♦♣❛❣❛t✐♦♥ ❢♦r✈✐s✉❛❧ tr❛❝❦✐♥❣✳ ■♥t❡r♥❛t✐♦♥❛❧ ❏♦✉r♥❛❧ ♦❢ ❈♦♠♣✉t❡r ❱✐s✐♦♥✱ ✷✾✿✺✕✷✽✳ ❏♦❤♥s♦♥✱ ❘✳ ❆✳ ✫ ❲✐❝❤❡r♥✱ ❉✳ ❲✳ ✭✷✵✵✼✮✳ ❆♣♣❧✐❡❞ ▼✉❧t✐✈❛r✐❛t❡ ❙t❛t✐st✐❝❛❧ ❆♥❛❧②s✐s✳P❡❛rs♦♥ ❊❞✉❝❛t✐♦♥ ■♥❝✳✱ ◆❡✇ ❏❡rs❡②✱ ✻t❤ ❡❞✐çã♦✳ ❏✉❛♥✲♣✐♥❣✱ ❩✳❀ ❏✐♥✲❣❛♥❣✱ ▲✳❀ ❳✐❛♥✲✇❡♥✱ ●✳ ✫ ❨✐♥❣✲q✐❛♦✱ ❈✳ ✭✷✵✶✵✮✳ ❘❡s❡❛r❝❤ ♦❢ ♣❛t❤♣❧❛♥♥✐♥❣ ❢♦r ♠♦❜✐❧❡ r♦❜♦t ❜❛s❡❞ ♦♥ ✐♠♣r♦✈❡❞ ❛♥t ❝♦❧♦♥② ♦♣t✐♠✐③❛t✐♦♥ ❛❧❣♦r✐t❤♠✳❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆❞✈❛♥❝❡❞ ❈♦♠♣✉t❡r ❈♦♥tr♦❧✱✈♦❧✉♠❡ ✸✱ ♣♣✳ ✷✹✶✕✷✹✺✳ ❏✉❧✐❡r✱ ❙✳ ✫ ❯❤❧♠❛♥♥✱ ❏✳ ❑✳ ✭✷✵✵✶✮✳ ●❡♥❡r❛❧ ❉❡❝❡♥tr❛❧✐③❡❞ ❉❛t❛ ❋✉s✐♦♥ ✇✐t❤ ❈♦✈❛r✐❛♥❝❡■♥t❡rs❡❝t✐♦♥ ✭❈■✮✳ ❊♠ ❍❛❧❧✱ ❉✳ ✫ ▲❧✐♥❛s✱ ❏✳✱ ❡❞✐t♦r❡s✱ ❍❛♥❞❜♦♦❦ ♦❢ ❉❛t❛ ❋✉s✐♦♥✳ ❈❘❈Pr❡ss✱ ❇♦❝❛ ❘❛t♦♥ ❋▲✱ ❯❙❆✳ ❏✉❧✐❡r✱ ❙✳ ❏✳ ✫ ❯❤❧♠❛♥♥✱ ❏✳ ❑✳ ✭✶✾✾✼✮✳ ❆ ◆♦♥✲❞✐✈❡r❣❡♥t ❊st✐♠❛t✐♦♥ ❆❧❣♦r✐t❤♠ ✐♥ t❤❡ Pr❡s❡♥❝❡ ♦❢ ❯♥❦♥♦✇♥ ❈♦rr❡❧❛t✐♦♥s✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ❆♠❡r✐❝❛♥ ❈♦♥tr♦❧❈♦♥❢❡r❡♥❝❡✱ ❆❧❜✉q✉❡rq✉❡✱ ◆▼✳ ❑❛❧♠❛♥✱ ❘✳ ❊✳ ✭✶✾✻✵✮✳ ❆ ♥❡✇ ❛♣♣r♦❛❝❤ t♦ ❧✐♥❡❛r ✜❧t❡r✐♥❣ ❛♥❞ ♣r❡❞✐❝t✐♦♥ ♣r♦❜❧❡♠s✳❚r❛♥s❛❝t✐♦♥s ♦❢ t❤❡ ❆❙▼❊ ✲ ❏♦✉r♥❛❧ ♦❢ ❇❛s✐❝ ❊♥❣✐♥❡❡r✐♥❣✱ ✽✷✭❙❡r✐❡s ❉✮✿✸✺✕✹✺✳ ❑❛r❛♠✱ ◆✳❀ ❈❤❛✉ss❡✱ ❋✳❀ ❆✉❢rèr❡✱ ❘✳ ✫ ❈❤❛♣✉✐s✱ ❘✳ ✭✷✵✵✻✮✳ ▲♦❝❛❧✐③❛t✐♦♥ ♦❢ ❛ ●r♦✉♣♦❢ ❈♦♠♠✉♥✐❝❛t✐♥❣ ❱❡❤✐❝❧❡s ❜② ❙t❛t❡ ❊①❝❤❛♥❣❡✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊✴❘❙❏■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ■♥t❡❧❧✐❣❡♥t ❘♦❜♦ts ❛♥❞ ❙②st❡♠s✱ ♣♣✳ ✺✶✾✕✺✷✹✱ ❇❡✐❥✐♥❣✱❈❤✐♥❛✳ ❑❡♠❡♥②✱ ❏✳ ●✳ ✫ ❙♥❡❧❧✱ ❏✳ ▲✳ ✭✶✾✽✸✮✳ ❋✐♥✐t❡ ▼❛r❦♦✈ ❈❤❛✐♥s✳ ❯♥❞❡r❣r❛❞✉❛t❡ ❚❡①ts ✐♥▼❛t❤❡♠❛t✐❝s✳ ❙♣r✐♥❣❡r✲❱❡r❧❛❣✱ ✸r❞ ❡❞✐çã♦✳ ❑♦♦✱ ❚✳ ❏✳ ✫ ❙❤❛❤r✉③✱ ❙✳ ▼✳ ✭✷✵✵✶✮✳ ❋♦r♠❛t✐♦♥ ♦❢ ❛ ❣r♦✉♣ ♦❢ ✉♥♠❛♥♥❡❞ ❛❡r✐❛❧ ✈❡❤✐❝❧❡s✭✉❛✈s✮✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ❆♠❡r✐❝❛♥ ❈♦♥tr♦❧ ❈♦♥❢❡r❡♥❝❡✳ ✶✸✻❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá❢✐❝❛s ❑✉❜❡✱ ❈✳ ❘✳ ✫ ❇♦♥❛❜❡❛✉✱ ❊✳ ✭✷✵✵✵✮✳ ❈♦♦♣❡r❛t✐✈❡ tr❛♥s♣♦rt ❜② ❛♥ts ❛♥❞ r♦❜♦ts✳ ❘♦✲❜♦t✐❝s ❛♥❞ ❆✉t♦♥♦♠♦✉s ❙②st❡♠s✱ ✸✵✿✽✺✕✶✵✶✳ ❑✉♠❛r✱ ▼✳ ✫ ●❛r❣✱ ❉✳ P✳ ✭✷✵✶✶✮✳ ❆❣❣r❡❣❛t✐♦♥ ♦❢ ❍❡t❡r♦❣❡♥❡♦✉s ❯♥✐ts ✐♥ ❛ ❙✇❛r♠♦❢ ❘♦❜♦t✐❝ ❆❣❡♥ts✳ ❊♠ ✹t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❙②♠♣♦s✐✉♠ ♦♥ ❘❡s✐❧✐❡♥t ❈♦♥tr♦❧ ❙②st❡♠s✭■❙❘❈❙✮✱ ♣♣✳ ✶✵✼✕✶✶✷✳ ❑✉♠❛r✱ ▼✳❀ ●❛r❣✱ ❉✳ P✳ ✫ ❑✉♠❛r✱ ❱✳ ✭✷✵✶✵✮✳ ❙❡❣r❡❣❛t✐♦♥ ♦❢ ❍❡t❡r♦❣❡♥❡♦✉s ❯♥✐ts ✐♥ ❛❙✇❛r♠ ♦❢ ❘♦❜♦t✐❝ ❆❣❡♥ts✳ ■❊❊❊ ❚r❛♥s❛❝t✐♦♥s ♦♥ ❆✉t♦♠❛t✐❝ ❈♦♥tr♦❧✱ ✺✺✭✸✮✿✼✹✸✕✼✹✽✳ ❑✉r❛③✉♠❡✱ ❘✳ ✫ ❍✐r♦s❡✱ ❙✳ ✭✶✾✾✽✮✳ ❙t✉❞② ♦♥ ❈♦♦♣❡r❛t✐✈❡ P♦s✐t✐♦♥✐♥❣ ❙②st❡♠ ✕ ❖♣✲ t✐♠✉♠ ▼♦✈✐♥❣ ❙tr❛t❡❣✐❡s ❢♦r ❈P❙✲■■■✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧❈♦♥❢❡r❡♥❝❡ ♦♥ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ✈♦❧✉♠❡ ✹✱ ♣♣✳ ✷✽✾✻✕✷✾✵✸✱ ▲❡✉✈❡♥✱ ❇❡❧❣✐✉♠✳ ❑✉r❛③✉♠❡✱ ❘✳ ✫ ❍✐r♦s❡✱ ❙✳ ✭✷✵✵✵❛✮✳ ❆♥ ❊①♣❡r✐♠❡♥t❛❧ ❙t✉❞② ♦❢ ❛ ❈♦♦♣❡r❛t✐✈❡ P♦s✐t✐♦✲♥✐♥❣ ❙②st❡♠✳ ❆✉t♦♥♦♠♦✉s ❘♦❜♦ts✱ ✽✭✶✮✿✹✸✕✺✷✳ ❑✉r❛③✉♠❡✱ ❘✳ ✫ ❍✐r♦s❡✱ ❙✳ ✭✷✵✵✵❜✮✳ ❉❡✈❡❧♦♣♠❡♥t ♦❢ ❛ ❈❧❡❛♥✐♥❣ ❘♦❜♦t ❙②st❡♠ ✇✐t❤❈♦♦♣❡r❛t✐✈❡ P♦s✐t✐♦♥✐♥❣ ❙②st❡♠✳ ❆✉t♦♥♦♠♦✉s ❘♦❜♦ts✱ ✾✿✷✸✼✕✷✹✻✳ ❑✉r❛③✉♠❡✱ ❘✳❀ ❍✐r♦s❡✱ ❙✳❀ ◆❛❣❛t❛✱ ❙✳ ✫ ❙❛s❤✐❞❛✱ ◆✳ ✭✶✾✾✻✮✳ ❙t✉❞② ♦♥ ❈♦♦♣❡r❛t✐✈❡P♦s✐t✐♦♥✐♥❣ ❙②st❡♠ ✭❇❛s✐❝ Pr✐♥❝✐♣❧❡ ❛♥❞ ▼❡❛s✉r❡♠❡♥t ❊①♣❡r✐♠❡♥t✮✳ ❊♠ Pr♦❝❡❡✲❞✐♥❣s ♦❢ t❤❡ ■❊❊❊✴❘❙❏ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ■♥t❡❧❧✐❣❡♥t ❘♦❜♦ts ❛♥❞ ❙②st❡♠s✱✈♦❧✉♠❡ ✷✱ ♣♣✳ ✶✹✷✶✕✶✹✷✻✱ ❖s❛❦❛✱ ❏❛♣❛♥✳ ❑✉r❛③✉♠❡✱ ❘✳❀ ◆❛❣❛t❛✱ ❙✳ ✫ ❍✐r♦s❡✱ ❙✳ ✭✶✾✾✹✮✳ ❈♦♦♣❡r❛t✐✈❡ P♦s✐t✐♦♥✐♥❣ ✇✐t❤ ▼✉❧t✐♣❧❡❘♦❜♦ts✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊✴❘❙❏ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ■♥t❡❧❧✐❣❡♥t❘♦❜♦ts ❛♥❞ ❙②st❡♠s✱ ♣♣✳ ✶✷✺✵✕✶✷✺✼✱ ▼✉♥✐❝❤✱ ●❡r♠❛♥②✳ ❑✉r❛③✉♠❡✱ ❘✳❀ ❚♦❜❛t❛✱ ❨✳❀ ■✇❛s❤✐t❛✱ ❨✳ ✫ ❍❛s❡❣❛✇❛✱ ❚✳ ✭✷✵✵✼✮✳ ✸❉ ❧❛s❡r ♠❡❛s✉r❡♠❡♥t s②st❡♠ ❢♦r ❧❛r❣❡ s❝❛❧❡ ❛r❝❤✐t❡❝t✉r❡s ✉s✐♥❣ ♠✉❧t✐♣❧❡ ♠♦❜✐❧❡ r♦❜♦ts✳ ❊♠ Pr♦❝❡❡❞✐♥❣s♦❢ ❙✐①t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ✸✲❉ ❉✐❣✐t❛❧ ■♠❛❣✐♥❣ ❛♥❞ ▼♦❞❡❧✐♥❣ ✭✸❉■▼✬✵✼✮✱♣♣✳ ✾✶✕✾✽✳ ▲❛❱❛❧❧❡✱ ❙✳ ▼✳ ✭✷✵✵✻✮✳ P❧❛♥♥✐♥❣ ❆❧❣♦r✐t❤♠s✳ ❈❛♠❜r✐❞❣❡ ❯♥✐✈❡rs✐t② Pr❡ss✱ ◆❡✇ ❨♦r❦✳▲❛③❛♥❛s✱ ❆✳ ✫ ▲❛t♦♠❜❡✱ ❏✳✲❈✳ ✭✶✾✾✺✮✳ ▲❛♥❞♠❛r❦✲❜❛s❡❞ r♦❜♦t ♥❛✈✐❣❛t✐♦♥✳ ❆❧❣♦r✐t❤♠✐❝❛✱ ✶✸✭✺✮✿✹✼✷✕✺✵✶✳▲✐✱ ❍✳ ✫ ◆❛s❤❛s❤✐❜✐✱ ❋✳ ✭✷✵✶✷✮✳ ❈♦♦♣❡r❛t✐✈❡ ♠✉❧t✐✲✈❡❤✐❝❧❡ ❧♦❝❛❧✐③❛t✐♦♥ ✉s✐♥❣ s♣❧✐t ❝♦✈❛r✐❛♥❝❡ ✐♥t❡rs❡❝t✐♦♥ ✜❧t❡r✳ ❊♠ ✷✵✶✷ ■♥t❡❧❧✐❣❡♥t ❱❡❤✐❝❧❡s ❙②♠♣♦s✐✉♠✱ ♣♣✳ ✷✶✶✕✷✶✻✱❆❧❝❛❧á ❞❡ ❍❡♥❛r❡s✱ ❙♣❛✐♥✳ ❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá❢✐❝❛s✶✸✼ ▲✐✱ ❍✳❀ ◆❛s❤❛s❤✐❜✐✱ ❋✳ ✫ ❨❛♥❣✱ ▼✳ ✭✷✵✶✸✮✳ ❙♣❧✐t ❝♦✈❛r✐❛♥❝❡ ✐♥t❡rs❡❝t✐♦♥ ✜❧t❡r✿ ❚❤❡✲♦r② ❛♥❞ ✐ts ❛♣♣❧✐❝❛t✐♦♥ t♦ ✈❡❤✐❝❧❡ ❧♦❝❛❧✐③❛t✐♦♥✳ ■❊❊❊ ❚r❛♥s❛❝t✐♦♥s ♦♥ ■♥t❡❧❧✐❣❡♥t❚r❛♥s♣♦rt❛t✐♦♥ ❙②st❡♠s✱ ✶✹✭✹✮✿✶✽✻✵✕✶✽✼✶✳ ▲✐✉✱ ❨✳ ✫ P❛ss✐♥♦✱ ❑✳ ▼✳ ✭✷✵✵✵✮✳ ❙✇❛r♠ ✐♥t❡❧❧✐❣❡♥❝❡✿ ▲✐t❡r❛t✉r❡ ♦✈❡r✈✐❡✇✳ ❉✐s♣♦♥í✈❡❧❡♠✿ ❤tt♣✿✴✴❡♥✳s❝✐❡♥t✐✜❝❝♦♠♠♦♥s✳♦r❣✴✹✷✻✵✹✻✾✾✳ ❆❝❡ss♦ ❡♠✿ ✵✸✴✶✷✴✷✵✶✷✳ ▼❛r✐♦tt✐♥✐✱ ●✳ ▲✳❀ ▼❛rt✐♥✐✱ ❙✳ ✫ ❊❣❡rst❡❞t✱ ▼✳ ❇✳ ✭✷✵✵✾✮✳ ❆ s✇✐t❝❤✐♥❣ ❛❝t✐✈❡ s❡♥s✐♥❣ str❛t❡❣② t♦ ♠❛✐♥t❛✐♥ ♦❜s❡r✈❛❜✐❧✐t② ❢♦r ✈✐s✐♦♥✲❜❛s❡❞ ❢♦r♠❛t✐♦♥ ❝♦♥tr♦❧✳ ❊♠ Pr♦❝❡❡❞✐♥❣s♦❢ t❤❡ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ♣♣✳ ✷✻✸✼✕✷✻✹✷✱❑♦❜❡✱ ❏❛♣❛♥✳ ▼❛rt✐♥✱ ▼✳❀ ❑❧✉♣❛r✱ P✳❀ ❑✐❧❜❡r❣✱ ❙✳ ✫ ❲✐♥t❡r✱ ❏✳ ✭✷✵✵✶✮✳ ❚❡❝❤s❛t ✷✶ ❛♥❞ r❡✈♦❧✉t✐♦♥✐③✐♥❣ s♣❛❝❡ ♠✐ss✐♦♥s ✉s✐♥❣ ♠✐❝r♦s❛t❡❧❧✐t❡s✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ❆■❆❆✴❯❙❯ ❈♦♥❢❡r❡♥❝❡♦♥ ❙♠❛❧❧ ❙❛t❡❧❧✐t❡s✱ ♣♣✳ ✶✺✼✹✕✶✺✼✾✱ ▲♦❣❛♥✱ ❯❚✳ ▼❛rt✐♥❡❧❧✐✱ ❆✳❀ P♦♥t✱ ❋✳ ✫ ❙✐❡❣✇❛rt✱ ❘✳ ✭✷✵✵✺✮✳ ▼✉❧t✐✲❘♦❜♦t ▲♦❝❛❧✐③❛t✐♦♥ ❯s✐♥❣ ❘❡❧❛t✐✈❡❖❜s❡r✈❛t✐♦♥s✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❘♦❜♦t✐❝s ❛♥❞❆✉t♦♠❛t✐♦♥✱ ♣♣✳ ✷✼✾✼✕✷✽✵✷✱ ❇❛r❝❡❧♦♥❛✱ ❙♣❛✐♥✳ ▼❝❧✉r❦✐♥✱ ❏✳ ✫ ❙♠✐t❤✱ ❏✳ ✭✷✵✵✹✮✳ ❉✐str✐❜✉t❡❞ ❛❧❣♦r✐t❤♠s ❢♦r ❞✐s♣❡rs✐♦♥ ✐♥ ✐♥❞♦♦r ❡♥✈✐✲ r♦♥♠❡♥ts ✉s✐♥❣ ❛ s✇❛r♠ ♦❢ ❛✉t♦♥♦♠♦✉s ♠♦❜✐❧❡ r♦❜♦ts✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ ■♥t❡r♥❛✲t✐♦♥❛❧ ❙②♠♣♦s✐✉♠ ♦♥ ❉✐str✐❜✉t❡❞ ❆✉t♦♥♦♠♦✉s ❘♦❜♦t✐❝ ❙②st❡♠s✳ ▼✐❝❤❛❡❧✱ ◆✳❀ ❋✐♥❦✱ ❏✳ ✫ ❑✉♠❛r✱ ❱✳ ✭✷✵✵✽✮✳ ❊①♣❡r✐♠❡♥t❛❧ ❚❡st❜❡❞ ❢♦r ▲❛r❣❡ ▼✉❧t✐r♦❜♦t❚❡❛♠s✳ ■❊❊❊ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥ ▼❛❣❛③✐♥❡✱ ✶✺✭✶✮✿✺✸✕✻✶✳ ▼♦❤❛♥✱ ❨✳ ✫ P♦♥♥❛♠❜❛❧❛♠✱ ❙✳ ●✳ ✭✷✵✵✾✮✳ ❆♥ ❡①t❡♥s✐✈❡ r❡✈✐❡✇ ♦❢ r❡s❡❛r❝❤ ✐♥ s✇❛r♠ r♦❜♦t✐❝s✳ ❊♠ ❆❜r❛❤❛♠✱ ❆✳❀ ❈❛r✈❛❧❤♦✱ ❆✳❀ ❍❡rr❡r❛✱ ❋✳ ✫ P❛✐✱ ❱✳✱ ❡❞✐t♦r❡s✱ Pr♦❝❡❡❞✐♥❣s♦❢ ✷✵✵✾ ❲♦r❧❞ ❈♦♥❣r❡ss ♦♥ ◆❛t✉r❡ ✫ ❇✐♦❧♦❣✐❝❛❧❧② ■♥s♣✐r❡❞ ❈♦♠♣✉t✐♥❣✱ ♣♣✳ ✶✹✵✕✶✹✺✱❈♦✐♠❜❛t♦r❡✱ ■♥❞✐❛✳ ▼♦♥❞❛❞❛✱ ❋✳❀ ❇♦♥❛♥✐✱ ▼✳❀ ❘❛❡♠②✱ ❳✳❀ P✉❣❤✱ ❏✳❀ ❈✐❛♥❝✐✱ ❈✳❀ ❑❧❛♣t♦❝③✱ ❆✳❀ ▼❛❣♥❡♥❛t✱ ❙✳❀❩✉✛❡r❡②✱ ❏✳✲❈✳❀ ❋❧♦r❡❛♥♦✱ ❉✳ ✫ ▼❛rt✐♥♦❧✐✱ ❆✳ ✭✷✵✵✾✮✳ ❚❤❡ ❡✲♣✉❝❦✱ ❛ ❘♦❜♦t ❉❡s✐❣♥❡❞❢♦r ❊❞✉❝❛t✐♦♥ ✐♥ ❊♥❣✐♥❡❡r✐♥❣✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✾t❤ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆✉t♦♥♦♠♦✉s❘♦❜♦t ❙②st❡♠s ❛♥❞ ❈♦♠♣❡t✐t✐♦♥s✱ ✈♦❧✉♠❡ ✶✱ ♣♣✳ ✺✾✕✻✺✳ ▼♦✉r✐❦✐s✱ ❆✳ ■✳ ✫ ❘♦✉♠❡❧✐♦t✐s✱ ❙✳ ■✳ ✭✷✵✵✻✮✳ ❖♣t✐♠❛❧ s❡♥s♦r s❝❤❡❞✉❧✐♥❣ ❢♦r r❡s♦✉r❝❡✲❝♦♥str❛✐♥❡❞ ❧♦❝❛❧✐③❛t✐♦♥ ♦❢ ♠♦❜✐❧❡ r♦❜♦t ❢♦r♠❛t✐♦♥s✳ ■❊❊❊ ❚r❛♥s❛❝t✐♦♥s ♦♥ ❘♦❜♦t✐❝s✱✷✷✭✺✮✿✾✶✼✕✾✸✶✳ ✶✸✽❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá❢✐❝❛s ◆❛✈❛rr♦✱ ■✳ ✫ ▼❛tí❛✱ ❋✳ ✭✷✵✶✸✮✳ ❆ ❙✉r✈❡② ♦❢ ❈♦❧❧❡❝t✐✈❡ ▼♦✈❡♠❡♥t ♦❢ ▼♦❜✐❧❡ ❘♦❜♦ts✳■♥t❡r♥❛t✐♦♥❛❧ ❏♦✉r♥❛❧ ♦❢ ❆❞✈❛♥❝❡❞ ❘♦❜♦t✐❝ ❙②st❡♠s✱ ✶✵✭✼✸✮✳ ◆❡r✉r❦❛r✱ ❊✳ ❉✳❀ ❘♦✉♠❡❧✐♦t✐s✱ ❙✳ ■✳ ✫ ▼❛rt✐♥❡❧❧✐✱ ❆✳ ✭✷✵✵✾✮✳ ❉✐str✐❜✉t❡❞ ♠❛①✐♠✉♠ ❛♣♦st❡r✐♦r✐ ❡st✐♠❛t✐♦♥ ❢♦r ♠✉❧t✐✲r♦❜♦t ❝♦♦♣❡r❛t✐✈❡ ❧♦❝❛❧✐③❛t✐♦♥✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ♣♣✳ ✶✹✵✷✕✶✹✵✾✱ ❑♦❜❡✱❏❛♣❛♥✳ ❖❧❢❛t✐✲❙❛❜❡r✱ ❘✳ ✭✷✵✵✻✮✳ ❋❧♦❝❦✐♥❣ ❢♦r ♠✉❧t✐✲❛❣❡♥t ❞②♥❛♠✐❝ s②st❡♠s✿ ❛❧❣♦r✐t❤♠s ❛♥❞ t❤❡♦r②✳ ■❊❊❊ ❚r❛♥s❛❝t✐♦♥s ♦♥ ❆✉t♦♠❛t✐❝ ❈♦♥tr♦❧✱ ✺✶✭✸✮✿✹✵✶✕✹✷✵✳❖❧❢❛t✐✲❙❛❜❡r✱ ❘✳ ✫ ▼✉rr❛②✱ ❘✳ ▼✳ ✭✷✵✵✷✮✳ ❉✐str✐❜✉t❡❞ ❈♦♦♣❡r❛t✐✈❡ ❈♦♥tr♦❧ ♦❢ ▼✉❧t✐✲ ♣❧❡ ❱❡❤✐❝❧❡ ❋♦r♠❛t✐♦♥s ❯s✐♥❣ ❙tr✉❝t✉r❛❧ P♦t❡♥t✐❛❧ ❋✉♥❝t✐♦♥s✳ ❊♠ ✐♥ ■❋❆❈ ❲♦r❧❞❈♦♥❣r❡ss✳ ❖✇❡♥✱ ❈✳ ✫ ◆❡❤♠③♦✇✱ ❯✳ ✭✶✾✾✽✮✳ ▲❛♥❞♠❛r❦✲❇❛s❡❞ ◆❛✈✐❣❛t✐♦♥ ❢♦r ❛ ▼♦❜✐❧❡ ❘♦❜♦t✳❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ❋✐❢t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❙✐♠✉❧❛t✐♦♥ ♦❢ ❆❞❛♣t✐✈❡❇❡❤❛✈✐♦r ♦♥ ❋r♦♠ ❛♥✐♠❛❧s t♦ ❛♥✐♠❛ts ✺✱ ♣♣✳ ✷✹✵✕✷✹✺✱ ❈❛♠❜r✐❞❣❡✱ ▼❆✱ ❯❙❆✳ ▼■❚Pr❡ss✳ P❛♥❛✐t✱ ▲✳ ✫ ▲✉❦❡✱ ❙✳ ✭✷✵✵✹✮✳ ❆ ♣❤❡r♦♠♦♥❡✲❜❛s❡❞ ✉t✐❧✐t② ♠♦❞❡❧ ❢♦r ❝♦❧❧❛❜♦r❛t✐✈❡ ❢♦r❛✲❣✐♥❣✳ ❊♠ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆✉t♦♥♦♠♦✉s ❆❣❡♥ts ❛♥❞ ▼✉❧t✐❛❣❡♥t ❙②st❡♠s✱♣♣✳ ✸✻✕✹✸✱ ◆❡✇ ❨♦r❦✱ ◆❨✱ ❯❙❆✳ ■❊❊❊ ❈♦♠♣✉t❡r ❙♦❝✐❡t②✳ P❛r❦❡r✱ ▲✳ ❊✳ ✭✶✾✾✸✮✳ ❉❡s✐❣♥✐♥❣ ❈♦♥tr♦❧ ▲❛✇s ❢♦r ❈♦♦♣❡r❛t✐✈❡ ❆❣❡♥t ❚❡❛♠s✳ ❊♠Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ♣♣✳✺✽✷✕✺✽✼✱ ❆t❧❛♥t❛✱ ●❆✱ ❯❙❆✳ P❛r❦❡r✱ ▲✳ ❊✳ ✭✷✵✵✽✮✳ ❉✐str✐❜✉t❡❞ ■♥t❡❧❧✐❣❡♥❝❡✿ ❖✈❡r✈✐❡✇ ♦❢ t❤❡ ❋✐❡❧❞ ❛♥❞ ✐ts ❆♣♣❧✐❝❛t✐♦♥✐♥ ▼✉❧t✐✲❘♦❜♦t ❙②st❡♠s✳ ❏♦✉r♥❛❧ ♦❢ P❤②s✐❝❛❧ ❆❣❡♥ts✱ ✷✭✶✮✿✺✕✶✹✳ P❛r❦✐♥s♦♥✱ ❇✳ ❲✳ ✫ ❙♣✐❧❦❡r ❏r✳✱ ❏✳ ❏✳✱ ❡❞✐t♦r❡s ✭✶✾✾✻✮✳ ●❧♦❜❛❧ P♦s✐t✐♦♥✐♥❣ ❙②st❡♠s✿ ❚❤❡✲♦r② ❛♥❞ ❆♣♣❧✐❝❛t✐♦♥s✱ ✈♦❧✉♠❡ ■✳ ❆♠❡r✐❝❛♥ ■♥st✐t✉t❡ ♦❢ ❆❡r♦♥❛✉t✐❝s ❛♥❞ ❆str♦♥❛✉t✐❝s■♥❝✳✱ ❯❙❆✳ P❛②t♦♥✱ ❉✳❀ ❊st❦♦✇s❦✐✱ ❘✳ ✫ ❍♦✇❛r❞✱ ▼✳ ✭✷✵✵✸✮✳ ❈♦♠♣♦✉♥❞ ❜❡❤❛✈✐♦rs ✐♥ ♣❤❡r♦♠♦♥❡ r♦❜♦t✐❝s✳ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♥♦♠♦✉s ❙②st❡♠s✱ ✹✹✿✷✷✾✕✷✹✵✳P✐♠❡♥t❛✱ ▲✳ ❈✳ ❞✳ ❆✳ ✭✷✵✵✾✮✳ ❚❡❝❤♥✐q✉❡s ❢♦r ❈♦♥tr♦❧❧✐♥❣ ❙✇❛r♠s ♦❢ ❘♦❜♦ts✳ P❤❉ t❤❡s✐s✱ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s✱ ❇❡❧♦ ❍♦r✐③♦♥t❡✳ ❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá❢✐❝❛s✶✸✾ Pr❡♠✈✉t✐✱ ❙✳ ✫ ❨✉t❛✱ ❙✳ ✭✶✾✾✵✮✳ ❈♦♥s✐❞❡r❛t✐♦♥ ♦♥ t❤❡ ❈♦♦♣❡r❛t✐♦♥ ♦❢ ▼✉❧t✐♣❧❡ ❆✉t♦✲♥♦♠♦✉s ▼♦❜✐❧❡ ❘♦❜♦ts✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊✴❘❙❏ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡♦♥ ■♥t❡❧❧✐❣❡♥t ❘♦❜♦ts ❛♥❞ ❙②st❡♠s✳ ✬❚♦✇❛r❞s ❛ ◆❡✇ ❋r♦♥t✐❡r ♦❢ ❆♣♣❧✐❝❛t✐♦♥s✬✱ ♣♣✳✺✾✕✻✸✱ ❇❛r❛❦✐✱ ❏❛♣❛♥✳ ■❊❊❊✳ Pr♦r♦❦✱ ❆✳❀ ❇❛❤r✱ ❆✳ ✫ ▼❛rt✐♥♦❧✐✱ ❆✳ ✭✷✵✶✷✮✳ ▲♦✇✲❈♦st ❈♦❧❧❛❜♦r❛t✐✈❡ ▲♦❝❛❧✐③❛t✐♦♥❢♦r ▲❛r❣❡✲❙❝❛❧❡ ▼✉❧t✐✲❘♦❜♦t ❙②st❡♠✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧❈♦♥❢❡r❡♥❝❡ ♦♥ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ♣♣✳ ✹✷✸✻✕✹✷✹✶✱ ❙❛✐♥t P❛✉❧✱ ▼✐♥♥❡s♦t❛✱❯❙❆✳ ◗✉✐❣❧❡②✱ ▼✳❀ ●❡r❦❡②✱ ❇✳❀ ❈♦♥❧❡②✱ ❑✳❀ ❋❛✉st✱ ❏✳❀ ❋♦♦t❡✱ ❚✳❀ ▲❡✐❜s✱ ❏✳❀ ❇❡r❣❡r✱ ❊✳❀ ❲❤❡❡❧❡r✱❘✳ ✫ ◆❣✱ ❆✳ ✭✷✵✵✾✮✳ ❘❖❙✿ ❛♥ ♦♣❡♥✲s♦✉r❝❡ ❘♦❜♦t ❖♣❡r❛t✐♥❣ ❙②st❡♠✳ ❊♠ ■❈❘❆✳ ❘❡❦❧❡✐t✐s✱ ■✳ ▼✳❀ ❉✉❞❡❦✱ ●✳ ✫ ▼✐❧✐♦s✱ ❊✳ ❊✳ ✭✶✾✾✼✮✳ ▼✉❧t✐✲❘♦❜♦t ❊①♣❧♦r❛t✐♦♥ ♦❢ ❛♥❯♥❦♥♦✇♥ ❊♥✈✐r♦♥♠❡♥t✱ ❊✣❝✐❡♥t❧② ❘❡❞✉❝✐♥❣ t❤❡ ❖❞♦♠❡tr② ❊rr♦r✳ ❊♠ Pr♦❝❡❡❞✐♥❣s♦❢ ■♥t❡r♥❛t✐♦♥❛❧ ❏♦✐♥t ❈♦♥❢❡r❡♥❝❡ ✐♥ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡✱ ✈♦❧✉♠❡ ✷✱ ♣♣✳ ✶✸✹✵✕✶✸✹✺✱❏❛♣❛♥✳ ❘❡❦❧❡✐t✐s✱ ■✳ ▼✳❀ ❉✉❞❡❦✱ ●✳ ✫ ▼✐❧✐♦s✱ ❊✳ ❊✳ ✭✶✾✾✽✮✳ ❖♥ ▼✉❧t✐❛❣❡♥t ❊①♣❧♦r❛t✐♦♥✳ ❊♠Pr♦❝❡❡❞✐♥❣s ♦❢ ❱✐s✐♦♥ ■♥t❡r❢❛❝❡✱ ♣♣✳ ✹✺✺✕✹✻✶✳ ❘❡❦❧❡✐t✐s✱ ■✳ ▼✳❀ ❉✉❞❡❦✱ ●✳ ✫ ▼✐❧✐♦s✱ ❊✳ ❊✳ ✭✷✵✵✵✮✳ ▼✉❧t✐✲❘♦❜♦t ❈♦❧❧❛❜♦r❛t✐♦♥ ❢♦r ❘♦✲❜✉st ❊①♣❧♦r❛t✐♦♥✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❘♦❜♦t✐❝s❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ✈♦❧✉♠❡ ✹✱ ♣♣✳ ✸✶✻✹✕✸✶✻✾✱ ❙❛♥ ❋r❛♥❝✐s❝♦✱ ❈❆✱ ❯❙❆✳ ❘❡❦❧❡✐t✐s✱ ■✳ ▼✳❀ ❉✉❞❡❦✱ ●✳ ✫ ▼✐❧✐♦s✱ ❊✳ ❊✳ ✭✷✵✵✷✮✳ ▼✉❧t✐✲❘♦❜♦t ❈♦♦♣❡r❛t✐✈❡ ▲♦❝❛❧✐③❛✲ t✐♦♥✿ ❆ ❙t✉❞② ♦❢ ❚r❛❞❡✲♦✛s ❇❡t✇❡❡♥ ❊✣❝✐❡♥❝② ❛♥❞ ❆❝❝✉r❛❝②✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡■❊❊❊✴❘❙❏ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ■♥t❡❧❧✐❣❡♥t ❘♦❜♦ts ❛♥❞ ❙②st❡♠s✱ ✈♦❧✉♠❡ ✸✱♣♣✳ ✷✻✾✵✕✷✻✾✺✱ ▲❛✉s❛♥♥❡✱ ❙✇✐t③❡r❧❛♥❞✳ ❘❡②♥♦❧❞s✱ ❈✳ ❲✳ ✭✶✾✽✼✮✳ ❋❧♦❝❦s✱ ❤❡r❞s✱ ❛♥❞ s❝❤♦♦❧s✿ ❆ ❞✐str✐❜✉t❡❞ ❜❡❤❛✈✐♦r❛❧ ♠♦❞❡❧✳❊♠ ❈♦♠♣✉t❡r ●r❛♣❤✐❝s✱ ♣♣✳ ✷✺✕✸✹✳ ❘♦❜♦t✐❝s ✫ ❊❧❡tr♦♥✐❝s P♦❧♦❧✉❧✉ ✭✷✵✶✷✮✳ ❍♦♠❡ ♣❛❣❡ ❞❛ ❡♠♣r❡s❛ ❘♦❜♦t✐❝s ✫❊❧❡tr♦♥✐❝s P♦❧♦❧✉❧✉✳ ❊♥❝♦❞❡r ❢♦r P♦❧♦❧✉ ❲❤❡❡❧ ✹✷①✶✾♠♠✳ ❉✐s♣♦♥í✈❡❧ ❡♠✿❤tt♣✿✴✴✇✇✇✳♣♦❧♦❧✉✳❝♦♠✴❝❛t❛❧♦❣✴♣r♦❞✉❝t✴✶✵✾✵✳ ❆❝❡ss♦ ❡♠✿ ✵✸✴✶✷✴✷✵✶✷✳ ❘♦✉♠❡❧✐♦t✐s✱ ❙✳ ■✳ ✫ ❇❡❦❡②✱ ●✳ ❆✳ ✭✷✵✵✵❛✮✳ ❈♦❧❧❡❝t✐✈❡ ▲♦❝❛❧✐③❛t✐♦♥✿ ❆ ❞✐str✐❜✉t❡❞❑❛❧♠❛♥ ✜❧t❡r ❛♣♣r♦❛❝❤ t♦ ❧♦❝❛❧✐③❛t✐♦♥ ♦❢ ❣r♦✉♣s ♦❢ ♠♦❜✐❧❡ r♦❜♦ts✳ ❊♠ Pr♦❝❡❡❞✐♥❣s♦❢ t❤❡ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ✈♦❧✉♠❡ ✸✱ ♣♣✳✷✾✺✽✕✷✾✻✺✱ ❙❛♥ ❋r❛♥❝✐s❝♦✱ ❈❆✱ ❯❙❆✳ ✶✹✵❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá❢✐❝❛s ❘♦✉♠❡❧✐♦t✐s✱ ❙✳ ■✳ ✫ ❇❡❦❡②✱ ●✳ ❆✳ ✭✷✵✵✵❜✮✳ ❙②♥❡r❣❡t✐❝ ▲♦❝❛❧✐③❛t✐♦♥ ❢♦r ●r♦✉♣s ♦❢ ▼♦❜✐❧❡❘♦❜♦ts✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✸✾t❤ ■❊❊❊ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❉❡❝✐s✐♦♥ ❛♥❞ ❈♦♥tr♦❧✱✈♦❧✉♠❡ ✹✱ ♣♣✳ ✸✹✼✼✕✸✹✽✷✳ ❘♦✉♠❡❧✐♦t✐s✱ ❙✳ ■✳ ✫ ❇❡❦❡②✱ ●✳ ❆✳ ✭✷✵✵✷✮✳ ❉✐str✐❜✉t❡❞ ▼✉❧t✐r♦❜♦t ▲♦❝❛❧✐③❛t✐♦♥✳ ■❊❊❊❚r❛♥s❛❝t✐♦♥s ♦♥ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ✶✽✭✺✮✿✼✽✶✕✼✾✺✳ ❘♦✉♠❡❧✐♦t✐s✱ ❙✳ ■✳ ✫ ❘❡❦❧❡✐t✐s✱ ■✳ ▼✳ ✭✷✵✵✹✮✳ Pr♦♣❛❣❛t✐♦♥ ♦❢ ✉♥❝❡rt❛✐♥t② ✐♥ ❝♦♦♣❡r❛t✐✈❡♠✉❧t✐r♦❜♦t ❧♦❝❛❧✐③❛t✐♦♥✿ ❆♥❛❧②s✐s ❛♥❞ ❡①♣❡r✐♠❡♥t❛❧ r❡s✉❧ts✳ ❆✉t♦♥♦♠♦✉s ❘♦❜♦ts✱✶✼✿✹✶✕✺✹✳ ❘✉ss❡❧❧✱ ❘✳ ❆✳ ✭✷✵✵✵✮✳ ❖❞♦✉r ❉❡t❡❝t✐♦♥ ❜② ▼♦❜✐❧❡ ❘♦❜♦ts✳ ❲♦r❧❞ ❙❝✐❡♥t✐✜❝ P✉❜❧✐s❤✐♥❣❈♦✳✱ ◆❡✇ ❏❡rs❡②✳ ❙❛❤✐♥✱ ❊✳ ✭✷✵✵✺✮✳ ❙✇❛r♠ r♦❜♦t✐❝s✿ ❋r♦♠ s♦✉r❝❡s ♦❢ ✐♥s♣✐r❛t✐♦♥ t♦ ❞♦♠❛✐♥s ♦❢ ❛♣♣❧✐❝❛✲ t✐♦♥✳ ❊♠ ❙❛❤✐♥✱ ❊✳ ✫ ❙♣❡❛rs✱ ❲✳ ▼✳✱ ❡❞✐t♦r❡s✱ ❙✇❛r♠ ❘♦❜♦t✐❝s ❲❙ ✷✵✵✹✱ ✈♦❧✉♠❡▲◆❈❙ ✸✸✹✷✱ ♣♣✳ ✶✵✕✷✵✳ ❙♣r✐♥❣❡r✲❱❡r❧❛❣✱ ❇❡r❧✐♥ ❍❡✐❞❡❧❜❡r❣✳ ❙❛❤✐♥✱ ❊✳❀ ●✐r❣✐♥✱ ❙✳❀ ❇❛②✐♥❞✐r✱ ▲✳ ✫ ❚✉r❣✉t✱ ❆✳ ❊✳ ✭✷✵✵✽✮✳ ❙✇❛r♠ ❘♦❜♦t✐❝s✳ ❊♠❇❧✉♠✱ ❈✳ ✫ ▼❡r❦❧❡✱ ❉✳✱ ❡❞✐t♦r❡s✱ ❙✇❛r♠ ■♥t❡❧❧✐❣❡♥❝❡✱ ◆❛t✉r❛❧ ❈♦♠♣✉t✐♥❣ ❙❡r✐❡s✱ ♣♣✳✽✼✕✶✵✵✳ ❙♣r✐♥❣❡r✳ ❙❛♥t♦s✱ ❱✳ ●✳ ✫ ❈❤❛✐♠♦✇✐❝③✱ ▲✳ ✭✷✵✶✶✮✳ ❍✐❡r❛r❝❤✐❝❛❧ ❈♦♥❣❡st✐♦♥ ❈♦♥tr♦❧ ❢♦r ❘♦❜♦t✐❝❙✇❛r♠s✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊✴❘❙❏ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ■♥t❡❧❧✐❣❡♥t❘♦❜♦ts ❛♥❞ ❙②st❡♠s✱ ♣♣✳ ✹✸✼✷✕✹✸✼✼✳ ❙❛♥t♦s✱ ❱✳ ●✳❀ P✐♠❡♥t❛✱ ▲✳ ❈✳ ❆✳ ✫ ❈❤❛✐♠♦✇✐❝③✱ ▲✳ ✭✷✵✶✹✮✳ ❙❡❣r❡❣❛t✐♦♥ ♦❢ ▼✉❧t✐♣❧❡❍❡t❡r♦❣❡♥❡♦✉s ❯♥✐ts ✐♥ ❛ ❘♦❜♦t✐❝ ❙✇❛r♠✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧❈♦♥❢❡r❡♥❝❡ ♦♥ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ♣♣✳ ✶✶✶✷✕✶✶✶✼✳ ❙❝❤❡✐♥❡r♠❛♥✱ ❊✳ ❘✳ ✭✶✾✾✻✮✳ ■♥✈✐t❛t✐♦♥ t♦ ❉②♥❛♠✐❝❛❧ ❙②st❡♠s✳ Pr❡♥t✐❝❡ ❍❛❧❧ ■♥❝✳✱ ◆❡✇❏❡rs❡②✳ ❙❝❤♥❡✐❞❡r✱ ❋✳ ❊✳ ✫ ❲✐❧❞❡r♠✉t❤✱ ❉✳ ✭✷✵✶✷✮✳ ■♥✢✉❡♥❝❡s ♦❢ t❤❡ r♦❜♦t ❣r♦✉♣ s✐③❡ ♦♥❝♦♦♣❡r❛t✐✈❡ ♠✉❧t✐✲r♦❜♦t ❧♦❝❛❧✐s❛t✐♦♥ ✕ ❆♥❛❧②s✐s ❛♥❞ ❡①♣❡r✐♠❡♥t❛❧ ✈❛❧✐❞❛t✐♦♥✳ ❘♦❜♦t✐❝s❛♥❞ ❆✉t♦♥♦♠♦✉s ❙②st❡♠s✱ ✻✵✭✶✶✮✿✶✹✷✶✕✶✹✷✽✳ ❙❤❛r❦❡②✱ ❆✳ ❏✳ ❈✳ ✭✷✵✵✼✮✳ ❙✇❛r♠ r♦❜♦t✐❝s ❛♥❞ ♠✐♥✐♠❛❧✐s♠✳ ❈♦♥♥❡❝t✐♦♥ ❙❝✐❡♥❝❡✱✶✾✭✸✮✿✷✹✺✕✷✻✵✳ ❙✐❡❣✇❛rt✱ ❘✳ ✫ ◆♦✉r❜❛❦❤s❤✱ ■✳ ❘✳ ✭✷✵✵✹✮✳ ■♥tr♦❞✉❝t✐♦♥ t♦ ❆✉t♦♥♦♠♦✉s ▼♦❜✐❧❡ ❘♦❜♦ts✳❚❤❡ ▼■❚ Pr❡ss✱ ❈❛♠❜r✐❞❣❡✱ ▼❛ss❛❝❤✉s❡tts✳ ❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá❢✐❝❛s✶✹✶ ❙✐♠♦♥✱ ❉✳ ✭✷✵✵✻✮✳ ❖♣t✐♠❛❧ ❙t❛t❡ ❊st✐♠❛t✐♦♥✿ ❑❛❧♠❛♥✱ ❍ ■♥✜♥✐t②✱ ❛♥❞ ◆♦♥❧✐♥❡❛r❆♣♣r♦❛❝❤❡s✳ ❏♦❤♥ ❲✐❧❡② ✫ ❙♦♥s✱ ■♥❝✳✱ ◆❡✇ ❏❡rs❡②✳ ❙♠✐t❤✱ ❘✳ ❈✳ ✫ ❈❤❡❡s❡♠❛♥✱ P✳ ✭✶✾✽✻✮✳ ❖♥ t❤❡ r❡♣r❡s❡♥t❛t✐♦♥ ❛♥❞ ❡st✐♠❛t✐♦♥ ♦❢ s♣❛t✐❛❧✉♥❝❡rt❛✐♥t②✳ ■♥t❡r♥❛t✐♦♥❛❧ ❏♦✉r♥❛❧ ♦❢ ❘♦❜♦t✐❝s ❘❡s❡❛r❝❤✱ ✹✿✺✻✕✻✽✳ ❙♦②s❛❧✱ ❖✳❀ ❇❛❤❝❡❝✐✱ ❊✳ ✫ ❙❛❤✐♥✱ ❊✳ ✭✷✵✵✼✮✳ ❆❣❣r❡❣❛t✐♦♥ ✐♥ s✇❛r♠ r♦❜♦t✐❝ s②st❡♠s✿❊✈♦❧✉t✐♦♥ ❛♥❞ ♣r♦❜❛❜✐❧✐st✐❝ ❝♦♥tr♦❧✳ ❚✉r❦✐s❤ ❏♦✉r♥❛❧ ♦❢ ❊❧❡❝tr✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞❈♦♠♣✉t❡r ❙❝✐❡♥❝❡s✱ ✶✺✿✶✾✾✕✷✷✺✳ ❙♣❡❛rs✱ ❲✳❀ ❙♣❡❛rs✱ ❉✳❀ ❍❛♠❛♥♥✱ ❏✳ ✫ ❍❡✐❧✱ ❘✳ ✭✷✵✵✹✮✳ ❉✐str✐❜✉t❡❞✱ ♣❤②s✐❝s✲❜❛s❡❞❝♦♥tr♦❧ ♦❢ s✇❛r♠s ♦❢ ✈❡❤✐❝❧❡s✳ ❆✉t♦♥♦♠♦✉s ❘♦❜♦ts✱ ✶✼✭✷✲✸✮✿✶✸✼✕✶✻✷✳ ❙✉♣❡r❉r♦✐❞ ❘♦❜♦ts ■♥❝✳ ✭✷✵✶✷✮✳ ❍♦♠❡ ♣❛❣❡ ❞❛ ❡♠♣r❡s❛ ❙✉♣❡r❉r♦✐❞❘♦❜♦ts ■♥❝✳ ▼✐♥✐ ❆❚❘ ▼❡❝❤❛♥✐❝❛❧ ❉❡s❝r✐♣t✐♦♥✳ ❉✐s♣♦♥✐✈❡❧ ❡♠✿❤tt♣✿✴✴✇✇✇✳s✉♣❡r❞r♦✐❞r♦❜♦ts✳❝♦♠✴❆❚❘❴♠✐♥✐✳❛s♣①✳ ❆❝❡ss♦ ❡♠✿ ✵✺✴✶✷✴✷✵✶✷✳ ❚❛♥♥❡r✱ ❍✳❀ ❏❛❞❜❛❜❛✐❡✱ ❆✳ ✫ P❛♣♣❛s✱ ●✳ ✭✷✵✵✺✮✳ ❋❧♦❝❦✐♥❣ ✐♥ t❡❛♠s ♦❢ ♥♦♥❤♦❧♦♥♦♠✐❝❛❣❡♥ts✳ ❊♠ ❑✉♠❛r✱ ❱✳❀ ▲❡♦♥❛r❞✱ ◆✳ ✫ ▼♦rs❡✱ ❆✳✱ ❡❞✐t♦r❡s✱ ❈♦♦♣❡r❛t✐✈❡ ❈♦♥tr♦❧✱ ✈♦✲❧✉♠❡ ✸✵✾ ♦❢ ▲❡❝t✉r❡ ◆♦t❡s ✐♥ ❈♦♥tr♦❧ ❛♥❞ ■♥❢♦r♠❛t✐♦♥ ❙❝✐❡♥❝❡✱ ♣♣✳ ✷✷✾✕✷✸✾✳ ❙♣r✐♥❣❡r❇❡r❧✐♥ ❍❡✐❞❡❧❜❡r❣✳ ❚❤r✉♥✱ ❙✳ ✭✷✵✵✷✮✳ ❘♦❜♦t✐❝ ▼❛♣♣✐♥❣✿ ❆ ❙✉r✈❡②✳ ❊♠ ▲❛❦❡♠❡②❡r✱ ●✳ ✫ ◆❡❜❡❧✱ ❇✳✱❡❞✐t♦r❡s✱ ❊①♣❧♦r✐♥❣ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ✐♥ t❤❡ ◆❡✇ ▼✐❧❧❡♥✐✉♠✱ ❝❤❛♣t❡r ✶✱ ♣♣✳ ✶✕✸✻✳▼♦r❣❛♥ ❑❛✉❢♠❛♥♥✳ ❚❤r✉♥✱ ❙✳❀ ❇✉r❣❛r❞✱ ❲✳ ✫ ❋♦①✱ ❉✳ ✭✷✵✵✺✮✳ Pr♦❜❛❜✐❧✐st✐❝ ❘♦❜♦t✐❝s✳ ■♥t❡❧❧✐❣❡♥t r♦❜♦t✐❝s❛♥❞ ❛✉t♦♥♦♠♦✉s ❛❣❡♥ts✳ ❚❤❡ ▼■❚ Pr❡ss✳ ❚❤r✉♥✱ ❙✳❀ ❋♦①✱ ❉✳ ✫ ❇✉r❣❛r❞✱ ❲✳ ✭✷✵✵✵✮✳ ▼♦♥t❡ ❈❛r❧♦ ▲♦❝❛❧✐③❛t✐♦♥ ✇✐t❤ ▼✐①t✉r❡Pr♦♣♦s❛❧ ❉✐str✐❜✉t✐♦♥✳ ❊♠ Pr♦❝❡❡❞✐♥❣s ♦❢ ❆❆❆■ ◆❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆rt✐✜❝✐❛❧■♥t❡❧❧✐❣❡♥❝❡✱ ♣♣✳ ✽✺✾✕✽✻✺✱ ❆✉st✐♥✱ ❚❡①❛s✳ ▼■❚ Pr❡ss✳ ❚❤r✉♥✱ ❙✳❀ ❋♦①✱ ❉✳❀ ❇✉r❣❛r❞✱ ❲✳ ✫ ❉❡❧❧❛❡rt✱ ❋✳ ✭✷✵✵✶✮✳ ❘♦❜✉st ▼♦♥t❡ ❈❛r