IDENTIFICACIÓN DE SUBCENTROS DE EMPLEO Y COMERCIO PARA LA
CIUDAD DE BOGOTÁ
AUTORES:
CARLOS MAURICIO GALEANO CAMPO
IVÁN DARÍO PÉREZ GÁNDARA
DIRECTORA:
ANA MARÍA DÍAZ ESCOBAR
PONTIFICIA UNIVERSIDAD JAVERIANA
FACULTAD DE CIENCIAS ECONÓMICAS Y ADMINISTRATIVAS
MAESTRÍA EN ECONOMÍA
❊▼P▲❖❨▼❊◆❚ ❆◆❉ ❈❖▼▼❊❘❈❊
❙❯❇❈❊◆❚❊❘ ■❉❊◆❚■❋■❈❆❚■❖◆ ❋❖❘
❇❖●❖❚❆
∗
❈❛r❧♦s ▼❛✉r✐❝✐♦ ●❛❧❡❛♥♦ ❈❛♠♣♦
†■✈á♥ ❉❛rí♦ Pér❡③ ●á♥❞❛r❛
❆❜str❛❝t
❯s✐♥❣ ✐♥❢♦r♠❛t✐♦♥ ❢r♦♠ t❤❡ ♠♦❜✐❧✐t② s✉r✈❡②s t❤❡ ✐❞❡♥t✐✜❝❛t✐♦♥ ♦❢ ❡♠✲ ♣❧♦②♠❡♥t ❛♥❞ ❝♦♠♠❡r❝❡ s✉❜❝❡♥t❡rs ✐s ♠❛❞❡ ❢♦r ❇♦❣♦t❛ ❝✐t② ❢♦r t❤❡ ②❡❛rs ✷✵✵✺ ❛♥❞ ✷✵✶✶✳ ❊st✐♠❛t✐♦♥s ❛r❡ ♠❛❞❡ ✉s✐♥❣ t❤❡ ♥♦♥ ♣❛r❛♠❡tr✐❝ ♠❡t❤♦❞ ♦❢ ❝♦♥t✐❣✉✐t② ♠❛tr✐❝❡s ❛♥❞ s✉❜s❡q✉❡♥t❧② ✉s✐♥❣ t❤❡ ♠❡t❤♦❞ ♦❢ q✉❛♥t✐❧❡ r❡✲ ❣r❡ss✐♦♥✳ ❚❤❡ ✐❞❡♥t✐✜❝❛t✐♦♥ ✉s❡s t✇♦ ❣❡♦❣r❛♣❤✐❝❛❧ ❛♥❛❧②s✐s ✉♥✐ts✿ ❩♦♥❛❧ P❧❛♥♥✐♥❣ ❯♥✐ts ✕❯P❩✲ ❛♥❞ tr❛♥s♣♦rt ❩♦♥❡s ✕❩❆❚✲✳ ❚❤❡ r❡s✉❧ts ♦❜t❛✐♥❡❞ ❧❡t ✉s t♦ ✐❞❡♥t✐❢② t❤❡ tr❛♥s❢♦r♠❛t✐♦♥ t❤❡ ❝✐t② ❤❛s s✉✛❡r❡❞ ❜❡t✇❡❡♥ ②❡❛rs ✷✵✵✺ ❛♥❞ ✷✵✶✶ ✐♥ t❡r♠s ♦❢ ✐ts ❡♠♣❧♦②♠❡♥t ❛♥❞ ❝♦♠♠❡r❝❡ s✉❜❝❡♥t❡rs ❞✐s✲ tr✐❜✉t✐♦♥✳ ▲✐❦❡✇✐s❡✱ t❤❡ r❡s✉❧ts ❝❛♥ ❜❡ ✉s❡❞ ❛s ❛♥ ✐♥♣✉t t♦ ❢❛❝✐❧✐t❛t❡ ♣✉❜❧✐❝ ♣♦❧✐❝② ❞❡❝✐s✐♦♥ t❛❦✐♥❣ s✐♥❝❡ t❤❡ ❝❤❛♥❣❡s ✐♥ t❤❡ t❡rr✐t♦r✐❛❧ str✉❝t✉r❡ ♦❢ t❤❡ ❝✐t② ❤❡❧♣ t♦ ❞❡t❡r♠✐♥❡ ❛ ❜❡tt❡r s✉♣♣❧② ♦❢ ♣✉❜❧✐❝ ❣♦♦❞s s✉❝❤ ❛s tr❛♥s♣♦rt ❛♥❞ ✐♥❢r❛str✉❝t✉r❡✳
❦❡②✇♦r❞s✿ ❡♠♣❧♦②♠❡♥t s✉❜❝❡♥t❡rs✱ ❝♦♠♠❡r❝❡ s✉❜❝❡♥t❡rs✱ ♠♦♥♦❝❡♥tr✐❝✱ ♣♦❧②❝❡♥tr✐❝✱ ❩♦♥❛❧ P❧❛♥♥✐♥❣ ❯♥✐ts ✭❯P❩✮✱ tr❛♥s♣♦rt ❩♦♥❡s ✭❩❆❚✮✱ ❝♦♥t✐✲ ❣✉✐t② ♠❛tr✐❝❡s✱ q✉❛♥t✐❧❡ r❡❣r❡ss✐♦♥
❏❊▲ ❈❧❛ss✐✜❝❛t✐♦♥✶✿ ❏✻✶✱ ❘✶✷✱ ❘✶✹
∗❚❤✐s ♣❛♣❡r ✐s ♣r❡s❡♥t❡❞ ❛s ❛ t❤❡s✐s t♦ ♦❜t❛✐♥ ❛ ♠❛st❡r✬s ❞❡❣r❡❡ ✐♥ ❡❝♦♥♦♠✐❝s
❢r♦♠ t❤❡ P♦♥t✐✜❝✐❛ ❯♥✐✈❡rs✐❞❛❞ ❏❛✈❡r✐❛♥❛
†❲❡ ❛♣♣r❡❝✐❛t❡ t❤❡ s✉♣♣♦rt ♣r♦✈✐❞❡❞ ❜② ❆♥❛ ▼❛r✐❛ ❉✐❛③✱ ♣r♦❢❡ss♦r ❛t t❤❡ ❯♥✐✈❡rs✐❞❛❞
❏❛✈❡r✐❛♥❛ ❊❝♦♥♦♠✐❝s ❉❡♣❛rt♠❡♥t✱ ✐♥ ❤❡r r♦❧❡ ❛s t❤❡s✐s ❞✐r❡❝t♦r✳ ❙✐♠✐❧❛r❧② ✇❡ ❛r❡ t❤❛♥❦❢✉❧ ✇✐t❤ Pr♦❢❡ss♦r ❏♦sé ❆♥t♦♥✐♦ ❆✈❡♥❞❛♥♦ ❆r♦s❡♠❡♥❛ ✇❤♦ s❤❛r❡❞ ✇✐t❤ ✉s s♦♠❡ ♦❢ ❤✐s r❡❝❡♥t ♣❛♣❡rs r❡❧❛t❡❞ t♦ ♦✉r t❤❡s✐s✳ ❲❡ t❤❛♥❦ t❤❡ ❞❛t❛❜❛s❡s ♦❢ t❤❡ ❉✐str✐❝t ▼♦❜✐❧✐t② ❙✉r✈❡②s ♣r♦✈✐❞❡❞ ❜② t❤❡ ❉❡♣❛rt♠❡♥t ♦❢ ❙❡❝t♦r✐❛❧ ❙t✉❞✐❡s ❛♥❞ ❙❡r✈✐❝❡s ♦❢ t❤❡ ▼♦❜✐❧✐t② ❉✐str✐❝t ❉❡♣❛rt♠❡♥t✱ ✐♥ ♣❛rt✐❝✉❧❛r t❤❡ ❢✉♥❝t✐♦♥❛r② ▲✉✐s P❧✐♥✐♦ ▼❡♥❞♦③❛ P❛rr❛ ✇❤♦ s♦❧✈❡❞ s❡✈❡r❛❧ q✉❡st✐♦♥s ❛ss♦❝✐❛t❡❞ ✇✐t❤ t❤❡ ❞❛t❛✳ ❋✐♥❛❧❧② ✇❡ t❤❛♥❦ t❤❡ s✉♣♣♦rt ♦❢ ❙■◆●❊❖ ●r♦✉♣ ♦❢ t❤❡ ❈♦❧♦♠❜✐❛♥ ●❡♦❧♦❣✐❝❛❧ ❙❡r✈✐❝❡ ❢♦r t❤❡✐r ❣✉✐❞❛♥❝❡ ✐♥ t❤❡ ❣❡♦r❡❢❡r❡♥❝✐❛t✐♦♥ ♦❢ s♦♠❡ ❞❛t❛✳ ❆♥② ♠✐st❛❦❡ ✐s t❤❡ s♦❧❡ r❡s♣♦♥s✐❜✐❧✐t② ♦❢ t❤❡ ❛✉t❤♦rs✳
✶❨♦✉ ❝❛♥ ✈✐s✐t ❤tt♣✿✴✴✇✇✇✳❡❝♦♥❧✐t✳♦r❣✴s✉❜❥❡❝t❴❞❡s❝r✐♣t♦rs✳❤t♠❧✳
■❉❊◆❚■❋■❈❆❈■Ó◆ ❉❊ ❙❯❇❈❊◆❚❘❖❙
❉❊ ❊▼P▲❊❖ ❨ ❈❖▼❊❘❈■❖ P❆❘❆ ▲❆
❈■❯❉❆❉ ❉❊ ❇❖●❖❚➪
✯
❈❛r❧♦s ▼❛✉r✐❝✐♦ ●❛❧❡❛♥♦ ❈❛♠♣♦
✯✯■✈á♥ ❉❛rí♦ Pér❡③ ●á♥❞❛r❛
❘❡s✉♠❡♥
❯t✐❧✐③❛♥❞♦ ✐♥❢♦r♠❛❝✐ó♥ ❞❡ ❧❛s ❡♥❝✉❡st❛s ❞❡ ♠♦✈✐❧✐❞❛❞ s❡ r❡❛❧✐③❛ ❧❛ ✐❞❡♥✲ t✐✜❝❛❝✐ó♥ ❞❡ s✉❜❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦ ② ❝♦♠❡r❝✐♦ ♣❛r❛ ❧❛ ❝✐✉❞❛❞ ❞❡ ❇♦❣♦tá ♣❛r❛ ❧♦s ❛ñ♦s ✷✵✵✺ ② ✷✵✶✶✳ ▲❛s ❡st✐♠❛❝✐♦♥❡s s❡ r❡❛❧✐③❛♥ ✉t✐❧✐③❛♥❞♦ ❡❧ ♠ét♦✲ ❞♦ ♥♦ ♣❛r❛♠étr✐❝♦ ❞❡ ♠❛tr✐❝❡s ❞❡ ❝♦♥t✐❣ü✐❞❛❞ ② ♣♦st❡r✐♦r♠❡♥t❡ ❤❛❝✐❡♥❞♦ ✉s♦ ❞❡❧ ♠ét♦❞♦ ❞❡ r❡❣r❡s✐ó♥ ❝✉❛♥tí❧✐❝❛✳ ▲❛ ✐❞❡♥t✐✜❝❛❝✐ó♥ s❡ ❜❛s❛ ❡♥ ❡❧ ❛♥á✲ ❧✐s✐s ❞❡ ❞♦s ✉♥✐❞❛❞❡s ❣❡♦❣rá✜❝❛s ❞❡ r❡❢❡r❡♥❝✐❛✿ ❧❛ ✉♥✐❞❛❞ ❞❡ ♣❧❛♥❡❛♠✐❡♥t♦ ③♦♥❛❧ ✲❯P❩✲ ② ❧❛ ③♦♥❛ ❞❡ tr❛♥s♣♦rt❡ ✲❩❆❚✲✳ ▲♦s r❡s✉❧t❛❞♦s ♦❜t❡♥✐❞♦s ♣❡r✲ ♠✐t❡♥ ✐❞❡♥t✐✜❝❛r ❧❛ tr❛♥s❢♦r♠❛❝✐ó♥ q✉❡ ❤❛ s✉❢r✐❞♦ ❧❛ ❝✐✉❞❛❞ ❡♥tr❡ ❧♦s ❛ñ♦s ✷✵✵✺ ② ✷✵✶✶ ❡♥ ❝✉❛♥t♦ ❛ s✉ ❞✐str✐❜✉❝✐ó♥ ❞❡ ❡♠♣❧❡♦ ② ❝♦♠❡r❝✐♦ s❡ r❡✜❡r❡✳ ❆sí ♠✐s♠♦ ❧♦s r❡s✉❧t❛❞♦s ♣✉❡❞❡♥ s❡r ✉t✐❧✐③❛❞♦s ❝♦♠♦ ✐♥s✉♠♦ ♣❛r❛ ❢❛❝✐✲ ❧✐t❛r ❧❛ t♦♠❛ ❞❡ ❞❡❝✐s✐♦♥❡s ❞❡ ♣♦❧ít✐❝❛ ♣ú❜❧✐❝❛ ②❛ q✉❡ ❧♦s ❝❛♠❜✐♦s ❡♥ ❧❛ ❡str✉❝t✉r❛ t❡rr✐t♦r✐❛❧ ❞❡ ❧❛ ❝✐✉❞❛❞ ❛②✉❞❛♥ ❛ ❞❡t❡r♠✐♥❛r ✉♥❛ ♠❡❥♦r ♦❢❡rt❛ ❞❡ ❜✐❡♥❡s ♣ú❜❧✐❝♦s t❛❧❡s ❝♦♠♦ ❡❧ tr❛♥s♣♦rt❡ ② ❧❛ ✐♥❢r❛❡str✉❝t✉r❛
P❛❧❛❜r❛s ❈❧❛✈❡✿ ❙✉❜❝❡♥tr♦ ❞❡ ❡♠♣❧❡♦✱ ❙✉❜❝❡♥tr♦ ❞❡ ❝♦♠❡r❝✐♦✱ ▼♦♥♦✲ ❝❡♥tr✐s♠♦✱ P♦❧✐❝❡♥tr✐s♠♦✱ ❯♥✐❞❛❞ ❞❡ P❧❛♥❡♠✐❡♥t♦ ❩♦♥❛❧ ✭❯P❩✮✱ ❩♦♥❛ ❞❡ ❚r❛♥s♣♦rt❡ ✭❩❆❚✮✱ ♠❛tr✐❝❡s ❞❡ ❝♦♥t✐❣ü✐❞❛❞✱ r❡❣r❡s✐ó♥ ❝✉❛♥tí❧✐❝❛✳
❈❧❛s✐✜❝❛❝✐ó♥ ❏❊▲✶✿ ❏✻✶✱ ❘✶✷✱ ❘✶✹
✯❚r❛❜❛❥♦ ♣r❡s❡♥t❛❞♦ ♣❛r❛ ♦♣t❛r ❛❧ tít✉❧♦ ❞❡ ▼❛❣✐st❡r ❡♥ ❊❝♦♥♦♠í❛ ❞❡ ❧❛ P♦♥✲
t✐✜❝✐❛ ❯♥✐✈❡rs✐❞❛❞ ❏❛✈❡r✐❛♥❛✳
✯✯❆❣r❛❞❡❝❡♠♦s ❡❧ ❛❝♦♠♣❛ñ❛♠✐❡♥t♦ ❞❡ ❧❛ ♣r♦❢❡s♦r❛ ❆♥❛ ▼❛rí❛ ❉✐❛③ ❞❡❧ ❉❡♣❛rt❛♠❡♥t♦ ❞❡
❊❝♦♥♦♠í❛ ❞❡ ❧❛ P♦♥t✐✜❝✐❛ ❯♥✐✈❡rs✐❞❛❞ ❏❛✈❡r✐❛♥❛ ❡♥ s✉ ❝❛❧✐❞❛❞ ❞❡ ❞✐r❡❝t♦r❛ ❞❡❧ ♣r❡s❡♥t❡ tr❛✲ ❜❛❥♦✳ ❉❡ ✐❣✉❛❧ ♠❛♥❡r❛ ❛❣r❛❞❡❝❡♠♦s ❡❧ ❛♣♦②♦ ♣r❡st❛❞♦ ♣♦r ❡❧ ♣r♦❢❡s♦r ❆♥t♦♥✐♦ ❏♦sé ❆✈❡♥❞❛ñ♦ ❆r♦s❡♠❡♥❛ ❛❧ ❢❛❝✐❧✐t❛r♥♦s ❛❧❣✉♥♦s ❞❡ s✉s tr❛❜❛❥♦s ❞❡ ✐♥✈❡st✐❣❛❝✐ó♥✳ ❆❣r❛❞❡❝❡♠♦s ❧❛s ❜❛s❡s ❞❡ ❞❛t♦s ❞❡ ❧❛s ❡♥❝✉❡st❛s ❞✐str✐t❛❧❡s ❞❡ ♠♦✈✐❧✐❞❛❞ s✉♠✐♥✐str❛❞❛s ♣♦r ❧❛ ❉✐r❡❝❝✐ó♥ ❞❡ ❊st✉❞✐♦s ❙❡❝t♦r✐❛❧❡s ② ❞❡ ❙❡r✈✐❝✐♦s ❞❡ ❙❡❝r❡t❛r✐❛ ❉✐str✐t❛❧ ❞❡ ▼♦✈✐❧✐❞❛❞ ② ❡♥ ♣❛rt✐❝✉❧❛r ❛❧ ❢✉♥❝✐♦♥❛r✐♦ ▲✉✐s P❧✐♥✐♦ ▼❡♥❞♦③❛ P❛rr❛ q✉✐❡♥ s♦❧✈❡♥t♦ ❞✐✈❡rs❛s ❞✉❞❛s ❛s♦❝✐❛❞❛s ❛ ❧♦s ❞❛t♦s✳ ❆❣r❛❞❡❝❡♠♦s ❛❧ ●r✉♣♦ ❙■◆●❊❖ ❞❡❧ ❙❡r✈✐❝✐♦ ●❡♦❧ó❣✐❝♦ ❈♦❧♦♠❜✐❛♥♦ ♣♦r s✉s ♦r✐❡♥t❛❝✐♦♥❡s ♣❛r❛ ❣❡♦r❡❢❡♥❝✐❛r ❣r❛♥ ♣❛rt❡ ❞❡ ❧❛ ✐♥❢♦r♠❛❝✐ó♥ ❈✉❛❧q✉✐❡r ❡rr♦r ♣r❡s❡♥t❛❞♦ ❡s ❞❡ ❡♥t❡r❛ r❡s♣♦♥s❛❜✐❧✐❞❛❞ ❞❡ ❧♦s ❛✉t♦r❡s✳
✶P✉❡❞❡ ❝♦♥s✉❧t❛r❧❛ ❡♥ ❤tt♣✿✴✴✇✇✇✳❡❝♦♥❧✐t✳♦r❣✴s✉❜❥❡❝t❴❞❡s❝r✐♣t♦rs✳❤t♠❧✳
❮♥❞✐❝❡
✶✳ ■◆❚❘❖❉❯❈❈■Ó◆ ✸
✷✳ ❘❊❱■❙■Ó◆ ❉❊ ▲■❚❊❘❆❚❯❘❆ ✹
✷✳✶✳ ❋✉♥❝✐♦♥❡s ❞❡ ❞❡♥s✐❞❛❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✷✳ ❘❡❣r❡s✐ó♥ ❝✉❛♥tí❧✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾
✸✳ ❉❆❚❖❙ ✶✵
✹✳ ▼❆❚❘■❈❊❙ ❉❊ ❈❖◆❚■●❯■❉❆❉ ✶✹
✺✳ ❆◆❆▲■❙■❙ ❈❯❆◆❚❮▲■❈❖ ✶✾
✺✳✶✳ ❙✉❜❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦ ✭❯P❩✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✺✳✷✳ ❙✉❜❝❡♥tr♦s ❞❡ ❝♦♠❡r❝✐♦ ✭❯P❩✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✺✳✸✳ ❙✉❜❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦ ✭❩❆❚✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✺✳✹✳ ❙✉❜❝❡♥tr♦s ❞❡ ❝♦♠❡r❝✐♦ ✭❩❆❚✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✻✳ ❈❖◆❈▲❯❙■❖◆❊❙ ✸✵
✶✳ ■◆❚❘❖❉❯❈❈■Ó◆
▲❛s ❝✐✉❞❛❞❡s ❤❛♥ ❥✉❣❛❞♦ ✉♥ ♣❛♣❡❧ tr❛s❝❡♥❞❡♥t❛❧ ❛ ❧♦ ❧❛r❣♦ ❞❡ ❧❛ ❤✐st♦r✐❛ ❞❡ ❧❛ ❤✉♠❛♥✐❞❛❞ ♣❡r♠✐t✐❡♥❞♦ ❞❡s❛rr♦❧❧❛r ❧❛s s♦❝✐❡❞❛❞❡s ❛ tr❛✈és ❞❡❧ ✐♥t❡r❝❛♠❜✐♦ ❝♦✲ ♠❡r❝✐❛❧✱ ❝✐❡♥tí✜❝♦✱ ❝✉❧t✉r❛❧ ② ♣♦❧ít✐❝♦✳ ▲❛s ❝✐✉❞❛❞❡s s♦♥ ❡str✉❝t✉r❛s ❝❛♠❜✐❛♥t❡s q✉❡ s❡ tr❛♥s❢♦r♠❛♥ ❞❡ ❛❝✉❡r❞♦ ❛ ❧❛ ♥❡❝❡s✐❞❛❞ ❞❡ s✉s ❤❛❜✐t❛♥t❡s❀ ❡♥ ✉♥ ♣r✐♥❝✐♣✐♦ ❡st❛❜❧❡❝✐❞❛s ❝♦♠♦ ❡s♣❛❝✐♦s ❞❡ r❡✉♥✐ó♥ ❡ ✐♥t❡r❝❛♠❜✐♦ ❞❡ ❜✐❡♥❡s✱ ♣❛s❛♥❞♦ ♣♦st❡✲ r✐♦r♠❡♥t❡✱ tr❛s ❧❛ r❡✈♦❧✉❝✐ó♥ ✐♥❞✉str✐❛❧✱ ❛ s❡r ❧♦s ❝❡♥tr♦s ❡❝♦♥ó♠✐❝♦s ② ♣♦❧ít✐❝♦s ❞❡ ❧♦s ♣❛ís❡s✳ ❊st♦ ❤❛ ❣❡♥❡r❛❞♦ ♠❛s✐✈❛s ♠✐❣r❛❝✐♦♥❡s ❞❡s❞❡ ❡❧ ❝❛♠♣♦ ❤❛❝✐❛ ❡st♦s ❝❡♥tr♦s ✉r❜❛♥♦s✳
❈♦❧♦♠❜✐❛ ♥♦ ❡s ✉♥ ❝❛s♦ ❛❧❡❥❛❞♦ ❛ ❞✐❝❤♦ ♣r♦❝❡s♦ ❞❡ ✉r❜❛♥✐③❛❝✐ó♥✳ ❉❡ ❛❝✉❡r❞♦ ❝♦♥ ❡❧ ❈❡♥s♦ ●❡♥❡r❛❧ r❡❛❧✐③❛❞♦ ♣♦r ❡❧ ❉❆◆❊✷✱ ❡♥ ❡❧ ❛ñ♦ ✷✵✵✺ ❡❧ ✼✻ ✪ ❞❡ ❧♦s
❝♦❧♦♠❜✐❛♥♦s ❤❛❜✐t❛♥ ❡♥ ③♦♥❛s ✉r❜❛♥❛s✱ s✐❡♥❞♦ ❇♦❣♦tá ❧❛ ❝✐✉❞❛❞ ♠ás ❣r❛♥❞❡ ❞❡❧ ♣❛ís ❝♦♥ ♠ás ❞❡ ✽ ♠✐❧❧♦♥❡s ❞❡ ❤❛❜✐t❛♥t❡s✱ ❝♦♥❝❡♥tr❛♥❞♦ ❛sí ❣r❛♥ ♣❛rt❡ ❞❡ ❧❛ ♦❢❡rt❛ ② ❞❡♠❛♥❞❛ ❞❡ ❜✐❡♥❡s ② s❡r✈✐❝✐♦s ❞❡❧ ♣❛ís✳
▲❛ ✐❞❡♥t✐✜❝❛❝✐ó♥ ❞❡ ❝❡♥tr♦s ❡❝♦♥ó♠✐❝♦s ❞❡ ❧❛s ❝✐✉❞❛❞❡s ② ár❡❛s ♠❡tr♦♣♦✲ ❧✐t❛♥❛s ❤❛ s✐❞♦ ❞❡ ❣r❛♥ ✐♥t❡rés ♣❛r❛ ❧❛ ❡❝♦♥♦♠í❛ ✉r❜❛♥❛ ♣✉❡st♦ q✉❡ ♣❡r♠✐t❡ ❝❛r❛❝t❡r✐③❛r✱ ❞❡ ✉♥❛ ✉ ♦tr❛ ❢♦r♠❛✱ ❧❛s r❡❧❛❝✐♦♥❡s ❡❝♦♥ó♠✐❝❛s ❞❡ ❧♦s ✐♥❞✐✈✐❞✉♦s ② s✉ ✐♠♣❛❝t♦ ❡♥ ❧❛ ❡❝♦♥♦♠í❛ ♥❛❝✐♦♥❛❧✳ ❉✐❝❤❛ ✐❞❡♥t✐✜❝❛❝✐ó♥ ❤❛ ❡✈♦❧✉❝✐♦♥❛❞♦ ❛ ♣❛rt✐r ❞❡ ❧❛ ✐♥❝✉rs✐ó♥ ❞❡ ♥✉❡✈❛s ② ♠❡❥♦r❡s té❝♥✐❝❛s ❛♥❛❧ít✐❝❛s ② ❝✉❛♥t✐t❛t✐✈❛s✳ ▲❛ ❣r❛♥ ♠❛②♦rí❛ ❞❡ ❧♦s ❡st✉❞✐♦s ✉t✐❧✐③❛♥ ♠✉② ❡str❡❝❤❛♠❡♥t❡ ❧❛ ❞❡♥s✐❞❛❞ ❞❡ ❡♠♣❧❡♦ ❞❡ ❞❡t❡r♠✐♥❛❞❛s ár❡❛s ❝♦♠♦ ♣r♦①② ❞❡ ❧❛ ❛❝t✐✈✐❞❛❞ ❡❝♦♥ó♠✐❝❛✳ ▲♦s ♣r✐♠❡r♦s ❡s✲ t✉❞✐♦s ❝♦♠♦ ❡❧ ❞❡ ❖❞❧❛♥❞ ✭✶✾✼✽✮ ♣❛rt❡♥ ❞❡ ❡str✉❝t✉r❛s ✉r❜❛♥❛s s✐♠♣❧❡s ❞♦♥❞❡ ❧❛ ♣r✐♥❝✐♣❛❧ ❛❝t✐✈✐❞❛❞ ❡❝♦♥ó♠✐❝❛ ❣✐r❛ ❡♥ t♦r♥♦ ❛ ✉♥ s♦❧♦ ❣r❛♥ ❝❡♥tr♦ ❞❡ ♥❡❣♦✲ ❝✐♦s ✭❈❡♥tr❛❧ ❇✉s✐♥❡ss ❉✐str✐❝t ♣♦r s✉s s✐❣❧❛s ❡♥ ✐♥❣❧és✮✱ ❧♦ q✉❡ s❡ ❝♦♥♦❝❡ ❡♥ ❧❛ ❧✐t❡r❛t✉r❛ ❝♦♠♦ ♠♦❞❡❧♦ ✉r❜❛♥♦ ♠♦♥♦❝é♥tr✐❝♦✳ ❊st✉❞✐♦s ♣♦st❡r✐♦r❡s ❝♦♠♦ ❧♦s ❞❡ ●✐✉❧✐❛♥♦ ✫ ❙♠❛❧❧ ✭✶✾✾✶✮✱ ▼❝❉♦♥❛❧❞ ✫ Pr❛t❤❡r ✭✶✾✾✹✮ ② ▼❝▼✐❧❧❡♥ ✫ ▼❝✲ ❉♦♥❛❧❞ ✭✶✾✾✼✮ ♣❛rt❡♥ ❞❡ ❡str✉❝t✉r❛s ♠♦♥♦❝é♥tr✐❝❛s ♣❛r❛ ♠♦str❛r ❡❧✱ ❝❛❞❛ ✈❡③ ♠ás ❛❝❡♣t❛❞♦✱ ❝❛rá❝t❡r ♣♦❧✐❝❡♥tr✐st❛ ❞❡ ❧❛s ❝✐✉❞❛❞❡s ❞♦♥❞❡ s❡ ❝✉❡♥t❛ ❝♦♥ ✈❛r✐♦s ❝❡♥tr♦s ♥❡❣♦❝✐♦s✳ P♦r s✉ ♣❛rt❡ ❡st✉❞✐♦s ❝♦♠♦ ❧♦ ❞❡ ❈r❛✐❣ ✫ ◆❣ ✭✷✵✵✶✮✱ ▼❝▼✐❧❧❡♥ ✭✷✵✵✸✮✱ ▼❝▼✐❧❧❡♥ ✭✷✵✵✹✮ ② ●❛r❝✐❛ ✭✷✵✵✽✮ ✐♥❝♦r♣♦r❛♥ té❝♥✐❝❛s ❡st❛❞íst✐❝❛s ♠ás s♦✜st✐❝❛❞❛s q✉❡ ♠❡❥♦r❛♥ ❧❛ ✐❞❡♥t✐✜❝❛❝✐ó♥ ❞❡ ❧♦s s✉❜❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦✳
▲♦s ❡st✉❞✐♦s s♦❜r❡ ❧❛ ❡str✉❝t✉r❛ ❞❡❧ ❡♠♣❧❡♦ ♣❛r❛ ❇♦❣♦tá s❡ ❤❛♥ ❡♥❢♦❝❛❞♦ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛❧ ❛♥á❧✐s✐s ❞❡❧ ❡♥t♦r♥♦ ♠❛❝r♦❡❝♦♥ó♠✐❝♦ ❞❡ ❧❛ ❝✐✉❞❛❞ ❝♦♥ ❡♥❢♦✲ q✉❡s ❞❡ ❡❝♦♥♦♠í❛ ❧❛❜♦r❛❧✱ ♥♦ ♦❜st❛♥t❡✱ ❡st✉❞✐♦s ❝♦♠♦ ❧♦s ❞❡ ❆✈❡♥❞❛ñ♦ ✭✷✵✵✽✮ ② ❘✉✐③ ✭✷✵✶✵✮ ❛❜♦r❞❛♥ ❡❧ ♣r♦❜❧❡♠❛ ❞❡s❞❡ ❧❛ ✐❞❡♥t✐✜❝❛❝✐ó♥ ❞❡ ❧♦s s✉❜❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦ ❡♥ ❧❛ ❝✐✉❞❛❞ ♠❡❞✐❛♥t❡ ❧❛ ❡st✐♠❛❝✐ó♥ ❞❡ ❢✉♥❝✐♦♥❡s ❞❡ ❞❡♥s✐❞❛❞ ❞❡ ❡♠♣❧❡♦✳
❊st❡ tr❛❜❛❥♦ r❡❛❧✐③❛ ❧❛ ✐❞❡♥t✐✜❝❛❝✐ó♥ ❞❡ ❧♦s s✉❜❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦ ❛ ♣❛rt✐r ❞❡❧ ✉s♦ ❞❡ ♠❛tr✐❝❡s ❞❡ ❝♦♥t✐❣ü✐❞❛❞ ❛sí ❝♦♠♦ ❡❧ ♠ét♦❞♦ ❞❡ r❡❣r❡s✐ó♥ ♣♦r ❝✉❛♥✲ t✐❧❡s ❝♦♥ ❡❧ ♦❜❥❡t✐✈♦ ❞❡ ✐❞❡♥t✐✜❝❛r ❧♦s ❝❛♠❜✐♦s ❞❡ ❧♦s s✉❜❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦ ❞❡
✷❉❡♣❛rt❛♠❡♥t♦ ❆❞♠✐♥✐str❛t✐✈♦ ◆❛❝✐♦♥❛❧ ❞❡ ❊st❛❞íst✐❝❛ ✭✇✇✇✳❞❛♥❡✳❣♦✈✳❝♦✮
❧❛ ❝✐✉❞❛❞ ❞❡ ❇♦❣♦tá ❡♥tr❡ ❡❧ ❛ñ♦ ✷✵✵✺ ② ✷✵✶✶✳ ❆❞✐❝✐♦♥❛❧♠❡♥t❡✱ s❡ ❛♥❛❧✐③❛rá ❡❧ ❡❢❡❝t♦ ❞❡ ❝❛♠❜✐❛r ❡❧ t❛♠❛ñ♦ ❞❡ ❧❛ ✉♥✐❞❛❞ ❣❡♦❣rá✜❝❛ ❞❡ ❛♥á❧✐s✐s ♣❛r❛ ❡❧ ❛ñ♦ ✷✵✶✶✳ ❊♥ s✉ ❝♦♥❥✉♥t♦ ❡❧ tr❛❜❛❥♦ r❡s✉❧t❛ s❡r ♥♦✈❡❞♦s♦ ❡♥ ❧❛ ♠❡❞✐❞❛ q✉❡ s❡ ❜✉s❝❛ ❤❛❝❡r ❝♦♠♣❛r❛❝✐♦♥❡s ♣♦❝♦ ❛❤♦♥❞❛❞❛s ❡♥ ❧❛ ❧✐t❡r❛t✉r❛✱ t❛❧❡s ❝♦♠♦ ✉♥❛ ❝♦♠♣❛r❛❝✐ó♥ ✐♥✲ t❡rt❡♠♣♦r❛❧ ❞❡ ❧♦s r❡s✉❧t❛❞♦s✳ P♦r ♦tr❛ ♣❛rt❡✱ ♦tr♦ ❛s♣❡❝t♦ ❢✉♥❞❛♠❡♥t❛❧ ❞❡ ❡st❡ tr❛❜❛❥♦ ❡s ❧❛ ✐❞❡♥t✐✜❝❛❝✐ó♥ ❞❡ s✉❜❝❡♥tr♦s ❞❡ ❝♦♠❡r❝✐♦ ❞❡ ❧❛ ❝✐✉❞❛❞ ❞❡ ❇♦❣♦tá✱ ❛s✲ ♣❡❝t♦ q✉❡ ❤❛ s✐❞♦ ♣♦❝♦ ♣r♦❢✉♥❞✐③❛❞♦ ❞❡s❞❡ ❧❛ ♣❡rs♣❡❝t✐✈❛ ❞❡ ❧❛ ❡❝♦♥♦♠í❛ ✉r❜❛♥❛✳
▲❛ ✐❞❡♥t✐✜❝❛❝✐ó♥ ❞❡ ❧♦s s✉❜❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦ ② ❝♦♠❡r❝✐♦ r❡s✉❧t❛ s❡r ❜❛st❛♥t❡ út✐❧ ❡♥ ❧❛ ❞❡✜♥✐❝✐ó♥ ❞❡ ♣♦❧ít✐❝❛s ♣ú❜❧✐❝❛s ❞❡ ❧❛ ❝✐✉❞❛❞ ♣✉❡st♦ q✉❡ ♣✉❡❞❡ s❡r ✉t✐❧✐③❛❞❛ ❝♦♠♦ ✐♥s✉♠♦ ❡♥ ❧❛ ❝♦♥str✉❝❝✐ó♥ ❞❡ s✐st❡♠❛s ❞❡ tr❛♥s♣♦rt❡✱ ❡♥ ❧❛ ♠❡❥♦r❛ ❞❡ ❧❛ ✐♥❢r❛❡str✉❝t✉r❛ ✉r❜❛♥❛ ✭✈í❛s✱ ♣❛rq✉❡s✱ ♣✉❡♥t❡s✱ ♣❛rq✉❡❛❞❡r♦s✱ ❡♥tr❡ ♦tr♦s✮✱ ❡♥ ❧❛ ❞❡✜♥✐❝✐ó♥ ❞❡ ♣❧❛♥❡s ❞❡ ♦r❞❡♥❛♠✐❡♥t♦ t❡rr✐t♦r✐❛❧ ❛sí ❝♦♠♦ ❧❛ ❧♦❝❛❧✐③❛❝✐ó♥ ❞❡ ❤♦s♣✐t❛❧❡s✱ ❝♦❧❡❣✐♦s✱ ✐♥❝❧✉s♦ ❜❛rr✐♦s✳ ❊❧ tr❛❜❛❥♦ ❡stá ❞✐✈✐❞✐❞♦ ❡♥ ❝✐♥❝♦ s❡❝❝✐♦♥❡s✱ ❡♥ ❧❛ ♣r✐♠❡r❛ s❡ ♣r❡s❡♥t❛ ✉♥❛ r❡✈✐s✐ó♥ ❛ ❧✐t❡r❛t✉r❛ ❞❡ ❡❝♦♥♦♠í❛ ✉r❜❛♥❛ ❛s♦❝✐❛❞❛ ❛ ❧❛ ✐❞❡♥t✐✜❝❛❝✐ó♥ ❞❡ s✉❜❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦ ② s❡ r❡❛❧✐③❛ ✉♥ ❛♥á❧✐s✐s t❡ór✐❝♦ ❞❡❧ ♣r♦❜❧❡♠❛ ❛ ❛❜♦r❞❛r✱ ♣r❡s❡♥t❛♥❞♦ ❧❛ ♠❡t♦❞♦❧♦❣í❛ ❞❡ ❧♦s ♠♦❞❡❧♦s ❛ ✉t✐❧✐③❛r✳ ❊♥ ❧❛ s❡❣✉♥❞❛ s❡❝❝✐ó♥ s❡ ❞❡s❝r✐❜❡♥ ❧♦s ❞❛t♦s ❛ ✉t✐❧✐③❛r✳ ❊♥ ❧❛s s❡❝❝✐♦♥❡s t❡r❝❡r❛ ② ❝✉❛rt❛ s❡ ♣r❡s❡♥t❛♥ ❧♦s ♣r✐♥❝✐♣❛❧❡s ❤❛❧❧❛③❣♦s ❞❡ ❧❛s ♠❡t♦❞♦❧♦❣í❛s ✉t✐❧✐③❛❞❛s✳ ❋✐♥❛❧♠❡♥t❡ ❝✐❡rr❛ ❧❛ ú❧t✐♠❛ s❡❝❝✐ó♥ ❝♦♥ ❧❛s ❝♦♥❝❧✉s✐♦♥❡s✳
✷✳ ❘❊❱■❙■Ó◆ ❉❊ ▲■❚❊❘❆❚❯❘❆
▲❛ ✐❞❡♥t✐✜❝❛❝✐ó♥ ❞❡ s✉❜❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦ ❞❡ ❧❛s ❝✐✉❞❛❞❡s ♦ r❡❣✐♦♥❡s ♠❡✲ tr♦♣♦❧✐t❛♥❛s ❤❛ s✐❞♦ ❞❡ ❣r❛♥ ✐♥t❡rés ❡♥ ❧❛ ❡❝♦♥♦♠í❛ ✉r❜❛♥❛ ② ❤❛ ❡✈♦❧✉❝✐♦♥❛❞♦ ❢❛✈♦r❛❜❧❡♠❡♥t❡ ❛ tr❛✈és ❞❡❧ ❞❡s❛rr♦❧❧♦ ❞❡ ♥✉❡✈♦s ♠ét♦❞♦s ❛♥❛❧ít✐❝♦s ② ❡❧ ✉s♦ ❞❡ ❤❡rr❛♠✐❡♥t❛s ♠ás r♦❜✉st❛s q✉❡ ♣❡r♠✐t❡♥ ❧♦❣r❛r ✉♥❛ ♠❡❥♦r ✐❞❡♥t✐✜❝❛❝✐ó♥✳ ▲♦s ♣r✐♠❡r♦s tr❛❜❛❥♦s s❡ ❜❛s❛❜❛♥ ❡♥ ❡str✉❝t✉r❛s ✉r❜❛♥❛s ♠♦♥♦❝é♥tr✐❝❛s✱ s✐♥ ❡♠❜❛r✲ ❣♦✱ ❖❞❧❛♥❞ ✭✶✾✼✽✮ ❧♦❣ró ❞❡♠♦str❛r q✉❡ ❛ ♣❡s❛r ❞❡ q✉❡ ❡❧ s✉♣✉❡st♦ ❞❡ ❡str✉❝t✉r❛ ♠♦♥♦❝é♥tr✐❝❛ ❧♦❣r❛ s✐♠♣❧✐✜❝❛r ❡❧ ❛♥á❧✐s✐s ❞❡ ❧♦s ♣❛tr♦♥❡s ✉r❜❛♥♦s✱ ❧❛s ❝✐✉❞❛❞❡s ❞❡ t❛♠❛ñ♦ ♠♦❞❡r❛❞♦ ♥♦ ❧♦❣r❛♥ s❡r ❞❡s❝r✐t❛s ♣♦r ✉♥ ♠♦❞❡❧♦ ♠♦♥♦❝é♥tr✐❝♦ ❞❡✲ ❜✐❞♦ ❛ q✉❡ ❡①✐st❡♥ ❝♦♠♣❧❡❥♦s ♣❛tr♦♥❡s ❞❡ ✉s♦ ❞❡ ❧❛ t✐❡rr❛ q✉❡ ♥♦ ❧♦❣r❛♥ s❡r ✐❞❡♥t✐✜❝❛❞♦s✳ ❱❛❧❡ ❧❛ ♣❡♥❛ ❛♥♦t❛r q✉❡ s❡ ❡♥t✐❡♥❞❡ ♠♦♥♦❝❡♥tr✐s♠♦ ❝♦♠♦ ❛q✉❡❧ s✐st❡♠❛ ✉r❜❛♥♦ ❡♥ ❡❧ ❝✉❛❧ ❡①✐st❡ ✉♥❛ ú♥✐❝❛ ❝♦♥❝❡♥tr❛❝✐ó♥ ❞❡ ❡♠♣❧❡♦ ② ❧❛ r❡♥t❛ ❞❡❧ s✉❡❧♦ ❡stá ❞❡t❡r♠✐♥❛❞❛ ♣♦r ❧❛ ❞✐st❛♥❝✐❛ ❛ ❞✐❝❤♦ ❝❡♥tr♦ ✭❆❛❧❜✉✱ ✷✵✵✹✮✳ P♦r ♦tr❛ ♣❛rt❡ ●❛r❝✐❛ ▲ó♣❡③ ✭✷✵✵✽✮ ❞❡✜♥❡ ❡❧ ♣♦❧✐❝❡♥tr✐s♠♦ ❝♦♠♦ ❧❛ ❝♦♠♣❡♥s❛❝✐ó♥ ❞❡ ♣❡r❞✐❞❛ ❞❡ ❡❝♦♥♦♠í❛s ❞❡ ❛❣❧♦♠❡r❛❝✐ó♥ ❡♥ ❡❧ ár❡❛ ❝❡♥tr❛❧ ❞❡ ❧❛ ❝✐✉❞❛❞✱ ❣❡♥❡r❛♥❞♦ ❝♦♥❝❡♥tr❛❝✐♦♥❡s ♣❡r✐❢ér✐❝❛s ♦ s✉❜❝❡♥tr♦s✳
❯♥ ❡st✉❞✐♦ ❞❡ r❡❢❡r❡♥❝✐❛ ❡♥ ❡❧ ❛♥á❧✐s✐s ❞❡ ❧❛ ❡str✉❝t✉r❛ ✉r❜❛♥❛ ❡s ❡❧ ❞❡ ●✐✉✲ ❧✐❛♥♦ ✫ ❙♠❛❧❧ ✭✶✾✾✶✮ q✉✐❡♥❡s ♣r❡s❡♥t❛♥ ✉♥ ❛♥á❧✐s✐s ❡♠♣ír✐❝♦ ❞❡ ❧♦s ♣❛tr♦♥❡s ❧❛❜♦r❛❧❡s ② ♣♦❜❧❛❝✐♦♥❛❧❡s ❞❡ ❧❛ r❡❣✐ó♥ ♠❡tr♦♣♦❧✐t❛♥❛ ❞❡ ▲♦s ➪♥❣❡❧❡s✱ ✉s❛♥❞♦ ♠ét♦❞♦s ♥♦ ♣❛r❛♠étr✐❝♦s ❞❡ ❡st✐♠❛❝✐ó♥ ❞❡ ❧❛ ❞❡♥s✐❞❛❞ ❞❡ ❡♠♣❧❡♦✱ t❛❧❡s ❝♦✲ ♠♦ ❧❛ ✐♥s♣❡❝❝✐ó♥ ✈✐s✉❛❧ ② ❧❛ ❡st✐♠❛❝✐ó♥ ❞❡ ✈❛❧♦r❡s ❝rít✐❝♦s ❞❡ ❝♦♥❝❡♥tr❛❝✐ó♥ ❞❡ ❡♠♣❧❡❛❞♦s ♣♦r ❛❝r❡✳ P♦r ♦tr♦ ❧❛❞♦✱ ▼❝❉♦♥❛❧❞ ✫ Pr❛t❤❡r ✭✶✾✾✹✮ r❡❛❧✐③❛♥ ✉♥❛
✐❞❡♥t✐✜❝❛❝✐ó♥ ❞❡ ❧❛ ❝✐✉❞❛❞ ❞❡ ❈❤✐❝❛❣♦✱ ♣❛rt✐❡♥❞♦ ❞❡ ✉♥ ♠♦❞❡❧♦ ♠♦♥♦❝é♥tr✐❝♦ ② ✉s❛♥❞♦ ✉♥❛ ❢✉♥❝✐ó♥ ❞❡ ❞❡♥s✐❞❛❞ ❡①♣♦♥❡♥❝✐❛❧ ♥❡❣❛t✐✈❛✳ ❆sí t❛♠❜✐é♥✱ ▼❝▼✐❧❧❡♥ ✫ ▼❝❉♦♥❛❧❞ ✭✶✾✾✼✮ ♣♦r ♠❡❞✐♦ ❞❡❧ ✉s♦ ❞❡ ✉♥❛ r❡❣r❡s✐ó♥ ❧♦❝❛❧♠❡♥t❡ ♣♦♥❞❡r❛❞❛✱ ♠✉❡str❛♥ ❡❧ ❝❛rá❝t❡r ♣♦❧✐❝❡♥tr✐st❛ ❞❡ ❧❛ ❝✐✉❞❛❞ ❞❡ ❈❤✐❝❛❣♦ ❛ tr❛✈és ❞❡ ❧❛ ❡st✐♠❛✲ ❝✐ó♥ ❞❡ ❧♦s s✉❜❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦✳ ❈r❛✐❣ ✫ ◆❣ ✭✷✵✵✶✮✱ ✉s❛♥❞♦ ✉♥❛ tr❛♥s❢♦r♠❛❝✐ó♥ ❞❡ ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞❡♥s✐❞❛❞ ❞❡ ❡♠♣❧❡♦✱ ✐❞❡♥t✐✜❝❛♥ ❧♦s s✉❜❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦ ❞❡ ❧❛ ❝✐✉❞❛❞ ❞❡ ❍♦✉st♦♥ ♣♦r ♠❡❞✐♦ ❞❡❧ ❛♥á❧✐s✐s ❞❡ ❧♦s ❣r❛❞✐❡♥t❡s ❞❡ ✉♥❛ ❡st✐♠❛✲ ❝✐ó♥ ❝✉❛♥tí❧✐❝❛ ❝♦♥ s♣❧✐♥❡s s✉❛✈✐③❛❞♦s✳ ▼❝▼✐❧❧❡♥ ✭✷✵✵✸✮ ✐♥tr♦❞✉❝❡ ✉♥ ♠ét♦❞♦ ❞❡ ✐❞❡♥t✐✜❝❛❝✐ó♥ ❜❛s❛❞♦ ❡♥ ❛❧❣♦r✐t♠♦ ② ✉s❛♥❞♦ ♠❛tr✐❝❡s ❞❡ ❝♦♥t✐❣ü✐❞❛❞✳ ▼❝▼✐❧❧❡♥ ✭✷✵✵✹✮✱ ✉s❛♥❞♦ ❢✉♥❝✐♦♥❡s ❞❡ ❞❡♥s✐❞❛❞✱ r❡❛❧✐③❛ ❡st✐♠❛❝✐♦♥❡s ♥♦ ♣❛r❛♠étr✐❝❛s ② s❡♠✐✲♣r❛♠❡tr✐❝❛s ❝♦♥ ❡❧ ✜♥ ✐❞❡♥t✐✜❝❛r s✉❜❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦ ❡♥ ❣r❛♥❞❡s ár❡❛s ♠❡tr♦♣♦❧✐t❛♥❛s✳ ●❛r❝✐❛ ✭✷✵✵✽✮ r❡❛❧✐③❛ ✉♥ ❛♥á❧✐s✐s ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ❧❛ r❡❣✐ó♥ ♠❡tr♦♣♦❧✐t❛♥❛ ❞❡ ❇❛r❝❡❧♦♥❛ ❡♥tr❡ ❧♦s ❛ñ♦s ✶✾✾✶ ② ✷✵✵✸ ❝♦♥ ❡❧ ✜♥ ❞❡ ❞❡t❡r♠✐♥❛r ❝❛♠❜✐♦s ❡♥ ❧❛ ❡str✉❝t✉r❛ ❡s♣❛❝✐❛❧✳
P❛r❛ ❡❧ ♣r❡s❡♥t❡ ❡st✉❞✐♦ ❡❧ ár❡❛ ✉r❜❛♥❛ ❞❡ ✐♥t❡rés ❡s ❧❛ ❝✐✉❞❛❞ ❞❡ ❇♦❣♦tá✱ ❞♦♥❞❡ ❡♥❝♦♥tr❛♠♦s ❧♦s tr❛❜❛❥♦s ❞❡ ❆✈❡♥❞❛ñ♦ ✭✷✵✵✽✮ ② ❘✉✐③ ✭✷✵✶✵✮✳ ❊❧ ♣r✐♠❡✲ r♦ ❝♦rr❡s♣♦♥❞❡ ❛ ❧❛ ✐♠♣❧❡♠❡♥t❛❝✐ó♥ ❞❡ ✉♥ ♠♦❞❡❧♦ ♣♦❧✐❝é♥tr✐❝♦ ❡st✐♠❛♥❞♦ ✉♥❛ ❢✉♥❝✐ó♥ ❞❡ ❞❡♥s✐❞❛❞ ❞❡ ❡♠♣❧❡♦ ❛ ♣❛rt✐r ❞❡❧ ❝❡♥s♦ ❞❡ ✶✾✾✸ ❛sí ❝♦♠♦ ❞❛t♦s ♣r♦✲ ♣♦r❝✐♦♥❛❞♦s ♣♦r ❧❛ ❙❡❝r❡t❛rí❛ ❉✐str✐t❛❧ ❞❡ ▼♦✈✐❧✐❞❛❞✳ P♦r s✉ ♣❛rt❡✱ ❡❧ s❡❣✉♥❞♦ tr❛❜❛❥♦ ❝♦rr❡s♣♦♥❞❡ ❛ ✉♥ ❛♥á❧✐s✐s ♣♦❧✐❝❡♥tr✐st❛ ❡♠♣❧❡❛♥❞♦ t❛♠❜✐é♥ ✉♥❛ ❢✉♥❝✐ó♥ ❞❡ ❞❡♥s✐❞❛❞ ❞❡ ❡♠♣❧❡♦ ② ✉t✐❧✐③❛♥❞♦ ✉♥❛ té❝♥✐❝❛ ✉♠❜r❛❧❡s ❞❡ r❡❢❡r❡♥❝✐❛ ❛ ♣❛rt✐r ❞❡ ❞❛t♦s ❞❡❧ ❝❡♥s♦ ❞❡ ✷✵✵✺ ② ❧❛ ❡♥❝✉❡st❛ ❞❡ ♠♦✈✐❧✐❞❛❞ ❞❡❧ ♠✐s♠♦ ❛ñ♦✳
P♦r ♦tr❛ ♣❛rt❡✱ ❛❧❣✉♥♦s ❛✉t♦r❡s s✉❡❧❡♥ r❡❢❡r✐rs❡ ❛ ❧❛s ❝✐✉❞❛❞❡s ❞❡❧ ♠✉♥❞♦ ❛❝t✉❛❧ ❝♦♥ ❞✐st✐♥t♦s tér♠✐♥♦s t❛❧❡s ❝♦♠♦ ♠❡❣❛ ❝✐✉❞❛❞❡s ✭❙❝♦tt✱ ✷✵✵✻✮✱ ❝✐✉❞❛❞❡s ♣♦st ✐♥❞✉str✐❛❧❡s ✭❍❛❧❧✱ ✷✵✵✻✮✱ ❝✐✉❞❛❞❡s r❡❣✐ó♥ ❣❧♦❜❛❧❡s ✭❉✐❡❧❡♠❛♥ ❛♥❞ ❋❛❧✉❞✐✱ ✶✾✾✽✮✱ ♣♦❧✐♥✉❝❧❡✐s♠♦ ✭❑❧♦♦st❡r♠❛♥ ❛♥❞ ▼✉st❡r❞✱ ✷✵✵✶✮✳ ▲♦ ❝✐❡rt♦ ❡s q✉❡ ❡s❛s ♣❛r❡❝✐❡s❡♥ s❡r ❧❛ ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ❧❛s ♣r✐♥❝✐♣❛❧❡s ❝❛♣✐t❛❧❡s ♠✉♥❞✐❛❧❡s✱ ❝✐✉❞❛❞❡s q✉❡ ♦❝✉♣❛♥ ✐♠♣♦rt❛♥t❡s ❡①t❡♥s✐♦♥❡s ❞❡ t❡rr✐t♦r✐♦ ❝♦♥ ✉♥ s✐♥❢í♥ ❞❡ r❡❧❛❝✐♦♥❡s ❡❝♦♥ó♠✐❝❛s✱ ❝❛❞❛ ✈❡③ ♠ás ❞❡s❝❡♥tr❛❧✐③❛❞❛s ② ❝♦♠♣❧❡❥❛s✳ ❊s ❛q✉í ❞♦♥❞❡ ❡♥tr❛ ❛ ❥✉❣❛r ❡♥ tér♠✐♥♦ ❞❡ ♣♦❧✐❝❡♥tr✐s♠♦ q✉❡✱ s✐❣✉✐❡♥❞♦ ❛ ❉❛✈♦✉❞✐ ✭✷✵✵✸✮✱ s❡ ♣✉❡❞❡ ❞❡✲ ✜♥✐r ❝♦♠♦ ❧❛ ❞❡s❝❡♥tr❛❧✐③❛❝✐ó♥ ❞❡ ❛❝t✐✈✐❞❛❞❡s ❡❝♦♥ó♠✐❝❛s✱ ♠♦✈✐❧✐❞❛❞ ❛✉♠❡♥t❛❞❛✱ ❞❡s♣❧❛③❛♠✐❡♥t♦s ❝♦♠♣❧❡❥♦s ② ❞✐str✐❜✉❝✐ó♥ ❡s♣❛❝✐❛❧ ❢r❛❣♠❡♥t❛❞❛ ❞❡ ❛❝t✐✈✐❞❛❞❡s✳
P♦r ♠✉❝❤♦s ❛ñ♦s ❡❧ ❛♥á❧✐s✐s ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❡s♣❛❝✐❛❧ ❞❡ ❧❛s ❝✐✉❞❛❞❡s s❡ r✐❣✐ó ❜❛❥♦ ❧♦s ♣♦st✉❧❛❞♦s ❞❡ ❧❛ ◆✉❡✈❛ ❊❝♦♥♦♠í❛ ❯r❜❛♥❛ ❞♦♥❞❡ s❡ ❛s✉♠í❛♥ ❧❛s ❝✐✉❞❛❞❡s ❜❛❥♦ ✉♥ ❡sq✉❡♠❛ ♠♦♥♦❝é♥tr✐❝♦ ❡♥ ❞♦♥❞❡ ❧❛ r❡♥t❛ ❞❡❧ s✉❡❧♦ ❡st❛❜❛ ❞❡t❡r♠✐♥❛❞❛ ♣♦r ❧❛ ❞✐st❛♥❝✐❛ ❛❧ ❈❡♥tr♦ ❞❡ ◆❡❣♦❝✐♦s ✭❈❇❉ ♣♦r s✉s s✐❣❧❛s ❡♥ ✐♥✲ ❣❧és✮✳ P♦❝♦ ❛ ♣♦❝♦✱ ❛ ❧♦s ♣♦st✉❧❛❞♦s ❞❡ ❧❛ ◆✉❡✈❛ ❊❝♦♥♦♠í❛ ❯r❜❛♥❛✸✱ s❡ ❢✉❡r♦♥
✐♥tr♦❞✉❝✐❡♥❞♦ tér♠✐♥♦s ❝♦♠♦ ❞✐s♣❡rs✐ó♥ ② ♣♦❧✐❝❡♥tr✐s♠♦ ❡♥ ❧❛ ♠❡❞✐❞❛ q✉❡ ❧❛s ❞✐st❛♥❝✐❛s ❛❧ ❈❇❉ ❛✉♠❡♥t❛❜❛♥ ❝♦♠♦ ❝♦♥s❡❝✉❡♥❝✐❛ ❞❡❧ ❝r❡❝✐♠✐❡♥t♦ ♣♦❜❧❛❝✐♦♥❛❧
✸❈♦rr✐❡♥t❡ ❞❡❧ ♣❡♥s❛♠✐❡♥t♦ s♦❜r❡ ❡❝♦♥♦♠í❛ ✉r❜❛♥❛ q✉❡ ♣r❡❞♦♠✐♥ó ❡♥ ❧♦s ❛ñ♦s s❡t❡♥t❛
② ♦❝❤❡♥t❛ ❜❛s❛❞♦ ❡♥ ❧❛ ✐❞❡❛ ❞❡ ❧❛ r❡♥t❛ ♦❢❡rt❛❞❛✱ s❡❣ú♥ ❧❛ ❝✉❛❧✱ ❛ ♠❡❞✐❞❛ q✉❡ ❛✉♠❡♥t❛ ❧❛ ❞✐st❛♥❝✐❛ ❛❧ ❈❡♥tr♦ ❞❡ ◆❡❣♦❝✐♦s✱ ② ♣♦r ❡♥❞❡ t❛♠❜✐é♥ ❞❡ ❧♦s ❝♦st♦s ❞❡ ❞❡s♣❧❛③❛♠✐❡♥t♦✱ ❞❡❜❡ ❝♦♠♣❡♥s❛rs❡ ❝♦♥ ✉♥❛ ♠❡♥♦r r❡♥t❛ ❞❡❧ s✉❡❧♦✳
✭❲❤✐t❡✱ ✶✾✾✶✮✳ ❆❧ r❡s♣❡❝t♦ ❈❤❛♠♣✐♦♥ ✭✷✵✵✶✮ ❞❡s❝r✐❜❡ ✸ ❢♦r♠❛s ✭✈❡r ✜❣✉r❛ ✶✮ ❡♥ ❧❛s ❝✉❛❧❡s s❡ ♣✉❡❞❡ ❧❧❡❣❛r ❛ ✉♥❛ ❝✐✉❞❛❞ ♣♦❧✐❝é♥tr✐❝❛ ✭❝❡♥trí❢✉❣❛✱ ✐♥❝♦r♣♦r❛❝✐ó♥✱ ❢✉s✐ó♥✮✳
❱❛❧❡ ❧❛ ♣❡♥❛ ♠❡♥❝✐♦♥❛r ❡♥ ❡st❡ ♣✉♥t♦ ❡❧ ❝♦♥t❡①t♦ ❤✐stór✐❝♦ ❞❡ ❧❛ ❝✉✐❞❛❞ ❞❡ ❇♦❣♦tá✳ ❉❡s❞❡ s✉s ❝♦♠✐❡♥③♦s ❧❛ ❝✐✉❞❛❞ ❤❛ t❡♥✐❞♦ ❝♦♠♦ ♣r✐♥❝✐♣❛❧ ③♦♥❛ ❞❡ ❞❡s❛rr♦❧❧♦ ❡♥ ❝❡♥tr♦ ❞❡ ❧❛ ❝❛♣✐t❛❧✳ ❋✉❡ ❛q✉í ❞♦♥❞❡ s❡ ❡st❛❜❧❡❝✐❡r♦♥ ❧♦s ♣r✐♠❡r♦s ❝♦❧♦♥✐③❛❞♦r❡s ❡ ✐♥❝❧✉s♦ ❡s ❡♥ ❡st❛ ③♦♥❛ ❞♦♥❞❡ ❤✐stór✐❝❛♠❡♥t❡ ❤❛ ❡st❛❞♦ ✉❜✐❝❛❞♦ ❧❛ s❡❞❡ ❞❡❧ ❣♦❜✐❡r♥♦ ◆❛❝✐♦♥❛❧ ❛sí ❝♦♠♦ ❧❛ ♠❛②♦rí❛ ❞❡ s✉s ❡♥t✐❞❛❞❡s ❞❡ ❛♣♦②♦✳ P♦r ♠✉❝❤♦s ❛ñ♦s ❧♦s ♦❥♦s ❞❡ ❧❛ ❞✐r✐❣❡♥❝✐❛ ❝❛♣✐t❛❧✐♥❛ ❡st✉✈✐❡r♦♥ ❡♥❢♦❝❛❞♦s ❤❛❝✐❛ ❡❧ ♥♦rt❡✱ ❡♥ ❡s♣❡❝✐❛❧ ❤❛❝✐❛ ❧❛ ❝✐✉❞❛❞ ❞❡ ❚✉♥❥❛ ② ❤❛❝✐❛ ❡❧ r✐♦ ▼❛❣❞❛❧❡♥❛ ❡❧ ❝✉❛❧ ❛ s✉ ✈❡③ ❝♦♠✉♥✐❝❛❜❛ ❝♦♥ ❧❛ ❝♦st❛ ❝❛r✐❜❡✳ ❉❡ ❡st❛ ❢♦r♠❛ ♣♦❜❧❛❝✐♦♥❡s ❛❧❡❞❛ñ❛s ❛ ❇♦❣♦tá✱ ❝♦♠♦ ❡❧ ♠✉♥✐❝✐♣✐♦ ❞❡ ❯s❛q✉é♥✱ ❡r❛♥ ♣❛s♦s ❝❛s✐ q✉❡ ♦❜❧✐❣❛❞♦s ♣❛r❛ ❧♦s ♣r✐♠❡r♦s ❤❛❜✐t❛♥t❡s ❞❡ ❧❛ ❝✐✉❞❛❞✳ ▼✉♥✐❝✐♣✐♦s ✐♥t❡r♠❡❞✐♦s ❝♦♠♦ ❡❧ ♠✉♥✐❝✐♣✐♦ ❞❡ ❈❤❛♣✐♥❡r♦ ❢✉❡r♦♥ ❛❞q✉✐r✐❡♥❞♦ ✐♠♣♦rt❛♥❝✐❛ t♦❞❛ ✈❡③ q✉❡ ❡r❛♥ ❝♦rr❡❞♦r❡s ✐♠♣♦r✲ t❛♥t❡s ❞❡ ♠❡r❝❛♥❝í❛s ❡♥tr❡ ❇♦❣♦tá✱ ❯s❛q✉é♥ ② ❡❧ ♥♦rt❡ ❞❡❧ ♣❛ís✳ P♦❝♦ ❛ ♣♦❝♦✱ ❞❡❜✐❞♦ ❛❧ ❝r❡❝✐♠✐❡♥t♦ ❞❡♠♦❣rá✜❝♦✱ ❞✐❝❤♦s ♠✉♥✐❝✐♣✐♦s ❢✉❡r♦♥ ❛❜s♦r❜✐❞♦s ♣♦r ❧❛ ❝✐✉❞❛❞ ❞❡ ❇♦❣♦tá✱ ♣❡r♠❛♥❡❝✐❡♥❞♦ ❝❛s✐ q✉❡ ✐♥t❛❝t♦s ❧♦s ❝♦rr❡❞♦r❡s ❝♦♠❡r❝✐❛❧❡s ❞❛♥❞♦ ❛sí ♦r✐❣❡♥ ❛ ❧♦ q✉❡ ❤♦② ❝♦♥♦❝❡♠♦s ❝♦♠♦ ❡❧ ❝❡♥tr♦ ❛♠♣❧✐❛❞♦ ❞❡ ❧❛ ❝✐✉❞❛❞✳
❆ ♣❛rt✐r ❞❡ ❧❛ s❡❣✉♥❞❛ ♠✐t❛❞ ❞❡❧ s✐❣❧♦ ❳❳ ❡❧ ♣❛ís ❝♦♠✐❡♥③❛ ❛ ✈✐✈✐r ✉♥❛ ♦❧❡❛✲ ❞❛ ❞❡ ✈✐♦❧❡♥❝✐❛ ❡♥tr❡ ♣❛rt✐❞♦s ♣♦❧ít✐❝♦s✱ ❧♦ ❝✉❛❧ ❤❛❝❡ q✉❡ ♠✉❝❤♦s ❤❛❜✐t❛♥t❡s ❞❡ ③♦♥❛s r✉r❛❧❡s ❝♦♠✐❡♥❝❡♥ ❛ ♠✐❣r❛r ❤❛❝✐❛ ❧❛s ❝✐✉❞❛❞❡s✱ ❡s♣❡❝✐❛❧♠❡♥t❡ ❇♦❣♦tá✳ ❆❧ ❧❧❡❣❛r s❡ ✉❜✐❝❛♥ ❡♥ ár❡❛s ❛❧❡❞❛ñ❛s ❛❧ ❝❡♥tr♦ ❤✐stór✐❝♦ ❝♦♥ ✉♥❛ t❡♥❞❡♥❝✐❛ ♣r❡❞♦✲ ♠✐♥❛♥t❡ ❤❛❝✐❛ ❛❧ s✉r ❞❡❜✐❞♦✱ ❡♥tr❡ ♦tr❛s✱ ❛❧ ❛❧t♦ ❝♦st♦ ❞❡ ❧❛ t✐❡rr❛ q✉❡ t❡♥í❛ ❡❧ ❝♦rr❡❞♦r ❝♦♠❡r❝✐❛❧ ❞❡❧ ♥♦rt❡✳ ❊st♦ s❡ tr❛❞✉❥♦ ❡♥ ✉♥❛ ❞❡♥s✐✜❝❛❝✐ó♥ ❞❡ ❧❛ ③♦♥❛ s✉r ② ♦❝❝✐❞❡♥t❛❧ ❞❡ ❧❛ ❝✐✉❞❛❞✳ P♦st❡r✐♦r♠❡♥t❡✱ ❤❛❝✐❛ ✜♥❛❧❡s ❞❡ ❧♦s ❛ñ♦s ✽✵ ② ❣r❛♥ ♣❛rt❡ ❞❡ ❧♦s ✾✵ s❡ ❛❣✉❞✐③❛ ❡❧ ❝♦♥✢✐❝t♦ ✐♥t❡r♥♦ ❝♦❧♦♠❜✐❛♥♦ ❧♦ q✉❡ s❡ tr❛❞✉❝❡ ❡♥ ✉♥❛ s❡❣✉♥❞❛ ♦❧❡❛❞❛ ❞❡ ❞❡s♣❧❛③❛♠✐❡♥t♦ r✉r❛❧ ❝♦♥❢♦r♠á♥❞♦s❡ ❛sí ♥✉❡✈♦s ❝✐♥t✉✲ r♦♥❡s ♣❡r✐❢ér✐❝♦s ❛❧t❛♠❡♥t❡ ♣♦❜❧❛❞♦s✱ ♥✉❡✈❛♠❡♥t❡ ❝♦♥ ♣r❡❢❡r❡♥❝✐❛ ♣♦r ❡❧ s✉r ② ❡❧ ♦❝❝✐❞❡♥t❡ ❞❡ ❧❛ ❝✐✉❞❛❞✳ ❚❡♥✐❡♥❞♦ ❡♥ ❝✉❡♥t❛ ❧♦ ❛♥t❡r✐♦r✱ s❡ ♣♦❞rí❛ ♣❡♥s❛r ❡♥ ✉♥ ♠♦❞❡❧♦ ❞❡ ✐♥❝♦r♣♦r❛❝✐ó♥ ♣❛r❛ ❡①♣❧✐❝❛r ❧❛ ❛♥❡①✐ó♥ ❞❡ ❝❡♥tr♦s ❝♦♠♦ ❯s♠❡✱ ❋♦♥t✐❜ó♥✱ ❊♥❣❛t✐✈á✱ ❙✉❜❛ ♦ ❯s❛q✉é♥ ✭❜❛❥♦ ❡❧ s✉♣✉❡st♦ q✉❡ ❞✐❝❤❛s r❡❣✐♦♥❡s s♦♥ s✉❜❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦✮✳
P♦r s✉ ♣❛rt❡✱ ❈❤❛♠♣✐♦♥ ✭✷✵✵✶✮ s❡ r❡✜❡r❡ ❛ ❞✐❢❡r❡♥t❡s ❡s❝❛❧❛s ❞❡ ♣♦❧✐❝❡♥tr✐s✲ ♠♦✱ r❡❛❧✐③❛♥❞♦ ✉♥❛ ❞✐st✐♥❝✐ó♥ ❡♥tr❡ ár❡❛s ♠❡tr♦♣♦❧✐t❛♥❛s ✐♥❞✐✈✐❞✉❛❧❡s✱ r❡❣✐♦♥❡s ♠❡tr♦♣♦❧✐t❛♥❛s ♣♦❧✐♥✉❝❧❡❛❞❛s ② ❝❛♠♣♦s ✉r❜❛♥♦s ♣♦❧✐♥✉❝❡❧❛❞♦s✳ ❖tr♦s ♥♦♠❜r❡s ✉s✉❛❧♠❡♥t❡ ❡♠♣❧❡❛❞♦s ❡♥ r❡✜❡r❡♥ ❛ ♠✐❝r♦✱ ♠❡s♦ ② ♠❛❝r♦ ♣♦❧✐❝❡♥tr✐s♠♦ r❡s♣❡❝✲ t✐✈❛♠❡♥t❡✳
❖tr♦ ❛s♣❡❝t♦ ❛ s❡r t❡♥✐❞♦ ❡♥ ❝✉❡♥t❛ ❛❧ ❤❛❜❧❛r ❞❡ ♣♦❧✐❝❡♥tr✐s♠♦ t✐❡♥❡ q✉❡ ✈❡r ❝♦♥ ❡❧ ❣r❛❞✐❡♥t❡✱ ♦ ❡♥ ♦tr♦s tér♠✐♥♦s✱ ❡❧ ❣r❛❞♦ ❞❡ ✐♥t❡r❞❡♣❡♥❞❡♥❝✐❛ q✉❡ ♣r❡s❡♥t❛♥ ❧♦s ❞✐st✐♥t♦s ❝❡♥tr♦s ✉r❜❛♥♦s ✭●r❡❡♥✱ ✷✵✵✼✮✳ ❙✉ ❢♦r♠❛ ♠ás ❜ás✐❝❛✱ ❡♥ ❧❛ ❝✉❛❧ ❧❛ ✐♥t❡r❞❡♣❡♥❞❡♥❝✐❛ ❡s ❡s❝❛s❛ ♦ ♥✉❧❛✱ s❡ ♣r❡s❡♥t❛ ❝✉❛♥❞♦ ♥♦ ❡①✐st❡ ♥✐♥❣✉♥❛ ③♦♥❛ ❞❡ ❧❛ ❝✐✉❞❛❞ ❝♦♥ r❡❧❡✈❛♥❝✐❛ ❝♦♥s✐❞❡r❛❜❧❡ s♦❜r❡ ♦tr❛s r❡❣✐♦♥❡s✱ ❡♥ ❡st❡ ❝❛s♦ s♦❧♦ ❤❛②
❋✐❣✉r❛ ✶✿❈❛♠✐♥♦s ❛❧t❡r♥❛t✐✈♦s ♣❛r❛ ❧❡ ❡✈♦❧✉❝✐ó♥ ❞❡ r❡❣✐♦♥❡s ✉r❜❛♥❛s ♣♦❧✐❝é♥tr✐❝❛s ✭❚♦♠❛❞♦ ❞❡✿ ❈❤❛♠♣✐♦♥✱ ✷✵✵✶✮
❞✐str✐❜✉❝✐ó♥ ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ s✐♥ ♥✐♥❣ú♥ t✐♣♦ ❞❡ ❣r❛✈❡❞❛❞ ♦ ❛tr❛❝❝✐ó♥ ❡♥tr❡ ✉♥♦ ✉ ♦tr♦ ✐♥❞✐✈✐❞✉♦✳ ❊❧ ♣♦❧♦ ♦♣✉❡st♦ s❡ ♠❛♥✐✜❡st❛ ❝✉❛♥❞♦ ❡①✐st❡ t♦t❛❧ ✐♥t❡r❛❝❝✐ó♥ ❡♥tr❡ ❧♦s ❞✐st✐♥t♦s s✉❜❝❡♥tr♦s ❞❡ ✉♥❛ ❝✐✉❞❛❞✳
❆❤♦r❛✱ ❡♥ ❝✉❛♥t♦ ❛ ❧❛s ✈❡♥t❛❥❛s ♦ ❞❡s✈❡♥t❛❥❛s ❞❡❧ ♣♦❧✐❝❡♥tr✐s♠♦ s❡ r❡✜❡r❡✱ ♥♦ ❤❛② ✉♥ ❝♦♥s❡♥s♦ ✉♥✐✜❝❛❞♦✳ ▼❛ ② ❇❛♥✐st❡r ✭✷✵✵✻✮✱ ♣♦r ❡❥❡♠♣❧♦✱ ❡✈✐❞❡♥❝✐❛♥ ❝♦♠♦ ❧❛s ❝✐✉❞❛❞❡s ♣♦❧✐❝é♥tr✐❝❛s ♣r❡s❡♥t❛♥ ✉♥ ❡①❝❡s♦ ❞❡ ✈✐❛❥❡s ❡♥tr❡ ❧♦s ❝✐✉❞❛❞❛♥♦s✳ ❖tr♦s✱ ❡♥ ❝❛♠❜✐♦✱ ♣r❡s❡♥t❛♥ ❡❧ ❝♦♥❝❡♣t♦ ❞❡ ❡❝♦♥♦♠í❛s ❞❡ ❛❣❧♦♠❡r❛❝✐ó♥ ❝♦♠♦ ✉♥❛ ✈❡♥t❛❥❛ ✐♥❞✐s❝✉t✐❜❧❡ ❞❡ ❧❛s ❝✐✉❞❛❞❡s ♣♦❧✐❝é♥tr✐❝❛s✱ ❆❣✉✐❧❡r❛ ✭✷✵✵✺✮✳
✷✳✶✳ ❋✉♥❝✐♦♥❡s ❞❡ ❞❡♥s✐❞❛❞
❱❛r✐♦s ♠ét♦❞♦s ❤❛♥ s✐❞♦ ✉t✐❧✐③❛❞♦s ♣♦r ❧♦s ✐♥✈❡st✐❣❛❞♦r❡s ♣❛r❛ ❧❛ ✐❞❡♥t✐✜✲ ❝❛❝✐ó♥ ❞❡ s✉❜❝❡♥tr♦s ❡♥ ❧❛s ❝✐✉❞❛❞❡s✳ ●r❡❡♥❡ ✭✶✾✽✵✮✱ ♣♦r ❡❥❡♠♣❧♦✱ ❞❡✜♥❡ ❧❛s ❝♦♥❝❡♥tr❛❝✐♦♥❡s ❞❡ ❡♠♣❧❡♦ ❝♦♠♦ ❛q✉❡❧❧❛s ③♦♥❛s ❡♥ ❧❛s ❝✉❛❧❡s ❡❧ ❡♠♣❧❡♦ ❡s ♠ás ❞❡❧ ❞♦❜❧❡ ❞❡❧ ♣r♦♠❡❞✐♦ ❞❡ ❡♠♣❧❡♦ ❞❡ ❧❛ ❝✐✉❞❛❞✳ ▼❝❉♦♥❛❧❞ ✭✶✾✽✼✮ ❞❡✜♥❡ ♣♦s✐✲ ❜❧❡s s✉❜❝❡♥tr♦s ❝♦♠♦ ❛q✉❡❧❧❛s ③♦♥❛s q✉❡ t✐❡♥❡♥ ✉♥❛ ❞❡♥s✐❞❛❞ ❞❡ ❡♠♣❧❡♦ ♠❛②♦r q✉❡ ❝✉❛❧q✉✐❡r❛ ❞❡ ❧❛s ③♦♥❛s ❝♦♥t✐❣✉❛s✳ ●✐✉❧✐❛♥♦ ② ❙♠❛❧❧ ✭✶✾✾✶✮ ✐❞❡♥t✐✜❝❛♥ s✉❜✲ ❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦ ❝♦♠♦ ❛q✉❡❧❧❛s ③♦♥❛s q✉❡ t✐❡♥❡♥ ❛❧ ♠❡♥♦s ✶✵ ❡♠♣❧❡❛❞♦s ♣♦r ❛❝r❡ ② ✉♥ t♦t❛❧ ❞❡ ❡♠♣❧❡♦ ❡♥tr❡ ❞✐❝❤❛s ③♦♥❛s ❞❡ ♥♦ ♠❡♥♦s ❞❡ ✶✵✵✵✵ ❡♠♣❧❡❛❞♦s✳ ❙❤✉❦❧❛ ❛♥❞ ❲❛❞❞❡❧ ✭✶✾✾✶✮ r❡❛❧✐③❛♥ ✉♥ ❛✈❛♥❝❡ ❛❧ ✐♥❝❧✉✐r ✈❛r✐❛❜❧❡s ❡①♣❧✐❝❛t✐✈❛s ❛❞✐❝✐♦♥❛❧❡s ♣❛r❛ ❞❡t❡r♠✐♥❛r ❧❛ ❞❡♥s✐❞❛❞ ❞❡ ❡♠♣❧❡♦✱ ✈❛r✐❛❜❧❡s t❛❧❡s ❝♦♠♦ ❛❝❝❡s♦ ❛❧ ❛❡r♦♣✉❡rt♦✱ ❛❝❝❡s♦ ❛ ❛✉t♦♣✐st❛s✱ ❝❛❧✐❞❛❞ ❞❡ ❧❛s ✈í❛s✱ ❛sí ❝♦♠♦ ✈❛r✐❛❜❧❡s ❞❡ ❛❣❧♦♠❡r❛❝✐ó♥ ❞❡ ❡♠♣❧❡♦✳
❊st✉❞✐♦s ♣♦st❡r✐♦r❡s ✐♥❝❧✉②❡♥ ✉♥ ♣♦❝♦ ♠ás ❞❡ r✐❣✉r♦s✐❞❛❞ ❡st❛❞íst✐❝❛ ♠❡❞✐❛♥✲ t❡ ❧❛ ✉t✐❧✐③❛❝✐ó♥ ❞❡ ❧❛ ❢✉♥❝✐ó♥ ❡①♣♦♥❡♥❝✐❛❧ ♥❡❣❛t✐✈❛ ♣❛r❛ ❞❡t❡r♠✐♥❛r ❞❡♥s✐❞❛❞❡s ❞❡ ❡♠♣❧❡♦✳ ❊❧ ♠♦❞❡❧♦ ❡♥ s✉ ❢♦r♠❛ ❡stá♥❞❛r s❡ ♣r❡s❡♥t❛ ❞❡ ❧❛ s✐❣✉✐❡♥t❡ ❢♦r♠❛✿
D(CBD) =d0e(−βd+u)
❉♦♥❞❡ ❉ ❡s ❧❛ ❞❡♥s✐❞❛❞ ❞❡ ❡♠♣❧❡♦ ♠❡❞✐❞❛ ❝♦♠♦ ❧❛ ❝❛♥t✐❞❛❞ ❞❡ ❡♠♣❧❡❛❞♦s ❡♥ ✉♥✐❞❛❞ ❣❡♦❣rá✜❝❛✱ ❞ ❡s ❧❛ ❞✐st❛♥❝✐❛ ❛❧ ❈❡♥tr♦ ❞❡ ◆❡❣♦❝✐♦s ✭❈❇❉ ♣♦r s✉s s✐❣❧❛s ❡♥ ✐♥❣❧és✮✱d0 ❡s ❧❛ ❞❡♥s✐❞❛❞ ❞❡ ❡♠♣❧❡♦ ❡♥ ❧❛ ❞✐st❛♥❝✐❛ ❝❡r♦✱β r❡♣r❡s❡♥t❛
❡❧ ❝♦❡✜❝✐❡♥t❡ q✉❡ ❝❛♣t✉r❛ ❡❧ ❣r❛❞✐❡♥t❡ ❞❡ ❞❡♥s✐❞❛❞ ② ✉ r❡♣r❡s❡♥t❛ ❡❧ tér♠✐♥♦ ❞❡ ❡rr♦r ❛❧❡❛t♦r✐♦✳ ❊❧ ♠♦❞❡❧♦ ❡♥ ❧♦❣❛r✐t♠♦ ♥❛t✉r❛❧ s❡rí❛ ❞❡ ❧❛ s✐❣✉✐❡♥t❡ ❢♦r♠❛✿
ln D(CBD) =ln d0−βd+u
❱❛r✐♦s ❡st✉❞✐♦s ❤❛♥ ✐♥✈❡st✐❣❛❞♦ ❞✐st✐♥t❛s ❢♦r♠❛s ❢✉♥❝✐♦♥❛❧❡s ❛ ♣❛rt✐r ❞❡ ❧❛ ❡❝✉❛❝✐ó♥ ❛♥t❡r✐♦r✳ P♦r ❡❥❡♠♣❧♦✱ ▼❝ ❉♦♥❛❧❞ ✭✶✾✽✾✮ ✉t✐❧✐③❛ s✐❡t❡ ❢♦r♠❛s ❢✉♥❝✐♦♥❛✲ ❧❡s ❞✐st✐♥t❛s ❡♥❝♦♥tr❛♥❞♦ ♣r♦❜❧❡♠❛s ❞❡ ❤❡t❡r♦❝❡❞❛st✐❝✐❞❛❞ ❡♥ ✈❛r✐❛s ❞❡ ❡❧❧❛s ❛sí ❝♦♠♦ r❡❧❛❝✐♦♥❡s ♥♦ ❧✐♥❡❛❧❡s s✐❣♥✐✜❝❛t✐✈❛s✳
▲❛ ❛♥t❡r✐♦r ❢✉♥❝✐ó♥ ❡①♣♦♥❡♥❝✐❛❧ ❡s ♠✉② út✐❧ ♣❛r❛ ❞❡s❝r✐❜✐r ♦r❞❡♥❛♠✐❡♥t♦s ✉r❜❛♥♦s ♠♦♥♦❝é♥tr✐❝♦s ❡♥ ❞♦♥❞❡ ❡❧ ♣r✐♥❝✐♣❛❧ ♣♦❧♦ ❞❡ ❞❡s❛rr♦❧❧♦ s❡ ❝♦♥❝❡♥tr❛ ❡♥ ✉♥ s♦❧♦ ❧✉❣❛r✳ ❙✐♥ ❡♠❜❛r❣♦✱ ❡♥ ❧❛ r❡❛❧✐❞❛❞ ❛❝♦♥t❡❝❡ q✉❡ ♣❛r❛ ❡❧ ❡st❛❜❧❡❝✐♠✐❡♥t♦ ❞❡ s✉❜❝❡♥tr♦s s❡ ❞❡❜❡ t❡♥❡r ❡♥ ❝✉❡♥t❛ ❧❛ r❡❧❛❝✐ó♥ ❞❡ ❡st♦s ❝♦♥ ♦tr♦s s✉❜❝❡♥tr♦s✳ ❉✐❝❤❛ r❡❧❛❝✐ó♥ ♣♦❞rí❛ ❜✐❡♥ ✐r ❡♥ ✉♥❛ s♦❧❛ ✈í❛✱ ❡s ❞❡❝✐r✱ ❝❛❞❛ s✉❜❝❡♥tr♦ ♣♦t❡♥✲ ❝✐❛❧ t✐❡♥❡ s♦❧♦ r❡❧❛❝✐ó♥ ❝♦♥ ❡❧ s✉❜❝❡♥tr♦ ♠ás ❝❡r❝❛♥♦✱ ♦ ❡❧ ❝❛s♦ ❡♥ ❡❧ q✉❡ ❝❛❞❛ s✉❜❝❡♥tr♦ ♣♦t❡♥❝✐❛❧ t✐❡♥❡ r❡❧❛❝✐ó♥ ❝♦♥ t♦❞♦s ❧♦s ♦tr♦s s✉❜❝❡♥tr♦s ❝♦♠♦ ❡①♣❧✐❝❛ ❍❡✐❦❦✐❧❛ ✭✶✾✽✾✮✳ ❯♥ ♣✉♥t♦ ✐♥t❡r♠❡❞✐♦ ❡s ❡❧ ♣r♦♣✉❡st♦ ♣♦r ●r✐✣t❤ ✭✶✾✽✶✮✱ ❡♥ ❞♦♥❞❡ s❡ ♣✉❡❞❡ ✉t✐❧✐③❛r ✉♥❛ ❢✉♥❝✐ó♥ ❞❡ ❞❡♥s✐❞❛❞ ❛❞✐t✐✈❛ ❡♥ ❧❛ ❝✉❛❧ s❡ ✐♥❝❧✉②❡ ❧❛ r❡❧❛❝✐ó♥ ❝♦♥ ❧♦s ❞❡♠ás s✉❜❝❡♥tr♦s✱ ❞❡ ❡st❛ ❢♦r♠❛ ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞❡♥s✐❞❛❞ ❞❡ ❡♠♣❧❡♦ t❡♥❞rí❛ ❧❛ s✐❣✉✐❡♥t❡ ❢♦r♠❛✿
D(d, X) =α+PN(n=1)βdn+PK(i=1)βXi+u
❉♦♥❞❡dn❡s ❧❛ ❞✐st❛♥❝✐❛ ❛ ❧❛ ③♦♥❛ ❡s♣❡❝í✜❝❛ ♥ ②Xi ❡❧ ❝♦♥❥✉♥t♦ ❞❡ ✈❛r✐❛❜❧❡s ❡①♣❧✐❝❛t✐✈❛s ❛❞✐❝✐♦♥❛❧❡s ♣❛r❛ ❡st✐♠❛r ❧❛ ❞❡♥s✐❞❛❞ ❞❡ ❡♠♣❧❡♦✳ ❉✐❝❤❛s ✈❛r✐❛❜❧❡s ♣✉❡❞❡♥ s❡r ❧❛ ❛❝t✐✈✐❞❛❞ ✐♥❞✉str✐❛❧ ❞❡ ❞❡t❡r♠✐♥❛❞❛ ③♦♥❛✱ ❡❧ ♥✐✈❡❧ ❞❡ ✐♥❢r❛❡str✉❝✲ t✉r❛✱ ❧❛ ❝❛♥t✐❞❛❞ ❞❡ ♣❛rq✉❡❛❞❡r♦s✱ ❡♥tr❡ ♦tr❛s✳
❆ ♣❛rt✐r ❞❡ ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞❡♥s✐❞❛❞ ❛♥t❡r✐♦r s❡ ❤❛♥ ❞❡s❛rr♦❧❧❛❞♦ ❞✐st✐♥t❛s ♠❡t♦❞♦❧♦❣í❛s ❡♥ ❛r❛s ❞❡ r❡❛❧✐③❛r ❝♦rr❡❝t❛s ❛♣r♦①✐♠❛❝✐♦♥❡s ❛ ❧♦s s✉❜❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦✳ ▼❝▼✐❧❧❡♥ ✭✷✵✵✶✮ ✉t✐❧✐③❛ ✉♥❛ r❡❣r❡s✐ó♥ ❡♥ ✷ ❡t❛♣❛s✱ ❡♥ ❧❛ ♣r✐♠❡r❛ r❡❛❧✐③❛ ✉♥❛ r❡❣r❡s✐ó♥ ❧♦❝❛❧♠❡♥t❡ ♣♦♥❞❡r❛❞❛ ✭▲❲❘ ♣♦r s✉s s✐❣❧❛s ❡♥ ✐♥❣❧és✮ q✉❡ s❡ r❡❛✲ ❧✐③❛ ❝♦♥ ❧❛ ✐♥t❡♥❝✐ó♥ ❞❡ ❞❛r ♠ás ♣❡s♦ ❛ ❧♦s s✉❜❝❡♥tr♦s ♠ás ❝❡r❝❛♥♦s ❛ ❧❛ ③♦♥❛ ❞❡ ❡st✉❞✐♦✳ ▲❛ s❡❣✉♥❞❛ ❡t❛♣❛ ❝♦♥s✐st❡ ❡♥ ✉t✐❧✐③❛r ✉♥ ♠♦❞❡❧♦ s❡♠✐♣❛r❛♠étr✐❝♦ ♣❛r❛ ❝♦♥♦❝❡r ❧❛ s✐❣♥✐✜❝❛♥❝✐❛ ❞❡ ❧❛s ③♦♥❛s ✐❞❡♥t✐✜❝❛❞❛s ❡♥ ❧❛ ♣r✐♠❡r❛ ❡t❛♣❛✳ ❯♥ ♣r♦✲ ❝❡❞✐♠✐❡♥t♦ s✐♠✐❧❛r ✉t✐❧✐③❛ ❘❡❞❢❡❛r♥ ✭✷✵✵✼✮ ♣❛r❛ ❡st✐♠❛r ❞❡♥s✐❞❛❞❡s ❞❡ ❡♠♣❧❡♦
❡♥ ❧❛ ❝✐✉❞❛❞ ❞❡ ▲♦s ➪♥❣❡❧❡s ❡st❛ ✈❡③✱ ❛ ❞✐❢❡r❡♥❝✐❛ ❞❡ ▼❝▼✐❧❧❡♥ ✭✷✵✵✶✮✱ ✉t✐❧✐③❛♥✲ ❞♦ s✉❜♠✉❡str❛s q✉❡ ♣❡r♠✐t❡♥ ✉s❛r ✉♥❛ ♠❛②♦r ✈❡♥t❛♥❛ ❞❡ ♣♦♥❞❡r❛❝✐ó♥✳ P♦r s✉ ♣❛rt❡ ❈r❛✐❣ ❛♥❞ ◆❣ ✭✷✵✵✶✮ ✉t✐❧✐③❛♥ s♣❧✐♥❡s ❝ú❜✐❝♦s ♣❛r❛ ✐❞❡♥t✐✜❝❛r s✉❜❝❡♥tr♦s✳ ❆q✉❡❧❧♦s s✉❜❝❡♥tr♦s q✉❡ s❡ ❡♥❝✉❡♥tr❡♥ ❡♥ ❛❧ ♠❡♥♦s ❡❧ ♣❡r❝❡♥t✐❧ ✾✺ ❞❡ ❧❛ ❞❡♥s✐❞❛❞ ❞❡ ❡♠♣❧❡♦ ♦ ❝♦♠❡r❝✐♦ s♦♥ ✜r♠❡s ❝❛♥❞✐❞❛t♦s ❛ ❝♦♠♣♦rt❛rs❡ ❝♦♠♦ s✉❜❝❡♥tr♦✳
✷✳✷✳ ❘❡❣r❡s✐ó♥ ❝✉❛♥tí❧✐❝❛
P❛r❛ ❡st❡ ❝❛s♦ ♣❛rt✐❝✉❧❛r ❡s✱ ❝♦♠♦ ❡♥ ❝❛s✐ t♦❞♦s ❧♦s ❛♥á❧✐s✐s ❡st❛❞íst✐❝♦s✱ ❞❡ ❣r❛♥ ✐♥t❡rés ♦❜t❡♥❡r ✉♥❛ ♣r♦❢✉♥❞❛ ❝❛r❛❝t❡r✐③❛❝✐ó♥ ❞❡ ❧♦s ❞❛t♦s ② ❡♥ ❡s♣❡❝✐❛❧ ❞❡ ❛q✉❡❧❧❛s ár❡❛s ❣❡♦❣rá✜❝❛s q✉❡ ❝♦♥❝❡♥tr❡♥ ❧❛ ♠❛②♦r ♣❛rt❡ ❞❡❧ ❡♠♣❧❡♦✳ ❊s ❛sí ❝♦✲ ♠♦ ❧❛ ♠❡t♦❞♦❧♦❣í❛ ❞❡ r❡❣r❡s✐ó♥ ❝✉❛♥tí❧✐❝❛ ♣r♦✈❡❡ ✐♥❢♦r♠❛❝✐ó♥ s♦❜r❡ ❧❛ ❞❡♥s✐❞❛❞ ❞❡ ❡♠♣❧❡♦ ❡♥ ♣❡r❝❡♥t✐❧❡s ❡s♣❡❝í✜❝♦s ❞❡ ❡st✉❞✐♦✱ ❝♦♠♦ ♣♦r ❡❥❡♠♣❧♦✱ ❧♦s ♣❡r❝❡♥t✐✲ ❧❡s ✾✵ ② ✾✺ ❡♥ ❞♦♥❞❡ ❡s♣❡r❛rí❛♠♦s ❡♥❝♦♥tr❛r ❧❛s ❞❡♥s✐❞❛❞❡s ❞❡ ❡♠♣❧❡♦ ♠ás ❛❧t❛s✳
❙✐❣✉✐❡♥❞♦ ❧♦ ❡①♣✉❡st♦ ♣♦r ❈❛♠❡r♦♥ ✫ ❚r✐✈❡❞✐ ✭✷✵✵✺✮ ♣♦❞❡♠♦s ❞❡✜♥✐r ❡❧ q✲és✐♠♦ ❝✉❛♥t✐❧ ❝♦♠♦ ❡❧ ✈❛❧♦r µq t❛❧ q✉❡ ❧❛ ✈❛r✐❛❜❧❡ ❞❡♣❡♥❞✐❡♥t❡ y ❡s ♠❡♥♦r ♦ ✐❣✉❛❧ q✉❡µq ❝♦♥ ♣r♦❜❛❜✐❧✐❞❛❞ q✳ ❊♥t♦♥❝❡s t❡♥❡♠♦s✿
q=P r[y≤µq] =Fy(µq)
❉♦♥❞❡ Fy ❡s ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❛❝✉♠✉❧❛❞❛ ❞❡ y✳ P❛r❛ ❡❧ ❝❛s♦ ❞❡❧ ♠♦❞❡❧♦ ❞❡ r❡❣r❡s✐ó♥✱ ❡❧ q✲és✐♠♦ ❝✉❛♥t✐❧ ♣♦❜❧❛❝✐♦♥❛❧ ❞❡y ❝♦♥❞✐❝✐♦♥❛❧ ❡♥ x❡s ❧❛ ❢✉♥❝✐ó♥ µq(x) t❛❧ q✉❡ ② ❝♦♥❞✐❝✐♦♥❛❧ ❡♥ ① ❡s ♠❡♥♦r ♦ ✐❣✉❛❧ q✉❡ µq(x)✳ ❉❡ ❡s❛
❢♦r♠❛ t❡♥❡♠♦s✿
q=F(y|x)(µq(x))
❆ ♥✐✈❡❧ ♠✉❡str❛❧ ❑♦❡♥❦❡r ❛♥❞ ❇❛ss❡tt ✭✶✾✼✽✮ ♦❜s❡r✈❛♥ q✉❡ ❡❧ ❝✉❛♥t✐❧ ♠✉❡s✲ tr❛❧ ♣✉❡❞❡ s❡r ❤❛❧❧❛❞♦ ❝♦♥ ❧❛ s♦❧✉❝✐ó♥ ❛❧ s✐❣✉✐❡♥t❡ ♣r♦❜❧❡♠❛ ❞❡ ♦♣t✐♠✐③❛❝✐ó♥✱ r❡s♣❡❝t♦ ❛ ✿
PN
(i:yi≥β)q|yi−β|+PN(i:yi<β)(1−q)|yi−β|
❊①t❡♥❞✐❡♥❞♦ ❡❧ ♠♦❞❡❧♦ ❛❧ ❝❛s♦ ❞❡ ✉♥❛ r❡❣r❡s✐ó♥ ❧✐♥❡❛❧ ❞❡ ❧❛ ❢♦r♠❛y=x′β+µ t❡♥❞rí❛♠♦s ❡❧ s✐❣✉✐❡♥t❡ ♣r♦❜❧❡♠❛ ❞❡ ♦♣t✐♠✐③❛❝✐ó♥✿
PN
(i:yi≥β)q|yi−x ′
β|+PN(i:yi<β)(1−q)|yi−x ′
β|
▲❛ ❡❝✉❛❝✐ó♥ ❛♥t❡r✐♦r ♥♦ ❡s ❞✐❢❡r❡♥❝✐❛❜❧❡ ❛sí q✉❡ ❧♦s ♠ét♦❞♦s ❞✐❢❡r❡♥❝✐❛❧❡s ❞❡ ♦♣t✐♠✐③❛❝✐ó♥ ♥♦ s♦♥ ❛♣❧✐❝❛❜❧❡s✱ ♣♦r ❡♥❞❡ t❛♠♣♦❝♦ ♠í♥✐♠♦s ❝✉❛❞r❛❞♦s ♦r❞✐♥❛r✐♦s ✭▼❈❖✮✳
❇✉❝❤✐♥s❦② ✭✶✾✾✽✮ ❞❡♠✉❡str❛ q✉❡✿
q
N(( ˆβq−βq)→N[0, A(−1)BA(−1)]
❉♦♥❞❡✿
A=plimn1Pn(i=1)f(µq)(0|xi)xix➫i
B=plimn1Pn(i=1)q(1−q)xix➫i
❙✐❡♥❞♦ f(µq) ❧❛ ❞❡♥s✐❞❛❞ ❝♦♥❞✐❝✐♦♥❛❧ ❞❡❧ t❡r♠✐♥♦ ❞❡ ❡rr♦r uq = y −x ′
βq ❡✈❛❧✉❛❞❛ ❡♥uq = 0✳ ▲❛ ❡st✐♠❛❝✐ó♥ ❞❡ ❧❛ ✈❛r✐❛♥③❛ ❞❡(βˆq)s✉❡❧❡ ♥❡❝❡s✐t❛r ❞❡❧ ✉s♦ ❞❡ ❜♦♦tstr❛♣✐♥❣✳
✸✳ ❉❆❚❖❙
P♦❧ít✐❝❛ ② ❣❡♦❣rá✜❝❛♠❡♥t❡ ❧❛ ❝✐✉❞❛❞ ❞❡ ❇♦❣♦tá ❡stá ❞✐✈✐❞✐❞❛ ❡♥ ✷✵ ❧♦❝❛❧✐✲ ❞❛❞❡s✳ ❊st❛s ❛ s✉ ✈❡③ s❡ ♣✉❡❞❡♥ ❞✐✈✐❞✐r ❡♥ ❯♥✐❞❛❞❡s ❞❡ P❧❛♥❡❛♠✐❡♥t♦ ❩♦♥❛❧ ✭❯P❩✮✱ ✶✶✼ ❡♥ t♦t❛❧ ♣❛r❛ ❇♦❣♦tá ✭❛♥❡①♦ ✶ ② ❛♥❡①♦ ✷✮✳ ▲❛s ❯P❩ ❛ s✉ ✈❡③ ❡stá♥ ❞✐✈✐❞✐❞❛s ❡♥ ❜❛rr✐♦s ② ❡st♦s ú❧t✐♠♦ ❡♥ ❩♦♥❛s ❞❡ ❚r❛♥s♣♦rt❡ ✭❩❆❚✮ ❝♦♥ ✉♥ t♦t❛❧ ♣❛r❛ ❡st❛s ú❧t✐♠❛s ❞❡ ✶✵✷✵ ♣❛r❛ ❇♦❣♦tá ✭❆♥❡①♦ ✸✮✳
❈♦♥ ❡❧ ✜♥ ❞❡ r❡❛❧✐③❛r ❧❛ ✐❞❡♥t✐✜❝❛❝✐ó♥ ❞❡ ❧♦s s✉❜❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦ ② ❝♦♠❡r❝✐♦ ♣❛r❛ ❧❛ ❝✐✉❞❛❞ ❞❡ ❇♦❣♦tá ❡♥ ❧♦s ❛ñ♦s ✷✵✵✺ ② ✷✵✶✶✱ s❡ ✉t✐❧✐③❛r♦♥ ❞❛t♦s ❣❡♥❡r❛❞♦s ♣♦r ❡♥t✐❞❛❞❡s ♣ú❜❧✐❝❛s ❞❡❧ ♦r❞❡♥ ❞✐str✐t❛❧✱ ❡♥ ♣❛rt✐❝✉❧❛r ❞❡ ❧❛ ❙❡❝r❡t❛r✐❛ ❉✐str✐✲ t❛❧ ❞❡ ▼♦✈✐❧✐❞❛❞ ② ❧❛ ❙❡❝r❡t❛r✐❛ ❉✐str✐t❛❧ ❞❡ P❧❛♥❡❛❝✐ó♥ ✉t✐❧✐③❛♥❞♦ ❧❛s ❡♥❝✉❡st❛s ❞✐str✐t❛❧❡s ❞❡ ♠♦✈✐❧✐❞❛❞ ♣❛r❛ ❧♦s ❛ñ♦s ✷✵✵✺ ② ✷✵✶✶✱ ❡❧ ✐♥✈❡♥t❛r✐♦ ❞❡ ✐♥❢♦r♠❛✲ ❝✐ó♥ ❡♥ ♠❛t❡r✐❛ ❡st❛❞íst✐❝❛ s♦❜r❡ ❇♦❣♦tá✱ ❡❧ s✐st❡♠❛ ❞❡ ❝♦♥s✉❧t❛ ❞❡ ❞❛t♦s ❞❡ ✐♥❢♦r♠❛❝✐ó♥ ❡st❛❞íst✐❝❛ ② ❧❛ ❝❛rt♦❣r❛❢í❛ ❞✐str✐t❛❧ ❞❡ ❧❛ ❯♥✐❞❛❞ ❆❞♠✐♥✐str❛t✐✈❛ ❞❡ ❈❛t❛str♦ ❉✐str✐t❛❧ ✕■❉❊❈❆✲✳
▲❛ ❡♥❝✉❡st❛ ❞✐str✐t❛❧ ❞❡ ♠♦✈✐❧✐❞❛❞ ❞❡❧ ❛ñ♦ ✷✵✵✺ ❡stá ❝♦♠♣✉❡st❛ ♣♦r ❝✉❛tr♦ ♠ó❞✉❧♦s q✉❡ ♣r❡s❡♥t❛♥ ❧❛ s✐❣✉✐❡♥t❡ ✐♥❢♦r♠❛❝✐ó♥✿ ❡❧ ♠♦❞✉❧♦ ❆ ❡s ❡❧ ❞❡ ✐❞❡♥t✐✜❝❛✲ ❝✐ó♥ ② ❝♦♥tr♦❧ ❞❡ ❧❛ ❡♥tr❡✈✐st❛❀ ❡❧ ♠♦❞✉❧♦ ❇ ❝♦♥t✐❡♥❡ ❧♦s ✈❡❤í❝✉❧♦s ❞❡ tr❛♥s♣♦rt❡ ❞✐s♣♦♥✐❜❧❡s ❡♥ ❡❧ ❤♦❣❛r❀ ❡❧ ♠♦❞✉❧♦ ❈ ♣r❡s❡♥t❛ ❧❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ❧♦s ♠✐❡♠❜r♦s ❞❡❧ ❤♦❣❛r ② ✜♥❛❧♠❡♥t❡ ❡❧ ♠ó❞✉❧♦ ❉ ❝♦♥t✐❡♥❡ ❧♦s ❞❡s♣❧❛③❛♠✐❡♥t♦s r❡❛❧✐③❛❞♦s ♣♦r ❧❛s ♣❡rs♦♥❛s ❞❡❧ ❤♦❣❛r✳ ▲❛ ✉♥✐❞❛❞ ❣❡♦❣rá✜❝❛ ❞❡ ❧❛ ❡♥❝✉❡st❛ ❞❡❧ ✷✵✵✺ ❡s ❧❛ ❯P❩✳
▲❛ ❡♥❝✉❡st❛ ❞✐str✐t❛❧ ❞❡ ♠♦✈✐❧✐❞❛❞ ❞❡❧ ❛ñ♦ ✷✵✶✶ ❡stá ❝♦♠♣✉❡st❛ ♣♦r ❝✉❛tr♦ ♠ó❞✉❧♦s ❞❡ ✐♥❢♦r♠❛❝✐ó♥❀ ❡❧ ♠ó❞✉❧♦ ❆ ♣r❡s❡♥t❛ ❧❛ ✐♥❢♦r♠❛❝✐ó♥ ❣❡♥❡r❛❧ ❞❡ ❧♦s ❤♦❣❛r❡s ❡♥❝✉❡st❛❞♦s❀ ❡❧ ♠ó❞✉❧♦ ❇ ❝♦♥t✐❡♥❡ ❧❛ ✐♥❢♦r♠❛❝✐ó♥ s♦❝✐♦❡❝♦♥ó♠✐❝❛ ❞❡❧ ❤♦❣❛r❀ ❡❧ ♠ó❞✉❧♦ ❈ ♣r❡s❡♥t❛ ❧❛ ✐♥❢♦r♠❛❝✐ó♥ ❞❡ ❧♦s ✈❡❤í❝✉❧♦s q✉❡ ❞✐s♣♦♥❡♥ ❧❛s ♣❡rs♦♥❛s ❞❡❧ ❤♦❣❛r ② ✜♥❛❧♠❡♥t❡ ❡❧ ♠ó❞✉❧♦ ❉ ♣r❡s❡♥t❛ ❧♦s ❞❡s♣❧❛③❛♠✐❡♥t♦s r❡❛✲ ❧✐③❛❞♦s ♣♦r ❧❛s ♣❡rs♦♥❛s ❞❡❧ ❤♦❣❛r✳ ▲❛ ✉♥✐❞❛❞ ❣❡♦❣rá✜❝❛ ❞❡ ❧❛ ❡♥❝✉❡st❛ ❞❡❧ ✷✵✶✶ ❡s ❧❛ ❩❆❚✱ s✐♥ ❡♠❜❛r❣♦✱ ❡st❛ ♣✉❡❞❡ s❡r ❢á❝✐❧♠❡♥t❡ ❝♦♠♣❛r❛❜❧❡ ❝♦♥ ❧❛ ❯P❩ r❛③ó♥ ♣♦r ❧❛ ❝✉❛❧ ❡❧ ❛♥á❧✐s✐s ♣♦r ❯P❩ s❡ ♣✉❡❞❡ ❤❛❝❡r t❛♥t♦ ♣❛r❛ ❡❧ ❛ñ♦ ✷✵✵✺ ❝♦♠♦ ❡❧ ✷✵✶✶✱ ❧♦ ❝✉❛❧ ♥♦ ♦❝✉rr❡ ❝♦♥ ❡❧ ❛♥á❧✐s✐s ❛ ♥✐✈❡❧ ❞❡ ❩❆❚ ❡❧ ❝✉❛❧ s♦❧♦ ♣✉❡❞❡ s❡r r❡❛❧✐③❛❞♦ ♣❛r❛ ❡❧ ❛ñ♦ ✷✵✶✶✳
❉❡❧ ■♥✈❡♥t❛r✐♦ ❊st❛❞íst✐❝♦ ❞❡ ❧❛ ❙❡❝r❡t❛r✐❛ ❉✐str✐t❛❧ ❞❡ P❧❛♥❡❛❝✐ó♥✱ s❡ ❤✐③♦ ✉s♦ ❞❡❧ ♠ó❞✉❧♦ ❞❡ ❛s♣❡❝t♦s ❣❡♦❣rá✜❝♦s ② ❞❡ ❧♦❝❛❧✐③❛❝✐ó♥✱ ❡♥ ♣❛rt✐❝✉❧❛r ❞❡ ❧❛ ✐♥❢♦r♠❛❝✐ó♥ ❞❡ ❡①t❡♥s✐ó♥ ❞❡ s✉❡❧♦ ✭✉r❜❛♥♦ ✕ r✉r❛❧✮ ② ❝❛♥t✐❞❛❞ ② s✉♣❡r✜❝✐❡✳ ❊❧ s✐st❡♠❛ ❞❡ ❝♦♥s✉❧t❛ ❞❡ ❞❛t♦s ❞❡ ✐♥❢♦r♠❛❝✐ó♥ ❡st❛❞íst✐❝❛ ❝♦♥t✐❡♥❡ ❛❞❡♠ás ✐♥✲ ❢♦r♠❛❝✐ó♥ ❞❡♠♦❣rá✜❝❛ ② ❡❝♦♥ó♠✐❝❛ ❞❡ ❧❛ ❝✐✉❞❛❞✱ ❡♥ ♣❛rt✐❝✉❧❛r ❡❧ ♠ó❞✉❧♦ ❞❡ ✐♥❢♦r♠❛❝✐ó♥ t❡rr✐t♦r✐❛❧ ❝♦♥t✐❡♥❡ ❡❧ ❝❡♥s♦ ❞✐str✐t❛❧ ❞❡ ❡❞✐✜❝❛❝✐♦♥❡s ❡❧ ❝✉❛❧ ♣❡r♠✐t❡ ❞❡t❡r♠✐♥❛r ❧❛s ✉♥✐❞❛❞❡s ❡❝♦♥ó♠✐❝❛s ♣♦r ❯P❩ ② ♣♦r s❡❝t♦r ❡❝♦♥ó♠✐❝♦✳
❆ ♣❛rt✐r ❞❡ ❧❛s ❢✉❡♥t❡s ❞❡ ✐♥❢♦r♠❛❝✐ó♥ ♣r❡s❡♥t❛❞❛s ❛♥t❡r✐♦r♠❡♥t❡ s❡ ❡st❛❜❧❡✲ ❝✐❡r♦♥ ❧❛s s✐❣✉✐❡♥t❡s ✈❛r✐❛❜❧❡s✿
❞tr❛❜❛❥♦✿ ❝♦rr❡s♣♦♥❞❡ ❛ ❧❛ ❞❡♥s✐❞❛❞ ❞❡ tr❛❜❛❥♦ ♣♦r ✉♥✐❞❛❞ ❣❡♦❣rá✜❝❛✱ ❧❛ ✈❛✲ r✐❛❜❧❡ s❡ ♦❜t✉✈♦ ❝♦♠♦ ❧❛ s✉♠❛ ❞❡ ❧♦s ✈✐❛❥❡s ❝✉②♦ ♠♦t✐✈♦ ❡r❛ tr❛❜❛❥❛r q✉❡ s❡ ❡♥❝✉❡♥tr❛ ❡♥ ❡❧ ♠ó❞✉❧♦ ❉ ❞❡ ❧❛s ❡♥❝✉❡st❛s ❞✐str✐t❛❧❡s ❞❡ ♠♦✈✐❧✐❞❛❞ ❞❡ ♣❛r❛ ❇♦✲ ❣♦tá ❞❡ ❧♦s ❛ñ♦s ✷✵✵✺ ② ✷✵✶✶✳
❞❝♦♠♣r❛s✿ ❝♦rr❡s♣♦♥❞❡ ❛ ❧❛ ❞❡♥s✐❞❛❞ ❞❡ ❝♦♠♣r❛s ♣♦r ✉♥✐❞❛❞ ❣❡♦❣rá✜❝❛✱ ❧❛ ✈❛r✐❛❜❧❡ s❡ ♦❜t✉✈♦ ❝♦♠♦ ❧❛ s✉♠❛ ❞❡ ❧♦s ✈✐❛❥❡s ❝✉②♦ ♠♦t✐✈♦ ❡r❛ ❝♦♠♣r❛s q✉❡ s❡ ❡♥❝✉❡♥tr❛ ❡♥ ❡❧ ♠ó❞✉❧♦ ❉ ❞❡ ❧❛s ❡♥❝✉❡st❛s ❞✐str✐t❛❧❡s ❞❡ ♠♦✈✐❧✐❞❛❞ ❞❡ ♣❛r❛ ❇♦❣♦tá ❞❡ ❧♦s ❛ñ♦s ✷✵✵✺ ② ✷✵✶✶✳
❡✐♥❞✉str✐❛✿ ❝♦rr❡s♣♦♥❞❡ ❛❧ ♥ú♠❡r♦ ❞❡ ✉♥✐❞❛❞❡s ❡❝♦♥ó♠✐❝❛s ❞❡❧ s❡❝t♦r ✐♥❞✉s✲ tr✐❛ ♣♦r ❯P❩ ♣❛r❛ ❧♦s ❛ñ♦s ✷✵✵✺ ② ✷✵✶✶✱ ❧❛ ✐♥❢♦r♠❛❝✐ó♥ ❢✉❡ ❡①tr❛í❞❛ ❞❡❧ ♠ó❞✉❧♦ ❞❡ ✐♥❢♦r♠❛❝✐ó♥ t❡rr✐t♦r✐❛❧ ❞❡❧ s✐st❡♠❛ ❞❡ ❝♦♥s✉❧t❛ ❞❡ ❞❛t♦s ❞❡ ✐♥❢♦r♠❛❝✐ó♥ ❡st❛✲ ❞íst✐❝❛✳
❡❝♦♠❡r❝✐♦✿ ❝♦rr❡s♣♦♥❞❡ ❛❧ ♥ú♠❡r♦ ❞❡ ✉♥✐❞❛❞❡s ❡❝♦♥ó♠✐❝❛s ❞❡❧ s❡❝t♦r ❝♦♠❡r✲ ❝✐♦ ♣♦r ❯P❩ ♣❛r❛ ❧♦s ❛ñ♦s ✷✵✵✺ ② ✷✵✶✶✱ ❧❛ ✐♥❢♦r♠❛❝✐ó♥ ❢✉❡ ❡①tr❛í❞❛ ❞❡❧ ♠ó❞✉❧♦ ❞❡ ✐♥❢♦r♠❛❝✐ó♥ t❡rr✐t♦r✐❛❧ ❞❡❧ s✐st❡♠❛ ❞❡ ❝♦♥s✉❧t❛ ❞❡ ❞❛t♦s ❞❡ ✐♥❢♦r♠❛❝✐ó♥ ❡st❛✲ ❞íst✐❝❛✳
❡s❡r✈✐❝✐♦s✿ ❝♦rr❡s♣♦♥❞❡ ❛❧ ♥ú♠❡r♦ ❞❡ ✉♥✐❞❛❞❡s ❡❝♦♥ó♠✐❝❛s ❞❡❧ s❡❝t♦r s❡r✈✐✲ ❝✐♦s ♣♦r ❯P❩ ♣❛r❛ ❧♦s ❛ñ♦s ✷✵✵✺ ② ✷✵✶✶✱ ❧❛ ✐♥❢♦r♠❛❝✐ó♥ ❢✉❡ ❡①tr❛í❞❛ ❞❡❧ ♠ó❞✉❧♦ ❞❡ ✐♥❢♦r♠❛❝✐ó♥ t❡rr✐t♦r✐❛❧ ❞❡❧ s✐st❡♠❛ ❞❡ ❝♦♥s✉❧t❛ ❞❡ ❞❛t♦s ❞❡ ✐♥❢♦r♠❛❝✐ó♥ ❡st❛✲ ❞íst✐❝❛✳
♣s✉❡❧♦❤❛❜✿ ❝♦rr❡s♣♦♥❞❡ ❛ ♣♦r❝❡♥t❛❥❡ ❞❡ s✉❡❧♦ ❤❛❜✐t❛❜❧❡ ♣♦r ❯P❩✳ ▲❛ ✈❛✲ r✐❛❜❧❡ ❢✉❡ ❝♦♥str✉✐❞❛ ❝♦♥ ✐♥❢♦r♠❛❝✐ó♥ ❞❡❧ ♠ó❞✉❧♦ ❞❡ ❛s♣❡❝t♦s ❣❡♦❣rá✜❝♦s ② ❞❡ ❧♦❝❛❧✐③❛❝✐ó♥ ❞❡❧ ✐♥✈❡♥t❛r✐♦ ❞❡ ✐♥❢♦r♠❛❝✐ó♥ ❡♥ ♠❛t❡r✐❛ ❡st❛❞íst✐❝❛ s♦❜r❡ ❇♦❣♦tá ❡♥ ❞♦♥❞❡ s❡ t♦♠ó ár❡❛ ❤❛❜✐t❛❜❧❡ ❞❡ ❧❛ ❯P❩ ② s❡ ❞✐✈✐❞✐ó ♣♦r ❡❧ ár❡❛ t♦t❛❧ ❞❡ ❧❛ ❯P❩✳
❛r❡❛✿ ❝♦rr❡s♣♦♥❞❡ ❛❧ ár❡❛ ❞❡ ❝❛❞❛ ✉♥❛ ❞❡ ❧❛s ③♦♥❛s ❣❡♦❣rá✜❝❛s ❞❡ ❡st✉❞✐♦✱ ❡❧ ❝á❧❝✉❧♦ ❢✉❡ r❡❛❧✐③❛❞♦ ♣♦r ❧♦s ❛✉t♦r❡s ❡♥ ❡❧ s✐st❡♠❛ ❞❡ ✐♥❢♦r♠❛❝✐ó♥ ❣❡♦❣rá✜❝❛ ❆r❝●■❙✹ ❛ ♣❛rt✐r ❞❡ ❧❛ ✐♥❢♦r♠❛❝✐ó♥ ❝❛rt♦❣rá✜❝❛ ■❉❊❈❆✳ ▲❛ ✉♥✐❞❛❞ ❞❡ ♠❡❞✐❞❛
✹❆r❝●■❙r❡s ✉♥ s♦❢t✇❛r❡ ❞❡ ✐♥❢♦r♠❛❝✐ó♥ ❣❡♦❣rá✜❝❛ q✉❡ ♣❡r♠✐t❡ ❧❛ ❡❧❛❜♦r❛❝✐ó♥ ❞❡ ♠❛♣❛s
❡s ❦✐❧ó♠❡tr♦s ❝✉❛❞r❛❞♦s✳
❞✐st❝❜❞✿ ❝♦rr❡s♣♦♥❞❡ ❛ ❧❛ ❞✐st❛♥❝✐❛ ❧✐♥❡❛❧ ❡♥ ❦✐❧ó♠❡tr♦s ❞❡ ❝❛❞❛ ✉♥❛ ❞❡ ❧❛s ③♦♥❛s ❣❡♦❣rá✜❝❛s ❞❡ ❡st✉❞✐♦ ❛❧ ❈❉❇ ✭❈❡♥tr❛❧ ❇✉s✐♥❡ss ❉✐str✐❝t✮✱ ❡❧ ❝á❧❝✉❧♦ ❢✉❡ r❡❛❧✐③❛❞♦ ♣♦r ❧♦s ❛✉t♦r❡s ❡♥ ❡❧ s✐st❡♠❛ ❞❡ ✐♥❢♦r♠❛❝✐ó♥ ❣❡♦❣rá✜❝❛ ❆r❝●■❙ ❛ ♣❛rt✐r ❞❡ ❧❛ ✐♥❢♦r♠❛❝✐ó♥ ❝❛rt♦❣rá✜❝❛ ■❉❊❈❆✳
❞✐st❛❡r♦✿ ❝♦rr❡s♣♦♥❞❡ ❛ ❧❛ ❞✐st❛♥❝✐❛ ❧✐♥❡❛❧ ❡♥ ❦✐❧ó♠❡tr♦s ❞❡ ❝❛❞❛ ✉♥❛ ❞❡ ❧❛s ③♦♥❛s ❣❡♦❣rá✜❝❛s ❞❡ ❡st✉❞✐♦ ❛❧ ❆❡r♦♣✉❡rt♦ ■♥t❡r♥❛❝✐♦♥❛❧ ❊❧ ❉♦r❛❞♦✱ ❡❧ ❝á❧❝✉❧♦ ❢✉❡ r❡❛❧✐③❛❞♦ ♣♦r ❧♦s ❛✉t♦r❡s ❡♥ ❡❧ s✐st❡♠❛ ❞❡ ✐♥❢♦r♠❛❝✐ó♥ ❣❡♦❣rá✜❝❛ ❆r❝●■❙ ❛ ♣❛rt✐r ❞❡ ❧❛ ✐♥❢♦r♠❛❝✐ó♥ ❝❛rt♦❣rá✜❝❛ ■❉❊❈❆✳
tr❛♥s♠✐✿ ❝♦rr❡s♣♦♥❞❡ ❛ ✉♥❛ ✈❛r✐❛❜❧❡ ❝❛t❡❣ór✐❝❛ ❝♦♥str✉✐❞❛ ♣♦r ❧♦s ❛✉t♦r❡s ❡♥ ❞♦♥❞❡ ❧❛ ③♦♥❛ ❣❡♦❣rá✜❝❛ ❞❡ ❡st✉❞✐♦ q✉❡ t✐❡♥❡ ❛❝❝❡s♦ ❞✐r❡❝t♦ ❛❧ ❚r❛♥s♠✐❧❡♥✐♦ s❡ ❧❡ ❛s✐❣♥❛ ✉♥ ✈❛❧♦r ❞❡ ✶ ② ❡♥ ❝❛s♦ ❝♦♥tr❛r✐♦ t✐❡♥❡ ✉♥ ✈❛❧♦r ❞❡ ✵✳
tr❛♥s♠✐❝♦♥s✿ ❝♦rr❡s♣♦♥❞❡ ❛ ✉♥❛ ✈❛r✐❛❜❧❡ ❝❛t❡❣ór✐❝❛ ❝♦♥str✉✐❞❛ ♣♦r ❧♦s ❛✉t♦✲ r❡s ❡♥ ❞♦♥❞❡ ❧❛ ③♦♥❛ ❣❡♦❣rá✜❝❛ ❞❡ ❡st✉❞✐♦ q✉❡ t✐❡♥❡ ❛❝❝❡s♦ ❞✐r❡❝t♦ ❛ ✉♥❛ tr♦♥❝❛❧ ❞❡ ❚r❛♥s♠✐❧❡♥✐♦ ❡♥ ❝♦♥str✉❝❝✐ó♥ s❡ ❧❡ ❛s✐❣♥❛ ✉♥ ✈❛❧♦r ❞❡ ✶ ② ❡♥ ❝❛s♦ ❝♦♥tr❛r✐♦ t✐❡♥❡ ✉♥ ✈❛❧♦r ❞❡ ✵✳
▲❛ ❊♥❝✉❡st❛ ❞❡ ▼♦✈✐❧✐❞❛❞ ❞❡❧ ❛ñ♦ ✷✵✵✺ ❝✉❡♥t❛ ❝♦♥ ✉♥❛ ♠✉❡str❛ ❞❡ ✉♥ ♣♦❝♦ ♠ás ❞❡ ✈❡✐♥t❡ ♠✐❧ ✈✐❛❥❡s r❡❛❧✐③❛❞♦s ♣♦r ❤❛❜✐t❛♥t❡s ❞❡ ❇♦❣♦tá ❤❛❝✐❛ s✉ ❞❡st✐♥♦ ❞❡ tr❛❜❛❥♦ ② ✻✶✾ ❝✉②♦ ♠♦t✐✈♦ ❞❡ ✈✐❛❥❡ ❢✉❡r♦♥ ❧❛s ❝♦♠♣r❛s✳ ❈❡r❝❛ ❞❡ ❧❛ ♠✐t❛❞ ❞❡ ❞✐❝❤♦s ✈✐❛❥❡s ❢✉❡r♦♥ r❡❛❧✐③❛❞♦s ❤❛❝✐❛ ❧❛s ❧♦❝❛❧✐❞❛❞❡s ❞❡ ❯s❛q✉é♥ ② ❈❤❛♣✐♥❡r♦✱ ❧♦❝❛❧✐❞❛❞❡s r❡❝♦♥♦❝✐❞❛s ❝♦♠♦ ✐♠♣♦rt❛♥t❡s ❝❡♥tr♦s ❞❡ ❡♠♣❧❡♦ ② ❝♦♠❡r❝✐♦ ❞❡ ❧❛ ❝✐✉❞❛❞✳ ▲❛ ❯P❩ ❝♦♥ ❡❧ ♠❛②♦r ♥ú♠❡r♦ ❞❡ ✈✐❛❥❡s ❝♦♥ ♠♦t✐✈♦ tr❛❜❛❥♦ ❡s ❧❛ ❯P❩ ✾✼ ✭❈❤✐❝ó ▲❛❣♦✮ ❝♦♥ ❝❡r❝❛ ❞❡❧ ✽ ✪ ❞❡❧ t♦t❛❧ ❞❡ ❡st❡ t✐♣♦ ❞❡ ✈✐❛❥❡s✳ ▲❡ s✐❣✉❡ ♠✉② ❞❡ ❝❡r❝❛ ❧❛ ❯P❩ ✾✸ ✭▲❛s ◆✐❡✈❡s✮ ❝♦♥ ✉♥ ✻ ✪✳ ▲❛s ❯P❩ ❝♦♥ ♠❡♥♦r❡s ✈✐❛❥❡s ❞❡ tr❛❜❛✲ ❥♦ s♦♥ ❧❛s ❯P❩ ✻✸ ② ❯P❩ ✻✹ ❡♥ ❧❛ ❧♦❝❛❧✐❞❛❞ ❞❡ ❈✐✉❞❛❞ ❇♦❧í✈❛r✳ ❊♥ ❝✉❛♥t♦ ❛ ❧♦s ✈✐❛❥❡s ❝♦♥ ❞❡st✐♥♦ ❝♦♠♣r❛s ❧❛ ❯P❩ ✶✻ ✭❙❛♥t❛ ❇ár❜❛r❛✮ ❡♥❝❛❜❡③❛ ❡❧ ❧✐st❛❞♦ ❝♦♥ ❡❧ ✽ ✪✱ s❡❣✉✐❞❛ ♠✉② ❞❡ ❝❡r❝❛ ♣♦r ❧❛ ❯P❩ ✾✸ ✭❧❛s ♥✐❡✈❡s✮ ❝♦♥ ❡❧ ✼ ✪✳ ❯♥ t♦t❛❧ ❞❡ ✶✵ ❯P❩ s❡ ❡♥❝✉❡♥tr❛♥ ❛❧ ✜♥❛❧ ❞❡ ❧❛ ❧✐st❛ ❝♦♥ ♥✐♥❣ú♥ ✈✐❛❥❡ ❝♦♥ ♠♦t✐✈♦ ❞❡ ❝♦♠♣r❛✳
❊♥ ❧❛ ❡♥❝✉❡st❛ ❞❡ ♠♦✈✐❧✐❞❛❞ ❞❡❧ ❛ñ♦ ✷✵✶✶ ❡❧ ♥ú♠❡r♦ ❞❡ ✈✐❛❥❡s ❝♦♥ ❞❡st✐♥♦ tr❛❜❛❥♦ ❡s ❞❡ ✼✸✻✺ ② ❞❡ ✷✾✼✵ ❝♦♥ ❞❡st✐♥♦ ❝♦♠♣r❛s✳ ▲❛ ❯P❩ ❝♦♥ ❡❧ ♠❛②♦r ♥ú♠❡r♦ ❞❡ ✈✐❛❥❡s ❝♦♥ ❞❡st✐♥♦ tr❛❜❛❥♦ s✐❣✉❡ s✐❡♥❞♦ ❧❛ ❯P❩ ✾✼ ✭❈❤✐❝ó ▲❛❣♦✮ ♣❡r♦ ❝♦♥ ✉♥❛ ♣❛rt✐❝✐♣❛❝✐ó♥ ♠❡♥♦r ❞❡❧ ♦r❞❡♥ ❞❡❧ ✺ ✪✱ s❡❣✉✐❞❛ ♣♦r ❧❛ ❯P❩ ✶✵✷ ✭▲❛ ❙❛❜❛♥❛✮ t❛♠❜✐é♥ ❝♦♥ ✉♥❛ ♣❛rt✐❝✐♣❛❝✐ó♥ ❝❡r❝❛♥❛ ❛❧ ✺ ✪✳ ▲❛ ❯P❩ ✾✸ ✭▲❛s ◆✐❡✈❡s✮ ♦❝✉♣❛ ❡❧ t❡r❝❡r ❧✉❣❛r ❡♥ ✐♠♣♦rt❛♥❝✐❛✳ ▲❛ ❯P❩ ✻✸ s❡ ♠❛♥t✐❡♥❡ ❡♥ ❡❧ ú❧t✐♠♦ ❧✉❣❛r ❧❛ ❧✐st❛ s✐♥ ♥✐♥❣ú♥ ✈✐❛❥❡ ❝♦♥ ❞❡st✐♥♦ tr❛❜❛❥♦✳ P❛r❛ ❧♦s ✈✐❛❥❡s ❝♦♥ ❞❡st✐♥♦ ❝♦♠♣r❛s ❛♣❛✲ r❡❝❡ ❧❛ ❯P❩ ✶✸ ✭▲♦s ❈❡❞r♦s✱ ❯s❛q✉é♥✮ ❝♦♥ ✹ ✪ ❞❡❧ t♦t❛❧ ❞❡ ✈✐❛❥❡s ❞❡ ❝♦♠♣r❛s✱ s❡❣✉✐❞❛ ❞❡ ❝❡r❝❛ ♣♦r ❧❛ ❯P❩ ✷✽ ✭❊❧ ❘✐♥❝ó♥✱ ❙✉❜❛✮ ❝♦♥ ✸ ✪ ❞❡ ❧❛ ♣❛rt✐❝✐♣❛❝✐ó♥✳ ② ❧❛ ❛❞♠✐♥✐str❛❝✐ó♥ ❞❡ ❞❛t♦s ❜❛❥♦ ❞✐st✐♥t❛s ♠♦❞❛❧✐❞❛❞❡s✳ P❛r❛ ❡st❡ tr❛❜❛❥♦ ❡❧ s♦❢t✇❛r❡ ❢✉❡ ❡♠♣❧❡❛❞♦ ❝♦♥ ❡❧ ✜♥ ❞❡ ❡❧❛❜♦r❛r ② ❣❡st✐♦♥❛r ❞❛t♦s ❣❡♦r❡❢❡♥❝✐❛❞♦s s♦❜r❡ ❧❛s ❞✐st✐♥t❛s ✉♥✐❞❛❞❡s ❣❡♦❣rá✜❝❛s ❞❡ r❡❢❡r❡♥❝✐❛ ♣❛r❛ ❧❛ ❝✐✉❞❛❞ ❞❡ ❇♦❣♦tá✳
