❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦
■♥st✐t✉t♦ ❞❡ ❋ís✐❝❛
▼♦❞❡❧❛❣❡♠ ❡st♦❝ást✐❝❛ ❞❡ ♥❡✉rô♥✐♦s ❡
s✉❛ ✐♥t❡r❛çã♦ ❡♠ t❡♠♣♦ r❡❛❧ ❝♦♠
♥❡✉rô♥✐♦s ❜✐♦❧ó❣✐❝♦s✳
P❡❞r♦ ❱❛❧❛❞ã♦ ❈❛r❡❧❧✐
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❘❡②♥❛❧❞♦ ❉❛♥✐❡❧ P✐♥t♦
❚❡s❡ ❞❡ ❞♦✉t♦r❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ ■♥st✐t✉t♦ ❞❡ ❋ís✐❝❛ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❈✐ê♥❝✐❛s
❇❛♥❝❛ ❡①❛♠✐♥❛❞♦r❛✿
Pr♦❢✳ ❉r✳ ❘❡②♥❛❧❞♦ ❉❛♥✐❡❧ P✐♥t♦ ✲ ■❋✲❯❙P
Pr♦❢✳ ❉r✳ ❏♦❛q✉✐♠ Pr♦❝ó♣✐♦ ❞❡ ❆r❛✉❥♦ ❋✐❧❤♦ ✲ ■❈❇✲❯❙P Pr♦❢✳ ❉r✳ ▼ár✐♦ ❏♦sé ❞❡ ❖❧✐✈❡✐r❛ ✲ ■❋✲❯❙P
Pr♦❢✳ ❉r✳ ❆♥tô♥✐♦ ❈❛r❧♦s ❘♦q✉❡ ❞❛ ❙✐❧✈❛ ❋✐❧❤♦ ✲ ❋❋❈▲❘P✲❯❙P Pr♦❢✳ ❉r✳ ❘✐t❛ ▼❛r✐❛ ❩♦r③❡♥♦♥ ❞♦s ❙❛♥t♦s ✲ ❯❋P❊
FICHA CATALOGRÁFICA
Preparada pelo Serviço de Biblioteca e Informação
do Instituto de Física da Universidade de São Paulo
Carelli, Pedro Valadão
Modelagem estocástica de neurônios e sua interação em tempo real com neurônios biológicos - 2008
Tese (Doutorado) – Universidade de São Paulo. Instituto de Física - Depto. de Física Geral
Orientador: Prof. Dr. Reynaldo Daniel Pinto
Área de Concentração: Física Geral
Unitermos: 1. Física; 2. Física Experimental; 3. Mecânica Estatística.
❆❣r❛❞❡❝✐♠❡♥t♦s
Em primeiro lugar agradeço ao Reynaldo, pela orientação
e ótima convivência que tivemos.
Ao Sartorelli por sua experiência e pelas conversas em
mo-mentos importantes.
Agradeço ao Marcelo pela ajuda no desenvolvimento do
trabalho, e muitas discussões proveitosas.
Ao Bóris pela ajuda no trabalho e na revisão do texto.
À Ludmila pelo apoio no laboratório.
À Vivi pela força na revisão final da tese.
Ao Thiagão, Caroline e todos do LFNL pela agradável
com-panhia no ambiente de trabalho.
À Carol pela companhia e confiança todos esses anos.
Gostaria de agradecer a todos que me acompanharam
❘❡s✉♠♦
❉❡s❡♥✈♦❧✈❡♠♦s ✉♠ ♠♦❞❡❧♦ ❡st♦❝ást✐❝♦ ❞❛ ❛t✐✈✐❞❛❞❡ ❡❧étr✐❝❛ ❞❡ ✉♠ ♥❡✉rô✲ ♥✐♦ ♠♦t♦r ❞♦ ❣â♥❣❧✐♦ ❡st♦♠❛t♦❣ástr✐❝♦ ❞❡ ❝r✉stá❝❡♦s✱ ❛ ♣❛rt✐r ❞❡ ✉♠ ♠♦❞❡❧♦ ❞❡t❡r♠✐♥íst✐❝♦ ❡❧❡tr♦✜s✐♦❧♦❣✐❝❛♠❡♥t❡ ♣❧❛✉sí✈❡❧✳ ❈♦♠ ✐ss♦ r❡❝✉♣❡r❛♠♦s ❝❛r❛❝✲ t❡ríst✐❝❛s ❞❛ ❞✐♥â♠✐❝❛ ♥❡✉r❛❧ s❡♠♣r❡ ♦❜s❡r✈❛❞❛s ❡♠ ♥❡✉rô♥✐♦s ✐s♦❧❛❞♦s✱ t❛✐s ❝♦♠♦ ✐rr❡❣✉❧❛r✐❞❛❞❡s ♥♦s ♣❛❞rõ❡s ❞❡ ❞✐s♣❛r♦s q✉❡ ♥ã♦ sã♦ r❡♣r♦❞✉③✐❞❛s ♣❡❧♦ ♠♦❞❡❧♦ ❞❡t❡r♠✐♥íst✐❝♦ ♦r✐❣✐♥❛❧✳
■♠♣❧❡♠❡♥t❛♠♦s ♦t✐♠✐③❛çõ❡s ❡ s✐♠♣❧✐✜❝❛çõ❡s ♥♦ ♠ét♦❞♦ ♥✉♠ér✐❝♦ ❞❡ s✐✲ ♠✉❧❛çã♦ ❡st♦❝ást✐❝❛ q✉❡ ♣❡r♠✐t✐r❛♠ r♦❞❛r ❛ s✐♠✉❧❛çã♦ ❡♠ t❡♠♣♦ r❡❛❧ ♣❛r❛ ✐♥t❡r❛❣✐r ♠♦❞❡❧♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❝♦♠ ♥❡✉rô♥✐♦s ❜✐♦❧ó❣✐❝♦s✱ ✐♠♣❧❡♠❡♥t❛♥❞♦ s✐♥❛♣s❡s ❛rt✐✜❝✐❛✐s ❡♥tr❡ ❡❧❡s✳
P♦r ✜♠ ✉t✐❧✐③❛♠♦s ♦ ♠♦❞❡❧♦ ❡ ♦s ♠ét♦❞♦s ❞❡ s✐♠✉❧❛çã♦ ❞❡s❡♥✈♦❧✈✐❞♦s ♣❛r❛ s✉❜st✐t✉✐r ♥❡✉rô♥✐♦s ❞♦ ❣â♥❣❧✐♦ ❡st♦♠❛t♦❣ástr✐❝♦ ❡ ❝♦♥str✉✐r s✐st❡♠❛s ❤í❜r✐❞♦s✱ q✉❡ ❢♦r❛♠ ✉s❛❞♦s ♣❛r❛ ✈❡r✐✜❝❛r ❝♦♠♦ ♦❝♦rr❡ ❛ tr❛♥s♠✐ssã♦ ❞❡ ✐♥✲ ❢♦r♠❛çã♦ ❡♥tr❡ ♥❡✉rô♥✐♦s ❜✐♦❧ó❣✐❝♦s ❡ ❛rt✐✜❝✐❛✐s✱ q✉❛♥❞♦ ❛ ❞✐♥â♠✐❝❛s ❞❡st❡s é ❡st♦❝ást✐❝❛ ♦✉ ❞❡t❡r♠✐♥íst✐❝❛✳
❆❜str❛❝t
❲❡ ❞❡✈❡❧♦♣❡❞ ❛ ♠❛t❤❡♠❛t✐❝❛❧ ♠♦❞❡❧ ♦❢ t❤❡ ❡❧❡❝tr✐❝❛❧ ❛❝t✐✈✐t② ♦❢ ❛ ♠♦t♦r ♥❡✉r♦♥ ❢r♦♠ t❤❡ st♦♠❛t♦❣❛str✐❝ ❣❛♥❣❧✐♦♥ ♦❢ ❝r✉st❛❝❡❛♥s✳ ■t ✇❛s ✐♥s♣✐r❡❞ ♦♥ ❛ ♣r❡✈✐♦✉s ❡①✐st✐♥❣ ❞❡t❡r♠✐♥✐st✐❝ ♠♦❞❡❧ ✇❤✐❝❤ ✐s ❝♦♥s✐❞❡r❡❞ ❛s ❡❧❡❝tr♦♣❤②s✐♦❧♦✲ ❣✐❝❛❧❧② ♣❧❛✉s✐❜❧❡ ✐♥ t❤❡ r❡❝❡♥t ❧✐t❡r❛t✉r❡✳ ❍♦✇❡✈❡r✱ t❤✐s ❞❡t❡r♠✐♥✐st✐❝ ♠♦❞❡❧ ✇❡r❡ ♥♦t ❛❜❧❡ t♦ r❡♣r♦❞✉❝❡ t❤❡ ✐rr❡❣✉❧❛r ❜✉rst✐♥❣ ❜❡❤❛✈✐♦r ❢♦✉♥❞ ✐♥ t❤♦s❡ ❜✐♦❧♦❣✐❝❛❧ ♥❡✉r♦♥s ✇❤❡♥ ✐s♦❧❛t❡❞ ❢r♦♠ t❤❡ ♥❡✉r❛❧ ❝✐r❝✉✐t✳ ❖✉r ♠♦❞❡❧✱ ❜❛s❡❞ ♦♥ t❤❡ ♠✐❝r♦s❝♦♣✐❝ st♦❝❤❛st✐❝ ❜❡❤❛✈✐♦r ♦❢ t❤❡ ♠❡♠❜r❛♥❡ ✐♦♥ ❝❤❛♥♥❡❧s✱ s✉❝✲ ❝❡ss❢✉❧❧② r❡♣r♦❞✉❝❡❞ t❤❡ ✐♥tr✐♥s✐❝ ✐rr❡❣✉❧❛r ♣r♦♣❡rt✐❡s t❤❛t ✇❡r❡ ♠✐ss✐♥❣ ✐♥ t❤❡ ♦r✐❣✐♥❛❧ ❞❡t❡r♠✐♥✐st✐❝ ♠♦❞❡❧✳
❚♦ ❛❧❧♦✇ t❤❡ r❡❛❧ t✐♠❡ ♣❡r❢♦r♠✐♥❣ ♦❢ t❤❡ st♦❝❤❛st✐❝ ♠♦❞❡❧ s✐♠✉❧❛t✐♦♥s ✇❡ ❤❛✈❡ t♦ ❞❡❛❧ ✇✐t❤ s♦♠❡ s✐♠♣❧✐✜❝❛t✐♦♥s ❛♥❞ t♦ ✐♠♣❧❡♠❡♥t s❡✈❡r❛❧ ♦♣t✐♠✐③❛t✐♦♥s t❤❛t ❛r❡ ❛❧s♦ ❞❡s❝r✐❜❡ ✐♥ ❞❡t❛✐❧✳ ❚❤❡ r❡❛❧ t✐♠❡ ✈❡rs✐♦♥ ♦❢ ♦✉r st♦❝❤❛st✐❝ ♠♦❞❡❧ ✇❛s ✐♠♣❧❡♠❡♥t❡❞ ✐♥ ❛ ❞②♥❛♠✐❝ ❝❧❛♠♣ ♣r♦t♦❝♦❧ t♦ ✐♥t❡r❢❛❝❡ t❤❡ ❝♦♠♣✉t❛t✐♦♥❛❧ ♠♦❞❡❧ t♦ r❡❛❧ ♥❡✉r♦♥s✳
❋✐♥❛❧❧②✱ ✇❡ ❛♣♣❧✐❡❞ t❤❡ ✐♠♣❧❡♠❡♥t❡❞ ✈❡rs✐♦♥s ♦❢ r❡❛❧ t✐♠❡ s✐♠✉❧❛t✐♦♥ ❛♥❞ ✐♥t❡r❢❛❝✐♥❣ ♣r♦t♦❝♦❧s t♦ r❡♣❧❛❝❡ s♦♠❡ ❜✐♦❧♦❣✐❝❛❧ ❜✉rst✐♥❣ ♥❡✉r♦♥s ♦❢ t❤❡ st♦♠❛✲ t♦❣❛str✐❝ ❣❛♥❣❧✐♦♥✳ ❚❤❡s❡ ❤✐❜r✐❞ ♥❡✉r❛❧ ♥❡t✇♦r❦s ✇❡r❡ ✉s❡❞ t♦ st✉❞② ❤♦✇ t❤❡ ✐♥❢♦r♠❛t✐♦♥ ✭❞✐✛❡r❡♥t ♣❛tt❡r♥s ♦❢ ✐♥t❡rs♣✐❦❡ ✐♥t❡r✈❛❧s✮ ✐s tr❛♥s♠✐tt❡❞ ❜❡t✇❡❡♥ ❜✐♦❧♦❣✐❝❛❧ ❛♥❞ t✇♦ t②♣❡s ♦❢ ❛rt✐✜❝✐❛❧ ♥❡✉r♦♥s✿ ❞❡t❡r♠✐♥✐st✐❝ ❛♥❞ st♦❝❤❛st✐❝✳
❈♦♥t❡ú❞♦
✶ ■♥tr♦❞✉çã♦ ✽
✷ ❆s♣❡❝t♦s ❣❡r❛✐s ✶✻
✷✳✶ ◆❡✉rô♥✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✶✳✶ Pr♦♣r✐❡❞❛❞❡s ♣❛ss✐✈❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✶✳✷ Pr♦♣r✐❡❞❛❞❡s ❡st♦❝ást✐❝❛s ❞♦s ❝❛♥❛✐s ✐ô♥✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✶✳✸ ❈❛♥❛✐s ✐ô♥✐❝♦s ❞❡♣❡♥❞❡♥t❡s ❞❡ ✈♦❧t❛❣❡♠ ❡ ♦ ♣♦t❡♥❝✐❛❧
❞❡ ❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✷✳✶✳✹ ❈❛♥❛✐s ✐ô♥✐❝♦s r❡s♣♦♥sá✈❡✐s ♣♦r r❛❥❛❞❛s ❞❡ ♣♦t❡♥❝✐❛✐s
♦✉ ❜✉rsts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✷ ❖ ♠♦❞❡❧♦ ❞❡ ❍♦❞❣❦✐♥✲❍✉①❧❡② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✸ ❇r❡✈❡ ❤✐stór✐❝♦ ❞❛ ♠♦❞❡❧❛❣❡♠ ❡st♦❝ást✐❝❛ ❞❡ ♥❡✉rô♥✐♦s ✳ ✳ ✳ ✳ ✸✵ ✷✳✹ ❖ ❣â♥❣❧✐♦ ❡st♦♠❛t♦❣ástr✐❝♦ ✭❙❚●✮ ❞❡ ❝r✉stá❝❡♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✳✺ ❈❡♥tr♦s ❣❡r❛❞♦r❡s ❞❡ ♣❛❞rõ❡s ✭❈P●s✮ ❞♦ ❙❚● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✳✻ ❚❡♦r✐❛ ❞❛ ✐♥❢♦r♠❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✸ ▼ét♦❞♦s ✹✵
✸✳✶ ❉✐ss❡❝❛çã♦ ❞♦ ❣â♥❣❧✐♦ ❡st♦♠❛t♦❣ástr✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✳✷ ❉②♥❛♠✐❝ ❝❧❛♠♣✿ ✐♥tr♦❞✉③✐♥❞♦ ❝♦♥❞✉tâ♥❝✐❛s ❛rt✐✜❝✐❛✐s ❡♠ ♥❡✉rô✲
♥✐♦s ❜✐♦❧ó❣✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
✸✳✸ ❚❡♦r✐❛ ❞❛ ✐♥❢♦r♠❛çã♦ ❡ ♦ ❈P● ♣✐❧ór✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻
✹ ■♠♣❧❡♠❡♥t❛çã♦ ❞❡ ♠♦❞❡❧♦s ✺✵
✹✳✶ ▼♦❞❡❧❛❣❡♠ ❞❡t❡r♠✐♥íst✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✷ ▼♦❞❡❧❛❣❡♠ ❡st♦❝ást✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✸ ❙✐♠✉❧❛çã♦ ❡st♦❝ást✐❝❛ ❡♠ t❡♠♣♦ r❡❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✹✳✹ ■♠♣❧❡♠❡♥t❛çã♦ ❞♦ ♠♦❞❡❧♦ ❡st♦❝ást✐❝♦ ♥♦ ❞②♥❛♠✐❝ ❝❧❛♠♣ ✳ ✳ ✳ ✺✾
✺ ❘❡s✉❧t❛❞♦s ❡ ❞✐s❝✉ssã♦ ✻✶
✺✳✶ ❙✐♠✉❧❛çã♦ ❞❛ ❛t✐✈✐❞❛❞❡ ❞❡ ♥❡✉rô♥✐♦s ✐s♦❧❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✺✳✷ P❡rt✉r❜❛♥❞♦ ❛s ✈❛r✐á✈❡✐s ❞✐♥â♠✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✺✳✸ ❚r❛♥s♠✐ssã♦ ❞❡ ✐♥❢♦r♠❛çã♦ ❡♥tr❡ ♠♦❞❡❧♦s ✏✐♥ s✐❧✐❝♦✑ ❡ ♦ ❈P●
♣✐❧ór✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✺✳✹ ❈P●s ❛rt✐✜❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✺✳✹✳✶ ❈P●s ❞❡ ♠♦❞❡❧♦s ❡st♦❝ást✐❝♦s ❡ ♥❡✉rô♥✐♦s ❡❧❡trô♥✐❝♦s ✳ ✽✶ ✺✳✹✳✷ ❈P●s ❞❡ ♠♦❞❡❧♦s ❡st♦❝ást✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✺✳✺ ▼♦❞❡❧♦s ❞❡ ❞♦✐s ❝♦♠♣❛rt✐♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✺✳✻ ▼♦❞❡❧♦ ❞❡t❡r♠✐♥íst✐❝♦ ♠✉❧t✐❝♦♠♣❛rt✐♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵
✻ ❈♦♥❝❧✉sõ❡s ✾✸
❘❡❢❡rê♥❝✐❛s ✾✻
❆♣ê♥❞✐❝❡s ✶✵✸
❆ ❱❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ❝♦♠ ❞✐str✐❜✉✐çã♦ ❣❛✉ss✐❛♥❛✳ ✶✵✹
❇ ❆rt✐❣♦ ♣✉❜❧✐❝❛❞♦ ✶✵✺
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
❖ ❡st✉❞♦ ❞❡ ♠♦❞❡❧♦s r❡❛❧✐st❛s ❞❛ ❛t✐✈✐❞❛❞❡ ❡❧étr✐❝❛ ❞❡ ♥❡✉rô♥✐♦s✱ ♦♥❞❡ ♣♦❞❡✲s❡ ❧✐✈r❡♠❡♥t❡ ♠❛♥✐♣✉❧❛r ❛ ❞✐♥â♠✐❝❛ ❞❡ ❝♦♥❞✉tâ♥❝✐❛s ✐♥❞✐✈✐❞✉❛✐s ❡ t❡s✲ t❛r ❞✐✈❡rs❛s ❤✐♣ót❡s❡s s♦❜r❡ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ❝é❧✉❧❛s✱ é ✉♠❛ ✐♠♣♦rt❛♥t❡ ❢❡rr❛♠❡♥t❛ ♣❛r❛ r❡s♣♦♥❞❡r q✉❡stõ❡s ❛❜❡rt❛s ❡♠ ♥❡✉r♦✜s✐♦❧♦❣✐❛✿ ❝♦♠♦ ❝♦♥❞✉✲ tâ♥❝✐❛s ✐ô♥✐❝❛s ✐♥❞✐✈✐❞✉❛✐s ♠♦❞✉❧❛♠ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❡❧étr✐❝♦ ❞❛ ❝é❧✉❧❛✱ ♦✉ q✉❛❧ ♦ ♣❛♣❡❧ ❞❡st❛s ♣r♦♣r✐❡❞❛❞❡s ❝❡❧✉❧❛r❡s ❡♠ ❞❡t❡r♠✐♥❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ✉♠❛ r❡❞❡ ❝♦♠♣❧❡①❛✭▼❛r❞❡r✱ ✶✾✾✽✮✳ ▼❡s♠♦ ♥❛s ♠❡♥♦r❡s r❡❞❡s ♥❡✉r❛✐s✱ ❡ss❛s q✉❡stõ❡s ❡stã♦ ❧♦♥❣❡ ❞❡ s❡r❡♠ r❡s♣♦♥❞✐❞❛s✱ ♣♦✐s ♦s ♥❡✉rô♥✐♦s sã♦ s✐st❡✲ ♠❛s ❛❧t❛♠❡♥t❡ ♥ã♦ ❧✐♥❡❛r❡s ❡ ❝♦♠♣❧❡①♦s ✭❍♦❧❞❡♥✱ ✶✾✾✼❀ ❘✐♥③❡❧ ❡ ❊r♠❡♥tr♦✉t✱ ✶✾✾✽❀ ■③❤✐❦❡✈✐❝❤✱ ✷✵✵✵✮✳
▼♦❞❡❧♦s ❞❡ ♥❡✉rô♥✐♦s✱ ❝♦♥str✉í❞♦s ❛ ♣❛rt✐r ❞❡ ❞❛❞♦s ❡❧❡tr♦✜s✐♦❧ó❣✐❝♦s✱ ♥ã♦ sã♦ ❛♣❡♥❛s út❡✐s ♣❛r❛ t❡st❛r ❤✐♣ót❡s❡s s♦❜r❡ ♦s ♣r♦❝❡ss♦s q✉❡ ❣❡r❛♠ ✉♠ ❝♦♠✲ ♣♦rt❛♠❡♥t♦ ♣❛rt✐❝✉❧❛r ♦❜s❡r✈❛❞♦ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✱ ♠❛s t❛♠❜é♠ ♣♦❞❡♠ s❡r ✉s❛❞♦s ♣❛r❛ ❢❛③❡r ♣r❡✈✐sõ❡s ❡ ♦r✐❡♥t❛r ♦ ♣❡sq✉✐s❛❞♦r ❛ ❢❛③❡r ❡①♣❡r✐♠❡♥t♦s q✉❡ r❡✈❡❧❡♠ ♥♦✈❛s ♣r♦♣r✐❡❞❛❞❡s ❞♦s ♥❡✉rô♥✐♦s ♦✉ ❞❛s r❡❞❡s ♥❡✉r❛✐s ✭▼❛r❞❡r✱ ✶✾✾✽❀ ❉❛②❛♥ ❡ ❆❜❜♦tt✱ ✷✵✵✶✮✳
❊st❡ ❝✐❝❧♦ ❞❡ tr♦❝❛ ❞❡ ✐♥❢♦r♠❛çõ❡s ❡♥tr❡ ❡①♣❡r✐♠❡♥t♦s ❡ ♠♦❞❡❧♦s ♣♦❞❡
❈❆P❮❚❯▲❖ ✶✳ ■◆❚❘❖❉❯➬➹❖ ✾
❛t✐♥❣✐r ♥í✈❡✐s ♠✉✐t♦ ✐♥t❡r❡ss❛♥t❡s q✉❛♥❞♦ ❝♦♥s✐❞❡r❛♠♦s ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ✐♥t❡r❛❣✐r✱ ❡♠ t❡♠♣♦ r❡❛❧✱ ♠♦❞❡❧♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❡ t❡❝✐❞♦ ✈✐✈♦ ♣❛r❛ ❝♦♥s✲ tr✉✐r s✐st❡♠❛s ❤í❜r✐❞♦s ✭❙③ü❝s ❡t ❛❧✳✱ ✷✵✵✵❀ P✐♥t♦ ❡t ❛❧✳✱ ✷✵✵✵❀ Pr✐♥③✱ ✷✵✵✹✮ ❡ t❡♥t❛r ❡♥t❡♥❞❡r ♠❡❧❤♦r ❝♦♠♦ r❡❞❡s ✈✐✈❛s ♦♣❡r❛♠ ✭❙❡❧✈❡rst♦♥ ❡t ❛❧✳✱ ✷✵✵✵✮✱ ♣❛r❛ r❡❝✉♣❡r❛r ♣r♦♣r✐❡❞❛❞❡s ❞❡ s✐st❡♠❛s ♥❡✉r❛✐s ❞❛♥✐✜❝❛❞♦s ✭❙③ü❝s ❡t ❛❧✳✱ ✷✵✵✵✮✱ ❝♦♥str✉✐r ❝✐r❝✉✐t♦s ❝♦♠ ♣r♦♣r✐❡❞❛❞❡s ♥♦✈❛s ✭❆②❡rs✱ ✷✵✵✹✮ ❡ ❛té ♠❡s♠♦ ❛❧✐♠❡♥t❛r ✉♠❛ r❡❞❡ ♥❡✉r❛❧ ✈✐✈❛ ❝♦♠ ❞❛❞♦s s❡♥s♦r✐❛✐s ✈✐♥❞♦s ❞❡ ❞✐s♣♦s✐t✐✈♦s ❛rt✐✜❝✐❛✐s ♦✉ ❝♦♥tr♦❧❛r ❞✐s♣♦s✐t✐✈♦s ❝♦♠♦ ✐♥t❡r❢❛❝❡s ❝ér❡❜r♦ ♠áq✉✐♥❛ ✭❈❛r✲ ♠❡♥❛ ❡t ❛❧✳✱ ✷✵✵✸✮✳
❉❡s❞❡ ♦ tr❛❜❛❧❤♦ ♣✐♦♥❡✐r♦ ✐♥tr♦❞✉③✐♥❞♦ ♦ ♠ét♦❞♦ ✈♦❧t❛❣❡✲❝❧❛♠♣ ❡ ❛ ♠♦❞❡✲ ❧❛❣❡♠ ♠❛t❡♠át✐❝❛ ❞❛ ❛t✐✈✐❞❛❞❡ ❞♦ ❛①ô♥✐♦ ❣✐❣❛♥t❡ ❞❛ ❧✉❧❛ ✭❍♦❞❣❦✐♥ ❡ ❍✉①❧❡②✱ ✶✾✺✷✮✱ ♠♦❞❡❧♦s ❞❡t❡r♠✐♥íst✐❝♦s q✉❡ ❞❡s❝r❡✈❡♠ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛s ❝♦♥❞✉✲ tâ♥❝✐❛s ✐ô♥✐❝❛s tê♠ s✐❞♦ ❛❞♦t❛❞♦s ♣♦r ♥❡✉r♦✜s✐♦❧♦❣✐st❛s ❝♦♠♦ ♦ ♣r✐♥❝✐♣❛❧ ♣❛r❛❞✐❣♠❛ ♣❛r❛ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❡❧étr✐❝♦ ♠❛❝r♦s❝ó♣✐❝♦ ❞❡ ♠❡♠❜r❛♥❛s ♥❡r✲ ✈♦s❛s✳
❆ r❛③ã♦ ♣r✐♥❝✐♣❛❧ ❞♦ s✉❝❡ss♦ ❞❡st❡s ♠♦❞❡❧♦s é q✉❡ ❡❧❡s sã♦ ❝❛♣❛③❡s ❞❡ ❡①♣❧✐❝❛r ♠✉✐t♦s ❛s♣❡❝t♦s ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❡❧étr✐❝♦ ❞❡ ❝é❧✉❧❛s ♥❡r✈♦s❛s✱ ✐♥✲ ❝❧✉✐♥❞♦ ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ❛çã♦✱ ✉s❛♥❞♦ ✉♠❛ ❡str✉t✉r❛ ♠❛t❡♠át✐❝❛ r✐❣♦r♦s❛✳ ❈♦♠♦ ❛ ♠❛✐♦r✐❛ ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ ♣♦❞❡♠ s❡r ✐♥❢❡r✐❞♦s q✉❛s❡ ❞✐r❡✲ t❛♠❡♥t❡ ❞❡ ❡①♣❡r✐♠❡♥t♦s ❞❡ ✈♦❧t❛❣❡✲❝❧❛♠♣ ✭❍♦❞❣❦✐♥ ❡ ❍✉①❧❡②✱ ✶✾✺✷❀ ❑❛♥❞❡❧ ❡t ❛❧✳✱ ✶✾✾✶✮✱ ♦♥❞❡ ❛s ❝♦♥tr✐❜✉✐çõ❡s ❞❡ ❝❛❞❛ ❝♦rr❡♥t❡ ✐ô♥✐❝❛ ❞❛ ♠❡♠❜r❛♥❛ ♣♦❞❡♠ s❡r s❡♣❛r❛❞❛s ❡ ❡st✉❞❛❞❛s ❡♠ ❞❡t❛❧❤❡s✱ ♦s ♠♦❞❡❧♦s ❞❡t❡r♠✐♥íst✐❝♦s s❡ t♦r♥❛r❛♠ ♠✉✐t♦ ♣♦♣✉❧❛r❡s ❡♥tr❡ ♦s ♣❡sq✉✐s❛❞♦r❡s ✭❑❛♥❞❡❧ ❡t ❛❧✳✱ ✶✾✾✶❀ ❉❛②❛♥ ❡ ❆❜❜♦tt✱ ✷✵✵✶✮✳
❈❆P❮❚❯▲❖ ✶✳ ■◆❚❘❖❉❯➬➹❖ ✶✵
❞♦ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛✳
◆♦ ❡♥t❛♥t♦✱ é ❜❡♠ ❝♦♥❤❡❝✐❞♦ q✉❡ ❛ ❛t✐✈✐❞❛❞❡ ❡❧étr✐❝❛ ✐♥trí♥s❡❝❛ ❞❡ ♠✉✐t♦s ♥❡✉rô♥✐♦s ✈✐✈♦s ❡stá ♠✉✐t♦ ❧♦♥❣❡ ❞❡ s❡r ❞❡t❡r♠✐♥íst✐❝❛✳ ❊①♣❡r✐♠❡♥t♦s ♦♥❞❡ ♥❡✉rô♥✐♦s ❞♦ ❝órt❡① sã♦ ✐s♦❧❛❞♦s s✉❥❡✐t♦s r❡♣❡t✐❞❛♠❡♥t❡ ✉♠ ♠❡s♠♦ ❡stí♠✉❧♦ ❞❡ ❝♦rr❡♥t❡ ❛rt✐✜❝✐❛❧♠❡♥t❡ ❣❡r❛❞♦ ✭▼❛✐♥❡♥ ❡ ❙❡❥♥♦✇s❦✐✱ ✶✾✾✺✮ ♠♦str❛r❛♠ q✉❡ ❛ ❝♦♥✜❛❜✐❧✐❞❛❞❡ ❞♦ ✐♥st❛♥t❡ ❞❡ ❞✐s♣❛r♦ ❞♦s ♣♦t❡♥❝✐❛✐s ❞❡ ❛çã♦ ❞❡♣❡♥❞❡ ❞❡ ♣r♦♣r✐❡❞❛❞❡s ❡st❛tíst✐❝❛s ❞♦ s✐♥❛❧ ❛♣❧✐❝❛❞♦✱ ❡♠ ❞❡s❛❝♦r❞♦ ❝♦♠ ♣r❡✈✐sõ❡s ❞❡t❡r♠✐♥íst✐❝❛s✳
❆té ♠❡s♠♦ ❡♠ ❝✐r❝✉✐t♦s ❡s♣❡❝✐❛❧✐③❛❞♦s ❡♠ ♣r♦✈❡r r✐t♠♦s ♣❡r✐ó❞✐❝♦s ❡ ❝♦♥✜á✈❡✐s ♣❛r❛ ❝♦♥tr♦❧❛r ❛ ❛t✐✈✐❞❛❞❡ ❞❡ ♠ús❝✉❧♦s✱ ❝♦♠♦ ♦ ❈❡♥tr♦ ●❡r❛❞♦r ❞❡ P❛❞rõ❡s ✭❈P●✮ ♣✐❧ór✐❝♦ ❞♦ ●â♥❣❧✐♦ ❊st♦♠❛t♦❣ástr✐❝♦ ✭❙❚●✮ ❞❡ ❝r✉stá✲ ❝❡♦s ✭▼✉❧❧♦♥❡② ❡ ❙❡❧✈❡rst♦♥✱ ✶✾✼✹❀ ❙❡❧✈❡rst♦♥ ❡ ▼♦✉❧✐♥s✱ ✶✾✽✻✮✱ ❛ ♠❛✐♦r✐❛ ❞♦s ♥❡✉rô♥✐♦s ♠♦t♦r❡s ❞♦ ❝✐r❝✉✐t♦ ❛♣r❡s❡♥t❛♠ ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ✐rr❡❣✉❧❛r ❞❡ r❛❥❛❞❛s ❞❡ ♣♦t❡♥❝✐❛✐s ❞❡ ❛çã♦ ✭❜✉rsts✮ q✉❛♥❞♦ ✐s♦❧❛❞♦s s✐♥❛♣t✐❝❛♠❡♥t❡ ✭❘❛❜✐♥♦✈✐❝❤ ❡t ❛❧✳✱ ✶✾✾✼❀ ❊❧s♦♥ ❡t ❛❧✳✱ ✶✾✾✾❀ ❙❡❧✈❡rst♦♥ ❡t ❛❧✳✱ ✷✵✵✵✮✳
❈❛❞❛ ✈❡③ q✉❡ ✉♠ ❞❡ss❡s ♥❡✉rô♥✐♦s é ✐s♦❧❛❞♦ ❞♦ ❈P● ♣✐❧ór✐❝♦✱ ❡❧❡ r❡✈❡❧❛ ✉♠ r❡♣❡rtór✐♦ s✐♠✐❧❛r ❞❡ ❝♦♠♣♦rt❛♠❡♥t♦s ✐rr❡❣✉❧❛r❡s✱ ♥♦ ❡♥t❛♥t♦ é s❛❜✐❞♦ q✉❡ ❡①✐st❡♠✱ ♣❡❧♦ ♠❡♥♦s ♣❡q✉❡♥❛s ❞✐❢❡r❡♥ç❛s ♥❛s ❝♦♥❞✉tâ♥❝✐❛s ✐ô♥✐❝❛s ❞❛ ♠❡♠❜r❛♥❛✱ ❞❡ ♥❡✉rô♥✐♦ ♣❛r❛ ♥❡✉rô♥✐♦ ❡ ❞❡ ❛♥✐♠❛❧ ♣❛r❛ ❛♥✐♠❛❧✳ ▼❛t❡♠❛✲ t✐❝❛♠❡♥t❡ ✐ss♦ s✐❣♥✐✜❝❛ q✉❡ s❡ ❢♦r ♣♦ssí✈❡❧ ❡s❝r❡✈❡r ❡q✉❛çõ❡s q✉❡ ♠♦❞❡❧❡♠ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ♦❜s❡r✈❛❞♦ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✱ ❡ss❛s ❡q✉❛çõ❡s ♥ã♦ ♣♦❞❡✲ r✐❛♠ s❡r ❡s♣❡❝✐✜❝❛❞❛s ❡①❛t❛♠❡♥t❡✱ s❡♥❞♦ ❡s♣❡r❛❞♦ q✉❡ ❡❧❛s ❛♣r❡s❡♥t❡♠ ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ s✐♠✐❧❛r q✉❛♥❞♦ s❡✉s ♣❛râ♠❡tr♦s sã♦ ❧✐❣❡✐r❛♠❡♥t❡ ✈❛r✐❛❞♦s✳ ❊ss❛ é ❛ ✐❞é✐❛ ❞❛ ❡st❛❜✐❧✐❞❛❞❡ ❡str✉t✉r❛❧✱ ♥❛ t❡♦r✐❛ ❞♦s s✐st❡♠❛s ❞✐♥â♠✐❝♦s ✭❆❜r❛❤❛♠ ❡ ❙❤❛✇✱ ✶✾✾✷✮✳
❈❆P❮❚❯▲❖ ✶✳ ■◆❚❘❖❉❯➬➹❖ ✶✶
❡str✉t✉r❛❧♠❡♥t❡ ❡stá✈❡❧ ❡♠ ✉♠ ❡s♣❛ç♦ ❞❡ ♣❛râ♠❡tr♦s ❡①♣❡r✐♠❡♥t❛❧ ❞❡ ❛❧t❛ ❞✐♠❡♥s✐♦♥❛❧✐❞❛❞❡✱ ♦♥❞❡ ♦s ♥❡✉rô♥✐♦s ❡stã♦ s✉❥❡✐t♦s ❛ ♣❡q✉❡♥❛s ✈❛r✐❛çõ❡s✱ ♥ã♦ ❛♣❡♥❛s ♥❛s s✉❛s ♣r♦♣r✐❡❞❛❞❡s ✐♥trí♥s❡❝❛s ♠❛s ❡♠ ❞✐✈❡rs♦s ♦✉tr♦s ♣❛râ♠❡tr♦s ❡①t❡r♥♦s✱ ❝♦♠♦ t❡♠♣❡r❛t✉r❛✱ ❝♦♥❝❡♥tr❛çõ❡s ✐ô♥✐❝❛s✱ ❡t❝✳
❆ ❡st❛❜✐❧✐❞❛❞❡ ❡str✉t✉r❛❧ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ✐rr❡❣✉❧❛r é ✉♠ sér✐♦ ♦❜s✲ tá❝✉❧♦ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♠♦❞❡❧♦s ❞♦ t✐♣♦ ❍♦❞❣❦✐♥✲❍✉①❧❡② ✭❍❍✮ ❞❡t❡r♠✐♥íst✐❝♦s✳ ❊♠ ♠♦❞❡❧♦s ❍❍ s✐♠♣❧❡s ❞❛ ❞✐♥â♠✐❝❛ ❞♦ ❛①ô♥✐♦✱ ✉♠ ❝♦♠✲ ♣♦rt❛♠❡♥t♦ ✐rr❡❣✉❧❛r ❝♦♠♣❛tí✈❡❧ ❝♦♠ ♦ ❡♥❝♦♥tr❛❞♦ ♥♦s ♥❡✉rô♥✐♦s ❜✐♦❧ó❣✐❝♦s é ❡str✉t✉r❛❧♠❡♥t❡ ✐♥stá✈❡❧✱ ♣♦✐s é ❝♦♥✜♥❛❞♦ ❛ ✉♠ ✈♦❧✉♠❡ ♠✉✐t♦ ♣❡q✉❡♥♦ ❞♦ ❡s♣❛ç♦ ❞❡ ♣❛râ♠❡tr♦s ✭●✉❝❦❡♥❤❡✐♠❡r ❡ ❖❧✐✈❛✱ ✷✵✵✷✮✳ ❊♠ ♠♦❞❡❧♦s ♠❛✐s r❡✲ ❛❧✐st❛s✱ ♦♥❞❡ s❡ t❡♠ ❞❡③❡♥❛s ❞❡ ❡q✉❛çõ❡s ♥ã♦ ❧✐♥❡❛r❡s ❛❝♦♣❧❛❞❛s✱ é ✐♥t✉✐t✐✈♦ ❡s♣❡r❛r q✉❡ ❛ ❛❧t❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❛✉♠❡♥t❛r✐❛ ❛s r❡❣✐õ❡s ❞♦ ❡s♣❛ç♦ ❞❡ ♣❛✲ râ♠❡tr♦s q✉❡ ❝♦rr❡s♣♦♥❞❡♠ ❛ ❝♦♠♣♦rt❛♠❡♥t♦ ✐rr❡❣✉❧❛r✱ ❞❛♥❞♦ ❡st❛❜✐❧✐❞❛❞❡ ❡str✉t✉r❛❧ ❛ ❡❧❡s✳ ❙✉r♣r❡❡♥❞❡♥t❡♠❡♥t❡ ❡st❡ ♥ã♦ é ♦ ❝❛s♦✳
❈❆P❮❚❯▲❖ ✶✳ ■◆❚❘❖❉❯➬➹❖ ✶✷
❈♦♠♣♦rt❛♠❡♥t♦ ❝❛ót✐❝♦ ❡str✉t✉r❛❧♠❡♥t❡ ❡stá✈❡❧ ❢♦✐ ❡♥❝♦♥tr❛❞♦ ❡♠ ❛❧❣✉♥s ♠♦❞❡❧♦s t✐♣♦ ❍❍ ❞❡t❡r♠✐♥íst✐❝♦s ✭❑♦♠❡♥❞❛♥t♦✈ ❡ ❑♦♥♦♥❡♥❦♦✱ ✶✾✾✻❀ ❋❛❧❝❦❡ ❡t ❛❧✳✱ ✷✵✵✵✮ q✉❡ ✐♥❝❧✉❡♠ ✉♠❛ ❞✐♥â♠✐❝❛ ♥ã♦ ❧✐♥❡❛r ❞❡ tr♦❝❛ ❞❡ ❝á❧❝✐♦ ❡♥tr❡ ♦ r❡tí❝✉❧♦ ❡♥❞♦♣❧❛s♠át✐❝♦ ❡ ♦ ❝✐t♦s♦❧✳ ❖ ♣r✐♥❝✐♣❛❧ ❛♣❡❧♦ ❞❡ss❡s ♠♦❞❡❧♦s é q✉❡ ❛ ♠♦❞✉❧❛çã♦ ❞❛ ❝♦♥❝❡♥tr❛çã♦ ✐♥tr❛❝❡❧✉❧❛r ❞❡ ❝á❧❝✐♦ é ✐♠♣♦rt❛♥t❡ ♣❛r❛ r❡❣✉❧❛r ♠✉✐t♦s ♣r♦❝❡ss♦s ❝❡❧✉❧❛r❡s ✭■❦❡❞❛✱ ✷✵✵✹✮✳ ❊ss❡s ♠♦❞❡❧♦s ♣r❡✈ê❡♠ q✉❡ ❛ ❝é✲ ❧✉❧❛ ♣r❡❝✐s❛ ❛♣r❡s❡♥t❛r ♦s❝✐❧❛çõ❡s ♠❛❝r♦s❝ó♣✐❝❛s ❧❡♥t❛s ❞♦s ♥í✈❡✐s ❝✐t♦só❧✐❝♦s ❞❡ ❝á❧❝✐♦✳ ◆♦ ❡♥t❛♥t♦✱ ♦s❝✐❧❛çõ❡s ❞❡ss❛ ❛♠♣❧✐t✉❞❡ ❢♦r❛♠ ♦❜s❡r✈❛❞❛s ❡①♣❡r✐✲ ♠❡♥t❛❧♠❡♥t❡ ❛♣❡♥❛s ❡♠ ❛❧❣✉♥s ♥❡✉rô♥✐♦s ❞❡ ✈❡rt❡❜r❛❞♦s ✭P❛rr✐ ❡ ❈r✉♥❡❧❧✐✱ ✷✵✵✶❀ ❩❤❛♥❣ ❡t ❛❧✳✱ ✷✵✵✸✮✱ ♠❛s ♥✉♥❝❛ ❡♠ ♥❡✉rô♥✐♦s ❞♦ ❙❚● ✭▲❡✈✐ ❡t ❛❧✳✱ ✷✵✵✸✮✳
❈❆P❮❚❯▲❖ ✶✳ ■◆❚❘❖❉❯➬➹❖ ✶✸
♥❡❝❡ssár✐♦s ♥❡♠ ❝♦♠♦ ❞✐str✐❜✉✐r ❛s ❝♦♥❞✉tâ♥❝✐❛s ✐ô♥✐❝❛s ❡♥tr❡ ♦s ❝♦♠♣❛rt✐✲ ♠❡♥t♦s✳
▼❡s♠♦ ❛ss✐♠✱ ❛❧❣✉♠❛s ❞❛s ♣r♦♣r✐❡❞❛❞❡s ♣❡r❞✐❞❛s ♣♦❞❡♠ s❡r r❡❝✉♣❡r❛✲ ❞❛s ♠❡s♠♦ ❡♠ ✉♠ ♠♦❞❡❧♦ s✐♠♣❧✐✜❝❛❞♦✱ ❞❡ ❝♦♠♣❛rt✐♠❡♥t♦ ú♥✐❝♦✱ ✉s❛♥❞♦✲s❡ ✉♠ ♠♦❞❡❧♦ ❡st♦❝ást✐❝♦ ❜❛s❡❛❞♦ ♥♦s ❡st❛❞♦s ♠❛r❦♦✈✐❛♥♦s ❞♦s ❝❛♥❛✐s ✐ô♥✐❝♦s ✭❉❡st❤❡①❤❡ ❡t ❛❧✳✱ ✶✾✾✹✮ ♦♥❞❡ ♦ ❝❛rát❡r ♣r♦❜❛❜✐❧íst✐❝♦ ❞♦s ❝❛♥❛✐s é ✉♠❛ ♣r♦✲ ♣r✐❡❞❛❞❡ ✐♥trí♥s❡❝❛ ✭❍✐❧❧❡✱ ✶✾✾✷❀ ❙❦❛✉❣❡♥ ❡ ❲❛❧❧♦❡✱ ✶✾✼✾❀ ❲❤✐t❡ ❡t ❛❧✳✱ ✶✾✾✽❀ ❲❤✐t❡ ❡t ❛❧✳✱ ✷✵✵✵✮ ❡ ♥❡♥❤✉♠ r✉í❞♦ ❛❞✐t✐✈♦ ♣r❡❝✐s❛ s❡r ✐♥❝❧✉í❞♦✳ ❙❡ ❝♦♥s✐❞❡✲ r❛r♠♦s ✉♠ ♠♦❞❡❧♦ ♠❛r❦♦✈✐❛♥♦ s✐♠♣❧❡s ♦♥❞❡ ✉♠❛ ♣♦♣✉❧❛çã♦ ❞❡ ❝❛♥❛✐s ❝♦♠ ❛♣❡♥❛s ❞♦✐s ❡st❛❞♦s ♣♦ssí✈❡✐s ✐♥❞❡♣❡♥❞❡♥t❡s ✭❢❡❝❤❛❞♦ ❡ ❛❜❡rt♦✮✱ ♦ ♥ú♠❡r♦ ♠é❞✐♦ ❞❡ ❝❛♥❛✐s ✭◆✮ q✉❡ s❡ ❡s♣❡r❛ q✉❡ s♦❢r❛ ❛ tr❛♥s✐çã♦ ❞♦ ❡st❛❞♦ ❢❡❝❤❛❞♦ ♣❛r❛ ♦ ❛❜❡rt♦✱ ❡♠ ✉♠ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ ∆t ♣♦❞❡ s❡r ❢❛❝✐❧♠❡♥t❡ ♦❜t✐❞♦ ❞❛s t❛①❛s ❞❡ ❛❜❡rt✉r❛ ❞♦ ♠♦❞❡❧♦ ❍❍✳ ❆ ✢✉t✉❛çã♦ ✭❞❡s✈✐♦ ♣❛❞rã♦✮ ❞♦ ♥ú♠❡r♦ ❞❡ ❝❛♥❛✐s ✐ô♥✐❝♦s q✉❡ ❡✈❡♥t✉❛❧♠❡♥t❡ s♦❢r❡♠ ❛ tr❛♥s✐çã♦ é ❞❛ ♦r❞❡♠ ❞❡ √N✳
❈♦♥s✐❞❡r❛♥❞♦ ◆ ❝♦♠♦ 106 ✭♣❛r❛ ♦s ❝❛♥❛✐s ❞❡ só❞✐♦✮ ❛s ✢✉t✉❛çõ❡s s❡rã♦ ❞❛
♦r❞❡♠ ❞❡ ✵✱✶✪ ❞❡ ◆✱ ❡ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❝♦rr❡♥t❡ ❡st♦❝ást✐❝❛ ❞❡ só❞✐♦ ❞❡✈❡ s❡r ♣r❛t✐❝❛♠❡♥t❡ ✐❣✉❛❧ ❛ s✉❛ ✈❡rsã♦ ❞❡t❡r♠✐♥íst✐❝❛✳ ◆♦ ❡♥t❛♥t♦✱ s❡ ❝♦♥✲ s✐❞❡r❛r♠♦s q✉❡ ♦s ♣♦t❡♥❝✐❛✐s ❞❡ ❛çã♦ sã♦ ❣❡r❛❞♦s ♥♦ ❝♦♥❡ ❞❡ ✐♠♣❧❛♥t❛çã♦ ❛①♦♥❛❧ ✭s♣✐❦❡ ✐♥✐t✐❛t✐♦♥ ③♦♥❡✮✱ r❡❣✐ã♦ ✭♣❛t❝❤✮ ❜❡♠ ♠❡♥♦r ❞♦ q✉❡ t♦❞♦ ♦ ❛①ô✲ ♥✐♦✱ ❝♦♠ ✉♠❛ q✉❛♥t✐❞❛❞❡ ❡♠ t♦r♥♦ ❞❡ 103 ♦✉ 104 ❝❛♥❛✐s ❞❡ só❞✐♦✱ ❡ ❡♥tã♦ ♦s s♣✐❦❡s sã♦ ♣r♦♣❛❣❛❞♦s ♣❛r❛ ♦✉tr❛s r❡❣✐õ❡s ❞❛ ♠❡♠❜r❛♥❛✱ ❛s ✢✉t✉❛çõ❡s ❞♦ ♥ú♠❡r♦ ❞❡ ❝❛♥❛✐s s♦❢r❡♥❞♦ ❛ tr❛♥s✐çã♦ ❞❡ ❢❡❝❤❛❞♦ ♣❛r❛ ❛❜❡rt♦ s❡rã♦ ❞❛ ♦r❞❡♠ ❞❡ ✷✪ ❞❡ ◆✱ s✉✜❝✐❡♥t❡s ♣❛r❛ ♣r♦❞✉③✐r ❡❢❡✐t♦s ♠❛❝r♦s❝ó♣✐❝♦s ♥♦ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛✳
❈❆P❮❚❯▲❖ ✶✳ ■◆❚❘❖❉❯➬➹❖ ✶✹
❞❡t❡r♠✐♥íst✐❝❛ ❡ ✈❡r✐✜❝♦✉✲s❡ q✉❡ ♦ ♠♦❞❡❧♦ ❡st♦❝ást✐❝♦ é ❝❛♣❛③ ❞❡ r❡♣r♦❞✉③✐r ❛s ♣r♦♣r✐❡❞❛❞❡s ❞❡ ♣r❡❝✐sã♦ ❡ ❝♦♥✜❛❜✐❧✐❞❛❞❡ ❡♥❝♦♥tr❛❞❛s ❡♠ ♥❡✉rô♥✐♦s ✈✐✈♦s ✭▼❛✐♥❡♥ ❡ ❙❡❥♥♦✇s❦✐✱ ✶✾✾✺✮ ❡♠ s✐t✉❛çõ❡s ❡♠ q✉❡ ♦ ♠♦❞❡❧♦ ❞❡t❡r♠✐♥íst✐❝♦ ❢❛❧❤❛✳
■♥s♣✐r❛❞♦s ♣❡❧♦ s✉❝❡ss♦ ❞♦ ✏♣❛t❝❤✑ ❡st♦❝ást✐❝♦ ❞♦ ❛①ô♥✐♦ ❡ ♣❡❧♦ ❢❛t♦ ❞♦s ♥❡✉rô♥✐♦s ❞♦ ❣â♥❣❧✐♦ ❡st♦♠❛t♦❣ástr✐❝♦ t❡r❡♠ s✉❛s ❝♦♥❞✉tâ♥❝✐❛s ✐ô♥✐❝❛s ❧❡♥✲ t❛s✱ q✉❡ sã♦ ❛s r❡s♣♦♥sá✈❡✐s ♣♦r ❝♦♠❡ç❛r ❡ ♣❛r❛r ✉♠ ❜✉rst ❞❡ ♣♦t❡♥❝✐❛✐s ❞❡ ❛çã♦✱ ♦r❞❡♥s ❞❡ ❣r❛♥❞❡③❛ ♠❡♥♦r❡s ❞♦ q✉❡ ❛s ❝♦♥❞✉tâ♥❝✐❛s ❛①♦♥❛✐s ❞❡ só✲ ❞✐♦ ❡ ♣♦táss✐♦ ✭Pr✐♥③ ❡t ❛❧✳✱ ✷✵✵✸❜✮✱ ❛♣r❡s❡♥t❛♠♦s ✉♠ ♠♦❞❡❧♦ ❡st♦❝ást✐❝♦ ❞❡ ❝♦♠♣❛rt✐♠❡♥t♦ ú♥✐❝♦ ♣❛r❛ ✉♠ ♥❡✉rô♥✐♦ ❡st♦♠❛t♦❣ástr✐❝♦✳
❖ ♠♦❞❡❧♦ ❡st♦❝ást✐❝♦ ❛q✉✐ ❛♣r❡s❡♥t❛❞♦ ❢♦✐ ♦❜t✐❞♦ ❞❛ tr❛❞✉çã♦ ❞❡ ✉♠ ♠♦❞❡❧♦ ❞❡t❡r♠✐♥íst✐❝♦ ❛t✉❛❧ ♣❛r❛ ✉♠ ♥❡✉rô♥✐♦ ❡st♦♠❛t♦❣ástr✐❝♦ ✭❚✉rr✐❣✐❛♥♦ ❡t ❛❧✳✱ ✶✾✾✺❀ Pr✐♥③ ❡t ❛❧✳✱ ✷✵✵✸❜✮✳ ◆♦ss♦ ❛❧❣♦r✐t♠♦ ❢♦✐ ❛❞❛♣t❛❞♦ ❞❡ ✉♠ ♠ét♦❞♦ ❞❡s❡♥✈♦❧✈✐❞♦ ♣❛r❛ s✐♠✉❧❛çã♦ ❞❡ r❡❛çõ❡s q✉í♠✐❝❛s ✭●✐❧❧❡s♣✐❡✱ ✶✾✼✼✮ ❡ ❞❡♣♦✐s ✐♠♣❧❡♠❡♥t❛❞♦ ♣❛r❛ ❛s ❝♦♥❞✉tâ♥❝✐❛s ✐ô♥✐❝❛s ❞❛ ♠❡♠❜r❛♥❛ ✭❙❦❛✉❣❡♥ ❡ ❲❛❧❧♦❡✱ ✶✾✼✾✮✳ ❊♠❜♦r❛ ❡ss❡ ♠ét♦❞♦ s❡❥❛ ❝♦♠♣✉t❛❝✐♦♥❛❧♠❡♥t❡ ❝❛r♦✱ ❡❧❡ é ❝♦♥s✐❞❡r❛❞♦ ✉♠ ❛❧❣♦r✐t♠♦ ❡①❛t♦ ✭▼✐♥♦ ❡t ❛❧✳✱ ✷✵✵✷✮✳
❆ tr❛❞✉çã♦ ❞♦ ♠♦❞❡❧♦ ❞❡t❡r♠✐♥íst✐❝♦ ❢♦✐ ❝✉✐❞❛❞♦s❛♠❡♥t❡ ❢❡✐t❛✱ ♣❛r❛ ♥ã♦ ♠✉❞❛r ♦✉ ✐♥❝❧✉✐r ♥❡♥❤✉♠❛ ♥♦✈❛ ❞✐♥â♠✐❝❛ ♦✉ ❢♦♥t❡ ❞❡ r✉í❞♦ q✉❡ ♥ã♦ ❡st✐✈❡ss❡ ♣r❡s❡♥t❡ ♥♦ ♠♦❞❡❧♦ ♦r✐❣✐♥❛❧✳ ❉❡ss❛ ❢♦r♠❛ ♣♦❞❡♠♦s ❝♦♠♣❛r❛r ❞✐r❡t❛♠❡♥t❡ ♥♦ss♦s r❡s✉❧t❛❞♦s ❝♦♠ ♦s ❞♦ ♠♦❞❡❧♦ ❞❡t❡r♠✐♥íst✐❝♦ q✉❛♥❞♦ s✉❜♠❡t✐❞♦s ❛♦s ♠❡s♠♦s ♣❛râ♠❡tr♦s ✭♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛s ❝♦♥❞✉tâ♥❝✐❛s ✐ô♥✐❝❛s ♠á①✐♠❛s ❞❡ ❞✐✲ ❢❡r❡♥t❡s t✐♣♦s ✐ô♥✐❝♦s✮✱ ♦ q✉❡ ❢❛③ ❝♦♠ q✉❡ q✉❛❧q✉❡r ❞✐♥â♠✐❝❛ ♥ã♦ ♣❡r✐ó❞✐❝❛ q✉❡ ❛♣❛r❡ç❛ ♣♦ss❛ s❡r t♦t❛❧♠❡♥t❡ ❛tr✐❜✉í❞❛ à ♥❛t✉r❡③❛ ❡st♦❝ást✐❝❛ ❞❛ ❞✐♥â✲ ♠✐❝❛ ❞♦s ❝❛♥❛✐s ✐ô♥✐❝♦s ❡ s✉❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❣❡r❛r ✢✉t✉❛çõ❡s ♠❛❝r♦s❝ó♣✐❝❛s ♥♦ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛✳
❈❆P❮❚❯▲❖ ✶✳ ■◆❚❘❖❉❯➬➹❖ ✶✺
✐rr❡❣✉❧❛r✐❞❛❞❡s ❡♥❝♦♥tr❛❞❛s ❡♠ ♥❡✉rô♥✐♦s r❡❛✐s✱ ❛♣r❡s❡♥t❛♥❞♦ ✉♠ ❝♦♠♣♦rt❛✲ ♠❡♥t♦ ❣❧♦❜❛❧ ❝❛ót✐❝♦ ❛ ♣❛rt✐r ❞❡ ✉♠❛ ❞✐♥â♠✐❝❛ ❡st♦❝ást✐❝❛ ❧♦❝❛❧✱ ❛ q✉❛❧ ❢♦✐ ❞✐✲ r❡t❛♠❡♥t❡ tr❛❞✉③✐❞❛ ❞❡ ✉♠ ♠♦❞❡❧♦ ❞❡t❡r♠✐♥íst✐❝♦ r❡❛❧✐st❛ ❞❡ ❝♦♠♣❛rt✐♠❡♥t♦ ú♥✐❝♦ q✉❡ ♥ã♦ ❛♣r❡s❡♥t❛ q✉❛❧q✉❡r ❝♦♠♣♦rt❛♠❡♥t♦ ✐rr❡❣✉❧❛r ❡str✉t✉r❛❧♠❡♥t❡ ❡stá✈❡❧✳ ❊st❡ t❡♠❛ é ❞❡ ✐♥t❡r❡ss❡ ❣❡r❛❧ ❡ ❝♦rr❡♥t❡♠❡♥t❡ ❡st✉❞❛❞♦ ♣♦r ❣r✉♣♦s q✉❡ tr❛❜❛❧❤❛♠ ❝♦♠ s✐st❡♠❛s ❞✐♥â♠✐❝♦s ✭▲✐✉ ❡t ❛❧✳✱ ✷✵✵✷✮✳
❚❛♠❜é♠ ❞❡s❝r❡✈❡♠♦s ❡♠ ❞❡t❛❧❤❡s ❛ ❡❧❛❜♦r❛çã♦ ❞❡ss❡ ♠♦❞❡❧♦ ❡st♦❝ást✐❝♦ ❡ ❞♦ ❛❧❣♦r✐t♠♦ ❛❞❛♣t❛❞♦ ♣❛r❛ s✐♠✉❧❛çõ❡s✱ ❛ss✐♠ ❝♦♠♦ ♦s r❡s✉❧t❛❞♦s ♦❜t✐✲ ❞♦s ❡♠ ❡①♣❡r✐♠❡♥t♦s ❡♠ q✉❡ ✐♥t❡r❛❣✐♠♦s ❡♠ t❡♠♣♦ r❡❛❧ ♦s ♠♦❞❡❧♦s ❝♦♠ t❡❝✐❞♦ ♥❡✉r❛❧ ✈✐✈♦✱ ♣❛r❛ ❡st✉❞❛r ❛ ❣❡r❛çã♦ ❞❡ ♣❛❞rõ❡s ❡ ♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ✐♥❢♦r♠❛çã♦ ❡♠ r❡❞❡s ♥❡✉r❛✐s ❜✐♦❧ó❣✐❝❛s✳
❈❛♣ít✉❧♦ ✷
❆s♣❡❝t♦s ❣❡r❛✐s
✷✳✶ ◆❡✉rô♥✐♦s
❖s ♥❡✉rô♥✐♦s sã♦ ❝é❧✉❧❛s ❡①❝✐tá✈❡✐s✱ ❝❛♣❛③❡s ❞❡ ♣r♦❞✉③✐r ❡ ♣r♦♣❛❣❛r s✐✲ ♥❛✐s ❡❧étr✐❝♦s✳ ❈♦♠♦ ❡st❛s ❝❛r❛❝t❡ríst✐❝❛s ♣❡r♠✐t❡♠ ♣r♦❝❡ss❛r ❡ tr❛♥s♠✐t✐r ✐♥❢♦r♠❛çõ❡s✱ ❡st❛s ❝é❧✉❧❛s t♦r♥❛r❛♠✲s❡ ♦s ❜❧♦❝♦s ❢✉♥❞❛♠❡♥t❛✐s ♣r❡s❡♥t❡s ♥♦s s✐st❡♠❛s ♥❡r✈♦s♦s ❞♦s ♠❛✐s ❞✐❢❡r❡♥t❡s ❛♥✐♠❛✐s✳ ❙ã♦ ♦s ♥❡✉rô♥✐♦s q✉❡ ❛t✐✈❛♠ ❞❡s❞❡ ❛ ❝♦❞✐✜❝❛çã♦ ❞❡ ❡stí♠✉❧♦s s❡♥s♦r✐❛✐s ❛té ❛ ❝♦♥tr❛çã♦ ❞❡ ♠ús❝✉❧♦s✱ ♣❛s✲ s❛♥❞♦ ♣♦r t♦❞❛s ❛s ❡t❛♣❛s ✐♥t❡r♠❡❞✐ár✐❛s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❞❛s ✐♥❢♦r♠❛çõ❡s s❡♥s♦r✐❛✐s✱ ♠❡♠ór✐❛✱ t♦♠❛❞❛ ❞❡ ❞❡❝✐sõ❡s✱ ❡t❝✳
◆❡st❡ ❝❛♣ít✉❧♦ ✈❛♠♦s ❛❜♦r❞❛r ❛♣❡♥❛s ❛s ♣r♦♣r✐❡❞❛❞❡s ❜ás✐❝❛s ❞♦s ♥❡✉rô✲ ♥✐♦s✱ ♥❡❝❡ssár✐❛s ♣❛r❛ ❡♥t❡♥❞❡r ❛ ❛t✐✈✐❞❛❞❡ ❡❧étr✐❝❛ ❞❡st❛s ❝é❧✉❧❛s ❡ s✉❛ ♠♦✲ ❞❡❧❛❣❡♠ ♠❛t❡♠át✐❝❛✳
✷✳✶✳✶ Pr♦♣r✐❡❞❛❞❡s ♣❛ss✐✈❛s
❆ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r é ✉♠❛ ❜✐❝❛♠❛❞❛ ❧✐♣í❞✐❝❛ q✉❡ ✐s♦❧❛ ♦s ♠❡✐♦s ✐♥tr❛ ❡ ❡①tr❛❝❡❧✉❧❛r❡s✳ ◗✉❛♥❞♦ ❤á ✉♠ ❞❡s❡q✉✐❧í❜r✐♦ ❞❡ ❝❛r❣❛s ❞❡♥tr♦ ❡ ❢♦r❛ ❞❛ ❝é✲ ❧✉❧❛✱ s❡✉ ❡①❝❡❞❡♥t❡ r❛♣✐❞❛♠❡♥t❡ s❡ ❛❝✉♠✉❧❛ ♥♦ ❡♥t♦r♥♦ ❞❛ ♠❡♠❜r❛♥❛✱ ❞❛♥❞♦
❈❆P❮❚❯▲❖ ✷✳ ❆❙P❊❈❚❖❙ ●❊❘❆■❙ ✶✼
♦r✐❣❡♠ ❛ ✉♠❛ ❞✐❢❡r❡♥ç❛ ❞❡ ♣♦t❡♥❝✐❛❧ ❝❤❛♠❛❞❛ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛ ✭❋✐❣✳ ✷✳✶✮✳
V♠=V✐♥tr❛−V❡①tr❛
s❡♥❞♦V♠♦ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛✱V✐♥tr❛ ♦ ♣♦t❡♥❝✐❛❧ ♥♦ ♠❡✐♦ ✐♥tr❛❝❡❧✉❧❛r✱
❡ V❡①tr❛ ♦ ♣♦t❡♥❝✐❛❧ ♥♦ ♠❡✐♦ ❡①tr❛❝❡❧✉❧❛r✳
❋✐❣✉r❛ ✷✳✶ ✕ ❖ ❡①❝❡✲ ❞❡♥t❡ ❞❡ ❝❛r❣❛s✱ ♣♦s✐t✐✲ ✈❛s ♦✉ ♥❡❣❛t✐✈❛s✱ s❡ ❛❝✉✲ ♠✉❧❛ ❡♠ t♦r♥♦ ❞❛ ♠❡♠✲ ❜r❛♥❛ ❝❡❧✉❧❛r✳ ❊①tr❛í❞♦ ❞❡ ✭❑❛♥❞❡❧ ❡t ❛❧✳✱ ✶✾✾✶✮✳
❆♣❡s❛r ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r ✐s♦❧❛r ♦s ❞♦✐s ♠❡✐♦s✱ ❡①✐st❡♠ ♣r♦t❡í♥❛s ✭❝❛✲ ♥❛✐s ✐ô♥✐❝♦s✮ q✉❡ ❛ ❛tr❛✈❡ss❛♠ ❢♦r♠❛♥❞♦ ✈❡r❞❛❞❡✐r♦s ♣♦r♦s q✉❡ ♣❡r♠✐t❡♠ ❛ ♣❛ss❛❣❡♠ ❞❡ ❝♦rr❡♥t❡s ✐ô♥✐❝❛s q✉❡ ❛❧t❡r❛♠ ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛✳ ❖s ❝❛✲ ♥❛✐s ✐ô♥✐❝♦s ♥♦ ❡♥t❛♥t♦✱ ♥ã♦ ❞❡✐①❛♠ ♣❛ss❛r q✉❛❧q✉❡r t✐♣♦ ❞❡ í♦♥✱ sã♦ s❡❧❡t✐✈♦s ❛ ✉♠ ♦✉ ♠❛✐s t✐♣♦s ✐ô♥✐❝♦s✳
❆❧é♠ ❞✐ss♦ ❛s ❝♦♥❝❡♥tr❛çõ❡s ✐ô♥✐❝❛s ♥ã♦ sã♦ s✐♠étr✐❝❛s ❞♦s ❞♦✐s ❧❛❞♦s
❞❛ ♠❡♠❜r❛♥❛✱ ♣♦r ❡①❡♠♣❧♦✱ t❡♠♦s ✉♠❛ ♣r❡❞♦♠✐♥â♥❝✐❛ ❞❡ só❞✐♦ ✭◆❛+✮ ❡
❝❧♦r❡t♦ ✭❈❧−
✮ ♥♦ ♠❡✐♦ ❡①tr❛❝❡❧✉❧❛r✱ ❡ ❞❡ ♣♦táss✐♦ ✭❑+✮ ❡ â♥✐♦♥s ♦r❣â♥✐❝♦s ✭❆−
❈❆P❮❚❯▲❖ ✷✳ ❆❙P❊❈❚❖❙ ●❊❘❆■❙ ✶✽
❋✐❣✉r❛ ✷✳✷ ✕ ✭❆✮ ❊sq✉❡♠❛ ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r ❝♦♠ ✉♠ ❝❛♥❛❧ ✐ô♥✐❝♦ ❞❡ ♣♦táss✐♦ q✉❡ ❛ ❛tr❛✈❡ss❛✳ ✭❇✮ ❈✐r❝✉✐t♦ ❡q✉✐✈❛❧❡♥t❡✱ ♦♥❞❡ ❛ ♠❡♠❜r❛♥❛ é r❡♣r❡s❡♥t❛❞❛ ♣♦r ✉♠ ❝❛♣❛❝✐t♦r✱ ❧✐❣❛❞♦ ❡♠ ♣❛r❛❧❡❧♦ ❝♦♠ ✉♠ r❡s✐st♦r ❡ ✉♠❛ ❜❛t❡r✐❛✱ q✉❡ r❡♣r❡s❡♥t❛♠ r❡s♣❡❝t✐✈❛♠❡♥t❡ ♦ ❝❛♥❛❧ ✐ô♥✐❝♦ ❞❡ ♣♦táss✐♦✱ ❡ ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ◆❡r♥st ✭❊q✳ ✷✳✶✮ ♣❛r❛ ♦ ♠❡s♠♦ í♦♥✳ ❊①tr❛í❞♦ ❞❡ ✭❑♦❝❤✱ ✶✾✾✾✮✳
♠♦str❛ ❛ ✜❣✉r❛ ✷✳✷✱ ❝♦♠♣♦st♦ ♣♦r ✉♠ ❝❛♣❛❝✐t♦r ✭q✉❡ r❡♣r❡s❡♥t❛ ❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r✮✱ ❧✐❣❛❞♦ ❡♠ ♣❛r❛❧❡❧♦ ❝♦♠ ✉♠ r❡s✐st♦r ✭❝❛♥❛❧ ✐ô♥✐❝♦✮ ❡♠ sér✐❡ ❝♦♠ ✉♠❛ ❜❛t❡r✐❛ ✭♣♦t❡♥❝✐❛❧ ❞✐❢✉s✐✈♦ ❞❡✈✐❞♦ ❛ ❞✐❢❡r❡♥ç❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦ ❞♦s ❞♦✐s ❧❛❞♦s ❞❛ ♠❡♠❜r❛♥❛✮✳
❉✐✈❡rs❛s ❝é❧✉❧❛s tê♠ ✉♠ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛ ✜①♦ ❛ ♠❡♥♦s q✉❡ s❡❥❛♠ ♣❡rt✉r❜❛❞❛s✱ q✉❡ é ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ♣♦t❡♥❝✐❛❧ ❞❡ r❡♣♦✉s♦✿ s✉❛ ♦r✐❣❡♠ é ❞❛❞❛ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❡❧❛ ❛ss✐♠❡tr✐❛ ❞❛s ❝♦♥❝❡♥tr❛çõ❡s ✐ô♥✐❝❛s ♥♦s ♠❡✐♦s ✐♥tr❛ ❡ ❡①tr❛❝❡❧✉❧❛r❡s ❡ ♣❡❧❛ ❞✐❢❡r❡♥ç❛ ♥❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ❞❛ ♠❡♠❜r❛♥❛ ❛ ❝❛❞❛ t✐♣♦ ✐ô♥✐❝♦✱ ❝♦♠♦ ❡①♣❧✐❝❛❞♦ ❛ s❡❣✉✐r✳
■♠❛❣✐♥❡♠♦s ✉♠❛ s✐t✉❛çã♦ ♦♥❞❡ t❡♠♦s ✉♠❛ ♠❡♠❜r❛♥❛ ✐♠♣❡r♠❡á✈❡❧✱ ❝♦♠ ❛❧t❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ◆❛+ ❡ ❈❧−
❈❆P❮❚❯▲❖ ✷✳ ❆❙P❊❈❚❖❙ ●❊❘❆■❙ ✶✾
❋✐❣✉r❛ ✷✳✸ ✕ ❊sq✉❡♠❛ ❡①♣❧✐❝❛t✐✈♦ ❞❛ ❢♦r♠❛çã♦ ❞♦ ♣♦t❡♥❝✐❛❧ ❞❡ r❡♣♦✉s♦✳ ✭❆✮ ◆❛ ❛✉sê♥❝✐❛
❞❡ ✉♠ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛✱ ❡ ❡st❛ s❡♥❞♦ ♣❡r♠❡á✈❡❧ ❛♣❡♥❛s ❛♦ ♣♦táss✐♦ ✭K+✮✱ ♦
♣♦t❡♥❝✐❛❧ ❞✐❢✉s✐✈♦ ❢❛③ ❝♦♠ q✉❡ ♦ ♣♦táss✐♦ ✈á ❞♦ ♠❡✐♦ ✐♥tr❛❝❡❧✉❧❛r ♣❛r❛ ♦ ♠❡✐♦ ❡①tr❛❝❡❧✉❧❛r✳ ✭❇✮ ❉❡✈✐❞♦ à s❛í❞❛ ❞❡ ♣♦táss✐♦ ❞❛ ❝é❧✉❧❛✱ ❢♦r♠❛✲s❡ ✉♠ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛ q✉❡ ❢♦rç❛ ♦ ♣♦táss✐♦ ♣❛r❛ ❞❡♥tr♦ ❞❛ ❝é❧✉❧❛✳ ◗✉❛♥❞♦ ❛t✐♥❣✐❞♦ ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ◆❡r♥st ✭❊q✳ ✷✳✶✮✱ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ♣♦táss✐♦ q✉❡ ❡♥tr❛ ♥❛ ❝é❧✉❧❛ é ✐❣✉❛❧ ❛ q✉❡ s❛✐✱ ❡ ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛ ♥ã♦ ✈❛r✐❛ ♠❛✐s✳
❞❡✈✐❞♦ ❛♦ s❡✉ ♣♦t❡♥❝✐❛❧ q✉í♠✐❝♦✳ ■ss♦ ❛❝❛rr❡t❛ ♥♦ ❛❝ú♠✉❧♦ ❞❡ ❝❛r❣❛s ♣♦s✐t✐✲ ✈❛s ♥♦ ♠❡✐♦ ❡①tr❛❝❡❧✉❧❛r ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❛ ❢♦r♠❛çã♦ ❞❡ ✉♠❛ ❞✐❢❡r❡♥ç❛ ❞❡ ♣♦t❡♥❝✐❛❧ ❛tr❛✈és ❞❛ ♠❡♠❜r❛♥❛ ✭❋✐❣✳ ✷✳✸✮✳ ❊ss❛ ❞✐❢❡r❡♥ç❛ ❞❡ ♣♦t❡♥❝✐❛❧ ❡①❡r❝❡ ✉♠❛ ❢♦rç❛ ❡❧étr✐❝❛ s♦❜r❡ ♦s í♦♥s ♥♦ s❡♥t✐❞♦ ❞❡ ❧❡✈á✲❧♦s ❞♦ ❧❛❞♦ ❝♦♠ ♠❡♥♦r ❝♦♥❝❡♥tr❛çã♦ ♣❛r❛ ♦ ❧❛❞♦ ❝♦♠ ♠❛✐♦r ❝♦♥❝❡♥tr❛çã♦✱ ♦ q✉❡ t❡♥❞❡ ❛ ❝♦♥✲ tr❛❜❛❧❛♥❝❡❛r ♦ ♣♦t❡♥❝✐❛❧ q✉í♠✐❝♦ ✭❋✐❣✳ ✷✳✸✮✳ ❆ ❡q✉❛çã♦ ❞❡ ◆❡r♥st ✭❊q✳ ✷✳✶✮ ♥♦s ❞á ♦ ♣♦t❡♥❝✐❛❧ ❡❧étr✐❝♦ ❡♠ q✉❡ ❛s ❞✉❛s t❡♥❞ê♥❝✐❛s ✭❞✐❢✉s✐✈❛ ❡ ❡❧étr✐❝❛✮ s❡ ❡q✉✐❧✐❜r❛♠✳
EK =
RT
ZF ln
[K]◦
[K]i ✭✷✳✶✮
❈❆P❮❚❯▲❖ ✷✳ ❆❙P❊❈❚❖❙ ●❊❘❆■❙ ✷✵
Vm =
P
kEk×gk
P
kgk ✭✷✳✷✮
❊st❛ ❡q✉❛çã♦ é ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❡q✉❛çã♦ ❞❡ ●♦❧❞♠❛♥✳ ❖ ♣♦t❡♥❝✐❛❧ ❞❡ r❡♣♦✉s♦ ✭❣❡r❛❧♠❡♥t❡ ❡♠ t♦r♥♦ ❞❡−65mV✮ é ❢♦r♠❛❞♦ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❞❡✈✐❞♦ ❛♦s ❝❛♥❛✐s ✐ô♥✐❝♦s ❞❡ ♣♦táss✐♦ q✉❡ tê♠ ✉♠ ♣♦t❡♥❝✐❛❧ ❞❡ ◆❡r♥st ✭EK✮ ❞❡ ✲✼✺
mV✱ ❝♦♠ ✉♠ ❡❢❡✐t♦ s❡❝✉♥❞ár✐♦ ❞♦s ❝❛♥❛✐s ❞❡ só❞✐♦✱ ❝♦♠ ✉♠ ♣♦t❡♥❝✐❛❧ ❞❡
◆❡r♥st ✭EN a✮ ❞❡ ✰✺✺ mV✳
✷✳✶✳✷ Pr♦♣r✐❡❞❛❞❡s ❡st♦❝ást✐❝❛s ❞♦s ❝❛♥❛✐s ✐ô♥✐❝♦s
❈♦♠ ❛ ❞❡s❝♦❜❡rt❛ ❞♦ ♠ét♦❞♦ ♣❛t❝❤✲❝❧❛♠♣ ✶✱ ❢♦✐ ♣♦ssí✈❡❧ ❡st✉❞❛r ♦ ❝♦♠✲ ♣♦rt❛♠❡♥t♦ ❞❡ ✉♠ ú♥✐❝♦ ❝❛♥❛❧ ✐ô♥✐❝♦ ✭❡str✉t✉r❛ ❜ás✐❝❛ r❡s♣♦♥sá✈❡❧ ♣❡❧❛ ❝♦♥✲ ❞✉tâ♥❝✐❛ ✐ô♥✐❝❛ ❛tr❛✈és ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r✮✱ ♠❡❞✐♥❞♦ ❛ ❝♦rr❡♥t❡ q✉❡ ♣❛ss❛ ♣♦r ❡❧❡✳
■♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞❛s ♣❛rt✐❝✉❧❛r✐❞❛❞❡s ❞❛s ❞✐♥â♠✐❝❛s ❞❡ ❛❜❡rt✉r❛✴❢❡✲ ❝❤❛♠❡♥t♦ ❞❡ ❝❛❞❛ t✐♣♦ ❞❡ ❝❛♥❛❧ ✐ô♥✐❝♦✱ é ❝♦♠✉♠ ❛ t♦❞♦s ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ t✐♣♦ t✉❞♦ ♦✉ ♥❛❞❛ ✭❋✐❣✳ ✷✳✹❛✮✳ ◗✉❛♥❞♦ ❡stã♦ ❢❡❝❤❛❞♦s✱ ♥ã♦ ❝♦♥❞✉③❡♠ ♥❡♥❤✉♠❛ ❝♦rr❡♥t❡ ✐ô♥✐❝❛✱ ❡ q✉❛♥❞♦ ❡stã♦ ❛❜❡rt♦s✱ tê♠ ✉♠❛ ❝♦♥❞✉tâ♥❝✐❛ ❜❡♠ ❞❡t❡r♠✐♥❛❞❛✱ s❡♥❞♦ ❛ ❝♦rr❡♥t❡ ✐ô♥✐❝❛ q✉❡ ♣❛ss❛ ♣♦r ❡❧❡s ❧✐♥❡❛r♠❡♥t❡ ♣r♦♣♦r✲ ❝✐♦♥❛❧ ❛♦ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛ ✭❋✐❣✳ ✷✳✹❜✮✭❝♦♥❞✉③❡♠ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❧❡✐ ❞❡ ❖❤♠ ✭❍✐❧❧❡✱ ✶✾✾✷❀ ❑❛♥❞❡❧ ❡t ❛❧✳✱ ✶✾✾✶✮✮✳
❆❧é♠ ❞✐ss♦✱ ❛ tr❛♥s✐çã♦ ❡♥tr❡ ♦s ❡st❛❞♦s ❛❜❡rt♦✴❢❡❝❤❛❞♦ é ❛❧❡❛tór✐❛ ✭❋✐❣✳ ✷✳✹❛✮✱ ♣♦❞❡♥❞♦ s❡r ❞❡s❝r✐t❛ ❛♣❡♥❛s ❡♠ t❡r♠♦s ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s✱ q✉❡ ❡♠ ❣❡r❛❧ ♣♦❞❡♠ ❞❡♣❡♥❞❡r ❞♦ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛✱ ❧✐❣❛çõ❡s ❝♦♠ ♠♦❧é❝✉❧❛s✱ ❡ ❞♦ t❡♠♣♦✳
✶▼ét♦❞♦ ❡①♣❡r✐♠❡♥t❛❧ q✉❡ ✉t✐❧✐③❛ ❝♦♠♦ ❡❧❡tr♦❞♦ ✉♠❛ ♠✐❝r♦♣✐♣❡t❛ ❞❡ ✈✐❞r♦ ♣r❡❡♥❝❤✐❞❛
❈❆P❮❚❯▲❖ ✷✳ ❆❙P❊❈❚❖❙ ●❊❘❆■❙ ✷✶
❈❆P❮❚❯▲❖ ✷✳ ❆❙P❊❈❚❖❙ ●❊❘❆■❙ ✷✷
❋✐❣✉r❛ ✷✳✺ ✕ ❈♦rr❡♥t❡s ✐ô♥✐✲ ❝❛s ❞❡✈✐❞♦ ❛ ❛t✐✈✐❞❛❞❡ ❝♦♥✲ ❥✉♥t❛ ❞❡ ❝❛♥❛✐s ✐ô♥✐❝♦s ✐♥❞✐✲ ✈✐❞✉❛✐s ❞✉r❛♥t❡ ✉♠❛ ❞❡s♣♦✲ ❧❛r✐③❛çã♦ s✉st❡♥t❛❞❛ ❞♦ ♣♦✲ t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛✱ ♣❛r❛ ❞✐❢❡r❡♥t❡s q✉❛♥t✐❞❛❞❡s ❞❡ ❝❛♥❛✐s ✐ô♥✐❝♦s✳ ❛✮ ✉♠ ❝❛✲ ♥❛❧✱ ❜✮ três ❝❛♥❛✐s✱ ❝✮ ❞❡③❡✲ ♥❛s ❞❡ ❝❛♥❛✐s✱ ❞✮ ♥ú♠❡r♦ ❛r✲ ❜✐tr❛r✐❛♠❡♥t❡ ❣r❛♥❞❡ ❞❡ ❝❛✲ ♥❛✐s✳ ✭❊①tr❛í❞♦ ❞❡ ✭▲❡✈✐t❛♥ ❡ ❑❛❝③♠❛r❡❦✱ ✶✾✾✼✮✮
✷✳✶✳✸ ❈❛♥❛✐s ✐ô♥✐❝♦s ❞❡♣❡♥❞❡♥t❡s ❞❡ ✈♦❧t❛❣❡♠ ❡ ♦ ♣♦✲
t❡♥❝✐❛❧ ❞❡ ❛çã♦
❆❧❣✉♥s t✐♣♦s ❞❡ ❝❛♥❛✐s ✐ô♥✐❝♦s sã♦ ❝❛♣❛③❡s ❞❡ ❛❜r✐r ❡ ❢❡❝❤❛r ♣❛r❛ ❛ ♣❛s✲ s❛❣❡♠ ❞❡ í♦♥s ♣❡❧❛ ❧✐❣❛çã♦ ❞❡ ♠♦❧é❝✉❧❛s✱ ♦✉tr♦s ♣❡❧❛ ❛♣❧✐❝❛çã♦ ❞❡ ✉♠ ❝❛♠♣♦ ❡❧étr✐❝♦✳ ❊st❡s ú❧t✐♠♦s sã♦ ❞❡ ♣❛rt✐❝✉❧❛r ✐♥t❡r❡ss❡ ♣♦✐s ❡①♣❧✐❝❛♠ ❛ ❢♦r♠❛çã♦ ❡ ♣r♦♣❛❣❛çã♦ ❞♦ ♣♦t❡♥❝✐❛❧ ❞❡ ❛çã♦ ✭P❆✮✳
❈❆P❮❚❯▲❖ ✷✳ ❆❙P❊❈❚❖❙ ●❊❘❆■❙ ✷✸
só❞✐♦ s❡ ✐♥❛t✐✈❛♠✱ ✐♥t❡rr♦♠♣❡♥❞♦ ❛ ❡♥tr❛❞❛ ❞❡ só❞✐♦ ♥❛ ❝é❧✉❧❛✳ ❊ss❡s ❞♦✐s ❢❡♥ô♠❡♥♦s ❢❛③❡♠ ❝♦♠ q✉❡ ❛ ♠❡♠❜r❛♥❛ ✈♦❧t❡ ❛ s❡ ♣♦❧❛r✐③❛r ✭❋✐❣✳ ✷✳✻✮✳
❖ ♠❡❝❛♥✐s♠♦ ❞❡ ❣❡r❛çã♦ ❞♦ ♣♦t❡♥❝✐❛❧ ❞❡ ❛çã♦ ✭❞❡s❝r✐t♦ ❛❝✐♠❛✮ ♣❡r♠✐t❡ q✉❡ ❡❧❡ s❡ ♣r♦♣❛❣✉❡ s❡♠ ❛t❡♥✉❛çã♦ ♣♦r ❣r❛♥❞❡s ❞✐stâ♥❝✐❛s ♥♦s ❛①ô♥✐♦s ❡✱ ❛❧é♠ ❞✐ss♦✱ ❢❛③ ❝♦♠ q✉❡ ❛ s✐♥❛❧✐③❛çã♦ ❞♦s ♥❡✉rô♥✐♦s t❡♥❤❛ ✉♠ ❝❛rát❡r ❞♦ t✐♣♦ t✉❞♦ ♦✉ ♥❛❞❛✳ ❆ ❞❡s❝r✐çã♦ ♠❛t❡♠át✐❝❛ ❞❡st❡ ❢❡♥ô♠❡♥♦ é ❡①♣❧✐❝❛❞❛ ♥❛ s❡çã♦ ✷✳✷✳
❋✐❣✉r❛ ✷✳✻ ✕ P♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛ ✭Em✮✱ ❡ ❝♦♥❞✉tâ♥❝✐❛s ❞❡ só❞✐♦ ❡ ♣♦✲
táss✐♦✱ ❞✉r❛♥t❡ ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ❛çã♦✱ ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦ ❡ ❞♦ ❡s♣❛ç♦✳ ✭❊①tr❛í❞♦ ❞❡ ✭❑❛♥❞❡❧ ❡t ❛❧✳✱ ✶✾✾✶✮✮
✷✳✶✳✹ ❈❛♥❛✐s ✐ô♥✐❝♦s r❡s♣♦♥sá✈❡✐s ♣♦r r❛❥❛❞❛s ❞❡ ♣♦t❡♥✲
❝✐❛✐s ♦✉ ❜✉rsts
❊①✐st❡♠ ❛❧❣✉♥s t✐♣♦s ❞❡ ❝❛♥❛✐s ✐ô♥✐❝♦s ❞❡♣❡♥❞❡♥t❡s ❞❛ ✈♦❧t❛❣❡♠ q✉❡ sã♦ ✐♠♣♦rt❛♥t❡s ♥❛ ❣❡r❛çã♦ ❞❡ ❛t✐✈✐❞❛❞❡ ❡s♣♦♥tâ♥❡❛ ♥♦s ♥❡✉rô♥✐♦s✱ ❡ ❡♠ ❡s♣❡❝✐❛❧ ♥❛ ❣❡r❛çã♦ ❞❡ ❜✉rsts✳ ❆q✉✐ ❞❡st❛❝❛♠♦s✿ ♦s ❝❛♥❛✐s ❞❡ ❝á❧❝✐♦✱ q✉❡ ♣♦❞❡♠ s❡r ❞❡ ❞✐♥â♠✐❝❛ rá♣✐❞❛ ❡ tr❛♥s✐❡♥t❡✱ ♦✉ ❞❡ ❞✐♥â♠✐❝❛ ♠❛✐s ❧❡♥t❛ ❡ ♣❡rs✐st❡♥t❡ ✭❈❛❚ ❡ ❈❛❙✮❀ ❡ ♦s ❝❛♥❛✐s ❞❡ ♣♦táss✐♦ ❞❡♣❡♥❞❡♥t❡ ❞❡ ❝á❧❝✐♦✱ q✉❡ t❡♠ ✉♠❛ ❞✐♥â♠✐❝❛ ❧❡♥t❛✱ ❛t✐✈❛❞❛ ❝♦♠ ❛ ❝♦♠❜✐♥❛çã♦ ❞❡ ❞❡s♣♦❧❛r✐③❛çã♦ ❞❛ ♠❡♠❜r❛♥❛ ❡ ❛✉♠❡♥t♦ ♥❛ ❝♦♥❝❡♥tr❛çã♦ ✐♥tr❛❝❡❧✉❧❛r ❞❡ ❝á❧❝✐♦✳
❈❆P❮❚❯▲❖ ✷✳ ❆❙P❊❈❚❖❙ ●❊❘❆■❙ ✷✹
❋✐❣✉r❛ ✷✳✼ ✕ ❆t✐✈✐❞❛❞❡ tí♣✐❝❛ ❞❡ ✉♠ ♥❡✉rô♥✐♦ ❧❛t❡r❛❧ ♣✐❧ór✐❝♦ ✭▲P✮ ❞♦ ❣â♥❣❧✐♦ ❡st♦♠❛✲ t♦❣ástr✐❝♦✳ ❚❡♠♦s ❞✉❛s ❡s❝❛❧❛s ❞❡ t❡♠♣♦ tí♣✐❝❛s ♥❡st❡ ❝♦♠♣♦rt❛♠❡♥t♦✱ ✉♠❛ rá♣✐❞❛ q✉❡ ❝♦rr❡s♣♦♥❞❡ ❛♦s ♣♦t❡♥❝✐❛✐s ❞❡ ❛çã♦✱ ❡ ✉♠❛ ❧❡♥t❛ q✉❡ ❝♦rr❡s♣♦♥❞❡ ❛♦s ♣❧❛tôs ❞❡ ❞❡s♣♦❧❛✲ r✐③❛çã♦ ❡ ❤✐♣❡r♣♦❧❛r✐③❛çõ❡s✳
❆ ❞✐♥â♠✐❝❛ rá♣✐❞❛ ❞♦s ♣♦t❡♥❝✐❛✐s ❞❡ ❛çã♦ é ❞❛❞❛ ♣❡❧♦s ❝❛♥❛✐s ❞❡ só❞✐♦ ❡ ♣♦táss✐♦ ❝♦♠♦ ✈✐♠♦s ♥❛ s❡çã♦ ❛♥t❡r✐♦r✳ ▼❛s ❛q✉✐ t❡♠♦s t❛♠❜é♠ ✉♠❛ ❞✐♥â♠✐❝❛ ❧❡♥t❛✱ ❞❡ ❞❡s♣♦❧❛r✐③❛çã♦ ❡ ♠❛♥✉t❡♥çã♦ ❞❡ ✉♠ ♣❛t❛♠❛r ❞❡ ❞❡s♣♦❧❛✲ r✐③❛çã♦ ✭♣❧❛tô✮✳ ❉✉r❛♥t❡ ❡ss❡ ♣❛t❛♠❛r ❞❡ ❞❡s♣♦❧❛r✐③❛çã♦✱ ♦❝♦rr❡♠ ❞✐✈❡rs♦s ♣♦t❡♥❝✐❛✐s ❞❡ ❛çã♦ ❡ ❡♥tã♦ ♦❝♦rr❡ ✉♠❛ ❤✐♣❡r♣♦❧❛r✐③❛çã♦✱ ❢❛③❡♥❞♦ ❝♦♠ q✉❡ ♦ ♥❡✉rô♥✐♦ ♣❡r♠❛♥❡ç❛ ✏s✐❧❡♥❝✐♦s♦✑ ♣♦r ❛❧❣✉♠ t❡♠♣♦✳
❆ ❞❡s♣♦❧❛r✐③❛çã♦ ❡ ♠❛♥✉t❡♥çã♦ ❞♦ ♣❧❛tô sã♦ ❝❛✉s❛❞❛s ♣❡❧❛ ❛❜❡rt✉r❛ ❞❡ ❝❛♥❛✐s ✐ô♥✐❝♦s ❞❡ ❝á❧❝✐♦ ✭Ca2+✮✳ ❊st❡✱ ❛♦ ❡♥tr❛r ♥❛ ❝é❧✉❧❛ ❛t✐✈❛ ✉♠ t✐♣♦ ❞❡ ❝❛♥❛❧ ✐ô♥✐❝♦ ❞❡ ♣♦táss✐♦ ❞❡♣❡♥❞❡♥t❡ ❞❡ ❝á❧❝✐♦ (K(Ca))✱ ♦ q✉❛❧ é ❝❛r❛❝t❡r✐✲ ③❛❞♦ ♣♦r ✉♠❛ ❞✐♥â♠✐❝❛ ❧❡♥t❛ ❝✉❥❛ ❛t✐✈❛çã♦ ❞❡♣❡♥❞❡ t❛♥t♦ ❞❡ ❝♦♥❝❡♥tr❛çã♦ ❞❡ í♦♥s ❞❡ ❝á❧❝✐♦ ✭[Ca2+]✮ ✐♥tr❛❝❡❧✉❧❛r ❝♦♠♦ ❞❛ ❞❡s♣♦❧❛r✐③❛çã♦ ❞❛ ♠❡♠❜r❛♥❛✳ ◗✉❛♥❞♦ ❡ss❡s ❝❛♥❛✐s s❡ ❛t✐✈❛♠✱ t❡♥❞❡♠ ❛ r❡♣♦❧❛r✐③❛r ❛ ♠❡♠❜r❛♥❛✱ t❡r♠✐✲ ♥❛♥❞♦ ♦ ♣❧❛tô ❡ ❝❛✉s❛♥❞♦ ❛ ❤✐♣❡r♣♦❧❛r✐③❛çã♦✳ ◆♦ ❝❛♣ít✉❧♦ ✹ ❛♣r❡s❡♥t❛♠♦s ✉♠❛ ❞❡s❝r✐çã♦ ♠❛t❡♠át✐❝❛ ❞❡t❛❧❤❛❞❛ ❞❛ ❞✐♥â♠✐❝❛ ❞❡ss❛s ❝♦rr❡♥t❡s✳
❈❆P❮❚❯▲❖ ✷✳ ❆❙P❊❈❚❖❙ ●❊❘❆■❙ ✷✺
❈❆P❮❚❯▲❖ ✷✳ ❆❙P❊❈❚❖❙ ●❊❘❆■❙ ✷✻
✷✳✷ ❖ ♠♦❞❡❧♦ ❞❡t❡r♠✐♥íst✐❝♦ ❞❡ ❍♦❞❣❦✐♥✲❍✉①❧❡②
❖ tr❛❜❛❧❤♦ ❞❡ ❍♦❞❣❦✐♥✲❍✉①❧❡② ✭❍♦❞❣❦✐♥ ❡ ❍✉①❧❡②✱ ✶✾✺✷✮ q✉❛♥t✐✜❝♦✉ ❛
❞❡♣❡♥❞ê♥❝✐❛ ❞❛s ❝♦♥❞✉tâ♥❝✐❛s ❞❡ N a+ ❡ K+ ❝♦♠ ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛
❡ ❝♦♠ ♦ t❡♠♣♦✳
❖ ♠♦❞❡❧♦✱ ❝♦♥s✐❞❡r❛r ❛ ♠❡♠❜r❛♥❛ ❝♦♠♦ ✉♠ ❝❛♣❛❝✐t♦r q✉❡ ❛❧t❡r❛ s❡✉ ♣♦t❡♥❝✐❛❧ ❡❧étr✐❝♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛s ❝♦rr❡♥t❡s ❡❧étr✐❝❛s ❛♣❧✐❝❛❞❛s✱ ❝♦♥s✐st❡ ❡♠ q✉❛tr♦ ❡q✉❛çõ❡s ❞✐❢❡r❡♥❝✐❛✐s✿ ✉♠❛ ♣❛r❛ ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛✱ ❞✉❛s ♣❛r❛ ❛ ❝♦rr❡♥t❡ ❞❡ só❞✐♦✱ ❡ ✉♠❛ ♣❛r❛ ❛ ❝♦rr❡♥t❡ ❞❡ ♣♦táss✐♦✳
Cm
dV
dt =gKn
4(V
−EK) +gN am3h(V −EN a) +gleak(V −Eleak) +I ✭✷✳✸✮
dm
dt =αm(1−m)−βmm ✭✷✳✹✮
dh
dt =αh(1−h)−βhh ✭✷✳✺✮
dn
dt =αn(1−n)−βnn ✭✷✳✻✮
αn(V)
0.01(10−V)
exp[(10−V)/10]−1
αm(V)
0.1(25−V)
exp[(25−V)/10]−1
αh(V) 0.07exp[−V /20]
βn(V) 0.125exp[−V /80]
βm(V) 4.0exp[−V /18]
βh(V)
1
exp[(30−V)/10] + 1
❈❆P❮❚❯▲❖ ✷✳ ❆❙P❊❈❚❖❙ ●❊❘❆■❙ ✷✼
❆ ❡q✉❛çã♦ ✷✳✸ é ❛ ❡q✉❛çã♦ ❞❡ ✉♠ ❝✐r❝✉✐t♦RC✱ s❡♥❞♦ Cm ❛ ❝❛♣❛❝✐tâ♥❝✐❛
❞❛ ♠❡♠❜r❛♥❛✱ V ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛✱ I ✉♠❛ ❝♦rr❡♥t❡ ❡①t❡r♥❛ ❛♣❧✐✲
❝❛❞❛✱ Ei(i =N a, K ou❧❡❛❦ ✲ ❝♦rr❡♥t❡ ❞❡ ❢✉❣❛)♦ ♣♦t❡♥❝✐❛❧ ❞❡ ◆❡r♥st ❞♦ í♦♥
i ❡ gi ❛ ❝♦♥❞✉tâ♥❝✐❛ ♠á①✐♠❛ ❞❛ ♠❡♠❜r❛♥❛ ❝♦♠ r❡❧❛çã♦ ❛♦ í♦♥ i✳ ❖s t❡r♠♦s
✐♥❝♦♠✉♥s sã♦ ♦ n4 ♠✉❧t✐♣❧✐❝❛♥❞♦ ❛ ❝♦♥❞✉tâ♥❝✐❛ ❞❡ K+ ❡ ♦s t❡r♠♦s m3 ❡ h
♠✉❧t✐♣❧✐❝❛♥❞♦ ❛ ❝♦♥❞✉tâ♥❝✐❛ ❞❡ N a+✱ q✉❡ ❝♦♥tê♠ ❛ ❞✐♥â♠✐❝❛ ❞❡ ❛❜❡rt✉r❛
❡ ❢❡❝❤❛♠❡♥t♦ ❞♦s ❝❛♥❛✐s ✐ô♥✐❝♦s ❡♠ ❢✉♥çã♦ ❞❡ V ❡ ❞♦ t❡♠♣♦✳ ❖s ❡①♣♦❡♥t❡s
❞❡ss❡s t❡r♠♦s ✭✹✱ ✸ ❡ ✶✮✱ ❢♦r❛♠ t✐r❛❞♦s ♦r✐❣✐♥❛❧♠❡♥t❡ ❞❡ ✉♠ ❛❥✉st❡ ♥✉♠ér✐❝♦ ❡ ❥✉st✐✜❝❛❞♦s ♣❡❧♦s ❛✉t♦r❡s ❝♦♠♦ s❡♥❞♦ ❞❡✈✐❞♦ ❛♦ ❞✐❢❡r❡♥t❡ ♥ú♠❡r♦ ❞❡ ✏♣❛rtí❝✉✲ ❧❛s ❞❡ ❛t✐✈❛çã♦ ❡ ✐♥❛t✐✈❛çã♦✑ q✉❡ ❝❛❞❛ ❝♦♥❞✉tâ♥❝✐❛ ♣♦ss✉í❛✳ ❈♦♠ ♦ ❛✈❛♥ç♦ ❞❡ té❝♥✐❝❛s ❞❡ ❝r✐st❛❧♦❣r❛✜❛ ❞❡ r❛✐♦ ❳ ❡ ❣❡♥ét✐❝❛✱ ✹✵ ❛♥♦s ❛♣ós ♦ ♠♦❞❡❧♦ t❡r s✐❞♦ ✐♥tr♦❞✉③✐❞♦ ♣♦r ❍❍✱ ❢♦✐ ♠♦str❛❞♦ q✉❡ ❡ss❡s ❡①♣♦❡♥t❡s r❡❛❧♠❡♥t❡ r❡✢❡t✐❛♠ ❛ ❡str✉t✉r❛ ♠✐❝r♦s❝ó♣✐❝❛ ❞♦s ❝❛♥❛✐s ✐ô♥✐❝♦s❝♦♠♦ ♣♦st✉❧❛❞♦ ♣❡❧♦s ❛✉t♦r❡s q✉❡ s❡q✉❡r s❛❜✐❛♠ ❞❡ s✉❛ ❡①✐stê♥❝✐❛✳
❖ ❝❛♥❛❧ ✐ô♥✐❝♦ ❞❡ ♣♦táss✐♦ é ✉♠❛ ♣r♦t❡í♥❛ q✉❡ t❡♠ ✹ ✭❞❛í ♦ ❡①♣♦❡♥t❡✮ s✉❜✉♥✐❞❛❞❡s ✐❞ê♥t✐❝❛s✱ q✉❡ s❡ ❛❜r❡♠ ❡ ❢❡❝❤❛♠ ❞❡ ❢♦r♠❛ ✐♥❞❡♣❡♥❞❡♥t❡✱ s❡♥❞♦
n ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠❛ s✉❜✉♥✐❞❛❞❡ s❡ ❡♥❝♦♥tr❛r ❛❜❡rt❛✳ P❛r❛ q✉❡ ❡st❡
❝❛♥❛❧ ✐ô♥✐❝♦ ❝♦♥❞✉③❛✱ é ♣r❡❝✐s♦ q✉❡ t♦❞❛s s✉❛s s✉❜✉♥✐❞❛❞❡s ❡st❡❥❛♠ ❛❜❡rt❛s✱ ♦ q✉❡ ❛❝♦♥t❡❝❡ ❝♦♠ ♣r♦❜❛❜✐❧✐❞❛❞❡ n4✳
P❛r❛ ♦ ❝❛♥❛❧ ✐ô♥✐❝♦ ❞❡ só❞✐♦ ❛ s✐t✉❛çã♦ é ❛♥á❧♦❣❛✳ ❊st❡ ❝❛♥❛❧ tê♠ ✸ s✉❜✉♥✐❞❛❞❡s m ❞❡ ❛t✐✈❛çã♦✱ ❡ ✉♠❛ s✉❜✉♥✐❞❛❞❡ h ❞❡ ✐♥❛t✐✈❛çã♦✳
❆s ❢✉♥çõ❡s αn,m,♦✉h ❡ βn,m,♦✉h ✭❚❛❜❡❧❛ ✷✳✶✮ sã♦ ❛s t❛①❛s ❞❡ ❛❜❡rt✉r❛ ❡
❢❡❝❤❛♠❡♥t♦ ❞❛s r❡s♣❡❝t✐✈❛s s✉❜✉♥✐❞❛❞❡s✳ ❋❛③❡♥❞♦ ❛ tr❛♥s❢♦r♠❛çã♦✿
n∞= αn
αn+βn
e τn=
1
❈❆P❮❚❯▲❖ ✷✳ ❆❙P❊❈❚❖❙ ●❊❘❆■❙ ✷✽
❚❡♠♦s ✉♠❛ ♠❛♥❡✐r❛ ❛❧t❡r♥❛t✐✈❛ ❞❡ ✈❡r ❛s ❡q✉❛çõ❡s ✷✳✹ ❛ ✷✳✻✿
dn
dt =
n∞−n
τn ✭✷✳✽✮
♦♥❞❡ n∞(V) r❡♣r❡s❡♥t❛ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠❛ s✉❜✉♥✐❞❛❞❡ ❞♦ ❝❛♥❛❧ ❞❡ ♣♦táss✐♦ ❡♥❝♦♥tr❛r✲s❡ ♥♦ ❡st❛❞♦ ❛❜❡rt♦ ♣❛r❛ ✉♠ ❞❛❞♦ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠✲
❜r❛♥❛ V ❡♠ ✉♠ t❡♠♣♦ ✐♥✜♥✐t♦✱ ❡ τn r❡♣r❡s❡♥t❛ ✉♠ t❡♠♣♦ ❞❡ r❡❧❛①❛çã♦✳ ◆❛
❧✐t❡r❛t✉r❛ ♣♦❞❡✲s❡ ❡♥❝♦♥tr❛r ❛s ❞✉❛s ❢♦r♠✉❧❛çõ❡s✱ q✉❡ sã♦ ❝♦♠♣❧❡t❛♠❡♥t❡ ❡q✉✐✈❛❧❡♥t❡s✳ ◆♦ ❡♥t❛♥t♦✱ ♣❛r❛ ❛ ♠♦❞❡❧❛❣❡♠ ❡st♦❝ást✐❝❛ ✭❈❛♣ít✉❧♦ ✹✮ é ♠❛✐s ❝♦♥✈❡♥✐❡♥t❡ ✉t✐❧✐③❛r ❛ ❢♦r♠✉❧❛çã♦ ♦r✐❣✐♥❛❧✱ ❡♠ t❡r♠♦s ❞❡ t❛①❛s ❞❡ tr❛♥s✐çã♦✳ ❊♠❜♦r❛ ❛s ❡q✉❛çõ❡s s❡❥❛♠ ♥ã♦ ❧✐♥❡❛r❡s ❡ ❞❡♣❡♥❞❛♠ ❞♦ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠✲ ❜r❛♥❛ ❛tr❛✈és ❞❡ ❢✉♥çõ❡s ❡①♣♦♥❡♥❝✐❛✐s ❡ s✐❣♠♦✐❞❛✐s✱ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ss❡ ♠♦❞❡❧♦ é ❜❛st❛♥t❡ s✐♠♣❧❡s✳ ❇❛s✐❝❛♠❡♥t❡ ❡❧❡ t❡♠ ❞♦✐s ❡st❛❞♦s ❡st❛❝✐♦♥ár✐♦s q✉❛❧✐t❛t✐✈❛♠❡♥t❡ ❞✐❢❡r❡♥t❡s✱ ❞❡♣❡♥❞❡♥❞♦ ❞❛ ❝♦rr❡♥t❡ ❉❈ ❛♣❧✐❝❛❞❛✳ ◗✉❛♥❞♦ ❡st❛ é ♠❡♥♦r ❞♦ q✉❡ ✉♠ ❝❡rt♦ ❧✐♠✐❛r✱ ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛ ❞♦ ♠♦❞❡❧♦ s❡ ❡st❛❜✐❧✐③❛ ❡♠ ✉♠ ✈❛❧♦r ❝♦♥st❛♥t❡✳ ❊ss❡ é ♦ ❡st❛❞♦ s✐❧❡♥❝✐♦s♦✳ ❙❡ ❛ ❝♦rr❡♥t❡ ❛♣❧✐❝❛❞❛ ✉❧tr❛♣❛ss❛r ❡ss❡ ❧✐♠✐❛r✱ ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛ ♣❛ss❛ ❛ ♦s❝✐❧❛r ♣❡✲ r✐♦❞✐❝❛♠❡♥t❡✱ ❣❡r❛♥❞♦ ♣✉❧s♦s ❞❡ ❞❡s♣♦❧❛r✐③❛çã♦ ❝❤❛♠❛❞♦s ♣♦t❡♥❝✐❛✐s ❞❡ ❛çã♦ ✭P✳❆✳✮✭❋✐❣✳ ✷✳✽✮✳ ◆♦ ❡st❛❞♦ s✐❧❡♥❝✐♦s♦✱ ♣❡q✉❡♥♦s ♣✉❧s♦s ❞❡ ❝♦rr❡♥t❡ ✭♣♦s✐t✐✲ ✈♦s ♦✉ ♥❡❣❛t✐✈♦s✮ sã♦ ❝❛♣❛③❡s ❞❡ ♣r♦❞✉③✐r ✉♠ P✳❆✳ ❛♣ós ♦ q✉❛❧ ♦ ♥❡✉rô♥✐♦ ♠♦❞❡❧❛❞♦ r❡t♦r♥❛ ❛♦ ❡st❛❞♦ s✐❧❡♥❝✐♦s♦✱ ♦✉ s❡❥❛ ❡❧❡ é ❡①❝✐tá✈❡❧✳
❈❆P❮❚❯▲❖ ✷✳ ❆❙P❊❈❚❖❙ ●❊❘❆■❙ ✷✾
❈❆P❮❚❯▲❖ ✷✳ ❆❙P❊❈❚❖❙ ●❊❘❆■❙ ✸✵
✷✳✸ ❇r❡✈❡ ❤✐stór✐❝♦ ❞❛ ♠♦❞❡❧❛❣❡♠ ❡st♦❝ást✐❝❛
❞❡ ♥❡✉rô♥✐♦s
❖ ♣r✐♠❡✐r♦ tr❛❜❛❧❤♦ ❡♥✈♦❧✈❡♥❞♦ ✉♠ ♠♦❞❡❧♦ t✐♣♦ ❍♦❞❣❦✐♥✲❍✉①❧❡② ❡st♦❝ás✲ t✐❝♦ ❢♦✐ ♦ ❞❡ ❙❦❛✉❣❡♥ ✶✾✼✾ ✭❙❦❛✉❣❡♥ ❡ ❲❛❧❧♦❡✱ ✶✾✼✾✮✳ ❊st❡ tr❛❜❛❧❤♦ ❡①♣❧♦r♦✉ ♦s ❡❢❡✐t♦s ❞❛s ❝♦♥❞✉tâ♥❝✐❛s ✐ô♥✐❝❛s ❞❡ só❞✐♦ ❡ ♣♦táss✐♦ s❡r❡♠ ❡st♦❝ást✐❝❛s ♥♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ✉♠ ♣❡q✉❡♥♦ tr❡❝❤♦ ❞♦ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛ ❞❡ ✉♠ ❛①ô✲ ♥✐♦✱ ❡♠ ❡s♣❡❝✐❛❧ ♥❛s ❝✉r✈❛s ❞❡ ❢r❡q✉ê♥❝✐❛ ♣♦r ❝♦rr❡♥t❡ ✐♥❥❡t❛❞❛✳ ◆❛ é♣♦❝❛✱ ♥ã♦ ❤❛✈✐❛ ❛✐♥❞❛ ♥❡♥❤✉♠❛ ❡st✐♠❛t✐✈❛ ❞❡ q✉❛♥t♦s ❝❛♥❛✐s ✐ô♥✐❝♦s ❤❛✈✐❛♠ ❡♠ ✉♠ ♥❡✉rô♥✐♦✱ ♣♦rt❛♥t♦ ❛s ✐♠♣❧✐❝❛çõ❡s ♣rát✐❝❛s ❞❡st❡ tr❛❜❛❧❤♦ ❡r❛♠ ♣✉r❛♠❡♥t❡ ❡s♣❡❝✉❧❛t✐✈❛s✳
▼❛✐s r❡❝❡♥t❡♠❡♥t❡✱ ♦✉tr♦s tr❛❜❛❧❤♦s ✭❈❤♦✇ ❡ ❲❤✐t❡✱ ✶✾✾✻❀ ❲❤✐t❡ ❡t ❛❧✳✱ ✷✵✵✵✮ ♠♦str❛♠ ♦✉tr♦s ❡❢❡✐t♦s ❞❡❝♦rr❡♥t❡s ❞❛ ❡st♦❝❛st✐❝✐❞❛❞❡ ❞♦s ❝❛♥❛✐s ✐ô✲ ♥✐❝♦s✱ t❛✐s ❝♦♠♦ ♣♦t❡♥❝✐❛✐s ❞❡ ❛çã♦ ❡s♣♦♥tâ♥❡♦s ✭q✉❡ ♥ã♦ s❡r✐❛♠ ❞✐s♣❛r❛❞♦s ♣♦r ♥❡✉rô♥✐♦s ❞❡t❡r♠✐♥íst✐❝♦s✮ ❡ ♣♦t❡♥❝✐❛✐s ❞❡ ❛çã♦ ♣❡r❞✐❞♦s ✭❢❛❧❤❛s ❡♠ ✉♠❛ ❛t✐✈✐❞❛❞❡ ❞❡ ❞✐s♣❛r♦ tô♥✐❝♦ ❞❡ ♣♦t❡♥❝✐❛✐s ❞❡ ❛çã♦✮✳ ❊st❡ ❢❡♥ô♠❡♥♦s tê♠ ❡s✲ ♣❡❝✐❛❧ r❡❧❡✈â♥❝✐❛ ❡♠ ♥ós ❞❡ ❘❛♥✈✐❡r ✭❘✉❜✐♥st❡✐♥✱ ✶✾✾✺✮ ❡ ♥❛ ♣r♦♣❛❣❛çã♦ ❞♦ ♣♦t❡♥❝✐❛❧ ❞❡ ❛çã♦ ❡♠ ❛①ô♥✐♦s ✜♥♦s ✭❋❛✐s❛❧ ❡ ▲❛✉❣❤❧✐♥✱ ✷✵✵✼✮✳ ❆❧é♠ ❞✐ss♦ ✉♠ ❛rt✐❣♦ ❞❡ r❡✈✐sã♦ ❛r❣✉♠❡♥t❛ q✉❡ ❛s ✢✉t✉❛çõ❡s ❡st♦❝ást✐❝❛s ❞♦s ❝❛♥❛✐s ✐ô♥✐❝♦s ✭t❛♠❜é♠ ❝♦♥❤❡❝✐❞❛❞❛ ♥❛ ❧✐t❡r❛t✉r❛ ❝♦♠♦ ✏❝❤❛♥♥❡❧ ♥♦✐s❡✑✮ sã♦ r❡s♣♦♥sá✈❡❧ ♣♦r ❛✉♠❡♥t❛r ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❝♦♠♣♦rt❛♠❡♥t♦s ❛❝❡ssí✈❡✐s à ❛❧❣✉♠❛s ♣♦♣✉❧❛çõ❡s ❞❡ ♥❡✉rô♥✐♦s ✭❲❤✐t❡ ❡t ❛❧✳✱ ✷✵✵✵✮✳
❈❆P❮❚❯▲❖ ✷✳ ❆❙P❊❈❚❖❙ ●❊❘❆■❙ ✸✶
❛♦ ✐♥í❝✐♦ ❞❛ ✐♥❥❡çã♦ ❞❡ ❝♦rr❡♥t❡ é s❡♠♣r❡ ♠✉✐t♦ ♣ró①✐♠♦✱ ❡♥q✉❛♥t♦ q✉❡ ♦s ♣ró①✐♠♦s ♣♦t❡♥❝✐❛✐s ❞❡ ❛çã♦ ✈ã♦ r❛♣✐❞❛♠❡♥t❡ ♣❡r❞❡♥❞♦ ❛ ❝♦♥✜❛❜✐❧✐❞❛❞❡ ❡ s❡ ❡♠❜❛r❛❧❤❛♥❞♦ ✭✜❣✉r❛ ✷✳✾ ❆✮✳ P❛r❛ ❝♦♠♣❛r❛r ❝♦♠ ❡st❡ r❡s✉❧t❛❞♦ ❡❧❡ ✜③❡r❛♠ t❛♠❜é♠ ❛ ♠❡s♠❛ ❡①♣❡r✐ê♥❝✐❛ ❛♣❧✐❝❛♥❞♦ ✈ár✐❛s ✈❡③❡s ✉♠❛ ❝♦rr❡♥t❡ r✉✐❞♦s❛ ❛♦ ✐♥✈és ❞❡ ✉♠ ❞❡❣r❛✉✳ ❖ q✉❡ s❡ ♦❜s❡r✈❛ s♦❜r❡♣♦♥❞♦ ♦s r❡s✉❧t❛❞♦s ♣❛r❛ ❛ ❝♦rr❡♥t❡ r✉✐❞♦s❛ é q✉❡ ♦ ✐♥st❛♥t❡ ❞❡ ♦❝♦rrê♥❝✐❛ ❞♦s ♣♦t❡♥❝✐❛✐s ❞❡ ❛çã♦ é ❜❛st❛♥t❡ ❝♦♥✜á✈❡❧ ✭✜❣✉r❛ ✷✳✾ ❇✮✳
❋✐❣✉r❛ ✷✳✾ ✕ ✭❆✮ ❆❝✐♠❛ t❡♠♦s ❛ s♦❜r❡♣♦s✐çã♦ ❞❛s r❡s♣♦st❛s ❞♦ ♥❡✉rô♥✐♦ ❞♦ ❝órt❡① ❞♦ r❛t♦ à ❛♣❧✐❝❛çã♦ ❞❡ ✉♠ ❞❡❣r❛✉ ❞❡ ❝♦rr❡♥t❡ ❞❡ ✷✵✵ ♣❆✱ ❡①✐❜✐❞♦ ♥❛ ✜❣✉r❛ ❞♦ ♠❡✐♦❀ ❛❜❛✐①♦ t❡♠♦s ♦s ✐♥st❛♥t❡s ❞❡ ♦❝♦rrê♥❝✐❛ ❞❡ ❝❛❞❛ ✉♠❛ ❞♦s ♣♦t❡♥❝✐❛✐s ❞❡ ❛çã♦ ♣❛r❛ ❝❛❞❛ ✉♠❛ ❞❛s ✷✺ t❡♥t❛t✐✈❛s✳ ✭❇✮ ❆❝✐♠❛ t❡♠♦s ❛ s♦❜r❡♣♦s✐çã♦ ❞❛s r❡s♣♦st❛s ❞♦ ♥❡✉rô♥✐♦ à ❛♣❧✐❝❛çã♦ ❞❡ ✉♠❛ ❝♦rr❡♥t❡ r✉✐❞♦s❛✱ ❡①✐❜✐❞❛ ♥❛ ✜❣✉r❛ ❞♦ ♠❡✐♦❀ ❛❜❛✐①♦ t❡♠♦s ♦s ✐♥st❛♥t❡s ❞❡ ♦❝♦rrê♥❝✐❛ ❞❡ ❝❛❞❛ ✉♠❛ ❞♦s ♣♦t❡♥❝✐❛✐s ❞❡ ❛çã♦ ♣❛r❛ ❝❛❞❛ ✉♠❛ ❞❛s ✷✺ t❡♥t❛t✐✈❛s✳ ❊①tr❛í❞♦ ❞❡ ✭▼❛✐♥❡♥ ❡ ❙❡❥♥♦✇s❦✐✱ ✶✾✾✺✮✳
❈❆P❮❚❯▲❖ ✷✳ ❆❙P❊❈❚❖❙ ●❊❘❆■❙ ✸✷
❢♦r♠❛✱ s✉❛ ❝♦♥✜❛❜✐❧✐❞❛❞❡ ✭r❡♣r♦❞✉t✐❜✐❧✐❞❛❞❡✮ ❞❡♣❡♥❞❡ ❞❡ ♣r♦♣r✐❡❞❛❞❡s ❡st❛✲ tíst✐❝❛s ❞♦ s✐♥❛❧ ❞❡ ❡stí♠✉❧♦✳ ◆♦ ❝❛s♦ ❞❡ ✉♠ ❡stí♠✉❧♦ ❝♦♥st❛♥t❡✱ ♦ ♥❡✉rô♥✐♦ ❞✐s♣❛r❛ ❝♦♠ ✉♠❛ ❝❡rt❛ ♣r❡❝✐sã♦ ♦s ♣r✐♠❡✐r♦s ♣♦t❡♥❝✐❛✐s ❞❡ ❛çã♦ ❡♥q✉❛♥t♦ ♦s ú❧t✐♠♦s sã♦ ❜❡♠ ♣♦✉❝♦ ❝♦♥✜á✈❡✐s✳ ◆♦ ❝❛s♦ ❞❡ ✉♠ ❡stí♠✉❧♦ r✉✐❞♦s♦✱ ❛s ♣♦s✐çõ❡s ❞♦s s♣✐❦❡s ❞♦ ♥❡✉rô♥✐♦ sã♦ ❜❡♠ ♠❛✐s ♣r❡❝✐s❛s✱ ❡ s✉❛ ❝♦♥✜❛❜✐❧✐❞❛❞❡ ❞❡♣❡♥❞❡ ❞❛ ✈❛r✐â♥❝✐❛ ❞♦ ❡stí♠✉❧♦✳
❈❆P❮❚❯▲❖ ✷✳ ❆❙P❊❈❚❖❙ ●❊❘❆■❙ ✸✸
❋✐❣✉r❛ ✷✳✶✵ ✕
❈♦♠♣❛r❛çã♦ ❡♥tr❡
♦s r❡s✉❧t❛❞♦s ❞❡ ♥❡✉rô✲ ♥✐♦s ♠♦❞❡❧♦ s✉❜♠❡t✐❞♦s ❛ ❝♦rr❡♥t❡s ❞♦ t✐♣♦
❞❡❣r❛✉ ❡ r✉✐❞♦s❛✳ ❖
▼♦❞❡❧♦ ❍❍ ❞❡t❡r♠✐♥ís✲ t✐❝♦ r❡s♣♦♥❞❡ s❡♠♣r❡
❞❛ ♠❡s♠❛ ♠❛♥❡✐r❛
t❛♥t♦ ♣❛r❛ ♦ ❞❡❣r❛✉ ❞❡ ❝♦rr❡♥t❡ q✉❛♥t♦ ♣❛r❛ ♦ s✐♥❛❧ r✉✐❞♦s♦✳ ❖ ♠♦❞❡❧♦ ❊st♦❝ást✐❝♦ ❝♦♠♣♦rt❛✲s❡ ❞❡ ♠♦❞♦ ♠❛✐s ❝♦♥✜á✈❡❧ ♣❛r❛ ♦ s✐♥❛❧ r✉✐❞♦s♦ q✉❡ ♣❛r❛ ♦ s✐♥❛❧ ❞❡ ❞❡❣r❛✉
❞❡ ❝♦rr❡♥t❡✳ ❊①tr❛í❞♦
