Essays in recursive equilibrium and market selection hypothesis

❋❯◆❉❆➬➹❖ ●❊❚❯▲■❖ ❱❆❘●❆❙

❊❙❈❖▲❆ ❞❡ PÓ❙✲●❘❆❉❯❆➬➹❖ ❡♠

❊❈❖◆❖▼■❆

❘♦❞r✐❣♦ ❏❛r❞✐♠ ❘❛❛❞

❊ss❛②s ✐♥ ❘❡❝✉rs✐✈❡ ❊q✉✐❧✐❜r✐✉♠ ❛♥❞

▼❛r❦❡t ❙❡❧❡❝t✐♦♥ ❍②♣♦t❤❡s✐s

❘♦❞r✐❣♦ ❏❛r❞✐♠ ❘❛❛❞

❊ss❛②s ✐♥ ❘❡❝✉rs✐✈❡ ❊q✉✐❧✐❜r✐✉♠ ❛♥❞

▼❛r❦❡t ❙❡❧❡❝t✐♦♥ ❍②♣♦t❤❡s✐s

❚❡s❡ s✉❜♠❡t✐❞❛ à ❊s❝♦❧❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊❝♦♥♦♠✐❛

❞❛ ❋✉♥❞❛çã♦ ●❡t✉❧✐♦ ❱❛r❣❛s ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❛ ♦❜t❡♥çã♦

❞♦ tít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❊❝♦♥♦♠✐❛✳

➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ♠✐❝r♦❡❝♦♥♦♠✐❛✳

❖r✐❡♥t❛❞♦r✿ ❆❧♦✐s✐♦ ❆r❛✉❥♦✳

❈♦✲♦r✐❡♥t❛❞♦r✿ ❱✐❝t♦r ❋✐❧✐♣❡ ▼❛rt✐♥s✲❞❛✲❘♦❝❤❛✳

❘✐♦ ❞❡ ❏❛♥❡✐r♦

✷✵✶✶

❘❛❛❞✱ ❘♦❞r✐❣♦ ❏❛r❞✐♠

❊ss❛②s ✐♥ r❡❝✉rs✐✈❡ ❡q✉✐❧✐❜r✐✉♠ ❛♥❞ ♠❛r❦❡t s❡❧❡❝✲ t✐♦♥ ❤②♣♦t❤❡s✐s ✴ ❘♦❞r✐❣♦ ❏❛r❞✐♠ ❘❛❛❞✳ ✲ ✷✵✶✶✳

✽✻❢✳

❚❡s❡ ✭❉♦✉t♦r❛❞♦✮ ❋✉♥❞❛çã♦ ●❡t✉❧✐♦ ❱❛r❣❛s✱ ❊s❝♦❧❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊❝♦♥♦♠✐❛✳

❖r✐❡♥t❛❞♦r✿ ❆❧♦✐s✐♦ ❆r❛✉❥♦✳

❈♦✲♦r✐❡♥t❛❞♦r✿ ❱✐❝t♦r ❋✐❧✐♣❡ ▼❛rt✐♥s✲❞❛✲❘♦❝❤❛✳ ■♥❝❧✉✐ ❜✐❜❧✐♦❣r❛✜❛✳

✶✳ ❊q✉✐❧í❜r✐♦ ❡❝♦♥ô♠✐❝♦✳ ✷✳ ■♥❝❡rt❡③❛ ✭❊❝♦♥♦♠✐❛✮✳ ✸✳ ❊①♣❡❝t❛t✐✈❛s r❛❝✐♦♥❛✐s ✭❚❡♦r✐❛ ❡❝♦♥ô♠✐❝❛✮✳ ✹✳ ❆♥á❧✐s❡ ♥✉♠ér✐❝❛✳ ■✳ ❆r❛ú❥♦✱ ❆❧♦ís✐♦ P❡ss♦❛ ❞❡✱ ✶✾✹✻✲✳ ■■✳ ▼❛rt✐♥s✲❞❛✲❘♦❝❤❛✱ ❱✐❝t♦r ❋✐❧✐♣❡✳ ■■■✳ ❋✉♥❞❛çã♦ ●❡t✉❧✐♦ ❱❛r❣❛s✳ ❊s❝♦❧❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊❝♦♥♦✲ ♠✐❛✳ ■❱✳ ❚ít✉❧♦✳

❈❉❉ ✲ ✸✸✾✳✺

❘♦❞r✐❣♦ ❏❛r❞✐♠ ❘❛❛❞

❊ss❛②s ✐♥ ❘❡❝✉rs✐✈❡ ❊q✉✐❧✐❜r✐✉♠ ❛♥❞

▼❛r❦❡t ❙❡❧❡❝t✐♦♥ ❍②♣♦t❤❡s✐s

❚❡s❡ s✉❜♠❡t✐❞❛ à ❊s❝♦❧❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊❝♦♥♦♠✐❛

❞❛ ❋✉♥❞❛çã♦ ●❡t✉❧✐♦ ❱❛r❣❛s ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❛ ♦❜t❡♥çã♦

❞♦ tít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❊❝♦♥♦♠✐❛✳

❊ ❛♣r♦✈❛❞❛ ❡♠ ✷✽✴✵✷✴✷✵✶✶ ♣❡❧❛ ❝♦♠✐ssã♦ ♦r❣❛♥✐③❛❞♦r❛

Pr♦❢✳ ❉r✳ ❆❧♦✐s✐♦ ❆r❛✉❥♦

Pr♦❢✳ ❉r✳

❱✐❝t♦r ❋✐❧✐♣❡ ▼❛rt✐♥s✲❞❛✲❘♦❝❤❛

Pr♦❢✳ ❉r✳ ▲✉✐s ❍✳ ❇✳ ❇r❛✐❞♦

Pr♦❢✳ ❉r✳

❏✉❛♥ P❛❜❧♦ ❚♦rr❡s✲▼❛rt✐♥❡③

Pr♦❢✳ ❉r✳ ❏♦sé ❍❡❧❡♥♦ ❋❛r♦

❆ ▲✉❝é❧✐❛ q✉❡ s❡♠♣r❡ ❡st❡✈❡ ❛♦ ♠❡✉ ❧❛❞♦ ♥♦s ♠♦♠❡♥t♦s ♠❛✐s ❞✐❢í❝❡✐s✳

❆❣r❛❞❡❝✐♠❡♥t♦s

❆❣r❛❞❡ç♦✱

❆ ♠✐♥❤❛ ❡s♣♦s❛✱ ♠❡✉s ♣❛✐s ❡ t♦❞❛s ❛s ♦✉tr❛s ♣❡ss♦❛s q✉❡ ❡st✐✈❡r❛♠ ♣r❡s❡♥t❡s ❞✐r❡t❛ ♦✉ ✐♥❞✐r❡t❛♠❡♥t❡ ♥❡ss❛ ❡t❛♣❛ ❞❛ ♠✐♥❤❛ ✈✐❞❛✳

❆♦s ♠❡✉s ♦r✐❡♥t❛❞♦r❡s✱ ❆❧♦✐s✐♦ P❡ss♦❛ ❆r❛✉❥♦ ❡ ❱✐❝t♦r ❋✐❧✐♣❡ ▼❛rt✐♥s✲❞❛✲❘♦❝❤❛✱ ♣❡❧❛ ❝♦♥tr✐❜✉✐çã♦ ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❛ t❡s❡✳

❆♦s ❛✉t♦r❡s ❈❤❛r❛❧❛♠❜♦s ❉✳ ❆❧✐♣r❛♥t✐s ✭✐♥ ♠❡♠♦r✐❛♥✮ ❡ ❑✐♠ ❈✳ ❇♦r❞❡r✱ ♣❡❧❛ ❡①❝❡❧❡♥t❡ ♦❜r❛ ■♥✜♥✐t❡ ❉✐♠❡♥s✐♦♥❛❧ ❆♥❛❧②s✐s✿ ❛ ❍✐t❝❤❤✐❦❡r✬s ●✉✐❞❡ r❡♣r❡s❡♥t❛♥❞♦ ✉♠❛ ❞❛s ♣r✐♥❝✐♣❛✐s r❡❢❡rê♥❝✐❛s ♣❛r❛ ❛s ❞❡♠♦♥str❛çõ❡s ❞♦s t❡♦r❡♠❛s ❝♦♥t✐❞♦s ♥❡st❛ t❡s❡✳

❆ t♦❞♦ ❝♦r♣♦ ❞♦❝❡♥t❡ ❞❛ ❊P●❊✳ ❆♦s ❢✉♥❝✐♦♥ár✐♦s ❞❛ ❝❛s❛✱ ♣❡❧♦ ❛♣♦✐♦ té❝♥✐❝♦ ✐♥❞✐s♣❡♥✲ sá✈❡❧✳

❆♦s ♠❡✉s ❝♦❧❡❣❛s ❞❛ ❊P●❊ ❡✱ ✜♥❛❧♠❡♥t❡✱

❆ ❉❡✉s P❛✐ ❡ ❈r✐❛❞♦r✱ s❡♠ ♦ q✉❛❧ ♥❛❞❛ s❡r✐❛ ♣♦ssí✈❡❧✳

❘❡s✉♠♦

❊st❛ t❡s❡ ❝♦♥s✐st❡ ❡♠ três ❡♥s❛✐♦s s♦❜r❡ ❡❝♦♥♦♠✐❛s ❡♠ ❤♦r✐③♦♥t❡ ✐♥✜♥✐t♦ ♣♦ss✉✐♥❞♦ ✐♥❝❡rt❡③❛ ❡①ó❣❡♥❛ ❡ ❡♥❞ó❣❡♥❛✳

◆♦ ♣r✐♠❡✐r♦ ❡♥s❛✐♦ ♣r♦✈❛♠♦s ❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠ ❡q✉✐❧í❜r✐♦ ♣❛r❛ ✉♠❛ ❝❧❛ss❡ ❞❡ ❡❝♦♥♦♠✐❛s ❞❡ ❤♦r✐③♦♥t❡ ✐♥✜♥✐t♦ ♦♥❞❡ ❛s tr♦❝❛s ♦❝♦rr❡♠ s❡qü❡♥❝✐❛❧♠❡♥t❡ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✳ ❊①✐st❡♠ ❞♦✐s t✐♣♦s ❞❡ ❛❣❡♥t❡s✿ ♦ ♣r✐♠❡✐r♦ ♣r❡✈ê ❝♦rr❡t❛♠❡♥t❡ t♦❞♦s ♦s ♣r❡ç♦s ❢✉t✉r♦s ❝♦♥t✐♥❣❡♥t❡s às ✈❛r✐á✈❡✐s ♦❜s❡r✈❛❞❛s ♥♦ ♣❛ss❛❞♦ ❡ ♦ s❡❣✉♥❞♦ t❡♠ ❡①♣❡❝t❛t✐✈❛s ❡①ó❣❡♥❛s s♦❜r❡ ♦s ♣r❡ç♦s ❢✉t✉r♦s ❝♦♠ ❜❛s❡ ♥❛s ✈❛r✐á✈❡✐s ❛❣r❡❣❛❞❛s ❛t✉❛✐s ❡ ♣❛ss❛❞❛s✳ ❖s ❛❣❡♥t❡s ♣♦❞❡♠ t❡r ♣❧❛♥♦s ✐♥❝♦♥s✐st❡♥t❡s ♣❛r❛ ♦ ❢✉t✉r♦✱ ♠❛s✱ ❡♠ q✉❛❧q✉❡r ❝❛s♦✱ ❡❧❡s tê♠ ♣r❡❢❡rê♥❝✐❛s ❞❛❞❛s ❝♦♠♦ ❡♠ ❇❧❛❝❦✇❡❧❧ ❛♥❞ ❉✉❜✐♥s ✭✶✾✻✷✮ q✉❡ ♥♦s ♣❡r♠✐t❡ ❝❛r❛❝t❡r✐③❛r ❛ ❞❡♠❛♥❞❛ ❞❡ ❢♦r♠❛ r❡❝✉rs✐✈❛ ❡ ❡✈✐t❛ tr✉♥❝❛♠❡♥t♦ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦ ♥❛ ♣r♦✈❛ ❞❡ ❡①✐stê♥❝✐❛ ✉s❛♥❞♦ ♦ t❡♦r❡♠❛ ❞♦ ♣♦♥t♦ ✜①♦ ❞❡ ❑❛❦✉t❛♥✐ ❋❛♥✲●❧✐❝❦s❜❡r❣✳

◆♦ s❡❣✉♥❞♦ ❡♥s❛✐♦ ❛❜♦r❞❛♠♦s ✉♠ ♠♦❞❡❧♦ ❞❡ ❡q✉✐❧í❜r✐♦ ❣❡r❛❧ ❝♦♠ ✉♠ ♥ú♠❡r♦ ✜♥✐t♦ ❞❡ ❛❣❡♥t❡s ❤❡t❡r♦❣ê♥❡♦s ♣♦ss✉✐♥❞♦ ❡①♣❡❝t❛t✐✈❛s ✐♥✈❛r✐❛♥t❡s ♥♦ t❡♠♣♦ ❡ ❡①ó❣❡♥❛s s♦❜r❡ ❛s ✈❛r✲ ✐á✈❡✐s ❡♥❞ó❣❡♥❛s✳ ▼♦str❛✲s❡ q✉❡ ❡①✐st❡ ✉♠ ❡q✉✐❧í❜r✐♦ r❡❝✉rs✐✈♦ ✐♠♣❧❡♠❡♥t❛♥❞♦ ♦ ❡q✉✐❧í❜r✐♦ s❡q✉❡♥❝✐❛❧ ❡♠ q✉❡ ♦ ❡s♣❛ç♦ ❞❡ ❡st❛❞♦ ❝♦♥s✐st❡ ♥❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣♦rt✐❢♦❧✐♦ ❛❣r❡❣❛❞♦ ♣❛ss❛❞♦ ❡ ♦ ❡st❛❞♦ ❛t✉❛❧ ❞❛ ♥❛t✉r❡③❛✳ ❊st❛❜❡❧❡❝❡♠♦s ❝♦♥❞✐çõ❡s ❡♠ q✉❡ ♦ ❡q✉✐❧í❜r✐♦ r❡❝✉rs✐✈♦ é ❝♦♥✲ tí♥✉♦✳ ❆❧é♠ ❞✐ss♦✱ ✉s❛♠♦s ❛ r❡❧❛çã♦ r❡❝✉rs✐✈❛ ❡ ❝♦♥tí♥✉❛ ❞❛s ✈❛r✐á✈❡✐s ❛❣r❡❣❛❞❛s ♣❛r❛ ♣r♦✈❛r q✉❡✱ ♥✉♠❛ ❡❝♦♥♦♠✐❛ ❝♦♠ ❞♦✐s t✐♣♦s ❞❡ ❛❣❡♥t❡s✱ ❛q✉❡❧❡ q✉❡ ❝♦♠❡t❡ ❡rr♦s ♣❡rs✐st❡♥t❡s s♦❜r❡ ❛s r❡❣r❛s ❞❡ ❡①♣❡❝t❛t✐✈❛ ❞❛s ✈❛r✐á✈❡✐s ❡♥❞ó❣❡♥❛s ♥♦ ❢✉t✉r♦ é ❡①♣✉❧s♦ ❞♦ ♠❡r❝❛❞♦ ♣❡❧♦s ♦✉t✲ r♦s ❝♦♠ ❛♥t❡❝✐♣❛çõ❡s ❝♦rr❡t❛s ❞❛s ✈❛r✐á✈❡✐s✱ ♦✉ s❡❥❛✱ ♦s ❛❣❡♥t❡s ❝♦♠ ❡①♣❡❝t❛t✐✈❛s r❛❝✐♦♥❛✐s✳ ❋✐♥❛❧♠❡♥t❡✱ ♣r♦✈❛♠♦s ❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠ ❡q✉✐❧í❜r✐♦ r❡❝✉rs✐✈♦ ❝♦♠ ♦ ♠❡s♠♦ ❡s♣❛ç♦ ❞❡ ❡st❛❞♦ ❛❝✐♠❛ ❡ t❛❧ q✉❡ ♣❡❧♦ ♠❡♥♦s ✉♠ t✐♣♦ tê♠ ❢✉♥çã♦ ❞❡ ❡①♣❡❝t❛t✐✈❛ ❞❡ ♣r❡ç♦ ❝♦rr❡t❛✳

◆♦ t❡r❝❡✐r♦ ❡♥s❛✐♦ ❡①✐❜✐♠♦s ❡①❡♠♣❧♦s ♥✉♠ér✐❝♦s ♣❛r❛ ♠♦❞❡❧♦s ❡st♦❝ást✐❝♦s ❞❡ ❡q✉✐❧í❜r✐♦ ❣❡r❛❧ ❝♦♠ ❛❣❡♥t❡s ❤❡t❡r♦❣ê♥❡♦s✱ ♠❡r❝❛❞♦s ✐♥❝♦♠♣❧❡t♦s ❡ ✐♥❝❡rt❡③❛ ❡①ó❣❡♥❛✳ ❊①❛♠✐♥❛♠♦s ❛ s♦❜r❡✈✐✈ê♥❝✐❛ ❞❡ ❛❣❡♥t❡s ❝♦♠ ♣r❡❢❡rê♥❝✐❛s q✉❡ ♥ã♦ s❛t✐s❢❛③❡♠ ♦s ♣r❡ss✉♣♦st♦s ❞❛ r❛❝✐♦♥❛❧✲ ✐❞❛❞❡ ❞♦ ♠♦❞❡❧♦ ❞❡ ❆rr♦✇✲❉❡❜r❡✉ ❡♠ ✉♠ ❡q✉✐❧í❜r✐♦ ♥♦ q✉❛❧ ♣❡❧♦ ♠❡♥♦s ✉♠ ❛❣❡♥t❡ t❡♠ ❡①♣❡❝t❛t✐✈❛s r❛❝✐♦♥❛✐s✳ ❈♦♥s✐❞❡r❛♠♦s✱ ❜❛s✐❝❛♠❡♥t❡✱ ♦s ❛❣❡♥t❡s ❝♦♠ ❛ ❛♠❜✐❣✉✐❞❛❞❡✱ ♦s ♥♦✐s❡ tr❛❞❡rs✱ ❛❣❡♥t❡s ❝♦♠ ♣r❡❢❡rê♥❝✐❛s ❝♦♠♦ ♥❛ t❡♦r✐❛ ❞❡ ✜♥❛♥ç❛ ❝♦♠♣♦rt❛♠❡♥t❛✐s ❡ ♥❛ t❡♦r✐❛ ♣r♦s♣❡❝t✐✈❛✱ ❡ ✜♥❡❧♠❡♥t❡✱ ❛❣❡♥t❡s ❝♦♠ ❡①♣❡❝t❛t✐✈❛s r❛❝✐♦♥❛✐s✱ ♠❛s r❡♥❞❛ ❤❡t❡r♦❣ê♥❡❛✳ ❆❧é♠ ❞✐ss♦✱ ♠♦str❛♠♦s q✉❡ s❡ ✉♠ ❡q✉✐❧í❜r✐♦ r❡❝✉rs✐✈♦ ❡①✐st❡✱ ❡♥tã♦ ❡❧❡ ✐♠♣❧❡♠❡♥t❛ ✉♠ ❡q✉✐❧í❜r✐♦ s❡q✉❡♥❝✐❛❧✱ ♠❡s♠♦ s❡ ❝♦♥s✐❞❡r❛r♠♦s ♦ ❡s♣❛ç♦ ❞❡ ❡st❛❞♦ ❝♦♠ ❛s ✈❛r✐á✈❡✐s ❞✐str✐❜✉✐çã♦ ❞❡ ♣♦r✲ t✐❢♦❧✐♦ ❛♥t❡r✐♦r ❛❣r❡❣❛❞♦ ❡ ❡st❛❞♦ ❛t✉❛❧ ❞❛ ♥❛t✉r❡③❛✳ ❊st❡ r❡s✉❧t❛❞♦ ♥♦s ♣❡r♠✐t❡ ❝❛❧❝✉❧❛r ♦ ❡q✉✐❧í❜r✐♦ s❡q✉❡♥❝✐❛❧ ✉s❛♥❞♦ ✉♠ ♠ét♦❞♦ ♥✉♠ér✐❝♦ ❝♦♥str✉í❞♦ ❡♠ ✉♠❛ ♠❛♥❡✐r❛ s✐♠✐❧❛r àq✉❡❧❛ ❡♥❝♦♥tr❛❞❛ ❡♠ ❏✉❞❞ ✭✶✾✾✽✮ q✉❡ ❝❛❧❝✉❧❛ s♦❧✉çõ❡s ❞❡ ❡q✉❛çõ❡s ❢✉♥❝✐♦♥❛✐s ✉s❛♥❞♦ ✉♠ ❛❧❣♦r✐t♠♦ ❞❡ ✐t❡r❛çã♦✳

P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❊q✉✐❧í❜r✐♦ ❘❡❝✉rs✐✈♦✱ ❍✐♣ót❡s❡ ❞❡ ❙❡❧❡çã♦ ❞❡ ▼❡r❝❛❞♦✱ ▼ét♦❞♦s ◆✉♠ér✐✲ ❝♦s✳

❆❜str❛❝t

❚❤✐s t❤❡s✐s ❝♦♥s✐sts ✐♥ t❤r❡❡ ❡ss❛②s ♦♥ ❛♥ ✐♥✜♥✐t❡ ❤♦r✐③♦♥ ❡❝♦♥♦♠② ✇✐t❤ ❡①♦❣❡♥♦✉s ❛♥❞ ❡♥✲ ❞♦❣❡♥♦✉s ✉♥❝❡rt❛✐♥t②✳

■♥ t❤❡ ✜rst ❡ss❛② ✇❡ ♣r♦✈❡ ❡①✐st❡♥❝❡ ♦❢ ❛♥ ❡q✉✐❧✐❜r✐✉♠ ❢♦r ❛ ❝❧❛ss ♦❢ ✐♥✜♥✐t❡ ❤♦r✐③♦♥ ❡❝♦♥♦♠✐❡s ✇❤❡r❡ tr❛❞❡ t❛❦❡s ♣❧❛❝❡ s❡q✉❡♥t✐❛❧❧② ♦✈❡r t✐♠❡✳ ❚❤❡r❡ ❡①✐st t✇♦ t②♣❡s ♦❢ ❛❣❡♥ts✿ t❤❡ ✜rst ❛♥t✐❝✐♣❛t❡s ❝♦rr❡❝t❧② ❛❧❧ ❢✉t✉r❡ ❝♦♥t✐♥❣❡♥t ♣r✐❝❡s ❛♥❞ t❤❡ s❡❝♦♥❞ ❤❛s ❡①♦❣❡♥♦✉s ❡①✲ ♣❡❝t❛t✐♦♥s ❛❜♦✉t ❢✉t✉r❡ ♣r✐❝❡s ❜❛s❡❞ ♦♥ t❤❡ ❝✉rr❡♥t ❛♥❞ ♣❛st ❛❣❣r❡❣❛t❡ ✈❛r✐❛❜❧❡s✳ ❆❣❡♥ts ♠❛② ❤❛✈❡ ✐♥❝♦♥s✐st❡♥t ♦♣t✐♠❛❧ ❢✉t✉r❡ ♣❧❛♥s ❜✉t✱ ✐♥ ❛♥② ❝❛s❡✱ t❤❡② ❤❛✈❡ ♣r❡❢❡r❡♥❝❡s ✇✐t❤ ♣r❡✲ ❞✐❝t✐✈❡ ❜❡❧✐❡❢s ✐♥ t❤❡ ❝♦♥t❡①t ♦❢ ❇❧❛❝❦✇❡❧❧ ❛♥❞ ❉✉❜✐♥s ✭✶✾✻✷✮ ✇❤✐❝❤ ❛❧❧♦✇s ✉s t♦ ❝❤❛r❛❝t❡r✐③❡ t❤❡✐r ❞❡♠❛♥❞ r❡❝✉rs✐✈❡❧② ❛♥❞ ❛✈♦✐❞s tr✉♥❝❛t✐♦♥ ♦✈❡r t✐♠❡ ✐♥ t❤❡ ❡①✐st❡♥❝❡ ♣r♦♦❢ ✉s✐♥❣ t❤❡ ❑❛❦✉t❛♥✐✲❋❛♥✲●❧✐❝❦s❜❡r❣ ❋✐①❡❞ P♦✐♥t ❚❤❡♦r❡♠✳

■♥ t❤❡ s❡❝♦♥❞ ❡ss❛② ✐t ✐s ❛❞❞r❡ss❡❞ ❛ ❣❡♥❡r❛❧ ❡q✉✐❧✐❜r✐✉♠ ♠♦❞❡❧ ✇✐t❤ ✜♥✐t❡ ❤❡t❡r♦❣❡♥❡♦✉s ❛❣❡♥ts ❤❛✈✐♥❣ t✐♠❡ ❤♦♠♦❣❡♥❡♦✉s ❡①♦❣❡♥♦✉s ❡①♣❡❝t❛t✐♦♥s ♦♥ ❡♥❞♦❣❡♥♦✉s ✈❛r✐❛❜❧❡s✳ ■t ✐s s❤♦✇♥ t❤❛t t❤❡r❡ ❡①✐sts ❛ r❡❝✉rs✐✈❡ ❡q✉✐❧✐❜r✐✉♠ ✐♠♣❧❡♠❡♥t✐♥❣ t❤❡ s❡q✉❡♥t✐❛❧ ❡q✉✐❧✐❜r✐✉♠ ❛♥❞ ✇✐t❤ t❤❡ st❛t❡ s♣❛❝❡ ❝♦♥s✐st✐♥❣ ♦❢ t❤❡ ♣❛st ❛❣❣r❡❣❛t❡ ♣♦rt❢♦❧✐♦ ❞✐str✐❜✉t✐♦♥ ❛♥❞ t❤❡ ❝✉rr❡♥t st❛t❡ ♦❢ t❤❡ ♥❛t✉r❡✳ ❲❡ ❡st❛❜❧✐s❤ ❝♦♥❞✐t✐♦♥s ✉♥❞❡r ✇❤✐❝❤ t❤❡ r❡❝✉rs✐✈❡ ❡q✉✐❧✐❜r✐✉♠ ✐s ❝♦♥t✐♥✉♦✉s✳ ▼♦r❡♦✈❡r✱ ✇❡ ✉s❡ t❤❡ ❝♦♥t✐♥✉♦✉s r❡❝✉rs✐✈❡ r❡❧❛t✐♦♥ ♦❢ t❤❡ ❛❣❣r❡❣❛t❡ ✈❛r✐❛❜❧❡s t♦ ♣r♦✈❡ t❤❛t ✐♥ ❛♥ ❡❝♦♥♦♠② ✇✐t❤ t✇♦ t②♣❡s ♦❢ ❛❣❡♥ts✱ t❤❡♥ t❤❡ ♦♥❡ ✇❤♦ ♠❛❦❡s ♣❡rs✐st❡♥t ♠✐st❛❦❡s ♦♥ t❤❡ ❡①♣❡❝t❛t✐♦♥ r✉❧❡s ♦❢ t❤❡ ❢✉t✉r❡ ❡♥❞♦❣❡♥♦✉s ✈❛r✐❛❜❧❡s ✐s ❞r✐✈❡♥ ♦✉t ♦❢ t❤❡ ♠❛r❦❡t ❜② t❤❡ ♦t❤❡rs ✇✐t❤ ❝♦rr❡❝t ❛♥t✐❝✐♣❛t✐♦♥s ♦❢ t❤❡ ✈❛r✐❛❜❧❡s✱ t❤❛t ✐s✱ t❤❡ r❛t✐♦♥❛❧ ❡①♣❡❝t❛t✐♦♥s ❛❣❡♥ts✳ ❋✐♥❛❧❧② ✇❡ ♣r♦✈❡ ❡①✐st❡♥❝❡ ♦❢ ❛ r❡❝✉rs✐✈❡ ❡q✉✐❧✐❜r✐✉♠ ✇✐t❤ t❤❡ s❛♠❡ st❛t❡ s♣❛❝❡ ❛s ❜❡❢♦r❡ ❛♥❞ s✉❝❤ t❤❛t ❛t ❧❡❛st ♦♥❡ t②♣❡ ❤❛✈❡ ❝♦rr❡❝t ♣r✐❝❡ ❡①♣❡❝t❛t✐♦♥ ❢✉♥❝t✐♦♥✳

■♥ t❤❡ t❤✐r❞ ❡ss❛② ✇❡ ♣r♦✈✐❞❡ ♥✉♠❡r✐❝❛❧ ❡①❛♠♣❧❡s ❢♦r st♦❝❤❛st✐❝ ♠♦❞❡❧s ♦❢ ❣❡♥❡r❛❧ ❡q✉✐❧✐❜✲ r✐✉♠ ✇✐t❤ ❤❡t❡r♦❣❡♥❡♦✉s ❛❣❡♥ts✱ ✐♥❝♦♠♣❧❡t❡ ♠❛r❦❡ts ❛♥❞ ❡①♦❣❡♥♦✉s ✉♥❝❡rt❛✐♥t②✳ ❲❡ ❡①❛♠✲ ✐♥❡ t❤❡ s✉r✈✐✈❛❧ ♦❢ ❛❣❡♥ts ✇✐t❤ ♣r❡❢❡r❡♥❝❡s t❤❛t ❞♦ ♥♦t s❛t✐s❢② t❤❡ r❛t✐♦♥❛❧✐t② ❛ss✉♠♣t✐♦♥s ♦❢ ❆rr♦✇✲❉❡❜r❡✉ ♠♦❞❡❧ ✐♥ ❛♥ ❡q✉✐❧✐❜r✐✉♠ ✐♥ ✇❤✐❝❤ ❛t ❧❡❛st ♦♥❡ ❛❣❡♥t ❤❛s r❛t✐♦♥❛❧ ❡①♣❡❝t❛t✐♦♥s✳ ❚❤❡ ❡①❛♠♣❧❡s ❝♦♥s✐❞❡r ❜❛s✐❝❛❧❧② ❛❣❡♥ts ✇✐t❤ ❛♠❜✐❣✉✐t②✱ ♥♦✐s❡ tr❛❞❡rs✱ ❜❡❤❛✈✐♦r❛❧ ✜♥❛♥❝❡✱ ♣r♦s♣❡❝t t❤❡♦r② ❛♥❞ ❛❣❡♥ts ✇✐t❤ r❛t✐♦♥❛❧ ❡①♣❡❝t❛t✐♦♥s ❜✉t ❤❡t❡r♦❣❡♥❡♦✉s ✐♥❝♦♠❡✳ ▼♦r❡♦✈❡r✱ ✇❡ s❤♦✇ t❤❛t ✐❢ ❛ r❡❝✉rs✐✈❡ ❡q✉✐❧✐❜r✐✉♠ ❡①✐sts t❤❡♥ ✐t ✐♠♣❧❡♠❡♥ts ❛ s❡q✉❡♥t✐❛❧ ❡q✉✐❧✐❜r✐✉♠✱ ❡✈❡♥ ✐❢ ✇❡ ❝♦♥s✐❞❡r t❤❡ st❛t❡ s♣❛❝❡ ❝♦♥s✐st✐♥❣ ♦❢ t❤❡ ♣r❡✈✐♦✉s ❛❣❣r❡❣❛t❡ ♣♦rt❢♦❧✐♦ ❞✐str✐❜✉t✐♦♥ ❛♥❞ t❤❡ ❝✉rr❡♥t st❛t❡ ♦❢ ♥❛t✉r❡✳ ❚❤✐s r❡s✉❧t ❛❧❧♦✇s ✉s t♦ ❝♦♠♣✉t❡ t❤❡ s❡q✉❡♥t✐❛❧ ❡q✉✐❧✐❜r✐✉♠ ❜② ✉s✐♥❣ ❛ ♥✉♠❡r✐❝❛❧ ♠❡t❤♦❞ ❝♦♥str✉❝t❡❞ ✐♥ ❛ ♠❛♥♥❡r s✐♠✐❧❛r t♦ t❤❛t ❢♦✉♥❞ ✐♥ ❏✉❞❞ ✭✶✾✾✽✮ ✇❤✐❝❤ ❝♦♠♣✉t❡s s♦❧✉t✐♦♥s ♦❢ ❢✉♥❝t✐♦♥❛❧ ❡q✉❛t✐♦♥s ❜② ✉s✐♥❣ ❛♥ ✐t❡r❛t✐♦♥ ❛❧❣♦r✐t❤♠✳

❑❡②✇♦r❞s✿ ❘❡❝✉rs✐✈❡ ❊q✉✐❧✐❜r✐✉♠✱ ▼❛r❦❡t ❙❡❧❡❝t✐♦♥ ❍②♣♦t❤❡s✐s✱ ◆✉♠❡r✐❝❛❧ ▼❡t❤♦❞s✳

❈♦♥t❡♥ts

✶ ❊①✐st❡♥❝❡ ♦❢ ❊q✉✐❧✐❜r✐✉♠ ✐♥ ▼❛r❦❡ts ✇✐t❤ ■♥✜♥✐t❡ ❍♦r✐③♦♥ ❛♥❞ ❊♥❞♦❣❡♥♦✉s

❯♥❝❡rt❛✐♥t② ✻

✶✳✶ ❚❤❡ ♠♦❞❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✶✳✶✳✶ ❇❛s✐❝ ❞❡✜♥✐t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✶✳✶✳✷ ❊①♦❣❡♥♦✉s ❡①♣❡❝t❛t✐♦♥s ❛❣❡♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✶✳✶✳✸ ❆❣❡♥ts ✇✐t❤ ❡♥❞♦❣❡♥♦✉s ❜❡❧✐❡❢s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✶✳✶✳✹ ❉❡✜♥✐t✐♦♥ ♦❢ ❡q✉✐❧✐❜r✐✉♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✶✳✷ ❇❡❧✐❡❢s ❝♦♥❝❡♣ts ❛♥❞ ❞❡♠❛♥❞ ♣r♦♣❡rt✐❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✶✳✷✳✶ ❊①♦❣❡♥♦✉s ❡①♣❡❝t❛t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✶✳✷✳✷ ❊♥❞♦❣❡♥♦✉s ❜❡❧✐❡❢s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✶✳✸ ❊①✐st❡♥❝❡ r❡s✉❧ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✶✳✹ ❆♣♣❡♥❞✐① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✶✳✹✳✶ ❘❡s✉❧ts r❡❧❛t❡❞ t♦ ❙✉❜s❡❝t✐♦♥ ✶✳✷✳✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✶✳✹✳✷ ❘❡s✉❧ts r❡❧❛t❡❞ t♦ ❙✉❜s❡❝t✐♦♥ ✶✳✷✳✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵

✷ ❊①♦❣❡♥♦✉s ❊①♣❡❝t❛t✐♦♥s ♦♥ ❊♥❞♦❣❡♥♦✉s ❱❛r✐❛❜❧❡s✿ ❘❡❝✉rs✐✈❡ ❊q✉✐❧✐❜r✐✉♠

❛♥❞ ❙✉r✈✐✈❛❧ ✸✷

✷✳✶ ❚❤❡ ♠♦❞❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✶✳✶ ❉❡✜♥✐t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✶✳✷ ❆❣❡♥ts✬ ❝❤❛r❛❝t❡r✐st✐❝s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✷ ❙❡q✉❡♥t✐❛❧ ❛♥❞ r❡❝✉rs✐✈❡ ❡q✉✐❧✐❜r✐✉♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✳✸ ❙✉r✈✐✈❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✷✳✸✳✶ ❊✉❧❡r ❡q✉❛t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✷✳✸✳✷ P❡r❢❡❝t ❢♦r❡s✐❣❤t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✷✳✸✳✸ ■♥❛❝❝✉r❛t❡ ❡①♣❡❝t❛t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✷✳✸✳✹ ❚❤❡ ❝❛s❡ S ❝♦♥✈❡① ♦r ✜♥✐t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺

✸ ❙✉r✈✐✈❛❧ ✐♥ ■♥❝♦♠♣❧❡t❡ ▼❛r❦❡ts ❲✐t❤♦✉t ❙❤♦rt ❙❛❧❡s✿ ◆✉♠❡r✐❝❛❧ ❊①❛♠✲

♣❧❡s✳ ✻✸

✸✳✶ ❚❤❡ ♠♦❞❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✸✳✶✳✶ ❉❡✜♥✐t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✸✳✶✳✷ ❆❣❡♥ts✬ ❢❡❛t✉r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✸✳✷ ❘❡❝✉rs✐✈❡ ❛♥❞ s❡q✉❡♥t✐❛❧ ❡q✉✐❧✐❜r✐✉♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✸✳✸ ◆✉♠❡r✐❝❛❧ ❡①❛♠♣❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✸✳✸✳✶ ❍❡t❡r♦❣❡♥❡♦✉s ✐♥❝♦♠❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✸✳✸✳✷ ❆♠❜✐❣✉✐t② ❆✈❡rs✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✸✳✸✳✸ ❆❝❝✉r❛t❡ ×■♥❛❝❝✉r❛t❡ ❜❡❧✐❡❢s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸

✸✳✸✳✹ ❇❡❤❛✈✐♦r❛❧ ❋✐♥❛♥❝❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✸✳✸✳✺ ◆♦✐s❡ tr❛❞❡rs ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✸✳✸✳✻ Pr♦s♣❡❝t t❤❡♦r② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✸✳✹ ❈♦♥❝❧✉s✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✸✳✺ ❆♣♣❡♥❞✐① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵

■♥tr♦❞✉❝t✐♦♥

▼♦st ❣❡♥❡r❛❧ ❡q✉✐❧✐❜r✐✉♠ ♠♦❞❡❧s ❞❡s❝r✐❜❡ ❤♦✇ ✉♥❝❡rt❛✐♥t② ❛✛❡❝ts ❛❣❡♥ts ❝❤♦✐❝❡s✳ ■♥ t❤❡ ✐♥t❡r♣r❡t❛t✐♦♥ ♦❢ t❤❡ ❆rr♦✇✲❉❡❜r❡✉ ♠♦❞❡❧✱ t❤❡r❡ ✐s ✉♥❝❡rt❛✐♥t② ❛❜♦✉t t❤❡ ✏st❛t❡ ♦❢ t❤❡ ✇♦r❞✑ ✇❤❡r❡ t❤❡ st❛t❡ ♦❢ t❤❡ ✇♦r❞ ✐♥✢✉❡♥❝❡s ❛❣❡♥ts✬ ❝❤❛r❛❝t❡r✐st✐❝s✳ ❆♥ ✐♠♣♦rt❛♥t ❢❡❛t✉r❡ ♦❢ t❤✐s ❦✐♥❞ ♦❢ ✉♥❝❡rt❛✐♥t② ✐s t❤❛t ✐t ✐s ❡①♦❣❡♥♦✉s✱ ✐♥ t❤❡ s❡♥s❡ ♦❢ ❜❡✐♥❣ ✐♥❞❡♣❡♥❞❡♥t ♦❢ ❛❣❡♥ts✬ ❛❝t✐♦♥s✳ ❊❛❝❤ ❛❣❡♥t ❦♥♦✇s t❤❡ ✇❤♦❧❡ s❡t ♦❢ ♣♦ss✐❜❧❡ st❛t❡s ♦❢ t❤❡ ✇♦r❞ ❛♥❞ tr❛❞❡ ❝♦♥t✐♥❣❡♥t ❝❧❛✐♠s✳ ■♥ t❤✐s t❤❡♦r②✱ ❡❛❝❤ ❝♦♠♠♦❞✐t② ✐s ❞❡s❝r✐❜❡❞ ❜② ✐ts ♣❤②s✐❝❛❧ ❝❤❛r❛❝t❡r✐st✐❝s✱ ❜② ✐ts ❧♦❝❛t✐♦♥✱ ✐ts ❞❛t❡ ♦❢ ❛✈❛✐❧❛❜✐❧✐t② ❛♥❞ ❜② t❤❡ st❛t❡ ♦❢ t❤❡ ❡♥✈✐r♦♥♠❡♥t ✐♥ ✇❤✐❝❤ ✐t ✐s ❛✈❛✐❧❛❜❧❡✳ ■t ✐s ❛ss✉♠❡❞ t❤❛t t❤❡r❡ ✐s ❛ ❝♦♠♣❧❡t❡ s❡t ♦❢ ❢✉t✉r❡s ♠❛r❦❡ts✱ ♦♥❡ ❢♦r ❡❛❝❤ s✉❝❤ ❝♦♥t✐♥❣❡♥t ❝❧❛✐♠✳ ❉❡s♣✐t❡ t❤❡ ❢❛❝t t❤❛t t❤✐s t❤❡♦r② ✐s ❛ ✈❡r② ✉s❡❢✉❧ ❢r❛♠❡✇♦r❦ ♦❢ r❡❢❡r❡♥❝❡✱ t❤❡r❡ ❛r❡ ♣❛♣❡rs ❛r❣✉✐♥❣ t❤❛t ✐ts ❡①tr❡♠❡ ❛ss✉♠♣t✐♦♥s ♠❛❦❡ ✐t ❛♥ ✐♥❛❞❡q✉❛t❡ t♦♦❧ ❢♦r r❡♣r❡s❡♥t✐♥❣ t❤❡ ✇♦r❧❞ ✇❡ ❧✐✈❡ ✐♥✳ ❚❤❡s❡ ✇♦r❦s ♣r♦✈✐❞❡ ❛♥♦t❤❡r ❡q✉✐❧✐❜r✐✉♠ ❝♦♥❝❡♣ts ✇❤✐❝❤ r❡❧❛① s♦♠❡ ❛ss✉♠♣t✐♦♥s ♦❢ t❤❡ ❆rr♦✇✲❉❡❜r❡✉ ♠♦❞❡❧✳ ❋♦r ❡①❛♠♣❧❡✱ ❘❛❞♥❡r ✭✶✾✼✷✮ ♣r❡s❡♥ts ❛ ❞❡✜♥✐t✐♦♥ ♦❢ ✐♥❝♦♠♣❧❡t❡ ♠❛r❦❡ts ❛♥❞ ✐♥tr♦❞✉❝❡s t❤❡ ❝♦♥❝❡♣t ♦❢ ❝♦♠♠♦♥ ✭❛♥❞ ❝♦rr❡❝t✮ ❡①♣❡❝t❛t✐♦♥s ✇❤✐❝❤ r❡q✉✐r❡s tr❛❞❡rs t♦ ❛ss♦❝✐❛t❡ t❤❡ s❛♠❡ ❢✉t✉r❡ ♣r✐❝❡s t♦ t❤❡ s❛♠❡ ❢✉t✉r❡ ❡①♦❣❡♥♦✉s ❡✈❡♥ts✱ ❜✉t ❞♦❡s ♥♦t r❡q✉✐r❡ t❤❡♠ t♦ ❛❣r❡❡ ♦♥ t❤❡ ✭s✉❜❥❡❝t✐✈❡✮ ♣r♦❜❛❜✐❧✐t✐❡s ❛ss♦❝✐❛t❡❞ ✇✐t❤ t❤♦s❡ ❡✈❡♥ts✳ ●r❛♥❞♠♦♥t ✭✶✾✼✼✮ ❛r❣✉❡s t❤❛t ✐♥ t❤❡ r❡❛❧ ✇♦r❧❞✱ t❤❡r❡ ✐s ♥♦ s✉❝❤ t❤✐♥❣ ❛s ❛ ❝♦♠♣❧❡t❡ s❡t ♦❢ ❢✉t✉r❡s ♠❛r❦❡ts✱ ♥♦r ❛r❡ t❤❡r❡ ❡♥♦✉❣❤ ✐♥st✐t✉t✐♦♥s ❡♥❛❜❧✐♥❣ t❤❡ ✐♥❞✐✈✐❞✉❛❧s t♦ tr❛♥s❢❡r ✇❡❛❧t❤ ❢r❡❡❧② ♦✈❡r t✐♠❡ ❛♥❞ ❛❝r♦ss st❛t❡s ♦❢ ♥❛t✉r❡✳ ❆❣❡♥ts ❤❛✈❡ ♥❡✐t❤❡r ❛ s✉✣❝✐❡♥t ❦♥♦✇❧❡❞❣❡ ♦❢ t❤❡ ❧❛✇s ♦❢ t❤❡ ❡❝♦♥♦♠✐❝ s②st❡♠ ♥♦r s✉✣❝✐❡♥t ❝♦♠♣✉t✐♥❣ ❝❛♣❛❜✐❧✐t✐❡s t♦ ❜❡ ❛❜❧❡ t♦ ❢♦r❡❝❛st t❤❡ ❢✉t✉r❡ ❛❝❝✉r❛t❡❧②✳ ■♥ ●r❛♥❞♠♦♥t✬s ❛♣♣r♦❛❝❤✱ ❡❝♦♥♦♠✐❝ ❛❣❡♥ts ♣♦ss✐❜❧② ♠❛❦❡ ♠✐st❛❦❡s ✐♥ t❤❡ ❛♥t✐❝✐♣❛t✐♦♥ ♦❢ t❤❡✐r ❢✉t✉r❡ ❡♥✈✐r♦♥♠❡♥t ❛♥❞✱ t❤❡r❡❢♦r❡✱ t❤❡ ♠♦❞❡❧ t❛❦❡s ✐♥t♦ ❛❝❝♦✉♥t ❛ ✏❞✐s❡q✉✐❧✐❜r✐✉♠✑ ♣❤❡♥♦♠❡♥♦♥ ✇❤✐❝❤ ✐s t❤❡ ❢❛❝t t❤❛t ❛t ❛ ❣✐✈❡♥ ❞❛t❡ ❛❣❡♥ts✬ ♣❧❛♥s ❢♦r t❤❡ ❢✉t✉r❡ ❛r❡ ♥♦t ❝♦♦r❞✐♥❛t❡❞ ❛♥❞✱ ❤❡♥❝❡✱ ♠❛② ❜❡ ✐♥❝♦♠♣❛t✐❜❧❡✱ t❤❛t ✐s✱ ❞♦ ♥♦t s❛t✐s❢② t❤❡ ♠❛r❦❡t ❝❧❡❛r✐♥❣ ❝♦♥❞✐t✐♦♥s✳ ●r❛♥❞♦♠♦♥t✬s ♠♦❞❡❧ ❛❧s♦ ❛❞❞r❡ss❡s ❛♥♦t❤❡r ❝♦♥❝❡♣t ♦❢ ✉♥❝❡rt❛✐♥t② ✜rst❧② st✉❞✐❡❞ ✐♥ ❙✈❡♥ss♦♥ ✭✶✾✽✶✮✱ ❝❛❧❧❡❞ ❡♥❞♦❣❡♥♦✉s ✉♥❝❡rt❛✐♥t②✱ ✇❤✐❝❤ ✐s t❤❡ ✐♥❛❝❝✉r❛❝② ✐♥ t❤❡ ❛♥t✐❝✐♣❛t✐♦♥ ♦❢ s♦♠❡ ❢✉t✉r❡ ❛❣❣r❡❣❛t❡ ❡♥❞♦❣❡♥♦✉s ✈❛r✐❛❜❧❡s ❛♥❞✱ ❝♦♥s❡q✉❡♥t❧②✱ ❞❡♣❡♥❞✐♥❣ ♦♥ ❛❣❡♥ts ❝❤♦✐❝❡s✳✶ _{❚❤❡ ❝♦♥❝❡♣t ♦❢ ✉♥❝❡rt❛✐♥t② ❛❜♦✉t ♣r✐❝❡s}

✇❛s ✜rst ❛❞❞r❡ss❡❞ ❜② ❍✐❝❦s ✭✶✾✹✻✱ ✶✾✻✺✮✱ ✉♥❞❡r t❤❡ ❧❛❜❡❧ t❡♠♣♦r❛r② ❡q✉✐❧✐❜r✐✉♠ ❛♥❞ ❛❢t❡r ❜② ❙t✐❣✉♠ ✭✶✾✻✾✮ ✇❤♦ ❛r❣✉❡s t❤❛t t❤❡ ✐♥❛❞❡q✉❛❝② ♦❢ t❤❡ ❆rr♦✇✲❉❡❜r❡✉ ♠♦❞❡❧ ❛r✐s❡s ❢r♦♠ s❡✈❡r❛❧ s♦✉r❝❡s✳ ❋✐rst✱ s✐♥❝❡ t❤❡ ❆rr♦✇✲❉❡❜r❡✉ ♠♦❞❡❧ ❝♦♥❝❡r♥s ❛ ✇♦r❧❞ ✐♥ ✇❤✐❝❤ ❜♦t❤ ❝✉rr❡♥t ❛♥❞ ❢✉t✉r❡ ♣r✐❝❡s ❛r❡ ❞❡t❡r♠✐♥❡❞ ✐♥ t❤❡ ♣r❡s❡♥t✱ ✐t ♥❡❡❞ ♥♦t ✐♥❝♦r♣♦r❛t❡ ❛♥② ❛ss✉♠♣t✐♦♥s ❛❜♦✉t ❤♦✇ ❛ ❝♦♥s✉♠❡r ❢♦r♠s ❤✐s ❡①♣❡❝t❛t✐♦♥s ❛❜♦✉t ❢✉t✉r❡ ♣r✐❝❡s✳ ■♥ ❝♦♥tr❛st✱ ❛ ♠♦❞❡❧ ✇❤✐❝❤ ♣✉r♣♦rts t♦ ❞❡s❝r✐❜❡ t❤❡ ✇❛② ❝♦♥s✉♠❡rs ❜❡❤❛✈❡ ✇❤❡♥ ❢✉t✉r❡ ♣r✐❝❡s ❛r❡ ❞❡t❡r♠✐♥❡❞ ✐♥ ❢✉t✉r❡ ♣❡r✐♦❞s s❤♦✉❧❞ ♣r♦✈✐❞❡ s♦♠❡ ♥♦t✐♦♥ ♦❢ ❤♦✇ t❤❡ ❝♦♥s✉♠❡r✬s ❡①♣❡❝t❛t✐♦♥s ❛❜♦✉t ❢✉t✉r❡ ♣r✐❝❡s

❛r❡ ❞❡t❡r♠✐♥❡❞✳ ❚❤❡ ✏❡q✉✐✈❛❧❡♥t✑ ♠♦❞❡❧✱ ✇❤✐❝❤ ❡st❛❜❧✐s❤❡s t❤❡ ❡q✉✐✈❛❧❡♥❝❡ ♦❢ t❤❡ ❘❛❞♥❡r ❛♥❞ ❆rr♦✇✲❉❡❜r❡✉ ❡q✉✐❧✐❜r✐✉♠ ✐♥ ❝♦♠♣❧❡t❡ ♠❛r❦❡ts✱ ❤♦✇❡✈❡r✱ ❞♦❡s ♥♦t ❞♦ t❤✐s✱ ❛♥❞ s♦ ♠✉st ❜❡ ❥✉❞❣❡❞ ✐♥❛❞❡q✉❛t❡✳ ❙❡❝♦♥❞✱ s✐♥❝❡ ✐♥ ❆rr♦✇ ❛♥❞ ❉❡❜r❡✉✬s ✇♦r❧❞ t❤❡ ❝✉rr❡♥t ❡✈❡♥t ✐s ✇❡❧❧ ❞❡✜♥❡❞ ✐♥❞❡♣❡♥❞❡♥t❧② ♦❢ ❝✉rr❡♥t ♣r✐❝❡s✱ t❤❡ ❝♦♥s✉♠❡r✬s ♣r❡❢❡r❡♥❝❡s ❢♦r ❞✐✛❡r❡♥t ❝♦♠♠♦❞✐t② ❜✉♥❞❧❡s ♠✉st ❜❡ ✐♥❞❡♣❡♥❞❡♥t ♦❢ ❝✉rr❡♥t ♣r✐❝❡s✳ ❚❤✐s ❝♦♥❞✐t✐♦♥✱ ❤♦✇❡✈❡r✱ ❝❛♥♥♦t ❤♦❧❞ ✐♥ ❛ ✇♦r❧❞ ✐♥ ✇❤✐❝❤ ❝♦♥s✉♠❡rs ❤❛✈❡ ♥♦ ♦♣♣♦rt✉♥✐t② t♦ tr❛❞❡ ✐♥ ❝♦♥t✐♥❣❡♥t ❝❧❛✐♠s ♦♥ ❢✉t✉r❡ ❣♦♦❞s✳ ■♥ s✉❝❤ ❛ ✇♦r❧❞ ❛ ❝♦♥s✉♠❡r✬s ❡①♣❡❝t❛t✐♦♥s ❝♦♥❝❡r♥✐♥❣ t❤❡ ❧✐❦❡❧✐❤♦♦❞ ♦❢ ❞✐✛❡r❡♥t ❢✉t✉r❡ ❡✈❡♥ts ✇✐❧❧ ❣❡♥❡r❛❧❧② ❞❡♣❡♥❞ ♦♥ ❝✉rr❡♥t ❛s ✇❡❧❧ ❛s ♣❛st ♣r✐❝❡s✱ ❛♥❞ ❛s ❛ r❡s✉❧t t❤❡ ❝♦♥s✉♠❡r✬s ♦r❞❡r✐♥❣ ♦❢ ❝✉rr❡♥t ❛♥❞ ♦❢ ❢✉t✉r❡ ❝♦♠♠♦❞✐t② ❜✉♥❞❧❡s ✇✐❧❧ ❛❧s♦ ❞❡♣❡♥❞ ♦♥ ❝✉rr❡♥t ♣r✐❝❡s✳

■♥ ❞❡❢❡♥s❡ ♦❢ ❆rr♦✇ ❉❡❜r❡✉ r❛t✐♦♥❛❧✐t②✱ ❜❛s✐❝❛❧❧②✱ t❤❡r❡ ❛r❡ t✇♦ ❡①♣❧❛♥❛t✐♦♥s ♦❢ ❤♦✇ tr❛❞❡rs ❛♥t✐❝✐♣❛t❡ ❡♥❞♦❣❡♥♦✉s ✈❛r✐❛❜❧❡s ❛♥❞ t❤❡ tr✉❡ ♣r♦❜❛❜✐❧✐t② ❞✐str✐❜✉t✐♦♥s ♦✈❡r st❛t❡s ♦❢ t❤❡ ♥❛✲ t✉r❡✳ ❖♥❡ ♣r♦♣♦s❡s t❤❛t ❝♦rr❡❝t ❜❡❧✐❡❢s ❝❛♥ ❜❡ ❧❡❛r♥❡❞✱ t❤❛t ✐s✱ r❛t✐♦♥❛❧ ❡①♣❡❝t❛t✐♦♥s ❛r❡ st❛❜❧❡ st❡❛❞② st❛t❡ ♦❢ ❧❡❛r♥✐♥❣ ❞②♥❛♠✐❝s✳ ❍♦✇❡✈❡r✱ ❇❧✉♠❡ ❛♥❞ ❊❛s❧❡② ✭✶✾✽✷✮ ❛r❣✉❡ t❤❛t ❧❡❛r♥✐♥❣ ❝❛♥♥♦t ♣r♦✈✐❞❡ ❛ s❛t✐s❢❛❝t♦r② ❢♦✉♥❞❛t✐♦♥ ❢♦r r❛t✐♦♥❛❧ ❡①♣❡❝t❛t✐♦♥s ❜❡❝❛✉s❡ ✐♥ ♠♦❞❡❧s ✇❤❡r❡ ❧❡❛r♥✐♥❣ ✇♦r❦s✱ t❤❡ ❧❡❛r♥✐♥❣ r✉❧❡ ✐s t✐❣❤t❧② ❝♦✉♣❧❡❞ t♦ t❤❡ ❡❝♦♥♦♠② ✐♥ q✉❡st✐♦♥✳ ▼♦r❡♦✈❡r✱ t❤❡② ❝❧❛✐♠ t❤❛t ♣♦s✐t✐✈❡ r❡s✉❧ts ❛r❡ ❞❡❧✐❝❛t❡ ❛♥❞ r♦❜✉st r❡s✉❧ts ❛r❡ ♠♦st❧② ♥❡❣❛t✐✈❡✳ ❚❤❡ ♦t❤❡r ❡①♣❧❛♥❛t✐♦♥ ♣♦s✐ts ✏♥❛t✉r❛❧ s❡❧❡❝t✐♦♥✑ ✐♥ ♠❛r❦❡t ❞②♥❛♠✐❝s✳ ❚❤❡ ♠❛r❦❡t s❡❧❡❝t✐♦♥ ❤②✲ ♣♦t❤❡s✐s t❤❛t ♠❛r❦❡ts ❢❛✈♦r r❛t✐♦♥❛❧ tr❛❞❡rs ♦✈❡r ✐rr❛t✐♦♥❛❧ tr❛❞❡rs ❤❛s ❛ ❧♦♥❣ tr❛❞✐t✐♦♥ ✐♥ ❡❝♦♥♦♠✐❝ ❛♥❛❧②s✐s✳ ❆❧❝❤✐❛♥ ✭✶✾✺✵✮ ❛♥❞ ❋r✐❡❞♠❛♥ ✭✶✾✺✸✮ ❜❡❧✐❡✈❡❞ t❤❛t ♠❛r❦❡t s❡❧❡❝t✐♦♥ ♣r❡s✲ s✉r❡ ✇♦✉❧❞ ❡✈❡♥t✉❛❧❧② r❡s✉❧t ✐♥ ❛❝❝✉r❛t❡ ❡①♣❡❝t❛t✐♦♥s❀ t❤♦s❡ ✇❤♦ ❜❡❤❛✈❡ ✐rr❛t✐♦♥❛❧❧② ✇✐❧❧ ❜❡ ❞r✐✈❡♥ ♦✉t ♦❢ t❤❡ ♠❛r❦❡t ❜② t❤♦s❡ ✇❤♦ ❜❡❤❛✈❡ ❛s ✐❢ t❤❡② ❛r❡ r❛t✐♦♥❛❧✳ ❋♦r ♠♦❞❡❧s ✇✐t❤ ❝♦♠♣❧❡t❡ ♠❛r❦❡ts ❛♥❞ ❝♦♠♠♦♥ ❡①♣❡❝t❛t✐♦♥s✱ ❇❧✉♠❡ ❛♥❞ ❊❛s❧❡② ✭✷✵✵✻✮ ❛♥❞ ❙❛♥❞r♦♥✐ ✭✷✵✵✵✮ ♣r♦✈✐❞❡ r❡s✉❧ts ❝♦♥✜r♠✐♥❣ t❤❡ s❡❧❡❝t✐♦♥ ❤②♣♦t❤❡s✐s✳ ❍♦✇❡✈❡r✱ ✐♥ ♠♦❞❡❧s ♦❢ t❡♠♣♦r❛r② ❡q✉✐❧✐❜✲ r✐✉♠ ❛s ✐♥ ●r❛♥❞♠♦♥t ✭✶✾✼✼✮ ✇❡ ❝♦✉❧❞ ❛s❦ ✐❢ ♠❛r❦❡ts ❡✈❡♥t✉❛❧❧② ❢❛✈♦r tr❛❞❡rs ✇✐t❤ ❝♦♠♠♦♥ ❡①♣❡❝t❛t✐♦♥s ✐❢ t❤❡② ❝♦❡①✐st ✇✐t❤ ❛❣❡♥ts ✇✐t❤♦✉t ❛❝❝✉r❛t❡ ❡①♣❡❝t❛t✐♦♥s ❛❜♦✉t t❤❡ ❢✉t✉r❡ ❡♥✲ ❞♦❣❡♥♦✉s ✈❛r✐❛❜❧❡s✱ ✐♥❝❧✉❞✐♥❣ ♣r✐❝❡s✳ ❖♥❡ ♦❢ t❤❡ ❝♦♥tr✐❜✉t✐♦♥s ♦❢ t❤✐s ✇♦r❦ ✐s t♦ ❥✉st✐❢② t❤❡ ❛ss✉♠♣t✐♦♥ ♦❢ ❝♦♠♠♦♥ ❡①♣❡❝t❛t✐♦♥s✱ ✉s✐♥❣ t❤❡ ❝♦♥❝❡♣t ♦❢ ♠❛r❦❡t s❡❧❡❝t✐♦♥ ❛♥❞ t❤❡ ❡①✐st❡♥❝❡ ♦❢ ❛ s❡q✉❡♥t✐❛❧ ❡q✉✐❧✐❜r✐❛ r❡❝✉rs✐✈❡❧② ✐♠♣❧❡♠❡♥t❛❜❧❡ ❜② ❛ r❡❧❛t✐✈❡❧② s✐♠♣❧❡ ❢✉♥❝t✐♦♥ ✇❤✐❝❤ ✐s ❛♥t✐❝✐♣❛t❡❞ ❜② t❤❡ r❛t✐♦♥❛❧ ❛❣❡♥ts✳ ❲❡ ❛❧s♦ ♠♦❞❡❧ ❛♥ ❡❝♦♥♦♠② ✇✐t❤ ❛♥❞ ✇✐t❤♦✉t ❛❣❡♥ts ❛♥t✐❝✐♣❛t✐♥❣ ❝♦rr❡❝t❧② t❤❡ ❡♥❞♦❣❡♥♦✉s ✈❛r✐❛❜❧❡s ❛♥❞ s❤♦✇ t❤❛t t❤❡r❡ ❡①✐sts ❛ s❡q✉❡♥t✐❛❧ ❡q✉✐✲ ❧✐❜r✐✉♠✳ ▼♦r❡♦✈❡r✱ ✇❡ ❣✐✈❡ ♥✉♠❡r✐❝❛❧ ❡①❛♠♣❧❡s ♦❢ ❡❝♦♥♦♠✐❡s ✇✐t❤ ✐♥❝♦♠♣❧❡t❡ ♠❛r❦❡ts ❛♥❞ ❛❧❧ ❛❣❡♥ts ❤❛✈✐♥❣ ❝♦♠♠♦♥ ❡①♣❡❝t❛t✐♦♥s s✉❝❤ t❤❛t ♦♥❡ ✇✐t❤ ✐♥❝♦rr❡❝t ❡①♣❡❝t❛t✐♦♥s ❞♦♠✐♥❛t❡s t❤❡ ♠❛r❦❡t ❡✈❡♥ ✐❢ t❤❡ ♦t❤❡r ❤❛s r❛t✐♦♥❛❧ ❡①♣❡❝t❛t✐♦♥s✳ ❇❧✉♠❡ ❛♥❞ ❊❛s❧❡② ✭✷✵✵✻✮ ♣r❡s❡♥t ❛♥ ❡①❛♠♣❧❡ ✐♥ ✇❤✐❝❤ t❤✐s ♣❤❡♥♦♠❡♥♦♥ ♦❝❝✉rs✳

■♥ ❈❤❛♣t❡r ✶ ✇❡ ♠♦❞❡❧ ❛ ❝❧❛ss ♦❢ ✐♥✜♥✐t❡ ❤♦r✐③♦♥ ❡❝♦♥♦♠✐❡s ✇✐t❤ t✇♦ t②♣❡s ♦❢ ❛❣❡♥ts✳ ❆❣❡♥ts ♦❢ t❤❡ ✜rst t②♣❡ ❛♥t✐❝✐♣❛t❡ ❝♦rr❡❝t❧② ❛❧❧ ❢✉t✉r❡ ❝♦♥t✐♥❣❡♥t ♣r✐❝❡s ✇✐t❤ ❝♦♠♠♦♥ ❡①♣❡❝✲ t❛t✐♦♥s ❛♥❞ ❛❣❡♥ts ♦❢ t❤❡ s❡❝♦♥❞ t②♣❡ ❤❛✈❡ ❡①♦❣❡♥♦✉s ❡①♣❡❝t❛t✐♦♥s ♦❢ ❢✉t✉r❡ ♣r✐❝❡s ❜❛s❡❞ ♦♥ t❤❡ ❝✉rr❡♥t ❛♥❞ ♣❛st ❛❣❣r❡❣❛t❡ ✈❛r✐❛❜❧❡s✳ ❲❡ ♣r♦✈❡ ❡①✐st❡♥❝❡ ♦❢ ❛♥ ❡q✉✐❧✐❜r✐✉♠ ✐♥ ✇❤✐❝❤ t❤❡s❡ t✇♦ t②♣❡s ❝♦❡①✐st ✐♥ ❡❛❝❤ ♣❡r✐♦❞✳✷ _{❆❣❡♥ts ♠❛② ❤❛✈❡ ✐♥❝♦♥s✐st❡♥t ♦♣t✐♠❛❧ ❢✉t✉r❡ ♣❧❛♥s ❜✉t}

♣r❡❢❡r❡♥❝❡s ✇✐t❤ ♣r❡❞✐❝t✐✈❡ ❜❡❧✐❡❢s ✐♥ t❤❡ ❝♦♥t❡①t ♦❢ ❇❧❛❝❦✇❡❧❧ ❛♥❞ ❉✉❜✐♥s ✭✶✾✻✷✮✳ ❚❤✐s ❝♦♥✲ str✉❝t✐♦♥ ❛❧❧♦✇s ✉s t♦ ❞❡✈❡❧♦♣ t❤✐s ♠♦❞❡❧ ✐♥ ❛♥ ❡♥✈✐r♦♥♠❡♥t ✇❤❡r❡ ❛❣❡♥ts ❤❛✈❡ ❤❡t❡r♦❣❡♥❡♦✉s ❜❡❧✐❡❢s ✭❝♦rr❡❝t ♦r ✐♥❝♦rr❡❝t✮ ✐♥ t❤❡ ❡♥❞♦❣❡♥♦✉s ✈❛r✐❛❜❧❡s✱ ✇❤✐❝❤ ❞♦❡s ♥♦t ❤❛♣♣❡♥ ✐♥ ♠♦❞❡❧s ♦❢

✷_{❍♦✇❡✈❡r ❛❧❧ r❡s✉❧ts ♦❢ t❤✐s ✇♦r❦ ❦❡❡♣ ✉♥❛❧t❡r❡❞ ✐❢ ✇❡ ❝♦♥s✐❞❡r ❛❣❣r❡❣❛t❡ ✈❛r✐❛❜❧❡s ❞❡♣❡♥❞✐♥❣ ♦♥ ♦t❤❡r}

❆rr♦✇✲❉❡❜r❡✉ ❛♥❞ ❘❛❞♥❡r✳ ▼♦r❡♦✈❡r✱ ✉♥❞❡r t❤❡ ❛ss✉♠♣t✐♦♥ ♦❢ ♣r❡❞✐❝t✐✈❡ ❜❡❧✐❡❢s✱ ✐t ✐s ♣♦ss✐✲ ❜❧❡ t♦ ✇r✐t❡ t❤❡ ❛❣❡♥ts✬ ❞❡♠❛♥❞ r❡❝✉rs✐✈❡❧②✱ t❤❛t ✐s✱ ❛❧❧ ❢✉t✉r❡ r❡❧❡✈❛♥t ❝❤♦✐❝❡s ❝❛♥ ❜❡ r❡❞✉❝❡❞ t♦ ❛ ❝✉rr❡♥t ♣❡r✐♦❞ ♠❛①✐♠✐③❛t✐♦♥ ♦❢ ❛ ✈❛❧✉❡ ❢✉♥❝t✐♦♥ ✇❤✐❝❤ ②✐❡❧❞s t❤❡ ✉t✐❧✐t② ♦❢ ❢✉t✉r❡ ♣❧❛♥s ❣✐✈❡♥ t❤❡ ❝✉rr❡♥t ❝❤♦✐❝❡s✳ ❚❤❡ ♠❛✐♥ ❝♦♥tr✐❜✉t✐♦♥ ♦❢ t❤✐s ❝❤❛♣t❡r ✐s t♦ s❤♦✇ t❤❛t t❤❡r❡ ❡①✐sts ❛ s❡q✉❡♥t✐❛❧ ❡q✉✐❧✐❜r✐✉♠ ❢♦r t❤✐s ❡❝♦♥♦♠②✱ t❤❛t ✐s✱ ❛❣❡♥ts ✇✐t❤ r❛t✐♦♥❛❧ ❡①♣❡❝t❛t✐♦♥s ❝♦❡①✐st ✇✐t❤ ❛❣❡♥ts ✇✐t❤ ❡①♦❣❡♥♦✉s ❡①♣❡❝t❛t✐♦♥s ✐♥ t❤✐s ❡q✉✐❧✐❜r✐✉♠✳ ❚❤❡r❡❢♦r❡ ✇❡ ❡①t❡♥❞ t❤❡ r❡s✉❧t ♦❢ ●r❛♥❞♠♦♥t ✭✶✾✼✼✮ ❛♥❞ ❏♦r❞❛♥ ✭✶✾✼✼✮✱ s❤♦✇✐♥❣ ❡①✐st❡♥❝❡ ♦❢ ❡q✉✐❧✐❜r✐✉♠ ❢♦r ❡❝♦♥♦♠✐❡s ✇✐t❤ ❛❣❡♥ts ❤❛✈✐♥❣ ❝♦♠♠♦♥ ✭❛♥❞ ❝♦rr❡❝t✮ ❡①♣❡❝t❛t✐♦♥s ❛♥❞ ❛❣❡♥ts ✇✐t❤ ❡①♦❣❡♥♦✉s ❡①♣❡❝t❛t✐♦♥s✳

■♥ ❈❤❛♣t❡r ✷ ✇❡ ♠♦❞❡❧ ❡❝♦♥♦♠✐❡s s✉❝❤ t❤❛t t❤❡ s❡q✉❡♥t✐❛❧ ❡q✉✐❧✐❜r✐✉♠ ❝❛♥ ❜❡ ✐♠♣❧❡✲ ♠❡♥t❡❞ ❜② ❛ tr❛♥s✐t✐♦♥ ❢✉♥❝t✐♦♥ ✇❤✐❝❤ ❛ss♦❝✐❛t❡s ❛♥ ❡❧❡♠❡♥t ♦❢ t❤❡ ❝✉rr❡♥t ♦❜s❡r✈❡❞ r❡❧❡✈❛♥t s❡t ♦❢ ❛❣❣r❡❣❛t❡ ✈❛r✐❛❜❧❡s✱ ✭❝❛❧❧❡❞ st❛t❡ s♣❛❝❡✮ ✇✐t❤ ♥❡①t ♣❡r✐♦❞ ❡q✉✐❧✐❜r✐✉♠ ✈❛r✐❛❜❧❡s ♦❢ t❤❡ ❡❝♦♥♦♠②✱ ❝❛❧❧❡❞ r❡❝✉rs✐✈❡ ❡q✉✐❧✐❜r✐✉♠ ✐♥ t❤✐s ❝❛s❡✳ ❘♦✉❣❤❧② s♣❡❛❦✐♥❣✱ ✇❡ tr② t♦ ✜♥❞ ❛ r❡❝✉r✲ s✐✈❡ ❡q✉✐❧✐❜r✐✉♠ ❢♦r t✇♦ ❡❝♦♥♦♠✐❡s✳ ■♥ t❤❡ ✜rst✱ ✇❡ s✉♣♣♦s❡ t❤❛t ❛❧❧ ❛❣❡♥ts ❤❛✈❡ ❡①♦❣❡♥♦✉s ❡①♣❡❝t❛t✐♦♥s ♦♥ ❡♥❞♦❣❡♥♦✉s ✈❛r✐❛❜❧❡s ❛♥❞ ✐♥ t❤❡ s❡❝♦♥❞ ✇❡ ❝♦♥s✐❞❡r ♦♥❡ t②♣❡ ❤❛✈✐♥❣ ❡①♦❣❡✲ ♥♦✉s ❡①♣❡❝t❛t✐♦♥s ♦♥ ❡♥❞♦❣❡♥♦✉s ✈❛r✐❛❜❧❡s ❛♥❞ ♦t❤❡r t②♣❡ ✇✐t❤ ❝♦rr❡❝t ❡①♣❡❝t❛t✐♦♥s ♦♥ t❤❡ ♣r✐❝❡ tr❛♥s✐t✐♦♥ ❢✉♥❝t✐♦♥✳

❛♥ ❖▲● ♠♦❞❡❧✱ ✇❤❡r❡ t❤❡r❡ ❛r❡ ✜♥✐t❡❧② ♠❛♥② ❝♦♠♠♦❞✐t✐❡s ❛♥❞ ❝♦♥s✉♠❡rs ✐♥ ❡❛❝❤ ♣❡r✐♦❞ ❛♥❞ t❤❡ st❛t❡ s♣❛❝❡ ✐s t❛❦❡♥ ❛s t❤❡ s❡t ♦❢ ❛❧❧ ♣❛②♦✛✲r❡❧❡✈❛♥t ✈❛r✐❛❜❧❡s✳ ■♥ ♠♦❞❡❧s s✉❝❤ t❤❛t ♠❛r❦❡ts r❡♦♣❡♥ s❡q✉❡♥t✐❛❧❧② ❛♥❞ t❤❡ s❡q✉❡♥t✐❛❧ ❡q✉✐❧✐❜r✐✉♠ ✐s ❞❡✜♥❡❞ ❢♦r ❡❛❝❤ ♣❡r✐♦❞ ♦❢ t✐♠❡✱ t❤❡ ❡①✐st❡♥❝❡ ♦❢ s✉❝❤ tr❛♥s✐t✐♦♥ ❢✉♥❝t✐♦♥ ❞❡✜♥❡❞ ✐♥ ❛ r❡❞✉❝❡❞ s❡t ♦❢ ✈❛r✐❛❜❧❡s ❛♥❞ ❞❡t❡r♠✐♥✲ ✐♥❣ t❤❡ ❡q✉✐❧✐❜r✐✉♠ ♦✈❡r ❝♦♥s❡❝✉t✐✈❡ ♣❡r✐♦❞s ♣r♦✈✐❞❡s ❛ t♦♦❧ t♦ ❝♦♠♣✉t❡ ✐t ❛♥❞ t♦ st✉❞② t❤❡ ❞②♥❛♠✐❝s ♦❢ t❤❡ st❛t❡ ✈❛r✐❛❜❧❡ ❡✈♦❧✉t✐♦♥✳ ■♥ t❤✐s ❝❤❛♣t❡r ✇❡ ❛❧s♦ ❡♠♣❤❛s✐③❡ t❤❡ ✐♠♣♦rt❛♥❝❡ ♦❢ t❤❡ r❡s✉❧ts ❛❜♦✉t ❡①✐st❡♥❝❡ ♦❢ r❡❝✉rs✐✈❡ ❡q✉✐❧✐❜r✐✉♠ ✇✐t❤ ❛ r❡❞✉❝❡❞ st❛t❡ s♣❛❝❡ ❜❡❝❛✉s❡ ✐t ❝❛♥ ❜❡ ✈✐❡✇❡❞ ❛s ❛ ❞❡❢❡♥s❡ ♦❢ t❤❡ ❝♦♠♠♦♥ ❡①♣❡❝t❛t✐♦♥s✳ ■♥❞❡❡❞✱ ✐❢ t❤❡ s❡q✉❡♥t✐❛❧ ❡q✉✐❧✐❜r✐✉♠ ✐s ✐♠♣❧❡♠❡♥t❡❞ ❜② ❛ r❡❝✉rs✐✈❡ ❡q✉✐❧✐❜r✐✉♠ ✇✐t❤ ❛ r❡❞✉❝❡❞ st❛t❡ s♣❛❝❡✱ t❤❡♥ ♣r✐❝❡s ❝❛♥ ❜❡ ❛♥t✐❝✐♣❛t❡❞ ❝♦rr❡❝t❧② ✉s✐♥❣ t❤❡ r❡❝✉rs✐✈❡ str✉❝t✉r❡ ❛♥❞ ❤❡♥❝❡ ❛❣❡♥ts ♦♥❧② ♥❡❡❞ t♦ ❛♥t✐❝✐♣❛t❡ ❛ r❡❧❛t✐✈❡ s✐♠♣❧❡ ♣r✐❝❡ tr❛♥s✐t✐♦♥ ❢✉♥❝t✐♦♥ ✐♥st❡❛❞ ♦❢ ❛❧❧ ❢✉t✉r❡ ❝♦♥t✐♥❣❡♥t ❡q✉✐❧✐❜r✐✉♠ ♣r✐❝❡s ✐ts❡❧❢ ❛s ❛ss✉♠❡❞ ✐♥ ❘❛❞♥❡r ✭✶✾✼✷✮ ♦r ▼❛❣✐❧❧ ❛♥❞ ◗✉✐♥③✐✐ ✭✶✾✾✹✮ ❢♦r ❡①❛♠♣❧❡✳ ❲❡ ❝❛♥ ✜♥❞ ❛✉t❤♦rs ✉s✐♥❣ t❤❡ ❡①✐st❡♥❝❡ ♦❢ r❡❝✉rs✐✈❡ ❡q✉✐❧✐❜r✐✉♠ ❛s ❛ ❞❡❢❡♥s❡ ♦❢ r❛t✐♦♥❛❧✐t②✱ ❢♦r ❡①❛♠♣❧❡✱ ●✉❡s♥❡r✐❡ ❛♥❞ ❲♦♦❞❢♦r❞ ✭✶✾✾✷✮ ❙❡❝t✐♦♥ ✸✱ ✏❛♥ ❡q✉✐❧✐❜r✐✉♠ ✇❤✐❝❤ ❞♦❡s ♥♦t ❞✐s♣❧❛② ♠✐♥✐♠❛❧ r❡❣✉❧❛r✐t② t❤r♦✉❣❤ t✐♠❡ ✲♠❛②❜❡ st❛t✐♦♥❛r✐t②✲ ✐s ✉♥❧✐❦❡❧② t♦ ❣❡♥❡r❛t❡ t❤❡ ❝♦♦r❞✐♥❛t✐♦♥ ❜❡t✇❡❡♥ ❛❣❡♥ts t❤❛t ✐t ❛ss✉♠❡s✳✑ ❚❤❡ ❡①✐st❡♥❝❡ ♦❢ r❡❝✉rs✐✈❡ ❡q✉✐❧✐❜r✐✉♠ ❝❛♥ ❛❧s♦ ❜❡ ✉s❡❞ t♦ ❥✉st✐❢② t❤❡ ❝♦rr❡❝t ❛♥t✐❝✐♣❛t✐♦♥ ♦❢ t❤❡ ❡♥❞♦❣❡♥♦✉s ✈❛r✐❛❜❧❡s ♦❢ t❤❡ ❡❝♦♥♦♠② ✉s✐♥❣ ❛ ♠❛r❦❡t s❡❧❡❝t✐♦♥ ❛r❣✉♠❡♥t✳ ■♥ ❢❛❝t✱ ✐♥ ❛♥ ❡❝♦♥♦♠② ✇✐t❤ ❛ s❡q✉❡♥t✐❛❧ ❡q✉✐❧✐❜r✐✉♠ ✐♠♣❧❡♠❡♥t❡❞ ❜② ❝♦♥t✐♥✉♦✉s r❡❝✉rs✐✈❡ ❡q✉✐❧✐❜r✐✉♠ ❛♥❞ t✇♦ t②♣❡s ♦❢ ❛❣❡♥ts✱ ✇❡ ♣r♦✈❡ t❤❛t t❤❡ ♦♥❡ ✇❤♦ ♠❛❦❡s ♣❡rs✐st❡♥t ♠✐st❛❦❡s ♦♥ t❤❡ r✉❧❡s ♦❢ ❛♥t✐❝✐♣❛t✐♦♥ ♦❢ t❤❡ ❢✉t✉r❡ ❡♥❞♦❣❡♥♦✉s ✈❛r✐❛❜❧❡s ✐s ❞r✐✈❡♥ ♦✉t ♦❢ t❤❡ ♠❛r❦❡t ❜② t❤❡ ♦t❤❡rs ✇✐t❤ ❝♦rr❡❝t ❡①♣❡❝t❛t✐♦♥ ❢✉♥❝t✐♦♥s ♦❢ t❤❡ ✈❛r✐❛❜❧❡s✱ t❤❛t ✐s✱ t❤❡ r❛t✐♦♥❛❧ ❡①♣❡❝t❛t✐♦♥s ❛❣❡♥ts✳ ❆❧t❤♦✉❣❤ ✇❡ ❞♦ ♥♦t s❤♦✇ ❡①✐st❡♥❝❡ ♦❢ ❛ ❝♦♥t✐♥✉♦✉s r❡❝✉rs✐✈❡ ❡q✉✐❧✐❜r✐✉♠ ✐♥ ✇❤✐❝❤ s♦♠❡ ❛❣❡♥t ❤❛✈❡ r❛t✐♦♥❛❧ ❡①♣❡❝t❛t✐♦♥s✱ ✇❡ ❣✐✈❡ ❛♥ ❡①❛♠♣❧❡ ♦❢ ❛♥ ❡❝♦♥♦♠② ✇✐t❤ t❤✐s ♣r♦♣❡rt② ❛♥❞ s❤♦✇ t❤❛t ✉♥✐q✉❡♥❡ss ♦❢ t❤❡ r❡❝✉rs✐✈❡ ❡q✉✐❧✐❜r✐✉♠ ✐♠♣❧✐❡s ❝♦♥t✐♥✉✐t②✱ ♣r♦✈✐❞✐♥❣ ❛♥♦t❤❡r ❡①❛♠♣❧❡ ♦❢ ❛♥ ❡❝♦♥♦♠② ✇✐t❤ ❛ ✉♥✐q✉❡ ❝♦♥t✐♥✉♦✉s r❡❝✉rs✐✈❡ ❡q✉✐❧✐❜r✐✉♠✳ ❆♥♦t❤❡r ❝♦♥tr✐❜✉t✐♦♥ ♦❢ t❤✐s ✇♦r❦ ✐s t♦ s❤♦✇ ❡①✐st❡♥❝❡ ♦❢ ❘❊ ✐♥ ❛ ♠♦❞❡❧ s✉❝❤ ❛s ●r❛♥❞♠♦♥t ✭✶✾✼✼✮ ✇❤❡r❡ ✐t ✐s ❛ss✉♠❡❞ t❤❛t ❛❣❡♥ts ❤❛✈❡ ❡①♦❣❡♥♦✉s ❡①♣❡❝t❛t✐♦♥s ♦♥ ❡♥❞♦❣❡♥♦✉s ✈❛r✐❛❜❧❡s✱ ❜✉t ❝♦♥tr❛r② t♦ ●r❛♥❞♠♦♥t ✭✶✾✼✼✮✱ ✇❡ ❞♦ ♥♦t ❛ss✉♠❡ t❤❛t ❛❣❡♥ts ❛r❡ ♠②♦♣✐❝✳✸ _{❚❤❡ st❛t❡ s♣❛❝❡}

✐s ❝♦♠♣♦s❡❞ ♦❢ ♣❛st ♠❡❛♥ ♣♦rt❢♦❧✐♦ ❞✐str✐❜✉t✐♦♥ ❛♥❞ t❤❡ ❝✉rr❡♥t st❛t❡ ♦❢ ♥❛t✉r❡ ❛♥❞ ❞♦❡s ♥♦t ✐♥❝❧✉❞❡ ❛❧❧ ♣❛②♦✛ r❡❧❡✈❛♥t ✈❛r✐❛❜❧❡s ❛s ✐♥ ❚❛❦❡♦❦❛ ✭✷✵✵✻✮ ♦r ❉✉✣❡ ❡t ❛❧✳ ✭✶✾✾✹✮✳ ■♥ t❤❡ ❝❛s❡ ♦❢ r❛t✐♦♥❛❧ ❡①♣❡❝t❛t✐♦♥s ❛♥❞ ❤❡t❡r♦❣❡♥❡♦✉s ❛❣❡♥ts✱ ❑✉❜❧❡r ❛♥❞ ❙❝❤♠❡❞❞❡rs ✭✷✵✵✷✮ ❤❛✈❡ s❤♦✇♥ ❡①❛♠♣❧❡s ✐♥ ✇❤✐❝❤ ❘❊ ♣r✐❝❡s ♠✉st ❞❡♣❡♥❞ ♦♥ ♣♦rt❢♦❧✐♦ ❞✐str✐❜✉t✐♦♥ ❛♥❞ ❝♦♥❝❧✉❞❡ t❤❛t t❤❡ ♠✐♥✐♠❛❧ st❛t❡ s♣❛❝❡ ♥❡❝❡ss❛r✐❧② ❝♦♥t❛✐♥s t❤❡ ❛❣❣r❡❣❛t❡ ♣♦rt❢♦❧✐♦ ❞✐str✐❜✉t✐♦♥ ♦❢ t❤❡ ❡❝♦♥♦♠②✳ ❙✐♥❝❡ ✇❡ ♣r♦✈❡ t❤❛t t❤❡ st❛t❡ s♣❛❝❡ ❝♦♥t❛✐♥s ♦♥❧② t❤❡ ♣❛st ❛❣❣r❡❣❛t❡ ♣♦rt❢♦❧✐♦ ❞✐str✐❜✉t✐♦♥ ❛♥❞ t❤❡ ❝✉rr❡♥t st❛t❡ ♦❢ ♥❛t✉r❡✱ ✐t ✐s ❛❧s♦ ❝❧❡❛r ❤❡r❡ t❤❛t t❤❡ ❘❊ ❤❛s ❛ ♠✐♥✐♠❛❧ st❛t❡ s♣❛❝❡ ❜② t❤❡ s❛♠❡ r❡❛s♦♥s ❣✐✈❡♥ ✐♥ ❑✉❜❧❡r ❛♥❞ ❙❝❤♠❡❞❞❡rs ✭✷✵✵✷✮✳ ❚❤❡ ✐♥t✉✐t✐♦♥ ❢♦r t❤✐s ❢❛❝t ✐s t❤❛t ✐♥ ❡❝♦♥♦♠✐❡s ✇✐t❤ r✐s❦ ❛✈❡rs✐♦♥ ❤❡t❡r♦❣❡♥❡✐t② ❢♦r ❡①❛♠♣❧❡✱ t❤❡ r❡❛❧❧♦❝❛t✐♦♥ ♦❢ t❤❡ ❛ss❡t s❤❛r❡s ❢r♦♠ ♦♥❡ ❛❣❡♥t t♦ ❛♥♦t❤❡r ✇✐t❤ ❣r❡❛t❡r r✐s❦ ❛✈❡rs✐♦♥ ✇♦✉❧❞ t②♣✐❝❛❧❧② r❡q✉✐r❡ ❛ ♥❡✇ s❡t ♦❢ ❡q✉✐❧✐❜r✐✉♠ ♣r✐❝❡s✳ ❯♥❞❡r s♦♠❡ ❝♦♥❞✐t✐♦♥s ♦♥ t❤❡ ❜❡❧✐❡❢s✱ ✇❡ ♣r♦✈❡ ❡①✐st❡♥❝❡ ♦❢ ❡q✉✐❧✐❜r✐✉♠ ✇✐t❤ ❛t ❧❡❛st ♦♥❡ ❛❣❡♥t ❛♥t✐❝✐♣❛t✐♥❣ ❝♦rr❡❝t❧② t❤❡ ♣r✐❝❡ tr❛♥s✐t✐♦♥ ❢✉♥❝t✐♦♥✱ ✇❤✐❝❤ ✐s ❛ ❞❡❢❡♥s❡ ♦❢ t❤❡ ❡①✐st❡♥❝❡ ♦❢ ♦♥❡ ❛❣❡♥t ✇✐t❤ ❛❝❝✉r❛❝② ♦♥ t❤❡ ♣r✐❝❡ ❡①♣❡❝t❛t✐♦♥s s✐♥❝❡ t❤✐s tr❛♥s✐t✐♦♥ ❢✉♥❝t✐♦♥ ✐♠♣❧❡♠❡♥ts ❛❧❧ ❢✉t✉r❡ ❝♦♥t✐♥❣❡♥t ♣r✐❝❡s ✐♥ t❤❡ ❡❝♦♥♦♠②✳

✸_{❇❛s✐❝❛❧❧②✱ ✇❡ s❛② t❤❛t ♦♥❡ ❛❣❡♥t ✐s ♠②♦♣✐❝ ✇❤❡♥ ❤❡ t❛❦❡s ✐♥t♦ ❛❝❝♦✉♥t ❛t ♠♦st ♦♥❡ ♣❡r✐♦❞ ❢♦r✇❛r❞ ♦❢ t❤❡}

■♥ ❝❤❛♣t❡r ✸ ✇❡ ♣r♦✈✐❞❡ s❡✈❡r❛❧ ♥✉♠❡r✐❝❛❧ ❡①❛♠♣❧❡s ❝❤❛♥❣✐♥❣ t❤❡ ♣r❡❢❡r❡♥❝❡s ❛♥❞ ❜❡❧✐❡❢s✱ ❦❡❡♣✐♥❣ t❤❡ ❝♦♠♠♦♥ ❡①♣❡❝t❛t✐♦♥s ❛ss✉♠♣t✐♦♥ ♦♥ ♣r✐❝❡s✳ ❚❤❡r❡ ✐s ❛ ❤✉❣❡ ❧✐t❡r❛t✉r❡ r❡❧❛t❡❞ t♦ s✉r✈✐✈❛❧ ✇✐t❤ ❝♦♠♠♦♥ ❡①♣❡❝t❛t✐♦♥s✳ ❚r❛❞✐t✐♦♥❛❧ ❡❝♦♥♦♠✐❝ t❤❡♦r② ❛r❣✉❡s t❤❛t ♠❛r❦❡ts ❢❛✈♦r r❛t✐♦♥❛❧ ✐♥✈❡st♦rs ♦✈❡r ✐rr❛t✐♦♥❛❧ ✐♥✈❡st♦rs ❛♥❞ ❛s ❛ ❝♦♥s❡q✉❡♥❝❡ ♦♥❧② t❤❡ r❛t✐♦♥❛❧ ♦♥❡s s✉r✈✐✈❡ ✭❙❡❡ ❆❧❝❤✐❛♥ ✭✶✾✺✵✮✱ ❋r✐❡❞♠❛♥ ✭✶✾✺✸✮✱ ❙❛♥❞r♦♥✐ ✭✷✵✵✵✮✱ ❇❧✉♠❡ ❛♥❞ ❊❛s❧❡② ✭✷✵✵✻✮ ❢♦r ❡①❛♠♣❧❡✮✳ ❋♦r ✐♥st❛♥❝❡✱ ✐♥❛❝❝✉r❛t❡ ❜❡❧✐❡❢s✱ ❛s ❛ ♣♦ss✐❜❧❡ ❢♦r♠ ♦❢ ✐rr❛t✐♦♥❛❧✐t②✱ ❝❛✉s❡ ❛❣❡♥ts t♦ ♠❛❦❡ ✇r♦♥❣ ✐♥✈❡st♠❡♥t ❞❡❝✐s✐♦♥s ❛♥❞ ❤❡♥❝❡ t♦ ❧♦s❡ t❤❡✐r ✇❡❛❧t❤ ✐♥ ❢❛✈♦r ♦❢ ❛❣❡♥ts ✇✐t❤ ♠♦r❡ ❛❝❝✉r❛t❡ ❜❡❧✐❡❢s✳ ❚❤❡r❡❢♦r❡✱ ❛❣❡♥ts ✇✐t❤ ❛❝❝✉r❛t❡ ❜❡❧✐❡❢s ❛❝❝✉♠✉❧❛t❡ ❛❧❧ t❤❡ ✇❡❛❧t❤ ❛♥❞ ❞r✐✈❡ t❤❡ ♦♥❡s ✇✐t❤ ✐♥❛❝❝✉r❛t❡ ❜❡❧✐❡❢s ♦✉t ♦❢ t❤❡ ♠❛r❦❡t✳ ❉❡▲♦♥❣ ❡t ❛❧✳ ✭✶✾✾✵✮ ❛♥❛❧②③❡ s❡❧❡❝t✐♦♥ ♦✈❡r tr❛❞❡rs ✇❤♦ ❛r❡ s✉❜❥❡❝t✐✈❡ ❡①♣❡❝t❡❞ ✉t✐❧✐t② ♠❛①✐♠✐③❡rs ✇✐t❤ ❞✐✛❡r✐♥❣ ❜❡❧✐❡❢s✳ ■♥ t❤❡✐r ♣❛♣❡r✱ t❤❡② ❛r❣✉❡ t❤❛t tr❛❞❡rs ✇❤♦s❡ ❜❡❧✐❡❢s r❡✢❡❝t ✐rr❛t✐♦♥❛❧ ♦✈❡r❝♦♥✜❞❡♥❝❡ ❝❛♥ ❡✈❡♥t✉❛❧❧② ❞♦♠✐♥❛t❡ ❛♥ ❛ss❡t ♠❛r❦❡t ✐♥ ✇❤✐❝❤ ♣r✐❝❡s ❛r❡ s❡t ❡①♦❣❡♥♦✉s❧②✳ ❚❤✐s r❡s✉❧t ❛♣♣❡❛rs t♦ ❝♦♥tr❛❞✐❝t t❤❡ ❝♦♥❝❧✉s✐♦♥s ♦❢ ❆❧❝❤✐❛♥ ❛♥❞ ❋r✐❡❞♠❛♥✳ ❍♦✇❡✈❡r✱ ❛s ♣r✐❝❡s ❛r❡ ❡①♦❣❡♥♦✉s✱ t❤❡s❡ tr❛❞❡rs ❛r❡ ♥♦t r❡❛❧❧② tr❛❞✐♥❣ ✇✐t❤ ❡❛❝❤ ♦t❤❡r❀ ✐❢ t❤❡② ✇❡r❡✱ t❤❡♥ ✇❤❡♥❡✈❡r tr❛❞❡rs ✇✐t❤ ✐♥❝♦rr❡❝t ❜❡❧✐❡❢s ❞♦♠✐♥❛t❡ t❤❡ ♠❛r❦❡t✱ ♣r✐❝❡s ✇♦✉❧❞ r❡✢❡❝t t❤❡✐r ❜❡❧✐❡❢s ❛♥❞ r❛t✐♦♥❛❧ tr❛❞❡rs ♠✐❣❤t ❜❡ ❛❜❧❡ t♦ t❛❦❡ ❛❞✈❛♥t❛❣❡ ♦❢ t❤❡♠✳ ■♥ ❛♥ ❡❝♦♥♦♠② ✇✐t❤ ❝♦♠♣❧❡t❡ ♠❛r❦❡ts✱ ❛♥❞ tr❛❞❡rs ✇✐t❤ ❛ ❝♦♠♠♦♥ ❞✐s❝♦✉♥t ❢❛❝t♦r✱ t❤❡ ✐♥t✉✐t✐♦♥s ♦❢ ❆❧❝❤✐❛♥ ❛♥❞ ❋r✐❡❞♠❛♥ ✇❡r❡ ❝♦rr❡❝t✳ ❙❛♥❞r♦♥✐ ✭✷✵✵✵✮ s❤♦✇s t❤❛t✱ ✐♥ ❛ ▲✉❝❛s tr❡❡ ❡❝♦♥♦♠②✱ t❤❡ tr❛❞❡rs ✇✐t❤ r❛t✐♦♥❛❧ ❡①♣❡❝t❛t✐♦♥s ❞♦♠✐♥❛t❡ t❤❡ ♠❛r❦❡t✳ ❇❧✉♠❡ ❛♥❞ ❊❛s❧❡② ✭✷✵✵✻✮ s❤♦✇ t❤❛t t❤✐s r❡s✉❧t ❤♦❧❞s ✐♥ ❛♥② P❛r❡t♦ ♦♣t✐♠❛❧ ❛❧❧♦❝❛t✐♦♥ ❢♦r ❛♥② ❜♦✉♥❞❡❞ ❝❧❛ss✐❝❛❧ ❡❝♦♥♦♠②✱ ❛♥❞ t❤✉s ❢♦r ❛♥② ❝♦♠♣❧❡t❡ ♠❛r❦❡ts ❡q✉✐❧✐❜r✐✉♠✳ ❖♥❡ ❝♦♥tr✐❜✉t✐♦♥ ♦❢ ❈❤❛♣t❡r ✸ ✐s t♦ s❤♦✇ t❤❛t ❛ r❡❝✉rs✐✈❡ ❡q✉✐❧✐❜r✐✉♠ ✇✐t❤ t❤❡ st❛t❡ s♣❛❝❡ ❝♦♥s✐st✐♥❣ ♦❢ t❤❡ ♣r❡✈✐♦✉s ❛❣❣r❡❣❛t❡ ♣♦rt❢♦❧✐♦ ❞✐str✐❜✉t✐♦♥ ❛♥❞ t❤❡ ❝✉rr❡♥t st❛t❡ ♦❢ ♥❛t✉r❡ ✐♠♣❧❡♠❡♥ts ❛♥ ❡q✉✐❧✐❜r✐✉♠ ♦❢ t❤❡ s❡q✉❡♥t✐❛❧ ❡❝♦♥♦♠②✳ ❚❤✐s r❡s✉❧t ❛❧❧♦✇s ✉s t♦ ❝♦♠♣✉t❡ ❛ s❡q✉❡♥t✐❛❧ ❡q✉✐❧✐❜r✐✉♠✹ _{❜② ✉s✐♥❣ ❛ ♥✉♠❡r✐❝❛❧ ♠❡t❤♦❞ ❝♦♥str✉❝t❡❞ ✐♥ ❛ ♠❛♥♥❡r}

s✐♠✐❧❛r t♦ t❤❛t ❢♦✉♥❞ ✐♥ ❏✉❞❞ ✭✶✾✾✽✮ ✇❤✐❝❤ ❝♦♠♣✉t❡s s♦❧✉t✐♦♥s ♦❢ ❢✉♥❝t✐♦♥❛❧ ❡q✉❛t✐♦♥s ❜② ❛♥ ✐t❡r❛t✐♦♥ ❛❧❣♦r✐t❤♠✳ ❚❤♦s❡ ❡①❛♠♣❧❡s ✐❧❧✉str❛t❡ t❤❛t t❤❡ r❡s✉❧ts ♦❢ ❙❛♥❞r♦♥✐ ✭✷✵✵✵✮ ❛♥❞ ❇❧✉♠❡ ❛♥❞ ❊❛s❧❡② ✭✷✵✵✻✮✱ ✇❤✐❝❤ ❛ss✉r❡ t❤❡ ❞♦♠✐♥❛♥❝❡ ♦❢ r❛t✐♦♥❛❧ ❛❣❡♥ts ✐♥ t❤❡ ❧♦♥❣ r✉♥✱ ♠❛② ❢❛✐❧ ✇❤❡♥ t❤❡ ✜♥❛♥❝✐❛❧ ♠❛r❦❡ts ❛r❡ ✐♥❝♦♠♣❧❡t❡✳ ◆♦t✐❝❡ t❤❛t ❇❧✉♠❡ ❛♥❞ ❊❛s❧❡② ✭✷✵✵✻✮ ❛❧s♦ ♣r❡s❡♥t ❛♥ ❡①❛♠♣❧❡ ♦❢ ❛♥ ❡❝♦♥♦♠② ✇✐t❤ ✐♥❝♦♠♣❧❡t❡ ♠❛r❦❡ts ❛♥❞ s❤♦rt s❛❧❡s ✐♥ ✇❤✐❝❤ ✐rr❛t✐♦♥❛❧ tr❛❞❡rs s✉r✈✐✈❡ ✐♥ ❛ ♠❛r❦❡t ❡♥❞♦✇❡❞ ✇✐t❤ r❛t✐♦♥❛❧ ❛❣❡♥ts✳ ❇❛s✐❝❛❧❧②✱ ✇❡ ❣✐✈❡ ❡①❛♠♣❧❡s ♦♥ t❤❡ ♠♦❞❡❧s ✇✐t❤ r❛t✐♦♥❛❧ ❡①♣❡❝t❛t✐♦♥s ❛♥❞ ❤❡t❡r♦❣❡♥❡♦✉s ✐♥❝♦♠❡✱ ♥♦✐s❡ tr❛❞❡rs✱ ❛♠❜✐❣✉✐t② ❛✈❡rs✐♦♥✱ ♣r♦s♣❡❝t t❤❡♦r② ❛♥❞ ❜❡❤❛✈✐♦r❛❧ ✜♥❛♥❝❡✳ ❘♦✉❣❤❧② s♣❡❛❦✐♥❣ ❛❜♦✉t t❤❡ ❡①❛♠♣❧❡s✱ ✇❡ ❝❛❧❧ ♥♦✐s❡ tr❛❞❡rs t❤♦s❡ ✇✐t❤ ❛❝❝✉r❛t❡ ♣r❡❝✐s✐♦♥ ❛❜♦✉t t❤❡ ♠❡❛♥ ❛ss❡t ♣r✐❝❡ ❛♥❞ ✐♥❛❝❝✉r❛t❡ ♣r❡❝✐s✐♦♥ ♦❢ t❤❡ ✈❛r✐❛♥❝❡✳ ❲❡ ❛❞❞r❡ss t❤❡ ❛♠❜✐❣✉✐t② ❛✈❡rs✐♦♥ ❝♦♥s✐❞❡r✐♥❣ ❛❣❡♥ts ✇✐t❤ ♠❛①♠✐♥ ❡①♣❡❝t❡❞ ✉t✐❧✐t② ♦✈❡r ❛❧❧ ♣r♦❜❛❜✐❧✐t② ❞✐str✐❜✉t✐♦♥s t❤❛t ❤❡ s✉♣♣♦s❡s ♣♦ss✐❜❧❡ ✉♥❞❡r ❤✐s ❜❡❧✐❡❢s✳ Pr♦s♣❡❝t t❤❡♦r② ✐s ❛♥ ❛♣♣r♦❛❝❤ ✐♥ ✇❤✐❝❤ ❛❣❡♥ts ♦✈❡r✇❡✐❣❤t ♦✉t❝♦♠❡s t❤❛t ❛r❡ ❝♦♥s✐❞❡r❡❞ ❝❡rt❛✐♥ r❡❧❛t✐✈❡ t♦ ♦✉t❝♦♠❡s t❤❛t ❛r❡ ❝♦♥s✐❞❡r❡❞ ✉♥❝❡rt❛✐♥✳ ❇❡❤❛✈✐♦r❛❧ ✜♥❛♥❝❡ ❝❤❛r❛❝t❡r✐③❡s ❛❣❡♥ts ❡st✐♠❛t✐♥❣ t❤❡ ❡①♦❣❡♥♦✉s s❤♦❝❦ ✇✐t❤ ❜❡❧✐❡❢s ❝❤❛r❛❝t❡r✐③❡❞ ❜② ❛ ▼❛r❦♦✈ s✇✐t❝❤✐♥❣ r❡❣✐♠❡ ✇❤✐❝❤ ✐s ❛ ❦✐♥❞ ♦❢ ❜❡❧✐❡❢s ❝♦♥s✐st❡♥t ✇✐t❤ ♣r✐❝❡ ✉♥❞❡rr❡❛❝t✐♦♥ t♦ ❤✐❣❤❡r s❤♦❝❦s ❛♥❞ ♣r✐❝❡ ♦✈❡rr❡❛❝t✐♦♥ t♦ ❧♦✇❡r s❤♦❝❦s✳ ■♥ t❤❡ ❡❝♦♥♦♠✐❡s ✇✐t❤ ♦♥❡ ❛ss❡t ❛♥❞ t✇♦ ❛❣❡♥ts ❛❧❧ ♥✉♠❡r✐❝❛❧ r❡s✉❧ts ❝♦♥✜r♠ ❇❡❦❡r ❛♥❞ ❈❤❛tt♦♣❛❞❤②❛② ✭✷✵✵✾✮ ✇❤✐❝❤ st❛t❡s t❤❛t ❛t ❧❡❛st ♦♥❡ ❛❣❡♥t ♠✉st ❤❛✈❡ ♥✉❧❧ ❛s②♠♣t♦t✐❝ ❝♦♥s✉♠♣t✐♦♥✱ ♣r♦✈✐❞❡❞ t❤❛t ❛❣❡♥ts ❞♦ ♥♦t ❤❛✈❡ ♣❡r✐♦❞✐❝ ✐♥❝♦♠❡✳

❈❤❛♣t❡r ✶

❊①✐st❡♥❝❡ ♦❢ ❊q✉✐❧✐❜r✐✉♠ ✐♥ ▼❛r❦❡ts ✇✐t❤

■♥✜♥✐t❡ ❍♦r✐③♦♥ ❛♥❞ ❊♥❞♦❣❡♥♦✉s

❯♥❝❡rt❛✐♥t②

❚❤✐s ❝❤❛♣t❡r ✐s ♦r❣❛♥✐③❡❞ ❛s ❢♦❧❧♦✇s✳ ■♥ ❙❡❝t✐♦♥ ✶ ✇❡ ❞❡✈❡❧♦♣ t❤❡ ❡♥✈✐r♦♥♠❡♥t ♦❢ t❤❡ ❡❝♦♥✲ ♦♠② ❛♥❞ ❞❡s❝r✐❜❡ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ ❛❣❡♥ts ✇✐t❤ ❡①♦❣❡♥♦✉s ❡①♣❡❝t❛t✐♦♥s ❛♥❞ ❛❣❡♥ts ✇✐t❤ r❛t✐♦♥❛❧ ❡①♣❡❝t❛t✐♦♥s ❛♥❞ ❞❡✜♥❡ t❤❡ ❡q✉✐❧✐❜r✐✉♠✳ ■♥ ❙❡❝t✐♦♥ ✷ ✇❡ ❞❡t❛✐❧ t❤❡ ❞❡♠❛♥❞ ❝❤❛r✲ ❛❝t❡r✐st✐❝s ❢♦r ❛❣❡♥ts ✇✐t❤ ❡①♦❣❡♥♦✉s ❡①♣❡❝t❛t✐♦♥s✳ ■♥ ❙❡❝t✐♦♥ ✹ ✇❡ s❤♦✇ t❤❡ ❡①✐st❡♥❝❡ ♦❢ ❡q✉✐❧✐❜r✐✉♠✳ ❙❡❝t✐♦♥ ✺ ✐s t❤❡ ❛♣♣❡♥❞✐①✳

✶✳✶ ❚❤❡ ♠♦❞❡❧

❚❤❡ ❡♥✈✐r♦♥♠❡♥t ♦❢ t❤❡ ♠♦❞❡❧s ✐♥ t❤✐s ❝❤❛♣t❡r ❤❛✈❡ t❤❡ ❢♦❧❧♦✇✐♥❣ ❢❡❛t✉r❡s✳ ❊❛❝❤ ❝♦♠♠♦❞✐t② ✐s ❞❡s❝r✐❜❡❞ ❜② ✐ts ♣❤②s✐❝❛❧ ❝❤❛r❛❝t❡r✐st✐❝s✱ ❜② ✐ts ❧♦❝❛t✐♦♥ ❛♥❞ ✐ts ❞❛t❡ ♦❢ ❛✈❛✐❧❛❜✐❧✐t②✱ ❛♥❞ ❜② t❤❡ st❛t❡ ♦❢ t❤❡ ❡♥✈✐r♦♥♠❡♥t✶ _{✐♥ ✇❤✐❝❤ ✐t ✐s ❛✈❛✐❧❛❜❧❡✳ ■t ✐s ❛ss✉♠❡❞ t❤❛t tr❛♥s❛❝t✐♦♥s}

❛r❡ ❝♦st❧❡ss✱ ❛♥❞ t❤❛t ❛❞❥✉st♠❡♥ts ❛r❡ ♠❛❞❡ ♦♥❧② ❜② ♣r✐❝❡ ♠♦✈❡♠❡♥ts✳ ▼❛r❦❡ts ♠❛② ❜❡ ✐♥❝♦♠♣❧❡t❡ ❛♥❞ r❡♦♣❡♥ s❡q✉❡♥t✐❛❧❧② ✇✐t❤ ❛❣❡♥ts ♠❛❦✐♥❣ ♣❧❛♥s ❢♦r ❢✉t✉r❡ ❝❤♦✐❝❡s ❝♦♥t✐♥❣❡♥t t♦ ❛❧❧ ♣♦ss✐❜❧❡ st❛t❡s ♦❢ t❤❡ ❡♥✈✐r♦♥♠❡♥t✳ ❆t ❡❛❝❤ ♣❡r✐♦❞✱ ❛♥ ❡q✉✐❧✐❜r✐✉♠ ✐s ❛ s❡t ♦❢ ♣r✐❝❡s ♦♥ t❤❡ ❝✉rr❡♥t ♣❡r✐♦❞ ❛♥❞ ❛ s❡t ♦❢ ✐♥❞✐✈✐❞✉❛❧ ♣❧❛♥s✱ ♦♥❡ ❢♦r ❡❛❝❤ tr❛❞❡r✱ s✉❝❤ t❤❛t✱ ❣✐✈❡♥ t❤❡ ❝✉rr❡♥t ♣r✐❝❡s✱ ❡❛❝❤ ✐♥❞✐✈✐❞✉❛❧ tr❛❞❡r✬s ♣❧❛♥ ✐s ♦♣t✐♠❛❧ ❢♦r ❤✐♠✱ s✉❜❥❡❝t t♦ ❛♥ ❛♣♣r♦♣r✐❛t❡ s❡q✉❡♥❝❡ ♦❢ ❜✉❞❣❡t ❝♦♥str❛✐♥ts✳ ▼♦r❡♦✈❡r✱ ❛t ❡❛❝❤ ♣❡r✐♦❞✱ t❤❡ ❝✉rr❡♥t ❝❤♦s❡♥ ❛❧❧♦❝❛t✐♦♥ ♦❢ ❣♦♦❞s ❛♥❞ ❛ss❡ts ✉♥❞❡r t❤♦s❡ ♣r✐❝❡s s❛t✐s❢② t❤❡ ♠❛r❦❡t ❝❧❡❛r✐♥❣ ❝♦♥❞✐t✐♦♥s✱ t❤❛t ✐s✱ ❛r❡ ❝♦♠♣❛t✐❜❧❡✳ ❆❣❡♥ts ♣♦ss✐❜❧② ♠❛❦❡ ♠✐st❛❦❡s ✐♥ t❤❡ ❛♥t✐❝✐♣❛t✐♦♥ ♦❢ t❤❡✐r ❢✉t✉r❡ ❡♥✈✐r♦♥♠❡♥t ❛♥❞✱ t❤❡r❡❢♦r❡✱ t❤❡ ♠♦❞❡❧ t❛❦❡s ✐♥t♦ ❛❝❝♦✉♥t ❛ ✏❞✐s❡q✉✐❧✐❜r✐✉♠✑ ♣❤❡♥♦♠❡♥♦♥ ✇❤✐❝❤ ✐s t❤❡ ❢❛❝t t❤❛t✱ ❛t ❛ ❣✐✈❡♥ ❞❛t❡✱ ❛❣❡♥ts✬ ♣❧❛♥s ❢♦r t❤❡ ❢✉t✉r❡ ❛r❡ ♥♦t ❝♦♦r❞✐♥❛t❡❞ ❛♥❞✱ ❤❡♥❝❡✱ ♠❛② ❜❡ ✐♥❝♦♠♣❛t✐❜❧❡✳

✼

✶✳✶✳✶ ❇❛s✐❝ ❞❡✜♥✐t✐♦♥s

❲❡ ❡①❛♠✐♥❡ ❛♥ ✐♥✜♥✐t❡ ❤♦r✐③♦♥ ❡❝♦♥♦♠② ✇✐t❤ ❛ ✜♥✐t❡ s❡t I ♦❢ ❤❡t❡r♦❣❡♥❡♦✉s ❛❣❡♥ts✳ ❚✐♠❡

✐s ✐♥❞❡①❡❞ ❜② t❤❡ s❡t N _{= {1,2,3...}} ❛♥❞ ✐s ❞❡♥♦t❡❞ ❜② _t ✇❤❡♥ ✐t r❡♣r❡s❡♥ts t❤❡ ❝✉rr❡♥t ♣❡r✐♦❞ ❛♥❞ r ∈ {0,1,2,3...} ✇❤❡♥ ✐t r❡♣r❡s❡♥ts ❛ ♣❧❛♥♥❡❞ ♣❡r✐♦❞✳ ❲❡ s✉♣♣♦s❡ t❤❛t t❤❡r❡

❡①✐sts ♦♥❧② ♦♥❡✷ _{♣❡r✐s❤❛❜❧❡ ❣♦♦❞ ✇✐t❤ ♣r✐❝❡ ❛t ♣❡r✐♦❞ t ❞❡♥♦t❡❞ ❜② q}c

t ❛♥❞✸ H = {1, ..., H}

❧♦♥❣✲❧✐✈❡❞ ❛ss❡ts t❤❛t ❛❧❧♦✇ ❛❣❡♥ts t♦ tr❛♥s❢❡r ✇❡❛❧t❤ ❜❡t✇❡❡♥ t✇♦ ❝♦♥s❡❝✉t✐✈❡ ♣❡r✐♦❞s ✇✐t❤ ♣r✐❝❡ ❛t ♣❡r✐♦❞t ❞❡♥♦t❡❞ ❜②qa

t = (qta1, ..., qtha)∈RH+✳ ❚❤❡r❡ ✐s ♥♦ ❡①♦❣❡♥♦✉s ✉♥❝❡rt❛✐♥t②✿ t❤❡

✉♥❝❡rt❛✐♥t② ✐s ❡♥❞♦❣❡♥♦✉s ✐♥ t❤❡ s❡♥s❡ t❤❛t ✐t ❞❡♣❡♥❞s ♦♥ ❛❣❡♥t✬s ❛❝t✐♦♥s ❜❡❝❛✉s❡ t❤❡② ♠❛② ❛♥t✐❝✐♣❛t❡ ✐♥❝♦rr❡❝t❧② t❤❡ ❡q✉✐❧✐❜r✐✉♠ ♣r✐❝❡s✳

❆❣❡♥ts ❤❛✈❡ t❤❡ ❢♦❧❧♦✇✐♥❣ ❝❤❛r❛❝t❡r✐st✐❝s✳ ✶✳ ❈♦♥✈❡① ❝♦♥s✉♠♣t✐♦♥ s❡t✿ Ci _⊂R

+ ❢♦r i∈I✳

✷✳ ❈♦♥✈❡① ♣♦rt❢♦❧✐♦ s❡t✿ Θi _⊂RH

+✳ ❖❜s❡r✈❡ t❤❛t ✇❡ ❛r❡ ♥♦t ❛❧❧♦✇✐♥❣ ❢♦r s❤♦rt✲s❛❧❡s✳

✸✳ ❊①♦❣❡♥♦✉s ✐♥✐t✐❛❧ ♣♦rt❢♦❧✐♦ θi

0 ∈Θi s❛t✐s❢②✐♥❣✹

P

i∈Iθ0i =1∈RH+✳

✹✳ ❊♥❞♦✇♠❡♥t ♦❢ ❣♦♦❞ ❛t ♣❡r✐♦❞ t✿ ei

t ∈ R+ ✉♥✐❢♦r♠❧② ❜♦✉♥❞❡❞ ❢r♦♠ ❛❜♦✈❡ ♦✈❡r t✐♠❡✱

t❤❛t ✐s✱ ei

t≤e¯∈R++ ❢♦r ❛❧❧ i∈I ❛♥❞ t∈N.

✺✳ ❉✐s❝♦✉♥t ❢❛❝t♦r 0< βi _<1✳

✻✳ ■♥st❛♥t❛♥❡♦✉s ✉t✐❧✐t② ❢✉♥❝t✐♦♥ ui

t : R+ → R+ ❝♦♥❝❛✈❡✱ ❝♦♥t✐♥✉♦✉s✱ str✐❝t❧② ✐♥❝r❡❛s✐♥❣

❛♥❞ ✉♥✐❢♦r♠❧② ❜♦✉♥❞❡❞ ♦✈❡r t✐♠❡✱ t❤❛t ✐s✱ t❤❡r❡ ❡①✐stsMi _{>0s✉❝❤ t❤❛tu}i

t(ci)≤Mi ❢♦r

❛❧❧t∈N❛♥❞ ❛❧❧_ci _∈Ci✳ ❚❤❡ ✈❛❧✉❡_ui

t(ci)✐s t❤❡ s❛t✐s❢❛❝t✐♦♥ ❛t ♣❡r✐♦❞t❢♦r ❝♦♥s✉♠✐♥❣ci

✉♥✐ts ♦❢ t❤❡ ❣♦♦❞✳ ❚❤❡ ❜♦✉♥❞❡❞♥❡ss ♦❢ ui

t r❡♣r❡s❡♥ts t❤❡ ✐♠♣❛t✐❡♥❝❡ ✐♥ t❤❡ ♣r❡❢❡r❡♥❝❡s

s✐♥❝❡ t❤❡ ❞✐s❝♦✉♥t ❢❛❝t♦r s❛t✐s✜❡s βi _{<1 ❛♥❞ ❤❡♥❝❡(β}i₎t_ui

t(cit) ✈❛♥✐s❤❡s ✐♥ t❤❡ ❧♦♥❣ r✉♥

❢♦r ❡✈❡r② str❡❛♠ ♦❢ ❝♦♥s✉♠♣t✐♦♥ {ci t}t∈N✳

❘♦✉❣❤❧② s♣❡❛❦✐♥❣✱ ❛t ❡❛❝❤ ❞❛t❡✱ ❛❣❡♥ts ♠❛❦❡ ♣❧❛♥s ❢♦r ❢✉t✉r❡ ❝♦♥s✉♠♣t✐♦♥ ❧❡✈❡❧ ❛♥❞ ♣♦rt✲ ❢♦❧✐♦ ❤♦❧❞✐♥❣s ❢❡❛s✐❜❧❡✺ _{❢r♦♠ ❛ ❝✉rr❡♥t ♣r✐❝❡ ❛♥❞ ♣❛st ❛ss❡t ❡♥❞♦✇♠❡♥ts✱ ❛♥❞ ❝♦♥t✐♥❣❡♥t t♦ ❛❧❧}

♣♦ss✐❜❧❡ r❡❛❧✐③❛t✐♦♥s ♦❢ ♣r✐❝❡s✳ ❚❤❡② ❝❤♦♦s❡ t❤❡ ♦♣t✐♠❛❧ ♣♦rt❢♦❧✐♦ ❛♥❞ ❝♦♥s✉♠♣t✐♦♥ ♠❛①✐♠✐③✲ ✐♥❣✱ ♦✈❡r ❛❧❧ ❢❡❛s✐❜❧❡ ❢✉t✉r❡ ❝♦♥s✉♠♣t✐♦♥ ♣❧❛♥s✱ t❤❡ ❡①♣❡❝t❡❞ ❞✐s❝♦✉♥t❡❞ s✉♠ ♦❢ ✐♥st❛♥t❛♥❡♦✉s ✉t✐❧✐t② ❢✉♥❝t✐♦♥s✱ ❡✈❛❧✉❛t❡❞ ❛t t❤❡s❡ ♣❧❛♥s✱ ✇✐t❤ r❡s♣❡❝t t♦ t❤❡✐r s✉❜❥❡❝t✐✈❡ ❜❡❧✐❡❢s✳ ❲❡ ❛ss✉♠❡ t❤❛t ❛❣❡♥ts ❤❛✈❡ ✐♥❢♦r♠❛t✐♦♥ ♦♥❧② ❛❜♦✉t t❤❡✐r ♦✇♥ ❜❡❧✐❡❢s ❛♥❞ ♣r❡❢❡r❡♥❝❡s✳

◆♦t❛t✐♦♥ ✶✳✶✳✶✳ ❲❡ ❞❡♥♦t❡ ❜② Q = {(qc_{, q}a_{) ∈ R}H+1

+ : qcs+q1a+...+qah = 1} ❜❡ t❤❡ s❡t ♦❢

❣♦♦❞ ❛♥❞ ❛ss❡t ♣r✐❝❡s ✇✐t❤ ❛ t②♣✐❝❛❧ ❡❧❡♠❡♥t q = (qc_{, q}a_{)✳ ❋♦r ❡❛❝❤ s ∈N ✇r✐t❡ C}i

s,Θis, Qs ❛

❝♦♣② ♦❢ t❤❡ s❡tsCi_,Θi_{, Qr❡s♣❡❝t✐✈❡❧②✳ ❉❡✜♥❡ ❢♦r ❛❧❧ r, s∈N✿}

Qr_s =Qs×Qs+1× · · · ×Qs+r−1 qrs = (qs, qs+1, ..., qs+r−1)∈Qrs

Q∞

s =Qs×Qs+1× · · · q∞s = (qs, qs+1, qs+2, ...)∈Q∞s

C_si,r =C_si ×C_si₊₁× · · · ×C_si_+r−1 ci,r

s = (cis, cis+1..., cis+r−1)∈Csi,r.

✷_{❚❤✐s ♠♦❞❡❧ ❝❛♥ ❜❡ ❣❡♥❡r❛❧✐③❡❞ ❢♦r ❛ ✜♥✐t❡ s❡t ♦❢ ❣♦♦❞s✳ ❆❧❧ r❡s✉❧ts r❡♠❛✐♥ ✉♥❝❤❛♥❣❡❞ s✐♥❝❡ ✇❡ ❞❡✜♥❡ t❤❡}

❞❡♠❛♥❞ ❛s ❛ ❝♦rr❡s♣♦♥❞❡♥❝❡ ❛♥❞ ❛❧❧ t❤❡ ❛r❣✉♠❡♥ts ✉s❡❞ ✐♥ t❤❡ ♣r♦♦❢s ❤♦❧❞ ❢♦r ❝♦rr❡s♣♦♥❞❡♥❝❡s✳

✸_{❲❡ ❞❡♥♦t❡ t❤❡ ❝❛r❞✐♥❛❧✐t② ♦❢ t❤❡ s❡t ✇✐t❤ t❤❡ s❛♠❡ s②♠❜♦❧ t♦ s✐♠♣❧✐❢②✳} ✹_{❲❡ ✇r✐t❡1:= (1, ...,1)∈}RH