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HAL Id: inria-00594908

https://hal.inria.fr/inria-00594908

Submitted on 21 May 2011

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3D Mapping of indoor environments with a time of

flight camera

Rodrigo Baravalle, Amaury Nègre

To cite this version:

Rodrigo Baravalle, Amaury Nègre. 3D Mapping of indoor environments with a time of flight camera.

[Technical Report] RT-0406, INRIA. 2011, 12p. �inria-00594908�

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a p p o r t

t e c h n i q u e

ISSN 0249-0803 ISRN INRIA/R T --0406--FR+ENG Domaine 1

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

3D Mapping of indoor environments with a time of

flight camera

Rodrigo Baravalle — Amaury Nègre

N° 0406

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Centre de recherche INRIA Grenoble – Rhône-Alpes 655, avenue de l’Europe, 38334 Montbonnot Saint Ismier

Téléphone : +33 4 76 61 52 00 — Télécopie +33 4 76 61 52 52

✸❉ ▼❛♣♣✐♥❣ ♦❢ ✐♥❞♦♦r ❡♥✈✐r♦♥♠❡♥ts ✇✐t❤ ❛ t✐♠❡

♦❢ ✢✐❣❤t ❝❛♠❡r❛

❘♦❞r✐❣♦ ❇❛r❛✈❛❧❧❡✱ ❆♠❛✉r② ◆è❣r❡

❉♦♠❛✐♥❡ ✿ ▼❛t❤é♠❛t✐q✉❡s ❛♣♣❧✐q✉é❡s✱ ❝❛❧❝✉❧ ❡t s✐♠✉❧❛t✐♦♥ ➱q✉✐♣❡✲Pr♦❥❡t ❡✲♠♦t✐♦♥ ❘❛♣♣♦rt t❡❝❤♥✐q✉❡ ♥➦ ✵✹✵✻ ✖ ❋❡❜r✉❛r② ✷✵✶✵ ✖ ✶✷ ♣❛❣❡s ❆❜str❛❝t✿ ■♥ t❤✐s ✇♦r❦ ✇❡ ♠❛❦❡ ❛ ✸❉ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ❛♥ ✐♥❞♦♦r ❡♥✈✐r♦♥♠❡♥t s✉rr♦✉♥❞✐♥❣ ❛ r♦❜♦t✳ ❙♦ ✇❡ ❛ss✉♠❡ ❛♥ st❛t✐❝ ❡♥✈✐r♦♥♠❡♥t✳ ❲❡ ✉s❡❞ ❛ ❙✇✐s✲ sr❛♥❣❡r ❙❘✹✵✵✵ ❝❛♠❡r❛ t♦ ❣❡t ✸❉ ♣♦✐♥t ❝❧♦✉❞s ♦❢ t❤❡ ❡♥✈✐r♦♥♠❡♥t✱ ❛♥❞ ❘❖❙ ❢♦r ✐♠♣❧❡♠❡♥t✐♥❣ t❤❡ s♦❢t✇❛r❡✳ ❲✐t❤ t❤❡s❡ ✐♥❢♦r♠❛t✐♦♥ ❛♥❞ t❤❡ ♣♦s✐t✐♦♥ ♦❢ t❤❡ r♦❜♦t✱ ✇❡ ❛r❡ ❛❜❧❡ t♦ ❝♦♥str✉❝t ❛ ✸❉ ♠❛♣ ✐♥ r❡❛❧ t✐♠❡✳ ❑❡②✲✇♦r❞s✿ ✸❞ ♠❛♣♣✐♥❣✱ s❧❛♠✱ ♦❝tr❡❡

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✸❉ ▼❛♣♣✐♥❣ ♦❢ ✐♥❞♦♦r ❡♥✈✐r♦♥♠❡♥ts ✇✐t❤ ❛ t✐♠❡

♦❢ ✢✐❣❤t ❝❛♠❡r❛

❘és✉♠é ✿ ❉❛♥s ❝❡t ❞♦❝✉♠❡♥t✱ ♥♦✉s ♣rés❡♥t♦♥s ♥♦s tr❛✈❛✉① s✉r ❧❛ ❝❛rt♦❣r❛♣❤✐❡ ✸❉ ❞✬✉♥ ❡♥✈✐r♦♥♥❡♠❡♥t ✐♥tér✐❡✉r st❛t✐q✉❡ ❞❛♥s ❧❡q✉❡❧ s❡ ❞é♣❧❛❝❡ ✉♥ r♦❜♦t✳ ◆♦✉s ✉t✐❧✐s♦♥s ✉♥❡ ❝❛♠ér❛ ✸❉ ❙✇✐ssr❛♥❣❡r ❙❘✹✵✵✵ ♣♦✉r ♦❜t❡♥✐r ✉♥ ♥✉❛❣❡ ❞❡ ♣♦✐♥ts ✸❉ ❞❡ ❧✬❡♥✈✐r♦♥♥❡♠❡♥t✳ ❆✈❡❝ ❝❡s ♠❡s✉r❡s ♣❧✉s ❧❛ ♣♦s✐t✐♦♥ ❞✉ r♦❜♦t ✭♦❜t❡♥✉ ❛✈❡❝ ✉♥ ❙▲❆▼ ✷❉✮✱ ♥♦✉s s♦♠♠❡ ❝❛♣❛❜❧❡s ❞❡ r❡❝♦♥str✉✐r❡ ❧✬❡♥✈✐r♦♥♥❡♠❡♥t ✸❉ ❡♥ t❡♠♣s ré❡❧✳ ▼♦ts✲❝❧és ✿ r❡❝♦♥str✉❝t✐♦♥ ✸❉✱ ♦❝tr❡❡

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✸❉ ▼❛♣♣✐♥❣ ♦❢ ✐♥❞♦♦r ❡♥✈✐r♦♥♠❡♥ts ✇✐t❤ ❛ t✐♠❡ ♦❢ ✢✐❣❤t ❝❛♠❡r❛ ✸

❈♦♥t❡♥ts

✶ ■♥tr♦❞✉❝t✐♦♥ ✹ ✷ ❍❛r❞✇❛r❡ ✹ ✷✳✶ s✇✐ssr❛♥❣❡r ❙❘✹✵✵✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✷✳✷ ▼❚✐ ①s❡♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✸ ❇❧✉❡ ❇♦t✐❝s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✸ ❙♦❢t✇❛r❡ ✺ ✸✳✶ ❘♦❜♦t ❖♣❡r❛t✐♥❣ ❙②st❡♠ ✭❘❖❙✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✸✳✶✳✶ ❯t✐❧✐t✐❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✹ ✸❉ ▼❛♣♣✐♥❣ ✼ ✹✳✶ ▼❛✐♥ ■❞❡❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✹✳✷ ▲♦❝❛❧✐③❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✹✳✸ ■♠♣❧❡♠❡♥t❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✺ ❘❡s✉❧ts ✶✵ ✻ ❈♦♥❝❧✉s✐♦♥s ✶✵ ✼ ❋✉t✉r❡ ❲♦r❦ ✶✷ ❘❚ ♥➦ ✵✹✵✻

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✸❉ ▼❛♣♣✐♥❣ ♦❢ ✐♥❞♦♦r ❡♥✈✐r♦♥♠❡♥ts ✇✐t❤ ❛ t✐♠❡ ♦❢ ✢✐❣❤t ❝❛♠❡r❛ ✹

✶ ■♥tr♦❞✉❝t✐♦♥

✸❉ ♠❛♣♣✐♥❣ ❤❛s ❜❡❡♥ r❡❝❡✐✈✐♥❣ ❣r❡❛t ❛tt❡♥t✐♦♥ ♦✈❡r t❤❡ ♣❛st ②❡❛rs✳ ❖♥❡ ♦❢ t❤❡ ♠❛✐♥ r❡❛s♦♥s ❢♦r t❤✐s ✐s t❤❡ ❡✈♦❧✉t✐♦♥ ♦❢ t❤❡ ❤❛r❞✇❛r❡ ❛♥❞ t❤❡ ♣♦ss✐❜✐❧✐t② ♦❢ ♠❛♥✲ ❛❣✐♥❣ ❣r❡❛t ❛♠♦✉♥ts ♦❢ ❞❛t❛✳ ✸❉ ♠❛♣s ❤❛✈❡ ❛♣♣❧✐❝❛t✐♦♥s ✐♥ r♦❜♦t ♥❛✈✐❣❛t✐♦♥✱ ♠❛♥✐♣✉❧❛t✐♦♥✱ t❡❧❡♣r❡s❡♥❝❡✱ ❣❛♠❡s✱ ❡t❝✳ ❚❤❡ ♣❛st ②❡❛r t❤❡ ❑✐♥❡❝t✶✱ ❛ ❝♦♥tr♦❧❧❡r ❞❡✈❡❧♦♣❡❞ ❢♦r t❤❡ ❳❜♦① ✸✻✵ ✇❛s ✉s❡❞ ❢♦r t❤✐s ♣✉r♣♦s❡✱ ❛s ❝❛♥ ❜❡ s❡❡♥ ✐♥ ❬✸❪✳ ▼❛♥② ✸❉ ♠❛♣♣✐♥❣ ❛❧❣♦r✐t❤♠s ❜✉✐❧❞ ✸❉ ♠❛♣s t❛❦✐♥❣ ✐♥t♦ ❛❝❝♦✉♥t ❛❝t✉❛❧ ❞❛t❛ ❝♦♠✐♥❣ ❢r♦♠ s❡♥s♦rs✱ ✇✐t❤♦✉t t❤❡ ❤❡❧♣ ♦❢ ❛♥② ♦t❤❡r ✐♥❢♦r♠❛t✐♦♥✳ ❍❡r❡✱ ✇❡ ♣r♦♣♦s❡ t♦ ✉s❡ ✷❉ ♠❛♣s ♦❢ t❤❡ s❛♠❡ ❡♥✈✐r♦♥♠❡♥t✱ ✐♥ ♦r❞❡r t♦ ✉s❡ ♣r❡✈✐♦✉s❧② ❝❛❧❝✉❧❛t❡❞ ✐♥❢♦r♠❛t✐♦♥✳ ▼♦r❡ s♣❡❝✐✜❝❛❧❧②✱ ✜rst ✇❡ ❜✉✐❧❞ ❛ ✷❉ ♠❛♣ ♦❢ t❤❡ ❡♥✈✐✲ r♦♥♠❡♥t✱ ✐♥ ✇❤✐❝❤ ✇❡ t❛❦❡ ✐♥t♦ ❛❝❝♦✉♥t t❤❡ ♣r♦❜❧❡♠ ♦❢ ❧♦♦♣ ❝❧♦s✉r❡✱ ❛♥❞ t❤❡♥ ✇❡ s✐♠♣❧② ❛❞❞ ❞❛t❛ ❝♦♠✐♥❣ ❢r♦♠ t❤❡ ✸❉ ❝❛♠❡r❛✳ ■♥ t❤✐s ✇❛②✱ ✇❡ ❝♦✉❧❞ s✐♠♣❧✐❢② t❤❡ ♠❛♣♣✐♥❣ ♣r♦❝❡ss✳ ❚❤❡ ❛✐♠ ♦❢ t❤✐s ✇♦r❦ ✐s t♦ ♦❜t❛✐♥ ❛ ✸❉ ♠❛♣ ♦❢ t❤❡ ❡♥✈✐r♦♥♠❡♥t ♦❢ t❤❡ r♦❜♦t✐❝ ✇❤❡❡❧❝❤❛✐r ✇❡ ❤❛✈❡✳ ❋♦r t❤❛t✱ ✇❡ ❤❛✈❡ ❛ s✇✐ssr❛♥❣❡r ❙❘✹✵✵✵ ❝❛♠❡r❛ ✇❤✐❝❤ ✐s ♠♦✉♥t❡❞ ♦♥ ✐t✳ ❚❤✐s ❝❛♠❡r❛ ❝❛♥ r❡tr✐❡✈❡ ✸❉ ♣♦✐♥t ❝❧♦✉❞s ♦❢ t❤❡ ❡♥✈✐r♦♥♠❡♥t ✐♥ r❡❛❧ t✐♠❡✳ ❲❡ ✐♠♣❧❡♠❡♥t❡❞ t❤❡ ❝♦❞❡ ✐♥ t❤❡ ❘❖❙ r♦❜♦t✐❝ ♣❧❛t❢♦r♠✳ ◆❡①t s❡❝t✐♦♥s ❣✐✈❡ ❛ ❜r✐❡❢ ❞❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ❤❛r❞✇❛r❡ ❛♥❞ s♦❢t✇❛r❡ ✉s❡❞ ❢♦r t❤❛t ♣✉r♣♦s❡✳

✷ ❍❛r❞✇❛r❡

■♥ t❤✐s s❡❝t✐♦♥ ✇❡ ❡①♣❧❛✐♥ t❤❡ ♠❛✐♥ ❝❤❛r❛❝t❡r✐st✐❝s ♦❢ t❤❡ ♠❛✐♥ ❝♦♠♣♦♥❡♥ts ♦❢ t❤❡ r♦❜♦t✐❝ s②st❡♠✳ ❲❡ ✉s❡❞ ❛ s✇✐ssr❛♥❣❡r ❝❛♠❡r❛✱ ❛ ▼❚✐ ①s❡♥s s❡♥s♦r ❛♥❞ ❛ ❇❧✉❡ ❇♦t✐❝s ✇❤❡❡❧❝❤❛✐r✳

✷✳✶ s✇✐ssr❛♥❣❡r ❙❘✹✵✵✵

❚❤✐s ❝❛♠❡r❛ ✐s ❞❡✈❡❧♦♣❡❞ ❜② ▼❡s❛ ■♠❛❣✐♥❣✷✳ ■t ✇♦r❦s ✇✐t❤ t❤❡ ❚✐♠❡ ♦❢ ❋❧✐❣❤t ✭❚❖❋✮ ♣r✐♥❝✐♣❧❡✳ ■ts ♠❛♥✉❛❧ ❡①♣❧❛✐♥s ✐♥ ❞❡t❛✐❧ t❤❡ ✇❛② ✐t ✇♦r❦s✿ ✏■♥ ❚✐♠❡ ♦❢ ❋❧✐❣❤t s②st❡♠s✱ t❤❡ t✐♠❡ t❛❦❡♥ ❢♦r ❧✐❣❤t t♦ tr❛✈❡❧ ❢r♦♠ ❛♥ ❛❝t✐✈❡ ✐❧❧✉♠✐♥❛t✐♦♥ s♦✉r❝❡ t♦ t❤❡ ♦❜❥❡❝ts ✐♥ t❤❡ ✜❡❧❞ ♦❢ ✈✐❡✇ ❛♥❞ ❜❛❝❦ t♦ t❤❡ s❡♥s♦r ✐s ♠❡❛s✉r❡❞✳ ●✐✈❡♥ t❤❡ s♣❡❡❞ ♦❢ ❧✐❣❤t ❝✱ t❤❡ ❞✐st❛♥❝❡ ❝❛♥ ❜❡ ❞❡t❡r♠✐♥❡❞ ❞✐r❡❝t❧② ❢r♦♠ t❤✐s r♦✉♥❞ tr✐♣ t✐♠❡✳ ❚♦ ❛❝❤✐❡✈❡ t❤❡ t✐♠❡ ♦❢ ✢✐❣❤t ♠❡❛s✉r❡♠❡♥t t❤❡ ❙❘✹✵✵✵ ♠♦❞✉❧❛t❡s ✐ts ✐❧❧✉♠✐♥❛t✐♦♥ ▲❊❉❙✱ ❛♥❞ t❤❡ ❈❈❉✴❈▼❖❙ ✐♠❛❣✐♥❣ s❡♥s♦r ♠❡❛s✉r❡s t❤❡ ♣❤❛s❡ ♦❢ t❤❡ r❡t✉r♥❡❞ ♠♦❞✉❧❛t❡❞ s✐❣♥❛❧ ❛t ❡❛❝❤ ♣✐①❡❧✳ ❚❤❡ ❞✐st❛♥❝❡ ❛t ❡❛❝❤ ♣✐①❡❧ ✐s ❞❡t❡r♠✐♥❡❞ ❛s ❛ ❢r❛❝t✐♦♥ ♦❢ t❤❡ ♦♥❡ ❢✉❧❧ ❝②❝❧❡ ♦❢ t❤❡ ♠♦❞✉❧❛t❡❞ s✐❣♥❛❧✱ ✇❤❡r❡ t❤❡ ❞✐st❛♥❝❡ ❝♦rr❡♣♦♥❞✐♥❣ t♦ ♦♥❡ ❢✉❧❧ ❝②❝❧❡ ✐s ❣✐✈❡♥ ❜② D=2fc ✇❤❡r❡ ❝ ✐s t❤❡ s♣❡❡❞ ♦❢ ❧✐❣❤t ❛♥❞ ❢ ✐s t❤❡ ♠♦❞✉❧❛t✐♦♥ ❢r❡q✉❡♥❝②✳ ■❢ ❢ ✐s ❡q✉❛❧ t♦ ✸✵▼❍③✱ t❤✐s ❞✐st❛♥❝❡ ✐s ✺♠✑✳ ❚❤✐s ❝❛♠❡r❛ ❤❛s ❛ r❡s♦❧✉t✐♦♥ ♦❢ ✶✼✻①✶✹✹ ♣✐①❡❧s✱ ✇❤✐❝❤ ✐s ❣♦♦❞ ❡♥♦✉❣❤ t♦ ❤❛✈❡ ❛ ❞❡t❛✐❧❡❞ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ♦❜❥❡❝ts✳ ■t ❤❛s s❡✈❡r❛❧ ♠♦❞✉❧❛t✐♦♥ ❢r❡q✉❡♥❝✐❡s✱ ✇❤✐❝❤ ❝❛♥ ❜❡ ❝♦♥✜❣✉r❡❞✱ ❛♥❞ ❡❛❝❤ ♦♥❡ ❤❛s ❛ ❞✐✛❡r❡♥t r❛♥❣❡ ♦❢ ❞❡♣t❤ ♠❡❛s✉r❡♠❡♥t✳ ▼❛✐♥❧②✱ t✇♦ ♦❢ t❤❡♠ ❛r❡ ✉s❡❞✿ ✵✲✺♠ ❛♥❞ ✵✲✶✵♠✳ ❲❤❡♥ ❛♥ ♦❜❥❡❝t ✐s ♦✉ts✐❞❡ t❤✐s ✏♥♦♥✲❛♠❜✐❣✉✐t② r❛♥❣❡✑✱ ❜✉t ❝❛♥ ❜❡ ❞❡t❡❝t❡❞ ❞✉❡ t♦ ✐ts ✐♥t❡♥s✐t②✱ ✐t ✐s ❢♦❧❞❡❞ ✐♥t♦ ✶❤tt♣✿✴✴❡♥✳✇✐❦✐♣❡❞✐❛✳♦r❣✴✇✐❦✐✴❑✐♥❡❝t❤tt♣✿✴✴✇✇✇✳♠❡s❛✲✐♠❛❣✐♥❣✳❝❤✴ ❘❚ ♥➦ ✵✹✵✻

(8)

✸❉ ▼❛♣♣✐♥❣ ♦❢ ✐♥❞♦♦r ❡♥✈✐r♦♥♠❡♥ts ✇✐t❤ ❛ t✐♠❡ ♦❢ ✢✐❣❤t ❝❛♠❡r❛ ✺ t❤❡ r❛♥❣❡✳ ❋♦r ✐♥st❛♥❝❡✱ ✐❢ ✉s✐♥❣ ❛ r❛♥❣❡ ♦❢ ✵✲✶✵♠✱ ❛♥❞ ❛ s❤✐♥② ♦❜❥❡❝t ✐s ✼ ♠❡t❡rs ❛✇❛② ❢r♦♠ t❤❡ ❝❛♠❡r❛✱ ✐t ✇✐❧❧ ❜❡ ❢♦❧❞❡❞ ❜❛❝❦✱ ❛♥❞ s♦ ✐t ✇✐❧❧ ❛♣♣❡❛r ❛s ✐❢ ✐t ✇❛s ♣❧❛❝❡❞ ❛t ✷ ♠❡t❡rs ♦❢ ❞✐st❛♥❝❡✳ ❲❤❡♥ t❤❡ ♠❡❛s✉r❡♠❡♥t ✐s t♦♦ ♥♦✐s②✱ ✐t ❛♣♣❡❛rs ❛s ❛ ❝♦♥❡ ♦❢ ♣♦✐♥ts ✭✇✐t❤ ❧♦✇ ✐♥t❡♥s✐t②✮ t❤❛t ❜❡❣✐♥s ✐♥ t❤❡ ♦r✐❣✐♥ ♦❢ ❝♦♦r❞✐♥❛t❡s ♦❢ t❤❡ ❝❛♠❡r❛✳ ❇❡❝❛✉s❡ ♦❢ t❤❛t✱ ✇❡ ✉s❡❞ t❤❡ r❛♥❣❡ ✵✲✶✵♠✱ ❛♥❞ ✇❡ ✜❧t❡r ♣♦✐♥ts ✭❜② ❤❛r❞✇❛r❡✮ ✇❤✐❝❤ ❤❛s ♥♦t ❡♥♦✉❣❤ ✐♥t❡♥s✐t②✱ ✉s✐♥❣ t❤❡ ♣❛r❛♠❡t❡r ✏❛♠♣❧✐t✉❞❡ t❤r❡s❤♦❧❞✑ ♦❢ t❤❡ ❝❛♠❡r❛✳ ■t ✐s ❧❡ss ♣r♦❜❛❜❧❡ t❤❛t ♦❜❥❡❝ts ✇✐t❤ ♠♦r❡ t❤❛♥ ✶✵♠ ♦❢ ❞✐st❛♥❝❡ ❢r♦♠ t❤❡ ❝❛♠❡r❛ ❝❛♥ ❜❡ ❝❛♣t✉r❡❞ ❡♥♦✉❣❤ ✐♥t❡♥s✐t②✳ ❆❧s♦✱ t❤❡ ❡♥✈✐r♦♥♠❡♥t ✐♥ ✇❤✐❝❤ t❤❡ ✇❤❡❡❧❝❤❛✐r ♠♦✈❡s ❤❛s ❞✐st❛♥❝❡s ❣r❡❛t❡r t❤❛♥ ✺ ♠❡t❡rs✳ ❆♣❛rt ❢r♦♠ t❤❡ r❛✇ ♣♦✐♥t ❝❧♦✉❞✱ t❤❡ ❝❛♠❡r❛ ♣r♦✈✐❞❡s ✐♥❢♦r♠❛t✐♦♥ ❛❜♦✉t ❝♦♥✜❞❡♥❝❡ ❛♥❞ ✐♥t❡♥s✐t② ♦❢ ❡❛❝❤ ♠❡❛s✉r❡♠❡♥t✳ ❚❤✐s ❝♦✉❧❞ ❜❡ ✉s❡❞ t♦ ✜❧t❡r ♣♦✐♥ts ✇❤✐❝❤ ❛r❡ ♣r♦✈❛❜❧② t❤❡ r❡s✉❧t ♦❢ ❜❛❞ ♠❡❛s✉r❡♠❡♥ts✳

✷✳✷ ▼❚✐ ①s❡♥s

❚❤✐s ♣r♦❞✉❝t ✐s ❞❡✈❡❧♦♣❡❞ ❜② ①s❡♥s✸✳ ❲❡ ✉s❡❞ ✐t ✇✐t❤ t❤❡ ✐❞❡❛ ♦❢ ❤❛✈✐♥❣ ❛❝❝✉r❛t❡ ✐♥❢♦r♠❛t✐♦♥ ❛❜♦✉t t❤❡ ♦r✐❡♥t❛t✐♦♥ ♦❢ t❤❡ ❝❛♠❡r❛✳ ❚❤❡ ❜❡st ✇❛② t♦ ✉♥❞❡rst❛♥❞ t❤❡ ❝❛♣❛❜✐❧✐t✐❡s ♦❢ t❤❡ s❡♥s♦r ✐s ❜② ✐ts ♠❛♥✉❛❧✿ ✏❚❤❡ ▼❚✐ ✐s ❛ ❝♦♠♣❧❡t❡ ♠✐♥✐❛t✉r❡ ✐♥❡rt✐❛❧ ♠❡❛s✉r❡♠❡♥t ✉♥✐t ✇✐t❤ ✐♥t❡❣r❛t❡❞ ✸❉ ♠❛❣♥❡t♦♠❡t❡rs ✭✸❉ ❝♦♠♣❛ss✮✱ ✇✐t❤ ❛♥ ❡♠❜❡❞❞❡❞ ♣r♦❝❡ss♦r ❝❛♣❛❜❧❡ ♦❢ ❝❛❧❝✉❧❛t✐♥❣ r♦❧❧✱ ♣✐t❝❤ ❛♥❞ ②❛✇ ✐♥ r❡❛❧ t✐♠❡✱ ❛s ✇❡❧❧ ❛s ♦✉t♣✉tt✐♥❣ ❝❛❧✐❜r❛t❡❞ ✸❉ ❧✐♥❡❛r ❛❝❝❡❧❡r❛t✐♦♥✱ r❛t❡ ♦❢ t✉r♥ ✭❣②r♦✮ ❛♥❞ ✭❡❛rt❤✮ ♠❛❣♥❡t✐❝ ✜❡❧❞ ❞❛t❛✳✑✳ ■ts ♠❛✐♥ ❛♣♣❧✐❝❛t✐♦♥s ❛r❡ r♦❜♦t✐❝s✱ ❛❡r♦s♣❛❝❡✱ ❛♥❞ ❛✉t♦♥♦♠♦✉s ✈❡❤✐❝❧❡s✳ ❲✐t❤ t❤✐s s❡♥s♦r✱ ✇❡ tr✐❡❞ t♦ ❣❡t t❤❡ ✸❉ ♦r✐❡♥t❛t✐♦♥ ♦❢ t❤❡ ❝❛♠❡r❛ ✐♥ s♣❛❝❡ ❛♥❞ t❤❡♥ ✉s❡ t❤❡s❡ ✈❛❧✉❡s t♦ tr❛♥s❢♦r♠ t❤❡ ❞❛t❛ ❛❝❝♦r❞✐♥❣❧②✳ ▼✐①✐♥❣ t❤❡ ✈❛❧✉❡s ♦❢ ♦r✐❡♥t❛t✐♦♥ ♦❢ t❤❡ ❝❛♠❡r❛✱ r❡tr✐❡✈❡❞ ❜② t❤✐s s❡♥s♦r✱ ❛♥❞ t❤❡ ♣♦s✐t✐♦♥ ♦❢ t❤❡ r♦❜♦t ✐♥ t❤❡ ♠❛♣✱ ✇❡ ✇❡r❡ ❛❜❧❡ t♦ tr❛♥s❢♦r♠ ♣♦✐♥t ❝❧♦✉❞s t♦ t❤❡ ♠❛♣ r❡❢❡r❡♥❝❡✳

✷✳✸ ❇❧✉❡ ❇♦t✐❝s

❚❤❡ ✇❤❡❡❧❝❤❛✐r ♣❧❛t❢♦r♠ ✇❡ ✉s❡❞ ✇❛s ❞❡✈❡❧♦♣❡❞ ❢♦r t❤❡ ▼❖❱❊▼❊◆❚✹ ♣r♦❥❡❝t✳ ■t ❤❛s ♦♥❡ ❙■❈❑✲▲▼❙ ✷✵✵ ❧❛s❡r ❛❧♦♥❣ ✇✐t❤ ✇❤❡❡❧s ❛♥❞ ❛ ❞r✐✈❡ ♠♦t♦r t♦ ♠♦✈❡ ✐t✳ ❚❤✐s r♦❜♦t ❝❛♥ ❜❡ ♦♣❡r❛t❡❞ ♠❛♥✉❛❧❧② t❤r♦✉❣❤ ❛ ❥♦②st✐❝❦ ✭t❤✐s ✐s t❤❡ ♠♦❞❡ ✇❡ ✉t✐❧✐③❡❞✮ ♦r ❛✉t♦♠❛t✐❝❛❧❧② t❤r♦✉❣❤ ✈❡❧♦❝✐t② ❝♦♠♠❛♥❞s✳ ■♥ ♦r❞❡r t♦ ✉s❡ t❤❡ ✇❤❡❡❧❝❤❛✐r✱ ✐t ✐s ♥❡❝❡ss❛r② t♦ ♣❛ss t❤❡ ✜r♠✇❛r❡ t♦ ✐t t❤r♦✉❣❤ ❛♥ ❊t❤❡r♥❡t ❝♦♥♥❡❝t✐♦♥✳ ❆❢t❡r t❤❛t✱ ✐t ✐s ♣♦ss✐❜❧❡ t♦ ❝♦♠♠✉♥✐❝❛t❡ ✇✐t❤ ✐t ✉s✐♥❣ ❛ ❈●■ ✐♥t❡r❢❛❝❡✳ ❚❤❡ ♣❧❛t❢♦r♠ ✐s ❝❛♣❛❜❧❡ ♦❢ r❡tr✐❡✈✐♥❣ ♦❞♦♠❡tr② ✐♥❢♦r♠❛t✐♦♥ ✭✇❤✐❝❤ ✐s ❛♥ ❡st✐♠❛t❡❞ ♣♦s✐t✐♦♥ ❛♥❞ ♦r✐❡♥t❛t✐♦♥✮✳ ❚❤✐s ✐♥❢♦r♠❛t✐♦♥ ✐♥ t✉r♥ ✐s ✉s❡❞ ❜② ✷❉ ♠❛♣♣✐♥❣ ❛❧❣♦r✐t❤♠s t♦ ❣❡t ❛ ♣♦s✐t✐♦♥ ✐♥ t❤❡ ✷❉ ♠❛♣✳

✸ ❙♦❢t✇❛r❡

■♥ t❤✐s s❡❝t✐♦♥ ✇❡ t❛❧❦ ❛❜♦✉t ❘❖❙✱ t❤❡ s♦❢t✇❛r❡ ♣❧❛t❢♦r♠ ✉s❡❞ ❢♦r ✐♠♣❧❡♠❡♥t✐♥❣ t❤❡ ❛❧❣♦r✐t❤♠✱ ❛♥❞ t❤❡♥ ✇❡ ♣r❡s❡♥t t❤❡ ❛❧❣♦r✐t❤♠ ♦❢ ♠❛♣♣✐♥❣ ✇❡ ❞❡✈❡❧♦♣❡❞✳ ✸❤tt♣✿✴✴✇✇✇✳①s❡♥s✳❝♦♠✴❡♥✴❣❡♥❡r❛❧✴♠t✐▼♦❞✉❧❛r ❱❡rs❛t✐❧❡ ▼♦❜✐❧✐t② ❊♥❤❛♥❝❡♠❡♥t ❚❡❝❤♥♦❧♦❣②✱ ❙♣❡❝✐✜❝ ❚❛r❣❡t❡❞ ❘❡s❡❛r❝❤ Pr♦❥❡❝t ♥r✳ ✺✶✶✻✼✵ ❘❚ ♥➦ ✵✹✵✻

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✸❉ ▼❛♣♣✐♥❣ ♦❢ ✐♥❞♦♦r ❡♥✈✐r♦♥♠❡♥ts ✇✐t❤ ❛ t✐♠❡ ♦❢ ✢✐❣❤t ❝❛♠❡r❛ ✻

✸✳✶ ❘♦❜♦t ❖♣❡r❛t✐♥❣ ❙②st❡♠ ✭❘❖❙✮

❘❖❙ ✐s ❛♥ ♦♣❡♥ s♦✉r❝❡ ♦♣❡r❛t✐♥❣ s②st❡♠ ❢♦r r♦❜♦ts✳ ■t ♣r♦✈✐❞❡s ❢❛❝✐❧✐t✐❡s ❧✐❦❡ ♠❡ss❛❣❡✲♣❛ss✐♥❣ ❜❡t✇❡❡♥ ♣r♦❝❡ss❡s✱ ❛♥❞ ❤❛r❞✇❛r❡ ❛❜str❛❝t✐♦♥✳ ❖♥❡ ♦❢ ✐ts ♠❛✐♥ ❝❤❛r❛❝t❡r✐st✐❝s ✐s t❤❛t ✐t ✐s ❛ ❞✐str✐❜✉t❡❞ s②st❡♠✱ ✐♥ ✇❤✐❝❤ ❞✐✛❡r❡♥t ♣r♦❝❡ss❡s ❝❛♥ ❝♦♠♠✉♥✐❝❛t❡ ❡❛❝❤ ♦t❤❡r ❜② ❛ st❛♥❞❛r❞ ✇❛② ♦❢ ♣❛ss✐♥❣ ♠❡ss❛❣❡s ❜❡t✇❡❡♥ t❤❡♠✳ ❊❛❝❤ s❡♣❛r❛t❡ ♣r♦❝❡ss ✐s ❝❛❧❧❡❞ ❛ ♥♦❞❡✳ ■t ❡①✐sts ❛ ❝❡♥tr❛❧ ♥♦❞❡ ✇❤✐❝❤ ✐s ❝❛❧❧❡❞ r♦s❝♦r❡✱ ✇❤✐❝❤ ✐s r❡s♣♦♥s✐❜❧❡ ❢♦r ❛❧❧ t❤❡ ❝♦♠♠✉♥✐❝❛t✐♦♥✳ ■♥ ❛ t✐♣✐❝❛❧ r♦❜♦t s②st❡♠ ✉s✉❛❧❧② ❡①✐sts ❛ ❧♦t ♦❢ ♥♦❞❡s✱ ❢♦r ✐♥st❛♥❝❡✱ ♦♥❡ ♥♦❞❡ ❝❛♥ ❜❡ r❡s♣♦♥s✐❜❧❡ ♦❢ s❡♥❞✐♥❣ t❤❡ ❛❝t✉❛❧ ♣♦s✐t✐♦♥ ♦❢ t❤❡ r♦❜♦t ✇❤✐❧❡ ♦t❤❡r ✐s ❝♦♥str✉❝t✐♥❣ ❛ ♠❛♣ ♦❢ t❤❡ ❡♥✈✐r♦♥♠❡♥t✳ ■t ❝♦✉❧❞ ❛❧s♦ ❜❡ ♦♥❡ ♥♦❞❡ ✇❤✐❝❤ ❝❛❧❝✉❧❛t❡s t❤❡ ❜❡st ♣❛t❤ t♦ r❡❛❝❤ ❛ ❣♦❛❧✱ ♦t❤❡r t❤❛t ❝♦♠♠✉♥✐❝❛t❡s ✇✐t❤ t❤❡ ❤❛r❞✇❛r❡ ♦❢ ❛ ❧❛s❡r ❛tt❛❝❤❡❞ t♦ t❤❡ r♦❜♦t✱ ❡t❝✳ ❖♥❡ ✐♠♣♦rt❛♥t ❛❞✈❛♥t❛❣❡ ♦❢ ❤❛✈✐♥❣ ❛ ❞✐str✐❜✉t❡❞ s②st❡♠ ✐s t❤❛t ②♦✉ ❝♦✉❧❞ ❤❛✈❡ ❡❛❝❤ ♣r♦❝❡ss r✉♥♥✐♥❣ ✐♥ ❞✐❢✲ ❢❡r❡♥t ♣r♦❝❡ss♦rs✱ ♦r ❡✈❡♥ ✐♥ ❞✐✛❡r❡♥t ❝♦♠♣✉t❡rs❀ t❤✐s ✐s ♣❛rt✐❝✉❧❛r❧② ✐♥t❡r❡st✐♥❣ ❢♦r ♣❡r❢♦r♠❛♥❝❡✳ ❆ ❝♦❧❧❡❝t✐♦♥ ♦❢ ♥♦❞❡s ✐s ❝❛❧❧❡❞ ❛ ♣❛❝❦❛❣❡✳ ■♥ ❛ ♣❛❝❦❛❣❡ ✐t ✉s✉❛❧❧② ❡①✐sts ❛ s❡t ♦❢ ♥♦❞❡s✱ t♦❣❡t❤❡r ✇✐t❤ ❧✐❜r❛r✐❡s✱ ❝♦♥✜❣✉r❛t✐♦♥ ✜❧❡s✱ ❞❛t❛s❡ts✱ ❡t❝✳ ❆ ❝♦❧❧❡❝t✐♦♥ ♦❢ ♣❛❝❦❛❣❡s ✐s ❝❛❧❧❡❞ ❛ st❛❝❦✳ ❯s✉❛❧❧② ❛ st❛❝❦ ❞❡♥♦t❡s s♦♠❡ s♣❡❝✐✜❝ s✉❜s❡t ♦❢ ❛ s②st❡♠✱ ❧✐❦❡ ❢♦r ✐♥st❛♥❝❡ t❤❡ ♥❛✈✐❣❛t✐♦♥ s✉❜s②st❡♠✳ ❋♦r ♥♦✇✱ t❤❡ ♦♥❧② ♦♣❡r❛t✐♥❣ s②st❡♠ ❢✉❧❧② s✉♣♣♦rt❡❞ ❢♦r ✉s✐♥❣ ❘❖❙ ✐s ❯❜✉♥t✉✳ ■t ✐s ♣♦ss✐❜❧❡ t♦ ✉s❡ ❈✰✰ ♦r P②t❤♦♥ t♦ ✐♥t❡❣r❛t❡ ❘❖❙ t♦ ❛♥ ❡①✐st✐♥❣ ❛♣♣❧✐❝❛t✐♦♥✳ ❋♦r t❤❛t✱ t❤❡ ❘❖❙ ♣❛❝❦❛❣❡s r♦s❝♣♣ ❛♥❞ r♦s♣② ❛r❡ ♣r♦✈✐❞❡❞✳ ❙✐♠♣❧② ❜② ✐♥❝❧✉❞✐♥❣ ✐t ✇✐t❤ ❛♥ ✐♥❝❧✉❞❡ ❞✐r❡❝t✐✈❡ ✐♥ ❛ ✳❝♣♣ ✇❡ ❝❛♥ st❛rt ✉s✐♥❣ ❘❖❙ ✐♥ ♦✉r ❛♣♣❧✐❝❛t✐♦♥✳ ❘❖❙ ❤❛s ♠❛♥② ❧✐❜r❛r✐❡s ❢♦r ❝♦♠♠♦♥ ✉s❡ ✇❤❡♥ ❜✉✐❧❞✐♥❣ s✉❝❤ ❛ s②st❡♠✳ ❍❡r❡ ✇❡ ✇✐❧❧ ❜r✐❡✢② ❞❡s❝r✐❜❡ t❤❡ ♦♥❡s ✇❤✐❝❤ ✇❡ ❤❛✈❡ ✉s❡❞✳ ✸✳✶✳✶ ❯t✐❧✐t✐❡s ❼ s❡♥s♦r❴♠s❣s✺ ❛ ❝♦❧❧❡❝t✐♦♥ ♦❢ ♠❡ss❛❣❡s ✉s❡❞ ❜② s❡♥s♦rs✱ ❧✐❦❡ ♣♦✐♥t ❝❧♦✉❞s✱ ♦r ✐♠❛❣❡s✳ ❚❤❡s❡ ♠❡ss❛❣❡s ❛r❡ ✉s❡❞ ❢♦r ❝♦♠♠✉♥✐❝❛t✐♦♥ ❜❡t✇❡❡♥ ❞✐✛❡r❡♥t ♥♦❞❡s✳ ❼ t❢✻ ✐s ❛ ❘❖❙ ❧✐❜r❛r② ✇❤✐❝❤ ❣✐✈❡s ❢❛❝✐❧✐t✐❡s ❢♦r ✉s✐♥❣ ❞✐✛❡r❡♥t ❝♦♦r❞✐♥❛t❡ s②st❡♠s t❤❛t ❛ r♦❜♦t✐❝ ♣❧❛t❢♦r♠ ❤❛s✳ ■t ♣r♦✈✐❞❡s ❛♥ ✐♥t❡r❢❛❝❡ ❢♦r ❦♥♦✇✐♥❣ ✇❤❡r❡ ❛r❡ t❤❡ ❞✐✛❡r❡♥t ❢r❛♠❡s ♦✈❡r t✐♠❡✱ ❛♥❞ t♦ r❡❛s♦♥ ❛❜♦✉t t❤❡♠✳ ■♥ ♦✉r ❝❛s❡✱ ✐t ✐s ✉s❡❢✉❧ ❢♦r tr❛♥s❢♦r♠✐♥❣ ♣♦✐♥t ❝❧♦✉❞s✱ ✇❤✐❝❤ ❝♦♠❡s ❢r♦♠ t❤❡ ❝❛♠❡r❛✱ t♦ t❤❡ ♠❛♣ r❡❢❡r❡♥❝❡ s②st❡♠✳ ❼ ♣❝❧ ✭♣♦✐♥t ❝❧♦✉❞ ❧✐❜r❛r②✼✮ ✐s ❛ ❝♦❧❧❡❝t✐♦♥ ♦❢ ✉t✐❧✐t✐❡s ❢♦r ♠❛♥❛❣✐♥❣ ♣♦✐♥t ❝❧♦✉❞s✳ ❆♠♦♥❣ t❤❡♠✱ ✇❡ ❝♦✉❧❞ ✜♥❞ ✜❧t❡r✐♥❣✱ s✉r❢❛❝❡ r❡❝♦♥str✉❝t✐♦♥✱ r❡❣✲ ✐str❛t✐♦♥✱ s❡❣♠❡♥t❛t✐♦♥✱ ❡t❝✳ ■♥ t❤❡ ♥❡①t s❡❝t✐♦♥ ✇❡ ✇✐❧❧ s❤♦✇ s♦♠❡ ❜✉♥❝❤❡s ♦❢ ❝♦❞❡ t❤❛t s❤♦✇ ❤♦✇ ✇❡ ✉s❡❞ ❘❖❙ ✐♥ t❤❡ ✐♠♣❧❡♠❡♥t❛t✐♦♥✳ ✺❤tt♣✿✴✴✇✇✇✳r♦s✳♦r❣✴✇✐❦✐✴s❡♥s♦r❴♠s❣s❤tt♣✿✴✴✇✇✇✳r♦s✳♦r❣✴✇✐❦✐✴t❢❤tt♣✿✴✴✇✇✇✳r♦s✳♦r❣✴✇✐❦✐✴♣❝❧ ❘❚ ♥➦ ✵✹✵✻

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✸❉ ▼❛♣♣✐♥❣ ♦❢ ✐♥❞♦♦r ❡♥✈✐r♦♥♠❡♥ts ✇✐t❤ ❛ t✐♠❡ ♦❢ ✢✐❣❤t ❝❛♠❡r❛ ✼

✹ ✸❉ ▼❛♣♣✐♥❣

■♥ t❤✐s s❡❝t✐♦♥ ✇❡ ✇✐❧❧ ❡①♣❧❛✐♥ t❤❡ ♠❛✐♥ ✐❞❡❛ ♦❢ t❤❡ ❛❧❣♦r✐t❤♠ ❛♥❞ t❤❡ ✇❛② ✇❡ ✐♠♣❧❡♠❡♥t❡❞ ✐t ♦✈❡r ❘❖❙✳

✹✳✶ ▼❛✐♥ ■❞❡❛

■❢✱ ❢♦r ❡❛❝❤ ✐♥❝♦♠✐♥❣ ✸❉ ♣♦✐♥t ❝❧♦✉❞✱ ✇❡ ❤❛✈❡ t❤❡ ♣♦s✐t✐♦♥ ♦❢ t❤❡ r♦❜♦t ✐♥ ❛ ✷❉ ❡♥✈✐r♦♥♠❡♥t✱ ✇❡ ❝♦✉❧❞ ❥✉st s✉♠ ✉♣ t❤❡ ❞✐✛❡r❡♥t r❛♥❣❡ ✐♠❛❣❡s ❝♦♠✐♥❣ ❢r♦♠ t❤❡ ❝❛♠❡r❛ t♦ ♦❜t❛✐♥ ❛ ✸❉ ♠❛♣ ♦❢ t❤❡ ❡♥✈✐r♦♥♠❡♥t✳ ❚❤❡ ❛❞✈❛♥t❛❣❡ ♦❢ ❞♦✐♥❣ t❤✐s ✐s t❤❛t ✇❡ s❛✈❡ ❝♦♠♣✉t❛t✐♦♥❛❧ t✐♠❡ r❡q✉✐r❡❞ t♦ ♣❡r❢♦r♠ ❛ ✸❉ ♣♦s✐t✐♦♥✐♥❣ ❛❧❣♦r✐t❤♠✱ ❜✉t ♦♥ t❤❡ ♦t❤❡r ❤❛♥❞ ✇❡ ❧♦s❡ ♣r❡❝✐s✐♦♥ ❛♥❞ ❛❧s♦ t❤❡ ✸❉ ♠❛♣ ❞❡♣❡♥❞s ♦♥ t❤❡ r❡s✉❧ts ♦❢ t❤❡ ✷❉ ♠❛♣♣✐♥❣ ❛❧❣♦r✐t❤♠✳ ❆♥②✇❛②✱ ✇❡ ❢♦✉♥❞ ✐t ✉s❡❢✉❧✱ ❜❡❝❛✉s❡ ♦✉r r♦❜♦t ❝❛♥ ♦♥❧② ♠♦✈❡ ✐♥ ✷❉✳

✹✳✷ ▲♦❝❛❧✐③❛t✐♦♥

❚♦ ♦❜t❛✐♥ t❤❡ ❧♦❝❛❧✐③❛t✐♦♥ ♦❢ t❤❡ r♦❜♦t ✇❡ ♠✉st ✜♥❞ ✐t✬s ♣♦s✐t✐♦♥ ✐♥ ❛ ♠❛♣✳ ❲❡ ❝♦♠♣❛r❡❞ t✇♦ ❞✐✛❡r❡♥t ✇❛②s ♦❢ ❞♦✐♥❣ t❤✐s✳ ❖♥❡ ♦❢ t❤❡♠ ✐s t♦ ❝♦♥str✉❝t t❤❡ ♠❛♣ ✐♥ ✷❉ ❛♥❞ t❤❡♥ ✉s❡ t❤❡ ♥♦❞❡ ❛♠❝❧ ❢r♦♠ ❘❖❙✱ ✇❤✐❝❤✱ ❜❛s❡❞ ♦♥ ❛❝t✉❛❧ ❧❛s❡r ✐♥❢♦r♠❛t✐♦♥✱ ❣✐✈❡s ✉s t❤❡ ❛❝t✉❛❧ ♣♦s✐t✐♦♥ ♦♥ t❤❛t ♠❛♣✳ ❆♥♦t❤❡r ✇❛② ✐s t♦ ✉s❡ t❤❡ s❧❛♠ ✷❞ ❛❧❣♦r✐t❤♠ t❤❛t ✐s ♣r❡s❡♥t ✐♥ ❘❖❙ t♦ ❤❛✈❡ t❤❡ ♣♦s✐t✐♦♥ ✐♥ ❛ ♠❛♣ ✇❤✐❝❤ ✐s ❜❡✐♥❣ ❝♦♥str✉❝t❡❞ ✇❤✐❧❡ t❤❡ r♦❜♦t ✐s ♠♦✈✐♥❣✳ ■♥ t❤❡ s❡❝♦♥❞ ❛♣♣r♦❛❝❤✱ ✐t ✐s ♥♦t ♥❡❝❡ss❛r② t♦ ❤❛✈❡ ❛ ♣r❡✈✐♦✉s❧② ❝♦♥str✉❝t❡❞ ♠❛♣✱ ❜✉t ❞✉❡ t♦ ❛❝t✉❛❧✐③❛t✐♦♥s t❤❛t t❤❡ ❛❧❣♦r✐t❤♠ ❞♦❡s✱ t❤❡ ♠❛♣ ✐s s♦♠❡t✐♠❡s ❛❞❥✉st❡❞ ❛♥❞ s♦ ✇❡ ❣♦t ❛ ❞✐st♦rt❡❞ ✸❉ ♠❛♣✳ ❖♥ t❤❡ ♦t❤❡r ❤❛♥❞✱ ❛♠❝❧ r❡q✉✐r❡s t♦ s❡t ✉♣ ❛♥ ✐♥✐t✐❛❧ ♣♦s✐t✐♦♥ ✐♥ t❤❛t ♠❛♣✳ ❲❡ ♦❜t❛✐♥❡❞ s✐♠✐❧❛r r❡s✉❧ts ✉s✐♥❣ ❜♦t❤ ❛♣♣r♦❛❝❤❡s✳ ❚❤❡ ♣r✐♥❝✐♣❛❧ ♣r♦❜❧❡♠ ♦❢ ❜♦t❤ ♦❝❝✉rs ✇❤❡♥ t❤❡② ❝♦♥str✉❝t ❞✐st♦rt❡❞ ♠❛♣s✱ ❞✉❡ t♦ ✐♥❛❝❝✉r❛❝② ♦♥ t❤✐s ♠❛♣s✳ ❖♥❡ s♦❧✉t✐♦♥ ✐s t♦ ❝♦♥str✉❝t t❤❡ ♠❛♣ ✜rst✱ ❛♥❞ t❤❡♥ ✉s❡ t❤❡ ♠❛♣ ♦♥❧② ✐❢ ✐t ❞♦❡s ♥♦t ❤❛✈❡ ✐♥❛❝❝✉r❛❝✐❡s✱ ✇✐t❤ ❛♠❝❧✳ ❲❡ ❝❛♥ ❛❧✇❛②s ❝♦♥str✉❝t ❛ ♥❡✇ ♠❛♣ ✐❢ t❤❡ ✜rst ✐s ♥♦t ❛s ❣♦♦❞ ❛s ✇❡ ✇❛♥t✳ ❆s ❛ ❢✉t✉r❡ ✇♦r❦✱ ✇❡ ♣r♦♣♦s❡ ❤❡r❡ t♦ ✐♠♣❧❡♠❡♥t ■❈P ❛❧❣♦r✐t❤♠s ✐♥ ♦r❞❡r t♦ ♠❛t❝❤ t❤❡ ❞✐✛❡r❡♥t ♣♦✐♥t ❝❧♦✉❞s✳ ❉♦✐♥❣ ✐t ✐♥ t❤✐s ✇❛② ✇✐❧❧ ❜r✐♥❣ ✉s ♠♦r❡ ❛❝❝✉r❛t❡ ✸❉ ♠❛♣s✳

✹✳✸ ■♠♣❧❡♠❡♥t❛t✐♦♥

❋✐rst ♦❢ ❛❧❧✱ ✇❡ s❤♦✉❧❞ ❝♦♥str✉❝t t❤❡ tr❛♥s❢♦r♠❛t✐♦♥ ❜❡t✇❡❡♥ t❤❡ s✇✐ssr❛♥❣❡r ❝❛♠❡r❛ ❛♥❞ t❤❡ ✇❤❡❡❧❝❤❛✐r✳ ❲❡ ♣❧❛❝❡❞ ✐t ✶✳✹ ♠ ❛❜♦✈❡ t❤❡ ❜❛s❡ ♦❢ t❤❡ r♦❜♦t ❛♥❞ ✵✳✼✼♠ ❜❛❝❦ ✐♥ t❤❡ ① ❝♦♦r❞✐♥❛t❡✳ ❙♦ ✇❡ ✇r✐t❡✿ s ✇ ✐ s s r ❛ ♥ ❣ ❡ r ✳ tr❛♥s❢♦r♠ ✳ t r ❛ ♥ s ❧ ❛ t ✐ ♦ ♥ ✳ ① ❂ ①❴s❝❛♥❴♦❢❢s❡t❴− ✵ ✳ ✼ ✼ ❀ s ✇ ✐ s s r ❛ ♥ ❣ ❡ r ✳ tr❛♥s❢♦r♠ ✳ t r ❛ ♥ s ❧ ❛ t ✐ ♦ ♥ ✳ ③ ❂ ✶ ✳ ✹ ❀ ❆❢t❡r t❤❛t ✇❡ ♦♥❧② ❤❛✈❡ t♦ s❡♥❞ t❤❡ tr❛♥s❢♦r♠❛t✐♦♥ ♦✈❡r ❘❖❙✱ ❛♥❞ s♦ ✐t ✇✐❧❧ ❜❡ ❛✈❛✐❧❛❜❧❡ ❢♦r ♠❛❦✐♥❣ t❤❡ ♥❡❝❡ss❛r② tr❛♥s❢♦r♠❛t✐♦♥s ♦❢ t❤❡ ♣♦✐♥t ❝❧♦✉❞s ❝♦♠✐♥❣ ❢r♦♠ t❤❡ ❝❛♠❡r❛ t♦ t❤❡ ♠❛♣ ✇❡ ❛r❡ ❝♦♥str✉❝t✐♥❣✳ ❘❖❙ ❛❧❧♦✇ ✉s t♦ tr❛❝❦ ❞✐✛❡r❡♥t ❝♦♦r❞✐♥❛t❡ s②st❡♠s ✉s✐♥❣ t❤❡ t❢ ❧✐❜r❛r②✳ ■♥ ♦r❞❡r t♦ ✉s❡ t❤❡ tr❛♥s❢♦r♠❛t✐♦♥ ✇❡ ❝r❡❛t❡❞✱ ✇❡ ❤❛✈❡ t♦ ❝❛❧❧ t❤✐s ❧✐❜r❛r② ❛s ❢♦❧❧♦✇s✿ s❡♥s♦r❴♠s❣s ✿ ✿ P♦✐♥t❈❧♦✉❞ ♣❝❴❝✉rr❡♥t ❀ ✳ ✳ ✳ ❘❚ ♥➦ ✵✹✵✻

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✸❉ ▼❛♣♣✐♥❣ ♦❢ ✐♥❞♦♦r ❡♥✈✐r♦♥♠❡♥ts ✇✐t❤ ❛ t✐♠❡ ♦❢ ✢✐❣❤t ❝❛♠❡r❛ ✽ t ❧ ✐ s t ❡ ♥ ❡ r ✳ ❧♦♦❦✉♣❚r❛♥s❢♦r♠ ✭✧✴♠❛♣✧✱ ♣❝❴❝✉rr❡♥t ✳ ❤❡❛❞❡r ✳ ❢r❛♠❡❴✐❞ ✱ ♣❝❴❝✉rr❡♥t ✳ ❤❡❛❞❡r ✳ st❛♠♣ ✱ ❜s✇✐sstr❛♥s❢♦r♠ ✮ ❀ ♣ ❝ ❧ ✿ ✿ tr❛♥s❢♦r♠❆s▼❛tr✐① ✭ ❜s✇✐sstr❛♥s❢♦r♠ ✱ ♠❛t ✮ ❀ ❆ ✇❛② t♦ ♦❜t❛✐♥ ❛ ♠♦r❡ ❛❝❝✉r❛t❡ tr❛♥s❢♦r♠❛t✐♦♥ ✐s t♦ ✉s❡ t❤❡ ♦✉t♣✉t ♦❢ ❛♥ ▼❚✐ ①s❡♥s s❡♥s♦r✱ ♣❛rt✐❝✉❧❛r❧②✱ ✇❡ ♦❜t❛✐♥❡❞ t❤❡ r♦t❛t✐♦♥ tr❛♥s❢♦r♠❛t✐♦♥ t❤r♦✉❣❤ t❤❡ ✈❛❧✉❡s ♦❢ t❤❡ ❣②r♦s❝♦♣❡s ✐♥ t❤❡ t❤r❡❡ ❡✉❝❧✐❞❡❛♥ ❡❞❣❡s✳ ❚❤✐s ✈❛❧✉❡s ✐♥ t✉r♥✱ ✇❡r❡ ✉s❡❞ t♦ ♠❛❦❡ ❛ tr❛♥s❢♦r♠❛t✐♦♥ ✇❤✐❝❤ ✐s s❡♥t ♦✈❡r ❘❖❙✳ ❚❤❡ ❝♦❞❡ r❡s✉❧ts✿ s❡♥s♦r❴♠s❣s ✿ ✿ P♦✐♥t❈❧♦✉❞ ♣❝❴❝✉rr❡♥t ❀ ✳ ✳ ✳ t ❧ ✐ s t ❡ ♥ ❡ r ✳ ❧♦♦❦✉♣❚r❛♥s❢♦r♠ ✭✧✴♠❛♣✧✱ ♣❝❴❝✉rr❡♥t ✳ ❤❡❛❞❡r ✳ ❢r❛♠❡❴✐❞ ✱ ♣❝❴❝✉rr❡♥t ✳ ❤❡❛❞❡r ✳ st❛♠♣ ✱ s ✇ ✐ s s t r ❛ ♥ s ❢ ♦ r ♠ ✮ ❀ ✳ ✳ ✳ ✴✴ ♦❜t❛✐♥ t❤❡ ✈ ❛ ❧ ✉ ❡ s ♦ ❢ t❤❡ ❣②r♦s❝♦♣❡s ✴✴ ❛♥❞ s❛✈❡ ✐ t ✐♥ str❛♥s❢♦r♠ t ❧ ✐ s t ❡ ♥ ❡ r ✳ ❧♦♦❦✉♣❚r❛♥s❢♦r♠ ✭✧ r♦t❴s✇✐ssr❛♥❣❡r ✧✱ ✧♠❛♣✧✱ ♣❝❴❝✉rr❡♥t ✳ ❤❡❛❞❡r ✳ st❛♠♣ ✱ str❛♥s❢♦r♠ ✮ ❀ ✳ ✳ ✳ ✴✴ ❢ ✐ ♥ ❛ ❧ t r ❛ ♥ s ❢ ♦ r ♠ ❛ t ✐ ♦ ♥ t r ❛ ♥ s ❢❂t ❢ ✿ ✿ ❚r❛♥s❢♦r♠ ✭ t ❢ ✿ ✿ ◗✉❛t❡r♥✐♦♥ ✭ str❛♥s❢♦r♠ ✳ ❣❡t❘♦t❛t✐♦♥ ✭ ✮ ✮ ✱ t ❢ ✿ ✿ ❱❡❝t♦r✸ ✭ s ✇ ✐ s s t r ❛ ♥ s ❢ ♦ r ♠ ✳ ❣ ❡ t ❖ r ✐ ❣ ✐ ♥ ✭ ✮ ✮ ✮ ❀ ■♥ t❤✐s ❝♦❞❡✱ r♦t❴s✇✐ssr❛♥❣❡r r❡♣r❡s❡♥ts t❤❡ tr❛♥s❢♦r♠❛t✐♦♥ ♦❢ t❤❡ ❣②r♦s❝♦♣❡s ✇✐t❤ r❡s♣❡❝t t♦ t❤❡ ♠❛♣✱ ✇❤✐❝❤ ✐s ✇❤❛t ✇❡ ❛❝t✉❛❧❧② ✇❛♥t✳ ❙♦ ✇❡ ♣✉t t♦❣❡t❤❡r t❤❡s❡ ✈❛❧✉❡s ✇✐t❤ t❤❡ ✈❛❧✉❡s ♦❢ t❤❡ ♣♦s✐t✐♦♥ (x, y) ♦❢ t❤❡ ❝❛♠❡r❛ ✐♥ t❤❡ ♠❛♣✳ ❚❤❡ r❡s✉❧ts ♦❜t❛✐♥❡❞ ✇❡r❡ s✐♠✐❧❛r✱ ❡①❝❡♣t ✐♥ t❤❡ ❝❛s❡ ✇❤❡♥ t❤❡ ✇❤❡❡❧❝❤❛✐r st♦♣s s✉❞❞❡♥❧② ❛♥❞ t❤❡ ❝❛♠❡r❛ ❝❤❛♥❣❡s ✐ts ♦r✐❡♥t❛t✐♦♥ ✈❡rt✐❝❛❧❧②✳ ❇✉t ❡✈❡♥ ✐♥ t❤✐s ❝❛s❡✱ t❤❡ ❡rr♦r ✇❛s ❛❝❝❡♣t❛❜❧❡ ✭❜❡❝❛✉s❡ t❤❡ ♠♦✈❡♠❡♥t ✐s s♠❛❧❧✮✳ ❲❡ ❞❡❝✐❞❡❞ s♦ ♥♦t t♦ ✉s❡ t❤❡ ▼❚✐ s❡♥s♦r ❢♦r t❤❡ s❛❦❡ ♦❢ s✐♠♣❧✐❝✐t②✳ ❆♥②✇❛②✱ t❤❡ ❝♦❞❡ ❝♦✉❧❞ ❜❡ ❝❤❛♥❣❡❞ ❡❛s✐❧② ✐♥ t❤❡ ❢✉t✉r❡✳ ❖♥❝❡ ✇❡ ❤❛✈❡ t❤❡ tr❛♥s❢♦r♠❛t✐♦♥ ❜❡t✇❡❡♥ t❤❡ ❝❛♠❡r❛ ❛♥❞ t❤❡ ♠❛♣✱ ✇❡ ✉s❡ t❤❡ ♣❝❧ ❘❖❙ ❧✐❜r❛r② t♦ ♣❛ss ✐t t♦ ❛ ♠❛tr✐① r❡♣r❡s❡♥t❛t✐♦♥✿ ♣ ❝ ❧ ✿ ✿ tr❛♥s❢♦r♠❆s▼❛tr✐① ✭ s✇✐sstr❛♥s❢♦r♠ ✱ ♠❛t ✮ ❀ ❆❢t❡r t❤❛t✱ ✇❡ ♣❡r❢♦r♠ t✇♦ ✜❧t❡r✐♥❣ st❡♣s ✐♥ ♦r❞❡r t♦ ❤❛✈❡ ❛ ❜❡tt❡r ❛♥❞ ♠♦r❡ ✉s❡❢✉❧ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ❡❛❝❤ ♣♦✐♥t ❝❧♦✉❞✳ ❇♦t❤ ♦❢ t❤❡♠ ❛r❡ ♣r♦✈✐❞❡❞ ❜② ♣❝❧✳ ❋✐rst✱ ❛♥ ♦✉t❧✐❡rs r❡♠♦✈❛❧✳ ■♥ ❡❛❝❤ ✐♥♣✉t✱ t❤❡r❡ ✉s✉❛❧❧② ❡①✐sts ♣♦✐♥ts ✇❤✐❝❤ ❞♦ ♥♦t r❡♣r❡s❡♥t r❡❛❧ ❞❛t❛✱ ❛♥❞ ✇❤❡♥ t❤❡r❡ ❡①✐sts ♠❛♥② ✐♥♣✉ts✱ t❤❡ ❡rr♦r ❝♦✉❧❞ ❜❡ ✐♥❝r❡♠❡♥t❡❞ ❛♥❞ ❞✐✣❝✉❧t t♦ ✜❧tr❛t❡✳ ❚❤❡② ✉s✉❛❧❧② ❛♣♣❡❛r ❛s ✐s♦❧❛t❡❞ ♣♦✐♥ts✳ ❲✐t❤ t❤✐s ✜❧t❡r ✇❡ ❛r❡ ❛❜❧❡ t♦ ❡❧✐♠✐♥❛t❡ ♠♦st ♦❢ t❤❡♠✳ ❚❤❡ ❝♦❞❡ ✐s ✐♠♣❧❡♠❡♥t❡❞ ❛s ❢♦❧❧♦✇s ✭s✐♠♣❧✐✜❡❞ ❢♦r ❜❡tt❡r ✉♥❞❡rst❛♥❞✐♥❣✮✿ ♣ ❝ ❧ ✿ ✿ ❙ t ❛ t ✐ s t ✐ ❝ ❛ ❧ ❖ ✉ t ❧ ✐ ❡ r ❘ ❡ ♠ ♦ ✈ ❛ ❧ ❁♣ ❝ ❧ ✿ ✿ P♦✐♥t❳❨❩❃ s ♦ r ❀ s ♦ r ✳ s❡t■♥♣✉t❈❧♦✉❞ ✭ ♣♦✐♥t❴❝❧♦✉❞❴✐♥ ✮ ❀ s ♦ r ✳ s❡t▼❡❛♥❑ ✭ ✺ ✵ ✮ ❀ ❘❚ ♥➦ ✵✹✵✻

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✸❉ ▼❛♣♣✐♥❣ ♦❢ ✐♥❞♦♦r ❡♥✈✐r♦♥♠❡♥ts ✇✐t❤ ❛ t✐♠❡ ♦❢ ✢✐❣❤t ❝❛♠❡r❛ ✾ s ♦ r ✳ s❡t❙t❞❞❡✈▼✉❧❚❤r❡s❤ ✭ ✶ ✳ ✵ ✮ ❀ s ♦ r ✳ ❢ ✐ ❧ t ❡ r ✭ ♣♦✐♥t❴❝❧♦✉❞❴♦✉t ✮ ❀ ■♥ t❤❡ ❝♦❞❡✱ ✇❡ ♣❛ss ♣♦✐♥t❴❝❧♦✉❞❴✐♥ ❛♥❞ ✇❡ ❣❡t t❤❡ ✜❧t❡r❡❞ ✈❡rs✐♦♥ ✐♥ ♣♦✐♥t❴❝❧♦✉❞❴♦✉t✳ ❚❤❡ s❡❝♦♥❞ ✜❧t❡r ✐s ✉s❡❢✉❧ ❢♦r st♦r❛❣❡ ❛♥❞ ❝♦♠♣✉t❛t✐♦♥❛❧ r❡s♦✉r❝❡s✳ ❇❡❝❛✉s❡ t❤❡ ♠❛♣ ❝♦✉❧❞ ❜❡ ❤✉❣❡✱ ✇❡ ♣❡r❢♦r♠ ❛ ❞♦✇♥s❛♠♣❧✐♥❣ ✐♥ ❡✈✲ ❡r② ✐♥♣✉t t♦ ❣❡t ❛ s✐♠♣❧✐✜❡❞ ✈❡rs✐♦♥✳ ❚❤❡r❡ ❡①✐sts ❛ ♣❛r❛♠❡t❡r t♦ ❝♦♥tr♦❧ t❤❡ r❡s♦❧✉t✐♦♥ ♦❢ t❤❡ ✜♥❛❧ ♣♦✐♥t❝❧♦✉❞✳ ❲❡ ♣❛ss t❤❡ r❡s✉❧t ♦❢ t❤❡ ♣r❡✈✐♦✉s ✜❧t❡r✐♥❣ t♦ t❤✐s st❡♣ ✭tr❛♥s❢♦r♠❡❞ t♦ ❛ s❡♥s♦r❴♠s❣s✿✿P♦✐♥t❈❧♦✉❞✷ ❞❛t❛t②♣❡✮✳ ♣ ❝ ❧ ✿ ✿ ❱♦①❡❧●r✐❞❁ s❡♥s♦r❴♠s❣s ✿ ✿ P♦✐♥t❈❧♦✉❞✷ ❃ ✈❣r✐❞ ❀ ✈❣r✐❞ ✳ s❡t■♥♣✉t❈❧♦✉❞ ✭ ♣❝❴❞♦✇♥s❛♠♣❧❡❞ ✮ ❀ ❞♦✉❜❧❡ r ❡ s ❂ ✵ ✳ ✵ ✶ ❀ ✈❣r✐❞ ✳ s ❡ t ▲ ❡ ❛ ❢ ❙ ✐ ③ ❡ ✭ r❡s ✱ r❡s ✱ r ❡ s ✮ ❀ ✈❣r✐❞ ✳ ❢ ✐ ❧ t ❡ r ✭ ♣❝❴♦✉t ✮ ❀ ■♥ ♣❝❴♦✉t t❤❡ ✜❧t❡r❡❞ ♣♦✐♥t ❝❧♦✉❞✳ ❍❡r❡ t❤❡ r❡s♦❧✉t✐♦♥ ✐s ❧♦✇❡r❡❞ ✶✵ t✐♠❡s✳ ❲✐t❤ t❤❛t r❡s♦❧✉t✐♦♥ t❤❡ q✉❛❧✐t② ♦❢ t❤❡ ♠❛♣ r❡♠❛✐♥s ❣♦♦❞ ❛♥❞ t❤❡ ♠❛♣ ❝♦✉❧❞ ❜❡ ❡✣❝✐❡♥t❧② ✉s❡❞ ❛♥❞ s❛✈❡❞✳ ■♥ ❡✐t❤❡r ❝❛s❡ t❤❡ r❡s♦❧✉t✐♦♥ ❝♦✉❧❞ ❜❡ ❛ ♣❛r❛♠❡t❡r ♦❢ t❤❡ ❛❧❣♦r✐t❤♠✱ ❞❡♣❡♥❞✐♥❣ ♦♥ ❡❛❝❤ ♥❡❝❡ss✐t②✳ ❚❤❡ ❛❧❣♦r✐t❤♠ ✉s❡s ❛ ❝❡♥tr♦✐❞✲ ❜❛s❡❞✽❞♦✇♥s❛♠♣❧✐♥❣✳ ❚❤❡ ♥❡①t st❡♣ ✐s s✐♠♣❧② t♦ ❛❞❞ t❤❡ ♥❡✇ ♣♦✐♥t❝❧♦✉❞✳ ❇❡❝❛✉s❡ ❛❞❞✐♥❣ ♣♦✐♥t ❝❧♦✉❞s ✐s ❝♦♠♣✉t❛t✐♦♥❛❧ ❡①♣❡♥s✐✈❡✱ ✇❡ ♠❛❞❡ ❛ ✈❡❝t♦r ♦❢ ♣♦✐♥t❝❧♦✉❞s✳ ❙♦ ✇❤❡♥ ❛ ♥❡✇ ♣♦✐♥t❝❧♦✉❞ ❛rr✐✈❡s ✇❡ ❝❛❧❝✉❧❛t❡ t❤❡ ♥✉♠❜❡r ♦❢ ♣♦✐♥ts ✇❡ ❛❧r❡❛❞② s✉♠♠❡❞ ❛♥❞ ✇❤❡♥ ✐t r❡❛❝❤❡s ❛ t❤r❡s❤♦❧❞✱ ✇❡ t❛❦❡ ❛ ♥❡✇ ❡❧❡♠❡♥t ✐♥ t❤❡ ✈❡❝t♦r✳ st❞ ✿ ✿ ✈❡❝t♦r ❁♣ ❝ ❧ ✿ ✿ P♦✐♥t❈❧♦✉❞❁♣ ❝ ❧ ✿ ✿ P♦✐♥t❳❨❩❃ ❃ ♣ ❝ ❧ s ❀ ✐ ❢✭ ✦ ❢ ✐ r s t P ♦ ✐ ♥ t ❈ ❧ ♦ ✉ ❞ ✫✫ ♣ ❝ ❧ s ❬ ♣❝❧❴❛❝t✉❛❧ ❪ ✳ ♣ ♦ ✐ ♥ t s ✳ s ✐ ③ ❡ ✭ ✮ ❃ t ❤ r ❡ s ❤ ♦ ❧ ❞ ✮ ④ ❘❖❙❴■◆❋❖✭✧ P♦✐♥t ❈❧♦✉❞ r❡❛❝❤❡❞ t ❤ r ❡ s ❤ ♦ ❧ ❞ ✧✮ ❀ ♣❝❧❴❛❝t✉❛❧✰✰❀ ❢ ✐ r s t P ♦ ✐ ♥ t ❈ ❧ ♦ ✉ ❞ ❂ tr✉❡❀ ⑥ ✐ ❢✭ ❢ ✐ r s t P ♦ ✐ ♥ t ❈ ❧ ♦ ✉ ❞ ✮ ④ ♣ ❝ ❧ s ✳ r ❡ s ✐ ③ ❡ ✭ ♣❝❧❴❛❝t✉❛❧ ✰✶✮❀ ♣ ❝ ❧ s ✳ ❛t ✭ ♣❝❧❴❛❝t✉❛❧ ✮ ❂ ♣ ♦ ✐ ♥ t ❝ ❧ ♦ ✉ ❞ ❴ ❢ ✐ ❧ t ❡ r ❡ ❞ ❀ ❢ ✐ r s t P ♦ ✐ ♥ t ❈ ❧ ♦ ✉ ❞ ❂ ❢ ❛ ❧ s ❡❀ ⑥ ❡ ❧ s ❡ ④ ♣ ❝ ❧ s ✳ ❛t ✭ ♣❝❧❴❛❝t✉❛❧ ✮ ✰❂ ♣ ♦ ✐ ♥ t ❝ ❧ ♦ ✉ ❞ ❴ ❢ ✐ ❧ t ❡ r ❡ ❞ ❀ ⑥ ❋✐♥❛❧❧②✱ ✇❡ s❛✈❡ t❤❡ ♠❛♣ ✐♥ ♣❝❞ ❢♦r♠❛t t♦ st♦r❡ ❛♥❞ ✈✐s✉❛❧✐③❡ ✐t✳ ❚❤❡ ♣❝❞ ❢♦r♠❛t ✐s ❞❡✜♥❡❞ ✐♥ ♣❝❧ ❛♥❞ ✐t ✐s ❥✉st ❛♥ ❛s❝✐✐ ✜❧❡ ✇✐t❤ t❤❡ ♣♦✐♥ts ♦❢ t❤❡ ♣♦✐♥t ❝❧♦✉❞ ❛❧♦♥❣ ✇✐t❤ ♠❡t❛❞❛t❛ ❛❜♦✉t t❤❡ ♣♦✐♥ts✳ ❚❤❡ ❧✐❜r❛r② ❛❧s♦ ♣r♦✈✐❞❡s ❛ ✈✐s✉❛❧✐③❡r ✭♣❝❞❴✈✐❡✇❡r✮ t♦ s❡❡ t❤❡ ♣♦✐♥ts s❛✈❡❞ ✐♥ t❤❛t ❢♦r♠❛t✳ ❲❡ ❞♦ ♦✉t❧✐❡rs r❡♠♦✈❛❧ ❛❣❛✐♥ ✇✐t❤ t❤❡ ✜♥❛❧ ♠❛♣ t♦ r❡♠♦✈❡ s♦♠❡ s♣✉r✐♦✉s ♣♦✐♥ts t❤❛t r❡s✉❧ts ❢r♦♠ t❤❡ ♠❡r❣✐♥❣ st❡♣✳ ✽❤tt♣✿✴✴❡♥✳✇✐❦✐♣❡❞✐❛✳♦r❣✴✇✐❦✐✴❈❡♥tr♦✐❞ ❘❚ ♥➦ ✵✹✵✻

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✸❉ ▼❛♣♣✐♥❣ ♦❢ ✐♥❞♦♦r ❡♥✈✐r♦♥♠❡♥ts ✇✐t❤ ❛ t✐♠❡ ♦❢ ✢✐❣❤t ❝❛♠❡r❛ ✶✵ ❋✐❣✉r❡ ✶✿ ✸❉ ♠❛♣ ♦❢ t❤❡ ✜rst ✢♦♦r ❛t ■◆❘■❆ ●r❡♥♦❜❧❡✳

✺ ❘❡s✉❧ts

❚❤❡ ❋✐❣✉r❡ ✶ s❤♦✇ s❝r❡❡♥s❤♦ts ✇✐t❤ t❤❡ r❡s✉❧t✐♥❣ ✸❉ ♠❛♣ ♦❢ t❤❡ ✜rst ✢♦♦r ♦❢ ■◆❘■❆ ●r❡♥♦❜❧❡✳ ❊✈❡♥ ❞♦✐♥❣ t❤❡ ♠❡♥t✐♦♥❡❞ ❞♦✇♥s❛♠♣❧✐♥❣✱ t❤❡ r❡s✉❧t✐♥❣ ♠❛♣ ❤❛s ❣r❡❛t ❞❡t❛✐❧ ♦❢ t❤❡ ❡♥✈✐r♦♥♠❡♥t ♦❢ t❤❡ r♦❜♦t✱ ❛s ❝❛♥ ❜❡ s❡❡♥ ✐♥ ❋✐❣✉r❡ ✷✳ ◆❡✈❡rt❤❡❧❡ss✱ ❞✉❡ t♦ ❧✐♠✐t❛t✐♦♥s ♦❢ t❤❡ ❝❛♠❡r❛✱ ✐t ❤❛s ♣r♦❜❧❡♠s ✇✐t❤ ❣❧❛ss❡s✳ ❚❤❡ ✜❣✉r❡ ✸ ❞❡♠♦♥str❛t❡s t❤❡s❡ ♣r♦❜❧❡♠s✳ ❚❤❡ ❜❛s✐❝ ♣r♦❜❧❡♠ ✐s t❤❛t ❜❡❝❛✉s❡ ✐t ✇♦r❦s ✇✐t❤ ❧✐❣❤t✱ ✇❤❡♥ ✐t r❡❛❝❤❡s ❛ ❣❧❛ss✱ ❧✐❣❤t ✐♥t❡r❛❝ts ✐♥ ❛ ❞✐✛❡r❡♥t ✇❛② ✇✐t❤ t❤❡ ❧✐❣❤t ❝♦♠✐♥❣ ❢r♦♠ t❤❡ ❝❛♠❡r❛✱ ❛♥❞ s♦ ♠❡❛s✉r❡s ❛r❡ ♥♦t ❛❝❝✉r❛t❡✳

✻ ❈♦♥❝❧✉s✐♦♥s

❲❡ ❤❛✈❡ ♠❛❞❡ ❛ s✐♠♣❧❡ ✸❉ ♠❛♣♣✐♥❣ ❛❧❣♦r✐t❤♠ ✉s✐♥❣ ❛♥ ♦♣❡♥ s♦✉r❝❡ s♦❢t✇❛r❡ ❞❡✈❡❧♦♣✐♥❣ ♣❧❛t❢♦r♠✳ ❯s✐♥❣ ❛ ✷❉ ❜❛s❡❞ s❧❛♠ ❧♦❝❛❧✐③❛t✐♦♥ ❛❧❣♦r✐t❤♠ ✇❡ ❛r❡ ❛❜❧❡ t♦ ❝♦♥str✉❝t ❛ ✸❉ ♠❛♣ ♦❢ t❤❡ s✉rr♦✉♥❞✐♥❣ ❡♥✈✐r♦♥♠❡♥t ♦❢ ❛ ♠♦✈✐♥❣ r♦❜♦t ✐♥ ❛♥ ✉♥❦♥♦✇♥ ❡♥✈✐r♦♥♠❡♥t✳ ❚❤❡ ❛❞✈❛♥t❛❣❡s ♦❢ t❤✐s ❛♣♣r♦❛❝❤ r❡❧✐❡s ♠♦st❧② ✐♥ ✐ts ❘❚ ♥➦ ✵✹✵✻

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✸❉ ▼❛♣♣✐♥❣ ♦❢ ✐♥❞♦♦r ❡♥✈✐r♦♥♠❡♥ts ✇✐t❤ ❛ t✐♠❡ ♦❢ ✢✐❣❤t ❝❛♠❡r❛ ✶✶

❋✐❣✉r❡ ✷✿ ❉❡t❛✐❧❧❡❞ ✈✐❡✇s ♦❢ t❤❡ ♠❛♣✳

❋✐❣✉r❡ ✸✿ Pr♦❜❧❡♠ ❞✉❡ t♦ t❤❡ ❧✐♠✐t❛t✐♦♥ ♦❢ t❤❡ ❝❛♠❡r❛ ✇❤❡♥ ❞❡t❡❝t✐♥❣ ❣❧❛ss❡s✳ ❘❚ ♥➦ ✵✹✵✻

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✸❉ ▼❛♣♣✐♥❣ ♦❢ ✐♥❞♦♦r ❡♥✈✐r♦♥♠❡♥ts ✇✐t❤ ❛ t✐♠❡ ♦❢ ✢✐❣❤t ❝❛♠❡r❛ ✶✷ s✐♠♣❧✐❝✐t② ❛♥❞ ♣♦✇❡r ♦❢ r❡♣r❡s❡♥t❛t✐♦♥✳ ▼❛♣s ♦❜t❛✐♥❡❞ ❤❛✈❡ ❣♦♦❞ q✉❛❧✐t② ❛♥❞ t❤❡ ❛❧❣♦r✐t❤♠ ❝❛♥ ❡❛s✐❧② ❣❡♥❡r❛t❡ t❤❡♠✳ ❚❤❡ ❞✐s❛❞✈❛♥t❛❣❡s ♦❢ t❤✐s ❛♣♣r♦❛❝❤ r❡❧✐❡s ✐♥ t❤❡ ❞❡♣❡♥❞❡♥❝❡ ♦♥ t❤❡ ✷❉ ♠❛♣✲ ♣✐♥❣ ❛❧❣♦r✐t❤♠✳ ❚❤✐s ♣r♦❜❧❡♠ ❝♦✉❧❞ ❜❡ s♦❧✈❡❞ ❜② ✉s✐♥❣ ❛ ✸❉ ♠❛t❝❤✐♥❣ ❛❧❣♦r✐t❤♠ ❧✐❦❡ ■❈P t❤❛t ❝♦✉❧❞ tr② t♦ ❛ss❡♠❜❧❡ t❤❡♠ ❝♦rr❡❝t❧②✳

✼ ❋✉t✉r❡ ❲♦r❦

■t ✐s ♣♦ss✐❜❧❡ t♦ ❝♦♥t✐♥✉❡ t❤✐s ✇♦r❦ t♦ ❣❡t ❛ ❜❡tt❡r r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ❡♥✈✐✲ r♦♥♠❡♥t✳ ❖♥❡ ♦❢ t❤❡ ♠♦st ✐♥t❡r❡st✐♥❣ ✇♦r❦s ✇✐❧❧ ❜❡ t♦ ✉s❡ s♦♠❡ ❛❧❣♦r✐t❤♠ t♦ ❥♦✐♥ t❤❡ ❞✐✛❡r❡♥t ♣♦✐♥t ❝❧♦✉❞s✳ ❚❤✐s ✇✐❧❧ ❣✐✈❡ ♠♦r❡ ✐♥❞❡♣❡♥❞❡♥❝❡ ✇✐t❤ t❤❡ ✷❉ ♠❛♣♣✐♥❣ ❛❧❣♦r✐t❤♠ ❛♥❞ ❧❡ss ❡rr♦rs✳ ❆♥♦t❤❡r ♣♦ss✐❜❧❡ ❢✉t✉r❡ ✇♦r❦ ✐s t♦ ♠❛❦❡ ❛♥ ♦♥❧✐♥❡ ❛❧❣♦r✐t❤♠✱ ❢♦r ✐♥st❛♥❝❡ ✉s✐♥❣ ♣❛r❛❧❧❡❧ ♣r♦❣r❛♠♠✐♥❣ ❛♥❞ ✐♠♣❧❡♠❡♥t✐♥❣ ✐t ✉s✐♥❣ ❈❯❉❆ ♦r ❖♣❡♥❈▲✳ ❲✐t❤ t❤❛t ✐t ✇✐❧❧ ❜❡ ♣♦ss✐❜❧❡ t♦ s❡❡ ✐♥ r❡❛❧ t✐♠❡ t❤❡ ❝♦♥str✉❝t✐♦♥ ♦❢ t❤❡ ✸❉ ♠❛♣✳ ■♥ ❛❞❞✐t✐♦♥✱ ✐t ✇✐❧❧ ❜❡ ✐♥t❡r❡st✐♥❣ t♦ ✐♠♣❧❡♠❡♥t ♣❡♦♣❧❡ ✜❧t❡r✐♥❣❬✷❪✳ ❙♦ t❤❡ ♠❛♣♣✐♥❣ ♣r♦❝❡ss ✇✐❧❧ ♥♦t ❞❡♣❡♥❞ ♦♥ t❤❡ ♣r❡s❡♥❝❡ ♦❢ ♣❡♦♣❧❡ ✐♥ t❤❡ ❡♥✈✐r♦♥♠❡♥t✳ ■r ♦r❞❡r t♦ ❤❡❧♣ r❡♥❞❡r✐♥❣✱ ✐t ✇✐❧❧ ❜❡ ✐♠♣♦rt❛♥t t♦ s❛✈❡ t❤❡ ♠❛♣ ✐♥ ❛ ❞✐✛❡r❡♥t ❞❛t❛ str✉❝t✉r❡✳ ❖♥❡ ♦❢ t❤❡ ♣♦ss✐❜✐❧✐t✐❡s ✐s r❡♣r❡s❡♥t❡❞ ❜② s✉r❢❛❝❡s❬✶❪✱ ❜❡❝❛✉s❡ t❤❡② ❛r❡ ❜❡tt❡r ❢♦r s❛✈✐♥❣ ❛♥❞ r❡♥❞❡r✐♥❣✱ ♦r ❡✈❡♥ s✉r❢❡❧s✱ ❛s ✐♥ ❬✸❪✳ ■♥ ❛❞❞✐t✐♦♥✱ ♦❝❝✉♣❛♥❝② ❣r✐❞s❬✹❪ ❛r❡ ❛ ❣♦♦❞ ♣♦ss✐❜✐❧✐t② t♦ ♠❛❦❡ t❤❡ ♠❛♣ ♠♦r❡ ✉s❡❢✉❧✳

❘❡❢❡r❡♥❝❡s

❬✶❪ ❇r✐❛♥ ▲ ❈✉r❧❡ss✳ ◆❡✇ ♠❡t❤♦❞s ❢♦r s✉r❢❛❝❡ r❡❝♦♥str✉❝t✐♦♥ ❢r♦♠ r❛♥❣❡ ✐♠❛❣❡s✳ ❚❡❝❤♥✐❝❛❧ r❡♣♦rt✱ ❙t❛♥❢♦r❞✱ ❈❆✱ ❯❙❆✱ ✶✾✾✼✳ ❬✷❪ ❉✐r❦ ❍ä❤♥❡❧✱ ❉✐r❦ ❙❝❤✉❧③✱ ❛♥❞ ❲♦❧❢r❛♠ ❇✉r❣❛r❞✳ ▼❛♣ ❜✉✐❧❞✐♥❣ ✇✐t❤ ♠♦❜✐❧❡ r♦❜♦ts ✐♥ ♣♦♣✉❧❛t❡❞ ❡♥✈✐r♦♥♠❡♥ts✱ ✷✵✵✷✳ ❬✸❪ P❡t❡r ❍❡♥r②✱ ▼✐❝❤❛❡❧ ❑r❛✐♥✐♥✱ ❊✈❛♥ ❍❡r❜st✱ ❳✐❛♦❢❡♥❣ ❘❡♥✱ ❛♥❞ ❉✐❡t❡r ❋♦①✳ ❘❣❜✲❞ ♠❛♣♣✐♥❣✿ ❯s✐♥❣ ❞❡♣t❤ ❝❛♠❡r❛s ❢♦r ❞❡♥s❡ ✸❞ ♠♦❞❡❧✐♥❣ ♦❢ ✐♥❞♦♦r ❡♥✲ ✈✐r♦♥♠❡♥ts✳ ■♥t❡r♥❛t✐♦♥❛❧ ❙②♠♣♦s✐✉♠ ♦♥ ❊①♣❡r✐♠❡♥t❛❧ ❘♦❜♦t✐❝s✱ ✷✵✶✵✳ ❬✹❪ ❙❡❜❛st✐❛♥ ❚❤r✉♥✱ ❲♦❧❢r❛♠ ❇✉r❣❛r❞✱ ❛♥❞ ❉✐❡t❡r ❋♦①✳ Pr♦❜❛❜✐❧✐st✐❝ ❘♦❜♦t✐❝s ✭■♥t❡❧❧✐❣❡♥t ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♥♦♠♦✉s ❆❣❡♥ts✮✳ ❚❤❡ ▼■❚ Pr❡ss✱ ✷✵✵✺✳ ❘❚ ♥➦ ✵✹✵✻

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