Évaluation des impacts des changements climatiques sur l ......résumé au cours des dernières...

© Edouard Mailhot, 2019

Évaluation des impacts des changements climatiques sur l'apport en eau des Grands Lacs d'Amérique du

Nord à l'aide de modèles régionaux du climat

Mémoire

Edouard Mailhot

Maîtrise en génie des eaux - avec mémoire

Maître ès sciences (M. Sc.)

Québec, Canada

❘és✉♠é

❆✉ ❝♦✉rs ❞❡s ❞❡r♥✐èr❡s ❞é❝❡♥♥✐❡s✱ ❧❛ ❝♦♠♠✉♥❛✉té s❝✐❡♥t✐✜q✉❡ s✬❡st ✐♥tér❡ssé❡ ❛✉① ✐♠♣❛❝ts ❞❡s

❝❤❛♥❣❡♠❡♥ts ❝❧✐♠❛t✐q✉❡s s✉r ♣❧✉s✐❡✉rs ❛s♣❡❝ts ❞❡ ♥♦tr❡ ❡♥✈✐r♦♥♥❡♠❡♥t ❡t ❞❡ ♥♦tr❡ q✉♦t✐❞✐❡♥✳

▲❡ ♣rés❡♥t ♠é♠♦✐r❡ ❝♦♥t✐♥✉❡ ❞❛♥s ❝❡tt❡ ✈♦✐❡ ❡♥ ❛♥❛❧②s❛♥t ❧❡s ❝♦♥séq✉❡♥❝❡s ❞✉ ❝❧✐♠❛t ❝❤❛♥❣❡❛♥t

s✉r ❧✬❤②❞r♦❧♦❣✐❡ ❞❡ ❧❛ ré❣✐♦♥ ❞❡s ●r❛♥❞s ▲❛❝s✳ P❧✉s ♣ré❝✐sé♠❡♥t✱ ❞❡s ♠♦❞è❧❡s ré❣✐♦♥❛✉① ❞✉

❝❧✐♠❛t s❡r✈❡♥t ❞✬♦✉t✐❧s ♣♦✉r ♣r♦❥❡t❡r✱ ❞❛♥s ❧❡ ❳❳■❡ s✐è❝❧❡✱ ❞❡s ✈❛r✐❛❜❧❡s r❡❧✐é❡s à ❧❛ ❞✐s♣♦♥✐❜✐❧✐té

❡♥ ❡❛✉ ❞❡ ❝❡tt❡ ré❣✐♦♥✳ ▲❛ ♥é❝❡ss✐té ❞✬✉♥❡ t❡❧❧❡ ét✉❞❡ ♥✬❛ ❜❡s♦✐♥ ❞✬❛✉❝✉♥❡ ❛r❣✉♠❡♥t❛t✐♦♥ ❧♦rsq✉❡

❧✬❛♠♣❧❡✉r ♣❤②s✐q✉❡ ❡t s♦❝✐❛❧❡ q✉❡ r❡♣rés❡♥t❡ ❧❡ t❡rr✐t♦✐r❡ t♦✉❝❤é ❡st ❝♦♠♣r✐s❡✳ ▲❛ ré❣✐♦♥ ❞❡s

●r❛♥❞s ▲❛❝s s✬ét❡♥❞ s✉r ♣rès ❞❡ ✼✽✵ ✵✵✵ ❦♠2 ❡t ✉♥❡ ♣♦♣✉❧❛t✐♦♥ ❞❡ ♣❧✉s ❞❡ ✹✵ ♠✐❧❧✐♦♥s ②

❤❛❜✐t❡✳ ❉❡ ♣❧✉s✱ ❧✬é❝♦♥♦♠✐❡ s✉r ❝❡ t❡rr✐t♦✐r❡ r❡♣rés❡♥t❡ ♣❧✉s ❞❡ ✷✵✵ ♠✐❧❧✐❛r❞s ❯❙❉ ❛♥♥✉❡❧❧❡♠❡♥t

✭▼❛❝❑❛② ❡t ❙❡❣❧❡♥✐❡❦s✱ ✷✵✶✸✮✳ ❯♥❡ ❝♦♠♣ré❤❡♥s✐♦♥ ♣❧✉s ✐♠♣♦rt❛♥t❡ ❞❡s ✐♠♣❛❝ts ♣♦t❡♥t✐❡❧s ❞❡s

❝❤❛♥❣❡♠❡♥ts ❝❧✐♠❛t✐q✉❡s s✉r ❧✬❤②❞r♦❧♦❣✐❡ ❞❡s ●r❛♥❞s ▲❛❝s ❡st ❞♦♥❝ ❞❡ ♠✐s❡✳ ▲❡ tr❛✈❛✐❧ ❞❡

r❡❝❤❡r❝❤❡ s❡ ❝♦♥❝❡♥tr❡ s✉r ❝❡rt❛✐♥❡s ✈❛r✐❛❜❧❡s q✉✐ ✐♥t❡r❛❣✐ss❡♥t ❞✐r❡❝t❡♠❡♥t ❛✈❡❝ ❧❛ ❞✐s♣♦♥✐❜✐❧✐té

❡♥ ❡❛✉ ❞❡s ❧❛❝s✳ ❖♥ ♣❛r❧❡ ✐❝✐ ❞❡ ❧❛ ♣ré❝✐♣✐t❛t✐♦♥ ❡t ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞❡s ❧❛❝s ❡t ❞✉

r✉✐ssè❧❡♠❡♥t à ❧✬✐♥tér✐❡✉r ❞❡ ❧❡✉r ❜❛ss✐♥ ✈❡rs❛♥t✳ ❈♦♠❜✐♥é❡s✱ ❝❡s ❝♦♠♣♦s❛♥t❡s ❞♦♥♥❡♥t ✉♥❡ ✐❞é❡

❞✉ ❜✐❧❛♥ ❤②❞r✐q✉❡ q✉✐ s❡rt à ❡st✐♠❡r ❧❡ ♥✐✈❡❛✉ ❞✬❡❛✉ ❞✬✉♥ ❧❛❝✳

▲❡s ♣r❡♠✐èr❡s s❡❝t✐♦♥s ♠❡ttr♦♥t ❧❛ t❛❜❧❡ ♣♦✉r ❧❡ ❈❤❛♣✐tr❡ ✷ q✉✐ ❝♦♥t✐❡♥t ✉♥ ❛rt✐❝❧❡ ♣rés❡♥t❛♥t

♥♦t❛♠♠❡♥t ❧❡s rés✉❧t❛ts ❧❡s ♣❧✉s ♠❛rq✉❛♥ts ❞❡ ❧✬ét✉❞❡✳ ▲❡ r❡st❡ ❞❡ ❝❡ ❞♦❝✉♠❡♥t ❝♦✉✈r✐r❛

❞✬❛✉tr❡s ❛s♣❡❝ts ✐♥tér❡ss❛♥ts ❞❡ ❧✬ét✉❞❡ q✉✐ ♥✬♦♥t ♣❛s été ✐♥❝❧✉s ❞❛♥s ❧✬❛rt✐❝❧❡✳

✐✐

❆❜str❛❝t

❋♦r ❞❡❝❛❞❡s ♥♦✇✱ t❤❡ s❝✐❡♥t✐✜❝ ❝♦♠♠✉♥✐t② ❤❛s ❜❡❡♥ ✐♥t❡r❡st❡❞ ❜② t❤❡ ✐♠♣❛❝ts ♦❢ ❝❧✐♠❛t❡

❝❤❛♥❣❡ ♦♥ s❡✈❡r❛❧ ❛s♣❡❝ts ♦❢ ♦✉r ❡♥✈✐r♦♥♠❡♥t ❛♥❞ ❡✈❡r②❞❛② ❧✐❢❡✳ ❚❤❡ ♣r❡s❡♥t ✇♦r❦ ❝♦♥t✐♥✉❡s

✐♥ t❤✐s tr❡♥❞ ❜② ❛ss❡ss✐♥❣ t❤❡ ❝♦♥s❡q✉❡♥❝❡s ♦♥ t❤❡ ❤②❞r♦❧♦❣② ♦❢ t❤❡ ●r❡❛t ▲❛❦❡s r❡❣✐♦♥✳ ▼♦r❡

♣r❡❝✐s❡❧②✱ r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧s ❛r❡ ✉s❡❞ ❛s t♦♦❧s t♦ ♣r♦❥❡❝t✱ ✐♥t♦ t❤❡ ✷✶st ❝❡♥t✉r②✱ s❡✈❡r❛❧

✈❛r✐❛❜❧❡s r❡❧❛t❡❞ t♦ ✇❛t❡r ❛✈❛✐❧❛❜✐❧✐t②✳ ❚❤❡ ✐♠♣♦rt❛♥❝❡ ❛♥❞ r❡❧❡✈❛♥❝❡ ♦❢ s✉❝❤ ❛♥ ❛♥❛❧②s✐s ♥❡❡❞

♥♦ ❡①♣❧❛✐♥✐♥❣ ✇❤❡♥ t❤❡ ♣❤②s✐❝❛❧ ❛♥❞ s♦❝✐❛❧ s❝♦♣❡ ♦❢ t❤❡ st✉❞✐❡❞ ❛r❡❛ ✐s ✉♥❞❡rst♦♦❞✳ ❚❤❡ ●r❡❛t

▲❛❦❡s r❡❣✐♦♥ ❝♦✈❡rs ❝❧♦s❡ t♦ ✼✽✵ ✵✵✵ ❦♠2 ❛♥❞ ✐s ❤♦♠❡ t♦ s♦♠❡ ✹✵ ♠✐❧❧✐♦♥ ♣❡♦♣❧❡✳ ❊❝♦♥♦♠✐✲

❝❛❧❧②✱ ❛❝t✐✈✐t✐❡s ♦♥ t❤✐s t❡rr✐t♦r② ❛r❡ ✇♦rt❤ ♠♦r❡ t❤❛♥ ✷✵✵ ❜✐❧❧✐♦♥s ❯❙❉ ❡❛❝❤ ②❡❛r ✭▼❛❝❑❛② ❡t

❙❡❣❧❡♥✐❡❦s✱ ✷✵✶✸✮✳ ❆ ❣r❡❛t❡r ✉♥❞❡rst❛♥❞✐♥❣ ♦❢ t❤❡ ♣♦t❡♥t✐❛❧ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞✐✜❝❛t✐♦♥s ❜r♦✉❣❤t

✉♣♦♥ t❤✐s r❡❣✐♦♥ ❜② ❝❧✐♠❛t❡ ❝❤❛♥❣❡ ✐s t❤✉s ✉♥❞♦✉❜t❡❞❧② ♥❡❡❞❡❞✳ ❚❤❡ ❢♦❝✉s ♦❢ t❤✐s ✇♦r❦ ✇✐❧❧

❜❡ ♦♥ ✈❛r✐❛❜❧❡s t❤❛t ❞✐r❡❝t❧② ✐♥t❡r❛❝t ✇✐t❤ ✇❛t❡r ❛✈❛✐❧❛❜✐❧✐t② ♦❢ t❤❡ ❧❛❦❡s✳ ❚❤♦s❡ ❛r❡✿ ♦✈❡r❧❛❦❡

♣r❡❝✐♣✐t❛t✐♦♥✱ ♦✈❡r❧❛❦❡ ❡✈❛♣♦r❛t✐♦♥ ❛♥❞ ❧❛♥❞ r✉♥♦✛ ✐♥s✐❞❡ t❤❡ ❧❛❦❡s✬ ✇❛t❡rs❤❡❞✳ ❈♦♠❜✐♥❡❞✱

t❤❡ ✈❛r✐❛❜❧❡s ❝❛♥ ②✐❡❧❞ ❛♥ ✐❞❡❛ ♦❢ t❤❡ ✇❛t❡r ❜✉❞❣❡t ✐♥ ❛ ❧❛❦❡ ❛♥❞✱ ❜② t❤❡ s❛♠❡ t♦❦❡♥✱ ❛ ✇❛t❡r

❧❡✈❡❧ ❡st✐♠❛t❡✳

❚❤❡ ✜rst s❡❝t✐♦♥s ♦❢ t❤✐s ❞♦❝✉♠❡♥t ✇✐❧❧ ♣r❡♣❛r❡ t❤❡ r❡❛❞❡r ❢♦r ❈❤❛♣t❡r ✷✱ ✇❤✐❝❤ ❝♦♥t❛✐♥s ❛♥

❛rt✐❝❧❡ ♣r❡s❡♥t✐♥❣✱ ❛♠♦♥❣ ♦t❤❡r t❤✐♥❣s✱ t❤❡ st✉❞②✬s ♠♦st ✐♥t❡r❡st✐♥❣ r❡s✉❧ts✳ ❚❤❡ r❡♠❛✐♥✐♥❣

s❡❝t✐♦♥s ✇✐❧❧ ❝♦✈❡r ♦t❤❡r ❛s♣❡❝ts ♦❢ t❤❡ st✉❞② t❤❛t ✇❡r❡ ♥♦t ✐♥❝❧✉❞❡❞ ✐♥ t❤❡ ❛rt✐❝❧❡✳

✐✐✐

❚❛❜❧❡ ❞❡s ♠❛t✐èr❡s

❘és✉♠é ✐✐

❆❜str❛❝t ✐✐✐

❚❛❜❧❡ ❞❡s ♠❛t✐èr❡s ✐✈

▲✐st❡ ❞❡s t❛❜❧❡❛✉① ✈✐

▲✐st❡ ❞❡s ✜❣✉r❡s ✈✐✐

▲✐st❡ ❞❡s s✐❣❧❡s ❡t ❛❜ré✈✐❛t✐♦♥s ①

❘❡♠❡r❝✐❡♠❡♥ts ①✐✐

❆✈❛♥t✲♣r♦♣♦s ①✐✐✐

■♥tr♦❞✉❝t✐♦♥ ✶

✶ ▼ét❤♦❞♦❧♦❣✐❡ ❣é♥ér❛❧❡ ✹✶✳✶ ▲❡s ♠♦❞è❧❡s ❝❧✐♠❛t✐q✉❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶✳✷ ❙❝é♥❛r✐♦s ❞✬é♠✐ss✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶✳✸ ▼♦❞è❧❡s ❞❡ ❧❛❝ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶✳✹ ❊t ❞❛♥s ❧❡ ❝♦♥t❡①t❡ ❞❡s ●r❛♥❞s ▲❛❝s ❄ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶✳✺ ❘❡✈✉❡ ❞❡ ❧❛ ❧✐ttér❛t✉r❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶✳✻ ❖✉t✐❧s ❞✬❛♥❛❧②s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶

✷ ❆rt✐❝❧❡ ✿ ❆ss❡ss♠❡♥t ♦❢ t❤❡ ▲❛✉r❡♥t✐❛♥ ●r❡❛t ▲❛❦❡s✬ ❤②❞r♦❧♦❣✐❝❛❧ ♠❡❛♥❛♥❞ ❡①tr❡♠❡ ❝♦♥❞✐t✐♦♥s ✐♥ ❛ ❝❤❛♥❣✐♥❣ ❝❧✐♠❛t❡ ✉s✐♥❣ r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡♠♦❞❡❧s ✶✹✷✳✶ ❘és✉♠é ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✷✳✷ ❆❜str❛❝t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✷✳✸ ❆rt✐❝❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺

✸ ❘és✉❧t❛ts ❝♦♠♣❧é♠❡♥t❛✐r❡s ✶✻✸✳✶ ❆♥❛❧②s❡ ❞❡s ❝♦♥❞✐t✐♦♥s ❤②❞r♦❧♦❣✐q✉❡s ♠♦②❡♥♥❡s ❞❡ ❝❤❛q✉❡ ❧❛❝ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✸✳✷ ➱✈♦❧✉t✐♦♥ ❞✉ ❝♦✉✈❡rt ❞❡ ❣❧❛❝❡ s✉r ❧❡s ●r❛♥❞s ▲❛❝s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

❈♦♥❝❧✉s✐♦♥s ✷✹

✐✈

❆ ❚❡♥❞❛♥❝❡s ♣♦✉r ❧❛❝s ✐♥❞✐✈✐❞✉❡❧s ✷✻

❇ Pr♦❥❡❝t✐♦♥s s✉r ❝❛rt❡s ✲ ▼❘❈❈✺ ✭❖✉r❛♥♦s✮ ✲ ❙❝é♥❛r✐♦ ❘❈P✽✳✺ ✸✹

❈ ❙❝r✐♣ts ▼❛t❧❛❜ ✉t✐❧✐sés ✹✶

❇✐❜❧✐♦❣r❛♣❤✐❡ ✹✷

✈

▲✐st❡ ❞❡s t❛❜❧❡❛✉①

✸✳✶ ▼♦②❡♥♥❡s ❛♥♥✉❡❧❧❡s ❞❡s ❝❤❛♥❣❡♠❡♥ts ❜✐❤❡❜❞♦♠❛❞❛✐r❡s ❞❡ ❧✬❡♥s❡♠❜❧❡ ❡♥tr❡ ✶✾✺✸✲✷✶✵✵ ♣♦✉r ❧❡s ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ❧❡ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠é s✉r ❧❡ ❧❛❝✱❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ❧❡ ◆❇❙ ♣♦✉r ❝❤❛❝✉♥ ❞❡s ●r❛♥❞s ▲❛❝s✳ ❙❝é♥❛r✐♦s❘❈P✹✳✺ ❡t ❘❈P✽✳✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼

✈✐

▲✐st❡ ❞❡s ✜❣✉r❡s

✵✳✶ ❈♦♠♣♦s❛♥t❡s ❞✉ ✓ ◆❡t ❇❛s✐♥ ❙✉♣♣❧② ✔ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷

✶✳✶ ●r✐❧❧❡ ✷❉ ❞❡ rés♦❧✉t✐♦♥ ❣r♦ss✐èr❡ ✭✻✵✵ ❦♠✮ ❞✬✉♥ ♠♦❞è❧❡ ❞❡ ❝✐r❝✉❧❛t✐♦♥ ❣é♥ér❛❧❡✭▼❈●✮✳ Pr♦❞✉✐t ♣❛r ❯❈ ❉❛✈✐s ❈❧✐♠❛t❡ ❛♥❞ ●❧♦❜❛❧ ❈❤❛♥❣❡ ●r♦✉♣✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺

✶✳✷ ❉♦♠❛✐♥❡ ❞❡ ❧✬❆♠ér✐q✉❡ ❞✉ ◆♦r❞ ❞✉ ♣r♦❥❡t ❈❖❘❉❊❳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶✳✸ ❍✐st♦r✐q✉❡ ❡t t❡♥❞❛♥❝❡s ❞❡s ❢♦rç❛❣❡s r❛❞✐❛t✐❢s t♦t❛✉① ❝♦rr❡s♣♦♥❞❛♥t ❛✉① ❘❈P✱

à ❞❡s s❝é♥❛r✐♦s ❞✉ ❙❘❊❙ ❡t ❞✬✉♥ s❝é♥❛r✐♦ ❞✬■❙✾✷ ✭✉♥❡ ❛✉tr❡ ❢❛♠✐❧❧❡ ❞❡ s❝é♥❛r✐♦✮❡♥tr❡ ✶✾✺✵ ❡t ✷✶✵✵✳ ❱❛❧❡✉rs r❡❧❛t✐✈❡s ❛✉① ♥✐✈❡❛✉① ♣ré✲✐♥❞✉str✐❡❧s ❞❡ ✶✼✻✺✳ ❋✐❣✉r❡t✐ré❡ ❞❡ ❙t♦❝❦❡r ✭✷✵✶✹✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

✶✳✹ ❱❛❧❡✉rs ❞❡s ❢r❛❝t✐♦♥s ❞❡ t❡rr❡ ♣❛r t✉✐❧❡ ❞❛♥s ❧❛ ré❣✐♦♥ ❞❡s ●r❛♥❞s ▲❛❝s ♣♦✉rq✉❛tr❡ ▼❈● ét✉❞✐és ❛✉ ❈❤❛♣✐tr❡ ✷✳ ❋✐❣✉r❡s t✐ré❡s ❞❡ ▼✉s✐❝ ❡t ■r❛♠❜♦♥❛ ✭✷✵✶✼✮✳ ✶✵

✶✳✺ ❉❡♥s✐té ❞❡ ♣r♦❜❛❜✐❧✐té ❞✬✉♥❡ ❧♦✐ ❞✬❡①tr❡♠✉♠ ❣é♥ér❛❧✐sé❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸

✸✳✶ ❚❡♥❞❛♥❝❡s ❞✉ ✭❛✮ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠é s✉r ❧❡ ❧❛❝ ❡t ❞✉ ✭❜✮ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝❖♥t❛r✐♦ ❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳❙❝é♥❛r✐♦ ✽✳✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽

✸✳✷ ❚❡♥❞❛♥❝❡s ❞❡ ✭❛✮ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ❞✉ ✭❜✮ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝❙✉♣ér✐❡✉r ❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳ ❙❝é♥❛r✐♦ ✽✳✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾

✸✳✸ ❈♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ s✉r ❧❡s ●r❛♥❞s ▲❛❝s ❧❡ ✷✶ ❢é✈r✐❡r ✶✾✽✽✳ ❋✐❣✉r❡ t✐ré❡ ❞❡ ❆ss❡❧✭✷✵✵✸✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶

✸✳✹ ❈♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ ♠❛①✐♠❛❧❡ ❞❡ ❧❛ ♣ér✐♦❞❡ ❏❛♥✈✐❡r✲❋é✈r✐❡r✲▼❛rs ♠♦②❡♥♥é❡❡♥tr❡ ✶✾✼✶ ❡t ✷✵✵✵ s✉r ❧❡s ●r❛♥❞s ▲❛❝s✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s♣✐❧♦té ♣❛r ❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷

✸✳✺ ❈♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ ♠❛①✐♠❛❧❡ ❞❡ ❧❛ ♣ér✐♦❞❡ ❏❛♥✈✐❡r✲❋é✈r✐❡r✲▼❛rs ♠♦②❡♥♥é❡❡♥tr❡ ✷✵✹✶ ❡t ✷✵✼✵ s✉r ❧❡s ●r❛♥❞s ▲❛❝s✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s♣✐❧♦té ♣❛r ❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸

✸✳✻ ❈♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ ♠❛①✐♠❛❧❡ ❞❡ ❧❛ ♣ér✐♦❞❡ ❏❛♥✈✐❡r✲❋é✈r✐❡r✲▼❛rs ♠♦②❡♥♥é❡❡♥tr❡ ✷✵✼✶ ❡t ✷✶✵✵ s✉r ❧❡s ●r❛♥❞s ▲❛❝s✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s♣✐❧♦té ♣❛r ❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸

❆✳✶ ❚❡♥❞❛♥❝❡s ❞❡s ✭❛✮ ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ✭❜✮ ❞✉ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠és✉r ❧❡ ❧❛❝✱ ✭❝✮ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ✭❞✮ ❞✉ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝❙✉♣ér✐❡✉r ❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳ ❙❝é♥❛r✐♦ ❘❈P✹✳✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻

✈✐✐

❆✳✷ ❚❡♥❞❛♥❝❡s ❞❡s ✭❛✮ ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ✭❜✮ ❞✉ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠és✉r ❧❡ ❧❛❝✱ ✭❝✮ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ✭❞✮ ❞✉ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝❙✉♣ér✐❡✉r ❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳ ❙❝é♥❛r✐♦ ❘❈P✽✳✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼

❆✳✸ ❚❡♥❞❛♥❝❡s ❞❡s ✭❛✮ ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ✭❜✮ ❞✉ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠és✉r ❧❡ ❧❛❝✱ ✭❝✮ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ✭❞✮ ❞✉ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝▼✐❝❤✐❣❛♥✲❍✉r♦♥ ❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡❚❤❡✐❧✲❙❡♥✳ ❙❝é♥❛r✐♦ ❘❈P✹✳✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽

❆✳✹ ❚❡♥❞❛♥❝❡s ❞❡s ✭❛✮ ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ✭❜✮ ❞✉ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠és✉r ❧❡ ❧❛❝✱ ✭❝✮ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ✭❞✮ ❞✉ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝▼✐❝❤✐❣❛♥✲❍✉r♦♥ ❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡❚❤❡✐❧✲❙❡♥✳ ❙❝é♥❛r✐♦ ❘❈P✽✳✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾

❆✳✺ ❚❡♥❞❛♥❝❡s ❞❡s ✭❛✮ ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ✭❜✮ ❞✉ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠és✉r ❧❡ ❧❛❝✱ ✭❝✮ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ✭❞✮ ❞✉ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝ ➱r✐é❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳ ❙❝é♥❛r✐♦❘❈P✹✳✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵

❆✳✻ ❚❡♥❞❛♥❝❡s ❞❡s ✭❛✮ ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ✭❜✮ ❞✉ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠és✉r ❧❡ ❧❛❝✱ ✭❝✮ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ✭❞✮ ❞✉ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝ ➱r✐é❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳ ❙❝é♥❛r✐♦❘❈P✽✳✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶

❆✳✼ ❚❡♥❞❛♥❝❡s ❞❡s ✭❛✮ ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ✭❜✮ ❞✉ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠és✉r ❧❡ ❧❛❝✱ ✭❝✮ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ✭❞✮ ❞✉ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝❖♥t❛r✐♦ ❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳❙❝é♥❛r✐♦ ❘❈P✹✳✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷

❆✳✽ ❚❡♥❞❛♥❝❡s ❞❡s ✭❛✮ ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ✭❜✮ ❞✉ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠és✉r ❧❡ ❧❛❝✱ ✭❝✮ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ✭❞✮ ❞✉ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝❖♥t❛r✐♦ ❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳❙❝é♥❛r✐♦ ❘❈P✽✳✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸

❇✳✶ ❱❛❧❡✉rs ♠♦②❡♥♥❡s ❞❡s t❡♠♣ér❛t✉r❡s ❞❡ ❧✬❛✐r ❞❛♥s ❧❛ ré❣✐♦♥ ❞❡s ●r❛♥❞s ▲❛❝s ♣♦✉r❧✬❤♦r✐③♦♥ ✶✾✼✶✲✷✵✵✵ ❡t ❝❤❛♥❣❡♠❡♥ts ❛❜s♦❧✉s ♣♦✉r ❧❡s ❤♦r✐③♦♥s ✷✵✹✶✲✷✵✼✵ ❡t ✷✵✼✶✲✷✶✵✵ ✭❝♦♠♣❛ré à ✶✾✼✶✲✷✵✵✵✮✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s ♣✐❧♦té ♣❛r❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹

❇✳✷ ❱❛❧❡✉rs ♠♦②❡♥♥❡s ❞❡s ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞❡s ●r❛♥❞s ▲❛❝s ♣♦✉r ❧✬❤♦r✐✲③♦♥ ✶✾✼✶✲✷✵✵✵ ❡t ❝❤❛♥❣❡♠❡♥ts r❡❧❛t✐❢s ♣♦✉r ❧❡s ❤♦r✐③♦♥s ✷✵✹✶✲✷✵✼✵ ❡t ✷✵✼✶✲✷✶✵✵✭❝♦♠♣❛ré à ✶✾✼✶✲✷✵✵✵✮✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s ♣✐❧♦té ♣❛r ❈❛✲♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺

❇✳✸ ❱❛❧❡✉rs ♠♦②❡♥♥❡s ❞❡ r✉✐ssè❧❡♠❡♥t ❞❛♥s ❧❡ ❜❛ss✐♥ ✈❡rs❛♥t ❞❡s ●r❛♥❞s ▲❛❝s ♣♦✉r❧✬❤♦r✐③♦♥ ✶✾✼✶✲✷✵✵✵ ❡t ❝❤❛♥❣❡♠❡♥ts r❡❧❛t✐❢s ♣♦✉r ❧❡s ❤♦r✐③♦♥s ✷✵✹✶✲✷✵✼✵ ❡t ✷✵✼✶✲✷✶✵✵ ✭❝♦♠♣❛ré à ✶✾✼✶✲✷✵✵✵✮✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s ♣✐❧♦té ♣❛r❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺

❇✳✹ ❱❛❧❡✉rs ♠♦②❡♥♥❡s ❞✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞❡s ●r❛♥❞s ▲❛❝s ♣♦✉r ❧✬❤♦r✐③♦♥ ✶✾✼✶✲✷✵✵✵ ❡t ❝❤❛♥❣❡♠❡♥ts r❡❧❛t✐❢s ♣♦✉r ❧❡s ❤♦r✐③♦♥s ✷✵✹✶✲✷✵✼✵ ❡t ✷✵✼✶✲✷✶✵✵ ✭❝♦♠♣❛réà ✶✾✼✶✲✷✵✵✵✮✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s ♣✐❧♦té ♣❛r ❈❛♥❊❙▼✷ ❡♥s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻

❇✳✺ ➱✈♦❧✉t✐♦♥ ❞❡s ♠♦②❡♥♥❡s ❞❡ ❧❛ ❝♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ ♠❛①✐♠❛❧❡ ❞✉r❛♥t ❧❡ ♠♦✐s ❞❡❏❛♥✈✐❡r s✉r ❧❡s ●r❛♥❞s ▲❛❝s ♣♦✉r ❞❡s ♣ér✐♦❞❡s ❞❡ ✸✵ ❛♥s✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡▼❘❈❈✺✲❖✉r❛♥♦s ♣✐❧♦té ♣❛r ❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼

✈✐✐✐

❇✳✻ ➱✈♦❧✉t✐♦♥ ❞❡s ♠♦②❡♥♥❡s ❞❡ ❧❛ ❝♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ ♠❛①✐♠❛❧❡ ❞✉r❛♥t ❧❡ ♠♦✐s ❞❡❋é✈r✐❡r s✉r ❧❡s ●r❛♥❞s ▲❛❝s ♣♦✉r ❞❡s ♣ér✐♦❞❡s ❞❡ ✸✵ ❛♥s✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡▼❘❈❈✺✲❖✉r❛♥♦s ♣✐❧♦té ♣❛r ❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽

❇✳✼ ➱✈♦❧✉t✐♦♥ ❞❡s ♠♦②❡♥♥❡s ❞❡ ❧❛ ❝♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ ♠❛①✐♠❛❧❡ ❞✉r❛♥t ❧❡ ♠♦✐s ❞❡▼❛rs s✉r ❧❡s ●r❛♥❞s ▲❛❝s ♣♦✉r ❞❡s ♣ér✐♦❞❡s ❞❡ ✸✵ ❛♥s✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡▼❘❈❈✺✲❖✉r❛♥♦s ♣✐❧♦té ♣❛r ❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾

❇✳✽ ➱✈♦❧✉t✐♦♥ ❞❡s ♠♦②❡♥♥❡s ❞❡ ❧❛ ❝♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ ♠❛①✐♠❛❧❡ ❞✉r❛♥t ❧❡ ♠♦✐s❞✬❆✈r✐❧ s✉r ❧❡s ●r❛♥❞s ▲❛❝s ♣♦✉r ❞❡s ♣ér✐♦❞❡s ❞❡ ✸✵ ❛♥s✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡▼❘❈❈✺✲❖✉r❛♥♦s ♣✐❧♦té ♣❛r ❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵

✐①

▲✐st❡ ❞❡s s✐❣❧❡s ❡t ❛❜ré✈✐❛t✐♦♥s

❈❖❘❉❊❳ ✳ ✳ ✳ ✳ ✳ ❈♦♦r❞✐♥❛t❡❞ ❘❡❣✐♦♥❛❧ ❈❧✐♠❛t❡ ❉♦✇♥s❝❛❧✐♥❣ ❊①♣❡r✐♠❡♥t

❈❛♥❊❙▼ ✳ ✳ ✳ ✳ ✳ ✳ ❈❛♥❛❞✐❛♥ ❊❛rt❤ ❙②st❡♠ ▼♦❞❡❧

❈❛♥❘❈▼ ✳ ✳ ✳ ✳ ✳ ✳ ❈❛♥❛❞✐❛♥ ❘❡❣✐♦♥❛❧ ❈❧✐♠❛t❡ ▼♦❞❡❧

●❊❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ●❛③ à ❊✛❡t ❞❡ ❙❡rr❡

●❋❉▲✲❊❙▼ ✳ ✳ ✳ ●❡♦♣❤②s✐❝❛❧ ❋❧✉✐❞ ❉②♥❛♠✐❝s ▲❛❜♦r❛t♦r② ✲ ❊❛rt❤ ❙②st❡♠ ▼♦❞❡❧

●■❊❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ●r♦✉♣❡ ❞✬❊①♣❡rts ■♥t❡r❣♦✉✈❡r♥❡♠❡♥t❛❧ s✉r ❧✬➱✈♦❧✉t✐♦♥ ❞✉ ❈❧✐♠❛t

▲❊● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ▲♦✐ ❞✬❊①tr❡♠✉♠ ●é♥ér❛❧✐sé❡

▼❈● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ▼♦❞è❧❡ ❞❡ ❈✐r❝✉❧❛t✐♦♥ ●é♥ér❛❧❡

▼P■✲❊❙▼✲▲❘ ▼❛① P❧❛♥❝❦ ■♥st✐t✉t❡ ✲ ❊❛rt❤ ❙②st❡♠ ▼♦❞❡❧

▼❘❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ▼♦❞è❧❡ ❘é❣✐♦♥❛❧ ❞✉ ❈❧✐♠❛t

▼❘❈❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ▼♦❞è❧❡ ❘é❣✐♦♥❛❧ ❈❛♥❛❞✐❡♥ ❞✉ ❈❧✐♠❛t

◆❇❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ◆❡t ❇❛s✐♥ ❙✉♣♣❧②

❘❈P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❘❡♣r❡s❡♥t❛t✐✈❡ ❈♦♥❝❡♥tr❛t✐♦♥ P❛t❤✇❛②

❙❘❊❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❙♣❡❝✐❛❧ ❘❡♣♦rt ♦♥ ❊♠✐ss✐♦♥s ❙❝❡♥❛r✐♦s

①

P♦✉r ❍✉❜✉❧❧❡ (20??− 2018)

①✐

❘❡♠❡r❝✐❡♠❡♥ts

❊♥ ♣r❡♠✐❡r ❧✐❡✉✱ ❥✬❛✐♠❡r❛✐s r❡♠❡r❝✐❡r ❉❛♥✐❡❧ ◆❛❞❡❛✉ ❡t ❇✐❧❥❛♥❛ ▼✉s✐❝ q✉✐ ♠✬♦♥t ❞✐r✐❣é ❡t s♦✉✲

t❡♥✉ ❞✉r❛♥t ♠❛ ♠❛îtr✐s❡✳ ❏❡ ♠❡ ❝♦♥s✐❞èr❡ très ❝❤❛♥❝❡✉① ❞✬❛✈♦✐r tr❛✈❛✐❧❧é ❛✈❡❝ ❞❡✉① ♣❡rs♦♥♥❡s

❛✉ss✐ ♠♦t✐✈❛♥t❡s✳

▼❡r❝✐ à ❆♥♥❡ ❋r✐❣♦♥✱ ❘✐❝❤❛r❞ ❚✉r❝♦tt❡ ❡t ❆❧❛✐♥ ▼❛✐❧❤♦t ♣♦✉r ❧❡✉rs ❥✉❞✐❝✐❡✉① ❝♦♥s❡✐❧s ❧♦rs ❞❡

♠❡s r❡❝❤❡r❝❤❡s ❡t ❞❡ ❧❛ ré❞❛❝t✐♦♥ ❞❡ ♠♦♥ ❛rt✐❝❧❡✳

▼❡r❝✐ à ❧✬éq✉✐♣❡ ❞✬❖✉r❛♥♦s ❞✬❛✈♦✐r ré♣♦♥❞✉ à ♠❡s q✉❡st✐♦♥s✳

▼❡r❝✐ à ♠❛ ❢❛♠✐❧❧❡ ♣♦✉r ❧❡✉r ♣rés❡♥❝❡ ❡t ❧❡✉rs ❡♥❝♦✉r❛❣❡♠❡♥ts✳

❏❡ r❡❝♦♥♥❛✐s ❡t r❡♠❡r❝✐❡ ▼✐t❛❝s ❡t ❖✉r❛♥♦s ♣♦✉r ❧❡ ✜♥❛♥❝❡♠❡♥t ❞❡ ♠♦♥ ♣r♦❥❡t ❞❡ r❡❝❤❡r❝❤❡✳

①✐✐

❆✈❛♥t✲♣r♦♣♦s

▲✬❛rt✐❝❧❡ ✐♥té❣ré ❞❛♥s ❝❡ ♠é♠♦✐r❡ ❡st ✐♥t✐t✉❧é ❆ss❡ss♠❡♥t ♦❢ t❤❡ ▲❛✉r❡♥t✐❛♥ ●r❡❛t ▲❛❦❡s✬ ❤②✲

❞r♦❧♦❣✐❝❛❧ ♠❡❛♥ ❛♥❞ ❡①tr❡♠❡ ❝♦♥❞✐t✐♦♥s ✐♥ ❛ ❝❤❛♥❣✐♥❣ ❝❧✐♠❛t❡ ✉s✐♥❣ r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧s✳

■❧ ❛ été s♦✉♠✐s ❛✉ ❥♦✉r♥❛❧ ❈❧✐♠❛t✐❝ ❈❤❛♥❣❡ ❧❡ ✶✾ ♥♦✈❡♠❜r❡ ✷✵✶✽ ❡t✱ ❛✉ ♠♦♠❡♥t ❞✉ ❞é♣ôt ❞❡

❝❡ ♠é♠♦✐r❡✱ ✉♥❡ ré♣♦♥s❡ ❡st ❛tt❡♥❞✉❡✳ ▲✬❛rt✐❝❧❡ s♦✉♠✐s ❛✉ ❥♦✉r♥❛❧ ❡t ❝❡❧✉✐ ✐♥séré ✐❝✐ s♦♥t ❧❡s

♠ê♠❡s✳ ❊❞♦✉❛r❞ ▼❛✐❧❤♦t ❡st ❧✬❛✉t❡✉r ♣r✐♥❝✐♣❛❧ ❡t ❝❡❧✉✐ q✉✐ ❛ ré❞✐❣é ❧✬❛rt✐❝❧❡✳ ❉❡ ♥♦♠❜r❡✉s❡s

ré✈✐s✐♦♥s ❡t ❝♦rr❡❝t✐♦♥s ♦♥t été ❛♣♣♦rté❡s ♣❛r ❧❡s ❝♦❛✉t❡✉rs ❇✐❧❥❛♥❛ ▼✉s✐❝ ❡t ❉❛♥✐❡❧ ◆❛❞❡❛✉✳

❯♥❡ ré✈✐s✐♦♥ s♦♠♠❛✐r❡ ❡t ❞❡s r❡❝♦♠♠❛♥❞❛t✐♦♥s ♦♥t été ❢♦✉r♥✐❡s ♣❛r ❧❡s ❝♦❛✉t❡✉rs ❆♥♥❡ ❋r✐❣♦♥

❡t ❘✐❝❤❛r❞ ❚✉r❝♦tt❡✳

▲❡s é✈❛❧✉❛t❡✉rs ❞✉ ♣rés❡♥t ♠é♠♦✐r❡ s♦♥t ◆❛t❤❛❧✐❡ ❇❛rr❡tt❡ ❡t ❋r❛♥ç♦✐s ❆♥❝t✐❧✳

①✐✐✐

■♥tr♦❞✉❝t✐♦♥

▲✬❡♥❥❡✉ ❞❡s ❝❤❛♥❣❡♠❡♥ts ❝❧✐♠❛t✐q✉❡ ♥✬❡st ♣❛s ré❝❡♥t✳ ❉✉r❛♥t ❧❛ ♣r❡♠✐èr❡ ♠♦✐t✐é ❞✉ ❳■❳❡ s✐è❝❧❡✱

❞é❥à✱ ♦♥ r❡♠❛rq✉❡ q✉❡ ❧✬❤✉♠❛✐♥ ❡t s❡s ❛❝t✐✈✐tés ✐♥❞✉str✐❡❧❧❡s ♣❡✉✈❡♥t t❤é♦r✐q✉❡♠❡♥t ♣r♦✈♦q✉❡r

❞❡s ❝❤❛♥❣❡♠❡♥ts ❛✉ ❝❧✐♠❛t ♣❧❛♥ét❛✐r❡ ✭❋♦✉r✐❡r✱ ✶✽✷✼✮✳ ◗✉❡❧q✉❡s ❞é❝❡♥♥✐❡s ❡t ❝♦♥tr✐❜✉t✐♦♥s

s❝✐❡♥t✐✜q✉❡s ♣❧✉s t❛r❞✱ ♦♥ ✐❞❡♥t✐✜❡ ❧❡s ❣❛③ q✉✐✱ ❧♦rsq✉❡ ♣rés❡♥ts ❞❛♥s ❧✬❛t♠♦s♣❤èr❡✱ ❝❛✉s❡♥t ✉♥

ré❝❤❛✉✛❡♠❡♥t ❞❡ ❧✬❛✐r ✭❚②♥❞❛❧❧✱ ✶✽✼✷✮✱ ♦♥ ❝❛❧❝✉❧❡ ❝❡❧✉✐✲❝✐ ♣♦✉r ❧❛ ♣r❡♠✐èr❡ ❢♦✐s ✭❆rr❤❡♥✐✉s ❡t

❍♦❧❞❡♥ ✶✽✾✼ ❀ ❈❤❛♠❜❡r❧✐♥ ✶✽✾✾✮ ❡t ♦♥ ❞♦♥♥❡ ✉♥ ♥♦♠ à ❝❡ ♣❤é♥♦♠è♥❡ ✿ ❧✬❡✛❡t ❞❡ s❡rr❡✳

▲✬❡✛❡t ❞❡ s❡rr❡✱ s✉❝❝✐♥❝t❡♠❡♥t✱ ❡st ✉♥ ♣r♦❝❡ss✉s ♥❛t✉r❡❧ ❝❛✉sé ♣❛r ❧✬❛t♠♦s♣❤èr❡ ❞✬✉♥❡ ♣❧❛♥èt❡✳

▲❛ ♣rés❡♥❝❡ ❡t ❧❛ ❝♦♠♣♦s✐t✐♦♥ ❞❡ ❝❡❧❧❡✲❝✐ ✐♥✢✉❡♥❝❡♥t✱ ❡♥tr❡ ❛✉tr❡s✱ ❧❡s ✢✉① ❞❡ r❛②♦♥♥❡♠❡♥t ♣r♦✲

✈❡♥❛♥t ❞✉ ❙♦❧❡✐❧ ❡t ❞✐❝t❡♥t ❝❡ q✉✐ ❡st ré✢é❝❤✐ ❞❛♥s ❧✬❡s♣❛❝❡✱ ❛❜s♦r❜é ♣❛r ❧✬❛t♠♦s♣❤èr❡ ❡t ❧❡ r❡st❡✱

❛❜s♦r❜é ♣❛r ❧❡ s♦❧✳ ▲❡ t❡❧ ❢r❛❝t✐♦♥♥❡♠❡♥t ❞❡s r❛②♦♥s s♦❧❛✐r❡s ✐♥✢✉❡♥❝❡ ❧❛ t❡♠♣ér❛t✉r❡ t❡rr❡str❡

à ✉♥ ♣♦✐♥t t❡❧ q✉❡ ♥♦tr❡ ♣❧❛♥èt❡✱ s❛♥s s♦♥ ❛t♠♦s♣❤èr❡✱ ❛✉r❛✐t ✉♥❡ t❡♠♣ér❛t✉r❡ ♠♦②❡♥♥❡ ❞❡

−19◦❈ ✭▲❡ ❚r❡✉t ❡t ❛❧✳✱ ✷✵✵✼✮✱ ❝✬❡st✲à✲❞✐r❡ 33◦❈ s♦✉s ❧❛ ✈❛❧❡✉r ❛❝t✉❡❧❧❡✳ ❯♥ t❡❧ é❝❛rt ✐♠♣❧✐q✉❡✱

é✈✐❞❡♠♠❡♥t✱ ❞❡s ❝♦♥❞✐t✐♦♥s ❝❧✐♠❛t✐q✉❡s ❜♦✉❧❡✈❡rsé❡s ❡t ✉♥ ❡♥✈✐r♦♥♥❡♠❡♥t ❝♦♠♣❧èt❡♠❡♥t ❞✐❢✲

❢ér❡♥t✱ ♠❛✐s ❧❛ ♠♦❞✐✜❝❛t✐♦♥ ❞❡s t❡♠♣ér❛t✉r❡s ♥✬❛ ♣❛s à êtr❡ ❞❡ ❝❡tt❡ ❡♥✈❡r❣✉r❡ ♣♦✉r ❛❧tér❡r ❧❡s

♣r♦❝❡ss✉s ♣❤②s✐q✉❡s ❛t♠♦s♣❤ér✐q✉❡s q✉✐ ❞é✜♥✐ss❡♥t ❧❡ ❝❧✐♠❛t✳ ❊♥ ❡✛❡t✱ ✉♥❡ ♣❛♥♦♣❧✐❡ ❞✬ét✉❞❡s

❞é❝r✐t ❧❡s rés✉❧t❛ts q✉✬✉♥❡ ❤❛✉ss❡ ❞✬à ♣❡✐♥❡ ✉♥ à tr♦✐s ❞❡❣rés ❈❡❧s✐✉s ❛✉r❛✐t s✉r ❧❡s s♣❤èr❡s

❝❧✐♠❛t✐q✉❡s✱ ❜✐♦❧♦❣✐q✉❡s ❡t s♦❝✐❛❧❡s ❞❡ ♥♦tr❡ ♣❧❛♥èt❡ ✭♣✳ ❡①✳ ❚r❡♥❜❡rt❤ ✷✵✶✶ ❀ ❉❛✐ ✷✵✶✶ ❀ ❆❧♦♥❣✐

✷✵✶✺✮✳ ❈♦♠♠❡ ❧❡ té♠♦✐❣♥❡r❛ ❧❛ ♣rés❡♥t❡ ét✉❞❡✱ ❧✬❤②❞r♦❧♦❣✐❡✱ ❡t✱ ♣❧✉s ♣❛rt✐❝✉❧✐èr❡♠❡♥t✱ ❧❡ ❝②❝❧❡

❞❡ ❧✬❡❛✉ ❞❛♥s ❧❡ ❜❛ss✐♥ ✈❡rs❛♥t ❞✬✉♥ ❧❛❝✱ ♥❡ s♦♥t ♣❛s ❡①❡♠♣ts ❞❡ ❧❛ ❧✐st❡ ❞❡s ❞♦♠❛✐♥❡s t♦✉❝❤és✳

P❛r♠✐s ❧❡s ❧❛❝s t❡rr❡str❡s✱ ❧❡s ●r❛♥❞s ▲❛❝s s❡ ❤✐ss❡♥t ❛✉ s♦♠♠❡t ❞✉ ♣❛❧♠❛rès ❡♥ t❡r♠❡ ❞❡ t❛✐❧❧❡

❡t ❞❡ r❡♥♦♠✳ ❋♦r♠é ❣é♦❧♦❣✐q✉❡♠❡♥t ✐❧ ② ❛ ✶✱✶ à ✶✱✷ ♠✐❧❧✐❛r❞s ❞✬❛♥♥é❡s ♣❛r ❧❛ sé♣❛r❛t✐♦♥ ❞❡ ❞❡✉①

♣❧❛q✉❡s t❡❝t♦♥✐q✉❡s ✭❱❛♥ ❙❝❤♠✉s ❡t ❍✐♥③❡✱ ✶✾✽✺✮✱ s❝✉❧♣té ♣❛r ❞❡ ♥♦♠❜r❡✉s❡s ❣❧❛❝✐❛t✐♦♥s ❡t

r❡♠♣❧✐ ✐❧ ② ❛ ❡♥✈✐r♦♥ ✶✶ ✵✵✵ ❛♥s ♣❛r ❧✬❡❛✉ ❞❡ ❢♦♥t❡ ❞❡s ❣❧❛❝✐❡rs ❞✉ ❞❡r♥✐❡r â❣❡ ❣❧❛❝✐❛✐r❡ ✭▲❛rs♦♥

❡t ❙❝❤❛❡t③❧✱ ✷✵✵✶✮✱ ❝❡ rés❡❛✉ ❞❡ ❝✐♥q ❧❛❝s ❡t ❧❡✉rs ❜❛ss✐♥s ✈❡rs❛♥ts ❝♦✉✈r❡♥t ❛✉❥♦✉r❞✬❤✉✐ ♣rès

❞❡ ✼✽✵ ✵✵✵ ❦♠2✳ ❉❡ ♣❧✉s✱ ❛♣♣r♦①✐♠❛t✐✈❡♠❡♥t ✷✵✪ ❞❡ ❧✬❡❛✉ ❞♦✉❝❡ t❡rr❡str❡ ❡st ❝♦♥t❡♥✉ ❞❛♥s

❧❡s ❧❛❝s ✭❍❛rt♠❛♥♥✱ ✶✾✾✵✮✳ ❈❡t ✐♠♠❡♥s❡ t❡rr✐t♦✐r❡ ❛❜r✐t❡ ✉♥❡ ♣♦♣✉❧❛t✐♦♥ ❞✬❡♥✈✐r♦♥ ✹✵ ♠✐❧✲

❧✐♦♥s ❞✬❤❛❜✐t❛♥ts ❡t ❧❡s ❛❝t✐✈✐tés é❝♦♥♦♠✐q✉❡s ② r❡♣rés❡♥t❡♥t ❞❡s ❝❡♥t❛✐♥❡s ❞❡ ♠✐❧❧✐❛r❞s ❯❙❉

✶

❋✐❣✉r❡ ✵✳✶ ✕ ❈♦♠♣♦s❛♥t❡s ❞✉ ✓ ◆❡t ❇❛s✐♥ ❙✉♣♣❧② ✔

❛♥♥✉❡❧❧❡♠❡♥t ✭▼❛❝❑❛② ❡t ❙❡❣❧❡♥✐❡❦s✱ ✷✵✶✸✮✳ ❱✉ ❧✬❛♠♣❧❡✉r ❞é♠♦❣r❛♣❤✐q✉❡ ❡t é❝♦♥♦♠✐q✉❡ ❞❡

❝❡tt❡ ré❣✐♦♥✱ ✐❧ ❡st ♣r✐♠♦r❞✐❛❧ ❞❡ ♠✐❡✉① ❝♦♠♣r❡♥❞r❡ ❧❛ ✈✉❧♥ér❛❜✐❧✐té ❞❡ s♦♥ ❤②❞r♦❧♦❣✐❡ ❛✉①

❝❤❛♥❣❡♠❡♥ts ❝❧✐♠❛t✐q✉❡s✳ ❇✐❡♥ q✉❡ ❧❡ ré❣✐♠❡ ❤②❞r♦❧♦❣✐q✉❡ ❞❡s ●r❛♥❞s ▲❛❝s s♦✐t ❝♦♠♣❧❡①❡✱ ✐❧

♣❡✉t êtr❡ s✐♠♣❧✐✜é ♣♦✉r ❢❛❝✐❧✐t❡r s♦♥ ❛♥❛❧②s❡✳ P♦✉r ❝❡ ❢❛✐r❡✱ ♦♥ ♥❡ ♣r❡♥❞ ❡♥ ❝♦♠♣t❡ q✉❡ ❧❡s

♣r♦❝❡ss✉s ❞❡ ❜❛s❡ ❞✉ ❝②❝❧❡ ❞❡ ❧✬❡❛✉✱ ❝✬❡st✲à✲❞✐r❡ ❧❛ ♣ré❝✐♣✐t❛t✐♦♥✱ ❧✬é✈❛♣♦r❛t✐♦♥ ❡t ❧❡ r✉✐ssè❧❡✲

♠❡♥t✳ ❆✈♦✐r ❞❡s ❡st✐♠❛t✐♦♥s q✉❛♥t✐t❛t✐✈❡s ❞❡ ❝❡s ✢✉① ♣❡r♠❡t ❞✬❛✈♦✐r ✉♥❡ ✐❞é❡ s♦♠♠❛✐r❡ ❞❡s

❛❝t✐✈✐tés ❤②❞r♦❧♦❣✐q✉❡s ❞❛♥s ✉♥ ❜❛ss✐♥ ✈❡rs❛♥t✳ ■❧ ❡st ♠ê♠❡ ♣♦ss✐❜❧❡✱ ❞✬❛♣rès ❝❡s ❡st✐♠❛t✐♦♥s✱

❞❡ ❧❡s ❝♦♠❜✐♥❡r ♣♦✉r ♦❜t❡♥✐r ✉♥ ❜✐❧❛♥ ❤②❞r✐q✉❡ q✉✐ s✬❛✈èr❡ ré✈é❧❛t❡✉r ❞✉ ♥✐✈❡❛✉ ❞✬❡❛✉ ❞✉ ❧❛❝

ét✉❞✐é✳ ▲❡ ❜✐❧❛♥ ❤②❞r✐q✉❡ ❞✬✉♥ ❧❛❝✱ ❞❛♥s ❝❡ ❞♦❝✉♠❡♥t✱ ❡st ❡①♣r✐♠é ♣❛r ❧❡ ◆❡t ❇❛s✐♥ ❙✉♣♣❧②

✭◆❇❙✮✱ ✉♥❡ ✈❛r✐❛❜❧❡ s♦✉✈❡♥t ✉t✐❧✐sé❡ ❡♥ ❤②❞r♦❧♦❣✐❡ ✭❈r♦❧❡② ✶✾✾✵ ❀ ▼✉s✐❝ ❡t ❛❧✳ ✷✵✶✺✮✳ ▲❡ ◆❇❙

r❡♣rés❡♥t❡ ✉♥❡ ❝♦✉❝❤❡ ❞✬❡❛✉ s✉r ✉♥ ❧❛❝ ❞✬✉♥❡ ❤❛✉t❡✉r ❞é✜♥✐❡ ♣❛r

◆❇❙ = P❧❛❝ + ❘t❡rr❡ − ❊❧❛❝, ✭✶✮

♦ù P❧❛❝ ❡st ❧❛ ♣ré❝✐♣✐t❛t✐♦♥ t♦♠❜❛♥t s✉r ❧❡ ❧❛❝✱ ❘t❡rr❡ ❡st ❧❡ r✉✐ssè❧❡♠❡♥t ♣r♦✈❡♥❛♥t ❞✉ ❜❛ss✐♥

✈❡rs❛♥t ❡t ❊❧❛❝ ❡st ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ✭✈♦✐r ❋✐❣✉r❡ ✵✳✶✮✳ ■❧ s✬❛❣✐t ❞❡ ❧❛ ❢❛ç♦♥ ❞✬❡①✲

♣r✐♠❡r ❧❡ ◆❇❙ ❞✐t❡ ♣❛r ❝♦♠♣♦s❛♥t❡s✳ ❈❡tt❡ ✈❛r✐❛❜❧❡ ❡st ❝❤♦✐s✐❡ ♣♦✉r ❧✬❛♥❛❧②s❡ ♣✉✐sq✉✬❡❧❧❡ ❡st

étr♦✐t❡♠❡♥t ❛ss♦❝✐é❡ ❛✉ ♥✐✈❡❛✉ ❞✬✉♥ ❧❛❝✱ ✉♥ ♣❛r❛♠ètr❡ ❝r✉❝✐❛❧ ♣♦✉r ❞é❝r✐r❡ ❝❡❧✉✐✲❝✐✳ ❊♥ ♣❧✉s

❞✉ ◆❇❙ ♣❛r ❝♦♠♣♦s❛♥t❡s✱ ✐❧ ❡①✐st❡ é❣❛❧❡♠❡♥t ❧❛ ♠ét❤♦❞❡ rés✐❞✉❡❧❧❡✱ q✉✐✱ ❡❧❧❡✱ rés♦✉t ❧❡ ❜✐❧❛♥

❞✬✉♥ ❧❛❝ ❡♥ ♣r❡♥❛♥t ❝♦♠♣t❡ ❞❡s ❞é❜✐ts ❡♥tr❛♥ts✱ ❡♥ ❛♠♦♥t✱ ❡t s♦rt❛♥ts✱ ❡♥ ❛✈❛❧✳ ❈❡tt❡ s❡❝♦♥❞❡

♠ét❤♦❞❡ ♥❡ s❡r❛ ♣❛s ❝♦✉✈❡rt❡ ✐❝✐✳ ❈✬❡st s✉r ❧❡ ◆❇❙ ❡t s❡s ❝♦♠♣♦s❛♥t❡s q✉❡ s❡r♦♥t ❜❛sé❡s ❧❡s

❞✐✛ér❡♥t❡s ❛♥❛❧②s❡s ❞❡ ❧❛ ♣rés❡♥t❡ ét✉❞❡✳

▲✬♦❜❥❡❝t✐❢ ♣r✐♥❝✐♣❛❧ ❞❡ ❝❡ ♣r♦❥❡t ❞❡ r❡❝❤❡r❝❤❡ ❡t ❞✬é✈❛❧✉❡r ❧❡s ✐♠♣❛❝ts ❞❡s ❝❤❛♥❣❡♠❡♥ts ❝❧✐♠❛✲

t✐q✉❡s s✉r ❧❡s ❛♣♣♦rts ❡♥ ❡❛✉ ❞❡s ●r❛♥❞s ▲❛❝s✳ P♦✉r ❛rr✐✈❡r à ❝❡t ♦❜❥❡❝t✐❢✱ q✉❡❧q✉❡s ♦❜❥❡❝t✐❢s

s❡❝♦♥❞❛✐r❡s ❞❡✈r♦♥t êtr❡ ré❛❧✐sés✳ ❖♥ ♣❛r❧❡ ✐❝✐ ❞❡ ❝♦♥str✉✐r❡ ❞❡s sér✐❡s t❡♠♣♦r❡❧❧❡s ♣♦✉r ❞✐✛é✲

r❡♥t❡s ✈❛r✐❛❜❧❡s ❤②❞r♦❧♦❣✐q✉❡s à ❧✬❛✐❞❡ ❞✬♦❜s❡r✈❛t✐♦♥s ♣♦✉r ❛rr✐✈❡r à ❞é❝r✐r❡ q✉❛♥t✐t❛t✐✈❡♠❡♥t

❧❡ ❝❧✐♠❛t ❤✐st♦r✐q✉❡ ❞❡ ❧❛ ré❣✐♦♥ à ❧✬ét✉❞❡✳ ■❧ ❡st é❣❛❧❡♠❡♥t ♥é❝❡ss❛✐r❡ ❞❡ ❝♦♥str✉✐r❡ ❞❡s sér✐❡s

❡♥ ♣r♦❥❡❝t✐♦♥ ❞❛♥s ❧❡ ❢✉t✉r ♣♦✉r ❧❡s ♠ê♠❡s ✈❛r✐❛❜❧❡s ❡♥ ✉t✐❧✐s❛♥t ❞❡s s✐♠✉❧❛t✐♦♥s ❣é♥éré❡s ♣❛r

✷

❞❡s ♠♦❞è❧❡s ré❣✐♦♥❛✉① ❞✉ ❝❧✐♠❛t ✭▼❘❈✮✳ ❋✐♥❛❧❡♠❡♥t✱ ❧❛ ❝♦♠♣❛r❛✐s♦♥ ❞❡s sér✐❡s ♦❜s❡r✈é❡s ❡t

s✐♠✉❧é❡s ❡♥ ✈✉❡ ❞✬é✈❛❧✉❡r ❧❡s ♣❡r❢♦r♠❛♥❝❡s ❞❡s ❞✐✛ér❡♥ts ♠♦❞è❧❡s ❡t ❧✬❛♥❛❧②s❡ st❛t✐st✐q✉❡ ❞❡s

♣r♦❥❡❝t✐♦♥s ✈♦♥t ♣❡r♠❡ttr❡ ❞✬❛tt❡✐♥❞r❡ ❧✬♦❜❥❡❝t✐❢ ♣r✐♥❝✐♣❛❧ ❞❡ ❧✬ét✉❞❡✳

✸

❈❤❛♣✐tr❡ ✶

▼ét❤♦❞♦❧♦❣✐❡ ❣é♥ér❛❧❡

✶✳✶ ▲❡s ♠♦❞è❧❡s ❝❧✐♠❛t✐q✉❡s

▲❛ ❢♦♥❝t✐♦♥ ❞✬✉♥ ♠♦❞è❧❡ ❝❧✐♠❛t✐q✉❡ ❡st ❞❡ s✐♠♣❧✐✜❡r ❡t s✐♠✉❧❡r ❞❡s ♣r♦❝❡ss✉s ♥❛t✉r❡❧s ♣♦✉r

r❡♣rés❡♥t❡r ✉♥❡ ✈❡rs✐♦♥ ❛rt✐✜❝✐❡❧❧❡ ❞✉ ❝❧✐♠❛t ❞✬✉♥ ❞♦♠❛✐♥❡ s♣❛t✐❛❧✳ ▲❡s ❝❛❧❝✉❧s ♣♦✉r ❡♥ ❛rr✐✈❡r

❧à s❡ ❜❛s❡♥t s✉r ❞❡s ❧♦✐s ❢♦♥❞❛♠❡♥t❛❧❡s ❞❡ ❧❛ ♣❤②s✐q✉❡ ❡t ❞❡s é❧é♠❡♥ts ❡♠♣✐r✐q✉❡s ✐♥é✈✐t❛❜❧❡s

✭▲❡ ❚r❡✉t✱ ✷✵✵✺✮✳ ▲✬é✈♦❧✉t✐♦♥ ❞❡ ❝❡ ❝❤❛♠♣ ❞✬❡①♣❡rt✐s❡ ét❛✐t✱ ❡t ❡st t♦✉❥♦✉rs très r❛♣✐❞❡✳ ❉ès

❧❡s ❜❛❧❜✉t✐❡♠❡♥ts ❞❡s ♠♦❞è❧❡s ❝❧✐♠❛t✐q✉❡s✱ ✈❡rs ✶✾✻✵✱ ❞❡s ♥♦✉✈❡❛✉① ♠♦❞è❧❡s✱ ❞❡s ✈❡rs✐♦♥s

❛♠é❧✐♦ré❡s ❞✬❛♥❝✐❡♥s ♠♦❞è❧❡s ❡t ❞❡s s✐♠✉❧❛t✐♦♥s ❞❡✈✐❡♥♥❡♥t ❞✐s♣♦♥✐❜❧❡s ❝❤❛q✉❡ ❛♥♥é❡ à ✉♥

r②t❤♠❡ ❡✛ré♥é✳ ▲❡ ❞♦♠❛✐♥❡ ✈✐sé ♣❛r ❧❡s ♠♦❞é❧✐s❛t✐♦♥s ❝♦✉✈r❡ ❛❧♦rs ❧❡ ❣❧♦❜❡ ❡♥t✐❡r ✭▲②♥❝❤✱

✷✵✵✻✮ ❡t ♦♥ ❛♣♣❡❧❧❡ ❝❡s ♦✉t✐❧s ❞❡s ♠♦❞è❧❡s ❞❡ ❝✐r❝✉❧❛t✐♦♥ ❣é♥ér❛❧❡ ✭▼❈●✮✳ ❈♦♠♠❡ ❧✬✐♥❞✐q✉❡

❧❛ ❋✐❣✉r❡ ✶✳✶✱ ❧❡s ▼❈● ❝♦✉✈r❡♥t ❧❛ s✉r❢❛❝❡ ❞❡ ❧❛ ♣❧❛♥èt❡ ❚❡rr❡ à ❧✬❛✐❞❡ ❞✬✉♥❡ ❣r✐❧❧❡ ❞❡ t②♣❡

❧❛t✐t✉❞❡✴❧♦♥❣✐t✉❞❡✳ ▲❛ rés♦❧✉t✐♦♥ s♣❛t✐❛❧❡ ❞❡s t✉✐❧❡s ❢♦r♠é❡s ♣❛r ❝❡tt❡ ❣r✐❧❧❡ ✈❛r✐❡✱ ♠❛✐s ❞❛♥s ❧❡

❝❛s ❞❡s ▼❈●✱ ❝❡❧❧❡✲❝✐ ❡st ❞✬❡♥✈✐r♦♥ ✷✵✵ ❦♠✳ ▲❡s ♠♦❞è❧❡s ❞❡ ❝✐r❝✉❧❛t✐♦♥ ❣é♥ér❛❧❡ s♦♥t s♦✉✈❡♥t

✉t✐❧✐sés ❞❛♥s ❧❡ ❝❛❞r❡ ❞✬ét✉❞❡s s✉r ❧❡s ❝❤❛♥❣❡♠❡♥ts ❝❧✐♠❛t✐q✉❡s✳ ❉❛♥s ❝❡s ❝❛s✱ ❧❡s s✐♠✉❧❛t✐♦♥s

s✉r ❞❡ ❣r❛♥❞❡s é❝❤❡❧❧❡s t❡♠♣♦r❡❧❧❡s ♣❡r♠❡tt❡♥t ❞✬❡♥tr❡✈♦✐r à q✉♦✐ ❧❡ ❝❧✐♠❛t ♣❧❛♥ét❛✐r❡ ♣♦✉rr❛✐t

r❡ss❡♠❜❧❡r ❡♥ ♣r♦❞✉✐s❛♥t ❞❡s sér✐❡s t❡♠♣♦r❡❧❧❡s ♣♦✉r ❞❡s ❝❡♥t❛✐♥❡s ❞❡ ✈❛r✐❛❜❧❡s ❞✐✛ér❡♥t❡s ✭❞✉

❝♦♥t❡♥✉ ❡♥ ❡❛✉ ❞✉ s♦❧ ❥✉sq✉✬à ❧❛ ✈✐t❡ss❡ ❡t ❧❛ ❞✐r❡❝t✐♦♥ ❞❡s ✈❡♥ts✮✳ ❉❡s ❛♥❛❧②s❡s ❞❡ t♦✉t❡s s♦rt❡s

♣❡✉✈❡♥t ❛❧♦rs ❣❡r♠❡r ❞❡s s♦rt✐❡s ❞❡s ▼❈●✳

▲❛ ♣❧✉♣❛rt ❞❡s ét✉❞❡s s❝✐❡♥t✐✜q✉❡s ét❛♥t à ❞❡s é❝❤❡❧❧❡s ♣❧✉s ♣❡t✐t❡s q✉❡ ❧❛ ♣❧❛♥èt❡ ❚❡rr❡✱ ❧❛

rés♦❧✉t✐♦♥ s♣❛t✐❛❧❡ ❢♦✉r♥✐❡ ♣❛r ❧❡s ▼❈● s✬❛✈èr❡ s♦✉✈❡♥t tr♦♣ ❣r♦ss✐èr❡✳ ❊♥ ❡✛❡t✱ ✉♥❡ ✈❛❧❡✉r

à ❝❤❛q✉❡ ✷✵✵ ❦✐❧♦♠ètr❡s ♥❡ s✉✣t ♣❛s ❧♦rsq✉❡ ❧❡ ❞♦♠❛✐♥❡ ❞✬ét✉❞❡ ❡st ✉♥ ♣❛②s✱ ✉♥❡ ré❣✐♦♥ ♦✉

✉♥❡ ✈✐❧❧❡✳ ❉❡ ♣❧✉s✱ ✉♥❡ ❤❛✉ss❡ ❞❡ ❧❛ rés♦❧✉t✐♦♥ ♣♦✉r ♣❡r♠❡ttr❡ ❛✉① ▼❈● ✉♥❡ ♣❧✉s ❣r❛♥❞❡

❝♦♥❝❡♥tr❛t✐♦♥ ❞❡ ❞♦♥♥é❡s ❝❛✉s❡ ✐♥é✈✐t❛❜❧❡♠❡♥t ✉♥❡ ❛✉❣♠❡♥t❛t✐♦♥ s✐❣♥✐✜❝❛t✐✈❡ ❞✉ t❡♠♣s ❡t

❞✉ ❝♦ût ❞❡s ❝❛❧❝✉❧s✳ P♦✉r tr♦✉✈❡r ✉♥ ❝♦♠♣r♦♠✐s✱ ♦♥ ♠❡t s✉r ♣✐❡❞ ❧❡s ♠♦❞è❧❡s ré❣✐♦♥❛✉① ❞✉

❝❧✐♠❛t✳ ■❧s ♦♥t ❧❡s ♠ê♠❡s ❢♦♥❝t✐♦♥s q✉❡ ❧❡s ▼❈●✱ ♠❛✐s ♦♣èr❡♥t s✉r ✉♥ ❞♦♠❛✐♥❡ s♣❛t✐❛❧ ❞é✜♥✐

❡t ♥♦♥ s✉r ❧✬❡♥t✐èr❡té ❞✉ ❣❧♦❜❡✳ ❈❡❧❛ ♣❡r♠❡t ❞✬❛✉❣♠❡♥t❡r ❧❡s rés♦❧✉t✐♦♥s ❥✉sq✉✬à ❞❡s ✈❛❧❡✉rs ❞❡✱

✹

❋✐❣✉r❡ ✶✳✶ ✕ ●r✐❧❧❡ ✷❉ ❞❡ rés♦❧✉t✐♦♥ ❣r♦ss✐èr❡ ✭✻✵✵ ❦♠✮ ❞✬✉♥ ♠♦❞è❧❡ ❞❡ ❝✐r❝✉❧❛t✐♦♥ ❣é♥ér❛❧❡✭▼❈●✮✳ Pr♦❞✉✐t ♣❛r ❯❈ ❉❛✈✐s ❈❧✐♠❛t❡ ❛♥❞ ●❧♦❜❛❧ ❈❤❛♥❣❡ ●r♦✉♣✳

❣é♥ér❛❧❡♠❡♥t✱ ✷✺ à ✺✵ ❦♠✳ ❈❡tt❡ rés♦❧✉t✐♦♥ ♣❧✉s ✜♥❡ ♣❡r♠❡t ❛✉① ▼❘❈ ❞❡ s✐♠✉❧❡r ❞❡s ♣r♦❝❡ss✉s

♥❛t✉r❡❧s ♣♦ssé❞❛♥ts ❞❡s ❡♥✈❡r❣✉r❡s ♣❧✉s ♣❡t✐t❡s✳ ▲❡s ❝②❝❧♦♥❡s✱ ♥♦t❛♠♠❡♥t✱ s♦♥t ♠❛❧ r❡♣rés❡♥tés

♣❛r ❧❡s ▼❈● ❡t ❞♦✐✈❡♥t ❞♦♥❝ êtr❡ ét✉❞✐és à ❧✬❛✐❞❡ ❞❡ ❣r✐❧❧❡s ❞❡ ❝❛❧❝✉❧ ♣❧✉s ✜♥❡s ❝♦♠♠❡✱ ♣❛r

❡①❡♠♣❧❡✱ ❝❡❧❧❡s ❞❡s ▼❘❈ ✭P♦❛♥ ❡t ❛❧✳✱ ✷✵✶✽✮✳ ❈❡s ❞❡r♥✐❡rs ♥❡ ♣❡✉✈❡♥t ❝❡♣❡♥❞❛♥t ♣❛s tr❛✈❛✐❧❧❡r

s❡✉❧s✳ ▲❡s ❝♦♥❞✐t✐♦♥s ❛✉① ❢r♦♥t✐èr❡s✱ ❡ss❡♥t✐❡❧❧❡s ♣♦✉r ❞✐❝t❡r ❧❡s ❝❛❧❝✉❧s à ❧✬✐♥tér✐❡✉r ❞✉ ❞♦♠❛✐♥❡✱

♣r♦✈✐❡♥♥❡♥t ❞✬✉♥ ▼❈● ✓ ♣✐❧♦t❡ ✔✳ ❙✉r ❧❛ ❋✐❣✉r❡ ✶✳✷✱ ♣❛r ❡①❡♠♣❧❡✱ ❧❡s ❝❛❧❝✉❧s ré❛❧✐sés ♣❛r ❧❡

▼❘❈ à ❧✬✐♥tér✐❡✉r ❞❡ ❧❛ ③♦♥❡ ❞é✜♥✐❡ ♣❛r ❧❡ tr❛✐t ♦r❛♥❣❡ s♦♥t ♣♦ss✐❜❧❡s ✉♥✐q✉❡♠❡♥t s✐ ❞❡s ❞♦♥♥é❡s

❧❛tér❛❧❡s ✭♣✳ ❡①✳ ♣r♦✜❧s ❞❡ t❡♠♣ér❛t✉r❡✱ ❤✉♠✐❞✐té r❡❧❛t✐✈❡ ❡t ✈✐t❡ss❡ ❞✉ ✈❡♥t✮ ❡t ❞❡ s✉r❢❛❝❡ ✭♣✳

❡①✳ ♣r❡ss✐♦♥ ❛t♠♦s♣❤ér✐q✉❡ ❡t t❡♠♣ér❛t✉r❡ ❞❡ s✉r❢❛❝❡ ❞❡s ♦❝é❛♥s✮ s♦♥t ❢♦✉r♥✐❡s ♣❛r ✉♥ ▼❈●

✭❯♥✐t❡❞ ❙t❛t❡s ●❡♦❧♦❣✐❝❛❧ ❙✉r✈❡②✱ ✷✵✶✶✮✳ ❉✬❛✐❧❧❡✉rs✱ ❧❡ ❞♦♠❛✐♥❡ ♣rés❡♥té à ❧❛ ❋✐❣✉r❡ ✶✳✷ ❡st

❝❡❧✉✐ ✉t✐❧✐sé ♣♦✉r t♦✉t❡s ❧❡s s✐♠✉❧❛t✐♦♥s ❞❡ ❧✬ét✉❞❡ ❞✉ ❈❤❛♣✐tr❡ ✷✱ ❝✬❡st✲à✲❞✐r❡ ❧❡ ❞♦♠❛✐♥❡ ❞❡

❧✬❆♠ér✐q✉❡ ❞✉ ◆♦r❞ ❞✉ ♣r♦❥❡t ❈❖❘❉❊❳ ✭❞❡ ♣❧✉s ❛♠♣❧❡s ❞ét❛✐❧s s❡r♦♥t ❢♦✉r♥✐s à ❝❡ s✉❥❡t ❛✉

♣r♦❝❤❛✐♥ ❝❤❛♣✐tr❡✮✳

✶✳✷ ❙❝é♥❛r✐♦s ❞✬é♠✐ss✐♦♥s

▲❡s s❝é♥❛r✐♦s ❞✬é♠✐ss✐♦♥s s❡r✈❡♥t à ♣r♦❥❡t❡r ❧❡s ✈❛❧❡✉rs ❞✬é♠✐ss✐♦♥s ❞❡ ❣❛③ à ❡✛❡t ❞❡ s❡rr❡ ✭●❊❙✮

❞❛♥s ❧❡ ❢✉t✉r ❡♥ ❝ré❛♥t ❛✐♥s✐ ❞❡s ❢✉t✉rs ♣♦ss✐❜❧❡s s❛♥s t♦✉t❡❢♦✐s q✉✬✐❧s s♦✐❡♥t ❞❡s ♣ré✈✐s✐♦♥s✳

✺

❋✐❣✉r❡ ✶✳✷ ✕ ❉♦♠❛✐♥❡ ❞❡ ❧✬❆♠ér✐q✉❡ ❞✉ ◆♦r❞ ❞✉ ♣r♦❥❡t ❈❖❘❉❊❳

◗✉❡ ❝❡ s♦✐t ❞❡s tr❛♥s❢♦r♠❛t✐♦♥s ❞é♠♦❣r❛♣❤✐q✉❡s✱ ❞❡s ❞é✈❡❧♦♣♣❡♠❡♥ts s♦❝✐♦✲é❝♦♥♦♠✐q✉❡s ♦✉

❞❡s ♣r♦❣rès t❡❝❤♥♦❧♦❣✐q✉❡s✱ ❞❡s ❝❡♥t❛✐♥❡s ❞❡ ❢❛❝t❡✉rs ❞ét❡r♠✐♥❡r♦♥t ❧❡s é♠✐ss✐♦♥s ❞❡ ●❊❙ ❞❛♥s

✷✵✱ ✺✵ ♦✉ ♠ê♠❡ ✶✵✵ ❛♥s✳ ▲❡s ❞✐✛ér❡♥ts s❝é♥❛r✐♦s ❞✬é♠✐ss✐♦♥s ✈♦♥t ❞♦♥❝ ♣r❡♥❞r❡ ❡♥ ❝♦♠♣t❡

❝❡rt❛✐♥s ❞❡ ❝❡s ❢❛❝t❡✉rs ♣♦✉r ❛rr✐✈❡r à ✉♥❡ é✈♦❧✉t✐♦♥ ♣♦ss✐❜❧❡ ❞❡s é♠✐ss✐♦♥s ❞❡ ❣❛③ ❝♦♠♠❡ ❧❡

❞✐♦①②❞❡ ❞❡ ❝❛r❜♦♥❡ ♦✉ ❧❡ ♠ét❤❛♥❡✳ ❖✉t✐❧❧és ❞❡ ❝❡s s❝é♥❛r✐♦s✱ ❧❡s ♠♦❞é❧✐s❛t❡✉rs ♣❡✉✈❡♥t ♣r♦❝é✲

❞❡r à ❞❡s s✐♠✉❧❛t✐♦♥s q✉✐ ✈♦♥t s✉✐✈r❡ ❞❡s ✈❛❧❡✉rs ❞✬é♠✐ss✐♦♥s ♣r❡s❝r✐t❡s ❞❛♥s ❧❡ t❡♠♣s✳

❚♦✉t ❝♦♠♠❡ ❧❡s ♠♦❞è❧❡s ❝❧✐♠❛t✐q✉❡s✱ ❧❡s s❝é♥❛r✐♦s ❞✬é♠✐ss✐♦♥s ♦♥t ❝❤❛♥❣é ❛✈❡❝ ❧❡ t❡♠♣s✳ ❉✐✛é✲

r❡♥t❡s ❛♣♣r♦❝❤❡s ❡①✐st❡♥t✱ ❞♦♥t ❝❡rt❛✐♥❡s s♦♥t q✉❛♥t✐t❛t✐✈❡s ❛❧♦rs q✉❡ ❞✬❛✉tr❡s s❡ ♣❡♥❝❤❡♥t ✈❡rs

✉♥❡ ❢❛ç♦♥ ❞❡ ❢❛✐r❡ q✉❛❧✐t❛t✐✈❡✳ ❊♥tr❡ ✷✵✵✵ ❡t ✷✵✶✹✱ ❧❡ ●r♦✉♣❡ ❞✬❡①♣❡rts ✐♥t❡r❣♦✉✈❡r♥❡♠❡♥t❛❧ s✉r

❧✬é✈♦❧✉t✐♦♥ ❞✉ ❝❧✐♠❛t ✭●■❊❈✮ ❛ ✉t✐❧✐sé ❧❡s s❝é♥❛r✐♦s ♣r♦✈❡♥❛♥t ❞❡ s♦♥ ❘❛♣♣♦rt s♣é❝✐❛❧ s✉r ❧❡s

s❝é♥❛r✐♦s ❞✬é♠✐ss✐♦♥s ✭❙❘❊❙✱ ◆❛❦✐❝❡♥♦✈✐❝ ❡t ❛❧✳ ✷✵✵✵✮✳ ▲❡s s❝é♥❛r✐♦s ❞✬é♠✐ss✐♦♥ ❞❡ ❝❡ r❛♣♣♦rt

s♦♥t ❝♦♥s✐❞érés ❝♦♠♠❡ ét❛♥t à ❧❛ ❢♦✐s q✉❛❧✐t❛t✐❢s ❡t q✉❛♥t✐t❛t✐❢s ❡t s♦♥t ❞✐str✐❜✉és ❡♥ q✉❛tr❡

❢❛♠✐❧❧❡s ❞✐st✐♥❝t❡s ✭❆✶✱ ❆✷✱ ❇✶ ❡t ❇✷✮✳ ▲❡s ❞✐st✐♥❝t✐♦♥s ❡♥tr❡ ❧❡s ❢❛♠✐❧❧❡s s♦♥t ❧❡ ♣♦✐♥t ❢♦❝❛❧ ❞✉

s❝é♥❛r✐♦ ✭é❝♦♥♦♠✐q✉❡ ♦✉ ❡♥✈✐r♦♥♥❡♠❡♥t❛❧✮ ❡t ❧✬❤♦♠♦❣é♥é✐té ❞❡s ré❣✐♦♥s ❞✉ ❣❧♦❜❡ ✭♠♦♥❞✐❛❧✐✲

s❛t✐♦♥ ♦✉ ré❣✐♦♥❛❧✐s❛t✐♦♥✮✳ ▲❡s s❝é♥❛r✐♦s ❞✉ ❙❘❊❙ ét❛❜❧✐ss❡♥t ❞❡s ❢✉t✉rs ❛❧❧❛♥t ❥✉sq✉✬à ❧✬❛♥♥é❡

✷✶✵✵✱ ❧❡s r❡♥❞❛♥t ♣♦♣✉❧❛✐r❡s ❝❤❡③ ❧❡s ét✉❞❡s ♣♦rt❛♥t s✉r ❧✬é✈♦❧✉t✐♦♥ ❞✉ ❝❧✐♠❛t ✭❍❛②❤♦❡ ❡t ❛❧✳

✷✵✶✵ ❀ ❆♥❣❡❧ ❡t ❑✉♥❦❡❧ ✷✵✶✵ ❀ ▼✉s✐❝ ❡t ❛❧✳ ✷✵✶✺✮✳ ❖♥ s✬❛♣❡rç♦✐t ♣❛r ❝♦♥tr❡ q✉❡✱ ✈✉ ❧❡s ❞✐✛é✲

r❡♥❝❡s ❡♥tr❡ ❧❡s ❢❛ç♦♥s ❞❡ tr❛✐t❡r ❧❡s é♠✐ss✐♦♥s ❞❡ ●❊❙ ♣❛r ❧❡s ❞✐✛ér❡♥ts ♠♦❞è❧❡s ❝❧✐♠❛t✐q✉❡s✱

✻

❧❡s ❝♦♥❝❡♥tr❛t✐♦♥s ❛t♠♦s♣❤ér✐q✉❡s rés✉❧t❛♥t❡s ❞✐✛èr❡♥t ❞✬✉♥ ♠♦❞è❧❡ à ❧✬❛✉tr❡ ♣♦✉r ✉♥ ♠ê♠❡

s❝é♥❛r✐♦ ❞✉ ❙❘❊❙ ✭❙t♦❝❦❡r✱ ✷✵✶✹✮✳

❊♥ ✷✵✶✹✱ ❧♦rs ❞❡ ❧❛ ♣✉❜❧✐❝❛t✐♦♥ ❞✉ ❝✐♥q✉✐è♠❡ ❘❛♣♣♦rt ❞✬é✈❛❧✉❛t✐♦♥ ❞✉ ●■❊❈ ✭❘❊✺✱ ❙t♦❝❦❡r

✷✵✶✹✮✱ ❧✬♦r❣❛♥✐s♠❡ ❛❞♦♣t❡ ✉♥ ♥♦✉✈❡❧ ❡♥s❡♠❜❧❡ ❞❡ s❝é♥❛r✐♦s ✿ ❧❡s ❘❡♣r❡s❡♥t❛t✐✈❡ ❈♦♥❝❡♥tr❛t✐♦♥

P❛t❤✇❛②s ✭❘❈P✱ ▼♦ss ❡t ❛❧✳ ✷✵✵✽ ❀ ▼♦ss ❡t ❛❧✳ ✷✵✶✵ ❀ ❱❛♥ ❱✉✉r❡♥ ❡t ❛❧✳ ✷✵✶✶✮✳ ❈♦♥tr❛✐r❡♠❡♥t

❛✉① s❝é♥❛r✐♦s ❞✉ ❙❘❊❙✱ ✐❧s ♣r♦❥❡tt❡♥t ♥♦♥ ♣❛s ❧❡s ✈❛❧❡✉rs ❞✬é♠✐ss✐♦♥s ❞❡s ●❊❙✱ ♠❛✐s ♣❧✉tôt ❧❡s

❝♦♥❝❡♥tr❛t✐♦♥s ❞❡ ❝❡s ❣❛③ ❞❛♥s ❧✬❛t♠♦s♣❤èr❡✱ ❛ss✉r❛♥t q✉❡ ❧❡s ♠♦❞è❧❡s ❝❧✐♠❛t✐q✉❡s s✉✐✈❛♥t ❧❡

♠ê♠❡ ❘❈P ♦❜t✐❡♥♥❡♥t ❞❡s ❝♦♥❝❡♥tr❛t✐♦♥s é❣❛❧❡s✳ ◗✉❛tr❡ ❘❈P ♦♥t été ❝❤♦✐s✐s ♣♦✉r r❡♣rés❡♥t❡r

❧✬ét❡♥❞✉❡ ❞❡s ♣♦ss✐❜❧❡s tr❛❥❡❝t♦✐r❡s ❞❡s ❢✉t✉rs ❛❧t❡r♥❛t✐❢s✳ ■❧s s✬é❝❤❡❧♦♥♥❡♥t ❞❡ ❝❡❧✉✐ ♣r♦❥❡t❛♥t ❧❡s

♣❧✉s ❢❛✐❜❧❡s ❝♦♥❝❡♥tr❛t✐♦♥s ❞❡ ●❊❙✱ ❧❡ ❘❈P✷✳✻✱ ❥✉sq✉✬❛✉ s❝é♥❛r✐♦ ❞❛♥s ❧❡q✉❡❧ ❧❡s ❝♦♥❝❡♥tr❛t✐♦♥s

s♦♥t ❧❡s ♣✐r❡s✱ ❧❡ ❘❈P✽✳✺✳ ❖♥ ♣❡✉t é❣❛❧❡♠❡♥t ♣❛r❧❡r ❞❡ ❝❡tt❡ ❣r❛❞❛t✐♦♥ ❝♦♠♠❡ ❝❡❧❧❡ ❞✉ s❝é♥❛r✐♦

❧❡ ♣❧✉s ♦♣t✐♠✐st❡ ❛✉ ♣❧✉s ♣❡ss✐♠✐st❡✳ ❯♥❡ ❝♦♠♣❛r❛✐s♦♥ ❞❡s ❢♦rç❛❣❡s r❛❞✐❛t✐❢s✱ ❝✬❡st✲à✲❞✐r❡ ❞❡s

♣❡rt✉r❜❛t✐♦♥s ❞✉ ❜✐❧❛♥ r❛❞✐❛t✐❢ ❞❡ ❧❛ ❚❡rr❡ ❡①♣r✐♠é❡s ❡♥ ❲ ♠−2✱ ♣♦✉r tr♦✐s t②♣❡s ❞❡ s❝é♥❛r✐♦s

❡st ♣rés❡♥té❡ à ❧❛ ❋✐❣✉r❡ ✶✳✸✳ ▲❡s ❘❈P ✹✳✺ ❡t ✽✳✺ ✭❧❡s ♣❧✉s ❝♦✉r❛♠♠❡♥t ✉t✐❧✐sés ❞❛♥s ❝❡ t②♣❡

❞✬ét✉❞❡✮ s♦♥t ❧❡s s❝é♥❛r✐♦s ✉t✐❧✐sés ♣♦✉r t♦✉t❡s ❧❡s s✐♠✉❧❛t✐♦♥s ét✉❞✐é❡s ❛✉ ❈❤❛♣✐tr❡ ✷✳

✶✳✸ ▼♦❞è❧❡s ❞❡ ❧❛❝

❈✬❡st ❜✐❡♥ ❝♦♥♥✉ q✉❡ ❧❡s ❧❛❝s ❞❡ ♠♦②❡♥♥❡s à ❣r❛♥❞❡s ❞✐♠❡♥s✐♦♥s ✐♥✢✉❡♥❝❡♥t ❧❡ ❝❧✐♠❛t ❞❡ ❧❡✉r

ré❣✐♦♥ ❡t✱ ❡♥ s❛❝❤❛♥t ❝❡❧❛✱ ✉♥❡ ❛tt❡♥t✐♦♥ ♣❛rt✐❝✉❧✐èr❡ ❞♦✐t êtr❡ ♣♦sé❡ s✉r ❝❡✉①✲❝✐✳ ▲❡s ❧❛❝s s♦♥t

❡♥ ❡✛❡t ❧❛ ❝❛✉s❡ ❞❡ ♣❧✉s✐❡✉rs ♣❤é♥♦♠è♥❡s ♠été♦r♦❧♦❣✐q✉❡s ✭♣✳ ❡①✳ ❜♦✉rr❛sq✉❡s ❞❡ ♥❡✐❣❡ ❡♥ ❛✈❛❧

❞❡s ❧❛❝s✱ ❜r✐s❡s ❞❡ ❧❛❝✮ ❡t ❧❡✉rs ❝❛r❛❝tér✐st✐q✉❡s ❞♦✐✈❡♥t ❞♦♥❝ êtr❡ ❛❞éq✉❛t❡♠❡♥t ❝♦♠♣r✐s❡s ❧♦rs

❞❡ ❧❛ ♠♦❞é❧✐s❛t✐♦♥ ❝❧✐♠❛t✐q✉❡ ❞✬✉♥❡ ré❣✐♦♥✳ ❈✬❡st ❡♥tr❡ ❛✉tr❡s ♣♦✉r ❝❡tt❡ r❛✐s♦♥ q✉❡ ❧❡s t✉✐❧❡s

q✉✐ ❝♦♠♣♦s❡♥t ❧❡s ❣r✐❧❧❡s ❞❡s ▼❈● ❡t ▼❘❈ s♦♥t ❞✐✈✐sé❡s ❡♥tr❡ ❝❡❧❧❡s r❡♣rés❡♥t❛♥t ❞❡ ❧❛ t❡rr❡ ❡t

❝❡❧❧❡s r❡♣rés❡♥t❛♥t ❞❡ ❧✬❡❛✉✳ P❛r ❧❡ ♣❛ssé✱ ❧❡s ✐♥t❡r❛❝t✐♦♥s ❡♥tr❡ ❧✬❛t♠♦s♣❤èr❡ ❡t ❧❡s t✉✐❧❡s ❞✬❡❛✉ à

❧✬✐♥tér✐❡✉r ❞❡s ♠♦❞è❧❡s ♠❛t❤é♠❛t✐q✉❡s ét❛✐❡♥t rés♦❧✉❡s ❞❡ ❢❛ç♦♥ r✉❞✐♠❡♥t❛✐r❡✱ ♠❛✐s à ♣❛rt✐r ❞❡

❧❛ ✜♥ ❞❡s ❛♥♥é❡s ✾✵✱ ❧❡s ♠♦❞è❧❡s ❞❡ ❧❛❝ ❛♠é❧✐♦r❡♥t ❣r❛♥❞❡♠❡♥t ❧❡✉rs ♣❡r❢♦r♠❛♥❝❡s✳ ▲✬♦❜❥❡❝t✐❢

❞✬✉♥ ♠♦❞è❧❡ ❞❡ ❧❛❝ ❡st ❞❡✱ à ❧✬❛✐❞❡ ❞❡s ❞♦♥♥é❡s ❞✬✉♥ ♠♦❞è❧❡ ❝❧✐♠❛t✐q✉❡ ❛✉q✉❡❧ ✐❧ ❡st ❝♦✉♣❧é✱ s✐✲

♠✉❧❡r ❧❡s ♣r♦❝❡ss✉s ♣❤②s✐q✉❡s ❞❛♥s ✉♥❡ ❝♦❧♦♥♥❡ ❞✬❡❛✉ ♣♦✉r ❛rr✐✈❡r à ❞❡s ❝❛r❛❝tér✐st✐q✉❡s t❡❧❧❡s

q✉❡ ❧❛ t❡♠♣ér❛t✉r❡ ❞❡ s✉r❢❛❝❡✱ ❧❛ str❛t✐✜❝❛t✐♦♥ t❤❡r♠✐q✉❡ ❡t ❧❛ ❝♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ ❡t ❞❡ ♥❡✐❣❡✳

❈❡s ❞♦♥♥é❡s ♣❡✉✈❡♥t êtr❡ ✉t✐❧✐sé❡s ❞✐r❡❝t❡♠❡♥t ♣♦✉r✱ ♣❛r ❡①❡♠♣❧❡✱ ❞❡s ét✉❞❡s s✉r ❧❡s ✐♠♣❛❝ts

❞❡s ❝❤❛♥❣❡♠❡♥ts ❝❧✐♠❛t✐q✉❡s s✉r ❧❡s ❝♦♥❞✐t✐♦♥s ❞❡s ❧❛❝s✱ ♠❛✐s ♣❡✉✈❡♥t é❣❛❧❡♠❡♥t s❡r✈✐r ❞✬✐♥❢♦r✲

♠❛t✐♦♥s ♣♦✉r ✉♥ ♠♦❞è❧❡ ❝❧✐♠❛t✐q✉❡✳ ❉❛♥s ❝❡ ❝❛s✱ ❧❡s ❝❛r❛❝tér✐st✐q✉❡s ♦❜t❡♥✉❡s ♣❛r ✉♥ ♠♦❞è❧❡

❞❡ ❧❛❝ s♦♥t ✉t✐❧✐sé❡s ♣❛r ✉♥ ▼❈● ♦✉ ✉♥ ▼❘❈ ❞❛♥s s❡s ❝❛❧❝✉❧s ♣♦✉r t❡♥t❡r ❞❡ ♠✐❡✉① r❡♣r♦❞✉✐r❡

❧❡s ♣r♦❝❡ss✉s ♥❛t✉r❡❧s ❛t♠♦s♣❤ér✐q✉❡s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✳ ❖♥ ❞✐t ❛❧♦rs q✉❡ ❧❡ ♠♦❞è❧❡ ❝❧✐♠❛t✐q✉❡

❡t ❧❡ ♠♦❞è❧❡ ❞❡ ❧❛❝ s♦♥t ❝♦✉♣❧és ❜✐❧❛tér❛❧❡♠❡♥t ❡♥ ♦♣♣♦s✐t✐♦♥ à ✉♥ s②stè♠❡ ❝♦✉♣❧é ✉♥✐❧❛tér❛✲

❧❡♠❡♥t✳ ❉❛♥s ❝❡ s❡❝♦♥❞ ❝❛s✱ ❧❡ ♠♦❞è❧❡ ❝❧✐♠❛t✐q✉❡ ♥❡ r❡ç♦✐t ♣❛s ❞✬✐♥❢♦r♠❛t✐♦♥ ❞✉ ♠♦❞è❧❡ ❞❡ ❧❛❝✳

✼

❋✐❣✉r❡ ✶✳✸ ✕ ❍✐st♦r✐q✉❡ ❡t t❡♥❞❛♥❝❡s ❞❡s ❢♦rç❛❣❡s r❛❞✐❛t✐❢s t♦t❛✉① ❝♦rr❡s♣♦♥❞❛♥t ❛✉① ❘❈P✱à ❞❡s s❝é♥❛r✐♦s ❞✉ ❙❘❊❙ ❡t ❞✬✉♥ s❝é♥❛r✐♦ ❞✬■❙✾✷ ✭✉♥❡ ❛✉tr❡ ❢❛♠✐❧❧❡ ❞❡ s❝é♥❛r✐♦✮ ❡♥tr❡ ✶✾✺✵ ❡t✷✶✵✵✳ ❱❛❧❡✉rs r❡❧❛t✐✈❡s ❛✉① ♥✐✈❡❛✉① ♣ré✲✐♥❞✉str✐❡❧s ❞❡ ✶✼✻✺✳ ❋✐❣✉r❡ t✐ré❡ ❞❡ ❙t♦❝❦❡r ✭✷✵✶✹✮✳

P❧✉s✐❡✉rs ♠♦❞è❧❡s ❞❡ ❧❛❝ ❡①✐st❡♥t ❡t ❝❤❛❝✉♥ ❛ s❡s ♣❛rt✐❝✉❧❛r✐tés ♣r♦♣r❡s✳ ■❧ ❡①✐st❡ ❞❡s ♠♦❞è❧❡s

r❡❧❛t✐✈❡♠❡♥t s✐♠♣❧❡s✱ à ✉♥❡ ❞✐♠❡♥s✐♦♥ ✭❍♦st❡t❧❡r ❡t ❛❧✳ ✶✾✾✸ ❀ ▼✐r♦♥♦✈ ❡t ❛❧✳ ✷✵✵✸✮ ♠❛✐s é❣❛✲

❧❡♠❡♥t ❞❡s ♠♦❞è❧❡s à ❞❡✉① ♦✉ tr♦✐s ❞✐♠❡♥s✐♦♥s ✭❳✉❡ ❡t ❛❧✳✱ ✷✵✶✼✮ q✉✐ ❡①✐❣❡♥t ♣❧✉s ❞❡ ❝❛❧❝✉❧s✳

▼❛❧❣ré ❧✬❡①✐st❡♥❝❡ ❞❡ ❝❡s ♠♦❞è❧❡s ♣❧✉s ❝♦♠♣❧❡①❡s✱ ❧❡s ♠♦❞è❧❡s ❞❡ ❧❛❝ ❧❡s ♣❧✉s ❝♦♠♠✉♥s ✭❡t

✉t✐❧✐sés ❞❛♥s ❧✬ét✉❞❡ ❞✉ ❈❤❛♣✐tr❡ ✷✮ ♦♣èr❡♥t ❡♥ ✉♥❡ ❞✐♠❡♥s✐♦♥✳ ▲❡s ♠♦❞è❧❡s à ✉♥❡ ❞✐♠❡♥s✐♦♥

✈❡rt✐❝❛❧❡ ♠❡♥t✐♦♥♥és ♣❧✉s tôt ♣❡r❢♦r♠❡♥t ❛❞éq✉❛t❡♠❡♥t ❞❛♥s ❧❡ ❝❛s ❞❡s ❧❛❝s ♣❡✉ ♣r♦❢♦♥❞s✱ ♠❛✐s

❧❡✉rs rés✉❧t❛ts ❧♦rs ❞❡ ❧❛ s✐♠✉❧❛t✐♦♥ ❞❡ ♣r♦❝❡ss✉s ❞❛♥s ❞❡s ❧❛❝s ♣r♦❢♦♥❞s ❧❛✐ss❡♥t à ❞és✐r❡r s❡❧♦♥

▼❛rt②♥♦✈ ❡t ❛❧✳ ✭✷✵✶✵✮✳ ❈❡ ♠ê♠❡ ❛rt✐❝❧❡ ♣r♦♣♦s❡ ❞✬❛✉❣♠❡♥t❡r ❧❡ ♥♦♠❜r❡ ❞❡ ♣r♦❝❡ss✉s ♣r✐s ❡♥

❝♦♠♣t❡ ❧♦rs ❞✉ ❝❛❧❝✉❧ ❞✉ ré❣✐♠❡ t❤❡r♠✐q✉❡✱ ❞❡ s❡ ♣❡♥❝❤❡r ❞❛✈❛♥t❛❣❡ s✉r ❧❡ rô❧❡ ❞❡ ❧❛ ♥❡✐❣❡

❛✉✲❞❡ss✉s ❞❡ ❧❛ ❣❧❛❝❡ ❡t✱ ✜♥❛❧❡♠❡♥t✱ ❞✬✐♥❝❧✉r❡ ❧✬✐♥✢✉❡♥❝❡ ❞❡s ♣r♦❝❡ss✉s tr✐❞✐♠❡♥s✐♦♥♥❡❧s s✉r

❧❛ ❝♦❧♦♥♥❡ ❞✬❡❛✉✳ ❈❡ ❞❡r♥✐❡r ♣♦✐♥t ♠❡t ❧✬❛❝❝❡♥t s✉r ❧✬❛✈❛♥t❛❣❡ ✐rré❢✉t❛❜❧❡ q✉❡ ♣♦ssè❞❡♥t ❧❡s

♠♦❞è❧❡s ❞❡ ❧❛❝ à tr♦✐s ❞✐♠❡♥s✐♦♥s ❛✉ ♣♦✐♥t ❞❡ ✈✉❡ ❞❡ ❧❛ r❡♣rés❡♥t❛t✐♦♥ ♣❤②s✐q✉❡✳ ▲✬❛✉❣♠❡♥✲

t❛t✐♦♥ ❞❡ ❧❛ ❝❤❛r❣❡ ♦♣ér❛t✐♦♥♥❡❧❧❡✱ q✉✐ ✈✐❡♥t ❛✈❡❝ ❝❡t ❛✈❛♥t❛❣❡✱ ❞❡✈r❛ êtr❡ s✉r♠♦♥té❡ ❞❛♥s ❧❡s

♣r♦❝❤❛✐♥❡s ❛♥♥é❡s s✐ ♦♥ ✈❡✉t ❛✉❣♠❡♥t❡r ❧❛ ❥✉st❡ss❡ ❞❡s s✐♠✉❧❛t✐♦♥s✳

✽

▲♦rsq✉✬✉♥ ▼❘❈ ♥✬❡st ♣❛s ❝♦✉♣❧é ❛✈❡❝ ✉♥ ♠♦❞è❧❡ ❞❡ ❧❛❝✱ ❧❡s ❝❛r❛❝tér✐st✐q✉❡s ♥♦r♠❛❧❡♠❡♥t ♦❜t❡✲

♥✉❡s ❛✈❡❝ ❝❡ ♠♦❞è❧❡ s♦♥t ✐♠♣♦rté❡s ❞❡♣✉✐s ❧❡ ▼❈● ♣✐❧♦t❡✳ ▲❡s ✐♥❢♦r♠❛t✐♦♥s s✉r ❧❛ t❡♠♣ér❛t✉r❡

❡t ❧❛ ❣❧❛❝❡ ❞❡ ❝❤❛q✉❡ t✉✐❧❡ ❞✬❡❛✉ ❞✉ ▼❘❈ ♣r♦✈✐❡♥♥❡♥t ❛❧♦rs ❞❡ ❧❛ t✉✐❧❡ ❞✉ ♠ê♠❡ t②♣❡ ❧❛ ♣❧✉s

♣r♦❝❤❡ s✉r ❧❛ ❣r✐❧❧❡ ❞✉ ▼❈●✳ ❈♦♠♠❡ ✐❧ s❡r❛ ♠❡♥t✐♦♥♥é ❞❛♥s ❧❛ ♣r♦❝❤❛✐♥❡ s❡❝t✐♦♥✱ ❝❡❝✐ ♣❡✉t

❝❛✉s❡r ❞❡s ❧❛❝✉♥❡s ✐♠♣♦rt❛♥t❡s✳ ❋✐♥❛❧❡♠❡♥t✱ ❝❡rt❛✐♥s ♠♦❞è❧❡s ✉t✐❧✐s❡♥t ♠ê♠❡ ❧✬✐♥t❡r♣♦❧❛t✐♦♥

❞❡s t❡♠♣ér❛t✉r❡s ❞❡s ♦❝é❛♥s P❛❝✐✜q✉❡ ❡t ❆t❧❛♥t✐q✉❡ ♣♦✉r ❛rr✐✈❡r à ❞❡s ✈❛❧❡✉rs ♣♦✉r ❧✬❡❛✉

❞❡ ❧❛❝s ❡♥ ❆♠ér✐q✉❡ ❞✉ ◆♦r❞ ❧♦rsq✉✬❛✉❝✉♥❡ t✉✐❧❡ ❞❡ ❧❛❝ ♥✬❡st ♣rés❡♥t❡ s✉r ❧❛ ❣r✐❧❧❡ ❞✉ ♣✐❧♦t❡

✭◆♦rt❤ ❆♠❡r✐❝❛♥ ❘❡❣✐♦♥❛❧ ❈❧✐♠❛t❡ ❈❤❛♥❣❡ ❆ss❡ss♠❡♥t Pr♦❣r❛♠✱ ✷✵✵✼✮✳

✶✳✹ ❊t ❞❛♥s ❧❡ ❝♦♥t❡①t❡ ❞❡s ●r❛♥❞s ▲❛❝s ❄

P❧✉s✐❡✉rs ♣❛rt✐❝✉❧❛r✐tés ❞♦✐✈❡♥t êtr❡ ❝♦♥s✐❞éré❡s ❧♦rsq✉✬✉♥❡ ét✉❞❡ ❝❧✐♠❛t✐q✉❡ ❡st ❡✛❡❝t✉é❡ ❞❛♥s

❧❛ ré❣✐♦♥ ❞❡s ●r❛♥❞s ▲❛❝s✳ ❈♦♠♠❡ ❝❡ ❢ût ♠❡♥t✐♦♥♥é ♣ré❝é❞❡♠♠❡♥t✱ ❧❡s ▼❈● ♥✬♦♥t ♣❛s t♦✉✲

❥♦✉rs ❞❡s rés♦❧✉t✐♦♥s s♣❛t✐❛❧❡s s✉✣s❛♠♠❡♥t ✜♥❡s ♣♦✉r ❜✐❡♥ ❞é✜♥✐r ❧❡s ét❡♥❞✉❡s ❞✬❡❛✉ ❞❡s

●r❛♥❞s ▲❛❝s ✭♠❛❧❣ré ❧❡✉rs t❛✐❧❧❡s✮✳ ❈♦♠♠❡ ♦♥ ❧✬♦❜s❡r✈❡ à ❧❛ ❋✐❣✉r❡ ✶✳✹✱ ❧❡s ▼❈● ♣♦ssè❞❡♥t

✉♥❡ ♣♦✐❣♥é❡ ❞❡ t✉✐❧❡s ❞✬❡❛✉ ♣♦✉r r❡♣rés❡♥t❡r ❝❡s ❧❛❝s✳ ❯♥ ❞❡s ♠♦❞è❧❡s ♣rés❡♥tés ✭●❋❉▲✲

❊❙▼✷▼✮ ♥❡ ♣♦ssè❞❡ ❛✉❝✉♥❡ t✉✐❧❡ ❛②❛♥t ✉♥❡ ❢r❛❝t✐♦♥ ❞✬❡❛✉ ❞❛♥s ❧❛ ré❣✐♦♥ ❞❡s ●r❛♥❞s ▲❛❝s✳

■❧ ❡st ❛r❞✉ ❞✬❛rr✐✈❡r à ❞❡s ❝♦♥❝❧✉s✐♦♥s ✐♥tér❡ss❛♥t❡s s✐ ❛✉ss✐ ♣❡✉ ❞❡ ♣♦✐♥ts s♦♥t ❝♦♥s✐❞érés ❡t

❝✬❡st ❧❛ r❛✐s♦♥ ♣♦✉r ❧❛q✉❡❧❧❡ ❧❡s ♠♦❞è❧❡s ré❣✐♦♥❛✉① s♦♥t ❞❡ ♠✐s❡ q✉❛♥❞ ♦♥ s♦✉❤❛✐t❡ ét✉❞✐❡r ❝❡

t❡rr✐t♦✐r❡✳

■❧ ❢❛✉t é❣❛❧❡♠❡♥t s♦✉❧✐❣♥❡r ❧✬✐♠♣♦rt❛♥❝❡ ❞❡s ♠♦❞è❧❡s ❞❡ ❧❛❝✳ ❱✉ ❧❡ ❜❛s ♥♦♠❜r❡ ❞❡ t✉✐❧❡s ❞✬❡❛✉

❞❡s ▼❈●✱ ❧❡s ❝❛r❛❝tér✐st✐q✉❡s ❞❡ ❧❛❝ ❞✐str✐❜✉é❡s ❛✉① ▼❘❈ q✉✐ ♥❡ ♣♦ssè❞❡♥t ♣❛s ❞❡ ♠♦❞è❧❡

❞❡ ❧❛❝ ♣r♦✈✐❡♥♥❡♥t ❞❡ s❡✉❧❡♠❡♥t q✉❡❧q✉❡s t✉✐❧❡s q✉✐ ❝♦✉✈r❡♥t ✉♥ t❡rr✐t♦✐r❡ ✐♠♠❡♥s❡ ❡t✱ ❞❛♥s

❜✐❡♥ ❞❡s ❝❛s✱ s❡ tr♦✉✈❡♥t ❣é♦❣r❛♣❤✐q✉❡♠❡♥t ❧♦✐♥ ❞❡ ❧❛ t✉✐❧❡ ré❝❡♣t✐✈❡✳ ❯♥ ♠♦❞è❧❡ ❞❡ ❧❛❝ ❝♦✉♣❧é

❛✉① ❘❈▼ ❡st ❞♦♥❝ ✐♠♣♦rt❛♥t ❧♦rs ❞✬✉♥❡ ♠♦❞é❧✐s❛t✐♦♥ ❝❧✐♠❛t✐q✉❡ ❞❡ ❝❡tt❡ ré❣✐♦♥✳ ❉❡✉① ▼❘❈

ét✉❞✐és ❛✉ ❈❤❛♣✐tr❡ ✷ ✭❈❛♥❘❈▼✹ ❡t ❍■❘❍❆▼✺✮ ♥✬❡♥ ♣♦ssè❞❡♥t ♣❛s✳

❋✐♥❛❧❡♠❡♥t✱ ♦♥ ❞♦✐t ré❛❧✐s❡r q✉❡ ❧❡s ♦❜s❡r✈❛t✐♦♥s s♦♥t très ❞✐✣❝✐❧❡s à ♦❜t❡♥✐r ❛✉✲❞❡ss✉s ❞❡s

●r❛♥❞s ▲❛❝s✳ ❉❡s ❜♦✉é❡s ❡t st❛t✐♦♥s ♠été♦r♦❧♦❣✐q✉❡s ❡①✐st❡♥t ♣♦✉r ❡♥ ré❝♦❧t❡r ✭◆❛t✐♦♥❛❧ ❖❝❡❛✲

♥✐❝ ❛♥❞ ❆t♠♦s♣❤❡r✐❝ ❆❞♠✐♥✐str❛t✐♦♥✱ ✶✾✾✾✮✱ ♠❛✐s ♣❛s s✉✣s❛♠♠❡♥t ♣♦✉r ❜✐❡♥ ❝♦✉✈r✐r ❧❡ ✈❛st❡

rés❡❛✉ ❞❡ ❧❛❝s✳ ❉❡s ♦❜s❡r✈❛t✐♦♥s ❞❡ t❡♠♣ér❛t✉r❡ ❞❡ ❧✬❡❛✉ ✭❙♣❡♥❝❡ ❡t ❛❧✳ ✷✵✶✸ ❀ ❱❛♥ ❈❧❡❛✈❡ ❡t ❛❧✳

✷✵✶✹✮✱ ❞❡ ❝♦✉✈❡rt ❞❡ ❣❧❛❝❡ ✭❆ss❡❧✱ ✷✵✵✸✮✱ ❞❡ ♣ré❝✐♣✐t❛t✐♦♥ ♣❛r té❧é❞ét❡❝t✐♦♥ ✭❈♦❧t♦♥✱ ✷✵✶✸✮ ❡t

❞❡ ✢✉① ❞❡ ❝❤❛❧❡✉r s❡♥s✐❜❧❡ ❡t ❧❛t❡♥t❡ ✭❇❧❛♥❦❡♥ ❡t ❛❧✳✱ ✷✵✶✶✮ ❡①✐st❡♥t✱ ♠❛✐s ❧❡✉r ✈❛❧✐❞✐té ♦✉

r❡♣rés❡♥t❛t✐✈✐té s♣❛t✐❛❧❡ ❡st ❞✐✣❝✐❧❡ à ♣r♦✉✈❡r ✭❙❤❛r♠❛ ❡t ❛❧✳✱ ✷✵✶✽✮✳ ◗✉❡❧q✉❡s ❝❛♠♣❛❣♥❡s ❞❡

♠❡s✉r❡ ♣❛r té❧é❞ét❡❝t✐♦♥ ♦♥t ré✉ss✐ à ♦❜t❡♥✐r ❞❡s ❞♦♥♥é❡s ♣ré❝✐s❡s✱ ♠❛✐s ♣♦✉r ❞❡s ♣ér✐♦❞❡s ❞❡✱

❣é♥ér❛❧❡♠❡♥t✱ s❡✉❧❡♠❡♥t q✉❡❧q✉❡s ❤❡✉r❡s ✭❇r❛❤❛♠ ❏r ❡t ❑❡❧❧② ✶✾✽✷ ❀ ❑r✐st♦✈✐❝❤ ❡t ❛❧✳ ✷✵✶✼✮✳

❙❡❧♦♥ ❉❡▼❛r❝❤✐ ❡t ❛❧✳ ✭✷✵✵✾✮✱ ❧❡s r❛✐s♦♥s q✉✐ ❝❛✉s❡♥t ❝❡ ♠❛♥q✉❡ ❞✬♦❜s❡r✈❛t✐♦♥s s♦♥t ❞❡s ❧✐♠✐✲

✾

❋✐❣✉r❡ ✶✳✹ ✕ ❱❛❧❡✉rs ❞❡s ❢r❛❝t✐♦♥s ❞❡ t❡rr❡ ♣❛r t✉✐❧❡ ❞❛♥s ❧❛ ré❣✐♦♥ ❞❡s ●r❛♥❞s ▲❛❝s ♣♦✉rq✉❛tr❡ ▼❈● ét✉❞✐és ❛✉ ❈❤❛♣✐tr❡ ✷✳ ❋✐❣✉r❡s t✐ré❡s ❞❡ ▼✉s✐❝ ❡t ■r❛♠❜♦♥❛ ✭✷✵✶✼✮✳

t❛t✐♦♥s ❛✉ ♥✐✈❡❛✉ ❞❡ ❧✬✐♥str✉♠❡♥t❛t✐♦♥✱ ✉♥❡ ❝♦✉✈❡rt✉r❡ tr♦♣ ❢❛✐❜❧❡ ❞✉ rés❡❛✉ ❞❡ s✉✐✈✐ ❡t ✉♥❡

❤étér♦❣é♥é✐té ❞❡s ❝♦♥❞✐t✐♦♥s s✉r ❧❡ t❡rr✐t♦✐r❡ à ❝♦✉✈r✐r✳ ❊♥ ❝♦♥séq✉❡♥❝❡✱ ❧❡ ♠❛♥q✉❡ ❞✬♦❜s❡r✈❛✲

t✐♦♥s ❛✉✲❞❡ss✉s ❞❡s ●r❛♥❞s ▲❛❝s ❞✐♠✐♥✉❡ ❧❛ ❝❛♣❛❝✐té ❞❡ ♣❛r❛♠étr❡r ❧❡s ♠♦❞è❧❡s ✭❝❧✐♠❛t✐q✉❡s

❡t ❞❡ ❧❛❝✮ ❡t✱ é❣❛❧❡♠❡♥t✱ ❞❡ t❡st❡r ❧❡s ♣❡r❢♦r♠❛♥❝❡s ❞❡ ❝❡✉①✲❝✐✳

✶✳✺ ❘❡✈✉❡ ❞❡ ❧❛ ❧✐ttér❛t✉r❡

P❧✉s✐❡✉rs s❝✐❡♥t✐✜q✉❡s s❡ s♦♥t ♣❡♥❝❤és s✉r ❧❛ q✉❡st✐♦♥ ❞❡ ❧✬✐♠♣❛❝t ❞✉ ré❝❤❛✉✛❡♠❡♥t ♣❧❛♥ét❛✐r❡

s✉r ❧✬❤②❞r♦❧♦❣✐❡ ❛✉ s❡✐♥ ❞✉ ❜❛ss✐♥ ❞❡s ●r❛♥❞s ▲❛❝s ❡♥ s❡ ❜❛s❛♥t s✉r ❧❡ ◆❇❙✳ ❆✉ ❞é♣❛rt✱ ❞ès ❧❡s

❛♥♥é❡s ✾✵✱ ❧❡s ét✉❞❡s ♦♣ér❛✐❡♥t ❛✈❡❝ ❧❛ ♠ét❤♦❞❡ ❞✉ ❢❛❝t❡✉r ❞❡ ❝❤❛♥❣❡♠❡♥t ♣♦✉r ♣❡r♠❡ttr❡ ✉♥❡

♣r♦❥❡❝t✐♦♥ ❞❡s ✈❛r✐❛❜❧❡s ét✉❞✐é❡s✳ ❈❡tt❡ ❢❛ç♦♥ ❞❡ ❢❛✐r❡ ✉t✐❧✐s❡ ❞❡s s♦rt✐❡s ❞❡ ▼❈● ♣♦✉r ✐❞❡♥t✐✲

✜❡r ❞❡s s✐❣♥❛✉① ❞❡ ❝❤❛♥❣❡♠❡♥ts ❝❧✐♠❛t✐q✉❡s✳ ❆✈❡❝ ❝❡s ❞❡r♥✐❡rs✱ ❞❡s ♠♦❞✐✜❝❛t✐♦♥s ✭❝✬❡st✲à✲❞✐r❡

✶✵

❞❡s ❛❞❞✐t✐♦♥s✴s♦✉str❛❝t✐♦♥s ♦✉ ❞❡s ♠✉❧t✐♣❧✐❝❛t✐♦♥s ♣❛r ❞❡s r❛t✐♦s✮ s✉r ❞❡s sér✐❡s ❞✬♦❜s❡r✈❛t✐♦♥s

t❡♥t❡♥t ❞❡ s✐♠✉❧❡r ✉♥❡ ♣r♦❥❡❝t✐♦♥ ❞❛♥s ❧❡ ❢✉t✉r✳ ▲❡s ♥♦✉✈❡❧❧❡s sér✐❡s ❛②❛♥t s✉❜✐ ❞❡s ❝❤❛♥❣❡✲

♠❡♥ts s♦♥t✱ ♣❛r ❧❛ s✉✐t❡✱ ✉t✐❧✐sé❡s ❝♦♠♠❡ ✐♥tr❛♥ts ❞❛♥s ✉♥❡ ❝❤❛î♥❡ ❞❡ ♠♦❞è❧❡s ❛✈❡❝ ❧❛q✉❡❧❧❡ ♦♥

♦❜t✐❡♥t✱ ❡♥tr❡ ❛✉tr❡s✱ ❞❡s sér✐❡s ❞❡ ◆❇❙✳ ▲❡s ét✉❞❡s ❞❡ ❝❡ t②♣❡ s♦♥t ❣é♥ér❛❧❡♠❡♥t ❛rr✐✈é❡s à ❞❡s

❝♦♥❝❧✉s✐♦♥s s✐♠✐❧❛✐r❡s ✿ ❞✬✐♠♣♦rt❛♥t❡s ❜❛✐ss❡s ❞✉ ◆❇❙ ♣♦✉r ❧❡s ●r❛♥❞s ▲❛❝s ❡♥ ❝❧✐♠❛t ❢✉t✉r ❡t

✉♥❡ ré♣❛rt✐t✐♦♥ é❣❛❧❡ ❞❡ ❝❡s ❞✐♠✐♥✉t✐♦♥s à ❧✬✐♥tér✐❡✉r ❞✉ ❝②❝❧❡ ❛♥♥✉❡❧✳ ❊♥ ❡✛❡t✱ ❞❡s ❜❛✐ss❡s ❞❡

✷✸ à ✺✶ ✪ ❞✉ ◆❇❙ s♦♥t ♣r♦❥❡té❡s ♣❛r ❈r♦❧❡② ✭✶✾✾✵✮✱ s❡ tr❛❞✉✐s❛♥t ♣❛r ❞❡s ❞✐♠✐♥✉t✐♦♥s ✈❛r✐❛♥t

❡♥tr❡ ✷✵ ❡t ✷✺✵ ❝♠ à ❧❛ ✜♥ ❞✉ ❳❳■❡ s✐è❝❧❡ ♣♦✉r ❧❡s ❞✐✛ér❡♥ts ❧❛❝s ❞✉ rés❡❛✉ ✭❍❛rt♠❛♥♥✱ ✶✾✾✵✮✳

❊♥ ✷✵✶✶✱ ✉♥❡ ét✉❞❡ ♣❛r ▲♦❢❣r❡♥ ❡t ❛❧✳ ✭✷✵✶✶✮ s♦✉❧è✈❡ ✉♥ ♣r♦❜❧è♠❡ ❛✈❡❝ ✉♥ ❞❡s ♠♦❞è❧❡s ❞❡ ❧❛

❝❤❛î♥❡ ✉t✐❧✐sé❡ ❞❛♥s ❧❛ ♠ét❤♦❞❡ ❞✉ ❢❛❝t❡✉r ❞❡ ❝❤❛♥❣❡♠❡♥t✳ ❈❡❧✉✐✲❝✐ ❝❛✉s❡ ✉♥❡ s✉r❡st✐♠❛t✐♦♥

❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✐♥s✐ q✉✬✉♥❡ s♦✉s✲❡st✐♠❛t✐♦♥ ❞✉ r✉✐ssè❧❡♠❡♥t✱ ♣r♦✈♦q✉❛♥t ❞❡s ❞✐♠✐♥✉t✐♦♥s

❡①❛❣éré❡s ❞✉ ◆❇❙ ❞❛♥s ❧❡s sér✐❡s ♣r♦❥❡té❡s✳ ■❧ ❡st ♣r♦♣♦sé✱ ♣♦✉r r❡♠é❞✐❡r ❛✉ ♣r♦❜❧è♠❡✱ ✉♥❡

♥♦✉✈❡❧❧❡ ❛♣♣r♦❝❤❡ ♣♦✉r ét✉❞✐❡r ❧❛ ♣r♦❥❡❝t✐♦♥ ❞❡s ✈❛❧❡✉rs ❞❡ ◆❇❙✳ ■❧ s✬❛❣✐t ❞❡ ❧✬✉t✐❧✐s❛t✐♦♥ ❞❡s

❞♦♥♥é❡s ❞❡ ▼❘❈ q✉✐ ♦♥t ❧✬❛✈❛♥t❛❣❡ ❞✬❛ss✉r❡r ❧❛ ❝♦♥s❡r✈❛t✐♦♥ ❞❡ ❧✬é♥❡r❣✐❡ ✭❝♦♥tr❛✐r❡♠❡♥t ❛✉

♠♦❞è❧❡ ♣r♦❜❧é♠❛t✐q✉❡ ❞❡ ❧❛ ♠ét❤♦❞❡ ♣ré❝é❞❡♥t❡✮✳ ❊♥ ♣❧✉s ❞✬✉t✐❧✐s❡r ❞❡s ♠♦❞è❧❡s ❛✈❡❝ ❞❡s

rés♦❧✉t✐♦♥s s♣❛t✐❛❧❡s ♣❧✉s ✜♥❡s✱ ❧❡s ❛✉t❡✉rs s✉❣❣èr❡♥t ❞♦♥❝ ❞✬✉t✐❧✐s❡r ❞✐r❡❝t❡♠❡♥t ❧❡s s♦rt✐❡s

❞❡ ▼❘❈ ♣♦✉r ❧❡s ❛♥❛❧②s❡s ♣❧✉tôt q✉❡ ❞❡ ♣❛ss❡r ♣❛r ✉♥❡ sér✐❡ ❞❡ ♠♦❞è❧❡s ❤②❞r♦❧♦❣✐q✉❡s ❡t

❤②❞r❛✉❧✐q✉❡s✳ ▲❡s ét✉❞❡s ✉t✐❧✐s❛♥t ❝❡tt❡ s❡❝♦♥❞❡ ❛♣♣r♦❝❤❡ ♦♥t ♦❜t❡♥✉ ❞❡s ❝❤❛♥❣❡♠❡♥ts ❞❡

◆❇❙ ❞✐✛ér❡♥ts ❞❡s ét✉❞❡s ❞✉ ♣r❡♠✐❡r t②♣❡✳ ❊♥ ❡✛❡t✱ ❧❡s ré❞✉❝t✐♦♥s ② s♦♥t ♠♦✐♥s ✐♠♣♦rt❛♥t❡s

❡t ❞❡s ❛✉❣♠❡♥t❛t✐♦♥s s♦♥t ♠ê♠❡ ♣r♦❥❡té❡s ✭▼❛❝❑❛② ❡t ❙❡❣❧❡♥✐❡❦s ✷✵✶✸ ❀ ▼✉s✐❝ ❡t ❛❧✳ ✷✵✶✺ ❀

◆♦t❛r♦ ❡t ❛❧✳ ✷✵✶✺✮✳ P❛r ❡①❡♠♣❧❡✱ ✉♥❡ ❝♦♠♣❛r❛✐s♦♥ ❡♥tr❡ ❧❡s ❤♦r✐③♦♥s ✶✾✻✷✲✶✾✾✵ ❡t ✷✵✷✶✲✷✵✺✵

ré✈è❧❡ ❞❡s ❝❤❛♥❣❡♠❡♥ts ❞❡ ◆❇❙ ❡♥tr❡ ✲✾ ❡t ✰✶✪ ❡t ❞❡ ❧é❣èr❡s ❜❛✐ss❡s ❞❡s ♥✐✈❡❛✉① ❞✬❡❛✉ ❞❡ ✸

à ✻ ❝❡♥t✐♠ètr❡s ✭▼❛❝❑❛② ❡t ❙❡❣❧❡♥✐❡❦s✱ ✷✵✶✸✮✳ ▼✉s✐❝ ❡t ❛❧✳ ✭✷✵✶✺✮✱ ❞❛♥s ✉♥❡ ét✉❞❡ s❡♠❜❧❛❜❧❡✱

♦❜t✐❡♥t ✉♥❡ ♠é❞✐❛♥❡ ❞✬❡♥s❡♠❜❧❡ ❞❡ ✵ ♠♠ ❥♦✉r−1 ♣♦✉r ❧❡s ❝❤❛♥❣❡♠❡♥ts ❞❡ ◆❇❙ ❡♥tr❡ ✶✾✼✶✲✶✾✾✾

❡t ✷✵✹✶✲✷✵✼✵ ♣♦✉r ❧❡ ❧❛❝ ▼✐❝❤✐❣❛♥✲❍✉r♦♥✳ ❊♥ ♣❧✉s ❞✬❛✈♦✐r ❞❡s rés✉❧t❛ts ❜✐❡♥ ❞✐✛ér❡♥ts à ❧♦♥❣

t❡r♠❡✱ ❧❡s ❞❡✉① ❛♣♣r♦❝❤❡s ♦♥t ✉♥❡ ❞✐✛ér❡♥❝❡ ♠❛rq✉é❡ ❞❛♥s ❧❡✉rs rés✉❧t❛ts ✐♥t❡r❛♥♥✉❡❧s✳ ❯♥❡

ré♣❛rt✐t✐♦♥ é❣❛❧❡ ❞❡s ❝❤❛♥❣❡♠❡♥ts ❞✉ ❜✐❧❛♥ ❤②❞r✐q✉❡ ❞❛♥s ❧✬❛♥♥é❡✱ ♣rés❡♥t❡ ♣♦✉r ❧❛ ♠ét❤♦❞❡ ❞✉

❢❛❝t❡✉r ❞❡ ❝❤❛♥❣❡♠❡♥t✱ ❡st ❡♥ ♦♣♣♦s✐t✐♦♥ ❛✉① ❧❛r❣❡s é❝❛rts ❞❡s rés✉❧t❛ts ❤✐✈❡r♥❛✉① ❡t ❡st✐✈❛✉①

q✉❡ ❧✬♦♥ ♦❜s❡r✈❡ ❞❛♥s ❧❡s ét✉❞❡s s❡ s❡r✈❛♥t ❞❡s ▼❘❈✳ ❈❡s ❞❡r♥✐èr❡s ♦❜t✐❡♥♥❡♥t ❡♥ ❡✛❡t ❞❡s

❛✉❣♠❡♥t❛t✐♦♥s ❞❡ ◆❇❙ ♣♦✉r ✉♥❡ ♣❛rt✐❡ ❞❡ ❧✬❛♥♥é❡ ❡t ❞❡s ❞✐♠✐♥✉t✐♦♥s ♣♦✉r ✉♥❡ ❛✉tr❡✳

✶✳✻ ❖✉t✐❧s ❞✬❛♥❛❧②s❡

❉✐✛ér❡♥ts t❡sts ❡t t❤é♦r✐❡s st❛t✐st✐q✉❡s s♦♥t ✉t✐❧✐sés ❞❛♥s ❝❡tt❡ ét✉❞❡ ♣♦✉r ❛♥❛❧②s❡r ❧❡s ❞♦♥♥é❡s

♣r♦❞✉✐t❡s ♣❛r ❧❡s ♠♦❞è❧❡s ❝❧✐♠❛t✐q✉❡s✳ ❈❡s ♦✉t✐❧s s❡r♦♥t ♠❡♥t✐♦♥♥és ❞❛♥s ❧✬❛rt✐❝❧❡ ❛✉ ❈❤❛♣✐tr❡

✷✱ ♠❛✐s ❞❡ ❢❛ç♦♥ très ❜rè✈❡✳ ❈❡tt❡ s❡❝t✐♦♥ s❡rt ❞♦♥❝ à ❢❛♠✐❧✐❛r✐s❡r ❧❡ ❧❡❝t❡✉r à ❝❡s t❡sts ♣♦✉r

♠✐❡✉① ❝♦♠♣r❡♥❞r❡ ❧❡s r❛✐s♦♥s ❞❡ ❧❡✉r ✉t✐❧✐s❛t✐♦♥ ❛✐♥s✐ q✉❡ ❧❡✉rs rés✉❧t❛ts✳

✶✶

▲✬❡st✐♠❛t❡✉r ❞❡ ❚❤❡✐❧✲❙❡♥ ❛ été ✐♥✐t✐❛❧❡♠❡♥t ❞é✈❡❧♦♣♣é ♣❛r ❚❤❡✐❧ ✭✶✾✺✵✮ ❡t ❡♥s✉✐t❡ ❛♠é❧✐♦ré

♣❛r ❙❡♥ ✭✶✾✻✽✮✳ ■❧ s✬❛❣✐t ❞✬✉♥❡ ré❣r❡ss✐♦♥ ❧✐♥é❛✐r❡ r♦❜✉st❡ ♣♦✉r ❞❡s sér✐❡s ❞❡ ♣♦✐♥ts ❛②❛♥t

❞❡s ❝♦♦r❞♦♥♥é❡s ❡♥ ❞❡✉① ❞✐♠❡♥s✐♦♥s ✭①✱②✮ q✉✐ ❡st s♦✉✈❡♥t ❡①♣r✐♠é❡ ❝♦♠♠❡ ✉♥❡ éq✉❛t✐♦♥

❢♦♥❝t✐♦♥♥❡❧❧❡ ❞❡ ❢♦r♠❡

y = ax+ b. ✭✶✳✶✮

▲❛ ♣❡♥t❡ ❛ ❡st ♦❜t❡♥✉❡ ❡♥ ♣r❡♥❛♥t ❧❛ ♠é❞✐❛♥❡ ❞❡s ♣❡♥t❡s ❡♥tr❡ ❝❤❛❝✉♥❡ ❞❡s

n(n− 1)

2✭✶✳✷✮

❝♦♠❜✐♥❛✐s♦♥s ❞❡ ♣♦✐♥ts ❞❛♥s ❧❛ sér✐❡✱ ♦ù ♥ ❡st ❧❡ ♥♦♠❜r❡ ❞❡ ♣♦✐♥ts ❞❛♥s ❝❡❧❧❡✲❝✐✳ P❛r ❡①❡♠♣❧❡✱

s✐ ♥♦✉s ❛✈♦♥s ✉♥❡ sér✐❡ ❞❡ q✉❛tr❡ ♣♦✐♥ts✱ s✐① ♣❛✐r❡s ❞❡ ♣♦✐♥ts ❞✐✛ér❡♥t❡s ❡①✐st❡♥t ❡t✱ ❞♦♥❝✱

❛✉t❛♥t ❞❡ ♣❡♥t❡s s♦♥t ♣r♦❞✉✐t❡s✳ ❖♥ ♦❜t✐❡♥❞r❛✐t ❛❧♦rs ❧❛ ♣❡♥t❡ ❛ ❛✈❡❝ ❧❛ ♠é❞✐❛♥❡ ❞❡s s✐①

♣❡♥t❡s✳ ❆✈❡❝ ❧❛ ♣❡♥t❡ ❡st✐♠é❡✱ ❧❛ ✈❛❧❡✉r ❞❡ ❧✬♦r❞♦♥♥é❡ à ❧✬♦r✐❣✐♥❡✱ ❜ ❞❛♥s ❧✬éq✉❛t✐♦♥ ✶✳✶✱ ❡st

♦❜t❡♥✉❡ ❡♥ ❝❛❧❝✉❧❛♥t ❧❛ ♠é❞✐❛♥❡ ❞❡

yi − axi ✭✶✳✸✮

♣♦✉r ❧❡s ♣♦✐♥ts i = 1, 2, ...n✳ ❱✉ s❛ s✐♠♣❧✐❝✐té✱ ❧❡ t❡st st❛t✐st✐q✉❡ ❞❡ ❚❤❡✐❧✲❙❡♥ ❡st s♦✉✈❡♥t

✉t✐❧✐sé✱ ❡t ❝❡✱ ❞❛♥s ♣❧✉s✐❡✉rs ❞♦♠❛✐♥❡s ✭♣✳ ❡①✳ ❛str♦♥♦♠✐❡✱ ❜✐♦❧♦❣✐❡✱ ❝❧✐♠❛t♦❧♦❣✐❡✱ ❡t❝✳✮✳ ❉❛♥s

❧✬ét✉❞❡ ❞✉ ❈❤❛♣✐tr❡ ✷✱ ❝❡ t❡st s❡rt à é✈❛❧✉❡r ❧❡s ❝❤❛♥❣❡♠❡♥ts ❞❡s ❝♦♥❞✐t✐♦♥s ❤②❞r♦❧♦❣✐q✉❡s

♠♦②❡♥♥❡s ❞❡s ●r❛♥❞s ▲❛❝s ❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵✳

P♦✉r ❧✬ét✉❞❡ ❞❡s ❡①trê♠❡s✱ ✉♥ ❛✉tr❡ ♦✉t✐❧ ❡st ❞✬✉♥❡ ♣❧✉s ❣r❛♥❞❡ ✉t✐❧✐té✳ ❈♦♠♠❡ ✐❧ s❡ ❢❛✐t

❢réq✉❡♠♠❡♥t ❞❛♥s ❧❡s ét✉❞❡s ❤②❞r♦❧♦❣✐q✉❡s q✉✐ t♦✉❝❤❡♥t ❛✉① é✈è♥❡♠❡♥ts r❛r❡s ✭❡♥ ❝♦♠♣❛r❛✲

✐s♦♥ ❛✉① ét✉❞❡s ❞❡s é✈è♥❡♠❡♥ts à ❢réq✉❡♥❝❡ ♠♦②❡♥♥❡✮✱ ❧❛ ❧♦✐ ❞✬❡①tr❡♠✉♠ ❣é♥ér❛❧✐sé❡ ✭▲❊●✱

♦✉ ✓●❊❱✔ ❡♥ ❛♥❣❧❛✐s✮ ❡st ✉t✐❧✐sé❡✳ ❈❡tt❡ ❧♦✐ ❡♥❣❧♦❜❡ ✉♥❡ ❢❛♠✐❧❧❡ ❞❡ ❞✐str✐❜✉t✐♦♥s q✉✐ s❡r✈❡♥t

à r❡♣rés❡♥t❡r ❞❡s ♣❤é♥♦♠è♥❡s ❛✉① ✈❛❧❡✉rs ❡①trê♠❡s ❡♥ ❤②❞r♦❧♦❣✐❡ ❡t ❞❛♥s ❞✬❛✉tr❡s ❞♦♠❛✐♥❡s

✭♣✳ ❡①✳ ♠été♦r♦❧♦❣✐❡ ❏❡♥❦✐♥s♦♥ ✶✾✺✺❀ ✜♥❛♥❝❡ ●✉é❣❛♥ ❡t ❍❛ss❛♥✐ ✷✵✶✹✮✳ ❉❛♥s ❧✬❛rt✐❝❧❡ ❞✉

❈❤❛♣✐tr❡ ✷✱ ❧❡s ♣❛r❛♠ètr❡s ♦♣t✐♠❛✉① ♣♦✉r ❞❡s ❞✐str✐❜✉t✐♦♥s ❞❡ ❧❛ ▲❊● s♦♥t ♦❜t❡♥✉s ♣♦✉r ❞✐❢✲

❢ér❡♥t❡s ✈❛r✐❛❜❧❡s s✉r ❞✐✛ér❡♥ts ❤♦r✐③♦♥s ✭✶✾✼✶✲✷✵✵✵✱ ✷✵✹✶✲✷✵✼✵ ❡t ✷✵✼✶✲✷✶✵✵✮ ♣♦✉r ♣❡r♠❡ttr❡

✉♥❡ ❝♦♠♣❛r❛✐s♦♥ ❞❛♥s ❧❡ t❡♠♣s✳ ❈❡s ♣❛r❛♠ètr❡s s♦♥t ❛✉ ♥♦♠❜r❡ ❞❡ tr♦✐s ❡t ❞é✜♥✐ss❡♥t ❧❛

♣♦s✐t✐♦♥ ✭µ✮✱ ❧❛ ❞✐s♣❡rs✐♦♥ ✭σ✮ ❡t ❧❛ ❢♦r♠❡ ✭ξ✮ ❞❡s ❞✐str✐❜✉t✐♦♥s✳ ➱q✉✐♣é❡s ❞❡s ❞✐✛ér❡♥t❡s ❞✐str✐✲

❜✉t✐♦♥s✱ ❞❡s ✈❛❧❡✉rs ❝♦rr❡s♣♦♥❞❛♥t❡s à ❞❡s ♣ér✐♦❞❡s ❞❡ r❡t♦✉r ❞é✜♥✐❡s ♣❡✉✈❡♥t êtr❡ ❝❛❧❝✉❧é❡s✳

P♦✉r ② ❛rr✐✈❡r✱ ♦♥ tr❛❝❡ ❧❛ ❢♦♥❝t✐♦♥ ❞❡ ❧❛ ❞❡♥s✐té ❞❡ ♣r♦❜❛❜✐❧✐té ❞♦♥t ❧✬éq✉❛t✐♦♥ ❡st

✶✷

❋✐❣✉r❡ ✶✳✺ ✕ ❉❡♥s✐té ❞❡ ♣r♦❜❛❜✐❧✐té ❞✬✉♥❡ ❧♦✐ ❞✬❡①tr❡♠✉♠ ❣é♥ér❛❧✐sé❡

P (x) =1

σt(x)ξ+1e−t(x), ✭✶✳✹✮

♦ù

t(x) =

(1 + ξ(x−µσ ))− 1/ξ, s✐ ξ 6= 0

e−(x − µ)/σ, s✐ ξ = 0

✭✶✳✺✮

▲❛ ✜❣✉r❡ ✶✳✺ ♣rés❡♥t❡ ✉♥ ❡①❡♠♣❧❡ ❞❡ ❢♦♥❝t✐♦♥ ❞❡ ❞❡♥s✐té ♣♦✉r ✉♥❡ ❞✐str✐❜✉t✐♦♥ ❞❡ ❧❛ ▲❊● ❛✈❡❝

❞❡s ♣❛r❛♠ètr❡s ❛r❜✐tr❛✐r❡s✳ ▲✬✐♥té❣r❛❧❡ ❞❡ ♠♦✐♥s ❧✬✐♥✜♥✐ à ❧✬✐♥✜♥✐ ❞✬✉♥❡ t❡❧❧❡ ❢♦♥❝t✐♦♥ ❡st é❣❛❧❡

à ✶✳ ❋✐♥❛❧❡♠❡♥t✱ ❝✬❡st ❧❛ ❢♦♥❝t✐♦♥ ❞❡ ❞❡♥s✐té q✉✐ ♣❡r♠❡t ❞❡ ré♣♦♥❞r❡ à ❞❡s q✉❡st✐♦♥s t❡❧❧❡s

q✉❡✿ ✓◗✉❡❧❧❡ ❡st ❧❛ ♣r♦❜❛❜✐❧✐té q✉✬✉♥❡ ✈❛❧❡✉r ❳ s♦✐t s✉♣ér✐❡✉r❡ à ❨ s✐ ❝❡ ♣❤é♥♦♠è♥❡ s✉✐t ✉♥❡

❞✐str✐❜✉t✐♦♥ ●❊❱ ❛②❛♥t ❞❡s ♣❛r❛♠ètr❡s µ✱ σ ❡t ξ❄✔✳ ▲❡s ✈❛❧❡✉rs ❞❡✱ ♣❛r ❡①❡♠♣❧❡✱ ♣ré❝✐♣✐t❛t✐♦♥s

♠❛①✐♠❛❧❡s ❛♥♥✉❡❧❧❡s ♣♦✉r ✉♥❡ ♣ér✐♦❞❡ ❞❡ r❡t♦✉r ❞❡ ✺✵ ❛♥s ✭❝✳✲à✲❞✳ q✉✐ s♦♥t ♦❜s❡r✈é❡s ❡♥

♠♦②❡♥♥❡ à ❝❤❛q✉❡ ✺✵ ❛♥s✮ ♣❡✉✈❡♥t ❞♦♥❝ êtr❡ ♦❜t❡♥✉❡s ❛✈❡❝ ❧✬éq✉❛t✐♦♥ ✶✳✹✳ ❈❡s ✈❛❧❡✉rs✱ ❞✐❝té❡s

♣❛r ❧❡s ❞✐str✐❜✉t✐♦♥s ❝♦rr❡s♣♦♥❞❛♥t❡s ❛✉① ❤♦r✐③♦♥s ❤✐st♦r✐q✉❡s ❡t ❢✉t✉rs✱ ♣❡r♠❡tt❡♥t ✜♥❛❧❡♠❡♥t

❞✬❛♥❛❧②s❡r ❧✬é✈♦❧✉t✐♦♥ ❞❡s ❡①trê♠❡s ❞❛♥s ❧❡ t❡♠♣s✳

✶✸

❈❤❛♣✐tr❡ ✷

❆rt✐❝❧❡ ✿ ❆ss❡ss♠❡♥t ♦❢ t❤❡ ▲❛✉r❡♥t✐❛♥

●r❡❛t ▲❛❦❡s✬ ❤②❞r♦❧♦❣✐❝❛❧ ♠❡❛♥ ❛♥❞

❡①tr❡♠❡ ❝♦♥❞✐t✐♦♥s ✐♥ ❛ ❝❤❛♥❣✐♥❣

❝❧✐♠❛t❡ ✉s✐♥❣ r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧s

✷✳✶ ❘és✉♠é

❯♥ ❡♥s❡♠❜❧❡ ❞❡ ✶✼ s✐♠✉❧❛t✐♦♥s ♣r♦✈❡♥❛♥t ❞❡ ✺ ♠♦❞è❧❡s ré❣✐♦♥❛✉① ❞✉ ❝❧✐♠❛t ❡st ✉t✐❧✐sé ❞❛♥s

❝❡tt❡ ét✉❞❡ ♣♦✉r é✈❛❧✉❡r ❧✬❛♣♣♦rt ❡♥ ❡❛✉ ❞❡s ●r❛♥❞s ▲❛❝s ❞❡ ✶✾✺✸ à ✷✶✵✵ ❡♥ s✉✐✈❛♥t ❧❡s

s❝é♥❛r✐♦s ❞✬é♠✐ss✐♦♥s ❘❈P ✹✳✺ ❡t ✽✳✺ ❛✈❡❝ ❝♦♠♠❡ ♣♦✐♥t ❝❡♥tr❛❧ ❧❡ ❝❤❛♥❣❡♠❡♥t ❞❡ ✈❛r✐❛❜❧❡s

❤②❞r♦❧♦❣✐q✉❡s ♠♦②❡♥♥❡s ❡t ❡①trê♠❡s ❜✐❤❡❜❞♦♠❛❞❛✐r❡s✳ ▲❡s ♠♦❞è❧❡s s♦♥t✱ ❡♥ ♣r❡♠✐❡r ❧✐❡✉✱

é✈❛❧✉és ❡♥ ❝♦♠♣❛r❛♥t ❧❡✉rs ❝②❝❧❡s ❛♥♥✉❡❧s ❞❡ ♣ré❝✐♣✐t❛t✐♦♥s✱ r✉✐ssè❧❡♠❡♥t✱ é✈❛♣♦r❛t✐♦♥ ❡t ◆❡t

❇❛s✐♥ ❙✉♣♣❧② ✭◆❇❙✮ ❛✈❡❝ ❞❡s ♦❜s❡r✈❛t✐♦♥s✳ ▲❡s t❡♥❞❛♥❝❡s ❞❛♥s ❧❡s ✈❛❧❡✉rs ♠♦②❡♥♥❡s s♦♥t

❡♥s✉✐t❡ ét✉❞✐é❡s ♣♦✉r ❝❤❛q✉❡ ✈❛r✐❛❜❧❡ à ❧✬❛✐❞❡ ❞✉ t❡st st❛t✐st✐q✉❡ ❞❡ ❚❤❡✐❧✲❙❡♥✳ ▲❡s ❝❤❛♥❣❡♠❡♥ts

❞❛♥s ❧❡s ✈❛❧❡✉rs ❡①trê♠❡s s♦♥t✱ q✉❛♥t à ❡✉①✱ ❛♥❛❧②sés ❛✈❡❝ ❧❛ ❧♦✐ ❞✬❡①tr❡♠✉♠ ❣é♥ér❛❧✐sé❡ ✭●❊❱✮

♣♦✉r ✉♥❡ ♣ér✐♦❞❡ ❞❡ ré❢ér❡♥❝❡ ✭✶✾✼✶✲✷✵✵✵✮ ❡t ❞❡✉① ♣ér✐♦❞❡s ❢✉t✉r❡s ✭✷✵✹✶✲✷✵✼✵ ❡t ✷✵✼✶✲✷✶✵✵✮✳

▲❡s t❡♥❞❛♥❝❡s ❞❡ ❧✬❡♥s❡♠❜❧❡ ✐♥❞✐q✉❡♥t ❞❡s ❛✉❣♠❡♥t❛t✐♦♥s ❞✬é✈❛♣♦r❛t✐♦♥ ❞❡ ✶✸✻ ❡t ✷✵✹ ♠♠

✭❘❈P✹✳✺ ❡t ❘❈P✽✳✺✮ ❛✉✲❞❡ss✉s ❞❡s ●r❛♥❞s ▲❛❝s ❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵✳ ▲❡s ♣ré❝✐♣✐t❛t✐♦♥s s♦♥t

❛❝❝❡♥t✉é❡s ❞❡ ✽✸ ❡t ✶✹✵ ♠♠ ❡t ❧❡ r✉✐ssè❧❡♠❡♥t ❞❡ ✻✽ ❡t ✶✸✺ ♠♠✳ ▲❡s ❝❤❛♥❣❡♠❡♥ts ♥❡ s♦♥t ♣❛s

❞✐str✐❜✉és é❣❛❧❡♠❡♥t ❛♥♥✉❡❧❧❡♠❡♥t ❡t✱ ❞♦♥❝✱ ❞❡s ❞✐✛ér❡♥❝❡s ✐♠♣♦rt❛♥t❡s ❡①✐st❡♥t ❞✬✉♥❡ s❛✐s♦♥

à ❧✬❛✉tr❡✳ P❛r ❝♦♥séq✉❡♥t✱ ❧❡s ❝❤❛♥❣❡♠❡♥ts ♣ré✈✉s ❞❛♥s ❧❡ ❜✐❧❛♥ ❤②❞r✐q✉❡ ❞❡s ●r❛♥❞s ▲❛❝s s♦♥t

♣♦s✐t✐❢s ❡♥ ❤✐✈❡r ❡t ❛✉ ♣r✐♥t❡♠♣s✱ ♠❛✐s ♥é❣❛t✐❢s ❡♥ été✳ ❙✉r ❧✬❛♥♥é❡ ❝♦♠♣❧èt❡✱ ❞❡s ❛✉❣♠❡♥t❛t✐♦♥s

❞❡ ✶✹ ❡t ✼✵ ♠♠ s♦♥t ♣r♦❥❡té❡s ♣♦✉r ❧❡s s❝é♥❛r✐♦s ❘❈P✹✳✺ ❡t ❘❈P✽✳✺ r❡s♣❡❝t✐✈❡♠❡♥t ♣♦✉r ✷✶✵✵✳

▲✬❛♥❛❧②s❡ s✉r ❧❡s ✈❛❧❡✉rs ❡①trê♠❡s ré✈è❧❡ ✉♥❡ ❤❛✉ss❡ ❞❡s ♠❛①✐♠❛ ❞❡ ♣ré❝✐♣✐t❛t✐♦♥s ❡t ❞❡ ◆❇❙

❞❡ ✶✶ à ✷✼✪ ❡t ❞❡ ✶ à ✾✪ r❡s♣❡❝t✐✈❡♠❡♥t t❛♥❞✐s q✉❡ ❧❡s ♠✐♥✐♠❛ ❞❡ ◆❇❙ ❜❛✐ss❡♥t ❞❡ ✶✽ à ✷✾✪

✶✹

❡♥tr❡ ✶✾✼✶✲✷✵✵✵ ❡t ✷✵✹✶✲✷✶✵✵✳

✷✳✷ ❆❜str❛❝t

❆ s❡t ♦❢ ✶✼ s✐♠✉❧❛t✐♦♥s ❢r♦♠ ✜✈❡ r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧s ✐s ✉s❡❞ ✐♥ t❤✐s st✉❞② t♦ ❛ss❡ss t❤❡

●r❡❛t ▲❛❦❡s✬ ✇❛t❡r s✉♣♣❧✐❡s ❢r♦♠ ✶✾✺✸ t♦ ✷✶✵✵ ❢♦❧❧♦✇✐♥❣ ❡♠✐ss✐♦♥s s❝❡♥❛r✐♦s ❘❈P✹✳✺ ❛♥❞

✽✳✺ ✇✐t❤ ❛ ❢♦❝✉s ♦♥ ❜✐✲✇❡❡❦❧② ❝❤❛♥❣❡s ♦♥ t❤❡ ♠❡❛♥s ❛♥❞ ❡①tr❡♠❡s ♦❢ ❤②❞r♦❧♦❣✐❝❛❧ ✈❛r✐❛❜❧❡s✳

▼♦❞❡❧s ❛r❡ ✜rst ❡✈❛❧✉❛t❡❞ ❜② ❝♦♠♣❛r✐♥❣ ❛♥♥✉❛❧ ❝②❝❧❡s ♦❢ ♣r❡❝✐♣✐t❛t✐♦♥✱ r✉♥♦✛✱ ❡✈❛♣♦r❛t✐♦♥

❛♥❞ ♥❡t ❜❛s✐♥ s✉♣♣❧② ✭◆❇❙✮ ✇✐t❤ ♦❜s❡r✈❛t✐♦♥s✳ ❚r❡♥❞s ✐♥ ♠❡❛♥ ✈❛❧✉❡s ❛r❡ t❤❡♥ st✉❞✐❡❞ ❢♦r

❡❛❝❤ ✈❛r✐❛❜❧❡ ✉s✐♥❣ ❚❤❡✐❧✲❙❡♥✬s st❛t✐st✐❝❛❧ t❡st✳ ❈❤❛♥❣❡s ✐♥ ❡①tr❡♠❡ ❝♦♥❞✐t✐♦♥s ❛r❡ ❛♥❛❧②③❡❞

✉s✐♥❣ ❣❡♥❡r❛❧✐③❡❞ ❡①tr❡♠❡ ✈❛❧✉❡s ❞✐str✐❜✉t✐♦♥s ❢♦r ❛ r❡❢❡r❡♥❝❡ ♣❡r✐♦❞ ✭✶✾✼✶✲✷✵✵✵✮ ❛♥❞ t✇♦

❢✉t✉r❡ ♣❡r✐♦❞s ✭✷✵✹✶✲✷✵✼✵ ❛♥❞ ✷✵✼✶✲✷✶✵✵✮✳ ❊♥s❡♠❜❧❡ tr❡♥❞ r❡s✉❧ts s❤♦✇ ❡✈❛♣♦r❛t✐♦♥ ✐♥❝r❡❛s❡s

♦❢ ✶✸✻ ❛♥❞ ✷✵✹ ♠♠ ✭❘❈P✹✳✺ ❛♥❞ ❘❈P✽✳✺✮ ♦✈❡r t❤❡ ●r❡❛t ▲❛❦❡s ❜❡t✇❡❡♥ ✶✾✺✸ ❛♥❞ ✷✶✵✵✳

Pr❡❝✐♣✐t❛t✐♦♥ r✐s❡s ❜② ✽✸ ❛♥❞ ✶✹✵ ♠♠ ❛♥❞ r✉♥♦✛ ✐♥❝r❡❛s❡s ❜② ✻✽ ❛♥❞ ✶✸✺ ♠♠✳ ❚r❡♥❞s ❛r❡ ♥♦t

❡q✉❛❧❧② ❞✐str✐❜✉t❡❞ t❤r♦✉❣❤♦✉t t❤❡ ②❡❛r ❛s s❡❛s♦♥❛❧ ❝❤❛♥❣❡s ❞✐✛❡r ❣r❡❛t❧②✳ ❆s ❛ r❡s✉❧t✱ ●r❡❛t

▲❛❦❡s ♥❡t ❜❛s✐♥ s✉♣♣❧② ✐s ❡①♣❡❝t❡❞ t♦ r✐s❡ ✐♥ ✇✐♥t❡r ❛♥❞ s♣r✐♥❣ ❛♥❞ ❞❡❝r❡❛s❡ ✐♥ s✉♠♠❡r✳ ❖✈❡r

t❤❡ ❡♥t✐r❡ ②❡❛r✱ ◆❇❙ ✐♥❝r❡❛s❡s ♦❢ ✶✹ ❛♥❞ ✼✵ ♠♠ ❛r❡ ♣r♦❥❡❝t❡❞ ❢♦r s❝❡♥❛r✐♦s ❘❈P✹✳✺ ❛♥❞ ✽✳✺

r❡s♣❡❝t✐✈❡❧② ❜② t❤❡ ②❡❛r ✷✶✵✵✳ ❊①tr❡♠❡ ✈❛❧✉❡s ❛♥❛❧②s✐s r❡✈❡❛❧s t❤❛t ♣r❡❝✐♣✐t❛t✐♦♥ ❛♥❞ ◆❇❙

♠❛①✐♠❛ ✐♥❝r❡❛s❡ ❜② ✶✶ t♦ ✷✼✪ ❛♥❞ ✶ t♦ ✾✪ r❡s♣❡❝t✐✈❡❧② ✇❤✐❧❡ ◆❇❙ ♠✐♥✐♠❛ ❞❡❝r❡❛s❡ ❜② ✶✽ t♦

✷✾✪ ❜❡t✇❡❡♥ ✶✾✼✶✲✷✵✵✵ ❛♥❞ ✷✵✹✶✲✷✶✵✵✳

✶✺

Noname manuscript No.

(will be inserted by the editor)

Assessment of the Laurentian Great Lakes’

hydrological mean and extreme conditions in a

changing climate using regional climate models

Edouard Mailhot · Biljana Music · Daniel

F. Nadeau · Anne Frigon · Richard

Turcotte

Received: date / Accepted: date

Abstract A set of 17 simulations from five regional climate models is used in thisstudy to assess the Great Lakes’ water supply from 1953 to 2100 following emis-sions scenarios RCP4.5 and 8.5 with a focus on bi-weekly changes in the meansand extremes of hydrological variables. Models are first evaluated by comparing an-nual cycles of precipitation, runoff, evaporation and net basin supply (NBS) withobservations. Trends in mean values are then studied for each variable using Theil-Sen’s statistical test. Changes in extreme conditions are analyzed using generalizedextreme values distributions for a reference period (1971-2000) and two future peri-ods (2041-2070 and 2071-2100). Ensemble trend results show evaporation increasesof 136 and 204 mm (RCP4.5 and RCP8.5) over the Great Lakes between 1953 and2100. Precipitation increases by 83 and 140 mm and runoff increases by 68 and135 mm. Trends are not equally distributed throughout the year as seasonal changesdiffer greatly. As a result, Great Lakes net basin supply is expected to increase inwinter and spring and decrease in summer. Over the entire year, NBS increases of14 and 70 mm are projected for scenarios RCP4.5 and 8.5 respectively by the year2100. An analysis of extreme values reveals that precipitation and NBS maximaincrease by 11 to 27% and 1 to 9% respectively, while NBS minima decrease by 18to 29% between 1971-2000 and 2041-2100.

Keywords Hydrology · Climate Change · Great Lakes · Regional ClimateModel · Net Basin Supply · Extreme Value Analysis · Lake Model · Water Budget

Ouranos, Universite Laval

Edouard Mailhot (�) · Biljana Music · Daniel F. NadeauUniversite Laval, 1065, av. de la Medecine, Quebec, G1V 0A6, QC, CanadaE-mail: [email protected]

Biljana Music · Anne FrigonOuranos - Consortium on Regional Climatology and Adaptation to Climate Change, 550 Sher-brooke West, West Tower, 19th floor, Montreal, H3A 1B9, QC, Canada

Richard TurcotteMinistere de l’Environnement et de la Lutte contre les changements climatiques du Quebec,675 Rene-Levesque Est, Quebec, G1R 5V7, QC, Canada

2 Edouard Mailhot et al.

1 Introduction

The Laurentian Great Lakes’ region, spanning close to 780 000 km2, is home tosome 40 million people and hosts economic activities worth hundreds of billions ofdollars each year (MacKay and Seglenieks 2013). In this context, anticipating howclimate change may alter the water balance of the lakes in the decades to come isof the utmost importance. In doing so, past studies have focused on estimating NetBasin Supply (NBS) as a main driver of lake levels (Croley 1990; Hartmann 1990;Lofgren et al. 2002; Deacu et al. 2012; MacKay and Seglenieks 2013; Music et al.2015). NBS represents the simplified hydrological balance of a lake, expressed asa water depth per unit area, such that

NBS = Plake + Rland − Elake, (1)

where Plake is over-lake precipitation, Rland is land runoff and Elake is lake evap-oration. The balance presented in (1) is the so-called component method. Otherapproaches exist, such as the residual method (see Deacu et al. 2012), but theywill not be explored in this paper.

The first climate change studies focusing on the hydrology of the Great Lakesregion have applied the change factor method to explore how climate variables

linked to the evaluation of (1) would evolve throughout the 21st century (Croley1990; Hartmann 1990; Angel and Kunkel 2010). This method consists in adjustingobservations by either adding the difference or multiplying the ratio between fu-ture and historical climate runs to produce new, disturbed time series. Then, thelatter are used as inputs in the Advanced Hydrological Prediction System (AHPS)to obtain projections for the Great Lakes NBS. In doing so, most studies relyingon Global Circulation Models (GCMs) have reported decreases in NBS rangingfrom 23 to 51% (Croley 1990), translating into declines of lake levels between 20

and 250 cm (Hartmann 1990) by the end of the 21st century.More recently, Lofgren et al. (2011) raised the issue that the hydrological model

used in AHPS lacked any constraint for conservation of energy at the earth’s sur-face. As a result, evapotranspiration (computed using temperature-based equa-tions) was likely overestimated and runoff underestimated, leading to artificialdrops in future net basin supply. Lofgren et al. (2013) argued that using hydrolog-ical outputs from climatic models directly would circumvent this issue as energyand water conservation is ensured by the model itself.

Within climate models, the vertical transport of heat and momentum betweenopen water surfaces and the atmosphere can be simulated by a lake model, whoserole is to capture the lake thermal regime and its ice cover. Lake schemes of vari-ous complexity have been proposed over the years, ranging from 1D simple models(used in MacKay and Seglenieks 2013) to two-way coupled 3D models fully resolv-ing the lake hydrodynamics (Xue et al. 2017). No matter its complexity, a lakemodel should ideally be coupled to the climate model to allow for two-way ex-changes of heat, momentum and water.

Unfortunately, most of previous studies either lacked a lake model (Deacu et al.2012) or used one in an offline mode (such as the AHPS, used in Angel and Kunkel2010). Regional Climate Models (RCMs), on the other hand, provide energy andwater conservation in addition to resolving smaller-scale processes given their highspatial resolution (typically 25-45 km versus ∼ 200 km for GCMs). As a result, a

Assessment of the Laurentian Great Lakes’ hydrology in a changing climate 3

better representation of feedback processes and a finer hydrological sensitivity canbe attained (Wood et al. 2004; Leung et al. 2004). As such, recent studies relyingon RCMs and coupled lake models have reported much less dramatic declines inNBS (e.g. MacKay and Seglenieks 2013; Music et al. 2015; Notaro et al. 2015). Acomparison between the 1962-1990 and 2021-2050 periods revealed NBS changesbetween −9 and +1% depending on the lake, and small water level decreasesranging from 3 to 6 cm (MacKay and Seglenieks 2013). Music et al. (2015) obtainedan ensemble median of 0mmday−1 for NBS changes between 1971-1999 and 2041-2070 for lake Michigan-Huron.

In recent years, the Coordinated Regional Climate Downscaling Experimentfor North America (NA-CORDEX; Mearns et al. 2017) coordinated the productionof regional downscaled climate projections to support impact assessment studiesover the continent. Using this project’s newest generation of RCM makes thisstudy relevant as it updates the results of older hydrological studies focusing onthe Great Lakes region. Along with recent models, representative concentrationpathways (RCPs) are used instead of previously applied scenarios from the SpecialReport on Emissions Scenarios (SRES; e.g. Angel and Kunkel 2010; Hayhoe et al.2010; Music et al. 2015). This paper also innovates by downscaling to two weeksthe time period for which the analyses are made. Doing this will increase ourunderstanding of climate change impacts within a monthly time threshold thatwas used in previous analyses (e.g. Notaro et al. 2015). This time scale is alsomore appropriate to the study of extreme events that were previously assessedusing monthly time series (Music et al. 2015).

The objective of this paper is to report impacts of climate change on meanand extreme values of the Great Lakes NBS and its components using a set ofRCM models, emissions scenarios and driving GCMs to better account for varioussources of uncertainty.

2 Methods

2.1 Models and Data

The plausible range of changes in NBS components are derived from five NA-CORDEX RCMs whose simulations recently became available (see NA-CORDEXwebsite). Table 1 presents the name, modeling institute, driving GCM, spatialresolution, emissions scenario and lake model of each simulation. The RCMs are:CanRCM4 (Scinocca et al. 2016), CRCM5-Ouranos, CRCM5-UQAM (for bothversions of CRCM5, see Martynov et al. 2013; Separovic et al. 2013), HIRHAM5(Christensen et al. 2006) and RCA4 (Kupiainen et al. 2011). Models will be referredto using the abbreviations in the first column of Table 1.

Three of the five RCMs (22 out of 28 simulations) are coupled to FLake, a1D lake model that uses a parametric representation of the changing temperatureprofiles inside a two-layer system while also taking into account the energy budgetinside the mentioned layers (Golosov et al. 2018). FLake was developed by Mironovet al. (2003) and has been successfully used in RCMs and GCMs (e.g. Samuelssonet al. 2010; Martynov et al. 2012).

When the land surface scheme does not include a lake model (CanRCM4 andHIRHAM5), the Great Lakes’ characteristics (surface temperature, ice cover, etc.),


Table 1 List of regional climate models used in this study for the period 1953-2100. A totalof 28 simulations are analysed. The RCP8.5 CRCM5-O simulation driven by CanESM2 is anensemble of 5 runs. The reanalysis run extends from 1979 to 2014. Institutes are the CanadianCentre for Climate Modelling and Analysis (CCCma), the University of Quebec in Montreal(UQAM), the Danish Meteorological Institute (DMI) and the Swedish Meteorological andHydrological Institute (SHMI).

RCM Institute Driving

GCM

Spatial

Resolution

Emissions

Scenario

Lake

Model

CanRCM4 CCCma CanESM2 0.22◦historical

NoneRCP4.5

RCP8.5

CRCM5-O Ouranos

CanESM2 0.22◦historical

FLake

RCP4.5

RCP8.5 (5)

CNRM-M5 0.22◦historical

RCP4.5

RCP8.5

GFDL-ESM2M 0.22◦historical

RCP4.5

RCP8.5

MPI-ESM-LR 0.22◦historical

RCP8.5

ERA-Interim 0.22◦ reanalysis

CRCM5-U UQAMCanESM2 0.44◦

historical

FLakeRCP4.5

MPI-ESM-LR 0.44◦historical

RCP4.5

HIRHAM5 DMI EC-EARTH 0.44◦historical

NoneRCP4.5

RCP8.5

RCA4 SHMI

CanESM2 0.44◦historical

FLake

RCP4.5

RCP8.5

EC-EARTH 0.44◦historical

RCP4.5

RCP8.5

are imported from the nearest lake tile of the driving GCM.All RCM runs are generated over the CORDEX North American domain at a

spatial resolution of 0.22◦ or 0.44◦ (∼ 25 or ∼ 50 km). They are all driven by aGCM except for a CRCM5-O run, which is driven by the ERA-Interim reanalysis.Given the focus of the paper, only model outputs located within the Great LakesBasin are considered. Figure 1 presents the basin with the model tiles of CRCM5-O(spatial resolution: 0.22◦) represented as dots. Note that lakes Michigan and Huronare considered as a single entity given that their water levels are at equilibrium.Only outputs of precipitation and evaporation over lake tiles are included in theanalysis since NBS is computed over a lake. Runoff values, taken on land tiles, aremultiplied by the ratio of lake to land surface areas of a particular watershed sothat they represent a water depth over a lake, allowing the computation of NBSvalues.


-94 -92 -90 -88 -86 -84 -82 -80 -78 -76 -74

Longitude (°)

40

41

42

43

44

45

46

47

48

49

50

51

La

titu

de

(°)

Lake Superior Watershed

Lake Michigan-Huron Watershed

Lake Erie Watershed

Lake Ontario Watershed

Water Grid Points

Fig. 1 Great Lakes Basin with CRCM5-O grid points indicated by colored dots. Blue dotsrepresent 100% lake tiles

RCPs 4.5 and 8.5 are used as greenhouse gas concentration scenarios for the sim-ulations in this study. Numbers represent increases in radiative forcing

(

W m−2)

in 2100 relative to pre-industrial values.

2.2 Validation

A comparison with the Great Lakes Monthly Hydrometeorological Database (GLM-HMD; Hunter et al. 2015) from the Great Lakes Environmental Research Labora-tory (GLERL) is undertaken to evaluate climate model outputs. The GLM-HMDis compiled with the use of a great amount of observations but model outputs stillmake up a major part. As such, the data used for the validation are not obser-vations but rather observation-based estimates. Their uncertainties are taken asthose reported in Neff and Nicholas (2005). The 1979-2005 period is selected formodel validation since it includes the largest overlap in model outputs and obser-vations. Finally, identifying RCM biases is important, but they will not greatlyimpact results since we assume that they partially cancel out when computingclimate change signals.

2.3 Trend Analysis

Trends within the RCM datasets are estimated with the Theil-Sen statistical test(Theil 1950; Sen 1968) over the study period. This test estimates the equation ofa line passing through sample points that minimizes the distances between datapoints and the produced linear regression. Each data point represents a bi-weeklymean averaged over the Great Lakes. February 29ths and December 31ths are re-moved from the dataset so as to create standard 364-day years (or 26 periods of two


weeks). The resulting Theil-Sen slope estimators have units of [mmday−1 year−1].By multiplying them by the number of days in a two-week period and by the num-ber of years in the study period (i.e. 148), the slopes can be converted to absolutechanges from 1953 to 2100 with units of [mm {14 days}−1].

2.4 Extreme Values Analysis

Along with an analysis of the average hydrological conditions, it is also relevant toassess possible changes in the highest and lowest values for two week periods. To dothis, bi-weekly annual time series of minima/maxima (i.e. the highest and lowestvalues over a period of 14 consecutive days for each year) are built to cover threetime periods (i.e. 1971-2000, 2041-2070 and 2071-2100) for over-lake precipitationand NBS. Extremes in evaporation and land runoff are not considered since theirresults were not statistically significant. As such, 30 minima and 30 maxima aregathered for each of the three periods. To compare differences between referenceand future years, a generalized extreme values (GEV) distribution is fitted to eachdataset of 30 combined minima and maxima for each 30-year period. Minimum andmaximum 14-day values of daily averages with return periods of 10 and 50 yearsare identified using the estimated parameters. The temporal changes in returnperiods are then analyzed to explore the evolution of extreme hydrological eventsin the Great Lakes region.

3 Results

3.1 Validation

Figure 2 presents the annual cycle of NBS and its components for the validation pe-riod. As seen in Figure 2a, over-lake precipitation has the annual cycle with the low-est variance throughout the year with values contained within a 100mmmonth−1

interval. The simulations are thus in relative agreement with each other. The RCMensemble mean has a positive bias of 180mm (+27.5%) for the whole year whencompared to GLM-HDM observations. Seasonally, the overestimation is greater inwinter and spring, with ensemble discrepancies reaching 29mmmonth−1 in March.RCM data are, generally, within the bounds of the shaded area of uncertaintiesbuilt around precipitation observations with a relative error of 45% (Neff andNicholas 2005).

Simulations from CRCM5 all follow a similar cycle for land runoff expressedover the lakes. Runs from this RCM are contained within a 35% uncertainty areaas shown in Figure 2b. Other RCMs do not perform as well. HIRAM5’s springpeak is overestimated by 59mmmonth−1 (+47%) and is one month earlier thanobservations. CanRCM4 and RCA4 values remain below GLM-HDM observationsfor almost all months. The ensemble mean has a small bias of −4.7% over theentire annual cycle. Monthly ensemble biases, on the other hand, oscillate between28.6% in March and −29.8% in October.

The lake evaporation annual cycle produced with the observation-based esti-mates from GLM-HDM has a different pattern than most model outputs. Indeed,Figure 2c shows that, starting in spring, observations and the RCM ensemble


differ by up to 48mmmonth−1 in their 1979-2005 monthly means. Most RCMsoverestimate evaporation in summer and display a peak in October rather thanin December. This is the case for CRCM5 and RCA4 simulations, which all useFLake as their lake model.

(a) (b)

(c) (d)

Fig. 2 Validation of over-lake precipitation (a), land runoff expressed over the lakes (b), lakeevaporation (c) and NBS (d) for the Great Lakes watershed over the 1979-2005 period usingannual cycles of monthly means.

Warmer water temperatures (not shown) may be responsible for the disparity.HIRAM5 displays a very different pattern than the rest of the simulations andunderestimates lake evaporation by 3 to 75mmmonth−1 from May to December.Condensation is even predicted by the model for a four-month period. The absence


of a lake model in HIRHAM5 and its dependence on EC-EARTH seem to be caus-ing a bias. Lake surface conditions (e.g. surface temperature and ice cover) overeach lake grid tile of this RCM are derived from the driving model’s nearest laketile. In the case of evaporation, this method leads to poor validation results forHIRHAM5. The other simulation using EC-EARTH (with RCA4 as the RCM) hasa very different behavior because it uses FLake to obtain lake surface conditions.Between the two, CanRCM4 shows excellent results as it closely follows observa-tions. Overall, the ensemble mean overestimates lake evaporation for almost allmonths, with a total annual bias of 199 mm (+35%).

Figure 2d presents the NBS validation. Annual cycles display similar pat-terns for most simulations, and are characterized by a mean ensemble peak of183mmmonth−1 in April due to snowmelt runoff and a subsided period in latesummer and early fall in which the lowest ensemble value reaches 4mmmonth−1

in September. All models, other than HIRHAM5, show significant NBS negativebiases of up to −138mmmonth−1 (−180%) in summer and fall. Overall, the sumof biases results in a difference of −0.3mmmonth−1 throughout the yearly cyclebut single month biases can go as high as 54.2mmmonth−1 (+50%) in March andas low as −57.2mmmonth−1 (−75%) in August.

It is interesting to note the performance of the CRCM5 run driven by theERA-Interim reanalysis. It is not, as expected, the closest to the observations butinstead shows a similar behavior to the other CRCM5 simulations. This suggeststhat the RCM and lake model, common to these runs, influence outputs moreheavily than the driving GCMs do.

The HIRHAM5 RCM is excluded from the rest of the study due to its signif-icant differences with the rest of the simulations in all validations and the occur-rence of negative evaporation above the lake tiles. It is believed that a model thatsimulates a historical climate that far from observed data cannot reliably be usedto estimate future changes in NBS. Other RCMs achieve satisfactory results andwill aid in assessing future hydrological changes of the Great Lakes.

3.2 Trend Analysis: changes in mean hydrological conditions

The trend analysis for the average conditions of NBS and its components is pre-sented in Figure 3 (RCP4.5) and Figure 4 (RCP8.5). The points indicating changesclose to a value of 0 have a small statistical significance. For steeper Theil-Senslopes, where points are further away from 0, the significance is greater. Statisti-cally significant results with confidence levels of 97.5% generally start with negativeand positive changes of 7mm(14 days)−1.

As seen in Figure 3a, RCP4.5 simulations, as an ensemble, show a rise of 83mm in over-lake precipitation for the whole year when comparing climates from1953 to 2100. On the other hand, a 140 mm increase is found over the Great Lakesusing the more pessimistic RCP8.5 scenario. Precipitation gains are not evenly dis-tributed throughout the year. Indeed, the four months between January and Junecontribute 68.4% (RCP4.5) and 73.6% (RCP8.5) of the annual increases. In bothcases, the summer months show no important changes while increases re-appearin the fall. Results agree with past studies in which positive trends in over-lakeprecipitation were found for the same region (e.g. Music et al. 2015; Notaro et al.2015).


Land runoff changes are similar in magnitude to those of precipitation, but theincreases are seen in winter (see Figures 3b and 4b). Winter increases are causedby warmer air temperatures which transform a fraction of the precipitation froma solid to a liquid state, thus inducing greater runoff.

(a) (b)

(c) (d)

Fig. 3 Trends in bi-weekly (a) over-lake precipitation, (b) land runoff expressed over thelakes, (c) lake evaporation and (d) NBS for the Great Lakes over the 1953-2100 period basedon Theil-Sen estimators from RCP4.5 simulations.

Temperature increases also have the effect of reducing snow water equivalent(SWE), as seen in Figure 5, and shortening the duration of the snow cover byapproximately a month. SWE annual maxima for RCP4.5 and 8.5 are lowered by16 and 26 mm respectively between 1971-2000 and 2071-2100 (−32% and −57%).


These phenomena contribute to increased winter runoff across the Great Lakeswatershed. The RCP4.5 ensemble runoff changes over the whole annual cycle rep-resent a 68 mm increase, which is mostly attributable to the winter months. Figure4b shows a similar pattern but with steeper trends for RCP8.5 as an annual in-crease of 135 mm is projected.

(a) (b)

(c) (d)

Fig. 4 Trends in bi-weekly (a) over-lake precipitation, (b) land runoff expressed over thelakes, (c) lake evaporation and (d) NBS for the Great Lakes over the 1953-2100 period basedon Theil-Sen estimators from RCP8.5 simulations.

A look at panels (c) of Figures 3 and 4 shows positive lake evaporation trendsall year long for both ensembles with only a few occurrences of declines for singlesimulations. Although average trends are positive for all two-week periods, theyare more important in summer months. Indeed, 62mm of the total annual increase


of 136mm (45.6%) happens during summer for RCP4.5, while summer increasesrepresent 91 of 204mm (44.6%) for scenario RCP8.5. Compared to net annualincreases of other variables, the Theil-Sen slope estimators for evaporation aresteeper. Lake evaporation is thus the NBS component most affected by climatechange.

(a) (b)

(c) (d)

Fig. 5 Evolution of snow water equivalent inside the Great Lakes watershed for scenarioRCP4.5 in (a) 1971-2000 and (b) 2071-2100 and for scenario RCP8.5 in (c) 1971-2000 and (d)2071-2100.

Changes in NBS are shown in Figures 3d and 4d. There is a large variabilityamong the trends computed from model outputs. The variability found for each


component is propagated to the water budget since NBS is the sum of land runoffand over-lake precipitation minus lake evaporation. Even with this larger rangeof changes, a clear pattern emerges from the data. Increases in precipitation andrunoff are found to cause positive NBS changes during winter and spring, whereasincreases in evaporation cause negative NBS trends in summer. Bi-weekly NBSchanges range from an increase of 13 mm in early March to a decrease of 15 mmin early July for RCP4.5. For RCP8.5, they range from a rise of 21 mm in lateApril (a 20 mm increase is also found in early February) to a decline of 18 mm inearly September. The winter maximum is caused by the increase in land runoff,whereas the subsequent spring peak value is a consequence of changes in precip-itation. Finally, the longer period of NBS decrease during summer and early fallresults from important increases in lake evaporation. A small positive change of14 mm is obtained for RCP4.5 and an increase of 70 mm for RCP8.5 for the wholeyear. The RCP4.5 change represents a relative increase of 1.7% when comparedto NBS values of the ensemble’s historical runs from the 1971-2000 period. In thesame manner, the RCP8.5 change is an increase of 9.2%. The conclusion that lakelevels will not undergo drastic changes annually can still be reached without evenrunning hydraulic routing models such as GLERL’s Hydrologic Response Model(HRM; Quinn 1978) to generate lake level values using the projected NBS timeseries. Changes will rather be felt on a seasonal basis since summer and fall resultsdiffer greatly from spring and summer ones.

We expect an amplification of the annual cycles of lake evaporation and NBSfor both emissions scenarios. Lake evaporation increases will occur mostly duringsummer and fall when observations already show the highest values (see Figure2c). Similarly, the NBS cycle is amplified by the projected changes since increasesare expected to occur during the spring when NBS values are already high, whiledecreases occur during the summer when values are historically the lowest (Figure2d).

Results of small positive annual increases in NBS (1.7 and 9.2%) strongly con-trast with earlier studies based on the change factor method in which negative NBSchanges of 23 to 51% (Croley 1990) and lake level drops of 20 to 250 cm (Hart-mann 1990) were reported. The methodology, and now, the results of the trendanalysis, bring this study more in line with studies based on RCMs. In those, NBSchanges from 1976 to 2036 vary between −9 and +1% (MacKay and Seglenieks2013). The seasonal amplification of the evaporation and NBS cycles is also dis-tinctive of the RCM approach to the assessment. Music et al. (2015) and Notaroet al. (2015) both obtained the highest evaporation increases between July andOctober. In addition, both found amplified NBS cycles due to increases betweenNovember and March and declines from May to October. In the case of changefactor studies, the NBS decreases were scattered evenly throughout all seasons(Croley 1990) causing lake level drops to remain close to, in Hartmann (1990) forexample, 120 cm all year long for lake Erie for one simulation between 1981 and2060. For a quick review of past and present results, see Figure 6. Please note thatthe compared studies do not use the same time period or physical scope for theiranalyses but a comparison remains of value nonetheless. Now that conclusions ofthe trend analysis have been compared to past studies, the results of the analysisof extreme events will continue the assessment at hand.


Fig. 6 Comparison of the present study’s NBS change results for average conditions withresults from two previous studies.

3.3 Extreme Values Analysis

Figure 7 presents the outcomes of the extreme values analysis for scenario RCP4.5,while results for RCP8.5 are shown in Figure 8. As seen in Figures 7a and 8a,there is a large uncertainty in projected changes of daily precipitation minima.RCP4.5 leads to a small decline while RCP8.5 indicates no change according tothe ensemble means. For maxima (b), daily precipitation return levels increasewhen comparing future periods to 1971-2000 for both scenarios. Increases of 0.7to 1.7mmday−1 (11 to 25%) with higher percentages for the 2041-2070 periodare observed for RCP4.5 while increases of 0.9 to 1.8mmday−1 (15 to 27%) areprojected by for RCP8.5.

NBS results are presented in Figures 7c, 7d, 8c and 8d. Minima tend to decreasewhile maxima tend to increase by small increments for both scenarios. Minimumvalues associated with 10 and 50-year return periods for this variable decrease by0.6 to 1.0mmday−1 (18 to 26%) for RCP4.5 and by 0.7 to 1.1mmday−1 (18 to29%) for RCP8.5. Maximum values increase by 0.1 to 0.3mmday−1 (1 to 3%) forRCP4.5 and by 0.1 to 1.2mmday−1 (1 to 9%) for RCP8.5. Values given here are,as mentioned previously, annual bi-weekly NBS minima/maxima for the entireGreat Lakes.

As is quite noticeable, changes worsen the extreme conditions of the historicperiod when they are observed in this analysis. Over-lake precipitation maxima getmore extreme, NBS minima decrease and NBS maxima increase in future periods.This is coherent with the results presented in Section 3.2 which emphasized theprojected aggravation of the annual cycles by climate change.

Precipitation results are coherent with Notaro et al. (2015) who found increasesin precipitation intensity. In their study, the 100-year precipitation quantile wasfound to increase by 7 to 8% by the end of the 21th century, while our analysissuggests an increase of 11−27% for 14-day maximum periods.Trends of NBS extremes can be compared with Music et al. (2015). NBS annual


minima changes between 1971-1999 and 2041-2070 range from −1.8 to 0mmday−1

for the 10 and 50-year return periods for the simulations used in the aforementionedstudy. In comparison, the present paper finds that, for the same periods, NBSminima changes vary between −0.8 and −0.6mmday−1 for the ensembles. Notethat changes reported in Music et al. 2015, unlike those obtained in our study,come from individual simulations. For NBS maxima, the results of both studiesare less convincing. The increases in this study are quite small (0.1 to 1.2mmday−1

for 1971-2000 to 2071-2100) while Music et al. (2015) obtained maximum changesthat are unclear due to overlapping confidence intervals.

4 Concluding remarks

Several studies have been published in the preceding decades on the issue of cli-mate change impacts on the Great Lakes region. Analyses using the change factormethod resulted in projections of important decreases in lake levels (Croley 1990;Hartmann 1990; Angel and Kunkel 2010) while others, using RCMs directly, ar-rived at lesser declines and even small increases in some instances (MacKay andSeglenieks 2013; Music et al. 2015; Notaro et al. 2015).

Our study is motivated by the availability of new RCM simulations withinNA-CORDEX. Modifications to the RCM’s physical parameterizations and an in-troduction of better performing lake models (Martynov et al. 2013) also testify tothe necessity of accomplishing this research. Furthermore, more detailed resultsare obtained due to changes to this study’s methodology when compared to itspredecessors that allow analyses of the data on a smaller, two-week, time scale.

Results show small increases in annual NBS from 1953 to 2100 that are notequally distributed throughout the year. Increases in over-lake precipitation andrunoff in winter and spring result in positive NBS changes for these seasons whilesummer is dominated by increased lake evaporation resulting in negative NBSchanges. Precipitation and NBS maximum extreme values are projected to growwhile negative trends are identified for NBS minimum extremes. Accordingly, anenhancement of the annual cycle of water availability is to be expected for theGreat Lakes region during the 21st century. No long-term changes can be confi-dently estimated for lake levels, but their annual cycle will be amplified by climatechange.

It will be useful for future studies to explore larger RCM ensembles to betterestimate the plausible range of NBS changes. Continued improvements to lake con-dition representations, among others, are also needed to reduce uncertainty relatedto model biases. Research on the topic at hand, with these recommendations, mustcontinue so that decision makers are adequately prepared in the coming years.


Acknowledgements The authors would like to thank Alain Mailhot for his helpful feed-back. The CRCM5 data were supplied by Ouranos (CRCM5-O) and by UQAM (CRCM5-U).CRCM5 computations were made on the Guillimin supercomputer from McGill University,managed by Calcul Quebec and Compute Canada. The operation of this supercomputer isfunded by the Canada Foundation for Innovation (CFI), the ministere de l’Economie, de lascience et de l’innovation du Quebec (MESI) and the Fonds de recherche du Quebec - Natureet technologies (FRQ-NT). The Canadian Regional Climate Model (CRCM5; Martynov et al.2013, Separovic et al. 2013) was developed by the ESCER Centre at UQAM (Universite duQuebec a Montreal) with the collaboration of Environment and Climate Change Canada. Datafrom other RCMs were extracted from the CORDEX database (Mearns et al. 2017). GreatLakes observations were provided by GLERL. This project was funded by Mitacs, the Ouranosconsortium and Fonds Verts Quebec under grant IT09276.


(a) (b)

(c) (d)

Fig. 7 Evolution of 10 and 50-year return periods values of 14-day (bi-weekly) annual min-imum (left) and maximum (right) for over-lake precipitation (a)-(b) and NBS (c)-(d) for theGreat Lakes. Data from scenario RCP4.5 and fitted to a GEV distribution for each period(e.g. 1971-2000).


(a) (b)

(c) (d)

Fig. 8 Evolution of 10 and 50-year return period values of 14-day (bi-weekly) annual minimum(left) and maximum (right) for over-lake precipitation (a)-(b) and NBS (c)-(d) for the GreatLakes. Data from scenario RCP8.5 and fitted to a GEV distribution for each period (e.g.1971-2000).


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❈❤❛♣✐tr❡ ✸

❘és✉❧t❛ts ❝♦♠♣❧é♠❡♥t❛✐r❡s

✸✳✶ ❆♥❛❧②s❡ ❞❡s ❝♦♥❞✐t✐♦♥s ❤②❞r♦❧♦❣✐q✉❡s ♠♦②❡♥♥❡s ❞❡ ❝❤❛q✉❡

❧❛❝

❉❛♥s ❝❡tt❡ s❡❝t✐♦♥✱ ❧❛ ♣r❡♠✐èr❡ ❛♥❛❧②s❡ ❞❡ ❧✬❛rt✐❝❧❡ ❞✉ ❈❤❛♣✐tr❡ ✷ ❡st ré♣été❡ ♠❛✐s✱ ❝❡tt❡ ❢♦✐s✲❝✐✱

❧❡s t❡sts s♦♥t ré❛❧✐sés ♣♦✉r ❝❤❛❝✉♥ ❞❡s ❧❛❝s ❞❡ ❢❛ç♦♥ ✐♥❞✐✈✐❞✉❡❧❧❡✳ ▲❡s t❡sts ❞❡ ❧✬❛rt✐❝❧❡ ❝♦✉✈r❛✐❡♥t

❧✬❡♥s❡♠❜❧❡ ❞❡s ●r❛♥❞s ▲❛❝s ✉♥✐❢♦r♠é♠❡♥t ❛❧♦rs q✉❡ ❝❡tt❡ s❡❝t✐♦♥ ❝❤❡r❝❤❡ ♣❧✉tôt à ✈♦✐r s✐ ❞❡s

❞✐✛ér❡♥❝❡s ❡①✐st❡♥t ❡♥tr❡ ❧❡s rés✉❧t❛ts ❞❡s ❧❛❝s✳ ❉❡s ❞✐s♣❛r✐tés s♦♥t ❛tt❡♥❞✉❡s ♣♦✉r ♣❧✉s✐❡✉rs

r❛✐s♦♥s✳ Pr❡♠✐èr❡♠❡♥t✱ ❧❡s ❝♦♥❞✐t✐♦♥s ❝❧✐♠❛t✐q✉❡s✱ ❡t ❞♦♥❝ ❧❡s ♣♦ss✐❜❧❡s ✐♠♣❛❝ts ❞❡s ❝❤❛♥❣❡✲

♠❡♥ts ❝❧✐♠❛t✐q✉❡s s✉r ❝❡❧❧❡s✲❝✐✱ s♦♥t ❞✐✛ér❡♥t❡s ❞✬✉♥ ❜❛ss✐♥ ✈❡rs❛♥t à ❧✬❛✉tr❡✳ ▲✬é❝❛rt ❡♥tr❡ ❧❡s

♠♦②❡♥♥❡s ❛♥♥✉❡❧❧❡s ❞❡s t❡♠♣ér❛t✉r❡s✱ ♣❛r ❡①❡♠♣❧❡✱ ✈❛ ❥✉sq✉✬à 7◦❈ ❡♥tr❡ ❧❡s ✈✐❧❧❡s ❞❡ ❚❤✉♥❞❡r

❇❛② ❡t ❈❤✐❝❛❣♦ ✭❊♥✈✐r♦♥♥❡♠❡♥t ❈❛♥❛❞❛ ✷✵✶✽ ❀ ◆❛t✐♦♥❛❧ ❖❝❡❛♥✐❝ ❛♥❞ ❆t♠♦s♣❤❡r✐❝ ❆❞♠✐♥✐s✲

tr❛t✐♦♥ ✷✵✶✽✮✳ ❉❡s é❝❛rts ✐♠♣♦rt❛♥ts ❡①✐st❡♥t é❣❛❧❡♠❡♥t ♣♦✉r ❧❡s ♣ré❝✐♣✐t❛t✐♦♥s ♠♦②❡♥♥❡s ❡♥

r❛✐s♦♥ ❞❡ ❧✬❡✛❡t ❞❡s ❧❛❝s✳ ❉❡✉①✐è♠❡♠❡♥t✱ ❧❡s ❧❛❝s ❡✉①✲♠ê♠❡s ❞✐✛èr❡♥t ❧❡s ✉♥s ❞❡s ❛✉tr❡s✳ ▲❛

s✉♣❡r✜❝✐❡ ❡t ❧❛ ♣r♦❢♦♥❞❡✉r ♠♦❞✐✜❡♥t ❧❡s ✐♥t❡r❛❝t✐♦♥s ❞✬✉♥ ❧❛❝ ❛✈❡❝ ❧✬❛t♠♦s♣❤èr❡ ❡t ❛✛❡❝t❡♥t

❛✐♥s✐ ❧❡ ❝❧✐♠❛t ❞❡ ❧❛ ré❣✐♦♥ ❞❛♥s ❧❛q✉❡❧❧❡ ✐❧ s❡ tr♦✉✈❡✳ ❉❡ ♣❧✉s✱ ❧❡s r❛♣♣♦rts ❡♥tr❡ ❧❛ s✉♣❡r✜❝✐❡

❞✉ ❧❛❝ ❡t ❝❡❧❧❡ ❞❡ s♦♥ ❜❛ss✐♥ ✈❡rs❛♥t ✈❛r✐❡♥t ❡♥tr❡ ❧❡s ❧❛❝s ❞✉ rés❡❛✉ ❞❡s ●r❛♥❞s ▲❛❝s✳ P❛r

❡①❡♠♣❧❡✱ ❧❡ ▲❛❝ ❙✉♣ér✐❡✉r ❛ ✉♥❡ s✉♣❡r✜❝✐❡ ❞❡ s❡✉❧❡♠❡♥t ✶✳✺✻ ❢♦✐s ❝❡❧❧❡ ❞❡ s♦♥ ❜❛ss✐♥ ✈❡rs❛♥t

t❛♥❞✐s q✉❡ ❝❡ r❛♣♣♦rt ❡st ❞❡ ✸✳✶✾ ❞❛♥s ❧❡ ❝❛s ❞✉ ▲❛❝ ❖♥t❛r✐♦✳ ❈❡ r❛♣♣♦rt ✐♥✢✉❡♥❝❡ ❧❡ ré❣✐♠❡

❞✉ r✉✐ssè❧❡♠❡♥t ❡t s♦♥ rô❧❡ ❞❛♥s ❧❡ ❝②❝❧❡ ❤②❞r✐q✉❡ ❞✬✉♥ ❧❛❝✳ ❋✐♥❛❧❡♠❡♥t✱ ❧❡s ré❝❤❛✉✛❡♠❡♥ts ❞✉s

❛✉① ❝❤❛♥❣❡♠❡♥ts ❝❧✐♠❛t✐q✉❡s ♥❡ s♦♥t ♣❛s é❣❛✉① ♣❛rt♦✉t à ❧✬✐♥tér✐❡✉r ❞❡ ❧❛ ré❣✐♦♥ ❞❡s ●r❛♥❞s

▲❛❝s✳ ▲❡s t❡♥❞❛♥❝❡s ❢✉t✉r❡s ❞❡s ❞✐✛ér❡♥t❡s ❝♦♥❞✐t✐♦♥s ❤②❞r♦❧♦❣✐q✉❡s ♣❡✉✈❡♥t ❞♦♥❝ êtr❡ ✐♥✢✉❡♥✲

❝é❡s ❞✐✛ér❡♠♠❡♥t s❡❧♦♥ ❧❡ ❧❛❝ ét✉❞✐é✳

▲❡ ❚❛❜❧❡❛✉ ✸✳✶ ♣rés❡♥t❡ ❧❡s rés✉❧t❛ts ❞❡s ♠♦②❡♥♥❡s ❞✬❡♥s❡♠❜❧❡ ✭♣♦✉r ♣❧✉s ❞✬✐♥❢♦r♠❛t✐♦♥s s✉r ❧❡s

♠♦❞è❧❡s ❝♦♠♣♦s❛♥t ❧✬❡♥s❡♠❜❧❡✱ ✈♦✐r ❧❡ ❚❛❜❧❡❛✉ ✶ ❞✉ ❈❤❛♣✐tr❡ ✷✮ ❞❡ ❧✬❛♥❛❧②s❡ s✉r ❧❡s ❝♦♥❞✐t✐♦♥s

♠♦②❡♥♥❡s ❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵ ❡♥ ✉t✐❧✐s❛♥t ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳ ❊♥ ♣❧✉s ❞❡ ❝❡ t❛❜❧❡❛✉✱

✶✻

❧✬❆♥♥❡①❡ ❆ r❡❣r♦✉♣❡ ❧❡s ✜❣✉r❡s ❞❡sq✉❡❧❧❡s ❧❡s rés✉❧t❛ts ♦♥t été t✐rés ❡t ❧✬❆♥♥❡①❡ ❇ ❝♦♥t✐❡♥t

q✉❡❧q✉❡s ❝❛rt❡s ❝♦♥t❡♥❛♥t ❞❡s ♣r♦❥❡❝t✐♦♥s ❞✉ ▼❘❈❈✺✲❖✉r❛♥♦s✳ ▲❡s ♣r♦❝❤❛✐♥s ♣❛r❛❣r❛♣❤❡s

✈♦♥t s♦✉❧✐❣♥❡r ❧❡s ❛s♣❡❝ts ❧❡s ♣❧✉s ✐♥tér❡ss❛♥ts ❞❡ ❝❡tt❡ ❛♥❛❧②s❡✳

❚❛❜❧❡ ✸✳✶ ✕ ▼♦②❡♥♥❡s ❛♥♥✉❡❧❧❡s ❞❡s ❝❤❛♥❣❡♠❡♥ts ❜✐❤❡❜❞♦♠❛❞❛✐r❡s ❞❡ ❧✬❡♥s❡♠❜❧❡ ❡♥tr❡ ✶✾✺✸✲✷✶✵✵ ♣♦✉r ❧❡s ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ❧❡ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠é s✉r ❧❡ ❧❛❝✱ ❧✬é✈❛♣♦r❛t✐♦♥❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ❧❡ ◆❇❙ ♣♦✉r ❝❤❛❝✉♥ ❞❡s ●r❛♥❞s ▲❛❝s✳ ❙❝é♥❛r✐♦s ❘❈P✹✳✺ ❡t ❘❈P✽✳✺✳

❬♠♠ ✭✶✹ ❥♦✉rs✮−1❪❙✉♣ér✐❡✉r ▼✐❝❤✐❣❛♥✲❍✉r♦♥ ➱r✐é ❖♥t❛r✐♦ ●r❛♥❞s ▲❛❝s

❘❈P✹✳✺ ❘❈P✽✳✺ ❘❈P✹✳✺ ❘❈P✽✳✺ ❘❈P✹✳✺ ❘❈P✽✳✺ ❘❈P✹✳✺ ❘❈P✽✳✺ ❘❈P✹✳✺ ❘❈P✽✳✺

Pré❝✐♣✐t❛t✐♦♥ ✷✱✾ ✹✱✹ ✸✱✵ ✺✱✶ ✷✱✶ ✺✱✶ ✷✱✵ ✹✱✾ ✸✱✷ ✺✱✹

❘✉✐ssè❧❡♠❡♥t ✶✱✼ ✷✱✽ ✸✱✵ ✺✱✹ ✶✱✾ ✺✱✽ ✶✱✾ ✻✱✷ ✷✱✻ ✺✱✷

➱✈❛♣♦r❛t✐♦♥ ✺✱✺ ✽✱✸ ✺✱✷ ✼✱✽ ✹✱✺ ✻✱✻ ✹✱✽ ✼✱✵ ✺✱✷ ✼✱✽

◆❇❙ ✲✵✱✾ ✲✶✱✶ ✶✱✵ ✷✱✼ ✲✵✱✺ ✹✱✾ ✲✶✱✷ ✹✱✸ ✵✱✺ ✷✱✼

❆✈❛♥t ❞❡ ❞✐s❝✉t❡r ❞❡s rés✉❧t❛ts ❞❡ ❝❤❛q✉❡ ✈❛r✐❛❜❧❡✱ ♦♥ r❡♠❛rq✉❡ q✉❡✱ ❣❧♦❜❛❧❡♠❡♥t✱ ❧❡s ré✲

s✉❧t❛ts ♣♦✉r ❧✬❡♥s❡♠❜❧❡ ❞❡s ●r❛♥❞s ▲❛❝s s♦♥t q✉❛s✐✲✐❞❡♥t✐q✉❡s à ❝❡✉① ♦❜t❡♥✉s ♣♦✉r ❧❡ ▲❛❝

▼✐❝❤✐❣❛♥✲❍✉r♦♥✳ ▲❡✉rs ❝❤❛♥❣❡♠❡♥ts ♣♦✉r ❧❡s ❝♦♠♣♦s❛♥t❡s ❞✉ ◆❇❙ ❡t ❧❡ ◆❇❙ ❧✉✐✲♠ê♠❡ ♦♥t

❞❡s ❞✐✛ér❡♥❝❡s ♠✐♥❡✉r❡s ♣♦✉r ❧❡s ❞❡✉① s❝é♥❛r✐♦s ❞✬é♠✐ss✐♦♥s✳ ❈❡❝✐ ❡st ❝❛✉sé ♣❛r ❧❡ ❢❛✐t q✉❡ ❧❡

▲❛❝ ▼✐❝❤✐❣❛♥✲❍✉r♦♥ ❡st ❝❡❧✉✐ q✉✐ ❝♦✉✈r❡ ❧❛ ♣❧✉s ❣r❛♥❞❡ s✉♣❡r✜❝✐❡ ❡t✱ ❞♦♥❝✱ q✉✐ ❝♦♥tr✐❜✉❡ ❧❡ ♣❧✉s

❞❡ ♣♦✐♥ts ❞❡ ❣r✐❧❧❡ ❧♦rs ❞✉ ❝❛❧❝✉❧ ❞❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥ s✉r ❧✬❡♥s❡♠❜❧❡ ❞❡s ●r❛♥❞s ▲❛❝s✳

▲❡s rés✉❧t❛ts ❞❡ ❝❡s ❞❡r♥✐❡rs t❡♥❞❡♥t ❛❧♦rs ✈❡rs ❧❡s ✈❛❧❡✉rs ❞❡s ❡st✐♠❛t❡✉rs ❞✉ ▲❛❝ ▼✐❝❤✐❣❛♥✲

❍✉r♦♥✳ ❯♥ ❞❡✉①✐è♠❡ ❢❛❝t❡✉r q✉✐ r❛♣♣r♦❝❤❡ ❧❡s rés✉❧t❛ts ❞❡s ❞❡✉① t❡sts ❡st ❧❛ s✐♠✐❧✐t✉❞❡ ❡♥tr❡

❧❡s r❛♣♣♦rts ❞❡ ❧❛ s✉♣❡r✜❝✐❡ ❞❡ ❧❛❝ s✉r ❝❡❧❧❡ ❞✉ ❜❛ss✐♥ ✈❡rs❛♥t✳ ❊♥ ❡✛❡t✱ ❧❡ ▲❛❝ ▼✐❝❤✐❣❛♥✲❍✉r♦♥

♣♦ssè❞❡ ❧❛ ✈❛❧❡✉r ✭✷✱✶✸✮ ❧❛ ♣❧✉s ♣r♦❝❤❡ ❞❡ ❝❡❧❧❡ ❞❡s q✉❛tr❡ ❧❛❝s ❝♦♥s✐❞érés ❝♦♠♠❡ ✉♥ ✭✷✱✵✹✮✳ ▲❡s

✈❛❧❡✉rs ♣♦✉r ❧❡s ❛✉tr❡s ❧❛❝s s♦♥t t♦✉t❡s s✉♣ér✐❡✉r❡s✱ ❝❡ q✉✐ ❝❛✉s❡ ❞❡s ❞✐✛ér❡♥❝❡s ♣❧✉s ♠❛rq✉é❡s

❞❛♥s ❧❡✉rs rés✉❧t❛ts ♣♦✉r ❧❡ r✉✐ssè❧❡♠❡♥t✳

▲❡s rés✉❧t❛ts ♣♦✉r ❧❡s ♣ré❝✐♣✐t❛t✐♦♥s s❡ r❡ss❡♠❜❧❡♥t ❞✬✉♥ ❧❛❝ à ❧✬❛✉tr❡✳ ❚♦✉t ❝♦♠♠❡ ❧❡s rés✉❧t❛ts

❞❡ ❧✬ét✉❞❡ ❛✉ ❈❤❛♣✐tr❡ ✷✱ ❞❡s ❤❛✉ss❡s✱ s✉rt♦✉t ♣r✐♥t❛♥✐èr❡s✱ ♠❛✐s é❣❛❧❡♠❡♥t ❤✐✈❡r♥❛❧❡s ❝❛✉s❡♥t

❞❡s ❛✉❣♠❡♥t❛t✐♦♥s ❡♥tr❡ ✷✱✵ ❡t ✺✱✶ ♠♠ ✭✶✹ ❥♦✉rs✮−1✱ ♠♦②❡♥♥é❡s s✉r ❧✬❛♥♥é❡ ❝♦♠♣❧èt❡✳ ■❧ ❡st

✐♥tér❡ss❛♥t ❞❡ r❡♠❛rq✉❡r q✉❡✱ ❡①❝❧✉s✐✈❡♠❡♥t ♣♦✉r ❧❡s ♣ré❝✐♣✐t❛t✐♦♥s✱ ❧❡s ❝❤❛♥❣❡♠❡♥ts s♦♥t ♣❧✉s

✐♠♣♦rt❛♥ts ♣♦✉r ❧✬❡♥s❡♠❜❧❡ ❞❡s ●r❛♥❞s ▲❛❝s q✉❡ ♣♦✉r ❧❡s ❧❛❝s ✐♥❞✐✈✐❞✉❡❧s✳ ❈❡ rés✉❧t❛t ❡st ét♦♥✲

♥❛♥t ❡t ❝♦♥tr❡✲✐♥t✉✐t✐❢ ♠❛✐s ❡st ♦❜t❡♥✉ ♣✉✐sq✉❡ ❧❡s ❤❛✉ss❡s ♣r✐♥t❛♥✐èr❡s ❧❡s ♣❧✉s ✐♠♣♦rt❛♥t❡s

✶✼

❛♣♣❛rt✐❡♥♥❡♥t ❛✉① ▲❛❝s ▼✐❝❤✐❣❛♥✲❍✉r♦♥ ❡t ❙✉♣ér✐❡✉r ♠❛✐s q✉✬❡❧❧❡s s♦♥t ❛❝❝♦♠♣❛❣♥é❡s ❞❡s

❜❛✐ss❡s ❧❡s ♣❧✉s ❢♦rt❡s ❡♥ été✳ ▲❡s ▲❛❝s ➱r✐é ❡t ❖♥t❛r✐♦✱ ❧♦rsq✉❡ ❧❡✉rs ❞♦♥♥é❡s s♦♥t ♣r✐s❡s ❡♥

❝♦♠♣t❡✱ ❞✐♠✐♥✉❡♥t ❧❡s ❤❛✉ss❡s ♠❛✐s ❛✉❣♠❡♥t❡♥t✱ ❡t ❞❡ ❢❛ç♦♥ ♣❧✉s ✐♠♣♦rt❛♥t❡✱ ❧❡s ♣ré❝✐♣✐t❛t✐♦♥s

❡st✐✈❛❧❡s✳ ■❧ ❡♥ rés✉❧t❡ ❞❡s ❛✉❣♠❡♥t❛t✐♦♥s ❧é❣èr❡♠❡♥t ♣❧✉s ❣r❛♥❞❡s s✉r ❧✬❛♥♥é❡ ❝♦♠♣❧èt❡ ♣♦✉r

❧❡ r❡❣r♦✉♣❡♠❡♥t ❞❡s ●r❛♥❞s ▲❛❝s q✉❡ ♣♦✉r ❧❡s ❧❛❝s ✐♥❞✐✈✐❞✉❡❧s✳

▲❡s ❞✐✛ér❡♥❝❡s ❧❡s ♣❧✉s ♠❛rq✉é❡s ❡♥tr❡ ❧❡s ❧❛❝s ♣r♦✈✐❡♥♥❡♥t ✐♥❞é♥✐❛❜❧❡♠❡♥t ❞✉ r✉✐ssè❧❡♠❡♥t✳

❈❡❝✐ ❡st ♣❛rt✐❝✉❧✐èr❡♠❡♥t ✢❛❣r❛♥t s✉r ❧❡s ❋✐❣✉r❡s ❆✳✼❜ ❡t ❆✳✽❜ ♦ù ❧✬♦♥ ✈♦✐t ❞❡s ✈❛❧❡✉rs très

✐♠♣♦rt❛♥t❡s ❞❡ ❝❤❛♥❣❡♠❡♥ts ❞✉ r✉✐ssè❧❡♠❡♥t ♣♦✉r ❧❡ ▲❛❝ ❖♥t❛r✐♦ ✭♥♦t❡③ ❧❛ ♠♦❞✐✜❝❛t✐♦♥ à

❧✬é❝❤❡❧❧❡ ❞❡ ❧✬❛①❡ ❞❡s ♦r❞♦♥♥é❡s ♣♦✉r ❝❡ ❧❛❝✮✳ ▲❡s ♣❧✉s ❣r❛♥❞s ❝❤❛♥❣❡♠❡♥ts s♦♥t s✐♠♣❧❡♠❡♥t

❝❛✉sés ♣❛r ✉♥ ♣❧✉s ✐♠♣♦rt❛♥t r❛♣♣♦rt ❞❡ ❧❛ s✉♣❡r✜❝✐❡ ❞✉ ❧❛❝ s✉r ❝❡❧❧❡ ❞✉ ❜❛ss✐♥ ✈❡rs❛♥t ♣♦✉r

❝❡ ❧❛❝✳ ❊♥ ❡✛❡t✱ ❧❛ ✈❛❧❡✉r ❞❡ ❝❡ r❛♣♣♦rt✱ ♣♦✉r ❧❡ ▲❛❝ ❖♥t❛r✐♦✱ ❡st ❞❡ ✸✱✷ t❛♥❞✐s q✉❡ ❧❡ s❡❝♦♥❞

r❛♥❣✱ ♦❝❝✉♣é ♣❛r ❧❡ ▲❛❝ ➱r✐é✱ ❛✣❝❤❡ ✷✱✸✳ ❈♦♠♠❡ ❝❡ ❢✉t ♠❡♥t✐♦♥♥é ❛✉♣❛r❛✈❛♥t✱ ❝❡ r❛♣♣♦rt s❡rt

à tr❛♥s❢♦r♠❡r ❧❡s ✈❛❧❡✉rs ❞❡ r✉✐ssè❧❡♠❡♥t ❞❡s t✉✐❧❡s ❞❡ t❡rr❡ à ❝❡❧❧❡s ❞❡ ❧❛❝✳ ❆✈❡❝ ✉♥ r❛♣♣♦rt

s✉♣ér✐❡✉r✱ ❧❡s ✈❛❧❡✉rs s♦♥t ♥é❝❡ss❛✐r❡♠❡♥t ♣❧✉s ❣r❛♥❞❡s ❡t ❧❡s ❝❤❛♥❣❡♠❡♥ts✱ q✉✬✐❧s s♦✐❡♥t ♣♦s✐✲

t✐❢s ♦✉ ♥é❣❛t✐❢s✱ s♦♥t ♣❧✉s ❞r❛st✐q✉❡s q✉❡ ♣♦✉r ❧❡s ❛✉tr❡s ❧❛❝s✳ ❉❛♥s ❧❡ ❝❛s ❞✉ r✉✐ssè❧❡♠❡♥t✱ ❝❡

s♦♥t ♠❛❥♦r✐t❛✐r❡♠❡♥t ❞❡s ❛✉❣♠❡♥t❛t✐♦♥s ❧♦rs ❞❡s ♠♦✐s ❞✬❤✐✈❡r✳ ❈❡s ❤❛✉ss❡s s✉r❞✐♠❡♥s✐♦♥♥é❡s

❞✐❝t❡♥t✱ ♣r❡sq✉❡ à ❡❧❧❡s s❡✉❧❡s✱ ❧❡ ❝②❝❧❡ ❞❡s ❝❤❛♥❣❡♠❡♥ts ❞❡ ◆❇❙ ♣♦✉r ❝❡ ❧❛❝ ✭❋✐❣✉r❡ ✸✳✶✮✳ ▲❛

❝♦♥✜❣✉r❛t✐♦♥ ❣é♦❣r❛♣❤✐q✉❡ ❞✉ ▲❛❝ ❖♥t❛r✐♦ s❡♠❜❧❡ ❞♦♥❝ ❛✈♦✐r ✉♥ ✐♠♣❛❝t ♠❛❥❡✉r à ❧✬é❝❤❡❧❧❡ ❞✉

❧❛❝ s❛♥s t♦✉t❡❢♦✐s s❡ ♣r♦♣❛❣❡r à ❧✬ét✉❞❡ ❞❡ t♦✉s ❧❡s ●r❛♥❞s ▲❛❝s ✈✉ s❛ ♣❧✉s ♣❡t✐t❡ t❛✐❧❧❡✳

✭❛✮ ✭❜✮

❋✐❣✉r❡ ✸✳✶ ✕ ❚❡♥❞❛♥❝❡s ❞✉ ✭❛✮ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠é s✉r ❧❡ ❧❛❝ ❡t ❞✉ ✭❜✮ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝❖♥t❛r✐♦ ❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳ ❙❝é♥❛r✐♦ ✽✳✺✳

✶✽

❈♦♠♠❡ ❧❡s rés✉❧t❛ts ♣♦✉r ❧✬é✈❛♣♦r❛t✐♦♥ s❡ r❡ss❡♠❜❧❡♥t ❡t ❛♣♣♦rt❡♥t ♣❡✉ ❞❡ ♥♦✉✈❡❧❧❡s ✐♥❢♦r✲

♠❛t✐♦♥s✱ ❧❡s ❞✐✛ér❡♥❝❡s ♣♦✉r ❧❡ ◆❇❙ ♣❡✉✈❡♥t êtr❡ é✈❛❧✉é❡s✳ ❈♦♥tr❛✐r❡♠❡♥t ❛✉① ❢❛✐❜❧❡s ❤❛✉ss❡s

❞❡ ❧✬ét✉❞❡ ❞❛♥s ❧❛q✉❡❧❧❡ ❧❡s ❧❛❝s s♦♥t r❡❣r♦✉♣és✱ ❞❡s ❜❛✐ss❡s ❞❡ ❝❡tt❡ ✈❛r✐❛❜❧❡ ❛♣♣❛r❛✐ss❡♥t à ❧❛

s✉✐t❡ ❞❡ ❧✬❛♥❛❧②s❡ s✉r ❧❡s ❧❛❝s ✐♥❞✐✈✐❞✉❡❧s ♣♦✉r ❧❡ s❝é♥❛r✐♦ ❘❈P✹✳✺✳ ❉❛♥s ❞❡✉① ❞❡s tr♦✐s ❝❛s ♦ù

❝❡❧❛ s❡ ♣r♦❞✉✐t✱ ♣♦✉r ❧❡s ▲❛❝s ➱r✐é ❡t ❖♥t❛r✐♦✱ ❧❡s ❜❛✐ss❡s s❡ tr❛♥s❢♦r♠❡♥t ❡♥ ❤❛✉ss❡ ❧♦rsq✉❡

❧❡ t❡st ❡st ré♣été s✉r ❧❡s ❞♦♥♥é❡s ❞✉ s❝é♥❛r✐♦ ❘❈P✽✳✺✳ ▲❡s ❜❛✐ss❡s ❡st✐✈❛❧❡s ❞❡ ◆❇❙ ❞✉ ▲❛❝

➱r✐é✱ ❝❛✉sé❡s ♣❛r ❞❡s ❜❛✐ss❡s ❞❡ ♣ré❝✐♣✐t❛t✐♦♥ ❡t ❞❡s ❛✉❣♠❡♥t❛t✐♦♥s ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥✱ s♦♥t s✉❢✲

✜s❛♥t❡s ♣♦✉r q✉❡✱ s✉r ❧❡ ❝②❝❧❡ ❛♥♥✉❡❧ ❡♥t✐❡r✱ ❧❡ ❜✐❧❛♥ ❞❡s ❝❤❛♥❣❡♠❡♥ts ❞❡ ◆❇❙ s♦✐t ❧é❣èr❡♠❡♥t

♥é❣❛t✐❢ ✭✲✵✱✺ ♠♠ ❬✶✹ ❥♦✉rs❪−1✮ ❀ ❋✐❣✉r❡ ❆✳✺✮✳ P❛r ❝♦♥tr❡✱ ❝❡ ❜✐❧❛♥ ❞❡✈✐❡♥t ♣♦s✐t✐❢ ✭✹✳✾ ♠♠ ❬✶✹

❥♦✉rs❪−1✮ ❧♦rs ❞❡ ❧✬❛♥❛❧②s❡ ❛✈❡❝ ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺ ✭❋✐❣✉r❡ ❆✳✻✮✳ ❈❡tt❡ ✐♠♣♦rt❛♥t❡ ❤❛✉ss❡ ❡st

❝❛✉sé❡ ♣❛r ❞❡ ♣❧✉s ❣r❛♥❞❡s q✉❛♥t✐tés ❞❡ ♣ré❝✐♣✐t❛t✐♦♥ ❥✉♠❡❧é❡s à ❞❡s ❤❛✉ss❡s ❞✉ r✉✐ssè❧❡♠❡♥t

❡♥ ❤✐✈❡r ❡t ❛✉ ♣r✐♥t❡♠♣s✳ ▲❡s ❛✉❣♠❡♥t❛t✐♦♥s ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ♥❡ s♦♥t ❛❧♦rs ♣❧✉s s✉✣s❛♥t❡s

♣♦✉r ♠❛✐♥t❡♥✐r ❧❡ ❜✐❧❛♥ ❞❡s ❝❤❛♥❣❡♠❡♥ts ❞❡ ◆❇❙ s♦✉s ③ér♦✳ ❯♥❡ s✐t✉❛t✐♦♥ s✐♠✐❧❛✐r❡ s❡ ♣r♦❞✉✐t

♣♦✉r ❧❡ ▲❛❝ ❖♥t❛r✐♦✱ ♠❛✐s ❝❡tt❡ ❢♦✐s ❧❡ ❝❤❛♥❣❡♠❡♥t ❞❡ s✐❣♥❡ ❡st ❞✐❝té ♣❛r ❧❡s ❢♦rt❡s ✈❛❧❡✉rs ❞❡

r✉✐ssè❧❡♠❡♥t ✭❋✐❣✉r❡s ❆✳✼ ❡t ❆✳✽✮✳ P♦✉r ❧❛ tr♦✐s✐è♠❡ ✐♥st❛♥❝❡ ❞✬✉♥❡ ❜❛✐ss❡ ❛♥♥✉❡❧❧❡ ❞✉ ◆❇❙

♣♦✉r ❧❡ s❝é♥❛r✐♦ ❘❈P✹✳✺✱ ❧✬❛♥❛❧②s❡ ❞✉ s❡❝♦♥❞ s❝é♥❛r✐♦ ♥❡ ❢❛✐t q✉✬❡♠♣✐r❡r ❝❡tt❡ ❞✐♠✐♥✉t✐♦♥✳ ❊♥

❡✛❡t✱ ❧❡ ▲❛❝ ❙✉♣ér✐❡✉r ❡st ❧❡ s❡✉❧ à ♣r♦❥❡t❡r ✉♥❡ ❜❛✐ss❡ ❞✉ ◆❇❙ ♣♦✉r ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺ ✭❋✐❣✉r❡

✸✳✷✮✳ ▲❛ ❝♦❧♦♥♥❡ ♣♦✉r ❝❡ ❧❛❝ ❛✉ ❚❛❜❧❡❛✉ ✸✳✶ ✐♥❞✐q✉❡ ❧❡s ❝❛✉s❡s ❞❡ ❝❡ ♣❤é♥♦♠è♥❡✳ ❯♥❡ ❤❛✉ss❡

❞✉ r✉✐ssè❧❡♠❡♥t ♠♦✐♥s ✐♠♣♦rt❛♥t❡ q✉❡ ❞❛♥s ❧❡ ❝❛s ❞❡s ❛✉tr❡s ❧❛❝s ❝♦✉♣❧é❡ à ✉♥❡ ✐♠♣♦rt❛♥t❡

❛✉❣♠❡♥t❛t✐♦♥ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ✭♣❛rt✐❝✉❧✐èr❡♠❡♥t ♣♦✉r ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺ ❀ ❋✐❣✉r❡ ❇✳✹ ❞❛♥s

❧✬❆♥♥❡①❡ ❇✮ ❝❛✉s❡ ❝❡tt❡ ❜❛✐ss❡ ❛♥♥✉❡❧❧❡ ❞✉ ◆❇❙✳

✭❛✮ ✭❜✮

❋✐❣✉r❡ ✸✳✷ ✕ ❚❡♥❞❛♥❝❡s ❞❡ ✭❛✮ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ❞✉ ✭❜✮ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝❙✉♣ér✐❡✉r ❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳ ❙❝é♥❛r✐♦ ✽✳✺✳

✶✾

❯♥ ❞❡✉①✐è♠❡ ❝♦✉♣ ❞✬÷✐❧ à ❧✬é✈♦❧✉t✐♦♥ ❞❡s ❝♦♥❞✐t✐♦♥s ❤②❞r♦❧♦❣✐q✉❡s ♠♦②❡♥♥❡s✱ ❛✈❡❝ ❝❡tt❡ ❢♦✐s

✉♥❡ ♥♦✉✈❡❧❧❡ ❛♣♣r♦❝❤❡✱ ♣r♦❝✉r❡ ✉♥ ❧♦t ❞✬✐♥❢♦r♠❛t✐♦♥s ✉t✐❧❡s✳ ■❧ ♣❡r♠❡t ❞❡ s❡ r❡♥❞r❡ ❝♦♠♣t❡ q✉❡

❧❡s ❧❛❝s ♥❡ ✈♦♥t ♣❛s ♥é❝❡ss❛✐r❡♠❡♥t s✉❜✐r ❧❡s ✐♠♣❛❝ts ❞❡s ❝❤❛♥❣❡♠❡♥ts ❝❧✐♠❛t✐q✉❡s ❞❡ ❧❛ ♠ê♠❡

❢❛ç♦♥ ❡t s♦✉❧✐❣♥❡ ❧❡s ♣❛rt✐❝✉❧❛r✐tés ❞❡ ❝❤❛❝✉♥ ❞❡ ❝❡✉①✲❝✐✳ ❖♥ r❡♠❛rq✉❡ ❛✉ss✐ q✉❡ ❧❛ tr❛❥❡❝t♦✐r❡

❢✉t✉r❡ ❞❡s é♠✐ss✐♦♥s ❞❡ ●❊❙ ♣❡✉t ❛✈♦✐r ✉♥ ✐♠♣❛❝t ♠❛❥❡✉r s✉r ❧❡ s❡♥s ❞❡s ❝❤❛♥❣❡♠❡♥ts ❞❡

◆❇❙✳

✸✳✷ ➱✈♦❧✉t✐♦♥ ❞✉ ❝♦✉✈❡rt ❞❡ ❣❧❛❝❡ s✉r ❧❡s ●r❛♥❞s ▲❛❝s

▲❡s ♠♦❞è❧❡s ❝❧✐♠❛t✐q✉❡s ❢♦✉r♥✐ss❡♥t à ❧✬✉t✐❧✐s❛t❡✉r ✉♥❡ ♣❛♥♦♣❧✐❡ ❞❡ ✈❛r✐❛❜❧❡s q✉✐ ❞é❝r✐✈❡♥t ❞❡s

❝♦♥❞✐t✐♦♥s ♣❤②s✐q✉❡s s✉r ✉♥ ❞♦♠❛✐♥❡ ❞✬ét✉❞❡✳ ❇♦♥ ♥♦♠❜r❡ ❞❡ ❝❡s ✈❛r✐❛❜❧❡s ♣r♦❥❡té❡s s❡r❛✐❡♥t

✐♥tér❡ss❛♥t❡s à ét✉❞✐❡r ♣♦✉r ♠✐❡✉① ❝♦♠♣r❡♥❞r❡ ❧✬❡♥❥❡✉ ❞❡s ❝❤❛♥❣❡♠❡♥ts ❝❧✐♠❛t✐q✉❡ ❡t ✉♥❡ ❞❡

❝❡❧❧❡s✲❝✐ s❡ tr♦✉✈❡ à êtr❡ ❧❛ ❝♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ s✉r ❧❡s ❧❛❝s✳ ❊①tr❛✐r❡ ❡t ❛♥❛❧②s❡r ❝❡s ❞♦♥♥é❡s

♣❡r♠❡t ❡♥ ❡✛❡t ❞✬❛❝q✉ér✐r ❞❡s ✐♥❢♦r♠❛t✐♦♥s ❝♦♠♣❧é♠❡♥t❛✐r❡s ❛✉① rés✉❧t❛ts ♦❜t❡♥✉s ♣ré❝é❞❡♠✲

♠❡♥t✳ ❈❡tt❡ s❡❝t✐♦♥ ♣♦rt❡r❛ ❞♦♥❝ s✉r ✉♥❡ ❜rè✈❡ ❞✐s❝✉ss✐♦♥ ❞❡s rés✉❧t❛ts ❞✬✉♥❡ ❛♥❛❧②s❡ s✉r ❧❡s

♣r♦❥❡❝t✐♦♥s ❞✉ ❝♦✉✈❡rt ❞❡ ❣❧❛❝❡ ❛✉✲❞❡ss✉s ❞❡s ●r❛♥❞s ▲❛❝s ❡♥tr❡ ✶✾✼✶ ❡t ✷✶✵✵✳ ▲❡s ✜❣✉r❡s

ré❢éré❡s s❡ tr♦✉✈❡♥t ❞❛♥s ❧✬❆♥♥❡①❡ ❇ à ♣❛rt✐r ❞❡ ❧❛ ❋✐❣✉r❡ ❇✳✺✳

❆✈❛♥t ❞❡ ❝♦♠♠❡♥❝❡r ❧✬❛♥❛❧②s❡ ❞❡s ♣r♦❞✉✐ts ❞❡s ♠♦❞è❧❡s ❝❧✐♠❛t✐q✉❡s✱ ✉♥❡ ét✉❞❡ ❞✬✉♥❡ ❜❛♥q✉❡

❞❡ ❞♦♥♥é❡s s✉r ❧❡ s✉❥❡t✱ ❝♦♠♣t❛❜✐❧✐sé❡ ♣❛r ❆ss❡❧ ✭✷✵✵✸✮✱ s✬✐♠♣♦s❡✳ ▲❡s ❞♦♥♥é❡s ❞❡ ❝❡❧❧❡✲❝✐ s✬é❝❤❡✲

❧♦♥♥❡♥t s✉r ✹✺ ❛♥s ✭✶✾✼✸✲✷✵✶✽✮ ❡t q✉❛♥t✐✜❡ ❧❡s ❝♦✉✈❡rt✉r❡s ❞❡ ❣❧❛❝❡ s✉r ❝❤❛q✉❡ ❧❛❝ à ❝❤❛q✉❡

❛♥♥é❡✳ ▲❡s ✐♥❢♦r♠❛t✐♦♥s ❞✐s♣♦♥✐❜❧❡s s♦♥t✱ ❡♥tr❡ ❛✉tr❡s✱ ❧❡s ♣♦✉r❝❡♥t❛❣❡s ❧❡s ♣❧✉s ❤❛✉ts ❛tt❡✐♥ts

❝❤❛q✉❡ ❤✐✈❡r ❡t ❞❡s ♠♦②❡♥♥❡s ❥♦✉r♥❛❧✐èr❡s q✉✐ ♣❡r♠❡tt❡♥t ❞❡ s✉✐✈r❡ ❧❡s ❝❤❛♥❣❡♠❡♥ts à ✉♥❡

é❝❤❡❧❧❡ t❡♠♣♦r❡❧❧❡ ♣❧✉s ♣❡t✐t❡✳ ❊♥tr❡ ✶✾✼✸ ❡t ✷✵✵✵✱ ❧❛ ❝♦✉✈❡rt✉r❡ ♠❛①✐♠❛❧❡ ❛tt❡✐♥t❡ ❛♥♥✉❡❧❧❡✲

♠❡♥t ❡♥ ♠♦②❡♥♥❡ ❡st ❞❡ ✺✽✱✽ ✪ s✉r ❧✬❡♥s❡♠❜❧❡ ❞❡s ❧❛❝s✳ ▲❛ ❋✐❣✉r❡ ✸✳✸ ♣rés❡♥t❡ ❧❛ ❝❛rt❡ ❞❡s

❝♦✉✈❡rt✉r❡s ❞❡ ❣❧❛❝❡ ♣♦✉r ❧❛ ❥♦✉r♥é❡ ❞✉ ✷✶ ❢é✈r✐❡r ✶✾✽✽ ✭❧❛ ❥♦✉r♥é❡ ❞✉r❛♥t ❧❛q✉❡❧❧❡ ❧❛ ❝♦✉✈❡r✲

t✉r❡ ❡st ❧❛ ♣❧✉s ❣r❛♥❞❡ ❞❛♥s ✉♥❡ ❛♥♥é❡ r❡♣rés❡♥t❛t✐✈❡ ❞❡ ❧❛ ♣ér✐♦❞❡ ✶✾✼✸✲✷✵✵✵✮ ♣♦✉r ✈✐s✉❛❧✐s❡r

♦ù s❡ ❢♦r♠❡ ❧❛ ❣❧❛❝❡ s✉r ❧❡s ●r❛♥❞s ▲❛❝s✳ ❉❡ ❢❛ç♦♥ ❣é♥ér❛❧❡✱ ❧❡s ♣♦✉r❝❡♥t❛❣❡s ❛✉❣♠❡♥t❡♥t ♣rès

❞❡s ❝ôt❡s ♦ù ❧❡s ♥✐✈❡❛✉① s♦♥t ♣❧✉s ❜❛s ❡t ❞♦♥❝ ❧✬❡❛✉ ② ❣è❧❡ ♣❧✉s ❢❛❝✐❧❡♠❡♥t✳

✷✵

❋✐❣✉r❡ ✸✳✸ ✕ ❈♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ s✉r ❧❡s ●r❛♥❞s ▲❛❝s ❧❡ ✷✶ ❢é✈r✐❡r ✶✾✽✽✳ ❋✐❣✉r❡ t✐ré❡ ❞❡ ❆ss❡❧✭✷✵✵✸✮

P♦✉r é✈❛❧✉❡r ❧❡s ❝❤❛♥❣❡♠❡♥ts ❞❛♥s ❧❡ ❢✉t✉r✱ ❧❡ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s ♣✐❧♦té ♣❛r ❈❛♥❊❙▼✷

❡t s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺ ❡st ✉t✐❧✐sé✳ ▲❡s ❋✐❣✉r❡s ✸✳✹✱ ✸✳✺ ❡t ✸✳✻ s♦♥t ✉♥❛♥✐♠❡s ❀ ❧❡s ❝♦✉✲

✈❡rt✉r❡s ❞❡ ❣❧❛❝❡s ♠❛①✐♠❛❧❡s ❛♥♥✉❡❧❧❡s ✈♦♥t êtr❡ ❞r❛st✐q✉❡♠❡♥t ré❞✉✐t❡s ♣❛r ❧❡ ré❝❤❛✉✛❡♠❡♥t

❝❧✐♠❛t✐q✉❡✳ ❊♥ ♠♦②❡♥♥❡✱ ❧❡✉rs ✈❛❧❡✉rs ♥❡ ❞é♣❛ss❡♥t q✉❡ très r❛r❡♠❡♥t ✺✵✪ s✉r ❧❡s ♣♦✐♥ts ❞❡

❣r✐❧❧❡ ❞✉ ♠♦❞è❧❡ ♣♦✉r ❧❡s ❤✐✈❡rs ❞❡ ❧✬❤♦r✐③♦♥ ✷✵✼✶✲✷✶✵✵✳ ❆✉ ♠♦✐s ❞❡ ♠❛rs✱ ✉♥❡ ❝♦✉✈❡rt✉r❡

❞❡ ✺✵✪ ♥✬❡st ❥❛♠❛✐s ❞é♣❛ssé❡ ♣♦✉r ❝❡t ❤♦r✐③♦♥ ❛❧♦rs q✉✬✉♥❡ ❝♦✉✈❡rt✉r❡ ♠♦②❡♥♥❡ ❞❡ ✸✵✪ s✉r

❧✬❡♥s❡♠❜❧❡ ❞❡s ●r❛♥❞s ▲❛❝s ét❛✐t s✐♠✉❧é❡ ❡♥ ♠❛rs ❡♥tr❡ ✶✾✼✶ ❡t ✷✵✵✵ ✭❋✐❣✉r❡ ❇✳✼✮✳ ▲❡ ♠ê♠❡

♣❤é♥♦♠è♥❡ s❡ ♣r♦❞✉✐t ❡♥ ❛✈r✐❧ ♠❛✐s ❧✬❛❜s❡♥❝❡ ❞✬✉♥❡ ❝♦✉✈❡rt✉r❡ à ✺✵✪ s❡ ♣r♦❞✉✐t ❞ès ❧✬❤♦r✐③♦♥

✷✵✹✶✲✷✵✼✵ ✭❋✐❣✉r❡ ❇✳✽✮✳ ➚ ✉♥❡ é❝❤❡❧❧❡ ♣❧✉s ✜♥❡✱ ❧❡ ▲❛❝ ❙✉♣ér✐❡✉r ♣❡r❞ ❧❡ ♣❧✉s ❞❡ ❣❧❛❝❡✳ ▲❛

♣r♦❥❡❝t✐♦♥ ✐♥❞✐q✉❡ ✉♥❡ ❛❜s❡♥❝❡ q✉❛s✐✲t♦t❛❧❡ ❞❡ ❣❧❛❝❡ ♣♦✉r ❝❡ ❧❛❝ à ❧❛ ✜♥ ❞✉ ❳❳■❡ s✐è❝❧❡ ❛❧♦rs

q✉❡ ❝❡❧✉✐✲❝✐ ♣♦ssé❞❛✐t ❧❛ ❝♦✉✈❡rt✉r❡ ❧❛ ♣❧✉s ✐♠♣♦rt❛♥t❡ ❡♥ ✶✾✼✶✲✷✵✵✵ à ❝❛✉s❡ ❞❡ s❛ ❧❛t✐t✉❞❡ ♣❧✉s

é❧❡✈é❡✳ ❈❡ ❞❡r♥✐❡r rés✉❧t❛t ❝♦rr♦❜♦r❡ ❧❡s ❞♦♥♥é❡s ❞✬é✈❛♣♦r❛t✐♦♥ ♣rés❡♥té❡s ❛✉ ❚❛❜❧❡❛✉ ✸✳✶ ♣♦✉r

❧❡ ▲❛❝ ❙✉♣ér✐❡✉r✳ ▲✬❛✉❣♠❡♥t❛t✐♦♥ ♣❧✉s ✐♠♣♦rt❛♥t❡ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ s✉r ❝❡ ❧❛❝ ❡st ❝❛✉sé❡ ♣❛r ❧❡

r❡tr❛✐t ❞✉ ❝♦✉✈❡rt ❞❡ ❣❧❛❝❡✳ ❊♥ ❡✛❡t✱ ❧♦rsq✉❡ ♣rés❡♥t❡✱ ❧❛ ❣❧❛❝❡ ré❞✉✐t s✐❣♥✐✜❝❛t✐✈❡♠❡♥t ❧❡ ✢✉①

❞❡ ✈❛♣❡✉r ❞✬❡❛✉ ✭s✉❜❧✐♠❛t✐♦♥✮ ❤✐✈❡r♥❛❧❡ ❡t r❡t❛r❞❡ ❝❡❧❧❡✲❝✐ ❥✉sq✉✬à ❧❛ ✜♥ ❞❡ ❧✬été ✭❱❛♥ ❈❧❡❛✈❡

❡t ❛❧✳✱ ✷✵✶✹✮✳ ❉❡ ♣❧✉s✱ ❧❛ ❣❧❛❝❡ s✉r ❧❡ ❧❛❝✱ ❛❣✐ss❛♥t ❝♦♠♠❡ ✉♥ ✐s♦❧❛♥t t❤❡r♠✐q✉❡✱ r❛❧❡♥t✐t ❧❡ ré✲

❝❤❛✉✛❡♠❡♥t ❞❡ ❧✬❡❛✉ ❞✉r❛♥t ❧❡s ♠♦✐s q✉✐ s✉✐✈❡♥t ❧✬❤✐✈❡r ❡t ré❞✉✐t ❞♦♥❝ ❧✬é✈❛♣♦r❛t✐♦♥ ❞✉r❛♥t ❧❛

♣ér✐♦❞❡ ❢♦rt❡✱ ❧✬❛✉t♦♠♥❡✳ ▲✬❛❜s❡♥❝❡ ❞✬✉♥ ❝♦✉✈❡rt ❞❡ ❣❧❛❝❡ ❡♥ ✷✵✼✶✲✷✶✵✵ ❡①♣❧✐q✉❡ ❞♦♥❝ ❧✬✐♠♣♦r✲

✷✶

❋✐❣✉r❡ ✸✳✹ ✕ ❈♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ ♠❛①✐♠❛❧❡ ❞❡ ❧❛ ♣ér✐♦❞❡ ❏❛♥✈✐❡r✲❋é✈r✐❡r✲▼❛rs ♠♦②❡♥♥é❡❡♥tr❡ ✶✾✼✶ ❡t ✷✵✵✵ s✉r ❧❡s ●r❛♥❞s ▲❛❝s✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s ♣✐❧♦té ♣❛r❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺

t❛♥t❡ ❤❛✉ss❡ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❞✉ ▲❛❝ ❙✉♣ér✐❡✉r ♣r♦❥❡té❡ ❛✉ ❝♦✉r❛♥t ❞✉ ❳❳■❡ s✐è❝❧❡✳ ❉✬❛✐❧❧❡✉rs✱

❧❡s ❞♦♥♥é❡s ❞❡s ❋✐❣✉r❡s ❆✳✶❝ ❡t ❆✳✷❝ ✐♥❞✐q✉❡♥t ❜✐❡♥ ❧❛ ❤❛✉ss❡ ❤✐✈❡r♥❛❧❡ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ♣♦✉r

❝❡ ❧❛❝✳ ❙❛♥s s✉r♣r✐s❡✱ ❧❡s ❛✉tr❡s ❧❛❝s s✉❜✐ss❡♥t é❣❛❧❡♠❡♥t ❞❡s ❞✐♠✐♥✉t✐♦♥s ❞❡ ❧❡✉rs ❝♦✉✈❡rts ❞❡

❣❧❛❝❡ q✉✐ ♣r♦✈♦q✉❡♥t ❞❡s ❛✉❣♠❡♥t❛t✐♦♥s s✉❜séq✉❡♥t❡s ❞✬é✈❛♣♦r❛t✐♦♥✳ ❈❡s ❤❛✉ss❡s ❛♣♣❛r❛✐ss❡♥t

❛✉ ❝♦✉r❛♥t ❞❡ ❧✬été ♥♦t❛♠♠❡♥t ♣❛r❝❡ q✉❡ ❧✬❡❛✉ s❡ ré❝❤❛✉✛❡ ♣❧✉s r❛♣✐❞❡♠❡♥t ❞✉r❛♥t ❧❡ ♣r✐♥✲

t❡♠♣s s✐ ❧✬❡✛❡t r❡❢r♦✐❞✐ss❛♥t ❞❡ ❧❛ ❣❧❛❝❡ ❞✐s♣❛r❛ît✳

✷✷

❋✐❣✉r❡ ✸✳✺ ✕ ❈♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ ♠❛①✐♠❛❧❡ ❞❡ ❧❛ ♣ér✐♦❞❡ ❏❛♥✈✐❡r✲❋é✈r✐❡r✲▼❛rs ♠♦②❡♥♥é❡❡♥tr❡ ✷✵✹✶ ❡t ✷✵✼✵ s✉r ❧❡s ●r❛♥❞s ▲❛❝s✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s ♣✐❧♦té ♣❛r❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺

❋✐❣✉r❡ ✸✳✻ ✕ ❈♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ ♠❛①✐♠❛❧❡ ❞❡ ❧❛ ♣ér✐♦❞❡ ❏❛♥✈✐❡r✲❋é✈r✐❡r✲▼❛rs ♠♦②❡♥♥é❡❡♥tr❡ ✷✵✼✶ ❡t ✷✶✵✵ s✉r ❧❡s ●r❛♥❞s ▲❛❝s✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s ♣✐❧♦té ♣❛r❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺

✷✸

❈♦♥❝❧✉s✐♦♥s

❉✬✐♥♥♦♠❜r❛❜❧❡s s✉❥❡ts ❞❡ r❡❝❤❡r❝❤❡ ✐♥tér❡ss❛♥ts ❛②❛♥t tr❛✐t ❛✉① ❝❤❛♥❣❡♠❡♥ts ❝❧✐♠❛t✐q✉❡s

❡①✐st❡♥t ♣✉✐sq✉❡ ❝✬❡st ✉♥ ♣❤é♥♦♠è♥❡ q✉✐ ❛✛❡❝t❡ ♣♦t❡♥t✐❡❧❧❡♠❡♥t ✉♥❡ ♠✉❧t✐t✉❞❡ ❞❡ ❞✐s❝✐♣❧✐♥❡s✳

▲❡ ♣rés❡♥t ❞♦❝✉♠❡♥t r❡♣rés❡♥t❡ ✉♥❡ ♠✐♥✉s❝✉❧❡ ✐♥❝✉rs✐♦♥ ❞❛♥s ✉♥ s❡✉❧ ❞❡ ❝❡s s✉❥❡ts ❡t t❡♥t❡

❞❡ ❢❛❝✐❧✐t❡r ❧❛ ❝♦♠♣ré❤❡♥s✐♦♥ ❞✉ ❧❡❝t❡✉r ❡♥ ❝♦✉✈r❛♥t✱ ❜✐❡♥ q✉❡ s✉❝❝✐♥❝t❡♠❡♥t✱ s❡s ♥♦t✐♦♥s ❞❡

❜❛s❡✳ ▲❡ s✉❥❡t tr❛✐té ✐❝✐ ❡st ❧✬✐♠♣❛❝t ❞❡s ❝❤❛♥❣❡♠❡♥ts ❝❧✐♠❛t✐q✉❡s s✉r ❧✬❤②❞r♦❧♦❣✐❡ ❞❡s ●r❛♥❞s

▲❛❝s ❞✬❆♠ér✐q✉❡ ❞✉ ◆♦r❞✳ ▲✬✐♥tr♦❞✉❝t✐♦♥ ❡t ❧❡ ♣r❡♠✐❡r ❝❤❛♣✐tr❡ ♣rés❡♥t❡♥t ❧❡s ❢♦♥❞❛t✐♦♥s s✉r

❧❡sq✉❡❧❧❡s s❡ ♣♦s❡ ❧❡ r❡st❡ ❞✉ ♠é♠♦✐r❡✳ ❊♥ ❝♦♠♠❡♥ç❛♥t ♣❛r ❞❡s ♥♦t✐♦♥s ❤✐st♦r✐q✉❡s ❡t ✉♥❡

❡①♣❧✐❝❛t✐♦♥ t❤é♦r✐q✉❡ ❞✉ ♣❤é♥♦♠è♥❡ ❞❡s ❝❤❛♥❣❡♠❡♥ts ❝❧✐♠❛t✐q✉❡s ❡t ❡♥ ♣♦✉rs✉✐✈❛♥t ❛✈❡❝ ✉♥❡

❞❡s❝r✐♣t✐♦♥ ❞✉ ❞♦♠❛✐♥❡ ♣❤②s✐q✉❡ s✉r ❧❡q✉❡❧ ♣♦rt❡r❛ ❧✬ét✉❞❡✱ ❧✬✐♥tr♦❞✉❝t✐♦♥ ♠❡t ❧❡ ♣r♦❥❡t ❞❡

r❡❝❤❡r❝❤❡ ❡♥ ❝♦♥t❡①t❡✳

▲✬❛rt✐❝❧❡ ✐♥séré ❛✉ ❈❤❛♣✐tr❡ ✷ r❡♥❢❡r♠❡ ❧❡s rés✉❧t❛ts ❞❡s ❛♥❛❧②s❡s ❧❡s ♣❧✉s ♣♦✉ssé❡s ❞❡ ❧✬ét✉❞❡

♠❛✐s ❧✬❛❝❝❡ss✐❜✐❧✐té ❞❡ ❝❡tt❡ s❡❝t✐♦♥ s❡r❛✐t ❝♦♠♣r♦♠✐s❡ s❛♥s ❧❛ ♣rés❡♥❝❡ ❞✉ ❈❤❛♣✐tr❡ ✶✳ ■❧ ❝♦✉✈r❡

♥♦♠❜r❡s ❞❡s s✉❥❡ts ❛❜♦r❞és ❞❛♥s ❧✬❛rt✐❝❧❡ s❝✐❡♥t✐✜q✉❡ ♠❛✐s ❡♥ s✬② ❛tt❛r❞❛♥t ❞✬❛✈❛♥t❛❣❡✳ ❆♣rès

❧❛ ❧❡❝t✉r❡ ❞✉ ❈❤❛♣✐tr❡ ✶✱ ❧❡s q✉❡st✐♦♥♥❡♠❡♥ts s♦✉❧❡✈és ♣❛r ❧❛ ♠✐s❡ ❡♥ ❝♦♥t❡①t❡ ❡t ❧❡s ♦❜❥❡❝t✐❢s

❞✉ ❞é❜✉t ❞✉ ❞♦❝✉♠❡♥t ♣❡✉✈❡♥t ✜♥❛❧❡♠❡♥t tr♦✉✈❡r ré♣♦♥s❡s✳

❯♥❡ ❢❛✐❜❧❡ ❤❛✉ss❡ ❞✉ ◆❇❙ ❛♥♥✉❡❧❧❡ ❞❡s ●r❛♥❞s ▲❛❝s ❡st ♣r♦❥❡té❡ ❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵ ♣❛r ❧✬❡♥✲

s❡♠❜❧❡ ❞❡ ♠♦❞è❧❡s ré❣✐♦♥❛✉① ❞✉ ❝❧✐♠❛t✳ ❚♦✉❥♦✉rs à ❧✬é❝❤❡❧❧❡ ❞❡ ❧✬❛♥♥é❡✱ ❧❡s ♣ré❝✐♣✐t❛t✐♦♥s ❡t

❧❡ r✉✐ssè❧❡♠❡♥t ❛✉❣♠❡♥t❡♥t✱ ❛❥♦✉t❛♥t ❛✉ ◆❇❙✳ ▲✬é✈❛♣♦r❛t✐♦♥ ❛✉❣♠❡♥t❡ é❣❛❧❡♠❡♥t ♠❛✐s ❛✈❡❝

❧✬❡✛❡t ❝♦♥tr❛✐r❡ s✉r ❧❡ ◆❇❙✳ ■❧ ② ❛ ✉♥ éq✉✐❧✐❜r❡ q✉❛s✐✲♣❛r❢❛✐t ❡♥tr❡ ❧❡s ❛✉❣♠❡♥t❛t✐♦♥s ❤②❞r✐q✉❡s

❞✬✉♥❡ ♣❛rt ❡t ❧❡s ❜❛✐ss❡s ❞✬✉♥❡ ❛✉tr❡✳ ▲❡s rés✉❧t❛ts ❜✐✲❤❡❜❞♦♠❛❞❛✐r❡s ♦✛r❡♥t ❞✬❛✈❛♥t❛❣❡ ❞❡

❞ét❛✐❧s✳ ■❧s ré✈è❧❡♥t ❞❡s ❞✐✛ér❡♥❝❡s ❡♥tr❡ ❧❡s t❡♥❞❛♥❝❡s à ❧✬✐♥tér✐❡✉r ❞✉ ❝②❝❧❡ ❛♥♥✉❡❧ ♣♦✉r ❧❡s ✈❛✲

r✐❛❜❧❡s ét✉❞✐é❡s✳ ▲❡s ♣ré❝✐♣✐t❛t✐♦♥s ❛✉❣♠❡♥t❡♥t s✉rt♦✉t ❛✉ ♣r✐♥t❡♠♣s✱ ❧❡ r✉✐ssè❧❡♠❡♥t ❡♥ ❤✐✈❡r

❡t ❧✬é✈❛♣♦r❛t✐♦♥ ❧✬été ❡t ❧✬❛✉t♦♠♥❡✳ ▲❡s ❝❤❛♥❣❡♠❡♥ts ♣r♦❥❡tés ♣♦✉r ❧❡ ◆❇❙ s♦♥t ❞✐❝tés ♣❛r ❝❡s

♣ér✐♦❞❡s ❞❡ ❤❛✉ss❡ ❡t ❧❡s ✈❛❧❡✉rs ✐♥t❡r❛♥♥✉❡❧❧❡s ✈❛r✐❡♥t ❞♦♥❝ ❧❛r❣❡♠❡♥t✳ ❉❡s ❤✐✈❡rs ❡t ♣r✐♥t❡♠♣s

❛✈❡❝✱ ❡♥ ♠♦②❡♥♥❡✱ ✉♥❡ ❞✐s♣♦♥✐❜✐❧✐té ❞❡ ❧✬❡❛✉ ♣❧✉s ✐♠♣♦rt❛♥t❡ ❞❛♥s ❧❡ ❜❛ss✐♥ ❞❡s ●r❛♥❞s ▲❛❝s

s♦♥t ❛tt❡♥❞✉s à ❧❛ ✜♥ ❞✉ ❳❳■❡ s✐è❝❧❡✳ ❊♥ r❡✈❛♥❝❤❡✱ ✉♥❡ ❞✐s♣♦♥✐❜✐❧✐té ❤②❞r✐q✉❡ ❡st✐✈❛❧❡ ♣❧✉s

❢❛✐❜❧❡ ❡st é❣❛❧❡♠❡♥t ♣ré✈✉❡ ♣❛r ❧❡s ♠♦❞è❧❡s✳ ❯♥❡ ❛♥❛❧②s❡ ❞❡s ❡①trê♠❡s ❝♦♥✜r♠❡ ❝❡s ❝♦♥❝❧✉s✐♦♥s

✷✹

❡♥ ré✈é❧❛♥t ❞❡s ♠❛①✐♠❛ ❛♥♥✉❡❧s s✉r ✉♥❡ ♣ér✐♦❞❡ ❞❡ ❞❡✉① s❡♠❛✐♥❡s q✉✐ ❛✉❣♠❡♥t❡♥t ♣♦✉r ❧❡s ♣ré✲

❝✐♣✐t❛t✐♦♥s ❡t ❧❡ ◆❇❙✳ ❱✉ ❧✬✐♥t❡♥s✐✜❝❛t✐♦♥ ❞✉ ❝②❝❧❡ ❤②❞r✐q✉❡✱ ❧❡s ♠✐♥✐♠❛ ❞❡ ◆❇❙✱ ❡✉①✱ ❜❛✐ss❡♥t✳

❉❡s rés✉❧t❛ts ❝♦♠♣❧é♠❡♥t❛✐r❡s à ❝❡✉① ❞❡ ❧✬❛rt✐❝❧❡ ❞✉ ❈❤❛♣✐tr❡ ✷ s♦♥t t✐rés ❞✬✉♥❡ ❛♥❛❧②s❡ ré❛❧✐sé❡

s✉r ❝❤❛❝✉♥ ❞❡s ❧❛❝s ♣❧✉tôt q✉❡ s✉r ❧✬❡♥s❡♠❜❧❡ ❞❡s ●r❛♥❞s ▲❛❝s✳ ❖♥ ② ❛♣♣r❡♥❞ q✉❡ ❧❡s ✐♠♣❛❝ts

♥❡ s♦♥t ♣❛s ✉♥✐❢♦r♠❡s s✉r t♦✉t ❧❡ t❡rr✐t♦✐r❡✳ ▲❡ ▲❛❝ ❙✉♣ér✐❡✉r s✉❜✐t ❞❡s ❤❛✉ss❡s ✐♠♣♦rt❛♥t❡s

❞✬é✈❛♣♦r❛t✐♦♥ q✉✐ ❝❛✉s❡♥t ❞❡s ❜❛✐ss❡s ❞❡ ◆❇❙ à ❧♦♥❣ t❡r♠❡ t❛♥❞✐s q✉❡✱ ♣♦✉r ❧❡ ▲❛❝ ▼✐❝❤✐❣❛♥✲

❍✉r♦♥✱ ❞❡ ❧é❣èr❡s ❤❛✉ss❡s ❞❡ ◆❇❙ s♦♥t ♣r♦❥❡té❡s ❞✬✐❝✐ ✷✶✵✵✳ ❋✐♥❛❧❡♠❡♥t✱ ✉♥❡ ❝♦✉rt❡ ét✉❞❡

s✉r ❧✬é✈♦❧✉t✐♦♥ ❞❡s ❝♦✉✈❡rts ❞❡ ❣❧❛❝❡ ❞❡s ●r❛♥❞s ▲❛❝s ✈✐❡♥t ❝❧♦r❡ ❧❡ ❈❤❛♣✐tr❡ ✸✳ ▲❡ ré❝❤❛✉✛❡✲

♠❡♥t ❞❡s t❡♠♣ér❛t✉r❡s ❞❡ ❧✬❛✐r ❛ ❞❡s ✐♠♣❛❝ts ❞r❛st✐q✉❡s s✉r ❧❛ ❣❧❛❝❡ ❡t ❡♥ ❝❛✉s❡ ❧❛ ❞✐s♣❛r✐t✐♦♥

♣r❡sq✉❡ t♦t❛❧❡ ❡♥tr❡ ✷✵✼✶ ❡t ✷✶✵✵ s❡❧♦♥ ❧❡s ❞♦♥♥é❡s ❞❡s s✐♠✉❧❛t✐♦♥s ❞✉ ▼❘❈❈✺✲❖✉r❛♥♦s ❛✈❡❝

❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺✳

P♦✉r ❛♠é❧✐♦r❡r ❧❡s ❛♥❛❧②s❡s ❡✛❡❝t✉é❡s ❞❛♥s ❝❡tt❡ ét✉❞❡✱ ❝❡rt❛✐♥s ♣♦✐♥ts ♣♦✉rr❛✐❡♥t êtr❡ ❡①♣❧♦rés

❞❛✈❛♥t❛❣❡✳ ▲❡ r♦✉t❛❣❡✱ ♣❛r ❡①❡♠♣❧❡✱ ♥✬❛ ♣❛s été ❝♦♥s✐❞éré ❧♦rs ❞❡ ❧✬❡①tr❛❝t✐♦♥ ❞❡s ❞♦♥♥é❡s ❞❡

r✉✐ssè❧❡♠❡♥t✳ ▲✬❤②♣♦t❤ès❡ q✉❡ ❧✬❡✛❡t ❞✉ r♦✉t❛❣❡ ❡st ♥é❣❧✐❣❡❛❜❧❡ s✉r ✉♥❡ é❝❤❡❧❧❡ t❡♠♣♦r❡❧❧❡ ❞❡

❞❡✉① s❡♠❛✐♥❡s ❞❛♥s ✉♥ ❜❛ss✐♥ ✈❡rs❛♥t ❛✉ss✐ ❣r❛♥❞ q✉❡ ❝❡❧✉✐ ❞❡s ●r❛♥❞s ▲❛❝s ❛ ♣❧✉tôt été

é♠✐s❡✳ ❉❡s t❡sts ♣♦✉r ✈ér✐✜❡r ❧❛ ✈❛❧✐❞✐té ❞❡ ❝❡tt❡ ❤②♣♦t❤ès❡ ❛✉r❛✐❡♥t été ✐♥tér❡ss❛♥ts✳ ❯♥❡

❡①♣❧♦r❛t✐♦♥ ❞❡s ✐♥❝❡rt✐t✉❞❡s s✉r ❧❡s rés✉❧t❛ts ♦❜t❡♥✉s ❡st é❣❛❧❡♠❡♥t ♠❛♥q✉❛♥t❡✳ P❛r ❡①❡♠♣❧❡✱

✉♥❡ ❛♥❛❧②s❡ ♣❧✉s ❛♣♣r♦❢♦♥❞✐❡ ♣♦✉r ❞ét❡r♠✐♥❡r ❧✬✐♠♣♦rt❛♥❝❡ à ❛❝❝♦r❞❡r ❛✉① ♠❡♠❜r❡s ❞✬✉♥ ●❈▼

♣❛r r❛♣♣♦rt à ✉♥❡ s✐♠✉❧❛t✐♦♥ ❞✬✉♥ ❛✉tr❡ ♠♦❞è❧❡ ❛♠é❧✐♦r❡r❛✐t ❧✬ét✉❞❡✳ ❈❡t ❡①❡r❝✐❝❡ ♣♦✉rr❛✐t

❛❜♦✉t✐r à ❧❛ ❝ré❛t✐♦♥ ❞✬✉♥❡ ❢♦✉r❝❤❡tt❡ ❞❡s ✐♥❝❡rt✐t✉❞❡s ❛✉t♦✉r ❞❡s t❡♥❞❛♥❝❡s ♦❜t❡♥✉❡s ❞❛♥s ❝❡

♣r♦❥❡t✱ ❛♣♣♦rt❛♥t s♦♥ ❧♦t ❞✬✐♥❢♦r♠❛t✐♦♥s ✐♥tér❡ss❛♥t❡s✳

❈❡ ♣r♦❥❡t ❞❡ r❡❝❤❡r❝❤❡ ❡st ✉♥ ♣❛s ❞❛♥s ❧❛ ❜♦♥♥❡ ❞✐r❡❝t✐♦♥ ♣♦✉r ♠✐❡✉① ❝♦♠♣r❡♥❞r❡ ❧✬❡♥❥❡✉

❞❡s ❝❤❛♥❣❡♠❡♥ts ❝❧✐♠❛t✐q✉❡s ❞❛♥s ❧❡ ❝♦♥t❡①t❡ ❞❡ ❧✬❤②❞r♦❧♦❣✐❡ ❞❡s ●r❛♥❞s ▲❛❝s✳ ■❧ ❝♦✉✈r❡ ❧❡s

❞♦♥♥é❡s ❞❡ ♣❧✉s✐❡✉rs ✈❛r✐❛❜❧❡s ❡t ♣r❡♥❞ ❡♥ ❝♦♠♣t❡ ❞✐✛ér❡♥ts s❝é♥❛r✐♦s ❞✬é♠✐ss✐♦♥s ❡t ♠♦❞è❧❡s

❝❧✐♠❛t✐q✉❡s✳ P❛r ❝♦♥tr❡✱ ❧❛ r❡❝❤❡r❝❤❡ s✉r ❝❡ s✉❥❡t ❞♦✐t ❝♦♥t✐♥✉❡r ❡♥ ♣r❡♥❛♥t ❡♥ ❝♦♥s✐❞ér❛t✐♦♥ ❧❡s

♥♦✉✈❡❛✉① ♠♦❞è❧❡s ❡t s✐♠✉❧❛t✐♦♥s ❞✐s♣♦♥✐❜❧❡s✳ ❉❡ ♣❧✉s✱ ❞❡s ❞✐③❛✐♥❡s ❞❡ ✈❛r✐❛❜❧❡s ✐♥tér❡ss❛♥t❡s

q✉✐ ♥✬♦♥t ♣❛s été ❝♦✉✈❡rt❡s ❞❛♥s ❝❡tt❡ ét✉❞❡ ♣♦✉rr❛✐❡♥t s❛♥s ❞♦✉t❡ ❛✐❞❡r à ❡♥ ❛♣♣r❡♥❞r❡

❞❛✈❛♥t❛❣❡✳ ▲❛ ❝♦♥t✐♥✉❛t✐♦♥ ❞❡ ❧❛ r❡❝❤❡r❝❤❡ s✉r ❧✬❤②❞r♦❧♦❣✐❡ ❞❡s ●r❛♥❞s ▲❛❝s ❞❛♥s ✉♥ ❝❧✐♠❛t

❝❤❛♥❣❡❛♥t✱ q✉❡ ❝❡ s♦✐t ❡♥ ✉t✐❧✐s❛♥t ❞❡ ♥♦✉✈❡❧❧❡s ♠ét❤♦❞♦❧♦❣✐❡s ♦✉ s✐♠♣❧❡♠❡♥t ❡♥ s❡ ❝♦♥❝❡♥tr❛♥t

s✉r ❞❡s ✈❛r✐❛❜❧❡s ❞✐✛ér❡♥t❡s✱ ❡st ❞✬✐♠♣♦rt❛♥❝❡ ❝❛♣✐t❛❧❡ ♣♦✉r ❛❞éq✉❛t❡♠❡♥t éq✉✐♣❡r ❧❡s ❞é❝✐❞❡✉rs

❢❛✐s❛♥t ❢❛❝❡ ❛✉① ❡♥❥❡✉① ❞❡ ❝❡tt❡ ré❣✐♦♥✳

✷✺

❆♥♥❡①❡ ❆

❚❡♥❞❛♥❝❡s ♣♦✉r ❧❛❝s ✐♥❞✐✈✐❞✉❡❧s

✭❛✮ ✭❜✮

✭❝✮ ✭❞✮

❋✐❣✉r❡ ❆✳✶ ✕ ❚❡♥❞❛♥❝❡s ❞❡s ✭❛✮ ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ✭❜✮ ❞✉ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠és✉r ❧❡ ❧❛❝✱ ✭❝✮ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ✭❞✮ ❞✉ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝ ❙✉♣ér✐❡✉r ❡♥tr❡✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳ ❙❝é♥❛r✐♦ ❘❈P✹✳✺✳

✷✻

✭❛✮ ✭❜✮

✭❝✮ ✭❞✮

❋✐❣✉r❡ ❆✳✷ ✕ ❚❡♥❞❛♥❝❡s ❞❡s ✭❛✮ ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ✭❜✮ ❞✉ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠és✉r ❧❡ ❧❛❝✱ ✭❝✮ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ✭❞✮ ❞✉ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝ ❙✉♣ér✐❡✉r ❡♥tr❡✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳ ❙❝é♥❛r✐♦ ❘❈P✽✳✺✳

✷✼

✭❛✮ ✭❜✮

✭❝✮ ✭❞✮

❋✐❣✉r❡ ❆✳✸ ✕ ❚❡♥❞❛♥❝❡s ❞❡s ✭❛✮ ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ✭❜✮ ❞✉ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠és✉r ❧❡ ❧❛❝✱ ✭❝✮ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ✭❞✮ ❞✉ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝ ▼✐❝❤✐❣❛♥✲❍✉r♦♥❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳ ❙❝é♥❛r✐♦ ❘❈P✹✳✺✳

✷✽

✭❛✮ ✭❜✮

✭❝✮ ✭❞✮

❋✐❣✉r❡ ❆✳✹ ✕ ❚❡♥❞❛♥❝❡s ❞❡s ✭❛✮ ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ✭❜✮ ❞✉ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠és✉r ❧❡ ❧❛❝✱ ✭❝✮ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ✭❞✮ ❞✉ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝ ▼✐❝❤✐❣❛♥✲❍✉r♦♥❡♥tr❡ ✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳ ❙❝é♥❛r✐♦ ❘❈P✽✳✺✳

✷✾

✭❛✮ ✭❜✮

✭❝✮ ✭❞✮

❋✐❣✉r❡ ❆✳✺ ✕ ❚❡♥❞❛♥❝❡s ❞❡s ✭❛✮ ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ✭❜✮ ❞✉ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠és✉r ❧❡ ❧❛❝✱ ✭❝✮ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ✭❞✮ ❞✉ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝ ➱r✐é ❡♥tr❡ ✶✾✺✸ ❡t✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳ ❙❝é♥❛r✐♦ ❘❈P✹✳✺✳

✸✵

✭❛✮ ✭❜✮

✭❝✮ ✭❞✮

❋✐❣✉r❡ ❆✳✻ ✕ ❚❡♥❞❛♥❝❡s ❞❡s ✭❛✮ ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ✭❜✮ ❞✉ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠és✉r ❧❡ ❧❛❝✱ ✭❝✮ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ✭❞✮ ❞✉ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝ ➱r✐é ❡♥tr❡ ✶✾✺✸ ❡t✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳ ❙❝é♥❛r✐♦ ❘❈P✽✳✺✳

✸✶

✭❛✮ ✭❜✮

✭❝✮ ✭❞✮

❋✐❣✉r❡ ❆✳✼ ✕ ❚❡♥❞❛♥❝❡s ❞❡s ✭❛✮ ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ✭❜✮ ❞✉ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠és✉r ❧❡ ❧❛❝✱ ✭❝✮ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ✭❞✮ ❞✉ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝ ❖♥t❛r✐♦ ❡♥tr❡✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳ ❙❝é♥❛r✐♦ ❘❈P✹✳✺✳

✸✷

✭❛✮ ✭❜✮

✭❝✮ ✭❞✮

❋✐❣✉r❡ ❆✳✽ ✕ ❚❡♥❞❛♥❝❡s ❞❡s ✭❛✮ ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞✉ ❧❛❝✱ ✭❜✮ ❞✉ r✉✐ssè❧❡♠❡♥t ❡①♣r✐♠és✉r ❧❡ ❧❛❝✱ ✭❝✮ ❞❡ ❧✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞✉ ❧❛❝ ❡t ✭❞✮ ❞✉ ◆❇❙ ♣♦✉r ❧❡ ▲❛❝ ❖♥t❛r✐♦ ❡♥tr❡✶✾✺✸ ❡t ✷✶✵✵✳ ❘és✉❧t❛ts ❜❛sés s✉r ❧❡s ❡st✐♠❛t❡✉rs ❞❡ ❚❤❡✐❧✲❙❡♥✳ ❙❝é♥❛r✐♦ ❘❈P✽✳✺✳

✸✸

❆♥♥❡①❡ ❇

Pr♦❥❡❝t✐♦♥s s✉r ❝❛rt❡s ✲ ▼❘❈❈✺

✭❖✉r❛♥♦s✮ ✲ ❙❝é♥❛r✐♦ ❘❈P✽✳✺

❋✐❣✉r❡ ❇✳✶ ✕ ❱❛❧❡✉rs ♠♦②❡♥♥❡s ❞❡s t❡♠♣ér❛t✉r❡s ❞❡ ❧✬❛✐r ❞❛♥s ❧❛ ré❣✐♦♥ ❞❡s ●r❛♥❞s ▲❛❝s♣♦✉r ❧✬❤♦r✐③♦♥ ✶✾✼✶✲✷✵✵✵ ❡t ❝❤❛♥❣❡♠❡♥ts ❛❜s♦❧✉s ♣♦✉r ❧❡s ❤♦r✐③♦♥s ✷✵✹✶✲✷✵✼✵ ❡t ✷✵✼✶✲✷✶✵✵✭❝♦♠♣❛ré à ✶✾✼✶✲✷✵✵✵✮✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s ♣✐❧♦té ♣❛r ❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺

✸✹

❋✐❣✉r❡ ❇✳✷ ✕ ❱❛❧❡✉rs ♠♦②❡♥♥❡s ❞❡s ♣ré❝✐♣✐t❛t✐♦♥s ❛✉✲❞❡ss✉s ❞❡s ●r❛♥❞s ▲❛❝s ♣♦✉r ❧✬❤♦r✐✲③♦♥ ✶✾✼✶✲✷✵✵✵ ❡t ❝❤❛♥❣❡♠❡♥ts r❡❧❛t✐❢s ♣♦✉r ❧❡s ❤♦r✐③♦♥s ✷✵✹✶✲✷✵✼✵ ❡t ✷✵✼✶✲✷✶✵✵ ✭❝♦♠♣❛ré à✶✾✼✶✲✷✵✵✵✮✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s ♣✐❧♦té ♣❛r ❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦❘❈P✽✳✺

❋✐❣✉r❡ ❇✳✸ ✕ ❱❛❧❡✉rs ♠♦②❡♥♥❡s ❞❡ r✉✐ssè❧❡♠❡♥t ❞❛♥s ❧❡ ❜❛ss✐♥ ✈❡rs❛♥t ❞❡s ●r❛♥❞s ▲❛❝s ♣♦✉r❧✬❤♦r✐③♦♥ ✶✾✼✶✲✷✵✵✵ ❡t ❝❤❛♥❣❡♠❡♥ts r❡❧❛t✐❢s ♣♦✉r ❧❡s ❤♦r✐③♦♥s ✷✵✹✶✲✷✵✼✵ ❡t ✷✵✼✶✲✷✶✵✵ ✭❝♦♠♣❛réà ✶✾✼✶✲✷✵✵✵✮✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s ♣✐❧♦té ♣❛r ❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦❘❈P✽✳✺

✸✺

❋✐❣✉r❡ ❇✳✹ ✕ ❱❛❧❡✉rs ♠♦②❡♥♥❡s ❞✬é✈❛♣♦r❛t✐♦♥ ❛✉✲❞❡ss✉s ❞❡s ●r❛♥❞s ▲❛❝s ♣♦✉r ❧✬❤♦r✐③♦♥ ✶✾✼✶✲✷✵✵✵ ❡t ❝❤❛♥❣❡♠❡♥ts r❡❧❛t✐❢s ♣♦✉r ❧❡s ❤♦r✐③♦♥s ✷✵✹✶✲✷✵✼✵ ❡t ✷✵✼✶✲✷✶✵✵ ✭❝♦♠♣❛ré à ✶✾✼✶✲✷✵✵✵✮✳❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s ♣✐❧♦té ♣❛r ❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺

✸✻

✭❛✮

✭❜✮

✭❝✮

❋✐❣✉r❡ ❇✳✺ ✕ ➱✈♦❧✉t✐♦♥ ❞❡s ♠♦②❡♥♥❡s ❞❡ ❧❛ ❝♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ ♠❛①✐♠❛❧❡ ❞✉r❛♥t ❧❡ ♠♦✐s ❞❡❏❛♥✈✐❡r s✉r ❧❡s ●r❛♥❞s ▲❛❝s ♣♦✉r ❞❡s ♣ér✐♦❞❡s ❞❡ ✸✵ ❛♥s✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s♣✐❧♦té ♣❛r ❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺

✸✼

✭❛✮

✭❜✮

✭❝✮

❋✐❣✉r❡ ❇✳✻ ✕ ➱✈♦❧✉t✐♦♥ ❞❡s ♠♦②❡♥♥❡s ❞❡ ❧❛ ❝♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ ♠❛①✐♠❛❧❡ ❞✉r❛♥t ❧❡ ♠♦✐s ❞❡❋é✈r✐❡r s✉r ❧❡s ●r❛♥❞s ▲❛❝s ♣♦✉r ❞❡s ♣ér✐♦❞❡s ❞❡ ✸✵ ❛♥s✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s♣✐❧♦té ♣❛r ❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺

✸✽

✭❛✮

✭❜✮

✭❝✮

❋✐❣✉r❡ ❇✳✼ ✕ ➱✈♦❧✉t✐♦♥ ❞❡s ♠♦②❡♥♥❡s ❞❡ ❧❛ ❝♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ ♠❛①✐♠❛❧❡ ❞✉r❛♥t ❧❡ ♠♦✐s ❞❡▼❛rs s✉r ❧❡s ●r❛♥❞s ▲❛❝s ♣♦✉r ❞❡s ♣ér✐♦❞❡s ❞❡ ✸✵ ❛♥s✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s♣✐❧♦té ♣❛r ❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺

✸✾

✭❛✮

✭❜✮

✭❝✮

❋✐❣✉r❡ ❇✳✽ ✕ ➱✈♦❧✉t✐♦♥ ❞❡s ♠♦②❡♥♥❡s ❞❡ ❧❛ ❝♦✉✈❡rt✉r❡ ❞❡ ❣❧❛❝❡ ♠❛①✐♠❛❧❡ ❞✉r❛♥t ❧❡ ♠♦✐s❞✬❆✈r✐❧ s✉r ❧❡s ●r❛♥❞s ▲❛❝s ♣♦✉r ❞❡s ♣ér✐♦❞❡s ❞❡ ✸✵ ❛♥s✳ ❉♦♥♥é❡s ❞✉ ♠♦❞è❧❡ ▼❘❈❈✺✲❖✉r❛♥♦s♣✐❧♦té ♣❛r ❈❛♥❊❙▼✷ ❡♥ s✉✐✈❛♥t ❧❡ s❝é♥❛r✐♦ ❘❈P✽✳✺

✹✵

❆♥♥❡①❡ ❈

❙❝r✐♣ts ▼❛t❧❛❜ ✉t✐❧✐sés

❱♦✐❝✐ ❧❡s s❝r✐♣ts ▼❛t❧❛❜ q✉✐ ♦♥t s❡r✈✐s ❛✉① ❛♥❛❧②s❡s ❝♦♥t❡♥✉❡s ❞❛♥s ❝❡ ❞♦❝✉♠❡♥t✳ ❈❡s ❝♦❞❡s

s♦♥t ❞✐s♣♦♥✐❜❧❡s s✉r ❧❡s s❡r✈❡✉rs ❞✬❖✉r❛♥♦s✳

✖ ❊①tr❛❝t✐♦♥❴❉♦♥♥❡❡s❴▼❈❴r❡❣✐♦♥❴s♣❡❝✐✜q✉❡ ✿ P❡r♠❡t ❞✬❡①tr❛✐r❡ ❞❡s ❞♦♥♥é❡s ❞❡s s❡r✲

✈❡✉rs ❞✬❖✉r❛♥♦s ♣♦✉r ✉♥❡ ré❣✐♦♥ s♣é❝✐✜q✉❡✳ ❋❛✐t ❛♣♣❡❧ ❛✉ s❝r✐♣t ▲♦❛❞❉❛t❛ q✉✐ ❢❛✐t ❛♣♣❡❧

à ♣❧✉s✐❡✉rs ❛✉tr❡s s❝r✐♣ts ❡t ❢♦♥❝t✐♦♥s à s♦♥ t♦✉r✳

✖ ▲♦♦♣❴❊①tr❛❝t✐♦♥❴▼❘❈❈✺ ✿ P❡r♠❡t ❞❡ ❝❤♦✐s✐r q✉❡❧❧❡s ✈❛r✐❛❜❧❡s ❡t s✐♠✉❧❛t✐♦♥s ❞✉ ▼❘❈❈✺

❧❡ s❝r✐♣t ❊①tr❛❝t✐♦♥❴❉♦♥♥❡❡s❴▼❈❴r❡❣✐♦♥❴s♣❡❝✐✜q✉❡ ❞♦✐t ❡①tr❛✐r❡✳

✖ ▲♦♦♣❴❊①tr❛❝t✐♦♥❴❈❖❘❉❊❳ ✿ P❡r♠❡t ❞❡ ❝❤♦✐s✐r q✉❡❧❧❡s ✈❛r✐❛❜❧❡s ❡t s✐♠✉❧❛t✐♦♥s ❞✬✉♥

♠♦❞è❧❡ ❈❖❘❉❊❳ ❧❡ s❝r✐♣t ❊①tr❛❝t✐♦♥❴❉♦♥♥❡❡s❴▼❈❴r❡❣✐♦♥❴s♣❡❝✐✜q✉❡ ❞♦✐t ❡①tr❛✐r❡✳

✖ ❍♦r❛✐r❡❴❛❴◗✉♦t✐❞✐❡♥❴▼❘❈❈✺r❡❣✐♦♥ ✿ ❚r❛♥s❢♦r♠❡ ❧❡s ❞♦♥♥é❡s ❞✉ ▼❘❈❈✺ ❛✉① ✸ ❡t ✽

❤❡✉r❡s ❡♥ ❞❡s ❞♦♥♥é❡s q✉♦t✐❞✐❡♥♥❡s✳

✖ ◗✉♦t✐❞✐❡♥❴❛❴❍❡❜❞♦♠❛❞❛✐r❡❴▼♦✐♥s✸✶❉❊❈ ✿ ❚r❛♥❢♦r♠❡ ❧❡s ❞♦♥♥é❡s q✉♦t✐❞✐❡♥♥❡s ❡♥ sé✲

r✐❡s ❤❡❜❞♦♠❛❞❛✐r❡s ❡♥ ❡♥❧❡✈❛♥t ❧❡s ✸✶ ❞é❝❡♠❜r❡✳

✖ ❈❛❧❝✉❧◆❇❙▼♦❞ ✿ P❡r♠❡t ❞❡ ❝❛❧❝✉❧❡r ❧❡ ◆❇❙ ❞❡ ❝❤❛❝✉♥ ❞❡s ●r❛♥❞s ▲❛❝s ❛✈❡❝ ❧❡s ❞♦♥♥é❡s

❞❡ ◗✉♦t✐❞✐❡♥❴❛❴❍❡❜❞♦♠❛❞❛✐r❡❴▼♦✐♥s✸✶❉❊❈ à ❝❤❛q✉❡ s❡♠❛✐♥❡ ♦✉ ❛✉① ✷ s❡♠❛✐♥❡s✳

✖ ❆ss❡♠❜❧❛❣❡❉❛t❛ ✿ ❆ss♦❝✐❛t✐♦♥ ❞❡s sér✐❡s ♣♦✉r q✉✬❡❧❧❡s ❞❡✈✐❡♥♥❡♥t ❞❡s sér✐❡s ❞❡ ✶✹✽ ❛♥s

✖ ❱❛❧✐❞❛t✐♦♥ ✿ ❱❛❧✐❞❛t✐♦♥ ❞❡s ❞♦♥♥é❡s ❞❡ ❈❛❧❝✉❧◆❇❙▼♦❞

✖ ❚❤❡✐❧❴❙❡♥❴❙t❛t❚❡st ✿ ❘é❛❧✐s❡ ❧❡ t❡st st❛t✐st✐q✉❡ ❞❡ ❚❤❡✐❧✲❙❡♥ s✉r ❧❡s sér✐❡s ❜✐❤❡❜❞♦♠❛✲

❞❛✐r❡s

✖ ❆ss❡♠❜❧❛❣❡❉❛t❛❈♦♠♣◗✉♦t ✿ ❖r❣❛♥✐s❡ ❡t ♠♦❞✐✜❡ ❧❡s sér✐❡s ❞❡ ❞♦♥♥é❡s

✖ ❆♥❛❧②s❡❊①tr❡♠❡s❴❇✐❲❡❡❦❴❆♥♥✉❛❧ ❡t ❆♥❛❧②s❡❊①tr❡♠❡s❴◆❇❙❴❇✐❲❡❡❦ ✿ ❚r♦✉✈❡ ❧❛ ♣✐r❡

♣ér✐♦❞❡ ❞❡ ❞❡✉① s❡♠❛✐♥❡s ✭♠✐♥✐♠✉♠ ❡t ♠❛①✐♠✉♠✮ ♣♦✉r ❝❤❛q✉❡ ❛♥♥é❡

✖ ❉✐str✐❜✉t✐♦♥s❴❊①tr❡♠❡s ✿ ❊st✐♠❛t✐♦♥ ❞❡s ♣❛r❛♠ètr❡s ❞❡ ❧❛ ❞✐str✐❜✉t✐♦♥ ●❊❱ ♣♦✉r ❧❡s

sér✐❡s ❞✬❡①trê♠❡s

✹✶

❇✐❜❧✐♦❣r❛♣❤✐❡

❉❛♥✐❡❧ ❆❧♦♥❣✐ ✿ ❚❤❡ ✐♠♣❛❝t ♦❢ ❝❧✐♠❛t❡ ❝❤❛♥❣❡ ♦♥ ♠❛♥❣r♦✈❡ ❢♦r❡sts✳ ❈✉rr✳ ❈❧✐♠✳ ❈❤❛♥❣✳

❘❡♣✳✱ ✶✭✶✮✿✸✵✕✸✾✱ ✷✵✶✺✳ ■❙❙◆ ✷✶✾✽✲✻✵✻✶✳

❏❛♠❡s ❘ ❆♥❣❡❧ ❡t ❑❡♥♥❡t❤ ❊ ❑✉♥❦❡❧ ✿ ❚❤❡ r❡s♣♦♥s❡ ♦❢ ●r❡❛t ▲❛❦❡s ✇❛t❡r ❧❡✈❡❧s t♦ ❢✉t✉r❡

❝❧✐♠❛t❡ s❝❡♥❛r✐♦s ✇✐t❤ ❛♥ ❡♠♣❤❛s✐s ♦♥ ▲❛❦❡ ▼✐❝❤✐❣❛♥✲❍✉r♦♥✳ ❏✳ ●r❡❛t ▲❛❦❡s ❘❡s✳✱ ✸✻✿✺✶✕✺✽✱

✷✵✶✵✳

❙✈❛♥t❡ ❆rr❤❡♥✐✉s ❡t ❊❞✇❛r❞ ❙ ❍♦❧❞❡♥ ✿ ❖♥ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ ❝❛r❜♦♥✐❝ ❛❝✐❞ ✐♥ t❤❡ ❛✐r ✉♣♦♥

t❤❡ t❡♠♣❡r❛t✉r❡ ♦❢ t❤❡ ❡❛rt❤✳ P✉❜❧✐❝❛t✐♦♥s ♦❢ t❤❡ ❆str♦♥♦♠✐❝❛❧ ❙♦❝✐❡t② ♦❢ t❤❡ P❛❝✐✜❝✱ ✾

✭✺✹✮✿✶✹✕✷✹✱ ✶✽✾✼✳

❘❆ ❆ss❡❧ ✿ ❆♥ ❡❧❡❝tr♦♥✐❝ ❛t❧❛s ♦❢ ❣r❡❛t ❧❛❦❡s ✐❝❡ ❝♦✈❡r✳ ✇✐♥t❡rs ✿ ✶✾✼✸✕✷✵✵✷✳ ♥♦❛❛✱ ❣r❡❛t ❧❛❦❡s

❡♥✈✐r♦♥♠❡♥t❛❧ r❡s❡❛r❝❤ ❧❛❜♦r❛t♦r②✳ ❉✐❣✐t❛❧ ▼❡❞✐❛✳❬❆✈❛✐❧❛❜❧❡ ♦♥❧✐♥❡ ❛t ❤tt♣ ✿✴✴✇✇✇✳ ❣❧❡r❧✳

♥♦❛❛✳ ❣♦✈✴❞❛t❛✴✐❝❡✴❛t❧❛s✳❪✱ ✷✵✵✸✳

P❡t❡r ❉ ❇❧❛♥❦❡♥✱ ❈❤r✐st♦♣❤❡r ❙♣❡♥❝❡✱ ◆❡✇❡❧❧ ❍❡❞str♦♠ ❡t ❏♦❤♥ ❉ ▲❡♥t❡rs ✿ ❊✈❛✲

♣♦r❛t✐♦♥ ❢r♦♠ ❧❛❦❡ s✉♣❡r✐♦r ✿ ✶✳ ♣❤②s✐❝❛❧ ❝♦♥tr♦❧s ❛♥❞ ♣r♦❝❡ss❡s✳ ❏✳ ●r❡❛t ▲❛❦❡s ❘❡s✳✱ ✸✼

✭✹✮✿✼✵✼✕✼✶✻✱ ✷✵✶✶✳

❘❘ ❇r❛❤❛♠ ❏r ❡t ❘❉ ❑❡❧❧② ✿ ▲❛❦❡✲❡✛❡❝t s♥♦✇ st♦r♠s ♦♥ ❧❛❦❡ ♠✐❝❤✐❣❛♥✱ ✉s❛✳ ❈❧♦✉❞ ❉②♥✳✱

♣❛❣❡s ✽✼✕✶✵✶✱ ✶✾✽✷✳

❚❤♦♠❛s ❈ ❈❤❛♠❜❡r❧✐♥ ✿ ❆♥ ❛tt❡♠♣t t♦ ❢r❛♠❡ ❛ ✇♦r❦✐♥❣ ❤②♣♦t❤❡s✐s ♦❢ t❤❡ ❝❛✉s❡ ♦❢ ❣❧❛❝✐❛❧

♣❡r✐♦❞s ♦♥ ❛♥ ❛t♠♦s♣❤❡r✐❝ ❜❛s✐s✳ ❚❤❡ ❏♦✉r♥❛❧ ♦❢ ●❡♦❧♦❣②✱ ✼✭✻✮✿✺✹✺✕✺✽✹✱ ✶✽✾✾✳

▼❛r✐❡ ❈ ❈♦❧t♦♥ ✿ ❉❡✈❡❧♦♣✐♥❣ ❛ ❣r❡❛t ❧❛❦❡s r❡♠♦t❡ s❡♥s✐♥❣ ❝♦♠♠✉♥✐t②✳ ❏✳ ●r❡❛t ▲❛❦❡s ❘❡s✳✱

✸✾✿✻✕✼✱ ✷✵✶✸✳

❚❤♦♠❛s ❊ ❈r♦❧❡② ✿ ▲❛✉r❡♥t✐❛♥ ●r❡❛t ▲❛❦❡s ❞♦✉❜❧❡✲❈❖ ✷ ❝❧✐♠❛t❡ ❝❤❛♥❣❡ ❤②❞r♦❧♦❣✐❝❛❧ ✐♠✲

♣❛❝ts✳ ❈❧✐♠✳ ❈❤❛♥❣❡✱ ✶✼✿✷✼✕✹✼✱ ✶✾✾✵✳

❆✐❣✉♦ ❉❛✐ ✿ ❉r♦✉❣❤t ✉♥❞❡r ❣❧♦❜❛❧ ✇❛r♠✐♥❣ ✿ ❛ r❡✈✐❡✇✳ ❲✐❧❡② ■♥t❡r❞✐s❝✐♣✳ ❘❡✈✳ ✿ ❈❧✐♠✳ ❈❤❛♥❣✳✱

✷✭✶✮✿✹✺✕✻✺✱ ✷✵✶✶✳

✹✷

❈❛r❧♦ ❉❡▼❛r❝❤✐✱ ◗✐❛♥❣ ❉❛✐✱ ▼❛r② ❊▼❡❧❧♦ ❡t ❚✐♠♦t❤② ❙ ❍✉♥t❡r ✿ ❊st✐♠❛t✐♦♥ ♦❢ ♦✈❡r❧❛❦❡

♣r❡❝✐♣✐t❛t✐♦♥ ❛♥❞ ❜❛s✐♥ r✉♥♦✛ ✉♥❝❡rt❛✐♥t②✳ ■♥t❡r♥❛t✐♦♥❛❧ ❯♣♣❡r ●r❡❛t ❧❛❦❡s ❙t✉❞②✱ ❈❛s❡

❲❡st❡r♥ ❘❡s❡r✈❡ ❯♥✐✈❡rs✐t②✱ ✷✵✵✾✳

❊♥✈✐r♦♥♥❡♠❡♥t ❈❛♥❛❞❛ ✿ ❉♦♥♥é❡s ❝❧✐♠❛t✐q✉❡s ❤✐st♦r✐q✉❡s✱ ✷✵✶✽✳ ❤tt♣✿✴✴❝❧✐♠❛t❡✳

✇❡❛t❤❡r✳❣❝✳❝❛✴✐♥❞❡①❴❢✳❤t♠❧✱ ▲❛st ❛❝❝❡ss❡❞ ♦♥ ✷✵✶✽✲✶✷✲✹✳

❏♦s❡♣❤ ❋♦✉r✐❡r ✿ ▼é♠♦✐r❡ s✉r ❧❡s t❡♠♣ér❛t✉r❡s ❞✉ ❣❧♦❜❡ t❡rr❡str❡ ❡t ❞❡s ❡s♣❛❝❡s ♣❧❛♥ét❛✐r❡s✳

▼é♠♦✐r❡s ❞❡ ❧✬❆❝❛❞é♠✐❡ ❘♦②❛❧❡ ❞❡s ❙❝✐❡♥❝❡s ❞❡ ❧✬■♥st✐t✉t ❞❡ ❋r❛♥❝❡✱ ✼✿✺✼✵✕✻✵✹✱ ✶✽✷✼✳

❉♦♠✐♥✐q✉❡ ●✉é❣❛♥ ❡t ❇❡rtr❛♥❞ ❍❛ss❛♥✐ ✿ ❆ ♠❛t❤❡♠❛t✐❝❛❧ r❡s✉r❣❡♥❝❡ ♦❢ r✐s❦ ♠❛♥❛❣❡♠❡♥t ✿

❛♥ ❡①tr❡♠❡ ♠♦❞❡❧✐♥❣ ♦❢ ❡①♣❡rt ♦♣✐♥✐♦♥s✳ ✷✵✶✹✳

❍♦❧❧② ❈ ❍❛rt♠❛♥♥ ✿ ❈❧✐♠❛t❡ ❝❤❛♥❣❡ ✐♠♣❛❝ts ♦♥ ▲❛✉r❡♥t✐❛♥ ●r❡❛t ▲❛❦❡s ❧❡✈❡❧s✳ ❈❧✐♠✳

❈❤❛♥❣❡✱ ✶✼✭✶✮✿✹✾✕✻✼✱ ✶✾✾✵✳

❑❛t❤❛r✐♥❡ ❍❛②❤♦❡✱ ❏❡✛ ❱❛♥❉♦r♥✱ ❚❤♦♠❛s ❈r♦❧❡② ■■✱ ◆✐❝♦❧❡ ❙❝❤❧❡❣❛❧ ❡t ❉♦♥❛❧❞

❲✉❡❜❜❧❡s ✿ ❘❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ❝❤❛♥❣❡ ♣r♦❥❡❝t✐♦♥s ❢♦r ❈❤✐❝❛❣♦ ❛♥❞ t❤❡ ❯❙ ●r❡❛t ▲❛❦❡s✳

❏✳ ●r❡❛t ▲❛❦❡s ❘❡s✳✱ ✸✻✿✼✕✷✶✱ ✷✵✶✵✳

❙ ❲ ❍♦st❡t❧❡r✱ ● ❚ ❇❛t❡s ❡t ❋✐❧✐♣♣♦ ●✐♦r❣✐ ✿ ■♥t❡r❛❝t✐✈❡ ❝♦✉♣❧✐♥❣ ♦❢ ❛ ❧❛❦❡ t❤❡r♠❛❧

♠♦❞❡❧ ✇✐t❤ ❛ r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧✳ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✿ ❆t♠✳✱ ✾✽✭❉✸✮✿✺✵✹✺✕✺✵✺✼✱ ✶✾✾✸✳

❆rt❤✉r ❋ ❏❡♥❦✐♥s♦♥ ✿ ❚❤❡ ❢r❡q✉❡♥❝② ❞✐str✐❜✉t✐♦♥ ♦❢ t❤❡ ❛♥♥✉❛❧ ♠❛①✐♠✉♠ ✭♦r ♠✐♥✐♠✉♠✮

✈❛❧✉❡s ♦❢ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❡❧❡♠❡♥ts✳ ◗✳ ❏✳ ❘✳ ▼❡t❡♦r♦❧♦❣✳ ❙♦❝✳✱ ✽✶✭✸✹✽✮✿✶✺✽✕✶✼✶✱ ✶✾✺✺✳

❉❛✈✐❞ ❆❘ ❑r✐st♦✈✐❝❤✱ ❘✐❝❤❛r❞ ❉ ❈❧❛r❦✱ ❏❡✛r❡② ❋r❛♠❡✱ ❇❛rt ●❡❡rts✱ ❑❡✈✐♥ ❘ ❑♥✉♣♣✱

❑❛r❡♥ ❆ ❑♦s✐❜❛✱ ◆❡✐❧ ❋ ▲❛✐r❞✱ ◆✐❝❤♦❧❛s ❉ ▼❡t③✱ ❏✉st✐♥ ❘ ▼✐♥❞❡r✱ ❚♦❞❞ ❉ ❙✐❦♦r❛

❡t ❛❧✳ ✿ ❚❤❡ ♦♥t❛r✐♦ ✇✐♥t❡r ❧❛❦❡✲❡✛❡❝t s②st❡♠s ✜❡❧❞ ❝❛♠♣❛✐❣♥ ✿ ❙❝✐❡♥t✐✜❝ ❛♥❞ ❡❞✉❝❛t✐♦♥❛❧

❛❞✈❡♥t✉r❡s t♦ ❢✉rt❤❡r ♦✉r ❦♥♦✇❧❡❞❣❡ ❛♥❞ ♣r❡❞✐❝t✐♦♥ ♦❢ ❧❛❦❡✲❡✛❡❝t st♦r♠s✳ ❇✉❧❧✳ ❆♠✳ ▼❡t❡♦r♦❧✳

❙♦❝✳✱ ✾✽✭✷✮✿✸✶✺✕✸✸✷✱ ✷✵✶✼✳

●r❛❤❛♠❡ ▲❛rs♦♥ ❡t ❘❛♥❞❛❧❧ ❙❝❤❛❡t③❧ ✿ ❖r✐❣✐♥ ❛♥❞ ❡✈♦❧✉t✐♦♥ ♦❢ t❤❡ ❣r❡❛t ❧❛❦❡s✳ ❏✳ ●r❡❛t

▲❛❦❡s ❘❡s✳✱ ✷✼✭✹✮✿✺✶✽✕✺✹✻✱ ✷✵✵✶✳

❍❡r✈é ▲❡ ❚r❡✉t ✿ ➱✈♦❧✉t✐♦♥ ❝❧✐♠❛t✐q✉❡ ✿ ❧❡s ♠♦❞è❧❡s ❡t ❧❡✉rs ❧✐♠✐t❡s✳ ■♠❛❣❡s ❞❡ ❧❛ ♣❤②s✳✱

♣❛❣❡s ✷✼✕✸✷✱ ✷✵✵✺✳

❍❡r✈é ▲❡ ❚r❡✉t✱ ❘✐❝❤❛r❞ ❙♦♠❡r✈✐❧❧❡✱ ❯❧r✐❝❤ ❈✉❜❛s❝❤✱ ❨✐❤✉✐ ❉✐♥❣✱ ❈❡❝✐❧✐❡ ▼❛✉r✐t③❡♥✱

❆❜❞❛❧❛❤▼♦❦ss✐t✱ ❚❤♦♠❛s P❡t❡rs♦♥ ❡t ▼✐❝❤❛❡❧ Pr❛t❤❡r ✿ ❍✐st♦r✐❝❛❧ ♦✈❡r✈✐❡✇ ♦❢ ❝❧✐♠❛t❡

❝❤❛♥❣❡ s❝✐❡♥❝❡✳ ❈❧✐♠✳ ❈❤❛♥❣❡✱ ✷✵✵✼✳

❇r❡♥t ▼ ▲♦❢❣r❡♥✱ ❚✐♠♦t❤② ❙ ❍✉♥t❡r ❡t ❏❡ss✐❝❛ ❲✐❧❜❛r❣❡r ✿ ❊✛❡❝ts ♦❢ ✉s✐♥❣ ❛✐r t❡♠✲

♣❡r❛t✉r❡ ❛s ❛ ♣r♦①② ❢♦r ♣♦t❡♥t✐❛❧ ❡✈❛♣♦tr❛♥s♣✐r❛t✐♦♥ ✐♥ ❝❧✐♠❛t❡ ❝❤❛♥❣❡ s❝❡♥❛r✐♦s ♦❢ ●r❡❛t

▲❛❦❡s ❜❛s✐♥ ❤②❞r♦❧♦❣②✳ ❏✳ ●r❡❛t ▲❛❦❡s ❘❡s✳✱ ✸✼✿✼✹✹✕✼✺✷✱ ✷✵✶✶✳

✹✸

P❡t❡r ▲②♥❝❤ ✿ ❚❤❡ ❡♥✐❛❝ ✐♥t❡❣r❛t✐♦♥s✳ ❚❤❡ ❊♠❡r❣❡♥❝❡ ♦❢ ◆✉♠❡r✳ ❲❡❛t❤❡r Pr❡❞✐❝t✐♦♥✱ ♣❛❣❡s

✷✵✻✕✷✵✽✱ ✷✵✵✻✳

▼✉rr❛②▼❛❝❑❛② ❡t ❋r❛♥❦ ❙❡❣❧❡♥✐❡❦s ✿ ❖♥ t❤❡ s✐♠✉❧❛t✐♦♥ ♦❢ ▲❛✉r❡♥t✐❛♥ ●r❡❛t ▲❛❦❡s ✇❛t❡r

❧❡✈❡❧s ✉♥❞❡r ♣r♦❥❡❝t✐♦♥s ♦❢ ❣❧♦❜❛❧ ❝❧✐♠❛t❡ ❝❤❛♥❣❡✳ ❈❧✐♠✳ ❈❤❛♥❣❡✱ ✶✶✼✿✺✺✕✻✼✱ ✷✵✶✸✳

❆♥❞r❡② ▼❛rt②♥♦✈✱ ▲❛①♠✐ ❙✉s❤❛♠❛ ❡t ❘❡♥é ▲❛♣r✐s❡ ✿ ❙✐♠✉❧❛t✐♦♥ ♦❢ t❡♠♣❡r❛t❡ ❢r❡❡③✐♥❣

❧❛❦❡s ❜② ♦♥❡✲❞✐♠❡♥s✐♦♥❛❧ ❧❛❦❡ ♠♦❞❡❧s ✿ ♣❡r❢♦r♠❛♥❝❡ ❛ss❡ss♠❡♥t ❢♦r ✐♥t❡r❛❝t✐✈❡ ❝♦✉♣❧✐♥❣ ✇✐t❤

r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧s✳ ❇♦r❡❛❧ ❊♥✈✐r♦♥✳ ❘❡s✳✱ ✷✵✶✵✳

❉♠✐tr✐✐▼✐r♦♥♦✈✱ ●❡♦r❣② ❑✐r✐❧❧✐♥✱ ❊r❞♠❛♥♥ ❍❡✐s❡✱ ❙❡r❣❡❥ ●♦❧♦s♦✈✱ ❆r❦❛❞② ❚❡r③❤❡✈✐❦

❡t ■❧②❛ ❩✈❡r❡✈ ✿ P❛r❛♠❡t❡r✐③❛t✐♦♥ ♦❢ ❧❛❦❡s ✐♥ ♥✉♠❡r✐❝❛❧ ♠♦❞❡❧s ❢♦r ❡♥✈✐r♦♥♠❡♥t❛❧ ❛♣♣❧✐✲

❝❛t✐♦♥s✳ ■♥ Pr♦❝✳ ✼t❤ ❲♦r❦s❤♦♣ ♦♥ P❤②s✐❝❛❧ Pr♦❝❡ss❡s ✐♥ ◆❛t✉r❛❧ ❲❛t❡rs✱ ♣❛❣❡s ✶✸✺✕✶✹✸✳

❈✐t❡s❡❡r✱ ✷✵✵✸✳

❘✐❝❤❛r❞ ▼♦ss✱ ❲ ❇❛❜✐❦❡r✱ ❙❛♥❞❡r ❇r✐♥❦♠❛♥✱ ❊❞✉❛r❞♦ ❈❛❧✈♦✱ ❚✐♠ ❈❛rt❡r✱ ❏❛❡ ❊❞✲

♠♦♥❞s✱ ■s♠❛✐❧ ❊❧❣✐③♦✉❧✐✱ ❙❡✐t❛ ❊♠♦r✐✱ ▲✐♥ ❊r❞❛✱ ❑❛t❤② ❍✐❜❜❛r❞ ❡t ❛❧✳ ✿ ❚♦✇❛r❞s ♥❡✇

s❝❡♥❛r✐♦s ❢♦r t❤❡ ❛♥❛❧②s✐s ♦❢ ❡♠✐ss✐♦♥s ✿ ❈❧✐♠❛t❡ ❝❤❛♥❣❡✱ ✐♠♣❛❝ts ❛♥❞ r❡s♣♦♥s❡ str❛t❡❣✐❡s✱

✷✵✵✽✳

❘✐❝❤❛r❞ ❍▼♦ss✱ ❏❛❡ ❆ ❊❞♠♦♥❞s✱ ❑❛t❤② ❆ ❍✐❜❜❛r❞✱ ▼❛rt✐♥ ❘▼❛♥♥✐♥❣✱ ❙t❡✈❡♥ ❑ ❘♦s❡✱

❉❡t❧❡❢ P ❱❛♥ ❱✉✉r❡♥✱ ❚✐♠♦t❤② ❘ ❈❛rt❡r✱ ❙❡✐t❛ ❊♠♦r✐✱ ▼✐❦✐❦♦ ❑❛✐♥✉♠❛✱ ❚♦♠ ❑r❛♠

❡t ❛❧✳ ✿ ❚❤❡ ♥❡①t ❣❡♥❡r❛t✐♦♥ ♦❢ s❝❡♥❛r✐♦s ❢♦r ❝❧✐♠❛t❡ ❝❤❛♥❣❡ r❡s❡❛r❝❤ ❛♥❞ ❛ss❡ss♠❡♥t✳ ◆❛t✳✱

✹✻✸✭✼✷✽✷✮✿✼✹✼✱ ✷✵✶✵✳

❇▼✉s✐❝ ❡t ❈ ■r❛♠❜♦♥❛ ✿ ❚r❡❛t♠❡♥t ♦❢ t❤❡ ●r❡❛t ▲❛❦❡s ✐♥ t❤❡ ❈❖❘❉❊❳✲◆❆ ❝❧✐♠❛t❡ ❝❤❛♥❣❡

r✉♥s✳ ❘❛♣♣♦rt t❡❝❤♥✐q✉❡✱ ❖✉r❛♥♦s✱ ✷✵✶✼✳

❇✐❧❥❛♥❛ ▼✉s✐❝✱ ❆♥♥❡ ❋r✐❣♦♥✱ ❇r❡♥t ▲♦❢❣r❡♥✱ ❘✐❝❤❛r❞ ❚✉r❝♦tt❡ ❡t ❏❡❛♥✲❋r❛♥ç♦✐s ❈②r ✿

Pr❡s❡♥t ❛♥❞ ❢✉t✉r❡ ▲❛✉r❡♥t✐❛♥ ●r❡❛t ▲❛❦❡s ❤②❞r♦❝❧✐♠❛t✐❝ ❝♦♥❞✐t✐♦♥s ❛s s✐♠✉❧❛t❡❞ ❜② r❡❣✐♦✲

♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧s ✇✐t❤ ❛♥ ❡♠♣❤❛s✐s ♦♥ ▲❛❦❡ ▼✐❝❤✐❣❛♥✲❍✉r♦♥✳ ❈❧✐♠✳ ❈❤❛♥❣❡✱ ✶✸✵✿✻✵✸✕✻✶✽✱

✷✵✶✺✳

◆❡❜♦❥s❛ ◆❛❦✐❝❡♥♦✈✐❝✱ ❏♦s❡♣❤ ❆❧❝❛♠♦✱ ❆ ●r✉❜❧❡r✱ ❑ ❘✐❛❤✐✱ ❘❆ ❘♦❡❤r❧✱ ❍✲❍ ❘♦❣♥❡r

❡t ◆ ❱✐❝t♦r ✿ ❙♣❡❝✐❛❧ r❡♣♦rt ♦♥ ❡♠✐ss✐♦♥s s❝❡♥❛r✐♦s ✭❙❘❊❙✮✱ ❛ s♣❡❝✐❛❧ r❡♣♦rt ♦❢ ❲♦r❦✐♥❣

●r♦✉♣ ■■■ ♦❢ t❤❡ ✐♥t❡r❣♦✈❡r♥♠❡♥t❛❧ ♣❛♥❡❧ ♦♥ ❝❧✐♠❛t❡ ❝❤❛♥❣❡✳ ❈❛♠❜r✐❞❣❡ ❯♥✐✈✳ Pr❡ss✱ ✷✵✵✵✳

◆❛t✐♦♥❛❧ ❖❝❡❛♥✐❝ ❛♥❞ ❆t♠♦s♣❤❡r✐❝ ❆❞♠✐♥✐str❛t✐♦♥ ✿ ❘❡❛❧t✐♠❡ ❣r❡❛t ❧❛❦❡s ✇❡❛t❤❡r

❞❛t❛ ❛♥❞ ♠❛r✐♥❡ ♦❜s❡r✈❛t✐♦♥s✱ ✶✾✾✾✳ ❤tt♣s✿✴✴❝♦❛st✇❛t❝❤✳❣❧❡r❧✳♥♦❛❛✳❣♦✈✴♠❛r♦❜s✴♣❤♣✴

❞❛t❛✳♣❤♣❄st❛❂✾✫✉♥✐ts❂❡✫③♦♦♠❂s✱ ▲❛st ❛❝❝❡ss❡❞ ♦♥ ✷✵✶✽✲✶✶✲✷✾✳

◆❛t✐♦♥❛❧ ❖❝❡❛♥✐❝ ❛♥❞ ❆t♠♦s♣❤❡r✐❝ ❆❞♠✐♥✐str❛t✐♦♥ ✿ ◆❛t✐♦♥❛❧ ✇❡❛t❤❡r s❡r✈✐❝❡✱ ✷✵✶✽✳

❤tt♣✿✴✴✇✇✇✳♥✇s✳♥♦❛❛✳❣♦✈✴❝❧✐♠❛t❡✳♣❤♣✴①♠❛❝✐s✳♣❤♣✪✸❢✇❢♦❂❧♦t✱ ▲❛st ❛❝❝❡ss❡❞ ♦♥ ✷✵✶✽✲

✶✷✲✹✳

✹✹

◆♦rt❤ ❆♠❡r✐❝❛♥ ❘❡❣✐♦♥❛❧ ❈❧✐♠❛t❡ ❈❤❛♥❣❡ ❆ss❡ss♠❡♥t Pr♦❣r❛♠ ✿ ❈❛✈❡❛ts ❢♦r

✉s❡rs✱ ✷✵✵✼✳ ❤tt♣✿✴✴✇✇✇✳♥❛r❝❝❛♣✳✉❝❛r✳❡❞✉✴❛❜♦✉t✴❝❛✈❡❛ts✳❤t♠❧✱ ▲❛st ❛❝❝❡ss❡❞ ♦♥ ✷✵✶✽✲

✶✶✲✷✻✳

▼✐❝❤❛❡❧ ◆♦t❛r♦✱ ❱❛❧ ❇❡♥♥✐♥❣t♦♥ ❡t ❇r❡♥t ▲♦❢❣r❡♥ ✿ ❉②♥❛♠✐❝❛❧ ❞♦✇♥s❝❛❧✐♥❣✕❜❛s❡❞ ♣r♦✲

❥❡❝t✐♦♥s ♦❢ ●r❡❛t ▲❛❦❡s ✇❛t❡r ❧❡✈❡❧s✳ ❏✳ ❈❧✐♠✳✱ ✷✽✿✾✼✷✶✕✾✼✹✺✱ ✷✵✶✺✳

❊❉ P♦❛♥✱ P ●❛❝❤♦♥✱ ❘❡♥é ▲❛♣r✐s❡✱ ❘❛❜❛❤ ❆✐❞❡r ❡t ●✉✐❧❧❛✉♠❡ ❉✉❡②♠❡s ✿ ■♥✈❡st✐❣❛t✐♥❣

❛❞❞❡❞ ✈❛❧✉❡ ♦❢ r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧✐♥❣ ✐♥ ♥♦rt❤ ❛♠❡r✐❝❛♥ ✇✐♥t❡r st♦r♠ tr❛❝❦ s✐♠✉❧❛t✐♦♥s✳

❈❧✐♠✳ ❉②♥✳✱ ✺✵✭✺✲✻✮✿✶✼✾✾✕✶✽✶✽✱ ✷✵✶✽✳

Pr❛♥❛❜ ❑✉♠❛r ❙❡♥ ✿ ❊st✐♠❛t❡s ♦❢ t❤❡ r❡❣r❡ss✐♦♥ ❝♦❡✣❝✐❡♥t ❜❛s❡❞ ♦♥ ❑❡♥❞❛❧❧✬s t❛✉✳ ❏✳ ❆♠✳

❙t❛t✳ ❆ss♦❝✳✱ ✻✸✿✶✸✼✾✕✶✸✽✾✱ ✶✾✻✽✳

❆ ❙❤❛r♠❛✱ ❆❋ ❍❛♠❧❡t✱ ❍❏❙ ❋❡r♥❛♥❞♦✱ ❈❊ ❈❛t❧❡tt✱ ❉❊ ❍♦rt♦♥✱ ❱❘ ❑♦t❛♠❛rt❤✐✱

❉❆❘ ❑r✐st♦✈✐❝❤✱ ❆■ P❛❝❦♠❛♥✱ ❏▲ ❚❛♥❦ ❡t ❉❏❲✉❡❜❜❧❡s ✿ ❚❤❡ ♥❡❡❞ ❢♦r ❛♥ ✐♥t❡❣r❛t❡❞

❧❛♥❞✲❧❛❦❡✲❛t♠♦s♣❤❡r❡ ♠♦❞❡❧✐♥❣ s②st❡♠✱ ❡①❡♠♣❧✐✜❡❞ ❜② ♥♦rt❤ ❛♠❡r✐❝❛✬s ❣r❡❛t ❧❛❦❡s r❡❣✐♦♥✳

❊❛rt❤s ❋✉t✉r❡✱ ✷✵✶✽✳

❈ ❙♣❡♥❝❡✱ P❉ ❇❧❛♥❦❡♥✱ ❏❉ ▲❡♥t❡rs ❡t ◆ ❍❡❞str♦♠ ✿ ❚❤❡ ✐♠♣♦rt❛♥❝❡ ♦❢ s♣r✐♥❣ ❛♥❞ ❛✉✲

t✉♠♥ ❛t♠♦s♣❤❡r✐❝ ❝♦♥❞✐t✐♦♥s ❢♦r t❤❡ ❡✈❛♣♦r❛t✐♦♥ r❡❣✐♠❡ ♦❢ ❧❛❦❡ s✉♣❡r✐♦r✳ ❏✳ ❍②❞r♦♠❡t❡♦r♦❧✳✱

✶✹✭✺✮✿✶✻✹✼✕✶✻✺✽✱ ✷✵✶✸✳

❚❤♦♠❛s ❙t♦❝❦❡r ✿ ❈❧✐♠❛t❡ ❝❤❛♥❣❡ ✷✵✶✸ ✿ t❤❡ ♣❤②s✐❝❛❧ s❝✐❡♥❝❡ ❜❛s✐s ✿ ❲♦r❦✐♥❣ ●r♦✉♣ ■ ❝♦♥tr✐✲

❜✉t✐♦♥ t♦ t❤❡ ❋✐❢t❤ ❛ss❡ss♠❡♥t r❡♣♦rt ♦❢ t❤❡ ■♥t❡r❣♦✈❡r♥♠❡♥t❛❧ P❛♥❡❧ ♦♥ ❈❧✐♠❛t❡ ❈❤❛♥❣❡✳

❈❛♠❜r✐❞❣❡ ❯♥✐✈❡rs✐t② Pr❡ss✱ ✷✵✶✹✳

❍❡♥r✐ ❚❤❡✐❧ ✿ ❆ r❛♥❦✲✐♥✈❛r✐❛♥t ♠❡t❤♦❞ ♦❢ ❧✐♥❡❛r ❛♥❞ ♣♦❧②♥♦♠✐♥❛❧ r❡❣r❡ss✐♦♥ ❛♥❛❧②s✐s ✭P❛rts

✶✲✸✮✳ ■♥ ◆❡❞✳ ❆❦❛❞✳ ❲❡t❡♥s❝❤✳ Pr♦❝✳ ❙❡r✳ ❆✱ ✈♦❧✉♠❡ ✺✸✱ ♣❛❣❡s ✶✸✾✼✕✶✹✶✷✱ ✶✾✺✵✳

❑❡✈✐♥ ❊ ❚r❡♥❜❡rt❤ ✿ ❈❤❛♥❣❡s ✐♥ ♣r❡❝✐♣✐t❛t✐♦♥ ✇✐t❤ ❝❧✐♠❛t❡ ❝❤❛♥❣❡✳ ❈❧✐♠✳ ❘❡s✳✱ ✹✼✭✶✲✷✮✿✶✷✸✕

✶✸✽✱ ✷✵✶✶✳

❏♦❤♥ ❚②♥❞❛❧❧ ✿ ❈♦♥tr✐❜✉t✐♦♥s t♦ ▼♦❧❡❝✉❧❛r P❤②s✐❝s ✐♥ t❤❡ ❉♦♠❛✐♥ ♦❢ ❘❛❞✐❛♥t ❍❡❛t ✿ ❆ ❙❡r✐❡s

♦❢ ▼❡♠♦✐rs P✉❜❧✐s❤❡❞ ✐♥ t❤❡✬P❤✐❧♦s♦♣❤✐❝❛❧ ❚r❛♥s❛❝t✐♦♥s✬ ❛♥❞✬P❤✐❧♦s♦♣❤✐❝❛❧ ▼❛❣❛③✐♥❡✱✬✇✐t❤

❆❞❞✐t✐♦♥s✳ ▲♦♥❣♠❛♥s✱ ●r❡❡♥✱ ❛♥❞ ❈♦♠♣❛♥②✱ ✶✽✼✷✳

❯♥✐t❡❞ ❙t❛t❡s ●❡♦❧♦❣✐❝❛❧ ❙✉r✈❡② ✿ ❘❡❣✐♦♥❛❧ ❛♥❞ ❣❧♦❜❛❧ ❝❧✐♠❛t❡ ✿ ❇❛❝❦❣r♦✉♥❞✱

✷✵✶✶✳ ❤tt♣✿✴✴r❡❣❝❧✐♠✳❝♦❛s✳♦r❡❣♦♥st❛t❡✳❡❞✉✴❞②♥❛♠✐❝❛❧✲❞♦✇♥s❝❛❧✐♥❣✴❜❛❝❦❣r♦✉♥❞✴

✐♥❞❡①✳❤t♠❧✱ ▲❛st ❛❝❝❡ss❡❞ ♦♥ ✷✵✶✽✲✶✶✲✷✻✳

❑❛t❤❡r✐♥❡ ❱❛♥ ❈❧❡❛✈❡✱ ❏♦❤♥ ❉ ▲❡♥t❡rs✱ ❏✐❛ ❲❛♥❣ ❡t ❊❞✇❛r❞ ▼ ❱❡r❤❛♠♠❡ ✿ ❆ r❡❣✐♠❡

s❤✐❢t ✐♥ ❧❛❦❡ s✉♣❡r✐♦r ✐❝❡ ❝♦✈❡r✱ ❡✈❛♣♦r❛t✐♦♥✱ ❛♥❞ ✇❛t❡r t❡♠♣❡r❛t✉r❡ ❢♦❧❧♦✇✐♥❣ t❤❡ ✇❛r♠ ❡❧

♥✐ñ ✇✐♥t❡r ♦❢ ✶✾✾✼✕✶✾✾✽✳ ▲✐♠♥♦❧✳ ❖❝❡❛♥♦❣r✳✱ ✺✾✭✻✮✿✶✽✽✾✕✶✽✾✽✱ ✷✵✶✹✳

✹✺

❲❘ ❱❛♥ ❙❝❤♠✉s ❡t ❲❏ ❍✐♥③❡ ✿ ❚❤❡ ♠✐❞❝♦♥t✐♥❡♥t r✐❢t s②st❡♠✳ ❆♥♥✉✳ ❘❡✈✳ ❊❛rt❤ P❧❛♥❡t✳

❙❝✐✳✱ ✶✸✭✶✮✿✸✹✺✕✸✽✸✱ ✶✾✽✺✳

❉❡t❧❡❢ P ❱❛♥ ❱✉✉r❡♥✱ ❏❛❡ ❊❞♠♦♥❞s✱ ▼✐❦✐❦♦ ❑❛✐♥✉♠❛✱ ❑❡②✇❛♥ ❘✐❛❤✐✱ ❆❧❧✐s♦♥ ❚❤♦♠s♦♥✱

❑❛t❤② ❍✐❜❜❛r❞✱ ●❡♦r❣❡ ❈ ❍✉rtt✱ ❚♦♠ ❑r❛♠✱ ❱♦❧❦❡r ❑r❡②✱ ❏❡❛♥✲❋r❛♥❝♦✐s ▲❛♠❛rq✉❡

❡t ❛❧✳ ✿ ❚❤❡ r❡♣r❡s❡♥t❛t✐✈❡ ❝♦♥❝❡♥tr❛t✐♦♥ ♣❛t❤✇❛②s ✿ ❛♥ ♦✈❡r✈✐❡✇✳ ❈❧✐♠✳ ❈❤❛♥❣❡✱ ✶✵✾✭✶✲✷✮✿✺✱

✷✵✶✶✳

P❡♥❣❢❡✐ ❳✉❡✱ ❏❡r❡♠② ❙ P❛❧✱ ❳✐♥②✉ ❨❡✱ ❏♦❤♥ ❉ ▲❡♥t❡rs✱ ❈❤❡♥❢✉ ❍✉❛♥❣ ❡t P❤✐❧✐♣ ❨

❈❤✉ ✿ ■♠♣r♦✈✐♥❣ t❤❡ s✐♠✉❧❛t✐♦♥ ♦❢ ❧❛r❣❡ ❧❛❦❡s ✐♥ r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧✐♥❣ ✿ ❚✇♦✲✇❛②

❧❛❦❡✕❛t♠♦s♣❤❡r❡ ❝♦✉♣❧✐♥❣ ✇✐t❤ ❛ ✸❉ ❤②❞r♦❞②♥❛♠✐❝ ♠♦❞❡❧ ♦❢ t❤❡ ●r❡❛t ▲❛❦❡s✳ ❏✳ ❈❧✐♠✳✱ ✸✵

✭✺✮✿✶✻✵✺✕✶✻✷✼✱ ✷✵✶✼✳

✹✻

Évaluation des impacts des changements climatiques sur l ......résumé au cours des dernières...

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