A Model of Emerald Ash Borer Spread in New York State
Herb Susmannvisibility
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❆ ▼♦❞❡❧ ♦❢ ❊♠❡r❛❧❞ ❆s❤ ❇♦r❡r ❙♣r❡❛❞ ✐♥ ◆❡✇ ❨♦r❦
❙t❛t❡
❍❡r❜ ❙✉s♠❛♥♥
❉❡❝❡♠❜❡r ✶✵✱ ✷✵✶✷
❈♦♥t❡♥ts
✶ ■♥tr♦❞✉❝t✐♦♥
✷
✷ ❉❛t❛
✹
✸ ❚❤❡ ▼♦❞❡❧
✺
✹ ❘❡s✉❧ts
✼
✺ ▼❛♣s
✽
✻ ❉✐s❝✉ss✐♦♥
✽
✼ ❈♦♥❝❧✉s✐♦♥
✶✵
❘❡❢❡r❡♥❝❡s
✶✶
✽ ❋✐❣✉r❡s
✶✸
✶
✶
■♥tr♦❞✉❝t✐♦♥
❆❣r✐❧✉s ♣❧❛♥✐♣❡♥♥✐s ✭❊♠❡r❛❧❞ ❆s❤ ❇♦r❡r✱ ♦r ❊❆❇✮ ✐s ❛ ❤✐❣❤❧② ❞❡str✉❝t✐✈❡ ✐♥✈❛s✐✈❡ s♣❡❝✐❡s
t❤❛t ❤❛s ❜❡❡♥ ❛tt❛❝❦✐♥❣ ❛s❤ tr❡❡ ♣♦♣✉❧❛t✐♦♥s ❛❝r♦ss t❤❡ ◆♦rt❤ ❊❛st✳ ❚❤❡ ✜rst ✐♥st❛♥❝❡ ♦❢
❊❆❇ ✐♥❢❡st❛t✐♦♥ ✐♥ t❤❡ ❯♥✐t❡❞ ❙t❛t❡s ✇❛s ❞✐s❝♦✈❡r❡❞ ✐♥ ▼✐❝❤✐❣❛♥ ✐♥ ✷✵✵✷✳ ❬❑✐♥❣✱ ✷✵✶✶❪ ❙✐♥❝❡
t❤❡♥✱ t❤❡ ❜❡❡t❧❡ ❤❛s s♣r❡❛❞ t♦ s✐①t❡❡♥ st❛t❡s✱ t❤❡ ♠♦st r❡❝❡♥t ❜❡✐♥❣ ▼❛ss❛❝❤✉s❡tts ✇❤✐❝❤
❛♥♥♦✉♥❝❡❞ ✐ts ✜rst ❝♦♥✜r♠❡❞ ✐♥❢❡st❛t✐♦♥ ✐♥ ❙❡♣t❡♠❜❡r ✷✵✶✷✳ ❬▲✐♥❞s❛②✱ ✷✵✶✷✱ ❉✐✈✐s✐♦♥ ♦❢
▲❛♥❞s ✫ ❋♦r❡sts✱ ✷✵✶✷❪ ■♥ ◆❡✇ ❨♦r❦ ❙t❛t❡✱ t❤❡ ❜❡❡t❧❡ ✇❛s ✜rst ❢♦✉♥❞ ✐♥ ✷✵✵✾✳❬❈♦✉♥❝✐❧✱ ✷✵✶✵❪
❙✐♥❝❡ t❤❡♥✱ ✐t ❤❛s ❜❡❡♥ ❞❡t❡❝t❡❞ ✐♥ t✇❡❧✈❡ ❝♦✉♥t✐❡s✳ ❬▲❛♥❞s ❛♥❞ ❋♦r❡sts✱ ✷✵✶✷❪ ❲❤✐❧❡ t❤❡
❜❡❡t❧❡ ❝✉rr❡♥t❧② ✐♥❢❡sts ❧❡ss t❤❛♥ ✶✪ ♦❢ ◆❡✇ ❨♦r❦✬s ❋♦r❡sts✱ ✐ts s♣r❡❛❞ ♣✉ts ❛t r✐s❦ ❛❧❧ ♦❢ t❤❡
✼✵✵ ♠✐❧❧✐♦♥ ❛s❤ tr❡❡s ✐♥ t❤❡ st❛t❡✳ ❬❊❆❇ ❍♦♠❡ P❛❣❡✱ ✷✵✶✷❪
❲❡ ❞❡s❝r✐❜❡ ❛ ♠❡t❤♦❞ ♦❢ ♠♦❞❡❧❧✐♥❣ t❤❡ s♣r❡❛❞ ♦❢ t❤❡ ❊❆❇ ✐♥ ♦r❞❡r t♦ ♣r❡❞✐❝t ❤♦✇ ✐t
✇✐❧❧ s♣r❡❛❞ ♦✈❡r ◆❡✇ ❨♦r❦ ❙t❛t❡✳ ❆ ♠♦❞❡❧ ♦❢ ❊❆❇ s♣r❡❛❞ ❤❛s ❛ ✈❛r✐❡t② ♦❢ ♣♦t❡♥t✐❛❧ ✉s❡s✳
Pr❡❞✐❝t✐♦♥s ❛r❡ ✈❛❧✉❛❜❧❡ ❢♦r ❧♦❝❛❧✱ st❛t❡ ❛♥❞ ❢❡❞❡r❛❧ ❣♦✈❡r♥♠❡♥ts ✇❤❡♥ ♣❧❛♥♥✐♥❣ ❛ r❡s♣♦♥s❡ t♦
t❤❡ ♣❡st✳ ❋✉rt❤❡r♠♦r❡✱ r❡s✉❧ts ❝❛♥ ❜❡ ❛♥❛❧②③❡❞ ✐♥ ♦r❞❡r t♦ ❞❡t❡r♠✐♥❡ ❤♦✇ ❞✐✛❡r❡♥t ✈❡❝t♦rs ♦❢
❊❆❇ s♣r❡❛❞ ❝♦♥tr✐❜✉t❡ t♦ ✐ts ♦✈❡r❛❧❧ ❞✐s♣❡rs✐♦♥ ♣❛tt❡r♥✳ ❙✉❝❤ r❡s✉❧ts ❛r❡ ♣❛rt✐❝✉❧❛r❧② ✉s❡❢✉❧
✐♥ ❞❡t❡r♠✐♥✐♥❣ t❤❡ ♠♦st ❡✣❝✐❡♥t ❝♦✉♥t❡r♠❡❛s✉r❡ ❛❣❛✐♥st t❤❡ ❊❆❇ ✐♥ ♦r❞❡r t♦ st♦♣ ♦r s❧♦✇
❞♦✇♥ ✐ts s♣r❡❛❞ ❛❝r♦ss t❤❡ st❛t❡✳
❙♣❡❝✐✜❝❛❧❧②✱ ✇❡ ♣r♦♣♦s❡ ❛ s♣❛t✐❛❧❧② ❡①♣❧✐❝✐t ❝❡❧❧✉❧❛r ❛✉t♦♠❛t❛ ♠♦❞❡❧ ♦❢ ❊❆❇ s♣r❡❛❞ ✐♥
◆❡✇ ❨♦r❦ ❙t❛t❡✳ ❖✉r ✇♦r❦ ✐s ❧❛r❣❡❧② ❜❛s❡❞ ♦♥ ♣r❡✈✐♦✉s ✇♦r❦s ❜② Pr❛s❛❞ ❡t✳ ❛❧✳ ❬✷✵✶✵❪ ✇❤♦
❞❡✈❡❧♦♣ ❛ s✐♠✐❧❛r ❝❡❧❧✉❧❛r ❛✉t♦♠❛t❛ ♠♦❞❡❧ ❛♥❞ ❇❡♥❉♦r ❡t✳ ❛❧✳ ❬✷✵✵✻❪ ✇❤♦ ❞❡✈❡❧♦♣ ❛ ♠♦❞❡❧ ♦❢
❊❆❇ s♣r❡❛❞ ✐♥ t❤❡ ❈❤✐❝❛❣♦ r❡❣✐♦♥ ♦❢ ■❧❧✐♥♦✐s✳ ❖✉r ♠♦❞❡❧ t❛❦❡s ✐♥t♦ ❛❝❝♦✉♥t ❊❆❇ ❞✐s♣❡rs✐♦♥
❜② ❜♦t❤ ✐♥s❡❝t ✢✐❣❤t ❛♥❞ ❤✉♠❛♥ r✐❞❡ ✈❡❝t♦rs ❛♥❞ ♣r❡❞✐❝ts t❤❡ s♣r❡❛❞ ♦❢ t❤❡ ❊❆❇ ✐♥ ◆❡✇
❨♦r❦ ❙t❛t❡ ❢r♦♠ ✷✵✶✷ t♦ ✷✵✷✷✳
❖✉r ♠♦❞❡❧ ❛❝❝♦✉♥ts ❢♦r t✇♦ ♦❢ t❤❡ ♠❛❥♦r ✈❡❝t♦rs ♦❢ ❊❆❇ s♣r❡❛❞✿ ✐♥s❡❝t ✢✐❣❤t ❛♥❞ ❤✉♠❛♥
r✐❞❡ t❤r♦✉❣❤ t❤❡ ❧♦♥❣ ❞✐st❛♥❝❡ tr❛♥s♣♦rt ♦❢ ✜r❡✇♦♦❞✳ ❬▼✉✐r❤❡❛❞ ❡t ❛❧✳✱ ✷✵✵✺❪ ❖t❤❡r ✈❡❝t♦rs
t❤❛t ❛r❡ ♥♦t t❛❦❡♥ ✐♥t♦ ❛❝❝♦✉♥t ✐♥ ♦✉r ♠♦❞❡❧ ✐♥❝❧✉❞❡ s♣r❡❛❞ t❤r♦✉❣❤ ♦t❤❡r ❤✉♠❛♥ ❛❝t✐✈✐t✐❡s
✷
s✉❝❤ ❛s tr❛♥s♣♦rt❛t✐♦♥ ♦❢ ✉♥tr❡❛t❡❞ ❛s❤ ❧♦❣s ❛♥❞ ❛s❤ ♥✉rs❡r② ♣r♦❞✉❝ts✳
❚❤❡ ♣r✐♠❛r② ♠❡t❤♦❞ ❜② ✇❤✐❝❤ t❤❡ ❜❡❡t❧❡ ❞✐s♣❡rs❡s ✐s ❜② s✐♠♣❧❡ ✐♥s❡❝t ✢✐❣❤t✳ ■♥ ❛♥ ❡①✲
♣❡r✐♠❡♥t t♦ ❞❡t❡r♠✐♥❡ ❊❆❇ ❜❡❡t❧❡ ✢✐❣❤t r❛♥❣❡s ✉s✐♥❣ ✢✐❣❤t ♠✐❧❧s✱ ✐t ✇❛s ❢♦✉♥❞ t❤❛t ❊♠❡r❛❧❞
❆s❤ ❇♦r❡r ❜❡❡t❧❡s ❝❛♥ ✢② ✉♣ t♦ ✷✳✽ ❦♠✴❞❛②✳ ❖✈❡r ❛ ✜✈❡ ❞❛② ♣❡r✐♦❞✱ t❤❡ ♠❛①✐♠✉♠ ❞✐st❛♥❝❡
✢♦✇♥ ❜② ❛ ❜❡❡t❧❡ ♦♥ ❛ ✢✐❣❤t ♠✐❧❧ ✇❛s ✾✳✽✹ ❦♠✳ ❚❤✐s ❡①♣❡r✐♠❡♥t❛❧ ❞❛t❛ s❤♦✉❧❞ ♥♦t ❜❡ t❛❦❡♥
❛s ❢❛❝t ✐♥ r❡❣❛r❞s ❊❆❇ ❜❡❡t❧❡ ❞✐s♣❡rs✐♦♥ ❞✐st❛♥❝❡s ✐♥ ♥❛t✉r❡ s✐♥❝❡ t❤❡ ❧❛❜♦r❛t♦r② ❝♦♥❞✐t✐♦♥s
✉s✐♥❣ ❛ ✢✐❣❤t ♠✐❧❧ ❛r❡ ✈❡r② ❞✐✛❡r❡♥t ❢r♦♠ t❤❡ ♦✉t❞♦♦rs✳❬❚❛②❧♦r ❡t ❛❧✳✱ ✷✵✵✼❪ ■✈❡rs♦♥ ❡t✳ ❛❧✳
❡st✐♠❛t❡❞ t❤❛t ❊❆❇ ✐♥❢❡st❛t✐♦♥ ❢r♦♥ts ❛s ❛ ✇❤♦❧❡ ❡①♣❛♥❞ ❛t ❛ r❛t❡ ♦❢ ❛♣♣r♦①✐♠❛t❡❧② ✷✵
❦♠✴②❡❛r✳
❬✷✵✶✵❪ ❚❤✐s ❡st✐♠❛t❡ ✇❛s ❜❛s❡❞ ♦♥ ❛ ✈❛r✐❡t② ♦❢ ❞❛t❛ s♦✉r❝❡s ❢r♦♠ ❛ ❊❆❇ ✐♥❢❡s✲
t❛t✐♦♥ ✐♥ ❉❡tr♦✐t✱ ▼✐❝❤✐❣❛♥✳
❇❛s❡❞ ♦♥ t❤❡ r❡s❡❛r❝❤ ❜② ■✈❡rs♦♥ ❛♥❞ ❚❛②❧♦r✱ ✐t ✐s ♣❧❛✉s✐❜❧❡
t❤❛t t❤❡ ❊❆❇ ❜❡❡t❧❡s ❝♦✉❧❞ ✢② ❢❛r ❡♥♦✉❣❤ ❜❛s❡❞ ♦♥ ✢✐❣❤t ❧❡♥❣t❤ ❞❛t❛ ✐♥ ♦r❞❡r t♦ s♣r❡❛❞ t❤❡
✐♥❢❡st❛t✐♦♥ ❜② ✷✵ ❦♠✴②❡❛r✳
▼❛♥② ✐♥❢❡st❛t✐♦♥ s✐t❡s ❝❛♥♥♦t ❜❡ ❛❝❝♦✉♥t❡❞ ❢♦r ❜② s✐♠♣❧❡ ✐♥s❡❝t ✢✐❣❤t ❞✐s♣❡rs✐♦♥ ❢r♦♠
♣r❡✈✐♦✉s❧② ✐♥❢❡st❡❞ ❛r❡❛s✱ ❛♥❞ ❛s s✉❝❤ ♦t❤❡r ♠❡❛♥s ♦❢ ❊❆❇ s♣r❡❛❞ ♠✉st ❜❡ ❝♦♥s✐❞❡r❡❞✳
❬▼✉✐r❤❡❛❞ ❡t ❛❧✳✱ ✷✵✵✺❪ ❍✉♠❛♥s ✐♥❛❞✈❡rt❛♥t❧② ❛ss✐st t❤❡ s♣r❡❛❞ ♦❢ t❤❡ ❊❆❇ ❜② ♠♦✈✐♥❣ ✐♥❢❡st❡❞
✜r❡✇♦♦❞ ❧♦♥❣❡r ❞✐st❛♥❝❡s t❤❛♥ t❤❡ ❊❆❇ ❝❛♥ ❞✐s♣❡rs❡✳ ■♥ s♦♠❡ ❝❛s❡s t❤✐s ♠❛② ❜❡ ❝❛✉s❡❞ ❜②
❝❛♠♣t❡rs ✇❤♦ ❜r✐♥❣ ✜r❡✇♦♦❞ ✇✐t❤ t❤❡♠ ♦♥ t❤❡✐r ❝❛♠♣✐♥❣ tr✐♣s✳ ❚♦ ✐❧❧✉str❛t❡ t❤✐s ♣♦t❡♥t✐❛❧
✈❡❝t♦r✱ ❝♦♥s✐❞❡r t❤❡ r❡s✉❧ts ♦❢ ❛ ✜r❡✇♦♦❞ s✉r✈❡② ✐♥ ▼✐❝❤✐❣❛♥✿
✏✇✐t❤✐♥ ❛ t✇♦✲❞❛② ♣❡r✐♦❞
✭❚❤✉rs❞❛②✴❋r✐❞❛②✮✱ t❤❡r❡ ✇❡r❡ ✶✷✽ r❡❢❡rr❛❧s ❢♦r ✜r❡✇♦♦❞ ✇✐t❤ ✶✵✶ q✉❛r❛♥t✐♥❡ ✈✐♦❧❛t✐♦♥s✳
❚❤❡r❡ ✇❡r❡ ✹✽✼✶ ♣✐❡❝❡s ♦❢ ✜r❡✇♦♦❞ s❡✐③❡❞❀ ♦♥❧② ❡✐❣❤t ♦❢ t❤❡s❡ ♣✐❡❝❡s ✇❡r❡ ❛s❤✱ ❜✉t ♦❢ t❤❡s❡✱
s✐① ✇❡r❡ ✐♥❢❡st❡❞ ✇✐t❤ ❊❆❇✳✑ ❬❯♥✐t❡❞ ❙t❛t❡s ❉❡♣❛rt♠❡♥t ♦❢ ❆❣r✐❝✉❧t✉r❡ ❛♥❞ ❙❡r✈✐❝❡✱ ✷✵✶✵❪
❈❛♠♣❡rs ♠♦✈✐♥❣ ✜r❡✇♦♦❞ ❝❛♥ ❝❡rt❛✐♥❧② ❜❡ ❛ ❝❛✉s❡ ♦❢ ❊❆❇ ❧♦♥❣ ❞✐st❛♥❝❡ ❞✐s♣❡rs❛❧✳ ❆s ♦❢
✷✵✶✵✱ t✇❡❧✈❡ st❛t❡s ❤❛❞ r❡❣✉❧❛t✐♦♥s ✐♥ ♣❧❛❝❡ r❡str✐❝t✐♥❣ ♠♦✈❡♠❡♥t ♦❢ ✜r❡✇♦♦❞ ❛s ❛ r❡s♣♦♥s❡
t♦ t❤❡ ❊❆❇✳ ❬❯♥✐t❡❞ ❙t❛t❡s ❉❡♣❛rt♠❡♥t ♦❢ ❆❣r✐❝✉❧t✉r❡ ❛♥❞ ❙❡r✈✐❝❡✱ ✷✵✶✵❪ ❲❡ ❛❝❝♦✉♥t ❢♦r
t❤✐s ✈❡❝t♦r ✐♥ ♦✉r ♠♦❞❡❧✳
✸
✷
❉❛t❛
❚❤❡ ♠♦❞❡❧ ✐s ❜❛s❡❞ ♦♥ s❡✈❡r❛❧ ❞❛t❛ ❧❛②❡rs ❝♦✈❡r✐♥❣ ❢❡❛t✉r❡s ♦❢ ◆❡✇ ❨♦r❦ ❙t❛t❡ r❡❧❛t❡❞
t♦ t❤❡ ❊♠❡r❛❧❞ ❆s❤ ❇♦r❡r✳ ❉❛t❛ ❢♦r t❤❡ ❞✐sr✐❜✉t✐♦♥ ♦❢ ❛s❤ tr❡❡s✱ ♣♦♣✉❧❛t✐♦♥✱ ❝❛♠♣❣r♦✉♥❞s✱
❛♥❞ ✷✵✶✷ ✐♥❢❡st❛t✐♦♥ s✐t❡s ❛❝r♦ss t❤❡ st❛t❡ ✇❛s ❝♦❧❧❡❝t❡❞ ❢r♦♠ ❛ ✈❛r✐❡t② ♦❢ s♦✉r❝❡s✳
❆ r❛st❡r ❧❛②❡r ❢♦r ❧✐✈❡ ❛s❤ tr❡❡ ❜❛s❛❧ ❛r❡❛ ✐♥ ◆❡✇ ❨♦r❦ ❙t❛t❡ ✇❛s ♣r♦✈✐❞❡❞ ❜② ❇❛rr②
❲✐❧s♦♥ ♦❢ t❤❡ ❯❙ ❋♦r❡st ❙❡r✈✐❝❡✳ ❚❤❡ r❛st❡r ✐s ❛ ❝♦♠❜✐♥❛t✐♦♥ ♦❢ t❤❡ ❜❛s❛❧ ❛r❡❛s ♦❢ ❛❧❧ t❤❡ ❛s❤
tr❡❡ s♣❡❝✐❡s ✐♥ t❤❡ st❛t❡✳ ❚❤✐s ❞❛t❛ ✇❛s ❣❛t❤❡r❡❞ ✉s✐♥❣ r❡♠♦t❡ s❡♥s✐♥❣ t❡❝❤♥♦❧♦❣② ✉s✐♥❣ ❛
♠❡t❤♦❞♦❧♦❣② ❞❡s❝r✐❜❡❞ ✐♥ ❛ ✷✵✶✷ ♣❛♣❡r ❜② ❲✐❧s♦♥ ❡t✳ ❛❧✳ ❬✷✵✶✷❪ ❚❤❡ r❛st❡r ✐s ❤✐❣❤ r❡s♦❧✉t✐♦♥
✇✐t❤ ❛ ♣✐①❡❧ s✐③❡ ♦❢ ✷✺✵♠ ❜② ✷✺✵♠✳ ❚❤❡ r❛st❡r ✈❛❧✉❡s ❛r❡ ✐♥ sq✉r❛r❡ ❢❡❡t ♣❡r ❛❝r❡ r❛♥❣❡❞
❢r♦♠ ✵ t♦ ✻✻✳
❈❛♠♣❣r♦✉♥❞ ❧♦❝❛t✐♦♥ ❞❛t❛ ✇❛s ❣❛t❤❡r❡❞ ❢r♦♠ s❡✈❡r❛❧ ♦♥❧✐♥❡ s♦✉r❝❡s✳
Pr✐✈❛t❡ ❝❛♠♣✲
❣r♦✉♥❞ ❛❞❞r❡ss❡s ✇❡r❡ ❝♦❧❧❡❝t❡❞ ❢r♦♠ ❛ ❧✐st ❢♦✉♥❞ ♦♥ t❤❡ ◆❡✇ ❨♦r❦ ❱✐s✐t♦rs ◆❡t✇♦r❦ ✇❡❜s✐t❡✳
❬✏❙❡❛r❝❤ ❢♦r ❝❛♠♣❣r♦✉♥❞s✑ ❪ ❊❛❝❤ ❛❞❞r❡ss ✇❛s ❣❡♦❝♦❞❡❞ ❜❛s❡❞ ♦♥ ❛❞❞r❡ss✱ ✇✐t❤ ✷✺✾ ♠❛t❝❤❡s✱
✷ t✐❡s✱ ❛♥❞ ✶✽ ✉♥♠❛t❝❤❡❞✳ P✉❜❧✐❝ ❝❛♠♣❣r♦✉♥❞s ✇❡r❡ ❣❛t❤❡r❡❞ ❢r♦♠ t✇♦ s♦✉r❝❡s✿ ❚❤❡ ◆❨❙
❉❡♣❛rt♠❡♥t ♦❢ P❛r❦s ❛♥❞ ❘❡❝r❡❛t✐♦♥ ❛♥❞ t❤❡ ◆❨❙ ❉❊❈✳ ❆ ♣✉❜❧✐❝❧② ❛✈❛✐❧❛❜❧❡ ❧✐st ♦❢ ❝❛♠♣✲
❣r♦✉♥❞ str❡❡t ❛❞❞r❡ss❡s ❢r♦♠ ❚❤❡ ❉❡♣❛rt♠❡♥t ♦❢ P❛r❦s ❛♥❞ ❘❡❝r❡❛t✐♦♥ ✇❛s ❣❡♦❝♦❞❡❞ ✇✐t❤
✺✷ ♠❛t❝❤❡s✱ ✷ t✐❡s✱ ❛♥❞ ✶✵ ✉♥♠❛t❝❤❡❞✳ ❚❤❡ ❉❊❈ ♣r♦✈✐❞❡s ❛ ❑▼❩ ✜❧❡ ♦❢ ❝❛♠♣❣r♦✉♥❞s ✇❤✐❝❤
❝♦♥t❛✐♥s s♣❛t✐❛❧ ✐♥❢♦r♠❛t✐♦♥ ❢♦r ❡❛❝❤ ♦❢ t❤❡ ✺✷ ❝❛♠♣❣r♦✉♥❞s✳ ❚❤✐s ❞❛t❛ ✇❛s ✐♠♣♦rt❡❞ ✉s✐♥❣
t❤❡ ✏❋r♦♠ ❑▼▲✑ t♦♦❧ ✐♥ ❆r❝❚♦♦❧❜♦①✳ ■♥ t♦t❛❧✱ t❤❡s❡ ❞❛t❛ s❡ts ②✐❡❧❞❡❞ s♣❛t✐❛❧ ✐♥❢♦r♠❛t✐♦♥
❢♦r ✸✻✼ ♣✉❜❧✐❝ ❛♥❞ ♣r✐✈❛t❡ ❝❛♠♣❣r♦✉♥❞s ✐♥ ◆❡✇ ❨♦r❦ ❙t❛t❡✳
❚❤❡ ❝❛♠♣❣r♦✉♥❞ str❡❡t ❛❞❞r❡ss❡s ✇❡r❡ ❣❡♦❝♦❞❡❞ ✉s✐♥❣ t❤❡ ◆♦rt❤ ❆♠❡r✐❝❛ ●❡♦❝♦❞❡ ❙❡r✲
✈✐❝❡✳ ▼❛♥✉❛❧ ♠❛t❝❤✐♥❣ ✇❛s ❛tt❡♠♣t❡❞ ❢♦r ❛❧❧ ✉♥♠❛t❝❤❡❞ ❛❞❞r❡ss❡s✳ ❚❤❡ ❘♦♦❢❚♦♣ ❧♦❝❛t♦r
✇❛s ✉s❡❞ ❢♦r t❤✐s ♣✉r♣♦s❡ ✇❤❡♥ ♣♦ss✐❜❧❡✱ ♦t❤❡r✇✐s❡ t❤❡ ❙tr❡❡ts ❧♦❝❛t♦r ✇❛s ✉s❡❞✳ ■t s❤♦✉❧❞
❜❡ ♥♦t❡❞ t❤❛t ❛♥② ❝❛♠♣❣r♦✉♥❞s ♠❛t❝❤❡❞ ✇✐t❤ t❤❡ ❙tr❡❡ts ❧♦❝❛t♦r ♠❛② ❜❡ s❧✐❣❤t❧② ✐♥❛❝❝✉r❛t❡
s✐♥❝❡ t❤✐s ❧♦❝❛t♦r ❛ss✐❣♥s s♣❛t✐❛❧ ❝♦♦r❞✐♥❛t❡s ❜❛s❡❞ ♦♥ t❤❡ ❣✐✈❡♥ str❡❡t✱ ♥♦t t❤❡ ♠♦r❡ s♣❡❝✐✜❝
❤♦✉s❡ ♥✉♠❜❡r ♦♥ t❤❡ str❡❡t✳
✹
●❡♦❝♦❞✐♥❣ ♣r♦❞✉❝❡❞ t❤r❡❡ ♣♦✐♥t ❢❡❛t✉r❡ ❝❧❛ss❡s ❝♦♥t❛✐♥✐♥❣ ❝❛♠♣❣r♦✉♥❞ ❧♦❝❛t✐♦♥s✳ ❊❛❝❤
❢❡❛t✉r❡ ❝❧❛ss ✇❛s ❝♦♥✈❡rt❡❞ t♦ ❛ r❛st❡r ✇✐t❤ t❤❡ s❛♠❡ ❣❡♦❣r❛♣❤✐❝ ❝♦♦r❞✐♥❛t❡ s②st❡♠✱ ❝❡❧❧ s✐③❡✱
❛♥❞ ❝❡❧❧ ❛❧✐❣♥♠❡♥t ❛s t❤❡ ❛s❤ tr❡❡ ❜❛s❛❧ ❛r❡❛ r❛st❡r ❧❛②❡r✳ ❚❤❡ t❤r❡❡ r❡s✉❧t✐♥❣ ❧❛②❡rs ✇❡r❡
♠❡r❣❡❞ ❛♥❞ r❡❝❧❛ss✐✜❡❞ ✐♥t♦ ❛ ❜♦♦❧❡❛♥ r❛st❡r ✐♥❞✐❝❛t✐♥❣ t❤❡ ♣r❡s❡♥❝❡ ♦❢ ❝❛♠♣❣r♦✉♥❞s ✐♥ t❤❡
st❛t❡✳ ■♥ t❤❡ ✜♥❛❧ ❜♦♦❧❡❛♥ ❧❛②❡r✱ t❤❡r❡ ✇❡r❡ ✷✹✸ ❝❡❧❧s ❝♦♥t❛✐♥✐♥❣ ♦♥❡ ♦r ♠♦r❡ ❝❛♠♣❣r♦✉♥❞s
✇✐t❤✐♥ t❤❡♠✳
❲❡ ❞❡r✐✈❡❞ ❛ ❝♦✉♥t② ❧❡✈❡❧ ♣♦♣✉❧❛t✐♦♥ r❛st❡r ❧❛②❡r ✇✐t❤ t❤❡ s❛♠❡ ♣✐①❡❧ s✐③❡ ❛♥❞ ❛❧✐❣♥♠❡♥t
❛s t❤❡ ❛s❤ tr❡❡ ❜❛s❛❧ ❛r❡❛ r❛st❡r ❢r♦♠ ❞❛t❛ ♣r♦✈✐❞❡❞ ✐♥ ▼❛st❡r✐♥❣ ❆r❝●■❙ ❜② ▼❛r✐❜❡t❤ Pr✐❝❡✳
❬✷✵✶✷❪ ❚❤❡
❝♦✉♥t✐❡s
♣♦❧②❣♦♥ ❢❡❛t✉r❡ ❝❧❛ss ❝♦♥t❛✐♥❡❞ ❛ ✜❡❧❞ ❢♦r ♣♦♣✉❧❛t✐♦♥ ♣❡r sq✉❛r❡ ♠✐❧❡✳
❚❤✐s ✇❛s ❝♦♥✈❡rt❡❞ ✐♥t♦ ❛ r❛st❡r ♦❢ ♣♦♣✉❧❛t✐♦♥ ♣❡r ✷✺✵♠✷ ✳
❋✐♥❛❧❧②✱ ❛ r❛st❡r ❧❛②❡r ♦❢ ✷✵✶✷ ✐♥❢❡st❛t✐♦♥ s✐t❡s ✇❛s ❝r❡❛t❡❞ ❜② ❞✐❣✐t✐③✐♥❣ ❛ ♠❛♣ ♣r♦✈✐❞❡❞
❜② t❤❡ ◆❡✇ ❨♦r❦ ❙t❛t❡ ❉❡♣❛rt♠❡♥t ♦❢ ❊♥✈✐r♦♥♠❡♥t❛❧ ❈♦♥s❡r✈❛t✐♦♥✳ ✭❋✐❣✉r❡ ✶✮ ❚❤❡ ♠❛♣
✇❛s ♠❛♥✉❛❧❧② ❞✐❣✐t✐③❡❞ ❜② ♣❧❛❝✐♥❣ ♣♦✐♥ts ✐♥t♦ ❛ ❢❡❛t✉r❡ ❝❧❛ss r♦✉❣❤❧② ❛t t❤❡ s❛♠❡ ❧♦❝❛t✐♦♥s
❛s t❤❡ ♣♦✐♥ts ♦♥ t❤❡ ♠❛♣✳ ❚❤✐s ❢❡❛t✉r❡ ❝❧❛ss ✇❛s t❤❡♥ ❝♦♥✈❡rt❡❞ ✐♥t♦ ❛ r❛st❡r ✇✐t❤ t❤❡ s❛♠❡
❝❡❧❧ s✐③❡ ❛♥❞ ❡①t❡♥t ❛s t❤❡ ❛s❤ tr❡❡ ❜❛s❛❧ ❛r❡❛ ❧❛②❡r s♦ ✐t ❝♦✉❧❞ ❜❡ ❢❡❞ ✐♥t♦ t❤❡ ♠♦❞❡❧ ❛s ✐♥♣✉t✳
✸
❚❤❡ ▼♦❞❡❧
❖✉r ♠♦❞❡❧ ✐s ❜❛s❡❞ ♦♥ ❛ ❣r✐❞ ♦❢ ✷✺✵♠ ❜② ✷✺✵♠ ❝❡❧❧s t❤❛t r❡♣r❡s❡♥t ◆❡✇ ❨♦r❦ ❙t❛t❡✳ ❊❛❝❤
❝❡❧❧ ❤♦❧❞s ❞❛t❛ r❡❣❛r❞✐♥❣ t❤❡ ❛s❤ tr❡❡ ❜❛s❛❧ ❛r❡❛✱ ❡①✐st❡♥❝❡ ♦❢ ❝❛♠♣❣r♦✉♥❞s✱ ✐♥❢❡❝t❡❞ st❛t✉s✱
❛♥❞ ♣♦♣✉❧❛t✐♦♥ ✇✐t❤✐♥ ✐t✳ ❊❛❝❤ t✐♠❡st❡♣ t❤❡ st❛t✉s ♦❢ ❡❛❝❤ ❝❡❧❧ ✐s ❞❡t❡r♠✐♥❡❞ ❜② t❤❡ st❛t✉s ♦❢
t❤❡ ♦t❤❡r ❝❡❧❧s ❛r♦✉♥❞ ✐t✳ ❋♦r ❡①❛♠♣❧❡✱ ✐❢ ❛ ❝❡❧❧ ✐s ♥❡①t t♦ ❛♥ ✐♥❢❡❝t❡❞ ❝❡❧❧✱ ✐t ❤❛s ❛ ♣r♦❜❛❜✐❧✐t②
♦❢ ❜❡✐♥❣ ✐♥❢❡❝t❡❞ ✐ts❡❧❢✳ ■♥ t❤✐s ♠❛♥♥❡r✱ ✇❡ ❝❛♥ ♠♦❞❡❧ t❤❡ s♣❛t✐❛❧ ❞✐♣❡rs✐♦♥ ♣❛tt❡r♥s ♦❢ t❤❡
❊❆❇✳
❚❤❡ ♠♦❞❡❧ ✐s ✐♥✐t✐❛❧✐③❡❞ ❜② ✐♥❢❡❝t✐♥❣ ❡❛❝❤ ❝❡❧❧ ✐♥ t❤❡ ✐♥✐t✐❛❧❧② ✐♥❢❡st❡❞ ③♦♥❡s ❛s ❣✐✈❡♥ ❜②
t❤❡ ✐♥♣✉t ❞❛t❛✳ ❊✈❡r② t✐♠❡st❡♣✱ ❡❛❝❤ ✐♥❢❡❝t❡❞ ❝❡❧❧ ✐s ✐♥s♣❡❝t❡❞ ❛♥❞ t❤❡ ✐♥❢❡❝t✐♦♥ ♣r♦❜❛❜✐❧✐t②
p ❢♦r ❡❛❝❤ ♥❡✐❣❤❜♦r ✐s ❝❛❧❝✉❧❛t❡❞✳ ❆ r❛♥❞♦♠ ♥✉♠❜❡r r ❜❡t✇❡❡♥ 0 ❛♥❞ 1 ✐s ❣❡♥❡r❛t❡❞✳ ■❢
✺
r < p✱ t❤❡♥ t❤❡ ♥❡✐❣❤❜♦r✐♥❣ ❝❡❧❧ ✐s ✐♥❢❡❝t❡❞✳ ◆♦t❡ t❤❛t ✐❢ ❛♥ ✉♥✐♥❢❡❝t❡❞ ❝❡❧❧ ❤❛s ♠✉❧t✐♣❧❡
♥❡❛r❜② ♥❡✐❣❤❜♦rs ✇❤♦ ❛r❡ ✐♥❢❡❝t❡❞✱ ✐t ❤❛s ♠✉❧t✐♣❧❡ ❝❤❛♥❝❡s ♦❢ ❜❡✐♥❣ ✐ts❡❧❢ ✐♥❢❡❝t❡❞✳ ❲❤❡♥ ❛❧❧
✐♥❢❡❝t❡❞ ❝❡❧❧s ❤❛✈❡ ❜❡❡♥ ✐♥s♣❡❝t❡❞✱ t❤❡ t✐♠❡st❡♣ ✐s ♦✈❡r ❛♥❞ t❤❡ ♣r♦❝❡ss r❡♣❡❛ts✳
❚❤❡ ♣r♦❜❛❜✐❧✐t② ❛♥ ✐♥❢❡st❡❞ ❝❡❧❧ ✐♥❢❡❝t✐♥❣ ❛ ♥❡❛r❜② ♥❡✐❣❤❜♦r ✐s ❝❛❧❝✉❧❛t❡❞ ❛s ❢♦❧❧♦✇s✳ ❲❡
❛ss✉♠❡ t❤❛t t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ ✐♥❢❡❝t✐♦♥ ❞❡❝❧✐♥❡s ❡①♣♦♥❡♥t✐❛❧❧② ❛s ❞✐st❛♥❝❡ t♦ t❤❡ ✐♥❢❡❝t❡❞
❝❡❧❧ ✐♥❝r❡❛s❡s✳ ❙♣❡❝✐✜❝❛❧❧②✱ ✐♥ ♦✉r ♠♦❞❡❧ t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ ❛♥ ✐♥❢❡❝t❡❞ ❝❡❧❧ ❛t x✱ y ✐♥❢❡❝t✐♥❣
❛ ❝❡❧❧ ❛t i✱ j ✐s ❣✐✈❡♥ ❜②
P1 =
Ax,y · Ai,j · Bx,y · C1
D x1
✇❤❡r❡ Ax,y ✐s t❤❡ ❛❜✉♥❞❛♥❝❡ ♦❢ ❛s❤ tr❡❡s ✐♥ t❤❡ ✐♥❢❡❝t❡❞ ❝❡❧❧✱ Ai,j ✐s t❤❡ ❛❜✉♥❞❛♥❝❡ ♦❢
❛s❤ tr❡❡s ✐♥ t❤❡ ♥♦♥✐♥❢❡❝t❡❞ ❝❡❧❧✱ ❛♥❞ Bx,y ✐s t❤❡ ❧❡✈❡❧ ♦❢ ❊❆❇ ✐♥❢❡st❛t✐♦♥ ✐♥ t❤❡ ✐♥❢❡❝t❡❞ ❝❡❧❧✳
D ✐s t❤❡ ❊✉❝❧✐❞✐❛♥ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ t❤❡ ✐♥❢❡❝t❡❞ ❛♥❞ ♥♦♥✐♥❢❡❝t❡❞ ❝❡❧❧s✱ ♠❡❛s✉r❡❞ ✐♥ ✉♥✐ts
♦❢ r❛st❡r ❣r✐❞ ❝❡❧❧s✳ ❚❤❡ r❛t❡ ❛t ✇❤✐❝❤ t❤❡ ♣r♦❜❛❜✐❧✐t② ❢❛❧❧s ♦✛ ❛ ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ ❞✐st❛♥❝❡
❝❛♥ ❜❡ ❝♦♥tr♦❧❧❡❞ ❜② t❤❡ x ♣❛r❛♠❡t❡r✳ ❋✐♥❛❧❧②✱ C ✐s ❛♥ ♦✈❡r❛❧❧ ♠✉❧t✐♣❧✐❡r ✉s❡❞ t♦ ❛❞❥✉st t❤❡
♣r♦❜❛❜✐❧✐t✐❡s ❢♦r ❛❧❧ ❝❡❧❧s✳ ❚❤❡ ♣❛r❛♠❡t❡rs x1 ❛♥❞ C1 ❛r❡ ✜tt❡❞ ❡♠♣✐r✐❝❛❧❧② ❜❛s❡❞ ♦♥ tr✐❛❧ r✉♥s
♦❢ t❤❡ ♠♦❞❡❧ t♦ ❡♥s✉r❡ t❤❛t t❤❡ ✐♥❢❡❝t✐♦♥ s♣r❡❛❞s ❛t 20 km/yr✱ t❤❡ ❡♠♣✐r✐❝❛❧ s♣r❡❛❞ r❛t❡ ❛s
❡st✐♠❛t❡❞ ❜② ■✈❡r♦♥✱ ❡t✳ ❛❧✳ ❬✷✵✶✵❪
❚❤❡ ❛s❤ tr❡❡ ❛❜✉♥❞❛♥❝❡ ✈❛r✐❛❜❧❡s Ax,y ❛♥❞ Ai,j r❛♥❣❡ ❢r♦♠ ✵ t♦ ✶ ❛♥❞ ❛r❡ ❞❡r✐✈❡❞ ❢r♦♠
t❤❡ ❛s❤ tr❡❡ ❜❛s❛❧ ❛r❡❛ r❛st❡r ❧❛②❡r✳ ❚❤❡ ❜❛s❛❧ ❛r❡❛ ✐♥ t❤❡ ❛♣♣r♦♣r✐❛t❡ ❝❡❧❧ ✐s ❞✐✈✐❞❡❞ ❜② t❤❡
♠❛①✐♠✉♠ ❜❛s❛❧ ❛r❡❛ ✐♥ t❤❡ r❛st❡r ✐♥ ♦r❞❡r t♦ ❛rr✐✈❡ ❛t ❛ ♥♦r♠❛❧✐③❡❞ ✈❛❧✉❡ ❢♦r ❛s❤ tr❡❡ ❜❛s❛❧
❛r❡❛ t❤❛t ✐s ✉s❡❞ ✐♥ t❤❡ ♣r♦❜❛❜✐❧✐t② ❝❛❧❝✉❧❛t✐♦♥s✳
❚❤❡ ❛❜♦✈❡ ❡q✉❛t✐♦♥ ❣✐✈❡s t❤❡ ♣r♦❜❛❜✐❧✐t② ❜❡t✇❡❡♥ ❛♥② t✇♦ ❝❡❧❧s ♦♥ t❤❡ ❣r✐❞✳ ■♥ ♦r❞❡r t♦
s❛✈❡ ❝♦♠♣✉t❛t✐♦♥❛❧ t✐♠❡✱ ❡❛❝❤ ✐♥❢❡❝t❡❞ ❝❡❧❧ ❞♦❡s ♥♦t tr② t♦ ✐♥❢❡❝t ❡✈❡r② ♦t❤❡r ❝❡❧❧ ♦♥ t❤❡ ❣r✐❞
s✐♥❝❡ t❤❡ ♣r♦❜❛❜✐❧✐t② ❢❛❧❧s ♦✛ ❡①♣♦♥❡♥t✐❛❧❧② ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ ❞✐st❛♥❝❡✳ ❘❛t❤❡r✱ ❡❛❝❤ ✐♥❢❡❝t❡❞
❝❡❧❧ ✐♥s♣❡❝ts ❛ ▼♦♦r❡ ♥❡✐❣❤❜♦r❤♦♦❞ ♦❢ r❛♥❣❡ ♥✐♥❡ ❝❡♥t❡r❡❞ ❛r♦✉♥❞ t❤❡ ✐♥❢❡❝t❡❞ ❝❡❧❧✳ ❆s s✉❝❤✱
❛♥ ✐♥❢❡❝t❡❞ ❝❡❧❧ ❝♦✉❧❞ ✐♥❢❡❝t ❛♥♦t❤❡r ❝❡❧❧ ❛t ♠❛①✐♠✉♠ ✸✳✶✽ ❦✐❧♦♠❡t❡rs ❛✇❛②✳ ❇② r❡str✐❝t✐♥❣ t❤❡
✻
❝❡❧❧s t❤❛t ❛r❡ ❝♦♥s✐❞❡r❡❞ ❢♦r ✐♥❢❡❝t✐♦♥ t❤❡ r✉♥♥✐♥❣ t✐♠❡ ♦❢ t❤❡ ♠♦❞❡❧ ✐s s✐❣♥✐✜❝❛♥t❧② r❡❞✉❝❡❞✳
❊❛❝❤ ✐♥❢❡❝t❡❞ ❝❡❧❧ ❝❛♥ ❛❧s♦ ✐♥❢❡❝t ❞✐st❛♥t ✉♥✐♥❢❡❝t❡❞ ❝❡❧❧s t❤❛t ❤♦✉s❡ ❝❛♠♣❣r♦✉♥❞s✳ ❚❤❡
♣r♦❜❛❜✐❧✐t② ♦❢ ✐♥❢❡❝t✐♦♥ ✐s r❡❧❛t❡❞ t♦ t❤❡ ❛s❤ ❛❜✉♥❞❛♥❝❡ ✐♥ ❡❛❝❤ ❝❡❧❧✱ t❤❡ ❧❡✈❡❧ ♦❢ ❊❆❇ ✐♥❢❡s✲
t❛t✐♦♥ ✐♥ t❤❡ ✐♥❢❡❝t❡❞ ❝❡❧❧✱ ❛♥❞ t❤❡ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ ❝❡❧❧s✱ ❛♥❞ t❤❡ ♣♦♣✉❧❛t✐♦♥ ✐♥ t❤❡ ✐♥❢❡❝t❡❞
❝❡❧❧✳ ■t ✐s ❛ss✉♠❡❞ t❤❛t ❛ ❝♦♥st❛♥t ♣❡r❝❡♥t❛❣❡ ♦❢ ✐♥❞✐✈✐❞✉❛❧s ✐♥ t❤❡ ♣♦♣✉❧❛t✐♦♥ ❛r❡ ❝❛♠♣❡rs❀
t❤❛t ✐s✱ t❤❡② ❛ ❝♦♥st❛♥t ♣❡r❝❡♥t❛❣❡ ♦❢ ✐♥❞✐✈✐❞✉❛❧s ✇❤♦ ♠❛② s♣r❡❛❞ t❤❡ ❊❆❇ ❜② ♠♦✈✐♥❣
✜r❡✇♦♦❞ t♦ ❛ ❝❛♠♣❣r♦✉♥❞✳
❚❤✉s✱ t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ ❛♥ ✐♥❢❡❝t❡❞ ❝❡❧❧ ❛t x✱ y ✐♥❢❡❝t✐♥❣ ❛ ❝❛♠♣❣r♦✉♥❞ ❝❡❧❧ ❛t i✱ j ✐s
❣✐✈❡♥ ❜②
P2 =
P opx,y · Ax,y · Ai,j · Bx,y · C2
D x2
❲❤❡r❡ P opx,y ✐s t❤❡ ♥♦r♠❛❧✐③❡❞ ♣♦♣✉❧❛t✐♦♥ ❛t x✱ y ✱ ❛♥❞ t❤❡ ♦t❤❡r ♣❛r❛♠❡t❡rs ❛r❡ s✐♠✐❧❛r
t♦ t❤♦s❡ ✐♥ P1 ✳ ❚❤❡ ❡♠♣✐r✐❝❛❧❧② ❞❡r✐✈❡❞ ♣❛r❛♠❡t❡rs x2 ❛♥❞ C2 ❛r❡ ❞✐✛❡r❡♥t ✐♥ ♦r❞❡r t♦ ❛❝❝♦✉♥t
❢♦r t❤❡ ❞✐✛❡r❡♥t ❞✐s♣❡rs✐♦♥ ❞②♥❛♠✐❝s ♦❢ ❝❛♠♣❡rs tr❛✈❡❧✐♥❣ t♦ ❝❛♠♣❣r♦✉♥❞s✳
✹
❘❡s✉❧ts
❚❤❡ ♠♦❞❡❧ ✇❛s r✉♥ ❢♦r ✶✷✵ t✐♠❡st❡♣s✳ ❚✇❡❧✈❡ t✐♠❡st❡♣s ✐s ❡q✉✐✈❛❧❡♥t t♦ ♦♥❡ ②❡❛r❀ t❤✉s✱
t❤❡ r❡s✉❧ts ❝♦✈❡r ✶✵ ②❡❛rs ❢r♦♠ r♦✉❣❤❧② ✷✵✶✷✲✷✵✷✷✳ ❚❤❡ ✈❛❧✉❡s ✉s❡❞ ❢♦r t❤❡ ♠♦❞❡❧ ♣❛r❛♠❡t❡rs
❛r❡ ❧✐st❡❞ ✐♥ ❋✐❣✉r❡ ✶✳
❚■❋ ❘❛st❡rs ✇❡r❡ ❣❡♥❡r❛t❡❞ ❡✈❡r② t✇❡❧✈❡ t✐♠❡st❡♣s ❛♥❞ ✐♠♣♦rt❡❞ ✐♥t♦ ❆r❝●■❙ ♦♥ ❲✐♥✲
❞♦✇s ✼ ❢♦r ❛♥❛❧②s✐s✳ ❚❤❡ ♦✉t♣✉t r❛st❡rs ✇❡r❡ ❣❡♦r❡❢❡r❡♥❝❡❞ ❜② r❡s✐③✐♥❣ ❛♥❞ s❤✐❢t✐♥❣ t❤❡
r❛st❡r t♦ ✐ts ❝♦rr❡❝t s♣❛t✐❛❧ ❧♦❝❛t✐♦♥✳ ❆♥ ❆r❝▼❛♣ ♠♦❞❡❧ ✇❛s ❞❡✈❡❧♦♣❡❞ t♦ ❢❛❝✐❧✐t❛t❡ t❤❡
❣❡♦r❡❢❡r❡♥❝✐♥❣ ♦❢ t❤❡ ♦✉t♣✉t r❛st❡rs✳ ✭❋✐❣✉r❡ ✷✮
✼
✺
▼❛♣s
❙❡✈❡r❛❧ ♠❛♣s ✇❡r❡ ♣r♦❞✉❝❡❞ ✐♥ ♦r❞❡r t♦ ✈✐s✉❛❧✐③❡ t❤❡ r❡s✉❧ts ♦❢ t❤❡ ♠♦❞❡❧✳ ❋✐rst✱ ❛ ♠❛♣
✇❛s ♣r♦❞✉❝❡❞ s❤♦✇✐♥❣ t❤❡ ❡①t❡♥t ♦❢ t❤❡ ✐♥❢❡st❛t✐♦♥ ♣❡r ②❡❛r ✭❋✐❣✉r❡ ✹✮✳ ❚❤❡ ♠♦❞❡❧ ♦✉t♣✉t
❧❛②❡rs ✇❡r❡ ❡❛❝❤ ❣✐✈❡♥ ❛ ❞✐✛❡r❡♥t ❝♦❧♦r ❛♥❞ ❧❛②❡r❡❞ ♦♥ t♦♣ ♦❢ ❡❛❝❤ ♦t❤❡r✳ ❚❤❡ ❝♦❧♦rs ✇❡r❡
❝❤♦s❡♥ s✉❝❤ t❤❛t t❤❡ ❡❛r❧✐❡st ✐♥❢❡❝t❡❞ ③♦♥❡s ✇❡r❡ t❤❡ ❜r✐❣❤t❡st s❤❛❞❡ ♦❢ r❡❞✳ ❆s t❤❡ ✐♥❢❡st❛t✐♦♥
❜❡❝❛♠❡ ♥❡✇❡r✱ t❤❡ ❝♦❧♦r t❛♣❡r❡❞ ♦✛ ✉♥t✐❧ ✐t ✇❛s ♥❡❛r❧② ✇❤✐t❡✳ ❚❤❡ ✐♥✐t✐t✐❛❧ ✐♥❢❡st❛t✐♦♥ ❝❡❧❧s
✇❡r❡ ❞❡♥♦t❡❞ ♦♥ t❤❡ ♠❛♣ ❜② ♣♦✐♥t ♠❛r❦❡rs✳
❆❞❞✐t✐♦♥❛❧ ♠❛♣s ✇❡r❡ ❝r❡❛t❡❞ s❤♦✇✐♥❣ t❤❡ ❡①t❡♥t ♦❢ t❤❡ ✐♥❢❡st❛t✐♦♥ ♦♥ ②❡❛rs ✷✱ ✺✱ ❛♥❞ ✶✵✳
❊❛❝❤ ❝❡❧❧ ✐s ❝♦✈❡r❡❞ ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ❧❡✈❡❧ ♦❢ ❊❆❇ ✐♥❢❡st❛t✐♦♥ ✐♥ t❤❛t ❝❡❧❧✳ ❆s ✐♥ t❤❡ ♣r❡✈✐♦✉s
♠❛♣✱ ♣♦✐♥t ♠❛r❦❡rs ❛r❡ ❛❞❞❡❞ t♦ ✐♥❞✐❝❛t❡ t❤❡ ❧♦❝❛t✐♦♥ ♦❢ t❤❡ ✐♥✐t✐❛❧ ✐♥❢❡st❛t✐♦♥s✳
✻
❉✐s❝✉ss✐♦♥
❆❝❝♦r❞✐♥❣ t♦ t❤❡ ♠♦❞❡❧✱ ❛❢t❡r t❡♥ ②❡❛rs✱ t❤❡ ❊❆❇ ✐♥❢❡st❛t✐♦♥ ❤❛s s♣r❡❛❞ ❢r♦♠ t❤❡ ✐♥✐t✐❛❧
✐♥❢❡❝t❡❞ s✐t❡s t♦ ❝♦✈❡r ♠♦st ♦❢ s♦✉t❤❡r♥ ◆❡✇ ❨♦r❦✳ ❆t t❤✐s ♣♦✐♥t✱ t❤❡ ✐♥❢❡st❛t✐♦♥ ✐s st✐❧❧
s♣r❡❛❞✐♥❣ t♦✇❛r❞s t❤❡ ♥♦rt❤❡r♥ r❡❣✐♦♥ ♦❢ t❤❡ st❛t❡✳ ■♥ ❣❡♥❡r❛❧✱ t❤❡ ✐♥❢❡❝t✐♦♥ s♣r❡❛❞s t❤r♦✉❣❤
❧♦❝❛❧ ✐♥s❡❝t ✢✐❣❤t ✇✐t❤ ♣❡r✐♦❞✐❝ ❤♦♣s t♦ ♥❡✇ ❛r❡❛s ❢❛❝✐❧✐t❛t❡❞ ❜② ❝❛♠♣❣r♦✉♥❞s✳ ❲❡ ❝❛♥ s❡❡
❛♥ ❡①❛♠♣❧❡ ♦❢ t❤✐s ✐♥ ❋✐❣✉r❡ ✹✱ ✇❤❡r❡ ❛ s♠❛❧❧ r❡❣✐♦♥ ✐♥ ♥♦rt❤❡r♥ ◆❡✇ ❨♦r❦ ✐s ✐♥❢❡❝t❡❞ ❞✉❡
t♦ t❤❡ ♣r❡s❡♥❝❡ ♦❢ ❛ ❝❛♠♣❣r♦✉♥❞✳
❍♦✇ ❛❝❝✉r❛t❡ ❛r❡ ♦✉r r❡s✉❧ts❄ ❲❡ ❝❛♥ ✐❞❡♥t✐❢② s♦♠❡ s♦✉r❝❡s ♦❢ ❡rr♦r ❜② ❡①❛♠✐♥✐♥❣
t❤❡ ♠♦❞❡❧✬s ❝♦r❡ ❛ss✉♠♣t✐♦♥s✳ ▼♦❞❡❧s ❛r❡ ❢✉♥❞❛♠❡♥t❛❧❧② ❜❛s❡❞ ♦♥ ❛ s❡r✐❡s ♦❢ ❛ss✉♠♣t✐♦♥s
❛❜♦✉t ❤♦✇ t❤❡ st✉❞② s✉❜❥❡❝t ❢✉♥❝t✐♦♥s✳ ❚❤❡ ❛❝❝✉r❛❝② ♦❢ t❤❡s❡ ✉♥❞❡r❧②✐♥❣ ❛ss✉♠♣t✐♦♥s ❝❛♥
❜❡ t❡st❡❞ ❜② ❝♦♠♣❛r✐♥❣ t❤❡ ♦✉t♣✉t ♦❢ t❤❡ ♠♦❞❡❧ t♦ s❡❡ ✐❢ ✐t ♠❛t❝❤❡s ♦❜s❡r✈❛t✐♦♥❛❧ ❞❛t❛✳
❆s s✉❝❤✱ ♠♦❞❡❧s ❝❛♥ ❜❡ ❛ ✈❡r② ✉s❡❢✉❧ t♦♦❧ ❢♦r ❞✐s❝♦✈❡r✐♥❣ t❤❡ ✉♥❞❡r❧②✐♥❣ ❞②♥❛♠✐❝s ❞r✐✈✐♥❣
♦❜s❡r✈❛❜❧❡ ♣❤❡♥♦♠❡♥❛✳
❚❤❡ ✜rst ❛ss✉♠♣t✐♦♥ ♦❢ t❤❡ ♠♦❞❡❧ ✐s t❤❛t t❤❡ ❊❆❇ ❞✐s♣❡rs❡s ❧♦❝❛❧❧② ❜② ✐♥s❡❝t ✢✐❣❤t✳
✽
❲❡ ❞❡✈❡❧♦♣❡❞ ❛ ♠♦❞❡❧ ❢r❛♠❡✇♦r❦ t❤❛t ❛❧❧♦✇s ❢♦r s✉❝❤ s♣r❡❛❞ t❤r♦✉❣❤ ❛ t②♣❡ ♦❢ ❝❡❧❧✉❧❛r
❛✉t♦♠❛t❛ ♠♦❞❡❧✳ ❙✐♥❝❡ ✇❡ ✇❡r❡ ❛❜❧❡ t♦ ❝❛❧✐❜r❛t❡ t❤✐s ♠♦❞❡❧ t♦ r❡s✉❧t ✐♥ ❛ ✷✵❦♠✴②❡❛r s♣r❡❛❞
♦❢ t❤❡ ✐♥❢❡st❛t✐♦♥ ❢r♦♥t ❛s ❤❛s ❜❡❡♥ ♦❜s❡r✈❡❞ ✐♥ t❤❡ ✇✐❧❞✱ ✐t ✐s r❡❛s♦♥❛❜❧❡ t♦ ❝♦♥❝❧✉❞❡ t❤❛t
t❤✐s ❛ss✉♠♣t✐♦♥ ✐s ✈❛❧✐❞✳ ❊①❛♠✐♥❛t✐♦♥ ♦❢ ♦t❤❡r ❛ss✉♠♣t✐♦♥s r❡✈❡❛❧ t❤❡ s❤♦rt❝♦♠✐♥❣s ♦❢ ♦✉r
♠♦❞❡❧✳
❉✉❡ t♦ t❤❡ ♥❛t✉r❡ ♦❢ ♦✉r ❞❛t❛ ✇❡ ❛r❡ ❢♦r❝❡❞ t♦ ♠❛❦❡ ❝❡rt❛✐♥ ❛ss✉♠♣t✐♦♥s ❛❜♦✉t t❤❡
❜❡❤❛✈✐♦✉r ♦❢ t❤❡ ❊❆❇✳ ❚❤❡ r❛st❡r ❞❛t❛s❡t ♦❢ ❛s❤ tr❡❡ ❜❛s❛❧ ❛r❡❛ r❡♣r❡s❡♥ts t❤❡ ❜❛s❛❧ ❛r❡❛
♦❢ ❛❧❧ s♣❡❝✐❡s ♦❢ ❛s❤ ✐♥ t❤❡ st❛t❡✳ ❆s s✉❝❤✱ ✇❡ ❛ss✉♠❡ t❤❛t t❤❡ ❜❡❡t❧❡ ❜❡❤❛✈❡s s✐♠✐❧❛r❧② ❢♦r
❛❧❧ s♣❡❝✐❡s✱ ✇❤✐❝❤ ✐s ♥♦t t❤❡ ❝❛s❡✳ ❇❡❡t❧❡s ♣r❡❢❡r❡♥t✐❛❧❧② ❛tt❛❝❦ s♦♠❡ s♣❡❝✐❡s ♦✈❡r ♦t❤❡rs✱ ❛♥❞
t❤❡ ❜❧✉❡ ❛s❤ tr❡❡s ❤❛✈❡ ❞✐s♣❧❛②❡❞ ❧✐♠✐t❡❞ r❡s✐st❛♥❝❡ t♦ t❤❡ ❜❡❡t❧❡✳ ❬❆♥✉❧❡✇✐❝③ ❡t ❛❧✳✱ ✷✵✵✼❪
❖♥❡ ♦❢ t❤❡ ❛ss✉♠♣t✐♦♥s ♦❢ t❤❡ ♠♦❞❡❧ ✐s t❤❛t ❝❛♠♣❡rs ♣r❡❢❡r❡♥t✐❛❧❧② ❝❤♦♦s❡ ❝❛♠♣❣r♦✉♥❞s
❝❧♦s❡r t♦ ❤♦♠❡✳ ❚❤✐s r❡str✐❝ts t❤❡ ❧♦♥❣ t❡r♠ s♣r❡❛❞ ♦❢ t❤❡ ❊❆❇✱ ❛s t❤❡ ✐♥❢❡st❛t✐♦♥ ❝❛♥ ❤♦♣
r❡❧❛t✐✈❡❧② s❤♦rt ❞✐st❛♥❝❡s ❜✉t ❝♦✉❧❞ ♥♦t✱ ❢♦r ❡①❛♠♣❧❡✱ ♠♦✈❡ ❛❧❧ t❤❡ ✇❛② ❛❝r♦ss t❤❡ st❛t❡ ✐♥ ❛
s✐♥❣❧❡ t✐♠❡st❡♣✳ ❚❤✐s ✐s t❤❡ r❡❛s♦♥ ✇❤② t❤❡ ✐♥❢❡st❛t✐♦♥ ❞♦❡s ♥♦t s♣r❡❛❞ ✐♥t♦ ◆♦rt❤❡r♥ ◆❡✇
❨♦r❦ ✐♥ ♦✉r r❡s✉❧ts✳ ❚❤❡ ❛❝❝✉r❛❝② ♦❢ t❤✐s ❛ss✉♠♣t✐♦♥ ✐s ✉♥❝❧❡❛r✳ ❋✉rt❤❡r r❡s❡❛r❝❤ ♠✉st ❜❡
❞♦♥❡ ✐♥t♦ t❤❡ ❜❡❤❛✈✐♦✉r ♦❢ ❝❛♠♣❡rs ✐♥ ◆❡✇ ❨♦r❦ ❙t❛t❡ ✐♥ ♦r❞❡r t♦ ✐♥❝♦r♣♦r❛t❡ t❤❡✐r tr❛✈❡❧✐♥❣
❜❡❤❛✈✐♦✉r ✐♥t♦ t❤❡ ❝❛❧✐❜r❛t✐♦♥ ♦❢ t❤❡ ♠♦❞❡❧✳ ❚❤✐s ✇♦✉❧❞ ❣r❡❛t❧② ✐♥❝r❡❛s❡ t❤❡ ❛❝❝✉r❛❝② ♦❢ t❤❡
♠♦❞❡❧✬s r❡s✉❧ts✳
❖❢ ❝♦✉rs❡✱ ♠♦✈✐♥❣ ✜r❡✇♦♦❞ ✐s ♥♦t t❤❡ ♦♥❧② ✇❛② ❤✉♠❛♥s ❛ss✐st t❤❡ ❞✐s♣❡rs✐♦♥ ♦❢ t❤❡
❊❆❇✳ ❚❤❡ ✐♥❢❡st❛t✐♦♥ ♠❛② ❛❧s♦ s♣r❡❛❞ ❜② ❤✐t❝❤❤✐❦✐♥❣ ♦♥ ❧♦❣❣✐♥❣ tr✉❝❦s ♦r ✇✐t❤ ♥✉rs❡r②
✐♥❞✉str② s❤✐♣♠❡♥ts✳ ❚❤❡s❡ ✈❡❝t♦rs ❛r❡ ❝✉rr❡♥t❧② ♥♦t ❛❝❝♦✉♥t❡❞ ❢♦r ✐♥ ♦✉r ♠♦❞❡❧✳ ❆ ♠♦r❡
❛❝❝✉r❛t❡ ✈❡rs✐♦♥ ✇♦✉❧❞ ✐♥t❡❣r❛t❡ ❞❛t❛ ♦♥ ✇♦♦❞ ❛♥❞ ♥✉rs❡r② ✐♥❞✉str② ❛❝t✐✈✐t② ✐♥ t❤❡ st❛t❡✳
❚r❛♥s♣♦rt❛t✐♦♥ ♥❡t✇♦r❦s ❝♦✉❧❞ ❛❧s♦ ❜❡ ✐♥t❡❣r❛t❡❞ ❛❧♦♥❣ ✇✐t❤ tr❛✣❝ ✐♥❢♦r♠❛t✐♦♥ ✐♥ ♦r❞❡r t♦
♠♦r❡ ❛❝❝✉r❛t❡❧② ♠♦❞❡❧ tr✉❝❦✐♥❣ ♣❛tt❡r♥s✳
❋✐♥❛❧❧②✱ ✇❡ ❛ss✉♠❡ t❤❛t t❤❡r❡ ✐s ♥♦ ♦r❣❛♥✐③❡❞ r❡s♣♦♥s❡ ❜② t❤❡ ❣♦✈❡r♥♠❡♥t t♦ t❤❡ s♣r❡❛❞
♦❢ t❤❡ ✐♥❢❡st❛t✐♦♥✳ ❆s s✉❝❤✱ ♦✉r ♠♦❞❡❧ s❤♦✇s ✇❤❛t ♠❛② ❤❛♣♣❡♥ ✇✐t❤♦✉t t❤❡ ✐♥t❡r❢❡r❡♥❝❡ ♦❢
❛♥② ♦✉ts✐❞❡ ❢♦r❝❡ tr②✐♥❣ t♦ ❦❡❡♣ t❤❡ ✐♥❢❡❝t✐♦♥ ❝♦♥t❛✐♥❡❞✳ ■♥ r❡❛❧✐t②✱ ✇❤✐❧❡ t❤❡ ❣♦✈❡r♥♠❡♥t
✾
❤❛s ❣✐✈❡♥ ✉♣ ♦♥ tr②✐♥❣ t♦ ❡r❛❞✐❝❛t❡ t❤❡ ❊❆❇✱ t❤❡② ❛r❡ ❛❝t✐✈❡❧② ♣✉rs✉❡✐♥❣ ♠❡t❤♦❞s ♦❢ s❧♦✇✐♥❣
❞♦✇♥ t❤❡ s♣r❡❛❞ ♦❢ t❤❡ ✐♥❢❡❝t✐♦♥✳
❚❤✉s✱ t❤❡ ♠♦❞❡❧ ❤❛s s❡✈❡r❛❧ s❤♦rt❝♦♠✐♥❣s✱ ❜♦t❤ ✐♥ s♦♠❡ ♦❢ t❤❡ ❛ss✉♠♣t✐♦♥s ✉s❡❞ t♦
❞❡✈❡❧♦♣ t❤❡ ♠♦❞❡❧ ❛s ✇❡❧❧ ❛s ❛s♣❡❝ts ♦❢ ❊❆❇ s♣r❡❛❞ ✐❣♥♦r❡❞ ❜② t❤❡ ♠♦❞❡❧✳ ❋✉rt❤❡r r❡s❡❛r❝❤
♠✉st ❜❡ ❞♦♥❡ t♦ ❞❡t❡r♠✐♥❡ t❤❡ ✈❛❧✐❞✐t② ♦❢ t❤❡ ❝♦r❡ ❛ss✉♠♣t✐♦♥s ♦❢ t❤❡ ♠♦❞❡❧❀ ❢✉rt❤❡r ❞❛t❛
♠✉st ❜❡ ❝♦❧❧❡❝t❡❞ ❛♥❞ ✐♥t❡❣r❛t❡❞ ✐♥ ♦r❞❡r t♦ ❡①♣❛♥❞ t❤❡ s❝♦♣❡ ♦❢ t❤❡ ♠♦❞❡❧ ✐♥ ♦r❞❡r t♦
✐♠♣r♦✈❡ t❤❡ ❛❝❝✉r❛❝② ♦❢ ✐ts ♣r❡❞✐❝t✐♦♥s✳
✼
❈♦♥❝❧✉s✐♦♥
❲❡ ❤❛✈❡ ❞❡s❝r✐❜❡❞ ❛ ♠♦❞❡❧ ♦❢ ❊❆❇ s♣r❡❛❞ ❜❛s❡❞ ♦♥ ✐♥s❡❝t ✢✐❣❤t ❛♥❞ ❤✉♠❛♥ ❛ss✐st❡❞ ❞✐s✲
♣❡rs✐♦♥ ♦❢ t❤❡ ❜❡❡t❧❡✳ ❇❛s❡❞ ♦♥ ♦✉r r❡s✉❧ts✱ ❜② ✷✵✷✷ t❤❡ ❊❆❇ ✐♥❢❡st❛t✐♦♥ ✇✐❧❧ ❝♦✈❡r ❛❧❧ ♦❢
❙♦✉t❤❡r♥ ◆❡✇ ❨♦r❦ ❛♥❞ ✇✐❧❧ ❜❡ s♣r❡❛❞✐♥❣ ◆♦rt❤✳ ❲❡ ♠❛❞❡ s❡✈❡r❛❧ s✐♠♣❧✐❢②✐♥❣ ❛ss✉♠♣t✐♦♥s
t❤❛t ♠❛② ❝♦♠♣r♦♠✐s❡ t❤❡ ❛❝❝✉r❛❝② ♦❢ t❤❡ ♠♦❞❡❧✳ ❋✉rt❤❡r r❡s❡❛r❝❤ ♠✉st ❜❡ ❞♦♥❡ ❛♥❞ ❞❛t❛
❝♦❧❧❡❝t❡❞ ✐♥ ♦r❞❡r t♦ ✈❡r✐❢② ♦r ❝♦rr❡❝t t❤❡s❡ ❛ss✉♠♣t✐♦♥s✳ ◆❡✈❡rt❤❡❧❡ss✱ ♦✉r ♠♦❞❡❧ ❢r❛♠❡✇♦r❦
✐s ✢❡①✐❜❧❡ ❛♥❞ ♦t❤❡r s♦✉r❝❡s ♦❢ ❞❛t❛ ❛♥❞ t②♣❡s ♦❢ ❊❆❇ s♣r❡❛❞ ❝❛♥ ❡❛s✐❧② ❜❡ ✐♥❝♦r♣♦r❛t❡❞ ✐♥
♦r❞❡r t♦ ✐♠♣r♦✈❡ ✐ts ❛❝❝✉r❛❝②✳
✶✵
❘❡❢❡r❡♥❝❡s
❆✳❈✳ ❆♥✉❧❡✇✐❝③✱ ❉✳●✳ ▼❝❈✉❧❧♦✉❣❤✱ ❛♥❞ ❉✳▲✳ ❈❛♣♣❛❡rt✳ ❊♠❡r❛❧❞ ❛s❤ ❜♦r❡r ✭❛❣r✐❧✉s ♣❧❛✲
♥✐♣❡♥♥✐s✮ ❞❡♥s✐t② ❛♥❞ ❝❛♥♦♣② ❞✐❡❜❛❝❦ ✐♥ t❤r❡❡ ♥♦rt❤ ❛♠❡r✐❝❛♥ ❛s❤ s♣❡❝✐❡s✳
❛♥❞ ❯r❜❛♥ ❋♦r❡str②✱
❆r❜♦r✐❝✉❧t✉r❡
✸✸✭✺✮✿✸✸✽✱ ✷✵✵✼✳
❚✳❑✳ ❇❡♥❉♦r✱ ❙✳❙✳ ▼❡t❝❛❧❢✱ ▲✳❊✳ ❋♦♥t❡♥♦t✱ ❇✳ ❙❛♥❣✉♥❡tt✱ ❛♥❞ ❇✳ ❍❛♥♥♦♥✳ ▼♦❞❡❧✐♥❣ t❤❡
s♣r❡❛❞ ♦❢ t❤❡ ❡♠❡r❛❧❞ ❛s❤ ❜♦r❡r✳
❊❝♦❧♦❣✐❝❛❧ ▼♦❞❡❧❧✐♥❣✱
✶✾✼✭✶✮✿✷✷✶✕✷✸✻✱ ✷✵✵✻✳
◆❡✇ ❨♦r❦ ❋♦r❡st ❍❡❛❧t❤ ❆❞✈✐s♦r② ❈♦✉♥❝✐❧✳ ■♠♣❛❝ts ❛♥❞ r❡❝♦♠♠❡♥❞❛t✐♦♥s r❡❧❛t❡❞ t♦ t❤❡
r❡❝❡♥t ❝♦♥✜r♠❛t✐♦♥ ♦❢ ❡♠❡r❛❧❞ ❛s❤ ❜♦r❡r ✐♥ st❡✉❜❡♥ ❛♥❞ ✉❧st❡r ❝♦✉♥t✐❡s✱ ♥②✳ Pr❡ss ❘❡❧❡❛s❡✱
❏✉♥ ✷✵✶✵✳
❇✉r❡❛✉ ♦❢ ❋♦r❡st ❍❡❛❧t❤ ❉✐✈✐s✐♦♥ ♦❢ ▲❛♥❞s ✫ ❋♦r❡sts✳ ❊♠❡r❛❧❞ ❛s❤ ❜♦r❡r ❢❛qs✱ ✷✵✶✷✳ ❯❘▲
❤tt♣✿✴✴✇✇✇✳❞❡❝✳♥②✳❣♦✈✴❛♥✐♠❛❧s✴✹✺✹✵✾✳❤t♠❧✳
▲♦✉✐s ❘✳ ■✈❡rs♦♥✱ ❆♥❛♥t❤❛ Pr❛s❛❞✱ ❏♦♥❛t❤❛♥ ❇♦ss❡♥❜r♦❡❦✱ ❉❛✈✐s ❙②❞♥♦r✱ ❛♥❞ ▼❛r❦ ❲✳
❙❝❤✇❛rt③✳ ▼♦❞❡❧✐♥❣ ♣♦t❡♥t✐❛❧ ♠♦✈❡♠❡♥ts ♦❢ t❤❡ ❡♠❡r❛❧❞ ❛s❤ ❜♦r❡r✿ t❤❡ ♠♦❞❡❧ ❢r❛♠❡✲
✇♦r❦✳
■♥ ❏♦❤♥ ▼✳ P②❡✱ ❍✳ ▼✐❝❤❛❡❧ ❘❛✉s❝❤❡r✱ ❨❛s♠❡❡♥ ❙❛♥❞s✱ ❉❛♥♥② ❈✳ ▲❡❡✱ ❛♥❞
❏❡r♦♠❡ ❙✳ ❇❡❛tt②✱ ❡❞✐t♦rs✱
❆❞✈❛♥❝❡s ✐♥ ❚❤r❡❛t ❆ss❡ss♠❡♥t ❛♥❞ ❚❤❡✐r ❆♣♣❧✐❝❛t✐♦♥ t♦ ❋♦r✲
❡st ❛♥❞ ❘❛♥❣❡❧❛♥❞ ▼❛♥❛❣❡♠❡♥t✱
✈♦❧✉♠❡ ✷✳ ❯✳❙✳ ❉❡♣❛rt♠❡♥t ♦❢ ❆❣r✐❝✉❧t✉r❡ ❋♦r❡st ❙❡r✈✐❝❡✱
❙❡♣t❡♠❜❡r ✷✵✶✵✳
▼❛r✐❛
❑✐♥❣✳
❚✐♥②
❜❡❡t❧❡✱
❜✐❣
♣r♦❜❧❡♠✱
❏✉♥
✷✵✶✶✳
❯❘▲
❤tt♣✿✴✴✇✇✇✳❞❡❝✳♥②✳❣♦✈✴♣✉❜s✴✼✹✻✽✷✳❤t♠❧✳
◆❨❙❉❊❈
▲❛♥❞s
❛♥❞
❋♦r❡sts✳
❊♠❡r❛❧❞
❛s❤
❜♦r❡r
✭❡❛❜✮✱
✷✵✶✷✳
❯❘▲
❙❡♣
✷✵✶✷✳
❯❘▲
❤tt♣✿✴✴✇✇✇✳❞❡❝✳♥②✳❣♦✈✴❛♥✐♠❛❧s✴✼✷✺✸✳❤t♠❧✳
❏❛②
▲✐♥❞s❛②✳
❊♠❡r❛❧❞
❛s❤
❜♦r❡r
❛rr✐✈❡s
✐♥
♠❛ss✳✱
❤tt♣✿✴✴✇✇✇✳t❡❧❡❣r❛♠✳❝♦♠✴❛rt✐❝❧❡✴✷✵✶✷✵✾✶✸✴◆❊❲❙✴✶✵✾✶✸✾✼✾✹✴✶✵✺✷✳
✶✶
❏✳❘✳ ▼✉✐r❤❡❛❞✱ ❇✳ ▲❡✉♥❣✱ ❈✳ ❖✈❡r❞✐❥❦✱ ❉✳❲✳ ❑❡❧❧②✱ ❑✳ ◆❛♥❞❛❦✉♠❛r✱ ❑✳❘✳ ▼❛r❝❤❛♥t✱ ❛♥❞
❍✳❏✳ ▼❛❝■s❛❛❝✳ ▼♦❞❡❧❧✐♥❣ ❧♦❝❛❧ ❛♥❞ ❧♦♥❣✲❞✐st❛♥❝❡ ❞✐s♣❡rs❛❧ ♦❢ ✐♥✈❛s✐✈❡ ❡♠❡r❛❧❞ ❛s❤ ❜♦r❡r
❛❣r✐❧✉s ♣❧❛♥✐♣❡♥♥✐s ✭❝♦❧❡♦♣t❡r❛✮ ✐♥ ♥♦rt❤ ❛♠❡r✐❝❛✳ ❉✐✈❡rs✐t② ❛♥❞ ❉✐str✐❜✉t✐♦♥s✱ ✶✷✭✶✮✿✼✶✕✼✾✱
✷✵✵✺✳
❆✳▼✳ Pr❛s❛❞✱ ▲✳❘✳ ■✈❡rs♦♥✱ ▼✳P✳ P❡t❡rs✱ ❏✳▼✳ ❇♦ss❡♥❜r♦❡❦✱ ❙✳◆✳ ▼❛tt❤❡✇s✱ ❚✳ ❉❛✈✐s ❙②❞♥♦r✱
❛♥❞ ▼✳❲✳ ❙❝❤✇❛rt③✳ ▼♦❞❡❧✐♥❣ t❤❡ ✐♥✈❛s✐✈❡ ❡♠❡r❛❧❞ ❛s❤ ❜♦r❡r r✐s❦ ♦❢ s♣r❡❛❞ ✉s✐♥❣ ❛
s♣❛t✐❛❧❧② ❡①♣❧✐❝✐t ❝❡❧❧✉❧❛r ♠♦❞❡❧✳
▼❛r✐❜❡t❤ ❍✉❣❤❡tt Pr✐❝❡✳
✱ ✷✺✭✸✮✿✸✺✸✕✸✻✾✱ ✷✵✶✵✳
▲❛♥❞s❝❛♣❡ ❡❝♦❧♦❣②
✳ ▼❝●r❛✇ ❍✐❧❧✱ ✺t❤ ❡❞✐t✐♦♥ ❡❞✐t✐♦♥✱ ✷✵✶✷✳
▼❛st❡r✐♥❣ ❆r❝●■❙
❘✳❆✳❏✳ ❚❛②❧♦r✱ ❚✳▼✳ P♦❧❛♥❞✱ ▲✳❙✳ ❇❛✉❡r✱ ❑✳◆✳ ❲✐♥❞❡❧❧✱ ❛♥❞ ❏✳▲✳ ❑❛✉t③✳ ❊♠❡r❛❧❞ ❛s❤ ❜♦r❡r
✢✐❣❤t ❡st✐♠❛t❡s r❡✈✐s❡❞✳
Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ❡♠❡r❛❧❞ ❛s❤ ❜♦r❡r✴❆s✐❛♥ ❧♦♥❣❤♦r♥❡❞ ❜❡❡t❧❡
r❡s❡❛r❝❤ ❛♥❞ ❚❡✳ ❋❍❚❊❚✲✷✵✵✼✲✵✹✳ ❯❙ ❉❡♣❛rt♠❡♥t ♦❢ ❆❣r✐❝✉❧t✉r❡ ❋♦r❡st ❙❡r✈✐❝❡✱ ❋♦r❡st
✱ ♣❛❣❡ ✶✵✱ ✷✵✵✼✳
❍❡❛❧t❤ ❚❡❝❤♥♦❧♦❣② ❊♥t❡r♣r✐s❡ ❚❡❛♠✱ ▼♦r❣❛♥t♦✇♥
❆♥✐♠❛❧ ❯♥✐t❡❞ ❙t❛t❡s ❉❡♣❛rt♠❡♥t ♦❢ ❆❣r✐❝✉❧t✉r❡ ❛♥❞ P❧❛♥t ❍❡❛❧t❤ ■♥s♣❡❝t✐♦♥ ❙❡r✈✐❝❡✳ ❘✐s❦
❛ss❡ss♠❡♥t ♦❢ t❤❡ ♠♦✈❡♠❡♥t ♦❢ ✜r❡✇♦♦❞ ✇✐t❤✐♥ t❤❡ ✉♥✐t❡❞ st❛t❡s✱ ▼❛② ✷✵✶✵✳
❇✳❚✳ ❲✐❧s♦♥✱ ❆✳❏✳ ▲✐st❡r✱ ❛♥❞ ❘✳■✳ ❘✐❡♠❛♥♥✳ ❆ ♥❡❛r❡st✲♥❡✐❣❤❜♦r ✐♠♣✉t❛t✐♦♥ ❛♣♣r♦❛❝❤ t♦
♠❛♣♣✐♥❣ tr❡❡ s♣❡❝✐❡s ♦✈❡r ❧❛r❣❡ ❛r❡❛s ✉s✐♥❣ ❢♦r❡st ✐♥✈❡♥t♦r② ♣❧♦ts ❛♥❞ ♠♦❞❡r❛t❡ r❡s♦❧✉t✐♦♥
r❛st❡r ❞❛t❛✳
✱ ✷✼✶✿✶✽✷✕✶✾✽✱ ✷✵✶✷✳
❋♦r❡st ❊❝♦❧♦❣② ❛♥❞ ▼❛♥❛❣❡♠❡♥t
✶✷
✽
❋✐❣✉r❡s
❋✐❣✉r❡ ✶✿ ◆❡✇ ❨♦r❦ ■♥❢❡st❛t✐♦♥s ❛s ♦❢ ✾✴✷✵✴✶✷
✶✸
❘❛st❡r ❖✉t♣✉t ●❡♦r❡❢❡r❡♥❝✐♥❣ ▼♦❞❡❧
P❛r❛♠❡t❡r
❉❡s❝r✐♣t✐♦♥
❱❛❧✉❡
❋✐❣✉r❡ ✷✿
C1
❊❆❇ ❙♣r❡❛❞ ▼✉❧t✐♣❧✐❡r
✼
x1
❊❆❇ ❘❛♥❣❡ P♦✇❡r
✵✳✸
C2
❈❛♠♣❣r♦✉♥❞ ❙♣r❡❛❞ ▼✉❧t✐♣❧✐❡r
✺✵✵
x2
❈❛♠♣❣r♦✉♥❞ ❘❛♥❣❡ P♦✇❡r
✷
❋✐❣✉r❡ ✸✿
▼♦❞❡❧ P❛r❛♠❡t❡rs
✶✹
❋✐❣✉r❡ ✹✿
Pr❡❞✐❝t❡❞ ❊♠❡r❛❧❞ ❆s❤ ❇♦r❡r ❙♣r❡❛❞
✷✵✶✷✲✷✵✷✷
✶✺
❋✐❣✉r❡ ✺✿ Pr❡❞✐❝t❡❞ ❊♠❡r❛❧❞ ❆s❤ ❇♦r❡r ❊①t❡♥t
❨❡❛r ✷
✶✻
❋✐❣✉r❡ ✻✿ Pr❡❞✐❝t❡❞ ❊♠❡r❛❧❞ ❆s❤ ❇♦r❡r ❊①t❡♥t
❨❡❛r ✺
✶✼
❋✐❣✉r❡ ✼✿ Pr❡❞✐❝t❡❞ ❊♠❡r❛❧❞ ❆s❤ ❇♦r❡r ❊①t❡♥t ❨❡❛r ✶✵
✶✽
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