The distance-based approach to the quantiﬁcation of the world convergences and imbalances - comparisons across countries and factors

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Munich Personal RePEc Archive

The distance-based approach to the

quantification of the world convergences and imbalances - comparisons across

countries and factors

Horvath, Denis and Sulikova, Veronika and Gazda, Vladimir and Sinicakova, Marianna

Faculty of Economics, Technical University of Kosice, Nemcovej 32, 040 01 Kosice, Slovakia, Universite de Nice Sophia Antipolis,

Institut Superieur d’Economie et de Management, Nice, France

2013

Online at https://mpra.ub.uni-muenchen.de/45033/

MPRA Paper No. 45033, posted 14 Mar 2013 14:14 UTC

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❚❤❡ ❞✐st❛♥❝❡✲❜❛s❡❞ ❛♣♣r♦❛❝❤ t♦ t❤❡

q✉❛♥t✐✜❝❛t✐♦♥ ♦❢ t❤❡ ✇♦r❧❞ ❝♦♥✈❡r❣❡♥❝❡s ❛♥❞

✐♠❜❛❧❛♥❝❡s ✲ ❝♦♠♣❛r✐s♦♥s ❛❝r♦ss ❝♦✉♥tr✐❡s ❛♥❞

❢❛❝t♦rs

❉❡♥✐s ❍♦r✈át❤

^∗^✶

✱ ❱❡r♦♥✐❦❛ ➆✉❧✐❦♦✈á

^†✶✱✷

✱ ❱❧❛❞✐♠ír ●❛③❞❛

^‡✶

✱

❛♥❞ ▼❛r✐❛♥♥❛ ❙✐♥✐↔á❦♦✈á

^§✶

✶

❋❛❝✉❧t② ♦❢ ❊❝♦♥♦♠✐❝s✱ ❚❡❝❤♥✐❝❛❧ ❯♥✐✈❡rs✐t② ♦❢ ❑♦➨✐❝❡✱ ◆❡♠❝♦✈❡❥

✸✷✱ ✵✹✵ ✵✶ ❑♦➨✐❝❡✱ ❙❧♦✈❛❦✐❛

✷

❯♥✐✈❡rs✐té ❞❡ ◆✐❝❡ ❙♦♣❤✐❛ ❆♥t✐♣♦❧✐s✱ ■♥st✐t✉t ❙✉♣ér✐❡✉r

❞✬❊❝♦♥♦♠✐❡ ❡t ❞❡ ▼❛♥❛❣❡♠❡♥t✱ ◆✐❝❡✱ ❋r❛♥❝❡

▼❛r❝❤ ✶✹✱ ✷✵✶✸

❆❜str❛❝t

❚❤❡ ♣❛♣❡r ♣r❡s❡♥ts ❛ ❣❡♥❡r❛❧ ❡♠♣✐r✐❝❛❧ ♠❡t❤♦❞ ♦❢ ❞✐st❛♥❝❡✲❜❛s❡❞

♠✉❧t✐❢❛❝❡t❡❞ s②st❡♠❛t✐❝ ✐❞❡♥t✐❢②✐♥❣ ♦❢ t❤❡ ♣♦s✐t✐♦♥s ♦❢ ❝♦✉♥tr✐❡s ✐♥ r❡✲

❧❛t✐♦♥ t♦ ✐♥❡q✉❛❧✐t✐❡s ❛♥❞ ✐♠❜❛❧❛♥❝❡s✳ ■♥ ♦r❞❡r t♦ ✉♥❞❡rst❛♥❞ t❤❡ ✇♦r❧❞

❡❝♦♥♦♠✐❝ r❡❧❛t✐♦♥s ✐♥ t❤❡✐r ❡♥t✐r❡t②✱ ✇❡ ❞❡❝✐❞❡❞ t♦ ❛♥❛❧②③❡ t✇❡❧✈❡ ♠♦st

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

♠♦❣r❛♣❤✐❝ ✐♥❞✐❝❛t♦rs r❡❧❡✈❛♥t t♦ t❤❡♠✳ ❖✉r ❛♥❛❧②s✐s ❝♦✈❡r✐♥❣ t❤❡ ♣❡✲

r✐♦❞ ✶✾✾✷✲✷✵✵✽ ❛tt❡♠♣ts t♦ ✐❞❡♥t✐❢② ❝♦r❡ ♣❛rts ♦❢ t❤❡ ❣❧♦❜❛❧ ❡❝♦♥♦♠✐❝

s②st❡♠ ❛♥❞ ❝♦✉♥tr✐❡s t❤❛t ♣♦s❡ ❛ ♣♦t❡♥t✐❛❧ r✐s❦ ♦❢ ✐♥st❛❜✐❧✐t②✳

❑❡②✇♦r❞s✿ ❣❧♦❜❛❧ ✐♠❜❛❧❛♥❝❡s✱ ❝♦♥✈❡r❣❡♥❝❡s✱ ❞✐st❛♥❝❡✲❜❛s❡❞ ♠❡t❤♦❞♦❧♦❣②✱

❝♦♠♣❧❡① ❞②♥❛♠✐❝s✱ ✇♦r❧❞ ❡❝♦♥♦♠②

∗❞❡♥✐s✳❤♦r✈❛t❤❅t✉❦❡✳s❦

†✈❡r♦♥✐❦❛✳s✉❧✐❦♦✈❛❅t✉❦❡✳s❦

‡✈❧❛❞✐♠✐r✳❣❛③❞❛❅t✉❦❡✳s❦

§♠❛r✐❛♥♥❛✳s✐♥✐❝❛❦♦✈❛❅t✉❦❡✳s❦

✶

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✶ ■♥tr♦❞✉❝t✐♦♥

❏✉st ❛ ❢❡✇ ②❡❛rs ❛❣♦✱ t❤❡r❡ ✇❡r❡ ✇✐❞❡s♣r❡❛❞ ❡①♣❡❝t❛t✐♦♥s ✭✭❇❡♥✲❉❛✈✐❞✱ ✶✾✾✻✱

✷✵✵✶❀ ❈②r✉s✱ ✷✵✵✹✮✮ t❤❛t ❛ ❣r❛❞✉❛❧ ♦♣❡♥✐♥❣ ♦❢ t❤❡ ❡❝♦♥♦♠✐❡s ✇✐❧❧ r❡s✉❧t ✐♥

❤✐❣❤❡r ✐♥t❡r❝♦✉♥tr② ❝♦♥✈❡r❣❡♥❝❡ ❧❡✈❡❧s ✐♥ t❤❡ ❢✉t✉r❡✳ ❚❤❡r❡ ✐s ❛ ✇✐❞❡ s♣r❡❛❞

♦♣✐♥✐♦♥ t❤❛t t❤❡ ♣❤❡♥♦♠❡♥♦♥ ♦❢ ❣❧♦❜❛❧✐③❛t✐♦♥ ❛♥❞ ✐ts ✐♠♣❧✐❝❛t✐♦♥s ❢♦r ✐♥✲

❝r❡❛s✐♥❣ ✐♥t❡r❞❡♣❡♥❞❡♥❝❡ ♣r♦♠♦t❡s ❝♦♥✈❡r❣❡♥❝❡ tr❡♥❞s ✐♥ t❤❡ ✇♦r❧❞✳ ❚❤❡

❝♦♥✈❡r❣❡♥❝❡ ❤❛s ❜❡❡♥ ❡❝♦♥♦♠❡tr✐❝❛❧❧② t❡st❡❞ ❜② ♥✉♠❡r♦✉s r❡s❡❛r❝❤❡rs ✭❇❛rr♦

❛♥❞ ❙❛❧❛✲✐✲▼❛rt✐♥✱ ✶✾✾✷❀ ▼❛t♦s ❛♥❞ ❋❛✉st✐♥♦✱ ✷✵✶✷❀ ❚②❦❤♦♥❡♥❦♦✱ ✷✵✵✺✮ ❢♦r

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

❜❡t✇❡❡♥ t❤❡ tr❛❞❡ ❧✐❜❡r❛❧✐③❛t✐♦♥ ❛♥❞ ❝♦♥✈❡r❣❡♥❝❡ ✭❙❧❛✉❣❤t❡r✱ ✷✵✵✶✮✳ ❚❤✐s

♣❛♣❡r s❤❛r❡s t❤❡ ✇✐❞❡✲s♣r❡❛❞ ❛♥t✐✲❝♦♥✈❡r❣❡♥❝❡ ✈✐❡✇ t❤❛t ❧✐❜❡r❛❧✐③❡❞ tr❛❞❡

✇✐❧❧ ❡✈❡♥ ❞❡❡♣❡♥ ❞✐s♣❛r✐t✐❡s ❛♠♦♥❣ t❤❡ ❝♦✉♥tr✐❡s✳ ❚❤❡ ♥❡✇ ❣❧♦❜❛❧✐③❡❞ ✇♦r❧❞✱

❛❝❝♦♠♣❛♥✐❡❞ ❜② t❤❡ ❝♦♥st❛♥t❧② ❡①♣❛♥❞✐♥❣ ✐♥t❡r♥❛t✐♦♥❛❧ tr❛❞❡ ❛♥❞ ✐♥❝r❡❛s✲

✐♥❣ ✐♥t❡❣r❛t✐♦♥ ❡✛♦rts ✐s ❣❡♥❡r❛❧❧② ❝❤❛r❛❝t❡r✐③❡❞ ❜② t❤❡ ❤✐❣❤ ❞❡❣r❡❡ ♦❢ ✐♥✲

t❡r♥❛t✐♦♥❛❧ s②♥❝❤r♦♥✐③❛t✐♦♥ ♦❢ t❤❡ ❡❝♦♥♦♠✐❝ ❝②❝❧❡s ✭❆rt✐s ❛♥❞ ❖❦✉❜♦✱ ✷✵✶✶❀

❆❣✉✐❛r✲❈♦♥r❛r✐❛ ❡t ❛❧✳✱ ✷✵✶✶❀ ❆❧❧❡❣r❡t ❡t ❛❧✳✱ ✷✵✶✶✮✳ ❲✐t❤ t❤❡ ♣r♦❣r❡ss✐♦♥ ♦❢

❣❧♦❜❛❧✐③❛t✐♦♥✱ ❡❝♦♥♦♠✐❡s ❜❡❝♦♠✐♥❣ ✐♥❝r❡❛s✐♥❣❧② ✐♥t❡r❝♦♥♥❡❝t❡❞ ❛♥❞ ✐♥t❡r❛❝t✲

✐♥❣ ❛s t❤❡② ❝♦✉❧❞ ❤❛r❞❧② ❡①✐st ✐♥❞❡♣❡♥❞❡♥t❧②✳ ❉✉❡ t♦ ♠✉❧t✐✲❝❤❛♥♥❡❧ ✐♥t❡r✲

❛❝t✐♦♥s ❜❡t✇❡❡♥ ❝♦✉♥tr✐❡s t❤❡r❡ ✐s ❛♥ ❛♠❜✐❣✉✐t② ✐♥ ❞❡t❡r♠✐♥✐♥❣ ❛ ❞❡❣r❡❡ ♦❢

❝♦♥✈❡r❣❡♥❝❡ s✐♥❝❡ t❤❡ ❝❤♦✐❝❡ ♦❢ ❢❛❝t♦rs✴✐♥❞✐❝❛t♦rs ❝♦♠♣❛r❡❞✳ ❚❤❡ ✐♥t✉✐t✐♦♥

❜❡❤✐♥❞ ✐♠❜❛❧❛♥❝❡s ✐s t❤❛t t❤❡✐r ✐♥✐t✐❛❧ ♣❤❛s❡ ✐s q✉✐t❡ ✉♥❝❡rt❛✐♥✳ ❚❤❡ ✐♥t❡r✲

❛❝t✐♦♥s ❛r❡ ❝r❡❛t✐♥❣ ❤✐❣❤❧② s✉s❝❡♣t✐❜❧❡ ❡♥✈✐r♦♥♠❡♥t✱ ✇❤❡r❡ ✐t ✐s ♣♦ss✐❜❧❡ t♦

❡①♣❡❝t t❤❛t ❡✈❡♥ t✐♥② ✐♥✐t✐❛❧ ❣❛♣ ❝❛♥ s♦✇ t❤❡ s❡❡❞ ♦❢ ❢✉t✉r❡ ♠❛❥♦r ✐♠❜❛❧❛♥❝❡

❛♥❞ r✐s❦✳

❆s t❤❡ ❜❛s✐s ♦❢ ❛ ♣✉r❡❧② ❡❝♦♥♦♠✐❝ s❝♦♣❡ ♦♥ t❤❡ ✇♦r❧❞ ✐♠❜❛❧❛♥❝❡s ♠❛② ❜❡

r❡❣❛r❞❡❞ ❞❡✜♥✐t✐♦♥ ♦❢ t❤❡ ❊✉r♦♣❡❛♥ ❈❡♥tr❛❧ ❇❛♥❦✱ ✇❤✐❝❤ s❡❡s t❤❡♠ ❛s ✧❡①✲

t❡r♥❛❧ ♣♦s✐t✐♦♥s ♦❢ s②st❡♠✐❝❛❧❧② ✐♠♣♦rt❛♥t ❡❝♦♥♦♠✐❡s t❤❛t r❡✢❡❝t ❞✐st♦rt✐♦♥s

♦r ❡♥t❛✐❧ r✐s❦s ❢♦r t❤❡ ❣❧♦❜❛❧ ❡❝♦♥♦♠②✧ ✭❇r❛❝❦❡ ❡t ❛❧✳✱ ✷✵✵✽✮✳ ❯♥❢♦rt✉♥❛t❡❧②✱

t❤✐s r❛t❤❡r ❣❡♥❡r❛❧ ❛♥❞ s♦♠❡✇❤❛t ✈❛❣✉❡ ❞❡✜♥✐t✐♦♥ ❞♦❡s ♥♦t ♣r♦✈✐❞❡ ❞✐r❡❝t q✉❛♥t✐✜❝❛t✐♦♥ ♦❢ ❝❤❛r❛❝t❡r✐st✐❝s ♦❢ ✐♠❜❛❧❛♥❝❡s✳ ❇✉t ❡✈❡♥ ✐❢ ✇❡ r❡❧② ♦♥❧② ♦♥

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

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

♣r♦❜❧❡♠ ✭❇❧❛♥❝❤❛r❞ ❛♥❞ ▼✐❧❡s✐✲❋❡rr❡tt✐✱ ✷✵✵✾✮ ♦❢t❡♥ ❞✐s❝✉ss❡❞ ❜② t❤❡ ❧❡❣✲

✐s❧❛t♦rs✱ ❡❝♦♥♦♠✐sts ❛♥❞ ♣♦❧✐❝② ♠❛❦❡rs✳ ❚❤❡ ♠❛✐♥ r❡❛s♦♥s ✇❤② ✇❡ t❤✐♥❦

♦❢ ✐♠❜❛❧❛♥❝❡s ❛s ❛ ❝♦♠♣❧❡① s②st❡♠ ✐ss✉❡s s♣r✐♥❣ ❢r♦♠ t❤❡ ❧❛r❣❡ ♥✉♠❜❡r ♦❢

t❤❡ ✈❛r✐❛❜❧❡s✱ ✇❤✐❝❤ s❡❡♠ t♦ ❜❡ ❛ss♦❝✐❛t❡❞ ✇✐t❤ ✐♠❜❛❧❛♥❝❡s✿ s❛✈✐♥❣s✱ ✐♥✈❡st✲

♠❡♥ts✱ ❡①t❡r♥❛❧ ❞❡❜ts✱ tr❛❞❡ ❛♥❞ ❝✉rr❡♥t ❛❝❝♦✉♥t ✐♠❜❛❧❛♥❝❡s✱ ❡t❝✳✳ ❇✉t ✐t✬s

♥♦t ♦♥❧② t❤❡ ❡❝♦♥♦♠② t❤❛t✬s s❤♦✇✐♥❣ s✐❣♥s ♦❢ ✐♠❜❛❧❛♥❝❡s✳ ❋♦r ❡①❛♠♣❧❡✱ t❤❡

✇✐❞❡ ✐♥t❡r❡st ❛❜♦✉t t❤❡ ✉♥❜❛❧❛♥❝❡❞ ♣♦♣✉❧❛t✐♦♥ ❣r♦✇t❤ ❞❛t❡s ❜❛❝❦ t♦ ❝❧❛ss✐❝❛❧

❞❡♠♦❣r❛♣❤✐❝ r❡s❡❛r❝❤ ✇♦r❦s ♦❢ ▼❛❧t❤✉s ❛♥❞ ❱❡r❤✉❧st ✭✶✽✸✽✮ ✇❤♦ ❞✐s♣✉t❡❞

✷

(4)

❛❜♦✉t t❤❡ ♣❤②s✐❝❛❧ ❧✐♠✐ts ❛♥❞ ❝❤❛♥❣❡♦✈❡r s❧♦✇✐♥❣ t❤❡ ♣♦♣✉❧❛t✐♦♥ ❣r♦✇t❤ ❜② t❤❡ ❞❡t❡r✐♦r❛t✐♥❣ ❡♥✈✐r♦♥♠❡♥t❛❧ ❝♦♥❞✐t✐♦♥s✳ ❯♥❞♦✉❜t❡❞❧②✱ t❤❡ s❝❛r❝✐t② ♦❢

♥❛t✉r❛❧ r❡s♦✉r❝❡s ❤❛s ❢❡❡❞❜❛❝❦ ❡✛❡❝ts ♦♥ t❤❡ ❧♦♥❣✲t❡r♠ ♣r♦❣r❡ss ♦❢ t❤❡ ✇♦r❧❞

❡❝♦♥♦♠②✳ ❈✉rr❡♥t❧②✱ t❤❡ ❜✐❣❣❡st ❦❡② ♥❛t✐♦♥❛❧ ❡❝♦♥♦♠✐❡s ❛r❡ ♥♦t ❤❛r♠♦♥✐③❡❞

r❡❣❛r❞✐♥❣ ❡✳❣✳ t❤❡✐r ♣♦♣✉❧❛t✐♦♥ ❣r♦✇t❤ ♥♦r ❛♥ ❡①❤❛✉st✐♦♥ ♦❢ t❤❡ ♥❛t✉r❛❧

r❡s♦✉r❝❡s✳

❚❤❡ str✉❝t✉r❡ ♦❢ t❤❡ ✇♦r❧❞ ❡❝♦♥♦♠② ✐s ❝♦♥t✐♥✉♦s❧② ❝❤❛♥❣✐♥❣ t♦✇❛r❞s ❡①✲

tr❡♠❡❧② ❝♦♠♣❧❡① s②st❡♠ ♦❢ ✐♥t❡r❝♦♥♥❡❝t❡❞ ❡♥t✐t✐❡s✳ ■♥ ♦r❞❡r t♦ ✉♥❞❡rst❛♥❞

✐ts ♥❛t✉r❡✱ ❛❧t❤♦✉❣❤ ✐♥ ❛ ✈❡r② r♦✉❣❤ ❛♥❞ ❡❧❡♠❡♥t❛r② ❧❡✈❡❧✱ ✇❡ ❤❛✈❡ t♦ ❞❡❛❧

✇✐t❤ ❛ ❧❛r❣❡ ♥✉♠❜❡r ♦❢ ✐♥❞✐❝❛t♦rs ❢♦r ♠♦♥✐t♦r✐♥❣ t❤❡ ♦✈❡r❛❧❧ s✐t✉❛t✐♦♥✳ ❚❤❡r❡✲

❢♦r❡✱ ♠✉❝❤ ❡✛♦rt ✐s ♥❡❡❞❡❞ t♦ ❡①♣❡r✐♠❡♥t ✇✐t❤ ✉♥❝♦♥✈❡♥t✐♦♥❛❧ ❛♥❞ ✐♥♥♦✈❛✲

t✐✈❡ ❡♠♣✐r✐❝❛❧ ✐❞❡❛s ❛♥❞ ❤❡✉r✐st✐❝ ❛♣♣r♦❛❝❤❡s✳ ■♥ t❤✐s r❡❣❛r❞✱ ❛t ❧❡❛st s❡✈❡r❛❧

♣❡rs♣❡❝t✐✈❡ ❛tt❡♠♣ts t♦ st✉❞② t❤❡ ❝♦♠♣❧❡① ❛♥❞ ✐♥t❡rr❡❧❛t❡❞ ❡❝♦♥♦♠✐❝ ✐ss✉❡s s❤♦✉❧❞ ❜❡ ♠❡♥t✐♦♥❡❞✳

❚❤❡ ❝♦♠♣r❡❤❡♥s✐✈❡ ❧♦♥❣✲t❡r♠ ✈✐❡✇ ♦♥ t❤❡ ✇♦r❧❞ ❞❡✈❡❧♦♣♠❡♥t r❡s♣❡❝t✲

✐♥❣ t❤❡ ♣♦♣✉❧❛t✐♦♥ ❜♦♦st ✉♥❞❡r t❤❡ r❡str✐❝t❡❞ r❡s♦✉r❝❡s ❤❛s ❜❡❡♥ ♣r❡s❡♥t❡❞

❜② ❊❤r❧✐❝❤ ❛♥❞ ❊❤r❧✐❝❤ ✭✶✾✾✵✮✳ ❯♥❢♦rt✉♥❛t❡❧②✱ ♠♦r❡ ♦♥ t❤❡ ♥❛rr❛t✐✈❡ t❤❛♥

q✉❛♥t✐t❛t✐✈❡ ❧❡✈❡❧✳ ❖✉r st✉❞② s❤♦✉❧❞ ❜❡ s❡❡♥ ♠♦r❡ ✐♥ t❤❡ ❧✐❣❤t ♦❢ ❡♠♣✐r✐❝❛❧

r❡s❡❛r❝❤✱ ✇❤❡r❡ t❤❡r❡ ✐s ✐♥t❡r❡st ✐♥ t❤❡ ✐♥tr✐♥s✐❝ ❝♦♠♣❧❡①✐t②✳ P♦ss✐❜❧② t❤❡ ♠♦st s✐❣♥✐✜❝❛♥t ❡♠♣✐r✐❝❛❧ ❡✛♦rt ✐♥ ✇❤✐❝❤ t❤❡ ❝♦♠♣❧❡①✐t② ❢r❛♠❡✇♦r❦ ✐s ❛ ❝❡♥t❡r ❢♦r r❡s❡❛r❝❤✱ r❡♣r❡s❡♥ts t❤❡ ✇♦r❦ ❜② ❍✐❞❛❧❣♦ ❡t ❛❧✳ ✭✷✵✵✾✮✳ ❚❤❡ ✇♦r❦ ❢♦❝✉s❡s

♦♥ t❤❡ ❡❝♦♥♦♠✐❝ ❣r♦✇t❤ ❛♥❛❧②③❡❞ ❢r♦♠ t❤❡ ♣❡rs♣❡❝t✐✈❡ ♦❢ t❤❡ ❝♦♠♣❧❡①✐t② ♦❢

t❤❡ ✇♦r❧❞ ♥❡t✇♦r❦ ✇✐t❤ ❧✐♥❦❛❣❡s ❢♦r♠❡❞ ❜② t❤❡ ✐♠♣♦rt ❛♥❞ ❡①♣♦rt ❜✉s✐♥❡ss

❞❛t❛✳ ❆s ❛♥♦t❤❡r ❡①❛♠♣❧❡ ✇❡ ❝♦✉❧❞ ♠❡♥t✐♦♥ t❤❡ ❡①t❡♥s✐✈❡ st✉❞② ❍✐❞❛❧❣♦ ❡t

❛❧✳ ✭✷✵✵✼✮ ❞❡❛❧✐♥❣ ✇✐t❤ t❤❡ ♥❡t✇♦r❦ t❡❝❤♥✐q✉❡s ❛♣♣❧✐❡❞ t♦ ❡✈❛❧✉❛t❡ t❤❡ ❧♦❝❛❧

❝♦♠♣❛r❛t✐✈❡ ❛❞✈❛♥t❛❣❡s ♦❢ t❤❡ ❝♦✉♥tr✐❡s✳

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

✇❤✐❝❤ ❝❛♥ ❜❡ ❡①♣❧❛✐♥❡❞ ❛s ❢♦❧❧♦✇s✳ ❆❝❝♦r❞✐♥❣ t♦ t❤❡ ❡❝♦♥♦♠✐❝ str❛t❡❣② ✐♥

✐♥t❡r♥❛t✐♦♥❛❧ tr❛❞❡ ❛♥❞ ❡①♣♦rt ♦r✐❡♥t❛t✐♦♥✱ t✇♦ ♠❛✐♥ ❝❛t❡❣♦r✐❡s ♦❢ ❝♦✉♥tr✐❡s

❝❛♥ ❜❡ ❞✐st✐♥❣✉✐s❤❡❞✿ t❤♦s❡ ✇✐t❤ ❞❡✜❝✐ts ❛♥❞ t❤♦s❡ ❛❝❝✉♠✉❧❛t✐♥❣ s✐❣♥✐✜❝❛♥t s✉r♣❧✉s❡s ✭✧♠❡r❝❛♥t✐❧✐st✧ ❡❝♦♥♦♠✐❡s✮✳ ❉❡✜❝✐t ♦r s✉r♣❧✉s tr❛❞❡ ❜❛❧❛♥❝❡✱ ❛s ❛

♣❛rt ♦❢ ❣r♦ss ❞♦♠❡st✐❝ ♣r♦❞✉❝t✱ ❞✐r❡❝t❧② ✐♥✢✉❡♥❝❡s ❡❝♦♥♦♠✐❝ ❣r♦✇t❤ ❛♥❞ ❝♦♥✲

s❡q✉❡♥t❧② ❡❝♦♥♦♠✐❝ ♣♦❧✐❝② str❛t❡❣② ✭❇r✉♥❡t ❛♥❞ ●✉✐❝❤❛r❞✱ ✷✵✶✶✮✳ ❚❤❡r❡❢♦r❡✱

✐❢ ❛ ❧❛r❣❡ ❡♠❡r❣✐♥❣ ❡❝♦♥♦♠✐❡s s✉❝❤ ❛s ❈❤✐♥❛ ❝♦♥t✐♥✉❡ t❤❡✐r ❛❣❣r❡ss✐✈❡ ♠❡r❝❛♥✲

t✐❧✐st str❛t❡❣② ❜❛s❡❞ ♦♥ t❤❡ st❡❛❞✐❧② ❣r♦✇✐♥❣ tr❛❞❡ ❜❛❧❛♥❝❡ s✉r♣❧✉s❡s ✭❇r✉♥❡t

❛♥❞ ●✉✐❝❤❛r❞ ✭✷✵✶✶✮✮✱ t❤❡ ❡❝♦♥♦♠✐❝ ♣❛rt♥❡rs ❛r❡ ❢❛❝✐♥❣ t❤❡ ♣❡r♠❛♥❡♥t ❛❝✲

❝✉♠✉❧❛t✐♦♥ ♦❢ t❤❡ tr❛❞❡ ❜❛❧❛♥❝❡ ❞❡✜❝✐ts ❛♥❞ ❧❛r❣❡r ❜✉❞❣❡t ❞❡✜❝✐ts✳ ■♥ ●✉ ❡t

❛❧✳ ✭✷✵✵✽✮ ✐t ✐s ❛r❣✉❡❞ t❤❛t ❈❤✐♥❛ ❞✐s♣❧❛②s ❛ ❤✐❣❤ ❞❡❣r❡❡ ♦❢ ❣❧♦❜❛❧ ♣♦✇❡r ❛♥❞

❣♦✈❡r♥❛♥❝❡ ❛♥❞ ✐ts str❛t❡❣② ❤❛✈❡ ❣❧♦❜❛❧❧② ✐♠♣♦rt❛♥t ❝♦♥s❡q✉❡♥❝❡s ❢♦r ♠❛♥②

♦t❤❡r ❛❝t♦rs✳ ❚❤✐s ✐♥tr♦❞✉❝❡s ♣♦ss✐❜✐❧✐t② t❤❛t ✐♠❜❛❧❛♥❝❡s ❛❝r♦ss ❝♦✉♥tr✐❡s

✸

(5)

❛r❡ ✇✐❞❡♥✐♥❣ ❛♥❞ ❞❡❡♣❡♥✐♥❣✳ ■♥ ❇❧❛♥❝❤❛r❞ ❛♥❞ ▼✐❧❡s✐✲❋❡rr❡tt✐ ✭✷✵✵✾✮ ✐t ✐s

♣♦✐♥t❡❞ ♦✉t t❤❛t ❢r♦♠ ✷✵✵✺ t✐❧❧ ❝✉rr❡♥t ❡❝♦♥♦♠✐❝ ❝r✐s✐s✱ t❤❡ ❣❧♦❜❛❧ ❡❝♦♥♦♠②

✐s ❝❤❛r❛❝t❡r✐③❡❞ ❜② ❛ ❛♥ ❡❝♦♥♦♠✐❝ ❜♦♦♠ ❛♥❞ ✐♥t❡r♥❛t✐♦♥❛❧ ❝❛♣✐t❛❧ ✢♦✇s ❡s♣❡✲

❝✐❛❧❧② ♦❜s❡r✈❡❞ ✐♥ t❤❡ ❞❡✈❡❧♦♣❡❞ ❡❝♦♥♦♠✐❡s✳ ❙✉❜s❡q✉❡♥t❧②✱ t❤✐s ❞❡✈❡❧♦♣♠❡♥t

❤❛s ❧❡❞ t♦ ♠✉❝❤ ✇✐❞❡r ❣❛♣s ✐♥ t❤❡ tr❛❞❡ ❜❛❧❛♥❝❡s ❛♥❞ ❝✉rr❡♥t ❛❝❝♦✉♥ts ✇♦r❧❞✲

✇✐❞❡✳ ❉♦ ✇❡ r❡❛❧❧② ❤❛✈❡ s♦ t♦✉❣❤ ♣r♦❜❧❡♠ ✇✐t❤ ❡①✐st✐♥❣ ❣❧♦❜❛❧ ✐♠❜❛❧❛♥❝❡s❄

■❢ s♦✱ ❤♦✇ ✇❡ ♠❛② ❝♦♣❡ ✇✐t❤ ✐t ❄ ❚❤❡ ✈✐❡✇s ❛r❡ ♦❢t❡♥ ❞✐✈❡rs❡ ❛♥❞ ❝♦♥tr♦✲

✈❡rs✐❛❧✳ ▼❛♥② ❡❝♦♥♦♠✐sts ✭s❡❡ ❡✳❣✳ ❇r✉♥❡t ❛♥❞ ●✉✐❝❤❛r❞ ✭✷✵✶✶✮❀ ❇❧❛♥❝❤❛r❞

❛♥❞ ▼✐❧❡s✐✲❋❡rr❡tt✐ ✭✷✵✵✾✮✮ ❝♦♥s✐❞❡r ✐♠❜❛❧❛♥❝❡s ❛s q✉✐t❡ s❡r✐♦✉s ❛♥❞ ♠♦st

❞❛♥❣❡r♦✉s t❤r❡❛t ❢♦r t❤❡ ♣r♦s♣❡r♦✉s ❢✉t✉r❡✳ ❆ ❞✐✛❡r❡♥t ✈✐❡✇ ❛♣♣❡❛rs ✐♥ t❤❡

✇♦r❦s ❈♦♦♣❡r ✭✷✵✵✼✮❀ P♦♣♦✈ ✭✷✵✶✵✮✳ ❚❤❡ r❡s❡❛r❝❤ ❤❡r❡ ✐s ❝♦♥❝❡r♥❡❞ ✇✐t❤

t❤❡ ❞❡✜❝✐t ❛♥❞ s✉r♣❧✉s ✐♠❜❛❧❛♥❝❡s ❛♠♦♥❣ ❝♦✉♥tr✐❡s✳ ■♥ t❤❡ ♣❛♣❡r ❈♦♦♣❡r

✭✷✵✵✼✮ ✐t ✐s ❞✐s❝✉ss❡❞ t❤❛t ❝✉rr❡♥t ❛❝❝♦✉♥t ❞❡✜❝✐t s❤♦✉❧❞ ♥♦t ❡①❝❧✉s✐✈❡❧② ❜❡

♣❡r❝❡✐✈❡❞ ❛s ♥❡❣❛t✐✈❡ ❢♦r t❤❡ ❧♦❝❛❧ ❡❝♦♥♦♠② ✐❢ ✐t ✐s ❝❛✉s❡❞ ❜② t❤❡ ❡①♣❡♥❞✐✲

t✉r❡s ♦♥ ❡❞✉❝❛t✐♦♥✱ r❡s❡❛r❝❤ ❛♥❞ ❞❡✈❡❧♦♣♠❡♥t ❛♥❞ ❝♦♥s✉♠❡r ❞✉r❛❜❧❡s✳ ❚❤❡s❡

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

t❤❡② ❝❛♥ ❝r❡❛t❡ s✉r♣❧✉s❡s ✐♥ t❤❡ ❢✉t✉r❡✳ ❚❤✐s ✐s ❛❧s♦ t❤❡ r❡❛s♦♥ ❢♦r t❤❡ ♦♣✐♥✐♦♥

♦❢ P♦♣♦✈ ✭✷✵✶✵✮ t❤❛t t❤❡ ✐♥t❡r✈❡♥t✐♦♥ ✐♥t♦ ❡❝♦♥♦♠② ✐s ♥♦t ♥❡❝❡ss❛r② ❜❡❝❛✉s❡

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

❚❤❡r❡ ✐s ❝❡rt❛✐♥❧② ♥♦ ❞♦✉❜t t❤❛t ❛ ❝♦✉♣❧✐♥❣ r❡❧❛t✐♦♥s❤✐♣ ❡①✐sts ❛♠♦♥❣ ❡❝♦✲

♥♦♠✐❝ ♣❡r❢♦r♠❛♥❝❡✱ ❞❡♠♦❣r❛♣❤✐❝ ❛♥❞ s♦❝✐❛❧ tr❡♥❞s✱ ❛♥❞ ❡❝♦❧♦❣✐❝❛❧ ♣r♦❝❡ss❡s✳

❚❤❡r❡❢♦r❡✱ ✐♥ ❛❞❞✐t✐♦♥ t♦ ♦✉r ♣r❡✈✐♦✉s ❡✈❛❧✉❛t✐♥❣ ♦❢ ❝✉rr❡♥t ❛❝❝♦✉♥t ❞❡✜❝✐ts

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

❧♦❣✐❝❛❧ ❞✐♠❡♥s✐♦♥ ♦❢ t❤❡ ♣r♦❜❧❡♠✳ ❘❡❧❛t✐♦♥s❤✐♣s ❜❡t✇❡❡♥ ❡❝♦❧♦❣✐❝❛❧ ✈❛r✐❛❜❧❡s s✉❝❤ ❛s ❈❖✷ ❡♠✐ss✐♦♥s ❛♥❞ ♣❡tr♦❧ ♦r ❝♦♥s✉♠♣t✐♦♥ ❤❛s ❜❡❡♥ ❦♥♦✇♥ ❛❧r❡❛❞② s✐♥❝❡ ✶✾✾✵s t❤❛♥❦s t♦ ●r♦ss♠❛♥ ❛♥❞ ❑r✉❡❣❡r ✭✶✾✾✶✮❀ ❇❡❝❦❡r♠❛♥ ✭✶✾✾✷✮ ❛♥❞

♦t❤❡rs✳ ❘❡❝❡♥t st✉❞✐❡s ❜② ❏♦❜❡rt ❡t ❛❧ ✭✷✵✶✵✮ tr❡❛ts ❈❖✷ ❡♠✐ss✐♦♥ ❝♦♥✈❡r✲

❣❡♥❝❡ ✐♥ t❤❡ ❊✉r♦♣❡❛♥ ❯♥✐♦♥✳ ❚❤❡② ✉s❡❞ t❤❡ ❇❛②❡s✐❛♥ s❤r✐♥❦❛❣❡ ❡st✐♠❛t✐♦♥

♠❡t❤♦❞ ✐♥ ✷✷ ❊✉r♦♣❡❛♥ ❝♦✉♥tr✐❡s s♣❛♥♥✐♥❣ t❤❡ ②❡❛rs ✶✾✼✶ t♦ ✷✵✵✻✳ ❚❤❡

r❡s✉❧ts ❝♦♥✜r♠❡❞ t❤❡ ❤②♣♦t❤❡s✐s ♦❢ ❛❜s♦❧✉t❡ ❝♦♥✈❡r❣❡♥❝❡ ♦❢ ♣❡r ❝❛♣✐t❛ ❈❖✷

❡♠✐ss✐♦♥s✳ ❚❤❡ r❡s❡❛r❝❤ r❡✈❡❛❧❡❞ ❛❧s♦ ❝♦rr❡❧❛t✐♦♥s ❜❡t✇❡❡♥ t❤❡ ✐♥❞✉str✐❛❧ s❡❝✲

t♦r ✐♥ ●❉P ❛♥❞ ❈❖✷ ❡♠✐ss✐♦♥s✳ ❚❤❡s❡ ✜♥❞✐♥❣s ♣❛rt❧✐❛❧❧② ❥✉st✐❢② ♦✉r ❢♦❝✉s

♦♥ ❈❖✷ ❡♠✐ss✐♦♥s ❞❛t❛✳ ■♥ ❣❡♥❡r❛❧✱ ❡♥❡r❣②✲r❡❧❛t❡❞ ❈❖✷ ♣r♦❞✉❝t✐♦♥ ❛♥❞ ❡♥✲

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

❚❤❡ ❛✐♠ ♦❢ t❤✐s ✇♦r❦ ✐s t♦ ✜♥❞ ♠❡t❤♦❞s ❢♦r ❛ss❡ss✐♥❣ ❛♥❞ ✐♥t❡r♣r❡t❛t✐♦♥

♦❢ t❤❡ ♠✉❧t✐♣❧❡ ❞❛t❛ s♦✉r❝❡s✳ ■♥ t❤❡ ♣❛♣❡r ✇❡ ❝♦♥s✐❞❡r ♠♦❞❡❧s ♦❢ ♠❡❛♥ ❞✐s✲

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

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

❡❧❡✈❡♥ ♠♦st ♣♦♣✉❧❛t❡❞ ❝♦✉♥tr✐❡s ❛♥❞ t❤❡ ❊❯✶✺ r❡❢❡rr❡❞ ❛s t✇❡❧❢t❤ ❝♦✉♥tr② ✐♥

❢✉rt❤❡r s❡❝t✐♦♥s✳ ❚❤❡ ♠✉t✉❛❧ ❡❝♦♥♦♠✐❝ ♣♦s✐t✐♦♥s ♦❢ t❤❡ ❝♦✉♥tr✐❡s ❛r❡ tr❡❛t❡❞

✹

(6)

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

♥♦♠✐❝ ✐♥❞✐❝❛t♦rs ✭✇❡ ❝❛❧❧ ❢❛❝t♦rs ✐♥ ✇❤❛t ❢♦❧❧♦✇s✮ ❝♦❧❧❡❝t❡❞ ♦✈❡r t❤❡ ♣❡r✐♦❞

❢r♦♠ ✶✾✾✷ t♦ ✷✵✵✽✳ ❆❢t❡r t❤❡ ❢♦r♠✉❧❛t✐♦♥ ♦❢ t❤❡ ❢♦✉♥❞❛t✐♦♥s ♦❢ ♦✉r ✐♥t✉✐t✐✈❡

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

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

♥♦t ♦♥❧② ❡❝♦♥♦♠✐❝ ✐ss✉❡s✱ ❜✉t ❛❧s♦ ❝♦♥❝❡♥tr❛t❡s ♦♥ ❛ ❤♦❧✐st✐❝ ✉♥❞❡rst❛♥❞✐♥❣

♦❢ t❤❡ ♣♦t❡♥t✐❛❧ s②st❡♠✐❝ r❡❧❛t✐♦♥s✳

❚❤❡ ♣❛♣❡r ✐s ♦r❣❛♥✐③❡❞ ❛s ✐t ❢♦❧❧♦✇s✳ ■♥ t❤❡ s❡❝t✐♦♥ ✷ ✇❡ ❞❡s❝r✐❜❡ t❤❡

s♦✉r❝❡s ❛♥❞ ❝♦❧❧❡❝t✐♦♥ ♦❢ ❞❛t❛✱ ✐♥ t❤❡ s❡❝t✐♦♥ ✸ ✇❡ ♣r❡s❡♥t t❤❡ ♠❡t❤♦❞ ❜❛s❡❞

♦♥ t❤❡ ❝♦♠❜✐♥❛t✐♦♥ ♦❢ t❤❡ ❞❛t❛ r❡s❝❛❧✐♥❣ ❛♥❞ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ❞✐st❛♥❝❡s

❜❡t✇❡❡♥ ❝♦✉♥tr✐❡s ❛♥❞ ❢❛❝t♦rs✳ ❚❤❡ s✉♣♣❧❡♠❡♥t❛r② ♠❡t❤♦❞♦❧♦❣✐❝❛❧ ✐ss✉❡s ❛r❡

❞✐s❝✉ss❡❞ ✐♥ t❤❡ s✉❜s❡❝t✐♦♥s ✸✳✶ ❛♥❞ ✸✳✷ ❞❡✈♦t❡❞ t♦ t❤❡ ❝♦♥❝❡♣ts ♦❢ ❞✐✈❡rs✐t②

♦❢ ❞✐st❛♥❝❡s✱ ❛♥❞ r❡s♣❡❝t✐✈❡❧②✱ t❡♠♣♦r❛❧ ✐♥st❛❜✐❧✐t② ❞❡s❝r✐❜❡❞ ❜② ♠❡❛♥s ♦❢

▲②❛♣✉♥♦✈✲t②♣❡ ❡①♣♦♥❡♥ts✳ ■♥ s❡❝t✐♦♥ ✺ t❤❡ ♠♦❞✐✜❡❞ ♠❡t❤♦❞♦❧♦❣② ✐s ❛♣♣❧✐❡❞

t♦ ❣r♦✉♣s ♦❢ ❝♦✉♥tr✐❡s✳ ❚❤❡ r❡s✉❧ts ♦❢ t❤❡ ✐♥✈❡st✐❣❛t✐♦♥ ❛♥❞ ✐♥t❡r♣r❡t❛t✐♦♥s

❛r❡ ❣✐✈❡♥ ✐♥ t❤❡ s❡❝t✐♦♥ ✹✳ ❋✐♥❛❧❧② t❤❡ ❝♦♥❝❧✉s✐♦♥s ❛r❡ ♣r❡s❡♥t❡❞✳

✷ ❉❛t❛

❚❤❡ ❛♥✉❛❧ ❞❛t❛ ❝♦✈❡r✐♥❣ ♣❡r✐♦❞ ❢r♦♠ ✶✾✾✷ t♦ ✷✵✵✽ ❤❛s ❜❡❡♥ r❡tr✐❡✈❡❞ ❢r♦♠

t❤❡ ❲♦r❧❞ ❇❛♥❦ ❞❛t❛❜❛s❡s ✭❲♦r❧❞ ❇❛♥❦ ✭✷✵✶✷✮✮✳ ❋♦r t❤❡ ♣✉r♣♦s❡ ♦❢ ♦✉r r❡s❡❛r❝❤ ✇❡ ❛♥❛❧②③❡❞ ✶✷ ✐♥❞✐❝❛t♦rs ✭❢❛❝t♦rs✮ ✐♥ t❤❡ ❤✐❣❤❧② ♣♦♣✉❧❛t❡❞ ❝♦✉♥✲

tr✐❡s ❇❛♥❣❧❛❞❡s❤ ✭❇❆◆✮✱ ❇r❛③✐❧ ✭❇❘❆✮✱ ❈❤✐♥❛ ✭❈❍■✮✱ ■♥❞✐❛ ✭■◆❉✮✱ ■♥❞♦♥❡✲

s✐❛ ✭■❉❖✮✱ ❏❛♣❛♥ ✭❏❆P✮✱ ▼❡①✐❝♦ ✭▼❊❳✮✱ ◆✐❣❡r✐❛ ✭◆■●✮✱ P❛❦✐st❛♥ ✭P❆❑✮✱

❘✉ss✐❛ ✭❘❯❙✮✱ ❯♥✐t❡❞ ❙t❛t❡s ♦❢ ❆♠❡r✐❝❛ ✭❯❙❆✮ ❛♥❞ t❤❡ ❊✉r♦♣❡❛♥ ❯♥✐♦♥

✭❊❯✶✺✮✳ ❚❤❡ s❡❧❡❝t✐♦♥ r❡♣r❡s❡♥ts ❛♣♣r♦①✐♠❛t❡❧② ✻✵✪ ♦❢ t❤❡ ✇♦r❧❞✬s ♣♦♣✉✲

❧❛t✐♦♥ ✐♥ ✷✵✶✷✳ ❚❤❡ ✐♥❞✐❝❛t♦rs ✇❡ ❢♦❝✉s ♦♥ ✐♥❝❧✉❞❡✿ ✐♥❝♦♠❡ ✭■◆❈✮ ❝❛r❜♦♥

❞✐♦①✐❞❡ ❡♠✐ss✐♦♥s ✭❈❖✷✮✱ ❝✉rr❡♥t ❛❝❝♦✉♥t ✭❈❆✮✱ ❡♥❡r❣② ✉s❡ ✭❊◆❯✮✱ ❡①t❡r✲

♥❛❧ ❞❡❜t ✭❊❳❉✮✱ ❣r♦ss ♥❛t✐♦♥❛❧ ✐♥❝♦♠❡ ✭●◆■✮✱ ✐♥✈❡st♠❡♥t ✭■◆❱✮✱ ❞♦♠❡s✲

t✐❝ s❛✈✐♥❣s ✭❙❆❱✮✱ ♣♦♣✉❧❛t✐♦♥ ✭P❖P✮✱ ❢♦r❡✐❣♥ ❡①❝❤❛♥❣❡ r❡s❡r✈❡s ✐♥❝❧✉❞✐♥❣

❣♦❧❞ ✭❋❊❘✮ ❛♥❞ ♦✐❧ ♣r♦❞✉❝t✐♦♥ ✭❖■▲✮✳ ❲❡ s❤♦✉❧❞ ♠❡♥t✐♦♥ t❤❛t ✐♥ s♦♠❡ ✐t❡♠s t❤❡ r❡❝♦r❞❡❞ ❞❛t❛ ✇❡r❡ ✐♥❝♦♠♣❧❡t❡✳ ❚❤❡ s✐t✉❛t✐♦♥ ❤❛s ❜❡❡♥ ♣❛rt✐❛❧❧② ❝♦r✲

r❡❝t❡❞ ❜② ❡①❝❧✉s✐♦♥ ♦❢ s✉♠♠❛t✐♦♥s ♦❢ t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❢❛❝t♦rs ✇✐t❤ ♣r♦♣❡r

♥♦r♠❛❧✐③❛t✐♦♥✳ ❚❤❡s❡ ♠✐ss✐♥❣ ❞❛t❛ ❞♦❡s ♥♦t ❡①❝❡❡❞ ♠♦r❡ t❤❛♥ ❢♦✉r ♣❡r❝❡♥t

♦❢ t❤❡ ✇❤♦❧❡ ❞❛t❛s❡t✳ ❉✉❡ t♦ r❡s❝❛❧✐♥❣ tr❛♥s❢♦r♠❛t✐♦♥s✱ ✇❤✐❝❤ ♣r❡❝❡❞❡ ❝❛❧❝✉✲

❧❛t✐♦♥ ♦❢ ❞✐st❛♥❝❡s ❜❡t✇❡❡♥ ❞❛t❛ s❡q✉❡♥❝❡s✱ ✐♥ ❢✉rt❤❡r ❝♦♥s✐❞❡r❛t✐♦♥s ✇❡ ✇✐❧❧

♥♦t ♣❛② ❛tt❡♥t✐♦♥ t♦ ❞❛t❛ ✉♥✐ts ✇❤✐❝❤ ❛r❡ ♥♦r♠❛❧❧② ♦❢ ✐♥t❡r❡st✳

✺

(7)

✸ ▼❡t❤♦❞ ❞❡s❝r✐♣t✐♦♥

❚❤❡ ❝♦♥❝❡♣t ♦❢ ❞✐st❛♥❝❡s ✐s ♦♥❡ ♦❢ t❤❡ ♠♦st ♣♦✇❡r❢✉❧ ❛♥❞ ✈❡rs❛t✐❧❡ t♦♦❧s t♦

st✉❞② t❤❡ r❡❧❛t✐✈❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ❝♦✉♥tr✐❡s ❛♥❞ ❢❛❝t♦rs ✇✐t❤♦✉t ❛❜s♦❧✉t✐③✐♥❣

t❤❡♠✳ ❚❤❡ ♣r♦❝❡❞✉r❡ ✇❡ ❛✐♠ t♦ ✉t✐❧✐③❡ t♦ ✜♥❞ ❛ss♦❝✐❛t✐♦♥ r❡❧❛t✐♦♥s❤✐♣s ✐♥

t❤❡ ❞❛t❛ ♠❛② ❜❡ r♦✉❣❤❧② ✈✐❡✇❡❞ ❛s ❛ ❞✐st❛♥❝❡✲❜❛s❡❞ ❛♣♣r♦❛❝❤ ✭❩❤❛♥❣ ❡t ❛❧✳✱

✷✵✵✾✮✳ ❇✉t ❡✈❡♥ t❤♦✉❣❤ ✐♥ ♦✉r ❝❛s❡✱ t❤❡ ❛♥❛❧②s✐s ❢♦❝✉s❡s ❛tt❡♥t✐♦♥ t♦ ❤✐❣❤✲

❞✐♠❡♥s✐♦♥❛❧ t✐♠❡ s❡r✐❡s ❞❛t❛s❡t✳ ❈♦♥s✐❞❡r t❤❡ t✐♠❡ ❞❡♣❡♥❞❡♥t ❞❛t❛ ♠❛tr✐①X

♦❢ ❡❧❡♠❡♥ts Xik(t)♦❢n×m❝♦♠❜✐♥❣ t❤❡ ✐♥❢♦r♠❛t✐♦♥ ❢r♦♠ t❤❡ s❡❧❡❝t❡❞ ❢❛❝t♦r k ∈ {1,2, . . . , m} ❝♦rr❡s♣♦♥❞✐♥❣ t♦ ❣✐✈❡♥ ❝♦✉♥tr②i∈ {1,2, . . . , n}✳ ❆s ✐t ❤❛s

❜❡❡♥ ♠❡♥t✐♦♥❡❞ ✐♥ t❤❡ ♣r❡✈✐♦✉s s❡❝t✐♦♥ ✇❡ st✉❞② t❤❡ s②st❡♠ ✇✐t❤ n = 12✱ m = 11✳ ❇❡❝❛✉s❡ t❤❡ t✐♠❡ ❞❡♣❡♥❞❡♥❝❡s Xik(t) ❛r❡ ♦❢ ✈❡r② ❞✐✛❡r❡♥t ✈❛❧✉❡

✭✉♥✐ts✮✱ ❢♦r t❤❡ ♣✉r♣♦s❡ ♦❢ r❡s❝❛❧✐♥❣ ✇❡ ✉s❡❞ t❡♠♣♦r❛r② st❛♥❞❛r❞✐③❛t✐♦♥

Xˆik(t) = Xik(t)−Xmin,ik(t)

Xmax,ik(t)−Xmin,ik(t). ✭✶✮

■♥ t❤✐s ❢♦r♠✉❧❛ ✇❡ ✉s❡ t❤❡ ✐♥st❛♥t ✭❧♦❝❛❧✮ ♠❛①✐♠✉♠ ❛♥❞ ♠✐♥✐♠✉♠ ✈❛❧✉❡s Xmax,ik(t) = max

τ∈W(t,T)Xik(τ), ✭✷✮

X_min,ik(t) = min

τ∈W(t,T)X_ik(τ), ✭✸✮

✇❤✐❝❤ ❛r❡ t♦ ❜❡ r❡❝❛❧❝✉❧❛t❡❞ ❢♦r r✉♥♥✐♥❣ t✐♠❡ r❡❝t❛♥❣✉❧❛r ✇✐♥❞♦✇ ❞❡✜♥❡❞ ❛s

❛ s❡t ♦❢ ♦❜s❡r✈❛t✐♦♥ t✐♠❡s ✐♥ ❝❤r♦♥♦❧♦❣✐❝❛❧ ♦r❞❡r

W(t, T) = {t−T + 1, t−T + 2, . . . , t−1, t}. ✭✹✮

❚❤❡ r✉♥♥✐♥❣ ✇✐♥❞♦✇ ✐s ♦❢ t❤❡ ❡①t❡♥t T✳ ❚❤✉s✱ ✐♥ ❝♦♠♣✉t❛t✐♦♥❛❧ ♣r❛❝t✐❝❡ ✇❡

❛r❡ ❢♦r❝❡❞ t♦ ✜♥❞ t❤❡ ❜❡st ❝♦♠♣r♦♠✐s❡ ❜❡t✇❡❡♥ t❤❡ ♠♦r❡ ❧♦❝❛❧✐③❡❞ ❢♦❝✉s ♦♥

t❤❡ ✐♥st❛♥t ❞❛t❛ ✈❛❧✉❡s ✭s♠❛❧❧ T✮ ♦r ❞❡s✐r❡❞ st❛t✐st✐❝❛❧ ♣♦✇❡r ✭❛❝❤✐❡✈❡❞ ❢♦r

❤✐❣❤❡rT✮✳ ✭❈❧❡❛r❧②✱ ✐♥ s✉❝❤ ❢♦r♠✉❧❛t✐♦♥✱ ❛s t❤❡ t✐♠❡ ♣❛ss❡s✱ t❤❡ ✇✐♥❞♦✇s ♠❛②

♦✈❡r❧❛♣✳✮ ◆♦✇ ❜❡❝❛✉s❡ ♦❢ ✐♠♣♦s❡❞ st❛♥❞❛r❞✐③❛t✐♦♥ ✭❧♦❝❛❧ r❡s❝❛❧✐♥❣✮✱ t❤❡ ✉♥✐ts

♦❢ X_ik ❜❡❝♦♠❡ ❝♦♠♣❧❡t❡❧② ✐rr❡❧❡✈❛♥t✳ ❆t ❛♥② ❣✐✈❡♥ t t❤❡ ♣❛✐r✇✐s❡ ♣r♦♣❡rt✐❡s

♦❢ t❤❡ s②st❡♠ ♠❛② ❜❡ ❛♥❛❧②③❡❞ ❜② ♠❡❛♥s ♦❢ t❤❡ ▼✐♥❦♦✇s❦✐✲t②♣❡ ❞✐st❛♥❝❡

Dik,jl(t) =





1 T

X

τ∈W(t,T)

Xˆik(t)−Xˆjl(t)

p





1/p

, ✭✺✮

✇❤❡r❡ p ✐s t❤❡ ❦♥♦✇♥ ✐♥❞❡① (p≥ 1)✳ ❇❡❝❛✉s❡ t❤❡ ❢♦✉r✲❞✐♠❡♥s✐♦♥❛❧ t❡♥s♦r✐❛❧

❢♦r♠ ♦❢ Dik,jl(t) ✐s t♦♦ ❡①❤❛✉st✐✈❡ ❢♦r t❤❡ ❞✐r❡❝t ✐♥t❡r♣r❡t❛t✐♦♥ ✇❡ ❤❛✈❡ t♦

✻

(8)

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

♦✈❡r t❤❡ ✐❞❡♥t✐❝❛❧ ❢❛❝t♦rs k✳ ❚❤❡ r❡❧❛t✐♦♥s D^cc_ij(t) = 1

m

X

k=1

Dik,jk(t), D_kl^ff(t) = 1 n

n

X

i=1

Dik,il(t). ✭✻✮

❞❡✜♥❡ ❛♥ ✐♥t❡r✲❝♦✉♥tr② ❛♥❞ ✐♥t❡r✲❢❛❝t♦r ♣❛✐r✇✐s❡ ♠❡❛♥ ❞✐st❛♥❝❡s✱ r❡s♣❡❝t✐✈❡❧②✳

❚❤✐s ✐♥❢♦r♠❛t✐♦♥ ❝♦♠♣r✐s❡❞ ✐♥ n² +m² ♠❛tr✐① ❡❧❡♠❡♥ts ✐s t❤❡♥ ❛❣❣r❡❣❛t❡❞

✐♥t♦ ✈❡❝t♦rs ♦❢ n ✭♦r m✮ ❝♦♠♣♦♥❡♥ts D_i^c(t) = 1

n−1

n

X

j=1,j6=i

D^cc_ij(t), D^f_k(t) = 1 m−1

m

X

l=1,l6=k

D^ff_kl(t). ✭✼✮

❚❤❡ ❝♦♠♣♦♥❡♥ts ❛r❡ ❛r✐t❤♠❡t✐❝ ♠❡❛♥ ❞✐st❛♥❝❡s ❜❡❧♦♥❣✐♥❣ t♦ ❝♦✉♥tr② ✭D_i^c✮

♦r ❢❛❝t♦r ✭D^f_k✮✳ ❋✐♥❛❧❧②✱ ✐♥ ♦r❞❡r t♦ ❡①tr❛❝t t❤❡ ♣r❡✈❛✐❧✐♥❣ ✧s♠♦♦t❤❡❞✧ ✇♦r❧❞

tr❡♥❞s ✇❡ ♣r♦♣♦s❡

D^c(t) = 1 n

m

X

l=1,l6=k

D_kl^c(t), D^f(t) = 1 m

m

X

l=1,l6=k

D^f_kl(t). ✭✽✮

❍♦✇❡✈❡r✱ ♠♦r❡ ❝r❡❞✐❜✐❧✐t② ❝❛♥ ❜❡ ❣✐✈❡♥ t♦ t❤❡ ♠❡❞✐❛♥ ❞❡s❝r✐♣t✐♦♥

D^cmed(t) = ♠❡❞✐❛♥(D^cc₁₁(t), D^cc₁₂(t)), . . . , D^cc_nn(t)) , ✭✾✮

D^fmed(t) = ♠❡❞✐❛♥D^ff₁₁(t), D₁₂^ff (t)), . . . , D^ff_mm(t) .

❆ ♠❡❛♥✐♥❣❢✉❧ ✇❛② t♦ ❤❛♥❞❧❡ ❞❛t❛ tr❛♥s❢♦r♠❡❞ ✐♥t♦ t❤❡ ✈❛r✐❛❜❧❡s D^cc_ij(t)✱

D^ff_ij(t)✱D^c(t)✱D^cmed(t)✱D^f(t)✱D^fmed(t)✐s ❜✉✐❧t✲✐♥ ✜✈❡✲♥✉♠❜❡r s✉♠♠❛r② ❜♦①✲

♣❧♦t ✇❡ ✉s❡ ✐♥ ❋✐❣✳✶✳ ❚❤❡ ❤✐❡r❛r❝❤② ♦❢ ❛❜♦✈❡ ✐♥❞✐❝❛t♦rs ♣r♦✈✐❞❡s ❛ ♣❛rt✐❝✉❧❛r

✈✐❡✇ ♦♥ t❤❡ ❞✐✛❡r❡♥t ❧❡✈❡❧s ♦❢ ❞✐st❛♥❝❡ ❝♦❛rs❡♥✐♥❣✳

■♥ t❤✐s ♣❛♣❡r ✇❡ r❡❝♦❣♥✐③❡❞ ❛❧s♦ ❛❞❞✐t✐♦♥❛❧ ❛♥❞ ✈❡r② ✐♠♣♦rt❛♥t ❢♦r♠s ♦❢

t❤❡ ❝❧❛ss✐✜❝❛t✐♦♥✴♦r❣❛♥✐③❛t✐♦♥ ♦❢ t❤❡ ❝❛❧❝✉❧❛t❡❞ ♦✉t♣✉ts✳ ❖♥❡ ♦❢ t❤❡ ♣♦t❡♥✲

t✐❛❧ ❜❡♥❡✜ts ♦❢ t❤❡ s✐♥❣❧❡ ✐♥❞❡①❡❞D^c_i ✐s t❤❛t ✐t ❛❧❧♦✇s s♦rt✐♥❣ ❛♥❞ ❝♦♥s❡q✉❡♥t r❛t✐♥❣ ♦❢ t❤❡ ❝♦✉♥tr✐❡s✳ ❲❤❡♥ t❤❡ ♠❡❛♥ ❞✐st❛♥❝❡s ❛r❡ s♦rt❡❞ D^c_i₁(t)< D_i^c₂ <

. . . < D_i^c_n(t)✱ t❤❡② ❜✉✐❧❞ ❛♥ ✐♥st❛♥t t✉♣❧❡ ♦❢ r❛♥❦si₁(t), i₂(t), . . . , i_n(t)✱ ✇❤❡r❡

❡❛❝❤ ❝♦✉♥tr② ✐♥❞❡① is ∈ 1,2, . . . , n✱ s ∈ {1,2, . . . , n}✮✳ ❖❜✈✐♦✉s❧②✱ ✉s✐♥❣

D^f_in(t)✱ t❤❡ ❛♥❛❧♦❣♦✉s ♣r♦❝❡❞✉r❡ ✐s ❛♣♣❧✐❝❛❜❧❡ t♦ t❤❡ ❢❛❝t♦rs✳ ■♥ t❤❡ s❡❝t✐♦♥ ✹ t❤❡ ❡❝♦♥♦♠✐❝ s✐❣♥✐✜❝❛♥❝❡ ❛♥❞ ✐♥t❡r♣r❡t❛t✐♦♥ ✐s ❛ttr✐❜✉t❡❞ t♦ t❤✐s ❢♦r♠❛❧ ❝❧❛s✲

s✐✜❝❛t✐♦♥ s②st❡♠✳

✸✳✶ ❚❤❡ ♣r♦♣❡rt✐❡s ♦❢ t❤❡ ❞✐str✐❜✉t✐♦♥ ♦❢ ❞✐st❛♥❝❡s

❚♦ ❣❛✐♥ ❛ ❝♦♠♣r❡❤❡♥s✐✈❡ ✈✐❡✇ ♦❢ t❤❡ ❞❛t❛ str✉❝t✉r❡✱ t❤❡ ❛❢♦r❡♠❡♥t✐♦♥❡❞ ❣❡♥✲

❡r❛❧✐③❡❞ ❛✈❡r❛❣❡s ♠✐❣❤t ♥♦t ♣r♦✈✐❞❡ ❣❛t❤❡r✐♥❣ ♦❢ ❛♥ ❛❞❡q✉❛t❡ ✐♥t❡r♣r❡t❛t✐♦♥✳

✼

(9)

❋♦r ❡①❛♠♣❧❡✱ t❤❡ ♣r♦❝❡ss ✇❤❡♥ ❞✐st❛♥❝❡ ✐s ❣♦✐♥❣ t♦ ❜❡ ❧❡ss ❞✐s♣❡rs❡❞ ❛r♦✉♥❞

t❤❡ ❝❡♥tr❛❧ t❡♥❞❡♥❝②✱ ♠❛② ✐♥❞✐❝❛t❡ ❛♥ ♦✈❡r❛❧❧ ❧❡✈❡❧ ♦❢ ❝❧✉st❡r✐♥❣✳ ❚❤❡r❡❢♦r❡✱

t❤❡ ♠❡t❤♦❞♦❧♦❣② s❤♦✉❧❞ ❜❡ str❡♥❣t❤❡♥❡❞ ❜② ♣r♦✈✐❞✐♥❣ t❤❡ ✐♥❢♦r♠❛t✐♦♥ ❛❜♦✉t t❤❡ ❞✐str✐❜✉t✐♦♥ ♦❢ ❞✐st❛♥❝❡s Dik,jl(t) ✭s❡❡ ❡✳❣✳❇✉r❣❤♦✉ts ❡t ❛❧✳✱ ✷✵✵✼✮✳ ❋♦r

❢✉rt❤❡r ❝♦♥✈❡♥✐❡♥❝❡ ♦❢ ❞❡s❝r✐♣t✐♦♥ ✇❡ ✐♥tr♦❞✉❝❡ t❤❡ s❡t ♦❢ ✐♥❞✐❝❡s

ID(t) ={(i, k, j, l); Dik,jl(t)>0}, ✭✶✵✮

✇❤✐❝❤ s✐♠♣❧② ❡①❝❧✉❞❡s t❤❡ ③❡r♦ ❞✐st❛♥❝❡s ❢r♦♠ t❤❡ ❝❛❧❝✉❧❛t✐♦♥s✳ ■t ❝❛♥ ❜❡

❞✐✈✐❞❡❞ ✐♥t♦ t❤❡ND ❞❛t❛ s❤❡❧❧s ♦❢ t❤❡ ❡q✉❛❧ ❡①t❡♥t∆D ❛♥❞ ❝❤❛r❛❝t❡r✐③❡❞ ❜② t❤❡✐r ❛❝t✉❛❧ ❝❛r❞✐♥❛❧✐t✐❡s

Cr(t) = ❝❛r❞{(i, k, j, l) ; (r−1) ∆D< Dik,jl(t)≤r∆D; ✭✶✶✮

i, j = 1, . . . , n;k, l = 1, . . . , m} ,

✇❤❡r❡ r = 1, . . . , ND ❛♥❞ ∆D = Dmax/ND✱ ✇❤❡r❡ Dmax ✐s ❛ ♠❛①✐♠✉♠ ♦❢

Dik,jl(t) ❢r♦♠ ❛❧❧ t❤❡ ❝♦♥s✐❞❡r❡❞ ❡♣♦❝❤s✳ ❚❤✉s✱ t❤❡ ✐♥st❛♥t ♣r♦❜❛❜✐❧✐t② ♦❢ t❤❡

❢❛❧❧ ♦❢ D_ik,jl(t) ✐♥t♦ t❤❡ ❜✐♥ s ♠❛② ❜❡ ❡st✐♠❛t❡❞ ❛s ˆ

πs(t) = Cs(t)

PND

r=1Cr(t), s= 1,2, . . . , ND. ✭✶✷✮

◆♦✇ t❤❡ ❧✐♥❦❛❣❡ t♦ t❤❡ ❙❤❛♥♥♦♥ ✐♥❞❡① ❜❡❝♦♠❡s str❛✐❣❤t❢♦r✇❛r❞

❙❍(t) = − 1 ln(N_D)

ND

X

s=1

ˆ

πs(t) ln(ˆπs(t)). ✭✶✸✮

❚❤❡ ❙❤❛♥♦♥ ✐♥❞❡① ✐s ♥♦r♠❛❧✐③❡❞✱ ✐✳❡✳ r❛♥❣❡s ❢r♦♠ ③❡r♦ t♦ ♦♥❡❀ ❛♣♣r♦❛❝❤✐♥❣

✉♥✐t② ♠❡❛♥s ❢♦r♠❛t✐♦♥ ♦❢ ✉♥✐❢♦r♠ ❞✐str✐❜✉t✐♦♥ ❛♥❞ ❛♣♣r♦❛❝❤✐♥❣ ③❡r♦ ♠❡❛♥s

❡✈❛❧✉❛t✐♦♥ ♦❢ t❤❡ ♠✐♥✐♠✉♠ ♦❢ ❞✐✈❡rs✐t② ♦❢ ❞✐st❛♥❝❡s✳ ❆❧t❡r♥❛t✐✈❡❧②✱ t❤❡ ❜✐♥✲

♥✐♥❣ ♦❢ ❞✐st❛♥❝❡s ✐s ♥♦t r❡q✉✐r❡❞ ❜② t❤❡ ❣❡♥❡r❛❧✐③❡❞ ❡♥tr♦♣② ✐♥❞❡① ✭❯❧❧❛❤ ❛♥❞

●✐❧❡s✱ ✶✾✾✽✮

●❊(α,{D}, t) = 1

α(α−1)❝❛r❞(ID(t))

X

(i,k,j,l)∈ID(t)

"

Dik,jl(t) D(t)

!α

−1

#

, ✭✶✹✮

✇❤❡r❡ α ✐s t❤❡ ❢r❡❡ ♣❛r❛♠❡t❡r ✇❡ ✈❛r②✳ ❚❤❡ ✐♥❞❡① r❡❢❡rs t♦ t❤❡ ✐♥st❛♥t ♠❡❛♥

D(t) = 1

❝❛r❞(ID(t))

X

(i,k,j,l)∈ID(t)

Dik,jl(t). ✭✶✺✮

▲❡t ✉s ♥♦t✐❝❡ ❛ ❣❡♥❡r❛❧ ♣r♦♣❡rt②✿ ✐♥ t❤❡ ❝❛s❡α→1t❤❡ ●❊ ✐♥❞❡① ❝♦♥✈❡rts t♦

t❤❡ ❦♥♦✇♥ ❚❤❡✐❧ ✐♥❞❡① ❚❍(t) ✇❡ ✉s❡ ❛s ❛♥ ❛❧t❡r♥❛t✐✈❡ ❢♦r t❤❡ q✉❛♥t✐✜❝❛t✐♦♥

♦❢ t❤❡ ❤❡t❡r♦❣❡♥❡✐t② ❛♥❞ r❡❞✉♥❞❛♥❝② ♦❢ D_ik,jl ❞✐st❛♥❝❡s✳

✽

(10)

✸✳✷ ❚❤❡ ▲②❛♣✉♥♦✈✲t②♣❡ ♠❡❛s✉r❡s❀ t❡♠♣♦r❛❧ ♥❡✐❣❤❜♦r✲

❤♦♦❞

❚❤❡ s❤♦rt✲t✐♠❡ st❛❜✐❧✐t② ♦❢ t❤❡ r❡❧❛t✐✈❡ ♣♦s✐t✐♦♥s ♦❢ t❤❡ ❡❧❡♠❡♥t❛r② ♣❛✐rs ♦❢

t❤❡ s②st❡♠ ✭❝♦✉♥tr✐❡s ♣❧✉s t❤❡✐r ❢❛❝t♦rs✮ ♠❛② ❜❡ q✉❛♥t✐✜❡❞ ❜② t❤❡ s❡♣❛r❛t✐♦♥

r❛t❡ ❞❡✜♥❡❞ ❜② t❤❡ ▲②❛♣✉♥♦✈✲t②♣❡ ❡①♣♦♥❡♥ts λik,jl(t) = ln Dik,jl(t+ 1)

Dik,jl(t)

!

. ✭✶✻✮

❋r♦♠ t❤❡ ❞②♥❛♠✐❝❛❧ s②st❡♠s ♣♦✐♥t ♦❢ ✈✐❡✇✱ t❤❡ t✇♦ ♣r✐♥❝✐♣❛❧ s②st❡♠✐❝ ❛❣❣r❡✲

❣❛t❡s ♠❛② ❜❡ ❞❡✜♥❡❞✳ ❚❤❡ ♣♦s✐t✐✈❡

λ₊(t) = 1

❝❛r❞(ID(t))

X

Λ+(t)

λ_ik,jl(t) ✭✶✼✮

s✉♠♠✐♥❣ ✉♣ t❤❡ ♣♦s✐t✐✈❡ ❡①♣♦♥❡♥ts✱ ✇❤✐❝❤ ❤❛✈❡ t❤❡ ♠❡❛♥✐♥❣ ♦❢ t❤❡ ♣❤❛s❡✲

s♣❛❝❡ ❡①♣❛♥s✐♦♥✳

❚❤❡ ♦♣♣♦s✐t❡ s✐❞❡ r❡♣r❡s❡♥ts ♥❡❣❛t✐✈❡ ❛❣❣r❡❣❛t❡ s❝♦r❡

λ−(t) = 1

❝❛r❞(ID(t))

X

Λ₋(t)

λik,jl(t). ✭✶✽✮

■t ❝❛♥ ❜❡ ✉s❡❞ t♦ r❡❧✐❡✈❡ s②♠♣t♦♠s ♦❢ t❤❡ ✐♥st❛♥t ❝♦♥✈❡r❣❡♥❝❡✳ ❚❤❡ ❛❜♦✈❡

❢♦r♠✉❧❛s ✐♥✈♦❧✈❡ t❤❡ s✉♠♠❛t✐♦♥ r✉♥♥✐♥❣ ♦✈❡r t❤❡ ♥♦♥✲✐♥t❡rs❡❝t✐♥❣ ❞②♥❛♠✐❝

s✉❜s❡ts ♦❢ ❢♦✉r✲t✉♣❧❡ ✐♥❞✐❝❡s

Λ+(t) = {(i, k, j, l) ; λik,jl(t)>0,∀(i, k, j, l)∈ID(t)} , ✭✶✾✮

Λ−(t) = {(i, k, j, l) ; λik,jl(t)<0,∀(i, k, j, l)∈ID(t)} .

✹ ❚❤❡ r❡s✉❧ts ❛♥❞ ✐♥t❡r♣r❡t❛t✐♦♥

❖✉r ❛❝t✉❛❧ ✐♥t❡r♣r❡t❛t✐♦♥ ♦❢ t❤❡ r❡s✉❧ts ✐s str♦♥❣❧② ❣✉✐❞❡❞ ❜② t❤❡ ♠✉❧t✐♣❧❡

❝♦♠♣❛r✐s♦♥s ♦❢ t❤❡ s✐♠✐❧❛r✐t✐❡s t❤❛t ❡①✐st ♦r ❡①✐st❡❞ ✇✐t❤ t❤❡ ♥✉♠❡r✐❝❛❧ ❛♥❛❧✲

②s✐s ♦❢ ❞❛t❛ ♦❜❥❡❝ts✳ ■♥ ♦✉r ✇♦r❦✱ ✐t ✇♦✉❧❞ ❜❡ ♠♦r❡ ❛❝❝✉r❛t❡ t♦ s♣❡❛❦ ♦❢ ❛

❜✐❞✐r❡❝t✐♦♥❛❧ ✐♥✢✉❡♥❝✐♥❣ ❜❡t✇❡❡♥ ♣r♦❝❡ss❡❞ ✐♥❢♦r♠❛t✐♦♥ ♦♥ t❤❡ ♦♥❡ s✐❞❡✱ ❛♥❞

✐ts ✐♥t❡r♣r❡t❛t✐♦♥ ♦♥ t❤❡ ♦t❤❡r s✐❞❡✳

▲♦♦❦✐♥❣ ❛t ❚❛❜✳✶✱ ✐♥❝❧✉❞✐♥❣ r❛♥❦✐♥❣ ❛❝❝♦r❞✐♥❣ t♦ ♠❡❛♥ ❞✐st❛♥❝❡s✱ t❤r❡❡

♠❛✐♥ ③♦♥❡s ♠❛② ❜❡ ✐❞❡♥t✐✜❡❞✳ ❚❤❡ ✜rst ❢♦✉r ♣♦s✐t✐♦♥s ♠❛② ❜❡ ❝♦♥s✐❞❡r❡❞

❛s t❤❡ ❝♦r❡ ♦❢ t❤❡ ✇♦r❧❞ ❡❝♦♥♦♠②✱ t❤❡ ❧❛st ❢♦✉r ❛r❡ ✐♥t❡r♣r❡t❡❞ ❛s ♣❡r✐♣❤❡r❛❧✳

❲❡ ❝❛♥ ❝❧❡❛r❧② ♦❜s❡r✈❡ t❤❛t t❤❡ ♣❡r✐♣❤❡r❛❧ ③♦♥❡ ♦❢ ❞✐ss✐♠✐❧❛r✐t② ❛♥❞ ♦✉t❧✐❡rs

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

✾

(11)

❚❛❜❧❡ ✶✿ ❚❤❡ ❝♦✉♥tr✐❡s ❛♥❞ ❢❛❝t♦rs s♦rt❡❞ ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ♠❡❛♥ ❞✐st❛♥❝❡s D^c_i(t)❛♥❞D_k^f(t)❀ ❤♦r✐③♦♥t❛❧ ♦r❣❛♥✐③❛t✐♦♥ ♦❞ t❤❡ t❛❜❧❡✿ ❛❝t✉❛❧ ❛♥♥✉❛❧ ❝♦✉♥tr②

✇✐t❤ s♠❛❧❧❡st D^c_i(t)✐s ♣♦s✐t✐♦♥❡❞ ❛t t❤❡ ♠♦st ❧❡❢t ♣♦s✐t✐♦♥✱ ✇❤❡r❡❛s t❤❡ ♠♦st

♣❡r✐♣❤❡r❛❧ ❝♦✉♥tr② ❛❝q✉✐r❡s t✇❡❧❢t❤ ♣♦s✐t✐♦♥ ✭n= 12✮✳ ❆♥❛❧♦❣♦✉s r❛♥❦✐♥❣ ✐s

❛✈❛✐❧❛❜❧❡ ❢♦r ❢❛❝t♦rs✳ ❚❤❡ ❞❛t❛ t❤❛t s❡r✈❡ t❤❡ ❜❛s✐s ❢♦r t❤❡ ❞❡t❡r♠✐♥❛t✐♦♥ ♦❢

r❛♥❦s ❡①tr❛❝t❡❞ ❢r♦♠ t❤❡ ❲♦r❧❞ ❇❛♥❦ ❞❛t❛❜❛s❡s ✭❲♦r❧❞ ❇❛♥❦✱ ✷✵✶✷✮✳ ❇❡✲

❝❛✉s❡T = 5✐s t❤❡ s✐③❡ ♦❢ t❤❡ t✐♠❡ ✇✐♥❞♦✇ ❢r♦♠ ❊q✳✭✹✮✱ t❤❡ ✐♥✐t✐❛❧ t❛❜❧❡ ❡♥tr②

✐s s❤✐❢t❡❞ ❢♦r✇❛r❞ t♦ t❤❡ ②❡❛r ✶✾✾✻✳

r❛♥❦✐♥❣ ✈✐❛D^c_i

year 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

1996 CHI IDO BAN USA IND PAK BRA JAP EU15 NIG MEX RUS 1997 CHI IDO IND BAN USA JAP EU15 BRA PAK MEX NIG RUS 1998 EU15 IND CHI USA PAK BAN JAP BRA IDO NIG MEX RUS 1999 IND PAK BAN USA MEX CHI NIG EU15 BRA JAP IDO RUS 2000 IND BAN PAK CHI USA BRA MEX EU15 NIG JAP IDO RUS 2001 PAK IND CHI BAN BRA MEX EU15 USA JAP NIG RUS IDO 2002 IND PAK BAN BRA MEX CHI EU15 IDO JAP RUS USA NIG 2003 PAK IND CHI BAN BRA MEX EU15 JAP IDO RUS USA NIG 2004 IND PAK CHI MEX BRA BAN EU15 JAP USA IDO RUS NIG 2005 IND MEX CHI PAK BRA USA BAN JAP RUS IDO EU15 NIG 2006 MEX CHI IND BAN BRA USA PAK JAP RUS IDO EU15 NIG 2007 MEX BRA IND CHI PAK BAN IDO USA JAP RUS EU15 NIG 2008 MEX IND BRA IDO CHI BAN PAK EU15 RUS NIG JAP USA

r❛♥❦✐♥❣ ✈✐❛ D_i^f

year 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

1996 GNI ENU POP INC CO2 INV SAV OIL FER EXD CA 1997 GNI POP ENU INC INV SAV CO2 OIL FER CA EXD 1998 POP GNI INC ENU SAV INV CO2 OIL FER CA EXD 1999 GNI INC POP ENU SAV INV CO2 OIL FER EXD CA 2000 GNI INC ENU POP INV SAV CO2 FER OIL EXD CA 2001 GNI ENU INC POP INV SAV CO2 FER OIL EXD CA 2002 GNI ENU POP CO2 INC SAV INV CA FER OIL EXD 2003 GNI ENU POP INC CO2 SAV FER CA INV OIL EXD 2004 GNI INC ENU CO2 POP SAV FER INV OIL CA EXD 2005 GNI INC ENU CO2 POP SAV INV FER OIL CA EXD 2006 GNI INC INV SAV ENU POP CO2 FER OIL CA EXD 2007 GNI INC INV SAV ENU POP CO2 FER OIL CA EXD 2008 GNI INC INV ENU SAV POP CO2 FER OIL CA EXD

♣♦s✐t✐♦♥s ✐♥ t❤❡ r❛♥❦✐♥❣ ❧♦❝❛t❡❞ ❜❡t✇❡❡♥ ❝♦r❡ ❛♥❞ ♣❡r✐♣❤❡r②✱ ✇✐❧❧ ❜❡ ❝❛❧❧❡❞

♥❡✉tr❛❧ ③♦♥❡✳ ■t s❤♦✉❧❞ ❜❡ ♥♦t❡❞ t❤❛t t❤❡ ❝♦♥t❡♥t ♦❢ ③♦♥❡s ❞♦❡s ♥♦t r❡♠❛✐♥

st❛t✐❝ ♦r st❛❜❧❡ ♦✈❡r t✐♠❡✳ ❈❧❡❛r❧②✱ t❤❡ ♣❧❛❝❡♠❡♥t ✐♥ t❤❡ ❝♦r❡ ✭❧❡❢t♠♦st ♣♦✲

s✐t✐♦♥ ✐♥ t❤❡ t❛❜❧❡✮ r❡♣r❡s❡♥ts t❤❡ ♣♦ss❡ss✐♦♥ ♦❢ t❤❡ ❝♦♠♠♦♥ ❢❡❛t✉r❡s ♦❢ t❤❡

✶✵

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❡♥t✐t✐❡s ❝♦♠♣❛r❡❞✱ ✐t ♠❛② r❡✢❡❝t t❤❡ s②♥❡r❣✐st✐❝ ♣❤❡♥♦♠❡♥❛✳ ❖✉r ❡♠♣✐r✐❝❛❧

r❡s❡❛r❝❤ ❤❛s ❧❡❞ ✉s t♦ ❝♦♥❝❧✉❞❡ t❤❛t ❛ ♣❡r✐♣❤❡r② ❝❛♥ ❜❡ ✈✐❡✇❡❞ ❛s ❛ ③♦♥❡

♦❢ t❤❡ ❛t②♣✐❝❛❧✱ ❧❡ss ✐♥✢✉❡♥t✐❛❧ ♦r ✉♥st❛❜❧❡ ❡♥t✐t✐❡s ♦❢ t❤❡ ❣❧♦❜❛❧ s②st❡♠✳ ❲❡

❤②♣♦t❤❡s✐③❡ t❤❛t ❝♦✉♥tr② ✭♦r ❢❛❝t♦r✮ ✐s ✐♥ ❛❝❝♦r❞❛♥❝❡ ✇✐t❤ ♠❛❥♦r ✇♦r❧❞ ❝♦♦r✲

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

♠❡❛♥ ❞✐st❛♥❝❡s ❝♦rr❡s♣♦♥❞ t♦ t❤❡ ❣❧♦❜❛❧ ♣❡r✐♣❤❡r❛❧s ❛♥❞ ♣♦ss✐❜❧❡ s♦✉r❝❡s ♦❢

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

r✐③❛t✐♦♥ ✐s t❡st❡❞ ❜② ❝♦♠♣❛r✐♥❣ ✇✐t❤ t❤❡ ♠❛✐♥ ❤✐st♦r✐❝❛❧ ❢❛❝ts✱ ♣♦❧✐❝② ❞❡❝✐s✐♦♥s

❛♥❞ ❤✐❣❤ ✐♠♣❛❝t ❡❝♦♥♦♠② ❡✈❡♥ts✳ ❆s ✇❡ s❤❛❧❧ s❡❡ ✐♥ ❢✉rt❤❡r✱ t❤❡ ♠❡t❤♦❞✲

♦❧♦❣② ❤❛s ♥♦t✐❝❡❛❜❧② ❣♦♦❞ ❝❛♣❛❜✐❧✐t② t♦ ❝❛♣t✉r❡✱ ❝❧❛ss✐❢② ❛♥❞ ✜♥❞ ❝♦♥t❡①ts

♦❢ t❤❡ ❣❧♦❜❛❧ ♠♦t✐♦♥s✳ ❚❤❡r❡ ✇✐❧❧ ❜❡ ❛❧s♦ ❛♥ ✐♥❞✐❝❛t✐♦♥ ♦❢ t❤❡ ❢♦r❡❝❛st✐♥❣

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

❆♥❛❧②③✐♥❣ t❤❡ r❛♥❦s ♦❢ t❤❡ ♣❛rt✐❝✉❧❛r ❝♦✉♥tr✐❡s ✇❡ ❝♦♠❡ t♦ t❤❡ ❢♦❧❧♦✇✐♥❣

❝♦♥❝❧✉s✐♦♥s✳ ❙✐♥❝❡ ✶✾✾✻✱ t❤❡ ❝♦✉♥tr✐❡s ❞✐✛❡r❡❞ ✐♥ t❡r♠s ♦❢ t❤❡✐r r❛♥❦✐♥❣ ✐♥

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

❤❛✈❡ ❧❡❢t t❤❡ ✉♥st❛❜❧❡ ♣❡r✐♣❤❡r② t♦ s❡tt❧❡ ✐♥ t❤❡ ❝♦r❡ ❛♥❞ ✈✐❝❡ ✈❡rs❛✳

❚❤❡ r❛♥❦✐♥❣ ♦♥ t❤❡ ❜❛s✐s ♦❢ D_k^f(t) ✭s❡❡ ❚❛❜✳✶✮ s❤♦✇s t❤❛t ❡①t❡r♥❛❧ ❞❡❜t

❛♥❞ ❝✉rr❡♥t ❛❝❝♦✉♥t ❛s ❛ ♠❛✐♥ ❢❛❝t♦r r❡s♣♦♥s✐❜❧❡ ❢♦r t❤❡ ♠❛❣♥✐❢②✐♥❣ ♦❢ t❤❡

❣❧♦❜❛❧ ❞✐✈❡r❣❡♥❝❡s✳ ❖✐❧ ♣r♦❞✉❝t✐♦♥ ❛♥❞ ❢♦r❡✐❣♥ ❡①❝❤❛♥❣❡ r❡s❡r✈❡s ❛r❡ ❛❧s♦

r❛t❤❡r ❞❡st❛❜✐❧✐③✐♥❣ ❡❧❡♠❡♥ts ✐♥ t❤❡ ❣❧♦❜❛❧ ❡❝♦♥♦♠②✳ ❲❡ ❝❛♥ ❝♦♥❝❧✉❞❡ t❤❛t

✐♥❝♦♠❡✱ ❣r♦ss ♥❛t✐♦♥❛❧ ✐♥❝♦♠❡✱ ❡♥❡r❣② ✉s❡ ❛♥❞ ♣♦♣✉❧❛t✐♦♥ ❣r♦✇t❤ ❛r❡ st❛❜✐❧✐③✲

✐♥❣ ❝♦r❡ ✐♥❞✐❝❛t♦rs✳ ❋✉rt❤❡r ❝♦♠♣❛r✐s♦♥ ♦❢ ❢❛❝t♦rs ✉♥❝♦✈❡r❡❞ ❤✐❣❤❡st st❛❜✐❧✐t②

♦❢ ❣r♦ss ♥❛t✐♦♥❛❧ ✐♥❝♦♠❡✱ ✇❤✐❝❤ ✐s ❝♦♥s✐st❡♥t ✇✐t❤ t❤❡ ✐❞❡❛ ♦❢ s②♥❝❤r♦♥✐③❛t✐♦♥

♦❢ t❤❡ ❡❝♦♥♦♠✐❝ ❝②❝❧❡s✳ ❋✐❣✳✶ ❞❡♣✐❝ts t❤❡ t✐♠❡ ❡✈♦❧✉t✐♦♥ ♦❢ D^c(t)✱ D^f(t) ❛♥❞

D^cmed(t)✱ D^fmed(t) ❛♥❞ ❝❛❧❝✉❧❛t❡❞ ❜② ♠❡❛♥s ♦❢ ❊q✳✭✽✮ ❛♥❞ ❊q✳✭✾✮ ❢♦r T = 5

✭❛♥❞ ❛❧s♦ T = 4✮ ❛♥❞ p = 1 ✭✇✐t❤ ❝❤❡❝❦ ❢♦r p = 2✮✳ ▲♦♦❦✐♥❣ ❛❣❛✐♥ ❛t t❤✐s

✜❣✉r❡ ✇❡ s❡❡ t❤❛t t❤❡ ♣❡r✐♦❞ ✶✾✾✷✲✷✵✵✺ ❝❛♥ ❜❡ ❝❤❛r❛❝t❡r✐③❡❞ ❜② t❤❡ r❡❧❛t✐✈❡❧② str♦♥❣ ❝♦♥✈❡r❣❡♥❝❡ ✇✐t❤ r❡s♣❡❝t t♦ t❤❡ ❛r✐t❤♠❡t✐❝ ❛♥❞ ❣❡♥❡r❛❧✐③❡❞ ♠❡❛♥✳ ❚❤❡

❝♦♥s❡❝✉t✐✈❡ ♣❡r✐♦❞ ❜❡t✇❡❡♥ ✷✵✵✺ ❛♥❞ ✷✵✵✼ s❡❡♠❡❞ ❡①❤✐❜✐t st❛❜✐❧✐③❛t✐♦♥✳ ❍♦✇✲

❡✈❡r✱ r❛❞✐❝❛❧ t✉r♥✐♥❣ ♣♦✐♥t ♦❝❝✉rr❡❞ ✐♥ ✷✵✵✽✱ ✇❤✐❝❤ ❝♦rr❡s♣♦♥❞s t♦ t❤❡ ❯✳❙✳

✜♥❛♥❝✐❛❧ ❝r✐s✐s ❛✛❡❝t✐♥❣ t❤❡ ✇♦r❧❞ ❡❝♦♥♦♠②✳ ■♥ t❤❡ ②❡❛r ♠❡♥t✐♦♥❡❞✱ ♣r❡❝❡❞❡❞

♥❡①t ❜② ❏❛♣❛♥✱ t❤❡ ❯✳❙✳ ♦❝❝✉♣✐❡❞ t❤❡ ❧❛st ♣♦s✐t✐♦♥ ✐♥ t❤❡ r❛♥❦✐♥❣ ❣✐✈❡♥ ✐♥

❚❛❜✳✶✳ ■♥ ❚❛❜✳✷✱ t❤❡ ♥❡✐❣❤❜♦r❤♦♦❞ ♦❢ t❤❡ ❯✳❙✳✱❏❛♣❛♥ ❛♥❞ t❤❡ ❊❯✶✺ ❛s ✇❡❧❧ ❛s

❛♥ ✐❞❡♥t✐✜❡❞ ❝❧✉st❡r ♦❢ ♦✉t❧✐❡rs ❝♦♥s✐st✐♥❣ ❝♦♥❝❧✉s✐✈❡❧② ♦❢ ❛❧❧ t❤❡s❡ ❝♦✉♥tr✐❡s

✐s ♦❜✈✐♦✉s✳ ❚❤❡ s✉♣♣❧❡♠❡♥t❛r② ✈✐❡✇ ♦♥ t❤❡ s✐♠✐❧❛r✐t✐❡s ♦✛❡r ❞❡♥❞r♦❣r❛♠s ✐♥

❋✐❣✳✷✳ ❚❤❡ ❝❛r❡❢✉❧ ❡①❛♠✐♥❛t✐♦♥ s❤♦✇s t❤❡② ❛r❡ ❝♦♥s✐st❡♥t ✇✐t❤ t❤❡ r❛♥❦✐♥❣

❝♦♠♣r✐s❡❞ ✐♥ ❚❛❜✳✷✳

❇❡❝❛✉s❡ t❤❡ ♦♣t✐♠❛❧ ♥✉♠❜❡r ❛♥❞ str✉❝t✉r❡ ♦❢ t❤❡ ❛❞♠✐ss✐❜❧❡ ❡❝♦♥♦♠✐❝

❢❛❝t♦rs ✐s ♥♦t ❦♥♦✇♥ ❛ ♣r✐♦r②✱ ✭♦✉r ✐♥t✉✐t✐✈❡ ❝❤♦✐❝❡ ✐sm= 11✮✱ t♦ s✉st❛✐♥ ♦✉r

❝♦♥❝❧✉s✐♦♥s ✇❡ t❡st❡❞ ✇❤❡t❤❡r t❤❡ ❝♦♥✈❡r❣✐♥❣✴❞✐✈❡r❣✐♥❣ s❝❡♥❛r✐♦ ❛❧s♦ r❡♠❛✐♥s

✶✶

(13)

✭❛✮

1996 1998 2000 2002 2004 2006 2008

0.200.250.300.350.40

year Dc , Dc med

✭❜✮

●

1996 1998 2000 2002 2004 2006 2008

0.200.250.300.350.40

year Df , Df med

❋✐❣✉r❡ ✶✿ ❚❤❡ ❞❛s❤❡❞ ❧✐♥❡s r❡♣r❡s❡♥t ♠❡❛♥ ❝❛❧❝✉❧❛t❡❞ ❢r♦♠ ❊q✳✭✽✮✳ ❚❤❡ ♠❡✲

❞✐❛♥ ✭❤♦r✐③♦♥t❛❧ ❧✐♥❡✮ ❜❡❧♦♥❣s ❊q✳✭✾✮✳ ❚❤❡ ❜♦①♣❧♦t ❢♦r ❝♦✉♥tr✐❡s ✐s ❝♦♥str✉❝t❡❞

❜② t❛❦✐♥❣ st❛t✐st✐❝s ♦♥ ✈❛❧✉❡s D^cc_ij✳ P❛rt ✭❛✮ s✉♠♠❛r✐③❡s ❝♦✉♥tr✐❡s✱ ♣❛rt ✭❜✮

✐♥❝❧✉❞❡s ❢❛❝t♦rs✳ ❲❡ s❡❡ t❤❛t ❣r♦✉♣✐♥❣ ♦❢ ✐♥t❡r✲❝♦✉♥tr② ❞✐st❛♥❝❡s ♣r♦✈✐❞❡s ❛

♠♦r❡ ♣r♦♥♦✉♥❝❡❞ ❛♥❞ ❧❡ss ♥♦✐s② ❞❡♣❡♥❞❡♥❝❡ t❤❛♥ t❤❡ s❛♠❡ ♣r♦❝❡❞✉r❡ ❛♣♣❧✐❡❞

t♦ ❢❛❝t♦rs✳

✶✷

(14)

EU15 BRA

IND JAP CHI IDO USA BAN PAK

MEX NIG RUS

0.1 0.3 0.5 0.7

1996

Height

BRA MEX

NIG PAK BAN

IND CHI USA EU15

RUS IDO

JAP

0.1 0.3 0.5 0.7 0.9

1999

Height

RUS BAN

CHI IND BRA

PAK IDO NIG EU15 MEX JAP USA

0.1 0.2 0.3 0.4 0.5 0.6

2002

Height NIG

RUS BRA MEX

JAP USA EU15 BAN

CHI IDO IND PAK

0.10 0.20 0.30 0.40

2006

Height

RUS MEX BRA PAK

IDO IND BAN

CHI

NIG JAP

USA EU15

0.10 0.20 0.30 0.40

2007

Height

USA JAP EU15 BAN

CHI IND PAK

NIG RUS IDO BRA MEX

0.1 0.2 0.3 0.4 0.5 0.6 0.7

2008

Height

❋✐❣✉r❡✷✿❚❤❡❞❡♥❞r♦❣r❛♠s♦❜t❛✐♥❡❞✈✐❛t❤❡❲❛r❞❧✐♥❦❛❣❡♠❡t❤♦❞✉s✐♥❣t❤❡❡✛❡❝t✐✈❡❞✐st❛♥❝❡♠❛tr✐①D cckl(t)❬❞❡✜♥❡❞❜②❊q✳✭✻✮❪❛s✐♥♣✉t✳❙❡❡t❤❡♥❡✐❣❤❜♦r❤♦♦❞str✉❝t✉r❡❞❡♣✐❝t❡❞✐♥t❛❜❧❡✷❢♦rt❤❡❝♦♠♣❛r✐s♦♥✳

✶✸