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UM MODELO ESPAÇO-TEMPORAL BASEADO EM PROCESSOS GAUSSIANOS PARA PREVISÃO DE INCIDÊNCIA DE DENGUE

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❯▼ ▼❖❉❊▲❖ ❊❙P❆➬❖✲❚❊▼P❖❘❆▲ ❇❆❙❊❆❉❖

❊▼ P❘❖❈❊❙❙❖❙ ●❆❯❙❙■❆◆❖❙ P❆❘❆ P❘❊❱■❙➹❖

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❏❯▲■❖ ❆▲❇■◆❆❚■ ❈❖❘❚❊❩

❯▼ ▼❖❉❊▲❖ ❊❙P❆➬❖✲❚❊▼P❖❘❆▲ ❇❆❙❊❆❉❖

❊▼ P❘❖❈❊❙❙❖❙ ●❆❯❙❙■❆◆❖❙ P❆❘❆ P❘❊❱■❙➹❖

❉❊ ■◆❈■❉✃◆❈■❆ ❉❊ ❉❊◆●❯❊

❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❞♦ ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❞❛ ❯♥✐✈❡r✲ s✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s ❝♦♠♦ r❡q✲ ✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳

❖r✐❡♥t❛❞♦r✿ ●✐s❡❧❡ ▲♦❜♦ P❛♣♣❛

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❏❯▲■❖ ❆▲❇■◆❆❚■ ❈❖❘❚❊❩

❆ ❙P❆❚■❖✲❚❊▼P❖❘❆▲ ●❆❯❙❙■❆◆

P❘❖❈❊❙❙✲❇❆❙❊❉ ▼❖❉❊▲ ❋❖❘ ❋❖❘❊❈❆❙❚■◆●

❉❊◆●❯❊ ❋❊❱❊❘ ■◆❈■❉❊◆❈❊

❉✐ss❡rt❛t✐♦♥ ♣r❡s❡♥t❡❞ t♦ t❤❡ ●r❛❞✉❛t❡ Pr♦❣r❛♠ ✐♥ ❈♦♠♣✉t❡r ❙❝✐❡♥❝❡ ♦❢ t❤❡ ❯♥✐✲ ✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s ✐♥ ♣❛r✲ t✐❛❧ ❢✉❧✜❧❧♠❡♥t ♦❢ t❤❡ r❡q✉✐r❡♠❡♥ts ❢♦r t❤❡ ❞❡❣r❡❡ ♦❢ ▼❛st❡r ✐♥ ❈♦♠♣✉t❡r ❙❝✐❡♥❝❡✳

❆❞✈✐s♦r✿ ●✐s❡❧❡ ▲♦❜♦ P❛♣♣❛

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© 2017, Júlio Albinati Cortez.

Todos os direitos reservados

.

Ficha catalográfica elaborada pela Biblioteca do ICEx - UFMG

Cortez, Júlio Albinati.

C828s A spatio-temporal gaussian process-based model for forecasting dengue fever incidence. / Júlio Albinati Cortez. – Belo Horizonte, 2017.

xxvi, 99 f.: il.; 29 cm.

Dissertação (mestrado) - Universidade Federal de

Minas Gerais – Departamento de Ciência da Computação.

Orientadora: Gisele Lobo Pappa.

1. Computação – Teses. 2. Dengue. 3. Processos gaussianos. 4. Teoria da previsão. 5. Early warning system 6. Multi-task regression. I. Orientadora. II. Título.

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❆❣r❛❞❡❝✐♠❡♥t♦s

Pr✐♠❡✐r❛♠❡♥t❡✱ ❣♦st❛r✐❛ ❞❡ ❛❣r❛❞❡❝❡r à ♠✐♥❤❛ ❡s♣♦s❛✱ q✉❡ ♠❡ ❛❝♦♠♣❛♥❤♦✉ ✭❧✐t❡r❛❧✲ ♠❡♥t❡✮ ♥❡ss❡ ♣❡r❝✉rs♦✳ ❈r❡✐♦ q✉❡ ♣♦❞❡♠♦s ❞✐③❡r q✉❡✱ ❡♠ r❡tr♦s♣❡❝t✐✈❛✱ ♦s ✜♥❛✐s ❞❡ s❡♠❛♥❛ ❡♠ ❝❛s❛ ❢❛③❡♥❞♦ ❧✐st❛s ❞❡ ❡①❡r❝í❝✐♦s ♦✉ ❚Ps ✈❛❧❡r❛♠ ❛ ♣❡♥❛✳ ❆❣r❛❞❡ç♦ t❛♠✲ ❜é♠ à ♠✐♥❤❛ ❢❛♠í❧✐❛✱ q✉❡ ♠❡ ✐♥s♣✐r❛r❛♠ ❞❡s❞❡ ♠✉✐t♦ ❝❡❞♦ ❛ ♠❡ ❞❡❞✐❝❛r ❛♦s ❡st✉❞♦s✳ ➱ ♦ ♠❛❧ ❞❡ t❡r ♣❛✐s ♣r♦❢❡ss♦r❡s✳✳✳

❆♦s ❝♦♠♣❛♥❤❡✐r♦s ❞♦ ❧❛❜♦r❛tór✐♦ ❙♣❡❡❞✱ ❡♠ ♣❛rt✐❝✉❧❛r ❱✐♥í❝✐✉s✱ P❛✉❧♦✱ ❙❛♠✉❡❧✱ ❉❡r✐❝❦✱ ❉❡♥✐s❡✱ ❲❛❧t❡r✱ ❖s✈❛❧❞♦ ❡ ❊❧✈❡rt♦♥ ✭❡ t❛♠❜é♠ ♦ ❘✉❜❡♥s✱ ❛♣❡s❛r ❞❛ tr❛✐r❛❣❡♠✮✱ ❞❡✐①♦ t❛♠❜é♠ ♠❡✉s ❛❣r❛❞❡❝✐♠❡♥t♦s✳ ❚✉❞♦ s❡r✐❛ ♠✉✐t♦ ♠❛✐s tr✐st❡ s❡♠ ♦s ♠♦♠❡♥t♦s ❞❡ ❞❡s❝♦♥tr❛çã♦ ♣r♦♣♦r❝✐♦♥❛❞♦ ♣♦r ✈♦❝ês✳ P♦❞❡♠♦s ♥ã♦ s❡r ♦ ❧❛❜♦r❛tór✐♦ ♠❛✐s ♦r❣❛♥✐③❛❞♦ ♦✉ ♦ ♠❛✐s ♣r♦❞✉t✐✈♦✱ ♠❛s ❞✉✈✐❞♦ q✉❡ ❡①✐st❛ ♦✉tr♦ ♠❛✐s ❛❝♦❧❤❡❞♦r✦

➚ ♠✐♥❤❛ ♦r✐❡♥t❛❞♦r❛✱ ●✐s❡❧❡✱ ❛❣r❛❞❡ç♦ ♣♦r t♦❞❛ ❛ ❝♦♥✜❛♥ç❛ ❞❡♣♦s✐t❛❞❛ ♥❛ ♠✐♥❤❛ ♣❡ss♦❛ ❡ ♣♦r ♠❡ ❛❝♦♠♣❛♥❤❛r ❞❡s❞❡ ♦ ✐♥í❝✐♦ ❞❛ ♠✐♥❤❛ ❣r❛❞✉❛çã♦✳ ❖❜r✐❣❛❞♦ ♣❡❧❛s ♣♦rt❛s ❛❜❡rt❛s✱ ❡ r❡❛❧♠❡♥t❡ ❡s♣❡r♦ q✉❡ ❛♣r♦✈❡✐t❡ ♠✉✐t♦ ❡ss❛ ♥♦✈❛ ❢❛s❡ ❞❛ s✉❛ ✈✐❞❛✦ ❆♦ ♣r♦❢❡ss♦r ❲❛❣♥❡r ▼❡✐r❛✱ t❛♠❜é♠ ❞❡✐①♦ ♦s ♠❡✉s ❛❣r❛❞❡❝✐♠❡♥t♦s ♣❡❧♦s ❝♦♥s❡❧❤♦s ❡ ♣❡❧❛s ♦♣♦rt✉♥✐❞❛❞❡s ❝♦♥❝❡❞✐❞❛s✳

◆ã♦ ♣♦ss♦ ❞❡✐①❛r ❞❡ ♠❡♥❝✐♦♥❛r ❛ s❡❝r❡t❛r✐❛ ❞♦ PP●❈❈✱ ❡♠ ♣❛rt✐❝✉❧❛r ❙ô♥✐❛✱ ▲✐♥❞❛ ❡ ❙❤❡✐❧❛✳ ❙❡♠ ❞ú✈✐❞❛s✱ s❡♠ ✈♦❝ês ♦ ❞❡♣❛rt❛♠❡♥t♦ ❡st❛r✐❛ ✐♠❡rs♦ ♥♦ ♠❛✐s ❝♦♠✲ ♣❧❡t♦ ❝❛♦s✳ P❛r❛❜é♥s ♣❡❧♦ ❡①❝❡❧❡♥t❡ tr❛❜❛❧❤♦ ❡♠ ♠❛♥t❡r t✉❞♦ ♥♦s s❡✉s ❞❡✈✐❞♦s ❡✐①♦s✦

P♦r ✜♠✱ ❛❣r❛❞❡ç♦ ❛♦ PP●❈❈ ❝♦♠♦ ✉♠ t♦❞♦ ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ r❡❛❧✐③❛r ♠❡✉ ♠❡str❛❞♦✳ ❙❡✐ q✉❡ é ✉♠ ♣r✐✈✐❧é❣✐♦ ♣♦❞❡r ❢❛③❡r ✉♠ ♠❡str❛❞♦ ❡♠ ✉♠ ♣r♦❣r❛♠❛ ❞❡ ♣r❡stí❣✐♦ ❡ ❞❡ ❢♦r♠❛ ❣r❛t✉✐t❛✳ ❊s♣❡r♦ ✉♠ ❞✐❛ ♣♦❞❡r r❡t♦r♥❛r ❛ t♦❞♦ ♦ ♠✉♥❞♦ ♦ q✉❡ ❡♠ ♠✐♠ ❢♦✐ ✐♥✈❡st✐❞♦✳

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❆❜str❛❝t

❉❡♥❣✉❡ ❢❡✈❡r ✐s ❛ ♠♦sq✉✐t♦✲❜♦r♥❡ ❞✐s❡❛s❡ ♣r❡s❡♥t ✐♥ ❛❧❧ tr♦♣✐❝❛❧ ③♦♥❡s ♦❢ t❤❡ ✇♦r❧❞ ❛♥❞ ❛✛❡❝ts ❛❧♠♦st ✹✵✵ ♠✐❧❧✐♦♥ ♣❡♦♣❧❡ ✇♦r❧❞✇✐❞❡ ❡✈❡r② ②❡❛r✳ ❍❛✈✐♥❣ ♥♦ tr❡❛t♠❡♥t ♥♦r ✈❛❝❝✐♥❡s ❛✈❛✐❧❛❜❧❡ ❢♦r ♣✉❜❧✐❝ ✉s❡✱ ❞❡♥❣✉❡ ❢❡✈❡r ❝❛♥ ♦♥❧② ❜❡ ❝♦♥tr♦❧❧❡❞ ❜② s✉♣♣r❡ss✐♥❣ t❤❡ ✈❡❝t♦r ♣♦♣✉❧❛t✐♦♥ ❛♥❞ q✉✐❝❦❧② ✐❞❡♥t✐❢②✐♥❣ ♦✉t❜r❡❛❦s t❤r♦✉❣❤ t❤❡ ✉s❛❣❡ ♦❢ ❛❝❝✉r❛t❡ ♣r❡❞✐❝t✐✈❡ ♠♦❞❡❧s ❝❛♣❛❜❧❡ ♦❢ ❡st✐♠❛t✐♥❣ t❤❡ ♥✉♠❜❡r ♦❢ ❞❡♥❣✉❡ ❝❛s❡s ✐♥ ❛ ❣✐✈❡♥ ❛r❡❛ ❛♥❞ ♣❡r✐♦❞ ♦❢ t✐♠❡✳

❇r❛③✐❧ ✐s r❡s♣♦♥s✐❜❧❡ ❢♦r t❤❡ ❧❛r❣❡st ♥✉♠❜❡r ♦❢ ❝♦♥✜r♠❡❞ ❝❛s❡s ✐♥ t❤❡ ❆♠❡r✐❝❛s✱ ❛❝❝♦✉♥t✐♥❣ ❢♦r ❛t ❧❡❛st ♦♥❡ ❢♦✉rt❤ ♦❢ t❤❡ t♦t❛❧ ♥✉♠❜❡r ♦❢ ❝❛s❡s ✐♥ t❤❡ ❝♦♥t✐♥❡♥t✳ ▼♦✲ t✐✈❛t❡❞ ❜② t❤✐s s❝❡♥❛r✐♦✱ t❤❡ ♠❛✐♥ ♦❜❥❡❝t✐✈❡ ♦❢ t❤✐s ✇♦r❦ ✐s t♦ ❞❡✈❡❧♦♣ ❛ ♥❡✇ ♠♦❞❡❧ ❢♦r ♣r❡❞✐❝t✐♥❣ ❞❡♥❣✉❡ ❢❡✈❡r ✐♥❝✐❞❡♥❝❡ ✭❉■❘✮ ✐♥ ❇r❛③✐❧✐❛♥ ❝✐t✐❡s✳ ❋♦r t❤❛t✱ ✇❡ ❡①♣❧♦r❡❞ t❤❡ ♥♦♥✲♣❛r❛♠❡tr✐❝ ❇❛②❡s✐❛♥ ❢r❛♠❡✇♦r❦ ♦❢ ✐♥❢❡r❡♥❝❡ ✉♥❞❡r ●❛✉ss✐❛♥ ♣r♦❝❡ss❡s ✭●P✮✱ ✇❤✐❝❤ ❧✐❡ ✐♥ t❤❡ ✐♥t❡rs❡❝t✐♦♥ ❜❡t✇❡❡♥ ✐♥t❡r♣r❡t❛❜❧❡ ❛♥❞ st❛t❡✲♦❢✲❛rt ♠❛❝❤✐♥❡ ❧❡❛r♥✐♥❣ ♠♦❞❡❧❧✐♥❣ ❢r❛♠❡✇♦r❦s✳

❚❤❡ ♣r♦♣♦s❡❞ ♠♦❞❡❧ ✐s ❛ ●P✲❜❛s❡❞ ♠♦❞❡❧ ❡q✉✐♣♣❡❞ ✇✐t❤ ❛ s♣❛t✐♦✲t❡♠♣♦r❛❧ ❝♦✲ ✈❛r✐❛♥❝❡ ❢✉♥❝t✐♦♥✳ ❚❤❡ t❡♠♣♦r❛❧ ❝♦♠♣♦♥❡♥t ❡①♣❧♦✐ts ❧♦❝❛❧ ❞❡♣❡♥❞❡♥❝❡s ❛♥❞ s❡❛s♦♥❛❧✲ ✐t②✱ ❡①♣r❡ss❡❞ t❤r♦✉❣❤ t❤❡ ❢♦r♠ ♦❢ ❛ q✉❛s✐✲♣❡r✐♦❞✐❝ ❝♦✈❛r✐❛♥❝❡ ❢✉♥❝t✐♦♥✳ ❚❤❡ s♣❛t✐❛❧ ❝♦♠♣♦♥❡♥t✱ ✐♥ t✉r♥✱ ✐s ❞❡✜♥❡❞ ❜② ❛♥ ✐♥t❡r✲❝✐t✐❡s ❝♦✈❛r✐❛♥❝❡ ♠❛tr✐① ❧❡❛r♥❡❞ ❢r♦♠ ❞❛t❛✱ ✇✐t❤♦✉t r❡q✉✐r✐♥❣ ❤✉♠❛♥ ✐♥t❡r✈❡♥t✐♦♥ ♦r s♣❡❝✐✜❝❛t✐♦♥✳ ❲❡ ❛❧s♦ ♣r♦♣♦s❡❞ ❛♥ ❡①t❡♥s✐♦♥ ♦❢ t❤❡ ♠♦❞❡❧ t❤❛t ✐s ❝❛♣❛❜❧❡ ♦❢ ✐♥❝♦r♣♦r❛t✐♥❣ ♦♥❧✐♥❡ ❞❛t❛✱ s✉❝❤ ❛s ❞❛t❛ ❢r♦♠ ❚✇✐tt❡r✱ t♦ ❛❝❝♦✉♥t ❢♦r t❤❡ t②♣✐❝❛❧ ❞❡❧❛② ✐♥ t❤❡ ♣r♦♣❛❣❛t✐♦♥ ♦❢ ❡♣✐❞❡♠✐♦❧♦❣✐❝❛❧ ❞❛t❛ ✐♥ ❛ ♠♦r❡ r❡❛❧✐st✐❝ s❝❡♥❛r✐♦✱ ✇❤❡r❡ ♦♥❧✐♥❡ ❞❛t❛ ❛❝ts ❛s ❛ ♣r♦①② ❢♦r ❡♣✐❞❡♠✐♦❧♦❣✐❝❛❧ ❞❛t❛✳

❲❡ ❝♦♥❞✉❝t❡❞ ❛♥ ❡①t❡♥s✐✈❡ ❡①♣❡r✐♠❡♥t❛❧ ❛♥❛❧②s✐s t♦ ❛ss❡ss t❤❡ ❛❝❝✉r❛❝② ♦❢ t❤❡ ♣r♦♣♦s❡❞ ♠♦❞❡❧ ❛♥❞ ❡①t❡♥s✐♦♥✱ ✈❡r✐❢②✐♥❣ t❤❛t t❤❡② ♦✉t♣❡r❢♦r♠❡❞ ❛❧t❡r♥❛t✐✈❡ ❛♣✲ ♣r♦❛❝❤❡s✱ ✐♥❝❧✉❞✐♥❣ ❛ ♠♦❞❡❧ s♣❡❝✐✜❝❛❧❧② ❞❡s✐❣♥❡❞ ❢♦r ❢♦r❡❝❛st✐♥❣ ❉■❘ ✐♥ ❇r❛③✐❧✳ ❖✉r r❡s✉❧ts ✇❡r❡ ♣❛rt✐❝✉❧❛r❧② ❡①♣r❡ss✐✈❡ ✐♥ t❤❡ s❝❡♥❛r✐♦ ✇❤❡r❡ ❉■❘ ✈❛❧✉❡s ❝❛♥ ❜❡ ❝❛t❡❣♦✲ r✐③❡❞ ✐♥t♦ t❤r❡❡ ✐♥❝✐❞❡♥❝❡ ❧❡✈❡❧s ✕ ❧♦✇✱ ♠❡❞✐✉♠ ❛♥❞ ❤✐❣❤ ✐♥❝✐❞❡♥❝❡ ✕ ✇❤❡r❡ t❤❡ ♣r♦♣♦s❡❞ ♠♦❞❡❧ ❛❝❤✐❡✈❡ ❛ ♠❡❞✐❛♥ ❛r❡❛ ✉♥❞❡r t❤❡ ❘❖❈ ❝✉r✈❡ ♦❢ ♠♦r❡ t❤❛♥ ✵✳✾✵✱ ❝♦♠♣❛r❡❞ t♦ ✵✳✼✹ ♦❜t❛✐♥❡❞ ❜② t❤❡ ❜❡st ❛❧t❡r♥❛t✐✈❡ ♠♦❞❡❧✳

(12)
(13)

❘❡s✉♠♦

❉❡♥❣✉❡ é ✉♠❛ ❞♦❡♥ç❛ ♣r❡s❡♥t❡ ❡♠ t♦❞❛s ③♦♥❛s tr♦♣✐❝❛✐s ❞♦ ♠✉♥❞♦✱ ❛❢❡t❛♥❞♦ q✉❛s❡ ✹✵✵ ♠✐❧❤õ❡s ❞❡ ♣❡ss♦❛s ❛♦ r❡❞♦r ❞♦ ♠✉♥❞♦ t♦❞♦s ♦s ❛♥♦s✳ ❈♦♠♦ ♥ã♦ ❤á tr❛t❛♠❡♥t♦ ♦✉ ✈❛❝✐♥❛s ❞✐s♣♦♥í✈❡✐s ♣❛r❛ ♦ ♣ú❜❧✐❝♦ ❣❡r❛❧✱ ❛ ❞❡♥❣✉❡ só ♣♦❞❡ s❡r ❝♦♥t✐❞❛ ❛tr❛✈és ❞♦ ❝♦♥tr♦❧❡ ♣♦♣✉❧❛❝✐♦♥❛❧ ❞♦ ♠♦sq✉✐t♦ tr❛♥s♠✐ss♦r ❞♦ ✈ír✉s ❡ ✐❞❡♥t✐✜❝❛♥❞♦ r❛♣✐❞❛♠❡♥t❡ ♥♦✈♦s ❢♦❝♦s ❞❛ ❞♦❡♥ç❛ ❛tr❛✈és ❞❡ ♠♦❞❡❧♦s ♣r❡❞✐t✐✈♦s ❝❛♣❛③❡s ❞❡ ❡st✐♠❛r✱ ❞❡ ❢♦r♠❛ ❛❝✉r❛❞❛✱ ♦ ♥ú♠❡r♦ ❞❡ ❝❛s♦s ❞❡ ❞❡♥❣✉❡ ❡♠ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ár❡❛ ❡ ♣❡rí♦❞♦ ❞❡ t❡♠♣♦✳ ❖ ❇r❛s✐❧ é r❡s♣♦♥sá✈❡❧ ♣❡❧♦ ♠❛✐♦r ♥ú♠❡r♦ ❞❡ ❝❛s♦s ❝♦♥✜r♠❛❞♦s ❞❡ ❞❡♥❣✉❡ ♥❛s ❆♠ér✐❝❛s✱ ❛t✐♥❣✐♥❞♦ ♠❛✐s ❞❡ ✉♠ q✉❛rt♦ ❞♦ ♥ú♠❡r♦ t♦t❛❧ ❞❡ ❝❛s♦s ♥♦ ❝♦♥t✐♥❡♥t❡✳ ▼♦t✐✲ ✈❛❞♦ ♣♦r ❡ss❡ ❝❡♥ár✐♦✱ ♦ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t✐✈♦ ❞❡ss❡ tr❛❜❛❧❤♦ é ❞❡s❡♥✈♦❧✈❡r ✉♠ ♠♦❞❡❧♦ ♣❛r❛ ♣r❡❞✐çã♦ ❞❡ ♥ú♠❡r♦ ❞❡ ❝❛s♦s ❞❡ ❞❡♥❣✉❡ ❡♠ ❝✐❞❛❞❡s ❜r❛s✐❧❡✐r❛s✳ P❛r❛ t❛♥t♦✱ ❡①♣❧♦r❛♠♦s ♦ ❢r❛♠❡✇♦r❦ ♥ã♦✲♣❛r❛♠étr✐❝♦ ❡ ❜❛②❡s✐❛♥♦ ❞❡ ✐♥❢❡rê♥❝✐❛ ✉t✐❧✐③❛♥❞♦ ♣r♦❝❡ss♦s ❣❛✉ss✐❛♥♦s✱ ✉♠ ♠ét♦❞♦ q✉❡ r❡s✐❞❡ ♥❛ ✐♥t❡rs❡çã♦ ❡♥tr❡ ♠♦❞❡❧♦s ✐♥t❡r♣r❡tá✈❡✐s ❡ ❡st❛❞♦✲❞❛✲❛rt❡✳

❖ ♠♦❞❡❧♦ ♣r♦♣♦st♦ é ❡q✉✐♣❛❞♦ ❝♦♠ ✉♠❛ ❢✉♥çã♦ ❞❡ ❝♦✈❛r✐â♥❝✐❛ ❡s♣❛ç♦✲t❡♠♣♦r❛❧✳ ❖ ❝♦♠♣♦♥❡♥t❡ t❡♠♣♦r❛❧ ❡①♣❧♦r❛ ❞❡♣❡♥❞ê♥❝✐❛s ❧♦❝❛✐s ❡ s❛③♦♥❛❧✐❞❛❞❡✱ s❡♥❞♦ ❡①♣r❡ss♦ ❛tr❛✈és ❞❡ ✉♠❛ ❢✉♥çã♦ q✉❛s✐✲♣❡r✐ó❞✐❝❛✳ ❏á ♦ ❝♦♠♣♦♥❡♥t❡ ❡s♣❛❝✐❛❧ é ❞❡✜♥✐❞♦ ♣♦r ♠❡✐♦ ❞❡ ✉♠❛ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛ ❡♥tr❡ ❝✐❞❛❞❡s✱ q✉❡ é ❛♣r❡♥❞✐❞❛ ❝♦♠ ❜❛s❡ ♥♦s ❞❛❞♦s ❛♣❡♥❛s✱ s❡♠ ♥❡♥❤✉♠❛ ✐♥t❡r✈❡♥çã♦ ❤✉♠❛♥❛✳ ❆❧é♠ ❞✐ss♦✱ ♣r♦♣✉s❡♠♦s ✉♠❛ ♠❡t♦❞♦❧♦❣✐❛ ♣❛r❛ ❡①t❡♥❞❡r ♦ ♠♦❞❡❧♦ ♣r♦♣♦st♦ ❞❡ ❢♦r♠❛ ❛ ✉t✐❧✐③❛r ❞❛❞♦s ❞❡ ❢♦♥t❡s ♦♥❧✐♥❡✱ ❝♦♠♦ ❞❛❞♦s ❞♦ ❚✇✐tt❡r✱ ♥♦ ❝❡♥ár✐♦ ♠❛✐s r❡❛❧✐st❛ ♦♥❞❡ ♦s ❞❛❞♦s ❡♣✐❞❡♠✐♦❧ó❣✐❝♦s sã♦ ❢♦r♥❡❝✐❞♦s ❝♦♠ ❛tr❛s♦✳ ❆ss✐♠✱ ♦s ❞❛❞♦s ♦♥❧✐♥❡ ❛t✉❛♠ ❝♦♠♦ ♣r♦①② ♣❛r❛ ♦s ❞❛❞♦s ❡♣✐❞❡♠✐♦❧ó❣✐❝♦s✳

❈♦♥❞✉③✐♠♦s ✉♠❛ ❛♥á❧✐s❡ ❡①♣❡r✐♠❡♥t❛❧ ❡①t❡♥s✐✈❛ ♣❛r❛ ❛♥❛❧✐③❛r ❛ ❛❝✉rá❝✐❛ ❞♦ ♠♦❞❡❧♦ ♣r♦♣♦st♦✱ ❜❡♠ ❝♦♠♦ ❛ s✉❛ ❡①t❡♥sã♦ ♣❛r❛ ♦ ❝❡♥ár✐♦ ❞❡s❝r✐t♦ ❛❝✐♠❛✳ ❱❡r✐✜❝❛♠♦s q✉❡ ❛s ♣r♦♣♦st❛s ♦❜t✐✈❡r❛♠ ♣r❡❞✐çõ❡s ♠❛✐s ❛❝✉r❛❞❛s q✉❛♥❞♦ ❝♦♠♣❛r❛❞❛s ❛ ❢♦r♠✉❧❛çõ❡s ❛❧t❡r♥❛t✐✈❛s✱ ✐♥❝❧✉✐♥❞♦ ✉♠ ♠♦❞❡❧♦ ♣r❡✈✐❛♠❡♥t❡ ♣r♦♣♦st♦ ♣❛r❛ ♣r❡✈✐sã♦ ❞❡ ✐♥❝✐❞ê♥❝✐❛ ❞❡ ❞❡♥❣✉❡ ♥♦ ❇r❛s✐❧✳ ◆♦ss♦s r❡s✉❧t❛❞♦s ❢♦r❛♠ ♣❛rt✐❝✉❧❛r♠❡♥t❡ ✐♥t❡r❡ss❛♥t❡s ♥♦ ❝❡♥ár✐♦ ♦♥❞❡ ♦s ✈❛❧♦r❡s ❞❡ ✐♥❝✐❞ê♥❝✐❛ sã♦ ❝❛t❡❣♦r✐③❛❞♦s ❡♠ ♥í✈❡✐s ❞❡ ✐♥❝✐❞ê♥❝✐❛ ✕ ❜❛✐①❛✱ ♠é❞✐❛ ♦✉ ❛❧t❛ ✕✱ ♦♥❞❡ ♦ ♠♦❞❡❧♦ ♦❜t❡✈❡ ✉♠❛ ár❡❛ s♦❜ ❛ ❝✉r✈❛ ❘❖❈ ♠❡❞✐❛♥❛ s✉♣❡r✐♦r ❛ ✵✳✾✵✱ ❝♦♠♣❛r❛❞❛ à ❛r❡❛ ❞❡ ✵✳✼✹ ♦❜t✐❞❛ ♣❡❧❛ ♠❡❧❤♦r ❢♦r♠✉❧❛çã♦ ❛❧t❡r♥❛t✐✈❛✳

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▲✐st ♦❢ ❋✐❣✉r❡s

✶✳✶ ●❧♦❜❛❧ ❞✐str✐❜✉t✐♦♥ ♦❢ ❞❡♥❣✉❡ ❢❡✈❡r✱ ❡①tr❛❝t❡❞ ❢r♦♠ ❙❛♠✐r ❡t ❛❧✳ ❬✷✵✶✸❪✳ ❚❤❡ ♠❛♣ ♦♥ t❤❡ t♦♣ ✭❛✮ s❤♦✇s t❤❡ ♣r❡s❡♥❝❡ ♦❢ ❞❡♥❣✉❡ ✈✐r✉s ❛r♦✉♥❞ t❤❡ ✇♦r❧❞✳ ❚❤❡ ♠❛♣ ♦♥ t❤❡ ♠✐❞❞❧❡ ✭❜✮ s❤♦✇s t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ ♦❝❝✉r❡♥❝❡ ♦❢ ❞❡♥❣✉❡ ❢❡✈❡r✳ ❚❤❡ ♠❛♣ ♦♥ t❤❡ ❜♦tt♦♠ ✭❝✮ ✐♥❞✐❝❛t❡s t❤❡ ♥✉♠❜❡r ♦❢ ❞❡♥❣✉❡ ❢❡✈❡r ✐♥❢❡❝t✐♦♥s ❛t ❝♦✉♥tr② ❧❡✈❡❧✱ ✇✐t❤ ❛r❡❛s ♣r♦♣♦rt✐♦♥❛❧ t♦ t❤❡ ♥✉♠❜❡r ♦❢ ❝❛s❡s✳ ✷

✷✳✶ ❖♥❡✲❞✐♠❡♥s✐♦♥❛❧ ❡①❛♠♣❧❡ ♦❢ sq✉❛r❡❞ ❡①♣♦♥❡♥t✐❛❧ ❝♦✈❛r✐❛♥❝❡ ❢✉♥❝t✐♦♥ ✇✐t❤ σ = 1 ❛♥❞ M = 10−2 ✭❧❡❢t ✜❣✉r❡✮ ❛♥❞ ❛ s❛♠♣❧❡ ❢r♦♠ ❛ ③❡r♦ ♠❡❛♥ ●P

❡q✉✐♣♣❡❞ ✇✐t❤ t❤❡ ✐❧❧✉str❛t❡❞ ❝♦✈❛r✐❛♥❝❡ ❢✉♥❝t✐♦♥ ✭r✐❣❤t ✜❣✉r❡✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✷ ❖♥❡✲❞✐♠❡♥s✐♦♥❛❧ ❡①❛♠♣❧❡ ♦❢ ▼❛tér♥ ❝♦✈❛r✐❛♥❝❡ ❢✉♥❝t✐♦♥ ✇✐t❤ σ = 1 ❛♥❞

M = 10−2 ✭❧❡❢t ✜❣✉r❡✮ ❛♥❞ ❛ s❛♠♣❧❡ ❢r♦♠ ❛ ③❡r♦ ♠❡❛♥ ●P ❡q✉✐♣♣❡❞ ✇✐t❤

t❤❡ ✐❧❧✉str❛t❡❞ ❝♦✈❛r✐❛♥❝❡ ❢✉♥❝t✐♦♥ ✭r✐❣❤t ✜❣✉r❡✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✸ ❖♥❡✲❞✐♠❡♥s✐♦♥❛❧ ❡①❛♠♣❧❡ ♦❢ ♣❡r✐♦❞✐❝ ❝♦✈❛r✐❛♥❝❡ ❢✉♥❝t✐♦♥ ✇✐t❤σ = 1✱p= 30

❛♥❞ ℓ = 1 ✭❧❡❢t ✜❣✉r❡✮ ❛♥❞ ❛ s❛♠♣❧❡ ❢r♦♠ ❛ ③❡r♦ ♠❡❛♥ ●P ❡q✉✐♣♣❡❞ ✇✐t❤

t❤❡ ✐❧❧✉str❛t❡❞ ❝♦✈❛r✐❛♥❝❡ ❢✉♥❝t✐♦♥ ✭r✐❣❤t ✜❣✉r❡✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✹ ❖♥❡✲❞✐♠❡♥s✐♦♥❛❧ ❡①❛♠♣❧❡ ♦❢ ❧✐♥❡❛r ❝♦✈❛r✐❛♥❝❡ ❢✉♥❝t✐♦♥ ✇✐t❤ σ = 1✱ M =

10−2 ✭❧❡❢t ✜❣✉r❡✮ ❛♥❞ ❛ s❛♠♣❧❡ ❢r♦♠ ❛ ③❡r♦ ♠❡❛♥ ●P ❡q✉✐♣♣❡❞ ✇✐t❤ t❤❡

✐❧❧✉str❛t❡❞ ❝♦✈❛r✐❛♥❝❡ ❢✉♥❝t✐♦♥ ✭r✐❣❤t ✜❣✉r❡✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✺ ❖♥❡✲❞✐♠❡♥s✐♦♥❛❧ ❡①❛♠♣❧❡ ♦❢ ❤♦♠♦❣❡♥❡♦✉s ♣♦❧②♥♦♠✐❛❧ ✭❞❡❣r❡❡ ✷✮ ❝♦✈❛r✐❛♥❝❡

❢✉♥❝t✐♦♥ ✇✐t❤ σ = 1 ❛♥❞ M = 10−2 ✭❧❡❢t ✜❣✉r❡✮ ❛♥❞ ❛ s❛♠♣❧❡ ❢r♦♠ ❛ ③❡r♦

♠❡❛♥ ●P ❡q✉✐♣♣❡❞ ✇✐t❤ t❤❡ ✐❧❧✉str❛t❡❞ ❝♦✈❛r✐❛♥❝❡ ❢✉♥❝t✐♦♥ ✭r✐❣❤t ✜❣✉r❡✮✳ ✳ ✶✹ ✷✳✻ ❖♥❡✲❞✐♠❡♥s✐♦♥❛❧ ❡①❛♠♣❧❡ ♦❢ ✸✲❝♦♠♣♦♥❡♥t s♣❡❝tr❛❧ ♠✐①t✉r❡ ❝♦✈❛r✐❛♥❝❡

❢✉♥❝t✐♦♥ ✇✐t❤ σ = (1,1,1)T v = (10−4,10−4,10−4)T ❛♥❞ µ = (10−1,10−2,10−3)T ✭❧❡❢t ✜❣✉r❡✮ ❛♥❞ ❛ s❛♠♣❧❡ ❢r♦♠ ❛ ③❡r♦ ♠❡❛♥ ●P ❡q✉✐♣♣❡❞

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✷✳✼ ❉✐❛❣r❛♠ ❢♦r ❝♦♥✈♦❧✉t✐♦♥✲❜❛s❡❞ ▼❚●P ✇✐t❤ t❤r❡❡ ✐♥❞❡♣❡♥❞❡♥t ●❛✉ss✐❛♥ ✇❤✐t❡ ♥♦✐s❡ ♣r♦❝❡ss❡s ✭X0✱ X1 ❛♥❞ X2✮✱ t✇♦ ♦✉t♣✉ts ✭Y1 ❛♥❞ Y2✮ ❛♥❞ ❢♦✉r

❦❡r♥❡❧s ✭h01✱ h02✱ h11 ❛♥❞ h22✮✳ ❑❡r♥❡❧s h12 ❛♥❞ h21 ❛r❡ ❛ss✉♠❡❞ t♦ ❜❡ ③❡r♦

❛♥❞ ♦♠✐tt❡❞✳ ❉❡♣❡♥❞❡♥❝❡ ❜❡t✇❡❡♥ Y1 ❛♥❞ Y2 ✐s ❞♦♥❡ ✈✐❛ U1 ❛♥❞ U2✱ ✇❤✐❝❤

s❤❛r❡ t❤❡ s❛♠❡ ●❛✉ss✐❛♥ ✇❤✐t❡ ♣r♦❝❡ss✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✽ ❉✐❛❣r❛♠ ❢♦r ●P❘◆ ✇✐t❤ t❤r❡❡ ❤✐❞❞❡♥ ♥♦❞❡s ✭f1✱f2 ❛♥❞f3✮ ❛♥❞ t✇♦ ♦✉t♣✉ts

✭Y1 ❛♥❞ Y2✮✳ ❈♦♠❜✐♥✐♥❣ ✇❡✐❣❤ts ❛r❡ s❤♦✇♥ ❛s w·· ❛♥❞ X ❛❝t ❛s ✐♥♣✉t ❢♦r t❤❡ ♥❡t✇♦r❦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷

✹✳✶ ❆✈❡r❛❣❡ ✇❡❡❦❧② ❉■❘ ✈❛❧✉❡s ♣❡r ❇r❛③✐❧✐❛♥ st❛t❡✱ ✇✐t❤ ❞❛r❦❡r ❝♦❧♦rs ✐♥❞✐❝❛t✐♥❣ ❤✐❣❤❡r ✐♥❝✐❞❡♥❝❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✹✳✷ ▼❡❞✐❛♥ ❡st✐♠❛t❡❞ t❡♠♣♦r❛❧ ❛✉t♦✲❝♦rr❡❧❛t✐♦♥ ✇❤❡♥ ❝♦♥s✐❞❡r✐♥❣ ❛❧❧ ❝✐t✐❡s ✉♥✲

❞❡r st✉❞②✳ ❙❤❛❞❡❞ ❛r❡❛ ✐♥❞✐❝❛t❡s ✐♥t❡r✲q✉❛rt✐❧❡ r❛♥❣❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹✳✸ ❊♠♣✐r✐❝❛❧ ❝✉♠✉❧❛t✐✈❡ ❞✐str✐❜✉t✐♦♥ ❢✉♥❝t✐♦♥ ♦❢ s♣❛t✐❛❧ ❝♦rr❡❧❛t✐♦♥s ✭❧❡❢t ✜❣✲

✉r❡✮ ❛♥❞ t❤❡ r♦❧❡ ♦❢ ❞✐st❛♥❝❡ ✐♥ s♣❛t✐❛❧ ❝♦rr❡❧❛t✐♦♥s ✭r✐❣❤t ✜❣✉r❡✮✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹✳✹ ❆✈❡r❛❣❡ ❡st✐♠❛t❡❞ ❝r♦ss✲❝♦rr❡❧❛t✐♦♥s ❜❡t✇❡❡♥ ❉■❘ ❛♥❞ ❝❧✐♠❛t❡ ❝♦✈❛r✐❛t❡s

❝♦♥s✐❞❡r✐♥❣ ❛❧❧ ❝✐t✐❡s ✉♥❞❡r st✉❞②✳ ❲❤✐s❦❡rs ✐♥❞✐❝❛t❡ ✾✺✪ ❝♦♥✜❞❡♥❝❡ ✐♥t❡r✈❛❧s✳ ✸✼ ✹✳✺ ❉✐str✐❜✉t✐♦♥ ♦❢ t❤❡ ♦♣t✐♠❛❧ ❧❛❣ ♣❡r ❝✐t② ❢♦r ❛❧❧ t❤r❡❡ ❝❧✐♠❛t❡✲r❡❧❛t❡❞ ❝♦✈❛r✐❛t❡s✳ ✸✽ ✹✳✻ ❆✈❡r❛❣❡ ❡st✐♠❛t❡❞ ❝r♦ss✲❝♦rr❡❧❛t✐♦♥s ❜❡t✇❡❡♥ ❉■❘ ❛♥❞ ✈♦❧✉♠❡ ♦❢ ❞❡♥❣✉❡✲

r❡❧❛t❡❞ t✇❡❡ts ❝♦♥s✐❞❡r✐♥❣ ❛❧❧ ❝✐t✐❡s ✉♥❞❡r st✉❞②✳ ❲❤✐s❦❡rs ✐♥❞✐❝❛t❡ ✾✺✪ ❝♦♥✜❞❡♥❝❡ ✐♥t❡r✈❛❧s✳ ◆❡❣❛t✐✈❡ ✈❛❧✉❡s ✐♥❞✐❝❛t❡ t❤❛t ❚✇✐tt❡r ❞❛t❛ ✐s ❞❡❧❛②❡❞ ✇✐t❤ r❡❧❛t✐♦♥ t♦ ❡♣✐❞❡♠✐♦❧♦❣✐❝❛❧ ❞❛t❛✱ ✇❤✐❧❡ ♣♦s✐t✐✈❡ ✈❛❧✉❡s ✐♥❞✐❝❛t❡ t❤❡ ♦♣♣♦s✐t❡ s❝❡♥❛r✐♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✹✳✼ ■♠♣❛❝t ♦❢ t❤❡ t♦t❛❧ ♥✉♠❜❡r ♦❢ ❞❡♥❣✉❡✲r❡❧❛t❡❞ t✇❡❡ts ♦♥ t❤❡ ❝♦rr❡❧❛t✐♦♥ ❜❡✲

t✇❡❡♥ ❉■❘ ✈❛❧✉❡s ❛♥❞ ❚✇✐tt❡r ❞❛t❛ ♣❡r ❝✐t②✳ ❊❛❝❤ s②♠❜♦❧ ❞❡♥♦t❡s ❛ ❝✐t②✱ ✇✐t❤ ❝♦❧♦r ❛♥❞ s❤❛♣❡ ✐♥❞✐❝❛t✐♥❣ ✐ts ❤✐❣❤❡st ✐♥❝✐❞❡♥❝❡ ❧❡✈❡❧ ❛❝❤✐❡✈❡❞ ✐♥ t❤❡ ♣❡r✐♦❞ ✉♥❞❡r st✉❞②✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵

✺✳✶ ❈♦♠♣❛r✐s♦♥ ❜❡t✇❡❡♥ ❛❧t❡r♥❛t✐✈❡ ❢♦r♠✉❧❛t✐♦♥s ♦❢ q✉❛s✐✲♣❡r✐♦❞✐❝ ❝♦✈❛r✐❛♥❝❡ ❢✉♥❝t✐♦♥s✳ ❊❛❝❤ s②♠❜♦❧ r❡♣r❡s❡♥ts ❛ ❝✐t② ❛♥❞ ❝♦❧♦r ❛♥❞ s❤❛♣❡ ✐♥❞✐❝❛t❡ t❤❡ ❤✐❣❤❡st ✐♥❝✐❞❡♥❝❡ ❧❡✈❡❧ ❛❝❤✐❡✈❡❞ ❜② t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝✐t②✳ ❚❤❡ s♦❧✐❞ ❜❧❛❝❦ ❧✐♥❡ ✐♥❞✐❝❛t❡s ❡q✉❛❧ ♣❡r❢♦r♠❛♥❝❡ ❜❡t✇❡❡♥ ♠♦❞❡❧s✳ ❈✐t✐❡s ❛❜♦✈❡ t❤❡ s♦❧✐❞ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② t❤❡ ②✲❛①✐s ❢♦r♠✉❧❛t✐♦♥✱ ✇❤✐❧❡ ❝✐t✐❡s ❜❡❧♦✇ t❤❡ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② ①✲❛①✐s ❢♦r♠✉❧❛t✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼

(17)

✺✳✷ ❈♦♠♣❛r✐s♦♥ ❜❡t✇❡❡♥ ❛❧t❡r♥❛t✐✈❡ ❢♦r♠✉❧❛t✐♦♥s ♦❢ t❤❡ ♣r♦♣♦s❡❞ ❝♦✈❛r✐❛♥❝❡ ❢✉♥❝t✐♦♥ ♦❜t❛✐♥❡❞ ❜② r❡♠♦✈✐♥❣ ♦♥❡ ♦❢ ✐ts t❤r❡❡ ❝♦♠♣♦♥❡♥ts✳ ❊❛❝❤ s②♠❜♦❧ r❡♣r❡s❡♥ts ❛ ❝✐t② ❛♥❞ ❝♦❧♦r ❛♥❞ s❤❛♣❡ ✐♥❞✐❝❛t❡ t❤❡ ❤✐❣❤❡st ✐♥❝✐❞❡♥❝❡ ❧❡✈❡❧ ❛❝❤✐❡✈❡❞ ❜② t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝✐t②✳ ❚❤❡ s♦❧✐❞ ❜❧❛❝❦ ❧✐♥❡ ✐♥❞✐❝❛t❡s ❡q✉❛❧ ♣❡r❢♦r♠❛♥❝❡ ❜❡t✇❡❡♥ ♠♦❞❡❧s✳ ❈✐t✐❡s ❛❜♦✈❡ t❤❡ s♦❧✐❞ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② t❤❡ ②✲❛①✐s ❢♦r♠✉❧❛t✐♦♥✱ ✇❤✐❧❡ ❝✐t✐❡s ❜❡❧♦✇ t❤❡ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② ①✲❛①✐s ❢♦r♠✉❧❛t✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽

✺✳✸ ❈♦♠♣❛r✐s♦♥ ❜❡t✇❡❡♥ t❤❡ ❝♦✈❛r✐❛♥❝❡ ❢✉♥❝t✐♦♥ ✇✐t❤ ❛ s✐♥❣❧❡ q✉❛s✐✲♣❡r✐♦❞✐❝ ❢✉♥❝t✐♦♥ ❛♥❞ t❤❡ s♣❡❝tr❛❧ ♠✐①t✉r❡ ❦❡r♥❡❧✳ ❊❛❝❤ s②♠❜♦❧ r❡♣r❡s❡♥ts ❛ ❝✐t② ❛♥❞ ❝♦❧♦r ❛♥❞ s❤❛♣❡ ✐♥❞✐❝❛t❡ t❤❡ ❤✐❣❤❡st ✐♥❝✐❞❡♥❝❡ ❧❡✈❡❧ ❛❝❤✐❡✈❡❞ ❜② t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝✐t②✳ ❚❤❡ s♦❧✐❞ ❜❧❛❝❦ ❧✐♥❡ ✐♥❞✐❝❛t❡s ❡q✉❛❧ ♣❡r❢♦r♠❛♥❝❡ ❜❡✲ t✇❡❡♥ ♠♦❞❡❧s✳ ❈✐t✐❡s ❛❜♦✈❡ t❤❡ s♦❧✐❞ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② t❤❡ ②✲❛①✐s ❢♦r♠✉❧❛t✐♦♥✱ ✇❤✐❧❡ ❝✐t✐❡s ❜❡❧♦✇ t❤❡ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② ①✲❛①✐s ❢♦r♠✉❧❛t✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾

✺✳✹ ■❧❧✉str❛t✐✈❡ ❡①❛♠♣❧❡ ♦❢ ❜❧♦❝❦✲❞✐❛❣♦♥❛❧✐③❛t✐♦♥ ♦❢ t❤❡ ❝♦✈❛r✐❛♥❝❡ ♠❛tr✐①K✳ ■♥ t❤❡ ❧❡❢t ✜❣✉r❡✱ ❡❛❝❤ s②♠❜♦❧ ❞❡♥♦t❡s ❛ ❝✐t②✱ ✇✐t❤ ❝♦❧♦r ✐♥❞✐❝❛t✐♥❣ t❤❡ ❝❧✉st❡r ✐t ❜❡❧♦♥❣s✳ ❚❤❡ r✐❣❤t ✜❣✉r❡ s❤♦✇s t❤❡ r❡s✉❧t✐♥❣ ❝♦✈❛r✐❛♥❝❡ ♠❛tr✐①✱ ✇✐t❤ ✇❤✐t❡ s♣❛❝❡ ✐♥❞✐❝❛t✐♥❣ ♥✉❧❧ ✈❛❧✉❡s ❛♥❞ ♥♦♥✲✇❤✐t❡ s♣❛❝❡ ✐♥❞✐❝❛t✐♥❣ ❝♦✈❛r✐✲ ❛♥❝❡s ❜❡t✇❡❡♥ ❝✐t✐❡s ✇✐t❤✐♥ t❤❡ s❛♠❡ ❝❧✉st❡r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹

✺✳✺ ❚❤❡ ❧❡❢t ✜❣✉r❡ s❤♦✇s t❤❡ ♥✉♠❜❡r ♦❢ ❝❧✉st❡rs ♦❜t❛✐♥❡❞ ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ♠❛①✐✲ ♠✉♠ s✐③❡ ❛❧❧♦✇❡❞ ✐♥ ❆❧❣♦r✐t❤♠ ✺✳✶✳ ❉♦tt❡❞ ❧✐♥❡s ✐♥❞✐❝❛t❡ ♥✉♠❜❡r ♦❢ ❝❧✉st❡rs ✇❤❡♥ ❝❧✉st❡r✐♥❣ ❜② st❛t❡ ❛♥❞ r❡❣✐♦♥ ❢♦r ❝♦♠♣❛r✐s♦♥✳ ❚❤❡ r✐❣❤t ✜❣✉r❡ s❤♦✇s t❤❡ ♣r♦♣♦rt✐♦♥ ♦❢ ❝✐t✐❡s ✇✐t❤✐♥ t❤❡ s❛♠❡ ❝❧✉st❡rs s❡♣❛r❛t❡❞ ❜② ❛ ❣✐✈❡♥ ❞✐s✲ t❛♥❝❡ ✇❤❡♥ ❝❧✉st❡r✐♥❣ ❜② st❛t❡s✱ ❜② r❡❣✐♦♥ ❛♥❞ ❜② ❝♦rr❡❧❛t✐♦♥ ✇✐t❤ ♠❛①✐♠✉♠ ❛❧❧♦✇❡❞ s✐③❡ ♦❢ ✶✵ ❝✐t✐❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

✺✳✻ ❘❡s✉❧ts ♦❜t❛✐♥❡❞ ❜② ❉●P ❢♦r ❞✐st✐♥❝t ❝❧✉st❡r✐♥❣ str❛t❡❣✐❡s ❛❝❝♦r❞✐♥❣ t♦ ❛❧❧ t❤r❡❡ ❡✈❛❧✉❛t✐♦♥ ♠❡tr✐❝s✳ ❊①♣❡r✐♠❡♥ts ✇✐t❤ ♦♣t✐♠✐③❡❞ ❝♦✈❛r✐❛♥❝❡ ♠❛tr✐① ❛♥❞ ❝❧✉st❡rs ♦❢ s✐③❡ ✉♣ t♦ ✺✵ ❝✐t✐❡s ♦r ❣r♦✉♣❡❞ ❜② st❛t❡s ✇❡r❡ ♥♦t ♣❡r❢♦r♠❡❞ ❞✉❡ t♦ t❤❡ ❧❛r❣❡ ❝♦♠♣✉t❛t✐♦♥❛❧ ❡✛♦rt r❡q✉✐r❡❞✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼

✺✳✼ ❚✐♠❡ r❡q✉✐r❡❞ ❢♦r ✐♥❢❡r❡♥❝❡ ✇✐t❤ N = 209 ✇❡❡❦s✱ M = 298 ❝✐t✐❡s ❛♥❞

(18)

✺✳✽ ❈♦♠♣❛r✐s♦♥ ❜❡t✇❡❡♥ ♦♣t✐♠✐③✐♥❣ ❝♦✈❛r✐❛♥❝❡s ❛♥❞ ✉s✐♥❣ ❡♠♣✐r✐❝❛❧ ❛♣♣r♦①✐✲ ♠❛t✐♦♥s ❛❝❝♦r❞✐♥❣ t♦ ❛❧❧ t❤r❡❡ ❡✈❛❧✉❛t✐♦♥ ♠❡tr✐❝s✳ ❊❛❝❤ s②♠❜♦❧ r❡♣r❡s❡♥ts ❛ ❝✐t② ❛♥❞ ❝♦❧♦r ❛♥❞ s❤❛♣❡ ✐♥❞✐❝❛t❡ t❤❡ ❤✐❣❤❡st ✐♥❝✐❞❡♥❝❡ ❧❡✈❡❧ ❛❝❤✐❡✈❡❞ ❜② t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝✐t②✳ ❚❤❡ s♦❧✐❞ ❜❧❛❝❦ ❧✐♥❡ ✐♥❞✐❝❛t❡s ❡q✉❛❧ ♣❡r❢♦r♠❛♥❝❡ ❜❡t✇❡❡♥ ♠♦❞❡❧s✳ ❈✐t✐❡s ❛❜♦✈❡ t❤❡ s♦❧✐❞ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② ❡♠♣✐r✐❝❛❧❧② ❛♣♣r♦①✐♠❛t✐♥❣KC✱ ✇❤✐❧❡ ❝✐t✐❡s ❜❡❧♦✇ t❤❡ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r

✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② ❧❡tt✐♥❣ ✐t ❜❡ ♦♣t✐♠✐③❡❞ ✈✐❛ ❧✐❦❡❧✐❤♦♦❞ ♠❛①✐♠✐③❛t✐♦♥✳ ✳ ✳ ✺✾ ✺✳✾ ❈♦♠♣❛r✐s♦♥ ❜❡t✇❡❡♥ t❡♠♣♦r❛❧✲♦♥❧② ❛♥❞ ❢✉❧❧ ✭✉s✐♥❣ ❝❧✐♠❛t❡✮ ❉●P ♠♦❞❡❧s

❛❝❝♦r❞✐♥❣ t♦ ❛❧❧ t❤r❡❡ ❡✈❛❧✉❛t✐♦♥ ♠❡tr✐❝s✳ ❊❛❝❤ s②♠❜♦❧ r❡♣r❡s❡♥ts ❛ ❝✐t② ❛♥❞ ❝♦❧♦r ❛♥❞ s❤❛♣❡ ✐♥❞✐❝❛t❡ t❤❡ ❤✐❣❤❡st ✐♥❝✐❞❡♥❝❡ ❧❡✈❡❧ ❛❝❤✐❡✈❡❞ ❜② t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝✐t②✳ ❚❤❡ s♦❧✐❞ ❜❧❛❝❦ ❧✐♥❡ ✐♥❞✐❝❛t❡s ❡q✉❛❧ ♣❡r❢♦r♠❛♥❝❡ ❜❡✲ t✇❡❡♥ ♠♦❞❡❧s✳ ❈✐t✐❡s ❛❜♦✈❡ t❤❡ s♦❧✐❞ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② t❡♠♣♦r❛❧✲♦♥❧② ❉●P✱ ✇❤✐❧❡ ❝✐t✐❡s ❜❡❧♦✇ t❤❡ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② ❢✉❧❧ ❉●P✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✺✳✶✵ ❈♦♠♣❛r✐s♦♥ ❜❡t✇❡❡♥ ❉●P ✇✐t❤ ❛♥❞ ✇✐t❤♦✉t s♣❛t✐❛❧ ❞❡♣❡♥❞❡♥❝❡s ❛❝❝♦r❞✐♥❣

t♦ ❛❧❧ t❤r❡❡ ❡✈❛❧✉❛t✐♦♥ ♠❡tr✐❝s✳ ❊❛❝❤ s②♠❜♦❧ r❡♣r❡s❡♥ts ❛ ❝✐t② ❛♥❞ ❝♦❧♦r ❛♥❞ s❤❛♣❡ ✐♥❞✐❝❛t❡ t❤❡ ❤✐❣❤❡st ✐♥❝✐❞❡♥❝❡ ❧❡✈❡❧ ❛❝❤✐❡✈❡❞ ❜② t❤❡ ❝♦rr❡s♣♦♥❞✲ ✐♥❣ ❝✐t②✳ ❚❤❡ s♦❧✐❞ ❜❧❛❝❦ ❧✐♥❡ ✐♥❞✐❝❛t❡s ❡q✉❛❧ ♣❡r❢♦r♠❛♥❝❡ ❜❡t✇❡❡♥ ♠♦❞❡❧s✳ ❈✐t✐❡s ❛❜♦✈❡ t❤❡ s♦❧✐❞ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② ✐❣♥♦r✐♥❣ s♣❛✲ t✐❛❧ ❞❡♣❡♥❞❡♥❝❡s✱ ✇❤✐❧❡ ❝✐t✐❡s ❜❡❧♦✇ t❤❡ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② ❡♥❢♦r❝✐♥❣ s♣❛t✐❛❧ ❞❡♣❡♥❞❡♥❝❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✻✳✶ ❈♦♠♣❛r✐s♦♥ ❜❡t✇❡❡♥ ❉●P✱ ▲▼✱ ❆❘ ❛♥❞ ◆❇ ❛❝❝♦r❞✐♥❣ t♦ ❛❧❧ t❤r❡❡ ❡✈❛❧✉✲

❛t✐♦♥ ♠❡tr✐❝s✳ ❊❛❝❤ s②♠❜♦❧ r❡♣r❡s❡♥ts ❛ ❝✐t② ❛♥❞ ❝♦❧♦r ❛♥❞ s❤❛♣❡ ✐♥❞✐❝❛t❡ t❤❡ ❤✐❣❤❡st ✐♥❝✐❞❡♥❝❡ ❧❡✈❡❧ ❛❝❤✐❡✈❡❞ ❜② t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝✐t②✳ ❚❤❡ s♦❧✐❞ ❜❧❛❝❦ ❧✐♥❡ ✐♥❞✐❝❛t❡s ❡q✉❛❧ ♣❡r❢♦r♠❛♥❝❡ ❜❡t✇❡❡♥ ♠♦❞❡❧s✳ ❈✐t✐❡s ❛❜♦✈❡ t❤❡ s♦❧✐❞ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② ▲▼✱ ❆❘ ♦r ◆❇ ✱ ✇❤✐❧❡ ❝✐t✐❡s ❜❡❧♦✇ t❤❡ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② ❉●P✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✻✳✷ P♦st❡r✐♦r ❞✐str✐❜✉t✐♦♥ ♦❢ ❝❧✐♠❛t❡✲r❡❧❛t❡❞ ❡✛❡❝ts ❢♦r t❤❡ ❝✐t② ♦❢ ❙ã♦ ❏♦sé ❞♦s

❈❛♠♣♦s✱ ❙ã♦ P❛✉❧♦✱ ✇❤❡♥ ◆❇ ✐s ✜tt❡❞ ♣❡r ❝✐t② ✭❜❧❛❝❦ ❧✐♥❡✮ ♦r ❥♦✐♥t❧② ✇✐t❤ ❛❧❧ ❝✐t✐❡s ✭r❡❞ ❧✐♥❡✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✻✳✸ ❊♠♣✐r✐❝❛❧ ❝✉♠✉❧❛t✐✈❡ ❞✐str✐❜✉t✐♦♥ ❢✉♥❝t✐♦♥ ❢♦r ❡❛❝❤ ❡✈❛❧✉❛t✐♦♥ ♠❡tr✐❝✳ ✳ ✳ ✳ ✼✵ ✻✳✹ ❙♣❛t✐❛❧ ❞✐str✐❜✉t✐♦♥ ♦❢ ❡✈❛❧✉❛t✐♦♥ ♠❡tr✐❝s ♣❡r ❝✐t② ♦❜t❛✐♥❡❞ ❜② ❉●P✳ ❊❛❝❤

s②♠❜♦❧ ❞❡♥♦t❡s ❛ ❝✐t②✱ ✇✐t❤ ❝♦❧♦r ❛♥❞ s❤❛♣❡ ❛ss♦❝✐❛t❡❞ t♦ t❤❡ ✈❛❧✉❡ ♦❜t❛✐♥❡❞ ✐♥ ❡❛❝❤ ♠❡tr✐❝ ♦♥ t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝✐t②✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✻✳✺ ❊✈❛❧✉❛t✐♦♥ ♠❡tr✐❝s str❛t✐✜❡❞ ♣❡r ❇r❛③✐❧✐❛♥ r❡❣✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶

(19)

✻✳✻ Pr❡❞✐❝t✐♦♥s ✐ss✉❡❞ ❢♦r t❤❡ s✐① ❇r❛③✐❧✐❛♥ ❝❛♣✐t❛❧ ❝✐t✐❡s ✇✐t❤ ❤✐❣❤❡st ❉■❘ ✈❛❧✲ ✉❡s✳ ❚❤❡ ❜❧❛❝❦ ❧✐♥❡ ✐♥❞✐❝❛t❡s r❡❛❧ ✈❛❧✉❡s✱ ✇❤✐❧❡ t❤❡ ❜❧✉❡ ❧✐♥❡ s❤♦✇ t❤❡ ♣r❡✲ ❞✐❝t✐♦♥s ♦❜t❛✐♥❡❞✳ ❚❤❡ ❜❧✉❡ s❤❛❞❡❞ ❛r❡❛ ✐♥❞✐❝❛t❡s t❤❡ ✾✺✪ ❝♦♥✜❞❡♥❝❡ ✐♥t❡r✈❛❧✳ ✼✷ ✼✳✶ ❚❤r❡❡✲st❡♣ ❤②❜r✐❞ ❛♣♣r♦❛❝❤ ♣r♦♣♦s❡❞ ❢♦r ✉s✐♥❣ ❚✇✐tt❡r ❞❛t❛ t♦ ✐♠♣r♦✈❡

❡♣✐❞❡♠✐♦❧♦❣✐❝❛❧ ♣r❡❞✐❝t✐✈❡ ♠♦❞❡❧s ❢♦r ❊❲❙s✳ ●r❛② ❜♦①❡s r❡♣r❡s❡♥t t❤❡ ❛♣✲ ♣r♦❛❝❤ ❝♦♠♣♦♥❡♥ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✼✳✷ ❚✇♦✲st❡♣ ♦♥❧✐♥❡✲♦♥❧② ❛♣♣r♦❛❝❤ ♣r♦♣♦s❡❞ ❢♦r ✉s✐♥❣ ❚✇✐tt❡r ❞❛t❛ t♦ ✐♠♣r♦✈❡

❊❲❙s ❢♦r ❞❡♥❣✉❡ ❢❡✈❡r✳ ●r❛② ❜♦①❡s r❡♣r❡s❡♥t t❤❡ ❛♣♣r♦❛❝❤ ❝♦♠♣♦♥❡♥ts✳ ✳ ✼✽ ✼✳✸ ■♠♣❛❝t ♦❢ t❤❡ ♥✉♠❜❡r ♦❢ ❞❡♥❣✉❡✲r❡❧❛t❡❞ t✇❡❡ts ❛♥❞ ❝♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥

❡♣✐❞❡♠✐♦❧♦❣✐❝❛❧ ❛♥❞ ♦♥❧✐♥❡ ❞❛t❛ ❢♦r ❡❛❝❤ ❝✐t② ♦♥ t❤❡ ❞✐✛❡r❡♥❝❡ ♦❢ ❛❝❝✉r❛❝② ❜❡t✇❡❡♥ ❍❆❛❊ ❛♥❞ ❍❆♥❊✳ ❊❛❝❤ s②♠❜♦❧ r❡♣r❡s❡♥ts ❛ ❝✐t② ❛♥❞ ❝♦❧♦r ❛♥❞ s❤❛♣❡ ✐♥❞✐❝❛t❡ t❤❡ ❤✐❣❤❡st ✐♥❝✐❞❡♥❝❡ ❧❡✈❡❧ ❛❝❤✐❡✈❡❞ ❜② t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝✐t②✳ ❚❤❡ ❞❛s❤❡❞ ❧✐♥❡ ✐♥❞✐❝❛t❡s ❡q✉❛❧ ♣❡r❢♦r♠❛♥❝❡✳ P♦✐♥ts ❛❜♦✈❡ t❤✐s ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② ❍❆❛❊✱ ✇❤✐❧❡ ♣♦✐♥ts ❜❡❧♦✇ t❤❡ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② ❍❆♥❊✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✼✳✹ ❈♦♠♣❛r✐s♦♥ ❜❡t✇❡❡♥ t❤❡ t✇♦ ♣r♦♣♦s❡❞ ❛♣♣r♦❛❝❤❡s✳ ❚❤❡ ①✲❛①✐s ❛♥❞ ②✲❛①✐s

❛r❡ r❡❧❛t❡❞ t♦ t❤❡ ✈❛❧✉❡ ❛❝❤✐❡✈❡❞ ✉s✐♥❣ ❛ ❣✐✈❡♥ ❡✈❛❧✉❛t✐♦♥ ♠❡tr✐❝ ❛♥❞ ❛ ❣✐✈❡♥ ❛♣♣r♦❛❝❤✳ ❊❛❝❤ s②♠❜♦❧ r❡♣r❡s❡♥ts ❛ ❝✐t② ❛♥❞ ❝♦❧♦r ❛♥❞ s❤❛♣❡ ✐♥❞✐❝❛t❡ t❤❡ ❤✐❣❤❡st ✐♥❝✐❞❡♥❝❡ ❧❡✈❡❧ ❛❝❤✐❡✈❡❞ ❜② t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝✐t②✳ ❚❤❡ ❞✐❛❣♦♥❛❧ ❧✐♥❡ ✐♥❞✐❝❛t❡s ❡q✉❛❧ ♣❡r❢♦r♠❛♥❝❡✳ P♦✐♥ts ❛❜♦✈❡ t❤✐s ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② ❖❆❚✱ ✇❤✐❧❡ ♣♦✐♥ts ❜❡❧♦✇ t❤❡ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② ❍❆ ♦r ❝❍❆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✼✳✺ ❈♦♠♣❛r✐s♦♥ ❜❡t✇❡❡♥ ❤②❜r✐❞ ❛♣♣r♦❛❝❤❡s ❛♥❞ st❛♥❞✲❛❧♦♥❡ ♠♦❞❡❧s✳ ❊❛❝❤ s②♠✲

❜♦❧ r❡♣r❡s❡♥ts ❛ ❝✐t② ❛♥❞ ❝♦❧♦r ❛♥❞ s❤❛♣❡ ✐♥❞✐❝❛t❡ t❤❡ ❤✐❣❤❡st ✐♥❝✐❞❡♥❝❡ ❧❡✈❡❧ ❛❝❤✐❡✈❡❞ ❜② t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝✐t②✳ ❚❤❡ s♦❧✐❞ ❜❧❛❝❦ ❧✐♥❡ ✐♥❞✐❝❛t❡s ❡q✉❛❧ ♣❡r✲ ❢♦r♠❛♥❝❡ ❜❡t✇❡❡♥ ♠♦❞❡❧s✳ ❈✐t✐❡s ❛❜♦✈❡ t❤❡ s♦❧✐❞ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② st❛♥❞✲❛❧♦♥❡ ♠♦❞❡❧s✱ ✇❤✐❧❡ ❝✐t✐❡s ❜❡❧♦✇ t❤❡ s♦❧✐❞ ❧✐♥❡ ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❜② ❤②❜r✐❞ ❛♣♣r♦❛❝❤❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✼✳✻ ❙♣❛t✐❛❧ ❞✐str✐❜✉t✐♦♥ ♦❢ ✇✐♥s ❛♥❞ ❧♦ss❡s ♦❜t❛✐♥❡❞ ❜② ❝❍❆✳ ❊❛❝❤ ♣♦✐♥t ❞❡♥♦t❡

❛ ❝✐t②✱ ✇✐t❤ ❝♦❧♦r ❛♥❞ s❤❛♣❡ ✐♥❞✐❝❛t✐♥❣ ✇❤❡t❤❡r ❝❍❆ ❝❤♦s❡ ❝♦rr❡❝t❧② t♦ ✉s❡ ❡st✐♠❛t❡❞ ❉■❘ ✈❛❧✉❡s ♦r ♥♦t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✼✳✼ Pr♦♣♦rt✐♦♥ ♦❢ ✇✐♥s✴❧♦ss❡s ♦❜t❛✐♥❡❞ ❜② t❤❡ ❝❍❆ str❛t✐✜❡❞ ❜② ❇r❛③✐❧✐❛♥ ❛❞✲

♠✐♥✐str❛t✐✈❡ r❡❣✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✼✳✽ ❉✐str✐❜✉t✐♦♥ ♦❢ ♥✉♠❜❡r ♦❢ t✇❡❡ts ❛♥❞ ❝♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ ❚✇✐tt❡r ❛♥❞

❞❡♥❣✉❡ ❞❛t❛ ❢♦r ❝✐t✐❡s ✇❤❡r❡ t❤❡ ♣r♦♣♦s❡❞ ❛♣♣r♦❛❝❤ ♦❜t❛✐♥❡❞ ❜❡tt❡r r❡s✉❧ts ❛♥❞ ✇❤❡r❡ ✐t ♦❜t❛✐♥❡❞ ✇♦rs❡ r❡s✉❧ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼

(20)

✼✳✾ ❉✐✛❡r❡♥❝❡ ✐♥ ❡❛❝❤ ❡✈❛❧✉❛t✐♦♥ ♠❡tr✐❝ ❢♦r ♣r❡❞✐❝t✐♦♥s ✐ss✉❡❞ ❜② ❝❍❆ ❛♥❞ ❍❆♥❊ ❢♦r ❡♣✐❞❡♠✐♦❧♦❣✐❝❛❧ ❞❛t❛ ❞❡❧❛② r❛♥❣✐♥❣ ❢r♦♠ ✷ t♦ ✶✻ ✇❡❡❦s✳ P♦s✐✲ t✐✈❡ ✈❛❧✉❡s ✐♥❞✐❝❛t❡ ❤✐❣❤❡r ✈❛❧✉❡s ❛❝❤✐❡✈❡❞ ❜② ❝❍❆✱ ✇❤✐❧❡ ♥❡❣❛t✐✈❡ ✈❛❧✉❡s ✐♥❞✐❝❛t❡ t❤❡ ♦♣♣♦s✐t❡ s❝❡♥❛r✐♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽

(21)

▲✐st ♦❢ ❚❛❜❧❡s

✸✳✶ ❙❡❧❡❝t❡❞ ♣r❡✈✐♦✉s ✇♦r❦ ♦♥ ❞❡♥❣✉❡ ✐♥❝✐❞❡♥❝❡ r❛t❡ ♣r❡❞✐❝t✐♦♥ ✭✷✵✵✻✲✷✵✶✶✮✳ ✳ ✳ ✷✺ ✸✳✷ ❙❡❧❡❝t❡❞ ♣r❡✈✐♦✉s ✇♦r❦ ♦♥ ❞❡♥❣✉❡ ✐♥❝✐❞❡♥❝❡ r❛t❡ ♣r❡❞✐❝t✐♦♥ ✭✷✵✶✷✲✷✵✶✺✮✳ ✳ ✳ ✷✻ ✹✳✶ ❈r♦ss✲❝♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ ❉■❘ ❛♥❞ ❝❧✐♠❛t❡ ❝♦✈❛r✐❛t❡s ✇❤❡♥ ❧❛❣s ❛r❡ ✜①❡❞

❛♥❞ ✇❤❡♥ ❧❛❣s ❛r❡ ❛❧❧♦✇❡❞ t♦ ✈❛r② ❢r♦♠ ♦♥❡ ❝✐t② t♦ ❛♥♦t❤❡r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✹✳✷ ❈r♦ss✲❝♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ ❉■❘ ❛♥❞ ✈♦❧✉♠❡ ♦❢ ❞❡♥❣✉❡✲r❡❧❛t❡❞ t✇❡❡ts ✇❤❡♥

❧❛❣s ❛r❡ ✜①❡❞ ❛♥❞ ✇❤❡♥ ❧❛❣s ❛r❡ ❛❧❧♦✇❡❞ t♦ ✈❛r② ❢r♦♠ ♦♥❡ ❝✐t② t♦ ❛♥♦t❤❡r✳ ✳ ✸✾ ✺✳✶ ❉✐✛❡r❡♥❝❡ ❛❝❝♦r❞✐♥❣ t♦ ❡❛❝❤ ❡✈❛❧✉❛t✐♦♥ ♠❡tr✐❝ ❜❡t✇❡❡♥ ❉●P ❡q✉✐♣♣❡❞ ✇✐t❤

♣r♦♣♦s❡❞ ❝♦✈❛r✐❛♥❝❡ ❢✉♥❝t✐♦♥ ❛♥❞ ✇✐t❤ ❛❧t❡r♥❛t✐✈❡ ❢♦r♠✉❧❛t✐♦♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✺✳✷ ❈♦♠♣✉t❛t✐♦♥❛❧ ❝♦♠♣❧❡①✐t② ✇❤❡♥ ✉s✐♥❣ ♣r♦♣♦s❡❞ str❛t❡❣✐❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✺✳✸ ❉✐✛❡r❡♥❝❡ ❛❝❝♦r❞✐♥❣ t♦ ❡❛❝❤ ❡✈❛❧✉❛t✐♦♥ ♠❡tr✐❝ ❜❡t✇❡❡♥ ❉●P ✐♥ ✐ts ❜❡st

❝♦♥✜❣✉r❛t✐♦♥ ✭t❡♠♣♦r❛❧✲♦♥❧②✱ S = 10 ❛♥❞ ❡♠♣✐r✐❝❛❧ ❛♣♣r♦①✐♠❛t✐♦♥ ♦❢ KC✮

❛♥❞ ❛❧t❡r♥❛t✐✈❡ ❢♦r♠✉❧❛t✐♦♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✺✳✹ ❚✐♠❡ r❡q✉✐r❡❞ ❢♦r ❤②♣❡r♣❛r❛♠❡t❡r ♦♣t✐♠✐③❛t✐♦♥ ❛♥❞ ✐♥❢❡r❡♥❝❡ ❢♦r ✈❛r✐❛♥ts

st✉❞✐❡❞✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✻✳✶ ❉✐✛❡r❡♥❝❡ ❛❝❝♦r❞✐♥❣ t♦ ❡❛❝❤ ❡✈❛❧✉❛t✐♦♥ ♠❡tr✐❝ ❜❡t✇❡❡♥ ❉●P ❛♥❞ ❛❧t❡r♥❛t✐✈❡

♠♦❞❡❧s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✻✳✷ ❍②♣❡r♣❛r❛♠❡t❡rs ♦❜t❛✐♥❡❞ ❜② ❉●P✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✼✳✶ ❊st✐♠❛t❡❞ ❝♦❡✣❝✐❡♥ts ❢♦r ❧✐♥❡❛r r❡❣r❡ss✐♦♥ ♦❢ ❞✐✛❡r❡♥❝❡ ✐♥ ❆❯❈ ♦✈❡r ❝♦rr❡✲

❧❛t✐♦♥ ❜❡t✇❡❡♥ ❚✇✐tt❡r ❛♥❞ ❞❡♥❣✉❡ ❞❛t❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✼✳✷ ❉✐✛❡r❡♥❝❡ ❛❝❝♦r❞✐♥❣ t♦ ❡❛❝❤ ❡✈❛❧✉❛t✐♦♥ ♠❡tr✐❝ ❜❡t✇❡❡♥ ❍❆ ❛♥❞ ❖❆❚✳ ✳ ✳ ✳ ✽✹ ✼✳✸ ❉✐✛❡r❡♥❝❡ ❛❝❝♦r❞✐♥❣ t♦ ❡❛❝❤ ❡✈❛❧✉❛t✐♦♥ ♠❡tr✐❝ ❜❡t✇❡❡♥ ❍❆ ❛♥❞ st❛♥❞✲❛❧♦♥❡

♠♦❞❡❧s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹

(22)
(23)

▲✐st ♦❢ ❆❧❣♦r✐t❤♠s

✷✳✶ ❆❧❣♦r✐t❤♠ ❢♦r ✐♥❢❡r❡♥❝❡ ✉♥❞❡r ●P ♠♦❞❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✷ ❆❧❣♦r✐t❤♠ ❢♦r ❝❛❧❝✉❧❛t✐♥❣z = (A⊗B)x ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾

✺✳✶ ❆❣❣❧♦♠❡r❛t✐✈❡ ❈♦♠♣❧❡t❡✲▲✐♥❦ ❍✐❡r❛r❝❤✐❝❛❧ ❈❧✉st❡r✐♥❣ ❆❧❣♦r✐t❤♠ ✳ ✳ ✳ ✳ ✺✸

(24)
(25)

❈♦♥t❡♥ts

❆❣r❛❞❡❝✐♠❡♥t♦s ✐①

❆❜str❛❝t ①✐

❘❡s✉♠♦ ①✐✐✐

▲✐st ♦❢ ❋✐❣✉r❡s ①✈

▲✐st ♦❢ ❚❛❜❧❡s ①①✐

✶ ■♥tr♦❞✉❝t✐♦♥ ✶

✶✳✶ ❖❜❥❡❝t✐✈❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✶✳✷ ❚❤❡s✐s ❖r❣❛♥✐③❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺

✷ ●❛✉ss✐❛♥ Pr♦❝❡ss❡s ✼

✷✳✶ ●❛✉ss✐❛♥ Pr♦❝❡ss ❛s ❛ ❉✐str✐❜✉t✐♦♥ ♦✈❡r ❋✉♥❝t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✷ ●❛✉ss✐❛♥ Pr♦❝❡ss ❛s ❛ ❑❡r♥❡❧ ▼❛❝❤✐♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✸ ❈♦✈❛r✐❛♥❝❡ ❋✉♥❝t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✸✳✶ ❋❛♠✐❧✐❡s ♦❢ ❈♦✈❛r✐❛♥❝❡ ❋✉♥❝t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✸✳✷ ❍②♣❡r♣❛r❛♠❡t❡r ❖♣t✐♠✐③❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✹ P✉tt✐♥❣ t❤❡ P✐❡❝❡s ❚♦❣❡t❤❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✺ ▼✉❧t✐✲t❛s❦ ●❛✉ss✐❛♥ Pr♦❝❡ss ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼

✸ ❘❡❧❛t❡❞ ❲♦r❦ ✷✸

✹ ❉❡♥❣✉❡ ❉❛t❛ ❈❤❛r❛❝t❡r✐③❛t✐♦♥ ✸✶

✹✳✶ ❉❡♥❣✉❡ ❉❛t❛ ❈♦❧❧❡❝t✐♦♥ ❛♥❞ Pr❡✲Pr♦❝❡ss✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✹✳✷ ❚❡♠♣♦r❛❧ ❆♥❛❧②s✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✹✳✸ ❙♣❛t✐❛❧ ❆♥❛❧②s✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✹✳✹ ❈❧✐♠❛t❡ ❉❡♣❡♥❞❡♥❝❡s ❆♥❛❧②s✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻

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✹✳✺ ❚✇✐tt❡r ❉❡♣❡♥❞❡♥❝❡s ❆♥❛❧②s✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✹✳✻ ❙✉♠♠❛r② ❛♥❞ ❉✐s❝✉ss✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵

✺ ❉❡♥❣✉❡ ❋❡✈❡r ■♥❝✐❞❡♥❝❡ ▼♦❞❡❧❧✐♥❣ ✹✸

✺✳✶ ❊①♣❡r✐♠❡♥t❛❧ ❙❡t✉♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✺✳✷ ❚❡♠♣♦r❛❧ ❛♥❞ ❈❧✐♠❛t❡✲❘❡❧❛t❡❞ ❈♦✈❛r✐❛♥❝❡ ❋✉♥❝t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✺✳✷✳✶ ❊✈❛❧✉❛t✐♦♥ ♦❢ ❈❛♥❞✐❞❛t❡ ❈♦✈❛r✐❛♥❝❡ ❋✉♥❝t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✺✳✸ ■♥❝❧✉❞✐♥❣ ❙♣❛t✐❛❧ ❉❡♣❡♥❞❡♥❝❡s t♦ t❤❡ ❈♦✈❛r✐❛♥❝❡ ❋✉♥❝t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✺✳✸✳✶ ■♠♣r♦✈✐♥❣ t❤❡ P❡r❢♦r♠❛♥❝❡ ♦❢ ❉●P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✺✳✸✳✷ ❊✈❛❧✉❛t✐♦♥ ♦❢ t❤❡ ❙♣❛t✐❛❧ ❈♦♠♣♦♥❡♥t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✺✳✹ ❙✉♠♠❛r② ❛♥❞ ❉✐s❝✉ss✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵

✻ ❊①♣❡r✐♠❡♥t❛❧ ❆♥❛❧②s✐s ✻✺

✻✳✶ ❈♦♠♣❛r✐s♦♥ ❇❡t✇❡❡♥ ❉●P ❛♥❞ Pr❡✈✐♦✉s ▼♦❞❡❧s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✻✳✷ ❆♥❛❧②s✐s ♦❢ ❍②♣❡r♣❛r❛♠❡t❡rs ❛♥❞ Pr❡❞✐❝t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✻✳✸ ❙✉♠♠❛r② ❛♥❞ ❉✐s❝✉ss✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷

✼ ❯s✐♥❣ Pr♦①✐❡s ❢♦r ❊♣✐❞❡♠✐♦❧♦❣✐❝❛❧ ❉❛t❛ ✼✺

✼✳✶ ❚✇♦ ❆♣♣r♦❛❝❤❡s ❢♦r ■♥❝♦r♣♦r❛t✐♥❣ ❖♥❧✐♥❡ ❉❛t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✼✳✶✳✶ ❍②❜r✐❞ ❆♣♣r♦❛❝❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✼✳✶✳✷ ❖♥❧✐♥❡✲♦♥❧② ❆♣♣r♦❛❝❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✼✳✶✳✸ ❈♦♠♣♦♥❡♥ts ❙♣❡❝✐✜❝❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✼✳✷ ❊①♣❡r✐♠❡♥t❛❧ ❘❡s✉❧ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✼✳✷✳✶ ❉❡t❡r♠✐♥✐♥❣ t❤❡ ❚❤r❡s❤♦❧❞ ❢♦r ❯s✐♥❣ t❤❡ ❍②❜r✐❞ ❆♣♣r♦❛❝❤ ✳ ✳ ✳ ✽✶ ✼✳✷✳✷ ❈♦♠♣❛r✐s♦♥ ❇❡t✇❡❡♥ ❖♥❧✐♥❡✲♦♥❧② ❛♥❞ ❍②❜r✐❞ ❆♣♣r♦❛❝❤❡s ✳ ✳ ✳ ✽✷ ✼✳✷✳✸ ❊✈❛❧✉❛t✐♦♥ ♦❢ t❤❡ Pr♦♣♦s❡❞ ❆♣♣r♦❛❝❤❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✼✳✷✳✹ ■♠♣❛❝t ♦❢ ❊♣✐❞❡♠✐♦❧♦❣✐❝❛❧ ❉❛t❛ ❉❡❧❛② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✼✳✸ ❙✉♠♠❛r② ❛♥❞ ❉✐s❝✉ss✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼

✽ ❈♦♥❝❧✉s✐♦♥s ❛♥❞ ❋✉t✉r❡ ❲♦r❦ ✽✾

❇✐❜❧✐♦❣r❛♣❤② ✾✸

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❈❤❛♣t❡r ✶

■♥tr♦❞✉❝t✐♦♥

❉❡♥❣✉❡ ❢❡✈❡r ✐s ❛ ♠♦sq✉✐t♦✲❜♦r♥❡ ✈✐r❛❧ ❞✐s❡❛s❡ tr❛♥s♠✐tt❡❞ ❜② ❢❡♠❛❧❡s ♠♦sq✉✐t♦❡s ♦❢ t❤❡ s♣❡❝✐❡s ❆❡❞❡s ❛❡❣②♣t✐✱ t❤❡ s❛♠❡ ♠♦sq✉✐t♦ t❤❛t ❝❛rr✐❡s t❤❡ ✈✐r✉s❡s ♦❢ ③✐❦❛✱ ②❡❧❧♦✇ ❢❡✈❡r ❛♥❞ ❝❤✐❦✉♥❣✉♥②❛✳ ❆s ❛♥② ✈❡❝t♦r✲❜♦r♥❡ ❞✐s❡❛s❡✱ ❞❡♥❣✉❡ ❢❡✈❡r ✐s ♥♦t tr❛♥s♠✐tt❡❞ ❞✐r❡❝t❧② ❜❡t✇❡❡♥ ❤✉♠❛♥s✱ r❡q✉✐r✐♥❣ t❤❡ ♣r❡s❡♥❝❡ ♦❢ ❛♥ ✐♥❢❡❝t❡❞ ✈❡❝t♦r✳ ■♥ t❤❡ s♣❡❝✐✜❝ ❝❛s❡ ♦❢ ❞❡♥❣✉❡ ❢❡✈❡r✱ ❛ ♠♦sq✉✐t♦ ✭✈❡❝t♦r✮ t❤❛t ❜✐t❡s ❛♥ ✐♥❢❡❝t❡❞ ❤✉♠❛♥ ♠❛② ❛❝q✉✐r❡ t❤❡ ✈✐r✉s✳ ❆❢t❡r ✈✐r✉s ✐♥❝✉❜❛t✐♦♥ ❢r♦♠ ✹ t♦ ✶✵ ❞❛②s✱ ❛♥ ✐♥❢❡❝t❡❞ ✈❡❝t♦r ✐s ❝❛♣❛❜❧❡ ♦❢ tr❛♥s♠✐tt✐♥❣ t❤❡ ✈✐r✉s ❢♦r t❤❡ r❡st ♦❢ ✐ts ❧✐❢❡ ❬❲♦r❧❞ ❍❡❛❧t❤ ❖r❣❛♥✐③❛t✐♦♥ ▼❡❞✐❛ ❈❡♥tr❡✱ ✷✵✶✻❪✳

❉❡♥❣✉❡ ❢❡✈❡r ✐s ❛ s❡✈❡r❡ ✢✉✲❧✐❦❡ ✐❧❧♥❡ss ❛♥❞ ♠❛② ❝❛✉s❡ ❤✐❣❤ ❢❡✈❡r✱ str♦♥❣ ❤❡❛❞❛❝❤❡✱ ♣❛✐♥ ❜❡❤✐♥❞ t❤❡ ❡②❡s✱ ♠✉s❝❧❡s ❛♥❞ ❥♦✐♥ts✱ ♥❛✉s❡❛✱ ✈♦♠✐t✐♥❣✱ s✇♦❧❧❡♥ ❣❧❛♥❞s ❛♥❞ r❛s❤✱ ✇❤✐❝❤ ♠❛② ❧❛st ❢♦r ♦♥❡ ✇❡❡❦✳ ❚❤❡r❡ ✐s ♥♦ s♣❡❝✐✜❝ tr❡❛t♠❡♥t ❢♦r ❞❡♥❣✉❡ ❢❡✈❡r ♥♦r ❛✈❛✐❧❛❜❧❡ ✈❛❝❝✐♥❡s ❛♥❞✱ t❤❡r❡❢♦r❡✱ ❝♦♥tr♦❧ ♦❢ t❤❡ ❞✐s❡❛s❡ ❝❛♥ ♦♥❧② ❜❡ ♠❛❞❡ ❜② s✉♣♣r❡ss✐♥❣ t❤❡ ✈❡❝t♦r ♣♦♣✉❧❛t✐♦♥✱ ❛s ✇❡❧❧ ❛s ✐❞❡♥t✐❢②✐♥❣ ♦✉t❜r❡❛❦s ❛s q✉✐❝❦❧② ❛s ♣♦ss✐❜❧❡ ❬❲♦r❧❞ ❍❡❛❧t❤ ❖r❣❛♥✐③❛t✐♦♥ ▼❡❞✐❛ ❈❡♥tr❡✱ ✷✵✶✻❪✳ ❆❧t❤♦✉❣❤ ❝❛s❡ ❢❛t❛❧✐t② r❛t❡ ❝❛♥ ❜❡ ❛s ❧♦✇ ❛s ✶✪ ✇✐t❤ ♣r♦♣❡r tr❡❛t♠❡♥t✱ t❤❡ ❞✐s❡❛s❡ ❝♦♠❡s ✇✐t❤ ❡❝♦♥♦♠✐❝❛❧ ❛♥❞ s♦❝✐❛❧ ❜✉r❞❡♥ ❬❙❛♠✐r ❡t ❛❧✳✱ ✷✵✶✸❪✳

❆❝❝♦r❞✐♥❣ t♦ ❙❛♠✐r ❡t ❛❧✳ ❬✷✵✶✸❪✱ ❞❡♥❣✉❡ ❢❡✈❡r ✐s ✉❜✐q✉✐t♦✉s t❤r♦✉❣❤♦✉t t❤❡ tr♦♣✲ ✐❝s✳ ❚❤❡ st✉❞② ❡st✐♠❛t❡s t❤❛t ❛❜♦✉t ✸✾✵ ♠✐❧❧✐♦♥ ♣❡♦♣❧❡ ✇♦r❧❞✇✐❞❡ ❝♦♥tr❛❝t ❞❡♥❣✉❡ ❢❡✈❡r ❡✈❡r② ②❡❛r✱ ✇✐t❤ ✾✻ ♠✐❧❧✐♦♥ ♦❢ t❤❡s❡ ❝❛s❡s ❜❡✐♥❣ s②♠♣t♦♠❛t✐❝✳ ❆❜♦✉t ✼✵✪ ♦❢ t❤❡ s②♠♣t♦♠❛t✐❝ ❝❛s❡s ❛r❡ ❢r♦♠ ❆s✐❛✱ ✇✐t❤ ■♥❞✐❛ ❛❧♦♥❡ ❝♦♥tr✐❜✉t✐♥❣ ✇✐t❤ ✸✹✪ ♦❢ t❤❡ ❣❧♦❜❛❧ ♥✉♠❜❡r ♦❢ ❝❛s❡s✳ ❚❤❡ ❆♠❡r✐❝❛s ❝♦♥tr✐❜✉t❡❞ ✇✐t❤ ✶✹✪ ♦❢ t❤❡ s②♠♣t♦♠❛t✐❝ ✐♥❢❡❝t✐♦♥s✱ ♦❢ ✇❤✐❝❤ ♦✈❡r ❤❛❧❢ ♦❝❝✉rr❡❞ ✐♥ ❇r❛③✐❧ ❛♥❞ ▼❡①✐❝♦✳ ❋✐♥❛❧❧②✱ t❤❡ st✉❞② ❡st✐♠❛t❡s ❛ s✐♠✐❧❛r s✐t✉❛t✐♦♥ ❢♦r ❆❢r✐❝❛ ✇❤❡♥ ❝♦♠♣❛r❡❞ t♦ t❤❡ ❆♠❡r✐❝❛s✳ ❋✐❣✉r❡ ✶✳✶ s✉♠♠❛r✐③❡s t❤❡ ❣❧♦❜❛❧ ❞✐str✐❜✉t✐♦♥ ♦❢ ❞❡♥❣✉❡ ❢❡✈❡r✳

■♥ ❇r❛③✐❧✱ ❞❡♥❣✉❡ ❢❡✈❡r ✇❛s ❡r❛❞✐❝❛t❡❞ ✐♥ t❤❡ ✜rst ❤❛❧❢ ♦❢ t❤❡ ✷✵t❤ ❝❡♥t✉r②✱ ❜✉t

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✷ ❈❤❛♣t❡r ✶✳ ■♥tr♦❞✉❝t✐♦♥

❋✐❣✉r❡ ✶✳✶✳ ●❧♦❜❛❧ ❞✐str✐❜✉t✐♦♥ ♦❢ ❞❡♥❣✉❡ ❢❡✈❡r✱ ❡①tr❛❝t❡❞ ❢r♦♠ ❙❛♠✐r ❡t ❛❧✳ ❬✷✵✶✸❪✳ ❚❤❡ ♠❛♣ ♦♥ t❤❡ t♦♣ ✭❛✮ s❤♦✇s t❤❡ ♣r❡s❡♥❝❡ ♦❢ ❞❡♥❣✉❡ ✈✐r✉s ❛r♦✉♥❞ t❤❡ ✇♦r❧❞✳ ❚❤❡ ♠❛♣ ♦♥ t❤❡ ♠✐❞❞❧❡ ✭❜✮ s❤♦✇s t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ ♦❝❝✉r❡♥❝❡ ♦❢ ❞❡♥❣✉❡ ❢❡✈❡r✳ ❚❤❡ ♠❛♣ ♦♥ t❤❡ ❜♦tt♦♠ ✭❝✮ ✐♥❞✐❝❛t❡s t❤❡ ♥✉♠❜❡r ♦❢ ❞❡♥❣✉❡ ❢❡✈❡r ✐♥❢❡❝t✐♦♥s ❛t ❝♦✉♥tr② ❧❡✈❡❧✱ ✇✐t❤ ❛r❡❛s ♣r♦♣♦rt✐♦♥❛❧ t♦ t❤❡ ♥✉♠❜❡r ♦❢ ❝❛s❡s✳

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❬❚❡✐①❡✐r❛ ❡t ❛❧✳✱ ✷✵✵✾❪✳ ❙✐♥❝❡ t❤❡♥✱ t❤❡ ♥✉♠❜❡r ♦❢ ✐♥❢❡❝t✐♦♥s ❤❛s ✐♥❝r❡❛s❡❞ s✐❣♥✐✜❝❛♥t❧②✳ ❚❤❡ s♣r❡❛❞ ♦❢ t❤❡ ♠♦sq✉✐t♦ ✭❛♥❞✱ ❝♦♥s❡q✉❡♥t❧②✱ ♦❢ t❤❡ ❞✐s❡❛s❡✮ ✇❛s ❢❛❝✐❧✐t❛t❡❞ ❜② t❤❡ ❝♦✉♥tr②✬s ❛♣♣r♦♣r✐❛t❡ ❝❧✐♠❛t❡ ❬❚❡✐①❡✐r❛ ❡t ❛❧✳✱ ✷✵✵✾❪ ❛♥❞ ♣♦♣✉❧❛t✐♦♥ ❣r♦✇t❤ ❬●✉❜❧❡r✱ ✷✵✵✷❪✳ ◆♦✇❛❞❛②s✱ ❞❡♥❣✉❡ ❢❡✈❡r ✐s ❡♥❞❡♠✐❝ ✐♥ ♠♦st ❇r❛③✐❧✐❛♥ r❡❣✐♦♥s ❛♥❞ t❤❡ ❝♦✉♥tr② ❤❛s t❤❡ ❧❛r❣❡st ♥✉♠❜❡r ♦❢ r❡♣♦rt❡❞ ❞❡♥❣✉❡ ❢❡✈❡r ❝❛s❡s ✐♥ t❤❡ ❆♠❡r✐❝❛s✱ ❛❝❝♦✉♥t✐♥❣ ❢♦r ❛t ❧❡❛st ♦♥❡✲❢♦✉rt❤ ♦❢ t❤❡ s②♠♣t♦♠❛t✐❝ ❝❛s❡s ✐♥ t❤❡ ❝♦♥t✐♥❡♥t ❬❙❛♠✐r ❡t ❛❧✳✱ ✷✵✶✸❪✳ ■♥ t❤✐s ❝♦♥t❡①t✱ ♣r♦✈✐❞✐♥❣ t♦♦❧s ❝❛♣❛❜❧❡ ♦❢ ❤❡❧♣✐♥❣ ✐❞❡♥t✐❢②✐♥❣ t❤❡ ❣r♦✇t❤ ✐♥ t❤❡ ♥✉♠❜❡r ♦❢ r❡♣♦rt❡❞ ❝❛s❡s✱ ❛❧❧♦✇✐♥❣ ❛ q✉✐❝❦ r❡s♣♦♥s❡ ❢r♦♠ t❤❡ ❣♦✈❡r♥♠❡♥t✱ ✐s ❡ss❡♥t✐❛❧ t♦ r❡❞✉❝❡ t❤❡ ❞✐s❡❛s❡ s♣r❡❛❞✳

❆♥ ❡❛r❧② ✇❛r♥✐♥❣ s②st❡♠ ✭❊❲❙✮ ✐s ❛ s②st❡♠ ❝❛♣❛❜❧❡ ♦❢ q✉✐❝❦❧② ✐❞❡♥t✐❢②✐♥❣ r✐s❦s ❛♥❞ ♣❧❛②s ❛ ♠❛❥♦r r♦❧❡ ♦♥ ❞✐s❛st❡r r✐s❦ r❡❞✉❝t✐♦♥ ❜② ♣r❡✈❡♥t✐♥❣ ❧♦ss ♦❢ ❧✐❢❡ ❛♥❞ ♠✐t✲ ✐❣❛t✐♥❣ t❤❡ ❡❝♦♥♦♠✐❝❛❧ ❛♥❞✴♦r ♠❛t❡r✐❛❧ ✐♠♣❛❝t ❬❲✐❧ts❤✐r❡✱ ✷✵✵✻❪✳ ■♥ t❤❡ ❝♦♥t❡①t ♦❢ ❡♣✐❞❡♠✐♦❧♦❣②✱ ❛♥ ❊❲❙ ✐s ❛ ❢✉♥❞❛♠❡♥t❛❧ st❡♣ ♦♥ ✐♠♣❧❡♠❡♥t✐♥❣ ❡✛❡❝t✐✈❡ ✐♥t❡r✈❡♥t✐♦♥s t♦ ❝♦♥tr♦❧ ✐♥❢❡❝t✐♦✉s ❞✐s❡❛s❡s✱ t❤✉s r❡❞✉❝✐♥❣ ♠♦rt❛❧✐t② ❛♥❞ ♠♦r❜✐❞✐t② ✐♥ ❤✉♠❛♥ ♣♦♣✉✲ ❧❛t✐♦♥s✳ ❍♦✇❡✈❡r✱ ✐❞❡♥t✐❢②✐♥❣ ❛♥ ❡♣✐❞❡♠✐❝ ✐s ♥♦t ❛♥ ❡❛s② t❛s❦✱ s✐♥❝❡ ✐t ❜❡❝♦♠❡s ❡✈✐❞❡♥t ♦♥❧② ❛❢t❡r ❛ ❧❛r❣❡ ♥✉♠❜❡r ♦❢ ✐♥❢❡❝t✐♦♥s ❤❛✈❡ ❛❧r❡❛❞② ❤❛♣♣❡♥❡❞ ❛♥❞ r❡❝♦r❞❡❞✳ ■♥ t❤✐s s❝❡♥❛r✐♦✱ ❞❡♥❣✉❡ ❢❡✈❡r ✐s ♥♦t ❛♥ ❡①❝❡♣t✐♦♥✳ ■♥ ❢❛❝t✱ t❤❡ ❲♦r❧❞ ❍❡❛❧t❤ ❖r❣❛♥✐③❛t✐♦♥ ❤❛s ✐♥❞✐❝❛t❡❞ ❞❡♥❣✉❡ ❢❡✈❡r ❛s ❛ ❞✐s❡❛s❡ ❢♦r ✇❤✐❝❤ ❜❡tt❡r ❊❲❙ ❛r❡ r❡q✉✐r❡❞ ❬❑✉❤♥ ❡t ❛❧✳✱ ✷✵✵✺❪✳

❆❝❝♦r❞✐♥❣ t♦ ❲✐❧ts❤✐r❡ ❬✷✵✵✻❪✱ ❛♥ ❊❲❙ ✐s ❝♦♠♣♦s❡❞ ♦❢ ❢♦✉r ❦❡② ❡❧❡♠❡♥ts✿ ✭✐✮ r✐s❦ ❦♥♦✇❧❡❞❣❡✱ ✭✐✐✮ ✇❛r♥✐♥❣ ❛♥❞ ♠♦♥✐t♦r✐♥❣ s❡r✈✐❝❡s✱ ✭✐✐✐✮ ❞✐ss❡♠✐♥❛t✐♦♥ ❛♥❞ ❝♦♠♠✉♥✐❝❛t✐♦♥ ❛♥❞ ✭✐✈✮ r❡s♣♦♥s❡ ❝❛♣❛❜✐❧✐t②✳ ❚❤❡ ❛✉t❤♦rs ♦❢ ❲✐❧ts❤✐r❡ ❬✷✵✵✻❪ ❛❧s♦ ✐♥❞✐❝❛t❡ t❤r❡❡ ♠❛❥♦r q✉❡st✐♦♥s t❤❛t ❛♥ ❛♣♣r♦♣r✐❛t❡ ✇❛r♥✐♥❣ s②st❡♠ ♠✉st ❛♥s✇❡r ❛✣r♠❛t✐✈❡❧②✿

✶✳ ❆r❡ t❤❡ r✐❣❤t ♣❛r❛♠❡t❡rs ❜❡✐♥❣ ♠♦♥✐t♦r❡❞❄

✷✳ ■s t❤❡r❡ ❛ s♦✉♥❞ s❝✐❡♥t✐✜❝ ❜❛s✐s ❢♦r ♠❛❦✐♥❣ ❢♦r❡❝❛sts❄ ✸✳ ❈❛♥ ❛❝❝✉r❛t❡ ❛♥❞ t✐♠❡❧② ✇❛r♥✐♥❣ ❜❡ ❣❡♥❡r❛t❡❞❄

Pr❡❞✐❝t✐✈❡ ♠♦❞❡❧s ❞❡s✐❣♥❡❞ ❢♦r ❢♦r❡❝❛st✐♥❣ ❞❡♥❣✉❡ ❢❡✈❡r ✐♥❝✐❞❡♥❝❡ t②♣✐❝❛❧❧② ✉s❡ ♣❛r❛♠❡tr✐❝ ♠♦❞❡❧s✶✱ s✉❝❤ ❛s ❣❡♥❡r❛❧✐③❡❞ ❧✐♥❡❛r ♦r ❆❘■▼❆ ♠♦❞❡❧s✱ ✇✐t❤ ❝♦✈❛r✐❛t❡s

❝♦♠♠♦♥❧② ❛ss♦❝✐❛t❡❞ t♦ ❞❡♥❣✉❡ ❢❡✈❡r✱ s✉❝❤ ❛s ❝❧✐♠❛t❡✲r❡❧❛t❡❞ ❢❛❝t♦rs✱ ✉r❜❛♥✐③❛t✐♦♥ ❛♥❞ s♦❝✐❛❧✲❡❝♦♥♦♠✐❝❛❧ ❝♦♥❞✐t✐♦♥s ✭❡✳❣✳✱ ▼❛rt✐♥❡③ ❡t ❛❧✳ ❬✷✵✶✶❪❀ ▲♦✇❡ ❡t ❛❧✳ ❬✷✵✶✸❪❀ ❙❤✐ ❡t ❛❧✳ ❬✷✵✶✻❪✮✳ ■♥ t❤✐s s❡♥s❡✱ t❤❡② ❛♥s✇❡r ❛✣r♠❛t✐✈❡❧② q✉❡st✐♦♥s ✶ ❛♥❞ ✷ ❧✐st❡❞ ❛❜♦✈❡✳

❍❡r❡✱ ✇❡ ❞❡✜♥❡ ❛ ♣❛r❛♠❡tr✐❝ ♠♦❞❡❧ ❛s ❛♥② ♠♦❞❡❧ t❤❛t ✐s ❢✉❧❧② s♣❡❝✐✜❡❞ ❜② ❛ ✜♥✐t❡ ♥✉♠❜❡r ♦❢

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✹ ❈❤❛♣t❡r ✶✳ ■♥tr♦❞✉❝t✐♦♥

❍♦✇❡✈❡r✱ t❤❡s❡ ♣❛r❛♠❡tr✐❝ ♠♦❞❡❧s ❤❛✈❡ ❧✐♠✐t❡❞ ❝♦♠♣❧❡①✐t② ✭❞❡✜♥❡❞ ❜② t❤❡ ♥✉♠❜❡r ♦❢ ♣❛r❛♠❡t❡rs✮ ❛♥❞✱ ❝♦♥s❡q✉❡♥t❧②✱ ♠❛② ❢❛✐❧ t♦ ❝❛♣t✉r❡ ❝♦♠♣❧❡① ♣❛tt❡r♥s t❤❛t ❝♦✉❧❞ ❜❡ ❡①♣❧♦✐t❡❞ t♦ ❡♥❤❛♥❝❡ t❤❡ ❛❝❝✉r❛❝② ♦❢ ♣r❡❞✐❝t✐♦♥s✳ ■♥ ♦r❞❡r t♦ ❛ss✉r❡ ❛❝❝✉r❛❝②✱ ♣❛r❛♠❡tr✐❝ ♠♦❞❡❧s ✉s✉❛❧❧② r❡q✉✐r❡ ❝❛r❡❢✉❧ ❛♥❛❧②s✐s ♦❢ ❞❛t❛✱ ❧❡❛❞✐♥❣ t♦ ♠♦❞❡❧s t❤❛t ❞♦ ♥♦t ❣❡♥❡r❛❧✐③❡ t♦ ♦t❤❡r ❝♦♥t❡①ts✳ ❋✐♥❛❧❧②✱ ❡♣✐❞❡♠✐♦❧♦❣✐❝❛❧ ❞❛t❛ t②♣✐❝❛❧❧② t❛❦❡s t✐♠❡ t♦ ❜❡ ❝♦♠♣✐❧❡❞ ❛♥❞ ♠❛❞❡ ❛✈❛✐❧❛❜❧❡ ❡✈❡♥ ❢♦r ❣♦✈❡r♥♠❡♥t❛❧ ❛✉t❤♦r✐t✐❡s✳ ❚❤❡r❡❢♦r❡✱ ❛t t✐♠❡t✱ ♦♥❧② ❡♣✐❞❡♠✐♦❧♦❣✐❝❛❧ ❞❛t❛ ❛ss♦❝✐❛t❡❞ ✉♣ t♦ t✐♠❡t−γ✱γ >0✱ ✐s ❛✈❛✐❧❛❜❧❡✳ ▼♦st

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

❖♥ t❤❡ ♦t❤❡r ❤❛♥❞✱ t❤❡ ♠❛❝❤✐♥❡ ❧❡❛r♥✐♥❣ ❝♦♠♠✉♥✐t② ❤❛s ♣r♦♣♦s❡❞ r✐❝❤❡r ❛♥❞ ♠♦r❡ ❣❡♥❡r❛❧ ♥♦♥✲♣❛r❛♠❡tr✐❝ ♠♦❞❡❧s ✇❤✐❝❤ ❝♦✉❧❞ ❜❡ ❡①♣❧♦✐t❡❞ t♦ ❜✉✐❧❞ ❡♣✐❞❡♠✐♦❧♦❣✐❝❛❧ ♠♦❞❡❧s✳ ■♥ t❤❡ ❝♦♥t❡①t ♦❢ ❡♣✐❞❡♠✐♦❧♦❣②✱ ✐♥t❡r♣r❡t❛❜✐❧✐t② ✐s ❛♥ ❡ss❡♥t✐❛❧ ♣r♦♣❡rt②✱ ❛s ✐♥❞✐❝❛t❡❞ ✐♥ q✉❡st✐♦♥ ✷ ❛❜♦✈❡✱ ♠❛❦✐♥❣ ♠❛♥② st❛t❡✲♦❢✲❛rt ♠♦❞❡❧s ✐♥❢❡❛s✐❜❧❡✳ ▼♦t✐✈❛t❡❞ ❜② t❤✐s ❝♦♥str❛✐♥t✱ t❤✐s ✇♦r❦ ❡①♣❧♦r❡s ●❛✉ss✐❛♥ ♣r♦❝❡ss❡s ❬❘❛s♠✉ss❡♥ ❛♥❞ ❲✐❧❧✐❛♠s✱ ✷✵✵✻❪✱ ❛ ❇❛②❡s✐❛♥ ♥♦♥✲♣❛r❛♠❡tr✐❝ ❢r❛♠❡✇♦r❦✱ t♦ ❜✉✐❧❞ ♣r❡❞✐❝t✐✈❡ ♠♦❞❡❧s ❢♦r ❞❡♥❣✉❡ ❢❡✈❡r ✐♥❝✐❞❡♥❝❡✱ ❛s t❤❡② ❧✐❡ ✐♥ t❤❡ ✐♥t❡rs❡❝t✐♦♥ ❜❡t✇❡❡♥ st❛t❡✲♦❢✲❛rt ❛♥❞ ✐♥t❡r♣r❡t❛❜❧❡ ♠♦❞❡❧s✳ ❇❡s✐❞❡s t❤❛t✱ ❛s ♣r❡✈✐♦✉s ✇♦r❦s ❤❛✈❡ ❛❧r❡❛❞② ✐♥❞✐❝❛t❡❞ ❛ss♦❝✐❛t✐♦♥s ❜❡t✇❡❡♥ ❡♣✐❞❡♠✐♦❧♦❣✐❝❛❧ ❞❛t❛ ❛♥❞ ♦♥❧✐♥❡ ❞❛t❛ s♦✉r❝❡s ❬●♦♠✐❞❡ ❡t ❛❧✳✱ ✷✵✶✶❀ ❆❧t❤♦✉s❡ ❡t ❛❧✳✱ ✷✵✶✶❀ ❙♦✉③❛ ❡t ❛❧✳✱ ✷✵✶✺❪✱ ✇❤✐❝❤ ❝❛♥ ❜❡ ♦❜t❛✐♥❡❞ ✐♥ r❡❛❧✲t✐♠❡ ❛♥❞ ✉s❡❞ t♦ ✜❧❧ t❤❡ ❣❛♣ ❝❛✉s❡❞ ❜② ❞❡❧❛②s ♦♥ ❡♣✐❞❡♠✐♦❧♦❣✐❝❛❧ ❞❛t❛✱ ✇❡ ❡①♣❧♦✐t ❚✇✐tt❡r ❞❛t❛ ❛s ❛ ♣r♦①② ❢♦r ❡♣✐❞❡♠✐♦❧♦❣✐❝❛❧ ❞❛t❛ t♦ ❜✉✐❧❞ ♠♦r❡ ❛❝❝✉r❛t❡ ♣r❡❞✐❝t✐✈❡ ❞❡♥❣✉❡ ♠♦❞❡❧s✳

✶✳✶ ❖❜❥❡❝t✐✈❡s

❚❤❡ ♠❛✐♥ ❣♦❛❧ ♦❢ t❤✐s ✇♦r❦ ✐s t♦ ❞❡✈❡❧♦♣ ❛ ♣r❡❞✐❝t✐✈❡ ♠♦❞❡❧ ❝❛♣❛❜❧❡ ♦❢ ❣❡♥❡r❛t✐♥❣ ✇❛r♥✐♥❣s ❛♥❞ ✇♦r❦✐♥❣ ❛s ❛ ♠♦♥✐t♦r✐♥❣ s❡r✈✐❝❡ ✇✐t❤✐♥ ❛♥ ❊❲❙✳ ❲❡ ♣r♦♣♦s❡ t♦ ❡①♣❧♦r❡ ●❛✉ss✐❛♥ ♣r♦❝❡ss❡s t♦ ❣❡♥❡r❛t❡ ♣r❡❞✐❝t✐✈❡ ♠♦❞❡❧s ❝❛♣❛❜❧❡ ♦❢ ❛✣r♠❛t✐✈❡❧② ❛♥s✇❡r✐♥❣ ❛❧❧ t❤r❡❡ q✉❡st✐♦♥s r❛✐s❡❞ ❛❜♦✈❡✳ ❲❡ ❛❧s♦ ♣r♦♣♦s❡ ❛ ❣❡♥❡r❛❧ ❢r❛♠❡✇♦r❦ ❢♦r ✉s✐♥❣ ♦♥❧✐♥❡ ❞❛t❛ t♦ ❞❡❛❧ ✇✐t❤ ❞❡❧❛②❡❞ ❡♣✐❞❡♠✐♦❧♦❣✐❝❛❧ ❞❛t❛✳ ■♥ s✉♠♠❛r②✱ ♦✉r ♠❛✐♥ ♦❜❥❡❝t✐✈❡s ❛♥❞ ❛ss♦❝✐❛t❡❞ ❝♦♥tr✐❜✉t✐♦♥s ❛r❡✿

• ❈❤❛r❛❝t❡r✐③❛t✐♦♥ ♦❢ ✇❡❡❦❧② ❡♣✐❞❡♠✐♦❧♦❣✐❝❛❧ ❞❡♥❣✉❡ ❞❛t❛ ✇✐t❤ r❡❧❛t✐♦♥ t♦ t❡♠♣♦r❛❧

❛s♣❡❝ts✱ ❝❧✐♠❛t❡ ❛♥❞ ✇❡❡❦❧② ♥✉♠❜❡r ♦❢ ❞❡♥❣✉❡✲r❡❧❛t❡❞ t✇❡❡ts❀

• ❉❡✈❡❧♦♣♠❡♥t ♦❢ ❛ s♣❛t✐♦✲t❡♠♣♦r❛❧ ♠♦❞❡❧ ❜❛s❡❞ ♦♥ ●❛✉ss✐❛♥ ♣r♦❝❡ss❡s ❢♦r ❢♦r❡✲

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✶✳✷✳ ❚❤❡s✐s ❖r❣❛♥✐③❛t✐♦♥ ✺

• ❉❡✈❡❧♦♣♠❡♥t ♦❢ ❛ ❣❡♥❡r❛❧ ❢r❛♠❡✇♦r❦ ❢♦r ❡♥❤❛♥❝✐♥❣ ❡♣✐❞❡♠✐♦❧♦❣✐❝❛❧ ♠♦❞❡❧s t❤❛t

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

✶✳✷ ❚❤❡s✐s ❖r❣❛♥✐③❛t✐♦♥

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Referências

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