Analisi di pathway biologici: studio e confronto di tecniche topologiche.
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Testo completo
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(3) ■♥❞✐❝❡. ✶ ■♥#$♦❞✉③✐♦♥❡. ✶. ✶✳✶. ◆♦③✐♦♥✐ ❞✐ ❜❛*❡ ❞❡❧❧❛ ❜✐♦❧♦❣✐❛ ♠♦❧❡❝♦❧❛0❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✶✳✷. ▲❛ 3❡❝♥♦❧♦❣✐❛ ❞✐. ❆✛②♠❡%&✐①. ✷. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹. ✶✳✷✳✶. ▲❛ ♠❛30✐❝❡ ❞❡✐ ❞❛3✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻. ✶✳✷✳✷. ▲❛ ♥♦0♠❛❧✐③③❛③✐♦♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼. ✶✳✸. ■ ❣❡♥✐ ❞✐✛❡0❡♥③✐❛❧♠❡♥3❡ ❡*♣0❡**✐ ✭❉❊●✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼. ✶✳✹. ▲♦ *3✉❞✐♦ 3♦♣♦❧♦❣✐❝♦ ❞❡✐ ♣❛3❤✇❛② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✾. ✶✳✺. ❙❝♦♣♦ ❞❡❧❧❛ 3❡*✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✶✷. ✷ ❚❡❝♥✐❝❤❡ /#❛#✐/#✐❝❤❡ ♣❡$ ❧✬✐❞❡♥#✐✜❝❛③✐♦♥❡ ❞❡✐ ❉❊●. ✶✺. ✷✳✶. ■♥30♦❞✉③✐♦♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✶✺. ✷✳✷. ■❧ ♠♦❞❡❧❧♦ ❧✐♥❡❛0❡ ♣❡0 ❞❛3✐ ❞✐ ♠✐❝0♦❛00❛② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✶✻. ✷✳✷✳✶. ▲❛ ♠❛30✐❝❡ ❞❡❧ ❞✐*❡❣♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✶✻. ✷✳✷✳✷. ■❧ 3✲3❡*3 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✶✽. ✷✳✷✳✸. ■❧ 3❡*3 ❇❛②❡*✐❛♥♦ ❊♠♣✐0✐❝♦ ❡❇❛②❡* ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✷✶. ✐.
(4) ■♥❞✐❝❡. ✸ ❆♥❛❧✐&✐ '♦♣♦❧♦❣✐❝❤❡ &✉✐ ♣❛'❤✇❛② ✸✳✶. ✸✳✷. ■♥%&♦❞✉③✐♦♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✷✺. ✸✳✶✳✶. ❉❡✜♥✐③✐♦♥❡ ❞❡❧ ♣❛"❤✇❛② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✷✻. ✸✳✶✳✷. ❈♦♥✈❡&5✐♦♥❡ ❞❡❧ ♣❛"❤✇❛② ✐♥ ♥❡"✇♦)❦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✷✾. ✸✳✶✳✸. ❈♦♥❝❡%%✐ ❜❛5❡ ❞❡❧❧❛ %❡♦&✐❛ ❞❡✐ ❣&❛✜ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✸. ❚♦♣♦❧♦❣②●❙❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✺. ✸✳✷✳✶. ❈♦♥✈❡&%✐&❡ ✉♥ ♥❡"✇♦)❦ ✐♥ ✉♥ ♠♦❞❡❧❧♦ ❣&❛✜❝♦ ✳ ✳ ✳. ✸✻. ✸✳✷✳✷. ❱❡&✐✜❝❛ ❞✬✐♣♦%❡5✐ ✐♥ ✉♥ ♠♦❞❡❧❧♦ ❣&❛✜❝♦ ✳ ✳ ✳ ✳ ✳ ✳. ✸✼. ✸✳✷✳✷✳✶. ✸✳✸. ✷✺. ❚❡5% 5✉❧❧✬✉❣✉❛❣❧✐❛♥③❛ ❞❡❧❧❡ ♠❛%&✐❝✐ ❞✐ ❝♦♥✲ ❝❡♥%&❛③✐♦♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✼. ✸✳✷✳✷✳✷. ❚❡5% ♣❡& ❧✬✉❣✉❛❣❧✐❛♥③❛ ❞❡❧❧❡ ♠❡❞✐❡ ✳ ✳ ✳ ✳. ✸✾. ✸✳✷✳✷✳✸. ❉❡❝♦♠♣♦5✐③✐♦♥❡ ❞❡❧ ❣&❛❢♦ ✐♥ ❝❧✐G✉❡5 ✳ ✳ ✳. ✹✵. ❙J■❆ ✭❙✐❣♥❛❧✐♥❣ ♣❛"❤✇❛② ■♠♣❛❝" ❆♥❛❧②3✐3 ✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✵. ✹ ❉❛'✐ 5❡❛❧✐ ❡ 5✐&✉❧'❛'✐. ✹✼. ✹✳✶. ■ ❞❛%✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✼. ✹✳✷. ■❧ ♣❛"❤✇❛② ❈❤)♦♥✐❝ ▼②❡❧♦✐❞ ▲❡✉❦❡♠✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✾. ✹✳✷✳✶. ■❧ ♣❛"❤✇❛② 5❡♠♣❧✐✜❝❛%♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✶. ✹✳✷✳✷. ■ G✉❛%%&♦ ❞❛%❛5❡% 5❡♠♣❧✐✜❝❛%✐. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✺. ✹✳✸. ■ ❣❡♥✐ ❞✐✛❡&❡♥③✐❛❧♠❡♥%❡ ❡5♣&❡55✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✼. ✹✳✹. ▲✬❛♥❛❧✐5✐ %♦♣♦❧♦❣✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✸. ▲❡ ❛♥❛❧✐5✐ 5✉❧❧❡ ❝❧✐9✉❡3 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✹. ▲✬❛♥❛❧✐5✐ ❙J■❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✹. ✹✳✹✳✶ ✹✳✺. ✺ ❈♦♥❝❧✉&✐♦♥✐. ✼✾. ✐✐.
(5) ✶ ■♥#$♦❞✉③✐♦♥❡ ▲❛ ❜✐♦✐♥❢♦'♠❛)✐❝❛✱ ♥❛)❛ ❛❧❧❛ ✜♥❡ ❞❡❣❧✐ ❛♥♥✐ ✼✵✱ 3 ✉♥❛ 5❝✐❡♥③❛ ❝❤❡ 5✐ 5)❛ '❛♣✐❞❛♠❡♥)❡ ❡✈♦❧✈❡♥❞♦✳ ◆❛)❛ ❝♦♠❡ ❜'❛♥❝❛ ❞❡❧❧❛ ❜✐♦❧♦❣✐❛✱ 3 ✉♥❛ ❞✐5❝✐♣❧✐✲ ♥❛ ❛❧)❛♠❡♥)❡ ✐♥)❡'❞✐5❝✐♣❧✐♥❛'❡ ❝❤❡ ❛♣♣❧✐❝❛ ❛ ♣'♦❜❧❡♠✐ ❞✐ ♥❛)✉'❛ ❜✐♦❧♦❣✐❝❛ ♥✉♠❡'♦5❡ )❡❝♥✐❝❤❡ ❡ ❝♦♥❝❡))✐ ❞❡'✐✈❛♥)✐ ❞❛❧❧✬✐♥❢♦'♠❛)✐❝❛✱ 5)❛)✐5)✐❝❛✱ ♠❛)❡✲ ♠❛)✐❝❛✱ ✜5✐❝❛✱ ❝❤✐♠✐❝❛ ❡ ❜✐♦❝❤✐♠✐❝❛✳ ■❧ ◆❛"✐♦♥❛❧ ❈❡♥"❡) ❢♦) ❇✐♦✐♥"❡❝♥♦❧♦✲. ❣② ■♥❢♦)♠❛"✐♦♥ ✭◆❈❇■✮ ❞❡✜♥✐5❝❡ ❧❛ ❜✐♦✐♥❢♦'♠❛)✐❝❛ ❝♦♠❡ ✧ ❧❛ 2❝✐❡♥③❛ ♥❡❧❧❛ 4✉❛❧❡ ❜✐♦❧♦❣✐❛✱ ✐♥❢♦)♠❛"✐❝❛ ❡ "❡❝♥♦❧♦❣✐❛ ❞❡❧❧✬✐♥❢♦)♠❛③✐♦♥❡ 2✐ ✉♥✐2❝♦♥♦ ✐♥ ✉♥✬✉♥✐❝❛ ❞✐2❝✐♣❧✐♥❛ ✧✳ ✶ ❯♥❛ ❞❡❧❧❡ ♣♦55✐❜✐❧✐ ❛♥❛❧✐5✐ ❞✐ ❞❛)✐ ❝❤❡ 5✐ ♣♦55♦♥♦ ❢❛'❡ ❛))'❛✈❡'5♦ ❧❛ ❜✐♦✐♥✲ ❢♦'♠❛)✐❝❛ 3 ❧✬❛♥❛❧✐5✐ ❞❡✐ ❞❛)✐ ❞✐ ❡5♣❡'✐♠❡♥)✐ ❞✐ ♠✐❝)♦❛))❛②✳ ❯♥ ♠✐❝)♦❛))❛②. ❞✐ ❉◆❆ ✭♦ ♠❛)'✐❝✐ ❛❞ ❛❧)❛ ❞❡♥5✐)E✮ 3 ❝♦5)✐)✉✐)♦ ❞❛ ✉♥ ✐♥5✐❡♠❡ ❞✐ ♠✐❝'♦✲ 5❝♦♣✐❝❤❡ 5♦♥❞❡ ❞✐ ❉◆❆✱ ❞❡))❡ ❛))❛②✱ ❛))❛❝❝❛)❡ ❛ ✉♥ ✈❡)'✐♥♦✳ ◗✉❡5)✐ ❛))❛② 5♦♥♦ ✉5❛)✐ ♣❡' ❡5❛♠✐♥❛'❡ ✐❧ ♣'♦✜❧♦ ❞✬❡5♣'❡55✐♦♥❡ ❞✐ ✉♥ ❣❡♥❡ ♦ ♣❡' ✐❞❡♥)✐✲ ✜❝❛'❡ ❧❛ ♣'❡5❡♥③❛ ❞✐ ✉♥ ❣❡♥❡✱ ♦ ❞✐ ✉♥❛ ❜'❡✈❡ 5❡I✉❡♥③❛✱ ❛❧❧✬✐♥)❡'♥♦ ❞✐ ✉♥❛ ♠✐5❝❡❧❛ ❞✐ ♠✐❣❧✐❛✐❛ ❞✐ ❣❡♥✐✳. ✶ ❤!!♣✿✴✴✇✇✇✳♥❝❜✐✳♥❧♠✳♥✐❤✳❣♦✈✴❆❜♦✉!✴♣2✐♠❡2✴❜✐♦✐♥❢♦2♠❛!✐❝6✳❤!♠❧. ✶.
(6) ✶ ■♥#$♦❞✉③✐♦♥❡. ✶✳✶ ◆♦③✐♦♥✐ ❞✐ ❜❛*❡ ❞❡❧❧❛ ❜✐♦❧♦❣✐❛ ♠♦❧❡❝♦❧❛0❡ ■❧ ❉◆❆ ✈❡♥♥❡ ✐♥✐③✐❛❧♠❡♥,❡ ✐-♦❧❛,♦ ❞❛❧ ❜✐♦❧♦❣♦ -✈✐③③❡2♦ ❋2✐❡❞2✐❝❤ ▼✐❡-❝❤❡2 ♥❡❧ ✶✽✻✾✱ ♠❛ -♦❧♦ ♥❡❧ ✶✾✺✸ ❏❛♠❡- ❲❛,-♦♥ ❡ ❋2❛♥❝✐- ❈2✐❝❦ ♣2❡-❡♥,❛♥♦ ✐❧ ♣2✐♠♦ ♠♦❞❡❧❧♦ ❛❝❝✉2❛,♦ ❞❡❧❧❛ -,2✉,,✉2❛ ❞✐ ❉◆❆✱ D✉❡❧❧♦ ❛ ❞♦♣♣✐❛ ❡❧✐❝❛✳ ◆❡❧ ✶✾✺✼ -❡♠♣2❡ ❈2✐❝❦ ♣2♦♣♦-❡ ✐❧ ❞♦❣♠❛ ❝❡♥,2❛❧❡ ❞❡❧❧❛ ❜✐♦❧♦❣✐❛ ♠♦❧❡❝♦❧❛2❡ ❝❤❡ ✜--❛ ❧❡ 2❡❧❛③✐♦♥✐ ,2❛ ❉◆❆✱ ❘◆❆ ❡ ♣2♦,❡✐♥❡✱ ♠❛ -♦❧♦ -✉❝❝❡--✐✈❛♠❡♥,❡ ❡❣❧✐ ❞✐♠♦-,2I ❝♦♠❡ ✐❧ ❝♦❞✐❝❡ ❣❡♥❡,✐❝♦ ❢♦--❡ ❜❛-❛,♦ -✉ ,2✐♣❧❡,,❡ ❞✐ ❜❛-✐ ♥♦♥ -♦✈2❛♣♣♦-,❡✱ ♣❡2♠❡,,❡♥❞♦ ❝♦-K ❛ ❍❛2 ●♦❜✐♥❞ ❑❤♦2❛♥❛✱ ❘♦❜❡2, ❍♦❧❧❡② ❡ ▼❛2-❤❛❧❧ ❲❛22❡♥ ◆✐2❡♥❜❡2❣ ❞✐ ❞❡❝✐❢2❛2❧♦✳ ◗✉❡-,❡ -❝♦♣❡2,❡ -♦♥♦ -,❛,❡ ❧❛ ❜❛-❡ ♣❡2 ❧♦ -✈✐❧✉♣♣♦ ❞❡❧❧❛ ♥✉♦✈❛ ❜✐♦❧♦❣✐❛ ♠♦❧❡❝♦❧❛2❡✳ ■❧ ❉◆❆✱ ❝♦♠❡ Q -,❛,♦ ❞❡,,♦✱ ❤❛ ✉♥❛ -,2✉,,✉2❛ ❛ ❞♦♣♣✐❛ ❡❧✐❝❛✱ -✐♠✐❧❡ ❛ ✉♥❛ -❝❛❧❛ ❛ ♣✐♦❧✐ ❞✐-♣♦-,❛ ❛ -♣✐2❛❧❡✳ ▲♦ -❝❤❡❧❡,2♦ ❞✐ D✉❡-,❛ ✧-❝❛❧❛✧ Q ❝♦♠♣♦-,♦ ❞❛ ③✉❝❝❤❡2♦ ❡ ✉♥ ❣2✉♣♣♦ ❢♦-❢❛,♦✱ ♠❡♥,2❡ ✐ ♣✐♦❧✐ -♦♥♦ ❝♦♠♣♦-,✐ ❞❛ D✉❛,,2♦ ❜❛-✐ ❛③♦,❛,❡ ✭❛❞❡♥✐♥❛ ✭❆✮✱ ❝✐,♦-✐♥❛ ✭❈✮✱ ❣✉❛♥✐♥❛ ✭●✮ ❡ ,✐♠✐♥❛ ✭❚✮✮✳ ❖❣♥✐ ❜❛-❡ ♣2❡-❡♥,❡ -✉ ✉♥ ✜❧❛♠❡♥,♦ -✐ ❧❡❣❛ ✐♥ ♠♦❞♦ ✉♥✐✈♦❝♦ ❛ ✉♥❛ ❜❛-❡ ❞❡❧ ✜❧❛♠❡♥,♦ ♦♣♣♦-,♦✿. •. ❆ ❛♣♣❛✐❛ ❝♦♥ ❚. •. ● ❛♣♣❛✐❛ ❝♦♥ ❈. ▲❛ ❞✐-♣♦-✐③✐♦♥❡ ✐♥ -❡D✉❡♥③❛ ❞✐ D✉❡-,❡ ✹ ❜❛-✐ ❝♦-,✐,✉✐-❝❡ ❧✬✐♥❢♦2♠❛③✐♦♥❡ ❣❡✲ ♥❡,✐❝❛✱ ❧❡❣❣✐❜✐❧❡ ❛,,2❛✈❡2-♦ ✐❧ ❝♦❞✐❝❡ ❣❡♥✐,✐❝♦✱ ❝❤❡ ♥❡ ♣❡2♠❡,,❡ ❧❛ ,2❛❞✉③✐♦✲ ♥❡ ✐♥ ❛♠♠✐♥♦❛❝✐❞✐✳ ■❧ ❣❡♥❡ ❝♦22✐-♣♦♥❞❡ ❛ ✉♥❛ ♣♦2③✐♦♥❡ ❞✐ ❝♦❞✐❝❡ ❣❡♥✐,✐❝♦. ✷.
(7) ✶ ■♥#$♦❞✉③✐♦♥❡ ❛❧❧✬✐♥%❡'♥♦ ❞❡❧❧❛ *❡+✉❡♥③❛ ❞✐ ❉◆❆✳ ■❧ ♣'♦❝❡**♦ ❞✐ %'❛❞✉③✐♦♥❡ ✭✜❣✉'❛ ✶✳✶✮ ❞❡❧ ❉◆❆ ✐♥ ♣'♦%❡✐♥❡ ❛✈✈✐❡♥❡ ✐♥ ❞✉❡ ❢❛*✐✿. • ▲❛ %'❛*❝'✐③✐♦♥❡❀ • ▲❛ %'❛❞✉③✐♦♥❡❀ ▲✬✐♥❢♦'♠❛③✐♦♥❡ ❝♦♥%❡♥✉%❛ ✐♥ ✉♥ ✜❧❛♠❡♥✲ %♦ ❞✐ ❉◆❆ ✈✐❡♥❡ %'❛*❝'✐%%❛ ✐♥ ✜❧❛♠❡♥%♦ ❞✐ ❘◆❆ ♠❡**❛❣❣❡'♦ ✭♠❘◆❆✮✱ ❝❤❡ *✉❝❝❡**✐✈❛✲ ♠❡♥%❡ ❡*❝❡ ❞❛❧ ♥✉❝❧❡♦✱ *✐ *♣♦*%❛ *✉✐ '✐❜♦*♦✲ ♠✐ ❞♦✈❡ ✐♥%❡'✈✐❡♥❡ ❧✬❘◆❆ ❞✐ %'❛*♣♦'%♦ ✭%❘✲ ◆❆✮✱ ❝♦*%✐%✉✐%♦ ❞❛ ✉♥❛ %'✐♣❧❡%%❛ ❞✐ ❜❛*✐ ❛③♦%❛✲ %❡ *♣❡❝✐✜❝❛ ♣❡' ❧✬❛♠♠✐♥♦❛❝✐❞♦ ❝❤❡ %'❛*♣♦'%❛✳ ■♥ +✉❡*%♦ ♠♦❞♦ ❣❧✐ ❛♠♠✐♥♦❛❝✐❞✐ ✈❡♥❣♦♥♦ ❛❧✲ ❧✐♥❡❛%✐ *❡❝♦♥❞♦ ❧❛ *❡+✉❡♥③❛ ✐♥✐③✐❛❧❡ ❞✐ ❉◆❆ ❡ ❢♦'♠❛♥♦ ❧❛ ❝❛%❡♥❛ ♣❡♣%✐❞✐❝❛✱ ♦✈✈❡'♦ ✉♥❛ ♣'♦%❡✐♥❛✳ ❉✉'❛♥%❡ ✐❧ ♣'♦❝❡**♦ ❞✐ %'❛❞✉③✐♦♥❡. ❋✐❣✉$❛ ✶✳✶✿ ■❧ ♣$♦❝❡//♦ ❞✐ 1$❛❞✉③✐♦♥❡ ❞❡❧ ❉◆❆. ♣♦**♦♥♦ ❛✈✈❡♥✐'❡ ❞❡✐ ❝❛♠❜✐❛♠❡♥%✐✱ ❝❤✐❛♠❛%❡ ♠✉%❛③✐♦♥✐✱ ❞❡❧❧❛ *❡+✉❡♥③❛ ❞❡❧❧❡ ❜❛*✐✱ ❝♦♠❡ ❧✬❛❣❣✐✉♥%❛✱ ❧❛ *♦*%✐%✉③✐♦♥❡ ♦ ❧✬❡✲ ❧✐♠✐♥❛③✐♦♥❡ ❞✐ ✉♥ ♥✉❝❧❡♦%✐❞❡✳ ◗✉❡*%♦ ♣♦'%❛ ❛ ❞❡❧❧❡ ♠✉%❛③✐♦♥✐ ♥❡✐ ❣❡♥✐ ❝❤❡ ❝♦❞✐✜❝❛♥♦ ❛❧❝✉♥❡ ♣'♦%❡✐♥❡✱ ❝❤❡ ♣♦**♦♥♦ +✉✐♥❞✐ ❞✐✈❡♥%❛'❡ ✐♥❛%%✐✈❡ ♦♣♣✉'❡ ❡**❡'❡ ❛❞❞✐'✐%%✉'❛ ♠❛♥❝❛♥%✐✳ ◗✉❡*%♦ ♣✉F ❡**❡'❡ ❧❛ ❝❛✉*❛ ❞❡❧❧✬✐♥*♦'❣❡♥③❛ ❞✐ ♠♦❧%❡ ♠❛❧❛%%✐❡ ❣❡♥❡%✐❝❤❡✳. ✸.
(8) ✶ ■♥#$♦❞✉③✐♦♥❡. ✶✳✷ ▲❛ %❡❝♥♦❧♦❣✐❛ ❞✐. ❆✛②♠❡%&✐①. ❈♦♠❡ ❣✐& ❞❡((♦ ✐♥ ♣+❡❝❡❞❡♥③❛ ❧❛ ❜✐♦✐♥❢♦+♠❛(✐❝❛ ❝✐ ❝♦♥2❡♥(❡ ❞✐ ❢❛+❡ ❛♥❛✲ ❧✐2✐ ❞❡✐ ❞❛(✐ ❞✐ ❡2♣❡+✐♠❡♥(✐ ❞✐ ♠✐❝#♦❛##❛②✳ ▲❛ (❡❝♥♦❧♦❣✐❛ ❞❡✐ ♠✐❝#♦❛##❛② ❝✐ ♣❡+♠❡((❡ ❞✐ ♠✐2✉+❛+❡ ❧✬❡2♣+❡22✐♦♥❡ ❣❡♥✐❝❛✱ ✐♥ ❞✐✛❡+❡♥(✐ ❝♦♥❞✐③✐♦♥✐✱ 2✉ ♠✐❣❧✐❛✐❛ ❞✐ ❣❡♥✐ 2✐♠✉❧(❛♥❡❛♠❡♥(❡✳ ❊2✐2(♦♥♦ ✈❛+✐ (✐♣✐ ❞✐ ♠✐❝+♦❛++❛② ✐♥ ❝♦♠♠❡+❝✐♦✱ ♠❛ ♥❡❧ ♣+❡2❡♥(❡ ❡❧❛❜♦+❛(♦ 2✐ ❢❛+& +✐❢❡+✐♠❡♥(♦ 2♦❧♦ ❛❧❧❛ (❡❝♥♦✲ ❧♦❣✐❛ ❛ 2✐♥❣♦❧♦ ❝❛♥❛❧❡ ♣+♦❞♦((❛ ❞❛ ❆✛②♠❡*#✐①✳ ●❧✐ ❡2♣❡+✐♠❡♥(✐ ❛ 2✐♥❣♦❧♦ ❝❛♥❛❧❡ 2♦♥♦ ❝❛+❛((❡+✐③③❛(✐ ❞❛ ✉♥ 2♦❧♦ ❝❛♠♣✐♦♥❡ ♣❡+ ❝❤✐♣ ✭✜❣✉+❛ ✶✳✷✮ ❡ ❢♦+♥✐2❝♦♥♦ ✉♥❛ ♠✐2✉+❛ ❞✐+❡((❛ ❡❞ ✐♥❞✐♣❡♥❞❡♥(❡ ❞❡❧ ❧✐✈❡❧❧♦ ❞✐ ❡2♣+❡22✐♦♥❡ ❣❡♥✐❝❛ ✐♥ ✉♥ ❝❛♠♣✐♦♥❡✳ ▲❛ (❡❝♥♦❧♦❣✐❛ ❞❡✐ ♠✐❝#♦❛##❛② ❛ ❉◆❆ 2✐ ❜❛2❛ 2✉❧❧❛ ❝❛♣❛❝✐(& ❞✐ ✐❜+✐❞❛③✐♦✲ ♥❡ ❞❡❣❧✐ ❛❝✐❞✐ ♥✉❝❧❡✐❝✐✱ ♦✈✈❡+♦ ❞✉❡ ✜❧❛♠❡♥(✐ ❞✐ ❉◆❆ +✐❡2❝♦♥♦ ❛ ✐❜+✐❞✐③③❛+❡ 2❡ 2♦♥♦ (+❛ ❞✐ ❧♦+♦ ❝♦♠♣❧❡♠❡♥(❛+✐✳ ▲❛ (❡❝♥♦❧♦❣✐❛ ❝♦♥2✐❞❡+❛(❛ ✐♥ F✉❡2(♦ ❡❧❛❜♦+❛(♦ ✉(✐❧✐③③❛ 2♦♥❞❡ ✭♦ ♣#♦❜❡ ✮ ❧✉♥❣❤❡ ❝✐+❝❛ ✷✺ ♣❛✐❛ ❞✐ ❜❛2✐ ❝❤❡ ✈❡♥❣♦✲ ♥♦ ❜❧♦❝❝❛(❡ 2✉ ✉♥❛ 2✉♣❡+✜❝✐❡ ❞✐ ✈❡(+♦ ✭✜❣✉+❛ ✶✳✸✮✳ ■♥ ♦❣♥✐ ✈❡(+✐♥♦ 2♦♥♦ ♣+❡2❡♥(✐ ❛❧❝✉♥❡ ❝❡♥(✐♥❛✐❛ ❞✐ ♠✐❣❧✐❛✐❛ ❞✐ ✜❧❛♠❡♥(✐✱ ❝✐❛2❝✉♥♦ ❞❡✐ F✉❛❧✐ ♣+❡✲ 2❡♥(❡ ✐♥ ♠✐❧✐♦♥✐ ❞✐ ❝♦♣✐❡✳ ❖❣♥✐ ❣❡♥❡ ♦ 2❡F✉❡♥③❛ ❣❡♥♦♠✐❝❛ ❞✐ ✐♥(❡+❡22❡ L +❛♣♣+❡2❡♥(❛(♦ ❞❛ ✉♥ ♣#♦❜❡/❡* ❢♦+♠❛(♦ ❞❛ ✶✶ ❛ ✷✵ ❝♦♣♣✐❡ ❞✐ ♣+♦❜❡ ✭ ♣#♦❜❡ ♣❛✐# ✮✳ ❖❣♥✐ ❝♦♣♣✐❛ L ❢♦+♠❛(❛ ❞❛ ✉♥ ♣❡#❢❡❝* ♠❛*❝❤ ✭2▼✮ ♣#♦❜❡ ❡ ❞❛ ✉♥ ♠✐/♠❛*❝❤ ✭▼▼✮ ♣#♦❜❡ ❝+❡❛(♦ ❝♦♥ ❧❛ (+❡❞✐❝❡2✐♠❛ ❜❛2❡ ❞✐✈❡+2❛✳ ■❧ ❧✐✈❡❧❧♦ ❞✐ ❡2♣+❡22✐♦♥❡ ❞✐ ✉♥ ❣❡♥❡✱ ✐♥ F✉❡2(♦ (✐♣♦ ❞✐ (❡❝♥♦❧♦❣✐❛✱ L ♦((❡♥✉(♦ ❞❛❧❧✬✐♥✲ (❡❣+❛③✐♦♥❡ ❞✐ (✉((✐ ✐ ❞❛(✐ ❞❡❧ ♣#♦❜❡/❡*✳. ✹.
(9) ✶ ■♥#$♦❞✉③✐♦♥❡. ❋✐❣✉$❛ ✶✳✷✿ ■❧ ●❡♥❡❈❤✐♣. ❋✐❣✉$❛ ✶✳✸✿ ■ ♣$♦❜❡ ♥❡❧ ●❡♥❡❈❤✐♣ ❛$$❛②. ❋✐❣✉$❛ ✶✳✹✿ ❙❝❛♥9✐♦♥❡ ❞❡❧ ●❡♥❡❈❤✐♣ ❝♦♥ 9❝❛♥♥❡$ ❧❛9❡$ ✺.
(10) ✶ ■♥#$♦❞✉③✐♦♥❡. ✶✳✷✳✶ ▲❛ ♠❛&'✐❝❡ ❞❡✐ ❞❛&✐. ❯♥❛ ✈♦❧&❛ ❝(❡❛&♦ ✐❧ ●❡♥❡❈❤✐♣ &(❛♠✐&❡ ✐❜(✐❞✐③③❛③✐♦♥❡ ❡ /❝❛♥/✐♦♥❛&♦ ❝♦♥ ❧✬✉&✐❧✐③③♦ ❞✐ ✉♥♦ /❝❛♥♥❡( ❧❛/❡(✱ ♦&&❡♥✐❛♠♦ ❧✬✐♠♠❛❣✐♥❡ ❞✐ &✉&&✐ ❣❧✐ /♣♦& ❝❤❡ /♦♥♦ /&❛&✐ ❝(❡❛&✐ ✭✜❣✉(❛ ✶✳✹✮✳ ❯♥❛ ✈♦❧&❛ ❝❤❡ < /&❛&❛ ✐❞❡♥&✐✜❝❛&❛ ❧❛ ♣♦/✐✲ ③✐♦♥❡ ❞✐ >✉❡/&✐ /♣♦& /✐ ♣✉? ♣❛//❛(❡ ❛❧ ❝❛❧❝♦❧♦ ❞❡❧❧❡ ✐♥&❡♥/✐&@ ❞✐ ♦❣♥✐ /♣♦& ❡ ❛❧ ❝❛❧❝♦❧♦ ❞❡❧ ❜❛❝❦❣,♦✉♥❞ ❧♦❝❛❧❡✳ ❉❛❧❧✬✐♠♠❛❣✐♥❡ /❝❛♥/✐♦♥❛&❛✱ >✉✐♥❞✐✱ /✐ ♣❛//❛ ❛❧❧❛ ♠❛&(✐❝❡ ❞✐ ✐♥&❡♥/✐&@✱ ❞♦✈❡ ♥❡❧ /❡♥/♦ ❞❡❧❧❡ (✐❣❤❡ ❛❜❜❜✐❛♠♦ ✐ ❞✐✈❡(/✐ /♣♦&/ ❡ ♥❡❧ /❡♥/♦ ❞❡❧❧❡ ❝♦❧♦♥♥❡ ❛❜❜✐❛♠♦ ✐ ❞✐✈❡(/✐ ✈❛❧♦(✐ ❞✐ ✐♥&❡♥/✐✲ &@ ♣❡( ♦❣♥✐ /♣♦&✳ ◆❡❧ ❝❛/♦ ♣❛(&✐❝♦❧❛(❡ ❞❡❧❧❛ &❡❝♥♦❧♦❣✐❛ ❆✛②♠❡4,✐① ✐ ❞❛&✐ ❣(❡③③✐ ♥♦♥ /♦♥♦ ♣(❡/❡♥&❛&✐ ❝♦♠❡ ✉♥❛ ♠❛&(✐❝❡ ❞✐ ❞❛&✐✱ ♠❛ /♦♥♦ ♣(❡/❡♥&❛&✐ ✐♥ ✜❧❡ ✳❈❊▲✱ ✐❧ ❝✉✐ ❢♦(♠❛&♦ < ✉♥ ✜❧❡ ❞✐ &❡/&♦ ❆❙❈■■✱ ❞❛ ❝✉✐ /✉❝❝❡//✐✈❛♠❡♥✲ &❡ ♣♦&(❡♠♦ ♦&&❡♥❡(❡ ❧❛ ♠❛&(✐❝❡ ❞❡✐ ❞❛&✐ ✭&❛❜❡❧❧❛ ✶✳✶✮✳ ◗✉❡/&♦ ❞❛&❛/❡& /✐ ♣(❡/❡♥&❛ ❝♦♠❡ ✉♥❛ ♠❛&(✐❝❡ ❝♦♥ n (✐❣❤❡ ❡ p ❝♦❧♦♥♥❡✱ ❞♦✈❡ ♥❡❧ /❡♥/♦ ❞❡❧❧❡ (✐❣❤❡ /✐ &(♦✈❛♥♦ ✐ ✈❛(✐ ❣❡♥✐✱ ❧❡ ✉♥✐&@ ❞✐ ✐♥&❡(❡//❡✱ ❡ ♥❡❧ /❡♥/♦ ❞❡❧❧❡ ❝♦❧♦♥♥❡ /✐ &(♦✈❛♥♦ ✐ ✈❛(✐ ❡/♣❡(✐♠❡♥&✐✳ ❊①♣✳✶. ❊①♣✳✷. ···. ❊①♣✳♣. x11. x12. ···. x1p. x21. x22. ···. x2p. ···. ···. ···. ···. ···. ●❡♥❡ ♥. xn1. xn2. ···. xnp. ●❡♥❡ ✶ ●❡♥❡ ✷. ❚❛❜❡❧❧❛ ✶✳✶✿ ❊!❡♠♣✐♦ ❞✐ ♠❛)*✐❝❡ ❞❡✐ ❞❛)✐. ✻.
(11) ✶ ■♥#$♦❞✉③✐♦♥❡. ✶✳✷✳✷ ▲❛ ♥♦'♠❛❧✐③③❛③✐♦♥❡. ❯♥♦ ❞❡✐ ♣✉♥(✐ ❝*✐(✐❝✐ ❞❡✐ ❞❛(✐ ❞✐ ♠✐❝#♦❛##❛② ,(❛ ♥❡❧❧❛ ♥♦*♠❛❧✐③③❛③✐♦♥❡✳ ❯♥❛ ♠❛(*✐❝❡ ❞✐ ❞❛(✐ ❝♦♥(✐❡♥❡ ✉♥ ♥✉♠❡*♦ ♠♦❧(♦ ❛❧(♦ ❞✐ ❣❡♥✐✱ ❛ ❢*♦♥(❡ ❞✐ ✉♥ ♥✉♠❡*♦ ♠♦❧(♦ ♣✐4 ❧✐♠✐(❛(♦ ❞✐ ❡,♣❡*✐♠❡♥(✐✳ ❙✐ ♣✉6 ❝♦♠♣*❡♥❞❡*❡ ❞✉♥7✉❡ ❝♦♠❡ ❛♥❝❤❡ ✉♥ ♣✐❝❝♦❧♦ ❡**♦*❡ ,✐,(❡♠❛(✐❝♦ ♣♦,,❛ ❝*❡❛*❡ ❞❡❧❧❡ ❞✐,(♦*,✐♦♥✐ ,✐❣♥✐✜❝❛(✐✈❡ ❞✉*❛♥(❡ ❧❛ ❢❛,❡ ❞✐ ✐♥❢❡*❡♥③❛✳ ▲❛ ♥♦*♠❛❧✐③③❛③✐♦♥❡ ❞❡✐ ❞❛(✐ ❛✈✈✐❡♥❡✱ 7✉✐♥❞✐✱ ✐♥ ✉♥❛ ❢❛,❡ ♣*❡❧✐♠✐♥❛*❡ ❛❧❧✬✐♥❢❡*❡♥③❛✳ ▲❛ ♥♦*♠❛❧✐③③❛③✐♦♥❡ (*❛ ❛##❛②✱ ❡,❡❣✉✐(❛ ♣*✐♥❝✐♣❛❧♠❡♥(❡ ♥❡❣❧✐ ❛##❛② ❛ ,✐♥❣♦❧♦ ❝❛♥❛❧❡✱ ♣❡*♠❡((❡ ❞✐ *✐,❝♦♥(*❛*❡ ❞❡❧❧❡ ❞✐✛❡*❡♥③❡ ❞✐ ✐♥(❡♥,✐(> ❞♦✈✉(❡ ❛ ❞✐✈❡*,❡ ♣♦(❡♥③❡ ❞❡✐ ❧❛,❡* ♦ ❛✐ ♣❛*❛♠❡(*✐ ❞✐ ,❝❛♥,✐♦♥❡✳ ■♥ 7✉❡,(♦ ❝❛,♦ ❧♦ ,❝♦♣♦ ❞✐ 7✉❡,(❛ ♥♦*♠❛❧✐③③❛③✐♦♥❡ @ 7✉❡❧❧♦ ❞✐ *❡♥❞❡*❡ ❝♦♥❢*♦♥(❛❜✐❧✐ ✐ ✈❛❧♦*✐ ❞✐ ❡,♣*❡,,✐♦♥❡ ❞✐ (✉((✐ ❣❧✐ ❡,♣❡*✐♠❡♥(✐ ❝♦♥,✐❞❡*❛(✐✳ ▲❛ ♠❛❣❣✐♦* ♣❛*(❡ ❞❡❧❧❡ ♣*♦❝❡❞✉*❡ ❞✐ ♥♦*♠❛❧✐③③❛③✐♦♥❡ ♣❡* ❧❛ *✐❞✉③✐♦♥❡ ❞❡❣❧✐ ❡**♦*✐ ,✐,(❡♠❛(✐❝✐ ,✐ ❜❛,❛ ,✉ (*❡ ❛,,✉♥③✐♦♥✐✿ •. C♦❝❤✐ ❣❡♥✐ ❞✐✛❡*❡♥③✐❛❧♠❡♥(❡ ❡,♣*❡,,✐ ♥❡❧❧❡ ❞✉❡ ❝♦♥❞✐③✐♦♥✐ ,♣❡*✐♠❡♥✲ (❛❧✐❀. •. ■❧ ♥✉♠❡*♦ ❞✐ ❣❡♥✐ ,♦✈*❛ ❡,♣*❡,,✐ ,✐❛ ,✐♠✐❧❡ ❛❧ ♥✉♠❡*♦ ❞✐ ❣❡♥✐ ,♦((♦ ❡,♣*❡,,✐❀. •. ▲❛ ❞✐✛❡*❡♥③✐❛❧❡ ❡,♣*❡,,✐♦♥❡ ♥♦♥ ❞✐♣❡♥❞❛ ❞❛❧❧❛ ♠❡❞✐❛ ❞❡❧ ,❡❣♥❛❧❡✳. ✶✳✸ ■ ❣❡♥✐ ❞✐✛❡*❡♥③✐❛❧♠❡♥/❡ ❡0♣*❡00✐ ✭❉❊●✮ ◆❡❣❧✐ ❡,♣❡*✐♠❡♥(✐ ❞✐ ♠✐❝#♦❛##❛② ✉♥ *✐,✉❧(❛(♦ ✐♠♣♦*(❛♥(❡ ❞❡❧❧✬❛♥❛❧✐,✐ ✐♥✲ ❢❡*❡③✐❛❧❡ @ 7✉❡❧❧♦ ❞❡❧❧✬✐❞❡♥(✐✜❝❛③✐♦♥❡ ❞❡✐ ❣❡♥✐ ❞✐✛❡*❡♥③✐❛❧♠❡♥(❡ ❡,♣*❡,,✐ ✼.
(12) ✶ ■♥#$♦❞✉③✐♦♥❡ ✭❉❊●✮✳ ❱❡♥❣♦♥♦ ❝❧❛..✐✜❝❛1✐ ❝♦♥ 2✉❡.1♦ ♥♦♠❡ ✐ ❣❡♥✐ ❝❤❡ ♠♦.16❛♥♦ ✉♥❛ .✐❣♥✐✜❝❛1✐✈❛ ❞✐✛❡6❡♥③❛ ♥❡✐ ❧✐✈❡❧❧✐ ❞✐ ❡.♣6❡..✐♦♥❡ ✐♥ ❞✉❡ ♦ ♣✐< ❣6✉♣♣✐ ❞✐ ❝❛♠♣✐♦♥✐ ❜✐♦❧♦❣✐❝✐ ♦❣❣❡11♦ ❞✐ .1✉❞✐♦✳ ■♥ ❧❡11❡6❛1✉6❛ .✐ 16♦✈❛♥♦ ♠♦❧1✐ 1❡.1 ❝❤❡ ♣♦..♦♥♦ ❡..❡6❡ ✉1✐❧✐③③❛1✐ ♣❡6 ❧✬✐❞❡♥1✐✜❝❛③✐♦♥❡ ❞✐ 1❛❧✐ ❣❡♥✐✳ ❙✐ 6✐♠❛♥❞❛ ❛❧ ❈❛♣✐1♦❧♦ ✷ ♣❡6 ✐❧ ❞❡11❛❣❧✐♦ ❞❡❧❧❡ 1❡❝♥✐❝❤❡ .1❛1✐.1✐❝❤❡ ✉.❛1❡ ✐♥ 2✉❡.1♦ ❡❧❛❜♦6❛1♦✳ ❱❛ 6✐❝♦6❞❛1♦✱ ✐♥♦❧16❡✱ ❝❤❡ ✐ 1❡.1 ♣❡6 ✐❞❡♥1✐✜❝❛6❡ ✐ ❣❡♥✐ ❉❊● ✈❛♥♥♦ ❝♦♥❞♦11✐ .✉ ♦❣♥✐ .✐♥❣♦❧♦ ❣❡♥❡✳ ■♥ ❛❧16❡ ♣❛6♦❧❡ ✈❛ ❡✛❡11✉❛1♦ ✉♥ 1❡.1 ♣❡6 ♦❣♥✐ 6✐❣❛ ❞❡❧❧❛ ♠❛16✐❝❡ ❞❡✐ ❞❛1✐ ❡ ♣❡6 ♦❣♥✐ ❣❡♥❡ .✐ ❛✈6D ✉♥ ❧✐✈❡❧❧♦ ❞✐ .✐❣♥✐✜❝❛1✐✈✐1D✳ ■❧ ♥✉♠❡6♦ ❞❡✐ ❣❡♥✐ ❞✐✛❡6❡♥③✐❛❧♠❡♥1❡ ❡.♣6❡..✐ ❞✐♣❡♥❞❡6D✱ 2✉✐♥❞✐✱ ❞❛ ✉♥ ❧✐✈❡❧❧♦ .♦❣❧✐❛ ✭ ❝✉"✲♦✛ ✮ ♦❧16❡ ✐❧ 2✉❛❧❡ .✐ 6✐✜✉1❛ ❧✬✐♣♦1❡.✐ ❞✐ ✉❣✉❛❣❧✐❛♥③❛ ❞❡✐ ✈❛❧♦6✐ ❞✐ ❡.♣6❡..✐♦♥❡ ♥❡✐ ❞✉❡✱ ♦ ♣✐<✱ ❣6✉♣♣✐✳ ❈♦♠❡ E .1❛✲ 1♦ ♣6❡❝❡❞❡♥1❡♠❡♥1❡ ❞❡11♦ ✐❧ ♥✉♠❡6♦ ❞✐ ❣❡♥✐ ♣6❡.❡♥1✐ ✐♥ ♦❣♥✐ ❡.♣❡6✐♠❡♥1♦ E ❞❡❧❧✬♦6❞✐♥❡ ❞✐ ❞❡❝✐♥❡ ❞✐ ♠✐❣❧✐❛✐❛✱ ❡ 2✉❡.1♦ ♣♦61❛ ✐♥❡✈✐1❛❜✐❧♠❡♥1❡ ❛ ✉♥ ♣6♦❜❧❡♠❛ ❞✐ ❝♦♥❢6♦♥1✐ ♠✉❧1✐♣❧✐✳ ❊✬ ♥♦1♦ ❝❤❡ ❧✬✉1✐❧✐③③♦ ❞✐ ♠♦❧1✐ ❝♦♥❢6♦♥1✐ ♠✉❧1✐♣❧✐ ❝♦♠♣♦61❛ ✉♥ ✐♥❝6❡♠❡♥1♦ ❞❡❧❧✬❡66♦6❡ ❞✐ ■ 1✐♣♦✱ ✐♥ 2✉❛♥1♦ ❛ ❧✐✈❡❧❧♦ ❣❧♦❜❛❧❡✱ ❧❛ ♣6♦❜❛❜✐❧✐1D ❞✐ 6✐✜✉1❛6❡ ❡66♦♥❡❛♠❡♥1❡ ✉♥✬✐♣♦1❡.✐ ♥✉❧❧❛ ❛✉♠❡♥✲ 1❛ ❝♦♥ ❧✬❛✉♠❡♥1❛6❡ ❞❡✐ ❝♦♥❢6♦♥1✐✳ ▼♦❧1♦ .♣❡..♦ .✐ ✉1✐❧✐③③❛♥♦ ♣6♦❝❡❞✉6❡ ❝❤❡ ❝♦♥16♦❧❧❛♥♦ ✐❧ ❋❛♠✐❧② ❲✐-❡ ❊00♦0 ❘❛"❡ ❬✶✻❪ ✭❋❲❊❘✮✱ ❞❡✜♥✐1♦ ❝♦♠❡ ❧❛ ♣6♦❜❛❜✐❧✐1D ❞✐ ❛✈❡6❡ ❛❧♠❡♥♦ ✉♥ ❢❛❧.♦ ♣♦.✐1✐✈♦ ❢6❛ 1✉11✐ ✐ 1❡.1 ❢❛11✐✱ ❝♦✲ ♠❡ ❧❛ ❝♦66❡③✐♦♥❡ ❞✐ ❇♦♥❢❡66♦♥✐ ♦ ❧❛ ❝♦66❡③✐♦♥❡ ❞✐ ❍♦❧♠✲❙✐❞❛❦✳ ❯♥✬❛❧16❛ 1❡❝♥✐❝❛ ❝❤❡ E ♠♦❧1♦ .♣❡..♦ ✉1✐❧✐③③❛1❛ ♣❡6 ❝♦♥16♦❧❧❛6❡ ✐❧ ✈❛❧♦6❡ ❞✐ .♦❣❧✐❛ E ✐❧ ❋❛❧-❡ ❉✐-❝♦✈❡0② ❘❛"❡ ✭❋❉❘✮✳ ◗✉❡.1♦ ♠❡1♦❞♦ E .1❛1♦ ♣6♦♣♦.1♦ ♣❡6 ❧❛ ♣6✐♠❛ ✈♦❧1❛ ♥❡❧ ✶✾✾✺ ❞❛ ❇❡♥❥❛♠✐♥✐ ❡ ❍♦❝❤❜❡6❣❬✶✻❪ ❡ 6✐.✉❧1❛ ❡..❡6❡ ✉♥ ❜✉♦♥ ❝♦♠♣6♦♠❡..♦ 16❛ ❧✬❡.✐❣❡♥③❛ ❞✐ 1❡♥❡6❡ .♦11♦ ❝♦♥16♦❧❧♦ ✐❧ 6✐.❝❤✐♦ ❞✐ ❝♦♠♠❡11❡6❡ ❡66♦6✐ ❞✐ ■ 1✐♣♦✱ ❝❤❡ ❛✉♠❡♥1❛ ❝♦♥ ❧✬❛✉♠❡♥1❛6❡ ❞❡✐ ❝♦♥❢6♦♥1✐✱. ✽.
(13) ✶ ■♥#$♦❞✉③✐♦♥❡ ❡ ❧❛ ♥❡❝❡%%✐'( ❞✐ ❡✈✐'❛+❡ ✉♥✬❡❝❝❡%%✐✈❛ +✐❞✉③✐♦♥❡ ❞❡❧❧❛ ♣♦'❡♥③❛ ❞❡❧ '❡%'✱ ❝❤❡ ❞✐♠✐♥✉✐%❝❡ 4✉❛♥'♦ ♣✐5 %✐ ❛❜❜❛%%❛ ❧❛ ♣+♦❜❛❜✐❧✐'( ❞✐ %♦❣❧✐❛ ♣❡+ ❧✬❡++♦+❡ ❞✐ ♣+✐♠♦ '✐♣♦✳ ■❧. ❋❛❧#❡ ❉✐#❝♦✈❡*② ❘❛-❡. : ❞❡✜♥✐'♦ ❝♦♠❡ ✐❧ ♥✉♠❡+♦ ❛''❡%♦ ❞✐. ❢❛❧%✐ ♣♦%✐'✐✈✐✱ ♦✈✈❡+♦ : ✐❧ +❛♣♣♦+'♦ '+❛ ✐❧ ♥✉♠❡+♦ ❞✐ ❣❡♥✐ ❝❤❡ %✐ ❞✐❝❤✐❛+❛♥♦ %✐❣♥✐✜❝❛'✐✈✐✱ ♦ ❞✐✛❡+❡♥③✐❛❧♠❡♥'❡ ❡%♣+❡%%✐✱ 4✉❛♥❞♦ ❧✬✐♣♦'❡%✐ ♥✉❧❧❛ : ✈❡+❛ ❡ ✐❧ ♥✉♠❡+♦ '♦'❛❧❡ ❞✐ ❣❡♥✐ ❞✐✛❡+❡♥③✐❛♠❡♥'❡ ❡%♣+❡%%✐✳ ❉❛ 4✉❡%'♦ ♥❡ ❝♦♥%❡❣✉❡ ❝❤❡ '❡♥❡+❡ ✉♥❛ %♦❣❧✐❛ ❞✐ ❋❉❘ ❜❛%%❛ ❡4✉✐✈❛❧❡ ❛ '❡♥❡+❡ ❜❛%%❛ ❧❛ ♣+♦❜❛❜✐❧✐'( ❞✐ ♦''❡♥❡+❡ ❢❛❧%✐ ♣♦%✐'✐✈✐✳. ✶✳✹ ▲♦ %&✉❞✐♦ &♦♣♦❧♦❣✐❝♦ ❞❡✐ ♣❛&❤✇❛② ❯♥❛ ✈♦❧'❛ %✈♦❧'❛ ❧✬❛♥❛❧✐%✐ ❞✐✛❡+❡♥③✐❛❧❡ %✐ ♦''✐❡♥❡ ✉♥❛ ❧✐%'❛ ❞✐ 4✉❛❧❝❤❡ ❝❡♥✲ '✐♥❛✐❛ ❞✐ ❣❡♥✐ ❞✐✛❡+❡♥③✐❛❧♠❡♥'❡ ❡%♣+❡%%✐✳ ▲❛ ❢❛%❡ ❞✐ ✐♥'❡+♣+❡'❛③✐♦♥❡ ❞❡✐ +✐%✉❧'❛'✐✱ 4✉✐♥❞✐✱ +✐%✉❧'❛ ♠♦❧'♦ ❝♦♠♣❧❡%%❛ %♦♣+❛''✉''♦ ♥❡❧ ❝❛%♦ ✐♥ ❝✉✐ ✐❧ ♣+♦❜❧❡♠❛ ❜✐♦❧♦❣✐❝♦ %'✉❞✐❛'♦ %✐❛ ♣♦❝♦ ♥♦'♦✳ ❙✐ ❝❡+❝❛ ❞✐ +✐%♦❧✈❡+❡ 4✉❡%'♦ ♣+♦❜❧❡♠❛ ✉'✐❧✐③③❛♥❞♦ ❧❡ ❛♥♥♦'❛③✐♦♥✐ ❢✉♥③✐♦♥❛❧✐ ❞❡✐ ❣❡♥✐ ✉%❛♥❞♦ ❧❛. ❖♥-♦❧♦❣②. ♦♣♣✉+❡ ✐❧ ❞❛'❛❜❛%❡ ❞✐ ♣❛'❤✇❛②. ❝②❝❧♦♣❡❞✐❛ ♦❢ ●❡♥❡# ❛♥❞ ●❡♥♦♠# ✮. ❑❊●●. ✭♣❛+'❡ ❞❡❧❧❛. ●❡♥❡. ❑②♦-♦ ❊♥✲. ❝♦♥ ✐ 4✉❛❧✐ %✐ ❝❡+❝❛ ❞✐ +❛❣❣+✉♣♣❛+❡ ✐. ❣❡♥✐ ✐♥ ❝❛'❡❣♦+✐❡✳ ❈♦♥ 4✉❡%'♦ '✐♣♦ ❞✐ ❛♥❛❧✐%✐ %✐ ❝❡+❝❛ ❞✐ +✐❝♦%'+✉✐+❡ ✐❧ ✜''♦ %❝❛♠❜✐♦ ❞✐ ✐♥❢♦+♠❛③✐♦♥✐ ❢+❛ ✐ ❣❡♥✐ ❝❤❡ ❛✈✈✐❡♥❡ ✐♥ ✉♥❛ ❝❡+'❛ ❝♦♥❞✐③✐♦♥❡ %♣❡✲ +✐♠❡♥'❛❧❡✳ ■❧. ❞❛-❛❜❛#❡. ❑❊●●✱ ❝❤❡ ✈❡++( ✉'✐❧✐③③❛'❛'♦ ❛♥❝❤❡ ♥❡❧❧❡ ❛♥❛❧✐%✐. %✉❝❝❡%%✐✈❡✱ ❝♦♥'✐❡♥❡ ✐♥❢♦+♠❛③✐♦♥✐ %✉✐ ♣❡+❝♦+%✐ ❞✐ ❝♦✲+❡❣♦❧❛③✐♦♥❡ ❝❤❡ %♦♥♦ ❛❧❧❛ ❜❛%❡ ❞❡❧❧❛ '+❛%♠✐%%✐♦♥❡ ❞❡❧ %❡❣♥❛❧❡ ❣❡♥❡'✐❝♦✳ ■♥ ❡%%❛ %♦♥♦ ♣+❡%❡♥'✐ ❧❡ ♠❛♣♣❡ ✭❝❤✐❛♠❛'❡. ♣❛-❤✇❛② ✮ ❝❤❡ ✈✐%✉❛❧✐③③❛♥♦ ✐♥ ♠♦❞♦ ❣+❛✜❝♦ ✐ ❞✐✛+❡♥✲. '✐ ❧✐✈❡❧❧✐ ❞✐ ✐♥'❡+❛③✐♦♥❡ ❢+❛ ✐ ❣❡♥✐✳ ◗✉❡%'❡ ✐♥❢♦+♠❛③✐♦♥✐ ❝✐ ❝♦♥%❡♥'♦♥♦ ❞✐. ✾.
(14) ✶ ■♥#$♦❞✉③✐♦♥❡ ❡❛❧✐③③❛ ❡ ❧❡ ❛♥❛❧✐'✐ ❞✐. ●❡♥❡ ❙❡$✱ ♦ ❛♥❛❧✐'✐ ❢✉♥③✐♦♥❛❧✐✱ ♦✈✈❡ ♦ ✉♥ .✐♣♦ ❞✐. ❛♥❛❧✐'✐ ❝❤❡ ♠✐ ❛ ❛❞ ✐❞❡♥.✐✜❝❛ ❡ ♥❡❧❧❛ ❧✐'.❛ ❞✐ ❣❡♥✐ ❉❊● ♣❛ .✐❝♦❧❛ ✐ ✐♥❢♦ ✲ ♠❛③✐♦♥✐ ❜✐♦❧♦❣✐❝❤❡✳ ◗✉❡'.♦ ❣❡♥❡ ❡ ❞✐ ❛♥❛❧✐'✐ '✐ ❞✐✈✐❞♦♥♦ ❡''❡♥③✐❛❧♠❡♥.❡ ✐♥ ❞✉❡ .✐♣✐✿. •. ◗✉❡❧❧❡ ❝❤❡ '♦✈ ❛♣♣♦♥❣♦♥♦ '❡♠♣❧✐❝❡♠❡♥.❡ ❧❛ ❧✐'.❛ ❞✐ ❣❡♥✐ ❉❊● ❛❧❧❡ ♠❛♣♣❡ ❞✐ ❝♦✲ ❡❣♦❧❛③✐♦♥❡✱. •. ❖✈❡' ❘❡♣'❡*❡♥$❛$✐♦♥ ❆♥❛❧②*✐*. ✭❖❘❆✮ ❀. ◗✉❡❧❧❡ ❝❤❡ ❝❡ ❝❛♥♦ ❞✐ ❛''♦❝✐❛ ❡ ✉♥ ♣❛ ❛♠❡. ♦ '.❛.✐'.✐❝♦ ❛❞ ✉♥. ♣❛$❤✲. ✇❛② ❝❤❡ '✐❛ ❡'♣❧✐❝❛.✐✈♦ ♥♦♥ '♦❧♦ ❞❡❧❧❡ ❞✐✛❡ ❡♥③❡ ❞✐ ❡'♣ ❡''✐♦♥❡✱ ♠❛ ❛♥❝❤❡ ❞❡❧❧❛ ❧♦ ♦ ♣♦'✐③✐♦♥❡ .♦♣♦❧♦❣✐❝❛✳. ❯♥. ♣❛$❤✇❛② ♠❡.❛❜♦❧✐❝♦ ✭✜❣✉ ❛ ✶✳✺✮ G ✉♥ ❞✐❛❣ ❛♠♠❛ ♥❡❧ H✉❛❧❡ '♦♥♦. ❛♣✲. ♣ ❡'❡♥.❛.❡ ❧❡ ❡❛③✐♦♥✐ ❝❤✐♠✐❝❤❡ ❝♦✐♥✈♦❧.❡ ✐♥ ✉♥♦ ♦ ♣✐I ♣ ♦❝❡''✐ ❝❡❧❧✉❧❛ ✐✳ ■ '✐♥❣♦❧✐ ♣❛''✐ ❞❡❧. ♣❛$❤✇❛② '♦♥♦. ❡❛③✐♦♥✐✱ ❝❛.❛❧✐③③❛.❡ ♥❡❧❧❛ ♠❛❣❣✐♦ ♣❛ .❡. ❞❡✐ ❝❛'✐ ❞❛ ❡♥③✐♠✐✱ ❝❤❡ ❛❣✐'❝♦♥♦ '✉ ✉♥❛ ♠♦❧❡❝♦❧❛ ❞✐ ♣❛ .❡♥③❛✱ ❝❤✐❛♠❛.❛ '✉❜'. ❛.♦✱ . ❛'❢♦ ♠❛♥❞♦❧❛ ✐♥ ✉♥ ♣ ♦❞♦..♦✱ ✐❧ H✉❛❧❡ '❛ K ✉.✐❧✐③③❛.♦ ❛ '✉❛ ✈♦❧.❛ ❝♦♠❡ '✉❜'. ❛.♦ ❛❧ ♣❛''♦ '✉❝❝❡''✐✈♦ ❞❡❧❧❛ ❡❛③✐♦♥❡ ❝❤✐♠✐❝❛✳ ■❧. ✇❛②. ♣❛$❤✲. ✐♥ ♣❛ .✐❝♦❧❛ ❡ ♣✉L ❡''❡ ❡ '.✉❞✐❛.♦ ❞❛ ✉♥ ♣✉♥.♦ ❞✐ ✈✐'.❛ '. ✉..✉ ❛❧❡. ❛.. ❛✈❡ '♦ ✉♥ ♠♦❞❡❧❧♦ ❜❛'❛.♦ '✉✐ ❣ ❛✜✳ ❯.✐❧✐③③❛ ❡ ✉♥ ❣ ❛❢♦ ♣❡ ♠♦❞❡❧❧❛ ❡. ♥❡$✇♦'❦ ✮ '✐❣♥✐✜❝❛ '❝❡❣❧✐❡ ❡ H✉❛❧✐ ❡♥.✐.K ❜✐♦❧♦❣✐❝❤❡ ❛''♦❝✐❛ ❡ ❛ ♥♦❞✐ ❡ ❛ ❝❤✐✳ ❯♥ ♥❡$✇♦'❦ ♠❡.❛❜♦❧✐❝♦ ✭✜❣✉ ❛ ✶✳✻✮✱ H✉✐♥❞✐✱ G. ✉♥❛ ❡.❡ ♠❡.❛❜♦❧✐❝❛ ✭♦. ✉♥ ✐♥'✐❡♠❡ ❞✐ ♥♦❞✐ ❝♦'.✐.✉✐.✐ ❞❛ ♣ ♦❞♦..✐ ❣❡♥✐❝✐✱ ✐♥ ♣❛ .✐❝♦❧❛ ❡ ♣ ♦.❡✐♥❡✱ ♠❛ ❛♥❝❤❡ ❘◆❆ ❡ ❝♦♠♣❧❡''✐✱ ❡❧❛③✐♦♥❛.✐ . ❛ ❞✐ ❧♦ ♦ . ❛♠✐.❡ ❛ ❝❤✐ ♦ ✐❡♥.❛.✐ ❛ '❡❝♦♥❞❛ ❞❡❧ .✐♣♦ ❞✐ ✐♥.❡ ❛③✐♦♥✐ ❢✉♥③✐♦♥❛❧✐ ❞❛ ❝✉✐ '♦♥♦ ❧❡❣❛.❡✳. ✶✵.
(15)
(16) ✶ ■♥#$♦❞✉③✐♦♥❡. ✶✳✺ ❙❝♦♣♦ ❞❡❧❧❛ +❡,✐ ❈♦♠❡ ❞❡%%♦ ♣'❡❝❡❞❡♥%❡♠❡♥%❡ ✐❧ ♣❛"❤✇❛②✱ ❝❤❡ ❢♦'♥✐/❝❡ ✐♠♣♦'%❛♥%✐ ✐♥❢♦'✲ ♠❛③✐♦♥✐ /✉❧❧❛ ❝♦''❡❧❛③✐♦♥❡ ❡/✐/%❡♥%❡ %'❛ ✐ ❣❡♥✐✱ 5 '❛♣♣'❡/❡♥%❛%♦ ❝♦♠❡ ✉♥ ❣'❛❢♦ ✐ ❝✉✐ ♥♦❞✐ ❝♦''✐/♣♦♥❞♦♥♦ ♠♦❧%♦ /♣❡//♦ ❛ ♣'♦❞♦%%✐ ❣❡♥✐❝✐✳ ◗✉❡/%✐ ♣♦//♦♥♦ ❡//❡'❡ ❞✐✈✐/✐ ✐♥ ❞✉❡ %✐♣✐✿ •. •. ❝♦♠♣❧❡//✐ ♣'♦%❡✐❝✐ ✭❣'✉♣♣✐ ❆◆❉✮✱ ❝❤❡ ♣♦//♦♥♦ ❡//❡'❡ ❡/♣❛♥/✐ ✐♥ ❝❧✐)✉❡, ✐♥ ❝✉✐ %✉%%❡ ❧❡ ♣'♦%❡✐♥❡ /♦♥♦ ❝♦❧❧❡❣❛%❡ %'❛ ❞✐ ❧♦'♦❀ ❣'✉♣♣✐ ❝♦♥ ❡❧❡♠❡♥%✐ %'❛ ❞✐ ❧♦'♦ /♦/%✐%✉✐❜✐❧✐✱ ❝♦♠❡ ❛❞ ❡/❡♠♣✐♦ ❧❡ ❢❛✲ ♠✐❣❧✐❡ ❣❡♥✐❝❤❡ ♦ ❣❡♥✐ ❝❤❡ ❤❛♥♥♦ ❢✉♥③✐♦♥✐ ❜✐♦❝❤✐♠✐❝❤❡ /✐♠✐❧✐ ✭❣'✉♣♣✐ ❖❘✮✳. ■❧ ❢❛%%♦ ❞✐ %❡♥❡' ❝♦♥%♦ ❞❡❧❧❛ ♣'❡/❡♥③❛ ❞✐ D✉❡/%✐ ❞✐✈❡'/✐ %✐♣✐ ❞✐ ♣'♦❞♦%%✐ ❣❡♥✐❝✐✱ ♣♦'%❛ ❛❞ ❛✈❡'❡ ❞❡❧❧❡ /%✐♠❡ ♣✐E ♣'❡❝✐/❡ ♥❡❧❧✬✐❞❡♥%✐✜❝❛③✐♦♥❡ ❞✐ /♦%%♦✲ ❣'✉♣♣✐ ❣❡♥✐❝✐ /'❡❣♦❧❛%✐ ❡ '✐❡/❝❡ ❛ ❡✈✐❞❡♥③✐❛'❡ D✉❡✐ /❡❣♥❛❧✐ ❝❤❡✱ ❛❧❧✬✐♥%❡'♥♦ ❞❡❧ ♣❛"❤✇❛②✱ /♦♥♦ ♣✐E ❝♦✐♥✈♦❧%✐ ♥❡❧❧❛ /✉❛ /'❡❣♦❧❛%❡③③❛✳ ■❧ ♣❛"❤✇❛②✱ ✐♥ D✉❡/%♦ ♠♦❞♦✱ ♣❡'H ❞✐✈❡♥%❛ ♠♦❧%♦ ♣✐E ❝♦♠♣❧❡//♦ ♥♦♥ /♦❧♦ ❞❛ ✉♥ ♣✉♥%♦ ❞✐ ✈✐/%❛ %♦♣♦❧♦❣✐❝♦✱ ♠❛ ❛♥❝❤❡ ❝♦♠♣✉%❛③✐♦♥❛❧❡✳ ▲✬✐♥%❡'❡//❡ ❞✐ D✉❡/%♦ ❡❧❛✲ ❜♦'❛%♦ 5 D✉❡❧❧♦ ❞✐ ❝❡'❝❛'❡ ❡ ✈❛❧✉%❛'❡ ✉♥ ♠❡%♦❞♦ ❝❤❡ ❝♦♥/❡♥%❛✱ ♣❛'%❡♥❞♦ ❞❛ ✉♥ ♣❛"❤✇❛② ✐♥ ❝✉✐ /✐❛ ✐ ❣'✉♣♣✐ ❆◆❉ ❝❤❡ ❖❘ /♦♥♦ /%❛%✐ ❡/♣❛♥/✐✱ ❞✐ /❡♠♣❧✐✜❝❛'❡ ❧❛ /%'✉%%✉'❛ ❞❡❧ ♣❛"❤✇❛② ♣❡' '❡♥❞❡'❡ D✉✐♥❞✐ ❛♥❝❤❡ ♣✐E ✈❡❧♦❝❡ ❧✬❛♥❛❧✐/✐✳ ■❧ ♣❛"❤✇❛② ❝♦♥/✐❞❡'❛%♦ 5 D✉❡❧❧♦ ❞✐ ❈❤'♦♥✐❝ ▼②❡❧♦✐❞ ▲❡✉❦❡♠✐❛✳ ▲❛ ❧❡✉❝❡♠✐❛ ♠✐❡❧♦✐❞❛❧❡ ❝'♦♥✐❝❛ 5 ✉♥❛ ❞❡❧❧❡ ♣'✐♠❡ ♠❛❧❛%%✐❡ ♣❡' ❝✉✐ /✐ 5 ✐♥❞✐✈✐❞✉❛%❛ ✉♥❛ /♣❡❝✐✜❝❛ ❛♥♦'♠❛❧✐%M ❝'♦♠♦/♦♠✐❝❛ %'❛ ❧❡ /✉❡ ❝❛✉/❡✳ ◆❡❧❧♦ /♣❡❝✐✜❝♦ ❧❛ %'❛/❧♦❝❛③✐♦♥❡ ❞❡❧ ❣❡♥❡ ❆❇▲ ❞❛❧ ❝'♦♠♦/♦♠❛ ✾ ❛❧ ❝'♦♠♦/♦♠❛ ✶✷.
(17) ✶ ■♥#$♦❞✉③✐♦♥❡ ✷✷ ❝♦♥ ❝♦♥$❡❣✉❡♥(❡ ❢♦*♠❛③✐♦♥❡ ❞✐ ✉♥ ❣❡♥❡ ❝❤✐♠❡*❛✳ ❙✐ $♦♥♦ ❝♦♥$✐❞❡*❛(❡✿. • ■❧ ❞❛"❛#❡" *❡❧❛(✐✈♦ ❛❧ ♣❛"❤✇❛② ✧❈❤*♦♥✐❝ ▼②❡❧♦✐❞ ▲❡✉❦❡♠✐❛✧ ✐♥ ❝✉✐ ✐ ❣*✉♣♣✐ ❆◆❉ ❡ ✐ ❣*✉♣♣✐ ❖❘ $♦♥♦ $(❛(✐ ❡$♣❛♥$✐ ✭♥❡❧ $❡❣✉✐(♦ ✧■♥✐③✐❛✲ ❧❡✧✮❀. • ■❧ ❞❛"❛#❡" ✐♥ ❝✉✐ ✐ ❣*✉♣♣✐ ❆◆❉ ❡ ❖❘ $♦♥♦ *❛♣♣*❡$❡♥(❛(✐ ❞❛❧❧❛ ♠❡❞✐❛ ❞❡✐ ❣❡♥✐ ❝❤❡ ❧✐ ❝♦♠♣♦♥❣♦♥♦ ✭✧▼❡❞✐❡✧✮❀. • ■❧ ❞❛"❛#❡" ✐♥ ❝✉✐ ✐ ❣*✉♣♣✐ ❖❘ $♦♥♦ *❛♣♣*❡$❡♥(❛(✐ ❞❛❧ ❣❡♥❡ ❝❤❡ ♠♦$(*❛ ✉♥❛ ♠❛❣❣✐♦*❡ ❞✐✛❡*❡♥③✐❛❧❡ ❡$♣*❡$$✐♦♥❡ ✐♥ ♠❡❞✐❛ ♥❡❧❧❡ ❞✉❡ ❝♦♥❞✐③✐♦✲ ♥✐ $♣❡*✐♠❡♥(❛❧✐✱ ♠❡♥(*❡ ✐ ❣*✉♣♣✐ ❆◆❉ ✈❡♥❣♦♥♦ *❛♣♣*❡$❡♥(❛*✐ $❡♠✲ ♣*❡ ❛((*❛✈❡*$♦ ❧❛ ♠❡❞✐❛ $❡♠♣❧✐❝❡ ✭✧▼❡❞✐❡ ❡ ▼❛$$✐♠❛ ❉✐✛❡*❡♥③✐❛❧❡ ❊$♣*❡$$✐♦♥❡✧✮❀. • ■❧ ❞❛"❛#❡" ✐♥ ❝✉✐ $✐❛ ✐ ❣*✉♣♣✐ ❆◆❉ ❝❤❡ ❖❘ $♦♥♦ *❛♣♣*❡$❡♥(❛(✐ ❞❛❧ ❣❡✲ ♥❡ ❝❤❡ ♠♦$(*❛ ✉♥❛ ♠❛❣❣✐♦*❡ ❞✐✛❡*❡♥③✐❛❧❡ ❡$♣*❡$$✐♦♥❡ ✐♥ ♠❡❞✐❛ ♥❡❧❧❡ ❞✉❡ ❝♦♥❞✐③✐♦♥✐ $♣❡*✐♠❡♥(❛❧✐ ✭✧▼❛$$✐♠❛ ❉✐✛❡*❡♥③✐❛❧❡ ❊$♣*❡$$✐♦♥❡✧✮❀. • ■❧ ❞❛"❛#❡" ✐♥ ❝✉✐ ❡♥(*❛♠❜❡ ❧❡ (✐♣♦❧♦❣✐❡ ❞✐ ❣*✉♣♣✐ ✈❡♥❣♦♥♦ ❡$♣*❡$$❡ $❡❝♦♥❞♦ ✐❧ ♠❡(♦❞♦ ❞❡❧❧❡ ❝♦♠♣♦♥❡(✐ ♣*✐♥❝✐♣❛❧✐ ✭✧❈♦♠♣♦♥❡♥(❡ K*✐♥✲ ❝✐♣❛❧❡✧✮❀ ❙✉ L✉❡$(✐ ❝✐♥L✉❡ ❞❛"❛#❡" $♦♥♦ $(❛(❡ $✈♦❧(❡ ❧❡ $(❡$$❡ ❛♥❛❧✐$✐✱ ♦✈✈❡*♦ ✐❞❡♥✲ (✐✜❝❛③✐♦♥❡ ❞❡✐ ❣❡♥✐ ❞✐✛❡*❡♥③✐❛❧♠❡♥(❡ ❡$♣*❡$$✐ ❡ ❛♥❛❧✐$✐ (♦♣♦❧♦❣✐❝❤❡ $✉✐. ♣❛"❤✇❛② ❝♦♥ ❚♦♣♦❧♦❣②●❙❆ ❡ ❙K■❆✳ ❙♦♥♦ $(❛(✐ ❝♦♥❢*♦♥(❛(✐ ♣♦✐ ✐ *✐$✉❧(❛(✐ ♦((❡♥✉(✐ ❞❛❧❧❡ L✉❛((*♦ ♠❛(*✐❝✐ $❡♠♣❧✐✜❝❛(❡ ❝♦♥ L✉❡❧❧✐ ♦((❡♥✉(✐ ❞❛❧❧❛ ♠❛(*✐✲. ✶✸.
(18) ✶ ■♥#$♦❞✉③✐♦♥❡ ❝❡ ❞❡✐ ❞❛%✐ ✐♥✐③✐❛❧❡✳ ❯♥♦ ,❝❤❡♠❛ ❣❡♥❡0❛❧❡ ❞✐ ❝♦♠❡ 1 ,%❛%❛ ,✈♦❧%❛ ❧✬❛♥❛❧✐,✐ 1 ✐♥❞✐❝❛%♦ ✐♥ ✜❣✉0❛ ✶✳✺✳. ❋✐❣✉$❛ ✶✳✺✿ ❙+$✉++✉$❛ ❞❡❧❧✬❛♥❛❧✐1✐ 1✈♦❧+❛. ✶✹.
(19) ✷ ❚❡❝♥✐❝❤❡ '(❛(✐'(✐❝❤❡ ♣❡+ ❧✬✐❞❡♥(✐✜❝❛③✐♦♥❡ ❞❡✐ ❉❊● ✷✳✶ ■♥%&♦❞✉③✐♦♥❡ ❈♦♠❡ ❣✐& ❛❝❝❡♥♥❛*♦✱ ❧✬✐❞❡♥*✐✜❝❛③✐♦♥❡ ❞✐ ❣❡♥✐ ❞✐✛❡2❡♥③✐❛❧♠❡♥*❡ ❡3♣2❡33✐ 5 ✉♥♦ ❞❡✐ 2✐3✉❧*❛*✐ ❞✐ ♠❛❣❣✐♦2 ✐♥*❡2❡33❡ 7✉❛♥❞♦ 3✐ ♣❛2❧❛ ❞✐ ❡3♣❡2✐♠❡♥*✐ ❞✐ ♠✐❝#♦❛##❛②✳ ◗✉❡3*❛ ❢❛3❡ ✐♥❢❡2❡♥③✐❛❧❡✱ ❝❤❡ ❛✈✈✐❡♥❡ 3✉❝❝❡33✐✈❛♠❡♥*❡ ❛❧❧❛ ❢❛3❡ ❞✐ ♥♦2♠❛❧✐③③❛③✐♦♥❡✱ ❤❛ ❧♦ 3❝♦♣♦✱ ❞✉♥7✉❡✱ ❞✐ ✐♥❞✐✈✐❞✉❛2❡ ✐ ❣❡♥✐ ❝❤❡ ❤❛♥♥♦ ✉♥ ✈❛❧♦2❡ ❞✐ ❡3♣2❡33✐♦♥❡ 3✐❣♥✐✜❝❛*✐✈❛♠❡♥*❡ ❞✐✈❡23♦ *2❛ ❞✉❡ ♦ ♣✐= ❝♦♥❞✐③✐♦♥✐ 3♣❡2✐♠❡♥*❛❧✐✳ ▲✬✐♣♦*❡3✐ ♥✉❧❧❛✱ ❞❡❧ 3✐3*❡♠❛ ❞✬✐♣♦*❡3✐ ❛ ❝✉✐ ❝✐ 3✐ 2✐❢❡2✐3❝❡✱ ❡3♣2✐♠❡ ❧✬✉❣✉❛❣❧✐❛♥③❛ ❞❡❧❧✬❡3♣2❡33✐♦♥❡ ❞❡❧ ❣❡♥❡ g ♥❡❧❧❡ ❞✉❡ ❝♦♥❞✐✲ ③✐♦♥✐ 3♣❡2✐♠❡♥*❛❧✐ ❡ ❧✬✐♣♦*❡3✐ ❛❧*❡2♥❛*✐✈❛ ♥❡ 2❛♣♣2❡3❡♥*❛ ❧❛ 3✉❛ ♥❡❣❛③✐♦♥❡✳ ❋♦2♠❛❧✐③③❛♥❞♦ 3✐ ❤❛✿ H0,g : µx (g) = µy (g) H1,g : µx (g) 6= µy (g). ✶✺. ✭✷✳✶✮.
(20) ✷ ❚❡❝♥✐❝❤❡ '(❛(✐'(✐❝❤❡ ♣❡+ ❧✬✐❞❡♥(✐✜❝❛③✐♦♥❡ ❞❡✐ ❉❊● ❝♦♥ g = 1, ..., n✱ ❞♦✈❡ µx (g) ' ✐❧ ✈❛❧♦+❡ ❛,,❡-♦ ❞❡❧❧✬❡-♣+❡--✐♦♥❡ ❞❡❧ ❣❡♥❡. g ♥❡❧❧❛ ♣+✐♠❛ ❝♦♥❞✐③✐♦♥❡ ❡ µy (g) ' ✐❧ ✈❛❧♦+❡ ❛,,❡-♦ ❞❡❧❧✬❡-♣+❡--✐♦♥❡ ❞❡❧ ❣❡♥❡ g ♥❡❧❧❛ -❡❝♦♥❞❛ ❝♦♥❞✐③✐♦♥❡✳ ■♥ ❧❡,,❡+❛,✉+❛ ❡-✐-,♦♥♦ ✈❛+✐ ,✐♣✐ ❞✐ ,❡-, ✉,✐❧✐③③❛,✐ ❝♦♥ ❧♦ -❝♦♣♦ ❞✐ ✐❞❡♥,✐✜❝❛+❡ ✐ ❣❡♥✐ ❞✐✛❡+❡♥③✐❛❧♠❡♥,❡ ❡-♣+❡--✐✱ ❝❤❡ ❛❞♦,,❛♥♦ -✐❛ ✉♥ ❛♣♣+♦❝❝✐♦ ♣❛+❛♠❡,+✐❝♦ ❝❤❡ ♥♦♥ ♣❛+❛♠❡,+✐❝♦✱ ♠❛ ✐♥ 9✉❡-,♦ ❡❧❛❜♦+❛,♦ ✈❡++; ✐♥,+♦❞♦,,❛ -♦❧♦ ❧❛ ♣❛+,❡ +❡❧❛,✐✈❛ ❛✐ ♠♦❞❡❧❧✐ ❧✐♥❡❛+✐ ♣❡+ ❞❛,✐ ❞✐. ♠✐❝#♦❛##❛②. ✭✐♥ 9✉❛♥,♦ ✈❡++❛♥♥♦ ✉,✐❧✐③③❛,✐ ♣♦✐ ♥❡❧❧❡ ❛♥❛❧✐-✐. -✉❝❝❡--✐✈❡✮✳ ❱❛ +✐❝♦+❞❛,♦ ❝❤❡ ✐ ♣+♦❜❧❡♠✐ ❝❤❡ -✐ +✐-❝♦♥,+❛♥♦ ♥❡✐ ❝+✐,❡+✐ ✉,✐❧✐③③❛,✐ ♥❡❧❧✬✐♥❢❡+❡♥③❛ ❝❧❛--✐❝❛ -♦♥♦ ♣+✐♥❝✐♣❛❧♠❡♥,❡ ❞✉❡✿. • ■❧ ❝♦♥,+♦❧❧♦ ❞❡❧❧✬❡++♦+❡ ❞✐ ♣+✐♠♦ ,✐♣♦ ✭ α✮✳ ❙♦♥♦ -,❛,✐ ♣+♦♣♦-,✐ ❛❧❝✉✲ ♥✐ ♠❡,♦❞✐ ❞✐ ❛❣❣✐✉-,❛♠❡♥,♦ ❞❡✐ ✈❛❧♦+✐✲ p -,✐♠❛,✐ ❝❤❡ ❝♦♥,+♦❧❧❛♥♦ ✐❧. ❢❛♠✐❧② ✇✐*❡ ❡##♦# #❛,❡ ♦✱ ✐♥ ❛❧,❡+♥❛,✐✈❛✱ ✐❧ ❢❛❧*❡ ❞✐*❝♦✈❡#② #❛,❡✳ • ▲❛ -,✐♠❛ ❞❡❧❧❛ ✈❛+✐❛♥③❛ ❣❡♥❡✲-♣❡❝✐✜❝❛ ✭ σg2 ✮✳ ■♥♦❧,+❡✱ 9✉❛♥❞♦ -✐ ♣❛+❧❛ ❞✐ ❛♣♣❧✐❝❛+❡ ❧✬✐♥❢❡+❡♥③❛ ❝❧❛--✐❝❛ ❛✐ ❞❛,✐ ❞✐. ♠✐✲. ❝#♦❛##❛② ❜✐-♦❣♥❛ ,❡♥❡+ ♣+❡-❡♥,❡ ❝❤❡ ✐❧ -✐-,❡♠❛ ❞✬✐♣♦,❡-✐ ✭✷✳✶✮ ❞❡✈❡ ❡--❡+❡ ,❡-,❛,♦ -✉ ♦❣♥✐ -✐♥❣♦❧♦ ❣❡♥❡ ❞❡❧❧❛ ♣✐❛,,❛❢♦+♠❛ ✭❝❤❡ ❝♦♥,✐❡♥❡ ❝❡♥,✐♥❛✐❛ ❞✐ ♠✐❣❧✐❛✐❛ ❞✐ ❣❡♥✐✮✱ ❡ ♥♦♥ ' ❞❡,,♦ ❝❤❡ -✐❛♥♦ +✐-♣❡,,❛,❡ ❧❡ ❛--✉♥③✐♦♥✐ ❞✐ ♥♦+♠❛❧✐,; ❞❡❧❧❛ ❞✐-,+✐❜✉③✐♦♥❡✱ ❞✐ ♦♠♦-❝❤❡❞❛-,✐❝✐,; ❡ ❞✐ ✐♥❞✐♣❡♥❞❡♥③❛✳. ✷✳✷ ■❧ ♠♦❞❡❧❧♦ ❧✐♥❡❛+❡ ♣❡+ ❞❛-✐ ❞✐ ♠✐❝+♦❛++❛② ✷✳✷✳✶ ▲❛ ♠❛&'✐❝❡ ❞❡❧ ❞✐-❡❣♥♦ ■ ♠♦❞❡❧❧✐ ❧✐♥❡❛+✐ ✈❡♥❣♦♥♦ ✉,✐❧✐③③❛,✐ ♣❡+ ❢❛+❡ ✐♥❢❡+❡♥③❛ -✐❛ ♣❡+ ❞❛,✐ ❝❤❡ ❞❡+✐✈❛♥♦ ❞❛ ,❡❝♥♦❧♦❣✐❡ ❛ -✐♥❣♦❧♦ ❝❛♥❛❧❡✱ -✐❛ ♣❡+ ❞❛,✐ ❝❤❡ ❞❡+✐✈❛♥♦ ❞❛. ✶✻.
(21) ✷ ❚❡❝♥✐❝❤❡ '(❛(✐'(✐❝❤❡ ♣❡+ ❧✬✐❞❡♥(✐✜❝❛③✐♦♥❡ ❞❡✐ ❉❊● ❡❝♥♦❧♦❣✐❡ ❛ ❞♦♣♣✐♦ ❝❛♥❛❧❡✳ ■♥ ❣❡♥❡-❛❧❡ .✐ ❛..✉♠❡ ❞✐ ❛✈❡-❡ ✉♥. p ♠✐❝(♦❛((❛②. ❞❛✐ 2✉❛❧✐ .✐ ♦. ✐❡♥❡ ✉♥ ✈❡. ♦-❡ ✭✈❡. ❝♦♥. ♦-❡ -✐.♣♦. ❛✮ ❝♦♥ ❡♥❡♥ ❡. ✐ ✈❛❧♦-✐ ❞✐ ❡.♣-❡..✐♦♥❡✱ ♣❡- ♦❣♥✐ .✐♥❣♦❧♦ ❣❡♥❡✳ 6❡- ✐❧ 2✉✐♥❞✐ ✐❧ ✈❡. ❞❛"❛#❡". g. ✲ ❡.✐♠♦ ❣❡♥❡ .✐ ❛✈-8. ♦-❡✿. . . yg1 yg2 yg = ··· ygp. ✭✷✳✷✮. ■❧ ✈❛❧♦-❡ ❞✐ ❡.♣-❡..✐♦♥❡✱ ❣❡♥❡-❛❧♠❡♥ ❡✱ ; ♣-❡.❡♥ ❛ ♦ ✐♥ ❡-♠✐♥✐ ❞✐ ❧♦❣❛-✐ ♠♦ ✐♥ ❜❛.❡ ✷ ❞❡❧ -❛♣♣♦- ♦ -❛ ❧❡ ✐♥ ❡♥.✐ 8 ❞❡❧❧❡ ❞✉❡ ❝♦♥❞✐③✐♦♥✐ .♣❡-✐♠❡♥ ❛❧✐ ♣❡- ❧❡ ❡❝♥♦❧♦❣✐❡ ❛ ❞♦♣♣✐♦ ❝❛♥❛❧❡ ❡ ✐♥ ❡-♠✐♥✐ ❞✐ ❧♦❣❛-✐ ♠♦ ✐♥ ❜❛.❡ ✷ ❞❡❧❧❡ ✐♥ ❡♥.✐ 8 ♥❡❧ ❝❛.♦ ❞✐. ❡❝♥♦❧♦❣✐❡ ❛ .✐♥❣♦❧♦ ❝❛♥❛❧❡✳. ■❧ ♠♦❞❡❧❧♦ ❝❤❡ ✈✐❡♥❡. ❞✉♥2✉❡ ❛..✉♥ ♦✱ ♣❡- ♦❣♥✐ .✐♥❣♦❧♦ ❣❡♥❡✱ ; ❞❡❧ ✐♣♦✿. yg = Xαg + ǫg ❞♦✈❡ -✐ ❡. ǫg. X. -❛♣♣-❡.❡♥ ❛ ❧❛ ♠❛ -✐❝❡ ❞❡❧ ❞✐.❡❣♥♦✱. ; ✉♥ ❢❛. ✭✷✳✸✮. αg. ; ✐❧ ✈❡. ♦-❡ ❞❡✐ ♣❛-❛♠❡✲. ♦-❡ ❞✬❡--♦-❡ ♥♦♥ ♥❡❝❡..❛-✐❛♠❡♥ ❡ ♥♦-♠❛❧❡✳ ▲❛ ♠❛ -✐❝❡. ❞❡❧ ❞✐.❡❣♥♦ ♥❡❧ ❝❛.♦ ❞✐. ❡❝♥♦❧♦❣✐❡ ❛ .✐♥❣♦❧♦ ❝❛♥❛❧❡ ❬✺❪ ; ✉❣✉❛❧❡ ❛ 2✉❡❧❧❛. ✉ ✐❧✐③③❛ ❛ ♥❡✐ ♠♦❞❡❧❧✐ ❧✐♥❡❛-✐ ❝❧❛..✐❝✐✱ ♦✈✈❡-♦✱ .✉♣♣♦♥❡♥❞♦ ❞✐ ❛✈❡-❡ ♣❡- ✐❧ ♣-✐♠♦ ❣-✉♣♣♦ ❡. j. ❛--❛② ♣❡- ✐❧ .❡❝♦♥❞♦ ❣-✉♣♣♦. ♣♦..✐❜✐❧❡ ♠❛ -✐❝❡ ❞❡❧ ❞✐.❡❣♥♦ .❛-8 ❞❡❧ ✐♣♦. ✶✼. i ❛--❛②. (i + j = p)✱. ✉♥❛.
(22) ✷ ❚❡❝♥✐❝❤❡ '(❛(✐'(✐❝❤❡ ♣❡+ ❧✬✐❞❡♥(✐✜❝❛③✐♦♥❡ ❞❡✐ ❉❊●. . X(p×2). = . 1 1. 0 0. ··· ··· 1. 0. 0. 1. 0. 1. ··· ··· 0. 1. . i − ma posizione . ✭✷✳✹✮. ✷✳✷✳✷ ■❧ $✲$❡'$ ❘✐♣(❡♥❞❡♥❞♦ ✐❧ ♠♦❞❡❧❧♦ ✭✷✳✸✮ ❞❡❧ ♣❛(❛❣(❛❢♦ ♣(❡❝❡❞❡♥4❡ 5✐ ❛55✉♠❡ ❝❤❡. ❞♦✈❡. Wg. E(yg ) = Xαg. ✭✷✳✺✮. var(yg ) = Wg σg2. ✭✷✳✻✮. ; ✉♥❛ ♠❛4(✐❝❡ ❞✐ ♣❡5✐✱ ♥♦4❛✱ ❞❡✜♥✐4❛ ♥♦♥ ♥❡❣❛4✐✈❛✳ ❙✐ ❛55✉♠❡✱. ✐♥♦❧4(❡✱ ❝❤❡ ❛❧❝✉♥✐ ❝♦♥4(❛54✐ 5✐❛♥♦ ❞✐ ✐♥4❡(❡55❡ ❜✐♦❧♦❣✐❝♦✱ ❡ @✉❡54✐ ♣♦55♦♥♦ ❡55❡(❡ ❞❡✜♥✐4✐ ❝♦♠❡✿. βg = C T αg. ✭✷✳✼✮. ■♥✜♥❡✱ 5✐ ❛55✉♠❡ ❝❤❡ 5✐❛ ❞✐ ✐♥4❡(❡55❡ 4❡54❛(❡ 5❡ ✐❧ 5✐♥❣♦❧♦ ✈❛❧♦(❡ ❞❡❧ ❝♦♥✲ 4(❛54♦. βgj. 5✐❛ ✉❣✉❛❧❡ ❛ ③❡(♦✱ ♦✈✈❡(♦. βgj = 0✳. 5✐54❡♠❛ ❞✐ ✐♣♦4❡5✐ 5✐❛ ❞❡❧ 4✐♣♦✿. ✶✽. ◆❡ ❝♦♥5❡❣✉❡✱ @✉✐♥❞✐✱ ❝❤❡ ✐❧.
(23) ✷ ❚❡❝♥✐❝❤❡ '(❛(✐'(✐❝❤❡ ♣❡+ ❧✬✐❞❡♥(✐✜❝❛③✐♦♥❡ ❞❡✐ ❉❊●. H0 : βgj = 0. ✭✷✳✽✮. H1 : βgj 6= 0 ❙✉❧ ✈❡**♦,❡ ❞❡❧❧❡ ,✐/♣♦/*❡ ✈✐❡♥❡ ❞✉♥2✉❡ /*✐♠❛*♦ ✐❧ ♠♦❞❡❧❧♦ ❧✐♥❡❛,❡ ✐♥ ♠♦❞♦ ❞❛ ♦**❡♥❡,❡✱ ♣❡, ♦❣♥✐ ❣❡♥❡✱ ✉♥❛ /*✐♠❛ ❞❡✐ /❡❣✉❡♥*✐ ❝♦❡✣❝✐❡♥*✐✿. • αˆg. ♣❡,. αg ❀. • s2g. /*✐♠❛ ♣❡,. σg2. ❞❛✐ 2✉❛❧✐ /✐ ♦**✐❡♥❡ ♣♦✐ ✉♥❛ /*✐♠❛ ❞❡❧❧❛ ♠❛*,✐❝❡ ❞✐ ✈❛,✐❛♥③❡ ❡ ❝♦✈❛,✐❛♥③❡. var(ˆ αg ) = Vg s2g ❞♦✈❡. Vg. = ✉♥❛ ♠❛*,✐❝❡ ❞❡✜♥✐*❛ ♣♦/✐*✐✈❛✱ ❝❤❡ ♥♦♥ ❞✐♣❡♥❞❡ ❞❛. ✭✷✳✾✮. s2g ✳. ✈♦❧*❛ ♦**❡♥✉*❡ 2✉❡/*❡ /*✐♠❡ /✐ ♦**✐❡♥❡ ✉♥❛ /*✐♠❛ ♣❡, ✐ ❝♦❡✣❝✐❡♥*✐. ❯♥❛. βg. ❝❤❡. ❞❡✜♥✐/❝♦♥♦ ✐ ❝♦♥*,❛/*✐. βˆg = C T α ˆg. ✭✷✳✶✵✮. ❧❛ ❝✉✐ ♠❛*,✐❝❡ ❞✐ ✈❛,✐❛♥③❡ ❡ ❝♦✈❛,✐❛♥③❡ /*✐♠❛*❛ =. var(βˆg ) = C T Vg Cs2g. ✭✷✳✶✶✮. ■❧ ♠♦❞❡❧❧♦ ♥♦♥ = ♥❡❝❡//❛,✐❛♠❡♥*❡ ❛//✉♥*♦ ♥♦,♠❛❧❡✱ ❡ 2✉✐♥❞✐ ♥♦♥ ✈❛ ♥❡❝❡/✲ /❛,✐❛♠❡♥*❡ ✉/❛*❛ ✉♥❛ /*✐♠❛ ❛✐ ♠✐♥✐♠✐ 2✉❛❞,❛*✐✳ ❆❞ ♦❣♥✐ ♠♦❞♦✱ /✐ ❛//✉♠❡ ❝❤❡ ❧❛ /*✐♠❛ ❞❡✐ ❝♦♥*,❛/*✐ /✐❛ ❛♣♣,♦//✐♠❛*✐✈❛♠❡♥*❡ ♥♦,♠❛❧❡ ❝♦♥ ♠❡❞✐❛. ✶✾. βg.
(24) ✷ ❚❡❝♥✐❝❤❡ '(❛(✐'(✐❝❤❡ ♣❡+ ❧✬✐❞❡♥(✐✜❝❛③✐♦♥❡ ❞❡✐ ❉❊● ❡ ♠❛#$✐❝❡ ❞✐ ✈❛$✐❛♥③❡ ❡ ❝♦✈❛$✐❛♥③❡ C T Vg Cs2g ❡ ❝❤❡ ❧❛ ✈❛$✐❛♥③❛ $❡.✐❞✉❛ s2g .❡❣✉❛ ❛♣♣$♦..✐♠❛#✐✈❛♠❡♥#❡ ✉♥❛ ❞✐.#$✐❜✉③✐♦♥❡ χ2 .❝❛❧❛#❛✳ ❉❡✜♥❡♥❞♦ ❝♦♥. vgj ❧✬❡❧❡♠❡♥#♦ ❞✐❛❣♦♥❛❧❡ j ✲❡.✐♠♦ ❞❡❧❧❛ ♠❛#$✐❝❡ C T Vg C ❧❡ ❛..✉♥③✐♦♥✐ .✉❧❧❡ ❞✐.#$✐❜✉③✐♦♥✐ ♣♦..♦♥♦ ❡..❡$❡ $✐❛..✉♥#❡ ❝♦♠❡ .❡❣✉❡✿. βˆgj ∼ N (βgj , vgj σg2 ). s2g. σg2 2 ∼ χdg dg. ✭✷✳✶✷✮. ✭✷✳✶✸✮. ❞♦✈❡ dg .♦♥♦ ✐ ❣$❛❞✐ ❞✐ ❧✐❜❡$#> $❡.✐❞✉✐ ❞❡❧ ♠♦❞❡❧❧♦ ❧✐♥❡❛$❡ ♣❡$ ✐❧ ❣❡♥❡ g ✳ ❙♦##♦ @✉❡.#❡ ❛..✉♥③✐♦♥✐ .✐ ♣✉A ❞❡✜♥✐$❡ ❧❛ .#❛#✐.#✐❝❛ #❡.# t ♦!❞✐♥❛!✐❛. tgj =. βˆgj ∼ tdg √ sg vgj. ✭✷✳✶✹✮. ❝❤❡ .❡❣✉❡ ❛♣♣$♦..✐♠❛#✐✈❛♠❡♥#❡ ❧❛ ❞✐.#$✐❜✉③✐♦♥❡ &✲❙&✉❞❡♥& ❝♦♥ dg ❣$❛❞✐ ❞✐ ❧✐❜❡$#>✳ ❉✐✈❡♥#❛✱ ♣❡$A✱ ❝♦♠♣❧❡..♦ ❞❛❧ ♣✉♥#♦ ❞✐ ✈✐.#❛ ❝♦♠♣✉#❛③✐♦♥❡ ❛♣✲ ♣❧✐❝❛$❡ @✉❡.#❛ .#❛#✐.#✐❝❛ #❡.# ❛ ❞❛#✐ ❞✐ ♠✐❝!♦❛!!❛②✱ ✐♥ @✉❛♥#♦✱ ❝♦♠❡ ❞❡##♦ ♣$❡❝❡❞❡♥#❡♠❡♥#❡✱ ✐♥ ♦❣♥✐ ♣✐❛##❛❢♦$♠❛ .♦♥♦ ♣$❡.❡♥#✐ ❝❡♥#✐♥❛✐❛ ❞✐ ♠✐❣❧✐❛✐❛ ❞✐ ❣❡♥✐✳ E❡$ @✉❡.#♦ ♠♦#✐✈♦ ❛❝❝❛❞❡ ❞✐ ❢$❡@✉❡♥#❡ ❝❤❡ ❛❧❝✉♥✐ ❣❡♥✐ ♣$❡.❡♥#✐♥♦ .♦♠♠❡ ❞✐ @✉❛❞$❛#✐ ♠♦❧#♦ ♣✐❝❝♦❧❡✱ ♦ ♠♦❧#♦ ❣$❛♥❞✐✱ ♣$♦❞✉❝❡♥❞♦ ❞✐ ❝♦♥✲ .❡❣✉❡♥③❛ ✈❛❧♦$✐ ❞❡❧ #❡.#✱ $✐.♣❡##✐✈❛♠❡♥#❡✱ ♠♦❧#♦ ❣$❛♥❞✐✱ ♦ ♠♦❧#♦ ♣✐❝❝♦❧✐✱ ♣✉$ ❡..❡♥❞♦ ❡.♣$❡..✐ ✐♥ @✉❛♥#✐#> .❝❛$.❡✳ E❡$ ❡✈✐#❛$❡ ✐❧ ♣$♦❜❧❡♠❛ ❝❤❡ @✉❡✲ .#✐ ❣❡♥✐ ❣❡♥❡$✐♥♦ ❞❡❣❧✐ ❡$$♦$✐ ❞✐ ✐❞❡♥#✐✜❝❛③✐♦♥❡ .♦♥♦ .#❛#❡ ♣$♦♣♦.#❡ ❞❡❧❧❡ .#❛#✐.#✐❝❤❡ ❛❧#❡$♥❛#✐✈❡✱ ❝❤❡ ❝♦♥.❡♥#♦♥♦ ❛❣❧✐ .#✐♠❛#♦$✐ ❞❡❧❧❡ ✈❛$✐❛♥③❡ ❞✐ $✐✲ ❞✉$$❡ ❧✬❡✛❡##♦ ❞❡✐ ✈❛❧♦$✐ ❡.❛❣❡$❛#❛♠❡♥#❡ ❣$❛♥❞✐ ❡ ❡.❛❣❡$❛#❛♠❡♥#❡ ♣✐❝❝♦❧✐✳. ✷✵.
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