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Multi-view dimensionality reduction for multi-modal biometrics

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(1)Multi-view dimensionality reduction for multi-modal biometrics Xuran Zhao. To cite this version: Xuran Zhao. Multi-view dimensionality reduction for multi-modal biometrics. Computer Vision and Pattern Recognition [cs.CV]. Télécom ParisTech, 2013. English. �NNT : 2013ENST0061�. �tel01236516�. HAL Id: tel-01236516 https://pastel.archives-ouvertes.fr/tel-01236516 Submitted on 1 Dec 2015. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) 2013-ENST-0061. EDITE - ED 130. Doctorat ParisTech THÈSE pour obtenir le grade de docteur délivré par. TELECOM ParisTech Spécialité « Signal and Image » présentée et soutenue publiquement par. Xuran ZHAO 24.10.2013. Réduction de la Dimensionalité Multivue pour la Biométrie Multimodal. Directeur de thèse : Nicholas Evans & Jean-Luc Dugelay. Jury M. Fabio Roli, Professeur, University of Cagliari M. Christophe Rosenburger, Professeur, ENSICAEN M. John Mason, Professeur, Swansea University M. Vincent Despiegel, Chercheur, MORPHO M. Nicholas Evans, Maitre de conférences, EURECOM M. Jean-Luc Dugelay, Professeur, EURECOM TELECOM ParisTech école de l’Institut Télécom - membre de ParisTech. Président Rapporteur Rapporteur Examinateur Directeur de thèse Directeur de thèse.

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(4) ❆❝❦♥♦✇❧❡❞❣❡♠❡♥+, ❚❤"❡❡ ②❡❛"& ❛❣♦ ✇❤❡♥ ■ ❣♦, ♠② ♠❛&,❡" ❞❡❣"❡❡✱ ■ &❛✐❞ ,♦ ♠②&❡❧❢✿ ✏■ ❞♦♥✬, ✇❛♥, ,♦ ❜❡ ❛ &♦❢,✇❛"❡ ❡♥❣✐♥❡❡"✱ &♦ ■ ✇✐❧❧ ❞♦ &♦♠❡ "❡&❡❛"❝❤ ✐♥&,❡❛❞✑✱ ❛♥❞ ,❤❛, ✇❛& ❤♦✇ ■ &,❛",❡❞ ♠② 9❤✳❉✳ ■ ,❤❡♥ ❢♦✉♥❞ ,❤❛, "❡&❡❛"❝❤ ✐& ♣"❡,,② ❧✐❦❡ ❛ ❣❛♠❡✳ ■ ✇❛& ❛&&✐❣♥❡❞ ✇✐,❤ ❛ ,♦♣✐❝✱ ♥❛♠❡❧② ♠✉❧,✐✲ ♠♦❞❛❧ ❜✐♦♠❡,"✐❝&✱ ♠✉❝❤ ❧✐❦❡ ❜❡✐♥❣ ,♦❧❞✿ ✏❚❤✐& ✐& ②♦✉" ❣❛♠❡ ❢♦" ,❤❡ ♥❡①, ,❤"❡❡ ②❡❛"&✑✳ ❙♦ ■ ✜❣✉"❡ ♦✉, ,❤❡ "✉❧❡&✱ ❧♦♦❦ ❛, ❤♦✇ ♦,❤❡"& ♣❧❛②✱ ❛♥❞ ,"② ,♦ ♣❧❛② ❜❡,,❡"✳ ❆❢,❡" ,❤"❡❡ ②❡❛"&✱ ■ ❛♠ &,✐❧❧ ♥♦, &✉"❡ ✐❢ ■ ❝❛♥ "❡❛❧❧② ♣❧❛② ❜❡,,❡" ,❤❛♥ ,❤❡ ♦,❤❡"&✱ ❜✉, ❛♠ ♣❛",✐❝✉❧❛"❧② ❤❛♣♣② ✇✐,❤ ,✇♦ ,❤✐♥❣&✿ ✜"&,✱ ■ ❡♥❥♦②❡❞ ,❤❡ ❣❛♠❡❀ ❛♥❞ &❡❝♦♥❞✱ ■ ❛♠ ✇✐❧❧✐♥❣ ,♦ ❝♦♥,✐♥✉❡ ♣❧❛②✐♥❣ ❛& ❛ ♣♦&,✲❞♦❝ "❛,❤❡" ,❤❛♥ ,♦ &❛② ✏■ F✉✐,✑✳ ■ ❤❛❞ ❛ ✈❡"② ❣♦♦❞ ,✐♠❡ &,✉❞②✐♥❣ ❛♥❞ ✇♦"❦✐♥❣ ❛, ❊❯❘❊❈❖▼✱ ❛♥❞ ❧✐✈✐♥❣ ✉♥❞❡" ,❤❡ &✉♥&❤✐♥❡ ♦❢ ❈♦,❡✲❞✬❆③✉"✳ ■ ✇♦✉❧❞ ❧✐❦❡ ,♦ ,❤❛♥❦ ❛ ❧♦, ♦❢ ♣❡♦♣❧❡✳ ❖❢ ❝♦✉"&❡✱ ■ ✇❛♥, ,♦ ✜"&, ❡①♣"❡&& ♠② ❣"❡❛,❡&, ❣"❛,✐,✉❞❡ ,♦ ♠② ,❤❡&✐& &✉♣❡"✈✐&♦"& ❉"✳ ◆✐❝❤♦❧❛& ❊✈❛♥& ❛♥❞ ❉"✳ ❏❡❛♥✲ ▲✉❝ ❉✉❣❡❧❛②✱ ✇❤♦ ❣❛✈❡ ♠❡ ,❤✐& ♦♣♣♦",✉♥✐,② ❛♥❞ ❤❡❧♣❡❞ ♠❡ ✐♥ ❛❧❧ ❛&♣❡❝,&✳ ■ "❡♠❡♠❜❡" ❛ ❋"✐❞❛② ❧❛,❡ ♥✐❣❤, ,❤"❡❡ ②❡❛"& ❛❣♦✱ ✇❤❡♥ ◆✐❝❦ ✇❛& ❛, ❤♦♠❡ ❜✉, &,✐❧❧ ✇♦"❦✐♥❣ ✇✐,❤ ♠❡ ♦♥ ♠② ✜"&, ♣❛♣❡" ❜② &❡♥❞✐♥❣ ❤✐& "❡✈✐&✐♦♥& ❜② ❊✲♠❛✐❧&✳ ❆, ✶✵✿✸✵ 9▼✱ ❤❡ ❊✲♠❛✐❧❡❞ ♠❡✿ ✏■ ❤❛✈❡ ,♦ ❧❡❛✈❡ ❢♦" ❛ ✇❤✐❧❡ ,♦ ❣✐✈❡ ♠② ❜❛❜② ❣✐"❧ ❛ &❤♦✇❡"✱ ❛♥❞ ✇✐❧❧ ❝♦♠❡ ❜❛❝❦ ✐♥ ❤❛❧❢ ❛♥ ❤♦✉"✳✑ ■, ✐& ❤❛"❞ ,♦ ❡①♣"❡&& ♠② ❣"❛,✐,✉❞❡ ,♦ ❤✐♠✱ ❜✉, ■ ❦♥♦✇ ,❤❛, ■ ♦✇❡ ❤✐♠ &♦ ♠✉❝❤✳ ■, ✐& ❛❧&♦ ♠② ❣"❡❛,❡&, ♣❧❡❛&✉"❡ ,♦ ✇♦"❦ ✉♥❞❡" ,❤❡ &✉♣❡"✈✐&✐♦♥ ♦❢ 9"♦❢✳ ❉✉❣❡❧❛② ✇❤♦ &❤❛"❡❞ ✇✐,❤ ♠❡ ❤✐& "✐❝❤ ❡①♣❡"✐❡♥❝❡ ✐♥ ❜♦,❤ "❡&❡❛"❝❤ ❛♥❞ ,❡❛❝❤✐♥❣✱ ❛♥❞ ❣❛✈❡ ♠❡ ❛ ❧♦, ♦❢ ✇♦♥❞❡"❢✉❧ ✐❞❡❛& ♦♥ ♠② "❡&❡❛"❝❤✳ ▼② &✐♥❝❡"❡ ❛♣♣"❡❝✐❛,✐♦♥ ❛❧&♦ ❣♦❡& ,♦ ♠② ,❤❡&✐& ❝♦♠♠✐,,❡❡ ♠❡♠❜❡"& ❢♦" ,❤❡✐" &✉♣♣♦",&✳ ■ ✇♦✉❧❞ ❧✐❦❡ ,♦ ,❤❛♥❦ ❛❧❧ ,❤❡ ❥✉"② ♠❡♠❜❡"& ❢♦" ,❤❡✐" ♣"❡❝✐♦✉& ,✐♠❡ ,♦ "❡❛❞ ♠② ♠❛♥✉&❝"✐♣,✳ ■ ❛❧&♦ ✇❛♥, ,♦ ,❤❛♥❦ ♠② ❝✉""❡♥, ❛♥❞ ♣"❡✈✐♦✉& ❝♦❧❧❡❣❡&✱ ✐♥❝❧✉❞✐♥❣ ❆♥,✐,③❛ ❉❛♥,❝❤❡✈❛✱ ◆❡&❧✐ ❊"❞♦❣♠✉&✱ ❈❛"♠❡❧♦ ❱❡❧❛"❞♦✱ ❘✉✐ ▼✐♥✱ ❍❛❥❡" ❋"❛❞✐✱ ◆❡&❧✐❤❛♥ ❑♦&❡✱ ❆♥❞"❡❛ ▼❊▲▲❊✱ ❆&♠❛❛ ❋✐❧❧❛,"❡✱ ❈❤"✐&,❡❧❧❡ ❨❡♠❞❥✐ ❚❝❤❛&&✐✱ ❋❡❞❡"✐❝♦ ❆❧❡❣"❡✱ ●✐♦✈❛♥♥✐ ❙♦❧❞✐ ❛♥❞ ▲❡❡❧❛ ●✉❞✉♣✉❞✐ ✇❤♦ &❤❛"❡❞ ❦♥♦✇❧❡❞❣❡ ❛♥❞ ❡①♣❡"✐❡♥❝❡ ✇✐,❤ ♠❡ ❤❛❞ ❤❛✈❡ ♣❧❡❛&❛♥, ❞✐&❝✉&&✐♦♥&✳ ■ ♠✉&, ❛❧&♦ ,❤❛♥❦ ,❤❡ ♠❡♠❜❡"& ♦❢ ✏❊❯❘❊❈❖▼ ❈❤✐♥❡&❡ ,❡❛♠✑✱ ✐♥❝❧✉❞✐♥❣ ❳✐❛♦❧❛♥ ❙❤❛✱ ❍❡♥❣ ❈✉✐✱.

(5) ✹ ❳✉❡❧✐❛♥❣ ▲✐✉✱ ❘✉✐ ▼✐♥✱ ❑❛✐❥✐❡ ❩❤♦✉✱ ❙❤❡♥❣②✉♥ ▲✐✉✱ ❳✐❛♦❤✉ ❲✉✱ ❍❛✐❢❛♥ ❨✐♥✱ ❳✐♥♣✐♥❣ ❨✐✱ ◗✐❛♥:✉✐ ▲✐✱ ❏✐♥②✉❛♥ ❈❤❡♥ ❢:♦♠ ✇❤♦♠ ■ ❤❛✈❡ ❧❡❛:♥A ❡♥♦:♠♦✉B ❦♥♦✇❧❡❞❣❡ ✐♥ ❜♦A❤ :❡B❡❛:❝❤ ❛♥❞ ❧✐❢❡✳ ■ ✇♦✉❧❞ ❧✐❦❡ A♦ A❤❛♥❦ ❛❧❧ ♠② ❢:✐❡♥❞B ❛A ❊❯❘❊❈❖▼ ❢♦: A❤❡ ❝♦❧♦✉:❢✉❧ ❧✐❢❡ ■ ❡♥❥♦②❡❞ ❞✉:✐♥❣ A❤❡ ♣❛BA A❤:❡❡ ②❡❛:B✳ ❆A ❧❛BA✱ ■ ✇♦✉❧❞ ❣✐✈❡ ♠② ❤❡❛:A❢❡❧A A❤❛♥❦B A♦ ♠② ❢❛♠✐❧②✳ ▼② ♣❛:❡♥AB ❛❧✇❛②B ❡♥❝♦✉:❛❣❡ ♠❡ ✇❤❡♥ ■ ❡①♣❡:✐❡♥❝❡❞ ❛ ❞✐✣❝✉❧A A✐♠❡✳ ❋✐♥❛❧❧②✱ ♠② ❧♦✈❡ ❣♦❡B A♦ ♠② ✇✐❢❡ ❏✐♦♥❣❥✐♦♥❣ ▼♦✱ ✇❤♦ ❤❛B B❤❛:❡❞ ✶✵✲②❡❛:B A✐♠❡ ✇✐A❤ ♠❡ ❛♥❞ ❛❧✇❛②B B✉♣♣♦:A❡❞ ♠❡✳.

(6) ❆❜"#$❛❝# ❇✐♦♠❡%&✐❝ ❞❛%❛ ✐* ♦❢%❡♥ &❡♣&❡*❡♥%❡❞ ❜② ❤✐❣❤✲❞✐♠❡♥*✐♦♥❛❧ ❢❡❛%✉&❡ ✈❡❝%♦&* ✇❤✐❝❤ ❝♦♥%❛✐♥ *✐❣♥✐❢✲ ✐❝❛♥% ✐♥%❡&✲*❡**✐♦♥ ✈❛&✐❛%✐♦♥✳ ❊✣❝✐❡♥% ❞✐♠❡♥*✐♦♥❛❧✐%② &❡❞✉❝%✐♦♥ %❡❝❤♥✐:✉❡* ❛&❡ %❤✉* ♥❡❡❞❡❞ ✐♥ ♦&❞❡& %♦ ❡①%&❛❝% ❝❧❛**✲❞✐*❝&✐♠✐♥❛%✐✈❡✱ ❧♦✇✲❞✐♠❡♥*✐♦♥❛❧ ❢❡❛%✉&❡* ❛♥❞ %♦ ❛%%❡♥✉❛%❡ ✉♥✇❛♥%❡❞ ✈❛&✐❛%✐♦♥* ✇❤✐❝❤ ✐* &❡❞✉♥❞❛♥% %♦ &❡❝♦❣♥✐%✐♦♥✳ ❙✉❝❤ ❞✐*❝&✐♠✐♥❛%✐✈❡ ❞✐♠❡♥*✐♦♥❛❧✐%② &❡❞✉❝%✐♦♥ %❡❝❤♥✐:✉❡* ❣❡♥❡&❛❧❧② ❢♦❧❧♦✇ ❛ *✉♣❡&✈✐*❡❞ ❧❡❛&♥✐♥❣ *❝❤❡♠❡✱ ✐♥ ✇❤✐❝❤ ❛ *✉❜*♣❛❝❡ ♣&♦❥❡❝%✐♦♥ ✐* ❧❡❛&♥❡❞ ✇✐%❤ ❢❡❛%✉&❡✲❧❛❜❡❧ ♣❛✐&*✳ ❍♦✇❡✈❡&✱ ❧❛❜❡❧❧❡❞ %&❛✐♥✐♥❣ ❞❛%❛ ✐* ❣❡♥❡&❛❧❧② ❧✐♠✐%❡❞ ✐♥ :✉❛♥%✐%② ❛♥❞ ♦❢%❡♥ ❞♦❡* ♥♦% &❡❧✐❛❜❧② &❡♣&❡*❡♥% %❤❡ ✐♥%❡&✲*❡**✐♦♥ ✈❛&✐❛%✐♦♥ ❡♥❝♦✉♥%❡&❡❞ ✐♥ %❡*% ❞❛%❛✳ ❚❤❡ ❧✐♠✐%❡❞ *✐③❡ ♦❢ ❧❛❜❡❧❧❡❞ %&❛✐♥✐♥❣ *❡% ♦❢%❡♥ ❧❡❛❞* %♦ ❜✐❛*❡❞ ♣&♦❥❡❝%✐♦♥ ♠❛%&✐❝❡* ❛♥❞ ❞❡❣&❛❞❡❞ &❡❝♦❣♥✐%✐♦♥ ♣❡&❢♦&♠❛♥❝❡✳ ❚❤✐* %❤❡*✐* ♣&♦♣♦*❡* %♦ ✉*❡ ♠✉❧%✐✲✈✐❡✇ ❞✐♠❡♥*✐♦♥❛❧✐%② &❡❞✉❝%✐♦♥ ✭▼❱❉❘✮ ✇❤✐❝❤ ❛✐♠* %♦ ❡①%&❛❝% ❞✐*❝&✐♠✐♥❛%✐✈❡ ❢❡❛%✉&❡* ✐♥ ♠✉❧%✐✲♠♦❞❛❧ ❜✐♦♠❡%&✐❝ *②*%❡♠*✱ ✇❤❡&❡ ❞✐✛❡&❡♥% ♠♦❞❛❧✲ ✐%✐❡* ❛&❡ &❡❣❛&❞❡❞ ❛* ❞✐✛❡&❡♥% ✈✐❡✇* ♦❢ %❤❡ *❛♠❡ ❞❛%❛✳ ■♥*%❡❛❞ ♦❢ %&❛✐♥✐♥❣ ♦♥ ❢❡❛%✉&❡✲❧❛❜❡❧ ♣❛✐&*✱ ▼❱❉❘ ♣&♦❥❡❝%✐♦♥* ❛&❡ %&❛✐♥❡❞ ♦♥ ❢❡❛%✉&❡✲❢❡❛%✉&❡ ♣❛✐&* ✇❤❡&❡ ❧❛❜❡❧ ✐♥❢♦&♠❛%✐♦♥ ✐* ♥♦% &❡:✉✐&❡❞✳ ❙✐♥❝❡ ✉♥❧❛❜❡❧❧❡❞ ❞❛%❛ ✐* ❡❛*✐❡& %♦ ❛❝:✉✐&❡ ✐♥ ❧❛&❣❡ :✉❛♥%✐%✐❡*✱ ❛♥❞ ❜❡❝❛✉*❡ ♦❢ %❤❡ ♥❛%✉&❛❧ ❝♦✲❡①✐*%❡♥❝❡ ♦❢ ♠✉❧%✐♣❧❡ ✈✐❡✇* ✐♥ ♠✉❧%✐✲♠♦❞❛❧ ❜✐♦♠❡%&✐❝ ♣&♦❜❧❡♠*✱ ❞✐*❝&✐♠✐♥❛♥%✱ ❧♦✇✲❞✐♠❡♥*✐♦♥❛❧ *✉❜*♣❛❝❡* ❝❛♥ ❜❡ ❧❡❛&♥% ✉*✐♥❣ %❤❡ ♣&♦♣♦*❡❞ ▼❱❉❘ ❛♣♣&♦❛❝❤❡* ✐♥ ❛ ❧❛&❣❡❧② ✉♥*✉♣❡&✈✐*❡❞ ♠❛♥♥❡&✳ ❆❝❝♦&❞✐♥❣ %♦ ❞✐✛❡&❡♥% ❢✉♥❝%✐♦♥❛❧✐%✐❡* ♦❢ ❜✐♦♠❡%&✐❝ *②*%❡♠*✱ ♥❛♠❡❧② &❡❝♦❣♥✐%✐♦♥ ✭✐♥❝❧✉❞✲ ✐♥❣ ✐❞❡♥%✐✜❝❛%✐♦♥ ❛♥❞ ✈❡&✐✜❝❛%✐♦♥✮✱ ❝❧✉*%❡&✐♥❣✱ ❛♥❞ &❡%&✐❡✈❛❧✱ ✇❡ ♣&♦♣♦*❡ %❤&❡❡ ▼❱❉❘ ❢&❛♠❡✲ ✇♦&❦* ✇❤✐❝❤ ♠❡❡% %❤❡ &❡:✉✐&❡♠❡♥%* ❢♦& ❡❛❝❤ ❢✉♥❝%✐♦♥❛❧✐%②✳ ❚❤❡ ♣&♦♣♦*❡❞ ❛♣♣&♦❛❝❤❡*✱ ❤♦✇✲ ❡✈❡&✱ *❤❛&❡ %❤❡ *❛♠❡ *♣✐&✐%✿ ❛❧❧ ♠❡%❤♦❞* ❛✐♠ %♦ ❧❡❛&♥ ❛ ♣&♦❥❡❝%✐♦♥ ❢♦& ❡❛❝❤ ✈✐❡✇ *✉❝❤ %❤❛% ❛ ❝❡&%❛✐♥ ❢♦&♠ ♦❢ ❛❣&❡❡♠❡♥% ✐* ❛%%❛✐♥❡❞ ✐♥ %❤❡ *✉❜*♣❛❝❡* ❛❝&♦** ❞✐✛❡&❡♥% ✈✐❡✇*✳ ❚❤❡ ♣&♦♣♦*❡❞ ▼❱❉❘ ❢&❛♠❡✇♦&❦* ❝❛♥ %❤✉* ❜❡ ✉♥✐✜❡❞ ✐♥%♦ ♦♥❡ ❣❡♥❡&❛❧ ❢&❛♠❡✇♦&❦ ❢♦& ♠✉❧%✐✲✈✐❡✇ ❞✐♠❡♥✲ *✐♦♥❛❧✐%② &❡❞✉❝%✐♦♥ %❤&♦✉❣❤ *✉❜*♣❛❝❡ ❛❣&❡❡♠❡♥%✳ ❲❡ &❡❣❛&❞ %❤✐* ♥♦✈❡❧ ❝♦♥❝❡♣% ♦❢ *✉❜*♣❛❝❡ ❛❣&❡❡♠❡♥% %♦ ❜❡ %❤❡ ♣&✐♠❛&② ❝♦♥%&✐❜✉%✐♦♥ ♦❢ %❤✐* %❤❡*✐*✳.

(7)

(8) ❈♦♥#❡♥#% ✶ ■♥#$♦❞✉❝#✐♦♥. ✶✶. ✶✳✶. ❈♦♥%&✐❜✉%✐♦♥* ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✶✷. ✶✳✷. ❖✉%❧✐♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✶✼. ✷ ❇✐♦♠❡#$✐❝ ❙②0#❡♠0 ❛♥❞ ❉✐♠❡♥0✐♦♥❛❧✐#② ❘❡❞✉❝#✐♦♥. ✶✾. ✷✳✶. ❇✐♦♠❡%&✐❝* ❙②*%❡♠* ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✶✾. ✷✳✷. ❋✉♥❝%✐♦♥❛❧✐%✐❡* ♦❢ ❇✐♦♠❡%&✐❝* ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✷✶. ✷✳✷✳✶. ❱❡&✐✜❝❛%✐♦♥ ❛♥❞ ✐❞❡♥%✐✜❝❛%✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✷✶. ✷✳✷✳✷. ❈❧✉*%❡&✐♥❣ ❛♥❞ &❡%&✐❡✈❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✷✸. ❇✐♦♠❡%&✐❝ ❋❡❛%✉&❡ ❘❡♣&❡*❡♥%❛%✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✷✺. ✷✳✸✳✶. ▲♦❝❛❧ ❜✐♥❛&② ♣❛%%❡&♥* ✭▲❇D✮ ❢♦& ❢❛❝❡ &❡♣&❡*❡♥%❛%✐♦♥. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✷✻. ✷✳✸✳✷. ●❛✉**✐❛♥ ♠✐①%✉&❡ ♠♦❞❡❧* ✭●▼▼✮ ❢♦& ✈♦✐❝❡ &❡♣&❡*❡♥%❛%✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳. ✷✽. ❈✉&*❡ ♦❢ ❉✐♠❡♥*✐♦♥❛❧✐%② ❛♥❞ ❉✐♠❡♥*✐♦♥❛❧✐%② ❘❡❞✉❝%✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✵. ✷✳✹✳✶. ❈✉&*❡ ♦❢ ❞✐♠❡♥*✐♦♥❛❧✐%② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✶. ✷✳✹✳✷. ❉✐♠❡♥*✐♦♥❛❧✐%② ❘❡❞✉❝%✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✷. ▼✉❧%✐♣❧❡ ❘❡♣&❡*❡♥%❛%✐♦♥ ♦❢ ❇✐♦♠❡%&✐❝ ❉❛%❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✻. ✷✳✺✳✶. ▼✉❧%✐✲♠♦❞❛❧ ❜✐♦♠❡%&✐❝* ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✻. ✷✳✺✳✷. ❋✉*✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✼. ✷✳✸. ✷✳✹. ✷✳✺. ✷✳✻ ✷✳✼. D&♦❜❧❡♠ ❙%❛%❡♠❡♥%✿ ❉✐*❝&✐♠✐♥❛%✐✈❡ ❋❡❛%✉&❡ ❊①%&❛❝%✐♦♥ ❢&♦♠ ❯♥❧❛❜❡❧❧❡❞✱ ▼✉❧%✐✲✈✐❡✇ ❉❛%❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✽. ❙✉♠♠❛&② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✽. ✸ ❙#❛#❡✲♦❢✲#❤❡✲❛$# ✐♥ ▼❱❉❘. ✹✶. ✸✳✶. ▼✉❧%✐✲❱✐❡✇ ❉✐♠❡♥*✐♦♥❛❧✐%② ❘❡❞✉❝%✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✶. ✸✳✷. ▼❱❉❘ ❇❛*❡❞ ♦♥ ❈❛♥♦♥✐❝❛❧ ❈♦&&❡❧❛%✐♦♥ ❆♥❛❧②*✐* ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✷.

(9) ❈♦♥#❡♥#%. ✽ ✸✳✷✳✶. %&✐♥❝✐♣❧❡- ♦❢ ❈❈❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✷. ✸✳✷✳✷. ❆♣♣❧✐❝❛4✐♦♥ ♦❢ ❈❈❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✸. ▼❱❉❘ ❇❛-❡❞ ♦♥ ❙✐♠✐❧❛&✐4② ●&❛♣❤- ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✹. ✸✳✸✳✶. ▼✉❧4✐✲✈✐❡✇ -♣❡❝4&❛❧ ❡♠❜❡❞❞✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✹. ✸✳✸✳✷. ▼✉❧4✐✲✈✐❡✇ ❙♣❡❝4&❛❧ ❝❧✉-4❡&✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✻. ✸✳✹. %&♦♣♦-❡❞ ▼❱❉❘ ❆♣♣&♦❛❝❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✽. ✸✳✺. ❙✉♠♠❛&② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✵. ✸✳✸. ✹ ▼❱❉❘ ❜② ■♥❝*❡♠❡♥-❛❧ ❈♦✲-*❛✐♥✐♥❣. ✺✶. ✹✳✶. ▼♦4✐✈❛4✐♦♥- ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✶. ✹✳✷. ▲❉❆ ✱❈♦✲4&❛✐♥✐♥❣ ❛♥❞ ❈♦✲▲❉❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✹. ✹✳✷✳✶. ▲❉❆ ❛♥❞ -♠❛❧❧ -❛♠♣❧❡ -✐③❡ ♣&♦❜❧❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✹. ✹✳✷✳✷. ❈♦✲4&❛✐♥✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✺. ✹✳✷✳✸. ❈♦✲▲❉❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✻. ❆♣♣❧✐❝❛4✐♦♥ 4♦ ❙❡♠✐✲-✉♣❡&✈✐-❡❞ ❆✉❞✐♦✲✈✐-✉❛❧ ❙♣❡❛❦❡& ❘❡❝♦❣♥✐4✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳. ✺✼. ✹✳✸✳✶. ❋❡❛4✉&❡ ❡①4&❛❝4✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✽. ✹✳✸✳✷. ❙✉❜-♣❛❝❡ ❧❡❛&♥✐♥❣. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✾. ✹✳✸✳✸. ■❞❡♥4✐✜❝❛4✐♦♥ ❛♥❞ ✈❡&✐✜❝❛4✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✵. ❊①♣❡&✐♠❡♥4❛❧ ✇♦&❦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✶. ✹✳✹✳✶. ▼♦❜✐♦ ❛✉❞✐♦✲✈✐-✉❛❧ ❞❛4❛❜❛-❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✶. ✹✳✹✳✷. ❊①♣❡&✐♠❡♥4❛❧ &❡-✉❧4- ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✷. ❈♦♣✐♥❣ ✇✐4❤ ❖✉4✲♦❢✲❝❧❛-- ❉❛4❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✹. ✹✳✺✳✶. ❙♣❛&-❡ &❡♣&❡-❡♥4❛4✐♦♥ ❝❧❛--✐✜❡& ❛♥❞ ♦✉4✲♦❢✲❝❧❛-- -❛♠♣❧❡ ❞❡4❡❝4✐♦♥ ✳ ✳. ✻✺. ✹✳✺✳✷. ❈♦✲▲❉❆✲❙❘❈ ❛❧❣♦&✐4❤♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✼. ❊①♣❡&✐♠❡♥4❛❧ ❘❡-✉❧4- ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✾. ✹✳✻✳✶. ❉❛4❛❜❛-❡ ❛♥❞ ♣&♦4♦❝♦❧- ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✾. ✹✳✻✳✷. ❘❡-✉❧4- ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✵. ❙✉♠♠❛&② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✷. ✹✳✸. ✹✳✹. ✹✳✺. ✹✳✻. ✹✳✼. ✺ ▼❱❉❘ ❜② ❙✉❜9♣❛❝❡ ❈❧✉9-❡*✐♥❣ ❆❣*❡❡♠❡♥-. ✼✸. ✺✳✶. ▼♦4✐✈❛4✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✹. ✺✳✷. ▲❉❆✱ ❦✲♠❡❛♥-✱ ❛♥❞ ❝♦✲4&❛✐♥✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✺. ✺✳✷✳✶. ▲❉❆ ❛♥❞ ❦✲♠❡❛♥- ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✺. ✺✳✷✳✷. ❈♦✲4&❛✐♥✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✻. ▼✉❧4✐✲✈✐❡✇ -✉❜-♣❛❝❡ ❝❧✉-4❡&✐♥❣✿ ❛ ❝♦✲4&❛✐♥✐♥❣ ❛❧❣♦&✐4❤♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✼. ✺✳✸.

(10) ❈♦♥#❡♥#%. ✾. ✺✳✸✳✶. ❆♥ ❛❧❣♦+✐-❤♠✿ ❈♦❑♠▲❉❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✼. ✺✳✸✳✷. ❆♥ ✐❧❧✉8-+❛-✐✈❡ ❡①❛♠♣❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✾. ✺✳✸✳✸. ▼❛-❤♠❛-✐❝❛❧ ❛♥❛❧②8✐8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✽✶. ✺✳✸✳✹. ❊①-❡♥8✐♦♥8 ♦❢ ❈♦❑♠▲❉❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✽✸. ✺✳✹. ❘❡❧❛-❡❞ ✇♦+❦8 ❛♥❞ ❛♥❛❧②8✐8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✽✺. ✺✳✺. ❊①♣❡+✐♠❡♥-8 ❛♥❞ ❞✐8❝✉88✐♦♥8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✽✼. ✺✳✺✳✶. ❊✈❛❧✉❛-✐♦♥ ♠❡-+✐❝8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✽✽. ✺✳✺✳✷. ❆✉❞✐♦✲✈✐8✉❛❧ 8♣❡❛❦❡+ ❝❧✉8-❡+✐♥❣ ✭❝♦♥❞✐-✐♦♥❛❧ ✐♥❞❡♣❡♥❞❡♥❝❡ ❛88✉♠♣-✐♦♥ 8❛-✐8✜❡❞✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✳✺✳✸ ✺✳✻. ✽✾. ❍❛♥❞✇+✐--❡♥ ❞✐❣✐- ❝❧✉8-❡+✐♥❣ ❛♥❞ -❡①- ❞♦❝✉♠❡♥- ❝❧✉8-❡+✐♥❣ ✭❈♦♥❞✐-✐♦♥❛❧ ✐♥❞❡♣❡♥❞❡♥❝❡ ❛88✉♠♣-✐♦♥ ♥♦- ❢✉❧❧② 8❛-✐8✜❡❞✮ ✳ ✳ ✳ ✳ ✳ ✳. ✾✸. ❙✉♠♠❛+② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✾✼. ✻ ▼❱❉❘ ❜② ❙✉❜)♣❛❝❡ ●/❛♣❤ ❆❣/❡❡♠❡♥5. ✾✾. ✻✳✶. ▼♦-✐✈❛-✐♦♥8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✳✷. ▲♦❝❛❧✐-② O+❡8❡+✈✐♥❣ O+♦❥❡❝-✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷. ✻✳✸. ❈♦✲▲OO ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸. ✻✳✹. ✻✳✺. ✾✾. ✻✳✸✳✶. ❖❜❥❡❝-✐✈❡ ❢✉♥❝-✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸. ✻✳✸✳✷. ❆❧❣♦+✐-❤♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹. ✻✳✸✳✸. ❆♣♣❧✐❝❛-✐♦♥ -♦ ♠✉❧-✐❜✐♦♠❡-+✐❝ +❡-+✐❡✈❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺. ❊①♣❡+✐♠❡♥-❛❧ +❡8✉❧-8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ✻✳✹✳✶. ❉❛-❛❜❛8❡8 ❛♥❞ O+♦-♦❝♦❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼. ✻✳✹✳✷. ❘❡8✉❧-8 ❛♥❞ ❛♥❛❧②8✐8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾. ❙✉♠♠❛+② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹. ✼ ❈♦♥❝❧✉)✐♦♥. ✶✶✺. ✼✳✶. ❈♦♥-+✐❜✉-✐♦♥8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺. ✼✳✷. ❋✉-✉+❡ ❲♦+❦. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼. ❆ ❙❡♠✐✲)✉♣❡/✈✐)❡❞ ❋❛❝❡ ❘❡❝♦❣♥✐5✐♦♥ ✇✐5❤ ▲❉❆ ❙❡❧❢✲5/❛✐♥✐♥❣. ✶✶✾. ❆✳✶ ■♥-+♦❞✉❝-✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ❆✳✷ ▲❉❆ ❙❡❧❢✲-+❛✐♥✐♥❣ ❆❧❣♦+✐-❤♠. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶. ❆✳✷✳✶ ❇❛8❡❧✐♥❡ 8②8-❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶ ❆✳✸ ▲❉❆ 8❡❧❢✲-+❛✐♥✐♥❣ ❛❧❣♦+✐-❤♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ❆✳✹ ❊①♣❡+✐♠❡♥-❛❧ ❘❡8✉❧-8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✸ ❆✳✹✳✶ ❚+❛♥❞✉❝-✐✈❡ ❝♦♥✜❣✉+❛-✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹.

(11) ❈♦♥#❡♥#%. ✶✵. ❆✳✹✳✷ ❙❡♠✐✲+✉♣❡.✈✐+❡❞ ❝♦♥✜❣✉.❛7✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺ ❆✳✹✳✸ ❙✐♥❣❧❡ 7.❛✐♥✐♥❣ ✐♠❛❣❡ 7❡+7 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✻ ❆✳✺ ❈♦♥❝❧✉+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✼. ❇✐❜❧✐♦❣&❛♣❤✐❡. ✶✸✽.

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(13) ❈❤❛♣$❡& ✶ ✕ ■♥$&♦❞✉❝$✐♦♥. ✶✷. ♦# ✇❤✐❝❤ ❡♥#♦❧❧❡❞ ✐❞❡♥,✐,② ,❤❡ ,❡., .❛♠♣❧❡ ❜❡❧♦♥❣. ,♦✳ ■♥ ♠♦., .,❛,❡✲♦❢✲,❤❡✲❛#, ❜✐♦♠❡,#✐❝ .②.,❡♠.✱ ❞❛,❛ .❛♠♣❧❡. ❛#❡ ♦❢,❡♥ #❡♣#❡.❡♥,❡❞ ❜② ❤✐❣❤✲❞✐♠❡♥.✐♦♥❛❧ ❢❡❛,✉#❡ ✈❡❝,♦#. ✭❡✳❣✳✱ ❧♦✲ ❝❛❧ ❜✐♥❛#② ♣❛,,❡#♥. ✭▲❇>✮ ❢♦# ❢❛❝❡ #❡❝♦❣♥✐,✐♦♥ ❬❆❤♦♥❡♥ ❡, ❛❧✳✱ ✷✵✵✻❪ ❛♥❞ ●❛✉..✐❛♥ ♠✐①,✉#❡ ♠♦❞❡❧ ✭●▼▼✮ .✉♣❡#✈❡❝,♦#. ❢♦# .♣❡❛❦❡# #❡❝♦❣♥✐,✐♦♥ ❬❈❛♠♣❜❡❧❧ ❡, ❛❧✳✱ ✷✵✵✻❪✮✳ ❚❤❡ ❤✐❣❤ ❞✐♠❡♥.✐♦♥❛❧✐,② ♦❢ ❜✐♦♠❡,#✐❝ ❢❡❛,✉#❡. ✐♥❝✉# ❤❡❛✈② .,♦#❛❣❡ ❛♥❞ ❝♦♠♣✉,❛,✐♦♥❛❧ ❜✉#❞❡♥.✱ ❛♥❞ ♠♦#❡ ✐♠♣♦#,❛♥,❧②✱ ,❤❡ .♦✲❝❛❧❧❡❞ ❝✉"#❡✲♦❢✲❞✐♠❡♥#✐♦♥❛❧✐.② ❬❇❡❧❧♠❛♥✱ ✶✾✻✶❪ ❝❛♥ ✐♠♣❛❝, ♦♥ ,❤❡ #❡❝♦❣♥✐,✐♦♥ ♣❡#❢♦#♠❛♥❝❡ ✐♥ ,❤❡ ❢♦❧❧♦✇✐♥❣ ❝♦♠♣❛#✐.♦♥ ♦# ❝❧❛..✐✜❝❛,✐♦♥ ♠♦❞✉❧❡✳ ❉✐✣❝✉❧,✐❡. ❛..♦❝✐❛,❡❞ ✇✐,❤ ,❤❡ ❤✐❣❤ ❞✐♠❡♥.✐♦♥❛❧✐,② ❛#❡ ❣❡♥❡#❛❧❧② ♦✈❡#❝♦♠❡ ,❤#♦✉❣❤ ,❤❡ ❛♣♣❧✐❝❛,✐♦♥ ♦❢ ❞✐♠❡♥.✐♦♥❛❧✐,② #❡❞✉❝,✐♦♥ ✭❉❘✮ ,❡❝❤♥✐P✉❡. ❬❏♦❧❧✐✛❡✱ ✷✵✵✺✱ ❇❛#,❧❡,, ❡, ❛❧✳✱ ✷✵✵✷✱ ◆✐②♦❣✐✱ ✷✵✵✹✱ ❇❡❧❤✉♠❡✉# ❡, ❛❧✳✱ ✶✾✾✼❪✱ ✇❤✐❝❤ ❧♦♦❦ ❢♦# ❛ ❧♦✇❡# ❞✐♠❡♥.✐♦♥❛❧ #❡♣#❡.❡♥,❛,✐♦♥ ♦❢ ,❤❡ ❤✐❣❤✲❞✐♠❡♥.✐♦♥❛❧ ❞❛,❛✳ ❉❡♣❡♥❞✐♥❣ ♦♥ ✇❤❡,❤❡# ❧❛❜❡❧ ✐♥❢♦#♠❛,✐♦♥ ✐. ♥❡❡❞❡❞✱ ❉❘ ,❡❝❤✲ ♥✐P✉❡. ❝❛♥ ❜❡ ❜#♦❛❞❧② ❝❛,❡❣♦#✐③❡❞ ✐♥,♦ .✉♣❡#✈✐.❡❞ ♦# ✉♥.✉♣❡#✈✐.❡❞ ♠❡,❤♦❞.✳ ❆ ❞✐❧❡♠♠❛ ❛#✐.❡. ❢#♦♠ ,❤❡ ,#❛❞❡✲♦✛ ❜❡,✇❡❡♥ ,❤❡ ❛✈❛✐❧❛❜✐❧✐,② ♦❢ ❧❛❜❡❧ ✐♥❢♦#♠❛,✐♦♥ ❛♥❞ ,❤❡ ❞✐.❝#✐♠✐♥❛✲ ,✐✈❡ ♣♦✇❡# ♦❢ ,❤❡ ❡①,#❛❝,❡❞ ❧♦✇✲❞✐♠❡♥.✐♦♥❛❧ ❢❡❛,✉#❡.✳ ❙✉♣❡#✈✐.❡❞ ♠❡,❤♦❞. .✉❝❤ ❛. ▲✐♥❡❛# ❉✐.❝#✐♠✐♥❛♥, ❆♥❛❧②.✐. ✭▲❉❆✮ ❬❇❡❧❤✉♠❡✉# ❡, ❛❧✳✱ ✶✾✾✼❪ ❤❛✈❡ ❤✐❣❤ ❞✐.❝#✐♠✐♥❛,✐✈❡ ♣♦✇❡#✱ ❜✉, #❡P✉✐#❡ ❧❛#❣❡ P✉❛♥,✐,② ♦❢ ♠❛♥✉❛❧❧② ❧❛❜❡❧❧❡❞ ,#❛✐♥✐♥❣ ❞❛,❛✳ ❯♥.✉♣❡#✈✐.❡❞ ♠❡,❤♦❞. .✉❝❤ ❛. >#✐♥❝✐♣❧❡ ❈♦♠♣♦♥❡♥, ❆♥❛❧②.✐. ✭>❈❆✮ ❬❏♦❧❧✐✛❡✱ ✷✵✵✺❪ ❞♦ ♥♦, #❡P✉✐#❡ ❝❧❛.. ❧❛❜❡❧.✱ ❜✉, ❣❡♥❡#❛❧❧② ❧❛❝❦ ❞✐.❝#✐♠✐♥❛,✐✈❡ ♣♦✇❡#✳ ■♥ ❜✐♦♠❡,#✐❝ ✐❞❡♥,✐✜❝❛,✐♦♥ ❛♥❞ ✈❡#✐✜❝❛,✐♦♥ .❡,,✐♥❣.✱ ♠❛♥✉❛❧❧② ❧❛❜❡❧❧❡❞ ❞❛,❛ ✐. ♥♦#♠❛❧❧② ❧✐♠✐,❡❞ ✐♥ ♥✉♠❜❡# ✇❤✐❧❡ ❧❛#❣❡ ❛♠♦✉♥, ♦❢ ✉♥❧❛❜❡❧❧❡❞ ❞❛,❛ ❝❛♥ ❜❡ ❡❛.✐❧② ❛❝P✉✐#❡❞ ❞✉#✐♥❣ ,❤❡ ♥♦#♠❛❧ .②.,❡♠ ✉.❡✳ ■♥ ♠✉❧,✐✲♠♦❞❛❧ ❜✐♦♠❡,#✐❝.✱ ❞✐✛❡#❡♥, ❜✐♦♠❡,#✐❝ ♠♦❞❛❧✐,✐❡. ❝❛♥ ❢♦#♠ ❞✐✛❡#❡♥, ✐♥♣✉,. ,♦ ❝❧❛..✐✜❝❛,✐♦♥ ❛❧❣♦#✐,❤♠.✳ ▼✉❧,✐♠♦❞❛❧ ❜✐♦♠❡,#✐❝ .②.,❡♠. ❝❛♥ ♦❜,❛✐♥ ♠✉❧,✐♣❧❡ .❡,. ♦❢ ✐♥❢♦#✲ ♠❛,✐♦♥ ❢#♦♠ ,❤❡ .❛♠❡ ♠♦❞❛❧✐,② ✭✐✳❡✳✱ ✷❉✰✸❉ ❢❛❝❡ #❡❝♦❣♥✐,✐♦♥✮ ❬❇♦✇②❡# ❡, ❛❧✳✱ ✷✵✵✻❪ ♦# ✐♥❢♦#♠❛,✐♦♥ ❢#♦♠ ❞✐✛❡#❡♥, ❜✐♦♠❡,#✐❝ ♠♦❞❛❧✐,✐❡. ✭✐✳❡✳ ❜✐♦♠❡,#✐❝ .②.,❡♠ ✇✐,❤ ❢❛❝❡ ❛♥❞ ✈♦✐❝❡✮✳ ❚❤❡ ❢✉.✐♦♥ ♦❢ ♠♦❞❛❧✐,✐❡. #❡♠❛✐♥. ❛ ❝❤❛❧❧❡♥❣✐♥❣ ♣#♦❜❧❡♠ ❛♥❞ ✐. ❣❡♥❡#❛❧❧② ,#❡❛,❡❞ ✐♥ ✐.♦❧❛,✐♦♥ ,♦ ,❤❛, ♦❢ ❤✐❣❤ ❞✐♠❡♥.✐♦♥❛❧✐,② ❬❘♦.. ❡, ❛❧✳✱ ✷✵✵✽❪✳ ❚❤✐. ,❤❡.✐. ,❛❝❦❧❡. ,❤❡ ❤✐❣❤ ❞✐♠❡♥.✐♦♥❛❧✐,② ♣#♦❜❧❡♠ ❛♥❞ ,❤❡ ♠✉❧,✐✲♠♦❞❛❧ ❢✉.✐♦♥ ♣#♦❜✲ ❧❡♠ ✐♥ ❛ ✉♥✐✜❡❞ ❢#❛♠❡✇♦#❦✳ ❯♥❞❡# ❛ ♠✉❧,✐✲♠♦❞❛❧ ❜✐♦♠❡,#✐❝ .❡,,✐♥❣ ❛♥❞ ❣✐✈❡♥ ❛❜✉♥❞❛♥, ✉♥❧❛❜❡❧❧❡❞ ❞❛,❛✱ ✇❡ ❛✐♠ ,♦ ❡①,#❛❝, ❤✐❣❤❧②✲❞✐.❝#✐♠✐♥❛,✐✈❡ ❢❡❛,✉#❡. ❢#♦♠ ♠✉❧,✐♣❧❡ ♠♦❞❛❧✐,✐❡. ✐♥ ❛♥ ✉♥.✉♣❡#✈✐.❡❞ ♠❛♥♥❡#✳. ✶✳✶ ❈♦♥%&✐❜✉%✐♦♥* ■♥ ,❤✐. .❡❝,✐♦♥✱ ✇❡ ❜#✐❡✢② .✉♠♠❛#✐③❡ ,❤❡ ❝♦♥,❡♥, ♦❢ ,❤❡ ,❤❡.✐. ❛♥❞ ,❤❡ ❝♦♥,#✐❜✉,✐♦♥.✳ ▼✉❧,✐✲♠♦❞❛❧ ❜✐♦♠❡,#✐❝ .②.,❡♠. ✉,✐❧✐③❡ ,✇♦ ♦# ♠♦#❡ ✐♥❞✐✈✐❞✉❛❧ ♠♦❞❛❧✐,✐❡. ,♦ ✐♠♣#♦✈❡ ,❤❡.

(14) ✶✳✶ ❈♦♥%&✐❜✉%✐♦♥*. ✶✸. "❡❝♦❣♥✐)✐♦♥ ❛❝❝✉"❛❝② ♦❢ ❝♦♥✈❡♥)✐♦♥❛❧ ✉♥✐✲♠♦❞❛❧ ♠❡)❤♦❞4✳ ■♥ ❛ ❜✐♠♦❞❛❧ ❜✐♦♠❡)"✐❝ 4②4)❡♠ ✇❤✐❝❤ ❡♠♣❧♦②4 )✇♦ ❞✐✛❡"❡♥) ♠♦❞❛❧✐)✐❡4✱ ❞❛)❛ 4❛♠♣❧❡4 ❝❛♥ ❜❡ "❡♣"❡4❡♥)❡❞ ❜② ♣❛✐"❡❞ ❢❡❛)✉"❡4. < X (1) , X (2) > ❛♥❞ ❛ 4✉❜❥❡❝) ✐❞❡♥)✐)② Y ❛4 ❛ )❛"❣❡) ✈❛"✐❛❜❧❡✳ ❙)❛)❡✲♦❢✲)❤❡✲❛") ❜✐♦♠❡)"✐❝ 4②4)❡♠4 ♦❢)❡♥ ♠❛❦❡ ✉4❡ ♦❢ ❤✐❣❤✲❞✐♠❡♥4✐♦♥❛❧ ❢❡❛)✉"❡4✱ )❤✉4 ❞✐♠❡♥4✐♦♥❛❧✐)② "❡❞✉❝)✐♦♥ ✭❉❘✮ )❡❝❤♥✐C✉❡4 ❛"❡ ♦❢)❡♥ ❛♣♣❧✐❡❞ )♦ ❛❧❧❡✈✐❛)❡ )❤❡ 4♦✲❝❛❧❧❡❞ ❝✉"4❡✲♦❢✲❞✐♠❡♥4✐♦♥❛❧✐)② ♣"♦❜❧❡♠ ✐♥ )❤❡ ❢♦❧❧♦✇✐♥❣ ❝❧❛44✐✜❝❛)✐♦♥ 4)❡♣✳ ❚❤✐4 )❤❡4✐4 "❡♣♦")4 ❛ 4)✉❞② ♦❢ ❉❘ ❛♣♣"♦❛❝❤❡4 ❢♦" ♠✉❧)✐✲♠♦❞❛❧ ❜✐♦♠❡)"✐❝4✳ ❈♦♠♠♦♥❧② "❡❢❡""❡❞ )♦ ❛4 ▼✉❧)✐✲✈✐❡✇ ❉✐♠❡♥4✐♦♥❛❧✐)② ❘❡❞✉❝)✐♦♥ ✭▼❱❉❘✮✱ )❤✐4 ✜❡❧❞ ❤❛4 ❛))"❛❝)❡❞ ❝♦♥4✐❞❡"❛❜❧❡ "❡4❡❛"❝❤ ✐♥)❡"❡4) ✐♥ "❡❝❡♥) ②❡❛"4✳ ▼♦4) ❡①✐4)✐♥❣ ▼❱❉❘ ❛❧❣♦"✐)❤♠4 ❛"❡ ❜❛4❡❞ ♦♥ ❈❛♥♦♥✐❝❛❧ ❈♦""❡❧❛)✐♦♥ ❆♥❛❧②4✐4 ✭❈❈❆✮ ❬❋♦4)❡" ❡) ❛❧✳✱ ✷✵✵✽❪ ❛♥❞ ✐)4 ✈❛"✐❛♥)4✳ ❚❤❡4❡ ❛❧❣♦"✐)❤♠4 ❣❡♥❡"❛❧❧② ❛✐♠ )♦ ❧❡❛"♥ ♣"♦❥❡❝)✐♦♥4 P (1) ❛♥❞ P (2) 4✉❝❤ )❤❛) )❤❡ ♣"♦❥❡❝)❡❞ 4❛♠♣❧❡4 P (1) X (1) ❛♥❞ P (2) X (2) ❛"❡ ♠❛①✐♠❛❧❧② ❝♦""❡❧❛)❡❞✳ ❲❤❡♥ ❛♣♣❧✐❡❞ )♦ ♣❛✐"❡❞ ❢❡❛)✉"❡4✱ )❤❡ ♠❛✐♥ ❛❞✈❛♥)❛❣❡ ♦❢ ▼❱❉❘ ♠❡)❤♦❞4 ♦✈❡" 4✐♥❣❧❡✲✈✐❡✇ ❉❘ ✐4 )❤❛) ♦♥❡ ✈✐❡✇ ❝❛♥ ❜❡ "❡❣❛"❞❡❞ ❛4 ✇❡❛❦ ❧❛❜❡❧4 ❢♦" )❤❡ ♦)❤❡"✳ ❆❝❝♦"❞✐♥❣❧②✱ ❝❧❛44✲4♣❡❝✐✜❝ ❞✐4❝"✐♠✐♥❛)✐✈❡ ❢❡❛)✉"❡4 ❝❛♥ )❤✉4 ❜❡ ❡①)"❛❝)❡❞ ❡✈❡♥ ✐❢ ❧❛❜❡❧❧❡❞ )"❛✐♥✐♥❣ 4❛♠♣❧❡4 ❛"❡ ❡✐)❤❡" ❧✐♠✐)❡❞ ✐♥ ♥✉♠❜❡" ♦" ❡♥)✐"❡❧② ❛❜4❡♥)✳ ■♥ ❝♦♥)"❛4) )♦ 4✉❝❤ ♣"❡✈✐♦✉4 ❛♣♣"♦❛❝❤❡4✱ )❤❡ ♥❡✇ ✇♦"❦ "❡♣♦")❡❞ ✐♥ )❤✐4 )❤❡4✐4 ❛❞❞"❡44❡4 )❤❡ ▼❱❉❘ ♣"♦❜❧❡♠ ❢"♦♠ ❛ ❞✐✛❡"❡♥) ❛♥❣❧❡✳ ■♥4♣✐"❡❞ ❜② )❤❡ ♣✐♦♥❡❡"✐♥❣ 4❡♠✐✲ 4✉♣❡"✈✐4❡❞ ❧❡❛"♥✐♥❣ ♠❡)❤♦❞ ❝♦✲#$❛✐♥✐♥❣ ❬❇❧✉♠ ❛♥❞ ▼✐)❝❤❡❧❧✱ ✶✾✾✽❜❪✱ )❤✐4 )❤❡4✐4 ✐♥)"♦❞✉❝❡4 ❛ ♥❡✇ ❝♦♥❝❡♣) ♦❢ )✉❜)♣❛❝❡ )#$✉❝#✉$❡ ❛❣$❡❡♠❡♥#✳ ❚❤❡ ♠❛✐♥ ✐❞❡❛ ✐♥✈♦❧✈❡4 ❧❡❛"♥✐♥❣ ♣"♦❥❡❝)✐♦♥4. P (1) ❛♥❞ P (2) ✱ 4✉❝❤ )❤❛) )❤❡ ❞❛)❛ 4)"✉❝)✉"❡ ♦❢ ♣"♦❥❡❝)❡❞ 4❛♠♣❧❡4 P (1) X (1) ❛♥❞ P (2) X (2) ✐4 ❛4 4✐♠✐❧❛" ❛4 ♣♦44✐❜❧❡✳ ❆❝❝♦"❞✐♥❣ )♦ ❞✐✛❡"❡♥) ❞❡✜♥✐)✐♦♥4 ♦❢ ❛❣$❡❡♠❡♥# ❛♥❞ ❞✐✛❡"❡♥) ❛♣✲ ♣❧✐❝❛)✐♦♥4✱ ♥❛♠❡❧② 4❡♠✐✲4✉♣❡"✈✐4❡❞ ❝❧❛44✐✜❝❛)✐♦♥✱ ✉♥4✉♣❡"✈✐4❡❞ ❝❧✉4)❡"✐♥❣ ❛♥❞ "❡)"✐❡✈❛❧✱ ✇❡ ♣"♦♣♦4❡ )❤"❡❡ ❞✐✛❡"❡♥) ▼❱❉❘ ❛♣♣"♦❛❝❤❡4✱ ✇❤✐❝❤ ❛"❡ ❞❡4❝"✐❜❡❞ ✐♥ )❤❡ ❢♦❧❧♦✇✐♥❣✳ ❚❤❡ ✜"4) ❛♣♣"♦❛❝❤ ✐4 ❛ ❞✐"❡❝) ❡①)❡♥4✐♦♥ ♦❢ ✐♥❝"❡♠❡♥)❛❧ ❝♦✲)"❛✐♥✐♥❣ )♦ 4❡♠✐✲4✉♣❡"✈✐4❡❞ ▼❱❉❘ ♣"♦❜❧❡♠4 ✈✐❛ )❤❡ ❝♦✲)"❛✐♥✐♥❣ ♦❢ ▲✐♥❡❛" ❉✐4❝"✐♠✐♥❛♥) ❆♥❛❧②4✐4 ✭▲❉❆✮ ❬❇❡❧❤✉♠❡✉" ❡) ❛❧✳✱ ✶✾✾✼❪ ♣"♦❥❡❝)✐♦♥4✳ ❚❤❡ ❛❧❣♦"✐)❤♠ ✐4 "❡❢❡""❡❞ )♦ ❛4 ❈♦✲▲❉❆ ❛♥❞ ✇❛4 ♣✉❜❧✐4❤❡❞ ✐♥ )❤❡ ♣"♦❝❡❡❞✐♥❣4 ♦❢ ■♥)❡"♥❛)✐♦♥❛❧ ❈♦♥❢❡"❡♥❝❡ ♦♥ ▼✉❧)✐♠❡❞✐❛ ❛♥❞ ❊①♣♦4✐)✐♦♥ ✭■❈▼❊✮ ✐♥ (1). (2). ✷✵✶✷✳ ❚❤❡ ✐♥♣✉) ✐♥✈♦❧✈❡4 ❛ 4♠❛❧❧ 4❡) ♦❢ )✇♦✲✈✐❡✇ ❧❛❜❡❧❧❡❞ )"❛✐♥✐♥❣ ❞❛)❛ {XL , XL ; Y } (1). (2). ❛♥❞ ❛ ❧❛"❣❡" ♣♦♦❧ ♦❢ ✉♥❧❛❜❡❧❧❡❞ ❞❛)❛ {XU , XU }✳ ❲❤✐❧❡ )❤❡ ❧❛"❣❡" ♣♦♦❧ ✐4 ✉♥❧❛❜❡❧❧❡❞✱ ✐)4. 4✐③❡ ✐4 ♠♦"❡ "❡♣"❡4❡♥)❛)✐✈❡ ♦❢ )❤❡ ✉♥❞❡"❧②✐♥❣ ❞❛)❛ ❞✐4)"✐❜✉)✐♦♥✳ ▲❉❆ ♣"♦❥❡❝)✐♦♥4 P (1) ❛♥❞. P (2) ❛"❡ ✐♥✐)✐❛❧❧② )"❛✐♥❡❞ ♦♥ ❡❛❝❤ ✈✐❡✇ ♦❢ )❤❡ ❧❛❜❡❧❧❡❞ )"❛✐♥✐♥❣ 4❡)✳ ❚❤❡ ✉♥❧❛❜❡❧❧❡❞ 4❡) ✐4 )❤❡♥ ♣"♦❥❡❝)❡❞ ✐♥)♦ )❤❡ 4❛♠❡ 4✉❜4♣❛❝❡4✱ ❛♥❞ 4❛♠♣❧❡4 ❛"❡ ❛44✐❣♥❡❞ ❧❛❜❡❧4 ❛❝❝♦"❞✐♥❣ )♦ ❛ ♥❡❛"❡4)✲❝❡♥)"♦✐❞ ❝❧❛44✐✜❡"✳ ❋♦" ❡❛❝❤ ✈✐❡✇✱ )❤❡ 4✉❜4❡) ♦❢ ✉♥❧❛❜❡❧❧❡❞ 4❛♠♣❧❡4 ✇❤✐❝❤ ❛"❡ ♠♦4) ❝♦♥✜❞❡♥)❧② ❧❛❜❡❧❧❡❞ ❛"❡ "❡♠♦✈❡❞ ❢"♦♠ )❤❡ ✉♥❧❛❜❡❧❧❡❞ 4❡) ❛♥❞ ❛❞❞❡❞ )♦ )❤❡ ❧❛❜❡❧❧❡❞ 4❡)✳ ❚❤❡ ▲❉❆ ♣"♦❥❡❝)✐♦♥4 ❛♥❞ ❝❧❛44✐✜❡"4 ❛"❡ )❤❡♥ "❡)"❛✐♥❡❞✳ ❚❤❡ ♣"♦❝❡44 ✐)❡"❛)❡4 ✉♥)✐❧ )❤❡ ✉♥❧❛✲ ❜❡❧❧❡❞ 4❡) ✐4 ❡♠♣)②✳ ❚❤❡ ♥❡✇ ❛❧❣♦"✐)❤♠ ✐4 4✉❝❝❡44❢✉❧ ✐♥ ✉)✐❧✐③✐♥❣ ✉♥❧❛❜❡❧❧❡❞ ❞❛)❛ )♦ ❛✈♦✐❞.

(15) ✶✹. ❈❤❛♣$❡& ✶ ✕ ■♥$&♦❞✉❝$✐♦♥. ♦✈❡%✲✜((✐♥❣ (♦ (❤❡ -♠❛❧❧❡% ❤❛♥❞✲❧❛❜❡❧❧❡❞ ❞❛(❛-❡(✳ ❲❤❡♥ (❡-(❡❞ ♦♥ (❤❡ ❜✐♠♦❞❛❧✱ ❢❛❝❡✲✈♦✐❝❡ ▼❖❇■❖ ❞❛(❛❜❛-❡ ❬▼❝❈♦♦❧ ❡( ❛❧✳✱ ✷✵✶✷❪✱ (❤❡ ♣%♦♣♦-❡❞ ❈♦✲▲❉❆ ❛❧❣♦%✐(❤♠ %❛✐-❡- ❛ ❜❛-❡❧✐♥❡ ✐❞❡♥(✐✜❝❛(✐♦♥ %❛(❡ ❢%♦♠ 71% (♦ 99% ✇❤✐❧❡ ✐♥ ❛ ✈❡%✐✜❝❛(✐♦♥ (❛-❦ (❤❡ ❊H✉❛❧ ❊%%♦% ❘❛(❡ ✭❊❊❘✮ ✐- %❡❞✉❝❡❞ ❢%♦♠ 16% (♦ ❧❡-- (❤❛♥ 1%✳ ■♥ ❛♥ ❡①(❡♥-✐♦♥ ♦❢ (❤✐- ✇♦%❦ ✇❤✐❝❤ ✇❛- ♣✉❜❧✐-❤❡❞ ✐♥ (❤❡ ♣%♦❝❡❡❞✐♥❣- ♦❢ ■♥(❡%♥❛(✐♦♥❛❧ ❈♦♥❢❡%❡♥❝❡ ♦♥ ❆❝♦✉-(✐❝-✱ ❙♣❡❡❝❤✱ ❛♥❞ ❙✐❣♥❛❧ O%♦❝❡--✐♥❣ ✭■❈❆❙❙O✮ ✷✵✶✸✱ ✇❡ -❤♦✇ (❤❛( ❙♣❛%-❡ ❘❡♣%❡-❡♥(❛(✐♦♥ ❈❧❛--✐✜❡% ✭❙❘❈✮ ❝♦✉❧❞ ❜❡ ❡♠♣❧♦②❡❞ (♦ %❡❥❡❝( ♦✉(✲♦❢✲❝❧❛-- -❛♠♣❧❡- ✇❤✐❝❤ ❜❡❧♦♥❣ (♦ ♥♦♥❡ ♦❢ (❤❡ %❡❣✐-(❡%❡❞ ❝❧❛--❡-✳ ■♥ %❡❧❛(❡❞ ✇♦%❦ ♣✉❜❧✐-❤❡❞ ✐♥ ♣%♦❝❡❡❞✐♥❣- ♦❢ ■♥(❡%♥❛(✐♦♥❛❧ ❈♦♥❢❡%❡♥❝❡ ♦♥ ■♠❛❣❡ O%♦❝❡--✐♥❣ ✭■❈■O✮ ✷✵✶✶ ❛♥❞ ❊✉%♦♣❡❛♥ ❙✐❣♥❛❧ O%♦❝❡--✐♥❣ ❈♦♥❢❡%❡♥❝❡ ✭❊❯❙■O❈❖✮ ✷✵✶✶✱ ✇❡ ❛❧-♦ ♣%♦♣♦-❡❞ ❛ -❡❧❢✲(%❛✐♥✐♥❣ ✈❡%-✐♦♥ ♦❢ (❤❡ ❛❧❣♦%✐(❤♠ ✇❤✐❝❤ ❝♦✉❧❞ ❜❡ ❛♣♣❧✐❡❞ (♦ -✐♥❣❧❡✲♠♦❞❛❧ -②-(❡♠-✳ ❚❤❡ -(❛♥❞❛%❞ ❝♦✲(%❛✐♥✐♥❣ ❛❧❣♦%✐(❤♠ ✐- -❡♠✐✲-✉♣❡%✈✐-❡❞ ❛♥❞ ♥❡❡❞- ❛( -♦♠❡ ❧❛❜❡❧❧❡❞ ❞❛(❛ ❢♦% ✐♥✐(✐❛❧✐③❛(✐♦♥✳ ❋♦% ♣✉%❡❧② ✉♥-✉♣❡%✈✐-❡❞ ❝❧✉-(❡%✐♥❣ ♣%♦❜❧❡♠-✱ ✇❡ ♣%♦♣♦-❡❞ ❛ ♠✉❧(✐✲✈✐❡✇ -✉❜-♣❛❝❡ ❝❧✉-(❡%✐♥❣ ❛❧❣♦%✐(❤♠ ✇❤✐❝❤ ✐- ❜❛-❡❞ ♦♥ ❛ ♠✉❧(✐✲✈✐❡✇ ❝❧✉-(❡% ❛❣%❡❡♠❡♥( ❛--✉♠♣(✐♦♥✳ ❲❡ ❝♦♥-✐❞❡% (❤❡ ♣%♦❜❧❡♠ ♦❢ ❝❧✉-(❡%✐♥❣ ❛ ❣%♦✉♣ ♦❢ ✉♥❧❛❜❡❧❧❡❞ (✇♦✲✈✐❡✇✱ ❤✐❣❤✲❞✐♠❡♥-✐♦♥❛❧ ❞❛(❛. X (1) , X (2) ✐♥(♦ k ❝❧✉-(❡%-✱ ❛♥❞ -❛♠♣❧❡- ✐♥ (❤❡ -❛♠❡ ❝❧❛-- ❛%❡ ❡①♣❡❝(❡❞ (♦ ❜❡ ❛--✐❣♥❡❞ (♦ (❤❡ -❛♠❡ ❝❧✉-(❡%✳ ❙✐♥❝❡ X (1) ❛♥❞ X (2) ❛%❡ ❞✐✛❡%❡♥( %❡♣%❡-❡♥(❛(✐♦♥- ♦❢ (❤❡ -❛♠❡ ✉♥❞❡%❧②✐♥❣ ❝❧❛--. Y ✱ ✐♥ ✐❞❡❛❧ ❝♦♥❞✐(✐♦♥-✱ ✐❞❡♥(✐❝❛❧ ❝❧✉-(❡%✐♥❣ %❡-✉❧(- ❛%❡ ❡①♣❡❝(❡❞ ✐%%❡-♣❡❝(✐✈❡ ♦❢ (❤❡ ✈✐❡✇ ✉-❡❞ ❢♦% ❝❧✉-(❡%✐♥❣✳ ❍♦✇❡✈❡%✱ (❤✐- ✐- ✉♥❧✐❦❡❧② ✐❢ ❝❧✉-(❡%✐♥❣ ✐- ♣❡%❢♦%♠❡❞ ✐♥ (❤❡ ♦%✐❣✐♥❛❧ ❢❡❛(✉%❡ -♣❛❝❡- X (1) ❛♥❞ X (2) -✐♥❝❡ (❤❡② ❛%❡ ❝♦%%✉♣(❡❞ ❜② ❞✐✛❡%❡♥( ✐♥(%❛✲❝❧❛-- ✈❛%✐❛(✐♦♥✳ ❚❤✐- (❤❡✲ -✐- ✐♥(%♦❞✉❝❡- ❛ ♥❡✇ ❛♣♣%♦❛❝❤ (♦ ♠✉❧(✐✲✈✐❡✇ -✉❜-♣❛❝❡ ❝❧✉-(❡%✐♥❣ ✇❤✐❝❤ -❡❡❦- ♣%♦❥❡❝(✐♦♥-. P (1) ❛♥❞ P (2) -✉❝❤ (❤❛( (❤❡ ❝❧✉-(❡%✐♥❣ %❡-✉❧(- ❛%❡ ✐♥ ♠❛①✐♠❛❧ ❛❣%❡❡♠❡♥( ✐♥ (❤❡ -✉❜-♣❛❝❡❛❝%♦-- ❡❛❝❤ ✈✐❡✇✳ ❲❡ -❤♦✇ (❤❛( (❤✐- ♦❜❥❡❝(✐✈❡ ❝❛♥ ❜❡ ♦❜(❛✐♥❡❞ ❜② ❝♦♠❜✐♥✐♥❣ (❤❡ -✐♠✲ ♣❧✐❝✐(② ♦❢ ❦✲♠❡❛♥- ❝❧✉-(❡%✐♥❣ ❛♥❞ ▲✐♥❡❛% ❉✐-❝%✐♠✐♥❛♥( ❆♥❛❧②-✐- ✭▲❉❆✮ ✇✐(❤✐♥ ❛ ❝♦✲(%❛✐♥✐♥❣ -❝❤❡♠❡✳ ❚❤❡ ♥❡✇ ❛❧❣♦%✐(❤♠ ❡①♣❧♦✐(- ❝❧✉-(❡% ✐♥❞✐❝❛(♦%- ♦❜(❛✐♥❡❞ ❢%♦♠ ❦✲♠❡❛♥- ❝❧✉-(❡%✐♥❣ ✐♥ ♦♥❡ ✈✐❡✇ (♦ ❧❡❛%♥ ❞✐-❝%✐♠✐♥❛(✐✈❡ -✉❜-♣❛❝❡- ✐♥ ❛♥♦(❤❡%✳ ❚❤❡ ❛❧❣♦%✐(❤♠ ✐- %❡❢❡%%❡❞ (♦ ❛❈♦❑♠▲❉❆✳ ❲❡ -❤♦✇ ♠❛(❤❡♠❛(✐❝❛❧❧② ❤♦✇ ▲❉❆ ♣%♦❥❡❝(✐♦♥- ❧❡❛%♥❡❞ ❢%♦♠ -❛♠♣❧❡- ✇✐(❤ %❛♥✲ ❞♦♠ ❧❛❜❡❧ ♥♦✐-❡ ❛%❡ ♣%♦❜❛❜✐❧✐-(✐❝❛❧❧② ❡H✉✐✈❛❧❡♥( (♦ (❤♦-❡ ❧❡❛%♥❡❞ ✇✐(❤ ❝❧❡❛♥ ❧❛❜❡❧- ❛♥❞ (❤❛( ❝%♦--✲✈✐❡✇ ❧❛❜❡❧❧✐♥❣✱ ♦% ❝♦✲(%❛✐♥✐♥❣✱ ✐- ❡✣❝✐❡♥( ✐♥ ❝♦%%❡❝(✐♥❣ ❡%%♦♥❡♦✉- -❛♠♣❧❡ ❧❛❜❡❧-✳ ❖❢ ♣❛%(✐❝✉❧❛% ♠❡%✐(✱ (❤❡ ❛❧❣♦%✐(❤♠ ❞♦❡- ♥♦( %❡H✉✐%❡ (❤❡ ♦♣(✐♠✐③❛(✐♦♥ ♦❢ ❛♥② ❤②♣❡%✲♣❛%❛♠❡(❡%-✳ ❚❤❡ ❡✛❡❝(✐✈❡♥❡-- ♦❢ (❤❡ ♣%♦♣♦-❡❞ ❛❧❣♦%✐(❤♠ ✐- ❞❡♠♦♥-(%❛(❡❞ ♥♦( ♦♥❧② ✐♥ -♣❡❛❦❡% ❝❧✉-(❡%✐♥❣ ❡①♣❡%✐♠❡♥(- ♦♥ (❤❡ -❛♠❡ ❜✐♠♦❞❛❧✱ ❢❛❝❡✲✈♦✐❝❡ ▼❖❇■❖ ❞❛(❛❜❛-❡✱ ❜✉( ❛❧-♦ ✐♥ ♠♦%❡ ❣❡♥❡%❛❧ ❝❧✉-(❡%✐♥❣ (❛-❦- -✉❝❤ ❛- ❤❛♥❞✇%✐((❡♥ ❞✐❣✐( ❝❧✉-(❡%✐♥❣ ❛♥❞ (❡①( ❞♦❝✉♠❡♥( ❝❧✉-(❡%✐♥❣✳ ❙✐❣✲ ♥✐✜❝❛♥( ✐♠♣%♦✈❡♠❡♥( ♦✈❡% ❛❧(❡%♥❛(✐✈❡ ♠✉❧(✐✲✈✐❡✇ ❝❧✉-(❡%✐♥❣ ❛♣♣%♦❛❝❤❡- -✉❝❤ ❛- ❈❈❆ ❛♥❞ ❝♦✲-♣❡❝(%❛❧ ❝❧✉-(❡%✐♥❣ ❛%❡ %❡♣♦%(❡❞✳ ❚❤✐- ✇♦%❦ ❤❛- ❜❡❡♥ -✉❜♠✐((❡❞ (♦ ❛ ❙♣❡❝✐❛❧ ■--✉❡ ♦♥ ❯♥-✉♣❡%✈✐-❡❞ ❛♥❞ ❙✉♣❡%✈✐-❡❞ ▲❡❛%♥✐♥❣ ✐♥ O❛((❡%♥ ❘❡❝♦❣♥✐(✐♦♥ ▲❡((❡%-✳.

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The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est

The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est

The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est

The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est

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The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est

The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est

The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est