Análise de sentimentos baseada em aspectos usando aprendizado semissupervisionado em redes heterogêneas

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Universidade de São Paulo

2015-10

Análise de sentimentos baseada em aspectos

usando aprendizado semissupervisionado em

redes heterogêneas

Symposium on Knowledge Discovery, Mining and Learning, III, 2015, Petrópolis.

http://www.producao.usp.br/handle/BDPI/50007

Downloaded from: Biblioteca Digital da Produção Intelectual - BDPI, Universidade de São Paulo

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3rd SYMPOSIUM ON KNOWLEDGE DISCOVERY,

MINING AND LEARNING

October 13th to 15th, 2015

Petr´opolis – RJ – Brazil

PROCEEDINGS

Organization

Fluminense Federal University – UFF

National Laboratory for Scientific Computing – LNCC

Federal Center of Technological Education of Rio de Janeiro – CEFET/RJ

Local Organization Chair

Alexandre Plastino, UFF

Program Committee Chairs

Sandra de Amo, UFU

Leandro Balby Marinho, UFCG

Steering Committee Chairs

Andr´e Ponce de Leon F. de Carvalho, ICMC-USP

Wagner Meira Jr., UFMG

Support

Brazilian Computer Society – SBC

International Association for Statistical Computing – IASC

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S989 Symposium on Knowledge Discovery, Mining and Learning (3.: 2015: Petrópolis, RJ).

Proceedings / 3rd Symposium on Knowledge Discovery, Mining and Learning ; Alexandre Plastino, Sandra de Amo, Leandro Balby Marinho, editors ; Universidade Federal Fluminense, Laboratório Nacional de Computação Científica, Centro Federal de Educação Tecnológica do Rio de Janeiro, organizadores. – Petrópolis : [s.n.], 2015.

97 p.

Evento realizado de 13 a 15 de outubro de 2015. ISSN 2318-1060

1. Mineração de dados. 2. Aprendizagem de máquina. 3. Ciência da Computação. I. Plastino, Alexandre. II. Amo, Sandra de. III. Marinho, Leandro Balby. IV. Universidade Federal Fluminense. V. Laboratório Nacional de Computação Científica. VI. Centro Federal de Educação Tecnológica do Rio de Janeiro. VII. Título.

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A Social Approach for the Cold-Start Issue on Recommender Systems Based on the

Extraction and Analysis of Web Resources . . . .

10 Antonio Felipe P. Bezerra, Julio Cesar Duarte

Predicting Student Dropout: A Case Study in Brazilian Higher Education . . . . .

18 Allan Sales, Leandro Balby, Adalberto Cajueiro

An Effective Strategy for Feature Selection in High-Dimensional Datasets . . . .

26 Mariana Tasca, Alexandre Plastino, Celso Ribeiro, Bianca Zadrozny

Prepara¸c˜ao de Dados Longitudinais: Estudo de Caso em Envelhecimento Humano

. . . .

34 Caio Eduardo Ribeiro, Luis Enrique Z´

arate

Aprendendo a Ranquear com Boosting e Florestas Aleat´orias: Um Modelo H´ıbrido

. . . .

42 Clebson S´

a, Marcos Gon¸calves, Daniel Sousa, Thiago Salles

Padrões de Alta Utilidade em Rela¸cões N-árias Fuzzy . . . .

50 Lo¨ıc Cerf

Initialization Heuristics for Greedy Bayesian Network Structure Learning . . . .

58 Walter Perez, Denis Mau´

a

Social PrefRec Framework: Leveraging Recommender Systems Based on Social

In-formation . . . .

66 Cr´ıcia Z. Fel´ıcio, Kl´

erisson Paix˜

ao, Guilherme Alves, Sandra de Amo

From the Sensor Data Streams to Linked Streaming Data. A Survey of Main

Ap-proaches. . . .

74 Kathrin Rodr´ıguez, Noel Moreno, Marco Antonio Casanova

Analyzing the Correlation Among Traffic Loop Sensors to Detect Anomalies in

Traf-fic Loop Data Streams . . . .

82

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An´alise de Sentimentos Baseada em Aspectos Usando Aprendizado

Semissupervisi-onado em Redes Heterogˆeneas (SHORT PAPER) . . . .

90 Ivone Penque Matsuno, Rafael Rossi, Ricardo Marcacini, Solange Rezende

Minera¸cão de Preferências do Usuário em Textos de Redes Sociais usando Senten¸cas

Comparativas (SHORT PAPER) . . . .

94

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■✈♦♥❡ %✳ ▼❛)*✉♥♦1,2_{✱ ❘❛❢❛❡❧ ●✳ ❘♦**✐}1_{✱ ❘✐❝❛3❞♦ ▼✳ ▼❛3❝❛❝✐♥✐}2_{✱ ❙♦❧❛♥❣❡ ❖✳ ❘❡③❡♥❞❡}1 1 _{■♥"#✐#✉#♦ ❞❡ ❈✐*♥❝✐❛" ▼❛#❡♠/#✐❝❛" ❡ ❞❡ ❈♦♠♣✉#❛12♦ ✭■❈▼❈✴❯❙7✮✱ ❇;❛"✐❧} 2 _{❯♥✐✈❡;"✐❞❛❞❡ ❋❡❞❡;❛❧ ❞❡ ▼❛#♦ ●;♦""♦ ❞♦ ❙✉❧ ✭❯❋▼❙✮✱ ❇;❛"✐❧} ❆❜"#$❛❝#✳ ◆❛ ❆♥$❧✐'❡ ❞❡ ❙❡♥+✐♠❡♥+♦' ❜❛'❡❛❞❛ ❡♠ ❆'♣❡❝+♦' ✭❆❙❇❆✮ 4 ♣♦''5✈❡❧ ❛♥❛❧✐'❛7 ♦ '❡♥+✐♠❡♥+♦ ❞❡ ❝❛❞❛ ❛'♣❡❝+♦ ❞❡ ✉♠ ♣7♦❞✉+♦✱ ♣♦7 ❡①❡♠♣❧♦✱ ❛ ;✉❛❧✐❞❛❞❡ ❞❛ ❝<♠❡7❛✱ '✐'+❡♠❛ ♦♣❡7❛❝✐♦♥❛❧ ❡ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❛7♠❛③❡♥❛♠❡♥+♦ ❞❡ ✉♠ ❙♠❛#$♣❤♦♥❡✳ ❚7❛❜❛❧❤♦' ❡①✐'+❡♥+❡' ✉+✐❧✐③❛♥❞♦ ❛♣7❡♥❞✐③❛❞♦ ❞❡ ♠$;✉✐♥❛ ♣❛7❛ ❆❙❇❆ 7❡;✉❡7❡♠ ✭✐✮ ❝♦♥❤❡❝❡7 ♣7❡✈✐❛♠❡♥+❡ ♦' ♣♦''5✈❡✐' ❛'♣❡❝+♦' ♦✉ ✭✐✐✮ 7♦+✉❧❛7 ✉♠❛ '✐❣♥✐✜❝❛+✐✈❛ ♣❛7❝❡❧❛ ❞♦' ❞❛❞♦'❀ ♦ ;✉❡ +♦7♥❛♠ '✉❛ ❛♣❧✐❝❛DE♦ ❧✐♠✐+❛❞❛ ❡♠ ❝❡♥$7✐♦' 7❡❛✐'✳ ❊♠ ✈✐'+❛ ❞✐''♦✱ ♥❡'+❡ +7❛❜❛❧❤♦ 4 ♣7♦♣♦'+❛ ✉♠❛ ❛❜♦7❞❛❣❡♠ ❞❡ ❛♣7❡♥❞✐③❛❞♦ '❡♠✐''✉♣❡7✈✐'✐♦♥❛❞♦ ;✉❡ ✐♥+❡❣7❛ ❞✐❢❡7❡♥+❡' ✐♥❢♦7♠❛DH❡' ❡♠ ✉♠❛ I♥✐❝❛ 7❡❞❡ +❛♥+♦ ♣❛7❛ ❞❡✜♥✐7 '❡ ✉♠ +❡7♠♦ 4 ✉♠ ❛'♣❡❝+♦ ;✉❛♥+♦ ♣❛7❛ ❞❡✜♥✐7 ❛ ♣♦❧❛7✐❞❛❞❡ ❞♦' '❡♥+✐♠❡♥+♦' ❡♠ 7❡❧❛DE♦ ❛♦' ❛'♣❡❝+♦'✳ ❖' 7❡'✉❧+❛❞♦' ❡①♣❡7✐♠❡♥+❛✐' 7❡✈❡❧❛♠ ;✉❡ ❛ ❛❜♦7❞❛❣❡♠ ♣7♦♣♦'+❛ ♦❜+4♠ 7❡'✉❧+❛❞♦' ♣7♦♠✐''♦7❡' ❡ ❝♦♠♣❡+✐+✐✈♦' ;✉❛♥❞♦ ❝♦♠♣❛7❛❞❛ ❝♦♠ ✉♠❛ ❛❜♦7❞❛❣❡♠ '✉♣❡7✈✐'✐♦♥❛❞❛✳ ❈❛+❡❣♦7✐❡' ❛♥❞ ❙✉❜❥❡❝+ ❉❡'❝7✐♣+♦7'✿ ●✳✷✳✷ ❬●$❛♣❤ ❚❤❡♦$②❪✿ ●7❛♣❤ ▲❛❜❡❧✐♥❣❀ ❍✳✷✳✽ ❬❉❛#❛❜❛"❡ ❆♣♣❧✐❝❛#✐♦♥"❪✿ ❉❛+❛ ▼✐♥✐♥❣❀ ❍✳✷✳✹ ❬❙②"#❡♠"❪✿ ❚❡①+✉❛❧ ❉❛+❛❜❛'❡' ❑❡②✇♦7❞'✿ ❛♥$❧✐'❡ ❞❡ '❡♥+✐♠❡♥+♦'✱ ❛♣7❡♥❞✐③❛❞♦ ❞❡ ♠$;✉✐♥❛✱ 7❡❞❡' ❤❡+❡7♦❣[♥❡❛' ✶✳ ■◆❚❘❖❉❯➬➹❖ ❆❜♦.❞❛❣❡♥4 5.❛❞✐❝✐♦♥❛✐4 ♣❛.❛ ❆♥9❧✐4❡ ❞❡ ❙❡♥5✐♠❡♥5♦4 ✭❆❙✮ ✈✐4❛♠ ❝❧❛44✐✜❝❛.✱ ❡♠ ❣❡.❛❧✱ ❛ ♣♦❧❛.✐❞❛❞❡ ❞♦ 4❡♥5✐♠❡♥5♦ ❞❡ ❞♦❝✉♠❡♥5♦4 5❡①5✉❛✐4 ❝♦♠♦ ♣♦4✐5✐✈❛✱ ♥❡❣❛5✐✈❛ ♦✉ ♥❡✉5.❛✳ ❊45❛ ❝❧❛44✐✜❝❛EF♦ G .❡❛❧✐③❛❞❛ ❛♥❛❧✐4❛♥❞♦ ♦ ❞♦❝✉♠❡♥5♦ ❝♦♠♦ ✉♠ 5♦❞♦ ✭❆❙ ❡♠ ♥I✈❡❧ ❞❡ ❞♦❝✉♠❡♥5♦✮ ♦✉ ❛♥❛❧✐4❛♥❞♦ ♦ 4❡♥5✐♠❡♥5♦ ❞❡ ❝❛❞❛ 4❡♥5❡♥E❛ ❞♦ ❞♦❝✉♠❡♥5♦ ✭❆❙ ❡♠ ♥I✈❡❧ ❞❡ 4❡♥5❡♥E❛✮ ❬▲✐✉ ✷✵✶✷❪✳ ◆❡44❡4 ❞♦✐4 ❝❛4♦4✱ ♥F♦ 4F♦ ❡①♣❧♦.❛❞❛4 ✐♥❢♦.♠❛EP❡4 4♦❜.❡ ❞❡5❡.♠✐♥❛❞♦4 ❛4♣❡❝5♦4 ❞❡ ✉♠ ♣.♦❞✉5♦ ♦✉ 4❡.✈✐E♦ ❛♥❛❧✐4❛❞♦✱ ♠❡4♠♦ 4❡♥❞♦ ❢.❡Q✉❡♥5❡ ❛ ❡①✐45R♥❝✐❛ ❞❡ 4❡♥5✐♠❡♥5♦4 ❞✐❢❡.❡♥5❡4 ♣❛.❛ ❛4♣❡❝5♦4 ❞✐45✐♥5♦4 ♥♦4 5❡①5♦4 ❛♥❛❧✐4❛❞♦4 ❬❈❤❡♥ ❡5 ❛❧✳ ✷✵✶✹❪✳ V♦. ❡①❡♠♣❧♦✱ ♥❛ 4❡♥5❡♥E❛ ✏ ❊✉ ❣♦$%❡✐ ❞❛ ✐♠❛❣❡♠ ❞❡$%❛ %❡❧❡✈✐$-♦✱ ♠❛$ ♦ ❝♦♥%1♦❧❡ 1❡♠♦%♦ ❞❡❧❛ 2 ❤♦114✈❡❧ ✑✱ 5❡♠♦4 ✉♠❛ ♦♣✐♥✐F♦ ♣♦4✐5✐✈❛ ❡ ♦✉5.❛ ♥❡❣❛5✐✈❛✳ ❆❧G♠ ❞✐44♦✱ ❝❛❞❛ ♦♣✐♥✐F♦ .❡❢❡.❡✲ 4❡ ❛ ❛4♣❡❝5♦4 ❞✐❢❡.❡♥5❡4 ✭✏✐♠❛❣❡♠✑ ❡ ✏❝♦♥5.♦❧❡ .❡♠♦5♦✑✮ ❞❛ ❡♥5✐❞❛❞❡ ❡♠ Q✉❡45F♦ ✭✏5❡❧❡✈✐4F♦✑✮ ❬❑✐♠ ❡5 ❛❧✳ ✷✵✶✸❪✳ V❛.❛ ❧✐❞❛. ❝♦♠ ❡44❡ 5✐♣♦ ❞❡ ❝❡♥9.✐♦ ❢♦✐ ♣.♦♣♦45❛ ❛ ❆♥9❧✐4❡ ❞❡ ❙❡♥5✐♠❡♥5♦4 ❜❛4❡❛❞❛ ❡♠ ❆4♣❡❝5♦4 ✭❆❙❇❆✮✱ Q✉❡ ♣♦5❡♥❝✐❛❧✐③❛ ♦ ❛♣♦✐♦ ] 5♦♠❛❞❛ ❞❡ ❞❡❝✐4F♦ ❣❡.❛♥❞♦ ✐♥❢♦.♠❛EP❡4 ♠❛✐4 ❡4♣❡❝I✜❝❛4 4♦❜.❡ ♦ 4❡♥5✐♠❡♥5♦ ❞❡ ❛4♣❡❝5♦4 ❞❡ ✉♠ ♣.♦❞✉5♦ ♦✉ 4❡.✈✐E♦✳ V♦.G♠✱ ❛ ❆❙❇❆ G ✉♠ ♣.♦❝❡44♦ ♠❛✐4 ❝♦♠♣❧❡①♦ ❡ ❞❡4❛✜❛❞♦. ❬▲✐✉ ✷✵✶✷❀ ❏✐♠G♥❡③✲❩❛❢.❛ ❡5 ❛❧✳ ✷✵✶✺❪✳ ❖4 5.❛❜❛❧❤♦4 ♠❛✐4 ♣.♦♠✐44♦.❡4 ❡♠ ❆❙❇❆ ❡①♣❧♦.❛♠ ✉♠❛ ❝♦♠❜✐♥❛EF♦ ❞❡ 5G❝♥✐❝❛4 ❞❡ V.♦❝❡44❛♠❡♥5♦ ❞❡ ▲✐♥❣✉❛❣❡♠ ◆❛5✉.❛❧ ✭V▲◆✮ ❡ ❆♣.❡♥❞✐③❛❞♦ ❞❡ ▼9Q✉✐♥❛ ✭❆▼✮ ♣❛.❛ ❛ ❡①5.❛EF♦ ❞❡ ❛4♣❡❝5♦4 ❡ ❝❧❛44✐✲ ✜❝❛EF♦ ❞❡ 4❡♥5✐♠❡♥5♦4✳ ❖4 5.❛❜❛❧❤♦4 Q✉❡ ❡①♣❧♦.❛♠ ❛♣"❡♥❞✐③❛❞♦ ♥)♦ *✉♣❡"✈✐*✐♦♥❛❞♦ ❣❡.❛❧♠❡♥5❡ 4F♦ ❜❛4❡❛❞♦4 ❡♠ ▼♦❞❡❧❛❣❡♠ ❞❡ ❚c♣✐❝♦4✱ ❝♦♠♦ ▲❉❆ ❡ ▲❙❆✱ ♣❛.❛ ♦❜5❡. ♦ ❝❤❛♠❛❞♦ ❚♦♣✐❝✲❙❡♥%✐♠❡♥% ▼♦❞❡❧ ❬❏✐♠G♥❡③✲❩❛❢.❛ ❡5 ❛❧✳ ✷✵✶✺❪✳ ❈❛❞❛ 5c♣✐❝♦ G ❝♦♠♣♦45♦ ♣♦. ✉♠ ❝♦♥❥✉♥5♦ ❞❡ ♣❛❧❛✈.❛4✳ ❯♠❛ ❧✐45❛ ♣.❡❞❡✜♥✐❞❛ ❞❡ ♣❛❧❛✈.❛4 ♣♦4✐5✐✈❛4 ❡ ♥❡❣❛5✐✈❛4✱ ❡ ✉♠❛ ❧✐45❛ ❞❡ ❛4♣❡❝5♦4 4F♦ ✉5✐❧✐③❛❞❛4 ♣❛.❛ ❞❡✜♥✐. ❛ ♣♦❧❛.✐❞❛❞❡ ❞♦ 4❡♥5✐♠❡♥5♦✳ ❈♦♠♦ ❞❡4✈❛♥5❛❣❡♠✱ ♠✉✐5♦4 ❛✉5♦.❡4 ❛✜.♠❛♠ Q✉❡ ❤9 ✉♠❛ ❣.❛♥❞❡ ❞✐✜❝✉❧✲ ❞❛❞❡ ❡♠ ❞❡✜♥✐. ✉♠ ♥e♠❡.♦ ❛❞❡Q✉❛❞♦ ❞❡ 5c♣✐❝♦4✳ ❆✐♥❞❛✱ ✉5✐❧✐③❛. ✉♠❛ ❧✐45❛ ♣.❡❞❡✜♥✐❞❛ ❞❡ ♣❛❧❛✈.❛4 ♣♦4✐5✐✈❛4 ♦✉ ♥❡❣❛5✐✈❛4 ♣♦❞❡ ♥F♦ ♦❜5❡. .❡4✉❧5❛❞♦4 4❛5✐4❢❛5c.✐♦4 ♣❛.❛ ❆❙❇❆✳ V♦. ❡①❡♠♣❧♦✱ ❛ ♣❛❧❛✈.❛ ✏1❛♣✐❞❛♠❡♥%❡✑ ♣♦❞❡ 5❡. ✉♠ 4❡♥5✐♠❡♥5♦ ♣♦4✐5✐✈♦ ❡♠ ✏ $✐$%❡♠❛ ❞♦ ❝❡❧✉❧❛1 ✐♥✐❝✐❛❧✐③❛ 1❛♣✐❞❛♠❡♥%❡ ✑✱ ♠❛4 ♥❡❣❛5✐✈♦ ❡♠ ✏❜❛%❡1✐❛ ❞♦ ❝❡❧✉❧❛1 ❞❡$❝❛11❡❣❛ 1❛♣✐❞❛♠❡♥%❡ ✑❀ ♦ Q✉❡ ❡①✐❣❡ ✉♠❛ ❛♥9❧✐4❡ ♣❛.❛ ❝❛❞❛ ❝♦♥5❡①5♦ ♦✉ ❞♦♠I♥✐♦ ❞❡ ❛♣❧✐❝❛EF♦✳ V♦. ✜♠✱ ❤9 ❝❡♥9.✐♦4 ❡♠ Q✉❡ ✉♠❛ ❧✐45❛ ❞❡ ❛4♣❡❝5♦4 ♥F♦ ❡459 ❞✐4♣♦♥I✈❡❧✳

❙②♠♣♦%✐✉♠ ♦♥ ❑♥♦✇❧❡❞❣❡ ❉✐%❝♦✈❡2②✱ ▼✐♥✐♥❣ ❛♥❞ ▲❡❛2♥✐♥❣✱ ❑❉▼■▲❊ ✷✵✶✺✳

3rd

KDMiLe – Proceedings – ISSN 2318-1060 October 13-15, 2015 – Petr´opolis, RJ, Brazil

KDMiLe:11

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■✳ #✳ ▼❛&'✉♥♦ ❛♥❞ ❘✳ ●✳ ❘♦''✐ ❛♥❞ ❘✳ ▼✳ ▼❛/❝❛❝✐♥✐ ❛♥❞ ❙✳ ❖✳ ❘❡③❡♥❞❡ ❏! ♦# $%❛❜❛❧❤♦# *✉❡ ❡①♣❧♦%❛♠ ❛♣"❡♥❞✐③❛❞♦ )✉♣❡"✈✐)✐♦♥❛❞♦ ✉$✐❧✐③❛♠ 2▲◆ ♣❛%❛ ❡①$%❛✐% ❛$%✐❜✉✲ $♦# ❣%❛♠❛$✐❝❛✐# ❞♦# $❡①$♦# ❡ ❛ ❝❧❛##✐✜❝❛:;♦ ❞❡ ❛#♣❡❝$♦# < ❜❛#❡❛❞❛ ♥❡##❡# ❛$%✐❜✉$♦# ❬▲✐✉ ✷✵✶✷❀ ❈❤❡♥ ❡$ ❛❧✳ ✷✵✶✹❪✳ 2♦% ❡①❡♠♣❧♦✱ ❛#♣❡❝$♦# ❣❡%❛❧♠❡♥$❡ #;♦ %❡♣%❡#❡♥$❛❞♦# ♣♦% #✉❜#$❛♥$✐✈♦# ❝♦♥❡❝$❛❞♦# ❛ ❛❞✲ ✈<%❜✐♦# ❡ ❛❞❥❡$✐✈♦#✳ ❆##✐♠✱ ♦# ❛#♣❡❝$♦# #;♦ %♦$✉❧❛❞♦# ♣❡❧♦# ✉#✉!%✐♦# ♣❛%❛✱ ♣♦#$❡%✐♦%♠❡♥$❡✱ ❛♣%❡♥❞❡% ✉♠ ❝❧❛##✐✜❝❛❞♦% *✉❡ ✐❞❡♥$✐✜*✉❡ ❛#♣❡❝$♦# ❡♠ ♥♦✈♦# $❡①$♦#✳ ❉❡ ❢♦%♠❛ ❛♥!❧♦❣❛✱ ♦# ✉#✉!%✐♦# $❛♠❜<♠ %♦$✉❧❛♠ ❡①❡♠♣❧♦# ♣♦#✐$✐✈♦# ❡ ♥❡❣❛$✐✈♦# *✉❡ ❡♥✈♦❧✈❛♠ ♦# ❛#♣❡❝$♦#✱ $❛♠❜<♠ ♣♦##✐❜✐❧✐$❛♥❞♦ ❛♣%❡♥❞❡% ✉♠ ❝❧❛##✐✜❝❛❞♦% *✉❡ ❞❡✜♥❛ ♦ #❡♥$✐♠❡♥$♦ ❞❡ ❛#♣❡❝$♦# ♥;♦ ✈✐#$♦#✳ ❊♠❜♦%❛ ♦❜$❡♥❤❛♠ ♠❛✐♦% ❛❝✉%!❝✐❛✱ $❛✐# $%❛❜❛❧❤♦# ❡①✐❣❡♠ ✉♠ ❣%❛♥❞❡ ❡#❢♦%:♦ ❤✉♠❛♥♦ ❞❡✈✐❞♦ ❛ ♥❡❝❡##✐❞❛❞❡ ❞❡ %♦$✉❧❛% ✉♠ ❣%❛♥❞❡ ❝♦♥❥✉♥$♦ ❞❡ $❡①$♦# ❬❈❤❡♥ ❡$ ❛❧✳ ✷✵✶✹❀ 2♦♥$✐❦✐ ❡$ ❛❧✳ ✷✵✶✹❪✳ ❊♠ ✈✐#$❛ ❞✐##♦✱ ♥❡#$❡ $%❛❜❛❧❤♦ < ♣%♦♣♦#$❛ ✉♠❛ ❛❜♦%❞❛❣❡♠ ♣❛%❛ ❆❙❇❆✱ ❞❡♥♦♠✐♥❛❞❛ ❆❙2❍◆ ✭❆!♣❡❝%✲ ❇❛!❡❞ ❙❡♥%✐♠❡♥% ./♦♣❛❣❛%✐♦♥ ♦♥ ❍❡%❡/♦❣❡♥❡♦✉! ◆❡%✇♦/❦! ✮✱ *✉❡ ✉$✐❧✐③❛ ❛♣%❡♥❞✐③❛❞♦ #❡♠✐##✉♣❡%✈✐#✐♦♥✲ ❛❞♦ $❛♥$♦ ♣❛%❛ ❝❧❛##✐✜❝❛:;♦ ❞❡ ❛#♣❡❝$♦#✱ *✉❛♥$♦ ♣❛%❛ ❝❧❛##✐✜❝❛:;♦ ❞❡ #❡♥$✐♠❡♥$♦ ❞♦# ❛#♣❡❝$♦#✳ ❖ ♦❜❥❡$✐✈♦ < ✉$✐❧✐③❛% ❛♣❡♥❛# ✉♠ ♣❡*✉❡♥♦ ❝♦♥❥✉♥$♦ ❞❡ ❡①❡♠♣❧♦# ♣%❡✈✐❛♠❡♥$❡ %♦$✉❧❛❞♦# ❡ %❡❛❧✐③❛% ♦ ❛♣%❡♥✲ ❞✐③❛❞♦ ♣♦% ♠❡✐♦ ❞❡ ♣%♦♣❛❣❛:;♦ ❞❡ %U$✉❧♦# ❡♠ %❡❞❡# ❤❡$❡%♦❣V♥❡❛# ❬❙✉♥ ❛♥❞ ❍❛♥ ✷✵✶✷❪✳ ◆❛ ❛❜♦%❞❛❣❡♠ ❆❙2❍◆✱ #;♦ ✐♥$❡❣%❛❞♦# ❞✐✈❡%#♦# $✐♣♦# ❞❡ ✐♥❢♦%♠❛:W❡# ❝♦♠♦ ✈<%$✐❝❡# ❡♠ ✉♠❛ X♥✐❝❛ %❡❞❡✿ ❛$%✐❜✉$♦# ❧✐♥❣✉Z#$✐❝♦#❀ ❝❛♥❞✐❞❛$♦# ❛ ❛#♣❡❝$♦# ❡ ✉♠ ❝♦♥❥✉♥$♦ ❞❡ $❡%♠♦#✳ ❖ ❛♣%❡♥❞✐③❛❞♦ < ❜❛#❡❛❞♦ ♥❛ ♣%♦♣❛✲ ❣❛:;♦ ❞❛ ✐♥❢♦%♠❛:;♦ ❞❡ ❡①❡♠♣❧♦# %♦$✉❧❛❞♦# ♣♦% ♠❡✐♦ ❞❛# %❡❧❛:W❡# $♦♣♦❧U❣✐❝❛# ❡♥$%❡ ♦# ✈<%$✐❝❡#✳ ❆ ❛❜♦%❞❛❣❡♠ ❆❙2❍◆ ❢♦✐ ❛✈❛❧✐❛❞❛ ❡①♣❡%✐♠❡♥$❛❧♠❡♥$❡ ❡ ♦❜$❡✈❡ %❡#✉❧$❛❞♦# ♣%♦♠✐##♦%❡# ❡ ❝♦♠♣❡$✐$✐✈♦# *✉❛♥❞♦ ❝♦♠♣❛%❛❞❛ ❝♦♠ ✉♠❛ ❛❜♦%❞❛❣❡♠ #✉♣❡%✈✐#✐♦♥❛❞❛✳ ✷✳ ❆❇❖❘❉❆●❊▼ 2❘❖2❖❙❚❆✿ ❆❙2❍◆ ✭❆❙.❊❈❚✲❇❆❙❊❉ ❙❊◆❚■▼❊◆❚ .❘❖.❆●❆❚■❖◆ ❋❖❘ ❍❊❚❊❘❖●❊◆❊❖❯❙ ◆❊❚❲❖❘❑❙ ✮ ❉❛❞♦ ✉♠ ❝♦♥❥✉♥$♦ ❞❡ ❞♦❝✉♠❡♥$♦# ❡#❝%✐$♦# ❡♠ ❧Z♥❣✉❛ ♥❛$✉%❛❧✱ %❡♣%❡#❡♥$❛♥❞♦ ♠❡♥#❛❣❡♥#✱ %❡✈✐#W❡#✱ ❛♥!❧✐#❡#✱ ♦✉ ♥♦$Z❝✐❛# #♦❜%❡ ❛##✉♥$♦ ❡#♣❡❝Z✜❝♦✱ ♦ ♣%♦❜❧❡♠❛ ❞❛ ❆❙❇❆ ♣♦❞❡ #❡% ❞❡✜♥✐❞♦ ❝♦♠♦ ❡①$%❛✐% ♦♣✐♥✐W❡# %❡♣%❡#❡♥$❛❞❛# ♣❡❧❛ $%✐♣❧❛ O = (ei, aij, sij)✱ ❡♠ *✉❡ ei < ✉♠❛ ❡♥$✐❞❛❞❡ i ✭❡✳❣✳ ♣%♦❞✉$♦ ♦✉ #❡%✈✐:♦✮✱ aij < ♦ ❛#♣❡❝$♦ j ✭♣%♦♣%✐❡❞❛❞❡✮ ❞❛ ❡♥$✐❞❛❞❡ i✱ ❡ sij < ❛ ♣♦❧❛%✐❞❛❞❡ ❞♦ #❡♥$✐♠❡♥$♦ ❡♠ %❡✲ ❧❛:;♦ ❛♦ ❛#♣❡❝$♦ aij ❞❛ ❡♥$✐❞❛❞❡ ei✱ ♣♦% ❡①❡♠♣❧♦✱ ♣♦#✐$✐✈❛✱ ♥❡❣❛$✐✈❛ ♦✉ ♥❡✉$%❛✳ ◆♦ ❡#❝♦♣♦ ❞❡#$❡ $%❛❜❛❧❤♦✱ ❛ ❡♥$✐❞❛❞❡ < ✉♠❛ ✐♥❢♦%♠❛:;♦ ♣%<✈✐❛ ❞♦ ♣%♦❜❧❡♠❛✱ ❞❡ ❢♦%♠❛ *✉❡ ♦ ♦❜❥❡$✐✈♦ ❞♦ ❛♣%❡♥❞✐③❛❞♦ < ❛ ✐❞❡♥$✐✜❝❛:;♦ ❞❡ ❛#♣❡❝$♦# ❡ ❝❧❛##✐✜❝❛:;♦ ❞♦# %❡#♣❡❝$✐✈♦# #❡♥$✐♠❡♥$♦# %❡❢❡%❡♥$❡# _ ❡♥$✐❞❛❞❡ ❞❡✜♥✐❞❛✳ ❆ ❛❜♦%❞❛❣❡♠ ♣%♦♣♦#$❛ ❞❡♥♦♠✐♥❛❞❛ ❆❙2❍◆ ✭❆!♣❡❝%✲❇❛!❡❞ ❙❡♥%✐♠❡♥% ./♦♣❛❣❛%✐♦♥ ❢♦/ ❍❡%❡/♦❣❡✲ ♥❡♦✉! ◆❡%✇♦/❦!✮ ✉$✐❧✐③❛ ✉♠❛ %❡❞❡ ❤❡$❡%♦❣V♥❡❛ ❝♦♠♣♦#$❛ ♣♦% ✭✐✮ ❛#♣❡❝$♦# A ❂ {a1, ..., ar}❀ ✭✐✐✮ ❛$%✐❜✉✲ $♦# ❣%❛♠❛$✐❝❛✐# G ❂ {g1, ..., gq}❝♦♥❡❝$❛❞♦# ❛♦# ❝❛♥❞✐❞❛$♦# _ ❛#♣❡❝$♦#❀ ❡ ♣♦% ✭✐✐✐✮ $❡%♠♦# T ❂ {t1, ..., tg} ❝♦♥❡❝$❛❞♦# ❛♦# ❛#♣❡❝$♦# ❝❧❛##✐✜❝❛❞♦#✱ ❝♦♥❢♦%♠❡ ✐❧✉#$%❛❞♦ ♥❛ ❋✐❣✉%❛ ✶✭❛✮✳ ❆# ❛%❡#$❛# ✐♥❞✐❝❛♠ ❛✉#V♥❝✐❛ ♦✉ ♣%❡#❡♥:❛ ❞❛# %❡❧❛:W❡#✱ ❡#♣❡❝✐✜❝❛♠❡♥$❡✱ ✭✐✮ *✉❛♥❞♦ ❛$%✐❜✉$♦ ❣%❛♠❛$✐❝❛❧ ❡#$! %❡❧❛❝✐♦♥❛❞♦ ❛♦ ❛#♣❡❝$♦ ❡ ✭✐✐✮ *✉❛♥❞♦ ✉♠ $❡%♠♦ ♦❝♦%%❡ ♥❛ ♠❡#♠❛ #❡♥$❡♥:❛ ❞❡ ✉♠ ❛#♣❡❝$♦✳ ◆❛ ♠♦❞❡❧❛❣❡♠ ❛*✉✐ ♣%♦♣♦#$❛✱ ♦# ❝❛♥❞✐❞❛$♦# _ ❛#♣❡❝$♦# #;♦ $❡%♠♦# ❝♦♠♣♦#$♦# ♣♦% #✉❜#$❛♥$✐✈♦#✱ ✈❡%❜♦#✱ ❛❞❥❡$✐✈♦# ❡ ❛❞✈<%❜✐♦# ✐❞❡♥✲ $✐✜❝❛❞♦# ♥❛ ❝♦❧❡:;♦ $❡①$✉❛❧✳ ❏! ♦# ❛$%✐❜✉$♦# ❣%❛♠❛$✐❝❛✐# #;♦ ❡①$%❛Z❞♦# ❞❛# #❡♥$❡♥:❛#✱ ❜❡♠ ❝♦♠♦ ❞❛ %❡#♣❡❝$✐✈❛ %❡❞❡ ❞❡ ❞❡♣❡♥❞V♥❝✐❛ #✐♥$!$✐❝❛✳ 2♦% ❡①❡♠♣❧♦✱ ♥❛ ❢%❛#❡ ❡♠ ✐♥❣❧V# ✏ ❚❤❡ ❢♦♦❞ ✇❛! ♥♦%❤✐♥❣ ♠✉❝❤✱ ❜✉% ■ ❧♦✈❡❞ %❤❡ !%❛✛✳✑ < ♣♦##Z✈❡❧ ♦❜$❡% ❛ ❡#$%✉$✉%❛ ✐❧✉#$%❛❞❛ ♥❛ ❋✐❣✉%❛ ✶✭❜✮✱ ❝♦♠ ✉#♦ ❞❛ ❢❡%%❛♠❡♥$❛ ❙%❛♥❢♦/❞ ❈♦/❡◆▲.✳ 2♦% ✜♠✱ ♦# $❡%♠♦# #;♦ ♣❛❧❛✈%❛# ❡①$%❛Z❞❛# ❞♦# $❡①$♦#✱ ❡❧✐♠✐♥❛♥❞♦✲#❡ ❛# !%♦♣✇♦/❞! ✭♣%❡♣♦#✐:W❡#✱ ❛%$✐❣♦#✱ ❝♦♥❥✉♥:W❡# ❡ ♣%♦♥♦♠❡#✮✳ ❆♣U# ❛ ♠♦❞❡❧❛❣❡♠ ❞❛ %❡❞❡ ❤❡$❡%♦❣V♥❡❛✱ ♦ ♣%♦❝❡##♦ ❛✈❛♥:❛ ♣❛%❛ ❛ ❡$❛♣❛ ❞❡ ❛♣%❡♥❞✐③❛❞♦ #❡♠✐#✲ #✉♣❡%✈✐#✐♦♥❛❞♦✳ ◆❡##❡ ❝❛#♦✱ ❛##✉♠❡✲#❡ *✉❡ ✉♠❛ ♣❡*✉❡♥❛ *✉❛♥$✐❞❛❞❡ ❞❡ ❛#♣❡❝$♦# ❥! ❢♦✐ %♦$✉❧❛❞❛✳ ❖ ❛♣%❡♥❞✐③❛❞♦ ♥❛ ❛❜♦%❞❛❣❡♠ ❆❙2❍◆ ❡♥✈♦❧✈❡ ❛ ♣%♦♣❛❣❛:;♦ ❞❡##❡# %U$✉❧♦#✱ ❝♦♥❢♦%♠❡ ❛ $♦♣♦❧♦❣✐❛ ❞❛ %❡❞❡✱ ❜❛#❡❛❞♦ ❡♠ ✉♠❛ ❡①$❡♥#;♦ ❛*✉✐ ♣%♦♣♦#$❛ ❞♦ ♠<$♦❞♦ ▲❛❜❡❧ ./♦♣❛❣❛%✐♦♥ ✉!✐♥❣ ❇✐♣❛/%✐%❡ ❍❡%❡/♦❣❡♥❡♦✉! ◆❡%✇♦/❦! ❬❘♦##✐ ❡$ ❛❧✳ ✷✵✶✹❪✱ *✉❡ < ✉♠ ❞♦# ❛❧❣♦%✐$♠♦# ❞♦ ❡#$❛❞♦ ❞❛ ❛%$❡ ♣❛%❛ ❡#$❛ $❛%❡❢❛✳ 2❛%❛ $❛❧✱ ❝♦♥#✐❞❡%❡ *✉❡ A = AL_{∪ A}U _{< ♦ ❝♦♥❥✉♥$♦ ❞❡ ✈<%$✐❝❡# ❞♦ $✐♣♦ ❛#♣❡❝$♦✱ ♥❛ *✉❛❧ A}L _{< ♦ ❝♦♥❥✉♥$♦ ❞❡} ❛#♣❡❝$♦# %♦$✉❧❛❞♦# ❡ AU _{< ♦ ❝♦♥❥✉♥$♦ ❞❡ ❛#♣❡❝$♦# ♥;♦ %♦$✉❧❛❞♦#✱ ❡ *✉❡ ✉♠ ❝♦♥❥✉♥$♦ X %❡❢❡%❡✲#❡ ❛ ✉♠} #❡❣✉♥❞♦ $✐♣♦ ❞❡ ✈<%$✐❝❡✳ ❆✐♥❞❛✱ ❝♦♥#✐❞❡%❡ *✉❡ ❛ ♣%♦❜❛❜✐❧✐❞❛❞❡ ❞♦ ✈<%$✐❝❡ ai❡#$❛% ❝♦♥❡❝$❛❞♦ ❛♦ ✈<%$✐❝❡ ❙②♠♣♦%✐✉♠ ♦♥ ❑♥♦✇❧❡❞❣❡ ❉✐%❝♦✈❡2②✱ ▼✐♥✐♥❣ ❛♥❞ ▲❡❛2♥✐♥❣✱ ❑❉▼■▲❊ ✷✵✶✺✳ 3rd

(9)

·

xj w(ai, xj) 1 0 xj ai p(ai, xj) = w(ai, xj)/ X ak∈A w(ak, xi) p(xj, ai) = w(ai, xj)/ X xk∈X w(ai, xk)   FAL FAU FX  =   PAL AL P AL AU P AL X PAU_AL P_AL_AL P_AU_X PXAL P_XAU P_XX     FAL FAU FX   FAL FAU FX X FAL FAU F_X Y FAL P PXAL X PAL_AL P_AL_AU P_AU_AL P_AL_AL P_XX Y FAU X FX ← PXAL F_AL+ P_XAU F_AU X FAU ← P AU X FX FAL ← P AL XFX FAL ← YL X X 3.044 3rd

(10)

✹

·

■✳ #✳ ▼❛&'✉♥♦ ❛♥❞ ❘✳ ●✳ ❘♦''✐ ❛♥❞ ❘✳ ▼✳ ▼❛/❝❛❝✐♥✐ ❛♥❞ ❙✳ ❖✳ ❘❡③❡♥❞❡ ❡ ♦ "❡❣✉♥❞♦ ♣♦( 3.048 (❡✈✐"+❡" ❡♠ ✐♥❣❧." "♦❜(❡ ❧❛♣1♦♣"✱ ❞✐"♣♦♥✐❜✐❧✐③❛❞♦" ❡♠ ❬5♦♥1✐❦✐ ❡1 ❛❧✳ ✷✵✶✹❪✳ ❆ ❡①1(❛?@♦ ❞❡ ❛1(✐❜✉1♦" ❣(❛♠❛1✐❝❛✐" ❢♦✐ (❡❛❧✐③❛❞♦ ♣♦( ♠❡✐♦ ❞❛ ❢❡((❛♠❡♥1❛ ❙!❛♥❢♦&❞ ❈♦&❡◆▲,✱ ❣❡(❛♥❞♦ 74❛1(✐❜✉1♦" ❝♦♠♣♦"1♦" ♣♦( ❡"1(✉1✉(❛" ❣(❛♠❛1✐❝❛✐" ❡ ❞❡♣❡♥❞.♥❝✐❛" "✐♥1C1✐❝❛"✳ ❆ ❛✈❛❧✐❛?@♦ D ❜❛"❡❛❞❛ ♥❛ 1❛①❛ ❞❡ ❛❝❡(1♦ ♠D❞✐❛ ❝♦♥"✐❞❡(❛♥❞♦ ✈❛❧✐❞❛?@♦ ❝(✉③❛❞❛ ✉"❛♥❞♦ 10✲❢♦❧❞/✳ ❖ ♣(♦❝❡""♦ ❞❡ ❛♣(❡♥❞✐③❛❞♦ "❡♠✐""✉♣❡(✈✐"✐♦♥❛❞♦ ❞❛ ❛❜♦(❞❛❣❡♠ ❆❙5❍◆ ❢♦✐ "✐♠✉❧❛❞♦ ❝♦♠ I✉❛1(♦ 1❛♠❛♥❤♦ ❞❡ ❛♠♦"1(❛" (♦1✉❧❛❞❛"✱ "❡❧❡❝✐♦♥❛♥❞♦✲"❡ ❛❧❡❛1♦(✐❛♠❡♥1❡ {1%, 10%, 20% e 30%} ❞♦ ❝♦♥❥✉♥1♦ ❞❡ 1(❡✐♥❛✲ ♠❡♥1♦ ❡♠ ❝❛❞❛ ✐1❡(❛?@♦ ❞❛ ✈❛❧✐❞❛?@♦ ❝(✉③❛❞❛✳ ❖" ❞❡♠❛✐" ❡①❡♠♣❧♦" ❢♦(❛♠ ❝♦♥"✐❞❡(❛❞♦" ❝♦♠♦ ❡①❡♠♣❧♦" ♥@♦ (♦1✉❧❛❞♦" ♣♦( ♣❛(1❡ ❞❛ ❛❜♦(❞❛❣❡♠ ❆❙5❍◆✳ ❆ ❛❜♦(❞❛❣❡♠ ❆❙5❍◆ ❢♦✐ ❝♦♠♣❛(❛❞❛ ❝♦♠ ✉♠❛ ❛❜♦(✲ ❞❛❣❡♠ "✉♣❡(✈✐"✐♦♥❛❞❛✱ I✉❡ ✉1✐❧✐③❛ 90% ❞❡ ❞❛❞♦" (♦1✉❧❛❞♦" ❡♠ ❝❛❞❛ ✐1❡(❛?@♦ ❞❛ ✈❛❧✐❞❛?@♦ ❝(✉③❛❞❛✳ ❋♦✐ "❡❧❡❝✐♦♥❛❞♦ ♦ ❛❧❣♦(✐1♠♦ ◆❛✐✈❡ ❇❛②❡/ ♣❛(❛ ❛ ❝♦♠♣❛(❛?@♦✱ ✉♠❛ ✈❡③ I✉❡ ❡"1❡ ♣❡(♠✐1❡ ✈❡(✐✜❝❛( ❛ ❝♦♥1(✐❜✉✐?@♦ ✭♣(♦❜❛❜✐❧✐❞❛❞❡✮ ❞❡ ❝❛❞❛ ❛1(✐❜✉1♦ ♣❛(❛ ❝❛❞❛ ❝❧❛""❡ ✭"✐♠✐❧❛( Q ❛❜♦(❞❛❣❡♠ ❆❙5❍◆✮✳ ! "# ! $ %$ &$ % ! "# $ %$ &$ ❋✐❣✳ ✷✳ ❈♦♠♣❛*❛+,♦ ❞❛ .❛①❛ ❞❡ ❛❝❡*.♦ ❡♥.*❡ ❛ ❆❙5❍◆ ❝♦♠ ✉♠❛ ❛❜♦*❞❛❣❡♠ :✉♣❡*✈✐:✐♦♥❛❞❛✳

❖! "❡!✉❧&❛❞♦! ❡①♣❡"✐♠❡♥&❛✐!✱ ❛♣"❡!❡♥&❛❞♦! ♥♦ 0✉❛❞"♦ ❞❛ ❋✐❣✉"❛ ✷ ✐♥❞✐❝❛♠ 0✉❡ ❛ ❛❜♦"❞❛❣❡♠ ♣"♦♣♦!&❛ ❆❙8❍◆✱ ♠❡!♠♦ ✉&✐❧✐③❛♥❞♦ ✉♠❛ 0✉❛♥&✐❞❛❞❡ ♠✉✐&♦ ✐♥❢❡"✐♦" ❞❡ ❡①❡♠♣❧♦! "♦&✉❧❛❞♦!✱ ♦❜&=♠ "❡!✉❧&❛❞♦! ❝♦♠♣❡&✐&✐✈♦! ❝♦♠ ✉♠❛ ❛❜♦"❞❛❣❡♠ !✉♣❡"✈✐!✐♦♥❛❞❛✳ ❯♠❛ ❛♥A❧✐!❡ ❡!&❛&B!&✐❝❛ ✉&✐❧✐③❛♥❞♦ ♦ &❡!&❡ ❚✲❙#✉❞❡♥# ♥C♦ ✐♥❞✐❝❛ ❞✐❢❡"❡♥D❛ !✐❣♥✐✜❝❛&✐✈❛ ❡♥&"❡ ❛! ❞✉❛! ❛❜♦"❞❛❣❡♥! 0✉❛♥❞♦ !C♦ ✉&✐❧✐③❛❞♦! 10% ♦✉ ♠❛✐! ❞❡ ❞❛❞♦! "♦&✉❧❛❞♦! ♥❛ ❛❜♦"❞❛❣❡♠ ❆❙8❍◆✳

✹✳ ❈❖◆❙■❉❊❘❆➬M❊❙ ❋■◆❆■❙

◆❡!&❡ &"❛❜❛❧❤♦ ❢♦✐ ♣"♦♣♦!&❛ ❛ ❛❜♦"❞❛❣❡♠ ❆❙8❍◆ ✭❆)♣❡❝#✲❇❛)❡❞ ❙❡♥#✐♠❡♥# 01♦♣❛❣❛#✐♦♥ ❢♦1 ❍❡#❡1♦✲ ❣❡♥❡♦✉) ◆❡#✇♦1❦)✮✱ 0✉❡ ♣❡"♠✐&❡ ✐❞❡♥&✐✜❝❛" ❛!♣❡❝&♦! ❡ ❝❧❛!!✐✜❝❛" ❛ ♣♦❧❛"✐❞❛❞❡ ❞♦ !❡♥&✐♠❡♥&♦ ❞❡ ❝❛❞❛ ❛!♣❡❝&♦ ✉!❛♥❞♦ ❛♣"❡♥❞✐③❛❞♦ !❡♠✐!!✉♣❡"✈✐!✐♦♥❛❞♦✳ ◆C♦ ❤A ♥❛ ❧✐&❡"❛&✉"❛ ✉♠❛ ❛❜♦"❞❛❣❡♠ 0✉❡ ❡①♣❧♦"❛ "❡❞❡! ❤❡&❡"♦❣Q♥❡❛! ♣❛"❛ ❛♥A❧✐!❡ ❞❡ !❡♥&✐♠❡♥&♦! ❜❛!❡❛❞❛ ❡♠ ❛!♣❡❝&♦! ❡ ♦! "❡!✉❧&❛❞♦! ♣"❡❧✐♠✐♥❛"❡! ♦❜&✐❞♦! ✐♥❞✐❝❛♠ 0✉❡ ❡!&❡ = ✉♠ ❝❛♠✐♥❤♦ ♣"♦♠✐!!♦"✳

❊♥&"❡ ❛! ❧✐♠✐&❛DR❡! ❡ ❞✐"❡DR❡! ♣❛"❛ &"❛❜❛❧❤♦! ❢✉&✉"♦!✱ ❛ ❛❜♦"❞❛❣❡♠ ❞❡✈❡ !❡" ❝♦♠♣❛"❛❞❛ ❝♦♠ ♦✉&"❛! ❡!&"❛&=❣✐❛! ❞❡ ❛♣"❡♥❞✐③❛❞♦ !❡♠✐!!✉♣❡"✈✐!✐♦♥❛❞♦✱ ❜❡♠ ❝♦♠♦ ❡♠ &❡①&♦! ❡!❝"✐&♦! ♥❛ ❧B♥❣✉❛ ♣♦"&✉❣✉❡!❛✳ ❆✐♥❞❛✱ ♦! ❛✉&♦"❡! ♣"❡&❡♥❞❡♠ ✐♥&❡❣"❛" ✉♠❛ ❡!&"❛&=❣✐❛ ❞❡ ❛♣"❡♥❞✐③❛❞♦ ❛&✐✈♦ ♣❛"❛ ❛♣♦✐❛" ❛ "♦&✉❧❛DC♦ ❞❛ ❛♠♦!&"❛ ✐♥✐❝✐❛❧✱ ❝♦♠ ❛✈❛❧✐❛DC♦ ❡♠ ♦✉&"♦! ❞♦♠B♥✐♦! ❡ ❝♦♥❥✉♥&♦! ❞❡ ❞❛❞♦!✳

❆❣"❛❞❡❝✐♠❡♥*♦,✿ ❖: ❛✉.♦*❡: ❛❣*❛❞❡❝❡♠ = ❋❆5❊❙5 ✭5*♦❝❡::♦: ✷✵✶✹✴✵✽✾✾✻✲✵ ❡ ✷✵✶✶✴✶✷✽✷✸✲✻ ✮ ❡ 5❘❖55✴❯❋▼❙ ✭5*♦.♦❝♦❧♦ ❙✐❣5*♦❥ ✶✻✵✸✹✸✳✻✻✾✳✶✻✾✼✻✺✳✶✷✶✶✷✵✶✸✮ ♣❡❧♦ ❛✉①Q❧✐♦ ❢♦*♥❡❝✐❞♦ ♣❛*❛ ❞❡:❡♥✈♦❧✈✐♠❡♥.♦ ❞❡:.❡ .*❛❜❛❧❤♦✳ ❘❊❋❊❘❊◆❈❊❙ ❈❤❡♥✱ ❩✳✱ ▼✉❦❤❡*❥❡❡✱ ❆✳✱ ❛♥❞ ▲✐✉✱ ❇✳ ❆:♣❡❝. ❡①.*❛❝.✐♦♥ ✇✐.❤ ❛✉.♦♠❛.❡❞ ♣*✐♦* ❦♥♦✇❧❡❞❣❡ ❧❡❛*♥✐♥❣✳ ■♥ !♦❝✳ ♦❢ ❆❈▲✳ ♣♣✳ ✸✹✼✕✸✺✽✱ ✷✵✶✹✳ ❏✐♠4♥❡③✲❩❛❢*❛✱ ❙✳ ▼✳✱ ▼❛*9:♥✲❱❛❧❞✐✈✐❛✱ ▼✳ ❚✳✱ ▼❛*9:♥❡③✲❈?♠❛*❛✱ ❊✳✱ ❛♥❞ ❯*❡B❛✲▲C♣❡③✱ ▲✳ ❆✳ ❈♦♠❜✐♥✐♥❣ *❡:♦✉*❝❡: .♦ ✐♠♣*♦✈❡ ✉♥:✉♣❡*✈✐:❡❞ :❡♥.✐♠❡♥. ❛♥❛❧②:✐: ❛. ❛:♣❡❝.✲❧❡✈❡❧✳ ❏♦✉!♥❛❧ ♦❢ ■♥❢♦!♠❛0✐♦♥ ❙❝✐❡♥❝❡✱ ✷✵✶✺✳ ❑✐♠✱ ❙✳✱ ❩❤❛♥❣✱ ❏✳✱ ❈❤❡♥✱ ❩✳✱ ❖❤✱ ❆✳ ❍✳✱ ❛♥❞ ▲✐✉✱ ❙✳ ❆ ❤✐❡*❛*❝❤✐❝❛❧ ❛:♣❡❝.✲:❡♥.✐♠❡♥. ♠♦❞❡❧ ❢♦* ♦♥❧✐♥❡ *❡✈✐❡✇:✳ ■♥ ❆❆❆■✱ ✷✵✶✸✳ ▲✐✉✱ ❇✳ ❙❡♥.✐♠❡♥. ❛♥❛❧②:✐: ❛♥❞ ♦♣✐♥✐♦♥ ♠✐♥✐♥❣✳ ▼♦!❣❛♥ ✫ ❈❧❛②♣♦♦❧ ✉❜❧✐:❤❡!:✱ ✷✵✶✷✳

I♦♥9✐❦✐✱ ▼✳✱ ●❛❧❛♥✐L✱ ❉✳✱ I❛✈❧♦♣♦✉❧♦L✱ ❏✳✱ I❛♣❛❣❡♦*❣✐♦✉✱ ❍✳✱ ❆♥❞*♦✉9L♦♣♦✉❧♦L✱ ■✳✱ ❛♥❞ ▼❛♥❛♥❞❤❛*✱ ❙✳ ❙❡♠❡✈❛❧✲✷✵✶✹ .❛:❦ ✹✿ ❆:♣❡❝. ❜❛:❡❞ :❡♥.✐♠❡♥. ❛♥❛❧②:✐:✳ ■♥ !♦❝✳ ❙❡♠❊✈❛❧✳ ♣♣✳ ✷✼✕✸✺✱ ✷✵✶✹✳ ❘♦LL✐✱ ❘✳ ●✳✱ ▲♦♣❡L✱ ❆✳ ❆✳✱ ❛♥❞ ❘❡③❡♥❞❡✱ ❙✳ ❖✳ ❆ ♣❛*❛♠❡.❡*✲❢*❡❡ ❧❛❜❡❧ ♣*♦♣❛❣❛.✐♦♥ ❛❧❣♦*✐.❤♠ ✉:✐♥❣ ❜✐♣❛*.✐.❡ ❤❡.❡*♦❣❡♥❡♦✉: ♥❡.✇♦*❦: ❢♦* .❡①. ❝❧❛::✐✜❝❛.✐♦♥✳ ■♥ !♦❝✳ ❙②♠♣♦:✐✉♠ ♦♥ ❆♣♣❧✐❡❞ ❈♦♠♣✉0✐♥❣✳ ❆❈▼✱ ♣♣✳ ✼✾✕✽✹✱ ✷✵✶✹✳ ❙✉♥✱ ❨✳ ❛♥❞ ❍❛♥✱ ❏✳ ▼✐♥✐♥❣ ❍❡0❡!♦❣❡♥❡♦✉: ■♥❢♦!♠❛0✐♦♥ ◆❡0✇♦!❦:✿ !✐♥❝✐♣❧❡: ❛♥❞ ▼❡0❤♦❞♦❧♦❣✐❡:✳ ▼♦*❣❛♥ ✫ ❈❧❛②♣♦♦❧ 5✉❜❧✐:❤❡*:✱ ✷✵✶✷✳ ❙②♠♣♦%✐✉♠ ♦♥ ❑♥♦✇❧❡❞❣❡ ❉✐%❝♦✈❡2②✱ ▼✐♥✐♥❣ ❛♥❞ ▲❡❛2♥✐♥❣✱ ❑❉▼■▲❊ ✷✵✶✺✳ 3rd