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Dissertations |
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DENISE LEMOS CARDOSO
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Advisor : ALLBENS ATMAN PICARDI FARIA
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COMMITTEE MEMBERS :
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ALLBENS ATMAN PICARDI FARIA
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BRENO RODRIGUES LAMAGHERE GALVAO
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FELIPE GALVÃO RAFAEL MAGALHÃES
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Data: Feb 10, 2023
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2
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CESAR AUGUSTO SOUZA DE OLIVEIRA
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Advisor : SERGIO RICARDO DE SOUZA
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COMMITTEE MEMBERS :
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SERGIO RICARDO DE SOUZA
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GUSTAVO CAMPOS MENEZES
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MARIA AMÉLIA LOPES SILVA
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Rodney Oliveira Marinho Diana
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Data: Feb 24, 2023
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3
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DIOGO SOUZA DE FIGUEIREDO
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Advisor : THIAGO DE SOUZA RODRIGUES
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COMMITTEE MEMBERS :
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GUSTAVO CAMPOS MENEZES
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SANDRO RENATO DIAS
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THIAGO DE SOUZA RODRIGUES
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Data: Feb 27, 2023
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View Dissertation/Thesis
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In almost every daily activity, the internet is always present. Many of these activities require the sharing of personal data (e.g. address, telephone, age, location, among others) and data considered sensitive (e.g. medical diagnosis, bank account, among others), generating a privacy concern. of this information to society. Sharing information requires the use of data protection tools, so the information in this data cannot be used to identify an individual. In order to comply with applicable laws and regulations, as well as informed data protection policies, a data protection mechanism called data anonymization has emerged. This mechanism basically consists of removing identifiers and hiding sensitive data, making it impossible to re-identify. As large amounts of data from individuals are disseminated, new challenges arise for the protection of their privacy. Various anonymization algorithms have been proposed, making publishing privacy-preserving data a very broad area of research. However, it is difficult to identify and select the most suitable algorithm, due to the large number of available algorithms and limited information about their performance. In this work, three anonymization algorithms called DataFly, Incognito and Mondrian are presented. Its efficiencies in data processing, its effectiveness in the amount of data used will be addressed, employing a wide set of different parameters, metrics and data sets. To guide the selection of an algorithm, a battery of experiments will be carried out among them to identify which factors can influence performance, presenting the conditions in which each algorithm outperforms each other in certain privacy requirements as well as their advantages and disadvantages
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4
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ALEXANDRE AUGUSTO AGUIAR GOMES
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Advisor : FLAVIO LUIS CARDEAL PADUA
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COMMITTEE MEMBERS :
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FLAVIO LUIS CARDEAL PADUA
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GUSTAVO CAMPOS MENEZES
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DANIEL HASAN DALIP
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MICHELE AMARAL BRANDÃO
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Data: Feb 27, 2023
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5
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WANDERLEY DA SILVA
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Advisor : ANTONIO PAULO BAETA SCARPELLI
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COMMITTEE MEMBERS :
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OSVALDO NEGRINI NETO
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ANTONIO PAULO BAETA SCARPELLI
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GIANCARLO QUEIROZ PELLEGRINO
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LUIZ CLEBER TAVARES DE BRITO
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Data: Mar 13, 2023
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6
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RODRIGO COIMBRA PEREIRA ALVES
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Advisor : ARTHUR RODRIGO BOSCO DE MAGALHAES
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COMMITTEE MEMBERS :
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ALLBENS ATMAN PICARDI FARIA
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ARTHUR RODRIGO BOSCO DE MAGALHAES
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CHARLENE CASSIA DE RESENDE
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CRISTIANO ARBEX VALLE
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Data: Jul 4, 2023
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7
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ROMARIO DOS SANTOS LOPES DE ASSIS
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Advisor : MARCONE JAMILSON FREITAS SOUZA
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COMMITTEE MEMBERS :
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TATIANA ALVES COSTA
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EDUARDO CAMARGO DE SIQUEIRA
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ELISANGELA MARTINS DE SA
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MARCONE JAMILSON FREITAS SOUZA
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MARIA AMÉLIA LOPES SILVA
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SERGIO RICARDO DE SOUZA
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Data: Jul 11, 2023
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8
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LEONARDO CORRÊA CARDOSO
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Advisor : ELISANGELA MARTINS DE SA
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COMMITTEE MEMBERS :
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ELISANGELA MARTINS DE SA
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GUSTAVO CAMPOS MENEZES
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Rodney Oliveira Marinho Diana
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SERGIO RICARDO DE SOUZA
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Data: Jul 14, 2023
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9
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RÓGENES REIS FIRMINO
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Advisor : FLAVIO LUIS CARDEAL PADUA
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COMMITTEE MEMBERS :
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FABÍOLA DE OLIVEIRA PAES LEME
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FLAVIO LUIS CARDEAL PADUA
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GUSTAVO CAMPOS MENEZES
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MARCO TULIO ALVES NOLASCO RODRIGUES
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NATALIA COSSE BATISTA
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Data: Aug 7, 2023
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10
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JOICE MARTINHA RODRIGUES
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Advisor : GUSTAVO CAMPOS MENEZES
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COMMITTEE MEMBERS :
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ELISANGELA MARTINS DE SA
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GUSTAVO ALVES FERNANDES
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GUSTAVO CAMPOS MENEZES
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THIAGO DE SOUZA RODRIGUES
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Data: Oct 5, 2023
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11
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MIRIAN GREINER DE OLIVEIRA PINHEIRO
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Advisor : GRAY FARIAS MOITA
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COMMITTEE MEMBERS :
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ELISANGELA MARTINS DE SA
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GRAY FARIAS MOITA
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GUILHERME DE CASTRO LEIVA
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MATHEUS HENRIQUE DE SOUSA OLIVEIRA
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RENATO GUIMARAES RIBEIRO
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Data: Oct 23, 2023
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12
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DANIEL LETO NEIVA COSTA
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Advisor : ELIZABETH FIALHO WANNER
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COMMITTEE MEMBERS :
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ELIZABETH FIALHO WANNER
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FLAVIO VINICIUS CRUZEIRO MARTINS
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ARTHUR RODRIGO BOSCO DE MAGALHAES
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JUAN PABLO NEIROTTI
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ROBERTO CASTRO ALAMINO
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Data: Dec 18, 2023
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13
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GERMANO TEIXEIRA DE MIRANDA
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Advisor : FLAVIO VINICIUS CRUZEIRO MARTINS
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COMMITTEE MEMBERS :
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LENIANA SANTOS NEVES
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ALISSON MARQUES DA SILVA
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FLAVIO VINICIUS CRUZEIRO MARTINS
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Data: Dec 21, 2023
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View Dissertation/Thesis
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Computer diagnostic aid systems are used in the various health sectors to facilitate the work of the most used health professionals. These computer systems help healthcare professionals to detect the chance of error, correct the accuracy of the diagnosis, in addition to reducing the time and cost of making the diagnosis. More specifically in the measures traced from cephalometric treatment in linear and not crucial to determine an orthodontic treatment. For the elaboration of this exam, measurements are made in a lateral medicine of the head called teleradiography. The diagnosis of a tracing tracing was obtained through the evaluation of measurements performed on teleradiography in comparison with the defined ideal pattern. This can be a comprehensive and well-defined feature as a candidate for the application of computational assessment techniques, without the possibility of automatic diagnosis, an intervention manual of the specialist. Research is evaluated as an existing computational research technique and currently applied. For the application of computer vision techniques, we intend to extract a basis from one of cephalometric tracing training tests performed in the most computerized tracing data collection tool of Cfaznet, one of the tracing data software in Latin America. . This training base will be used for nutritional calculation as a computer vision technique that can best perform the task of anatomical points in a teleradiography. In order to find the techniques it is best to carry out the tracing exam, most likely the job of searching to find the best techniques comparatively. In this way, computer vision techniques were studied today capable of performing a projected cephalometric determination exam without a theoretical intervention.
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Thesis |
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1
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SOLANGE CONCEIÇÃO DE OLIVEIRA
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Advisor : LEONARDO DOS SANTOS LIMA
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COMMITTEE MEMBERS :
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ADRIANO CESAR MACHADO PEREIRA
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ADÉLCIO CARLOS DE OLIVEIRA
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FELIPE DIAS PAIVA
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JOSE LUIZ ACEBAL FERNANDES
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LEONARDO DOS SANTOS LIMA
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Data: Feb 23, 2023
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2
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PRISCILA FLÁVIA SOUZA DA SILVA
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Advisor : GRAY FARIAS MOITA
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COMMITTEE MEMBERS :
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ALISSON MARQUES DA SILVA
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ELIENE PIRES CARVALHO
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GRAY FARIAS MOITA
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GUSTAVO CAMPOS MENEZES
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MOACIR KRIPKA
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ROQUE LUIZ DA SILVA PITANGUEIRA
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Data: Feb 24, 2023
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3
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DANIEL DE OLIVEIRA CAPANEMA
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Advisor : ADRIANO CESAR MACHADO PEREIRA
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COMMITTEE MEMBERS :
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ADRIANO CESAR MACHADO PEREIRA
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ADRIANO LIMA ALVES
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ELIZABETH FIALHO WANNER
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FLAVIO LUIS CARDEAL PADUA
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JOÃO GUSTAVO CLAUDINO
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PAULO ROBERTO PEREIRA SANTIAGO
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Data: Feb 27, 2023
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4
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JOSENILDO SILVA DE LIMA
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Advisor : RODRIGO TOMAS NOGUEIRA CARDOSO
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COMMITTEE MEMBERS :
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ANA PAULA PINTADO WYSE
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ARTHUR RODRIGO BOSCO DE MAGALHAES
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JOSE LUIZ ACEBAL FERNANDES
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RICARDO HIROSHI CALDEIRA TAKAHASHI
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RODRIGO TOMAS NOGUEIRA CARDOSO
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Data: Feb 27, 2023
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5
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SINAIDE NUNES BEZERRA
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Advisor : MARCONE JAMILSON FREITAS SOUZA
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COMMITTEE MEMBERS :
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ELISANGELA MARTINS DE SA
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ELIZABETH FIALHO WANNER
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LUIZ SATORU OCHI
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MARCONE JAMILSON FREITAS SOUZA
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PUCA HUACHI VAZ PENNA
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SERGIO RICARDO DE SOUZA
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Data: Feb 27, 2023
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View Dissertation/Thesis
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6
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FLÁVIA DA SILVA CORDEIRO
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Advisor : JOSE LUIZ ACEBAL FERNANDES
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COMMITTEE MEMBERS :
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ALLBENS ATMAN PICARDI FARIA
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ARTHUR RODRIGO BOSCO DE MAGALHAES
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CLÁUDIA MAZZA DIAS
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FABIO ROCHA DA SILVA
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JOSE LUIZ ACEBAL FERNANDES
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LUCY TIEMI TAKAHASHI
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Data: Feb 28, 2023
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7
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LUIZ OTAVIO RODRIGUES ALVES SERENO
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Advisor : JOSE LUIZ ACEBAL FERNANDES
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COMMITTEE MEMBERS :
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JOSE LUIZ ACEBAL FERNANDES
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ARTHUR RODRIGO BOSCO DE MAGALHAES
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JOSE GERALDO PEIXOTO DE FARIA
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LUIS ALBERTO D AFONSECA
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Ana Paula de Paiva Pereira
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CARLOS ALEXANDRE SILVA
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Data: Feb 28, 2023
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View Dissertation/Thesis
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TNormal diffusion is a process observed in many phenomena in nature. For these processes there are well-developed simulations and theory, namely the random walk (RW) and the diffusion equation, or Fokker-Planck. However, in systems with long-range interactions between individuals or between individuals and the environment, there may be deviations from this regime and present anomalous behaviour. This class of more general processes is called anomalous diffusion. Systems in which there are interactions between individuals or between individuals and the environment, for example, deviate from the usual description of diffusion, presenting an anomalous behaviour. The theoretical approach to these phenomena ranges from analytical representation through partial differential equations, stochastic equations and computational simulations that mimic the phenomenon. From displacement data and characteristic times of a phenomenon on a microscopic scale, it is possible to identify the theoretical parameters of the models that macroscopically describe these data. For this purpose, a theoretical study is carried out in which datasets are generated by simulations with controlled microdynamic parameters and adjusted to a function associated with the phenomenon. In this study, flights are generated via continuous time random walk (CTRW) and the anomalous diffusion models are fractional partial differential equations with solutions obtained by Fractional Calculus. An evolutionary algorithm capable of obtaining parameters that describe the phenomenon is presented, with only a limitation in the parameter space being a prerequisite. Furthermore, in the discretization process of the theoretical model associated with the phenomenon, new parameters emerge whose behaviours are investigated, as their role can influence the study of anomalous diffusion. As an immediate application of superdiffusion is included the study of specialized proteins, called transcription factors, in cells that allow the transcription of deoxyribonucleic acid (DNA).
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8
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IZABELA MARQUES DE OLIVEIRA
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Advisor : ALLBENS ATMAN PICARDI FARIA
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COMMITTEE MEMBERS :
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ALLBENS ATMAN PICARDI FARIA
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ANTONIO PAULO BAETA SCARPELLI
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ARTHUR RODRIGO BOSCO DE MAGALHAES
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BRUNA AMIN GONCALVES
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LAURA CORINA CARPI
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TIAGO ALVES SCHIEBER DE JESUS
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Data: Mar 20, 2023
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Air transportation remains the best option to connect distant regions and support world social and economic development, despite environmental challenges. Brazil depends strongly in this mode of transportation due to its continental dimensions. In this work, we conducted a study using the multiplex approach of complex networks to analyze the air transport network of Brazilian passengers, BATMN. In this context, we create the multiplex efficiency index (MEI) and its versions for targeted and/or weighted networks, which allow to quantify the level of connection heterogeneity of a multiplex network on a scale of 0 to 1, considering the characteristics of direction and importance level of edges, being appropriate for research in transportation networks. We used the MEI to evaluate the diversification of routes of airlines in Brazil between 2010 and 2021, a period of occurrence of major events in the country. We analyzed the influence of some of these events on network efficiency, such as the FIFA World Cup in 2014 and the Rio Olympic Games in 2016, as well as other sector changes, including the merger between airlines, airport privatization, the closure of operations of an important air carrier and COVID-19 pandemic. In addition, we investigated whether the diversification of routes affected the prices of air tickets in Brazil. Additionally, through a recently introduced methodology in the literature, we examined the network’s diffusion capacity and observed the relative gain that occurred in the diffusion of the air transportation system when the flight connections between different airlines are considered, outlining a scenario possible partnerships between airlines. The evaluations carried out in this work provide new and significant information about the passenger air transportation network in Brazil, contributing to optimize the offer of this type of transportation in the country and, consequently, reduce the costs involved. In addition, the proposed methodology allows not only a differentiated analysis of air transportation networks, but also the quantification of the efficiency of multiplex networks in general.
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9
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DANIEL MORAIS DOS REIS
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Advisor : SERGIO RICARDO DE SOUZA
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COMMITTEE MEMBERS :
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IGOR MACHADO COELHO
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ANOLAN YAMILE MILANES BARRIENTOS
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GUSTAVO ALVES FERNANDES
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GUSTAVO CAMPOS MENEZES
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MARCONE JAMILSON FREITAS SOUZA
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SERGIO RICARDO DE SOUZA
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Data: Aug 18, 2023
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View Dissertation/Thesis
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This work optimizes sequential methods and proposes parallelized heuristic methods on Nvidia CUDA GPUs to solve the Fiber Installation Problem in Optical Networks PIFRO. PIFRO consists of allocating, in an optical network that uses Wavelength Division Multiplexing (WDM) technology, a set of previously known requests with multiple origins and destinations. The objective is to minimize the total cost of the devices required to operate the network. After proving that the decision version of PIFRO is NP-Hard, a mathematical formulation is carried out and two parallelized metaheuristics are implemented in new formats, seeking to improve the results in the literature. One of the heuristics is based on Biased Random Key Genetic Algorithm (BRKGA) and the other is based on Iterated Local Search (ILS) which were selected due to the good results available for the problem. The basic concepts of parallel processing are analyzed and selected for executing new metaheuristics in heterogeneous environments with GPUs.
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10
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OTAVIANO MARTINS MONTEIRO
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Advisor : THIAGO DE SOUZA RODRIGUES
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COMMITTEE MEMBERS :
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THIAGO DE SOUZA RODRIGUES
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ALISSON MARQUES DA SILVA
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GUSTAVO CAMPOS MENEZES
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ANDRE RODRIGUES DA CRUZ
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ROGERIO MARTINS GOMES
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SANDRO RENATO DIAS
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Data: Aug 24, 2023
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11
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GILSON VIEIRA SOARES
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Advisor : JOSE GERALDO PEIXOTO DE FARIA
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COMMITTEE MEMBERS :
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ADÉLCIO CARLOS DE OLIVEIRA
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ALLBENS ATMAN PICARDI FARIA
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GIANCARLO QUEIROZ PELLEGRINO
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JOSE GERALDO PEIXOTO DE FARIA
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LUIS ARGEL POVEDA CALVINO
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MAURICIO REIS E SILVA JUNIOR
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THIAGO GOMES DE MATTOS
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Data: Aug 29, 2023
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In this study, we investigate the two-mode Bose-Hubbard model with atom-atom interactions harmonically tuned over time. The classical Hamiltonian is derived through an expansion of the quantum Hamiltonian in terms of 1/N. Chaotic behavior is observed in classical dynamics, and we map the parameter and phase space using the dominant Lyapunov exponent and quantum measures such as Loschmidt echo, generalized purity, and linear entropy. In the quantum counterpart of chaos, irregular Josephson oscillations are noted. In the regular regime, we identify collapses, revivals, quasi-periodicity, and coherent control of Josephson oscillations.
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12
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TULIO PHILIPE FERREIRA E VIEIRA
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Advisor : GRAY FARIAS MOITA
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COMMITTEE MEMBERS :
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MARCOS PAULINO RORIZ JUNIOR
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ALISSON MARQUES DA SILVA
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ELISANGELA MARTINS DE SA
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GRAY FARIAS MOITA
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GUILHERME DE CASTRO LEIVA
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MAGALI REZENDE GOUVEA MEIRELES
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RENATO GUIMARAES RIBEIRO
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Data: Aug 29, 2023
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View Dissertation/Thesis
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According to data from the United Nations (UN), there are currently more than 3.8 billion people living in cities and in 2050, almost 70% of the world’s population will live in urbana reas. Cities are considered places of economic, political, cultural and social development, but disorderly urbanization, especially in developing countries, has deteriorated the quality of various systems and services offered to citizens. Among the systems that make up the urban infrastructure, the transportation system can be seen as an indicator of the residents’ quality of life. This is because, through the analysis of the transport system, from wich people gain access to medical, educational, cultural and leisure services, it is possible to identify social, economical and cultural differences. Thus, in order to ensure the construction of sustainable cities that offer a good quality of life to their inhabitants, the planning and efficient management of urban mobility is essential. In order to contribute to the construction of an efficient transport system, this work presents the development of a framework composed of low cost hardware and software, which can be used to generate and monitor real time indicators for the transport system. The proposedframeworkuses data from different sources such asprobe request, census and smart card and employs machine learning algorithms such as Kalman Filter and Artificial Neural Networks to generate the origin-destination matrix and other indicators of the transportation system. Preliminary results indicate that the strategy used manages to reduce errors in forecasting indicators to less than 5%.
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13
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RENAN JOSÉ DOS SANTOS VIANA
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Advisor : FLAVIO VINICIUS CRUZEIRO MARTINS
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COMMITTEE MEMBERS :
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CLAUDIO LUCIO DO VAL LOPES
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ELIZABETH FIALHO WANNER
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FLAVIO VINICIUS CRUZEIRO MARTINS
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MARCONE JAMILSON FREITAS SOUZA
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RICARDO HIROSHI CALDEIRA TAKAHASHI
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SERGIO RICARDO DE SOUZA
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Data: Aug 30, 2023
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View Dissertation/Thesis
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Several problems encountered in science, engineering, industry, among other fields of knowledge, involve the simultaneous optimization of two or more often conflicting objectives. Problems with such characteristics are known in the literature as Multiobjective Optimization Problems. Due to the existence of a certain level of conflict between the optimized objectives, for this class of problems, there is no single optimal solution (global) as in mono-objective problems; instead, they produce a set of solutions that represent the possible trade-offs between objectives. Generally, in multiobjective optimization, the Pareto dominance relation is adopted to compare solutions. Thus, the optimal solutions to the problem are called Pareto-optimal solutions, and the image of this set in the objective space is called the Pareto-Optimal front.
Over the past few years, both experimental and theoretical research has indicated that the increase in the number of optimized objectives promotes new and complex challenges. For example, the increase in the proportion of non-dominated solutions, the exponential growth in the number of solutions necessary to achieve a complete approximation of the Pareto-optimal front, the ineffectiveness of traditional solutions visualization techniques, difficulty in ensuring the maintenance of diversity population, among others. However, it is known that a multiobjective problem does not necessarily become more complicated when new objectives are added. Other properties of the problem can also increase its complexity, such as the characteristics of the test problems used. Also, combinatorial problems have not received as much attention as continuous problems, so it is still an area of research with questions to be explored.
In this context, in the first part of this thesis, we aimed for a deeper understanding of the challenges associated with combinatorial problems with many objectives. To achieve this goal, we conducted two analyses using a many-objective formulation of the popular logistics problem "Dial-a-Ride Problem" (DARP). Initially, we conducted a fitness landscape study to expand our understanding of the geometry of the obtained Pareto front for the problem and identify relationships between the objectives. Subsequently, we performed a performance analysis, involving some of the prominent multi-objective evolutionary algorithms from different classes. The results of these analyses revealed that, even considering the same problem formulation, different observations could be made both on the characteristics of the problem and the algorithms’ behavior when using different test sets.
In a second phase, diverging from the main focus of current research, which centers on developing new MOEAs and creating innovative selection strategies, we present an approach that generates and optimizes various alternative formulations of the addressed multi-objective optimization problem. In these formulations, artificial linear correlations between the objective functions are induced. The proposed approach adopts the divide-and-conquer paradigm, via allocating an evolutionary process (execution of the MOEA) for the original formulation and each constructed formulation with correlated objectives. At the end of each execution, the obtained approximation set is converted back to the original formulation, and all non-dominated solutions are returned as the algorithm’s output. By conducting independent searches using different formulations of the addressed MOP/MaOP, the aim is to guide the search in different directions of the objective space, thus reaching regions that would be challenging to explore solely by optimizing the original problem formulation using state-of-the-art MOEAs. When integrated with MOEAs from different classes, the proposed approach demonstrated effectiveness in enhancing the performance of these algorithms when applied to a well-known combinatorial optimization problem. Given the performance improvement of various MOEAs through the proposed approach, we introduced two new MOEAs based on the optimization of formulations with correlated objectives. The presented results showcased the superiority of the proposed MOEAs compared to renowned MOEAs in the literature, when applied to the multi-objective knapsack problem containing 4 to 10 objectives.
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14
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CRISTIANO FRAGA GUIMARÃES NUNES
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Advisor : FLAVIO LUIS CARDEAL PADUA
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COMMITTEE MEMBERS :
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ADRIANO CESAR MACHADO PEREIRA
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Celso Luiz de Souza
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DARLAN NUNES DE BRITO
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ELIZABETH FIALHO WANNER
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FLAVIO LUIS CARDEAL PADUA
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Data: Aug 31, 2023
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15
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LUCIENE LOPES BORGES MIRANDA
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Advisor : LEONARDO DOS SANTOS LIMA
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COMMITTEE MEMBERS :
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GIANCARLO QUEIROZ PELLEGRINO
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LEONARDO FERREIRA CALAZANS
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LUIS ARGEL POVEDA CALVINO
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THIAGO DE SOUZA RODRIGUES
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THIAGO GOMES DE MATTOS
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Data: Nov 30, 2023
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View Dissertation/Thesis
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Show Abstract
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The complexity of behavior and studies on the financial market and the Itô-Langevin Calculations, become an attractive field of studies for researchers in several areas, such as: Economics, Systems Analysis, Mathematics and Physics. We can emphasize its importance for such studies in interdisciplinary areas, such as: Econophysics, which relate elements of Economics and Physics in the study of markets and financial systems. Statistical mechanics is one of the main tools for modeling these financial systems, more precisely the price dynamics. To understand such facts, the Itô stochastic differential equations were used, with additive white noise as a mathematical model for the price dynamics of the financial market. Mathematical methods of Statistical Physics have been applied in the description of economic systems to time series to investigate the behavior of financial markets at different scales. Among the tools used for this, are measures of central dispersion, probability distribution, stochastic dynamics, and methods to estimate the correlations. Financial instruments such as assets, options and stock exchange indices fluctuate over time, so they can be modeled by stochastic processes. In this way this thesis intends to verify if a stochastic differential equation (interfered by white and non-white noise) attend a stylized fact of the market. More specifically, if the heavy tail of the distribution of absolute returns generated by the proposed equation follows an empirical power law. Furthermore, we estimate the Hurst exponent through R/S Analysis and DFA to verify the long-range dependence, or long memory of the obtained time series. As the noise term that composes the equation is non-differentiable, we introduce the stochastic calculus to analytically obtain its solution.
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16
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BRUNO ZANOTELLI FELIPPE
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Advisor : ANTONIO PAULO BAETA SCARPELLI
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COMMITTEE MEMBERS :
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MARCOS DONIZETI RODRIGUES SAMPAIO
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ALEXANDRE RODRIGUES VIEIRA
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ANTONIO PAULO BAETA SCARPELLI
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ARTHUR RODRIGO BOSCO DE MAGALHAES
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JOSE LUIZ ACEBAL FERNANDES
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LUIS ALBERTO D AFONSECA
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Data: Dec 4, 2023
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View Dissertation/Thesis
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Show Abstract
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The perturbative calculations in Quantum Field Theory can be represented, graphically, in terms of Feynman diagrams. The calculations of amplitudes represented by Feynman diagrams involve integrals, often divergent beyond tree level. These integrals require a treatment known as regularization, in order to extract the physical content of the amplitude. One of the most powerful techniques, Dimensional Regularization, involve dimensional extensions of space-time. However, there are models that involve mathematical objects whose the dimensional extension is ambiguous or ill-defined. A technique, called Implicit Regularization, proved to be appropriate for the treatment of models whose dimensional extension is not well defined. The method allows the calculations to be performed in the own theory dimension and prescribes simple rules for the preservation of the symmetries of the models. However, for a single Feynman integral, the expansion to separate divergences can generate a large set of finite integrals in the case of high degrees of divergence. In addition, expansions generate high powers of momenta in the numerator and denominator, which results in long and labor-intensive calculations. In this thesis, we developed a new procedure for the application of Constrained Implicit Regularization that simplifies the calculation of amplitudes, including finite parts.
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