http://www.bdtd.uerj.br/handle/1/21508 2026-04-13T04:47:59Z http://www.bdtd.uerj.br/handle/1/25546 Título: Representações Monte Carlo, Las Vegas e Determinística de Grafos Massivos Autor: Leão, Paulo Diogo Rodrigues Primeiro orientador: Oliveira, Fabiano de Souza Abstract: Lossless compact and probabilistic graph representations aim to reduce the space occupied by classical representations, such as the adjacency list and edge list, without compromising the accuracy of adjacency tests. In the literature, there are several techniques for compact graph representation. However, many of these approaches are limited to modifying vertex labels in order to produce more compact classical representations, or to representing more restricted classes of graphs. Few proposals exist for modeling general graphs with an emphasis on compactness of representation. This thesis investigates a recent variant of the XOR filter, called Spatial XOR, which introduces the concept of contiguous windows in the mapping vector of hash functions. We developed an empirical and computational methodology to estimate the optimal size of these windows and the maximum load factor, employing machine learning techniques (leave-one-out validation) and large-scale empirical analysis. Additionally, two new lossless graph representations are proposed. The first is based on the use of hash functions, combining explicit and implicit neighborhood lists, resulting in a Las Vegas–type randomized data structure; the second employs modular arithmetic to represent neighborhoods through systems of congruences. The experiments demonstrated that the probabilistic representation achieves greater compactness, while the modular representation provides a significantly shorter construction time, maintaining space efficiency compared to traditional adjacency lists. Instituição: Universidade do Estado do Rio de Janeiro Tipo do documento: Tese 2025-12-05T00:00:00Z http://www.bdtd.uerj.br/handle/1/23480 Título: Modelagem Fuzzy Intuicionista no Reconhecimento de Padrões em Registros no Prontuário Eletrônico de Pacientes atendidos no Hospital Universitário durante a Pandemia da Covid-19 Autor: Cruz, Carla Cristina Passos Primeiro orientador: Lanzillotti, Regina Serrão Abstract: Text Mining corresponds to pre-processing for the use of algorithms, as it organizes, links and transforms the contents of written language into reliable information that anticipates the subsequent use of modeling that seeks pattern recognition. It is noteworthy that 80% of the data generated is unstructured and of these, 80% are in textual format that deals with uncertainty and ambiguity. Information Retrieval and Natural Language Processing account for the frequency of occurrence of words, which allows the approach of Inferential Statistics and Computational Intelligence. Objective: Applying Fuzzy Intuitionist modeling to obtain patterns according to linguistic terms in records in the electronic medical record of patients treated in a Public University Hospital Unit during the Covid-19 pandemic. Method: Case study, Fuzzy Intuitionist Grouping was chosen, which considers the degree of relevance, non- pertinence and hesitation to describe scenarios. Applying this modeling, which was used to obtain patterns according to linguistic terms, we used the records made in the electronic medical records of patients at the Pedro Ernesto University Hospital during the period of the Covid-19 pandemic. The unstructured information, written incorrectly and not complying with the International Classification of Diseases, went through the Pre-Processing stage, where variables were created for entry into the Fuzzy System. The Elbow method was applied to indicate the probable number of clusters and ratification by the Fuzzy Intuitionist C-Means model. Results: Pre-processing organized and adjusted the data and enabled the construction of a textual database associated with the incidence of Covid-19 in cases treated at HUPE, which can be used in other research. Two Standard Classes were established to allow the classification of a patient suffering from Covid-19 based on the Cosine of the Intuitionist Fuzzy Sets according to the symptoms: fever, shortness of breath and fatigue; and comorbidities: hypertension, cerebrovascular disease and cardiovascular disease. Conclusion: The results confirm that a patient can be classified into a certain standard class by estimating the pertinences of the Fuzzy Intuitionist Logic System, taking into account the relevance of the similarity. Instituição: Universidade do Estado do Rio de Janeiro Tipo do documento: Tese 2024-11-05T00:00:00Z http://www.bdtd.uerj.br/handle/1/23479 Título: Métodos de Diferenças Finitas para a Equação de Difusão Fracionária Autor: Negreiros, Jhoab Pessoa de Primeiro orientador: Faria, Cristiane Oliveira de Abstract: There is an extensive range of formulations involving the term fractional derivative, and this number continues to increase. This is due to the fact that fractional derivative is a complex and comprehensive mathematical concept that can be used to describe a wide range of phenomena. Considering the growing number of definitions, this work presents a study using numerical methods with six fractional derivatives: Riemann-Liouville, Caputo, Chen, Katugampola, Caputo-Fabrizio, and Atangana-Baleanu. These derivatives are applied to the fractional diffusion equation in one dimension with a constant coefficient, where the fractional temporal variation is simulated in the diffusion term. The selection of these operators was based on the classification carried out by Teodoro in his doctoral thesis, which, based on the criterion proposed by Ortigueira and Machado in 2015 − composed of five properties that help us conclude when a specific operator is a fractional derivative − verified whether these or many other operators can be considered fractional derivatives, according to the aforementioned criterion. The numerical approach adopted is the finite difference method, employing schemes based on the classical progressive and regressive Euler methods. The numerical analysis of stability and convergence is carried out using the forward and backward Euler-type method with the fractional derivative according to Riemann-Liouville. The imbalance generated by the fractional derivative in the fractional diffusion equation is corrected by inserting the dimensional correction parameter T into the model. The central contribution of this work was the development of numerical methods and the construction of respective codes for fractional-order diffusion. Numerical experiments are presented, displaying results with the aim of confirming theoretical conclusions, verifying the convergence rate, making comparisons between different approaches, and understanding the importance of the validity of the properties of the Ortigueira and Machado criterion for modeling. Algorithms, along with their corresponding Python language codes, are available. Instituição: Universidade do Estado do Rio de Janeiro Tipo do documento: Tese 2023-12-18T00:00:00Z http://www.bdtd.uerj.br/handle/1/23352 Título: Árvore de decisão por agrupamento com DBSCAN aproximativo Autor: Goulart, Jorge Luiz de Jesus Primeiro orientador: Oliveira, Fabiano de Souza Abstract: Machine learning aims to create systems that can learn from data, identify patterns, and make decisions with minimal human intervention. Generally, machine learning methods employ various geometric concepts involving points in multidimensional space. On the other hand, in the literature of algorithms for solving geometric concepts, there are numerous algorithms of this nature that involve randomized and approximate procedures. These procedures sometimes result in an improvement in expected time complexity and at other times in simplifying the implementation of these algorithms. This thesis presents a variant of the decision tree model, where new predicates are considered to partition the data. Instead of using only univariate predicates (associated with a single feature of the data), as is the case with the ordinary decision tree, the new variant also considers multi-feature predicates. Such predicates involve separating the data by their relevance to each of the groups produced by the unsupervised clustering model DBSCAN. The DBSCAN algorithm has a high computational time complexity to be directly integrated into decision trees. Therefore, the proposal involves using an approximate version with linear time complexity of the DBSCAN algorithm to mitigate this impact. The thesis not only proposes this but also conducts experiments on various machine learning benchmark datasets. Instituição: Universidade do Estado do Rio de Janeiro Tipo do documento: Tese 2024-02-22T00:00:00Z