We consider the Minimum 0-Extension Problem for a given fixed undirected graph with positive weights. We study the computational com- plexity of the threshold decision variant with respect to properties of the fixed graph, in particular modularity and orientability, as defined by Karzanov in [Eur. J. Comb., 19/1 (1998)]. We approach the problem from the viewpoint of the Finite-Valued CSP, which allows us to employ the rich theory that was developed to prove the Dichotomy Conjecture. On the negative side, we provide an explicit reduction from the Max-Cut Problem to obtain NP-hardness for non-modular graphs. For non-orientable graphs, we express a cost function that satisfies a certain condition which guarantees the existence of an implicit reduction from the Max-Cut Problem. On the positive side, we construct symmetric fractional polymorphisms in order to show that the so-called Basic LP Relaxation can solve two special cases of weighted modular orientable graphs: paths and rectangles. 1

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No. of bitstreams: 1 DissACIZ.pdf: 2734710 bytes, checksum: bf061fead4f2a8becfcbedc457a68b25 (MD5) Previous issue date: 2016-03-29 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / The Automatic Multi-Document Summarization (MDS) aims at creating a single summary, coherent and cohesive, from a collection of different sources texts, on the same topic. The creation of these summaries, in general extracts (informative and generic), requires the selection of the most important sentences from the collection. Therefore, one may use superficial linguistic knowledge (or statistic) or deep knowledge. It is important to note that deep methods, although more expensive and less robust, produce more informative extracts and with more linguistic quality. For the Portuguese language, the sole deep methods that use lexical-conceptual knowledge are based on the frequency of the occurrence of the concepts in the collection for the selection of a content. Considering the potential for application of semantic-conceptual knowledge, the proposition is to investigate MDS methods that start with representation of lexical concepts of source texts in a hierarchy for further exploration of certain hierarchical properties able to distinguish the most relevant concepts (in other words, the topics from a collection of texts) from the others. Specifically, 3 out of 50 CSTNews (multi-document corpus of Portuguese reference) collections were selected and the names that have occurred in the source texts of each collection were manually indexed to the concepts of the WordNet from Princenton (WN.Pr), engendering at the end, an hierarchy with the concepts derived from the collection and other concepts inherited from the WN.PR for the construction of the hierarchy. The hierarchy concepts were characterized in 5 graph metrics (of relevancy) potentially relevant to identify the concepts that compose a summary: Centrality, Simple Frequency, Cumulative Frequency, Closeness and Level. Said characterization was analyzed manually and by machine learning algorithms (ML) with the purpose of verifying the most suitable measures to identify the relevant concepts of the collection. As a result, the measure Centrality was disregarded and the other ones were used to propose content selection methods to MDS. Specifically, 2 sentences selection methods were selected which make up the extractive methods: (i) CFSumm whose content selection is exclusively based on the metric Simple Frequency, and (ii) LCHSumm whose selection is based on rules learned by machine learning algorithms from the use of all 4 relevant measures as attributes. These methods were intrinsically evaluated concerning the informativeness, by means of the package of measures called ROUGE, and the evaluation of linguistic quality was based on the criteria from the TAC conference. Therefore, the 6 human abstracts available in each CSTNews collection were used. Furthermore, the summaries generated by the proposed methods were compared to the extracts generated by the GistSumm summarizer, taken as baseline. The two methods got satisfactory results when compared to the GistSumm baseline and the CFSumm method stands out upon the LCHSumm method. / Na Sumarização Automática Multidocumento (SAM), busca-se gerar um único sumário, coerente e coeso, a partir de uma coleção de textos, de diferentes fontes, que tratam de um mesmo assunto. A geração de tais sumários, comumente extratos (informativos e genéricos), requer a seleção das sentenças mais importantes da coleção. Para tanto, pode-se empregar conhecimento linguístico superficial (ou estatística) ou conhecimento profundo. Quanto aos métodos profundos, destaca-se que estes, apesar de mais caros e menos robustos, produzem extratos mais informativos e com mais qualidade linguística. Para o português, os únicos métodos profundos que utilizam conhecimento léxico-conceitual baseiam na frequência de ocorrência dos conceitos na coleção para a seleção de conteúdo. Tendo em vista o potencial de aplicação do conhecimento semântico-conceitual, propôs-se investigar métodos de SAM que partem da representação dos conceitos lexicais dos textos-fonte em uma hierarquia para a posterior exploração de certas propriedades hierárquicas capazes de distinguir os conceitos mais relevantes (ou seja, os tópicos da coleção) dos demais. Especificamente, selecionaram-se 3 das 50 coleções do CSTNews, corpus multidocumento de referência do português, e os nomes que ocorrem nos textos-fonte de cada coleção foram manualmente indexados aos conceitos da WordNet de Princeton (WN.Pr), gerando, ao final, uma hierarquia com os conceitos constitutivos da coleção e demais conceitos herdados da WN.Pr para a construção da hierarquia. Os conceitos da hierarquia foram caracterizados em função de 5 métricas (de relevância) de grafo potencialmente pertinentes para a identificação dos conceitos a comporem um sumário: Centrality, Simple Frequency, Cumulative Frequency, Closeness e Level. Tal caracterização foi analisada de forma manual e por meio de algoritmos de Aprendizado de Máquina (AM) com o objetivo de verificar quais medidas seriam as mais adequadas para identificar os conceitos relevantes da coleção. Como resultado, a medida Centrality foi descartada e as demais utilizadas para propor métodos de seleção de conteúdo para a SAM. Especificamente, propuseram-se 2 métodos de seleção de sentenças, os quais compõem os métodos extrativos: (i) CFSumm, cuja seleção de conteúdo se baseia exclusivamente na métrica Simple Frequency, e (ii) LCHSumm, cuja seleção se baseia em regras aprendidas por algoritmos de AM a partir da utilização em conjunto das 4 medidas relevantes como atributos. Tais métodos foram avaliados intrinsecamente quanto à informatividade, por meio do pacote de medidas ROUGE, e qualidade linguística, com base nos critérios da conferência TAC. Para tanto, utilizaram-se os 6 abstracts humanos disponíveis em cada coleção do CSTNews. Ademais, os sumários gerados pelos métodos propostos foram comparados aos extratos gerados pelo sumarizador GistSumm, tido como baseline. Os dois métodos obtiveram resultados satisfatórios quando comparados ao baseline GistSumm e o método CFSumm se sobressai ao método LCHSumm. / FAPESP 2014/12817-4

The aim of the thesis is to define the dependency of the classification of patients affected by neurodegenerative diseases on the choice of the parcellation atlas. Part of this thesis is the application of the functional connectivity analysis and the calculation of graph metrics according to the method published by Olaf Sporns and Mikail Rubinov [1] on fMRI data measured at CEITEC MU. The application is preceded by the theoretical research of parcellation atlases for brain segmentation from fMRI frames and the research of mathematical methods for classification as well as classifiers of neurodegenerative diseases. The first chapters of the thesis brings a theoretical basis of knowledge from the field of magnetic and functional magnetic resonance imaging. The physical principles of the method, the conditions and the course of acquisition of image data are defined. The third chapter summarizes the graph metrics used in the diploma thesis for analyzing and classifying graphs. The paper presents a brief overview of the brain segmentation methods, with the focuse on the atlas-based segmentation. After a theoretical research of functional connectivity methods and mathematical classification methods, the findings were used for segmentation, calculation of graph metrics and for classification of fMRI images obtained from 96 subjects into the one of two classes using Binary classifications by support vector machines and linear discriminatory analysis. The data classified in this study was measured on patiens with Parkinson’s disease (PD), Alzheimer’s disease (AD), Mild cognitive impairment (MCI), a combination of PD and MCI and subjects belonging to the control group of healthy individuals. For pre-processing and analysis, the MATLAB environment, the SPM12 toolbox and The Brain Connectivity Toolbox were used.