Networks (also known as graphs) are everywhere. People-contact networks, social networks, email communication networks, internet networks (among others) are examples of graphs in our daily life. The increasing size of these networks makes it harder to understand them. Instead, summarizing these graphs can reveal key patterns and also help in sensemaking as well as accelerating existing graph algorithms. Intuitively, different summarizes are desired for different purposes. For example, to stop viral infections, one may want to find an effective policy to immunize people in a people-contact network. In this case, a high-quality network summary should highlight roughly structurally important nodes. Others may want to detect communities in the same people-contact network, and hence, the summary should show cohesive groups of nodes. This implies that for each task, we should design a specific method to reveal related patterns. Despite the importance of task-specific summarization, there has not been much work in this area. Hence, in this thesis, we design task-specific summarization frameworks for univariate and multivariate networks. We start with optimization-based approaches to summarize graphs for a particular task and finally propose general frameworks which automatically learn how to summarize for a given task and generalize it to similar networks. 1. Optimization-based approaches: Given a large network and a task, we propose summarization algorithms to highlight specific characteristics of the graph (i.e., structure, attributes, labels, dynamics) with respect to the task. We develop effective and efficient algorithms for various tasks such as content-aware influence maximization and time segmentation. In addition, we study many real-world networks and their summary graphs such as people-contact, news-blogs, etc. and visualize them to make sense of their characteristics given the input task. 2. Learning-based approaches: As our next step, we propose a unified framework which learns the process of summarization itself for a given task. First, we design a generalizable algorithm to learn to summarize graphs for a set of graph optimization problems. Next, we go further and add sparse human feedback to the learning process for the given optimization task. To the best of our knowledge, we are the first to systematically bring the necessity of considering the given task to the forefront and emphasize the importance of learning-based approaches in network summarization. Our models and frameworks lead to meaningful discoveries. We also solve problems from various domains such as epidemiology, marketing, social media, cybersecurity, and interactive visualization. / Doctor of Philosophy / Networks (also known as graphs) are everywhere. People-contact networks, social networks, email communication networks, internet networks (among others) are examples of graphs in our daily life. The increasing size of these networks makes it harder to understand them. Instead, summarizing these graphs can reveal key information and also help in sensemaking as well as accelerating existing graph analysis methods. Intuitively, different summarizes are desired for different purposes. For example, to stop viral infections, one may want to find an effective policy to immunize people in a people-contact network. In this case, a high-quality network summary should highlight roughly important nodes. Others may want to detect friendship communities in the same people-contact network, and hence, the summary should show cohesive groups of nodes. This implies that for each task, we should design a specific method to reveal related patterns. Despite the importance of task-specific summarization, there has not been much work in this area. Hence, in this thesis, we design task-specific summarization frameworks for various type of networks with different approaches. To the best of our knowledge, we are the first to systematically bring the necessity of considering the given task to the forefront and emphasize the importance of learning-based approaches in network summarization. Our models and frameworks lead to meaningful discoveries. We also solve problems from various domains such as epidemiology, marketing, social media, cybersecurity, and interactive visualization.

This study proposes a new spectral representation called the Zeros of Z-Transform (ZZT), which is an all-zero representation of the z-transform of the signal. In addition, new chirp group delay processing techniques are developed for analysis of resonances of a signal. The combination of the ZZT representation with the chirp group delay processing algorithms provides a useful domain to study resonance characteristics of source and filter components of speech. Using the two representations, effective algorithms are developed for: source-tract decomposition of speech, glottal flow parameter estimation, formant tracking and feature extraction for speech recognition. The ZZT representation is mainly important for theoretical studies. Studying the ZZT of a signal is essential to be able to develop effective chirp group delay processing methods. Therefore, first the ZZT representation of the source-filter model of speech is studied for providing a theoretical background. We confirm through ZZT representation that anti-causality of the glottal flow signal introduces mixed-phase characteristics in speech signals. The ZZT of windowed speech signals is also studied since windowing cannot be avoided in practical signal processing algorithms and the effect of windowing on ZZT representation is drastic. We show that separate patterns exist in ZZT representations of windowed speech signals for the glottal flow and the vocal tract contributions. A decomposition method for source-tract separation is developed based on these patterns in ZZT. We define chirp group delay as group delay calculated on a circle other than the unit circle in z-plane. The need to compute group delay on a circle other than the unit circle comes from the fact that group delay spectra are often very noisy and cannot be easily processed for formant tracking purposes (the reasons are explained through ZZT representation). In this thesis, we propose methods to avoid such problems by modifying the ZZT of a signal and further computing the chirp group delay spectrum. New algorithms based on processing of the chirp group delay spectrum are developed for formant tracking and feature estimation for speech recognition. The proposed algorithms are compared to state-of-the-art techniques. Equivalent or higher efficiency is obtained for all proposed algorithms. The theoretical parts of the thesis further discuss a mixed-phase model for speech and phase processing problems in detail.

FREIRE, Márcio de Melo. Funções de Green em Mecânica Estatística. 2014. 56 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2014. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2014-09-12T19:48:53Z No. of bitstreams: 1 2014_dis_mmfreire.pdf: 935092 bytes, checksum: 28a3a9a1ed16462d01e40ff411a01564 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2014-09-12T19:50:01Z (GMT) No. of bitstreams: 1 2014_dis_mmfreire.pdf: 935092 bytes, checksum: 28a3a9a1ed16462d01e40ff411a01564 (MD5) / Made available in DSpace on 2014-09-12T19:50:01Z (GMT). No. of bitstreams: 1 2014_dis_mmfreire.pdf: 935092 bytes, checksum: 28a3a9a1ed16462d01e40ff411a01564 (MD5) Previous issue date: 2014 / Neste trabalho estabeleceremos as definições das funções de Green em mecânica estatística e suas propriedades básicas. Estas funções dependem duplamente do tempo e da temperatura. Isto pode ser observado por meio de suas definições, onde aparecem os valores médios dos produtos de operadores. Neste caso a média é feita sobre o ensemble grão-canônico. Os operadores envolvidos nestas funções satisfazem a equação de movimento de Heisenberg, o que nos permite descrever as equações de evolução para as funções de Green. Por meio da representação espectral das funções de correlação temporal, que é feita através da introdução de uma transformada de Fourier para mudar o sistema do espaço dos tempos para o espaço das frequências, podemos obter as representações espectrais para as funções de Green retardada, avançada e causal. Por último, faremos o uso da função de Green retardada para descrever a condutividade elétrica de um sistema de elétrons submetido a um campo elétrico externo dependente de tempo, em outras palavras, descreveremos o tensor de condutividade elétrica em termos da função de Green retardada e, por último, calcularemos a condutividade elétrica de um sistema de elétrons e fônons.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Neste trabalho estabeleceremos as definiÃÃes das funÃÃes de Green em mecÃnica estatÃstica e suas propriedades bÃsicas. Estas funÃÃes dependem duplamente do tempo e da temperatura. Isto pode ser observado por meio de suas definiÃÃes, onde aparecem os valores mÃdios dos produtos de operadores. Neste caso a mÃdia à feita sobre o ensemble grÃo-canÃnico. Os operadores envolvidos nestas funÃÃes satisfazem a equaÃÃo de movimento de Heisenberg, o que nos permite descrever as equaÃÃes de evoluÃÃo para as funÃÃes de Green. Por meio da representaÃÃo espectral das funÃÃes de correlaÃÃo temporal, que à feita atravÃs da introduÃÃo de uma transformada de Fourier para mudar o sistema do espaÃo dos tempos para o espaÃo das frequÃncias, podemos obter as representaÃÃes espectrais para as funÃÃes de Green retardada, avanÃada e causal. Por Ãltimo, faremos o uso da funÃÃo de Green retardada para descrever a condutividade elÃtrica de um sistema de elÃtrons submetido a um campo elÃtrico externo dependente de tempo, em outras palavras, descreveremos o tensor de condutividade elÃtrica em termos da funÃÃo de Green retardada e, por Ãltimo, calcularemos a condutividade elÃtrica de um sistema de elÃtrons e fÃnons.

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