Depuis plusieurs années, l’aéronautique est confrontée à une mutation majeure due à l’émergence des matériaux composites. Ce changement, justifié par les excellentes propriétés mécaniques des matériaux composites et un gain de masse important, implique une révision complète des réseaux de retour de courant. Pour faciliter cette révision, la thèse propose de lier au travers de l’analyse spectrale des graphes les performances des réseaux électriques avec leur topologie. Deux objectifs couplés sont étudiés : un dimensionnement topologique visant un bon compromis masse/robustesse et une stratégie de surveillance de ces réseaux. / The principles of the electrical system design in future aircrafts have to be reconsidered due to the emergence of new composite materials. The use of these materials for the aircraft structure has indeed implied a complete revision of on-board current return path networks. To facilitate this revision, it is proposed to link through the spectral graph analysis the performances of electrical networks with their topology. The aim of this thesis is to give topological drivers that could help the aeronautical engineers during the design process and then to propose a monitoring methodology.

This thesis advances the theory of network specialization by characterizing the effect of network specialization on the eigenvectors of a network. We prove and provide explicit formulas for the eigenvectors of specialized graphs based on the eigenvectors of their parent graphs. The second portion of this thesis applies network specialization to learning problems. Our work focuses on training reservoir computers to mimic the Lorentz equations. We experiment with random graph, preferential attachment and small world topologies and demonstrate that the random removal of directed edges increases predictive capability of a reservoir topology. We then create a new network model by growing networks via targeted application of the specialization model. This is accomplished iteratively by selecting top preforming nodes within the reservoir computer and specializing them. Our generated topology out-preforms all other topologies on average.

A well-known result in spectral graph theory states that if a graph has an equitable partition then the eigenvalues of the associated divisor graph are a subset of the graph's eigenvalues. A natural question question is whether it is possible to recover the remaining eigenvalues of the graph. Here we show that if a graph has a Hermitian adjacency matrix then the spectrum of the graph can be decomposed into a collection of smaller graphs whose eigenvalues are collectively the remaining eigenvalues of the graph. This we refer to as a complete equitable decomposition of the graph.

Additive manufacturing (AM) is a powerful emerging technology for fabrication of components with complex geometries using a variety of materials. However, despite promising potential, due to the complexity of the process dynamics, how to ensure product quality and consistency of AM parts efficiently during the process still remains challenging. Therefore, the objective of this dissertation is to develop effective methodologies for online automatic quality monitoring and improvement, i.e., to build a basis for smart additive manufacturing. The fast-growing sensor technology can easily generate a massive amount of real-time process data, which provides excellent opportunities to address the barriers of online quality assurance in AM through data-driven perspectives. Although this direction is very promising, the online sensing data typically have high dimensionality and complex inherent structure, which causes the tasks of real-time data-driven analytics and decision-making to be very challenging. To address these challenges, multiple data-driven approaches have been developed in this dissertation to achieve effective feature extraction, process modeling, and closed-loop quality control. These methods are successfully validated by a typical AM process, namely, fused filament fabrication (FFF). Specifically, four new methodologies are proposed and developed as listed below, (1) To capture the variation of hidden patterns in sensor signals, a feature extraction approach based on spectral graph theory is developed for defect detection in online quality monitoring of AM. The most informative feature is extracted and integrated with a statistical control chart, which can effectively detect the anomalies caused by cyber-physical attack. (2) To understand the underlying structure of high dimensional sensor data, an effective dimension reduction method based on an integrated manifold learning approach termed multi-kernel metric learning embedded isometric feature mapping (MKML-ISOMAP) is proposed for online process monitoring and defect diagnosis of AM. Based on the proposed method, process defects can be accurately identified by supervised classification algorithms. (3) To quantify the layer-wise quality correlation in AM by taking into consideration of reheating effects, a novel bilateral time series modeling approach termed extended autoregressive (EAR) model is proposed, which successfully correlates the quality characteristics of the current layer with not only past but also future layers. The resulting model is able to online predict the defects in a layer-wise manner. (4) To achieve online defect mitigation for AM process, a closed-loop quality control system is implemented using an image analysis-based proportional-integral-derivative (PID) controller, which can mitigate the defects by adaptively adjusting machine parameters during the printing process in a timely manner. By fully utilizing the online sensor data with innovative data analytics and closed-loop control approaches, the above-proposed methodologies are expected to have excellent performance in online quality assurance for AM. In addition, these methodologies are inherently integrated into a generic framework. Thus, they can be easily transformed for applications in other advanced manufacturing processes. / Doctor of Philosophy / Additive manufacturing (AM) technology is rapidly changing the industry; and online sensor-based data analytics is one of the most effective enabling techniques to further improve AM product quality. The objective of this dissertation is to develop methodologies for online quality assurance of AM processes using sensor technology, advanced data analytics, and closed-loop control. It aims to build a basis for the implementation of smart additive manufacturing. The proposed new methodologies in this dissertation are focused to address the quality issues in AM through effective feature extraction, advanced statistical modeling, and closed-loop control. To validate their effectiveness and efficiency, a widely used AM process, namely, fused filament fabrication (FFF), is selected as the experimental platform for testing and validation. The results demonstrate that the proposed methods are very promising to detect and mitigate quality defects during AM operations. Consequently, with the research outcome in this dissertation, our capability of online defect detection, diagnosis, and mitigation for the AM process is significantly improved. However, the future applications of the accomplished work in this dissertation are not just limited to AM. The developed generic methodological framework can be further extended to many other types of advanced manufacturing processes.

La maladie de Huntington est une maladie neurodégénérative héréditaire qui est devenue un modèle d'étude pour comprendre la physiopathologie des maladies du cerveau associées à la production de protéines mal conformées et à la neurodégénérescence. Bien que plusieurs mécanismes aient été mis en avant pour cette maladie, dont plusieurs seraient aussi impliqués dans des pathologies plus fréquentes comme la maladie d’Alzheimer ou la maladie de Parkinson, nous ne savons toujours pas quels sont les mécanismes ou les profils moléculaires qui déterminent fondamentalement la dynamique des processus de dysfonction et de dégénérescence neuronale dans cette maladie. De même, nous ne savons toujours pas comment le cerveau peut résister aussi longtemps à la production de protéines mal conformées, ce qui suggère en fait que ces protéines ne présentent qu’une toxicité modérée ou que le cerveau dispose d'une capacité de compensation et de résilience considérable. L'hypothèse de mon travail de thèse est que l'intégration de données génomiques et transcriptomiques au travers des modèles qui récapitulent différentes phases biologiques de la maladie de Huntington peut permettre de répondre à ces questions. Dans cette optique, l'utilisation des réseaux de gènes et la mise en application de concepts issus de la théorie des graphes sont particulièrement bien adaptés à l'intégration de données hétérogènes, au travers des modèles et au travers des espèces. Les résultats de mon travail suggèrent que l'altération précoce (avant les symptômes, avant la mort cellulaire) et éventuellement dès le développement cérébral) des grandes voies de développement et de maintenance neuronale, puis la persistance voire l'aggravation de ces effets, sont à la base des processus physiopathologiques qui conduisent à la dysfonction puis à la mort neuronale. Ces résultats permettent aussi de prioriser des gènes et de générer des hypothèses fortes sur les cibles thérapeutiques les plus intéressantes à étudier d'un point de vue expérimental. En conclusion, mes recherches ont un impact à la fois fondamental et translationnel sur l'étude de la maladie de Huntington, permettant de dégager des méthodes d'analyse et des hypothèses qui pourraient avoir valeur thérapeutique pour les maladies neurodégénératives en général. / Huntington’s disease is a hereditary neurodegenerative disease that has become a model to understand physiopathological mechanisms associated to misfolded proteins that ocurs in brain diseases. Despite exciting findings that have uncover pathological mechanisms occurring in this disease and that might also be relevant to Alzheimer’s disease and Parkinson’s disease, we still do not know yet which are the mechanisms and molecular profiles that rule the dynamic of neurodegenerative processes in Huntington’s disease. Also, we do not understand clearly how the brain resist over such a long time to misfolded proteins, which suggest that the toxicity of these proteins is mild, and that the brain have exceptional compensation capacities. My work is based on the hypothesis that integration of ‘omics’ data from models that depicts various stages of the disease might be able to give us clues to answer these questions. Within this framework, the use of network biology and graph theory concepts seems particularly well suited to help us integrate heterogeneous data across models and species. So far, the outcome of my work suggest that early, pre-symptomatic alterations of signaling pathways and cellular maintenance processes, and persistency and worthening of these phenomenon are at the basis of physiopathological processes that lead to neuronal dysfunction and death. These results might allow to prioritize targets and formulate new hypotheses that are interesting to further study and test experimentally. To conclude, this work shall have a fundamental and translational impact to the field of Huntington’s disease, by pinpointing methods and hypotheses that could be valuable in a therapeutic perspective.

La maladie de Huntington est une maladie neurodégénérative héréditaire qui est devenue un modèle d'étude pour comprendre la physiopathologie des maladies du cerveau associées à la production de protéines mal conformées et à la neurodégénérescence. Bien que plusieurs mécanismes aient été mis en avant pour cette maladie, dont plusieurs seraient aussi impliqués dans des pathologies plus fréquentes comme la maladie d’Alzheimer ou la maladie de Parkinson, nous ne savons toujours pas quels sont les mécanismes ou les profils moléculaires qui déterminent fondamentalement la dynamique des processus de dysfonction et de dégénérescence neuronale dans cette maladie. De même, nous ne savons toujours pas comment le cerveau peut résister aussi longtemps à la production de protéines mal conformées, ce qui suggère en fait que ces protéines ne présentent qu’une toxicité modérée ou que le cerveau dispose d'une capacité de compensation et de résilience considérable. L'hypothèse de mon travail de thèse est que l'intégration de données génomiques et transcriptomiques au travers des modèles qui récapitulent différentes phases biologiques de la maladie de Huntington peut permettre de répondre à ces questions. Dans cette optique, l'utilisation des réseaux de gènes et la mise en application de concepts issus de la théorie des graphes sont particulièrement bien adaptés à l'intégration de données hétérogènes, au travers des modèles et au travers des espèces. Les résultats de mon travail suggèrent que l'altération précoce (avant les symptômes, avant la mort cellulaire) et éventuellement dès le développement cérébral) des grandes voies de développement et de maintenance neuronale, puis la persistance voire l'aggravation de ces effets, sont à la base des processus physiopathologiques qui conduisent à la dysfonction puis à la mort neuronale. Ces résultats permettent aussi de prioriser des gènes et de générer des hypothèses fortes sur les cibles thérapeutiques les plus intéressantes à étudier d'un point de vue expérimental. En conclusion, mes recherches ont un impact à la fois fondamental et translationnel sur l'étude de la maladie de Huntington, permettant de dégager des méthodes d'analyse et des hypothèses qui pourraient avoir valeur thérapeutique pour les maladies neurodégénératives en général. / Huntington’s disease is a hereditary neurodegenerative disease that has become a model to understand physiopathological mechanisms associated to misfolded proteins that ocurs in brain diseases. Despite exciting findings that have uncover pathological mechanisms occurring in this disease and that might also be relevant to Alzheimer’s disease and Parkinson’s disease, we still do not know yet which are the mechanisms and molecular profiles that rule the dynamic of neurodegenerative processes in Huntington’s disease. Also, we do not understand clearly how the brain resist over such a long time to misfolded proteins, which suggest that the toxicity of these proteins is mild, and that the brain have exceptional compensation capacities. My work is based on the hypothesis that integration of ‘omics’ data from models that depicts various stages of the disease might be able to give us clues to answer these questions. Within this framework, the use of network biology and graph theory concepts seems particularly well suited to help us integrate heterogeneous data across models and species. So far, the outcome of my work suggest that early, pre-symptomatic alterations of signaling pathways and cellular maintenance processes, and persistency and worthening of these phenomenon are at the basis of physiopathological processes that lead to neuronal dysfunction and death. These results might allow to prioritize targets and formulate new hypotheses that are interesting to further study and test experimentally. To conclude, this work shall have a fundamental and translational impact to the field of Huntington’s disease, by pinpointing methods and hypotheses that could be valuable in a therapeutic perspective.

Image segmentation is an essential tool to enhance the ability of computer systems to efficiently perform elementary cognitive tasks such as detection, recognition and tracking. In this thesis we concentrate on the investigation of two fundamental topics in the context of image segmentation: spectral clustering and seeded image segmentation. We introduce two new algorithms for those topics that, in summary, rely on Laplacian-based operators, spectral graph theory, and minimization of energy functionals. The effectiveness of both segmentation algorithms is verified by visually evaluating the resulting partitions against state-of-the-art methods as well as through a variety of quantitative measures typically employed as benchmark by the image segmentation community. Our spectral-based segmentation algorithm combines image decomposition, similarity metrics, and spectral graph theory into a concise and powerful framework. An image decomposition is performed to split the input image into texture and cartoon components. Then, an affinity graph is generated and weights are assigned to the edges of the graph according to a gradient-based inner-product function. From the eigenstructure of the affinity graph, the image is partitioned through the spectral cut of the underlying graph. Moreover, the image partitioning can be improved by changing the graph weights by sketching interactively. Visual and numerical evaluation were conducted against representative spectral-based segmentation techniques using boundary and partition quality measures in the well-known BSDS dataset. Unlike most existing seed-based methods that rely on complex mathematical formulations that typically do not guarantee unique solution for the segmentation problem while still being prone to be trapped in local minima, our segmentation approach is mathematically simple to formulate, easy-to-implement, and it guarantees to produce a unique solution. Moreover, the formulation holds an anisotropic behavior, that is, pixels sharing similar attributes are preserved closer to each other while big discontinuities are naturally imposed on the boundary between image regions, thus ensuring better fitting on object boundaries. We show that the proposed approach significantly outperforms competing techniques both quantitatively as well as qualitatively, using the classical GrabCut dataset from Microsoft as a benchmark. While most of this research concentrates on the particular problem of segmenting an image, we also develop two new techniques to address the problem of image inpainting and photo colorization. Both methods couple the developed segmentation tools with other computer vision approaches in order to operate properly. / Segmentar uma image é visto nos dias de hoje como uma prerrogativa para melhorar a capacidade de sistemas de computador para realizar tarefas complexas de natureza cognitiva tais como detecção de objetos, reconhecimento de padrões e monitoramento de alvos. Esta pesquisa de doutorado visa estudar dois temas de fundamental importância no contexto de segmentação de imagens: clusterização espectral e segmentação interativa de imagens. Foram propostos dois novos algoritmos de segmentação dentro das linhas supracitadas, os quais se baseiam em operadores do Laplaciano, teoria espectral de grafos e na minimização de funcionais de energia. A eficácia de ambos os algoritmos pode ser constatada através de avaliações visuais das segmentações originadas, como também através de medidas quantitativas computadas com base nos resultados obtidos por técnicas do estado-da-arte em segmentação de imagens. Nosso primeiro algoritmo de segmentação, o qual ´e baseado na teoria espectral de grafos, combina técnicas de decomposição de imagens e medidas de similaridade em grafos em uma única e robusta ferramenta computacional. Primeiramente, um método de decomposição de imagens é aplicado para dividir a imagem alvo em duas componentes: textura e cartoon. Em seguida, um grafo de afinidade é gerado e pesos são atribuídos às suas arestas de acordo com uma função escalar proveniente de um operador de produto interno. Com base no grafo de afinidade, a imagem é então subdividida por meio do processo de corte espectral. Além disso, o resultado da segmentação pode ser refinado de forma interativa, mudando-se, desta forma, os pesos do grafo base. Experimentos visuais e numéricos foram conduzidos tomando-se por base métodos representativos do estado-da-arte e a clássica base de dados BSDS a fim de averiguar a eficiência da metodologia proposta. Ao contrário de grande parte dos métodos existentes de segmentação interativa, os quais são modelados por formulações matemáticas complexas que normalmente não garantem solução única para o problema de segmentação, nossa segunda metodologia aqui proposta é matematicamente simples de ser interpretada, fácil de implementar e ainda garante unicidade de solução. Além disso, o método proposto possui um comportamento anisotrópico, ou seja, pixels semelhantes são preservados mais próximos uns dos outros enquanto descontinuidades bruscas são impostas entre regiões da imagem onde as bordas são mais salientes. Como no caso anterior, foram realizadas diversas avaliações qualitativas e quantitativas envolvendo nossa técnica e métodos do estado-da-arte, tomando-se como referência a base de dados GrabCut da Microsoft. Enquanto a maior parte desta pesquisa de doutorado concentra-se no problema específico de segmentar imagens, como conteúdo complementar de pesquisa foram propostas duas novas técnicas para tratar o problema de retoque digital e colorização de imagens.

We consider the problem of maximizing the second smallest eigenvalue of the weighted Laplacian of a (simple) graph over all nonnegative edge weightings with bounded total weight. We generalize this problem by introducing node significances and edge lengths. We give a formulation of this generalized problem as a semidefinite program. The dual program can be equivalently written as embedding problem. This is fifinding an embedding of the n nodes of the graph in n-space so that their barycenter is at the origin, the distance between adjacent nodes is bounded by the respective edge length, and the embedded nodes are spread as much as possible. (The sum of the squared norms is maximized.) We proof the following necessary condition for optimal embeddings. For any separator of the graph at least one of the components fulfills the following property: Each straight-line segment between the origin and an embedded node of the component intersects the convex hull of the embedded nodes of the separator. There exists always an optimal embedding of the graph whose dimension is bounded by the tree-width of the graph plus one. We defifine the rotational dimension of a graph. This is the minimal dimension k such that for all choices of the node significances and edge lengths an optimal embedding of the graph can be found in k-space. The rotational dimension of a graph is a minor monotone graph parameter. We characterize the graphs with rotational dimension up to two.

The focus of this thesis is to develop computational techniques for analysis of protein structures. We model protein structures as points in 3-dimensional space which in turn are modeled as weighted graphs. The problem of protein structure comparison is posed as a weighted graph matching problem and an algorithm motivated from the spectral graph matching techniques is developed. The thesis also proposes novel similarity measures by deriving kernel functions. These kernel functions allow the data to be mapped to a suitably defined Reproducing kernel Hilbert Space(RKHS), paving the way for efficient algorithms for protein structure classification. Protein structure comparison (structure alignment)is a classical method of determining overall similarity between two protein structures. This problem can be posed as the approximate weighted subgraph matching problem, which is a well known NP-Hard problem. Spectral graph matching techniques provide efficient heuristic solution for the weighted graph matching problem using eigenvectors of adjacency matrices of the graphs. We propose a novel and efficient algorithm for protein structure comparison using the notion of neighborhood preserving projections (NPP) motivated from spectral graph matching. Empirically, we demonstrate that comparing the NPPs of two protein structures gives the correct equivalences when the sizes of proteins being compared are roughly similar. Also, the resulting algorithm is 3 -20 times faster than the existing state of the art techniques. This algorithm was used for retrieval of protein structures from standard databases with accuracies comparable to the state of the art. A limitation of the above method is that it gives wrong results when the number of unmatched residues, also called insertions and deletions (indels), are very high. This problem was tackled by matching neighborhoods, rather than entire structures. For each pair of neighborhoods, we grow the neighborhood alignments to get alignments for entire structures. This results in a robust method that has outperformed the existing state of the art methods on standard benchmark datasets. This method was also implemented using MPI on a cluster for database search. Another important problem in computational biology is classification of protein structures into classes exhibiting high structural similarity. Many manual and semi-automatic structural classification databases exist. Kernel methods along with support vector machines (SVM) have proved to be a robust and principled tool for classification. We have proposed novel positive semidefinite kernel functions on protein structures based on spatial neighborhoods. The kernels were derived using a general technique called convolution kernel, and showed to be related to the spectral alignment score in a limiting case. These kernels have outperformed the existing tools when validated on a well known manual classification scheme called SCOP. The kernels were designed keeping the general problem of capturing structural similarity in mind, and have been successfully applied to problems in other domains, e.g. computer vision.

Image segmentation is an essential tool to enhance the ability of computer systems to efficiently perform elementary cognitive tasks such as detection, recognition and tracking. In this thesis we concentrate on the investigation of two fundamental topics in the context of image segmentation: spectral clustering and seeded image segmentation. We introduce two new algorithms for those topics that, in summary, rely on Laplacian-based operators, spectral graph theory, and minimization of energy functionals. The effectiveness of both segmentation algorithms is verified by visually evaluating the resulting partitions against state-of-the-art methods as well as through a variety of quantitative measures typically employed as benchmark by the image segmentation community. Our spectral-based segmentation algorithm combines image decomposition, similarity metrics, and spectral graph theory into a concise and powerful framework. An image decomposition is performed to split the input image into texture and cartoon components. Then, an affinity graph is generated and weights are assigned to the edges of the graph according to a gradient-based inner-product function. From the eigenstructure of the affinity graph, the image is partitioned through the spectral cut of the underlying graph. Moreover, the image partitioning can be improved by changing the graph weights by sketching interactively. Visual and numerical evaluation were conducted against representative spectral-based segmentation techniques using boundary and partition quality measures in the well-known BSDS dataset. Unlike most existing seed-based methods that rely on complex mathematical formulations that typically do not guarantee unique solution for the segmentation problem while still being prone to be trapped in local minima, our segmentation approach is mathematically simple to formulate, easy-to-implement, and it guarantees to produce a unique solution. Moreover, the formulation holds an anisotropic behavior, that is, pixels sharing similar attributes are preserved closer to each other while big discontinuities are naturally imposed on the boundary between image regions, thus ensuring better fitting on object boundaries. We show that the proposed approach significantly outperforms competing techniques both quantitatively as well as qualitatively, using the classical GrabCut dataset from Microsoft as a benchmark. While most of this research concentrates on the particular problem of segmenting an image, we also develop two new techniques to address the problem of image inpainting and photo colorization. Both methods couple the developed segmentation tools with other computer vision approaches in order to operate properly. / Segmentar uma image é visto nos dias de hoje como uma prerrogativa para melhorar a capacidade de sistemas de computador para realizar tarefas complexas de natureza cognitiva tais como detecção de objetos, reconhecimento de padrões e monitoramento de alvos. Esta pesquisa de doutorado visa estudar dois temas de fundamental importância no contexto de segmentação de imagens: clusterização espectral e segmentação interativa de imagens. Foram propostos dois novos algoritmos de segmentação dentro das linhas supracitadas, os quais se baseiam em operadores do Laplaciano, teoria espectral de grafos e na minimização de funcionais de energia. A eficácia de ambos os algoritmos pode ser constatada através de avaliações visuais das segmentações originadas, como também através de medidas quantitativas computadas com base nos resultados obtidos por técnicas do estado-da-arte em segmentação de imagens. Nosso primeiro algoritmo de segmentação, o qual ´e baseado na teoria espectral de grafos, combina técnicas de decomposição de imagens e medidas de similaridade em grafos em uma única e robusta ferramenta computacional. Primeiramente, um método de decomposição de imagens é aplicado para dividir a imagem alvo em duas componentes: textura e cartoon. Em seguida, um grafo de afinidade é gerado e pesos são atribuídos às suas arestas de acordo com uma função escalar proveniente de um operador de produto interno. Com base no grafo de afinidade, a imagem é então subdividida por meio do processo de corte espectral. Além disso, o resultado da segmentação pode ser refinado de forma interativa, mudando-se, desta forma, os pesos do grafo base. Experimentos visuais e numéricos foram conduzidos tomando-se por base métodos representativos do estado-da-arte e a clássica base de dados BSDS a fim de averiguar a eficiência da metodologia proposta. Ao contrário de grande parte dos métodos existentes de segmentação interativa, os quais são modelados por formulações matemáticas complexas que normalmente não garantem solução única para o problema de segmentação, nossa segunda metodologia aqui proposta é matematicamente simples de ser interpretada, fácil de implementar e ainda garante unicidade de solução. Além disso, o método proposto possui um comportamento anisotrópico, ou seja, pixels semelhantes são preservados mais próximos uns dos outros enquanto descontinuidades bruscas são impostas entre regiões da imagem onde as bordas são mais salientes. Como no caso anterior, foram realizadas diversas avaliações qualitativas e quantitativas envolvendo nossa técnica e métodos do estado-da-arte, tomando-se como referência a base de dados GrabCut da Microsoft. Enquanto a maior parte desta pesquisa de doutorado concentra-se no problema específico de segmentar imagens, como conteúdo complementar de pesquisa foram propostas duas novas técnicas para tratar o problema de retoque digital e colorização de imagens.