O aumento constante da demanda por sistemas computacionais cada vez mais eficientes tem motivado a busca por sistemas híbridos customizados compostos por GPP (General Purpose Processor), FPGAs (Field-Programmable Gate Array) e GPUs (Graphics Processing Units). Quando utilizados em conjunto possibilitam otimizar a relação entre desempenho e consumo de energia. Tais sistemas dependem de técnicas que façam o mapeamento mais adequado considerando o perfil do código fonte. Nesse sentido, este projeto propõe uma técnica para realizar o mapeamento entre GPP e FPGA. Para isso, utilizou-se como base uma abordagem de mineração de dados que avalia a similaridade entre código fonte. A técnica aqui desenvolvida obteve taxas de acertos de 65,67% para códigos sintetizados para FPGA com a ferramenta LegUP e 59,19% para Impulse C, considerando que para GPP o código foi compilado com o GCC (GNU Compiler Collection) utilizando o suporte a OpenMP. Os resultados demonstraram que esta abordagem pode ser empregada como um ponto de decisão inicial no processo de mapeamento em sistemas híbridos, somente analisando o perfil do código fonte sem que haja a necessidade de execução do mesmo para a tomada de decisão. / The steady increasing on demand for efficient computer systems has been motivated the search for customized hybrid systems composed by GPP (general purpose processors), FPGAs (Field- Programmable Gate Array) and GPUs (Graphics Processing Units). When they are used together allow to exploit their computing resources to optimize performance and power consumption. Such systems rely on techniques make the most appropriate mapping considering the profile of source code. Thus, this project proposes a technique to perform the mapping between GPP and FPGA. For this, it is applied a technique based on a data mining approach that evaluates the similarity between source code. The proposed method obtained hit rate 65.67% for codes synthesized in FPGA using LegUP tool and 59.19% for Impulse C tool, whereas for GPP, the source code was compiled on GCC (GNU Compiler Collection) using OpenMP. The results demonstrated that this approach can be used as an initial decision point on the mapping process in hybrid systems, only analyzing the profile of the source code without the need for implementing it for decision-making.

O aumento constante da demanda por sistemas computacionais cada vez mais eficientes tem motivado a busca por sistemas híbridos customizados compostos por GPP (General Purpose Processor), FPGAs (Field-Programmable Gate Array) e GPUs (Graphics Processing Units). Quando utilizados em conjunto possibilitam otimizar a relação entre desempenho e consumo de energia. Tais sistemas dependem de técnicas que façam o mapeamento mais adequado considerando o perfil do código fonte. Nesse sentido, este projeto propõe uma técnica para realizar o mapeamento entre GPP e FPGA. Para isso, utilizou-se como base uma abordagem de mineração de dados que avalia a similaridade entre código fonte. A técnica aqui desenvolvida obteve taxas de acertos de 65,67% para códigos sintetizados para FPGA com a ferramenta LegUP e 59,19% para Impulse C, considerando que para GPP o código foi compilado com o GCC (GNU Compiler Collection) utilizando o suporte a OpenMP. Os resultados demonstraram que esta abordagem pode ser empregada como um ponto de decisão inicial no processo de mapeamento em sistemas híbridos, somente analisando o perfil do código fonte sem que haja a necessidade de execução do mesmo para a tomada de decisão. / The steady increasing on demand for efficient computer systems has been motivated the search for customized hybrid systems composed by GPP (general purpose processors), FPGAs (Field- Programmable Gate Array) and GPUs (Graphics Processing Units). When they are used together allow to exploit their computing resources to optimize performance and power consumption. Such systems rely on techniques make the most appropriate mapping considering the profile of source code. Thus, this project proposes a technique to perform the mapping between GPP and FPGA. For this, it is applied a technique based on a data mining approach that evaluates the similarity between source code. The proposed method obtained hit rate 65.67% for codes synthesized in FPGA using LegUP tool and 59.19% for Impulse C tool, whereas for GPP, the source code was compiled on GCC (GNU Compiler Collection) using OpenMP. The results demonstrated that this approach can be used as an initial decision point on the mapping process in hybrid systems, only analyzing the profile of the source code without the need for implementing it for decision-making.

Positive kernels and their associated reproducing kernel Hilbert spaces have played a key role in the development of complex analysis and Hilbert-space operator theory, and they have recently been extended to the setting of free noncommutative function theory. In this paper, we develop the subject further in a number of directions. We give a characterization of completely positive noncommutative kernels in the setting of Hilbert C*-modules and Hilbert W*-modules. We prove an Arveson-type extension theorem for completely positive noncommutative kernels, and we show that a uniformly bounded noncommutative kernel can be decomposed into a linear combination of completely positive noncommutative kernels. / Ph. D.

Probabilistic modeling with latent variables is a powerful paradigm that has led to key advances in many applications such natural language processing, text mining, and computational biology. Unfortunately, while introducing latent variables substantially increases representation power, learning and modeling can become considerably more complicated. Most existing solutions largely ignore non-identifiability issues in modeling and formulate learning as a nonconvex optimization problem, where convergence to the optimal solution is not guaranteed due to local minima. In this thesis, we propose to tackle these problems through the lens of linear/multi-linear algebra. Viewing latent variable models from this perspective allows us to approach key problems such as structure learning and parameter learning using tools such as matrix/tensor decompositions, inversion, and additive metrics. These new tools enable us to develop novel solutions to learning in latent variable models with theoretical and practical advantages. For example, our spectral parameter learning methods for latent trees and junction trees are provably consistent, local-optima-free, and 1-2 orders of magnitude faster thanEMfor large sample sizes. In addition, we focus on applications in Natural Language Processing, using our insights to not only devise new algorithms, but also to propose new models. Our method for unsupervised parsing is the first algorithm that has both theoretical guarantees and is also practical, performing favorably to theCCMmethod of Klein and Manning. We also developed power low rank ensembles, a framework for language modeling that generalizes existing n-gram techniques to non-integer n. It consistently outperforms state-of-the-art Kneser Ney baselines and can train on billion-word datasets in a few hours.

This thesis consists of an introduction and five research papers on topics related to conformal mapping, the Loewner equation and its applications, and Bergman-type spaces of holomorphic functions. The first two papers are devoted to the study of integral means of derivatives of conformal mappings. In Paper I, we present improved upper estimates of the universal means spectrum of conformal mappingsof the unit disk. These estimates rely on inequalities  obtained by Hedenmalm and Shimorin using Bergman space techniques, and on computer calculations. Paper II is a survey of recent results on the universal means spectrum, with particular emphasis on Bergman spacetechniques.Paper III concerns Bergman-type spaces of holomorphic functions in subsets of $\textbf{C}^d$ and their reproducing kernel functions. By expanding the norm of a function in a Bergman space along the zero variety of a polynomial, we obtain a series expansion of reproducing kernel functions in terms of kernels associated with lower-dimensionalspaces of holomorphic functions. We show how this general approach can be used to explicitly compute kernel functions for certain weighted Bergman and Bargmann-Fock spaces defined in domains in $\textbf{C}^2$.The last two papers contribute to the theory of Loewner chains and theirapplications in the analysis of planar random growth model defined in terms of compositions of conformal maps.In Paper IV, we study Loewner chains generated by unimodular L\'evy processes.We first establish the existence of a capacity scaling limit for the associated growing hulls in terms of whole-plane Loewner chains driven by a time-reversed process. We then analyze the properties of Loewner chains associated with a class of two-parameter compound Poisson processes, and we describe the dependence of the geometric properties of the hulls on the parameters of the driving process. In Paper V, we consider a variation of the Hastings-Levitov growth model, with anisotropic growth. We again establish results concerning scaling limits, when the number of compositions increases and the basic conformal mappings tends to the identity. We show that the resulting limit sets can be associated with solutions to the Loewner equation.We also prove that, in the limit, the evolution of harmonic measure on the boundary is deterministic and is determined by the flow associated with an ordinary differential equation, and we give a description of the fluctuations around this deterministic limit flow. / <p>QC 20100414</p>

In this work, we generalize three famous results obtained by Schoenberg: I) the characterization of the continuous positive definite isotropic kernels defined on a real sphere; II) the characterization of the continuous positive definite radial kernels defined on an Euclidean space; III) the characterization of the continuous conditionally negative radial kernels defined on an Euclidean space. From this new approach, we reobtain several results in the literature and obtain some new ones as well. With the exception of S1 and R , we obtain necessary and sufficient conditions in order that these kernels be strictly positive definite and strictly conditionally negative definite. / Neste trabalho, nós generalizamos três resultados famosos obtidos por Schoenberg: I) a caracterização dos núcleos contínuos isotrópicos positivos definidos em esferas reais; II) a caracterização dos núcleos contínuos radiais positivos definidos em espaços Euclidianos; III) a caracterização dos núcleos contínuos radiais condicionalmente negativos definidos em espaços Euclidianos. A partir destas novas abordagens, reobtemos vários resultados da literatura assim como obtemos novos. Com a exceção de S1 e R, obtemos condições necessárias e suficientes para que estes núcleos sejam estritamente positivos definidos e estritamente condicionalmente negativos definidos.

Ces dernières années, les réseaux sont devenus une source importante d’informations dans différents domaines aussi variés que les sciences sociales, la physique ou les mathématiques. De plus, la taille de ces réseaux n’a cessé de grandir de manière conséquente. Ce constat a vu émerger de nouveaux défis, comme le besoin de mesures précises et intuitives pour caractériser et analyser ces réseaux de grandes tailles en un temps raisonnable. La première partie de cette thèse introduit une nouvelle mesure de similarité entre deux noeuds d’un réseau dirigé et pondéré : la covariance “sum-over-paths”. Celle-ci a une interprétation claire et précise : en dénombrant tous les chemins possibles deux noeuds sont considérés comme fortement corrélés s’ils apparaissent souvent sur un même chemin – de préférence court. Cette mesure dépend d’une distribution de probabilités, définie sur l’ensemble infini dénombrable des chemins dans le graphe, obtenue en minimisant l'espérance du coût total entre toutes les paires de noeuds du graphe sachant que l'entropie relative totale injectée dans le réseau est fixée à priori. Le paramètre d’entropie permet de biaiser la distribution de probabilité sur un large spectre : allant de marches aléatoires naturelles où tous les chemins sont équiprobables à des marches biaisées en faveur des plus courts chemins. Cette mesure est alors appliquée à des problèmes de classification semi-supervisée sur des réseaux de taille moyennes et comparée à l’état de l’art. La seconde partie de la thèse introduit trois nouveaux algorithmes de classification de noeuds en sein d’un large réseau dont les noeuds sont partiellement étiquetés. Ces algorithmes ont un temps de calcul linéaire en le nombre de noeuds, de classes et d’itérations, et peuvent dés lors être appliqués sur de larges réseaux. Ceux-ci ont obtenus des résultats compétitifs en comparaison à l’état de l’art sur le large réseaux de citations de brevets américains et sur huit autres jeux de données. De plus, durant la thèse, nous avons collecté un nouveau jeu de données, déjà mentionné : le réseau de citations de brevets américains. Ce jeu de données est maintenant disponible pour la communauté pour la réalisation de tests comparatifs. La partie finale de cette thèse concerne la combinaison d’un graphe de citations avec les informations présentes sur ses noeuds. De manière empirique, nous avons montré que des données basées sur des citations fournissent de meilleurs résultats de classification que des données basées sur des contenus textuels. Toujours de manière empirique, nous avons également montré que combiner les différentes sources d’informations (contenu et citations) doit être considéré lors d’une tâche de classification de textes. Par exemple, lorsqu’il s’agit de catégoriser des articles de revues, s’aider d’un graphe de citations extrait au préalable peut améliorer considérablement les performances. Par contre, dans un autre contexte, quand il s’agit de directement classer les noeuds du réseau de citations, s’aider des informations présentes sur les noeuds n’améliora pas nécessairement les performances. La théorie, les algorithmes et les applications présentés dans cette thèse fournissent des perspectives intéressantes dans différents domaines. In recent years, networks have become a major data source in various fields ranging from social sciences to mathematical and physical sciences. Moreover, the size of available networks has grow substantially as well. This has brought with it a number of new challenges, like the need for precise and intuitive measures to characterize and analyze large scale networks in a reasonable time. The first part of this thesis introduces a novel measure between two nodes of a weighted directed graph: The sum-over-paths covariance. It has a clear and intuitive interpretation: two nodes are considered as highly correlated if they often co-occur on the same -- preferably short -- paths. This measure depends on a probability distribution over the (usually infinite) countable set of paths through the graph which is obtained by minimizing the total expected cost between all pairs of nodes while fixing the total relative entropy spread in the graph. The entropy parameter allows to bias the probability distribution over a wide spectrum: going from natural random walks (where all paths are equiprobable) to walks biased towards shortest-paths. This measure is then applied to semi-supervised classification problems on medium-size networks and compared to state-of-the-art techniques. The second part introduces three novel algorithms for within-network classification in large-scale networks, i.e., classification of nodes in partially labeled graphs. The algorithms have a linear computing time in the number of edges, classes and steps and hence can be applied to large scale networks. They obtained competitive results in comparison to state-of-the-art technics on the large scale U.S.~patents citation network and on eight other data sets. Furthermore, during the thesis, we collected a novel benchmark data set: the U.S.~patents citation network. This data set is now available to the community for benchmarks purposes. The final part of the thesis concerns the combination of a citation graph with information on its nodes. We show that citation-based data provide better results for classification than content-based data. We also show empirically that combining both sources of information (content-based and citation-based) should be considered when facing a text categorization problem. For instance, while classifying journal papers, considering to extract an external citation graph may considerably boost the performance. However, in another context, when we have to directly classify the network citation nodes, then the help of features on nodes will not improve the results. The theory, algorithms and applications presented in this thesis provide interesting perspectives in various fields.

Habitat loss is the greatest contributor to the decline of species globally and thus understanding habitat use and the consequences fragmentation has on biodiversity is a fundamental step towards management and recovery. I conducted a radio-telemetry study to examine the spatial ecology and the effects of roads on Eastern Hognose Snakes (Heterodon platirhinos), a species at risk, in the Long Point Region of Ontario, Canada. I tested habitat selection at multiple spatial scales and I found that within the home range, snakes avoided agricultural land and selected open sand barrens, particularly for nesting. At the local scale, snakes avoided mature overstory trees and used younger patches of forest. Used locations had more woody debris, logs and low-vegetative coverage than locations selected at random. Eastern Hognose Snakes also showed avoidance of paved road crossings in their seasonal movements, but readily crossed unpaved roads. Management efforts for this species at risk should be placed on the conservation of sand barrens and on the construction of road underpasses to prevent genetic isolation of populations.

Habitat loss is the greatest contributor to the decline of species globally and thus understanding habitat use and the consequences fragmentation has on biodiversity is a fundamental step towards management and recovery. I conducted a radio-telemetry study to examine the spatial ecology and the effects of roads on Eastern Hognose Snakes (Heterodon platirhinos), a species at risk, in the Long Point Region of Ontario, Canada. I tested habitat selection at multiple spatial scales and I found that within the home range, snakes avoided agricultural land and selected open sand barrens, particularly for nesting. At the local scale, snakes avoided mature overstory trees and used younger patches of forest. Used locations had more woody debris, logs and low-vegetative coverage than locations selected at random. Eastern Hognose Snakes also showed avoidance of paved road crossings in their seasonal movements, but readily crossed unpaved roads. Management efforts for this species at risk should be placed on the conservation of sand barrens and on the construction of road underpasses to prevent genetic isolation of populations.

This dissertation investigates the problem of estimating a kernel over a large graph based on a sample of noisy observations of linear measurements of the kernel. We are interested in solving this estimation problem in the case when the sample size is much smaller than the ambient dimension of the kernel. As is typical in high-dimensional statistics, we are able to design a suitable estimator based on a small number of samples only when the target kernel belongs to a subset of restricted complexity. In our study, we restrict the complexity by considering scenarios where the target kernel is both low-rank and smooth over a graph. Using standard tools of non-parametric estimation, we derive a minimax lower bound on the least squares error in terms of the rank and the degree of smoothness of the target kernel. To prove the optimality of our lower-bound, we proceed to develop upper bounds on the error for a least-square estimator based on a non-convex penalty. The proof of these upper bounds depends on bounds for estimators over uniformly bounded function classes in terms of Rademacher complexities. We also propose a computationally tractable estimator based on least-squares with convex penalty. We derive an upper bound for the computationally tractable estimator in terms of a coherence function introduced in this work. Finally, we present some scenarios wherein this upper bound achieves a near-optimal rate. The motivations for studying such problems come from various real-world applications like recommender systems and social network analysis.