Abstract Vehicular Ad Hoc Networks (VANET) can provide strong safety for vehicles by taking the advantages of the information which are interchanged among themselves and some infrastructures. Due to this significant application of VANET, message authentication and privacy in VANET is quite critical. Pseudonym PKI technology is a practical solution to ensure the above two properties. However, the performance of the previous works cannot satisfy the requirement for the applications in VANET, such as efficiency and management cost. Most of all pseudonym PKI technologies are comprehensive schemes, like group key and ID-based public key cryptosystem. This also increases the implementation complexity of VANET security. Therefore, we will propose an efficient pseudonym PKI mechanism based on bilinear mapping to improve the performance of the message authentication protocol, certificate tracing and certificate revocation, implementation cost, and management cost.

Many problems in signal processing, machine learning and computer vision can be solved by learning low rank models from data. In computer vision, problems such as rigid structure from motion have been formulated as an optimization over subspaces with fixed rank. These hard-rank constraints have traditionally been imposed by a factorization that parameterizes subspaces as a product of two matrices of fixed rank. Whilst factorization approaches lead to efficient and kernelizable optimization algorithms, they have been shown to be NP-Hard in presence of missing data. Inspired by recent work in compressed sensing, hard-rank constraints have been replaced by soft-rank constraints, such as the nuclear norm regularizer. Vis-a-vis hard-rank approaches, soft-rank models are convex even in presence of missing data: but how is convex optimization solving a NP-Hard problem? This thesis addresses this question by analyzing the relationship between hard and soft rank constraints in the unsupervised factorization with missing data problem. Moreover, we extend soft rank models to weakly supervised and fully supervised learning problems in computer vision. There are four main contributions of our work: (1) The analysis of a new unified low-rank model for matrix factorization with missing data. Our model subsumes soft and hard-rank approaches and merges advantages from previous formulations, such as efficient algorithms and kernelization. It also provides justifications on the choice of algorithms and regions that guarantee convergence to global minima. (2) A deterministic \rank continuation" strategy for the NP-hard unsupervised factorization with missing data problem, that is highly competitive with the state-of-the-art and often achieves globally optimal solutions. In preliminary work, we show that this optimization strategy is applicable to other NP-hard problems which are typically relaxed to convex semidentite programs (e.g., MAX-CUT, quadratic assignment problem). (3) A new soft-rank fully supervised robust regression model. This convex model is able to deal with noise, outliers and missing data in the input variables. (4) A new soft-rank model for weakly supervised image classification and localization. Unlike existing multiple-instance approaches for this problem, our model is convex.

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Quasi-keyhole, including plasma keyhole and double-sided welding, is a novel approach proposed to operate the keyhole arc welding process. It can result in a high quality weld, but also raise higher demand of the operator. A computer control system to detect the keyhole and control the arc current can improve the performance of the welding process. To this effect, developing automatic pipe welding, instead of manual welding, is a hot research topic in the welding field. The objective of this research is to design an automatic quasi-keyhole pipe welding system that can monitor the keyhole and control its establishment time to track the reference trajectory as the dynamic behavior of welding processes changes. For this reason, an automatic plasma welding system is proposed, in which an additional electrode is added on the back side of the workpiece to detect the keyhole, as well as to provide the double-side arc in the double-sided arc welding mode. In the automatic pipe welding system the arc current can be controlled by the computer controller. Based on the designed automatic plasma pipe welding system, two kinds of model predictive controller − linear and bilinear − are developed, and an optimal algorithm is designed to optimize the keyhole weld process. The result of the proposed approach has been verified by using both linear and bilinear model structures in the quasi-keyhole plasma welding (QKPW) process experiments, both in normal plasma keyhole and double-sided arc welding modes.

The Alpha Magnetic Spectrometer is an International Space Station Experiment that features a unique nonlinear support system with no previous flight heritage. The experiment consists of multiple straps with piecewise-linear stiffness curves that support a cryogenic magnet in three-dimensional space inside of a vacuum chamber. The stiffness curves for each strap are essentially bilinear and switch between two distinct slopes at a specified displacement. This highly nonlinear support system poses many questions in regards to feasible computational methods of analysis and possible response behavior. This thesis develops a numerical model for a multi-bilinear-spring support system motivated by the Alpha Magnetic Spectrometer design. Methods of analysis applied to the single bilinear oscillator served as the foundation of the model developed in this thesis. The model is developed using MATLAB and proves to be more computationally efficient than ANSYS finite element software. Numerical simulations contained herein demonstrate the variety of response behaviors possible in a multi-bilinear-spring support system, thus aiding future endeavors which may use a support system similar to the Alpha Magnetic Spectrometer. Classic nonlinear responses, such as subharmonic and chaotic, were found to exist.

Orientador: Aparecido Nilceu Marana / Banca: João Paulo Papa / Banca: Marcelo Andrade da Costa Vieira / Resumo: Neste trabalho é proposto um método para reconhecer veículos em imagens coloridas baseado em uma rede neural Perceptron Multicamadas pré-treinada por meio de técnicas de aprendizado em profundidade, sendo uma das técnicas composta por Máquinas de Boltzmann Profundas e projeção bilinear e a outra composta por Máquinas de Boltzmann Profundas Multinomiais e projeção bilinear. A proposição deste método justifica-se pela demanda cada vez maior da área de Sistemas de Transporte Inteligentes. Para se obter um reconhecedor de veículos robusto, a proposta é utilizar o método de treinamento inferencial não-supervisionado Divergência por Contraste em conjunto com o método inferencial Campos Intermediários, para treinar múltiplas instâncias das redes profundas. Na fase de pré-treinamento local do método proposto são utilizadas projeções bilineares para reduzir o número de nós nas camadas da rede. A junção das estruturas em redes profundas treinadas separadamente forma a arquitetura final da rede neural, que passa por uma etapa de pré- treinamento global por Campos Intermediários. Na última etapa de treinamentos a rede neural Perceptron Multicamadas (MLP) é inicializada com os parâmetros pré-treinados globalmente e a partir deste ponto, inicia-se um processo de treinamento supervisionado utilizando gradiente conjugado de segunda ordem. O método proposto foi avaliado sobre a base BIT-Vehicle de imagens frontais de veículos coletadas de um ambiente de tráfego real... / Abstract: In this work it is proposed a vehicle recognition method for color images based on a Multilayer Perceptron neural network pre-trained through deep learning techniques (one technique composed by Deep Boltzmann Machines and bilinear projections and the other composed by Multinomial Deep Boltzmann Machines and bilinear projections). This proposition is justified by the increasing demand in Traffic Engineering area for the class of Intelligent Transportation Systems. In order to create a robust vehicle recognizer, the proposal is to use the inferential unsupervised training method of Contrastive Divergence together with the Mean Field inferential method, for training multiple instances of deep models. In the local pre-training phase of the proposed method, bilinear projections are used to reduce the number of nodes of the neural network. The combination of the separated trained deep models constitutes the final recognizer's architecture, that yet will be global pre-trained through Mean Field. In the last phase of training the Multilayer Perceptron neural network is initialized with globally pre-trained parameters and from this point, a process of supervised training starts using second order conjugate gradient. The proposed method was evaluated over the BIT-Vehicle database of frontal images of vehicles collected from a real road traffic environment. The best results obtained by the proposed method that used multinomial deep models were 81.83% of mean accuracy in ... / Mestre

[pt] É considerado o problema da estabilidade de sistemas dinâmicos bilineares em ambiente estocástico. Após a apresentação de uma coletânea de resultados já existentes, são propostas novas condições de estabilidade para sistemas discretos utilizando o método direto de Lyapunov. Tais resultados são comparados com os já existentes. / [en] The stability of bilinear dynamic systems in a stochastic environment is considered, including a survey on this field. New conditions for stability of discrete systems using the direct method of Lyapunov are proposed. The results developed here are compared with chose in the current literature.

Doctor of Philosophy / Department of Mathematics / Virginia Naibo / Leibniz-type rules associated to bilinear pseudodifferential operators have received considerable attention due to their applications in obtaining fractional Leibniz rules and the study of various partial differential equations. Generally speaking, fractional Leibniz rules provide a way of estimating the size and smoothness of a product of functions in terms of the size and smoothness of the individual functions themselves. Such rules are helpful in determining well-posedness results for solutions of PDEs modeling a variety of real world phenomena, ranging from Euler and Navier-Stokes equations (which model incompressible fluid flow, such as airflow over a wing) to Korteweg-de Vries equations (which model waves on shallow water surfaces). Bilinear pseudodifferential operators act to combine two functions using their Fourier transforms and a symbol, which is a function that assigns different weights to the functions’ frequency components as they are combined. Thus, Leibniz-type rules associated to bilinear pseudodifferential operators serve as a generalization of fractional Leibniz rules by providing estimates on the size and smoothness of some combination of two functions, for which pointwise multiplication is recoverable by choosing a symbol identically equal to one. A variety of function spaces may be used to measure the size and smoothness of functions involved, including Lebesgue spaces, Sobolev spaces, and Besov and Triebel-Lizorkin spaces. Further, bilinear pseudodifferential operators may be considered in association with different classes of symbols, which is to say that the symbol itself (and possibly its derivatives) will possess certain decay properties. New Leibniz-type rules in two different settings will be presented in this manuscript. In the first setting, Leibniz-type rules associated to bilinear pseudodifferential operators with homogeneous symbols in a certain class are proved, where the sizes of the functions involved are measured using a combination of Lebesgue space norms and norms corresponding to function spaces admitting appropriate molecular decompositions, specifically focusing on the case of homogeneous Besov-type and Triebel-Lizorkin-type spaces. In the second setting, Leibniz-type rules and biparameter counterparts are proved in weighted Lebesgue and Sobolev spaces associated to Coifman-Meyer multiplier operators. All of the new Leibniz-type rules proved in the manuscript yield corresponding new fractional Leibniz rules, which are highlighted as appropriate. Various techniques from Fourier analysis serve as important tools in the proofs of these new results, such as obtaining paraproduct decompositions for bilinear pseudodifferential operators and utilizing Littlewood-Paley theory and square function-type estimates.

[pt] É considerado o problema de estabilidade de sistemas dinâmicos bilineares a tempo discreto em ambiente determinístico. São propostas novas condições de estabilidade para três modelos diferentes. Tais resultados são comparados com os já existentes. / [en] The stability of bilinear dynamic discrete-time systems in a deterministic environment is considered. New conditions for stability of three types of systems are proposed. The results developed here are compared with those in the current literature.

Cette thèse intitulée « Une approche exacte de résolution de problèmes de pooling appliquée à la fabrication d’aliments », porte sur la résolution (par des méthodes exactes d’optimisation) de problèmes industriels liés à la fabrication d’aliments. Ces problèmes industriels traitent de l’aide à la décision pour la fabrication d’aliments pour des animaux et se rapprochent de problèmes biens connus de la littérature scientifique, à savoir les problèmes de pooling. La méthode présentée dans cet exposé permet de résoudre les problèmes d’optimisation bilinéaires issus de cette problématique industrielle. Elle est basée un branch-and-bound résolvant des linéarisations. Une approche lagrangienne a aussi été explorée et testée pour calculer des bornes inférieures. / « A global approach to solve pooling problem applied to feed mix industry » deals with the resolution of non linear non convex optimization problem which can occur in the feed mix industry. Feed mix industry problems are close to pooling problem, well-known in the literature. They are aimed to help decision maker in formulating feed, ie. To decide how to blend raw material to make a product satisfying nutrient and production constraints. The brand-and-bound algorithm presented in this these is aimed to solved large-scaled bilinear problems with bilinear constraints. A lagrangian approach has also been developed to obtain valid lower bound.