[pt] Este trabalho faz parte de um projeto para a implementação de um programa que possa simular problemas com milhões de graus de liberdade em um computador pessoal. Para isto, combina-se o Método Fast Multipole (FMM) com o Método Expedito dos Elementos de Contorno (EBEM), além de serem utilizados resolvedores iterativos de sistemas de equações. O EBEM é especialmente vantajoso em problemas de complicada topologia, ou que usem funções fundamentais muito complexas. Neste trabalho apresenta-se uma formulação para o Método Fast Multipole (FMM) que pode ser usada para, virtualmente, qualquer função e também para contornos curvos, o que parece ser uma contribuição original. Esta formulação apresenta um formato mais compacto do que as já existentes na literatura, e também pode ser diretamente aplicada a diversos tipos de problemas praticamente sem modificação de sua estrutura básica. É apresentada a validação numérica da formulação proposta. Sua utilização em um contexto do EBEM permite que um programa prescinda de integrações sobre segmentos – mesmo curvos – do contorno quando estes estão distantes do ponto fonte. / [en] This is part of a larger project that aims to develop a program able to simulate problems with millions of degrees of freedom on a personal computer. The Fast Multipole Method (FMM) is combined with the Expedite Boundary Element Method (EBEM) for integration, in the project s final version, with iterative equations solvers. The EBEM is especially advantageous when applied to problems with complicated topology as well as in the case of highly complex fundamental solutions. In this work, a FMM formulation is proposed for the use with virtually any type of fundamental solution and considering curved boundaries, which seems to be an original contribution. This formulation presents a more compact format than the ones shown in the technical literature, and can be directly applied to different kinds of problems without the need of manipulation of its basic structure, being numerically validated for a few applications. Its application in the context of the EBEM leads to the straightforward implementation of higher-order elements for generally curved boundaries that dispenses integration when the boundary segment is relatively far from the source point.

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Orientador: Yuri Dimitrov Bozhkov / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-27T01:04:06Z (GMT). No. of bitstreams: 1 SilvaJunior_ValterAparecido_M.pdf: 1356319 bytes, checksum: e64224c844e48a46487c6d387ec0f3e7 (MD5) Previous issue date: 2015 / Resumo: Nesta dissertação, obteremos as soluções exatas do Problema de Liouville-Gelfand (em uma e em duas dimensões) via grupos de Lie de simetrias / Abstract: In this dissertation, we shall obtain the exact solutions of the Liouville-Gelfand Problem (in one and in two dimensions) via Lie groups of symmetries / Mestrado / Matematica Aplicada / Mestre em Matemática Aplicada

[pt] Neste trabalho obtém-se a matriz de espalhamento de obstáculos cilíndricos em guias de ondas retangulares. O método de análise utilizado é o método dos momentos juntamente com o método das imagens. São analisadas descontinuidades formadas por um poste vertical inteiro, postes verticais contendo um gap central, postes horizontais contendo um gap central e postes localizados nas quatro paredes do guia de ondas retangular. Os resultados obtidos são comparados com valores experimentais para as 4 geometrias descritas acima. Além disso é feita a comparação dos resultados obtidos com os do método variacional para o caso do poste vertical inteiro. / [en] In this work the scattering matrix of cylindrical obstacles in rectangular wavwguides is obtained. The analysis method adopted is the moment method in junction with the image method. Discontinuities formed by a single vertivcal post, vetical posts with a central gap, horizontal posts with a central gap, and posts on the four waveguides walls are analyzed. The results are compared with experimental data for the four geometries described above. Moreover the results are also compared with those obtained by variational method in the case of the single vertical post.

abstract: This thesis introduces new techniques for clustering distributional data according to their geometric similarities. This work builds upon the optimal transportation (OT) problem that seeks global minimum cost for matching distributional data and leverages the connection between OT and power diagrams to solve different clustering problems. The OT formulation is based on the variational principle to differentiate hard cluster assignments, which was missing in the literature. This thesis shows multiple techniques to regularize and generalize OT to cope with various tasks including clustering, aligning, and interpolating distributional data. It also discusses the connections of the new formulation to other OT and clustering formulations to better understand their gaps and the means to close them. Finally, this thesis demonstrates the advantages of the proposed OT techniques in solving machine learning problems and their downstream applications in computer graphics, computer vision, and image processing. / Dissertation/Thesis / Doctoral Dissertation Computer Engineering 2020

A defining feature of quantum many-body systems is the presence of entanglement among their constituents. Besides providing valuable insights on several physical properties, entanglement is also responsible for the computational complexity of simulating quantum systems with variational methods. This thesis explores several aspects of entanglement in many-body systems, with the primary goal of devising efficient approaches for the study of topological properties and quantum dynamics of lattice models. The first focus of this work is the development of variational wavefunctions inspired by artificial neural networks. These can efficiently encode long-range and extensive entanglement in their structure, as opposed to the case of tensor network states. This feature makes them promising tools for the study of topologically ordered phases, quantum critical states as well as dynamical properties of quantum systems. In this thesis, we characterize the representational power of a specific class of artificial neural network states, constructed from Boltzmann machines. First, we show that wavefunctions obtained from restricted Boltzmann machines can efficiently parametrize chiral topological phases, such as fractional quantum Hall states. We then turn our attention to deep Boltzmann machines. In this framework, we propose a new class of variational wavefunctions, coined generalized transfer matrix states, which encompass restricted Boltzmann machine and tensor network states. We investigate the entanglement properties of this ansatz, as well as its capability of representing physical states. Understanding how the entanglement properties of a system evolve in time is the second focus of this thesis. In this context, we first investigate the manifestation of topological properties in the unitary dynamics of systems after a quench, using the degeneracy of the entanglement spectrum as a possible signature. We then analyze the phenomenon of entanglement growth, which limits to short timescales the applicability of tensor network methods in out-of-equilibrium problems. We investigate whether these limitations can be overcome by exploiting the dependence of entanglement entropies on the chosen computational basis. Specifically, we study how the spreading of quantum correlations can be contained by means of time-dependent basis rotations of the state, using exact diagonalization to simulate its dynamics after a quench. Going beyond the case of sudden quenches, we then show how, in certain weakly interacting problems, the asymptotic value of the entanglement entropy can be tuned by modifying the velocity at which the parameters in the Hamiltonian are changed. This enables the simulation of longer timescales using tensor network approaches. We present preliminary results obtained with matrix product states methods, with the goal of studying how equilibration affects the transport properties of interacting systems at long times.

Cette thèse porte sur l’étude de nouveaux modèles de jeux à champ moyen. On étudie dans un premier temps des modèles d’arrêt optimal et de contrôle impulsionnel en l’absence de bruit commun. On construit pour ces modèles une notion de solution adaptée pour laquelle on prouve des résultats d’existence et d’unicité sous des hypothèses naturelles. Ensuite, on s’intéresse à plusieurs propriétés des jeux à champ moyen. On étudie la limite de ces modèles vers des modèles d’évolution pures lorsque l’anticipation des joueurs tend vers 0. On montre l’unicité des équilibres pour des systèmes fortement couples (couples par les stratégies) sous certaines hypothèses. On prouve ensuite certains résultats de régularités sur une ”master equation” qui modélise un jeu à champ moyen avec bruit commun dans un espace d’états discret. Par la suite on présente une généralisation de l’algorithme standard d’Uzawa et on l’applique à la résolution numérique de certains modèles de jeux à champ moyen, notamment d’arrêt optimal ou de contrôle impulsionnel. Enfin on présente un cas concret de jeu à champ moyen qui provient de problèmes faisant intervenir un grand nombre d’appareils connectés dans les télécommunications. / This thesis is concerned with new models of mean field games. First, we study models of optimal stopping and impulse control in the case when there is no common noise. We build an appropriate notion of solutions for those models. We prove the existence and the uniqueness of such solutions under natural assumptions. Then, we are interested with several properties of mean field games. We study the limit of such models when the anticipation of the players vanishes. We show that uniqueness holds for strongly coupled mean field games (coupled via strategies) under certain assumptions. We then prove some regularity results for the master equation in a discrete state space case with common noise. We continue by giving a generalization of Uzawa’s algorithm and we apply it to solve numerically some mean field games, especially optimal stopping and impulse control problems. The last chapter presents an application of mean field games. This application originates from problems in telecommunications which involve a huge number of connected devices.

Deep learning is usually applied to static datasets. If used for classification based on data streams, it is not easy to take into account a non-stationarity. This thesis presents work in progress on a new method for online deep classifi- cation learning in data streams with slow or moderate drift, highly relevant for the application domain of malware detection. The method uses a combination of multilayer perceptron and variational autoencoder to achieve constant mem- ory consumption by encoding past data to a generative model. This can make online learning of neural networks more accessible for independent adaptive sys- tems with limited memory. First results for real-world malware stream data are presented, and they look promising. 1

Wireless communications technologies have experienced an exponential development during the last decades. 5G is a prominent exponent whose one of its crucial component is the Massive MIMO technology. By supporting multiple streams of signals it allows a revamped signal reconstruction in terms of mobile traffic size, data rate, latency, and reliability. In this thesis work, we isolated this technology into a SIMOapproach (Single-Input Multiple-Output) to explore a Machine Learning modeling to address the so-called Channel Prediction problem. Generally, the algorithms available to perform Channel Estimation in FDD and TDD deployments incur computational complexity downsides and require explicit feedback from client devices, which is typically prohibitive. This thesis work focuses on Channel Prediction by aims of employing Machine and deep Learning models in order to reduce the computational complexity by further relying in statistical modeling/learning. We explored the cross-Frequency Subband prediction intra-TTI (Transmission Time Interval) by means of proposing 3 three models. These intended to leverage frequency Multipath Components dependencies along TTIs. The first two ones are Probabilistic Principal Components Analysis (PPCA) and its Bayesiancounterpart, Bayesian Principal Components Analysis (BPCA). Then, we implemented Deep Learning Variational Encoder-Decoder (VED) architecture. These three models are intended to deal with the hugely high-dimensional space of the 4 datasets used by its intrinsic dimensionality reduction. The PPCA method was on average five times better than the VED alternative in terms of MSE accounting for all the datasets used.

Providing high quality of topics inference in today's large and dynamic corpora, such as Twitter, is a challenging task. This is especially challenging taking into account that the content in this environment contains short texts and many abbreviations. This project proposes an improvement of a popular online topics modelling algorithm for Latent Dirichlet Allocation (LDA), by incorporating supervision to make it suitable for Twitter context. This improvement is motivated by the need for a single algorithm that achieves both objectives: analyzing huge amounts of documents, including new documents arriving in a stream, and, at the same time, achieving high quality of topics’ detection in special case environments, such as Twitter. The proposed algorithm is a combination of an online algorithm for LDA and a supervised variant of LDA - labeled LDA. The performance and quality of the proposed algorithm is compared with these two algorithms. The results demonstrate that the proposed algorithm has shown better performance and quality when compared to the supervised variant of LDA, and it achieved better results in terms of quality in comparison to the online algorithm. These improvements make our algorithm an attractive option when applied to dynamic environments, like Twitter. An environment for analyzing and labelling data is designed to prepare the dataset before executing the experiments. Possible application areas for the proposed algorithm are tweets recommendation and trends detection. / Tillhandahålla högkvalitativa ämnen slutsats i dagens stora och dynamiska korpusar, såsom Twitter, är en utmanande uppgift. Detta är särskilt utmanande med tanke på att innehållet i den här miljön innehåller korta texter och många förkortningar. Projektet föreslår en förbättring med en populär online ämnen modellering algoritm för Latent Dirichlet Tilldelning (LDA), genom att införliva tillsyn för att göra den lämplig för Twitter sammanhang. Denna förbättring motiveras av behovet av en enda algoritm som uppnår båda målen: analysera stora mängder av dokument, inklusive nya dokument som anländer i en bäck, och samtidigt uppnå hög kvalitet på ämnen "upptäckt i speciella fall miljöer, till exempel som Twitter. Den föreslagna algoritmen är en kombination av en online-algoritm för LDA och en övervakad variant av LDA - Labeled LDA. Prestanda och kvalitet av den föreslagna algoritmen jämförs med dessa två algoritmer. Resultaten visar att den föreslagna algoritmen har visat bättre prestanda och kvalitet i jämförelse med den övervakade varianten av LDA, och det uppnådde bättre resultat i fråga om kvalitet i jämförelse med den online-algoritmen. Dessa förbättringar gör vår algoritm till ett attraktivt alternativ när de tillämpas på dynamiska miljöer, som Twitter. En miljö för att analysera och märkning uppgifter är utformad för att förbereda dataset innan du utför experimenten. Möjliga användningsområden för den föreslagna algoritmen är tweets rekommendation och trender upptäckt.