abstract: For a (N+1)-bus power system, possibly 2N solutions exists. One of these solutions is known as the high-voltage (HV) solution or operable solution. The rest of the solutions are the low-voltage (LV), or large-angle, solutions. In this report, a recently developed non-iterative algorithm for solving the power- flow (PF) problem using the holomorphic embedding (HE) method is shown as being capable of finding the HV solution, while avoiding converging to LV solutions nearby which is a drawback to all other iterative solutions. The HE method provides a novel non-iterative procedure to solve the PF problems by eliminating the non-convergence and initial-estimate dependency issues appeared in the traditional iterative methods. The detailed implementation of the HE method is discussed in the report. While published work focuses mainly on finding the HV PF solution, modified holomorphically embedded formulations are proposed in this report to find the LV/large-angle solutions of the PF problem. It is theoretically proven that the proposed method is guaranteed to find a total number of 2N solutions to the PF problem and if no solution exists, the algorithm is guaranteed to indicate such by the oscillations in the maximal analytic continuation of the coefficients of the voltage power series obtained. After presenting the derivation of the LV/large-angle formulations for both PQ and PV buses, numerical tests on the five-, seven- and 14-bus systems are conducted to find all the solutions of the system of nonlinear PF equations for those systems using the proposed HE method. After completing the derivation to find all the PF solutions using the HE method, it is shown that the proposed HE method can be used to find only the of interest PF solutions (i.e. type-1 PF solutions with one positive real-part eigenvalue in the Jacobian matrix), with a proper algorithm developed. The closet unstable equilibrium point (UEP), one of the type-1 UEP’s, can be obtained by the proposed HE method with limited dynamic models included. The numerical performance as well as the robustness of the proposed HE method is investigated and presented by implementing the algorithm on the problematic cases and large-scale power system. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2015

abstract: Power flow calculation plays a significant role in power system studies and operation. To ensure the reliable prediction of system states during planning studies and in the operating environment, a reliable power flow algorithm is desired. However, the traditional power flow methods (such as the Gauss Seidel method and the Newton-Raphson method) are not guaranteed to obtain a converged solution when the system is heavily loaded. This thesis describes a novel non-iterative holomorphic embedding (HE) method to solve the power flow problem that eliminates the convergence issues and the uncertainty of the existence of the solution. It is guaranteed to find a converged solution if the solution exists, and will signal by an oscillation of the result if there is no solution exists. Furthermore, it does not require a guess of the initial voltage solution. By embedding the complex-valued parameter α into the voltage function, the power balance equations become holomorphic functions. Then the embedded voltage functions are expanded as a Maclaurin power series, V(α). The diagonal Padé approximant calculated from V(α) gives the maximal analytic continuation of V(α), and produces a reliable solution of voltages. The connection between mathematical theory and its application to power flow calculation is described in detail. With the existing bus-type-switching routine, the models of phase shifters and three-winding transformers are proposed to enable the HE algorithm to solve practical large-scale systems. Additionally, sparsity techniques are used to store the sparse bus admittance matrix. The modified HE algorithm is programmed in MATLAB. A study parameter β is introduced in the embedding formula βα + (1- β)α^2. By varying the value of β, numerical tests of different embedding formulae are conducted on the three-bus, IEEE 14-bus, 118-bus, 300-bus, and the ERCOT systems, and the numerical performance as a function of β is analyzed to determine the “best” embedding formula. The obtained power-flow solutions are validated using MATPOWER. / Dissertation/Thesis / Flow chart of the HE algorithm / Presentation for mater's thesis defense / Masters Thesis Electrical Engineering 2015

abstract: High-level inference tasks in video applications such as recognition, video retrieval, and zero-shot classification have become an active research area in recent years. One fundamental requirement for such applications is to extract high-quality features that maintain high-level information in the videos. Many video feature extraction algorithms have been purposed, such as STIP, HOG3D, and Dense Trajectories. These algorithms are often referred to as “handcrafted” features as they were deliberately designed based on some reasonable considerations. However, these algorithms may fail when dealing with high-level tasks or complex scene videos. Due to the success of using deep convolution neural networks (CNNs) to extract global representations for static images, researchers have been using similar techniques to tackle video contents. Typical techniques first extract spatial features by processing raw images using deep convolution architectures designed for static image classifications. Then simple average, concatenation or classifier-based fusion/pooling methods are applied to the extracted features. I argue that features extracted in such ways do not acquire enough representative information since videos, unlike images, should be characterized as a temporal sequence of semantically coherent visual contents and thus need to be represented in a manner considering both semantic and spatio-temporal information. In this thesis, I propose a novel architecture to learn semantic spatio-temporal embedding for videos to support high-level video analysis. The proposed method encodes video spatial and temporal information separately by employing a deep architecture consisting of two channels of convolutional neural networks (capturing appearance and local motion) followed by their corresponding Fully Connected Gated Recurrent Unit (FC-GRU) encoders for capturing longer-term temporal structure of the CNN features. The resultant spatio-temporal representation (a vector) is used to learn a mapping via a Fully Connected Multilayer Perceptron (FC-MLP) to the word2vec semantic embedding space, leading to a semantic interpretation of the video vector that supports high-level analysis. I evaluate the usefulness and effectiveness of this new video representation by conducting experiments on action recognition, zero-shot video classification, and semantic video retrieval (word-to-video) retrieval, using the UCF101 action recognition dataset. / Dissertation/Thesis / Masters Thesis Computer Science 2016

abstract: In recent years, several methods have been proposed to encode sentences into fixed length continuous vectors called sentence representation or sentence embedding. With the recent advancements in various deep learning methods applied in Natural Language Processing (NLP), these representations play a crucial role in tasks such as named entity recognition, question answering and sentence classification. Traditionally, sentence vector representations are learnt from its constituent word representations, also known as word embeddings. Various methods to learn the distributed representation (embedding) of words have been proposed using the notion of Distributional Semantics, i.e. “meaning of a word is characterized by the company it keeps”. However, principle of compositionality states that meaning of a sentence is a function of the meanings of words and also the way they are syntactically combined. In various recent methods for sentence representation, the syntactic information like dependency or relation between words have been largely ignored. In this work, I have explored the effectiveness of sentence representations that are composed of the representation of both, its constituent words and the relations between the words in a sentence. The word and relation embeddings are learned based on their context. These general-purpose embeddings can also be used as off-the- shelf semantic and syntactic features for various NLP tasks. Similarity Evaluation tasks was performed on two datasets showing the usefulness of the learned word embeddings. Experiments were conducted on three different sentence classification tasks showing that our sentence representations outperform the original word-based sentence representations, when used with the state-of-the-art Neural Network architectures. / Dissertation/Thesis / Masters Thesis Computer Science 2017

Made available in DSpace on 2015-05-15T11:45:59Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 941118 bytes, checksum: f8ae9b800c3284a22de7188884029167 (MD5) Previous issue date: 2011-05-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this dissertation we expose the solve the four line problem in Schubert Calculus using the Plucker embedding, giving emphasis to the study of the relative position of the four given lines in P3, this allows us to obtain an explicit description of the solution's set as well as to give the precise meaning to the notion of general position. In chapter 1, we insert the notion of projective space and other related, which are the basic notions for addressing the problem that we treat. In chapter 2, we introduce the Plucker embedding, !, which allows us to identify the set of lines that meet a xed given line l0 with the intersection of the Plucker's quadric, Q, and the tangent space of Q at !(l0). We also give the description of all the linear varieties contained in the Plucker's quadric Q. Finally, in chapter 3 we demonstrate the Theorem 3.0.3 which is a key ingredient to and solutions for our problem. Moreover, we establish a relationship between the relative position of the four given lines and their solution's set. Finally, we conclude in the appendix with the Shapiro-Shapiro conjecture in the case of the four line problem in Schubert Calculus. / Neste trabalho expomos a resolução do problema das 4 retas do Cálculo de Schubert utilizando o mergulho de Plücker, com ênfase no estudo da posição relativa das 4 retas dadas em P3, o que nos permite obter uma descrição explícita do conjunto de soluções é dar sentido preciso à noção de posição geral. No capítulo 1 inserimos a noção de espaço projetivo e outras correlatas que servirão de base no estudo do problema a ser resolvido. No capítulo 2 introduzimos o Mergulho de Plücker, ω, o qual nos permite identificar o conjunto das retas que encontram uma reta fixa l0 com a interseção da quádrica de Plücker e o espaço tangente à mesma no ponto ω l0. Além disso damos a descrição das variedades lineares contidas na quádrica de Plücker. Porém, no capítulo 3 demonstramos o Teorema 3.0.3 que é a chave para resolução do nosso problema e fazemos a descrição do conjunto solução cada para posição relativa possível das 4 retas. Concluímos com um apêndice onde tratamos da conjectura de Shapiro-Shapiro no caso do problema das quatro retas do cálculo de Shubert.

A virtualização de redes tem se tornado cada vez mais proeminente nos últimos anos. Tal técnica permite a criação de infraestruturas de rede que se adaptam a necessidades específicas de aplicações de rede distintas, além de dar suporte à instanciação de ambientes favoráveis para o desenvolvimento e avaliação de novas arquiteturas e protocolos. Apesar de esforços recentes (motivados principalmente pela busca de mecanismos para avaliar propostas relacionadas à Internet do Futuro) terem contribuído substancialmente para a materialização desse conceito, nenhum preocupou-se em conciliar alocação eficiente de recursos e satisfação de requisitos de segurança (e.g., confidencialidade). É importante ressaltar que, no contexto de redes virtuais, a proteção de infraestruturas de rede compartilhadas constitui condição fundamental para seu uso em larga escala. É de grande importância que o impacto negativo causado pelo aprovisionamento de segurança seja considerado no processo de mapeamento de redes virtuais, de forma a permitir o uso integral dos recursos físicos sem subestimar requisitos de capacidade. Portanto, nesta dissertação, são propostos um modelo ótimo e um al- goritmo heurístico para realizar o mapeamento de redes virtuais em substratos físicos que têm por objetivo otimizar a utilização de recursos físicos garantindo a satisfação de requisitos de segurança. Ambas as abordagens possuem uma modelagem precisa de custos adicionais associados a mecanismos de segurança usados para proteger re- des virtuais, e são capazes de atender requisições de redes virtuais de forma online. Além disso, são apresentados os resultados de um extensivo processo de avaliação realizado, incluindo uma comparação detalhada entre o modelo ótimo e o algoritmo heurístico. Os experimentos revelam que o modelo baseado em Programação Linear Inteira é capaz de alocar redes virtuais de forma ótima em substratos físicos com até cem roteadores, enquanto que o algoritmo heurístico é capaz de adaptar-se a infraestruturas maiores, provendo mapeamentos sub-ótimos em um curto espaço de tempo. / Network virtualization has become increasingly prominent in recent years. It enables the creation of network infrastructures that are specifically tailored to the needs of distinct network applications and supports the instantiation of favorable en- vironments for the development and evaluation of new architectures and protocols. Although recent efforts (motivated mainly by the search for mechanisms to eval- uate Future Internet proposals) have contributed substantially to materialize this concept, none of them has attempted to combine efficient resource mapping with ful- fillment of security requirements (e.g., confidentiality). It is important to note that, in the context of virtual networks, the protection of shared network infrastructures constitutes a fundamental condition to enable its use in large scale. Considering the negative impact of security provisions in the virtual network embedding process is of paramount importance in order to fully utilize physical re- sources without underestimating capacity requirements. Therefore, in this thesis we propose both an optimal model and a heuristic algorithm for embedding virtual networks on physical substrates that aim to optimize physical resource usage while meeting security requirements. Both approaches feature precise modeling of over- head costs of security mechanisms used to protect virtual networks, and are able to handle virtual network requests in an online manner. In addition, we present the results of an extensive evaluation we carried out, including a detailed comparison of both the optimal model and the heuristic algorithm. Our experiments show that the Integer Linear Programming (ILP) model is capable of optimally embedding virtual networks on physical infrastructures with up to a hundred routers, while the heuristic algorithm is capable of scaling to larger infrastructures, providing timely, sub-optimal mappings.

A virtualização de redes é um mecanismo que permite a coexistência de múltiplas redes virtuais sobre um mesmo substrato físico. Um dos desafios de pesquisa abordados na literatura é o mapeamento eficiente de recursos virtuais em infraestruturas físicas. Embora o referido desafio tenha recebido considerável atenção, as abordagens que constituem o estado-da-arte apresentam alta taxa de rejeição, i.e., a proporção de solicitações de redes virtuais negadas em relação ao total de solicitações efetuadas ao substrato é elevada. Nesta dissertação, caracteriza-se, inicialmente, a relação entre a qualidade dos mapeamentos de redes virtuais e as estruturas topológicas dos substratos subjacentes. Avalia-se as soluções exatas de um modelo de mapeamento online sob diferentes classes de topologias de rede. A partir do entendimento dos fatores topológicos que influenciam diretamente o processo de mapeamento de redes virtuais, propõe-se uma estratégia para planejar a expansão de redes de provedores de infraestrutura de forma a reduzir consistentemente a taxa de rejeição de requisições de redes virtuais e melhor aproveitar os recursos ociosos da mesma. Os resultados obtidos evidenciam que grande parte das rejeições de redes virtuais ocorre em situações em que há grande disponibilidade de recursos, mas alguns poucos já saturados acabam inviabilizando, em função de características de conectividade do substrato, o atendimento de novas requisições. Ademais, os resultados obtidos utilizando a estratégia proposta evidenciam que o fortalecimento de partes-chave da infraestrutura levam a uma ocupação muito mais satisfatória. Uma expansão de 10% a 20% dos recursos da infraestrutura contribui para um aumento sustentado de até 30% no número de redes virtuais aceitas e de até 45% no aproveitamento dos recursos em comparação com a rede original. / Network virtualization is a mechanism that allows the coexistence of multiple virtual networks on top of a single physical substrate. One of the research challenges addressed recently in the literature is the efficient mapping of virtual resources on physical infrastructures. Although this challenge has received considerable attention, state-of-the-art approaches present, in general, a high rejection rate, i.e., the ratio between the number of denied virtual network requests and the total amount of requests is considerably high. In this thesis, we characterize the relationship between the quality of virtual network mappings and the topological structures of the underlying substrates. Exact solutions of an online embedding model are evaluated under different classes of network topologies. From the understanding of the topological factors that directly influence the virtual network embedding process, we propose an expansion strategy of physical infrastructure in order to suggest adjustments that lead to higher virtual network acceptance and, in consequence, to improved physical resource utilization. The obtained results demonstrate that most of rejections occur in situations in which a significant amount of resource is available, but a few saturated devices and links, depending on connectivity features of the physical substrate, hinder the acceptance of new requests. Moreover, the obtained results using the proposed strategy evidence that an expansion of 10% to 20% of the infrastructure resources leads to a sustained increase of up to 30% in the number of accepted virtual networks and of up to 45% in resource usage compared to the original network.

Virtualização permite o compartilhamento de uma rede física entre uma ou mais redes virtuais. O Problema de Mapeamento de Redes Virtuais é um dos principais desafios na virtualização de redes. Esse problema consiste em mapear uma rede virtual em uma rede física, respeitando restrições de capacidade. O presente trabalho mostra que encontrar uma solução factível para esse problema é NP-Difícil. Mesmo assim, muitas instâncias podem ser pode ser resolvidas na prática através da exploração de sua estrutura. Nós apresentamos um algoritmo de Branch & Price aplicado a instâncias de diferentes topologias e tamanhos. Os experimentos realizados sugerem que o algoritmo proposto é superior ao modelo de programação linear resolvido com CPLEX. / Virtualization allows one or more virtual networks to share physical infrastructures. The Virtual Network Embedding problem (VNEP) is one of the main challenges in the virtualization of physical networks. This problem consists in mapping a virtual network into a physical network while respecting capacity constraints. This work shows that finding a feasible solution for this problem is NP-Hard. However, many instances can be solved up to optimality in practice by exploiting the problem structure. We present a Branch & Price algorithm applied to instances of different topologies and sizes. The experimental results suggest that the proposed algorithm is superior to the Integer Linear Programming model solved by CPLEX.

abstract: Recently, a novel non-iterative power flow (PF) method known as the Holomorphic Embedding Method (HEM) was applied to the power-flow problem. Its superiority over other traditional iterative methods such as Gauss-Seidel (GS), Newton-Raphson (NR), Fast Decoupled Load Flow (FDLF) and their variants is that it is theoretically guaranteed to find the operable solution, if one exists, and will unequivocally signal if no solution exists. However, while theoretical convergence is guaranteed by Stahl’s theorem, numerical convergence is not. Numerically, the HEM may require extended precision to converge, especially for heavily-loaded and ill-conditioned power system models. In light of the advantages and disadvantages of the HEM, this report focuses on three topics: 1. Exploring the effect of double and extended precision on the performance of HEM, 2. Investigating the performance of different embedding formulations of HEM, and 3. Estimating the saddle-node bifurcation point (SNBP) from HEM-based Thévenin-like networks using pseudo-measurements. The HEM algorithm consists of three distinct procedures that might accumulate roundoff error and cause precision loss during the calculations: the matrix equation solution calculation, the power series inversion calculation and the Padé approximant calculation. Numerical experiments have been performed to investigate which aspect of the HEM algorithm causes the most precision loss and needs extended precision. It is shown that extended precision must be used for the entire algorithm to improve numerical performance. A comparison of two common embedding formulations, a scalable formulation and a non-scalable formulation, is conducted and it is shown that these two formulations could have extremely different numerical properties on some power systems. The application of HEM to the SNBP estimation using local-measurements is explored. The maximum power transfer theorem (MPTT) obtained for nonlinear Thévenin-like networks is validated with high precision. Different numerical methods based on MPTT are investigated. Numerical results show that the MPTT method works reasonably well for weak buses in the system. The roots method, as an alternative, is also studied. It is shown to be less effective than the MPTT method but the roots of the Padé approximant can be used as a research tool for determining the effects of noisy measurements on the accuracy of SNBP prediction. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2018

abstract: With the power system being increasingly operated near its limits, there is an increasing need for a power-flow (PF) solution devoid of convergence issues. Traditional iterative methods are extremely initial-estimate dependent and not guaranteed to converge to the required solution. Holomorphic Embedding (HE) is a novel non-iterative procedure for solving the PF problem. While the theory behind a restricted version of the method is well rooted in complex analysis, holomorphic functions and algebraic curves, the practical implementation of the method requires going beyond the published details and involves numerical issues related to Taylor's series expansion, Padé approximants, convolution and solving linear matrix equations. The HE power flow was developed by a non-electrical engineer with language that is foreign to most engineers. One purpose of this document to describe the approach using electric-power engineering parlance and provide an understanding rooted in electric power concepts. This understanding of the methodology is gained by applying the approach to a two-bus dc PF problem and then gradually from moving from this simple two-bus dc PF problem to the general ac PF case. Software to implement the HE method was developed using MATLAB and numerical tests were carried out on small and medium sized systems to validate the approach. Implementation of different analytic continuation techniques is included and their relevance in applications such as evaluating the voltage solution and estimating the bifurcation point (BP) is discussed. The ability of the HE method to trace the PV curve of the system is identified. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2014