Finding the smallest eigenvalue by the inverse Monte Carlo method with refinement

Finding the smallest eigenvalue of a given square matrix A of order n is computationally very intensive problem. The most popular method for this problem is the Inverse Power Method which uses LU-decomposition and forward and backward solving of the factored system at every iteration step. An alternative to this method is the Resolvent Monte Carlo method which uses representation of the resolvent matrix [I -qA](-m) as a series and then performs Monte Carlo iterations (random walks) on the elements of the matrix. This leads to great savings in computations, but the method has many restrictions and a very slow convergence. In this paper we propose a method that includes fast Monte Carlo procedure for finding the inverse matrix, refinement procedure to improve approximation of the inverse if necessary, and Monte Carlo power iterations to compute the smallest eigenvalue. We provide not only theoretical estimations about accuracy and convergence but also results from numerical tests performed on a number of test matrices.

Intrinsic subspace convergence in TDD MIMO communication

In numerical linear algebra, students encounter earlythe iterative power method, which finds eigenvectors of a matrixfrom an arbitrary starting point through repeated normalizationand multiplications by the matrix itself. In practice, more sophisticatedmethods are used nowadays, threatening to make the powermethod a historical and pedagogic footnote. However, in the contextof communication over a time-division duplex (TDD) multipleinputmultiple-output (MIMO) channel, the power method takes aspecial position. It can be viewed as an intrinsic part of the uplinkand downlink communication switching, enabling estimationof the eigenmodes of the channel without extra overhead. Generalizingthe method to vector subspaces, communication in thesubspaces with the best receive and transmit signal-to-noise ratio(SNR) is made possible. In exploring this intrinsic subspace convergence(ISC), we show that several published and new schemes canbe cast into a common framework where all members benefit fromthe ISC.

A brain-computer interface for navigation in virtual reality

L'interface cerveau-ordinateur (ICO) décode les signaux électriques du cerveau requise par l’électroencéphalographie et transforme ces signaux en commande pour contrôler un appareil ou un logiciel. Un nombre limité de tâches mentales ont été détectés et classifier par différents groupes de recherche. D’autres types de contrôle, par exemple l’exécution d'un mouvement du pied, réel ou imaginaire, peut modifier les ondes cérébrales du cortex moteur. Nous avons utilisé un ICO pour déterminer si nous pouvions faire une classification entre la navigation de type marche avant et arrière, en temps réel et en temps différé, en utilisant différentes méthodes. Dix personnes en bonne santé ont participé à l’expérience sur les ICO dans un tunnel virtuel. L’expérience fut a était divisé en deux séances (48 min chaque). Chaque séance comprenait 320 essais. On a demandé au sujets d’imaginer un déplacement avant ou arrière dans le tunnel virtuel de façon aléatoire d’après une commande écrite sur l'écran. Les essais ont été menés avec feedback. Trois électrodes ont été montées sur le scalp, vis-à-vis du cortex moteur. Durant la 1re séance, la classification des deux taches (navigation avant et arrière) a été réalisée par les méthodes de puissance de bande, de représentation temporel-fréquence, des modèles autorégressifs et des rapports d’asymétrie du rythme β avec classificateurs d’analyse discriminante linéaire et SVM. Les seuils ont été calculés en temps différé pour former des signaux de contrôle qui ont été utilisés en temps réel durant la 2e séance afin d’initier, par les ondes cérébrales de l'utilisateur, le déplacement du tunnel virtuel dans le sens demandé. Après 96 min d'entrainement, la méthode « online biofeedback » de la puissance de bande a atteint une précision de classification moyenne de 76 %, et la classification en temps différé avec les rapports d’asymétrie et puissance de bande, a atteint une précision de classification d’environ 80 %.

Borlänge, Dalarnas köpstad no 1 : Hur centrum, Kupolen och Norra Backa kan bindas samman för att tillsammans vinna köpkraften

Thesis:The aim of our study is to identify how IKEA's externalestablishment at Norra Backa can affect Kupolen and the centre. This in order to provide suggestions on how these trade areas can be connected and create a whole to thereby gain the purchasing power.Method:In our study we used triangulation. That means we have used both a quantitative and a qualitative approach. The quantitative method based on a survey with 100 respondents. The qualitative method is based on interviews with the centre conductors of Borlänge, Laila G Prosén and Anna Timander.Theory:The theories we have used is STP, substitution effects and effects of overspill, important factors for an attractive market town, Town Centre Management, Urban Retail Product.Conclusion: We found how IKEA's establishment at Norra Backa may affect Kupolen and the center of Borlänge then we gave suggestions on how these trade areas can be connected.

Métodos numéricos para resolução de equações diferenciais ordinárias lineares baseados em interpolação por spline

In this work we have elaborated a spline-based method of solution of inicial value problems involving ordinary differential equations, with emphasis on linear equations. The method can be seen as an alternative for the traditional solvers such as Runge-Kutta, and avoids root calculations in the linear time invariant case. The method is then applied on a central problem of control theory, namely, the step response problem for linear EDOs with possibly varying coefficients, where root calculations do not apply. We have implemented an efficient algorithm which uses exclusively matrix-vector operations. The working interval (till the settling time) was determined through a calculation of the least stable mode using a modified power method. Several variants of the method have been compared by simulation. For general linear problems with fine grid, the proposed method compares favorably with the Euler method. In the time invariant case, where the alternative is root calculation, we have indications that the proposed method is competitive for equations of sifficiently high order.

Parallel relaxed and extrapolated algorithms for computing PageRank

In this paper, parallel Relaxed and Extrapolated algorithms based on the Power method for accelerating the PageRank computation are presented. Different parallel implementations of the Power method and the proposed variants are analyzed using different data distribution strategies. The reported experiments show the behavior and effectiveness of the designed algorithms for realistic test data using either OpenMP, MPI or an hybrid OpenMP/MPI approach to exploit the benefits of shared memory inside the nodes of current SMP supercomputers.

Aproveitamento de subproduto de maçã da indústria agroalimentar

Neste trabalho foi estudado um subproduto derivado da indústria agroalimentar produtora de sumo concentrado de maçã, conhecido por bagaço de maçã, com o objetivo de avaliar condições de extração de compostos fenólicos, o teor de compostos fenólicos totais, flavonóides e proantocianidinas e ainda a atividade antioxidante. Foram efetuadas extrações a partir do bagaço de maçã variando as condições de tempo, temperatura, razão massa:volume e solvente e os extratos obtidos avaliados quanto ao seu teor em compostos fenólicos totais pelo método FolinCiocalteu. O extrato aquoso do bagaço de maçã para uma temperatura de 100 ºC a um tempo de 2x4h e concentração de 50 mg/mL, apresentou o teor de compostos fenólicos mais elevado (9,37 mgEAG/g de bagaço de maçã, na base seca) em relação a todas as outras temperaturas, tempos de extração e solventes utilizados, como etanol (50% e 70%) e metanol. O doseamento de flavonóides totais baseou-se no método espetrofotométrico, usando o reagente cloreto de alumínio e a rutina como padrão. Os melhores resultados foram obtidos usando etanol (70%) como solvente à temperatura ambiente, cerca de 4,35 mgER/g. A amostra extraída com água apresentou valores bastante similares ao etanol, cerca de 4,27 mgER/g, usando uma temperatura de 100 ºC durante 2x4h. O conteúdo em proantocianidinas foi determinado pelo método 4-dimetilamino cinamaldeído (DMAC). O bagaço de maçã estudado demonstrou ser pobre no seu conteúdo de proantocianidinas, obtendo valores de 0,77 mgEEC/g. A atividade antioxidante do bagaço de maçã foi avaliada através de dois métodos distintos: 2,2-difenil-1-picril-hidrazilo (DPPH∙) e método do poder redutor (FRAP). O extrato aquoso obtido a 100 ºC a um tempo de 2x4h, demonstrou ser aquele com maior potencial, com uma capacidade antioxidante mais elevada que os restantes extratos, com valores de IC50 de 0,48 mg/mL e 0,65 mg/mL, para os métodos de DPPH∙ e FRAP, respetivamente.

Um estudo sobre polinômios matriciais

This research work aims to make a study of the algebraic theory of matrix monic polynomials, as well as the definitions, concepts and properties with respect to block eigenvalues, block eigenvectors and solvents of P(X). We investigte the main relations between the matrix polynomial and the Companion and Vandermonde matrices. We study the construction of matrix polynomials with certain solvents and the extention of the Power Method, to calculate block eigenvalues and solvents of P(X). Through the relationship between the dominant block eigenvalue of the Companion matrix and the dominant solvent of P(X) it is possible to obtain the convergence of the algorithm for the dominant solvent of the matrix polynomial. We illustrate with numerical examples for diferent cases of convergence.

Desenvolvimento de uma bancada para a realização de ensaios de auto-amortecimento em cabos condutores de energia elétrica

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Mecânica, 2015.

Power Secant Method applied to natural frequency extraction of Timoshenko beam structures

This work deals with an improved plane frame formulation whose exact dynamic stiffness matrix (DSM) presents, uniquely, null determinant for the natural frequencies. In comparison with the classical DSM, the formulation herein presented has some major advantages: local mode shapes are preserved in the formulation so that, for any positive frequency, the DSM will never be ill-conditioned; in the absence of poles, it is possible to employ the secant method in order to have a more computationally efficient eigenvalue extraction procedure. Applying the procedure to the more general case of Timoshenko beams, we introduce a new technique, named ""power deflation"", that makes the secant method suitable for the transcendental nonlinear eigenvalue problems based on the improved DSM. In order to avoid overflow occurrences that can hinder the secant method iterations, limiting frequencies are formulated, with scaling also applied to the eigenvalue problem. Comparisons with results available in the literature demonstrate the strength of the proposed method. Computational efficiency is compared with solutions obtained both by FEM and by the Wittrick-Williams algorithm.

Power imbalance application region method for distributed synchronous generator anti-islanding protection design and evaluation

This paper presents a novel graphical approach to adjust and evaluate frequency-based relays employed in anti-islanding protection schemes of distributed synchronous generators, in order to meet the anti-islanding and abnormal frequency variation requirements, simultaneously. The proposed method defines a region in the power mismatch space, inside which the relay non-detection zone should be located, if the above-mentioned requirements must be met. Such region is called power imbalance application region. Results show that this method can help protection engineers to adjust frequency-based relays to improve the anti-islanding capability and to minimize false operation occurrences, keeping the abnormal frequency variation utility requirements satisfied. Moreover, the proposed method can be employed to coordinate different types of frequency-based relays, aiming at improving overall performance of the distributed generator frequency protection scheme. (C) 2011 Elsevier B.V. All rights reserved.

Power Factor Calculation by the Finite Element Method

The use of finite element analysis (FEA) to design electrical motors has increased significantly in the past few years due the increasingly better performance of modern computers. Even though the analytical software remains the most used tool, the FEA is widely used to refine the analysis and gives the final design to be prototyped. The power factor, a standard data of motor manufactures data sheet is important because it shows how much reactive power is consumed by the motor. This data becomes important when the motor is connected to network. However, the calculation of power factor is not an easy task. Due to the saturation phenomena the input motor current has a high level of harmonics that cannot be neglected. In this work the FEA is used to evaluate a proposed (not limitative) methodology to estimate the power factor or displacement factor of a small single-phase induction motor. Results of simulations and test are compared.

Hybrid Method to Assess Sensitive Process Interruption Costs Due to Faults in Electric Power Distribution Networks

This paper shows a new hybrid method for risk assessment regarding interruptions in sensitive processes due to faults in electric power distribution systems. This method determines indices related to long duration interruptions and short duration voltage variations (SDVV), such as voltage sags and swells in each customer supplied by the distribution network. Frequency of such occurrences and their impact on customer processes are determined for each bus and classified according to their corresponding magnitude and duration. The method is based on information regarding network configuration, system parameters and protective devices. It randomly generates a number of fault scenarios in order to assess risk areas regarding long duration interruptions and voltage sags and swells in an especially inventive way, including frequency of events according to their magnitude and duration. Based on sensitivity curves, the method determines frequency indices regarding disruption in customer processes that represent equipment malfunction and possible process interruptions due to voltage sags and swells. Such approach allows for the assessment of the annual costs associated with each one of the evaluated power quality indices.

Risk-based decision making method for maintenance policy selection of thermal power plant equipment

This study presents a decision-making method for maintenance policy selection of power plants equipment. The method is based on risk analysis concepts. The method first step consists in identifying critical equipment both for power plant operational performance and availability based on risk concepts. The second step involves the proposal of a potential maintenance policy that could be applied to critical equipment in order to increase its availability. The costs associated with each potential maintenance policy must be estimated, including the maintenance costs and the cost of failure that measures the critical equipment failure consequences for the power plant operation. Once the failure probabilities and the costs of failures are estimated, a decision-making procedure is applied to select the best maintenance policy. The decision criterion is to minimize the equipment cost of failure, considering the costs and likelihood of occurrence of failure scenarios. The method is applied to the analysis of a lubrication oil system used in gas turbines journal bearings. The turbine has more than 150 MW nominal output, installed in an open cycle thermoelectric power plant. A design modification with the installation of a redundant oil pump is proposed for lubricating oil system availability improvement. (C) 2009 Elsevier Ltd. All rights reserved.