Generalized power method for sparse principal component analysis

In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant principal component of a data matrix, or more components at once, respectively. While the initial formulations involve nonconvex functions, and are therefore computationally intractable, we rewrite them into the form of an optimization program involving maximization of a convex function on a compact set. The dimension of the search space is decreased enormously if the data matrix has many more columns (variables) than rows. We then propose and analyze a simple gradient method suited for the task. It appears that our algorithm has best convergence properties in the case when either the objective function or the feasible set are strongly convex, which is the case with our single-unit formulations and can be enforced in the block case. Finally, we demonstrate numerically on a set of random and gene expression test problems that our approach outperforms existing algorithms both in quality of the obtained solution and in computational speed. © 2010 Michel Journée, Yurii Nesterov, Peter Richtárik and Rodolphe Sepulchre.

IMPROVED PEAK POWER METHOD FOR MEASURING FREQUENCY RESPONSES OF PHOTODETECTORS IN A SELF-HETERODYNE SYSTEM

An improved peak power method for measuring frequency responses of photodetectors in a self-heterodyne system consisting of a distributed Bragg reflector laser is proposed. The time-resolved spectrum technique is used to measure the peak power of the beat signal and the intrinsic linewidth of heat signal for calibration. The experimental results show that the impact of the thermal-induced frequency drift, which is the main reason for producing an error in measurement by conventional peak power method and spectrum power method, can be removed.

Metabolic power method underestimates energy expenditure in field sport movements using a GPS tracking system

The purpose of this study was to assess the validity of a GPS tracking system to estimate energy expenditure (EE) during exercise and field sport locomotor movements. Twenty-seven participants each completed one 90 minute exercise session on an outdoor synthetic futsal pitch. During the exercise session participants wore a 5 Hz GPS unit interpolated to 15 Hz (SPI HPU, GPSports Pty Ltd, Australia) and a portable gas analyser (Metamax® 3B, Cortex Pty Ltd, Germany) which acted as the criterion measure of EE. The exercise session was comprised of alternating five minute exercise bouts of randomised walking, jogging, running or a field sport circuit (x3) followed by 10 minutes of recovery. One-way ANOVA showed significant (p<0.01) and very large underestimations between GPS metabolic power derived EE and VO2 derived EE for all field sport circuits (% difference ≈ -44%). No differences in EE were observed for the jog (7.8%) and run (4.8%) while very large overestimations were found for the walk (43.0%). The GPS metabolic power EE over the entire 90 minute session was significantly lower (p<0.01) than the VO2 EE, resulting in a moderate underestimation overall (-19%). The results of this study suggest that a GPS tracking system using the metabolic power model of EE does not accurately estimate EE in field sport movements or over an exercise session consisting of mixed locomotor activities interspersed with recovery periods; however is able to provide a reasonably accurate estimation of EE during continuous jogging and running.

Proportional resonant controller based circulating power setup for thermal testing of multilevel inverter

A regenerative or circulating-power method is presented in this paper for heat run test on the legs of a three-level neutral point clamped (NPC) inverter. This test ensures that only losses are drawn from the dc supply, while rated power is circulated between the two legs, thus minimising wastage of energy. A proportional-resonant (PR) controller based current control scheme is proposed here for the circulating power test setup in NPC inverter. Simulation and experimental results are presented to validate the controller design at various operating conditions. Results of thermal test on the inverter legs are presented at two different operating conditions.

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.

Physical Layer Data Fusion Via Distributed Co-Phasing With General Signal Constellations

This paper studies a pilot-assisted physical layer data fusion technique known as Distributed Co-Phasing (DCP). In this two-phase scheme, the sensors first estimate the channel to the fusion center (FC) using pilots sent by the latter; and then they simultaneously transmit their common data by pre-rotating them by the estimated channel phase, thereby achieving physical layer data fusion. First, by analyzing the symmetric mutual information of the system, it is shown that the use of higher order constellations (HOC) can improve the throughput of DCP compared to the binary signaling considered heretofore. Using an HOC in the DCP setting requires the estimation of the composite DCP channel at the FC for data decoding. To this end, two blind algorithms are proposed: 1) power method, and 2) modified K-means algorithm. The latter algorithm is shown to be computationally efficient and converges significantly faster than the conventional K-means algorithm. Analytical expressions for the probability of error are derived, and it is found that even at moderate to low SNRs, the modified K-means algorithm achieves a probability of error comparable to that achievable with a perfect channel estimate at the FC, while requiring no pilot symbols to be transmitted from the sensor nodes. Also, the problem of signal corruption due to imperfect DCP is investigated, and constellation shaping to minimize the probability of signal corruption is proposed and analyzed. The analysis is validated, and the promising performance of DCP for energy-efficient physical layer data fusion is illustrated, using Monte Carlo simulations.

Introduction of boulders to the R. Ribble: a short geomorphological evaluation

The placement of artificial in-channel structures (including large cobbles / boulders) into any fluvial system needs to be considered carefully. This brief report summarises considerations for boulder introductions into the River Ribble from a geomorphological perspective. This includes boulder placement and shape. Bagnold's Excess Stream Power Method is used to calculate the boulder sizing.

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.