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Phase unwrapping is an important problem in the areas of optical metrology, synthetic aperture radar (SAR) image analysis, and magnetic resonance imaging (MRI) analysis. These images are becoming larger in size and, particularly, the availability and need for processing of SAR and MRI data have increased significantly with the acquisition of remote sensing data and the popularization of magnetic resonators in clinical diagnosis. Therefore, it is important to develop faster and accurate phase unwrapping algorithms. We propose a parallel multigrid algorithm of a phase unwrapping method named accumulation of residual maps, which builds on a serial algorithm that consists of the minimization of a cost function; minimization achieved by means of a serial Gauss-Seidel kind algorithm. Our algorithm also optimizes the original cost function, but unlike the original work, our algorithm is a parallel Jacobi class with alternated minimizations. This strategy is known as the chessboard type, where red pixels can be updated in parallel at same iteration since they are independent. Similarly, black pixels can be updated in parallel in an alternating iteration. We present parallel implementations of our algorithm for different parallel multicore architecture such as CPU-multicore, Xeon Phi coprocessor, and Nvidia graphics processing unit. In all the cases, we obtain a superior performance of our parallel algorithm when compared with the original serial version. In addition, we present a detailed comparative performance of the developed parallel versions. [ABSTRACT FROM AUTHOR]

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In this paper we study the harmonic functions and the Dirichlet eigenfunctions of the Hata set, and their restrictions to the interval , its main edge. We prove that these restrictions of the harmonic functions are singular, i.e. monotone and with zero derivatives almost everywhere, and provide numerical evidence that this is also the case for the Dirichlet eigenfunctions. [ABSTRACT FROM AUTHOR]

Group testing is a procedure in which groups that contain several units (plants) are analysed without having to inspect individual plants, with the purpose of estimating the prevalence of genetically modified plants (adventitious presence of unwanted transgenic plants, AP) in a population at a low cost, without losing precision. When pool (group) testing is used to estimate the proportion of AP (p), there are several procedures that can be used for computing the confidence interval (CI); however, they usually do not ensure precision in the estimation of p. This research proposes a formula for determining the required number of pools (g), given a pool size (k), for estimating the proportion of AP plants using the Dorfman model. The proposed formula ensures precision in the estimated proportion of AP because it guarantees that the width (W) of the CI will be equal to, or narrower than, the desired width (ω), with a probability of γ. This probability accounts for the stochastic nature of the sample variance of p. We give examples to show how to use the proposed sample-size formula. Simulated data were created and tables are presented showing the different scenarios that a researcher may encounter. The Monte Carlo method was used to study the coverage and the level of assurance achieved by the proposed sample sizes. An R program that reproduces the results in the tables and makes it easy for the researcher to create other scenarios is given in the Appendix. [ABSTRACT FROM PUBLISHER]

We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on little sinc functions, which discretizes the Schrödinger equation on a uniform grid. The different boundary conditions are naturally implemented using sets of functions with the appropriate behavior. Good convergence properties are observed. A comparison with results based on a Wentzel-Kramers-Brillouin analysis is performed. [ABSTRACT FROM AUTHOR]

The quarantine is an intervention procedure to control the spread of infectious diseases among farms. However, the dilemma persists of which and how many farms need to be quarantined to achieve effective control, or at least, to make the losses minimum. In the present paper we propose an SEIR modified stochastic model to decide with high objectivity and rapidity the best quarantine strategy. Three quarantine strategies with different percentage of quarantine farms are compared by means of Monte Carlo simulation. We find that the minimum final size of an epidemic is obtained if a small fraction of farms with a high number of edges is quarantined. In addition, the proposed model was applied to a set of real data for avian influenza reported in the northwest of Tehuacán Valley, Puebla, México in 1995. [ABSTRACT FROM AUTHOR]