The algorithm generates a sequence of triangulations of the domain of f. The triangulations include triangles with high aspect ratio along the curve where f has jumps. The sequence of functions generated by the algorithm are obtained by interpolating f on the triangulations using continuous piecewise polynomial functions.

## The UK and Brexit: The laughing stock of Europe – VoxEurop (English)

The procedure employed here is a generalization to 3-D of the method of central corrections for logarithmic singularities [1] in one dimension, and [2] in two dimensions. As in one and two dimensions, the correction coefficients for high-order trapezoidal rules for J v are independent of the number of sampling points used to discretize the cube D. When v is compactly supported in D, the approximation is the trapezoidal rule plus a local weighted sum of the values of v around the point of singularity.

These quadrature rules provide an efficient, stable and accurate way of approximating J v. We demonstrate the performance of these quadratures of orders up to 17 for highly oscillatory functions v. These type of integrals appear in scattering calculations in 3-D. We present a high-order, fast, iterative solver for the direct scattering calculation for the Helmholtz equation in two dimensions.

Our algorithm solves the scattering problem formulated as the Lippmann-Schwinger integral equation for compactly supported, smoothly vanishing scatterers. There are two main components to this algorithm. First, the integral equation is discretized with quadratures based on high-order corrected trapezoidal rules for the logarithmic singularity present in the kernel of the integral equation.

Second, on the uniform mesh required for the trapezoidal rule we rewrite the discretized integral operator as a composition of two linear operators: a discrete convolution followed by a diagonal multiplication; therefore, the application of these operators to an arbitrary vector, required by an iterative method for the solution of the discretized linear system, will cost N 2 log N for a N-by-N mesh, with the help of FFT. We will demonstrate the performance of the algorithm for scatterers of complex structures and at large wave numbers.

For numerical implementations, CMRES iterations will be used, and corrected trapezoidal rules up to order 20 will be tested. The procedure we use is a generalization to 2-D of the method of central corrections for logarithmic singularities described in [1]. As in 1-D, the correction coefficients are independent of the number of sampling points used to discretize the square D. When v has compact support contained in D, the approximation is the trapezoidal rule plus a local weighted sum of the values of v around the point of singularity. These quadrature rules give an efficient, stable, and accurate way of approximating J v.

We provide the correction coefficients to obtain corrected trapezoidal quadrature rules up to order This paper addresses the problem of the optimal design of batch plants with imprecise demands in product amounts. The design of such plants necessarily involves the way that equipment may be utilized, which means that plant scheduling and production must form an integral part of the design problem.

This work relies on a previous study, which proposed an alternative treatment of the imprecision demands by introducing fuzzy concepts, embedded in a multi-objective Genetic Algorithm GA that takes into account simultaneously maximization of the net present value NPV and two other performance criteria, i. The results showed that an additional interpretation step might be necessary to help the managers choosing among the non-dominated solutions provided by the GA. The analytic hierarchy process AHP is a strategy commonly used in Operations Research for the solution of this kind of multicriteria decision problems, allowing the apprehension of manager subjective judgments.

The major aim of this study is thus to propose a software integrating the AHP theory for the analysis of the GA Pareto-optimal solutions, as an alternative decision-support tool for the batch plant design problem solution. A workflow is a set of steps or tasks that model the execution of a process, e.

## Publicaciones de la facultad

Workflow applications commonly require large computational resources. Hence, distributed computing approaches such as Grid and Cloud computing emerge as a feasible solution to execute them.

Two important factors for executing workflows in distributed computing platforms are 1 workflow scheduling and 2 resource allocation. As a consequence, there is a myriad of workflow scheduling algorithms that map workflow tasks to distributed resources subject to task dependencies, time and budget constraints. In this paper, we present a taxonomy of workflow scheduling algorithms, which categorizes the algorithms into 1 best-effort algorithms including heuristics, metaheuristics, and approximation algorithms and 2 quality-of-service algorithms including budget-constrained, deadline-constrained and algorithms simultaneously constrained by deadline and budget.

In addition, a workflow engine simulator was developed to quantitatively compare the performance of scheduling algorithms. We study the behavior of a decision maker who prefers alternative x to alternative y in menu A if the utility of x exceeds that of y by at least a threshold associated with y and A. Hence the decision maker's preferences are given by menu-dependent interval orders. In every menu, her choice set comprises of undominated alternatives according to this preference.

We axiomatize this broad model when thresholds are monotone, i. We also obtain novel characterizations in two special cases that have appeared in the literature: the maximization of a fixed interval order where the thresholds depend on the alternative and not on the menu, and the maximization of monotone semiorders where the thresholds are independent of the alternatives but monotonic in menus.

Shelf life experiments have as an outcome a matrix of zeroes and ones that represent the acceptance or no acceptance of customers when presented with samples of the product under evaluation in a random fashion within a designed experiment. This kind of response is called a Bernoulli response due to the dichotomous nature 0,1 of its values. It is not rare to find inconsistent sequences of responses, that is when a customer rejects a less aged sample and does not reject an older sample. That is, we find a zero before a one. This is due to the human factor present in the experiment.

In the presence of this kind of inconsistencies some conventions have been taken in the literature in order to estimate shelf life distribution using methods and software from the reliability field which requires numerical responses. In this work we propose a method that does not require coding the original responses into numerical values.

We use a more reliable coding by using the Bernoulli response directly and using a Bayesian approach. The resulting method is based on solid Bayesian theory and proved computer programs. We show by means of an example and simulation studies that the new methodology clearly beats the methodology proposed by Hough. We also provide the R software necessary for the implementation. Definitive Screening Designs DSD are a class of experimental designs that have the possibility to estimate linear, quadratic and interaction effects with relatively little experimental effort.

The linear or main effects are completely independent of two factor interactions and quadratic effects. The two factor interactions are not completely confounded with other two factor interactions, and quadratic effects are estimable. The number of experimental runs is twice the number of factors of interest plus one. Several approaches have been proposed to analyze the results of these experimental plans, some of these approaches take into account the structure of the design, others do not.

The first author of this paper proposed a Bayesian sequential procedure that takes into account the structure of the design, this procedure consider normal and non normal responses. The creators of the DSD originally performed a forward stepwise regression programmed in JMP, and also used the minimization of a bias corrected version of Akaike's information criterion, and later they proposed a frequentist procedure that considers the structure of the DSD.

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Both the frequentist and Bayesian procedures, when the number of experimental runs is twice the number of factors of interest plus one, use as initial step fitting a model with only main effects and then check the significance of these effects to proceed. In this paper we present modification of the Bayesian procedure that incorporates the Bayesian factor identification which is an approach that computes, for each factor, the posterior probability that it is active, this includes the possibility that it is present in linear, quadratic or two factor interactions.

This a more comprehensive approach than just testing the significance of an effect. Definitive Screening Designs are a class of experimental designs that under factor sparsity have the potential to estimate linear, quadratic and interaction effects with little experimental effort. BAYESDEF is a package that performs a five step strategy to analyze this kind of experiments that makes use of tools coming from the Bayesian approach.

It also includes the least absolute shrinkage and selection operator lasso as a check Aguirre VM. With the advent of widespread computing and availability of open source programs to perform many different programming tasks, nowadays there is a trend in Statistics to program tailor made applications for non statistical customers in various areas. This is an alternative to having a large statistical package with many functions many of which never are used.

Consonance Analysis is a useful numerical and graphical exploratory approach for evaluating the consistency of the measurements and the panel of people involved in sensory evaluation. It makes use of several uni and multivariate techniques either graphical or analytical, particularly Principal Components Analysis.

The package is implemented in a graphical user interface in order to get a user friendly package. Definitive screening designs DSDs are a class of experimental designs that allow the estimation of linear, quadratic, and interaction effects with little experimental effort if there is effect sparsity. Many industrial experiments involve nonnormal responses.

Generalized linear models GLMs are a useful alternative for analyzing these kind of data. The analysis of GLMs is based on asymptotic theory, something very debatable, for example, in the case of the DSD with only 13 experimental runs. So far, analysis of DSDs considers a normal response. In this work, we show a five-step strategy that makes use of tools coming from the Bayesian approach to analyze this kind of experiment when the response is nonnormal. We consider the case of binomial, gamma, and Poisson responses without having to resort to asymptotic approximations.

We use posterior odds that effects are active and posterior probability intervals for the effects and use them to evaluate the significance of the effects. We also combine the results of the Bayesian procedure with the lasso estimation procedure to enhance the scope of the method. It is not uncommon to deal with very small experiments in practice. For example, if the experiment is conducted on the production process, it is likely that only a very few experimental runs will be allowed. If testing involves the destruction of expensive experimental units, we might only have very small fractions as experimental plans.

In this paper, we will consider the analysis of very small factorial experiments with only four or eight experimental runs. In addition, the methods presented here could be easily applied to larger experiments. A Daniel plot of the effects to judge significance may be useless for this type of situation.

Instead, we will use different tools based on the Bayesian approach to judge significance. The first tool consists of the computation of the posterior probability that each effect is significant. The second tool is referred to in Bayesian analysis as the posterior distribution for each effect. Combining these tools with the Daniel plot gives us more elements to judge the signiicance of an effect. Because, in practice, the response may not necessarily be normally distributed, we will extend our approach to the generalized linear model setup.

By simulation, we will show that not only in the case of discrete responses and very small experiments, the usual large sample approach for modeling generalized linear models may produce a very biased and variable estimators, but also that the Bayesian approach provides a very sensible results. Inference for quantile regression parameters presents two problems.

First, it is computationally costly because estimation requires optimising a non-differentiable objective function which is a formidable numerical task, specially with many number of observations and regressors. Second, it is controversial because standard asymptotic inference requires the choice of smoothing parameters and different choices may lead to different conclusions.

Bootstrap methods solve the latter problem at the price of enlarging the former. We give a theoretical justification for a new inference method consisting of the construction of asymptotic pivots based on a small number of bootstrap replications. We show its usefulness to draw inferences on linear or non-linear functions of the parameters of quantile regression models.

The existing methods for analyzing unreplicated fractional factorial experiments that do not contemplate the possibility of outliers in the data have a poor performance for detecting the active effects when that contingency becomes a reality. There are some methods to detect active effects under this experimental setup that consider outliers. We propose a new procedure based on robust regression methods to estimate the effects that allows for outliers.

We perform a simulation study to compare its behavior relative to existing methods and find that the new method has a very competitive or even better power. The relative power improves as the contamination and size of outliers increase when the number of active effects is up to four.

The paper presents the asymptotic theory of the efficient method of moments when the model of interest is not correctly specified.