10 research outputs found

    Third International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC98)

    Full text link

    Are quasi-Monte Carlo algorithms efficient for two-stage stochastic programs?

    Get PDF
    Quasi-Monte Carlo algorithms are studied for designing discrete approximations of two-stage linear stochastic programs with random right-hand side and continuous probability distribution. The latter should allow for a transformation to a distribution with independent marginals. The two-stage integrands are piecewise linear, but neither smooth nor lie in the function spaces considered for QMC error analysis. We show that under some weak geometric condition on the two-stage model all terms of their ANOVA decomposition, except the one of highest order, are continuously differentiable and that first and second order ANOVA terms have mixed first order partial derivatives. Hence, randomly shifted lattice rules (SLR) may achieve the optimal rate of convergence not depending on the dimension if the effective superposition dimension is at most two. We discuss effective dimensions and dimension reduction for two-stage integrands. The geometric condition is shown to be satisfied almost everywhere if the underlying probability distribution is normal and principal component analysis (PCA) is used for transforming the covariance matrix. Numerical experiments for a large scale two-stage stochastic production planning model with normal demand show that indeed convergence rates close to the optimal are achieved when using SLR and randomly scrambled Sobol' point sets accompanied with PCA for dimension reduction

    Quasi-Monte Carlo rules for numerical integration over the unit sphere S2\mathbb{S}^2

    Full text link
    We study numerical integration on the unit sphere S2R3\mathbb{S}^2 \subset \mathbb{R}^3 using equal weight quadrature rules, where the weights are such that constant functions are integrated exactly. The quadrature points are constructed by lifting a (0,m,2)(0,m,2)-net given in the unit square [0,1]2[0,1]^2 to the sphere S2\mathbb{S}^2 by means of an area preserving map. A similar approach has previously been suggested by Cui and Freeden [SIAM J. Sci. Comput. 18 (1997), no. 2]. We prove three results. The first one is that the construction is (almost) optimal with respect to discrepancies based on spherical rectangles. Further we prove that the point set is asymptotically uniformly distributed on S2\mathbb{S}^2. And finally, we prove an upper bound on the spherical cap L2L_2-discrepancy of order N1/2(logN)1/2N^{-1/2} (\log N)^{1/2} (where NN denotes the number of points). This slightly improves upon the bound on the spherical cap L2L_2-discrepancy of the construction by Lubotzky, Phillips and Sarnak [Comm. Pure Appl. Math. 39 (1986), 149--186]. Numerical results suggest that the (0,m,2)(0,m,2)-nets lifted to the sphere S2\mathbb{S}^2 have spherical cap L2L_2-discrepancy converging with the optimal order of N3/4N^{-3/4}

    A Study of Adaptation Mechanisms for Simulation Algorithms

    Get PDF
    The performance of a program can sometimes greatly improve if it was known in advance the features of the input the program is supposed to process, the actual operating parameters it is supposed to work with, or the specific environment it is to run on. However, this information is typically not available until too late in the program’s operation to take advantage of it. This is especially true for simulation algorithms, which are sensitive to this late-arriving information, and whose role in the solution of decision-making, inference and valuation problems is crucial. To overcome this limitation we need to provide the flexibility for a program to adapt its behaviour to late-arriving information once it becomes available. In this thesis, I study three adaptation mechanisms: run-time code generation, model-specific (quasi) Monte Carlo sampling and dynamic computation offloading, and evaluate their benefits on Monte Carlo algorithms. First, run-time code generation is studied in the context of Monte Carlo algorithms for time-series filtering in the form of the Input-Adaptive Kalman filter, a dynamically generated state estimator for non-linear, non-Gaussian dynamic systems. The second adaptation mechanism consists of the application of the functional-ANOVA decomposition to generate model-specific QMC-samplers which can then be used to improve Monte Carlo-based integration. The third adaptive mechanism treated here, dynamic computation offloading, is applied to wireless communication management, where network conditions are assessed via option valuation techniques to determine whether a program should offload computations or carry them out locally in order to achieve higher run-time (and correspondingly battery-usage) efficiency. This ability makes the program well suited for operation in mobile environments. At their core, all these applications carry out or make use of (quasi) Monte Carlo simulations on dynamic Bayesian networks (DBNs). The DBN formalism and its associated simulation-based algorithms are of great value in the solution to problems with a large uncertainty component. This characteristic makes adaptation techniques like those studied here likely to gain relevance in a world where computers are endowed with perception capabilities and are expected to deal with an ever-increasing stream of sensor and time-series data

    Four essays on sequential Monte Carlo and quasi-Monte Carlo methods

    Get PDF

    Vol. 4, No. 2 (Full Issue)

    Get PDF

    Complex Concentrated Alloys (CCAs)

    Get PDF
    This book is a collection of several unique articles on the current state of research on complex concentrated alloys, as well as their compelling future opportunities in wide ranging applications. Complex concentrated alloys consist of multiple principal elements and represent a new paradigm in structural alloy design. They show a range of exceptional properties that are unachievable in conventional alloys, including high strength–ductility combination, resistance to oxidation, corrosion/wear resistance, and excellent high-temperature properties. The research articles, reviews, and perspectives are intended to provide a wholistic view of this multidisciplinary subject of interest to scientists and engineers
    corecore