1,354 research outputs found

    Domination in generalized Petersen graphs

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    3D APIs in Interactive Real-Time Systems: Comparison of OpenGL, Direct3D and Java3D.

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    Since the first display of a few computer-generated lines on a Cathode-ray tube (CRT) over 40 years ago, graphics has progressed rapidly towards the computer generation of detailed images and interactive environments in real time (Angel, 1997). In the last twenty years a number of Application Programmer's Interfaces (APIs) have been developed to provide access to three-dimensional graphics systems. Currently, there are numerous APIs used for many different types of applications. This paper will look at three of these: OpenGL, Direct3D, and one of the newest entrants, Java3D. They will be discussed in relation to their level of versatility, programability, and how innovative they are in introducing new features and furthering the development of 3D-interactive programming

    A Bayesian conjugate gradient method (with Discussion)

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    A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is employed. However, for more challenging systems a substantial error can be present even after many iterations have been performed. The estimates obtained in this case are of little value unless further information can be provided about the numerical error. In this paper we propose a novel statistical model for this numerical error set in a Bayesian framework. Our approach is a strict generalisation of the conjugate gradient method, which is recovered as the posterior mean for a particular choice of prior. The estimates obtained are analysed with Krylov subspace methods and a contraction result for the posterior is presented. The method is then analysed in a simulation study as well as being applied to a challenging problem in medical imaging

    Vertices contained in all or in no minimum total dominating set of a tree

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    AbstractA set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. We characterize the set of vertices of a tree that are contained in all, or in no, minimum total dominating sets of the tree

    Radiative transfer as a Bayesian linear regression problem

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    Electromagnetic radiation plays a crucial role in various physical and chemical processes. Hence, almost all astrophysical simulations require some form of radiative transfer model. Despite many innovations in radiative transfer algorithms and their implementation, realistic radiative transfer models remain very computationally expensive, such that one often has to resort to approximate descriptions. The complexity of these models makes it difficult to assess the validity of any approximation and to quantify uncertainties on the model results. This impedes scientific rigour, in particular, when comparing models to observations, or when using their results as input for other models. We present a probabilistic numerical approach to address these issues by treating radiative transfer as a Bayesian linear regression problem. This allows us to model uncertainties on the input and output of the model with the variances of the associated probability distributions. Furthermore, this approach naturally allows us to create reduced-order radiative transfer models with a quantifiable accuracy. These are approximate solutions to exact radiative transfer models, in contrast to the exact solutions to approximate models that are often used. As a first demonstration, we derive a probabilistic version of the method of characteristics, a commonly-used technique to solve radiative transfer problems

    Stable and Metastable InGaAs/GaAs Island Shapes and Surfactantlike Suppression of the Wetting Transformation

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    Contrasting behaviors are observed in InGaAs/GaAs island formation during vapor phase epitaxy: variation of group V partial pressures gives different critical thicknesses for the onset of the Stranski-Krastanow transformation, surface coverages, ratios between coherent and incoherent islands, and dissimilar morphologies upon annealing. The latter experiments show that small lens-shaped islands can be found in equilibrium if InGaAs surface energies are minimized, leading to the conclusion that AsH3 can raise surface energies and act as an impurity-free "morphactant.
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