4,664 research outputs found

    Galaxy correlations and the BAO in a void universe: structure formation as a test of the Copernican Principle

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    A suggested solution to the dark energy problem is the void model, where accelerated expansion is replaced by Hubble-scale inhomogeneity. In these models, density perturbations grow on a radially inhomogeneous background. This large scale inhomogeneity distorts the spherical Baryon Acoustic Oscillation feature into an ellipsoid which implies that the bump in the galaxy correlation function occurs at different scales in the radial and transverse correlation functions. We compute these for the first time, under the approximation that curvature gradients do not couple the scalar modes to vector and tensor modes. The radial and transverse correlation functions are very different from those of the concordance model, even when the models have the same average BAO scale. This implies that if void models are fine-tuned to satisfy average BAO data, there is enough extra information in the correlation functions to distinguish a void model from the concordance model. We expect these new features to remain when the full perturbation equations are solved, which means that the radial and transverse galaxy correlation functions can be used as a powerful test of the Copernican Principle.Comment: 12 pages, 8 figures, matches published versio

    A functional analysis of change propagation

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    A thorough understanding of change propagation is fundamental to effective change management during product redesign. A new model of change propagation, as a result of the interaction of form and function is presented and used to develop an analysis method that determines how change is likely to propagate. The analysis produces a Design Structure Matrix, which clearly illustrates change propagation paths and highlights connections that could otherwise be ignored. This provides the user with an in-depth knowledge of product connectivity, which has the potential to support the design process and reduce the product's susceptibility to future change

    Randomized Extended Kaczmarz for Solving Least-Squares

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    We present a randomized iterative algorithm that exponentially converges in expectation to the minimum Euclidean norm least squares solution of a given linear system of equations. The expected number of arithmetic operations required to obtain an estimate of given accuracy is proportional to the square condition number of the system multiplied by the number of non-zeros entries of the input matrix. The proposed algorithm is an extension of the randomized Kaczmarz method that was analyzed by Strohmer and Vershynin.Comment: 19 Pages, 5 figures; code is available at https://github.com/zouzias/RE
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