3,399 research outputs found
Interpolating point spread function anisotropy
Planned wide-field weak lensing surveys are expected to reduce the
statistical errors on the shear field to unprecedented levels. In contrast,
systematic errors like those induced by the convolution with the point spread
function (PSF) will not benefit from that scaling effect and will require very
accurate modeling and correction. While numerous methods have been devised to
carry out the PSF correction itself, modeling of the PSF shape and its spatial
variations across the instrument field of view has, so far, attracted much less
attention. This step is nevertheless crucial because the PSF is only known at
star positions while the correction has to be performed at any position on the
sky. A reliable interpolation scheme is therefore mandatory and a popular
approach has been to use low-order bivariate polynomials. In the present paper,
we evaluate four other classical spatial interpolation methods based on splines
(B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and
ordinary Kriging (OK). These methods are tested on the Star-challenge part of
the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and
are compared with the classical polynomial fitting (Polyfit). We also test all
our interpolation methods independently of the way the PSF is modeled, by
interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are
known exactly at star positions). We find in that case RBF to be the clear
winner, closely followed by the other local methods, IDW and OK. The global
methods, Polyfit and B-splines, are largely behind, especially in fields with
(ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all
interpolators reach a variance on PSF systematics better than
the upper bound expected by future space-based surveys, with
the local interpolators performing better than the global ones
Robust localization methods for passivity enforcement of linear macromodels
In this paper we solve a non-smooth convex formulation for passivity enforcement of linear macromodels using robust localization based algorithms such as the ellipsoid and the cutting plane methods. Differently from existing perturbation based techniques, we solve the formulation based on the direct ââ norm minimization through perturbation of state-space model parameters. We provide a systematic way of defining an initial set which is guaranteed to contain the global optimum. We also provide a lower bound on the global minimum, that grows tighter at each iteration and hence guarantees ÎŽ - optimality of the computed solution. We demonstrate the robustness of our implementation by generating accurate passive models for challenging examples for which existing algorithms either failed or exhibited extremely slow convergenc
Actions for signature change
This is a contribution on the controversy about junction conditions for
classical signature change. The central issue in this debate is whether the
extrinsic curvature on slices near the hypersurface of signature change has to
be continuous ({\it weak} signature change) or to vanish ({\it strong}
signature change). Led by a Lagrangian point of view, we write down eight
candidate action functionals ,\dots as possible generalizations of
general relativity and investigate to what extent each of these defines a
sensible variational problem, and which junction condition is implied. Four of
the actions involve an integration over the total manifold. A particular
subtlety arises from the precise definition of the Einstein-Hilbert Lagrangian
density . The other four actions are constructed as sums of
integrals over singe-signature domains. The result is that {\it both} types of
junction conditions occur in different models, i.e. are based on different
first principles, none of which can be claimed to represent the ''correct''
one, unless physical predictions are taken into account. From a point of view
of naturality dictated by the variational formalism, {\it weak} signature
change is slightly favoured over {\it strong} one, because it requires less
{\it \`a priori} restrictions for the class of off-shell metrics. In addition,
a proposal for the use of the Lagrangian framework in cosmology is made.Comment: 36 pages, LaTeX, no figures; some corrections have been made, several
Comments and further references are included and a note has been added
A Comparative Review of Dimension Reduction Methods in Approximate Bayesian Computation
Approximate Bayesian computation (ABC) methods make use of comparisons
between simulated and observed summary statistics to overcome the problem of
computationally intractable likelihood functions. As the practical
implementation of ABC requires computations based on vectors of summary
statistics, rather than full data sets, a central question is how to derive
low-dimensional summary statistics from the observed data with minimal loss of
information. In this article we provide a comprehensive review and comparison
of the performance of the principal methods of dimension reduction proposed in
the ABC literature. The methods are split into three nonmutually exclusive
classes consisting of best subset selection methods, projection techniques and
regularization. In addition, we introduce two new methods of dimension
reduction. The first is a best subset selection method based on Akaike and
Bayesian information criteria, and the second uses ridge regression as a
regularization procedure. We illustrate the performance of these dimension
reduction techniques through the analysis of three challenging models and data
sets.Comment: Published in at http://dx.doi.org/10.1214/12-STS406 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A comparative study of surrogate musculoskeletal models using various neural network configurations
Title from PDF of title page, viewed on August 13, 2013Thesis advisor: Reza R. DerakhshaniVitaIncludes bibliographic references (pages 85-88)Thesis (M.S.)--School of Computing and Engineering. University of Missouri--Kansas City, 2013The central idea in musculoskeletal modeling is to be able to predict body-level
(e.g. muscle forces) as well as tissue-level information (tissue-level stress, strain, etc.). To
develop computationally efficient techniques to analyze such models, surrogate models
have been introduced which concurrently predict both body-level and tissue-level
information using multi-body and finite-element analysis, respectively. However, this
kind of surrogate model is not an optimum solution as it involves the usage of finite
element models which are computation intensive and involve complex meshing methods
especially during real-time movement simulations. An alternative surrogate modeling
method is the use of artificial neural networks in place of finite-element models. The ultimate objective of this research is to predict tissue-level stresses
experienced by the cartilage and ligaments during movement and achieve concurrent
simulation of muscle force and tissue stress using various surrogate neural network
models, where stresses obtained from finite-element models provide the frame of
reference. Over the last decade, neural networks have been successfully implemented in
several biomechanical modeling applications. Their adaptive ability to learn from
examples, simple implementation techniques, and fast simulation times make neural networks versatile and robust when compared to other techniques. The neural network
models are trained with reaction forces from multi-body models and stresses from finite
element models obtained at the interested elements. Several configurations of static and
dynamic neural networks are modeled, and accuracies close to 93% were achieved, where
the correlation coefficient is the chosen measure of goodness. Using neural networks, the
simulation time was reduced nearly 40,000 times when compared to the finite-element
models. This study also confirms theoretical concepts that special network
configurations--including average committee, stacked generalization, and negative
correlation learning--provide considerably better results when compared to individual
networks themselves.Introduction -- Methods -- Results -- Conclusion -- Future work -- Appendix A. Various linear and non-linear modeling techniques -- Appendix B. Error analysi
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