1,834 research outputs found
Sequential Monte Carlo samplers for semilinear inverse problems and application to magnetoencephalography
We discuss the use of a recent class of sequential Monte Carlo methods for
solving inverse problems characterized by a semi-linear structure, i.e. where
the data depend linearly on a subset of variables and nonlinearly on the
remaining ones. In this type of problems, under proper Gaussian assumptions one
can marginalize the linear variables. This means that the Monte Carlo procedure
needs only to be applied to the nonlinear variables, while the linear ones can
be treated analytically; as a result, the Monte Carlo variance and/or the
computational cost decrease. We use this approach to solve the inverse problem
of magnetoencephalography, with a multi-dipole model for the sources. Here,
data depend nonlinearly on the number of sources and their locations, and
depend linearly on their current vectors. The semi-analytic approach enables us
to estimate the number of dipoles and their location from a whole time-series,
rather than a single time point, while keeping a low computational cost.Comment: 26 pages, 6 figure
Numerical hyperinterpolation over nonstandard planar regions
We discuss an algorithm (implemented in Matlab) that computes numerically total-degree bivariate orthogonal polynomials (OPs) given an algebraic cubature formula with positive weights, and constructs the orthogonal projection (hyperinterpolation) of a function sampled at the cubature nodes. The method is applicable to nonstandard regions where OPs are not known analytically, for example convex and concave polygons, or circular sections such as sectors, lenses and lunes
On the computation of sets of points with low Lebesgue constant on the unit disk
In this paper of numerical nature, we test the Lebesgue constant of several available point sets on the disk and propose new ones that enjoy low Lebesgue constant. Furthermore we extend some results in Cuyt (2012), analyzing the case of Bos arrays whose radii are nonnegative Gauss–Gegenbauer–Lobatto nodes with exponent, noticing that the optimal still allows to achieve point sets on with low Lebesgue constant for degrees. Next we introduce an algorithm that through optimization determines point sets with the best known Lebesgue constants for. Finally, we determine theoretically a point set with the best Lebesgue constant for the case
Subperiodic trigonometric subsampling: A numerical approach
We show that Gauss-Legendre quadrature applied to trigonometric poly- nomials on subintervals of the period can be competitive with subperiodic trigonometric Gaussian quadrature. For example with intervals correspond- ing to few angular degrees, relevant for regional scale models on the earth surface, we see a subsampling ratio of one order of magnitude already at moderate trigonometric degrees
Caratheodory-Tchakaloff Subsampling
We present a brief survey on the compression of discrete measures by
Caratheodory-Tchakaloff Subsampling, its implementation by Linear or Quadratic
Programming and the application to multivariate polynomial Least Squares. We
also give an algorithm that computes the corresponding Caratheodory-Tchakaloff
(CATCH) points and weights for polynomial spaces on compact sets and manifolds
in 2D and 3D
Optimal polynomial meshes and Caratheodory-Tchakaloff submeshes on the sphere
Using the notion of Dubiner distance, we give an elementary proof of the fact
that good covering point configurations on the 2-sphere are optimal polynomial
meshes. From these we extract Caratheodory-Tchakaloff (CATCH) submeshes for
compressed Least Squares fitting
Bayesian multi--dipole localization and uncertainty quantification from simultaneous EEG and MEG recordings
We deal with estimation of multiple dipoles from combined MEG and EEG
time--series. We use a sequential Monte Carlo algorithm to characterize the
posterior distribution of the number of dipoles and their locations. By
considering three test cases, we show that using the combined data the method
can localize sources that are not easily (or not at all) visible with either of
the two individual data alone. In addition, the posterior distribution from
combined data exhibits a lower variance, i.e. lower uncertainty, than the
posterior from single device.Comment: 4 pages, 3 figures -- conference paper from EMBEC 2017, Tampere,
Finlan
Polynomial Meshes: Computation and Approximation
We present the software package WAM, written in Matlab, that generates Weakly
Admissible Meshes and Discrete Extremal Sets of Fekete and Leja type, for 2d and 3d
polynomial least squares and interpolation on compact sets with various geometries.
Possible applications range from data fitting to high-order methods for PDEs
L'umanista Angelo Sabino e l'Odyssea decurtata del ms. Diez. B. Sant. 41 di Berlino
Angelus Sabinus’ paternity of the Odyssey in epistolary form (Odyssea decurtata) preserved in ms. Diez. B. Sant. 41 in Berlin is confirmed by Angelus himself, who, in his poem in praise of pope Pius II (Epaeneticum) claims to have composed in his youth, under the pontificate of Callistus III (1455-1458), verses about Ulysses, the Naritius dux. The evidence that Angelus Sabinus is the author of the Odyssea decurtata may also shed new light on the vexata quaestio of the authorship of the three epistles composed in response to three of Ovid’s Heroides, generally ascribed to Angelus, but newly attributed by Häuptli, the latest editor of the Ovidiana, to the ancient poet Sabinus, Ovid’s contemporary and friend. The essay also debates the question of the identity of Fatius, scriptor of the ms
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