Reduced Ambiguity Calibration for LOFAR

Interferometric calibration always yields non unique solutions. It is therefore essential to remove these ambiguities before the solutions could be used in any further modeling of the sky, the instrument or propagation effects such as the ionosphere. We present a method for LOFAR calibration which does not yield a unitary ambiguity, especially under ionospheric distortions. We also present exact ambiguities we get in our solutions, in closed form. Casting this as an optimization problem, we also present conditions for this approach to work. The proposed method enables us to use the solutions obtained via calibration for further modeling of instrumental and propagation effects. We provide extensive simulation results on the performance of our method. Moreover, we also give cases where due to degeneracy, this method fails to perform as expected and in such cases, we suggest exploiting diversity in time, space and frequency.Comment: Draft version. Final version published on 10 April 201

Error Analysis of TT-Format Tensor Algorithms

The tensor train (TT) decomposition is a representation technique for arbitrary tensors, which allows efficient storage and computations. For a d-dimensional tensor with d 65 2, that decomposition consists of two ordinary matrices and d 12 2 third-order tensors. In this paper we prove that the TT decomposition of an arbitrary tensor can be computed (or approximated, for data compression purposes) by means of a backward stable algorithm based on computations with Householder matrices. Moreover, multilinear forms with tensors represented in TT format can be computed efficiently with a small backward error

An algorithm to compute the polar decomposition of a 3 × 3 matrix

We propose an algorithm for computing the polar decomposition of a 3 × 3 real matrix that is based on the connection between orthogonal matrices and quaternions. An important application is to 3D transformations in the level 3 Cascading Style Sheets specification used in web browsers. Our algorithm is numerically reliable and requires fewer arithmetic operations than the alternative of computing the polar decomposition via the singular value decomposition

Performance Analysis of Effective Methods for Solving Band Matrix SLAEs after Parabolic Nonlinear PDEs

This paper presents an experimental performance study of implementations of three different types of algorithms for solving band matrix systems of linear algebraic equations (SLAEs) after parabolic nonlinear partial differential equations -- direct, symbolic, and iterative, the former two of which were introduced in Veneva and Ayriyan (arXiv:1710.00428v2). An iterative algorithm is presented -- the strongly implicit procedure (SIP), also known as the Stone method. This method uses the incomplete LU (ILU(0)) decomposition. An application of the Hotelling-Bodewig iterative algorithm is suggested as a replacement of the standard forward-backward substitutions. The upsides and the downsides of the SIP method are discussed. The complexity of all the investigated methods is presented. Performance analysis of the implementations is done using the high-performance computing (HPC) clusters "HybriLIT" and "Avitohol". To that purpose, the experimental setup and the results from the conducted computations on the individual computer systems are presented and discussed.Comment: 10 pages, 2 figure

Novel Modifications of Parallel Jacobi Algorithms

We describe two main classes of one-sided trigonometric and hyperbolic Jacobi-type algorithms for computing eigenvalues and eigenvectors of Hermitian matrices. These types of algorithms exhibit significant advantages over many other eigenvalue algorithms. If the matrices permit, both types of algorithms compute the eigenvalues and eigenvectors with high relative accuracy. We present novel parallelization techniques for both trigonometric and hyperbolic classes of algorithms, as well as some new ideas on how pivoting in each cycle of the algorithm can improve the speed of the parallel one-sided algorithms. These parallelization approaches are applicable to both distributed-memory and shared-memory machines. The numerical testing performed indicates that the hyperbolic algorithms may be superior to the trigonometric ones, although, in theory, the latter seem more natural.Comment: Accepted for publication in Numerical Algorithm

A note on "symmetric" vielbeins in bimetric, massive, perturbative and non perturbative gravities

We consider a manifold endowed with two different vielbeins $E^{A}{}_{\mu}$ and $L^{A}{}_{\mu}$ corresponding to two different metrics $g_{\mu\nu}$ and $f_{\mu\nu}$. Such a situation arises generically in bimetric or massive gravity (including the recently discussed version of de Rham, Gabadadze and Tolley), as well as in perturbative quantum gravity where one vielbein parametrizes the background space-time and the other the dynamical degrees of freedom. We determine the conditions under which the relation $g^{\mu\nu} E^{A}{}_{\mu} L^{B}{}_{\nu} = g^{\mu\nu} E^{B}{}_{\mu} L^{A}{}_{\nu}$ can be imposed (or the "Deser-van Nieuwenhuizen" gauge chosen). We clarify and correct various statements which have been made about this issue.Comment: 20 pages. Section 7, prop. 6 and 7. added. Some results made more precis

Neandertal-Modern Human Contact in Western Eurasia: Issues of Dating, Taxonomy, and Cultural Associations

Supporting Assimilation views of Neandertal/modern human interaction, chronostratigraphic reasoning indicates that the “transitional” industries of Europe predate modern human immigration, in agreement with their association with Neandertals in the Châtelperronian at the Grotte du Renne and St.-Césaire. Supporting the Neandertals' species separateness and less developed cognition, those industries are alternatively claimed to relate to pioneer groups of modern humans; the latter would have been the true makers of the precocious instances of symbolic material culture that, under Assimilation, are assigned to the Neandertals. However, the taxonomy of the Kent's Cavern and Grotta del Cavallo dental remains is uncertain, and their poor stratigraphic context precludes dating by association. The opposite happens at the Grotte du Renne, whose stratigraphic integrity is corroborated by both taphonomy and dating. Not questioning that the Early Ahmarian is a cultural proxy for modern humans and a source for the Protoaurignacian of Europe, its claimed emergence ~46–49 ka ago at Kebara refl ects the dating of Middle Paleolithic charcoal—to be expected, because the Early Ahmarian units at the back of the cave are made up of reworked Middle Paleolithic sediments derived from the entrance. The dating of inherited material also explains the old results for the Aurignacian of Willendorf II and Geissenklösterle. At the latter, the dates on anthropically modified samples of the hunted taxa (reindeer and horse) place its Aurignacian occupations in the same time range as elsewhere in Europe, after ~40 ka ago. The hypothesis that Neandertal/modern human contact in Europe resulted in a process of assimilation in connection with the spread of the Protoaurignacian ~41.5 ka ago remains unfalsified.info:eu-repo/semantics/publishedVersio