3,615 research outputs found
Weight hierarchies of a family of linear codes associated with degenerate quadratic forms
We restrict a degenerate quadratic form over a finite field of odd
characteristic to subspaces. Thus, a quotient space related to is
introduced. Then we get a non-degenerate quadratic form induced by over the
quotient space. Some related results on the subspaces and quotient space are
obtained. Based on this, we solve the weight hierarchies of a family of linear
codes related to Comment: 12 page
3-D inelastic analysis methods for hot section components. Volume 2: Advanced special functions models
This Annual Status Report presents the results of work performed during the third year of the 3-D Inelastic Analysis Methods for Hot Sections Components program (NASA Contract NAS3-23697). The objective of the program is to produce a series of computer codes that permit more accurate and efficient three-dimensional analyses of selected hot section components, i.e., combustor liners, turbine blades, and turbine vanes. The computer codes embody a progression of mathematical models and are streamlined to take advantage of geometrical features, loading conditions, and forms of material response that distinguish each group of selected components
Efficiently Generating Geometric Inhomogeneous and Hyperbolic Random Graphs
Hyperbolic random graphs (HRG) and geometric inhomogeneous random graphs (GIRG) are two similar generative network models that were designed to resemble complex real world networks. In particular, they have a power-law degree distribution with controllable exponent beta, and high clustering that can be controlled via the temperature T.
We present the first implementation of an efficient GIRG generator running in expected linear time. Besides varying temperatures, it also supports underlying geometries of higher dimensions. It is capable of generating graphs with ten million edges in under a second on commodity hardware. The algorithm can be adapted to HRGs. Our resulting implementation is the fastest sequential HRG generator, despite the fact that we support non-zero temperatures. Though non-zero temperatures are crucial for many applications, most existing generators are restricted to T = 0. We also support parallelization, although this is not the focus of this paper. Moreover, we note that our generators draw from the correct probability distribution, i.e., they involve no approximation.
Besides the generators themselves, we also provide an efficient algorithm to determine the non-trivial dependency between the average degree of the resulting graph and the input parameters of the GIRG model. This makes it possible to specify the desired expected average degree as input.
Moreover, we investigate the differences between HRGs and GIRGs, shedding new light on the nature of the relation between the two models. Although HRGs represent, in a certain sense, a special case of the GIRG model, we find that a straight-forward inclusion does not hold in practice. However, the difference is negligible for most use cases
A unified pseudo- framework
The pseudo- is an algorithm for estimating the angular power and
cross-power spectra that is very fast and, in realistic cases, also nearly
optimal. The algorithm can be extended to deal with contaminant deprojection
and purification, and can therefore be applied in a wide variety of
scenarios of interest for current and future cosmological observations. This
paper presents NaMaster, a public, validated, accurate and easy-to-use software
package that, for the first time, provides a unified framework to compute
angular cross-power spectra of any pair of spin-0 or spin-2 fields,
contaminated by an arbitrary number of linear systematics and requiring - or
-mode purification, both on the sphere or in the flat-sky approximation. We
describe the mathematical background of the estimator, including all the
features above, and its software implementation in NaMaster. We construct a
validation suite that aims to resemble the types of observations that
next-generation large-scale structure and ground-based CMB experiments will
face, and use it to show that the code is able to recover the input power
spectra in the most complex scenarios with no detectable bias. NaMaster can be
found at https://github.com/LSSTDESC/NaMaster, and is provided with
comprehensive documentation and a number of code examples.Comment: 27 pages, 17 figures, accepted in MNRAS. Code can be found at
https://github.com/LSSTDESC/NaMaste
Discontinuities in numerical radiative transfer
Observations and magnetohydrodynamic simulations of solar and stellar
atmospheres reveal an intermittent behavior or steep gradients in physical
parameters, such as magnetic field, temperature, and bulk velocities. The
numerical solution of the stationary radiative transfer equation is
particularly challenging in such situations, because standard numerical methods
may perform very inefficiently in the absence of local smoothness. However, a
rigorous investigation of the numerical treatment of the radiative transfer
equation in discontinuous media is still lacking. The aim of this work is to
expose the limitations of standard convergence analyses for this problem and to
identify the relevant issues. Moreover, specific numerical tests are performed.
These show that discontinuities in the atmospheric physical parameters
effectively induce first-order discontinuities in the radiative transfer
equation, reducing the accuracy of the solution and thwarting high-order
convergence. In addition, a survey of the existing numerical schemes for
discontinuous ordinary differential systems and interpolation techniques for
discontinuous discrete data is given, evaluating their applicability to the
radiative transfer problem
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