184 research outputs found
Fast Computation of Minimal Interpolation Bases in Popov Form for Arbitrary Shifts
We compute minimal bases of solutions for a general interpolation problem,
which encompasses Hermite-Pad\'e approximation and constrained multivariate
interpolation, and has applications in coding theory and security.
This problem asks to find univariate polynomial relations between vectors
of size ; these relations should have small degree with respect to an
input degree shift. For an arbitrary shift, we propose an algorithm for the
computation of an interpolation basis in shifted Popov normal form with a cost
of field operations, where
is the exponent of matrix multiplication and the notation
indicates that logarithmic terms are omitted.
Earlier works, in the case of Hermite-Pad\'e approximation and in the general
interpolation case, compute non-normalized bases. Since for arbitrary shifts
such bases may have size , the cost bound
was feasible only with restrictive
assumptions on the shift that ensure small output sizes. The question of
handling arbitrary shifts with the same complexity bound was left open.
To obtain the target cost for any shift, we strengthen the properties of the
output bases, and of those obtained during the course of the algorithm: all the
bases are computed in shifted Popov form, whose size is always . Then, we design a divide-and-conquer scheme. We recursively reduce
the initial interpolation problem to sub-problems with more convenient shifts
by first computing information on the degrees of the intermediate bases.Comment: 8 pages, sig-alternate class, 4 figures (problems and algorithms
Verification of Gyrokinetic codes: theoretical background and applications
In fusion plasmas the strong magnetic field allows the fast gyro-motion to be
systematically removed from the description of the dynamics, resulting in a
considerable model simplification and gain of computational time. Nowadays, the
gyrokinetic (GK) codes play a major role in the understanding of the
development and the saturation of turbulence and in the prediction of the
subsequent transport. Naturally, these codes require thorough verification and
validation.
Here we present a new and generic theoretical framework and specific
numerical applications to test the faithfulness of the implemented models to
theory and to verify the domain of applicability of existing GK codes. For a
sound verification process, the underlying theoretical GK model and the
numerical scheme must be considered at the same time, which has rarely been
done and therefore makes this approach pioneering. At the analytical level, the
main novelty consists in using advanced mathematical tools such as variational
formulation of dynamics for systematization of basic GK code's equations to
access the limits of their applicability. The verification of numerical scheme
is proposed via the benchmark effort.
In this work, specific examples of code verification are presented for two GK
codes: the multi-species electromagnetic ORB5 (PIC) and the radially global
version of GENE (Eulerian). The proposed methodology can be applied to any
existing GK code. We establish a hierarchy of reduced GK Vlasov-Maxwell
equations implemented in the ORB5 and GENE codes using the Lagrangian
variational formulation. At the computational level, detailed verifications of
global electromagnetic test cases developed from the CYCLONE Base Case are
considered, including a parametric -scan covering the transition from
ITG to KBM and the spectral properties at the nominal value.Comment: 16 pages, 2 Figures, APS DPP 2016 invited pape
Computing minimal interpolation bases
International audienceWe consider the problem of computing univariate polynomial matrices over afield that represent minimal solution bases for a general interpolationproblem, some forms of which are the vector M-Pad\'e approximation problem in[Van Barel and Bultheel, Numerical Algorithms 3, 1992] and the rationalinterpolation problem in [Beckermann and Labahn, SIAM J. Matrix Anal. Appl. 22,2000]. Particular instances of this problem include the bivariate interpolationsteps of Guruswami-Sudan hard-decision and K\"otter-Vardy soft-decisiondecodings of Reed-Solomon codes, the multivariate interpolation step oflist-decoding of folded Reed-Solomon codes, and Hermite-Pad\'e approximation. In the mentioned references, the problem is solved using iterative algorithmsbased on recurrence relations. Here, we discuss a fast, divide-and-conquerversion of this recurrence, taking advantage of fast matrix computations overthe scalars and over the polynomials. This new algorithm is deterministic, andfor computing shifted minimal bases of relations between vectors of size it uses field operations, where is the exponent of matrix multiplication, and is the sum of theentries of the input shift , with . This complexity boundimproves in particular on earlier algorithms in the case of bivariateinterpolation for soft decoding, while matching fastest existing algorithms forsimultaneous Hermite-Pad\'e approximation
3D Detection and Characterisation of ALMA Sources through Deep Learning
We present a Deep-Learning (DL) pipeline developed for the detection and
characterization of astronomical sources within simulated Atacama Large
Millimeter/submillimeter Array (ALMA) data cubes. The pipeline is composed of
six DL models: a Convolutional Autoencoder for source detection within the
spatial domain of the integrated data cubes, a Recurrent Neural Network (RNN)
for denoising and peak detection within the frequency domain, and four Residual
Neural Networks (ResNets) for source characterization. The combination of
spatial and frequency information improves completeness while decreasing
spurious signal detection. To train and test the pipeline, we developed a
simulation algorithm able to generate realistic ALMA observations, i.e. both
sky model and dirty cubes. The algorithm simulates always a central source
surrounded by fainter ones scattered within the cube. Some sources were
spatially superimposed in order to test the pipeline deblending capabilities.
The detection performances of the pipeline were compared to those of other
methods and significant improvements in performances were achieved. Source
morphologies are detected with subpixel accuracies obtaining mean residual
errors of pixel ( mas) and mJy/beam on positions and
flux estimations, respectively. Projection angles and flux densities are also
recovered within of the true values for and of all sources
in the test set, respectively. While our pipeline is fine-tuned for ALMA data,
the technique is applicable to other interferometric observatories, as SKA,
LOFAR, VLBI, and VLTI
Faster Algorithms for Multivariate Interpolation with Multiplicities and Simultaneous Polynomial Approximations
The interpolation step in the Guruswami-Sudan algorithm is a bivariate
interpolation problem with multiplicities commonly solved in the literature
using either structured linear algebra or basis reduction of polynomial
lattices. This problem has been extended to three or more variables; for this
generalization, all fast algorithms proposed so far rely on the lattice
approach. In this paper, we reduce this multivariate interpolation problem to a
problem of simultaneous polynomial approximations, which we solve using fast
structured linear algebra. This improves the best known complexity bounds for
the interpolation step of the list-decoding of Reed-Solomon codes,
Parvaresh-Vardy codes, and folded Reed-Solomon codes. In particular, for
Reed-Solomon list-decoding with re-encoding, our approach has complexity
, where are the
list size, the multiplicity, the number of sample points and the dimension of
the code, and is the exponent of linear algebra; this accelerates the
previously fastest known algorithm by a factor of .Comment: Version 2: Generalized our results about Problem 1 to distinct
multiplicities. Added Section 4 which details several applications of our
results to the decoding of Reed-Solomon codes (list-decoding with re-encoding
technique, Wu algorithm, and soft-decoding). Reorganized the sections, added
references and corrected typo
Correction: Exome-wide association study reveals novel susceptibility genes to sporadic dilated cardiomyopathy
This corrects the article DOI: 10.1371/journal.pone.017299
Bayesian and Machine Learning Methods in the Big Data era for astronomical imaging
The Atacama Large Millimeter/submillimeter Array with the planned electronic
upgrades will deliver an unprecedented amount of deep and high resolution
observations. Wider fields of view are possible with the consequential cost of
image reconstruction. Alternatives to commonly used applications in image
processing have to be sought and tested. Advanced image reconstruction methods
are critical to meet the data requirements needed for operational purposes.
Astrostatistics and astroinformatics techniques are employed. Evidence is given
that these interdisciplinary fields of study applied to synthesis imaging meet
the Big Data challenges and have the potentials to enable new scientific
discoveries in radio astronomy and astrophysics.Comment: 8 pages, 5 figures, proceedings International Workshop on Bayesian
Inference and Maximum Entropy Methods in Science and Engineering, IHP, Paris,
July 18-22, 202
First principles gyrokinetic analysis of electromagnetic plasma instabilities
A two-fold analysis of electromagnetic core tokamak instabilities in the
framework of the gyrokinetic theory is presented. First principle theoretical
foundations of the gyrokinetic theory are used to explain and justify the
numerical results obtained with the global electromagnetic particle-in-cell
code Orb5 whose model is derived from the Lagrangian formalism. The energy
conservation law corresponding to the Orb5 model is derived from the Noether
theorem and implemented in the code as a diagnostics for energy balance and
conservation verification. An additional Noether theorem based diagnostics is
implemented in order to analyse destabilising mechanisms for the electrostatic
and the electromagnetic Ion Temperature Gradient (ITG) instabilities in the
core region of the tokamak. The transition towards the Kinetic Ballooning Modes
(KBM) at high electromagnetic is also investigated.Comment: 22 pages, 10 Figures, material form the ICPP conference 2018, invite
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