3,001 research outputs found
Extrapolation-Based Super-Convergent Implicit-Explicit Peer Methods with A-stable Implicit Part
In this paper, we extend the implicit-explicit (IMEX) methods of Peer type
recently developed in [Lang, Hundsdorfer, J. Comp. Phys., 337:203--215, 2017]
to a broader class of two-step methods that allow the construction of
super-convergent IMEX-Peer methods with A-stable implicit part. IMEX schemes
combine the necessary stability of implicit and low computational costs of
explicit methods to efficiently solve systems of ordinary differential
equations with both stiff and non-stiff parts included in the source term. To
construct super-convergent IMEX-Peer methods with favourable stability
properties, we derive necessary and sufficient conditions on the coefficient
matrices and apply an extrapolation approach based on already computed stage
values. Optimised super-convergent IMEX-Peer methods of order s+1 for s=2,3,4
stages are given as result of a search algorithm carefully designed to balance
the size of the stability regions and the extrapolation errors. Numerical
experiments and a comparison to other IMEX-Peer methods are included.Comment: 22 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1610.0051
Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant K
We consider systems A_\ell(t) y(q^\ell t) + ... + A_0(t) y(t) = b(t) of
higher order q-recurrence equations with rational coefficients. We extend a
method for finding a bound on the maximal power of t in the denominator of
arbitrary rational solutions y(t) as well as a method for bounding the degree
of polynomial solutions from the scalar case to the systems case. The approach
is direct and does not rely on uncoupling or reduction to a first order system.
Unlike in the scalar case this usually requires an initial transformation of
the system.Comment: 8 page
Pre main sequence: Accretion & Outflows
Low-mass pre-main sequence (PMS) stars are strong X-ray sources, because they
possess hot corona like their older main-sequence counterparts. Unique to young
stars, however, are X-rays from accretion and outflows, and both processes are
of pivotal importance for star and planet formation. We describe how X-ray data
provide important insight into the physics of accretion and outflows. First,
mass accreted from a circumstellar disk onto the stellar surface reaches
velocities up to a few hundred km/s, fast enough to generate soft X-rays in the
post-shock region of the accretion shock. X-ray observations together with
laboratory experiments and numerical simulations show that the accretion
geometry is complex in young stars. Specifically, the center of the accretion
column is likely surrounded by material shielding the inner flow from view but
itself also hot enough to emit X-rays. Second, X-rays are observed in two
locations of protostellar jets: an inner stationary emission component probably
related to outflow collimation and outer components, which evolve withing years
and are likely related to working surfaces where the shock travels through the
jet. Jet-powered X-rays appear to trace the fastest jet component and provide
novel information on jet launching in young stars. We conclude that X-ray data
will continue to be highly important for understanding star and planet
formation, because they directly probe the origin of many emission features
studied in other wavelength regimes. In addition, future X-ray missions will
improve sensitivity and spectral resolution to probe key model parameters (e.g.
velocities) in large samples of PMS stars.Comment: Invited chapter for the "Handbook of X-ray and Gamma-ray
Astrophysics" (Eds. C. Bambi and A. Santangelo, Springer Nature, 2022),
accepted (34 pages, 11 figures
Evaluating the Effectiveness of Natural Language Inference for Hate Speech Detection in Languages with Limited Labeled Data
Most research on hate speech detection has focused on English where a
sizeable amount of labeled training data is available. However, to expand hate
speech detection into more languages, approaches that require minimal training
data are needed. In this paper, we test whether natural language inference
(NLI) models which perform well in zero- and few-shot settings can benefit hate
speech detection performance in scenarios where only a limited amount of
labeled data is available in the target language. Our evaluation on five
languages demonstrates large performance improvements of NLI fine-tuning over
direct fine-tuning in the target language. However, the effectiveness of
previous work that proposed intermediate fine-tuning on English data is hard to
match. Only in settings where the English training data does not match the test
domain, can our customised NLI-formulation outperform intermediate fine-tuning
on English. Based on our extensive experiments, we propose a set of
recommendations for hate speech detection in languages where minimal labeled
training data is available.Comment: 15 pages, 7 figures, Accepted at the 7th Workshop on Online Abuse and
Harms (WOAH), ACL 202
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