972 research outputs found
Automated Feedback for 'Fill in the Gap' Programming Exercises
Timely feedback is a vital component in the learning process. It is especially important for beginner students in Information Technology since many have not yet formed an effective internal model of a computer that they can use to construct viable knowledge. Research has shown that learning efficiency is increased if immediate feedback is provided for students. Automatic analysis of student programs has the potential to provide immediate feedback for students and to assist teaching staff in the marking process. This paper describes a “fill in the gap” programming analysis framework which tests students’ solutions and gives feedback on their correctness, detects logic errors and provides hints on how to fix these errors. Currently, the framework is being used with the Environment for Learning to Programming (ELP) system at Queensland University of Technology (QUT); however, the framework can be integrated into any existing online learning environment or programming Integrated Development Environment (IDE
Generalizing Topological Graph Neural Networks with Paths
While Graph Neural Networks (GNNs) have made significant strides in diverse
areas, they are hindered by a theoretical constraint known as the
1-Weisfeiler-Lehmann test. Even though latest advancements in higher-order GNNs
can overcome this boundary, they typically center around certain graph
components like cliques or cycles. However, our investigation goes a different
route. We put emphasis on paths, which are inherent in every graph. We are able
to construct a more general topological perspective and form a bridge to
certain established theories about other topological domains. Interestingly,
without any assumptions on graph sub-structures, our approach surpasses earlier
techniques in this field, achieving state-of-the-art performance on several
benchmarks
Time-Dependent Stochastic Particle Acceleration in Astrophysical Plasmas: Exact Solutions Including Momentum-Dependent Escape
Stochastic acceleration of charged particles due to interactions with
magnetohydrodynamic (MHD) plasma waves is the dominant process leading to the
formation of the high-energy electron and ion distributions in a variety of
astrophysical systems. Collisions with the waves influence both the
energization and the spatial transport of the particles, and therefore it is
important to treat these two aspects of the problem in a self-consistent
manner. We solve the representative Fokker-Planck equation to obtain a new,
closed-form solution for the time-dependent Green's function describing the
acceleration and escape of relativistic ions interacting with Alfven or
fast-mode waves characterized by momentum diffusion coefficient and mean particle escape timescale , where
is the particle momentum and is the power-law index of the MHD wave
spectrum. In particular, we obtain solutions for the momentum distribution of
the ions in the plasma and also for the momentum distribution of the escaping
particles, which may form an energetic outflow. The general features of the
solutions are illustrated via examples based on either a Kolmogorov or
Kraichnan wave spectrum. The new expressions complement the results obtained by
Park and Petrosian, who presented exact solutions for the hard-sphere
scattering case () in addition to other scenarios in which the escape
timescale has a power-law dependence on the momentum. Our results have direct
relevance for models of high-energy radiation and cosmic-ray production in
astrophysical environments such as -ray bursts, active galaxies, and
magnetized coronae around black holes.Comment: Accepted for publication in Ap
Particle Acceleration and the Formation of Relativistic Outflows in Viscous Accretion Disks with Shocks
In this Letter, we present a new self-consistent theory for the production of
the relativistic outflows observed from radio-loud black hole candidates and
active galaxies as a result of particle acceleration in hot, viscous accretion
disks containing standing, centrifugally-supported isothermal shocks. This is
the first work to obtain the structure of such disks for a relatively large
value of the Shakura-Sunyaev viscosity parameter (), and to
consider the implications of the shock for the acceleration of relativistic
particles in viscous disks. In our approach, the hydrodynamics and the particle
acceleration are coupled and the solutions are obtained self-consistently based
on a rigorous mathematical method. We find that particle acceleration in the
vicinity of the shock can provide enough energy to power the observed
relativistic jet in M87.Comment: published in ApJ
Images of Multilinear Polynomials on Generalized Quaternion Algebras
The main goal of this paper is to extend [J. Algebra Appl. 20 (2021),
2150074] to generalized quaternion algebras, even when these algebras are not
necessarily division rings. More precisely, in such cases, the image of a
multilinear polynomial evaluated on a quaternion algebra is a vector space and
we additionally provide a classification of possible images.Comment: One new section is added, namely Section 3, and thus the paper is now
18 page
Particle Acceleration in Advection-Dominated Accretion Disks with Shocks: Green's Function Energy Distribution
The distribution function describing the acceleration of relativistic
particles in an advection-dominated accretion disk is analyzed using a
transport formalism that includes first-order Fermi acceleration, advection,
spatial diffusion, and the escape of particles through the upper and lower
surfaces of the disk. When a centrifugally-supported shock is present in the
disk, the concentrated particle acceleration occurring in the vicinity of the
shock channels a significant fraction of the binding energy of the accreting
gas into a population of relativistic particles. These high-energy particles
diffuse vertically through the disk and escape, carrying away both energy and
entropy and allowing the remaining gas to accrete. The dynamical structure of
the disk/shock system is computed self-consistently using a model previously
developed by the authors that successfully accounts for the production of the
observed relativistic outflows (jets) in M87 and \SgrA. This ensures that the
rate at which energy is carried away from the disk by the escaping relativistic
particles is equal to the drop in the radial energy flux at the shock location,
as required for energy conservation. We investigate the influence of advection,
diffusion, and acceleration on the particle distribution by computing the
nonthermal Green's function, which displays a relatively flat power-law tail at
high energies. We also obtain the energy distribution for the particles
escaping from the disk, and we conclude by discussing the spectrum of the
observable secondary radiation produced by the escaping particles.Comment: Published in Ap
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