Many natural and formal languages contain words or symbols that require a matching counterpart for making an expression wellformed. The combination of opening and closing brackets is a typical example of such a construction. Due to their commonness, the ability to follow such rules is important for language modeling. Currently, recurrent neural networks (RNNs) are extensively used for this task. We investigate whether they are capable of learning the rules of opening and closing brackets by applying them to synthetic Dyck languages that consist of different types of brackets. We provide an analysis of the statistical properties of these languages as a baseline and show strengths and limits of Elman-RNNs, GRUs and LSTMs in experiments on random samples of these languages. In terms of perplexity and prediction accuracy, the RNNs get close to the theoretical baseline in most cases.

Received xx; revised xx; accepted xx)Recent efforts to include kinetic effects in fluid simulations of plasmas have been very promising. Concerning collisionless magnetic reconnection, it has been found before that damping of the pressure tensor to isotropy leads to good agreement with kinetic runs in certain scenarios. An accurate representation of kinetic effects in reconnection was achieved in a study by Wang et al. (Phys. Plasmas, volume 22, 2015, 012108) with a closure derived from earlier work by Hammett and Perkins (PRL, volume 64, 1990, 3019). Here, their approach is analyzed on the basis of heat flux data from a Vlasov simulation. As a result, we propose a new local closure in which heat flux is driven by temperature gradients. That way, a more realistic approximation of Landau damping in the collisionless regime is achieved. Previous issues are addressed and the agreement with kinetic simulations in different reconnection setups is improved significantly. To the authors' knowledge, the new fluid model is the first to perform well in simulations of the coalescence of large magnetic islands.

We present a way to combine Vlasov and two-fluid codes for the simulation of a collisionless plasma in large domains while keeping full information of the velocity distribution in localized areas of interest. This is made possible by solving the full Vlasov equation in one region while the remaining area is treated by a 5-moment two-fluid code. In such a treatment, the main challenge of coupling kinetic and fluid descriptions is the interchange of physically correct boundary conditions between the different plasma models. In contrast to other treatments, we do not rely on any specific form of the distribution function, e.g. a Maxwellian type. Instead, we combine an extrapolation of the distribution function and a correction of the moments based on the fluid data. Thus, throughout the simulation both codes provide the necessary boundary conditions for each other. A speed-up factor of around 20 is achieved by using GPUs for the computationally expensive solution of the Vlasov equation and an overall factor of at least 60 using the coupling strategy combined with the GPU computation. The coupled codes were then tested on the GEM reconnection challenge

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