On the existence and convergence of polyhomogeneous expansions of zero-rest-mass fields

The convergence of polyhomogeneous expansions of zero-rest-mass fields in asymptotically flat spacetimes is discussed. An existence proof for the asymptotic characteristic initial value problem for a zero-rest-mass field with polyhomogeneous initial data is given. It is shown how this non-regular problem can be properly recast as a set of regular initial value problems for some auxiliary fields. The standard techniques of symmetric hyperbolic systems can be applied to these new auxiliary problems, thus yielding a positive answer to the question of existence in the original problem.Comment: 10 pages, 1 eps figur

Combinatorial optimization model for railway engine assignment problem

This paper presents an experimental study for the Hungarian State Railway Company (M\'AV). The engine assignment problem was solved at M\'AV by their experts without using any explicit operations research tool. Furthermore, the operations research model was not known at the company. The goal of our project was to introduce and solve an operations research model for the engine assignment problem on real data sets. For the engine assignment problem we are using a combinatorial optimization model. At this stage of research the single type train that is pulled by a single type engine is modeled and solved for real data. There are two regions in Hungary where the methodology described in this paper can be used and M\'AV started to use it regularly. There is a need to generalize the model for multiple type trains and multiple type engines

Can one detect a non-smooth null infinity?

It is shown that the precession of a gyroscope can be used to elucidate the nature of the smoothness of the null infinity of an asymptotically flat spacetime (describing an isolated body). A model for which the effects of precession in the non-smooth null infinity case are of order $r^{-2}\ln r$ is proposed. By contrast, in the smooth version the effects are of order $r^{-3}$. This difference should provide an effective criterion to decide on the nature of the smoothness of null infinity.Comment: 6 pages, to appear in Class. Quantum Gra

Polyhomogeneity and zero-rest-mass fields with applications to Newman-Penrose constants

A discussion of polyhomogeneity (asymptotic expansions in terms of $1/r$ and $\ln r$) for zero-rest-mass fields and gravity and its relation with the Newman-Penrose (NP) constants is given. It is shown that for spin-$s$ zero-rest-mass fields propagating on Minkowski spacetime, the logarithmic terms in the asymptotic expansion appear naturally if the field does not obey the ``Peeling theorem''. The terms that give rise to the slower fall-off admit a natural interpretation in terms of advanced field. The connection between such fields and the NP constants is also discussed. The case when the background spacetime is curved and polyhomogeneous (in general) is considered. The free fields have to be polyhomogeneous, but the logarithmic terms due to the connection appear at higher powers of $1/r$. In the case of gravity, it is shown that it is possible to define a new auxiliary field, regular at null infinity, and containing some relevant information on the asymptotic behaviour of the spacetime. This auxiliary zero-rest-mass field ``evaluated at future infinity ($i^+$)'' yields the logarithmic NP constants.Comment: 19 page

Context dependent differences in working memory related brain activity in heavy cannabis users

Rationale  Compromised cognitive control in cannabis use–tempting situations is thought to play a key role in the development of cannabis use disorders. However, little is known about how exposure to cannabis cues and contexts may influence cognitive control and the underlying neural mechanisms in cannabis users.  Objectives  Working memory (WM) is an attention reliant executive function central to cognitive control. In this study, we investigated how distracting cannabis words affected WM load–dependent performance and related brain activity in near-daily cannabis users (N = 36) relative to controls (N = 33).  Methods  Brain activity was recorded during a novel N-back flanker WM task with neutral and cannabis flankers added as task-irrelevant distractors.  Results  On a behavioural level, WM performance did not differ between groups, and the presence of cannabis flankers did not affect performance. However, in cannabis users compared to controls, the presence of cannabis flankers reduced WM load–related activity in multiple regions, including the insula, thalamus, superior parietal lobe and supramarginal gyrus.  Conclusions  The group specificity of these effects suggest that cannabis users might differ from controls in the way they process cannabis-related cues and that cannabis cue exposure could interfere with other cognitive processes under cognitively demanding circumstances. Future studies should focus on the role of context in cognitive control–related processes like WM and attention to further elucidate potential cognitive impairments in heavy cannabis users and how these relate to loss of control over drug seeking itself