A Forward Reachability Algorithm for Bounded Timed-Arc Petri Nets

Timed-arc Petri nets (TAPN) are a well-known time extension of the Petri net model and several translations to networks of timed automata have been proposed for this model. We present a direct, DBM-based algorithm for forward reachability analysis of bounded TAPNs extended with transport arcs, inhibitor arcs and age invariants. We also give a complete proof of its correctness, including reduction techniques based on symmetries and extrapolation. Finally, we augment the algorithm with a novel state-space reduction technique introducing a monotonic ordering on markings and prove its soundness even in the presence of monotonicity-breaking features like age invariants and inhibitor arcs. We implement the algorithm within the model-checker TAPAAL and the experimental results document an encouraging performance compared to verification approaches that translate TAPN models to UPPAAL timed automata.Comment: In Proceedings SSV 2012, arXiv:1211.587

Universal correlators for multi-arc complex matrix models

The correlation functions of the multi-arc complex matrix model are shown to be universal for any finite number of arcs. The universality classes are characterized by the support of the eigenvalue density and are conjectured to fall into the same classes as the ones recently found for the Hermitian model. This is explicitly shown to be true for the case of two arcs, apart from the known result for one arc. The basic tool is the iterative solution of the loop equation for the complex matrix model with multiple arcs, which provides all multi-loop correlators up to an arbitrary genus. Explicit results for genus one are given for any number of arcs. The two-arc solution is investigated in detail, including the double-scaling limit. In addition universal expressions for the string susceptibility are given for both the complex and Hermitian model

A simple prescription for simulating and characterizing gravitational arcs

Simple models of gravitational arcs are crucial to simulate large samples of these objects with full control of the input parameters. These models also provide crude and automated estimates of the shape and structure of the arcs, which are necessary when trying to detect and characterize these objects on massive wide area imaging surveys. We here present and explore the ArcEllipse, a simple prescription to create objects with shape similar to gravitational arcs. We also present PaintArcs, which is a code that couples this geometrical form with a brightness distribution and adds the resulting object to images. Finally, we introduce ArcFitting, which is a tool that fits ArcEllipses to images of real gravitational arcs. We validate this fitting technique using simulated arcs and apply it to CFHTLS and HST images of tangential arcs around clusters of galaxies. Our simple ArcEllipse model for the arc, associated to a S\'ersic profile for the source, recovers the total signal in real images typically within 10%-30%. The ArcEllipse+S\'ersic models also automatically recover visual estimates of length-to-width ratios of real arcs. Residual maps between data and model images reveal the incidence of arc substructure. They may thus be used as a diagnostic for arcs formed by the merging of multiple images. The incidence of these substructures is the main factor preventing ArcEllipse models from accurately describing real lensed systems.Comment: 12 pages, 11 figures, accepted for publication in A&

New JVLA observations at 3 GHz and 5.5 GHz of the `Kite' radio source in Abell 2626

We report on new JVLA observations performed at 3 GHz and 5.5 GHz of Abell 2626. The cluster has been the object of several studies in the recent years due to its peculiar radio emission, which shows a complex system of symmetric radio arcs characterized by a steep spectrum. The origin of these radio sources is still unclear. Due to their mirror symmetry toward the center, it has been proposed that they may be created by pairs of precessing jets powered by the inner AGN. The new JVLA observations were requested with the specific aim of detecting extended emission on frequencies higher than 1.4 GHz, in order to constrain the jet-precession model by analyzing the spectral index and radiative age patterns alongs the arcs. We performed a standard data reduction of the JVLA datasets with the software CASA. By combining the new 3 GHz data with the archival 1.4 GHz VLA dataset we produced a spectral index maps of the extended emission, and then we estimated the radiative age of the arcs by assuming that the plasma was accelerated in moving hot-spots tracing the arcs. Thanks to the high sensitivity of the JVLA, we achieve the detection of the arcs at 3 GHz and extended emission at 5.5 GHz. We measure a mean spectral index <-2.5 for the arcs up to 3 GHz. No clear spectral index, or radiative age, trend is detected across the arcs which may challenge the interpretation based on precession or put strong constraints on the jet-precession period. In particular, by analyzing the radiative age distribution along the arcs, we were able to provide for the first time a time-scale < 26 Myr of the jet-precession period.Comment: 8 pages, 5 figures. Accepted for publication in A&

Discovery of hard X-ray features around hotspots of Cygnus A

We present results of analysis of a Chandra observation of Cygnus A in which the X-ray hotspots at the ends of the jets are mapped in detail. A hardness map reveals previously unknown structure in the form of outer and inner hard arcs around the hotspots, with hardness significantly enhanced compared with the hotspot central regions. The outer hard arcs may constitute the first detection of the bow shock; the inner hard arcs may reveal where the jets impact on the hotspots. We argue that these features cannot result from electrons radiating by the synchrotron self-Compton process. Instead we consider two possible sources of the hard emission: the outer arcs may be due to thermal radiation of hot intracluster gas compressed at the bow shock. Alternatively, both outer and inner arcs may be due to synchrotron radiation of electrons accelerated in turbulent regions highly perturbed by shocks and shear flows. Comparison of measured hardness ratios with simulations of the hardness ratios resulting from these processes show that it is more diffcult to explain the observations with a thermal model. Although we cannot rule out a thermal model, we argue in favour of the non-thermal explanation. The hard regions in the secondary hotspots suggest that jet activity is still powering these hotspots.Comment: MNRAS in press; 5 pages, 3 figures (2 figures in colour in jpeg format should be printed separately

Arc Statistics in Clusters: Galaxy Contribution

The frequency with which background galaxies appear as long arcs as a result of gravitational lensing by foreground clusters of galaxies has recently been found to be a very sensitive probe of cosmological models by Bartelmann et al. (1998). They have found that such arcs would be expected far less frequently than observed (by an order of magnitude) in the currently favored model for the universe, with a large cosmological constant $\Omega_\Lambda \sim 0.7$. Here we analyze whether including the effect of cluster galaxies on the likelihood of clusters to generate long-arc images of background galaxies can change the statistics. Taking into account a variety of constraints on the properties of cluster galaxies, we find that there are not enough sufficiently massive galaxies in a cluster for them to significantly enhance the cross section of clusters to generate long arcs. We find that cluster galaxies typically enhance the cross section by only $\lesssim 15$.Comment: 19 pages, 1 figure, uses aasms4.sty, submitted to Ap

Topological transition in disordered planar matching: combinatorial arcs expansion

In this paper, we investigate analytically the properties of the disordered Bernoulli model of planar matching. This model is characterized by a topological phase transition, yielding complete planar matching solutions only above a critical density threshold. We develop a combinatorial procedure of arcs expansion that explicitly takes into account the contribution of short arcs, and allows to obtain an accurate analytical estimation of the critical value by reducing the global constrained problem to a set of local ones. As an application to a toy representation of the RNA secondary structures, we suggest generalized models that incorporate a one-to-one correspondence between the contact matrix and the RNA-type sequence, thus giving sense to the notion of effective non-integer alphabets.Comment: 28 pages, 6 figures, published versio