On The Complexity and Completeness of Static Constraints for Breaking Row and Column Symmetry

We consider a common type of symmetry where we have a matrix of decision variables with interchangeable rows and columns. A simple and efficient method to deal with such row and column symmetry is to post symmetry breaking constraints like DOUBLELEX and SNAKELEX. We provide a number of positive and negative results on posting such symmetry breaking constraints. On the positive side, we prove that we can compute in polynomial time a unique representative of an equivalence class in a matrix model with row and column symmetry if the number of rows (or of columns) is bounded and in a number of other special cases. On the negative side, we show that whilst DOUBLELEX and SNAKELEX are often effective in practice, they can leave a large number of symmetric solutions in the worst case. In addition, we prove that propagating DOUBLELEX completely is NP-hard. Finally we consider how to break row, column and value symmetry, correcting a result in the literature about the safeness of combining different symmetry breaking constraints. We end with the first experimental study on how much symmetry is left by DOUBLELEX and SNAKELEX on some benchmark problems.Comment: To appear in the Proceedings of the 16th International Conference on Principles and Practice of Constraint Programming (CP 2010

Tractable Combinations of Global Constraints

We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used; indeed, they are one of the key reasons for the success of constraint programming in solving real-world problems. Previous work has focused on the development of efficient propagators for individual constraints. In this paper, we identify a new tractable class of constraint problems involving global constraints of unbounded arity. To do so, we combine structural restrictions with the observation that some important types of global constraint do not distinguish between large classes of equivalent solutions.Comment: To appear in proceedings of CP'13, LNCS 8124. arXiv admin note: text overlap with arXiv:1307.179

VLT FORS2 optical imaging and spectroscopy of nine luminous type 2 AGN at 0.3 < z < 0.6-I. Ionized gas nebulae

We present optical imaging and long slit spectroscopic observations of nine luminous type 2 active galactic nuclei (AGN) within the redshift range 0.3 <z< 0.6 based on Very Large Telescope Focal Reducer and Low Dispersion Spectrograph (VLT FORS2) data. Most objects (6/9) are high luminosity Seyfert 2, and three are type 2 quasars (QSO2), with our sample extending to lower luminosity than previous works. Seven out of nine objects (78 per cent) show morphological evidence for interactions or mergers in the form of disturbed morphologies and/or peculiar features such as tidal tails, amorphous haloes, or compact emission line knots. The detection rate of morphological evidence for interaction is consistent with those found during previous studies of QSO2 at similar z, suggesting that the merger rate is independent of AGN power at the high end of the AGN luminosity function. We find the emission line flux spatial profiles are often dominated by the often spatially unresolved central source. In addition, all but one of our samples is associated with much fainter, extended line emission. We find these extended emission line structures have a variety of origins and ionization mechanisms: star-forming companions, tidal features, or extended ionized nebulae. AGN related processes dominate the excitation of the nuclear gas. Stellar photoionization sometimes plays a role in extended structures often related to mergers/interactions

A distributed optimization method for the geographically distributed data centres problem

The geographically distributed data centres problem (GDDC) is a naturally distributed resource allocation problem. The problem involves allocating a set of virtual machines (VM) amongst the data centres (DC) in each time period of an operating horizon. The goal is to optimize the allocation of workload across a set of DCs such that the energy cost is minimized, while respecting limitations on data centre capacities, migrations of VMs, etc. In this paper, we propose a distributed optimization method for GDDC using the distributed constraint optimization (DCOP) framework. First, we develop a new model of the GDDC as a DCOP where each DC operator is represented by an agent. Secondly, since traditional DCOP approaches are unsuited to these types of large-scale problem with multiple variables per agent and global constraints, we introduce a novel semi-asynchronous distributed algorithm for solving such DCOPs. Preliminary results illustrate the benefits of the new method

Young stellar populations in type II quasars: timing the onset of star formation and nuclear activity

Despite the emerging morphological evidence that luminous quasar-like active galactic nuclei (AGN) are triggered in galaxy mergers, the natures of the triggering mergers and the order of events in the triggering sequence remain uncertain. In this work, we present a detailed study of the stellar populations of the host galaxies of 21 type II quasars, with the aim of understanding the sequence of events between the onset of the merger, the triggering of the associated starburst and the initiation of the quasar activity. To this end, we model highquality, wide spectral coverage, intermediate-resolution optical spectra of the type II quasars. We find that of the 21 objects, the higher order Balmer absorption lines, characteristic of young stellar populations (YSPs), are directly detected in ∼62 per cent of the sample. We also fit these spectra using a number of combinations of stellar and/or power-law components, representative of viable formation histories, as well as including the possibility of scattered AGN light. We find that ∼90 per cent of the type II quasar host galaxies require the inclusion of a YSP to adequately model their spectra, whilst 71 per cent of the sample require the inclusion of a YSP with age <100 Myr. Since the ages of the YSP in most type II quasar host galaxies are comparable with the expected lifetimes of the AGN activity, these results provide strong evidence that the quasars are triggered close to the peaks of the merger-induced starbursts

Mergers and interactions in SDSS type 2 quasars at z~0.3-0.4. SDSS J143027.66-005614.8: a case study

We present a compilation of HST images of 58 luminous SDSS type 2 AGNs at 0.3<z<0.4. 42 of them are type 2 quasars, which are a good representation of all optically selected SDSS type 2 quasars in this range. We find that the majority of the host galaxies are ellipticals (30/42 or 71%). This is consistent with studies of radio loud and radio quiet type 1 quasars which show that their host galaxies are in general ellipticals. A significant fraction of type 2 quasars (>25/42 or >59%) show clear signatures of morphological disturbance which are in most cases identified with merger/interaction processes. We discuss this in the context of related works on type 2 quasars and powerful radio galaxies. We study in detail the particular case of the radio quiet type 2 quasar SDSS J143027.66-005614.8 at z=0.32 based on VLT, HST and SDSS imaging and spectroscopic data. We discuss the global properties of the object in the context of theoretical and observational studies of galaxy mergers/interactions and their role in the triggering of the nuclear and star formation activities in the most luminous active galaxies.Comment: Accepted for publication in MNRAS. 25 pages, 21 figure

Investigating the impact of quasar-driven outflows on galaxies at redshift 0.3-0.4

We present a detailed study of the kinematics of 19 QSO2s in the range 0.3 10^{8.5}$L$_{\odot}$. We aim at advancing our understanding of the AGN feedback phenomenon by correlating outflow properties with the presence of young stellar populations (YSPs) with ages <100 Myr, the optical morphology and the environment of the galaxies, and the radio luminosity. We characterize the ionized gas kinematics using the [OIII]$\lambda$5007$\r{A}$profiles, through three different outflow detection methods: multi-component parametric and flux-weighted and peak-weighted non-parametric. We detect ionized outflows in 18 QSO2s using the parametric analysis, and in all of them using the non-parametric methods. We find higher outflow masses using the parametric analysis (log M$_{OF}$(M$_{\odot}$)=6.47$\pm$0.50), and larger mass rates and kinetic powers with the flux-weighted non-parametric method (\.M$_{OF}$=4.0$\pm$4.4 M$_{\odot}$yr$^{-1}$and log(\.E$_{kin}$)=41.9$\pm$0.6 erg~s$^{-1}$). However, it is when we use the parametric method and the maximum outflow velocities that we measure the highest outflow mass rates and kinetic energies (23$\pm$35 M$_{\odot}$yr$^{-1}$and 42.9$\pm$0.6 erg s$^{-1}$). We do not find any significant correlation between the outflow properties and the previously mentioned galaxy properties. 4 out of 5 QSO2s without a YS<100 Myr show highly disturbed kinematics, whereas only 5 out of the 14 QSO2s with YSPs show similarly asymmetric [OIII] profiles. This might be indicative of negative feedback. The lack of correlation between the outflow properties and the presence of mergers in different interaction stages might be due to their different dynamical timescales. Lastly, the small radio luminosity range covered by our sample may be impeding the detection of any correlation between radio emission and outflow properties.Comment: 26 pages, 9 figures. Accepted for publication in A&

Galaxy-wide radio-induced feedback in a radio-quiet quasar

We report the discovery of a radio-quiet type 2 quasar (SDSS J165315.06+234943.0 nicknamed the ‘Beetle’ at z = 0.103) with unambiguous evidence for active galactic nucleus (AGN) radio-induced feedback acting across a total extension of ∼46 kpc and up to ∼26 kpc from the AGN. To the best of our knowledge, this is the first radio-quiet system where radio-induced feedback has been securely identified at ≫several kpc from the AGN. The morphological, ionization and kinematic properties of the extended ionized gas are correlated with the radio structures. We find along the radio axis (a) enhancement of the optical line emission at the location of the radio hotspots (b) turbulent gas kinematics (FWHM ∼ 380–470 km s−1) across the entire spatial range circumscribed by them (c) ionization minima for the turbulent gas at the location of the hot spots, (d) high temperature Te ≳ 1.9 × 104 K at the NE hotspot. Turbulent gas is also found far from the radio axis, ∼25 kpc in the perpendicular direction. We propose a scenario in which the radio structures have perforated the interstellar medium of the galaxy and escaped into the circumgalactic medium. While advancing, they have interacted with in situ gas modifying its properties. Our results show that jets of modest power can be the dominant feedback mechanism acting across huge volumes in radio-quiet systems, including highly accreting luminous AGNs, where radiative mode feedback may be expected

Consistency Checking for the Evolution of Cardinality-based Feature Models

International audienceFeature models (FMs) are a widely used approach to specify the commonalities and variability in variable systems and software product lines. Various works have addressed edits to FMs for FM evolution and tool support to ensure consistency of FMs. An important extension to FMs are feature cardinalities and related constraints, as extensively used e.g., when modeling variability of cloud computing environments. Since cardinality-based FMs pose additional complexity, additional support for evolution and consistency checking with respect to feature cardinalities would be desirable, but has not been addressed yet. In this paper, we discuss common cardinality-based FM edits and resulting inconsistencies based on experiences with FMs in cloud domain. We introduce tool-support for automated inconsistency detection and explanation based on an off-the-shelf solver. We demonstrate the feasibility of the approach by an empirical evaluation showing the performance of the tool