Complexity of Inconsistency-Tolerant Query Answering in Datalog+/- under Cardinality-Based Repairs

Querying inconsistent ontological knowledge bases is an important problem in practice, for which several inconsistency-tolerant semantics have been proposed. In these semantics, the input database is erroneous, and a repair is a maximally consistent database subset. Different notions of maximality (such as subset and cardinality maximality) have been considered. In this paper, we give a precise picture of the computational complexity of inconsistency-tolerant query answering in a wide range of Datalog+/– languages under the cardinality-based versions of three prominent repair semantic

The IBISCO survey: I. Multiphase discs and winds in the Seyfert galaxy Markarian 509

We present the analysis of the ALMA CO(2 1) emission line and the underlying 1.2mm continuum of Mrk 509 with spatial resolution of similar to 270 pc. This local Seyfert 1.5 galaxy, optically classified as a spheroid, is known to host an ionised disc, a starburst ring, and ionised gas winds on both nuclear (ultra-fast outflows) and galactic scales. From CO(2 1) we estimate a molecular gas reservoir of M-H2 = 1.7 x10(9) M-circle dot, located within a disc of size similar to 5.2 kpc, with M-dyn = (2.0 +/- 1.1) x 10(10) M-circle dot inclined at 44 +/- 10 deg. The molecular gas fraction within the disc is mu(gas) = 5%, consistent with that of local star-forming galaxies with similar stellar mass. The gas kinematics in the nuclear region within r similar to 700 pc, that is only marginally resolved at the current angular resolution, suggests the presence of a warped nuclear disc. Both the presence of a molecular disc with ongoing star formation in a starburst ring, and the signatures of a minor merger, are in agreement with the scenario where galaxy mergers produce gas destabilisation, feeding both star formation and AGN activity. The spatially resolved Toomre Q-parameter across the molecular disc is in the range Q(gas) = 0.5-10, and shows that the disc is marginally unstable across the starburst ring, and stable against fragmentation at nucleus and in a lopsided ring-like structure located inside of the starburst ring. We find complex molecular gas kinematics and significant kinematics perturbations at two locations, one within 300 pc of the nucleus and one 1.4 kpc away close to the region with high Q(gas), that we interpret as molecular winds with velocity v(98) = 200-250 km s(-1). The total molecular outflow rate is in the range 6.4-17.0 M-circle dot yr(-1) for the optically thin and thick cases, respectively. The molecular wind total kinetic energy is consistent with a multiphase momentum-conserving wind driven by the AGN with P-of/P-rad in the range 0.06-0.5. The spatial overlap of the inner molecular wind with the ionised wind, and their similar velocity suggest a cooling sequence within a multiphase wind driven by the AGN. The second outer molecular wind component overlaps with the starburst ring, and its energy is consistent with a supernova-driven wind arising from the starburst ring

NGC 2992: The interplay between the multiphase disk, wind and radio bubbles

We present an analysis of the gas kinematics in NGC 2992, based on VLT/MUSE, ALMA and VLA data, aimed at characterising the disk, the wind and their interplay in the cold molecular and warm ionised phases. CO(2-1) and H$\rm \alpha~$ arise from a multiphase disk with inclination 80 deg and radii 1.5 and 1.8 kpc, respectively. We find that the velocity dispersion of the cold molecular phase is consistent with that of star forming galaxies at the same redshift, except in the inner 600 pc region, and in the region between the cone walls and the disk. This suggests that a disk-wind interaction locally boosts the gas turbulence. We detect a clumpy ionised wind distributed in two wide opening angle ionisation cones reaching scales of 7 kpc. The [O III] wind expands with velocity exceeding -1000 km/s in the inner 600 pc, a factor of 5 larger than the previously reported wind velocity. Based on spatially resolved electron density and ionisation parameter maps, we infer an ionised outflow mass of $M_{\rm of,ion} = (3.2 \pm 0.3) \times \, 10^7 \, M_{\odot}$, and a total ionised outflow rate of $\dot M_{\rm of,ion}=13.5\pm1$ \sfr. We detected clumps of cold molecular gas located above and below the disk reaching maximum projected distances and velocities of 1.7 kpc and 200 km/s, respectively. On these scales, the wind is multiphase, with a fast ionised component and a slower molecular one, and a total mass of $M_{\rm of, ion+mol}= 5.8 \times 10^7 \, M_{\odot}$, of which the molecular component carries the bulk of the mass. The dusty molecular outflowing clumps and the turbulent ionised gas are located at the edges of the radio bubbles, suggesting that the bubbles interact with the surrounding medium through shocks. We detect a dust reservoir co-spatial with the molecular disk, with a cold dust mass $M_{\rm dust} = (4.04 \pm 0.03) \times \, 10^{6} \, M_{\odot}$.Comment: 19 pages, 17 figures, 6 tables; Accepted by A&

On the Complexity of Core, Kernel, and Bargaining Set

Coalitional games are mathematical models suited to analyze scenarios where players can collaborate by forming coalitions in order to obtain higher worths than by acting in isolation. A fundamental problem for coalitional games is to single out the most desirable outcomes in terms of appropriate notions of worth distributions, which are usually called solution concepts. Motivated by the fact that decisions taken by realistic players cannot involve unbounded resources, recent computer science literature reconsidered the definition of such concepts by advocating the relevance of assessing the amount of resources needed for their computation in terms of their computational complexity. By following this avenue of research, the paper provides a complete picture of the complexity issues arising with three prominent solution concepts for coalitional games with transferable utility, namely, the core, the kernel, and the bargaining set, whenever the game worth-function is represented in some reasonable compact form (otherwise, if the worths of all coalitions are explicitly listed, the input sizes are so large that complexity problems are---artificially---trivial). The starting investigation point is the setting of graph games, about which various open questions were stated in the literature. The paper gives an answer to these questions, and in addition provides new insights on the setting, by characterizing the computational complexity of the three concepts in some relevant generalizations and specializations.Comment: 30 pages, 6 figure

Infeasibility Certificates and the Complexity of the Core in Coalitional Games

This paper characterizes the complexity of the core in coalitional games. There are different proposals for representing coalitional games in a compact way, where the worths of coalitions may be computed in polynomial time. In all those frameworks, it was shown that core non-emptiness is a co-NPhard problem. However, for the most general of them, it was left as an open problem whether it belongs to co-NP or it actually is an harder problem. We solve this open problem in a positive way; indeed, we are able to show that, for the case of transferable payoffs, the problem belongs to co-NP for any compact representation of the game where the worths of coalitions may be computed in polynomial time (also, non-deterministic polynomial time), encompassing all previous proposals of this kind. This is proved by showing that games with empty cores have small infeasibility certificates. The picture is completed by looking at coalitional games with non-transferable payoffs. We propose a compact representation based on marginal contribution nets. Also in this case, we are able to settle the precise complexity of core non-emptiness, which turns out to be Σ P 2-complete.

How much navigable is the Web of Linked Data?

Abstract. Millions of RDF links connect data providers on the Web of Linked Data. Here, navigability is a key issue. This poster provides a preliminary quantitative analysis of this fundamental feature.