Generalized bisimulation metrics

International audienceThe pseudometric based on the Kantorovich lifting is one of the most popular notion of distance between probabilistic processes proposed in the literature. However, its application in verification is limited to linear properties. We propose a generalization which allows to deal with a wider class of properties, such as those used in security and privacy. More precisely, we propose a family of pseudometrics, parametrized on a notion of distance which depends on the property we want to verify. Furthermore, we show that the members of this family still characterize bisimilarity in terms of their kernel, and provide a bound on the corresponding distance between trace distributions. Finally, we study the instance corresponding to differential privacy, and we show that it has a dual form, easier to compute. We also prove that the typical process-algebra constructs are non-expansive, thus paving the way to a modular approach to verification

Approximating a Behavioural Pseudometric without Discount for<br> Probabilistic Systems

Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of behavioural pseudometrics for probabilistic transition systems. These pseudometrics are a quantitative analogue of probabilistic bisimilarity. Distance zero captures probabilistic bisimilarity. Each pseudometric has a discount factor, a real number in the interval (0, 1]. The smaller the discount factor, the more the future is discounted. If the discount factor is one, then the future is not discounted at all. Desharnais et al. showed that the behavioural distances can be calculated up to any desired degree of accuracy if the discount factor is smaller than one. In this paper, we show that the distances can also be approximated if the future is not discounted. A key ingredient of our algorithm is Tarski's decision procedure for the first order theory over real closed fields. By exploiting the Kantorovich-Rubinstein duality theorem we can restrict to the existential fragment for which more efficient decision procedures exist

HST images and properties of the most distant radio galaxies

We present Hubble Space Telescope images of 11 high redshift radio galaxies (between $z=2.3$ and $z=3.6$). The galaxies were observed with the WFPC2 camera in a broad band filter (F606W or F707W, roughly equivalent to V or R-band), for 2 orbits each. We find that on the scale of the HST observations there is a wide variety of morphological structures of the hosting galaxies: most objects have a clumpy, irregular appearance, consisting of a bright nucleus and a number of smaller components, suggestive of merging systems. Some observed structures could be due (at least partly) to the presence of dust distributed through the galaxies. The UV continuum emission is generally elongated and aligned with the axis of the radio sources, however the characteristics of the ``alignment effect'' differ from case to case, suggesting that the phenomenon cannot be explained by a single physical mechanism. We compare the properties of our radio galaxies with those of the UV dropout galaxies and conclude that (i) the most massive radio galaxies may well evolve from an aggregate of UV dropout galaxies and (ii) high redshift radio galaxies probably evolve into present day brightest cluster galaxies.Comment: 22 pages, 30 figures, accepted by A&

Radiative Shock-Induced Collapse of Intergalactic Clouds

Accumulating observational evidence for a number of radio galaxies suggests an association between their jets and regions of active star formation. The standard picture is that shocks generated by the jet propagate through an inhomogeneous medium and trigger the collapse of overdense clouds, which then become active star-forming regions. In this contribution, we report on recent hydrodynamic simulations of radiative shock-cloud interactions using two different cooling models: an equilibrium cooling-curve model assuming solar metallicities and a non-equilibrium chemistry model appropriate for primordial gas clouds. We consider a range of initial cloud densities and shock speeds in order to quantify the role of cooling in the evolution. Our results indicate that for moderate cloud densities (>1 cm^{-3}) and shock Mach numbers (<20), cooling processes can be highly efficient and result in more than 50% of the initial cloud mass cooling to below 100 K. We also use our results to estimate the final H_2 mass fraction for the simulations that use the non-equilibrium chemistry package. This is an important measurement, since H_2 is the dominant coolant for a primordial gas cloud. We find peak H_2 mass fractions of >0.01 and total H_2 mass fractions of >10^{-5} for the cloud gas. Finally, we compare our results with the observations of jet-induced star formation in ``Minkowski's Object.'' We conclude that its morphology, star formation rate (~ 0.3M_solar/yr) and stellar mass (~ 1.2 x 10^7 M_solar) can be explained by the interaction of a 90,000 km/s jet with an ensemble of moderately dense (~ 10 cm^{-3}), warm (10^4 K) intergalactic clouds in the vicinity of its associated radio galaxy at the center of the galaxy cluster.Comment: 30 pages, 7 figures, submitted to Astrophysical Journa

Magnetic Fields in the 3C 129 Cluster

We present multi-frequency VLA observations of the two radio galaxies 3C 129 and 3C 129.1 embedded in a luminous X-ray cluster. These radio observations reveal a substantial difference in the Faraday Rotation Measures (RMs) toward 3C 129.1 at the cluster center and 3C 129 at the cluster periphery. After deriving the density profile from available X-ray data, we find that the RM structure of both radio galaxies can be fit by a tangled cluster magnetic field with strength 6 microGauss extending at least 3 core radii (450 kpc) from the cluster center. The magnetic field makes up a small contribution to the total pressure (5%) in the central regions of the cluster. The radio morphology of 3C 129.1 appears disturbed on the southern side, perhaps by the higher pressure environment. In contrast with earlier claims for the presence of a moderately strong cooling flow in the 3C 129 cluster, our analysis of the X-ray data places a limit on the mass deposition rate from any such flow of <1.2 Msun/yr.Comment: in press at MNRA