On the Hardness of the Strongly Dependent Decision Problem

We present necessary and sufficient conditions for solving the strongly dependent decision (SDD) problem in various distributed systems. Our main contribution is a novel characterization of the SDD problem based on point-set topology. For partially synchronous systems, we show that any algorithm that solves the SDD problem induces a set of executions that is closed with respect to the point-set topology. We also show that the SDD problem is not solvable in the asynchronous system augmented with any arbitrarily strong failure detectors.Comment: Appeared in ICDCN 201

Solving k-Set Agreement with Stable Skeleton Graphs

In this paper we consider the k-set agreement problem in distributed message-passing systems using a round-based approach: Both synchrony of communication and failures are captured just by means of the messages that arrive within a round, resulting in round-by-round communication graphs that can be characterized by simple communication predicates. We introduce the weak communication predicate PSources(k) and show that it is tight for k-set agreement, in the following sense: We (i) prove that there is no algorithm for solving (k-1)-set agreement in systems characterized by PSources(k), and (ii) present a novel distributed algorithm that achieves k-set agreement in runs where PSources(k) holds. Our algorithm uses local approximations of the stable skeleton graph, which reflects the underlying perpetual synchrony of a run. We prove that this approximation is correct in all runs, regardless of the communication predicate, and show that graph-theoretic properties of the stable skeleton graph can be used to solve k-set agreement if PSources(k) holds.Comment: to appear in 16th IEEE Workshop on Dependable Parallel, Distributed and Network-Centric System

Recent advances in the simulation of particle-laden flows

A substantial number of algorithms exists for the simulation of moving particles suspended in fluids. However, finding the best method to address a particular physical problem is often highly non-trivial and depends on the properties of the particles and the involved fluid(s) together. In this report we provide a short overview on a number of existing simulation methods and provide two state of the art examples in more detail. In both cases, the particles are described using a Discrete Element Method (DEM). The DEM solver is usually coupled to a fluid-solver, which can be classified as grid-based or mesh-free (one example for each is given). Fluid solvers feature different resolutions relative to the particle size and separation. First, a multicomponent lattice Boltzmann algorithm (mesh-based and with rather fine resolution) is presented to study the behavior of particle stabilized fluid interfaces and second, a Smoothed Particle Hydrodynamics implementation (mesh-free, meso-scale resolution, similar to the particle size) is introduced to highlight a new player in the field, which is expected to be particularly suited for flows including free surfaces.Comment: 16 pages, 4 figure

Austerity and old-age mortality in England: a longitudinal cross-local area analysis, 2007-2013

Objective: There has been significant concern that austerity measures have negatively impacted health in the UK. We examined whether budgetary reductions in Pension Credit and social care have been associated with recent rises in mortality rates among pensioners aged 85 years and over. Design: Cross-local authority longitudinal study. Setting: Three hundred and twenty-four lower tier local authorities in England. Main outcome measure: Annual percentage changes in mortality rates among pensioners aged 85 years or over. Results: Between 2007 and 2013, each 1% decline in Pension Credit spending (support for low income pensioners) per beneficiary was associated with an increase in 0.68% in old-age mortality (95% CI: 0.41 to 0.95). Each reduction in the number of beneficiaries per 1000 pensioners was associated with an increase in 0.20% (95% CI: 0.15 to 0.24). Each 1% decline in social care spending was associated with a significant rise in old-age mortality (0.08%, 95% CI: 0.0006–0.12) but not after adjusting for Pension Credit spending. Similar patterns were seen in both men and women. Weaker associations observed for those aged 75 to 84 years, and none among those 65 to 74 years. Categories of service expenditure not expected to affect old-age mortality, such as transportation, showed no association. Conclusions: Rising mortality rates among pensioners aged 85 years and over were linked to reductions in spending on income support for poor pensioners and social care. Findings suggest austerity measures in England have affected vulnerable old-age adults

Emission lines and optical continuum in low-luminosity radio galaxies

We present spectroscopic observations of a complete sub-sample of 13 low-luminosity radio galaxies selected from the 2Jy sample. The underlying continuum in these sources is carefully modelled in order to make a much-needed comparison between the emission line and continuum properties of FRIs with those of other classes of radio sources. We find that 5 galaxies in the sample show a measurable UV excess: 2 of the these sources are BL Lacs and in the remaining 3 galaxies we argue that the most likely contributor to the UV excess is a young stellar component. Excluding the BL Lacs, we therefore find that \~30% of the sample show evidence for young stars, which is similar to the results obtained for higher luminosity samples. We compare our results with far-infrared measurements in order to investigate the far-infrared-starburst link. The nature of the optical-radio correlations is investigated in light of this new available data and, in contrast to previous studies, we find that the FRI sources follow the correlations with a similar slope to that found for the FRIIs. Finally, we compare the luminosity of the emission lines in the FRI and BL Lac sources and find a significant difference in the [OIII] line luminosities of the two groups. Our results are discussed in the context of the unified schemes.Comment: 18 pages, 31 figures, MNRAS in press, (all enquiries to Clive Tadhunter ([email protected])

Static solutions from the point of view of comparison geometry

We analyze (the harmonic map representation of) static solutions of the Einstein Equations in dimension three from the point of view of comparison geometry. We find simple monotonic quantities capturing sharply the influence of the Lapse function on the focussing of geodesics. This allows, in particular, a sharp estimation of the Laplacian of the distance function to a given (hyper)-surface. We apply the technique to asymptotically flat solutions with regular and connected horizons and, after a detailed analysis of the distance function to the horizon, we recover the Penrose inequality and the uniqueness of the Schwarzschild solution. The proof of this last result does not require proving conformal flatness at any intermediate step.Comment: 41 page