A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws

In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve random initial data and random flux functions. Based on these results we present an a posteriori error analysis for a numerical approximation of the random entropy admissible solution. For the stochastic discretization, we consider a non-intrusive approach, the Stochastic Collocation method. The spatio-temporal discretization relies on the Runge--Kutta Discontinuous Galerkin method. We derive the a posteriori estimator using continuous reconstructions of the discrete solution. Combined with the relative entropy stability framework this yields computable error bounds for the entire space-stochastic discretization error. The estimator admits a splitting into a stochastic and a deterministic (space-time) part, allowing for a novel residual-based space-stochastic adaptive mesh refinement algorithm. We conclude with various numerical examples investigating the scaling properties of the residuals and illustrating the efficiency of the proposed adaptive algorithm

Molecular and Cellular Basis of Microvascular Perfusion Deficits Induced by Clostridium perfringens and Clostridium septicum

Reduced tissue perfusion leading to tissue ischemia is a central component of the pathogenesis of myonecrosis caused by Clostridium perfringens. The C. perfringens α-toxin has been shown capable of inducing these changes, but its potential synergy with perfringolysin O (θ-toxin) is less well understood. Similarly, Clostridium septicum is a highly virulent causative agent of spontaneous gas gangrene, but its effect on the microcirculation has not been examined. Therefore, the aim of this study was to use intravital microscopy to examine the effects of C. perfringens and C. septicum on the functional microcirculation, coupled with the use of isogenic toxin mutants to elucidate the role of particular toxins in the resultant microvascular perfusion deficits. This study represents the first time this integrated approach has been used in the analysis of the pathological response to clostridial toxins. Culture supernatants from wild-type C. perfringens induced extensive cell death within 30 min, as assessed by in vivo uptake of propidium iodide. Furthermore, significant reductions in capillary perfusion were observed within 60 min. Depletion of either platelets or neutrophils reduced the alteration in perfusion, consistent with a role for these blood-borne cells in obstructing perfusion. In addition, mutation of either the α-toxin or perfringolysin O structural genes attenuated the reduction in perfusion, a process that was reversed by genetic complementation. C. septicum also induced a marked reduction in perfusion, with the degree of microvascular compromise correlating with the level of the C. septicum α-toxin. Together, these data indicate that as a result of its ability to produce α-toxin and perfringolysin O, C. perfringens rapidly induces irreversible cellular injury and a marked reduction in microvascular perfusion. Since C. septicum induces a similar reduction in microvascular perfusion, it is postulated that this function is central to the pathogenesis of clostridial myonecrosis, irrespective of the causative bacterium

Centrally concentrated molecular gas driving galactic-scale ionized gas outflows in star-forming galaxies

We perform a joint analysis of high spatial resolution molecular gas and star-formation rate (SFR) maps in main-sequence star-forming galaxies experiencing galactic-scale outflows of ionized gas. Our aim is to understand the mechanism that determines which galaxies are able to launch these intense winds. We observed CO(1→0) at 1-arcsec resolution with ALMA in 16 edge-on galaxies, which also have 2-arcsec spatial-resolution optical integral field observations from the SAMI Galaxy Survey. Half the galaxies in the sample were previously identified as harbouring intense and large-scale outflows of ionized gas (‘outflow types’) and the rest serve as control galaxies. The data set is complemented by integrated CO(1→0) observations from the IRAM 30-m telescope to probe the total molecular gas reservoirs. We find that the galaxies powering outflows do not possess significantly different global gas fractions or star-formation efficiencies when compared with a control sample. However, the ALMA maps reveal that the molecular gas in the outflow-type galaxies is distributed more centrally than in the control galaxies. For our outflow-type objects, molecular gas and star-formation are largely confined within their inner effective radius (reff), whereas in the control sample, the distribution is more diffuse, extending far beyond reff. We infer that outflows in normal star-forming galaxies may be caused by dynamical mechanisms that drive molecular gas into their central regions, which can result in locally enhanced gas surface density and star-formation

The SAMI Galaxy Survey: Decomposed stellar kinematics of galaxy bulges and disks

We investigate the stellar kinematics of the bulge and disk components in 826 galaxies with a wide range of morphology from the Sydney-AAO Multi-object Integral-field spectroscopy Galaxy Survey. The spatially resolved rotation velocity (V) and velocity dispersion (σ ) of bulge and disk components have been simultaneously estimated using the penalized pixel fitting (PPXF) method with photometrically defined weights for the two components. We introduce a new subroutine of PPXF for dealing with degeneracy in the solutions. We show that the V and σ distributions in each galaxy can be reconstructed using the kinematics and weights of the bulge and disk components. The combination of two distinct components provides a consistent description of the major kinematic features of galaxies over a wide range of morphological types. We present Tully-Fisher and Faber-Jackson relations showing that the galaxy stellar mass scales with both V and σ for both components of all galaxy types. We find a tight Faber-Jackson relation even for the disk component. We show that the bulge and disk components are kinematically distinct: (1) the two components show scaling relations with similar slopes, but different intercepts; (2) the spin parameter λR indicates bulges are pressure-dominated systems and disks are supported by rotation; and (3) the bulge and disk components have, respectively, low and high values in intrinsic ellipticity. Our findings suggest that the relative contributions of the two components explain, at least to first order, the complex kinematic behaviour of galaxies

The SAMI Galaxy Survey: The role of disc fading and progenitor bias in kinematic transitions

We use comparisons between the Sydney-AAO Multi-object Integral Field Spectrograph (SAMI) Galaxy Survey and equilibrium galaxy models to infer the importance of disc fading in the transition of spirals into lenticular (S0) galaxies. The local S0 population has both higher photometric concentration and lower stellar spin than spiral galaxies of comparable mass and we test whether this separation can be accounted for by passive aging alone. We construct a suite of dynamically self-consistent galaxy models, with a bulge, disc, and halo using the galactics code. The dispersion-dominated bulge is given a uniformly old stellar population, while the disc is given a current star formation rate putting it on the main sequence, followed by sudden instantaneous quenching. We then generate mock observables (r-band images, stellar velocity, and dispersion maps) as a function of time since quenching for a range of bulge/total (B/T) mass ratios. The disc fading leads to a decline in measured spin as the bulge contribution becomes more dominant, and also leads to increased concentration. However, the quantitative changes observed after 5 Gyr of disc fading cannot account for all of the observed difference. We see similar results if we instead subdivide our SAMI Galaxy Survey sample by star formation (relative to the main sequence). We use EAGLE simulations to also take into account progenitor bias, using size evolution to infer quenching time. The EAGLE simulations suggest that the progenitors of current passive galaxies typically have slightly higher spin than present day star-forming disc galaxies of the same mass. As a result, progenitor bias moves the data further from the disc fading model scenario, implying that intrinsic dynamical evolution must be important in the transition from star-forming discs to passive discs

The SAMI galaxy survey: Stellar populations of passive spiral galaxies in different environments

We investigate the stellar populations of passive spiral galaxies as a function of mass and environment, using integral field spectroscopy data from the Sydney-AAO Multi-object Integral field spectrograph Galaxy Survey. Our sample consists of 52 cluster passive spirals and 18 group/field passive spirals, as well as a set of S0s used as a control sample. The age and [Z/H] estimated by measuring Lick absorption line strength indices both at the center and within 1Re do not show a significant difference between the cluster and the field/group passive spirals. However, the field/group passive spirals with log(Må/Me)∈10.5 show decreasing [α/Fe] along with stellar mass, which is ∼0.1 dex smaller than that of the cluster passive spirals. We also compare the stellar populations of passive spirals with S0s. In the clusters, we find that passive spirals show slightly younger age and lower [α/Fe] than the S0s over the whole mass range. In the field/group, stellar populations show a similar trend between passive spirals and S0s. In particular, [α/Fe] of the field/group S0s tend to be flattening with increasing mass above log(Må/Me)∈10.5, similar to the field/group passive spirals. We relate the age and [α/Fe] of passive spirals to their mean infall time in phase space; we find a positive correlation, in agreement with the prediction of numerical simulations. We discuss the environmental processes that can explain the observed trends. The results lead us to conclude that the formation of the passive spirals and their transformation into S0s may significantly depend on their environments

The SAMI galaxy survey: Rules of behaviour for spin-ellipticity radial tracks in galaxies

We study the behaviour of the spin-ellipticity radial tracks for 507 galaxies from the Sydney AAO Multiobject Integral Field (SAMI) Galaxy Survey with stellar kinematics out to ≥1.5Re. We advocate for a morpho-dynamical classification of galaxies, relying on spatially resolved photometric and kinematic data. We find the use of spin-ellipticity radial tracks is valuable in identifying substructures within a galaxy, including embedded and counter-rotating discs, that are easily missed in unilateral studies of the photometry alone. Conversely, bars are rarely apparent in the stellar kinematics but are readily identified on images. Consequently, we distinguish the spin-ellipticity radial tracks of seven morpho-dynamical types: elliptical, lenticular, early spiral, late spiral, barred spiral, embedded disc, and 2σ galaxies. The importance of probing beyond the inner radii of galaxies is highlighted by the characteristics of galactic features in the spin-ellipticity radial tracks present at larger radii. The density of information presented through spin-ellipticity radial tracks emphasizes a clear advantage to representing galaxies as a track, rather than a single point, in spin-ellipticity parameter space

Association of food security status with overweight and dietary intake: exploration of White British and Pakistani-origin families in the Born in Bradford cohort.

BACKGROUND: Food insecurity has been associated with dietary intake and weight status in UK adults and children although results have been mixed and ethnicity has not been explored. We aimed to compare prevalence and trajectories of weight and dietary intakes among food secure and insecure White British and Pakistani-origin families. METHODS: At 12 months postpartum, mothers in the Born in Bradford cohort completed a questionnaire on food security status and a food frequency questionnaire (FFQ) assessing their child's intake in the previous month; at 18 months postpartum, mothers completed a short-form FFQ assessing dietary intake in the previous 12 months. Weights and heights of mothers and infants were assessed at 12-, 24-, and 36-months postpartum, with an additional measurement of children taken at 4-5 years. Associations between food security status and dietary intakes were assessed using Wilcoxon-Mann-Whitney for continuous variables and χ2 or Fisher's exact tests for categorical variables. Quantile and logistic regression were used to determine dietary intakes adjusting for mother's age. Linear mixed effects models were used to assess longitudinal changes in body mass index (BMI) in mothers and BMI z-scores in children. RESULTS: At 12 months postpartum, White British mothers reported more food insecurity than Pakistani-origin mothers (11% vs 7%; p < 0.01) and more food insecure mothers were overweight. Between 12 and 36 months postpartum, BMI increased more among food insecure Pakistani-origin mothers (β = 0.77 units, [95% Confidence Interval [CI]: 0.40, 1.10]) than food secure (β = 0.44 units, 95% CI: 0.33, 0.55). This was also found in Pakistani-origin children (BMI z-score: food insecure β = 0.40 units, 95% CI: 0.22, 0.59; food secure β = 0.25 units, 95% CI: 0.20, 0.29). No significant increases in BMI were observed for food secure or insecure White British mothers while BMI z-score increased by 0.17 (95% CI: 0.13, 0.21) for food secure White British children. Food insecure mothers and children had dietary intakes of poorer quality, with fewer vegetables and higher consumption of sugar-sweetened drinks. CONCLUSIONS: Food security status is associated with body weight and dietary intakes differentially by ethnicity. These are important considerations for developing targeted interventions

MCMAS: an open-source model checker for the verification of multi-agent systems

We present MCMAS, a model checker for the verification of multi-agent systems. MCMAS supports efficient symbolic techniques for the verification of multi-agent systems against specifications representing temporal, epistemic and strategic properties. We present the underlying semantics of the specification language supported and the algorithms implemented in MCMAS, including its fairness and counterexample generation features. We provide a detailed description of the implementation. We illustrate its use by discussing a number of examples and evaluate its performance by comparing it against other model checkers for multi-agent systems on a common case study

Towards a resolution of some outstanding issues in transitive research: an empirical test on middle childhood

Transitive Inference (deduce B > D from B > C and C > D) can help us to understand other areas of sociocognitive development. Across three experiments, learning, memory, and the validity of two transitive paradigms were investigated. In Experiment 1 (N = 121), 7-year-olds completed a three-term nontraining task or a five-term task requiring extensive-training. Performance was superior on the three-term task. Experiment 2 presented 5–10-year-olds with a new five-term task, increasing learning opportunities without lengthening training (N = 71). Inferences improved, suggesting children can learn five-term series rapidly. Regarding memory, the minor (CD) premise was the best predictor of BD-inferential performance in both task-types. However, tasks exhibited different profiles according to associations between the major (BC) premise and BD inference, correlations between the premises, and the role of age. Experiment 3 (N = 227) helped rule out the possible objection that the above findings simply stemmed from three-term tasks with real objects being easier to solve than computer-tasks. It also confirmed that, unlike for five-term task (Experiments 1 & 2), inferences on three-term tasks improve with age, whether the age range is wide (Experiment 3) or narrow (Experiment 2). I conclude that the tasks indexed different routes within a dual-process conception of transitive reasoning: The five-term tasks indexes Type 1 (associative) processing, and the three-term task indexes Type 2 (analytic) processing. As well as demonstrating that both tasks are perfectly valid, these findings open up opportunities to use transitive tasks for educability, to investigate the role of transitivity in other domains of reasoning, and potentially to benefit the lived experiences of persons with developmental issues