Operator systems from discrete groups

We express various sets of quantum correlations studied in the theoretical physics literature in terms of different tensor products of operator systems of discrete groups. We thus recover earlier results of Tsirelson and formulate a new approach for the study of quantum correlations. To do this we formulate a general framework for the study of operator systems arising from discrete groups. We study in detail the operator system of the free group Fn on n generators, as well as the operator systems of the free products of finitely many copies of the two-element group Z2. We examine various tensor products of group operator systems, including the minimal, the maximal, and the commuting tensor products. We introduce a new tensor product in the category of operator systems and formulate necessary and sufficient conditions for its equality to the commuting tensor product in the case of group operator systems.

Perceptual Watermarking for Discrete Shearlet Transform

This paper presents a new perceptual watermarking model for Discrete Shearlet transform (DST). DST provides the optimal representation [10] of the image features based on multi-resolution and multi-directional analysis. This property can be exploited on for watermark embedding to achieve the watermarking imperceptibility by introducing the human visual system using Chou’s model. In this model, a spatial JND profile is adapted to fit the sub-band structure. The combination of DST and the Just-Noticeable Distortion (JND) profile improves the levels of robustness against certain attacks while minimizing the distortion; by assigning a visibility threshold of distortion to each DST sub-band coefficient in the case of grey scale image watermarking.

On the complexity of solving polytree-shaped limited memory influence diagrams with binary variables

Influence diagrams are intuitive and concise representations of structured decision problems. When the problem is non-Markovian, an optimal strategy can be exponentially large in the size of the diagram. We can avoid the inherent intractability by constraining the size of admissible strategies, giving rise to limited memory influence diagrams. A valuable question is then how small do strategies need to be to enable efficient optimal planning. Arguably, the smallest strategies one can conceive simply prescribe an action for each time step, without considering past decisions or observations. Previous work has shown that finding such optimal strategies even for polytree-shaped diagrams with ternary variables and a single value node is NP-hard, but the case of binary variables was left open. In this paper we address such a case, by first noting that optimal strategies can be obtained in polynomial time for polytree-shaped diagrams with binary variables and a single value node. We then show that the same problem is NP-hard if the diagram has multiple value nodes. These two results close the fixed-parameter complexity analysis of optimal strategy selection in influence diagrams parametrized by the shape of the diagram, the number of value nodes and the maximum variable cardinality.

Variables to be considered when assessing the photocatalytic destruction of bacterial pathogens

The current study sought to assess the importance of three common variables on the outcome of TiO₂ photocatalysis experiments with bacteria. Factors considered were (a) ability of test species to withstand osmotic pressure, (b) incubation period of agar plates used for colony counts following photocatalysis and (c) chemical nature of suspension medium used for bacteria and TiO₂. Staphylococcus aureus, Escherichia coli, Salmonella ser. Typhimurium and Pseudomonas aeruginosa were found to vary greatly in their ability to withstand osmotic pressure, raising the possibility that osmotic lysis may be contributing to loss of viability in some photocatalytic disinfection studies. Agar plate incubation time was also found to influence results, as bacteria treated with UV light only grew more slowly than those treated with a combination of UV and TiO_2. The chemical nature of the suspension medium used was found to have a particularly pronounced effect upon results. Greatest antibacterial activity was detected when aqueous sodium chloride solution was utilised, with ∼1 × 10⁶ CFU mL^-1 S. aureus being completely killed after 60 min. Moderate activity was observed when distilled water was employed with bacteria being killed after 2 h and 30 min, and no antibacterial activity at all was detected when aqueous tryptone solution was used. Interestingly, the antibacterial activity of UV light on its own appeared to be very much reduced in experiments where aqueous sodium chloride was employed instead of distilled water. 

Deriving meteorological variables across Africa for the study and control of vector-borne disease:a comparison of remote sensing and spatial interpolation of climate

This paper presents the results of an investigation into the utility of remote sensing (RS) using meteorological satellites sensors and spatial interpolation (SI) of data from meteorological stations, for the prediction of spatial variation in monthly climate across continental Africa in 1990. Information from the Advanced Very High Resolution Radiometer (AVHRR) of the National Oceanic and Atmospheric Administration's (NOAA) polar-orbiting meteorological satellites was used to estimate land surface temperature (LST) and atmospheric moisture. Cold cloud duration (CCD) data derived from the High Resolution Radiometer (HRR) onboard the European Meteorological Satellite programme's (EUMETSAT) Meteosat satellite series were also used as a RS proxy measurement of rainfall. Temperature, atmospheric moisture and rainfall surfaces were independently derived from SI of measurements from the World Meteorological Organization (WMO) member stations of Africa. These meteorological station data were then used to test the accuracy of each methodology, so that the appropriateness of the two techniques for epidemiological research could be compared. SI was a more accurate predictor of temperature, whereas RS provided a better surrogate for rainfall; both were equally accurate at predicting atmospheric moisture. The implications of these results for mapping short and long-term climate change and hence their potential for the study anti control of disease vectors are considered. Taking into account logistic and analytical problems, there were no clear conclusions regarding the optimality of either technique, but there was considerable potential for synergy.

Discrete cyclic di-GMP-dependent control of bacterial predation versus axenic growth in Bdellovibrio bacteriovorus

Bdellovibrio bacteriovorus is a Delta-proteobacterium that oscillates between free-living growth and predation on Gram-negative bacteria including important pathogens of man, animals and plants. After entering the prey periplasm, killing the prey and replicating inside the prey bdelloplast, several motile B. bacteriovorus progeny cells emerge. The B. bacteriovorus HD100 genome encodes numerous proteins predicted to be involved in signalling via the secondary messenger cyclic di-GMP (c-di-GMP), which is known to affect bacterial lifestyle choices. We investigated the role of c-di-GMP signalling in B. bacteriovorus, focussing on the five GGDEF domain proteins that are predicted to function as diguanylyl cyclases initiating c-di-GMP signalling cascades. Inactivation of individual GGDEF domain genes resulted in remarkably distinct phenotypes. Deletion of dgcB (Bd0742) resulted in a predation impaired, obligately axenic mutant, while deletion of dgcC (Bd1434) resulted in the opposite, obligately predatory mutant. Deletion of dgcA (Bd0367) abolished gliding motility, producing bacteria capable of predatory invasion but unable to leave the exhausted prey. Complementation was achieved with wild type dgc genes, but not with GGAAF versions. Deletion of cdgA (Bd3125) substantially slowed predation; this was restored by wild type complementation. Deletion of dgcD (Bd3766) had no observable phenotype. In vitro assays showed that DgcA, DgcB, and DgcC were diguanylyl cyclases. CdgA lacks enzymatic activity but functions as a c-di-GMP receptor apparently in the DgcB pathway. Activity of DgcD was not detected. Deletion of DgcA strongly decreased the extractable c-di-GMP content of axenic Bdellovibrio cells. We show that c-di-GMP signalling pathways are essential for both the free-living and predatory lifestyles of B. bacteriovorus and that obligately predatory dgcC- can be made lacking a propensity to survive without predation of bacterial pathogens and thus possibly useful in anti-pathogen applications. In contrast to many studies in other bacteria, Bdellovibrio shows specificity and lack of overlap in c-di-GMP signalling pathways.

Optimal design of cold-formed steel portal frames for stressed-skin action using genetic algorithm

This paper describes a stressed-skin diaphragm approach to the optimal design of the internal frame of a cold-formed steel portal framing system, in conjunction with the effect of semi-rigid joints. Both ultimate and serviceability limit states are considered. Wind load combinations are included. The designs are optimized using a real-coded niching genetic algorithm, in which both discrete and continuous decision variables are processed. For a building with two internal frames, it is shown that the material cost of the internal frame can be reduced by as much as 53%, compared with a design that ignores stressed-skin action.

The impact of accretion disc winds on the optical spectra of cataclysmic variables

Many high-state non-magnetic cataclysmic variables (CVs) exhibit blueshifted absorption or P-Cygni profiles associated with ultraviolet (UV) resonance lines. These features imply the existence of powerful accretion disc winds in CVs. Here, we use our Monte Carlo ionization and radiative transfer code to investigate whether disc wind models that produce realistic UV line profiles are also likely to generate observationally significant recombination line and continuum emission in the optical waveband. We also test whether outflows may be responsible for the single-peaked emission line profiles often seen in high-state CVs and for the weakness of the Balmer absorption edge (relative to simple models of optically thick accretion discs). We find that a standard disc wind model that is successful in reproducing the UV spectra of CVs also leaves a noticeable imprint on the optical spectrum, particularly for systems viewed at high inclination. The strongest optical wind-formed recombination lines are H alpha and He ii lambda 4686. We demonstrate that a higher density outflow model produces all the expected H and He lines and produces a recombination continuum that can fill in the Balmer jump at high inclinations. This model displays reasonable verisimilitude with the optical spectrum of RW Trianguli. No single-peaked emission is seen, although we observe a narrowing of the double-peaked emission lines from the base of the wind. Finally, we show that even denser models can produce a single-peaked H alpha line. On the basis of our results, we suggest that winds can modify, and perhaps even dominate, the line and continuum emission from CVs.

Optimal design of long-span steel portal frames using fabricated beams

This paper considers the optimal design of fabricated steel beams for long-span portal frames. The design optimisation takes into account ultimate as well as serviceability limit states, adopting deflection limits recommended by the Steel Construction Institute (SCI). Results for three benchmark frames demonstrate the efficiency of the optimisation methodology. A genetic algorithm (GA) was used to optimise the dimensions of the plates used for the columns, rafters and haunches. Discrete decision variables were adopted for the thickness of the steel plates and continuous variables for the breadth and depth of the plates. Strategies were developed to enhance the performance of the GA including solution space reduction and a hybrid initial population half of which is derived using Latin hypercube sampling. The results show that the proposed GA-based optimisation model generates optimal and near-optimal solutions consistently. A parametric study is then conducted on frames of different spans. A significant variation in weight between fabricated and conventional hot-rolled steel portal frames is shown; for a 50 m span frame, a 14–19% saving in weight was achieved. Furthermore, since Universal Beam sections in the UK come from a discrete section library, the results could also provide overall dimensions of other beams that could be more efficient for portal frames. Eurocode 3 was used for illustrative purposes; any alternative code of practice may be used.

Selection of burst-like transients and stochastic variables using multi-brand image differencing in the Pan-STARRS1 Medium Deep Survey

We present a novel method for the light-curve characterization of Pan-STARRS1 Medium Deep Survey (PS1 MDS) extragalactic sources into stochastic variables (SVs) and burst-like (BL) transients, using multi-band image-differencing time-series data. We select detections in difference images associated with galaxy hosts using a star/galaxy catalog extracted from the deep PS1 MDS stacked images, and adopt a maximum a posteriori formulation to model their difference-flux time-series in four Pan-STARRS1 photometric bands gP1, rP1, iP1, and zP1. We use three deterministic light-curve models to fit BL transients; a Gaussian, a Gamma distribution, and an analytic supernova (SN) model, and one stochastic light-curve model, the Ornstein-Uhlenbeck process, in order to fit variability that is characteristic of active galactic nuclei (AGNs). We assess the quality of fit of the models band-wise and source-wise, using their estimated leave-out-one cross-validation likelihoods and corrected Akaike information criteria. We then apply a K-means clustering algorithm on these statistics, to determine the source classification in each band. The final source classification is derived as a combination of the individual filter classifications, resulting in two measures of classification quality, from the averages across the photometric filters of (1) the classifications determined from the closest K-means cluster centers, and (2) the square distances from the clustering centers in the K-means clustering spaces. For a verification set of AGNs and SNe, we show that SV and BL occupy distinct regions in the plane constituted by these measures. We use our clustering method to characterize 4361 extragalactic image difference detected sources, in the first 2.5 yr of the PS1 MDS, into 1529 BL, and 2262 SV, with a purity of 95.00% for AGNs, and 90.97% for SN based on our verification sets. We combine our light-curve classifications with their nuclear or off-nuclear host galaxy offsets, to define a robust photometric sample of 1233 AGNs and 812 SNe. With these two samples, we characterize their variability and host galaxy properties, and identify simple photometric priors that would enable their real-time identification in future wide-field synoptic surveys.