Solution-free sets for sums of binary forms

In this paper, we obtain quantitative estimates for the asymptotic density of subsets of the integer lattice Z2 that contain only trivial solutions to an additive equation involving binary forms. In the process we develop an analogue of Vinogradov’s mean value theorem applicable to binary forms.

Antipathogenic activity of probiotics against Salmonella Typhimurium and Clostridium difficile in anaerobic batch culture systems: is it due to synergies in probiotic mixtures or the specificity of single strains?

Probiotics are currently being investigated for prevention of infections caused by enteric pathogens. The aim of this in vitro study was to evaluate the influence of three single probiotics: Lactobacillus casei NCIMB 30185 (PXN 37), Lactobacillus acidophilus NCIMB 30184 (PXN 35), Bifidobacterium breve NCIMB 30180 (PXN 25) and a probiotic mixture containing the above strains plus twelve other strains belonging to the Lactobacillus, Bifidobacterium, Lactococcus, Streptococcus and Bacillus genera on the survival of Salmonella Typhimurium and Clostridium difficile using pH-controlled anaerobic batch cultures containing mixed fecal bacteria. Changes in relevant bacterial groups and effects of probiotic addition on survival of the two pathogens were assessed over 24 h. Quantitative analysis of bacterial populations revealed that there was a significant increase in lactobacilli and/or bifidobacteria numbers, depending on probiotic addition, compared with the control (no added probiotic). There was also a significant reduction in S. Typhimurium and C. difficile numbers in the presence of certain probiotics compared with controls. Of the probiotic treatments, two single strains namely L. casei NCIMB 30185 (PXN 37), and B. breve NCIMB 30180 (PXN 25) were the most potent in reducing the numbers of S. Typhimurium and C. difficile. In addition, the supplementation with probiotics into the systems influenced some fermentations parameters. Acetate was found in the largest concentrations in all vessels and lactate and formate were generally detected in higher amounts in vessels with probiotic addition compared to controls.

Analytical and numerical solutions describing the inward solidification of a binary melt

We present a mathematical model describing the inward solidification of a slab, a circular cylinder and a sphere of binary melt kept below its equilibrium freezing temperature. The thermal and physical properties of the melt and solid are assumed to be identical. An asymptotic method, valid in the limit of large Stefan number is used to decompose the moving boundary problem for a pure substance into a hierarchy of fixed-domain diffusion problems. Approximate, analytical solutions are derived for the inward solidification of a slab and a sphere of a binary melt which are compared with numerical solutions of the unapproximated system. The solutions are found to agree within the appropriate asymptotic regime of large Stefan number and small time. Numerical solutions are used to demonstrate the dependence of the solidification process upon the level of impurity and other parameters. We conclude with a discussion of the solutions obtained, their stability and possible extensions and refinements of our study.

Problems with binary pattern measures for flood model evaluation

As the calibration and evaluation of flood inundation models are a prerequisite for their successful application, there is a clear need to ensure that the performance measures that quantify how well models match the available observations are fit for purpose. This paper evaluates the binary pattern performance measures that are frequently used to compare flood inundation models with observations of flood extent. This evaluation considers whether these measures are able to calibrate and evaluate model predictions in a credible and consistent way, i.e. identifying the underlying model behaviour for a number of different purposes such as comparing models of floods of different magnitudes or on different catchments. Through theoretical examples, it is shown that the binary pattern measures are not consistent for floods of different sizes, such that for the same vertical error in water level, a model of a flood of large magnitude appears to perform better than a model of a smaller magnitude flood. Further, the commonly used Critical Success Index (usually referred to as F<2 >) is biased in favour of overprediction of the flood extent, and is also biased towards correctly predicting areas of the domain with smaller topographic gradients. Consequently, it is recommended that future studies consider carefully the implications of reporting conclusions using these performance measures. Additionally, future research should consider whether a more robust and consistent analysis could be achieved by using elevation comparison methods instead.

New RGD-peptide amphiphile mixtures containing a negatively charged diluent

Here, we studied the self-assembly of two peptide amphiphiles, C16-Gly-Gly-Gly-Arg-Gly- Asp (PA 1: C16-GGG-RGD) and C16-Gly-Gly-Gly-Arg-Gly-Asp-Ser (PA 2: C16-GGG-RGDS).We showed that PA 1 and PA 2 self-assemble into nanotapes with an internal bilayer structure. C16 chains were highly interdigitated within the nanotape cores, while the peptide blocks formed water-exposed b-sheets too. PA 1 nanotapes were characterized by one spacing distribution, corresponding to a more regular internal structure than that of PA 2 nanotapes, which presented two different spacing distributions. We showed that it is possible to obtain homogeneous nanotapes in water by co-assembling PA 1 or PA 2 with the negatively charged diluent C16-Glu-Thr-Thr-Glu- Ser (PA 3: C16-ETTES). The homogeneous tapes formed by PA 1–PA 3 or PA 2–PA 3 mixtures presented a structure similar to that observed for the corresponding pure PA 1 or PA 2 nanotapes. The mixed nanotapes, which were able to form a stabilized matrix containing homogeneously distributed cell adhesive RGD groups, represent promising materials for designing new cell adhesion substrates.

The inclusion of forage mixtures in the diet of growing dairy heifers: impacts on digestion, energy utilisation, and methane emissions

Intensive farming focusing on monoculture grass species to maximise forage production has led to a reduction in the extent and diversity of species-rich grasslands. However, plant communities with higher species number (richness) are a potential strategy for more sustainable production and mitigation of greenhouse gas (GHG) emissions. Research has indicated the need to understand opportunities that forage mixtures can offer sustainable ruminant production systems. The objective of the two experiments reported here were to evaluate multiple species forage mixtures in comparison to ryegrass-dominant pasture, when conserved or grazed, on digestion, energy utilisation, N excretion, and methane emissions by growing 10–15 month old heifers. Experiment 1 was a 4 × 4 Latin square design with five week periods. Four forage treatments of: (1) ryegrass (control); permanent pasture with perennial ryegrass (Lolium perenne); (2) clover; a ryegrass:red clover (Trifolium pratense) mixture; (3) trefoil; a ryegrass:birdsfoot trefoil (Lotus corniculatus) mixture; and (4) flowers; a ryegrass:wild flower mixture of predominately sorrel (Rumex acetosa), ox-eye daisy (Leucanthemum vulgare), yarrow (Achillea millefolium), knapweed (Centaurea nigra) and ribwort plantain (Plantago lanceolata), were fed as haylages to four dairy heifers. Measurements included digestibility, N excretion, and energy utilisation (including methane emissions measured in respiration chambers). Experiment 2 used 12 different dairy heifers grazing three of the same forage treatments used to make haylage in experiment 1 (ryegrass, clover and flowers) and methane emissions were estimated using the sulphur hexafluoride (SF6) tracer technique. Distribution of ryegrass to other species (dry matter (DM) basis) was approximately 70:30 (clover), 80:20 (trefoil), and 40:60 (flowers) for experiment 1. During the first and second grazing rotations (respectively) in experiment 2, perennial ryegrass accounted for 95 and 98% of DM in ryegrass, and 84 and 52% of DM in clover, with red clover accounting for almost all of the remainder. In the flowers mixture, perennial ryegrass was 52% of the DM in the first grazing rotation and only 30% in the second, with a variety of other flower species occupying the remainder. Across both experiments, compared to the forage mixtures (clover, trefoil and flowers), ryegrass had a higher crude protein (CP) content (P < 0.001, 187 vs. 115 g kg −1 DM) and DM intake (P < 0.05, 9.0 vs. 8.1 kg day −1). Heifers in experiment 1 fed ryegrass, compared to the forage mixtures, had greater total tract digestibility (g kg −1) of DM (DMD; P < 0.008, 713 vs. 641) and CP (CPD, P < 0.001, 699 vs. 475), and used more intake energy (%) for body tissue deposition (P < 0.05, 2.6 vs. −4.9). For both experiments, heifers fed flowers differed the most compared to the ryegrass control for a number of measurements. Compared to ryegrass, flowers had 40% lower CP content (P < 0.001, 113 vs. 187 g kg −1), 18% lower DMD (P < 0.01, 585 vs. 713 g kg −1), 42% lower CPD (P < 0.001, 407 vs. 699 g kg −1), and 10% lower methane yield (P < 0.05, 22.6 vs. 25.1 g kg −1 DM intake). This study has shown inclusion of flowers in forage mixtures resulted in a lower CP concentration, digestibility and intake. These differences were due in part to sward management and maturity at harvest. Further research is needed to determine how best to exploit the potential environmental benefits of forage mixtures in sustainable ruminant production systems.

Folding of graphene slit like pore walls—a simple method of improving CO2 separation from mixtures with CH4 or N2

We report for the first time a detailed procedure for creating a simulation model of energetically stable, folded graphene-like pores and simulation results of CO2/CH4 and CO2/N2 separation using these structures. We show that folding of graphene structures is a very promising method to improve the separation of CO2 from mixtures with CH4 and N2. The separation properties of the analyzed materials are compared with carbon nanotubes having similar diameters or S/V ratio. The presented results have potential importance in the field of CO2 capture and sequestration.

Multiwalled nanotubes formed by catanionic mixtures of drug amphiphiles

Mixing of oppositely charged amphiphilic molecules (catanionic mixing) offers an attractive strategy to produce morphologies different from those formed by individual molecules. We report here on the use of catanionic mixing of anticancer drug amphiphiles to construct multiwalled nanotubes containing a fixed and high drug loading. We found that the molecular mixing ratio, the solvent composition, the overall drug concentrations, as well as the molecular design of the studied amphiphiles are all important experimental parameters contributing to the tubular morphology. We believe these results demonstrate the remarkable potential that anticancer drugs could offer to self-assemble into discrete nanostructures and also provide important insight into the formation mechanism of nanotubes by catanionic mixtures. Our preliminary animal studies reveal that the CPT nanotubes show significantly prolonged retention time in the tumor site after intratumoral injection.

Effect of azole fungicide mixtures, alternations and dose on azole sensitivity in the wheat pathogen Zymoseptoria tritici

The evolution of fungicide resistance in the cereal pathogen Zymoseptoria tritici, is a serious threat to the sustainability and profitability of wheat production in Europe. Application of azole fungicides has been shown to affect fitness of Z. tritici variants differentially, so it has been hypothesised that combinations of azoles could slow the evolution of resistance. This work was initiated to assess the effects of dose, mixtures and alternations of two azoles on selection for isolates with reduced sensitivity and on disease control. Naturally infected field trials were carried out at six sites across Ireland and the sensitivity of Z. tritici isolates monitored pre- and post-treatment. The azoles epoxiconazole and metconazole were applied as solo products, in alternation with each other and as a pre-formulated mixture. Full and half label doses were tested. The two azoles were partially cross-resistant, with a common azole resistance principal component accounting for 75% of the variation between isolates. Selection for isolates with reduced azole sensitivity was correlated with disease control. Decreased doses were related to decreases in sensitivity but the effect was barely significant (P = 0.1) and control was reduced. Single applications of an active ingredient (a.i.) caused smaller decreases in sensitivity than double applications. Shifts in sensitivity to the a.i. applied to a plot were greater than to the a.i. not applied, and the decrease in sensitivity was greater to the a.i. applied at the second timing. These results confirm the need to mix a.i.s with different modes of action.

Sample size considerations in active-control non-inferiority trials with binary data based on the odds ratio

This paper presents an approximate closed form sample size formula for determining non-inferiority in active-control trials with binary data. We use the odds-ratio as the measure of the relative treatment effect, derive the sample size formula based on the score test and compare it with a second, well-known formula based on the Wald test. Both closed form formulae are compared with simulations based on the likelihood ratio test. Within the range of parameter values investigated, the score test closed form formula is reasonably accurate when non-inferiority margins are based on odds-ratios of about 0.5 or above and when the magnitude of the odds ratio under the alternative hypothesis lies between about 1 and 2.5. The accuracy generally decreases as the odds ratio under the alternative hypothesis moves upwards from 1. As the non-inferiority margin odds ratio decreases from 0.5, the score test closed form formula increasingly overestimates the sample size irrespective of the magnitude of the odds ratio under the alternative hypothesis. The Wald test closed form formula is also reasonably accurate in the cases where the score test closed form formula works well. Outside these scenarios, the Wald test closed form formula can either underestimate or overestimate the sample size, depending on the magnitude of the non-inferiority margin odds ratio and the odds ratio under the alternative hypothesis. Although neither approximation is accurate for all cases, both approaches lead to satisfactory sample size calculation for non-inferiority trials with binary data where the odds ratio is the parameter of interest.

Assessing the carcinogenic potential of low-dose exposures to chemical mixtures in the environment: the challenge ahead

Lifestyle factors are responsible for a considerable portion of cancer incidence worldwide, but credible estimates from the World Health Organization and the International Agency for Research on Cancer (IARC) suggest that the fraction of cancers attributable to toxic environmental exposures is between 7% and 19%. To explore the hypothesis that low-dose exposures to mixtures of chemicals in the environment may be combining to contribute to environmental carcinogenesis, we reviewed 11 hallmark phenotypes of cancer, multiple priority target sites for disruption in each area and prototypical chemical disruptors for all targets, this included dose-response characterizations, evidence of low-dose effects and cross-hallmark effects for all targets and chemicals. In total, 85 examples of chemicals were reviewed for actions on key pathways/mechanisms related to carcinogenesis. Only 15% (13/85) were found to have evidence of a dose-response threshold, whereas 59% (50/85) exerted low-dose effects. No dose-response information was found for the remaining 26% (22/85). Our analysis suggests that the cumulative effects of individual (non-carcinogenic) chemicals acting on different pathways, and a variety of related systems, organs, tissues and cells could plausibly conspire to produce carcinogenic synergies. Additional basic research on carcinogenesis and research focused on low-dose effects of chemical mixtures needs to be rigorously pursued before the merits of this hypothesis can be further advanced. However, the structure of the World Health Organization International Programme on Chemical Safety 'Mode of Action' framework should be revisited as it has inherent weaknesses that are not fully aligned with our current understanding of cancer biology.

The potential for chemical mixtures from the environment to enable the cancer hallmark of sustained proliferative signalling

The aim of this work is to review current knowledge relating the established cancer hallmark, sustained cell proliferation to the existence of chemicals present as low dose mixtures in the environment. Normal cell proliferation is under tight control, i.e. cells respond to a signal to proliferate, and although most cells continue to proliferate into adult life, the multiplication ceases once the stimulatory signal disappears or if the cells are exposed to growth inhibitory signals. Under such circumstances, normal cells remain quiescent until they are stimulated to resume further proliferation. In contrast, tumour cells are unable to halt proliferation, either when subjected to growth inhibitory signals or in the absence of growth stimulatory signals. Environmental chemicals with carcinogenic potential may cause sustained cell proliferation by interfering with some cell proliferation control mechanisms committing cells to an indefinite proliferative span.

Comparative analysis of performance and stability among composite cross populations, variety mixtures and pure lines of winter wheat in organic and conventional cropping systems

This study investigated the effects of increased genetic diversity in winter wheat (Triticum aestivum L.), either from hybridization across genotypes or from physical mixing of lines, on grain yield, grain quality, and yield stability in different cropping environments. Sets of pure lines (no diversity), chosen for high yielding ability or high quality, were compared with line mixtures (intermediate level of diversity), and lines crossed with each other in composite cross populations (CCPn, high diversity). Additional populations containing male sterility genes (CCPms) to increase outcrossing rates were also tested. Grain yield, grain protein content, and protein yield were measured at four sites (two organically-managed and two conventionally-managed) over three years, using seed harvested locally in each preceding year. CCPn and mixtures out-yielded the mean of the parents by 2.4% and 3.6%, respectively. These yield differences were consistent across genetic backgrounds but partly inconsistent across cropping environments and years. Yield stability measured by environmental variance was higher in CCPn and CCPms than the mean of the parents. An index of yield reliability tended to be higher in CCPn, CCPms and mixtures than the mean of the parents. Lin and Binns’ superiority values of yield and protein yield were consistently and significantly lower (i.e. better) in the CCPs than in the mean of the parents, but not different between CCPs and mixtures. However, CCPs showed greater early ground cover and plant height than mixtures. When compared with the (locally non-predictable) best-yielding pure line, CCPs and mixtures exhibited lower mean yield and somewhat lower yield reliability but comparable superiority values. Thus, establishing CCPs from smaller sets of high-performing parent lines might optimize their yielding ability. On the whole, the results demonstrate that using increased within-crop genetic diversity can produce wheat crops with improved yield stability and good yield reliability across variable and unpredictable cropping environments.

To what extent can mutual shifting of folded carbonaceous walls in slit-like pores affect their adsorption properties?

We have performed systematic Monte Carlo studies on the influence of shifting the walls in slit-like systems constructed from folded graphene sheets on their adsorption properties. Specifically, we have analysed the effect on the mechanism of argon adsorption (T = 87 K) and on adsorption and separation of three binary gas mixtures: CO2/N2, CO2/CH4 and CH4/N2 (T = 298 K). The effects of the changes in interlayer distance were also determined. We show that folding of the walls significantly improves the adsorption and separation properties in comparison to ideal slit-like systems. Moreover, we demonstrate that mutual shift of sheets (for small interlayer distances) causes the appearance of small pores between opposite bulges. This causes an increase in vapour adsorption at low pressures. Due to overlapping of interactions with opposite walls causing an increase in adsorption energy, the mutual shift of sheets is also connected with the rise in efficiency of mixtures separation. The effects connected with sheet orientation vanish as the interlayer distance increases.