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.

Extended optimal estimation techniques for sea surface temperature from the Spinning Enhanced Visible and Infra-Red Imager (SEVIRI)

Sea surface temperature (SST) can be estimated from day and night observations of the Spinning Enhanced Visible and Infra-Red Imager (SEVIRI) by optimal estimation (OE). We show that exploiting the 8.7 μm channel, in addition to the “traditional” wavelengths of 10.8 and 12.0 μm, improves OE SST retrieval statistics in validation. However, the main benefit is an improvement in the sensitivity of the SST estimate to variability in true SST. In a fair, single-pixel comparison, the 3-channel OE gives better results than the SST estimation technique presently operational within the Ocean and Sea Ice Satellite Application Facility. This operational technique is to use SST retrieval coefficients, followed by a bias-correction step informed by radiative transfer simulation. However, the operational technique has an additional “atmospheric correction smoothing”, which improves its noise performance, and hitherto had no analogue within the OE framework. Here, we propose an analogue to atmospheric correction smoothing, based on the expectation that atmospheric total column water vapour has a longer spatial correlation length scale than SST features. The approach extends the observations input to the OE to include the averaged brightness temperatures (BTs) of nearby clear-sky pixels, in addition to the BTs of the pixel for which SST is being retrieved. The retrieved quantities are then the single-pixel SST and the clear-sky total column water vapour averaged over the vicinity of the pixel. This reduces the noise in the retrieved SST significantly. The robust standard deviation of the new OE SST compared to matched drifting buoys becomes 0.39 K for all data. The smoothed OE gives SST sensitivity of 98% on average. This means that diurnal temperature variability and ocean frontal gradients are more faithfully estimated, and that the influence of the prior SST used is minimal (2%). This benefit is not available using traditional atmospheric correction smoothing.

Temperature-dependent reduction pathways of complexes fac-[Re(CO)3(N-R-imidazole)(1,10-phenanthroline)]+ (R = H, CH3)

Peculiar reduction pathways of the complexes fac-[Re(imH)(CO)3(phen)]+ and fac-[Re(imCH3)(CO)3(phen)]+ (imH = imidazole, imCH3 = N-methylimidazole and phen = 1,10-phenanthroline) have been unravelled by performing combined cyclic voltammetric and in situ IR spectroelectrochemical experiments. In the temperature range of 293–233 K, the initial reduction of the phen ligand in [Re(imH)(CO)3(phen)]+ results in irreversible conversion of the imidazole ligand to 3-imidazolate by a rapid phen•−→ imH intramolecular electron transfer coupled with N H bond cleavage. This process is followed by second phen-localized 1e− reduction producing [ReI(3-im−)(CO)3(phen•−)]−, similar to the analogous 2,2'-bipyridine complex. In contrast to the bpy analogue, the stability of the phen•−-containing complexes is significantly affected by lowering the temperature. At 233 K, a secondary reaction occurs in both [Re(3-im−)(CO)3(phen•−)]− and [Re(imCH3)(CO)3(phen•−)]. The resulting products exhibit v(CO) wavenumbers indistinguishable from those of the parent phen•− complexes; however, their oxidation occurs at a considerably more positive electrode potential. It is proposed that these species are produced by a new C C bond formation between the C(2) site of 3-im− or imCH3 and the C(2) site of the phen•−ligand.

Investigating flavonoids as molecular templates for the design of small-molecule inhibitors of cell signaling

Epidemiological and clinical trials reveal compelling evidence for the ability of dietary flavonoids to lower cardiovascular disease risk. The mechanisms of action of these polyphenolic compounds are diverse, and of particular interest is their ability to function as protein and lipid kinase inhibitors. We have previously described structure-activity studies that reinforce the possibility for using flavonoid structures as templates for drug design. In the present study, we aim to begin constructing rational screening strategies for exploiting these compounds as templates for the design of clinically relevant, antiplatelet agents. We used the platelet as a model system to dissect the structural influence of flavonoids, stilbenes, anthocyanidins, and phenolic acids on inhibition of cell signaling and function. Functional groups identified as relevant for potent inhibition of platelet function included at least 2 benzene rings, a hydroxylated B ring, a planar C ring, a C ring ketone group, and a C-2 positioned B ring. Hydroxylation of the B ring with either a catechol group or a single C-4' hydroxyl may be required for efficient inhibition of collagen-stimulated tyrosine phosphorylated proteins of 125 to 130 kDa, but may not be necessary for that of phosphotyrosine proteins at approximately 29 kDa. The removal of the C ring C-3 hydroxyl together with a hydroxylated B ring (apigenin) may confer selectivity for 37 to 38 kDa phosphotyrosine proteins. We conclude that this study may form the basis for construction of maps of flavonoid inhibitory activity on kinase targets that may allow a multitargeted therapeutic approach with analogue counterparts and parent compounds.

The climate and biomes of Europe at 6000 yr BP: comparison of model simulations and pollen-based reconstructions

14C-dated pollen and lake-level data from Europe are used to assess the spatial patterns of climate change between 6000 yr BP and present, as simulated by the NCAR CCM1 (National Center for Atmospheric Research, Community Climate Model, version 1) in response to the change in the Earth’s orbital parameters during this perod. First, reconstructed 6000 yr BP values of bioclimate variables obtained from pollen and lake-level data with the constrained-analogue technique are compared with simulated values. Then a 6000 yr BP biome map obtained from pollen data with an objective biome reconstruction (biomization) technique is compared with BIOME model results derived from the same simulation. Data and simulations agree in some features: warmer-than-present growing seasons in N and C Europe allowed forests to extend further north and to higher elevations than today, and warmer winters in C and E Europe prevented boreal conifers from spreading west. More generally, however, the agreement is poor. Predominantly deciduous forest types in Fennoscandia imply warmer winters than the model allows. The model fails to simulate winters cold enough, or summers wet enough, to allow temperate deciduous forests their former extended distribution in S Europe, and it incorrectly simulates a much expanded area of steppe vegetation in SE Europe. Similar errors have also been noted in numerous 6000 yr BP simulations with prescribed modern sea surface temperatures. These errors are evidently not resolved by the inclusion of interactive sea-surface conditions in the CCM1. Accurate representation of mid-Holocene climates in Europe may require the inclusion of dynamical ocean–atmosphere and/or vegetation–atmosphere interactions that most palaeoclimate model simulations have so far disregarded.

Salt forms of Amides: protonation and polymorphism of Carbamazepine and Cytenamide

In situ generation of HCl or HBr in alcohol leads to O-protonation of the amide group of carbamazepine. Six salt phases have been produced using this method and their crystal structures determined by single crystal diffraction. A new polymorph of carbamazepine hydrochloride is described as are two polymorphs of carbamazepine hydrobromide. All are protonated at the amide O atom to give RC(OH)NH2 cations. Prolonged exposure to air results in addition of water to the solid salt forms. Such hydration of carbamazepine hydrobromide simply gives a monohydrated phase, but similar treatment of the equivalent hydrochloride results in partial loss of HCl and the transfer of the remaining proton from the amide group to water to give [carbamazepine][H3O]0.5[Cl]0.5·H2O. A similar hydronium chloride species is the only product isolated after reaction of the carbamazepine analogue cytenamide with HCl generated in methanol.

Addition of different fats to a carbohydrate food: impact on gastric emptying, glycaemic and satiety responses and comparison with in vitro digestion

In vitro, the addition of lipids to a carbohydrate food has been found to increase the digestibility of starch. In contrast, in vivo studies have shown that the addition of fat to a food can reduce the glycaemic response (GR). The aim of this study was to assess if delayed gastric emptying (GE) causes reduced GR with the addition of lipids to a carbohydrate food and if a relationship between GR and in vitro digestion of starch exists for high fat foods. Ten healthy volunteers were tested on five occasions after consuming pancakes containing 50 g of available carbohydrate and 202 kcal of sunflower oil, olive oil, butter, medium chain triglyceride (MCT) oil or a control containing no oil. GR was measured using fingerpick blood samples, satiety using visual analogue scales and GE using the 13C octanoic acid breath test. There was a significant difference in GR between the different pancake breakfasts (p = 0.05). The highest GR was observed following the control pancakes and the lowest following the olive oil pancakes. There were significant differences in GE half time, lag phase and ascension time (p < 0.05) between the different pancakes with the control pancakes having the shortest GE time and the MCT pancakes the longest. There was a significant difference in satiety parameters fullness (p = 0.003) and prospective consumption (p = 0.050), with satiety being lowest following the control pancakes. There was a significant inverse correlation between the GR and all satiety parameters. A significant inverse correlation (p = 0.009) was also observed between the digestibility of starch in vitro and GR in vivo. The paper indicates that the digestibility of starch in vitro does not predict the GR for high fat containing foods

The climate of Europe 6000 years ago

Palaeoclimates across Europe for 6000 y BP were estimated from pollen data using the modern pollen analogue technique constrained with lake-level data. The constraint consists of restricting the set of modern pollen samples considered as analogues of the fossil samples to those locations where the implied change in annual precipitation minus evapotranspiration (P–E) is consistent with the regional change in moisture balance as indicated by lakes. An artificial neural network was used for the spatial interpolation of lake-level changes to the pollen sites, and for mapping palaeoclimate anomalies. The climate variables reconstructed were mean temperature of the coldest month (T c ), growing degree days above 5  °C (GDD), moisture availability expressed as the ratio of actual to equilibrium evapotranspiration (α), and P–E. The constraint improved the spatial coherency of the reconstructed palaeoclimate anomalies, especially for P–E. The reconstructions indicate clear spatial and seasonal patterns of Holocene climate change, which can provide a quantitative benchmark for the evaluation of palaeoclimate model simulations. Winter temperatures (T c ) were 1–3 K greater than present in the far N and NE of Europe, but 2–4 K less than present in the Mediterranean region. Summer warmth (GDD) was greater than present in NW Europe (by 400–800 K day at the highest elevations) and in the Alps, but >400 K day less than present at lower elevations in S Europe. P–E was 50–250 mm less than present in NW Europe and the Alps, but α was 10–15% greater than present in S Europe and P–E was 50–200 mm greater than present in S and E Europe.

Risk-taking and inhibitory control in behaviourally inhibited and disinhibited preschool children

The temperament style Behavioural Inhibition (BI) has been implicated as a risk factor for the development of internalising disorders such as anxiety. Of interest is what factors influence the developmental trajectories of both inhibited and disinhibited children and the development of psychopathology. One such factor is risk-taking behaviour. Using the computer based Balloon Analogue Risk Task, we assessed risk taking behaviour in behaviourally inhibited (n = 27) and behaviourally disinhibited (n = 43) children. This is the first study to examine the relationship between BI, executive functioning and risk-taking. The results indicated Behavioural Inhibition was not related to risk-taking but that inhibitory control predicted reward focused results. These findings illustrate how inhibitory control affects risk-taking and risk avoidance in both inhibited and disinhibited children.

Dyspnea-related cues engage the prefrontal cortex - evidence from functional brain imaging in COPD

Dyspnea is the major source of disability in chronic obstructive pulmonary disease (COPD). In COPD, environmental cues (e.g. the prospect of having to climb stairs) become associated with dyspnea, and may trigger dyspnea even before physical activity commences. We hypothesised that brain activation relating to such cues would be different between COPD patients and healthy controls, reflecting greater engagement of emotional mechanisms in patients. Methods: Using FMRI, we investigated brain responses to dyspnea-related word cues in 41 COPD patients and 40 healthy age-matched controls. We combined these findings with scores of self-report questionnaires thus linking the FMRI task with clinically relevant measures. This approach was adapted from studies in pain that enables identification of brain networks responsible for pain processing despite absence of a physical challenge. Results: COPD patients demonstrate activation in the medial prefrontal cortex (mPFC), and anterior cingulate cortex (ACC) which correlated with the visual analogue scale (VAS) response to word cues. This activity independently correlated with patient-reported questionnaires of depression, fatigue and dyspnea vigilance. Activation in the anterior insula, lateral prefrontal cortex (lPFC) and precuneus correlated with the VAS dyspnea scale but not the questionnaires. Conclusions: Our findings suggest that engagement of the brain's emotional circuitry is important for interpretation of dyspnea-related cues in COPD, and is influenced by depression, fatigue, and vigilance. A heightened response to salient cues is associated with increased symptom perception in chronic pain and asthma, and our findings suggest such mechanisms may be relevant in COPD.

Human versus animal: contrasting decomposition dynamics of mammalian analogues in experimental taphonomy

Taphonomic studies regularly employ animal analogues for human decomposition due to ethical restrictions relating to the use of human tissue. However, the validity of using animal analogues in soil decomposition studies is still questioned. This study compared the decomposition of skeletal muscle tissues (SMTs) from human (Homo sapiens), pork (Sus scrofa), beef (Bos taurus), and lamb (Ovis aries) interred in soil microcosms. Fixed interval samples were collected from the SMT for microbial activity and mass tissue loss determination; samples were also taken from the underlying soil for pH, electrical conductivity, and nutrient (potassium, phosphate, ammonium, and nitrate) analysis. The overall patterns of nutrient fluxes and chemical changes in nonhuman SMT and the underlying soil followed that of human SMT. Ovine tissue was the most similar to human tissue in many of the measured parameters. Although no single analogue was a precise predictor of human decomposition in soil, all models offered close approximations in decomposition dynamics.

Predicting fatty acid profiles in blood based on food intake and the FADS1 rs174546 SNP

SCOPE: A high intake of n-3 PUFA provides health benefits via changes in the n-6/n-3 ratio in blood. In addition to such dietary PUFAs, variants in the fatty acid desaturase 1 (FADS1) gene are also associated with altered PUFA profiles. METHODS AND RESULTS: We used mathematical modelling to predict levels of PUFA in whole blood, based on MHT and bolasso selected food items, anthropometric and lifestyle factors, and the rs174546 genotypes in FADS1 from 1,607 participants (Food4Me Study). The models were developed using data from the first reported time point (training set) and their predictive power was evaluated using data from the last reported time point (test set). Amongst other food items, fish, pizza, chicken and cereals were identified as being associated with the PUFA profiles. Using these food items and the rs174546 genotypes as predictors, models explained 26% to 43% of the variability in PUFA concentrations in the training set and 22% to 33% in the test set. CONCLUSIONS: Selecting food items using MHT is a valuable contribution to determine predictors, as our models' predictive power is higher compared to analogue studies. As unique feature, we additionally confirmed our models' power based on a test set.

The grass-free lawn: floral performance and management implications

Grass lawns are a ubiquitous feature of urban green-space throughout much of the temperate world. Species poor and intensively managed, lawns are ecologically impoverished, however environmentally aware lawn owners are reluctant to implement alternatives due to aesthetic concerns. Developing an alternative lawn format which is both biodiversity friendly and aesthetically pleasing is an imperative for urban greening. We suggest that such an alternative can be provided by replacing the grass lawn by a forb-based mix. To advance this, we tested the floral performance of three groups of clonal perennial forbs (native, non-native and mixed), each maintained using standard lawn management mowing regimes. Our findings show that both the frequency of mowing and the height at which mowing is applied influence floral performance and lawn aesthetics. Species origin was found to influence floral productivity, floral visibility and floral variety within grass-free lawns, with native species providing the greatest floral performance. The behaviour and management of grass lawns was not found to be a suitable analogue for the management of grass-free lawns and grass-free lawns are sufficiently different from grass lawns to require an entirely original management approach. We suggest that the grass-free lawn can provide an aesthetically and environmentally relevant replacement for the ubiquitous and ecologically-poor grass lawn.

Generalised golden ratios over integer alphabets

It is a well known result that for β ∈ (1,1+√52) and x ∈ (0,1β−1) there exists uncountably many (ǫi)∞i=1 ∈ {0,1}N such that x = P∞i=1ǫiβ−i. When β ∈ (1+√52,2] there exists x ∈ (0,1β−1) for which there exists a unique (ǫi)∞i=1 ∈ {0,1}N such that x=P∞i=1ǫiβ−i. In this paper we consider the more general case when our sequences are elements of {0, . . . , m}N. We show that an analogue of the golden ratio exists and give an explicit formula for it.

The new Hollywood, 1981–1999: special/visual effects

The emergence and development of digital imaging technologies and their impact on mainstream filmmaking is perhaps the most familiar special effects narrative associated with the years 1981-1999. This is in part because some of the questions raised by the rise of the digital still concern us now, but also because key milestone films showcasing advancements in digital imaging technologies appear in this period, including Tron (1982) and its computer generated image elements, the digital morphing in The Abyss (1989) and Terminator 2: Judgment Day (1991), computer animation in Jurassic Park (1993) and Toy Story (1995), digital extras in Titanic (1997), and ‘bullet time’ in The Matrix (1999). As a result it is tempting to characterize 1981-1999 as a ‘transitional period’ in which digital imaging processes grow in prominence and technical sophistication, and what we might call ‘analogue’ special effects processes correspondingly become less common. But such a narrative risks eliding the other practices that also shape effects sequences in this period. Indeed, the 1980s and 1990s are striking for the diverse range of effects practices in evidence in both big budget films and lower budget productions, and for the extent to which analogue practices persist independently of or alongside digital effects work in a range of production and genre contexts. The chapter seeks to document and celebrate this diversity and plurality, this sustaining of earlier traditions of effects practice alongside newer processes, this experimentation with materials and technologies old and new in the service of aesthetic aspirations alongside budgetary and technical constraints. The common characterization of the period as a series of rapid transformations in production workflows, practices and technologies will be interrogated in relation to the persistence of certain key figures as Douglas Trumbull, John Dykstra, and James Cameron, but also through a consideration of the contexts for and influences on creative decision-making. Comparative analyses of the processes used to articulate bodies, space and scale in effects sequences drawn from different generic sites of special effects work, including science fiction, fantasy, and horror, will provide a further frame for the chapter’s mapping of the commonalities and specificities, continuities and variations in effects practices across the period. In the process, the chapter seeks to reclaim analogue processes’ contribution both to moments of explicit spectacle, and to diegetic verisimilitude, in the decades most often associated with the digital’s ‘arrival’.