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Female genital schistosomiasis (FGS) is a chronic disease manifestation of the waterborne parasitic infection Schistosoma haematobium that affects up to 56 million women and girls, predominantly in sub-Saharan Africa. Starting from early childhood, this stigmatizing gynaecological condition is caused by the presence of Schistosoma eggs and associated toxins within the genital tract. Schistosoma haematobium typically causes debilitating urogenital symptoms, mostly as a consequence of inflammation, which includes bleeding, discharge and lower abdominal pelvic pain. Chronic complications of FGS include adverse sexual and reproductive health and rights outcomes such as infertility, ectopic pregnancy and miscarriage. FGS is associated with prevalent human immunodeficiency virus and may increase the susceptibility of women to high-risk human papillomavirus infection. Across SSA, and even in clinics outside endemic areas, the lack of awareness and available resources among both healthcare professionals and the public means FGS is underreported, misdiagnosed and inadequately treated. Several studies have highlighted research needs and priorities in FGS, including better training, accessible and accurate diagnostic tools, and treatment guidelines. On 6 September, 2024, LifeArc, the Global Schistosomiasis Alliance and partners from the BILGENSA Research Network (Genital Bilharzia in Southern Africa) convened a consultative, collaborative and translational workshop: ‘Female Genital Schistosomiasis: Translational Challenges and Opportunities’. Its ambition was to identify practical solutions that could address these research needs and drive appropriate actions towards progress in tackling FGS. Here, we present the outcomes of that workshop – a series of discrete translational actions to better galvanize the community and research funders.
This research paper describes a test of association of sire with susceptibility to mastitis, using a custom-bred population of dairy cattle. We hypothesised that sire daughters ranked as more resistant to intramammary infections in their first two lactations would be more resistant to an intramammary challenge in their third lactation. Mastitis phenotypes were generated for a Holstein-Friesian × Jersey crossbred research herd of 864 cows, bred from six defined sires and managed as two cohorts in a seasonal calving system in New Zealand. Naturally occurring new intramammary infections (IMI) and clinical mastitis (CM) were monitored in their first two lactations from herd records, milking staff observations and bacteriology of quarter milk samples collected at four time-points during each lactation. The animals retained to their third lactation were then exposed to a single intramammary challenge with Streptococcus uberis. We used a relative risk (RR) analysis to rank performance of sire daughters for pathogen-specific phenotypes for new IMI and CM, and somatic cell count (SCC) traits, and their clinical outcomes to the challenge. Generally, daughters of sire B had the highest RR for new IMI or CM by a major pathogen, whereas daughters of sires A and C had a consistently lower risk. The RR for sires E, D and F were intermediate and inconsistent across major pathogens. Daughters of sire B ranked highest for all CM cases and SCC traits whereas sires A and C ranked lowest. Following intramammary challenge, daughters of sires A and C were more likely to develop CM, whereas daughters of sire B and F were less likely to develop CM. Thus, the hypothesis was rejected. The results revealed strong associations between sire and pathogen-specific mastitis phenotypes, and validated use of SCC and CM traits in sire selection and breeding programmes to improve mastitis resistance.
Richard Wagner’s musical and prose works are shot through with ideas, imagery, and speculation relating to race. Given the influence of racial theorising on almost every area of nineteenth-century European thought and culture, this is hardly surprising. Yet Wagner did not just absorb theories of race: he actively disseminated them, a fact that remains a troubling, if unavoidable part of his legacy. This chapter provides a selective overview of the history of scientific racism in Europe (especially Germany) from the Enlightenment era to the early twentieth century, focusing on the intersections of racial theory with aesthetics, comparative philology, and religious ideologies, including antisemitism. Special attention is devoted to Arthur de Gobineau’s influence on Wagner’s late essays, and the impact of those writings on the Bayreuth Circle, including Houston Stewart Chamberlain.
To determine the association between blood markers of white matter injury (e.g., serum neurofilament light and phosphorylated neurofilament heavy) and a novel neuroimaging technique measuring microstructural white matter changes (e.g., diffusion kurtosis imaging) in regions (e.g., anterior thalamic radiation and uncinate fasciculus) known to be impacted in traumatic brain injury (TBI) and associated with symptoms common in those with chronic TBI (e.g., sleep disruption, cognitive and emotional disinhibition) in a heterogeneous sample of Veterans and non-Veterans with a history of remote TBI (i.e., >6 months).
Participants and Methods:
Participants with complete imaging and blood data (N=24) were sampled from a larger multisite study of chronic mild-moderate TBI. Participants ranged in age from young to middle-aged (mean age = 34.17, SD age = 10.96, range = 19-58) and primarily male (66.7%). The number of distinct TBIs ranged from 1-5 and the time since most recent TBI ranged from 0-30 years. Scores on a cognitive screener (MoCA) ranged from 22-30 (mean = 26.75). We performed bivariate correlations with mean kurtosis (MK) in the anterior thalamic radiation (ATR; left, right) uncinate fasciculus (UF; left, right), and serum neurofilament light (NFL), and phosphorylated neurofilament heavy (pNFH). Both were log transformed for non-normality. Significance threshold was set at p<0.05.
Results:
pNFH was significantly and negatively correlated to MK in the right (r=-0.446) and left (r=-0.599) UF and right (r=-0.531) and left (r=-0.469) ATR. NFL showed moderate associations with MK in the right (r=-0.345) and left (r=-0.361) UF and little to small association in the right (r=-0.063) and left (r=-0.215) ATR. In post-hoc analyses, MK in both the left (r=0.434) and right (r=0.514) UF was positively associated with performance on a frontally-mediated list-learning task (California Verbal Learning Test, 2nd Edition; Trials 1-5 total).
Conclusions:
Results suggest that serum pNFH may be a more sensitive blood marker of microstructural complexity in white matter regions frequently impacted by TBI in a chronic mild-moderate TBI sample. Further, it suggests that even years after a mild-moderate TBI, levels of pNFH may be informative regarding white matter integrity in regions related to executive functioning and emotional disinhibition, both of which are common presenting problems when these patients are seen in a clinical setting.
To determine the association between in-vivo spectroscopy metabolite data, the local connectome, and markers of initial injury severity (I.e., history of loss of consciousness; LoC) in traumatic brain injury (TBI), in a heterogenous sample of Veterans and non-Veterans with a history of remote mild-to-moderate TBI (I.e., >6 months).
Participants and Methods:
Participants with complete PRESS magnetic resonance spectroscopy (MRS) and diffusion weighted imaging (DWI) data (N = 41) were sampled from a larger multisite study of chronic mild-to-moderate TBI (Nmiid = 38; Nmoderate = 3; 54% with LoC; 46% with multiple TBI). The sample was predominantly male (76%) with ages ranging from 23-59 (M = 36.9, SD = 10.1), with 98% holding at least a high school degree (M = 14.5 years of education, SD = 2.4). Fully tissue-and-relaxation-corrected metabolite concentration estimates in the dorsal anterior cingulate (30x30x30mm voxel) were modeled using Osprey 2.4.0. Total creatine (tCr), total choline (tCho), total N-acetylaspartate (tNAA), glutamate/glutamine (Glx), and myo-inositol (mI) were analyzed. Logistic regression was used to measure the association between metabolites and history of TBI with LoC. Correlational connectometry using the normalized spin distribution function was performed for metabolites associated with LoC, to characterize the local connectome associated with metabolites of interest, controlling for age and sex, and correcting for multiple comparisons (FDR < .050 with 4000 permutations). A profile approach was used to interpret diffusion metrics, contrasting quantitative anisotropy (QA) with fractional anisotropy (FA). Local connectome tracks were then clustered to identify the larger white matter tract.
Results:
Glx (p = .008) and tCr (p = .032) were significantly associated with history of TBI with LoC. Increased Glx was associated with increased QA in 11,001 tracks, accounting for 1.4% of the total white matter tracks in the brain. 90% of tracks were identified in bilateral cingulum (33%), bilateral thalamic (13%), bilateral corticospinal (13%), corpus callosum (12%), left arcuate fasciculus (9%), left frontoparietal aslant tracts (6%), and bilateral inferior fronto-occipital fasciculus (4%) tracts. In contrast, FA was not associated with Glx. The same pattern emerged for tCr, with 10,542 tracks identified predominantly in bilateral cingulum (29%), corpus callosum (21%), bilateral corticospinal (15%), bilateral corticostriatal (7%), bilateral medial lemniscus (7%), left cortico-pontine (3%), left thalamic (2%), and bilateral superior longitudinal fasciculus (2%) tracts. Post-hoc exploratory analyses of mean QA across regions of cingulum found that increased QA was associated with self-report measures of headache intensity, fatigue, and perceived change in executive functioning.
Conclusions:
Results provided evidence that multimodal imaging can identify subtle markers of initial TBI severity years after injury. Neurometabolite concentrations were associated with diffuse changes in the local connectome; the pattern of discrepancy between FA and QA was suggestive of reduced potential for neuroplasticity. Exploratory analyses further indicated that variability in white matter density in the cingulum, an important connection for limbic regions, was associated with a range of problems commonly reported in clinical settings, which may be informative for diagnosis and treatment planning.
Real-world data, such as administrative claims and electronic health records, are increasingly used for safety monitoring and to help guide regulatory decision-making. In these settings, it is important to document analytic decisions transparently and objectively to assess and ensure that analyses meet their intended goals.
Methods:
The Causal Roadmap is an established framework that can guide and document analytic decisions through each step of the analytic pipeline, which will help investigators generate high-quality real-world evidence.
Results:
In this paper, we illustrate the utility of the Causal Roadmap using two case studies previously led by workgroups sponsored by the Sentinel Initiative – a program for actively monitoring the safety of regulated medical products. Each case example focuses on different aspects of the analytic pipeline for drug safety monitoring. The first case study shows how the Causal Roadmap encourages transparency, reproducibility, and objective decision-making for causal analyses. The second case study highlights how this framework can guide analytic decisions beyond inference on causal parameters, improving outcome ascertainment in clinical phenotyping.
Conclusion:
These examples provide a structured framework for implementing the Causal Roadmap in safety surveillance and guide transparent, reproducible, and objective analysis.
Antibiotic overuse is high in patients hospitalized with coronavirus disease 2019 (COVID-19) despite a low documented prevalence of bacterial infections in many studies. In this study evaluating 65 COVID-19 patients in the intensive care unit, empiric broad-spectrum antibiotics were often overutilized with an inertia to de-escalate despite negative culture results.
The protagonist of Winterreise wanders through a landscape that is both real and imagined. Banished from one home but unable to conceive another, he follows a path that circles back on itself repeatedly, leading only to exhaustion and defeat. Yet while the singer of Winterreise appears to inhabit a lonely landscape, Wilhelm Müller’s verses and their musical setting by Franz Schubert would also have evoked a concrete social world for their audiences, that of the road (Landstrasse). The road, by its very nature, was filled with people on the move, some of them (journeymen, pilgrims) heading purposefully from one place to another, but others with no particular destination, whose poverty, criminality, or “dishonorable” status banished them from their towns and villages. These last types, the “wandering people” (fahrendes Volk), had become well established as an object of public fascination and state scrutiny by the eighteenth century.
To examine associations between diet and risk of developing gastro-oesophageal reflux disease (GERD).
Design:
Prospective cohort with a median follow-up of 15·8 years. Baseline diet was measured using a FFQ. GERD was defined as self-reported current or history of daily heartburn or acid regurgitation beginning at least 2 years after baseline. Sex-specific logistic regressions were performed to estimate OR for GERD associated with diet quality scores and intakes of nutrients, food groups and individual foods and beverages. The effect of substituting saturated fat for monounsaturated or polyunsaturated fat on GERD risk was examined.
Setting:
Melbourne, Australia.
Participants:
A cohort of 20 926 participants (62 % women) aged 40–59 years at recruitment between 1990 and 1994.
Results:
For men, total fat intake was associated with increased risk of GERD (OR 1·05 per 5 g/d; 95 % CI 1·01, 1·09; P = 0·016), whereas total carbohydrate (OR 0·89 per 30 g/d; 95 % CI 0·82, 0·98; P = 0·010) and starch intakes (OR 0·84 per 30 g/d; 95 % CI 0·75, 0·94; P = 0·005) were associated with reduced risk. Nutrients were not associated with risk for women. For both sexes, substituting saturated fat for polyunsaturated or monounsaturated fat did not change risk. For both sexes, fish, chicken, cruciferous vegetables and carbonated beverages were associated with increased risk, whereas total fruit and citrus were associated with reduced risk. No association was observed with diet quality scores.
Conclusions:
Diet is a possible risk factor for GERD, but food considered as triggers of GERD symptoms might not necessarily contribute to disease development. Potential differential associations for men and women warrant further investigation.
High-fidelity measurements of velocity and concentration are carried out in a neutral jet (NJ) and a negatively buoyant jet (NBJ) by injecting a jet of fresh water vertically downwards into ambient fresh and saline water, respectively. The Reynolds number ($Re$) based on the pipe inlet diameter ($d$) and the source velocity ($W_o$) is approximately 5900 in all the experiments, while the source Froude number based on density difference is approximately 30 in the NBJ experiments. Velocity and concentration measurements are obtained in the region $17 \leq z/d \leq 40$ ($z$ being the axial coordinate) using particle image velocimetry and planar laser induced fluorescence techniques, respectively. Consistent with the literature on jets, the centreline velocity ($W_c$) decays as $z^{-1}$ in the NJ, but in the NBJ, $W_c$ decays faster along $z$ due to the action of negative buoyancy. Nonetheless, the mean velocity ($W$) and concentration ($C$) profiles in both the flows exhibit self-similar Gaussian form, when scaled by the local centreline parameters ($W_c,C_c$) and the jet half-widths ($r^\ast _{W},r^\ast _{C}$). On the other hand, the turbulence statistics and Reynolds stress in the NBJ do not scale with $W_c$. The results of autocorrelation functions, integral length scales and two-dimensional correlation maps show the similarity of turbulence structure in the NJ and the NBJ when the axial and radial distances are normalised by the local jet half-width. Further, the spectra and probability density functions are similar on the axis and only minor differences are seen near the jet interface. The above findings are fundamentally consistent with our recent analysis (Milton-McGurk et al., J. Fluid Mech., 2020b), where we observed that the mean and turbulence statistics in the NBJ have different development characteristics. Overall, we find that the turbulence structure of the NBJ (when scaled by local velocity and length scales) is very similar to the momentum-driven NJ, and the differences (e.g. spreading rate, scaling of turbulence intensities, etc.) between the NJ and the NBJ seem to be of secondary importance.
Gonorrhoea cases in women have been rising in Australia in the 2010s but the cause of the increase is not well understood. This cross-sectional study aimed to describe the characteristics of genital gonorrhoea infection in women attending the Melbourne Sexual Health Centre, Australia. Gonorrhoea cases were diagnosed by nucleic acid amplification test (NAAT) and/or culture. Genitourinary specimens were obtained in 12 869 clinic visits in women aged 16 years or above between August 2017 and August 2018. Genital gonorrhoea was detected in 142 (1.1%) of the visits. Almost half of the cases were asymptomatic, 47.9% [95% confidence interval (CI) 39.8–56.1%]; yellow, green or pus-like vaginal discharge was present in 11.3% (95% CI 7.0–17.6%) and other genital symptoms in 40.8% (95% CI 33.1–49.1%) of the cases. The mean time between last sexual contact and onset of symptoms was 7.3 days and between the onset of symptoms to presentation to the clinic was 12.1 days. Half of the cases of genital gonorrhoea among women are asymptomatic and these cases would have been missed by testing of only symptomatic women. Further epidemiological and behavioural research is required to understand the temporal changes in sexual practices among women in Australia.
The present study concerns a temporally developing parallel natural convection boundary layer with Prandtl number $\textit {Pr} = 0.71$ over an isothermally heated vertical plate. Three-dimensional direct numerical simulations (DNS) with different initial conditions were carried out to investigate the turbulent statistical profiles of mean velocity and temperature up to ${\textit {Gr}}_\delta =7.7\times 10^7$, where $Gr_\delta$ is the Grashof number based on the boundary layer thickness $\delta$. By virtue of DNS, we have identified a constant heat flux layer (George & Capp, Intl J. Heat Mass Transfer, vol. 22, issue 6, 1979, pp. 813–826; Hölling & Herwig, J. Fluid Mech., vol. 541, 2005, pp. 383–397) and a constant forcing layer in the near-wall region. In the close vicinity of the wall ($y^+<5$) a laminar-like sublayer has developed, and the temperature profile follows the linear relation, consistent with the studies of spatially developing flows (Tsuji & Nagano, Intl J. Heat Mass Transfer, vol. 31, issue 8, 1988, pp. 1723–1734); whereas such a linear relation cannot be observed for the velocity profile due to the extra buoyancy. Similar to earlier studies (Ng et al., J. Fluid Mech., vol. 825, 2017, pp. 550–572) we show that this buoyancy effect would asymptotically become zero if the ${\textit {Gr}}_\delta$ is sufficiently large. Further away from the wall ($y^+>50$), there is a log-law region for the mean temperature profile as reported by Tsuji & Nagano (1988). In this region, the turbulent length scale which characterises mixing scales linearly with the distance from the wall once ${\textit {Gr}}_\delta$ is sufficiently large. By taking the varying buoyancy into consideration with the robust mixing length model, a modified log-law for the mean velocity profile for $y^+>50$ is proposed. The effect of the initialization is shown to persist until relatively high ${\textit {Gr}}_\delta$ as a result of slow adjustment of the buoyancy (temperature) profile. Once these differences are accounted for, we find excellent agreement with our two DNS cases and with the spatially developing data of Tsuji & Nagano (1988). In the limit of higher ${\textit {Gr}}_\delta$ the velocity profile is expected to become asymptotic to momentum-dominated behaviour as buoyancy becomes increasingly weak in comparison with shear in the near-wall region.
Destratification of thermally stratified open-channel flow by surface cooling is investigated using direct numerical simulation. The initial states are the equilibrium states resulting from radiative heating. Using these states as initial conditions, a series of direct numerical simulations was run with radiative heating removed and a constant, uniform cooling flux applied at the upper surface. The flow evolves until the initial stable stratification is broken down and replaced by unstable stratification driven by surface cooling. The destratification process is described with reference to the evolution of the internal structure of the turbulent flow field. Based on these observations, we conclude that the dominant time scales in the flow from the perspective of destratification are the time scales associated with shear ${t}_{\tau }$, convection ${t}_*$ and stable density stratification ${t}_N$. Scaling arguments are then used to derive a scaling relationship for destratification rate as a function of a friction Richardson number $Ri_{\tau } = ( {t}_{\tau }/ {t}_N)^2$ and a convection Richardson number $Ri_* = ( {t}_*/ {t}_N)^2$. The relationship takes the form ${\mathcal {D}}_N = C_1Ri_{\tau }^{-1} + C_2Ri_*^{-1}$, where ${\mathcal {D}}_N$ is the destratification rate non-dimensionalised with respect to $ {t}_N$ and $C_1$ and $C_2$ are model coefficients. The relationship is compared with simulation results and is shown to accurately predict the destratification rate in the simulations across a range of parameters. This relationship is then integrated to give a formula for the time taken for the flow to destratify.
We forward the hypothesis and empirically establish that variations in the strength of family ties are rooted in culture. In particular, we show that individualism is associated with looser family ties. We exploit the associations between contemporary individualism and historical climatic and disease environments to establish a causal relationship. At both the individual- and country-levels, we find strong support that individualism reduces family ties. The estimated effects are economically large and robust to a wide variety of potentially confounding variables.
NOT VERY LONG AGO, the playwright and polemicist August von Kotzebue (1761–1819) was considered beneath the consideration of serious scholars of German literature. If he was remembered, it was as an antipode to Goethe, an exponent of Trivialliteratur, or as the unfortunate though perhaps deserved victim of the student nationalist Carl Ludwig Sand. Despite his enormous literary output and his influence on the cultural lives of his contemporaries, a recent history of German literature mentions Kotzebue not a single time. In recent years this tide has turned, as scholars have discovered the importance of Kotzebue for postcolonial studies, the Baltic Enlightenment, the cultural politics of the Napoleonic era, and debates regarding the meaning and function of literature. The 200th anniversary of Kotzebue's assassination brought forth a number of remembrances that were quite favorable to him, certainly more sympathetic than most of what was written in the immediate aftermath of that event.
Despite the growing interest in Kotzebue's literary and polemical output, barriers exist to a closer study of his life, with most biographers still relying on the accounts in his literary memoir and in the autobiographical pieces that were published after his death. The Kotzebue Nachlass, held in the Staatsbibliothek zu Berlin, is extensive but fragmentary, and there has been no concerted attempt to collect and publish Kotzebue's personal papers and correspondence, which, in any case, are strewn across archives and libraries throughout Germany and beyond. With that said, one key source on Kotzebue's life has remained largely unexplored, despite lying more or less in plain view for many years—namely, the manuscript Mein Umgang mit dem schönen Geschlecht (My relations with the fair sex) which forms part of the Kotzebue Nachlass in the Staatsbibliothek zu Berlin and is published here for the first time.
The manuscript consists of twenty-six pages, written in what looks to be Kotzebue's hand on thin, somewhat transparent paper. Although the manuscript is undated, its opening line indicates that Kotzebue was 56 when he wrote it, placing its origin around 1817. This also means that it was written in the same time period that Kotzebue penned two other autobiographical texts, Betrachtungen über mich selbst (Reflections on myself) and Woher kommt es daß ich so viele Feinde haben?
Advances in immunohistochemistry have spearheaded major developments in our understanding and classification of sinonasal tumours. In the last decade, several new distinct histopathological entities of sinonasal cancer have been characterised.
Objectives
This review aims to provide a clinical update of the major emerging subtypes for the ENT surgeon and an overview of the management strategies available for this heterogeneous group of pathologies.
Conclusion
Although rare, knowledge of sinonasal neoplasm subtypes has implications for prognosis, treatment strategies and the development of novel therapeutic targets.
The prevalence of many diseases in pigs displays seasonal distributions. Despite growing concerns about the impacts of climate change, we do not yet have a good understanding of the role that weather factors play in explaining such seasonal patterns. In this study, national and county-level aggregated abattoir inspection data were assessed for England and Wales during 2010–2015. Seasonally-adjusted relationships were characterised between weekly ambient maximum temperature and the prevalence of both respiratory conditions and tail biting detected at slaughter. The prevalence of respiratory conditions showed cyclical annual patterns with peaks in the summer months and troughs in the winter months each year. However, there were no obvious associations with either high or low temperatures. The prevalence of tail biting generally increased as temperatures decreased, but associations were not supported by statistical evidence: across all counties there was a relative risk of 1.028 (95% CI 0.776–1.363) for every 1 °C fall in temperature. Whilst the seasonal patterns observed in this study are similar to those reported in previous studies, the lack of statistical evidence for an explicit association with ambient temperature may possibly be explained by the lack of information on date of disease onset. There is also the possibility that other time-varying factors not investigated here may be driving some of the seasonal patterns.
Telomeres are nucleoprotein complexes that form the ends of eukaryotic chromosomes where they protect DNA from genomic instability, prevent end-to-end fusion and limit cellular replicative capabilities. Increased telomere attrition rates, and relatively shorter telomere length, is associated with genomic instability and has been linked with several chronic diseases, malignancies and reduced longevity. Telomeric DNA is highly susceptible to oxidative damage and dietary habits may make an impact on telomere attrition rates through the mediation of oxidative stress and chronic inflammation. The aim of this study was to examine the association between leucocyte telomere length (LTL) with both the Dietary Inflammatory Index® 2014 (DII®) and the Alternative Healthy Eating Index 2010 (AHEI-2010). This is a cross-sectional analysis using baseline data from 263 postmenopausal women from the Alberta Physical Activity and Breast Cancer Prevention (ALPHA) Trial, in Calgary and Edmonton, Alberta, Canada. No statistically significant association was detected between LTL z-score and the AHEI-2010 (P = 0·20) or DII® (P = 0·91) in multivariable adjusted models. An exploratory analysis of AHEI-2010 and DII® parameters and LTL revealed anthocyanidin intake was associated with LTL (P < 0·01); however, this association was non-significant after a Bonferroni correction was applied (P = 0·27). No effect modification by age, smoking history, or recreational physical activity was detected for either relationship. Increased dietary antioxidant and decreased oxidant intake were not associated with LTL in this analysis.
The stability properties of a natural convection boundary layer adjacent to an isothermally heated vertical wall, with Prandtl number 0.71, are numerically investigated in the configuration of a temporally evolving parallel flow. The instantaneous linear stability of the flow is first investigated by solving the eigenvalue problem with a quasi-steady assumption, whereby the unsteady base flow is frozen in time. Temporal responses of the discrete perturbation modes are numerically obtained by solving the two-dimensional linearized disturbance equations using a‘frozen’ base flow as an initial-value problem at various $Gr_{\unicode[STIX]{x1D6FF}}$, where $Gr_{\unicode[STIX]{x1D6FF}}$ is the Grashof number based on the velocity integral boundary layer thickness $\unicode[STIX]{x1D6FF}$. The resultant amplification rates of the discrete modes are compared with the quasi-steady eigenvalue analysis, and both two-dimensional and three-dimensional direct numerical simulations (DNS) of the temporally evolving flow. The amplification rate predicted by the linear theory compares well with the result of direct numerical simulation up to a transition point. The extent of the linear regime where the perturbations linearly interact with the base flow is thus identified. The value of the transition $Gr_{\unicode[STIX]{x1D6FF}}$, according to the three-dimensional DNS results, is dependent on the initial perturbation amplitude. Beyond the transition point, the DNS results diverge from the linear stability predictions as nonlinear mechanisms become important.