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Let$f:X\rightarrow X$be a continuous dynamical system on a compact metric space$X$and let$\unicode[STIX]{x1D6F7}:X\rightarrow \mathbb{R}^{m}$be an$m$-dimensional continuous potential. The (generalized) rotation set$\text{Rot}(\unicode[STIX]{x1D6F7})$is defined as the set of all$\unicode[STIX]{x1D707}$-integrals of$\unicode[STIX]{x1D6F7}$, where$\unicode[STIX]{x1D707}$runs over all invariant probability measures. Analogous to the classical topological entropy, one can associate the localized entropy$\unicode[STIX]{x210B}(w)$to each$w\in \text{Rot}(\unicode[STIX]{x1D6F7})$. In this paper, we study the computability of rotation sets and localized entropy functions by deriving conditions that imply their computability. Then we apply our results to study the case where$f$is a subshift of finite type. We prove that$\text{Rot}(\unicode[STIX]{x1D6F7})$is computable and that$\unicode[STIX]{x210B}(w)$is computable in the interior of the rotation set. Finally, we construct an explicit example that shows that, in general,$\unicode[STIX]{x210B}$is not continuous on the boundary of the rotation set when considered as a function of$\unicode[STIX]{x1D6F7}$and$w$. In particular,$\unicode[STIX]{x210B}$is, in general, not computable at the boundary of$\text{Rot}(\unicode[STIX]{x1D6F7})$.

Data depth functions are a generalization of one-dimensional order statistics and medians to real spaces of dimension greater than one; in particular, a data depth function quantifies the centrality of a point with respect to a data set or a probability distribution. One of the most commonly studied data depth functions is halfspace depth. Halfspace depth is of interest to computational geometers because it is highly geometric, and it is of interest to statisticians because it shares many desirable theoretical properties with the one-dimensional median. It is known that as the sample size increases, the halfspace depth for a sample converges to the halfspace depth for the underlying distribution, almost surely. In this paper, we use the geometry and structure of halfspace depth to reduce a high-dimensional problem into many one-dimensional problems. This bound requires only mild assumptions on the distribution, and it leads to an improved convergence rate when the underlying distribution decays exponentially, i.e., the probability that a sample point has magnitude at least R is O ( exp ( − λ R 2 / 2 ) ) . We also provide examples and show that our bounds are tight.

We develop algorithms for certifying an approximation to a nonsingular solution of a square system of equations built from univariate analytic functions. These algorithms are based on the existence of oracles for evaluating basic data about the input analytic functions. One approach for certification is based on alpha-theory while the other is based on the Krawczyk generalization of Newton's iteration. We show that the necessary oracles exist for D-finite functions and compare the two algorithmic approaches for this case using our software implementation in SageMath., 16 pages

A full-scale fire test was conducted on a kitchen arrangement containing a refrigerator, dishwasher, and electric clothes dryer. The fire was ignited by a heat source external to the appliances. Post fire analysis established the presence of arc faults on the appliances’ internal electrical wiring. This fire test establishes that while faults indicate that the appliances were energized when attacked by fire, they are not necessarily indicators that the fire originated inside the appliance. This fire test also demonstrates that an arc mapping analysis of an appliance requires knowledge of the internal configuration of the appliance and its wiring.

Homotopy continuation is a well-known method in numerical root-finding. Recently, certified algorithms for homotopy continuation based on Smale's alpha-theory have been developed. This approach enforces very strong requirements at each step, leading to small step sizes. In this paper, we propose an approach that is independent of alpha-theory. It is based on the weaker notion of well-isolated approximations to the roots. We apply it to univariate polynomials and provide experimental evidence of its feasibility.

International audience; We present a general framework for analyzing the complexity of subdivision-based algorithms whose tests are based on the sizes of regions and their distance to certain sets (often varieties) intrinsic to the problem under study. We call such tests diameter-distance tests. We illustrate that diameter-distance tests are common in the literature by proving that many interval arithmetic-based tests are, in fact, diameter-distance tests. For this class of algorithms, we provide both non-adaptive bounds for the complexity, based on separation bounds, as well as adaptive bounds, by applying the framework of continuous amortization. Using this structure, we provide the first complexity analysis for the algorithm by Plantinga and Vegeter for approximating real implicit curves and surfaces. We present both adaptive and non-adaptive a priori worst-case bounds on the complexity of this algorithm both in terms of the number of subregions constructed and in terms of the bit complexity for the construction. Finally, we construct families of hypersurfaces to prove that our bounds are tight.

A microgrid presents a challenging package to finance. The primary difficulty arises from the fact that a microgrid is not just one type of asset but rather a portfolio of assets that represent different value streams, technology risks, and depreciation lives.

Background Eczema is common in infancy; however, there is little evidence about its natural history to adulthood. Objectives To study the natural history of eczema from birth to young adult life with particular reference to its relation to atopy. Methods A birth cohort of children with atopic family histories was followed for 23 years. Clinical examinations were conducted until the age of 7 years, skin-prick tests and serum total IgE were recorded in infancy and at ages 7 and 23 years, and questionnaires about eczema symptoms were completed at 15 and 23 years. Results Information was obtained on 497 subjects at birth, 482 at 1 year, 440 at 7 years, 363 at 15 years and 304 at 23 years. Eczema usually remitted from age 1 to 7 years but became more persistent from the age of 15 years, especially in those who were atopic. The prevalence of eczema rose in women from age 15 to 23 years but declined in men. Adults with eczema had higher IgE than those without at 3 months (geometric mean 3·0 vs. 1·7 kU L-1; P = 0·01), 7 years (107·9 vs. 45·2 kU L-1; P = 0·01) and 23 years (123·4 vs. 42·3 kU L-1; P = 0·01), and were more likely to have had positive skin-prick tests at 1 year of age. Current eczema was associated with raised IgE in infancy and adulthood but not in childhood. Conclusions Predisposed infants and children with eczema usually grow out of the disease, but in adolescence it is more likely to persist. Adult eczema is related to atopy from the age of 3 months. What's already known about this topic? Eczema is associated with atopy, asthma and rhinoconjunctivitis. Eczema in infancy usually remits but is more likely to persist if the child is atopic. After puberty eczema often persists to adult life. What does this study add? Adult eczema is associated with atopy from the age of 3 months. Atopy increases the likelihood of persistence after adolescence.

Authors were provided two sets of 24 exemplar candles. Of these, 24 were identified as the same that the provider had observed “flaring”. Fourier Transform Infrared Spectroscopy (FTIR) analysis of the material showed that the candles that did not flare were soy based wax and that those that did flare were petroleum based wax. Burning the candles showed that melted wax in some petroleum based candles was ignited by the wick flame and produced a pool fire inside the candles’ glass container. Based on measured mass loss rate and the heat of combustion of petroleum based wax, the calculated power output of a normal burning candle is ca. 30 W. When the liquid wax pool ignited, the output was ca. 230 W, with significant flame extension above the top edge of candle’s glass container. The FTIR analysis also showed that twelve of the petroleum based wax candles had a simple hydroxyl compound, likely an alcohol, peak that was not present in the second sample of one dozen petroleum based wax candles. Burn testing showed that the candles from the sample with hydroxyl ignite a pool fire after burning for 15 to 30 min; the second sample of petroleum based wax candles, those that did not have the hydroxyl compound, did not ignite a pool fire. This suggests that the hydroxyl compound reduces the flashpoint of the wax to an ignition temperature attained after burning the candle for tens of minutes. Once the hydroxyl compound petroleum based wax melts and reaches a temperature above its flashpoint/flame point, it vaporizes sufficiently to be ignited, with flame extension of 152 mm (6 in) or more above the wax pool. This flame extension or “flaring” represents a significant fire hazard in that it may ignite nearby combustibles or fracture the candle’s glass container and release burning wax.

For a complex irreducible projective variety, the volume function and the higher asymptotic cohomological functions have proven to be useful in understanding the positivity of divisors as well as other geometric properties of the variety. In this paper, we study the vanishing properties of these functions on hypersurfaces of ℙn × ℙn. In particular, we show that very general hypersurfaces of bidegree (k, k) obey a very strong vanishing property, which we define as asymptotic purity: at most one asymptotic cohomological function is nonzero for each divisor. This provides evidence for the truth of a conjecture of Bogomolov and also suggests some general conditions for asymptotic purity.

This Part II paper describes source apportionment (SA) for 10 source categories at a 12 km horizontal grid resolution over the eastern U.S. for January and July of 2002 using the Comprehensive Air Quality Model with extensions/Particulate Source Apportionment Technology (CAMx/PSAT). SA results from CAMx/PSAT are contrasted with those from CMAQ/BFM in Part I. The top three sources domainwide in January are identified to be coal combustion (with a monthly–mean contribution of 14.0%, or 1.1 µg m –3 ), biomass burning (11.3%, 0.9 µg m –3 ) and other mobile sources (6.8%, 0.6 µg m –3 ) by CAMx/PSAT but biomass burning (13.7%, 1.1 µg m –3 ), miscellaneous area sources (11.8%, 0.9 µg m –3 ), and coal combustion (10.8%, 0.9 µg m –3 ) by CMAQ/BFM. Both agree that coal combustion, industrial processes, and miscellaneous area sources are the top three sources in July, though they differ in the magnitude of contributions. Both give similar contributions for primary PM, but they differ substantially in SA results for secondary PM, due primarily to their treatments for oxidant–limiting and indirect effects. While CMAQ/BFM inherently accounts for these effects and can provide useful information for primary and secondary PM species, CAMx/PSAT neglects them by linking each PM species only with its direct primary emission precursor. These effects are enhanced in January due to the increased importance of NO 3 – and lower concentrations of oxidants relative to July. CAMx/PSAT is thus accurate for SA of the primary PM species but incorrect in its SA for secondary PM species. For a highly non–linear system studied here, the true SA cannot be obtained with current SA methods. Policy–makers must be mindful of relative strengths and weaknesses of each method, as well as the limitation of current SA methods in the SA of secondary PM species, when using such information in support of state implementation plan and epidemiological studies.

We design efficient data structures for dynamically maintaining a ham-sandwich cut of two point sets in the plane subject to insertions and deletions of points in either set. A ham-sandwich cut is a line that simultaneously bisects the cardinality of both point sets. For general point sets, our first data structure supports each operation in O(n^1^/^3^+^@e) amortized time and O(n^4^/^3^+^@e) space. Our second data structure performs faster when each point set decomposes into a small number k of subsets in convex position: it supports insertions and deletions in O(logn) time and ham-sandwich queries in O(klog^4n) time. In addition, if each point set has convex peeling depth k, then we can maintain the decomposition automatically using O(klogn) time per insertion and deletion. Alternatively, we can view each convex point set as a convex polygon, and we show how to find a ham-sandwich cut that bisects the total areas or total perimeters of these polygons in O(klog^4n) time plus the O((kb)polylog(kb)) time required to approximate the root of a polynomial of degree O(k) up to b bits of precision. We also show how to maintain a partition of the plane by two lines into four regions each containing a quarter of the total point count, area, or perimeter in polylogarithmic time.

Background: A study was undertaken to see whether the prevalence of asthma has changed since a survey was conducted in 1988, using the same methods that showed an increase during the previous 15 years. Methods: A survey of 12 year old children was conducted in schools in South Wales where surveys had taken place in 1973 and 1988. The survey comprised a parentally completed questionnaire and an exercise challenge test, performed when no bronchodilator had been recently used. Results: In 1973, 1988, and 2003, questionnaires were obtained for 817, 965 and 1148 children, respectively; the exercise test was performed by 812, 960 and 1019 children, respectively. The prevalence of reported wheeze in the last year rose during each 15 year period (9.8%, 15.2%, 19.7%), with an even steeper rise in reported asthma ever (5.5%, 12.0%, 27.3%). There was a continued increase in wheeze attributed to running, in terms of all children (5.8%, 10.5%, 16.0%) and also as the proportion of those with a history of wheeze (34.1%, 47.0%, 57.3%). The use of inhaled corticosteroids (not available in 1973) increased fourfold between 1988 and 2003. The prevalence of exercise induced bronchoconstriction rose between 1973 and 1988 but had declined by 2003. Conclusions: The rise in the prevalence of asthmatic symptoms has continued since 1988. This appears to conflict with a reported recent decline, unless asthma prevalence peaked in the 1990s. The decline in exercise induced bronchoconstriction is probably attributable to better control of the disease as more children are now using inhaled corticosteroids as preventive treatment.

Two successive randomized trials examined the effect of an increased intake of fatty fish, or the use of fish oil supplements, in reducing mortality in men with heart disease. The Diet and Reinfarction Trial (DART) was conducted in 2033 men who were recovering from acute myocardial infarction (MI). Those who were advised to eat fatty fish (or who opted to take fish oil capsules instead) had a 29% reduction in all-cause mortality over the following two years compared with those not so advised. The effect appeared in the first few months of the trial. The Diet and Angina Randomized Trial (DART 2) involved 3114 men with stable angina. Advice to eat fatty fish did not reduce mortality, and taking fish oil capsules was associated with a higher risk of cardiac and sudden death. The adverse effects of fish or fish oil were restricted to men not taking beta-blockers or dihydropyridine calcium-channel blockers, and were greater in those taking digoxin. Evidence from other sources strongly suggests an anti-arrhythmic action of fish oil, particularly after MI or in the presence of acute ischemia. The apparently conflicting results of the two trials may reflect different actions of n-3 fatty acids in acute and chronic conditions, together with different effects of eating fish and taking fish oil capsules. A mechanism is proposed that could account for these findings.

Objective To address the risk factors for coronary heart disease (CHD) and back pain in workplaces employing less than 50 people in the Merthyr/Cynon area of South Wales. Design A comparative study of small workplaces randomly allocated into either CHD or musculo-skeletal intervention groups. Setting Small workplaces, employing 50 staff or less. Method Following random allocation into CHD or musculo-skeletal groups, participating workplaces received a dual approach consisting of organisational health promotion policy advice and support with individual employee health screening, advice and limited intervention. Results Stress was the most commonly reported CHD risk factor amongst respondents and was more prevalent amongst women, although there was also an important differentiation identified between 'workplace' and 'domestic' stress. Advice about stress was twice as often reported in the private than in the public sector, although the prevalence of'current stress' was slightly higher among the public than the private workers. Most smokers wanted to stop. Over 50 per cent of respondents reported some form of musculo-skeletal problem and physical inactivity was generally high across all sectors. There appeared to be an increased awareness of health messages following the interventions but no statistically significant changes in behaviour were evident. Nearly all workplaces (97 per cent) had smoking policies. The commonest obstacle to health promotion was lack of obvious benefit as perceived by the employer. Conclusions Overall, there appeared to be a resistance to workplace health promotion, which was viewed as not benefiting the business, requiring too much time, and not the employer's responsibility. Most small businesses do not have the resources available to larger employers to address the health needs of their workforce and alternative ways of helping these workplaces needs to be explored. The major issue that needs to be addressed is stress, which may originate in the workplace or at home. Other important health related matters include exercise, diet, smoking and spinal pain.

Background: Although there is growing knowledge about factors that may predispose to the onset of atopic dermatitis (AD), little is known about factors which may exacerbate existing disease. AD sufferers and those involved in the management of the disease are often aware of factors that influence its course and severity. However, there is little available evidence on the distribution and relative importance of such factors, and what information exists is derived from selected groups such as hospital patients and may not therefore be representative of the AD population as a whole. Objectives: To determine the distribution and relative importance of 19 potential exacerbating and relieving factors as perceived by a population-based sample of schoolchildren with AD. Methods: A questionnaire was used to identify all children with AD in years 8 and 9 (12–14-year-olds) from eight comprehensive schools across Wales. These individuals were then requested to complete a supplementary questionnaire which asked them to state for each of 19 factors whether (i) it makes their eczema better, (ii) it makes their eczema worse, (iii) it has no effect, or (iv) they do not know its effects. Results: Almost 10% (250 of 2501) of children surveyed were considered to have AD, and 90% (225 of 250) of these completed the supplementary questionnaire. Most AD sufferers found that none to two factors relieve their symptoms whilst none to five factors exacerbate them. Sweating from exercise, fabrics (especially wool) and hot weather were the three most common exacerbators, affecting 41·8%, 40% and 39·1%, respectively, of AD responders. The three key relievers were steroid creams (22·2% of AD responders), moisturizers/makeup (16·4%) and medicines/tablets (13·8%). Almost 60% of respondents believed foods have no effect on their symptoms. There was also evidence to suggest that 12·4% (28 of 225) of participants may use creams which they are not aware contain steroids. Conclusions: These findings shed light on the relative perceived importance of factors such as food, aeroallergens, sweat, climate, illness, stress and therapies for the course of AD in a representative population sample of AD sufferers. Such information might be explored during clinical consultations given the increasing participation of sufferers and their carers in the management of this chronic disease. These findings also form the basis of hypothesis generation for future analytical studies.

To determine whether residents of congested streets have a higher prevalence of respiratory symptoms than residents of nearby uncongested streets, and whether their respiratory health improves following a reduction in exposure to traffic related air pollutants.An area was identified where certain streets were subject to air pollution from heavy road traffic, which was likely to improve following the construction of a by-pass. A respiratory survey was conducted among the residents, together with the residents of nearby uncongested streets, at baseline and again a year after the by-pass opened. Measurements were made of air pollutant concentrations in both areas on both occasions.Initial concentrations of PM10 and PM2.5 were substantially higher in the congested than in the uncongested streets. When the by-pass opened, the volume of heavy goods traffic fell by nearly 50%. PM10 decreased by 23% (8.0 microg/m3) in the congested streets and by 29% (3.4 microg/m3) in the uncongested streets, with similar proportionate falls in PM2.5. There were no clear or consistent differences between the residents of the two areas initially in terms of symptoms or peak flow variability. Repeat questionnaires were obtained from 165 and 283 subjects in the congested and uncongested areas respectively, and showed a tendency for most symptoms to improve in both areas. For chest symptoms, the improvement tended to be greater in the uncongested area, although the difference between the areas was not statistically significant. Rhinitis and rhinoconjunctivitis tended to improve to a greater extent in the congested streets; the difference between the areas was significant for the degree to which rhinitis interfered with daily activities. Peak flow variability tended to improve in the uncongested area.The by-pass reduced pollutant levels to a degree that probably alleviates rhinitis and rhinoconjunctivitis but has little effect on lower respiratory symptoms.

Background Although pollens are major allergens associated with allergic rhinoconjunctivitis and asthma, there is little information about the relative prevalence of these conditions in populations with different pollen exposures. Objective The purpose of this study was to investigate the relationship between pollen exposure and allergic symptoms among children in different countries. Methods An ecological analysis was conducted to see whether pollen exposure (pollen counts, and duration and severity of pollen seasons) is associated with symptoms of allergic rhinoconjunctivitis, asthma and atopic eczema in 28 centres within 11 countries (nine being in Europe). Data on the prevalence of symptoms in 13–14-year olds were based on the responses to the written questionnaires from the International Study of Asthma and Allergies in Childhood (ISAAC). The analysis was adjusted for gross national product and mean annual relative humidity. Results There was little relationship between pollen exposure and symptom prevalence, except for a significant inverse association between grass pollen counts and lifetime prevalence of the symptoms of allergic rhinitis (P=0.03). Almost all the regression coefficients were negative. The associations were even weaker and all non-significant when the analyses were conducted within countries, using a random intercept fixed slope model, but there was still no evidence of a positive association between pollen exposure and symptoms. Conclusion There is a weak but consistent tendency for the prevalence of allergic symptoms to be inversely associated with pollen exposure. This finding accords with evidence from several countries, suggesting that the prevalence of hayfever and asthma tends to be lower in rural than in urban areas, and lowest among people living on farms. Exposure to allergenic pollen in early life does not appear to increase the risk of acquiring symptoms of respiratory allergy, and may even give some protection against them.

Objective: To assess and compare the effects of natural folate (100 microg) with those of folic acid from fortified sources (100 microg/day) on plasma folate and homocysteine. Design: Randomized controlled trial (parallel groups). Setting: Men and women living in South Wales, UK. Subjects: A total of 135 healthy individuals recruited from the local workforce and blood donor sessions. All subjects possessed the 'wild-type' CC genotype for C677T polymorphism in methylenetetrahydrofolate reductase (MTHFR). Interventions: Subjects underwent one of the following dietary interventions for 4 months: (1) fortified diet—usual diet plus 100 microg/day folic acid from fortified foods; (2) natural folate diet—usual diet plus 100 microg/day folate from natural sources; (3) control—usual diet. Results: The fortified group increased reported intake of folic acid from fortified foods compared to other groups (P

Objective: To assess the long-term effect of dietary advice on diet and mortality after a randomised trial of men with a recent history of myocardial infarction. Design: Questionnaire survey and mortality follow-up after a trial of dietary advice. Setting: Twenty-one hospitals in south Wales and south-west England. Subjects: Former participants in the Diet and Reinfarction Trial. Main outcome measures: Current fish intake and cereal fibre intake. All-cause mortality, stroke mortality and coronary mortality. Results: By February 2000, after 21147 person years of follow-up, 1083 (53%) of the men had died. Completed questionnaires were obtained from 879 (85%) of the 1030 men alive at the beginning of 1999. Relative increases in fish and fibre intake were still present at 10 y but were much smaller. The early reduction in all-cause mortality observed in those given fish advice (unadjusted hazard 0.70 (95% CI 0.54, 0.92)) was followed by an increased risk over the next 3 y (unadjusted hazard 1.31 (95% CI 1.01, 1.70). Fat and fibre advice had no clear effect on coronary or all-cause mortality. The risk of stroke death was increased in the fat advice group¾the overall unadjusted hazard was 2.03 (95% CI 1.14, 3.63). Conclusions: In this follow-up of a trial of intensive dietary advice following myocardial infarction we did not observe any substantial long-term survival benefit. Further trials of fish and fibre advice are feasible and necessary to clarify the role of these foods in coronary disease.

Objective:To study the effect of advice to increase dietary soluble fibre, including fruit and vegetables, on plasma folate and homocysteine in men with angina.Design:Data were collected on a subset of subjects from the Diet and Angina Randomised Trial (DART II). In a randomised (2 × 2) factorial design, subjects received advice on either, neither or both interventions to: (1) increase soluble fibre intake to 8.0 g day−1(fruit, vegetables and oats); (2) increase oily fish intake to 2 portions week−1. Those who received soluble fibre advice were compared with those who did not. Subjects were genotyped for C677T variant 5,10-methylenetetrahydrofolate reductase (MTHFR).Setting/subjects:Seven hundred and fifty-three male angina patients were recruited from general practice.Results:Plasma homocysteine concentrations were at the upper end of the normal range (median 11.5, 25% 9.4, 75% 14.0 μmol l−1). Baseline intake of fruit and vegetables was positively correlated with plasma folate (rs= 0.29,P< 0.01). Smokers had lower intakes of fruit and vegetables, lower plasma folate and higher homocysteine (allP< 0.01). Homozygotes for variant MTHFR had higher homocysteine concentrations at low plasma folate (P< 0.01). Reported intakes of fruit and vegetables and estimated dietary folate increased in the intervention group (ca.+75 g day−1,P< 0.01 andca.+20 g day−1,P< 0.05, respectively). However, neither plasma folate (baseline/follow-up 4.5 vs. 4.4 μg l−1,P= 0.40) nor homocysteine (baseline/follow-up 11.7 vs. 11.7 μmol l−1,P= 0.31) changed.Conclusions:Plasma homocysteine, a cardiovascular risk factor, is influenced by MTHFR genotype, plasma folate and smoking status. Dietary advice successfully led to changes in fruit and vegetable intake, but not to changes in plasma folate or homocysteine, possibly because the fruits and vegetables that were chosen were not those richest in folate.

OBJECTIVESWe sought to study the effect of low-dose folic acid supplementation or optimization of dietary folate intake on plasma homocysteine and endothelial function in healthy adults.BACKGROUNDElevated homocysteine is associated with cardiovascular disease, but it is not known whether this relationship is causal. Individuals homozygous (TT) for the C677T mutation in the methylenetetrahydrofolate reductase (MTHFR) gene (∼12% of the population) have increased homocysteine levels, particularly in association with suboptimal folate intake.METHODSHealthy subjects (n = 126; 42 of each MTHFR genotype) were included in this cross-over study of three interventions of four months each: 1) placebo plus natural diet; 2) daily 400-μg folic acid supplement plus natural diet; and 3) increased dietary folate intake to 400 μg/day.RESULTSAt baseline, homocysteine was inversely related to plasma folate and was higher in TT homozygotes. For the whole group, plasma folate increased by 46% after dietary folate and by 79% after supplementation, with reductions of homocysteine of 14% and 16%, respectively. Within the genotype, TT homozygotes exhibited the most marked changes in these variables. Brachial artery endothelial function, as determined by a change in end-diastolic diameter in response to increased flow, was not changed by increased folate intake (98 ± 73 μm at baseline, 110 ± 69 μm after a high-folate diet, 114 ± 59 μm after supplementation and 118 ± 68 μm after placebo). Plasma von Willebrand factor antigen was unaltered.CONCLUSIONSOptimization of dietary folate or low-dose folic acid supplementation reduces plasma homocysteine but does not enhance endothelial function, irrespective of the MTHFR (C667T) genotype.