The maximum modulus of a trigonometric trinomial

Let Lambda be a set of three integers and let C_Lambda be the space of 2pi-periodic functions with spectrum in Lambda endowed with the maximum modulus norm. We isolate the maximum modulus points x of trigonometric trinomials T in C_Lambda and prove that x is unique unless |T| has an axis of symmetry. This permits to compute the exposed and the extreme points of the unit ball of C_Lambda, to describe how the maximum modulus of T varies with respect to the arguments of its Fourier coefficients and to compute the norm of unimodular relative Fourier multipliers on C_Lambda. We obtain in particular the Sidon constant of Lambda

Decreased production of low density lipoprotein by atorvastatin after apheresis in homozygous familial hypercholesterolemia

Apheresis only partially controls raised low density lipoprotein cholesterol levels in patients with homozygous familial hypercholesterolemia, who usually respond poorly to lipid-lowering drugs. The efficacy and mechanism of action of a new 3-hydroxy-3-methylglutaryl coenzyme A reductase inhibitor, atorvastatin, was therefore investigated in seven homozygotes undergoing apheresis. One receptor-negative and six receptor-defective homozygotes undergoing plasma exchange or LDL apheresis every 2 weeks were studied during 2 months each on placebo and on atorvastatin 80 mg daily. Changes in plasma lipids and mevalonic acid, an index of cholesterol synthesis, were measured and the kinetics of the rebound of low density lipoprotein cholesterol and apolipoprotein B after apheresis were analyzed. All subjects had significant improvements on atorvastatin. Mean decreases in low density lipoprotein cholesterol were 31% greater both pre- and post-apheresis on atorvastatin compared with placebo, accompanied by a 63% decrease in mevalonic acid. Percentage changes in low density lipoprotein cholesterol and mevalonic acid were closely correlated (r = 0.89, P = 0.007). The mean production rates of low density lipoprotein cholesterol and apolipoprotein B were 21% and 25% lower, respectively, on atorvastatin than on placebo (P < 0.005 and <0.02) but changes in mean fractional clearance rates were not statistically significant. We conclude that atorvastatin enhances the efficacy of plasma exchange and low density lipoprotein apheresis in patients who lack low density lipoprotein receptors. This effect appears to be due to marked inhibition of cholesterol synthesis which results in a decreased rate of production of low density lipoprotein

Return to driving after traumatic brain injury : a British perspective

Primary Objective: to identify current legal situation, and professional practice in assisting persons with traumatic brain injury (TBI) to return to safe driving after injury. Methods and Procedures A brief review of relevant literature, a description of the current statutory and quasi-statutory authorities regulating return to driving after TBI in the UK, and a description of the nature and resolution of clinical and practical dilemmas facing professionals helping return to safe driving after TBI. Each of the 15 UK mobility centres was contacted and literature requested; in addition a representative of each centre responded to a structured telephone survey. Main Outcome and Results: The current situation in Great Britain is described, with a brief analysis of the strengths and weaknesses both of the current statutory situation, and also the practical situation (driving centres), with suggestions for improvements in practice. Conclusion Although brain injury may cause serious limitations in driving ability, previous drivers are not routinely assessed or advised regarding return to driving after TBI

Noncommutative Figa-Talamanca-Herz algebras for Schur multipliers

We introduce a noncommutative analogue of the Fig\'a-Talamanca-Herz algebra $A_p(G)$ on the natural predual of the operator space $\frak{M}_{p,cb}$ of completely bounded Schur multipliers on Schatten space $S_p$. We determine the isometric Schur multipliers and prove that the space $\frak{M}_{p}$ of bounded Schur multipliers on Schatten space $S_p$ is the closure in the weak operator topology of the span of isometric multipliers.Comment: 24 pages; corrected typo

Thin Melanoma with Nodal Involvement: Analysis of Demographic, Pathologic, and Treatment Factors with Regard to Prognosis.

BACKGROUND: Although only a small proportion of thin melanomas result in lymph node metastasis, the abundance of these lesions results in a relatively large absolute number of patients with a diagnosis of nodal metastases, determined by either sentinel lymph node (SLN) biopsy or clinical nodal recurrence (CNR). METHODS: Independent cohorts with thin melanoma and either SLN metastasis or CNR were identified at two melanoma referral centers. At both centers, SLN metastasis patients were included. At center 1, the CNR cohort included patients with initial negative clinical nodal evaluation followed by CNR. At center 2, the CNR cohort was restricted to those presenting in the era before the use of SLN biopsy. Uni- and multivariable analyses of melanoma-specific survival (MSS) were performed. RESULTS: At center 1, 427 CNR patients were compared with 91 SLN+ patients. The 5- and 10-year survival rates in the SLN group were respectively 88 and 84 % compared with 72 and 49 % in the CNR group (p \u3c 0.0001). The multivariate analysis showed age older than 50 years (hazard ratio [HR] 1.5; 95 % confidence interval [CI] 1.2-1.9), present ulceration (HR 1.9; 95 % CI 1.2-2.9), unknown ulceration (HR 1.6; 95 % CI 1.3-2.1), truncal site (HR 1.6; 95 % CI 1.2-2.2), and CNR (HR 3.3; 95 % CI 1.8-6.0) to be associated significantly with decreased MSS (p \u3c 0.01 for each). The center 2 cohort demonstrated remarkably similar findings, with a 5-year MSS of 88 % in the SLN (n = 29) group and 76 % in the CNR group (n = 39, p = 0.09). CONCLUSION: Patients with nodal metastases from thin melanomas have a substantial risk of melanoma death. This risk is lower among patients whose disease is discovered by SLN biopsy rather than CNR

Pioglitazone Improves Myocardial Blood Flow and Glucose Utilization in Nondiabetic Patients With Combined Hyperlipidemia A Randomized, Double-Blind, Placebo-Controlled Study

ObjectivesThis study’s aim was to examine whether treatment with pioglitazone, added to conventional lipid-lowering therapy, would improve myocardial glucose utilization (MGU) and blood flow (MBF) in nondiabetic patients with familial combined hyperlipidemia (FCHL).BackgroundThiazolidinediones were found to improve insulin sensitivity and MGU in type 2 diabetes and MBF in Mexican Americans with insulin resistance. Familial combined hyperlipidemia is a complex genetic disorder conferring a high risk of premature coronary artery disease, characterized by high serum cholesterol and/or triglyceride, low high-density lipoprotein (HDL) cholesterol, and insulin resistance.MethodsWe undertook a randomized, double-blind, placebo-controlled study in 26 patients with FCHL, treated with pioglitazone or matching placebo 30 mg daily for 4 weeks, followed by 45 mg daily for 12 weeks. Positron emission tomography was used to measure MBF at rest and during adenosine-induced hyperemia and MGU during euglycemic hyperinsulinemic clamp at baseline and after treatment.ResultsWhereas no change was observed in the placebo group after treatment, patients receiving pioglitazone showed a significant increase in whole body glucose disposal (3.93 ± 1.59 mg/kg/min to 5.24 ± 1.65 mg/kg/min; p = 0.004) and MGU (0.62 ± 0.26 μmol/g/min to 0.81 ± 0.14 μmol/g/min; p = 0.0007), accompanied by a significant improvement in resting MBF (1.11 ± 0.20 ml/min/g to 1.25 ± 0.21 ml/min/g; p = 0.008). Furthermore, in the pioglitazone group HDL cholesterol (+28%; p = 0.003) and adiponectin (+156.2%; p = 0.0001) were increased and plasma insulin (−35%; p = 0.017) was reduced.ConclusionsIn patients with FCHL treated with conventional lipid-lowering therapy, the addition of pioglitazone led to significant improvements in MGU and MBF, with a favorable effect on blood lipid and metabolic parameters. (A study to investigate the effect of pioglitazone on whole body and myocardial glucose uptake and myocardial blood flow/coronary vasodilator reserve in patients with familial combined hyperlipidaemia; http://www.controlled-trials.com/mrct/trial/230761/ISRCTN78563659; ISRCTN78563659

Daylight entanglement-based quantum key distribution with a quantum dot source

Entanglement-based quantum key distribution can enable secure communication in trusted node-free networks and over long distances. Although implementations exist both in fiber and in free space, the latter approach is often considered challenging due to environmental factors. Here, we implement a quantum communication protocol during daytime for the first time using a quantum dot source. This technology presents advantages in terms of narrower spectral bandwidth-beneficial for filtering out sunlight-and negligible multiphoton emission at peak brightness. We demonstrate continuous operation over the course of three days, across an urban 270 m-long free-space optical link, under different light and weather conditions

Quantum key distribution with entangled photons generated on demand by a quantum dot

Quantum key distribution-exchanging a random secret key relying on a quantum mechanical resource-is the core feature of secure quantum networks. Entanglement-based protocols offer additional layers of security and scale favorably with quantum repeaters, but the stringent requirements set on the photon source have made their use situational so far. Semiconductor-based quantum emitters are a promising solution in this scenario, ensuring on-demand generation of near-unity-fidelity entangled photons with record-low multiphoton emission, the latter feature countering some of the best eavesdropping attacks. Here, we use a coherently driven quantum dot to experimentally demonstrate a modified Ekert quantum key distribution protocol with two quantum channel approaches: both a 250-m-long single-mode fiber and in free space, connecting two buildings within the campus of Sapienza University in Rome. Our field study highlights that quantum-dot entangled photon sources are ready to go beyond laboratory experiments, thus opening the way to real-life quantum communication

Specialists in ancient trees are more affected by climate than generalists

Ancient trees are considered one of the most important habitats for biodiversity in Europe and North America. They support exceptional numbers of specialized species, including a range of rare and endangered wood-living insects. In this study, we use a dataset of 105 sites spanning a climatic gradient along the oak range of Norway and Sweden to investigate the importance of temperature and precipitation on beetle species richness in ancient, hollow oak trees. We expected that increased summer temperature would positively influence all wood-living beetle species whereas precipitation would be less important with a negligible or negative impact. Surprisingly, only oak-specialist beetles with a northern distribu- tion increased in species richness with temperature. Few specialist beetles and no generalist beetles responded to the rise of 4°C in summer as covered by our cli- matic gradient. The negative effect of precipitation affected more specialist species than did temperature, whereas the generalists remained unaffected. In summary, we suggest that increased summer temperature is likely to benefit a few specialist beetles within this dead wood community, but a larger number of specialists are likely to decline due to increased precipitation. In addition, generalist species will remain unaffected. To minimize adverse impacts of climate change on this impor- tant community, long-term management plans for ancient trees are important

Squatter settlements and slums and sustainable development

Squatter settlement is defined as a low residential area, which has developed without legal right to the land or permission from the concerned authorities to build, and as a result, of their illegal status, infrastructure and services are usually inadequate (UN-Habitat 2003). On the other hand, slums are contiguous settlements where inhabitants are characterized by insecure residential status, inadequate access to safe water, inadequate access to sanitation and other basic infrastructure and services, poor housing quality, and overcrowding (UN-Habitat 2003). Both are form of informal settlements that are not formally planned