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

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

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

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

Assessment of the reliability of the motor unit size index (MUSIX) in single subject “round-robin” and multi-centre settings

Objective The motor unit size index (MUSIX) is incorporated into the motor unit number index (MUNIX). Our objective was to assess the intra-/inter-rater reliability of MUSIX in healthy volunteers across single subject “round robin” and multi-centre settings. Methods Data were obtained from i). a round-robin assessment in which 12 raters (6 with prior experience and 6 without) assessed six muscles (abductor pollicis brevis, abductor digiti minimi, biceps brachii, tibialis anterior, extensor digitorum brevis and abductor hallucis) and ii). a multi-centre study with 6 centres studying the same muscles in 66 healthy volunteers. Intra/inter-rater data were provided by 5 centres, 1 centre provided only intra-rater data. Intra/inter-rater variability was assessed using the coefficient of variation (COV), Bland-Altman plots, bias and 95% limits of agreement. Results In the round-robin assessment intra-rater COVs for MUSIX ranged from 7.8% to 28.4%. Inter-rater variability was between 7.8% and 16.2%. Prior experience did not impact on MUSIX values. In the multi-centre study MUSIX was more consistent than the MUNIX. Abductor hallucis was the least reliable muscle. Conclusions The MUSIX is a reliable neurophysiological biomarker of reinnervation. Significance MUSIX could provide insights into the pathophysiology of a range of neuromuscular disorders, providing a quantitative biomarker of reinnervation

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

Old World megadroughts and pluvials during the Common Era

Climate model projections suggest widespread drying in the Mediterranean Basin and wetting in Fennoscandia in the coming decades largely as a consequence of greenhouse gas forcing of climate. To place these and other “Old World” climate projections into historical perspective based on more complete estimates of natural hydroclimatic variability, we have developed the “Old World Drought Atlas” (OWDA), a set of year-to-year maps of tree-ring reconstructed summer wetness and dryness over Europe and the Mediterranean Basin during the Common Era. The OWDA matches historical accounts of severe drought and wetness with a spatial completeness not previously available. In addition, megadroughts reconstructed over north-central Europe in the 11th and mid-15th centuries reinforce other evidence from North America and Asia that droughts were more severe, extensive, and prolonged over Northern Hemisphere land areas before the 20th century, with an inadequate understanding of their causes. The OWDA provides new data to determine the causes of Old World drought and wetness and attribute past climate variability to forced and/or internal variability

Genomic patterns in the widespread Eurasian lynx shaped by Late Quaternary climatic fluctuations and anthropogenic impacts.

Disentangling the contribution of long-term evolutionary processes and recent anthropogenic impacts to current genetic patterns of wildlife species is key for assessing genetic risks and designing conservation strategies. Here, we used 80 whole nuclear genomes and 96 mitogenomes from populations of the Eurasian lynx covering a range of conservation statuses, climatic zones and subspecies across Eurasia to infer the demographic history, reconstruct genetic patterns and discuss the influence of long-term isolation and/or more recent human-driven changes. Our results show that Eurasian lynx populations shared a common history until 100 kya, when Asian and European populations started to diverge and both entered a period of continuous and widespread decline, with western populations, except Kirov, maintaining lower effective sizes than eastern populations. Population declines and increased isolation in more recent times likely drove the genetic differentiation between geographically and ecologically close westernmost European populations. By contrast, and despite the wide range of habitats covered, populations are quite homogeneous genetically across the Asian range, showing a pattern of isolation by distance and providing little genetic support for the several proposed subspecies. Mitogenomic and nuclear divergences and population declines starting during the Late Pleistocene can be mostly attributed to climatic fluctuations and early human influence, but the widespread and sustained decline since the Holocene is more probably the consequence of anthropogenic impacts which intensified during the last centuries, especially in western Europe. Genetic erosion in isolated European populations and lack of evidence for long-term isolation argue for the restoration of lost population connectivity