A simple construction of complex equiangular lines

A set of vectors of equal norm in $\mathbb{C}^d$ represents equiangular lines if the magnitudes of the inner product of every pair of distinct vectors in the set are equal. The maximum size of such a set is $d^2$, and it is conjectured that sets of this maximum size exist in $\mathbb{C}^d$ for every $d \geq 2$. We describe a new construction for maximum-sized sets of equiangular lines, exposing a previously unrecognized connection with Hadamard matrices. The construction produces a maximum-sized set of equiangular lines in dimensions 2, 3 and 8.Comment: 11 pages; minor revisions and comments added in section 1 describing a link to previously known results; correction to Theorem 1 and updates to reference

Consistent perturbations in an imperfect fluid

We present a new prescription for analysing cosmological perturbations in a more-general class of scalar-field dark-energy models where the energy-momentum tensor has an imperfect-fluid form. This class includes Brans-Dicke models, f(R) gravity, theories with kinetic gravity braiding and generalised galileons. We employ the intuitive language of fluids, allowing us to explicitly maintain a dependence on physical and potentially measurable properties. We demonstrate that hydrodynamics is not always a valid description for describing cosmological perturbations in general scalar-field theories and present a consistent alternative that nonetheless utilises the fluid language. We apply this approach explicitly to a worked example: k-essence non-minimally coupled to gravity. This is the simplest case which captures the essential new features of these imperfect-fluid models. We demonstrate the generic existence of a new scale separating regimes where the fluid is perfect and imperfect. We obtain the equations for the evolution of dark-energy density perturbations in both these regimes. The model also features two other known scales: the Compton scale related to the breaking of shift symmetry and the Jeans scale which we show is determined by the speed of propagation of small scalar-field perturbations, i.e. causality, as opposed to the frequently used definition of the ratio of the pressure and energy-density perturbations.Comment: 40 pages plus appendices. v2 reflects version accepted for publication in JCAP (new summary of notation, extra commentary on choice of gauge and frame, extra references to literature

Time-of-arrival distributions from position-momentum and energy-time joint measurements

The position-momentum quasi-distribution obtained from an Arthurs and Kelly joint measurement model is used to obtain indirectly an ``operational'' time-of-arrival (TOA) distribution following a quantization procedure proposed by Kocha\'nski and W\'odkiewicz [Phys. Rev. A 60, 2689 (1999)]. This TOA distribution is not time covariant. The procedure is generalized by using other phase-space quasi-distributions, and sufficient conditions are provided for time covariance that limit the possible phase-space quasi-distributions essentially to the Wigner function, which, however, provides a non-positive TOA quasi-distribution. These problems are remedied with a different quantization procedure which, on the other hand, does not guarantee normalization. Finally an Arthurs and Kelly measurement model for TOA and energy (valid also for arbitrary conjugate variables when one of the variables is bounded from below) is worked out. The marginal TOA distribution so obtained, a distorted version of Kijowski's distribution, is time covariant, positive, and normalized

Insulin-like growth factor 1 (IGF1), IGF binding protein 3 (IGFBP3), and breast cancer risk: Pooled individual data analysis of 17 prospective studies

Background: Insulin-like growth factor 1 (IGF1) stimulates mitosis and inhibits apoptosis. Some published results have shown an association between circulating IGF1 and breast-cancer risk, but it has been unclear whether this relationship is consistent or whether it is modified by IGF binding protein 3 (IGFBP3), menopausal status, oestrogen receptor status or other factors. The relationship of IGF1 (and IGFBP3) with breast-cancer risk factors is also unclear. The Endogenous Hormones and Breast Cancer Collaborative Group was established to analyse pooled individual data from prospective studies to increase the precision of the estimated associations of endogenous hormones with breast-cancer risk. Methods: Individual data on prediagnostic IGF1 and IGFBP3 concentrations were obtained from 17 prospective studies in 12 countries. The associations of IGF1 with risk factors for breast cancer in controls were examined by calculating geometric mean concentrations in categories of these factors. The odds ratios (ORs) with 95% CIs of breast cancer associated with increasing IGF1 concentrations were estimated by conditional logistic regression in 4790 cases and 9428 matched controls, with stratification by study, age at baseline, and date of baseline. All statistical tests were two-sided, and a p value of less than 0\ub705 was considered significant. Findings: IGF1 concentrations, adjusted for age, were positively associated with height and age at first pregnancy, inversely associated with age at menarche and years since menopause, and were higher in moderately overweight women and moderate alcohol consumers than in other women. The OR for breast cancer for women in the highest versus the lowest fifth of IGF1 concentration was 1\ub728 (95% CI 1\ub714-1\ub744; p<0\ub70001). This association was not altered by adjusting for IGFBP3, and did not vary significantly by menopausal status at blood collection. The ORs for a difference in IGF1 concentration between the highest and lowest fifth were 1\ub738 (95% CI 1\ub714-1\ub768) for oestrogen-receptor-positive tumours and 0\ub780 (0\ub757-1\ub713) for oestrogen-receptor-negative tumours (p for heterogeneity=0\ub7007). Interpretation: Circulating IGF1 is positively associated with breast-cancer risk. The association is not substantially modified by IGFBP3, and does not differ markedly by menopausal status, but seems to be confined to oestrogen-receptor-positive tumours

Whole-genome sequencing of chronic lymphocytic leukemia identifies subgroups with distinct biological and clinical features

The value of genome-wide over targeted driver analyses for predicting clinical outcomes of cancer patients is debated. Here, we report the whole-genome sequencing of 485 chronic lymphocytic leukemia patients enrolled in clinical trials as part of the United Kingdom’s 100,000 Genomes Project. We identify an extended catalog of recurrent coding and noncoding genetic mutations that represents a source for future studies and provide the most complete high-resolution map of structural variants, copy number changes and global genome features including telomere length, mutational signatures and genomic complexity. We demonstrate the relationship of these features with clinical outcome and show that integration of 186 distinct recurrent genomic alterations defines five genomic subgroups that associate with response to therapy, refining conventional outcome prediction. While requiring independent validation, our findings highlight the potential of whole-genome sequencing to inform future risk stratification in chronic lymphocytic leukemia

A História da Alimentação: balizas historiográficas

Os M. pretenderam traçar um quadro da História da Alimentação, não como um novo ramo epistemológico da disciplina, mas como um campo em desenvolvimento de práticas e atividades especializadas, incluindo pesquisa, formação, publicações, associações, encontros acadêmicos, etc. Um breve relato das condições em que tal campo se assentou faz-se preceder de um panorama dos estudos de alimentação e temas correia tos, em geral, segundo cinco abardagens Ia biológica, a econômica, a social, a cultural e a filosófica!, assim como da identificação das contribuições mais relevantes da Antropologia, Arqueologia, Sociologia e Geografia. A fim de comentar a multiforme e volumosa bibliografia histórica, foi ela organizada segundo critérios morfológicos. A seguir, alguns tópicos importantes mereceram tratamento à parte: a fome, o alimento e o domínio religioso, as descobertas européias e a difusão mundial de alimentos, gosto e gastronomia. O artigo se encerra com um rápido balanço crítico da historiografia brasileira sobre o tema

Convalescent plasma in patients admitted to hospital with COVID-19 (RECOVERY): a randomised controlled, open-label, platform trial

Background: Many patients with COVID-19 have been treated with plasma containing anti-SARS-CoV-2 antibodies. We aimed to evaluate the safety and efficacy of convalescent plasma therapy in patients admitted to hospital with COVID-19. Methods: This randomised, controlled, open-label, platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]) is assessing several possible treatments in patients hospitalised with COVID-19 in the UK. The trial is underway at 177 NHS hospitals from across the UK. Eligible and consenting patients were randomly assigned (1:1) to receive either usual care alone (usual care group) or usual care plus high-titre convalescent plasma (convalescent plasma group). The primary outcome was 28-day mortality, analysed on an intention-to-treat basis. The trial is registered with ISRCTN, 50189673, and ClinicalTrials.gov, NCT04381936. Findings: Between May 28, 2020, and Jan 15, 2021, 11558 (71%) of 16287 patients enrolled in RECOVERY were eligible to receive convalescent plasma and were assigned to either the convalescent plasma group or the usual care group. There was no significant difference in 28-day mortality between the two groups: 1399 (24%) of 5795 patients in the convalescent plasma group and 1408 (24%) of 5763 patients in the usual care group died within 28 days (rate ratio 1·00, 95% CI 0·93–1·07; p=0·95). The 28-day mortality rate ratio was similar in all prespecified subgroups of patients, including in those patients without detectable SARS-CoV-2 antibodies at randomisation. Allocation to convalescent plasma had no significant effect on the proportion of patients discharged from hospital within 28 days (3832 [66%] patients in the convalescent plasma group vs 3822 [66%] patients in the usual care group; rate ratio 0·99, 95% CI 0·94–1·03; p=0·57). Among those not on invasive mechanical ventilation at randomisation, there was no significant difference in the proportion of patients meeting the composite endpoint of progression to invasive mechanical ventilation or death (1568 [29%] of 5493 patients in the convalescent plasma group vs 1568 [29%] of 5448 patients in the usual care group; rate ratio 0·99, 95% CI 0·93–1·05; p=0·79). Interpretation: In patients hospitalised with COVID-19, high-titre convalescent plasma did not improve survival or other prespecified clinical outcomes. Funding: UK Research and Innovation (Medical Research Council) and National Institute of Health Research