The BCS Functional for General Pair Interactions

The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.Comment: Revised Version. To appear in Commun. Math. Phys

Association of Sex with Neurobehavioral Markers of Executive Function in 2-Year-Olds at High and Low Likelihood of Autism

Importance: Children with autism and their siblings exhibit executive function (EF) deficits early in development, but associations between EF and biological sex or early brain alterations in this population are largely unexplored. Objective: To investigate the interaction of sex, autism likelihood group, and structural magnetic resonance imaging alterations on EF in 2-year-old children at high familial likelihood (HL) and low familial likelihood (LL) of autism, based on having an older sibling with autism or no family history of autism in first-degree relatives. Design, Setting, and Participants: This prospective cohort study assessed 165 toddlers at HL (n = 110) and LL (n = 55) of autism at 4 university-based research centers. Data were collected from January 1, 2007, to December 31, 2013, and analyzed between August 2021 and June 2022 as part of the Infant Brain Imaging Study. Main Outcomes and Measures: Direct assessments of EF and acquired structural magnetic resonance imaging were performed to determine frontal lobe, parietal lobe, and total cerebral brain volume. Results: A total of 165 toddlers (mean [SD] age, 24.61 [0.95] months; 90 [54%] male, 137 [83%] White) at HL for autism (n = 110; 17 diagnosed with ASD) and LL for autism (n = 55) were studied. The toddlers at HL for autism scored lower than the toddlers at LL for autism on EF tests regardless of sex (mean [SE] B = -8.77 [4.21]; 95% CI, -17.09 to -0.45; η2p= 0.03). With the exclusion of toddlers with autism, no group (HL vs LL) difference in EF was found in boys (mean [SE] difference, -7.18 [4.26]; 95% CI, 1.24-15.59), but EF was lower in HL girls than LL girls (mean [SE] difference, -9.75 [4.34]; 95% CI, -18.32 to -1.18). Brain-behavior associations were examined, controlling for overall cerebral volume and developmental level. Sex differences in EF-frontal (B [SE] = 16.51 [7.43]; 95% CI, 1.36-31.67; η2p= 0.14) and EF-parietal (B [SE] = 17.68 [6.99]; 95% CI, 3.43-31.94; η2p= 0.17) associations were found in the LL group but not the HL group (EF-frontal: B [SE] = -1.36 [3.87]; 95% CI, -9.07 to 6.35; η2p= 0.00; EF-parietal: B [SE] = -2.81 [4.09]; 95% CI, -10.96 to 5.34; η2p= 0.01). Autism likelihood group differences in EF-frontal (B [SE] = -9.93 [4.88]; 95% CI, -19.73 to -0.12; η2p= 0.08) and EF-parietal (B [SE] = -15.44 [5.18]; 95% CI, -25.86 to -5.02; η2p= 0.16) associations were found in girls not boys (EF-frontal: B [SE] = 6.51 [5.88]; 95% CI, -5.26 to 18.27; η2p= 0.02; EF-parietal: B [SE] = 4.18 [5.48]; 95% CI, -6.78 to 15.15; η2p= 0.01). Conclusions and Relevance: This cohort study of toddlers at HL and LL of autism suggests that there is an association between sex and EF and that brain-behavior associations in EF may be altered in children at HL of autism. Furthermore, EF deficits may aggregate in families, particularly in girls

Decadal variations in a Venus general circulation model

International audienceThe Community Atmosphere Model (CAM), a 3-dimensional Earth-based climate model, has been modified to simulate the dynamics of the Venus atmosphere. The most current finite volume version of CAM is used with Earth-related processes removed, parameters appropriate for Venus introduced, and some basic physics approximations adopted. A simplified Newtonian cooling approximation has been used for the radiation scheme. We use a high resolution (1° by 1° in latitude and longitude) to take account of small-scale dynamical processes that might be important on Venus. A Rayleigh friction approach is used at the lower boundary to represent surface drag, and a similar approach is implemented in the uppermost few model levels providing a 'sponge layer' to prevent wave reflection from the upper boundary. The simulations generate superrotation with wind velocities comparable to those measured in the Venus atmosphere by probes and around 50-60% of those measured by cloud tracking. At cloud heights and above the atmosphere is always superrotating with mid-latitude zonal jets that wax and wane on an approximate 10 year cycle. However, below the clouds, the zonal winds vary periodically on a decadal timescale between superrotation and subrotation. Both subrotating and superrotating mid-latitude jets are found in the approximate 40-60. km altitude range. The growth and decay of the sub-cloud level jets also occur on the decadal timescale. Though subrotating zonal winds are found below the clouds, the total angular momentum of the atmosphere is always in the sense of superrotation. The global relative angular momentum of the atmosphere oscillates with an amplitude of about 5% on the approximate 10 year timescale. Symmetric instability in the near surface equatorial atmosphere might be the source of the decadal oscillation in the atmospheric state. Analyses of angular momentum transport show that all the jets are built up by poleward transport by a meridional circulation while angular momentum is redistributed to lower latitudes primarily by transient eddies. Possible changes in the structure of Venus' cloud level mid-latitude jets measured by Mariner 10, Pioneer Venus, and Venus Express suggest that a cyclic variation similar to that found in the model might occur in the real Venus atmosphere, although no subrotating winds below the cloud level have been observed to date. Venus' atmosphere must be observed over multi-year timescales and below the clouds if we are to understand its dynamics. © 2010 Elsevier Inc

Seeding uniformity for vacuum precision seeders Uniformidade de semeaduras para semeadeiras de precisão a vácuo

The performance of three vacuum precision seeders was investigated in a field study. Seeding uniformity was determined in three different within-row distances: 14, 18 and 21 cm. The seeders were operated at 1.8, 3.6, 5.4 and 7.2 km h-1. Successive seed spacing along of 3 m of row was measured in three replications on each row. For evaluating the seeding uniformity of seeders, seed spacings were analyzed using the methods (MISS, MULT, QFI and PREC). There were no differences between seeders. For P < 0.01, operating speed affected MISS and QFI values, and the within-row seed spacing affected MULT and PREC values. The best operating speed was 1.8 km h-1 because of the highest QFI value (88.5%). There was no difference between 1.8 and 3.6 km h-1. The speeds, 1.8 and 3.6 km h-1, were different from 5.4 and 7.2 km h-1. The best within-row distance was 18 cm because the QFI value was higher than those of 14 and 20 cm, 86.9%, 82.0% and 81.8%, respectively. The best PREC value was obtained for 21 cm within-row distance (17.4%). PREC values were acceptable for precision seeding in all trials.<br>O comportamento de três semeadeiras de precisão a vácuo foi investigado em um estudo de campo. A uniformidade de semeadura foi determinada para três distâncias de entrelinha: 14, 18 e 21 cm. As semeadeiras operaram nas velocidades de 1,8; 3,6; 5,4 e 7,2 km h-1. O espaçamento entre sementes sucessivas foi feito ao longo de 3 m de linha, com três repetições em cada linha. Para avaliar a uniformidade, os espaçamentos entre sementes foram analisados usando os métodos (MISS, MULT, QFI e PREC) e nos resultados não foi achada diferença entre semeadeiras. Para P < 0,001 a velocidade de operação afetou MISS e QFI e o espaçamento entre linhas afetou MULT e PREC. A melhor velocidade de operação foi de 1,8 km h-1 devido ao seu mais alto valor de QFI (88,5%). Não houve diferença entre as velocidades de 1,8 e 3,6 km h-1, mas elas foram diferentes das velocidades 5,4 e 7,2 km h-1. A melhor distância entre linhas foi de 18 cm, pois seu QFI foi maior em relação à 14 e 20 cm, 86,9%, 82,0% e 81,8%, respectivamente. O melhor PREC foi obtido para 21 cm de entrelinha (17,4) e os valores de PREC foram aceitáveis para todos experimentos