Solvability of subprincipal type operators

In this paper we consider the solvability of pseudodifferential operators in the case when the principal symbol vanishes of order $k \ge 2$ at a nonradial involutive manifold $\Sigma_2$. We shall assume that the operator is of subprincipal type, which means that the $k$:th inhomogeneous blowup at $\Sigma_2$ of the refined principal symbol is of principal type with Hamilton vector field parallel to the base $\Sigma_2$, but transversal to the symplectic leaves of $\Sigma_2$ at the characteristics. When $k = \infty$ this blowup reduces to the subprincipal symbol. We also assume that the blowup is essentially constant on the leaves of $\Sigma_2$, and does not satisfying the Nirenberg-Treves condition (${\Psi}$). We also have conditions on the vanishing of the normal gradient and the Hessian of the blowup at the characteristics. Under these conditions, we show that $P$ is not solvable.Comment: Changed the formulation of Theorem 2.15, added an assuption. Corrected errors and clarified the arguments. Added reference

Risks associated with obesity in pregnancy, for the mother and baby: a systematic review of reviews

Maternal obesity is linked with adverse outcomes for mothers and babies. To get an overview of risks related to obesity in pregnant women, a systematic review of reviews was conducted. For inclusion, reviews had to compare pregnant women of healthy weight with women with obesity, and measure a health outcome for mother and/or baby. Authors conducted full-text screening, quality assurance using the AMSTAR tool and data extraction steps in pairs. Narrative analysis of the 22 reviews included show gestational diabetes, pre-eclampsia, gestational hypertension, depression, instrumental and caesarean birth, and surgical site infection to be more likely to occur in pregnant women with obesity compared with women with a healthy weight. Maternal obesity is also linked to greater risk of preterm birth, large-for-gestational-age babies, foetal defects, congenital anomalies and perinatal death. Furthermore, breastfeeding initiation rates are lower and there is greater risk of early breastfeeding cessation in women with obesity compared with healthy weight women. These adverse outcomes may result in longer duration of hospital stay, with concomitant resource implications. It is crucial to reduce the burden of adverse maternal and foetal/child outcomes caused by maternal obesity. Women with obesity need support to lose weight before they conceive, and to minimize their weight gain in pregnancy

Probabilistic Weyl laws for quantized tori

For the Toeplitz quantization of complex-valued functions on a $2n$-dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law. In numerical experiments the same Weyl law also holds for ``false'' eigenvalues created by pseudospectral effects.Comment: 33 pages, 3 figures, v2 corrected listed titl

Knowledge Acquisition Activities, Prior Knowledge and Experience & the Survival of New Firms

Knowledge acquisition activities occurring may be just as critical to firm survival as pre-existing knowledge and experience, because knowledge acquisition activities enable the augmentation of existing knowledge and the exploration and pursuit of new strategic directions. Drawing from organization theory and entrepreneurship theory, we examine two important sets of knowledge acquisition activities: knowledge acquired through planning and knowledge acquired through learning by doing. We examine the direct impact of these activities on the survival of new firms and examine the extent to which planning and learning by doing can compensate for low prior knowledge and/or management experience. We find that while learning by doing promotes firm survival and can compensate, planning deters firm survival and can not compensate

Cardiorespiratory fitness is associated with hard and light intensity physical activity but not time spent sedentary in 10–14 year old schoolchildren: the HAPPY study

Sedentary behaviour is a major risk factor for developing chronic diseases and is associated with low cardiorespiratory fitness in adults. It remains unclear how sedentary behaviour and different physical activity subcomponents are related to cardiorespiratory fitness in children. The purpose of this study was to assess how sedentary behaviour and different physical activity subcomponents are associated with 10–14 year-old schoolchildren's cardiorespiratory fitness

Quadricuspid aortic valve by using intraoperative transesophageal echocardiography

Quadricuspid aortic valve is a rare congenital malformation of the aortic valve. Its diagnosis is often missed even with the use of transthoracic echocardiogram. Many of these patients progress to aortic incompetence later in life, hence requiring surgical intervention

Characterization of Single-Mode Vertical Cavity Surface-Emitting Lasers

A high-quality single-mode beam is desirable for the efficient use of lasers as light sources for optical data communications and interconnects, however there is little data which characterizes operating ranges and near-field beam qualities of Vertical Cavity Surface Emitting Lasers (VCSELs), which has resulted in a lack of analysis of these devices. Measures of beam quality include beam-quality factor (M2 ), Side-Mode-Suppression-Ratio (SMSR) and RMS linewidth. M2 is a measurement of how closely the beam is to an ideal Gaussian. SMSR is the difference, in dB, between the amplitude of the primary peak and the amplitude of the next highest peak of the output spectrum, with single-mode operation defined by a SMSR \u3e 30 dB. RMS linewidth is a second moment calculation involving the power spectral density, where smaller RMS linewidth indicates higher beam quality. Utilizing a novel vertical M2 setup in which on-wafer VCSEL M2 can be measured, a study was conducted on the relation between M2 , SMSR and RMS linewidth, for various oxide-confined VCSELs of varying aperture sizes and Photonic Crystal (PhC) VCSELs of varying aperture sizes and photonic crystal configurations. First, the operating range of the VCSEL was determined utilizing a Semiconductor Parameter Analyzer to obtain the LIV characteristics. Along with this measurement, spectral data was collected using an Optical Spectrum Analyzer at several key operating points, which allowed the RMS linewidths and SMSRs of the devices to be calculated at these points. The novel beam-profiler setup was used to measure the device’s M2 . Initial results show a strong correlation between the measures of beam quality, with increasing SMSR, corresponding to M2 values closer to 1, and single-mode operation characterized by a M2 of less than 1.5. A strong correlation between RMS linewidth and M2 was also seen, with increasing RMS linewidths corresponding to an increase in M2

Childbirth experience questionnaire: validating its use in the United Kingdom

BACKGROUND: The Childbirth Experience Questionnaire (CEQ) was developed in Sweden in 2010 and validated in 920 primiparous women. It has not been validated in the United Kingdom (UK). Measuring the impact of an intervention on a woman's childbirth experience is arguably as important as measuring its impact on outcomes such as caesarean delivery and perinatal morbidity or mortality and yet surprisingly it is rarely done. The lack of a robust validated tool for evaluating labour experience in the UK is a topical issue in the UK at present. Indeed NICE say 'A standardised method to measure and quantify women's psychological and emotional wellbeing and their birth experiences is urgently required to support any study investigating the effectiveness of interventions, techniques or strategies during birth.' METHODS: The Childbirth Experience Questionnaire and part of the Care Quality Commission Maternity Survey (2010) was sent to 350 women at one month postnatal. The CEQ was sent again two weeks later. The CEQ was tested for face validity among 25 postnatal mothers. Demographic data and delivery data was used to establish construct validity of the CEQ using the method of known-groups validation. The results of the scored CEQ sent out twice were used to measure test-retest reliability of the CEQ by calculating the quadratic weighted index of agreement between the two scores. Criterion validity was measured by calculating the Pearson correlation coefficient for the CEQ and Maternity Survey scores. RESULTS: Face validity of the CEQ in a UK population was demonstrated with all respondents stating it was easy to understand and complete. A statistically significantly higher CEQ score for subgroups of women known to report a better birth outcome demonstrated construct validity of the CEQ. A weighted kappa of 0.68 demonstrated test-retest reliability of the CEQ. A Pearson correlation co-efficient of 0.73 demonstrated a strong correlation between the results of the CEQ and the results of the 'gold standard' assessment of childbirth experience in the UK: the Maternity Survey and hence criterion validity of the CEQ. CONCLUSIONS: The Childbirth Experience Questionnaire is a valid and reliable measure of childbirth experience in the UK population

Characterization of Single-Mode Vertical Cavity Surface-Emitting Lasers

A high-quality single-mode beam is desirable for the efficient use of lasers as light sources for optical data communications and interconnects, however there is little data which characterizes operating ranges and near-field beam qualities of Vertical Cavity Surface Emitting Lasers (VCSELs), which has resulted in a lack of analysis of these devices. Measures of beam quality include beam-quality factor (M2 ), Side-Mode-Suppression-Ratio (SMSR) and RMS linewidth. M2 is a measurement of how closely the beam is to an ideal Gaussian. SMSR is the difference, in dB, between the amplitude of the primary peak and the amplitude of the next highest peak of the output spectrum, with single-mode operation defined by a SMSR \u3e 30 dB. RMS linewidth is a second moment calculation involving the power spectral density, where smaller RMS linewidth indicates higher beam quality. Utilizing a novel vertical M2 setup in which on-wafer VCSEL M2 can be measured, a study was conducted on the relation between M2 , SMSR and RMS linewidth, for various oxide-confined VCSELs of varying aperture sizes and Photonic Crystal (PhC) VCSELs of varying aperture sizes and photonic crystal configurations. First, the operating range of the VCSEL was determined utilizing a Semiconductor Parameter Analyzer to obtain the LIV characteristics. Along with this measurement, spectral data was collected using an Optical Spectrum Analyzer at several key operating points, which allowed the RMS linewidths and SMSRs of the devices to be calculated at these points. The novel beam-profiler setup was used to measure the device’s M2 . Initial results show a strong correlation between the measures of beam quality, with increasing SMSR, corresponding to M2 values closer to 1, and single-mode operation characterized by a M2 of less than 1.5. A strong correlation between RMS linewidth and M2 was also seen, with increasing RMS linewidths corresponding to an increase in M2

Objectively measured physical activity and fat mass in a large cohort of children

Background Previous studies have been unable to characterise the association between physical activity and obesity, possibly because most relied on inaccurate measures of physical activity and obesity. Methods and Findings We carried out a cross sectional analysis on 5,500 12-year-old children enrolled in the Avon Longitudinal Study of Parents and Children. Total physical activity and minutes of moderate and vigorous physical activity (MVPA) were measured using the Actigraph accelerometer. Fat mass and obesity (defined as the top decile of fat mass) were measured using the Lunar Prodigy dual x-ray emission absorptiometry scanner. We found strong negative associations between MVPA and fat mass that were unaltered after adjustment for total physical activity. We found a strong negative dose-response association between MVPA and obesity. The odds ratio for obesity in adjusted models between top and the bottom quintiles of minutes of MVPA was 0.03 (95% confidence interval [CI] 0.01-0.13, p-value for trend < 0.0001) in boys and 0.36 (95% CI 0.17-0.74, p-value for trend = 0.006) in girls. Conclusions We demonstrated a strong graded inverse association between physical activity and obesity that was stronger in boys. Our data suggest that higher intensity physical activity may be more important than total activity