Large Sums of Fourier Coefficients of Cusp Forms

Let $N$ be a fixed positive integer, and let $f\in S_k(N)$ be a primitive cusp form given by the Fourier expansion $f(z)=\sum_{n=1}^{\infty} \lambda_f(n)n^{\frac{k-1}{2}}e(nz)$. We consider the partial sum $S(x,f)=\sum_{n\leq x}\lambda_f(x)$. It is conjectured that $S(x,f)=o(x\log x)$ in the range $x\geq k^{\epsilon}$. Lamzouri proved in arXiv:1703.10582 [math.NT] that this is true under the assumption of the Generalized Riemann Hypothesis (GRH) for $L(s,f)$. In this paper, we prove that this conjecture holds under a weaker assumption than GRH. In particular, we prove that given $\epsilon>(\log k)^{-\frac{1}{8}}$ and $1\leq T\leq (\log k)^{\frac{1}{200}}$, we have $S(x,f)\ll \frac{x\log x}{T}$ in the range $x\geq k^{\epsilon}$ provided that $L(s,f)$ has no more than $\epsilon^2\log k/5000$ zeros in the region $\left\{s\,:\, \Re(s)\geq \frac34, \, |\Im(s)-\phi| \leq \frac14\right\}$ for every real number $\phi$ with $|\phi|\leq T$.Comment: 14 page

Positive mindset and exercise capacity in school-aged children and adolescents with congenital heart disease

IntroductionPatients with congenital heart disease (CHD) have variable degrees of peak oxygen consumption (VO2) that can be improved with supervised fitness training. The ability to exercise is affected by anatomy, hemodynamics, and motivation. Motivation is in part related to mindset, or personal attitudes and beliefs, and a more positive mindset around exercise has been associated with better outcomes. It is unknown whether variations in measured peak VO2 in patients with CHD are related to having a positive mindset.MethodsPatient's ages 8–17 years with CHD were administered quality of life and physical activity questionnaires at the time of their routine cardiopulmonary exercise test. Those with severe hemodynamic burden were excluded. Patients were grouped based on disease classification. Mindset was evaluated via validated questionnaires including a PROMIS Meaning and Purpose (MaP) survey and an Anxiety survey. Pearson correlation coefficients were calculated to estimate the magnitude of the association between percent predicted peak oxygen consumption (pppVO2) and questionnaire scores overall and within CHD subgroups.ResultsEighty-five patients participated; median age was 14.7 years, 53% were female, 66% had complex CHD, 20% had simple CHD, and 14% had single ventricle heart disease. Mean MaP scores were significantly lower in all CHD groups compared to population norms (p < 0.001). As a group, MaP scores were positively associated with the amount of reported physical activity (p = 0.017). In patients with simple CHD, MaP scores were positively associated with pppVO2 (p = 0.015). The association was even stronger for MaP:Anxiety, with worse ratios associated with lower pppVO2 (p = 0.005). Patients with complex and single ventricle CHD did not show a similar association.ConclusionsPatients with CHD, regardless of severity, had lower meaning and purpose scores than the general population, and these scores were associated with amount of reported physical activity. In the simple CHD subset, having a more positive mindset was associated with higher peak VO2 and a more negative mindset with lower peak VO2. This relationship was not seen with more significant CHD. While underlying CHD diagnoses are not modifiable, mindset and peak VO2 are, and consideration should be given to measuring both as each may be a target for intervention

Right ventricular contraction patterns in healthy children using three-dimensional echocardiography

Background: The right ventricle (RV) has complex geometry and function, with motion along three separate axes—longitudinal, radial, and anteroposterior. Quantitative assessment of RV function by two-dimension echocardiography (2DE) has been limited as a consequence of this complexity, whereas newer three dimensional (3D) analysis offers the potential for more comprehensive assessment of the contributors to RV function. The aims of this study were to quantify the longitudinal, radial and anteroposterior components of global RV function using 3D echocardiography in a cohort of healthy children and to examine maturational changes in these parameters. Methods: Three-dimensional contours of the RV were generated from a cohort of healthy pediatric patients with structurally normal hearts at two centers. Traditional 2D and 3D echo characteristics were recorded. Using offline analysis of 3D datasets, RV motion was decomposed into three components, and ejection fractions (EF) were calculated (longitudinal-LEF; radial-REF; and anteroposterior-AEF). The individual decomposed EF values were indexed against the global RVEF. Strain values were calculated as well. Results: Data from 166 subjects were included in the analysis; median age was 13.5 years (range 0 to 17.4 years). Overall, AEF was greater than REF and LEF (29.2 ± 6.2% vs. 25.1 ± 7.2% and 25.7 ± 6.0%, respectively; p < 0.001). This remained true when indexed to overall EF (49.8 ± 8.7% vs. 43.3 ± 11.6% and 44.4 ± 10%, respectively; p < 0.001). Age-related differences were present for global RVEF, REF, and all components of RV strain. Conclusions: In healthy children, anteroposterior shortening is the dominant component of RV contraction. Evaluation of 3D parameters of the RV in children is feasible and enhances the overall understanding of RV function, which may allow improvements in recognition of dysfunction and assessment of treatment effects in the future

ehealth technology in cardiac exercise therapeutics for pediatric patients with congenital and acquired heart conditions: a summary of evidence and future directions

Many children and adolescents with congenital and acquired heart disease (CHD) are physically inactive and participate in an insufficient amount of moderate-to-vigorous intensity exercise. Although physical activity (PA) and exercise interventions are effective at improving short- and long-term physiological and psychosocial outcomes in youth with CHD, several barriers including resource limitations, financial costs, and knowledge inhibit widespread implementation and dissemination of these beneficial programs. New and developing eHealth, mHealth, and remote monitoring technologies offer a potentially transformative and cost-effective solution to increase access to PA and exercise programs for youth with CHD, yet little has been written on this topic. In this review, a cardiac exercise therapeutics (CET) model is presented as a systematic approach to PA and exercise, with assessment and testing guiding three sequential PA and exercise intervention approaches of progressive intensity and resource requirements: (1) PA and exercise promotion within a clinical setting; (2) unsupervised exercise prescription; and (3) medically supervised fitness training intervention (i.e., cardiac rehabilitation). Using the CET model, the goal of this review is to summarize the current evidence describing the application of novel technologies within CET in populations of children and adolescents with CHD and introduce potential future applications of these technologies with an emphasis on improving equity and access to patients in low-resource settings and underserved communities

Risk of endometrial cancer in relationship to cigarette smoking: results from the EPIC study

Abstract is not availabl

Core components of a rehabilitation program in pediatric cardiac disease

There is increasing effort in both the inpatient and outpatient setting to improve care, function, and quality of life for children with congenital heart disease, and to decrease complications. As the mortality rates of surgical procedures for congenital heart disease decrease, improvement in perioperative morbidity and quality of life have become key metrics of quality of care. Quality of life and function in patients with congenital heart disease can be affected by multiple factors: the underlying heart condition, cardiac surgery, complications, and medical treatment. Some of the functional areas affected are motor abilities, exercise capacity, feeding, speech, cognition, and psychosocial adjustment. Rehabilitation interventions aim to enhance and restore functional ability and quality of life for those with physical impairments or disabilities. Interventions such as exercise training have been extensively evaluated in adults with acquired heart disease, and rehabilitation interventions for pediatric patients with congenital heart disease have similar potential to improve perioperative morbidity and quality of life. However, literature regarding the pediatric population is limited. We have gathered a multidisciplinary team of experts from major institutions to create evidence- and practice-based guidelines for pediatric cardiac rehabilitation programs in both inpatient and outpatient settings. To improve the quality of life of pediatric patients with congenital heart disease, we propose the use of individualized multidisciplinary rehabilitation programs that include: medical management; neuropsychology; nursing care; rehabilitation equipment; physical, occupational, speech, and feeding therapies; and exercise training

Gender-Specific Effects of Unemployment on Family Formation: A Cross-National Perspective

This paper investigates the impact of unemployment on the propensity to start a family. Unemployment is accompanied by bad occupational prospects and impending economic deprivation, placing the well-being of a future family at risk. I analyze unemployment at the intersection of state-dependence and the reduced opportunity costs of parenthood, distinguishing between men and women across a set of welfare states. Using micro-data from the European Community Household Panel (ECHP), I apply event history methods to analyze longitudinal samples of first-birth transitions in France, Finland, Germany, and the UK (1994-2001). The results highlight spurious negative effects of unemployment on family formation among men, which can be attributed to the lack of breadwinner capabilities in the inability to financially support a family. Women, in contrast, show positive effects of unemployment on the propensity to have a first child in all countries except France. These effects prevail even after ontrolling for labour market and income-related factors. The findings are pronounced in Germany and the UK where work-family conflicts are the cause of high opportunity costs of motherhood, and the gender-specific division of labour is still highly traditional. Particularly among women with a moderate and low level of education, unemployment clearly increases the likelihood to have a first child

The SuperCam Instrument Suite on the Mars 2020 Rover: Science Objectives and Mast-Unit Description

On the NASA 2020 rover mission to Jezero crater, the remote determination of the texture, mineralogy and chemistry of rocks is essential to quickly and thoroughly characterize an area and to optimize the selection of samples for return to Earth. As part of the Perseverance payload, SuperCam is a suite of five techniques that provide critical and complementary observations via Laser-Induced Breakdown Spectroscopy (LIBS), Time-Resolved Raman and Luminescence (TRR/L), visible and near-infrared spectroscopy (VISIR), high-resolution color imaging (RMI), and acoustic recording (MIC). SuperCam operates at remote distances, primarily 2-7 m, while providing data at sub-mm to mm scales. We report on SuperCam's science objectives in the context of the Mars 2020 mission goals and ways the different techniques can address these questions. The instrument is made up of three separate subsystems: the Mast Unit is designed and built in France; the Body Unit is provided by the United States; the calibration target holder is contributed by Spain, and the targets themselves by the entire science team. This publication focuses on the design, development, and tests of the Mast Unit; companion papers describe the other units. The goal of this work is to provide an understanding of the technical choices made, the constraints that were imposed, and ultimately the validated performance of the flight model as it leaves Earth, and it will serve as the foundation for Mars operations and future processing of the data.In France was provided by the Centre National d'Etudes Spatiales (CNES). Human resources were provided in part by the Centre National de la Recherche Scientifique (CNRS) and universities. Funding was provided in the US by NASA's Mars Exploration Program. Some funding of data analyses at Los Alamos National Laboratory (LANL) was provided by laboratory-directed research and development funds