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In this paper, we show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.

\"Among the many instruments devised by students of mathematical sciences in ancient Greece, the monochord provides one of the best opportunities to examine the methodologies of those who employed it in their investigations. Consisting of a single string which could be divided at measured points by means of movable bridges, it was used to demonstrate theorems about the arithmetical relationships between pitched sounds in music. This book traces the history of the monochord and its multiple uses down to Ptolemy, bringing together all the relevant evidence in one comprehensive study. By comparing the monochord with a number of other ancient scientific instruments and their uses, David Creese shows how the investigation of music in ancient Greece not only shares in the patterns of demonstrative and argumentative instrument use common to other sciences, but also goes beyond them in offering the possibility of a rigorous empiricism unparalleled in Greek science\"--Provided by publisher.

In the practice of data analysis, there is a conceptual distinction between hypothesis testing, on the one hand, and estimation with quantified uncertainty on the other. Among frequentists in psychology, a shift of emphasis from hypothesis testing to estimation has been dubbed “the New Statistics” (Cumming 2014 ). A second conceptual distinction is between frequentist methods and Bayesian methods. Our main goal in this article is to explain how Bayesian methods achieve the goals of the New Statistics better than frequentist methods. The article reviews frequentist and Bayesian approaches to hypothesis testing and to estimation with confidence or credible intervals. The article also describes Bayesian approaches to meta-analysis, randomized controlled trials, and power analysis.

The purpose of this paper is to propose methodologies for statistical inference of low dimensional parameters with high dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of several of them in a linear regression model, although our ideas are applicable in a much broader context. The theoretical results that are presented provide sufficient conditions for the asymptotic normality of the proposed estimators along with a consistent estimator for their finite dimensional covariance matrices. These sufficient conditions allow the number of variables to exceed the sample size and the presence of many small non‐zero coefficients. Our methods and theory apply to interval estimation of a preconceived regression coefficient or contrast as well as simultaneous interval estimation of many regression coefficients. Moreover, the method proposed turns the regression data into an approximate Gaussian sequence of point estimators of individual regression coefficients, which can be used to select variables after proper thresholding. The simulation results that are presented demonstrate the accuracy of the coverage probability of the confidence intervals proposed as well as other desirable properties, strongly supporting the theoretical results.

IntroductionTranscatheter aortic valve implantation (TAVI) is an established treatment for patients with severe symptomatic aortic stenosis at high and intermediate operative risk. Permanent pacemaker (PPM) implantation, after TAVI, remains a common occurrence. Identifying the predictors of post TAVI PPM requirement and long-term consequences are important as TAVI extends to low-risk patients.MethodsWe report the rate of PPM implantation for all patients that had TAVI in Northern Ireland (n=1033) between February 2008 and December 2018. 7% (n=72) had a PPM at baseline and were excluded from the analysis. The remaining 961 patients were investigated and after performing an initial univariate analysis, we identified predictors of new PPM at 1 year via an adjusted multivariate model (table 1). Survival was predicted using Kaplan-Meier analysis.ResultsAt 30-days and 1 year, respectively, new PPM was required in 14.6% (n=140) and 17% (n=163) patients, with males having a higher rate of PPM at 1 year (20% vs. 14.4%, p 0.022). There was no significant difference in age (81.3±6.4 y vs. 81.7±6.8 y, p 0.602) or EuroScore2 (7.8±6.5% vs. 8.4±8.1%, p 0.357) between patients requiring/not requiring a PPM at 1 year. Right bundle branch block (RBBB (8% vs. 1.6%, p<0.0005)) was associated with a 5-fold increase risk in PPM implantation at 1 year. The presence of 1st degree AV block (12.9% vs. 4.4%, p<0.0005), at baseline, was associated with a 3-fold increase risk of PPM implantation at 1 year. We compared the early pre multi-slice CT (MSCT) era and current time period using routine MSCT for procedural planning. We found that the routine use of MSCT was associated with a significantly lower rate of new PPM implantation at 1 year (13.6% vs. 33.1%, p<0.0005). Mechanical- (n=58) and self-expandable (n=641) valves were associated with higher rates of PPM at 1 year, compared to balloon-expandable (n=262) valves (25.9% vs. 18.9% vs. 10.3%, p 0.001). There was no significant difference in long-term survival for patients that had PPM implantation at 1 year (median survival 4.6 y vs. 5.1 y, p.336). Heart failure (HF) readmissions, at any time, were significantly higher for patients that required a PPM at 1 year (19% vs. 12.7%, p 0.032), even after adjusting for impaired left ventricular systolic function. There was no significant difference in post-TAVI infective endocarditis (IE) between the two groups (0.6% (n=1) vs. 1.9% (n=15), p 0.497). Abstract 56 Table 1Predictors of new PPM implantation at 1 year after TAVI Predictors of new PPM implantation at 1 year after TAVI Variable Odds Ratio 95% Confidence interval p value (unadj.) Odds ratio 95% Confidence interval p value (adjust.) Age, years 0.99 0.97–1.02 0.602 Male sex 1.49 1.06–2.09 0.022 1.47 1.03–2.103 0.034 CrCl mL/min 0.99 0.99–1.01 0.556 EuroScore 2 0.99 0.97–1.00 0.091 Prior Cardiac Surgery 1.25 0.82–1.90 0.298 AF/flutter 1.19 0.83–1.70 0.343 LBBB 1.13 0.60–2.11 0.709 RBBB 5.23 2.40–11.51 <.0005 5.48 2.40–12.53 <0.0005 1st degree AV Block 3.22 1.82–5.70 <.0005 3.30 1.81–6.00 <0.0005 MSCT era 0.60 0.43-.84 0.003 0.64 0.37–1.33 0.013 BE valve 0.476 0.31-.74 0.001 0.29 0.14-.61 0.001 ConclusionWe identified baseline characteristics predictive of PPM implantation at 1 year. The need for a new PPM, after TAVI, decreased with time. This is likely explained by the routine use of MSCT for procedural planning, improved operator implantation technique and improvements in valve technology. While there was no difference in long-term mortality or IE, there was an increase in HF readmissions in patients that required a PPM after TAVI. The long-term effects of PPM implantation on morbidity, after TAVI, requires further and more prolonged follow-up.

We propose a robust method for constructing conditionally valid prediction intervals based on models for conditional distributions such as quantile and distribution regression. Our approach can be applied to important prediction problems, including cross-sectional prediction, k–step-ahead forecasts, synthetic controls and counterfactual prediction, and individual treatment effects prediction. Our method exploits the probability integral transform and relies on permuting estimated ranks. Unlike regression residuals, ranks are independent of the predictors, allowing us to construct conditionally valid prediction intervals under heteroskedasticity. We establish approximate conditional validity under consistent estimation and provide approximate unconditional validity under model misspecification, under overfitting, and with time series data. We also propose a simple “shape” adjustment of our baseline method that yields optimal prediction intervals.