Scaling asymptotics for quantized Hamiltonian flows

In recent years, the near diagonal asymptotics of the equivariant components of the Szeg\"{o} kernel of a positive line bundle on a compact symplectic manifold have been studied extensively by many authors. As a natural generalization of this theme, here we consider the local scaling asymptotics of the Toeplitz quantization of a Hamiltonian symplectomorphism, and specifically how they concentrate on the graph of the underlying classical map

Is a combination of varenicline and nicotine patch more effective in helping smokers quit than varenicline alone? A randomised controlled trial

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Local trace formulae and scaling asymptotics in Toeplitz quantization

A trace formula for Toeplitz operators was proved by Boutet de Monvel and Guillemin in the setting of general Toeplitz structures. Here we give a local version of this result for a class of Toeplitz operators related to continuous groups of symmetries on quantizable compact symplectic manifolds. The local trace formula involves certain scaling asymptotics along the clean fixed locus of the Hamiltonian flow of the symbol, reminiscent of the scaling asymptotics of the equivariant components of the Szeg\"o kernel along the diagonal

Rapid reduction versus abrupt quitting for smokers who want to stop soon: a randomised controlled non-inferiority trial

Background: The standard way to stop smoking is to stop abruptly on a quit day with no prior reduction in consumption of cigarettes. Many smokers feel that reduction is natural and if reduction programmes were offered, many more might take up treatment. Few trials of reduction versus abrupt cessation have been completed. Most are small, do not use pharmacotherapy, and do not meet the standards necessary to obtain a marketing authorisation for a pharmacotherapy.\ud Design/Methods: We will conduct a non-inferiority andomised trial of rapid reduction versus standard abrupt cessation among smokers who want to stop smoking. In the reduction arm,participants will be advised to reduce smoking consumption by half in the first week and to 25% of baseline in the second, leading up to a quit day at which participants will stop smoking completely.This will be assisted by nicotine patches and an acute form of nicotine replacement therapy. In the abrupt arm participants will use nicotine patches only, whilst smoking as normal, for two weeks prior to a quit day, at which they will also stop smoking completely. Smokers in either arm will have standard withdrawal orientated behavioural support programme with a combination of nicotine patches and acute nicotine replacement therapy post-cessation.\ud Outcomes/Follow-up: The primary outcome of interest will be prolonged abstinence from smoking, with secondary trial outcomes of point prevalence, urges to smoke and withdrawal\ud symptoms. Follow up will take place at 4 weeks, 8 weeks and 6 months post-quit day

Analysis of 17,576 Potentially Functional SNPs in Three Case–Control Studies of Myocardial Infarction

Myocardial infarction (MI) is a common complex disease with a genetic component. While several single nucleotide polymorphisms (SNPs) have been reported to be associated with risk of MI, they do not fully explain the observed genetic component of MI. We have been investigating the association between MI and SNPs that are located in genes and have the potential to affect gene function or expression. We have previously published studies that tested about 12,000 SNPs for association with risk of MI, early-onset MI, or coronary stenosis. In the current study we tested 17,576 SNPs that could affect gene function or expression. In order to use genotyping resources efficiently, we staged the testing of these SNPs in three case–control studies of MI. In the first study (762 cases, 857 controls) we tested 17,576 SNPs and found 1,949 SNPs that were associated with MI (P<0.05). We tested these 1,949 SNPs in a second study (579 cases and 1159 controls) and found that 24 SNPs were associated with MI (1-sided P<0.05) and had the same risk alleles in the first and second study. Finally, we tested these 24 SNPs in a third study (475 cases and 619 controls) and found that 5 SNPs in 4 genes (ENO1, FXN (2 SNPs), HLA-DPB2, and LPA) were associated with MI in the third study (1-sided P<0.05), and had the same risk alleles in all three studies. The false discovery rate for this group of 5 SNPs was 0.23. Thus, we have identified 5 SNPs that merit further examination for their potential association with MI. One of these SNPs (in LPA), has been previously shown to be associated with risk of cardiovascular disease in other studies