Detecting squarefree numbers

We present an algorithm, based on the explicit formula for $L$-functions and conditional on GRH, for proving that a given integer is squarefree with little or no knowledge of its factorization. We analyze the algorithm both theoretically and practically, and use it to prove that several RSA challenge numbers are not squarefull.Comment: 31 pages, 3 figures, latest versio

Pair correlation and twin primes revisited

We use the methods developed in our papers on moments and divisor correlations to derive heuristically the conjectural ratios formula for two zetas over two zetas

Random Matrix Theory and the Fourier Coefficients of Half-Integral Weight Forms

Conjectured links between the distribution of values taken by the characteristic polynomials of random orthogonal matrices and that for certain families of L-functions at the centre of the critical strip are used to motivate a series of conjectures concerning the value-distribution of the Fourier coefficients of half-integral weight modular forms related to these L-functions. Our conjectures may be viewed as being analogous to the Sato-Tate conjecture for integral weight modular forms. Numerical evidence is presented in support of them.Comment: 28 pages, 8 figure

On the joint moments of the characteristic polynomials of random unitary matrices

We establish the asymptotics of the joint moments of the characteristic polynomial of a random unitary matrix and its derivative for general real values of the exponents, proving a conjecture made by Hughes in 2001. Moreover, we give a probabilistic representation for the leading order coefficient in the asymptotic in terms of a real-valued random variable that plays an important role in the ergodic decomposition of the Hua-Pickrell measures. This enables us to establish connections between the characteristic function of this random variable and the $\sigma$-Painlev\'{e} III' equation.Comment: Minor revision according to referee reports. To appear IMR

Lower order terms in the full moment conjecture for the Riemann zeta function

We describe an algorithm for obtaining explicit expressions for lower terms for the conjectured full asymptotics of the moments of the Riemann zeta function, and give two distinct methods for obtaining numerical values of these coefficients. We also provide some numerical evidence in favour of the conjecture.Comment: 37 pages, 4 figure

Evaluation of a student-run smoking cessation clinic for a medically underserved population

<p>Abstract</p> <p>Background</p> <p>Smoking is common among medically underserved populations. Accessible resources to encourage and support smoking cessation among these patients are limited. Volunteer medical student-run free smoking cessation clinics may provide an effective option to help these individuals achieve smoking abstinence. In order to demonstrate the feasibility and cost-effectiveness of a student-run clinic, we analyzed a case series of patients receiving care in a medical student-run Smoking Cessation Clinic (SCC) at the Rochester, Minnesota Salvation Army Good Samaritan Health Clinic (GSHC).</p> <p>Findings</p> <p>Between January 2005 and March 2009, 282 cigarette smokers seeking care at the SCC were analyzed. Student providers at the SCC conducted 1652 weekly individual counseling sessions averaging 18 minutes per encounter. Patients were offered a choice of pharmacotherapies including nicotine replacement therapy (NRT), bupropion, and varenicline for up to 12 weeks. Smoking abstinence was confirmed with exhaled carbon monoxide (CO). Thirty-two patients completed the entire 12-week program (11.3%). At last contact, 94 patients (33.3%) abstained from smoking for ≥ 7 days and 39 patients (13.8%) were continuously abstinent for ≥ 4 weeks. The 7-day point prevalence abstinence rates at last contact were 58.6% for varenicline, 41.2% for bupropion, 33.9% for NRT, and 23.5% for bupropion and NRT. Analyzing missing patients as smoking, the 7-day point prevalence abstinence rates were 7.1%, 8.9%, and 8.2%, at 1 month, 2 months, and 3 months after program enrollment, respectively. No serious adverse drug reactions were recorded.</p> <p>Conclusions</p> <p>Our medical student-run smoking cessation clinic provided an effective and safe experience for medically underserved patients who might not otherwise have access to conventional smoking cessation programs because of high cost, lack of insurance, or other disparities. Similar medical student initiatives focusing on healthy lifestyles may be feasible and beneficial for individuals with limited access to healthcare resources.</p

Adult height, coronary heart disease and stroke: a multi-locus Mendelian randomization meta-analysis

BACKGROUND: We investigated causal effect of completed growth, measured by adult height, on coronary heart disease (CHD), stroke and cardiovascular traits, using instrumental variable (IV) Mendelian randomization meta-analysis. METHODS: We developed an allele score based on 69 single nucleotide polymorphisms (SNPs) associated with adult height, identified by the IBCCardioChip, and used it for IV analysis against cardiovascular risk factors and events in 21 studies and 60 028 participants. IV analysis on CHD was supplemented by summary data from 180 height-SNPs from the GIANT consortium and their corresponding CHD estimates derived from CARDIoGRAMplusC4D. RESULTS: IV estimates from IBCCardioChip and GIANT-CARDIoGRAMplusC4D showed that a 6.5-cm increase in height reduced the odds of CHD by 10% [odds ratios 0.90; 95% confidence intervals (CIs): 0.78 to 1.03 and 0.85 to 0.95, respectively],which agrees with the estimate from the Emerging Risk Factors Collaboration (hazard ratio 0.93; 95% CI: 0.91 to 0.94). IV analysis revealed no association with stroke (odds ratio 0.97; 95% CI: 0.79 to 1.19). IV analysis showed that a 6.5-cm increase in height resulted in lower levels of body mass index (P < 0.001), triglycerides (P < 0.001), non high-density (non-HDL) cholesterol (P < 0.001), C-reactive protein (P = 0.042), and systolic blood pressure (P = 0.064) and higher levels of forced expiratory volume in 1 s and forced vital capacity (P < 0.001 for both). CONCLUSIONS: Taller individuals have a lower risk of CHD with potential explanations being that taller people have a better lung function and lower levels of body mass index, cholesterol and blood pressure

Population genomics of cardiometabolic traits: design of the University College London-London School of Hygiene and Tropical Medicine-Edinburgh-Bristol (UCLEB) Consortium.

Substantial advances have been made in identifying common genetic variants influencing cardiometabolic traits and disease outcomes through genome wide association studies. Nevertheless, gaps in knowledge remain and new questions have arisen regarding the population relevance, mechanisms, and applications for healthcare. Using a new high-resolution custom single nucleotide polymorphism (SNP) array (Metabochip) incorporating dense coverage of genomic regions linked to cardiometabolic disease, the University College-London School-Edinburgh-Bristol (UCLEB) consortium of highly-phenotyped population-based prospective studies, aims to: (1) fine map functionally relevant SNPs; (2) precisely estimate individual absolute and population attributable risks based on individual SNPs and their combination; (3) investigate mechanisms leading to altered risk factor profiles and CVD events; and (4) use Mendelian randomisation to undertake studies of the causal role in CVD of a range of cardiovascular biomarkers to inform public health policy and help develop new preventative therapies