Super congruences and Euler numbers

Let $p>3$ be a prime. We prove that $$\sum_{k=0}^{p-1}\binom{2k}{k}/2^k=(-1)^{(p-1)/2}-p^2E_{p-3} (mod p^3),$$ $$\sum_{k=1}^{(p-1)/2}\binom{2k}{k}/k=(-1)^{(p+1)/2}8/3*pE_{p-3} (mod p^2),$$ $$\sum_{k=0}^{(p-1)/2}\binom{2k}{k}^2/16^k=(-1)^{(p-1)/2}+p^2E_{p-3} (mod p^3)$$, where E_0,E_1,E_2,... are Euler numbers. Our new approach is of combinatorial nature. We also formulate many conjectures concerning super congruences and relate most of them to Euler numbers or Bernoulli numbers. Motivated by our investigation of super congruences, we also raise a conjecture on 7 new series for $\pi^2$, $\pi^{-2}$ and the constant $K:=\sum_{k>0}(k/3)/k^2$ (with (-) the Jacobi symbol), two of which are $$\sum_{k=1}^\infty(10k-3)8^k/(k^3\binom{2k}{k}^2\binom{3k}{k})=\pi^2/2$$ and $$\sum_{k>0}(15k-4)(-27)^{k-1}/(k^3\binom{2k}{k}^2\binom{3k}k)=K.$

Measurements of single top quark production cross sections and |Vtb| in ppbar collisions at sqrt{s}=1.96 TeV

We present measurements of production cross sections of single top quarks in \ppbar collisions at $\sqrt{s}=1.96\;\rm TeV$ in a data sample corresponding to an integrated luminosity of $5.4\;\rm fb^{-1}$ collected by the D0 detector at the Fermilab Tevatron Collider. We select events with an isolated electron or muon, an imbalance in transverse energy, and two, three, or four jets, with one or two of them containing a bottom hadron. We obtain an inclusive cross section of \sigma({\ppbar}{\rargap}tb+X, tqb+X) = 3.43\pm^{0.73}_{0.74}\;\rm pb and use it to extract the CKM matrix element $0.79 < |V_{tb}| \leq 1$ at the 95% C.L. We also measure \sigma({\ppbar}{\rargap}tb+X) = 0.68\pm^{0.38}_{0.35}\;\rm pb and \sigma({\ppbar}{\rargap}tqb+X) = 2.86\pm^{0.69}_{0.63}\;\rm pb when assuming, respectively, $tqb$ and $tb$ production rates as predicted by the standard model.Comment: 11 pages, 8 figures, submitted to Phys. Rev.

The state of the Martian climate

60°N was +2.0°C, relative to the 1981–2010 average value (Fig. 5.1). This marks a new high for the record. The average annual surface air temperature (SAT) anomaly for 2016 for land stations north of starting in 1900, and is a significant increase over the previous highest value of +1.2°C, which was observed in 2007, 2011, and 2015. Average global annual temperatures also showed record values in 2015 and 2016. Currently, the Arctic is warming at more than twice the rate of lower latitudes

The Role of Practitioner Resilience and Mindfulness in Effective Practice: A Practice-Based Feasibility Study.

A growing body of literature attests to the existence of therapist effects with little explanation of this phenomenon. This study therefore investigated the role of resilience and mindfulness as factors related to practitioner wellbeing and associated effective practice. Data comprised practitioners (n = 37) and their patient outcome data (n = 4980) conducted within a stepped care model of service delivery. Analyses employed benchmarking and multilevel modeling to identify more and less effective practitioners via yoking of therapist factors and nested patient outcomes. A therapist effect of 6.7 % was identified based on patient depression (PHQ-9) outcome scores. More effective practitioners compared to less effective practitioners displayed significantly higher levels of mindfulness as well as resilience and mindfulness combined. Implications for policy, research and practice are discussed

Mutations in the UBIAD1 Gene, Encoding a Potential Prenyltransferase, Are Causal for Schnyder Crystalline Corneal Dystrophy

Schnyder crystalline corneal dystrophy (SCCD, MIM 121800) is a rare autosomal dominant disease characterized by progressive opacification of the cornea resulting from the local accumulation of lipids, and associated in some cases with systemic dyslipidemia. Although previous studies of the genetics of SCCD have localized the defective gene to a 1.58 Mbp interval on chromosome 1p, exhaustive sequencing of positional candidate genes has thus far failed to reveal causal mutations. We have ascertained a large multigenerational family in Nova Scotia affected with SCCD in which we have confirmed linkage to the same general area of chromosome 1. Intensive fine mapping in our family revealed a 1.3 Mbp candidate interval overlapping that previously reported. Sequencing of genes in our interval led to the identification of five putative causal mutations in gene UBIAD1, in our family as well as in four other small families of various geographic origins. UBIAD1 encodes a potential prenyltransferase, and is reported to interact physically with apolipoprotein E. UBIAD1 may play a direct role in intracellular cholesterol biochemistry, or may prenylate other proteins regulating cholesterol transport and storage

Genomic correlates of glatiramer acetate adverse cardiovascular effects lead to a novel locus mediating coronary risk

Glatiramer acetate is used therapeutically in multiple sclerosis but also known for adverse effects including elevated coronary artery disease (CAD) risk. The mechanisms underlying the cardiovascular side effects of the medication are unclear. Here, we made use of the chromosomal variation in the genes that are known to be affected by glatiramer treatment. Focusing on genes and gene products reported by drug-gene interaction database to interact with glatiramer acetate we explored a large meta-analysis on CAD genome-wide association studies aiming firstly, to investigate whether variants in these genes also affect cardiovascular risk and secondly, to identify new CAD risk genes. We traced association signals in a 200-kb region around genomic positions of genes interacting with glatiramer in up to 60 801 CAD cases and 123 504 controls. We validated the identified association in additional 21 934 CAD cases and 76 087 controls. We identified three new CAD risk alleles within the TGFB1 region on chromosome 19 that independently affect CAD risk. The lead SNP rs12459996 was genome-wide significantly associated with CAD in the extended meta-analysis (odds ratio 1.09, p = 1.58×10-12). The other two SNPs at the locus were not in linkage disequilibrium with the lead SNP and by a conditional analysis showed p-values of 4.05 × 10-10 and 2.21 × 10-6. Thus, studying genes reported to interact with glatiramer acetate we identified genetic variants that concordantly with the drug increase the risk of CAD. Of these, TGFB1 displayed signal for association. Indeed, the gene has been associated with CAD previously in both in vivo and in vitro studies. Here we establish genome-wide significant association with CAD in large human samples.This work was supported by grants from the Fondation Leducq (CADgenomics: Understanding CAD Genes, 12CVD02), the German Federal Ministry of Education and Research (BMBF) within the framework of the e:Med research and funding concept (e:AtheroSysMed, grant 01ZX1313A-2014 and SysInflame, grant 01ZX1306A), and the European Union Seventh Framework Programme FP7/2007-2013 under grant agreement no HEALTH-F2-2013-601456 (CVgenes-at-target). Further grants were received from the DFG as part of the Sonderforschungsbereich CRC 1123 (B2). T.K. was supported by a DZHK Rotation Grant. I.B. was supported by the Deutsche Forschungsgemeinschaft (DFG) cluster of excellence ‘Inflammation at Interfaces’. F.W.A. is supported by a Dekker scholarship-Junior Staff Member 2014T001 - Netherlands Heart Foundation and UCL Hospitals NIHR Biomedical Research Centre

Model-independent measurement of t\boldsymbol{t}-channel single top quark production in ppˉ\boldsymbol{p\bar{p}} collisions at s=1.96\boldsymbol{\sqrt{s}=1.96} TeV

We present a model-independent measurement of $t$-channel electroweak production of single top quarks in \ppbar collisions at $\sqrt{s}=1.96\;\rm TeV$. Using $5.4\;\rm fb^{-1}$ of integrated luminosity collected by the D0 detector at the Fermilab Tevatron Collider, and selecting events containing an isolated electron or muon, missing transverse energy and one or two jets originating from the fragmentation of $b$ quarks, we measure a cross section \sigma({\ppbar}{\rargap}tqb+X) = 2.90 \pm 0.59\;\rm (stat+syst)\; pb for a top quark mass of $172.5\;\rm GeV$. The probability of the background to fluctuate and produce a signal as large as the one observed is $1.6\times10^{-8}$, corresponding to a significance of 5.5 standard deviations.Comment: 8 pages, 4 figures, submitted to Phys. Lett.

Genome-wide association identifies nine common variants associated with fasting proinsulin levels and provides new insights into the pathophysiology of type 2 diabetes.

OBJECTIVE: Proinsulin is a precursor of mature insulin and C-peptide. Higher circulating proinsulin levels are associated with impaired β-cell function, raised glucose levels, insulin resistance, and type 2 diabetes (T2D). Studies of the insulin processing pathway could provide new insights about T2D pathophysiology. RESEARCH DESIGN AND METHODS: We have conducted a meta-analysis of genome-wide association tests of ∼2.5 million genotyped or imputed single nucleotide polymorphisms (SNPs) and fasting proinsulin levels in 10,701 nondiabetic adults of European ancestry, with follow-up of 23 loci in up to 16,378 individuals, using additive genetic models adjusted for age, sex, fasting insulin, and study-specific covariates. RESULTS: Nine SNPs at eight loci were associated with proinsulin levels (P < 5 × 10(-8)). Two loci (LARP6 and SGSM2) have not been previously related to metabolic traits, one (MADD) has been associated with fasting glucose, one (PCSK1) has been implicated in obesity, and four (TCF7L2, SLC30A8, VPS13C/C2CD4A/B, and ARAP1, formerly CENTD2) increase T2D risk. The proinsulin-raising allele of ARAP1 was associated with a lower fasting glucose (P = 1.7 × 10(-4)), improved β-cell function (P = 1.1 × 10(-5)), and lower risk of T2D (odds ratio 0.88; P = 7.8 × 10(-6)). Notably, PCSK1 encodes the protein prohormone convertase 1/3, the first enzyme in the insulin processing pathway. A genotype score composed of the nine proinsulin-raising alleles was not associated with coronary disease in two large case-control datasets. CONCLUSIONS: We have identified nine genetic variants associated with fasting proinsulin. Our findings illuminate the biology underlying glucose homeostasis and T2D development in humans and argue against a direct role of proinsulin in coronary artery disease pathogenesis

New genetic loci link adipose and insulin biology to body fat distribution.

Body fat distribution is a heritable trait and a well-established predictor of adverse metabolic outcomes, independent of overall adiposity. To increase our understanding of the genetic basis of body fat distribution and its molecular links to cardiometabolic traits, here we conduct genome-wide association meta-analyses of traits related to waist and hip circumferences in up to 224,459 individuals. We identify 49 loci (33 new) associated with waist-to-hip ratio adjusted for body mass index (BMI), and an additional 19 loci newly associated with related waist and hip circumference measures (P < 5 × 10(-8)). In total, 20 of the 49 waist-to-hip ratio adjusted for BMI loci show significant sexual dimorphism, 19 of which display a stronger effect in women. The identified loci were enriched for genes expressed in adipose tissue and for putative regulatory elements in adipocytes. Pathway analyses implicated adipogenesis, angiogenesis, transcriptional regulation and insulin resistance as processes affecting fat distribution, providing insight into potential pathophysiological mechanisms