Quantum duality and Bethe-ansatz for the Hofstadter problem on hexagonal lattice

The Hofstadter problem is studied on hexagonal lattice. We first establish a relation between the spectra for the hexagonal lattice and for its dual he triangular lattice. Following the idea of Faddeev and Kashaev, we then obtain the Bethe-ansatz equations for this system.Comment: 8 pages, latex, revised version for Phys. Lett.

Local Dynamics and Strong Correlation Physics I: 1D and 2D Half-filled Hubbard Models

We report on a non-perturbative approach to the 1D and 2D Hubbard models that is capable of recovering both strong and weak-coupling limits. We first show that even when the on-site Coulomb repulsion, U, is much smaller than the bandwith, the Mott-Hubbard gap never closes at half-filling in both 1D and 2D. Consequently, the Hubbard model at half-filling is always in the strong-coupling non-perturbative regime. For both large and small U, we find that the population of nearest-neighbour singlet states approaches a value of order unity as $T\to 0$ as would be expected for antiferromagnetic order. We also find that the double occupancy is a smooth monotonic function of U and approaches the anticipated non-interacting limit and large U limits. Finally, in our results for the heat capacity in 1D differ by no more than 1% from the Bethe ansatz predictions. In addition, we find that in 2D, the heat capacity vs T for different values of U exhibits a universal crossing point at two characteristic temperatures as is seen experimentally in a wide range of strongly-correlated systems such as $^3He$, $UBe_3$, and $CeCu_{6-x}Al_x$. The success of this method in recovering well-established results that stem fundamentally from the Coulomb interaction suggests that local dynamics are at the heart of the physics of strongly correlated systems.Comment: 10 pages, 16 figures included in text, Final version for publication with a reference added and minor corrections. Phys. Rev. B, in pres

Dilute Bose gas in two dimensions: Density expansions and the Gross-Pitaevskii equation

A dilute two-dimensional (2D) Bose gas at zero temperature is studied by the method developed earlier by the authors. Low density expansions are derived for the chemical potential, ground state energy, kinetic and interaction energies. The expansion parameter is found to be a dimensionless in-medium scattering amplitude u obeying the equation 1/u+\ln u=-\ln(na^2\pi)-2\gamma, where na^2 and \gamma are the gas parameter and the Euler constant, respectively. It is shown that the ground state energy is mostly kinetic in the low density limit; this result does not depend on a specific form of the pairwise interaction potential, contrary to 3D case. A new form of 2D Gross-Pitaevskii equation is proposed within our scheme.Comment: 4 pages, REVTeX, no figure

Trans-ancestry genome-wide association study identifies 12 genetic loci influencing blood pressure and implicates a role for DNA methylation

We carried out a trans-ancestry genome-wide association and replication study of blood pressure phenotypes among up to 320,251 individuals of East Asian, European and South Asian ancestry. We find genetic variants at 12 new loci to be associated with blood pressure (P = 3.9 × 10-11 to 5.0 × 10-21). The sentinel blood pressure SNPs are enriched for association with DNA methylation at multiple nearby CpG sites, suggesting that, at some of the loci identified, DNA methylation may lie on the regulatory pathway linking sequence variation to blood pressure. The sentinel SNPs at the 12 new loci point to genes involved in vascular smooth muscle (IGFBP3, KCNK3, PDE3A and PRDM6) and renal (ARHGAP24, OSR1, SLC22A7 and TBX2) function. The new and known genetic variants predict increased left ventricular mass, circulating levels of NT-proBNP, and cardiovascular and all-cause mortality (P = 0.04 to 8.6 × 10-6). Our results provide new evidence for the role of DNA methylation in blood pressure regulation

Associations of autozygosity with a broad range of human phenotypes

In many species, the offspring of related parents suffer reduced reproductive success, a phenomenon known as inbreeding depression. In humans, the importance of this effect has remained unclear, partly because reproduction between close relatives is both rare and frequently associated with confounding social factors. Here, using genomic inbreeding coefficients (F-ROH) for >1.4 million individuals, we show that F-ROH is significantly associated (p <0.0005) with apparently deleterious changes in 32 out of 100 traits analysed. These changes are associated with runs of homozygosity (ROH), but not with common variant homozygosity, suggesting that genetic variants associated with inbreeding depression are predominantly rare. The effect on fertility is striking: F-ROH equivalent to the offspring of first cousins is associated with a 55% decrease [95% CI 44-66%] in the odds of having children. Finally, the effects of F-ROH are confirmed within full-sibling pairs, where the variation in F-ROH is independent of all environmental confounding.Peer reviewe

Genome-wide association meta-analyses and fine-mapping elucidate pathways influencing albuminuria

Increased levels of the urinary albumin-to-creatinine ratio (UACR) are associated with higher risk of kidney disease progression and cardiovascular events, but underlying mechanisms are incompletely understood. Here, we conduct trans-ethnic (n = 564,257) and European-ancestry specific meta-analyses of genome-wide association studies of UACR, including ancestry- and diabetes-specific analyses, and identify 68 UACR-associated loci. Genetic correlation analyses and risk score associations in an independent electronic medical records database (n = 192,868) reveal connections with proteinuria, hyperlipidemia, gout, and hypertension. Fine-mapping and trans-Omics analyses with gene expression in 47 tissues and plasma protein levels implicate genes potentially operating through differential expression in kidney (including TGFB1, MUC1, PRKCI, and OAF), and allow coupling of UACR associations to altered plasma OAF concentrations. Knockdown of OAF and PRKCI orthologs in Drosophila nephrocytes reduces albumin endocytosis. Silencing fly PRKCI further impairs slit diaphragm formation. These results generate a priority list of genes and pathways for translational research to reduce albuminuria

Genetic insights into resting heart rate and its role in cardiovascular disease.

Resting heart rate is associated with cardiovascular diseases and mortality in observational and Mendelian randomization studies. The aims of this study are to extend the number of resting heart rate associated genetic variants and to obtain further insights in resting heart rate biology and its clinical consequences. A genome-wide meta-analysis of 100 studies in up to 835,465 individuals reveals 493 independent genetic variants in 352 loci, including 68 genetic variants outside previously identified resting heart rate associated loci. We prioritize 670 genes and in silico annotations point to their enrichment in cardiomyocytes and provide insights in their ECG signature. Two-sample Mendelian randomization analyses indicate that higher genetically predicted resting heart rate increases risk of dilated cardiomyopathy, but decreases risk of developing atrial fibrillation, ischemic stroke, and cardio-embolic stroke. We do not find evidence for a linear or non-linear genetic association between resting heart rate and all-cause mortality in contrast to our previous Mendelian randomization study. Systematic alteration of key differences between the current and previous Mendelian randomization study indicates that the most likely cause of the discrepancy between these studies arises from false positive findings in previous one-sample MR analyses caused by weak-instrument bias at lower P-value thresholds. The results extend our understanding of resting heart rate biology and give additional insights in its role in cardiovascular disease development