Quantum Hamiltonians with Quasi-Ballistic Dynamics and Point Spectrum

Consider the family of Schr\"odinger operators (and also its Dirac version) on $\ell^2(\mathbb{Z})$ or $\ell^2(\mathbb{N})$ $$H^W_{\omega,S}=\Delta + \lambda F(S^n\omega) + W, \quad \omega\in\Omega,$$ where $S$ is a transformation on (compact metric) $\Omega$, $F$ a real Lipschitz function and $W$ a (sufficiently fast) power-decaying perturbation. Under certain conditions it is shown that $H^W_{\omega,S}$ presents quasi-ballistic dynamics for $\omega$ in a dense $G_{\delta}$ set. Applications include potentials generated by rotations of the torus with analytic condition on $F$, doubling map, Axiom A dynamical systems and the Anderson model. If $W$ is a rank one perturbation, examples of $H^W_{\omega,S}$ with quasi-ballistic dynamics and point spectrum are also presented.Comment: 17 pages; to appear in Journal of Differential Equation

Dynamical Delocalization for the 1D Bernoulli Discrete Dirac Operator

An 1D tight-binding version of the Dirac equation is considered; after checking that it recovers the usual discrete Schr?odinger equation in the nonrelativistic limit, it is found that for two-valued Bernoulli potentials the zero mass case presents absence of dynamical localization for specific values of the energy, albeit it has no continuous spectrum. For the other energy values (again excluding some very specific ones) the Bernoulli Dirac system is localized, independently of the mass.Comment: 9 pages, no figures - J. Physics A: Math. Ge

Dynamical Lower Bounds for 1D Dirac Operators

Quantum dynamical lower bounds for continuous and discrete one-dimensional Dirac operators are established in terms of transfer matrices. Then such results are applied to various models, including the Bernoulli-Dirac one and, in contrast to the discrete case, critical energies are also found for the continuous Dirac case with positive mass.Comment: 18 pages; to appear in Math.

Role of Adiponectin in Coronary Heart Disease Risk:A Mendelian Randomization Study

RATIONALE: Hypoadiponectinemia correlates with several coronary heart disease (CHD) risk factors. However, it is unknown whether adiponectin is causally implicated in CHD pathogenesis. OBJECTIVE: We aimed to investigate the causal effect of adiponectin on CHD risk. METHODS AND RESULTS: We undertook a Mendelian randomization study using data from genome-wide association studies consortia. We used the ADIPOGen consortium to identify genetic variants that could be used as instrumental variables for the effect of adiponectin. Data on the association of these genetic variants with CHD risk were obtained from CARDIoGRAM (22 233 CHD cases and 64 762 controls of European ancestry) and from CARDIoGRAMplusC4D Metabochip (63 746 cases and 130 681 controls; ≈ 91% of European ancestry) consortia. Data on the association of genetic variants with adiponectin levels and with CHD were combined to estimate the influence of blood adiponectin on CHD risk. In the conservative approach (restricted to using variants within the adiponectin gene as instrumental variables), each 1 U increase in log blood adiponectin concentration was associated with an odds ratio for CHD of 0.83 (95% confidence interval, 0.68–1.01) in CARDIoGRAM and 0.97 (95% confidence interval, 0.84–1.12) in CARDIoGRAMplusC4D Metabochip. Findings from the liberal approach (including variants in any locus across the genome) indicated a protective effect of adiponectin that was attenuated to the null after adjustment for known CHD predictors. CONCLUSIONS: Overall, our findings do not support a causal role of adiponectin levels in CHD pathogenesis

Iron content affects lipogenic gene expression in the muscle of nelore beef cattle.

Iron (Fe) is an essential mineral for metabolism and plays a central role in a range of biochemical processes. Therefore, this study aimed to identify differentially expressed (DE) genes and metabolic pathways in Longissimus dorsi (LD) muscle from cattle with divergent iron content, as well as to investigate the likely role of these DE genes in biological processes underlying beef quality parameters. Samples for RNA extraction for sequencing and iron, copper, manganese, and zinc determination were collected from LD muscles at slaughter. Eight Nelore steers, with extreme genomic estimated breeding values for iron content (Fe-GEBV), were selected from a reference population of 373 animals. From the 49 annotated DE genes (FDR<0.05) found between the two groups, 18 were upregulated and 31 down-regulated for the animals in the low Fe-GEBV group. The functional enrichment analyses identified several biological processes, such as lipid transport and metabolism, and cell growth. Lipid metabolism was the main pathway observed in the analysis of metabolic and canonical signaling pathways for the genes identified as DE, including the genes FASN, FABP4, and THRSP, which are functional candidates for beef quality, suggesting reduced lipogenic activities with lower iron content. Our results indicate metabolic pathways that are partially influenced by iron, contributing to a better understanding of its participation in skeletal muscle physiology