Entanglement entropy dynamics of Heisenberg chains

By means of the time dependent density matrix renormalization group algorithm we study the zero-temperature dynamics of the Von Neumann entropy of a block of spins in a Heisenberg chain after a sudden quench in the anisotropy parameter. In the absence of any disorder the block entropy increases linearly with time and then saturates. We analyse the velocity of propagation of the entanglement as a function of the initial and final anisotropies and compare our results, wherever possible, with those obtained by means of conformal field theory. In the disordered case we find a slower ( logarithmic) evolution which may signal the onset of entanglement localization.

The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.

Cardiopulmonary function in two human disorders of the hypoxia-inducible factor (HIF) pathway: von Hippel-Lindau disease and HIF-2 alpha gain-of-function mutation

The hypoxia-inducible factors (HIFs; isoforms HIF-1 alpha, HIF-2 alpha, HIF-3 alpha) mediate many responses to hypoxia. Their regulation is principally by oxygen-dependent degradation, which is initiated by hydroxylation of specific proline residues followed by binding of von Hippel-Lindau (VHL) protein. Chuvash polycythemia is a disorder with elevated HIF. It arises through germline homozygosity for hypomorphic VHL alleles and has a phenotype of hematological, cardiopulmonary, and metabolic abnormalities. This study explores the phenotype of two other HIF pathway diseases: classic VHL disease and HIF-2 alpha gain-of-function mutation. No cardiopulmonary abnormalities were detected in classic VHL disease. HIF-2 alpha gain-of-function mutations were associated with pulmonary hypertension, increased cardiac output, increased heart rate, and increased pulmonary ventilation relative to metabolism. Comparison of the HIF-2 alpha gain-of-function responses with data from studies of Chuvash polycythemia suggested that other aspects of the Chuvash phenotype were diminished or absent. In classic VHL disease, patients are germline heterozygous for mutations in VHL, and the present results suggest that a single wild-type allele for VHL is sufficient to maintain normal cardiopulmonary function. The HIF-2 alpha gain-of-function phenotype may be more limited than the Chuvash phenotype either because HIF-1 alpha is not elevated in the former condition, or because other HIF-independent functions of VHL are perturbed in Chuvash polycythemia.-Formenti, F., Beer, P. A., Croft, Q. P. P., Dorrington, K. L., Gale, D. P., Lappin, T. R. J., Lucas, G. S., Maher, E. R., Maxwell, P. H., McMullin, M. F., O'Connor, D. F., Percy, M. J., Pugh, C. W., Ratcliffe, P. J., Smith, T. G., Talbot, N. P., Robbins, P. A. Cardiopulmonary function in two human disorders of the hypoxia-inducible factor (HIF) pathway: von Hippel-Lindau disease and HIF-2 alpha gain-of-function mutation. FASEB J. 25, 2001-2011 (2011). www.fasebj.org

Convergence of products from Povarov and von Miller reactions: approaches to helquinoline

Yttrium triflate or triflic acid catalysed Povarov reaction of methyl anthranilate with ethyl vinyl ether, both as aldehyde surrogate and as alkene, gave the desired 2-methyl-4-ethoxytetrahydroquinoline diastereoisomers as the major products along with four component coupling von Miller adducts. A proton NMR-study, using yttrium triflate as catalyst, revealed that the cis-diastereoisomers were the initial major products in both the Povarov and von Miller reactions but that these isomerised to the trans-diastereoisomers under the reaction conditions. Two distinct pathways for forming von Miller adducts were uncovered with the initial Povarov products being converted to von Miller adducts under the reaction conditions. Replacement of the 4-ethoxy with a 4-methoxy group under acidic conditions gave predominantly the trans-diastereoisomer, which was subsequently converted to a cis/trans mixture of the tetrahydroquinoline antibiotic helquinoline. It was also possible to convert the von Miller products to Povarov products under acidic conditions

Increasing Prevalence of Myopia in Europe and the Impact of Education

PURPOSE: To investigate whether myopia is becoming more common across Europe and explore whether increasing education levels, an important environmental risk factor for myopia, might explain any temporal trend.

DESIGN: Meta-analysis of population-based, cross-sectional studies from the European Eye Epidemiology (E(3)) Consortium.

PARTICIPANTS: The E(3) Consortium is a collaborative network of epidemiological studies of common eye diseases in adults across Europe. Refractive data were available for 61 946 participants from 15 population-based studies performed between 1990 and 2013; participants had a range of median ages from 44 to 78 years.

METHODS: Noncycloplegic refraction, year of birth, and highest educational level achieved were obtained for all participants. Myopia was defined as a mean spherical equivalent ≤-0.75 diopters. A random-effects meta-analysis of age-specific myopia prevalence was performed, with sequential analyses stratified by year of birth and highest level of educational attainment.

MAIN OUTCOME MEASURES: Variation in age-specific myopia prevalence for differing years of birth and educational level.

RESULTS: There was a significant cohort effect for increasing myopia prevalence across more recent birth decades; age-standardized myopia prevalence increased from 17.8% (95% confidence interval [CI], 17.6-18.1) to 23.5% (95% CI, 23.2-23.7) in those born between 1910 and 1939 compared with 1940 and 1979 (P = 0.03). Education was significantly associated with myopia; for those completing primary, secondary, and higher education, the age-standardized prevalences were 25.4% (CI, 25.0-25.8), 29.1% (CI, 28.8-29.5), and 36.6% (CI, 36.1-37.2), respectively. Although more recent birth cohorts were more educated, this did not fully explain the cohort effect. Compared with the reference risk of participants born in the 1920s with only primary education, higher education or being born in the 1960s doubled the myopia prevalence ratio-2.43 (CI, 1.26-4.17) and 2.62 (CI, 1.31-5.00), respectively-whereas individuals born in the 1960s and completing higher education had approximately 4 times the reference risk: a prevalence ratio of 3.76 (CI, 2.21-6.57).

CONCLUSIONS: Myopia is becoming more common in Europe; although education levels have increased and are associated with myopia, higher education seems to be an additive rather than explanatory factor. Increasing levels of myopia carry significant clinical and economic implications, with more people at risk of the sight-threatening complications associated with high myopia.