Periodic and discrete Zak bases

Weyl's displacement operators for position and momentum commute if the product of the elementary displacements equals Planck's constant. Then, their common eigenstates constitute the Zak basis, each state specified by two phase parameters. Upon enforcing a periodic dependence on the phases, one gets a one-to-one mapping of the Hilbert space on the line onto the Hilbert space on the torus. The Fourier coefficients of the periodic Zak bases make up the discrete Zak bases. The two bases are mutually unbiased. We study these bases in detail, including a brief discussion of their relation to Aharonov's modular operators, and mention how they can be used to associate with the single degree of freedom of the line a pair of genuine qubits.Comment: 15 pages, 3 figures; displayed abstract is shortened, see the paper for the complete abstrac

Minimax mean estimator for the trine

We explore the question of state estimation for a qubit restricted to the $x$-$z$ plane of the Bloch sphere, with the trine measurement. In our earlier work [H. K. Ng and B.-G. Englert, eprint arXiv:1202.5136[quant-ph] (2012)], similarities between quantum tomography and the tomography of a classical die motivated us to apply a simple modification of the classical estimator for use in the quantum problem. This worked very well. In this article, we adapt a different aspect of the classical estimator to the quantum problem. In particular, we investigate the mean estimator, where the mean is taken with a weight function identical to that in the classical estimator but now with quantum constraints imposed. Among such mean estimators, we choose an optimal one with the smallest worst-case error-the minimax mean estimator-and compare its performance with that of other estimators. Despite the natural generalization of the classical approach, this minimax mean estimator does not work as well as one might expect from the analogous performance in the classical problem. While it outperforms the often-used maximum-likelihood estimator in having a smaller worst-case error, the advantage is not significant enough to justify the more complicated procedure required to construct it. The much simpler adapted estimator introduced in our earlier work is still more effective. Our previous work emphasized the similarities between classical and quantum state estimation; in contrast, this paper highlights how intuition gained from classical problems can sometimes fail in the quantum arena.Comment: 18 pages, 3 figure

Non-local anomaly of the axial-vector current for bound states

We demonstrate that the amplitude $<\rho\gamma|\partial_\nu (\bar q\gamma_\nu \gamma_5 q)|0>$ does not vanish in the limit of zero quark masses. This represents a new kind of violation of the classical equation of motion for the axial current and should be interpreted as the axial anomaly for bound states. The anomaly emerges in spite of the fact that the one loop integrals are ultraviolet-finite as guaranteed by the presence of the bound-state wave function. As a result, the amplitude behaves like $\sim 1/p^2$ in the limit of a large momentum $p$ of the current. This is to be compared with the amplitude $$ which remains finite in the limit $p^2\to\infty$. The observed effect leads to the modification of the classical equation of motion of the axial-vector current in terms of the non-local operator and can be formulated as a non-local axial anomaly for bound states.Comment: revtex, 4 pages, numerical value for $\kappa$ in Eq. (19) is corrected, Eqs. (22) and (23) are modified. New references added. Results remain unchange

Migrating Songbirds on Stopover Prepare for, and Recover from, Oxidative Challenges Posed by Long-Distance Flight

Managing oxidative stress is an important physiological function for all aerobic organisms, particularly during periods of prolonged high metabolic activity, such as long-distance migration across ecological barriers. However, no previous study has investigated the oxidative status of birds at different stages of migration and whether that oxidative status depends on the condition of the birds. In this study, we compared (1) energy stores and circulating oxidative status measures in (a) two species of Neotropical migrants with differing migration strategies that were sampled at an autumn stopover site before an ecological barrier; and (b) a species of trans-Saharan migrant sampled at a spring stopover site after crossing an ecological barrier; and (2) circulating oxidative measures and indicators of fat metabolism in a trans-Saharan migrant after stopovers of varying duration (0–8 nights), based on recapture records. We found fat stores to be positively correlated with circulating antioxidant capacity in Blackpoll Warblers and Red-eyed Vireos preparing for fall migration on Block Island, USA, but uncorrelated in Garden Warblers on the island of Ponza, Italy, after a spring crossing of the Sahara Desert and Mediterranean Sea. In all circumstances, fat stores were positively correlated with circulating lipid oxidation levels. Among Garden Warblers on the island of Ponza, fat anabolism increased with stopover duration while oxidative damage levels decreased. Our study provides evidence that birds build antioxidant capacity as they build fat stores at stopover sites before long flights, but does not support the idea that antioxidant stores remain elevated in birds with high fuel levels after an ecological barrier. Our results further suggest that lipid oxidation may be an inescapable hazard of using fats as the primary fuel for flight. Yet, we also show that birds on stopover are capable of recovering from the oxidative damage they have accrued during migration, as lipid oxidation levels decrease with time on stopover. Thus, the physiological strategy of migrating songbirds may be to build prophylactic antioxidant capacity in concert with fuel stores at stopover sites before a long-distance flight, and then repair oxidative damage while refueling at stopover sites after long-distance flight

Precision Measurement of the 29Si, 33S, and 36Cl Binding Energies

The binding energies of 29Si, 33S, and 36Cl have been measured with a relative uncertainty $< 0.59 \times 10^{-6}$ using a flat-crystal spectrometer. The unique features of these measurements are 1) nearly perfect crystals whose lattice spacing is known in meters, 2) a highly precise angle scale that is derived from first principles, and 3) a gamma-ray measurement facility that is coupled to a high flux reactor with near-core source capability. The binding energy is obtained by measuring all gamma-rays in a cascade scheme connecting the capture and ground states. The measurements require the extension of precision flat-crystal diffraction techniques to the 5 to 6 MeV energy region, a significant precision measurement challenge. The binding energies determined from these gamma-ray measurements are consistent with recent highly accurate atomic mass measurements within a relative uncertainty of $4.3 \times 10^{-7}$. The gamma-ray measurement uncertainties are the dominant contributors to the uncertainty of this consistency test. The measured gamma-ray energies are in agreement with earlier precision gamma-ray measurements.Comment: 13 pages, 4 figure

Pseudo-Jahn-Teller origin of the low barrier hydrogen bond in N2H7+

The microscopic origin and quantum effects of the low barrier hydrogen bond (LBHB) in the proton-bound ammonia dimer cation N2H7+ were studied by means of ab initio and density-functional theory(DFT) methods. These results were analyzed in the framework of vibronic theory and compared to those obtained for the Zundel cation H5O2+. All geometry optimizations carried out using wavefunction-based methods [Hartree–Fock, second and fourth order Möller–Plesset theory (MP2 and MP4), and quadratic configuration interaction with singles and doubles excitations (QCISD)] lead to an asymmetrical H3N–H+⋯NH3 conformation (C3v symmetry) with a small energy barrier (1.26kcal/mol in MP4 and QCISD calculations) between both equivalent minima. The value of this barrier is underestimated in DFT calculations particularly at the local density approximation level where geometry optimization leads to a symmetric H3N⋯H+⋯NH3 structure (D3d point group). The instability of the symmetric D3d structure is shown to originate from the pseudo-Jahn–Teller mixing of the electronic A1g1ground state with five low lying excited states of A2u symmetry through the asymmetric α2u vibrational mode. A molecular orbital study of the pseudo-Jahn–Teller coupling has allowed us to discuss the origin of the proton displacement and the LBHB formation in terms of the polarization of the NH3 molecules and the transfer of electronic charge between the proton and the NH3 units (rebonding). The parallel study of the H5O2+ cation, which presents a symmetric single-well structure, allows us to analyze why these similar molecules behave differently with respect to proton transfer. From the vibronic analysis, a unified view of the Rudle–Pimentel three-center four-electron and charge transfer models of LBHBs is given. Finally, the large difference in the N–N distance in the D3d and C3v configurations of N2H7+ indicates a large anharmonic coupling between α2u-α1g modes along the proton-transfer dynamics. This issue was explored by solving numerically the vibrational Schrödinger equation corresponding to the bidimensional E[Q(α2u),Q(α1g)] energy surface calculated at the MP4/6-311++G** level of theory

Sex differences in the association of phospholipids with components of the metabolic syndrome in young adults

BACKGROUND: There are differences in the prevalence and severity of diseases between males, females not taking hormonal contraceptives (non-HC females) and females taking hormonal contraceptives (HC females). The aim of this study was to identify sex-specific differences in the metabolome and its relation to components of the metabolic syndrome in a young adult population. METHODS: The subjects analysed are from the 20-year follow-up of the Western Australian Pregnancy Cohort (Raine) Study. Two hundred fifteen plasma metabolites were analysed in 1021 fasted plasma samples by a targeted liquid chromatography coupled to tandem mass spectrometry (LC-MS/MS) metabolomics approach. Principal component analysis between males (n = 550), non-HC females (n = 199) and HC females (n = 269) was applied. Regression analysis with a sex x metabolite concentration interaction was performed on components of the MetS, namely waist circumference, systolic blood pressure, and plasma HDL-C, triglycerides and glucose concentration, as outcome to select the significant metabolites of the interaction. Those selected metabolites were used as predictors in a sex group stratified analysis to compare the different beta coefficients and therefore the sex group-dependent associations. RESULTS: Principal component analysis between males, non-HC females, and HC females showed a general discriminating trend between males and HC females. One hundred twenty-seven metabolites were significantly different between males and non-HC females, whereas 97 differed between non-HC females and HC females. Males and non-HC females mainly differed in sphingomyelin, lyso-phosphatidylcholine, acyl-carnitine and amino acid species, whilst non-HC females and HC females mainly differed in phosphatidylcholine, lyso-phosphatidylcholine and acyl-carnitine concentrations. Forty-one metabolites (phosphatidylcholines, sphingomyelines, lyso-phosphatidylcholine) were significantly differently associated with the MetS factors in the different groups. CONCLUSIONS: We have shown clear differences between plasma metabolite concentrations in males, and HC or non-HC females, especially in lyso-phosphatidylcholine, sphingomyelin and phosphatidylcholine, which have been shown to associate with obesity in other studies. The association of these metabolites differed between sexes with components of the metabolic syndrome, which means that development of diseases like obesity and diabetes may differ between the sexes. Our findings highlight the importance of considering sex differences when conducting a metabolomics study and the need to account for the effect of HC usage in females in future studies

The promoter polymorphism -232C/G of the PCK1 gene is associated with type 2 diabetes in a UK-resident South Asian population

Background: The PCK1 gene, encoding cytosolic phosphoenolpyruvate carboxykinase (PEPCK-C), has previously been implicated as a candidate gene for type 2 diabetes (T2D) susceptibility. Rodent models demonstrate that over-expression of Pck1 can result in T2D development and a single nucleotide polymorphism (SNP) in the promoter region of human PCK1 (-232C/G) has exhibited significant association with the disease in several cohorts. Within the UK-resident South Asian population, T2D is 4 to 6 times more common than in indigenous white Caucasians. Despite this, few studies have reported on the genetic susceptibility to T2D in this ethnic group and none of these has investigated the possible effect of PCK1 variants. We therefore aimed to investigate the association between common variants of the PCK1 gene and T2D in a UK-resident South Asian population of Punjabi ancestry, originating predominantly from the Mirpur area of Azad Kashmir, Pakistan. \ud \ud Methods: We used TaqMan assays to genotype five tagSNPs covering the PCK1 gene, including the -232C/G variant, in 903 subjects with T2D and 471 normoglycaemic controls. \ud \ud Results: Of the variants studied, only the minor allele (G) of the -232C/G SNP demonstrated a significant association with T2D, displaying an OR of 1.21 (95% CI: 1.03 - 1.42, p = 0.019). \ud \ud Conclusion: This study is the first to investigate the association between variants of the PCK1 gene and T2D in South Asians. Our results suggest that the -232C/G promoter polymorphism confers susceptibility to T2D in this ethnic group. \ud \ud Trial registration: UKADS Trial Registration: ISRCTN38297969

Plants lacking the main light-harvesting complex retain photosystem II macro-organization

Photosystem II (PSII) is a key component of photosynthesis, the process of converting sunlight into the chemical energy of life. In plant cells, it forms a unique oligomeric macrostructure in membranes of the chloroplasts. Several light-harvesting antenna complexes are organized precisely in the PSII macrostructure—the major trimeric complexes (LHCII) that bind 70% of PSII chlorophyll and three minor monomeric complexes—which together form PSII supercomplexes. The antenna complexes are essential for collecting sunlight and regulating photosynthesis, but the relationship between these functions and their molecular architecture is unresolved. Here we report that antisense Arabidopsis plants lacking the proteins that form LHCII trimers have PSII supercomplexes with almost identical abundance and structure to those found in wild-type plants. The place of LHCII is taken by a normally minor and monomeric complex, CP26, which is synthesized in large amounts and organized into trimers. Trimerization is clearly not a specific attribute of LHCII. Our results highlight the importance of the PSII macrostructure: in the absence of one of its main components, another protein is recruited to allow it to assemble and function

(Micro)evolutionary changes and the evolutionary potential of bird migration

Seasonal migration is the yearly long-distance movement of individuals between their breeding and wintering grounds. Individuals from nearly every animal group exhibit this behavior, but probably the most iconic migration is carried out by birds, from the classic V-shape formation of geese on migration to the amazing nonstop long-distance flights undertaken by Arctic Terns Sterna paradisaea. In this chapter, we discuss how seasonal migration has shaped the field of evolution. First, this behavior is known to turn on and off quite rapidly, but controversy remains concerning where this behavior first evolved geographically and whether the ancestral state was sedentary or migratory (Fig. 7.1d, e). We review recent work using new analytical techniques to provide insight into this topic. Second, it is widely accepted that there is a large genetic basis to this trait, especially in groups like songbirds that migrate alone and at night precluding any opportunity for learning. Key hypotheses on this topic include shared genetic variation used by different populations to migrate and only few genes being involved in its control. We summarize recent work using new techniques for both phenotype and genotype characterization to evaluate and challenge these hypotheses. Finally, one topic that has received less attention is the role these differences in migratory phenotype could play in the process of speciation. Specifically, many populations breed next to one another but take drastically different routes on migration (Fig. 7.2). This difference could play an important role in reducing gene flow between populations, but our inability to track most birds on migration has so far precluded evaluations of this hypothesis. The advent of new tracking techniques means we can track many more birds with increasing accuracy on migration, and this work has provided important insight into migration's role in speciation that we will review here