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

A Predictive Minimal Model for Neutrino Masses and Mixings

A model is considered in which the scale of the heavy singlet neutrinos is a few orders of magnitude below the grand unification scale and where right-handed vector bosons play still a negligible role. In a basis with diagonal up-quark and Dirac-neutrino mass matrices it is assumed that the heavy neutrino mass matrix has only zero elements in its diagonal, in analogy to the light neutrino mass matrix in the Zee model. Connecting then the remaining matrix elements with the small parameter describing the hierarchy of quark masses and mixings and by assuming commutativity of the charged lepton with the down-quark mass matrix, the calculation of all neutrino properties can be performed in terms of the two mass differences relevant for atmospheric and solar neutrino oscillations. CP-violation is directly related to CP-violation in the quark sector.Comment: revtex, 9 pages, two references added, to be published in Phys. Rev. D presented at Neutrino' 2000, Sudbury, Canad

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

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

Critical Micronutrients in Pregnancy, Lactation, and Infancy: Considerations on Vitamin D, Folic Acid, and Iron, and Priorities for Future Research

The Early Nutrition Academy and the European Commission-funded EURRECA Network of Excellence jointly sponsored a scientific workshop on critical micronutrients in pregnancy, lactation, and infancy. Current knowledge and unresolved questions on the supply of vitamin D, folic acid, and iron for pregnant women, lactating women, and infants, and their health effects were discussed. The question was addressed of whether, and under which circumstances, supplementation with these micronutrients in addition to usual dietary intakes is advisable. The workshop participants concluded that public health strategies for improving supplementation with these micronutrients in pregnancy, lactation, and infancy are required. Further research priorities should focus on adequately powered human intervention trials to obtain a stronger evidence base for the amounts of vitamin D, folic acid, and iron that have optimal effects on health. The conclusions of the workshop should help to inform the scientific community as well as public health policy strategies. Copyright (C) 2011 S. Karger AG, Base

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

(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

Quantitative wave-particle duality and non-erasing quantum erasure

The notion of wave-particle duality may be quantified by the inequality V^2+K^2 <=1, relating interference fringe visibility V and path knowledge K. With a single-photon interferometer in which polarization is used to label the paths, we have investigated the relation for various situations, including pure, mixed, and partially-mixed input states. A quantum eraser scheme has been realized that recovers interference fringes even when no which-way information is available to erase.Comment: 6 pages, 4 figures. To appear in Phys. Rev.