Neutrino mixing, interval matrices and singular values

We study the properties of singular values of mixing matrices embedded within an experimentally determined interval matrix. We argue that any physically admissible mixing matrix needs to have the property of being a contraction. This condition constrains the interval matrix, by imposing correlations on its elements and leaving behind only physical mixings that may unveil signs of new physics in terms of extra neutrino species. We propose a description of the admissible three-dimensional mixing space as a convex hull over experimentally determined unitary mixing matrices parametrized by Euler angles which allows us to select either unitary or nonunitary mixing matrices. The unitarity-breaking cases are found through singular values and we construct unitary extensions yielding a complete theory of minimal dimensionality larger than three through the theory of unitary matrix dilations. We discuss further applications to the quark sector.Comment: Misprints correcte

Capillary electrophoretic separation of herbicidal enantiomers applying ergot alkaloids

Abstract The capillary electrophoretic separation of some herbicidal enantiomers is shown applying 1-allylterguride as chiral selector. Baseline separation is shown for the enantiomers of fluazifop, halossifop and fenoxaprop, whereas the optical isomers of flamprop could be partially resolved. Separation times are short compared to similar analyses, applying HPLC and a terguride chiral stationary phase. The degree of dissociation of the acidic analytes, as well as the amount of methanol present in the background electrolyte, are shown to have a major influence on enantioresolution, as expected form earlier studies. © 1997 Elsevier Science B. V

Off-Diagonal Elements of the DeWitt Expansion from the Quantum Mechanical Path Integral

The DeWitt expansion of the matrix element M_{xy} = \left\langle x \right| \exp -[\case{1}{2} (p-A)^2 + V]t \left| y \right\rangle, $(p=-i\partial)$ in powers of $t$ can be made in a number of ways. For $x=y$ (the case of interest when doing one-loop calculations) numerous approaches have been employed to determine this expansion to very high order; when $x \neq y$ (relevant for doing calculations beyond one-loop) there appear to be but two examples of performing the DeWitt expansion. In this paper we compute the off-diagonal elements of the DeWitt expansion coefficients using the Fock-Schwinger gauge. Our technique is based on representing $M_{xy}$ by a quantum mechanical path integral. We also generalize our method to the case of curved space, allowing us to determine the DeWitt expansion of \tilde M_{xy} = \langle x| \exp \case{1}{2} [\case{1}{\sqrt {g}} (\partial_\mu - i A_\mu)g^{\mu\nu}{\sqrt{g}}(\partial_\nu - i A_\nu) ] t| y \rangle by use of normal coordinates. By comparison with results for the DeWitt expansion of this matrix element obtained by the iterative solution of the diffusion equation, the relative merit of different approaches to the representation of $\tilde M_{xy}$ as a quantum mechanical path integral can be assessed. Furthermore, the exact dependence of $\tilde M_{xy}$ on some geometric scalars can be determined. In two appendices, we discuss boundary effects in the one-dimensional quantum mechanical path integral, and the curved space generalization of the Fock-Schwinger gauge.Comment: 16pp, REVTeX. One additional appendix concerning end-point effects for finite proper-time intervals; inclusion of these effects seem to make our results consistent with those from explicit heat-kernel method

Reply to Guy et al.: Support for a bottleneck in the 2011 Escherichia coli O104:H4 outbreak in Germany

In our paper (1), we analyzed isolates from the Escherichia coli O104:H4 outbreaks in Germany and France in May to July 2011. We concluded that, although the German outbreak was larger, the German isolates represent a clade within the greater diversity of the French outbreak. We proposed several hypotheses to explain these findings, including that the lineage leading to the German outbreak went through a narrow bottleneck that purged diversity. Guy et al. (2) report the genomes of eight additional E. coli O104:H4 isolates sampled from the German outbreak. By focusing on the numbers of SNPs in their samples, they suggest that the German outbreak is more diverse than we reported and is similar to the French outbreak. In fact, Guy et al.’s data (2) strongly support our conclusion that the German outbreak represents a clade within the diversity

The influence of long-term treadmill exercise on bone mass and articular cartilage in ovariectomized rats

<p>Abstract</p> <p>Background</p> <p>Loss of bone quality and deterioration of articular cartilage are commonly seen after menopause. While exercise may protect against tissue degeneration, a clear link has yet to be established. The aim of the present study is to investigate the influence of long-term treadmill exercise on changes in bone mass and articular cartilage in ovariectomized rats.</p> <p>Methods</p> <p>Sixty female Sprague-Dawley rats were randomly assigned to 4 groups: ovariectomized (OVX), ovariectomized plus treadmill exercise (OVX-RUN), treadmill exercise alone (RUN), and control (CON) groups. After 36 weeks, the following variables were compared among the 4 groups. Bone mass was evaluated by trabecular bone volume and bone mineral density (BMD). Articular cartilage in the knee joints was evaluated by histology analysis and a modified Mankin score.</p> <p>Results</p> <p>Rats in the ovariectomized groups (OVX and OVX-RUN) had significantly lower BMD and bone mass than the non-ovariectomized rats (CON and RUN), indicating that exercise did little to preserve bone mass. However, the sedentary OVX group had a significantly worse modified Mankin score (7.7 ± 1.4) than the OVX-RUN group (4.8 ± 1.0), whose scores did not differ significantly from the other 2 non-operated groups. The articular cartilage in the sedentary OVX rats was relatively thinner, hypocellular, and had more clefts than in the other 3 groups.</p> <p>Conclusion</p> <p>This study suggests that long-term exercise protects articular cartilage in OVX rats but does not retard the loss of bone mass seen in after menopause.</p

Low-frequency vibratory exercise reduces the risk of bone fracture more than walking: a randomized controlled trial

BACKGROUND: Whole-body vibration (WBV) is a new type of exercise that has been increasingly tested for the ability to prevent bone fractures and osteoporosis in frail people. There are two currently marketed vibrating plates: a) the whole plate oscillates up and down; b) reciprocating vertical displacements on the left and right side of a fulcrum, increasing the lateral accelerations. A few studies have shown recently the effectiveness of the up-and-down plate for increasing Bone Mineral Density (BMD) and balance; but the effectiveness of the reciprocating plate technique remains mainly unknown. The aim was to compare the effects of WBV using a reciprocating platform at frequencies lower than 20 Hz and a walking-based exercise programme on BMD and balance in post-menopausal women. METHODS: Twenty-eight physically untrained post-menopausal women were assigned at random to a WBV group or a Walking group. Both experimental programmes consisted of 3 sessions per week for 8 months. Each vibratory session included 6 bouts of 1 min (12.6 Hz in frequency and 3 cm in amplitude with 60° of knee flexion) with 1 min rest between bouts. Each walking session was 55 minutes of walking and 5 minutes of stretching. Hip and lumbar BMD (g·cm(-2)) were measured using dual-energy X-ray absorptiometry and balance was assessed by the blind flamingo test. ANOVA for repeated measurements was adjusted by baseline data, weight and age. RESULTS: After 8 months, BMD at the femoral neck in the WBV group was increased by 4.3% (P = 0.011) compared to the Walking group. In contrast, the BMD at the lumbar spine was unaltered in both groups. Balance was improved in the WBV group (29%) but not in the Walking group. CONCLUSION: The 8-month course of vibratory exercise using a reciprocating plate is feasible and is more effective than walking to improve two major determinants of bone fractures: hip BMD and balance

High expression of Lewis(y/b )antigens is associated with decreased survival in lymph node negative breast carcinomas

INTRODUCTION: There is sufficient evidence that blood group related Lewis antigens are tumour-associated molecules. The Lewis(y )and Lewis(b )antigens are complex carbohydrates that are over-expressed by breast, lung, colon and ovarian cancers. The SC101 mAb is a unique Lewis(y/b )binding antibody that binds to native and extended Lewis(y )and Lewis(b )haptens, displaying no cross reactivity with H type 1, H type 2, Lewis(x )or normal blood group antigens. METHODS: Immunohistochemical detection of Lewis(y/b )was performed on 660 formalin-fixed, paraffin embedded breast tumour specimens using a streptavidin-biotin peroxidase technique. Tissue from these patients had previously been included in tissue microarrays. This cohort comprises a well characterized series of patients with primary operable breast cancer diagnosed between 1987 and 1992, obtained from the Nottingham Tenovus Primary Breast Carcinoma Series. This includes patients 70 years of age or less, with a mean follow up of 7 years. RESULTS: Of the breast carcinomas, 370 of 660 (56%) were negative for Lewis(y/b )expression, 110 (17%) cases showed a low level of expression (<25% of positive cells) and only 54 cases (8%) showed extensive expression of Lewis(y/b )(>75% of positive cells). We found significant positive associations between histological grade (p < 0.001), Nottingham Prognostic Index (p = 0.016), tumour type (p = 0.007) and the level of Lewis (y/b )expression. There was a significant correlation between the proportion of Lewis(y/b )positive tumour cells and survival in lymph-node negative patients (p = 0.006). CONCLUSION: The unique epitope recognised by SC101 mAb on Lewis(y/b )hapten is over-expressed on breast tumour tissue compared with normal breast. In this large series of invasive breast cancers, higher expression of Lewis(y/b )was more often found in high grade and poor prognosis tumours compared to good prognosis cancers. Moreover, in lymph node negative breast carcinomas, over-expression of Lewis(y/b )hapten was associated with significantly decreased patient survival