A Bloch-Sphere-Type Model for Two Qubits in the Geometric Algebra of a 6-D Euclidean Vector Space

Geometric algebra is a mathematical structure that is inherent in any metric vector space, and defined by the requirement that the metric tensor is given by the scalar part of the product of vectors. It provides a natural framework in which to represent the classical groups as subgroups of rotation groups, and similarly their Lie algebras. In this article we show how the geometric algebra of a six-dimensional real Euclidean vector space naturally allows one to construct the special unitary group on a two-qubit (quantum bit) Hilbert space, in a fashion similar to that used in the well-established Bloch sphere model for a single qubit. This is then used to illustrate the Cartan decompositions and subalgebras of the four-dimensional special unitary group, which have recently been used by J. Zhang, J. Vala, S. Sastry and K. B. Whaley [Phys. Rev. A 67, 042313, 2003] to study the entangling capabilities of two-qubit unitaries.Comment: 14 pages, 2 figures, in press (Proceedings of SPIE Conference on Defense & Security

The costs of inequality: whole-population modelling study of lifetime inpatient hospital costs in the English National Health Service by level of neighbourhood deprivation : Whole-population modelling study of lifetime inpatient hospital costs in the English National Health Service by level of neighbourhood deprivation

BACKGROUND: There are substantial socioeconomic inequalities in both life expectancy and healthcare use in England. In this study, we describe how these two sets of inequalities interact by estimating the social gradient in hospital costs across the life course. METHODS: Hospital episode statistics, population and index of multiple deprivation data were combined at lower-layer super output area level to estimate inpatient hospital costs for 2011/2012 by age, sex and deprivation quintile. Survival curves were estimated for each of the deprivation groups and used to estimate expected annual costs and cumulative lifetime costs. RESULTS: A steep social gradient was observed in overall inpatient hospital admissions, with rates ranging from 31 298/100 000 population in the most affluent fifth of areas to 43 385 in the most deprived fifth. This gradient was steeper for emergency than for elective admissions. The total cost associated with this inequality in 2011/2012 was £4.8 billion. A social gradient was also observed in the modelled lifetime costs where the lower life expectancy was not sufficient to outweigh the higher average costs in the more deprived populations. Lifetime costs for women were 14% greater than for men, due to higher costs in the reproductive years and greater life expectancy. CONCLUSIONS: Socioeconomic inequalities result in increased morbidity and decreased life expectancy. Interventions to reduce inequality and improve health in more deprived neighbourhoods have the potential to save money for health systems not only within years but across peoples' entire lifetimes, despite increased costs due to longer life expectancies

Comparison of chicken 7SK and U6 RNA polymerase III promoters for short hairpin RNA expression

Background: RNA polymerase III (pol III) type 3 promoters such as U6 or 7SK are commonly used to express short-hairpin RNA (shRNA) effectors for RNA interference (RNAi). To extend the use of RNAi for studies of development using the chicken as a model system, we have developed a system for expressing shRNAs using the chicken 7SK (ch7SK) promoter. Results: We identified and characterised the ch7SK promoter sequence upstream of the full-length 7SK small nuclear RNA (snRNA) sequence in the chicken genome and used this to construct vectors to express shRNAs targeting enhanced green fluorescent protein (EGFP). We transfected chicken DF-1 cells with these constructs and found that anti-EGFP-shRNAs (shEGFP) expressed from the ch7SK promoter could induce efficient knockdown of EGFP expression. We further compared the efficiency of ch7SK-directed knockdown to that of chicken U6 (cU6) promoters and found that the efficiency of the ch7SK promoter was not greater than, but comparable to the efficiency of cU6 promoters. Conclusion: In this study we have demonstrated that the ch7SK promoter can express shRNAs capable of mediating efficient RNAi in a chicken cell line. However, our finding that RNAi driven by the ch7SK promoter is not more efficient than cU6 promoters contrasts previous comparisons of mammalian U6 and 7SK promoters. Since the ch7SK promoter is the first non-mammalian vertebrate 7SK promoter to be characterised, this finding may be helpful in understanding the divergence of pol III promoter activities between mammalian and non-mammalian vertebrates. This aside, our results clearly indicate that the ch7SK promoter is an efficient alternative to U6-based shRNA expression systems for inducing efficient RNAi activity in chicken cells.<br /

Reflection Symmetries for Multiqubit Density Operators

For multiqubit density operators in a suitable tensorial basis, we show that a number of nonunitary operations used in the detection and synthesis of entanglement are classifiable as reflection symmetries, i.e., orientation changing rotations. While one-qubit reflections correspond to antiunitary symmetries, as is known for example from the partial transposition criterion, reflections on the joint density of two or more qubits are not accounted for by the Wigner Theorem and are well-posed only for sufficiently mixed states. One example of such nonlocal reflections is the unconditional NOT operation on a multiparty density, i.e., an operation yelding another density and such that the sum of the two is the identity operator. This nonphysical operation is admissible only for sufficiently mixed states.Comment: 9 page

The impact of out-of-hours admission on patient mortality: longitudinal analysis in a tertiary acute hospital

Background Emergency hospital admission at weekends is associated with an increased risk of mortality. Previous studies have been limited to examining single years and assessing day – not time – of admission. We used an enhanced longitudinal dataset to estimate the ‘weekend effect’ over time and the effect of night-time admission on the mortality rate. Method We examined 246,350 emergency spells from a large teaching hospital in England between April 2004 and March 2014. Outcomes included 7-day, 30-day and in-hospital mortality rates. We conducted probit regressions to estimate the impact of two key predictors on mortality: i) admission at weekends (7.00 pm Friday to 6.59 am Monday); ii) night-time admission (7.00 pm to 6.59 am). Logistic regressions were estimated to produce odds ratios. Results Crude 30-day mortality rate decreased from 6.6% in 2004/05 to 5.2% in 2013/14. Adjusted mortality risk was elevated for all out-of-hours periods. The highest risk was associated with admission at weekend night-times: 30-day mortality increased by 0.6 percentage points (adjusted OR: 1.168), 7-day mortality by 0.4 percentage points (adjusted OR: 1.225), and in-hospital mortality by 0.5 percentage points (adjusted OR: 1.140) compared with admission on weekday day-times. Weekend night-time admission was associated with increased mortality risk in 9 out of 10 years, but this was only statistically significant (P≤ 0.05) in 5 out of 10 years. Conclusions There is an increased risk of mortality for patients admitted as emergencies both at weekends and during the night-time. These effects are additive, so that the greatest risk of mortality occurs in patients admitted during the night at weekends. This increased risk appears to be consistent over time, but the effects are small and are not statistically significant in individual hospitals in every year

Expressing the operations of quantum computing in multiparticle geometric algebra

We show how the basic operations of quantum computing can be expressed and manipulated in a clear and concise fashion using a multiparticle version of geometric (aka Clifford) algebra. This algebra encompasses the product operator formalism of NMR spectroscopy, and hence its notation leads directly to implementations of these operations via NMR pulse sequences.Comment: RevTeX, 10 pages, no figures; Physics Letters A, in pres