Fuzzy Line Bundles, the Chern Character and Topological Charges over the Fuzzy Sphere

Using the theory of quantized equivariant vector bundles over compact coadjoint orbits we determine the Chern characters of all noncommutative line bundles over the fuzzy sphere with regard to its derivation based differential calculus. The associated Chern numbers (topological charges) arise to be non-integer, in the commutative limit the well known integer Chern numbers of the complex line bundles over the 2-sphere are recovered.Comment: Latex2e, 13 pages, 1 figure. This paper continues and supersedes math-ph/0103003. v2: Typos correcte

Do Not Keep Calm and Carry on: School-Based Mindfulness Programmes Should Test Making Mindfulness Practice Available in the School Day

Recently, the largest test of a school-based mindfulness programme to date, the My Resilience In Adolescence (MYRIAD) trial, found that participating in weekly mindfulness lessons did not improve students’ well-being compared to teaching as usual, with low uptake of recommended home mindfulness practice. One potential explanation for the null result and low uptake is that adolescents might be unlikely to adhere to home mindfulness practice recommendations when choosing between mindfulness and their graded homework or more stimulating activities. Indeed, many studies of school-based mindfulness programmes have reported low adherence to home practice recommendations. Home practice recommendations also create equity issues, as many students may find it difficult to make the time for home mindfulness practice, a factor that is more likely to affect students who are disadvantaged. As such, we argue in this article that research needs to test whether school-based mindfulness programmes that make mindfulness practice time available in the school day result in higher adherence to mindfulness practice recommendations, and whether these programmes are effective at improving student mental health. Unfortunately, very little research has examined how much mindfulness practice is required to obtain meaningful effects. We summarise the small volume of mindfulness dose-response literature to provide guidelines for how much school-based mindfulness practice might be sufficient and provide suggestions for further testing. While making mindfulness practice time available in the school day may be difficult to implement, its efficacy is currently untested. Youth mental health remains a critical issue, providing strong justification for testing whether mindfulness practice made available in the school day results in better outcomes, despite the challenges posed in pursuing this research avenue

The noncommutative Lorentzian cylinder as an isospectral deformation

We present a new example of a finite-dimensional noncommutative manifold, namely the noncommutative cylinder. It is obtained by isospectral deformation of the canonical triple associated to the Euclidean cylinder. We discuss Connes' character formula for the cylinder. In the second part, we discuss noncommutative Lorentzian manifolds. Here, the definition of spectral triples involves Krein spaces and operators on Krein spaces. A central role is played by the admissible fundamental symmetries on the Krein space of square integrable sections of a spin bundle over a Lorentzian manifold. Finally, we discuss isospectral deformation of the Lorentzian cylinder and determine all admissible fundamental symmetries of the noncommutative cylinder.Comment: 30 page

Estimating the nuclear level density with the Monte Carlo shell model

A method for making realistic estimates of the density of levels in even-even nuclei is presented making use of the Monte Carlo shell model (MCSM). The procedure follows three basic steps: (1) computation of the thermal energy with the MCSM, (2) evaluation of the partition function by integrating the thermal energy, and (3) evaluating the level density by performing the inverse Laplace transform of the partition function using Maximum Entropy reconstruction techniques. It is found that results obtained with schematic interactions, which do not have a sign problem in the MCSM, compare well with realistic shell-model interactions provided an important isospin dependence is accounted for.Comment: 14 pages, 3 postscript figures. Latex with RevTex. Submitted as a rapid communication to Phys. Rev.

Microlocal analysis of quantum fields on curved spacetimes: Analytic wavefront sets and Reeh-Schlieder theorems

We show in this article that the Reeh-Schlieder property holds for states of quantum fields on real analytic spacetimes if they satisfy an analytic microlocal spectrum condition. This result holds in the setting of general quantum field theory, i.e. without assuming the quantum field to obey a specific equation of motion. Moreover, quasifree states of the Klein-Gordon field are further investigated in this work and the (analytic) microlocal spectrum condition is shown to be equivalent to simpler conditions. We also prove that any quasifree ground- or KMS-state of the Klein-Gordon field on a stationary real analytic spacetime fulfills the analytic microlocal spectrum condition.Comment: 31 pages, latex2

Randomized, double-blind, parallel-group, 48-week study for efficacy and safety of a higher-dose rivastigmine patch (15 vs. 10 cm(2)) in Alzheimer’s disease

Aim: Determine whether patients with Alzheimer’s disease demonstrating functional and cognitive decline, following 24-48 weeks of open-label treatment with 9.5 mg/24 h (10 cm(2)) rivastigmine patch, benefit from a dose increase in a double-blind (DB) comparative trial of two patch doses. Methods: Patients meeting prespecified decline criteria were randomized to receive 9.5 or 13.3 mg/24 h (15 cm(2)) patch during a 48-week, DB phase. Coprimary outcomes were change from baseline to week 48 on the Instrumental Activities of Daily Living domain of the Alzheimer’s Disease Cooperative Study-Activities of Daily Living (ADCS-IADL) scale and the Alzheimer’s Disease Assessment Scale-cognitive subscale (ADAS-cog). Safety and tolerability were assessed. Results: Of 1,584 patients enrolled, 567 met decline criteria and were randomized. At all timepoints, ADCS-IADL and ADAS-cog scores favoured the 13.3 mg/24 h patch. The 13.3 mg/24 h patch was statistically superior to the 9.5 mg/24 h patch on the ADCS-IADL scale from week 16 (p = 0.025) onwards including week 48 (p = 0.002), and ADAScog at week 24 (p = 0.027), but not at week 48 (p = 0.227). No unexpected safety concerns were observed. Conclusions: The 13.3 mg/24 h rivastigmine patch significantly reduced deterioration in IADL, compared with the 9.5 mg/24 h patch, and was well tolerated. Copyright © 2012 S. Karger AG, Base

A geometrical origin for the covariant entropy bound

Causal diamond-shaped subsets of space-time are naturally associated with operator algebras in quantum field theory, and they are also related to the Bousso covariant entropy bound. In this work we argue that the net of these causal sets to which are assigned the local operator algebras of quantum theories should be taken to be non orthomodular if there is some lowest scale for the description of space-time as a manifold. This geometry can be related to a reduction in the degrees of freedom of the holographic type under certain natural conditions for the local algebras. A non orthomodular net of causal sets that implements the cutoff in a covariant manner is constructed. It gives an explanation, in a simple example, of the non positive expansion condition for light-sheet selection in the covariant entropy bound. It also suggests a different covariant formulation of entropy bound.Comment: 20 pages, 8 figures, final versio

Quantum Energy Inequalities in Pre-Metric Electrodynamics

Pre-metric electrodynamics is a covariant framework for electromagnetism with a general constitutive law. Its lightcone structure can be more complicated than that of Maxwell theory as is shown by the phenomenon of birefringence. We study the energy density of quantized pre-metric electrodynamics theories with linear constitutive laws admitting a single hyperbolicity double-cone and show that averages of the energy density along the worldlines of suitable observers obey a Quantum Energy Inequality (QEI) in states that satisfy a microlocal spectrum condition. The worldlines must meet two conditions: (a) the classical weak energy condition must hold along them, and (b) their velocity vectors have positive contractions with all positive frequency null covectors (we call such trajectories `subluminal'). After stating our general results, we explicitly quantize the electromagnetic potential in a translationally invariant uniaxial birefringent crystal. Since the propagation of light in such a crystal is governed by two nested lightcones, the theory shows features absent in ordinary (quantized) Maxwell electrodynamics. We then compute a QEI bound for worldlines of inertial `subluminal' observers, which generalizes known results from the Maxwell theory. Finally, it is shown that the QEIs fail along trajectories that have velocity vectors which are timelike with respect to only one of the lightcones