Local Differential Geometry as a Representation of the SUSY Oscillator

This work proposes a natural extension of the Bargmann-Fock representation to a SUSY system. The main objective is to show that all essential structures of the n-dimensional SUSY oscillator are supplied by basic differential geometrical notions on an analytical R^n, except for the scalar product which is the only additional ingredient. The restriction to real numbers implies only a minor loss of structure but makes the essential features clearer. In particular, euclidean evolution is enforced naturally by identification with the 1-parametric group of dilations.Comment: 10 pages, late

Generalised boundary conditions for the Aharonov-Bohm effect combined with a homogeneous magnetic field

The most general admissible boundary conditions are derived for an idealised Aharonov-Bohm flux intersecting the plane at the origin on the background of a homogeneous magnetic field. A standard technique based on self-adjoint extensions yields a four-parameter family of boundary conditions; other two parameters of the model are the Aharonov-Bohm flux and the homogeneous magnetic field. The generalised boundary conditions may be regarded as a combination of the Aharonov-Bohm effect with a point interaction. Spectral properties of the derived Hamiltonians are studied in detail.Comment: 32 pages, a LaTeX source file with 2 eps figures; submitted to J. Math. Phy

A Generalization of the Bargmann-Fock Representation to Supersymmetry by Holomorphic Differential Geometry

In the Bargmann-Fock representation the coordinates $z^i$ act as bosonic creation operators while the partial derivatives $\partial_{z^j}$ act as annihilation operators on holomorphic $0$-forms as states of a $D$-dimensional bosonic oscillator. Considering also $p$-forms and further geometrical objects as the exterior derivative and Lie derivatives on a holomorphic ${\bf C}^D$, we end up with an analogous representation for the $D$-dimensional supersymmetric oscillator. In particular, the supersymmetry multiplet structure of the Hilbert space corresponds to the cohomology of the exterior derivative. In addition, a 1-complex parameter group emerges naturally and contains both time evolution and a homotopy related to cohomology. Emphasis is on calculus.Comment: 11 pages, LaTe

Zero modes in a system of Aharonov-Bohm fluxes

We study zero modes of two-dimensional Pauli operators with Aharonov--Bohm fluxes in the case when the solenoids are arranged in periodic structures like chains or lattices. We also consider perturbations to such periodic systems which may be infinite and irregular but they are always supposed to be sufficiently scarce

Inhibition of IL-1beta improves Glycaemia in a Mouse Model for Gestational Diabetes

Gestational diabetes mellitus (GDM) is one of the most common diseases associated with pregnancy, however, the underlying mechanisms remain unclear. Based on the well documented role of inflammation in type 2 diabetes, the aim was to investigate the role of inflammation in GDM. We established a mouse model for GDM on the basis of its two major risk factors, obesity and aging. In these GDM mice, we observed increased Interleukin-1β (IL-1β) expression in the uterus and the placenta along with elevated circulating IL-1β concentrations compared to normoglycemic pregnant mice. Treatment with an anti-IL-1β antibody improved glucose-tolerance of GDM mice without apparent deleterious effects for the fetus. Finally, IL-1β antagonism showed a tendency for reduced plasma corticosterone concentrations, possibly explaining the metabolic improvement. We conclude that IL-1β is a causal driver of impaired glucose tolerance in GDM

Electrophysiological, cognitive and clinical profiles of at-risk mental state: the longitudinal minds in transition (MinT) study

The onset of schizophrenia is typically preceded by a prodromal period lasting several years during which sub-threshold symptoms may be identified retrospectively. Clinical interviews are currently used to identify individuals who have an ultra-high risk (UHR) of developing a psychotic illness with a view to provision of interventions that prevent, delay or reduce severity of future mental health issues. The utility of bio-markers as an adjunct in the identification of UHR individuals is not yet established. Several event-related potential measures, especially mismatch-negativity (MMN), have been identified as potential biomarkers for schizophrenia. In this 12-month longitudinal study, demographic, clinical and neuropsychological data were acquired from 102 anti-psychotic naive UHR and 61 healthy controls, of whom 80 UHR and 58 controls provided valid EEG data during a passive auditory task at baseline. Despite widespread differences between UHR and controls on demographic, clinical and neuropsychological measures, MMN and P3a did not differ between these groups. Of 67 UHR at the 12-month follow-up, 7 (10%) had transitioned to a psychotic illness. The statistical power to detect differences between those who did or did not transition was limited by the lower than expected transition rate. ERPs did not predict transition, with trends in the opposite direction to that predicted. In exploratory analysis, the strongest predictors of transition were measures of verbal memory and subjective emotional disturbance.Rebbekah J. Atkinson, W. Ross Fulham, Patricia T. Michie, Philip B. Ward, Juanita Todd, Helen Stain ... et al