The Dirichlet problem for constant mean curvature surfaces in Heisenberg space

We study constant mean curvature graphs in the Riemannian 3-dimensional Heisenberg spaces ${\cal H}={\cal H}(\tau)$. Each such ${\cal H}$ is the total space of a Riemannian submersion onto the Euclidean plane $\mathbb{R}^2$ with geodesic fibers the orbits of a Killing field. We prove the existence and uniqueness of CMC graphs in ${\cal H}$ with respect to the Riemannian submersion over certain domains $\Omega\subset\mathbb{R}^2$ taking on prescribed boundary values

Resolving ambiguities in the LF/HF Ratio: LF-HF scatter plots for the categorization of mental and physical stress from HRV

It is generally accepted that the activities of the autonomic nervous system (ANS), which consists of the sympathetic (SNS) and parasympathetic nervous systems (PNS), are reflected in the low- (LF) and high-frequency (HF) bands in heart rate variability (HRV)—while, not without some controversy, the ratio of the powers in those frequency bands, the so called LF-HF ratio (LF/HF), has been used to quantify the degree of sympathovagal balance. Indeed, recent studies demonstrate that, in general: (i) sympathovagal balance cannot be accurately measured via the ratio of the LF- and HF- power bands; and (ii) the correspondence between the LF/HF ratio and the psychological and physiological state of a person is not unique. Since the standard LF/HF ratio provides only a single degree of freedom for the analysis of this 2D phenomenon, we propose a joint treatment of the LF and HF powers in HRV within a two-dimensional representation framework, thus providing the required degrees of freedom. By virtue of the proposed 2D representation, the restrictive assumption of the linear dependence between the activity of the autonomic nervous system (ANS) and the LF-HF frequency band powers is demonstrated to become unnecessary. The proposed analysis framework also opens up completely new possibilities for a more comprehensive and rigorous examination of HRV in relation to physical and mental states of an individual, and makes possible the categorization of different stress states based on HRV. In addition, based on instantaneous amplitudes of Hilbert-transformed LF- and HF-bands, a novel approach to estimate the markers of stress in HRV is proposed and is shown to improve the robustness to artifacts and irregularities, critical issues in real-world recordings. The proposed approach for resolving the ambiguities in the standard LF/HF-ratio analyses is verified over a number of real-world stress-invoking scenarios

Ideal evolution of MHD turbulence when imposing Taylor-Green symmetries

We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the four-fold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a re-gridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of $6144^3$ points, and three different configurations on grids of $4096^3$ points. At the highest resolution, two different current and vorticity sheet systems are found to collide, producing two successive accelerations in the development of small scales. At the latest time, a convergence of magnetic field lines to the location of maximum current is probably leading locally to a strong bending and directional variability of such lines. A novel analytical method, based on sharp analysis inequalities, is used to assess the validity of the finite-time singularity scenario. This method allows one to rule out spurious singularities by evaluating the rate at which the logarithmic decrement of the analyticity-strip method goes to zero. The result is that the finite-time singularity scenario cannot be ruled out, and the singularity time could be somewhere between $t=2.33$ and $t=2.70.$ More robust conclusions will require higher resolution runs and grid-point interpolation measurements of maximum current and vorticity.Comment: 18 pages, 13 figures, 2 tables; submitted to Physical Review

Pain prediction from ECG in vascular surgery

Varicose vein surgeries are routine outpatient procedures, which are often performed under local anaesthesia. The use of local anaesthesia both minimises the risk to patients and is cost effective, however, a number of patients still experience pain during surgery. Surgical teams must therefore decide to administer either a general or local anaesthetic based on their subjective qualitative assessment of patient anxiety and sensitivity to pain, without any means to objectively validate their decision. To this end, we develop a 3-D polynomial surface fit, of physiological metrics and numerical pain ratings from patients, in order to model the link between the modulation of cardiovascular responses and pain in varicose vein surgeries. Spectral and structural complexity features found in heart rate variability signals, recorded immediately prior to 17 varicose vein surgeries, are used as pain metrics. The so obtained pain prediction model is validated through a leave-one-out validation, and achieved a Kappa coefficient of 0.72 (substantial agreement) and an area below a receiver operating characteristic curve of 0.97 (almost perfect accuracy). This proof-of-concept study conclusively demonstrates the feasibility of the accurate classification of pain sensitivity, and introduces a mathematical model to aid clinicians in the objective administration of the safest and most cost-effective anaesthetic to individual patients

Variability in Demand for Special Education Teachers: Indicators, Explanations, and Impacts

After decades of growth, the number of special education teachers (SETs) has begun to decline. In 2009, U.S. schools employed 13% fewer SETs than in 2006. The number of annual new hires of SETs also dropped dramatically in some states. The onset of these declines predated the economic downturn of 2008 and resulted in part from a steady decline since 2005 in the number of students with disabilities (SWD) served. We consider factors that may be contributing to declining demand for SETs, among them the number of SWD, service delivery, the economic downturn, and present supporting evidence. We also consider the potential impact of reduced demand on SET supply, teacher education, equitable distribution of teachers, and, most importantly, outcomes for SWD. We call for vigilance and monitoring of SET employment data to assure that all students receive the appropriate education to which they are entitled

Properties of Galaxies in and around Voids

Two surveys for intrinsically faint galaxies towards nearby voids have been conducted at the MPI f\"ur Astronomie, Heidelberg. One selected targets from a new diameter limited ($\Phi \ge 5''$) catalog with morphological criteria while the other used digitized objective prism Schmidt plates to select mainly HII dwarf galaxies. For some 450 galaxies, redshifts and other optical data were obtained. We studied the spatial distribution of the sample objects, their luminosity function, and their intrinsic properties. Most of the galaxies belong to already well known sheets and filaments. But we found about a dozen highly isolated galaxies in each sample (nearest neighborhood distance $\ge 3 h_{75}^{-1} Mpc$). These tend to populate additional structures and are not distributed homogeneously throughout the voids. As our results on 'void galaxies' still suffer from small sample statistics, I also tried to combine similar existing surveys of nearby voids to get further hints on the larger structure and on the luminosity function of the isolated galaxies. No differences in the luminosity function of sheet and void galaxies could be found. The optical and infrared properties of both samples are in the normal range for samples dominated by late-type dwarfs. Follow-up HI studies show that the isolated dwarfs in both samples have unusual high amount of neutral gas for a given luminosity.Comment: 10 pages, 4 figures, latex, to appear in the proceedings of the 'Ringberg workshop on Large Scale Structure', hold Sep. 23-28, 199

Systematically Asymmetric Heliospheric Magnetic Field: Evidence for a Quadrupole Mode and Non-axisymmetry with Polarity Flip-flops

Recent studies of the heliospheric magnetic field (HMF) have detected interesting, systematic hemispherical and longitudinal asymmetries which have a profound significance for the understanding of solar magnetic fields. The in situ HMF measurements since 1960s show that the heliospheric current sheet (HCS) is systematically shifted (coned) southward during solar minimum times, leading to the concept of a bashful ballerina. While temporary shifts can be considerably larger, the average HCS shift (coning) angle is a few degrees, less than the $7.2^{\circ}$ tilt of the solar rotation axis. Recent solar observations during the last two solar cycles verify these results and show that the magnetic areas in the northern solar hemisphere are larger and their intensity weaker than in the south during long intervals in the late declining to minimum phase. The multipole expansion reveals a strong quadrupole term which is oppositely directed to the dipole term. These results imply that the Sun has a symmetric quadrupole S0 dynamo mode that oscillates in phase with the dominant dipole A0 mode. Moreover, the heliospheric magnetic field has a strong tendency to produce solar tilts that are roughly opposite in longitudinal phase. This implies is a systematic longitudinal asymmetry and leads to a "flip-flop" type behaviour in the dominant HMF sector whose period is about 3.2 years. This agrees very well with the similar flip-flop period found recently in sunspots, as well as with the observed ratio of three between the activity cycle period and the flip-flop period of sun-like stars. Accordingly, these results require that the solar dynamo includes three modes, A0, S0 and a non-axisymmetric mode. Obviously, these results have a great impact on solar modelling.Comment: 13 pages, 4 figures, Solar Physics, Topical Issue of Space Climate Symposium, in pres

Association between skirt size and chronic liver disease in post-menopausal women: a prospective cohort study within the United Kingdom Trial of Ovarian Cancer Screening (UKCTOCS)

BACKGROUND: We investigated the association between self-reported skirt size (SS) and change in SS, and incidence of chronic liver disease (CLD) in a prospective cohort study of women recruited to the UKCTOCS trial. METHODS: Women recruited to UKCTOCS in England without documented CLD self-reported their current UK SS during trial participation and were asked to recall their SS when aged in 20s (via completion of a questionnaire 3-5 years after recruitment). Participants were followed up via electronic health record linkage and hazard ratios (HR) calculated for incident liver-related events (LRE). RESULTS: Three hundred twenty-two (0.3%) of 94,124 women experienced a first LRE. Compared to SS ≤ 16, rates of LRE were higher in the SS ≥ 18 groups (both when aged in 20s and at questionnaire completion). Event rates were higher if there was no change in SS or an increase in SS, compared to a decrease in SS. In the models adjusted for potential confounders, HRs for LRE were higher in the groups of women reporting SS ≥ 18 both when aged in 20s (HR = 1.39 (95% CI; 0.87-2.23)) and at questionnaire completion (HR = 1.37 (95% CI; 1.07-1.75)). Compared to a decrease in SS, HRs were higher in the no change (HR = 1.78 (95% CI; 0.95-3.34)) and increase (HR = 1.80 (95% CI; 1.01-3.21)) groups. CONCLUSION: CLD is associated with high SS and an increase in SS over time. These data suggest SS can be used in simple public health messages about communicating the risk of liver disease. TRIAL REGISTRATION: UKCTOCS is registered as an International Standard Randomised Controlled Trial, number ISRCTN22488978 . Registered 06/04/2000