Vector-valued covariant differential operators for the M\"obius transformation

We obtain a family of functional identities satisfied by vector-valued functions of two variables and their geometric inversions. For this we introduce particular differential operators of arbitrary order attached to Gegenbauer polynomials. These differential operators are symmetry breaking for the pair of Lie groups $(SL(2,\mathbb C), SL(2,\mathbb R))$ that arise from conformal geometry.Comment: To appear in Springer Proceedings in Mathematics and Statistic

A retrospective study on the effects of illness severity and atrial fibrillation on outcomes in the intensive care unit

Introduction: Atrial fibrillation (AF) is common in patients in the intensive care unit (ICU) and has been associated with worse outcomes. However, it is unclear whether AF itself adds to the risk of death or is merely a marker of illness severity. We aimed to record the incidence and outcomes of all patients with different categories of AF and determine whether AF was an independent predictor of death.<p></p> Methods: This retrospective cohort study was undertaken in the ICU of a tertiary-referral university hospital. Category of AF, sex, C-reactive protein (CRP) level, APACHE II score, predicted hospital mortality and survival outcomes were analysed from 1084 records. Percentages, medians and interquartile ranges were used to describe the sample. Chi-square test and the non-parametric Mann–Whitney U test were used, as appropriate, for statistical analysis. Logistic regression analyses were performed to evaluate the association of AF with death in the ICU adjusting for age, sex, CRP level and APACHE II score.<p></p> Results: Overall, 13.6% of patients developed new-onset AF during their critical illness, while 4.3% had a pre-existing history. The hospital mortality rate was higher in those with AF compared with those without (47.9% vs. 30.9%, p<0.001) and higher in those with newly diagnosed AF compared with those with a prior history (53.1% vs. 31.9%, p=0.012). CRP levels were higher in those with AF (p<0.001) compared with those without and higher in those with newly diagnosed AF compared with those with a prior history (p=0.012). On multivariate logistic regression analysis, only the APACHE II score was found to be an independent predictor of death.<p></p> Conclusion: Despite the higher mortality rate in patients with AF, the APACHE II score was the only independent predictor of death within the ICU. Prospective studies are required to explore the apparently reduced risk of dying among those with a prior history of AF.<p></p&gt

Patients' request for and emergency physicians' prescription of antimicrobial prophylaxis for anthrax during the 2001 bioterrorism-related outbreak

BACKGROUND: Inappropriate use of antibiotics by individuals worried about biological agent exposures during bioterrorism events is an important public health concern. However, little is documented about the extent to which individuals with self-identified risk of anthrax exposure approached physicians for antimicrobial prophylaxis during the 2001 bioterrorism attacks in the United States. METHODS: We conducted a telephone survey of randomly selected members of the Pennsylvania Chapter of the American College of Emergency Physicians to assess patients' request for and emergency physicians' prescription of antimicrobial agents during the 2001 anthrax attacks. RESULTS: Ninety-seven physicians completed the survey. Sixty-four (66%) respondents had received requests from patients for anthrax prophylaxis; 16 (25%) of these physicians prescribed antibiotics to a total of 23 patients. Ten physicians prescribed ciprofloxacin while 8 physicians prescribed doxycycline. CONCLUSION: During the 2001 bioterrorist attacks, the majority of the emergency physicians we surveyed encountered patients who requested anthrax prophylaxis. Public fears may lead to a high demand for antibiotic prophylaxis during bioterrorism events. Elucidation of the relationship between public health response to outbreaks and outcomes would yield insights to ease burden on frontline clinicians and guide strategies to control inappropriate antibiotic allocation during bioterrorist events

RF model of the distribution system as a communication channel, phase 2. Volume 3: Appendices

Program documentation concerning the design, implementation, and verification of a computerized model for predicting the steady-state sinusoidal response of radial configured distribution feeders is presented in these appendices

Absolute emission altitude of pulsars: PSRs B1839+09, B1916+14 and B2111+46

We study the mean profiles of the multi--component pulsars PSRs B1839+09, B1916+14 and B2111+46. We estimate the emission height of the core components, and hence find the absolute emission altitudes corresponding to the conal components. By fitting Gaussians to the emission components, we determine the phase location of the component peaks. Our findings indicate that the emission beams of these pulsars have the nested core--cone structures. Based on the phase location of the component peaks, we estimate the aberration--retardation (A/R) phase shifts in the profiles. Due to the A/R phase shift, the peak of the core component in the intensity profile and the inflection point of the polarization angle swing are found to be symmetrically shifted in the opposite directions with respect to the meridional plane in such a way that the core shifts towards the leading side and the polarization angle inflection point towards the trailing side. We have been able to locate the phase location of the meridional plane and to estimate the absolute emission altitude of both the core and the conal components relative to the neutron star centre, using the exact expression for the A/R phase shift given by Gangadhara (2005).Comment: 10 pages, 6 figures, Accepted for Publication in A&

The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability

We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter $\epsilon$ uncouples the system at $\epsilon=0$. Using a normal form for $N=2$ identical systems undergoing Hopf bifurcation, we explore the dynamical properties. Matching the normal form coefficients to a coupled Wilson-Cowan oscillator network gives an understanding of different types of behaviour that arise in a model of perceptual bistability. Notably, we find bistability between in-phase and anti-phase solutions that demonstrates the feasibility for synchronisation to act as the mechanism by which periodic inputs can be segregated (rather than via strong inhibitory coupling, as in existing models). Using numerical continuation we confirm our theoretical analysis for small coupling strength and explore the bifurcation diagrams for large coupling strength, where the normal form approximation breaks down

Stokes tomography of radio pulsar magnetospheres. I. Linear polarization

Polarimetric studies of pulsar radio emission traditionally concentrate on how the Stokes vector (I, Q, U, V) varies with pulse longitude, with special emphasis on the position angle (PA) swing of the linearly polarized component. The interpretation of the PA swing in terms of the rotating vector model is limited by the assumption of an axisymmetric magnetic field and the degeneracy of the output with respect to the orientation and magnetic geometry of the pulsar; different combinations of the latter two properties can produce similar PA swings. This paper introduces Stokes phase portraits as a supplementary diagnostic tool with which the orientation and magnetic geometry can be inferred more accurately. The Stokes phase portraits feature unique patterns in the I-Q, I-U, and Q-U planes, whose shapes depend sensitively on the magnetic geometry, inclination angle, beam and polarization patterns, and emission altitude. We construct look-up tables of Stokes phase portraits and PA swings for pure and current-modified dipole fields, filled core and hollow cone beams, and two empirical linear polarization models, L/I = \cos \theta_0 and L/I = \sin \theta_0, where \theta_0 is the colatitude of the emission point. We compare our look-up tables to the measured phase portraits of 24 pulsars in the European Pulsar Network online database. We find evidence in 60% of the objects that the radio emission region may depart significantly from low altitudes, even when the PA swing is S-shaped and/or the pulse-width-period relation is well satisfied. On the other hand, the data are explained adequately if the emission altitude exceeds ~10% of the light cylinder radius. We conclude that Stokes phase portraits should be analysed concurrently with the PA swing and pulse profiles in future when interpreting radio pulsar polarization data.Comment: 60 pages, 58 figures, submitted to MNRAS, accepted 13 Oct 201

Is pulsar B0656+14 a very nearby RRAT source?

The recently discovered RRAT sources are characterized by very bright radio bursts which, while being periodically related, occur infrequently. We find bursts with the same characteristics for the known pulsar B0656+14. These bursts represent pulses from the bright end of an extended smooth pulse-energy distribution and are shown to be unlike giant pulses, giant micropulses or the pulses of normal pulsars. The extreme peak-fluxes of the brightest of these pulses indicates that PSR B0656+14, were it not so near, could only have been discovered as an RRAT source. Longer observations of the RRATs may reveal that they, like PSR B0656+14, emit weaker emission in addition to the bursts.Comment: 4 pages, 4 figures, accepted by ApJ

Geography of conservation spending, biodiversity, and culture

We used linear and multivariate models to examine the associations between geography, biodiversity, per capita economic output, national spending on conservation, governance, and cultural traits in 55 countries. Cultural traits and social metrics of modernization correlated positively with national spending on conservation. The global distribution of this spending culture was poorly aligned with the distribution of biodiversity. Specifically, biodiversity was greater in the tropics where cultures tended to spend relatively less on conservation and tended to have higher collectivism, formalized and hierarchical leadership, and weaker governance. Consequently, nations lacking social traits frequently associated with modernization, environmentalism, and conservation spending have the largest component of Earth's biodiversity. This has significant implications for setting policies and priorities for resource management given that biological diversity is rapidly disappearing and cultural traits change slowly. Therefore, we suggest natural resource management adapt to and use characteristics of existing social organization rather than wait for or promote social values associated with conservation spending. Supporting biocultural traditions, engaging leaders to increase conservation commitments, cross-national efforts that complement attributes of cultures, and avoiding interference with nature may work best to conserve nature in collective and hierarchical societies. Spending in modernized nations may be a symbolic response to a symptom of economic development and environmental degradation, and here conservation actions need to ensure that biodiversity is not being lost