Global MHD Simulations of Neptune's Magnetosphere

A global magnetohydrodynamic (MHD) simulation has been performed in order to investigate the outer boundaries of Neptune's magnetosphere at the time of Voyager 2's flyby in 1989 and to better understand the dynamics of magnetospheres formed by highly inclined planetary dipoles. Using the MHD code Gorgon, we have implemented a precessing dipole to mimic Neptune's tilted magnetic field and rotation axes. By using the solar wind parameters measured by Voyager 2, the simulation is verified by finding good agreement with Voyager 2 magnetometer observations. Overall, there is a large-scale reconfiguration of magnetic topology and plasma distribution. During the “pole-on” magnetospheric configuration, there only exists one tail current sheet, contained between a rarefied lobe region which extends outward from the dayside cusp, and a lobe region attached to the nightside cusp. It is found that the tail current always closes to the magnetopause current system, rather than closing in on itself, as suggested by other models. The bow shock position and shape is found to be dependent on Neptune's daily rotation, with maximum standoff being during the pole-on case. Reconnection is found on the magnetopause but is highly modulated by the interplanetary magnetic field (IMF) and time of day, turning “off” and “on” when the magnetic shear between the IMF and planetary fields is large enough. The simulation shows that the most likely location for reconnection to occur during Voyager 2's flyby was far from the spacecraft trajectory, which may explain the relative lack of associated signatures in the observations

Prolongations of Geometric Overdetermined Systems

We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on the dimension of the solution space.Comment: 22 pages. In the second version, a comparison with the classical theory of prolongations was added. In this third version more details were added concerning our construction and especially the use of Kostant's computation of Lie algebra cohomolog

Statistical modelling of transcript profiles of differentially regulated genes

Background: The vast quantities of gene expression profiling data produced in microarray studies, and the more precise quantitative PCR, are often not statistically analysed to their full potential. Previous studies have summarised gene expression profiles using simple descriptive statistics, basic analysis of variance (ANOVA) and the clustering of genes based on simple models fitted to their expression profiles over time. We report the novel application of statistical non-linear regression modelling techniques to describe the shapes of expression profiles for the fungus Agaricus bisporus, quantified by PCR, and for E. coli and Rattus norvegicus, using microarray technology. The use of parametric non-linear regression models provides a more precise description of expression profiles, reducing the "noise" of the raw data to produce a clear "signal" given by the fitted curve, and describing each profile with a small number of biologically interpretable parameters. This approach then allows the direct comparison and clustering of the shapes of response patterns between genes and potentially enables a greater exploration and interpretation of the biological processes driving gene expression. Results: Quantitative reverse transcriptase PCR-derived time-course data of genes were modelled. "Splitline" or "broken-stick" regression identified the initial time of gene up-regulation, enabling the classification of genes into those with primary and secondary responses. Five-day profiles were modelled using the biologically-oriented, critical exponential curve, y(t) = A + (B + Ct)Rt + ε. This non-linear regression approach allowed the expression patterns for different genes to be compared in terms of curve shape, time of maximal transcript level and the decline and asymptotic response levels. Three distinct regulatory patterns were identified for the five genes studied. Applying the regression modelling approach to microarray-derived time course data allowed 11% of the Escherichia coli features to be fitted by an exponential function, and 25% of the Rattus norvegicus features could be described by the critical exponential model, all with statistical significance of p < 0.05. Conclusion: The statistical non-linear regression approaches presented in this study provide detailed biologically oriented descriptions of individual gene expression profiles, using biologically variable data to generate a set of defining parameters. These approaches have application to the modelling and greater interpretation of profiles obtained across a wide range of platforms, such as microarrays. Through careful choice of appropriate model forms, such statistical regression approaches allow an improved comparison of gene expression profiles, and may provide an approach for the greater understanding of common regulatory mechanisms between genes

Super-Alfv\'enic propagation of reconnection signatures and Poynting flux during substorms

The propagation of reconnection signatures and their associated energy are examined using kinetic particle-in-cell simulations and Cluster satellite observations. It is found that the quadrupolar out-of-plane magnetic field near the separatrices is associated with a kinetic Alfv\'en wave. For magnetotail parameters, the parallel propagation of this wave is super-Alfv\'enic (V_parallel ~ 1500 - 5500 km/s) and generates substantial Poynting flux (S ~ 10^-5 - 10^-4 W/m^2) consistent with Cluster observations of magnetic reconnection. This Poynting flux substantially exceeds that due to frozen-in ion bulk outflows and is sufficient to generate white light aurora in the Earth's ionosphere.Comment: Submitted to PRL on 11/1/2010. Resubmitted on 4/5/201

Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities

We survey our recently proposed method for constructing biholomorphic invariants of quasihomogeneous isolated hypersurface singularities and, more generally, invariants of graded Artinian Gorenstein algebras. The method utilizes certain polynomials associated to such algebras, called nil-polynomials, and we compare them with two other classes of polynomials that have also been used to produce invariants.Comment: 13 page

Bowen-York Tensors

There is derived, for a conformally flat three-space, a family of linear second-order partial differential operators which send vectors into tracefree, symmetric two-tensors. These maps, which are parametrized by conformal Killing vectors on the three-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular these maps send source-free electric fields into TT-tensors. Moreover, if the original vector field is the Coulomb field on $\mathbb{R}^3\backslash \lbrace0\rbrace$, the resulting tensor fields on $\mathbb{R}^3\backslash \lbrace0\rbrace$ are nothing but the family of TT-tensors originally written down by Bowen and York.Comment: 12 pages, Contribution to CQG Special Issue "A Spacetime Safari: Essays in Honour of Vincent Moncrief

A Review of Literature on Health-Related Quality of Life of Retinoblastoma Survivors.

Background: Retinoblastoma is a malignant tumor of the eye that typically presents in early childhood and occurs in approximately 1 in 20,000 births. While active treatment of the tumor is typically completed in childhood, survivors often suffer from long-term effects from treatment including visual impairment, facial deformities, and fear of recurrence or secondary cancer. However, little is known how these long-term effects affect their health-related quality of life (HRQOL). Purpose: To review the literature on HRQOL in retinoblastoma survivors. Method: We searched three electronic databases from January 2005 to December 2018 for original research articles reporting on HRQOL or individual domains such as function, cognition, and psychosocial outcomes in retinoblastoma survivors. Results: A total of 59 articles were reviewed and 15 were identified as eligible. Five of the studies reported worse HRQOL in retinoblastoma survivors than controls or general population norms. Parent-proxy ratings were worse than survivors' self-reports. Conclusion: Our findings confirm the need for further HRQOL research to assess the factors influencing long-term outcomes associated with treatment in adolescent and young adult retinoblastoma survivors. By identifying any potential deficits in specific domains of HRQOL, early interventions might be developed to improve HRQOL in retinoblastoma survivors

Physical Activity Clinical Champions: A Peer-to-Peer Physical Activity Education Programme in England.

Physical inactivity is a key risk factor for morbidity and mortality worldwide1. Targeted interventions aim to increase activity participation, with healthcare professionals (HCPs) having a vital role in its promotion. The England-based Physical Activity Clinical Champion Programme is a global example of a professional development programme designed to harness HCPs influence. This editorial reflects its history, with insight from some key individuals who shaped it