Conical: an extended module for computing a numerically satisfactory pair of solutions of the differential equation for conical functions

Conical functions appear in a large number of applications in physics and engineering. In this paper we describe an extension of our module CONICAL for the computation of conical functions. Specifically, the module includes now a routine for computing the function ${{\rm R}}^{m}_{-\frac{1}{2}+i\tau}(x)$, a real-valued numerically satisfactory companion of the function ${\rm P}^m_{-\tfrac12+i\tau}(x)$ for $x>1$. In this way, a natural basis for solving Dirichlet problems bounded by conical domains is provided.Comment: To appear in Computer Physics Communication

The State of the Circumstellar Medium Surrounding Gamma-Ray Burst Sources and its Effect on the Afterglow Appearance

We present a numerical investigation of the contribution of the presupernova ejecta of Wolf-Rayet stars to the environment surrounding gamma-ray bursts (GRBs), and describe how this external matter can affect the observable afterglow characteristics. An implicit hydrodynamic calculation for massive stellar evolution is used here to provide the inner boundary conditions for an explicit hydrodynamical code to model the circumstellar gas dynamics. The resulting properties of the circumstellar medium are then used to calculate the deceleration of a relativistic, gas-dynamic jet and the corresponding afterglow light curve produced as the shock wave propagates through the shocked-wind medium. We find that variations in the stellar wind drive instabilities that may produce radial filaments in the shocked-wind region. These comet-like tails of clumps could give rise to strong temporal variations in the early afterglow lightcurve. Afterglows may be expected to differ widely among themselves, depending on the angular anisotropy of the jet and the properties of the stellar progenitor; a wide diversity of behaviors may be the rule, rather than the exception.Comment: 17 pages, 7 figures, ApJ in pres

Controlled Release of Vancomycin and Tigecycline from an Orthopaedic Implant Coating Prevents Staphylococcus aureus Infection in an Open Fracture Animal Model.

Introduction:Treatment of open fractures routinely involves multiple surgeries and delayed definitive fracture fixation because of concern for infection. If implants were made less susceptible to infection, a one-stage procedure with intramedullary nailing would be more feasible, which would reduce morbidity and improve outcomes. Methods:In this study, a novel open fracture mouse model was developed using Staphylococcus aureus (S. aureus) and single-stage intramedullary fixation. The model was used to evaluate whether implants coated with a novel "smart" polymer coating containing vancomycin or tigecycline would be colonized by bacteria in an open fracture model infected with S. aureus. In vivo bioluminescence, ex vivo CFUs, and X-ray images were evaluated over a 42-day postoperative period. Results:We found evidence of a markedly decreased bacterial burden with the local release of vancomycin and tigecycline from the PEG-PPS polymer compared to polymer alone. Vancomycin was released in a controlled fashion and maintained local drug concentrations above the minimum inhibition concentration for S. aureus for greater than 7 days postoperatively. Bacteria were reduced 139-fold from implants containing vancomycin and undetected from the bone and soft tissue. Tigecycline coatings led to a 5991-fold reduction in bacteria isolated from bone and soft tissue and 15-fold reduction on the implants compared to polymer alone. Antibiotic coatings also prevented osteomyelitis and implant loosening as observed on X-ray. Conclusion:Vancomycin and tigecycline can be encapsulated in a polymer coating and released over time to maintain therapeutic levels during the perioperative period. Our results suggest that antibiotic coatings can be used to prevent implant infection and osteomyelitis in the setting of open fracture. This novel open fracture mouse model can be used as a powerful in vivo preclinical tool to evaluate and optimize the treatment of open fractures before further studies in humans

High-pressure study of substrate material ScAlMgO4

We report on the structural properties of ScAlMgO4 studied under quasi-hydrostatic pressure using synchrotron high-pressure x-ray diffraction up to 40 GPa. We also report on single-crystal studies of ScAlMgO4 performed at 300 K and 100 K. We found that the low-pressure phase remains stable up to 24 GPa. At 28 GPa, we detected a reversible phase transformation. The high-pressure phase is assigned to a monoclinic distortion of the low-pressure phase. No additional phase transition is observed up to 40 GPa. In addition, the equation of state, compressibility tensor, and thermal expansion coefficients of ScAlMgO4 are determined. The bulk modulus of ScAlMgO4 is found to be 143(8) GPa, with a strong compressibility anisotropy. For the trigonal low-pressure phase, the compressibility along the c-axis is twice than perpendicular one. A perfect lattice match with ZnO is retained under pressure in the pressure range of stability of wurtzite ZnO.Comment: 22 pages, 5 figures, 4 tables, 24 reference

Computation of parabolic cylinder functions having complex argument

Numerical methods for the computation of the parabolic cylinder $U(a,z)$ for real $a$ and complex $z$ are presented. The main tools are recent asymptotic expansions involving exponential and Airy functions, with slowly varying analytic coefficient functions involving simple coefficients, and stable integral representations; these two main main methods can be complemented with Maclaurin series and a Poincar\'e asymptotic expansion. We provide numerical evidence showing that the combination of these methods is enough for computing the function with $5\times 10^{-13}$ relative accuracy in double precision floating point arithmetic

Predictive modelling using pathway scores: robustness and significance of pathway collections

Background Transcriptomic data is often used to build statistical models which are predictive of a given phenotype, such as disease status. Genes work together in pathways and it is widely thought that pathway representations will be more robust to noise in the gene expression levels. We aimed to test this hypothesis by constructing models based on either genes alone, or based on sample specific scores for each pathway, thus transforming the data to a ‘pathway space’. We progressively degraded the raw data by addition of noise and examined the ability of the models to maintain predictivity. Results Models in the pathway space indeed had higher predictive robustness than models in the gene space. This result was independent of the workflow, parameters, classifier and data set used. Surprisingly, randomised pathway mappings produced models of similar accuracy and robustness to true mappings, suggesting that the success of pathway space models is not conferred by the specific definitions of the pathway. Instead, predictive models built on the true pathway mappings led to prediction rules with fewer influential pathways than those built on randomised pathways. The extent of this effect was used to differentiate pathway collections coming from a variety of widely used pathway databases. Conclusions Prediction models based on pathway scores are more robust to degradation of gene expression information than the equivalent models based on ungrouped genes. While models based on true pathway scores are not more robust or accurate than those based on randomised pathways, true pathways produced simpler prediction rules, emphasizing a smaller number of pathways