Cyclic Lorentzian Lie Groups

We consider Lie groups equipped with a left-invariant cyclic Lorentzian metric. As in the Riemannian case, in terms of homogeneous structures, such metrics can be considered as different as possible from bi-invariant metrics. We show that several results concerning cyclic Riemannian metrics do not extend to their Lorentzian analogues, and obtain a full classification of three- and four-dimensional cyclic Lorentzian metrics

A stochastic collocation approach for parabolic PDEs with random domain deformations

This work considers the problem of numerically approximating statistical moments of a Quantity of Interest (QoI) that depends on the solution of a linear parabolic partial differential equation. The geometry is assumed to be random and is parameterized by $N$ random variables. The parabolic problem is remapped to a fixed deterministic domain with random coefficients and shown to admit an extension on a well defined region embedded in the complex hyperplane. A Stochastic collocation method with an isotropic Smolyak sparse grid is used to compute the statistical moments of the QoI. In addition, convergence rates for the stochastic moments are derived and compared to numerical experiments

Peripheral Intravenous Infiltrates: Engaging Staff to Increase Reporting

A large free standing children’s academic hospital aimed to improve patient safety and outcomes by decreasing the overall severity of peripheral intravenous infiltration and extravasations (PIVIEs). A care bundle was developed by creating a PIVIE measurement tool within the electronic medical record (EMR) and integrating the tool into standardized daily practice for nurses. The care bundle included creating a team of clinical leaders consisting of empowered bedside nurses acting as mobilized resources embedded into each unit. The initiative resulted in a large scale increase in reported PIVIEs system-wide within 1 month of education dissemination to bedside RN staff. The QI interventions captured a realistic interpretation allowing for a more global and accurate reflection of the number and severity of PIVIE events system-wide, while creating documentation for the PIVIE tool in the EMR and a clinical leader model. The results reflected a dramatic rise in the number of reported PIVIE events, increase in staff awareness of PIVIEs, increased peripheral intravenous line assessments, and decreased severity of PIVIEs that do occur

Four-dimensional naturally reductive pseudo-Riemannian spaces

The classification of 4-dimensional naturally reductive pseudo-Riemannian spaces is given. This classification comprises symmetric spaces, the product of 3-dimensional naturally reductive spaces with the real line and new families of indecomposable manifolds which are studied at the end of the article. The oscillator group is also analyzed from the point of view of this classification

Covariant un-reduction for curve matching

The process of un-reduction, a sort of reversal of reduction by the Lie group symmetries of a variational problem, is explored in the setting of field theories. This process is applied to the problem of curve matching in the plane, when the curves depend on more than one independent variable. This situation occurs in a variety of instances such as matching of surfaces or comparison of evolution between species. A discussion of the appropriate Lagrangian involved in the variational principle is given, as well as some initial numerical investigations.Comment: Conference paper for MFCA201