Group-invariant soliton equations and bi-Hamiltonian geometric curve flows in Riemannian symmetric spaces

Universal bi-Hamiltonian hierarchies of group-invariant (multicomponent) soliton equations are derived from non-stretching geometric curve flows \map(t,x) in Riemannian symmetric spaces $M=G/H$, including compact semisimple Lie groups $M=K$ for $G=K\times K$, $H={\rm diag} G$. The derivation of these soliton hierarchies utilizes a moving parallel frame and connection 1-form along the curve flows, related to the Klein geometry of the Lie group $G\supset H$ where $H$ is the local frame structure group. The soliton equations arise in explicit form from the induced flow on the frame components of the principal normal vector N=\covder{x}\mapder{x} along each curve, and display invariance under the equivalence subgroup in $H$ that preserves the unit tangent vector T=\mapder{x} in the framing at any point $x$ on a curve. Their bi-Hamiltonian integrability structure is shown to be geometrically encoded in the Cartan structure equations for torsion and curvature of the parallel frame and its connection 1-form in the tangent space T_\map M of the curve flow. The hierarchies include group-invariant versions of sine-Gordon (SG) and modified Korteweg-de Vries (mKdV) soliton equations that are found to be universally given by curve flows describing non-stretching wave maps and mKdV analogs of non-stretching Schrodinger maps on $G/H$. These results provide a geometric interpretation and explicit bi-Hamiltonian formulation for many known multicomponent soliton equations. Moreover, all examples of group-invariant (multicomponent) soliton equations given by the present geometric framework can be constructed in an explicit fashion based on Cartan's classification of symmetric spaces.Comment: Published version, with a clarification to Theorem 4.5 and a correction to the Hamiltonian flow in Proposition 5.1

Relativistic Compact Objects in Isotropic Coordinates

We present a matrix method for obtaining new classes of exact solutions for Einstein's equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein's equations to two independent Riccati type differential equations for which three classes of solutions are obtained. One class of the solutions corresponding to the linear barotropic type fluid with an equation of state $p=\gamma \rho$ is discussed in detail.Comment: 9 pages, no figures, accepted for publication in Pramana-Journal of Physic

Behaviour of Magnetic Tubes in Neutron Star's Interior

It is found from Maxwell's equations that the magnetic field lines are good analogues of relativistic strings. It is shown that the super-conducting current in the neutron star's interior causes local rotation of magnetic flux tubes carrying quantized flux.Comment: 6 pages, no figure

Cholesterol efflux promoting function of high-density lipoproteins in calcific aortic valve stenosis

Background and aims: Cholesterol efflux capacity is a functional property of high-density lipoproteins (HDL) reflecting the efficiency of the atheroprotective reverse cholesterol transport process in humans. Its relationship with calcific aortic valve stenosis (CAVS) has not been fully assessed yet. Methods: We evaluated HDL-CEC in a patient population with varying degrees of aortic valvular calcific disease, assessed using echocardiography and cardiac computed tomography. Measurement of biomarkers that reflect osteogenic and tissue remodeling, along with dietary and gut microbiota-derived metabolites were performed. Results: Patients with moderate-severe CAVS had significantly lower HDL-CEC compared to both control and aortic sclerosis subjects (mean: 6.09%, 7.32% and 7.26%, respectively). HDL-CEC displayed negative correlations with peak aortic jet velocity and aortic valve calcium score, indexes of CAVS severity (ρ = -0.298, p = 0.002 and ρ = -0.358, p = 0.005, respectively). In multivariable regression model, HDL-CEC had independent association with aortic valve calcium score (B: -0.053, SE: 0.014, p < 0.001), GFR (B: -0.034, SE: 0.012, p = 0.007), as well as with levels of total cholesterol (B: 0.018, SE: 0.005, p = 0.002). Conclusion: These results indicate an impairment of HDL-CEC in moderate-severe CAVS and may contribute to identify potential novel targets for CAVS management

Impact of a Multifaceted Early Mobility Intervention for Critically Ill Children - the PICU Up! Trial: Study Protocol for a Multicenter Stepped-Wedge Cluster Randomized Controlled Trial

BACKGROUND: Over 50% of all critically ill children develop preventable intensive care unit-acquired morbidity. Early and progressive mobility is associated with improved outcomes in critically ill adults including shortened duration of mechanical ventilation and improved muscle strength. However, the clinical effectiveness of early and progressive mobility in the pediatric intensive care unit has never been rigorously studied. The objective of the study is to evaluate if the PICU Up! intervention, delivered in real-world conditions, decreases mechanical ventilation duration (primary outcome) and improves delirium and functional status compared to usual care in critically ill children. Additionally, the study aims to identify factors associated with reliable PICU Up! delivery. METHODS: The PICU Up! trial is a stepped-wedge, cluster-randomized trial of a pragmatic, interprofessional, and multifaceted early mobility intervention (PICU Up!) conducted in 10 pediatric intensive care units (PICUs). The trial\u27s primary outcome is days alive free of mechanical ventilation (through day 21). Secondary outcomes include days alive and delirium- and coma-free (ADCF), days alive and coma-free (ACF), days alive, as well as functional status at the earlier of PICU discharge or day 21. Over a 2-year period, data will be collected on 1,440 PICU patients. The study includes an embedded process evaluation to identify factors associated with reliable PICU Up! delivery. DISCUSSION: This study will examine whether a multifaceted strategy to optimize early mobility affects the duration of mechanical ventilation, delirium incidence, and functional outcomes in critically ill children. This study will provide new and important evidence on ways to optimize short and long-term outcomes for pediatric patients. TRIAL REGISTRATION: ClinicalTrials.gov NCT04989790. Registered on August 4, 2021

Type D spacetimes and the Weyl double copy

We study the double-copy relation between classical solutions in gauge theory and gravity, focusing on four-dimensional vacuum metrics of algebraic type D, a class that includes several important solutions. We present a double copy of curvatures that applies to all spacetimes of this type—the Weyl double copy—relating the curvature of the spacetime to an electromagnetic field strength. We show that the Weyl double copy is consistent with the previously known Kerr–Schild double copy, and in fact resolves certain ambiguities of the latter. The most interesting new example of the classical double copy presented here is that of the C-metric. This well-known solution, which represents a pair of uniformly accelerated black holes, is mapped to the Liénard–Wiechert potential for a pair of uniformly accelerated charges. We also present a new double-copy interpretation of the Eguchi–Hanson instanton

Dynamics and stability of the Godel universe

We use covariant techniques to describe the properties of the Godel universe and then consider its linear response to a variety of perturbations. Against matter aggregations, we find that the stability of the Godel model depends primarily upon the presence of gradients in the centrifugal energy, and secondarily on the equation of state of the fluid. The latter dictates the behaviour of the model when dealing with homogeneous perturbations. The vorticity of the perturbed Godel model is found to evolve as in almost-FRW spacetimes, with some additional directional effects due to shape distortions. We also consider gravitational-wave perturbations by investigating the evolution of the magnetic Weyl component. This tensor obeys a simple plane-wave equation, which argues for the neutral stability of the Godel model against linear gravity-wave distortions. The implications of the background rotation for scalar-field Godel cosmologies are also discussed.Comment: Revised version, to match paper published in Class. Quantum Gra

Weak signals in healthcare: The case study of the Mid-Staffordshire NHS Foundation Trust

Most organisational disasters have warning signals prior to the event occurring, which are increasingly appearing in accident reports. In the case of the Mid-Staffordshire Disaster, the disaster was not as a result of component failure or human error but rather an organisation that drifted into failure with precursory warning signals being ignored. It has been estimated that between 400 and 1200 patients died as a result of poor care between 2004 and 2009. The aim of this study was to identify the precursory signals and their rationalizations that occurred during this event. Qualitative document analysis was used to analyse the independent and public inquiry reports. Signals were present on numerous system levels. At a person level, there were cases of staff trying to make management aware of the problems, as well as the campaign “Cure the NHS” started by bereaved relatives. At an organisational level, examples of missed signals included the decrease in the trust’s star rating due to failure to meet targets, the NHS care regulator voicing concern regarding the unusually high death rates and auditors’ reports highlighting concerns regarding risk management. At an external level, examples included negative peer reviews from various external organizations