Geodesics on Lie groups: Euler equations and totally geodesic subgroup

The geodesic motion on a Lie group equipped with a left or right invariant Riemannian metric is governed by the Euler-Arnold equation. This paper investigates conditions on the metric in order for a given subgroup to be totally geodesic. Results on the construction and characterisation of such metrics are given. The setting works both in the classical nite dimensional case, and in the category of in nite dimensional Fr echet Lie groups, in which di eomorphism groups are included. Using the framework we give new examples of both nite and in nite dimensional totally geodesic subgroups. In particular, based on the cross helicity, we construct right invariant metrics such that a given subgroup of exact volume preserving di eomorphisms is totally geodesic. The paper also gives a general framework for the representation of Euler-Arnold equations in arbitrary choice of dual pairing

Geodesic Warps by Conformal Mappings

In recent years there has been considerable interest in methods for diffeomorphic warping of images, with applications e.g.\ in medical imaging and evolutionary biology. The original work generally cited is that of the evolutionary biologist D'Arcy Wentworth Thompson, who demonstrated warps to deform images of one species into another. However, unlike the deformations in modern methods, which are drawn from the full set of diffeomorphism, he deliberately chose lower-dimensional sets of transformations, such as planar conformal mappings. In this paper we study warps of such conformal mappings. The approach is to equip the infinite dimensional manifold of conformal embeddings with a Riemannian metric, and then use the corresponding geodesic equation in order to obtain diffeomorphic warps. After deriving the geodesic equation, a numerical discretisation method is developed. Several examples of geodesic warps are then given. We also show that the equation admits totally geodesic solutions corresponding to scaling and translation, but not to affine transformations

Geometric Integration of Hamiltonian Systems Perturbed by Rayleigh Damping

Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the symplectic structure in the case $\epsilon=0$. In the case $0<\epsilon\ll 1$ the energy dissipation rate is shown to be asymptotically correct by backward error analysis. Theoretical results on monotone decrease of the modified Hamiltonian function for small enough step sizes are given. Further, an analysis proving near conservation of relative equilibria for small enough step sizes is conducted. Numerical examples, verifying the analyses, are given for a planar pendulum and an elastic 3--D pendulum. The results are superior in comparison with a conventional explicit Runge-Kutta method of the same order

Diffeomorphic random sampling using optimal information transport

In this article we explore an algorithm for diffeomorphic random sampling of nonuniform probability distributions on Riemannian manifolds. The algorithm is based on optimal information transport (OIT)---an analogue of optimal mass transport (OMT). Our framework uses the deep geometric connections between the Fisher-Rao metric on the space of probability densities and the right-invariant information metric on the group of diffeomorphisms. The resulting sampling algorithm is a promising alternative to OMT, in particular as our formulation is semi-explicit, free of the nonlinear Monge--Ampere equation. Compared to Markov Chain Monte Carlo methods, we expect our algorithm to stand up well when a large number of samples from a low dimensional nonuniform distribution is needed.Comment: 8 pages, 3 figure

Geometric Generalisations of SHAKE and RATTLE

A geometric analysis of the Shake and Rattle methods for constrained Hamiltonian problems is carried out. The study reveals the underlying differential geometric foundation of the two methods, and the exact relation between them. In addition, the geometric insight naturally generalises Shake and Rattle to allow for a strictly larger class of constrained Hamiltonian systems than in the classical setting. In order for Shake and Rattle to be well defined, two basic assumptions are needed. First, a nondegeneracy assumption, which is a condition on the Hamiltonian, i.e., on the dynamics of the system. Second, a coisotropy assumption, which is a condition on the geometry of the constrained phase space. Non-trivial examples of systems fulfilling, and failing to fulfill, these assumptions are given

A Case Series on Genotype and Outcome of Liver Transplantation in Children with Niemann-Pick Disease Type C

Background: To report on clinical presentation and outcomes of children who underwent liver transplantation (LTx) and were subsequently diagnosed to have Niemann-Pick type C (NPC). Methods: Retrospective, descriptive, multi-centre review of children diagnosed with NPC who underwent LTx (2003–2018). Diagnosis was made by filipin skin test or genetic testing. Results: Nine children were identified (six centres). Neonatal acute liver failure was the most common indication for LTx (seven children). Median age at first presentation: 7 days (range: 0–37). The most prevalent presenting symptoms: jaundice (8/9), hepatosplenomegaly (8/9) and ascites (6/9). 8/9 children had a LTx before the diagnosis of NPC. Genetic testing revealed mutations in NPC1 correlating with a severe biochemical phenotype in 5 patients. All 9 children survived beyond early infancy. Seven children are still alive (median follow-up time of 9 (range: 6–13) years). Neurological symptoms developed in 4/7 (57%) patients at median 9 (range: 5–13) years following LTx. Conclusion: Early diagnosis of NPC continues to be a challenge and a definitive diagnosis is often made only after LTx. Neurological disease is not prevented in the majority of patients. Genotype does not appear to predict neurological outcome after LTx. LTx still remains controversial in NPC

Towards all-non-vacuum-processed photovoltaic systems: a water-based screen-printed Cu(In,Ga)Se2 Photoabsorber with a 6.6% efficiency

During the last few decades, major advances have been made in photovoltaic systems based on Cu(In,Ga)Se2 chalcopyrite. However, the most efficient photovoltaic cells are processed under high-energy-demanding vacuum conditions. To lower the costs and facilitate high-throughput production, printing/coating processes are proving to be effective solutions. This work combined printing, coating, and chemical bath deposition processes of photoabsorber, buffer, and transparent conductive layers for the development of solution-processed photovoltaic systems. Using a sustainable approach, all inks were formulated using water and ethanol as solvents. Screen printing of the photoabsorber on fluorine-doped tin-oxide-coated glass followed by selenization, chemical bath deposition of the cadmium sulfide buffer, and final sputtering of the intrinsic zinc oxide and aluminum-doped zinc oxide top conductive layers delivered a 6.6% maximum efficiency solar cell, a record for screen-printed Cu(In,Ga)Se2 solar cells. On the other hand, the all-non-vacuum-processed device with spray-coated intrinsic zinc-oxide- and tin-doped indium oxide top conductive layers delivered a 2.2% efficiency. The given approaches represent relevant steps towards the fabrication of sustainable and efficient Cu(In,Ga)Se2 solar cells.This study was conducted with financial support from the Portuguese Foundation for Science and Technology (PTDC/CTM-ENE/5387/2014, PTDC/NAN-MAT/28745/2017, UID/FIS/04650/2020, UID/QUI/0686/2020, PTDC/FIS-MAC/28157/2017, SFRH/BD/121780/2016 and SFRH/BD/143750/2019) and the Basque Government Industry Department (ELKARTEK and HAZITEK)

Family physicians' effort to stay in charge of the medical treatment when patients have home care by district nurses. A grounded theory study

<p>Abstract</p> <p>Background</p> <p>District nurses (DNs) provide home care for old persons with a mixture of chronic diseases, symptoms and reduced functional ability. Family physicians (FPs) have been criticised for their lack of involvement in this care. The aim of this study was to obtain increased knowledge concerning the FP's experience of providing medical treatment for patients with home care provided by DNs by developing a theoretical model that elucidates how FPs handle the problems they encounter regarding the individual patients and their conditions.</p> <p>Methods</p> <p>Semi-structured interviews were conducted with 13 Swedish FPs concerning one of their registered patients with home care by a DN, and the treatment of this patient. Grounded theory methodology (GTM) was used in the analyses.</p> <p>Results</p> <p>The core category was the effort to stay in charge of the medical treatment. This involved three types of problems: gaining sufficient insight, making adequate decisions, and maintaining appropriate medical treatment. For three categories of patients, the FPs had problems staying in charge. Patients with reduced functional ability had problems providing information and maintaining treatment. Patients who were "fixed in their ways" did not provide information and did not comply with recommendations, and for patients with complex conditions, making adequate decisions could be problematic. To overcome the problems, four different strategies were used: relying on information from others, supporting close observation and follow-up by others, being constantly ready to change the goal of the treatment, and relying on others to provide treatment.</p> <p>Conclusion</p> <p>The patients in this study differed from most other patients seen at the healthcare centre as the consultation with the patient could not provide the usual foundation for decisions concerning medical treatment. Information from and collaboration with the DN and other home care providers was essential for the FP's effort to stay in charge of the medical treatment. The complexity of the situation made it problematic for the FP to make adequate decisions about the goal of the medical treatment. The goal of the treatment had to be constantly evaluated based on information from the DN and other care providers, and thus this information was absolutely crucial.</p

Profiling social, emotional and behavioural difficulties of children involved in direct and indirect bullying behaviours

Being involved in bullying places a child at risk of poor psychosocial and educational outcomes. This study aimed to examine the profile of behavioural, emotional and social functioning for two subtypes of bullying; direct and indirect (relational). Pupils aged between seven and eleven years old completed sociometric measures of social inclusion and bullying behaviour to identify 192 pupils considered to be involved in either direct, indirect, both or neither types of bullying. These pupils and their teachers completed a battery of assessments relating to behaviour, social competence and self-perception. All bully-groups experienced similar levels of significant social rejection. ‘Direct’ and ‘both’ groups showed the greatest number of behavioural, emotional and social difficulties, while the ‘indirect’ group showed weaknesses in self-perception, but no teacher-rated problems. Understanding the behavioural, emotional and social correlates of bullying is of particular importance for early identification of children at risk of becoming bullies and for developing targeted interventions