Symplectic integrators for index one constraints

We show that symplectic Runge-Kutta methods provide effective symplectic integrators for Hamiltonian systems with index one constraints. These include the Hamiltonian description of variational problems subject to position and velocity constraints nondegenerate in the velocities, such as those arising in sub-Riemannian geometry and control theory.Comment: 13 pages, accepted in SIAM J Sci Compu

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

The key role of nitric oxide in hypoxia: hypoxic vasodilation and energy supply-demand matching

Significance: a mismatch between energy supply and demand induces tissue hypoxia with the potential to cause cell death and organ failure. Whenever arterial oxygen concentration is reduced, increases in blood flow - 'hypoxic vasodilation' - occur in an attempt to restore oxygen supply. Nitric oxide is a major signalling and effector molecule mediating the body's response to hypoxia, given its unique characteristics of vasodilation (improving blood flow and oxygen supply) and modulation of energetic metabolism (reducing oxygen consumption and promoting utilization of alternative pathways). Recent advances: this review covers the role of oxygen in metabolism and responses to hypoxia, the hemodynamic and metabolic effects of nitric oxide, and mechanisms underlying the involvement of nitric oxide in hypoxic vasodilation. Recent insights into nitric oxide metabolism will be discussed, including the role for dietary intake of nitrate, endogenous nitrite reductases, and release of nitric oxide from storage pools. The processes through which nitric oxide levels are elevated during hypoxia are presented, namely (i) increased synthesis from nitric oxide synthases, increased reduction of nitrite to nitric oxide by heme- or pterin-based enzymes and increased release from nitric oxide stores, and (ii) reduced deactivation by mitochondrial cytochrome c oxidase. Critical issues: several reviews covered modulation of energetic metabolism by nitric oxide, while here we highlight the crucial role NO plays in achieving cardiocirculatory homeostasis during acute hypoxia through both vasodilation and metabolic suppression Future directions: we identify a key position for nitric oxide in the body's adaptation to an acute energy supply-demand mismatc

Continuous Aquatic Soundings of the Lake Tere-Khol’ Water Area in the Republic of Tuva (Russia)

Introduction The archaeological site of Por-Bajin (meaning « Clay House » in the local Tuva language) occupies a small island in Lake Tere-Khol’, eight kilometers west of the Kungurtuk settlement in the southwestern part of the Republic of Tuva, Southern Siberia (Fig. 1).It consists of a rectangular enclosure around a complex of buildings and courtyards which is dominated by a central building. Its building materials and technology suggest that Por-Bajin was erected within the framework of th..

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

Geophysical investigations on Por-Bajin island, Tuva (Russia)

In 2007-2008, the cultural fund « Fortress Por-Bajin » undertook extensive archaeological excavations on the 8th/9th century AD monument of Por-Bajin. By the end of the summer season 2008, the total excavated area was about 2 hectares. Some 1 000 people took part in this project: archaeologists, architects, soil scientists, geomorphologists and other specialists. Considering the extreme remoteness of the site, the fund developed its own infrastructure for transport, accommodation and safety o..

Social origin, schooling and individual change in intelligence during childhood influence long-term mortality: a 68-year follow-up study

Background Intelligence at a single time-point has been linked to health outcomes. An individual's IQ increases with longer schooling, but the validity of such increase is unclear. In this study, we assess the hypothesis that individual change in the performance on IQ tests between ages 10 and 20 years is associated with mortality later in life