Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space

The problem of the invariant classification of the orthogonal coordinate webs defined in Euclidean space is solved within the framework of Felix Klein's Erlangen Program. The results are applied to the problem of integrability of the Calogero-Moser model

Theory of algebraic invariants of vector spaces of Killing tensors: Methods for computing the fundamental invariants

We review computational techniques that can be used in the determination of fundamental invariants of vector spaces of Killing tensors under the action of the isometry group. In particular, for the first time in this study, we employ for these purposes the method of moving frames introduced by Fels and Olver. Illustrative examples are provided

Hypoxia Disruption of Vertebrate CNS Pathfinding through EphrinB2 Is Rescued by Magnesium

The mechanisms of hypoxic injury to the developing human brain are poorly understood, despite being a major cause of chronic neurodevelopmental impairments. Recent work in the invertebrate Caenorhabditis elegans has shown that hypoxia causes discrete axon pathfinding errors in certain interneurons and motorneurons. However, it is unknown whether developmental hypoxia would have similar effects in a vertebrate nervous system. We have found that developmental hypoxic injury disrupts pathfinding of forebrain neurons in zebrafish (Danio rerio), leading to errors in which commissural axons fail to cross the midline. The pathfinding defects result from activation of the hypoxia-inducible transcription factor (hif1) pathway and are mimicked by chemical inducers of the hif1 pathway or by expression of constitutively active hif1α. Further, we found that blocking transcriptional activation by hif1α helped prevent the guidance defects. We identified ephrinB2a as a target of hif1 pathway activation, showed that knock-down of ephrinB2a rescued the guidance errors, and showed that the receptor ephA4a is expressed in a pattern complementary to the misrouting axons. By targeting a constitutively active form of ephrinB2a to specific neurons, we found that ephrinB2a mediates the pathfinding errors via a reverse-signaling mechanism. Finally, magnesium sulfate, used to improve neurodevelopmental outcomes in preterm births, protects against pathfinding errors by preventing upregulation of ephrinB2a. These results demonstrate that evolutionarily conserved genetic pathways regulate connectivity changes in the CNS in response to hypoxia, and they support a potential neuroprotective role for magnesium

Effect of remote ischaemic conditioning on clinical outcomes in patients with acute myocardial infarction (CONDI-2/ERIC-PPCI): a single-blind randomised controlled trial.

BACKGROUND: Remote ischaemic conditioning with transient ischaemia and reperfusion applied to the arm has been shown to reduce myocardial infarct size in patients with ST-elevation myocardial infarction (STEMI) undergoing primary percutaneous coronary intervention (PPCI). We investigated whether remote ischaemic conditioning could reduce the incidence of cardiac death and hospitalisation for heart failure at 12 months. METHODS: We did an international investigator-initiated, prospective, single-blind, randomised controlled trial (CONDI-2/ERIC-PPCI) at 33 centres across the UK, Denmark, Spain, and Serbia. Patients (age >18 years) with suspected STEMI and who were eligible for PPCI were randomly allocated (1:1, stratified by centre with a permuted block method) to receive standard treatment (including a sham simulated remote ischaemic conditioning intervention at UK sites only) or remote ischaemic conditioning treatment (intermittent ischaemia and reperfusion applied to the arm through four cycles of 5-min inflation and 5-min deflation of an automated cuff device) before PPCI. Investigators responsible for data collection and outcome assessment were masked to treatment allocation. The primary combined endpoint was cardiac death or hospitalisation for heart failure at 12 months in the intention-to-treat population. This trial is registered with ClinicalTrials.gov (NCT02342522) and is completed. FINDINGS: Between Nov 6, 2013, and March 31, 2018, 5401 patients were randomly allocated to either the control group (n=2701) or the remote ischaemic conditioning group (n=2700). After exclusion of patients upon hospital arrival or loss to follow-up, 2569 patients in the control group and 2546 in the intervention group were included in the intention-to-treat analysis. At 12 months post-PPCI, the Kaplan-Meier-estimated frequencies of cardiac death or hospitalisation for heart failure (the primary endpoint) were 220 (8·6%) patients in the control group and 239 (9·4%) in the remote ischaemic conditioning group (hazard ratio 1·10 [95% CI 0·91-1·32], p=0·32 for intervention versus control). No important unexpected adverse events or side effects of remote ischaemic conditioning were observed. INTERPRETATION: Remote ischaemic conditioning does not improve clinical outcomes (cardiac death or hospitalisation for heart failure) at 12 months in patients with STEMI undergoing PPCI. FUNDING: British Heart Foundation, University College London Hospitals/University College London Biomedical Research Centre, Danish Innovation Foundation, Novo Nordisk Foundation, TrygFonden

Immunomodulation of multiple myeloma bone disease

Multiple myeloma (MM) is a clonal malignancy of terminally differentiated plasma cells. Myeloma patients often have extensive skeletal complications, including bone pain, osteolytic lesions and pathological fractures, which represent the major cause of morbidity and possible mortality. Osteolysis is due to the uncoupling of bone cell activity, caused by osteoclast activation and osteoblast inhibition. Osteoclast biology is dominantly regulated by the RANK/RANKL/OPG axis. A disruption of RANKL/OPG ratio, due to the prevalence of RANKL and/or inactivation of OPG, has been reported in MM bone disease by different mechanisms involving either malignant plasma cells and/or other cells of immune system. Despite the major involvement of RANKL in MM is well documented, a dysregulated production of other cytokines either with pro- or anti-osteoclastogenic activity can also contribute to the development of osteolytic lesions by acting directly on bone cells or altering RANKL/OPG axis. This review focuses on molecules produced by cells of immune system able to induce bone destruction in MM bone disease