Weak and strong solutions of equations of compressible magnetohydrodynamics

International audienceThis article proposes a review of the analysis of the system of magnetohydrodynamics (MHD). First, we give an account of the modelling asumptions. Then, the results of existence of weak solutions, using the notion of renormalized solutions. Then, existence of strong solutions in the neighbourhood of equilibrium states is reviewed, in particular with the method of Kawashima and Shizuta. Finally, the special case of dimension one is highlighted : the use of Lagrangian coordinates gives a simpler system, which is solved by standard techniques

Development and validation of self-reported line drawings of the modified Beighton score for the assessment of generalised joint hypermobility

Background: The impracticalities and comparative expense of carrying out a clinical assessment is an obstacle in many large epidemiological studies. The purpose of this study was to develop and validate a series of electronic self-reported line drawing instruments based on the modified Beighton scoring system for the assessment of selfreported generalised joint hypermobility.Methods: Five sets of line drawings were created to depict the 9-point Beighton score criteria. Each instrument consisted of an explanatory question whereby participants were asked to select the line drawing which best represented their joints. Fifty participants completed the self-report online instrument on two occasions, before attending a clinical assessment. A blinded expert clinical observer then assessed participants’ on two occasions,using a standardised goniometry measurement protocol. Validity of the instrument was assessed by participant observeragreement and reliability by participant repeatability and observer repeatability using unweighted Cohen’s kappa (k). Validity and reliability were assessed for each item in the self-reported instrument separately, and for the sum of the total scores. An aggregate score for generalised joint hypermobility was determined based on a Beighton score of 4 or more out of 9.Results: Observer-repeatability between the two clinical assessments demonstrated perfect agreement (k 1.00; 95%CI 1.00, 1.00). Self-reported participant-repeatability was lower but it was still excellent (k 0.91; 95% CI 0.74, 1.00). Theparticipant-observer agreement was excellent (k 0.96; 95% CI 0.87, 1.00). Validity was excellent for the self-report instrument, with a good sensitivity of 0.87 (95% CI 0.81, 0.91) and excellent specificity of 0.99 (95% CI 0.98, 1.00).Conclusions: The self-reported instrument provides a valid and reliable assessment of the presence of generalisedjoint hypermobility and may have practical use in epidemiological studie