Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensemble

The paper studies the spectral properties of large Wigner, band and sample covariance random matrices with heavy tails of the marginal distributions of matrix entries.Comment: This is an extended version of my talk at the QMath 9 conference at Giens, France on September 13-17, 200

Cell shape analysis of random tessellations based on Minkowski tensors

To which degree are shape indices of individual cells of a tessellation characteristic for the stochastic process that generates them? Within the context of stochastic geometry and the physics of disordered materials, this corresponds to the question of relationships between different stochastic models. In the context of image analysis of synthetic and biological materials, this question is central to the problem of inferring information about formation processes from spatial measurements of resulting random structures. We address this question by a theory-based simulation study of shape indices derived from Minkowski tensors for a variety of tessellation models. We focus on the relationship between two indices: an isoperimetric ratio of the empirical averages of cell volume and area and the cell elongation quantified by eigenvalue ratios of interfacial Minkowski tensors. Simulation data for these quantities, as well as for distributions thereof and for correlations of cell shape and volume, are presented for Voronoi mosaics of the Poisson point process, determinantal and permanental point processes, and Gibbs hard-core and random sequential absorption processes as well as for Laguerre tessellations of polydisperse spheres and STIT- and Poisson hyperplane tessellations. These data are complemented by mechanically stable crystalline sphere and disordered ellipsoid packings and area-minimising foam models. We find that shape indices of individual cells are not sufficient to unambiguously identify the generating process even amongst this limited set of processes. However, we identify significant differences of the shape indices between many of these tessellation models. Given a realization of a tessellation, these shape indices can narrow the choice of possible generating processes, providing a powerful tool which can be further strengthened by density-resolved volume-shape correlations.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jense

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

INELASTIC PROPERTIES OF ICE Ih AT LOW TEMPERATURES AND HIGH PRESSURES

Le but de notre programme de recherche est d'étudier le comportement rhéologique de glaces soumises aux mêmes conditions que celles existant à l'intérieur de satellites des planètes extérieures afin de connaître leurs lois de déformation. Pour cela, nous avons effectué 100 essais de compression à vitesse de déformation constante pour des pressions allant jusqu'à 500 MPa et pour des températures aussi basses que 77 K. Pour P > 30 MPa, la glace Ih se fracture par instabilité de cisaillement produisant des fautes dans la direction du maximum de contrainte de cisaillement et la contrainte de fissuration est indépendante de la pression. Ce comportement inhabituel peut-être associé à des transformations de phases localisées dans les zones de cisaillement. La résistance en régime stationnaire suit des lois rhéologiques thermiquement activées décrites par des lois de puissance, avec différents paramètres d'écoulement dépendant des gammes de températures étudiées. Les lois d'écoulement seront discutées en relation avec les divers mécanismes de déformation déduits des microstructures observées optiquement et en comparaison avec d'autres travaux.The aim of our research programme is to explore the rheological behavior of H2O ices under conditions appropriate to the interiors of the icy satellites of the outer planets in order to give insight into their deformation. To this end, we have performed over 100 constant-strain-rate compression tests at pressures to 500 MPa and temperatures as low as 77 K. At P > 30 MPa, ice Ih fails by a shear instability producing faults in the maximum shear stress orientation and failure strength typically is independent of pressure. This unusual faulting behavior is thought to be connected with phase transformations localized in the shear zones. The steady-state strength follows rheological laws of the thermally-activated power-law type, with different flow law parameters depending on the range of test temperatures. The flow laws will be discussed with reference to the operating deformation mechanisms as deduced from optical-scale microstructures and comparison with other work