Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary

Consider an essentially nonbranching metric measure space with the measure contraction property of Ohta and Sturm, or with a Ricci curvature lower bound in the sense of Lott, Sturm and Villani. We prove a sharp upper bound on the inscribed radius of any subset whose boundary has a suitably signed lower bound on its generalized mean curvature. This provides a nonsmooth analog to a result of Kasue (1983) and Li (2014). We prove a stability statement concerning such bounds and - in the Riemannian curvature-dimension (RCD) setting - characterize the cases of equality

A conformal Hopf-Rinow theorem for semi-Riemannian spacetimes

The famous Hopf-Rinow theorem states that a Riemannian manifold is metrically complete if and only if it is geodesically complete. The compact Clifton-Pohl torus fails to be geodesically complete, leading many mathematicians and Wikipedia to conclude that "the theorem does not generalize to Lorentzian manifolds". Recall now that in their 1931 paper Hopf and Rinow characterized metric completeness also by properness. Recently, the author and Garc\'{\i}a-Heveling obtained a Lorentzian completeness-compactness result with a similar flavor. In this manuscript, we extend our theorem to cone structures and to a new class of semi-Riemannian manifolds, dubbed $(n-\nu,\nu)$-spacetimes. Moreover, we demonstrate that our result implies, and hence generalizes, the metric part of the Hopf-Rinow theorem.Comment: 40 page

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Best practices for HPM-assisted performance engineering on modern multicore processors

Many tools and libraries employ hardware performance monitoring (HPM) on modern processors, and using this data for performance assessment and as a starting point for code optimizations is very popular. However, such data is only useful if it is interpreted with care, and if the right metrics are chosen for the right purpose. We demonstrate the sensible use of hardware performance counters in the context of a structured performance engineering approach for applications in computational science. Typical performance patterns and their respective metric signatures are defined, and some of them are illustrated using case studies. Although these generic concepts do not depend on specific tools or environments, we restrict ourselves to modern x86-based multicore processors and use the likwid-perfctr tool under the Linux OS.Comment: 10 pages, 2 figure

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