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Background: Surgical mortality data are collected routinely in high-income countries, yet virtually no low-or middle-income countries have outcome surveillance in place. The aim was prospectively to collect worldwide mortality data following emergency abdominal surgery, comparing findings across countries with a low, middle or high Human Development Index (HDI).Methods: This was a prospective, multicentre, cohort study. Self-selected hospitals performing emergency surgery submitted prespecified data for consecutive patients from at least one 2-week interval during July to December 2014. Postoperative mortality was analysed by hierarchical multivariable logistic regression.

We derive improved bounds on the number of fc-dimensional simplices spanned by a set of n points in R'^ that are congruent to a given fc-simplex, for fc < d -1. Let f^ '{n) be the maximum number of fc-simplices spanned by a set of n points in R"* that are congruent to a given fc-simplex. We prove that /j (n) = 0("5/3 .20(a^(n)))_ y(4)(") ^ 0{n^+n, A^\n) = 0(n^/3), and /^^'(n) = 0(TI^/**+^). We also derive a recurrence to bound fjf'^ (n) for arbitrary values of k and d, and use it to derive the bound fjfhn) = 0{n^/'^) for d < 7 and A; < d -2. Following Erdos and Purdy, we conjecture that this bound holds for laxger values of d as well, and for fc < d -2.

A box-tree is a bounding-volume hierarchy that uses axisaligned boxes as bounding volumes. The query complexity of a box-tree with respect to a given type of query is the maximum number of nodes visited when answering such a query. We describe several new algorithms for constructing box-trees with small worst-case query complexity with respect to queries with axis-parallel boxes and with points. We also prove lower bounds on the worst-case query complexity for box-trees, which show that our results are optimal or close to optimal. Finally, we present algorithn^ to convert box-trees to R-trees, resulting in R-trees with (almost) optimal query complexity.