A Second-Order Distributed Trotter-Suzuki Solver with a Hybrid Kernel

The Trotter-Suzuki approximation leads to an efficient algorithm for solving the time-dependent Schr\"odinger equation. Using existing highly optimized CPU and GPU kernels, we developed a distributed version of the algorithm that runs efficiently on a cluster. Our implementation also improves single node performance, and is able to use multiple GPUs within a node. The scaling is close to linear using the CPU kernels, whereas the efficiency of GPU kernels improve with larger matrices. We also introduce a hybrid kernel that simultaneously uses multicore CPUs and GPUs in a distributed system. This kernel is shown to be efficient when the matrix size would not fit in the GPU memory. Larger quantum systems scale especially well with a high number nodes. The code is available under an open source license.Comment: 11 pages, 10 figure

Linear extensions and order-preserving poset partitions

We examine the lattice of all order congruences of a finite poset from the viewpoint of combinatorial algebraic topology. We will prove that the order complex of the lattice of all nontrivial order congruences (or order-preserving partitions) of a finite $n$-element poset $P$ with $n\geq 3$ is homotopy equivalent to a wedge of spheres of dimension $n-3$. If $P$ is connected, then the number of spheres is equal to the number of linear extensions of $P$. In general, the number of spheres is equal to the number of cyclic extensions of $P$

Assessing the impacts of the first year of rotavirus vaccination in the United Kingdom

The United Kingdom (UK) added rotavirus (RV) vaccine (Rotarix GlaxoSmithKline) to the national vaccine schedule in July 2013. During the 2012–2014 rotavirus seasons, children presenting to the Bristol Royal Hospital for Children Emergency Department with gastroenteritis symptoms had stool virology analysis (real-time PCR) and clinical outcome recorded. Nosocomial cases were identified as patients with non-gastroenteritis diagnosis testing positive for rotavirus > 48h after admission. In comparison to average pre-vaccine seasons, in the first year after vaccine introduction there were 48% fewer attendances diagnosed with gastroenteritis, 53% reduction in gastroenteritis admissions and a total saving of 330 bed-days occupancy. There was an overall reduction in number of rotavirus-positive stool samples with 94% reduction in children aged under one year and a 65% reduction in those too old to have been vaccinated. In the first year after the introduction of universal vaccination against rotavirus we observed a profound reduction in gastroenteritis presentations and admissions with a substantial possible herd effect seen in older children. Extrapolating these findings to the UK population we estimate secondary healthcare savings in the first year of ca £7.5 (€10.5) million. Ongoing surveillance will be required to determine the long-term impact of the RV immunisation programme