Efficient Irregular Wavefront Propagation Algorithms on Hybrid CPU-GPU Machines

In this paper, we address the problem of efficient execution of a computation pattern, referred to here as the irregular wavefront propagation pattern (IWPP), on hybrid systems with multiple CPUs and GPUs. The IWPP is common in several image processing operations. In the IWPP, data elements in the wavefront propagate waves to their neighboring elements on a grid if a propagation condition is satisfied. Elements receiving the propagated waves become part of the wavefront. This pattern results in irregular data accesses and computations. We develop and evaluate strategies for efficient computation and propagation of wavefronts using a multi-level queue structure. This queue structure improves the utilization of fast memories in a GPU and reduces synchronization overheads. We also develop a tile-based parallelization strategy to support execution on multiple CPUs and GPUs. We evaluate our approaches on a state-of-the-art GPU accelerated machine (equipped with 3 GPUs and 2 multicore CPUs) using the IWPP implementations of two widely used image processing operations: morphological reconstruction and euclidean distance transform. Our results show significant performance improvements on GPUs. The use of multiple CPUs and GPUs cooperatively attains speedups of 50x and 85x with respect to single core CPU executions for morphological reconstruction and euclidean distance transform, respectively.Comment: 37 pages, 16 figure

Exact Casimir interaction of perfectly conducting three-spheres in four euclidean dimensions

Exploiting conformal symmetry, we derive a simple exact formula for the classical electromagnetic Casimir interaction of two perfectly conducting three-spheres, including the sphere-plate geometry as a special case, in four euclidean dimensions. We verify that the short distance expansion of the Casimir energy agrees to leading order with the Proximity Force Approximation (PFA), while the next-to-leading-order is in agreement with a recently proposed derivative expansion of the Casimir energy. At the next-to-next-to-leading order we find a non-analytic correction to PFA, which for a sphere-plate system is of the order of $(d/R)^{3/2} \log(d/R)$, where $d$ is the separation and $R$ the sphere radius.Comment: 19 pages, 2 figure

On the minimum orbital intersection distance computation: a new effective method

The computation of the Minimum Orbital Intersection Distance (MOID) is an old, but increasingly relevant problem. Fast and precise methods for MOID computation are needed to select potentially hazardous asteroids from a large catalogue. The same applies to debris with respect to spacecraft. An iterative method that strictly meets these two premises is presented.Comment: 13 pages, 10 figures, article accepted for publication in MNRA

Wilson Loops and Minimal Surfaces

The AdS/CFT correspondence suggests that the Wilson loop of the large N gauge theory with N=4 supersymmetry in 4 dimensions is described by a minimal surface in AdS_5 x S^5. We examine various aspects of this proposal, comparing gauge theory expectations with computations of minimal surfaces. There is a distinguished class of loops, which we call BPS loops, whose expectation values are free from ultra-violet divergence. We formulate the loop equation for such loops. To the extent that we have checked, the minimal surface in AdS_5 x S^5 gives a solution of the equation. We also discuss the zig-zag symmetry of the loop operator. In the N=4 gauge theory, we expect the zig-zag symmetry to hold when the loop does not couple the scalar fields in the supermultiplet. We will show how this is realized for the minimal surface.Comment: 51 pages, 7 figure