Load-Balancing for Parallel Delaunay Triangulations

Computing the Delaunay triangulation (DT) of a given point set in $\mathbb{R}^D$ is one of the fundamental operations in computational geometry. Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm that merges two partial triangulations by re-triangulating a small subset of their vertices - the border vertices - and combining the three triangulations efficiently via parallel hash table lookups. The input point division should therefore yield roughly equal-sized partitions for good load-balancing and also result in a small number of border vertices for fast merging. In this paper, we present a novel divide-step based on partitioning the triangulation of a small sample of the input points. In experiments on synthetic and real-world data sets, we achieve nearly perfectly balanced partitions and small border triangulations. This almost cuts running time in half compared to non-data-sensitive division schemes on inputs exhibiting an exploitable underlying structure.Comment: Short version submitted to EuroPar 201

Approximating Nearest Neighbor Distances

Several researchers proposed using non-Euclidean metrics on point sets in Euclidean space for clustering noisy data. Almost always, a distance function is desired that recognizes the closeness of the points in the same cluster, even if the Euclidean cluster diameter is large. Therefore, it is preferred to assign smaller costs to the paths that stay close to the input points. In this paper, we consider the most natural metric with this property, which we call the nearest neighbor metric. Given a point set P and a path $\gamma$, our metric charges each point of $\gamma$ with its distance to P. The total charge along $\gamma$ determines its nearest neighbor length, which is formally defined as the integral of the distance to the input points along the curve. We describe a $(3+\varepsilon)$-approximation algorithm and a $(1+\varepsilon)$-approximation algorithm to compute the nearest neighbor metric. Both approximation algorithms work in near-linear time. The former uses shortest paths on a sparse graph using only the input points. The latter uses a sparse sample of the ambient space, to find good approximate geodesic paths.Comment: corrected author nam

Analysis of and workarounds for element reversal for a finite element-based algorithm for warping triangular and tetrahedral meshes

We consider an algorithm called FEMWARP for warping triangular and tetrahedral finite element meshes that computes the warping using the finite element method itself. The algorithm takes as input a two- or three-dimensional domain defined by a boundary mesh (segments in one dimension or triangles in two dimensions) that has a volume mesh (triangles in two dimensions or tetrahedra in three dimensions) in its interior. It also takes as input a prescribed movement of the boundary mesh. It computes as output updated positions of the vertices of the volume mesh. The first step of the algorithm is to determine from the initial mesh a set of local weights for each interior vertex that describes each interior vertex in terms of the positions of its neighbors. These weights are computed using a finite element stiffness matrix. After a boundary transformation is applied, a linear system of equations based upon the weights is solved to determine the final positions of the interior vertices. The FEMWARP algorithm has been considered in the previous literature (e.g., in a 2001 paper by Baker). FEMWARP has been succesful in computing deformed meshes for certain applications. However, sometimes FEMWARP reverses elements; this is our main concern in this paper. We analyze the causes for this undesirable behavior and propose several techniques to make the method more robust against reversals. The most successful of the proposed methods includes combining FEMWARP with an optimization-based untangler.Comment: Revision of earlier version of paper. Submitted for publication in BIT Numerical Mathematics on 27 April 2010. Accepted for publication on 7 September 2010. Published online on 9 October 2010. The final publication is available at http://www.springerlink.co

Evaluating Elevated Convection with the Downdraft Convective Inhibition

A method for evaluating the penetration of a stable layer by an elevated convective downdraft is discussed. Some controversy exists on the community’s ability to define truly elevated convection from surface-based convection. By comparing the downdraft convective inhibition (DCIN) to the downdraft convective available potential energy (DCAPE), we determine that downdraft penetration potential is progressively enabled as the DCIN is progressively smaller than the DCAPE; inversely as DCIN increases over DCAPE, so does the likelihood of purely elevated convection. Serial vertical soundings and accompanying analyses are provided to support this finding

Streaming Compression of Tetrahedral Volume Meshes

Geometry processing algorithms have traditionally assumed that the input data is entirely in main memory and available for random access. This assumption does not scale to large data sets, as exhausting the physical memory typically leads to IO-inefficient thrashing. Recent works advocate processing geometry in a 'streaming' manner, where computation and output begin as soon as possible. Streaming is suitable for tasks that require only local neighbor information and batch process an entire data set. We describe a streaming compression scheme for tetrahedral volume meshes that encodes vertices and tetrahedra in the order they are written. To keep the memory footprint low, the compressor is informed when vertices are referenced for the last time (i.e. are finalized). The compression achieved depends on how coherent the input order is and how many tetrahedra are buffered for local reordering. For reasonably coherent orderings and a buffer of 10,000 tetrahedra, we achieve compression rates that are only 25 to 40 percent above the state-of-the-art, while requiring drastically less memory resources and less than half the processing time

Comparison between a μFE model and DEM for an assembly of spheres under triaxial compression

This paper presents a simple case of a Face Centred Cubic (FCC) array of 2,000 spheres under triaxial compression to compare the results obtained using the Discrete Element Method (DEM) and a micro finite element model (μFE). This μFE approach was developed so that the internal structure of the soil can be obtained using x-ray computed tomography and converted into a numerical fabric. The individual grains are represented as continuum deformable bodies and the inter-granular interaction based on the defined contact laws. In order to demonstrate the simple contact constitutive behaviour used in this μFE model, the response for two contacting elastic spheres is compared with theoretical equations. The strength at failure of the packing of 2,000 spheres is seen to yield similar values for DEM, μFE and the analytical solution. When comparing the evolving void ratio, a good agreement between the two numerical models was observed for very small strains but as the strain increases, the values start to diverge, which is believed to be related with the rigidity of the grains used in DEM

Evidence on anti-malarial and diagnostic markets in Cambodia to guide malaria elimination strategies and policies

BACKGROUND: Understanding Cambodia's anti-malarial and diagnostic landscape in 2015 is critical for informing and monitoring strategies and policies as Cambodia moves forward with national efforts to eliminate malaria. The aim of this paper is to present timely and key findings on the public and private sector anti-malarial and diagnostic landscape in Cambodia. This evidence can serve as a baseline benchmark for guiding implementation of national strategies as well as other regional initiatives to address malaria elimination activities. METHODS: From August 17th to October 1st, 2015, a cross sectional, nationally-representative malaria outlet survey was conducted in Cambodia. A census of all public and private outlets with potential to distribute malaria testing and/or treatment was conducted among 180 communes. An audit was completed for all anti-malarials, malaria rapid diagnostic tests (RDT) and microscopy. RESULTS: A total of 26,664 outlets were screened, and 1303 outlets were eligible and interviewed. Among all screened outlets in the public sector, 75.9% of public health facilities and 67.7% of community health workers stocked both malaria diagnostic testing and a first-line artemisinin-based combination therapy (ACT). Among anti-malarial-stocking private sector outlets, 64.7% had malaria blood testing available, and 70.9% were stocking a first-line ACT. Market share data illustrate that most of the anti-malarials were sold or distributed through the private sector (58.4%), including itinerant drug vendors (23.4%). First-line ACT accounted for the majority of the market share across the public and private sectors (90.3%). Among private sector outlets stocking any anti-malarial, the proportion of outlets with a first-line ACT or RDT was higher among outlets that had reportedly received one or more forms of 'support' (e.g. reportedly received training in the previous year on malaria diagnosis [RDT and/or microscopy] and/or the national treatment guidelines for malaria) compared to outlets that did not report receiving any support (ACT: 82.1 and 60.6%, respectively; RDT: 78.2 and 64.0%, respectively). CONCLUSION: The results point to high availability and distribution of first-line ACT and widespread availability of malaria diagnosis, especially in the public sector. This suggests that there is a strong foundation for achieving elimination goals in Cambodia. However, key gaps in terms of availability of malaria commodities for case management must be addressed, particularly in the private sector where most people seek treatment. Continued engagement with the private sector will be important to ensure accelerated progress towards malaria elimination

Whirling Hexagons and Defect Chaos in Hexagonal Non-Boussinesq Convection

We study hexagon patterns in non-Boussinesq convection of a thin rotating layer of water. For realistic parameters and boundary conditions we identify various linear instabilities of the pattern. We focus on the dynamics arising from an oscillatory side-band instability that leads to a spatially disordered chaotic state characterized by oscillating (whirling) hexagons. Using triangulation we obtain the distribution functions for the number of pentagonal and heptagonal convection cells. In contrast to the results found for defect chaos in the complex Ginzburg-Landau equation and in inclined-layer convection, the distribution functions can show deviations from a squared Poisson distribution that suggest non-trivial correlations between the defects.Comment: 4 mpg-movies are available at http://www.esam.northwestern.edu/~riecke/lit/lit.html submitted to New J. Physic

What Hispanic parents do to encourage or discourage 3-5 year old children to be active: a qualitative study

Conference Theme: Promoting healthy eating and physical activity: The latest international researchabstract no. O8.2PURPOSE: Hispanic preschool children may be less active than Anglo-American children. Our aim was to identify what parents do to encourage or discourage physical activity (PA) among Hispanic preschool children. METHODS: Nominal Group Technique (NGT), a structured multi-step group procedure, was used to elicit and prioritize responses from 10 groups of Hispanic parents regarding what parents do to encourage (5 groups) or discourage (5 groups) preschool children to be active. Five groups consisted of parents with low education (less than high school) and 5 with high education (high school or greater) split between the two NGT questions: What …postprin