Mapping polygons to the grid with small Hausdorff and Fréchet distance

We show how to represent a simple polygon P by a (pixel-based) grid polygon Q that is simple and whose Hausdorff or Fréchet distance to P is small. For any simple polygon P, a grid polygon exists with constant Hausdorff distance between their boundaries and their interiors. Moreover, we show that with a realistic input assumption we can also realize constant Fréchet distance between the boundaries. We present algorithms accompanying these constructions, heuristics to improve their output while keeping the distance bounds, and experiments to assess the output

Visual Encoding of Dissimilarity Data via Topology-Preserving Map Deformation

We present an efficient technique for topology-preserving map deformation and apply it to the visualization of dissimilarity data in a geographic context. Map deformation techniques such as value-by-area cartograms are well studied. However, using deformation to highlight (dis)similarity between locations on a map in terms of their underlying data attributes is novel. We also identify an alternative way to represent dissimilarities on a map through the use of visual overlays. These overlays are complementary to deformation techniques and enable us to assess the quality of the deformation as well as to explore the design space of blending the two methods. Finally, we demonstrate how these techniques can be useful in several—quite different—applied contexts: travel-time visualization, social demographics research and understanding energy flowing in a wide-area power-grid

An integrative multi-omics analysis to identify candidate DNA methylation biomarkers related to prostate cancer risk

It remains elusive whether some of the associations identified in genome-wide association studies of prostate cancer (PrCa) may be due to regulatory effects of genetic variants on CpG sites, which may further influence expression of PrCa target genes. To search for Cp