Medial Axis Isoperimetric Profiles

Recently proposed as a stable means of evaluating geometric compactness, the isoperimetric profile of a planar domain measures the minimum perimeter needed to inscribe a shape with prescribed area varying from 0 to the area of the domain. While this profile has proven valuable for evaluating properties of geographic partitions, existing algorithms for its computation rely on aggressive approximations and are still computationally expensive. In this paper, we propose a practical means of approximating the isoperimetric profile and show that for domains satisfying a "thick neck" condition, our approximation is exact. For more general domains, we show that our bound is still exact within a conservative regime and is otherwise an upper bound. Our method is based on a traversal of the medial axis which produces efficient and robust results. We compare our technique with the state-of-the-art approximation to the isoperimetric profile on a variety of domains and show significantly tighter bounds than were previously achievable.Comment: Code and supplemental available here: https://github.com/pzpzpzp1/isoperimetric_profil

An Image-Based High-Content Screening Assay for Compounds Targeting Intracellular Leishmania donovani Amastigotes in Human Macrophages

Leishmaniasis is a tropical disease threatening 350 million people from endemic regions. The available drugs for treatment are inadequate, with limitations such as serious side effects, parasite resistance or high cost. Driven by this need for new drugs, we developed a high-content, high-throughput image-based screening assay targeting the intracellular amastigote stage of different species of Leishmania in infected human macrophages. The in vitro infection protocol was adapted to a 384-well-plate format, enabling acquisition of a large amount of readouts by automated confocal microscopy. The reading method was based on DNA staining and required the development of a customized algorithm to analyze the images, which enabled the use of non-modified parasites. The automated analysis generated parameters used to quantify compound activity, including infection ratio as well as the number of intracellular amastigote parasites and yielded cytotoxicity information based on the number of host cells. Comparison of this assay with one that used the promastigote form to screen 26,500 compounds showed that 50% of the hits selected against the intracellular amastigote were not selected in the promastigote screening. These data corroborate the idea that the intracellular amastigote form of the parasite is the most appropriate to be used in primary screening assay for Leishmania

Spatial Shape-Preserving Interpolation Using Nu-Splines

Introduction Shape-preserving interpolation, via functional, as well as parametric splines, can be regarded as a well studied topic for the planar case. Indeed, there exists an abundance of papers, that provide schemes for constructing monotonicity- and/or convexitypreserving planar splines. On the contrary, the literature on shape-preserving interpolation in the three-dimensional space is apparently limited. This may be partially attributed to the fact that, introducing and validating a notion of shape-preserving interpolation in 3D is not as straightforward as it is in 2D. As a consequence, the first relevant papers in the literature have been devoted to introducing and investigating alternative notions of shape-preserving spatial interpolation, such as the inflection count of a curve in Good- 218 M. I. Karavelas, P. D. Kaklis / Shape-preserving interpolation using -splines man [4] and the shape properties o

Geometric Extensions of Cutwidth in any Dimension

International audienceWe define a multi-dimensional geometric extension of cutwidth. A graph has d-cutwidth at most k if it can be embedded in the d-dimensional euclidean space so that no hyperplane can intersect more than k of its edges. We prove a series of combinatorial results on d-cutwidth which imply that for every d and k, there is a linear time algorithm checking whether the d-cutwidth of a graph G is at most k

Prototype Implementation of the Algebraic Kernel

In this report we describe the current progress with respect to prototype implementations of algebraic kernels within the ACS project. More specifically, we report on: (1) the Cgal package Algebraic_kernel_for_circles_2_2 aimed at providing the necessary algebraic functionality required for treating circular arcs; (2) an interface between Cgal and SYNAPS for accessing the algebraic functionality in the SYNAPS library; (3) the NumeriX library (part of the EXACUS project) which is a prototype implementation of a set of algebraic tools on univariate polynomials, needed to built an algebraic kernel and (4) a rough CGAL-like prototype implementation of a set of algebraic tools on univariate polynomials