Snapping Graph Drawings to the Grid Optimally

In geographic information systems and in the production of digital maps for small devices with restricted computational resources one often wants to round coordinates to a rougher grid. This removes unnecessary detail and reduces space consumption as well as computation time. This process is called snapping to the grid and has been investigated thoroughly from a computational-geometry perspective. In this paper we investigate the same problem for given drawings of planar graphs under the restriction that their combinatorial embedding must be kept and edges are drawn straight-line. We show that the problem is NP-hard for several objectives and provide an integer linear programming formulation. Given a plane graph G and a positive integer w, our ILP can also be used to draw G straight-line on a grid of width w and minimum height (if possible).Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Simultaneous determination of natural and synthetic steroid estrogens and their conjugates in aqueous matrices by liquid chromatography / mass spectrometry

An analytical method for the simultaneous determination of nine free and conjugated steroid estrogens was developed with application to environmental aqueous matrices. Solid phase extraction (SPE) was employed for isolation and concentration, with detection by liquid chromatography/mass spectrometry (LC/MS) using electrospray ionisation (ESI) in the negative mode. Method recoveries for various aqueous matrices (wastewater, lake and drinking water) were determined, recoveries proving to be sample dependent. When spiked at 50 ng/l concentrations in sewage influent, recoveries ranged from 62-89 % with relative standard deviations (RSD) < 8.1 %. In comparison, drinking water spiked at the same concentrations had recoveries between 82-100 % with an RSD < 5%. Ion suppression is a known phenomenon when using ESI; hence its impact on method recovery was elucidated for raw sewage. Both ion suppression from matrix interferences and the extraction procedure has bearing on the overall method recovery. Analysis of municipal raw sewage identified several of the analytes of interest at ng/l concentrations, estriol (E3) being the most abundant. Only one conjugate, estrone 3-sulphate (E1-3S) was observe

A unified treatment of single component replacement models

In this paper we discuss a general framework for single component replacement models. This framework is based on the regenerative structure of these models and by using results from renewal theory a unified presentation of the discounted and average finite and infinite horizon cost models is given. Finally, some well-known replacement models are discussed, and making use of the previous results an easy derivation of their cost functions is presented

Ramified rectilinear polygons: coordinatization by dendrons

Simple rectilinear polygons (i.e. rectilinear polygons without holes or cutpoints) can be regarded as finite rectangular cell complexes coordinatized by two finite dendrons. The intrinsic $l_1$-metric is thus inherited from the product of the two finite dendrons via an isometric embedding. The rectangular cell complexes that share this same embedding property are called ramified rectilinear polygons. The links of vertices in these cell complexes may be arbitrary bipartite graphs, in contrast to simple rectilinear polygons where the links of points are either 4-cycles or paths of length at most 3. Ramified rectilinear polygons are particular instances of rectangular complexes obtained from cube-free median graphs, or equivalently simply connected rectangular complexes with triangle-free links. The underlying graphs of finite ramified rectilinear polygons can be recognized among graphs in linear time by a Lexicographic Breadth-First-Search. Whereas the symmetry of a simple rectilinear polygon is very restricted (with automorphism group being a subgroup of the dihedral group $D_4$), ramified rectilinear polygons are universal: every finite group is the automorphism group of some ramified rectilinear polygon.Comment: 27 pages, 6 figure