We introduce a new problem in the study of doubling spaces: Given a point set S and a target dimension d∗, remove from S the fewest number of points so that the remaining set has doubling dimension at most d∗. We present a bicriteria approximation for this problem, and extend this algorithm to solve a group of proximity problems.

RATIONALE Ambient air pollution has been associated with heart failure morbidity and mortality. The mechanisms responsible for these associations are unknown but may include the effects of traffic-related pollutants on vascular or autonomic function. OBJECTIVES We assessed the cross-sectional relation between long-term air pollution, traffic exposures, and important end-organ measures of alte...

In vitro three dimensional (3D) cancer models were developed to observe the invasive capacity of melanoma cell spheroids co-cultured with the vascular-formed endothelial cell network. An array-like multicellular pattern of mouse melanoma cell line B16F1 was developed by magnetic cell labeling using a pin-holder device for allocation of magnetic force. When the B16F1 patterned together with a va...

Hilar cholangiocarcinoma is a rare malignancy that occurs at the bifurcation of the bile ducts. Complete surgical excision with negative histologic margins remains the only hope for cure or long-term survival. Because of its location and proximity to the vascular inflow of the liver, surgical resection is technically difficult and may require advanced vascular reconstructions to achieve complet...

Erosion of vascular grafts is not uncommon as seen in the recent literature. There have been many case reports documenting the work up and management of erosion of these grafts into bowel. We report a case of a crossover femoral-femoral graft that eroded into the anterior bladder wall and was incidentally found as an adherent bladder stone during cystoscopy. We demonstrate the importance of hav...

The best approximation problem in a hyperconvex metric space consists of finding conditions for given set-valued mappings F andG and a setX such that there is a point x0 ∈ X satisfying d G x0 , F x0 ≤ d x, F x0 for x ∈ X. When G I, the identity mapping, and when the set X is compact, best approximation theorems for mappings in hyperconvex metric spaces are given for the single-valued case in 1–...

Many algorithms have to deal with multiple representations of the same object. The process of aligning these representations is called registration. In this paper we present a new approach for the registration of free-form surfaces which is not based on finding closest points. Instead, our algorithm takes advantage of the graphics hardware and uses the depth buffer for determining the distance ...

The proximity relations inherent in triangulations of geometric data can be exploited in the implementation of nearest-neighbour search procedures. This is relevant to applications such as terrain analysis, cartography and robotics, in which triangulations may be used to model the spatial data. Here we describe neighbourhood search procedures within constrained Delaunay triangulations of the ve...