We introduce a number of new tools for the study of relatively hyperbolic groups. First, given a relatively hyperbolic group G, we construct a nice combinatorial Gromov hyperbolic model space acted on properly by G, which reflects the relative hyperbolicity of G in many natural ways. Second, we construct two useful bicombings on this space. The first of these, preferred paths, is combinatorial ...

The interesting subsets of a Peano space which were later called the arc-sets or A -sets were defined independently and in a different manner by G. T. Whyburn and the author, and each studied the properties of these sets which have proved so useful in the later theory. The similarity of the properties led shortly to the conjecture that a relation existed between the two definitions, and investi...

Using space-filling curves to order multidimensional data has been found to be useful in a variety of application domains. This paper examines the space-filling curve induced ordering of multidimensional data that has been transformed using shape preserving transformations. It is demonstrated that, although the orderings are not invariant under these transformations, the probability of an order...

Nowadays there are different kinds of attacks on Field Programmable Gate Array (FPGA). As FPGAs are used in many different applications, its security becomes an important concern, especially in Internet of Things (IoT) applications. Hardware Trojan Horse (HTH) insertion is one of the major security threats that can be implemented in unused space of the FPGA. This unused space is unavoidable to ...

Die corner filling is very important in tube hydroforming process. Definition of the internal pressure path is a key factor in improving the corner filling.  However, the factors that cause improvement of corner filling are still unclear. In this paper, effect of bilinear pressure path on corner filling in hydroforming of tube in box-shape die is studied using both finite element simulation and...

A data depth is one of the most important concepts of nonparametric multivariate analysis. Several depth functions have been introduced since 1980. The halfspace depth is probably the most popular. This depth function has many desirable properties (they are stated in the general definition of statictical depth function). We show a way of generalization of the halfspace depth finding a broader c...

This paper studies single-image depth perception in the wild, i.e., recovering depth from a single image taken in unconstrained settings. We introduce a new dataset “Depth in the Wild” consisting of images in the wild annotated with relative depth between pairs of random points. We also propose a new algorithm that learns to estimate metric depth using annotations of relative depth. Compared to...

BACKGROUND Mercury vapor poses a known health risk with no clearly established safe level of exposure. Consequently there is debate over whether the level of prolonged exposure to mercury vapor from dental amalgam fillings, combining approximately 50% mercury with other metals, is sufficiently high to represent a risk to health. The objective of our study is to determine if mercury exposure fro...