For most algorithms dealing with sets of points in the plane, the only relevant information carried by the input is the combinatorial configuration of the points: the orientation of each triple of points in the set (clockwise, counterclockwise, or collinear). This information is called the order type of the point set. In the dual, realizable order types and abstract order types are combinatoria...

We consider the inverse boundary value problem in the case of discrete electrical networks containing nonlinear (non-ohmic) conductors. For a fixed nonlinear electrical network, we show that under reasonable assumptions, there are well-defined Dirichletto-Neumann and Neumann-to-Dirichlet maps relating boundary voltages and boundary currents. We also generalize work of Curtis, Morrow, and others...

The associahedron is a polytope whose graph is the graph of flips on triangulations of a convex polygon. Pseudotriangulations and multitriangulations generalize triangulations in two different ways, which have been unified by Pilaud and Pocchiola in their study of pseudoline arrangements with contacts supported by a given network. In this paper, we construct the “brick polytope” of a network, o...

The arrangement design of a submarine depends on the past design data and experts’ experiences. Delay in design can occur due to data missing or the absence of experts. In addition, various compartments and equipment are placed on the limited space called pressure hull in the submarine, so that the relation between the compartments and equipment should be considered carefully when designing the...

A Weyl arrangement is the arrangement defined by the root system of a finite Weyl group. When a set of positive roots is an ideal in the root poset, we call the corresponding arrangement an ideal subarrangement. Our main theorem asserts that any ideal subarrangement is a free arrangement and that its exponents are given by the dual partition of the height distribution, which was conjectured by ...

An arrangement of pseudocircles is a collection of simple closed curves on the sphere or in the plane such that every pair is either disjoint or intersects in exactly two crossing points. We call an arrangement intersecting if every pair of pseudocircles intersects twice. An arrangement is circularizable if there is a combinatorially equivalent arrangement of circles. Kang and Müller showed tha...

In Ayurvedic practice Butea monosperma (Palash) is in clinical use for hundreds of years as a contraceptive. Seeds of Butea monosperma are also used as an anthelmitic (Ansani et al., 1979) and antimicrobial (Avirutnant & Pongpan, 1983). Butea monosperma (Fabaceae family) locally known as Palash (Dhak) if given for 3 consecutive days acts as an antifertility agent for which it has been is tradit...