We show that an arrangement A of n lines in general position in the plane has an inducing polygon of size O(n). Additionally, we present a simple algorithm for finding an inducing n-path for A in O(n log n) time and an algorithm that constructs an inducing n-gon for a special class of line arrangements within the same time bound. Eligible for best student paper

A convex polyhedron P is k-equiprojective if all of its orthogonal projections, i.e., shadows, except those parallel to the faces of P are k-gon for some fixed value of k. Since 1968 it is an open problem to construct all equiprojective polyhedra. Recently, Hasan and Lubiw [8] have given a characterization of equiprojective polyhedra. Based on their characterization, in this paper we discover s...

We present an O(n log n)-time algorithm that determines whether a given planar n-gon is weakly simple. This improves upon an O(n log n)-time algorithm by Chang, Erickson, and Xu [5]. Weakly simple polygons are required as input for several geometric algorithms. As such, how to recognize simple or weakly simple polygons is a fundamental question.

The scattering equations on the Riemann sphere give rise to remarkable formulas for tree-level gauge theory and gravity amplitudes. Adamo, Casali, and Skinner conjectured a one-loop formula for supergravity amplitudes based on scattering equations on a torus. We use a residue theorem to transform this into a formula on the Riemann sphere. What emerges is a framework for loop integrands on the R...

Abstract The current lack of consensus for diagnosing glaucoma makes it difficult to develop diagnostic tests derived from deep learning (DL) algorithms. In the present study, we propose an objective definition glaucomatous optic neuropathy (GON) using clearly defined parameters optical coherence tomography and standard automated perimetry. We then use proposed as reference a DL algorithm detec...

Although surgical procedures are often performed over the posterior head and neck, surgical landmarks for avoiding the cutaneous nerves in this region are surprisingly lacking in the literature. Twelve adult cadaveric specimens underwent dissection of the cutaneous nerves overlying the posterior head and neck, and mensuration was made between these structures and easily identifiable surrounding...

Nnam gon, a cake made by steam cooking a mixture of Cucurbitaceae seeds paste and others ingredients specially spices, is a highly prized dish in Central African region. A preliminary investigation conducted as part of this study highlighted that formulations used in the processing of Nnam gon vary according to the spices used. This study was carried out to determine the best formulation for th...

The Delta-Notch signaling system plays an essential role in various morphogenetic systems of multicellular animal development [1]. Here we analyzed the mechanism of Notch-dependent boundary formation in the Drosophila large intestine by experimental manipulation of Delta expression and computational modeling and simulation by Genomic Object Net (GON) [3]. GON is proved to be a useful and flexib...

of the ONH, and the lack of autonomic innervation of retinal vessels. In addition to structural vascular abnormalities, the dysregulation of arteries and veins is also important. Intraretinal haemorrhages are often a consequence of disturbed BRB. Venous dysregulation increases RVP and can lead to RVO. While hypoxia plays a major pathophysiological role in diabetic retinopathy and in wet AMD, an...