An n-gon is called Napoleon if the centers of the regular ngons erected outwardly on its sides are vertices of a regular n-gon. In this note we obtain a new geometric characterization of Napoleon ngons and give a new proof of the well-known theorem of Barlotti Greber ([1], [3]) that an n-gon is Napoleon if and only if it is affine regular. Moreover, we generalize this theorem by obtaining an an...

Occipital neuralgia a type of headache that involves irritation and inflammation of the Greater Occipital Nerve (GON). Diagnosis of this headache is achieved mainly through clinical examinations where tenderness is noted along the distribution of the GON. However, anatomical studies have demonstrated its various course and distribution that may be distant from the conventional landmarks where r...

PURPOSE To determine whether an unsupervised machine learning classifier can identify patterns of visual field loss in standard visual fields consistent with typical patterns learned by decades of human experience. METHODS Standard perimetry thresholds for 52 locations plus age from one eye of each of 156 patients with glaucomatous optic neuropathy (GON) and 189 eyes of healthy subjects were ...

The gon-2 gene of Caenorhabditis elegans encodes a TRPM cation channel required for gonadal cell divisions. In this article, we demonstrate that the gonadogenesis defects of gon-2 loss-of-function mutants (including a null allele) can be suppressed by gain-of-function mutations in the gem-1 (gon-2 extragenic modifier) locus. gem-1 encodes a multipass transmembrane protein that is similar to SLC...

The classical Erdős-Szekeres theorem states that a convex k-gon exists in every sufficiently large point set. This problem has been well studied and finding tight asymptotic bounds is considered a challenging open problem. Several variants of the Erdős-Szekeres problem have been posed and studied in the last two decades. The well studied variants include the empty convex k-gon problem, convex k...

Classical Gon£arov polynomials are polynomials which interpolate derivatives. Delta Gon£arov polynomials are polynomials which interpolate delta operators, e.g., forward and backward difference operators. We extend fundamental aspects of the theory of classical bivariate Gon£arov polynomials and univariate delta Gon£arov polynomials to the multivariate setting using umbral calculus. After intro...

ADAMTS9 is a metalloprotease that cleaves components of the extracellular matrix and is also implicated in transport from the endoplasmic reticulum (ER) to the Golgi. It has been reported that an ADAMTS9 gene variant is associated with type 2 diabetes. The underlying pathology of type 2 diabetes is insulin resistance and beta-cell dysfunction. However, the molecular mechanisms underlying ADAMTS...

We find necessary and sufficient conditions on m and n for inscribing a regular m-gon in a regular n-gon. Mathematics Subject Classification (2010). Primary 51M20; Secondary 52C15.

We show that the nonconvex twisted prism over an n-gon cannot be triangulated without new vertices. For this, it does not matter what the coordinates of the n-gon are as long as the top and the bottom n-gon are congruent and the twist is not too large. This generalizes Schönhardt’s polyhedron, which is the nonconvex twisted prism over a triangle.

Purpose To examine the association between intraocular pressure (IOP) and the prevalence of glaucomatous optic neuropathy (GON) in high myopia. Methods The hospital-based observational study consisted of patients treated in the Tokyo High Myopia Clinics and for whom fundus photographs and IOP readings were available. The appearance of the optic nerve head on fundus photographs was the basis f...