On the Areas of Cyclic and Semicyclic Polygons

We investigate the ``generalized Heron polynomial'' that relates the squared area of an n-gon inscribed in a circle to the squares of its side lengths. For a (2m+1)-gon or (2m+2)-gon, we express it as the defining polynomial of a certain variety derived from the variety of binary (2m-1)-forms having m-1 double roots. Thus we obtain explicit formulas for the areas of cyclic heptagons and octagons, and illuminate some mysterious features of Robbins' formulas for the areas of cyclic pentagons and hexagons. We also introduce a companion family of polynomials that relate the squared area of an n-gon inscribed in a circle, one of whose sides is a diameter, to the squared lengths of the other sides. By similar algebraic techniques we obtain explicit formulas for these polynomials for all n <= 7.Comment: 22 page

Collective pinning of imperfect vortex lattices by material line defects in extreme type-II superconductors

The critical current density shown by a superconductor at the extreme type-II limit is predicted to follow an inverse square-root power law with external magnetic field if the vortex lattice is weakly pinned by material line defects. It acquires an additional inverse dependence with thickness along the line direction once pinning of the interstitial vortex lines by material point defects is included. Moderate quantitative agreement with the critical current density shown by second-generation wires of high-temperature superconductors in kG magnetic fields is achieved at liquid-nitrogen temperature.Comment: 10 pages, 3 figures, 2 tables. To appear in Physical Review

Minimum Separation for Single-Layer Channel Routing

We present a linear-time algorithm for determining the minimum height of a single-layer routing channel. The algorithm handles single-sided connections and multiterminal nets. It yields a simple routability test for single-layer switchboxes, correcting an error in the literature

An Efficient Targeting Strategy for Multiobject Spectrograph Surveys: the Sloan Digital Sky Survey "Tiling" Algorithm

Large surveys using multiobject spectrographs require automated methods for deciding how to efficiently point observations and how to assign targets to each pointing. The Sloan Digital Sky Survey (SDSS) will observe around 10 6 spectra from targets distributed over an area of about 10,000 deg2, using a multiobject fiber spectrograph that can simultaneously observe 640 objects in a circular field of view (referred to as a "tile") 1°.49 in radius. No two fibers can be placed closer than 55Prime; during the same observation; multiple targets closer than this distance are said to "collide." We present here a method of allocating fibers to desired targets given a set of tile centers that includes the effects of collisions and that is nearly optimally efficient and uniform. Because of large-scale structure in the galaxy distribution (which form the bulk of the SDSS targets), a naive covering of the sky with equally spaced tiles does not yield uniform sampling. Thus, we present a heuristic for perturbing the centers of the tiles from the equally spaced distribution that provides more uniform completeness. For the SDSS sample, we can attain a sampling rate of greater than 92% for all targets, and greater than 99% for the set of targets that do not collide with each other, with an efficiency greater than 90% (defined as the fraction of available fibers assigned to targets). The methods used here may prove useful to those planning other large surveys

The late Holocene palaeoenvironment in the lake Njupi area, west Cameroon : implications regarding the history of lake Nyos

Le lac Njupi, au sein de la ligne volcanique du Cameroun, s'est constitué par barrage d'une dépression à 1 km à l'est du lac Nyos. Les deux sondages du lac Nyos analysés ont traversé les sédiments déposés au marges du lac. Les dépôts les plus anciens sont datés à 3400 BP, cet âge est proposé comme un minimum pour l'apparition du lac Njupi. Des études sédimentologiques, palynologiques et géochimiques d'une coupe de 2 m permettent de reconstituer l'histoire fini-holocène de cet environnement. Il s'agit d'un dépôt tourbeux (plus de 30% de carbone organique) avec une importante fraction de spicules silicieux de Spongiaires. La sédimentation a été relativement régulière, entrecoupée seulement durant les 800 ans du dépôt, de cinq lamines plus grossières caractérisées par des grains de quartz et de gros débris ligneux. Ces flux sont soulignés par des concentrations de carbohydrates ou parfois par des composés phénoliques bien conservés. Cette étude confirme et précise l'existence d'une phase aride qui s'intensifie ici entre 2500 et 2000 ans BP. Cette crise climatique qui a débuté vers 3000 ans BP est, en fait, très générale dans l'Afrique centrale Atlantique (sud Cameroun). Le lac Njupi, situé aujourd'hui dans un paysage essentiellement composé de savanes d'où sa dénomination de "Grass Fields", permet d'observer avant 2500 ans BP un paysage mixte de forêts et savane en mosaïque, puis son évolution vers une savane avec quelques îlots forestiers, couvert défini alors par 75% à 85% de pollens herbacés. La végétation montagnarde, caractérisée par #Podocarpus et #Olea capensis, régresse vers 2300 ans BP, au moment où #Elaeis guineensis$ (le Palmier à Huile) initie son expansion, d'abord comme un arbre pionnier, offrant ainsi ultérieurement à l'Homme l'opportunité de sa culture. (Résumé d'auteur

A Review of the Pathophysiology and Novel Treatments for Erectile Dysfunction

Erectile dysfunction (ED) affects up to 50% of men between the ages of 40 and 70. Treatment with PDE-5 inhibitors is effective in the majority of men with ED. However, PDE-5 inhibitors are not effective when levels of nitric oxide (NO), the principle mediator of erection, are low. The pharmacologic actions of three new potential treatments for ED are discussed in this paper: (1) sGC stimulators/activators, (2) Rho-kinase inhibitors, and (3) sodium nitrite

An Efficient Targeting Strategy for Multiobject Spectrograph Surveys: the Sloan Digital Sky Survey “Tiling” Algorithm

Large surveys using multiobject spectrographs require automated methods for deciding how to efficiently point observations and how to assign targets to each pointing. The Sloan Digital Sky Survey (SDSS) will observe around 106 spectra from targets distributed over an area of about 10,000 deg2 , using a multiobject fiber spectrograph that can simultaneously observe 640 objects in a circular field of view (referred to as a ‘‘ tile ’’) 1= 49 in radius. No two fibers can be placed closer than 5500 during the same observation; multiple targets closer than this distance are said to ‘‘ collide.’’ We present here a method of allocating fibers to desired targets given a set of tile centers that includes the effects of collisions and that is nearly optimally efficient and uniform. Because of large-scale structure in the galaxy distribution (which form the bulk of the SDSS targets), a naive covering of the sky with equally spaced tiles does not yield uniform sampling. Thus, we present a heuristic for perturbing the centers of the tiles from the equally spaced distribution that provides more uniform completeness. For the SDSS sample, we can attain a sampling rate of greater than 92% for all targets, and greater than 99% for the set of targets that do not collide with each other, with an efficiency greater than 90% (defined as the fraction of available fibers assigned to targets). The methods used here may prove useful to those planning other large surveys

Optical Properties of Crystals with Spatial Dispersion: Josephson Plasma Resonance in Layered Superconductors

We derive the transmission coefficient, $T(\omega)$, for grazing incidence of crystals with spatial dispersion accounting for the excitation of multiple modes with different wave vectors ${\bf k}$ for a given frequency $\omega$. The generalization of the Fresnel formulas contains the refraction indices of these modes as determined by the dielectric function $\epsilon(\omega,{\bf k})$. Near frequencies $\omega_e$, where the group velocity vanishes, $T(\omega)$ depends also on an additional parameter determined by the crystal microstructure. The transmission $T$ is significantly suppressed, if one of the excited modes is decaying into the crystal. We derive these features microscopically for the Josephson plasma resonance in layered superconductors.Comment: 4 pages, 2 figures, epl.cls style file, minor change

Dynamic clonal equilibrium and predetermined cancer risk in Barrett's oesophagus

abstract: Surveillance of Barrett’s oesophagus allows us to study the evolutionary dynamics of a human neoplasm over time. Here we use multicolour fluorescence in situ hybridization on brush cytology specimens, from two time points with a median interval of 37 months in 195 non-dysplastic Barrett's patients, and a third time point in a subset of 90 patients at a median interval of 36 months, to study clonal evolution at single-cell resolution. Baseline genetic diversity predicts progression and remains in a stable dynamic equilibrium over time. Clonal expansions are rare, being detected once every 36.8 patient years, and growing at an average rate of 1.58 cm[superscript 2] (95% CI: 0.09–4.06) per year, often involving the p16 locus. This suggests a lack of strong clonal selection in Barrett’s and that the malignant potential of ‘benign’ Barrett’s lesions is predetermined, with important implications for surveillance programs.The final version of this article, as published in Nature Communications, can be viewed online at: https://www.nature.com/articles/ncomms1215