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

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

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

An in vitro co-culture model of esophageal cells identifies ascorbic acid as a modulator of cell competition

<p>Abstract</p> <p>Background</p> <p>The evolutionary dynamics between interacting heterogeneous cell types are fundamental properties of neoplastic progression but can be difficult to measure and quantify. Cancers are heterogeneous mixtures of mutant clones but the direct effect of interactions between these clones is rarely documented. The implicit goal of most preventive interventions is to bias competition in favor of normal cells over neoplastic cells. However, this is rarely explicitly tested. Here we have developed a cell culture competition model to allow for direct observation of the effect of chemopreventive or therapeutic agents on two interacting cell types. We have examined competition between normal and Barrett's esophagus cell lines, in the hopes of identifying a system that could screen for potential chemopreventive agents.</p> <p>Methods</p> <p>One fluorescently-labeled normal squamous esophageal cell line (EPC2-hTERT) was grown in competition with one of four Barrett's esophagus cell lines (CP-A, CP-B, CP-C, CP-D) under varying conditions and the outcome of competition measured over 14 days by flow cytometry.</p> <p>Results</p> <p>We demonstrate that ascorbic acid (vitamin C) can help squamous cells outcompete Barrett's cells in this system. We are also able to show that ascorbic acid's boost to the relative fitness of squamous cells was increased in most cases by mimicking the pH conditions of gastrointestinal reflux in the lower esophagus.</p> <p>Conclusions</p> <p>This model is able to integrate differential fitness effects on various cell types, allowing us to simultaneously capture effects on interacting cell types without having to perform separate experiments. This model system may be used to screen for new classes of cancer prevention agents designed to modulate the competition between normal and neoplastic cells.</p

Antibody Evasion by a Gammaherpesvirus O-Glycan Shield

All gammaherpesviruses encode a major glycoprotein homologous to the Epstein-Barr virus gp350. These glycoproteins are often involved in cell binding, and some provide neutralization targets. However, the capacity of gammaherpesviruses for long-term transmission from immune hosts implies that in vivo neutralization is incomplete. In this study, we used Bovine Herpesvirus 4 (BoHV-4) to determine how its gp350 homolog - gp180 - contributes to virus replication and neutralization. A lack of gp180 had no impact on the establishment and maintenance of BoHV-4 latency, but markedly sensitized virions to neutralization by immune sera. Antibody had greater access to gB, gH and gL on gp180-deficient virions, including neutralization epitopes. Gp180 appears to be highly O-glycosylated, and removing O-linked glycans from virions also sensitized them to neutralization. It therefore appeared that gp180 provides part of a glycan shield for otherwise vulnerable viral epitopes. Interestingly, this O-glycan shield could be exploited for neutralization by lectins and carbohydrate-specific antibody. The conservation of O-glycosylation sites in all gp350 homologs suggests that this is a general evasion mechanism that may also provide a therapeutic target